LMFDB - Embedded newform 2142.2.p.h.1135.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [2142,2,Mod(1135,2142)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2142, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 0, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("2142.1135"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 2142 = 2 \cdot 3^{2} \cdot 7 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2142.p (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [16,0,0,-16,0,0,0,0,0,0,-4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

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

Self dual:	no
Analytic conductor:	$17.1039561130$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8 x^{15} + 36 x^{14} - 108 x^{13} + 244 x^{12} - 424 x^{11} + 674 x^{10} - 1804 x^{9} + \cdots + 388 $ x^16 - 8x^15 + 36x^14 - 108x^13 + 244x^12 - 424x^11 + 674x^10 - 1804x^9 + 6149x^8 - 16208x^7 + 30950x^6 - 42696x^5 + 41270x^4 - 26632x^3 + 10964x^2 - 2792*x + 388
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			1135.3
Root			$0.343636 + 1.58460i$ of defining polynomial
Character	$\chi$	$=$	2142.1135
Dual form			2142.2.p.h.1891.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.00000i q^{2} -1.00000 q^{4} +(-1.26230 - 1.26230i) q^{5} +(0.707107 - 0.707107i) q^{7} -1.00000i q^{8} +(1.26230 - 1.26230i) q^{10} +(-0.256310 + 0.256310i) q^{11} -7.02105 q^{13} +(0.707107 + 0.707107i) q^{14} +1.00000 q^{16} +(1.73795 - 3.73892i) q^{17} +5.90462i q^{19} +(1.26230 + 1.26230i) q^{20} +(-0.256310 - 0.256310i) q^{22} +(-4.08539 + 4.08539i) q^{23} -1.81321i q^{25} -7.02105i q^{26} +(-0.707107 + 0.707107i) q^{28} +(2.89759 + 2.89759i) q^{29} +(6.39559 + 6.39559i) q^{31} +1.00000i q^{32} +(3.73892 + 1.73795i) q^{34} -1.78516 q^{35} +(3.75382 + 3.75382i) q^{37} -5.90462 q^{38} +(-1.26230 + 1.26230i) q^{40} +(7.96346 - 7.96346i) q^{41} +6.12644i q^{43} +(0.256310 - 0.256310i) q^{44} +(-4.08539 - 4.08539i) q^{46} +12.7093 q^{47} -1.00000i q^{49} +1.81321 q^{50} +7.02105 q^{52} -9.23249i q^{53} +0.647080 q^{55} +(-0.707107 - 0.707107i) q^{56} +(-2.89759 + 2.89759i) q^{58} +4.37397i q^{59} +(1.28967 - 1.28967i) q^{61} +(-6.39559 + 6.39559i) q^{62} -1.00000 q^{64} +(8.86266 + 8.86266i) q^{65} -2.23388 q^{67} +(-1.73795 + 3.73892i) q^{68} -1.78516i q^{70} +(3.98590 + 3.98590i) q^{71} +(4.62068 + 4.62068i) q^{73} +(-3.75382 + 3.75382i) q^{74} -5.90462i q^{76} +0.362477i q^{77} +(6.00332 - 6.00332i) q^{79} +(-1.26230 - 1.26230i) q^{80} +(7.96346 + 7.96346i) q^{82} -9.38309i q^{83} +(-6.91344 + 2.52581i) q^{85} -6.12644 q^{86} +(0.256310 + 0.256310i) q^{88} +13.0683 q^{89} +(-4.96463 + 4.96463i) q^{91} +(4.08539 - 4.08539i) q^{92} +12.7093i q^{94} +(7.45338 - 7.45338i) q^{95} +(6.72848 + 6.72848i) q^{97} +1.00000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 16 q^{4} - 4 q^{11} - 24 q^{13} + 16 q^{16} + 8 q^{17} - 4 q^{22} - 4 q^{29} + 24 q^{31} + 8 q^{34} + 8 q^{35} - 12 q^{37} + 8 q^{38} + 4 q^{44} - 32 q^{47} - 8 q^{50} + 24 q^{52} - 16 q^{55} + 4 q^{58}+ \cdots + 16 q^{98}+O(q^{100}) $ 16 * q - 16 * q^4 - 4 * q^11 - 24 * q^13 + 16 * q^16 + 8 * q^17 - 4 * q^22 - 4 * q^29 + 24 * q^31 + 8 * q^34 + 8 * q^35 - 12 * q^37 + 8 * q^38 + 4 * q^44 - 32 * q^47 - 8 * q^50 + 24 * q^52 - 16 * q^55 + 4 * q^58 - 24 * q^62 - 16 * q^64 + 32 * q^65 - 40 * q^67 - 8 * q^68 - 32 * q^71 + 16 * q^73 + 12 * q^74 - 8 * q^79 + 16 * q^85 + 4 * q^88 + 4 * q^91 + 40 * q^95 + 16 * q^97 + 16 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2142\mathbb{Z}\right)^\times$.

$n$	$1261$	$1667$	$1837$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$		0			0
$3$		0			0
$4$	−1.00000			−0.500000
$5$	−1.26230	−	1.26230i	−0.564517	−	0.564517i	0.366071	−	0.930587i	$-0.380703\pi$
$5$	−1.26230	−	1.26230i	−0.564517	−	0.564517i	−0.930587	+	0.366071i	$0.880703\pi$
$6$		0			0
$7$	0.707107	−	0.707107i	0.267261	−	0.267261i
$7$	0.707107	−	0.707107i	0.267261	−	0.267261i
$8$		−	1.00000i		−	0.353553i
$9$		0			0
$10$	1.26230	−	1.26230i	0.399174	−	0.399174i
$11$	−0.256310	+	0.256310i	−0.0772805	+	0.0772805i	−0.744690	−	0.667410i	$-0.767403\pi$
$11$	−0.256310	+	0.256310i	−0.0772805	+	0.0772805i	0.667410	+	0.744690i	$0.267403\pi$
$12$		0			0
$13$	−7.02105			−1.94729			−0.973645	−	0.228070i	$-0.926759\pi$
$13$	−7.02105			−1.94729			−0.973645	+	0.228070i	$0.926759\pi$
$14$	0.707107	+	0.707107i	0.188982	+	0.188982i
$15$		0			0
$16$	1.00000			0.250000
$17$	1.73795	−	3.73892i	0.421516	−	0.906821i
$17$	1.73795	−	3.73892i	0.421516	−	0.906821i
$18$		0			0
$19$			5.90462i			1.35461i	0.735701	+	0.677306i	$0.236853\pi$
$19$			5.90462i			1.35461i	−0.735701	+	0.677306i	$0.763147\pi$
$20$	1.26230	+	1.26230i	0.282258	+	0.282258i
$21$		0			0
$22$	−0.256310	−	0.256310i	−0.0546455	−	0.0546455i
$23$	−4.08539	+	4.08539i	−0.851863	+	0.851863i	−0.990363	−	0.138499i	$-0.955772\pi$
$23$	−4.08539	+	4.08539i	−0.851863	+	0.851863i	0.138499	+	0.990363i	$0.455772\pi$
$24$		0			0
$25$		−	1.81321i		−	0.362642i
$26$		−	7.02105i		−	1.37694i
$27$		0			0
$28$	−0.707107	+	0.707107i	−0.133631	+	0.133631i
$29$	2.89759	+	2.89759i	0.538070	+	0.538070i	0.922962	−	0.384892i	$-0.125761\pi$
$29$	2.89759	+	2.89759i	0.538070	+	0.538070i	−0.384892	+	0.922962i	$0.625761\pi$
$30$		0			0
$31$	6.39559	+	6.39559i	1.14868	+	1.14868i	0.986812	+	0.161871i	$0.0517528\pi$
$31$	6.39559	+	6.39559i	1.14868	+	1.14868i	0.161871	+	0.986812i	$0.448247\pi$
$32$			1.00000i			0.176777i
$33$		0			0
$34$	3.73892	+	1.73795i	0.641219	+	0.298057i
$35$	−1.78516			−0.301747
$36$		0			0
$37$	3.75382	+	3.75382i	0.617124	+	0.617124i	0.944793	−	0.327669i	$-0.106263\pi$
$37$	3.75382	+	3.75382i	0.617124	+	0.617124i	−0.327669	+	0.944793i	$0.606263\pi$
$38$	−5.90462			−0.957855
$39$		0			0
$40$	−1.26230	+	1.26230i	−0.199587	+	0.199587i
$41$	7.96346	−	7.96346i	1.24368	−	1.24368i	0.285222	−	0.958462i	$-0.407933\pi$
$41$	7.96346	−	7.96346i	1.24368	−	1.24368i	0.958462	−	0.285222i	$-0.0920672\pi$
$42$		0			0
$43$			6.12644i			0.934273i	0.884185	+	0.467137i	$0.154714\pi$
$43$			6.12644i			0.934273i	−0.884185	+	0.467137i	$0.845286\pi$
$44$	0.256310	−	0.256310i	0.0386402	−	0.0386402i
$45$		0			0
$46$	−4.08539	−	4.08539i	−0.602358	−	0.602358i
$47$	12.7093			1.85385			0.926924	−	0.375249i	$-0.122443\pi$
$47$	12.7093			1.85385			0.926924	+	0.375249i	$0.122443\pi$
$48$		0			0
$49$		−	1.00000i		−	0.142857i
$50$	1.81321			0.256427
$51$		0			0
$52$	7.02105			0.973645
$53$		−	9.23249i		−	1.26818i	−0.773259	−	0.634090i	$-0.781375\pi$
$53$		−	9.23249i		−	1.26818i	0.773259	−	0.634090i	$-0.218625\pi$
$54$		0			0
$55$	0.647080			0.0872522
$56$	−0.707107	−	0.707107i	−0.0944911	−	0.0944911i
$57$		0			0
$58$	−2.89759	+	2.89759i	−0.380473	+	0.380473i
$59$			4.37397i			0.569443i	0.958610	+	0.284721i	$0.0919011\pi$
$59$			4.37397i			0.569443i	−0.958610	+	0.284721i	$0.908099\pi$
$60$		0			0
