LMFDB - Embedded newform 900.2.k.l.307.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [900,2,Mod(307,900)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(900, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 0, 1]))

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

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

chi := DirichletCharacter("900.307");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	900.k (of order $4$, degree $2$, 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:	$7.18653618192$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 300)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			307.1
Root			$-0.965926 - 0.258819i$ of defining polynomial
Character	$\chi$	$=$	900.307
Dual form			900.2.k.l.343.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.22474 - 0.707107i) q^{2} +(1.00000 + 1.73205i) q^{4} +(3.15660 - 3.15660i) q^{7} -2.82843i q^{8} +O(q^{10})$	\(q+(-1.22474 - 0.707107i) q^{2} +(1.00000 + 1.73205i) q^{4} +(3.15660 - 3.15660i) q^{7} -2.82843i q^{8} -2.00000i q^{11} +(1.60368 - 1.60368i) q^{13} +(-6.09808 + 1.63397i) q^{14} +(-2.00000 + 3.46410i) q^{16} +(-4.24264 - 4.24264i) q^{17} -3.19615 q^{19} +(-1.41421 + 2.44949i) q^{22} +(5.27792 + 5.27792i) q^{23} +(-3.09808 + 0.830127i) q^{26} +(8.62398 + 2.31079i) q^{28} -0.535898i q^{29} +3.73205i q^{31} +(4.89898 - 2.82843i) q^{32} +(2.19615 + 8.19615i) q^{34} +(-7.72741 - 7.72741i) q^{37} +(3.91447 + 2.26002i) q^{38} -1.46410 q^{41} +(-3.15660 - 3.15660i) q^{43} +(3.46410 - 2.00000i) q^{44} +(-2.73205 - 10.1962i) q^{46} +(0.656339 - 0.656339i) q^{47} -12.9282i q^{49} +(4.38134 + 1.17398i) q^{52} +(3.86370 - 3.86370i) q^{53} +(-8.92820 - 8.92820i) q^{56} +(-0.378937 + 0.656339i) q^{58} +11.4641 q^{59} +3.00000 q^{61} +(2.63896 - 4.57081i) q^{62} -8.00000 q^{64} +(-3.91447 + 3.91447i) q^{67} +(3.10583 - 11.5911i) q^{68} +2.53590i q^{71} +(-2.82843 + 2.82843i) q^{73} +(4.00000 + 14.9282i) q^{74} +(-3.19615 - 5.53590i) q^{76} +(-6.31319 - 6.31319i) q^{77} +7.46410 q^{79} +(1.79315 + 1.03528i) q^{82} +(-9.14162 - 9.14162i) q^{83} +(1.63397 + 6.09808i) q^{86} -5.65685 q^{88} -6.92820i q^{89} -10.1244i q^{91} +(-3.86370 + 14.4195i) q^{92} +(-1.26795 + 0.339746i) q^{94} +(-6.88160 - 6.88160i) q^{97} +(-9.14162 + 15.8338i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{4}+O(q^{10}) $ 8 * q + 8 * q^4	$ 8 q + 8 q^{4} - 28 q^{14} - 16 q^{16} + 16 q^{19} - 4 q^{26} - 24 q^{34} + 16 q^{41} - 8 q^{46} - 16 q^{56} + 64 q^{59} + 24 q^{61} - 64 q^{64} + 32 q^{74} + 16 q^{76} + 32 q^{79} + 20 q^{86} - 24 q^{94}+O(q^{100}) $ 8 * q + 8 * q^4 - 28 * q^14 - 16 * q^16 + 16 * q^19 - 4 * q^26 - 24 * q^34 + 16 * q^41 - 8 * q^46 - 16 * q^56 + 64 * q^59 + 24 * q^61 - 64 * q^64 + 32 * q^74 + 16 * q^76 + 32 * q^79 + 20 * q^86 - 24 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/900\mathbb{Z}\right)^\times$.

$n$	$101$	$451$	$577$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−1.22474	−	0.707107i	−0.866025	−	0.500000i
$2$	−1.22474	−	0.707107i	−0.866025	−	0.500000i
$3$		0			0
$3$		0			0
$4$	1.00000	+	1.73205i	0.500000	+	0.866025i
$5$		0			0
$5$		0			0
$6$		0			0
$7$	3.15660	−	3.15660i	1.19308	−	1.19308i	0.216884	−	0.976197i	$-0.430411\pi$
$7$	3.15660	−	3.15660i	1.19308	−	1.19308i	0.976197	−	0.216884i	$-0.0695893\pi$
$8$		−	2.82843i		−	1.00000i
$9$		0			0
$10$		0			0
$11$		−	2.00000i		−	0.603023i	−0.953463	−	0.301511i	$-0.902509\pi$
$11$		−	2.00000i		−	0.603023i	0.953463	−	0.301511i	$-0.0974911\pi$
$12$		0			0
$13$	1.60368	−	1.60368i	0.444781	−	0.444781i	−0.448834	−	0.893615i	$-0.648160\pi$
$13$	1.60368	−	1.60368i	0.444781	−	0.444781i	0.893615	+	0.448834i	$0.148160\pi$
$14$	−6.09808	+	1.63397i	−1.62978	+	0.436698i
$15$		0			0
$16$	−2.00000	+	3.46410i	−0.500000	+	0.866025i
$17$	−4.24264	−	4.24264i	−1.02899	−	1.02899i	−0.999567	−	0.0294245i	$-0.990633\pi$
$17$	−4.24264	−	4.24264i	−1.02899	−	1.02899i	−0.0294245	−	0.999567i	$-0.509367\pi$
$18$		0			0
$19$	−3.19615			−0.733248			−0.366624	−	0.930369i	$-0.619486\pi$
$19$	−3.19615			−0.733248			−0.366624	+	0.930369i	$0.619486\pi$
$20$		0			0
$21$		0			0
$22$	−1.41421	+	2.44949i	−0.301511	+	0.522233i
$23$	5.27792	+	5.27792i	1.10052	+	1.10052i	0.994348	+	0.106174i	$0.0338601\pi$
$23$	5.27792	+	5.27792i	1.10052	+	1.10052i	0.106174	+	0.994348i	$0.466140\pi$
$24$		0			0
$25$		0			0
$26$	−3.09808	+	0.830127i	−0.607583	+	0.162801i
$27$		0			0
$28$	8.62398	+	2.31079i	1.62978	+	0.436698i
$29$		−	0.535898i		−	0.0995138i	−0.998761	−	0.0497569i	$-0.984155\pi$
$29$		−	0.535898i		−	0.0995138i	0.998761	−	0.0497569i	$-0.0158447\pi$
$30$		0			0
$31$			3.73205i			0.670296i	0.942165	+	0.335148i	$0.108786\pi$
$31$			3.73205i			0.670296i	−0.942165	+	0.335148i	$0.891214\pi$
$32$	4.89898	−	2.82843i	0.866025	−	0.500000i
$33$		0			0
$34$	2.19615	+	8.19615i	0.376637	+	1.40563i
$35$		0			0
$36$		0			0
$37$	−7.72741	−	7.72741i	−1.27038	−	1.27038i	−0.945890	−	0.324488i	$-0.894808\pi$
$37$	−7.72741	−	7.72741i	−1.27038	−	1.27038i	−0.324488	−	0.945890i	$-0.605192\pi$
$38$	3.91447	+	2.26002i	0.635011	+	0.366624i
$39$		0			0
$40$		0			0
$41$	−1.46410			−0.228654			−0.114327	−	0.993443i	$-0.536471\pi$
$41$	−1.46410			−0.228654			−0.114327	+	0.993443i	$0.536471\pi$
$42$		0			0
$43$	−3.15660	−	3.15660i	−0.481376	−	0.481376i	0.424195	−	0.905571i	$-0.360557\pi$
$43$	−3.15660	−	3.15660i	−0.481376	−	0.481376i	−0.905571	+	0.424195i	$0.860557\pi$
$44$	3.46410	−	2.00000i	0.522233	−	0.301511i
$45$		0			0
$46$	−2.73205	−	10.1962i	−0.402819	−	1.50334i
$47$	0.656339	−	0.656339i	0.0957369	−	0.0957369i	−0.657616	−	0.753353i	$-0.728435\pi$
$47$	0.656339	−	0.656339i	0.0957369	−	0.0957369i	0.753353	+	0.657616i	$0.228435\pi$
$48$		0			0
$49$		−	12.9282i		−	1.84689i
$50$		0			0
$51$		0			0
$52$	4.38134	+	1.17398i	0.607583	+	0.162801i
$53$	3.86370	−	3.86370i	0.530720	−	0.530720i	−0.390066	−	0.920787i	$-0.627548\pi$
$53$	3.86370	−	3.86370i	0.530720	−	0.530720i	0.920787	+	0.390066i	$0.127548\pi$
$54$		0			0
$55$		0			0
$56$	−8.92820	−	8.92820i	−1.19308	−	1.19308i
$57$		0			0
$58$	−0.378937	+	0.656339i	−0.0497569	+	0.0861815i
$59$	11.4641			1.49250			0.746249	−	0.665666i	$-0.231853\pi$
$59$	11.4641			1.49250			0.746249	+	0.665666i	$0.231853\pi$
$60$		0			0
$61$	3.00000			0.384111			0.192055	−	0.981384i	$-0.438485\pi$
$61$	3.00000			0.384111			0.192055	+	0.981384i	$0.438485\pi$
$62$	2.63896	−	4.57081i	0.335148	−	0.580493i
$63$		0			0
$64$	−8.00000			−1.00000
$65$		0			0
$66$		0			0
$67$	−3.91447	+	3.91447i	−0.478229	+	0.478229i	−0.904565	−	0.426336i	$-0.859804\pi$
$67$	−3.91447	+	3.91447i	−0.478229	+	0.478229i	0.426336	+	0.904565i	$0.359804\pi$
