LMFDB - Embedded newform 570.2.d.c.229.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,2,Mod(229,570)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(570, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 0]))

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

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

chi := DirichletCharacter("570.229");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.d (of order $2$, degree $1$, 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:	$4.55147291521$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.0.350464.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} + 2x^{4} + 2x^{3} + 4x^{2} - 4x + 2 $ x^6 - 2x^5 + 2x^4 + 2x^3 + 4x^2 - 4*x + 2
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			229.1
Root			$0.403032 + 0.403032i$ of defining polynomial
Character	$\chi$	$=$	570.229
Dual form			570.2.d.c.229.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} -1.00000i q^{3} -1.00000 q^{4} +(-1.67513 - 1.48119i) q^{5} -1.00000 q^{6} -3.35026i q^{7} +1.00000i q^{8} -1.00000 q^{9} +O(q^{10})$	\(q-1.00000i q^{2} -1.00000i q^{3} -1.00000 q^{4} +(-1.67513 - 1.48119i) q^{5} -1.00000 q^{6} -3.35026i q^{7} +1.00000i q^{8} -1.00000 q^{9} +(-1.48119 + 1.67513i) q^{10} -0.962389 q^{11} +1.00000i q^{12} +1.61213i q^{13} -3.35026 q^{14} +(-1.48119 + 1.67513i) q^{15} +1.00000 q^{16} -0.387873i q^{17} +1.00000i q^{18} -1.00000 q^{19} +(1.67513 + 1.48119i) q^{20} -3.35026 q^{21} +0.962389i q^{22} +0.962389i q^{23} +1.00000 q^{24} +(0.612127 + 4.96239i) q^{25} +1.61213 q^{26} +1.00000i q^{27} +3.35026i q^{28} -6.96239 q^{29} +(1.67513 + 1.48119i) q^{30} +3.35026 q^{31} -1.00000i q^{32} +0.962389i q^{33} -0.387873 q^{34} +(-4.96239 + 5.61213i) q^{35} +1.00000 q^{36} -1.61213i q^{37} +1.00000i q^{38} +1.61213 q^{39} +(1.48119 - 1.67513i) q^{40} -9.27504 q^{41} +3.35026i q^{42} -6.18664i q^{43} +0.962389 q^{44} +(1.67513 + 1.48119i) q^{45} +0.962389 q^{46} +0.962389i q^{47} -1.00000i q^{48} -4.22425 q^{49} +(4.96239 - 0.612127i) q^{50} -0.387873 q^{51} -1.61213i q^{52} -6.00000i q^{53} +1.00000 q^{54} +(1.61213 + 1.42548i) q^{55} +3.35026 q^{56} +1.00000i q^{57} +6.96239i q^{58} -10.3127 q^{59} +(1.48119 - 1.67513i) q^{60} +11.9248 q^{61} -3.35026i q^{62} +3.35026i q^{63} -1.00000 q^{64} +(2.38787 - 2.70052i) q^{65} +0.962389 q^{66} -7.22425i q^{67} +0.387873i q^{68} +0.962389 q^{69} +(5.61213 + 4.96239i) q^{70} +7.22425 q^{71} -1.00000i q^{72} +3.22425i q^{73} -1.61213 q^{74} +(4.96239 - 0.612127i) q^{75} +1.00000 q^{76} +3.22425i q^{77} -1.61213i q^{78} +3.35026 q^{79} +(-1.67513 - 1.48119i) q^{80} +1.00000 q^{81} +9.27504i q^{82} -15.0132i q^{83} +3.35026 q^{84} +(-0.574515 + 0.649738i) q^{85} -6.18664 q^{86} +6.96239i q^{87} -0.962389i q^{88} -4.64974 q^{89} +(1.48119 - 1.67513i) q^{90} +5.40105 q^{91} -0.962389i q^{92} -3.35026i q^{93} +0.962389 q^{94} +(1.67513 + 1.48119i) q^{95} -1.00000 q^{96} -10.9624i q^{97} +4.22425i q^{98} +0.962389 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{4} - 6 q^{6} - 6 q^{9}+O(q^{10}) $ 6 * q - 6 * q^4 - 6 * q^6 - 6 * q^9	$ 6 q - 6 q^{4} - 6 q^{6} - 6 q^{9} + 2 q^{10} + 16 q^{11} + 2 q^{15} + 6 q^{16} - 6 q^{19} + 6 q^{24} + 2 q^{25} + 8 q^{26} - 20 q^{29} - 4 q^{34} - 8 q^{35} + 6 q^{36} + 8 q^{39} - 2 q^{40} + 8 q^{41} - 16 q^{44} - 16 q^{46} - 22 q^{49} + 8 q^{50} - 4 q^{51} + 6 q^{54} + 8 q^{55} - 20 q^{59} - 2 q^{60} + 28 q^{61} - 6 q^{64} + 16 q^{65} - 16 q^{66} - 16 q^{69} + 32 q^{70} + 40 q^{71} - 8 q^{74} + 8 q^{75} + 6 q^{76} + 6 q^{81} + 20 q^{85} - 12 q^{86} - 48 q^{89} - 2 q^{90} - 48 q^{91} - 16 q^{94} - 6 q^{96} - 16 q^{99}+O(q^{100}) $ 6 * q - 6 * q^4 - 6 * q^6 - 6 * q^9 + 2 * q^10 + 16 * q^11 + 2 * q^15 + 6 * q^16 - 6 * q^19 + 6 * q^24 + 2 * q^25 + 8 * q^26 - 20 * q^29 - 4 * q^34 - 8 * q^35 + 6 * q^36 + 8 * q^39 - 2 * q^40 + 8 * q^41 - 16 * q^44 - 16 * q^46 - 22 * q^49 + 8 * q^50 - 4 * q^51 + 6 * q^54 + 8 * q^55 - 20 * q^59 - 2 * q^60 + 28 * q^61 - 6 * q^64 + 16 * q^65 - 16 * q^66 - 16 * q^69 + 32 * q^70 + 40 * q^71 - 8 * q^74 + 8 * q^75 + 6 * q^76 + 6 * q^81 + 20 * q^85 - 12 * q^86 - 48 * q^89 - 2 * q^90 - 48 * q^91 - 16 * q^94 - 6 * q^96 - 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

$n$	$191$	$211$	$457$
$\chi(n)$	$1$	$1$	$-1$

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 $

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$		−	1.00000i		−	0.577350i
$3$		−	1.00000i		−	0.577350i
$4$	−1.00000			−0.500000
$5$	−1.67513	−	1.48119i	−0.749141	−	0.662410i
$5$	−1.67513	−	1.48119i	−0.749141	−	0.662410i
$6$	−1.00000			−0.408248
$7$		−	3.35026i		−	1.26628i	−0.774037	−	0.633140i	$-0.781766\pi$
$7$		−	3.35026i		−	1.26628i	0.774037	−	0.633140i	$-0.218234\pi$
$8$			1.00000i			0.353553i
$9$	−1.00000			−0.333333
$10$	−1.48119	+	1.67513i	−0.468395	+	0.529723i
$11$	−0.962389			−0.290171			−0.145086	−	0.989419i	$-0.546346\pi$
$11$	−0.962389			−0.290171			−0.145086	+	0.989419i	$0.546346\pi$
$12$			1.00000i			0.288675i
$13$			1.61213i			0.447124i	0.974690	+	0.223562i	$0.0717684\pi$
$13$			1.61213i			0.447124i	−0.974690	+	0.223562i	$0.928232\pi$
$14$	−3.35026			−0.895395
$15$	−1.48119	+	1.67513i	−0.382443	+	0.432517i
$16$	1.00000			0.250000
$17$		−	0.387873i		−	0.0940731i	−0.998893	−	0.0470365i	$-0.985022\pi$
$17$		−	0.387873i		−	0.0940731i	0.998893	−	0.0470365i	$-0.0149777\pi$
$18$			1.00000i			0.235702i
$19$	−1.00000			−0.229416
$19$	−1.00000			−0.229416
$20$	1.67513	+	1.48119i	0.374571	+	0.331205i
$21$	−3.35026			−0.731087
$22$			0.962389i			0.205182i
$23$			0.962389i			0.200672i	0.994954	+	0.100336i	$0.0319918\pi$
$23$			0.962389i			0.200672i	−0.994954	+	0.100336i	$0.968008\pi$
$24$	1.00000			0.204124
$25$	0.612127	+	4.96239i	0.122425	+	0.992478i
$26$	1.61213			0.316164
$27$			1.00000i			0.192450i
$28$			3.35026i			0.633140i
$29$	−6.96239			−1.29288			−0.646442	−	0.762964i	$-0.723744\pi$
$29$	−6.96239			−1.29288			−0.646442	+	0.762964i	$0.723744\pi$
$30$	1.67513	+	1.48119i	0.305836	+	0.270428i
$31$	3.35026			0.601725			0.300862	−	0.953668i	$-0.402726\pi$
$31$	3.35026			0.601725			0.300862	+	0.953668i	$0.402726\pi$
$32$		−	1.00000i		−	0.176777i
$33$			0.962389i			0.167530i
$34$	−0.387873			−0.0665197
$35$	−4.96239	+	5.61213i	−0.838797	+	0.948623i
$36$	1.00000			0.166667
$37$		−	1.61213i		−	0.265032i	−0.991181	−	0.132516i	$-0.957694\pi$
$37$		−	1.61213i		−	0.265032i	0.991181	−	0.132516i	$-0.0423056\pi$
$38$			1.00000i			0.162221i
$39$	1.61213			0.258147
$40$	1.48119	−	1.67513i	0.234197	−	0.264861i
$41$	−9.27504			−1.44852			−0.724259	−	0.689528i	$-0.757818\pi$
$41$	−9.27504			−1.44852			−0.724259	+	0.689528i	$0.757818\pi$
$42$			3.35026i			0.516957i
$43$		−	6.18664i		−	0.943454i	−0.881745	−	0.471727i	$-0.843631\pi$
$43$		−	6.18664i		−	0.943454i	0.881745	−	0.471727i	$-0.156369\pi$
$44$	0.962389			0.145086
$45$	1.67513	+	1.48119i	0.249714	+	0.220803i
$46$	0.962389			0.141896
$47$			0.962389i			0.140379i	0.997534	+	0.0701894i	$0.0223604\pi$
$47$			0.962389i			0.140379i	−0.997534	+	0.0701894i	$0.977640\pi$
$48$		−	1.00000i		−	0.144338i
$49$	−4.22425			−0.603465
$50$	4.96239	−	0.612127i	0.701788	−	0.0865678i
$51$	−0.387873			−0.0543131
$52$		−	1.61213i		−	0.223562i
