LMFDB - Embedded newform 450.2.p.h.293.2

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			293.2
Root			$0.500000 - 0.589118i$ of defining polynomial
Character	$\chi$	$=$	450.293
Dual form			450.2.p.h.407.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.258819 + 0.965926i) q^{2} +(1.45865 + 0.933998i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(-1.27970 + 1.16721i) q^{6} +(2.56188 + 0.686453i) q^{7} +(0.707107 - 0.707107i) q^{8} +(1.25529 + 2.72474i) q^{9} +O(q^{10})$	\(q+(-0.258819 + 0.965926i) q^{2} +(1.45865 + 0.933998i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(-1.27970 + 1.16721i) q^{6} +(2.56188 + 0.686453i) q^{7} +(0.707107 - 0.707107i) q^{8} +(1.25529 + 2.72474i) q^{9} +(4.15512 - 2.39896i) q^{11} +(-0.796225 - 1.53819i) q^{12} +(-0.581838 + 0.155903i) q^{13} +(-1.32613 + 2.29692i) q^{14} +(0.500000 + 0.866025i) q^{16} +(-4.40865 - 4.40865i) q^{17} +(-2.95680 + 0.507306i) q^{18} +5.19145i q^{19} +(3.09573 + 3.39408i) q^{21} +(1.24179 + 4.63444i) q^{22} +(0.681226 + 2.54237i) q^{23} +(1.69185 - 0.370982i) q^{24} -0.602363i q^{26} +(-0.713876 + 5.14688i) q^{27} +(-1.87542 - 1.87542i) q^{28} +(-0.920201 - 1.59383i) q^{29} +(-2.03888 + 3.53145i) q^{31} +(-0.965926 + 0.258819i) q^{32} +(8.30148 + 0.381642i) q^{33} +(5.39948 - 3.11739i) q^{34} +(0.275255 - 2.98735i) q^{36} +(-0.632057 + 0.632057i) q^{37} +(-5.01456 - 1.34365i) q^{38} +(-0.994309 - 0.316029i) q^{39} +(-5.58550 - 3.22479i) q^{41} +(-4.07966 + 2.11179i) q^{42} +(0.644420 - 2.40501i) q^{43} -4.79792 q^{44} -2.63206 q^{46} +(1.02538 - 3.82678i) q^{47} +(-0.0795432 + 1.73022i) q^{48} +(0.0298240 + 0.0172189i) q^{49} +(-2.31299 - 10.5483i) q^{51} +(0.581838 + 0.155903i) q^{52} +(1.31215 - 1.31215i) q^{53} +(-4.78674 - 2.02166i) q^{54} +(2.29692 - 1.32613i) q^{56} +(-4.84881 + 7.57249i) q^{57} +(1.77769 - 0.476331i) q^{58} +(-0.0645473 + 0.111799i) q^{59} +(6.27251 + 10.8643i) q^{61} +(-2.88341 - 2.88341i) q^{62} +(1.34550 + 7.84217i) q^{63} -1.00000i q^{64} +(-2.51722 + 7.91984i) q^{66} +(-2.85782 - 10.6655i) q^{67} +(1.61368 + 6.02233i) q^{68} +(-1.38090 + 4.34468i) q^{69} -10.4203i q^{71} +(2.81431 + 1.03906i) q^{72} +(-3.30021 - 3.30021i) q^{73} +(-0.446932 - 0.774109i) q^{74} +(2.59573 - 4.49593i) q^{76} +(12.2917 - 3.29355i) q^{77} +(0.562606 - 0.878635i) q^{78} +(3.62792 - 2.09458i) q^{79} +(-5.84847 + 6.84072i) q^{81} +(4.56054 - 4.56054i) q^{82} +(-11.1098 - 2.97686i) q^{83} +(-0.983937 - 4.48722i) q^{84} +(2.15627 + 1.24492i) q^{86} +(0.146391 - 3.18431i) q^{87} +(1.24179 - 4.63444i) q^{88} +2.04989 q^{89} -1.59762 q^{91} +(0.681226 - 2.54237i) q^{92} +(-6.27237 + 3.24682i) q^{93} +(3.43100 + 1.98089i) q^{94} +(-1.65068 - 0.524648i) q^{96} +(16.7115 + 4.47782i) 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 $\left(\mathbb{Z}/450\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−0.258819	+	0.965926i	−0.183013	+	0.683013i
$2$	−0.258819	+	0.965926i	−0.183013	+	0.683013i
$3$	1.45865	+	0.933998i	0.842150	+	0.539244i
$3$	1.45865	+	0.933998i	0.842150	+	0.539244i
$4$	−0.866025	−	0.500000i	−0.433013	−	0.250000i
$5$		0			0
$5$		0			0
$6$	−1.27970	+	1.16721i	−0.522435	+	0.476510i
$7$	2.56188	+	0.686453i	0.968299	+	0.259455i	0.708109	−	0.706103i	$-0.249548\pi$
$7$	2.56188	+	0.686453i	0.968299	+	0.259455i	0.260189	+	0.965558i	$0.416215\pi$
$8$	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	$0.0759512\pi$
$12$	−0.796225	−	1.53819i	−0.229850	−	0.444037i
$13$	−0.581838	+	0.155903i	−0.161373	+	0.0432397i	−0.338601	−	0.940930i	$-0.609954\pi$
$13$	−0.581838	+	0.155903i	−0.161373	+	0.0432397i	0.177228	+	0.984170i	$0.443287\pi$
$14$	−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	−0.997416	−	0.0718393i	$-0.977113\pi$
$17$	−4.40865	−	4.40865i	−1.06926	−	1.06926i	−0.0718393	−	0.997416i	$-0.522887\pi$
$18$	−2.95680	+	0.507306i	−0.696923	+	0.119573i
$19$			5.19145i			1.19100i	0.803355	+	0.595501i	$0.203046\pi$
$19$			5.19145i			1.19100i	−0.803355	+	0.595501i	$0.796954\pi$
$20$		0			0
$21$	3.09573	+	3.39408i	0.675543	+	0.740649i
$22$	1.24179	+	4.63444i	0.264751	+	0.988065i
$23$	0.681226	+	2.54237i	0.142046	+	0.530121i	0.999869	+	0.0161770i	$0.00514951\pi$
$23$	0.681226	+	2.54237i	0.142046	+	0.530121i	−0.857824	+	0.513944i	$0.828184\pi$
$24$	1.69185	−	0.370982i	0.345348	−	0.0757264i
$25$		0			0
$26$		−	0.602363i		−	0.118133i
$27$	−0.713876	+	5.14688i	−0.137386	+	0.990518i
$28$	−1.87542	−	1.87542i	−0.354422	−	0.354422i
$29$	−0.920201	−	1.59383i	−0.170877	−	0.295968i	0.767850	−	0.640630i	$-0.221327\pi$
$29$	−0.920201	−	1.59383i	−0.170877	−	0.295968i	−0.938727	+	0.344662i	$0.887993\pi$
$30$		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	$0.286006\pi$
$32$	−0.965926	+	0.258819i	−0.170753	+	0.0457532i
$33$	8.30148	+	0.381642i	1.44510	+	0.0664354i
$34$	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	−0.757150	−	0.653241i	$-0.773409\pi$
$37$	−0.632057	+	0.632057i	−0.103910	+	0.103910i	0.653241	+	0.757150i	$0.273409\pi$
$38$	−5.01456	−	1.34365i	−0.813469	−	0.217968i
$39$	−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	$0.834668\pi$
$42$	−4.07966	+	2.11179i	−0.629506	+	0.325856i
$43$	0.644420	−	2.40501i	0.0982731	−	0.366760i	−0.899222	−	0.437492i	$-0.855867\pi$
$43$	0.644420	−	2.40501i	0.0982731	−	0.366760i	0.997495	+	0.0707320i	$0.0225335\pi$
$44$	−4.79792			−0.723314
$45$		0			0
$46$	−2.63206			−0.388076
$47$	1.02538	−	3.82678i	0.149568	−	0.558194i	−0.849942	−	0.526876i	$-0.823363\pi$
$47$	1.02538	−	3.82678i	0.149568	−	0.558194i	0.999509	−	0.0313173i	$-0.00997024\pi$
$48$	−0.0795432	+	1.73022i	−0.0114811	+	0.249736i
$49$	0.0298240	+	0.0172189i	0.00426058	+	0.00245984i
$50$		0			0
$51$	−2.31299	−	10.5483i	−0.323883	−	1.47706i
$52$	0.581838	+	0.155903i	0.0806865	+	0.0216199i
$53$	1.31215	−	1.31215i	0.180237	−	0.180237i	−0.611222	−	0.791459i	$-0.709322\pi$
$53$	1.31215	−	1.31215i	0.180237	−	0.180237i	0.791459	+	0.611222i	$0.209322\pi$
$54$	−4.78674	−	2.02166i	−0.651393	−	0.275113i
$55$		0			0
$56$	2.29692	−	1.32613i	0.306938	−	0.177211i
$57$	−4.84881	+	7.57249i	−0.642240	+	1.00300i
$58$	1.77769	−	0.476331i	0.233422	−	0.0625453i
$59$	−0.0645473	+	0.111799i	−0.00840334	+	0.0145550i	−0.870196	−	0.492705i	$-0.836008\pi$
$59$	−0.0645473	+	0.111799i	−0.00840334	+	0.0145550i	0.861793	+	0.507260i	$0.169342\pi$
$60$		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
$63$	1.34550	+	7.84217i	0.169517	+	0.988020i
$64$		−	1.00000i		−	0.125000i
$65$		0			0
$66$	−2.51722	+	7.91984i	−0.309848	+	0.974864i
$67$	−2.85782	−	10.6655i	−0.349138	−	1.30300i	−0.887703	−	0.460416i	$-0.847700\pi$
$67$	−2.85782	−	10.6655i	−0.349138	−	1.30300i	0.538566	−	0.842584i	$-0.318966\pi$
$68$	1.61368	+	6.02233i	0.195687	+	0.730315i