$68$	3.10583	−	11.5911i	0.376637	−	1.40563i
$69$		0			0
$70$		0			0
$71$			2.53590i			0.300956i	0.988613	+	0.150478i	$0.0480812\pi$
$71$			2.53590i			0.300956i	−0.988613	+	0.150478i	$0.951919\pi$
$72$		0			0
$73$	−2.82843	+	2.82843i	−0.331042	+	0.331042i	−0.852982	−	0.521940i	$-0.825209\pi$
$73$	−2.82843	+	2.82843i	−0.331042	+	0.331042i	0.521940	+	0.852982i	$0.325209\pi$
$74$	4.00000	+	14.9282i	0.464991	+	1.73537i
$75$		0			0
$76$	−3.19615	−	5.53590i	−0.366624	−	0.635011i
$77$	−6.31319	−	6.31319i	−0.719455	−	0.719455i
$78$		0			0
$79$	7.46410			0.839777			0.419889	−	0.907576i	$-0.362069\pi$
$79$	7.46410			0.839777			0.419889	+	0.907576i	$0.362069\pi$
$80$		0			0
$81$		0			0
$82$	1.79315	+	1.03528i	0.198020	+	0.114327i
$83$	−9.14162	−	9.14162i	−1.00342	−	1.00342i	−0.999994	−	0.00342905i	$-0.998908\pi$
$83$	−9.14162	−	9.14162i	−1.00342	−	1.00342i	−0.00342905	−	0.999994i	$-0.501092\pi$
$84$		0			0
$85$		0			0
$86$	1.63397	+	6.09808i	0.176196	+	0.657572i
$87$		0			0
$88$	−5.65685			−0.603023
$89$		−	6.92820i		−	0.734388i	−0.930144	−	0.367194i	$-0.880318\pi$
$89$		−	6.92820i		−	0.734388i	0.930144	−	0.367194i	$-0.119682\pi$
$90$		0			0
$91$		−	10.1244i		−	1.06132i
$92$	−3.86370	+	14.4195i	−0.402819	+	1.50334i
$93$		0			0
$94$	−1.26795	+	0.339746i	−0.130779	+	0.0350421i
$95$		0			0
$96$		0			0
$97$	−6.88160	−	6.88160i	−0.698721	−	0.698721i	0.265414	−	0.964135i	$-0.414491\pi$
$97$	−6.88160	−	6.88160i	−0.698721	−	0.698721i	−0.964135	+	0.265414i	$0.914491\pi$
$98$	−9.14162	+	15.8338i	−0.923443	+	1.59945i
$99$		0			0
$100$		0			0
$101$	−5.46410			−0.543698			−0.271849	−	0.962340i	$-0.587635\pi$
$101$	−5.46410			−0.543698			−0.271849	+	0.962340i	$0.587635\pi$
$102$		0			0
$103$	4.89898	+	4.89898i	0.482711	+	0.482711i	0.905996	−	0.423286i	$-0.139123\pi$
$103$	4.89898	+	4.89898i	0.482711	+	0.482711i	−0.423286	+	0.905996i	$0.639123\pi$
$104$	−4.53590	−	4.53590i	−0.444781	−	0.444781i
$105$		0			0
$106$	−7.46410	+	2.00000i	−0.724978	+	0.194257i
$107$	9.52056	−	9.52056i	0.920387	−	0.920387i	−0.0766695	−	0.997057i	$-0.524429\pi$
$107$	9.52056	−	9.52056i	0.920387	−	0.920387i	0.997057	+	0.0766695i	$0.0244286\pi$
$108$		0			0
$109$		−	7.00000i		−	0.670478i	−0.942133	−	0.335239i	$-0.891183\pi$
$109$		−	7.00000i		−	0.670478i	0.942133	−	0.335239i	$-0.108817\pi$
$110$		0			0
$111$		0			0
$112$	4.62158	+	17.2480i	0.436698	+	1.62978i
$113$	−9.79796	+	9.79796i	−0.921714	+	0.921714i	−0.997151	−	0.0754362i	$-0.975965\pi$
$113$	−9.79796	+	9.79796i	−0.921714	+	0.921714i	0.0754362	+	0.997151i	$0.475965\pi$
$114$		0			0
$115$		0			0
$116$	0.928203	−	0.535898i	0.0861815	−	0.0497569i
$117$		0			0
$118$	−14.0406	−	8.10634i	−1.29254	−	0.746249i
$119$	−26.7846			−2.45534
$120$		0			0
$121$	7.00000			0.636364
$122$	−3.67423	−	2.12132i	−0.332650	−	0.192055i
$123$		0			0
$124$	−6.46410	+	3.73205i	−0.580493	+	0.335148i
$125$		0			0
$126$		0			0
$127$	7.72741	−	7.72741i	0.685696	−	0.685696i	−0.275581	−	0.961278i	$-0.588870\pi$
$127$	7.72741	−	7.72741i	0.685696	−	0.685696i	0.961278	+	0.275581i	$0.0888703\pi$
$128$	9.79796	+	5.65685i	0.866025	+	0.500000i
$129$		0			0
$130$		0			0
$131$		−	2.53590i		−	0.221562i	−0.993845	−	0.110781i	$-0.964665\pi$
$131$		−	2.53590i		−	0.221562i	0.993845	−	0.110781i	$-0.0353353\pi$
$132$		0			0
$133$	−10.0890	+	10.0890i	−0.874824	+	0.874824i
$134$	7.56218	−	2.02628i	0.653273	−	0.175044i
$135$		0			0
$136$	−12.0000	+	12.0000i	−1.02899	+	1.02899i
$137$	10.9348	+	10.9348i	0.934221	+	0.934221i	0.997966	−	0.0637456i	$-0.0203046\pi$
$137$	10.9348	+	10.9348i	0.934221	+	0.934221i	−0.0637456	+	0.997966i	$0.520305\pi$
$138$		0			0
$139$	12.5359			1.06328			0.531641	−	0.846970i	$-0.321576\pi$
$139$	12.5359			1.06328			0.531641	+	0.846970i	$0.321576\pi$
$140$		0			0
$141$		0			0
$142$	1.79315	−	3.10583i	0.150478	−	0.260635i
$143$	−3.20736	−	3.20736i	−0.268213	−	0.268213i
$144$		0			0
$145$		0			0
$146$	5.46410	−	1.46410i	0.452212	−	0.121170i
$147$		0			0
$148$	5.65685	−	21.1117i	0.464991	−	1.73537i
$149$		−	11.8564i		−	0.971315i	−0.874149	−	0.485657i	$-0.838580\pi$
$149$		−	11.8564i		−	0.971315i	0.874149	−	0.485657i	$-0.161420\pi$
$150$		0			0
$151$			7.73205i			0.629225i	0.949220	+	0.314613i	$0.101875\pi$
$151$			7.73205i			0.629225i	−0.949220	+	0.314613i	$0.898125\pi$
$152$			9.04008i			0.733248i
$153$		0			0
$154$	3.26795	+	12.1962i	0.263339	+	0.982794i
$155$		0			0
$156$		0			0
$157$	4.43211	+	4.43211i	0.353721	+	0.353721i	0.861492	−	0.507771i	$-0.169530\pi$
$157$	4.43211	+	4.43211i	0.353721	+	0.353721i	−0.507771	+	0.861492i	$0.669530\pi$
$158$	−9.14162	−	5.27792i	−0.727268	−	0.419889i
$159$		0			0
$160$		0			0
$161$	33.3205			2.62602
$162$		0			0
$163$	5.32868	+	5.32868i	0.417375	+	0.417375i	0.884298	−	0.466923i	$-0.154638\pi$
$163$	5.32868	+	5.32868i	0.417375	+	0.417375i	−0.466923	+	0.884298i	$0.654638\pi$
$164$	−1.46410	−	2.53590i	−0.114327	−	0.198020i
$165$		0			0
$166$	4.73205	+	17.6603i	0.367278	+	1.37070i
$167$	−11.5911	+	11.5911i	−0.896947	+	0.896947i	−0.995165	−	0.0982179i	$-0.968686\pi$
$167$	−11.5911	+	11.5911i	−0.896947	+	0.896947i	0.0982179	+	0.995165i	$0.468686\pi$
$168$		0			0
$169$			7.85641i			0.604339i
$170$		0			0
$171$		0			0
$172$	2.31079	−	8.62398i	0.176196	−	0.657572i
$173$	3.48477	−	3.48477i	0.264942	−	0.264942i	−0.562116	−	0.827058i	$-0.690013\pi$
$173$	3.48477	−	3.48477i	0.264942	−	0.264942i	0.827058	+	0.562116i	$0.190013\pi$
$174$		0			0
$175$		0			0
$176$	6.92820	+	4.00000i	0.522233	+	0.301511i
$177$		0			0
$178$	−4.89898	+	8.48528i	−0.367194	+	0.635999i
$179$	9.32051			0.696647			0.348324	−	0.937374i	$-0.386751\pi$
$179$	9.32051			0.696647			0.348324	+	0.937374i	$0.386751\pi$
$180$		0			0
$181$	−0.0717968			−0.00533661			−0.00266831	−	0.999996i	$-0.500849\pi$
$181$	−0.0717968			−0.00533661			−0.00266831	+	0.999996i	$0.500849\pi$
$182$	−7.15900	+	12.3998i	−0.530660	+	0.919131i
$183$		0			0
$184$	14.9282	−	14.9282i	1.10052	−	1.10052i
$185$		0			0
$186$		0			0
$187$	−8.48528	+	8.48528i	−0.620505	+	0.620505i
$188$	1.79315	+	0.480473i	0.130779	+	0.0350421i
$189$		0			0
$190$		0			0
$191$			3.07180i			0.222267i	0.993805	+	0.111134i	$0.0354482\pi$
$191$			3.07180i			0.222267i	−0.993805	+	0.111134i	$0.964552\pi$
$192$		0			0
$193$	7.26054	−	7.26054i	0.522625	−	0.522625i	−0.395738	−	0.918363i	$-0.629511\pi$
$193$	7.26054	−	7.26054i	0.522625	−	0.522625i	0.918363	+	0.395738i	$0.129511\pi$
$194$	3.56218	+	13.2942i	0.255749	+	0.954470i
$195$		0			0
$196$	22.3923	−	12.9282i	1.59945	−	0.923443i
$197$	−4.52004	−	4.52004i	−0.322040	−	0.322040i	0.527509	−	0.849549i	$-0.323126\pi$
$197$	−4.52004	−	4.52004i	−0.322040	−	0.322040i	−0.849549	+	0.527509i	$0.823126\pi$
$198$		0			0
