LMFDB - Embedded newform 484.2.g.g.215.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [484,2,Mod(215,484)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(484, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 9]))

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

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

chi := DirichletCharacter("484.215");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 484 = 2^{2} \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	484.g (of order $10$, degree $4$, not 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:	$3.86475945783$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{10})$
Coefficient field:	16.0.26873856000000000000.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2x^{14} + 8x^{10} - 16x^{8} + 32x^{6} - 128x^{2} + 256 $ x^16 - 2x^14 + 8x^10 - 16x^8 + 32x^6 - 128*x^2 + 256
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	no (minimal twist has level 44)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			215.1
Root			$-1.29195 - 0.575212i$ of defining polynomial
Character	$\chi$	$=$	484.215
Dual form			484.2.g.g.475.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.38331 - 0.294032i) q^{2} +(1.01807 - 1.40126i) q^{3} +(1.82709 + 0.813473i) q^{4} +(-0.309017 + 0.951057i) q^{5} +(-1.82033 + 1.63903i) q^{6} +(-2.28825 + 1.66251i) q^{7} +(-2.28825 - 1.66251i) q^{8} +O(q^{10})$	\(q+(-1.38331 - 0.294032i) q^{2} +(1.01807 - 1.40126i) q^{3} +(1.82709 + 0.813473i) q^{4} +(-0.309017 + 0.951057i) q^{5} +(-1.82033 + 1.63903i) q^{6} +(-2.28825 + 1.66251i) q^{7} +(-2.28825 - 1.66251i) q^{8} +(0.707107 - 1.22474i) q^{10} +(3.00000 - 1.73205i) q^{12} +(4.65921 - 1.51387i) q^{13} +(3.65418 - 1.62695i) q^{14} +(1.01807 + 1.40126i) q^{15} +(2.67652 + 2.97258i) q^{16} +(4.65921 + 1.51387i) q^{17} +(2.28825 + 1.66251i) q^{19} +(-1.33826 + 1.48629i) q^{20} +4.89898i q^{21} -5.19615i q^{23} +(-4.65921 + 1.51387i) q^{24} +(3.23607 + 2.35114i) q^{25} +(-6.89025 + 0.724194i) q^{26} +(4.94183 + 1.60570i) q^{27} +(-5.53324 + 1.17613i) q^{28} +(-0.996297 - 2.23772i) q^{30} +(-1.64728 + 0.535233i) q^{31} +(-2.82843 - 4.89898i) q^{32} +(-6.00000 - 3.46410i) q^{34} +(-0.874032 - 2.68999i) q^{35} +(-2.42705 + 1.76336i) q^{37} +(-2.67652 - 2.97258i) q^{38} +(2.62210 - 8.06998i) q^{39} +(2.28825 - 1.66251i) q^{40} +(-2.87955 + 3.96336i) q^{41} +(1.44045 - 6.77681i) q^{42} +5.65685 q^{43} +(-1.52783 + 7.18789i) q^{46} +(2.03615 - 2.80252i) q^{47} +(6.89025 - 0.724194i) q^{48} +(0.309017 - 0.951057i) q^{49} +(-3.78517 - 4.20386i) q^{50} +(6.86474 - 4.98752i) q^{51} +(9.74428 + 1.02417i) q^{52} +(-0.618034 - 1.90211i) q^{53} +(-6.36396 - 3.67423i) q^{54} +8.00000 q^{56} +(4.65921 - 1.51387i) q^{57} +(-1.01807 - 1.40126i) q^{59} +(0.720227 + 3.38840i) q^{60} +(9.31841 + 3.02774i) q^{61} +(2.43607 - 0.256041i) q^{62} +(2.47214 + 7.60845i) q^{64} +4.89898i q^{65} +8.66025i q^{67} +(7.28130 + 6.55611i) q^{68} +(-7.28115 - 5.29007i) q^{69} +(0.418114 + 3.97809i) q^{70} +(-11.5309 - 3.74663i) q^{71} +(-2.87955 - 3.96336i) q^{73} +(3.87585 - 1.72564i) q^{74} +(6.58911 - 2.14093i) q^{75} +(2.82843 + 4.89898i) q^{76} +(-6.00000 + 10.3923i) q^{78} +(-3.49613 - 10.7600i) q^{79} +(-3.65418 + 1.62695i) q^{80} +(7.28115 - 5.29007i) q^{81} +(5.14866 - 4.63587i) q^{82} +(-3.98519 + 8.95088i) q^{84} +(-2.87955 + 3.96336i) q^{85} +(-7.82518 - 1.66329i) q^{86} -1.00000 q^{89} +(-8.14459 + 11.2101i) q^{91} +(4.22693 - 9.49384i) q^{92} +(-0.927051 + 2.85317i) q^{93} +(-3.64065 + 3.27806i) q^{94} +(-2.28825 + 1.66251i) q^{95} +(-9.74428 - 1.02417i) q^{96} +(2.16312 + 6.65740i) q^{97} +(-0.707107 + 1.22474i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{4} + 4 q^{5}+O(q^{10}) $ 16 * q + 4 * q^4 + 4 * q^5	$ 16 q + 4 q^{4} + 4 q^{5} + 48 q^{12} + 8 q^{14} + 8 q^{16} - 4 q^{20} + 16 q^{25} - 24 q^{26} - 96 q^{34} - 12 q^{37} - 8 q^{38} + 24 q^{42} + 24 q^{48} - 4 q^{49} + 8 q^{53} + 128 q^{56} + 12 q^{60} - 32 q^{64} - 36 q^{69} - 8 q^{70} - 96 q^{78} - 8 q^{80} + 36 q^{81} - 24 q^{82} + 16 q^{86} - 16 q^{89} + 36 q^{92} + 12 q^{93} - 28 q^{97}+O(q^{100}) $ 16 * q + 4 * q^4 + 4 * q^5 + 48 * q^12 + 8 * q^14 + 8 * q^16 - 4 * q^20 + 16 * q^25 - 24 * q^26 - 96 * q^34 - 12 * q^37 - 8 * q^38 + 24 * q^42 + 24 * q^48 - 4 * q^49 + 8 * q^53 + 128 * q^56 + 12 * q^60 - 32 * q^64 - 36 * q^69 - 8 * q^70 - 96 * q^78 - 8 * q^80 + 36 * q^81 - 24 * q^82 + 16 * q^86 - 16 * q^89 + 36 * q^92 + 12 * q^93 - 28 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/484\mathbb{Z}\right)^\times$.

$n$	$243$	$365$
$\chi(n)$	$-1$	$e\left(\frac{9}{10}\right)$

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 $

$2$	−1.38331	−	0.294032i	−0.978148	−	0.207912i
$2$	−1.38331	−	0.294032i	−0.978148	−	0.207912i
$3$	1.01807	−	1.40126i	0.587785	−	0.809017i	−0.406737	−	0.913545i	$-0.633333\pi$
$3$	1.01807	−	1.40126i	0.587785	−	0.809017i	0.994522	+	0.104528i	$0.0333333\pi$
$4$	1.82709	+	0.813473i	0.913545	+	0.406737i
$5$	−0.309017	+	0.951057i	−0.138197	+	0.425325i	−0.996074	−	0.0885298i	$-0.971783\pi$
$5$	−0.309017	+	0.951057i	−0.138197	+	0.425325i	0.857877	+	0.513855i	$0.171783\pi$
$6$	−1.82033	+	1.63903i	−0.743145	+	0.669131i
$7$	−2.28825	+	1.66251i	−0.864876	+	0.628369i	−0.929207	−	0.369560i	$-0.879509\pi$
$7$	−2.28825	+	1.66251i	−0.864876	+	0.628369i	0.0643314	+	0.997929i	$0.479509\pi$
$8$	−2.28825	−	1.66251i	−0.809017	−	0.587785i
$9$		0			0
$10$	0.707107	−	1.22474i	0.223607	−	0.387298i
$11$		0			0
$11$		0			0
$12$	3.00000	−	1.73205i	0.866025	−	0.500000i
$13$	4.65921	−	1.51387i	1.29223	−	0.419871i	0.419359	−	0.907820i	$-0.362255\pi$
$13$	4.65921	−	1.51387i	1.29223	−	0.419871i	0.872872	+	0.487949i	$0.162255\pi$
$14$	3.65418	−	1.62695i	0.976621	−	0.434820i
$15$	1.01807	+	1.40126i	0.262866	+	0.361803i
$16$	2.67652	+	2.97258i	0.669131	+	0.743145i
$17$	4.65921	+	1.51387i	1.13002	+	0.367167i	0.813585	−	0.581446i	$-0.197513\pi$
$17$	4.65921	+	1.51387i	1.13002	+	0.367167i	0.316439	+	0.948613i	$0.397513\pi$
$18$		0			0
$19$	2.28825	+	1.66251i	0.524960	+	0.381405i	0.818469	−	0.574551i	$-0.194823\pi$
$19$	2.28825	+	1.66251i	0.524960	+	0.381405i	−0.293509	+	0.955956i	$0.594823\pi$
$20$	−1.33826	+	1.48629i	−0.299244	+	0.332344i
$21$			4.89898i			1.06904i
$22$		0			0
$23$		−	5.19615i		−	1.08347i	−0.840548	−	0.541736i	$-0.817767\pi$
$23$		−	5.19615i		−	1.08347i	0.840548	−	0.541736i	$-0.182233\pi$
$24$	−4.65921	+	1.51387i	−0.951057	+	0.309017i
$25$	3.23607	+	2.35114i	0.647214	+	0.470228i
$26$	−6.89025	+	0.724194i	−1.35129	+	0.142026i
$27$	4.94183	+	1.60570i	0.951057	+	0.309017i
$28$	−5.53324	+	1.17613i	−1.04568	+	0.222267i
$29$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$29$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$30$	−0.996297	−	2.23772i	−0.181898	−	0.408550i
$31$	−1.64728	+	0.535233i	−0.295860	+	0.0961307i	−0.453186	−	0.891416i	$-0.649713\pi$
$31$	−1.64728	+	0.535233i	−0.295860	+	0.0961307i	0.157326	+	0.987547i	$0.449713\pi$
$32$	−2.82843	−	4.89898i	−0.500000	−	0.866025i
$33$		0			0
$34$	−6.00000	−	3.46410i	−1.02899	−	0.594089i
$35$	−0.874032	−	2.68999i	−0.147738	−	0.454692i
$36$		0			0
$37$	−2.42705	+	1.76336i	−0.399005	+	0.289894i	−0.769135	−	0.639086i	$-0.779313\pi$
$37$	−2.42705	+	1.76336i	−0.399005	+	0.289894i	0.370131	+	0.928980i	$0.379313\pi$
$38$	−2.67652	−	2.97258i	−0.434189	−	0.482216i
$39$	2.62210	−	8.06998i	0.419871	−	1.29223i
$40$	2.28825	−	1.66251i	0.361803	−	0.262866i
$41$	−2.87955	+	3.96336i	−0.449710	+	0.618972i	−0.972335	−	0.233590i	$-0.924953\pi$
$41$	−2.87955	+	3.96336i	−0.449710	+	0.618972i	0.522625	+	0.852562i	$0.324953\pi$
$42$	1.44045	−	6.77681i	0.222267	−	1.04568i
$43$	5.65685			0.862662			0.431331	−	0.902194i	$-0.358044\pi$
$43$	5.65685			0.862662			0.431331	+	0.902194i	$0.358044\pi$
$44$		0			0
$45$		0			0
$46$	−1.52783	+	7.18789i	−0.225267	+	1.05980i
$47$	2.03615	−	2.80252i	0.297003	−	0.408789i	−0.634270	−	0.773111i	$-0.718699\pi$
$47$	2.03615	−	2.80252i	0.297003	−	0.408789i	0.931273	+	0.364322i	$0.118699\pi$
$48$	6.89025	−	0.724194i	0.994522	−	0.104528i
$49$	0.309017	−	0.951057i	0.0441453	−	0.135865i
$50$	−3.78517	−	4.20386i	−0.535304	−	0.594516i
$51$	6.86474	−	4.98752i	0.961255	−	0.698393i
$52$	9.74428	+	1.02417i	1.35129	+	0.142026i
$53$	−0.618034	−	1.90211i	−0.0848935	−	0.261275i	0.899595	−	0.436726i	$-0.143862\pi$
$53$	−0.618034	−	1.90211i	−0.0848935	−	0.261275i	−0.984488	+	0.175450i	$0.943862\pi$
$54$	−6.36396	−	3.67423i	−0.866025	−	0.500000i
$55$		0			0
$56$	8.00000			1.06904
$57$	4.65921	−	1.51387i	0.617127	−	0.200517i
$58$		0			0
$59$	−1.01807	−	1.40126i	−0.132542	−	0.182428i	0.737588	−	0.675252i	$-0.235965\pi$