$69$	−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	$-0.212190\pi$
$72$	2.81431	+	1.03906i	0.331670	+	0.122454i
$73$	−3.30021	−	3.30021i	−0.386261	−	0.386261i	0.487091	−	0.873351i	$-0.338058\pi$
$73$	−3.30021	−	3.30021i	−0.386261	−	0.386261i	−0.873351	+	0.487091i	$0.838058\pi$
$74$	−0.446932	−	0.774109i	−0.0519548	−	0.0899883i
$75$		0			0
$76$	2.59573	−	4.49593i	0.297750	−	0.515719i
$77$	12.2917	−	3.29355i	1.40077	−	0.375335i
$78$	0.562606	−	0.878635i	0.0637026	−	0.0994858i
$79$	3.62792	−	2.09458i	0.408173	−	0.235659i	−0.281832	−	0.959464i	$-0.590942\pi$
$79$	3.62792	−	2.09458i	0.408173	−	0.235659i	0.690004	+	0.723805i	$0.257609\pi$
$80$		0			0
$81$	−5.84847	+	6.84072i	−0.649830	+	0.760080i
$82$	4.56054	−	4.56054i	0.503628	−	0.503628i
$83$	−11.1098	−	2.97686i	−1.21946	−	0.326753i	−0.408992	−	0.912538i	$-0.634119\pi$
$83$	−11.1098	−	2.97686i	−1.21946	−	0.326753i	−0.810466	+	0.585785i	$0.800786\pi$
$84$	−0.983937	−	4.48722i	−0.107356	−	0.489596i
$85$		0			0
$86$	2.15627	+	1.24492i	0.232517	+	0.134243i
$87$	0.146391	−	3.18431i	0.0156948	−	0.341393i
$88$	1.24179	−	4.63444i	0.132376	−	0.494033i
$89$	2.04989			0.217288			0.108644	−	0.994081i	$-0.465349\pi$
$89$	2.04989			0.217288			0.108644	+	0.994081i	$0.465349\pi$
$90$		0			0
$91$	−1.59762			−0.167476
$92$	0.681226	−	2.54237i	0.0710228	−	0.265061i
$93$	−6.27237	+	3.24682i	−0.650414	+	0.336679i
$94$	3.43100	+	1.98089i	0.353881	+	0.204313i
$95$		0			0
$96$	−1.65068	−	0.524648i	−0.168472	−	0.0535466i
$97$	16.7115	+	4.47782i	1.69679	+	0.454654i	0.972128	−	0.234450i	$-0.0753290\pi$
$97$	16.7115	+	4.47782i	1.69679	+	0.454654i	0.724663	+	0.689104i	$0.241996\pi$
$98$	−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	$0.536232\pi$
$102$	10.7876	+	0.495934i	1.06813	+	0.0491048i
$103$	10.4055	−	2.78816i	1.02529	−	0.274725i	0.293285	−	0.956025i	$-0.405252\pi$
$103$	10.4055	−	2.78816i	1.02529	−	0.274725i	0.732004	+	0.681300i	$0.238585\pi$
$104$	−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	$-0.346190\pi$
$107$	−4.35367	−	4.35367i	−0.420885	−	0.420885i	−0.885508	+	0.464623i	$0.846190\pi$
$108$	3.19168	−	4.10039i	0.307119	−	0.394560i
$109$		−	15.4546i		−	1.48028i	−0.672452	−	0.740141i	$-0.734759\pi$
$109$		−	15.4546i		−	1.48028i	0.672452	−	0.740141i	$-0.265241\pi$
$110$		0			0
$111$	−1.51229	+	0.331607i	−0.143540	+	0.0314748i
$112$	0.686453	+	2.56188i	0.0648637	+	0.242075i
$113$	−1.53568	−	5.73124i	−0.144465	−	0.539150i	−0.999779	−	0.0210396i	$-0.993302\pi$
$113$	−1.53568	−	5.73124i	−0.144465	−	0.539150i	0.855314	−	0.518110i	$-0.173364\pi$
$114$	−6.05950	−	6.64349i	−0.567524	−	0.622220i
$115$		0			0
$116$			1.84040i			0.170877i
$117$	−1.15518	−	1.38966i	−0.106796	−	0.128474i
$118$	−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
$122$	−12.1176	+	3.24689i	−1.09707	+	0.293960i
$123$	−5.13532	−	9.92068i	−0.463036	−	0.894517i
$124$	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	−0.809957	−	0.586489i	$-0.800510\pi$
$127$	−2.51837	+	2.51837i	−0.223469	+	0.223469i	0.586489	+	0.809957i	$0.300510\pi$
$128$	0.965926	+	0.258819i	0.0853766	+	0.0228766i
$129$	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	$0.473406\pi$
$132$	−6.99847	−	4.48125i	−0.609139	−	0.390043i
$133$	−3.56369	+	13.2999i	−0.309011	+	1.15325i
$134$	11.0417			0.953862
$135$		0			0
$136$	−6.23478			−0.534628
$137$	−0.840942	+	3.13844i	−0.0718465	+	0.268135i	−0.992500	−	0.122246i	$-0.960990\pi$
$137$	−0.840942	+	3.13844i	−0.0718465	+	0.268135i	0.920653	+	0.390381i	$0.127657\pi$
$138$	−3.83924	−	2.45834i	−0.326818	−	0.209267i
$139$	−19.0478	−	10.9973i	−1.61561	−	0.932775i	−0.988036	−	0.154221i	$-0.950713\pi$
$139$	−19.0478	−	10.9973i	−1.61561	−	0.932775i	−0.627578	−	0.778554i	$-0.715953\pi$
$140$		0			0
$141$	5.06988	−	4.62421i	0.426961	−	0.389429i
$142$	10.0652	+	2.69696i	0.844653	+	0.226324i
$143$	−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
$147$	0.0274203	+	0.0529719i	0.00226159	+	0.00436905i
$148$	0.863406	−	0.231349i	0.0709715	−	0.0190168i
$149$	6.56668	−	11.3738i	0.537964	−	0.931780i	−0.461050	−	0.887374i	$-0.652527\pi$
$149$	6.56668	−	11.3738i	0.537964	−	0.931780i	0.999014	−	0.0444061i	$-0.0141396\pi$
$150$		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
$153$	6.47830	−	17.5466i	0.523739	−	1.41856i
$154$			12.7253i			1.02543i
$155$		0			0
$156$	0.703083	+	0.770843i	0.0562917	+	0.0617169i
$157$	1.17992	+	4.40352i	0.0941678	+	0.351439i	0.996892	−	0.0787808i	$-0.0251027\pi$
$157$	1.17992	+	4.40352i	0.0941678	+	0.351439i	−0.902724	+	0.430220i	$0.858436\pi$
$158$	1.08423	+	4.04642i	0.0862571	+	0.321916i
$159$	3.13950	−	0.688415i	0.248979	−	0.0545948i
$160$		0			0
$161$			6.98088i			0.550170i
$162$	−5.09393	−	7.41970i	−0.400217	−	0.582946i
$163$	−9.01496	−	9.01496i	−0.706106	−	0.706106i	0.259608	−	0.965714i	$-0.416407\pi$
$163$	−9.01496	−	9.01496i	−0.706106	−	0.706106i	−0.965714	+	0.259608i	$0.916407\pi$
$164$	3.22479	+	5.58550i	0.251814	+	0.436154i
$165$		0			0
$166$	5.75085	−	9.96076i	0.446353	−	0.773105i
$167$	0.00858342	−	0.00229992i	0.000664205	−	0.000177973i	−0.258487	−	0.966015i	$-0.583224\pi$
$167$	0.00858342	−	0.00229992i	0.000664205	−	0.000177973i	0.259151	+	0.965837i	$0.416557\pi$
$168$	4.58899	+	0.210969i	0.354048	+	0.0162766i
$169$	−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
$173$	10.0291	+	2.68729i	0.762500	+	0.204311i	0.619056	−	0.785347i	$-0.287516\pi$
$173$	10.0291	+	2.68729i	0.762500	+	0.204311i	0.143444	+	0.989658i	$0.454182\pi$
$174$	3.03791	+	0.965562i	0.230304	+	0.0731991i
$175$		0			0
$176$	4.15512	+	2.39896i	0.313204	+	0.180829i
$177$	−0.198572	+	0.102788i	−0.0149256	+	0.00772605i
$178$	−0.530550	+	1.98004i	−0.0397664	+	0.148410i
$179$	1.46292			0.109343			0.0546717	−	0.998504i	$-0.482589\pi$
$179$	1.46292			0.109343			0.0546717	+	0.998504i	$0.482589\pi$
$180$		0			0
$181$	−8.68576			−0.645607			−0.322804	−	0.946466i	$-0.604625\pi$
$181$	−8.68576			−0.645607			−0.322804	+	0.946466i	$0.604625\pi$
$182$	0.413494	−	1.54318i	0.0306502	−	0.114388i
$183$	−0.997872	+	21.7057i	−0.0737648	+	1.60453i
$184$	2.27943	+	1.31603i	0.168042	+	0.0970189i
$185$		0			0
$186$	−1.51278	−	6.89898i	−0.110922	−	0.505858i
$187$	−28.8947	−	7.74231i	−2.11299	−	0.566174i
$188$	−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	$0.391338\pi$
$192$	0.933998	−	1.45865i	0.0674055	−	0.105269i
$193$	3.25355	−	0.871785i	0.234195	−	0.0627524i	−0.139812	−	0.990178i	$-0.544650\pi$
$193$	3.25355	−	0.871785i	0.234195	−	0.0627524i	0.374008	+	0.927426i	$0.377983\pi$
$194$	−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	0.993858	+	0.110665i	$0.0352980\pi$
$197$	15.5027	+	15.5027i	1.10452	+	1.10452i	0.110665	+	0.993858i	$0.464702\pi$
