LMFDB - Embedded newform 900.2.k.g.343.3

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			343.3
Root			$-0.965926 + 0.258819i$ of defining polynomial
Character	$\chi$	$=$	900.343
Dual form			900.2.k.g.307.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 1.22474i) q^{2} +(-1.00000 - 1.73205i) q^{4} +(3.15660 + 3.15660i) q^{7} -2.82843 q^{8} +O(q^{10})$	\(q+(0.707107 - 1.22474i) q^{2} +(-1.00000 - 1.73205i) q^{4} +(3.15660 + 3.15660i) q^{7} -2.82843 q^{8} -2.00000i q^{11} +(-1.60368 - 1.60368i) q^{13} +(6.09808 - 1.63397i) q^{14} +(-2.00000 + 3.46410i) q^{16} +(4.24264 - 4.24264i) q^{17} +3.19615 q^{19} +(-2.44949 - 1.41421i) q^{22} +(5.27792 - 5.27792i) q^{23} +(-3.09808 + 0.830127i) q^{26} +(2.31079 - 8.62398i) q^{28} +0.535898i q^{29} +3.73205i q^{31} +(2.82843 + 4.89898i) q^{32} +(-2.19615 - 8.19615i) q^{34} +(7.72741 - 7.72741i) q^{37} +(2.26002 - 3.91447i) q^{38} -1.46410 q^{41} +(-3.15660 + 3.15660i) q^{43} +(-3.46410 + 2.00000i) q^{44} +(-2.73205 - 10.1962i) q^{46} +(0.656339 + 0.656339i) q^{47} +12.9282i q^{49} +(-1.17398 + 4.38134i) q^{52} +(-3.86370 - 3.86370i) q^{53} +(-8.92820 - 8.92820i) q^{56} +(0.656339 + 0.378937i) q^{58} -11.4641 q^{59} +3.00000 q^{61} +(4.57081 + 2.63896i) q^{62} +8.00000 q^{64} +(-3.91447 - 3.91447i) q^{67} +(-11.5911 - 3.10583i) q^{68} +2.53590i q^{71} +(2.82843 + 2.82843i) q^{73} +(-4.00000 - 14.9282i) q^{74} +(-3.19615 - 5.53590i) q^{76} +(6.31319 - 6.31319i) q^{77} -7.46410 q^{79} +(-1.03528 + 1.79315i) q^{82} +(-9.14162 + 9.14162i) q^{83} +(1.63397 + 6.09808i) q^{86} +5.65685i q^{88} +6.92820i q^{89} -10.1244i q^{91} +(-14.4195 - 3.86370i) q^{92} +(1.26795 - 0.339746i) q^{94} +(6.88160 - 6.88160i) q^{97} +(15.8338 + 9.14162i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/900\mathbb{Z}\right)^\times$.

$n$	$101$	$451$	$577$
$\chi(n)$	$1$	$-1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	0.707107	−	1.22474i	0.500000	−	0.866025i
$2$	0.707107	−	1.22474i	0.500000	−	0.866025i
$3$		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	0.976197	+	0.216884i	$0.0695893\pi$
$7$	3.15660	+	3.15660i	1.19308	+	1.19308i	0.216884	+	0.976197i	$0.430411\pi$
$8$	−2.82843			−1.00000
$9$		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	$-0.351840\pi$
$13$	−1.60368	−	1.60368i	−0.444781	−	0.444781i	−0.893615	+	0.448834i	$0.851840\pi$
$14$	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	0.0294245	−	0.999567i	$-0.490633\pi$
$17$	4.24264	−	4.24264i	1.02899	−	1.02899i	0.999567	−	0.0294245i	$-0.00936746\pi$
$18$		0			0
$19$	3.19615			0.733248			0.366624	−	0.930369i	$-0.380514\pi$
$19$	3.19615			0.733248			0.366624	+	0.930369i	$0.380514\pi$
$20$		0			0
$21$		0			0
$22$	−2.44949	−	1.41421i	−0.522233	−	0.301511i
$23$	5.27792	−	5.27792i	1.10052	−	1.10052i	0.106174	−	0.994348i	$-0.466140\pi$
$23$	5.27792	−	5.27792i	1.10052	−	1.10052i	0.994348	−	0.106174i	$-0.0338601\pi$
$24$		0			0
$25$		0			0
$26$	−3.09808	+	0.830127i	−0.607583	+	0.162801i
$27$		0			0
$28$	2.31079	−	8.62398i	0.436698	−	1.62978i
$29$			0.535898i			0.0995138i	0.998761	+	0.0497569i	$0.0158447\pi$
$29$			0.535898i			0.0995138i	−0.998761	+	0.0497569i	$0.984155\pi$
$30$		0			0
$31$			3.73205i			0.670296i	0.942165	+	0.335148i	$0.108786\pi$
$31$			3.73205i			0.670296i	−0.942165	+	0.335148i	$0.891214\pi$
$32$	2.82843	+	4.89898i	0.500000	+	0.866025i
$33$		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	0.324488	−	0.945890i	$-0.394808\pi$
$37$	7.72741	−	7.72741i	1.27038	−	1.27038i	0.945890	−	0.324488i	$-0.105192\pi$
$38$	2.26002	−	3.91447i	0.366624	−	0.635011i
$39$		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	−0.905571	−	0.424195i	$-0.860557\pi$
$43$	−3.15660	+	3.15660i	−0.481376	+	0.481376i	0.424195	+	0.905571i	$0.360557\pi$
$44$	−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	0.753353	−	0.657616i	$-0.228435\pi$
$47$	0.656339	+	0.656339i	0.0957369	+	0.0957369i	−0.657616	+	0.753353i	$0.728435\pi$
$48$		0			0
$49$			12.9282i			1.84689i
$50$		0			0
$51$		0			0
$52$	−1.17398	+	4.38134i	−0.162801	+	0.607583i
$53$	−3.86370	−	3.86370i	−0.530720	−	0.530720i	0.390066	−	0.920787i	$-0.372452\pi$
$53$	−3.86370	−	3.86370i	−0.530720	−	0.530720i	−0.920787	+	0.390066i	$0.872452\pi$
$54$		0			0
$55$		0			0
$56$	−8.92820	−	8.92820i	−1.19308	−	1.19308i
$57$		0			0
$58$	0.656339	+	0.378937i	0.0861815	+	0.0497569i
$59$	−11.4641			−1.49250			−0.746249	−	0.665666i	$-0.768147\pi$
$59$	−11.4641			−1.49250			−0.746249	+	0.665666i	$0.768147\pi$
$60$		0			0
