LMFDB - Embedded newform 570.2.f.d.341.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,2,Mod(341,570)]

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([1, 0, 1]))

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

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

chi := DirichletCharacter("570.341");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.f (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:	$8$
Coefficient field:	8.0.7278137344.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} + x^{6} + 6x^{5} - 20x^{4} + 18x^{3} + 9x^{2} - 54x + 81 $ x^8 - 2x^7 + x^6 + 6x^5 - 20x^4 + 18x^3 + 9x^2 - 54x + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			341.5
Root			$0.209196 + 1.71937i$ of defining polynomial
Character	$\chi$	$=$	570.341
Dual form			570.2.f.d.341.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +(-0.209196 - 1.71937i) q^{3} +1.00000 q^{4} -1.00000i q^{5} +(-0.209196 - 1.71937i) q^{6} +0.264536 q^{7} +1.00000 q^{8} +(-2.91247 + 0.719371i) q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +(-0.209196 - 1.71937i) q^{3} +1.00000 q^{4} -1.00000i q^{5} +(-0.209196 - 1.71937i) q^{6} +0.264536 q^{7} +1.00000 q^{8} +(-2.91247 + 0.719371i) q^{9} -1.00000i q^{10} -2.00000i q^{11} +(-0.209196 - 1.71937i) q^{12} -5.43874i q^{13} +0.264536 q^{14} +(-1.71937 + 0.209196i) q^{15} +1.00000 q^{16} +3.28489i q^{17} +(-2.91247 + 0.719371i) q^{18} +(1.41839 - 4.12167i) q^{19} -1.00000i q^{20} +(-0.0553398 - 0.454835i) q^{21} -2.00000i q^{22} +3.96781i q^{23} +(-0.209196 - 1.71937i) q^{24} -1.00000 q^{25} -5.43874i q^{26} +(1.84614 + 4.85713i) q^{27} +0.264536 q^{28} -0.418392 q^{29} +(-1.71937 + 0.209196i) q^{30} -3.56041i q^{31} +1.00000 q^{32} +(-3.43874 + 0.418392i) q^{33} +3.28489i q^{34} -0.264536i q^{35} +(-2.91247 + 0.719371i) q^{36} -0.307712i q^{37} +(1.41839 - 4.12167i) q^{38} +(-9.35122 + 1.13776i) q^{39} -1.00000i q^{40} +2.15386 q^{41} +(-0.0553398 - 0.454835i) q^{42} +1.71427 q^{43} -2.00000i q^{44} +(0.719371 + 2.91247i) q^{45} +3.96781i q^{46} +5.71427i q^{47} +(-0.209196 - 1.71937i) q^{48} -6.93002 q^{49} -1.00000 q^{50} +(5.64794 - 0.687185i) q^{51} -5.43874i q^{52} -3.29588 q^{53} +(1.84614 + 4.85713i) q^{54} -2.00000 q^{55} +0.264536 q^{56} +(-7.38340 - 1.57651i) q^{57} -0.418392 q^{58} +12.5486 q^{59} +(-1.71937 + 0.209196i) q^{60} +9.18520 q^{61} -3.56041i q^{62} +(-0.770454 + 0.190299i) q^{63} +1.00000 q^{64} -5.43874 q^{65} +(-3.43874 + 0.418392i) q^{66} +0.666330i q^{67} +3.28489i q^{68} +(6.82214 - 0.830051i) q^{69} -0.264536i q^{70} +10.3484 q^{71} +(-2.91247 + 0.719371i) q^{72} +12.7024 q^{73} -0.307712i q^{74} +(0.209196 + 1.71937i) q^{75} +(1.41839 - 4.12167i) q^{76} -0.529072i q^{77} +(-9.35122 + 1.13776i) q^{78} +8.08948i q^{79} -1.00000i q^{80} +(7.96501 - 4.19030i) q^{81} +2.15386 q^{82} +16.7456i q^{83} +(-0.0553398 - 0.454835i) q^{84} +3.28489 q^{85} +1.71427 q^{86} +(0.0875259 + 0.719371i) q^{87} -2.00000i q^{88} -10.6829 q^{89} +(0.719371 + 2.91247i) q^{90} -1.43874i q^{91} +3.96781i q^{92} +(-6.12167 + 0.744824i) q^{93} +5.71427i q^{94} +(-4.12167 - 1.41839i) q^{95} +(-0.209196 - 1.71937i) q^{96} +1.47093i q^{97} -6.93002 q^{98} +(1.43874 + 5.82495i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{2} - 2 q^{3} + 8 q^{4} - 2 q^{6} + 4 q^{7} + 8 q^{8} + 2 q^{9}+O(q^{10}) $ 8 * q + 8 * q^2 - 2 * q^3 + 8 * q^4 - 2 * q^6 + 4 * q^7 + 8 * q^8 + 2 * q^9	$ 8 q + 8 q^{2} - 2 q^{3} + 8 q^{4} - 2 q^{6} + 4 q^{7} + 8 q^{8} + 2 q^{9} - 2 q^{12} + 4 q^{14} + 8 q^{16} + 2 q^{18} + 12 q^{19} - 2 q^{21} - 2 q^{24} - 8 q^{25} + 16 q^{27} + 4 q^{28} - 4 q^{29} + 8 q^{32} + 2 q^{36} + 12 q^{38} - 22 q^{39} + 16 q^{41} - 2 q^{42} - 40 q^{43} - 8 q^{45} - 2 q^{48} + 4 q^{49} - 8 q^{50} + 18 q^{51} + 28 q^{53} + 16 q^{54} - 16 q^{55} + 4 q^{56} - 30 q^{57} - 4 q^{58} - 4 q^{59} + 16 q^{61} - 34 q^{63} + 8 q^{64} - 16 q^{65} - 2 q^{69} + 24 q^{71} + 2 q^{72} - 4 q^{73} + 2 q^{75} + 12 q^{76} - 22 q^{78} + 34 q^{81} + 16 q^{82} - 2 q^{84} - 40 q^{86} + 26 q^{87} - 88 q^{89} - 8 q^{90} - 24 q^{93} - 8 q^{95} - 2 q^{96} + 4 q^{98} - 16 q^{99}+O(q^{100}) $ 8 * q + 8 * q^2 - 2 * q^3 + 8 * q^4 - 2 * q^6 + 4 * q^7 + 8 * q^8 + 2 * q^9 - 2 * q^12 + 4 * q^14 + 8 * q^16 + 2 * q^18 + 12 * q^19 - 2 * q^21 - 2 * q^24 - 8 * q^25 + 16 * q^27 + 4 * q^28 - 4 * q^29 + 8 * q^32 + 2 * q^36 + 12 * q^38 - 22 * q^39 + 16 * q^41 - 2 * q^42 - 40 * q^43 - 8 * q^45 - 2 * q^48 + 4 * q^49 - 8 * q^50 + 18 * q^51 + 28 * q^53 + 16 * q^54 - 16 * q^55 + 4 * q^56 - 30 * q^57 - 4 * q^58 - 4 * q^59 + 16 * q^61 - 34 * q^63 + 8 * q^64 - 16 * q^65 - 2 * q^69 + 24 * q^71 + 2 * q^72 - 4 * q^73 + 2 * q^75 + 12 * q^76 - 22 * q^78 + 34 * q^81 + 16 * q^82 - 2 * q^84 - 40 * q^86 + 26 * q^87 - 88 * q^89 - 8 * q^90 - 24 * q^93 - 8 * q^95 - 2 * q^96 + 4 * q^98 - 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 $

$2$	1.00000			0.707107
$2$	1.00000			0.707107
$3$	−0.209196	−	1.71937i	−0.120779	−	0.992679i
$3$	−0.209196	−	1.71937i	−0.120779	−	0.992679i
$4$	1.00000			0.500000
$5$		−	1.00000i		−	0.447214i
$5$		−	1.00000i		−	0.447214i
$6$	−0.209196	−	1.71937i	−0.0854039	−	0.701930i
$7$	0.264536			0.0999851			0.0499926	−	0.998750i	$-0.484080\pi$
$7$	0.264536			0.0999851			0.0499926	+	0.998750i	$0.484080\pi$
$8$	1.00000			0.353553
$9$	−2.91247	+	0.719371i	−0.970825	+	0.239790i
$10$		−	1.00000i		−	0.316228i
$11$		−	2.00000i		−	0.603023i	−0.953463	−	0.301511i	$-0.902509\pi$
$11$		−	2.00000i		−	0.603023i	0.953463	−	0.301511i	$-0.0974911\pi$
$12$	−0.209196	−	1.71937i	−0.0603897	−	0.496340i
$13$		−	5.43874i		−	1.50844i	−0.656624	−	0.754218i	$-0.728016\pi$
$13$		−	5.43874i		−	1.50844i	0.656624	−	0.754218i	$-0.271984\pi$
$14$	0.264536			0.0707002
$15$	−1.71937	+	0.209196i	−0.443940	+	0.0540142i
$16$	1.00000			0.250000
$17$			3.28489i			0.796702i	0.917233	+	0.398351i	$0.130417\pi$
$17$			3.28489i			0.796702i	−0.917233	+	0.398351i	$0.869583\pi$
$18$	−2.91247	+	0.719371i	−0.686477	+	0.169557i
$19$	1.41839	−	4.12167i	0.325401	−	0.945576i
$19$	1.41839	−	4.12167i	0.325401	−	0.945576i
$20$		−	1.00000i		−	0.223607i
$21$	−0.0553398	−	0.454835i	−0.0120761	−	0.0992532i
$22$		−	2.00000i		−	0.426401i
$23$			3.96781i			0.827346i	0.910425	+	0.413673i	$0.135754\pi$
$23$			3.96781i			0.827346i	−0.910425	+	0.413673i	$0.864246\pi$
$24$	−0.209196	−	1.71937i	−0.0427020	−	0.350965i
$25$	−1.00000			−0.200000
$26$		−	5.43874i		−	1.06663i
$27$	1.84614	+	4.85713i	0.355291	+	0.934756i
$28$	0.264536			0.0499926
$29$	−0.418392			−0.0776934			−0.0388467	−	0.999245i	$-0.512368\pi$
$29$	−0.418392			−0.0776934			−0.0388467	+	0.999245i	$0.512368\pi$
$30$	−1.71937	+	0.209196i	−0.313913	+	0.0381938i
$31$		−	3.56041i		−	0.639469i	−0.947507	−	0.319734i	$-0.896406\pi$
$31$		−	3.56041i		−	0.639469i	0.947507	−	0.319734i	$-0.103594\pi$
$32$	1.00000			0.176777
$33$	−3.43874	+	0.418392i	−0.598608	+	0.0728327i
$34$			3.28489i			0.563353i
$35$		−	0.264536i		−	0.0447147i
$36$	−2.91247	+	0.719371i	−0.485412	+	0.119895i
$37$		−	0.307712i		−	0.0505876i	−0.999680	−	0.0252938i	$-0.991948\pi$
$37$		−	0.307712i		−	0.0505876i	0.999680	−	0.0252938i	$-0.00805212\pi$
$38$	1.41839	−	4.12167i	0.230094	−	0.668623i
$39$	−9.35122	+	1.13776i	−1.49739	+	0.182188i
$40$		−	1.00000i		−	0.158114i
$41$	2.15386			0.336376			0.168188	−	0.985755i	$-0.446208\pi$
$41$	2.15386			0.336376			0.168188	+	0.985755i	$0.446208\pi$
$42$	−0.0553398	−	0.454835i	−0.00853912	−	0.0701826i
$43$	1.71427			0.261423			0.130712	−	0.991420i	$-0.458274\pi$
$43$	1.71427			0.261423			0.130712	+	0.991420i	$0.458274\pi$
$44$		−	2.00000i		−	0.301511i
$45$	0.719371	+	2.91247i	0.107238	+	0.434166i
$46$			3.96781i			0.585022i
$47$			5.71427i			0.833512i	0.909018	+	0.416756i	$0.136833\pi$
$47$			5.71427i			0.833512i	−0.909018	+	0.416756i	$0.863167\pi$