$198$	−11.0688	+	9.20116i	−0.786628	+	0.653898i
$199$			18.4607i			1.30864i	0.756217	+	0.654321i	$0.227045\pi$
$199$			18.4607i			1.30864i	−0.756217	+	0.654321i	$0.772955\pi$
$200$		0			0
$201$	5.79303	−	18.2264i	0.408609	−	1.28559i
$202$	−3.09598	−	11.5544i	−0.217832	−	0.812962i
$203$	−1.26335	−	4.71488i	−0.0886697	−	0.330920i
$204$	−3.27106	+	10.2916i	−0.229020	+	0.720558i
$205$		0			0
$206$			10.7726i			0.750564i
$207$	−6.07217	+	5.04759i	−0.422045	+	0.350832i
$208$	−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	$0.152320\pi$
$212$	−1.79243	+	0.480279i	−0.123104	+	0.0329857i
$213$	9.73251	−	15.1995i	0.666860	−	1.04145i
$214$	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
$218$	14.9280	+	3.99994i	1.01105	+	0.270910i
$219$	−1.73145	−	7.89624i	−0.117001	−	0.533578i
$220$		0			0
$221$	3.25245	+	1.87780i	0.218783	+	0.126315i
$222$	0.0711008	−	1.54658i	0.00477197	−	0.103800i
$223$	−5.42903	+	20.2614i	−0.363555	+	1.35681i	0.505814	+	0.862643i	$0.331192\pi$
$223$	−5.42903	+	20.2614i	−0.363555	+	1.35681i	−0.869369	+	0.494163i	$0.835474\pi$
$224$	−2.65225			−0.177211
$225$		0			0
$226$	5.93342			0.394685
$227$	−1.54126	+	5.75206i	−0.102297	+	0.381778i	−0.998025	−	0.0628257i	$-0.979989\pi$
$227$	−1.54126	+	5.75206i	−0.102297	+	0.381778i	0.895727	+	0.444604i	$0.146655\pi$
$228$	7.98544	−	4.13357i	0.528848	−	0.273752i
$229$	10.1822	+	5.87872i	0.672862	+	0.388477i	0.797160	−	0.603768i	$-0.206335\pi$
$229$	10.1822	+	5.87872i	0.672862	+	0.388477i	−0.124298	+	0.992245i	$0.539668\pi$
$230$		0			0
$231$	21.0054	+	6.67630i	1.38205	+	0.439268i
$232$	−1.77769	−	0.476331i	−0.116711	−	0.0312727i
$233$	−13.4322	+	13.4322i	−0.879973	+	0.879973i	−0.993531	−	0.113558i	$-0.963775\pi$
$233$	−13.4322	+	13.4322i	−0.879973	+	0.879973i	0.113558	+	0.993531i	$0.463775\pi$
$234$	1.64129	−	0.756144i	0.107294	−	0.0494307i
$235$		0			0
$236$	0.111799	−	0.0645473i	0.00727751	−	0.00420167i
$237$	7.24818	+	0.333219i	0.470820	+	0.0216449i
$238$	15.9727	−	4.27988i	1.03536	−	0.277424i
$239$	−2.27943	+	3.94809i	−0.147444	+	0.255380i	−0.930282	−	0.366845i	$-0.880438\pi$
$239$	−2.27943	+	3.94809i	−0.147444	+	0.255380i	0.782838	+	0.622225i	$0.213771\pi$
$240$		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
$243$	−14.9201	+	4.51572i	−0.957122	+	0.289684i
$244$		−	12.5450i		−	0.803113i
$245$		0			0
$246$	10.9118	−	2.39268i	0.695708	−	0.152552i
$247$	−0.809364	−	3.02059i	−0.0514986	−	0.192195i
$248$	1.05540	+	3.93882i	0.0670181	+	0.250115i
$249$	−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	$-0.204663\pi$
$252$	2.75584	−	7.46427i	0.173602	−	0.470205i
$253$	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
$257$	−3.23709	+	0.867374i	−0.201924	+	0.0541053i	−0.358363	−	0.933582i	$-0.616665\pi$
$257$	−3.23709	+	0.867374i	−0.201924	+	0.0541053i	0.156439	+	0.987688i	$0.449998\pi$
$258$	1.98248	+	3.82985i	0.123424	+	0.238436i
$259$	−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
$263$	16.1748	+	4.33402i	0.997380	+	0.267247i	0.720347	−	0.693614i	$-0.243982\pi$
$263$	16.1748	+	4.33402i	0.997380	+	0.267247i	0.277032	+	0.960861i	$0.410649\pi$
$264$	6.13989	−	5.60017i	0.377884	−	0.344667i
$265$		0			0
$266$	−11.9243	−	6.88452i	−0.731128	−	0.422117i
$267$	2.99006	+	1.91459i	0.182989	+	0.117171i
$268$	−2.85782	+	10.6655i	−0.174569	+	0.651500i
$269$	0.535741			0.0326647			0.0163324	−	0.999867i	$-0.494801\pi$
$269$	0.535741			0.0326647			0.0163324	+	0.999867i	$0.494801\pi$
$270$		0			0
$271$	−15.5412			−0.944063			−0.472032	−	0.881582i	$-0.656479\pi$
$271$	−15.5412			−0.944063			−0.472032	+	0.881582i	$0.656479\pi$
$272$	1.61368	−	6.02233i	0.0978437	−	0.365158i
$273$	−2.33036	−	1.49217i	−0.141040	−	0.0903104i
$274$	−2.81385	−	1.62458i	−0.169991	−	0.0981442i
$275$		0			0
$276$	3.36824	−	3.07216i	0.202744	−	0.184922i
$277$	−16.7200	−	4.48011i	−1.00461	−	0.269184i	−0.281232	−	0.959640i	$-0.590743\pi$
$277$	−16.7200	−	4.48011i	−1.00461	−	0.269184i	−0.723374	+	0.690456i	$0.757410\pi$
$278$	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	$0.588971\pi$
$282$	3.15447	+	6.09396i	0.187846	+	0.362890i
$283$	−15.9876	+	4.28387i	−0.950365	+	0.254649i	−0.700517	−	0.713636i	$-0.747047\pi$
$283$	−15.9876	+	4.28387i	−0.950365	+	0.254649i	−0.249848	+	0.968285i	$0.580381\pi$
$284$	−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
$288$	−1.91774	−	2.30701i	−0.113004	−	0.135942i
$289$			21.8725i			1.28661i
$290$		0			0
$291$	20.1938	+	22.1400i	1.18378	+	1.29787i
$292$	1.20796	+	4.50818i	0.0706906	+	0.263821i
$293$	−4.18032	−	15.6012i	−0.244217	−	0.911431i	−0.973775	−	0.227512i	$-0.926941\pi$
$293$	−4.18032	−	15.6012i	−0.244217	−	0.911431i	0.729558	−	0.683919i	$-0.239726\pi$
$294$	−0.0582638	+	0.0127758i	−0.00339801	+	0.000745100i
$295$		0			0
$296$			0.893864i			0.0519548i
$297$	9.38093	+	23.0985i	0.544337	+	1.34031i
$298$	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
$302$	0.324356	−	0.0869109i	0.0186646	−	0.00500116i
$303$	−20.6968	−	0.951492i	−1.18900	−	0.0546618i
$304$	−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	−0.664323	−	0.747445i	$-0.731280\pi$
$307$	1.45642	−	1.45642i	0.0831222	−	0.0831222i	0.747445	+	0.664323i	$0.231280\pi$
$308$	−12.2917	−	3.29355i	−0.700384	−	0.187667i
$309$	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	$0.685588\pi$
$312$	−0.926549	+	0.479617i	−0.0524555	+	0.0271530i
$313$	5.11217	−	19.0789i	0.288957	−	1.07840i	−0.656942	−	0.753941i	$-0.728150\pi$
$313$	5.11217	−	19.0789i	0.288957	−	1.07840i	0.945899	−	0.324461i	$-0.105183\pi$
$314$	−4.55886			−0.257271
$315$		0			0
$316$	−4.18916			−0.235659
$317$	−8.82217	+	32.9248i	−0.495503	+	1.84924i	0.0316937	+	0.999498i	$0.489910\pi$
$317$	−8.82217	+	32.9248i	−0.495503	+	1.84924i	−0.527196	+	0.849743i	$0.676757\pi$
$318$	−0.147605	+	3.21070i	−0.00827727	+	0.180047i
$319$	−7.64709	−	4.41505i	−0.428155	−	0.247195i
$320$		0			0
$321$	−2.28414	−	10.4168i	−0.127488	−	0.581408i
$322$	−6.74301	−	1.80678i	−0.375773	−	0.100688i
$323$	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
$327$	14.4346	−	22.5428i	0.798233	−	1.24662i
$328$	−6.22982	+	1.66927i	−0.343984	+	0.0921703i
$329$	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
$333$	−2.51561	−	0.928776i	−0.137855	−	0.0508966i
$334$			0.00888621i			0.000486232i
$335$		0			0
$336$	−1.39150	+	4.37802i	−0.0759124	+	0.238841i
$337$	−3.17090	−	11.8340i	−0.172730	−	0.644637i	−0.996927	−	0.0783338i	$-0.975040\pi$
$337$	−3.17090	−	11.8340i	−0.172730	−	0.644637i	0.824197	−	0.566303i	$-0.191627\pi$
$338$	−3.27074	−	12.2066i	−0.177905	−	0.663949i
$339$	3.11295	−	9.79417i	0.169072	−	0.531947i
$340$		0			0
$341$			19.5648i			1.05949i
$342$	−2.63366	−	15.3501i	−0.142412	−	0.830037i
$343$	−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