$61$	3.00000			0.384111			0.192055	−	0.981384i	$-0.438485\pi$
$61$	3.00000			0.384111			0.192055	+	0.981384i	$0.438485\pi$
$62$	4.57081	+	2.63896i	0.580493	+	0.335148i
$63$		0			0
$64$	8.00000			1.00000
$65$		0			0
$66$		0			0
$67$	−3.91447	−	3.91447i	−0.478229	−	0.478229i	0.426336	−	0.904565i	$-0.359804\pi$
$67$	−3.91447	−	3.91447i	−0.478229	−	0.478229i	−0.904565	+	0.426336i	$0.859804\pi$
$68$	−11.5911	−	3.10583i	−1.40563	−	0.376637i
$69$		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	$-0.174791\pi$
$73$	2.82843	+	2.82843i	0.331042	+	0.331042i	−0.521940	+	0.852982i	$0.674791\pi$
$74$	−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	$-0.637931\pi$
$79$	−7.46410			−0.839777			−0.419889	+	0.907576i	$0.637931\pi$
$80$		0			0
$81$		0			0
$82$	−1.03528	+	1.79315i	−0.114327	+	0.198020i
$83$	−9.14162	+	9.14162i	−1.00342	+	1.00342i	−0.00342905	+	0.999994i	$0.501092\pi$
$83$	−9.14162	+	9.14162i	−1.00342	+	1.00342i	−0.999994	+	0.00342905i	$0.998908\pi$
$84$		0			0
$85$		0			0
$86$	1.63397	+	6.09808i	0.176196	+	0.657572i
$87$		0			0
$88$			5.65685i			0.603023i
$89$			6.92820i			0.734388i	0.930144	+	0.367194i	$0.119682\pi$
$89$			6.92820i			0.734388i	−0.930144	+	0.367194i	$0.880318\pi$
$90$		0			0
$91$		−	10.1244i		−	1.06132i
$92$	−14.4195	−	3.86370i	−1.50334	−	0.402819i
$93$		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	$-0.585509\pi$
$97$	6.88160	−	6.88160i	0.698721	−	0.698721i	0.964135	+	0.265414i	$0.0855086\pi$
$98$	15.8338	+	9.14162i	1.59945	+	0.923443i
$99$		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	−0.423286	−	0.905996i	$-0.639123\pi$
$103$	4.89898	−	4.89898i	0.482711	−	0.482711i	0.905996	+	0.423286i	$0.139123\pi$
$104$	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	0.997057	−	0.0766695i	$-0.0244286\pi$
$107$	9.52056	+	9.52056i	0.920387	+	0.920387i	−0.0766695	+	0.997057i	$0.524429\pi$
$108$		0			0
$109$			7.00000i			0.670478i	0.942133	+	0.335239i	$0.108817\pi$
$109$			7.00000i			0.670478i	−0.942133	+	0.335239i	$0.891183\pi$
$110$		0			0
$111$		0			0
$112$	−17.2480	+	4.62158i	−1.62978	+	0.436698i
$113$	9.79796	+	9.79796i	0.921714	+	0.921714i	0.997151	−	0.0754362i	$-0.0240349\pi$
$113$	9.79796	+	9.79796i	0.921714	+	0.921714i	−0.0754362	+	0.997151i	$0.524035\pi$
$114$		0			0
$115$		0			0
$116$	0.928203	−	0.535898i	0.0861815	−	0.0497569i
$117$		0			0
$118$	−8.10634	+	14.0406i	−0.746249	+	1.29254i
$119$	26.7846			2.45534
$120$		0			0
$121$	7.00000			0.636364
$122$	2.12132	−	3.67423i	0.192055	−	0.332650i
$123$		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	0.961278	−	0.275581i	$-0.0888703\pi$
$127$	7.72741	+	7.72741i	0.685696	+	0.685696i	−0.275581	+	0.961278i	$0.588870\pi$
$128$	5.65685	−	9.79796i	0.500000	−	0.866025i
$129$		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	$-0.979695\pi$
$137$	−10.9348	+	10.9348i	−0.934221	+	0.934221i	0.0637456	+	0.997966i	$0.479695\pi$
$138$		0			0
$139$	−12.5359			−1.06328			−0.531641	−	0.846970i	$-0.678424\pi$
$139$	−12.5359			−1.06328			−0.531641	+	0.846970i	$0.678424\pi$
$140$		0			0
$141$		0			0
$142$	3.10583	+	1.79315i	0.260635	+	0.150478i
$143$	−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
$148$	−21.1117	−	5.65685i	−1.73537	−	0.464991i
$149$			11.8564i			0.971315i	0.874149	+	0.485657i	$0.161420\pi$
$149$			11.8564i			0.971315i	−0.874149	+	0.485657i	$0.838580\pi$
$150$		0			0
$151$			7.73205i			0.629225i	0.949220	+	0.314613i	$0.101875\pi$
$151$			7.73205i			0.629225i	−0.949220	+	0.314613i	$0.898125\pi$
$152$	−9.04008			−0.733248
$153$		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	$-0.830470\pi$
$157$	−4.43211	+	4.43211i	−0.353721	+	0.353721i	0.507771	+	0.861492i	$0.330470\pi$
$158$	−5.27792	+	9.14162i	−0.419889	+	0.727268i
$159$		0			0
$160$		0			0
$161$	33.3205			2.62602
$162$		0			0
$163$	5.32868	−	5.32868i	0.417375	−	0.417375i	−0.466923	−	0.884298i	$-0.654638\pi$
$163$	5.32868	−	5.32868i	0.417375	−	0.417375i	0.884298	+	0.466923i	$0.154638\pi$
$164$	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	0.0982179	−	0.995165i	$-0.468686\pi$
$167$	−11.5911	−	11.5911i	−0.896947	−	0.896947i	−0.995165	+	0.0982179i	$0.968686\pi$
$168$		0			0
$169$		−	7.85641i		−	0.604339i
$170$		0			0
$171$		0			0
$172$	8.62398	+	2.31079i	0.657572	+	0.176196i
$173$	−3.48477	−	3.48477i	−0.264942	−	0.264942i	0.562116	−	0.827058i	$-0.309987\pi$
$173$	−3.48477	−	3.48477i	−0.264942	−	0.264942i	−0.827058	+	0.562116i	$0.809987\pi$
$174$		0			0
$175$		0			0
$176$	6.92820	+	4.00000i	0.522233	+	0.301511i
