LMFDB - Embedded newform 975.2.i.l.451.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [975,2,Mod(451,975)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(975, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 4]))

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

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

chi := DirichletCharacter("975.451");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 975 = 3 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	975.i (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.78541419707$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.1714608.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} + 12x^{4} - 19x^{3} + 30x^{2} - 21x + 7 $ x^6 - 3x^5 + 12x^4 - 19x^3 + 30x^2 - 21*x + 7
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 195)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			451.1
Root			$0.500000 + 2.23871i$ of defining polynomial
Character	$\chi$	$=$	975.451
Dual form			975.2.i.l.601.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.13090 + 1.95878i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-1.55787 - 2.69832i) q^{4} +(-1.13090 - 1.95878i) q^{6} +(-0.630901 - 1.09275i) q^{7} +2.52360 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-1.13090 + 1.95878i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-1.55787 - 2.69832i) q^{4} +(-1.13090 - 1.95878i) q^{6} +(-0.630901 - 1.09275i) q^{7} +2.52360 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-2.26180 + 3.91756i) q^{11} +3.11575 q^{12} +(3.45058 - 1.04571i) q^{13} +2.85395 q^{14} +(0.261802 - 0.453455i) q^{16} +(-2.24665 - 3.89131i) q^{17} +2.26180 q^{18} +(-2.55787 - 4.43037i) q^{19} +1.26180 q^{21} +(-5.11575 - 8.86074i) q^{22} +(1.11575 - 1.93253i) q^{23} +(-1.26180 + 2.18551i) q^{24} +(-1.85395 + 7.94151i) q^{26} +1.00000 q^{27} +(-1.96573 + 3.40474i) q^{28} +(0.688776 - 1.19299i) q^{29} +8.87085 q^{31} +(3.11575 + 5.39664i) q^{32} +(-2.26180 - 3.91756i) q^{33} +10.1630 q^{34} +(-1.55787 + 2.69832i) q^{36} +(-0.115749 + 0.200484i) q^{37} +11.5708 q^{38} +(-0.819677 + 3.51114i) q^{39} +(-0.573026 + 0.992511i) q^{41} +(-1.42697 + 2.47159i) q^{42} +(3.18878 + 5.52312i) q^{43} +14.0944 q^{44} +(2.52360 + 4.37101i) q^{46} +10.7854 q^{47} +(0.261802 + 0.453455i) q^{48} +(2.70393 - 4.68334i) q^{49} +4.49330 q^{51} +(-8.19723 - 7.68167i) q^{52} -4.52360 q^{53} +(-1.13090 + 1.95878i) q^{54} +(-1.59214 - 2.75768i) q^{56} +5.11575 q^{57} +(1.55787 + 2.69832i) q^{58} +(0.426974 + 0.739540i) q^{59} +(-2.31968 - 4.01780i) q^{61} +(-10.0321 + 17.3760i) q^{62} +(-0.630901 + 1.09275i) q^{63} -13.0472 q^{64} +10.2315 q^{66} +(6.56633 - 11.3732i) q^{67} +(-7.00000 + 12.1244i) q^{68} +(1.11575 + 1.93253i) q^{69} +(4.80453 + 8.32168i) q^{71} +(-1.26180 - 2.18551i) q^{72} -13.7854 q^{73} +(-0.261802 - 0.453455i) q^{74} +(-7.96970 + 13.8039i) q^{76} +5.70789 q^{77} +(-5.95058 - 5.57632i) q^{78} -8.87085 q^{79} +(-0.500000 + 0.866025i) q^{81} +(-1.29607 - 2.24486i) q^{82} +8.23150 q^{83} +(-1.96573 - 3.40474i) q^{84} -14.4248 q^{86} +(0.688776 + 1.19299i) q^{87} +(-5.70789 + 9.88636i) q^{88} +(-3.31122 + 5.73521i) q^{89} +(-3.31968 - 3.11089i) q^{91} -6.95279 q^{92} +(-4.43543 + 7.68238i) q^{93} +(-12.1972 + 21.1262i) q^{94} -6.23150 q^{96} +(5.33483 + 9.24019i) q^{97} +(6.11575 + 10.5928i) q^{98} +4.52360 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 3 q^{3} - 6 q^{4} + 3 q^{7} - 12 q^{8} - 3 q^{9}+O(q^{10}) $ 6 * q - 3 * q^3 - 6 * q^4 + 3 * q^7 - 12 * q^8 - 3 * q^9	$ 6 q - 3 q^{3} - 6 q^{4} + 3 q^{7} - 12 q^{8} - 3 q^{9} + 12 q^{12} - 3 q^{13} + 24 q^{14} - 12 q^{16} - 12 q^{19} - 6 q^{21} - 24 q^{22} + 6 q^{24} - 18 q^{26} + 6 q^{27} + 12 q^{28} - 6 q^{29} + 6 q^{31} + 12 q^{32} - 6 q^{36} + 6 q^{37} - 12 q^{38} + 12 q^{39} - 12 q^{42} + 9 q^{43} - 24 q^{44} - 12 q^{46} + 24 q^{47} - 12 q^{48} + 6 q^{49} - 12 q^{52} - 30 q^{56} + 24 q^{57} + 6 q^{58} + 6 q^{59} + 3 q^{61} - 6 q^{62} + 3 q^{63} - 24 q^{64} + 48 q^{66} + 9 q^{67} - 42 q^{68} + 12 q^{71} + 6 q^{72} - 42 q^{73} + 12 q^{74} - 48 q^{76} + 48 q^{77} - 12 q^{78} - 6 q^{79} - 3 q^{81} - 18 q^{82} + 36 q^{83} + 12 q^{84} - 12 q^{86} - 6 q^{87} - 48 q^{88} - 30 q^{89} - 3 q^{91} - 96 q^{92} - 3 q^{93} - 36 q^{94} - 24 q^{96} + 15 q^{97} + 30 q^{98}+O(q^{100}) $ 6 * q - 3 * q^3 - 6 * q^4 + 3 * q^7 - 12 * q^8 - 3 * q^9 + 12 * q^12 - 3 * q^13 + 24 * q^14 - 12 * q^16 - 12 * q^19 - 6 * q^21 - 24 * q^22 + 6 * q^24 - 18 * q^26 + 6 * q^27 + 12 * q^28 - 6 * q^29 + 6 * q^31 + 12 * q^32 - 6 * q^36 + 6 * q^37 - 12 * q^38 + 12 * q^39 - 12 * q^42 + 9 * q^43 - 24 * q^44 - 12 * q^46 + 24 * q^47 - 12 * q^48 + 6 * q^49 - 12 * q^52 - 30 * q^56 + 24 * q^57 + 6 * q^58 + 6 * q^59 + 3 * q^61 - 6 * q^62 + 3 * q^63 - 24 * q^64 + 48 * q^66 + 9 * q^67 - 42 * q^68 + 12 * q^71 + 6 * q^72 - 42 * q^73 + 12 * q^74 - 48 * q^76 + 48 * q^77 - 12 * q^78 - 6 * q^79 - 3 * q^81 - 18 * q^82 + 36 * q^83 + 12 * q^84 - 12 * q^86 - 6 * q^87 - 48 * q^88 - 30 * q^89 - 3 * q^91 - 96 * q^92 - 3 * q^93 - 36 * q^94 - 24 * q^96 + 15 * q^97 + 30 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/975\mathbb{Z}\right)^\times$.

$n$	$301$	$326$	$352$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.13090	+	1.95878i	−0.799668	+	1.38507i	0.120165	+	0.992754i	$0.461658\pi$
$2$	−1.13090	+	1.95878i	−0.799668	+	1.38507i	−0.919832	+	0.392311i	$0.871676\pi$
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$4$	−1.55787	−	2.69832i	−0.778937	−	1.34916i
$5$		0			0
$5$		0			0
$6$	−1.13090	−	1.95878i	−0.461688	−	0.799668i
$7$	−0.630901	−	1.09275i	−0.238458	−	0.413022i	0.721814	−	0.692087i	$-0.243309\pi$
$7$	−0.630901	−	1.09275i	−0.238458	−	0.413022i	−0.960272	+	0.279066i	$0.909975\pi$
$8$	2.52360			0.892229
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$		0			0
$11$	−2.26180	+	3.91756i	−0.681959	+	1.18119i	0.292423	+	0.956289i	$0.405538\pi$
$11$	−2.26180	+	3.91756i	−0.681959	+	1.18119i	−0.974382	+	0.224899i	$0.927795\pi$
$12$	3.11575			0.899439
$13$	3.45058	−	1.04571i	0.957018	−	0.290028i
$13$	3.45058	−	1.04571i	0.957018	−	0.290028i
$14$	2.85395			0.762749
$15$		0			0
$16$	0.261802	−	0.453455i	0.0654506	−	0.113364i
$17$	−2.24665	−	3.89131i	−0.544893	−	0.943782i	−0.998614	−	0.0526381i	$-0.983237\pi$
$17$	−2.24665	−	3.89131i	−0.544893	−	0.943782i	0.453721	−	0.891144i	$-0.350096\pi$
$18$	2.26180			0.533112
$19$	−2.55787	−	4.43037i	−0.586817	−	1.01640i	−0.994646	−	0.103338i	$-0.967048\pi$
$19$	−2.55787	−	4.43037i	−0.586817	−	1.01640i	0.407830	−	0.913058i	$-0.366286\pi$
$20$		0			0
$21$	1.26180			0.275348
$22$	−5.11575	−	8.86074i	−1.09068	−	1.88912i
$23$	1.11575	−	1.93253i	0.232650	−	0.402961i	−0.725937	−	0.687761i	$-0.758594\pi$
$23$	1.11575	−	1.93253i	0.232650	−	0.402961i	0.958587	+	0.284800i	$0.0919271\pi$
$24$	−1.26180	+	2.18551i	−0.257564	+	0.446114i
$25$		0			0
$26$	−1.85395	+	7.94151i	−0.363589	+	1.55746i
$27$	1.00000			0.192450
$28$	−1.96573	+	3.40474i	−0.371488	+	0.643436i
$29$	0.688776	−	1.19299i	0.127902	−	0.221534i	−0.794961	−	0.606660i	$-0.792509\pi$
$29$	0.688776	−	1.19299i	0.127902	−	0.221534i	0.922864	+	0.385127i	$0.125842\pi$
$30$		0			0
$31$	8.87085			1.59325			0.796626	−	0.604472i	$-0.206616\pi$
$31$	8.87085			1.59325			0.796626	+	0.604472i	$0.206616\pi$
$32$	3.11575	+	5.39664i	0.550792	+	0.954000i
$33$	−2.26180	−	3.91756i	−0.393729	−	0.681959i
$34$	10.1630			1.74293
$35$		0			0
$36$	−1.55787	+	2.69832i	−0.259646	+	0.449720i
$37$	−0.115749	+	0.200484i	−0.0190291	+	0.0329593i	−0.875383	−	0.483430i	$-0.839391\pi$
$37$	−0.115749	+	0.200484i	−0.0190291	+	0.0329593i	0.856354	+	0.516389i	$0.172724\pi$
$38$	11.5708			1.87703
$39$	−0.819677	+	3.51114i	−0.131253	+	0.562233i
$40$		0			0
$41$	−0.573026	+	0.992511i	−0.0894917	+	0.155004i	−0.907296	−	0.420492i	$-0.861858\pi$
$41$	−0.573026	+	0.992511i	−0.0894917	+	0.155004i	0.817805	+	0.575496i	$0.195191\pi$
$42$	−1.42697	+	2.47159i	−0.220187	+	0.381375i
$43$	3.18878	+	5.52312i	0.486284	+	0.842268i	0.999876	−	0.0157664i	$-0.00501881\pi$
$43$	3.18878	+	5.52312i	0.486284	+	0.842268i	−0.513592	+	0.858035i	$0.671685\pi$
$44$	14.0944			2.12481
$45$		0			0
