LMFDB - Embedded newform 450.2.p.h.257.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [450,2,Mod(257,450)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(450, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([10, 3]))

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

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

chi := DirichletCharacter("450.257");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 450 = 2 \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	450.p (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$3.59326809096$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{12})$
Coefficient field:	16.0.9349208943630483456.9
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8 x^{15} + 48 x^{14} - 196 x^{13} + 642 x^{12} - 1668 x^{11} + 3580 x^{10} - 6328 x^{9} + \cdots + 25 $ x^16 - 8x^15 + 48x^14 - 196x^13 + 642x^12 - 1668x^11 + 3580x^10 - 6328x^9 + 9297x^8 - 11276x^7 + 11224x^6 - 9024x^5 + 5736x^4 - 2780x^3 + 972x^2 - 220*x + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 90)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			257.2
Root			$0.500000 - 0.331082i$ of defining polynomial
Character	$\chi$	$=$	450.257
Dual form			450.2.p.h.443.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.965926 - 0.258819i) q^{2} +(0.933998 - 1.45865i) q^{3} +(0.866025 + 0.500000i) q^{4} +(-1.27970 + 1.16721i) q^{6} +(-0.686453 + 2.56188i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-1.25529 - 2.72474i) q^{9} +O(q^{10})$	\(q+(-0.965926 - 0.258819i) q^{2} +(0.933998 - 1.45865i) q^{3} +(0.866025 + 0.500000i) q^{4} +(-1.27970 + 1.16721i) q^{6} +(-0.686453 + 2.56188i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-1.25529 - 2.72474i) q^{9} +(4.15512 - 2.39896i) q^{11} +(1.53819 - 0.796225i) q^{12} +(0.155903 + 0.581838i) q^{13} +(1.32613 - 2.29692i) q^{14} +(0.500000 + 0.866025i) q^{16} +(4.40865 - 4.40865i) q^{17} +(0.507306 + 2.95680i) q^{18} -5.19145i q^{19} +(3.09573 + 3.39408i) q^{21} +(-4.63444 + 1.24179i) q^{22} +(2.54237 - 0.681226i) q^{23} +(-1.69185 + 0.370982i) q^{24} -0.602363i q^{26} +(-5.14688 - 0.713876i) q^{27} +(-1.87542 + 1.87542i) q^{28} +(0.920201 + 1.59383i) q^{29} +(-2.03888 + 3.53145i) q^{31} +(-0.258819 - 0.965926i) q^{32} +(0.381642 - 8.30148i) q^{33} +(-5.39948 + 3.11739i) q^{34} +(0.275255 - 2.98735i) q^{36} +(-0.632057 - 0.632057i) q^{37} +(-1.34365 + 5.01456i) q^{38} +(0.994309 + 0.316029i) q^{39} +(-5.58550 - 3.22479i) q^{41} +(-2.11179 - 4.07966i) q^{42} +(-2.40501 - 0.644420i) q^{43} +4.79792 q^{44} -2.63206 q^{46} +(3.82678 + 1.02538i) q^{47} +(1.73022 + 0.0795432i) q^{48} +(-0.0298240 - 0.0172189i) q^{49} +(-2.31299 - 10.5483i) q^{51} +(-0.155903 + 0.581838i) q^{52} +(-1.31215 - 1.31215i) q^{53} +(4.78674 + 2.02166i) q^{54} +(2.29692 - 1.32613i) q^{56} +(-7.57249 - 4.84881i) q^{57} +(-0.476331 - 1.77769i) q^{58} +(0.0645473 - 0.111799i) q^{59} +(6.27251 + 10.8643i) q^{61} +(2.88341 - 2.88341i) q^{62} +(7.84217 - 1.34550i) q^{63} +1.00000i q^{64} +(-2.51722 + 7.91984i) q^{66} +(10.6655 - 2.85782i) q^{67} +(6.02233 - 1.61368i) q^{68} +(1.38090 - 4.34468i) q^{69} -10.4203i q^{71} +(-1.03906 + 2.81431i) q^{72} +(-3.30021 + 3.30021i) q^{73} +(0.446932 + 0.774109i) q^{74} +(2.59573 - 4.49593i) q^{76} +(3.29355 + 12.2917i) q^{77} +(-0.878635 - 0.562606i) q^{78} +(-3.62792 + 2.09458i) q^{79} +(-5.84847 + 6.84072i) q^{81} +(4.56054 + 4.56054i) q^{82} +(-2.97686 + 11.1098i) q^{83} +(0.983937 + 4.48722i) q^{84} +(2.15627 + 1.24492i) q^{86} +(3.18431 + 0.146391i) q^{87} +(-4.63444 - 1.24179i) q^{88} -2.04989 q^{89} -1.59762 q^{91} +(2.54237 + 0.681226i) q^{92} +(3.24682 + 6.27237i) q^{93} +(-3.43100 - 1.98089i) q^{94} +(-1.65068 - 0.524648i) q^{96} +(-4.47782 + 16.7115i) q^{97} +(0.0243512 + 0.0243512i) q^{98} +(-11.7525 - 8.31025i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{7}+O(q^{10}) $ 16 * q - 8 * q^7	$ 16 q - 8 q^{7} + 8 q^{16} + 24 q^{21} - 8 q^{22} + 24 q^{23} + 16 q^{28} - 8 q^{31} + 24 q^{36} - 24 q^{38} + 24 q^{41} - 24 q^{42} - 32 q^{46} - 48 q^{47} - 48 q^{51} + 24 q^{56} - 24 q^{57} - 16 q^{58} - 24 q^{61} + 48 q^{63} - 48 q^{66} + 16 q^{67} + 24 q^{68} + 24 q^{72} - 16 q^{73} + 16 q^{76} + 72 q^{77} + 24 q^{81} + 16 q^{82} - 48 q^{83} - 48 q^{86} + 48 q^{87} - 8 q^{88} + 24 q^{92} - 72 q^{93} + 48 q^{97}+O(q^{100}) $ 16 * q - 8 * q^7 + 8 * q^16 + 24 * q^21 - 8 * q^22 + 24 * q^23 + 16 * q^28 - 8 * q^31 + 24 * q^36 - 24 * q^38 + 24 * q^41 - 24 * q^42 - 32 * q^46 - 48 * q^47 - 48 * q^51 + 24 * q^56 - 24 * q^57 - 16 * q^58 - 24 * q^61 + 48 * q^63 - 48 * q^66 + 16 * q^67 + 24 * q^68 + 24 * q^72 - 16 * q^73 + 16 * q^76 + 72 * q^77 + 24 * q^81 + 16 * q^82 - 48 * q^83 - 48 * q^86 + 48 * q^87 - 8 * q^88 + 24 * q^92 - 72 * q^93 + 48 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/450\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−0.965926	−	0.258819i	−0.683013	−	0.183013i
$2$	−0.965926	−	0.258819i	−0.683013	−	0.183013i
$3$	0.933998	−	1.45865i	0.539244	−	0.842150i
$3$	0.933998	−	1.45865i	0.539244	−	0.842150i
$4$	0.866025	+	0.500000i	0.433013	+	0.250000i
$5$		0			0
$5$		0			0
$6$	−1.27970	+	1.16721i	−0.522435	+	0.476510i
$7$	−0.686453	+	2.56188i	−0.259455	+	0.968299i	0.706103	+	0.708109i	$0.250452\pi$
$7$	−0.686453	+	2.56188i	−0.259455	+	0.968299i	−0.965558	+	0.260189i	$0.916215\pi$
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$	−1.25529	−	2.72474i	−0.418432	−	0.908248i
$10$		0			0
$11$	4.15512	−	2.39896i	1.25282	−	0.723314i	0.281149	−	0.959664i	$-0.409285\pi$
$11$	4.15512	−	2.39896i	1.25282	−	0.723314i	0.971668	+	0.236350i	$0.0759512\pi$
$12$	1.53819	−	0.796225i	0.444037	−	0.229850i
$13$	0.155903	+	0.581838i	0.0432397	+	0.161373i	0.984170	−	0.177228i	$-0.0567130\pi$
$13$	0.155903	+	0.581838i	0.0432397	+	0.161373i	−0.940930	+	0.338601i	$0.890046\pi$
$14$	1.32613	−	2.29692i	0.354422	−	0.613877i
$15$		0			0
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	4.40865	−	4.40865i	1.06926	−	1.06926i	0.0718393	−	0.997416i	$-0.477113\pi$
$17$	4.40865	−	4.40865i	1.06926	−	1.06926i	0.997416	−	0.0718393i	$-0.0228869\pi$
$18$	0.507306	+	2.95680i	0.119573	+	0.696923i
$19$		−	5.19145i		−	1.19100i	−0.803355	−	0.595501i	$-0.796954\pi$
$19$		−	5.19145i		−	1.19100i	0.803355	−	0.595501i	$-0.203046\pi$
$20$		0			0
$21$	3.09573	+	3.39408i	0.675543	+	0.740649i
$22$	−4.63444	+	1.24179i	−0.988065	+	0.264751i
$23$	2.54237	−	0.681226i	0.530121	−	0.142046i	0.0161770	−	0.999869i	$-0.494850\pi$
$23$	2.54237	−	0.681226i	0.530121	−	0.142046i	0.513944	+	0.857824i	$0.328184\pi$
$24$	−1.69185	+	0.370982i	−0.345348	+	0.0757264i
$25$		0			0
$26$		−	0.602363i		−	0.118133i
$27$	−5.14688	−	0.713876i	−0.990518	−	0.137386i
$28$	−1.87542	+	1.87542i	−0.354422	+	0.354422i
$29$	0.920201	+	1.59383i	0.170877	+	0.295968i	0.938727	−	0.344662i	$-0.112007\pi$
$29$	0.920201	+	1.59383i	0.170877	+	0.295968i	−0.767850	+	0.640630i	$0.778673\pi$
$30$		0			0
$31$	−2.03888	+	3.53145i	−0.366194	+	0.634266i	−0.988967	−	0.148136i	$-0.952673\pi$
$31$	−2.03888	+	3.53145i	−0.366194	+	0.634266i	0.622773	+	0.782402i	$0.286006\pi$
$32$	−0.258819	−	0.965926i	−0.0457532	−	0.170753i
$33$	0.381642	−	8.30148i	0.0664354	−	1.44510i
$34$	−5.39948	+	3.11739i	−0.926002	+	0.534628i
$35$		0			0
$36$	0.275255	−	2.98735i	0.0458759	−	0.497891i
$37$	−0.632057	−	0.632057i	−0.103910	−	0.103910i	0.653241	−	0.757150i	$-0.273409\pi$
$37$	−0.632057	−	0.632057i	−0.103910	−	0.103910i	−0.757150	+	0.653241i	$0.773409\pi$
$38$	−1.34365	+	5.01456i	−0.217968	+	0.813469i
$39$	0.994309	+	0.316029i	0.159217	+	0.0506051i
$40$		0			0
$41$	−5.58550	−	3.22479i	−0.872309	−	0.503628i	−0.00419400	−	0.999991i	$-0.501335\pi$
$41$	−5.58550	−	3.22479i	−0.872309	−	0.503628i	−0.868115	+	0.496363i	$0.834668\pi$
$42$	−2.11179	−	4.07966i	−0.325856	−	0.629506i
$43$	−2.40501	−	0.644420i	−0.366760	−	0.0982731i	0.0707320	−	0.997495i	$-0.477466\pi$
$43$	−2.40501	−	0.644420i	−0.366760	−	0.0982731i	−0.437492	+	0.899222i	$0.644133\pi$
$44$	4.79792			0.723314
$45$		0			0
$46$	−2.63206			−0.388076
$47$	3.82678	+	1.02538i	0.558194	+	0.149568i	0.526876	−	0.849942i	$-0.323363\pi$
$47$	3.82678	+	1.02538i	0.558194	+	0.149568i	0.0313173	+	0.999509i	$0.490030\pi$
$48$	1.73022	+	0.0795432i	0.249736	+	0.0114811i
$49$	−0.0298240	−	0.0172189i	−0.00426058	−	0.00245984i
$50$		0			0
$51$	−2.31299	−	10.5483i	−0.323883	−	1.47706i
$52$	−0.155903	+	0.581838i	−0.0216199	+	0.0806865i
$53$	−1.31215	−	1.31215i	−0.180237	−	0.180237i	0.611222	−	0.791459i	$-0.290678\pi$
$53$	−1.31215	−	1.31215i	−0.180237	−	0.180237i	−0.791459	+	0.611222i	$0.790678\pi$
$54$	4.78674	+	2.02166i	0.651393	+	0.275113i
$55$		0			0
$56$	2.29692	−	1.32613i	0.306938	−	0.177211i