$53$		−	6.00000i		−	0.824163i	−0.911147	−	0.412082i	$-0.864802\pi$
$53$		−	6.00000i		−	0.824163i	0.911147	−	0.412082i	$-0.135198\pi$
$54$	1.00000			0.136083
$55$	1.61213	+	1.42548i	0.217379	+	0.192212i
$56$	3.35026			0.447698
$57$			1.00000i			0.132453i
$58$			6.96239i			0.914206i
$59$	−10.3127			−1.34259			−0.671296	−	0.741189i	$-0.734262\pi$
$59$	−10.3127			−1.34259			−0.671296	+	0.741189i	$0.734262\pi$
$60$	1.48119	−	1.67513i	0.191221	−	0.216258i
$61$	11.9248			1.52681			0.763406	−	0.645919i	$-0.223526\pi$
$61$	11.9248			1.52681			0.763406	+	0.645919i	$0.223526\pi$
$62$		−	3.35026i		−	0.425484i
$63$			3.35026i			0.422093i
$64$	−1.00000			−0.125000
$65$	2.38787	−	2.70052i	0.296179	−	0.334959i
$66$	0.962389			0.118462
$67$		−	7.22425i		−	0.882583i	−0.897364	−	0.441292i	$-0.854520\pi$
$67$		−	7.22425i		−	0.882583i	0.897364	−	0.441292i	$-0.145480\pi$
$68$			0.387873i			0.0470365i
$69$	0.962389			0.115858
$70$	5.61213	+	4.96239i	0.670777	+	0.593119i
$71$	7.22425			0.857361			0.428681	−	0.903456i	$-0.358979\pi$
$71$	7.22425			0.857361			0.428681	+	0.903456i	$0.358979\pi$
$72$		−	1.00000i		−	0.117851i
$73$			3.22425i			0.377370i	0.982038	+	0.188685i	$0.0604226\pi$
$73$			3.22425i			0.377370i	−0.982038	+	0.188685i	$0.939577\pi$
$74$	−1.61213			−0.187406
$75$	4.96239	−	0.612127i	0.573007	−	0.0706823i
$76$	1.00000			0.114708
$77$			3.22425i			0.367438i
$78$		−	1.61213i		−	0.182537i
$79$	3.35026			0.376934			0.188467	−	0.982080i	$-0.439648\pi$
$79$	3.35026			0.376934			0.188467	+	0.982080i	$0.439648\pi$
$80$	−1.67513	−	1.48119i	−0.187285	−	0.165603i
$81$	1.00000			0.111111
$82$			9.27504i			1.02426i
$83$		−	15.0132i		−	1.64791i	−0.566655	−	0.823955i	$-0.691763\pi$
$83$		−	15.0132i		−	1.64791i	0.566655	−	0.823955i	$-0.308237\pi$
$84$	3.35026			0.365544
$85$	−0.574515	+	0.649738i	−0.0623150	+	0.0704740i
$86$	−6.18664			−0.667123
$87$			6.96239i			0.746446i
$88$		−	0.962389i		−	0.102591i
$89$	−4.64974			−0.492871			−0.246436	−	0.969159i	$-0.579259\pi$
$89$	−4.64974			−0.492871			−0.246436	+	0.969159i	$0.579259\pi$
$90$	1.48119	−	1.67513i	0.156132	−	0.176574i
$91$	5.40105			0.566184
$92$		−	0.962389i		−	0.100336i
$93$		−	3.35026i		−	0.347406i
$94$	0.962389			0.0992628
$95$	1.67513	+	1.48119i	0.171865	+	0.151967i
$96$	−1.00000			−0.102062
$97$		−	10.9624i		−	1.11306i	−0.830827	−	0.556531i	$-0.812132\pi$
$97$		−	10.9624i		−	1.11306i	0.830827	−	0.556531i	$-0.187868\pi$
$98$			4.22425i			0.426714i
$99$	0.962389			0.0967237
$100$	−0.612127	−	4.96239i	−0.0612127	−	0.496239i
$101$	2.72496			0.271144			0.135572	−	0.990768i	$-0.456713\pi$
$101$	2.72496			0.271144			0.135572	+	0.990768i	$0.456713\pi$
$102$			0.387873i			0.0384052i
$103$		−	0.574515i		−	0.0566087i	−0.999599	−	0.0283043i	$-0.990989\pi$
$103$		−	0.574515i		−	0.0566087i	0.999599	−	0.0283043i	$-0.00901076\pi$
$104$	−1.61213			−0.158082
$105$	5.61213	+	4.96239i	0.547688	+	0.484280i
$106$	−6.00000			−0.582772
$107$			10.7005i			1.03446i	0.855847	+	0.517229i	$0.173037\pi$
$107$			10.7005i			1.03446i	−0.855847	+	0.517229i	$0.826963\pi$
$108$		−	1.00000i		−	0.0962250i
$109$	−10.1260			−0.969896			−0.484948	−	0.874543i	$-0.661161\pi$
$109$	−10.1260			−0.969896			−0.484948	+	0.874543i	$0.661161\pi$
$110$	1.42548	−	1.61213i	0.135915	−	0.153710i
$111$	−1.61213			−0.153016
$112$		−	3.35026i		−	0.316570i
$113$		−	20.5501i		−	1.93319i	−0.256311	−	0.966594i	$-0.582507\pi$
$113$		−	20.5501i		−	1.93319i	0.256311	−	0.966594i	$-0.417493\pi$
$114$	1.00000			0.0936586
$115$	1.42548	−	1.61213i	0.132927	−	0.150332i
$116$	6.96239			0.646442
$117$		−	1.61213i		−	0.149041i
$118$			10.3127i			0.949356i
$119$	−1.29948			−0.119123
$120$	−1.67513	−	1.48119i	−0.152918	−	0.135214i
$121$	−10.0738			−0.915801
$122$		−	11.9248i		−	1.07962i
$123$			9.27504i			0.836302i
$124$	−3.35026			−0.300862
$125$	6.32487	−	9.21933i	0.565713	−	0.824602i
$126$	3.35026			0.298465
$127$			1.35026i			0.119816i	0.998204	+	0.0599082i	$0.0190808\pi$
$127$			1.35026i			0.119816i	−0.998204	+	0.0599082i	$0.980919\pi$
$128$			1.00000i			0.0883883i
$129$	−6.18664			−0.544703
$130$	−2.70052	−	2.38787i	−0.236852	−	0.209430i
$131$	12.4387			1.08677			0.543385	−	0.839483i	$-0.317142\pi$
$131$	12.4387			1.08677			0.543385	+	0.839483i	$0.317142\pi$
$132$		−	0.962389i		−	0.0837652i
$133$			3.35026i			0.290505i
$134$	−7.22425			−0.624080
$135$	1.48119	−	1.67513i	0.127481	−	0.144172i
$136$	0.387873			0.0332598
$137$		−	18.1622i		−	1.55170i	−0.630916	−	0.775851i	$-0.717321\pi$
$137$		−	18.1622i		−	1.55170i	0.630916	−	0.775851i	$-0.282679\pi$
$138$		−	0.962389i		−	0.0819240i
$139$	−8.77575			−0.744349			−0.372175	−	0.928163i	$-0.621388\pi$
$139$	−8.77575			−0.744349			−0.372175	+	0.928163i	$0.621388\pi$
$140$	4.96239	−	5.61213i	0.419398	−	0.474311i
$141$	0.962389			0.0810477
$142$		−	7.22425i		−	0.606246i
$143$		−	1.55149i		−	0.129742i
$144$	−1.00000			−0.0833333
$145$	11.6629	+	10.3127i	0.968552	+	0.856419i
$146$	3.22425			0.266841
$147$			4.22425i			0.348411i
$148$			1.61213i			0.132516i
$149$	−15.9756			−1.30877			−0.654385	−	0.756162i	$-0.727072\pi$
$149$	−15.9756			−1.30877			−0.654385	+	0.756162i	$0.727072\pi$
$150$	−0.612127	−	4.96239i	−0.0499799	−	0.405177i
$151$	18.4241			1.49933			0.749665	−	0.661818i	$-0.230215\pi$
$151$	18.4241			1.49933			0.749665	+	0.661818i	$0.230215\pi$
$152$		−	1.00000i		−	0.0811107i
$153$			0.387873i			0.0313577i
$154$	3.22425			0.259818
$155$	−5.61213	−	4.96239i	−0.450777	−	0.398589i
$156$	−1.61213			−0.129073
$157$		−	13.7889i		−	1.10048i	−0.835008	−	0.550238i	$-0.814537\pi$
$157$		−	13.7889i		−	1.10048i	0.835008	−	0.550238i	$-0.185463\pi$
$158$		−	3.35026i		−	0.266533i
$159$	−6.00000			−0.475831
$160$	−1.48119	+	1.67513i	−0.117099	+	0.132431i
$161$	3.22425			0.254107
$162$		−	1.00000i		−	0.0785674i
$163$			3.73813i			0.292793i	0.989226	+	0.146397i	$0.0467676\pi$
$163$			3.73813i			0.292793i	−0.989226	+	0.146397i	$0.953232\pi$
$164$	9.27504			0.724259
$165$	1.42548	−	1.61213i	0.110974	−	0.125504i
$166$	−15.0132			−1.16525
$167$			15.4763i			1.19759i	0.800902	+	0.598795i	$0.204354\pi$
$167$			15.4763i			1.19759i	−0.800902	+	0.598795i	$0.795646\pi$
$168$		−	3.35026i		−	0.258478i
$169$	10.4010			0.800081
$170$	0.649738	+	0.574515i	0.0498326	+	0.0440633i
$171$	1.00000			0.0764719
$172$			6.18664i			0.471727i
$173$			1.47627i			0.112239i	0.998424	+	0.0561194i	$0.0178727\pi$
$173$			1.47627i			0.112239i	−0.998424	+	0.0561194i	$0.982127\pi$
$174$	6.96239			0.527817
$175$	16.6253	−	2.05079i	1.25675	−	0.155025i
$176$	−0.962389			−0.0725428
$177$			10.3127i			0.775146i
$178$			4.64974i			0.348513i
$179$	14.3127			1.06978			0.534889	−	0.844922i	$-0.320353\pi$
$179$	14.3127			1.06978			0.534889	+	0.844922i	$0.320353\pi$
$180$	−1.67513	−	1.48119i	−0.124857	−	0.110402i
$181$	−8.82653			−0.656071			−0.328035	−	0.944665i	$-0.606387\pi$
$181$	−8.82653			−0.656071			−0.328035	+	0.944665i	$0.606387\pi$
$182$		−	5.40105i		−	0.400352i
$183$		−	11.9248i		−	0.881505i
$184$	−0.962389			−0.0709482
$185$	−2.38787	+	2.70052i	−0.175560	+	0.198546i
$186$	−3.35026			−0.245653
$187$			0.373285i			0.0272973i
$188$		−	0.962389i		−	0.0701894i
$189$	3.35026			0.243696
$190$	1.48119	−	1.67513i	0.107457	−	0.121527i
$191$	2.31265			0.167338			0.0836688	−	0.996494i	$-0.473336\pi$