$199$	10.1244			0.717697			0.358848	−	0.933396i	$-0.383170\pi$
$199$	10.1244			0.717697			0.358848	+	0.933396i	$0.383170\pi$
$200$		0			0
$201$		0			0
$202$	6.69213	+	3.86370i	0.470857	+	0.271849i
$203$	−1.69161	−	1.69161i	−0.118728	−	0.118728i
$204$		0			0
$205$		0			0
$206$	−2.53590	−	9.46410i	−0.176684	−	0.659395i
$207$		0			0
$208$	2.34795	+	8.76268i	0.162801	+	0.607583i
$209$			6.39230i			0.442165i
$210$		0			0
$211$			3.19615i			0.220032i	0.993930	+	0.110016i	$0.0350902\pi$
$211$			3.19615i			0.220032i	−0.993930	+	0.110016i	$0.964910\pi$
$212$	10.5558	+	2.82843i	0.724978	+	0.194257i
$213$		0			0
$214$	−18.3923	+	4.92820i	−1.25727	+	0.336885i
$215$		0			0
$216$		0			0
$217$	11.7806	+	11.7806i	0.799718	+	0.799718i
$218$	−4.94975	+	8.57321i	−0.335239	+	0.580651i
$219$		0			0
$220$		0			0
$221$	−13.6077			−0.915353
$222$		0			0
$223$	−6.64136	−	6.64136i	−0.444739	−	0.444739i	0.448862	−	0.893601i	$-0.351829\pi$
$223$	−6.64136	−	6.64136i	−0.444739	−	0.444739i	−0.893601	+	0.448862i	$0.851829\pi$
$224$	6.53590	−	24.3923i	0.436698	−	1.62978i
$225$		0			0
$226$	18.9282	−	5.07180i	1.25909	−	0.337371i
$227$	−5.93426	+	5.93426i	−0.393870	+	0.393870i	−0.876064	−	0.482194i	$-0.839840\pi$
$227$	−5.93426	+	5.93426i	−0.393870	+	0.393870i	0.482194	+	0.876064i	$0.339840\pi$
$228$		0			0
$229$		−	2.85641i		−	0.188757i	−0.995536	−	0.0943783i	$-0.969914\pi$
$229$		−	2.85641i		−	0.188757i	0.995536	−	0.0943783i	$-0.0300863\pi$
$230$		0			0
$231$		0			0
$232$	−1.51575			−0.0995138
$233$	5.93426	−	5.93426i	0.388766	−	0.388766i	−0.485481	−	0.874247i	$-0.661356\pi$
$233$	5.93426	−	5.93426i	0.388766	−	0.388766i	0.874247	+	0.485481i	$0.161356\pi$
$234$		0			0
$235$		0			0
$236$	11.4641	+	19.8564i	0.746249	+	1.29254i
$237$		0			0
$238$	32.8043	+	18.9396i	2.12639	+	1.22767i
$239$	10.5359			0.681511			0.340755	−	0.940152i	$-0.389317\pi$
$239$	10.5359			0.681511			0.340755	+	0.940152i	$0.389317\pi$
$240$		0			0
$241$	12.8564			0.828154			0.414077	−	0.910242i	$-0.364104\pi$
$241$	12.8564			0.828154			0.414077	+	0.910242i	$0.364104\pi$
$242$	−8.57321	−	4.94975i	−0.551107	−	0.318182i
$243$		0			0
$244$	3.00000	+	5.19615i	0.192055	+	0.332650i
$245$		0			0
$246$		0			0
$247$	−5.12561	+	5.12561i	−0.326135	+	0.326135i
$248$	10.5558			0.670296
$249$		0			0
$250$		0			0
$251$			29.8564i			1.88452i	0.334883	+	0.942260i	$0.391303\pi$
$251$			29.8564i			1.88452i	−0.334883	+	0.942260i	$0.608697\pi$
$252$		0			0
$253$	10.5558	−	10.5558i	0.663640	−	0.663640i
$254$	−14.9282	+	4.00000i	−0.936679	+	0.250982i
$255$		0			0
$256$	−8.00000	−	13.8564i	−0.500000	−	0.866025i
$257$	20.3538	+	20.3538i	1.26963	+	1.26963i	0.946277	+	0.323358i	$0.104812\pi$
$257$	20.3538	+	20.3538i	1.26963	+	1.26963i	0.323358	+	0.946277i	$0.395188\pi$
$258$		0			0
$259$	−48.7846			−3.03133
$260$		0			0
$261$		0			0
$262$	−1.79315	+	3.10583i	−0.110781	+	0.191879i
$263$	10.2784	+	10.2784i	0.633795	+	0.633795i	0.949018	−	0.315223i	$-0.102079\pi$
$263$	10.2784	+	10.2784i	0.633795	+	0.633795i	−0.315223	+	0.949018i	$0.602079\pi$
$264$		0			0
$265$		0			0
$266$	19.4904	−	5.22243i	1.19503	−	0.320208i
$267$		0			0
$268$	−10.6945	−	2.86559i	−0.653273	−	0.175044i
$269$			22.3923i			1.36528i	0.730753	+	0.682641i	$0.239169\pi$
$269$			22.3923i			1.36528i	−0.730753	+	0.682641i	$0.760831\pi$
$270$		0			0
$271$			24.2487i			1.47300i	0.676435	+	0.736502i	$0.263524\pi$
$271$			24.2487i			1.47300i	−0.676435	+	0.736502i	$0.736476\pi$
$272$	23.1822	−	6.21166i	1.40563	−	0.376637i
$273$		0			0
$274$	−5.66025	−	21.1244i	−0.341948	−	1.27617i
$275$		0			0
$276$		0			0
$277$	−6.50266	−	6.50266i	−0.390707	−	0.390707i	0.484232	−	0.874939i	$-0.339099\pi$
$277$	−6.50266	−	6.50266i	−0.390707	−	0.390707i	−0.874939	+	0.484232i	$0.839099\pi$
$278$	−15.3533	−	8.86422i	−0.920828	−	0.531641i
$279$		0			0
$280$		0			0
$281$	−6.39230			−0.381333			−0.190666	−	0.981655i	$-0.561065\pi$
$281$	−6.39230			−0.381333			−0.190666	+	0.981655i	$0.561065\pi$
$282$		0			0
$283$	−0.429705	−	0.429705i	−0.0255433	−	0.0255433i	0.694220	−	0.719763i	$-0.255750\pi$
$283$	−0.429705	−	0.429705i	−0.0255433	−	0.0255433i	−0.719763	+	0.694220i	$0.755750\pi$
$284$	−4.39230	+	2.53590i	−0.260635	+	0.150478i
$285$		0			0
$286$	1.66025	+	6.19615i	0.0981729	+	0.366386i
$287$	−4.62158	+	4.62158i	−0.272803	+	0.272803i
$288$		0			0
$289$			19.0000i			1.11765i
$290$		0			0
$291$		0			0
$292$	−7.72741	−	2.07055i	−0.452212	−	0.121170i
$293$	−13.7632	+	13.7632i	−0.804055	+	0.804055i	−0.983727	−	0.179672i	$-0.942496\pi$
$293$	−13.7632	+	13.7632i	−0.804055	+	0.804055i	0.179672	+	0.983727i	$0.442496\pi$
$294$		0			0
$295$		0			0
$296$	−21.8564	+	21.8564i	−1.27038	+	1.27038i
$297$		0			0
$298$	−8.38375	+	14.5211i	−0.485657	+	0.841183i
$299$	16.9282			0.978983
$300$		0			0
$301$	−19.9282			−1.14864
$302$	5.46739	−	9.46979i	0.314613	−	0.544925i
$303$		0			0
$304$	6.39230	−	11.0718i	0.366624	−	0.635011i
$305$		0			0
$306$		0			0
$307$	−5.22715	+	5.22715i	−0.298329	+	0.298329i	−0.840359	−	0.542030i	$-0.817656\pi$
$307$	−5.22715	+	5.22715i	−0.298329	+	0.298329i	0.542030	+	0.840359i	$0.317656\pi$
$308$	4.62158	−	17.2480i	0.263339	−	0.982794i
$309$		0			0
$310$		0			0
$311$		−	20.5359i		−	1.16448i	−0.813016	−	0.582242i	$-0.802176\pi$
$311$		−	20.5359i		−	1.16448i	0.813016	−	0.582242i	$-0.197824\pi$
$312$		0			0
$313$	−11.4016	+	11.4016i	−0.644459	+	0.644459i	−0.951648	−	0.307190i	$-0.900611\pi$
$313$	−11.4016	+	11.4016i	−0.644459	+	0.644459i	0.307190	+	0.951648i	$0.400611\pi$
$314$	−2.29423	−	8.56218i	−0.129471	−	0.483192i
$315$		0			0
$316$	7.46410	+	12.9282i	0.419889	+	0.727268i
$317$	−4.89898	−	4.89898i	−0.275154	−	0.275154i	0.556017	−	0.831171i	$-0.312329\pi$
$317$	−4.89898	−	4.89898i	−0.275154	−	0.275154i	−0.831171	+	0.556017i	$0.812329\pi$
$318$		0			0
$319$	−1.07180			−0.0600091
$320$		0			0
$321$		0			0
$322$	−40.8091	−	23.5612i	−2.27420	−	1.31301i
$323$	13.5601	+	13.5601i	0.754506	+	0.754506i
$324$		0			0
$325$		0			0
$326$	−2.75833	−	10.2942i	−0.152770	−	0.570145i
$327$		0			0
$328$			4.14110i			0.228654i
$329$		−	4.14359i		−	0.228444i
$330$		0			0
$331$		−	18.3923i		−	1.01093i	−0.862846	−	0.505466i	$-0.831321\pi$
$331$		−	18.3923i		−	1.01093i	0.862846	−	0.505466i	$-0.168679\pi$
$332$	6.69213	−	24.9754i	0.367278	−	1.37070i
$333$		0			0
$334$	22.3923	−	6.00000i	1.22525	−	0.328305i
$335$		0			0
$336$		0			0
$337$	20.2659	+	20.2659i	1.10395	+	1.10395i	0.993929	+	0.110023i	$0.0350923\pi$
$337$	20.2659	+	20.2659i	1.10395	+	1.10395i	0.110023	+	0.993929i	$0.464908\pi$
$338$	5.55532	−	9.62209i	0.302169	−	0.523373i
$339$		0			0
$340$		0			0
$341$	7.46410			0.404204
$342$		0			0
$343$	−18.7129	−	18.7129i	−1.01040	−	1.01040i