$61$	1.28967	−	1.28967i	0.165125	−	0.165125i	−0.619708	−	0.784833i	$-0.712749\pi$
$61$	1.28967	−	1.28967i	0.165125	−	0.165125i	0.784833	+	0.619708i	$0.212749\pi$
$62$	−6.39559	+	6.39559i	−0.812241	+	0.812241i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	8.86266	+	8.86266i	1.09928	+	1.09928i
$66$		0			0
$67$	−2.23388			−0.272912			−0.136456	−	0.990646i	$-0.543571\pi$
$67$	−2.23388			−0.272912			−0.136456	+	0.990646i	$0.543571\pi$
$68$	−1.73795	+	3.73892i	−0.210758	+	0.453411i
$69$		0			0
$70$		−	1.78516i		−	0.213367i
$71$	3.98590	+	3.98590i	0.473039	+	0.473039i	0.902897	−	0.429858i	$-0.141436\pi$
$71$	3.98590	+	3.98590i	0.473039	+	0.473039i	−0.429858	+	0.902897i	$0.641436\pi$
$72$		0			0
$73$	4.62068	+	4.62068i	0.540809	+	0.540809i	0.923766	−	0.382957i	$-0.125094\pi$
$73$	4.62068	+	4.62068i	0.540809	+	0.540809i	−0.382957	+	0.923766i	$0.625094\pi$
$74$	−3.75382	+	3.75382i	−0.436373	+	0.436373i
$75$		0			0
$76$		−	5.90462i		−	0.677306i
$77$			0.362477i			0.0413081i
$78$		0			0
$79$	6.00332	−	6.00332i	0.675426	−	0.675426i	−0.283535	−	0.958962i	$-0.591507\pi$
$79$	6.00332	−	6.00332i	0.675426	−	0.675426i	0.958962	+	0.283535i	$0.0915073\pi$
$80$	−1.26230	−	1.26230i	−0.141129	−	0.141129i
$81$		0			0
$82$	7.96346	+	7.96346i	0.879417	+	0.879417i
$83$		−	9.38309i		−	1.02993i	−0.857212	−	0.514964i	$-0.827805\pi$
$83$		−	9.38309i		−	1.02993i	0.857212	−	0.514964i	$-0.172195\pi$
$84$		0			0
$85$	−6.91344	+	2.52581i	−0.749868	+	0.273963i
$86$	−6.12644			−0.660631
$87$		0			0
$88$	0.256310	+	0.256310i	0.0273228	+	0.0273228i
$89$	13.0683			1.38524			0.692619	−	0.721303i	$-0.256457\pi$
$89$	13.0683			1.38524			0.692619	+	0.721303i	$0.256457\pi$
$90$		0			0
$91$	−4.96463	+	4.96463i	−0.520435	+	0.520435i
$92$	4.08539	−	4.08539i	0.425932	−	0.425932i
$93$		0			0
$94$			12.7093i			1.31087i
$95$	7.45338	−	7.45338i	0.764701	−	0.764701i
$96$		0			0
$97$	6.72848	+	6.72848i	0.683174	+	0.683174i	0.960714	−	0.277540i	$-0.0895192\pi$
$97$	6.72848	+	6.72848i	0.683174	+	0.683174i	−0.277540	+	0.960714i	$0.589519\pi$
$98$	1.00000			0.101015
$99$		0			0
$100$			1.81321i			0.181321i
$101$	11.7639			1.17055			0.585276	−	0.810834i	$-0.300986\pi$
$101$	11.7639			1.17055			0.585276	+	0.810834i	$0.300986\pi$
$102$		0			0
$103$	−15.4955			−1.52682			−0.763410	−	0.645914i	$-0.776476\pi$
$103$	−15.4955			−1.52682			−0.763410	+	0.645914i	$0.776476\pi$
$104$			7.02105i			0.688471i
$105$		0			0
$106$	9.23249			0.896739
$107$	−4.66108	−	4.66108i	−0.450604	−	0.450604i	0.444951	−	0.895555i	$-0.353221\pi$
$107$	−4.66108	−	4.66108i	−0.450604	−	0.450604i	−0.895555	+	0.444951i	$0.853221\pi$
$108$		0			0
$109$	0.449863	−	0.449863i	0.0430890	−	0.0430890i	−0.685234	−	0.728323i	$-0.740300\pi$
$109$	0.449863	−	0.449863i	0.0430890	−	0.0430890i	0.728323	+	0.685234i	$0.240300\pi$
$110$			0.647080i			0.0616966i
$111$		0			0
$112$	0.707107	−	0.707107i	0.0668153	−	0.0668153i
$113$	−8.79800	+	8.79800i	−0.827646	+	0.827646i	−0.987191	−	0.159545i	$-0.948997\pi$
$113$	−8.79800	+	8.79800i	−0.827646	+	0.827646i	0.159545	+	0.987191i	$0.448997\pi$
$114$		0			0
$115$	10.3140			0.961782
$116$	−2.89759	−	2.89759i	−0.269035	−	0.269035i
$117$		0			0
$118$	−4.37397			−0.402657
$119$	−1.41490	−	3.87273i	−0.129703	−	0.355013i
$120$		0			0
$121$			10.8686i			0.988055i
$122$	1.28967	+	1.28967i	0.116761	+	0.116761i
$123$		0			0
$124$	−6.39559	−	6.39559i	−0.574341	−	0.574341i
$125$	−8.60030	+	8.60030i	−0.769234	+	0.769234i
$126$		0			0
$127$			21.8018i			1.93459i	0.253649	+	0.967296i	$0.418369\pi$
$127$			21.8018i			1.93459i	−0.253649	+	0.967296i	$0.581631\pi$
$128$		−	1.00000i		−	0.0883883i
$129$		0			0
$130$	−8.86266	+	8.86266i	−0.777306	+	0.777306i
$131$	−0.0814023	−	0.0814023i	−0.00711215	−	0.00711215i	0.703542	−	0.710654i	$-0.251601\pi$
$131$	−0.0814023	−	0.0814023i	−0.00711215	−	0.00711215i	−0.710654	+	0.703542i	$0.751601\pi$
$132$		0			0
$133$	4.17520	+	4.17520i	0.362035	+	0.362035i
$134$		−	2.23388i		−	0.192978i
$135$		0			0
$136$	−3.73892	−	1.73795i	−0.320610	−	0.149028i
$137$	−0.499607			−0.0426843			−0.0213421	−	0.999772i	$-0.506794\pi$
$137$	−0.499607			−0.0426843			−0.0213421	+	0.999772i	$0.506794\pi$
$138$		0			0
$139$	6.91600	+	6.91600i	0.586608	+	0.586608i	0.936711	−	0.350103i	$-0.113854\pi$
$139$	6.91600	+	6.91600i	0.586608	+	0.586608i	−0.350103	+	0.936711i	$0.613854\pi$
$140$	1.78516			0.150873
$141$		0			0
$142$	−3.98590	+	3.98590i	−0.334489	+	0.334489i
$143$	1.79957	−	1.79957i	0.150487	−	0.150487i
$144$		0			0
$145$		−	7.31525i		−	0.607498i
$146$	−4.62068	+	4.62068i	−0.382410	+	0.382410i
$147$		0			0
$148$	−3.75382	−	3.75382i	−0.308562	−	0.308562i
$149$	−11.3616			−0.930782			−0.465391	−	0.885105i	$-0.654086\pi$
$149$	−11.3616			−0.930782			−0.465391	+	0.885105i	$0.654086\pi$
$150$		0			0
$151$			8.78206i			0.714674i	0.933975	+	0.357337i	$0.116315\pi$
$151$			8.78206i			0.714674i	−0.933975	+	0.357337i	$0.883685\pi$
$152$	5.90462			0.478928
$153$		0			0
$154$	−0.362477			−0.0292093
$155$		−	16.1463i		−	1.29690i
$156$		0			0
$157$	2.46419			0.196664			0.0983320	−	0.995154i	$-0.468649\pi$
$157$	2.46419			0.196664			0.0983320	+	0.995154i	$0.468649\pi$
$158$	6.00332	+	6.00332i	0.477599	+	0.477599i
$159$		0			0
$160$	1.26230	−	1.26230i	0.0997934	−	0.0997934i
$161$			5.77762i			0.455340i
$162$		0			0
$163$	−10.1778	+	10.1778i	−0.797187	+	0.797187i	−0.982651	−	0.185464i	$-0.940621\pi$
$163$	−10.1778	+	10.1778i	−0.797187	+	0.797187i	0.185464	+	0.982651i	$0.440621\pi$
$164$	−7.96346	+	7.96346i	−0.621842	+	0.621842i
$165$		0			0
$166$	9.38309			0.728269
$167$	9.74825	+	9.74825i	0.754342	+	0.754342i	0.975286	−	0.220944i	$-0.0709139\pi$
$167$	9.74825	+	9.74825i	0.754342	+	0.754342i	−0.220944	+	0.975286i	$0.570914\pi$
$168$		0			0
$169$	36.2952			2.79194
$170$	−2.52581	−	6.91344i	−0.193721	−	0.530237i
$171$		0			0
$172$		−	6.12644i		−	0.467137i
$173$	−11.2812	−	11.2812i	−0.857695	−	0.857695i	0.133371	−	0.991066i	$-0.457420\pi$
$173$	−11.2812	−	11.2812i	−0.857695	−	0.857695i	−0.991066	+	0.133371i	$0.957420\pi$
$174$		0			0
$175$	−1.28213	−	1.28213i	−0.0969202	−	0.0969202i
$176$	−0.256310	+	0.256310i	−0.0193201	+	0.0193201i
$177$		0			0
$178$			13.0683i			0.979511i
$179$			2.00990i			0.150227i	0.997175	+	0.0751134i	$0.0239319\pi$
$179$			2.00990i			0.150227i	−0.997175	+	0.0751134i	$0.976068\pi$
$180$		0			0
$181$	15.0900	−	15.0900i	1.12163	−	1.12163i	0.130135	−	0.991496i	$-0.458459\pi$
$181$	15.0900	−	15.0900i	1.12163	−	1.12163i	0.991496	−	0.130135i	$-0.0415412\pi$
$182$	−4.96463	−	4.96463i	−0.368003	−	0.368003i
$183$		0			0
$184$	4.08539	+	4.08539i	0.301179	+	0.301179i
$185$		−	9.47687i		−	0.696754i
$186$		0			0
$187$	0.512868	+	1.40378i	0.0375046	+	0.102654i
$188$	−12.7093			−0.926924
$189$		0			0
$190$	7.45338	+	7.45338i	0.540725	+	0.540725i
$191$	−8.62703			−0.624230			−0.312115	−	0.950044i	$-0.601037\pi$
$191$	−8.62703			−0.624230			−0.312115	+	0.950044i	$0.601037\pi$
$192$		0			0