$347$	17.9559	−	4.81127i	0.963924	−	0.258283i	0.257663	−	0.966235i	$-0.417047\pi$
$347$	17.9559	−	4.81127i	0.963924	−	0.258283i	0.706260	+	0.707952i	$0.250381\pi$
$348$	−1.71893	+	2.68449i	−0.0921444	+	0.143904i
$349$	27.2305	−	15.7215i	1.45761	−	0.841553i	0.458720	−	0.888581i	$-0.348308\pi$
$349$	27.2305	−	15.7215i	1.45761	−	0.841553i	0.998894	+	0.0470278i	$0.0149749\pi$
$350$		0			0
$351$	−0.387054	−	3.10595i	−0.0206594	−	0.165783i
$352$	−3.39264	+	3.39264i	−0.180829	+	0.180829i
$353$	−11.7440	−	3.14681i	−0.625073	−	0.167488i	−0.0676398	−	0.997710i	$-0.521547\pi$
$353$	−11.7440	−	3.14681i	−0.625073	−	0.167488i	−0.557433	+	0.830222i	$0.688214\pi$
$354$	−0.0478918	−	0.218409i	−0.00254542	−	0.0116083i
$355$		0			0
$356$	−1.77526	−	1.02494i	−0.0940883	−	0.0543219i
$357$	1.31534	−	28.6113i	0.0696153	−	1.51427i
$358$	−0.378631	+	1.41307i	−0.0200112	+	0.0746830i
$359$	−4.31606			−0.227793			−0.113896	−	0.993493i	$-0.536333\pi$
$359$	−4.31606			−0.227793			−0.113896	+	0.993493i	$0.536333\pi$
$360$		0			0
$361$	−7.95119			−0.418484
$362$	2.24804	−	8.38980i	0.118154	−	0.440958i
$363$	18.4891	−	9.57068i	0.970428	−	0.502330i
$364$	1.38358	+	0.798810i	0.0725192	+	0.0418690i
$365$		0			0
$366$	−20.7078	−	6.58172i	−1.08242	−	0.344032i
$367$	19.2008	+	5.14485i	1.00228	+	0.268559i	0.722399	−	0.691477i	$-0.243040\pi$
$367$	19.2008	+	5.14485i	1.00228	+	0.268559i	0.279877	+	0.960036i	$0.409706\pi$
$368$	−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
$372$	7.05544	+	0.324358i	0.365807	+	0.0168172i
$373$	−2.53800	+	0.680056i	−0.131413	+	0.0352120i	−0.323926	−	0.946082i	$-0.605003\pi$
$373$	−2.53800	+	0.680056i	−0.131413	+	0.0352120i	0.192513	+	0.981294i	$0.438336\pi$
$374$	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
$378$	−10.8753	−	8.46512i	−0.559363	−	0.435399i
$379$			3.03124i			0.155705i	0.996965	+	0.0778523i	$0.0248063\pi$
$379$			3.03124i			0.155705i	−0.996965	+	0.0778523i	$0.975194\pi$
$380$		0			0
$381$	−6.02555	+	1.32125i	−0.308698	+	0.0676899i
$382$	−1.29643	−	4.83835i	−0.0663313	−	0.247552i
$383$	6.14717	+	22.9416i	0.314106	+	1.17226i	0.924819	+	0.380407i	$0.124216\pi$
$383$	6.14717	+	22.9416i	0.314106	+	1.17226i	−0.610713	+	0.791852i	$0.709117\pi$
$384$	1.16721	+	1.27970i	0.0595638	+	0.0653043i
$385$		0			0
$386$			3.36832i			0.171443i
$387$	7.36197	−	1.26311i	0.374230	−	0.0642077i
$388$	−12.2336	−	12.2336i	−0.621069	−	0.621069i
$389$	3.33254	+	5.77213i	0.168966	+	0.292659i	0.938057	−	0.346482i	$-0.112624\pi$
$389$	3.33254	+	5.77213i	0.168966	+	0.292659i	−0.769090	+	0.639140i	$0.779290\pi$
$390$		0			0
$391$	8.20515	−	14.2117i	0.414952	−	0.718718i
$392$	0.0332644	−	0.00891317i	0.00168011	−	0.000450183i
$393$	10.3987	+	20.0887i	0.524543	+	1.01334i
$394$	−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	−0.292548	−	0.956251i	$-0.594503\pi$
$397$	13.2242	−	13.2242i	0.663703	−	0.663703i	0.956251	+	0.292548i	$0.0945031\pi$
$398$	−17.8316	−	4.77797i	−0.893819	−	0.239498i
$399$	−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	$0.623684\pi$
$402$	16.1060	+	10.3130i	0.803294	+	0.514364i
$403$	0.635736	−	2.37260i	0.0316683	−	0.118188i
$404$	11.9619			0.595129
$405$		0			0
$406$	4.88121			0.242250
$407$	−1.10999	+	4.14256i	−0.0550204	+	0.205339i
$408$	−9.09433	−	5.82327i	−0.450237	−	0.288295i
$409$	−7.43574	−	4.29303i	−0.367674	−	0.212277i	0.304768	−	0.952427i	$-0.401421\pi$
$409$	−7.43574	−	4.29303i	−0.367674	−	0.212277i	−0.672442	+	0.740150i	$0.734754\pi$
$410$		0			0
$411$	−4.15793	+	3.79243i	−0.205096	+	0.187067i
$412$	−10.4055	−	2.78816i	−0.512644	−	0.137363i
$413$	−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
$417$	−17.5126	−	33.8317i	−0.857595	−	1.65675i
$418$	−24.0595	+	6.44672i	−1.17679	+	0.315319i
$419$	7.72749	−	13.3844i	0.377512	−	0.653871i	−0.613187	−	0.789938i	$-0.710113\pi$
$419$	7.72749	−	13.3844i	0.377512	−	0.653871i	0.990700	+	0.136067i	$0.0434462\pi$
$420$		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
$423$	11.7142	−	2.00983i	0.569562	−	0.0977214i
$424$		−	1.85566i		−	0.0901186i
$425$		0			0
$426$	12.1626	+	13.3348i	0.589280	+	0.646073i
$427$	8.61157	+	32.1388i	0.416743	+	1.55531i
$428$	1.59355	+	5.94722i	0.0770273	+	0.287470i
$429$	−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	$0.969948\pi$
$432$	−4.81427	+	1.95521i	−0.231627	+	0.0940699i
$433$	27.2049	+	27.2049i	1.30738	+	1.30738i	0.923297	+	0.384086i	$0.125483\pi$
$433$	27.2049	+	27.2049i	1.30738	+	1.30738i	0.384086	+	0.923297i	$0.374517\pi$
$434$	−5.40762	−	9.36628i	−0.259574	−	0.449596i
$435$		0			0
$436$	−7.72730	+	13.3841i	−0.370070	+	0.640981i
$437$	−13.1986	+	3.53656i	−0.631375	+	0.169176i
$438$	8.07531	+	0.371245i	0.385853	+	0.0177388i
$439$	−13.2725	+	7.66286i	−0.633460	+	0.365728i	−0.782091	−	0.623164i	$-0.785847\pi$
$439$	−13.2725	+	7.66286i	−0.633460	+	0.365728i	0.148631	+	0.988893i	$0.452513\pi$
$440$		0			0
$441$	−0.00947919	+	0.102878i	−0.000451390	+	0.00489894i
$442$	−2.65561	+	2.65561i	−0.126315	+	0.126315i
$443$	26.8719	+	7.20031i	1.27672	+	0.342097i	0.832603	−	0.553870i	$-0.186850\pi$
$443$	26.8719	+	7.20031i	1.27672	+	0.342097i	0.444120	+	0.895967i	$0.353516\pi$
$444$	1.47548	+	0.468963i	0.0700233	+	0.0222560i
$445$		0			0
$446$	−18.1659	−	10.4881i	−0.860180	−	0.496625i
$447$	20.2016	−	10.4571i	0.955503	−	0.494605i
$448$	0.686453	−	2.56188i	0.0324319	−	0.121037i
$449$	−24.3627			−1.14975			−0.574874	−	0.818242i	$-0.694949\pi$
$449$	−24.3627			−1.14975			−0.574874	+	0.818242i	$0.694949\pi$
$450$		0			0
$451$	−30.9446			−1.45712
$452$	−1.53568	+	5.73124i	−0.0722324	+	0.269575i
$453$	0.0267105	−	0.581006i	0.00125497	−	0.0272980i
$454$	−5.15716	−	2.97749i	−0.242037	−	0.139740i
$455$		0			0
$456$	1.92594	+	8.78319i	0.0901902	+	0.411310i
$457$	12.6705	+	3.39506i	0.592702	+	0.158814i	0.542688	−	0.839935i	$-0.317407\pi$
$457$	12.6705	+	3.39506i	0.592702	+	0.158814i	0.0500141	+	0.998749i	$0.484073\pi$
$458$	−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	$-0.0511948\pi$
$462$	−11.8854	+	18.5617i	−0.552959	+	0.863569i
$463$	11.5688	−	3.09986i	0.537649	−	0.144063i	0.0202307	−	0.999795i	$-0.493560\pi$
$463$	11.5688	−	3.09986i	0.537649	−	0.144063i	0.517418	+	0.855733i	$0.326893\pi$
$464$	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	$-0.341138\pi$
$467$	−8.63124	−	8.63124i	−0.399406	−	0.399406i	−0.878024	+	0.478617i	$0.841138\pi$
$468$	0.305583	+	1.78107i	0.0141256	+	0.0823298i
$469$		−	29.2855i		−	1.35228i
$470$		0			0
$471$	−2.39179	+	7.52521i	−0.110208	+	0.346744i
$472$	0.0334121	+	0.124696i	0.00153792	+	0.00573959i
$473$	−3.09188	−	11.5390i	−0.142165	−	0.530565i
$474$	−2.19783	+	6.91496i	−0.100950	+	0.317615i
$475$		0			0
$476$			16.5362i			0.757935i
