LMFDB - Embedded newform 1470.2.m.f.1273.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1470,2,Mod(97,1470)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1470, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1, 2]))

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

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

chi := DirichletCharacter("1470.97");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1470.m (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$11.7380090971$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 32 x^{13} + 2 x^{12} + 352 x^{10} - 288 x^{9} + 2 x^{8} - 1440 x^{7} + 8800 x^{6} + \cdots + 390625 $ x^16 - 32x^13 + 2x^12 + 352x^10 - 288x^9 + 2x^8 - 1440x^7 + 8800x^6 + 1250x^4 - 100000*x^3 + 390625
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			1273.3
Root			$-1.22045 + 1.87363i$ of defining polynomial
Character	$\chi$	$=$	1470.1273
Dual form			1470.2.m.f.97.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} +(0.707107 - 0.707107i) q^{3} -1.00000i q^{4} +(1.84456 - 1.26397i) q^{5} +1.00000i q^{6} +(0.707107 + 0.707107i) q^{8} -1.00000i q^{9} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} +(0.707107 - 0.707107i) q^{3} -1.00000i q^{4} +(1.84456 - 1.26397i) q^{5} +1.00000i q^{6} +(0.707107 + 0.707107i) q^{8} -1.00000i q^{9} +(-0.410538 + 2.19806i) q^{10} +5.16148 q^{11} +(-0.707107 - 0.707107i) q^{12} +(-0.184778 + 0.184778i) q^{13} +(0.410538 - 2.19806i) q^{15} -1.00000 q^{16} +(0.750926 + 0.750926i) q^{17} +(0.707107 + 0.707107i) q^{18} +4.08523 q^{19} +(-1.26397 - 1.84456i) q^{20} +(-3.64972 + 3.64972i) q^{22} +(-2.36811 - 2.36811i) q^{23} +1.00000 q^{24} +(1.80477 - 4.66292i) q^{25} -0.261316i q^{26} +(-0.707107 - 0.707107i) q^{27} -0.387531i q^{29} +(1.26397 + 1.84456i) q^{30} +10.6134i q^{31} +(0.707107 - 0.707107i) q^{32} +(3.64972 - 3.64972i) q^{33} -1.06197 q^{34} -1.00000 q^{36} +(2.51162 - 2.51162i) q^{37} +(-2.88869 + 2.88869i) q^{38} +0.261316i q^{39} +(2.19806 + 0.410538i) q^{40} +7.05881i q^{41} +(-2.13217 - 2.13217i) q^{43} -5.16148i q^{44} +(-1.26397 - 1.84456i) q^{45} +3.34901 q^{46} +(-7.37446 - 7.37446i) q^{47} +(-0.707107 + 0.707107i) q^{48} +(2.02101 + 4.57335i) q^{50} +1.06197 q^{51} +(0.184778 + 0.184778i) q^{52} +(7.15311 + 7.15311i) q^{53} +1.00000 q^{54} +(9.52064 - 6.52395i) q^{55} +(2.88869 - 2.88869i) q^{57} +(0.274026 + 0.274026i) q^{58} -9.70992 q^{59} +(-2.19806 - 0.410538i) q^{60} -11.0100i q^{61} +(-7.50483 - 7.50483i) q^{62} +1.00000i q^{64} +(-0.107280 + 0.574387i) q^{65} +5.16148i q^{66} +(-0.0355377 + 0.0355377i) q^{67} +(0.750926 - 0.750926i) q^{68} -3.34901 q^{69} +15.7253 q^{71} +(0.707107 - 0.707107i) q^{72} +(3.22877 - 3.22877i) q^{73} +3.55196i q^{74} +(-2.02101 - 4.57335i) q^{75} -4.08523i q^{76} +(-0.184778 - 0.184778i) q^{78} -7.46114i q^{79} +(-1.84456 + 1.26397i) q^{80} -1.00000 q^{81} +(-4.99134 - 4.99134i) q^{82} +(0.409165 - 0.409165i) q^{83} +(2.33427 + 0.435979i) q^{85} +3.01534 q^{86} +(-0.274026 - 0.274026i) q^{87} +(3.64972 + 3.64972i) q^{88} -14.1264 q^{89} +(2.19806 + 0.410538i) q^{90} +(-2.36811 + 2.36811i) q^{92} +(7.50483 + 7.50483i) q^{93} +10.4291 q^{94} +(7.53543 - 5.16359i) q^{95} -1.00000i q^{96} +(-1.32497 - 1.32497i) q^{97} -5.16148i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{5}+O(q^{10}) $ 16 * q + 8 * q^5	$ 16 q + 8 q^{5} + 8 q^{13} - 16 q^{16} - 8 q^{17} - 48 q^{19} - 8 q^{22} - 8 q^{23} + 16 q^{24} + 8 q^{25} + 8 q^{33} - 16 q^{36} + 8 q^{37} - 8 q^{38} + 16 q^{47} - 8 q^{52} + 8 q^{53} + 16 q^{54} + 8 q^{57} + 24 q^{58} + 48 q^{59} - 8 q^{62} + 72 q^{65} - 48 q^{67} - 8 q^{68} + 16 q^{73} + 8 q^{78} - 8 q^{80} - 16 q^{81} - 16 q^{82} - 72 q^{85} - 24 q^{87} + 8 q^{88} - 64 q^{89} - 8 q^{92} + 8 q^{93} + 64 q^{94} + 48 q^{95} - 64 q^{97}+O(q^{100}) $ 16 * q + 8 * q^5 + 8 * q^13 - 16 * q^16 - 8 * q^17 - 48 * q^19 - 8 * q^22 - 8 * q^23 + 16 * q^24 + 8 * q^25 + 8 * q^33 - 16 * q^36 + 8 * q^37 - 8 * q^38 + 16 * q^47 - 8 * q^52 + 8 * q^53 + 16 * q^54 + 8 * q^57 + 24 * q^58 + 48 * q^59 - 8 * q^62 + 72 * q^65 - 48 * q^67 - 8 * q^68 + 16 * q^73 + 8 * q^78 - 8 * q^80 - 16 * q^81 - 16 * q^82 - 72 * q^85 - 24 * q^87 + 8 * q^88 - 64 * q^89 - 8 * q^92 + 8 * q^93 + 64 * q^94 + 48 * q^95 - 64 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1470\mathbb{Z}\right)^\times$.

$n$	$491$	$1081$	$1177$
$\chi(n)$	$1$	$-1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$3$	0.707107	−	0.707107i	0.408248	−	0.408248i
$3$	0.707107	−	0.707107i	0.408248	−	0.408248i
$4$		−	1.00000i		−	0.500000i
$5$	1.84456	−	1.26397i	0.824910	−	0.565263i
$5$	1.84456	−	1.26397i	0.824910	−	0.565263i
$6$			1.00000i			0.408248i
$7$		0			0
$7$		0			0
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$		−	1.00000i		−	0.333333i
$10$	−0.410538	+	2.19806i	−0.129824	+	0.695087i
$11$	5.16148			1.55625			0.778123	−	0.628112i	$-0.216172\pi$
$11$	5.16148			1.55625			0.778123	+	0.628112i	$0.216172\pi$
$12$	−0.707107	−	0.707107i	−0.204124	−	0.204124i
$13$	−0.184778	+	0.184778i	−0.0512483	+	0.0512483i	−0.732266	−	0.681018i	$-0.761537\pi$
$13$	−0.184778	+	0.184778i	−0.0512483	+	0.0512483i	0.681018	+	0.732266i	$0.261537\pi$
$14$		0			0
$15$	0.410538	−	2.19806i	0.106000	−	0.567536i
$16$	−1.00000			−0.250000
$17$	0.750926	+	0.750926i	0.182126	+	0.182126i	0.792282	−	0.610155i	$-0.208893\pi$
$17$	0.750926	+	0.750926i	0.182126	+	0.182126i	−0.610155	+	0.792282i	$0.708893\pi$
$18$	0.707107	+	0.707107i	0.166667	+	0.166667i
$19$	4.08523			0.937215			0.468608	−	0.883406i	$-0.344756\pi$
$19$	4.08523			0.937215			0.468608	+	0.883406i	$0.344756\pi$
$20$	−1.26397	−	1.84456i	−0.282632	−	0.412455i
$21$		0			0
$22$	−3.64972	+	3.64972i	−0.778123	+	0.778123i
$23$	−2.36811	−	2.36811i	−0.493785	−	0.493785i	0.415712	−	0.909496i	$-0.363533\pi$
$23$	−2.36811	−	2.36811i	−0.493785	−	0.493785i	−0.909496	+	0.415712i	$0.863533\pi$
$24$	1.00000			0.204124
$25$	1.80477	−	4.66292i	0.360955	−	0.932583i
$26$		−	0.261316i		−	0.0512483i
$27$	−0.707107	−	0.707107i	−0.136083	−	0.136083i
$28$		0			0
$29$		−	0.387531i		−	0.0719627i	−0.999352	−	0.0359813i	$-0.988544\pi$
$29$		−	0.387531i		−	0.0719627i	0.999352	−	0.0359813i	$-0.0114557\pi$
$30$	1.26397	+	1.84456i	0.230768	+	0.336768i
$31$			10.6134i			1.90623i	0.302611	+	0.953114i	$0.402142\pi$
$31$			10.6134i			1.90623i	−0.302611	+	0.953114i	$0.597858\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$	3.64972	−	3.64972i	0.635335	−	0.635335i
$34$	−1.06197			−0.182126
$35$		0			0
$36$	−1.00000			−0.166667
$37$	2.51162	−	2.51162i	0.412907	−	0.412907i	−0.469843	−	0.882750i	$-0.655689\pi$
$37$	2.51162	−	2.51162i	0.412907	−	0.412907i	0.882750	+	0.469843i	$0.155689\pi$
$38$	−2.88869	+	2.88869i	−0.468608	+	0.468608i
$39$			0.261316i			0.0418440i
$40$	2.19806	+	0.410538i	0.347543	+	0.0649118i
$41$			7.05881i			1.10240i	0.834373	+	0.551201i	$0.185830\pi$
$41$			7.05881i			1.10240i	−0.834373	+	0.551201i	$0.814170\pi$
$42$		0			0
$43$	−2.13217	−	2.13217i	−0.325153	−	0.325153i	0.525587	−	0.850740i	$-0.323846\pi$
$43$	−2.13217	−	2.13217i	−0.325153	−	0.325153i	−0.850740	+	0.525587i	$0.823846\pi$
$44$		−	5.16148i		−	0.778123i
$45$	−1.26397	−	1.84456i	−0.188421	−	0.274970i
$46$	3.34901			0.493785
$47$	−7.37446	−	7.37446i	−1.07568	−	1.07568i	−0.996892	−	0.0787836i	$-0.974896\pi$
$47$	−7.37446	−	7.37446i	−1.07568	−	1.07568i	−0.0787836	−	0.996892i	$-0.525104\pi$
$48$	−0.707107	+	0.707107i	−0.102062	+	0.102062i
$49$		0			0
$50$	2.02101	+	4.57335i	0.285814	+	0.646769i
$51$	1.06197			0.148706
$52$	0.184778	+	0.184778i	0.0256241	+	0.0256241i
$53$	7.15311	+	7.15311i	0.982556	+	0.982556i	0.999850	−	0.0172949i	$-0.00550540\pi$
$53$	7.15311	+	7.15311i	0.982556	+	0.982556i	−0.0172949	+	0.999850i	$0.505505\pi$
$54$	1.00000			0.136083
$55$	9.52064	−	6.52395i	1.28376	−	0.879689i
$56$		0			0
$57$	2.88869	−	2.88869i	0.382617	−	0.382617i
$58$	0.274026	+	0.274026i	0.0359813	+	0.0359813i