$48$	−0.209196	−	1.71937i	−0.0301948	−	0.248170i
$49$	−6.93002			−0.990003
$50$	−1.00000			−0.141421
$51$	5.64794	−	0.687185i	0.790870	−	0.0962252i
$52$		−	5.43874i		−	0.754218i
$53$	−3.29588			−0.452723			−0.226362	−	0.974043i	$-0.572683\pi$
$53$	−3.29588			−0.452723			−0.226362	+	0.974043i	$0.572683\pi$
$54$	1.84614	+	4.85713i	0.251228	+	0.660972i
$55$	−2.00000			−0.269680
$56$	0.264536			0.0353501
$57$	−7.38340	−	1.57651i	−0.977956	−	0.208813i
$58$	−0.418392			−0.0549376
$59$	12.5486			1.63369			0.816843	−	0.576860i	$-0.195722\pi$
$59$	12.5486			1.63369			0.816843	+	0.576860i	$0.195722\pi$
$60$	−1.71937	+	0.209196i	−0.221970	+	0.0270071i
$61$	9.18520			1.17604			0.588022	−	0.808845i	$-0.299907\pi$
$61$	9.18520			1.17604			0.588022	+	0.808845i	$0.299907\pi$
$62$		−	3.56041i		−	0.452173i
$63$	−0.770454	+	0.190299i	−0.0970681	+	0.0239755i
$64$	1.00000			0.125000
$65$	−5.43874			−0.674593
$66$	−3.43874	+	0.418392i	−0.423280	+	0.0515005i
$67$			0.666330i			0.0814052i	0.999171	+	0.0407026i	$0.0129596\pi$
$67$			0.666330i			0.0814052i	−0.999171	+	0.0407026i	$0.987040\pi$
$68$			3.28489i			0.398351i
$69$	6.82214	−	0.830051i	0.821290	−	0.0999264i
$70$		−	0.264536i		−	0.0316181i
$71$	10.3484			1.22813			0.614065	−	0.789255i	$-0.289533\pi$
$71$	10.3484			1.22813			0.614065	+	0.789255i	$0.289533\pi$
$72$	−2.91247	+	0.719371i	−0.343238	+	0.0847787i
$73$	12.7024			1.48671			0.743354	−	0.668899i	$-0.233234\pi$
$73$	12.7024			1.48671			0.743354	+	0.668899i	$0.233234\pi$
$74$		−	0.307712i		−	0.0357708i
$75$	0.209196	+	1.71937i	0.0241559	+	0.198536i
$76$	1.41839	−	4.12167i	0.162701	−	0.472788i
$77$		−	0.529072i		−	0.0602933i
$78$	−9.35122	+	1.13776i	−1.05882	+	0.128826i
$79$			8.08948i			0.910138i	0.890456	+	0.455069i	$0.150385\pi$
$79$			8.08948i			0.910138i	−0.890456	+	0.455069i	$0.849615\pi$
$80$		−	1.00000i		−	0.111803i
$81$	7.96501	−	4.19030i	0.885001	−	0.465589i
$82$	2.15386			0.237854
$83$			16.7456i			1.83807i	0.394177	+	0.919035i	$0.371030\pi$
$83$			16.7456i			1.83807i	−0.394177	+	0.919035i	$0.628970\pi$
$84$	−0.0553398	−	0.454835i	−0.00603807	−	0.0496266i
$85$	3.28489			0.356296
$86$	1.71427			0.184854
$87$	0.0875259	+	0.719371i	0.00938376	+	0.0771247i
$88$		−	2.00000i		−	0.213201i
$89$	−10.6829			−1.13239			−0.566194	−	0.824272i	$-0.691585\pi$
$89$	−10.6829			−1.13239			−0.566194	+	0.824272i	$0.691585\pi$
$90$	0.719371	+	2.91247i	0.0758284	+	0.307002i
$91$		−	1.43874i		−	0.150821i
$92$			3.96781i			0.413673i
$93$	−6.12167	+	0.744824i	−0.634788	+	0.0772347i
$94$			5.71427i			0.589382i
$95$	−4.12167	−	1.41839i	−0.422874	−	0.145524i
$96$	−0.209196	−	1.71937i	−0.0213510	−	0.175483i
$97$			1.47093i			0.149350i	0.997208	+	0.0746751i	$0.0237920\pi$
$97$			1.47093i			0.149350i	−0.997208	+	0.0746751i	$0.976208\pi$
$98$	−6.93002			−0.700038
$99$	1.43874	+	5.82495i	0.144599	+	0.585429i
$100$	−1.00000			−0.100000
$101$		−	6.28404i		−	0.625285i	−0.949871	−	0.312643i	$-0.898786\pi$
$101$		−	6.28404i		−	0.625285i	0.949871	−	0.312643i	$-0.101214\pi$
$102$	5.64794	−	0.687185i	0.559229	−	0.0680415i
$103$			9.42854i			0.929021i	0.885568	+	0.464511i	$0.153770\pi$
$103$			9.42854i			0.929021i	−0.885568	+	0.464511i	$0.846230\pi$
$104$		−	5.43874i		−	0.533313i
$105$	−0.454835	+	0.0553398i	−0.0443874	+	0.00540062i
$106$	−3.29588			−0.320124
$107$	10.1734			0.983496			0.491748	−	0.870738i	$-0.336358\pi$
$107$	10.1734			0.983496			0.491748	+	0.870738i	$0.336358\pi$
$108$	1.84614	+	4.85713i	0.177645	+	0.467378i
$109$			4.99915i			0.478832i	0.970917	+	0.239416i	$0.0769560\pi$
$109$			4.99915i			0.478832i	−0.970917	+	0.239416i	$0.923044\pi$
$110$	−2.00000			−0.190693
$111$	−0.529072	+	0.0643722i	−0.0502173	+	0.00610994i
$112$	0.264536			0.0249963
$113$	−18.6325			−1.75279			−0.876397	−	0.481590i	$-0.840060\pi$
$113$	−18.6325			−1.75279			−0.876397	+	0.481590i	$0.840060\pi$
$114$	−7.38340	−	1.57651i	−0.691519	−	0.147653i
$115$	3.96781			0.370001
$116$	−0.418392			−0.0388467
$117$	3.91247	+	15.8402i	0.361708	+	1.46443i
$118$	12.5486			1.15519
$119$			0.868970i			0.0796584i
$120$	−1.71937	+	0.209196i	−0.156956	+	0.0190969i
$121$	7.00000			0.636364
$122$	9.18520			0.831589
$123$	−0.450578	−	3.70328i	−0.0406273	−	0.333913i
$124$		−	3.56041i		−	0.319734i
$125$			1.00000i			0.0894427i
$126$	−0.770454	+	0.190299i	−0.0686375	+	0.0169532i
$127$		−	2.83678i		−	0.251724i	−0.992048	−	0.125862i	$-0.959830\pi$
$127$		−	2.83678i		−	0.251724i	0.992048	−	0.125862i	$-0.0401696\pi$
$128$	1.00000			0.0883883
$129$	−0.358618	−	2.94746i	−0.0315746	−	0.259510i
$130$	−5.43874			−0.477009
$131$		−	3.08012i		−	0.269112i	−0.990906	−	0.134556i	$-0.957039\pi$
$131$		−	3.08012i		−	0.269112i	0.990906	−	0.134556i	$-0.0429608\pi$
$132$	−3.43874	+	0.418392i	−0.299304	+	0.0364163i
$133$	0.375216	−	1.09033i	0.0325353	−	0.0945436i
$134$			0.666330i			0.0575622i
$135$	4.85713	−	1.84614i	0.418036	−	0.158891i
$136$			3.28489i			0.281677i
$137$		−	4.79651i		−	0.409794i	−0.978784	−	0.204897i	$-0.934314\pi$
$137$		−	4.79651i		−	0.409794i	0.978784	−	0.204897i	$-0.0656859\pi$
$138$	6.82214	−	0.830051i	0.580740	−	0.0706586i
$139$	11.7550			0.997043			0.498522	−	0.866877i	$-0.333876\pi$
$139$	11.7550			0.997043			0.498522	+	0.866877i	$0.333876\pi$
$140$		−	0.264536i		−	0.0223574i
$141$	9.82495	−	1.19540i	0.827410	−	0.100671i
$142$	10.3484			0.868420
$143$	−10.8775			−0.909621
$144$	−2.91247	+	0.719371i	−0.242706	+	0.0599476i
$145$			0.418392i			0.0347456i
$146$	12.7024			1.05126
$147$	1.44973	+	11.9153i	0.119572	+	0.982756i
$148$		−	0.307712i		−	0.0252938i
$149$		−	17.4473i		−	1.42933i	−0.699464	−	0.714667i	$-0.746578\pi$
$149$		−	17.4473i		−	1.42933i	0.699464	−	0.714667i	$-0.253422\pi$
$150$	0.209196	+	1.71937i	0.0170808	+	0.140386i
$151$			13.2934i			1.08180i	0.841086	+	0.540901i	$0.181917\pi$
$151$			13.2934i			1.08180i	−0.841086	+	0.540901i	$0.818083\pi$
$152$	1.41839	−	4.12167i	0.115047	−	0.334312i
$153$	−2.36305	−	9.56715i	−0.191041	−	0.773458i
$154$		−	0.529072i		−	0.0426338i
$155$	−3.56041			−0.285979
$156$	−9.35122	+	1.13776i	−0.748697	+	0.0910940i
$157$	−4.39720			−0.350934			−0.175467	−	0.984485i	$-0.556144\pi$
$157$	−4.39720			−0.350934			−0.175467	+	0.984485i	$0.556144\pi$
$158$			8.08948i			0.643565i
$159$	0.689484	+	5.66683i	0.0546797	+	0.449409i
$160$		−	1.00000i		−	0.0790569i
$161$			1.04963i			0.0827224i
$162$	7.96501	−	4.19030i	0.625790	−	0.329221i
$163$	−11.7330			−0.918999			−0.459499	−	0.888178i	$-0.651971\pi$
$163$	−11.7330			−0.918999			−0.459499	+	0.888178i	$0.651971\pi$
$164$	2.15386			0.168188
$165$	0.418392	+	3.43874i	0.0325718	+	0.267706i
$166$			16.7456i			1.29971i
$167$	6.24334			0.483124			0.241562	−	0.970385i	$-0.422340\pi$
$167$	6.24334			0.483124			0.241562	+	0.970385i	$0.422340\pi$
$168$	−0.0553398	−	0.454835i	−0.00426956	−	0.0350913i
$169$	−16.5799			−1.27538
$170$	3.28489			0.251939
$171$	−1.16602	+	13.0246i	−0.0891677	+	0.996017i
$172$	1.71427			0.130712
$173$	−15.3422			−1.16644			−0.583222	−	0.812313i	$-0.698208\pi$
$173$	−15.3422			−1.16644			−0.583222	+	0.812313i	$0.698208\pi$
$174$	0.0875259	+	0.719371i	0.00663532	+	0.0545354i
$175$	−0.264536			−0.0199970
$176$		−	2.00000i		−	0.150756i
$177$	−2.62511	−	21.5757i	−0.197315	−	1.62173i
$178$	−10.6829			−0.800719
$179$	−20.6812			−1.54579			−0.772894	−	0.634535i	$-0.781192\pi$
$179$	−20.6812			−1.54579			−0.772894	+	0.634535i	$0.781192\pi$
$180$	0.719371	+	2.91247i	0.0536188	+	0.217083i
$181$		−	9.76305i		−	0.725682i	−0.931851	−	0.362841i	$-0.881807\pi$
$181$		−	9.76305i		−	0.725682i	0.931851	−	0.362841i	$-0.118193\pi$
$182$		−	1.43874i		−	0.106647i
$183$	−1.92151	−	15.7928i	−0.142042	−	1.16743i
$184$			3.96781i			0.292511i
$185$	−0.307712			−0.0226235
$186$	−6.12167	+	0.744824i	−0.448863	+	0.0546131i
$187$	6.56977			0.480429
$188$			5.71427i			0.416756i