$477$	5.22240	+	1.92813i	0.239117	+	0.0882832i
$478$	−3.22360	−	3.22360i	−0.147444	−	0.147444i
$479$	5.13488	+	8.89388i	0.234619	+	0.406372i	0.959162	−	0.282858i	$-0.0912825\pi$
$479$	5.13488	+	8.89388i	0.234619	+	0.406372i	−0.724543	+	0.689230i	$0.757949\pi$
$480$		0			0
$481$	0.269215	−	0.466295i	0.0122752	−	0.0212612i
$482$	−15.5148	+	4.15717i	−0.706678	+	0.189354i
$483$	−6.52013	+	10.1826i	−0.296676	+	0.463326i
$484$	−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	−0.982140	−	0.188153i	$-0.939750\pi$
$487$	−17.5218	+	17.5218i	−0.793987	+	0.793987i	0.188153	+	0.982140i	$0.439750\pi$
$488$	12.1176	+	3.24689i	0.548536	+	0.146980i
$489$	−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	$0.730973\pi$
$492$	−0.513021	+	11.1592i	−0.0231288	+	0.503096i
$493$	−2.96982	+	11.0835i	−0.133754	+	0.499176i
$494$	3.12714			0.140697
$495$		0			0
$496$	−4.07776			−0.183097
$497$	7.15302	−	26.6954i	0.320857	−	1.19745i
$498$	17.6918	−	9.15794i	0.792788	−	0.410377i
$499$	25.4186	+	14.6754i	1.13789	+	0.656963i	0.945908	−	0.324435i	$-0.105174\pi$
$499$	25.4186	+	14.6754i	1.13789	+	0.656963i	0.191985	+	0.981398i	$0.438507\pi$
$500$		0			0
$501$	0.0146683	+	0.00466213i	0.000655331	+	0.000208288i
$502$	18.3507	+	4.91707i	0.819034	+	0.219459i
$503$	−10.0766	+	10.0766i	−0.449293	+	0.449293i	−0.895120	−	0.445826i	$-0.852910\pi$
$503$	−10.0766	+	10.0766i	−0.449293	+	0.449293i	0.445826	+	0.895120i	$0.352910\pi$
$504$	6.49666	+	4.59383i	0.289384	+	0.204626i
$505$		0			0
$506$	−10.9365	+	6.31420i	−0.486188	+	0.280701i
$507$	−21.8651	−	1.00520i	−0.971063	−	0.0446425i
$508$	3.44015	−	0.921786i	0.152632	−	0.0408976i
$509$	−15.0024	+	25.9849i	−0.664970	+	1.15176i	0.314323	+	0.949316i	$0.398223\pi$
$509$	−15.0024	+	25.9849i	−0.664970	+	1.15176i	−0.979293	+	0.202446i	$0.935111\pi$
$510$		0			0
$511$	−6.18930	−	10.7202i	−0.273799	−	0.474233i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	−26.7198	−	3.70605i	−1.17971	−	0.163626i
$514$		−	3.35128i		−	0.147819i
$515$		0			0
$516$	−4.21246	+	0.923688i	−0.185443	+	0.0406631i
$517$	−4.91971	−	18.3606i	−0.216369	−	0.807499i
$518$	−0.613596	−	2.28997i	−0.0269598	−	0.100615i
$519$	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	$0.955193\pi$
$522$	3.52941	+	4.24582i	0.154478	+	0.185834i
$523$	−16.0596	−	16.0596i	−0.702237	−	0.702237i	0.262653	−	0.964890i	$-0.415403\pi$
$523$	−16.0596	−	16.0596i	−0.702237	−	0.702237i	−0.964890	+	0.262653i	$0.915403\pi$
$524$	−6.52997	−	11.3102i	−0.285263	−	0.494090i
$525$		0			0
$526$	−8.37268	+	14.5019i	−0.365066	+	0.632313i
$527$	24.5576	−	6.58020i	1.06975	−	0.286638i
$528$	3.82023	+	7.38011i	0.166254	+	0.321178i
$529$	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
$533$	3.75261	+	1.00551i	0.162544	+	0.0435535i
$534$	−2.62324	+	2.39264i	−0.113519	+	0.103540i
$535$		0			0
$536$	−9.56244	−	5.52087i	−0.413034	−	0.238465i
$537$	2.13388	+	1.36636i	0.0920836	+	0.0589628i
$538$	−0.138660	+	0.517486i	−0.00597806	+	0.0223104i
$539$	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	$0.0908026\pi$
$542$	4.02237	−	15.0117i	0.172776	−	0.644807i
$543$	−12.6694	−	8.11248i	−0.543698	−	0.348140i
$544$	5.39948	+	3.11739i	0.231501	+	0.133657i
$545$		0			0
$546$	2.04447	−	1.86475i	0.0874953	−	0.0798040i
$547$	−5.15053	−	1.38008i	−0.220221	−	0.0590080i	0.147022	−	0.989133i	$-0.453031\pi$
$547$	−5.15053	−	1.38008i	−0.220221	−	0.0590080i	−0.367242	+	0.930125i	$0.619698\pi$
$548$	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
$552$	2.09571	+	4.04860i	0.0891994	+	0.172320i
$553$	10.7321	−	2.87566i	0.456376	−	0.122286i
$554$	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	$-0.289232\pi$
$557$	−4.10329	−	4.10329i	−0.173862	−	0.173862i	−0.788674	+	0.614812i	$0.789232\pi$
$558$	4.23703	−	11.4761i	0.179368	−	0.485822i
$559$			1.49979i			0.0634344i
$560$		0			0
$561$	−34.9158	−	38.2809i	−1.47415	−	1.61622i
$562$	−6.24341	−	23.3007i	−0.263362	−	0.982882i
$563$	−1.53547	−	5.73047i	−0.0647125	−	0.241510i	0.925992	−	0.377544i	$-0.123231\pi$
$563$	−1.53547	−	5.73047i	−0.0647125	−	0.241510i	−0.990704	+	0.136033i	$0.956565\pi$
$564$	−6.70275	+	1.46975i	−0.282237	+	0.0618875i
$565$		0			0
$566$		−	16.5516i		−	0.695715i
$567$	−19.6789	+	13.5104i	−0.826436	+	0.567383i
$568$	−7.36824	−	7.36824i	−0.309164	−	0.309164i
$569$	17.6714	+	30.6077i	0.740822	+	1.28314i	0.952122	+	0.305720i	$0.0988971\pi$
$569$	17.6714	+	30.6077i	0.740822	+	1.28314i	−0.211300	+	0.977421i	$0.567770\pi$
$570$		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	$0.146602\pi$
$572$	2.79162	−	0.748011i	0.116723	−	0.0312759i
$573$	−8.66674	−	0.398435i	−0.362058	−	0.0166448i
$574$	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	−0.424990	−	0.905198i	$-0.639722\pi$
$577$	11.5350	−	11.5350i	0.480208	−	0.480208i	0.905198	+	0.424990i	$0.139722\pi$
$578$	−21.1272	−	5.66101i	−0.878774	−	0.235467i
$579$	5.56002	+	1.76718i	0.231066	+	0.0734415i
$580$		0			0
$581$	−26.4185	−	15.2527i	−1.09602	−	0.632789i
$582$	−26.6122	+	13.7755i	−1.10311	+	0.571011i
$583$	2.30434	−	8.59992i	0.0954361	−	0.356172i
$584$	−4.66721			−0.193130
$585$		0			0
$586$	16.1515			0.667214
$587$	2.95165	−	11.0157i	0.121828	−	0.454666i	−0.877879	−	0.478882i	$-0.841042\pi$
$587$	2.95165	−	11.0157i	0.121828	−	0.454666i	0.999707	+	0.0242156i	$0.00770882\pi$
$588$	0.00273930	−	0.0595851i	0.000112967	−	0.00245725i
$589$	−18.3333	−	10.5848i	−0.755412	−	0.436137i
$590$		0			0
$591$	8.13346	+	37.0925i	0.334566	+	1.52578i
$592$	−0.863406	−	0.231349i	−0.0354858	−	0.00950838i
$593$	−23.4664	+	23.4664i	−0.963651	+	0.963651i	−0.999362	−	0.0357109i	$-0.988630\pi$
$593$	−23.4664	+	23.4664i	−0.963651	+	0.963651i	0.0357109	+	0.999362i	$0.488630\pi$
$594$	−24.7394	+	3.08295i	−1.01507	+	0.126495i
$595$		0			0
$596$	−11.3738	+	6.56668i	−0.465890	+	0.268982i
$597$	−17.2422	+	26.9276i	−0.705678	+	1.10207i
$598$	1.53143	−	0.410346i	0.0626249	−	0.0167803i
$599$	−17.2683	+	29.9097i	−0.705566	+	1.22208i	0.260922	+	0.965360i	$0.415974\pi$
$599$	−17.2683	+	29.9097i	−0.705566	+	1.22208i	−0.966487	+	0.256715i	$0.917360\pi$
$600$		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
$603$	25.4734	−	21.1752i	1.03736	−	0.862320i
$604$			0.335798i			0.0136634i
$605$		0			0
$606$	6.27581	−	19.7454i	0.254937	−	0.802100i
$607$	−1.32070	−	4.92890i	−0.0536054	−	0.200058i	0.933930	−	0.357456i	$-0.116356\pi$
$607$	−1.32070	−	4.92890i	−0.0536054	−	0.200058i	−0.987535	+	0.157399i	$0.949689\pi$
$608$	−1.34365	−	5.01456i	−0.0544921	−	0.203367i
$609$	2.56091	−	8.05731i	0.103773	−	0.326499i
$610$		0			0
$611$			2.38643i			0.0965446i
$612$	−14.3837	+	11.9567i	−0.581426	+	0.483320i
$613$	9.09622	+	9.09622i	0.367393	+	0.367393i	0.866525	−	0.499133i	$-0.166348\pi$