$59$	−1.01807	−	1.40126i	−0.132542	−	0.182428i	−0.870129	+	0.492823i	$0.835965\pi$
$60$	0.720227	+	3.38840i	0.0929809	+	0.437441i
$61$	9.31841	+	3.02774i	1.19310	+	0.387662i	0.837218	−	0.546869i	$-0.184180\pi$
$61$	9.31841	+	3.02774i	1.19310	+	0.387662i	0.355882	+	0.934531i	$0.384180\pi$
$62$	2.43607	−	0.256041i	0.309381	−	0.0325173i
$63$		0			0
$64$	2.47214	+	7.60845i	0.309017	+	0.951057i
$65$			4.89898i			0.607644i
$66$		0			0
$67$			8.66025i			1.05802i	0.848616	+	0.529009i	$0.177436\pi$
$67$			8.66025i			1.05802i	−0.848616	+	0.529009i	$0.822564\pi$
$68$	7.28130	+	6.55611i	0.882988	+	0.795046i
$69$	−7.28115	−	5.29007i	−0.876548	−	0.636849i
$70$	0.418114	+	3.97809i	0.0499742	+	0.475472i
$71$	−11.5309	−	3.74663i	−1.36847	−	0.444643i	−0.469609	−	0.882874i	$-0.655605\pi$
$71$	−11.5309	−	3.74663i	−1.36847	−	0.444643i	−0.898862	+	0.438231i	$0.855605\pi$
$72$		0			0
$73$	−2.87955	−	3.96336i	−0.337026	−	0.463876i	0.606544	−	0.795050i	$-0.292555\pi$
$73$	−2.87955	−	3.96336i	−0.337026	−	0.463876i	−0.943570	+	0.331174i	$0.892555\pi$
$74$	3.87585	−	1.72564i	0.450558	−	0.200601i
$75$	6.58911	−	2.14093i	0.760845	−	0.247214i
$76$	2.82843	+	4.89898i	0.324443	+	0.561951i
$77$		0			0
$78$	−6.00000	+	10.3923i	−0.679366	+	1.17670i
$79$	−3.49613	−	10.7600i	−0.393345	−	1.21059i	−0.930243	−	0.366945i	$-0.880404\pi$
$79$	−3.49613	−	10.7600i	−0.393345	−	1.21059i	0.536898	−	0.843647i	$-0.319596\pi$
$80$	−3.65418	+	1.62695i	−0.408550	+	0.181898i
$81$	7.28115	−	5.29007i	0.809017	−	0.587785i
$82$	5.14866	−	4.63587i	0.568574	−	0.511947i
$83$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$83$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$84$	−3.98519	+	8.95088i	−0.434820	+	0.976621i
$85$	−2.87955	+	3.96336i	−0.312331	+	0.429886i
$86$	−7.82518	−	1.66329i	−0.843811	−	0.179358i
$87$		0			0
$88$		0			0
$89$	−1.00000			−0.106000			−0.0529999	−	0.998595i	$-0.516878\pi$
$89$	−1.00000			−0.106000			−0.0529999	+	0.998595i	$0.516878\pi$
$90$		0			0
$91$	−8.14459	+	11.2101i	−0.853785	+	1.17513i
$92$	4.22693	−	9.49384i	0.440688	−	0.989802i
$93$	−0.927051	+	2.85317i	−0.0961307	+	0.295860i
$94$	−3.64065	+	3.27806i	−0.375505	+	0.338106i
$95$	−2.28825	+	1.66251i	−0.234769	+	0.170570i
$96$	−9.74428	−	1.02417i	−0.994522	−	0.104528i
$97$	2.16312	+	6.65740i	0.219631	+	0.675956i	0.998792	+	0.0491321i	$0.0156455\pi$
$97$	2.16312	+	6.65740i	0.219631	+	0.675956i	−0.779161	+	0.626824i	$0.784354\pi$
$98$	−0.707107	+	1.22474i	−0.0714286	+	0.123718i
$99$		0			0
$100$	4.00000	+	6.92820i	0.400000	+	0.692820i
$101$	−4.65921	+	1.51387i	−0.463608	+	0.150635i	−0.531502	−	0.847057i	$-0.678372\pi$
$101$	−4.65921	+	1.51387i	−0.463608	+	0.150635i	0.0678936	+	0.997693i	$0.478372\pi$
$102$	−10.9625	+	4.88084i	−1.08545	+	0.483275i
$103$	−2.03615	−	2.80252i	−0.200628	−	0.276140i	0.696834	−	0.717232i	$-0.254591\pi$
$103$	−2.03615	−	2.80252i	−0.200628	−	0.276140i	−0.897462	+	0.441092i	$0.854591\pi$
$104$	−13.1782	−	4.28187i	−1.29223	−	0.419871i
$105$	−4.65921	−	1.51387i	−0.454692	−	0.147738i
$106$	0.295651	+	2.81293i	0.0287162	+	0.273216i
$107$	−6.86474	−	4.98752i	−0.663639	−	0.482162i	0.204251	−	0.978919i	$-0.434524\pi$
$107$	−6.86474	−	4.98752i	−0.663639	−	0.482162i	−0.867890	+	0.496757i	$0.834524\pi$
$108$	7.72299	+	6.95381i	0.743145	+	0.669131i
$109$		−	9.79796i		−	0.938474i	−0.883072	−	0.469237i	$-0.844529\pi$
$109$		−	9.79796i		−	0.938474i	0.883072	−	0.469237i	$-0.155471\pi$
$110$		0			0
$111$			5.19615i			0.493197i
$112$	−11.0665	−	2.35225i	−1.04568	−	0.222267i
$113$	4.04508	+	2.93893i	0.380530	+	0.276471i	0.761564	−	0.648090i	$-0.224432\pi$
$113$	4.04508	+	2.93893i	0.380530	+	0.276471i	−0.381034	+	0.924561i	$0.624432\pi$
$114$	−6.89025	+	0.724194i	−0.645331	+	0.0678270i
$115$	4.94183	+	1.60570i	0.460828	+	0.149732i
$116$		0			0
$117$		0			0
$118$	0.996297	+	2.23772i	0.0917166	+	0.205999i
$119$	−13.1782	+	4.28187i	−1.20805	+	0.392518i
$120$		−	4.89898i		−	0.447214i
$121$		0			0
$122$	−12.0000	−	6.92820i	−1.08643	−	0.627250i
$123$	2.62210	+	8.06998i	0.236426	+	0.727646i
$124$	−3.44512	−	0.362097i	−0.309381	−	0.0325173i
$125$	−7.28115	+	5.29007i	−0.651246	+	0.473158i
$126$		0			0
$127$	−4.37016	+	13.4500i	−0.387789	+	1.19349i	0.546648	+	0.837363i	$0.315904\pi$
$127$	−4.37016	+	13.4500i	−0.387789	+	1.19349i	−0.934437	+	0.356129i	$0.884096\pi$
$128$	−1.18260	−	11.2517i	−0.104528	−	0.994522i
$129$	5.75910	−	7.92672i	0.507060	−	0.697908i
$130$	1.44045	−	6.77681i	0.126336	−	0.594365i
$131$	−2.82843			−0.247121			−0.123560	−	0.992337i	$-0.539431\pi$
$131$	−2.82843			−0.247121			−0.123560	+	0.992337i	$0.539431\pi$
$132$		0			0
$133$	−8.00000			−0.693688
$134$	2.54639	−	11.9798i	0.219974	−	1.03490i
$135$	−3.05422	+	4.20378i	−0.262866	+	0.361803i
$136$	−8.14459	−	11.2101i	−0.698393	−	0.961255i
$137$	5.87132	−	18.0701i	0.501621	−	1.54383i	−0.304757	−	0.952430i	$-0.598575\pi$
$137$	5.87132	−	18.0701i	0.501621	−	1.54383i	0.806378	−	0.591400i	$-0.201425\pi$
$138$	8.51664	+	9.45869i	0.724985	+	0.805177i
$139$	−16.0177	+	11.6376i	−1.35861	+	0.987084i	−0.360073	+	0.932924i	$0.617248\pi$
$139$	−16.0177	+	11.6376i	−1.35861	+	0.987084i	−0.998532	+	0.0541603i	$0.982752\pi$
$140$	0.591302	−	5.62587i	0.0499742	−	0.475472i
$141$	−1.85410	−	5.70634i	−0.156144	−	0.480560i
$142$	14.8492	+	8.57321i	1.24612	+	0.719448i
$143$		0			0
$144$		0			0
$145$		0			0
$146$	2.81795	+	6.32923i	0.233216	+	0.523811i
$147$	−1.01807	−	1.40126i	−0.0839693	−	0.115574i
$148$	−5.86889	+	1.24747i	−0.482419	+	0.102541i
$149$	−13.9776	−	4.54160i	−1.14509	−	0.372063i	−0.325799	−	0.945439i	$-0.605633\pi$
$149$	−13.9776	−	4.54160i	−1.14509	−	0.372063i	−0.819292	+	0.573376i	$0.805633\pi$
$150$	−9.74428	+	1.02417i	−0.795618	+	0.0836228i
$151$	4.57649	+	3.32502i	0.372430	+	0.270586i	0.758218	−	0.652001i	$-0.226070\pi$
$151$	4.57649	+	3.32502i	0.372430	+	0.270586i	−0.385788	+	0.922587i	$0.626070\pi$
$152$	−2.47214	−	7.60845i	−0.200517	−	0.617127i
$153$		0			0
$154$		0			0
$155$		−	1.73205i		−	0.139122i
$156$	11.3555	−	12.6116i	0.909169	−	1.00973i
$157$	−8.89919	−	6.46564i	−0.710232	−	0.516014i	0.173016	−	0.984919i	$-0.444649\pi$
$157$	−8.89919	−	6.46564i	−0.710232	−	0.516014i	−0.883249	+	0.468905i	$0.844649\pi$
$158$	1.67246	+	15.9124i	0.133053	+	1.26592i
$159$	−3.29456	−	1.07047i	−0.261275	−	0.0848935i
$160$	5.53324	−	1.17613i	0.437441	−	0.0929809i
$161$	8.63864	+	11.8901i	0.680820	+	0.937069i
$162$	−11.6275	+	5.17691i	−0.913545	+	0.406737i
$163$	16.4728	−	5.35233i	1.29025	−	0.419227i	0.418070	−	0.908415i	$-0.362707\pi$
$163$	16.4728	−	5.35233i	1.29025	−	0.419227i	0.872178	+	0.489188i	$0.162707\pi$
$164$	−8.48528	+	4.89898i	−0.662589	+	0.382546i
$165$		0			0
$166$		0			0
$167$	6.11822	+	18.8300i	0.473442	+	1.45711i	0.848047	+	0.529921i	$0.177779\pi$
$167$	6.11822	+	18.8300i	0.473442	+	1.45711i	−0.374604	+	0.927185i	$0.622221\pi$
$168$	8.14459	−	11.2101i	0.628369	−	0.864876i
$169$	8.89919	−	6.46564i	0.684553	−	0.497357i
$170$	5.14866	−	4.63587i	0.394884	−	0.355555i
$171$		0			0
$172$	10.3356	+	4.60170i	0.788081	+	0.350876i
$173$	5.75910	−	7.92672i	0.437856	−	0.602657i	−0.531878	−	0.846821i	$-0.678514\pi$
$173$	5.75910	−	7.92672i	0.437856	−	0.602657i	0.969734	+	0.244164i	$0.0785135\pi$
$174$		0			0
$175$	−11.3137			−0.855236
$176$		0			0
$177$	−3.00000			−0.225494
$178$	1.38331	+	0.294032i	0.103683	+	0.0220386i
$179$	5.09037	−	7.00629i	0.380472	−	0.523675i	−0.575237	−	0.817986i	$-0.695090\pi$
$179$	5.09037	−	7.00629i	0.380472	−	0.523675i	0.955710	+	0.294312i	$0.0950903\pi$
$180$		0			0
$181$	−6.48936	+	19.9722i	−0.482350	+	1.48452i	0.353432	+	0.935460i	$0.385014\pi$
$181$	−6.48936	+	19.9722i	−0.482350	+	1.48452i	−0.835782	+	0.549061i	$0.814986\pi$
$182$	14.5626	−	13.1122i	1.07945	−	0.971943i
$183$	13.7295	−	9.97505i	1.01491	−	0.737377i
$184$	−8.63864	+	11.8901i	−0.636849	+	0.876548i
$185$	−0.927051	−	2.85317i	−0.0681581	−	0.209769i
$186$	2.12132	−	3.67423i	0.155543	−	0.269408i
$187$		0			0
$188$	6.00000	−	3.46410i	0.437595	−	0.252646i
$189$	−13.9776	+	4.54160i	−1.01672	+	0.330353i
$190$	3.65418	−	1.62695i	0.265102	−	0.118031i
$191$	3.05422	+	4.20378i	0.220996	+	0.304175i	0.905091	−	0.425218i	$-0.139803\pi$
$191$	3.05422	+	4.20378i	0.220996	+	0.304175i	−0.684095	+	0.729393i	$0.739803\pi$
$192$	13.1782	+	4.28187i	0.951057	+	0.309017i
$193$	−9.31841	−	3.02774i	−0.670754	−	0.217941i	−0.0462111	−	0.998932i	$-0.514715\pi$
$193$	−9.31841	−	3.02774i	−0.670754	−	0.217941i	−0.624543	+	0.780991i	$0.714715\pi$
$194$	−1.03478	−	9.84526i	−0.0742928	−	0.706849i
$195$	6.86474	+	4.98752i	0.491594	+	0.357164i
$196$	1.33826	−	1.48629i	0.0955901	−	0.106164i