$189$	0.488371	+	1.28489i	0.0355238	+	0.0934617i
$190$	−4.12167	−	1.41839i	−0.299017	−	0.102901i
$191$			19.3100i			1.39722i	0.715501	+	0.698611i	$0.246198\pi$
$191$			19.3100i			1.39722i	−0.715501	+	0.698611i	$0.753802\pi$
$192$	−0.209196	−	1.71937i	−0.0150974	−	0.124085i
$193$			15.0565i			1.08379i	0.840447	+	0.541894i	$0.182292\pi$
$193$			15.0565i			1.08379i	−0.840447	+	0.541894i	$0.817708\pi$
$194$			1.47093i			0.105606i
$195$	1.13776	+	9.35122i	0.0814769	+	0.669655i
$196$	−6.93002			−0.495001
$197$		−	15.5116i		−	1.10516i	−0.833461	−	0.552579i	$-0.813644\pi$
$197$		−	15.5116i		−	1.10516i	0.833461	−	0.552579i	$-0.186356\pi$
$198$	1.43874	+	5.82495i	0.102247	+	0.413961i
$199$	15.8469			1.12336			0.561680	−	0.827355i	$-0.310155\pi$
$199$	15.8469			1.12336			0.561680	+	0.827355i	$0.310155\pi$
$200$	−1.00000			−0.0707107
$201$	1.14567	−	0.139394i	0.0808093	−	0.00983207i
$202$		−	6.28404i		−	0.442144i
$203$	−0.110680			−0.00776819
$204$	5.64794	−	0.687185i	0.395435	−	0.0481126i
$205$		−	2.15386i		−	0.150432i
$206$			9.42854i			0.656917i
$207$	−2.85433	−	11.5562i	−0.198390	−	0.803208i
$208$		−	5.43874i		−	0.377109i
$209$	−8.24334	−	2.83678i	−0.570204	−	0.196224i
$210$	−0.454835	+	0.0553398i	−0.0313866	+	0.00381881i
$211$		−	6.88600i		−	0.474052i	−0.971503	−	0.237026i	$-0.923827\pi$
$211$		−	6.88600i		−	0.474052i	0.971503	−	0.237026i	$-0.0761726\pi$
$212$	−3.29588			−0.226362
$213$	−2.16485	−	17.7928i	−0.148333	−	1.21914i
$214$	10.1734			0.695437
$215$		−	1.71427i		−	0.116912i
$216$	1.84614	+	4.85713i	0.125614	+	0.330486i
$217$		−	0.941857i		−	0.0639374i
$218$			4.99915i			0.338585i
$219$	−2.65730	−	21.8402i	−0.179564	−	1.47582i
$220$	−2.00000			−0.134840
$221$	17.8656			1.20177
$222$	−0.529072	+	0.0643722i	−0.0355090	+	0.00432038i
$223$		−	6.67484i		−	0.446981i	−0.974706	−	0.223490i	$-0.928255\pi$
$223$		−	6.67484i		−	0.446981i	0.974706	−	0.223490i	$-0.0717451\pi$
$224$	0.264536			0.0176750
$225$	2.91247	−	0.719371i	0.194165	−	0.0479581i
$226$	−18.6325			−1.23941
$227$	−13.8656			−0.920295			−0.460148	−	0.887842i	$-0.652204\pi$
$227$	−13.8656			−0.920295			−0.460148	+	0.887842i	$0.652204\pi$
$228$	−7.38340	−	1.57651i	−0.488978	−	0.104407i
$229$	−9.64990			−0.637683			−0.318842	−	0.947808i	$-0.603294\pi$
$229$	−9.64990			−0.637683			−0.318842	+	0.947808i	$0.603294\pi$
$230$	3.96781			0.261630
$231$	−0.909671	+	0.110680i	−0.0598519	+	0.00728219i
$232$	−0.418392			−0.0274688
$233$			26.3548i			1.72656i	0.504725	+	0.863280i	$0.331594\pi$
$233$			26.3548i			1.72656i	−0.504725	+	0.863280i	$0.668406\pi$
$234$	3.91247	+	15.8402i	0.255766	+	1.03551i
$235$	5.71427			0.372758
$236$	12.5486			0.816843
$237$	13.9088	−	1.69229i	0.903475	−	0.109926i
$238$			0.868970i			0.0563270i
$239$		−	13.3149i		−	0.861273i	−0.902526	−	0.430636i	$-0.858289\pi$
$239$		−	13.3149i		−	0.861273i	0.902526	−	0.430636i	$-0.141711\pi$
$240$	−1.71937	+	0.209196i	−0.110985	+	0.0135035i
$241$		−	22.0627i		−	1.42118i	−0.703605	−	0.710591i	$-0.748428\pi$
$241$		−	22.0627i		−	1.42118i	0.703605	−	0.710591i	$-0.251572\pi$
$242$	7.00000			0.449977
$243$	−8.87093	−	12.8182i	−0.569070	−	0.822289i
$244$	9.18520			0.588022
$245$			6.93002i			0.442743i
$246$	−0.450578	−	3.70328i	−0.0287278	−	0.236112i
$247$	−22.4167	−	7.71427i	−1.42634	−	0.490847i
$248$		−	3.56041i		−	0.226086i
$249$	28.7919	−	3.50311i	1.82461	−	0.222001i
$250$			1.00000i			0.0632456i
$251$			20.6137i			1.30113i	0.759452	+	0.650564i	$0.225467\pi$
$251$			20.6137i			1.30113i	−0.759452	+	0.650564i	$0.774533\pi$
$252$	−0.770454	+	0.190299i	−0.0485340	+	0.0119877i
$253$	7.93563			0.498909
$254$		−	2.83678i		−	0.177996i
$255$	−0.687185	−	5.64794i	−0.0430332	−	0.353688i
$256$	1.00000			0.0625000
$257$	−13.4066			−0.836278			−0.418139	−	0.908383i	$-0.637318\pi$
$257$	−13.4066			−0.836278			−0.418139	+	0.908383i	$0.637318\pi$
$258$	−0.358618	−	2.94746i	−0.0223266	−	0.183501i
$259$		−	0.0814009i		−	0.00505801i
$260$	−5.43874			−0.337296
$261$	1.21856	−	0.300979i	0.0754267	−	0.0186301i
$262$		−	3.08012i		−	0.190291i
$263$		−	14.6748i		−	0.904890i	−0.891792	−	0.452445i	$-0.850552\pi$
$263$		−	14.6748i		−	0.904890i	0.891792	−	0.452445i	$-0.149448\pi$
$264$	−3.43874	+	0.418392i	−0.211640	+	0.0257502i
$265$			3.29588i			0.202464i
$266$	0.375216	−	1.09033i	0.0230059	−	0.0668524i
$267$	2.23483	+	18.3679i	0.136769	+	1.12410i
$268$			0.666330i			0.0407026i
$269$	−13.3235			−0.812346			−0.406173	−	0.913796i	$-0.633137\pi$
$269$	−13.3235			−0.812346			−0.406173	+	0.913796i	$0.633137\pi$
$270$	4.85713	−	1.84614i	0.295596	−	0.112353i
$271$	21.5579			1.30955			0.654776	−	0.755823i	$-0.272763\pi$
$271$	21.5579			1.30955			0.654776	+	0.755823i	$0.272763\pi$
$272$			3.28489i			0.199175i
$273$	−2.47373	+	0.300979i	−0.149717	+	0.0182161i
$274$		−	4.79651i		−	0.289768i
$275$			2.00000i			0.120605i
$276$	6.82214	−	0.830051i	0.410645	−	0.0499632i
$277$	−20.0471			−1.20451			−0.602257	−	0.798303i	$-0.705732\pi$
$277$	−20.0471			−1.20451			−0.602257	+	0.798303i	$0.705732\pi$
$278$	11.7550			0.705016
$279$	2.56126	+	10.3696i	0.153338	+	0.620812i
$280$		−	0.264536i		−	0.0158090i
$281$	−6.33282			−0.377785			−0.188892	−	0.981998i	$-0.560490\pi$
$281$	−6.33282			−0.377785			−0.188892	+	0.981998i	$0.560490\pi$
$282$	9.82495	−	1.19540i	0.585067	−	0.0711852i
$283$	−33.2022			−1.97367			−0.986834	−	0.161738i	$-0.948290\pi$
$283$	−33.2022			−1.97367			−0.986834	+	0.161738i	$0.948290\pi$
$284$	10.3484			0.614065
$285$	−1.57651	+	7.38340i	−0.0933841	+	0.437355i
$286$	−10.8775			−0.643199
$287$	0.569772			0.0336326
$288$	−2.91247	+	0.719371i	−0.171619	+	0.0423893i
$289$	6.20952			0.365266
$290$			0.418392i			0.0245688i
$291$	2.52907	−	0.307712i	0.148257	−	0.0180384i
$292$	12.7024			0.743354
$293$	29.4748			1.72194			0.860969	−	0.508657i	$-0.169858\pi$
$293$	29.4748			1.72194			0.860969	+	0.508657i	$0.169858\pi$
$294$	1.44973	+	11.9153i	0.0845501	+	0.694913i
$295$		−	12.5486i		−	0.730606i
$296$		−	0.307712i		−	0.0178854i
$297$	9.71427	−	3.69229i	0.563679	−	0.214248i
$298$		−	17.4473i		−	1.01069i
$299$	21.5799			1.24800
$300$	0.209196	+	1.71937i	0.0120779	+	0.0992679i
$301$	0.453485			0.0261385
$302$			13.2934i			0.764949i
$303$	−10.8046	+	1.31460i	−0.620708	+	0.0755216i
$304$	1.41839	−	4.12167i	0.0813504	−	0.236394i
$305$		−	9.18520i		−	0.525943i
$306$	−2.36305	−	9.56715i	−0.135087	−	0.546917i
$307$			1.81934i			0.103835i	0.998651	+	0.0519176i	$0.0165333\pi$
$307$			1.81934i			0.103835i	−0.998651	+	0.0519176i	$0.983467\pi$
$308$		−	0.529072i		−	0.0301467i
$309$	16.2112	−	1.97241i	0.922220	−	0.112207i
$310$	−3.56041			−0.202218
$311$		−	15.9898i		−	0.906698i	−0.891333	−	0.453349i	$-0.850229\pi$
$311$		−	15.9898i		−	0.906698i	0.891333	−	0.453349i	$-0.149771\pi$
$312$	−9.35122	+	1.13776i	−0.529408	+	0.0644132i
$313$	21.4416			1.21195			0.605977	−	0.795482i	$-0.292782\pi$
$313$	21.4416			1.21195			0.605977	+	0.795482i	$0.292782\pi$
$314$	−4.39720			−0.248148
$315$	0.190299	+	0.770454i	0.0107222	+	0.0434102i
$316$			8.08948i			0.455069i
$317$	−6.44037			−0.361727			−0.180864	−	0.983508i	$-0.557889\pi$
$317$	−6.44037			−0.361727			−0.180864	+	0.983508i	$0.557889\pi$
$318$	0.689484	+	5.66683i	0.0386644	+	0.317780i
$319$			0.836784i			0.0468509i
$320$		−	1.00000i		−	0.0559017i
$321$	−2.12823	−	17.4918i	−0.118786	−	0.976296i
$322$			1.04963i			0.0584935i
$323$	13.5392	+	4.65926i	0.753342	+	0.259248i
$324$	7.96501	−	4.19030i	0.442501	−	0.232794i
$325$			5.43874i			0.301687i
$326$	−11.7330			−0.649830
$327$	8.59540	−	1.04580i	0.475327	−	0.0578330i
$328$	2.15386			0.118927
$329$			1.51163i			0.0833388i
$330$	0.418392	+	3.43874i	0.0230317	+	0.189297i
$331$			24.6239i			1.35345i	0.736234	+	0.676727i	$0.236602\pi$
$331$			24.6239i			1.35345i	−0.736234	+	0.676727i	$0.763398\pi$
