LMFDB - Embedded newform 1890.2.i.g.1171.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1890,2,Mod(991,1890)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1890, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1890.991");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1890 = 2 \cdot 3^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1890.i (of order $3$, degree $2$, not 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:	$15.0917259820$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} + 7 x^{10} - 3 x^{9} - 2 x^{8} + 24 x^{7} - 21 x^{6} + 72 x^{5} - 18 x^{4} + \cdots + 729 $ x^12 - 3x^11 + 7x^10 - 3x^9 - 2x^8 + 24x^7 - 21x^6 + 72x^5 - 18x^4 - 81x^3 + 567x^2 - 729*x + 729
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 3^{4} $
Twist minimal:	no (minimal twist has level 630)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			1171.5
Root			$-1.67391 - 0.444996i$ of defining polynomial
Character	$\chi$	$=$	1890.1171
Dual form			1890.2.i.g.991.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{4} +(0.500000 + 0.866025i) q^{5} +(1.85185 - 1.88962i) q^{7} -1.00000 q^{8} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{4} +(0.500000 + 0.866025i) q^{5} +(1.85185 - 1.88962i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{10} +(-3.22352 + 5.58330i) q^{11} +(0.332016 - 0.575068i) q^{13} +(-1.85185 + 1.88962i) q^{14} +1.00000 q^{16} +(-0.411850 - 0.713345i) q^{17} +(-2.77668 + 4.80936i) q^{19} +(0.500000 + 0.866025i) q^{20} +(3.22352 - 5.58330i) q^{22} +(-1.74387 - 3.02046i) q^{23} +(-0.500000 + 0.866025i) q^{25} +(-0.332016 + 0.575068i) q^{26} +(1.85185 - 1.88962i) q^{28} +(-2.03452 - 3.52389i) q^{29} -7.63703 q^{31} -1.00000 q^{32} +(0.411850 + 0.713345i) q^{34} +(2.56238 + 0.658939i) q^{35} +(-5.32042 + 9.21523i) q^{37} +(2.77668 - 4.80936i) q^{38} +(-0.500000 - 0.866025i) q^{40} +(-0.511800 + 0.886464i) q^{41} +(-4.15005 - 7.18810i) q^{43} +(-3.22352 + 5.58330i) q^{44} +(1.74387 + 3.02046i) q^{46} -2.60076 q^{47} +(-0.141315 - 6.99857i) q^{49} +(0.500000 - 0.866025i) q^{50} +(0.332016 - 0.575068i) q^{52} +(3.27668 + 5.67538i) q^{53} -6.44704 q^{55} +(-1.85185 + 1.88962i) q^{56} +(2.03452 + 3.52389i) q^{58} +2.91633 q^{59} -0.767506 q^{61} +7.63703 q^{62} +1.00000 q^{64} +0.664031 q^{65} +7.28641 q^{67} +(-0.411850 - 0.713345i) q^{68} +(-2.56238 - 0.658939i) q^{70} -3.44704 q^{71} +(4.71172 + 8.16093i) q^{73} +(5.32042 - 9.21523i) q^{74} +(-2.77668 + 4.80936i) q^{76} +(4.58083 + 16.4306i) q^{77} -5.40500 q^{79} +(0.500000 + 0.866025i) q^{80} +(0.511800 - 0.886464i) q^{82} +(-0.897166 - 1.55394i) q^{83} +(0.411850 - 0.713345i) q^{85} +(4.15005 + 7.18810i) q^{86} +(3.22352 - 5.58330i) q^{88} +(2.06497 - 3.57663i) q^{89} +(-0.471816 - 1.69232i) q^{91} +(-1.74387 - 3.02046i) q^{92} +2.60076 q^{94} -5.55337 q^{95} +(-8.98652 - 15.5651i) q^{97} +(0.141315 + 6.99857i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 12 q^{2} + 12 q^{4} + 6 q^{5} + 4 q^{7} - 12 q^{8}+O(q^{10}) $ 12 * q - 12 * q^2 + 12 * q^4 + 6 * q^5 + 4 * q^7 - 12 * q^8	$ 12 q - 12 q^{2} + 12 q^{4} + 6 q^{5} + 4 q^{7} - 12 q^{8} - 6 q^{10} - 3 q^{11} - 2 q^{13} - 4 q^{14} + 12 q^{16} - q^{17} + 8 q^{19} + 6 q^{20} + 3 q^{22} - 11 q^{23} - 6 q^{25} + 2 q^{26} + 4 q^{28} - 13 q^{29} - 42 q^{31} - 12 q^{32} + q^{34} - 4 q^{35} + 18 q^{37} - 8 q^{38} - 6 q^{40} - 5 q^{41} - 11 q^{43} - 3 q^{44} + 11 q^{46} - 46 q^{47} + 6 q^{50} - 2 q^{52} - 2 q^{53} - 6 q^{55} - 4 q^{56} + 13 q^{58} + 2 q^{59} + 2 q^{61} + 42 q^{62} + 12 q^{64} - 4 q^{65} - 4 q^{67} - q^{68} + 4 q^{70} + 30 q^{71} + 22 q^{73} - 18 q^{74} + 8 q^{76} + 31 q^{77} - 54 q^{79} + 6 q^{80} + 5 q^{82} - 6 q^{83} + q^{85} + 11 q^{86} + 3 q^{88} + 18 q^{89} + 14 q^{91} - 11 q^{92} + 46 q^{94} + 16 q^{95} - 4 q^{97}+O(q^{100}) $ 12 * q - 12 * q^2 + 12 * q^4 + 6 * q^5 + 4 * q^7 - 12 * q^8 - 6 * q^10 - 3 * q^11 - 2 * q^13 - 4 * q^14 + 12 * q^16 - q^17 + 8 * q^19 + 6 * q^20 + 3 * q^22 - 11 * q^23 - 6 * q^25 + 2 * q^26 + 4 * q^28 - 13 * q^29 - 42 * q^31 - 12 * q^32 + q^34 - 4 * q^35 + 18 * q^37 - 8 * q^38 - 6 * q^40 - 5 * q^41 - 11 * q^43 - 3 * q^44 + 11 * q^46 - 46 * q^47 + 6 * q^50 - 2 * q^52 - 2 * q^53 - 6 * q^55 - 4 * q^56 + 13 * q^58 + 2 * q^59 + 2 * q^61 + 42 * q^62 + 12 * q^64 - 4 * q^65 - 4 * q^67 - q^68 + 4 * q^70 + 30 * q^71 + 22 * q^73 - 18 * q^74 + 8 * q^76 + 31 * q^77 - 54 * q^79 + 6 * q^80 + 5 * q^82 - 6 * q^83 + q^85 + 11 * q^86 + 3 * q^88 + 18 * q^89 + 14 * q^91 - 11 * q^92 + 46 * q^94 + 16 * q^95 - 4 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1890\mathbb{Z}\right)^\times$.

