LMFDB - Embedded newform 450.2.h.d.91.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [450,2,Mod(91,450)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(450, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("450.91");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 450 = 2 \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	450.h (of order $5$, 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:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.1064390625.3
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} - 3x^{6} - 5x^{5} + 36x^{4} - 35x^{3} + 23x^{2} - 171x + 361 $ x^8 - 2x^7 - 3x^6 - 5x^5 + 36x^4 - 35x^3 + 23x^2 - 171*x + 361
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 150)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			91.1
Root			$-1.86886 - 1.45788i$ of defining polynomial
Character	$\chi$	$=$	450.91
Dual form			450.2.h.d.361.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.809017 - 0.587785i) q^{2} +(0.309017 + 0.951057i) q^{4} +(-2.17787 + 0.506822i) q^{5} -2.31003 q^{7} +(0.309017 - 0.951057i) q^{8} +O(q^{10})$	\(q+(-0.809017 - 0.587785i) q^{2} +(0.309017 + 0.951057i) q^{4} +(-2.17787 + 0.506822i) q^{5} -2.31003 q^{7} +(0.309017 - 0.951057i) q^{8} +(2.05984 + 0.870094i) q^{10} +(2.77305 + 2.01474i) q^{11} +(3.98689 - 2.89665i) q^{13} +(1.86886 + 1.35780i) q^{14} +(-0.809017 + 0.587785i) q^{16} +(2.36886 - 7.29059i) q^{17} +(1.00000 - 3.07768i) q^{19} +(-1.15502 - 1.91466i) q^{20} +(-1.05921 - 3.25992i) q^{22} +(3.61803 + 2.62866i) q^{23} +(4.48626 - 2.20759i) q^{25} -4.92807 q^{26} +(-0.713839 - 2.19697i) q^{28} +(2.13279 + 6.56405i) q^{29} +(1.09581 - 3.37254i) q^{31} +1.00000 q^{32} +(-6.20175 + 4.50583i) q^{34} +(5.03096 - 1.17078i) q^{35} +(-3.20175 + 2.32620i) q^{37} +(-2.61803 + 1.90211i) q^{38} +(-0.190983 + 2.22790i) q^{40} +(-0.132788 + 0.0964762i) q^{41} +6.71149 q^{43} +(-1.05921 + 3.25992i) q^{44} +(-1.38197 - 4.25325i) q^{46} +(-1.92807 - 5.93398i) q^{47} -1.66375 q^{49} +(-4.92705 - 0.850981i) q^{50} +(3.98689 + 2.89665i) q^{52} +(-3.69971 - 11.3865i) q^{53} +(-7.06047 - 2.98240i) q^{55} +(-0.713839 + 2.19697i) q^{56} +(2.13279 - 6.56405i) q^{58} +(8.62715 - 6.26799i) q^{59} +(0.249178 + 0.181038i) q^{61} +(-2.86886 + 2.08435i) q^{62} +(-0.809017 - 0.587785i) q^{64} +(-7.21486 + 8.32917i) q^{65} +(-1.42642 + 4.39008i) q^{67} +7.66578 q^{68} +(-4.75830 - 2.00995i) q^{70} +(-0.117646 - 0.362077i) q^{71} +(0.0608552 + 0.0442139i) q^{73} +3.95758 q^{74} +3.23607 q^{76} +(-6.40584 - 4.65411i) q^{77} +(4.72296 + 14.5358i) q^{79} +(1.46403 - 1.69015i) q^{80} +0.164135 q^{82} +(-0.403806 + 1.24279i) q^{83} +(-1.46403 + 17.0786i) q^{85} +(-5.42971 - 3.94492i) q^{86} +(2.77305 - 2.01474i) q^{88} +(3.58371 + 2.60372i) q^{89} +(-9.20985 + 6.69135i) q^{91} +(-1.38197 + 4.25325i) q^{92} +(-1.92807 + 5.93398i) q^{94} +(-0.618034 + 7.20963i) q^{95} +(-5.31876 - 16.3695i) q^{97} +(1.34600 + 0.977926i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{2} - 2 q^{4} + 4 q^{5} - 2 q^{7} - 2 q^{8}+O(q^{10}) $ 8 * q - 2 * q^2 - 2 * q^4 + 4 * q^5 - 2 * q^7 - 2 * q^8	$ 8 q - 2 q^{2} - 2 q^{4} + 4 q^{5} - 2 q^{7} - 2 q^{8} + 4 q^{10} + 5 q^{11} + 6 q^{13} - 2 q^{14} - 2 q^{16} + 2 q^{17} + 8 q^{19} - q^{20} + 20 q^{23} + 14 q^{25} - 14 q^{26} + 3 q^{28} + 18 q^{29} + 9 q^{31} + 8 q^{32} - 3 q^{34} + 4 q^{35} + 21 q^{37} - 12 q^{38} - 6 q^{40} - 2 q^{41} - 32 q^{43} - 20 q^{46} + 10 q^{47} + 22 q^{49} - 26 q^{50} + 6 q^{52} - 7 q^{53} - 40 q^{55} + 3 q^{56} + 18 q^{58} + 25 q^{59} + 10 q^{61} - 6 q^{62} - 2 q^{64} - 37 q^{65} - 2 q^{67} + 2 q^{68} - 11 q^{70} - 24 q^{73} + 26 q^{74} + 8 q^{76} - 35 q^{77} - 6 q^{79} - q^{80} - 42 q^{82} - 11 q^{83} + q^{85} - 2 q^{86} + 5 q^{88} - 9 q^{89} - 4 q^{91} - 20 q^{92} + 10 q^{94} + 4 q^{95} + q^{97} + 7 q^{98}+O(q^{100}) $ 8 * q - 2 * q^2 - 2 * q^4 + 4 * q^5 - 2 * q^7 - 2 * q^8 + 4 * q^10 + 5 * q^11 + 6 * q^13 - 2 * q^14 - 2 * q^16 + 2 * q^17 + 8 * q^19 - q^20 + 20 * q^23 + 14 * q^25 - 14 * q^26 + 3 * q^28 + 18 * q^29 + 9 * q^31 + 8 * q^32 - 3 * q^34 + 4 * q^35 + 21 * q^37 - 12 * q^38 - 6 * q^40 - 2 * q^41 - 32 * q^43 - 20 * q^46 + 10 * q^47 + 22 * q^49 - 26 * q^50 + 6 * q^52 - 7 * q^53 - 40 * q^55 + 3 * q^56 + 18 * q^58 + 25 * q^59 + 10 * q^61 - 6 * q^62 - 2 * q^64 - 37 * q^65 - 2 * q^67 + 2 * q^68 - 11 * q^70 - 24 * q^73 + 26 * q^74 + 8 * q^76 - 35 * q^77 - 6 * q^79 - q^80 - 42 * q^82 - 11 * q^83 + q^85 - 2 * q^86 + 5 * q^88 - 9 * q^89 - 4 * q^91 - 20 * q^92 + 10 * q^94 + 4 * q^95 + q^97 + 7 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−0.809017	−	0.587785i	−0.572061	−	0.415627i
$2$	−0.809017	−	0.587785i	−0.572061	−	0.415627i
$3$		0			0
$3$		0			0
$4$	0.309017	+	0.951057i	0.154508	+	0.475528i
$5$	−2.17787	+	0.506822i	−0.973974	+	0.226658i
$5$	−2.17787	+	0.506822i	−0.973974	+	0.226658i
$6$		0			0
$7$	−2.31003			−0.873110			−0.436555	−	0.899677i	$-0.643802\pi$
$7$	−2.31003			−0.873110			−0.436555	+	0.899677i	$0.643802\pi$
$8$	0.309017	−	0.951057i	0.109254	−	0.336249i
$9$		0			0
$10$	2.05984	+	0.870094i	0.651378	+	0.275148i
$11$	2.77305	+	2.01474i	0.836106	+	0.607467i	0.921280	−	0.388899i	$-0.127145\pi$
$11$	2.77305	+	2.01474i	0.836106	+	0.607467i	−0.0851740	+	0.996366i	$0.527145\pi$
$12$		0			0
$13$	3.98689	−	2.89665i	1.10576	−	0.803385i	0.123773	−	0.992311i	$-0.460501\pi$
$13$	3.98689	−	2.89665i	1.10576	−	0.803385i	0.981991	+	0.188926i	$0.0605005\pi$
$14$	1.86886	+	1.35780i	0.499473	+	0.362888i
$15$		0			0
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	2.36886	−	7.29059i	0.574532	−	1.76823i	−0.0632354	−	0.997999i	$-0.520142\pi$
$17$	2.36886	−	7.29059i	0.574532	−	1.76823i	0.637767	−	0.770229i	$-0.279858\pi$
$18$		0			0
$19$	1.00000	−	3.07768i	0.229416	−	0.706069i	−0.768398	−	0.639973i	$-0.778946\pi$
$19$	1.00000	−	3.07768i	0.229416	−	0.706069i	0.997813	−	0.0660962i	$-0.0210544\pi$
$20$	−1.15502	−	1.91466i	−0.258270	−	0.428132i
$21$		0			0
$22$	−1.05921	−	3.25992i	−0.225825	−	0.695017i
$23$	3.61803	+	2.62866i	0.754412	+	0.548113i	0.897191	−	0.441642i	$-0.145604\pi$
$23$	3.61803	+	2.62866i	0.754412	+	0.548113i	−0.142779	+	0.989755i	$0.545604\pi$
$24$		0			0
$25$	4.48626	−	2.20759i	0.897252	−	0.441518i
$26$	−4.92807			−0.966473
$27$		0			0
$28$	−0.713839	−	2.19697i	−0.134903	−	0.415189i
$29$	2.13279	+	6.56405i	0.396049	+	1.21891i	0.928142	+	0.372227i	$0.121406\pi$
$29$	2.13279	+	6.56405i	0.396049	+	1.21891i	−0.532093	+	0.846686i	$0.678594\pi$
$30$		0			0
$31$	1.09581	−	3.37254i	0.196812	−	0.605727i	−0.803138	−	0.595793i	$-0.796838\pi$
$31$	1.09581	−	3.37254i	0.196812	−	0.605727i	0.999951	−	0.00993372i	$-0.00316205\pi$
$32$	1.00000			0.176777
$33$		0			0
$34$	−6.20175	+	4.50583i	−1.06359	+	0.772744i
$35$	5.03096	−	1.17078i	0.850387	−	0.197897i
$36$		0			0
$37$	−3.20175	+	2.32620i	−0.526364	+	0.382426i	−0.818996	−	0.573799i	$-0.805469\pi$
$37$	−3.20175	+	2.32620i	−0.526364	+	0.382426i	0.292632	+	0.956225i	$0.405469\pi$
$38$	−2.61803	+	1.90211i	−0.424701	+	0.308563i
$39$		0			0
$40$	−0.190983	+	2.22790i	−0.0301971	+	0.352261i
$41$	−0.132788	+	0.0964762i	−0.0207380	+	0.0150670i	−0.598106	−	0.801417i	$-0.704080\pi$
$41$	−0.132788	+	0.0964762i	−0.0207380	+	0.0150670i	0.577368	+	0.816484i	$0.304080\pi$
$42$		0			0
$43$	6.71149			1.02349			0.511746	−	0.859137i	$-0.328999\pi$
$43$	6.71149			1.02349			0.511746	+	0.859137i	$0.328999\pi$
$44$	−1.05921	+	3.25992i	−0.159682	+	0.491451i
$45$		0			0
$46$	−1.38197	−	4.25325i	−0.203760	−	0.627108i
$47$	−1.92807	−	5.93398i	−0.281237	−	0.865560i	−0.987501	−	0.157611i	$-0.949621\pi$
$47$	−1.92807	−	5.93398i	−0.281237	−	0.865560i	0.706264	−	0.707949i	$-0.250379\pi$
$48$		0			0
$49$	−1.66375			−0.237678
$50$	−4.92705	−	0.850981i	−0.696790	−	0.120347i
$51$		0			0
$52$	3.98689	+	2.89665i	0.552882	+	0.401692i
$53$	−3.69971	−	11.3865i	−0.508195	−	1.56406i	−0.795333	−	0.606173i	$-0.792704\pi$