$59$	−9.70992			−1.26412			−0.632062	−	0.774918i	$-0.717791\pi$
$59$	−9.70992			−1.26412			−0.632062	+	0.774918i	$0.717791\pi$
$60$	−2.19806	−	0.410538i	−0.283768	−	0.0530002i
$61$		−	11.0100i		−	1.40969i	−0.709361	−	0.704846i	$-0.751016\pi$
$61$		−	11.0100i		−	1.40969i	0.709361	−	0.704846i	$-0.248984\pi$
$62$	−7.50483	−	7.50483i	−0.953114	−	0.953114i
$63$		0			0
$64$			1.00000i			0.125000i
$65$	−0.107280	+	0.574387i	−0.0133065	+	0.0712440i
$66$			5.16148i			0.635335i
$67$	−0.0355377	+	0.0355377i	−0.00434163	+	0.00434163i	−0.709274	−	0.704933i	$-0.750977\pi$
$67$	−0.0355377	+	0.0355377i	−0.00434163	+	0.00434163i	0.704933	+	0.709274i	$0.250977\pi$
$68$	0.750926	−	0.750926i	0.0910632	−	0.0910632i
$69$	−3.34901			−0.403174
$70$		0			0
$71$	15.7253			1.86625			0.933127	−	0.359546i	$-0.117068\pi$
$71$	15.7253			1.86625			0.933127	+	0.359546i	$0.117068\pi$
$72$	0.707107	−	0.707107i	0.0833333	−	0.0833333i
$73$	3.22877	−	3.22877i	0.377899	−	0.377899i	−0.492445	−	0.870344i	$-0.663897\pi$
$73$	3.22877	−	3.22877i	0.377899	−	0.377899i	0.870344	+	0.492445i	$0.163897\pi$
$74$			3.55196i			0.412907i
$75$	−2.02101	−	4.57335i	−0.233366	−	0.528085i
$76$		−	4.08523i		−	0.468608i
$77$		0			0
$78$	−0.184778	−	0.184778i	−0.0209220	−	0.0209220i
$79$		−	7.46114i		−	0.839444i	−0.907653	−	0.419722i	$-0.862128\pi$
$79$		−	7.46114i		−	0.839444i	0.907653	−	0.419722i	$-0.137872\pi$
$80$	−1.84456	+	1.26397i	−0.206228	+	0.141316i
$81$	−1.00000			−0.111111
$82$	−4.99134	−	4.99134i	−0.551201	−	0.551201i
$83$	0.409165	−	0.409165i	0.0449117	−	0.0449117i	−0.684294	−	0.729206i	$-0.739890\pi$
$83$	0.409165	−	0.409165i	0.0449117	−	0.0449117i	0.729206	+	0.684294i	$0.239890\pi$
$84$		0			0
$85$	2.33427	+	0.435979i	0.253187	+	0.0472886i
$86$	3.01534			0.325153
$87$	−0.274026	−	0.274026i	−0.0293786	−	0.0293786i
$88$	3.64972	+	3.64972i	0.389061	+	0.389061i
$89$	−14.1264			−1.49739			−0.748695	−	0.662914i	$-0.769319\pi$
$89$	−14.1264			−1.49739			−0.748695	+	0.662914i	$0.769319\pi$
$90$	2.19806	+	0.410538i	0.231696	+	0.0432745i
$91$		0			0
$92$	−2.36811	+	2.36811i	−0.246892	+	0.246892i
$93$	7.50483	+	7.50483i	0.778215	+	0.778215i
$94$	10.4291			1.07568
$95$	7.53543	−	5.16359i	0.773119	−	0.529774i
$96$		−	1.00000i		−	0.102062i
$97$	−1.32497	−	1.32497i	−0.134530	−	0.134530i	0.636635	−	0.771165i	$-0.280326\pi$
$97$	−1.32497	−	1.32497i	−0.134530	−	0.134530i	−0.771165	+	0.636635i	$0.780326\pi$
$98$		0			0
$99$		−	5.16148i		−	0.518749i
$100$	−4.66292	−	1.80477i	−0.466292	−	0.180477i
$101$			2.60028i			0.258737i	0.991597	+	0.129369i	$0.0412951\pi$
$101$			2.60028i			0.258737i	−0.991597	+	0.129369i	$0.958705\pi$
$102$	−0.750926	+	0.750926i	−0.0743528	+	0.0743528i
$103$	6.20799	−	6.20799i	0.611691	−	0.611691i	−0.331695	−	0.943387i	$-0.607621\pi$
$103$	6.20799	−	6.20799i	0.611691	−	0.611691i	0.943387	+	0.331695i	$0.107621\pi$
$104$	−0.261316			−0.0256241
$105$		0			0
$106$	−10.1160			−0.982556
$107$	−13.6366	+	13.6366i	−1.31830	+	1.31830i	−0.403183	+	0.915119i	$0.632096\pi$
$107$	−13.6366	+	13.6366i	−1.31830	+	1.31830i	−0.915119	+	0.403183i	$0.867904\pi$
$108$	−0.707107	+	0.707107i	−0.0680414	+	0.0680414i
$109$		−	7.24117i		−	0.693578i	−0.937943	−	0.346789i	$-0.887272\pi$
$109$		−	7.24117i		−	0.693578i	0.937943	−	0.346789i	$-0.112728\pi$
$110$	−2.11899	+	11.3452i	−0.202037	+	1.08173i
$111$		−	3.55196i		−	0.337137i
$112$		0			0
$113$	−5.46766	−	5.46766i	−0.514354	−	0.514354i	0.401503	−	0.915858i	$-0.368488\pi$
$113$	−5.46766	−	5.46766i	−0.514354	−	0.514354i	−0.915858	+	0.401503i	$0.868488\pi$
$114$			4.08523i			0.382617i
$115$	−7.36132	−	1.37490i	−0.686447	−	0.128210i
$116$	−0.387531			−0.0359813
$117$	0.184778	+	0.184778i	0.0170828	+	0.0170828i
$118$	6.86595	−	6.86595i	0.632062	−	0.632062i
$119$		0			0
$120$	1.84456	−	1.26397i	0.168384	−	0.115384i
$121$	15.6409			1.42190
$122$	7.78528	+	7.78528i	0.704846	+	0.704846i
$123$	4.99134	+	4.99134i	0.450054	+	0.450054i
$124$	10.6134			0.953114
$125$	−2.56477	−	10.8822i	−0.229400	−	0.973332i
$126$		0			0
$127$	13.3115	−	13.3115i	1.18120	−	1.18120i	0.201770	−	0.979433i	$-0.435331\pi$
$127$	13.3115	−	13.3115i	1.18120	−	1.18120i	0.979433	−	0.201770i	$-0.0646693\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$	−3.01534			−0.265486
$130$	−0.330295	−	0.482012i	−0.0289688	−	0.0422752i
$131$			10.9119i			0.953376i	0.879073	+	0.476688i	$0.158163\pi$
$131$			10.9119i			0.953376i	−0.879073	+	0.476688i	$0.841837\pi$
$132$	−3.64972	−	3.64972i	−0.317667	−	0.317667i
$133$		0			0
$134$		−	0.0502580i		−	0.00434163i
$135$	−2.19806	−	0.410538i	−0.189179	−	0.0353335i
$136$			1.06197i			0.0910632i
$137$	−2.89316	+	2.89316i	−0.247180	+	0.247180i	−0.819812	−	0.572633i	$-0.805922\pi$
$137$	−2.89316	+	2.89316i	−0.247180	+	0.247180i	0.572633	+	0.819812i	$0.305922\pi$
$138$	2.36811	−	2.36811i	0.201587	−	0.201587i
$139$	10.3841			0.880769			0.440384	−	0.897809i	$-0.354842\pi$
$139$	10.3841			0.880769			0.440384	+	0.897809i	$0.354842\pi$
$140$		0			0
$141$	−10.4291			−0.878285
$142$	−11.1195	+	11.1195i	−0.933127	+	0.933127i
$143$	−0.953730	+	0.953730i	−0.0797549	+	0.0797549i
$144$			1.00000i			0.0833333i
$145$	−0.489826	−	0.714822i	−0.0406779	−	0.0593628i
$146$			4.56617i			0.377899i
$147$		0			0
$148$	−2.51162	−	2.51162i	−0.206454	−	0.206454i
$149$		−	16.7852i		−	1.37510i	−0.726139	−	0.687548i	$-0.758687\pi$
$149$		−	16.7852i		−	1.37510i	0.726139	−	0.687548i	$-0.241313\pi$
$150$	4.66292	+	1.80477i	0.380726	+	0.147359i
$151$	9.76485			0.794652			0.397326	−	0.917677i	$-0.369938\pi$
$151$	9.76485			0.794652			0.397326	+	0.917677i	$0.369938\pi$
$152$	2.88869	+	2.88869i	0.234304	+	0.234304i
$153$	0.750926	−	0.750926i	0.0607088	−	0.0607088i
$154$		0			0
$155$	13.4150	+	19.5771i	1.07752	+	1.57247i
$156$	0.261316			0.0209220
$157$	−8.66837	−	8.66837i	−0.691811	−	0.691811i	0.270819	−	0.962630i	$-0.412705\pi$
$157$	−8.66837	−	8.66837i	−0.691811	−	0.691811i	−0.962630	+	0.270819i	$0.912705\pi$
$158$	5.27582	+	5.27582i	0.419722	+	0.419722i
$159$	10.1160			0.802253
$160$	0.410538	−	2.19806i	0.0324559	−	0.173772i
$161$		0			0
$162$	0.707107	−	0.707107i	0.0555556	−	0.0555556i
$163$	13.7694	+	13.7694i	1.07850	+	1.07850i	0.996644	+	0.0818553i	$0.0260845\pi$
$163$	13.7694	+	13.7694i	1.07850	+	1.07850i	0.0818553	+	0.996644i	$0.473915\pi$
$164$	7.05881			0.551201
$165$	2.11899	−	11.3452i	0.164963	−	0.883226i
$166$			0.578647i			0.0449117i
$167$	−4.32056	−	4.32056i	−0.334335	−	0.334335i	0.519895	−	0.854230i	$-0.325971\pi$
$167$	−4.32056	−	4.32056i	−0.334335	−	0.334335i	−0.854230	+	0.519895i	$0.825971\pi$
$168$		0			0
$169$			12.9317i			0.994747i
$170$	−1.95886	+	1.34230i	−0.150238	+	0.102949i
$171$		−	4.08523i		−	0.312405i
$172$	−2.13217	+	2.13217i	−0.162576	+	0.162576i
$173$	−14.3204	+	14.3204i	−1.08876	+	1.08876i	−0.0931075	+	0.995656i	$0.529680\pi$
$173$	−14.3204	+	14.3204i	−1.08876	+	1.08876i	−0.995656	+	0.0931075i	$0.970320\pi$
$174$	0.387531			0.0293786
$175$		0			0
$176$	−5.16148			−0.389061
$177$	−6.86595	+	6.86595i	−0.516076	+	0.516076i
$178$	9.98884	−	9.98884i	0.748695	−	0.748695i
$179$			22.2204i			1.66083i	0.557144	+	0.830416i	$0.311897\pi$
$179$			22.2204i			1.66083i	−0.557144	+	0.830416i	$0.688103\pi$
$180$	−1.84456	+	1.26397i	−0.137485	+	0.0942106i
$181$			25.1301i			1.86791i	0.357397	+	0.933953i	$0.383664\pi$
$181$			25.1301i			1.86791i	−0.357397	+	0.933953i	$0.616336\pi$
$182$		0			0
$183$	−7.78528	−	7.78528i	−0.575504	−	0.575504i
$184$		−	3.34901i		−	0.246892i
$185$	1.45822	−	7.80742i	0.107210	−	0.574013i
$186$	−10.6134			−0.778215
$187$	3.87589	+	3.87589i	0.283433	+	0.283433i
$188$	−7.37446	+	7.37446i	−0.537838	+	0.537838i
$189$		0			0
$190$	−1.67714	+	8.97957i	−0.121673	+	0.651446i
$191$	1.53994			0.111426			0.0557130	−	0.998447i	$-0.482257\pi$
$191$	1.53994			0.111426			0.0557130	+	0.998447i	$0.482257\pi$
$192$	0.707107	+	0.707107i	0.0510310	+	0.0510310i