$46$	2.52360	+	4.37101i	0.372085	+	0.644470i
$47$	10.7854			1.57321			0.786607	−	0.617454i	$-0.211836\pi$
$47$	10.7854			1.57321			0.786607	+	0.617454i	$0.211836\pi$
$48$	0.261802	+	0.453455i	0.0377879	+	0.0654506i
$49$	2.70393	−	4.68334i	0.386275	−	0.669049i
$50$		0			0
$51$	4.49330			0.629188
$52$	−8.19723	−	7.68167i	−1.13675	−	1.06526i
$53$	−4.52360			−0.621365			−0.310682	−	0.950514i	$-0.600558\pi$
$53$	−4.52360			−0.621365			−0.310682	+	0.950514i	$0.600558\pi$
$54$	−1.13090	+	1.95878i	−0.153896	+	0.266556i
$55$		0			0
$56$	−1.59214	−	2.75768i	−0.212759	−	0.368510i
$57$	5.11575			0.677598
$58$	1.55787	+	2.69832i	0.204559	+	0.354307i
$59$	0.426974	+	0.739540i	0.0555872	+	0.0962799i	0.892480	−	0.451087i	$-0.148964\pi$
$59$	0.426974	+	0.739540i	0.0555872	+	0.0962799i	−0.836893	+	0.547367i	$0.815630\pi$
$60$		0			0
$61$	−2.31968	−	4.01780i	−0.297004	−	0.514426i	0.678445	−	0.734651i	$-0.262654\pi$
$61$	−2.31968	−	4.01780i	−0.297004	−	0.514426i	−0.975449	+	0.220225i	$0.929321\pi$
$62$	−10.0321	+	17.3760i	−1.27407	+	2.20676i
$63$	−0.630901	+	1.09275i	−0.0794861	+	0.137674i
$64$	−13.0472			−1.63090
$65$		0			0
$66$	10.2315			1.25941
$67$	6.56633	−	11.3732i	0.802205	−	1.38946i	−0.115958	−	0.993254i	$-0.536994\pi$
$67$	6.56633	−	11.3732i	0.802205	−	1.38946i	0.918162	−	0.396205i	$-0.129673\pi$
$68$	−7.00000	+	12.1244i	−0.848875	+	1.47029i
$69$	1.11575	+	1.93253i	0.134320	+	0.232650i
$70$		0			0
$71$	4.80453	+	8.32168i	0.570192	+	0.987602i	0.996546	+	0.0830453i	$0.0264646\pi$
$71$	4.80453	+	8.32168i	0.570192	+	0.987602i	−0.426354	+	0.904557i	$0.640202\pi$
$72$	−1.26180	−	2.18551i	−0.148705	−	0.257564i
$73$	−13.7854			−1.61346			−0.806730	−	0.590920i	$-0.798765\pi$
$73$	−13.7854			−1.61346			−0.806730	+	0.590920i	$0.798765\pi$
$74$	−0.261802	−	0.453455i	−0.0304339	−	0.0527130i
$75$		0			0
$76$	−7.96970	+	13.8039i	−0.914187	+	1.58342i
$77$	5.70789			0.650475
$78$	−5.95058	−	5.57632i	−0.673770	−	0.631394i
$79$	−8.87085			−0.998049			−0.499024	−	0.866588i	$-0.666308\pi$
$79$	−8.87085			−0.998049			−0.499024	+	0.866588i	$0.666308\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−1.29607	−	2.24486i	−0.143127	−	0.247904i
$83$	8.23150			0.903524			0.451762	−	0.892138i	$-0.350796\pi$
$83$	8.23150			0.903524			0.451762	+	0.892138i	$0.350796\pi$
$84$	−1.96573	−	3.40474i	−0.214479	−	0.371488i
$85$		0			0
$86$	−14.4248			−1.55546
$87$	0.688776	+	1.19299i	0.0738445	+	0.127902i
$88$	−5.70789	+	9.88636i	−0.608464	+	1.05389i
$89$	−3.31122	+	5.73521i	−0.350989	+	0.607931i	−0.986423	−	0.164224i	$-0.947488\pi$
$89$	−3.31122	+	5.73521i	−0.350989	+	0.607931i	0.635434	+	0.772155i	$0.280821\pi$
$90$		0			0
$91$	−3.31968	−	3.11089i	−0.347997	−	0.326110i
$92$	−6.95279			−0.724879
$93$	−4.43543	+	7.68238i	−0.459932	+	0.796626i
$94$	−12.1972	+	21.1262i	−1.25805	+	2.17900i
$95$		0			0
$96$	−6.23150			−0.636000
$97$	5.33483	+	9.24019i	0.541670	+	0.938200i	0.998808	+	0.0488041i	$0.0155410\pi$
$97$	5.33483	+	9.24019i	0.541670	+	0.938200i	−0.457139	+	0.889395i	$0.651126\pi$
$98$	6.11575	+	10.5928i	0.617784	+	1.07003i
$99$	4.52360			0.454639
$100$		0			0
$101$	8.52360	−	14.7633i	0.848130	−	1.46900i	−0.0347444	−	0.999396i	$-0.511062\pi$
$101$	8.52360	−	14.7633i	0.848130	−	1.46900i	0.882875	−	0.469609i	$-0.155605\pi$
$102$	−5.08148	+	8.80138i	−0.503141	+	0.871466i
$103$	13.9484			1.37437			0.687187	−	0.726481i	$-0.258845\pi$
$103$	13.9484			1.37437			0.687187	+	0.726481i	$0.258845\pi$
$104$	8.70789	−	2.63896i	0.853879	−	0.258771i
$105$		0			0
$106$	5.11575	−	8.86074i	0.496886	−	0.860631i
$107$	6.24665	−	10.8195i	0.603886	−	1.04596i	−0.388340	−	0.921516i	$-0.626951\pi$
$107$	6.24665	−	10.8195i	0.603886	−	1.04596i	0.992226	−	0.124446i	$-0.0397153\pi$
$108$	−1.55787	−	2.69832i	−0.149907	−	0.259646i
$109$	−2.27871			−0.218261			−0.109130	−	0.994027i	$-0.534807\pi$
$109$	−2.27871			−0.218261			−0.109130	+	0.994027i	$0.534807\pi$
$110$		0			0
$111$	−0.115749	−	0.200484i	−0.0109864	−	0.0190291i
$112$	−0.660685			−0.0624289
$113$	−0.738198	−	1.27860i	−0.0694438	−	0.120280i	0.829213	−	0.558933i	$-0.188789\pi$
$113$	−0.738198	−	1.27860i	−0.0694438	−	0.120280i	−0.898657	+	0.438653i	$0.855456\pi$
$114$	−5.78541	+	10.0206i	−0.541853	+	0.938517i
$115$		0			0
$116$	−4.29211			−0.398512
$117$	−2.63090	−	2.46543i	−0.243227	−	0.227929i
$118$	−1.93146			−0.177805
$119$	−2.83483	+	4.91007i	−0.259868	+	0.450105i
$120$		0			0
$121$	−4.73150	−	8.19520i	−0.430136	−	0.745018i
$122$	10.4933			0.950019
$123$	−0.573026	−	0.992511i	−0.0516681	−	0.0894917i
$124$	−13.8197	−	23.9364i	−1.24104	−	2.14955i
$125$		0			0
$126$	−1.42697	−	2.47159i	−0.127125	−	0.220187i
$127$	−8.89270	+	15.4026i	−0.789100	+	1.36676i	0.137419	+	0.990513i	$0.456119\pi$
$127$	−8.89270	+	15.4026i	−0.789100	+	1.36676i	−0.926519	+	0.376248i	$0.877214\pi$
$128$	8.52360	−	14.7633i	0.753387	−	1.30491i
$129$	−6.37755			−0.561512
$130$		0			0
$131$	11.6697			1.01958			0.509791	−	0.860298i	$-0.329723\pi$
$131$	11.6697			1.01958			0.509791	+	0.860298i	$0.329723\pi$
$132$	−7.04721	+	12.2061i	−0.613381	+	1.06241i
$133$	−3.22753	+	5.59025i	−0.279863	+	0.484736i
$134$	14.8517	+	25.7240i	1.28299	+	2.22221i
$135$		0			0
$136$	−5.66966	−	9.82013i	−0.486169	−	0.842070i
$137$	−10.0321	−	17.3760i	−0.857096	−	1.48453i	−0.874686	−	0.484689i	$-0.838933\pi$
$137$	−10.0321	−	17.3760i	−0.857096	−	1.48453i	0.0175898	−	0.999845i	$-0.494401\pi$
$138$	−5.04721			−0.429647
$139$	−8.16966	−	14.1503i	−0.692941	−	1.20021i	−0.970870	−	0.239608i	$-0.922981\pi$
$139$	−8.16966	−	14.1503i	−0.692941	−	1.20021i	0.277928	−	0.960602i	$-0.410352\pi$
$140$		0			0
$141$	−5.39270	+	9.34044i	−0.454148	+	0.786607i
$142$	−21.7338			−1.82386
$143$	−3.70789	+	15.8830i	−0.310070	+	1.32821i
$144$	−0.523604			−0.0436337
$145$		0			0
$146$	15.5899	−	27.0026i	1.29023	−	2.23475i
$147$	2.70393	+	4.68334i	0.223016	+	0.386275i
$148$	0.721292			0.0592899
$149$	1.62245	+	2.81016i	0.132916	+	0.230218i	0.924799	−	0.380455i	$-0.124233\pi$
$149$	1.62245	+	2.81016i	0.132916	+	0.230218i	−0.791883	+	0.610672i	$0.790899\pi$
$150$		0			0
$151$	5.69996			0.463856			0.231928	−	0.972733i	$-0.425497\pi$
$151$	5.69996			0.463856			0.231928	+	0.972733i	$0.425497\pi$
$152$	−6.45506	−	11.1805i	−0.523575	−	0.906858i
$153$	−2.24665	+	3.89131i	−0.181631	+	0.314594i
$154$	−6.45506	+	11.1805i	−0.520164	+	0.900950i
$155$		0			0
$156$	10.7511	−	3.25817i	0.860780	−	0.260863i
$157$	3.85395			0.307578			0.153789	−	0.988104i	$-0.450852\pi$
$157$	3.85395			0.307578			0.153789	+	0.988104i	$0.450852\pi$
$158$	10.0321	−	17.3760i	0.798108	−	1.38236i
$159$	2.26180	−	3.91756i	0.179373	−	0.310682i
$160$		0			0
$161$	−2.81571			−0.221909
$162$	−1.13090	−	1.95878i	−0.0888520	−	0.153896i
$163$	−4.86240	−	8.42192i	−0.380853	−	0.659656i	0.610332	−	0.792146i	$-0.291036\pi$
$163$	−4.86240	−	8.42192i	−0.380853	−	0.659656i	−0.991184	+	0.132490i	$0.957703\pi$
$164$	3.57081			0.278834
$165$		0			0
$166$	−9.30901	+	16.1237i	−0.722519	+	1.25144i
$167$	−9.63935	+	16.6959i	−0.745916	+	1.29196i	0.203850	+	0.979002i	$0.434654\pi$
$167$	−9.63935	+	16.6959i	−0.745916	+	1.29196i	−0.949766	+	0.312962i	$0.898679\pi$
$168$	3.18429			0.245673
$169$	10.8130	−	7.21661i	0.831768	−	0.555124i
$170$		0			0
$171$	−2.55787	+	4.43037i	−0.195606	+	0.338799i
$172$	9.93543	−	17.2087i	0.757569	−	1.31215i
$173$	−1.50845	−	2.61272i	−0.114686	−	0.198641i	0.802968	−	0.596022i	$-0.203253\pi$
$173$	−1.50845	−	2.61272i	−0.114686	−	0.198641i	−0.917654	+	0.397380i	$0.869919\pi$
$174$	−3.11575			−0.236204
$175$		0			0
$176$	1.18429	+	2.05125i	0.0892692	+	0.154619i
$177$	−0.853947			−0.0641866
$178$	−7.48933	−	12.9719i	−0.561349	−	0.972286i
$179$	2.65847	−	4.60461i	0.198704	−	0.344165i	−0.749405	−	0.662112i	$-0.769660\pi$
$179$	2.65847	−	4.60461i	0.198704	−	0.344165i	0.948108	+	0.317947i	$0.102994\pi$
$180$		0			0
$181$	25.8709			1.92297			0.961483	−	0.274866i	$-0.0886333\pi$
$181$	25.8709			1.92297			0.961483	+	0.274866i	$0.0886333\pi$
$182$	9.84777	−	2.98440i	0.729965	−	0.221219i
$183$	4.63935			0.342951
$184$	2.81571	−	4.87695i	0.207577	−	0.359534i
$185$		0			0
$186$	−10.0321	−	17.3760i	−0.735586	−	1.27407i