$332$			16.7456i			0.919035i
$333$	0.221359	+	0.896204i	0.0121304	+	0.0491117i
$334$	6.24334			0.341620
$335$	0.666330			0.0364055
$336$	−0.0553398	−	0.454835i	−0.00301904	−	0.0248133i
$337$		−	25.6686i		−	1.39826i	−0.714995	−	0.699129i	$-0.753571\pi$
$337$		−	25.6686i		−	1.39826i	0.714995	−	0.699129i	$-0.246429\pi$
$338$	−16.5799			−0.901829
$339$	3.89783	+	32.0361i	0.211701	+	1.73996i
$340$	3.28489			0.178148
$341$	−7.12082			−0.385614
$342$	−1.16602	+	13.0246i	−0.0630511	+	0.704290i
$343$	−3.68499			−0.198971
$344$	1.71427			0.0924272
$345$	−0.830051	−	6.82214i	−0.0446884	−	0.367292i
$346$	−15.3422			−0.824801
$347$			3.23398i			0.173609i	0.996225	+	0.0868046i	$0.0276656\pi$
$347$			3.23398i			0.173609i	−0.996225	+	0.0868046i	$0.972334\pi$
$348$	0.0875259	+	0.719371i	0.00469188	+	0.0385623i
$349$	−17.9576			−0.961249			−0.480624	−	0.876927i	$-0.659590\pi$
$349$	−17.9576			−0.961249			−0.480624	+	0.876927i	$0.659590\pi$
$350$	−0.264536			−0.0141400
$351$	26.4167	−	10.0407i	1.41002	−	0.535933i
$352$		−	2.00000i		−	0.106600i
$353$		−	7.59260i		−	0.404113i	−0.979374	−	0.202057i	$-0.935237\pi$
$353$		−	7.59260i		−	0.404113i	0.979374	−	0.202057i	$-0.0647625\pi$
$354$	−2.62511	−	21.5757i	−0.139523	−	1.14673i
$355$		−	10.3484i		−	0.549237i
$356$	−10.6829			−0.566194
$357$	1.49408	−	0.181785i	0.0790752	−	0.00962109i
$358$	−20.6812			−1.09304
$359$		−	36.7605i		−	1.94015i	−0.242814	−	0.970073i	$-0.578070\pi$
$359$		−	36.7605i		−	1.94015i	0.242814	−	0.970073i	$-0.421930\pi$
$360$	0.719371	+	2.91247i	0.0379142	+	0.153501i
$361$	−14.9763	−	11.6923i	−0.788228	−	0.615384i
$362$		−	9.76305i		−	0.513135i
$363$	−1.46437	−	12.0356i	−0.0768596	−	0.631705i
$364$		−	1.43874i		−	0.0754106i
$365$		−	12.7024i		−	0.664876i
$366$	−1.92151	−	15.7928i	−0.100439	−	0.825501i
$367$	−35.2917			−1.84221			−0.921106	−	0.389312i	$-0.872713\pi$
$367$	−35.2917			−1.84221			−0.921106	+	0.389312i	$0.872713\pi$
$368$			3.96781i			0.206837i
$369$	−6.27305	+	1.54942i	−0.326562	+	0.0806597i
$370$	−0.307712			−0.0159972
$371$	−0.871877			−0.0452656
$372$	−6.12167	+	0.744824i	−0.317394	+	0.0386173i
$373$			21.6821i			1.12266i	0.827594	+	0.561328i	$0.189709\pi$
$373$			21.6821i			1.12266i	−0.827594	+	0.561328i	$0.810291\pi$
$374$	6.56977			0.339715
$375$	1.71937	−	0.209196i	0.0887879	−	0.0108028i
$376$			5.71427i			0.294691i
$377$			2.27553i			0.117196i
$378$	0.488371	+	1.28489i	0.0251191	+	0.0660874i
$379$		−	13.1750i		−	0.676754i	−0.941011	−	0.338377i	$-0.890122\pi$
$379$		−	13.1750i		−	0.676754i	0.941011	−	0.338377i	$-0.109878\pi$
$380$	−4.12167	−	1.41839i	−0.211437	−	0.0727620i
$381$	−4.87748	+	0.593444i	−0.249881	+	0.0304031i
$382$			19.3100i			0.987985i
$383$	27.2354			1.39166			0.695832	−	0.718204i	$-0.255036\pi$
$383$	27.2354			1.39166			0.695832	+	0.718204i	$0.255036\pi$
$384$	−0.209196	−	1.71937i	−0.0106755	−	0.0877413i
$385$	−0.529072			−0.0269640
$386$			15.0565i			0.766353i
$387$	−4.99276	+	1.23320i	−0.253796	+	0.0626868i
$388$			1.47093i			0.0746751i
$389$		−	27.4236i		−	1.39043i	−0.718801	−	0.695215i	$-0.755309\pi$
$389$		−	27.4236i		−	1.39043i	0.718801	−	0.695215i	$-0.244691\pi$
$390$	1.13776	+	9.35122i	0.0576129	+	0.473517i
$391$	−13.0338			−0.659148
$392$	−6.93002			−0.350019
$393$	−5.29588	+	0.644350i	−0.267142	+	0.0325031i
$394$		−	15.5116i		−	0.781465i
$395$	8.08948			0.407026
$396$	1.43874	+	5.82495i	0.0722995	+	0.292715i
$397$	4.00313			0.200911			0.100456	−	0.994942i	$-0.467970\pi$
$397$	4.00313			0.200911			0.100456	+	0.994942i	$0.467970\pi$
$398$	15.8469			0.794335
$399$	−1.95317	−	0.417042i	−0.0977810	−	0.0208782i
$400$	−1.00000			−0.0500000
$401$	−6.98569			−0.348849			−0.174424	−	0.984671i	$-0.555806\pi$
$401$	−6.98569			−0.348849			−0.174424	+	0.984671i	$0.555806\pi$
$402$	1.14567	−	0.139394i	0.0571408	−	0.00695232i
$403$	−19.3642			−0.964598
$404$		−	6.28404i		−	0.312643i
$405$	−4.19030	−	7.96501i	−0.208218	−	0.395785i
$406$	−0.110680			−0.00549294
$407$	−0.615425			−0.0305055
$408$	5.64794	−	0.687185i	0.279615	−	0.0340207i
$409$			25.9763i			1.28445i	0.766518	+	0.642223i	$0.221988\pi$
$409$			25.9763i			1.28445i	−0.766518	+	0.642223i	$0.778012\pi$
$410$		−	2.15386i		−	0.106371i
$411$	−8.24699	+	1.00341i	−0.406794	+	0.0494947i
$412$			9.42854i			0.464511i
$413$	3.31955			0.163344
$414$	−2.85433	−	11.5562i	−0.140283	−	0.567954i
$415$	16.7456			0.822010
$416$		−	5.43874i		−	0.266656i
$417$	−2.45909	−	20.2112i	−0.120422	−	0.989744i
$418$	−8.24334	−	2.83678i	−0.403195	−	0.138752i
$419$			15.1395i			0.739615i	0.929108	+	0.369808i	$0.120576\pi$
$419$			15.1395i			0.739615i	−0.929108	+	0.369808i	$0.879424\pi$
$420$	−0.454835	+	0.0553398i	−0.0221937	+	0.00270031i
$421$		−	28.7728i		−	1.40230i	−0.713013	−	0.701151i	$-0.752670\pi$
$421$		−	28.7728i		−	1.40230i	0.713013	−	0.701151i	$-0.247330\pi$
$422$		−	6.88600i		−	0.335205i
$423$	−4.11068	−	16.6427i	−0.199868	−	0.809194i
$424$	−3.29588			−0.160062
$425$		−	3.28489i		−	0.159340i
$426$	−2.16485	−	17.7928i	−0.104887	−	0.862062i
$427$	2.42981			0.117587
$428$	10.1734			0.491748
$429$	2.27553	+	18.7024i	0.109863	+	0.902962i
$430$		−	1.71427i		−	0.0826694i
$431$	−20.4485			−0.984971			−0.492486	−	0.870321i	$-0.663912\pi$
$431$	−20.4485			−0.984971			−0.492486	+	0.870321i	$0.663912\pi$
$432$	1.84614	+	4.85713i	0.0888226	+	0.233689i
$433$			35.3422i			1.69844i	0.528042	+	0.849218i	$0.322926\pi$
$433$			35.3422i			1.69844i	−0.528042	+	0.849218i	$0.677074\pi$
$434$		−	0.941857i		−	0.0452106i
$435$	0.719371	−	0.0875259i	0.0344912	−	0.00419655i
$436$			4.99915i			0.239416i
$437$	16.3540	+	5.62792i	0.782319	+	0.269220i
$438$	−2.65730	−	21.8402i	−0.126971	−	1.04356i
$439$			22.1741i			1.05831i	0.848524	+	0.529157i	$0.177492\pi$
$439$			22.1741i			1.05831i	−0.848524	+	0.529157i	$0.822508\pi$
$440$	−2.00000			−0.0953463
$441$	20.1835	−	4.98526i	0.961119	−	0.237393i
$442$	17.8656			0.849782
$443$			21.4205i			1.01772i	0.860850	+	0.508858i	$0.169932\pi$
$443$			21.4205i			1.01772i	−0.860850	+	0.508858i	$0.830068\pi$
$444$	−0.529072	+	0.0643722i	−0.0251086	+	0.00305497i
$445$			10.6829i			0.506419i
$446$		−	6.67484i		−	0.316063i
$447$	−29.9983	+	3.64990i	−1.41887	+	0.172634i
$448$	0.264536			0.0124981
$449$	−9.43662			−0.445342			−0.222671	−	0.974894i	$-0.571478\pi$
$449$	−9.43662			−0.445342			−0.222671	+	0.974894i	$0.571478\pi$
$450$	2.91247	−	0.719371i	0.137295	−	0.0339115i
$451$		−	4.30771i		−	0.202842i
$452$	−18.6325			−0.876397
$453$	22.8563	−	2.78093i	1.07388	−	0.130659i
$454$	−13.8656			−0.650747
$455$	−1.43874			−0.0674493
$456$	−7.38340	−	1.57651i	−0.345759	−	0.0738266i
$457$	−26.1921			−1.22521			−0.612607	−	0.790388i	$-0.709879\pi$
$457$	−26.1921			−1.22521			−0.612607	+	0.790388i	$0.709879\pi$
$458$	−9.64990			−0.450910
$459$	−15.9551	+	6.06437i	−0.744722	+	0.283061i
$460$	3.96781			0.185000
$461$			17.2828i			0.804939i	0.915433	+	0.402469i	$0.131848\pi$
$461$			17.2828i			0.804939i	−0.915433	+	0.402469i	$0.868152\pi$
$462$	−0.909671	+	0.110680i	−0.0423217	+	0.00514928i
$463$	1.17880			0.0547837			0.0273918	−	0.999625i	$-0.491280\pi$
$463$	1.17880			0.0547837			0.0273918	+	0.999625i	$0.491280\pi$
$464$	−0.418392			−0.0194234
$465$	0.744824	+	6.12167i	0.0345404	+	0.283886i
$466$			26.3548i			1.22086i
$467$		−	2.25142i		−	0.104183i	−0.998642	−	0.0520917i	$-0.983411\pi$
$467$		−	2.25142i		−	0.104183i	0.998642	−	0.0520917i	$-0.0165888\pi$
$468$	3.91247	+	15.8402i	0.180854	+	0.732213i
$469$			0.176268i			0.00813931i
$470$	5.71427			0.263580
$471$	0.919876	+	7.56041i	0.0423856	+	0.348365i
$472$	12.5486			0.577595
$473$		−	3.42854i		−	0.157644i
$474$	13.9088	−	1.69229i	0.638853	−	0.0777293i
$475$	−1.41839	+	4.12167i	−0.0650803	+	0.189115i
$476$			0.868970i			0.0398292i
$477$	9.59915	−	2.37096i	0.439515	−	0.108559i
$478$		−	13.3149i		−	0.609012i