$191$	2.31265			0.167338			0.0836688	+	0.996494i	$0.473336\pi$
$192$			1.00000i			0.0721688i
$193$		−	7.58769i		−	0.546174i	−0.961989	−	0.273087i	$-0.911955\pi$
$193$		−	7.58769i		−	0.546174i	0.961989	−	0.273087i	$-0.0880447\pi$
$194$	−10.9624			−0.787054
$195$	−2.70052	−	2.38787i	−0.193389	−	0.170999i
$196$	4.22425			0.301732
$197$		−	18.8119i		−	1.34030i	−0.742228	−	0.670148i	$-0.766231\pi$
$197$		−	18.8119i		−	1.34030i	0.742228	−	0.670148i	$-0.233769\pi$
$198$		−	0.962389i		−	0.0683940i
$199$	9.40105			0.666423			0.333211	−	0.942852i	$-0.391868\pi$
$199$	9.40105			0.666423			0.333211	+	0.942852i	$0.391868\pi$
$200$	−4.96239	+	0.612127i	−0.350894	+	0.0432839i
$201$	−7.22425			−0.509560
$202$		−	2.72496i		−	0.191728i
$203$			23.3258i			1.63715i
$204$	0.387873			0.0271566
$205$	15.5369	+	13.7381i	1.08514	+	0.959513i
$206$	−0.574515			−0.0400284
$207$		−	0.962389i		−	0.0668906i
$208$			1.61213i			0.111781i
$209$	0.962389			0.0665698
$210$	4.96239	−	5.61213i	0.342437	−	0.387274i
$211$	4.77575			0.328776			0.164388	−	0.986396i	$-0.447435\pi$
$211$	4.77575			0.328776			0.164388	+	0.986396i	$0.447435\pi$
$212$			6.00000i			0.412082i
$213$		−	7.22425i		−	0.494998i
$214$	10.7005			0.731473
$215$	−9.16362	+	10.3634i	−0.624954	+	0.706780i
$216$	−1.00000			−0.0680414
$217$		−	11.2243i		−	0.761952i
$218$			10.1260i			0.685820i
$219$	3.22425			0.217875
$220$	−1.61213	−	1.42548i	−0.108690	−	0.0961061i
$221$	0.625301			0.0420623
$222$			1.61213i			0.108199i
$223$			24.6761i			1.65243i	0.563353	+	0.826216i	$0.309511\pi$
$223$			24.6761i			1.65243i	−0.563353	+	0.826216i	$0.690489\pi$
$224$	−3.35026			−0.223849
$225$	−0.612127	−	4.96239i	−0.0408085	−	0.330826i
$226$	−20.5501			−1.36697
$227$			15.4763i			1.02720i	0.858031	+	0.513598i	$0.171688\pi$
$227$			15.4763i			1.02720i	−0.858031	+	0.513598i	$0.828312\pi$
$228$		−	1.00000i		−	0.0662266i
$229$	−21.3258			−1.40925			−0.704625	−	0.709580i	$-0.748885\pi$
$229$	−21.3258			−1.40925			−0.704625	+	0.709580i	$0.748885\pi$
$230$	−1.61213	−	1.42548i	−0.106300	−	0.0939937i
$231$	3.22425			0.212140
$232$		−	6.96239i		−	0.457103i
$233$			9.01317i			0.590473i	0.955424	+	0.295236i	$0.0953984\pi$
$233$			9.01317i			0.590473i	−0.955424	+	0.295236i	$0.904602\pi$
$234$	−1.61213			−0.105388
$235$	1.42548	−	1.61213i	0.0929884	−	0.105164i
$236$	10.3127			0.671296
$237$		−	3.35026i		−	0.217623i
$238$			1.29948i			0.0842326i
$239$	0.135857			0.00878787			0.00439393	−	0.999990i	$-0.498601\pi$
$239$	0.135857			0.00878787			0.00439393	+	0.999990i	$0.498601\pi$
$240$	−1.48119	+	1.67513i	−0.0956107	+	0.108129i
$241$	−25.8496			−1.66512			−0.832558	−	0.553938i	$-0.813125\pi$
$241$	−25.8496			−1.66512			−0.832558	+	0.553938i	$0.813125\pi$
$242$			10.0738i			0.647569i
$243$		−	1.00000i		−	0.0641500i
$244$	−11.9248			−0.763406
$245$	7.07618	+	6.25694i	0.452080	+	0.399741i
$246$	9.27504			0.591355
$247$		−	1.61213i		−	0.102577i
$248$			3.35026i			0.212742i
$249$	−15.0132			−0.951421
$250$	−9.21933	−	6.32487i	−0.583082	−	0.400020i
$251$	−10.1114			−0.638227			−0.319114	−	0.947716i	$-0.603385\pi$
$251$	−10.1114			−0.638227			−0.319114	+	0.947716i	$0.603385\pi$
$252$		−	3.35026i		−	0.211047i
$253$		−	0.926192i		−	0.0582292i
$254$	1.35026			0.0847230
$255$	0.649738	+	0.574515i	0.0406882	+	0.0359776i
$256$	1.00000			0.0625000
$257$			26.9986i			1.68413i	0.539380	+	0.842063i	$0.318659\pi$
$257$			26.9986i			1.68413i	−0.539380	+	0.842063i	$0.681341\pi$
$258$			6.18664i			0.385164i
$259$	−5.40105			−0.335605
$260$	−2.38787	+	2.70052i	−0.148090	+	0.167479i
$261$	6.96239			0.430961
$262$		−	12.4387i		−	0.768463i
$263$		−	15.0376i		−	0.927259i	−0.886029	−	0.463629i	$-0.846547\pi$
$263$		−	15.0376i		−	0.927259i	0.886029	−	0.463629i	$-0.153453\pi$
$264$	−0.962389			−0.0592309
$265$	−8.88717	+	10.0508i	−0.545934	+	0.617415i
$266$	3.35026			0.205418
$267$			4.64974i			0.284559i
$268$			7.22425i			0.441292i
$269$	4.51388			0.275216			0.137608	−	0.990487i	$-0.456059\pi$
$269$	4.51388			0.275216			0.137608	+	0.990487i	$0.456059\pi$
$270$	−1.67513	−	1.48119i	−0.101945	−	0.0901426i
$271$	15.8496			0.962792			0.481396	−	0.876503i	$-0.340130\pi$
$271$	15.8496			0.962792			0.481396	+	0.876503i	$0.340130\pi$
$272$		−	0.387873i		−	0.0235183i
$273$		−	5.40105i		−	0.326886i
$274$	−18.1622			−1.09722
$275$	−0.589104	−	4.77575i	−0.0355243	−	0.287988i
$276$	−0.962389			−0.0579290
$277$			10.3127i			0.619627i	0.950797	+	0.309814i	$0.100267\pi$
$277$			10.3127i			0.619627i	−0.950797	+	0.309814i	$0.899733\pi$
$278$			8.77575i			0.526334i
$279$	−3.35026			−0.200575
$280$	−5.61213	−	4.96239i	−0.335389	−	0.296559i
$281$	24.3488			1.45253			0.726265	−	0.687415i	$-0.241254\pi$
$281$	24.3488			1.45253			0.726265	+	0.687415i	$0.241254\pi$
$282$		−	0.962389i		−	0.0573094i
$283$		−	26.2882i		−	1.56267i	−0.624111	−	0.781336i	$-0.714539\pi$
$283$		−	26.2882i		−	1.56267i	0.624111	−	0.781336i	$-0.285461\pi$
$284$	−7.22425			−0.428681
$285$	1.48119	−	1.67513i	0.0877384	−	0.0992262i
$286$	−1.55149			−0.0917417
$287$			31.0738i			1.83423i
$288$			1.00000i			0.0589256i
$289$	16.8496			0.991150
$290$	10.3127	−	11.6629i	0.605580	−	0.684870i
$291$	−10.9624			−0.642627
$292$		−	3.22425i		−	0.188685i
$293$			13.0738i			0.763780i	0.924208	+	0.381890i	$0.124727\pi$
$293$			13.0738i			0.763780i	−0.924208	+	0.381890i	$0.875273\pi$
$294$	4.22425			0.246363
$295$	17.2750	+	15.2750i	1.00579	+	0.889347i
$296$	1.61213			0.0937030
$297$		−	0.962389i		−	0.0558435i
$298$			15.9756i			0.925439i
$299$	−1.55149			−0.0897251
$300$	−4.96239	+	0.612127i	−0.286504	+	0.0353412i
$301$	−20.7269			−1.19468
$302$		−	18.4241i		−	1.06019i
$303$		−	2.72496i		−	0.156545i
$304$	−1.00000			−0.0573539
$305$	−19.9756	−	17.6629i	−1.14380	−	1.01138i
$306$	0.387873			0.0221732
$307$		−	7.07381i		−	0.403724i	−0.979414	−	0.201862i	$-0.935301\pi$
$307$		−	7.07381i		−	0.403724i	0.979414	−	0.201862i	$-0.0646992\pi$
$308$		−	3.22425i		−	0.183719i
$309$	−0.574515			−0.0326830
$310$	−4.96239	+	5.61213i	−0.281845	+	0.318747i
$311$	26.3127			1.49205			0.746027	−	0.665916i	$-0.231959\pi$
$311$	26.3127			1.49205			0.746027	+	0.665916i	$0.231959\pi$
$312$			1.61213i			0.0912687i
$313$			18.7005i			1.05702i	0.848928	+	0.528508i	$0.177248\pi$
$313$			18.7005i			1.05702i	−0.848928	+	0.528508i	$0.822752\pi$
$314$	−13.7889			−0.778154
$315$	4.96239	−	5.61213i	0.279599	−	0.316208i
$316$	−3.35026			−0.188467
$317$			26.4749i			1.48698i	0.668749	+	0.743488i	$0.266830\pi$
$317$			26.4749i			1.48698i	−0.668749	+	0.743488i	$0.733170\pi$
$318$			6.00000i			0.336463i
$319$	6.70052			0.375157
$320$	1.67513	+	1.48119i	0.0936427	+	0.0828013i
$321$	10.7005			0.597245
$322$		−	3.22425i		−	0.179681i
$323$			0.387873i			0.0215818i
$324$	−1.00000			−0.0555556
$325$	−8.00000	+	0.986826i	−0.443760	+	0.0547393i
$326$	3.73813			0.207036
$327$			10.1260i			0.559970i
$328$		−	9.27504i		−	0.512128i
$329$	3.22425			0.177759
$330$	−1.61213	−	1.42548i	−0.0887447	−	0.0784703i
$331$	−30.7005			−1.68745			−0.843727	−	0.536773i	$-0.819643\pi$
$331$	−30.7005			−1.68745			−0.843727	+	0.536773i	$0.819643\pi$
$332$			15.0132i			0.823955i
$333$			1.61213i			0.0883440i
$334$	15.4763			0.846824
$335$	−10.7005	+	12.1016i	−0.584632	+	0.661179i