$197$		0			0		1.00000			$0$
$197$		0			0		−1.00000			$\pi$
$198$		0			0
$199$		−	10.3923i		−	0.736691i	−0.929689	−	0.368345i	$-0.879924\pi$
$199$		−	10.3923i		−	0.736691i	0.929689	−	0.368345i	$-0.120076\pi$
$200$	−3.49613	−	10.7600i	−0.247214	−	0.760845i
$201$	12.1353	+	8.81678i	0.855955	+	0.621888i
$202$	6.89025	−	0.724194i	0.484796	−	0.0509541i
$203$		0			0
$204$	16.5997	−	3.52838i	1.16221	−	0.247036i
$205$	−2.87955	−	3.96336i	−0.201116	−	0.276813i
$206$	1.99259	+	4.47544i	0.138831	+	0.311819i
$207$		0			0
$208$	16.9706	+	9.79796i	1.17670	+	0.679366i
$209$		0			0
$210$	6.00000	+	3.46410i	0.414039	+	0.239046i
$211$	1.74806	+	5.37999i	0.120342	+	0.370374i	0.993024	−	0.117915i	$-0.0376212\pi$
$211$	1.74806	+	5.37999i	0.120342	+	0.370374i	−0.872682	+	0.488289i	$0.837621\pi$
$212$	0.418114	−	3.97809i	0.0287162	−	0.273216i
$213$	−16.9894	+	12.3435i	−1.16409	+	0.845762i
$214$	8.02957	+	8.91774i	0.548890	+	0.609604i
$215$	−1.74806	+	5.37999i	−0.119217	+	0.366912i
$216$	−8.63864	−	11.8901i	−0.587785	−	0.809017i
$217$	2.87955	−	3.96336i	0.195476	−	0.269050i
$218$	−2.88091	+	13.5536i	−0.195120	+	0.917966i
$219$	−8.48528			−0.573382
$220$		0			0
$221$	24.0000			1.61441
$222$	1.52783	−	7.18789i	0.102541	−	0.482419i
$223$	13.2350	−	18.2164i	0.886279	−	1.21986i	−0.0883636	−	0.996088i	$-0.528164\pi$
$223$	13.2350	−	18.2164i	0.886279	−	1.21986i	0.974642	−	0.223769i	$-0.0718363\pi$
$224$	14.6167	+	6.50779i	0.976621	+	0.434820i
$225$		0			0
$226$	−4.73147	−	5.25483i	−0.314733	−	0.349546i
$227$	6.86474	−	4.98752i	0.455629	−	0.331034i	−0.336185	−	0.941796i	$-0.609137\pi$
$227$	6.86474	−	4.98752i	0.455629	−	0.331034i	0.791814	+	0.610762i	$0.209137\pi$
$228$	9.74428	+	1.02417i	0.645331	+	0.0678270i
$229$	−0.309017	−	0.951057i	−0.0204204	−	0.0628476i	0.940327	−	0.340272i	$-0.110519\pi$
$229$	−0.309017	−	0.951057i	−0.0204204	−	0.0628476i	−0.960747	+	0.277424i	$0.910519\pi$
$230$	−6.36396	−	3.67423i	−0.419627	−	0.242272i
$231$		0			0
$232$		0			0
$233$	−18.6368	+	6.05547i	−1.22094	+	0.396707i	−0.847424	−	0.530917i	$-0.821848\pi$
$233$	−18.6368	+	6.05547i	−1.22094	+	0.396707i	−0.373515	+	0.927624i	$0.621848\pi$
$234$		0			0
$235$	2.03615	+	2.80252i	0.132824	+	0.182816i
$236$	−0.720227	−	3.38840i	−0.0468828	−	0.220566i
$237$	−18.6368	−	6.05547i	−1.21059	−	0.393345i
$238$	19.4886	−	2.04833i	1.26326	−	0.132774i
$239$	−4.57649	−	3.32502i	−0.296029	−	0.215077i	0.429850	−	0.902900i	$-0.358567\pi$
$239$	−4.57649	−	3.32502i	−0.296029	−	0.215077i	−0.725878	+	0.687823i	$0.758567\pi$
$240$	−1.44045	+	6.77681i	−0.0929809	+	0.437441i
$241$		−	29.3939i		−	1.89343i	−0.322078	−	0.946713i	$-0.604381\pi$
$241$		−	29.3939i		−	1.89343i	0.322078	−	0.946713i	$-0.395619\pi$
$242$		0			0
$243$		0			0
$244$	14.5626	+	13.1122i	0.932275	+	0.839424i
$245$	0.809017	+	0.587785i	0.0516862	+	0.0375522i
$246$	−1.25434	−	11.9343i	−0.0799739	−	0.760901i
$247$	13.1782	+	4.28187i	0.838510	+	0.272449i
$248$	4.65921	+	1.51387i	0.295860	+	0.0961307i
$249$		0			0
$250$	11.6275	−	5.17691i	0.735390	−	0.327417i
$251$	−21.4146	+	6.95803i	−1.35168	+	0.439187i	−0.893256	−	0.449548i	$-0.851585\pi$
$251$	−21.4146	+	6.95803i	−1.35168	+	0.439187i	−0.458422	+	0.888735i	$0.651585\pi$
$252$		0			0
$253$		0			0
$254$	10.0000	−	17.3205i	0.627456	−	1.08679i
$255$	2.62210	+	8.06998i	0.164202	+	0.505362i
$256$	−1.67246	+	15.9124i	−0.104528	+	0.994522i
$257$	17.7984	−	12.9313i	1.11023	−	0.806631i	0.127532	−	0.991834i	$-0.459294\pi$
$257$	17.7984	−	12.9313i	1.11023	−	0.806631i	0.982700	+	0.185204i	$0.0592945\pi$
$258$	−10.2973	+	9.27175i	−0.641083	+	0.577234i
$259$	2.62210	−	8.06998i	0.162929	−	0.501444i
$260$	−3.98519	+	8.95088i	−0.247151	+	0.555110i
$261$		0			0
$262$	3.91259	+	0.831647i	0.241721	+	0.0513793i
$263$	14.1421			0.872041			0.436021	−	0.899937i	$-0.356387\pi$
$263$	14.1421			0.872041			0.436021	+	0.899937i	$0.356387\pi$
$264$		0			0
$265$	2.00000			0.122859
$266$	11.0665	+	2.35225i	0.678529	+	0.144226i
$267$	−1.01807	+	1.40126i	−0.0623051	+	0.0857556i
$268$	−7.04489	+	15.8231i	−0.430335	+	0.966548i
$269$	−3.09017	+	9.51057i	−0.188411	+	0.579869i	−0.999990	−	0.00437267i	$-0.998608\pi$
$269$	−3.09017	+	9.51057i	−0.188411	+	0.579869i	0.811579	+	0.584242i	$0.198608\pi$
$270$	5.46098	−	4.91709i	0.332344	−	0.299244i
$271$	2.28825	−	1.66251i	0.139001	−	0.100990i	−0.516112	−	0.856521i	$-0.672621\pi$
$271$	2.28825	−	1.66251i	0.139001	−	0.100990i	0.655113	+	0.755531i	$0.272621\pi$
$272$	7.97038	+	17.9018i	0.483275	+	1.08545i
$273$	7.41641	+	22.8254i	0.448861	+	1.38145i
$274$	−13.4350	+	23.2702i	−0.811640	+	1.40580i
$275$		0			0
$276$	−9.00000	−	15.5885i	−0.541736	−	0.938315i
$277$	9.31841	−	3.02774i	0.559889	−	0.181919i	−0.0153821	−	0.999882i	$-0.504896\pi$
$277$	9.31841	−	3.02774i	0.559889	−	0.181919i	0.575271	+	0.817963i	$0.304896\pi$
$278$	25.5793	−	11.3886i	1.53414	−	0.683044i
$279$		0			0
$280$	−2.47214	+	7.60845i	−0.147738	+	0.454692i
$281$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$281$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$282$	0.886953	+	8.43880i	0.0528173	+	0.502523i
$283$	−9.15298	−	6.65003i	−0.544088	−	0.395303i	0.281513	−	0.959557i	$-0.409164\pi$
$283$	−9.15298	−	6.65003i	−0.544088	−	0.395303i	−0.825601	+	0.564254i	$0.809164\pi$
$284$	−18.0203	−	16.2256i	−1.06931	−	0.962810i
$285$			4.89898i			0.290191i
$286$		0			0
$287$		−	13.8564i		−	0.817918i
$288$		0			0
$289$	5.66312	+	4.11450i	0.333125	+	0.242029i
$290$		0			0
$291$	11.5309	+	3.74663i	0.675956	+	0.219631i
$292$	−2.03711	−	9.58385i	−0.119213	−	0.560852i
$293$	2.87955	+	3.96336i	0.168225	+	0.231542i	0.884803	−	0.465965i	$-0.154293\pi$
$293$	2.87955	+	3.96336i	0.168225	+	0.231542i	−0.716578	+	0.697507i	$0.754293\pi$
$294$	0.996297	+	2.23772i	0.0581052	+	0.130506i
$295$	1.64728	−	0.535233i	0.0959082	−	0.0311625i
$296$	8.48528			0.493197
$297$		0			0
$298$	18.0000	+	10.3923i	1.04271	+	0.602010i
$299$	−7.86629	−	24.2099i	−0.454919	−	1.40010i
$300$	13.7805	+	1.44839i	0.795618	+	0.0836228i
$301$	−12.9443	+	9.40456i	−0.746095	+	0.542070i
$302$	−5.35304	−	5.94516i	−0.308033	−	0.342105i
$303$	−2.62210	+	8.06998i	−0.150635	+	0.463608i
$304$	1.18260	+	11.2517i	0.0678270	+	0.645331i
$305$	−5.75910	+	7.92672i	−0.329765	+	0.453882i
$306$		0			0
$307$	−19.7990			−1.12999			−0.564994	−	0.825095i	$-0.691122\pi$
$307$	−19.7990			−1.12999			−0.564994	+	0.825095i	$0.691122\pi$
$308$		0			0
$309$	−6.00000			−0.341328
$310$	−0.509278	+	2.39596i	−0.0289250	+	0.136082i
$311$	−6.10844	+	8.40755i	−0.346378	+	0.476748i	−0.946291	−	0.323317i	$-0.895202\pi$
$311$	−6.10844	+	8.40755i	−0.346378	+	0.476748i	0.599913	+	0.800065i	$0.295202\pi$
$312$	−19.4164	+	14.1068i	−1.09924	+	0.798643i
$313$	8.34346	−	25.6785i	0.471600	−	1.45144i	−0.378888	−	0.925442i	$-0.623694\pi$
$313$	8.34346	−	25.6785i	0.471600	−	1.45144i	0.850488	−	0.525994i	$-0.176306\pi$
$314$	10.4092	+	11.5606i	0.587427	+	0.652404i
$315$		0			0
$316$	2.36521	−	22.5035i	0.133053	−	1.26592i
$317$	−7.72542	−	23.7764i	−0.433903	−	1.33542i	−0.894206	−	0.447655i	$-0.852259\pi$
$317$	−7.72542	−	23.7764i	−0.433903	−	1.33542i	0.460303	−	0.887762i	$-0.347741\pi$
$318$	4.24264	+	2.44949i	0.237915	+	0.137361i
$319$		0			0
$320$	−8.00000			−0.447214
$321$	−13.9776	+	4.54160i	−0.780155	+	0.253488i
$322$	−8.45386	−	18.9877i	−0.471115	−	1.05814i
$323$	8.14459	+	11.2101i	0.453177	+	0.623745i
$324$	17.6067	−	3.74241i	0.978148	−	0.207912i
$325$	18.6368	+	6.05547i	1.03379	+	0.335897i
$326$	−24.3607	+	2.56041i	−1.34922	+	0.141808i
$327$	−13.7295	−	9.97505i	−0.759242	−	0.551621i
$328$	13.1782	−	4.28187i	0.727646	−	0.236426i
$329$			9.79796i			0.540179i
$330$		0			0
$331$		−	5.19615i		−	0.285606i	−0.989751	−	0.142803i	$-0.954388\pi$
$331$		−	5.19615i		−	0.285606i	0.989751	−	0.142803i	$-0.0456116\pi$
$332$		0			0
$333$		0			0
$334$	−2.92680	−	27.8466i	−0.160147	−	1.52370i
$335$	−8.23639	−	2.67617i	−0.450002	−	0.146215i
$336$	−14.5626	+	13.1122i	−0.794455	+	0.715331i
$337$	−20.1568	−	27.7435i	−1.09801	−	1.51128i	−0.837992	−	0.545682i	$-0.816271\pi$
$337$	−20.1568	−	27.7435i	−1.09801	−	1.51128i	−0.260020	−	0.965603i	$-0.583729\pi$
$338$	−14.2114	+	6.32734i	−0.773000	+	0.344162i
$339$	8.23639	−	2.67617i	0.447339	−	0.145349i
$340$	−8.48528	+	4.89898i	−0.460179	+	0.265684i
$341$		0			0
$342$		0			0
$343$	−5.24419	−	16.1400i	−0.283160	−	0.871476i
$344$	−12.9443	−	9.40456i	−0.697908	−	0.507060i
$345$	7.28115	−	5.29007i	0.392004	−	0.284808i
$346$	−10.2973	+	9.27175i	−0.553587	+	0.498452i
$347$	−7.86629	+	24.2099i	−0.422284	+	1.29966i	0.483286	+	0.875462i	$0.339443\pi$
$347$	−7.86629	+	24.2099i	−0.422284	+	1.29966i	−0.905571	+	0.424196i	$0.860557\pi$