$344$	−8.92820	+	8.92820i	−0.481376	+	0.481376i
$345$		0			0
$346$	−6.73205	+	1.80385i	−0.361917	+	0.0969754i
$347$	17.6269	−	17.6269i	0.946262	−	0.946262i	−0.0523663	−	0.998628i	$-0.516676\pi$
$347$	17.6269	−	17.6269i	0.946262	−	0.946262i	0.998628	+	0.0523663i	$0.0166763\pi$
$348$		0			0
$349$			23.8564i			1.27700i	0.769620	+	0.638502i	$0.220446\pi$
$349$			23.8564i			1.27700i	−0.769620	+	0.638502i	$0.779554\pi$
$350$		0			0
$351$		0			0
$352$	−5.65685	−	9.79796i	−0.301511	−	0.522233i
$353$	−8.38375	+	8.38375i	−0.446222	+	0.446222i	−0.894096	−	0.447875i	$-0.852181\pi$
$353$	−8.38375	+	8.38375i	−0.446222	+	0.446222i	0.447875	+	0.894096i	$0.352181\pi$
$354$		0			0
$355$		0			0
$356$	12.0000	−	6.92820i	0.635999	−	0.367194i
$357$		0			0
$358$	−11.4152	−	6.59059i	−0.603314	−	0.348324i
$359$	−3.60770			−0.190407			−0.0952034	−	0.995458i	$-0.530350\pi$
$359$	−3.60770			−0.190407			−0.0952034	+	0.995458i	$0.530350\pi$
$360$		0			0
$361$	−8.78461			−0.462348
$362$	0.0879327	+	0.0507680i	0.00462164	+	0.00266831i
$363$		0			0
$364$	17.5359	−	10.1244i	0.919131	−	0.530660i
$365$		0			0
$366$		0			0
$367$	22.1977	−	22.1977i	1.15871	−	1.15871i	0.173958	−	0.984753i	$-0.444344\pi$
$367$	22.1977	−	22.1977i	1.15871	−	1.15871i	0.984753	−	0.173958i	$-0.0556557\pi$
$368$	−28.8391	+	7.72741i	−1.50334	+	0.402819i
$369$		0			0
$370$		0			0
$371$		−	24.3923i		−	1.26639i
$372$		0			0
$373$	25.9227	−	25.9227i	1.34223	−	1.34223i	0.448388	−	0.893839i	$-0.351998\pi$
$373$	25.9227	−	25.9227i	1.34223	−	1.34223i	0.893839	−	0.448388i	$-0.148002\pi$
$374$	16.3923	−	4.39230i	0.847626	−	0.227121i
$375$		0			0
$376$	−1.85641	−	1.85641i	−0.0957369	−	0.0957369i
$377$	−0.859411	−	0.859411i	−0.0442619	−	0.0442619i
$378$		0			0
$379$	−12.2679			−0.630162			−0.315081	−	0.949065i	$-0.602032\pi$
$379$	−12.2679			−0.630162			−0.315081	+	0.949065i	$0.602032\pi$
$380$		0			0
$381$		0			0
$382$	2.17209	−	3.76217i	0.111134	−	0.192489i
$383$	−17.5254	−	17.5254i	−0.895504	−	0.895504i	0.0995302	−	0.995035i	$-0.468266\pi$
$383$	−17.5254	−	17.5254i	−0.895504	−	0.895504i	−0.995035	+	0.0995302i	$0.968266\pi$
$384$		0			0
$385$		0			0
$386$	−14.0263	+	3.75833i	−0.713919	+	0.191294i
$387$		0			0
$388$	5.03768	−	18.8009i	0.255749	−	0.954470i
$389$			21.4641i			1.08827i	0.838997	+	0.544137i	$0.183143\pi$
$389$			21.4641i			1.08827i	−0.838997	+	0.544137i	$0.816857\pi$
$390$		0			0
$391$		−	44.7846i		−	2.26486i
$392$	−36.5665			−1.84689
$393$		0			0
$394$	2.33975	+	8.73205i	0.117875	+	0.439914i
$395$		0			0
$396$		0			0
$397$	8.19428	+	8.19428i	0.411259	+	0.411259i	0.882177	−	0.470918i	$-0.156077\pi$
$397$	8.19428	+	8.19428i	0.411259	+	0.411259i	−0.470918	+	0.882177i	$0.656077\pi$
$398$	−12.3998	−	7.15900i	−0.621543	−	0.358848i
$399$		0			0
$400$		0			0
$401$	−29.1769			−1.45703			−0.728513	−	0.685032i	$-0.759788\pi$
$401$	−29.1769			−1.45703			−0.728513	+	0.685032i	$0.759788\pi$
$402$		0			0
$403$	5.98502	+	5.98502i	0.298135	+	0.298135i
$404$	−5.46410	−	9.46410i	−0.271849	−	0.470857i
$405$		0			0
$406$	0.875644	+	3.26795i	0.0434575	+	0.162186i
$407$	−15.4548	+	15.4548i	−0.766067	+	0.766067i
$408$		0			0
$409$		−	13.7846i		−	0.681605i	−0.940135	−	0.340803i	$-0.889301\pi$
$409$		−	13.7846i		−	0.681605i	0.940135	−	0.340803i	$-0.110699\pi$
$410$		0			0
$411$		0			0
$412$	−3.58630	+	13.3843i	−0.176684	+	0.659395i
$413$	36.1875	−	36.1875i	1.78067	−	1.78067i
$414$		0			0
$415$		0			0
$416$	3.32051	−	12.3923i	0.162801	−	0.607583i
$417$		0			0
$418$	4.52004	−	7.82894i	0.221082	−	0.382926i
$419$	−33.4641			−1.63483			−0.817414	−	0.576050i	$-0.804593\pi$
$419$	−33.4641			−1.63483			−0.817414	+	0.576050i	$0.804593\pi$
$420$		0			0
$421$	−34.7846			−1.69530			−0.847649	−	0.530557i	$-0.821983\pi$
$421$	−34.7846			−1.69530			−0.847649	+	0.530557i	$0.821983\pi$
$422$	2.26002	−	3.91447i	0.110016	−	0.190553i
$423$		0			0
$424$	−10.9282	−	10.9282i	−0.530720	−	0.530720i
$425$		0			0
$426$		0			0
$427$	9.46979	−	9.46979i	0.458275	−	0.458275i
$428$	26.0106	+	6.96953i	1.25727	+	0.336885i
$429$		0			0
$430$		0			0
$431$		−	29.7128i		−	1.43122i	−0.698502	−	0.715608i	$-0.746150\pi$
$431$		−	29.7128i		−	1.43122i	0.698502	−	0.715608i	$-0.253850\pi$
$432$		0			0
$433$	−25.1648	+	25.1648i	−1.20935	+	1.20935i	−0.238106	+	0.971239i	$0.576526\pi$
$433$	−25.1648	+	25.1648i	−1.20935	+	1.20935i	−0.971239	+	0.238106i	$0.923474\pi$
$434$	−6.09808	−	22.7583i	−0.292717	−	1.09243i
$435$		0			0
$436$	12.1244	−	7.00000i	0.580651	−	0.335239i
$437$	−16.8690	−	16.8690i	−0.806955	−	0.806955i
$438$		0			0
$439$	23.9808			1.14454			0.572270	−	0.820066i	$-0.306063\pi$
$439$	23.9808			1.14454			0.572270	+	0.820066i	$0.306063\pi$
$440$		0			0
$441$		0			0
$442$	16.6660	+	9.62209i	0.792719	+	0.457676i
$443$	20.3538	+	20.3538i	0.967038	+	0.967038i	0.999474	−	0.0324359i	$-0.0103265\pi$
$443$	20.3538	+	20.3538i	0.967038	+	0.967038i	−0.0324359	+	0.999474i	$0.510326\pi$
$444$		0			0
$445$		0			0
$446$	3.43782	+	12.8301i	0.162786	+	0.607524i
$447$		0			0
$448$	−25.2528	+	25.2528i	−1.19308	+	1.19308i
$449$			6.14359i			0.289934i	0.989436	+	0.144967i	$0.0463076\pi$
$449$			6.14359i			0.289934i	−0.989436	+	0.144967i	$0.953692\pi$
$450$		0			0
$451$			2.92820i			0.137884i
$452$	−26.7685	−	7.17260i	−1.25909	−	0.337371i
$453$		0			0
$454$	11.4641	−	3.07180i	0.538037	−	0.144167i
$455$		0			0
$456$		0			0
$457$	13.9391	+	13.9391i	0.652042	+	0.652042i	0.953484	−	0.301442i	$-0.0974681\pi$
$457$	13.9391	+	13.9391i	0.652042	+	0.652042i	−0.301442	+	0.953484i	$0.597468\pi$
$458$	−2.01978	+	3.49837i	−0.0943783	+	0.163468i
$459$		0			0
$460$		0			0
$461$	−36.3923			−1.69496			−0.847479	−	0.530828i	$-0.821881\pi$
$461$	−36.3923			−1.69496			−0.847479	+	0.530828i	$0.821881\pi$
$462$		0			0
$463$	19.0411	+	19.0411i	0.884916	+	0.884916i	0.994029	−	0.109114i	$-0.0348012\pi$
$463$	19.0411	+	19.0411i	0.884916	+	0.884916i	−0.109114	+	0.994029i	$0.534801\pi$
$464$	1.85641	+	1.07180i	0.0861815	+	0.0497569i
$465$		0			0
$466$	−11.4641	+	3.07180i	−0.531064	+	0.142298i
$467$	−2.44949	+	2.44949i	−0.113349	+	0.113349i	−0.761506	−	0.648157i	$-0.775540\pi$
$467$	−2.44949	+	2.44949i	−0.113349	+	0.113349i	0.648157	+	0.761506i	$0.275540\pi$
$468$		0			0
$469$			24.7128i			1.14113i
$470$		0			0
$471$		0			0
$472$		−	32.4254i		−	1.49250i
$473$	−6.31319	+	6.31319i	−0.290281	+	0.290281i
$474$		0			0
$475$		0			0
$476$	−26.7846	−	46.3923i	−1.22767	−	2.12639i
$477$		0			0
$478$	−12.9038	−	7.45001i	−0.590206	−	0.340755i
$479$	21.3205			0.974159			0.487079	−	0.873358i	$-0.338062\pi$
$479$	21.3205			0.974159			0.487079	+	0.873358i	$0.338062\pi$
$480$		0			0
$481$	−24.7846			−1.13008
