LMFDB - Embedded newform 570.2.f.c.341.3

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			341.3
Root			$0.209196 - 1.71937i$ of defining polynomial
Character	$\chi$	$=$	570.341
Dual form			570.2.f.c.341.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +(0.209196 - 1.71937i) q^{3} +1.00000 q^{4} +1.00000i q^{5} +(-0.209196 + 1.71937i) q^{6} +0.264536 q^{7} -1.00000 q^{8} +(-2.91247 - 0.719371i) q^{9} +O(q^{10})$	\(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} +(-6.78996 - 3.30098i) 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} + 26 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 + 26 * 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	$0.0974911\pi$
$11$			2.00000i			0.603023i	−0.953463	+	0.301511i	$0.902509\pi$
$12$	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	$-0.869583\pi$
$17$		−	3.28489i		−	0.796702i	0.917233	−	0.398351i	$-0.130417\pi$
$18$	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	$-0.864246\pi$
$23$		−	3.96781i		−	0.827346i	0.910425	−	0.413673i	$-0.135754\pi$
$24$	−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	$-0.487632\pi$
$29$	0.418392			0.0776934			0.0388467	+	0.999245i	$0.487632\pi$
$30$	−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	$-0.553792\pi$
$41$	−2.15386			−0.336376			−0.168188	+	0.985755i	$0.553792\pi$
$42$	−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	$-0.863167\pi$
$47$		−	5.71427i		−	0.833512i	0.909018	−	0.416756i	$-0.136833\pi$
$48$	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	$-0.427317\pi$
$53$	3.29588			0.452723			0.226362	+	0.974043i	$0.427317\pi$
$54$	1.84614	−	4.85713i	0.251228	−	0.660972i
$55$	−2.00000			−0.269680
$56$	−0.264536			−0.0353501
$57$	−6.78996	−	3.30098i	−0.899352	−	0.437225i
$58$	−0.418392			−0.0549376
$59$	−12.5486			−1.63369			−0.816843	−	0.576860i	$-0.804278\pi$
$59$	−12.5486			−1.63369			−0.816843	+	0.576860i	$0.804278\pi$
$60$	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	$-0.710467\pi$
$71$	−10.3484			−1.22813			−0.614065	+	0.789255i	$0.710467\pi$
$72$	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	$-0.628970\pi$
$83$		−	16.7456i		−	1.83807i	0.394177	−	0.919035i	$-0.371030\pi$
$84$	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	$-0.308415\pi$
$89$	10.6829			1.13239			0.566194	+	0.824272i	$0.308415\pi$
$90$	−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	$0.101214\pi$
$101$			6.28404i			0.625285i	−0.949871	+	0.312643i	$0.898786\pi$
$102$	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	$-0.663642\pi$
$107$	−10.1734			−0.983496			−0.491748	+	0.870738i	$0.663642\pi$
$108$	−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	$-0.159940\pi$
$113$	18.6325			1.75279			0.876397	+	0.481590i	$0.159940\pi$
$114$	6.78996	+	3.30098i	0.635938	+	0.309165i
$115$	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	$0.0429608\pi$
$131$			3.08012i			0.269112i	−0.990906	+	0.134556i	$0.957039\pi$
$132$	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	$0.0656859\pi$
$137$			4.79651i			0.409794i	−0.978784	+	0.204897i	$0.934314\pi$
$138$	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	$0.253422\pi$
$149$			17.4473i			1.42933i	−0.699464	+	0.714667i	$0.746578\pi$
$150$	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	$-0.577660\pi$
$167$	−6.24334			−0.483124			−0.241562	+	0.970385i	$0.577660\pi$
$168$	−0.0553398	+	0.454835i	−0.00426956	+	0.0350913i
$169$	−16.5799			−1.27538
$170$	−3.28489			−0.251939
$171$	−7.09604	+	10.9839i	−0.542648	+	0.839960i
$172$	1.71427			0.130712
$173$	15.3422			1.16644			0.583222	−	0.812313i	$-0.301792\pi$
$173$	15.3422			1.16644			0.583222	+	0.812313i	$0.301792\pi$
$174$	−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	$-0.218808\pi$
$179$	20.6812			1.54579			0.772894	+	0.634535i	$0.218808\pi$
$180$	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	$-0.753802\pi$