$348$		0			0
$349$	−2.87955	+	3.96336i	−0.154139	+	0.212154i	−0.879102	−	0.476634i	$-0.841857\pi$
$349$	−2.87955	+	3.96336i	−0.154139	+	0.212154i	0.724963	+	0.688788i	$0.241857\pi$
$350$	15.6504	+	3.32659i	0.836547	+	0.177814i
$351$	25.4558			1.35873
$352$		0			0
$353$	−17.0000			−0.904819			−0.452409	−	0.891810i	$-0.649435\pi$
$353$	−17.0000			−0.904819			−0.452409	+	0.891810i	$0.649435\pi$
$354$	4.14993	+	0.882095i	0.220566	+	0.0468828i
$355$	7.12652	−	9.80881i	0.378236	−	0.520598i
$356$	−1.82709	−	0.813473i	−0.0968356	−	0.0431140i
$357$	−7.41641	+	22.8254i	−0.392518	+	1.20805i
$358$	−9.10163	+	8.19514i	−0.481036	+	0.433127i
$359$	−6.86474	+	4.98752i	−0.362307	+	0.263231i	−0.754014	−	0.656859i	$-0.771885\pi$
$359$	−6.86474	+	4.98752i	−0.362307	+	0.263231i	0.391707	+	0.920090i	$0.371885\pi$
$360$		0			0
$361$	−3.39919	−	10.4616i	−0.178905	−	0.550612i
$362$	14.8492	−	25.7196i	0.780459	−	1.35179i
$363$		0			0
$364$	−24.0000	+	13.8564i	−1.25794	+	0.726273i
$365$	4.65921	−	1.51387i	0.243874	−	0.0792395i
$366$	−21.9251	+	9.76168i	−1.14604	+	0.510251i
$367$	−1.01807	−	1.40126i	−0.0531430	−	0.0731451i	0.781618	−	0.623757i	$-0.214394\pi$
$367$	−1.01807	−	1.40126i	−0.0531430	−	0.0731451i	−0.834761	+	0.550612i	$0.814394\pi$
$368$	15.4460	−	13.9076i	0.805177	−	0.724985i
$369$		0			0
$370$	0.443477	+	4.21940i	0.0230553	+	0.219356i
$371$	4.57649	+	3.32502i	0.237600	+	0.172626i
$372$	−4.01478	+	4.45887i	−0.208157	+	0.231182i
$373$		−	14.6969i		−	0.760979i	−0.924785	−	0.380489i	$-0.875756\pi$
$373$		−	14.6969i		−	0.760979i	0.924785	−	0.380489i	$-0.124244\pi$
$374$		0			0
$375$			15.5885i			0.804984i
$376$	−9.31841	+	3.02774i	−0.480560	+	0.156144i
$377$		0			0
$378$	20.6707	−	2.17258i	1.06319	−	0.111746i
$379$	−11.5309	−	3.74663i	−0.592305	−	0.192452i	−0.00249946	−	0.999997i	$-0.500796\pi$
$379$	−11.5309	−	3.74663i	−0.592305	−	0.192452i	−0.589806	+	0.807545i	$0.700796\pi$
$380$	−5.53324	+	1.17613i	−0.283849	+	0.0603340i
$381$	14.3977	+	19.8168i	0.737619	+	1.01524i
$382$	−2.98889	−	6.71316i	−0.152925	−	0.343475i
$383$	31.2983	−	10.1694i	1.59927	−	0.519634i	0.632341	−	0.774690i	$-0.282094\pi$
$383$	31.2983	−	10.1694i	1.59927	−	0.519634i	0.966926	+	0.255056i	$0.0820940\pi$
$384$	−16.9706	−	9.79796i	−0.866025	−	0.500000i
$385$		0			0
$386$	12.0000	+	6.92820i	0.610784	+	0.352636i
$387$		0			0
$388$	−1.46340	+	13.9233i	−0.0742928	+	0.706849i
$389$	−15.3713	+	11.1679i	−0.779357	+	0.566236i	−0.904786	−	0.425867i	$-0.859969\pi$
$389$	−15.3713	+	11.1679i	−0.779357	+	0.566236i	0.125429	+	0.992103i	$0.459969\pi$
$390$	−8.02957	−	8.91774i	−0.406593	−	0.451567i
$391$	7.86629	−	24.2099i	0.397815	−	1.22435i
$392$	−2.28825	+	1.66251i	−0.115574	+	0.0839693i
$393$	−2.87955	+	3.96336i	−0.145254	+	0.199925i
$394$		0			0
$395$	11.3137			0.569254
$396$		0			0
$397$	6.00000			0.301131			0.150566	−	0.988600i	$-0.451890\pi$
$397$	6.00000			0.301131			0.150566	+	0.988600i	$0.451890\pi$
$398$	−3.05567	+	14.3758i	−0.153167	+	0.720592i
$399$	−8.14459	+	11.2101i	−0.407740	+	0.561205i
$400$	1.67246	+	15.9124i	0.0836228	+	0.795618i
$401$	3.09017	−	9.51057i	0.154316	−	0.474935i	−0.843775	−	0.536697i	$-0.819672\pi$
$401$	3.09017	−	9.51057i	0.154316	−	0.474935i	0.998091	+	0.0617618i	$0.0196719\pi$
$402$	−14.1944	−	15.7645i	−0.707953	−	0.786261i
$403$	−6.86474	+	4.98752i	−0.341957	+	0.248446i
$404$	−9.74428	−	1.02417i	−0.484796	−	0.0509541i
$405$	2.78115	+	8.55951i	0.138197	+	0.425325i
$406$		0			0
$407$		0			0
$408$	−24.0000			−1.18818
$409$	27.9552	−	9.08321i	1.38230	−	0.449136i	0.478874	−	0.877884i	$-0.341045\pi$
$409$	27.9552	−	9.08321i	1.38230	−	0.449136i	0.903424	+	0.428748i	$0.141045\pi$
$410$	2.81795	+	6.32923i	0.139169	+	0.312578i
$411$	−19.3434	−	26.6239i	−0.954140	−	1.31326i
$412$	−1.44045	−	6.77681i	−0.0709661	−	0.333869i
$413$	4.65921	+	1.51387i	0.229265	+	0.0744926i
$414$		0			0
$415$		0			0
$416$	−20.5946	−	18.5435i	−1.00973	−	0.909169i
$417$			34.2929i			1.67933i
$418$		0			0
$419$			10.3923i			0.507697i	0.967244	+	0.253849i	$0.0816965\pi$
$419$			10.3923i			0.507697i	−0.967244	+	0.253849i	$0.918303\pi$
$420$	−7.28130	−	6.55611i	−0.355291	−	0.319906i
$421$	−24.2705	−	17.6336i	−1.18287	−	0.859407i	−0.190380	−	0.981711i	$-0.560972\pi$
$421$	−24.2705	−	17.6336i	−1.18287	−	0.859407i	−0.992493	+	0.122304i	$0.960972\pi$
$422$	−0.836228	−	7.95618i	−0.0407069	−	0.387301i
$423$		0			0
$424$	−1.74806	+	5.37999i	−0.0848935	+	0.261275i
$425$	11.5182	+	15.8534i	0.558714	+	0.769004i
$426$	27.1309	−	12.0795i	1.31450	−	0.585252i
$427$	−26.3565	+	8.56373i	−1.27548	+	0.414428i
$428$	−8.48528	−	14.6969i	−0.410152	−	0.710403i
$429$		0			0
$430$	4.00000	−	6.92820i	0.192897	−	0.334108i
$431$	4.37016	+	13.4500i	0.210503	+	0.647862i	0.999442	+	0.0333909i	$0.0106306\pi$
$431$	4.37016	+	13.4500i	0.210503	+	0.647862i	−0.788939	+	0.614471i	$0.789369\pi$
$432$	8.45386	+	18.9877i	0.406737	+	0.913545i
$433$	16.9894	−	12.3435i	0.816456	−	0.593190i	−0.0992389	−	0.995064i	$-0.531641\pi$
$433$	16.9894	−	12.3435i	0.816456	−	0.593190i	0.915695	+	0.401873i	$0.131641\pi$
$434$	−5.14866	+	4.63587i	−0.247144	+	0.222529i
$435$		0			0
$436$	7.97038	−	17.9018i	0.381712	−	0.857339i
$437$	8.63864	−	11.8901i	0.413242	−	0.568779i
$438$	11.7378	+	2.49494i	0.560852	+	0.119213i
$439$	−22.6274			−1.07995			−0.539974	−	0.841682i	$-0.681566\pi$
$439$	−22.6274			−1.07995			−0.539974	+	0.841682i	$0.681566\pi$
$440$		0			0
$441$		0			0
$442$	−33.1994	−	7.05676i	−1.57914	−	0.335656i
$443$	−3.05422	+	4.20378i	−0.145110	+	0.199727i	−0.875385	−	0.483426i	$-0.839392\pi$
$443$	−3.05422	+	4.20378i	−0.145110	+	0.199727i	0.730275	+	0.683154i	$0.239392\pi$
$444$	−4.22693	+	9.49384i	−0.200601	+	0.450558i
$445$	0.309017	−	0.951057i	0.0146488	−	0.0450844i
$446$	−23.6642	+	21.3074i	−1.12053	+	1.00893i
$447$	−20.5942	+	14.9626i	−0.974073	+	0.707705i
$448$	−18.3060	−	13.3001i	−0.864876	−	0.628369i
$449$	7.10739	+	21.8743i	0.335419	+	1.03231i	0.966516	+	0.256608i	$0.0826050\pi$
$449$	7.10739	+	21.8743i	0.335419	+	1.03231i	−0.631097	+	0.775704i	$0.717395\pi$
$450$		0			0
$451$		0			0
$452$	5.00000	+	8.66025i	0.235180	+	0.407344i
$453$	9.31841	−	3.02774i	0.437817	−	0.142255i
$454$	−10.9625	+	4.88084i	−0.514498	+	0.229069i
$455$	−8.14459	−	11.2101i	−0.381824	−	0.525536i
$456$	−13.1782	−	4.28187i	−0.617127	−	0.200517i
$457$	18.6368	+	6.05547i	0.871794	+	0.283263i	0.710546	−	0.703651i	$-0.248448\pi$
$457$	18.6368	+	6.05547i	0.871794	+	0.283263i	0.161248	+	0.986914i	$0.448448\pi$
$458$	0.147826	+	1.40647i	0.00690744	+	0.0657199i
$459$	20.5942	+	14.9626i	0.961255	+	0.698393i
$460$	7.72299	+	6.95381i	0.360086	+	0.324223i
$461$			29.3939i			1.36901i	0.729008	+	0.684505i	$0.239981\pi$
$461$			29.3939i			1.36901i	−0.729008	+	0.684505i	$0.760019\pi$
$462$		0			0
$463$			36.3731i			1.69040i	0.534450	+	0.845200i	$0.320519\pi$
$463$			36.3731i			1.69040i	−0.534450	+	0.845200i	$0.679481\pi$
$464$		0			0
$465$	−2.42705	−	1.76336i	−0.112552	−	0.0817737i
$466$	27.5610	−	2.89678i	1.27674	−	0.134191i
$467$	−31.2983	−	10.1694i	−1.44831	−	0.470585i	−0.523834	−	0.851820i	$-0.675499\pi$
$467$	−31.2983	−	10.1694i	−1.44831	−	0.470585i	−0.924478	+	0.381235i	$0.875499\pi$
$468$		0			0
$469$	−14.3977	−	19.8168i	−0.664826	−	0.915054i
$470$	−1.99259	−	4.47544i	−0.0919115	−	0.206437i
$471$	−18.1201	+	5.88756i	−0.834928	+	0.271285i
$472$			4.89898i			0.225494i
$473$		0			0
$474$	24.0000	+	13.8564i	1.10236	+	0.636446i
$475$	3.49613	+	10.7600i	0.160413	+	0.493702i
$476$	−27.5610	−	2.89678i	−1.26326	−	0.132774i
$477$		0			0
$478$	5.35304	+	5.94516i	0.244843	+	0.271925i
$479$	9.61435	−	29.5899i	0.439291	−	1.35200i	−0.449334	−	0.893364i	$-0.648339\pi$
$479$	9.61435	−	29.5899i	0.439291	−	1.35200i	0.888625	−	0.458635i	$-0.151661\pi$
$480$	3.98519	−	8.95088i	0.181898	−	0.408550i
$481$	−8.63864	+	11.8901i	−0.393888	+	0.542141i
$482$	−8.64273	+	40.6608i	−0.393665	+	1.85205i
$483$	25.4558			1.15828
$484$		0			0
$485$	−7.00000			−0.317854
$486$		0			0
$487$	−23.4157	+	32.2289i	−1.06107	+	1.46043i	−0.182263	+	0.983250i	$0.558342\pi$
$487$	−23.4157	+	32.2289i	−1.06107	+	1.46043i	−0.878804	+	0.477183i	$0.841658\pi$
$488$	−16.2892	−	22.4201i	−0.737377	−	1.01491i
$489$	9.27051	−	28.5317i	0.419227	−	1.29025i
$490$	−0.946294	−	1.05097i	−0.0427492	−	0.0474778i
$491$	27.4589	−	19.9501i	1.23920	−	0.900335i	0.241660	−	0.970361i	$-0.422308\pi$
$491$	27.4589	−	19.9501i	1.23920	−	0.900335i	0.997545	+	0.0700259i	$0.0223082\pi$
$492$	−1.77391	+	16.8776i	−0.0799739	+	0.760901i
$493$		0			0
$494$	−16.9706	−	9.79796i	−0.763542	−	0.440831i
$495$		0			0
$496$	−6.00000	−	3.46410i	−0.269408	−	0.155543i