$177$		0			0
$178$	8.48528	+	4.89898i	0.635999	+	0.367194i
$179$	−9.32051			−0.696647			−0.348324	−	0.937374i	$-0.613249\pi$
$179$	−9.32051			−0.696647			−0.348324	+	0.937374i	$0.613249\pi$
$180$		0			0
$181$	−0.0717968			−0.00533661			−0.00266831	−	0.999996i	$-0.500849\pi$
$181$	−0.0717968			−0.00533661			−0.00266831	+	0.999996i	$0.500849\pi$
$182$	−12.3998	−	7.15900i	−0.919131	−	0.530660i
$183$		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
$188$	0.480473	−	1.79315i	0.0350421	−	0.130779i
$189$		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	$-0.370489\pi$
$193$	−7.26054	−	7.26054i	−0.522625	−	0.522625i	−0.918363	+	0.395738i	$0.870489\pi$
$194$	−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	$-0.676874\pi$
$197$	4.52004	−	4.52004i	0.322040	−	0.322040i	0.849549	+	0.527509i	$0.176874\pi$
$198$		0			0
$199$	−10.1244			−0.717697			−0.358848	−	0.933396i	$-0.616830\pi$
$199$	−10.1244			−0.717697			−0.358848	+	0.933396i	$0.616830\pi$
$200$		0			0
$201$		0			0
$202$	−3.86370	+	6.69213i	−0.271849	+	0.470857i
$203$	−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
$208$	8.76268	−	2.34795i	0.607583	−	0.162801i
$209$		−	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	$0.964910\pi$
$212$	−2.82843	+	10.5558i	−0.194257	+	0.724978i
$213$		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
$218$	8.57321	+	4.94975i	0.580651	+	0.335239i
$219$		0			0
$220$		0			0
$221$	−13.6077			−0.915353
$222$		0			0
$223$	−6.64136	+	6.64136i	−0.444739	+	0.444739i	−0.893601	−	0.448862i	$-0.851829\pi$
$223$	−6.64136	+	6.64136i	−0.444739	+	0.444739i	0.448862	+	0.893601i	$0.351829\pi$
$224$	−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	0.482194	−	0.876064i	$-0.339840\pi$
$227$	−5.93426	−	5.93426i	−0.393870	−	0.393870i	−0.876064	+	0.482194i	$0.839840\pi$
$228$		0			0
$229$			2.85641i			0.188757i	0.995536	+	0.0943783i	$0.0300863\pi$
$229$			2.85641i			0.188757i	−0.995536	+	0.0943783i	$0.969914\pi$
$230$		0			0
$231$		0			0
$232$		−	1.51575i		−	0.0995138i
$233$	−5.93426	−	5.93426i	−0.388766	−	0.388766i	0.485481	−	0.874247i	$-0.338644\pi$
$233$	−5.93426	−	5.93426i	−0.388766	−	0.388766i	−0.874247	+	0.485481i	$0.838644\pi$
$234$		0			0
$235$		0			0
$236$	11.4641	+	19.8564i	0.746249	+	1.29254i
$237$		0			0
$238$	18.9396	−	32.8043i	1.22767	−	2.12639i
$239$	−10.5359			−0.681511			−0.340755	−	0.940152i	$-0.610683\pi$
$239$	−10.5359			−0.681511			−0.340755	+	0.940152i	$0.610683\pi$
$240$		0			0
$241$	12.8564			0.828154			0.414077	−	0.910242i	$-0.364104\pi$
$241$	12.8564			0.828154			0.414077	+	0.910242i	$0.364104\pi$
$242$	4.94975	−	8.57321i	0.318182	−	0.551107i
$243$		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
$248$		−	10.5558i		−	0.670296i
$249$		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	−0.323358	+	0.946277i	$0.604812\pi$
$257$	−20.3538	+	20.3538i	−1.26963	+	1.26963i	−0.946277	+	0.323358i	$0.895188\pi$
$258$		0			0
$259$	48.7846			3.03133
$260$		0			0
$261$		0			0
$262$	−3.10583	−	1.79315i	−0.191879	−	0.110781i
$263$	10.2784	−	10.2784i	0.633795	−	0.633795i	−0.315223	−	0.949018i	$-0.602079\pi$
$263$	10.2784	−	10.2784i	0.633795	−	0.633795i	0.949018	+	0.315223i	$0.102079\pi$
$264$		0			0
$265$		0			0
$266$	19.4904	−	5.22243i	1.19503	−	0.320208i
$267$		0			0
$268$	−2.86559	+	10.6945i	−0.175044	+	0.653273i
$269$		−	22.3923i		−	1.36528i	−0.730753	−	0.682641i	$-0.760831\pi$
$269$		−	22.3923i		−	1.36528i	0.730753	−	0.682641i	$-0.239169\pi$
$270$		0			0
$271$			24.2487i			1.47300i	0.676435	+	0.736502i	$0.263524\pi$
$271$			24.2487i			1.47300i	−0.676435	+	0.736502i	$0.736476\pi$
$272$	6.21166	+	23.1822i	0.376637	+	1.40563i
$273$		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	$-0.660901\pi$
$277$	6.50266	−	6.50266i	0.390707	−	0.390707i	0.874939	+	0.484232i	$0.160901\pi$
$278$	−8.86422	+	15.3533i	−0.531641	+	0.920828i
$279$		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	−0.719763	−	0.694220i	$-0.755750\pi$
$283$	−0.429705	+	0.429705i	−0.0255433	+	0.0255433i	0.694220	+	0.719763i	$0.255750\pi$
$284$	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
$292$	2.07055	−	7.72741i	0.121170	−	0.452212i
$293$	13.7632	+	13.7632i	0.804055	+	0.804055i	0.983727	−	0.179672i	$-0.0575036\pi$
$293$	13.7632	+	13.7632i	0.804055	+	0.804055i	−0.179672	+	0.983727i	$0.557504\pi$
$294$		0			0
$295$		0			0
$296$	−21.8564	+	21.8564i	−1.27038	+	1.27038i
$297$		0			0
$298$	14.5211	+	8.38375i	0.841183	+	0.485657i
$299$	−16.9282			−0.978983
$300$		0			0