$187$	20.3259			1.48638
$188$	−16.8023	−	29.1025i	−1.22543	−	2.12251i
$189$	−0.630901	−	1.09275i	−0.0458913	−	0.0794861i
$190$		0			0
$191$	−5.32813	−	9.22859i	−0.385530	−	0.667757i	0.606313	−	0.795226i	$-0.292648\pi$
$191$	−5.32813	−	9.22859i	−0.385530	−	0.667757i	−0.991843	+	0.127469i	$0.959315\pi$
$192$	6.52360	−	11.2992i	0.470801	−	0.815451i
$193$	3.99155	−	6.91356i	0.287318	−	0.497649i	−0.685851	−	0.727742i	$-0.740570\pi$
$193$	3.99155	−	6.91356i	0.287318	−	0.497649i	0.973169	+	0.230093i	$0.0739031\pi$
$194$	−24.1327			−1.73262
$195$		0			0
$196$	−16.8495			−1.20354
$197$	8.66966	−	15.0163i	0.617688	−	1.06987i	−0.372219	−	0.928145i	$-0.621403\pi$
$197$	8.66966	−	15.0163i	0.617688	−	1.06987i	0.989907	−	0.141721i	$-0.0452637\pi$
$198$	−5.11575	+	8.86074i	−0.363560	+	0.629705i
$199$	0.615749	+	1.06651i	0.0436493	+	0.0756028i	0.887025	−	0.461722i	$-0.152768\pi$
$199$	0.615749	+	1.06651i	0.0436493	+	0.0756028i	−0.843375	+	0.537325i	$0.819435\pi$
$200$		0			0
$201$	6.56633	+	11.3732i	0.463153	+	0.802205i
$202$	19.2787	+	33.3917i	1.35645	+	2.34943i
$203$	−1.73820			−0.121998
$204$	−7.00000	−	12.1244i	−0.490098	−	0.848875i
$205$		0			0
$206$	−15.7742	+	27.3218i	−1.09904	+	1.90360i
$207$	−2.23150			−0.155100
$208$	0.429187	−	1.83845i	0.0297587	−	0.127474i
$209$	23.1416			1.60074
$210$		0			0
$211$	−5.16966	+	8.95411i	−0.355894	+	0.616426i	−0.987271	−	0.159050i	$-0.949157\pi$
$211$	−5.16966	+	8.95411i	−0.355894	+	0.616426i	0.631377	+	0.775476i	$0.282490\pi$
$212$	7.04721	+	12.2061i	0.484004	+	0.838320i
$213$	−9.60905			−0.658401
$214$	14.1287	+	24.4716i	0.965817	+	1.67284i
$215$		0			0
$216$	2.52360			0.171710
$217$	−5.59663	−	9.69365i	−0.379924	−	0.658048i
$218$	2.57699	−	4.46348i	0.174536	−	0.302305i
$219$	6.89270	−	11.9385i	0.465766	−	0.806730i
$220$		0			0
$221$	−11.8214	−	11.0779i	−0.795195	−	0.745182i
$222$	0.523604			0.0351420
$223$	10.7854	−	18.6809i	0.722244	−	1.25096i	−0.237854	−	0.971301i	$-0.576444\pi$
$223$	10.7854	−	18.6809i	0.722244	−	1.25096i	0.960098	−	0.279663i	$-0.0902227\pi$
$224$	3.93146	−	6.80949i	0.262682	−	0.454978i
$225$		0			0
$226$	3.33931			0.222128
$227$	2.72305	+	4.71645i	0.180735	+	0.313042i	0.942131	−	0.335245i	$-0.108819\pi$
$227$	2.72305	+	4.71645i	0.180735	+	0.313042i	−0.761396	+	0.648287i	$0.775486\pi$
$228$	−7.96970	−	13.8039i	−0.527806	−	0.914187i
$229$	21.9315			1.44927			0.724636	−	0.689132i	$-0.242008\pi$
$229$	21.9315			1.44927			0.724636	+	0.689132i	$0.242008\pi$
$230$		0			0
$231$	−2.85395	+	4.94318i	−0.187776	+	0.325237i
$232$	1.73820	−	3.01065i	0.114118	−	0.197659i
$233$	−25.3125			−1.65828			−0.829139	−	0.559042i	$-0.811169\pi$
$233$	−25.3125			−1.65828			−0.829139	+	0.559042i	$0.811169\pi$
$234$	7.80453	−	2.36519i	0.510198	−	0.154617i
$235$		0			0
$236$	1.33034	−	2.30422i	0.0865979	−	0.149992i
$237$	4.43543	−	7.68238i	0.288112	−	0.499024i
$238$	−6.41182	−	11.1056i	−0.415617	−	0.719869i
$239$	22.5236			1.45693			0.728465	−	0.685083i	$-0.240234\pi$
$239$	22.5236			1.45693			0.728465	+	0.685083i	$0.240234\pi$
$240$		0			0
$241$	−5.55787	−	9.62652i	−0.358014	−	0.620099i	0.629615	−	0.776907i	$-0.283213\pi$
$241$	−5.55787	−	9.62652i	−0.358014	−	0.620099i	−0.987629	+	0.156809i	$0.949879\pi$
$242$	21.4034			1.37586
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$	−7.22753	+	12.5185i	−0.462695	+	0.801412i
$245$		0			0
$246$	2.59214			0.165269
$247$	−13.4590	−	12.6125i	−0.856378	−	0.802516i
$248$	22.3865			1.42155
$249$	−4.11575	+	7.12869i	−0.260825	+	0.451762i
$250$		0			0
$251$	−5.52360	−	9.56716i	−0.348647	−	0.603874i	0.637363	−	0.770564i	$-0.280025\pi$
$251$	−5.52360	−	9.56716i	−0.348647	−	0.603874i	−0.986009	+	0.166690i	$0.946692\pi$
$252$	3.93146			0.247659
$253$	5.04721	+	8.74202i	0.317315	+	0.549606i
$254$	−20.1135	−	34.8377i	−1.26204	−	2.18591i
$255$		0			0
$256$	6.23150	+	10.7933i	0.389469	+	0.674580i
$257$	−1.01515	+	1.75829i	−0.0633234	+	0.109679i	−0.895949	−	0.444157i	$-0.853503\pi$
$257$	−1.01515	+	1.75829i	−0.0633234	+	0.109679i	0.832626	+	0.553836i	$0.186837\pi$
$258$	7.21238	−	12.4922i	0.449023	−	0.777731i
$259$	0.292106			0.0181506
$260$		0			0
$261$	−1.37755			−0.0852683
$262$	−13.1972	+	22.8583i	−0.815328	+	1.41219i
$263$	1.62420	−	2.81320i	0.100153	−	0.173469i	−0.811595	−	0.584221i	$-0.801400\pi$
$263$	1.62420	−	2.81320i	0.100153	−	0.173469i	0.911747	+	0.410751i	$0.134734\pi$
$264$	−5.70789	−	9.88636i	−0.351297	−	0.608464i
$265$		0			0
$266$	−7.30004	−	12.6440i	−0.447594	−	0.775256i
$267$	−3.31122	−	5.73521i	−0.202644	−	0.350989i
$268$	−40.9181			−2.49947
$269$	−13.4742	−	23.3380i	−0.821535	−	1.42294i	−0.904539	−	0.426392i	$-0.859784\pi$
$269$	−13.4742	−	23.3380i	−0.821535	−	1.42294i	0.0830032	−	0.996549i	$-0.473549\pi$
$270$		0			0
$271$	9.92476	−	17.1902i	0.602886	−	1.04423i	−0.389495	−	0.921028i	$-0.627351\pi$
$271$	9.92476	−	17.1902i	0.602886	−	1.04423i	0.992382	−	0.123201i	$-0.0393161\pi$
$272$	−2.35271			−0.142654
$273$	4.35395	−	1.31948i	0.263513	−	0.0798586i
$274$	45.3811			2.74157
$275$		0			0
$276$	3.47640	−	6.02129i	0.209254	−	0.362439i
$277$	8.04721	+	13.9382i	0.483510	+	0.837464i	0.999821	−	0.0189376i	$-0.00602837\pi$
$277$	8.04721	+	13.9382i	0.483510	+	0.837464i	−0.516311	+	0.856401i	$0.672695\pi$
$278$	36.9563			2.21649
$279$	−4.43543	−	7.68238i	−0.265542	−	0.459932i
$280$		0			0
$281$	−5.37755			−0.320798			−0.160399	−	0.987052i	$-0.551278\pi$
$281$	−5.37755			−0.320798			−0.160399	+	0.987052i	$0.551278\pi$
$282$	−12.1972	−	21.1262i	−0.726334	−	1.25805i
$283$	13.4332	−	23.2670i	0.798522	−	1.38308i	−0.122057	−	0.992523i	$-0.538949\pi$
$283$	13.4332	−	23.2670i	0.798522	−	1.38308i	0.920579	−	0.390557i	$-0.127718\pi$
$284$	14.9697	−	25.9283i	0.888288	−	1.53856i
$285$		0			0
$286$	−26.9181	−	25.2251i	−1.59170	−	1.49159i
$287$	1.44609			0.0853601
$288$	3.11575	−	5.39664i	0.183597	−	0.318000i
$289$	−1.59488	+	2.76241i	−0.0938163	+	0.162495i
$290$		0			0
$291$	−10.6697			−0.625466
$292$	21.4759	+	37.1974i	1.25678	+	2.17681i
$293$	10.7096	+	18.5497i	0.625664	+	1.08368i	0.988412	+	0.151795i	$0.0485054\pi$
$293$	10.7096	+	18.5497i	0.625664	+	1.08368i	−0.362748	+	0.931887i	$0.618161\pi$
$294$	−12.2315			−0.713355
$295$		0			0
$296$	−0.292106	+	0.505942i	−0.0169783	+	0.0294073i
$297$	−2.26180	+	3.91756i	−0.131243	+	0.227320i
$298$	−7.33931			−0.425155
$299$	1.82911	−	7.83511i	0.105780	−	0.453116i
$300$		0			0
$301$	4.02360	−	6.96909i	0.231917	−	0.401692i
$302$	−6.44609	+	11.1650i	−0.370931	+	0.642471i
$303$	8.52360	+	14.7633i	0.489668	+	0.848130i
$304$	−2.67863			−0.153630
$305$		0			0
$306$	−5.08148	−	8.80138i	−0.290489	−	0.503141i
$307$	7.85395			0.448248			0.224124	−	0.974561i	$-0.428048\pi$
$307$	7.85395			0.448248			0.224124	+	0.974561i	$0.428048\pi$
$308$	−8.89218	−	15.4017i	−0.506679	−	0.877594i
$309$	−6.97418	+	12.0796i	−0.396747	+	0.687187i
$310$		0			0
$311$	−27.8744			−1.58061			−0.790305	−	0.612714i	$-0.790078\pi$
$311$	−27.8744			−1.58061			−0.790305	+	0.612714i	$0.790078\pi$
$312$	−2.06854	+	8.86074i	−0.117108	+	0.501641i
$313$	−7.88776			−0.445842			−0.222921	−	0.974836i	$-0.571559\pi$
$313$	−7.88776			−0.445842			−0.222921	+	0.974836i	$0.571559\pi$
$314$	−4.35843	+	7.54903i	−0.245961	+	0.426016i
$315$		0			0
$316$	13.8197	+	23.9364i	0.777418	+	1.34653i
$317$	−13.2181			−0.742403			−0.371201	−	0.928552i	$-0.621054\pi$
$317$	−13.2181			−0.742403			−0.371201	+	0.928552i	$0.621054\pi$
$318$	5.11575	+	8.86074i	0.286877	+	0.496886i
$319$	3.11575	+	5.39664i	0.174448	+	0.302154i
$320$		0			0
$321$	6.24665	+	10.8195i	0.348654	+	0.603886i
$322$	3.18429	−	5.51535i	0.177454	−	0.307359i
$323$	−11.4933	+	19.9070i	−0.639504	+	1.10765i
$324$	3.11575			0.173097
$325$		0			0
$326$	21.9956			1.21822
$327$	1.13935	−	1.97342i	0.0630064	−	0.109130i
$328$	−1.44609	+	2.50470i	−0.0798471	+	0.138299i
$329$	−6.80453	−	11.7858i	−0.375146	−	0.649771i
$330$		0			0
$331$	11.9248	+	20.6543i	0.655444	+	1.13526i	0.981782	+	0.190009i	$0.0608519\pi$
$331$	11.9248	+	20.6543i	0.655444	+	1.13526i	−0.326338	+	0.945253i	$0.605815\pi$
$332$	−12.8236	−	22.2112i	−0.703789	−	1.21900i
$333$	0.231499			0.0126861
$334$	−21.8023	−	37.7627i	−1.19297	−	2.06628i