$n$	$757$	$1081$	$1541$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$		0			0
$3$		0			0
$4$	1.00000			0.500000
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$		0			0
$7$	1.85185	−	1.88962i	0.699933	−	0.714209i
$7$	1.85185	−	1.88962i	0.699933	−	0.714209i
$8$	−1.00000			−0.353553
$9$		0			0
$10$	−0.500000	−	0.866025i	−0.158114	−	0.273861i
$11$	−3.22352	+	5.58330i	−0.971927	+	1.68343i	−0.282204	+	0.959354i	$0.591065\pi$
$11$	−3.22352	+	5.58330i	−0.971927	+	1.68343i	−0.689723	+	0.724073i	$0.742268\pi$
$12$		0			0
$13$	0.332016	−	0.575068i	0.0920846	−	0.159495i	−0.816304	−	0.577623i	$-0.803980\pi$
$13$	0.332016	−	0.575068i	0.0920846	−	0.159495i	0.908388	+	0.418128i	$0.137314\pi$
$14$	−1.85185	+	1.88962i	−0.494927	+	0.505022i
$15$		0			0
$16$	1.00000			0.250000
$17$	−0.411850	−	0.713345i	−0.0998883	−	0.173012i	0.811750	−	0.584005i	$-0.198515\pi$
$17$	−0.411850	−	0.713345i	−0.0998883	−	0.173012i	−0.911638	+	0.410994i	$0.865182\pi$
$18$		0			0
$19$	−2.77668	+	4.80936i	−0.637015	+	1.10334i	0.349070	+	0.937097i	$0.386498\pi$
$19$	−2.77668	+	4.80936i	−0.637015	+	1.10334i	−0.986084	+	0.166245i	$0.946836\pi$
$20$	0.500000	+	0.866025i	0.111803	+	0.193649i
$21$		0			0
$22$	3.22352	−	5.58330i	0.687256	−	1.19036i
$23$	−1.74387	−	3.02046i	−0.363621	−	0.629810i	0.624933	−	0.780679i	$-0.285126\pi$
$23$	−1.74387	−	3.02046i	−0.363621	−	0.629810i	−0.988554	+	0.150868i	$0.951793\pi$
$24$		0			0
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	−0.332016	+	0.575068i	−0.0651136	+	0.112780i
$27$		0			0
$28$	1.85185	−	1.88962i	0.349966	−	0.357104i
$29$	−2.03452	−	3.52389i	−0.377800	−	0.654369i	0.612942	−	0.790128i	$-0.289986\pi$
$29$	−2.03452	−	3.52389i	−0.377800	−	0.654369i	−0.990742	+	0.135759i	$0.956653\pi$
$30$		0			0
$31$	−7.63703			−1.37165			−0.685826	−	0.727766i	$-0.740559\pi$
$31$	−7.63703			−1.37165			−0.685826	+	0.727766i	$0.740559\pi$
$32$	−1.00000			−0.176777
$33$		0			0
$34$	0.411850	+	0.713345i	0.0706317	+	0.122338i
$35$	2.56238	+	0.658939i	0.433122	+	0.111381i
$36$		0			0
$37$	−5.32042	+	9.21523i	−0.874671	+	1.51497i	−0.0175583	+	0.999846i	$0.505589\pi$
$37$	−5.32042	+	9.21523i	−0.874671	+	1.51497i	−0.857113	+	0.515129i	$0.827744\pi$
$38$	2.77668	−	4.80936i	0.450437	−	0.780181i
$39$		0			0
$40$	−0.500000	−	0.866025i	−0.0790569	−	0.136931i
$41$	−0.511800	+	0.886464i	−0.0799298	+	0.138442i	−0.903219	−	0.429179i	$-0.858803\pi$
$41$	−0.511800	+	0.886464i	−0.0799298	+	0.138442i	0.823290	+	0.567621i	$0.192136\pi$
$42$		0			0
$43$	−4.15005	−	7.18810i	−0.632877	−	1.09618i	−0.986961	−	0.160961i	$-0.948541\pi$
$43$	−4.15005	−	7.18810i	−0.632877	−	1.09618i	0.354084	−	0.935214i	$-0.384793\pi$
$44$	−3.22352	+	5.58330i	−0.485964	+	0.841714i
$45$		0			0
$46$	1.74387	+	3.02046i	0.257119	+	0.445343i
$47$	−2.60076			−0.379361			−0.189680	−	0.981846i	$-0.560745\pi$
$47$	−2.60076			−0.379361			−0.189680	+	0.981846i	$0.560745\pi$
$48$		0			0
$49$	−0.141315	−	6.99857i	−0.0201879	−	0.999796i
$50$	0.500000	−	0.866025i	0.0707107	−	0.122474i
$51$		0			0
$52$	0.332016	−	0.575068i	0.0460423	−	0.0797476i
$53$	3.27668	+	5.67538i	0.450087	+	0.779574i	0.998391	−	0.0567055i	$-0.0180596\pi$
$53$	3.27668	+	5.67538i	0.450087	+	0.779574i	−0.548304	+	0.836279i	$0.684726\pi$
$54$		0			0
$55$	−6.44704			−0.869318
$56$	−1.85185	+	1.88962i	−0.247464	+	0.252511i
$57$		0			0
$58$	2.03452	+	3.52389i	0.267145	+	0.462709i
$59$	2.91633			0.379674			0.189837	−	0.981816i	$-0.439204\pi$
$59$	2.91633			0.379674			0.189837	+	0.981816i	$0.439204\pi$
$60$		0			0
$61$	−0.767506			−0.0982691			−0.0491346	−	0.998792i	$-0.515646\pi$
$61$	−0.767506			−0.0982691			−0.0491346	+	0.998792i	$0.515646\pi$
$62$	7.63703			0.969904
$63$		0			0
$64$	1.00000			0.125000
$65$	0.664031			0.0823629
$66$		0			0
$67$	7.28641			0.890176			0.445088	−	0.895487i	$-0.353172\pi$