$497$	32.6144	−	10.5971i	1.46296	−	0.475344i
$498$		0			0
$499$	10.1807	+	14.0126i	0.455752	+	0.627289i	0.973621	−	0.228171i	$-0.0732744\pi$
$499$	10.1807	+	14.0126i	0.455752	+	0.627289i	−0.517869	+	0.855460i	$0.673274\pi$
$500$	−17.6067	+	3.74241i	−0.787394	+	0.167366i
$501$	32.6144	+	10.5971i	1.45711	+	0.473442i
$502$	31.6689	−	3.32854i	1.41345	−	0.148560i
$503$	32.0354	+	23.2751i	1.42839	+	1.03779i	0.990314	+	0.138848i	$0.0443399\pi$
$503$	32.0354	+	23.2751i	1.42839	+	1.03779i	0.438076	+	0.898938i	$0.355660\pi$
$504$		0			0
$505$		−	4.89898i		−	0.218002i
$506$		0			0
$507$		−	19.0526i		−	0.846154i
$508$	−18.9259	+	21.0193i	−0.839700	+	0.932581i
$509$	0.809017	+	0.587785i	0.0358590	+	0.0260531i	0.605570	−	0.795792i	$-0.292945\pi$
$509$	0.809017	+	0.587785i	0.0358590	+	0.0260531i	−0.569711	+	0.821845i	$0.692945\pi$
$510$	−1.25434	−	11.9343i	−0.0555432	−	0.528458i
$511$	13.1782	+	4.28187i	0.582970	+	0.189419i
$512$	6.99226	−	21.5200i	0.309017	−	0.951057i
$513$	8.63864	+	11.8901i	0.381405	+	0.524960i
$514$	−28.4229	+	12.6547i	−1.25368	+	0.558174i
$515$	3.29456	−	1.07047i	0.145176	−	0.0471704i
$516$	16.9706	−	9.79796i	0.747087	−	0.431331i
$517$		0			0
$518$	−6.00000	+	10.3923i	−0.263625	+	0.456612i
$519$	−5.24419	−	16.1400i	−0.230194	−	0.708466i
$520$	8.14459	−	11.2101i	0.357164	−	0.491594i
$521$	13.7533	−	9.99235i	0.602543	−	0.437773i	−0.244238	−	0.969715i	$-0.578538\pi$
$521$	13.7533	−	9.99235i	0.602543	−	0.437773i	0.846780	+	0.531943i	$0.178538\pi$
$522$		0			0
$523$	11.3624	−	34.9699i	0.496844	−	1.52913i	−0.317220	−	0.948352i	$-0.602749\pi$
$523$	11.3624	−	34.9699i	0.496844	−	1.52913i	0.814063	−	0.580776i	$-0.197251\pi$
$524$	−5.16779	−	2.30085i	−0.225756	−	0.100513i
$525$	−11.5182	+	15.8534i	−0.502695	+	0.691900i
$526$	−19.5630	−	4.15823i	−0.852985	−	0.181308i
$527$	−8.48528			−0.369625
$528$		0			0
$529$	−4.00000			−0.173913
$530$	−2.76662	−	0.588063i	−0.120174	−	0.0255438i
$531$		0			0
$532$	−14.6167	−	6.50779i	−0.633715	−	0.282148i
$533$	−7.41641	+	22.8254i	−0.321240	+	0.988676i
$534$	1.82033	−	1.63903i	0.0787732	−	0.0709277i
$535$	6.86474	−	4.98752i	0.296788	−	0.215629i
$536$	14.3977	−	19.8168i	0.621888	−	0.855955i
$537$	−4.63525	−	14.2658i	−0.200026	−	0.615617i
$538$	7.07107	−	12.2474i	0.304855	−	0.528025i
$539$		0			0
$540$	−9.00000	+	5.19615i	−0.387298	+	0.223607i
$541$	13.9776	−	4.54160i	0.600945	−	0.195259i	0.00728303	−	0.999973i	$-0.497682\pi$
$541$	13.9776	−	4.54160i	0.600945	−	0.195259i	0.593662	+	0.804715i	$0.297682\pi$
$542$	−3.65418	+	1.62695i	−0.156961	+	0.0698833i
$543$	21.3796	+	29.4264i	0.917484	+	1.26281i
$544$	−5.76182	−	27.1072i	−0.247036	−	1.16221i
$545$	9.31841	+	3.02774i	0.399157	+	0.129694i
$546$	−3.54781	−	33.7552i	−0.151832	−	1.44459i
$547$	−4.57649	−	3.32502i	−0.195677	−	0.142167i	0.485633	−	0.874163i	$-0.338589\pi$
$547$	−4.57649	−	3.32502i	−0.195677	−	0.142167i	−0.681309	+	0.731995i	$0.738589\pi$
$548$	25.4270	−	28.2395i	1.08619	−	1.20633i
$549$		0			0
$550$		0			0
$551$		0			0
$552$	7.86629	+	24.2099i	0.334811	+	1.03044i
$553$	25.8885	+	18.8091i	1.10089	+	0.799845i
$554$	−13.7805	+	1.44839i	−0.585477	+	0.0615361i
$555$	−4.94183	−	1.60570i	−0.209769	−	0.0681581i
$556$	−38.7327	+	8.23288i	−1.64263	+	0.349152i
$557$	−14.3977	−	19.8168i	−0.610052	−	0.839664i	0.386530	−	0.922277i	$-0.373674\pi$
$557$	−14.3977	−	19.8168i	−0.610052	−	0.839664i	−0.996582	+	0.0826126i	$0.973674\pi$
$558$		0			0
$559$	26.3565	−	8.56373i	1.11476	−	0.362207i
$560$	5.65685	−	9.79796i	0.239046	−	0.414039i
$561$		0			0
$562$		0			0
$563$	3.49613	+	10.7600i	0.147344	+	0.453479i	0.997305	−	0.0733671i	$-0.0233745\pi$
$563$	3.49613	+	10.7600i	0.147344	+	0.453479i	−0.849961	+	0.526846i	$0.823374\pi$
$564$	1.25434	−	11.9343i	0.0528173	−	0.502523i
$565$	−4.04508	+	2.93893i	−0.170178	+	0.123642i
$566$	10.7061	+	11.8903i	0.450011	+	0.499787i
$567$	−7.86629	+	24.2099i	−0.330353	+	1.01672i
$568$	20.1568	+	27.7435i	0.845762	+	1.16409i
$569$	11.5182	−	15.8534i	0.482868	−	0.664610i	−0.496185	−	0.868217i	$-0.665266\pi$
$569$	11.5182	−	15.8534i	0.482868	−	0.664610i	0.979053	+	0.203606i	$0.0652663\pi$
$570$	1.44045	−	6.77681i	0.0603340	−	0.283849i
$571$	−5.65685			−0.236732			−0.118366	−	0.992970i	$-0.537766\pi$
$571$	−5.65685			−0.236732			−0.118366	+	0.992970i	$0.537766\pi$
$572$		0			0
$573$	9.00000			0.375980
$574$	−4.07422	+	19.1677i	−0.170055	+	0.800044i
$575$	12.2169	−	16.8151i	0.509479	−	0.701238i
$576$		0			0
$577$	−5.25329	+	16.1680i	−0.218697	+	0.673081i	0.780173	+	0.625564i	$0.215131\pi$
$577$	−5.25329	+	16.1680i	−0.218697	+	0.673081i	−0.998870	+	0.0475174i	$0.984869\pi$
$578$	−6.62406	−	7.35676i	−0.275524	−	0.306001i
$579$	−13.7295	+	9.97505i	−0.570577	+	0.414549i
$580$		0			0
$581$		0			0
$582$	−14.8492	−	8.57321i	−0.615521	−	0.355371i
$583$		0			0
$584$			13.8564i			0.573382i
$585$		0			0
$586$	−2.81795	−	6.32923i	−0.116409	−	0.261458i
$587$	−6.10844	−	8.40755i	−0.252122	−	0.347017i	0.664131	−	0.747616i	$-0.268802\pi$
$587$	−6.10844	−	8.40755i	−0.252122	−	0.347017i	−0.916253	+	0.400600i	$0.868802\pi$
$588$	−0.720227	−	3.38840i	−0.0297017	−	0.139735i
$589$	−4.65921	−	1.51387i	−0.191979	−	0.0623778i
$590$	−2.43607	+	0.256041i	−0.100291	+	0.0105411i
$591$		0			0
$592$	−11.7378	−	2.49494i	−0.482419	−	0.102541i
$593$			9.79796i			0.402354i	0.979555	+	0.201177i	$0.0644766\pi$
$593$			9.79796i			0.402354i	−0.979555	+	0.201177i	$0.935523\pi$
$594$		0			0
$595$		−	13.8564i		−	0.568057i
$596$	−21.8439	−	19.6683i	−0.894761	−	0.805647i
$597$	−14.5623	−	10.5801i	−0.595996	−	0.433016i
$598$	3.76302	+	35.8028i	0.153882	+	1.46408i
$599$	42.8292	+	13.9161i	1.74996	+	0.568595i	0.996083	−	0.0884261i	$-0.0281837\pi$
$599$	42.8292	+	13.9161i	1.74996	+	0.568595i	0.753872	+	0.657021i	$0.228184\pi$
$600$	−18.6368	−	6.05547i	−0.760845	−	0.247214i
$601$	2.87955	+	3.96336i	0.117459	+	0.161669i	0.863698	−	0.504009i	$-0.168142\pi$
$601$	2.87955	+	3.96336i	0.117459	+	0.161669i	−0.746239	+	0.665678i	$0.768142\pi$
$602$	20.6712	−	9.20340i	0.842494	−	0.375103i
$603$		0			0
$604$	5.65685	+	9.79796i	0.230174	+	0.398673i
$605$		0			0
$606$	6.00000	−	10.3923i	0.243733	−	0.422159i
$607$	−6.99226	−	21.5200i	−0.283807	−	0.873468i	−0.986754	−	0.162225i	$-0.948133\pi$
$607$	−6.99226	−	21.5200i	−0.283807	−	0.873468i	0.702947	−	0.711242i	$-0.251867\pi$
$608$	1.67246	−	15.9124i	0.0678270	−	0.645331i
$609$		0			0
$610$	10.2973	−	9.27175i	0.416926	−	0.375402i
$611$	5.24419	−	16.1400i	0.212157	−	0.652953i
$612$		0			0
$613$	−5.75910	+	7.92672i	−0.232608	+	0.320157i	−0.909326	−	0.416085i	$-0.863402\pi$
$613$	−5.75910	+	7.92672i	−0.232608	+	0.320157i	0.676718	+	0.736242i	$0.263402\pi$
$614$	27.3881	+	5.82153i	1.10530	+	0.234938i
$615$	−8.48528			−0.342160
$616$		0			0
$617$	2.00000			0.0805170			0.0402585	−	0.999189i	$-0.487182\pi$
$617$	2.00000			0.0805170			0.0402585	+	0.999189i	$0.487182\pi$
$618$	8.29986	+	1.76419i	0.333869	+	0.0709661i
$619$	1.01807	−	1.40126i	0.0409198	−	0.0563213i	−0.788067	−	0.615590i	$-0.788918\pi$
$619$	1.01807	−	1.40126i	0.0409198	−	0.0563213i	0.828987	+	0.559268i	$0.188918\pi$
$620$	1.40898	−	3.16461i	0.0565859	−	0.127094i
$621$	8.34346	−	25.6785i	0.334811	−	1.03044i
$622$	10.9220	−	9.83417i	0.437930	−	0.394314i
$623$	2.28825	−	1.66251i	0.0916766	−	0.0666070i
$624$	31.0068	−	13.8051i	1.24126	−	0.552646i
$625$	3.39919	+	10.4616i	0.135967	+	0.418465i
$626$	−19.0919	+	33.0681i	−0.763065	+	1.32167i
$627$		0			0
$628$	−11.0000	−	19.0526i	−0.438948	−	0.760280i
$629$	−13.9776	+	4.54160i	−0.557324	+	0.181086i
$630$		0			0
$631$	−21.3796	−	29.4264i	−0.851107	−	1.17145i	−0.983618	−	0.180266i	$-0.942304\pi$
$631$	−21.3796	−	29.4264i	−0.851107	−	1.17145i	0.132511	−	0.991181i	$-0.457696\pi$
$632$	−9.88854	+	30.4338i	−0.393345	+	1.21059i
$633$	9.31841	+	3.02774i	0.370374	+	0.120342i
$634$	3.69564	+	35.1617i	0.146773	+	1.39645i
$635$	−11.4412	−	8.31254i	−0.454031	−	0.329873i
$636$	−5.14866	−	4.63587i	−0.204158	−	0.183824i
$637$		−	4.89898i		−	0.194105i
$638$		0			0
$639$		0			0
$640$	11.0665	+	2.35225i	0.437441	+	0.0929809i
$641$	−15.3713	−	11.1679i	−0.607131	−	0.441106i	0.241272	−	0.970458i	$-0.422435\pi$
$641$	−15.3713	−	11.1679i	−0.607131	−	0.441106i	−0.848403	+	0.529351i	$0.822435\pi$
$642$	20.6707	−	2.17258i	0.815809	−	0.0857450i
$643$	−24.7092	−	8.02850i	−0.974435	−	0.316613i	−0.221830	−	0.975085i	$-0.571203\pi$
$643$	−24.7092	−	8.02850i	−0.974435	−	0.316613i	−0.752605	+	0.658472i	$0.771203\pi$
$644$	6.11133	+	28.7516i	0.240820	+	1.13297i
$645$	5.75910	+	7.92672i	0.226764	+	0.312114i
$646$	−7.97038	−	17.9018i	−0.313590	−	0.704335i