$335$		0			0
$336$	0.330343	−	0.572170i	0.0180217	−	0.0312144i
$337$	−5.68306			−0.309576			−0.154788	−	0.987948i	$-0.549469\pi$
$337$	−5.68306			−0.309576			−0.154788	+	0.987948i	$0.549469\pi$
$338$	1.90734	+	29.3415i	0.103745	+	1.59597i
$339$	1.47640			0.0801868
$340$		0			0
$341$	−20.0641	+	34.7521i	−1.08653	+	1.88193i
$342$	−5.78541	−	10.0206i	−0.312839	−	0.541853i
$343$	−15.6563			−0.845359
$344$	8.04721	+	13.9382i	0.433876	+	0.751496i
$345$		0			0
$346$	6.82364			0.366841
$347$	−10.7248	−	18.5759i	−0.575737	−	0.997206i	−0.995961	−	0.0897859i	$-0.971382\pi$
$347$	−10.7248	−	18.5759i	−0.575737	−	0.997206i	0.420224	−	0.907421i	$-0.361952\pi$
$348$	2.14605	−	3.71707i	0.115041	−	0.199256i
$349$	−3.43543	+	5.95033i	−0.183894	+	0.318514i	−0.943203	−	0.332216i	$-0.892204\pi$
$349$	−3.43543	+	5.95033i	−0.183894	+	0.318514i	0.759309	+	0.650730i	$0.225537\pi$
$350$		0			0
$351$	3.45058	−	1.04571i	0.184178	−	0.0558159i
$352$	−28.1888			−1.50247
$353$	17.2484	−	29.8751i	0.918040	−	1.59009i	0.115651	−	0.993290i	$-0.463104\pi$
$353$	17.2484	−	29.8751i	0.918040	−	1.59009i	0.802389	−	0.596802i	$-0.203562\pi$
$354$	0.965730	−	1.67269i	0.0513280	−	0.0889026i
$355$		0			0
$356$	20.6339			1.09359
$357$	−2.83483	−	4.91007i	−0.150035	−	0.259868i
$358$	6.01294	+	10.4147i	0.317794	+	0.550435i
$359$	−8.15945			−0.430639			−0.215320	−	0.976544i	$-0.569079\pi$
$359$	−8.15945			−0.430639			−0.215320	+	0.976544i	$0.569079\pi$
$360$		0			0
$361$	−3.58545	+	6.21017i	−0.188708	+	0.326851i
$362$	−29.2574	+	50.6753i	−1.53773	+	2.66343i
$363$	9.46300			0.496679
$364$	−3.22253	+	13.8039i	−0.168906	+	0.723522i
$365$		0			0
$366$	−5.24665	+	9.08747i	−0.274247	+	0.475009i
$367$	−3.42027	+	5.92409i	−0.178537	+	0.309235i	−0.941380	−	0.337349i	$-0.890470\pi$
$367$	−3.42027	+	5.92409i	−0.178537	+	0.309235i	0.762843	+	0.646584i	$0.223803\pi$
$368$	−0.584211	−	1.01188i	−0.0304541	−	0.0527481i
$369$	1.14605			0.0596611
$370$		0			0
$371$	2.85395	+	4.94318i	0.148170	+	0.256637i
$372$	27.6394			1.43303
$373$	6.90961	+	11.9678i	0.357766	+	0.619669i	0.987587	−	0.157071i	$-0.0502052\pi$
$373$	6.90961	+	11.9678i	0.357766	+	0.619669i	−0.629821	+	0.776740i	$0.716872\pi$
$374$	−22.9866	+	39.8140i	−1.18861	+	2.05873i
$375$		0			0
$376$	27.2181			1.40367
$377$	1.12915	−	4.83678i	0.0581540	−	0.249107i
$378$	2.85395			0.146791
$379$	−5.75784	+	9.97286i	−0.295760	+	0.512272i	−0.975161	−	0.221495i	$-0.928906\pi$
$379$	−5.75784	+	9.97286i	−0.295760	+	0.512272i	0.679401	+	0.733767i	$0.262240\pi$
$380$		0			0
$381$	−8.89270	−	15.4026i	−0.455587	−	0.789100i
$382$	24.1024			1.23318
$383$	11.4399	+	19.8145i	0.584552	+	1.01247i	0.994931	+	0.100559i	$0.0320631\pi$
$383$	11.4399	+	19.8145i	0.584552	+	1.01247i	−0.410379	+	0.911915i	$0.634604\pi$
$384$	8.52360	+	14.7633i	0.434968	+	0.753387i
$385$		0			0
$386$	9.02809	+	15.6371i	0.459518	+	0.795908i
$387$	3.18878	−	5.52312i	0.162095	−	0.280756i
$388$	16.6220	−	28.7901i	0.843854	−	1.46160i
$389$	−4.35271			−0.220691			−0.110346	−	0.993893i	$-0.535196\pi$
$389$	−4.35271			−0.220691			−0.110346	+	0.993893i	$0.535196\pi$
$390$		0			0
$391$	−10.0268			−0.507077
$392$	6.82364	−	11.8189i	0.344646	−	0.596944i
$393$	−5.83483	+	10.1062i	−0.294328	+	0.509791i
$394$	19.6091	+	33.9639i	0.987890	+	1.71108i
$395$		0			0
$396$	−7.04721	−	12.2061i	−0.354136	−	0.613381i
$397$	3.81122	+	6.60123i	0.191280	+	0.331306i	0.945675	−	0.325115i	$-0.105403\pi$
$397$	3.81122	+	6.60123i	0.191280	+	0.331306i	−0.754395	+	0.656421i	$0.772070\pi$
$398$	−2.78541			−0.139620
$399$	−3.22753	−	5.59025i	−0.161579	−	0.279863i
$400$		0			0
$401$	−10.4248	+	18.0562i	−0.520588	+	0.901684i	0.479126	+	0.877746i	$0.340954\pi$
$401$	−10.4248	+	18.0562i	−0.520588	+	0.901684i	−0.999713	+	0.0239381i	$0.992380\pi$
$402$	−29.7035			−1.48147
$403$	30.6096	−	9.27635i	1.52477	−	0.462088i
$404$	−53.1148			−2.64256
$405$		0			0
$406$	1.96573	−	3.40474i	0.0975575	−	0.168975i
$407$	−0.523604	−	0.906910i	−0.0259541	−	0.0449538i
$408$	11.3393			0.561380
$409$	8.48264	+	14.6924i	0.419439	+	0.726490i	0.995883	−	0.0906466i	$-0.0288934\pi$
$409$	8.48264	+	14.6924i	0.419439	+	0.726490i	−0.576444	+	0.817137i	$0.695560\pi$
$410$		0			0
$411$	20.0641			0.989690
$412$	−21.7298	−	37.6371i	−1.07055	−	1.85425i
$413$	0.538756	−	0.933153i	0.0265105	−	0.0459175i
$414$	2.52360	−	4.37101i	0.124028	−	0.214823i
$415$		0			0
$416$	16.3945	+	15.3633i	0.803804	+	0.753250i
$417$	16.3393			0.800140
$418$	−26.1709	+	45.3293i	−1.28006	+	2.21713i
$419$	−1.04942	+	1.81765i	−0.0512676	+	0.0887981i	−0.890520	−	0.454943i	$-0.849659\pi$
$419$	−1.04942	+	1.81765i	−0.0512676	+	0.0887981i	0.839253	+	0.543742i	$0.182993\pi$
$420$		0			0
$421$	−39.6598			−1.93290			−0.966449	−	0.256857i	$-0.917313\pi$
$421$	−39.6598			−1.93290			−0.966449	+	0.256857i	$0.917313\pi$
$422$	−11.6927	−	20.2524i	−0.569194	−	0.985873i
$423$	−5.39270	−	9.34044i	−0.262202	−	0.454148i
$424$	−11.4158			−0.554400
$425$		0			0
$426$	10.8669	−	18.8220i	0.526502	−	0.911929i
$427$	−2.92697	+	5.06967i	−0.141646	+	0.245338i
$428$	−38.9260			−1.88156
$429$	−11.9012	−	11.1526i	−0.574593	−	0.538455i
$430$		0			0
$431$	11.0641	−	19.1636i	0.532940	−	0.923079i	−0.466320	−	0.884616i	$-0.654421\pi$
$431$	11.0641	−	19.1636i	0.532940	−	0.923079i	0.999260	−	0.0384626i	$-0.0122461\pi$
$432$	0.261802	−	0.453455i	0.0125960	−	0.0218169i
$433$	−15.6781	−	27.1553i	−0.753442	−	1.30500i	−0.946145	−	0.323743i	$-0.895059\pi$
$433$	−15.6781	−	27.1553i	−0.753442	−	1.30500i	0.192703	−	0.981257i	$-0.438275\pi$
$434$	25.3169			1.21525
$435$		0			0
$436$	3.54994	+	6.14868i	0.170011	+	0.294468i
$437$	−11.4158			−0.546091
$438$	15.5899	+	27.0026i	0.744916	+	1.29023i
$439$	−2.15672	+	3.73555i	−0.102935	+	0.178288i	−0.912892	−	0.408200i	$-0.866157\pi$
$439$	−2.15672	+	3.73555i	−0.102935	+	0.178288i	0.809958	+	0.586488i	$0.199490\pi$
$440$		0			0
$441$	−5.40786			−0.257517
$442$	35.0681	−	10.6275i	1.66802	−	0.505499i
$443$	−0.493301			−0.0234374			−0.0117187	−	0.999931i	$-0.503730\pi$
$443$	−0.493301			−0.0234374			−0.0117187	+	0.999931i	$0.503730\pi$
$444$	−0.360646	+	0.624657i	−0.0171155	+	0.0296449i
$445$		0			0
$446$	24.3945	+	42.2524i	1.15511	+	2.00071i
$447$	−3.24490			−0.153478
$448$	8.23150	+	14.2574i	0.388902	+	0.673598i
$449$	11.6563	+	20.1892i	0.550093	+	0.952789i	0.998267	+	0.0588427i	$0.0187410\pi$
$449$	11.6563	+	20.1892i	0.550093	+	0.952789i	−0.448174	+	0.893946i	$0.647926\pi$
$450$		0			0
$451$	−2.59214	−	4.48973i	−0.122059	−	0.211413i
$452$	−2.30004	+	3.98378i	−0.108185	+	0.187381i
$453$	−2.84998	+	4.93631i	−0.133904	+	0.231928i
$454$	−12.3180			−0.578112
$455$		0			0
$456$	12.9101			0.604572
$457$	3.33483	−	5.77609i	0.155997	−	0.270194i	−0.777425	−	0.628976i	$-0.783474\pi$
$457$	3.33483	−	5.77609i	0.155997	−	0.270194i	0.933422	+	0.358782i	$0.116808\pi$
$458$	−24.8023	+	42.9589i	−1.15894	+	2.00734i
$459$	−2.24665	−	3.89131i	−0.104865	−	0.181631i
$460$		0			0
$461$	−14.5596	−	25.2180i	−0.678110	−	1.17452i	−0.975550	−	0.219780i	$-0.929466\pi$
$461$	−14.5596	−	25.2180i	−0.678110	−	1.17452i	0.297440	−	0.954740i	$-0.403867\pi$
$462$	−6.45506	−	11.1805i	−0.300317	−	0.520164i
$463$	1.79334			0.0833436			0.0416718	−	0.999131i	$-0.486732\pi$
$463$	1.79334			0.0833436			0.0416718	+	0.999131i	$0.486732\pi$
$464$	−0.360646	−	0.624657i	−0.0167426	−	0.0289990i
$465$		0			0
$466$	28.6260	−	49.5816i	1.32607	−	2.29682i
$467$	−16.8192			−0.778301			−0.389150	−	0.921174i	$-0.627231\pi$
$467$	−16.8192			−0.778301			−0.389150	+	0.921174i	$0.627231\pi$
$468$	−2.55391	+	10.9398i	−0.118054	+	0.505694i
$469$	−16.5708			−0.765169
$470$		0			0
$471$	−1.92697	+	3.33762i	−0.0887903	+	0.153789i
$472$	1.07751	+	1.86631i	0.0495965	+	0.0859037i
$473$	−28.8495			−1.32650
$474$	10.0321	+	17.3760i	0.460788	+	0.798108i
$475$		0			0
$476$	17.6652			0.809685
$477$	2.26180	+	3.91756i	0.103561	+	0.179373i
$478$	−25.4720	+	44.1187i	−1.16506	+	2.01794i
$479$	−17.5765	+	30.4434i	−0.803092	+	1.39100i	0.114479	+	0.993426i	$0.463480\pi$
$479$	−17.5765	+	30.4434i	−0.803092	+	1.39100i	−0.917571	+	0.397571i	$0.869853\pi$
$480$		0			0
$481$	−0.189754	+	0.812826i	−0.00865205	+	0.0370617i