$301$	−19.9282			−1.14864
$302$	9.46979	+	5.46739i	0.544925	+	0.314613i
$303$		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	0.542030	−	0.840359i	$-0.317656\pi$
$307$	−5.22715	−	5.22715i	−0.298329	−	0.298329i	−0.840359	+	0.542030i	$0.817656\pi$
$308$	−17.2480	−	4.62158i	−0.982794	−	0.263339i
$309$		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	$-0.0993885\pi$
$313$	11.4016	+	11.4016i	0.644459	+	0.644459i	−0.307190	+	0.951648i	$0.599389\pi$
$314$	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	$-0.687671\pi$
$317$	4.89898	−	4.89898i	0.275154	−	0.275154i	0.831171	+	0.556017i	$0.187671\pi$
$318$		0			0
$319$	1.07180			0.0600091
$320$		0			0
$321$		0			0
$322$	23.5612	−	40.8091i	1.31301	−	2.27420i
$323$	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
$328$	4.14110			0.228654
$329$			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	$-0.168679\pi$
$332$	24.9754	+	6.69213i	1.37070	+	0.367278i
$333$		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	−0.110023	+	0.993929i	$0.535092\pi$
$337$	−20.2659	+	20.2659i	−1.10395	+	1.10395i	−0.993929	+	0.110023i	$0.964908\pi$
$338$	−9.62209	−	5.55532i	−0.523373	−	0.302169i
$339$		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	0.998628	−	0.0523663i	$-0.0166763\pi$
$347$	17.6269	+	17.6269i	0.946262	+	0.946262i	−0.0523663	+	0.998628i	$0.516676\pi$
$348$		0			0
$349$		−	23.8564i		−	1.27700i	−0.769620	−	0.638502i	$-0.779554\pi$
$349$		−	23.8564i		−	1.27700i	0.769620	−	0.638502i	$-0.220446\pi$
$350$		0			0
$351$		0			0
$352$	9.79796	−	5.65685i	0.522233	−	0.301511i
$353$	8.38375	+	8.38375i	0.446222	+	0.446222i	0.894096	−	0.447875i	$-0.147819\pi$
$353$	8.38375	+	8.38375i	0.446222	+	0.446222i	−0.447875	+	0.894096i	$0.647819\pi$
$354$		0			0
$355$		0			0
$356$	12.0000	−	6.92820i	0.635999	−	0.367194i
$357$		0			0
$358$	−6.59059	+	11.4152i	−0.348324	+	0.603314i
$359$	3.60770			0.190407			0.0952034	−	0.995458i	$-0.469650\pi$
$359$	3.60770			0.190407			0.0952034	+	0.995458i	$0.469650\pi$
$360$		0			0
$361$	−8.78461			−0.462348
$362$	−0.0507680	+	0.0879327i	−0.00266831	+	0.00462164i
$363$		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	0.984753	+	0.173958i	$0.0556557\pi$
$367$	22.1977	+	22.1977i	1.15871	+	1.15871i	0.173958	+	0.984753i	$0.444344\pi$
$368$	7.72741	+	28.8391i	0.402819	+	1.50334i
$369$		0			0
$370$		0			0
$371$		−	24.3923i		−	1.26639i
$372$		0			0
$373$	−25.9227	−	25.9227i	−1.34223	−	1.34223i	−0.893839	−	0.448388i	$-0.851998\pi$
$373$	−25.9227	−	25.9227i	−1.34223	−	1.34223i	−0.448388	−	0.893839i	$-0.648002\pi$
$374$	−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	$-0.397968\pi$
$379$	12.2679			0.630162			0.315081	+	0.949065i	$0.397968\pi$
$380$		0			0
$381$		0			0
$382$	3.76217	+	2.17209i	0.192489	+	0.111134i
$383$	−17.5254	+	17.5254i	−0.895504	+	0.895504i	−0.995035	−	0.0995302i	$-0.968266\pi$
$383$	−17.5254	+	17.5254i	−0.895504	+	0.895504i	0.0995302	+	0.995035i	$0.468266\pi$
$384$		0			0
$385$		0			0
$386$	−14.0263	+	3.75833i	−0.713919	+	0.191294i
$387$		0			0
$388$	−18.8009	−	5.03768i	−0.954470	−	0.255749i
$389$		−	21.4641i		−	1.08827i	−0.838997	−	0.544137i	$-0.816857\pi$
$389$		−	21.4641i		−	1.08827i	0.838997	−	0.544137i	$-0.183143\pi$
$390$		0			0
$391$		−	44.7846i		−	2.26486i
$392$		−	36.5665i		−	1.84689i
$393$		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	$-0.843923\pi$
$397$	−8.19428	+	8.19428i	−0.411259	+	0.411259i	0.470918	+	0.882177i	$0.343923\pi$
$398$	−7.15900	+	12.3998i	−0.358848	+	0.621543i
$399$		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	$0.110699\pi$
$409$			13.7846i			0.681605i	−0.940135	+	0.340803i	$0.889301\pi$
$410$		0			0
$411$		0			0
$412$	−13.3843	−	3.58630i	−0.659395	−	0.176684i
$413$	−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
$418$	−7.82894	−	4.52004i	−0.382926	−	0.221082i
$419$	33.4641			1.63483			0.817414	−	0.576050i	$-0.195407\pi$
$419$	33.4641			1.63483			0.817414	+	0.576050i	$0.195407\pi$
$420$		0			0
$421$	−34.7846			−1.69530			−0.847649	−	0.530557i	$-0.821983\pi$
$421$	−34.7846			−1.69530			−0.847649	+	0.530557i	$0.821983\pi$
$422$	3.91447	+	2.26002i	0.190553	+	0.110016i
$423$		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
$428$	6.96953	−	26.0106i	0.336885	−	1.25727i
$429$		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	0.971239	+	0.238106i	$0.0765265\pi$
$433$	25.1648	+	25.1648i	1.20935	+	1.20935i	0.238106	+	0.971239i	$0.423474\pi$
$434$	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	$-0.693937\pi$