$336$	−3.35026			−0.182772
$337$			6.81194i			0.371070i	0.982638	+	0.185535i	$0.0594018\pi$
$337$			6.81194i			0.371070i	−0.982638	+	0.185535i	$0.940598\pi$
$338$		−	10.4010i		−	0.565742i
$339$	−20.5501			−1.11613
$340$	0.574515	−	0.649738i	0.0311575	−	0.0352370i
$341$	−3.22425			−0.174603
$342$		−	1.00000i		−	0.0540738i
$343$		−	9.29948i		−	0.502125i
$344$	6.18664			0.333561
$345$	−1.61213	−	1.42548i	−0.0867940	−	0.0767455i
$346$	1.47627			0.0793648
$347$			18.3879i			0.987113i	0.869714	+	0.493556i	$0.164303\pi$
$347$			18.3879i			0.987113i	−0.869714	+	0.493556i	$0.835697\pi$
$348$		−	6.96239i		−	0.373223i
$349$	−31.1490			−1.66737			−0.833685	−	0.552241i	$-0.813773\pi$
$349$	−31.1490			−1.66737			−0.833685	+	0.552241i	$0.813773\pi$
$350$	−2.05079	−	16.6253i	−0.109619	−	0.888660i
$351$	−1.61213			−0.0860490
$352$			0.962389i			0.0512955i
$353$		−	7.61213i		−	0.405153i	−0.979266	−	0.202576i	$-0.935069\pi$
$353$		−	7.61213i		−	0.405153i	0.979266	−	0.202576i	$-0.0649314\pi$
$354$	10.3127			0.548111
$355$	−12.1016	−	10.7005i	−0.642285	−	0.567925i
$356$	4.64974			0.246436
$357$			1.29948i			0.0687756i
$358$		−	14.3127i		−	0.756447i
$359$	35.3112			1.86366			0.931828	−	0.362901i	$-0.118214\pi$
$359$	35.3112			1.86366			0.931828	+	0.362901i	$0.118214\pi$
$360$	−1.48119	+	1.67513i	−0.0780658	+	0.0882871i
$361$	1.00000			0.0526316
$362$			8.82653i			0.463912i
$363$			10.0738i			0.528738i
$364$	−5.40105			−0.283092
$365$	4.77575	−	5.40105i	0.249974	−	0.282704i
$366$	−11.9248			−0.623318
$367$			31.9756i			1.66911i	0.550924	+	0.834555i	$0.314275\pi$
$367$			31.9756i			1.66911i	−0.550924	+	0.834555i	$0.685725\pi$
$368$			0.962389i			0.0501680i
$369$	9.27504			0.482839
$370$	2.70052	+	2.38787i	0.140394	+	0.124140i
$371$	−20.1016			−1.04362
$372$			3.35026i			0.173703i
$373$		−	26.4894i		−	1.37157i	−0.727804	−	0.685786i	$-0.759459\pi$
$373$		−	26.4894i		−	1.37157i	0.727804	−	0.685786i	$-0.240541\pi$
$374$	0.373285			0.0193021
$375$	−9.21933	−	6.32487i	−0.476084	−	0.326615i
$376$	−0.962389			−0.0496314
$377$		−	11.2243i		−	0.578078i
$378$		−	3.35026i		−	0.172319i
$379$	19.3258			0.992701			0.496350	−	0.868122i	$-0.334673\pi$
$379$	19.3258			0.992701			0.496350	+	0.868122i	$0.334673\pi$
$380$	−1.67513	−	1.48119i	−0.0859324	−	0.0759837i
$381$	1.35026			0.0691760
$382$		−	2.31265i		−	0.118325i
$383$		−	3.37470i		−	0.172439i	−0.996276	−	0.0862195i	$-0.972521\pi$
$383$		−	3.37470i		−	0.172439i	0.996276	−	0.0862195i	$-0.0274786\pi$
$384$	1.00000			0.0510310
$385$	4.77575	−	5.40105i	0.243395	−	0.275263i
$386$	−7.58769			−0.386203
$387$			6.18664i			0.314485i
$388$			10.9624i			0.556531i
$389$	11.3503			0.575481			0.287741	−	0.957708i	$-0.407096\pi$
$389$	11.3503			0.575481			0.287741	+	0.957708i	$0.407096\pi$
$390$	−2.38787	+	2.70052i	−0.120915	+	0.136746i
$391$	0.373285			0.0188778
$392$		−	4.22425i		−	0.213357i
$393$		−	12.4387i		−	0.627447i
$394$	−18.8119			−0.947732
$395$	−5.61213	−	4.96239i	−0.282377	−	0.249685i
$396$	−0.962389			−0.0483618
$397$		−	18.8364i		−	0.945371i	−0.881231	−	0.472685i	$-0.843285\pi$
$397$		−	18.8364i		−	0.945371i	0.881231	−	0.472685i	$-0.156715\pi$
$398$		−	9.40105i		−	0.471232i
$399$	3.35026			0.167723
$400$	0.612127	+	4.96239i	0.0306063	+	0.248119i
$401$	−4.12601			−0.206043			−0.103022	−	0.994679i	$-0.532851\pi$
$401$	−4.12601			−0.206043			−0.103022	+	0.994679i	$0.532851\pi$
$402$			7.22425i			0.360313i
$403$			5.40105i			0.269045i
$404$	−2.72496			−0.135572
$405$	−1.67513	−	1.48119i	−0.0832379	−	0.0736011i
$406$	23.3258			1.15764
$407$			1.55149i			0.0769046i
$408$		−	0.387873i		−	0.0192026i
$409$	−2.52373			−0.124790			−0.0623952	−	0.998052i	$-0.519874\pi$
$409$	−2.52373			−0.124790			−0.0623952	+	0.998052i	$0.519874\pi$
$410$	13.7381	−	15.5369i	0.678478	−	0.767313i
$411$	−18.1622			−0.895875
$412$			0.574515i			0.0283043i
$413$			34.5501i			1.70010i
$414$	−0.962389			−0.0472988
$415$	−22.2374	+	25.1490i	−1.09159	+	1.23452i
$416$	1.61213			0.0790410
$417$			8.77575i			0.429750i
$418$		−	0.962389i		−	0.0470720i
$419$	−7.51247			−0.367008			−0.183504	−	0.983019i	$-0.558744\pi$
$419$	−7.51247			−0.367008			−0.183504	+	0.983019i	$0.558744\pi$
$420$	−5.61213	−	4.96239i	−0.273844	−	0.242140i
$421$	3.67750			0.179230			0.0896152	−	0.995976i	$-0.471436\pi$
$421$	3.67750			0.179230			0.0896152	+	0.995976i	$0.471436\pi$
$422$		−	4.77575i		−	0.232480i
$423$		−	0.962389i		−	0.0467929i
$424$	6.00000			0.291386
$425$	1.92478	−	0.237428i	0.0933654	−	0.0115169i
$426$	−7.22425			−0.350016
$427$		−	39.9511i		−	1.93337i
$428$		−	10.7005i		−	0.517229i
$429$	−1.55149			−0.0749068
$430$	10.3634	+	9.16362i	0.499769	+	0.441909i
$431$	−10.3272			−0.497446			−0.248723	−	0.968575i	$-0.580011\pi$
$431$	−10.3272			−0.497446			−0.248723	+	0.968575i	$0.580011\pi$
$432$			1.00000i			0.0481125i
$433$		−	31.5877i		−	1.51801i	−0.651086	−	0.759004i	$-0.725686\pi$
$433$		−	31.5877i		−	1.51801i	0.651086	−	0.759004i	$-0.274314\pi$
$434$	−11.2243			−0.538781
$435$	10.3127	−	11.6629i	0.494454	−	0.559194i
$436$	10.1260			0.484948
$437$		−	0.962389i		−	0.0460373i
$438$		−	3.22425i		−	0.154061i
$439$	38.1524			1.82091			0.910456	−	0.413605i	$-0.135731\pi$
$439$	38.1524			1.82091			0.910456	+	0.413605i	$0.135731\pi$
$440$	−1.42548	+	1.61213i	−0.0679573	+	0.0768551i
$441$	4.22425			0.201155
$442$		−	0.625301i		−	0.0297425i
$443$		−	16.3127i		−	0.775037i	−0.921862	−	0.387519i	$-0.873332\pi$
$443$		−	16.3127i		−	0.775037i	0.921862	−	0.387519i	$-0.126668\pi$
$444$	1.61213			0.0765082
$445$	7.78892	+	6.88717i	0.369230	+	0.326483i
$446$	24.6761			1.16845
$447$			15.9756i			0.755618i
$448$			3.35026i			0.158285i
$449$	37.5271			1.77101			0.885506	−	0.464629i	$-0.153812\pi$
$449$	37.5271			1.77101			0.885506	+	0.464629i	$0.153812\pi$
$450$	−4.96239	+	0.612127i	−0.233929	+	0.0288559i
$451$	8.92619			0.420318
$452$			20.5501i			0.966594i
$453$		−	18.4241i		−	0.865638i
$454$	15.4763			0.726337
$455$	−9.04746	−	8.00000i	−0.424151	−	0.375046i
$456$	−1.00000			−0.0468293
$457$		−	8.00000i		−	0.374224i	−0.982339	−	0.187112i	$-0.940087\pi$
$457$		−	8.00000i		−	0.374224i	0.982339	−	0.187112i	$-0.0599128\pi$
$458$			21.3258i			0.996490i
$459$	0.387873			0.0181044
$460$	−1.42548	+	1.61213i	−0.0664636	+	0.0751658i
$461$	12.3780			0.576502			0.288251	−	0.957555i	$-0.406926\pi$
$461$	12.3780			0.576502			0.288251	+	0.957555i	$0.406926\pi$
$462$		−	3.22425i		−	0.150006i
$463$		−	32.4504i		−	1.50810i	−0.656818	−	0.754049i	$-0.728098\pi$
$463$		−	32.4504i		−	1.50810i	0.656818	−	0.754049i	$-0.271902\pi$
$464$	−6.96239			−0.323221
$465$	−4.96239	+	5.61213i	−0.230125	+	0.260256i
$466$	9.01317			0.417527
$467$			7.53690i			0.348766i	0.984678	+	0.174383i	$0.0557931\pi$
$467$			7.53690i			0.348766i	−0.984678	+	0.174383i	$0.944207\pi$
$468$			1.61213i			0.0745206i
$469$	−24.2031			−1.11760
$470$	−1.61213	−	1.42548i	−0.0743619	−	0.0657527i
$471$	−13.7889			−0.635360
$472$		−	10.3127i		−	0.474678i
$473$			5.95395i			0.273763i
$474$	−3.35026			−0.153883
$475$	−0.612127	−	4.96239i	−0.0280863	−	0.227690i
$476$	1.29948			0.0595614
$477$			6.00000i			0.274721i
$478$		−	0.135857i		−	0.00621396i
$479$	−15.2097			−0.694947			−0.347474	−	0.937690i	$-0.612960\pi$
