LMFDB - Embedded newform 675.2.l.f.151.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [675,2,Mod(76,675)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(675, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([14, 0]))

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

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

chi := DirichletCharacter("675.76");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 675 = 3^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	675.l (of order $9$, degree $6$, 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:	$5.38990213644$
Analytic rank:	$0$
Dimension:	$66$
Relative dimension:	$11$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			151.6
Character	$\chi$	$=$	675.151
Dual form			675.2.l.f.76.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.194784 + 0.163444i) q^{2} +(-1.72511 - 0.154950i) q^{3} +(-0.336069 - 1.90594i) q^{4} +(-0.310698 - 0.312139i) q^{6} +(-0.449901 + 2.55151i) q^{7} +(0.500326 - 0.866590i) q^{8} +(2.95198 + 0.534610i) q^{9} +O(q^{10})$	\(q+(0.194784 + 0.163444i) q^{2} +(-1.72511 - 0.154950i) q^{3} +(-0.336069 - 1.90594i) q^{4} +(-0.310698 - 0.312139i) q^{6} +(-0.449901 + 2.55151i) q^{7} +(0.500326 - 0.866590i) q^{8} +(2.95198 + 0.534610i) q^{9} +(2.07133 - 0.753901i) q^{11} +(0.284429 + 3.34003i) q^{12} +(1.11074 - 0.932020i) q^{13} +(-0.504662 + 0.423462i) q^{14} +(-3.39816 + 1.23683i) q^{16} +(1.17819 + 2.04069i) q^{17} +(0.487621 + 0.586616i) q^{18} +(2.22207 - 3.84874i) q^{19} +(1.17148 - 4.33192i) q^{21} +(0.526682 + 0.191697i) q^{22} +(-1.22504 - 6.94755i) q^{23} +(-0.997394 + 1.41743i) q^{24} +0.368687 q^{26} +(-5.00964 - 1.37967i) q^{27} +5.01424 q^{28} +(-4.88786 - 4.10140i) q^{29} +(-1.13861 - 6.45736i) q^{31} +(-2.74467 - 0.998979i) q^{32} +(-3.69007 + 0.979608i) q^{33} +(-0.104044 + 0.590063i) q^{34} +(0.0268659 - 5.80597i) q^{36} +(2.27172 + 3.93474i) q^{37} +(1.06188 - 0.386492i) q^{38} +(-2.06056 + 1.43572i) q^{39} +(5.08374 - 4.26577i) q^{41} +(0.936211 - 0.652319i) q^{42} +(5.79479 - 2.10913i) q^{43} +(-2.13300 - 3.69447i) q^{44} +(0.896913 - 1.55350i) q^{46} +(1.65920 - 9.40977i) q^{47} +(6.05384 - 1.60712i) q^{48} +(0.270040 + 0.0982866i) q^{49} +(-1.71630 - 3.70297i) q^{51} +(-2.14966 - 1.80378i) q^{52} -13.3683 q^{53} +(-0.750303 - 1.08753i) q^{54} +(1.98602 + 1.66647i) q^{56} +(-4.42967 + 6.29518i) q^{57} +(-0.281731 - 1.59778i) q^{58} +(3.10061 + 1.12853i) q^{59} +(-1.57865 + 8.95295i) q^{61} +(0.833631 - 1.44389i) q^{62} +(-2.69216 + 7.29150i) q^{63} +(3.24491 + 5.62035i) q^{64} +(-0.878880 - 0.412306i) q^{66} +(4.09170 - 3.43334i) q^{67} +(3.49349 - 2.93138i) q^{68} +(1.03680 + 12.1751i) q^{69} +(-1.67410 - 2.89963i) q^{71} +(1.94024 - 2.29068i) q^{72} +(2.55076 - 4.41805i) q^{73} +(-0.200612 + 1.13773i) q^{74} +(-8.08225 - 2.94170i) q^{76} +(0.991698 + 5.62420i) q^{77} +(-0.636024 - 0.0571280i) q^{78} +(3.14132 + 2.63588i) q^{79} +(8.42838 + 3.15632i) q^{81} +1.68745 q^{82} +(-2.65602 - 2.22867i) q^{83} +(-8.65009 - 0.776955i) q^{84} +(1.47346 + 0.536295i) q^{86} +(7.79656 + 7.83272i) q^{87} +(0.383015 - 2.17219i) q^{88} +(7.60791 - 13.1773i) q^{89} +(1.87834 + 3.25338i) q^{91} +(-12.8299 + 4.66971i) q^{92} +(0.963650 + 11.3161i) q^{93} +(1.86115 - 1.56169i) q^{94} +(4.58006 + 2.14863i) q^{96} +(3.94072 - 1.43431i) q^{97} +(0.0365353 + 0.0632810i) q^{98} +(6.51756 - 1.11815i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 66 q - 6 q^{2} - 6 q^{6} - 6 q^{7} - 12 q^{8} - 6 q^{9}+O(q^{10}) $ 66 * q - 6 * q^2 - 6 * q^6 - 6 * q^7 - 12 * q^8 - 6 * q^9	$ 66 q - 6 q^{2} - 6 q^{6} - 6 q^{7} - 12 q^{8} - 6 q^{9} + 15 q^{11} - 18 q^{12} + 15 q^{14} + 18 q^{16} - 30 q^{17} + 12 q^{18} + 12 q^{19} + 12 q^{21} + 45 q^{22} - 36 q^{23} - 39 q^{24} + 6 q^{26} - 51 q^{27} + 36 q^{28} - 15 q^{29} + 3 q^{31} - 27 q^{32} + 3 q^{33} + 30 q^{36} - 6 q^{37} + 12 q^{38} - 15 q^{39} + 39 q^{41} - 48 q^{42} - 12 q^{43} + 51 q^{44} + 9 q^{46} - 30 q^{47} + 132 q^{48} - 6 q^{49} - 9 q^{52} + 24 q^{53} + 75 q^{54} + 144 q^{56} - 33 q^{57} - 27 q^{58} + 45 q^{59} - 54 q^{61} - 66 q^{62} + 120 q^{63} - 24 q^{64} + 48 q^{66} - 9 q^{67} + 69 q^{68} + 51 q^{69} - 15 q^{71} - 9 q^{72} + 15 q^{73} + 96 q^{74} - 48 q^{76} + 36 q^{77} + 18 q^{78} + 48 q^{79} - 54 q^{81} + 36 q^{82} - 30 q^{83} + 57 q^{84} - 111 q^{86} + 33 q^{87} - 36 q^{88} - 12 q^{89} + 9 q^{91} + 219 q^{92} - 63 q^{93} + 36 q^{94} - 249 q^{96} - 57 q^{97} - 75 q^{98} - 48 q^{99}+O(q^{100}) $ 66 * q - 6 * q^2 - 6 * q^6 - 6 * q^7 - 12 * q^8 - 6 * q^9 + 15 * q^11 - 18 * q^12 + 15 * q^14 + 18 * q^16 - 30 * q^17 + 12 * q^18 + 12 * q^19 + 12 * q^21 + 45 * q^22 - 36 * q^23 - 39 * q^24 + 6 * q^26 - 51 * q^27 + 36 * q^28 - 15 * q^29 + 3 * q^31 - 27 * q^32 + 3 * q^33 + 30 * q^36 - 6 * q^37 + 12 * q^38 - 15 * q^39 + 39 * q^41 - 48 * q^42 - 12 * q^43 + 51 * q^44 + 9 * q^46 - 30 * q^47 + 132 * q^48 - 6 * q^49 - 9 * q^52 + 24 * q^53 + 75 * q^54 + 144 * q^56 - 33 * q^57 - 27 * q^58 + 45 * q^59 - 54 * q^61 - 66 * q^62 + 120 * q^63 - 24 * q^64 + 48 * q^66 - 9 * q^67 + 69 * q^68 + 51 * q^69 - 15 * q^71 - 9 * q^72 + 15 * q^73 + 96 * q^74 - 48 * q^76 + 36 * q^77 + 18 * q^78 + 48 * q^79 - 54 * q^81 + 36 * q^82 - 30 * q^83 + 57 * q^84 - 111 * q^86 + 33 * q^87 - 36 * q^88 - 12 * q^89 + 9 * q^91 + 219 * q^92 - 63 * q^93 + 36 * q^94 - 249 * q^96 - 57 * q^97 - 75 * q^98 - 48 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/675\mathbb{Z}\right)^\times$.