$439$	−23.9808			−1.14454			−0.572270	+	0.820066i	$0.693937\pi$
$440$		0			0
$441$		0			0
$442$	−9.62209	+	16.6660i	−0.457676	+	0.792719i
$443$	20.3538	−	20.3538i	0.967038	−	0.967038i	−0.0324359	−	0.999474i	$-0.510326\pi$
$443$	20.3538	−	20.3538i	0.967038	−	0.967038i	0.999474	+	0.0324359i	$0.0103265\pi$
$444$		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	$-0.953692\pi$
$449$		−	6.14359i		−	0.289934i	0.989436	−	0.144967i	$-0.0463076\pi$
$450$		0			0
$451$			2.92820i			0.137884i
$452$	7.17260	−	26.7685i	0.337371	−	1.25909i
$453$		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	$-0.902532\pi$
$457$	−13.9391	+	13.9391i	−0.652042	+	0.652042i	0.301442	+	0.953484i	$0.402532\pi$
$458$	3.49837	+	2.01978i	0.163468	+	0.0943783i
$459$		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	−0.109114	−	0.994029i	$-0.534801\pi$
$463$	19.0411	−	19.0411i	0.884916	−	0.884916i	0.994029	+	0.109114i	$0.0348012\pi$
$464$	−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	0.648157	−	0.761506i	$-0.275540\pi$
$467$	−2.44949	−	2.44949i	−0.113349	−	0.113349i	−0.761506	+	0.648157i	$0.775540\pi$
$468$		0			0
$469$		−	24.7128i		−	1.14113i
$470$		0			0
$471$		0			0
$472$	32.4254			1.49250
$473$	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
$478$	−7.45001	+	12.9038i	−0.340755	+	0.590206i
$479$	−21.3205			−0.974159			−0.487079	−	0.873358i	$-0.661938\pi$
$479$	−21.3205			−0.974159			−0.487079	+	0.873358i	$0.661938\pi$
$480$		0			0
$481$	−24.7846			−1.13008
$482$	9.09085	−	15.7458i	0.414077	−	0.717202i
$483$		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	0.0843846	−	0.996433i	$-0.473108\pi$
$487$	−20.1272	−	20.1272i	−0.912049	−	0.912049i	−0.996433	+	0.0843846i	$0.973108\pi$
$488$	−8.48528			−0.384111
$489$		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	$-0.735544\pi$
$499$	−30.1244			−1.34855			−0.674276	+	0.738480i	$0.735544\pi$
$500$		0			0
$501$		0			0
$502$	36.5665	+	21.1117i	1.63204	+	0.942260i
$503$	0.277401	−	0.277401i	0.0123687	−	0.0123687i	−0.700895	−	0.713264i	$-0.747216\pi$
$503$	0.277401	−	0.277401i	0.0123687	−	0.0123687i	0.713264	+	0.700895i	$0.247216\pi$
$504$		0			0
$505$		0			0
$506$	−20.3923	+	5.46410i	−0.906549	+	0.242909i
$507$		0			0
$508$	5.65685	−	21.1117i	0.250982	−	0.936679i
$509$			24.9282i			1.10492i	0.833538	+	0.552462i	$0.186311\pi$
$509$			24.9282i			1.10492i	−0.833538	+	0.552462i	$0.813689\pi$
$510$		0			0
$511$			17.8564i			0.789921i
$512$	−22.6274			−1.00000
$513$		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
$518$	34.4959	−	59.7487i	1.51566	−	2.62521i
$519$		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	−0.685254	−	0.728304i	$-0.740309\pi$
$523$	0.984508	−	0.984508i	0.0430495	−	0.0430495i	0.728304	+	0.685254i	$0.240309\pi$
$524$	−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
$532$	7.38563	−	27.5636i	0.320208	−	1.19503i
$533$	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
$538$	−27.4249	−	15.8338i	−1.18237	−	0.682641i
$539$	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	$0.446481\pi$
$542$	29.6985	+	17.1464i	1.27566	+	0.736502i
$543$		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	0.406285	−	0.913746i	$-0.366824\pi$
$547$	−11.8685	−	11.8685i	−0.507461	−	0.507461i	−0.913746	+	0.406285i	$0.866824\pi$
$548$	29.8744	+	8.00481i	1.27617	+	0.341948i
$549$		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	$-0.666443\pi$
$557$	8.66115	−	8.66115i	0.366985	−	0.366985i	0.866376	+	0.499392i	$0.166443\pi$
$558$		0			0
$559$	10.1244			0.428215
$560$		0			0
$561$		0			0
$562$	−4.52004	+	7.82894i	−0.190666	+	0.330244i
$563$	−27.7023	+	27.7023i	−1.16751	+	1.16751i	−0.184720	+	0.982791i	$0.559138\pi$
$563$	−27.7023	+	27.7023i	−1.16751	+	1.16751i	−0.982791	+	0.184720i	$0.940862\pi$
$564$		0			0
$565$		0			0
$566$	0.222432	+	0.830127i	0.00934951	+	0.0348928i
$567$		0			0
$568$		−	7.17260i		−	0.300956i
$569$			17.3205i			0.726113i	0.931767	+	0.363057i	$0.118267\pi$
$569$			17.3205i			0.726113i	−0.931767	+	0.363057i	$0.881733\pi$
$570$		0			0
$571$			27.1962i			1.13812i	0.822295	+	0.569062i	$0.192693\pi$
$571$			27.1962i			1.13812i	−0.822295	+	0.569062i	$0.807307\pi$
$572$	8.76268	+	2.34795i	0.366386	+	0.0981729i
$573$		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	$-0.512053\pi$
$577$	23.0943	−	23.0943i	0.961428	−	0.961428i	0.999283	+	0.0378555i	$0.0120527\pi$
$578$	−23.2702	−	13.4350i	−0.967911	−	0.558824i
$579$		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	0.894401	−	0.447266i	$-0.147602\pi$