$482$	−15.7458	−	9.09085i	−0.717202	−	0.414077i
$483$		0			0
$484$	7.00000	+	12.1244i	0.318182	+	0.551107i
$485$		0			0
$486$		0			0
$487$	−20.1272	+	20.1272i	−0.912049	+	0.912049i	−0.996433	−	0.0843846i	$-0.973108\pi$
$487$	−20.1272	+	20.1272i	−0.912049	+	0.912049i	0.0843846	+	0.996433i	$0.473108\pi$
$488$		−	8.48528i		−	0.384111i
$489$		0			0
$490$		0			0
$491$			34.6410i			1.56333i	0.623700	+	0.781664i	$0.285629\pi$
$491$			34.6410i			1.56333i	−0.623700	+	0.781664i	$0.714371\pi$
$492$		0			0
$493$	−2.27362	+	2.27362i	−0.102399	+	0.102399i
$494$	9.90192	−	2.65321i	0.445509	−	0.119374i
$495$		0			0
$496$	−12.9282	−	7.46410i	−0.580493	−	0.335148i
$497$	8.00481	+	8.00481i	0.359065	+	0.359065i
$498$		0			0
$499$	30.1244			1.34855			0.674276	−	0.738480i	$-0.264456\pi$
$499$	30.1244			1.34855			0.674276	+	0.738480i	$0.264456\pi$
$500$		0			0
$501$		0			0
$502$	21.1117	−	36.5665i	0.942260	−	1.63204i
$503$	0.277401	+	0.277401i	0.0123687	+	0.0123687i	0.713264	−	0.700895i	$-0.247216\pi$
$503$	0.277401	+	0.277401i	0.0123687	+	0.0123687i	−0.700895	+	0.713264i	$0.747216\pi$
$504$		0			0
$505$		0			0
$506$	−20.3923	+	5.46410i	−0.906549	+	0.242909i
$507$		0			0
$508$	21.1117	+	5.65685i	0.936679	+	0.250982i
$509$		−	24.9282i		−	1.10492i	−0.833538	−	0.552462i	$-0.813689\pi$
$509$		−	24.9282i		−	1.10492i	0.833538	−	0.552462i	$-0.186311\pi$
$510$		0			0
$511$			17.8564i			0.789921i
$512$			22.6274i			1.00000i
$513$		0			0
$514$	−10.5359	−	39.3205i	−0.464719	−	1.73435i
$515$		0			0
$516$		0			0
$517$	−1.31268	−	1.31268i	−0.0577315	−	0.0577315i
$518$	59.7487	+	34.4959i	2.62521	+	1.51566i
$519$		0			0
$520$		0			0
$521$	38.3923			1.68200			0.840999	−	0.541037i	$-0.181968\pi$
$521$	38.3923			1.68200			0.840999	+	0.541037i	$0.181968\pi$
$522$		0			0
$523$	0.984508	+	0.984508i	0.0430495	+	0.0430495i	0.728304	−	0.685254i	$-0.240309\pi$
$523$	0.984508	+	0.984508i	0.0430495	+	0.0430495i	−0.685254	+	0.728304i	$0.740309\pi$
$524$	4.39230	−	2.53590i	0.191879	−	0.110781i
$525$		0			0
$526$	−5.32051	−	19.8564i	−0.231985	−	0.865780i
$527$	15.8338	−	15.8338i	0.689729	−	0.689729i
$528$		0			0
$529$			32.7128i			1.42230i
$530$		0			0
$531$		0			0
$532$	−27.5636	−	7.38563i	−1.19503	−	0.320208i
$533$	−2.34795	+	2.34795i	−0.101701	+	0.101701i
$534$		0			0
$535$		0			0
$536$	11.0718	+	11.0718i	0.478229	+	0.478229i
$537$		0			0
$538$	15.8338	−	27.4249i	0.682641	−	1.18237i
$539$	−25.8564			−1.11371
$540$		0			0
$541$	7.78461			0.334687			0.167343	−	0.985899i	$-0.446481\pi$
$541$	7.78461			0.334687			0.167343	+	0.985899i	$0.446481\pi$
$542$	17.1464	−	29.6985i	0.736502	−	1.27566i
$543$		0			0
$544$	−32.7846	−	8.78461i	−1.40563	−	0.376637i
$545$		0			0
$546$		0			0
$547$	−11.8685	+	11.8685i	−0.507461	+	0.507461i	−0.913746	−	0.406285i	$-0.866824\pi$
$547$	−11.8685	+	11.8685i	−0.507461	+	0.507461i	0.406285	+	0.913746i	$0.366824\pi$
$548$	−8.00481	+	29.8744i	−0.341948	+	1.27617i
$549$		0			0
$550$		0			0
$551$			1.71281i			0.0729683i
$552$		0			0
$553$	23.5612	−	23.5612i	1.00192	−	1.00192i
$554$	3.36603	+	12.5622i	0.143009	+	0.533716i
$555$		0			0
$556$	12.5359	+	21.7128i	0.531641	+	0.920828i
$557$	−8.66115	−	8.66115i	−0.366985	−	0.366985i	0.499392	−	0.866376i	$-0.333557\pi$
$557$	−8.66115	−	8.66115i	−0.366985	−	0.366985i	−0.866376	+	0.499392i	$0.833557\pi$
$558$		0			0
$559$	−10.1244			−0.428215
$560$		0			0
$561$		0			0
$562$	7.82894	+	4.52004i	0.330244	+	0.190666i
$563$	−27.7023	−	27.7023i	−1.16751	−	1.16751i	−0.982791	−	0.184720i	$-0.940862\pi$
$563$	−27.7023	−	27.7023i	−1.16751	−	1.16751i	−0.184720	−	0.982791i	$-0.559138\pi$
$564$		0			0
$565$		0			0
$566$	0.222432	+	0.830127i	0.00934951	+	0.0348928i
$567$		0			0
$568$	7.17260			0.300956
$569$		−	17.3205i		−	0.726113i	−0.931767	−	0.363057i	$-0.881733\pi$
$569$		−	17.3205i		−	0.726113i	0.931767	−	0.363057i	$-0.118267\pi$
$570$		0			0
$571$			27.1962i			1.13812i	0.822295	+	0.569062i	$0.192693\pi$
$571$			27.1962i			1.13812i	−0.822295	+	0.569062i	$0.807307\pi$
$572$	2.34795	−	8.76268i	0.0981729	−	0.366386i
$573$		0			0
$574$	8.92820	−	2.39230i	0.372656	−	0.0998529i
$575$		0			0
$576$		0			0
$577$	−23.0943	−	23.0943i	−0.961428	−	0.961428i	0.0378555	−	0.999283i	$-0.487947\pi$
$577$	−23.0943	−	23.0943i	−0.961428	−	0.961428i	−0.999283	+	0.0378555i	$0.987947\pi$
$578$	13.4350	−	23.2702i	0.558824	−	0.967911i
$579$		0			0
$580$		0			0
$581$	−57.7128			−2.39433
$582$		0			0
$583$	−7.72741	−	7.72741i	−0.320036	−	0.320036i
$584$	8.00000	+	8.00000i	0.331042	+	0.331042i
$585$		0			0
$586$	26.5885	−	7.12436i	1.09836	−	0.294304i
$587$	10.8332	−	10.8332i	0.447135	−	0.447135i	−0.447266	−	0.894401i	$-0.647602\pi$
$587$	10.8332	−	10.8332i	0.447135	−	0.447135i	0.894401	+	0.447266i	$0.147602\pi$
$588$		0			0
$589$		−	11.9282i		−	0.491493i
$590$		0			0
$591$		0			0
$592$	42.2233	−	11.3137i	1.73537	−	0.464991i
$593$	8.20788	−	8.20788i	0.337057	−	0.337057i	−0.518201	−	0.855259i	$-0.673398\pi$
$593$	8.20788	−	8.20788i	0.337057	−	0.337057i	0.855259	+	0.518201i	$0.173398\pi$
$594$		0			0
$595$		0			0
$596$	20.5359	−	11.8564i	0.841183	−	0.485657i
$597$		0			0
$598$	−20.7327	−	11.9700i	−0.847824	−	0.489492i
$599$	−22.6410			−0.925087			−0.462543	−	0.886597i	$-0.653063\pi$
$599$	−22.6410			−0.925087			−0.462543	+	0.886597i	$0.653063\pi$
$600$		0			0
$601$	21.7846			0.888613			0.444306	−	0.895875i	$-0.353450\pi$
$601$	21.7846			0.888613			0.444306	+	0.895875i	$0.353450\pi$
$602$	24.4070	+	14.0914i	0.994754	+	0.574321i
$603$		0			0
$604$	−13.3923	+	7.73205i	−0.544925	+	0.314613i
$605$		0			0
$606$		0			0
$607$	−25.2528	+	25.2528i	−1.02498	+	1.02498i	−0.0252985	+	0.999680i	$0.508054\pi$
$607$	−25.2528	+	25.2528i	−1.02498	+	1.02498i	−0.999680	+	0.0252985i	$0.991946\pi$
$608$	−15.6579	+	9.04008i	−0.635011	+	0.366624i
$609$		0			0
$610$		0			0
$611$		−	2.10512i		−	0.0851639i
$612$		0			0
$613$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$613$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$614$	10.0981	−	2.70577i	0.407525	−	0.109196i
$615$		0			0
$616$	−17.8564	+	17.8564i	−0.719455	+	0.719455i
$617$	24.2175	+	24.2175i	0.974960	+	0.974960i	0.999694	−	0.0247344i	$-0.00787400\pi$
$617$	24.2175	+	24.2175i	0.974960	+	0.974960i	−0.0247344	+	0.999694i	$0.507874\pi$
$618$		0			0
$619$	15.9808			0.642321			0.321161	−	0.947025i	$-0.395927\pi$
$619$	15.9808			0.642321			0.321161	+	0.947025i	$0.395927\pi$
$620$		0			0
$621$		0			0
$622$	−14.5211	+	25.1512i	−0.582242	+	1.00847i
$623$	−21.8695	−	21.8695i	−0.876185	−	0.876185i
$624$		0			0
$625$		0			0
$626$	22.0263	−	5.90192i	0.880347	−	0.235888i
$627$		0			0
$628$	−3.24453	+	12.1087i	−0.129471	+	0.483192i
$629$			65.5692i			2.61442i