$n$	$326$	$352$
$\chi(n)$	$e\left(\frac{2}{9}\right)$	$1$

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 $

$2$	0.194784	+	0.163444i	0.137733	+	0.115572i	0.709052	−	0.705157i	$-0.249123\pi$
$2$	0.194784	+	0.163444i	0.137733	+	0.115572i	−0.571318	+	0.820729i	$0.693568\pi$
$3$	−1.72511	−	0.154950i	−0.995990	−	0.0894603i
$3$	−1.72511	−	0.154950i	−0.995990	−	0.0894603i
$4$	−0.336069	−	1.90594i	−0.168035	−	0.952971i
$5$		0			0
$5$		0			0
$6$	−0.310698	−	0.312139i	−0.126842	−	0.127430i
$7$	−0.449901	+	2.55151i	−0.170046	+	0.964381i	0.773661	+	0.633600i	$0.218423\pi$
$7$	−0.449901	+	2.55151i	−0.170046	+	0.964381i	−0.943707	+	0.330781i	$0.892688\pi$
$8$	0.500326	−	0.866590i	0.176892	−	0.306386i
$9$	2.95198	+	0.534610i	0.983994	+	0.178203i
$10$		0			0
$11$	2.07133	−	0.753901i	0.624528	−	0.227310i	−0.0103197	−	0.999947i	$-0.503285\pi$
$11$	2.07133	−	0.753901i	0.624528	−	0.227310i	0.634848	+	0.772637i	$0.281063\pi$
$12$	0.284429	+	3.34003i	0.0821077	+	0.964183i
$13$	1.11074	−	0.932020i	0.308063	−	0.258496i	−0.475628	−	0.879647i	$-0.657779\pi$
$13$	1.11074	−	0.932020i	0.308063	−	0.258496i	0.783691	+	0.621151i	$0.213335\pi$
$14$	−0.504662	+	0.423462i	−0.134877	+	0.113175i
$15$		0			0
$16$	−3.39816	+	1.23683i	−0.849541	+	0.309208i
$17$	1.17819	+	2.04069i	0.285754	+	0.494940i	0.972792	−	0.231681i	$-0.0744227\pi$
$17$	1.17819	+	2.04069i	0.285754	+	0.494940i	−0.687038	+	0.726622i	$0.741089\pi$
$18$	0.487621	+	0.586616i	0.114933	+	0.138267i
$19$	2.22207	−	3.84874i	0.509778	−	0.882962i	−0.490157	−	0.871634i	$-0.663061\pi$
$19$	2.22207	−	3.84874i	0.509778	−	0.882962i	0.999936	−	0.0113281i	$-0.00360593\pi$
$20$		0			0
$21$	1.17148	−	4.33192i	0.255638	−	0.945302i
$22$	0.526682	+	0.191697i	0.112289	+	0.0408699i
$23$	−1.22504	−	6.94755i	−0.255439	−	1.44866i	−0.794944	−	0.606682i	$-0.792500\pi$
$23$	−1.22504	−	6.94755i	−0.255439	−	1.44866i	0.539506	−	0.841982i	$-0.318611\pi$
$24$	−0.997394	+	1.41743i	−0.203592	+	0.289333i
$25$		0			0
$26$	0.368687			0.0723055
$27$	−5.00964	−	1.37967i	−0.964106	−	0.265517i
$28$	5.01424			0.947602
$29$	−4.88786	−	4.10140i	−0.907652	−	0.761611i	0.0640188	−	0.997949i	$-0.479608\pi$
$29$	−4.88786	−	4.10140i	−0.907652	−	0.761611i	−0.971671	+	0.236338i	$0.924053\pi$
$30$		0			0
$31$	−1.13861	−	6.45736i	−0.204500	−	1.15978i	−0.898225	−	0.439536i	$-0.855143\pi$
$31$	−1.13861	−	6.45736i	−0.204500	−	1.15978i	0.693725	−	0.720240i	$-0.255968\pi$
$32$	−2.74467	−	0.998979i	−0.485194	−	0.176596i
$33$	−3.69007	+	0.979608i	−0.642359	+	0.170528i
$34$	−0.104044	+	0.590063i	−0.0178434	+	0.101195i
$35$		0			0
$36$	0.0268659	−	5.80597i	0.00447766	−	0.967662i
$37$	2.27172	+	3.93474i	0.373469	+	0.646868i	0.990097	−	0.140387i	$-0.0448348\pi$
$37$	2.27172	+	3.93474i	0.373469	+	0.646868i	−0.616627	+	0.787255i	$0.711501\pi$
$38$	1.06188	−	0.386492i	0.172259	−	0.0626972i
$39$	−2.06056	+	1.43572i	−0.329953	+	0.229900i
$40$		0			0
$41$	5.08374	−	4.26577i	0.793947	−	0.666201i	−0.152772	−	0.988262i	$-0.548820\pi$
$41$	5.08374	−	4.26577i	0.793947	−	0.666201i	0.946719	+	0.322061i	$0.104375\pi$
$42$	0.936211	−	0.652319i	0.144460	−	0.100655i
$43$	5.79479	−	2.10913i	0.883697	−	0.321640i	0.139996	−	0.990152i	$-0.455291\pi$
$43$	5.79479	−	2.10913i	0.883697	−	0.321640i	0.743701	+	0.668512i	$0.233069\pi$
$44$	−2.13300	−	3.69447i	−0.321562	−	0.556962i
$45$		0			0
$46$	0.896913	−	1.55350i	0.132243	−	0.229051i
$47$	1.65920	−	9.40977i	0.242019	−	1.37256i	−0.585297	−	0.810819i	$-0.699022\pi$
$47$	1.65920	−	9.40977i	0.242019	−	1.37256i	0.827316	−	0.561737i	$-0.189867\pi$
$48$	6.05384	−	1.60712i	0.873797	−	0.231968i
$49$	0.270040	+	0.0982866i	0.0385772	+	0.0140409i
$50$		0			0
$51$	−1.71630	−	3.70297i	−0.240331	−	0.518519i
$52$	−2.14966	−	1.80378i	−0.298104	−	0.250139i
$53$	−13.3683			−1.83627			−0.918137	−	0.396263i	$-0.870307\pi$
$53$	−13.3683			−1.83627			−0.918137	+	0.396263i	$0.870307\pi$
$54$	−0.750303	−	1.08753i	−0.102103	−	0.147994i
$55$		0			0
$56$	1.98602	+	1.66647i	0.265393	+	0.222691i
$57$	−4.42967	+	6.29518i	−0.586724	+	0.833817i
$58$	−0.281731	−	1.59778i	−0.0369931	−	0.209798i
$59$	3.10061	+	1.12853i	0.403665	+	0.146922i	0.535870	−	0.844300i	$-0.319984\pi$
$59$	3.10061	+	1.12853i	0.403665	+	0.146922i	−0.132205	+	0.991222i	$0.542206\pi$
$60$		0			0
$61$	−1.57865	+	8.95295i	−0.202125	+	1.14631i	0.699775	+	0.714363i	$0.253284\pi$
$61$	−1.57865	+	8.95295i	−0.202125	+	1.14631i	−0.901900	+	0.431945i	$0.857828\pi$
$62$	0.833631	−	1.44389i	0.105871	−	0.183374i
$63$	−2.69216	+	7.29150i	−0.339181	+	0.918642i
$64$	3.24491	+	5.62035i	0.405614	+	0.702543i
$65$		0			0
$66$	−0.878880	−	0.412306i	−0.108183	−	0.0507514i
$67$	4.09170	−	3.43334i	0.499881	−	0.419450i	−0.357671	−	0.933848i	$-0.616429\pi$
$67$	4.09170	−	3.43334i	0.499881	−	0.419450i	0.857552	+	0.514398i	$0.171985\pi$
$68$	3.49349	−	2.93138i	0.423647	−	0.355482i
$69$	1.03680	+	12.1751i	0.124816	+	1.46571i
$70$		0			0
$71$	−1.67410	−	2.89963i	−0.198680	−	0.344123i	0.749421	−	0.662094i	$-0.230332\pi$
$71$	−1.67410	−	2.89963i	−0.198680	−	0.344123i	−0.948101	+	0.317971i	$0.896999\pi$
$72$	1.94024	−	2.29068i	0.228660	−	0.269959i
$73$	2.55076	−	4.41805i	0.298544	−	0.517094i	−0.677259	−	0.735745i	$-0.736832\pi$
$73$	2.55076	−	4.41805i	0.298544	−	0.517094i	0.975803	+	0.218651i	$0.0701656\pi$
$74$	−0.200612	+	1.13773i	−0.0233206	+	0.132258i
$75$		0			0
$76$	−8.08225	−	2.94170i	−0.927098	−	0.337436i
$77$	0.991698	+	5.62420i	0.113014	+	0.640937i
$78$	−0.636024	−	0.0571280i	−0.0720156	−	0.00646847i
$79$	3.14132	+	2.63588i	0.353426	+	0.296560i	0.802164	−	0.597104i	$-0.203682\pi$
$79$	3.14132	+	2.63588i	0.353426	+	0.296560i	−0.448738	+	0.893663i	$0.648126\pi$
$80$		0			0
$81$	8.42838	+	3.15632i	0.936487	+	0.350702i
$82$	1.68745			0.186347
$83$	−2.65602	−	2.22867i	−0.291536	−	0.244628i	0.485275	−	0.874362i	$-0.338720\pi$
$83$	−2.65602	−	2.22867i	−0.291536	−	0.244628i	−0.776811	+	0.629734i	$0.783164\pi$
$84$	−8.65009	−	0.776955i	−0.943802	−	0.0847727i
$85$		0			0
$86$	1.47346	+	0.536295i	0.158887	+	0.0578302i
$87$	7.79656	+	7.83272i	0.835879	+	0.839756i
$88$	0.383015	−	2.17219i	0.0408296	−	0.231556i
$89$	7.60791	−	13.1773i	0.806437	−	1.39679i	−0.108880	−	0.994055i	$-0.534726\pi$
$89$	7.60791	−	13.1773i	0.806437	−	1.39679i	0.915317	−	0.402734i	$-0.131940\pi$
$90$		0			0
$91$	1.87834	+	3.25338i	0.196903	+	0.341047i
$92$	−12.8299	+	4.66971i	−1.33761	+	0.486851i
$93$	0.963650	+	11.3161i	0.0999259	+	1.17342i
$94$	1.86115	−	1.56169i	0.191963	−	0.161076i
$95$		0			0
$96$	4.58006	+	2.14863i	0.467450	+	0.219294i
$97$	3.94072	−	1.43431i	0.400120	−	0.145632i	−0.134119	−	0.990965i	$-0.542821\pi$
$97$	3.94072	−	1.43431i	0.400120	−	0.145632i	0.534239	+	0.845334i	$0.320598\pi$
$98$	0.0365353	+	0.0632810i	0.00369063	+	0.00639235i
$99$	6.51756	−	1.11815i	0.655039	−	0.112378i
$100$		0			0
$101$	−2.48305	+	14.0821i	−0.247073	+	1.40122i	0.568557	+	0.822644i	$0.307502\pi$
$101$	−2.48305	+	14.0821i	−0.247073	+	1.40122i	−0.815629	+	0.578575i	$0.803609\pi$
$102$	0.270917	−	1.00180i	0.0268248	−	0.0991929i
$103$	8.11392	+	2.95323i	0.799489	+	0.290990i	0.709275	−	0.704932i	$-0.249023\pi$
$103$	8.11392	+	2.95323i	0.799489	+	0.290990i	0.0902141	+	0.995922i	$0.471245\pi$
$104$	−0.251948	−	1.42887i	−0.0247055	−	0.140112i
$105$		0			0
$106$	−2.60393	−	2.18496i	−0.252916	−	0.212222i
$107$	5.67259			0.548390			0.274195	−	0.961674i	$-0.411589\pi$
$107$	5.67259			0.548390			0.274195	+	0.961674i	$0.411589\pi$