$587$	10.8332	+	10.8332i	0.447135	+	0.447135i	−0.447266	+	0.894401i	$0.647602\pi$
$588$		0			0
$589$			11.9282i			0.491493i
$590$		0			0
$591$		0			0
$592$	11.3137	+	42.2233i	0.464991	+	1.73537i
$593$	−8.20788	−	8.20788i	−0.337057	−	0.337057i	0.518201	−	0.855259i	$-0.326602\pi$
$593$	−8.20788	−	8.20788i	−0.337057	−	0.337057i	−0.855259	+	0.518201i	$0.826602\pi$
$594$		0			0
$595$		0			0
$596$	20.5359	−	11.8564i	0.841183	−	0.485657i
$597$		0			0
$598$	−11.9700	+	20.7327i	−0.489492	+	0.847824i
$599$	22.6410			0.925087			0.462543	−	0.886597i	$-0.346937\pi$
$599$	22.6410			0.925087			0.462543	+	0.886597i	$0.346937\pi$
$600$		0			0
$601$	21.7846			0.888613			0.444306	−	0.895875i	$-0.353450\pi$
$601$	21.7846			0.888613			0.444306	+	0.895875i	$0.353450\pi$
$602$	−14.0914	+	24.4070i	−0.574321	+	0.994754i
$603$		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	−0.999680	−	0.0252985i	$-0.991946\pi$
$607$	−25.2528	−	25.2528i	−1.02498	−	1.02498i	−0.0252985	−	0.999680i	$-0.508054\pi$
$608$	9.04008	+	15.6579i	0.366624	+	0.635011i
$609$		0			0
$610$		0			0
$611$		−	2.10512i		−	0.0851639i
$612$		0			0
$613$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$613$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$614$	−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	$-0.992126\pi$
$617$	−24.2175	+	24.2175i	−0.974960	+	0.974960i	0.0247344	+	0.999694i	$0.492126\pi$
$618$		0			0
$619$	−15.9808			−0.642321			−0.321161	−	0.947025i	$-0.604073\pi$
$619$	−15.9808			−0.642321			−0.321161	+	0.947025i	$0.604073\pi$
$620$		0			0
$621$		0			0
$622$	−25.1512	−	14.5211i	−1.00847	−	0.582242i
$623$	−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
$628$	12.1087	+	3.24453i	0.483192	+	0.129471i
$629$		−	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	$-0.200458\pi$
$632$	21.1117			0.839777
$633$		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
$638$	0.757875	−	1.31268i	0.0300045	−	0.0519694i
$639$		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	−0.129172	−	0.991622i	$-0.541232\pi$
$643$	21.8695	−	21.8695i	0.862451	−	0.862451i	0.991622	+	0.129172i	$0.0412318\pi$
$644$	−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	0.919434	−	0.393244i	$-0.128647\pi$
$647$	13.3843	+	13.3843i	0.526190	+	0.526190i	−0.393244	+	0.919434i	$0.628647\pi$
$648$		0			0
$649$			22.9282i			0.900011i
$650$		0			0
$651$		0			0
$652$	−14.5582	−	3.90087i	−0.570145	−	0.152770i
$653$	−7.34847	−	7.34847i	−0.287568	−	0.287568i	0.548550	−	0.836118i	$-0.315180\pi$
$653$	−7.34847	−	7.34847i	−0.287568	−	0.287568i	−0.836118	+	0.548550i	$0.815180\pi$
$654$		0			0
$655$		0			0
$656$	2.92820	−	5.07180i	0.114327	−	0.198020i
$657$		0			0
$658$	5.07484	+	2.92996i	0.197838	+	0.114222i
$659$	−21.4641			−0.836123			−0.418061	−	0.908419i	$-0.637290\pi$
$659$	−21.4641			−0.836123			−0.418061	+	0.908419i	$0.637290\pi$
$660$		0			0
$661$	19.8564			0.772325			0.386162	−	0.922431i	$-0.373800\pi$
$661$	19.8564			0.772325			0.386162	+	0.922431i	$0.373800\pi$
$662$	−22.5259	−	13.0053i	−0.875493	−	0.505466i
$663$		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
$668$	−8.48528	+	31.6675i	−0.328305	+	1.22525i
$669$		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	$-0.274564\pi$
$673$	−2.82843	−	2.82843i	−0.109028	−	0.109028i	−0.759516	+	0.650488i	$0.774564\pi$
$674$	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	$-0.534181\pi$
$677$	23.0807	−	23.0807i	0.887063	−	0.887063i	0.994240	+	0.107177i	$0.0341812\pi$
$678$		0			0
$679$	43.4449			1.66726
$680$		0			0
$681$		0			0
$682$	5.27792	−	9.14162i	0.202102	−	0.350051i
$683$	13.3843	−	13.3843i	0.512135	−	0.512135i	−0.403045	−	0.915180i	$-0.632048\pi$
$683$	13.3843	−	13.3843i	0.512135	−	0.512135i	0.915180	+	0.403045i	$0.132048\pi$
$684$		0			0
$685$		0			0
$686$	9.68653	+	36.1506i	0.369834	+	1.38024i
$687$		0			0
$688$	−4.62158	−	17.2480i	−0.176196	−	0.657572i
$689$			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	$0.943269\pi$
$692$	−2.55103	+	9.52056i	−0.0969754	+	0.361917i
$693$		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
$698$	−29.2180	−	16.8690i	−1.10592	−	0.638502i
$699$		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	$0.0170815\pi$
$709$			2.85641i			0.107275i	−0.998560	+	0.0536373i	$0.982919\pi$
$710$		0			0
$711$		0			0
$712$		−	19.5959i		−	0.734388i
$713$	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
$718$	2.55103	−	4.41851i	0.0952034	−	0.164897i
$719$	−0.928203			−0.0346161			−0.0173081	−	0.999850i	$-0.505510\pi$