$191$		−	19.3100i		−	1.39722i	0.715501	−	0.698611i	$-0.246198\pi$
$192$	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	$0.186356\pi$
$197$			15.5116i			1.10516i	−0.833461	+	0.552579i	$0.813644\pi$
$198$	−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	$-0.347796\pi$
$227$	13.8656			0.920295			0.460148	+	0.887842i	$0.347796\pi$
$228$	−6.78996	−	3.30098i	−0.449676	−	0.218613i
$229$	−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	$-0.668406\pi$
$233$		−	26.3548i		−	1.72656i	0.504725	−	0.863280i	$-0.331594\pi$
$234$	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	$0.141711\pi$
$239$			13.3149i			0.861273i	−0.902526	+	0.430636i	$0.858289\pi$
$240$	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	$-0.774533\pi$
$251$		−	20.6137i		−	1.30113i	0.759452	−	0.650564i	$-0.225467\pi$
$252$	−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	$-0.362682\pi$
$257$	13.4066			0.836278			0.418139	+	0.908383i	$0.362682\pi$
$258$	−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	$0.149448\pi$
$263$			14.6748i			0.904890i	−0.891792	+	0.452445i	$0.850552\pi$
$264$	−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	$-0.366863\pi$
$269$	13.3235			0.812346			0.406173	+	0.913796i	$0.366863\pi$
$270$	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	$-0.439510\pi$
$281$	6.33282			0.377785			0.188892	+	0.981998i	$0.439510\pi$
$282$	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
$285$	3.30098	−	6.78996i	0.195533	−	0.402202i
$286$	−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	$-0.830142\pi$
$293$	−29.4748			−1.72194			−0.860969	+	0.508657i	$0.830142\pi$
$294$	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	$0.149771\pi$
$311$			15.9898i			0.906698i	−0.891333	+	0.453349i	$0.850229\pi$
$312$	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	$-0.442111\pi$
$317$	6.44037			0.361727			0.180864	+	0.983508i	$0.442111\pi$
$318$	−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
$342$	7.09604	−	10.9839i	0.383710	−	0.593942i
$343$	−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	$-0.972334\pi$
$347$		−	3.23398i		−	0.173609i	0.996225	−	0.0868046i	$-0.0276656\pi$
$348$	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	$0.0647625\pi$
$353$			7.59260i			0.404113i	−0.979374	+	0.202057i	$0.935237\pi$
$354$	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	$0.421930\pi$
$359$			36.7605i			1.94015i	−0.242814	+	0.970073i	$0.578070\pi$
$360$	−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	$-0.744964\pi$
$383$	−27.2354			−1.39166			−0.695832	+	0.718204i	$0.744964\pi$
$384$	−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	$0.244691\pi$
$389$			27.4236i			1.39043i	−0.718801	+	0.695215i	$0.755309\pi$
$390$	−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
$399$	−1.79619	−	0.873227i	−0.0899218	−	0.0437160i
$400$	−1.00000			−0.0500000
$401$	6.98569			0.348849			0.174424	−	0.984671i	$-0.444194\pi$
$401$	6.98569			0.348849			0.174424	+	0.984671i	$0.444194\pi$
$402$	−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	$-0.879424\pi$
$419$		−	15.1395i		−	0.739615i	0.929108	−	0.369808i	$-0.120576\pi$
$420$	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	$-0.336088\pi$
$431$	20.4485			0.984971			0.492486	+	0.870321i	$0.336088\pi$
$432$	−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	$-0.830068\pi$
$443$		−	21.4205i		−	1.01772i	0.860850	−	0.508858i	$-0.169932\pi$
$444$	−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	$-0.428522\pi$
$449$	9.43662			0.445342			0.222671	+	0.974894i	$0.428522\pi$
$450$	−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
$456$	6.78996	+	3.30098i	0.317969	+	0.154583i
$457$	−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	$-0.868152\pi$
$461$		−	17.2828i		−	0.804939i	0.915433	−	0.402469i	$-0.131848\pi$
$462$	−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	$0.0165888\pi$
