LMFDB - Embedded newform 588.2.n.d.275.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [588,2,Mod(263,588)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("588.263"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(588, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 3, 4])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 588 = 2^{2} \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	588.n (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [24,0,0,-12,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(6)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.69520363885$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			275.1
Character	$\chi$	$=$	588.275
Dual form			588.2.n.d.263.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.13414 + 0.844822i) q^{2} +(-1.36816 - 1.06214i) q^{3} +(0.572551 - 1.91629i) q^{4} +(3.44057 + 1.98641i) q^{5} +(2.44900 + 0.0487576i) q^{6} +(0.969574 + 2.65705i) q^{8} +(0.743736 + 2.90635i) q^{9} +(-5.58025 + 0.653796i) q^{10} +(1.65172 + 2.86086i) q^{11} +(-2.81871 + 2.01367i) q^{12} -0.850601 q^{13} +(-2.59742 - 6.37208i) q^{15} +(-3.34437 - 2.19435i) q^{16} +(0.499236 - 0.288234i) q^{17} +(-3.29885 - 2.66788i) q^{18} +(-3.11023 - 1.79569i) q^{19} +(5.77645 - 5.45582i) q^{20} +(-4.29021 - 1.84921i) q^{22} +(-1.98085 + 3.43094i) q^{23} +(1.49561 - 4.66510i) q^{24} +(5.39167 + 9.33865i) q^{25} +(0.964701 - 0.718606i) q^{26} +(2.06938 - 4.76630i) q^{27} +3.37929i q^{29} +(8.32911 + 5.03249i) q^{30} +(4.24264 - 2.44949i) q^{31} +(5.64683 - 0.336691i) q^{32} +(0.778803 - 5.66848i) q^{33} +(-0.322697 + 0.748663i) q^{34} +(5.99525 + 0.238815i) q^{36} +(-2.14510 + 3.71543i) q^{37} +(5.04449 - 0.591024i) q^{38} +(1.16376 + 0.903453i) q^{39} +(-1.94212 + 11.0677i) q^{40} -5.35550i q^{41} +7.66518i q^{43} +(6.42795 - 1.52719i) q^{44} +(-3.21433 + 11.4769i) q^{45} +(-0.651966 - 5.56464i) q^{46} +(-4.54525 + 7.87260i) q^{47} +(2.24494 + 6.55441i) q^{48} +(-14.0044 - 6.03634i) q^{50} +(-0.989179 - 0.135905i) q^{51} +(-0.487013 + 1.63000i) q^{52} +(-0.527096 + 0.304319i) q^{53} +(1.67971 + 7.15392i) q^{54} +13.1240i q^{55} +(2.34803 + 5.76029i) q^{57} +(-2.85490 - 3.83259i) q^{58} +(3.93980 + 6.82394i) q^{59} +(-13.6979 + 1.32907i) q^{60} +(4.87315 - 8.44054i) q^{61} +(-2.74237 + 6.36234i) q^{62} +(-6.11985 + 5.15242i) q^{64} +(-2.92655 - 1.68964i) q^{65} +(3.90558 + 7.08680i) q^{66} +(7.83384 - 4.52287i) q^{67} +(-0.266503 - 1.12171i) q^{68} +(6.35425 - 2.59015i) q^{69} +9.15654 q^{71} +(-7.00121 + 4.79407i) q^{72} +(0.707107 + 1.22474i) q^{73} +(-0.706026 - 6.02605i) q^{74} +(2.54223 - 18.5035i) q^{75} +(-5.22185 + 4.93200i) q^{76} +(-2.08312 - 0.0414733i) q^{78} +(6.00000 + 3.46410i) q^{79} +(-7.14764 - 14.1931i) q^{80} +(-7.89371 + 4.32311i) q^{81} +(4.52445 + 6.07390i) q^{82} -4.13877 q^{83} +2.29021 q^{85} +(-6.47571 - 8.69339i) q^{86} +(3.58926 - 4.62341i) q^{87} +(-6.00000 + 7.16253i) q^{88} +(4.98550 + 2.87838i) q^{89} +(-6.05039 - 15.7319i) q^{90} +(5.44055 + 5.76029i) q^{92} +(-8.40631 - 1.15496i) q^{93} +(-1.49600 - 12.7686i) q^{94} +(-7.13398 - 12.3564i) q^{95} +(-8.08339 - 5.53705i) q^{96} -13.5487 q^{97} +(-7.08622 + 6.92820i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 12 q^{4} - 36 q^{16} - 12 q^{18} + 12 q^{25} + 12 q^{30} + 12 q^{36} + 96 q^{39} - 96 q^{46} - 12 q^{51} - 24 q^{57} - 120 q^{58} - 84 q^{60} - 48 q^{64} + 48 q^{67} - 72 q^{72} - 24 q^{78} + 144 q^{79}+ \cdots - 24 q^{93}+O(q^{100}) $ 24 * q - 12 * q^4 - 36 * q^16 - 12 * q^18 + 12 * q^25 + 12 * q^30 + 12 * q^36 + 96 * q^39 - 96 * q^46 - 12 * q^51 - 24 * q^57 - 120 * q^58 - 84 * q^60 - 48 * q^64 + 48 * q^67 - 72 * q^72 - 24 * q^78 + 144 * q^79 + 12 * q^81 - 48 * q^85 - 144 * q^88 - 24 * q^93

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/588\mathbb{Z}\right)^\times$.

$n$	$197$	$295$	$493$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.13414	+	0.844822i	−0.801959	+	0.597379i
$2$	−1.13414	+	0.844822i	−0.801959	+	0.597379i
$3$	−1.36816	−	1.06214i	−0.789909	−	0.613224i
$3$	−1.36816	−	1.06214i	−0.789909	−	0.613224i
$4$	0.572551	−	1.91629i	0.286276	−	0.958147i
$5$	3.44057	+	1.98641i	1.53867	+	0.888351i	0.998917	+	0.0465264i	$0.0148152\pi$
$5$	3.44057	+	1.98641i	1.53867	+	0.888351i	0.539752	+	0.841824i	$0.318518\pi$
$6$	2.44900	+	0.0487576i	0.999802	+	0.0199052i
$7$		0			0
$7$		0			0
$8$	0.969574	+	2.65705i	0.342796	+	0.939410i
$9$	0.743736	+	2.90635i	0.247912	+	0.968783i
$10$	−5.58025	+	0.653796i	−1.76463	+	0.206748i
$11$	1.65172	+	2.86086i	0.498013	+	0.862583i	0.999997	−	0.00229340i	$-0.000730012\pi$
$11$	1.65172	+	2.86086i	0.498013	+	0.862583i	−0.501985	+	0.864876i	$0.667397\pi$
$12$	−2.81871	+	2.01367i	−0.813691	+	0.581298i
$13$	−0.850601			−0.235914			−0.117957	−	0.993019i	$-0.537635\pi$
$13$	−0.850601			−0.235914			−0.117957	+	0.993019i	$0.537635\pi$
$14$		0			0
$15$	−2.59742	−	6.37208i	−0.670650	−	1.64527i
$16$	−3.34437	−	2.19435i	−0.836092	−	0.548589i
$17$	0.499236	−	0.288234i	0.121082	−	0.0699070i	−0.438236	−	0.898860i	$-0.644396\pi$
$17$	0.499236	−	0.288234i	0.121082	−	0.0699070i	0.559318	+	0.828953i	$0.311063\pi$
$18$	−3.29885	−	2.66788i	−0.777546	−	0.628826i
$19$	−3.11023	−	1.79569i	−0.713537	−	0.411960i	0.0988326	−	0.995104i	$-0.468489\pi$
$19$	−3.11023	−	1.79569i	−0.713537	−	0.411960i	−0.812369	+	0.583144i	$0.801822\pi$
$20$	5.77645	−	5.45582i	1.29165	−	1.21996i
$21$		0			0
$22$	−4.29021	−	1.84921i	−0.914675	−	0.394254i
$23$	−1.98085	+	3.43094i	−0.413037	+	0.715401i	−0.995220	−	0.0976569i	$-0.968865\pi$
$23$	−1.98085	+	3.43094i	−0.413037	+	0.715401i	0.582183	+	0.813057i	$0.302199\pi$
$24$	1.49561	−	4.66510i	0.305291	−	0.952259i
$25$	5.39167	+	9.33865i	1.07833	+	1.86773i
$26$	0.964701	−	0.718606i	0.189193	−	0.140930i
$27$	2.06938	−	4.76630i	0.398253	−	0.917276i
$28$		0			0
$29$			3.37929i			0.627518i	0.949503	+	0.313759i	$0.101588\pi$
$29$			3.37929i			0.627518i	−0.949503	+	0.313759i	$0.898412\pi$
$30$	8.32911	+	5.03249i	1.52068	+	0.918802i
$31$	4.24264	−	2.44949i	0.762001	−	0.439941i	−0.0680129	−	0.997684i	$-0.521666\pi$
$31$	4.24264	−	2.44949i	0.762001	−	0.439941i	0.830014	+	0.557743i	$0.188333\pi$
$32$	5.64683	−	0.336691i	0.998227	−	0.0595191i
$33$	0.778803	−	5.66848i	0.135572	−	0.986755i
$34$	−0.322697	+	0.748663i	−0.0553421	+	0.128395i
$35$		0			0
$36$	5.99525	+	0.238815i	0.999208	+	0.0398026i
$37$	−2.14510	+	3.71543i	−0.352653	+	0.610812i	−0.986713	−	0.162471i	$-0.948054\pi$
$37$	−2.14510	+	3.71543i	−0.352653	+	0.610812i	0.634061	+	0.773283i	$0.281387\pi$
$38$	5.04449	−	0.591024i	0.818324	−	0.0958767i
$39$	1.16376	+	0.903453i	0.186351	+	0.144668i
$40$	−1.94212	+	11.0677i	−0.307076	+	1.74996i
$41$		−	5.35550i		−	0.836389i	−0.908357	−	0.418195i	$-0.862663\pi$
$41$		−	5.35550i		−	0.836389i	0.908357	−	0.418195i	$-0.137337\pi$
$42$		0			0
$43$			7.66518i			1.16893i	0.811419	+	0.584464i	$0.198695\pi$
$43$			7.66518i			1.16893i	−0.811419	+	0.584464i	$0.801305\pi$
$44$	6.42795	−	1.52719i	0.969050	−	0.230233i
$45$	−3.21433	+	11.4769i	−0.479164	+	1.71087i
$46$	−0.651966	−	5.56464i	−0.0961272	−	0.820461i
$47$	−4.54525	+	7.87260i	−0.662993	+	1.14834i	0.316833	+	0.948481i	$0.397381\pi$
$47$	−4.54525	+	7.87260i	−0.662993	+	1.14834i	−0.979825	+	0.199856i	$0.935953\pi$
$48$	2.24494	+	6.55441i	0.324029	+	0.946047i
$49$		0			0
$50$	−14.0044	−	6.03634i	−1.98052	−	0.853667i
$51$	−0.989179	−	0.135905i	−0.138513	−	0.0190305i
$52$	−0.487013	+	1.63000i	−0.0675365	+	0.226041i
$53$	−0.527096	+	0.304319i	−0.0724023	+	0.0418015i	−0.535764	−	0.844368i	$-0.679976\pi$
$53$	−0.527096	+	0.304319i	−0.0724023	+	0.0418015i	0.463362	+	0.886169i	$0.346643\pi$
$54$	1.67971	+	7.15392i	0.228579	+	0.973525i
$55$			13.1240i			1.76964i
$56$		0			0
$57$	2.34803	+	5.76029i	0.311005	+	0.762969i
$58$	−2.85490	−	3.83259i	−0.374866	−	0.503244i
$59$	3.93980	+	6.82394i	0.512919	+	0.888401i	0.999888	+	0.0149820i	$0.00476911\pi$
$59$	3.93980	+	6.82394i	0.512919	+	0.888401i	−0.486969	+	0.873419i	$0.661898\pi$
$60$	−13.6979	+	1.32907i	−1.76840	+	0.171582i
$61$	4.87315	−	8.44054i	0.623943	−	1.08070i	−0.364802	−	0.931085i	$-0.618863\pi$
$61$	4.87315	−	8.44054i	0.623943	−	1.08070i	0.988744	−	0.149615i	$-0.0478034\pi$
$62$	−2.74237	+	6.36234i	−0.348281	+	0.808018i
$63$		0			0
$64$	−6.11985	+	5.15242i	−0.764982	+	0.644052i
$65$	−2.92655	−	1.68964i	−0.362994	−	0.209575i
$66$	3.90558	+	7.08680i	0.480744	+	0.872325i
$67$	7.83384	−	4.52287i	0.957056	−	0.552557i	0.0617904	−	0.998089i	$-0.480319\pi$
$67$	7.83384	−	4.52287i	0.957056	−	0.552557i	0.895266	+	0.445532i	$0.146986\pi$
$68$	−0.266503	−	1.12171i	−0.0323182	−	0.136027i