$719$	−0.928203			−0.0346161			−0.0173081	+	0.999850i	$0.505510\pi$
$720$		0			0
$721$	30.9282			1.15183
$722$	−6.21166	+	10.7589i	−0.231174	+	0.400405i
$723$		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	0.976915	−	0.213629i	$-0.0685284\pi$
$727$	20.5804	+	20.5804i	0.763286	+	0.763286i	−0.213629	+	0.976915i	$0.568528\pi$
$728$			28.6360i			1.06132i
$729$		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	$-0.0207505\pi$
$733$	25.2528	+	25.2528i	0.932732	+	0.932732i	−0.0651435	+	0.997876i	$0.520751\pi$
$734$	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	$-0.462489\pi$
$739$	6.39230			0.235145			0.117572	+	0.993064i	$0.462489\pi$
$740$		0			0
$741$		0			0
$742$	−29.8744	−	17.2480i	−1.09672	−	0.633193i
$743$	12.0716	−	12.0716i	0.442863	−	0.442863i	−0.450110	−	0.892973i	$-0.648615\pi$
$743$	12.0716	−	12.0716i	0.442863	−	0.442863i	0.892973	+	0.450110i	$0.148615\pi$
$744$		0			0
$745$		0			0
$746$	−50.0788	+	13.4186i	−1.83352	+	0.491289i
$747$		0			0
$748$	−6.21166	+	23.1822i	−0.227121	+	0.847626i
$749$			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	$-0.0263731\pi$
$752$	−3.58630	+	0.960947i	−0.130779	+	0.0350421i
$753$		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	$-0.861009\pi$
$757$	−13.2963	+	13.2963i	−0.483263	+	0.483263i	0.422909	+	0.906172i	$0.361009\pi$
$758$	8.67475	−	15.0251i	0.315081	−	0.545736i
$759$		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	$0.0935828\pi$
$769$			16.0718i			0.579564i	−0.957093	+	0.289782i	$0.906417\pi$
$770$		0			0
$771$		0			0
$772$	−5.31508	+	19.8362i	−0.191294	+	0.713919i
$773$	−20.6312	−	20.6312i	−0.742052	−	0.742052i	0.230920	−	0.972973i	$-0.425826\pi$
$773$	−20.6312	−	20.6312i	−0.742052	−	0.742052i	−0.972973	+	0.230920i	$0.925826\pi$
$774$		0			0
$775$		0			0
$776$	−19.4641	+	19.4641i	−0.698721	+	0.698721i
$777$		0			0
$778$	−26.2880	−	15.1774i	−0.942472	−	0.544137i
$779$	−4.67949			−0.167660
$780$		0			0
$781$	5.07180			0.181483
$782$	−54.8497	−	31.6675i	−1.96142	−	1.13243i
$783$		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	0.969588	+	0.244741i	$0.0787030\pi$
$787$	34.0662	+	34.0662i	1.21433	+	1.21433i	0.244741	+	0.969588i	$0.421297\pi$
$788$	−12.3490	−	3.30890i	−0.439914	−	0.117875i
$789$		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	$-0.828922\pi$
$797$	−9.79796	+	9.79796i	−0.347062	+	0.347062i	0.511952	+	0.859014i	$0.328922\pi$
$798$		0			0
$799$	5.56922			0.197025
$800$		0			0
$801$		0			0
$802$	−20.6312	+	35.7343i	−0.728513	+	1.26182i
$803$	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
$808$	15.4548			0.543698
$809$		−	13.1769i		−	0.463276i	−0.972802	−	0.231638i	$-0.925592\pi$
$809$		−	13.1769i		−	0.463276i	0.972802	−	0.231638i	$-0.0744084\pi$
$810$		0			0
$811$			1.87564i			0.0658628i	0.999458	+	0.0329314i	$0.0104843\pi$
$811$			1.87564i			0.0658628i	−0.999458	+	0.0329314i	$0.989516\pi$
$812$	4.62158	+	1.23835i	0.162186	+	0.0434575i
$813$		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
$818$	16.8826	+	9.74719i	0.590287	+	0.340803i
$819$		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	−0.954391	−	0.298559i	$-0.903494\pi$
$823$	−18.8145	+	18.8145i	−0.655832	+	0.655832i	0.298559	+	0.954391i	$0.403494\pi$
$824$	−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	−0.968936	−	0.247313i	$-0.920452\pi$
$827$	−34.9764	−	34.9764i	−1.21625	−	1.21625i	−0.247313	−	0.968936i	$-0.579548\pi$
$828$		0			0
$829$			37.7128i			1.30982i	0.755707	+	0.654910i	$0.227294\pi$
$829$			37.7128i			1.30982i	−0.755707	+	0.654910i	$0.772706\pi$
$830$		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
$838$	23.6627	−	40.9850i	0.817414	−	1.41580i
$839$	−28.6410			−0.988798			−0.494399	−	0.869235i	$-0.664612\pi$
$839$	−28.6410			−0.988798			−0.494399	+	0.869235i	$0.664612\pi$
$840$		0			0
$841$	28.7128			0.990097
$842$	−24.5964	+	42.6023i	−0.847649	+	1.46817i
$843$		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
$848$	21.1117	−	5.65685i	0.724978	−	0.194257i
$849$		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	$-0.164011\pi$
$853$	11.0227	+	11.0227i	0.377410	+	0.377410i	−0.492757	+	0.870167i	$0.664011\pi$
$854$	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	$-0.792054\pi$
$857$	−5.45378	+	5.45378i	−0.186298	+	0.186298i	0.607796	+	0.794093i	$0.292054\pi$
$858$		0			0
$859$	−42.3923			−1.44641			−0.723203	−	0.690635i	$-0.757331\pi$
$859$	−42.3923			−1.44641			−0.723203	+	0.690635i	$0.757331\pi$
$860$		0			0
$861$		0			0