$467$			2.25142i			0.104183i	−0.998642	+	0.0520917i	$0.983411\pi$
$468$	−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	$-0.880570\pi$
$479$		−	16.0407i		−	0.732918i	0.930434	−	0.366459i	$-0.119430\pi$
$480$	−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	$-0.949946\pi$
$491$		−	6.94017i		−	0.313205i	0.987662	−	0.156603i	$-0.0500542\pi$
$492$	−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	$0.0458592\pi$
$503$			6.44002i			0.287146i	−0.989640	+	0.143573i	$0.954141\pi$
$504$	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	$-0.743592\pi$
$509$	−31.2574			−1.38546			−0.692730	+	0.721197i	$0.743592\pi$
$510$	−0.687185	+	5.64794i	−0.0304291	+	0.250095i
$511$	3.36025			0.148649
$512$	−1.00000			−0.0441942
$513$	17.4009	+	14.4985i	0.768271	+	0.640125i
$514$	−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	$-0.507794\pi$
$521$	−1.11769			−0.0489670			−0.0244835	+	0.999700i	$0.507794\pi$
$522$	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	$0.0127707\pi$
$557$			1.89324i			0.0802190i	−0.999195	+	0.0401095i	$0.987229\pi$
$558$	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	$-0.670516\pi$
$563$	−24.2229			−1.02087			−0.510437	+	0.859915i	$0.670516\pi$
$564$	−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	$-0.215355\pi$
$569$	37.1991			1.55947			0.779734	+	0.626111i	$0.215355\pi$
$570$	−3.30098	+	6.78996i	−0.138263	+	0.284400i
$571$	−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	$-0.580046\pi$
$587$		−	46.9321i		−	1.93709i	0.248830	−	0.968547i	$-0.419954\pi$
$588$	−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	$-0.868893\pi$
$593$		−	19.4977i		−	0.800676i	0.916368	−	0.400338i	$-0.131107\pi$
$594$	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	$-0.415421\pi$
$599$	12.8538			0.525193			0.262596	+	0.964906i	$0.415421\pi$
$600$	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	$-0.760124\pi$
$617$		−	33.9935i		−	1.36853i	0.729235	−	0.684263i	$-0.239876\pi$
$618$	−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
$627$	6.60196	−	13.5799i	0.263657	−	0.542330i
$628$	−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	$-0.169775\pi$
$641$	43.6027			1.72220			0.861101	+	0.508434i	$0.169775\pi$
$642$	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	$0.177894\pi$
$647$			26.9740i			1.06046i	−0.847854	+	0.530230i	$0.822106\pi$
$648$	−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	$-0.720378\pi$
$653$		−	39.3405i		−	1.53951i	0.638338	−	0.769756i	$-0.279622\pi$
$654$	−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	$-0.687039\pi$
$659$	−28.4622			−1.10873			−0.554365	+	0.832273i	$0.687039\pi$
$660$	−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	$-0.374356\pi$
$677$	20.0114			0.769101			0.384551	+	0.923104i	$0.374356\pi$
$678$	−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	$-0.741443\pi$
$683$	−35.9527			−1.37569			−0.687845	+	0.725858i	$0.741443\pi$
$684$	−7.09604	+	10.9839i	−0.271324	+	0.419980i
$685$	−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	$-0.831156\pi$
$701$		−	26.7894i		−	1.01182i	0.862585	−	0.505912i	$-0.168844\pi$
$702$	−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	$0.245094\pi$
$719$			37.3320i			1.39225i	−0.717922	+	0.696124i	$0.754906\pi$
$720$	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
$741$	−17.9532	+	36.9288i	−0.659526	+	1.35661i
$742$	−0.871877			−0.0320076
$743$	−35.7330			−1.31092			−0.655458	−	0.755232i	$-0.727524\pi$
$743$	−35.7330			−1.31092			−0.655458	+	0.755232i	$0.727524\pi$
$744$	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	$0.0718571\pi$
$761$			12.3494i			0.447666i	−0.974627	+	0.223833i	$0.928143\pi$
$762$	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	$-0.271529\pi$
$773$	36.5720			1.31540			0.657702	+	0.753279i	$0.271529\pi$
$774$	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	$-0.527946\pi$