$479$			16.0407i			0.732918i	0.930434	+	0.366459i	$0.119430\pi$
$479$			16.0407i			0.732918i	−0.930434	+	0.366459i	$0.880570\pi$
$480$	−1.71937	+	0.209196i	−0.0784782	+	0.00954845i
$481$	−1.67357			−0.0763081
$482$		−	22.0627i		−	1.00493i
$483$	1.80470	−	0.219578i	0.0821168	−	0.00999115i
$484$	7.00000			0.318182
$485$	1.47093			0.0667914
$486$	−8.87093	−	12.8182i	−0.402393	−	0.581446i
$487$		−	2.59344i		−	0.117520i	−0.998272	−	0.0587601i	$-0.981285\pi$
$487$		−	2.59344i		−	0.117520i	0.998272	−	0.0587601i	$-0.0187147\pi$
$488$	9.18520			0.415794
$489$	2.45449	+	20.1734i	0.110996	+	0.912271i
$490$			6.93002i			0.313066i
$491$			6.94017i			0.313205i	0.987662	+	0.156603i	$0.0500542\pi$
$491$			6.94017i			0.313205i	−0.987662	+	0.156603i	$0.949946\pi$
$492$	−0.450578	−	3.70328i	−0.0203136	−	0.166957i
$493$		−	1.37437i		−	0.0618985i
$494$	−22.4167	−	7.71427i	−1.00858	−	0.347081i
$495$	5.82495	−	1.43874i	0.261812	−	0.0646667i
$496$		−	3.56041i		−	0.159867i
$497$	2.73753			0.122795
$498$	28.7919	−	3.50311i	1.29020	−	0.156978i
$499$	22.4111			1.00326			0.501629	−	0.865083i	$-0.332734\pi$
$499$	22.4111			1.00326			0.501629	+	0.865083i	$0.332734\pi$
$500$			1.00000i			0.0447214i
$501$	−1.30608	−	10.7346i	−0.0583514	−	0.479587i
$502$			20.6137i			0.920036i
$503$		−	6.44002i		−	0.287146i	−0.989640	−	0.143573i	$-0.954141\pi$
$503$		−	6.44002i		−	0.287146i	0.989640	−	0.143573i	$-0.0458592\pi$
$504$	−0.770454	+	0.190299i	−0.0343187	+	0.00847661i
$505$	−6.28404			−0.279636
$506$	7.93563			0.352782
$507$	3.46845	+	28.5070i	0.154039	+	1.26604i
$508$		−	2.83678i		−	0.125862i
$509$	31.2574			1.38546			0.692730	−	0.721197i	$-0.256408\pi$
$509$	31.2574			1.38546			0.692730	+	0.721197i	$0.256408\pi$
$510$	−0.687185	−	5.64794i	−0.0304291	−	0.250095i
$511$	3.36025			0.148649
$512$	1.00000			0.0441942
$513$	22.6381	−	0.719875i	0.999495	−	0.0317833i
$514$	−13.4066			−0.591338
$515$	9.42854			0.415471
$516$	−0.358618	−	2.94746i	−0.0157873	−	0.129755i
$517$	11.4285			0.502626
$518$		−	0.0814009i		−	0.00357655i
$519$	3.20952	+	26.3789i	0.140882	+	1.15791i
$520$	−5.43874			−0.238505
$521$	1.11769			0.0489670			0.0244835	−	0.999700i	$-0.492206\pi$
$521$	1.11769			0.0489670			0.0244835	+	0.999700i	$0.492206\pi$
$522$	1.21856	−	0.300979i	0.0533347	−	0.0131735i
$523$			15.4794i			0.676869i	0.940990	+	0.338434i	$0.109897\pi$
$523$			15.4794i			0.676869i	−0.940990	+	0.338434i	$0.890103\pi$
$524$		−	3.08012i		−	0.134556i
$525$	0.0553398	+	0.454835i	0.00241523	+	0.0198506i
$526$		−	14.6748i		−	0.639854i
$527$	11.6955			0.509466
$528$	−3.43874	+	0.418392i	−0.149652	+	0.0182082i
$529$	7.25645			0.315498
$530$			3.29588i			0.143164i
$531$	−36.5474	+	9.02708i	−1.58602	+	0.391742i
$532$	0.375216	−	1.09033i	0.0162677	−	0.0472718i
$533$		−	11.7143i		−	0.507401i
$534$	2.23483	+	18.3679i	0.0967104	+	0.794858i
$535$		−	10.1734i		−	0.439833i
$536$			0.666330i			0.0287811i
$537$	4.32643	+	35.5587i	0.186699	+	1.53447i
$538$	−13.3235			−0.574415
$539$			13.8600i			0.596994i
$540$	4.85713	−	1.84614i	0.209018	−	0.0794454i
$541$	25.4032			1.09217			0.546084	−	0.837731i	$-0.316118\pi$
$541$	25.4032			1.09217			0.546084	+	0.837731i	$0.316118\pi$
$542$	21.5579			0.925993
$543$	−16.7863	+	2.04239i	−0.720369	+	0.0876474i
$544$			3.28489i			0.140838i
$545$	4.99915			0.214140
$546$	−2.47373	+	0.300979i	−0.105866	+	0.0128807i
$547$			8.46965i			0.362136i	0.983471	+	0.181068i	$0.0579554\pi$
$547$			8.46965i			0.362136i	−0.983471	+	0.181068i	$0.942045\pi$
$548$		−	4.79651i		−	0.204897i
$549$	−26.7516	+	6.60757i	−1.14173	+	0.282004i
$550$			2.00000i			0.0852803i
$551$	−0.593444	+	1.72447i	−0.0252816	+	0.0734651i
$552$	6.82214	−	0.830051i	0.290370	−	0.0353293i
$553$			2.13996i			0.0910003i
$554$	−20.0471			−0.851719
$555$	0.0643722	+	0.529072i	0.00273245	+	0.0224578i
$556$	11.7550			0.498522
$557$		−	1.89324i		−	0.0802190i	−0.999195	−	0.0401095i	$-0.987229\pi$
$557$		−	1.89324i		−	0.0802190i	0.999195	−	0.0401095i	$-0.0127707\pi$
$558$	2.56126	+	10.3696i	0.108427	+	0.438981i
$559$		−	9.32346i		−	0.394341i
$560$		−	0.264536i		−	0.0111787i
$561$	−1.37437	−	11.2959i	−0.0580259	−	0.476912i
$562$	−6.33282			−0.267134
$563$	24.2229			1.02087			0.510437	−	0.859915i	$-0.329484\pi$
$563$	24.2229			1.02087			0.510437	+	0.859915i	$0.329484\pi$
$564$	9.82495	−	1.19540i	0.413705	−	0.0503355i
$565$			18.6325i			0.783873i
$566$	−33.2022			−1.39559
$567$	2.10703	−	1.10848i	0.0884870	−	0.0465520i
$568$	10.3484			0.434210
$569$	−37.1991			−1.55947			−0.779734	−	0.626111i	$-0.784645\pi$
$569$	−37.1991			−1.55947			−0.779734	+	0.626111i	$0.784645\pi$
$570$	−1.57651	+	7.38340i	−0.0660325	+	0.309257i
$571$	−34.0847			−1.42640			−0.713199	−	0.700961i	$-0.752755\pi$
$571$	−34.0847			−1.42640			−0.713199	+	0.700961i	$0.752755\pi$
$572$	−10.8775			−0.454810
$573$	33.2011	−	4.03957i	1.38699	−	0.168756i
$574$	0.569772			0.0237818
$575$		−	3.96781i		−	0.165469i
$576$	−2.91247	+	0.719371i	−0.121353	+	0.0299738i
$577$	34.2522			1.42594			0.712969	−	0.701196i	$-0.247350\pi$
$577$	34.2522			1.42594			0.712969	+	0.701196i	$0.247350\pi$
$578$	6.20952			0.258282
$579$	25.8876	−	3.14975i	1.07585	−	0.130899i
$580$			0.418392i			0.0173728i
$581$			4.42981i			0.183780i
$582$	2.52907	−	0.307712i	0.104833	−	0.0127551i
$583$			6.59175i			0.273003i
$584$	12.7024			0.525630
$585$	15.8402	−	3.91247i	0.654911	−	0.161761i
$586$	29.4748			1.21759
$587$			46.9321i			1.93709i	0.248830	+	0.968547i	$0.419954\pi$
$587$			46.9321i			1.93709i	−0.248830	+	0.968547i	$0.580046\pi$
$588$	1.44973	+	11.9153i	0.0597860	+	0.491378i
$589$	−14.6748	−	5.05006i	−0.604666	−	0.208084i
$590$		−	12.5486i		−	0.516617i
$591$	−26.6702	+	3.24497i	−1.09707	+	0.133480i
$592$		−	0.307712i		−	0.0126469i
$593$			19.4977i			0.800676i	0.916368	+	0.400338i	$0.131107\pi$
$593$			19.4977i			0.800676i	−0.916368	+	0.400338i	$0.868893\pi$
$594$	9.71427	−	3.69229i	0.398581	−	0.151496i
$595$	0.868970			0.0356243
$596$		−	17.4473i		−	0.714667i
$597$	−3.31511	−	27.2468i	−0.135679	−	1.11514i
$598$	21.5799			0.882468
$599$	−12.8538			−0.525193			−0.262596	−	0.964906i	$-0.584579\pi$
$599$	−12.8538			−0.525193			−0.262596	+	0.964906i	$0.584579\pi$
$600$	0.209196	+	1.71937i	0.00854039	+	0.0701930i
$601$			38.3280i			1.56343i	0.623635	+	0.781716i	$0.285655\pi$
$601$			38.3280i			1.56343i	−0.623635	+	0.781716i	$0.714345\pi$
$602$	0.453485			0.0184827
$603$	−0.479339	−	1.94067i	−0.0195202	−	0.0790302i
$604$			13.2934i			0.540901i
$605$		−	7.00000i		−	0.284590i
$606$	−10.8046	+	1.31460i	−0.438907	+	0.0534018i
$607$		−	9.26078i		−	0.375884i	−0.982180	−	0.187942i	$-0.939818\pi$
$607$		−	9.26078i		−	0.375884i	0.982180	−	0.187942i	$-0.0601816\pi$
$608$	1.41839	−	4.12167i	0.0575234	−	0.167156i
$609$	0.0231537	+	0.190299i	0.000938237	+	0.00771132i
$610$		−	9.18520i		−	0.371898i
$611$	31.0784			1.25730
$612$	−2.36305	−	9.56715i	−0.0955207	−	0.386729i
$613$	36.0691			1.45682			0.728408	−	0.685144i	$-0.240261\pi$
$613$	36.0691			1.45682			0.728408	+	0.685144i	$0.240261\pi$
$614$			1.81934i			0.0734226i
$615$	−3.70328	+	0.450578i	−0.149331	+	0.0181691i
$616$		−	0.529072i		−	0.0213169i
$617$			33.9935i			1.36853i	0.729235	+	0.684263i	$0.239876\pi$
$617$			33.9935i			1.36853i	−0.729235	+	0.684263i	$0.760124\pi$
$618$	16.2112	−	1.97241i	0.652108	−	0.0793421i
$619$	0.772412			0.0310459			0.0155229	−	0.999880i	$-0.495059\pi$
$619$	0.772412			0.0310459			0.0155229	+	0.999880i	$0.495059\pi$
$620$	−3.56041			−0.142990
$621$	−19.2722	+	7.32516i	−0.773367	+	0.293948i
$622$		−	15.9898i		−	0.641132i
$623$	−2.82602			−0.113222
$624$	−9.35122	+	1.13776i	−0.374348	+	0.0455470i
$625$	1.00000			0.0400000
$626$	21.4416			0.856981
$627$	−3.15301	+	14.7668i	−0.125919	+	0.589729i
$628$	−4.39720			−0.175467
$629$	1.01080			0.0403032