$53$	−3.69971	−	11.3865i	−0.508195	−	1.56406i	0.287138	−	0.957889i	$-0.407296\pi$
$54$		0			0
$55$	−7.06047	−	2.98240i	−0.952033	−	0.402147i
$56$	−0.713839	+	2.19697i	−0.0953908	+	0.293583i
$57$		0			0
$58$	2.13279	−	6.56405i	0.280049	−	0.861902i
$59$	8.62715	−	6.26799i	1.12316	−	0.816023i	0.138475	−	0.990366i	$-0.455780\pi$
$59$	8.62715	−	6.26799i	1.12316	−	0.816023i	0.984685	+	0.174343i	$0.0557801\pi$
$60$		0			0
$61$	0.249178	+	0.181038i	0.0319040	+	0.0231796i	0.603623	−	0.797270i	$-0.293723\pi$
$61$	0.249178	+	0.181038i	0.0319040	+	0.0231796i	−0.571719	+	0.820450i	$0.693723\pi$
$62$	−2.86886	+	2.08435i	−0.364345	+	0.264712i
$63$		0			0
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$	−7.21486	+	8.32917i	−0.894893	+	1.03311i
$66$		0			0
$67$	−1.42642	+	4.39008i	−0.174265	+	0.536333i	−0.999599	−	0.0283116i	$-0.990987\pi$
$67$	−1.42642	+	4.39008i	−0.174265	+	0.536333i	0.825334	+	0.564645i	$0.190987\pi$
$68$	7.66578			0.929612
$69$		0			0
$70$	−4.75830	−	2.00995i	−0.568725	−	0.240234i
$71$	−0.117646	−	0.362077i	−0.0139620	−	0.0429706i	0.943833	−	0.330423i	$-0.107192\pi$
$71$	−0.117646	−	0.362077i	−0.0139620	−	0.0429706i	−0.957795	+	0.287453i	$0.907192\pi$
$72$		0			0
$73$	0.0608552	+	0.0442139i	0.00712256	+	0.00517484i	0.591341	−	0.806422i	$-0.298599\pi$
$73$	0.0608552	+	0.0442139i	0.00712256	+	0.00517484i	−0.584218	+	0.811597i	$0.698599\pi$
$74$	3.95758			0.460059
$75$		0			0
$76$	3.23607			0.371202
$77$	−6.40584	−	4.65411i	−0.730013	−	0.530386i
$78$		0			0
$79$	4.72296	+	14.5358i	0.531374	+	1.63540i	0.751355	+	0.659898i	$0.229400\pi$
$79$	4.72296	+	14.5358i	0.531374	+	1.63540i	−0.219981	+	0.975504i	$0.570600\pi$
$80$	1.46403	−	1.69015i	0.163684	−	0.188964i
$81$		0			0
$82$	0.164135			0.0181257
$83$	−0.403806	+	1.24279i	−0.0443235	+	0.136414i	−0.970769	−	0.240014i	$-0.922848\pi$
$83$	−0.403806	+	1.24279i	−0.0443235	+	0.136414i	0.926446	+	0.376428i	$0.122848\pi$
$84$		0			0
$85$	−1.46403	+	17.0786i	−0.158797	+	1.85243i
$86$	−5.42971	−	3.94492i	−0.585501	−	0.425391i
$87$		0			0
$88$	2.77305	−	2.01474i	0.295608	−	0.214772i
$89$	3.58371	+	2.60372i	0.379873	+	0.275994i	0.761293	−	0.648408i	$-0.224565\pi$
$89$	3.58371	+	2.60372i	0.379873	+	0.275994i	−0.381420	+	0.924402i	$0.624565\pi$
$90$		0			0
$91$	−9.20985	+	6.69135i	−0.965454	+	0.701444i
$92$	−1.38197	+	4.25325i	−0.144080	+	0.443432i
$93$		0			0
$94$	−1.92807	+	5.93398i	−0.198865	+	0.612043i
$95$	−0.618034	+	7.20963i	−0.0634089	+	0.739692i
$96$		0			0
$97$	−5.31876	−	16.3695i	−0.540039	−	1.66207i	−0.732503	−	0.680764i	$-0.761648\pi$
$97$	−5.31876	−	16.3695i	−0.540039	−	1.66207i	0.192464	−	0.981304i	$-0.438352\pi$
$98$	1.34600	+	0.977926i	0.135966	+	0.0987854i
$99$		0			0
$100$	3.48587	+	3.58451i	0.348587	+	0.358451i
$101$	−5.70946			−0.568112			−0.284056	−	0.958808i	$-0.591680\pi$
$101$	−5.70946			−0.568112			−0.284056	+	0.958808i	$0.591680\pi$
$102$		0			0
$103$	5.36013	+	16.4968i	0.528149	+	1.62548i	0.758004	+	0.652250i	$0.226175\pi$
$103$	5.36013	+	16.4968i	0.528149	+	1.62548i	−0.229855	+	0.973225i	$0.573825\pi$
$104$	−1.52286	−	4.68687i	−0.149328	−	0.459585i
$105$		0			0
$106$	−3.69971	+	11.3865i	−0.359348	+	1.10596i
$107$	1.57154			0.151927			0.0759635	−	0.997111i	$-0.475797\pi$
$107$	1.57154			0.151927			0.0759635	+	0.997111i	$0.475797\pi$
$108$		0			0
$109$	10.3447	−	7.51584i	0.990840	−	0.719887i	0.0307348	−	0.999528i	$-0.490215\pi$
$109$	10.3447	−	7.51584i	0.990840	−	0.719887i	0.960105	+	0.279641i	$0.0902153\pi$
$110$	3.95903	+	6.56285i	0.377478	+	0.625743i
$111$		0			0
$112$	1.86886	−	1.35780i	0.176590	−	0.128300i
$113$	4.08536	−	2.96818i	0.384318	−	0.279223i	−0.378805	−	0.925476i	$-0.623665\pi$
$113$	4.08536	−	2.96818i	0.384318	−	0.279223i	0.763123	+	0.646253i	$0.223665\pi$
$114$		0			0
$115$	−9.21188	−	3.89118i	−0.859012	−	0.362854i
$116$	−5.58371	+	4.05680i	−0.518435	+	0.376665i
$117$		0			0
$118$	−10.6637			−0.981677
$119$	−5.47214	+	16.8415i	−0.501630	+	1.54386i
$120$		0			0
$121$	0.231449	+	0.712325i	0.0210408	+	0.0647569i
$122$	−0.0951775	−	0.292926i	−0.00861697	−	0.0265203i
$123$		0			0
$124$	3.54610			0.318449
$125$	−8.65165	+	7.08159i	−0.773827	+	0.633397i
$126$		0			0
$127$	−4.51076	−	3.27726i	−0.400265	−	0.290810i	0.369384	−	0.929277i	$-0.379569\pi$
$127$	−4.51076	−	3.27726i	−0.400265	−	0.290810i	−0.769649	+	0.638467i	$0.779569\pi$
$128$	0.309017	+	0.951057i	0.0273135	+	0.0840623i
$129$		0			0
$130$	10.7327	−	2.49765i	0.941320	−	0.219059i
$131$	−1.89856	+	5.84316i	−0.165878	+	0.510520i	−0.999100	−	0.0424190i	$-0.986494\pi$
$131$	−1.89856	+	5.84316i	−0.165878	+	0.510520i	0.833222	+	0.552939i	$0.186494\pi$
$132$		0			0
$133$	−2.31003	+	7.10955i	−0.200305	+	0.616476i
$134$	3.73442	−	2.71322i	0.322605	−	0.234386i
$135$		0			0
$136$	−6.20175	−	4.50583i	−0.531795	−	0.386372i
$137$	4.10657	−	2.98360i	0.350848	−	0.254906i	−0.398377	−	0.917222i	$-0.630426\pi$
$137$	4.10657	−	2.98360i	0.350848	−	0.254906i	0.749225	+	0.662316i	$0.230426\pi$
$138$		0			0
$139$	−4.80636	−	3.49202i	−0.407670	−	0.296189i	0.364988	−	0.931012i	$-0.381073\pi$
$139$	−4.80636	−	3.49202i	−0.407670	−	0.296189i	−0.772658	+	0.634823i	$0.781073\pi$
$140$	2.66813	+	4.42294i	0.225498	+	0.373806i
$141$		0			0
$142$	−0.117646	+	0.362077i	−0.00987262	+	0.0303848i
$143$	16.8918			1.41257
$144$		0			0
$145$	−7.97175	−	13.2147i	−0.662018	−	1.09742i
$146$	−0.0232446	−	0.0715396i	−0.00192374	−	0.00592066i
$147$		0			0
$148$	−3.20175	−	2.32620i	−0.263182	−	0.191213i
$149$	−9.88361			−0.809697			−0.404848	−	0.914384i	$-0.632676\pi$
$149$	−9.88361			−0.809697			−0.404848	+	0.914384i	$0.632676\pi$
$150$		0			0
$151$	−2.63424			−0.214371			−0.107186	−	0.994239i	$-0.534184\pi$
$151$	−2.63424			−0.214371			−0.107186	+	0.994239i	$0.534184\pi$
$152$	−2.61803	−	1.90211i	−0.212351	−	0.154282i
$153$		0			0
$154$	2.44681	+	7.53051i	0.197170	+	0.606826i
$155$	−0.677245	+	7.90035i	−0.0543976	+	0.634571i
$156$		0			0
$157$	−3.71822			−0.296746			−0.148373	−	0.988931i	$-0.547404\pi$
$157$	−3.71822			−0.296746			−0.148373	+	0.988931i	$0.547404\pi$
$158$	4.72296	−	14.5358i	0.375738	−	1.15640i
$159$		0			0
$160$	−2.17787	+	0.506822i	−0.172176	+	0.0400678i
$161$	−8.35778	−	6.07228i	−0.658685	−	0.478563i
$162$		0			0
$163$	11.3262	−	8.22899i	0.887139	−	0.644545i	−0.0479912	−	0.998848i	$-0.515282\pi$
$163$	11.3262	−	8.22899i	0.887139	−	0.644545i	0.935131	+	0.354303i	$0.115282\pi$
$164$	−0.132788	−	0.0964762i	−0.0103690	−	0.00753352i
$165$		0			0
$166$	1.05718	−	0.768085i	0.0820530	−	0.0596150i
$167$	−7.66452	+	23.5890i	−0.593099	+	1.82537i	−0.0291269	+	0.999576i	$0.509273\pi$
$167$	−7.66452	+	23.5890i	−0.593099	+	1.82537i	−0.563972	+	0.825794i	$0.690727\pi$
$168$		0			0
$169$	3.48752	−	10.7335i	0.268271	−	0.825652i
$170$	11.2230	−	12.9563i	0.860762	−	0.993704i
$171$		0			0
$172$	2.07397	+	6.38301i	0.158138	+	0.486700i
$173$	17.2347	+	12.5218i	1.31033	+	0.952012i	0.999999	+	0.00138481i	$0.000440800\pi$
$173$	17.2347	+	12.5218i	1.31033	+	0.952012i	0.310334	+	0.950628i	$0.399559\pi$
$174$		0			0
$175$	−10.3634	+	5.09961i	−0.783400	+	0.385494i
$176$	−3.42768			−0.258371
$177$		0			0
$178$	−1.36886	−	4.21291i	−0.102600	−	0.315771i
$179$	−2.94991	−	9.07888i	−0.220486	−	0.678587i	−0.998718	−	0.0506106i	$-0.983883\pi$
$179$	−2.94991	−	9.07888i	−0.220486	−	0.678587i	0.778232	−	0.627977i	$-0.216117\pi$
$180$		0			0
$181$	−0.222958	+	0.686194i	−0.0165723	+	0.0510044i	−0.959001	−	0.283404i	$-0.908536\pi$
$181$	−0.222958	+	0.686194i	−0.0165723	+	0.0510044i	0.942428	+	0.334408i	$0.108536\pi$
$182$	11.3840			0.843838
$183$		0			0
$184$	3.61803	−	2.62866i	0.266725	−	0.193787i
$185$	5.79402	−	6.68889i	0.425985	−	0.491777i
$186$		0			0
$187$	21.2576	−	15.4445i	1.55451	−	1.12942i
$188$	5.04775	−	3.66740i	0.368145	−	0.267473i
$189$		0			0
$190$	4.73771	−	5.46944i	0.343710	−	0.396795i