$630$		0			0
$631$		−	29.5885i		−	1.17790i	−0.808170	−	0.588949i	$-0.799542\pi$
$631$		−	29.5885i		−	1.17790i	0.808170	−	0.588949i	$-0.200458\pi$
$632$		−	21.1117i		−	0.839777i
$633$		0			0
$634$	2.53590	+	9.46410i	0.100713	+	0.375867i
$635$		0			0
$636$		0			0
$637$	−20.7327	−	20.7327i	−0.821461	−	0.821461i
$638$	1.31268	+	0.757875i	0.0519694	+	0.0300045i
$639$		0			0
$640$		0			0
$641$	44.7846			1.76889			0.884443	−	0.466648i	$-0.154539\pi$
$641$	44.7846			1.76889			0.884443	+	0.466648i	$0.154539\pi$
$642$		0			0
$643$	21.8695	+	21.8695i	0.862451	+	0.862451i	0.991622	−	0.129172i	$-0.0412318\pi$
$643$	21.8695	+	21.8695i	0.862451	+	0.862451i	−0.129172	+	0.991622i	$0.541232\pi$
$644$	33.3205	+	57.7128i	1.31301	+	2.27420i
$645$		0			0
$646$	−7.01924	−	26.1962i	−0.276168	−	1.03067i
$647$	13.3843	−	13.3843i	0.526190	−	0.526190i	−0.393244	−	0.919434i	$-0.628647\pi$
$647$	13.3843	−	13.3843i	0.526190	−	0.526190i	0.919434	+	0.393244i	$0.128647\pi$
$648$		0			0
$649$		−	22.9282i		−	0.900011i
$650$		0			0
$651$		0			0
$652$	−3.90087	+	14.5582i	−0.152770	+	0.570145i
$653$	7.34847	−	7.34847i	0.287568	−	0.287568i	−0.548550	−	0.836118i	$-0.684820\pi$
$653$	7.34847	−	7.34847i	0.287568	−	0.287568i	0.836118	+	0.548550i	$0.184820\pi$
$654$		0			0
$655$		0			0
$656$	2.92820	−	5.07180i	0.114327	−	0.198020i
$657$		0			0
$658$	−2.92996	+	5.07484i	−0.114222	+	0.197838i
$659$	21.4641			0.836123			0.418061	−	0.908419i	$-0.362710\pi$
$659$	21.4641			0.836123			0.418061	+	0.908419i	$0.362710\pi$
$660$		0			0
$661$	19.8564			0.772325			0.386162	−	0.922431i	$-0.373800\pi$
$661$	19.8564			0.772325			0.386162	+	0.922431i	$0.373800\pi$
$662$	−13.0053	+	22.5259i	−0.505466	+	0.875493i
$663$		0			0
$664$	−25.8564	+	25.8564i	−1.00342	+	1.00342i
$665$		0			0
$666$		0			0
$667$	2.82843	−	2.82843i	0.109517	−	0.109517i
$668$	−31.6675	−	8.48528i	−1.22525	−	0.328305i
$669$		0			0
$670$		0			0
$671$		−	6.00000i		−	0.231627i
$672$		0			0
$673$	2.82843	−	2.82843i	0.109028	−	0.109028i	−0.650488	−	0.759516i	$-0.725436\pi$
$673$	2.82843	−	2.82843i	0.109028	−	0.109028i	0.759516	+	0.650488i	$0.225436\pi$
$674$	−10.4904	−	39.1506i	−0.404074	−	1.50803i
$675$		0			0
$676$	−13.6077	+	7.85641i	−0.523373	+	0.302169i
$677$	−23.0807	−	23.0807i	−0.887063	−	0.887063i	0.107177	−	0.994240i	$-0.465819\pi$
$677$	−23.0807	−	23.0807i	−0.887063	−	0.887063i	−0.994240	+	0.107177i	$0.965819\pi$
$678$		0			0
$679$	−43.4449			−1.66726
$680$		0			0
$681$		0			0
$682$	−9.14162	−	5.27792i	−0.350051	−	0.202102i
$683$	13.3843	+	13.3843i	0.512135	+	0.512135i	0.915180	−	0.403045i	$-0.132048\pi$
$683$	13.3843	+	13.3843i	0.512135	+	0.512135i	−0.403045	+	0.915180i	$0.632048\pi$
$684$		0			0
$685$		0			0
$686$	9.68653	+	36.1506i	0.369834	+	1.38024i
$687$		0			0
$688$	17.2480	−	4.62158i	0.657572	−	0.176196i
$689$		−	12.3923i		−	0.472109i
$690$		0			0
$691$			9.32051i			0.354569i	0.984160	+	0.177284i	$0.0567312\pi$
$691$			9.32051i			0.354569i	−0.984160	+	0.177284i	$0.943269\pi$
$692$	9.52056	+	2.55103i	0.361917	+	0.0969754i
$693$		0			0
$694$	−34.0526	+	9.12436i	−1.29262	+	0.346356i
$695$		0			0
$696$		0			0
$697$	6.21166	+	6.21166i	0.235283	+	0.235283i
$698$	16.8690	−	29.2180i	0.638502	−	1.10592i
$699$		0			0
$700$		0			0
$701$	8.53590			0.322396			0.161198	−	0.986922i	$-0.448464\pi$
$701$	8.53590			0.322396			0.161198	+	0.986922i	$0.448464\pi$
$702$		0			0
$703$	24.6980	+	24.6980i	0.931502	+	0.931502i
$704$			16.0000i			0.603023i
$705$		0			0
$706$	16.1962	−	4.33975i	0.609550	−	0.163328i
$707$	−17.2480	+	17.2480i	−0.648676	+	0.648676i
$708$		0			0
$709$		−	2.85641i		−	0.107275i	−0.998560	−	0.0536373i	$-0.982919\pi$
$709$		−	2.85641i		−	0.107275i	0.998560	−	0.0536373i	$-0.0170815\pi$
$710$		0			0
$711$		0			0
$712$	−19.5959			−0.734388
$713$	−19.6975	+	19.6975i	−0.737675	+	0.737675i
$714$		0			0
$715$		0			0
$716$	9.32051	+	16.1436i	0.348324	+	0.603314i
$717$		0			0
$718$	4.41851	+	2.55103i	0.164897	+	0.0952034i
$719$	0.928203			0.0346161			0.0173081	−	0.999850i	$-0.494490\pi$
$719$	0.928203			0.0346161			0.0173081	+	0.999850i	$0.494490\pi$
$720$		0			0
$721$	30.9282			1.15183
$722$	10.7589	+	6.21166i	0.400405	+	0.231174i
$723$		0			0
$724$	−0.0717968	−	0.124356i	−0.00266831	−	0.00462164i
$725$		0			0
$726$		0			0
$727$	20.5804	−	20.5804i	0.763286	−	0.763286i	−0.213629	−	0.976915i	$-0.568528\pi$
$727$	20.5804	−	20.5804i	0.763286	−	0.763286i	0.976915	+	0.213629i	$0.0685284\pi$
$728$	−28.6360			−1.06132
$729$		0			0
$730$		0			0
$731$			26.7846i			0.990665i
$732$		0			0
$733$	−25.2528	+	25.2528i	−0.932732	+	0.932732i	−0.997876	−	0.0651435i	$-0.979249\pi$
$733$	−25.2528	+	25.2528i	−0.932732	+	0.932732i	0.0651435	+	0.997876i	$0.479249\pi$
$734$	−42.8827	+	11.4904i	−1.58283	+	0.424118i
$735$		0			0
$736$	40.7846	+	10.9282i	1.50334	+	0.402819i
$737$	7.82894	+	7.82894i	0.288383	+	0.288383i
$738$		0			0
$739$	−6.39230			−0.235145			−0.117572	−	0.993064i	$-0.537511\pi$
$739$	−6.39230			−0.235145			−0.117572	+	0.993064i	$0.537511\pi$
$740$		0			0
$741$		0			0
$742$	−17.2480	+	29.8744i	−0.633193	+	1.09672i
$743$	12.0716	+	12.0716i	0.442863	+	0.442863i	0.892973	−	0.450110i	$-0.148615\pi$
$743$	12.0716	+	12.0716i	0.442863	+	0.442863i	−0.450110	+	0.892973i	$0.648615\pi$
$744$		0			0
$745$		0			0
$746$	−50.0788	+	13.4186i	−1.83352	+	0.491289i
$747$		0			0
$748$	−23.1822	−	6.21166i	−0.847626	−	0.227121i
$749$		−	60.1051i		−	2.19619i
$750$		0			0
$751$		−	4.53590i		−	0.165517i	−0.996570	−	0.0827586i	$-0.973627\pi$
$751$		−	4.53590i		−	0.165517i	0.996570	−	0.0827586i	$-0.0263731\pi$
$752$	0.960947	+	3.58630i	0.0350421	+	0.130779i
$753$		0			0
$754$	0.444864	+	1.66025i	0.0162010	+	0.0604629i
$755$		0			0
$756$		0			0
$757$	13.2963	+	13.2963i	0.483263	+	0.483263i	0.906172	−	0.422909i	$-0.138991\pi$
$757$	13.2963	+	13.2963i	0.483263	+	0.483263i	−0.422909	+	0.906172i	$0.638991\pi$
$758$	15.0251	+	8.67475i	0.545736	+	0.315081i
$759$		0			0
$760$		0			0
$761$	22.6410			0.820736			0.410368	−	0.911920i	$-0.365400\pi$
$761$	22.6410			0.820736			0.410368	+	0.911920i	$0.365400\pi$
$762$		0			0
$763$	−22.0962	−	22.0962i	−0.799935	−	0.799935i
$764$	−5.32051	+	3.07180i	−0.192489	+	0.111134i
$765$		0			0
$766$	9.07180	+	33.8564i	0.327777	+	1.22328i
$767$	18.3848	−	18.3848i	0.663836	−	0.663836i
$768$		0			0
$769$		−	16.0718i		−	0.579564i	−0.957093	−	0.289782i	$-0.906417\pi$
$769$		−	16.0718i		−	0.579564i	0.957093	−	0.289782i	$-0.0935828\pi$
$770$		0			0
$771$		0			0
$772$	19.8362	+	5.31508i	0.713919	+	0.191294i
$773$	20.6312	−	20.6312i	0.742052	−	0.742052i	−0.230920	−	0.972973i	$-0.574174\pi$
$773$	20.6312	−	20.6312i	0.742052	−	0.742052i	0.972973	+	0.230920i	$0.0741736\pi$