$67$	7.28641			0.890176			0.445088	+	0.895487i	$0.353172\pi$
$68$	−0.411850	−	0.713345i	−0.0499442	−	0.0865058i
$69$		0			0
$70$	−2.56238	−	0.658939i	−0.306263	−	0.0787582i
$71$	−3.44704			−0.409088			−0.204544	−	0.978857i	$-0.565571\pi$
$71$	−3.44704			−0.409088			−0.204544	+	0.978857i	$0.565571\pi$
$72$		0			0
$73$	4.71172	+	8.16093i	0.551465	+	0.955165i	0.998169	+	0.0604835i	$0.0192642\pi$
$73$	4.71172	+	8.16093i	0.551465	+	0.955165i	−0.446704	+	0.894682i	$0.647402\pi$
$74$	5.32042	−	9.21523i	0.618486	−	1.07125i
$75$		0			0
$76$	−2.77668	+	4.80936i	−0.318507	+	0.551671i
$77$	4.58083	+	16.4306i	0.522034	+	1.87244i
$78$		0			0
$79$	−5.40500			−0.608110			−0.304055	−	0.952654i	$-0.598341\pi$
$79$	−5.40500			−0.608110			−0.304055	+	0.952654i	$0.598341\pi$
$80$	0.500000	+	0.866025i	0.0559017	+	0.0968246i
$81$		0			0
$82$	0.511800	−	0.886464i	0.0565189	−	0.0978936i
$83$	−0.897166	−	1.55394i	−0.0984768	−	0.170567i	0.812578	−	0.582853i	$-0.198064\pi$
$83$	−0.897166	−	1.55394i	−0.0984768	−	0.170567i	−0.911054	+	0.412286i	$0.864730\pi$
$84$		0			0
$85$	0.411850	−	0.713345i	0.0446714	−	0.0773732i
$86$	4.15005	+	7.18810i	0.447512	+	0.775113i
$87$		0			0
$88$	3.22352	−	5.58330i	0.343628	−	0.595181i
$89$	2.06497	−	3.57663i	0.218886	−	0.379122i	−0.735582	−	0.677436i	$-0.763091\pi$
$89$	2.06497	−	3.57663i	0.218886	−	0.379122i	0.954468	+	0.298314i	$0.0964244\pi$
$90$		0			0
$91$	−0.471816	−	1.69232i	−0.0494598	−	0.177404i
$92$	−1.74387	−	3.02046i	−0.181811	−	0.314905i
$93$		0			0
$94$	2.60076			0.268248
$95$	−5.55337			−0.569763
$96$		0			0
$97$	−8.98652	−	15.5651i	−0.912443	−	1.58040i	−0.810603	−	0.585596i	$-0.800861\pi$
$97$	−8.98652	−	15.5651i	−0.912443	−	1.58040i	−0.101839	−	0.994801i	$-0.532473\pi$
$98$	0.141315	+	6.99857i	0.0142750	+	0.706963i
$99$		0			0
$100$	−0.500000	+	0.866025i	−0.0500000	+	0.0866025i
$101$	3.30960	−	5.73239i	0.329317	−	0.570394i	−0.653059	−	0.757307i	$-0.726515\pi$
$101$	3.30960	−	5.73239i	0.329317	−	0.570394i	0.982377	+	0.186912i	$0.0598481\pi$
$102$		0			0
$103$	3.05265	+	5.28735i	0.300787	+	0.520978i	0.976314	−	0.216357i	$-0.0694175\pi$
$103$	3.05265	+	5.28735i	0.300787	+	0.520978i	−0.675528	+	0.737335i	$0.736084\pi$
$104$	−0.332016	+	0.575068i	−0.0325568	+	0.0563901i
$105$		0			0
$106$	−3.27668	−	5.67538i	−0.318260	−	0.551242i
$107$	−7.32418	+	12.6859i	−0.708056	+	1.22639i	0.257522	+	0.966272i	$0.417094\pi$
$107$	−7.32418	+	12.6859i	−0.708056	+	1.22639i	−0.965577	+	0.260116i	$0.916239\pi$
$108$		0			0
$109$	−0.492869	−	0.853674i	−0.0472083	−	0.0817671i	0.841456	−	0.540326i	$-0.181699\pi$
$109$	−0.492869	−	0.853674i	−0.0472083	−	0.0817671i	−0.888664	+	0.458559i	$0.848366\pi$
$110$	6.44704			0.614701
$111$		0			0
$112$	1.85185	−	1.88962i	0.174983	−	0.178552i
$113$	−4.06408	+	7.03919i	−0.382317	+	0.662192i	−0.991393	−	0.130920i	$-0.958207\pi$
$113$	−4.06408	+	7.03919i	−0.382317	+	0.662192i	0.609076	+	0.793112i	$0.291540\pi$
$114$		0			0
$115$	1.74387	−	3.02046i	0.162616	−	0.281660i
$116$	−2.03452	−	3.52389i	−0.188900	−	0.327185i
$117$		0			0
$118$	−2.91633			−0.268470
$119$	−2.11063	−	0.542768i	−0.193482	−	0.0497554i
$120$		0			0
$121$	−15.2821	−	26.4694i	−1.38929	−	2.40631i
$122$	0.767506			0.0694868
$123$		0			0
$124$	−7.63703			−0.685826
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	6.95639			0.617280			0.308640	−	0.951179i	$-0.400126\pi$
$127$	6.95639			0.617280			0.308640	+	0.951179i	$0.400126\pi$
$128$	−1.00000			−0.0883883
$129$		0			0
$130$	−0.664031			−0.0582394
$131$	−4.88725	−	8.46497i	−0.427001	−	0.739588i	0.569604	−	0.821920i	$-0.307097\pi$
$131$	−4.88725	−	8.46497i	−0.427001	−	0.739588i	−0.996605	+	0.0823314i	$0.973763\pi$
$132$		0			0
$133$	3.94585	+	14.1531i	0.342149	+	1.22723i
$134$	−7.28641			−0.629450
$135$		0			0
$136$	0.411850	+	0.713345i	0.0353159	+	0.0611689i
$137$	−6.42809	+	11.1338i	−0.549189	+	0.951223i	0.449142	+	0.893461i	$0.351730\pi$