$69$	6.35425	−	2.59015i	0.764962	−	0.311817i
$70$		0			0
$71$	9.15654			1.08668			0.543341	−	0.839512i	$-0.317159\pi$
$71$	9.15654			1.08668			0.543341	+	0.839512i	$0.317159\pi$
$72$	−7.00121	+	4.79407i	−0.825100	+	0.564986i
$73$	0.707107	+	1.22474i	0.0827606	+	0.143346i	0.904435	−	0.426612i	$-0.140293\pi$
$73$	0.707107	+	1.22474i	0.0827606	+	0.143346i	−0.821674	+	0.569958i	$0.806960\pi$
$74$	−0.706026	−	6.02605i	−0.0820738	−	0.700514i
$75$	2.54223	−	18.5035i	0.293551	−	2.13660i
$76$	−5.22185	+	4.93200i	−0.598987	+	0.565739i
$77$		0			0
$78$	−2.08312	−	0.0414733i	−0.235867	−	0.00469593i
$79$	6.00000	+	3.46410i	0.675053	+	0.389742i	0.797988	−	0.602673i	$-0.205898\pi$
$79$	6.00000	+	3.46410i	0.675053	+	0.389742i	−0.122936	+	0.992415i	$0.539231\pi$
$80$	−7.14764	−	14.1931i	−0.799130	−	1.58684i
$81$	−7.89371	+	4.32311i	−0.877079	+	0.480346i
$82$	4.52445	+	6.07390i	0.499642	+	0.670750i
$83$	−4.13877			−0.454289			−0.227144	−	0.973861i	$-0.572939\pi$
$83$	−4.13877			−0.454289			−0.227144	+	0.973861i	$0.572939\pi$
$84$		0			0
$85$	2.29021			0.248408
$86$	−6.47571	−	8.69339i	−0.698294	−	0.937433i
$87$	3.58926	−	4.62341i	0.384809	−	0.495682i
$88$	−6.00000	+	7.16253i	−0.639602	+	0.763528i
$89$	4.98550	+	2.87838i	0.528462	+	0.305108i	0.740390	−	0.672177i	$-0.234641\pi$
$89$	4.98550	+	2.87838i	0.528462	+	0.305108i	−0.211928	+	0.977285i	$0.567974\pi$
$90$	−6.05039	−	15.7319i	−0.637768	−	1.65829i
$91$		0			0
$92$	5.44055	+	5.76029i	0.567217	+	0.600552i
$93$	−8.40631	−	1.15496i	−0.871694	−	0.119764i
$94$	−1.49600	−	12.7686i	−0.154300	−	1.31698i
$95$	−7.13398	−	12.3564i	−0.731931	−	1.26774i
$96$	−8.08339	−	5.53705i	−0.825007	−	0.565122i
$97$	−13.5487			−1.37567			−0.687833	−	0.725869i	$-0.741438\pi$
$97$	−13.5487			−1.37567			−0.687833	+	0.725869i	$0.741438\pi$
$98$		0			0
$99$	−7.08622	+	6.92820i	−0.712192	+	0.696311i
$100$	20.9826	−	4.98517i	2.09826	−	0.498517i
$101$	6.18294	−	3.56972i	0.615225	−	0.355200i	−0.159782	−	0.987152i	$-0.551079\pi$
$101$	6.18294	−	3.56972i	0.615225	−	0.355200i	0.775008	+	0.631952i	$0.217746\pi$
$102$	1.23668	−	0.681544i	0.122450	−	0.0674829i
$103$	9.10090	+	5.25441i	0.896738	+	0.517732i	0.876141	−	0.482056i	$-0.160110\pi$
$103$	9.10090	+	5.25441i	0.896738	+	0.517732i	0.0205978	+	0.999788i	$0.493443\pi$
$104$	−0.824720	−	2.26009i	−0.0808705	−	0.221620i
$105$		0			0
$106$	0.340706	−	0.790444i	0.0330923	−	0.0767747i
$107$	−0.616561	+	1.06792i	−0.0596052	+	0.103239i	−0.894288	−	0.447491i	$-0.852318\pi$
$107$	−0.616561	+	1.06792i	−0.0596052	+	0.103239i	0.834683	+	0.550731i	$0.185651\pi$
$108$	−7.94881	−	6.69450i	−0.764875	−	0.644179i
$109$	1.60147	+	2.77382i	0.153393	+	0.265684i	0.932473	−	0.361241i	$-0.117647\pi$
$109$	1.60147	+	2.77382i	0.153393	+	0.265684i	−0.779080	+	0.626925i	$0.784313\pi$
$110$	−11.0874	−	14.8845i	−1.05715	−	1.41918i
$111$	6.88114	−	2.80492i	0.653128	−	0.266231i
$112$		0			0
$113$		−	19.9097i		−	1.87294i	−0.350744	−	0.936471i	$-0.614071\pi$
$113$		−	19.9097i		−	1.87294i	0.350744	−	0.936471i	$-0.385929\pi$
$114$	−7.52942	−	4.54931i	−0.705195	−	0.426082i
$115$	−13.6305	+	7.86959i	−1.27105	+	0.733843i
$116$	6.47571	+	1.93482i	0.601255	+	0.179643i
$117$	−0.632623	−	2.47214i	−0.0584860	−	0.228550i
$118$	−10.2333	−	4.41088i	−0.942052	−	0.406054i
$119$		0			0
$120$	14.4126	−	13.0797i	1.31568	−	1.19401i
$121$	0.0436371	−	0.0755817i	0.00396701	−	0.00687107i
$122$	1.60392	+	13.6897i	0.145212	+	1.23941i
$123$	−5.68827	+	7.32720i	−0.512894	+	0.660671i
$124$	−2.26481	−	9.53261i	−0.203386	−	0.856053i
$125$			22.9762i			2.05505i
$126$		0			0
$127$		−	16.4426i		−	1.45904i	−0.683957	−	0.729522i	$-0.739742\pi$
$127$		−	16.4426i		−	1.45904i	0.683957	−	0.729522i	$-0.260258\pi$
$128$	2.58790	−	11.0138i	0.228740	−	0.973488i
$129$	8.14146	−	10.4872i	0.716815	−	0.923347i
$130$	4.74657	−	0.556119i	0.416302	−	0.0487749i
$131$	1.13845	−	1.97186i	0.0994670	−	0.172282i	−0.811997	−	0.583661i	$-0.801620\pi$
$131$	1.13845	−	1.97186i	0.0994670	−	0.172282i	0.911464	+	0.411379i	$0.134953\pi$
$132$	−10.4166	−	4.73791i	−0.906646	−	0.412382i
$133$		0			0
$134$	−5.06366	+	11.7478i	−0.437434	+	1.01485i
$135$	16.5877	−	12.2881i	1.42764	−	1.05759i
$136$	1.24990	+	1.04703i	0.107178	+	0.0897822i
$137$	−7.97118	+	4.60216i	−0.681024	+	0.393189i	−0.800241	−	0.599679i	$-0.795295\pi$
$137$	−7.97118	+	4.60216i	−0.681024	+	0.393189i	0.119217	+	0.992868i	$0.461962\pi$
$138$	−5.01841	+	8.30581i	−0.427195	+	0.707037i
$139$		−	11.1056i		−	0.941960i	−0.882144	−	0.470980i	$-0.843900\pi$
$139$		−	11.1056i		−	0.941960i	0.882144	−	0.470980i	$-0.156100\pi$
$140$		0			0
$141$	14.5804	−	5.94333i	1.22789	−	0.500519i
$142$	−10.3848	+	7.73565i	−0.871474	+	0.649161i
$143$	−1.40495	−	2.43345i	−0.117488	−	0.203496i
$144$	3.89023	−	11.3519i	0.324186	−	0.945994i
$145$	−6.71266	+	11.6267i	−0.557456	+	0.965542i
$146$	−1.83665	−	0.791654i	−0.152002	−	0.0655177i
$147$		0			0
$148$	5.89167	+	6.23792i	0.484292	+	0.512754i
$149$	5.81744	+	3.35870i	0.476584	+	0.275156i	0.718992	−	0.695019i	$-0.244604\pi$
$149$	5.81744	+	3.35870i	0.476584	+	0.275156i	−0.242408	+	0.970174i	$0.577937\pi$
$150$	12.7489	+	23.1333i	1.04094	+	1.88882i
$151$	11.4426	−	6.60641i	0.931188	−	0.537622i	0.0440012	−	0.999031i	$-0.485989\pi$
$151$	11.4426	−	6.60641i	0.931188	−	0.537622i	0.887187	+	0.461410i	$0.152656\pi$
$152$	1.75565	−	10.0051i	0.142402	−	0.811522i
$153$	1.20901	+	1.23658i	0.0977425	+	0.0999718i
$154$		0			0
$155$	19.4628			1.56329
$156$	2.39759	−	1.71283i	0.191961	−	0.137136i
$157$	1.19412	+	2.06828i	0.0953011	+	0.165066i	0.909734	−	0.415191i	$-0.136285\pi$
$157$	1.19412	+	2.06828i	0.0953011	+	0.165066i	−0.814433	+	0.580257i	$0.802952\pi$
$158$	−9.73140	+	1.14015i	−0.774188	+	0.0907057i
$159$	1.04438	+	0.143490i	0.0828249	+	0.0113795i
$160$	20.0971	+	10.0585i	1.58881	+	0.795196i
$161$		0			0
$162$	5.30032	−	11.5718i	0.416433	−	0.909167i
$163$	−15.8412	−	9.14590i	−1.24078	−	0.716362i	−0.271524	−	0.962432i	$-0.587528\pi$
$163$	−15.8412	−	9.14590i	−1.24078	−	0.716362i	−0.969252	+	0.246069i	$0.920861\pi$
$164$	−10.2627	−	3.06630i	−0.801384	−	0.239438i
$165$	13.9395	−	17.9558i	1.08519	−	1.39785i
$166$	4.69394	−	3.49652i	0.364321	−	0.271383i
$167$	−19.3650			−1.49851			−0.749253	−	0.662284i	$-0.769587\pi$
$167$	−19.3650			−1.49851			−0.749253	+	0.662284i	$0.769587\pi$
$168$		0			0
$169$	−12.2765			−0.944344
$170$	−2.59742	+	1.93482i	−0.199213	+	0.148394i
$171$	2.90572	−	10.3749i	0.222206	−	0.793392i
$172$	14.6887	+	4.38871i	1.12001	+	0.334636i
$173$	−4.83696	−	2.79262i	−0.367748	−	0.212319i	0.304726	−	0.952440i	$-0.401435\pi$
$173$	−4.83696	−	2.79262i	−0.367748	−	0.212319i	−0.672474	+	0.740121i	$0.734768\pi$
$174$	−0.164766	+	8.27589i	−0.0124909	+	0.627394i
$175$		0			0
$176$	0.753784	−	13.1922i	0.0568186	−	0.994403i
$177$	1.85766	−	13.5209i	0.139630	−	1.01629i
$178$	−8.08598	+	0.947373i	−0.606070	+	0.0710086i
$179$	9.68969	+	16.7830i	0.724241	+	1.25442i	0.959286	+	0.282438i	$0.0911432\pi$
$179$	9.68969	+	16.7830i	0.724241	+	1.25442i	−0.235044	+	0.971985i	$0.575523\pi$
$180$	20.1527	+	12.7307i	1.50209	+	0.948890i
$181$	10.8735			0.808222			0.404111	−	0.914710i	$-0.367581\pi$
$181$	10.8735			0.808222			0.404111	+	0.914710i	$0.367581\pi$
$182$		0			0
$183$	−15.6323	+	6.37208i	−1.15557	+	0.471038i
$184$	−11.0368	−	1.93668i	−0.813642	−	0.142774i
$185$	−14.7607	+	8.52212i	−1.08523	+	0.626559i
$186$	10.5097	−	5.79195i	0.770607	−	0.424686i
$187$	1.64920	+	0.952164i	0.120601	+	0.0696291i
$188$	12.4838	+	13.2175i	0.910477	+	0.963986i
$189$		0			0
$190$	18.5299	+	7.98697i	1.34430	+	0.579436i
$191$	−0.616561	+	1.06792i	−0.0446128	+	0.0772716i	−0.887470	−	0.460866i	$-0.847539\pi$
$191$	−0.616561	+	1.06792i	−0.0446128	+	0.0772716i	0.842857	+	0.538138i	$0.180872\pi$
$192$	13.8455	−	0.549231i	0.999214	−	0.0396373i
$193$	−7.89167	−	13.6688i	−0.568055	−	0.983900i	−0.996758	−	0.0804546i	$-0.974363\pi$
$193$	−7.89167	−	13.6688i	−0.568055	−	0.983900i	0.428703	−	0.903445i	$-0.358971\pi$
$194$	15.3662	−	11.4463i	1.10323	−	0.821795i
$195$	2.20936	+	5.42010i	0.158216	+	0.388141i
$196$		0			0
$197$			17.3868i			1.23876i	0.785092	+	0.619379i	$0.212615\pi$
$197$			17.3868i			1.23876i	−0.785092	+	0.619379i	$0.787385\pi$
$198$	2.18367	−	13.8442i	0.155187	−	0.983861i
$199$	−3.95565	+	2.28380i	−0.280409	+	0.161894i	−0.633608	−	0.773654i	$-0.718427\pi$
$199$	−3.95565	+	2.28380i	−0.280409	+	0.161894i	0.353200	+	0.935548i	$0.385094\pi$
$200$	−19.5857	+	23.3805i	−1.38491	+	1.65325i
$201$	−15.5219	−	2.13258i	−1.09483	−	0.150421i
$202$	−3.99654	+	9.27205i	−0.281196	+	0.652379i
$203$		0			0
$204$	−0.826790	+	1.81775i	−0.0578869	+	0.127268i