$193$	−10.9385	+	10.9385i	−0.787367	+	0.787367i	−0.981062	−	0.193695i	$-0.937953\pi$
$193$	−10.9385	+	10.9385i	−0.787367	+	0.787367i	0.193695	+	0.981062i	$0.437953\pi$
$194$	−6.72848	+	6.72848i	−0.483077	+	0.483077i
$195$		0			0
$196$			1.00000i			0.0714286i
$197$	−10.8246	+	10.8246i	−0.771221	+	0.771221i	−0.978320	−	0.207099i	$-0.933598\pi$
$197$	−10.8246	+	10.8246i	−0.771221	+	0.771221i	0.207099	+	0.978320i	$0.433598\pi$
$198$		0			0
$199$	−9.06251	−	9.06251i	−0.642424	−	0.642424i	0.308727	−	0.951151i	$-0.400097\pi$
$199$	−9.06251	−	9.06251i	−0.642424	−	0.642424i	−0.951151	+	0.308727i	$0.900097\pi$
$200$	−1.81321			−0.128213
$201$		0			0
$202$			11.7639i			0.827706i
$203$	4.09782			0.287610
$204$		0			0
$205$	−20.1045			−1.40416
$206$		−	15.4955i		−	1.07962i
$207$		0			0
$208$	−7.02105			−0.486822
$209$	−1.51341	−	1.51341i	−0.104685	−	0.104685i
$210$		0			0
$211$	10.3530	−	10.3530i	0.712728	−	0.712728i	−0.254377	−	0.967105i	$-0.581871\pi$
$211$	10.3530	−	10.3530i	0.712728	−	0.712728i	0.967105	+	0.254377i	$0.0818706\pi$
$212$			9.23249i			0.634090i
$213$		0			0
$214$	4.66108	−	4.66108i	0.318625	−	0.318625i
$215$	7.73339	−	7.73339i	0.527413	−	0.527413i
$216$		0			0
$217$	9.04474			0.613997
$218$	0.449863	+	0.449863i	0.0304685	+	0.0304685i
$219$		0			0
$220$	−0.647080			−0.0436261
$221$	−12.2023	+	26.2511i	−0.820813	+	1.76584i
$222$		0			0
$223$			14.7723i			0.989228i	0.869113	+	0.494614i	$0.164691\pi$
$223$			14.7723i			0.989228i	−0.869113	+	0.494614i	$0.835309\pi$
$224$	0.707107	+	0.707107i	0.0472456	+	0.0472456i
$225$		0			0
$226$	−8.79800	−	8.79800i	−0.585234	−	0.585234i
$227$	−10.3677	+	10.3677i	−0.688129	+	0.688129i	−0.961818	−	0.273690i	$-0.911756\pi$
$227$	−10.3677	+	10.3677i	−0.688129	+	0.688129i	0.273690	+	0.961818i	$0.411756\pi$
$228$		0			0
$229$		−	19.3079i		−	1.27590i	−0.770078	−	0.637950i	$-0.779783\pi$
$229$		−	19.3079i		−	1.27590i	0.770078	−	0.637950i	$-0.220217\pi$
$230$			10.3140i			0.680083i
$231$		0			0
$232$	2.89759	−	2.89759i	0.190236	−	0.190236i
$233$	11.3972	+	11.3972i	0.746658	+	0.746658i	0.973850	−	0.227192i	$-0.0729544\pi$
$233$	11.3972	+	11.3972i	0.746658	+	0.746658i	−0.227192	+	0.973850i	$0.572954\pi$
$234$		0			0
$235$	−16.0430	−	16.0430i	−1.04653	−	1.04653i
$236$		−	4.37397i		−	0.284721i
$237$		0			0
$238$	3.87273	−	1.41490i	0.251032	−	0.0917141i
$239$	8.31892			0.538106			0.269053	−	0.963125i	$-0.413289\pi$
$239$	8.31892			0.538106			0.269053	+	0.963125i	$0.413289\pi$
$240$		0			0
$241$	−18.4359	−	18.4359i	−1.18756	−	1.18756i	−0.977739	−	0.209824i	$-0.932711\pi$
$241$	−18.4359	−	18.4359i	−1.18756	−	1.18756i	−0.209824	−	0.977739i	$-0.567289\pi$
$242$	−10.8686			−0.698661
$243$		0			0
$244$	−1.28967	+	1.28967i	−0.0825624	+	0.0825624i
$245$	−1.26230	+	1.26230i	−0.0806452	+	0.0806452i
$246$		0			0
$247$		−	41.4566i		−	2.63782i
$248$	6.39559	−	6.39559i	0.406121	−	0.406121i
$249$		0			0
$250$	−8.60030	−	8.60030i	−0.543931	−	0.543931i
$251$	20.3603			1.28513			0.642564	−	0.766232i	$-0.277871\pi$
$251$	20.3603			1.28513			0.642564	+	0.766232i	$0.277871\pi$
$252$		0			0
$253$		−	2.09426i		−	0.131665i
$254$	−21.8018			−1.36796
$255$		0			0
$256$	1.00000			0.0625000
$257$		−	19.5012i		−	1.21645i	−0.793765	−	0.608225i	$-0.791882\pi$
$257$		−	19.5012i		−	1.21645i	0.793765	−	0.608225i	$-0.208118\pi$
$258$		0			0
$259$	5.30870			0.329867
$260$	−8.86266	−	8.86266i	−0.549639	−	0.549639i
$261$		0			0
$262$	0.0814023	−	0.0814023i	0.00502905	−	0.00502905i
$263$		−	15.2627i		−	0.941141i	−0.882363	−	0.470570i	$-0.844048\pi$
$263$		−	15.2627i		−	0.941141i	0.882363	−	0.470570i	$-0.155952\pi$
$264$		0			0
$265$	−11.6541	+	11.6541i	−0.715909	+	0.715909i
$266$	−4.17520	+	4.17520i	−0.255998	+	0.255998i
$267$		0			0
$268$	2.23388			0.136456
$269$	−20.6722	−	20.6722i	−1.26041	−	1.26041i	−0.950897	−	0.309508i	$-0.899836\pi$
$269$	−20.6722	−	20.6722i	−1.26041	−	1.26041i	−0.309508	−	0.950897i	$-0.600164\pi$
$270$		0			0
$271$	−21.6579			−1.31563			−0.657813	−	0.753182i	$-0.728518\pi$
$271$	−21.6579			−1.31563			−0.657813	+	0.753182i	$0.728518\pi$
$272$	1.73795	−	3.73892i	0.105379	−	0.226705i
$273$		0			0
$274$		−	0.499607i		−	0.0301823i
$275$	0.464744	+	0.464744i	0.0280251	+	0.0280251i
$276$		0			0
$277$	5.66374	+	5.66374i	0.340301	+	0.340301i	0.856480	−	0.516179i	$-0.172646\pi$
$277$	5.66374	+	5.66374i	0.340301	+	0.340301i	−0.516179	+	0.856480i	$0.672646\pi$
$278$	−6.91600	+	6.91600i	−0.414794	+	0.414794i
$279$		0			0
$280$			1.78516i			0.106684i
$281$			12.1004i			0.721847i	0.932595	+	0.360923i	$0.117538\pi$
$281$			12.1004i			0.721847i	−0.932595	+	0.360923i	$0.882462\pi$
$282$		0			0
$283$	0.170593	−	0.170593i	0.0101407	−	0.0101407i	−0.702018	−	0.712159i	$-0.747718\pi$
$283$	0.170593	−	0.170593i	0.0101407	−	0.0101407i	0.712159	+	0.702018i	$0.247718\pi$
$284$	−3.98590	−	3.98590i	−0.236519	−	0.236519i
$285$		0			0
$286$	1.79957	+	1.79957i	0.106411	+	0.106411i
$287$		−	11.2620i		−	0.664777i
$288$		0			0
$289$	−10.9590	−	12.9961i	−0.644649	−	0.764479i
$290$	7.31525			0.429566
$291$		0			0
$292$	−4.62068	−	4.62068i	−0.270405	−	0.270405i
$293$	−3.48214			−0.203429			−0.101714	−	0.994814i	$-0.532433\pi$
$293$	−3.48214			−0.203429			−0.101714	+	0.994814i	$0.532433\pi$
$294$		0			0
$295$	5.52125	−	5.52125i	0.321460	−	0.321460i
$296$	3.75382	−	3.75382i	0.218186	−	0.218186i
$297$		0			0
$298$		−	11.3616i		−	0.658162i
$299$	28.6838	−	28.6838i	1.65882	−	1.65882i
$300$		0			0
$301$	4.33205	+	4.33205i	0.249695	+	0.249695i
$302$	−8.78206			−0.505351
$303$		0			0
$304$			5.90462i			0.338653i
$305$	−3.25589			−0.186431
$306$		0			0
$307$	29.2933			1.67186			0.835928	−	0.548839i	$-0.184930\pi$
$307$	29.2933			1.67186			0.835928	+	0.548839i	$0.184930\pi$
$308$		−	0.362477i		−	0.0206541i
$309$		0			0
$310$	16.1463			0.917047
$311$	12.4156	+	12.4156i	0.704025	+	0.704025i	0.965272	−	0.261247i	$-0.0841338\pi$
$311$	12.4156	+	12.4156i	0.704025	+	0.704025i	−0.261247	+	0.965272i	$0.584134\pi$
$312$		0			0
$313$	6.97350	−	6.97350i	0.394166	−	0.394166i	−0.482004	−	0.876169i	$-0.660091\pi$
$313$	6.97350	−	6.97350i	0.394166	−	0.394166i	0.876169	+	0.482004i	$0.160091\pi$
$314$			2.46419i			0.139062i
$315$		0			0
$316$	−6.00332	+	6.00332i	−0.337713	+	0.337713i
$317$	−18.9765	+	18.9765i	−1.06583	+	1.06583i	−0.0681525	+	0.997675i	$0.521710\pi$
$317$	−18.9765	+	18.9765i	−1.06583	+	1.06583i	−0.997675	+	0.0681525i	$0.978290\pi$
$318$		0			0
$319$	−1.48537			−0.0831645
$320$	1.26230	+	1.26230i	0.0705646	+	0.0705646i
$321$		0			0
$322$	−5.77762			−0.321974
$323$	22.0769	+	10.2620i	1.22839	+	0.570990i
$324$		0			0
$325$			12.7306i			0.706169i
$326$	−10.1778	−	10.1778i	−0.563697	−	0.563697i
$327$		0			0
$328$	−7.96346	−	7.96346i	−0.439708	−	0.439708i
$329$	8.98686	−	8.98686i	0.495462	−	0.495462i
$330$		0			0
$331$			5.12997i			0.281969i	0.990012	+	0.140984i	$0.0450267\pi$
$331$			5.12997i			0.281969i	−0.990012	+	0.140984i	$0.954973\pi$