$137$	−6.42809	+	11.1338i	−0.549189	+	0.951223i	−0.998330	+	0.0577621i	$0.981604\pi$
$138$		0			0
$139$	−9.29552	+	16.1003i	−0.788436	+	1.36561i	0.138489	+	0.990364i	$0.455775\pi$
$139$	−9.29552	+	16.1003i	−0.788436	+	1.36561i	−0.926925	+	0.375247i	$0.877558\pi$
$140$	2.56238	+	0.658939i	0.216561	+	0.0556905i
$141$		0			0
$142$	3.44704			0.289269
$143$	2.14052	+	3.70748i	0.178999	+	0.310035i
$144$		0			0
$145$	2.03452	−	3.52389i	0.168957	−	0.292643i
$146$	−4.71172	−	8.16093i	−0.389945	−	0.675404i
$147$		0			0
$148$	−5.32042	+	9.21523i	−0.437336	+	0.757487i
$149$	−4.81823	−	8.34542i	−0.394725	−	0.683684i	0.598341	−	0.801242i	$-0.295827\pi$
$149$	−4.81823	−	8.34542i	−0.394725	−	0.683684i	−0.993066	+	0.117558i	$0.962493\pi$
$150$		0			0
$151$	−8.83973	+	15.3109i	−0.719367	+	1.24598i	0.241883	+	0.970305i	$0.422235\pi$
$151$	−8.83973	+	15.3109i	−0.719367	+	1.24598i	−0.961251	+	0.275675i	$0.911098\pi$
$152$	2.77668	−	4.80936i	0.225219	−	0.390090i
$153$		0			0
$154$	−4.58083	−	16.4306i	−0.369134	−	1.32402i
$155$	−3.81852	−	6.61386i	−0.306711	−	0.531238i
$156$		0			0
$157$	−13.0284			−1.03978			−0.519888	−	0.854234i	$-0.674026\pi$
$157$	−13.0284			−1.03978			−0.519888	+	0.854234i	$0.674026\pi$
$158$	5.40500			0.429999
$159$		0			0
$160$	−0.500000	−	0.866025i	−0.0395285	−	0.0684653i
$161$	−8.93690	−	2.29820i	−0.704326	−	0.181124i
$162$		0			0
$163$	−4.56357	+	7.90433i	−0.357446	+	0.619115i	−0.987533	−	0.157410i	$-0.949686\pi$
$163$	−4.56357	+	7.90433i	−0.357446	+	0.619115i	0.630087	+	0.776524i	$0.283019\pi$
$164$	−0.511800	+	0.886464i	−0.0399649	+	0.0692212i
$165$		0			0
$166$	0.897166	+	1.55394i	0.0696336	+	0.120609i
$167$	−2.33645	+	4.04686i	−0.180800	+	0.313155i	−0.942153	−	0.335182i	$-0.891202\pi$
$167$	−2.33645	+	4.04686i	−0.180800	+	0.313155i	0.761353	+	0.648337i	$0.224535\pi$
$168$		0			0
$169$	6.27953	+	10.8765i	0.483041	+	0.836651i
$170$	−0.411850	+	0.713345i	−0.0315875	+	0.0547111i
$171$		0			0
$172$	−4.15005	−	7.18810i	−0.316438	−	0.548088i
$173$	25.6473			1.94993			0.974966	−	0.222356i	$-0.0713747\pi$
$173$	25.6473			1.94993			0.974966	+	0.222356i	$0.0713747\pi$
$174$		0			0
$175$	0.710533	+	2.54856i	0.0537113	+	0.192653i
$176$	−3.22352	+	5.58330i	−0.242982	+	0.420857i
$177$		0			0
$178$	−2.06497	+	3.57663i	−0.154776	+	0.268079i
$179$	2.98463	+	5.16954i	0.223082	+	0.386389i	0.955742	−	0.294205i	$-0.0950549\pi$
$179$	2.98463	+	5.16954i	0.223082	+	0.386389i	−0.732660	+	0.680594i	$0.761722\pi$
$180$		0			0
$181$	−5.42323			−0.403105			−0.201553	−	0.979478i	$-0.564599\pi$
$181$	−5.42323			−0.403105			−0.201553	+	0.979478i	$0.564599\pi$
$182$	0.471816	+	1.69232i	0.0349734	+	0.125443i
$183$		0			0
$184$	1.74387	+	3.02046i	0.128559	+	0.222672i
$185$	−10.6408			−0.782330
$186$		0			0
$187$	5.31042			0.388337
$188$	−2.60076			−0.189680
$189$		0			0
$190$	5.55337			0.402884
$191$	−4.97914			−0.360278			−0.180139	−	0.983641i	$-0.557655\pi$
$191$	−4.97914			−0.360278			−0.180139	+	0.983641i	$0.557655\pi$
$192$		0			0
$193$	−23.4191			−1.68575			−0.842873	−	0.538112i	$-0.819138\pi$
$193$	−23.4191			−1.68575			−0.842873	+	0.538112i	$0.819138\pi$
$194$	8.98652	+	15.5651i	0.645194	+	1.11751i
$195$		0			0
$196$	−0.141315	−	6.99857i	−0.0100939	−	0.499898i
$197$	11.5441			0.822480			0.411240	−	0.911527i	$-0.365096\pi$
$197$	11.5441			0.822480			0.411240	+	0.911527i	$0.365096\pi$
$198$		0			0
$199$	8.07725	+	13.9902i	0.572581	+	0.991740i	0.996300	+	0.0859457i	$0.0273912\pi$
$199$	8.07725	+	13.9902i	0.572581	+	0.991740i	−0.423719	+	0.905794i	$0.639275\pi$
$200$	0.500000	−	0.866025i	0.0353553	−	0.0612372i
$201$		0			0
$202$	−3.30960	+	5.73239i	−0.232863	+	0.403330i
$203$	−10.4264	−	2.68124i	−0.731791	−	0.188186i
$204$		0			0
$205$	−1.02360			−0.0714914
$206$	−3.05265	−	5.28735i	−0.212688	−	0.368387i
$207$		0			0