$205$	10.6382	−	18.4260i	0.743007	−	1.28693i
$206$	−14.7607	+	1.72940i	−1.02843	+	0.120493i
$207$	−11.4447	−	3.20534i	−0.795464	−	0.222786i
$208$	2.84472	+	1.86652i	0.197246	+	0.129420i
$209$		−	11.8639i		−	0.820646i
$210$		0			0
$211$			1.11224i			0.0765696i	0.999267	+	0.0382848i	$0.0121894\pi$
$211$			1.11224i			0.0765696i	−0.999267	+	0.0382848i	$0.987811\pi$
$212$	0.281376	+	1.18431i	0.0193250	+	0.0813388i
$213$	−12.5276	−	9.72549i	−0.858379	−	0.666379i
$214$	−0.202931	−	1.73205i	−0.0138721	−	0.118401i
$215$	−15.2262	+	26.3726i	−1.03842	+	1.79859i
$216$	14.6707	+	0.877174i	0.998217	+	0.0596841i
$217$		0			0
$218$	−4.15967	−	1.79295i	−0.281729	−	0.121434i
$219$	0.333408	−	2.42669i	0.0225296	−	0.163981i
$220$	25.1494	+	7.51416i	1.69558	+	0.506605i
$221$	−0.424650	+	0.245172i	−0.0285651	+	0.0164920i
$222$	−5.43452	+	8.99451i	−0.364741	+	0.603672i
$223$		−	23.6328i		−	1.58257i	−0.611447	−	0.791285i	$-0.709412\pi$
$223$		−	23.6328i		−	1.58257i	0.611447	−	0.791285i	$-0.290588\pi$
$224$		0			0
$225$	−23.1314	+	22.6156i	−1.54209	+	1.50770i
$226$	16.8201	+	22.5804i	1.11886	+	1.50202i
$227$	6.14917	+	10.6507i	0.408135	+	0.706910i	0.994681	−	0.103006i	$-0.0328461\pi$
$227$	6.14917	+	10.6507i	0.408135	+	0.706910i	−0.586546	+	0.809916i	$0.699513\pi$
$228$	12.3828	−	1.20146i	0.820070	−	0.0795688i
$229$	−4.51474	+	7.81976i	−0.298342	+	0.516744i	−0.975757	−	0.218857i	$-0.929767\pi$
$229$	−4.51474	+	7.81976i	−0.298342	+	0.516744i	0.677414	+	0.735602i	$0.263100\pi$
$230$	8.81054	−	20.4406i	0.580950	−	1.34781i
$231$		0			0
$232$	−8.97895	+	3.27647i	−0.589497	+	0.215111i
$233$	6.55912	+	3.78691i	0.429703	+	0.248089i	0.699220	−	0.714907i	$-0.253531\pi$
$233$	6.55912	+	3.78691i	0.429703	+	0.248089i	−0.269517	+	0.962996i	$0.586864\pi$
$234$	2.80600	+	2.26930i	0.183434	+	0.148349i
$235$	−31.2765	+	18.0575i	−2.04025	+	1.17794i
$236$	15.3324	−	3.64277i	0.998055	−	0.237124i
$237$	−4.52963	−	11.1123i	−0.294231	−	0.721819i
$238$		0			0
$239$	−9.25206			−0.598466			−0.299233	−	0.954180i	$-0.596731\pi$
$239$	−9.25206			−0.598466			−0.299233	+	0.954180i	$0.596731\pi$
$240$	−5.29589	+	27.0103i	−0.341848	+	1.74350i
$241$	−7.83018	−	13.5623i	−0.504386	−	0.873623i	−0.999987	−	0.00507224i	$-0.998385\pi$
$241$	−7.83018	−	13.5623i	−0.504386	−	0.873623i	0.495601	−	0.868550i	$-0.334948\pi$
$242$	0.0143625	+	0.122586i	0.000923254	+	0.00788012i
$243$	15.3916	+	2.46947i	0.987372	+	0.158417i
$244$	−13.3844	−	14.1710i	−0.856850	−	0.907207i
$245$		0			0
$246$	0.261122	−	13.1157i	0.0166485	−	0.836223i
$247$	2.64557	+	1.52742i	0.168333	+	0.0971873i
$248$	10.6220	+	8.89796i	0.674496	+	0.565021i
$249$	5.66250	+	4.39593i	0.358847	+	0.278581i
$250$	−19.4108	−	26.0583i	−1.22765	−	1.64807i
$251$	−3.08987			−0.195031			−0.0975155	−	0.995234i	$-0.531090\pi$
$251$	−3.08987			−0.195031			−0.0975155	+	0.995234i	$0.531090\pi$
$252$		0			0
$253$	−13.0873			−0.822790
$254$	13.8911	+	18.6482i	0.871603	+	1.17009i
$255$	−3.13337	−	2.43251i	−0.196219	−	0.152330i
$256$	6.36962	+	14.6775i	0.398101	+	0.917341i
$257$	−6.38190	−	3.68459i	−0.398092	−	0.229839i	0.287568	−	0.957760i	$-0.407153\pi$
$257$	−6.38190	−	3.68459i	−0.398092	−	0.229839i	−0.685660	+	0.727922i	$0.740486\pi$
$258$	−0.373736	+	18.7721i	−0.0232678	+	1.16870i
$259$		0			0
$260$	−4.91346	+	4.64072i	−0.304720	+	0.287805i
$261$	−9.82139	+	2.51330i	−0.607929	+	0.155569i
$262$	0.374703	+	3.19815i	0.0231492	+	0.197583i
$263$	−11.1017	−	19.2288i	−0.684563	−	1.18570i	−0.973574	−	0.228372i	$-0.926660\pi$
$263$	−11.1017	−	19.2288i	−0.684563	−	1.18570i	0.289011	−	0.957326i	$-0.406673\pi$
$264$	15.8165	−	3.42669i	0.973441	−	0.210898i
$265$	−2.41801			−0.148537
$266$		0			0
$267$	−3.76375	−	9.23337i	−0.230338	−	0.565073i
$268$	−4.18188	−	17.6015i	−0.255449	−	1.07518i
$269$	8.67226	−	5.00693i	0.528757	−	0.305278i	−0.211753	−	0.977323i	$-0.567917\pi$
$269$	8.67226	−	5.00693i	0.528757	−	0.305278i	0.740510	+	0.672045i	$0.234584\pi$
$270$	−8.43149	+	27.9501i	−0.513124	+	1.70099i
$271$	−20.4250	−	11.7924i	−1.24073	−	0.716335i	−0.271486	−	0.962442i	$-0.587515\pi$
$271$	−20.4250	−	11.7924i	−1.24073	−	0.716335i	−0.969243	+	0.246107i	$0.920848\pi$
$272$	−2.30212	−	0.131539i	−0.139586	−	0.00797574i
$273$		0			0
$274$	5.15243	−	11.9537i	0.311270	−	0.722151i
$275$	−17.8111	+	30.8497i	−1.07405	+	1.86031i
$276$	−1.32535	−	13.6596i	−0.0797767	−	0.822212i
$277$	−14.5299	−	25.1665i	−0.873018	−	1.51211i	−0.858860	−	0.512211i	$-0.828826\pi$
$277$	−14.5299	−	25.1665i	−0.873018	−	1.51211i	−0.0141582	−	0.999900i	$-0.504507\pi$
$278$	9.38221	+	12.5953i	0.562708	+	0.755413i
$279$	10.2745	+	10.5088i	0.615117	+	0.629146i
$280$		0			0
$281$		−	23.2889i		−	1.38930i	−0.719347	−	0.694651i	$-0.755559\pi$
$281$		−	23.2889i		−	1.38930i	0.719347	−	0.694651i	$-0.244441\pi$
$282$	−11.5152	+	19.0584i	−0.685719	+	1.13491i
$283$	15.0916	−	8.71312i	0.897101	−	0.517941i	0.0208421	−	0.999783i	$-0.493365\pi$
$283$	15.0916	−	8.71312i	0.897101	−	0.517941i	0.876258	+	0.481842i	$0.160032\pi$
$284$	5.24259	−	17.5466i	0.311090	−	1.04120i
$285$	−3.36375	+	24.4828i	−0.199251	+	1.45024i
$286$	3.64925	+	1.57294i	0.215785	+	0.0930100i
$287$		0			0
$288$	5.17829	+	16.1612i	0.305134	+	0.952310i
$289$	−8.33384	+	14.4346i	−0.490226	+	0.849096i
$290$	−2.20936	−	18.8573i	−0.129738	−	1.10734i
$291$	18.5369	+	14.3906i	1.08665	+	0.843592i
$292$	2.75183	−	0.653796i	0.161038	−	0.0382605i
$293$			1.20747i			0.0705412i	0.999378	+	0.0352706i	$0.0112293\pi$
$293$			1.20747i			0.0705412i	−0.999378	+	0.0352706i	$0.988771\pi$
$294$		0			0
$295$			31.3043i			1.82261i
$296$	−11.9519	−	2.09727i	−0.694691	−	0.121901i
$297$	17.0538	−	1.95238i	0.989561	−	0.113289i
$298$	−9.43531	+	1.10546i	−0.546573	+	0.0640377i
$299$	1.68492	−	2.91836i	0.0974412	−	0.168773i
$300$	−34.0025	−	15.4658i	−1.96314	−	0.892921i
$301$		0			0
$302$	−7.39632	+	17.1596i	−0.425610	+	0.987423i
$303$	−12.2508	−	1.68316i	−0.703789	−	0.0966950i
$304$	6.46138	+	12.8304i	0.370586	+	0.735875i
$305$	33.5328	−	19.3602i	1.92008	−	1.10856i
$306$	−2.41588	−	0.381063i	−0.138106	−	0.0217839i
$307$			34.0275i			1.94205i	0.238973	+	0.971026i	$0.423189\pi$
$307$			34.0275i			1.94205i	−0.238973	+	0.971026i	$0.576811\pi$
$308$		0			0
$309$	−6.87062	−	16.8553i	−0.390856	−	0.958863i
$310$	−22.0735	+	16.4426i	−1.25369	+	0.933877i
$311$	−13.3558	−	23.1329i	−0.757337	−	1.31175i	−0.944204	−	0.329361i	$-0.893167\pi$
$311$	−13.3558	−	23.1329i	−0.757337	−	1.31175i	0.186867	−	0.982385i	$-0.440167\pi$
$312$	−1.27217	+	3.96814i	−0.0720225	+	0.224651i
$313$	−4.66276	+	8.07614i	−0.263555	+	0.456490i	−0.967184	−	0.254077i	$-0.918228\pi$
$313$	−4.66276	+	8.07614i	−0.263555	+	0.456490i	0.703629	+	0.710567i	$0.251562\pi$
$314$	−3.10162	−	1.33690i	−0.175035	−	0.0754455i
$315$		0			0
$316$	10.0735	−	9.51439i	0.566681	−	0.535226i
$317$	23.3767	+	13.4966i	1.31297	+	0.758043i	0.982587	−	0.185805i	$-0.0594891\pi$
$317$	23.3767	+	13.4966i	1.31297	+	0.758043i	0.330382	+	0.943847i	$0.392822\pi$
$318$	−1.30570	+	0.719579i	−0.0732200	+	0.0403520i
$319$	−9.66769	+	5.58164i	−0.541286	+	0.312512i
$320$	−31.2906	+	5.57069i	−1.74920	+	0.311411i
$321$	1.97783	−	0.806210i	0.110392	−	0.0449982i
$322$		0			0
$323$	−2.07032			−0.115196
$324$	3.76480	+	17.6019i	0.209156	+	0.977882i
$325$	−4.58616	−	7.94346i	−0.254394	−	0.440624i
$326$	25.6928	−	3.01023i	1.42299	−	0.166721i
$327$	0.755108	−	5.49601i	0.0417575	−	0.303930i
$328$	14.2299	−	5.19256i	0.785712	−	0.286711i
$329$		0			0
$330$	−0.639895	+	32.1407i	−0.0352251	+	1.76929i
$331$	12.6382	+	7.29669i	0.694660	+	0.401062i	0.805356	−	0.592792i	$-0.201974\pi$
$331$	12.6382	+	7.29669i	0.694660	+	0.401062i	−0.110695	+	0.993854i	$0.535308\pi$
$332$	−2.36966	+	7.93109i	−0.130052	+	0.435275i
$333$	−12.3937	−	3.47112i	−0.679171	−	0.190216i
$334$	21.9626	−	16.3600i	1.20174	−	0.895177i
$335$	35.9372			1.96346
$336$		0			0
$337$	31.6823			1.72585			0.862924	−	0.505335i	$-0.168631\pi$
$337$	31.6823			1.72585			0.862924	+	0.505335i	$0.168631\pi$
$338$	13.9233	−	10.3714i	0.757325	−	0.564132i
$339$	−21.1468	+	27.2396i	−1.14853	+	1.47945i
$340$	1.31126	−	4.38871i	0.0711131	−	0.238011i
$341$	14.0153	+	8.09175i	0.758972	+	0.438193i
$342$	5.46949	+	14.2215i	0.295756	+	0.769009i
$343$		0			0
$344$	−20.3668	+	7.43196i	−1.09810	+	0.400704i
$345$	27.0073	+	3.71059i	1.45403	+	0.199772i
$346$	7.84507	−	0.919147i	0.421753	−	0.0494136i
$347$	−1.07687	−	1.86519i	−0.0578092	−	0.100128i	0.835673	−	0.549228i	$-0.185078\pi$
$347$	−1.07687	−	1.86519i	−0.0578092	−	0.100128i	−0.893482	+	0.449100i	$0.851745\pi$
$348$	−6.80479	−	9.52523i	−0.364775	−	0.510606i
$349$	33.0517			1.76922			0.884608	−	0.466335i	$-0.154426\pi$