$193$	−12.7329	−	12.7329i	−0.916533	−	0.916533i	0.0802420	−	0.996775i	$-0.474431\pi$
$193$	−12.7329	−	12.7329i	−0.916533	−	0.916533i	−0.996775	+	0.0802420i	$0.974431\pi$
$194$	1.87379			0.134530
$195$	0.330295	+	0.482012i	0.0236529	+	0.0345176i
$196$		0			0
$197$	12.0158	−	12.0158i	0.856087	−	0.856087i	−0.134787	−	0.990875i	$-0.543035\pi$
$197$	12.0158	−	12.0158i	0.856087	−	0.856087i	0.990875	+	0.134787i	$0.0430351\pi$
$198$	3.64972	+	3.64972i	0.259374	+	0.259374i
$199$	9.42226			0.667926			0.333963	−	0.942586i	$-0.391614\pi$
$199$	9.42226			0.667926			0.333963	+	0.942586i	$0.391614\pi$
$200$	4.57335	−	2.02101i	0.323385	−	0.142907i
$201$			0.0502580i			0.00354492i
$202$	−1.83867	−	1.83867i	−0.129369	−	0.129369i
$203$		0			0
$204$		−	1.06197i		−	0.0743528i
$205$	8.92211	+	13.0204i	0.623147	+	0.909383i
$206$			8.77942i			0.611691i
$207$	−2.36811	+	2.36811i	−0.164595	+	0.164595i
$208$	0.184778	−	0.184778i	0.0128121	−	0.0128121i
$209$	21.0858			1.45854
$210$		0			0
$211$	14.4641			0.995748			0.497874	−	0.867249i	$-0.334114\pi$
$211$	14.4641			0.995748			0.497874	+	0.867249i	$0.334114\pi$
$212$	7.15311	−	7.15311i	0.491278	−	0.491278i
$213$	11.1195	−	11.1195i	0.761895	−	0.761895i
$214$		−	19.2851i		−	1.31830i
$215$	−6.62790	−	1.23791i	−0.452019	−	0.0844250i
$216$		−	1.00000i		−	0.0680414i
$217$		0			0
$218$	5.12028	+	5.12028i	0.346789	+	0.346789i
$219$		−	4.56617i		−	0.308553i
$220$	−6.52395	−	9.52064i	−0.439844	−	0.641882i
$221$	−0.277510			−0.0186673
$222$	2.51162	+	2.51162i	0.168569	+	0.168569i
$223$	−7.80302	+	7.80302i	−0.522529	+	0.522529i	−0.918334	−	0.395805i	$-0.870465\pi$
$223$	−7.80302	+	7.80302i	−0.522529	+	0.522529i	0.395805	+	0.918334i	$0.370465\pi$
$224$		0			0
$225$	−4.66292	−	1.80477i	−0.310861	−	0.120318i
$226$	7.73244			0.514354
$227$	−7.43269	−	7.43269i	−0.493325	−	0.493325i	0.416027	−	0.909352i	$-0.363422\pi$
$227$	−7.43269	−	7.43269i	−0.493325	−	0.493325i	−0.909352	+	0.416027i	$0.863422\pi$
$228$	−2.88869	−	2.88869i	−0.191308	−	0.191308i
$229$	−10.5109			−0.694583			−0.347291	−	0.937757i	$-0.612899\pi$
$229$	−10.5109			−0.694583			−0.347291	+	0.937757i	$0.612899\pi$
$230$	6.17744	−	4.23304i	0.407328	−	0.279118i
$231$		0			0
$232$	0.274026	−	0.274026i	0.0179907	−	0.0179907i
$233$	−16.2668	−	16.2668i	−1.06568	−	1.06568i	−0.997686	−	0.0679900i	$-0.978341\pi$
$233$	−16.2668	−	16.2668i	−1.06568	−	1.06568i	−0.0679900	−	0.997686i	$-0.521659\pi$
$234$	−0.261316			−0.0170828
$235$	−22.9237	−	4.28153i	−1.49538	−	0.279296i
$236$			9.70992i			0.632062i
$237$	−5.27582	−	5.27582i	−0.342702	−	0.342702i
$238$		0			0
$239$			19.4914i			1.26080i	0.776272	+	0.630398i	$0.217108\pi$
$239$			19.4914i			1.26080i	−0.776272	+	0.630398i	$0.782892\pi$
$240$	−0.410538	+	2.19806i	−0.0265001	+	0.141884i
$241$			8.15049i			0.525019i	0.964929	+	0.262509i	$0.0845501\pi$
$241$			8.15049i			0.525019i	−0.964929	+	0.262509i	$0.915450\pi$
$242$	−11.0598	+	11.0598i	−0.710950	+	0.710950i
$243$	−0.707107	+	0.707107i	−0.0453609	+	0.0453609i
$244$	−11.0100			−0.704846
$245$		0			0
$246$	−7.05881			−0.450054
$247$	−0.754861	+	0.754861i	−0.0480307	+	0.0480307i
$248$	−7.50483	+	7.50483i	−0.476557	+	0.476557i
$249$		−	0.578647i		−	0.0366702i
$250$	9.50843	+	5.88130i	0.601366	+	0.371966i
$251$			8.93480i			0.563960i	0.959420	+	0.281980i	$0.0909911\pi$
$251$			8.93480i			0.563960i	−0.959420	+	0.281980i	$0.909009\pi$
$252$		0			0
$253$	−12.2230	−	12.2230i	−0.768450	−	0.768450i
$254$			18.8253i			1.18120i
$255$	1.95886	−	1.34230i	0.122669	−	0.0840578i
$256$	1.00000			0.0625000
$257$	−2.26445	−	2.26445i	−0.141253	−	0.141253i	0.632944	−	0.774197i	$-0.281846\pi$
$257$	−2.26445	−	2.26445i	−0.141253	−	0.141253i	−0.774197	+	0.632944i	$0.781846\pi$
$258$	2.13217	−	2.13217i	0.132743	−	0.132743i
$259$		0			0
$260$	0.574387	+	0.107280i	0.0356220	+	0.00665323i
$261$	−0.387531			−0.0239876
$262$	−7.71587	−	7.71587i	−0.476688	−	0.476688i
$263$	8.87987	+	8.87987i	0.547556	+	0.547556i	0.925733	−	0.378177i	$-0.123449\pi$
$263$	8.87987	+	8.87987i	0.547556	+	0.547556i	−0.378177	+	0.925733i	$0.623449\pi$
$264$	5.16148			0.317667
$265$	22.2356	+	4.15302i	1.36592	+	0.255118i
$266$		0			0
$267$	−9.98884	+	9.98884i	−0.611307	+	0.611307i
$268$	0.0355377	+	0.0355377i	0.00217081	+	0.00217081i
$269$	7.38784			0.450445			0.225222	−	0.974307i	$-0.427689\pi$
$269$	7.38784			0.450445			0.225222	+	0.974307i	$0.427689\pi$
$270$	1.84456	−	1.26397i	0.112256	−	0.0769226i
$271$		−	2.27382i		−	0.138124i	−0.997612	−	0.0690622i	$-0.977999\pi$
$271$		−	2.27382i		−	0.138124i	0.997612	−	0.0690622i	$-0.0220007\pi$
$272$	−0.750926	−	0.750926i	−0.0455316	−	0.0455316i
$273$		0			0
$274$		−	4.09155i		−	0.247180i
$275$	9.31531	−	24.0676i	0.561734	−	1.45133i
$276$			3.34901i			0.201587i
$277$	−17.8539	+	17.8539i	−1.07274	+	1.07274i	−0.0755979	+	0.997138i	$0.524087\pi$
$277$	−17.8539	+	17.8539i	−1.07274	+	1.07274i	−0.997138	+	0.0755979i	$0.975913\pi$
$278$	−7.34268	+	7.34268i	−0.440384	+	0.440384i
$279$	10.6134			0.635410
$280$		0			0
$281$	−27.1380			−1.61892			−0.809458	−	0.587178i	$-0.800239\pi$
$281$	−27.1380			−1.61892			−0.809458	+	0.587178i	$0.800239\pi$
$282$	7.37446	−	7.37446i	0.439143	−	0.439143i
$283$	2.30592	−	2.30592i	0.137073	−	0.137073i	−0.635241	−	0.772314i	$-0.719099\pi$
$283$	2.30592	−	2.30592i	0.137073	−	0.137073i	0.772314	+	0.635241i	$0.219099\pi$
$284$		−	15.7253i		−	0.933127i
$285$	1.67714	−	8.97957i	0.0993453	−	0.531904i
$286$		−	1.34878i		−	0.0797549i
$287$		0			0
$288$	−0.707107	−	0.707107i	−0.0416667	−	0.0416667i
$289$		−	15.8722i		−	0.933660i
$290$	0.851815	+	0.159096i	0.0500203	+	0.00934245i
$291$	−1.87379			−0.109843
$292$	−3.22877	−	3.22877i	−0.188949	−	0.188949i
$293$	−22.8732	+	22.8732i	−1.33627	+	1.33627i	−0.436625	+	0.899643i	$0.643826\pi$
$293$	−22.8732	+	22.8732i	−1.33627	+	1.33627i	−0.899643	+	0.436625i	$0.856174\pi$
$294$		0			0
$295$	−17.9105	+	12.2730i	−1.04279	+	0.714563i
$296$	3.55196			0.206454
$297$	−3.64972	−	3.64972i	−0.211778	−	0.211778i
$298$	11.8689	+	11.8689i	0.687548	+	0.687548i
$299$	0.875150			0.0506112
$300$	−4.57335	+	2.02101i	−0.264042	+	0.116683i
$301$		0			0
$302$	−6.90479	+	6.90479i	−0.397326	+	0.397326i
$303$	1.83867	+	1.83867i	0.105629	+	0.105629i
$304$	−4.08523			−0.234304
$305$	−13.9163	−	20.3086i	−0.796847	−	1.16287i
$306$			1.06197i			0.0607088i
$307$	−2.06248	−	2.06248i	−0.117712	−	0.117712i	0.645797	−	0.763509i	$-0.276525\pi$
$307$	−2.06248	−	2.06248i	−0.117712	−	0.117712i	−0.763509	+	0.645797i	$0.776525\pi$
$308$		0			0
$309$		−	8.77942i		−	0.499444i
$310$	−23.3289	−	4.35722i	−1.32499	−	0.247473i
$311$		−	5.67250i		−	0.321658i	−0.986982	−	0.160829i	$-0.948583\pi$
$311$		−	5.67250i		−	0.321658i	0.986982	−	0.160829i	$-0.0514168\pi$
$312$	−0.184778	+	0.184778i	−0.0104610	+	0.0104610i
$313$	−23.7286	+	23.7286i	−1.34122	+	1.34122i	−0.446374	+	0.894847i	$0.647285\pi$
$313$	−23.7286	+	23.7286i	−1.34122	+	1.34122i	−0.894847	+	0.446374i	$0.852715\pi$
$314$	12.2589			0.691811
$315$		0			0
$316$	−7.46114			−0.419722
$317$	−7.61158	+	7.61158i	−0.427509	+	0.427509i	−0.887779	−	0.460270i	$-0.847753\pi$
$317$	−7.61158	+	7.61158i	−0.427509	+	0.427509i	0.460270	+	0.887779i	$0.347753\pi$
$318$	−7.15311	+	7.15311i	−0.401127	+	0.401127i
$319$		−	2.00023i		−	0.111992i
$320$	1.26397	+	1.84456i	0.0706579	+	0.103114i
$321$			19.2851i			1.07639i
$322$		0			0
$323$	3.06770	+	3.06770i	0.170692	+	0.170692i
$324$			1.00000i			0.0555556i
$325$	0.528123	+	1.19509i	0.0292950	+	0.0662916i
$326$	−19.4728			−1.07850
$327$	−5.12028	−	5.12028i	−0.283152	−	0.283152i
$328$	−4.99134	+	4.99134i	−0.275600	+	0.275600i
$329$		0			0
$330$	6.52395	+	9.52064i	0.359131	+	0.524094i
$331$	−5.09546			−0.280072			−0.140036	−	0.990146i	$-0.544722\pi$
$331$	−5.09546			−0.280072			−0.140036	+	0.990146i	$0.544722\pi$
$332$	−0.409165	−	0.409165i	−0.0224558	−	0.0224558i
$333$	−2.51162	−	2.51162i	−0.137636	−	0.137636i
$334$	6.11020			0.334335