$630$	0.190299	+	0.770454i	0.00758171	+	0.0306956i
$631$	25.9339			1.03241			0.516207	−	0.856464i	$-0.327344\pi$
$631$	25.9339			1.03241			0.516207	+	0.856464i	$0.327344\pi$
$632$			8.08948i			0.321782i
$633$	−11.8396	+	1.44052i	−0.470581	+	0.0572557i
$634$	−6.44037			−0.255780
$635$	−2.83678			−0.112574
$636$	0.689484	+	5.66683i	0.0273398	+	0.224705i
$637$			37.6906i			1.49336i
$638$			0.836784i			0.0331286i
$639$	−30.1395	+	7.44435i	−1.19230	+	0.294494i
$640$		−	1.00000i		−	0.0395285i
$641$	−43.6027			−1.72220			−0.861101	−	0.508434i	$-0.830225\pi$
$641$	−43.6027			−1.72220			−0.861101	+	0.508434i	$0.830225\pi$
$642$	−2.12823	−	17.4918i	−0.0839944	−	0.690346i
$643$	15.6312			0.616433			0.308217	−	0.951316i	$-0.400268\pi$
$643$	15.6312			0.616433			0.308217	+	0.951316i	$0.400268\pi$
$644$			1.04963i			0.0413612i
$645$	−2.94746	+	0.358618i	−0.116056	+	0.0141206i
$646$	13.5392	+	4.65926i	0.532693	+	0.183316i
$647$		−	26.9740i		−	1.06046i	−0.847854	−	0.530230i	$-0.822106\pi$
$647$		−	26.9740i		−	1.06046i	0.847854	−	0.530230i	$-0.177894\pi$
$648$	7.96501	−	4.19030i	0.312895	−	0.164611i
$649$		−	25.0972i		−	0.985149i
$650$			5.43874i			0.213325i
$651$	−1.61940	+	0.197033i	−0.0634693	+	0.00772232i
$652$	−11.7330			−0.459499
$653$			39.3405i			1.53951i	0.638338	+	0.769756i	$0.279622\pi$
$653$			39.3405i			1.53951i	−0.638338	+	0.769756i	$0.720378\pi$
$654$	8.59540	−	1.04580i	0.336107	−	0.0408941i
$655$	−3.08012			−0.120350
$656$	2.15386			0.0840940
$657$	−36.9955	+	9.13776i	−1.44333	+	0.356498i
$658$			1.51163i			0.0589294i
$659$	28.4622			1.10873			0.554365	−	0.832273i	$-0.312961\pi$
$659$	28.4622			1.10873			0.554365	+	0.832273i	$0.312961\pi$
$660$	0.418392	+	3.43874i	0.0162859	+	0.133853i
$661$		−	8.93478i		−	0.347523i	−0.984788	−	0.173761i	$-0.944408\pi$
$661$		−	8.93478i		−	0.347523i	0.984788	−	0.173761i	$-0.0555921\pi$
$662$			24.6239i			0.957037i
$663$	−3.73742	−	30.7177i	−0.145149	−	1.19298i
$664$			16.7456i			0.649856i
$665$	−1.09033	−	0.375216i	−0.0422812	−	0.0145502i
$666$	0.221359	+	0.896204i	0.00857750	+	0.0347272i
$667$		−	1.66010i		−	0.0642794i
$668$	6.24334			0.241562
$669$	−11.4765	+	1.39635i	−0.443708	+	0.0539860i
$670$	0.666330			0.0257426
$671$		−	18.3704i		−	0.709181i
$672$	−0.0553398	−	0.454835i	−0.00213478	−	0.0175457i
$673$		−	19.1411i		−	0.737836i	−0.929462	−	0.368918i	$-0.879728\pi$
$673$		−	19.1411i		−	0.737836i	0.929462	−	0.368918i	$-0.120272\pi$
$674$		−	25.6686i		−	0.988718i
$675$	−1.84614	−	4.85713i	−0.0710581	−	0.186951i
$676$	−16.5799			−0.637689
$677$	−20.0114			−0.769101			−0.384551	−	0.923104i	$-0.625644\pi$
$677$	−20.0114			−0.769101			−0.384551	+	0.923104i	$0.625644\pi$
$678$	3.89783	+	32.0361i	0.149695	+	1.23034i
$679$			0.389113i			0.0149328i
$680$	3.28489			0.125970
$681$	2.90064	+	23.8402i	0.111153	+	0.913558i
$682$	−7.12082			−0.272670
$683$	35.9527			1.37569			0.687845	−	0.725858i	$-0.258557\pi$
$683$	35.9527			1.37569			0.687845	+	0.725858i	$0.258557\pi$
$684$	−1.16602	+	13.0246i	−0.0445839	+	0.498008i
$685$	−4.79651			−0.183265
$686$	−3.68499			−0.140694
$687$	2.01872	+	16.5918i	0.0770190	+	0.633015i
$688$	1.71427			0.0653559
$689$			17.9254i			0.682904i
$690$	−0.830051	−	6.82214i	−0.0315995	−	0.259715i
$691$	−14.9419			−0.568415			−0.284208	−	0.958763i	$-0.591730\pi$
$691$	−14.9419			−0.568415			−0.284208	+	0.958763i	$0.591730\pi$
$692$	−15.3422			−0.583222
$693$	0.380599	+	1.54091i	0.0144578	+	0.0585342i
$694$			3.23398i			0.122760i
$695$		−	11.7550i		−	0.445891i
$696$	0.0875259	+	0.719371i	0.00331766	+	0.0272677i
$697$			7.07517i			0.267991i
$698$	−17.9576			−0.679706
$699$	45.3137	−	5.51332i	1.71392	−	0.208533i
$700$	−0.264536			−0.00999851
$701$			26.7894i			1.01182i	0.862585	+	0.505912i	$0.168844\pi$
$701$			26.7894i			1.01182i	−0.862585	+	0.505912i	$0.831156\pi$
$702$	26.4167	−	10.0407i	0.997034	−	0.378962i
$703$	−1.26829	−	0.436457i	−0.0478344	−	0.0164613i
$704$		−	2.00000i		−	0.0753778i
$705$	−1.19540	−	9.82495i	−0.0450214	−	0.370029i
$706$		−	7.59260i		−	0.285751i
$707$		−	1.66235i		−	0.0625193i
$708$	−2.62511	−	21.5757i	−0.0986577	−	0.810863i
$709$	−41.3861			−1.55429			−0.777145	−	0.629322i	$-0.783333\pi$
$709$	−41.3861			−1.55429			−0.777145	+	0.629322i	$0.783333\pi$
$710$		−	10.3484i		−	0.388369i
$711$	−5.81934	−	23.5604i	−0.218242	−	0.883584i
$712$	−10.6829			−0.400360
$713$	14.1271			0.529062
$714$	1.49408	−	0.181785i	0.0559146	−	0.00680314i
$715$			10.8775i			0.406795i
$716$	−20.6812			−0.772894
$717$	−22.8933	+	2.78543i	−0.854967	+	0.104024i
$718$		−	36.7605i		−	1.37189i
$719$		−	37.3320i		−	1.39225i	−0.717922	−	0.696124i	$-0.754906\pi$
$719$		−	37.3320i		−	1.39225i	0.717922	−	0.696124i	$-0.245094\pi$
$720$	0.719371	+	2.91247i	0.0268094	+	0.108541i
$721$			2.49419i			0.0928883i
$722$	−14.9763	−	11.6923i	−0.557361	−	0.435142i
$723$	−37.9339	+	4.61542i	−1.41078	+	0.171649i
$724$		−	9.76305i		−	0.362841i
$725$	0.418392			0.0155387
$726$	−1.46437	−	12.0356i	−0.0543479	−	0.446683i
$727$	38.4900			1.42752			0.713758	−	0.700393i	$-0.246992\pi$
$727$	38.4900			1.42752			0.713758	+	0.700393i	$0.246992\pi$
$728$		−	1.43874i		−	0.0533233i
$729$	−20.1835	+	17.9339i	−0.747537	+	0.664220i
$730$		−	12.7024i		−	0.470138i
$731$			5.63118i			0.208277i
$732$	−1.92151	−	15.7928i	−0.0710209	−	0.583717i
$733$	3.30004			0.121890			0.0609449	−	0.998141i	$-0.480589\pi$
$733$	3.30004			0.121890			0.0609449	+	0.998141i	$0.480589\pi$
$734$	−35.2917			−1.30264
$735$	11.9153	−	1.44973i	0.439502	−	0.0534742i
$736$			3.96781i			0.146256i
$737$	1.33266			0.0490892
$738$	−6.27305	+	1.54942i	−0.230914	+	0.0570350i
$739$	0.119548			0.00439764			0.00219882	−	0.999998i	$-0.499300\pi$
$739$	0.119548			0.00439764			0.00219882	+	0.999998i	$0.499300\pi$
$740$	−0.307712			−0.0113117
$741$	−8.57421	+	40.1564i	−0.314981	+	1.47518i
$742$	−0.871877			−0.0320076
$743$	35.7330			1.31092			0.655458	−	0.755232i	$-0.272476\pi$
$743$	35.7330			1.31092			0.655458	+	0.755232i	$0.272476\pi$
$744$	−6.12167	+	0.744824i	−0.224431	+	0.0273066i
$745$	−17.4473			−0.639218
$746$			21.6821i			0.793837i
$747$	−12.0463	−	48.7712i	−0.440751	−	1.78444i
$748$	6.56977			0.240215
$749$	2.69122			0.0983350
$750$	1.71937	−	0.209196i	0.0627826	−	0.00763876i
$751$		−	24.9370i		−	0.909965i	−0.890500	−	0.454983i	$-0.849645\pi$
$751$		−	24.9370i		−	0.909965i	0.890500	−	0.454983i	$-0.150355\pi$
$752$			5.71427i			0.208378i
$753$	35.4427	−	4.31231i	1.29160	−	0.157149i
$754$			2.27553i			0.0828698i
$755$	13.2934			0.483796
$756$	0.488371	+	1.28489i	0.0177619	+	0.0467309i
$757$	5.45534			0.198278			0.0991388	−	0.995074i	$-0.468391\pi$
$757$	5.45534			0.198278			0.0991388	+	0.995074i	$0.468391\pi$
$758$		−	13.1750i		−	0.478537i
$759$	−1.66010	−	13.6443i	−0.0602579	−	0.495256i
$760$	−4.12167	−	1.41839i	−0.149509	−	0.0514505i
$761$		−	12.3494i		−	0.447666i	−0.974627	−	0.223833i	$-0.928143\pi$
$761$		−	12.3494i		−	0.447666i	0.974627	−	0.223833i	$-0.0718571\pi$
$762$	−4.87748	+	0.593444i	−0.176693	+	0.0214982i
$763$			1.32246i			0.0478761i
$764$			19.3100i			0.698611i
$765$	−9.56715	+	2.36305i	−0.345901	+	0.0854363i
$766$	27.2354			0.984056
$767$		−	68.2485i		−	2.46431i
$768$	−0.209196	−	1.71937i	−0.00754871	−	0.0620425i
$769$	−13.0932			−0.472154			−0.236077	−	0.971734i	$-0.575862\pi$
$769$	−13.0932			−0.472154			−0.236077	+	0.971734i	$0.575862\pi$
$770$	−0.529072			−0.0190664
$771$	2.80460	+	23.0508i	0.101005	+	0.830156i
$772$			15.0565i			0.541894i
$773$	−36.5720			−1.31540			−0.657702	−	0.753279i	$-0.728471\pi$
$773$	−36.5720			−1.31540			−0.657702	+	0.753279i	$0.728471\pi$
$774$	−4.99276	+	1.23320i	−0.179461	+	0.0443263i
$775$			3.56041i			0.127894i
$776$			1.47093i			0.0528032i
$777$	−0.139958	+	0.0170288i	−0.00502098	+	0.000610903i
$778$		−	27.4236i		−	0.983183i