$349$	33.0517			1.76922			0.884608	+	0.466335i	$0.154426\pi$
$350$		0			0
$351$	−1.76022	+	4.05422i	−0.0939535	+	0.216398i
$352$	10.2902	+	15.5987i	0.548470	+	0.831413i
$353$	13.5161	−	7.80351i	0.719388	−	0.415339i	−0.0951392	−	0.995464i	$-0.530330\pi$
$353$	13.5161	−	7.80351i	0.719388	−	0.415339i	0.814528	+	0.580125i	$0.196996\pi$
$354$	9.31588	+	16.9040i	0.495133	+	0.898435i
$355$	31.5037	+	18.1887i	1.67204	+	0.965354i
$356$	8.37028	−	7.90567i	0.443624	−	0.419000i
$357$		0			0
$358$	−25.1681	−	10.8483i	−1.33018	−	0.573348i
$359$	16.8237	−	29.1394i	0.887919	−	1.53792i	0.0455885	−	0.998960i	$-0.485484\pi$
$359$	16.8237	−	29.1394i	0.887919	−	1.53792i	0.842331	−	0.538961i	$-0.181183\pi$
$360$	−33.6111	+	2.58701i	−1.77146	+	0.136348i
$361$	−3.05096	−	5.28443i	−0.160577	−	0.278128i
$362$	−12.3321	+	9.18619i	−0.648161	+	0.482815i
$363$	−0.139981	+	0.0570595i	−0.00734708	+	0.00299485i
$364$		0			0
$365$			5.61842i			0.294082i
$366$	12.3459	−	20.4333i	0.645331	−	1.06807i
$367$	6.79444	−	3.92277i	0.354667	−	0.204767i	−0.312072	−	0.950059i	$-0.601023\pi$
$367$	6.79444	−	3.92277i	0.354667	−	0.204767i	0.666739	+	0.745291i	$0.267690\pi$
$368$	14.1534	−	7.12764i	0.737797	−	0.371554i
$369$	15.5650	−	3.98308i	0.810279	−	0.207351i
$370$	9.54109	−	22.1355i	0.496018	−	1.15077i
$371$		0			0
$372$	−7.02629	+	15.4477i	−0.364296	+	0.800926i
$373$	−0.493136	+	0.854137i	−0.0255336	+	0.0442256i	−0.878510	−	0.477724i	$-0.841462\pi$
$373$	−0.493136	+	0.854137i	−0.0255336	+	0.0442256i	0.852976	+	0.521950i	$0.174795\pi$
$374$	−2.67483	+	0.313389i	−0.138312	+	0.0162050i
$375$	24.4038	−	31.4352i	1.26021	−	1.62331i
$376$	−25.3249	−	4.44389i	−1.30603	−	0.229176i
$377$		−	2.87443i		−	0.148040i
$378$		0			0
$379$		−	18.8285i		−	0.967153i	−0.875302	−	0.483576i	$-0.839337\pi$
$379$		−	18.8285i		−	0.967153i	0.875302	−	0.483576i	$-0.160663\pi$
$380$	−27.7631	+	6.59612i	−1.42422	+	0.338374i
$381$	−17.4643	+	22.4961i	−0.894721	+	1.15251i
$382$	−0.202931	−	1.73205i	−0.0103829	−	0.0886194i
$383$	−1.81144	+	3.13750i	−0.0925602	+	0.160319i	−0.908588	−	0.417694i	$-0.862838\pi$
$383$	−1.81144	+	3.13750i	−0.0925602	+	0.160319i	0.816028	+	0.578013i	$0.196172\pi$
$384$	−15.2388	+	12.3199i	−0.777650	+	0.628697i
$385$		0			0
$386$	20.4979	+	8.83526i	1.04332	+	0.449703i
$387$	−22.2777	+	5.70087i	−1.13244	+	0.289792i
$388$	−7.75735	+	25.9634i	−0.393820	+	1.31809i
$389$	−12.6579	+	7.30807i	−0.641783	+	0.370534i	−0.785301	−	0.619114i	$-0.787492\pi$
$389$	−12.6579	+	7.30807i	−0.641783	+	0.370534i	0.143518	+	0.989648i	$0.454159\pi$
$390$	−7.08475	−	4.28064i	−0.358750	−	0.216759i
$391$			2.28380i			0.115497i
$392$		0			0
$393$	−3.65197	+	1.48863i	−0.184217	+	0.0750914i
$394$	−14.6887	−	19.7191i	−0.740008	−	0.993432i
$395$	13.7623	+	23.8370i	0.692455	+	1.19937i
$396$	9.21925	+	17.5460i	0.463285	+	0.881722i
$397$	3.04852	−	5.28019i	0.153001	−	0.265005i	−0.779328	−	0.626616i	$-0.784440\pi$
$397$	3.04852	−	5.28019i	0.153001	−	0.265005i	0.932329	+	0.361610i	$0.117773\pi$
$398$	2.55687	−	5.93197i	0.128164	−	0.297343i
$399$		0			0
$400$	2.46056	−	43.0631i	0.123028	−	2.15316i
$401$	−6.31340	−	3.64505i	−0.315276	−	0.182025i	0.334009	−	0.942570i	$-0.391598\pi$
$401$	−6.31340	−	3.64505i	−0.315276	−	0.182025i	−0.649285	+	0.760545i	$0.724932\pi$
$402$	19.4056	−	10.6946i	0.967865	−	0.533397i
$403$	−3.60879	+	2.08354i	−0.179767	+	0.103788i
$404$	−3.30059	−	13.8922i	−0.164210	−	0.691162i
$405$	−35.7463	−	0.806210i	−1.77625	−	0.0400609i
$406$		0			0
$407$	−14.1724			−0.702502
$408$	−0.597975	−	2.76007i	−0.0296042	−	0.136644i
$409$	10.0950	+	17.4850i	0.499165	+	0.864580i	1.00000		0.000963491i	$-0.000306689\pi$
$409$	10.0950	+	17.4850i	0.499165	+	0.864580i	−0.500834	+	0.865543i	$0.666973\pi$
$410$	3.50140	+	29.8851i	0.172922	+	1.47592i
$411$	15.7940	+	2.16997i	0.779060	+	0.107037i
$412$	15.2797	−	14.4316i	0.752778	−	0.710993i
$413$		0			0
$414$	15.6879	−	6.03347i	0.771018	−	0.296529i
$415$	−14.2397	−	8.22130i	−0.699000	−	0.403568i
$416$	−4.80319	+	0.286389i	−0.235496	+	0.0140414i
$417$	−11.7956	+	15.1942i	−0.577633	+	0.744063i
$418$	10.0229	+	13.4554i	0.490237	+	0.658124i
$419$	−1.32886			−0.0649189			−0.0324594	−	0.999473i	$-0.510334\pi$
$419$	−1.32886			−0.0649189			−0.0324594	+	0.999473i	$0.510334\pi$
$420$		0			0
$421$	−7.31859			−0.356686			−0.178343	−	0.983968i	$-0.557074\pi$
$421$	−7.31859			−0.356686			−0.178343	+	0.983968i	$0.557074\pi$
$422$	−0.939643	−	1.26143i	−0.0457411	−	0.0614057i
$423$	−26.2610	−	7.35493i	−1.27685	−	0.357609i
$424$	−1.31965	−	1.10546i	−0.0640879	−	0.0536860i
$425$	5.38343	+	3.10812i	0.261135	+	0.150766i
$426$	22.4244	+	0.446451i	1.08647	+	0.0216306i
$427$		0			0
$428$	1.69343	+	1.79295i	0.0818549	+	0.0866655i
$429$	−0.662451	+	4.82161i	−0.0319834	+	0.232790i
$430$	−5.01146	−	42.7736i	−0.241674	−	2.06273i
$431$	0.0894647	+	0.154957i	0.00430936	+	0.00746403i	0.868172	−	0.496263i	$-0.165295\pi$
$431$	0.0894647	+	0.154957i	0.00430936	+	0.00746403i	−0.863863	+	0.503727i	$0.831962\pi$
$432$	−17.3797	+	11.3993i	−0.836183	+	0.548450i
$433$	15.2499			0.732866			0.366433	−	0.930444i	$-0.380579\pi$
$433$	15.2499			0.732866			0.366433	+	0.930444i	$0.380579\pi$
$434$		0			0
$435$	21.5331	−	8.77742i	1.03243	−	0.420845i
$436$	6.23238	−	1.48073i	0.298477	−	0.0709139i
$437$	12.3218	−	7.11402i	0.589434	−	0.340310i
$438$	1.67199	+	3.03388i	0.0798909	+	0.144965i
$439$	−25.8988	−	14.9527i	−1.23608	−	0.713654i	−0.267793	−	0.963476i	$-0.586294\pi$
$439$	−25.8988	−	14.9527i	−1.23608	−	0.713654i	−0.968292	+	0.249823i	$0.919628\pi$
$440$	−34.8711	+	12.7247i	−1.66242	+	0.606626i
$441$		0			0
$442$	0.274487	−	0.636813i	0.0130560	−	0.0302901i
$443$	2.50795	−	4.34390i	0.119156	−	0.206385i	−0.800277	−	0.599630i	$-0.795314\pi$
$443$	2.50795	−	4.34390i	0.119156	−	0.206385i	0.919434	+	0.393245i	$0.128648\pi$
$444$	−1.43524	−	14.7922i	−0.0681137	−	0.702009i
$445$	11.4353	+	19.8065i	0.542086	+	0.938920i
$446$	19.9655	+	26.8029i	0.945395	+	1.26916i
$447$	−4.39181	−	10.7742i	−0.207725	−	0.509601i
$448$		0			0
$449$			14.4978i			0.684195i	0.939664	+	0.342098i	$0.111137\pi$
$449$			14.4978i			0.684195i	−0.939664	+	0.342098i	$0.888863\pi$
$450$	7.12811	−	45.1911i	0.336023	−	2.13033i
$451$	15.3214	−	8.84580i	0.721455	−	0.416532i
$452$	−38.1528	−	11.3993i	−1.79456	−	0.536178i
$453$	−22.6723	−	3.11499i	−1.06524	−	0.146355i
$454$	−15.9719	−	6.88441i	−0.749600	−	0.323101i
$455$		0			0
$456$	−13.0288	+	11.8239i	−0.610129	+	0.553704i
$457$	9.92844	−	17.1966i	0.464433	−	0.804422i	−0.534743	−	0.845015i	$-0.679591\pi$
$457$	9.92844	−	17.1966i	0.464433	−	0.804422i	0.999176	+	0.0405933i	$0.0129248\pi$
$458$	−1.48595	−	12.6829i	−0.0694341	−	0.592631i
$459$	−0.340700	−	2.97598i	−0.0159025	−	0.138907i
$460$	7.27627	+	30.6259i	0.339258	+	1.42794i
$461$		−	17.3910i		−	0.809978i	−0.914322	−	0.404989i	$-0.867275\pi$
$461$		−	17.3910i		−	0.809978i	0.914322	−	0.404989i	$-0.132725\pi$
$462$		0			0
$463$		−	15.3304i		−	0.712462i	−0.934398	−	0.356231i	$-0.884062\pi$
$463$		−	15.3304i		−	0.712462i	0.934398	−	0.356231i	$-0.115938\pi$
$464$	7.41536	−	11.3016i	0.344249	−	0.524663i
$465$	−26.6283	−	20.6721i	−1.23486	−	0.958647i
$466$	−10.6382	+	1.24640i	−0.492807	+	0.0577384i
$467$	10.5410	−	18.2575i	0.487778	−	0.844857i	−0.512123	−	0.858912i	$-0.671141\pi$
$467$	10.5410	−	18.2575i	0.487778	−	0.844857i	0.999901	+	0.0140554i	$0.00447412\pi$
$468$	−5.09956	−	0.203137i	−0.235727	−	0.00938999i
$469$		0			0
$470$	20.2166	−	46.9028i	0.932521	−	2.16346i
$471$	0.563040	−	4.09805i	0.0259435	−	0.188828i
$472$	−14.3116	+	17.0846i	−0.658746	+	0.786381i
$473$	−21.9290	+	12.6607i	−1.00830	+	0.582141i
$474$	14.5251	+	8.77615i	0.667161	+	0.403102i
$475$		−	38.7272i		−	1.77692i
$476$		0			0
$477$	−1.27648	−	1.30559i	−0.0584459	−	0.0597790i
$478$	10.4931	−	7.81634i	0.479945	−	0.357511i
$479$	3.79982	+	6.58149i	0.173618	+	0.300716i	0.939682	−	0.342049i	$-0.111121\pi$
$479$	3.79982	+	6.58149i	0.173618	+	0.300716i	−0.766064	+	0.642764i	$0.777787\pi$
$480$	−16.8126	−	35.1075i	−0.767386	−	1.60243i
$481$	1.82463	−	3.16034i	0.0831958	−	0.144099i
$482$	20.3382	+	8.76642i	0.926381	+	0.399299i
$483$		0			0
$484$	−0.119852	−	0.126896i	−0.00544784	−	0.00576800i
$485$	−46.6154	−	26.9134i	−2.11670	−	1.22207i
$486$	−19.5425	+	10.2024i	−0.886467	+	0.462792i
$487$	13.3691	−	7.71865i	0.605811	−	0.349765i	−0.165513	−	0.986208i	$-0.552928\pi$
$487$	13.3691	−	7.71865i	0.605811	−	0.349765i	0.771324	+	0.636442i	$0.219595\pi$
$488$	27.1518	+	4.76448i	1.22911	+	0.215678i
$489$	11.9591	+	29.3386i	0.540809	+	1.32674i
$490$		0			0
$491$	40.5166			1.82849			0.914243	−	0.405165i	$-0.132786\pi$