$647$	−1.64728	+	0.535233i	−0.0647612	+	0.0210422i	−0.341218	−	0.939984i	$-0.610840\pi$
$647$	−1.64728	+	0.535233i	−0.0647612	+	0.0210422i	0.276457	+	0.961026i	$0.410840\pi$
$648$	−25.4558			−1.00000
$649$		0			0
$650$	−24.0000	−	13.8564i	−0.941357	−	0.543493i
$651$	−2.62210	−	8.06998i	−0.102768	−	0.316288i
$652$	34.4512	+	3.62097i	1.34922	+	0.141808i
$653$	−25.0795	+	18.2213i	−0.981438	+	0.713056i	−0.958029	−	0.286670i	$-0.907452\pi$
$653$	−25.0795	+	18.2213i	−0.981438	+	0.713056i	−0.0234083	+	0.999726i	$0.507452\pi$
$654$	16.0591	+	17.8355i	0.627962	+	0.697422i
$655$	0.874032	−	2.68999i	0.0341513	−	0.105107i
$656$	−19.4886	+	2.04833i	−0.760901	+	0.0799739i
$657$		0			0
$658$	2.88091	−	13.5536i	0.112310	−	0.528375i
$659$	45.2548			1.76288			0.881439	−	0.472298i	$-0.156575\pi$
$659$	45.2548			1.76288			0.881439	+	0.472298i	$0.156575\pi$
$660$		0			0
$661$	−17.0000			−0.661223			−0.330612	−	0.943767i	$-0.607255\pi$
$661$	−17.0000			−0.661223			−0.330612	+	0.943767i	$0.607255\pi$
$662$	−1.52783	+	7.18789i	−0.0593809	+	0.279365i
$663$	24.4338	−	33.6302i	0.948929	−	1.30609i
$664$		0			0
$665$	2.47214	−	7.60845i	0.0958653	−	0.295043i
$666$		0			0
$667$		0			0
$668$	−4.13912	+	39.3811i	−0.160147	+	1.52370i
$669$	−12.0517	−	37.0912i	−0.465944	−	1.43403i
$670$	10.6066	+	6.12372i	0.409769	+	0.236580i
$671$		0			0
$672$	24.0000	−	13.8564i	0.925820	−	0.534522i
$673$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$673$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$674$	19.7257	+	44.3046i	0.759805	+	1.70655i
$675$	12.2169	+	16.8151i	0.470228	+	0.647214i
$676$	21.5192	−	4.57406i	0.827663	−	0.175925i
$677$	−23.2960	−	7.56934i	−0.895339	−	0.290913i	−0.175027	−	0.984564i	$-0.556001\pi$
$677$	−23.2960	−	7.56934i	−0.895339	−	0.290913i	−0.720312	+	0.693650i	$0.756001\pi$
$678$	−12.1804	+	1.28021i	−0.467784	+	0.0491661i
$679$	−16.0177	−	11.6376i	−0.614704	−	0.446608i
$680$	13.1782	−	4.28187i	0.505362	−	0.164202i
$681$		−	14.6969i		−	0.563188i
$682$		0			0
$683$		−	3.46410i		−	0.132550i	−0.997801	−	0.0662751i	$-0.978889\pi$
$683$		−	3.46410i		−	0.132550i	0.997801	−	0.0662751i	$-0.0211115\pi$
$684$		0			0
$685$	15.3713	+	11.1679i	0.587308	+	0.426704i
$686$	2.50868	+	23.8685i	0.0957820	+	0.911305i
$687$	−1.64728	−	0.535233i	−0.0628476	−	0.0204204i
$688$	15.1407	+	16.8154i	0.577234	+	0.641083i
$689$	−5.75910	−	7.92672i	−0.219404	−	0.301984i
$690$	−11.6275	+	5.17691i	−0.442653	+	0.197082i
$691$	−14.8255	+	4.81710i	−0.563989	+	0.183251i	−0.577115	−	0.816663i	$-0.695822\pi$
$691$	−14.8255	+	4.81710i	−0.563989	+	0.183251i	0.0131264	+	0.999914i	$0.495822\pi$
$692$	16.9706	−	9.79796i	0.645124	−	0.372463i
$693$		0			0
$694$	18.0000	−	31.1769i	0.683271	−	1.18346i
$695$	−6.11822	−	18.8300i	−0.232077	−	0.714261i
$696$		0			0
$697$	−19.4164	+	14.1068i	−0.735449	+	0.534335i
$698$	5.14866	−	4.63587i	0.194880	−	0.175470i
$699$	−10.4884	+	32.2799i	−0.396707	+	1.22094i
$700$	−20.6712	−	9.20340i	−0.781297	−	0.347856i
$701$	−20.1568	+	27.7435i	−0.761313	+	1.04786i	0.235791	+	0.971804i	$0.424232\pi$
$701$	−20.1568	+	27.7435i	−0.761313	+	1.04786i	−0.997104	+	0.0760538i	$0.975768\pi$
$702$	−35.2133	−	7.48482i	−1.32904	−	0.282496i
$703$	−8.48528			−0.320028
$704$		0			0
$705$	6.00000			0.225973
$706$	23.5163	+	4.99854i	0.885046	+	0.188122i
$707$	8.14459	−	11.2101i	0.306309	−	0.421598i
$708$	−5.48127	−	2.44042i	−0.205999	−	0.0917166i
$709$	−7.72542	+	23.7764i	−0.290134	+	0.892942i	0.694678	+	0.719321i	$0.255547\pi$
$709$	−7.72542	+	23.7764i	−0.290134	+	0.892942i	−0.984813	+	0.173621i	$0.944453\pi$
$710$	−12.7423	+	11.4732i	−0.478209	+	0.430582i
$711$		0			0
$712$	2.28825	+	1.66251i	0.0857556	+	0.0623051i
$713$	2.78115	+	8.55951i	0.104155	+	0.320556i
$714$	16.9706	−	29.3939i	0.635107	−	1.10004i
$715$		0			0
$716$	15.0000	−	8.66025i	0.560576	−	0.323649i
$717$	−9.31841	+	3.02774i	−0.348003	+	0.113073i
$718$	10.9625	−	4.88084i	0.409119	−	0.182151i
$719$	−9.16267	−	12.6113i	−0.341710	−	0.470323i	0.603230	−	0.797567i	$-0.293880\pi$
$719$	−9.16267	−	12.6113i	−0.341710	−	0.470323i	−0.944940	+	0.327244i	$0.893880\pi$
$720$		0			0
$721$	9.31841	+	3.02774i	0.347036	+	0.112759i
$722$	1.62608	+	15.4711i	0.0605165	+	0.575776i
$723$	−41.1884	−	29.9251i	−1.53181	−	1.11293i
$724$	−28.1035	+	31.2121i	−1.04446	+	1.15999i
$725$		0			0
$726$		0			0
$727$		−	25.9808i		−	0.963573i	−0.876289	−	0.481787i	$-0.839988\pi$
$727$		−	25.9808i		−	0.963573i	0.876289	−	0.481787i	$-0.160012\pi$
$728$	37.2737	−	12.1109i	1.38145	−	0.448861i
$729$	21.8435	+	15.8702i	0.809017	+	0.587785i
$730$	−6.89025	+	0.724194i	−0.255020	+	0.0268036i
$731$	26.3565	+	8.56373i	0.974829	+	0.316741i
$732$	33.1994	−	7.05676i	1.22709	−	0.260825i
$733$	−5.75910	−	7.92672i	−0.212717	−	0.292780i	0.689304	−	0.724472i	$-0.257917\pi$
$733$	−5.75910	−	7.92672i	−0.212717	−	0.292780i	−0.902021	+	0.431693i	$0.857917\pi$
$734$	0.996297	+	2.23772i	0.0367740	+	0.0825958i
$735$	1.64728	−	0.535233i	0.0607608	−	0.0197424i
$736$	−25.4558	+	14.6969i	−0.938315	+	0.541736i
$737$		0			0
$738$		0			0
$739$	−1.74806	−	5.37999i	−0.0643036	−	0.197906i	0.913743	−	0.406293i	$-0.133179\pi$
$739$	−1.74806	−	5.37999i	−0.0643036	−	0.197906i	−0.978046	+	0.208387i	$0.933179\pi$
$740$	0.627171	−	5.96713i	0.0230553	−	0.219356i
$741$	19.4164	−	14.1068i	0.713280	−	0.518228i
$742$	−5.35304	−	5.94516i	−0.196516	−	0.218254i
$743$	−10.4884	+	32.2799i	−0.384782	+	1.18424i	0.551857	+	0.833939i	$0.313919\pi$
$743$	−10.4884	+	32.2799i	−0.384782	+	1.18424i	−0.936639	+	0.350297i	$0.886081\pi$
$744$	6.86474	−	4.98752i	0.251673	−	0.182851i
$745$	8.63864	−	11.8901i	0.316495	−	0.435619i
$746$	−4.32136	+	20.3304i	−0.158216	+	0.744349i
$747$		0			0
$748$		0			0
$749$	24.0000			0.876941
$750$	4.58350	−	21.5637i	0.167366	−	0.787394i
$751$	−3.05422	+	4.20378i	−0.111450	+	0.153398i	−0.861098	−	0.508439i	$-0.830223\pi$
$751$	−3.05422	+	4.20378i	−0.111450	+	0.153398i	0.749648	+	0.661837i	$0.230223\pi$
$752$	13.7805	−	1.44839i	0.502523	−	0.0528173i
$753$	−12.0517	+	37.0912i	−0.439187	+	1.35168i
$754$		0			0
$755$	−4.57649	+	3.32502i	−0.166556	+	0.121010i
$756$	−29.2329	−	3.07250i	−1.06319	−	0.111746i
$757$	9.27051	+	28.5317i	0.336942	+	1.03700i	0.965757	+	0.259447i	$0.0835403\pi$
$757$	9.27051	+	28.5317i	0.336942	+	1.03700i	−0.628815	+	0.777555i	$0.716460\pi$
$758$	14.8492	+	8.57321i	0.539349	+	0.311393i
$759$		0			0
$760$	8.00000			0.290191
$761$	−41.9329	+	13.6248i	−1.52006	+	0.493899i	−0.945794	−	0.324766i	$-0.894714\pi$
$761$	−41.9329	+	13.6248i	−1.52006	+	0.493899i	−0.574271	+	0.818666i	$0.694714\pi$
$762$	−14.0898	−	31.6461i	−0.510419	−	1.14642i
$763$	16.2892	+	22.4201i	0.589708	+	0.811663i
$764$	2.16068	+	10.1652i	0.0781707	+	0.367764i
$765$		0			0
$766$	−46.2854	+	4.86479i	−1.67236	+	0.175772i
$767$	−6.86474	−	4.98752i	−0.247871	−	0.180089i
$768$	20.5946	+	18.5435i	0.743145	+	0.669131i
$769$		−	4.89898i		−	0.176662i	−0.996091	−	0.0883309i	$-0.971847\pi$
$769$		−	4.89898i		−	0.176662i	0.996091	−	0.0883309i	$-0.0281533\pi$
$770$		0			0
$771$		−	38.1051i		−	1.37232i
$772$	−14.5626	−	13.1122i	−0.524120	−	0.471919i
$773$	8.09017	+	5.87785i	0.290983	+	0.211412i	0.723694	−	0.690121i	$-0.242443\pi$
$773$	8.09017	+	5.87785i	0.290983	+	0.211412i	−0.432711	+	0.901533i	$0.642443\pi$
$774$		0			0
$775$	−6.58911	−	2.14093i	−0.236688	−	0.0769046i
$776$	6.11822	−	18.8300i	0.219631	−	0.675956i
$777$	−8.63864	−	11.8901i	−0.309910	−	0.426554i
$778$	24.5470	−	10.9290i	0.880053	−	0.391825i
$779$	−13.1782	+	4.28187i	−0.472159	+	0.153414i
$780$	8.48528	+	14.6969i	0.303822	+	0.526235i
$781$		0			0
$782$	−18.0000	+	31.1769i	−0.643679	+	1.11488i
$783$		0			0
$784$	3.65418	−	1.62695i	0.130506	−	0.0581052i
$785$	8.89919	−	6.46564i	0.317626	−	0.230769i
$786$	5.14866	−	4.63587i	0.183647	−	0.165356i
$787$	−8.74032	+	26.8999i	−0.311559	+	0.958879i	0.665589	+	0.746318i	$0.268180\pi$
$787$	−8.74032	+	26.8999i	−0.311559	+	0.958879i	−0.977148	+	0.212561i	$0.931820\pi$
$788$		0			0
$789$	14.3977	−	19.8168i	0.512573	−	0.705496i
$790$	−15.6504	−	3.32659i	−0.556815	−	0.118355i
$791$	−14.1421			−0.502836
$792$		0			0
$793$	48.0000			1.70453
$794$	−8.29986	−	1.76419i	−0.294551	−	0.0626087i
$795$	2.03615	−	2.80252i	0.0722147	−	0.0993950i
$796$	8.45386	−	18.9877i	0.299639	−	0.673001i
$797$	2.16312	−	6.65740i	0.0766216	−	0.235817i	−0.905408	−	0.424542i	$-0.860435\pi$
$797$	2.16312	−	6.65740i	0.0766216	−	0.235817i	0.982030	+	0.188724i	$0.0604353\pi$
$798$	14.5626	−	13.1122i	0.515511	−	0.464168i
$799$	13.7295	−	9.97505i	0.485714	−	0.352892i
$800$	2.36521	−	22.5035i	0.0836228	−	0.795618i
$801$		0			0
$802$	−7.07107	+	12.2474i	−0.249688	+	0.432472i
$803$		0			0