$335$	−0.0206328	+	0.110470i	−0.00112729	+	0.00603562i
$336$		0			0
$337$	8.29846	−	8.29846i	0.452046	−	0.452046i	−0.443987	−	0.896033i	$-0.646436\pi$
$337$	8.29846	−	8.29846i	0.452046	−	0.452046i	0.896033	+	0.443987i	$0.146436\pi$
$338$	−9.14410	−	9.14410i	−0.497374	−	0.497374i
$339$	−7.73244			−0.419969
$340$	0.435979	−	2.33427i	0.0236443	−	0.126594i
$341$			54.7810i			2.96656i
$342$	2.88869	+	2.88869i	0.156203	+	0.156203i
$343$		0			0
$344$		−	3.01534i		−	0.162576i
$345$	−6.17744	+	4.23304i	−0.332582	+	0.227899i
$346$		−	20.2522i		−	1.08876i
$347$	−9.94950	+	9.94950i	−0.534117	+	0.534117i	−0.921795	−	0.387678i	$-0.873277\pi$
$347$	−9.94950	+	9.94950i	−0.534117	+	0.534117i	0.387678	+	0.921795i	$0.373277\pi$
$348$	−0.274026	+	0.274026i	−0.0146893	+	0.0146893i
$349$	−25.7633			−1.37908			−0.689540	−	0.724247i	$-0.742187\pi$
$349$	−25.7633			−1.37908			−0.689540	+	0.724247i	$0.742187\pi$
$350$		0			0
$351$	0.261316			0.0139480
$352$	3.64972	−	3.64972i	0.194531	−	0.194531i
$353$	0.116111	−	0.116111i	0.00617997	−	0.00617997i	−0.704010	−	0.710190i	$-0.748609\pi$
$353$	0.116111	−	0.116111i	0.00617997	−	0.00617997i	0.710190	+	0.704010i	$0.248609\pi$
$354$		−	9.70992i		−	0.516076i
$355$	29.0063	−	19.8763i	1.53949	−	1.05493i
$356$			14.1264i			0.748695i
$357$		0			0
$358$	−15.7122	−	15.7122i	−0.830416	−	0.830416i
$359$		−	11.3365i		−	0.598319i	−0.954203	−	0.299159i	$-0.903294\pi$
$359$		−	11.3365i		−	0.598319i	0.954203	−	0.299159i	$-0.0967062\pi$
$360$	0.410538	−	2.19806i	0.0216373	−	0.115848i
$361$	−2.31092			−0.121627
$362$	−17.7697	−	17.7697i	−0.933953	−	0.933953i
$363$	11.0598	−	11.0598i	0.580488	−	0.580488i
$364$		0			0
$365$	1.87459	−	10.0367i	0.0981203	−	0.525345i
$366$	11.0100			0.575504
$367$	−9.84215	−	9.84215i	−0.513756	−	0.513756i	0.401919	−	0.915675i	$-0.368343\pi$
$367$	−9.84215	−	9.84215i	−0.513756	−	0.513756i	−0.915675	+	0.401919i	$0.868343\pi$
$368$	2.36811	+	2.36811i	0.123446	+	0.123446i
$369$	7.05881			0.367467
$370$	4.48957	+	6.55180i	0.233401	+	0.340612i
$371$		0			0
$372$	7.50483	−	7.50483i	0.389107	−	0.389107i
$373$	−9.17514	−	9.17514i	−0.475071	−	0.475071i	0.428480	−	0.903551i	$-0.359049\pi$
$373$	−9.17514	−	9.17514i	−0.475071	−	0.475071i	−0.903551	+	0.428480i	$0.859049\pi$
$374$	−5.48134			−0.283433
$375$	−9.50843	−	5.88130i	−0.491013	−	0.303709i
$376$		−	10.4291i		−	0.537838i
$377$	0.0716073	+	0.0716073i	0.00368796	+	0.00368796i
$378$		0			0
$379$		−	24.7501i		−	1.27133i	−0.771967	−	0.635663i	$-0.780727\pi$
$379$		−	24.7501i		−	1.27133i	0.771967	−	0.635663i	$-0.219273\pi$
$380$	−5.16359	−	7.53543i	−0.264887	−	0.386559i
$381$		−	18.8253i		−	0.964448i
$382$	−1.08890	+	1.08890i	−0.0557130	+	0.0557130i
$383$	13.7562	−	13.7562i	0.702908	−	0.702908i	−0.262126	−	0.965034i	$-0.584423\pi$
$383$	13.7562	−	13.7562i	0.702908	−	0.702908i	0.965034	+	0.262126i	$0.0844235\pi$
$384$	−1.00000			−0.0510310
$385$		0			0
$386$	18.0070			0.916533
$387$	−2.13217	+	2.13217i	−0.108384	+	0.108384i
$388$	−1.32497	+	1.32497i	−0.0672650	+	0.0672650i
$389$		−	8.60539i		−	0.436310i	−0.975914	−	0.218155i	$-0.929996\pi$
$389$		−	8.60539i		−	0.436310i	0.975914	−	0.218155i	$-0.0700039\pi$
$390$	−0.574387	−	0.107280i	−0.0290852	−	0.00543234i
$391$		−	3.55655i		−	0.179862i
$392$		0			0
$393$	7.71587	+	7.71587i	0.389214	+	0.389214i
$394$			16.9929i			0.856087i
$395$	−9.43064	−	13.7625i	−0.474507	−	0.692466i
$396$	−5.16148			−0.259374
$397$	19.1209	+	19.1209i	0.959649	+	0.959649i	0.999217	−	0.0395679i	$-0.0125981\pi$
$397$	19.1209	+	19.1209i	0.959649	+	0.959649i	−0.0395679	+	0.999217i	$0.512598\pi$
$398$	−6.66254	+	6.66254i	−0.333963	+	0.333963i
$399$		0			0
$400$	−1.80477	+	4.66292i	−0.0902387	+	0.233146i
$401$	−6.66995			−0.333082			−0.166541	−	0.986035i	$-0.553260\pi$
$401$	−6.66995			−0.333082			−0.166541	+	0.986035i	$0.553260\pi$
$402$	−0.0355377	−	0.0355377i	−0.00177246	−	0.00177246i
$403$	−1.96113	−	1.96113i	−0.0976909	−	0.0976909i
$404$	2.60028			0.129369
$405$	−1.84456	+	1.26397i	−0.0916567	+	0.0628070i
$406$		0			0
$407$	12.9637	−	12.9637i	0.642585	−	0.642585i
$408$	0.750926	+	0.750926i	0.0371764	+	0.0371764i
$409$	17.0199			0.841579			0.420789	−	0.907158i	$-0.361753\pi$
$409$	17.0199			0.841579			0.420789	+	0.907158i	$0.361753\pi$
$410$	−15.5157	−	2.89791i	−0.766265	−	0.143118i
$411$			4.09155i			0.201821i
$412$	−6.20799	−	6.20799i	−0.305846	−	0.305846i
$413$		0			0
$414$		−	3.34901i		−	0.164595i
$415$	0.237556	−	1.27190i	0.0116612	−	0.0624350i
$416$			0.261316i			0.0128121i
$417$	7.34268	−	7.34268i	0.359572	−	0.359572i
$418$	−14.9099	+	14.9099i	−0.729269	+	0.729269i
$419$	−2.00407			−0.0979052			−0.0489526	−	0.998801i	$-0.515588\pi$
$419$	−2.00407			−0.0979052			−0.0489526	+	0.998801i	$0.515588\pi$
$420$		0			0
$421$	1.44745			0.0705444			0.0352722	−	0.999378i	$-0.488770\pi$
$421$	1.44745			0.0705444			0.0352722	+	0.999378i	$0.488770\pi$
$422$	−10.2276	+	10.2276i	−0.497874	+	0.497874i
$423$	−7.37446	+	7.37446i	−0.358558	+	0.358558i
$424$			10.1160i			0.491278i
$425$	4.85676	−	2.14626i	0.235587	−	0.104109i
$426$			15.7253i			0.761895i
$427$		0			0
$428$	13.6366	+	13.6366i	0.659151	+	0.659151i
$429$			1.34878i			0.0651196i
$430$	5.56197	−	3.81129i	0.268222	−	0.183797i
$431$	16.8876			0.813447			0.406724	−	0.913551i	$-0.366671\pi$
$431$	16.8876			0.813447			0.406724	+	0.913551i	$0.366671\pi$
$432$	0.707107	+	0.707107i	0.0340207	+	0.0340207i
$433$	−20.5784	+	20.5784i	−0.988934	+	0.988934i	−0.999939	−	0.0110055i	$-0.996497\pi$
$433$	−20.5784	+	20.5784i	−0.988934	+	0.988934i	0.0110055	+	0.999939i	$0.496497\pi$
$434$		0			0
$435$	−0.851815	−	0.159096i	−0.0408414	−	0.00762808i
$436$	−7.24117			−0.346789
$437$	−9.67426	−	9.67426i	−0.462783	−	0.462783i
$438$	3.22877	+	3.22877i	0.154276	+	0.154276i
$439$	2.72617			0.130113			0.0650564	−	0.997882i	$-0.479277\pi$
$439$	2.72617			0.130113			0.0650564	+	0.997882i	$0.479277\pi$
$440$	11.3452	+	2.11899i	0.540863	+	0.101019i
$441$		0			0
$442$	0.196229	−	0.196229i	0.00933366	−	0.00933366i
$443$	−0.586605	−	0.586605i	−0.0278705	−	0.0278705i	0.693034	−	0.720905i	$-0.256273\pi$
$443$	−0.586605	−	0.586605i	−0.0278705	−	0.0278705i	−0.720905	+	0.693034i	$0.756273\pi$
$444$	−3.55196			−0.168569
$445$	−26.0569	+	17.8553i	−1.23521	+	0.846420i
$446$		−	11.0351i		−	0.522529i
$447$	−11.8689	−	11.8689i	−0.561380	−	0.561380i
$448$		0			0
$449$			26.3699i			1.24447i	0.782830	+	0.622235i	$0.213775\pi$
$449$			26.3699i			1.24447i	−0.782830	+	0.622235i	$0.786225\pi$
$450$	4.57335	−	2.02101i	0.215590	−	0.0952715i
$451$			36.4339i			1.71561i
$452$	−5.46766	+	5.46766i	−0.257177	+	0.257177i
$453$	6.90479	−	6.90479i	0.324415	−	0.324415i
$454$	10.5114			0.493325
$455$		0			0
$456$	4.08523			0.191308
$457$	−18.1053	+	18.1053i	−0.846929	+	0.846929i	−0.989749	−	0.142820i	$-0.954383\pi$
$457$	−18.1053	+	18.1053i	−0.846929	+	0.846929i	0.142820	+	0.989749i	$0.454383\pi$
$458$	7.43236	−	7.43236i	0.347291	−	0.347291i
$459$		−	1.06197i		−	0.0495685i
$460$	−1.37490	+	7.36132i	−0.0641049	+	0.343223i
$461$		−	4.45597i		−	0.207535i	−0.994602	−	0.103768i	$-0.966910\pi$
$461$		−	4.45597i		−	0.207535i	0.994602	−	0.103768i	$-0.0330898\pi$
$462$		0			0
$463$	−12.4474	−	12.4474i	−0.578482	−	0.578482i	0.356003	−	0.934485i	$-0.384139\pi$
$463$	−12.4474	−	12.4474i	−0.578482	−	0.578482i	−0.934485	+	0.356003i	$0.884139\pi$
$464$			0.387531i			0.0179907i
$465$	23.3289	+	4.35722i	1.08185	+	0.202061i
$466$	23.0048			1.06568
$467$	8.34972	+	8.34972i	0.386379	+	0.386379i	0.873394	−	0.487015i	$-0.161914\pi$
$467$	8.34972	+	8.34972i	0.386379	+	0.386379i	−0.487015	+	0.873394i	$0.661914\pi$
$468$	0.184778	−	0.184778i	0.00854138	−	0.00854138i
$469$		0			0
$470$	19.2370	−	13.1820i	0.887336	−	0.608040i
$471$	−12.2589			−0.564861
$472$	−6.86595	−	6.86595i	−0.316031	−	0.316031i
$473$	−11.0052	−	11.0052i	−0.506018	−	0.506018i
$474$	7.46114			0.342702
$475$	7.37291	−	19.0491i	0.338292	−	0.874032i
$476$		0			0