$57$	−7.57249	−	4.84881i	−1.00300	−	0.642240i
$58$	−0.476331	−	1.77769i	−0.0625453	−	0.233422i
$59$	0.0645473	−	0.111799i	0.00840334	−	0.0145550i	−0.861793	−	0.507260i	$-0.830658\pi$
$59$	0.0645473	−	0.111799i	0.00840334	−	0.0145550i	0.870196	+	0.492705i	$0.163992\pi$
$60$		0			0
$61$	6.27251	+	10.8643i	0.803113	+	1.39103i	0.917558	+	0.397603i	$0.130158\pi$
$61$	6.27251	+	10.8643i	0.803113	+	1.39103i	−0.114445	+	0.993430i	$0.536509\pi$
$62$	2.88341	−	2.88341i	0.366194	−	0.366194i
$63$	7.84217	−	1.34550i	0.988020	−	0.169517i
$64$			1.00000i			0.125000i
$65$		0			0
$66$	−2.51722	+	7.91984i	−0.309848	+	0.974864i
$67$	10.6655	−	2.85782i	1.30300	−	0.349138i	0.460416	−	0.887703i	$-0.347700\pi$
$67$	10.6655	−	2.85782i	1.30300	−	0.349138i	0.842584	+	0.538566i	$0.181034\pi$
$68$	6.02233	−	1.61368i	0.730315	−	0.195687i
$69$	1.38090	−	4.34468i	0.166241	−	0.523039i
$70$		0			0
$71$		−	10.4203i		−	1.23666i	−0.785919	−	0.618329i	$-0.787810\pi$
$71$		−	10.4203i		−	1.23666i	0.785919	−	0.618329i	$-0.212190\pi$
$72$	−1.03906	+	2.81431i	−0.122454	+	0.331670i
$73$	−3.30021	+	3.30021i	−0.386261	+	0.386261i	−0.873351	−	0.487091i	$-0.838058\pi$
$73$	−3.30021	+	3.30021i	−0.386261	+	0.386261i	0.487091	+	0.873351i	$0.338058\pi$
$74$	0.446932	+	0.774109i	0.0519548	+	0.0899883i
$75$		0			0
$76$	2.59573	−	4.49593i	0.297750	−	0.515719i
$77$	3.29355	+	12.2917i	0.375335	+	1.40077i
$78$	−0.878635	−	0.562606i	−0.0994858	−	0.0637026i
$79$	−3.62792	+	2.09458i	−0.408173	+	0.235659i	−0.690004	−	0.723805i	$-0.742391\pi$
$79$	−3.62792	+	2.09458i	−0.408173	+	0.235659i	0.281832	+	0.959464i	$0.409058\pi$
$80$		0			0
$81$	−5.84847	+	6.84072i	−0.649830	+	0.760080i
$82$	4.56054	+	4.56054i	0.503628	+	0.503628i
$83$	−2.97686	+	11.1098i	−0.326753	+	1.21946i	0.585785	+	0.810466i	$0.300786\pi$
$83$	−2.97686	+	11.1098i	−0.326753	+	1.21946i	−0.912538	+	0.408992i	$0.865881\pi$
$84$	0.983937	+	4.48722i	0.107356	+	0.489596i
$85$		0			0
$86$	2.15627	+	1.24492i	0.232517	+	0.134243i
$87$	3.18431	+	0.146391i	0.341393	+	0.0156948i
$88$	−4.63444	−	1.24179i	−0.494033	−	0.132376i
$89$	−2.04989			−0.217288			−0.108644	−	0.994081i	$-0.534651\pi$
$89$	−2.04989			−0.217288			−0.108644	+	0.994081i	$0.534651\pi$
$90$		0			0
$91$	−1.59762			−0.167476
$92$	2.54237	+	0.681226i	0.265061	+	0.0710228i
$93$	3.24682	+	6.27237i	0.336679	+	0.650414i
$94$	−3.43100	−	1.98089i	−0.353881	−	0.204313i
$95$		0			0
$96$	−1.65068	−	0.524648i	−0.168472	−	0.0535466i
$97$	−4.47782	+	16.7115i	−0.454654	+	1.69679i	0.234450	+	0.972128i	$0.424671\pi$
$97$	−4.47782	+	16.7115i	−0.454654	+	1.69679i	−0.689104	+	0.724663i	$0.741996\pi$
$98$	0.0243512	+	0.0243512i	0.00245984	+	0.00245984i
$99$	−11.7525	−	8.31025i	−1.18117	−	0.835211i
$100$		0			0
$101$	−10.3594	+	5.98097i	−1.03079	+	0.595129i	−0.917212	−	0.398399i	$-0.869566\pi$
$101$	−10.3594	+	5.98097i	−1.03079	+	0.595129i	−0.113582	+	0.993529i	$0.536232\pi$
$102$	−0.495934	+	10.7876i	−0.0491048	+	1.06813i
$103$	−2.78816	−	10.4055i	−0.274725	−	1.02529i	−0.956025	−	0.293285i	$-0.905252\pi$
$103$	−2.78816	−	10.4055i	−0.274725	−	1.02529i	0.681300	−	0.732004i	$-0.261415\pi$
$104$	0.301182	−	0.521662i	0.0295333	−	0.0511532i
$105$		0			0
$106$	0.927828	+	1.60704i	0.0901186	+	0.156090i
$107$	4.35367	−	4.35367i	0.420885	−	0.420885i	−0.464623	−	0.885508i	$-0.653810\pi$
$107$	4.35367	−	4.35367i	0.420885	−	0.420885i	0.885508	+	0.464623i	$0.153810\pi$
$108$	−4.10039	−	3.19168i	−0.394560	−	0.307119i
$109$			15.4546i			1.48028i	0.672452	+	0.740141i	$0.265241\pi$
$109$			15.4546i			1.48028i	−0.672452	+	0.740141i	$0.734759\pi$
$110$		0			0
$111$	−1.51229	+	0.331607i	−0.143540	+	0.0314748i
$112$	−2.56188	+	0.686453i	−0.242075	+	0.0648637i
$113$	−5.73124	+	1.53568i	−0.539150	+	0.144465i	−0.518110	−	0.855314i	$-0.673364\pi$
$113$	−5.73124	+	1.53568i	−0.539150	+	0.144465i	−0.0210396	+	0.999779i	$0.506698\pi$
$114$	6.05950	+	6.64349i	0.567524	+	0.622220i
$115$		0			0
$116$			1.84040i			0.170877i
$117$	1.38966	−	1.15518i	0.128474	−	0.106796i
$118$	−0.0912837	+	0.0912837i	−0.00840334	+	0.00840334i
$119$	8.26810	+	14.3208i	0.757935	+	1.31278i
$120$		0			0
$121$	6.01003	−	10.4097i	0.546367	−	0.946335i
$122$	−3.24689	−	12.1176i	−0.293960	−	1.09707i
$123$	−9.92068	+	5.13532i	−0.894517	+	0.463036i
$124$	−3.53145	+	2.03888i	−0.317133	+	0.183097i
$125$		0			0
$126$	−7.92319	−	0.730046i	−0.705854	−	0.0650377i
$127$	−2.51837	−	2.51837i	−0.223469	−	0.223469i	0.586489	−	0.809957i	$-0.300510\pi$
$127$	−2.51837	−	2.51837i	−0.223469	−	0.223469i	−0.809957	+	0.586489i	$0.800510\pi$
$128$	0.258819	−	0.965926i	0.0228766	−	0.0853766i
$129$	−3.18625	+	2.90617i	−0.280534	+	0.255874i
$130$		0			0
$131$	11.3102	+	6.52997i	0.988181	+	0.570526i	0.904730	−	0.425985i	$-0.140073\pi$
$131$	11.3102	+	6.52997i	0.988181	+	0.570526i	0.0834508	+	0.996512i	$0.473406\pi$
$132$	4.48125	−	6.99847i	0.390043	−	0.609139i
$133$	13.2999	+	3.56369i	1.15325	+	0.309011i
$134$	−11.0417			−0.953862
$135$		0			0
$136$	−6.23478			−0.534628
$137$	−3.13844	−	0.840942i	−0.268135	−	0.0718465i	0.122246	−	0.992500i	$-0.460990\pi$
$137$	−3.13844	−	0.840942i	−0.268135	−	0.0718465i	−0.390381	+	0.920653i	$0.627657\pi$
$138$	−2.45834	+	3.83924i	−0.209267	+	0.326818i
$139$	19.0478	+	10.9973i	1.61561	+	0.932775i	0.988036	+	0.154221i	$0.0492868\pi$
$139$	19.0478	+	10.9973i	1.61561	+	0.932775i	0.627578	+	0.778554i	$0.284047\pi$
$140$		0			0
$141$	5.06988	−	4.62421i	0.426961	−	0.389429i
$142$	−2.69696	+	10.0652i	−0.226324	+	0.844653i
$143$	2.04360	+	2.04360i	0.170895	+	0.170895i
$144$	1.73205	−	2.44949i	0.144338	−	0.204124i
$145$		0			0
$146$	4.04192	−	2.33360i	0.334512	−	0.193130i
$147$	−0.0529719	+	0.0274203i	−0.00436905	+	0.00226159i
$148$	−0.231349	−	0.863406i	−0.0190168	−	0.0709715i
$149$	−6.56668	+	11.3738i	−0.537964	+	0.931780i	0.461050	+	0.887374i	$0.347473\pi$
$149$	−6.56668	+	11.3738i	−0.537964	+	0.931780i	−0.999014	+	0.0444061i	$0.985860\pi$
$150$		0			0
$151$	−0.167899	−	0.290810i	−0.0136634	−	0.0236658i	0.859113	−	0.511786i	$-0.171016\pi$
$151$	−0.167899	−	0.290810i	−0.0136634	−	0.0236658i	−0.872776	+	0.488120i	$0.837683\pi$
$152$	−3.67091	+	3.67091i	−0.297750	+	0.297750i
$153$	−17.5466	−	6.47830i	−1.41856	−	0.523739i
$154$		−	12.7253i		−	1.02543i
$155$		0			0
$156$	0.703083	+	0.770843i	0.0562917	+	0.0617169i
$157$	−4.40352	+	1.17992i	−0.351439	+	0.0941678i	−0.430220	−	0.902724i	$-0.641564\pi$
$157$	−4.40352	+	1.17992i	−0.351439	+	0.0941678i	0.0787808	+	0.996892i	$0.474897\pi$
$158$	4.04642	−	1.08423i	0.321916	−	0.0862571i
$159$	−3.13950	+	0.688415i	−0.248979	+	0.0545948i
$160$		0			0
$161$			6.98088i			0.550170i
$162$	7.41970	−	5.09393i	0.582946	−	0.400217i
$163$	−9.01496	+	9.01496i	−0.706106	+	0.706106i	−0.965714	−	0.259608i	$-0.916407\pi$
$163$	−9.01496	+	9.01496i	−0.706106	+	0.706106i	0.259608	+	0.965714i	$0.416407\pi$
$164$	−3.22479	−	5.58550i	−0.251814	−	0.436154i
$165$		0			0
$166$	5.75085	−	9.96076i	0.446353	−	0.773105i
$167$	0.00229992	+	0.00858342i	0.000177973	+	0.000664205i	0.966015	−	0.258487i	$-0.0832239\pi$
$167$	0.00229992	+	0.00858342i	0.000177973	+	0.000664205i	−0.965837	+	0.259151i	$0.916557\pi$
$168$	0.210969	−	4.58899i	0.0162766	−	0.354048i
$169$	10.9441	−	6.31858i	0.841854	−	0.486045i
$170$		0			0
$171$	−14.1454	+	6.51681i	−1.08172	+	0.498353i
$172$	−1.76059	−	1.76059i	−0.134243	−	0.134243i
$173$	2.68729	−	10.0291i	0.204311	−	0.762500i	−0.785347	−	0.619056i	$-0.787516\pi$
$173$	2.68729	−	10.0291i	0.204311	−	0.762500i	0.989658	−	0.143444i	$-0.0458178\pi$
$174$	−3.03791	−	0.965562i	−0.230304	−	0.0731991i
$175$		0			0
$176$	4.15512	+	2.39896i	0.313204	+	0.180829i
$177$	−0.102788	−	0.198572i	−0.00772605	−	0.0149256i
$178$	1.98004	+	0.530550i	0.148410	+	0.0397664i
$179$	−1.46292			−0.109343			−0.0546717	−	0.998504i	$-0.517411\pi$
$179$	−1.46292			−0.109343			−0.0546717	+	0.998504i	$0.517411\pi$
$180$		0			0
$181$	−8.68576			−0.645607			−0.322804	−	0.946466i	$-0.604625\pi$
$181$	−8.68576			−0.645607			−0.322804	+	0.946466i	$0.604625\pi$
$182$	1.54318	+	0.413494i	0.114388	+	0.0306502i
$183$	21.7057	+	0.997872i	1.60453	+	0.0737648i
$184$	−2.27943	−	1.31603i	−0.168042	−	0.0970189i
$185$		0			0
$186$	−1.51278	−	6.89898i	−0.110922	−	0.505858i
$187$	7.74231	−	28.8947i	0.566174	−	2.11299i
$188$	2.80140	+	2.80140i	0.204313	+	0.204313i
$189$	5.36196	−	12.6956i	0.390025	−	0.923472i
$190$		0			0
$191$	−4.33795	+	2.50452i	−0.313883	+	0.181220i	−0.648663	−	0.761076i	$-0.724671\pi$
$191$	−4.33795	+	2.50452i	−0.313883	+	0.181220i	0.334780	+	0.942296i	$0.391338\pi$
$192$	1.45865	+	0.933998i	0.105269	+	0.0674055i
$193$	−0.871785	−	3.25355i	−0.0627524	−	0.234195i	0.927426	−	0.374008i	$-0.122017\pi$