$804$	15.0000	+	25.9808i	0.529009	+	0.916271i
$805$	−13.9776	+	4.54160i	−0.492646	+	0.160070i
$806$	10.9625	−	4.88084i	0.386139	−	0.171920i
$807$	10.1807	+	14.0126i	0.358379	+	0.493266i
$808$	13.1782	+	4.28187i	0.463608	+	0.150635i
$809$	−41.9329	−	13.6248i	−1.47428	−	0.479023i	−0.541882	−	0.840454i	$-0.682288\pi$
$809$	−41.9329	−	13.6248i	−1.47428	−	0.479023i	−0.932399	+	0.361432i	$0.882288\pi$
$810$	−1.33043	−	12.6582i	−0.0467465	−	0.444764i
$811$	32.0354	+	23.2751i	1.12492	+	0.817300i	0.984947	−	0.172856i	$-0.0552996\pi$
$811$	32.0354	+	23.2751i	1.12492	+	0.817300i	0.139969	+	0.990156i	$0.455300\pi$
$812$		0			0
$813$		−	4.89898i		−	0.171815i
$814$		0			0
$815$			17.3205i			0.606711i
$816$	33.1994	+	7.05676i	1.16221	+	0.247036i
$817$	12.9443	+	9.40456i	0.452863	+	0.329024i
$818$	−41.3415	+	4.34517i	−1.44547	+	0.151925i
$819$		0			0
$820$	−2.03711	−	9.58385i	−0.0711390	−	0.334683i
$821$	28.7955	+	39.6336i	1.00497	+	1.38322i	0.922226	+	0.386650i	$0.126368\pi$
$821$	28.7955	+	39.6336i	1.00497	+	1.38322i	0.0827428	+	0.996571i	$0.473632\pi$
$822$	18.9296	+	42.5167i	0.660247	+	1.48294i
$823$	−8.23639	+	2.67617i	−0.287103	+	0.0932853i	−0.449028	−	0.893518i	$-0.648230\pi$
$823$	−8.23639	+	2.67617i	−0.287103	+	0.0932853i	0.161925	+	0.986803i	$0.448230\pi$
$824$			9.79796i			0.341328i
$825$		0			0
$826$	−6.00000	−	3.46410i	−0.208767	−	0.120532i
$827$	7.86629	+	24.2099i	0.273538	+	0.841862i	0.989603	+	0.143829i	$0.0459414\pi$
$827$	7.86629	+	24.2099i	0.273538	+	0.841862i	−0.716065	+	0.698034i	$0.754059\pi$
$828$		0			0
$829$	13.7533	−	9.99235i	0.477671	−	0.347049i	−0.322752	−	0.946484i	$-0.604608\pi$
$829$	13.7533	−	9.99235i	0.477671	−	0.347049i	0.800423	+	0.599435i	$0.204608\pi$
$830$		0			0
$831$	5.24419	−	16.1400i	0.181919	−	0.559889i
$832$	23.0364	+	31.7069i	0.798643	+	1.09924i
$833$	2.87955	−	3.96336i	0.0997704	−	0.137322i
$834$	10.0832	−	47.4376i	0.349152	−	1.64263i
$835$	−19.7990			−0.685172
$836$		0			0
$837$	−9.00000			−0.311086
$838$	3.05567	−	14.3758i	0.105556	−	0.496603i
$839$	−15.2711	+	21.0189i	−0.527217	+	0.725652i	−0.986703	−	0.162533i	$-0.948034\pi$
$839$	−15.2711	+	21.0189i	−0.527217	+	0.725652i	0.459486	+	0.888185i	$0.348034\pi$
$840$	8.14459	+	11.2101i	0.281015	+	0.386784i
$841$	8.96149	−	27.5806i	0.309017	−	0.951057i
$842$	28.3888	+	31.5290i	0.978343	+	1.08656i
$843$		0			0
$844$	−1.18260	+	11.2517i	−0.0407069	+	0.387301i
$845$	3.39919	+	10.4616i	0.116936	+	0.359891i
$846$		0			0
$847$		0			0
$848$	4.00000	−	6.92820i	0.137361	−	0.237915i
$849$	−18.6368	+	6.05547i	−0.639614	+	0.207823i
$850$	−11.2718	−	25.3169i	−0.386620	−	0.868363i
$851$	9.16267	+	12.6113i	0.314092	+	0.432311i
$852$	−41.0822	+	8.73229i	−1.40745	+	0.299163i
$853$	−37.2737	−	12.1109i	−1.27623	−	0.414671i	−0.408976	−	0.912545i	$-0.634114\pi$
$853$	−37.2737	−	12.1109i	−1.27623	−	0.414671i	−0.867249	+	0.497874i	$0.834114\pi$
$854$	38.9771	−	4.09666i	1.33377	−	0.140185i
$855$		0			0
$856$	7.41641	+	22.8254i	0.253488	+	0.780155i
$857$		−	29.3939i		−	1.00408i	−0.864846	−	0.502038i	$-0.832584\pi$
$857$		−	29.3939i		−	1.00408i	0.864846	−	0.502038i	$-0.167416\pi$
$858$		0			0
$859$			15.5885i			0.531871i	0.963991	+	0.265936i	$0.0856809\pi$
$859$			15.5885i			0.531871i	−0.963991	+	0.265936i	$0.914319\pi$
$860$	−7.57035	+	8.40772i	−0.258147	+	0.286701i
$861$	−19.4164	−	14.1068i	−0.661709	−	0.480760i
$862$	−2.09057	−	19.8904i	−0.0712051	−	0.677471i
$863$	29.6510	+	9.63420i	1.00933	+	0.327952i	0.766589	−	0.642139i	$-0.221953\pi$
$863$	29.6510	+	9.63420i	1.00933	+	0.327952i	0.242744	+	0.970091i	$0.421953\pi$
$864$	−6.11133	−	28.7516i	−0.207912	−	0.978148i
$865$	5.75910	+	7.92672i	0.195815	+	0.269516i
$866$	−27.1309	+	12.0795i	−0.921946	+	0.410477i
$867$	11.5309	−	3.74663i	0.391612	−	0.127242i
$868$	8.48528	−	4.89898i	0.288009	−	0.166282i
$869$		0			0
$870$		0			0
$871$	13.1105	+	40.3499i	0.444232	+	1.36720i
$872$	−16.2892	+	22.4201i	−0.551621	+	0.759242i
$873$		0			0
$874$	−15.4460	+	13.9076i	−0.522468	+	0.470432i
$875$	7.86629	−	24.2099i	0.265929	−	0.818446i
$876$	−15.5034	−	6.90255i	−0.523811	−	0.233216i
$877$	31.6750	−	43.5969i	1.06959	−	1.47216i	0.199099	−	0.979979i	$-0.436199\pi$
$877$	31.6750	−	43.5969i	1.06959	−	1.47216i	0.870491	−	0.492184i	$-0.163801\pi$
$878$	31.3007	+	6.65317i	1.05635	+	0.224534i
$879$	8.48528			0.286201
$880$		0			0
$881$	−49.0000			−1.65085			−0.825426	−	0.564510i	$-0.809065\pi$
$881$	−49.0000			−1.65085			−0.825426	+	0.564510i	$0.809065\pi$
$882$		0			0
$883$	14.2530	−	19.6176i	0.479653	−	0.660185i	−0.498785	−	0.866726i	$-0.666220\pi$
$883$	14.2530	−	19.6176i	0.479653	−	0.660185i	0.978438	+	0.206540i	$0.0662204\pi$
$884$	43.8502	+	19.5234i	1.47484	+	0.656642i
$885$	0.927051	−	2.85317i	0.0311625	−	0.0959082i
$886$	5.46098	−	4.91709i	0.183465	−	0.165193i
$887$	−13.7295	+	9.97505i	−0.460991	+	0.334929i	−0.793920	−	0.608023i	$-0.791963\pi$
$887$	−13.7295	+	9.97505i	−0.460991	+	0.334929i	0.332929	+	0.942952i	$0.391963\pi$
$888$	8.63864	−	11.8901i	0.289894	−	0.399005i
$889$	−12.3607	−	38.0423i	−0.414564	−	1.27590i
$890$	−0.707107	+	1.22474i	−0.0237023	+	0.0410535i
$891$		0			0
$892$	39.0000	−	22.5167i	1.30582	−	0.753914i
$893$	9.31841	−	3.02774i	0.311829	−	0.101319i
$894$	32.8876	−	14.6425i	1.09993	−	0.489719i
$895$	5.09037	+	7.00629i	0.170152	+	0.234195i
$896$	21.4122	+	23.7806i	0.715331	+	0.794455i
$897$	−41.9329	−	13.6248i	−1.40010	−	0.454919i
$898$	−3.39999	−	32.3487i	−0.113459	−	1.07949i
$899$		0			0
$900$		0			0
$901$		−	9.79796i		−	0.326417i
$902$		0			0
$903$			27.7128i			0.922225i
$904$	−4.37016	−	13.4500i	−0.145349	−	0.447339i
$905$	−16.9894	−	12.3435i	−0.564745	−	0.410312i
$906$	−13.7805	+	1.44839i	−0.457826	+	0.0481195i
$907$	−3.29456	−	1.07047i	−0.109394	−	0.0355442i	0.253809	−	0.967254i	$-0.418317\pi$
$907$	−3.29456	−	1.07047i	−0.109394	−	0.0355442i	−0.363202	+	0.931710i	$0.618317\pi$
$908$	16.5997	−	3.52838i	0.550881	−	0.117093i
$909$		0			0
$910$	7.97038	+	17.9018i	0.264215	+	0.593438i
$911$	23.0619	−	7.49326i	0.764075	−	0.248263i	0.0990481	−	0.995083i	$-0.468420\pi$
$911$	23.0619	−	7.49326i	0.764075	−	0.248263i	0.665027	+	0.746820i	$0.268420\pi$
$912$	16.9706	+	9.79796i	0.561951	+	0.324443i
$913$		0			0
$914$	−24.0000	−	13.8564i	−0.793849	−	0.458329i
$915$	5.24419	+	16.1400i	0.173368	+	0.533571i
$916$	0.209057	−	1.98904i	0.00690744	−	0.0657199i
$917$	6.47214	−	4.70228i	0.213729	−	0.155283i
$918$	−24.0887	−	26.7532i	−0.795046	−	0.882988i
$919$	−3.49613	+	10.7600i	−0.115327	+	0.354939i	−0.992015	−	0.126120i	$-0.959748\pi$
$919$	−3.49613	+	10.7600i	−0.115327	+	0.354939i	0.876688	+	0.481059i	$0.159748\pi$
$920$	−8.63864	−	11.8901i	−0.284808	−	0.392004i
$921$	−20.1568	+	27.7435i	−0.664190	+	0.914180i
$922$	8.64273	−	40.6608i	0.284633	−	1.33909i
$923$	−59.3970			−1.95508
$924$		0			0
$925$	−12.0000			−0.394558
$926$	10.6948	−	50.3152i	0.351454	−	1.65346i
$927$		0			0
$928$		0			0
$929$	−6.79837	+	20.9232i	−0.223047	+	0.686469i	0.775437	+	0.631426i	$0.217530\pi$
$929$	−6.79837	+	20.9232i	−0.223047	+	0.686469i	−0.998484	+	0.0550438i	$0.982470\pi$
$930$	2.83888	+	3.15290i	0.0930906	+	0.103388i
$931$	2.28825	−	1.66251i	0.0749942	−	0.0544865i
$932$	−38.9771	−	4.09666i	−1.27674	−	0.134191i
$933$	5.56231	+	17.1190i	0.182102	+	0.560451i
$934$	40.3051	+	23.2702i	1.31882	+	0.761423i
$935$		0			0
$936$		0			0
$937$	4.65921	−	1.51387i	0.152210	−	0.0494559i	−0.231921	−	0.972735i	$-0.574501\pi$
$937$	4.65921	−	1.51387i	0.152210	−	0.0494559i	0.384131	+	0.923279i	$0.374501\pi$
$938$	14.0898	+	31.6461i	0.460047	+	1.03328i
$939$	−27.4880	−	37.8340i	−0.897037	−	1.23467i
$940$	1.44045	+	6.77681i	0.0469824	+	0.221035i
$941$	37.2737	+	12.1109i	1.21509	+	0.394805i	0.845290	−	0.534307i	$-0.179428\pi$
$941$	37.2737	+	12.1109i	1.21509	+	0.394805i	0.369796	+	0.929113i	$0.379428\pi$
$942$	26.7968	−	2.81646i	0.873086	−	0.0917651i
$943$	20.5942	+	14.9626i	0.670640	+	0.487248i
$944$	1.44045	−	6.77681i	0.0468828	−	0.220566i
$945$		−	14.6969i		−	0.478091i
$946$		0			0
$947$			43.3013i			1.40710i	0.710645	+	0.703551i	$0.248403\pi$
$947$			43.3013i			1.40710i	−0.710645	+	0.703551i	$0.751597\pi$
$948$	−29.1252	−	26.2245i	−0.945943	−	0.851731i
$949$	−19.4164	−	14.1068i	−0.630283	−	0.457928i
$950$	−1.67246	−	15.9124i	−0.0542616	−	0.516265i
$951$	−41.1820	−	13.3808i	−1.33542	−	0.433903i
$952$	37.2737	+	12.1109i	1.20805	+	0.392518i
$953$	−20.1568	−	27.7435i	−0.652944	−	0.898700i	0.346278	−	0.938132i	$-0.387445\pi$
$953$	−20.1568	−	27.7435i	−0.652944	−	0.898700i	−0.999222	+	0.0394316i	$0.987445\pi$
$954$		0			0
$955$	−4.94183	+	1.60570i	−0.159914	+	0.0519592i