$191$	−1.00000	+	0.726543i	−0.0723575	+	0.0525708i	−0.623376	−	0.781922i	$-0.714239\pi$
$191$	−1.00000	+	0.726543i	−0.0723575	+	0.0525708i	0.551018	+	0.834493i	$0.314239\pi$
$192$		0			0
$193$	−26.9529			−1.94011			−0.970055	−	0.242884i	$-0.921907\pi$
$193$	−26.9529			−1.94011			−0.970055	+	0.242884i	$0.921907\pi$
$194$	−5.31876	+	16.3695i	−0.381865	+	1.17526i
$195$		0			0
$196$	−0.514126	−	1.58232i	−0.0367233	−	0.113023i
$197$	−7.85473	−	24.1744i	−0.559626	−	1.72235i	−0.683402	−	0.730043i	$-0.739500\pi$
$197$	−7.85473	−	24.1744i	−0.559626	−	1.72235i	0.123775	−	0.992310i	$-0.460500\pi$
$198$		0			0
$199$	21.7585			1.54242			0.771208	−	0.636583i	$-0.219653\pi$
$199$	21.7585			1.54242			0.771208	+	0.636583i	$0.219653\pi$
$200$	−0.713211	−	4.94887i	−0.0504317	−	0.349938i
$201$		0			0
$202$	4.61905	+	3.35594i	0.324995	+	0.236123i
$203$	−4.92681	−	15.1632i	−0.345794	−	1.06425i
$204$		0			0
$205$	0.240299	−	0.277413i	0.0167832	−	0.0193754i
$206$	5.36013	−	16.4968i	0.373458	−	1.14938i
$207$		0			0
$208$	−1.52286	+	4.68687i	−0.105591	+	0.324976i
$209$	8.97378	−	6.51983i	0.620729	−	0.450986i
$210$		0			0
$211$	17.9476	+	13.0397i	1.23556	+	0.897688i	0.997294	−	0.0735122i	$-0.0234208\pi$
$211$	17.9476	+	13.0397i	1.23556	+	0.897688i	0.238267	+	0.971200i	$0.423421\pi$
$212$	9.68598	−	7.03727i	0.665236	−	0.483322i
$213$		0			0
$214$	−1.27141	−	0.923731i	−0.0869116	−	0.0631449i
$215$	−14.6168	+	3.40153i	−0.996856	+	0.231983i
$216$		0			0
$217$	−2.53135	+	7.79069i	−0.171839	+	0.528866i
$218$	−12.7867			−0.866026
$219$		0			0
$220$	0.654628	−	7.63652i	0.0441350	−	0.514854i
$221$	−11.6739	−	35.9285i	−0.785270	−	2.41681i
$222$		0			0
$223$	−6.39108	−	4.64339i	−0.427979	−	0.310945i	0.352861	−	0.935676i	$-0.385209\pi$
$223$	−6.39108	−	4.64339i	−0.427979	−	0.310945i	−0.780840	+	0.624731i	$0.785209\pi$
$224$	−2.31003			−0.154346
$225$		0			0
$226$	−5.04978			−0.335906
$227$	−2.15502	−	1.56571i	−0.143033	−	0.103920i	0.513967	−	0.857810i	$-0.328175\pi$
$227$	−2.15502	−	1.56571i	−0.143033	−	0.103920i	−0.657001	+	0.753890i	$0.728175\pi$
$228$		0			0
$229$	−2.90685	−	8.94638i	−0.192090	−	0.591193i	−0.999998	−	0.00188454i	$-0.999400\pi$
$229$	−2.90685	−	8.94638i	−0.192090	−	0.591193i	0.807908	−	0.589309i	$-0.200600\pi$
$230$	5.16539	+	8.56264i	0.340596	+	0.564603i
$231$		0			0
$232$	6.90185			0.453128
$233$	−4.56935	+	14.0630i	−0.299348	+	0.921298i	0.682378	+	0.730999i	$0.260946\pi$
$233$	−4.56935	+	14.0630i	−0.299348	+	0.921298i	−0.981726	+	0.190299i	$0.939054\pi$
$234$		0			0
$235$	7.20656	+	11.9463i	0.470104	+	0.779289i
$236$	8.62715	+	6.26799i	0.561580	+	0.408012i
$237$		0			0
$238$	14.3262	−	10.4086i	0.928632	−	0.674691i
$239$	−10.2098	−	7.41789i	−0.660420	−	0.479823i	0.206385	−	0.978471i	$-0.433830\pi$
$239$	−10.2098	−	7.41789i	−0.660420	−	0.479823i	−0.866805	+	0.498648i	$0.833830\pi$
$240$		0			0
$241$	13.9247	−	10.1169i	0.896969	−	0.651686i	−0.0407167	−	0.999171i	$-0.512964\pi$
$241$	13.9247	−	10.1169i	0.896969	−	0.651686i	0.937686	+	0.347485i	$0.112964\pi$
$242$	0.231449	−	0.712325i	0.0148781	−	0.0457900i
$243$		0			0
$244$	−0.0951775	+	0.292926i	−0.00609312	+	0.0187527i
$245$	3.62343	−	0.843224i	0.231492	−	0.0538716i
$246$		0			0
$247$	−4.92807	−	15.1670i	−0.313565	−	0.965055i
$248$	−2.86886	−	2.08435i	−0.182173	−	0.132356i
$249$		0			0
$250$	11.1618	−	0.643811i	0.705933	−	0.0407182i
$251$	18.1097			1.14307			0.571536	−	0.820577i	$-0.306348\pi$
$251$	18.1097			1.14307			0.571536	+	0.820577i	$0.306348\pi$
$252$		0			0
$253$	4.73694	+	14.5788i	0.297809	+	0.916561i
$254$	1.72296	+	5.30272i	0.108108	+	0.332722i
$255$		0			0
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	1.07193			0.0668653			0.0334327	−	0.999441i	$-0.489356\pi$
$257$	1.07193			0.0668653			0.0334327	+	0.999441i	$0.489356\pi$
$258$		0			0
$259$	7.39614	−	5.37361i	0.459574	−	0.333900i
$260$	−10.1510	−	4.28788i	−0.629540	−	0.265923i
$261$		0			0
$262$	4.97049	−	3.61127i	0.307078	−	0.223105i
$263$	−19.8756	+	14.4405i	−1.22558	+	0.890439i	−0.996551	−	0.0829801i	$-0.973556\pi$
$263$	−19.8756	+	14.4405i	−1.22558	+	0.890439i	−0.229032	+	0.973419i	$0.573556\pi$
$264$		0			0
$265$	13.8285	+	22.9234i	0.849476	+	1.40817i
$266$	6.04775	−	4.39394i	0.370811	−	0.269410i
$267$		0			0
$268$	−4.61600			−0.281967
$269$	6.23670	−	19.1946i	0.380258	−	1.17031i	−0.559604	−	0.828760i	$-0.689047\pi$
$269$	6.23670	−	19.1946i	0.380258	−	1.17031i	0.939862	−	0.341554i	$-0.110953\pi$
$270$		0			0
$271$	−1.55174	−	4.77575i	−0.0942613	−	0.290106i	0.892799	−	0.450455i	$-0.148738\pi$
$271$	−1.55174	−	4.77575i	−0.0942613	−	0.290106i	−0.987060	+	0.160349i	$0.948738\pi$
$272$	2.36886	+	7.29059i	0.143633	+	0.442057i
$273$		0			0
$274$	−5.07600			−0.306652
$275$	16.8883	+	2.91689i	1.01841	+	0.175895i
$276$		0			0
$277$	7.50975	+	5.45615i	0.451217	+	0.327828i	0.790076	−	0.613009i	$-0.210041\pi$
$277$	7.50975	+	5.45615i	0.451217	+	0.327828i	−0.338859	+	0.940837i	$0.610041\pi$
$278$	1.83586	+	5.65021i	0.110108	+	0.338877i
$279$		0			0
$280$	0.441177	−	5.14652i	0.0263654	−	0.307563i
$281$	−8.45092	+	26.0093i	−0.504140	+	1.55158i	0.298072	+	0.954543i	$0.403656\pi$
$281$	−8.45092	+	26.0093i	−0.504140	+	1.55158i	−0.802212	+	0.597039i	$0.796344\pi$
$282$		0			0
$283$	4.33829	−	13.3519i	0.257884	−	0.793686i	−0.735363	−	0.677673i	$-0.762988\pi$
$283$	4.33829	−	13.3519i	0.257884	−	0.793686i	0.993248	−	0.116013i	$-0.0370115\pi$
$284$	0.308001	−	0.223776i	0.0182765	−	0.0132786i
$285$		0			0
$286$	−13.6658	−	9.92877i	−0.808074	−	0.587100i
$287$	0.306745	−	0.222863i	0.0181066	−	0.0131552i
$288$		0			0
$289$	−33.7879	−	24.5484i	−1.98752	−	1.44402i
$290$	−1.31814	+	15.3766i	−0.0774036	+	0.902945i
$291$		0			0
$292$	−0.0232446	+	0.0715396i	−0.00136029	+	0.00418654i
$293$	1.70695			0.0997210			0.0498605	−	0.998756i	$-0.484122\pi$
$293$	1.70695			0.0997210			0.0498605	+	0.998756i	$0.484122\pi$
$294$		0			0
$295$	−15.6121	+	18.0233i	−0.908971	+	1.04936i
$296$	1.22296	+	3.76388i	0.0710830	+	0.218771i
$297$		0			0
$298$	7.99601	+	5.80944i	0.463196	+	0.336532i
$299$	22.0390			1.27455
$300$		0			0
$301$	−15.5038			−0.893622
$302$	2.13114	+	1.54837i	0.122634	+	0.0890985i
$303$		0			0
$304$	1.00000	+	3.07768i	0.0573539	+	0.176517i
$305$	−0.634432	−	0.267990i	−0.0363275	−	0.0153450i
$306$		0			0
$307$	−17.5669			−1.00259			−0.501297	−	0.865276i	$-0.667143\pi$
$307$	−17.5669			−1.00259			−0.501297	+	0.865276i	$0.667143\pi$
$308$	2.44681	−	7.53051i	0.139420	−	0.429091i
$309$		0			0
$310$	5.19161	−	5.99344i	0.294864	−	0.340405i
$311$	6.78546	+	4.92992i	0.384768	+	0.279550i	0.763308	−	0.646035i	$-0.223574\pi$
$311$	6.78546	+	4.92992i	0.384768	+	0.279550i	−0.378540	+	0.925585i	$0.623574\pi$
$312$		0			0
$313$	−20.3407	+	14.7784i	−1.14972	+	0.835323i	−0.988444	−	0.151586i	$-0.951562\pi$
$313$	−20.3407	+	14.7784i	−1.14972	+	0.835323i	−0.161279	+	0.986909i	$0.551562\pi$
$314$	3.00810	+	2.18551i	0.169757	+	0.123336i
$315$		0			0
$316$	−12.3649	+	8.98360i	−0.695578	+	0.505367i
$317$	−1.83857	+	5.65854i	−0.103264	+	0.317815i	−0.989319	−	0.145765i	$-0.953436\pi$
$317$	−1.83857	+	5.65854i	−0.103264	+	0.317815i	0.886055	+	0.463581i	$0.153436\pi$
$318$		0			0
$319$	−7.31051	+	22.4994i	−0.409310	+	1.25973i
$320$	2.05984	+	0.870094i	0.115149	+	0.0486397i
$321$		0			0
$322$	3.19239	+	9.82516i	0.177905	+	0.547535i
$323$	−20.0693	−	14.5812i	−1.11668	−	0.811318i
$324$		0			0
$325$	11.4916	−	21.7965i	0.637441	−	1.20905i
$326$	−14.0000			−0.775388
$327$		0			0
$328$	0.0507205	+	0.156102i	0.00280057	+	0.00861928i
$329$	4.45390	+	13.7077i	0.245551	+	0.755729i
$330$		0			0
$331$	7.47339	−	23.0007i	0.410775	−	1.26423i	−0.505201	−	0.863002i	$-0.668582\pi$
$331$	7.47339	−	23.0007i	0.410775	−	1.26423i	0.915976	−	0.401233i	$-0.131418\pi$
$332$	−1.30674			−0.0717169
$333$		0			0
$334$	20.0660	−	14.5788i	1.09796	−	0.797716i
$335$	0.881578	−	10.2840i	0.0481657	−	0.561874i
$336$		0			0