$491$	40.5166			1.82849			0.914243	+	0.405165i	$0.132786\pi$
$492$	10.7842	+	15.0956i	0.486191	+	0.680562i
$493$	0.974025	+	1.68706i	0.0438679	+	0.0759814i
$494$	−4.29084	+	0.502725i	−0.193054	+	0.0226187i
$495$	−38.1429	+	9.76079i	−1.71440	+	0.438715i
$496$	−19.5640	−	1.11786i	−0.878450	−	0.0501932i
$497$		0			0
$498$	−10.1359	−	0.201796i	−0.454199	−	0.00904272i
$499$	26.2986	+	15.1835i	1.17729	+	0.679707i	0.955385	−	0.295362i	$-0.0954403\pi$
$499$	26.2986	+	15.1835i	1.17729	+	0.679707i	0.221902	+	0.975069i	$0.428774\pi$
$500$	44.0292	+	13.1551i	1.96904	+	0.588312i
$501$	26.4944	+	20.5682i	1.18368	+	0.918921i
$502$	3.50435	−	2.61039i	0.156407	−	0.116507i
$503$	−13.8974			−0.619652			−0.309826	−	0.950793i	$-0.600271\pi$
$503$	−13.8974			−0.619652			−0.309826	+	0.950793i	$0.600271\pi$
$504$		0			0
$505$	28.3638			1.26217
$506$	14.8428	−	11.0564i	0.659844	−	0.491518i
$507$	16.7962	+	13.0393i	0.745946	+	0.579095i
$508$	−31.5089	−	9.41423i	−1.39798	−	0.417689i
$509$	−25.6830	−	14.8281i	−1.13838	−	0.657243i	−0.192350	−	0.981326i	$-0.561611\pi$
$509$	−25.6830	−	14.8281i	−1.13838	−	0.657243i	−0.946029	+	0.324083i	$0.894944\pi$
$510$	5.60872	+	0.111665i	0.248358	+	0.00494461i
$511$		0			0
$512$	−19.6239	−	11.2651i	−0.867262	−	0.497853i
$513$	−14.9951	+	11.1083i	−0.662049	+	0.490445i
$514$	10.3508	−	1.21272i	0.456554	−	0.0534909i
$515$	20.8748	+	36.1563i	0.919855	+	1.59324i
$516$	−15.4352	−	21.6059i	−0.679496	−	0.951147i
$517$	−30.0299			−1.32071
$518$		0			0
$519$	3.65161	+	8.95827i	0.160288	+	0.393225i
$520$	1.65197	−	9.41423i	0.0724435	−	0.412841i
$521$	−29.0727	+	16.7851i	−1.27370	+	0.735369i	−0.975682	−	0.219192i	$-0.929658\pi$
$521$	−29.0727	+	16.7851i	−1.27370	+	0.735369i	−0.298015	+	0.954561i	$0.596325\pi$
$522$	9.01555	−	11.1478i	0.394600	−	0.487924i
$523$	8.82946	+	5.09769i	0.386085	+	0.222906i	0.680463	−	0.732783i	$-0.261779\pi$
$523$	8.82946	+	5.09769i	0.386085	+	0.222906i	−0.294377	+	0.955689i	$0.595112\pi$
$524$	−3.12684	−	3.31060i	−0.136596	−	0.144624i
$525$		0			0
$526$	28.8358	+	12.4291i	1.25730	+	0.541937i
$527$	1.41205	−	2.44575i	0.0615099	−	0.106538i
$528$	−15.0433	+	17.2485i	−0.654674	+	0.750645i
$529$	3.65243	+	6.32620i	0.158801	+	0.275052i
$530$	2.74237	−	2.04279i	0.119121	−	0.0887332i
$531$	−16.9026	+	16.5256i	−0.733509	+	0.717152i
$532$		0			0
$533$			4.55539i			0.197316i
$534$	12.0692	+	7.29225i	0.522284	+	0.315567i
$535$	−4.24264	+	2.44949i	−0.183425	+	0.105901i
$536$	19.6130	+	16.4297i	0.847152	+	0.709654i
$537$	4.56879	−	33.2537i	0.197158	−	1.43500i
$538$	−5.60560	+	13.0051i	−0.241675	+	0.560689i
$539$		0			0
$540$	−14.0504	−	38.8225i	−0.604633	−	1.67065i
$541$	−5.15243	+	8.92427i	−0.221520	+	0.383684i	−0.955270	−	0.295736i	$-0.904435\pi$
$541$	−5.15243	+	8.92427i	−0.221520	+	0.383684i	0.733750	+	0.679420i	$0.237769\pi$
$542$	33.1272	−	3.88127i	1.42294	−	0.166715i
$543$	−14.8767	−	11.5492i	−0.638422	−	0.495622i
$544$	2.72205	−	1.79569i	0.116707	−	0.0769898i
$545$			12.7247i			0.545066i
$546$		0			0
$547$			5.44070i			0.232628i	0.993213	+	0.116314i	$0.0371078\pi$
$547$			5.44070i			0.232628i	−0.993213	+	0.116314i	$0.962892\pi$
$548$	4.25519	+	17.9101i	0.181773	+	0.765081i
$549$	28.1555	+	7.88552i	1.20165	+	0.336546i
$550$	−5.86223	−	50.0351i	−0.249966	−	2.13350i
$551$	6.06817	−	10.5104i	0.258513	−	0.447757i
$552$	13.0431	+	14.3722i	0.555150	+	0.611723i
$553$		0			0
$554$	37.7402	+	16.2672i	1.60343	+	0.691128i
$555$	29.2467	+	4.01827i	1.24145	+	0.170566i
$556$	−21.2815	−	6.35850i	−0.902537	−	0.269660i
$557$	3.84264	−	2.21855i	0.162818	−	0.0940030i	−0.416377	−	0.909192i	$-0.636700\pi$
$557$	3.84264	−	2.21855i	0.162818	−	0.0940030i	0.579195	+	0.815189i	$0.303367\pi$
$558$	−20.5308	−	3.23837i	−0.869137	−	0.137091i
$559$		−	6.52001i		−	0.275767i
$560$		0			0
$561$	−1.24504	−	3.05438i	−0.0525657	−	0.128956i
$562$	19.6750	+	26.4129i	0.829940	+	1.11416i
$563$	−19.5639	−	33.8857i	−0.824522	−	1.42811i	−0.902284	−	0.431141i	$-0.858111\pi$
$563$	−19.5639	−	33.8857i	−0.824522	−	1.42811i	0.0777627	−	0.996972i	$-0.475222\pi$
$564$	−3.04113	−	31.3432i	−0.128055	−	1.31979i
$565$	39.5488	−	68.5005i	1.66383	−	2.88184i
$566$	−9.75493	+	22.6316i	−0.410030	+	0.951277i
$567$		0			0
$568$	8.87794	+	24.3294i	0.372510	+	1.02084i
$569$	−38.4653	−	22.2079i	−1.61255	−	0.931005i	−0.988777	−	0.149398i	$-0.952266\pi$
$569$	−38.4653	−	22.2079i	−1.61255	−	0.931005i	−0.623771	−	0.781607i	$-0.714400\pi$
$570$	−16.8687	−	30.6088i	−0.706551	−	1.28206i
$571$	2.15883	−	1.24640i	0.0903442	−	0.0521603i	−0.454147	−	0.890927i	$-0.650056\pi$
$571$	2.15883	−	1.24640i	0.0903442	−	0.0521603i	0.544491	+	0.838766i	$0.316723\pi$
$572$	−5.46762	+	1.29903i	−0.228613	+	0.0543152i
$573$	1.97783	−	0.806210i	0.0826249	−	0.0336799i
$574$		0			0
$575$	−42.7205			−1.78157
$576$	−19.5263	−	13.9544i	−0.813595	−	0.581432i
$577$	18.2933	+	31.6849i	0.761560	+	1.31906i	0.942046	+	0.335482i	$0.108899\pi$
$577$	18.2933	+	31.6849i	0.761560	+	1.31906i	−0.180487	+	0.983577i	$0.557767\pi$
$578$	−2.74295	−	23.4115i	−0.114092	−	0.973791i
$579$	−3.72100	+	27.0831i	−0.154640	+	1.12554i
$580$	18.4368	+	19.5203i	0.765546	+	0.810536i
$581$		0			0
$582$	−33.1809	−	0.660605i	−1.37539	−	0.0273830i
$583$	−1.74123	−	1.00530i	−0.0721145	−	0.0416353i
$584$	−2.56862	+	3.06630i	−0.106290	+	0.126884i
$585$	2.73411	−	9.76222i	0.113042	−	0.403618i
$586$	−1.02010	−	1.36944i	−0.0421398	−	0.0565711i
$587$	−36.8412			−1.52060			−0.760299	−	0.649573i	$-0.774948\pi$
$587$	−36.8412			−1.52060			−0.760299	+	0.649573i	$0.774948\pi$
$588$		0			0
$589$	−17.5941			−0.724954
$590$	−26.4466	−	35.5035i	−1.08879	−	1.46166i
$591$	18.4671	−	23.7879i	0.759636	−	0.978505i
$592$	15.3270	−	7.71865i	0.629935	−	0.317234i
$593$	14.9125	+	8.60972i	0.612382	+	0.353559i	0.773897	−	0.633311i	$-0.218305\pi$
$593$	14.9125	+	8.60972i	0.612382	+	0.353559i	−0.161515	+	0.986870i	$0.551638\pi$
$594$	−17.6920	+	16.6217i	−0.725911	+	0.681996i
$595$		0			0
$596$	9.76705	−	9.22491i	0.400074	−	0.377867i
$597$	7.83768	+	1.07683i	0.320775	+	0.0440719i
$598$	0.554563	+	4.73329i	0.0226778	+	0.193558i
$599$	−9.51076	−	16.4731i	−0.388599	−	0.673073i	0.603662	−	0.797240i	$-0.293708\pi$
$599$	−9.51076	−	16.4731i	−0.388599	−	0.673073i	−0.992261	+	0.124167i	$0.960374\pi$
$600$	51.6296	−	11.1857i	2.10777	−	0.456652i
$601$	−7.95144			−0.324346			−0.162173	−	0.986762i	$-0.551850\pi$
$601$	−7.95144			−0.324346			−0.162173	+	0.986762i	$0.551850\pi$
$602$		0			0
$603$	18.9713	+	19.4040i	0.772573	+	0.790194i
$604$	−6.10833	−	25.7100i	−0.248544	−	1.04612i
$605$	0.300273	−	0.173363i	0.0122078	−	0.00704820i
$606$	15.3161	−	8.44080i	0.622174	−	0.342884i
$607$	−20.5976	−	11.8920i	−0.836030	−	0.482682i	0.0198827	−	0.999802i	$-0.493671\pi$
$607$	−20.5976	−	11.8920i	−0.836030	−	0.482682i	−0.855913	+	0.517120i	$0.827004\pi$
$608$	−18.1675	−	9.09279i	−0.736791	−	0.368761i
$609$		0			0
$610$	−21.6750	+	50.2864i	−0.877596	+	2.03604i
$611$	3.86619	−	6.69644i	0.156409	−	0.270909i
$612$	3.06187	−	1.60881i	0.123769	−	0.0650322i
$613$	14.8779	+	25.7694i	0.600914	+	1.04081i	0.992683	+	0.120751i	$0.0385301\pi$
$613$	14.8779	+	25.7694i	0.600914	+	1.04081i	−0.391768	+	0.920064i	$0.628137\pi$
$614$	−28.7472	−	38.5920i	−1.16014	−	1.55745i
$615$	−34.1257	+	13.9105i	−1.37608	+	0.560924i
$616$		0			0
$617$			28.7008i			1.15545i	0.816232	+	0.577724i	$0.196059\pi$
$617$			28.7008i			1.15545i	−0.816232	+	0.577724i	$0.803941\pi$
$618$	22.0320	+	13.3118i	0.886255	+	0.535479i
$619$	−19.9082	+	11.4940i	−0.800177	+	0.461983i	−0.843533	−	0.537077i	$-0.819528\pi$
$619$	−19.9082	+	11.4940i	−0.800177	+	0.461983i	0.0433558	+	0.999060i	$0.486195\pi$
$620$	11.1434	−	37.2964i	0.447532	−	1.49786i
$621$	12.2538	+	16.5413i	0.491726	+	0.663779i
$622$	34.6905	+	14.9527i	1.39096	+	0.599549i
$623$		0			0
$624$	−1.90955	−	5.57518i	−0.0764431	−	0.223186i
$625$	−18.6819	+	32.3580i	−0.747275	+	1.29432i
$626$	−1.53467	−	13.0987i	−0.0613378	−	0.523529i
$627$	−12.6011	+	16.2318i	−0.503240	+	0.648236i
$628$	4.64712	−	1.10409i	0.185440	−	0.0440580i
$629$			2.47316i			0.0986115i
$630$		0			0
$631$		−	15.3304i		−	0.610292i	−0.952306	−	0.305146i	$-0.901295\pi$
$631$		−	15.3304i		−	0.610292i	0.952306	−	0.305146i	$-0.0987052\pi$
$632$	−3.38685	+	19.3010i	−0.134722	+	0.767753i
$633$	1.18135	−	1.52172i	0.0469543	−	0.0604830i
$634$	−37.9147	+	4.44218i	−1.50579	+	0.176421i
$635$	32.6618	−	56.5719i	1.29614	−	2.24499i
$636$	0.872931	−	1.91919i	0.0346140	−	0.0761008i
$637$		0			0
$638$	6.24902	−	14.4978i	0.247401	−	0.573975i
$639$	6.81005	+	26.6121i	0.269401	+	1.05276i
$640$	30.7817	−	32.7529i	1.21675	−	1.29467i