$208$	0.332016	−	0.575068i	0.0230211	−	0.0398738i
$209$	−17.9014	−	31.0061i	−1.23826	−	2.14474i
$210$		0			0
$211$	13.0581	−	22.6172i	0.898954	−	1.55703i	0.0701210	−	0.997538i	$-0.477661\pi$
$211$	13.0581	−	22.6172i	0.898954	−	1.55703i	0.828833	−	0.559496i	$-0.189005\pi$
$212$	3.27668	+	5.67538i	0.225044	+	0.389787i
$213$		0			0
$214$	7.32418	−	12.6859i	0.500671	−	0.867188i
$215$	4.15005	−	7.18810i	0.283031	−	0.490224i
$216$		0			0
$217$	−14.1426	+	14.4311i	−0.960064	+	0.979645i
$218$	0.492869	+	0.853674i	0.0333813	+	0.0578181i
$219$		0			0
$220$	−6.44704			−0.434659
$221$	−0.546963			−0.0367927
$222$		0			0
$223$	−0.452684	−	0.784071i	−0.0303139	−	0.0525053i	0.850470	−	0.526023i	$-0.176317\pi$
$223$	−0.452684	−	0.784071i	−0.0303139	−	0.0525053i	−0.880784	+	0.473518i	$0.842984\pi$
$224$	−1.85185	+	1.88962i	−0.123732	+	0.126255i
$225$		0			0
$226$	4.06408	−	7.03919i	0.270339	−	0.468240i
$227$	−10.7112	+	18.5524i	−0.710928	+	1.23136i	0.253581	+	0.967314i	$0.418392\pi$
$227$	−10.7112	+	18.5524i	−0.710928	+	1.23136i	−0.964509	+	0.264050i	$0.914942\pi$
$228$		0			0
$229$	7.96073	+	13.7884i	0.526060	+	0.911163i	0.999539	+	0.0303576i	$0.00966460\pi$
$229$	7.96073	+	13.7884i	0.526060	+	0.911163i	−0.473479	+	0.880805i	$0.657002\pi$
$230$	−1.74387	+	3.02046i	−0.114987	+	0.199164i
$231$		0			0
$232$	2.03452	+	3.52389i	0.133573	+	0.231354i
$233$	3.45390	−	5.98232i	0.226272	−	0.391915i	−0.730428	−	0.682990i	$-0.760679\pi$
$233$	3.45390	−	5.98232i	0.226272	−	0.391915i	0.956700	+	0.291075i	$0.0940128\pi$
$234$		0			0
$235$	−1.30038	−	2.25233i	−0.0848276	−	0.146926i
$236$	2.91633			0.189837
$237$		0			0
$238$	2.11063	+	0.542768i	0.136812	+	0.0351824i
$239$	−7.95013	+	13.7700i	−0.514251	+	0.890709i	0.485612	+	0.874174i	$0.338597\pi$
$239$	−7.95013	+	13.7700i	−0.514251	+	0.890709i	−0.999863	+	0.0165346i	$0.994737\pi$
$240$		0			0
$241$	−4.67555	+	8.09830i	−0.301179	+	0.521657i	−0.976403	−	0.215955i	$-0.930713\pi$
$241$	−4.67555	+	8.09830i	−0.301179	+	0.521657i	0.675224	+	0.737612i	$0.264047\pi$
$242$	15.2821	+	26.4694i	0.982373	+	1.70152i
$243$		0			0
$244$	−0.767506			−0.0491346
$245$	5.99028	−	3.62167i	0.382705	−	0.231380i
$246$		0			0
$247$	1.84380	+	3.19356i	0.117318	+	0.203202i
$248$	7.63703			0.484952
$249$		0			0
$250$	1.00000			0.0632456
$251$	−14.3111			−0.903310			−0.451655	−	0.892193i	$-0.649166\pi$
$251$	−14.3111			−0.903310			−0.451655	+	0.892193i	$0.649166\pi$
$252$		0			0
$253$	22.4855			1.41365
$254$	−6.95639			−0.436483
$255$		0			0
$256$	1.00000			0.0625000
$257$	−4.08461	−	7.07475i	−0.254791	−	0.441311i	0.710048	−	0.704153i	$-0.248673\pi$
$257$	−4.08461	−	7.07475i	−0.254791	−	0.441311i	−0.964839	+	0.262843i	$0.915340\pi$
$258$		0			0
$259$	7.56067	+	27.1188i	0.469797	+	1.68508i
$260$	0.664031			0.0411815
$261$		0			0
$262$	4.88725	+	8.46497i	0.301936	+	0.522968i
$263$	8.24002	−	14.2721i	0.508101	−	0.880057i	−0.491855	−	0.870677i	$-0.663681\pi$
$263$	8.24002	−	14.2721i	0.508101	−	0.880057i	0.999956	−	0.00937977i	$-0.00298572\pi$
$264$		0			0
$265$	−3.27668	+	5.67538i	−0.201285	+	0.348636i
$266$	−3.94585	−	14.1531i	−0.241936	−	0.867780i
$267$		0			0
$268$	7.28641			0.445088
$269$	12.8752	+	22.3005i	0.785015	+	1.35969i	0.928990	+	0.370104i	$0.120678\pi$
$269$	12.8752	+	22.3005i	0.785015	+	1.35969i	−0.143976	+	0.989581i	$0.545989\pi$
$270$		0			0
$271$	−10.3794	+	17.9777i	−0.630504	+	1.09207i	0.356944	+	0.934126i	$0.383819\pi$
$271$	−10.3794	+	17.9777i	−0.630504	+	1.09207i	−0.987449	+	0.157940i	$0.949515\pi$
$272$	−0.411850	−	0.713345i	−0.0249721	−	0.0432529i
$273$		0			0
$274$	6.42809	−	11.1338i	0.388335	−	0.672616i
$275$	−3.22352	−	5.58330i	−0.194385	−	0.336685i
$276$		0			0
$277$	15.5538	−	26.9400i	0.934540	−	1.61867i	0.159087	−	0.987265i	$-0.449145\pi$
$277$	15.5538	−	26.9400i	0.934540	−	1.61867i	0.775453	−	0.631405i	$-0.217522\pi$