$193$	−0.871785	−	3.25355i	−0.0627524	−	0.234195i	−0.990178	+	0.139812i	$0.955350\pi$
$194$	8.65048	−	14.9831i	0.621069	−	1.07572i
$195$		0			0
$196$	−0.0172189	−	0.0298240i	−0.00122992	−	0.00213029i
$197$	−15.5027	+	15.5027i	−1.10452	+	1.10452i	−0.110665	+	0.993858i	$0.535298\pi$
$197$	−15.5027	+	15.5027i	−1.10452	+	1.10452i	−0.993858	+	0.110665i	$0.964702\pi$
$198$	9.20116	+	11.0688i	0.653898	+	0.786628i
$199$		−	18.4607i		−	1.30864i	−0.756217	−	0.654321i	$-0.772955\pi$
$199$		−	18.4607i		−	1.30864i	0.756217	−	0.654321i	$-0.227045\pi$
$200$		0			0
$201$	5.79303	−	18.2264i	0.408609	−	1.28559i
$202$	11.5544	−	3.09598i	0.812962	−	0.217832i
$203$	−4.71488	+	1.26335i	−0.330920	+	0.0886697i
$204$	3.27106	−	10.2916i	0.229020	−	0.720558i
$205$		0			0
$206$			10.7726i			0.750564i
$207$	−5.04759	−	6.07217i	−0.350832	−	0.422045i
$208$	−0.425935	+	0.425935i	−0.0295333	+	0.0295333i
$209$	−12.4541	−	21.5711i	−0.861468	−	1.49211i
$210$		0			0
$211$	0.654465	−	1.13357i	0.0450552	−	0.0780380i	−0.842618	−	0.538511i	$-0.818987\pi$
$211$	0.654465	−	1.13357i	0.0450552	−	0.0780380i	0.887674	+	0.460473i	$0.152320\pi$
$212$	−0.480279	−	1.79243i	−0.0329857	−	0.123104i
$213$	−15.1995	−	9.73251i	−1.04145	−	0.666860i
$214$	−5.33213	+	3.07851i	−0.364497	+	0.210442i
$215$		0			0
$216$	3.13461	+	4.14418i	0.213283	+	0.281976i
$217$	−7.64754	−	7.64754i	−0.519149	−	0.519149i
$218$	3.99994	−	14.9280i	0.270910	−	1.01105i
$219$	1.73145	+	7.89624i	0.117001	+	0.533578i
$220$		0			0
$221$	3.25245	+	1.87780i	0.218783	+	0.126315i
$222$	1.54658	+	0.0711008i	0.103800	+	0.00477197i
$223$	20.2614	+	5.42903i	1.35681	+	0.363555i	0.862643	−	0.505814i	$-0.168808\pi$
$223$	20.2614	+	5.42903i	1.35681	+	0.363555i	0.494163	+	0.869369i	$0.335474\pi$
$224$	2.65225			0.177211
$225$		0			0
$226$	5.93342			0.394685
$227$	−5.75206	−	1.54126i	−0.381778	−	0.102297i	0.0628257	−	0.998025i	$-0.479989\pi$
$227$	−5.75206	−	1.54126i	−0.381778	−	0.102297i	−0.444604	+	0.895727i	$0.646655\pi$
$228$	−4.13357	−	7.98544i	−0.273752	−	0.528848i
$229$	−10.1822	−	5.87872i	−0.672862	−	0.388477i	0.124298	−	0.992245i	$-0.460332\pi$
$229$	−10.1822	−	5.87872i	−0.672862	−	0.388477i	−0.797160	+	0.603768i	$0.793665\pi$
$230$		0			0
$231$	21.0054	+	6.67630i	1.38205	+	0.439268i
$232$	0.476331	−	1.77769i	0.0312727	−	0.116711i
$233$	13.4322	+	13.4322i	0.879973	+	0.879973i	0.993531	−	0.113558i	$-0.0362249\pi$
$233$	13.4322	+	13.4322i	0.879973	+	0.879973i	−0.113558	+	0.993531i	$0.536225\pi$
$234$	−1.64129	+	0.756144i	−0.107294	+	0.0494307i
$235$		0			0
$236$	0.111799	−	0.0645473i	0.00727751	−	0.00420167i
$237$	−0.333219	+	7.24818i	−0.0216449	+	0.470820i
$238$	−4.27988	−	15.9727i	−0.277424	−	1.03536i
$239$	2.27943	−	3.94809i	0.147444	−	0.255380i	−0.782838	−	0.622225i	$-0.786229\pi$
$239$	2.27943	−	3.94809i	0.147444	−	0.255380i	0.930282	+	0.366845i	$0.119562\pi$
$240$		0			0
$241$	8.03104	+	13.9102i	0.517325	+	0.896032i	0.999798	+	0.0201215i	$0.00640532\pi$
$241$	8.03104	+	13.9102i	0.517325	+	0.896032i	−0.482473	+	0.875911i	$0.660261\pi$
$242$	−8.49947	+	8.49947i	−0.546367	+	0.546367i
$243$	4.51572	+	14.9201i	0.289684	+	0.957122i
$244$			12.5450i			0.803113i
$245$		0			0
$246$	10.9118	−	2.39268i	0.695708	−	0.152552i
$247$	3.02059	−	0.809364i	0.192195	−	0.0514986i
$248$	3.93882	−	1.05540i	0.250115	−	0.0670181i
$249$	13.4249	+	14.7187i	0.850766	+	0.932760i
$250$		0			0
$251$		−	18.9981i		−	1.19915i	−0.800319	−	0.599574i	$-0.795337\pi$
$251$		−	18.9981i		−	1.19915i	0.800319	−	0.599574i	$-0.204663\pi$
$252$	7.46427	+	2.75584i	0.470205	+	0.173602i
$253$	8.92963	−	8.92963i	0.561401	−	0.561401i
$254$	1.78075	+	3.08436i	0.111734	+	0.193530i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−0.867374	−	3.23709i	−0.0541053	−	0.201924i	0.933582	−	0.358363i	$-0.116665\pi$
$257$	−0.867374	−	3.23709i	−0.0541053	−	0.201924i	−0.987688	+	0.156439i	$0.949998\pi$
$258$	3.82985	−	1.98248i	0.238436	−	0.123424i
$259$	2.05313	−	1.18538i	0.127575	−	0.0736557i
$260$		0			0
$261$	3.18767	−	4.50804i	0.197312	−	0.279041i
$262$	−9.23478	−	9.23478i	−0.570526	−	0.570526i
$263$	4.33402	−	16.1748i	0.267247	−	0.997380i	−0.693614	−	0.720347i	$-0.743982\pi$
$263$	4.33402	−	16.1748i	0.267247	−	0.997380i	0.960861	−	0.277032i	$-0.0893509\pi$
$264$	−6.13989	+	5.60017i	−0.377884	+	0.344667i
$265$		0			0
$266$	−11.9243	−	6.88452i	−0.731128	−	0.422117i
$267$	−1.91459	+	2.99006i	−0.117171	+	0.182989i
$268$	10.6655	+	2.85782i	0.651500	+	0.174569i
$269$	−0.535741			−0.0326647			−0.0163324	−	0.999867i	$-0.505199\pi$
$269$	−0.535741			−0.0326647			−0.0163324	+	0.999867i	$0.505199\pi$
$270$		0			0
$271$	−15.5412			−0.944063			−0.472032	−	0.881582i	$-0.656479\pi$
$271$	−15.5412			−0.944063			−0.472032	+	0.881582i	$0.656479\pi$
$272$	6.02233	+	1.61368i	0.365158	+	0.0978437i
$273$	−1.49217	+	2.33036i	−0.0903104	+	0.141040i
$274$	2.81385	+	1.62458i	0.169991	+	0.0981442i
$275$		0			0
$276$	3.36824	−	3.07216i	0.202744	−	0.184922i
$277$	4.48011	−	16.7200i	0.269184	−	1.00461i	−0.690456	−	0.723374i	$-0.742590\pi$
$277$	4.48011	−	16.7200i	0.269184	−	1.00461i	0.959640	−	0.281232i	$-0.0907432\pi$
$278$	−15.5525	−	15.5525i	−0.932775	−	0.932775i
$279$	12.1817	+	1.12242i	0.729298	+	0.0671978i
$280$		0			0
$281$	−20.8909	+	12.0613i	−1.24624	+	0.719519i	−0.970358	−	0.241671i	$-0.922304\pi$
$281$	−20.8909	+	12.0613i	−1.24624	+	0.719519i	−0.275886	+	0.961190i	$0.588971\pi$
$282$	−6.09396	+	3.15447i	−0.362890	+	0.187846i
$283$	4.28387	+	15.9876i	0.254649	+	0.950365i	0.968285	+	0.249848i	$0.0803805\pi$
$283$	4.28387	+	15.9876i	0.254649	+	0.950365i	−0.713636	+	0.700517i	$0.752953\pi$
$284$	5.21013	−	9.02421i	0.309164	−	0.535489i
$285$		0			0
$286$	−1.44505	−	2.50289i	−0.0854474	−	0.147999i
$287$	12.0957	−	12.0957i	0.713987	−	0.713987i
$288$	−2.30701	+	1.91774i	−0.135942	+	0.113004i
$289$		−	21.8725i		−	1.28661i
$290$		0			0
$291$	20.1938	+	22.1400i	1.18378	+	1.29787i
$292$	−4.50818	+	1.20796i	−0.263821	+	0.0706906i
$293$	−15.6012	+	4.18032i	−0.911431	+	0.244217i	−0.683919	−	0.729558i	$-0.739726\pi$
$293$	−15.6012	+	4.18032i	−0.911431	+	0.244217i	−0.227512	+	0.973775i	$0.573059\pi$
$294$	0.0582638	−	0.0127758i	0.00339801	−	0.000745100i
$295$		0			0
$296$			0.893864i			0.0519548i
$297$	−23.0985	+	9.38093i	−1.34031	+	0.544337i
$298$	9.28669	−	9.28669i	0.537964	−	0.537964i
$299$	0.792727	+	1.37304i	0.0458446	+	0.0794052i
$300$		0			0
$301$	3.30185	−	5.71897i	0.190315	−	0.329636i
$302$	0.0869109	+	0.324356i	0.00500116	+	0.0186646i
$303$	−0.951492	+	20.6968i	−0.0546618	+	1.18900i
$304$	4.49593	−	2.59573i	0.257859	−	0.148875i
$305$		0			0
$306$	15.2720	+	10.7990i	0.873043	+	0.617335i
$307$	1.45642	+	1.45642i	0.0831222	+	0.0831222i	0.747445	−	0.664323i	$-0.231280\pi$
$307$	1.45642	+	1.45642i	0.0831222	+	0.0831222i	−0.664323	+	0.747445i	$0.731280\pi$
$308$	−3.29355	+	12.2917i	−0.187667	+	0.700384i
$309$	−17.7821	−	5.65183i	−1.01159	−	0.321521i
$310$		0			0
$311$	−1.81462	−	1.04767i	−0.102898	−	0.0594081i	0.447668	−	0.894200i	$-0.352255\pi$
$311$	−1.81462	−	1.04767i	−0.102898	−	0.0594081i	−0.550566	+	0.834792i	$0.685588\pi$
$312$	−0.479617	−	0.926549i	−0.0271530	−	0.0524555i
$313$	−19.0789	−	5.11217i	−1.07840	−	0.288957i	−0.324461	−	0.945899i	$-0.605183\pi$
$313$	−19.0789	−	5.11217i	−1.07840	−	0.288957i	−0.753941	+	0.656942i	$0.771850\pi$
$314$	4.55886			0.257271
$315$		0			0
$316$	−4.18916			−0.235659
$317$	−32.9248	−	8.82217i	−1.84924	−	0.495503i	−0.849743	−	0.527196i	$-0.823243\pi$
$317$	−32.9248	−	8.82217i	−1.84924	−	0.495503i	−0.999498	+	0.0316937i	$0.989910\pi$
$318$	3.21070	+	0.147605i	0.180047	+	0.00827727i
$319$	7.64709	+	4.41505i	0.428155	+	0.247195i
$320$		0			0
$321$	−2.28414	−	10.4168i	−0.127488	−	0.581408i
$322$	1.80678	−	6.74301i	0.100688	−	0.375773i
$323$	−22.8873	−	22.8873i	−1.27348	−	1.27348i
$324$	−8.48528	+	3.00000i	−0.471405	+	0.166667i
$325$		0			0
$326$	11.0410	−	6.37454i	0.611506	−	0.353053i
$327$	22.5428	+	14.4346i	1.24662	+	0.798233i
$328$	1.66927	+	6.22982i	0.0921703	+	0.343984i
$329$	−5.25381	+	9.09987i	−0.289652	+	0.501692i
$330$		0			0
$331$	−12.0140	−	20.8088i	−0.660348	−	1.14376i	−0.980524	−	0.196399i	$-0.937075\pi$
$331$	−12.0140	−	20.8088i	−0.660348	−	1.14376i	0.320176	−	0.947358i	$-0.396258\pi$
$332$	−8.13293	+	8.13293i	−0.446353	+	0.446353i
$333$	−0.928776	+	2.51561i	−0.0508966	+	0.137855i
$334$		−	0.00888621i		−	0.000486232i
$335$		0			0
$336$	−1.39150	+	4.37802i	−0.0759124	+	0.238841i
$337$	11.8340	−	3.17090i	0.644637	−	0.172730i	0.0783338	−	0.996927i	$-0.475040\pi$
$337$	11.8340	−	3.17090i	0.644637	−	0.172730i	0.566303	+	0.824197i	$0.308373\pi$
$338$	−12.2066	+	3.27074i	−0.663949	+	0.177905i
$339$	−3.11295	+	9.79417i	−0.169072	+	0.531947i