$482$	25.1416			1.14517
$483$	1.40786	−	2.43848i	0.0640596	−	0.110955i
$484$	−14.7422	+	25.5342i	−0.670098	+	1.16064i
$485$		0			0
$486$	2.26180			0.102597
$487$	−4.31298	−	7.47030i	−0.195440	−	0.338511i	0.751605	−	0.659614i	$-0.229280\pi$
$487$	−4.31298	−	7.47030i	−0.195440	−	0.338511i	−0.947045	+	0.321102i	$0.895947\pi$
$488$	−5.85395	−	10.1393i	−0.264996	−	0.458986i
$489$	9.72480			0.439771
$490$		0			0
$491$	11.6068	−	20.1036i	0.523809	−	0.907264i	−0.475807	−	0.879550i	$-0.657844\pi$
$491$	11.6068	−	20.1036i	0.523809	−	0.907264i	0.999616	−	0.0277143i	$-0.00882287\pi$
$492$	−1.78541	+	3.09242i	−0.0804924	+	0.139417i
$493$	−6.18975			−0.278773
$494$	39.9260	−	12.0997i	1.79636	−	0.544392i
$495$		0			0
$496$	2.32241	−	4.02253i	0.104279	−	0.180617i
$497$	6.06236	−	10.5003i	0.271934	−	0.471004i
$498$	−9.30901	−	16.1237i	−0.417147	−	0.722519i
$499$	29.0393			1.29998			0.649988	−	0.759944i	$-0.274774\pi$
$499$	29.0393			1.29998			0.649988	+	0.759944i	$0.274774\pi$
$500$		0			0
$501$	−9.63935	−	16.6959i	−0.430655	−	0.745916i
$502$	24.9866			1.11521
$503$	−8.69996	−	15.0688i	−0.387912	−	0.671883i	0.604256	−	0.796790i	$-0.293470\pi$
$503$	−8.69996	−	15.0688i	−0.387912	−	0.671883i	−0.992169	+	0.124906i	$0.960137\pi$
$504$	−1.59214	+	2.75768i	−0.0709198	+	0.122837i
$505$		0			0
$506$	−22.8316			−1.01499
$507$	0.843281	+	12.9726i	0.0374514	+	0.576134i
$508$	55.4149			2.45864
$509$	11.4382	−	19.8115i	0.506987	−	0.878128i	−0.492980	−	0.870041i	$-0.664092\pi$
$509$	11.4382	−	19.8115i	0.506987	−	0.878128i	0.999967	−	0.00808731i	$-0.00257430\pi$
$510$		0			0
$511$	8.69723	+	15.0640i	0.384743	+	0.666394i
$512$	5.90558			0.260992
$513$	−2.55787	−	4.43037i	−0.112933	−	0.195606i
$514$	−2.29607	−	3.97691i	−0.101275	−	0.175414i
$515$		0			0
$516$	9.93543	+	17.2087i	0.437383	+	0.757569i
$517$	−24.3945	+	42.2524i	−1.07287	+	1.85826i
$518$	−0.330343	+	0.572170i	−0.0145144	+	0.0251397i
$519$	3.01691			0.132427
$520$		0			0
$521$	−26.3642			−1.15503			−0.577517	−	0.816378i	$-0.695978\pi$
$521$	−26.3642			−1.15503			−0.577517	+	0.816378i	$0.695978\pi$
$522$	1.55787	−	2.69832i	0.0681863	−	0.118102i
$523$	−13.1461	+	22.7696i	−0.574837	+	0.995646i	0.421223	+	0.906957i	$0.361601\pi$
$523$	−13.1461	+	22.7696i	−0.574837	+	0.995646i	−0.996059	+	0.0886892i	$0.971732\pi$
$524$	−18.1799	−	31.4884i	−0.794191	−	1.37558i
$525$		0			0
$526$	3.67362	+	6.36290i	0.160178	+	0.277436i
$527$	−19.9297	−	34.5193i	−0.868152	−	1.50368i
$528$	−2.36858			−0.103079
$529$	9.01021	+	15.6061i	0.391748	+	0.678528i
$530$		0			0
$531$	0.426974	−	0.739540i	0.0185291	−	0.0320933i
$532$	20.1124			0.871981
$533$	−0.939393	+	4.02396i	−0.0406896	+	0.174297i
$534$	14.9787			0.648190
$535$		0			0
$536$	16.5708	−	28.7015i	0.715750	−	1.23972i
$537$	2.65847	+	4.60461i	0.114722	+	0.198704i
$538$	60.9519			2.62782
$539$	12.2315	+	21.1856i	0.526848	+	0.912527i
$540$		0			0
$541$	−0.107816			−0.00463537			−0.00231768	−	0.999997i	$-0.500738\pi$
$541$	−0.107816			−0.00463537			−0.00231768	+	0.999997i	$0.500738\pi$
$542$	22.4478	+	38.8808i	0.964218	+	1.67007i
$543$	−12.9354	+	22.4048i	−0.555112	+	0.961483i
$544$	14.0000	−	24.2487i	0.600245	−	1.03965i
$545$		0			0
$546$	−2.33931	+	10.0206i	−0.100113	+	0.428843i
$547$	−12.1193			−0.518182			−0.259091	−	0.965853i	$-0.583423\pi$
$547$	−12.1193			−0.518182			−0.259091	+	0.965853i	$0.583423\pi$
$548$	−31.2574	+	54.1394i	−1.33525	+	2.31272i
$549$	−2.31968	+	4.01780i	−0.0990014	+	0.171475i
$550$		0			0
$551$	−7.04721			−0.300221
$552$	2.81571	+	4.87695i	0.119845	+	0.207577i
$553$	5.59663	+	9.69365i	0.237993	+	0.412216i
$554$	−36.4024			−1.54659
$555$		0			0
$556$	−25.4546	+	44.0887i	−1.07952	+	1.86978i
$557$	19.0035	−	32.9150i	0.805204	−	1.39466i	−0.110948	−	0.993826i	$-0.535389\pi$
$557$	19.0035	−	32.9150i	0.805204	−	1.39466i	0.916153	−	0.400829i	$-0.131278\pi$
$558$	20.0641			0.849382
$559$	16.7787	+	15.7234i	0.709664	+	0.665030i
$560$		0			0
$561$	−10.1630	+	17.6028i	−0.429080	+	0.743189i
$562$	6.08148	−	10.5334i	0.256532	−	0.444326i
$563$	7.75510	+	13.4322i	0.326839	+	0.566101i	0.981883	−	0.189490i	$-0.0606833\pi$
$563$	7.75510	+	13.4322i	0.326839	+	0.566101i	−0.655044	+	0.755591i	$0.727350\pi$
$564$	33.6046			1.41501
$565$		0			0
$566$	30.3833	+	52.6254i	1.27710	+	2.21201i
$567$	1.26180			0.0529907
$568$	12.1247	+	21.0006i	0.508742	+	0.881167i
$569$	−9.62024	+	16.6627i	−0.403301	+	0.698538i	−0.994122	−	0.108265i	$-0.965471\pi$
$569$	−9.62024	+	16.6627i	−0.403301	+	0.698538i	0.590821	+	0.806803i	$0.298804\pi$
$570$		0			0
$571$	27.7338			1.16062			0.580311	−	0.814395i	$-0.302931\pi$
$571$	27.7338			1.16062			0.580311	+	0.814395i	$0.302931\pi$
$572$	48.6339	−	14.7387i	2.03349	−	0.616255i
$573$	10.6563			0.445172
$574$	−1.63539	+	2.83257i	−0.0682597	+	0.118229i
$575$		0			0
$576$	6.52360	+	11.2992i	0.271817	+	0.470801i
$577$	−26.9866			−1.12347			−0.561733	−	0.827318i	$-0.689865\pi$
$577$	−26.9866			−1.12347			−0.561733	+	0.827318i	$0.689865\pi$
$578$	−3.60730	−	6.24802i	−0.150044	−	0.259883i
$579$	3.99155	+	6.91356i	0.165883	+	0.287318i
$580$		0			0
$581$	−5.19326	−	8.99499i	−0.215453	−	0.373175i
$582$	12.0663	−	20.8995i	0.500165	−	0.866312i
$583$	10.2315	−	17.7215i	0.423745	−	0.733949i
$584$	−34.7889			−1.43958
$585$		0			0
$586$	−48.4462			−2.00129
$587$	−15.4265	+	26.7195i	−0.636720	+	1.10283i	0.349427	+	0.936963i	$0.386376\pi$
$587$	−15.4265	+	26.7195i	−0.636720	+	1.10283i	−0.986148	+	0.165869i	$0.946957\pi$
$588$	8.42476	−	14.5921i	0.347431	−	0.601769i
$589$	−22.6905	−	39.3012i	−0.934947	−	1.61938i
$590$		0			0
$591$	8.66966	+	15.0163i	0.356622	+	0.617688i
$592$	0.0606069	+	0.104974i	0.00249093	+	0.00431441i
$593$	−4.29211			−0.176256			−0.0881278	−	0.996109i	$-0.528088\pi$
$593$	−4.29211			−0.176256			−0.0881278	+	0.996109i	$0.528088\pi$
$594$	−5.11575	−	8.86074i	−0.209902	−	0.363560i
$595$		0			0
$596$	5.05514	−	8.75576i	0.207067	−	0.358650i
$597$	−1.23150			−0.0504019
$598$	13.2787	+	12.4436i	0.543007	+	0.508855i
$599$	−24.0224			−0.981527			−0.490764	−	0.871293i	$-0.663282\pi$
$599$	−24.0224			−0.981527			−0.490764	+	0.871293i	$0.663282\pi$
$600$		0			0
$601$	−1.26577	+	2.19238i	−0.0516318	+	0.0894289i	−0.890686	−	0.454619i	$-0.849776\pi$
$601$	−1.26577	+	2.19238i	−0.0516318	+	0.0894289i	0.839054	+	0.544048i	$0.183109\pi$
$602$	9.10060	+	15.7627i	0.370913	+	0.642440i
$603$	−13.1327			−0.534803
$604$	−8.87982	−	15.3803i	−0.361315	−	0.625816i
$605$		0			0
$606$	−38.5574			−1.56629
$607$	5.72083	+	9.90877i	0.232201	+	0.402185i	0.958456	−	0.285242i	$-0.0920738\pi$
$607$	5.72083	+	9.90877i	0.232201	+	0.402185i	−0.726254	+	0.687426i	$0.758740\pi$
$608$	15.9394	−	27.6078i	0.646428	−	1.11965i
$609$	0.869099	−	1.50532i	0.0352177	−	0.0609988i
$610$		0			0
$611$	37.2159	−	11.2784i	1.50559	−	0.456276i
$612$	14.0000			0.565916
$613$	−3.59663	+	6.22955i	−0.145267	+	0.251609i	−0.929472	−	0.368892i	$-0.879737\pi$
$613$	−3.59663	+	6.22955i	−0.145267	+	0.251609i	0.784206	+	0.620501i	$0.213071\pi$
$614$	−8.88204	+	15.3841i	−0.358450	+	0.620853i
$615$		0			0
$616$	14.4045			0.580373
$617$	12.7854	+	22.1450i	0.514721	+	0.891523i	0.999854	+	0.0170827i	$0.00543786\pi$
$617$	12.7854	+	22.1450i	0.514721	+	0.891523i	−0.485133	+	0.874440i	$0.661229\pi$
$618$	−15.7742	−	27.3218i	−0.634532	−	1.09904i
$619$	5.98660			0.240622			0.120311	−	0.992736i	$-0.461611\pi$
$619$	5.98660			0.240622			0.120311	+	0.992736i	$0.461611\pi$
$620$		0			0
$621$	1.11575	−	1.93253i	0.0447735	−	0.0775499i
$622$	31.5231	−	54.5997i	1.26396	−	2.18925i
$623$	8.35622			0.334785
$624$	1.37755	+	1.29091i	0.0551462	+	0.0516778i
$625$		0			0
$626$	8.92027	−	15.4504i	0.356526	−	0.617521i
$627$	−11.5708	+	20.0412i	−0.462094	+	0.800370i
$628$	−6.00397	−	10.3992i	−0.239584	−	0.414972i
$629$	1.04019			0.0414752
$630$		0			0
$631$	21.5129	+	37.2615i	0.856417	+	1.48336i	0.875325	+	0.483536i	$0.160648\pi$
$631$	21.5129	+	37.2615i	0.856417	+	1.48336i	−0.0189080	+	0.999821i	$0.506019\pi$
$632$	−22.3865			−0.890488
$633$	−5.16966	−	8.95411i	−0.205475	−	0.355894i
$634$	14.9484	−	25.8913i	0.593675	−	1.02828i
$635$		0			0
$636$	−14.0944			−0.558880