$337$	9.18218	−	6.67124i	0.500185	−	0.363406i	−0.308903	−	0.951094i	$-0.599962\pi$
$337$	9.18218	−	6.67124i	0.500185	−	0.363406i	0.809088	+	0.587688i	$0.199962\pi$
$338$	−9.13044	+	6.63365i	−0.496631	+	0.360823i
$339$		0			0
$340$	−16.6951	+	3.88519i	−0.905419	+	0.210704i
$341$	9.83352	−	7.14447i	0.532515	−	0.386895i
$342$		0			0
$343$	20.0135			1.08063
$344$	2.07397	−	6.38301i	0.111821	−	0.344149i
$345$		0			0
$346$	−6.58308	−	20.2606i	−0.353909	−	1.08922i
$347$	3.56086	+	10.9592i	0.191157	+	0.588320i	1.00000		0.000295559i	$9.40792e-5\pi$
$347$	3.56086	+	10.9592i	0.191157	+	0.588320i	−0.808843	+	0.588024i	$0.799906\pi$
$348$		0			0
$349$	−1.81216			−0.0970025			−0.0485013	−	0.998823i	$-0.515444\pi$
$349$	−1.81216			−0.0970025			−0.0485013	+	0.998823i	$0.515444\pi$
$350$	11.3817	+	1.96579i	0.608375	+	0.105076i
$351$		0			0
$352$	2.77305	+	2.01474i	0.147804	+	0.107386i
$353$	0.939338	+	2.89099i	0.0499959	+	0.153872i	0.972938	−	0.231068i	$-0.0742221\pi$
$353$	0.939338	+	2.89099i	0.0499959	+	0.153872i	−0.922942	+	0.384940i	$0.874222\pi$
$354$		0			0
$355$	0.439726	+	0.728932i	0.0233383	+	0.0386877i
$356$	−1.36886	+	4.21291i	−0.0725492	+	0.223284i
$357$		0			0
$358$	−2.94991	+	9.07888i	−0.155907	+	0.479834i
$359$	4.93136	−	3.58284i	0.260267	−	0.189095i	−0.449998	−	0.893030i	$-0.648575\pi$
$359$	4.93136	−	3.58284i	0.260267	−	0.189095i	0.710265	+	0.703935i	$0.248575\pi$
$360$		0			0
$361$	6.89919	+	5.01255i	0.363115	+	0.263819i
$362$	0.583712	−	0.424091i	0.0306792	−	0.0222897i
$363$		0			0
$364$	−9.20985	−	6.69135i	−0.482727	−	0.350722i
$365$	−0.154943	−	0.0654495i	−0.00811011	−	0.00342578i
$366$		0			0
$367$	−8.14152	+	25.0570i	−0.424984	+	1.30797i	0.478026	+	0.878346i	$0.341352\pi$
$367$	−8.14152	+	25.0570i	−0.424984	+	1.30797i	−0.903010	+	0.429620i	$0.858648\pi$
$368$	−4.47214			−0.233126
$369$		0			0
$370$	−8.61910	+	2.00579i	−0.448085	+	0.104276i
$371$	8.54646	+	26.3033i	0.443710	+	1.36560i
$372$		0			0
$373$	−11.4742	−	8.33647i	−0.594110	−	0.431646i	0.249673	−	0.968330i	$-0.419677\pi$
$373$	−11.4742	−	8.33647i	−0.594110	−	0.431646i	−0.843783	+	0.536684i	$0.819677\pi$
$374$	−26.2758			−1.35869
$375$		0			0
$376$	−6.23936			−0.321770
$377$	27.5169	+	19.9922i	1.41719	+	1.02965i
$378$		0			0
$379$	9.82663	+	30.2432i	0.504760	+	1.55349i	0.801174	+	0.598432i	$0.204209\pi$
$379$	9.82663	+	30.2432i	0.504760	+	1.55349i	−0.296414	+	0.955060i	$0.595791\pi$
$380$	−7.04775	+	1.64011i	−0.361542	+	0.0841360i
$381$		0			0
$382$	1.23607			0.0632427
$383$	−7.16336	+	22.0466i	−0.366031	+	1.12653i	0.583303	+	0.812255i	$0.301760\pi$
$383$	−7.16336	+	22.0466i	−0.366031	+	1.12653i	−0.949333	+	0.314271i	$0.898240\pi$
$384$		0			0
$385$	16.3099	+	6.88945i	0.831230	+	0.351119i
$386$	21.8053	+	15.8425i	1.10986	+	0.806362i
$387$		0			0
$388$	13.9247	−	10.1169i	0.706920	−	0.513607i
$389$	−10.3323	−	7.50683i	−0.523866	−	0.380611i	0.294192	−	0.955746i	$-0.404949\pi$
$389$	−10.3323	−	7.50683i	−0.523866	−	0.380611i	−0.818058	+	0.575135i	$0.804949\pi$
$390$		0			0
$391$	27.7350	−	20.1507i	1.40262	−	1.01906i
$392$	−0.514126	+	1.58232i	−0.0259673	+	0.0799191i
$393$		0			0
$394$	−7.85473	+	24.1744i	−0.395716	+	1.21789i
$395$	−17.6531	−	29.2634i	−0.888222	−	1.47240i
$396$		0			0
$397$	5.21110	+	16.0381i	0.261538	+	0.804931i	0.992471	+	0.122481i	$0.0390852\pi$
$397$	5.21110	+	16.0381i	0.261538	+	0.804931i	−0.730933	+	0.682449i	$0.760915\pi$
$398$	−17.6030	−	12.7893i	−0.882357	−	0.641070i
$399$		0			0
$400$	−2.33187	+	4.42294i	−0.116594	+	0.221147i
$401$	−2.02027			−0.100887			−0.0504437	−	0.998727i	$-0.516064\pi$
$401$	−2.02027			−0.100887			−0.0504437	+	0.998727i	$0.516064\pi$
$402$		0			0
$403$	−5.40020	−	16.6201i	−0.269003	−	0.827907i
$404$	−1.76432	−	5.43002i	−0.0877782	−	0.270154i
$405$		0			0
$406$	−4.92681	+	15.1632i	−0.244514	+	0.752535i
$407$	−13.5653			−0.672407
$408$		0			0
$409$	−3.07827	+	2.23649i	−0.152211	+	0.110587i	−0.661284	−	0.750136i	$-0.729988\pi$
$409$	−3.07827	+	2.23649i	−0.152211	+	0.110587i	0.509073	+	0.860723i	$0.329988\pi$
$410$	−0.357465	+	0.0831873i	−0.0176540	+	0.00410833i
$411$		0			0
$412$	−14.0330	+	10.1956i	−0.691356	+	0.502299i
$413$	−19.9290	+	14.4793i	−0.980642	+	0.712478i
$414$		0			0
$415$	0.249566	−	2.91129i	0.0122507	−	0.142910i
$416$	3.98689	−	2.89665i	0.195473	−	0.142020i
$417$		0			0
$418$	−11.0922			−0.542537
$419$	2.33265	−	7.17916i	0.113957	−	0.350725i	−0.877771	−	0.479081i	$-0.840970\pi$
$419$	2.33265	−	7.17916i	0.113957	−	0.350725i	0.991728	+	0.128356i	$0.0409700\pi$
$420$		0			0
$421$	4.73955	+	14.5868i	0.230992	+	0.710919i	0.997628	+	0.0688374i	$0.0219290\pi$
$421$	4.73955	+	14.5868i	0.230992	+	0.710919i	−0.766636	+	0.642082i	$0.778071\pi$
$422$	−6.85536	−	21.0986i	−0.333714	−	1.02706i
$423$		0			0
$424$	−11.9725			−0.581437
$425$	−5.46732	−	37.9370i	−0.265204	−	1.84021i
$426$		0			0
$427$	−0.575609	−	0.418205i	−0.0278557	−	0.0202383i
$428$	0.485634	+	1.49463i	0.0234740	+	0.0722456i
$429$		0			0
$430$	13.8246	+	5.83963i	0.666681	+	0.281612i
$431$	−2.89981	+	8.92471i	−0.139679	+	0.429888i	−0.996288	−	0.0860773i	$-0.972567\pi$
$431$	−2.89981	+	8.92471i	−0.139679	+	0.429888i	0.856609	+	0.515966i	$0.172567\pi$
$432$		0			0
$433$	−9.34803	+	28.7703i	−0.449238	+	1.38261i	0.428531	+	0.903527i	$0.359031\pi$
$433$	−9.34803	+	28.7703i	−0.449238	+	1.38261i	−0.877769	+	0.479085i	$0.840969\pi$
$434$	6.62715	−	4.81491i	0.318114	−	0.231123i
$435$		0			0
$436$	10.3447	+	7.51584i	0.495420	+	0.359944i
$437$	11.7082	−	8.50651i	0.560079	−	0.406921i
$438$		0			0
$439$	−30.8108	−	22.3853i	−1.47052	−	1.06839i	−0.980463	−	0.196703i	$-0.936977\pi$
$439$	−30.8108	−	22.3853i	−1.47052	−	1.06839i	−0.490055	−	0.871691i	$-0.663023\pi$
$440$	−5.01824	+	5.79329i	−0.239235	+	0.276184i
$441$		0			0
$442$	−11.6739	+	35.9285i	−0.555270	+	1.70895i
$443$	1.53797			0.0730713			0.0365356	−	0.999332i	$-0.488368\pi$
$443$	1.53797			0.0730713			0.0365356	+	0.999332i	$0.488368\pi$
$444$		0			0
$445$	−9.12449	−	3.85426i	−0.432542	−	0.182710i
$446$	2.44118	+	7.51317i	0.115593	+	0.355759i
$447$		0			0
$448$	1.86886	+	1.35780i	0.0882951	+	0.0641502i
$449$	−14.0449			−0.662822			−0.331411	−	0.943487i	$-0.607525\pi$
$449$	−14.0449			−0.662822			−0.331411	+	0.943487i	$0.607525\pi$
$450$		0			0
$451$	−0.562602			−0.0264919
$452$	4.08536	+	2.96818i	0.192159	+	0.139612i
$453$		0			0
$454$	0.823143	+	2.53337i	0.0386320	+	0.118897i
$455$	16.6666	−	19.2407i	0.781340	−	0.902016i
$456$		0			0
$457$	14.5748			0.681782			0.340891	−	0.940103i	$-0.389271\pi$
$457$	14.5748			0.681782			0.340891	+	0.940103i	$0.389271\pi$
$458$	−2.90685	+	8.94638i	−0.135828	+	0.418037i
$459$		0			0
$460$	0.854102	−	9.96346i	0.0398227	−	0.464549i
$461$	14.6187	+	10.6211i	0.680862	+	0.494675i	0.873644	−	0.486566i	$-0.161751\pi$
$461$	14.6187	+	10.6211i	0.680862	+	0.494675i	−0.192781	+	0.981242i	$0.561751\pi$
$462$		0			0
$463$	−16.6322	+	12.0840i	−0.772964	+	0.561591i	−0.902859	−	0.429936i	$-0.858536\pi$
$463$	−16.6322	+	12.0840i	−0.772964	+	0.561591i	0.129895	+	0.991528i	$0.458536\pi$
$464$	−5.58371	−	4.05680i	−0.259217	−	0.188332i
$465$		0			0
$466$	11.9627	−	8.69141i	0.554161	−	0.402622i
$467$	−7.78691	+	23.9656i	−0.360335	+	1.10900i	0.592516	+	0.805559i	$0.298135\pi$
$467$	−7.78691	+	23.9656i	−0.360335	+	1.10900i	−0.952851	+	0.303439i	$0.901865\pi$
$468$		0			0
$469$	3.29508	−	10.1412i	0.152153	−	0.468278i
$470$	1.19161	−	13.9006i	0.0549649	−	0.641189i
$471$		0			0
$472$	−3.29528	−	10.1418i	−0.151678	−	0.466815i
$473$	18.6113	+	13.5219i	0.855749	+	0.621738i
$474$		0			0
$475$	−2.30800	−	16.0149i	−0.105898	−	0.734813i
$476$	−17.7082			−0.811654
$477$		0			0
$478$	3.89981	+	12.0024i	0.178373	+	0.548977i
$479$	−0.809645	−	2.49183i	−0.0369936	−	0.113855i	0.930854	−	0.365390i	$-0.119064\pi$
$479$	−0.809645	−	2.49183i	−0.0369936	−	0.113855i	−0.967848	+	0.251536i	$0.919064\pi$
$480$		0			0