$477$	7.15311	−	7.15311i	0.327519	−	0.327519i
$478$	−13.7825	−	13.7825i	−0.630398	−	0.630398i
$479$	11.9092			0.544147			0.272073	−	0.962276i	$-0.412291\pi$
$479$	11.9092			0.544147			0.272073	+	0.962276i	$0.412291\pi$
$480$	−1.26397	−	1.84456i	−0.0576920	−	0.0841921i
$481$			0.928184i			0.0423216i
$482$	−5.76326	−	5.76326i	−0.262509	−	0.262509i
$483$		0			0
$484$		−	15.6409i		−	0.710950i
$485$	−4.11869	−	0.769261i	−0.187020	−	0.0349303i
$486$		−	1.00000i		−	0.0453609i
$487$	−24.0514	+	24.0514i	−1.08987	+	1.08987i	−0.0943340	+	0.995541i	$0.530072\pi$
$487$	−24.0514	+	24.0514i	−1.08987	+	1.08987i	−0.995541	+	0.0943340i	$0.969928\pi$
$488$	7.78528	−	7.78528i	0.352423	−	0.352423i
$489$	19.4728			0.880591
$490$		0			0
$491$	−32.7719			−1.47898			−0.739488	−	0.673169i	$-0.764932\pi$
$491$	−32.7719			−1.47898			−0.739488	+	0.673169i	$0.764932\pi$
$492$	4.99134	−	4.99134i	0.225027	−	0.225027i
$493$	0.291007	−	0.291007i	0.0131063	−	0.0131063i
$494$		−	1.06753i		−	0.0480307i
$495$	−6.52395	−	9.52064i	−0.293230	−	0.427921i
$496$		−	10.6134i		−	0.476557i
$497$		0			0
$498$	0.409165	+	0.409165i	0.0183351	+	0.0183351i
$499$			29.0636i			1.30107i	0.759478	+	0.650533i	$0.225454\pi$
$499$			29.0636i			1.30107i	−0.759478	+	0.650533i	$0.774546\pi$
$500$	−10.8822	+	2.56477i	−0.486666	+	0.114700i
$501$	−6.11020			−0.272984
$502$	−6.31786	−	6.31786i	−0.281980	−	0.281980i
$503$	−2.02797	+	2.02797i	−0.0904226	+	0.0904226i	−0.750871	−	0.660449i	$-0.770366\pi$
$503$	−2.02797	+	2.02797i	−0.0904226	+	0.0904226i	0.660449	+	0.750871i	$0.270366\pi$
$504$		0			0
$505$	3.28667	+	4.79636i	0.146255	+	0.213435i
$506$	17.2859			0.768450
$507$	9.14410	+	9.14410i	0.406104	+	0.406104i
$508$	−13.3115	−	13.3115i	−0.590601	−	0.590601i
$509$	−5.18151			−0.229666			−0.114833	−	0.993385i	$-0.536633\pi$
$509$	−5.18151			−0.229666			−0.114833	+	0.993385i	$0.536633\pi$
$510$	−0.435979	+	2.33427i	−0.0193055	+	0.103363i
$511$		0			0
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	−2.88869	−	2.88869i	−0.127539	−	0.127539i
$514$	3.20242			0.141253
$515$	3.60429	−	19.2977i	0.158824	−	0.850357i
$516$			3.01534i			0.132743i
$517$	−38.0631	−	38.0631i	−1.67401	−	1.67401i
$518$		0			0
$519$			20.2522i			0.888972i
$520$	−0.482012	+	0.330295i	−0.0211376	+	0.0144844i
$521$		−	4.08595i		−	0.179009i	−0.995986	−	0.0895044i	$-0.971472\pi$
$521$		−	4.08595i		−	0.179009i	0.995986	−	0.0895044i	$-0.0285283\pi$
$522$	0.274026	−	0.274026i	0.0119938	−	0.0119938i
$523$	−3.85548	+	3.85548i	−0.168588	+	0.168588i	−0.786359	−	0.617770i	$-0.788036\pi$
$523$	−3.85548	+	3.85548i	−0.168588	+	0.168588i	0.617770	+	0.786359i	$0.288036\pi$
$524$	10.9119			0.476688
$525$		0			0
$526$	−12.5580			−0.547556
$527$	−7.96990	+	7.96990i	−0.347174	+	0.347174i
$528$	−3.64972	+	3.64972i	−0.158834	+	0.158834i
$529$		−	11.7841i		−	0.512353i
$530$	−18.6596	+	12.7863i	−0.810520	+	0.555403i
$531$			9.70992i			0.421375i
$532$		0			0
$533$	−1.30432	−	1.30432i	−0.0564962	−	0.0564962i
$534$		−	14.1264i		−	0.611307i
$535$	−7.91727	+	42.3898i	−0.342293	+	1.83267i
$536$	−0.0502580			−0.00217081
$537$	15.7122	+	15.7122i	0.678032	+	0.678032i
$538$	−5.22400	+	5.22400i	−0.225222	+	0.225222i
$539$		0			0
$540$	−0.410538	+	2.19806i	−0.0176667	+	0.0945894i
$541$	30.1052			1.29432			0.647162	−	0.762353i	$-0.275956\pi$
$541$	30.1052			1.29432			0.647162	+	0.762353i	$0.275956\pi$
$542$	1.60783	+	1.60783i	0.0690622	+	0.0690622i
$543$	17.7697	+	17.7697i	0.762569	+	0.762569i
$544$	1.06197			0.0455316
$545$	−9.15260	−	13.3567i	−0.392054	−	0.572140i
$546$		0			0
$547$	−5.00208	+	5.00208i	−0.213873	+	0.213873i	−0.805911	−	0.592037i	$-0.798324\pi$
$547$	−5.00208	+	5.00208i	−0.213873	+	0.213873i	0.592037	+	0.805911i	$0.298324\pi$
$548$	2.89316	+	2.89316i	0.123590	+	0.123590i
$549$	−11.0100			−0.469897
$550$	10.4314	+	23.6053i	0.444797	+	1.00653i
$551$		−	1.58315i		−	0.0674445i
$552$	−2.36811	−	2.36811i	−0.100793	−	0.100793i
$553$		0			0
$554$		−	25.2492i		−	1.07274i
$555$	−4.48957	−	6.55180i	−0.190571	−	0.278108i
$556$		−	10.3841i		−	0.440384i
$557$	22.4314	−	22.4314i	0.950451	−	0.950451i	−0.0483784	−	0.998829i	$-0.515405\pi$
$557$	22.4314	−	22.4314i	0.950451	−	0.950451i	0.998829	+	0.0483784i	$0.0154053\pi$
$558$	−7.50483	+	7.50483i	−0.317705	+	0.317705i
$559$	0.787957			0.0333270
$560$		0			0
$561$	5.48134			0.231422
$562$	19.1894	−	19.1894i	0.809458	−	0.809458i
$563$	−15.6424	+	15.6424i	−0.659247	+	0.659247i	−0.955202	−	0.295955i	$-0.904362\pi$
$563$	−15.6424	+	15.6424i	−0.659247	+	0.659247i	0.295955	+	0.955202i	$0.404362\pi$
$564$			10.4291i			0.439143i
$565$	−16.9964	−	3.17446i	−0.715042	−	0.133551i
$566$			3.26106i			0.137073i
$567$		0			0
$568$	11.1195	+	11.1195i	0.466564	+	0.466564i
$569$			36.8555i			1.54506i	0.634977	+	0.772531i	$0.281010\pi$
$569$			36.8555i			1.54506i	−0.634977	+	0.772531i	$0.718990\pi$
$570$	5.16359	+	7.53543i	0.216279	+	0.315624i
$571$	34.4042			1.43977			0.719885	−	0.694093i	$-0.244194\pi$
$571$	34.4042			1.43977			0.719885	+	0.694093i	$0.244194\pi$
$572$	0.953730	+	0.953730i	0.0398774	+	0.0398774i
$573$	1.08890	−	1.08890i	0.0454895	−	0.0454895i
$574$		0			0
$575$	−15.3162	+	6.76839i	−0.638729	+	0.282262i
$576$	1.00000			0.0416667
$577$	32.5072	+	32.5072i	1.35329	+	1.35329i	0.881949	+	0.471346i	$0.156232\pi$
$577$	32.5072	+	32.5072i	1.35329	+	1.35329i	0.471346	+	0.881949i	$0.343768\pi$
$578$	11.2234	+	11.2234i	0.466830	+	0.466830i
$579$	−18.0070			−0.748346
$580$	−0.714822	+	0.489826i	−0.0296814	+	0.0203389i
$581$		0			0
$582$	1.32497	−	1.32497i	0.0549217	−	0.0549217i
$583$	36.9207	+	36.9207i	1.52910	+	1.52910i
$584$	4.56617			0.188949
$585$	0.574387	+	0.107280i	0.0237480	+	0.00443549i
$586$		−	32.3476i		−	1.33627i
$587$	6.93980	+	6.93980i	0.286436	+	0.286436i	0.835669	−	0.549233i	$-0.185080\pi$
$587$	6.93980	+	6.93980i	0.286436	+	0.286436i	−0.549233	+	0.835669i	$0.685080\pi$
$588$		0			0
$589$			43.3583i			1.78655i
$590$	3.98629	−	21.3430i	0.164113	−	0.878676i
$591$		−	16.9929i		−	0.698992i
$592$	−2.51162	+	2.51162i	−0.103227	+	0.103227i
$593$	28.8960	−	28.8960i	1.18662	−	1.18662i	0.208621	−	0.977997i	$-0.433103\pi$
$593$	28.8960	−	28.8960i	1.18662	−	1.18662i	0.977997	−	0.208621i	$-0.0668974\pi$
$594$	5.16148			0.211778
$595$		0			0
$596$	−16.7852			−0.687548
$597$	6.66254	−	6.66254i	0.272680	−	0.272680i
$598$	−0.618824	+	0.618824i	−0.0253056	+	0.0253056i
$599$			25.5344i			1.04331i	0.853157	+	0.521654i	$0.174685\pi$
$599$			25.5344i			1.04331i	−0.853157	+	0.521654i	$0.825315\pi$
$600$	1.80477	−	4.66292i	0.0736796	−	0.190363i
$601$			8.12886i			0.331583i	0.986161	+	0.165792i	$0.0530179\pi$
$601$			8.12886i			0.331583i	−0.986161	+	0.165792i	$0.946982\pi$
$602$		0			0
$603$	0.0355377	+	0.0355377i	0.00144721	+	0.00144721i
$604$		−	9.76485i		−	0.397326i
$605$	28.8505	−	19.7696i	1.17294	−	0.803748i
$606$	−2.60028			−0.105629
$607$	17.5109	+	17.5109i	0.710744	+	0.710744i	0.966691	−	0.255947i	$-0.0823871\pi$
$607$	17.5109	+	17.5109i	0.710744	+	0.710744i	−0.255947	+	0.966691i	$0.582387\pi$
$608$	2.88869	−	2.88869i	0.117152	−	0.117152i
$609$		0			0
$610$	24.2007	+	4.52004i	0.979858	+	0.183011i
$611$	2.72528			0.110253
$612$	−0.750926	−	0.750926i	−0.0303544	−	0.0303544i
$613$	−18.1428	−	18.1428i	−0.732780	−	0.732780i	0.238389	−	0.971170i	$-0.423381\pi$
$613$	−18.1428	−	18.1428i	−0.732780	−	0.732780i	−0.971170	+	0.238389i	$0.923381\pi$
$614$	2.91679			0.117712
$615$	15.5157	+	2.89791i	0.625653	+	0.116855i
$616$		0			0
$617$	10.6259	−	10.6259i	0.427784	−	0.427784i	−0.460089	−	0.887873i	$-0.652182\pi$
$617$	10.6259	−	10.6259i	0.427784	−	0.427784i	0.887873	+	0.460089i	$0.152182\pi$
$618$	6.20799	+	6.20799i	0.249722	+	0.249722i
$619$	−35.7243			−1.43588			−0.717940	−	0.696105i	$-0.754915\pi$
$619$	−35.7243			−1.43588			−0.717940	+	0.696105i	$0.754915\pi$
$620$	19.5771	−	13.4150i	0.786234	−	0.538761i
$621$			3.34901i			0.134391i
$622$	4.01106	+	4.01106i	0.160829	+	0.160829i