$332$			9.38309i			0.514964i
$333$		0			0
$334$	−9.74825	+	9.74825i	−0.533400	+	0.533400i
$335$	2.81982	+	2.81982i	0.154063	+	0.154063i
$336$		0			0
$337$	2.77812	+	2.77812i	0.151334	+	0.151334i	0.778713	−	0.627380i	$-0.215873\pi$
$337$	2.77812	+	2.77812i	0.151334	+	0.151334i	−0.627380	+	0.778713i	$0.715873\pi$
$338$			36.2952i			1.97420i
$339$		0			0
$340$	6.91344	−	2.52581i	0.374934	−	0.136982i
$341$	−3.27851			−0.177541
$342$		0			0
$343$	−0.707107	−	0.707107i	−0.0381802	−	0.0381802i
$344$	6.12644			0.330316
$345$		0			0
$346$	11.2812	−	11.2812i	0.606482	−	0.606482i
$347$	8.57595	−	8.57595i	0.460381	−	0.460381i	−0.438399	−	0.898780i	$-0.644454\pi$
$347$	8.57595	−	8.57595i	0.460381	−	0.460381i	0.898780	+	0.438399i	$0.144454\pi$
$348$		0			0
$349$		−	0.594539i		−	0.0318249i	−0.999873	−	0.0159125i	$-0.994935\pi$
$349$		−	0.594539i		−	0.0318249i	0.999873	−	0.0159125i	$-0.00506531\pi$
$350$	1.28213	−	1.28213i	0.0685329	−	0.0685329i
$351$		0			0
$352$	−0.256310	−	0.256310i	−0.0136614	−	0.0136614i
$353$	27.2958			1.45281			0.726406	−	0.687266i	$-0.241189\pi$
$353$	27.2958			1.45281			0.726406	+	0.687266i	$0.241189\pi$
$354$		0			0
$355$		−	10.0628i		−	0.534077i
$356$	−13.0683			−0.692619
$357$		0			0
$358$	−2.00990			−0.106226
$359$			15.7415i			0.830802i	0.909638	+	0.415401i	$0.136359\pi$
$359$			15.7415i			0.830802i	−0.909638	+	0.415401i	$0.863641\pi$
$360$		0			0
$361$	−15.8645			−0.834974
$362$	15.0900	+	15.0900i	0.793113	+	0.793113i
$363$		0			0
$364$	4.96463	−	4.96463i	0.260218	−	0.260218i
$365$		−	11.6653i		−	0.610592i
$366$		0			0
$367$	6.22217	−	6.22217i	0.324795	−	0.324795i	−0.525808	−	0.850603i	$-0.676237\pi$
$367$	6.22217	−	6.22217i	0.324795	−	0.324795i	0.850603	+	0.525808i	$0.176237\pi$
$368$	−4.08539	+	4.08539i	−0.212966	+	0.212966i
$369$		0			0
$370$	9.47687			0.492679
$371$	−6.52836	−	6.52836i	−0.338935	−	0.338935i
$372$		0			0
$373$	2.51310			0.130123			0.0650617	−	0.997881i	$-0.479276\pi$
$373$	2.51310			0.130123			0.0650617	+	0.997881i	$0.479276\pi$
$374$	−1.40378	+	0.512868i	−0.0725877	+	0.0265198i
$375$		0			0
$376$		−	12.7093i		−	0.655434i
$377$	−20.3442	−	20.3442i	−1.04778	−	1.04778i
$378$		0			0
$379$	14.8107	+	14.8107i	0.760772	+	0.760772i	0.976462	−	0.215690i	$-0.0691999\pi$
$379$	14.8107	+	14.8107i	0.760772	+	0.760772i	−0.215690	+	0.976462i	$0.569200\pi$
$380$	−7.45338	+	7.45338i	−0.382351	+	0.382351i
$381$		0			0
$382$		−	8.62703i		−	0.441397i
$383$			35.6542i			1.82184i	0.412580	+	0.910921i	$0.364628\pi$
$383$			35.6542i			1.82184i	−0.412580	+	0.910921i	$0.635372\pi$
$384$		0			0
$385$	0.457554	−	0.457554i	0.0233191	−	0.0233191i
$386$	−10.9385	−	10.9385i	−0.556752	−	0.556752i
$387$		0			0
$388$	−6.72848	−	6.72848i	−0.341587	−	0.341587i
$389$			26.6867i			1.35307i	0.736411	+	0.676534i	$0.236519\pi$
$389$			26.6867i			1.35307i	−0.736411	+	0.676534i	$0.763481\pi$
$390$		0			0
$391$	8.17473	+	22.3752i	0.413414	+	1.13156i
$392$	−1.00000			−0.0505076
$393$		0			0
$394$	−10.8246	−	10.8246i	−0.545336	−	0.545336i
$395$	−15.1560			−0.762579
$396$		0			0
$397$	−23.2453	+	23.2453i	−1.16665	+	1.16665i	−0.183656	+	0.982991i	$0.558793\pi$
$397$	−23.2453	+	23.2453i	−1.16665	+	1.16665i	−0.982991	+	0.183656i	$0.941207\pi$
$398$	9.06251	−	9.06251i	0.454262	−	0.454262i
$399$		0			0
$400$		−	1.81321i		−	0.0906605i
$401$	−4.94397	+	4.94397i	−0.246890	+	0.246890i	−0.819693	−	0.572803i	$-0.805856\pi$
$401$	−4.94397	+	4.94397i	−0.246890	+	0.246890i	0.572803	+	0.819693i	$0.305856\pi$
$402$		0			0
$403$	−44.9038	−	44.9038i	−2.23682	−	2.23682i
$404$	−11.7639			−0.585276
$405$		0			0
$406$			4.09782i			0.203371i
$407$	−1.92428			−0.0953833
$408$		0			0
$409$	24.4249			1.20773			0.603867	−	0.797085i	$-0.293626\pi$
$409$	24.4249			1.20773			0.603867	+	0.797085i	$0.293626\pi$
$410$		−	20.1045i		−	0.992891i
$411$		0			0
$412$	15.4955			0.763410
$413$	3.09287	+	3.09287i	0.152190	+	0.152190i
$414$		0			0
$415$	−11.8443	+	11.8443i	−0.581411	+	0.581411i
$416$		−	7.02105i		−	0.344235i
$417$		0			0
$418$	1.51341	−	1.51341i	0.0740235	−	0.0740235i
$419$	−8.83294	+	8.83294i	−0.431517	+	0.431517i	−0.889144	−	0.457627i	$-0.848700\pi$
$419$	−8.83294	+	8.83294i	−0.431517	+	0.431517i	0.457627	+	0.889144i	$0.348700\pi$
$420$		0			0
$421$	0.570702			0.0278143			0.0139071	−	0.999903i	$-0.495573\pi$
$421$	0.570702			0.0278143			0.0139071	+	0.999903i	$0.495573\pi$
$422$	10.3530	+	10.3530i	0.503974	+	0.503974i
$423$		0			0
$424$	−9.23249			−0.448369
$425$	−6.77945	−	3.15127i	−0.328851	−	0.152859i
$426$		0			0
$427$		−	1.82386i		−	0.0882630i
$428$	4.66108	+	4.66108i	0.225302	+	0.225302i
$429$		0			0
$430$	7.73339	+	7.73339i	0.372937	+	0.372937i
$431$	25.5324	−	25.5324i	1.22985	−	1.22985i	0.265835	−	0.964018i	$-0.414352\pi$
$431$	25.5324	−	25.5324i	1.22985	−	1.22985i	0.964018	−	0.265835i	$-0.0856478\pi$
$432$		0			0
$433$		−	4.54033i		−	0.218194i	−0.994031	−	0.109097i	$-0.965204\pi$
$433$		−	4.54033i		−	0.218194i	0.994031	−	0.109097i	$-0.0347960\pi$
$434$			9.04474i			0.434161i
$435$		0			0
$436$	−0.449863	+	0.449863i	−0.0215445	+	0.0215445i
$437$	−24.1227	−	24.1227i	−1.15394	−	1.15394i
$438$		0			0
$439$	4.10702	+	4.10702i	0.196017	+	0.196017i	0.798290	−	0.602273i	$-0.205738\pi$
$439$	4.10702	+	4.10702i	0.196017	+	0.196017i	−0.602273	+	0.798290i	$0.705738\pi$
$440$		−	0.647080i		−	0.0308483i
$441$		0			0
$442$	−26.2511	−	12.2023i	−1.24864	−	0.580402i
$443$	34.5919			1.64351			0.821755	−	0.569841i	$-0.192995\pi$
$443$	34.5919			1.64351			0.821755	+	0.569841i	$0.192995\pi$
$444$		0			0
$445$	−16.4961	−	16.4961i	−0.781990	−	0.781990i
$446$	−14.7723			−0.699490
$447$		0			0
$448$	−0.707107	+	0.707107i	−0.0334077	+	0.0334077i
$449$	4.26160	−	4.26160i	0.201117	−	0.201117i	−0.599361	−	0.800479i	$-0.704579\pi$
$449$	4.26160	−	4.26160i	0.201117	−	0.201117i	0.800479	+	0.599361i	$0.204579\pi$
$450$		0			0
$451$			4.08223i			0.192225i
$452$	8.79800	−	8.79800i	0.413823	−	0.413823i
$453$		0			0
$454$	−10.3677	−	10.3677i	−0.486580	−	0.486580i
$455$	12.5337			0.587588
$456$		0			0
$457$		−	39.3436i		−	1.84042i	−0.391427	−	0.920209i	$-0.628019\pi$
$457$		−	39.3436i		−	1.84042i	0.391427	−	0.920209i	$-0.371981\pi$
$458$	19.3079			0.902198
$459$		0			0
$460$	−10.3140			−0.480891
$461$			34.4718i			1.60551i	0.596308	+	0.802756i	$0.296634\pi$
$461$			34.4718i			1.60551i	−0.596308	+	0.802756i	$0.703366\pi$
$462$		0			0
$463$	−2.39896			−0.111489			−0.0557446	−	0.998445i	$-0.517753\pi$
$463$	−2.39896			−0.111489			−0.0557446	+	0.998445i	$0.517753\pi$
$464$	2.89759	+	2.89759i	0.134517	+	0.134517i
$465$		0			0
$466$	−11.3972	+	11.3972i	−0.527967	+	0.527967i
$467$		−	24.3491i		−	1.12674i	−0.826203	−	0.563372i	$-0.809504\pi$
$467$		−	24.3491i		−	1.12674i	0.826203	−	0.563372i	$-0.190496\pi$
$468$		0			0
$469$	−1.57959	+	1.57959i	−0.0729387	+	0.0729387i
$470$	16.0430	−	16.0430i	0.740007	−	0.740007i
$471$		0			0
$472$	4.37397			0.201328