$108$	−0.945981	+	10.0118i	−0.0910271	+	0.963382i
$109$	18.9591			1.81595			0.907975	−	0.419025i	$-0.137628\pi$
$109$	18.9591			1.81595			0.907975	+	0.419025i	$0.137628\pi$
$110$		0			0
$111$	−3.30928	−	7.13985i	−0.314103	−	0.677685i
$112$	−1.62695	−	9.22691i	−0.153733	−	0.871861i
$113$	−10.7438	−	3.91044i	−1.01070	−	0.367863i	−0.216996	−	0.976172i	$-0.569626\pi$
$113$	−10.7438	−	3.91044i	−1.01070	−	0.367863i	−0.793700	+	0.608309i	$0.791848\pi$
$114$	−1.89174	+	0.502201i	−0.177177	+	0.0470355i
$115$		0			0
$116$	−6.17437	+	10.6943i	−0.573276	+	0.992943i
$117$	3.77714	−	2.15749i	0.349197	−	0.199460i
$118$	0.419500	+	0.726595i	0.0386181	+	0.0668884i
$119$	−5.73692	+	2.08807i	−0.525903	+	0.191413i
$120$		0			0
$121$	−4.70446	+	3.94751i	−0.427679	+	0.358865i
$122$	−1.77080	+	1.48588i	−0.160321	+	0.134525i
$123$	−9.43098	+	6.57118i	−0.850362	+	0.592503i
$124$	−11.9247	+	4.34024i	−1.07087	+	0.389765i
$125$		0			0
$126$	−1.71614	+	0.980254i	−0.152886	+	0.0873279i
$127$	1.65219	−	2.86168i	0.146608	−	0.253933i	−0.783363	−	0.621564i	$-0.786498\pi$
$127$	1.65219	−	2.86168i	0.146608	−	0.253933i	0.929972	+	0.367631i	$0.119831\pi$
$128$	−1.30094	+	7.37801i	−0.114988	+	0.652130i
$129$	−10.3234	+	2.74057i	−0.908928	+	0.241294i
$130$		0			0
$131$	2.70616	+	15.3474i	0.236439	+	1.34091i	0.839563	+	0.543263i	$0.182811\pi$
$131$	2.70616	+	15.3474i	0.236439	+	1.34091i	−0.603124	+	0.797647i	$0.706078\pi$
$132$	3.10720	+	6.70385i	0.270447	+	0.583496i
$133$	8.82040	+	7.40120i	0.764826	+	0.641765i
$134$	1.35816			0.117327
$135$		0			0
$136$	2.35792			0.202190
$137$	−9.21811	−	7.73491i	−0.787556	−	0.660838i	0.157583	−	0.987506i	$-0.449630\pi$
$137$	−9.21811	−	7.73491i	−0.787556	−	0.660838i	−0.945139	+	0.326668i	$0.894074\pi$
$138$	−1.78799	+	2.54098i	−0.152203	+	0.216302i
$139$	−3.09573	−	17.5568i	−0.262577	−	1.48915i	−0.775848	−	0.630920i	$-0.782677\pi$
$139$	−3.09573	−	17.5568i	−0.262577	−	1.48915i	0.513271	−	0.858227i	$-0.328434\pi$
$140$		0			0
$141$	−4.32033	+	15.9758i	−0.363838	+	1.34540i
$142$	0.147837	−	0.838425i	0.0124062	−	0.0703591i
$143$	1.59805	−	2.76790i	0.133636	−	0.231464i
$144$	−10.6925	+	1.83441i	−0.891045	+	0.152867i
$145$		0			0
$146$	1.21895	−	0.443662i	0.100881	−	0.0367177i
$147$	−0.450619	−	0.211398i	−0.0371664	−	0.0174358i
$148$	6.73594	−	5.65212i	0.553691	−	0.464602i
$149$	−16.4176	+	13.7760i	−1.34498	+	1.12857i	−0.364664	+	0.931139i	$0.618816\pi$
$149$	−16.4176	+	13.7760i	−1.34498	+	1.12857i	−0.980316	+	0.197433i	$0.936739\pi$
$150$		0			0
$151$	−7.24523	+	2.63705i	−0.589608	+	0.214600i	−0.619557	−	0.784952i	$-0.712688\pi$
$151$	−7.24523	+	2.63705i	−0.589608	+	0.214600i	0.0299488	+	0.999551i	$0.490466\pi$
$152$	−2.22352	−	3.85125i	−0.180351	−	0.312378i
$153$	2.38703	+	6.65396i	0.192980	+	0.537940i
$154$	−0.726071	+	1.25759i	−0.0585085	+	0.101340i
$155$		0			0
$156$	3.42890	+	3.44480i	0.274532	+	0.275805i
$157$	0.728013	+	0.264975i	0.0581018	+	0.0211473i	0.370908	−	0.928670i	$-0.379047\pi$
$157$	0.728013	+	0.264975i	0.0581018	+	0.0211473i	−0.312806	+	0.949817i	$0.601269\pi$
$158$	0.181063	+	1.02686i	0.0144046	+	0.0816924i
$159$	23.0617	+	2.07141i	1.82891	+	0.164274i
$160$		0			0
$161$	18.2779			1.44050
$162$	1.12584	+	1.99237i	0.0884542	+	0.156535i
$163$	−16.3075			−1.27731			−0.638653	−	0.769495i	$-0.720508\pi$
$163$	−16.3075			−1.27731			−0.638653	+	0.769495i	$0.720508\pi$
$164$	−9.83880	−	8.25573i	−0.768281	−	0.644664i
$165$		0			0
$166$	−0.153090	−	0.868219i	−0.0118821	−	0.0673869i
$167$	−6.51098	−	2.36980i	−0.503835	−	0.183381i	0.0775833	−	0.996986i	$-0.475280\pi$
$167$	−6.51098	−	2.36980i	−0.503835	−	0.183381i	−0.581418	+	0.813605i	$0.697502\pi$
$168$	−3.16787	−	3.18257i	−0.244407	−	0.245540i
$169$	−1.89235	+	10.7320i	−0.145565	+	0.825542i
$170$		0			0
$171$	8.61709	−	10.1735i	0.658965	−	0.777985i
$172$	−5.96733	−	10.3357i	−0.455005	−	0.788092i
$173$	7.00660	−	2.55019i	0.532702	−	0.193888i	−0.0616426	−	0.998098i	$-0.519634\pi$
$173$	7.00660	−	2.55019i	0.532702	−	0.193888i	0.594344	+	0.804211i	$0.297412\pi$
$174$	0.238441	+	2.79999i	0.0180762	+	0.212267i
$175$		0			0
$176$	−6.10626	+	5.12376i	−0.460277	+	0.386218i
$177$	−5.17401	−	2.42727i	−0.388903	−	0.182445i
$178$	3.63564	−	1.32327i	0.272503	−	0.0991830i
$179$	7.25608	+	12.5679i	0.542345	+	0.939369i	0.998769	+	0.0496065i	$0.0157967\pi$
$179$	7.25608	+	12.5679i	0.542345	+	0.939369i	−0.456424	+	0.889762i	$0.650870\pi$
$180$		0			0
$181$	−4.13864	+	7.16833i	−0.307622	+	0.532818i	−0.977842	−	0.209345i	$-0.932867\pi$
$181$	−4.13864	+	7.16833i	−0.307622	+	0.532818i	0.670219	+	0.742163i	$0.266200\pi$
$182$	−0.165873	+	0.940710i	−0.0122953	+	0.0697301i
$183$	4.11059	−	15.2002i	0.303864	−	1.12363i
$184$	−6.63360	−	2.41443i	−0.489035	−	0.177994i
$185$		0			0
$186$	−1.66183	+	2.36169i	−0.121851	+	0.173168i
$187$	3.97890	+	3.33870i	0.290966	+	0.244150i
$188$	−18.4921			−1.34867
$189$	5.77408	−	12.1615i	0.420003	−	0.884616i
$190$		0			0
$191$	−18.3309	−	15.3815i	−1.32638	−	1.11297i	−0.984909	−	0.173074i	$-0.944630\pi$
$191$	−18.3309	−	15.3815i	−1.32638	−	1.11297i	−0.341472	−	0.939892i	$-0.610925\pi$
$192$	−4.72694	−	10.1985i	−0.341137	−	0.736013i
$193$	4.17280	+	23.6651i	0.300364	+	1.70345i	0.644560	+	0.764553i	$0.277040\pi$
$193$	4.17280	+	23.6651i	0.300364	+	1.70345i	−0.344196	+	0.938898i	$0.611848\pi$
$194$	1.00202	+	0.364705i	0.0719408	+	0.0261843i
$195$		0			0
$196$	0.0965765	−	0.547712i	0.00689832	−	0.0391223i
$197$	11.7231	−	20.3050i	0.835235	−	1.44667i	−0.0586045	−	0.998281i	$-0.518665\pi$
$197$	11.7231	−	20.3050i	0.835235	−	1.44667i	0.893839	−	0.448388i	$-0.148002\pi$
$198$	1.45227	+	0.847455i	0.103209	+	0.0602260i
$199$	3.92254	+	6.79404i	0.278061	+	0.481617i	0.970903	−	0.239473i	$-0.0769748\pi$
$199$	3.92254	+	6.79404i	0.278061	+	0.481617i	−0.692841	+	0.721090i	$0.743641\pi$
$200$		0			0
$201$	−7.59061	+	5.28887i	−0.535401	+	0.373048i
$202$	−2.78528	+	2.33713i	−0.195972	+	0.164440i
$203$	12.6638	−	10.6262i	0.888826	−	0.745814i
$204$	−6.48085	+	4.51563i	−0.453750	+	0.316157i
$205$		0			0
$206$	1.09778	+	1.90141i	0.0764860	+	0.132478i
$207$	0.0979318	−	21.1640i	0.00680673	−	1.47100i
$208$	−2.62172	+	4.54095i	−0.181784	+	0.314858i
$209$	1.70107	−	9.64722i	0.117665	−	0.667312i
$210$		0			0
$211$	4.73989	+	1.72518i	0.326307	+	0.118766i	0.499979	−	0.866037i	$-0.333341\pi$
$211$	4.73989	+	1.72518i	0.326307	+	0.118766i	−0.173672	+	0.984804i	$0.555563\pi$
$212$	4.49267	+	25.4792i	0.308558	+	1.74992i
$213$	2.43871	+	5.26158i	0.167098	+	0.360517i
$214$	1.10493	+	0.927148i	0.0755316	+	0.0633785i
$215$		0			0
$216$	−3.70206	+	3.65102i	−0.251893	+	0.248421i
$217$	16.9883			1.15324
$218$	3.69293	+	3.09874i	0.250117	+	0.209873i
$219$	−5.08492	+	7.22637i	−0.343607	+	0.488313i
$220$		0			0
$221$	3.21063	+	1.16857i	0.215970	+	0.0786067i
$222$	0.522367	−	1.93161i	0.0350590	−	0.129641i
$223$	3.27908	−	18.5966i	0.219583	−	1.24532i	−0.653191	−	0.757193i	$-0.726570\pi$
$223$	3.27908	−	18.5966i	0.219583	−	1.24532i	0.872774	−	0.488125i	$-0.162319\pi$
$224$	3.78374	−	6.55363i	0.252812	−	0.437883i
$225$		0			0
$226$	−1.45360	−	2.51771i	−0.0966919	−	0.167475i
$227$	3.51591	−	1.27969i	0.233359	−	0.0849358i	−0.222694	−	0.974888i	$-0.571485\pi$
$227$	3.51591	−	1.27969i	0.233359	−	0.0849358i	0.456053	+	0.889953i	$0.349263\pi$
$228$	13.4869	+	6.32709i	0.893194	+	0.419022i
$229$	6.44759	−	5.41017i	0.426069	−	0.357514i	−0.404397	−	0.914583i	$-0.632519\pi$