$774$		0			0
$775$		0			0
$776$	−19.4641	+	19.4641i	−0.698721	+	0.698721i
$777$		0			0
$778$	15.1774	−	26.2880i	0.544137	−	0.942472i
$779$	4.67949			0.167660
$780$		0			0
$781$	5.07180			0.181483
$782$	−31.6675	+	54.8497i	−1.13243	+	1.96142i
$783$		0			0
$784$	44.7846	+	25.8564i	1.59945	+	0.923443i
$785$		0			0
$786$		0			0
$787$	34.0662	−	34.0662i	1.21433	−	1.21433i	0.244741	−	0.969588i	$-0.421297\pi$
$787$	34.0662	−	34.0662i	1.21433	−	1.21433i	0.969588	−	0.244741i	$-0.0787030\pi$
$788$	3.30890	−	12.3490i	0.117875	−	0.439914i
$789$		0			0
$790$		0			0
$791$			61.8564i			2.19936i
$792$		0			0
$793$	4.81105	−	4.81105i	0.170845	−	0.170845i
$794$	−4.24167	−	15.8301i	−0.150531	−	0.561790i
$795$		0			0
$796$	10.1244	+	17.5359i	0.358848	+	0.621543i
$797$	9.79796	+	9.79796i	0.347062	+	0.347062i	0.859014	−	0.511952i	$-0.171078\pi$
$797$	9.79796	+	9.79796i	0.347062	+	0.347062i	−0.511952	+	0.859014i	$0.671078\pi$
$798$		0			0
$799$	−5.56922			−0.197025
$800$		0			0
$801$		0			0
$802$	35.7343	+	20.6312i	1.26182	+	0.728513i
$803$	5.65685	+	5.65685i	0.199626	+	0.199626i
$804$		0			0
$805$		0			0
$806$	−3.09808	−	11.5622i	−0.109125	−	0.407260i
$807$		0			0
$808$			15.4548i			0.543698i
$809$			13.1769i			0.463276i	0.972802	+	0.231638i	$0.0744084\pi$
$809$			13.1769i			0.463276i	−0.972802	+	0.231638i	$0.925592\pi$
$810$		0			0
$811$			1.87564i			0.0658628i	0.999458	+	0.0329314i	$0.0104843\pi$
$811$			1.87564i			0.0658628i	−0.999458	+	0.0329314i	$0.989516\pi$
$812$	1.23835	−	4.62158i	0.0434575	−	0.162186i
$813$		0			0
$814$	29.8564	−	8.00000i	1.04647	−	0.280400i
$815$		0			0
$816$		0			0
$817$	10.0890	+	10.0890i	0.352968	+	0.352968i
$818$	−9.74719	+	16.8826i	−0.340803	+	0.590287i
$819$		0			0
$820$		0			0
$821$	27.5692			0.962172			0.481086	−	0.876673i	$-0.340242\pi$
$821$	27.5692			0.962172			0.481086	+	0.876673i	$0.340242\pi$
$822$		0			0
$823$	−18.8145	−	18.8145i	−0.655832	−	0.655832i	0.298559	−	0.954391i	$-0.403494\pi$
$823$	−18.8145	−	18.8145i	−0.655832	−	0.655832i	−0.954391	+	0.298559i	$0.903494\pi$
$824$	13.8564	−	13.8564i	0.482711	−	0.482711i
$825$		0			0
$826$	−69.9090	+	18.7321i	−2.43244	+	0.651771i
$827$	−34.9764	+	34.9764i	−1.21625	+	1.21625i	−0.247313	+	0.968936i	$0.579548\pi$
$827$	−34.9764	+	34.9764i	−1.21625	+	1.21625i	−0.968936	+	0.247313i	$0.920452\pi$
$828$		0			0
$829$		−	37.7128i		−	1.30982i	−0.755707	−	0.654910i	$-0.772706\pi$
$829$		−	37.7128i		−	1.30982i	0.755707	−	0.654910i	$-0.227294\pi$
$830$		0			0
$831$		0			0
$832$	−12.8295	+	12.8295i	−0.444781	+	0.444781i
$833$	−54.8497	+	54.8497i	−1.90043	+	1.90043i
$834$		0			0
$835$		0			0
$836$	−11.0718	+	6.39230i	−0.382926	+	0.221082i
$837$		0			0
$838$	40.9850	+	23.6627i	1.41580	+	0.817414i
$839$	28.6410			0.988798			0.494399	−	0.869235i	$-0.335388\pi$
$839$	28.6410			0.988798			0.494399	+	0.869235i	$0.335388\pi$
$840$		0			0
$841$	28.7128			0.990097
$842$	42.6023	+	24.5964i	1.46817	+	0.847649i
$843$		0			0
$844$	−5.53590	+	3.19615i	−0.190553	+	0.110016i
$845$		0			0
$846$		0			0
$847$	22.0962	−	22.0962i	0.759234	−	0.759234i
$848$	5.65685	+	21.1117i	0.194257	+	0.724978i
$849$		0			0
$850$		0			0
$851$		−	81.5692i		−	2.79616i
$852$		0			0
$853$	−11.0227	+	11.0227i	−0.377410	+	0.377410i	−0.870167	−	0.492757i	$-0.835989\pi$
$853$	−11.0227	+	11.0227i	−0.377410	+	0.377410i	0.492757	+	0.870167i	$0.335989\pi$
$854$	−18.2942	+	4.90192i	−0.626016	+	0.167740i
$855$		0			0
$856$	−26.9282	−	26.9282i	−0.920387	−	0.920387i
$857$	5.45378	+	5.45378i	0.186298	+	0.186298i	0.794093	−	0.607796i	$-0.207946\pi$
$857$	5.45378	+	5.45378i	0.186298	+	0.186298i	−0.607796	+	0.794093i	$0.707946\pi$
$858$		0			0
$859$	42.3923			1.44641			0.723203	−	0.690635i	$-0.242669\pi$
$859$	42.3923			1.44641			0.723203	+	0.690635i	$0.242669\pi$
$860$		0			0
$861$		0			0
$862$	−21.0101	+	36.3906i	−0.715608	+	1.23947i
$863$	21.6665	+	21.6665i	0.737535	+	0.737535i	0.972100	−	0.234565i	$-0.0753666\pi$
$863$	21.6665	+	21.6665i	0.737535	+	0.737535i	−0.234565	+	0.972100i	$0.575367\pi$
$864$		0			0
$865$		0			0
$866$	48.6147	−	13.0263i	1.65200	−	0.442651i
$867$		0			0
$868$	−8.62398	+	32.1851i	−0.292717	+	1.09243i
$869$		−	14.9282i		−	0.506405i
$870$		0			0
$871$			12.5551i			0.425415i
$872$	−19.7990			−0.670478
$873$		0			0
$874$	8.73205	+	32.5885i	0.295366	+	1.10232i
$875$		0			0
$876$		0			0
$877$	−33.8260	−	33.8260i	−1.14222	−	1.14222i	−0.988043	−	0.154180i	$-0.950727\pi$
$877$	−33.8260	−	33.8260i	−1.14222	−	1.14222i	−0.154180	−	0.988043i	$-0.549273\pi$
$878$	−29.3703	−	16.9570i	−0.991200	−	0.572270i
$879$		0			0
$880$		0			0
$881$	37.0718			1.24898			0.624490	−	0.781033i	$-0.285307\pi$
$881$	37.0718			1.24898			0.624490	+	0.781033i	$0.285307\pi$
$882$		0			0
$883$	−22.7525	−	22.7525i	−0.765683	−	0.765683i	0.211660	−	0.977343i	$-0.432113\pi$
$883$	−22.7525	−	22.7525i	−0.765683	−	0.765683i	−0.977343	+	0.211660i	$0.932113\pi$
$884$	−13.6077	−	23.5692i	−0.457676	−	0.792719i
$885$		0			0
$886$	−10.5359	−	39.3205i	−0.353960	−	1.32100i
$887$	−14.0406	+	14.0406i	−0.471437	+	0.471437i	−0.902379	−	0.430942i	$-0.858181\pi$
$887$	−14.0406	+	14.0406i	−0.471437	+	0.471437i	0.430942	+	0.902379i	$0.358181\pi$
$888$		0			0
$889$		−	48.7846i		−	1.63618i
$890$		0			0
$891$		0			0
$892$	4.86181	−	18.1445i	0.162786	−	0.607524i
$893$	−2.09776	+	2.09776i	−0.0701988	+	0.0701988i
$894$		0			0
$895$		0			0
$896$	48.7846	−	13.0718i	1.62978	−	0.436698i
$897$		0			0
$898$	4.34418	−	7.52433i	0.144967	−	0.251090i
$899$	2.00000			0.0667037
$900$		0			0
$901$	−32.7846			−1.09221
$902$	2.07055	−	3.58630i	0.0689419	−	0.119411i
$903$		0			0
$904$	27.7128	+	27.7128i	0.921714	+	0.921714i
$905$		0			0
$906$		0			0
$907$	−12.6264	+	12.6264i	−0.419252	+	0.419252i	−0.884946	−	0.465694i	$-0.845805\pi$
$907$	−12.6264	+	12.6264i	−0.419252	+	0.419252i	0.465694	+	0.884946i	$0.345805\pi$
$908$	−16.2127	−	4.34418i	−0.538037	−	0.144167i
$909$		0			0
$910$		0			0
$911$			5.60770i			0.185791i	0.995676	+	0.0928956i	$0.0296123\pi$
$911$			5.60770i			0.185791i	−0.995676	+	0.0928956i	$0.970388\pi$
$912$		0			0
$913$	−18.2832	+	18.2832i	−0.605087	+	0.605087i
$914$	−7.21539	−	26.9282i	−0.238664	−	0.890706i
$915$		0			0
$916$	4.94744	−	2.85641i	0.163468	−	0.0943783i
$917$	−8.00481	−	8.00481i	−0.264342	−	0.264342i
$918$		0			0
$919$	26.6603			0.879441			0.439720	−	0.898135i	$-0.355078\pi$
$919$	26.6603			0.879441			0.439720	+	0.898135i	$0.355078\pi$
$920$		0			0
$921$		0			0
$922$	44.5713	+	25.7332i	1.46788	+	0.847479i
$923$	4.06678	+	4.06678i	0.133860	+	0.133860i
$924$		0			0
$925$		0			0
$926$	−9.85641	−	36.7846i	−0.323902	−	1.20882i
$927$		0			0
$928$	−1.51575	−	2.62536i	−0.0497569	−	0.0861815i