$473$	−1.57027	−	1.57027i	−0.0722011	−	0.0722011i
$474$		0			0
$475$	10.7063			0.491239
$476$	1.41490	+	3.87273i	0.0648517	+	0.177506i
$477$		0			0
$478$			8.31892i			0.380498i
$479$	5.89635	+	5.89635i	0.269411	+	0.269411i	0.828863	−	0.559452i	$-0.188988\pi$
$479$	5.89635	+	5.89635i	0.269411	+	0.269411i	−0.559452	+	0.828863i	$0.688988\pi$
$480$		0			0
$481$	−26.3558	−	26.3558i	−1.20172	−	1.20172i
$482$	18.4359	−	18.4359i	0.839734	−	0.839734i
$483$		0			0
$484$		−	10.8686i		−	0.494028i
$485$		−	16.9867i		−	0.771326i
$486$		0			0
$487$	16.7497	−	16.7497i	0.759000	−	0.759000i	−0.217140	−	0.976140i	$-0.569673\pi$
$487$	16.7497	−	16.7497i	0.759000	−	0.759000i	0.976140	+	0.217140i	$0.0696729\pi$
$488$	−1.28967	−	1.28967i	−0.0583805	−	0.0583805i
$489$		0			0
$490$	−1.26230	−	1.26230i	−0.0570248	−	0.0570248i
$491$			13.6628i			0.616593i	0.951290	+	0.308297i	$0.0997590\pi$
$491$			13.6628i			0.616593i	−0.951290	+	0.308297i	$0.900241\pi$
$492$		0			0
$493$	15.8698	−	5.79799i	0.714738	−	0.261128i
$494$	41.4566			1.86522
$495$		0			0
$496$	6.39559	+	6.39559i	0.287171	+	0.287171i
$497$	5.63691			0.252850
$498$		0			0
$499$	−4.38730	+	4.38730i	−0.196402	+	0.196402i	−0.798456	−	0.602053i	$-0.794349\pi$
$499$	−4.38730	+	4.38730i	−0.196402	+	0.196402i	0.602053	+	0.798456i	$0.294349\pi$
$500$	8.60030	−	8.60030i	0.384617	−	0.384617i
$501$		0			0
$502$			20.3603i			0.908723i
$503$	3.82151	−	3.82151i	0.170393	−	0.170393i	−0.616759	−	0.787152i	$-0.711555\pi$
$503$	3.82151	−	3.82151i	0.170393	−	0.170393i	0.787152	+	0.616759i	$0.211555\pi$
$504$		0			0
$505$	−14.8496	−	14.8496i	−0.660796	−	0.660796i
$506$	2.09426			0.0931011
$507$		0			0
$508$		−	21.8018i		−	0.967296i
$509$	−17.2922			−0.766464			−0.383232	−	0.923652i	$-0.625189\pi$
$509$	−17.2922			−0.766464			−0.383232	+	0.923652i	$0.625189\pi$
$510$		0			0
$511$	6.53462			0.289075
$512$			1.00000i			0.0441942i
$513$		0			0
$514$	19.5012			0.860160
$515$	19.5600	+	19.5600i	0.861915	+	0.861915i
$516$		0			0
$517$	−3.25754	+	3.25754i	−0.143266	+	0.143266i
$518$			5.30870i			0.233251i
$519$		0			0
$520$	8.86266	−	8.86266i	0.388653	−	0.388653i
$521$	21.2438	−	21.2438i	0.930707	−	0.930707i	−0.0670431	−	0.997750i	$-0.521356\pi$
$521$	21.2438	−	21.2438i	0.930707	−	0.930707i	0.997750	+	0.0670431i	$0.0213565\pi$
$522$		0			0
$523$	−0.0942759			−0.00412240			−0.00206120	−	0.999998i	$-0.500656\pi$
$523$	−0.0942759			−0.00412240			−0.00206120	+	0.999998i	$0.500656\pi$
$524$	0.0814023	+	0.0814023i	0.00355607	+	0.00355607i
$525$		0			0
$526$	15.2627			0.665487
$527$	35.0279	−	12.7974i	1.52584	−	0.557462i
$528$		0			0
$529$		−	10.3809i		−	0.451342i
$530$	−11.6541	−	11.6541i	−0.506224	−	0.506224i
$531$		0			0
$532$	−4.17520	−	4.17520i	−0.181018	−	0.181018i
$533$	−55.9119	+	55.9119i	−2.42181	+	2.42181i
$534$		0			0
$535$			11.7674i			0.508747i
$536$			2.23388i			0.0964888i
$537$		0			0
$538$	20.6722	−	20.6722i	0.891241	−	0.891241i
$539$	0.256310	+	0.256310i	0.0110401	+	0.0110401i
$540$		0			0
$541$	−0.162766	−	0.162766i	−0.00699785	−	0.00699785i	0.703599	−	0.710597i	$-0.251575\pi$
$541$	−0.162766	−	0.162766i	−0.00699785	−	0.00699785i	−0.710597	+	0.703599i	$0.751575\pi$
$542$		−	21.6579i		−	0.930288i
$543$		0			0
$544$	3.73892	+	1.73795i	0.160305	+	0.0745141i
$545$	−1.13572			−0.0486489
$546$		0			0
$547$	−12.7921	−	12.7921i	−0.546951	−	0.546951i	0.378606	−	0.925558i	$-0.376403\pi$
$547$	−12.7921	−	12.7921i	−0.546951	−	0.546951i	−0.925558	+	0.378606i	$0.876403\pi$
$548$	0.499607			0.0213421
$549$		0			0
$550$	−0.464744	+	0.464744i	−0.0198168	+	0.0198168i
$551$	−17.1092	+	17.1092i	−0.728876	+	0.728876i
$552$		0			0
$553$		−	8.48998i		−	0.361031i
$554$	−5.66374	+	5.66374i	−0.240629	+	0.240629i
$555$		0			0
$556$	−6.91600	−	6.91600i	−0.293304	−	0.293304i
$557$	−7.62887			−0.323245			−0.161623	−	0.986853i	$-0.551673\pi$
$557$	−7.62887			−0.323245			−0.161623	+	0.986853i	$0.551673\pi$
$558$		0			0
$559$		−	43.0141i		−	1.81930i
$560$	−1.78516			−0.0754367
$561$		0			0
$562$	−12.1004			−0.510423
$563$			7.74927i			0.326593i	0.986577	+	0.163296i	$0.0522127\pi$
$563$			7.74927i			0.326593i	−0.986577	+	0.163296i	$0.947787\pi$
$564$		0			0
$565$	22.2114			0.934440
$566$	0.170593	+	0.170593i	0.00717057	+	0.00717057i
$567$		0			0
$568$	3.98590	−	3.98590i	0.167244	−	0.167244i
$569$		−	33.8165i		−	1.41766i	−0.705380	−	0.708830i	$-0.749223\pi$
$569$		−	33.8165i		−	1.41766i	0.705380	−	0.708830i	$-0.250777\pi$
$570$		0			0
$571$	−32.9181	+	32.9181i	−1.37758	+	1.37758i	−0.528885	+	0.848694i	$0.677390\pi$
$571$	−32.9181	+	32.9181i	−1.37758	+	1.37758i	−0.848694	+	0.528885i	$0.822610\pi$
$572$	−1.79957	+	1.79957i	−0.0752437	+	0.0752437i
$573$		0			0
$574$	11.2620			0.470068
$575$	7.40768	+	7.40768i	0.308921	+	0.308921i
$576$		0			0
$577$	40.5091			1.68642			0.843208	−	0.537587i	$-0.180664\pi$
$577$	40.5091			1.68642			0.843208	+	0.537587i	$0.180664\pi$
$578$	12.9961	−	10.9590i	0.540568	−	0.455836i
$579$		0			0
$580$			7.31525i			0.303749i
$581$	−6.63485	−	6.63485i	−0.275260	−	0.275260i
$582$		0			0
$583$	2.36638	+	2.36638i	0.0980055	+	0.0980055i
$584$	4.62068	−	4.62068i	0.191205	−	0.191205i
$585$		0			0
$586$		−	3.48214i		−	0.143846i
$587$		−	13.2004i		−	0.544837i	−0.962179	−	0.272418i	$-0.912176\pi$
$587$		−	13.2004i		−	0.544837i	0.962179	−	0.272418i	$-0.0878235\pi$
$588$		0			0
$589$	−37.7635	+	37.7635i	−1.55602	+	1.55602i
$590$	5.52125	+	5.52125i	0.227306	+	0.227306i
$591$		0			0
$592$	3.75382	+	3.75382i	0.154281	+	0.154281i
$593$			28.4113i			1.16671i	0.812216	+	0.583357i	$0.198261\pi$
$593$			28.4113i			1.16671i	−0.812216	+	0.583357i	$0.801739\pi$
$594$		0			0
$595$	−3.10252	+	6.67456i	−0.127191	+	0.273630i
$596$	11.3616			0.465391
$597$		0			0
$598$	28.6838	+	28.6838i	1.17297	+	1.17297i
$599$	−14.3208			−0.585132			−0.292566	−	0.956245i	$-0.594509\pi$
$599$	−14.3208			−0.585132			−0.292566	+	0.956245i	$0.594509\pi$
$600$		0			0
$601$	−9.92695	+	9.92695i	−0.404929	+	0.404929i	−0.879966	−	0.475037i	$-0.842435\pi$
$601$	−9.92695	+	9.92695i	−0.404929	+	0.404929i	0.475037	+	0.879966i	$0.342435\pi$
$602$	−4.33205	+	4.33205i	−0.176561	+	0.176561i
$603$		0			0
$604$		−	8.78206i		−	0.357337i
$605$	13.7194	−	13.7194i	0.557774	−	0.557774i
$606$		0			0
$607$	−3.04883	−	3.04883i	−0.123748	−	0.123748i	0.642520	−	0.766269i	$-0.277889\pi$
$607$	−3.04883	−	3.04883i	−0.123748	−	0.123748i	−0.766269	+	0.642520i	$0.777889\pi$
$608$	−5.90462			−0.239464
$609$		0			0
$610$		−	3.25589i		−	0.131827i
$611$	−89.2330			−3.60998
$612$		0			0
$613$	−44.9795			−1.81670			−0.908352	−	0.418207i	$-0.862659\pi$
$613$	−44.9795			−1.81670			−0.908352	+	0.418207i	$0.862659\pi$
$614$			29.2933i			1.18218i
$615$		0			0
$616$	0.362477			0.0146046
$617$	−11.7456	−	11.7456i	−0.472862	−	0.472862i	0.429978	−	0.902840i	$-0.358521\pi$
$617$	−11.7456	−	11.7456i	−0.472862	−	0.472862i	−0.902840	+	0.429978i	$0.858521\pi$
$618$		0			0