$229$	6.44759	−	5.41017i	0.426069	−	0.357514i	0.830466	+	0.557069i	$0.188074\pi$
$230$		0			0
$231$	−0.839315	−	9.85600i	−0.0552229	−	0.648477i
$232$	−5.99975	+	2.18373i	−0.393903	+	0.143369i
$233$	5.62166	+	9.73700i	0.368287	+	0.637892i	0.989298	−	0.145910i	$-0.0466110\pi$
$233$	5.62166	+	9.73700i	0.368287	+	0.637892i	−0.621011	+	0.783802i	$0.713278\pi$
$234$	1.08836	+	0.197104i	0.0711481	+	0.0128851i
$235$		0			0
$236$	1.10889	−	6.28885i	0.0721828	−	0.409369i
$237$	−5.01068	−	5.03392i	−0.325479	−	0.326988i
$238$	−1.45874	−	0.530939i	−0.0945563	−	0.0344157i
$239$	3.13312	+	17.7688i	0.202665	+	1.14937i	0.901073	+	0.433668i	$0.142781\pi$
$239$	3.13312	+	17.7688i	0.202665	+	1.14937i	−0.698408	+	0.715700i	$0.746108\pi$
$240$		0			0
$241$	11.6762	+	9.79751i	0.752131	+	0.631113i	0.936066	−	0.351826i	$-0.114439\pi$
$241$	11.6762	+	9.79751i	0.752131	+	0.631113i	−0.183934	+	0.982939i	$0.558883\pi$
$242$	−1.56155			−0.100380
$243$	−14.0508	−	6.75096i	−0.901358	−	0.433074i
$244$	17.5943			1.12636
$245$		0			0
$246$	−2.91102	−	0.261470i	−0.185600	−	0.0166707i
$247$	−1.11896	−	6.34596i	−0.0711980	−	0.403784i
$248$	−6.16556	−	2.24408i	−0.391513	−	0.142499i
$249$	4.23659	+	4.25624i	0.268483	+	0.269728i
$250$		0			0
$251$	10.1160	−	17.5214i	0.638515	−	1.10594i	−0.347244	−	0.937775i	$-0.612882\pi$
$251$	10.1160	−	17.5214i	0.638515	−	1.10594i	0.985759	−	0.168165i	$-0.0537843\pi$
$252$	14.8019	+	2.68066i	0.932434	+	0.168866i
$253$	−7.77522	−	13.4671i	−0.488824	−	0.846668i
$254$	0.789545	−	0.287371i	0.0495405	−	0.0180312i
$255$		0			0
$256$	8.48369	−	7.11866i	0.530230	−	0.444916i
$257$	22.3026	−	18.7141i	1.39120	−	1.16735i	0.426347	−	0.904560i	$-0.359800\pi$
$257$	22.3026	−	18.7141i	1.39120	−	1.16735i	0.964852	−	0.262795i	$-0.0846442\pi$
$258$	−2.45877	−	1.15348i	−0.153077	−	0.0718124i
$259$	−11.0616	+	4.02609i	−0.687334	+	0.250169i
$260$		0			0
$261$	−12.2362	−	14.7203i	−0.757402	−	0.911167i
$262$	−1.98132	+	3.43174i	−0.122406	+	0.212014i
$263$	0.202359	−	1.14764i	0.0124780	−	0.0707663i	−0.977933	−	0.208919i	$-0.933005\pi$
$263$	0.202359	−	1.14764i	0.0124780	−	0.0707663i	0.990411	+	0.138153i	$0.0441165\pi$
$264$	−0.997322	+	3.68791i	−0.0613809	+	0.226975i
$265$		0			0
$266$	0.508399	+	2.88328i	0.0311720	+	0.176785i
$267$	−15.1663	+	21.5534i	−0.928160	+	1.31904i
$268$	−7.91885	−	6.64471i	−0.483721	−	0.405890i
$269$	3.89377			0.237407			0.118704	−	0.992930i	$-0.462126\pi$
$269$	3.89377			0.237407			0.118704	+	0.992930i	$0.462126\pi$
$270$		0			0
$271$	−1.01175			−0.0614596			−0.0307298	−	0.999528i	$-0.509783\pi$
$271$	−1.01175			−0.0614596			−0.0307298	+	0.999528i	$0.509783\pi$
$272$	−6.52769	−	5.47738i	−0.395799	−	0.332115i
$273$	−2.73622	−	5.90347i	−0.165604	−	0.357294i
$274$	−0.531323	−	3.01328i	−0.0320984	−	0.182039i
$275$		0			0
$276$	22.8566	−	6.06776i	1.37580	−	0.365236i
$277$	−5.38133	+	30.5191i	−0.323333	+	1.83371i	0.197807	+	0.980241i	$0.436618\pi$
$277$	−5.38133	+	30.5191i	−0.323333	+	1.83371i	−0.521140	+	0.853471i	$0.674493\pi$
$278$	2.26654	−	3.92577i	0.135938	−	0.235452i
$279$	0.0910221	−	19.6707i	0.00544935	−	1.17765i
$280$		0			0
$281$	−2.69096	+	0.979428i	−0.160529	+	0.0584278i	−0.421035	−	0.907045i	$-0.638333\pi$
$281$	−2.69096	+	0.979428i	−0.160529	+	0.0584278i	0.260506	+	0.965472i	$0.416111\pi$
$282$	−3.45267	+	2.40570i	−0.205603	+	0.143257i
$283$	−18.8737	+	15.8369i	−1.12192	+	0.941405i	−0.998700	−	0.0509739i	$-0.983767\pi$
$283$	−18.8737	+	15.8369i	−1.12192	+	0.941405i	−0.123223	+	0.992379i	$0.539323\pi$
$284$	−4.96392	+	4.16523i	−0.294555	+	0.247161i
$285$		0			0
$286$	0.763671	−	0.277954i	0.0451568	−	0.0164357i
$287$	8.59698	+	14.8904i	0.507464	+	0.878953i
$288$	−7.56816	−	4.41630i	−0.445958	−	0.260233i
$289$	5.72372	−	9.91377i	0.336689	−	0.583163i
$290$		0			0
$291$	−7.02041	+	1.86371i	−0.411544	+	0.109253i
$292$	−9.27779	−	3.37684i	−0.542942	−	0.197615i
$293$	1.00740	+	5.71323i	0.0588527	+	0.333771i	0.999991	−	0.00425146i	$-0.00135329\pi$
$293$	1.00740	+	5.71323i	0.0588527	+	0.333771i	−0.941138	+	0.338022i	$0.890242\pi$
$294$	−0.0532219	−	0.114828i	−0.00310397	−	0.00669688i
$295$		0			0
$296$	4.54641			0.264255
$297$	−11.4167	+	0.919033i	−0.662466	+	0.0533277i
$298$	−5.44948			−0.315680
$299$	−7.83595	−	6.57515i	−0.453165	−	0.380250i
$300$		0			0
$301$	2.77440	+	15.7344i	0.159914	+	0.906915i
$302$	−1.84227	−	0.670530i	−0.106011	−	0.0385847i
$303$	6.46554	−	23.9083i	0.371435	−	1.37350i
$304$	−2.79073	+	15.8270i	−0.160059	+	0.907740i
$305$		0			0
$306$	−0.622589	+	1.68623i	−0.0355911	+	0.0963955i
$307$	15.4802	+	26.8124i	0.883500	+	1.53027i	0.847424	+	0.530917i	$0.178152\pi$
$307$	15.4802	+	26.8124i	0.883500	+	1.53027i	0.0360759	+	0.999349i	$0.488514\pi$
$308$	10.3861	−	3.78024i	0.591804	−	0.215399i
$309$	−13.5398	−	6.35188i	−0.770251	−	0.361346i
$310$		0			0
$311$	7.44776	−	6.24942i	0.422324	−	0.354372i	−0.406722	−	0.913552i	$-0.633328\pi$
$311$	7.44776	−	6.24942i	0.422324	−	0.354372i	0.829046	+	0.559180i	$0.188884\pi$
$312$	0.213234	+	2.50399i	0.0120720	+	0.141760i
$313$	11.4133	−	4.15409i	0.645116	−	0.234803i	0.00131881	−	0.999999i	$-0.499580\pi$
$313$	11.4133	−	4.15409i	0.645116	−	0.234803i	0.643797	+	0.765196i	$0.277358\pi$
$314$	0.0984972	+	0.170602i	0.00555852	+	0.00962763i
$315$		0			0
$316$	3.96814	−	6.87301i	0.223225	−	0.386637i
$317$	−0.918600	+	5.20964i	−0.0515937	+	0.292603i	−0.999677	−	0.0254200i	$-0.991908\pi$
$317$	−0.918600	+	5.20964i	−0.0515937	+	0.292603i	0.948083	+	0.318023i	$0.103019\pi$
$318$	4.15350	+	4.17276i	0.232917	+	0.233997i
$319$	−13.2164	−	4.81037i	−0.739976	−	0.269329i
$320$		0			0
$321$	−9.78581	−	0.878966i	−0.546191	−	0.0490591i
$322$	3.56025	+	2.98741i	0.198405	+	0.166482i
$323$	10.4721			0.582685
$324$	3.18324	−	17.1248i	0.176847	−	0.951376i
$325$		0			0
$326$	−3.17646	−	2.66536i	−0.175928	−	0.147621i
$327$	−32.7064	−	2.93770i	−1.80867	−	0.162455i
$328$	−1.15314	−	6.53980i	−0.0636717	−	0.361100i
$329$	23.2627	+	8.46692i	1.28251	+	0.466797i
$330$		0			0
$331$	4.36397	−	24.7493i	0.239866	−	1.36035i	−0.592255	−	0.805750i	$-0.701762\pi$
$331$	4.36397	−	24.7493i	0.239866	−	1.36035i	0.832121	−	0.554595i	$-0.187127\pi$
$332$	−3.35510	+	5.81121i	−0.184135	+	0.318932i
$333$	4.60254	+	12.8298i	0.252217	+	0.703067i
$334$	−0.880908	−	1.52578i	−0.0482012	−	0.0834868i
$335$		0			0
$336$	1.37696	+	16.1695i	0.0751193	+	0.882118i
$337$	3.87282	−	3.24968i	0.210966	−	0.177021i	−0.531182	−	0.847258i	$-0.678252\pi$
$337$	3.87282	−	3.24968i	0.210966	−	0.177021i	0.742147	+	0.670237i	$0.233807\pi$
$338$	−2.12268	+	1.78114i	−0.115459	+	0.0968814i
$339$	17.9284	+	8.41068i	0.973734	+	0.456806i
$340$		0			0
$341$	−7.22663	−	12.5169i	−0.391344	−	0.677828i
$342$	3.34126	−	0.573226i	0.180675	−	0.0309965i
$343$	−9.44033	+	16.3511i	−0.509730	+	0.882878i
$344$	1.07153	−	6.07696i	0.0577732	−	0.327648i
$345$		0			0
$346$	1.78159	+	0.648445i	0.0957788	+	0.0348606i
$347$	4.69131	+	26.6058i	0.251843	+	1.42827i	0.804048	+	0.594564i	$0.202675\pi$
$347$	4.69131	+	26.6058i	0.251843	+	1.42827i	−0.552206	+	0.833708i	$0.686214\pi$
$348$	12.3085	−	17.4921i	0.659807	−	0.937677i
$349$	−17.9519	−	15.0634i	−0.960941	−	0.806326i	0.0201645	−	0.999797i	$-0.493581\pi$
$349$	−17.9519	−	15.0634i	−0.960941	−	0.806326i	−0.981106	+	0.193471i	$0.938025\pi$
$350$		0			0
$351$	−6.85028	+	3.13664i	−0.365641	+	0.167421i
$352$	−6.43824			−0.343160