$278$	9.29552	−	16.1003i	0.557508	−	0.965633i
$279$		0			0
$280$	−2.56238	−	0.658939i	−0.153132	−	0.0393791i
$281$	−15.0816	−	26.1221i	−0.899692	−	1.55831i	−0.827888	−	0.560894i	$-0.810458\pi$
$281$	−15.0816	−	26.1221i	−0.899692	−	1.55831i	−0.0718045	−	0.997419i	$-0.522876\pi$
$282$		0			0
$283$	22.2721			1.32394			0.661969	−	0.749531i	$-0.269721\pi$
$283$	22.2721			1.32394			0.661969	+	0.749531i	$0.269721\pi$
$284$	−3.44704			−0.204544
$285$		0			0
$286$	−2.14052	−	3.70748i	−0.126571	−	0.219228i
$287$	0.727303	+	2.60871i	0.0429313	+	0.153987i
$288$		0			0
$289$	8.16076	−	14.1348i	0.480045	−	0.831462i
$290$	−2.03452	+	3.52389i	−0.119471	+	0.206930i
$291$		0			0
$292$	4.71172	+	8.16093i	0.275732	+	0.477583i
$293$	−10.9592	+	18.9818i	−0.640242	+	1.10893i	0.345137	+	0.938552i	$0.387832\pi$
$293$	−10.9592	+	18.9818i	−0.640242	+	1.10893i	−0.985379	+	0.170379i	$0.945501\pi$
$294$		0			0
$295$	1.45817	+	2.52562i	0.0848978	+	0.147047i
$296$	5.32042	−	9.21523i	0.309243	−	0.535624i
$297$		0			0
$298$	4.81823	+	8.34542i	0.279113	+	0.483437i
$299$	−2.31596			−0.133936
$300$		0			0
$301$	−21.2680	−	5.46926i	−1.22587	−	0.315243i
$302$	8.83973	−	15.3109i	0.508670	−	0.881041i
$303$		0			0
$304$	−2.77668	+	4.80936i	−0.159254	+	0.275836i
$305$	−0.383753	−	0.664680i	−0.0219736	−	0.0380595i
$306$		0			0
$307$	−8.76843			−0.500441			−0.250220	−	0.968189i	$-0.580503\pi$
$307$	−8.76843			−0.500441			−0.250220	+	0.968189i	$0.580503\pi$
$308$	4.58083	+	16.4306i	0.261017	+	0.936222i
$309$		0			0
$310$	3.81852	+	6.61386i	0.216877	+	0.375642i
$311$	−28.7971			−1.63293			−0.816466	−	0.577394i	$-0.804070\pi$
$311$	−28.7971			−1.63293			−0.816466	+	0.577394i	$0.804070\pi$
$312$		0			0
$313$	15.0040			0.848073			0.424037	−	0.905645i	$-0.360613\pi$
$313$	15.0040			0.848073			0.424037	+	0.905645i	$0.360613\pi$
$314$	13.0284			0.735233
$315$		0			0
$316$	−5.40500			−0.304055
$317$	23.7437			1.33358			0.666791	−	0.745245i	$-0.267668\pi$
$317$	23.7437			1.33358			0.666791	+	0.745245i	$0.267668\pi$
$318$		0			0
$319$	26.2332			1.46878
$320$	0.500000	+	0.866025i	0.0279508	+	0.0484123i
$321$		0			0
$322$	8.93690	+	2.29820i	0.498034	+	0.128074i
$323$	4.57431			0.254521
$324$		0			0
$325$	0.332016	+	0.575068i	0.0184169	+	0.0318990i
$326$	4.56357	−	7.90433i	0.252753	−	0.437780i
$327$		0			0
$328$	0.511800	−	0.886464i	0.0282595	−	0.0489468i
$329$	−4.81622	+	4.91445i	−0.265527	+	0.270943i
$330$		0			0
$331$	−3.51509			−0.193207			−0.0966033	−	0.995323i	$-0.530798\pi$
$331$	−3.51509			−0.193207			−0.0966033	+	0.995323i	$0.530798\pi$
$332$	−0.897166	−	1.55394i	−0.0492384	−	0.0852834i
$333$		0			0
$334$	2.33645	−	4.04686i	0.127845	−	0.221434i
$335$	3.64320	+	6.31021i	0.199049	+	0.344764i
$336$		0			0
$337$	16.6235	−	28.7927i	0.905538	−	1.56844i	0.0853438	−	0.996352i	$-0.472801\pi$
$337$	16.6235	−	28.7927i	0.905538	−	1.56844i	0.820194	−	0.572086i	$-0.193866\pi$
$338$	−6.27953	−	10.8765i	−0.341561	−	0.591602i
$339$		0			0
$340$	0.411850	−	0.713345i	0.0223357	−	0.0386866i
$341$	24.6181	−	42.6398i	1.33315	−	2.30908i
$342$		0			0
$343$	−13.4863	−	12.6933i	−0.728193	−	0.685372i
$344$	4.15005	+	7.18810i	0.223756	+	0.387556i
$345$		0			0
$346$	−25.6473			−1.37881
$347$	−5.36573			−0.288047			−0.144024	−	0.989574i	$-0.546004\pi$
$347$	−5.36573			−0.288047			−0.144024	+	0.989574i	$0.546004\pi$
$348$		0			0
$349$	2.39917	+	4.15548i	0.128424	+	0.222438i	0.923066	−	0.384641i	$-0.125675\pi$
$349$	2.39917	+	4.15548i	0.128424	+	0.222438i	−0.794642	+	0.607078i	$0.792341\pi$
$350$	−0.710533	−	2.54856i	−0.0379796	−	0.136226i
$351$		0			0
$352$	3.22352	−	5.58330i	0.171814	−	0.297591i
$353$	−16.2100	+	28.0765i	−0.862770	+	1.49436i	0.00647381	+	0.999979i	$0.497939\pi$
$353$	−16.2100	+	28.0765i	−0.862770	+	1.49436i	−0.869244	+	0.494383i	$0.835394\pi$
$354$		0			0
$355$	−1.72352	−	2.98522i	−0.0914748	−	0.158439i