$613$	9.09622	+	9.09622i	0.367393	+	0.367393i	−0.499133	+	0.866525i	$0.666348\pi$
$614$	1.02984	+	1.78374i	0.0415611	+	0.0719859i
$615$		0			0
$616$	6.36265	−	11.0204i	0.256358	−	0.444026i
$617$	−23.2998	+	6.24315i	−0.938013	+	0.251340i	−0.695268	−	0.718751i	$-0.744714\pi$
$617$	−23.2998	+	6.24315i	−0.938013	+	0.251340i	−0.242745	+	0.970090i	$0.578048\pi$
$618$	−10.0616	+	15.7134i	−0.404737	+	0.632087i
$619$	26.9280	−	15.5469i	1.08233	−	0.624883i	0.150806	−	0.988563i	$-0.451813\pi$
$619$	26.9280	−	15.5469i	1.08233	−	0.624883i	0.931524	+	0.363680i	$0.118480\pi$
$620$		0			0
$621$	−13.5716	+	1.69125i	−0.544609	+	0.0678677i
$622$	1.48163	−	1.48163i	0.0594081	−	0.0594081i
$623$	5.25156	+	1.40715i	0.210399	+	0.0563764i
$624$	−0.223466	−	1.01911i	−0.00894580	−	0.0407971i
$625$		0			0
$626$	17.1057	+	9.87595i	0.683679	+	0.394723i
$627$	−1.98128	+	43.0967i	−0.0791246	+	1.72112i
$628$	1.17992	−	4.40352i	0.0470839	−	0.175719i
$629$	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	$0.129153\pi$
$632$	1.08423	−	4.04642i	0.0431285	−	0.160958i
$633$	2.01338	−	1.04220i	0.0800247	−	0.0414239i
$634$	−29.5196	−	17.0431i	−1.17237	−	0.676869i
$635$		0			0
$636$	−3.06309	−	0.973565i	−0.121460	−	0.0386044i
$637$	−0.0200372	−	0.00536896i	−0.000793905	−	0.000212726i
$638$	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	$0.358117\pi$
$642$	10.6530	+	0.489749i	0.420441	+	0.0193288i
$643$	29.9917	−	8.03625i	1.18276	−	0.316919i	0.386737	−	0.922190i	$-0.373602\pi$
$643$	29.9917	−	8.03625i	1.18276	−	0.316919i	0.796019	+	0.605271i	$0.206935\pi$
$644$	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	$-0.0821824\pi$
$647$	18.0986	+	18.0986i	0.711531	+	0.711531i	−0.255325	+	0.966855i	$0.582182\pi$
$648$	0.701625	+	8.97261i	0.0275624	+	0.352477i
$649$			0.619386i			0.0243130i
$650$		0			0
$651$	−18.2978	+	4.01226i	−0.717149	+	0.157253i
$652$	3.29971	+	12.3147i	0.129226	+	0.482280i
$653$	−3.63685	−	13.5729i	−0.142321	−	0.531148i	−0.999860	−	0.0167299i	$-0.994674\pi$
$653$	−3.63685	−	13.5729i	−0.142321	−	0.531148i	0.857539	−	0.514419i	$-0.171992\pi$
$654$	18.0387	+	19.7772i	0.705369	+	0.773350i
$655$		0			0
$656$		−	6.44958i		−	0.251814i
$657$	4.84950	−	13.1350i	0.189197	−	0.512444i
$658$	7.43002	+	7.43002i	0.289652	+	0.289652i
$659$	−18.2709	−	31.6462i	−0.711734	−	1.23276i	−0.964206	−	0.265155i	$-0.914577\pi$
$659$	−18.2709	−	31.6462i	−0.711734	−	1.23276i	0.252471	−	0.967604i	$-0.418757\pi$
$660$		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	$0.920896\pi$
$662$	23.2092	−	6.21890i	0.902053	−	0.241704i
$663$	2.99030	+	5.77683i	0.116134	+	0.224353i
$664$	−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
$668$	−0.00858342	−	0.00229992i	−0.000332102	−	8.89866e-5i
$669$	−26.8432	+	24.4835i	−1.03782	+	0.946588i
$670$		0			0
$671$	52.1261	+	30.0950i	2.01231	+	1.16181i
$672$	−3.86870	−	2.47720i	−0.149238	−	0.0955600i
$673$	6.49200	−	24.2285i	0.250248	−	0.933939i	−0.720424	−	0.693534i	$-0.756053\pi$
$673$	6.49200	−	24.2285i	0.250248	−	0.933939i	0.970673	−	0.240406i	$-0.0772804\pi$
$674$	12.2514			0.471907
$675$		0			0
$676$	12.6372			0.486045
$677$	−1.40152	+	5.23054i	−0.0538647	+	0.201026i	−0.987614	−	0.156901i	$-0.949850\pi$
$677$	−1.40152	+	5.23054i	−0.0538647	+	0.201026i	0.933750	+	0.357927i	$0.116516\pi$
$678$	8.65475	+	5.54180i	0.332384	+	0.212832i
$679$	39.7389	+	22.9433i	1.52504	+	0.880481i
$680$		0			0
$681$	−7.62057	+	6.95069i	−0.292021	+	0.266351i
$682$	−18.8981	−	5.06374i	−0.723647	−	0.193901i
$683$	−14.3302	+	14.3302i	−0.548331	+	0.548331i	−0.925958	−	0.377627i	$-0.876740\pi$
$683$	−14.3302	+	14.3302i	−0.548331	+	0.548331i	0.377627	+	0.925958i	$0.376740\pi$
$684$	15.5087	+	1.42897i	0.592989	+	0.0546382i
$685$		0			0
$686$	15.9993	−	9.23721i	0.610857	−	0.352678i
$687$	9.36157	+	18.0852i	0.357166	+	0.689992i
$688$	2.40501	−	0.644420i	0.0916900	−	0.0245683i
$689$	−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
$693$	24.4038	+	29.3574i	0.927023	+	1.11519i
$694$			18.5893i			0.705641i
$695$		0			0
$696$	−2.14813	−	2.35516i	−0.0814246	−	0.0892720i
$697$	10.4076	+	38.8415i	0.394214	+	1.47123i
$698$	8.13805	+	30.3716i	0.308030	+	1.14958i
$699$	−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	$-0.197028\pi$
$702$	3.10029	+	0.430013i	0.117013	+	0.0162298i
$703$	−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
$707$	−30.6451	+	8.21132i	−1.15253	+	0.308818i
$708$	0.223362	+	0.0102686i	0.00839448	+	0.000385918i
$709$	−27.4879	+	15.8701i	−1.03233	+	0.596015i	−0.917651	−	0.397387i	$-0.869917\pi$
$709$	−27.4879	+	15.8701i	−1.03233	+	0.596015i	−0.114678	+	0.993403i	$0.536584\pi$
$710$		0			0
$711$	10.2613	+	7.25584i	0.384829	+	0.272115i
$712$	1.44949	−	1.44949i	0.0543219	−	0.0543219i
$713$	−10.3672	−	2.77788i	−0.388254	−	0.104032i
$714$	27.2960	+	8.67568i	1.02153	+	0.324679i
$715$		0			0
$716$	−1.26692	−	0.731458i	−0.0473471	−	0.0273359i
$717$	−7.01238	+	3.62988i	−0.261882	+	0.135560i
$718$	1.11708	−	4.16899i	0.0416890	−	0.155585i
$719$	−7.79879			−0.290846			−0.145423	−	0.989370i	$-0.546454\pi$
$719$	−7.79879			−0.290846			−0.145423	+	0.989370i	$0.546454\pi$
$720$		0			0
$721$	28.5717			1.06407
$722$	2.05792	−	7.68026i	0.0765878	−	0.285830i
$723$	−1.27763	+	27.7910i	−0.0475155	+	1.03356i
$724$	7.52209	+	4.34288i	0.279556	+	0.161402i
$725$		0			0
$726$	4.45923	+	20.3362i	0.165497	+	0.754747i
$727$	42.7863	+	11.4645i	1.58685	+	0.425196i	0.941039	−	0.338297i	$-0.109851\pi$
$727$	42.7863	+	11.4645i	1.58685	+	0.425196i	0.645815	+	0.763494i	$0.276518\pi$
$728$	−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
$732$	11.7170	−	18.2987i	0.433074	−	0.676341i
$733$	−26.9304	+	7.21598i	−0.994697	+	0.266528i	−0.719222	−	0.694780i	$-0.755502\pi$
$733$	−26.9304	+	7.21598i	−0.994697	+	0.266528i	−0.275475	+	0.961308i	$0.588835\pi$
$734$	−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
$738$	18.1511	+	6.70149i	0.668153	+	0.246685i
$739$		−	10.8068i		−	0.397536i	−0.980047	−	0.198768i	$-0.936306\pi$
$739$		−	10.8068i		−	0.397536i	0.980047	−	0.198768i	$-0.0636941\pi$
$740$		0			0
$741$	1.64065	−	5.16191i	0.0602707	−	0.189628i
$742$	1.27382	+	4.75396i	0.0467634	+	0.174523i
$743$	5.75762	+	21.4877i	0.211227	+	0.788309i	0.987461	+	0.157864i	$0.0504608\pi$
$743$	5.75762	+	21.4877i	0.211227	+	0.788309i	−0.776234	+	0.630445i	$0.782873\pi$
$744$	−2.13939	+	6.73108i	−0.0784338	+	0.246773i
$745$		0			0
$746$		−	2.62754i		−	0.0962009i
$747$	−5.83488	−	34.0082i	−0.213487	−	1.24429i
$748$	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	$0.895485\pi$
$752$	3.82678	−	1.02538i	0.139548	−	0.0373919i
$753$	17.7442	−	27.7115i	0.646634	−	1.00986i
$754$	−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	−0.227743	−	0.973721i	$-0.573135\pi$