$353$	13.6706	+	11.4710i	0.727611	+	0.610538i	0.929479	−	0.368875i	$-0.120257\pi$
$353$	13.6706	+	11.4710i	0.727611	+	0.610538i	−0.201868	+	0.979413i	$0.564701\pi$
$354$	−0.611095	−	1.31845i	−0.0324794	−	0.0700750i
$355$		0			0
$356$	−27.6719	−	10.0718i	−1.46661	−	0.533802i
$357$	10.2203	−	2.71320i	0.540918	−	0.143598i
$358$	−0.640771	+	3.63399i	−0.0338658	+	0.192062i
$359$	12.7067	−	22.0086i	0.670633	−	1.16157i	−0.307092	−	0.951680i	$-0.599356\pi$
$359$	12.7067	−	22.0086i	0.670633	−	1.16157i	0.977725	−	0.209891i	$-0.0673108\pi$
$360$		0			0
$361$	−0.375211	−	0.649885i	−0.0197480	−	0.0342045i
$362$	−1.97776	+	0.719845i	−0.103949	+	0.0378342i
$363$	8.72737	−	6.08092i	0.458068	−	0.319166i
$364$	5.56950	−	4.67337i	0.291921	−	0.244951i
$365$		0			0
$366$	3.28505	−	2.28891i	0.171712	−	0.119643i
$367$	−33.4606	+	12.1787i	−1.74663	+	0.635721i	−0.999578	−	0.0290451i	$-0.990753\pi$
$367$	−33.4606	+	12.1787i	−1.74663	+	0.635721i	−0.747051	+	0.664766i	$0.768531\pi$
$368$	12.7558	+	22.0938i	0.664944	+	1.15172i
$369$	17.2876	−	9.87465i	0.899958	−	0.514054i
$370$		0			0
$371$	6.01439	−	34.1093i	0.312252	−	1.77087i
$372$	21.2439	−	5.63964i	1.10144	−	0.292402i
$373$	5.43137	+	1.97686i	0.281226	+	0.102358i	0.478782	−	0.877934i	$-0.341078\pi$
$373$	5.43137	+	1.97686i	0.281226	+	0.102358i	−0.197557	+	0.980291i	$0.563301\pi$
$374$	0.229340	+	1.30065i	0.0118589	+	0.0672551i
$375$		0			0
$376$	−7.32428	−	6.14580i	−0.377721	−	0.316945i
$377$	−9.25171			−0.476487
$378$	3.11241	−	1.42513i	0.160085	−	0.0733006i
$379$	−27.7158			−1.42366			−0.711832	−	0.702350i	$-0.752134\pi$
$379$	−27.7158			−1.42366			−0.711832	+	0.702350i	$0.752134\pi$
$380$		0			0
$381$	−3.29362	+	4.68070i	−0.168737	+	0.239799i
$382$	−1.05658	−	5.99215i	−0.0540592	−	0.306585i
$383$	5.17297	+	1.88281i	0.264326	+	0.0962069i	0.470784	−	0.882249i	$-0.343971\pi$
$383$	5.17297	+	1.88281i	0.264326	+	0.0962069i	−0.206457	+	0.978456i	$0.566193\pi$
$384$	3.38748	−	12.5263i	0.172867	−	0.639228i
$385$		0			0
$386$	−3.05511	+	5.29161i	−0.155501	+	0.269336i
$387$	18.2337	−	3.12816i	0.926870	−	0.159014i
$388$	−4.05806	−	7.02876i	−0.206017	−	0.356831i
$389$	−33.7465	+	12.2827i	−1.71101	+	0.622758i	−0.997002	−	0.0773745i	$-0.975346\pi$
$389$	−33.7465	+	12.2827i	−1.71101	+	0.622758i	−0.714013	+	0.700133i	$0.753124\pi$
$390$		0			0
$391$	12.7345	−	10.6855i	0.644010	−	0.540388i
$392$	0.220282	−	0.184839i	0.0111259	−	0.00933577i
$393$	−2.29034	−	26.8952i	−0.115532	−	1.35669i
$394$	5.60219	−	2.03903i	0.282234	−	0.102725i
$395$		0			0
$396$	−4.32148	−	12.0463i	−0.217163	−	0.605350i
$397$	4.23035	−	7.32719i	0.212315	−	0.367741i	−0.740123	−	0.672471i	$-0.765233\pi$
$397$	4.23035	−	7.32719i	0.212315	−	0.367741i	0.952439	+	0.304730i	$0.0985663\pi$
$398$	−0.346392	+	1.96449i	−0.0173631	+	0.0984708i
$399$	−14.0693	−	14.1346i	−0.704347	−	0.707614i
$400$		0			0
$401$	4.71483	+	26.7391i	0.235447	+	1.33529i	0.841669	+	0.539993i	$0.181573\pi$
$401$	4.71483	+	26.7391i	0.235447	+	1.33529i	−0.606222	+	0.795296i	$0.707316\pi$
$402$	−2.34297	−	0.210446i	−0.116857	−	0.0104961i
$403$	−7.28308	−	6.11123i	−0.362796	−	0.304422i
$404$	27.6741			1.37684
$405$		0			0
$406$	4.20350			0.208616
$407$	7.67189	+	6.43748i	0.380281	+	0.319094i
$408$	−4.06767	−	0.365360i	−0.201380	−	0.0180880i
$409$	−0.359891	−	2.04104i	−0.0177954	−	0.100923i	0.974616	−	0.223882i	$-0.0718729\pi$
$409$	−0.359891	−	2.04104i	−0.0177954	−	0.100923i	−0.992412	+	0.122959i	$0.960762\pi$
$410$		0			0
$411$	14.7037	+	14.7719i	0.725280	+	0.728643i
$412$	2.90184	−	16.4572i	0.142964	−	0.810786i
$413$	−4.27442	+	7.40352i	−0.210331	+	0.364303i
$414$	3.47819	−	4.10640i	0.170944	−	0.201819i
$415$		0			0
$416$	−3.97968	+	1.44849i	−0.195120	+	0.0710178i
$417$	2.62005	+	30.7670i	0.128304	+	1.50667i
$418$	1.90812	−	1.60110i	0.0933291	−	0.0783124i
$419$	−19.8184	+	16.6296i	−0.968190	+	0.812408i	−0.982266	−	0.187493i	$-0.939964\pi$
$419$	−19.8184	+	16.6296i	−0.968190	+	0.812408i	0.0140758	+	0.999901i	$0.495519\pi$
$420$		0			0
$421$	9.37834	−	3.41344i	0.457073	−	0.166361i	−0.103215	−	0.994659i	$-0.532913\pi$
$421$	9.37834	−	3.41344i	0.457073	−	0.166361i	0.560287	+	0.828298i	$0.310691\pi$
$422$	0.641287	+	1.11074i	0.0312174	+	0.0540700i
$423$	9.92847	−	26.8904i	0.482739	−	1.30746i
$424$	−6.68850	+	11.5848i	−0.324822	+	0.562608i
$425$		0			0
$426$	−0.384948	+	1.42347i	−0.0186508	+	0.0689671i
$427$	−22.1333	−	8.05588i	−1.07111	−	0.389851i
$428$	−1.90638	−	10.8116i	−0.0921484	−	0.522600i
$429$	−3.18569	+	4.52731i	−0.153807	+	0.218581i
$430$		0			0
$431$	2.41940			0.116538			0.0582692	−	0.998301i	$-0.481442\pi$
$431$	2.41940			0.116538			0.0582692	+	0.998301i	$0.481442\pi$
$432$	18.7300	−	1.50774i	0.901148	−	0.0725413i
$433$	−19.8081			−0.951915			−0.475957	−	0.879468i	$-0.657898\pi$
$433$	−19.8081			−0.951915			−0.475957	+	0.879468i	$0.657898\pi$
$434$	3.30906	+	2.77663i	0.158840	+	0.133282i
$435$		0			0
$436$	−6.37156	−	36.1349i	−0.305142	−	1.73055i
$437$	−29.4615	−	10.7231i	−1.40933	−	0.512955i
$438$	−2.17157	+	0.576488i	−0.103761	+	0.0275457i
$439$	0.697642	−	3.95652i	0.0332966	−	0.188835i	−0.963623	−	0.267266i	$-0.913880\pi$
$439$	0.697642	−	3.95652i	0.0332966	−	0.188835i	0.996920	+	0.0784310i	$0.0249910\pi$
$440$		0			0
$441$	0.744609	+	0.434506i	0.0354576	+	0.0206908i
$442$	0.434385	+	0.752376i	0.0206616	+	0.0357869i
$443$	−4.71098	+	1.71466i	−0.223826	+	0.0814658i	−0.451499	−	0.892272i	$-0.649110\pi$
$443$	−4.71098	+	1.71466i	−0.223826	+	0.0814658i	0.227673	+	0.973738i	$0.426888\pi$
$444$	−12.4960	+	8.70678i	−0.593034	+	0.413205i
$445$		0			0
$446$	3.67820	−	3.08638i	0.174168	−	0.146144i
$447$	30.4566	−	21.2211i	1.44055	−	1.00373i
$448$	−15.8003	+	5.75083i	−0.746493	+	0.271701i
$449$	9.48026	+	16.4203i	0.447401	+	0.774922i	0.998216	−	0.0597059i	$-0.0190163\pi$
$449$	9.48026	+	16.4203i	0.447401	+	0.774922i	−0.550815	+	0.834627i	$0.685683\pi$
$450$		0			0
$451$	7.31412	−	12.6684i	0.344409	−	0.596533i
$452$	−3.84240	+	21.7913i	−0.180731	+	1.02498i
$453$	12.9074	−	3.42654i	0.606442	−	0.160993i
$454$	0.894001	+	0.325390i	0.0419575	+	0.0152713i
$455$		0			0
$456$	3.23906	+	6.98835i	0.151683	+	0.327260i
$457$	−8.71986	−	7.31683i	−0.407898	−	0.342267i	0.415639	−	0.909530i	$-0.363558\pi$
$457$	−8.71986	−	7.31683i	−0.407898	−	0.342267i	−0.823537	+	0.567263i	$0.808002\pi$
$458$	2.14015			0.100002
$459$	−3.08685	−	11.8486i	−0.144082	−	0.553048i
$460$		0			0
$461$	−3.34271	−	2.80487i	−0.155686	−	0.130636i	0.561617	−	0.827397i	$-0.310179\pi$
$461$	−3.34271	−	2.80487i	−0.155686	−	0.130636i	−0.717303	+	0.696761i	$0.754624\pi$
$462$	1.44741	−	2.05698i	0.0673398	−	0.0956992i
$463$	1.25780	+	7.13335i	0.0584550	+	0.331515i	0.999985	−	0.00541334i	$-0.00172313\pi$
$463$	1.25780	+	7.13335i	0.0584550	+	0.331515i	−0.941530	+	0.336928i	$0.890612\pi$
$464$	21.6825	+	7.89178i	1.00658	+	0.366367i
$465$		0			0
$466$	−0.496438	+	2.81544i	−0.0229970	+	0.130423i
$467$	−1.79131	+	3.10264i	−0.0828919	+	0.143573i	−0.904491	−	0.426493i	$-0.859749\pi$
$467$	−1.79131	+	3.10264i	−0.0828919	+	0.143573i	0.821599	+	0.570066i	$0.193082\pi$
$468$	−5.38144	−	6.47395i	−0.248757	−	0.299259i
$469$	6.91936	+	11.9847i	0.319507	+	0.553402i
$470$		0			0
$471$	−1.21484	−	0.569916i	−0.0559770	−	0.0262603i
$472$	2.52929	−	2.12232i	0.116420	−	0.0976879i
$473$	10.4128	−	8.73740i	0.478782	−	0.401746i
$474$	−0.153241	−	1.79949i	−0.00703858	−	0.0826534i
$475$		0			0
$476$	5.90774	+	10.2325i	0.270781	+	0.469006i