$637$	4.43269	−	18.9878i	0.175630	−	0.752322i
$638$	−14.0944			−0.558003
$639$	4.80453	−	8.32168i	0.190064	−	0.329201i
$640$		0			0
$641$	3.34725	+	5.79760i	0.132208	+	0.228992i	0.924528	−	0.381115i	$-0.124460\pi$
$641$	3.34725	+	5.79760i	0.132208	+	0.228992i	−0.792319	+	0.610107i	$0.791127\pi$
$642$	−28.2574			−1.11523
$643$	4.09039	+	7.08477i	0.161309	+	0.279396i	0.935338	−	0.353754i	$-0.115095\pi$
$643$	4.09039	+	7.08477i	0.161309	+	0.279396i	−0.774029	+	0.633150i	$0.781762\pi$
$644$	4.38652	+	7.59768i	0.172853	+	0.299391i
$645$		0			0
$646$	−25.9956	−	45.0257i	−1.02278	−	1.77151i
$647$	−5.63935	+	9.76765i	−0.221706	+	0.384006i	−0.955326	−	0.295554i	$-0.904496\pi$
$647$	−5.63935	+	9.76765i	−0.221706	+	0.384006i	0.733620	+	0.679560i	$0.237829\pi$
$648$	−1.26180	+	2.18551i	−0.0495683	+	0.0858548i
$649$	−3.86292			−0.151633
$650$		0			0
$651$	11.1933			0.438699
$652$	−15.1500	+	26.2406i	−0.593321	+	1.02766i
$653$	13.6242	−	23.5978i	0.533156	−	0.923454i	−0.466094	−	0.884735i	$-0.654339\pi$
$653$	13.6242	−	23.5978i	0.533156	−	0.923454i	0.999250	−	0.0387184i	$-0.0123275\pi$
$654$	2.57699	+	4.46348i	0.100768	+	0.174536i
$655$		0			0
$656$	0.300039	+	0.519683i	0.0117146	+	0.0202902i
$657$	6.89270	+	11.9385i	0.268910	+	0.465766i
$658$	30.7810			1.19997
$659$	−3.37755	−	5.85009i	−0.131571	−	0.227887i	0.792711	−	0.609597i	$-0.208669\pi$
$659$	−3.37755	−	5.85009i	−0.131571	−	0.227887i	−0.924282	+	0.381710i	$0.875335\pi$
$660$		0			0
$661$	13.2551	−	22.9585i	0.515564	−	0.892983i	−0.484273	−	0.874917i	$-0.660916\pi$
$661$	13.2551	−	22.9585i	0.515564	−	0.892983i	0.999837	−	0.0180657i	$-0.00575081\pi$
$662$	−53.9429			−2.09655
$663$	15.5045	−	4.69869i	0.602144	−	0.182482i
$664$	20.7730			0.806151
$665$		0			0
$666$	−0.261802	+	0.453455i	−0.0101446	+	0.0175710i
$667$	−1.53700	−	2.66217i	−0.0595130	−	0.103079i
$668$	60.0676			2.32409
$669$	10.7854	+	18.6809i	0.416988	+	0.722244i
$670$		0			0
$671$	20.9866			0.810179
$672$	3.93146	+	6.80949i	0.151659	+	0.262682i
$673$	−0.338795	+	0.586811i	−0.0130596	+	0.0226199i	−0.872481	−	0.488647i	$-0.837490\pi$
$673$	−0.338795	+	0.586811i	−0.0130596	+	0.0226199i	0.859422	+	0.511267i	$0.170824\pi$
$674$	6.42697	−	11.1318i	0.247558	−	0.428783i
$675$		0			0
$676$	−36.3180	−	17.9343i	−1.39685	−	0.689780i
$677$	10.4630			0.402126			0.201063	−	0.979578i	$-0.435560\pi$
$677$	10.4630			0.402126			0.201063	+	0.979578i	$0.435560\pi$
$678$	−1.66966	+	2.89193i	−0.0641228	+	0.111064i
$679$	6.73150	−	11.6593i	0.258331	−	0.447443i
$680$		0			0
$681$	−5.44609			−0.208695
$682$	−45.3811	−	78.6023i	−1.73773	−	3.00984i
$683$	−9.37580	−	16.2394i	−0.358755	−	0.621382i	0.628998	−	0.777407i	$-0.283465\pi$
$683$	−9.37580	−	16.2394i	−0.358755	−	0.621382i	−0.987753	+	0.156025i	$0.950132\pi$
$684$	15.9394			0.609458
$685$		0			0
$686$	17.7057	−	30.6671i	0.676006	−	1.17088i
$687$	−10.9657	+	18.9932i	−0.418369	+	0.724636i
$688$	3.33931			0.127310
$689$	−15.6091	+	4.73038i	−0.594657	+	0.180213i
$690$		0			0
$691$	−21.7827	+	37.7287i	−0.828652	+	1.43527i	0.0704440	+	0.997516i	$0.477558\pi$
$691$	−21.7827	+	37.7287i	−0.828652	+	1.43527i	−0.899096	+	0.437752i	$0.855775\pi$
$692$	−4.69996	+	8.14057i	−0.178666	+	0.309458i
$693$	−2.85395	−	4.94318i	−0.108412	−	0.187776i
$694$	48.5148			1.84159
$695$		0			0
$696$	1.73820	+	3.01065i	0.0658862	+	0.114118i
$697$	5.14956			0.195054
$698$	−7.77026	−	13.4585i	−0.294108	−	0.509411i
$699$	12.6563	−	21.9213i	0.478704	−	0.829139i
$700$		0			0
$701$	−19.0810			−0.720680			−0.360340	−	0.932821i	$-0.617339\pi$
$701$	−19.0810			−0.720680			−0.360340	+	0.932821i	$0.617339\pi$
$702$	−1.85395	+	7.94151i	−0.0699727	+	0.299733i
$703$	1.18429			0.0446663
$704$	29.5102	−	51.1132i	1.11221	−	1.92640i
$705$		0			0
$706$	39.0125	+	67.5716i	1.46825	+	2.54309i
$707$	−21.5102			−0.808975
$708$	1.33034	+	2.30422i	0.0499973	+	0.0865979i
$709$	−22.3023	−	38.6287i	−0.837581	−	1.45073i	−0.891912	−	0.452210i	$-0.850636\pi$
$709$	−22.3023	−	38.6287i	−0.837581	−	1.45073i	0.0543307	−	0.998523i	$-0.482697\pi$
$710$		0			0
$711$	4.43543	+	7.68238i	0.166341	+	0.288112i
$712$	−8.35622	+	14.4734i	−0.313163	+	0.542414i
$713$	9.89765	−	17.1432i	0.370670	−	0.642019i
$714$	12.8236			0.479913
$715$		0			0
$716$	−16.5663			−0.619110
$717$	−11.2618	+	19.5060i	−0.420580	+	0.728465i
$718$	9.22753	−	15.9826i	0.344368	−	0.596464i
$719$	6.49109	+	11.2429i	0.242077	+	0.419289i	0.961306	−	0.275484i	$-0.0888381\pi$
$719$	6.49109	+	11.2429i	0.242077	+	0.419289i	−0.719229	+	0.694773i	$0.755505\pi$
$720$		0			0
$721$	−8.80004	−	15.2421i	−0.327731	−	0.567646i
$722$	−8.10957	−	14.0462i	−0.301807	−	0.522745i
$723$	11.1157			0.413399
$724$	−40.3035	−	69.8078i	−1.49787	−	2.59439i
$725$		0			0
$726$	−10.7017	+	18.5359i	−0.397178	+	0.687932i
$727$	−17.3980			−0.645255			−0.322627	−	0.946526i	$-0.604566\pi$
$727$	−17.3980			−0.645255			−0.322627	+	0.946526i	$0.604566\pi$
$728$	−8.37755	−	7.85065i	−0.310493	−	0.290965i
$729$	1.00000			0.0370370
$730$		0			0
$731$	14.3281	−	24.8170i	0.529945	−	0.917892i
$732$	−7.22753	−	12.5185i	−0.267137	−	0.462695i
$733$	−45.8272			−1.69266			−0.846332	−	0.532655i	$-0.821194\pi$
$733$	−45.8272			−1.69266			−0.846332	+	0.532655i	$0.821194\pi$
$734$	−7.73598	−	13.3991i	−0.285540	−	0.494570i
$735$		0			0
$736$	13.9056			0.512567
$737$	29.7035	+	51.4479i	1.09414	+	1.89511i
$738$	−1.29607	+	2.24486i	−0.0477091	+	0.0826346i
$739$	−8.78541	+	15.2168i	−0.323176	+	0.559758i	−0.981142	−	0.193290i	$-0.938084\pi$
$739$	−8.78541	+	15.2168i	−0.323176	+	0.559758i	0.657965	+	0.753048i	$0.271417\pi$
$740$		0			0
$741$	17.6523	−	5.34959i	0.648473	−	0.196522i
$742$	−12.9101			−0.473946
$743$	−15.1781	+	26.2893i	−0.556831	+	0.964459i	0.440928	+	0.897543i	$0.354650\pi$
$743$	−15.1781	+	26.2893i	−0.556831	+	0.964459i	−0.997759	+	0.0669167i	$0.978684\pi$
$744$	−11.1933	+	19.3873i	−0.410365	+	0.710773i
$745$		0			0
$746$	−31.2563			−1.14438
$747$	−4.11575	−	7.12869i	−0.150587	−	0.260825i
$748$	−31.6652	−	54.8458i	−1.15780	−	2.00536i
$749$	−15.7641			−0.576007
$750$		0			0
$751$	−1.90162	+	3.29369i	−0.0693909	+	0.120189i	−0.898633	−	0.438700i	$-0.855439\pi$
$751$	−1.90162	+	3.29369i	−0.0693909	+	0.120189i	0.829242	+	0.558889i	$0.188772\pi$
$752$	2.82364	−	4.89069i	0.102968	−	0.178345i
$753$	11.0472			0.402583
$754$	8.19723	+	7.68167i	0.298525	+	0.279750i
$755$		0			0
$756$	−1.96573	+	3.40474i	−0.0714929	+	0.123829i
$757$	−1.70393	+	2.95129i	−0.0619303	+	0.107266i	−0.895328	−	0.445407i	$-0.853059\pi$
$757$	−1.70393	+	2.95129i	−0.0619303	+	0.107266i	0.833398	+	0.552673i	$0.186392\pi$
$758$	−13.0231	−	22.5566i	−0.473020	−	0.819294i
$759$	−10.0944			−0.366404
$760$		0			0
$761$	−3.62245	−	6.27426i	−0.131314	−	0.227442i	0.792870	−	0.609391i	$-0.208586\pi$
$761$	−3.62245	−	6.27426i	−0.131314	−	0.227442i	−0.924183	+	0.381949i	$0.875253\pi$
$762$	40.2271			1.45727
$763$	1.43764	+	2.49006i	0.0520460	+	0.0901464i
$764$	−16.6011	+	28.7540i	−0.600607	+	1.04028i
$765$		0			0
$766$	−51.7496			−1.86979
$767$	2.24665	+	2.10535i	0.0811218	+	0.0760198i
$768$	−12.4630			−0.449720
$769$	−15.5882	+	26.9995i	−0.562124	+	0.973627i	0.435187	+	0.900340i	$0.356682\pi$
$769$	−15.5882	+	26.9995i	−0.562124	+	0.973627i	−0.997311	+	0.0732873i	$0.976651\pi$
$770$		0			0
$771$	−1.01515	−	1.75829i	−0.0365598	−	0.0633234i
$772$	−24.8733			−0.895210
$773$	9.73026	+	16.8533i	0.349973	+	0.606172i	0.986244	−	0.165294i	$-0.0528573\pi$
$773$	9.73026	+	16.8533i	0.349973	+	0.606172i	−0.636271	+	0.771466i	$0.719524\pi$
$774$	7.21238	+	12.4922i	0.259244	+	0.449023i
$775$		0			0
$776$	13.4630	+	23.3186i	0.483293	+	0.837089i
$777$	−0.146053	+	0.252971i	−0.00523962	+	0.00907528i
$778$	4.92249	−	8.52600i	0.176480	−	0.305672i
$779$	5.86292			0.210061
$780$		0			0
$781$	−43.4675			−1.55539
$782$	11.3393	−	19.6403i	0.405493	−	0.702335i
$783$	0.688776	−	1.19299i	0.0246148	−	0.0426342i
$784$	−1.41579	−	2.45222i	−0.0505639	−	0.0875792i
$785$		0			0
$786$	−13.1972	−	22.8583i	−0.470730	−	0.815328i
$787$	7.20171	+	12.4737i	0.256713	+	0.444641i	0.965359	−	0.260923i	$-0.0840270\pi$
$787$	7.20171	+	12.4737i	0.256713	+	0.444641i	−0.708646	+	0.705564i	$0.750694\pi$