$481$	−6.02682	+	18.5486i	−0.274799	+	0.845745i
$482$	−17.2119			−0.783980
$483$		0			0
$484$	−0.605940	+	0.440241i	−0.0275427	+	0.0200110i
$485$	19.8800	+	32.9550i	0.902705	+	1.49641i
$486$		0			0
$487$	−20.3452	+	14.7817i	−0.921930	+	0.669821i	−0.944004	−	0.329935i	$-0.892973\pi$
$487$	−20.3452	+	14.7817i	−0.921930	+	0.669821i	0.0220737	+	0.999756i	$0.492973\pi$
$488$	0.249178	−	0.181038i	0.0112798	−	0.00819522i
$489$		0			0
$490$	−3.42705	−	1.44762i	−0.154818	−	0.0653966i
$491$	25.5824	−	18.5867i	1.15452	−	0.838805i	0.165442	−	0.986220i	$-0.447095\pi$
$491$	25.5824	−	18.5867i	1.15452	−	0.838805i	0.989075	+	0.147414i	$0.0470950\pi$
$492$		0			0
$493$	52.9080			2.38286
$494$	−4.92807	+	15.1670i	−0.221724	+	0.682397i
$495$		0			0
$496$	1.09581	+	3.37254i	0.0492031	+	0.151432i
$497$	0.271766	+	0.836409i	0.0121904	+	0.0375181i
$498$		0			0
$499$	−28.6266			−1.28150			−0.640752	−	0.767748i	$-0.721377\pi$
$499$	−28.6266			−1.28150			−0.640752	+	0.767748i	$0.721377\pi$
$500$	−9.40850	−	6.03988i	−0.420761	−	0.270112i
$501$		0			0
$502$	−14.6510	−	10.6446i	−0.653907	−	0.475091i
$503$	−1.48960	−	4.58451i	−0.0664178	−	0.204413i	0.912340	−	0.409434i	$-0.134274\pi$
$503$	−1.48960	−	4.58451i	−0.0664178	−	0.204413i	−0.978758	+	0.205021i	$0.934274\pi$
$504$		0			0
$505$	12.4345	−	2.89368i	0.553327	−	0.128767i
$506$	4.73694	−	14.5788i	0.210582	−	0.648106i
$507$		0			0
$508$	1.72296	−	5.30272i	0.0764439	−	0.235270i
$509$	−10.8604	+	7.89057i	−0.481380	+	0.349743i	−0.801860	−	0.597512i	$-0.796156\pi$
$509$	−10.8604	+	7.89057i	−0.481380	+	0.349743i	0.320479	+	0.947255i	$0.396156\pi$
$510$		0			0
$511$	−0.140578	−	0.102136i	−0.00621878	−	0.00451821i
$512$	−0.809017	+	0.587785i	−0.0357538	+	0.0259767i
$513$		0			0
$514$	−0.867212	−	0.630066i	−0.0382511	−	0.0277910i
$515$	−20.0346	−	33.2112i	−0.882830	−	1.46346i
$516$		0			0
$517$	6.60880	−	20.3398i	0.290654	−	0.894543i
$518$	−9.14213			−0.401682
$519$		0			0
$520$	5.69200	+	9.43559i	0.249611	+	0.413778i
$521$	1.15710	+	3.56117i	0.0506933	+	0.156018i	0.973198	−	0.229967i	$-0.0738618\pi$
$521$	1.15710	+	3.56117i	0.0506933	+	0.156018i	−0.922505	+	0.385985i	$0.873862\pi$
$522$		0			0
$523$	10.5938	+	7.69688i	0.463237	+	0.336561i	0.794800	−	0.606872i	$-0.207576\pi$
$523$	10.5938	+	7.69688i	0.463237	+	0.336561i	−0.331563	+	0.943433i	$0.607576\pi$
$524$	−6.14387			−0.268396
$525$		0			0
$526$	24.5676			1.07120
$527$	−21.9920	−	15.9781i	−0.957987	−	0.696019i
$528$		0			0
$529$	−0.927051	−	2.85317i	−0.0403066	−	0.124051i
$530$	2.28655	−	26.6736i	0.0993213	−	1.15863i
$531$		0			0
$532$	−7.47542			−0.324101
$533$	−0.249954	+	0.769280i	−0.0108267	+	0.0333212i
$534$		0			0
$535$	−3.42262	+	0.796494i	−0.147973	+	0.0344354i
$536$	3.73442	+	2.71322i	0.161303	+	0.117193i
$537$		0			0
$538$	−16.3279	+	11.8629i	−0.703945	+	0.511446i
$539$	−4.61365	−	3.35202i	−0.198724	−	0.144382i
$540$		0			0
$541$	−17.0349	+	12.3766i	−0.732390	+	0.532112i	−0.890319	−	0.455338i	$-0.849518\pi$
$541$	−17.0349	+	12.3766i	−0.732390	+	0.532112i	0.157929	+	0.987450i	$0.449518\pi$
$542$	−1.55174	+	4.77575i	−0.0666528	+	0.205136i
$543$		0			0
$544$	2.36886	−	7.29059i	0.101564	−	0.312581i
$545$	−18.7202	+	21.6115i	−0.801884	+	0.925733i
$546$		0			0
$547$	−4.24608	−	13.0681i	−0.181549	−	0.558752i	0.818322	−	0.574759i	$-0.194904\pi$
$547$	−4.24608	−	13.0681i	−0.181549	−	0.558752i	−0.999872	+	0.0160078i	$0.994904\pi$
$548$	4.10657	+	2.98360i	0.175424	+	0.127453i
$549$		0			0
$550$	−11.9485	−	12.2865i	−0.509484	−	0.523900i
$551$	22.3348			0.951496
$552$		0			0
$553$	−10.9102	−	33.5781i	−0.463948	−	1.42789i
$554$	−2.86847	−	8.82824i	−0.121870	−	0.375076i
$555$		0			0
$556$	1.83586	−	5.65021i	0.0778580	−	0.239622i
$557$	16.0148			0.678569			0.339284	−	0.940684i	$-0.389815\pi$
$557$	16.0148			0.678569			0.339284	+	0.940684i	$0.389815\pi$
$558$		0			0
$559$	26.7580	−	19.4408i	1.13174	−	0.822259i
$560$	−3.38197	+	3.90430i	−0.142914	+	0.164987i
$561$		0			0
$562$	22.1248	−	16.0746i	0.933279	−	0.678067i
$563$	24.9328	−	18.1147i	1.05079	−	0.763445i	0.0784295	−	0.996920i	$-0.475009\pi$
$563$	24.9328	−	18.1147i	1.05079	−	0.763445i	0.972363	+	0.233474i	$0.0750094\pi$
$564$		0			0
$565$	−7.39304	+	8.53488i	−0.311028	+	0.359065i
$566$	−11.3578	+	8.25191i	−0.477403	+	0.346854i
$567$		0			0
$568$	−0.380710			−0.0159742
$569$	11.0326	−	33.9549i	0.462511	−	1.42346i	−0.399576	−	0.916700i	$-0.630842\pi$
$569$	11.0326	−	33.9549i	0.462511	−	1.42346i	0.862086	−	0.506762i	$-0.169158\pi$
$570$		0			0
$571$	9.21188	+	28.3513i	0.385505	+	1.18646i	0.936113	+	0.351699i	$0.114396\pi$
$571$	9.21188	+	28.3513i	0.385505	+	1.18646i	−0.550608	+	0.834764i	$0.685604\pi$
$572$	5.21986	+	16.0651i	0.218253	+	0.671715i
$573$		0			0
$574$	−0.379157			−0.0158257
$575$	22.0344	+	3.80570i	0.918900	+	0.158709i
$576$		0			0
$577$	11.6772	+	8.48402i	0.486130	+	0.353194i	0.803694	−	0.595043i	$-0.202865\pi$
$577$	11.6772	+	8.48402i	0.486130	+	0.353194i	−0.317564	+	0.948237i	$0.602865\pi$
$578$	12.9058	+	39.7201i	0.536812	+	1.65214i
$579$		0			0
$580$	10.1045	−	11.6652i	0.419568	−	0.484369i
$581$	0.932806	−	2.87088i	0.0386993	−	0.119104i
$582$		0			0
$583$	12.6814	−	39.0294i	0.525211	−	1.61643i
$584$	0.0608552	−	0.0442139i	0.00251821	−	0.00182958i
$585$		0			0
$586$	−1.38095	−	1.00332i	−0.0570465	−	0.0414467i
$587$	8.65134	−	6.28557i	0.357079	−	0.259433i	−0.394754	−	0.918787i	$-0.629170\pi$
$587$	8.65134	−	6.28557i	0.357079	−	0.259433i	0.751833	+	0.659354i	$0.229170\pi$
$588$		0			0
$589$	−9.28381	−	6.74509i	−0.382533	−	0.277926i
$590$	23.2243	−	5.40463i	0.956129	−	0.222505i
$591$		0			0
$592$	1.22296	−	3.76388i	0.0502633	−	0.154694i
$593$	−1.89856			−0.0779645			−0.0389822	−	0.999240i	$-0.512412\pi$
$593$	−1.89856			−0.0779645			−0.0389822	+	0.999240i	$0.512412\pi$
$594$		0			0
$595$	3.38197	−	39.4521i	0.138647	−	1.61738i
$596$	−3.05420	−	9.39987i	−0.125105	−	0.385034i
$597$		0			0
$598$	−17.8299	−	12.9542i	−0.729119	−	0.529736i
$599$	8.35410			0.341339			0.170670	−	0.985328i	$-0.445407\pi$
$599$	8.35410			0.341339			0.170670	+	0.985328i	$0.445407\pi$
$600$		0			0
$601$	2.38816			0.0974149			0.0487075	−	0.998813i	$-0.484490\pi$
$601$	2.38816			0.0974149			0.0487075	+	0.998813i	$0.484490\pi$
$602$	12.5428	+	9.11289i	0.511207	+	0.371414i
$603$		0			0
$604$	−0.814025	−	2.50531i	−0.0331222	−	0.101940i
$605$	−0.865088	−	1.43405i	−0.0351708	−	0.0583025i
$606$		0			0
$607$	−16.3129			−0.662122			−0.331061	−	0.943609i	$-0.607407\pi$
$607$	−16.3129			−0.662122			−0.331061	+	0.943609i	$0.607407\pi$
$608$	1.00000	−	3.07768i	0.0405554	−	0.124817i
$609$		0			0
$610$	0.355746	+	0.589718i	0.0144037	+	0.0238770i
$611$	−24.8756	−	18.0732i	−1.00636	−	0.731163i
$612$		0			0
$613$	−11.4823	+	8.34236i	−0.463765	+	0.336945i	−0.795006	−	0.606601i	$-0.792532\pi$
$613$	−11.4823	+	8.34236i	−0.463765	+	0.336945i	0.331242	+	0.943546i	$0.392532\pi$
$614$	14.2119	+	10.3255i	0.573545	+	0.416705i
$615$		0			0
$616$	−6.40584	+	4.65411i	−0.258099	+	0.187520i
$617$	−9.01449	+	27.7437i	−0.362910	+	1.11692i	0.588370	+	0.808592i	$0.299770\pi$
$617$	−9.01449	+	27.7437i	−0.362910	+	1.11692i	−0.951280	+	0.308329i	$0.900230\pi$
$618$		0			0
$619$	−8.16617	+	25.1329i	−0.328226	+	1.01018i	0.641737	+	0.766924i	$0.278214\pi$
$619$	−8.16617	+	25.1329i	−0.328226	+	1.01018i	−0.969963	+	0.243251i	$0.921786\pi$
$620$	−7.72296	+	1.79724i	−0.310161	+	0.0721790i
$621$		0			0
$622$	−2.59181	−	7.97678i	−0.103922	−	0.319840i
$623$	−8.27849	−	6.01468i	−0.331671	−	0.240973i
$624$		0			0
$625$	15.2531	−	19.8077i	0.610124	−	0.792306i
$626$	25.1425			1.00489
$627$		0			0
$628$	−1.14899	−	3.53624i	−0.0458498	−	0.141111i
$629$	9.37493	+	28.8531i	0.373803	+	1.15045i
$630$		0			0
$631$	1.06192	−	3.26825i	0.0422743	−	0.130107i	−0.927692	−	0.373347i	$-0.878210\pi$
$631$	1.06192	−	3.26825i	0.0422743	−	0.130107i	0.969966	+	0.243240i	$0.0782102\pi$