$956$	−5.65685	−	9.79796i	−0.182956	−	0.316889i
$957$		0			0
$958$	−22.0000	+	38.1051i	−0.710788	+	1.23112i
$959$	16.6066	+	51.1099i	0.536255	+	1.65042i
$960$	−8.14459	+	11.2101i	−0.262866	+	0.361803i
$961$	−22.6525	+	16.4580i	−0.730725	+	0.530903i
$962$	15.4460	−	13.9076i	0.497998	−	0.448400i
$963$		0			0
$964$	23.9111	−	53.7053i	0.770126	−	1.72973i
$965$	5.75910	−	7.92672i	0.185392	−	0.255170i
$966$	−35.2133	−	7.48482i	−1.13297	−	0.240820i
$967$	45.2548			1.45530			0.727649	−	0.685950i	$-0.240613\pi$
$967$	45.2548			1.45530			0.727649	+	0.685950i	$0.240613\pi$
$968$		0			0
$969$	24.0000			0.770991
$970$	9.68317	+	2.05822i	0.310908	+	0.0660855i
$971$	−19.3434	+	26.6239i	−0.620759	+	0.854402i	−0.997408	−	0.0719542i	$-0.977076\pi$
$971$	−19.3434	+	26.6239i	−0.620759	+	0.854402i	0.376649	+	0.926356i	$0.377076\pi$
$972$		0			0
$973$	17.3050	−	53.2592i	0.554771	−	1.70741i
$974$	41.8675	−	37.6977i	1.34152	−	1.20791i
$975$	27.4589	−	19.9501i	0.879390	−	0.638914i
$976$	15.9408	+	35.8035i	0.510251	+	1.14604i
$977$	5.87132	+	18.0701i	0.187840	+	0.578113i	0.999986	−	0.00534212i	$-0.00170046\pi$
$977$	5.87132	+	18.0701i	0.187840	+	0.578113i	−0.812145	+	0.583455i	$0.801700\pi$
$978$	−21.2132	+	36.7423i	−0.678323	+	1.17489i
$979$		0			0
$980$	1.00000	+	1.73205i	0.0319438	+	0.0553283i
$981$		0			0
$982$	−43.8502	+	19.5234i	−1.39932	+	0.623015i
$983$	−1.01807	−	1.40126i	−0.0324715	−	0.0446932i	0.792473	−	0.609908i	$-0.208793\pi$
$983$	−1.01807	−	1.40126i	−0.0324715	−	0.0446932i	−0.824944	+	0.565214i	$0.808793\pi$
$984$	7.41641	−	22.8254i	0.236426	−	0.727646i
$985$		0			0
$986$		0			0
$987$	13.7295	+	9.97505i	0.437014	+	0.317509i
$988$	20.5946	+	18.5435i	0.655203	+	0.589947i
$989$		−	29.3939i		−	0.934671i
$990$		0			0
$991$		−	51.9615i		−	1.65061i	−0.564686	−	0.825306i	$-0.691003\pi$
$991$		−	51.9615i		−	1.65061i	0.564686	−	0.825306i	$-0.308997\pi$
$992$	7.28130	+	6.55611i	0.231182	+	0.208157i
$993$	−7.28115	−	5.29007i	−0.231060	−	0.167875i
$994$	−48.2317	+	5.06936i	−1.52982	+	0.160790i
$995$	9.88367	+	3.21140i	0.313333	+	0.101808i
$996$		0			0
$997$	−2.87955	−	3.96336i	−0.0911962	−	0.125521i	0.760981	−	0.648774i	$-0.224718\pi$
$997$	−2.87955	−	3.96336i	−0.0911962	−	0.125521i	−0.852177	+	0.523254i	$0.824718\pi$
$998$	−9.96297	−	22.3772i	−0.315372	−	0.708338i
$999$	−14.8255	+	4.81710i	−0.469058	+	0.152406i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	484.2.g.g.215.1		16
4.3	odd	2	inner	484.2.g.g.215.2		16
11.2	odd	10	inner	484.2.g.g.475.2		16
11.3	even	5		44.2.c.a.43.2	yes	4
11.4	even	5	inner	484.2.g.g.239.2		16
11.5	even	5	inner	484.2.g.g.403.4		16
11.6	odd	10	inner	484.2.g.g.403.1		16
11.7	odd	10	inner	484.2.g.g.239.3		16
11.8	odd	10		44.2.c.a.43.3	yes	4
11.9	even	5	inner	484.2.g.g.475.3		16
11.10	odd	2	inner	484.2.g.g.215.4		16
33.8	even	10		396.2.h.b.307.2		4
33.14	odd	10		396.2.h.b.307.3		4
44.3	odd	10		44.2.c.a.43.4	yes	4
44.7	even	10	inner	484.2.g.g.239.4		16
44.15	odd	10	inner	484.2.g.g.239.1		16
44.19	even	10		44.2.c.a.43.1	✓	4
44.27	odd	10	inner	484.2.g.g.403.3		16
44.31	odd	10	inner	484.2.g.g.475.4		16
44.35	even	10	inner	484.2.g.g.475.1		16
44.39	even	10	inner	484.2.g.g.403.2		16
44.43	even	2	inner	484.2.g.g.215.3		16
88.3	odd	10		704.2.e.b.703.3		4
88.19	even	10		704.2.e.b.703.4		4
88.69	even	10		704.2.e.b.703.2		4
88.85	odd	10		704.2.e.b.703.1		4
132.47	even	10		396.2.h.b.307.1		4
132.107	odd	10		396.2.h.b.307.4		4
176.3	odd	20		2816.2.g.b.1407.8		8
176.19	even	20		2816.2.g.b.1407.7		8
176.69	even	20		2816.2.g.b.1407.5		8
176.85	odd	20		2816.2.g.b.1407.6		8
176.91	odd	20		2816.2.g.b.1407.2		8
176.107	even	20		2816.2.g.b.1407.1		8
176.157	even	20		2816.2.g.b.1407.3		8
176.173	odd	20		2816.2.g.b.1407.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
44.2.c.a.43.1	✓	4	44.19	even	10
44.2.c.a.43.2	yes	4	11.3	even	5
44.2.c.a.43.3	yes	4	11.8	odd	10
44.2.c.a.43.4	yes	4	44.3	odd	10
396.2.h.b.307.1		4	132.47	even	10
396.2.h.b.307.2		4	33.8	even	10
396.2.h.b.307.3		4	33.14	odd	10
396.2.h.b.307.4		4	132.107	odd	10
484.2.g.g.215.1		16	1.1	even	1	trivial
484.2.g.g.215.2		16	4.3	odd	2	inner
484.2.g.g.215.3		16	44.43	even	2	inner
484.2.g.g.215.4		16	11.10	odd	2	inner
484.2.g.g.239.1		16	44.15	odd	10	inner
484.2.g.g.239.2		16	11.4	even	5	inner
484.2.g.g.239.3		16	11.7	odd	10	inner
484.2.g.g.239.4		16	44.7	even	10	inner
484.2.g.g.403.1		16	11.6	odd	10	inner
484.2.g.g.403.2		16	44.39	even	10	inner
484.2.g.g.403.3		16	44.27	odd	10	inner
484.2.g.g.403.4		16	11.5	even	5	inner
484.2.g.g.475.1		16	44.35	even	10	inner
484.2.g.g.475.2		16	11.2	odd	10	inner
484.2.g.g.475.3		16	11.9	even	5	inner
484.2.g.g.475.4		16	44.31	odd	10	inner
704.2.e.b.703.1		4	88.85	odd	10
704.2.e.b.703.2		4	88.69	even	10
704.2.e.b.703.3		4	88.3	odd	10
704.2.e.b.703.4		4	88.19	even	10
2816.2.g.b.1407.1		8	176.107	even	20
2816.2.g.b.1407.2		8	176.91	odd	20
2816.2.g.b.1407.3		8	176.157	even	20
2816.2.g.b.1407.4		8	176.173	odd	20
2816.2.g.b.1407.5		8	176.69	even	20
2816.2.g.b.1407.6		8	176.85	odd	20
2816.2.g.b.1407.7		8	176.19	even	20
2816.2.g.b.1407.8		8	176.3	odd	20

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:	\( N \)	\(=\)	\( 484 = 2^{2} \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	484.g (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.38331 - 0.294032i) q^{2} +(1.01807 - 1.40126i) q^{3} +(1.82709 + 0.813473i) q^{4} +(-0.309017 + 0.951057i) q^{5} +(-1.82033 + 1.63903i) q^{6} +(-2.28825 + 1.66251i) q^{7} +(-2.28825 - 1.66251i) q^{8} +O(q^{10})\)	\(q+(-1.38331 - 0.294032i) q^{2} +(1.01807 - 1.40126i) q^{3} +(1.82709 + 0.813473i) q^{4} +(-0.309017 + 0.951057i) q^{5} +(-1.82033 + 1.63903i) q^{6} +(-2.28825 + 1.66251i) q^{7} +(-2.28825 - 1.66251i) q^{8} +(0.707107 - 1.22474i) q^{10} +(3.00000 - 1.73205i) q^{12} +(4.65921 - 1.51387i) q^{13} +(3.65418 - 1.62695i) q^{14} +(1.01807 + 1.40126i) q^{15} +(2.67652 + 2.97258i) q^{16} +(4.65921 + 1.51387i) q^{17} +(2.28825 + 1.66251i) q^{19} +(-1.33826 + 1.48629i) q^{20} +4.89898i q^{21} -5.19615i q^{23} +(-4.65921 + 1.51387i) q^{24} +(3.23607 + 2.35114i) q^{25} +(-6.89025 + 0.724194i) q^{26} +(4.94183 + 1.60570i) q^{27} +(-5.53324 + 1.17613i) q^{28} +(-0.996297 - 2.23772i) q^{30} +(-1.64728 + 0.535233i) q^{31} +(-2.82843 - 4.89898i) q^{32} +(-6.00000 - 3.46410i) q^{34} +(-0.874032 - 2.68999i) q^{35} +(-2.42705 + 1.76336i) q^{37} +(-2.67652 - 2.97258i) q^{38} +(2.62210 - 8.06998i) q^{39} +(2.28825 - 1.66251i) q^{40} +(-2.87955 + 3.96336i) q^{41} +(1.44045 - 6.77681i) q^{42} +5.65685 q^{43} +(-1.52783 + 7.18789i) q^{46} +(2.03615 - 2.80252i) q^{47} +(6.89025 - 0.724194i) q^{48} +(0.309017 - 0.951057i) q^{49} +(-3.78517 - 4.20386i) q^{50} +(6.86474 - 4.98752i) q^{51} +(9.74428 + 1.02417i) q^{52} +(-0.618034 - 1.90211i) q^{53} +(-6.36396 - 3.67423i) q^{54} +8.00000 q^{56} +(4.65921 - 1.51387i) q^{57} +(-1.01807 - 1.40126i) q^{59} +(0.720227 + 3.38840i) q^{60} +(9.31841 + 3.02774i) q^{61} +(2.43607 - 0.256041i) q^{62} +(2.47214 + 7.60845i) q^{64} +4.89898i q^{65} +8.66025i q^{67} +(7.28130 + 6.55611i) q^{68} +(-7.28115 - 5.29007i) q^{69} +(0.418114 + 3.97809i) q^{70} +(-11.5309 - 3.74663i) q^{71} +(-2.87955 - 3.96336i) q^{73} +(3.87585 - 1.72564i) q^{74} +(6.58911 - 2.14093i) q^{75} +(2.82843 + 4.89898i) q^{76} +(-6.00000 + 10.3923i) q^{78} +(-3.49613 - 10.7600i) q^{79} +(-3.65418 + 1.62695i) q^{80} +(7.28115 - 5.29007i) q^{81} +(5.14866 - 4.63587i) q^{82} +(-3.98519 + 8.95088i) q^{84} +(-2.87955 + 3.96336i) q^{85} +(-7.82518 - 1.66329i) q^{86} -1.00000 q^{89} +(-8.14459 + 11.2101i) q^{91} +(4.22693 - 9.49384i) q^{92} +(-0.927051 + 2.85317i) q^{93} +(-3.64065 + 3.27806i) q^{94} +(-2.28825 + 1.66251i) q^{95} +(-9.74428 - 1.02417i) q^{96} +(2.16312 + 6.65740i) q^{97} +(-0.707107 + 1.22474i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{4} + 4 q^{5}+O(q^{10}) \) 16 * q + 4 * q^4 + 4 * q^5	\( 16 q + 4 q^{4} + 4 q^{5} + 48 q^{12} + 8 q^{14} + 8 q^{16} - 4 q^{20} + 16 q^{25} - 24 q^{26} - 96 q^{34} - 12 q^{37} - 8 q^{38} + 24 q^{42} + 24 q^{48} - 4 q^{49} + 8 q^{53} + 128 q^{56} + 12 q^{60} - 32 q^{64} - 36 q^{69} - 8 q^{70} - 96 q^{78} - 8 q^{80} + 36 q^{81} - 24 q^{82} + 16 q^{86} - 16 q^{89} + 36 q^{92} + 12 q^{93} - 28 q^{97}+O(q^{100}) \) 16 * q + 4 * q^4 + 4 * q^5 + 48 * q^12 + 8 * q^14 + 8 * q^16 - 4 * q^20 + 16 * q^25 - 24 * q^26 - 96 * q^34 - 12 * q^37 - 8 * q^38 + 24 * q^42 + 24 * q^48 - 4 * q^49 + 8 * q^53 + 128 * q^56 + 12 * q^60 - 32 * q^64 - 36 * q^69 - 8 * q^70 - 96 * q^78 - 8 * q^80 + 36 * q^81 - 24 * q^82 + 16 * q^86 - 16 * q^89 + 36 * q^92 + 12 * q^93 - 28 * q^97

Introduction

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