$477$	−39.4629	−	7.14681i	−1.80688	−	0.327230i
$478$	−2.29391	+	3.97317i	−0.104921	+	0.181729i
$479$	0.329444	−	1.86837i	0.0150527	−	0.0853680i	−0.976356	−	0.216169i	$-0.930644\pi$
$479$	0.329444	−	1.86837i	0.0150527	−	0.0853680i	0.991409	+	0.130801i	$0.0417549\pi$
$480$		0			0
$481$	6.19055	+	2.25318i	0.282265	+	0.102736i
$482$	0.673006	+	3.81680i	0.0306546	+	0.173851i
$483$	−31.5313	−	2.83216i	−1.43473	−	0.128868i
$484$	9.10476	+	7.63980i	0.413853	+	0.347264i
$485$		0			0
$486$	−1.63347	−	3.61149i	−0.0740959	−	0.163821i
$487$	13.6444			0.618286			0.309143	−	0.951016i	$-0.399958\pi$
$487$	13.6444			0.618286			0.309143	+	0.951016i	$0.399958\pi$
$488$	6.96870	+	5.84743i	0.315458	+	0.264701i
$489$	28.1322	+	2.52685i	1.27218	+	0.114268i
$490$		0			0
$491$	−37.0378	−	13.4806i	−1.67149	−	0.608373i	−0.679386	−	0.733781i	$-0.737754\pi$
$491$	−37.0378	−	13.4806i	−1.67149	−	0.608373i	−0.992105	+	0.125408i	$0.959976\pi$
$492$	15.6937	+	15.7665i	0.707529	+	0.710810i
$493$	2.61085	−	14.8068i	0.117587	−	0.666867i
$494$	0.819249	−	1.41898i	0.0368598	−	0.0638430i
$495$		0			0
$496$	11.8558	+	20.5349i	0.532343	+	0.922044i
$497$	8.15164	−	2.96695i	0.365651	−	0.133086i
$498$	0.129567	+	1.52149i	0.00580603	+	0.0681797i
$499$	−20.0062	+	16.7872i	−0.895599	+	0.751497i	−0.969325	−	0.245781i	$-0.920955\pi$
$499$	−20.0062	+	16.7872i	−0.895599	+	0.751497i	0.0737260	+	0.997279i	$0.476511\pi$
$500$		0			0
$501$	10.8649	+	5.09703i	0.485409	+	0.227719i
$502$	4.83419	−	1.75950i	0.215761	−	0.0785304i
$503$	−3.26454	−	5.65434i	−0.145558	−	0.252115i	0.784023	−	0.620732i	$-0.213165\pi$
$503$	−3.26454	−	5.65434i	−0.145558	−	0.252115i	−0.929581	+	0.368618i	$0.879831\pi$
$504$	4.97178	+	5.98113i	0.221461	+	0.266421i
$505$		0			0
$506$	0.686615	−	3.89399i	0.0305238	−	0.173109i
$507$	4.92743	−	18.2207i	0.218835	−	0.809209i
$508$	−6.00945	−	2.18726i	−0.266626	−	0.0970441i
$509$	−0.633039	−	3.59014i	−0.0280590	−	0.159130i	0.967559	−	0.252646i	$-0.0813007\pi$
$509$	−0.633039	−	3.59014i	−0.0280590	−	0.159130i	−0.995618	+	0.0935154i	$0.970190\pi$
$510$		0			0
$511$	10.1251	+	8.49600i	0.447910	+	0.375841i
$512$	17.7996			0.786640
$513$	−16.4418	+	16.2151i	−0.725922	+	0.715914i
$514$	7.40290			0.326528
$515$		0			0
$516$	8.69277	+	18.7549i	0.382678	+	0.825637i
$517$	−3.65730	−	20.7416i	−0.160848	−	0.912214i
$518$	−2.81267	−	1.02373i	−0.123581	−	0.0449800i
$519$	−12.4823	+	3.31368i	−0.547911	+	0.145454i
$520$		0			0
$521$	5.35490	−	9.27496i	0.234603	−	0.406344i	−0.724555	−	0.689217i	$-0.757954\pi$
$521$	5.35490	−	9.27496i	0.234603	−	0.406344i	0.959157	+	0.282874i	$0.0912878\pi$
$522$	0.0225221	−	4.86722i	0.000985764	−	0.213033i
$523$	1.48990	+	2.58057i	0.0651486	+	0.112841i	0.896760	−	0.442517i	$-0.145915\pi$
$523$	1.48990	+	2.58057i	0.0651486	+	0.112841i	−0.831611	+	0.555358i	$0.812581\pi$
$524$	28.3418	−	10.3156i	1.23812	−	0.450639i
$525$		0			0
$526$	0.226990	−	0.190467i	0.00989724	−	0.00830477i
$527$	11.8360	−	9.93156i	0.515583	−	0.432626i
$528$	11.3279	−	7.89287i	0.492982	−	0.343493i
$529$	−25.1548	+	9.15560i	−1.09369	+	0.398069i
$530$		0			0
$531$	8.54962	+	4.98901i	0.371022	+	0.216505i
$532$	11.1420	−	19.2985i	0.483067	−	0.836696i
$533$	1.67093	−	9.47630i	0.0723759	−	0.410464i
$534$	−6.47691	+	1.71943i	−0.280283	+	0.0744071i
$535$		0			0
$536$	−0.928118	−	5.26362i	−0.0400886	−	0.227354i
$537$	−10.5701	−	22.8053i	−0.456134	−	0.984121i
$538$	0.758445	+	0.636411i	0.0326989	+	0.0274376i
$539$	0.633440			0.0272842
$540$		0			0
$541$	9.02469			0.388002			0.194001	−	0.981001i	$-0.437854\pi$
$541$	9.02469			0.388002			0.194001	+	0.981001i	$0.437854\pi$
$542$	−0.197074	−	0.165364i	−0.00846504	−	0.00710301i
$543$	8.25032	−	11.7248i	0.354055	−	0.503161i
$544$	−1.19515	−	6.77802i	−0.0512415	−	0.290605i
$545$		0			0
$546$	0.431911	−	1.59712i	0.0184841	−	0.0683505i
$547$	−1.85977	+	10.5473i	−0.0795180	+	0.450969i	0.918887	+	0.394520i	$0.129089\pi$
$547$	−1.85977	+	10.5473i	−0.0795180	+	0.450969i	−0.998405	+	0.0564494i	$0.982022\pi$
$548$	−11.6444	+	20.1687i	−0.497423	+	0.861562i
$549$	−9.44647	+	25.5850i	−0.403166	+	1.09194i
$550$		0			0
$551$	−26.6464	+	9.69849i	−1.13517	+	0.413170i
$552$	11.0695	+	5.19303i	0.471151	+	0.221030i
$553$	−8.13876	+	6.82923i	−0.346095	+	0.290409i
$554$	−6.03634	+	5.06509i	−0.256460	+	0.215195i
$555$		0			0
$556$	−32.4218	+	11.8006i	−1.37499	+	0.500456i
$557$	−5.12647	−	8.87931i	−0.217216	−	0.376228i	0.736740	−	0.676176i	$-0.236364\pi$
$557$	−5.12647	−	8.87931i	−0.217216	−	0.376228i	−0.953956	+	0.299948i	$0.903031\pi$
$558$	3.23278	−	3.81667i	0.136855	−	0.161573i
$559$	4.47074	−	7.74355i	0.189092	−	0.327517i
$560$		0			0
$561$	−6.34670	−	6.37613i	−0.267958	−	0.269201i
$562$	−0.684238	−	0.249042i	−0.0288628	−	0.0105052i
$563$	7.26542	+	41.2043i	0.306201	+	1.73655i	0.617797	+	0.786338i	$0.288025\pi$
$563$	7.26542	+	41.2043i	0.306201	+	1.73655i	−0.311596	+	0.950215i	$0.600864\pi$
$564$	31.9008	+	2.86535i	1.34327	+	0.120653i
$565$		0			0
$566$	−6.26473			−0.263326
$567$	−11.8453	+	20.0851i	−0.497457	+	0.843495i
$568$	−3.35039			−0.140579
$569$	−6.82704	−	5.72857i	−0.286205	−	0.240154i	0.488370	−	0.872637i	$-0.337592\pi$
$569$	−6.82704	−	5.72857i	−0.286205	−	0.240154i	−0.774575	+	0.632482i	$0.782036\pi$
$570$		0			0
$571$	3.12283	+	17.7104i	0.130686	+	0.741159i	0.977767	+	0.209695i	$0.0672470\pi$
$571$	3.12283	+	17.7104i	0.130686	+	0.741159i	−0.847081	+	0.531464i	$0.821642\pi$
$572$	−5.81252	−	2.11558i	−0.243034	−	0.0884570i
$573$	29.2395	+	29.3751i	1.22150	+	1.22716i
$574$	−0.759183	+	4.30554i	−0.0316877	+	0.179710i
$575$		0			0
$576$	6.57422	+	18.3259i	0.273926	+	0.763580i
$577$	−3.64403	−	6.31165i	−0.151703	−	0.262757i	0.780151	−	0.625592i	$-0.215142\pi$
$577$	−3.64403	−	6.31165i	−0.151703	−	0.262757i	−0.931854	+	0.362834i	$0.881809\pi$
$578$	2.73523	−	0.995544i	0.113771	−	0.0414092i
$579$	−3.53161	−	41.4714i	−0.146769	−	1.72349i
$580$		0			0
$581$	6.88142	−	5.77419i	0.285489	−	0.239554i
$582$	−1.67208	−	0.784418i	−0.0693099	−	0.0325152i
$583$	−27.6901	+	10.0784i	−1.14680	+	0.417403i
$584$	−2.55243	−	4.42094i	−0.105620	−	0.182940i
$585$		0			0
$586$	−0.737566	+	1.27750i	−0.0304686	+	0.0527731i
$587$	5.23392	−	29.6830i	0.216027	−	1.22515i	−0.663089	−	0.748541i	$-0.730755\pi$
$587$	5.23392	−	29.6830i	0.216027	−	1.22515i	0.879116	−	0.476608i	$-0.158134\pi$
$588$	−0.251473	+	0.929897i	−0.0103706	+	0.0383483i
$589$	−27.3828	−	9.96652i	−1.12829	−	0.410663i
$590$		0			0
$591$	−23.3698	+	33.2117i	−0.961305	+	1.36615i
$592$	−12.5863	−	10.5612i	−0.517294	−	0.434061i
$593$	−3.49473			−0.143511			−0.0717557	−	0.997422i	$-0.522860\pi$
$593$	−3.49473			−0.143511			−0.0717557	+	0.997422i	$0.522860\pi$
$594$	−2.37401	−	1.68698i	−0.0974069	−	0.0692176i
$595$		0			0
$596$	31.7737	+	26.6613i	1.30150	+	1.09209i
$597$	−5.71406	−	12.3282i	−0.233861	−	0.504561i
$598$	−0.451657	−	2.56147i	−0.0184696	−	0.104746i
$599$	24.8902	+	9.05928i	1.01698	+	0.370152i	0.796111	−	0.605150i	$-0.206887\pi$
$599$	24.8902	+	9.05928i	1.01698	+	0.370152i	0.220873	+	0.975302i	$0.429109\pi$
$600$		0			0
$601$	−2.02684	+	11.4948i	−0.0826764	+	0.468881i	0.915157	+	0.403096i	$0.132066\pi$
$601$	−2.02684	+	11.4948i	−0.0826764	+	0.468881i	−0.997834	+	0.0657845i	$0.979045\pi$
$602$	−2.03127	+	3.51827i	−0.0827886	+	0.143394i
$603$	13.9141	−	7.94770i	0.566627	−	0.323656i
$604$	7.46096	+	12.9228i	0.303582	+	0.525820i
$605$		0			0