$479$	−15.2097			−0.694947			−0.347474	+	0.937690i	$0.612960\pi$
$480$	1.67513	+	1.48119i	0.0764589	+	0.0676070i
$481$	2.59895			0.118502
$482$			25.8496i			1.17741i
$483$		−	3.22425i		−	0.146709i
$484$	10.0738			0.457900
$485$	−16.2374	+	18.3634i	−0.737304	+	0.833841i
$486$	−1.00000			−0.0453609
$487$		−	1.19982i		−	0.0543689i	−0.999630	−	0.0271844i	$-0.991346\pi$
$487$		−	1.19982i		−	0.0543689i	0.999630	−	0.0271844i	$-0.00865414\pi$
$488$			11.9248i			0.539809i
$489$	3.73813			0.169044
$490$	6.25694	−	7.07618i	0.282660	−	0.319669i
$491$	−5.11283			−0.230739			−0.115369	−	0.993323i	$-0.536805\pi$
$491$	−5.11283			−0.230739			−0.115369	+	0.993323i	$0.536805\pi$
$492$		−	9.27504i		−	0.418151i
$493$			2.70052i			0.121625i
$494$	−1.61213			−0.0725330
$495$	−1.61213	−	1.42548i	−0.0724597	−	0.0640708i
$496$	3.35026			0.150431
$497$		−	24.2031i		−	1.08566i
$498$			15.0132i			0.672756i
$499$	−14.2981			−0.640069			−0.320035	−	0.947406i	$-0.603695\pi$
$499$	−14.2981			−0.640069			−0.320035	+	0.947406i	$0.603695\pi$
$500$	−6.32487	+	9.21933i	−0.282857	+	0.412301i
$501$	15.4763			0.691429
$502$			10.1114i			0.451295i
$503$		−	11.5125i		−	0.513316i	−0.966502	−	0.256658i	$-0.917379\pi$
$503$		−	11.5125i		−	0.513316i	0.966502	−	0.256658i	$-0.0826213\pi$
$504$	−3.35026			−0.149233
$505$	−4.56467	−	4.03620i	−0.203125	−	0.179608i
$506$	−0.926192			−0.0411742
$507$		−	10.4010i		−	0.461927i
$508$		−	1.35026i		−	0.0599082i
$509$	31.9610			1.41665			0.708323	−	0.705889i	$-0.249452\pi$
$509$	31.9610			1.41665			0.708323	+	0.705889i	$0.249452\pi$
$510$	0.574515	−	0.649738i	0.0254400	−	0.0287709i
$511$	10.8021			0.477857
$512$		−	1.00000i		−	0.0441942i
$513$		−	1.00000i		−	0.0441511i
$514$	26.9986			1.19086
$515$	−0.850969	+	0.962389i	−0.0374982	+	0.0424079i
$516$	6.18664			0.272352
$517$		−	0.926192i		−	0.0407339i
$518$			5.40105i			0.237308i
$519$	1.47627			0.0648010
$520$	2.70052	+	2.38787i	0.118426	+	0.104715i
$521$	−33.2750			−1.45781			−0.728903	−	0.684617i	$-0.759969\pi$
$521$	−33.2750			−1.45781			−0.728903	+	0.684617i	$0.759969\pi$
$522$		−	6.96239i		−	0.304735i
$523$			9.29948i			0.406638i	0.979113	+	0.203319i	$0.0651728\pi$
$523$			9.29948i			0.406638i	−0.979113	+	0.203319i	$0.934827\pi$
$524$	−12.4387			−0.543385
$525$	−2.05079	−	16.6253i	−0.0895036	−	0.725588i
$526$	−15.0376			−0.655671
$527$		−	1.29948i		−	0.0566061i
$528$			0.962389i			0.0418826i
$529$	22.0738			0.959731
$530$	10.0508	+	8.88717i	0.436578	+	0.386034i
$531$	10.3127			0.447531
$532$		−	3.35026i		−	0.145252i
$533$		−	14.9525i		−	0.647666i
$534$	4.64974			0.201214
$535$	15.8496	−	17.9248i	0.685236	−	0.774956i
$536$	7.22425			0.312040
$537$		−	14.3127i		−	0.617636i
$538$		−	4.51388i		−	0.194607i
$539$	4.06537			0.175108
$540$	−1.48119	+	1.67513i	−0.0637405	+	0.0720862i
$541$	28.5501			1.22746			0.613732	−	0.789515i	$-0.289668\pi$
$541$	28.5501			1.22746			0.613732	+	0.789515i	$0.289668\pi$
$542$		−	15.8496i		−	0.680797i
$543$			8.82653i			0.378783i
$544$	−0.387873			−0.0166299
$545$	16.9624	+	14.9986i	0.726589	+	0.642469i
$546$	−5.40105			−0.231143
$547$		−	28.4749i		−	1.21750i	−0.793363	−	0.608748i	$-0.791672\pi$
$547$		−	28.4749i		−	1.21750i	0.793363	−	0.608748i	$-0.208328\pi$
$548$			18.1622i			0.775851i
$549$	−11.9248			−0.508937
$550$	−4.77575	+	0.589104i	−0.203639	+	0.0251195i
$551$	6.96239			0.296608
$552$			0.962389i			0.0409620i
$553$		−	11.2243i		−	0.477304i
$554$	10.3127			0.438143
$555$	2.70052	+	2.38787i	0.114631	+	0.101360i
$556$	8.77575			0.372175
$557$		−	4.88717i		−	0.207076i	−0.994626	−	0.103538i	$-0.966984\pi$
$557$		−	4.88717i		−	0.207076i	0.994626	−	0.103538i	$-0.0330163\pi$
$558$			3.35026i			0.141828i
$559$	9.97365			0.421841
$560$	−4.96239	+	5.61213i	−0.209699	+	0.237156i
$561$	0.373285			0.0157601
$562$		−	24.3488i		−	1.02709i
$563$		−	30.8021i		−	1.29815i	−0.760723	−	0.649077i	$-0.775155\pi$
$563$		−	30.8021i		−	1.29815i	0.760723	−	0.649077i	$-0.224845\pi$
$564$	−0.962389			−0.0405239
$565$	−30.4387	+	34.4241i	−1.28056	+	1.44823i
$566$	−26.2882			−1.10498
$567$		−	3.35026i		−	0.140698i
$568$			7.22425i			0.303123i
$569$	24.1260			1.01141			0.505707	−	0.862705i	$-0.331232\pi$
$569$	24.1260			1.01141			0.505707	+	0.862705i	$0.331232\pi$
$570$	−1.67513	−	1.48119i	−0.0701635	−	0.0620404i
$571$	−5.67276			−0.237398			−0.118699	−	0.992930i	$-0.537872\pi$
$571$	−5.67276			−0.237398			−0.118699	+	0.992930i	$0.537872\pi$
$572$			1.55149i			0.0648712i
$573$		−	2.31265i		−	0.0966124i
$574$	31.0738			1.29700
$575$	−4.77575	+	0.589104i	−0.199162	+	0.0245673i
$576$	1.00000			0.0416667
$577$		−	32.0000i		−	1.33218i	−0.745873	−	0.666089i	$-0.767967\pi$
$577$		−	32.0000i		−	1.33218i	0.745873	−	0.666089i	$-0.232033\pi$
$578$		−	16.8496i		−	0.700849i
$579$	−7.58769			−0.315334
$580$	−11.6629	−	10.3127i	−0.484276	−	0.428209i
$581$	−50.2981			−2.08672
$582$			10.9624i			0.454406i
$583$			5.77433i			0.239148i
$584$	−3.22425			−0.133421
$585$	−2.38787	+	2.70052i	−0.0987264	+	0.111653i
$586$	13.0738			0.540074
$587$		−	13.6121i		−	0.561833i	−0.959732	−	0.280916i	$-0.909362\pi$
$587$		−	13.6121i		−	0.561833i	0.959732	−	0.280916i	$-0.0906383\pi$
$588$		−	4.22425i		−	0.174205i
$589$	−3.35026			−0.138045
$590$	15.2750	−	17.2750i	0.628863	−	0.711202i
$591$	−18.8119			−0.773820
$592$		−	1.61213i		−	0.0662580i
$593$		−	23.4617i		−	0.963456i	−0.876321	−	0.481728i	$-0.840009\pi$
$593$		−	23.4617i		−	0.963456i	0.876321	−	0.481728i	$-0.159991\pi$
$594$	−0.962389			−0.0394873
$595$	2.17679	+	1.92478i	0.0892398	+	0.0789082i
$596$	15.9756			0.654385
$597$		−	9.40105i		−	0.384759i
$598$			1.55149i			0.0634452i
$599$	−10.0263			−0.409665			−0.204833	−	0.978797i	$-0.565665\pi$
$599$	−10.0263			−0.409665			−0.204833	+	0.978797i	$0.565665\pi$
$600$	0.612127	+	4.96239i	0.0249900	+	0.202589i
$601$	11.7743			0.480285			0.240143	−	0.970738i	$-0.422806\pi$
$601$	11.7743			0.480285			0.240143	+	0.970738i	$0.422806\pi$
$602$			20.7269i			0.844764i
$603$			7.22425i			0.294194i
$604$	−18.4241			−0.749665
$605$	16.8749	+	14.9213i	0.686064	+	0.606636i
$606$	−2.72496			−0.110694
$607$			38.4993i			1.56264i	0.624132	+	0.781319i	$0.285453\pi$
$607$			38.4993i			1.56264i	−0.624132	+	0.781319i	$0.714547\pi$
$608$			1.00000i			0.0405554i
$609$	23.3258			0.945210
$610$	−17.6629	+	19.9756i	−0.715150	+	0.808787i
$611$	−1.55149			−0.0627667
$612$		−	0.387873i		−	0.0156788i
$613$			7.61213i			0.307451i	0.988114	+	0.153725i	$0.0491271\pi$
$613$			7.61213i			0.307451i	−0.988114	+	0.153725i	$0.950873\pi$
$614$	−7.07381			−0.285476
$615$	13.7381	−	15.5369i	0.553975	−	0.626508i
$616$	−3.22425			−0.129909
$617$		−	29.5369i		−	1.18911i	−0.804055	−	0.594555i	$-0.797328\pi$
$617$		−	29.5369i		−	1.18911i	0.804055	−	0.594555i	$-0.202672\pi$
$618$			0.574515i			0.0231104i
$619$	22.5501			0.906364			0.453182	−	0.891418i	$-0.350289\pi$
$619$	22.5501			0.906364			0.453182	+	0.891418i	$0.350289\pi$
$620$	5.61213	+	4.96239i	0.225388	+	0.199294i
$621$	−0.962389			−0.0386193
$622$		−	26.3127i		−	1.05504i
$623$			15.5778i			0.624113i
$624$	1.61213			0.0645367
$625$	−24.2506	+	6.07522i	−0.970024	+	0.243009i
$626$	18.7005			0.747423
$627$		−	0.962389i		−	0.0384341i
$628$			13.7889i			0.550238i
$629$	−0.625301			−0.0249324