$632$	15.2838			0.607957
$633$		0			0
$634$	4.81344	−	3.49717i	0.191166	−	0.138890i
$635$	11.4849	+	4.85130i	0.455763	+	0.192518i
$636$		0			0
$637$	−6.63318	+	4.81928i	−0.262816	+	0.190947i
$638$	19.1392	−	13.9054i	0.757727	−	0.550521i
$639$		0			0
$640$	−1.15502	−	1.91466i	−0.0456560	−	0.0756837i
$641$	−7.17071	+	5.20983i	−0.283226	+	0.205776i	−0.720323	−	0.693638i	$-0.756007\pi$
$641$	−7.17071	+	5.20983i	−0.283226	+	0.205776i	0.437097	+	0.899414i	$0.356007\pi$
$642$		0			0
$643$	−10.9508			−0.431859			−0.215930	−	0.976409i	$-0.569278\pi$
$643$	−10.9508			−0.431859			−0.215930	+	0.976409i	$0.569278\pi$
$644$	3.19239	−	9.82516i	0.125798	−	0.387165i
$645$		0			0
$646$	7.66578	+	23.5928i	0.301606	+	0.928248i
$647$	11.2381	+	34.5873i	0.441815	+	1.35977i	0.885939	+	0.463802i	$0.153515\pi$
$647$	11.2381	+	34.5873i	0.441815	+	1.35977i	−0.444124	+	0.895966i	$0.646485\pi$
$648$		0			0
$649$	36.5519			1.43479
$650$	−22.1086	+	10.8792i	−0.867171	+	0.426715i
$651$		0			0
$652$	11.3262	+	8.22899i	0.443570	+	0.322272i
$653$	−3.58386	−	11.0300i	−0.140247	−	0.431637i	0.856122	−	0.516774i	$-0.172867\pi$
$653$	−3.58386	−	11.0300i	−0.140247	−	0.431637i	−0.996369	+	0.0851371i	$0.972867\pi$
$654$		0			0
$655$	1.17337	−	13.6879i	0.0458475	−	0.534831i
$656$	0.0507205	−	0.156102i	0.00198030	−	0.00609475i
$657$		0			0
$658$	4.45390	−	13.7077i	0.173631	−	0.534381i
$659$	−39.1957	+	28.4774i	−1.52685	+	1.10932i	−0.568890	+	0.822414i	$0.692627\pi$
$659$	−39.1957	+	28.4774i	−1.52685	+	1.10932i	−0.957959	+	0.286907i	$0.907373\pi$
$660$		0			0
$661$	−1.33751	−	0.971757i	−0.0520231	−	0.0377970i	0.561470	−	0.827497i	$-0.310236\pi$
$661$	−1.33751	−	0.971757i	−0.0520231	−	0.0377970i	−0.613493	+	0.789700i	$0.710236\pi$
$662$	−19.5656	+	14.2152i	−0.760438	+	0.552491i
$663$		0			0
$664$	1.05718	+	0.768085i	0.0410265	+	0.0298075i
$665$	1.42768	−	16.6545i	0.0553630	−	0.645833i
$666$		0			0
$667$	−9.53812	+	29.3553i	−0.369317	+	1.13664i
$668$	−24.8029			−0.959654
$669$		0			0
$670$	−6.75798	+	7.80173i	−0.261084	+	0.301407i
$671$	0.326238	+	1.00406i	0.0125943	+	0.0387612i
$672$		0			0
$673$	7.79971	+	5.66682i	0.300657	+	0.218440i	0.727877	−	0.685708i	$-0.240507\pi$
$673$	7.79971	+	5.66682i	0.300657	+	0.218440i	−0.427220	+	0.904147i	$0.640507\pi$
$674$	−11.3498			−0.437178
$675$		0			0
$676$	11.2858			0.434071
$677$	−7.61063	−	5.52945i	−0.292500	−	0.212514i	0.431851	−	0.901945i	$-0.357861\pi$
$677$	−7.61063	−	5.52945i	−0.292500	−	0.212514i	−0.724351	+	0.689431i	$0.757861\pi$
$678$		0			0
$679$	12.2865	+	37.8140i	0.471513	+	1.45117i
$680$	15.7903	+	6.66995i	0.605529	+	0.255781i
$681$		0			0
$682$	−12.1549			−0.465435
$683$	3.20637	−	9.86818i	0.122688	−	0.377595i	−0.870785	−	0.491665i	$-0.836389\pi$
$683$	3.20637	−	9.86818i	0.122688	−	0.377595i	0.993473	+	0.114069i	$0.0363886\pi$
$684$		0			0
$685$	−7.43143	+	8.57920i	−0.283940	+	0.327794i
$686$	−16.1913	−	11.7637i	−0.618187	−	0.449139i
$687$		0			0
$688$	−5.42971	+	3.94492i	−0.207006	+	0.150399i
$689$	−47.7331	−	34.6802i	−1.81849	−	1.32121i
$690$		0			0
$691$	−3.19568	+	2.32179i	−0.121569	+	0.0883252i	−0.646908	−	0.762568i	$-0.723938\pi$
$691$	−3.19568	+	2.32179i	−0.121569	+	0.0883252i	0.525339	+	0.850893i	$0.323938\pi$
$692$	−6.58308	+	20.2606i	−0.250251	+	0.770194i
$693$		0			0
$694$	3.56086	−	10.9592i	0.135168	−	0.416005i
$695$	12.2375	+	5.16921i	0.464194	+	0.196079i
$696$		0			0
$697$	0.388812	+	1.19664i	0.0147273	+	0.0453260i
$698$	1.46607	+	1.06516i	0.0554914	+	0.0403169i
$699$		0			0
$700$	−8.05248	−	8.28033i	−0.304355	−	0.312967i
$701$	14.6454			0.553148			0.276574	−	0.960993i	$-0.410801\pi$
$701$	14.6454			0.553148			0.276574	+	0.960993i	$0.410801\pi$
$702$		0			0
$703$	3.95758	+	12.1802i	0.149263	+	0.459384i
$704$	−1.05921	−	3.25992i	−0.0399205	−	0.122863i
$705$		0			0
$706$	0.939338	−	2.89099i	0.0353525	−	0.108804i
$707$	13.1890			0.496025
$708$		0			0
$709$	37.2889	−	27.0920i	1.40042	−	1.01746i	0.405785	−	0.913968i	$-0.366998\pi$
$709$	37.2889	−	27.0920i	1.40042	−	1.01746i	0.994630	−	0.103493i	$-0.0330020\pi$
$710$	0.0727091	−	0.848183i	0.00272873	−	0.0318317i
$711$		0			0
$712$	3.58371	−	2.60372i	0.134305	−	0.0975785i
$713$	12.8299	−	9.32148i	0.480484	−	0.349092i
$714$		0			0
$715$	−36.7883	+	8.56116i	−1.37580	+	0.320169i
$716$	7.72296	−	5.61106i	0.288620	−	0.209695i
$717$		0			0
$718$	−6.09549			−0.227482
$719$	−7.22238	+	22.2282i	−0.269349	+	0.828971i	0.721310	+	0.692612i	$0.243540\pi$
$719$	−7.22238	+	22.2282i	−0.269349	+	0.828971i	−0.990659	+	0.136359i	$0.956460\pi$
$720$		0			0
$721$	−12.3821	−	38.1081i	−0.461132	−	1.41922i
$722$	−2.63525	−	8.11048i	−0.0980740	−	0.301841i
$723$		0			0
$724$	−0.721507			−0.0268146
$725$	24.0590	+	24.7397i	0.893528	+	0.918810i
$726$		0			0
$727$	6.97049	+	5.06436i	0.258521	+	0.187827i	0.709495	−	0.704711i	$-0.248923\pi$
$727$	6.97049	+	5.06436i	0.258521	+	0.187827i	−0.450974	+	0.892537i	$0.648923\pi$
$728$	3.51785	+	10.8268i	0.130380	+	0.401269i
$729$		0			0
$730$	0.0868817	+	0.144023i	0.00321564	+	0.00533054i
$731$	15.8986	−	48.9307i	0.588029	−	1.80977i
$732$		0			0
$733$	−4.61959	+	14.2176i	−0.170628	+	0.525140i	−0.999407	−	0.0344367i	$-0.989036\pi$
$733$	−4.61959	+	14.2176i	−0.170628	+	0.525140i	0.828779	+	0.559577i	$0.189036\pi$
$734$	21.3148	−	15.4861i	0.786743	−	0.571602i
$735$		0			0
$736$	3.61803	+	2.62866i	0.133363	+	0.0968935i
$737$	−12.8004	+	9.30004i	−0.471509	+	0.342571i
$738$		0			0
$739$	33.0484	+	24.0110i	1.21570	+	0.883261i	0.995736	−	0.0922465i	$-0.0294048\pi$
$739$	33.0484	+	24.0110i	1.21570	+	0.883261i	0.219968	+	0.975507i	$0.429405\pi$
$740$	8.15197	+	3.44346i	0.299672	+	0.126584i
$741$		0			0
$742$	8.54646	−	26.3033i	0.313750	−	0.965625i
$743$	−13.6476			−0.500683			−0.250342	−	0.968158i	$-0.580543\pi$
$743$	−13.6476			−0.500683			−0.250342	+	0.968158i	$0.580543\pi$
$744$		0			0
$745$	21.5252	−	5.00924i	0.788624	−	0.183524i
$746$	4.38274	+	13.4887i	0.160464	+	0.493856i
$747$		0			0
$748$	21.2576	+	15.4445i	0.777255	+	0.564709i
$749$	−3.63032			−0.132649
$750$		0			0
$751$	41.3014			1.50711			0.753555	−	0.657385i	$-0.228337\pi$
$751$	41.3014			1.50711			0.753555	+	0.657385i	$0.228337\pi$
$752$	5.04775	+	3.66740i	0.184072	+	0.133736i
$753$		0			0
$754$	−10.5105	−	32.3481i	−0.382771	−	1.17805i
$755$	5.73704	−	1.33509i	0.208792	−	0.0485889i
$756$		0			0
$757$	18.1132			0.658337			0.329169	−	0.944271i	$-0.393232\pi$
$757$	18.1132			0.658337			0.329169	+	0.944271i	$0.393232\pi$
$758$	9.82663	−	30.2432i	0.356919	−	1.09848i
$759$		0			0
$760$	6.66578	+	2.81568i	0.241793	+	0.102136i
$761$	−7.95941	−	5.78285i	−0.288529	−	0.209628i	0.434100	−	0.900865i	$-0.357066\pi$
$761$	−7.95941	−	5.78285i	−0.288529	−	0.209628i	−0.722629	+	0.691236i	$0.757066\pi$
$762$		0			0
$763$	−23.8965	+	17.3618i	−0.865112	+	0.628541i
$764$	−1.00000	−	0.726543i	−0.0361787	−	0.0262854i
$765$		0			0
$766$	18.7539	−	13.6255i	0.677607	−	0.492310i
$767$	16.2394	−	49.9796i	0.586369	−	1.80466i
$768$		0			0
$769$	−16.8687	+	51.9166i	−0.608302	+	1.87216i	−0.136040	+	0.990703i	$0.543438\pi$
$769$	−16.8687	+	51.9166i	−0.608302	+	1.87216i	−0.472262	+	0.881458i	$0.656562\pi$
$770$	−9.14548	−	15.1604i	−0.329580	−	0.546343i
$771$		0			0
$772$	−8.32890	−	25.6337i	−0.299764	−	0.922578i
$773$	−25.9764	−	18.8729i	−0.934305	−	0.678812i	0.0127381	−	0.999919i	$-0.495945\pi$
$773$	−25.9764	−	18.8729i	−0.934305	−	0.678812i	−0.947043	+	0.321107i	$0.895945\pi$
$774$		0			0
$775$	−2.52912	−	17.5492i	−0.0908487	−	0.630386i
$776$	−17.2119			−0.617870
$777$		0			0
$778$	3.94657	+	12.1463i	0.141491	+	0.435466i
$779$	0.164135	+	0.505156i	0.00588075	+	0.0180991i
$780$		0			0
$781$	0.403252	−	1.24108i	0.0144295	−	0.0444094i
$782$	−34.2824			−1.22594
$783$		0			0
$784$	1.34600	−	0.977926i	0.0480714	−	0.0349259i
$785$	8.09781	−	1.88448i	0.289023	−	0.0672599i
$786$		0			0
$787$	43.1703	−	31.3651i	1.53886	−	1.11804i	0.587808	−	0.809000i	$-0.299991\pi$