$340$		0			0
$341$			19.5648i			1.05949i
$342$	15.3501	−	2.63366i	0.830037	−	0.142412i
$343$	−13.0634	+	13.0634i	−0.705357	+	0.705357i
$344$	1.24492	+	2.15627i	0.0671217	+	0.116258i
$345$		0			0
$346$	−5.19145	+	8.99186i	−0.279094	+	0.483405i
$347$	4.81127	+	17.9559i	0.258283	+	0.963924i	0.966235	+	0.257663i	$0.0829525\pi$
$347$	4.81127	+	17.9559i	0.258283	+	0.963924i	−0.707952	+	0.706260i	$0.750381\pi$
$348$	2.68449	+	1.71893i	0.143904	+	0.0921444i
$349$	−27.2305	+	15.7215i	−1.45761	+	0.841553i	−0.998894	−	0.0470278i	$-0.985025\pi$
$349$	−27.2305	+	15.7215i	−1.45761	+	0.841553i	−0.458720	+	0.888581i	$0.651692\pi$
$350$		0			0
$351$	−0.387054	−	3.10595i	−0.0206594	−	0.165783i
$352$	−3.39264	−	3.39264i	−0.180829	−	0.180829i
$353$	−3.14681	+	11.7440i	−0.167488	+	0.625073i	0.830222	+	0.557433i	$0.188214\pi$
$353$	−3.14681	+	11.7440i	−0.167488	+	0.625073i	−0.997710	+	0.0676398i	$0.978453\pi$
$354$	0.0478918	+	0.218409i	0.00254542	+	0.0116083i
$355$		0			0
$356$	−1.77526	−	1.02494i	−0.0940883	−	0.0543219i
$357$	28.6113	+	1.31534i	1.51427	+	0.0696153i
$358$	1.41307	+	0.378631i	0.0746830	+	0.0200112i
$359$	4.31606			0.227793			0.113896	−	0.993493i	$-0.463667\pi$
$359$	4.31606			0.227793			0.113896	+	0.993493i	$0.463667\pi$
$360$		0			0
$361$	−7.95119			−0.418484
$362$	8.38980	+	2.24804i	0.440958	+	0.118154i
$363$	−9.57068	−	18.4891i	−0.502330	−	0.970428i
$364$	−1.38358	−	0.798810i	−0.0725192	−	0.0418690i
$365$		0			0
$366$	−20.7078	−	6.58172i	−1.08242	−	0.344032i
$367$	−5.14485	+	19.2008i	−0.268559	+	1.00228i	0.691477	+	0.722399i	$0.256960\pi$
$367$	−5.14485	+	19.2008i	−0.268559	+	1.00228i	−0.960036	+	0.279877i	$0.909706\pi$
$368$	1.86115	+	1.86115i	0.0970189	+	0.0970189i
$369$	−1.77528	+	19.2671i	−0.0924174	+	1.00301i
$370$		0			0
$371$	4.26229	−	2.46083i	0.221287	−	0.127760i
$372$	−0.324358	+	7.05544i	−0.0168172	+	0.365807i
$373$	0.680056	+	2.53800i	0.0352120	+	0.131413i	0.981294	−	0.192513i	$-0.0616638\pi$
$373$	0.680056	+	2.53800i	0.0352120	+	0.131413i	−0.946082	+	0.323926i	$0.894997\pi$
$374$	−14.9570	+	25.9063i	−0.773408	+	1.33958i
$375$		0			0
$376$	−1.98089	−	3.43100i	−0.102157	−	0.176940i
$377$	−0.783892	+	0.783892i	−0.0403725	+	0.0403725i
$378$	−8.46512	+	10.8753i	−0.435399	+	0.559363i
$379$		−	3.03124i		−	0.155705i	−0.996965	−	0.0778523i	$-0.975194\pi$
$379$		−	3.03124i		−	0.155705i	0.996965	−	0.0778523i	$-0.0248063\pi$
$380$		0			0
$381$	−6.02555	+	1.32125i	−0.308698	+	0.0676899i
$382$	4.83835	−	1.29643i	0.247552	−	0.0663313i
$383$	22.9416	−	6.14717i	1.17226	−	0.314106i	0.380407	−	0.924819i	$-0.375784\pi$
$383$	22.9416	−	6.14717i	1.17226	−	0.314106i	0.791852	+	0.610713i	$0.209117\pi$
$384$	−1.16721	−	1.27970i	−0.0595638	−	0.0653043i
$385$		0			0
$386$			3.36832i			0.171443i
$387$	1.26311	+	7.36197i	0.0642077	+	0.374230i
$388$	−12.2336	+	12.2336i	−0.621069	+	0.621069i
$389$	−3.33254	−	5.77213i	−0.168966	−	0.292659i	0.769090	−	0.639140i	$-0.220710\pi$
$389$	−3.33254	−	5.77213i	−0.168966	−	0.292659i	−0.938057	+	0.346482i	$0.887376\pi$
$390$		0			0
$391$	8.20515	−	14.2117i	0.414952	−	0.718718i
$392$	0.00891317	+	0.0332644i	0.000450183	+	0.00168011i
$393$	20.0887	−	10.3987i	1.01334	−	0.524543i
$394$	18.9869	−	10.9621i	0.956545	−	0.552261i
$395$		0			0
$396$	−6.02281	−	13.0731i	−0.302658	−	0.656949i
$397$	13.2242	+	13.2242i	0.663703	+	0.663703i	0.956251	−	0.292548i	$-0.0945031\pi$
$397$	13.2242	+	13.2242i	0.663703	+	0.663703i	−0.292548	+	0.956251i	$0.594503\pi$
$398$	−4.77797	+	17.8316i	−0.239498	+	0.893819i
$399$	17.6202	−	16.0713i	0.882114	−	0.804572i
$400$		0			0
$401$	4.66934	+	2.69585i	0.233176	+	0.134624i	0.612036	−	0.790830i	$-0.290351\pi$
$401$	4.66934	+	2.69585i	0.233176	+	0.134624i	−0.378860	+	0.925454i	$0.623684\pi$
$402$	−10.3130	+	16.1060i	−0.514364	+	0.803294i
$403$	−2.37260	−	0.635736i	−0.118188	−	0.0316683i
$404$	−11.9619			−0.595129
$405$		0			0
$406$	4.88121			0.242250
$407$	−4.14256	−	1.10999i	−0.205339	−	0.0550204i
$408$	−5.82327	+	9.09433i	−0.288295	+	0.450237i
$409$	7.43574	+	4.29303i	0.367674	+	0.212277i	0.672442	−	0.740150i	$-0.265246\pi$
$409$	7.43574	+	4.29303i	0.367674	+	0.212277i	−0.304768	+	0.952427i	$0.598579\pi$
$410$		0			0
$411$	−4.15793	+	3.79243i	−0.205096	+	0.187067i
$412$	2.78816	−	10.4055i	0.137363	−	0.512644i
$413$	0.242107	+	0.242107i	0.0119133	+	0.0119133i
$414$	3.30401	+	7.17168i	0.162383	+	0.352469i
$415$		0			0
$416$	0.521662	−	0.301182i	0.0255766	−	0.0147666i
$417$	33.8317	−	17.5126i	1.65675	−	0.857595i
$418$	6.44672	+	24.0595i	0.315319	+	1.17679i
$419$	−7.72749	+	13.3844i	−0.377512	+	0.653871i	−0.990700	−	0.136067i	$-0.956554\pi$
$419$	−7.72749	+	13.3844i	−0.377512	+	0.653871i	0.613187	+	0.789938i	$0.289887\pi$
$420$		0			0
$421$	9.45129	+	16.3701i	0.460628	+	0.797831i	0.998992	−	0.0448812i	$-0.0142909\pi$
$421$	9.45129	+	16.3701i	0.460628	+	0.797831i	−0.538364	+	0.842712i	$0.680958\pi$
$422$	−0.925553	+	0.925553i	−0.0450552	+	0.0450552i
$423$	−2.00983	−	11.7142i	−0.0977214	−	0.569562i
$424$			1.85566i			0.0901186i
$425$		0			0
$426$	12.1626	+	13.3348i	0.589280	+	0.646073i
$427$	−32.1388	+	8.61157i	−1.55531	+	0.416743i
$428$	5.94722	−	1.59355i	0.287470	−	0.0770273i
$429$	4.88962	−	1.07217i	0.236073	−	0.0517650i
$430$		0			0
$431$			3.91428i			0.188544i	0.995546	+	0.0942720i	$0.0300523\pi$
$431$			3.91428i			0.188544i	−0.995546	+	0.0942720i	$0.969948\pi$
$432$	−1.95521	−	4.81427i	−0.0940699	−	0.231627i
$433$	27.2049	−	27.2049i	1.30738	−	1.30738i	0.384086	−	0.923297i	$-0.374517\pi$
$433$	27.2049	−	27.2049i	1.30738	−	1.30738i	0.923297	−	0.384086i	$-0.125483\pi$
$434$	5.40762	+	9.36628i	0.259574	+	0.449596i
$435$		0			0
$436$	−7.72730	+	13.3841i	−0.370070	+	0.640981i
$437$	−3.53656	−	13.1986i	−0.169176	−	0.631375i
$438$	0.371245	−	8.07531i	0.0177388	−	0.385853i
$439$	13.2725	−	7.66286i	0.633460	−	0.365728i	−0.148631	−	0.988893i	$-0.547487\pi$
$439$	13.2725	−	7.66286i	0.633460	−	0.365728i	0.782091	+	0.623164i	$0.214153\pi$
$440$		0			0
$441$	−0.00947919	+	0.102878i	−0.000451390	+	0.00489894i
$442$	−2.65561	−	2.65561i	−0.126315	−	0.126315i
$443$	7.20031	−	26.8719i	0.342097	−	1.27672i	−0.553870	−	0.832603i	$-0.686850\pi$
$443$	7.20031	−	26.8719i	0.342097	−	1.27672i	0.895967	−	0.444120i	$-0.146484\pi$
$444$	−1.47548	−	0.468963i	−0.0700233	−	0.0222560i
$445$		0			0
$446$	−18.1659	−	10.4881i	−0.860180	−	0.496625i
$447$	10.4571	+	20.2016i	0.494605	+	0.955503i
$448$	−2.56188	−	0.686453i	−0.121037	−	0.0324319i
$449$	24.3627			1.14975			0.574874	−	0.818242i	$-0.305051\pi$
$449$	24.3627			1.14975			0.574874	+	0.818242i	$0.305051\pi$
$450$		0			0
$451$	−30.9446			−1.45712
$452$	−5.73124	−	1.53568i	−0.269575	−	0.0722324i
$453$	−0.581006	−	0.0267105i	−0.0272980	−	0.00125497i
$454$	5.15716	+	2.97749i	0.242037	+	0.139740i
$455$		0			0
$456$	1.92594	+	8.78319i	0.0901902	+	0.411310i
$457$	−3.39506	+	12.6705i	−0.158814	+	0.592702i	0.839935	+	0.542688i	$0.182593\pi$
$457$	−3.39506	+	12.6705i	−0.158814	+	0.592702i	−0.998749	+	0.0500141i	$0.984073\pi$
$458$	8.31377	+	8.31377i	0.388477	+	0.388477i
$459$	−25.8380	+	19.5436i	−1.20602	+	0.912216i
$460$		0			0
$461$	34.7684	−	20.0736i	1.61933	−	0.934919i	0.632233	−	0.774778i	$-0.282139\pi$
$461$	34.7684	−	20.0736i	1.61933	−	0.934919i	0.987094	−	0.160141i	$-0.0511948\pi$
$462$	−18.5617	−	11.8854i	−0.863569	−	0.552959i
$463$	−3.09986	−	11.5688i	−0.144063	−	0.537649i	−0.999795	−	0.0202307i	$-0.993560\pi$
$463$	−3.09986	−	11.5688i	−0.144063	−	0.537649i	0.855733	−	0.517418i	$-0.173107\pi$
$464$	−0.920201	+	1.59383i	−0.0427192	+	0.0739919i
$465$		0			0
$466$	−9.49800	−	16.4510i	−0.439986	−	0.762079i
$467$	8.63124	−	8.63124i	0.399406	−	0.399406i	−0.478617	−	0.878024i	$-0.658862\pi$
$467$	8.63124	−	8.63124i	0.399406	−	0.399406i	0.878024	+	0.478617i	$0.158862\pi$
$468$	1.78107	−	0.305583i	0.0823298	−	0.0141256i
$469$			29.2855i			1.35228i
$470$		0			0
$471$	−2.39179	+	7.52521i	−0.110208	+	0.346744i
$472$	−0.124696	+	0.0334121i	−0.00573959	+	0.00153792i
$473$	−11.5390	+	3.09188i	−0.530565	+	0.142165i
$474$	2.19783	−	6.91496i	0.100950	−	0.317615i
$475$		0			0
$476$			16.5362i			0.757935i
$477$	−1.92813	+	5.22240i	−0.0882832	+	0.239117i
$478$	−3.22360	+	3.22360i	−0.147444	+	0.147444i
$479$	−5.13488	−	8.89388i	−0.234619	−	0.406372i	0.724543	−	0.689230i	$-0.242051\pi$
$479$	−5.13488	−	8.89388i	−0.234619	−	0.406372i	−0.959162	+	0.282858i	$0.908718\pi$
$480$		0			0
$481$	0.269215	−	0.466295i	0.0122752	−	0.0212612i
$482$	−4.15717	−	15.5148i	−0.189354	−	0.706678i
$483$	10.1826	+	6.52013i	0.463326	+	0.296676i
$484$	10.4097	−	6.01003i	0.473167	−	0.273183i
$485$		0			0
$486$	−0.500258	−	15.5804i	−0.0226921	−	0.706743i