$623$		0			0
$624$		−	0.261316i		−	0.0104610i
$625$	−18.4856	−	16.8310i	−0.739423	−	0.673241i
$626$		−	33.5573i		−	1.34122i
$627$	14.9099	−	14.9099i	0.595445	−	0.595445i
$628$	−8.66837	+	8.66837i	−0.345906	+	0.345906i
$629$	3.77208			0.150403
$630$		0			0
$631$	11.8871			0.473220			0.236610	−	0.971605i	$-0.423964\pi$
$631$	11.8871			0.473220			0.236610	+	0.971605i	$0.423964\pi$
$632$	5.27582	−	5.27582i	0.209861	−	0.209861i
$633$	10.2276	−	10.2276i	0.406512	−	0.406512i
$634$		−	10.7644i		−	0.427509i
$635$	7.72849	−	41.3790i	0.306696	−	1.64208i
$636$		−	10.1160i		−	0.401127i
$637$		0			0
$638$	1.41438	+	1.41438i	0.0559958	+	0.0559958i
$639$		−	15.7253i		−	0.622085i
$640$	−2.19806	−	0.410538i	−0.0868859	−	0.0162279i
$641$	4.10018			0.161947			0.0809736	−	0.996716i	$-0.474197\pi$
$641$	4.10018			0.161947			0.0809736	+	0.996716i	$0.474197\pi$
$642$	−13.6366	−	13.6366i	−0.538195	−	0.538195i
$643$	−0.865126	+	0.865126i	−0.0341173	+	0.0341173i	−0.723960	−	0.689842i	$-0.757680\pi$
$643$	−0.865126	+	0.865126i	−0.0341173	+	0.0341173i	0.689842	+	0.723960i	$0.257680\pi$
$644$		0			0
$645$	−5.56197	+	3.81129i	−0.219002	+	0.150070i
$646$	−4.33839			−0.170692
$647$	21.6196	+	21.6196i	0.849956	+	0.849956i	0.990127	−	0.140171i	$-0.0447653\pi$
$647$	21.6196	+	21.6196i	0.849956	+	0.849956i	−0.140171	+	0.990127i	$0.544765\pi$
$648$	−0.707107	−	0.707107i	−0.0277778	−	0.0277778i
$649$	−50.1176			−1.96729
$650$	−1.21849	−	0.471616i	−0.0477933	−	0.0184983i
$651$		0			0
$652$	13.7694	−	13.7694i	0.539250	−	0.539250i
$653$	13.9720	+	13.9720i	0.546768	+	0.546768i	0.925505	−	0.378736i	$-0.123641\pi$
$653$	13.9720	+	13.9720i	0.546768	+	0.546768i	−0.378736	+	0.925505i	$0.623641\pi$
$654$	7.24117			0.283152
$655$	13.7923	+	20.1276i	0.538909	+	0.786450i
$656$		−	7.05881i		−	0.275600i
$657$	−3.22877	−	3.22877i	−0.125966	−	0.125966i
$658$		0			0
$659$			37.7204i			1.46938i	0.678403	+	0.734690i	$0.262672\pi$
$659$			37.7204i			1.46938i	−0.678403	+	0.734690i	$0.737328\pi$
$660$	−11.3452	−	2.11899i	−0.441613	−	0.0824814i
$661$			9.49534i			0.369326i	0.982802	+	0.184663i	$0.0591193\pi$
$661$			9.49534i			0.369326i	−0.982802	+	0.184663i	$0.940881\pi$
$662$	3.60303	−	3.60303i	0.140036	−	0.140036i
$663$	−0.196229	+	0.196229i	−0.00762090	+	0.00762090i
$664$	0.578647			0.0224558
$665$		0			0
$666$	3.55196			0.137636
$667$	−0.917715	+	0.917715i	−0.0355341	+	0.0355341i
$668$	−4.32056	+	4.32056i	−0.167168	+	0.167168i
$669$			11.0351i			0.426643i
$670$	−0.0635244	−	0.0927036i	−0.00245416	−	0.00358145i
$671$		−	56.8281i		−	2.19383i
$672$		0			0
$673$	8.09653	+	8.09653i	0.312098	+	0.312098i	0.845722	−	0.533624i	$-0.179170\pi$
$673$	8.09653	+	8.09653i	0.312098	+	0.312098i	−0.533624	+	0.845722i	$0.679170\pi$
$674$			11.7358i			0.452046i
$675$	−4.57335	+	2.02101i	−0.176028	+	0.0777888i
$676$	12.9317			0.497374
$677$	−3.17891	−	3.17891i	−0.122176	−	0.122176i	0.643375	−	0.765551i	$-0.277533\pi$
$677$	−3.17891	−	3.17891i	−0.122176	−	0.122176i	−0.765551	+	0.643375i	$0.777533\pi$
$678$	5.46766	−	5.46766i	0.209984	−	0.209984i
$679$		0			0
$680$	1.34230	+	1.95886i	0.0514747	+	0.0751190i
$681$	−10.5114			−0.402798
$682$	−38.7360	−	38.7360i	−1.48328	−	1.48328i
$683$	22.6023	+	22.6023i	0.864852	+	0.864852i	0.991897	−	0.127045i	$-0.0405494\pi$
$683$	22.6023	+	22.6023i	0.864852	+	0.864852i	−0.127045	+	0.991897i	$0.540549\pi$
$684$	−4.08523			−0.156203
$685$	−1.67974	+	8.99346i	−0.0641795	+	0.343622i
$686$		0			0
$687$	−7.43236	+	7.43236i	−0.283562	+	0.283562i
$688$	2.13217	+	2.13217i	0.0812882	+	0.0812882i
$689$	−2.64348			−0.100709
$690$	1.37490	−	7.36132i	0.0523414	−	0.280241i
$691$		−	29.0533i		−	1.10524i	−0.833434	−	0.552620i	$-0.813628\pi$
$691$		−	29.0533i		−	1.10524i	0.833434	−	0.552620i	$-0.186372\pi$
$692$	14.3204	+	14.3204i	0.544382	+	0.544382i
$693$		0			0
$694$		−	14.0707i		−	0.534117i
$695$	19.1541	−	13.1252i	0.726555	−	0.497866i
$696$		−	0.387531i		−	0.0146893i
$697$	−5.30065	+	5.30065i	−0.200776	+	0.200776i
$698$	18.2174	−	18.2174i	0.689540	−	0.689540i
$699$	−23.0048			−0.870121
$700$		0			0
$701$	−3.75353			−0.141769			−0.0708844	−	0.997485i	$-0.522582\pi$
$701$	−3.75353			−0.141769			−0.0708844	+	0.997485i	$0.522582\pi$
$702$	−0.184778	+	0.184778i	−0.00697400	+	0.00697400i
$703$	10.2605	−	10.2605i	0.386983	−	0.386983i
$704$			5.16148i			0.194531i
$705$	−19.2370	+	13.1820i	−0.724507	+	0.496462i
$706$			0.164206i			0.00617997i
$707$		0			0
$708$	6.86595	+	6.86595i	0.258038	+	0.258038i
$709$		−	30.2423i		−	1.13577i	−0.823106	−	0.567887i	$-0.807761\pi$
$709$		−	30.2423i		−	1.13577i	0.823106	−	0.567887i	$-0.192239\pi$
$710$	−6.45585	+	34.5652i	−0.242284	+	1.29721i
$711$	−7.46114			−0.279815
$712$	−9.98884	−	9.98884i	−0.374348	−	0.374348i
$713$	25.1338	−	25.1338i	0.941267	−	0.941267i
$714$		0			0
$715$	−0.553725	+	2.96469i	−0.0207081	+	0.110873i
$716$	22.2204			0.830416
$717$	13.7825	+	13.7825i	0.514718	+	0.514718i
$718$	8.01613	+	8.01613i	0.299159	+	0.299159i
$719$	2.97972			0.111125			0.0555624	−	0.998455i	$-0.482305\pi$
$719$	2.97972			0.111125			0.0555624	+	0.998455i	$0.482305\pi$
$720$	1.26397	+	1.84456i	0.0471053	+	0.0687425i
$721$		0			0
$722$	1.63406	−	1.63406i	0.0608136	−	0.0608136i
$723$	5.76326	+	5.76326i	0.214338	+	0.214338i
$724$	25.1301			0.933953
$725$	−1.80702	−	0.699405i	−0.0671112	−	0.0259753i
$726$			15.6409i			0.580488i
$727$	18.0738	+	18.0738i	0.670321	+	0.670321i	0.957790	−	0.287469i	$-0.0928139\pi$
$727$	18.0738	+	18.0738i	0.670321	+	0.670321i	−0.287469	+	0.957790i	$0.592814\pi$
$728$		0			0
$729$			1.00000i			0.0370370i
$730$	5.77149	+	8.42255i	0.213612	+	0.311733i
$731$		−	3.20220i		−	0.118438i
$732$	−7.78528	+	7.78528i	−0.287752	+	0.287752i
$733$	−14.5519	+	14.5519i	−0.537486	+	0.537486i	−0.922790	−	0.385304i	$-0.874097\pi$
$733$	−14.5519	+	14.5519i	−0.537486	+	0.537486i	0.385304	+	0.922790i	$0.374097\pi$
$734$	13.9189			0.513756
$735$		0			0
$736$	−3.34901			−0.123446
$737$	−0.183427	+	0.183427i	−0.00675664	+	0.00675664i
$738$	−4.99134	+	4.99134i	−0.183734	+	0.183734i
$739$		−	15.1843i		−	0.558562i	−0.960209	−	0.279281i	$-0.909904\pi$
$739$		−	15.1843i		−	0.558562i	0.960209	−	0.279281i	$-0.0900961\pi$
$740$	−7.80742	−	1.45822i	−0.287007	−	0.0536051i
$741$			1.06753i			0.0392169i
$742$		0			0
$743$	−26.7267	−	26.7267i	−0.980509	−	0.980509i	0.0193046	−	0.999814i	$-0.493855\pi$
$743$	−26.7267	−	26.7267i	−0.980509	−	0.980509i	−0.999814	+	0.0193046i	$0.993855\pi$
$744$			10.6134i			0.389107i
$745$	−21.2159	−	30.9612i	−0.777291	−	1.13433i
$746$	12.9756			0.475071
$747$	−0.409165	−	0.409165i	−0.0149706	−	0.0149706i
$748$	3.87589	−	3.87589i	0.141717	−	0.141717i
$749$		0			0
$750$	10.8822	−	2.56477i	0.397361	−	0.0936521i
$751$	15.8471			0.578268			0.289134	−	0.957289i	$-0.406633\pi$
$751$	15.8471			0.578268			0.289134	+	0.957289i	$0.406633\pi$
$752$	7.37446	+	7.37446i	0.268919	+	0.268919i
$753$	6.31786	+	6.31786i	0.230236	+	0.230236i
$754$	−0.101268			−0.00368796
$755$	18.0118	−	12.3425i	0.655517	−	0.449188i
$756$		0			0
$757$	3.96309	−	3.96309i	0.144041	−	0.144041i	−0.631409	−	0.775450i	$-0.717523\pi$
$757$	3.96309	−	3.96309i	0.144041	−	0.144041i	0.775450	+	0.631409i	$0.217523\pi$
$758$	17.5009	+	17.5009i	0.635663	+	0.635663i
$759$	−17.2859			−0.627437
$760$	8.97957	+	1.67714i	0.325723	+	0.0608363i
$761$		−	13.6146i		−	0.493529i	−0.969075	−	0.246765i	$-0.920633\pi$
$761$		−	13.6146i		−	0.493529i	0.969075	−	0.246765i	$-0.0793675\pi$
$762$	13.3115	+	13.3115i	0.482224	+	0.482224i
$763$		0			0
$764$		−	1.53994i		−	0.0557130i
$765$	0.435979	−	2.33427i	0.0157629	−	0.0843958i
$766$			19.4542i			0.702908i
$767$	1.79418	−	1.79418i	0.0647841	−	0.0647841i
$768$	0.707107	−	0.707107i	0.0255155	−	0.0255155i
$769$	6.93519			0.250089			0.125045	−	0.992151i	$-0.460093\pi$
$769$	6.93519			0.250089			0.125045	+	0.992151i	$0.460093\pi$
$770$		0			0
$771$	−3.20242			−0.115332
$772$	−12.7329	+	12.7329i	−0.458267	+	0.458267i