$641$	11.6038	−	6.69943i	0.458321	−	0.264612i	−0.253017	−	0.967462i	$-0.581423\pi$
$641$	11.6038	−	6.69943i	0.458321	−	0.264612i	0.711338	+	0.702850i	$0.248090\pi$
$642$	−1.56203	+	2.58527i	−0.0616484	+	0.102032i
$643$			2.68122i			0.105737i	0.998601	+	0.0528684i	$0.0168364\pi$
$643$			2.68122i			0.105737i	−0.998601	+	0.0528684i	$0.983164\pi$
$644$		0			0
$645$	48.8432	−	19.9097i	1.92320	−	0.783942i
$646$	2.34803	−	1.74905i	0.0923822	−	0.0688155i
$647$	9.86799	+	17.0919i	0.387951	+	0.671950i	0.992174	−	0.124865i	$-0.0398497\pi$
$647$	9.86799	+	17.0919i	0.387951	+	0.671950i	−0.604223	+	0.796815i	$0.706516\pi$
$648$	−19.1403	−	16.7824i	−0.751901	−	0.659276i
$649$	−13.0149	+	22.5425i	−0.510880	+	0.884870i
$650$	11.9122	+	5.13452i	0.467233	+	0.201392i
$651$		0			0
$652$	−26.5961	+	25.1198i	−1.04158	+	0.983769i
$653$	30.5038	+	17.6114i	1.19371	+	0.689186i	0.959145	−	0.282915i	$-0.0913015\pi$
$653$	30.5038	+	17.6114i	1.19371	+	0.689186i	0.234561	+	0.972101i	$0.424635\pi$
$654$	3.78675	+	6.87118i	0.148074	+	0.268684i
$655$	7.83384	−	4.52287i	0.306094	−	0.176723i
$656$	−11.7519	+	17.9108i	−0.458833	+	0.699299i
$657$	−3.03363	+	2.96599i	−0.118353	+	0.115714i
$658$		0			0
$659$	−39.7628			−1.54894			−0.774469	−	0.632612i	$-0.781983\pi$
$659$	−39.7628			−1.54894			−0.774469	+	0.632612i	$0.781983\pi$
$660$	−26.4275	−	36.9927i	−1.02869	−	1.43994i
$661$	−7.46659	−	12.9325i	−0.290417	−	0.503017i	0.683492	−	0.729958i	$-0.260461\pi$
$661$	−7.46659	−	12.9325i	−0.290417	−	0.503017i	−0.973908	+	0.226942i	$0.927127\pi$
$662$	−20.4979	+	2.40159i	−0.796675	+	0.0933404i
$663$	0.841396	+	0.115601i	0.0326771	+	0.00448957i
$664$	−4.01284	−	10.9969i	−0.155728	−	0.426763i
$665$		0			0
$666$	16.9887	−	6.53375i	0.658298	−	0.253178i
$667$	−11.5941	−	6.69388i	−0.448927	−	0.259188i
$668$	−11.0874	+	37.1090i	−0.428986	+	1.43579i
$669$	−25.1012	+	32.3335i	−0.970470	+	1.25009i
$670$	−40.7578	+	30.3605i	−1.57461	+	1.17293i
$671$	32.1963			1.24292
$672$		0			0
$673$	1.52059			0.0586145			0.0293072	−	0.999570i	$-0.490670\pi$
$673$	1.52059			0.0586145			0.0293072	+	0.999570i	$0.490670\pi$
$674$	−35.9322	+	26.7659i	−1.38406	+	1.03099i
$675$	55.6683	−	6.37310i	2.14267	−	0.245301i
$676$	−7.02891	+	23.5253i	−0.270343	+	0.904821i
$677$	14.2074	+	8.20266i	0.546036	+	0.315254i	0.747522	−	0.664238i	$-0.231244\pi$
$677$	14.2074	+	8.20266i	0.546036	+	0.315254i	−0.201486	+	0.979491i	$0.564577\pi$
$678$	0.970748	−	48.7588i	0.0372813	−	1.87257i
$679$		0			0
$680$	2.22052	+	6.08520i	0.0851532	+	0.233357i
$681$	2.89940	−	21.1031i	0.111105	−	0.808672i
$682$	−22.7314	+	2.66327i	−0.870431	+	0.101982i
$683$	4.57827	+	7.92980i	0.175183	+	0.303425i	0.940224	−	0.340555i	$-0.110615\pi$
$683$	4.57827	+	7.92980i	0.175183	+	0.303425i	−0.765042	+	0.643981i	$0.777282\pi$
$684$	−18.2178	−	11.5084i	−0.696574	−	0.440035i
$685$	−36.5672			−1.39716
$686$		0			0
$687$	14.4825	−	5.90343i	0.552543	−	0.225230i
$688$	16.8201	−	25.6352i	0.641261	−	0.977333i
$689$	0.448349	−	0.258854i	0.0170807	−	0.00986156i
$690$	−33.7649	+	18.6081i	−1.28541	+	0.708397i
$691$	−28.7221	−	16.5827i	−1.09264	−	0.630836i	−0.158362	−	0.987381i	$-0.550621\pi$
$691$	−28.7221	−	16.5827i	−1.09264	−	0.630836i	−0.934278	+	0.356545i	$0.883955\pi$
$692$	−8.12090	+	7.67013i	−0.308710	+	0.291575i
$693$		0			0
$694$	2.79707	+	1.20562i	0.106175	+	0.0457649i
$695$	22.0602	−	38.2094i	0.836791	−	1.44937i
$696$	15.7647	+	5.05411i	0.597560	+	0.191576i
$697$	−1.54364	−	2.67366i	−0.0584694	−	0.101272i
$698$	−37.4853	+	27.9228i	−1.41884	+	1.05689i
$699$	−4.95173	−	12.1478i	−0.187292	−	0.459472i
$700$		0			0
$701$		−	38.1529i		−	1.44101i	−0.693448	−	0.720507i	$-0.743909\pi$
$701$		−	38.1529i		−	1.44101i	0.693448	−	0.720507i	$-0.256091\pi$
$702$	−1.42876	−	6.08513i	−0.0539251	−	0.229668i
$703$	13.3435	−	7.70390i	0.503261	−	0.290558i
$704$	−24.8487	−	8.99771i	−0.936519	−	0.339114i
$705$	61.9708	+	8.51429i	2.33396	+	0.320667i
$706$	−8.73656	+	20.2690i	−0.328805	+	0.762833i
$707$		0			0
$708$	−24.8464	−	11.3012i	−0.933783	−	0.424725i
$709$	−6.97895	+	12.0879i	−0.262100	+	0.453970i	−0.966800	−	0.255535i	$-0.917748\pi$
$709$	−6.97895	+	12.0879i	−0.262100	+	0.453970i	0.704700	+	0.709505i	$0.251082\pi$
$710$	−51.0958	+	5.98651i	−1.91759	+	0.224670i
$711$	−5.60547	+	20.0145i	−0.210221	+	0.750601i
$712$	−2.81420	+	16.0375i	−0.105466	+	0.601032i
$713$			19.4083i			0.726848i
$714$		0			0
$715$		−	11.1633i		−	0.417483i
$716$	37.7091	−	8.95915i	1.40925	−	0.334819i
$717$	12.6583	+	9.82694i	0.472733	+	0.366994i
$718$	5.53724	+	47.2612i	0.206648	+	1.76377i
$719$	−10.0890	+	17.4746i	−0.376255	+	0.651693i	−0.990514	−	0.137412i	$-0.956122\pi$
$719$	−10.0890	+	17.4746i	−0.376255	+	0.651693i	0.614259	+	0.789105i	$0.289455\pi$
$720$	35.9342	−	31.3295i	1.33919	−	1.16758i
$721$		0			0
$722$	7.92462	+	3.41576i	0.294924	+	0.127121i
$723$	−3.69201	+	26.8721i	−0.137307	+	0.999384i
$724$	6.22565	−	20.8369i	0.231374	−	0.774396i
$725$	−31.5580	+	18.2200i	−1.17203	+	0.676674i
$726$	0.110553	−	0.182972i	0.00410300	−	0.00679074i
$727$			1.62103i			0.0601206i	0.999548	+	0.0300603i	$0.00956993\pi$
$727$			1.62103i			0.0601206i	−0.999548	+	0.0300603i	$0.990430\pi$
$728$		0			0
$729$	−18.4353	−	19.7266i	−0.682789	−	0.730615i
$730$	−4.74657	−	6.37208i	−0.175678	−	0.235841i
$731$	2.20936	+	3.82673i	0.0817163	+	0.141537i
$732$	3.26052	+	33.6043i	0.120512	+	1.24205i
$733$	−13.9026	+	24.0801i	−0.513505	+	0.889417i	0.486372	+	0.873752i	$0.338320\pi$
$733$	−13.9026	+	24.0801i	−0.513505	+	0.889417i	−0.999877	+	0.0156654i	$0.995013\pi$
$734$	−4.39181	+	10.1891i	−0.162105	+	0.376086i
$735$		0			0
$736$	−10.0304	+	20.0409i	−0.369725	+	0.738716i
$737$	25.8786	+	14.9410i	0.953252	+	0.550360i
$738$	−14.2879	+	17.6670i	−0.525943	+	0.650331i
$739$	25.1030	−	14.4932i	0.923429	−	0.533142i	0.0387013	−	0.999251i	$-0.487678\pi$
$739$	25.1030	−	14.4932i	0.923429	−	0.533142i	0.884727	+	0.466109i	$0.154345\pi$
$740$	7.87961	+	33.1653i	0.289660	+	1.21918i
$741$	−1.99724	−	4.89971i	−0.0733704	−	0.179995i
$742$		0			0
$743$	10.4018			0.381604			0.190802	−	0.981629i	$-0.438891\pi$
$743$	10.4018			0.381604			0.190802	+	0.981629i	$0.438891\pi$
$744$	−5.08175	−	23.4558i	−0.186306	−	0.859932i
$745$	13.3435	+	23.1117i	0.488870	+	0.846747i
$746$	−0.162308	−	1.38532i	−0.00594251	−	0.0507203i
$747$	−3.07815	−	12.0287i	−0.112624	−	0.440107i
$748$	2.76888	−	2.61518i	0.101240	−	0.0956205i
$749$		0			0
$750$	−1.12027	+	56.2688i	−0.0409063	+	2.05465i
$751$	14.7045	+	8.48962i	0.536573	+	0.309791i	0.743689	−	0.668526i	$-0.233074\pi$
$751$	14.7045	+	8.48962i	0.536573	+	0.309791i	−0.207116	+	0.978316i	$0.566408\pi$
$752$	32.4763	−	16.3550i	1.18429	−	0.596406i
$753$	4.22745	+	3.28186i	0.154057	+	0.119598i
$754$	2.42838	+	3.26000i	0.0884363	+	0.118722i
$755$	52.4922			1.91039
$756$		0			0
$757$	−10.9716			−0.398770			−0.199385	−	0.979921i	$-0.563894\pi$
$757$	−10.9716			−0.398770			−0.199385	+	0.979921i	$0.563894\pi$
$758$	15.9067	+	21.3541i	0.577757	+	0.775617i
$759$	17.9055	+	13.9005i	0.649929	+	0.504555i
$760$	25.9147	−	30.9358i	0.940026	−	1.12216i
$761$	−10.0723	−	5.81526i	−0.365121	−	0.210803i	0.306204	−	0.951966i	$-0.400941\pi$
$761$	−10.0723	−	5.81526i	−0.365121	−	0.210803i	−0.671325	+	0.741163i	$0.734274\pi$
$762$	0.801702	−	40.2680i	0.0290426	−	1.45876i
$763$		0			0
$764$	1.69343	+	1.79295i	0.0612660	+	0.0648666i
$765$	1.70331	+	6.65613i	0.0615833	+	0.240653i
$766$	−0.596206	−	5.08871i	−0.0215418	−	0.183863i
$767$	−3.35120	−	5.80445i	−0.121005	−	0.209586i
$768$	6.87478	−	26.8466i	0.248072	−	0.968742i
$769$	0.123424			0.00445080			0.00222540	−	0.999998i	$-0.499292\pi$
$769$	0.123424			0.00445080			0.00222540	+	0.999998i	$0.499292\pi$
$770$		0			0
$771$	4.81794	+	11.8196i	0.173514	+	0.425671i
$772$	−30.7118	+	7.29669i	−1.10534	+	0.262614i
$773$	−13.4620	+	7.77229i	−0.484194	+	0.279550i	−0.722163	−	0.691723i	$-0.756852\pi$
$773$	−13.4620	+	7.77229i	−0.484194	+	0.279550i	0.237968	+	0.971273i	$0.423519\pi$
$774$	20.4498	−	25.2863i	0.735053	−	0.908896i
$775$	45.7498	+	26.4137i	1.64338	+	0.948808i
$776$	−13.1365	−	35.9997i	−0.471573	−	1.29231i
$777$		0			0
$778$	8.18188	−	18.9821i	0.293334	−	0.680541i
$779$	−9.61685	+	16.6569i	−0.344559	+	0.596794i
$780$	11.6515	−	1.13051i	0.417190	−	0.0404786i
$781$	15.1240	+	26.1956i	0.541181	+	0.937353i
$782$	−1.92940	−	2.59015i	−0.0689953	−	0.0926235i
$783$	16.1067	+	6.99304i	0.575607	+	0.249911i
$784$		0			0
$785$			9.48806i			0.338643i
$786$	2.88422	−	4.77358i	0.102877	−	0.170268i
$787$	−36.3048	+	20.9606i	−1.29413	+	0.747164i	−0.979383	−	0.202014i	$-0.935252\pi$