$862$	−36.3906	−	21.0101i	−1.23947	−	0.715608i
$863$	21.6665	−	21.6665i	0.737535	−	0.737535i	−0.234565	−	0.972100i	$-0.575367\pi$
$863$	21.6665	−	21.6665i	0.737535	−	0.737535i	0.972100	+	0.234565i	$0.0753666\pi$
$864$		0			0
$865$		0			0
$866$	48.6147	−	13.0263i	1.65200	−	0.442651i
$867$		0			0
$868$	32.1851	+	8.62398i	1.09243	+	0.292717i
$869$			14.9282i			0.506405i
$870$		0			0
$871$			12.5551i			0.425415i
$872$		−	19.7990i		−	0.670478i
$873$		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	0.154180	−	0.988043i	$-0.450727\pi$
$877$	33.8260	−	33.8260i	1.14222	−	1.14222i	0.988043	−	0.154180i	$-0.0492734\pi$
$878$	−16.9570	+	29.3703i	−0.572270	+	0.991200i
$879$		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	−0.977343	−	0.211660i	$-0.932113\pi$
$883$	−22.7525	+	22.7525i	−0.765683	+	0.765683i	0.211660	+	0.977343i	$0.432113\pi$
$884$	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	0.430942	−	0.902379i	$-0.358181\pi$
$887$	−14.0406	−	14.0406i	−0.471437	−	0.471437i	−0.902379	+	0.430942i	$0.858181\pi$
$888$		0			0
$889$			48.7846i			1.63618i
$890$		0			0
$891$		0			0
$892$	18.1445	+	4.86181i	0.607524	+	0.162786i
$893$	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
$898$	−7.52433	−	4.34418i	−0.251090	−	0.144967i
$899$	−2.00000			−0.0667037
$900$		0			0
$901$	−32.7846			−1.09221
$902$	3.58630	+	2.07055i	0.119411	+	0.0689419i
$903$		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	0.465694	−	0.884946i	$-0.345805\pi$
$907$	−12.6264	−	12.6264i	−0.419252	−	0.419252i	−0.884946	+	0.465694i	$0.845805\pi$
$908$	−4.34418	+	16.2127i	−0.144167	+	0.538037i
$909$		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	$-0.644922\pi$
$919$	−26.6603			−0.879441			−0.439720	+	0.898135i	$0.644922\pi$
$920$		0			0
$921$		0			0
$922$	−25.7332	+	44.5713i	−0.847479	+	1.46788i
$923$	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
$928$	−2.62536	+	1.51575i	−0.0861815	+	0.0497569i
$929$			0.535898i			0.0175823i	0.999961	+	0.00879113i	$0.00279834\pi$
$929$			0.535898i			0.0175823i	−0.999961	+	0.00879113i	$0.997202\pi$
$930$		0			0
$931$			41.3205i			1.35422i
$932$	−4.34418	+	16.2127i	−0.142298	+	0.531064i
$933$		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	$-0.682374\pi$
$937$	9.12802	−	9.12802i	0.298199	−	0.298199i	0.840308	+	0.542109i	$0.182374\pi$
$938$	−30.2669	−	17.4746i	−0.988249	−	0.570566i
$939$		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	0.231765	−	0.972772i	$-0.425550\pi$
$947$	−22.8033	−	22.8033i	−0.741007	−	0.741007i	−0.972772	+	0.231765i	$0.925550\pi$
$948$		0			0
$949$		−	9.07180i		−	0.294483i
$950$		0			0
$951$		0			0
$952$	−75.7583			−2.45534
$953$	−28.0812	−	28.0812i	−0.909639	−	0.909639i	0.0866036	−	0.996243i	$-0.472399\pi$
$953$	−28.0812	−	28.0812i	−0.909639	−	0.909639i	−0.996243	+	0.0866036i	$0.972399\pi$
$954$		0			0
$955$		0			0
$956$	10.5359	+	18.2487i	0.340755	+	0.590206i
$957$		0			0
$958$	−15.0759	+	26.1122i	−0.487079	+	0.843646i
$959$	−69.0333			−2.22920
$960$		0			0
$961$	17.0718			0.550703
$962$	−17.5254	+	30.3548i	−0.565040	+	0.978679i
$963$		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	−0.995372	−	0.0961015i	$-0.969363\pi$
$967$	−33.9411	−	33.9411i	−1.09147	−	1.09147i	−0.0961015	−	0.995372i	$-0.530637\pi$
$968$	−19.7990			−0.636364
$969$		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	$-0.629101\pi$
$977$	16.3886	−	16.3886i	0.524316	−	0.524316i	0.918872	+	0.394556i	$0.129101\pi$
$978$		0			0
$979$	13.8564			0.442853
$980$		0			0
$981$		0			0
$982$	42.4264	+	24.4949i	1.35388	+	0.781664i
$983$	−1.31268	+	1.31268i	−0.0418679	+	0.0418679i	−0.727731	−	0.685863i	$-0.759425\pi$
$983$	−1.31268	+	1.31268i	−0.0418679	+	0.0418679i	0.685863	+	0.727731i	$0.259425\pi$
$984$		0			0
$985$		0			0
$986$	4.39230	−	1.17691i	0.139879	−	0.0374806i
$987$		0			0
$988$	−3.75221	+	14.0034i	−0.119374	+	0.445509i
$989$			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	$0.862207\pi$
$992$	−18.2832	+	10.5558i	−0.580493	+	0.335148i
$993$		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	$-0.605391\pi$
$997$	19.5959	−	19.5959i	0.620609	−	0.620609i	0.945687	+	0.325078i	$0.105391\pi$
$998$	−21.3011	+	36.8947i	−0.674276	+	1.16788i
$999$		0			0

Twists

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

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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)

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

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more