$773$	−26.7038	+	26.7038i	−0.960469	+	0.960469i	−0.999248	−	0.0387784i	$-0.987653\pi$
$773$	−26.7038	+	26.7038i	−0.960469	+	0.960469i	0.0387784	+	0.999248i	$0.487653\pi$
$774$		−	3.01534i		−	0.108384i
$775$	49.4895	+	19.1548i	1.77772	+	0.688062i
$776$		−	1.87379i		−	0.0672650i
$777$		0			0
$778$	6.08493	+	6.08493i	0.218155	+	0.218155i
$779$			28.8369i			1.03319i
$780$	0.482012	−	0.330295i	0.0172588	−	0.0118264i
$781$	81.1661			2.90435
$782$	2.51486	+	2.51486i	0.0899312	+	0.0899312i
$783$	−0.274026	+	0.274026i	−0.00979288	+	0.00979288i
$784$		0			0
$785$	−26.9458	−	5.03276i	−0.961738	−	0.179627i
$786$	−10.9119			−0.389214
$787$	26.9827	+	26.9827i	0.961828	+	0.961828i	0.999298	−	0.0374699i	$-0.0119298\pi$
$787$	26.9827	+	26.9827i	0.961828	+	0.961828i	−0.0374699	+	0.999298i	$0.511930\pi$
$788$	−12.0158	−	12.0158i	−0.428044	−	0.428044i
$789$	12.5580			0.447078
$790$	16.4000	+	3.06308i	0.583487	+	0.108980i
$791$		0			0
$792$	3.64972	−	3.64972i	0.129687	−	0.129687i
$793$	2.03442	+	2.03442i	0.0722442	+	0.0722442i
$794$	−27.0410			−0.959649
$795$	18.6596	−	12.7863i	0.661787	−	0.453484i
$796$		−	9.42226i		−	0.333963i
$797$	−27.7007	−	27.7007i	−0.981208	−	0.981208i	0.0186189	−	0.999827i	$-0.494073\pi$
$797$	−27.7007	−	27.7007i	−0.981208	−	0.981208i	−0.999827	+	0.0186189i	$0.994073\pi$
$798$		0			0
$799$		−	11.0753i		−	0.391818i
$800$	−2.02101	−	4.57335i	−0.0714536	−	0.161692i
$801$			14.1264i			0.499130i
$802$	4.71637	−	4.71637i	0.166541	−	0.166541i
$803$	16.6652	−	16.6652i	0.588103	−	0.588103i
$804$	0.0502580			0.00177246
$805$		0			0
$806$	2.77346			0.0976909
$807$	5.22400	−	5.22400i	0.183893	−	0.183893i
$808$	−1.83867	+	1.83867i	−0.0646843	+	0.0646843i
$809$		−	37.1345i		−	1.30558i	−0.757540	−	0.652789i	$-0.773599\pi$
$809$		−	37.1345i		−	1.30558i	0.757540	−	0.652789i	$-0.226401\pi$
$810$	0.410538	−	2.19806i	0.0144248	−	0.0772319i
$811$		−	50.9815i		−	1.79020i	−0.445863	−	0.895101i	$-0.647103\pi$
$811$		−	50.9815i		−	1.79020i	0.445863	−	0.895101i	$-0.352897\pi$
$812$		0			0
$813$	−1.60783	−	1.60783i	−0.0563891	−	0.0563891i
$814$			18.3334i			0.642585i
$815$	42.8024	+	7.99433i	1.49930	+	0.280029i
$816$	−1.06197			−0.0371764
$817$	−8.71040	−	8.71040i	−0.304738	−	0.304738i
$818$	−12.0349	+	12.0349i	−0.420789	+	0.420789i
$819$		0			0
$820$	13.0204	−	8.92211i	0.454691	−	0.311574i
$821$	−27.8441			−0.971765			−0.485882	−	0.874024i	$-0.661502\pi$
$821$	−27.8441			−0.971765			−0.485882	+	0.874024i	$0.661502\pi$
$822$	−2.89316	−	2.89316i	−0.100911	−	0.100911i
$823$	22.0442	+	22.0442i	0.768412	+	0.768412i	0.977827	−	0.209415i	$-0.0671560\pi$
$823$	22.0442	+	22.0442i	0.768412	+	0.768412i	−0.209415	+	0.977827i	$0.567156\pi$
$824$	8.77942			0.305846
$825$	−10.4314	−	23.6053i	−0.363175	−	0.821829i
$826$		0			0
$827$	−2.46031	+	2.46031i	−0.0855533	+	0.0855533i	−0.748588	−	0.663035i	$-0.769268\pi$
$827$	−2.46031	+	2.46031i	−0.0855533	+	0.0855533i	0.663035	+	0.748588i	$0.269268\pi$
$828$	2.36811	+	2.36811i	0.0822975	+	0.0822975i
$829$	23.1065			0.802523			0.401262	−	0.915964i	$-0.368572\pi$
$829$	23.1065			0.802523			0.401262	+	0.915964i	$0.368572\pi$
$830$	0.731390	+	1.06735i	0.0253869	+	0.0370481i
$831$			25.2492i			0.875885i
$832$	−0.184778	−	0.184778i	−0.00640603	−	0.00640603i
$833$		0			0
$834$			10.3841i			0.359572i
$835$	−13.4306	−	2.50847i	−0.464784	−	0.0868092i
$836$		−	21.0858i		−	0.729269i
$837$	7.50483	−	7.50483i	0.259405	−	0.259405i
$838$	1.41709	−	1.41709i	0.0489526	−	0.0489526i
$839$	17.5563			0.606112			0.303056	−	0.952973i	$-0.401993\pi$
$839$	17.5563			0.606112			0.303056	+	0.952973i	$0.401993\pi$
$840$		0			0
$841$	28.8498			0.994821
$842$	−1.02350	+	1.02350i	−0.0352722	+	0.0352722i
$843$	−19.1894	+	19.1894i	−0.660920	+	0.660920i
$844$		−	14.4641i		−	0.497874i
$845$	16.3453	+	23.8533i	0.562294	+	0.820577i
$846$		−	10.4291i		−	0.358558i
$847$		0			0
$848$	−7.15311	−	7.15311i	−0.245639	−	0.245639i
$849$		−	3.26106i		−	0.111919i
$850$	−1.91662	+	4.95188i	−0.0657394	+	0.169848i
$851$	−11.8956			−0.407775
$852$	−11.1195	−	11.1195i	−0.380948	−	0.380948i
$853$	16.6127	−	16.6127i	0.568806	−	0.568806i	−0.362988	−	0.931794i	$-0.618243\pi$
$853$	16.6127	−	16.6127i	0.568806	−	0.568806i	0.931794	+	0.362988i	$0.118243\pi$
$854$		0			0
$855$	−5.16359	−	7.53543i	−0.176591	−	0.257706i
$856$	−19.2851			−0.659151
$857$	13.2049	+	13.2049i	0.451071	+	0.451071i	0.895710	−	0.444639i	$-0.146668\pi$
$857$	13.2049	+	13.2049i	0.451071	+	0.451071i	−0.444639	+	0.895710i	$0.646668\pi$
$858$	−0.953730	−	0.953730i	−0.0325598	−	0.0325598i
$859$	−21.2126			−0.723764			−0.361882	−	0.932224i	$-0.617866\pi$
$859$	−21.2126			−0.723764			−0.361882	+	0.932224i	$0.617866\pi$
$860$	−1.23791	+	6.62790i	−0.0422125	+	0.226009i
$861$		0			0
$862$	−11.9413	+	11.9413i	−0.406724	+	0.406724i
$863$	−0.653661	−	0.653661i	−0.0222509	−	0.0222509i	0.695894	−	0.718145i	$-0.255008\pi$
$863$	−0.653661	−	0.653661i	−0.0222509	−	0.0222509i	−0.718145	+	0.695894i	$0.755008\pi$
$864$	−1.00000			−0.0340207
$865$	−8.31429	+	44.5154i	−0.282694	+	1.51357i
$866$		−	29.1022i		−	0.988934i
$867$	−11.2234	−	11.2234i	−0.381165	−	0.381165i
$868$		0			0
$869$		−	38.5106i		−	1.30638i
$870$	0.714822	−	0.489826i	0.0242347	−	0.0166067i
$871$		−	0.0131332i		−	0.000445002i
$872$	5.12028	−	5.12028i	0.173395	−	0.173395i
$873$	−1.32497	+	1.32497i	−0.0448433	+	0.0448433i
$874$	13.6815			0.462783
$875$		0			0
$876$	−4.56617			−0.154276
$877$	32.5505	−	32.5505i	1.09915	−	1.09915i	0.104641	−	0.994510i	$-0.466631\pi$
$877$	32.5505	−	32.5505i	1.09915	−	1.09915i	0.994510	−	0.104641i	$-0.0333694\pi$
$878$	−1.92769	+	1.92769i	−0.0650564	+	0.0650564i
$879$			32.3476i			1.09106i
$880$	−9.52064	+	6.52395i	−0.320941	+	0.219922i
$881$			42.4620i			1.43058i	0.698826	+	0.715291i	$0.253706\pi$
$881$			42.4620i			1.43058i	−0.698826	+	0.715291i	$0.746294\pi$
$882$		0			0
$883$	31.4976	+	31.4976i	1.05998	+	1.05998i	0.998083	+	0.0618962i	$0.0197148\pi$
$883$	31.4976	+	31.4976i	1.05998	+	1.05998i	0.0618962	+	0.998083i	$0.480285\pi$
$884$			0.277510i			0.00933366i
$885$	−3.98629	+	21.3430i	−0.133998	+	0.717436i
$886$	0.829585			0.0278705
$887$	−18.9884	−	18.9884i	−0.637567	−	0.637567i	0.312388	−	0.949955i	$-0.398871\pi$
$887$	−18.9884	−	18.9884i	−0.637567	−	0.637567i	−0.949955	+	0.312388i	$0.898871\pi$
$888$	2.51162	−	2.51162i	0.0842844	−	0.0842844i
$889$		0			0
$890$	5.79941	−	31.0505i	0.194397	−	1.04082i
$891$	−5.16148			−0.172916
$892$	7.80302	+	7.80302i	0.261264	+	0.261264i
$893$	−30.1263	−	30.1263i	−1.00814	−	1.00814i
$894$	16.7852			0.561380
$895$	28.0859	+	40.9868i	0.938807	+	1.37004i
$896$		0			0
$897$	0.618824	−	0.618824i	0.0206619	−	0.0206619i
$898$	−18.6463	−	18.6463i	−0.622235	−	0.622235i
$899$	4.11303			0.137177
$900$	−1.80477	+	4.66292i	−0.0601591	+	0.155431i
$901$			10.7429i			0.357899i
$902$	−25.7627	−	25.7627i	−0.857804	−	0.857804i
$903$		0			0
$904$		−	7.73244i		−	0.257177i
$905$	31.7636	+	46.3539i	1.05586	+	1.54085i
$906$			9.76485i			0.324415i
$907$	39.9794	−	39.9794i	1.32750	−	1.32750i	0.419947	−	0.907549i	$-0.362049\pi$
$907$	39.9794	−	39.9794i	1.32750	−	1.32750i	0.907549	−	0.419947i	$-0.137951\pi$
$908$	−7.43269	+	7.43269i	−0.246663	+	0.246663i
$909$	2.60028			0.0862457
$910$		0			0
$911$	16.7618			0.555342			0.277671	−	0.960676i	$-0.410437\pi$
$911$	16.7618			0.555342			0.277671	+	0.960676i	$0.410437\pi$
$912$	−2.88869	+	2.88869i	−0.0956542	+	0.0956542i
$913$	2.11190	−	2.11190i	0.0698936	−	0.0698936i
$914$		−	25.6047i		−	0.846929i
$915$	−24.2007	−	4.52004i	−0.800051	−	0.149428i
$916$			10.5109i			0.347291i
$917$		0			0
$918$	0.750926	+	0.750926i	0.0247843	+	0.0247843i
$919$		−	37.8718i		−	1.24928i	−0.780914	−	0.624638i	$-0.785246\pi$
$919$		−	37.8718i		−	1.24928i	0.780914	−	0.624638i	$-0.214754\pi$
$920$	−4.23304	−	6.17744i	−0.139559	−	0.203664i
$921$	−2.91679			−0.0961114
$922$	3.15084	+	3.15084i	0.103768	+	0.103768i