$619$	17.8630	−	17.8630i	0.717974	−	0.717974i	−0.250216	−	0.968190i	$-0.580502\pi$
$619$	17.8630	−	17.8630i	0.717974	−	0.717974i	0.968190	+	0.250216i	$0.0805017\pi$
$620$			16.1463i			0.648450i
$621$		0			0
$622$	−12.4156	+	12.4156i	−0.497821	+	0.497821i
$623$	9.24069	−	9.24069i	0.370221	−	0.370221i
$624$		0			0
$625$	12.6462			0.505849
$626$	6.97350	+	6.97350i	0.278717	+	0.278717i
$627$		0			0
$628$	−2.46419			−0.0983320
$629$	20.5592	−	7.51126i	0.819749	−	0.299494i
$630$		0			0
$631$			3.53435i			0.140700i	0.997522	+	0.0703501i	$0.0224116\pi$
$631$			3.53435i			0.140700i	−0.997522	+	0.0703501i	$0.977588\pi$
$632$	−6.00332	−	6.00332i	−0.238799	−	0.238799i
$633$		0			0
$634$	−18.9765	−	18.9765i	−0.753654	−	0.753654i
$635$	27.5203	−	27.5203i	1.09211	−	1.09211i
$636$		0			0
$637$			7.02105i			0.278184i
$638$		−	1.48537i		−	0.0588062i
$639$		0			0
$640$	−1.26230	+	1.26230i	−0.0498967	+	0.0498967i
$641$	1.94227	+	1.94227i	0.0767150	+	0.0767150i	0.744423	−	0.667708i	$-0.232725\pi$
$641$	1.94227	+	1.94227i	0.0767150	+	0.0767150i	−0.667708	+	0.744423i	$0.732725\pi$
$642$		0			0
$643$	13.4629	+	13.4629i	0.530924	+	0.530924i	0.920847	−	0.389923i	$-0.127499\pi$
$643$	13.4629	+	13.4629i	0.530924	+	0.530924i	−0.389923	+	0.920847i	$0.627499\pi$
$644$		−	5.77762i		−	0.227670i
$645$		0			0
$646$	−10.2620	+	22.0769i	−0.403751	+	0.868604i
$647$	−20.4010			−0.802047			−0.401024	−	0.916068i	$-0.631345\pi$
$647$	−20.4010			−0.802047			−0.401024	+	0.916068i	$0.631345\pi$
$648$		0			0
$649$	−1.12109	−	1.12109i	−0.0440068	−	0.0440068i
$650$	−12.7306			−0.499337
$651$		0			0
$652$	10.1778	−	10.1778i	0.398594	−	0.398594i
$653$	30.4618	−	30.4618i	1.19206	−	1.19206i	0.215575	−	0.976487i	$-0.430838\pi$
$653$	30.4618	−	30.4618i	1.19206	−	1.19206i	0.976487	−	0.215575i	$-0.0691624\pi$
$654$		0			0
$655$			0.205508i			0.00802985i
$656$	7.96346	−	7.96346i	0.310921	−	0.310921i
$657$		0			0
$658$	8.98686	+	8.98686i	0.350344	+	0.350344i
$659$	12.4422			0.484678			0.242339	−	0.970192i	$-0.422085\pi$
$659$	12.4422			0.484678			0.242339	+	0.970192i	$0.422085\pi$
$660$		0			0
$661$			20.2314i			0.786911i	0.919344	+	0.393456i	$0.128720\pi$
$661$			20.2314i			0.786911i	−0.919344	+	0.393456i	$0.871280\pi$
$662$	−5.12997			−0.199382
$663$		0			0
$664$	−9.38309			−0.364135
$665$		−	10.5407i		−	0.408750i
$666$		0			0
$667$	−23.6756			−0.916723
$668$	−9.74825	−	9.74825i	−0.377171	−	0.377171i
$669$		0			0
$670$	−2.81982	+	2.81982i	−0.108939	+	0.108939i
$671$			0.661110i			0.0255219i
$672$		0			0
$673$	24.3330	−	24.3330i	0.937970	−	0.937970i	−0.0602153	−	0.998185i	$-0.519179\pi$
$673$	24.3330	−	24.3330i	0.937970	−	0.937970i	0.998185	+	0.0602153i	$0.0191787\pi$
$674$	−2.77812	+	2.77812i	−0.107009	+	0.107009i
$675$		0			0
$676$	−36.2952			−1.39597
$677$	−7.19287	−	7.19287i	−0.276444	−	0.276444i	0.555243	−	0.831688i	$-0.312625\pi$
$677$	−7.19287	−	7.19287i	−0.276444	−	0.276444i	−0.831688	+	0.555243i	$0.812625\pi$
$678$		0			0
$679$	9.51551			0.365172
$680$	2.52581	+	6.91344i	0.0968606	+	0.265118i
$681$		0			0
$682$		−	3.27851i		−	0.125541i
$683$	−12.4713	−	12.4713i	−0.477202	−	0.477202i	0.427034	−	0.904236i	$-0.359559\pi$
$683$	−12.4713	−	12.4713i	−0.477202	−	0.477202i	−0.904236	+	0.427034i	$0.859559\pi$
$684$		0			0
$685$	0.630652	+	0.630652i	0.0240960	+	0.0240960i
$686$	0.707107	−	0.707107i	0.0269975	−	0.0269975i
$687$		0			0
$688$			6.12644i			0.233568i
$689$			64.8218i			2.46951i
$690$		0			0
$691$	31.3551	−	31.3551i	1.19280	−	1.19280i	0.216526	−	0.976277i	$-0.430527\pi$
$691$	31.3551	−	31.3551i	1.19280	−	1.19280i	0.976277	−	0.216526i	$-0.0694727\pi$
$692$	11.2812	+	11.2812i	0.428848	+	0.428848i
$693$		0			0
$694$	8.57595	+	8.57595i	0.325539	+	0.325539i
$695$		−	17.4601i		−	0.662300i
$696$		0			0
$697$	−15.9346	−	43.6148i	−0.603566	−	1.65203i
$698$	0.594539			0.0225036
$699$		0			0
$700$	1.28213	+	1.28213i	0.0484601	+	0.0484601i
$701$	−5.31490			−0.200741			−0.100370	−	0.994950i	$-0.532003\pi$
$701$	−5.31490			−0.200741			−0.100370	+	0.994950i	$0.532003\pi$
$702$		0			0
$703$	−22.1649	+	22.1649i	−0.835964	+	0.835964i
$704$	0.256310	−	0.256310i	0.00966006	−	0.00966006i
$705$		0			0
$706$			27.2958i			1.02729i
$707$	8.31834	−	8.31834i	0.312843	−	0.312843i
$708$		0			0
$709$	35.3451	+	35.3451i	1.32741	+	1.32741i	0.907621	+	0.419792i	$0.137897\pi$
$709$	35.3451	+	35.3451i	1.32741	+	1.32741i	0.419792	+	0.907621i	$0.362103\pi$
$710$	10.0628			0.377649
$711$		0			0
$712$		−	13.0683i		−	0.489756i
$713$	−52.2570			−1.95704
$714$		0			0
$715$	−4.54318			−0.169905
$716$		−	2.00990i		−	0.0751134i
$717$		0			0
$718$	−15.7415			−0.587466
$719$	4.49360	+	4.49360i	0.167583	+	0.167583i	0.785916	−	0.618333i	$-0.212192\pi$
$719$	4.49360	+	4.49360i	0.167583	+	0.167583i	−0.618333	+	0.785916i	$0.712192\pi$
$720$		0			0
$721$	−10.9570	+	10.9570i	−0.408060	+	0.408060i
$722$		−	15.8645i		−	0.590416i
$723$		0			0
$724$	−15.0900	+	15.0900i	−0.560816	+	0.560816i
$725$	5.25395	−	5.25395i	0.195127	−	0.195127i
$726$		0			0
$727$	41.1826			1.52738			0.763689	−	0.645584i	$-0.223386\pi$
$727$	41.1826			1.52738			0.763689	+	0.645584i	$0.223386\pi$
$728$	4.96463	+	4.96463i	0.184002	+	0.184002i
$729$		0			0
$730$	11.6653			0.431753
$731$	22.9063	+	10.6475i	0.847219	+	0.393811i
$732$		0			0
$733$		−	9.83517i		−	0.363270i	−0.983366	−	0.181635i	$-0.941861\pi$
$733$		−	9.83517i		−	0.363270i	0.983366	−	0.181635i	$-0.0581390\pi$
$734$	6.22217	+	6.22217i	0.229664	+	0.229664i
$735$		0			0
$736$	−4.08539	−	4.08539i	−0.150590	−	0.150590i
$737$	0.572566	−	0.572566i	0.0210907	−	0.0210907i
$738$		0			0
$739$		−	22.4548i		−	0.826015i	−0.910728	−	0.413007i	$-0.864478\pi$
$739$		−	22.4548i		−	0.826015i	0.910728	−	0.413007i	$-0.135522\pi$
$740$			9.47687i			0.348377i
$741$		0			0
$742$	6.52836	−	6.52836i	0.239663	−	0.239663i
$743$	−28.9164	−	28.9164i	−1.06084	−	1.06084i	−0.998025	−	0.0628155i	$-0.979992\pi$
$743$	−28.9164	−	28.9164i	−1.06084	−	1.06084i	−0.0628155	−	0.998025i	$-0.520008\pi$
$744$		0			0
$745$	14.3418	+	14.3418i	0.525442	+	0.525442i
$746$			2.51310i			0.0920111i
$747$		0			0
$748$	−0.512868	−	1.40378i	−0.0187523	−	0.0513272i
$749$	−6.59177			−0.240858
$750$		0			0
$751$	−1.73255	−	1.73255i	−0.0632218	−	0.0632218i	0.674789	−	0.738011i	$-0.264235\pi$
$751$	−1.73255	−	1.73255i	−0.0632218	−	0.0632218i	−0.738011	+	0.674789i	$0.764235\pi$
$752$	12.7093			0.463462
$753$		0			0
$754$	20.3442	−	20.3442i	0.740890	−	0.740890i
$755$	11.0856	−	11.0856i	0.403445	−	0.403445i
$756$		0			0
$757$			23.6189i			0.858445i	0.903199	+	0.429222i	$0.141212\pi$
$757$			23.6189i			0.858445i	−0.903199	+	0.429222i	$0.858788\pi$
$758$	−14.8107	+	14.8107i	−0.537947	+	0.537947i
$759$		0			0
$760$	−7.45338	−	7.45338i	−0.270363	−	0.270363i
$761$	30.4905			1.10528			0.552639	−	0.833421i	$-0.313621\pi$
$761$	30.4905			1.10528			0.552639	+	0.833421i	$0.313621\pi$
$762$		0			0
$763$		−	0.636202i		−	0.0230321i