$487$	−17.5218	−	17.5218i	−0.793987	−	0.793987i	0.188153	−	0.982140i	$-0.439750\pi$
$487$	−17.5218	−	17.5218i	−0.793987	−	0.793987i	−0.982140	+	0.188153i	$0.939750\pi$
$488$	3.24689	−	12.1176i	0.146980	−	0.548536i
$489$	4.72968	+	21.5696i	0.213884	+	0.975411i
$490$		0			0
$491$	−7.70100	−	4.44617i	−0.347541	−	0.200653i	0.316061	−	0.948739i	$-0.397640\pi$
$491$	−7.70100	−	4.44617i	−0.347541	−	0.200653i	−0.663602	+	0.748086i	$0.730973\pi$
$492$	−11.1592	−	0.513021i	−0.503096	−	0.0231288i
$493$	11.0835	+	2.96982i	0.499176	+	0.133754i
$494$	−3.12714			−0.140697
$495$		0			0
$496$	−4.07776			−0.183097
$497$	26.6954	+	7.15302i	1.19745	+	0.320857i
$498$	−9.15794	−	17.6918i	−0.410377	−	0.792788i
$499$	−25.4186	−	14.6754i	−1.13789	−	0.656963i	−0.191985	−	0.981398i	$-0.561493\pi$
$499$	−25.4186	−	14.6754i	−1.13789	−	0.656963i	−0.945908	+	0.324435i	$0.894826\pi$
$500$		0			0
$501$	0.0146683	+	0.00466213i	0.000655331	+	0.000208288i
$502$	−4.91707	+	18.3507i	−0.219459	+	0.819034i
$503$	10.0766	+	10.0766i	0.449293	+	0.449293i	0.895120	−	0.445826i	$-0.147090\pi$
$503$	10.0766	+	10.0766i	0.449293	+	0.449293i	−0.445826	+	0.895120i	$0.647090\pi$
$504$	−6.49666	−	4.59383i	−0.289384	−	0.204626i
$505$		0			0
$506$	−10.9365	+	6.31420i	−0.486188	+	0.280701i
$507$	1.00520	−	21.8651i	0.0446425	−	0.971063i
$508$	−0.921786	−	3.44015i	−0.0408976	−	0.152632i
$509$	15.0024	−	25.9849i	0.664970	−	1.15176i	−0.314323	−	0.949316i	$-0.601777\pi$
$509$	15.0024	−	25.9849i	0.664970	−	1.15176i	0.979293	−	0.202446i	$-0.0648892\pi$
$510$		0			0
$511$	−6.18930	−	10.7202i	−0.273799	−	0.474233i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	−3.70605	+	26.7198i	−0.163626	+	1.17971i
$514$			3.35128i			0.147819i
$515$		0			0
$516$	−4.21246	+	0.923688i	−0.185443	+	0.0406631i
$517$	18.3606	−	4.91971i	0.807499	−	0.216369i
$518$	−2.28997	+	0.613596i	−0.100615	+	0.0269598i
$519$	−12.1190	−	13.2870i	−0.531965	−	0.583234i
$520$		0			0
$521$			6.40485i			0.280602i	0.990109	+	0.140301i	$0.0448070\pi$
$521$			6.40485i			0.280602i	−0.990109	+	0.140301i	$0.955193\pi$
$522$	−4.24582	+	3.52941i	−0.185834	+	0.154478i
$523$	−16.0596	+	16.0596i	−0.702237	+	0.702237i	−0.964890	−	0.262653i	$-0.915403\pi$
$523$	−16.0596	+	16.0596i	−0.702237	+	0.702237i	0.262653	+	0.964890i	$0.415403\pi$
$524$	6.52997	+	11.3102i	0.285263	+	0.494090i
$525$		0			0
$526$	−8.37268	+	14.5019i	−0.365066	+	0.632313i
$527$	6.58020	+	24.5576i	0.286638	+	1.06975i
$528$	7.38011	−	3.82023i	0.321178	−	0.166254i
$529$	−13.9190	+	8.03614i	−0.605174	+	0.349397i
$530$		0			0
$531$	−0.385650	−	0.0355339i	−0.0167358	−	0.00154204i
$532$	9.73618	+	9.73618i	0.422117	+	0.422117i
$533$	1.00551	−	3.75261i	0.0435535	−	0.162544i
$534$	2.62324	−	2.39264i	0.113519	−	0.103540i
$535$		0			0
$536$	−9.56244	−	5.52087i	−0.413034	−	0.238465i
$537$	−1.36636	+	2.13388i	−0.0589628	+	0.0920836i
$538$	0.517486	+	0.138660i	0.0223104	+	0.00597806i
$539$	−0.165230			−0.00711696
$540$		0			0
$541$	44.6389			1.91917			0.959587	−	0.281412i	$-0.0908026\pi$
$541$	44.6389			1.91917			0.959587	+	0.281412i	$0.0908026\pi$
$542$	15.0117	+	4.02237i	0.644807	+	0.172776i
$543$	−8.11248	+	12.6694i	−0.348140	+	0.543698i
$544$	−5.39948	−	3.11739i	−0.231501	−	0.133657i
$545$		0			0
$546$	2.04447	−	1.86475i	0.0874953	−	0.0798040i
$547$	1.38008	−	5.15053i	0.0590080	−	0.220221i	−0.930125	−	0.367242i	$-0.880302\pi$
$547$	1.38008	−	5.15053i	0.0590080	−	0.220221i	0.989133	+	0.147022i	$0.0469687\pi$
$548$	−2.29750	−	2.29750i	−0.0981442	−	0.0981442i
$549$	21.7286	−	30.7289i	0.927355	−	1.31148i
$550$		0			0
$551$	8.27432	−	4.77718i	0.352498	−	0.203515i
$552$	−4.04860	+	2.09571i	−0.172320	+	0.0891994i
$553$	−2.87566	−	10.7321i	−0.122286	−	0.456376i
$554$	−8.65490	+	14.9907i	−0.367712	+	0.636895i
$555$		0			0
$556$	10.9973	+	19.0478i	0.466388	+	0.807807i
$557$	4.10329	−	4.10329i	0.173862	−	0.173862i	−0.614812	−	0.788674i	$-0.710768\pi$
$557$	4.10329	−	4.10329i	0.173862	−	0.173862i	0.788674	+	0.614812i	$0.210768\pi$
$558$	−11.4761	−	4.23703i	−0.485822	−	0.179368i
$559$		−	1.49979i		−	0.0634344i
$560$		0			0
$561$	−34.9158	−	38.2809i	−1.47415	−	1.61622i
$562$	23.3007	−	6.24341i	0.982882	−	0.263362i
$563$	−5.73047	+	1.53547i	−0.241510	+	0.0647125i	−0.377544	−	0.925992i	$-0.623231\pi$
$563$	−5.73047	+	1.53547i	−0.241510	+	0.0647125i	0.136033	+	0.990704i	$0.456565\pi$
$564$	6.70275	−	1.46975i	0.282237	−	0.0618875i
$565$		0			0
$566$		−	16.5516i		−	0.695715i
$567$	−13.5104	−	19.6789i	−0.567383	−	0.826436i
$568$	−7.36824	+	7.36824i	−0.309164	+	0.309164i
$569$	−17.6714	−	30.6077i	−0.740822	−	1.28314i	−0.952122	−	0.305720i	$-0.901103\pi$
$569$	−17.6714	−	30.6077i	−0.740822	−	1.28314i	0.211300	−	0.977421i	$-0.432230\pi$
$570$		0			0
$571$	1.50529	−	2.60725i	0.0629946	−	0.109110i	−0.832808	−	0.553562i	$-0.813268\pi$
$571$	1.50529	−	2.60725i	0.0629946	−	0.109110i	0.895803	+	0.444452i	$0.146602\pi$
$572$	0.748011	+	2.79162i	0.0312759	+	0.116723i
$573$	−0.398435	+	8.66674i	−0.0166448	+	0.362058i
$574$	−14.8142	+	8.55296i	−0.618331	+	0.356993i
$575$		0			0
$576$	2.72474	−	1.25529i	0.113531	−	0.0523040i
$577$	11.5350	+	11.5350i	0.480208	+	0.480208i	0.905198	−	0.424990i	$-0.139722\pi$
$577$	11.5350	+	11.5350i	0.480208	+	0.480208i	−0.424990	+	0.905198i	$0.639722\pi$
$578$	−5.66101	+	21.1272i	−0.235467	+	0.878774i
$579$	−5.56002	−	1.76718i	−0.231066	−	0.0734415i
$580$		0			0
$581$	−26.4185	−	15.2527i	−1.09602	−	0.632789i
$582$	−13.7755	−	26.6122i	−0.571011	−	1.10311i
$583$	−8.59992	−	2.30434i	−0.356172	−	0.0954361i
$584$	4.66721			0.193130
$585$		0			0
$586$	16.1515			0.667214
$587$	11.0157	+	2.95165i	0.454666	+	0.121828i	0.478882	−	0.877879i	$-0.341042\pi$
$587$	11.0157	+	2.95165i	0.454666	+	0.121828i	−0.0242156	+	0.999707i	$0.507709\pi$
$588$	−0.0595851	−	0.00273930i	−0.00245725	−	0.000112967i
$589$	18.3333	+	10.5848i	0.755412	+	0.436137i
$590$		0			0
$591$	8.13346	+	37.0925i	0.334566	+	1.52578i
$592$	0.231349	−	0.863406i	0.00950838	−	0.0354858i
$593$	23.4664	+	23.4664i	0.963651	+	0.963651i	0.999362	−	0.0357109i	$-0.0113696\pi$
$593$	23.4664	+	23.4664i	0.963651	+	0.963651i	−0.0357109	+	0.999362i	$0.511370\pi$
$594$	24.7394	−	3.08295i	1.01507	−	0.126495i
$595$		0			0
$596$	−11.3738	+	6.56668i	−0.465890	+	0.268982i
$597$	−26.9276	−	17.2422i	−1.10207	−	0.705678i
$598$	−0.410346	−	1.53143i	−0.0167803	−	0.0626249i
$599$	17.2683	−	29.9097i	0.705566	−	1.22208i	−0.260922	−	0.965360i	$-0.584026\pi$
$599$	17.2683	−	29.9097i	0.705566	−	1.22208i	0.966487	−	0.256715i	$-0.0826403\pi$
$600$		0			0
$601$	−1.57759	−	2.73247i	−0.0643513	−	0.111460i	0.832055	−	0.554694i	$-0.187164\pi$
$601$	−1.57759	−	2.73247i	−0.0643513	−	0.111460i	−0.896406	+	0.443234i	$0.853831\pi$
$602$	−4.66952	+	4.66952i	−0.190315	+	0.190315i
$603$	−21.1752	−	25.4734i	−0.862320	−	1.03736i
$604$		−	0.335798i		−	0.0136634i
$605$		0			0
$606$	6.27581	−	19.7454i	0.254937	−	0.802100i
$607$	4.92890	−	1.32070i	0.200058	−	0.0536054i	−0.157399	−	0.987535i	$-0.550311\pi$
$607$	4.92890	−	1.32070i	0.200058	−	0.0536054i	0.357456	+	0.933930i	$0.383644\pi$
$608$	−5.01456	+	1.34365i	−0.203367	+	0.0544921i
$609$	−2.56091	+	8.05731i	−0.103773	+	0.326499i
$610$		0			0
$611$			2.38643i			0.0965446i
$612$	−11.9567	−	14.3837i	−0.483320	−	0.581426i
$613$	9.09622	−	9.09622i	0.367393	−	0.367393i	−0.499133	−	0.866525i	$-0.666348\pi$
$613$	9.09622	−	9.09622i	0.367393	−	0.367393i	0.866525	+	0.499133i	$0.166348\pi$
$614$	−1.02984	−	1.78374i	−0.0415611	−	0.0719859i
$615$		0			0
$616$	6.36265	−	11.0204i	0.256358	−	0.444026i
$617$	−6.24315	−	23.2998i	−0.251340	−	0.938013i	−0.970090	−	0.242745i	$-0.921952\pi$
$617$	−6.24315	−	23.2998i	−0.251340	−	0.938013i	0.718751	−	0.695268i	$-0.244714\pi$
$618$	15.7134	+	10.0616i	0.632087	+	0.404737i
$619$	−26.9280	+	15.5469i	−1.08233	+	0.624883i	−0.931524	−	0.363680i	$-0.881520\pi$
$619$	−26.9280	+	15.5469i	−1.08233	+	0.624883i	−0.150806	+	0.988563i	$0.548187\pi$
$620$		0			0
$621$	−13.5716	+	1.69125i	−0.544609	+	0.0678677i
$622$	1.48163	+	1.48163i	0.0594081	+	0.0594081i
$623$	1.40715	−	5.25156i	0.0563764	−	0.210399i
$624$	0.223466	+	1.01911i	0.00894580	+	0.0407971i
$625$		0			0
$626$	17.1057	+	9.87595i	0.683679	+	0.394723i
$627$	−43.0967	−	1.98128i	−1.72112	−	0.0791246i
$628$	−4.40352	−	1.17992i	−0.175719	−	0.0470839i
$629$	−5.57304			−0.222212
$630$		0			0
$631$	46.1604			1.83762			0.918809	−	0.394703i	$-0.129153\pi$
$631$	46.1604			1.83762			0.918809	+	0.394703i	$0.129153\pi$
$632$	4.04642	+	1.08423i	0.160958	+	0.0431285i
$633$	−1.04220	−	2.01338i	−0.0414239	−	0.0800247i
$634$	29.5196	+	17.0431i	1.17237	+	0.676869i
$635$		0			0
$636$	−3.06309	−	0.973565i	−0.121460	−	0.0386044i
$637$	0.00536896	−	0.0200372i	0.000212726	−	0.000793905i