$788$	−54.0250			−1.92456
$789$	1.62420	+	2.81320i	0.0578231	+	0.100153i
$790$		0			0
$791$	−0.931460	+	1.61334i	−0.0331189	+	0.0573636i
$792$	11.4158			0.405642
$793$	−12.2057	−	11.4380i	−0.433436	−	0.406176i
$794$	−17.2405			−0.611841
$795$		0			0
$796$	1.91852	−	3.32298i	0.0680002	−	0.117780i
$797$	−11.8006	−	20.4392i	−0.417997	−	0.723992i	0.577741	−	0.816220i	$-0.303934\pi$
$797$	−11.8006	−	20.4392i	−0.417997	−	0.723992i	−0.995738	+	0.0922279i	$0.970601\pi$
$798$	14.6001			0.516837
$799$	−24.2310	−	41.9694i	−0.857233	−	1.48477i
$800$		0			0
$801$	6.62245			0.233993
$802$	−23.5787	−	40.8396i	−0.832595	−	1.44210i
$803$	31.1799	−	54.0051i	1.10031	−	1.90580i
$804$	20.4590	−	35.4361i	0.721534	−	1.24973i
$805$		0			0
$806$	−16.4461	+	70.4480i	−0.579289	+	2.48142i
$807$	26.9484			0.948627
$808$	21.5102	−	37.2568i	0.756726	−	1.31069i
$809$	−13.3776	+	23.1706i	−0.470330	+	0.814635i	−0.999424	−	0.0339280i	$-0.989198\pi$
$809$	−13.3776	+	23.1706i	−0.470330	+	0.814635i	0.529095	+	0.848563i	$0.322532\pi$
$810$		0			0
$811$	−3.58421			−0.125859			−0.0629293	−	0.998018i	$-0.520044\pi$
$811$	−3.58421			−0.125859			−0.0629293	+	0.998018i	$0.520044\pi$
$812$	2.70789	+	4.69021i	0.0950285	+	0.164594i
$813$	9.92476	+	17.1902i	0.348077	+	0.602886i
$814$	2.36858			0.0830187
$815$		0			0
$816$	1.17636	−	2.03751i	0.0411807	−	0.0713271i
$817$	16.3130	−	28.2549i	0.570719	−	0.988514i
$818$	−38.3721			−1.34165
$819$	−1.03427	+	4.43037i	−0.0361403	+	0.154810i
$820$		0			0
$821$	−7.91806	+	13.7145i	−0.276342	+	0.478639i	−0.970473	−	0.241210i	$-0.922456\pi$
$821$	−7.91806	+	13.7145i	−0.276342	+	0.478639i	0.694131	+	0.719849i	$0.255789\pi$
$822$	−22.6905	+	39.3012i	−0.791423	+	1.37079i
$823$	3.70789	+	6.42226i	0.129249	+	0.223866i	0.923386	−	0.383873i	$-0.125410\pi$
$823$	3.70789	+	6.42226i	0.129249	+	0.223866i	−0.794137	+	0.607739i	$0.792077\pi$
$824$	35.2002			1.22626
$825$		0			0
$826$	1.21856	+	2.11061i	0.0423991	+	0.0734374i
$827$	16.6036			0.577363			0.288682	−	0.957425i	$-0.406783\pi$
$827$	16.6036			0.577363			0.288682	+	0.957425i	$0.406783\pi$
$828$	3.47640	+	6.02129i	0.120813	+	0.209254i
$829$	14.6421	−	25.3608i	0.508541	−	0.880818i	−0.491410	−	0.870928i	$-0.663518\pi$
$829$	14.6421	−	25.3608i	0.508541	−	0.880818i	0.999951	−	0.00989015i	$-0.00314819\pi$
$830$		0			0
$831$	−16.0944			−0.558309
$832$	−45.0204	+	13.6436i	−1.56080	+	0.473007i
$833$	−24.2991			−0.841915
$834$	−18.4781	+	32.0051i	−0.639846	+	1.10825i
$835$		0			0
$836$	−36.0518	−	62.4435i	−1.24688	−	2.15965i
$837$	8.87085			0.306622
$838$	−2.37358	−	4.11117i	−0.0819941	−	0.142018i
$839$	15.0810	+	26.1211i	0.520655	+	0.901800i	0.999712	+	0.0240164i	$0.00764541\pi$
$839$	15.0810	+	26.1211i	0.520655	+	0.901800i	−0.479057	+	0.877784i	$0.659021\pi$
$840$		0			0
$841$	13.5512	+	23.4713i	0.467282	+	0.809356i
$842$	44.8513	−	77.6847i	1.54568	−	2.67719i
$843$	2.68878	−	4.65710i	0.0926064	−	0.160399i
$844$	32.2147			1.10888
$845$		0			0
$846$	24.3945			0.838699
$847$	−5.97022	+	10.3407i	−0.205139	+	0.355311i
$848$	−1.18429	+	2.05125i	−0.0406687	+	0.0704402i
$849$	13.4332	+	23.2670i	0.461027	+	0.798522i
$850$		0			0
$851$	0.258295	+	0.447379i	0.00885423	+	0.0153360i
$852$	14.9697	+	25.9283i	0.512853	+	0.888288i
$853$	2.50670			0.0858277			0.0429139	−	0.999079i	$-0.486336\pi$
$853$	2.50670			0.0858277			0.0429139	+	0.999079i	$0.486336\pi$
$854$	−6.62024	−	11.4666i	−0.226540	−	0.392378i
$855$		0			0
$856$	15.7641	−	27.3042i	0.538805	−	0.933238i
$857$	24.4327			0.834605			0.417302	−	0.908768i	$-0.362976\pi$
$857$	24.4327			0.834605			0.417302	+	0.908768i	$0.362976\pi$
$858$	35.3046	−	10.6992i	1.20528	−	0.365264i
$859$	−7.10235			−0.242329			−0.121165	−	0.992632i	$-0.538663\pi$
$859$	−7.10235			−0.242329			−0.121165	+	0.992632i	$0.538663\pi$
$860$		0			0
$861$	−0.723046	+	1.25235i	−0.0246413	+	0.0426801i
$862$	25.0248	+	43.3443i	0.852349	+	1.47631i
$863$	3.24490			0.110458			0.0552288	−	0.998474i	$-0.482411\pi$
$863$	3.24490			0.110458			0.0552288	+	0.998474i	$0.482411\pi$
$864$	3.11575	+	5.39664i	0.106000	+	0.183597i
$865$		0			0
$866$	70.9216			2.41001
$867$	−1.59488	−	2.76241i	−0.0541649	−	0.0938163i
$868$	−17.4377	+	30.2030i	−0.591874	+	1.02516i
$869$	20.0641	−	34.7521i	0.680628	−	1.17888i
$870$		0			0
$871$	10.7645	−	46.1106i	0.364742	−	1.56240i
$872$	−5.75056			−0.194738
$873$	5.33483	−	9.24019i	0.180557	−	0.312733i
$874$	12.9101	−	22.3610i	0.436692	−	0.756372i
$875$		0			0
$876$	−42.9519			−1.45121
$877$	9.49330	+	16.4429i	0.320566	+	0.555237i	0.980605	−	0.195995i	$-0.0627936\pi$
$877$	9.49330	+	16.4429i	0.320566	+	0.555237i	−0.660039	+	0.751231i	$0.729460\pi$
$878$	−4.87807	−	8.44907i	−0.164627	−	0.285142i
$879$	−21.4193			−0.722455
$880$		0			0
$881$	9.73820	−	16.8671i	0.328088	−	0.568265i	−0.654044	−	0.756456i	$-0.726929\pi$
$881$	9.73820	−	16.8671i	0.328088	−	0.568265i	0.982132	+	0.188191i	$0.0602623\pi$
$882$	6.11575	−	10.5928i	0.205928	−	0.356678i
$883$	50.5664			1.70169			0.850847	−	0.525413i	$-0.176089\pi$
$883$	50.5664			1.70169			0.850847	+	0.525413i	$0.176089\pi$
$884$	−11.4755	+	49.1560i	−0.385962	+	1.65330i
$885$		0			0
$886$	0.557875	−	0.966267i	0.0187422	−	0.0324624i
$887$	−6.26356	+	10.8488i	−0.210310	+	0.364267i	−0.951811	−	0.306684i	$-0.900781\pi$
$887$	−6.26356	+	10.8488i	−0.210310	+	0.364267i	0.741502	+	0.670951i	$0.234114\pi$
$888$	−0.292106	−	0.505942i	−0.00980243	−	0.0169783i
$889$	22.4417			0.752669
$890$		0			0
$891$	−2.26180	−	3.91756i	−0.0757732	−	0.131243i
$892$	−67.2092			−2.25033
$893$	−27.5877	−	47.7833i	−0.923188	−	1.59901i
$894$	3.66966	−	6.35603i	0.122732	−	0.212578i
$895$		0			0
$896$	−21.5102			−0.718606
$897$	5.87085	+	5.50161i	0.196022	+	0.183693i
$898$	−52.7283			−1.75957
$899$	6.11003	−	10.5829i	0.203781	−	0.352959i
$900$		0			0
$901$	10.1630	+	17.6028i	0.338577	+	0.586433i
$902$	11.7258			0.390428
$903$	4.02360	+	6.96909i	0.133897	+	0.231917i
$904$	−1.86292	−	3.22667i	−0.0619598	−	0.107317i
$905$		0			0
$906$	−6.44609	−	11.1650i	−0.214157	−	0.370931i
$907$	14.0209	−	24.2849i	0.465555	−	0.806366i	−0.533671	−	0.845692i	$-0.679188\pi$
$907$	14.0209	−	24.2849i	0.465555	−	0.806366i	0.999226	+	0.0393265i	$0.0125213\pi$
$908$	8.48433	−	14.6953i	0.281562	−	0.487680i
$909$	−17.0472			−0.565420
$910$		0			0
$911$	16.1977			0.536653			0.268327	−	0.963328i	$-0.413529\pi$
$911$	16.1977			0.536653			0.268327	+	0.963328i	$0.413529\pi$
$912$	1.33931	−	2.31976i	0.0443491	−	0.0768150i
$913$	−18.6180	+	32.2474i	−0.616167	+	1.06723i
$914$	7.54272	+	13.0644i	0.249491	+	0.432131i
$915$		0			0
$916$	−34.1665	−	59.1781i	−1.12889	−	1.95530i
$917$	−7.36240	−	12.7521i	−0.243128	−	0.421110i
$918$	10.1630			0.335428
$919$	21.6389	+	37.4797i	0.713801	+	1.23634i	0.963420	+	0.267996i	$0.0863614\pi$
$919$	21.6389	+	37.4797i	0.713801	+	1.23634i	−0.249619	+	0.968344i	$0.580305\pi$
$920$		0			0
$921$	−3.92697	+	6.80172i	−0.129398	+	0.224124i
$922$	65.8620			2.16905
$923$	25.2805	+	23.6905i	0.832117	+	0.779781i
$924$	17.7844			0.585063
$925$		0			0
$926$	−2.02809	+	3.51276i	−0.0666472	+	0.115436i
$927$	−6.97418	−	12.0796i	−0.229062	−	0.396747i
$928$	8.58421			0.281791
$929$	−6.88425	−	11.9239i	−0.225865	−	0.391210i	0.730714	−	0.682684i	$-0.239187\pi$
$929$	−6.88425	−	11.9239i	−0.225865	−	0.391210i	−0.956579	+	0.291475i	$0.905854\pi$
$930$		0			0
$931$	−27.6652			−0.906691
$932$	39.4337	+	68.3012i	1.29169	+	2.23728i
$933$	13.9372	−	24.1399i	0.456283	−	0.790305i
$934$	19.0209	−	32.9451i	0.622382	−	1.07800i
$935$		0			0
$936$	−6.63935	−	6.22178i	−0.217014	−	0.203365i
$937$	38.1888			1.24757			0.623787	−	0.781594i	$-0.285593\pi$
$937$	38.1888			1.24757			0.623787	+	0.781594i	$0.285593\pi$
$938$	18.7400	−	32.4585i	0.611881	−	1.05981i
$939$	3.94388	−	6.83100i	0.128704	−	0.222921i
$940$		0			0
$941$	−13.9618			−0.455140			−0.227570	−	0.973762i	$-0.573078\pi$
$941$	−13.9618			−0.455140			−0.227570	+	0.973762i	$0.573078\pi$
$942$	−4.35843	−	7.54903i	−0.142005	−	0.245961i
$943$	1.27871	+	2.21479i	0.0416405	+	0.0721234i
$944$	0.447131			0.0145529
$945$		0			0
$946$	32.6260	−	56.5098i	1.06076	−	1.83729i