$764$	8.62703			0.312115
$765$		0			0
$766$	−35.6542			−1.28824
$767$		−	30.7099i		−	1.10887i
$768$		0			0
$769$	−1.17195			−0.0422614			−0.0211307	−	0.999777i	$-0.506727\pi$
$769$	−1.17195			−0.0422614			−0.0211307	+	0.999777i	$0.506727\pi$
$770$	0.457554	+	0.457554i	0.0164891	+	0.0164891i
$771$		0			0
$772$	10.9385	−	10.9385i	0.393683	−	0.393683i
$773$			4.60742i			0.165718i	0.996561	+	0.0828588i	$0.0264050\pi$
$773$			4.60742i			0.165718i	−0.996561	+	0.0828588i	$0.973595\pi$
$774$		0			0
$775$	11.5966	−	11.5966i	0.416561	−	0.416561i
$776$	6.72848	−	6.72848i	0.241538	−	0.241538i
$777$		0			0
$778$	−26.6867			−0.956764
$779$	47.0212	+	47.0212i	1.68471	+	1.68471i
$780$		0			0
$781$	−2.04325			−0.0731133
$782$	−22.3752	+	8.17473i	−0.800135	+	0.292328i
$783$		0			0
$784$		−	1.00000i		−	0.0357143i
$785$	−3.11055	−	3.11055i	−0.111020	−	0.111020i
$786$		0			0
$787$	−16.7085	−	16.7085i	−0.595595	−	0.595595i	0.343542	−	0.939137i	$-0.388373\pi$
$787$	−16.7085	−	16.7085i	−0.595595	−	0.595595i	−0.939137	+	0.343542i	$0.888373\pi$
$788$	10.8246	−	10.8246i	0.385611	−	0.385611i
$789$		0			0
$790$		−	15.1560i		−	0.539225i
$791$			12.4422i			0.442395i
$792$		0			0
$793$	−9.05482	+	9.05482i	−0.321546	+	0.321546i
$794$	−23.2453	−	23.2453i	−0.824944	−	0.824944i
$795$		0			0
$796$	9.06251	+	9.06251i	0.321212	+	0.321212i
$797$			15.9167i			0.563797i	0.959444	+	0.281899i	$0.0909642\pi$
$797$			15.9167i			0.563797i	−0.959444	+	0.281899i	$0.909036\pi$
$798$		0			0
$799$	22.0882	−	47.5192i	0.781426	−	1.68111i
$800$	1.81321			0.0641067
$801$		0			0
$802$	−4.94397	−	4.94397i	−0.174578	−	0.174578i
$803$	−2.36865			−0.0835880
$804$		0			0
$805$	7.29307	−	7.29307i	0.257047	−	0.257047i
$806$	44.9038	−	44.9038i	1.58167	−	1.58167i
$807$		0			0
$808$		−	11.7639i		−	0.413853i
$809$	−19.9363	+	19.9363i	−0.700923	+	0.700923i	−0.964609	−	0.263686i	$-0.915062\pi$
$809$	−19.9363	+	19.9363i	−0.700923	+	0.700923i	0.263686	+	0.964609i	$0.415062\pi$
$810$		0			0
$811$	−25.3306	−	25.3306i	−0.889477	−	0.889477i	0.104996	−	0.994473i	$-0.466517\pi$
$811$	−25.3306	−	25.3306i	−0.889477	−	0.889477i	−0.994473	+	0.104996i	$0.966517\pi$
$812$	−4.09782			−0.143805
$813$		0			0
$814$		−	1.92428i		−	0.0674462i
$815$	25.6948			0.900051
$816$		0			0
$817$	−36.1743			−1.26558
$818$			24.4249i			0.853996i
$819$		0			0
$820$	20.1045			0.702080
$821$	17.8482	+	17.8482i	0.622908	+	0.622908i	0.946274	−	0.323366i	$-0.104815\pi$
$821$	17.8482	+	17.8482i	0.622908	+	0.622908i	−0.323366	+	0.946274i	$0.604815\pi$
$822$		0			0
$823$	10.3518	−	10.3518i	0.360842	−	0.360842i	−0.503281	−	0.864123i	$-0.667874\pi$
$823$	10.3518	−	10.3518i	0.360842	−	0.360842i	0.864123	+	0.503281i	$0.167874\pi$
$824$			15.4955i			0.539812i
$825$		0			0
$826$	−3.09287	+	3.09287i	−0.107615	+	0.107615i
$827$	−26.0979	+	26.0979i	−0.907512	+	0.907512i	−0.996071	−	0.0885592i	$-0.971774\pi$
$827$	−26.0979	+	26.0979i	−0.907512	+	0.907512i	0.0885592	+	0.996071i	$0.471774\pi$
$828$		0			0
$829$	8.45739			0.293737			0.146869	−	0.989156i	$-0.453081\pi$
$829$	8.45739			0.293737			0.146869	+	0.989156i	$0.453081\pi$
$830$	−11.8443	−	11.8443i	−0.411120	−	0.411120i
$831$		0			0
$832$	7.02105			0.243411
$833$	−3.73892	−	1.73795i	−0.129546	−	0.0602165i
$834$		0			0
$835$		−	24.6104i		−	0.851677i
$836$	1.51341	+	1.51341i	0.0523425	+	0.0523425i
$837$		0			0
$838$	−8.83294	−	8.83294i	−0.305129	−	0.305129i
$839$	−20.0774	+	20.0774i	−0.693150	+	0.693150i	−0.962924	−	0.269774i	$-0.913051\pi$
$839$	−20.0774	+	20.0774i	−0.693150	+	0.693150i	0.269774	+	0.962924i	$0.413051\pi$
$840$		0			0
$841$		−	12.2079i		−	0.420962i
$842$			0.570702i			0.0196677i
$843$		0			0
$844$	−10.3530	+	10.3530i	−0.356364	+	0.356364i
$845$	−45.8153	−	45.8153i	−1.57609	−	1.57609i
$846$		0			0
$847$	7.68527	+	7.68527i	0.264069	+	0.264069i
$848$		−	9.23249i		−	0.317045i
$849$		0			0
$850$	3.15127	−	6.77945i	0.108088	−	0.232533i
$851$	−30.6717			−1.05141
$852$		0			0
$853$	22.4310	+	22.4310i	0.768021	+	0.768021i	0.977758	−	0.209737i	$-0.0672606\pi$
$853$	22.4310	+	22.4310i	0.768021	+	0.768021i	−0.209737	+	0.977758i	$0.567261\pi$
$854$	1.82386			0.0624113
$855$		0			0
$856$	−4.66108	+	4.66108i	−0.159313	+	0.159313i
$857$	−24.6896	+	24.6896i	−0.843382	+	0.843382i	−0.989297	−	0.145915i	$-0.953387\pi$
$857$	−24.6896	+	24.6896i	−0.843382	+	0.843382i	0.145915	+	0.989297i	$0.453387\pi$
$858$		0			0
$859$			12.1397i			0.414201i	0.978320	+	0.207100i	$0.0664027\pi$
$859$			12.1397i			0.414201i	−0.978320	+	0.207100i	$0.933597\pi$
$860$	−7.73339	+	7.73339i	−0.263706	+	0.263706i
$861$		0			0
$862$	25.5324	+	25.5324i	0.869638	+	0.869638i
$863$	11.3223			0.385417			0.192709	−	0.981256i	$-0.438273\pi$
$863$	11.3223			0.385417			0.192709	+	0.981256i	$0.438273\pi$
$864$		0			0
$865$			28.4805i			0.968367i
$866$	4.54033			0.154287
$867$		0			0
$868$	−9.04474			−0.306998
$869$			3.07743i			0.104395i
$870$		0			0
$871$	15.6842			0.531438
$872$	−0.449863	−	0.449863i	−0.0152343	−	0.0152343i
$873$		0			0
$874$	24.1227	−	24.1227i	0.815962	−	0.815962i
$875$			12.1627i			0.411173i
$876$		0			0
$877$	4.09408	−	4.09408i	0.138247	−	0.138247i	−0.634596	−	0.772844i	$-0.718834\pi$
$877$	4.09408	−	4.09408i	0.138247	−	0.138247i	0.772844	+	0.634596i	$0.218834\pi$
$878$	−4.10702	+	4.10702i	−0.138605	+	0.138605i
$879$		0			0
$880$	0.647080			0.0218131
$881$	8.25200	+	8.25200i	0.278017	+	0.278017i	0.832317	−	0.554300i	$-0.187014\pi$
$881$	8.25200	+	8.25200i	0.278017	+	0.278017i	−0.554300	+	0.832317i	$0.687014\pi$
$882$		0			0
$883$	−19.4147			−0.653355			−0.326678	−	0.945136i	$-0.605929\pi$
$883$	−19.4147			−0.653355			−0.326678	+	0.945136i	$0.605929\pi$
$884$	12.2023	−	26.2511i	0.410406	−	0.882922i
$885$		0			0
$886$			34.5919i			1.16214i
$887$	−33.4898	−	33.4898i	−1.12448	−	1.12448i	−0.991060	−	0.133417i	$-0.957405\pi$
$887$	−33.4898	−	33.4898i	−1.12448	−	1.12448i	−0.133417	−	0.991060i	$-0.542595\pi$
$888$		0			0
$889$	15.4162	+	15.4162i	0.517042	+	0.517042i
$890$	16.4961	−	16.4961i	0.552950	−	0.552950i
$891$		0			0
$892$		−	14.7723i		−	0.494614i
$893$			75.0438i			2.51125i
$894$		0			0
$895$	2.53709	−	2.53709i	0.0848056	−	0.0848056i
$896$	−0.707107	−	0.707107i	−0.0236228	−	0.0236228i
$897$		0			0
$898$	4.26160	+	4.26160i	0.142211	+	0.142211i
$899$			37.0637i			1.23614i
$900$		0			0
$901$	−34.5195	−	16.0456i	−1.15001	−	0.534558i
$902$	−4.08223			−0.135923
$903$		0			0
$904$	8.79800	+	8.79800i	0.292617	+	0.292617i
$905$	−38.0962			−1.26636
$906$		0			0
$907$	−5.54811	+	5.54811i	−0.184222	+	0.184222i	−0.793193	−	0.608971i	$-0.791583\pi$
$907$	−5.54811	+	5.54811i	−0.184222	+	0.184222i	0.608971	+	0.793193i	$0.291583\pi$
$908$	10.3677	−	10.3677i	0.344064	−	0.344064i
$909$		0			0
$910$			12.5337i			0.415488i
$911$	−26.1612	+	26.1612i	−0.866759	+	0.866759i	−0.992112	−	0.125353i	$-0.959994\pi$
$911$	−26.1612	+	26.1612i	−0.866759	+	0.866759i	0.125353	+	0.992112i	$0.459994\pi$