$779$	3.05501	−	8.87748i	0.109457	−	0.318069i
$780$	1.13776	+	9.35122i	0.0407385	+	0.334827i
$781$		−	20.6968i		−	0.740591i
$782$	−13.0338			−0.466088
$783$	−0.772412	−	2.03219i	−0.0276037	−	0.0726244i
$784$	−6.93002			−0.247501
$785$			4.39720i			0.156943i
$786$	−5.29588	+	0.644350i	−0.188898	+	0.0229832i
$787$		−	13.0919i		−	0.466676i	−0.972396	−	0.233338i	$-0.925035\pi$
$787$		−	13.0919i		−	0.466676i	0.972396	−	0.233338i	$-0.0749648\pi$
$788$		−	15.5116i		−	0.552579i
$789$	−25.2315	+	3.06992i	−0.898265	+	0.109292i
$790$	8.08948			0.287811
$791$	−4.92895			−0.175253
$792$	1.43874	+	5.82495i	0.0511235	+	0.206981i
$793$		−	49.9559i		−	1.77399i
$794$	4.00313			0.142066
$795$	5.66683	−	0.689484i	0.200982	−	0.0244535i
$796$	15.8469			0.561680
$797$	4.95072			0.175364			0.0876818	−	0.996149i	$-0.472054\pi$
$797$	4.95072			0.175364			0.0876818	+	0.996149i	$0.472054\pi$
$798$	−1.95317	−	0.417042i	−0.0691416	−	0.0147631i
$799$	−18.7707			−0.664060
$800$	−1.00000			−0.0353553
$801$	31.1138	−	7.68499i	1.09935	−	0.271536i
$802$	−6.98569			−0.246673
$803$		−	25.4049i		−	0.896518i
$804$	1.14567	−	0.139394i	0.0404046	−	0.00491604i
$805$	1.04963			0.0369946
$806$	−19.3642			−0.682074
$807$	2.78722	+	22.9080i	0.0981146	+	0.806399i
$808$		−	6.28404i		−	0.221072i
$809$		−	16.6443i		−	0.585184i	−0.956237	−	0.292592i	$-0.905482\pi$
$809$		−	16.6443i		−	0.585184i	0.956237	−	0.292592i	$-0.0945178\pi$
$810$	−4.19030	−	7.96501i	−0.147232	−	0.279862i
$811$		−	27.2913i		−	0.958326i	−0.877726	−	0.479163i	$-0.840940\pi$
$811$		−	27.2913i		−	0.958326i	0.877726	−	0.479163i	$-0.159060\pi$
$812$	−0.110680			−0.00388410
$813$	−4.50983	−	37.0661i	−0.158167	−	1.29996i
$814$	−0.615425			−0.0215706
$815$			11.7330i			0.410989i
$816$	5.64794	−	0.687185i	0.197717	−	0.0240563i
$817$	2.43150	−	7.06565i	0.0850676	−	0.247196i
$818$			25.9763i			0.908241i
$819$	1.03499	+	4.19030i	0.0361655	+	0.146421i
$820$		−	2.15386i		−	0.0752159i
$821$			15.6279i			0.545418i	0.962097	+	0.272709i	$0.0879196\pi$
$821$			15.6279i			0.545418i	−0.962097	+	0.272709i	$0.912080\pi$
$822$	−8.24699	+	1.00341i	−0.287647	+	0.0349980i
$823$	28.1358			0.980752			0.490376	−	0.871511i	$-0.336859\pi$
$823$	28.1358			0.980752			0.490376	+	0.871511i	$0.336859\pi$
$824$			9.42854i			0.328459i
$825$	3.43874	−	0.418392i	0.119722	−	0.0145665i
$826$	3.31955			0.115502
$827$	−4.58615			−0.159476			−0.0797380	−	0.996816i	$-0.525408\pi$
$827$	−4.58615			−0.159476			−0.0797380	+	0.996816i	$0.525408\pi$
$828$	−2.85433	−	11.5562i	−0.0991948	−	0.401604i
$829$		−	27.6773i		−	0.961271i	−0.876920	−	0.480635i	$-0.840406\pi$
$829$		−	27.6773i		−	0.961271i	0.876920	−	0.480635i	$-0.159594\pi$
$830$	16.7456			0.581249
$831$	4.19377	+	34.4684i	0.145480	+	1.19570i
$832$		−	5.43874i		−	0.188554i
$833$		−	22.7643i		−	0.788737i
$834$	−2.45909	−	20.2112i	−0.0851514	−	0.699855i
$835$		−	6.24334i		−	0.216060i
$836$	−8.24334	−	2.83678i	−0.285102	−	0.0981122i
$837$	17.2934	−	6.57303i	0.597747	−	0.227197i
$838$			15.1395i			0.522987i
$839$	−34.9497			−1.20660			−0.603299	−	0.797515i	$-0.706147\pi$
$839$	−34.9497			−1.20660			−0.603299	+	0.797515i	$0.706147\pi$
$840$	−0.454835	+	0.0553398i	−0.0156933	+	0.00190941i
$841$	−28.8249			−0.993964
$842$		−	28.7728i		−	0.991578i
$843$	1.32480	+	10.8885i	0.0456286	+	0.375019i
$844$		−	6.88600i		−	0.237026i
$845$			16.5799i			0.570366i
$846$	−4.11068	−	16.6427i	−0.141328	−	0.572186i
$847$	1.85175			0.0636269
$848$	−3.29588			−0.113181
$849$	6.94577	+	57.0869i	0.238378	+	1.95922i
$850$		−	3.28489i		−	0.112671i
$851$	1.22095			0.0418535
$852$	−2.16485	−	17.7928i	−0.0741664	−	0.609570i
$853$	−3.25270			−0.111370			−0.0556852	−	0.998448i	$-0.517734\pi$
$853$	−3.25270			−0.111370			−0.0556852	+	0.998448i	$0.517734\pi$
$854$	2.42981			0.0831465
$855$	13.0246	+	1.16602i	0.445432	+	0.0398770i
$856$	10.1734			0.347718
$857$	−16.6893			−0.570096			−0.285048	−	0.958513i	$-0.592010\pi$
$857$	−16.6893			−0.570096			−0.285048	+	0.958513i	$0.592010\pi$
$858$	2.27553	+	18.7024i	0.0776852	+	0.638491i
$859$	38.9589			1.32926			0.664630	−	0.747173i	$-0.268589\pi$
$859$	38.9589			1.32926			0.664630	+	0.747173i	$0.268589\pi$
$860$		−	1.71427i		−	0.0584561i
$861$	−0.119194	−	0.979650i	−0.00406212	−	0.0333864i
$862$	−20.4485			−0.696480
$863$	−12.5773			−0.428136			−0.214068	−	0.976819i	$-0.568671\pi$
$863$	−12.5773			−0.428136			−0.214068	+	0.976819i	$0.568671\pi$
$864$	1.84614	+	4.85713i	0.0628071	+	0.165243i
$865$			15.3422i			0.521650i
$866$			35.3422i			1.20098i
$867$	−1.29901	−	10.6765i	−0.0441166	−	0.362592i
$868$		−	0.941857i		−	0.0319687i
$869$	16.1790			0.548834
$870$	0.719371	−	0.0875259i	0.0243890	−	0.00296741i
$871$	3.62400			0.122795
$872$			4.99915i			0.169293i
$873$	−1.05814	−	4.28404i	−0.0358127	−	0.144993i
$874$	16.3540	+	5.62792i	0.553183	+	0.190367i
$875$			0.264536i			0.00894294i
$876$	−2.65730	−	21.8402i	−0.0897818	−	0.737912i
$877$			8.78588i			0.296678i	0.988937	+	0.148339i	$0.0473927\pi$
$877$			8.78588i			0.296678i	−0.988937	+	0.148339i	$0.952607\pi$
$878$			22.1741i			0.748341i
$879$	−6.16602	−	50.6782i	−0.207975	−	1.70933i
$880$	−2.00000			−0.0674200
$881$			48.3043i			1.62741i	0.581275	+	0.813707i	$0.302554\pi$
$881$			48.3043i			1.62741i	−0.581275	+	0.813707i	$0.697446\pi$
$882$	20.1835	−	4.98526i	0.679614	−	0.167862i
$883$	5.38953			0.181372			0.0906860	−	0.995880i	$-0.471094\pi$
$883$	5.38953			0.181372			0.0906860	+	0.995880i	$0.471094\pi$
$884$	17.8656			0.600887
$885$	−21.5757	+	2.62511i	−0.725258	+	0.0882422i
$886$			21.4205i			0.719634i
$887$	−0.127053			−0.00426604			−0.00213302	−	0.999998i	$-0.500679\pi$
$887$	−0.127053			−0.00426604			−0.00213302	+	0.999998i	$0.500679\pi$
$888$	−0.529072	+	0.0643722i	−0.0177545	+	0.00216019i
$889$		−	0.750431i		−	0.0251686i
$890$			10.6829i			0.358093i
$891$	−8.38060	−	15.9300i	−0.280761	−	0.533676i
$892$		−	6.67484i		−	0.223490i
$893$	23.5523	+	8.10507i	0.788149	+	0.271226i
$894$	−29.9983	+	3.64990i	−1.00329	+	0.122071i
$895$			20.6812i			0.691298i
$896$	0.264536			0.00883752
$897$	−4.51443	−	37.1039i	−0.150733	−	1.23886i
$898$	−9.43662			−0.314904
$899$			1.48965i			0.0496825i
$900$	2.91247	−	0.719371i	0.0970825	−	0.0239790i
$901$		−	10.8266i		−	0.360686i
$902$		−	4.30771i		−	0.143431i
$903$	−0.0948673	−	0.779710i	−0.00315699	−	0.0259471i
$904$	−18.6325			−0.619706
$905$	−9.76305			−0.324535
$906$	22.8563	−	2.78093i	0.759349	−	0.0923901i
$907$		−	36.7510i		−	1.22030i	−0.792287	−	0.610148i	$-0.791110\pi$
$907$		−	36.7510i		−	1.22030i	0.792287	−	0.610148i	$-0.208890\pi$
$908$	−13.8656			−0.460148
$909$	4.52056	+	18.3021i	0.149937	+	0.607043i
$910$	−1.43874			−0.0476938
$911$	11.3734			0.376816			0.188408	−	0.982091i	$-0.439667\pi$
$911$	11.3734			0.376816			0.188408	+	0.982091i	$0.439667\pi$
$912$	−7.38340	−	1.57651i	−0.244489	−	0.0522033i
$913$	33.4912			1.10840
$914$	−26.1921			−0.866357
$915$	−15.7928	+	1.92151i	−0.522093	+	0.0635230i
$916$	−9.64990			−0.318842
$917$		−	0.814803i		−	0.0269072i
$918$	−15.9551	+	6.06437i	−0.526598	+	0.200154i
$919$	20.8026			0.686213			0.343106	−	0.939297i	$-0.388521\pi$
$919$	20.8026			0.686213			0.343106	+	0.939297i	$0.388521\pi$
$920$	3.96781			0.130815
$921$	3.12812	−	0.380599i	0.103075	−	0.0125412i
$922$			17.2828i			0.569178i
$923$		−	56.2823i		−	1.85256i
$924$	−0.909671	+	0.110680i	−0.0299260	+	0.00364109i
$925$			0.307712i			0.0101175i
$926$	1.17880			0.0387379
$927$	−6.78262	−	27.4604i	−0.222770	−	0.901917i
$928$	−0.418392			−0.0137344
$929$		−	38.4603i		−	1.26184i	−0.775847	−	0.630921i	$-0.782677\pi$
$929$		−	38.4603i		−	1.26184i	0.775847	−	0.630921i	$-0.217323\pi$
$930$	0.744824	+	6.12167i	0.0244237	+	0.200737i
$931$	−9.82949	+	28.5633i	−0.322148	+	0.936123i
$932$			26.3548i			0.863280i
$933$	−27.4924	+	3.34500i	−0.900060	+	0.109510i