$947$	3.68481	−	6.38228i	0.119740	−	0.207396i	−0.799924	−	0.600101i	$-0.795127\pi$
$947$	3.68481	−	6.38228i	0.119740	−	0.207396i	0.919665	+	0.392705i	$0.128461\pi$
$948$	−27.6394			−0.897684
$949$	−47.5676	+	14.4155i	−1.54411	+	0.467948i
$950$		0			0
$951$	6.60905	−	11.4472i	0.214313	−	0.371201i
$952$	−7.15399	+	12.3911i	−0.231862	+	0.401597i
$953$	11.6091	+	20.1075i	0.376054	+	0.651345i	0.990484	−	0.137627i	$-0.0439474\pi$
$953$	11.6091	+	20.1075i	0.376054	+	0.651345i	−0.614430	+	0.788971i	$0.710614\pi$
$954$	−10.2315			−0.331257
$955$		0			0
$956$	−35.0890	−	60.7759i	−1.13486	−	1.96563i
$957$	−6.23150			−0.201436
$958$	−39.7546	−	68.8571i	−1.28441	−	2.22467i
$959$	−12.6585	+	21.9251i	−0.408763	+	0.707999i
$960$		0			0
$961$	47.6920			1.53845
$962$	−1.37755	−	1.29091i	−0.0444140	−	0.0416207i
$963$	−12.4933			−0.402591
$964$	−17.3169	+	29.9938i	−0.557741	+	0.966036i
$965$		0			0
$966$	3.18429	+	5.51535i	0.102453	+	0.177454i
$967$	7.54402			0.242599			0.121300	−	0.992616i	$-0.461294\pi$
$967$	7.54402			0.242599			0.121300	+	0.992616i	$0.461294\pi$
$968$	−11.9404	−	20.6814i	−0.383780	−	0.664726i
$969$	−11.4933	−	19.9070i	−0.369218	−	0.639504i
$970$		0			0
$971$	15.2921	+	26.4867i	0.490747	+	0.849999i	0.999943	−	0.0106517i	$-0.00339059\pi$
$971$	15.2921	+	26.4867i	0.490747	+	0.849999i	−0.509196	+	0.860650i	$0.670057\pi$
$972$	−1.55787	+	2.69832i	−0.0499689	+	0.0865486i
$973$	−10.3085	+	17.8548i	−0.330475	+	0.572400i
$974$	19.5102			0.625147
$975$		0			0
$976$	−2.42919			−0.0777564
$977$	−17.8405	+	30.9007i	−0.570770	+	0.988602i	0.425717	+	0.904856i	$0.360022\pi$
$977$	−17.8405	+	30.9007i	−0.570770	+	0.988602i	−0.996487	+	0.0837460i	$0.973312\pi$
$978$	−10.9978	+	19.0487i	−0.351670	+	0.609111i
$979$	−14.9787	−	25.9438i	−0.478720	−	0.829168i
$980$		0			0
$981$	1.13935	+	1.97342i	0.0363768	+	0.0630064i
$982$	26.2524	+	45.4704i	0.837747	+	1.45102i
$983$	−12.9866			−0.414208			−0.207104	−	0.978319i	$-0.566404\pi$
$983$	−12.9866			−0.414208			−0.207104	+	0.978319i	$0.566404\pi$
$984$	−1.44609	−	2.50470i	−0.0460997	−	0.0798471i
$985$		0			0
$986$	7.00000	−	12.1244i	0.222925	−	0.386118i
$987$	13.6091			0.433181
$988$	−13.0652	+	55.9655i	−0.415658	+	1.78050i
$989$	14.2315			0.452535
$990$		0			0
$991$	11.3736	−	19.6996i	0.361294	−	0.625779i	−0.626880	−	0.779116i	$-0.715668\pi$
$991$	11.3736	−	19.6996i	0.361294	−	0.625779i	0.988174	+	0.153336i	$0.0490018\pi$
$992$	27.6394	+	47.8728i	0.877550	+	1.51996i
$993$	−23.8495			−0.756842
$994$	13.7119	+	23.7496i	0.434914	+	0.753293i
$995$		0			0
$996$	25.6473			0.812665
$997$	−6.92301	−	11.9910i	−0.219254	−	0.379759i	0.735326	−	0.677713i	$-0.237029\pi$
$997$	−6.92301	−	11.9910i	−0.219254	−	0.379759i	−0.954580	+	0.297955i	$0.903696\pi$
$998$	−32.8405	+	56.8815i	−1.03955	+	1.80055i
$999$	−0.115749	+	0.200484i	−0.00366215	+	0.00634303i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	975.2.i.l.451.1		6
5.2	odd	4		975.2.bb.k.724.2		12
5.3	odd	4		975.2.bb.k.724.5		12
5.4	even	2		195.2.i.d.61.3	yes	6
13.3	even	3	inner	975.2.i.l.601.1		6
15.14	odd	2		585.2.j.f.451.1		6
65.3	odd	12		975.2.bb.k.874.2		12
65.4	even	6		2535.2.a.ba.1.3		3
65.9	even	6		2535.2.a.bb.1.1		3
65.29	even	6		195.2.i.d.16.3	✓	6
65.42	odd	12		975.2.bb.k.874.5		12
195.29	odd	6		585.2.j.f.406.1		6
195.74	odd	6		7605.2.a.bv.1.3		3
195.134	odd	6		7605.2.a.bw.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.2.i.d.16.3	✓	6	65.29	even	6
195.2.i.d.61.3	yes	6	5.4	even	2
585.2.j.f.406.1		6	195.29	odd	6
585.2.j.f.451.1		6	15.14	odd	2
975.2.i.l.451.1		6	1.1	even	1	trivial
975.2.i.l.601.1		6	13.3	even	3	inner
975.2.bb.k.724.2		12	5.2	odd	4
975.2.bb.k.724.5		12	5.3	odd	4
975.2.bb.k.874.2		12	65.3	odd	12
975.2.bb.k.874.5		12	65.42	odd	12
2535.2.a.ba.1.3		3	65.4	even	6
2535.2.a.bb.1.1		3	65.9	even	6
7605.2.a.bv.1.3		3	195.74	odd	6
7605.2.a.bw.1.1		3	195.134	odd	6

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:	\( N \)	\(=\)	\( 975 = 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	975.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.13090 + 1.95878i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-1.55787 - 2.69832i) q^{4} +(-1.13090 - 1.95878i) q^{6} +(-0.630901 - 1.09275i) q^{7} +2.52360 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-1.13090 + 1.95878i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-1.55787 - 2.69832i) q^{4} +(-1.13090 - 1.95878i) q^{6} +(-0.630901 - 1.09275i) q^{7} +2.52360 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-2.26180 + 3.91756i) q^{11} +3.11575 q^{12} +(3.45058 - 1.04571i) q^{13} +2.85395 q^{14} +(0.261802 - 0.453455i) q^{16} +(-2.24665 - 3.89131i) q^{17} +2.26180 q^{18} +(-2.55787 - 4.43037i) q^{19} +1.26180 q^{21} +(-5.11575 - 8.86074i) q^{22} +(1.11575 - 1.93253i) q^{23} +(-1.26180 + 2.18551i) q^{24} +(-1.85395 + 7.94151i) q^{26} +1.00000 q^{27} +(-1.96573 + 3.40474i) q^{28} +(0.688776 - 1.19299i) q^{29} +8.87085 q^{31} +(3.11575 + 5.39664i) q^{32} +(-2.26180 - 3.91756i) q^{33} +10.1630 q^{34} +(-1.55787 + 2.69832i) q^{36} +(-0.115749 + 0.200484i) q^{37} +11.5708 q^{38} +(-0.819677 + 3.51114i) q^{39} +(-0.573026 + 0.992511i) q^{41} +(-1.42697 + 2.47159i) q^{42} +(3.18878 + 5.52312i) q^{43} +14.0944 q^{44} +(2.52360 + 4.37101i) q^{46} +10.7854 q^{47} +(0.261802 + 0.453455i) q^{48} +(2.70393 - 4.68334i) q^{49} +4.49330 q^{51} +(-8.19723 - 7.68167i) q^{52} -4.52360 q^{53} +(-1.13090 + 1.95878i) q^{54} +(-1.59214 - 2.75768i) q^{56} +5.11575 q^{57} +(1.55787 + 2.69832i) q^{58} +(0.426974 + 0.739540i) q^{59} +(-2.31968 - 4.01780i) q^{61} +(-10.0321 + 17.3760i) q^{62} +(-0.630901 + 1.09275i) q^{63} -13.0472 q^{64} +10.2315 q^{66} +(6.56633 - 11.3732i) q^{67} +(-7.00000 + 12.1244i) q^{68} +(1.11575 + 1.93253i) q^{69} +(4.80453 + 8.32168i) q^{71} +(-1.26180 - 2.18551i) q^{72} -13.7854 q^{73} +(-0.261802 - 0.453455i) q^{74} +(-7.96970 + 13.8039i) q^{76} +5.70789 q^{77} +(-5.95058 - 5.57632i) q^{78} -8.87085 q^{79} +(-0.500000 + 0.866025i) q^{81} +(-1.29607 - 2.24486i) q^{82} +8.23150 q^{83} +(-1.96573 - 3.40474i) q^{84} -14.4248 q^{86} +(0.688776 + 1.19299i) q^{87} +(-5.70789 + 9.88636i) q^{88} +(-3.31122 + 5.73521i) q^{89} +(-3.31968 - 3.11089i) q^{91} -6.95279 q^{92} +(-4.43543 + 7.68238i) q^{93} +(-12.1972 + 21.1262i) q^{94} -6.23150 q^{96} +(5.33483 + 9.24019i) q^{97} +(6.11575 + 10.5928i) q^{98} +4.52360 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{3} - 6 q^{4} + 3 q^{7} - 12 q^{8} - 3 q^{9}+O(q^{10}) \) 6 * q - 3 * q^3 - 6 * q^4 + 3 * q^7 - 12 * q^8 - 3 * q^9	\( 6 q - 3 q^{3} - 6 q^{4} + 3 q^{7} - 12 q^{8} - 3 q^{9} + 12 q^{12} - 3 q^{13} + 24 q^{14} - 12 q^{16} - 12 q^{19} - 6 q^{21} - 24 q^{22} + 6 q^{24} - 18 q^{26} + 6 q^{27} + 12 q^{28} - 6 q^{29} + 6 q^{31} + 12 q^{32} - 6 q^{36} + 6 q^{37} - 12 q^{38} + 12 q^{39} - 12 q^{42} + 9 q^{43} - 24 q^{44} - 12 q^{46} + 24 q^{47} - 12 q^{48} + 6 q^{49} - 12 q^{52} - 30 q^{56} + 24 q^{57} + 6 q^{58} + 6 q^{59} + 3 q^{61} - 6 q^{62} + 3 q^{63} - 24 q^{64} + 48 q^{66} + 9 q^{67} - 42 q^{68} + 12 q^{71} + 6 q^{72} - 42 q^{73} + 12 q^{74} - 48 q^{76} + 48 q^{77} - 12 q^{78} - 6 q^{79} - 3 q^{81} - 18 q^{82} + 36 q^{83} + 12 q^{84} - 12 q^{86} - 6 q^{87} - 48 q^{88} - 30 q^{89} - 3 q^{91} - 96 q^{92} - 3 q^{93} - 36 q^{94} - 24 q^{96} + 15 q^{97} + 30 q^{98}+O(q^{100}) \) 6 * q - 3 * q^3 - 6 * q^4 + 3 * q^7 - 12 * q^8 - 3 * q^9 + 12 * q^12 - 3 * q^13 + 24 * q^14 - 12 * q^16 - 12 * q^19 - 6 * q^21 - 24 * q^22 + 6 * q^24 - 18 * q^26 + 6 * q^27 + 12 * q^28 - 6 * q^29 + 6 * q^31 + 12 * q^32 - 6 * q^36 + 6 * q^37 - 12 * q^38 + 12 * q^39 - 12 * q^42 + 9 * q^43 - 24 * q^44 - 12 * q^46 + 24 * q^47 - 12 * q^48 + 6 * q^49 - 12 * q^52 - 30 * q^56 + 24 * q^57 + 6 * q^58 + 6 * q^59 + 3 * q^61 - 6 * q^62 + 3 * q^63 - 24 * q^64 + 48 * q^66 + 9 * q^67 - 42 * q^68 + 12 * q^71 + 6 * q^72 - 42 * q^73 + 12 * q^74 - 48 * q^76 + 48 * q^77 - 12 * q^78 - 6 * q^79 - 3 * q^81 - 18 * q^82 + 36 * q^83 + 12 * q^84 - 12 * q^86 - 6 * q^87 - 48 * q^88 - 30 * q^89 - 3 * q^91 - 96 * q^92 - 3 * q^93 - 36 * q^94 - 24 * q^96 + 15 * q^97 + 30 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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