$757$	20.5246	−	20.5246i	0.745978	−	0.745978i	0.973721	+	0.227743i	$0.0731346\pi$
$758$	−2.92796	−	0.784544i	−0.106348	−	0.0284959i
$759$	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	$0.353078\pi$
$762$	0.283294	−	6.16220i	0.0102626	−	0.223233i
$763$	10.6089	−	39.5928i	0.384066	−	1.43335i
$764$	5.00903			0.181220
$765$		0			0
$766$	−23.7508			−0.858153
$767$	0.0201262	−	0.0751122i	0.000726717	−	0.00271214i
$768$	−1.53819	+	0.796225i	−0.0555046	+	0.0287313i
$769$	26.6702	+	15.3980i	0.961752	+	0.555268i	0.896712	−	0.442615i	$-0.145949\pi$
$769$	26.6702	+	15.3980i	0.961752	+	0.555268i	0.0650399	+	0.997883i	$0.479283\pi$
$770$		0			0
$771$	−5.53189	−	1.75824i	−0.199226	−	0.0633215i
$772$	−3.25355	−	0.871785i	−0.117098	−	0.0313762i
$773$	−29.6376	+	29.6376i	−1.06599	+	1.06599i	−0.0683287	+	0.997663i	$0.521767\pi$
$773$	−29.6376	+	29.6376i	−1.06599	+	1.06599i	−0.997663	+	0.0683287i	$0.978233\pi$
$774$	−0.685343	+	7.43803i	−0.0246341	+	0.267354i
$775$		0			0
$776$	14.9831	−	8.65048i	0.537861	−	0.310534i
$777$	−4.10193	−	0.188577i	−0.147156	−	0.00676517i
$778$	−6.43797	+	1.72505i	−0.230813	+	0.0618460i
$779$	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
$783$	8.86018	−	3.59836i	0.316637	−	0.128595i
$784$			0.0344378i			0.00122992i
$785$		0			0
$786$	−22.0955	+	4.84500i	−0.788122	+	0.172816i
$787$	6.98316	+	26.0615i	0.248923	+	0.928993i	0.971371	+	0.237568i	$0.0763501\pi$
$787$	6.98316	+	26.0615i	0.248923	+	0.928993i	−0.722448	+	0.691425i	$0.756983\pi$
$788$	−5.67439	−	21.1771i	−0.202142	−	0.754403i
$789$	19.5453	+	21.4290i	0.695831	+	0.762893i
$790$		0			0
$791$		−	15.7369i		−	0.559540i
$792$	14.1865	−	2.43401i	0.504095	−	0.0864890i
$793$	−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
$797$	−6.28188	+	1.68322i	−0.222515	+	0.0596228i	−0.368354	−	0.929686i	$-0.620079\pi$
$797$	−6.28188	+	1.68322i	−0.222515	+	0.0596228i	0.145839	+	0.989308i	$0.453412\pi$
$798$	−10.9633	−	21.1794i	−0.388095	−	0.749742i
$799$	−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
$803$	−21.6299	−	5.79571i	−0.763302	−	0.204526i
$804$	−14.1301	+	12.8880i	−0.498330	+	0.454525i
$805$		0			0
$806$	2.12721	+	1.22815i	0.0749279	+	0.0432596i
$807$	0.781457	+	0.500381i	0.0275086	+	0.0176143i
$808$	−3.09598	+	11.5544i	−0.108916	+	0.406481i
$809$	−5.79431			−0.203717			−0.101859	−	0.994799i	$-0.532479\pi$
$809$	−5.79431			−0.203717			−0.101859	+	0.994799i	$0.532479\pi$
$810$		0			0
$811$	1.90498			0.0668929			0.0334465	−	0.999441i	$-0.489352\pi$
$811$	1.90498			0.0668929			0.0334465	+	0.999441i	$0.489352\pi$
$812$	−1.26335	+	4.71488i	−0.0443349	+	0.165460i
$813$	−22.6692	−	14.5155i	−0.795042	−	0.509080i
$814$	−3.71411	−	2.14434i	−0.130180	−	0.0751592i
$815$		0			0
$816$	7.97863	−	7.27728i	0.279308	−	0.254756i
$817$	12.4855	+	3.34547i	0.436812	+	0.117043i
$818$	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	$0.568764\pi$
$822$	−2.58706	−	4.99781i	−0.0902339	−	0.174319i
$823$	−20.6711	+	5.53879i	−0.720548	+	0.193070i	−0.600416	−	0.799688i	$-0.704998\pi$
$823$	−20.6711	+	5.53879i	−0.720548	+	0.193070i	−0.120132	+	0.992758i	$0.538332\pi$
$824$	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	$-0.442855\pi$
$827$	−23.1603	−	23.1603i	−0.805364	−	0.805364i	−0.983928	+	0.178564i	$0.942855\pi$
$828$	7.78245	−	1.33526i	0.270459	−	0.0464034i
$829$		−	34.1116i		−	1.18475i	−0.805664	−	0.592373i	$-0.798191\pi$
$829$		−	34.1116i		−	1.18475i	0.805664	−	0.592373i	$-0.201809\pi$
$830$		0			0
$831$	−20.2041	−	22.1513i	−0.700873	−	0.768421i
$832$	0.155903	+	0.581838i	0.00540497	+	0.0201716i
$833$	−0.0555716	−	0.207396i	−0.00192544	−	0.00718585i
$834$	37.2115	−	8.15957i	1.28853	−	0.282543i
$835$		0			0
$836$		−	24.9082i		−	0.861468i
$837$	−16.7204	−	13.0149i	−0.577942	−	0.449860i
$838$	10.9283	+	10.9283i	0.377512	+	0.377512i
$839$	18.8058	+	32.5726i	0.649249	+	1.12453i	0.983303	+	0.181978i	$0.0582500\pi$
$839$	18.8058	+	32.5726i	0.649249	+	1.12453i	−0.334054	+	0.942554i	$0.608417\pi$
$840$		0			0
$841$	12.8065	−	22.1814i	0.441602	−	0.764877i
$842$	−18.2585	+	4.89235i	−0.629229	+	0.168602i
$843$	−41.7376	−	1.91880i	−1.43752	−	0.0660868i
$844$	−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
$848$	1.79243	+	0.480279i	0.0615521	+	0.0164928i
$849$	−27.3214	−	8.68375i	−0.937667	−	0.298026i
$850$		0			0
$851$	−2.03750	−	1.17635i	−0.0698445	−	0.0403248i
$852$	−16.0283	+	8.29688i	−0.549122	+	0.284246i
$853$	1.98742	−	7.41714i	0.0680478	−	0.253958i	−0.923519	−	0.383552i	$-0.874701\pi$
$853$	1.98742	−	7.41714i	0.0680478	−	0.253958i	0.991567	+	0.129594i	$0.0413674\pi$
$854$	−33.2726			−1.13856
$855$		0			0
$856$	−6.15702			−0.210442
$857$	−1.87635	+	7.00264i	−0.0640949	+	0.239206i	−0.990540	−	0.137224i	$-0.956182\pi$
$857$	−1.87635	+	7.00264i	−0.0640949	+	0.239206i	0.926445	+	0.376430i	$0.122848\pi$
$858$	0.229887	−	5.00051i	0.00784823	−	0.170714i
$859$	−1.50446	−	0.868601i	−0.0513316	−	0.0296363i	0.474115	−	0.880463i	$-0.342768\pi$
$859$	−1.50446	−	0.868601i	−0.0513316	−	0.0296363i	−0.525446	+	0.850827i	$0.676102\pi$
$860$		0			0
$861$	−6.34598	−	28.9407i	−0.216271	−	0.986297i
$862$	−3.78090	−	1.01309i	−0.128778	−	0.0345060i
$863$	36.4612	−	36.4612i	1.24115	−	1.24115i	0.281630	−	0.959523i	$-0.409125\pi$
$863$	36.4612	−	36.4612i	1.24115	−	1.24115i	0.959523	−	0.281630i	$-0.0908751\pi$
$864$	−0.642559	−	5.15627i	−0.0218603	−	0.175420i
$865$		0			0
$866$	−33.3190	+	19.2368i	−1.13223	+	0.653692i
$867$	−20.4288	+	31.9042i	−0.693799	+	1.08352i
$868$	10.4467	−	2.79919i	0.354585	−	0.0950108i
$869$	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
$873$	8.77688	+	51.1554i	0.297052	+	1.73135i
$874$		−	13.6642i		−	0.462199i
$875$		0			0
$876$	−2.44864	+	7.70407i	−0.0827318	+	0.260296i
$877$	−2.68194	−	10.0092i	−0.0905628	−	0.337985i	0.905747	−	0.423820i	$-0.139311\pi$
$877$	−2.68194	−	10.0092i	−0.0905628	−	0.337985i	−0.996309	+	0.0858347i	$0.972644\pi$
$878$	−3.96659	−	14.8035i	−0.133866	−	0.499594i
$879$	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	$0.993687\pi$
$882$	−0.0969188	−	0.0357829i	−0.00326343	−	0.00120487i
$883$	22.1929	+	22.1929i	0.746850	+	0.746850i	0.973886	−	0.227036i	$-0.0729035\pi$
$883$	22.1929	+	22.1929i	0.746850	+	0.746850i	−0.227036	+	0.973886i	$0.572903\pi$
$884$	−1.87780	−	3.25245i	−0.0631573	−	0.109392i
$885$		0			0
$886$	−13.9099	+	24.0927i	−0.467313	+	0.809410i
$887$	−8.80492	+	2.35927i	−0.295640	+	0.0792166i	−0.403590	−	0.914940i	$-0.632238\pi$
$887$	−8.80492	+	2.35927i	−0.295640	+	0.0792166i	0.107950	+	0.994156i	$0.465571\pi$
$888$	−0.834867	+	1.30383i	−0.0280163	+	0.0437537i
$889$	−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
$893$	19.8666	+	5.32323i	0.664809	+	0.178135i