$356$	2.06497	−	3.57663i	0.109443	−	0.189561i
$357$		0			0
$358$	−2.98463	−	5.16954i	−0.157743	−	0.273218i
$359$	5.80951	−	10.0624i	0.306614	−	0.531072i	−0.671005	−	0.741453i	$-0.734137\pi$
$359$	5.80951	−	10.0624i	0.306614	−	0.531072i	0.977619	+	0.210381i	$0.0674705\pi$
$360$		0			0
$361$	−5.91994	−	10.2536i	−0.311576	−	0.539665i
$362$	5.42323			0.285039
$363$		0			0
$364$	−0.471816	−	1.69232i	−0.0247299	−	0.0887018i
$365$	−4.71172	+	8.16093i	−0.246623	+	0.427163i
$366$		0			0
$367$	8.36773	−	14.4933i	0.436792	−	0.756546i	−0.560648	−	0.828054i	$-0.689448\pi$
$367$	8.36773	−	14.4933i	0.436792	−	0.756546i	0.997440	+	0.0715082i	$0.0227812\pi$
$368$	−1.74387	−	3.02046i	−0.0909053	−	0.157453i
$369$		0			0
$370$	10.6408			0.553191
$371$	16.7922	+	4.31827i	0.871809	+	0.224193i
$372$		0			0
$373$	6.07788	+	10.5272i	0.314701	+	0.545078i	0.979374	−	0.202057i	$-0.0647625\pi$
$373$	6.07788	+	10.5272i	0.314701	+	0.545078i	−0.664673	+	0.747134i	$0.731429\pi$
$374$	−5.31042			−0.274596
$375$		0			0
$376$	2.60076			0.134124
$377$	−2.70197			−0.139158
$378$		0			0
$379$	−18.5422			−0.952448			−0.476224	−	0.879324i	$-0.657995\pi$
$379$	−18.5422			−0.952448			−0.476224	+	0.879324i	$0.657995\pi$
$380$	−5.55337			−0.284882
$381$		0			0
$382$	4.97914			0.254755
$383$	4.16276	+	7.21011i	0.212707	+	0.368420i	0.952561	−	0.304348i	$-0.0984386\pi$
$383$	4.16276	+	7.21011i	0.212707	+	0.368420i	−0.739854	+	0.672768i	$0.765105\pi$
$384$		0			0
$385$	−11.9389	+	12.1824i	−0.608464	+	0.620875i
$386$	23.4191			1.19200
$387$		0			0
$388$	−8.98652	−	15.5651i	−0.456221	−	0.790198i
$389$	−6.54784	+	11.3412i	−0.331988	+	0.575021i	−0.982902	−	0.184131i	$-0.941053\pi$
$389$	−6.54784	+	11.3412i	−0.331988	+	0.575021i	0.650913	+	0.759152i	$0.274386\pi$
$390$		0			0
$391$	−1.43642	+	2.48796i	−0.0726430	+	0.125821i
$392$	0.141315	+	6.99857i	0.00713749	+	0.353481i
$393$		0			0
$394$	−11.5441			−0.581581
$395$	−2.70250	−	4.68087i	−0.135978	−	0.235520i
$396$		0			0
$397$	13.2600	−	22.9670i	0.665501	−	1.15268i	−0.313648	−	0.949539i	$-0.601551\pi$
$397$	13.2600	−	22.9670i	0.665501	−	1.15268i	0.979149	−	0.203143i	$-0.0651156\pi$
$398$	−8.07725	−	13.9902i	−0.404876	−	0.701266i
$399$		0			0
$400$	−0.500000	+	0.866025i	−0.0250000	+	0.0433013i
$401$	−14.6317	−	25.3429i	−0.730672	−	1.26556i	−0.956596	−	0.291417i	$-0.905873\pi$
$401$	−14.6317	−	25.3429i	−0.730672	−	1.26556i	0.225924	−	0.974145i	$-0.427460\pi$
$402$		0			0
$403$	−2.53561	+	4.39181i	−0.126308	+	0.218772i
$404$	3.30960	−	5.73239i	0.164659	−	0.285197i
$405$		0			0
$406$	10.4264	+	2.68124i	0.517454	+	0.133068i
$407$	−34.3009	−	59.4109i	−1.70023	−	2.94489i
$408$		0			0
$409$	14.1459			0.699470			0.349735	−	0.936849i	$-0.386272\pi$
$409$	14.1459			0.699470			0.349735	+	0.936849i	$0.386272\pi$
$410$	1.02360			0.0505520
$411$		0			0
$412$	3.05265	+	5.28735i	0.150393	+	0.260489i
$413$	5.40061	−	5.51076i	0.265747	−	0.271167i
$414$		0			0
$415$	0.897166	−	1.55394i	0.0440402	−	0.0762798i
$416$	−0.332016	+	0.575068i	−0.0162784	+	0.0281950i
$417$		0			0
$418$	17.9014	+	31.0061i	0.875585	+	1.51656i
$419$	16.6209	−	28.7882i	0.811982	−	1.40639i	−0.0994931	−	0.995038i	$-0.531722\pi$
$419$	16.6209	−	28.7882i	0.811982	−	1.40639i	0.911475	−	0.411356i	$-0.134945\pi$
$420$		0			0
$421$	9.58351	+	16.5991i	0.467072	+	0.808992i	0.999292	−	0.0376136i	$-0.0119756\pi$
$421$	9.58351	+	16.5991i	0.467072	+	0.808992i	−0.532220	+	0.846606i	$0.678642\pi$
$422$	−13.0581	+	22.6172i	−0.635657	+	1.10099i
$423$		0			0
$424$	−3.27668	−	5.67538i	−0.159130	−	0.275621i
$425$	0.823700			0.0399553
$426$		0			0
$427$	−1.42131	+	1.45029i	−0.0687818	+	0.0701847i
$428$	−7.32418	+	12.6859i	−0.354028	+	0.613194i
$429$		0			0
$430$	−4.15005	+	7.18810i	−0.200133	+	0.346641i
$431$	−9.77141	−	16.9246i	−0.470672	−	0.815228i	0.528765	−	0.848768i	$-0.322655\pi$