$630$	−5.61213	−	4.96239i	−0.223592	−	0.197706i
$631$	−37.9248			−1.50976			−0.754881	−	0.655862i	$-0.772305\pi$
$631$	−37.9248			−1.50976			−0.754881	+	0.655862i	$0.772305\pi$
$632$			3.35026i			0.133266i
$633$		−	4.77575i		−	0.189819i
$634$	26.4749			1.05145
$635$	2.00000	−	2.26187i	0.0793676	−	0.0897594i
$636$	6.00000			0.237915
$637$		−	6.81003i		−	0.269823i
$638$		−	6.70052i		−	0.265276i
$639$	−7.22425			−0.285787
$640$	1.48119	−	1.67513i	0.0585493	−	0.0662154i
$641$	6.67609			0.263690			0.131845	−	0.991270i	$-0.457910\pi$
$641$	6.67609			0.263690			0.131845	+	0.991270i	$0.457910\pi$
$642$		−	10.7005i		−	0.422316i
$643$			25.2605i			0.996175i	0.867127	+	0.498087i	$0.165964\pi$
$643$			25.2605i			0.996175i	−0.867127	+	0.498087i	$0.834036\pi$
$644$	−3.22425			−0.127053
$645$	10.3634	+	9.16362i	0.408060	+	0.360817i
$646$	0.387873			0.0152607
$647$		−	16.9135i		−	0.664939i	−0.943114	−	0.332469i	$-0.892118\pi$
$647$		−	16.9135i		−	0.664939i	0.943114	−	0.332469i	$-0.107882\pi$
$648$			1.00000i			0.0392837i
$649$	9.92478			0.389582
$650$	0.986826	+	8.00000i	0.0387065	+	0.313786i
$651$	−11.2243			−0.439913
$652$		−	3.73813i		−	0.146397i
$653$			24.1114i			0.943553i	0.881718	+	0.471776i	$0.156387\pi$
$653$			24.1114i			0.943553i	−0.881718	+	0.471776i	$0.843613\pi$
$654$	10.1260			0.395958
$655$	−20.8364	−	18.4241i	−0.814145	−	0.719888i
$656$	−9.27504			−0.362129
$657$		−	3.22425i		−	0.125790i
$658$		−	3.22425i		−	0.125694i
$659$	20.3879			0.794199			0.397099	−	0.917776i	$-0.370017\pi$
$659$	20.3879			0.794199			0.397099	+	0.917776i	$0.370017\pi$
$660$	−1.42548	+	1.61213i	−0.0554869	+	0.0627520i
$661$	17.6023			0.684649			0.342325	−	0.939582i	$-0.388786\pi$
$661$	17.6023			0.684649			0.342325	+	0.939582i	$0.388786\pi$
$662$			30.7005i			1.19321i
$663$		−	0.625301i		−	0.0242847i
$664$	15.0132			0.582624
$665$	4.96239	−	5.61213i	0.192433	−	0.217629i
$666$	1.61213			0.0624686
$667$		−	6.70052i		−	0.259445i
$668$		−	15.4763i		−	0.598795i
$669$	24.6761			0.954033
$670$	12.1016	+	10.7005i	0.467524	+	0.413397i
$671$	−11.4763			−0.443036
$672$			3.35026i			0.129239i
$673$			44.3634i			1.71008i	0.518558	+	0.855042i	$0.326469\pi$
$673$			44.3634i			1.71008i	−0.518558	+	0.855042i	$0.673531\pi$
$674$	6.81194			0.262386
$675$	−4.96239	+	0.612127i	−0.191002	+	0.0235608i
$676$	−10.4010			−0.400040
$677$		−	8.70052i		−	0.334388i	−0.985924	−	0.167194i	$-0.946529\pi$
$677$		−	8.70052i		−	0.334388i	0.985924	−	0.167194i	$-0.0534707\pi$
$678$			20.5501i			0.789221i
$679$	−36.7269			−1.40945
$680$	−0.649738	−	0.574515i	−0.0249163	−	0.0220317i
$681$	15.4763			0.593052
$682$			3.22425i			0.123463i
$683$		−	37.8759i		−	1.44928i	−0.689127	−	0.724641i	$-0.742006\pi$
$683$		−	37.8759i		−	1.44928i	0.689127	−	0.724641i	$-0.257994\pi$
$684$	−1.00000			−0.0382360
$685$	−26.9018	+	30.4241i	−1.02786	+	1.16244i
$686$	−9.29948			−0.355056
$687$			21.3258i			0.813631i
$688$		−	6.18664i		−	0.235864i
$689$	9.67276			0.368503
$690$	−1.42548	+	1.61213i	−0.0542673	+	0.0613726i
$691$	−0.775746			−0.0295108			−0.0147554	−	0.999891i	$-0.504697\pi$
$691$	−0.775746			−0.0295108			−0.0147554	+	0.999891i	$0.504697\pi$
$692$		−	1.47627i		−	0.0561194i
$693$		−	3.22425i		−	0.122479i
$694$	18.3879			0.697994
$695$	14.7005	+	12.9986i	0.557623	+	0.493064i
$696$	−6.96239			−0.263909
$697$			3.59754i			0.136266i
$698$			31.1490i			1.17901i
$699$	9.01317			0.340910
$700$	−16.6253	+	2.05079i	−0.628377	+	0.0775124i
$701$	42.3752			1.60049			0.800245	−	0.599674i	$-0.204703\pi$
$701$	42.3752			1.60049			0.800245	+	0.599674i	$0.204703\pi$
$702$			1.61213i			0.0608458i
$703$			1.61213i			0.0608025i
$704$	0.962389			0.0362714
$705$	−1.61213	−	1.42548i	−0.0607162	−	0.0536869i
$706$	−7.61213			−0.286486
$707$		−	9.12933i		−	0.343344i
$708$		−	10.3127i		−	0.387573i
$709$	−36.2784			−1.36246			−0.681231	−	0.732068i	$-0.738555\pi$
$709$	−36.2784			−1.36246			−0.681231	+	0.732068i	$0.738555\pi$
$710$	−10.7005	+	12.1016i	−0.401583	+	0.454164i
$711$	−3.35026			−0.125645
$712$		−	4.64974i		−	0.174256i
$713$			3.22425i			0.120749i
$714$	1.29948			0.0486317
$715$	−2.29806	+	2.59895i	−0.0859426	+	0.0971953i
$716$	−14.3127			−0.534889
$717$		−	0.135857i		−	0.00507368i
$718$		−	35.3112i		−	1.31780i
$719$	42.5355			1.58631			0.793153	−	0.609022i	$-0.208438\pi$
$719$	42.5355			1.58631			0.793153	+	0.609022i	$0.208438\pi$
$720$	1.67513	+	1.48119i	0.0624284	+	0.0552009i
$721$	−1.92478			−0.0716824
$722$		−	1.00000i		−	0.0372161i
$723$			25.8496i			0.961355i
$724$	8.82653			0.328035
$725$	−4.26187	−	34.5501i	−0.158282	−	1.28316i
$726$	10.0738			0.373874
$727$			0.378024i			0.0140201i	0.999975	+	0.00701007i	$0.00223139\pi$
$727$			0.378024i			0.0140201i	−0.999975	+	0.00701007i	$0.997769\pi$
$728$			5.40105i			0.200176i
$729$	−1.00000			−0.0370370
$730$	−5.40105	−	4.77575i	−0.199902	−	0.176758i
$731$	−2.39963			−0.0887536
$732$			11.9248i			0.440752i
$733$			26.0118i			0.960766i	0.877059	+	0.480383i	$0.159502\pi$
$733$			26.0118i			0.960766i	−0.877059	+	0.480383i	$0.840498\pi$
$734$	31.9756			1.18024
$735$	6.25694	−	7.07618i	0.230791	−	0.261009i
$736$	0.962389			0.0354741
$737$			6.95254i			0.256100i
$738$		−	9.27504i		−	0.341419i
$739$	44.8773			1.65084			0.825419	−	0.564520i	$-0.190939\pi$
$739$	44.8773			1.65084			0.825419	+	0.564520i	$0.190939\pi$
$740$	2.38787	−	2.70052i	0.0877800	−	0.0992732i
$741$	−1.61213			−0.0592230
$742$			20.1016i			0.737952i
$743$		−	4.67418i		−	0.171479i	−0.996318	−	0.0857394i	$-0.972675\pi$
$743$		−	4.67418i		−	0.171479i	0.996318	−	0.0857394i	$-0.0273253\pi$
$744$	3.35026			0.122827
$745$	26.7612	+	23.6629i	0.980453	+	0.866942i
$746$	−26.4894			−0.969847
$747$			15.0132i			0.549303i
$748$		−	0.373285i		−	0.0136486i
$749$	35.8496			1.30991
$750$	−6.32487	+	9.21933i	−0.230952	+	0.336642i
$751$	−6.57452			−0.239907			−0.119954	−	0.992779i	$-0.538275\pi$
$751$	−6.57452			−0.239907			−0.119954	+	0.992779i	$0.538275\pi$
$752$			0.962389i			0.0350947i
$753$			10.1114i			0.368481i
$754$	−11.2243			−0.408763
$755$	−30.8627	−	27.2896i	−1.12321	−	0.993171i
$756$	−3.35026			−0.121848
$757$			15.5633i			0.565656i	0.959171	+	0.282828i	$0.0912726\pi$
$757$			15.5633i			0.565656i	−0.959171	+	0.282828i	$0.908727\pi$
$758$		−	19.3258i		−	0.701946i
$759$	−0.926192			−0.0336186
$760$	−1.48119	+	1.67513i	−0.0537286	+	0.0607634i
$761$	−23.8759			−0.865501			−0.432750	−	0.901514i	$-0.642457\pi$
$761$	−23.8759			−0.865501			−0.432750	+	0.901514i	$0.642457\pi$
$762$		−	1.35026i		−	0.0489148i
$763$			33.9248i			1.22816i
$764$	−2.31265			−0.0836688
$765$	0.574515	−	0.649738i	0.0207717	−	0.0234913i
$766$	−3.37470			−0.121933
$767$		−	16.6253i		−	0.600305i
$768$		−	1.00000i		−	0.0360844i
$769$	−30.4749			−1.09895			−0.549476	−	0.835510i	$-0.685173\pi$
$769$	−30.4749			−1.09895			−0.549476	+	0.835510i	$0.685173\pi$
$770$	−5.40105	−	4.77575i	−0.194640	−	0.172106i
$771$	26.9986			0.972330
$772$			7.58769i			0.273087i
$773$			16.3272i			0.587250i	0.955921	+	0.293625i	$0.0948617\pi$
$773$			16.3272i			0.587250i	−0.955921	+	0.293625i	$0.905138\pi$
$774$	6.18664			0.222374
$775$	2.05079	+	16.6253i	0.0736664	+	0.597198i
$776$	10.9624			0.393527
$777$			5.40105i			0.193761i
$778$		−	11.3503i		−	0.406927i
$779$	9.27504			0.332313