$638$	−6.24383	−	6.24383i	−0.247195	−	0.247195i
$639$	−28.3926	+	13.0805i	−1.12319	+	0.517457i
$640$		0			0
$641$	−3.41084	+	1.96925i	−0.134720	+	0.0777808i	−0.565845	−	0.824511i	$-0.691450\pi$
$641$	−3.41084	+	1.96925i	−0.134720	+	0.0777808i	0.431125	+	0.902292i	$0.358117\pi$
$642$	−0.489749	+	10.6530i	−0.0193288	+	0.420441i
$643$	−8.03625	−	29.9917i	−0.316919	−	1.18276i	−0.922190	−	0.386737i	$-0.873602\pi$
$643$	−8.03625	−	29.9917i	−0.316919	−	1.18276i	0.605271	−	0.796019i	$-0.293065\pi$
$644$	−3.49044	+	6.04562i	−0.137543	+	0.238231i
$645$		0			0
$646$	16.1838	+	28.0311i	0.636742	+	1.10287i
$647$	−18.0986	+	18.0986i	−0.711531	+	0.711531i	−0.966855	−	0.255325i	$-0.917818\pi$
$647$	−18.0986	+	18.0986i	−0.711531	+	0.711531i	0.255325	+	0.966855i	$0.417818\pi$
$648$	8.97261	−	0.701625i	0.352477	−	0.0275624i
$649$		−	0.619386i		−	0.0243130i
$650$		0			0
$651$	−18.2978	+	4.01226i	−0.717149	+	0.157253i
$652$	−12.3147	+	3.29971i	−0.482280	+	0.129226i
$653$	−13.5729	+	3.63685i	−0.531148	+	0.142321i	−0.514419	−	0.857539i	$-0.671992\pi$
$653$	−13.5729	+	3.63685i	−0.531148	+	0.142321i	−0.0167299	+	0.999860i	$0.505326\pi$
$654$	−18.0387	−	19.7772i	−0.705369	−	0.773350i
$655$		0			0
$656$		−	6.44958i		−	0.251814i
$657$	13.1350	+	4.84950i	0.512444	+	0.189197i
$658$	7.43002	−	7.43002i	0.289652	−	0.289652i
$659$	18.2709	+	31.6462i	0.711734	+	1.23276i	0.964206	+	0.265155i	$0.0854233\pi$
$659$	18.2709	+	31.6462i	0.711734	+	1.23276i	−0.252471	+	0.967604i	$0.581243\pi$
$660$		0			0
$661$	−17.9365	+	31.0670i	−0.697650	+	1.20836i	0.271629	+	0.962402i	$0.412438\pi$
$661$	−17.9365	+	31.0670i	−0.697650	+	1.20836i	−0.969279	+	0.245963i	$0.920896\pi$
$662$	6.21890	+	23.2092i	0.241704	+	0.902053i
$663$	5.77683	−	2.99030i	0.224353	−	0.116134i
$664$	9.96076	−	5.75085i	0.386553	−	0.223176i
$665$		0			0
$666$	1.54822	−	2.18951i	0.0599922	−	0.0848418i
$667$	3.42525	+	3.42525i	0.132626	+	0.132626i
$668$	−0.00229992	+	0.00858342i	−8.89866e−5	+	0.000332102i
$669$	26.8432	−	24.4835i	1.03782	−	0.946588i
$670$		0			0
$671$	52.1261	+	30.0950i	2.01231	+	1.16181i
$672$	2.47720	−	3.86870i	0.0955600	−	0.149238i
$673$	−24.2285	−	6.49200i	−0.933939	−	0.250248i	−0.240406	−	0.970673i	$-0.577280\pi$
$673$	−24.2285	−	6.49200i	−0.933939	−	0.250248i	−0.693534	+	0.720424i	$0.743947\pi$
$674$	−12.2514			−0.471907
$675$		0			0
$676$	12.6372			0.486045
$677$	−5.23054	−	1.40152i	−0.201026	−	0.0538647i	0.156901	−	0.987614i	$-0.449850\pi$
$677$	−5.23054	−	1.40152i	−0.201026	−	0.0538647i	−0.357927	+	0.933750i	$0.616516\pi$
$678$	5.54180	−	8.65475i	0.212832	−	0.332384i
$679$	−39.7389	−	22.9433i	−1.52504	−	0.880481i
$680$		0			0
$681$	−7.62057	+	6.95069i	−0.292021	+	0.266351i
$682$	5.06374	−	18.8981i	0.193901	−	0.723647i
$683$	14.3302	+	14.3302i	0.548331	+	0.548331i	0.925958	−	0.377627i	$-0.123260\pi$
$683$	14.3302	+	14.3302i	0.548331	+	0.548331i	−0.377627	+	0.925958i	$0.623260\pi$
$684$	−15.5087	−	1.42897i	−0.592989	−	0.0546382i
$685$		0			0
$686$	15.9993	−	9.23721i	0.610857	−	0.352678i
$687$	−18.0852	+	9.36157i	−0.689992	+	0.357166i
$688$	−0.644420	−	2.40501i	−0.0245683	−	0.0916900i
$689$	0.558889	−	0.968025i	0.0212920	−	0.0368788i
$690$		0			0
$691$	−5.85991	−	10.1497i	−0.222921	−	0.386111i	0.732772	−	0.680474i	$-0.238226\pi$
$691$	−5.85991	−	10.1497i	−0.222921	−	0.386111i	−0.955694	+	0.294363i	$0.904893\pi$
$692$	7.34182	−	7.34182i	0.279094	−	0.279094i
$693$	29.3574	−	24.4038i	1.11519	−	0.927023i
$694$		−	18.5893i		−	0.705641i
$695$		0			0
$696$	−2.14813	−	2.35516i	−0.0814246	−	0.0892720i
$697$	−38.8415	+	10.4076i	−1.47123	+	0.394214i
$698$	30.3716	−	8.13805i	1.14958	−	0.308030i
$699$	32.1385	−	7.04717i	1.21559	−	0.266549i
$700$		0			0
$701$		−	30.7235i		−	1.16041i	−0.814471	−	0.580205i	$-0.802972\pi$
$701$		−	30.7235i		−	1.16041i	0.814471	−	0.580205i	$-0.197028\pi$
$702$	−0.430013	+	3.10029i	−0.0162298	+	0.117013i
$703$	−3.28129	+	3.28129i	−0.123756	+	0.123756i
$704$	2.39896	+	4.15512i	0.0904143	+	0.156602i
$705$		0			0
$706$	6.07917	−	10.5294i	0.228792	−	0.396280i
$707$	−8.21132	−	30.6451i	−0.308818	−	1.15253i
$708$	0.0102686	−	0.223362i	0.000385918	−	0.00839448i
$709$	27.4879	−	15.8701i	1.03233	−	0.596015i	0.114678	−	0.993403i	$-0.463416\pi$
$709$	27.4879	−	15.8701i	1.03233	−	0.596015i	0.917651	+	0.397387i	$0.130083\pi$
$710$		0			0
$711$	10.2613	+	7.25584i	0.384829	+	0.272115i
$712$	1.44949	+	1.44949i	0.0543219	+	0.0543219i
$713$	−2.77788	+	10.3672i	−0.104032	+	0.388254i
$714$	−27.2960	−	8.67568i	−1.02153	−	0.324679i
$715$		0			0
$716$	−1.26692	−	0.731458i	−0.0473471	−	0.0273359i
$717$	−3.62988	−	7.01238i	−0.135560	−	0.261882i
$718$	−4.16899	−	1.11708i	−0.155585	−	0.0416890i
$719$	7.79879			0.290846			0.145423	−	0.989370i	$-0.453546\pi$
$719$	7.79879			0.290846			0.145423	+	0.989370i	$0.453546\pi$
$720$		0			0
$721$	28.5717			1.06407
$722$	7.68026	+	2.05792i	0.285830	+	0.0765878i
$723$	27.7910	+	1.27763i	1.03356	+	0.0475155i
$724$	−7.52209	−	4.34288i	−0.279556	−	0.161402i
$725$		0			0
$726$	4.45923	+	20.3362i	0.165497	+	0.754747i
$727$	−11.4645	+	42.7863i	−0.425196	+	1.58685i	0.338297	+	0.941039i	$0.390149\pi$
$727$	−11.4645	+	42.7863i	−0.425196	+	1.58685i	−0.763494	+	0.645815i	$0.776518\pi$
$728$	1.12969	+	1.12969i	0.0418690	+	0.0418690i
$729$	25.9808	+	7.34847i	0.962250	+	0.272166i
$730$		0			0
$731$	−13.4439	+	7.76182i	−0.497239	+	0.287081i
$732$	18.2987	+	11.7170i	0.676341	+	0.433074i
$733$	7.21598	+	26.9304i	0.266528	+	0.994697i	0.961308	+	0.275475i	$0.0888350\pi$
$733$	7.21598	+	26.9304i	0.266528	+	0.994697i	−0.694780	+	0.719222i	$0.744498\pi$
$734$	9.93909	−	17.2150i	0.366858	−	0.635418i
$735$		0			0
$736$	−1.31603	−	2.27943i	−0.0485095	−	0.0840208i
$737$	37.4607	−	37.4607i	1.37988	−	1.37988i
$738$	6.70149	−	18.1511i	0.246685	−	0.668153i
$739$			10.8068i			0.397536i	0.980047	+	0.198768i	$0.0636941\pi$
$739$			10.8068i			0.397536i	−0.980047	+	0.198768i	$0.936306\pi$
$740$		0			0
$741$	1.64065	−	5.16191i	0.0602707	−	0.189628i
$742$	−4.75396	+	1.27382i	−0.174523	+	0.0467634i
$743$	21.4877	−	5.75762i	0.788309	−	0.211227i	0.157864	−	0.987461i	$-0.449539\pi$
$743$	21.4877	−	5.75762i	0.788309	−	0.211227i	0.630445	+	0.776234i	$0.282873\pi$
$744$	2.13939	−	6.73108i	0.0784338	−	0.246773i
$745$		0			0
$746$		−	2.62754i		−	0.0962009i
$747$	34.0082	−	5.83488i	1.24429	−	0.213487i
$748$	21.1524	−	21.1524i	0.773408	−	0.773408i
$749$	8.16498	+	14.1422i	0.298342	+	0.516743i
$750$		0			0
$751$	−20.6235	+	35.7209i	−0.752561	+	1.30347i	0.194017	+	0.980998i	$0.437848\pi$
$751$	−20.6235	+	35.7209i	−0.752561	+	1.30347i	−0.946578	+	0.322476i	$0.895485\pi$
$752$	1.02538	+	3.82678i	0.0373919	+	0.139548i
$753$	−27.7115	−	17.7442i	−1.00986	−	0.646634i
$754$	0.960067	−	0.554295i	0.0349636	−	0.0201862i
$755$		0			0
$756$	10.9914	−	8.31377i	0.399754	−	0.302369i
$757$	20.5246	+	20.5246i	0.745978	+	0.745978i	0.973721	−	0.227743i	$-0.0731346\pi$
$757$	20.5246	+	20.5246i	0.745978	+	0.745978i	−0.227743	+	0.973721i	$0.573135\pi$
$758$	−0.784544	+	2.92796i	−0.0284959	+	0.106348i
$759$	−4.68491	−	21.3654i	−0.170051	−	0.775516i
$760$		0			0
$761$	39.8188	+	22.9894i	1.44343	+	0.833365i	0.998077	−	0.0619904i	$-0.0197448\pi$
$761$	39.8188	+	22.9894i	1.44343	+	0.833365i	0.445353	+	0.895355i	$0.353078\pi$
$762$	6.16220	+	0.283294i	0.223233	+	0.0102626i
$763$	−39.5928	−	10.6089i	−1.43335	−	0.384066i
$764$	−5.00903			−0.181220
$765$		0			0
$766$	−23.7508			−0.858153
$767$	0.0751122	+	0.0201262i	0.00271214	+	0.000726717i
$768$	0.796225	+	1.53819i	0.0287313	+	0.0555046i
$769$	−26.6702	−	15.3980i	−0.961752	−	0.555268i	−0.0650399	−	0.997883i	$-0.520717\pi$
$769$	−26.6702	−	15.3980i	−0.961752	−	0.555268i	−0.896712	+	0.442615i	$0.854051\pi$
$770$		0			0
$771$	−5.53189	−	1.75824i	−0.199226	−	0.0633215i
$772$	0.871785	−	3.25355i	0.0313762	−	0.117098i
$773$	29.6376	+	29.6376i	1.06599	+	1.06599i	0.997663	+	0.0683287i	$0.0217667\pi$
$773$	29.6376	+	29.6376i	1.06599	+	1.06599i	0.0683287	+	0.997663i	$0.478233\pi$
$774$	0.685343	−	7.43803i	0.0246341	−	0.267354i
$775$		0			0
$776$	14.9831	−	8.65048i	0.537861	−	0.310534i
$777$	0.188577	−	4.10193i	0.00676517	−	0.147156i
$778$	1.72505	+	6.43797i	0.0618460	+	0.230813i
$779$	−16.7414	+	28.9969i	−0.599821	+	1.03892i
$780$		0			0
$781$	−24.9978	−	43.2975i	−0.894492	−	1.54931i
$782$	−11.6038	+	11.6038i	−0.414952	+	0.414952i
$783$	−3.59836	−	8.86018i	−0.128595	−	0.316637i
$784$		−	0.0344378i		−	0.00122992i
$785$		0			0
$786$	−22.0955	+	4.84500i	−0.788122	+	0.172816i
$787$	−26.0615	+	6.98316i	−0.928993	+	0.248923i	−0.691425	−	0.722448i	$-0.743017\pi$
$787$	−26.0615	+	6.98316i	−0.928993	+	0.248923i	−0.237568	+	0.971371i	$0.576350\pi$