$787$	−36.3048	+	20.9606i	−1.29413	+	0.747164i	−0.314743	+	0.949177i	$0.601918\pi$
$788$	33.3182	+	9.95483i	1.18691	+	0.354626i
$789$	−5.23459	+	38.0996i	−0.186356	+	1.35638i
$790$	−35.7463	−	15.4078i	−1.27180	−	0.548185i
$791$		0			0
$792$	−25.2792	−	12.1111i	−0.898258	−	0.430348i
$793$	−4.14510	+	7.17953i	−0.147197	+	0.254953i
$794$	1.00337	+	8.56394i	0.0356083	+	0.303923i
$795$	3.30824	+	2.56826i	0.117331	+	0.0910868i
$796$	2.11161	+	8.88779i	0.0748442	+	0.315019i
$797$		−	20.7831i		−	0.736175i	−0.929791	−	0.368088i	$-0.880013\pi$
$797$		−	20.7831i		−	0.736175i	0.929791	−	0.368088i	$-0.119987\pi$
$798$		0			0
$799$			5.24038i			0.185391i
$800$	33.5901	+	50.9184i	1.18759	+	1.80024i
$801$	−4.65768	+	16.6304i	−0.164571	+	0.587605i
$802$	10.2397	−	1.19971i	0.361577	−	0.0423632i
$803$	−2.33589	+	4.04587i	−0.0824316	+	0.142776i
$804$	−12.9737	+	28.5235i	−0.457548	+	1.00595i
$805$		0			0
$806$	2.33266	−	5.41181i	0.0821645	−	0.190623i
$807$	−17.1831	−	2.36082i	−0.604874	−	0.0831048i
$808$	15.4797	+	12.9673i	0.544576	+	0.456187i
$809$	1.65777	−	0.957115i	0.0582842	−	0.0336504i	−0.470575	−	0.882360i	$-0.655953\pi$
$809$	1.65777	−	0.957115i	0.0582842	−	0.0336504i	0.528859	+	0.848710i	$0.322620\pi$
$810$	41.2225	−	29.2849i	1.44841	−	1.02897i
$811$			4.68171i			0.164397i	0.996616	+	0.0821986i	$0.0261942\pi$
$811$			4.68171i			0.164397i	−0.996616	+	0.0821986i	$0.973806\pi$
$812$		0			0
$813$	15.4196	+	37.8280i	0.540789	+	1.32668i
$814$	16.0735	−	11.9732i	0.563378	−	0.419660i
$815$	−36.3351	−	62.9342i	−1.27276	−	2.20449i
$816$	3.00996	+	2.62513i	0.105370	+	0.0918978i
$817$	13.7643	−	23.8405i	0.481552	−	0.834073i
$818$	−26.2209	−	11.3020i	−0.916792	−	0.395166i
$819$		0			0
$820$	−29.2186	−	30.9358i	−1.02036	−	1.08033i
$821$	1.44771	+	0.835834i	0.0505253	+	0.0291708i	0.525050	−	0.851071i	$-0.324047\pi$
$821$	1.44771	+	0.835834i	0.0505253	+	0.0291708i	−0.474525	+	0.880242i	$0.657380\pi$
$822$	−19.7458	+	10.8821i	−0.688715	+	0.379555i
$823$	23.7559	−	13.7155i	0.828078	−	0.478091i	−0.0251160	−	0.999685i	$-0.507996\pi$
$823$	23.7559	−	13.7155i	0.828078	−	0.478091i	0.853194	+	0.521593i	$0.174662\pi$
$824$	−5.13724	+	29.2761i	−0.178964	+	1.01988i
$825$	57.1350	−	23.2896i	1.98918	−	0.810840i
$826$		0			0
$827$	−25.9621			−0.902789			−0.451395	−	0.892324i	$-0.649073\pi$
$827$	−25.9621			−0.902789			−0.451395	+	0.892324i	$0.649073\pi$
$828$	−12.6951	+	20.0963i	−0.441184	+	0.698394i
$829$	−14.5674	−	25.2315i	−0.505948	−	0.876328i	−0.999976	−	0.00688179i	$-0.997809\pi$
$829$	−14.5674	−	25.2315i	−0.505948	−	0.876328i	0.494028	−	0.869446i	$-0.335524\pi$
$830$	23.0954	−	2.70591i	0.801652	−	0.0939234i
$831$	−6.85100	+	49.8646i	−0.237659	+	1.72979i
$832$	5.20555	−	4.38265i	0.180470	−	0.151941i
$833$		0			0
$834$	0.541480	−	27.1975i	0.0187499	−	0.941774i
$835$	−66.6265	−	38.4668i	−2.30571	−	1.33120i
$836$	−22.7348	−	6.79272i	−0.786300	−	0.234931i
$837$	−2.89536	−	25.2906i	−0.100078	−	0.874173i
$838$	1.50711	−	1.12265i	0.0520623	−	0.0387812i
$839$	14.3863			0.496671			0.248336	−	0.968674i	$-0.420116\pi$
$839$	14.3863			0.496671			0.248336	+	0.968674i	$0.420116\pi$
$840$		0			0
$841$	17.5804			0.606221
$842$	8.30031	−	6.18290i	0.286048	−	0.213077i
$843$	−24.7360	+	31.8631i	−0.851954	+	1.09742i
$844$	2.13138	+	0.636813i	0.0733650	+	0.0219200i
$845$	−42.2381	−	24.3862i	−1.45303	−	0.838909i
$846$	35.9973	−	13.8443i	1.23761	−	0.475978i
$847$		0			0
$848$	2.43059	+	0.138880i	0.0834668	+	0.00476916i
$849$	−29.9022	−	4.10833i	−1.02624	−	0.140997i
$850$	−8.73138	+	1.02299i	−0.299484	+	0.0350882i
$851$	−8.49827	−	14.7194i	−0.291317	−	0.504576i
$852$	−25.8096	+	18.4383i	−0.884223	+	0.631686i
$853$	49.4483			1.69308			0.846539	−	0.532327i	$-0.178682\pi$
$853$	49.4483			1.69308			0.846539	+	0.532327i	$0.178682\pi$
$854$		0			0
$855$	30.6062	−	29.9237i	1.04671	−	1.02337i
$856$	−3.43531	−	0.602812i	−0.117416	−	0.0206037i
$857$	−10.0283	+	5.78983i	−0.342560	+	0.197777i	−0.661403	−	0.750030i	$-0.730039\pi$
$857$	−10.0283	+	5.78983i	−0.342560	+	0.197777i	0.318844	+	0.947807i	$0.396705\pi$
$858$	−3.32209	−	6.02804i	−0.113414	−	0.205794i
$859$	6.27765	+	3.62441i	0.214191	+	0.123663i	0.603258	−	0.797546i	$-0.293869\pi$
$859$	6.27765	+	3.62441i	0.214191	+	0.123663i	−0.389067	+	0.921210i	$0.627202\pi$
$860$	41.8198	+	44.2775i	1.42604	+	1.50985i
$861$		0			0
$862$	−0.232377	−	0.100162i	−0.00791479	−	0.00341152i
$863$	−10.4435	+	18.0886i	−0.355500	+	0.615744i	−0.987203	−	0.159466i	$-0.949023\pi$
$863$	−10.4435	+	18.0886i	−0.355500	+	0.615744i	0.631703	+	0.775210i	$0.282356\pi$
$864$	10.0807	−	27.6112i	0.342952	−	0.939353i
$865$	−11.0946	−	19.2164i	−0.377228	−	0.653378i
$866$	−17.2956	+	12.8835i	−0.587728	+	0.437799i
$867$	26.7336	−	10.8973i	0.907920	−	0.370090i
$868$		0			0
$869$			22.8869i			0.776385i
$870$	−17.0062	+	28.1465i	−0.576565	+	0.954255i
$871$	−6.66347	+	3.84716i	−0.225783	+	0.130356i
$872$	−5.81744	+	6.94460i	−0.197004	+	0.235174i
$873$	−10.0767	−	39.3774i	−0.341044	−	1.33272i
$874$	−7.96462	+	18.4781i	−0.269407	+	0.625030i
$875$		0			0
$876$	−4.45937	−	2.02831i	−0.150668	−	0.0685304i
$877$	28.5877	−	49.5154i	0.965339	−	1.67202i	0.256639	−	0.966507i	$-0.417385\pi$
$877$	28.5877	−	49.5154i	0.965339	−	1.67202i	0.708701	−	0.705509i	$-0.249282\pi$
$878$	42.0053	−	4.92144i	1.41761	−	0.166091i
$879$	1.28250	−	1.65202i	0.0432576	−	0.0557211i
$880$	28.7987	−	43.8915i	0.970804	−	1.47958i
$881$		−	26.8284i		−	0.903870i	−0.892051	−	0.451935i	$-0.850734\pi$
$881$		−	26.8284i		−	0.903870i	0.892051	−	0.451935i	$-0.149266\pi$
$882$		0			0
$883$			27.6059i			0.929012i	0.885570	+	0.464506i	$0.153768\pi$
$883$			27.6059i			0.929012i	−0.885570	+	0.464506i	$0.846232\pi$
$884$	0.226688	+	0.954128i	0.00762433	+	0.0320908i
$885$	33.2494	−	42.8294i	1.11767	−	1.43969i
$886$	0.825451	+	7.04537i	0.0277316	+	0.236694i
$887$	13.1703	−	22.8116i	0.442215	−	0.765939i	−0.555639	−	0.831424i	$-0.687526\pi$
$887$	13.1703	−	22.8116i	0.442215	−	0.765939i	0.997854	+	0.0654853i	$0.0208595\pi$
$888$	14.1246	+	15.5640i	0.473990	+	0.522292i
$889$		0			0
$890$	−29.7022	−	12.8026i	−0.995622	−	0.429144i
$891$	−25.4060	−	15.4423i	−0.851135	−	0.517335i
$892$	−45.2874	−	13.5310i	−1.51634	−	0.453051i
$893$	28.2736	−	16.3238i	0.946139	−	0.546254i
$894$	14.0832	+	8.50912i	0.471012	+	0.284588i
$895$			76.9909i			2.57352i
$896$		0			0
$897$	−5.40493	+	2.20318i	−0.180465	+	0.0735621i
$898$	−12.2481	−	16.4426i	−0.408724	−	0.548696i
$899$	8.27753	+	14.3371i	0.276071	+	0.478169i
$900$	30.0942	+	57.2751i	1.00314	+	1.90917i
$901$	−0.175430	+	0.303854i	−0.00584443	+	0.0101228i
$902$	−9.90347	+	22.9762i	−0.329749	+	0.765024i
$903$		0			0
$904$	52.9010	−	19.3039i	1.75946	−	0.642038i
$905$	37.4111	+	21.5993i	1.24359	+	0.717985i
$906$	28.3452	−	15.6212i	0.941705	−	0.518980i
$907$	9.51618	−	5.49417i	0.315980	−	0.182431i	−0.333619	−	0.942708i	$-0.608270\pi$
$907$	9.51618	−	5.49417i	0.315980	−	0.182431i	0.649599	+	0.760277i	$0.274937\pi$
$908$	23.9305	−	5.68556i	0.794163	−	0.188682i
$909$	14.9733	+	15.3148i	0.496634	+	0.507961i
$910$		0			0
$911$	6.42795			0.212968			0.106484	−	0.994314i	$-0.466041\pi$
$911$	6.42795			0.212968			0.106484	+	0.994314i	$0.466041\pi$
$912$	4.78742	−	24.4170i	0.158527	−	0.808526i
$913$	−6.83609	−	11.8404i	−0.226241	−	0.391862i
$914$	3.26779	+	27.8911i	0.108089	+	0.922556i
$915$	−66.4414	−	9.12852i	−2.19649	−	0.301779i
$916$	12.4000	+	13.1288i	0.409709	+	0.433787i
$917$		0			0
$918$	2.90057	+	3.08734i	0.0957331	+	0.101898i
$919$	47.7559	+	27.5719i	1.57532	+	0.909512i	0.995499	+	0.0947691i	$0.0302113\pi$
$919$	47.7559	+	27.5719i	1.57532	+	0.909512i	0.579822	+	0.814743i	$0.303122\pi$
$920$	−34.1257	−	28.5869i	−1.12509	−	0.942481i
$921$	36.1418	−	46.5552i	1.19091	−	1.53404i
$922$	14.6923	+	19.7238i	0.483864	+	0.649569i
$923$	−7.78856			−0.256364
$924$		0			0
$925$	−46.2628			−1.52111
$926$	12.9514	+	17.3868i	0.425610	+	0.571365i
$927$	−8.50246	+	30.3583i	−0.279258	+	0.997096i
$928$	1.13777	+	19.0823i	0.0373493	+	0.626406i
$929$	−41.5330	−	23.9791i	−1.36265	−	0.786728i	−0.372677	−	0.927961i	$-0.621560\pi$
$929$	−41.5330	−	23.9791i	−1.36265	−	0.786728i	−0.989976	+	0.141233i	$0.954893\pi$
$930$	47.6645	+	0.948960i	1.56298	+	0.0311176i
$931$		0			0
$932$	11.0123	−	10.4010i	0.360719	−	0.340697i
$933$	−6.29739	+	45.8352i	−0.206167	+	1.50058i
$934$	3.46939	+	29.6118i	0.113522	+	0.968929i
$935$	3.78278	+	6.55197i	0.123710	+	0.214272i
$936$	5.95523	−	4.07784i	0.194653	−	0.133288i
$937$	−36.7501			−1.20057			−0.600287	−	0.799784i	$-0.704947\pi$
$937$	−36.7501			−1.20057			−0.600287	+	0.799784i	$0.704947\pi$
$938$		0			0
$939$	14.9574	−	6.09698i	0.488115	−	0.198968i