$606$	5.16705	−	3.60022i	0.209897	−	0.146249i
$607$	−4.18061	+	3.50795i	−0.169686	+	0.142383i	−0.723676	−	0.690140i	$-0.757549\pi$
$607$	−4.18061	+	3.50795i	−0.169686	+	0.142383i	0.553990	+	0.832523i	$0.313105\pi$
$608$	−9.94367	+	8.34373i	−0.403269	+	0.338383i
$609$	−23.4930	+	16.3691i	−0.951983	+	0.663308i
$610$		0			0
$611$	−6.92716	−	11.9982i	−0.280243	−	0.485395i
$612$	11.8799	−	6.78574i	0.480215	−	0.274297i
$613$	3.48113	−	6.02950i	0.140602	−	0.243529i	−0.787122	−	0.616798i	$-0.788430\pi$
$613$	3.48113	−	6.02950i	0.140602	−	0.243529i	0.927723	+	0.373269i	$0.121763\pi$
$614$	−1.36702	+	7.75278i	−0.0551686	+	0.312877i
$615$		0			0
$616$	5.37005	+	1.95454i	0.216365	+	0.0787505i
$617$	3.30719	+	18.7560i	0.133143	+	0.755089i	0.976135	+	0.217164i	$0.0696806\pi$
$617$	3.30719	+	18.7560i	0.133143	+	0.755089i	−0.842993	+	0.537925i	$0.819208\pi$
$618$	−1.59916	−	3.45024i	−0.0643278	−	0.138789i
$619$	10.9809	+	9.21409i	0.441360	+	0.370345i	0.836218	−	0.548397i	$-0.184762\pi$
$619$	10.9809	+	9.21409i	0.441360	+	0.370345i	−0.394858	+	0.918742i	$0.629206\pi$
$620$		0			0
$621$	−3.44829	+	36.4949i	−0.138375	+	1.46449i
$622$	2.47214			0.0991236
$623$	30.1992	+	25.3401i	1.20991	+	1.01523i
$624$	5.22636	−	7.42739i	0.209222	−	0.297333i
$625$		0			0
$626$	2.90209	+	1.05627i	0.115991	+	0.0422172i
$627$	−4.42935	+	16.3789i	−0.176891	+	0.654110i
$628$	0.260365	−	1.47660i	0.0103897	−	0.0589228i
$629$	−5.35306	+	9.27178i	−0.213441	+	0.369690i
$630$		0			0
$631$	−5.23437	−	9.06620i	−0.208377	−	0.360920i	0.742826	−	0.669484i	$-0.233485\pi$
$631$	−5.23437	−	9.06620i	−0.208377	−	0.360920i	−0.951203	+	0.308564i	$0.900151\pi$
$632$	3.85591	−	1.40344i	0.153380	−	0.0558257i
$633$	−7.90949	−	3.71056i	−0.314374	−	0.147481i
$634$	−1.03041	+	0.864618i	−0.0409229	+	0.0343384i
$635$		0			0
$636$	−3.80233	−	44.6504i	−0.150772	−	1.77050i
$637$	0.391549	−	0.142512i	0.0155137	−	0.00564654i
$638$	−1.78812	−	3.09712i	−0.0707925	−	0.122616i
$639$	−3.39175	−	9.45466i	−0.134176	−	0.374021i
$640$		0			0
$641$	−1.94620	+	11.0374i	−0.0768701	+	0.435952i	0.921947	+	0.387317i	$0.126598\pi$
$641$	−1.94620	+	11.0374i	−0.0768701	+	0.435952i	−0.998817	+	0.0486349i	$0.984513\pi$
$642$	−1.76246	−	1.77064i	−0.0695588	−	0.0698815i
$643$	3.76197	+	1.36924i	0.148357	+	0.0539977i	0.415132	−	0.909761i	$-0.363736\pi$
$643$	3.76197	+	1.36924i	0.148357	+	0.0539977i	−0.266774	+	0.963759i	$0.585958\pi$
$644$	−6.14264	−	34.8367i	−0.242054	−	1.37276i
$645$		0			0
$646$	2.03981	+	1.71160i	0.0802551	+	0.0673421i
$647$	23.5060			0.924118			0.462059	−	0.886849i	$-0.347111\pi$
$647$	23.5060			0.924118			0.462059	+	0.886849i	$0.347111\pi$
$648$	6.95217	−	5.72477i	0.273107	−	0.224890i
$649$	7.27317			0.285497
$650$		0			0
$651$	−29.3066	−	2.63233i	−1.14862	−	0.103169i
$652$	5.48046	+	31.0812i	0.214631	+	1.21724i
$653$	10.0562	+	3.66017i	0.393531	+	0.143233i	0.531203	−	0.847244i	$-0.321740\pi$
$653$	10.0562	+	3.66017i	0.393531	+	0.143233i	−0.137673	+	0.990478i	$0.543962\pi$
$654$	−5.89055	−	5.91787i	−0.230339	−	0.231407i
$655$		0			0
$656$	−11.9994	+	20.7835i	−0.468497	+	0.811460i
$657$	9.89175	−	11.6783i	0.385914	−	0.455616i
$658$	3.14734	+	5.45136i	0.122696	+	0.212516i
$659$	−5.16703	+	1.88064i	−0.201279	+	0.0732595i	−0.440692	−	0.897658i	$-0.645267\pi$
$659$	−5.16703	+	1.88064i	−0.201279	+	0.0732595i	0.239414	+	0.970918i	$0.423045\pi$
$660$		0			0
$661$	−29.3397	+	24.6189i	−1.14118	+	0.957565i	−0.999477	−	0.0323440i	$-0.989703\pi$
$661$	−29.3397	+	24.6189i	−1.14118	+	0.957565i	−0.141705	+	0.989909i	$0.545258\pi$
$662$	4.89515	−	4.10752i	0.190255	−	0.159643i
$663$	−5.35760	−	2.51340i	−0.208072	−	0.0976123i
$664$	−3.26022	+	1.18662i	−0.126521	+	0.0460499i
$665$		0			0
$666$	−1.20044	+	3.25130i	−0.0465161	+	0.125985i
$667$	−22.5068	+	38.9830i	−0.871469	+	1.50943i
$668$	−2.32857	+	13.2060i	−0.0900950	+	0.510954i
$669$	−8.53829	+	31.5730i	−0.330109	+	1.22068i
$670$		0			0
$671$	3.47975	+	19.7346i	0.134334	+	0.761847i
$672$	−7.54283	+	10.7194i	−0.290971	+	0.413510i
$673$	16.1006	+	13.5100i	0.620631	+	0.520771i	0.898002	−	0.439992i	$-0.145019\pi$
$673$	16.1006	+	13.5100i	0.620631	+	0.520771i	−0.277371	+	0.960763i	$0.589463\pi$
$674$	1.28550			0.0495158
$675$		0			0
$676$	21.0906			0.811178
$677$	2.14171	+	1.79711i	0.0823126	+	0.0690685i	0.683016	−	0.730404i	$-0.260668\pi$
$677$	2.14171	+	1.79711i	0.0823126	+	0.0690685i	−0.600703	+	0.799472i	$0.705113\pi$
$678$	2.11749	+	4.56854i	0.0813218	+	0.175454i
$679$	1.88672	+	10.7001i	0.0724055	+	0.410632i
$680$		0			0
$681$	−6.26360	+	1.66280i	−0.240022	+	0.0637188i
$682$	0.638170	−	3.61924i	0.0244368	−	0.138588i
$683$	1.12135	−	1.94224i	0.0429073	−	0.0743176i	−0.843774	−	0.536698i	$-0.819671\pi$
$683$	1.12135	−	1.94224i	0.0429073	−	0.0743176i	0.886681	+	0.462381i	$0.153005\pi$
$684$	−22.2860	−	13.0047i	−0.852126	−	0.497247i
$685$		0			0
$686$	−4.51132	+	1.64199i	−0.172243	+	0.0626913i
$687$	−11.9611	+	8.33406i	−0.456343	+	0.317964i
$688$	−17.0830	+	14.3344i	−0.651284	+	0.546492i
$689$	−14.8487	+	12.4595i	−0.565689	+	0.474669i
$690$		0			0
$691$	27.0475	−	9.84448i	1.02893	−	0.374502i	0.228260	−	0.973600i	$-0.426697\pi$
$691$	27.0475	−	9.84448i	1.02893	−	0.374502i	0.800675	+	0.599099i	$0.204474\pi$
$692$	−7.21522	−	12.4971i	−0.274282	−	0.475070i
$693$	−0.0792780	+	17.1327i	−0.00301152	+	0.650817i
$694$	−3.43474	+	5.94915i	−0.130381	+	0.225827i
$695$		0			0
$696$	10.6886	−	2.83751i	0.405150	−	0.107555i
$697$	14.6947	+	5.34845i	0.556603	+	0.202587i
$698$	−1.03473	−	5.86823i	−0.0391650	−	0.222116i
$699$	−8.18921	−	17.6684i	−0.309744	−	0.668281i
$700$		0			0
$701$	−19.7581			−0.746255			−0.373127	−	0.927780i	$-0.621715\pi$
$701$	−19.7581			−0.746255			−0.373127	+	0.927780i	$0.621715\pi$
$702$	−1.84699	−	0.508666i	−0.0697102	−	0.0191983i
$703$	20.1917			0.761546
$704$	10.9584	+	9.19523i	0.413012	+	0.346558i
$705$		0			0
$706$	0.787958	+	4.46873i	0.0296552	+	0.168183i
$707$	−34.8135	−	12.6711i	−1.30930	−	0.476544i
$708$	−2.88741	+	10.6771i	−0.108516	+	0.401270i
$709$	−0.688034	+	3.90203i	−0.0258397	+	0.146544i	−0.994998	−	0.0998949i	$-0.968149\pi$
$709$	−0.688034	+	3.90203i	−0.0258397	+	0.146544i	0.969158	+	0.246439i	$0.0792605\pi$
$710$		0			0
$711$	7.86395	+	9.46045i	0.294921	+	0.354795i
$712$	−7.61287	−	13.1859i	−0.285304	−	0.494162i
$713$	−43.4680	+	15.8211i	−1.62789	+	0.592503i
$714$	2.43422	+	1.14196i	0.0910984	+	0.0427367i
$715$		0			0
$716$	21.5152	−	18.0534i	0.804059	−	0.674686i
$717$	−2.65169	−	31.1385i	−0.0990291	−	1.16289i
$718$	6.07223	−	2.21011i	0.226614	−	0.0824806i
$719$	−13.6807	−	23.6957i	−0.510204	−	0.883699i	−0.999930	−	0.0118228i	$-0.996237\pi$
$719$	−13.6807	−	23.6957i	−0.510204	−	0.883699i	0.489726	−	0.871876i	$-0.337097\pi$
$720$		0			0
$721$	−11.1857	+	19.3741i	−0.416576	+	0.721530i
$722$	0.0331342	−	0.187913i	0.00123313	−	0.00699341i
$723$	−18.6246	−	18.7110i	−0.692656	−	0.695868i
$724$	15.0533	+	5.47895i	0.559451	+	0.203624i
$725$		0			0
$726$	2.69384	+	0.241962i	0.0999779	+	0.00898006i
$727$	9.42789	+	7.91094i	0.349661	+	0.293401i	0.800654	−	0.599127i	$-0.204486\pi$
$727$	9.42789	+	7.91094i	0.349661	+	0.293401i	−0.450993	+	0.892528i	$0.648930\pi$
$728$	3.75913			0.139323
$729$	23.1930	+	13.8233i	0.859001	+	0.511973i
$730$		0			0
$731$	11.1315	+	9.34041i	0.411712	+	0.345468i
$732$	−30.3521	−	2.72624i	−1.12185	−	0.100765i
$733$	−0.405710	−	2.30089i	−0.0149852	−	0.0849854i	0.976398	−	0.215979i	$-0.0692943\pi$