$894$	4.87224	+	22.2197i	0.162952	+	0.743140i
$895$		0			0
$896$	2.29692	+	1.32613i	0.0767346	+	0.0443028i
$897$	0.126112	−	2.74319i	0.00421076	−	0.0915925i
$898$	6.30553	−	23.5326i	0.210418	−	0.785292i
$899$	7.50472			0.250296
$900$		0			0
$901$	−11.5696			−0.385439
$902$	8.00905	−	29.8902i	0.266672	−	0.995234i
$903$	10.1577	−	5.25803i	0.338028	−	0.174976i
$904$	−5.13849	−	2.96671i	−0.170904	−	0.0986713i
$905$		0			0
$906$	0.554295	+	0.176176i	0.0184152	+	0.00585304i
$907$	−7.35203	−	1.96997i	−0.244120	−	0.0654118i	0.134684	−	0.990889i	$-0.456998\pi$
$907$	−7.35203	−	1.96997i	−0.244120	−	0.0654118i	−0.378804	+	0.925477i	$0.623665\pi$
$908$	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	$0.0629846\pi$
$912$	−8.98237	−	0.412945i	−0.297436	−	0.0136740i
$913$	−53.3039	+	14.2827i	−1.76410	+	0.472690i
$914$	−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
$918$	12.1903	+	30.0159i	0.402339	+	0.990672i
$919$		−	19.9726i		−	0.658836i	−0.944184	−	0.329418i	$-0.893148\pi$
$919$		−	19.9726i		−	0.658836i	0.944184	−	0.329418i	$-0.106852\pi$
$920$		0			0
$921$	3.48469	−	0.764106i	0.114824	−	0.0251782i
$922$	10.3908	+	38.7791i	0.342204	+	1.27712i
$923$	1.62455	+	6.06291i	0.0534728	+	0.199563i
$924$	−14.8531	−	16.2845i	−0.488630	−	0.535722i
$925$		0			0
$926$			11.9769i			0.393586i
$927$	20.6590	+	24.8525i	0.678532	+	0.816263i
$928$	1.30136	+	1.30136i	0.0427192	+	0.0427192i
$929$	−24.8920	−	43.1142i	−0.816681	−	1.41453i	−0.908115	−	0.418721i	$-0.862478\pi$
$929$	−24.8920	−	43.1142i	−0.816681	−	1.41453i	0.0914341	−	0.995811i	$-0.470855\pi$
$930$		0			0
$931$	−0.0893912	+	0.154830i	−0.00292968	+	0.00507435i
$932$	18.3487	−	4.91653i	0.601033	−	0.161046i
$933$	−1.66837	−	3.22304i	−0.0546199	−	0.105518i
$934$	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	−0.998117	−	0.0613453i	$-0.980461\pi$
$937$	−28.6750	+	28.6750i	−0.936771	+	0.936771i	0.0613453	+	0.998117i	$0.480461\pi$
$938$	28.2876	+	7.57964i	0.923623	+	0.247484i
$939$	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	$0.961365\pi$
$942$	−6.64976	−	4.25796i	−0.216661	−	0.138732i
$943$	4.39363	−	16.3972i	0.143076	−	0.533967i
$944$	−0.129095			−0.00420167
$945$		0			0
$946$	11.9461			0.388401
$947$	−11.6667	+	43.5407i	−0.379117	+	1.41488i	0.468119	+	0.883665i	$0.344932\pi$
$947$	−11.6667	+	43.5407i	−0.379117	+	1.41488i	−0.847236	+	0.531217i	$0.821735\pi$
$948$	−6.11050	−	3.91267i	−0.198460	−	0.127078i
$949$	2.43470	+	1.40568i	0.0790339	+	0.0456302i
$950$		0			0
$951$	−43.6201	+	39.7857i	−1.41448	+	1.29014i
$952$	−15.9727	−	4.27988i	−0.517679	−	0.138712i
$953$	2.71971	−	2.71971i	0.0881001	−	0.0881001i	−0.661683	−	0.749783i	$-0.730158\pi$
$953$	2.71971	−	2.71971i	0.0881001	−	0.0881001i	0.749783	+	0.661683i	$0.230158\pi$
$954$	−3.21409	+	4.54541i	−0.104060	+	0.147163i
$955$		0			0
$956$	3.94809	−	2.27943i	0.127690	−	0.0737220i
$957$	−7.03075	−	13.5824i	−0.227272	−	0.439056i
$958$	−9.91983	+	2.65801i	−0.320495	+	0.0858764i
$959$	−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
$963$	6.39750	−	17.3278i	0.206156	−	0.558380i
$964$		−	16.0621i		−	0.517325i
$965$		0			0
$966$	−8.14813	−	8.93342i	−0.262162	−	0.287428i
$967$	−8.10886	−	30.2627i	−0.260763	−	0.973182i	−0.964793	−	0.263011i	$-0.915284\pi$
$967$	−8.10886	−	30.2627i	−0.260763	−	0.973182i	0.704029	−	0.710171i	$-0.251382\pi$
$968$	−3.11102	−	11.6105i	−0.0999920	−	0.373175i
$969$	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	$-0.171448\pi$
$972$	15.1790	+	3.54930i	0.486867	+	0.113844i
$973$	−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
$977$	8.45932	−	2.26667i	0.270638	−	0.0725171i	−0.120948	−	0.992659i	$-0.538593\pi$
$977$	8.45932	−	2.26667i	0.270638	−	0.0725171i	0.391585	+	0.920142i	$0.371927\pi$
$978$	22.0588	+	1.01410i	0.705361	+	0.0324275i
$979$	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
$983$	−40.7397	−	10.9162i	−1.29940	−	0.348172i	−0.458174	−	0.888863i	$-0.651496\pi$
$983$	−40.7397	−	10.9162i	−1.29940	−	0.348172i	−0.841222	+	0.540691i	$0.818163\pi$
$984$	−10.6462	−	3.38376i	−0.339388	−	0.107870i
$985$		0			0
$986$	−9.93720	−	5.73725i	−0.316465	−	0.182711i
$987$	16.1627	−	8.36644i	0.514465	−	0.266307i
$988$	−0.809364	+	3.02059i	−0.0257493	+	0.0960977i
$989$	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	$0.570920\pi$
$992$	1.05540	−	3.93882i	0.0335091	−	0.125058i
$993$	1.91126	−	41.5738i	0.0606521	−	1.31930i
$994$	23.9345	+	13.8186i	0.759156	+	0.438299i
$995$		0			0
$996$	4.26692	+	19.4592i	0.135203	+	0.616589i
$997$	−29.2374	−	7.83414i	−0.925958	−	0.248110i	−0.235828	−	0.971795i	$-0.575780\pi$
$997$	−29.2374	−	7.83414i	−0.925958	−	0.248110i	−0.690130	+	0.723685i	$0.742447\pi$
$998$	−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.293.2		16
3.2	odd	2		1350.2.q.h.1043.4		16
5.2	odd	4	inner	450.2.p.h.257.2		16
5.3	odd	4		90.2.l.b.77.3	yes	16
5.4	even	2		90.2.l.b.23.3	✓	16
9.2	odd	6	inner	450.2.p.h.443.2		16
9.7	even	3		1350.2.q.h.143.3		16
15.2	even	4		1350.2.q.h.557.3		16
15.8	even	4		270.2.m.b.17.1		16
15.14	odd	2		270.2.m.b.233.1		16
20.3	even	4		720.2.cu.b.257.3		16
20.19	odd	2		720.2.cu.b.113.4		16
45.2	even	12	inner	450.2.p.h.407.2		16
45.4	even	6		810.2.f.c.323.5		16
45.7	odd	12		1350.2.q.h.1007.4		16
45.13	odd	12		810.2.f.c.647.4		16
45.14	odd	6		810.2.f.c.323.4		16
45.23	even	12		810.2.f.c.647.5		16
45.29	odd	6		90.2.l.b.83.3	yes	16
45.34	even	6		270.2.m.b.143.1		16
45.38	even	12		90.2.l.b.47.3	yes	16
45.43	odd	12		270.2.m.b.197.1		16
180.83	odd	12		720.2.cu.b.497.4		16
180.119	even	6		720.2.cu.b.353.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
90.2.l.b.23.3	✓	16	5.4	even	2
90.2.l.b.47.3	yes	16	45.38	even	12
90.2.l.b.77.3	yes	16	5.3	odd	4
90.2.l.b.83.3	yes	16	45.29	odd	6
270.2.m.b.17.1		16	15.8	even	4
270.2.m.b.143.1		16	45.34	even	6
270.2.m.b.197.1		16	45.43	odd	12
270.2.m.b.233.1		16	15.14	odd	2
450.2.p.h.257.2		16	5.2	odd	4	inner
450.2.p.h.293.2		16	1.1	even	1	trivial
450.2.p.h.407.2		16	45.2	even	12	inner
450.2.p.h.443.2		16	9.2	odd	6	inner
720.2.cu.b.113.4		16	20.19	odd	2
720.2.cu.b.257.3		16	20.3	even	4
720.2.cu.b.353.3		16	180.119	even	6
720.2.cu.b.497.4		16	180.83	odd	12
810.2.f.c.323.4		16	45.14	odd	6
810.2.f.c.323.5		16	45.4	even	6
810.2.f.c.647.4		16	45.13	odd	12
810.2.f.c.647.5		16	45.23	even	12
1350.2.q.h.143.3		16	9.7	even	3
1350.2.q.h.557.3		16	15.2	even	4
1350.2.q.h.1007.4		16	45.7	odd	12
1350.2.q.h.1043.4		16	3.2	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:	\( N \)	\(=\)	\( 450 = 2 \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	450.p (of order \(12\), degree \(4\), minimal)

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

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more