$780$	2.70052	+	2.38787i	0.0966943	+	0.0854996i
$781$	−6.95254			−0.248781
$782$		−	0.373285i		−	0.0133486i
$783$		−	6.96239i		−	0.248815i
$784$	−4.22425			−0.150866
$785$	−20.4241	+	23.0982i	−0.728966	+	0.824412i
$786$	−12.4387			−0.443672
$787$		−	30.9525i		−	1.10334i	−0.834063	−	0.551669i	$-0.813991\pi$
$787$		−	30.9525i		−	1.10334i	0.834063	−	0.551669i	$-0.186009\pi$
$788$			18.8119i			0.670148i
$789$	−15.0376			−0.535353
$790$	−4.96239	+	5.61213i	−0.176554	+	0.199671i
$791$	−68.8481			−2.44796
$792$			0.962389i			0.0341970i
$793$			19.2243i			0.682673i
$794$	−18.8364			−0.668478
$795$	10.0508	+	8.88717i	0.356465	+	0.315195i
$796$	−9.40105			−0.333211
$797$		−	14.8773i		−	0.526982i	−0.964662	−	0.263491i	$-0.915126\pi$
$797$		−	14.8773i		−	0.526982i	0.964662	−	0.263491i	$-0.0848739\pi$
$798$		−	3.35026i		−	0.118598i
$799$	0.373285			0.0132059
$800$	4.96239	−	0.612127i	0.175447	−	0.0216420i
$801$	4.64974			0.164290
$802$			4.12601i			0.145694i
$803$		−	3.10299i		−	0.109502i
$804$	7.22425			0.254780
$805$	−5.40105	−	4.77575i	−0.190362	−	0.168323i
$806$	5.40105			0.190244
$807$		−	4.51388i		−	0.158896i
$808$			2.72496i			0.0958638i
$809$	−25.4471			−0.894672			−0.447336	−	0.894366i	$-0.647627\pi$
$809$	−25.4471			−0.894672			−0.447336	+	0.894366i	$0.647627\pi$
$810$	−1.48119	+	1.67513i	−0.0520439	+	0.0588581i
$811$	−53.3522			−1.87345			−0.936724	−	0.350069i	$-0.886158\pi$
$811$	−53.3522			−1.87345			−0.936724	+	0.350069i	$0.886158\pi$
$812$		−	23.3258i		−	0.818576i
$813$		−	15.8496i		−	0.555868i
$814$	1.55149			0.0543798
$815$	5.53690	−	6.26187i	0.193949	−	0.219344i
$816$	−0.387873			−0.0135783
$817$			6.18664i			0.216443i
$818$			2.52373i			0.0882402i
$819$	−5.40105			−0.188728
$820$	−15.5369	−	13.7381i	−0.542572	−	0.479756i
$821$	−27.9756			−0.976354			−0.488177	−	0.872745i	$-0.662338\pi$
$821$	−27.9756			−0.976354			−0.488177	+	0.872745i	$0.662338\pi$
$822$			18.1622i			0.633480i
$823$		−	7.87399i		−	0.274470i	−0.990539	−	0.137235i	$-0.956178\pi$
$823$		−	7.87399i		−	0.274470i	0.990539	−	0.137235i	$-0.0438216\pi$
$824$	0.574515			0.0200142
$825$	−4.77575	+	0.589104i	−0.166270	+	0.0205100i
$826$	34.5501			1.20215
$827$		−	40.1016i		−	1.39447i	−0.716843	−	0.697234i	$-0.754414\pi$
$827$		−	40.1016i		−	1.39447i	0.716843	−	0.697234i	$-0.245586\pi$
$828$			0.962389i			0.0334453i
$829$	−47.2262			−1.64023			−0.820116	−	0.572197i	$-0.806091\pi$
$829$	−47.2262			−1.64023			−0.820116	+	0.572197i	$0.806091\pi$
$830$	25.1490	+	22.2374i	0.872936	+	0.771872i
$831$	10.3127			0.357742
$832$		−	1.61213i		−	0.0558904i
$833$			1.63847i			0.0567698i
$834$	8.77575			0.303879
$835$	22.9234	−	25.9248i	0.793296	−	0.897164i
$836$	−0.962389			−0.0332849
$837$			3.35026i			0.115802i
$838$			7.51247i			0.259514i
$839$	3.89843			0.134589			0.0672944	−	0.997733i	$-0.478563\pi$
$839$	3.89843			0.134589			0.0672944	+	0.997733i	$0.478563\pi$
$840$	−4.96239	+	5.61213i	−0.171219	+	0.193637i
$841$	19.4749			0.671547
$842$		−	3.67750i		−	0.126735i
$843$		−	24.3488i		−	0.838619i
$844$	−4.77575			−0.164388
$845$	−17.4231	−	15.4060i	−0.599373	−	0.529982i
$846$	−0.962389			−0.0330876
$847$			33.7499i			1.15966i
$848$		−	6.00000i		−	0.206041i
$849$	−26.2882			−0.902209
$850$	−0.237428	−	1.92478i	−0.00814370	−	0.0660193i
$851$	1.55149			0.0531845
$852$			7.22425i			0.247499i
$853$			35.1900i			1.20488i	0.798164	+	0.602441i	$0.205805\pi$
$853$			35.1900i			1.20488i	−0.798164	+	0.602441i	$0.794195\pi$
$854$	−39.9511			−1.36710
$855$	−1.67513	−	1.48119i	−0.0572883	−	0.0506558i
$856$	−10.7005			−0.365736
$857$			12.1768i			0.415951i	0.978134	+	0.207976i	$0.0666875\pi$
$857$			12.1768i			0.415951i	−0.978134	+	0.207976i	$0.933313\pi$
$858$			1.55149i			0.0529671i
$859$	−57.3522			−1.95683			−0.978415	−	0.206648i	$-0.933745\pi$
$859$	−57.3522			−1.95683			−0.978415	+	0.206648i	$0.933745\pi$
$860$	9.16362	−	10.3634i	0.312477	−	0.353390i
$861$	31.0738			1.05899
$862$			10.3272i			0.351747i
$863$			14.0752i			0.479126i	0.970881	+	0.239563i	$0.0770042\pi$
$863$			14.0752i			0.479126i	−0.970881	+	0.239563i	$0.922996\pi$
$864$	1.00000			0.0340207
$865$	2.18664	−	2.47295i	0.0743481	−	0.0840827i
$866$	−31.5877			−1.07339
$867$		−	16.8496i		−	0.572241i
$868$			11.2243i			0.380976i
$869$	−3.22425			−0.109375
$870$	−11.6629	−	10.3127i	−0.395410	−	0.349632i
$871$	11.6464			0.394624
$872$		−	10.1260i		−	0.342910i
$873$			10.9624i			0.371021i
$874$	−0.962389			−0.0325533
$875$	−30.8872	−	21.1900i	−1.04418	−	0.716352i
$876$	−3.22425			−0.108937
$877$			18.8627i			0.636949i	0.947931	+	0.318475i	$0.103171\pi$
$877$			18.8627i			0.636949i	−0.947931	+	0.318475i	$0.896829\pi$
$878$		−	38.1524i		−	1.28758i
$879$	13.0738			0.440969
$880$	1.61213	+	1.42548i	0.0543448	+	0.0480531i
$881$	−19.1490			−0.645147			−0.322574	−	0.946544i	$-0.604548\pi$
$881$	−19.1490			−0.645147			−0.322574	+	0.946544i	$0.604548\pi$
$882$		−	4.22425i		−	0.142238i
$883$		−	42.9135i		−	1.44415i	−0.691812	−	0.722077i	$-0.743187\pi$
$883$		−	42.9135i		−	1.44415i	0.691812	−	0.722077i	$-0.256813\pi$
$884$	−0.625301			−0.0210311
$885$	15.2750	−	17.2750i	0.513465	−	0.580694i
$886$	−16.3127			−0.548034
$887$			22.7005i			0.762209i	0.924532	+	0.381104i	$0.124456\pi$
$887$			22.7005i			0.762209i	−0.924532	+	0.381104i	$0.875544\pi$
$888$		−	1.61213i		−	0.0540994i
$889$	4.52373			0.151721
$890$	6.88717	−	7.78892i	0.230858	−	0.261085i
$891$	−0.962389			−0.0322412
$892$		−	24.6761i		−	0.826216i
$893$		−	0.962389i		−	0.0322051i
$894$	15.9756			0.534303
$895$	−23.9756	−	21.1998i	−0.801415	−	0.708632i
$896$	3.35026			0.111924
$897$			1.55149i			0.0518028i
$898$		−	37.5271i		−	1.25229i
$899$	−23.3258			−0.777960
$900$	0.612127	+	4.96239i	0.0204042	+	0.165413i
$901$	−2.32724			−0.0775316
$902$		−	8.92619i		−	0.297210i
$903$			20.7269i			0.689747i
$904$	20.5501			0.683485
$905$	14.7856	+	13.0738i	0.491490	+	0.434588i
$906$	−18.4241			−0.612099
$907$			14.5501i			0.483127i	0.970385	+	0.241564i	$0.0776603\pi$
$907$			14.5501i			0.483127i	−0.970385	+	0.241564i	$0.922340\pi$
$908$		−	15.4763i		−	0.513598i
$909$	−2.72496			−0.0903813
$910$	−8.00000	+	9.04746i	−0.265197	+	0.299920i
$911$	−0.998585			−0.0330846			−0.0165423	−	0.999863i	$-0.505266\pi$
$911$	−0.998585			−0.0330846			−0.0165423	+	0.999863i	$0.505266\pi$
$912$			1.00000i			0.0331133i
$913$			14.4485i			0.478176i
$914$	−8.00000			−0.264616
$915$	−17.6629	+	19.9756i	−0.583918	+	0.660372i
$916$	21.3258			0.704625
$917$		−	41.6728i		−	1.37616i
$918$		−	0.387873i		−	0.0128017i
$919$	33.7743			1.11411			0.557056	−	0.830475i	$-0.311931\pi$
$919$	33.7743			1.11411			0.557056	+	0.830475i	$0.311931\pi$
$920$	1.61213	+	1.42548i	0.0531502	+	0.0469968i
$921$	−7.07381			−0.233090
$922$		−	12.3780i		−	0.407649i
$923$			11.6464i			0.383346i
$924$	−3.22425			−0.106070
$925$	8.00000	−	0.986826i	0.263038	−	0.0324466i
$926$	−32.4504			−1.06639
$927$			0.574515i			0.0188696i
$928$			6.96239i			0.228552i
$929$	−14.8773			−0.488109			−0.244054	−	0.969762i	$-0.578478\pi$
$929$	−14.8773			−0.488109			−0.244054	+	0.969762i	$0.578478\pi$
$930$	5.61213	+	4.96239i	0.184029	+	0.162723i
$931$	4.22425			0.138444
$932$		−	9.01317i		−	0.295236i
$933$		−	26.3127i		−	0.861437i
$934$	7.53690			0.246615