$733$	−0.405710	−	2.30089i	−0.0149852	−	0.0849854i	−0.991383	+	0.130994i	$0.958183\pi$
$734$	−8.50813	−	3.09671i	−0.314041	−	0.114302i
$735$		0			0
$736$	−3.57812	+	20.2925i	−0.131891	+	0.747993i
$737$	5.88684	−	10.1963i	0.216845	−	0.375586i
$738$	4.98131	+	0.902125i	0.183365	+	0.0332077i
$739$	−26.0513	−	45.1221i	−0.958311	−	1.65984i	−0.726602	−	0.687059i	$-0.758901\pi$
$739$	−26.0513	−	45.1221i	−0.958311	−	1.65984i	−0.231710	−	0.972785i	$-0.574432\pi$
$740$		0			0
$741$	0.947026	+	11.1208i	0.0347899	+	0.408534i
$742$	6.74646	−	5.66095i	0.247670	−	0.207820i
$743$	30.9313	−	25.9544i	1.13476	−	0.952175i	0.135504	−	0.990777i	$-0.456735\pi$
$743$	30.9313	−	25.9544i	1.13476	−	0.952175i	0.999255	+	0.0386016i	$0.0122903\pi$
$744$	10.2885	+	4.82663i	0.377195	+	0.176953i
$745$		0			0
$746$	0.734841	+	1.27278i	0.0269045	+	0.0465999i
$747$	−6.64906	−	7.99892i	−0.243276	−	0.292665i
$748$	5.02618	−	8.70559i	0.183775	−	0.318308i
$749$	−2.55210	+	14.4737i	−0.0932517	+	0.528857i
$750$		0			0
$751$	−25.8917	−	9.42382i	−0.944803	−	0.343880i	−0.176742	−	0.984257i	$-0.556556\pi$
$751$	−25.8917	−	9.42382i	−0.944803	−	0.343880i	−0.768061	+	0.640377i	$0.778778\pi$
$752$	6.00007	+	34.0281i	0.218800	+	1.24088i
$753$	−20.1661	+	28.6588i	−0.734892	+	1.04438i
$754$	−1.80209	−	1.51213i	−0.0656282	−	0.0550686i
$755$		0			0
$756$	−25.1195	−	6.91798i	−0.913588	−	0.251604i
$757$	−13.2447			−0.481386			−0.240693	−	0.970601i	$-0.577375\pi$
$757$	−13.2447			−0.481386			−0.240693	+	0.970601i	$0.577375\pi$
$758$	−5.39860	−	4.52996i	−0.196086	−	0.164536i
$759$	11.3264	+	24.4369i	0.411121	+	0.887004i
$760$		0			0
$761$	35.4594	+	12.9062i	1.28540	+	0.467848i	0.892215	−	0.451611i	$-0.149150\pi$
$761$	35.4594	+	12.9062i	1.28540	+	0.467848i	0.393187	+	0.919459i	$0.371373\pi$
$762$	−1.40658	+	0.373405i	−0.0509549	+	0.0135270i
$763$	−8.52970	+	48.3743i	−0.308796	+	1.75127i
$764$	−23.1558	+	40.1070i	−0.837747	+	1.45102i
$765$		0			0
$766$	0.699881	+	1.21223i	0.0252877	+	0.0437997i
$767$	4.49578	−	1.63633i	0.162333	−	0.0590844i
$768$	−15.7383	+	10.9659i	−0.567907	+	0.395698i
$769$	39.2960	−	32.9733i	1.41705	−	1.18905i	0.464153	−	0.885755i	$-0.346359\pi$
$769$	39.2960	−	32.9733i	1.41705	−	1.18905i	0.952898	−	0.303292i	$-0.0980856\pi$
$770$		0			0
$771$	−41.3741	+	28.8280i	−1.49005	+	1.03822i
$772$	43.7020	−	15.9062i	1.57287	−	0.572477i
$773$	−21.4439	−	37.1420i	−0.771285	−	1.33590i	−0.936859	−	0.349707i	$-0.886281\pi$
$773$	−21.4439	−	37.1420i	−0.771285	−	1.33590i	0.165574	−	0.986197i	$-0.447052\pi$
$774$	4.06291	+	2.37086i	0.146038	+	0.0852188i
$775$		0			0

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:	\( N \)	\(=\)	\( 675 = 3^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	675.l (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.194784 + 0.163444i) q^{2} +(-1.72511 - 0.154950i) q^{3} +(-0.336069 - 1.90594i) q^{4} +(-0.310698 - 0.312139i) q^{6} +(-0.449901 + 2.55151i) q^{7} +(0.500326 - 0.866590i) q^{8} +(2.95198 + 0.534610i) q^{9} +O(q^{10})\)	\(q+(0.194784 + 0.163444i) q^{2} +(-1.72511 - 0.154950i) q^{3} +(-0.336069 - 1.90594i) q^{4} +(-0.310698 - 0.312139i) q^{6} +(-0.449901 + 2.55151i) q^{7} +(0.500326 - 0.866590i) q^{8} +(2.95198 + 0.534610i) q^{9} +(2.07133 - 0.753901i) q^{11} +(0.284429 + 3.34003i) q^{12} +(1.11074 - 0.932020i) q^{13} +(-0.504662 + 0.423462i) q^{14} +(-3.39816 + 1.23683i) q^{16} +(1.17819 + 2.04069i) q^{17} +(0.487621 + 0.586616i) q^{18} +(2.22207 - 3.84874i) q^{19} +(1.17148 - 4.33192i) q^{21} +(0.526682 + 0.191697i) q^{22} +(-1.22504 - 6.94755i) q^{23} +(-0.997394 + 1.41743i) q^{24} +0.368687 q^{26} +(-5.00964 - 1.37967i) q^{27} +5.01424 q^{28} +(-4.88786 - 4.10140i) q^{29} +(-1.13861 - 6.45736i) q^{31} +(-2.74467 - 0.998979i) q^{32} +(-3.69007 + 0.979608i) q^{33} +(-0.104044 + 0.590063i) q^{34} +(0.0268659 - 5.80597i) q^{36} +(2.27172 + 3.93474i) q^{37} +(1.06188 - 0.386492i) q^{38} +(-2.06056 + 1.43572i) q^{39} +(5.08374 - 4.26577i) q^{41} +(0.936211 - 0.652319i) q^{42} +(5.79479 - 2.10913i) q^{43} +(-2.13300 - 3.69447i) q^{44} +(0.896913 - 1.55350i) q^{46} +(1.65920 - 9.40977i) q^{47} +(6.05384 - 1.60712i) q^{48} +(0.270040 + 0.0982866i) q^{49} +(-1.71630 - 3.70297i) q^{51} +(-2.14966 - 1.80378i) q^{52} -13.3683 q^{53} +(-0.750303 - 1.08753i) q^{54} +(1.98602 + 1.66647i) q^{56} +(-4.42967 + 6.29518i) q^{57} +(-0.281731 - 1.59778i) q^{58} +(3.10061 + 1.12853i) q^{59} +(-1.57865 + 8.95295i) q^{61} +(0.833631 - 1.44389i) q^{62} +(-2.69216 + 7.29150i) q^{63} +(3.24491 + 5.62035i) q^{64} +(-0.878880 - 0.412306i) q^{66} +(4.09170 - 3.43334i) q^{67} +(3.49349 - 2.93138i) q^{68} +(1.03680 + 12.1751i) q^{69} +(-1.67410 - 2.89963i) q^{71} +(1.94024 - 2.29068i) q^{72} +(2.55076 - 4.41805i) q^{73} +(-0.200612 + 1.13773i) q^{74} +(-8.08225 - 2.94170i) q^{76} +(0.991698 + 5.62420i) q^{77} +(-0.636024 - 0.0571280i) q^{78} +(3.14132 + 2.63588i) q^{79} +(8.42838 + 3.15632i) q^{81} +1.68745 q^{82} +(-2.65602 - 2.22867i) q^{83} +(-8.65009 - 0.776955i) q^{84} +(1.47346 + 0.536295i) q^{86} +(7.79656 + 7.83272i) q^{87} +(0.383015 - 2.17219i) q^{88} +(7.60791 - 13.1773i) q^{89} +(1.87834 + 3.25338i) q^{91} +(-12.8299 + 4.66971i) q^{92} +(0.963650 + 11.3161i) q^{93} +(1.86115 - 1.56169i) q^{94} +(4.58006 + 2.14863i) q^{96} +(3.94072 - 1.43431i) q^{97} +(0.0365353 + 0.0632810i) q^{98} +(6.51756 - 1.11815i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 66 q - 6 q^{2} - 6 q^{6} - 6 q^{7} - 12 q^{8} - 6 q^{9}+O(q^{10}) \) 66 * q - 6 * q^2 - 6 * q^6 - 6 * q^7 - 12 * q^8 - 6 * q^9	\( 66 q - 6 q^{2} - 6 q^{6} - 6 q^{7} - 12 q^{8} - 6 q^{9} + 15 q^{11} - 18 q^{12} + 15 q^{14} + 18 q^{16} - 30 q^{17} + 12 q^{18} + 12 q^{19} + 12 q^{21} + 45 q^{22} - 36 q^{23} - 39 q^{24} + 6 q^{26} - 51 q^{27} + 36 q^{28} - 15 q^{29} + 3 q^{31} - 27 q^{32} + 3 q^{33} + 30 q^{36} - 6 q^{37} + 12 q^{38} - 15 q^{39} + 39 q^{41} - 48 q^{42} - 12 q^{43} + 51 q^{44} + 9 q^{46} - 30 q^{47} + 132 q^{48} - 6 q^{49} - 9 q^{52} + 24 q^{53} + 75 q^{54} + 144 q^{56} - 33 q^{57} - 27 q^{58} + 45 q^{59} - 54 q^{61} - 66 q^{62} + 120 q^{63} - 24 q^{64} + 48 q^{66} - 9 q^{67} + 69 q^{68} + 51 q^{69} - 15 q^{71} - 9 q^{72} + 15 q^{73} + 96 q^{74} - 48 q^{76} + 36 q^{77} + 18 q^{78} + 48 q^{79} - 54 q^{81} + 36 q^{82} - 30 q^{83} + 57 q^{84} - 111 q^{86} + 33 q^{87} - 36 q^{88} - 12 q^{89} + 9 q^{91} + 219 q^{92} - 63 q^{93} + 36 q^{94} - 249 q^{96} - 57 q^{97} - 75 q^{98} - 48 q^{99}+O(q^{100}) \) 66 * q - 6 * q^2 - 6 * q^6 - 6 * q^7 - 12 * q^8 - 6 * q^9 + 15 * q^11 - 18 * q^12 + 15 * q^14 + 18 * q^16 - 30 * q^17 + 12 * q^18 + 12 * q^19 + 12 * q^21 + 45 * q^22 - 36 * q^23 - 39 * q^24 + 6 * q^26 - 51 * q^27 + 36 * q^28 - 15 * q^29 + 3 * q^31 - 27 * q^32 + 3 * q^33 + 30 * q^36 - 6 * q^37 + 12 * q^38 - 15 * q^39 + 39 * q^41 - 48 * q^42 - 12 * q^43 + 51 * q^44 + 9 * q^46 - 30 * q^47 + 132 * q^48 - 6 * q^49 - 9 * q^52 + 24 * q^53 + 75 * q^54 + 144 * q^56 - 33 * q^57 - 27 * q^58 + 45 * q^59 - 54 * q^61 - 66 * q^62 + 120 * q^63 - 24 * q^64 + 48 * q^66 - 9 * q^67 + 69 * q^68 + 51 * q^69 - 15 * q^71 - 9 * q^72 + 15 * q^73 + 96 * q^74 - 48 * q^76 + 36 * q^77 + 18 * q^78 + 48 * q^79 - 54 * q^81 + 36 * q^82 - 30 * q^83 + 57 * q^84 - 111 * q^86 + 33 * q^87 - 36 * q^88 - 12 * q^89 + 9 * q^91 + 219 * q^92 - 63 * q^93 + 36 * q^94 - 249 * q^96 - 57 * q^97 - 75 * q^98 - 48 * q^99

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