$787$	43.1703	−	31.3651i	1.53886	−	1.11804i	0.951048	−	0.309044i	$-0.100009\pi$
$788$	20.5640	−	14.9406i	0.732560	−	0.532236i
$789$		0			0
$790$	−2.91895	+	34.0508i	−0.103852	+	1.21147i
$791$	−9.43731	+	6.85661i	−0.335552	+	0.243793i
$792$		0			0
$793$	1.51785			0.0539004
$794$	5.21110	−	16.0381i	0.184935	−	0.569172i
$795$		0			0
$796$	6.72373	+	20.6935i	0.238316	+	0.733463i
$797$	−3.52634	−	10.8530i	−0.124909	−	0.384431i	0.868975	−	0.494856i	$-0.164779\pi$
$797$	−3.52634	−	10.8530i	−0.124909	−	0.384431i	−0.993885	+	0.110424i	$0.964779\pi$
$798$		0			0
$799$	−47.8295			−1.69209
$800$	4.48626	−	2.20759i	0.158613	−	0.0780501i
$801$		0			0
$802$	1.63443	+	1.18748i	0.0577138	+	0.0419315i
$803$	0.0796751	+	0.245215i	0.00281167	+	0.00865344i
$804$		0			0
$805$	21.2797	+	8.98875i	0.750013	+	0.316812i
$806$	−5.40020	+	16.6201i	−0.190214	+	0.585419i
$807$		0			0
$808$	−1.76432	+	5.43002i	−0.0620686	+	0.191027i
$809$	22.9630	−	16.6836i	0.807337	−	0.586564i	−0.105721	−	0.994396i	$-0.533715\pi$
$809$	22.9630	−	16.6836i	0.807337	−	0.586564i	0.913057	+	0.407831i	$0.133715\pi$
$810$		0			0
$811$	−32.0027	−	23.2513i	−1.12377	−	0.816463i	−0.138990	−	0.990294i	$-0.544386\pi$
$811$	−32.0027	−	23.2513i	−1.12377	−	0.816463i	−0.984776	+	0.173831i	$0.944386\pi$
$812$	12.8986	−	9.37135i	0.452651	−	0.328870i
$813$		0			0
$814$	10.9746	+	7.97348i	0.384658	+	0.279470i
$815$	−20.4965	+	23.6621i	−0.717960	+	0.828847i
$816$		0			0
$817$	6.71149	−	20.6558i	0.234805	−	0.722657i
$818$	3.80495			0.133037
$819$		0			0
$820$	0.338092	+	0.142813i	0.0118067	+	0.00498724i
$821$	7.65811	+	23.5692i	0.267270	+	0.822572i	0.991162	+	0.132659i	$0.0423514\pi$
$821$	7.65811	+	23.5692i	0.267270	+	0.822572i	−0.723892	+	0.689913i	$0.757649\pi$
$822$		0			0
$823$	−5.39437	−	3.91924i	−0.188036	−	0.136616i	0.489785	−	0.871843i	$-0.337075\pi$
$823$	−5.39437	−	3.91924i	−0.188036	−	0.136616i	−0.677821	+	0.735227i	$0.737075\pi$
$824$	17.3457			0.604267
$825$		0			0
$826$	24.6336			0.857113
$827$	8.30060	+	6.03074i	0.288640	+	0.209709i	0.722677	−	0.691186i	$-0.242911\pi$
$827$	8.30060	+	6.03074i	0.288640	+	0.209709i	−0.434037	+	0.900895i	$0.642911\pi$
$828$		0			0
$829$	−13.0307	−	40.1043i	−0.452575	−	1.39288i	−0.873959	−	0.485999i	$-0.838456\pi$
$829$	−13.0307	−	40.1043i	−0.452575	−	1.39288i	0.421385	−	0.906882i	$-0.361544\pi$
$830$	−1.91312	+	2.20859i	−0.0664053	+	0.0766614i
$831$		0			0
$832$	−4.92807			−0.170850
$833$	−3.94118	+	12.1297i	−0.136554	+	0.420269i
$834$		0			0
$835$	4.73694	−	55.2583i	0.163928	−	1.91229i
$836$	8.97378	+	6.51983i	0.310365	+	0.225493i
$837$		0			0
$838$	−6.10696	+	4.43696i	−0.210961	+	0.153272i
$839$	−37.9625	−	27.5814i	−1.31061	−	0.952215i	−0.999999	−	0.00167835i	$-0.999466\pi$
$839$	−37.9625	−	27.5814i	−1.31061	−	0.952215i	−0.310613	−	0.950537i	$-0.600534\pi$
$840$		0			0
$841$	−15.0764	+	10.9537i	−0.519877	+	0.377713i
$842$	4.73955	−	14.5868i	0.163336	−	0.502696i
$843$		0			0
$844$	−6.85536	+	21.0986i	−0.235971	+	0.726245i
$845$	−2.15540	+	25.1437i	−0.0741482	+	0.864970i
$846$		0			0
$847$	−0.534654	−	1.64550i	−0.0183709	−	0.0565399i
$848$	9.68598	+	7.03727i	0.332618	+	0.241661i
$849$		0			0
$850$	−17.8756	+	33.9053i	−0.613129	+	1.16294i
$851$	−17.6988			−0.606708
$852$		0			0
$853$	−2.49257	−	7.67135i	−0.0853440	−	0.262662i	0.899273	−	0.437388i	$-0.144096\pi$
$853$	−2.49257	−	7.67135i	−0.0853440	−	0.262662i	−0.984617	+	0.174726i	$0.944096\pi$
$854$	0.219863	+	0.676669i	0.00752356	+	0.0231551i
$855$		0			0
$856$	0.485634	−	1.49463i	0.0165986	−	0.0510853i
$857$	−15.1446			−0.517331			−0.258666	−	0.965967i	$-0.583283\pi$
$857$	−15.1446			−0.517331			−0.258666	+	0.965967i	$0.583283\pi$
$858$		0			0
$859$	−7.55268	+	5.48734i	−0.257694	+	0.187226i	−0.709130	−	0.705078i	$-0.750912\pi$
$859$	−7.55268	+	5.48734i	−0.257694	+	0.187226i	0.451436	+	0.892304i	$0.350912\pi$
$860$	−7.75188	−	12.8502i	−0.264337	−	0.438190i
$861$		0			0
$862$	7.59181	−	5.51578i	0.258578	−	0.187868i
$863$	−6.85207	+	4.97832i	−0.233247	+	0.169464i	−0.698270	−	0.715835i	$-0.746046\pi$
$863$	−6.85207	+	4.97832i	−0.233247	+	0.169464i	0.465022	+	0.885299i	$0.346046\pi$
$864$		0			0
$865$	−43.8814	−	18.5359i	−1.49201	−	0.630239i
$866$	24.4735	−	17.7810i	0.831642	−	0.604223i
$867$		0			0
$868$	−8.19161			−0.278041
$869$	−16.1888	+	49.8240i	−0.549167	+	1.69016i
$870$		0			0
$871$	7.02951	+	21.6346i	0.238186	+	0.733061i
$872$	−3.95131	−	12.1609i	−0.133808	−	0.411820i
$873$		0			0
$874$	−14.4721			−0.489527
$875$	19.9856	−	16.3587i	0.675637	−	0.553025i
$876$		0			0
$877$	15.8678	+	11.5287i	0.535819	+	0.389295i	0.822530	−	0.568722i	$-0.192562\pi$
$877$	15.8678	+	11.5287i	0.535819	+	0.389295i	−0.286711	+	0.958017i	$0.592562\pi$
$878$	11.7687	+	36.2202i	0.397173	+	1.22237i
$879$		0			0
$880$	7.46505	−	1.73722i	0.251647	−	0.0585618i
$881$	0.663267	−	2.04133i	0.0223460	−	0.0687740i	−0.939262	−	0.343202i	$-0.888488\pi$
$881$	0.663267	−	2.04133i	0.0223460	−	0.0687740i	0.961608	+	0.274428i	$0.0884885\pi$
$882$		0			0
$883$	−0.291020	+	0.895667i	−0.00979360	+	0.0301416i	−0.955834	−	0.293907i	$-0.905044\pi$
$883$	−0.291020	+	0.895667i	−0.00979360	+	0.0301416i	0.946040	+	0.324049i	$0.105044\pi$
$884$	30.5626	−	22.2050i	1.02793	−	0.746836i
$885$		0			0
$886$	−1.24425	−	0.903997i	−0.0418012	−	0.0303704i
$887$	−26.5838	+	19.3143i	−0.892598	+	0.648510i	−0.936554	−	0.350523i	$-0.886004\pi$
$887$	−26.5838	+	19.3143i	−0.892598	+	0.648510i	0.0439563	+	0.999033i	$0.486004\pi$
$888$		0			0
$889$	10.4200	+	7.57058i	0.349476	+	0.253909i
$890$	5.11639	+	8.48141i	0.171502	+	0.284297i
$891$		0			0
$892$	2.44118	−	7.51317i	0.0817367	−	0.251560i
$893$	−20.1910			−0.675665
$894$		0			0
$895$	11.0259	+	18.2776i	0.368555	+	0.610952i
$896$	−0.713839	−	2.19697i	−0.0238477	−	0.0733957i
$897$		0			0
$898$	11.3626	+	8.25541i	0.379175	+	0.275486i
$899$	24.4746			0.816275
$900$		0			0
$901$	−91.7787			−3.05759
$902$	0.455155	+	0.330689i	0.0151550	+	0.0110108i
$903$		0			0
$904$	−1.56047	−	4.80262i	−0.0519004	−	0.159733i
$905$	0.137796	−	1.60744i	0.00458048	−	0.0534332i
$906$		0			0
$907$	−54.8128			−1.82003			−0.910014	−	0.414577i	$-0.863930\pi$
$907$	−54.8128			−1.82003			−0.910014	+	0.414577i	$0.863930\pi$
$908$	0.823143	−	2.53337i	0.0273170	−	0.0840730i
$909$		0			0
$910$	−24.7929	+	5.76967i	−0.821877	+	0.191263i
$911$	10.0457	+	7.29864i	0.332829	+	0.241815i	0.741630	−	0.670809i	$-0.234053\pi$
$911$	10.0457	+	7.29864i	0.332829	+	0.241815i	−0.408801	+	0.912624i	$0.634053\pi$
$912$		0			0
$913$	−3.62367	+	2.63275i	−0.119926	+	0.0871313i
$914$	−11.7913	−	8.56687i	−0.390021	−	0.283367i
$915$		0			0
$916$	7.61024	−	5.52917i	0.251450	−	0.182689i
$917$	4.38573	−	13.4979i	0.144830	−	0.445740i
$918$		0			0
$919$	10.1076	−	31.1081i	0.333420	−	1.02616i	−0.634075	−	0.773271i	$-0.718619\pi$
$919$	10.1076	−	31.1081i	0.333420	−	1.02616i	0.967495	−	0.252890i	$-0.0813810\pi$
$920$	−6.54736	+	7.55858i	−0.215860	+	0.249199i
$921$		0			0
$922$	−5.58386	−	17.1854i	−0.183895	−	0.565969i
$923$	−1.51785	−	1.10278i	−0.0499606	−	0.0362985i
$924$		0			0
$925$	−9.22856	+	17.5041i	−0.303433	+	0.575531i
$926$	20.5585			0.675595
$927$		0			0
$928$	2.13279	+	6.56405i	0.0700122	+	0.215475i
$929$	11.6232	+	35.7724i	0.381344	+	1.17365i	0.939098	+	0.343649i	$0.111663\pi$
$929$	11.6232	+	35.7724i	0.381344	+	1.17365i	−0.557755	+	0.830006i	$0.688337\pi$
$930$		0			0
$931$	−1.66375	+	5.12049i	−0.0545271	+	0.167817i
$932$	−14.7867			−0.484355
$933$		0			0
$934$	20.3864	−	14.8116i	0.667063	−	0.484650i
$935$	−38.4687	+	44.4101i	−1.25806	+	1.45237i
$936$		0			0
$937$	−21.7311	+	15.7885i	−0.709923	+	0.515789i	−0.883149	−	0.469093i	$-0.844581\pi$
$937$	−21.7311	+	15.7885i	−0.709923	+	0.515789i	0.173226	+	0.984882i	$0.444581\pi$
$938$	−8.62664	+	6.26762i	−0.281670	+	0.204645i
$939$		0			0
$940$	−9.13463	+	10.5454i	−0.297939	+	0.343955i