$935$	0.552907	−	0.625301i	0.0180820	−	0.0204495i
$936$	1.61213			0.0526940
$937$			22.2981i			0.728446i	0.931312	+	0.364223i	$0.118665\pi$
$937$			22.2981i			0.728446i	−0.931312	+	0.364223i	$0.881335\pi$
$938$			24.2031i			0.790261i
$939$	18.7005			0.610269
$940$	−1.42548	+	1.61213i	−0.0464942	+	0.0525818i
$941$	−36.3634			−1.18541			−0.592707	−	0.805418i	$-0.701941\pi$
$941$	−36.3634			−1.18541			−0.592707	+	0.805418i	$0.701941\pi$
$942$			13.7889i			0.449267i
$943$		−	8.92619i		−	0.290677i
$944$	−10.3127			−0.335648
$945$	−5.61213	−	4.96239i	−0.182563	−	0.161427i
$946$	5.95395			0.193580
$947$			50.3390i			1.63580i	0.575362	+	0.817899i	$0.304861\pi$
$947$			50.3390i			1.63580i	−0.575362	+	0.817899i	$0.695139\pi$
$948$			3.35026i			0.108811i
$949$	−5.19791			−0.168731
$950$	−4.96239	+	0.612127i	−0.161001	+	0.0198600i
$951$	26.4749			0.858506
$952$		−	1.29948i		−	0.0421163i
$953$			16.3272i			0.528891i	0.964401	+	0.264446i	$0.0851890\pi$
$953$			16.3272i			0.528891i	−0.964401	+	0.264446i	$0.914811\pi$
$954$	6.00000			0.194257
$955$	−3.87399	−	3.42548i	−0.125359	−	0.110846i
$956$	−0.135857			−0.00439393
$957$		−	6.70052i		−	0.216597i
$958$			15.2097i			0.491402i
$959$	−60.8481			−1.96489
$960$	1.48119	−	1.67513i	0.0478053	−	0.0540646i
$961$	−19.7757			−0.637927
$962$		−	2.59895i		−	0.0837936i
$963$		−	10.7005i		−	0.344820i
$964$	25.8496			0.832558
$965$	−11.2388	+	12.7104i	−0.361791	+	0.409161i
$966$	−3.22425			−0.103739
$967$			0.276454i			0.00889015i	0.999990	+	0.00444507i	$0.00141492\pi$
$967$			0.276454i			0.00889015i	−0.999990	+	0.00444507i	$0.998585\pi$
$968$		−	10.0738i		−	0.323784i
$969$	0.387873			0.0124603
$970$	18.3634	+	16.2374i	0.589614	+	0.521352i
$971$	37.9102			1.21660			0.608298	−	0.793709i	$-0.291853\pi$
$971$	37.9102			1.21660			0.608298	+	0.793709i	$0.291853\pi$
$972$			1.00000i			0.0320750i
$973$			29.4010i			0.942554i
$974$	−1.19982			−0.0384446
$975$	0.986826	+	8.00000i	0.0316037	+	0.256205i
$976$	11.9248			0.381703
$977$			28.3996i			0.908585i	0.890853	+	0.454292i	$0.150108\pi$
$977$			28.3996i			0.908585i	−0.890853	+	0.454292i	$0.849892\pi$
$978$		−	3.73813i		−	0.119532i
$979$	4.47486			0.143017
$980$	−7.07618	−	6.25694i	−0.226040	−	0.199871i
$981$	10.1260			0.323299
$982$			5.11283i			0.163157i
$983$			0.926192i			0.0295409i	0.999891	+	0.0147705i	$0.00470176\pi$
$983$			0.926192i			0.0295409i	−0.999891	+	0.0147705i	$0.995298\pi$
$984$	−9.27504			−0.295677
$985$	−27.8641	+	31.5125i	−0.887825	+	1.00407i
$986$	2.70052			0.0860022
$987$		−	3.22425i		−	0.102629i
$988$			1.61213i			0.0512886i
$989$	5.95395			0.189325
$990$	−1.42548	+	1.61213i	−0.0453049	+	0.0512368i
$991$	30.5256			0.969679			0.484839	−	0.874603i	$-0.338878\pi$
$991$	30.5256			0.969679			0.484839	+	0.874603i	$0.338878\pi$
$992$		−	3.35026i		−	0.106371i
$993$			30.7005i			0.974252i
$994$	−24.2031			−0.767677
$995$	−15.7480	−	13.9248i	−0.499245	−	0.441445i
$996$	15.0132			0.475711
$997$			21.0132i			0.665494i	0.943016	+	0.332747i	$0.107975\pi$
$997$			21.0132i			0.665494i	−0.943016	+	0.332747i	$0.892025\pi$
$998$			14.2981i			0.452597i
$999$	1.61213			0.0510054

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.d.c.229.1	✓	6
3.2	odd	2		1710.2.d.f.1369.6		6
5.2	odd	4		2850.2.a.bm.1.3		3
5.3	odd	4		2850.2.a.bl.1.1		3
5.4	even	2	inner	570.2.d.c.229.4	yes	6
15.2	even	4		8550.2.a.ce.1.3		3
15.8	even	4		8550.2.a.cq.1.1		3
15.14	odd	2		1710.2.d.f.1369.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.d.c.229.1	✓	6	1.1	even	1	trivial
570.2.d.c.229.4	yes	6	5.4	even	2	inner
1710.2.d.f.1369.3		6	15.14	odd	2
1710.2.d.f.1369.6		6	3.2	odd	2
2850.2.a.bl.1.1		3	5.3	odd	4
2850.2.a.bm.1.3		3	5.2	odd	4
8550.2.a.ce.1.3		3	15.2	even	4
8550.2.a.cq.1.1		3	15.8	even	4

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:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	570.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} -1.00000i q^{3} -1.00000 q^{4} +(-1.67513 - 1.48119i) q^{5} -1.00000 q^{6} -3.35026i q^{7} +1.00000i q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} -1.00000i q^{3} -1.00000 q^{4} +(-1.67513 - 1.48119i) q^{5} -1.00000 q^{6} -3.35026i q^{7} +1.00000i q^{8} -1.00000 q^{9} +(-1.48119 + 1.67513i) q^{10} -0.962389 q^{11} +1.00000i q^{12} +1.61213i q^{13} -3.35026 q^{14} +(-1.48119 + 1.67513i) q^{15} +1.00000 q^{16} -0.387873i q^{17} +1.00000i q^{18} -1.00000 q^{19} +(1.67513 + 1.48119i) q^{20} -3.35026 q^{21} +0.962389i q^{22} +0.962389i q^{23} +1.00000 q^{24} +(0.612127 + 4.96239i) q^{25} +1.61213 q^{26} +1.00000i q^{27} +3.35026i q^{28} -6.96239 q^{29} +(1.67513 + 1.48119i) q^{30} +3.35026 q^{31} -1.00000i q^{32} +0.962389i q^{33} -0.387873 q^{34} +(-4.96239 + 5.61213i) q^{35} +1.00000 q^{36} -1.61213i q^{37} +1.00000i q^{38} +1.61213 q^{39} +(1.48119 - 1.67513i) q^{40} -9.27504 q^{41} +3.35026i q^{42} -6.18664i q^{43} +0.962389 q^{44} +(1.67513 + 1.48119i) q^{45} +0.962389 q^{46} +0.962389i q^{47} -1.00000i q^{48} -4.22425 q^{49} +(4.96239 - 0.612127i) q^{50} -0.387873 q^{51} -1.61213i q^{52} -6.00000i q^{53} +1.00000 q^{54} +(1.61213 + 1.42548i) q^{55} +3.35026 q^{56} +1.00000i q^{57} +6.96239i q^{58} -10.3127 q^{59} +(1.48119 - 1.67513i) q^{60} +11.9248 q^{61} -3.35026i q^{62} +3.35026i q^{63} -1.00000 q^{64} +(2.38787 - 2.70052i) q^{65} +0.962389 q^{66} -7.22425i q^{67} +0.387873i q^{68} +0.962389 q^{69} +(5.61213 + 4.96239i) q^{70} +7.22425 q^{71} -1.00000i q^{72} +3.22425i q^{73} -1.61213 q^{74} +(4.96239 - 0.612127i) q^{75} +1.00000 q^{76} +3.22425i q^{77} -1.61213i q^{78} +3.35026 q^{79} +(-1.67513 - 1.48119i) q^{80} +1.00000 q^{81} +9.27504i q^{82} -15.0132i q^{83} +3.35026 q^{84} +(-0.574515 + 0.649738i) q^{85} -6.18664 q^{86} +6.96239i q^{87} -0.962389i q^{88} -4.64974 q^{89} +(1.48119 - 1.67513i) q^{90} +5.40105 q^{91} -0.962389i q^{92} -3.35026i q^{93} +0.962389 q^{94} +(1.67513 + 1.48119i) q^{95} -1.00000 q^{96} -10.9624i q^{97} +4.22425i q^{98} +0.962389 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{4} - 6 q^{6} - 6 q^{9}+O(q^{10}) \) 6 * q - 6 * q^4 - 6 * q^6 - 6 * q^9	\( 6 q - 6 q^{4} - 6 q^{6} - 6 q^{9} + 2 q^{10} + 16 q^{11} + 2 q^{15} + 6 q^{16} - 6 q^{19} + 6 q^{24} + 2 q^{25} + 8 q^{26} - 20 q^{29} - 4 q^{34} - 8 q^{35} + 6 q^{36} + 8 q^{39} - 2 q^{40} + 8 q^{41} - 16 q^{44} - 16 q^{46} - 22 q^{49} + 8 q^{50} - 4 q^{51} + 6 q^{54} + 8 q^{55} - 20 q^{59} - 2 q^{60} + 28 q^{61} - 6 q^{64} + 16 q^{65} - 16 q^{66} - 16 q^{69} + 32 q^{70} + 40 q^{71} - 8 q^{74} + 8 q^{75} + 6 q^{76} + 6 q^{81} + 20 q^{85} - 12 q^{86} - 48 q^{89} - 2 q^{90} - 48 q^{91} - 16 q^{94} - 6 q^{96} - 16 q^{99}+O(q^{100}) \) 6 * q - 6 * q^4 - 6 * q^6 - 6 * q^9 + 2 * q^10 + 16 * q^11 + 2 * q^15 + 6 * q^16 - 6 * q^19 + 6 * q^24 + 2 * q^25 + 8 * q^26 - 20 * q^29 - 4 * q^34 - 8 * q^35 + 6 * q^36 + 8 * q^39 - 2 * q^40 + 8 * q^41 - 16 * q^44 - 16 * q^46 - 22 * q^49 + 8 * q^50 - 4 * q^51 + 6 * q^54 + 8 * q^55 - 20 * q^59 - 2 * q^60 + 28 * q^61 - 6 * q^64 + 16 * q^65 - 16 * q^66 - 16 * q^69 + 32 * q^70 + 40 * q^71 - 8 * q^74 + 8 * q^75 + 6 * q^76 + 6 * q^81 + 20 * q^85 - 12 * q^86 - 48 * q^89 - 2 * q^90 - 48 * q^91 - 16 * q^94 - 6 * q^96 - 16 * q^99

Introduction

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