$940$	16.6961	+	70.2738i	0.544566	+	2.29208i
$941$	−34.3080	+	19.8077i	−1.11841	+	0.645714i	−0.940994	−	0.338422i	$-0.890107\pi$
$941$	−34.3080	+	19.8077i	−1.11841	+	0.645714i	−0.177415	+	0.984136i	$0.556774\pi$
$942$	2.82356	+	5.12344i	0.0919965	+	0.166931i
$943$	18.3744	+	10.6085i	0.598353	+	0.345459i
$944$	1.79798	−	31.4671i	0.0585193	−	1.02417i
$945$		0			0
$946$	14.1745	−	32.8852i	0.460854	−	1.06919i
$947$	−5.92594	+	10.2640i	−0.192567	+	0.333536i	−0.946100	−	0.323874i	$-0.895015\pi$
$947$	−5.92594	+	10.2640i	−0.192567	+	0.333536i	0.753533	+	0.657410i	$0.228348\pi$
$948$	−23.8878	+	2.31776i	−0.775840	+	0.0752773i
$949$	−0.601466	−	1.04177i	−0.0195244	−	0.0338172i
$950$	32.7176	+	43.9221i	1.06150	+	1.42502i
$951$	−17.6480	−	43.2948i	−0.572275	−	1.40393i
$952$		0			0
$953$			39.8193i			1.28987i	0.764236	+	0.644937i	$0.223116\pi$
$953$			39.8193i			1.28987i	−0.764236	+	0.644937i	$0.776884\pi$
$954$	2.55070	+	0.402328i	0.0825819	+	0.0130259i
$955$	−4.24264	+	2.44949i	−0.137289	+	0.0792636i
$956$	−5.29728	+	17.7297i	−0.171326	+	0.573418i
$957$	19.1554	+	2.63180i	0.619207	+	0.0850741i
$958$	−9.86972	−	4.25416i	−0.318876	−	0.137446i
$959$		0			0
$960$	48.7274	+	25.6132i	1.57267	+	0.826664i
$961$	−3.50000	+	6.06218i	−0.112903	+	0.195554i
$962$	0.600546	+	5.12576i	0.0193624	+	0.165261i
$963$	−3.56229	−	0.997694i	−0.114793	−	0.0321502i
$964$	−30.4725	+	7.23984i	−0.981453	+	0.233179i
$965$		−	62.7045i		−	2.01853i
$966$		0			0
$967$		−	23.4388i		−	0.753741i	−0.926266	−	0.376871i	$-0.877000\pi$
$967$		−	23.4388i		−	0.753741i	0.926266	−	0.376871i	$-0.123000\pi$
$968$	0.243134	+	0.0426641i	0.00781462	+	0.00137127i
$969$	2.83253	+	2.19896i	0.0909941	+	0.0706408i
$970$	75.6054	−	8.85811i	2.42754	−	0.284417i
$971$	5.55718	−	9.62532i	0.178338	−	0.308891i	−0.762973	−	0.646430i	$-0.776261\pi$
$971$	5.55718	−	9.62532i	0.178338	−	0.308891i	0.941312	+	0.337539i	$0.109595\pi$
$972$	13.5447	−	28.0810i	0.434447	−	0.900697i
$973$		0			0
$974$	−8.64155	+	20.0485i	−0.276893	+	0.642396i
$975$	−2.16242	+	15.7391i	−0.0692529	+	0.504054i
$976$	−34.8191	+	17.5349i	−1.11453	+	0.561278i
$977$	9.58812	−	5.53570i	0.306751	−	0.177103i	−0.338721	−	0.940887i	$-0.609994\pi$
$977$	9.58812	−	5.53570i	0.306751	−	0.177103i	0.645472	+	0.763784i	$0.276661\pi$
$978$	−38.3492	−	23.1707i	−1.22627	−	0.740918i
$979$			19.0171i			0.607790i
$980$		0			0
$981$	−6.87062	+	6.71741i	−0.219362	+	0.214470i
$982$	−45.9515	+	34.2293i	−1.46637	+	1.09230i
$983$	15.9716	+	27.6637i	0.509416	+	0.882334i	0.999941	+	0.0109070i	$0.00347189\pi$
$983$	15.9716	+	27.6637i	0.509416	+	0.882334i	−0.490524	+	0.871427i	$0.663195\pi$
$984$	−24.9839	−	8.00977i	−0.796459	−	0.255342i
$985$	−34.5373	+	59.8204i	−1.10045	+	1.90604i
$986$	−2.52995	−	1.09049i	−0.0805700	−	0.0347282i
$987$		0			0
$988$	4.44171	−	4.19516i	0.141310	−	0.133466i
$989$	−26.2988	−	15.1836i	−0.836252	−	0.482811i
$990$	35.0133	−	43.2941i	1.11280	−	1.37598i
$991$	−18.0000	+	10.3923i	−0.571789	+	0.330122i	−0.757863	−	0.652413i	$-0.773757\pi$
$991$	−18.0000	+	10.3923i	−0.571789	+	0.330122i	0.186075	+	0.982536i	$0.440423\pi$
$992$	23.1327	−	15.2603i	0.734465	−	0.484515i
$993$	−9.54109	−	23.4066i	−0.302777	−	0.742785i
$994$		0			0
$995$	−18.1463			−0.575275
$996$	11.6660	−	8.33413i	0.369650	−	0.264077i
$997$	−20.7685	−	35.9721i	−0.657745	−	1.13925i	−0.981198	−	0.193003i	$-0.938177\pi$
$997$	−20.7685	−	35.9721i	−0.657745	−	1.13925i	0.323453	−	0.946244i	$-0.395156\pi$
$998$	−42.6537	+	4.99740i	−1.35018	+	0.158190i
$999$	13.2698	+	17.9129i	0.419838	+	0.566738i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	588.2.n.d.275.1		24
3.2	odd	2	inner	588.2.n.d.275.12		24
4.3	odd	2		588.2.n.h.275.8		24
7.2	even	3		588.2.e.f.491.24	yes	24
7.3	odd	6		588.2.n.h.263.6		24
7.4	even	3		588.2.n.h.263.5		24
7.5	odd	6		588.2.e.f.491.23	yes	24
7.6	odd	2	inner	588.2.n.d.275.2		24
12.11	even	2		588.2.n.h.275.5		24
21.2	odd	6		588.2.e.f.491.1	✓	24
21.5	even	6		588.2.e.f.491.2	yes	24
21.11	odd	6		588.2.n.h.263.8		24
21.17	even	6		588.2.n.h.263.7		24
21.20	even	2	inner	588.2.n.d.275.11		24
28.3	even	6	inner	588.2.n.d.263.11		24
28.11	odd	6	inner	588.2.n.d.263.12		24
28.19	even	6		588.2.e.f.491.4	yes	24
28.23	odd	6		588.2.e.f.491.3	yes	24
28.27	even	2		588.2.n.h.275.7		24
84.11	even	6	inner	588.2.n.d.263.1		24
84.23	even	6		588.2.e.f.491.22	yes	24
84.47	odd	6		588.2.e.f.491.21	yes	24
84.59	odd	6	inner	588.2.n.d.263.2		24
84.83	odd	2		588.2.n.h.275.6		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
588.2.e.f.491.1	✓	24	21.2	odd	6
588.2.e.f.491.2	yes	24	21.5	even	6
588.2.e.f.491.3	yes	24	28.23	odd	6
588.2.e.f.491.4	yes	24	28.19	even	6
588.2.e.f.491.21	yes	24	84.47	odd	6
588.2.e.f.491.22	yes	24	84.23	even	6
588.2.e.f.491.23	yes	24	7.5	odd	6
588.2.e.f.491.24	yes	24	7.2	even	3
588.2.n.d.263.1		24	84.11	even	6	inner
588.2.n.d.263.2		24	84.59	odd	6	inner
588.2.n.d.263.11		24	28.3	even	6	inner
588.2.n.d.263.12		24	28.11	odd	6	inner
588.2.n.d.275.1		24	1.1	even	1	trivial
588.2.n.d.275.2		24	7.6	odd	2	inner
588.2.n.d.275.11		24	21.20	even	2	inner
588.2.n.d.275.12		24	3.2	odd	2	inner
588.2.n.h.263.5		24	7.4	even	3
588.2.n.h.263.6		24	7.3	odd	6
588.2.n.h.263.7		24	21.17	even	6
588.2.n.h.263.8		24	21.11	odd	6
588.2.n.h.275.5		24	12.11	even	2
588.2.n.h.275.6		24	84.83	odd	2
588.2.n.h.275.7		24	28.27	even	2
588.2.n.h.275.8		24	4.3	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 588 = 2^{2} \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	588.n (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.13414 + 0.844822i) q^{2} +(-1.36816 - 1.06214i) q^{3} +(0.572551 - 1.91629i) q^{4} +(3.44057 + 1.98641i) q^{5} +(2.44900 + 0.0487576i) q^{6} +(0.969574 + 2.65705i) q^{8} +(0.743736 + 2.90635i) q^{9} +(-5.58025 + 0.653796i) q^{10} +(1.65172 + 2.86086i) q^{11} +(-2.81871 + 2.01367i) q^{12} -0.850601 q^{13} +(-2.59742 - 6.37208i) q^{15} +(-3.34437 - 2.19435i) q^{16} +(0.499236 - 0.288234i) q^{17} +(-3.29885 - 2.66788i) q^{18} +(-3.11023 - 1.79569i) q^{19} +(5.77645 - 5.45582i) q^{20} +(-4.29021 - 1.84921i) q^{22} +(-1.98085 + 3.43094i) q^{23} +(1.49561 - 4.66510i) q^{24} +(5.39167 + 9.33865i) q^{25} +(0.964701 - 0.718606i) q^{26} +(2.06938 - 4.76630i) q^{27} +3.37929i q^{29} +(8.32911 + 5.03249i) q^{30} +(4.24264 - 2.44949i) q^{31} +(5.64683 - 0.336691i) q^{32} +(0.778803 - 5.66848i) q^{33} +(-0.322697 + 0.748663i) q^{34} +(5.99525 + 0.238815i) q^{36} +(-2.14510 + 3.71543i) q^{37} +(5.04449 - 0.591024i) q^{38} +(1.16376 + 0.903453i) q^{39} +(-1.94212 + 11.0677i) q^{40} -5.35550i q^{41} +7.66518i q^{43} +(6.42795 - 1.52719i) q^{44} +(-3.21433 + 11.4769i) q^{45} +(-0.651966 - 5.56464i) q^{46} +(-4.54525 + 7.87260i) q^{47} +(2.24494 + 6.55441i) q^{48} +(-14.0044 - 6.03634i) q^{50} +(-0.989179 - 0.135905i) q^{51} +(-0.487013 + 1.63000i) q^{52} +(-0.527096 + 0.304319i) q^{53} +(1.67971 + 7.15392i) q^{54} +13.1240i q^{55} +(2.34803 + 5.76029i) q^{57} +(-2.85490 - 3.83259i) q^{58} +(3.93980 + 6.82394i) q^{59} +(-13.6979 + 1.32907i) q^{60} +(4.87315 - 8.44054i) q^{61} +(-2.74237 + 6.36234i) q^{62} +(-6.11985 + 5.15242i) q^{64} +(-2.92655 - 1.68964i) q^{65} +(3.90558 + 7.08680i) q^{66} +(7.83384 - 4.52287i) q^{67} +(-0.266503 - 1.12171i) q^{68} +(6.35425 - 2.59015i) q^{69} +9.15654 q^{71} +(-7.00121 + 4.79407i) q^{72} +(0.707107 + 1.22474i) q^{73} +(-0.706026 - 6.02605i) q^{74} +(2.54223 - 18.5035i) q^{75} +(-5.22185 + 4.93200i) q^{76} +(-2.08312 - 0.0414733i) q^{78} +(6.00000 + 3.46410i) q^{79} +(-7.14764 - 14.1931i) q^{80} +(-7.89371 + 4.32311i) q^{81} +(4.52445 + 6.07390i) q^{82} -4.13877 q^{83} +2.29021 q^{85} +(-6.47571 - 8.69339i) q^{86} +(3.58926 - 4.62341i) q^{87} +(-6.00000 + 7.16253i) q^{88} +(4.98550 + 2.87838i) q^{89} +(-6.05039 - 15.7319i) q^{90} +(5.44055 + 5.76029i) q^{92} +(-8.40631 - 1.15496i) q^{93} +(-1.49600 - 12.7686i) q^{94} +(-7.13398 - 12.3564i) q^{95} +(-8.08339 - 5.53705i) q^{96} -13.5487 q^{97} +(-7.08622 + 6.92820i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 12 q^{4} - 36 q^{16} - 12 q^{18} + 12 q^{25} + 12 q^{30} + 12 q^{36} + 96 q^{39} - 96 q^{46} - 12 q^{51} - 24 q^{57} - 120 q^{58} - 84 q^{60} - 48 q^{64} + 48 q^{67} - 72 q^{72} - 24 q^{78} + 144 q^{79}+ \cdots - 24 q^{93}+O(q^{100}) \) 24 * q - 12 * q^4 - 36 * q^16 - 12 * q^18 + 12 * q^25 + 12 * q^30 + 12 * q^36 + 96 * q^39 - 96 * q^46 - 12 * q^51 - 24 * q^57 - 120 * q^58 - 84 * q^60 - 48 * q^64 + 48 * q^67 - 72 * q^72 - 24 * q^78 + 144 * q^79 + 12 * q^81 - 48 * q^85 - 144 * q^88 - 24 * q^93

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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