$941$	−34.6644	+	25.1852i	−1.13003	+	0.821014i	−0.985699	−	0.168516i	$-0.946103\pi$
$941$	−34.6644	+	25.1852i	−1.13003	+	0.821014i	−0.144330	+	0.989530i	$0.546103\pi$
$942$		0			0
$943$	−0.734034			−0.0239035
$944$	−3.29528	+	10.1418i	−0.107252	+	0.330088i
$945$		0			0
$946$	−7.10889	−	21.8789i	−0.231130	−	0.711345i
$947$	−10.4191	−	32.0668i	−0.338577	−	1.04203i	−0.964933	−	0.262495i	$-0.915455\pi$
$947$	−10.4191	−	32.0668i	−0.338577	−	1.04203i	0.626357	−	0.779537i	$-0.284545\pi$
$948$		0			0
$949$	0.370695			0.0120333
$950$	−7.54610	+	14.3129i	−0.244828	+	0.464373i
$951$		0			0
$952$	14.3262	+	10.4086i	0.464316	+	0.337345i
$953$	4.02931	+	12.4010i	0.130522	+	0.401706i	0.994867	−	0.101194i	$-0.0322663\pi$
$953$	4.02931	+	12.4010i	0.130522	+	0.401706i	−0.864344	+	0.502900i	$0.832266\pi$
$954$		0			0
$955$	1.80964	−	2.08914i	0.0585587	−	0.0676030i
$956$	3.89981	−	12.0024i	0.126129	−	0.388185i
$957$		0			0
$958$	−0.809645	+	2.49183i	−0.0261584	+	0.0805074i
$959$	−9.48631	+	6.89221i	−0.306329	+	0.222561i
$960$		0			0
$961$	14.9063	+	10.8300i	0.480848	+	0.349356i
$962$	15.7784	−	11.4637i	0.508717	−	0.369604i
$963$		0			0
$964$	13.9247	+	10.1169i	0.448485	+	0.325843i
$965$	58.7000	−	13.6603i	1.88962	−	0.439741i
$966$		0			0
$967$	−6.53843	+	20.1232i	−0.210262	+	0.647119i	0.789194	+	0.614144i	$0.210498\pi$
$967$	−6.53843	+	20.1232i	−0.210262	+	0.647119i	−0.999456	+	0.0329758i	$0.989502\pi$
$968$	0.748983			0.0240732
$969$		0			0
$970$	3.28718	−	38.3463i	0.105545	−	1.23123i
$971$	−1.55251	−	4.77814i	−0.0498225	−	0.153338i	0.923050	−	0.384680i	$-0.125688\pi$
$971$	−1.55251	−	4.77814i	−0.0498225	−	0.153338i	−0.972872	+	0.231342i	$0.925688\pi$
$972$		0			0
$973$	11.1028	+	8.06669i	0.355941	+	0.258606i
$974$	25.1481			0.805796
$975$		0			0
$976$	−0.308001			−0.00985887
$977$	49.4746	+	35.9454i	1.58283	+	1.15000i	0.913356	+	0.407162i	$0.133482\pi$
$977$	49.4746	+	35.9454i	1.58283	+	1.15000i	0.669477	+	0.742833i	$0.266518\pi$
$978$		0			0
$979$	4.69200	+	14.4405i	0.149957	+	0.461520i
$980$	1.92166	+	3.18552i	0.0613850	+	0.101758i
$981$		0			0
$982$	−31.6216			−1.00908
$983$	9.94678	−	30.6131i	0.317253	−	0.976405i	−0.657564	−	0.753399i	$-0.728413\pi$
$983$	9.94678	−	30.6131i	0.317253	−	0.976405i	0.974817	−	0.223006i	$-0.0715870\pi$
$984$		0			0
$985$	29.3587	+	48.6678i	0.935447	+	1.55068i
$986$	−42.8035	−	31.0986i	−1.36314	−	0.990380i
$987$		0			0
$988$	12.9018	−	9.37374i	0.410462	−	0.298218i
$989$	24.2824	+	17.6422i	0.772136	+	0.560989i
$990$		0			0
$991$	−22.8588	+	16.6079i	−0.726135	+	0.527568i	−0.888338	−	0.459189i	$-0.848140\pi$
$991$	−22.8588	+	16.6079i	−0.726135	+	0.527568i	0.162203	+	0.986757i	$0.448140\pi$
$992$	1.09581	−	3.37254i	0.0347919	−	0.107078i
$993$		0			0
$994$	0.271766	−	0.836409i	0.00861989	−	0.0265293i
$995$	−47.3872	+	11.0277i	−1.50227	+	0.349601i
$996$		0			0
$997$	1.06317	+	3.27211i	0.0336711	+	0.103629i	0.966480	−	0.256744i	$-0.0826496\pi$
$997$	1.06317	+	3.27211i	0.0336711	+	0.103629i	−0.932808	+	0.360372i	$0.882650\pi$
$998$	23.1594	+	16.8263i	0.733099	+	0.532628i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	450.2.h.d.91.1		8
3.2	odd	2		150.2.g.c.91.2	yes	8
15.2	even	4		750.2.h.e.49.1		16
15.8	even	4		750.2.h.e.49.4		16
15.14	odd	2		750.2.g.d.451.2		8
25.11	even	5	inner	450.2.h.d.361.1		8
75.2	even	20		750.2.h.e.199.3		16
75.8	even	20		3750.2.c.h.1249.7		8
75.11	odd	10		150.2.g.c.61.2	✓	8
75.14	odd	10		750.2.g.d.301.2		8
75.17	even	20		3750.2.c.h.1249.2		8
75.23	even	20		750.2.h.e.199.2		16
75.44	odd	10		3750.2.a.q.1.3		4
75.56	odd	10		3750.2.a.l.1.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
150.2.g.c.61.2	✓	8	75.11	odd	10
150.2.g.c.91.2	yes	8	3.2	odd	2
450.2.h.d.91.1		8	1.1	even	1	trivial
450.2.h.d.361.1		8	25.11	even	5	inner
750.2.g.d.301.2		8	75.14	odd	10
750.2.g.d.451.2		8	15.14	odd	2
750.2.h.e.49.1		16	15.2	even	4
750.2.h.e.49.4		16	15.8	even	4
750.2.h.e.199.2		16	75.23	even	20
750.2.h.e.199.3		16	75.2	even	20
3750.2.a.l.1.2		4	75.56	odd	10
3750.2.a.q.1.3		4	75.44	odd	10
3750.2.c.h.1249.2		8	75.17	even	20
3750.2.c.h.1249.7		8	75.8	even	20

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.h (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.809017 - 0.587785i) q^{2} +(0.309017 + 0.951057i) q^{4} +(-2.17787 + 0.506822i) q^{5} -2.31003 q^{7} +(0.309017 - 0.951057i) q^{8} +O(q^{10})\)	\(q+(-0.809017 - 0.587785i) q^{2} +(0.309017 + 0.951057i) q^{4} +(-2.17787 + 0.506822i) q^{5} -2.31003 q^{7} +(0.309017 - 0.951057i) q^{8} +(2.05984 + 0.870094i) q^{10} +(2.77305 + 2.01474i) q^{11} +(3.98689 - 2.89665i) q^{13} +(1.86886 + 1.35780i) q^{14} +(-0.809017 + 0.587785i) q^{16} +(2.36886 - 7.29059i) q^{17} +(1.00000 - 3.07768i) q^{19} +(-1.15502 - 1.91466i) q^{20} +(-1.05921 - 3.25992i) q^{22} +(3.61803 + 2.62866i) q^{23} +(4.48626 - 2.20759i) q^{25} -4.92807 q^{26} +(-0.713839 - 2.19697i) q^{28} +(2.13279 + 6.56405i) q^{29} +(1.09581 - 3.37254i) q^{31} +1.00000 q^{32} +(-6.20175 + 4.50583i) q^{34} +(5.03096 - 1.17078i) q^{35} +(-3.20175 + 2.32620i) q^{37} +(-2.61803 + 1.90211i) q^{38} +(-0.190983 + 2.22790i) q^{40} +(-0.132788 + 0.0964762i) q^{41} +6.71149 q^{43} +(-1.05921 + 3.25992i) q^{44} +(-1.38197 - 4.25325i) q^{46} +(-1.92807 - 5.93398i) q^{47} -1.66375 q^{49} +(-4.92705 - 0.850981i) q^{50} +(3.98689 + 2.89665i) q^{52} +(-3.69971 - 11.3865i) q^{53} +(-7.06047 - 2.98240i) q^{55} +(-0.713839 + 2.19697i) q^{56} +(2.13279 - 6.56405i) q^{58} +(8.62715 - 6.26799i) q^{59} +(0.249178 + 0.181038i) q^{61} +(-2.86886 + 2.08435i) q^{62} +(-0.809017 - 0.587785i) q^{64} +(-7.21486 + 8.32917i) q^{65} +(-1.42642 + 4.39008i) q^{67} +7.66578 q^{68} +(-4.75830 - 2.00995i) q^{70} +(-0.117646 - 0.362077i) q^{71} +(0.0608552 + 0.0442139i) q^{73} +3.95758 q^{74} +3.23607 q^{76} +(-6.40584 - 4.65411i) q^{77} +(4.72296 + 14.5358i) q^{79} +(1.46403 - 1.69015i) q^{80} +0.164135 q^{82} +(-0.403806 + 1.24279i) q^{83} +(-1.46403 + 17.0786i) q^{85} +(-5.42971 - 3.94492i) q^{86} +(2.77305 - 2.01474i) q^{88} +(3.58371 + 2.60372i) q^{89} +(-9.20985 + 6.69135i) q^{91} +(-1.38197 + 4.25325i) q^{92} +(-1.92807 + 5.93398i) q^{94} +(-0.618034 + 7.20963i) q^{95} +(-5.31876 - 16.3695i) q^{97} +(1.34600 + 0.977926i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{2} - 2 q^{4} + 4 q^{5} - 2 q^{7} - 2 q^{8}+O(q^{10}) \) 8 * q - 2 * q^2 - 2 * q^4 + 4 * q^5 - 2 * q^7 - 2 * q^8	\( 8 q - 2 q^{2} - 2 q^{4} + 4 q^{5} - 2 q^{7} - 2 q^{8} + 4 q^{10} + 5 q^{11} + 6 q^{13} - 2 q^{14} - 2 q^{16} + 2 q^{17} + 8 q^{19} - q^{20} + 20 q^{23} + 14 q^{25} - 14 q^{26} + 3 q^{28} + 18 q^{29} + 9 q^{31} + 8 q^{32} - 3 q^{34} + 4 q^{35} + 21 q^{37} - 12 q^{38} - 6 q^{40} - 2 q^{41} - 32 q^{43} - 20 q^{46} + 10 q^{47} + 22 q^{49} - 26 q^{50} + 6 q^{52} - 7 q^{53} - 40 q^{55} + 3 q^{56} + 18 q^{58} + 25 q^{59} + 10 q^{61} - 6 q^{62} - 2 q^{64} - 37 q^{65} - 2 q^{67} + 2 q^{68} - 11 q^{70} - 24 q^{73} + 26 q^{74} + 8 q^{76} - 35 q^{77} - 6 q^{79} - q^{80} - 42 q^{82} - 11 q^{83} + q^{85} - 2 q^{86} + 5 q^{88} - 9 q^{89} - 4 q^{91} - 20 q^{92} + 10 q^{94} + 4 q^{95} + q^{97} + 7 q^{98}+O(q^{100}) \) 8 * q - 2 * q^2 - 2 * q^4 + 4 * q^5 - 2 * q^7 - 2 * q^8 + 4 * q^10 + 5 * q^11 + 6 * q^13 - 2 * q^14 - 2 * q^16 + 2 * q^17 + 8 * q^19 - q^20 + 20 * q^23 + 14 * q^25 - 14 * q^26 + 3 * q^28 + 18 * q^29 + 9 * q^31 + 8 * q^32 - 3 * q^34 + 4 * q^35 + 21 * q^37 - 12 * q^38 - 6 * q^40 - 2 * q^41 - 32 * q^43 - 20 * q^46 + 10 * q^47 + 22 * q^49 - 26 * q^50 + 6 * q^52 - 7 * q^53 - 40 * q^55 + 3 * q^56 + 18 * q^58 + 25 * q^59 + 10 * q^61 - 6 * q^62 - 2 * q^64 - 37 * q^65 - 2 * q^67 + 2 * q^68 - 11 * q^70 - 24 * q^73 + 26 * q^74 + 8 * q^76 - 35 * q^77 - 6 * q^79 - q^80 - 42 * q^82 - 11 * q^83 + q^85 - 2 * q^86 + 5 * q^88 - 9 * q^89 - 4 * q^91 - 20 * q^92 + 10 * q^94 + 4 * q^95 + q^97 + 7 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more