$912$		0			0
$913$	2.40498	+	2.40498i	0.0795933	+	0.0795933i
$914$	39.3436			1.30137
$915$		0			0
$916$			19.3079i			0.637950i
$917$	−0.115120			−0.00380160
$918$		0			0
$919$	1.76526			0.0582305			0.0291152	−	0.999576i	$-0.490731\pi$
$919$	1.76526			0.0582305			0.0291152	+	0.999576i	$0.490731\pi$
$920$		−	10.3140i		−	0.340041i
$921$		0			0
$922$	−34.4718			−1.13527
$923$	−27.9852	−	27.9852i	−0.921144	−	0.921144i
$924$		0			0
$925$	6.80646	−	6.80646i	0.223795	−	0.223795i
$926$		−	2.39896i		−	0.0788348i
$927$		0			0
$928$	−2.89759	+	2.89759i	−0.0951182	+	0.0951182i
$929$	−4.48787	+	4.48787i	−0.147242	+	0.147242i	−0.776885	−	0.629643i	$-0.783201\pi$
$929$	−4.48787	+	4.48787i	−0.147242	+	0.147242i	0.629643	+	0.776885i	$0.283201\pi$
$930$		0			0
$931$	5.90462			0.193516
$932$	−11.3972	−	11.3972i	−0.373329	−	0.373329i
$933$		0			0
$934$	24.3491			0.796728
$935$	1.12459	−	2.41938i	0.0367782	−	0.0791221i
$936$		0			0
$937$			32.7891i			1.07117i	0.844480	+	0.535587i	$0.179910\pi$
$937$			32.7891i			1.07117i	−0.844480	+	0.535587i	$0.820090\pi$
$938$	−1.57959	−	1.57959i	−0.0515754	−	0.0515754i
$939$		0			0
$940$	16.0430	+	16.0430i	0.523264	+	0.523264i
$941$	−8.37437	+	8.37437i	−0.272997	+	0.272997i	−0.830305	−	0.557309i	$-0.811834\pi$
$941$	−8.37437	+	8.37437i	−0.272997	+	0.272997i	0.557309	+	0.830305i	$0.311834\pi$
$942$		0			0
$943$			65.0677i			2.11890i
$944$			4.37397i			0.142361i
$945$		0			0
$946$	1.57027	−	1.57027i	0.0510539	−	0.0510539i
$947$	26.6181	+	26.6181i	0.864972	+	0.864972i	0.991911	−	0.126938i	$-0.0405151\pi$
$947$	26.6181	+	26.6181i	0.864972	+	0.864972i	−0.126938	+	0.991911i	$0.540515\pi$
$948$		0			0
$949$	−32.4420	−	32.4420i	−1.05311	−	1.05311i
$950$			10.7063i			0.347359i
$951$		0			0
$952$	−3.87273	+	1.41490i	−0.125516	+	0.0458571i
$953$	−2.71517			−0.0879530			−0.0439765	−	0.999033i	$-0.514003\pi$
$953$	−2.71517			−0.0879530			−0.0439765	+	0.999033i	$0.514003\pi$
$954$		0			0
$955$	10.8899	+	10.8899i	0.352388	+	0.352388i
$956$	−8.31892			−0.269053
$957$		0			0
$958$	−5.89635	+	5.89635i	−0.190502	+	0.190502i
$959$	−0.353275	+	0.353275i	−0.0114079	+	0.0114079i
$960$		0			0
$961$			50.8073i			1.63894i
$962$	26.3558	−	26.3558i	0.849744	−	0.849744i
$963$		0			0
$964$	18.4359	+	18.4359i	0.593782	+	0.593782i
$965$	27.6152			0.888963
$966$		0			0
$967$			32.1282i			1.03317i	0.856235	+	0.516587i	$0.172798\pi$
$967$			32.1282i			1.03317i	−0.856235	+	0.516587i	$0.827202\pi$
$968$	10.8686			0.349330
$969$		0			0
$970$	16.9867			0.545410
$971$		−	25.2962i		−	0.811795i	−0.913919	−	0.405898i	$-0.866959\pi$
$971$		−	25.2962i		−	0.811795i	0.913919	−	0.405898i	$-0.133041\pi$
$972$		0			0
$973$	9.78070			0.313555
$974$	16.7497	+	16.7497i	0.536694	+	0.536694i
$975$		0			0
$976$	1.28967	−	1.28967i	0.0412812	−	0.0412812i
$977$		−	2.37227i		−	0.0758957i	−0.999280	−	0.0379479i	$-0.987918\pi$
$977$		−	2.37227i		−	0.0758957i	0.999280	−	0.0379479i	$-0.0120821\pi$
$978$		0			0
$979$	−3.34954	+	3.34954i	−0.107052	+	0.107052i
$980$	1.26230	−	1.26230i	0.0403226	−	0.0403226i
$981$		0			0
$982$	−13.6628			−0.435997
$983$	−30.4349	−	30.4349i	−0.970723	−	0.970723i	0.0288603	−	0.999583i	$-0.490812\pi$
$983$	−30.4349	−	30.4349i	−0.970723	−	0.970723i	−0.999583	+	0.0288603i	$0.990812\pi$
$984$		0			0
$985$	27.3277			0.870734
$986$	5.79799	+	15.8698i	0.184645	+	0.505396i
$987$		0			0
$988$			41.4566i			1.31891i
$989$	−25.0289	−	25.0289i	−0.795873	−	0.795873i
$990$		0			0
$991$	−22.5640	−	22.5640i	−0.716770	−	0.716770i	0.251173	−	0.967942i	$-0.419184\pi$
$991$	−22.5640	−	22.5640i	−0.716770	−	0.716770i	−0.967942	+	0.251173i	$0.919184\pi$
$992$	−6.39559	+	6.39559i	−0.203060	+	0.203060i
$993$		0			0
$994$			5.63691i			0.178792i
$995$			22.8792i			0.725318i
$996$		0			0
$997$	−22.2438	+	22.2438i	−0.704468	+	0.704468i	−0.965366	−	0.260899i	$-0.915981\pi$
$997$	−22.2438	+	22.2438i	−0.704468	+	0.704468i	0.260899	+	0.965366i	$0.415981\pi$
$998$	−4.38730	−	4.38730i	−0.138877	−	0.138877i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2142.2.p.h.1135.3	✓	16
3.2	odd	2		2142.2.p.i.1135.6	yes	16
17.4	even	4	inner	2142.2.p.h.1891.3	yes	16
51.38	odd	4		2142.2.p.i.1891.6	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2142.2.p.h.1135.3	✓	16	1.1	even	1	trivial
2142.2.p.h.1891.3	yes	16	17.4	even	4	inner
2142.2.p.i.1135.6	yes	16	3.2	odd	2
2142.2.p.i.1891.6	yes	16	51.38	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2142 = 2 \cdot 3^{2} \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2142.p (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} -1.00000 q^{4} +(-1.26230 - 1.26230i) q^{5} +(0.707107 - 0.707107i) q^{7} -1.00000i q^{8} +(1.26230 - 1.26230i) q^{10} +(-0.256310 + 0.256310i) q^{11} -7.02105 q^{13} +(0.707107 + 0.707107i) q^{14} +1.00000 q^{16} +(1.73795 - 3.73892i) q^{17} +5.90462i q^{19} +(1.26230 + 1.26230i) q^{20} +(-0.256310 - 0.256310i) q^{22} +(-4.08539 + 4.08539i) q^{23} -1.81321i q^{25} -7.02105i q^{26} +(-0.707107 + 0.707107i) q^{28} +(2.89759 + 2.89759i) q^{29} +(6.39559 + 6.39559i) q^{31} +1.00000i q^{32} +(3.73892 + 1.73795i) q^{34} -1.78516 q^{35} +(3.75382 + 3.75382i) q^{37} -5.90462 q^{38} +(-1.26230 + 1.26230i) q^{40} +(7.96346 - 7.96346i) q^{41} +6.12644i q^{43} +(0.256310 - 0.256310i) q^{44} +(-4.08539 - 4.08539i) q^{46} +12.7093 q^{47} -1.00000i q^{49} +1.81321 q^{50} +7.02105 q^{52} -9.23249i q^{53} +0.647080 q^{55} +(-0.707107 - 0.707107i) q^{56} +(-2.89759 + 2.89759i) q^{58} +4.37397i q^{59} +(1.28967 - 1.28967i) q^{61} +(-6.39559 + 6.39559i) q^{62} -1.00000 q^{64} +(8.86266 + 8.86266i) q^{65} -2.23388 q^{67} +(-1.73795 + 3.73892i) q^{68} -1.78516i q^{70} +(3.98590 + 3.98590i) q^{71} +(4.62068 + 4.62068i) q^{73} +(-3.75382 + 3.75382i) q^{74} -5.90462i q^{76} +0.362477i q^{77} +(6.00332 - 6.00332i) q^{79} +(-1.26230 - 1.26230i) q^{80} +(7.96346 + 7.96346i) q^{82} -9.38309i q^{83} +(-6.91344 + 2.52581i) q^{85} -6.12644 q^{86} +(0.256310 + 0.256310i) q^{88} +13.0683 q^{89} +(-4.96463 + 4.96463i) q^{91} +(4.08539 - 4.08539i) q^{92} +12.7093i q^{94} +(7.45338 - 7.45338i) q^{95} +(6.72848 + 6.72848i) q^{97} +1.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 16 q^{4} - 4 q^{11} - 24 q^{13} + 16 q^{16} + 8 q^{17} - 4 q^{22} - 4 q^{29} + 24 q^{31} + 8 q^{34} + 8 q^{35} - 12 q^{37} + 8 q^{38} + 4 q^{44} - 32 q^{47} - 8 q^{50} + 24 q^{52} - 16 q^{55} + 4 q^{58}+ \cdots + 16 q^{98}+O(q^{100}) \) 16 * q - 16 * q^4 - 4 * q^11 - 24 * q^13 + 16 * q^16 + 8 * q^17 - 4 * q^22 - 4 * q^29 + 24 * q^31 + 8 * q^34 + 8 * q^35 - 12 * q^37 + 8 * q^38 + 4 * q^44 - 32 * q^47 - 8 * q^50 + 24 * q^52 - 16 * q^55 + 4 * q^58 - 24 * q^62 - 16 * q^64 + 32 * q^65 - 40 * q^67 - 8 * q^68 - 32 * q^71 + 16 * q^73 + 12 * q^74 - 8 * q^79 + 16 * q^85 + 4 * q^88 + 4 * q^91 + 40 * q^95 + 16 * q^97 + 16 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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