$797$	−4.95072			−0.175364			−0.0876818	+	0.996149i	$0.527946\pi$
$798$	1.79619	+	0.873227i	0.0635843	+	0.0309119i
$799$	−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	$0.0945178\pi$
$809$			16.6443i			0.585184i	−0.956237	+	0.292592i	$0.905482\pi$
$810$	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	$-0.912080\pi$
$821$		−	15.6279i		−	0.545418i	0.962097	−	0.272709i	$-0.0879196\pi$
$822$	−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	$-0.474592\pi$
$827$	4.58615			0.159476			0.0797380	+	0.996816i	$0.474592\pi$
$828$	−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	$-0.293853\pi$
$839$	34.9497			1.20660			0.603299	+	0.797515i	$0.293853\pi$
$840$	−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
$855$	−10.9839	−	7.09604i	−0.375642	−	0.242679i
$856$	10.1734			0.347718
$857$	16.6893			0.570096			0.285048	−	0.958513i	$-0.407990\pi$
$857$	16.6893			0.570096			0.285048	+	0.958513i	$0.407990\pi$
$858$	−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	$-0.431329\pi$
$863$	12.5773			0.428136			0.214068	+	0.976819i	$0.431329\pi$
$864$	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	$-0.697446\pi$
$881$		−	48.3043i		−	1.62741i	0.581275	−	0.813707i	$-0.302554\pi$
$882$	−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	$-0.499321\pi$
$887$	0.127053			0.00426604			0.00213302	+	0.999998i	$0.499321\pi$
$888$	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	$-0.560333\pi$
$911$	−11.3734			−0.376816			−0.188408	+	0.982091i	$0.560333\pi$
$912$	−6.78996	−	3.30098i	−0.224838	−	0.109306i
$913$	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	$0.217323\pi$
$929$			38.4603i			1.26184i	−0.775847	+	0.630921i	$0.782677\pi$
$930$	−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	$-0.273838\pi$
$941$	40.0147			1.30444			0.652221	+	0.758029i	$0.273838\pi$
$942$	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	$0.0801588\pi$
$947$			15.3358i			0.498346i	−0.968459	+	0.249173i	$0.919841\pi$
$948$	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	$-0.741392\pi$
$953$	−42.4613			−1.37546			−0.687728	+	0.725968i	$0.741392\pi$
$954$	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
$969$	−10.8433	+	22.3042i	−0.348338	+	0.716515i
$970$	1.47093			0.0472287
$971$	−54.7439			−1.75682			−0.878408	−	0.477912i	$-0.841394\pi$
$971$	−54.7439			−1.75682			−0.878408	+	0.477912i	$0.841394\pi$
$972$	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	$-0.662779\pi$
$977$	−30.5934			−0.978771			−0.489385	+	0.872068i	$0.662779\pi$
$978$	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	$-0.214647\pi$
$983$	48.9809			1.56225			0.781124	+	0.624377i	$0.214647\pi$
$984$	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.c.341.3	✓	8
3.2	odd	2		570.2.f.d.341.5	yes	8
19.18	odd	2		570.2.f.d.341.6	yes	8
57.56	even	2	inner	570.2.f.c.341.4	yes	8

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
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} +(-6.78996 - 3.30098i) 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	\( 8 q - 8 q^{2} + 2 q^{3} + 8 q^{4} - 2 q^{6} + 4 q^{7} - 8 q^{8} + 2 q^{9} + 2 q^{12} - 4 q^{14} + 8 q^{16} - 2 q^{18} + 12 q^{19} + 2 q^{21} - 2 q^{24} - 8 q^{25} - 16 q^{27} + 4 q^{28} + 4 q^{29} - 8 q^{32} + 2 q^{36} - 12 q^{38} - 22 q^{39} - 16 q^{41} - 2 q^{42} - 40 q^{43} - 8 q^{45} + 2 q^{48} + 4 q^{49} + 8 q^{50} - 18 q^{51} - 28 q^{53} + 16 q^{54} - 16 q^{55} - 4 q^{56} + 26 q^{57} - 4 q^{58} + 4 q^{59} + 16 q^{61} - 34 q^{63} + 8 q^{64} + 16 q^{65} + 2 q^{69} - 24 q^{71} - 2 q^{72} - 4 q^{73} - 2 q^{75} + 12 q^{76} + 22 q^{78} + 34 q^{81} + 16 q^{82} + 2 q^{84} + 40 q^{86} + 26 q^{87} + 88 q^{89} + 8 q^{90} - 24 q^{93} + 8 q^{95} - 2 q^{96} - 4 q^{98} - 16 q^{99}+O(q^{100}) \) 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 + 26 * 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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