$788$	−21.1771	+	5.67439i	−0.754403	+	0.202142i
$789$	−19.5453	−	21.4290i	−0.695831	−	0.762893i
$790$		0			0
$791$		−	15.7369i		−	0.559540i
$792$	2.43401	+	14.1865i	0.0864890	+	0.504095i
$793$	−5.34337	+	5.34337i	−0.189749	+	0.189749i
$794$	−9.35091	−	16.1963i	−0.331852	−	0.574784i
$795$		0			0
$796$	9.23033	−	15.9874i	0.327161	−	0.566659i
$797$	−1.68322	−	6.28188i	−0.0596228	−	0.222515i	0.929686	−	0.368354i	$-0.120079\pi$
$797$	−1.68322	−	6.28188i	−0.0596228	−	0.222515i	−0.989308	+	0.145839i	$0.953412\pi$
$798$	−21.1794	+	10.9633i	−0.749742	+	0.388095i
$799$	21.3915	−	12.3504i	0.756778	−	0.436926i
$800$		0			0
$801$	2.57321	+	5.58542i	0.0909200	+	0.197351i
$802$	−3.81250	−	3.81250i	−0.134624	−	0.134624i
$803$	−5.79571	+	21.6299i	−0.204526	+	0.763302i
$804$	14.1301	−	12.8880i	0.498330	−	0.454525i
$805$		0			0
$806$	2.12721	+	1.22815i	0.0749279	+	0.0432596i
$807$	−0.500381	+	0.781457i	−0.0176143	+	0.0275086i
$808$	11.5544	+	3.09598i	0.406481	+	0.108916i
$809$	5.79431			0.203717			0.101859	−	0.994799i	$-0.467521\pi$
$809$	5.79431			0.203717			0.101859	+	0.994799i	$0.467521\pi$
$810$		0			0
$811$	1.90498			0.0668929			0.0334465	−	0.999441i	$-0.489352\pi$
$811$	1.90498			0.0668929			0.0334465	+	0.999441i	$0.489352\pi$
$812$	−4.71488	−	1.26335i	−0.165460	−	0.0443349i
$813$	−14.5155	+	22.6692i	−0.509080	+	0.795042i
$814$	3.71411	+	2.14434i	0.130180	+	0.0751592i
$815$		0			0
$816$	7.97863	−	7.27728i	0.279308	−	0.254756i
$817$	−3.34547	+	12.4855i	−0.117043	+	0.436812i
$818$	−6.07126	−	6.07126i	−0.212277	−	0.212277i
$819$	2.00548	+	4.35310i	0.0700773	+	0.152110i
$820$		0			0
$821$	−33.4503	+	19.3125i	−1.16742	+	0.674012i	−0.953072	−	0.302745i	$-0.902097\pi$
$821$	−33.4503	+	19.3125i	−1.16742	+	0.674012i	−0.214351	+	0.976757i	$0.568764\pi$
$822$	4.99781	−	2.58706i	0.174319	−	0.0902339i
$823$	5.53879	+	20.6711i	0.193070	+	0.720548i	0.992758	+	0.120132i	$0.0383317\pi$
$823$	5.53879	+	20.6711i	0.193070	+	0.720548i	−0.799688	+	0.600416i	$0.795002\pi$
$824$	−5.38631	+	9.32936i	−0.187641	+	0.325004i
$825$		0			0
$826$	−0.171196	−	0.296520i	−0.00595666	−	0.0103172i
$827$	23.1603	−	23.1603i	0.805364	−	0.805364i	−0.178564	−	0.983928i	$-0.557145\pi$
$827$	23.1603	−	23.1603i	0.805364	−	0.805364i	0.983928	+	0.178564i	$0.0571453\pi$
$828$	−1.33526	−	7.78245i	−0.0464034	−	0.270459i
$829$			34.1116i			1.18475i	0.805664	+	0.592373i	$0.201809\pi$
$829$			34.1116i			1.18475i	−0.805664	+	0.592373i	$0.798191\pi$
$830$		0			0
$831$	−20.2041	−	22.1513i	−0.700873	−	0.768421i
$832$	−0.581838	+	0.155903i	−0.0201716	+	0.00540497i
$833$	−0.207396	+	0.0555716i	−0.00718585	+	0.00192544i
$834$	−37.2115	+	8.15957i	−1.28853	+	0.282543i
$835$		0			0
$836$		−	24.9082i		−	0.861468i
$837$	13.0149	−	16.7204i	0.449860	−	0.577942i
$838$	10.9283	−	10.9283i	0.377512	−	0.377512i
$839$	−18.8058	−	32.5726i	−0.649249	−	1.12453i	−0.983303	−	0.181978i	$-0.941750\pi$
$839$	−18.8058	−	32.5726i	−0.649249	−	1.12453i	0.334054	−	0.942554i	$-0.391583\pi$
$840$		0			0
$841$	12.8065	−	22.1814i	0.441602	−	0.764877i
$842$	−4.89235	−	18.2585i	−0.168602	−	0.629229i
$843$	−1.91880	+	41.7376i	−0.0660868	+	1.43752i
$844$	1.13357	−	0.654465i	0.0390190	−	0.0225276i
$845$		0			0
$846$	−1.09050	+	11.8352i	−0.0374921	+	0.406903i
$847$	22.5427	+	22.5427i	0.774577	+	0.774577i
$848$	0.480279	−	1.79243i	0.0164928	−	0.0615521i
$849$	27.3214	+	8.68375i	0.937667	+	0.298026i
$850$		0			0
$851$	−2.03750	−	1.17635i	−0.0698445	−	0.0403248i
$852$	−8.29688	−	16.0283i	−0.284246	−	0.549122i
$853$	−7.41714	−	1.98742i	−0.253958	−	0.0680478i	0.129594	−	0.991567i	$-0.458633\pi$
$853$	−7.41714	−	1.98742i	−0.253958	−	0.0680478i	−0.383552	+	0.923519i	$0.625299\pi$
$854$	33.2726			1.13856
$855$		0			0
$856$	−6.15702			−0.210442
$857$	−7.00264	−	1.87635i	−0.239206	−	0.0640949i	0.137224	−	0.990540i	$-0.456182\pi$
$857$	−7.00264	−	1.87635i	−0.239206	−	0.0640949i	−0.376430	+	0.926445i	$0.622848\pi$
$858$	−5.00051	−	0.229887i	−0.170714	−	0.00784823i
$859$	1.50446	+	0.868601i	0.0513316	+	0.0296363i	0.525446	−	0.850827i	$-0.323898\pi$
$859$	1.50446	+	0.868601i	0.0513316	+	0.0296363i	−0.474115	+	0.880463i	$0.657232\pi$
$860$		0			0
$861$	−6.34598	−	28.9407i	−0.216271	−	0.986297i
$862$	1.01309	−	3.78090i	0.0345060	−	0.128778i
$863$	−36.4612	−	36.4612i	−1.24115	−	1.24115i	−0.959523	−	0.281630i	$-0.909125\pi$
$863$	−36.4612	−	36.4612i	−1.24115	−	1.24115i	−0.281630	−	0.959523i	$-0.590875\pi$
$864$	0.642559	+	5.15627i	0.0218603	+	0.175420i
$865$		0			0
$866$	−33.3190	+	19.2368i	−1.13223	+	0.653692i
$867$	−31.9042	−	20.4288i	−1.08352	−	0.693799i
$868$	−2.79919	−	10.4467i	−0.0950108	−	0.354585i
$869$	−10.0496	+	17.4065i	−0.340911	+	0.590474i
$870$		0			0
$871$	3.32557	+	5.76006i	0.112683	+	0.195172i
$872$	10.9280	−	10.9280i	0.370070	−	0.370070i
$873$	51.1554	−	8.77688i	1.73135	−	0.297052i
$874$			13.6642i			0.462199i
$875$		0			0
$876$	−2.44864	+	7.70407i	−0.0827318	+	0.260296i
$877$	10.0092	−	2.68194i	0.337985	−	0.0905628i	−0.0858347	−	0.996309i	$-0.527356\pi$
$877$	10.0092	−	2.68194i	0.337985	−	0.0905628i	0.423820	+	0.905747i	$0.360689\pi$
$878$	−14.8035	+	3.96659i	−0.499594	+	0.133866i
$879$	−8.47386	+	26.6610i	−0.285816	+	0.899254i
$880$		0			0
$881$			1.17719i			0.0396604i	0.999803	+	0.0198302i	$0.00631257\pi$
$881$			1.17719i			0.0396604i	−0.999803	+	0.0198302i	$0.993687\pi$
$882$	0.0357829	−	0.0969188i	0.00120487	−	0.00326343i
$883$	22.1929	−	22.1929i	0.746850	−	0.746850i	−0.227036	−	0.973886i	$-0.572903\pi$
$883$	22.1929	−	22.1929i	0.746850	−	0.746850i	0.973886	+	0.227036i	$0.0729035\pi$
$884$	1.87780	+	3.25245i	0.0631573	+	0.109392i
$885$		0			0
$886$	−13.9099	+	24.0927i	−0.467313	+	0.809410i
$887$	−2.35927	−	8.80492i	−0.0792166	−	0.295640i	0.914940	−	0.403590i	$-0.132238\pi$
$887$	−2.35927	−	8.80492i	−0.0792166	−	0.295640i	−0.994156	+	0.107950i	$0.965571\pi$
$888$	1.30383	+	0.834867i	0.0437537	+	0.0280163i
$889$	8.18049	−	4.72301i	0.274365	−	0.158405i
$890$		0			0
$891$	−7.89049	+	42.4543i	−0.264341	+	1.42227i
$892$	14.8324	+	14.8324i	0.496625	+	0.496625i
$893$	5.32323	−	19.8666i	0.178135	−	0.664809i
$894$	−4.87224	−	22.2197i	−0.162952	−	0.743140i
$895$		0			0
$896$	2.29692	+	1.32613i	0.0767346	+	0.0443028i
$897$	2.74319	+	0.126112i	0.0915925	+	0.00421076i
$898$	−23.5326	−	6.30553i	−0.785292	−	0.210418i
$899$	−7.50472			−0.250296
$900$		0			0
$901$	−11.5696			−0.385439
$902$	29.8902	+	8.00905i	0.995234	+	0.266672i
$903$	−5.25803	−	10.1577i	−0.174976	−	0.338028i
$904$	5.13849	+	2.96671i	0.170904	+	0.0986713i
$905$		0			0
$906$	0.554295	+	0.176176i	0.0184152	+	0.00585304i
$907$	1.96997	−	7.35203i	0.0654118	−	0.244120i	−0.925477	−	0.378804i	$-0.876335\pi$
$907$	1.96997	−	7.35203i	0.0654118	−	0.244120i	0.990889	+	0.134684i	$0.0430020\pi$
$908$	−4.21080	−	4.21080i	−0.139740	−	0.139740i
$909$	29.3007	+	20.7187i	0.971842	+	0.687196i
$910$		0			0
$911$	39.2522	−	22.6623i	1.30048	−	0.750835i	0.319997	−	0.947418i	$-0.396318\pi$
$911$	39.2522	−	22.6623i	1.30048	−	0.750835i	0.980487	+	0.196583i	$0.0629846\pi$
$912$	0.412945	−	8.98237i	0.0136740	−	0.297436i
$913$	14.2827	+	53.3039i	0.472690	+	1.76410i
$914$	6.55874	−	11.3601i	0.216944	−	0.375758i
$915$		0			0
$916$	−5.87872	−	10.1822i	−0.194238	−	0.336431i
$917$	−24.4930	+	24.4930i	−0.808829	+	0.808829i
$918$	30.0159	−	12.1903i	0.990672	−	0.402339i
$919$			19.9726i			0.658836i	0.944184	+	0.329418i	$0.106852\pi$
$919$			19.9726i			0.658836i	−0.944184	+	0.329418i	$0.893148\pi$
$920$		0			0
$921$	3.48469	−	0.764106i	0.114824	−	0.0251782i
$922$	−38.7791	+	10.3908i	−1.27712	+	0.342204i
$923$	6.06291	−	1.62455i	0.199563	−	0.0534728i
$924$	14.8531	+	16.2845i	0.488630	+	0.535722i
$925$		0			0
$926$			11.9769i			0.393586i
$927$	−24.8525	+	20.6590i	−0.816263	+	0.678532i
$928$	1.30136	−	1.30136i	0.0427192	−	0.0427192i
$929$	24.8920	+	43.1142i	0.816681	+	1.41453i	0.908115	+	0.418721i	$0.137522\pi$
$929$	24.8920	+	43.1142i	0.816681	+	1.41453i	−0.0914341	+	0.995811i	$0.529145\pi$
$930$		0			0
$931$	−0.0893912	+	0.154830i	−0.00292968	+	0.00507435i
$932$	4.91653	+	18.3487i	0.161046	+	0.601033i
$933$	−3.22304	+	1.66837i	−0.105518	+	0.0546199i
$934$	−10.5711	+	6.10321i	−0.345896	+	0.199703i
$935$		0			0
$936$	−1.79947	−	0.165804i	−0.0588174	−	0.00541946i
$937$	−28.6750	−	28.6750i	−0.936771	−	0.936771i	0.0613453	−	0.998117i	$-0.480461\pi$
$937$	−28.6750	−	28.6750i	−0.936771	−	0.936771i	−0.998117	+	0.0613453i	$0.980461\pi$
$938$	7.57964	−	28.2876i	0.247484	−	0.923623i
$939$	−25.2765	+	23.0546i	−0.824867	+	0.752357i
$940$		0			0
$941$	−42.4585	−	24.5134i	−1.38411	−	0.799115i	−0.391464	−	0.920193i	$-0.628031\pi$
$941$	−42.4585	−	24.5134i	−1.38411	−	0.799115i	−0.992643	+	0.121078i	$0.961365\pi$