$923$	−2.90570	+	2.90570i	−0.0956423	+	0.0956423i
$924$		0			0
$925$	−7.17856	−	16.2444i	−0.236030	−	0.534111i
$926$	17.6033			0.578482
$927$	−6.20799	−	6.20799i	−0.203897	−	0.203897i
$928$	−0.274026	−	0.274026i	−0.00899533	−	0.00899533i
$929$	1.03579			0.0339832			0.0169916	−	0.999856i	$-0.494591\pi$
$929$	1.03579			0.0339832			0.0169916	+	0.999856i	$0.494591\pi$
$930$	−19.5771	+	13.4150i	−0.641957	+	0.439896i
$931$		0			0
$932$	−16.2668	+	16.2668i	−0.532838	+	0.532838i
$933$	−4.01106	−	4.01106i	−0.131316	−	0.131316i
$934$	−11.8083			−0.386379
$935$	12.0483	+	2.25030i	0.394022	+	0.0735927i
$936$			0.261316i			0.00854138i
$937$	16.4902	+	16.4902i	0.538713	+	0.538713i	0.923151	−	0.384438i	$-0.125605\pi$
$937$	16.4902	+	16.4902i	0.538713	+	0.538713i	−0.384438	+	0.923151i	$0.625605\pi$
$938$		0			0
$939$			33.5573i			1.09510i
$940$	−4.28153	+	22.9237i	−0.139648	+	0.747688i
$941$		−	4.78578i		−	0.156012i	−0.996953	−	0.0780060i	$-0.975145\pi$
$941$		−	4.78578i		−	0.156012i	0.996953	−	0.0780060i	$-0.0248553\pi$
$942$	8.66837	−	8.66837i	0.282431	−	0.282431i
$943$	16.7160	−	16.7160i	0.544349	−	0.544349i
$944$	9.70992			0.316031
$945$		0			0
$946$	15.5636			0.506018
$947$	18.9447	−	18.9447i	0.615620	−	0.615620i	−0.328785	−	0.944405i	$-0.606639\pi$
$947$	18.9447	−	18.9447i	0.615620	−	0.615620i	0.944405	+	0.328785i	$0.106639\pi$
$948$	−5.27582	+	5.27582i	−0.171351	+	0.171351i
$949$			1.19321i			0.0387333i
$950$	8.25630	+	18.6832i	0.267870	+	0.606162i
$951$			10.7644i			0.349060i
$952$		0			0
$953$	−13.9822	−	13.9822i	−0.452927	−	0.452927i	0.443398	−	0.896325i	$-0.353773\pi$
$953$	−13.9822	−	13.9822i	−0.452927	−	0.452927i	−0.896325	+	0.443398i	$0.853773\pi$
$954$			10.1160i			0.327519i
$955$	2.84050	−	1.94643i	0.0919165	−	0.0629850i
$956$	19.4914			0.630398
$957$	−1.41438	−	1.41438i	−0.0457204	−	0.0457204i
$958$	−8.42110	+	8.42110i	−0.272073	+	0.272073i
$959$		0			0
$960$	2.19806	+	0.410538i	0.0709420	+	0.0132501i
$961$	−81.6449			−2.63371
$962$	−0.656326	−	0.656326i	−0.0211608	−	0.0211608i
$963$	13.6366	+	13.6366i	0.439434	+	0.439434i
$964$	8.15049			0.262509
$965$	−39.5805	−	7.39257i	−1.27414	−	0.237975i
$966$		0			0
$967$	−0.721442	+	0.721442i	−0.0232000	+	0.0232000i	−0.718612	−	0.695412i	$-0.755222\pi$
$967$	−0.721442	+	0.721442i	−0.0232000	+	0.0232000i	0.695412	+	0.718612i	$0.255222\pi$
$968$	11.0598	+	11.0598i	0.355475	+	0.355475i
$969$	4.33839			0.139369
$970$	3.45630	−	2.36841i	0.110975	−	0.0760449i
$971$		−	8.21543i		−	0.263646i	−0.991273	−	0.131823i	$-0.957917\pi$
$971$		−	8.21543i		−	0.263646i	0.991273	−	0.131823i	$-0.0420830\pi$
$972$	0.707107	+	0.707107i	0.0226805	+	0.0226805i
$973$		0			0
$974$		−	34.0139i		−	1.08987i
$975$	1.21849	+	0.471616i	0.0390230	+	0.0151038i
$976$			11.0100i			0.352423i
$977$	−26.3124	+	26.3124i	−0.841808	+	0.841808i	−0.989094	−	0.147286i	$-0.952946\pi$
$977$	−26.3124	+	26.3124i	−0.841808	+	0.841808i	0.147286	+	0.989094i	$0.452946\pi$
$978$	−13.7694	+	13.7694i	−0.440296	+	0.440296i
$979$	−72.9129			−2.33031
$980$		0			0
$981$	−7.24117			−0.231193
$982$	23.1733	−	23.1733i	0.739488	−	0.739488i
$983$	−19.0672	+	19.0672i	−0.608150	+	0.608150i	−0.942462	−	0.334312i	$-0.891496\pi$
$983$	−19.0672	+	19.0672i	−0.608150	+	0.608150i	0.334312	+	0.942462i	$0.391496\pi$
$984$			7.05881i			0.225027i
$985$	6.97621	−	37.3513i	0.222281	−	1.19011i
$986$			0.411546i			0.0131063i
$987$		0			0
$988$	0.754861	+	0.754861i	0.0240153	+	0.0240153i
$989$			10.0984i			0.321111i
$990$	11.3452	+	2.11899i	0.360575	+	0.0673458i
$991$	−3.65897			−0.116231			−0.0581155	−	0.998310i	$-0.518509\pi$
$991$	−3.65897			−0.116231			−0.0581155	+	0.998310i	$0.518509\pi$
$992$	7.50483	+	7.50483i	0.238279	+	0.238279i
$993$	−3.60303	+	3.60303i	−0.114339	+	0.114339i
$994$		0			0
$995$	17.3799	−	11.9094i	0.550980	−	0.377554i
$996$	−0.578647			−0.0183351
$997$	−31.9803	−	31.9803i	−1.01283	−	1.01283i	−0.999917	−	0.0129095i	$-0.995891\pi$
$997$	−31.9803	−	31.9803i	−1.01283	−	1.01283i	−0.0129095	−	0.999917i	$-0.504109\pi$
$998$	−20.5511	−	20.5511i	−0.650533	−	0.650533i
$999$	−3.55196			−0.112379

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1470.2.m.f.1273.3	yes	16
5.2	odd	4		1470.2.m.c.97.2	✓	16
7.6	odd	2		1470.2.m.c.1273.2	yes	16
35.27	even	4	inner	1470.2.m.f.97.3	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1470.2.m.c.97.2	✓	16	5.2	odd	4
1470.2.m.c.1273.2	yes	16	7.6	odd	2
1470.2.m.f.97.3	yes	16	35.27	even	4	inner
1470.2.m.f.1273.3	yes	16	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1470.m (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} +(0.707107 - 0.707107i) q^{3} -1.00000i q^{4} +(1.84456 - 1.26397i) q^{5} +1.00000i q^{6} +(0.707107 + 0.707107i) q^{8} -1.00000i q^{9} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} +(0.707107 - 0.707107i) q^{3} -1.00000i q^{4} +(1.84456 - 1.26397i) q^{5} +1.00000i q^{6} +(0.707107 + 0.707107i) q^{8} -1.00000i q^{9} +(-0.410538 + 2.19806i) q^{10} +5.16148 q^{11} +(-0.707107 - 0.707107i) q^{12} +(-0.184778 + 0.184778i) q^{13} +(0.410538 - 2.19806i) q^{15} -1.00000 q^{16} +(0.750926 + 0.750926i) q^{17} +(0.707107 + 0.707107i) q^{18} +4.08523 q^{19} +(-1.26397 - 1.84456i) q^{20} +(-3.64972 + 3.64972i) q^{22} +(-2.36811 - 2.36811i) q^{23} +1.00000 q^{24} +(1.80477 - 4.66292i) q^{25} -0.261316i q^{26} +(-0.707107 - 0.707107i) q^{27} -0.387531i q^{29} +(1.26397 + 1.84456i) q^{30} +10.6134i q^{31} +(0.707107 - 0.707107i) q^{32} +(3.64972 - 3.64972i) q^{33} -1.06197 q^{34} -1.00000 q^{36} +(2.51162 - 2.51162i) q^{37} +(-2.88869 + 2.88869i) q^{38} +0.261316i q^{39} +(2.19806 + 0.410538i) q^{40} +7.05881i q^{41} +(-2.13217 - 2.13217i) q^{43} -5.16148i q^{44} +(-1.26397 - 1.84456i) q^{45} +3.34901 q^{46} +(-7.37446 - 7.37446i) q^{47} +(-0.707107 + 0.707107i) q^{48} +(2.02101 + 4.57335i) q^{50} +1.06197 q^{51} +(0.184778 + 0.184778i) q^{52} +(7.15311 + 7.15311i) q^{53} +1.00000 q^{54} +(9.52064 - 6.52395i) q^{55} +(2.88869 - 2.88869i) q^{57} +(0.274026 + 0.274026i) q^{58} -9.70992 q^{59} +(-2.19806 - 0.410538i) q^{60} -11.0100i q^{61} +(-7.50483 - 7.50483i) q^{62} +1.00000i q^{64} +(-0.107280 + 0.574387i) q^{65} +5.16148i q^{66} +(-0.0355377 + 0.0355377i) q^{67} +(0.750926 - 0.750926i) q^{68} -3.34901 q^{69} +15.7253 q^{71} +(0.707107 - 0.707107i) q^{72} +(3.22877 - 3.22877i) q^{73} +3.55196i q^{74} +(-2.02101 - 4.57335i) q^{75} -4.08523i q^{76} +(-0.184778 - 0.184778i) q^{78} -7.46114i q^{79} +(-1.84456 + 1.26397i) q^{80} -1.00000 q^{81} +(-4.99134 - 4.99134i) q^{82} +(0.409165 - 0.409165i) q^{83} +(2.33427 + 0.435979i) q^{85} +3.01534 q^{86} +(-0.274026 - 0.274026i) q^{87} +(3.64972 + 3.64972i) q^{88} -14.1264 q^{89} +(2.19806 + 0.410538i) q^{90} +(-2.36811 + 2.36811i) q^{92} +(7.50483 + 7.50483i) q^{93} +10.4291 q^{94} +(7.53543 - 5.16359i) q^{95} -1.00000i q^{96} +(-1.32497 - 1.32497i) q^{97} -5.16148i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{5}+O(q^{10}) \) 16 * q + 8 * q^5	\( 16 q + 8 q^{5} + 8 q^{13} - 16 q^{16} - 8 q^{17} - 48 q^{19} - 8 q^{22} - 8 q^{23} + 16 q^{24} + 8 q^{25} + 8 q^{33} - 16 q^{36} + 8 q^{37} - 8 q^{38} + 16 q^{47} - 8 q^{52} + 8 q^{53} + 16 q^{54} + 8 q^{57} + 24 q^{58} + 48 q^{59} - 8 q^{62} + 72 q^{65} - 48 q^{67} - 8 q^{68} + 16 q^{73} + 8 q^{78} - 8 q^{80} - 16 q^{81} - 16 q^{82} - 72 q^{85} - 24 q^{87} + 8 q^{88} - 64 q^{89} - 8 q^{92} + 8 q^{93} + 64 q^{94} + 48 q^{95} - 64 q^{97}+O(q^{100}) \) 16 * q + 8 * q^5 + 8 * q^13 - 16 * q^16 - 8 * q^17 - 48 * q^19 - 8 * q^22 - 8 * q^23 + 16 * q^24 + 8 * q^25 + 8 * q^33 - 16 * q^36 + 8 * q^37 - 8 * q^38 + 16 * q^47 - 8 * q^52 + 8 * q^53 + 16 * q^54 + 8 * q^57 + 24 * q^58 + 48 * q^59 - 8 * q^62 + 72 * q^65 - 48 * q^67 - 8 * q^68 + 16 * q^73 + 8 * q^78 - 8 * q^80 - 16 * q^81 - 16 * q^82 - 72 * q^85 - 24 * q^87 + 8 * q^88 - 64 * q^89 - 8 * q^92 + 8 * q^93 + 64 * q^94 + 48 * q^95 - 64 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more