$934$		−	2.25142i		−	0.0736688i
$935$		−	6.56977i		−	0.214855i
$936$	3.91247	+	15.8402i	0.127883	+	0.517753i
$937$	51.4357			1.68033			0.840166	−	0.542330i	$-0.182458\pi$
$937$	51.4357			1.68033			0.840166	+	0.542330i	$0.182458\pi$
$938$			0.176268i			0.00575536i
$939$	−4.48551	−	36.8662i	−0.146379	−	1.20308i
$940$	5.71427			0.186379
$941$	−40.0147			−1.30444			−0.652221	−	0.758029i	$-0.726162\pi$
$941$	−40.0147			−1.30444			−0.652221	+	0.758029i	$0.726162\pi$
$942$	0.919876	+	7.56041i	0.0299712	+	0.246332i
$943$			8.54610i			0.278299i
$944$	12.5486			0.408421
$945$	1.28489	−	0.488371i	0.0417973	−	0.0158867i
$946$		−	3.42854i		−	0.111471i
$947$		−	15.3358i		−	0.498346i	−0.968459	−	0.249173i	$-0.919841\pi$
$947$		−	15.3358i		−	0.498346i	0.968459	−	0.249173i	$-0.0801588\pi$
$948$	13.9088	−	1.69229i	0.451738	−	0.0549629i
$949$		−	69.0853i		−	2.24260i
$950$	−1.41839	+	4.12167i	−0.0460187	+	0.133725i
$951$	1.34730	+	11.0734i	0.0436892	+	0.359079i
$952$			0.868970i			0.0281635i
$953$	42.4613			1.37546			0.687728	−	0.725968i	$-0.258608\pi$
$953$	42.4613			1.37546			0.687728	+	0.725968i	$0.258608\pi$
$954$	9.59915	−	2.37096i	0.310784	−	0.0767626i
$955$	19.3100			0.624857
$956$		−	13.3149i		−	0.430636i
$957$	1.43874	−	0.175052i	0.0465079	−	0.00565862i
$958$			16.0407i			0.518252i
$959$		−	1.26885i		−	0.0409733i
$960$	−1.71937	+	0.209196i	−0.0554925	+	0.00675177i
$961$	18.3235			0.591079
$962$	−1.67357			−0.0539580
$963$	−29.6296	+	7.31842i	−0.954802	+	0.235833i
$964$		−	22.0627i		−	0.710591i
$965$	15.0565			0.484684
$966$	1.80470	−	0.219578i	0.0580653	−	0.00706481i
$967$	−30.8652			−0.992557			−0.496278	−	0.868164i	$-0.665300\pi$
$967$	−30.8652			−0.992557			−0.496278	+	0.868164i	$0.665300\pi$
$968$	7.00000			0.224989
$969$	5.17864	−	24.2536i	0.166362	−	0.779139i
$970$	1.47093			0.0472287
$971$	54.7439			1.75682			0.878408	−	0.477912i	$-0.158606\pi$
$971$	54.7439			1.75682			0.878408	+	0.477912i	$0.158606\pi$
$972$	−8.87093	−	12.8182i	−0.284535	−	0.411144i
$973$	3.10961			0.0996895
$974$		−	2.59344i		−	0.0830993i
$975$	9.35122	−	1.13776i	0.299479	−	0.0364376i
$976$	9.18520			0.294011
$977$	30.5934			0.978771			0.489385	−	0.872068i	$-0.337221\pi$
$977$	30.5934			0.978771			0.489385	+	0.872068i	$0.337221\pi$
$978$	2.45449	+	20.1734i	0.0784861	+	0.645073i
$979$			21.3659i			0.682856i
$980$			6.93002i			0.221371i
$981$	−3.59625	−	14.5599i	−0.114819	−	0.464862i
$982$			6.94017i			0.221470i
$983$	−48.9809			−1.56225			−0.781124	−	0.624377i	$-0.785353\pi$
$983$	−48.9809			−1.56225			−0.781124	+	0.624377i	$0.785353\pi$
$984$	−0.450578	−	3.70328i	−0.0143639	−	0.118056i
$985$	−15.5116			−0.494242
$986$		−	1.37437i		−	0.0437689i
$987$	2.59905	−	0.316227i	0.0827287	−	0.0100656i
$988$	−22.4167	−	7.71427i	−0.713170	−	0.245424i
$989$			6.80190i			0.216288i
$990$	5.82495	−	1.43874i	0.185129	−	0.0457262i
$991$		−	55.7394i		−	1.77062i	−0.465002	−	0.885310i	$-0.653946\pi$
$991$		−	55.7394i		−	1.77062i	0.465002	−	0.885310i	$-0.346054\pi$
$992$		−	3.56041i		−	0.113043i
$993$	42.3377	−	5.15123i	1.34355	−	0.163469i
$994$	2.73753			0.0868291
$995$		−	15.8469i		−	0.502381i
$996$	28.7919	−	3.50311i	0.912307	−	0.111000i
$997$	34.1252			1.08076			0.540378	−	0.841422i	$-0.318281\pi$
$997$	34.1252			1.08076			0.540378	+	0.841422i	$0.318281\pi$
$998$	22.4111			0.709411
$999$	1.49460	−	0.568081i	0.0472871	−	0.0179733i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.f.d.341.5	yes	8
3.2	odd	2		570.2.f.c.341.3	✓	8
19.18	odd	2		570.2.f.c.341.4	yes	8
57.56	even	2	inner	570.2.f.d.341.6	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.f.c.341.3	✓	8	3.2	odd	2
570.2.f.c.341.4	yes	8	19.18	odd	2
570.2.f.d.341.5	yes	8	1.1	even	1	trivial
570.2.f.d.341.6	yes	8	57.56	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +(-0.209196 - 1.71937i) q^{3} +1.00000 q^{4} -1.00000i q^{5} +(-0.209196 - 1.71937i) q^{6} +0.264536 q^{7} +1.00000 q^{8} +(-2.91247 + 0.719371i) q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +(-0.209196 - 1.71937i) q^{3} +1.00000 q^{4} -1.00000i q^{5} +(-0.209196 - 1.71937i) q^{6} +0.264536 q^{7} +1.00000 q^{8} +(-2.91247 + 0.719371i) q^{9} -1.00000i q^{10} -2.00000i q^{11} +(-0.209196 - 1.71937i) q^{12} -5.43874i q^{13} +0.264536 q^{14} +(-1.71937 + 0.209196i) q^{15} +1.00000 q^{16} +3.28489i q^{17} +(-2.91247 + 0.719371i) q^{18} +(1.41839 - 4.12167i) q^{19} -1.00000i q^{20} +(-0.0553398 - 0.454835i) q^{21} -2.00000i q^{22} +3.96781i q^{23} +(-0.209196 - 1.71937i) q^{24} -1.00000 q^{25} -5.43874i q^{26} +(1.84614 + 4.85713i) q^{27} +0.264536 q^{28} -0.418392 q^{29} +(-1.71937 + 0.209196i) q^{30} -3.56041i q^{31} +1.00000 q^{32} +(-3.43874 + 0.418392i) q^{33} +3.28489i q^{34} -0.264536i q^{35} +(-2.91247 + 0.719371i) q^{36} -0.307712i q^{37} +(1.41839 - 4.12167i) q^{38} +(-9.35122 + 1.13776i) q^{39} -1.00000i q^{40} +2.15386 q^{41} +(-0.0553398 - 0.454835i) q^{42} +1.71427 q^{43} -2.00000i q^{44} +(0.719371 + 2.91247i) q^{45} +3.96781i q^{46} +5.71427i q^{47} +(-0.209196 - 1.71937i) q^{48} -6.93002 q^{49} -1.00000 q^{50} +(5.64794 - 0.687185i) q^{51} -5.43874i q^{52} -3.29588 q^{53} +(1.84614 + 4.85713i) q^{54} -2.00000 q^{55} +0.264536 q^{56} +(-7.38340 - 1.57651i) q^{57} -0.418392 q^{58} +12.5486 q^{59} +(-1.71937 + 0.209196i) q^{60} +9.18520 q^{61} -3.56041i q^{62} +(-0.770454 + 0.190299i) q^{63} +1.00000 q^{64} -5.43874 q^{65} +(-3.43874 + 0.418392i) q^{66} +0.666330i q^{67} +3.28489i q^{68} +(6.82214 - 0.830051i) q^{69} -0.264536i q^{70} +10.3484 q^{71} +(-2.91247 + 0.719371i) q^{72} +12.7024 q^{73} -0.307712i q^{74} +(0.209196 + 1.71937i) q^{75} +(1.41839 - 4.12167i) q^{76} -0.529072i q^{77} +(-9.35122 + 1.13776i) q^{78} +8.08948i q^{79} -1.00000i q^{80} +(7.96501 - 4.19030i) q^{81} +2.15386 q^{82} +16.7456i q^{83} +(-0.0553398 - 0.454835i) q^{84} +3.28489 q^{85} +1.71427 q^{86} +(0.0875259 + 0.719371i) q^{87} -2.00000i q^{88} -10.6829 q^{89} +(0.719371 + 2.91247i) q^{90} -1.43874i q^{91} +3.96781i q^{92} +(-6.12167 + 0.744824i) q^{93} +5.71427i q^{94} +(-4.12167 - 1.41839i) q^{95} +(-0.209196 - 1.71937i) q^{96} +1.47093i q^{97} -6.93002 q^{98} +(1.43874 + 5.82495i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{2} - 2 q^{3} + 8 q^{4} - 2 q^{6} + 4 q^{7} + 8 q^{8} + 2 q^{9}+O(q^{10}) \) 8 * q + 8 * q^2 - 2 * q^3 + 8 * q^4 - 2 * q^6 + 4 * q^7 + 8 * q^8 + 2 * q^9	\( 8 q + 8 q^{2} - 2 q^{3} + 8 q^{4} - 2 q^{6} + 4 q^{7} + 8 q^{8} + 2 q^{9} - 2 q^{12} + 4 q^{14} + 8 q^{16} + 2 q^{18} + 12 q^{19} - 2 q^{21} - 2 q^{24} - 8 q^{25} + 16 q^{27} + 4 q^{28} - 4 q^{29} + 8 q^{32} + 2 q^{36} + 12 q^{38} - 22 q^{39} + 16 q^{41} - 2 q^{42} - 40 q^{43} - 8 q^{45} - 2 q^{48} + 4 q^{49} - 8 q^{50} + 18 q^{51} + 28 q^{53} + 16 q^{54} - 16 q^{55} + 4 q^{56} - 30 q^{57} - 4 q^{58} - 4 q^{59} + 16 q^{61} - 34 q^{63} + 8 q^{64} - 16 q^{65} - 2 q^{69} + 24 q^{71} + 2 q^{72} - 4 q^{73} + 2 q^{75} + 12 q^{76} - 22 q^{78} + 34 q^{81} + 16 q^{82} - 2 q^{84} - 40 q^{86} + 26 q^{87} - 88 q^{89} - 8 q^{90} - 24 q^{93} - 8 q^{95} - 2 q^{96} + 4 q^{98} - 16 q^{99}+O(q^{100}) \) 8 * q + 8 * q^2 - 2 * q^3 + 8 * q^4 - 2 * q^6 + 4 * q^7 + 8 * q^8 + 2 * q^9 - 2 * q^12 + 4 * q^14 + 8 * q^16 + 2 * q^18 + 12 * q^19 - 2 * q^21 - 2 * q^24 - 8 * q^25 + 16 * q^27 + 4 * q^28 - 4 * q^29 + 8 * q^32 + 2 * q^36 + 12 * q^38 - 22 * q^39 + 16 * q^41 - 2 * q^42 - 40 * q^43 - 8 * q^45 - 2 * q^48 + 4 * q^49 - 8 * q^50 + 18 * q^51 + 28 * q^53 + 16 * q^54 - 16 * q^55 + 4 * q^56 - 30 * q^57 - 4 * q^58 - 4 * q^59 + 16 * q^61 - 34 * q^63 + 8 * q^64 - 16 * q^65 - 2 * q^69 + 24 * q^71 + 2 * q^72 - 4 * q^73 + 2 * q^75 + 12 * q^76 - 22 * q^78 + 34 * q^81 + 16 * q^82 - 2 * q^84 - 40 * q^86 + 26 * q^87 - 88 * q^89 - 8 * q^90 - 24 * q^93 - 8 * q^95 - 2 * q^96 + 4 * q^98 - 16 * q^99

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