$942$	4.25796	−	6.64976i	0.138732	−	0.216661i
$943$	−16.3972	−	4.39363i	−0.533967	−	0.143076i
$944$	0.129095			0.00420167
$945$		0			0
$946$	11.9461			0.388401
$947$	−43.5407	−	11.6667i	−1.41488	−	0.379117i	−0.531217	−	0.847236i	$-0.678265\pi$
$947$	−43.5407	−	11.6667i	−1.41488	−	0.379117i	−0.883665	+	0.468119i	$0.844932\pi$
$948$	−3.91267	+	6.11050i	−0.127078	+	0.198460i
$949$	−2.43470	−	1.40568i	−0.0790339	−	0.0456302i
$950$		0			0
$951$	−43.6201	+	39.7857i	−1.41448	+	1.29014i
$952$	4.27988	−	15.9727i	0.138712	−	0.517679i
$953$	−2.71971	−	2.71971i	−0.0881001	−	0.0881001i	0.661683	−	0.749783i	$-0.269842\pi$
$953$	−2.71971	−	2.71971i	−0.0881001	−	0.0881001i	−0.749783	+	0.661683i	$0.769842\pi$
$954$	3.21409	−	4.54541i	0.104060	−	0.147163i
$955$		0			0
$956$	3.94809	−	2.27943i	0.127690	−	0.0737220i
$957$	13.5824	−	7.03075i	0.439056	−	0.227272i
$958$	2.65801	+	9.91983i	0.0858764	+	0.320495i
$959$	4.30878	−	7.46303i	0.139138	−	0.240994i
$960$		0			0
$961$	7.18593	+	12.4464i	0.231804	+	0.401497i
$962$	−0.380728	+	0.380728i	−0.0122752	+	0.0122752i
$963$	−17.3278	−	6.39750i	−0.558380	−	0.206156i
$964$			16.0621i			0.517325i
$965$		0			0
$966$	−8.14813	−	8.93342i	−0.262162	−	0.287428i
$967$	30.2627	−	8.10886i	0.973182	−	0.260763i	0.263011	−	0.964793i	$-0.415284\pi$
$967$	30.2627	−	8.10886i	0.973182	−	0.260763i	0.710171	+	0.704029i	$0.248618\pi$
$968$	−11.6105	+	3.11102i	−0.373175	+	0.0999920i
$969$	−54.7612	+	12.0078i	−1.75918	+	0.385745i
$970$		0			0
$971$		−	31.9680i		−	1.02590i	−0.858418	−	0.512951i	$-0.828552\pi$
$971$		−	31.9680i		−	1.02590i	0.858418	−	0.512951i	$-0.171448\pi$
$972$	−3.54930	+	15.1790i	−0.113844	+	0.486867i
$973$	−41.2491	+	41.2491i	−1.32238	+	1.32238i
$974$	12.3898	+	21.4597i	0.396993	+	0.687613i
$975$		0			0
$976$	−6.27251	+	10.8643i	−0.200778	+	0.347758i
$977$	2.26667	+	8.45932i	0.0725171	+	0.270638i	0.992659	−	0.120948i	$-0.0385934\pi$
$977$	2.26667	+	8.45932i	0.0725171	+	0.270638i	−0.920142	+	0.391585i	$0.871927\pi$
$978$	1.01410	−	22.0588i	0.0324275	−	0.705361i
$979$	−8.51754	+	4.91760i	−0.272222	+	0.157167i
$980$		0			0
$981$	42.1098	−	19.4001i	1.34446	−	0.619397i
$982$	6.28784	+	6.28784i	0.200653	+	0.200653i
$983$	−10.9162	+	40.7397i	−0.348172	+	1.29940i	0.540691	+	0.841222i	$0.318163\pi$
$983$	−10.9162	+	40.7397i	−0.348172	+	1.29940i	−0.888863	+	0.458174i	$0.848504\pi$
$984$	10.6462	+	3.38376i	0.339388	+	0.107870i
$985$		0			0
$986$	−9.93720	−	5.73725i	−0.316465	−	0.182711i
$987$	8.36644	+	16.1627i	0.266307	+	0.514465i
$988$	3.02059	+	0.809364i	0.0960977	+	0.0257493i
$989$	−6.55342			−0.208387
$990$		0			0
$991$	−13.9120			−0.441929			−0.220964	−	0.975282i	$-0.570920\pi$
$991$	−13.9120			−0.441929			−0.220964	+	0.975282i	$0.570920\pi$
$992$	3.93882	+	1.05540i	0.125058	+	0.0335091i
$993$	−41.5738	−	1.91126i	−1.31930	−	0.0606521i
$994$	−23.9345	−	13.8186i	−0.759156	−	0.438299i
$995$		0			0
$996$	4.26692	+	19.4592i	0.135203	+	0.616589i
$997$	7.83414	−	29.2374i	0.248110	−	0.925958i	−0.723685	−	0.690130i	$-0.757553\pi$
$997$	7.83414	−	29.2374i	0.248110	−	0.925958i	0.971795	−	0.235828i	$-0.0757801\pi$
$998$	20.7542	+	20.7542i	0.656963	+	0.656963i
$999$	2.80191	+	3.70433i	0.0886486	+	0.117200i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	450.2.p.h.257.2		16
3.2	odd	2		1350.2.q.h.557.3		16
5.2	odd	4		90.2.l.b.23.3	✓	16
5.3	odd	4	inner	450.2.p.h.293.2		16
5.4	even	2		90.2.l.b.77.3	yes	16
9.2	odd	6	inner	450.2.p.h.407.2		16
9.7	even	3		1350.2.q.h.1007.4		16
15.2	even	4		270.2.m.b.233.1		16
15.8	even	4		1350.2.q.h.1043.4		16
15.14	odd	2		270.2.m.b.17.1		16
20.7	even	4		720.2.cu.b.113.4		16
20.19	odd	2		720.2.cu.b.257.3		16
45.2	even	12		90.2.l.b.83.3	yes	16
45.4	even	6		810.2.f.c.647.4		16
45.7	odd	12		270.2.m.b.143.1		16
45.14	odd	6		810.2.f.c.647.5		16
45.22	odd	12		810.2.f.c.323.5		16
45.29	odd	6		90.2.l.b.47.3	yes	16
45.32	even	12		810.2.f.c.323.4		16
45.34	even	6		270.2.m.b.197.1		16
45.38	even	12	inner	450.2.p.h.443.2		16
45.43	odd	12		1350.2.q.h.143.3		16
180.47	odd	12		720.2.cu.b.353.3		16
180.119	even	6		720.2.cu.b.497.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
90.2.l.b.23.3	✓	16	5.2	odd	4
90.2.l.b.47.3	yes	16	45.29	odd	6
90.2.l.b.77.3	yes	16	5.4	even	2
90.2.l.b.83.3	yes	16	45.2	even	12
270.2.m.b.17.1		16	15.14	odd	2
270.2.m.b.143.1		16	45.7	odd	12
270.2.m.b.197.1		16	45.34	even	6
270.2.m.b.233.1		16	15.2	even	4
450.2.p.h.257.2		16	1.1	even	1	trivial
450.2.p.h.293.2		16	5.3	odd	4	inner
450.2.p.h.407.2		16	9.2	odd	6	inner
450.2.p.h.443.2		16	45.38	even	12	inner
720.2.cu.b.113.4		16	20.7	even	4
720.2.cu.b.257.3		16	20.19	odd	2
720.2.cu.b.353.3		16	180.47	odd	12
720.2.cu.b.497.4		16	180.119	even	6
810.2.f.c.323.4		16	45.32	even	12
810.2.f.c.323.5		16	45.22	odd	12
810.2.f.c.647.4		16	45.4	even	6
810.2.f.c.647.5		16	45.14	odd	6
1350.2.q.h.143.3		16	45.43	odd	12
1350.2.q.h.557.3		16	3.2	odd	2
1350.2.q.h.1007.4		16	9.7	even	3
1350.2.q.h.1043.4		16	15.8	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 450 = 2 \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	450.p (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.965926 - 0.258819i) q^{2} +(0.933998 - 1.45865i) q^{3} +(0.866025 + 0.500000i) q^{4} +(-1.27970 + 1.16721i) q^{6} +(-0.686453 + 2.56188i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-1.25529 - 2.72474i) q^{9} +O(q^{10})\)	\(q+(-0.965926 - 0.258819i) q^{2} +(0.933998 - 1.45865i) q^{3} +(0.866025 + 0.500000i) q^{4} +(-1.27970 + 1.16721i) q^{6} +(-0.686453 + 2.56188i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-1.25529 - 2.72474i) q^{9} +(4.15512 - 2.39896i) q^{11} +(1.53819 - 0.796225i) q^{12} +(0.155903 + 0.581838i) q^{13} +(1.32613 - 2.29692i) q^{14} +(0.500000 + 0.866025i) q^{16} +(4.40865 - 4.40865i) q^{17} +(0.507306 + 2.95680i) q^{18} -5.19145i q^{19} +(3.09573 + 3.39408i) q^{21} +(-4.63444 + 1.24179i) q^{22} +(2.54237 - 0.681226i) q^{23} +(-1.69185 + 0.370982i) q^{24} -0.602363i q^{26} +(-5.14688 - 0.713876i) q^{27} +(-1.87542 + 1.87542i) q^{28} +(0.920201 + 1.59383i) q^{29} +(-2.03888 + 3.53145i) q^{31} +(-0.258819 - 0.965926i) q^{32} +(0.381642 - 8.30148i) q^{33} +(-5.39948 + 3.11739i) q^{34} +(0.275255 - 2.98735i) q^{36} +(-0.632057 - 0.632057i) q^{37} +(-1.34365 + 5.01456i) q^{38} +(0.994309 + 0.316029i) q^{39} +(-5.58550 - 3.22479i) q^{41} +(-2.11179 - 4.07966i) q^{42} +(-2.40501 - 0.644420i) q^{43} +4.79792 q^{44} -2.63206 q^{46} +(3.82678 + 1.02538i) q^{47} +(1.73022 + 0.0795432i) q^{48} +(-0.0298240 - 0.0172189i) q^{49} +(-2.31299 - 10.5483i) q^{51} +(-0.155903 + 0.581838i) q^{52} +(-1.31215 - 1.31215i) q^{53} +(4.78674 + 2.02166i) q^{54} +(2.29692 - 1.32613i) q^{56} +(-7.57249 - 4.84881i) q^{57} +(-0.476331 - 1.77769i) q^{58} +(0.0645473 - 0.111799i) q^{59} +(6.27251 + 10.8643i) q^{61} +(2.88341 - 2.88341i) q^{62} +(7.84217 - 1.34550i) q^{63} +1.00000i q^{64} +(-2.51722 + 7.91984i) q^{66} +(10.6655 - 2.85782i) q^{67} +(6.02233 - 1.61368i) q^{68} +(1.38090 - 4.34468i) q^{69} -10.4203i q^{71} +(-1.03906 + 2.81431i) q^{72} +(-3.30021 + 3.30021i) q^{73} +(0.446932 + 0.774109i) q^{74} +(2.59573 - 4.49593i) q^{76} +(3.29355 + 12.2917i) q^{77} +(-0.878635 - 0.562606i) q^{78} +(-3.62792 + 2.09458i) q^{79} +(-5.84847 + 6.84072i) q^{81} +(4.56054 + 4.56054i) q^{82} +(-2.97686 + 11.1098i) q^{83} +(0.983937 + 4.48722i) q^{84} +(2.15627 + 1.24492i) q^{86} +(3.18431 + 0.146391i) q^{87} +(-4.63444 - 1.24179i) q^{88} -2.04989 q^{89} -1.59762 q^{91} +(2.54237 + 0.681226i) q^{92} +(3.24682 + 6.27237i) q^{93} +(-3.43100 - 1.98089i) q^{94} +(-1.65068 - 0.524648i) q^{96} +(-4.47782 + 16.7115i) q^{97} +(0.0243512 + 0.0243512i) q^{98} +(-11.7525 - 8.31025i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{7}+O(q^{10}) \) 16 * q - 8 * q^7	\( 16 q - 8 q^{7} + 8 q^{16} + 24 q^{21} - 8 q^{22} + 24 q^{23} + 16 q^{28} - 8 q^{31} + 24 q^{36} - 24 q^{38} + 24 q^{41} - 24 q^{42} - 32 q^{46} - 48 q^{47} - 48 q^{51} + 24 q^{56} - 24 q^{57} - 16 q^{58} - 24 q^{61} + 48 q^{63} - 48 q^{66} + 16 q^{67} + 24 q^{68} + 24 q^{72} - 16 q^{73} + 16 q^{76} + 72 q^{77} + 24 q^{81} + 16 q^{82} - 48 q^{83} - 48 q^{86} + 48 q^{87} - 8 q^{88} + 24 q^{92} - 72 q^{93} + 48 q^{97}+O(q^{100}) \) 16 * q - 8 * q^7 + 8 * q^16 + 24 * q^21 - 8 * q^22 + 24 * q^23 + 16 * q^28 - 8 * q^31 + 24 * q^36 - 24 * q^38 + 24 * q^41 - 24 * q^42 - 32 * q^46 - 48 * q^47 - 48 * q^51 + 24 * q^56 - 24 * q^57 - 16 * q^58 - 24 * q^61 + 48 * q^63 - 48 * q^66 + 16 * q^67 + 24 * q^68 + 24 * q^72 - 16 * q^73 + 16 * q^76 + 72 * q^77 + 24 * q^81 + 16 * q^82 - 48 * q^83 - 48 * q^86 + 48 * q^87 - 8 * q^88 + 24 * q^92 - 72 * q^93 + 48 * q^97

Introduction

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