$929$		−	0.535898i		−	0.0175823i	−0.999961	−	0.00879113i	$-0.997202\pi$
$929$		−	0.535898i		−	0.0175823i	0.999961	−	0.00879113i	$-0.00279834\pi$
$930$		0			0
$931$			41.3205i			1.35422i
$932$	16.2127	+	4.34418i	0.531064	+	0.142298i
$933$		0			0
$934$	4.73205	−	1.26795i	0.154837	−	0.0414886i
$935$		0			0
$936$		0			0
$937$	−9.12802	−	9.12802i	−0.298199	−	0.298199i	0.542109	−	0.840308i	$-0.317626\pi$
$937$	−9.12802	−	9.12802i	−0.298199	−	0.298199i	−0.840308	+	0.542109i	$0.817626\pi$
$938$	17.4746	−	30.2669i	0.570566	−	0.988249i
$939$		0			0
$940$		0			0
$941$	−11.0718			−0.360930			−0.180465	−	0.983581i	$-0.557760\pi$
$941$	−11.0718			−0.360930			−0.180465	+	0.983581i	$0.557760\pi$
$942$		0			0
$943$	−7.72741	−	7.72741i	−0.251639	−	0.251639i
$944$	−22.9282	+	39.7128i	−0.746249	+	1.29254i
$945$		0			0
$946$	12.1962	−	3.26795i	0.396531	−	0.106250i
$947$	−22.8033	+	22.8033i	−0.741007	+	0.741007i	−0.972772	−	0.231765i	$-0.925550\pi$
$947$	−22.8033	+	22.8033i	−0.741007	+	0.741007i	0.231765	+	0.972772i	$0.425550\pi$
$948$		0			0
$949$			9.07180i			0.294483i
$950$		0			0
$951$		0			0
$952$			75.7583i			2.45534i
$953$	28.0812	−	28.0812i	0.909639	−	0.909639i	−0.0866036	−	0.996243i	$-0.527601\pi$
$953$	28.0812	−	28.0812i	0.909639	−	0.909639i	0.996243	+	0.0866036i	$0.0276014\pi$
$954$		0			0
$955$		0			0
$956$	10.5359	+	18.2487i	0.340755	+	0.590206i
$957$		0			0
$958$	−26.1122	−	15.0759i	−0.843646	−	0.487079i
$959$	69.0333			2.22920
$960$		0			0
$961$	17.0718			0.550703
$962$	30.3548	+	17.5254i	0.978679	+	0.565040i
$963$		0			0
$964$	12.8564	+	22.2679i	0.414077	+	0.717202i
$965$		0			0
$966$		0			0
$967$	−33.9411	+	33.9411i	−1.09147	+	1.09147i	−0.0961015	+	0.995372i	$0.530637\pi$
$967$	−33.9411	+	33.9411i	−1.09147	+	1.09147i	−0.995372	+	0.0961015i	$0.969363\pi$
$968$		−	19.7990i		−	0.636364i
$969$		0			0
$970$		0			0
$971$		−	43.1769i		−	1.38561i	−0.721123	−	0.692807i	$-0.756374\pi$
$971$		−	43.1769i		−	1.38561i	0.721123	−	0.692807i	$-0.243626\pi$
$972$		0			0
$973$	39.5708	−	39.5708i	1.26858	−	1.26858i
$974$	38.8827	−	10.4186i	1.24588	−	0.333833i
$975$		0			0
$976$	−6.00000	+	10.3923i	−0.192055	+	0.332650i
$977$	−16.3886	−	16.3886i	−0.524316	−	0.524316i	0.394556	−	0.918872i	$-0.370899\pi$
$977$	−16.3886	−	16.3886i	−0.524316	−	0.524316i	−0.918872	+	0.394556i	$0.870899\pi$
$978$		0			0
$979$	−13.8564			−0.442853
$980$		0			0
$981$		0			0
$982$	24.4949	−	42.4264i	0.781664	−	1.35388i
$983$	−1.31268	−	1.31268i	−0.0418679	−	0.0418679i	0.685863	−	0.727731i	$-0.259425\pi$
$983$	−1.31268	−	1.31268i	−0.0418679	−	0.0418679i	−0.727731	+	0.685863i	$0.759425\pi$
$984$		0			0
$985$		0			0
$986$	4.39230	−	1.17691i	0.139879	−	0.0374806i
$987$		0			0
$988$	−14.0034	−	3.75221i	−0.445509	−	0.119374i
$989$		−	33.3205i		−	1.05953i
$990$		0			0
$991$			26.4115i			0.838990i	0.907758	+	0.419495i	$0.137793\pi$
$991$			26.4115i			0.838990i	−0.907758	+	0.419495i	$0.862207\pi$
$992$	10.5558	+	18.2832i	0.335148	+	0.580493i
$993$		0			0
$994$	−4.14359	−	15.4641i	−0.131427	−	0.490492i
$995$		0			0
$996$		0			0
$997$	−19.5959	−	19.5959i	−0.620609	−	0.620609i	0.325078	−	0.945687i	$-0.394609\pi$
$997$	−19.5959	−	19.5959i	−0.620609	−	0.620609i	−0.945687	+	0.325078i	$0.894609\pi$
$998$	−36.8947	−	21.3011i	−1.16788	−	0.674276i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	900.2.k.l.307.1		8
3.2	odd	2		300.2.j.c.7.4	yes	8
4.3	odd	2		900.2.k.g.307.1		8
5.2	odd	4		900.2.k.g.343.3		8
5.3	odd	4		900.2.k.g.343.2		8
5.4	even	2	inner	900.2.k.l.307.4		8
12.11	even	2		300.2.j.a.7.4	yes	8
15.2	even	4		300.2.j.a.43.2	yes	8
15.8	even	4		300.2.j.a.43.3	yes	8
15.14	odd	2		300.2.j.c.7.1	yes	8
20.3	even	4	inner	900.2.k.l.343.2		8
20.7	even	4	inner	900.2.k.l.343.3		8
20.19	odd	2		900.2.k.g.307.4		8
60.23	odd	4		300.2.j.c.43.3	yes	8
60.47	odd	4		300.2.j.c.43.2	yes	8
60.59	even	2		300.2.j.a.7.1	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
300.2.j.a.7.1	✓	8	60.59	even	2
300.2.j.a.7.4	yes	8	12.11	even	2
300.2.j.a.43.2	yes	8	15.2	even	4
300.2.j.a.43.3	yes	8	15.8	even	4
300.2.j.c.7.1	yes	8	15.14	odd	2
300.2.j.c.7.4	yes	8	3.2	odd	2
300.2.j.c.43.2	yes	8	60.47	odd	4
300.2.j.c.43.3	yes	8	60.23	odd	4
900.2.k.g.307.1		8	4.3	odd	2
900.2.k.g.307.4		8	20.19	odd	2
900.2.k.g.343.2		8	5.3	odd	4
900.2.k.g.343.3		8	5.2	odd	4
900.2.k.l.307.1		8	1.1	even	1	trivial
900.2.k.l.307.4		8	5.4	even	2	inner
900.2.k.l.343.2		8	20.3	even	4	inner
900.2.k.l.343.3		8	20.7	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	900.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.22474 - 0.707107i) q^{2} +(1.00000 + 1.73205i) q^{4} +(3.15660 - 3.15660i) q^{7} -2.82843i q^{8} +O(q^{10})\)	\(q+(-1.22474 - 0.707107i) q^{2} +(1.00000 + 1.73205i) q^{4} +(3.15660 - 3.15660i) q^{7} -2.82843i q^{8} -2.00000i q^{11} +(1.60368 - 1.60368i) q^{13} +(-6.09808 + 1.63397i) q^{14} +(-2.00000 + 3.46410i) q^{16} +(-4.24264 - 4.24264i) q^{17} -3.19615 q^{19} +(-1.41421 + 2.44949i) q^{22} +(5.27792 + 5.27792i) q^{23} +(-3.09808 + 0.830127i) q^{26} +(8.62398 + 2.31079i) q^{28} -0.535898i q^{29} +3.73205i q^{31} +(4.89898 - 2.82843i) q^{32} +(2.19615 + 8.19615i) q^{34} +(-7.72741 - 7.72741i) q^{37} +(3.91447 + 2.26002i) q^{38} -1.46410 q^{41} +(-3.15660 - 3.15660i) q^{43} +(3.46410 - 2.00000i) q^{44} +(-2.73205 - 10.1962i) q^{46} +(0.656339 - 0.656339i) q^{47} -12.9282i q^{49} +(4.38134 + 1.17398i) q^{52} +(3.86370 - 3.86370i) q^{53} +(-8.92820 - 8.92820i) q^{56} +(-0.378937 + 0.656339i) q^{58} +11.4641 q^{59} +3.00000 q^{61} +(2.63896 - 4.57081i) q^{62} -8.00000 q^{64} +(-3.91447 + 3.91447i) q^{67} +(3.10583 - 11.5911i) q^{68} +2.53590i q^{71} +(-2.82843 + 2.82843i) q^{73} +(4.00000 + 14.9282i) q^{74} +(-3.19615 - 5.53590i) q^{76} +(-6.31319 - 6.31319i) q^{77} +7.46410 q^{79} +(1.79315 + 1.03528i) q^{82} +(-9.14162 - 9.14162i) q^{83} +(1.63397 + 6.09808i) q^{86} -5.65685 q^{88} -6.92820i q^{89} -10.1244i q^{91} +(-3.86370 + 14.4195i) q^{92} +(-1.26795 + 0.339746i) q^{94} +(-6.88160 - 6.88160i) q^{97} +(-9.14162 + 15.8338i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{4}+O(q^{10}) \) 8 * q + 8 * q^4	\( 8 q + 8 q^{4} - 28 q^{14} - 16 q^{16} + 16 q^{19} - 4 q^{26} - 24 q^{34} + 16 q^{41} - 8 q^{46} - 16 q^{56} + 64 q^{59} + 24 q^{61} - 64 q^{64} + 32 q^{74} + 16 q^{76} + 32 q^{79} + 20 q^{86} - 24 q^{94}+O(q^{100}) \) 8 * q + 8 * q^4 - 28 * q^14 - 16 * q^16 + 16 * q^19 - 4 * q^26 - 24 * q^34 + 16 * q^41 - 8 * q^46 - 16 * q^56 + 64 * q^59 + 24 * q^61 - 64 * q^64 + 32 * q^74 + 16 * q^76 + 32 * q^79 + 20 * q^86 - 24 * q^94

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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