$431$	−9.77141	−	16.9246i	−0.470672	−	0.815228i	−0.999437	+	0.0335402i	$0.989322\pi$
$432$		0			0
$433$	20.6650			0.993097			0.496548	−	0.868009i	$-0.334601\pi$
$433$	20.6650			0.993097			0.496548	+	0.868009i	$0.334601\pi$
$434$	14.1426	−	14.4311i	0.678868	−	0.692714i
$435$		0			0
$436$	−0.492869	−	0.853674i	−0.0236041	−	0.0408836i
$437$	19.3687			0.926528
$438$		0			0
$439$	17.5808			0.839088			0.419544	−	0.907735i	$-0.362190\pi$
$439$	17.5808			0.839088			0.419544	+	0.907735i	$0.362190\pi$
$440$	6.44704			0.307350
$441$		0			0
$442$	0.546963			0.0260164
$443$	−16.3960			−0.778996			−0.389498	−	0.921027i	$-0.627352\pi$
$443$	−16.3960			−0.778996			−0.389498	+	0.921027i	$0.627352\pi$
$444$		0			0
$445$	4.12993			0.195778
$446$	0.452684	+	0.784071i	0.0214352	+	0.0371268i
$447$		0			0
$448$	1.85185	−	1.88962i	0.0874916	−	0.0892761i
$449$	33.5534			1.58348			0.791740	−	0.610858i	$-0.209175\pi$
$449$	33.5534			1.58348			0.791740	+	0.610858i	$0.209175\pi$
$450$		0			0
$451$	−3.29960	−	5.71507i	−0.155372	−	0.269112i
$452$	−4.06408	+	7.03919i	−0.191158	+	0.331096i
$453$		0			0
$454$	10.7112	−	18.5524i	0.502702	−	0.870706i
$455$	1.22969	−	1.25477i	0.0576485	−	0.0588243i
$456$		0			0
$457$	19.5171			0.912971			0.456486	−	0.889731i	$-0.349108\pi$
$457$	19.5171			0.912971			0.456486	+	0.889731i	$0.349108\pi$
$458$	−7.96073	−	13.7884i	−0.371981	−	0.644289i
$459$		0			0
$460$	1.74387	−	3.02046i	0.0813082	−	0.140830i
$461$	15.2287	+	26.3769i	0.709272	+	1.22850i	0.965127	+	0.261781i	$0.0843097\pi$
$461$	15.2287	+	26.3769i	0.709272	+	1.22850i	−0.255855	+	0.966715i	$0.582357\pi$
$462$		0			0
$463$	−7.56973	+	13.1112i	−0.351795	+	0.609327i	−0.986564	−	0.163375i	$-0.947762\pi$
$463$	−7.56973	+	13.1112i	−0.351795	+	0.609327i	0.634769	+	0.772702i	$0.281095\pi$
$464$	−2.03452	−	3.52389i	−0.0944501	−	0.163592i
$465$		0			0
$466$	−3.45390	+	5.98232i	−0.159999	+	0.277126i
$467$	−0.118683	+	0.205565i	−0.00549199	+	0.00951241i	−0.868758	−	0.495236i	$-0.835081\pi$
$467$	−0.118683	+	0.205565i	−0.00549199	+	0.00951241i	0.863266	+	0.504749i	$0.168415\pi$
$468$		0			0
$469$	13.4933	−	13.7685i	0.623064	−	0.635772i
$470$	1.30038	+	2.25233i	0.0599822	+	0.103892i
$471$		0			0
$472$	−2.91633			−0.134235
$473$	53.5111			2.46044
$474$		0			0
$475$	−2.77668	−	4.80936i	−0.127403	−	0.220668i
$476$	−2.11063	−	0.542768i	−0.0967408	−	0.0248777i
$477$		0			0
$478$	7.95013	−	13.7700i	0.363630	−	0.629826i
$479$	−6.76029	+	11.7092i	−0.308885	+	0.535005i	−0.978119	−	0.208047i	$-0.933289\pi$
$479$	−6.76029	+	11.7092i	−0.308885	+	0.535005i	0.669233	+	0.743052i	$0.266623\pi$
$480$		0			0
$481$	3.53292	+	6.11920i	0.161087	+	0.279012i
$482$	4.67555	−	8.09830i	0.212966	−	0.368867i
$483$		0			0
$484$	−15.2821	−	26.4694i	−0.694643	−	1.20316i
$485$	8.98652	−	15.5651i	0.408057	−	0.706775i
$486$		0			0
$487$	19.3582	+	33.5294i	0.877203	+	1.51936i	0.854397	+	0.519620i	$0.173927\pi$
$487$	19.3582	+	33.5294i	0.877203	+	1.51936i	0.0228055	+	0.999740i	$0.492740\pi$
$488$	0.767506			0.0347434
$489$		0			0
$490$	−5.99028	+	3.62167i	−0.270613	+	0.163610i
$491$	−5.10089	+	8.83500i	−0.230200	+	0.398718i	−0.957867	−	0.287213i	$-0.907271\pi$
$491$	−5.10089	+	8.83500i	−0.230200	+	0.398718i	0.727667	+	0.685931i	$0.240605\pi$
$492$		0			0
$493$	−1.67583	+	2.90263i	−0.0754757	+	0.130728i
$494$	−1.84380	−	3.19356i	−0.0829567	−	0.143685i
$495$		0			0
$496$	−7.63703			−0.342913
$497$	−6.38339	+	6.51358i	−0.286334	+	0.292174i
$498$		0			0
$499$	5.34312	+	9.25456i	0.239191	+	0.414291i	0.960482	−	0.278341i	$-0.0897845\pi$
$499$	5.34312	+	9.25456i	0.239191	+	0.414291i	−0.721291	+	0.692632i	$0.756451\pi$
$500$	−1.00000			−0.0447214
$501$		0			0
$502$	14.3111			0.638736
$503$	5.82335			0.259651			0.129825	−	0.991537i	$-0.458558\pi$
$503$	5.82335			0.259651			0.129825	+	0.991537i	$0.458558\pi$
$504$		0			0
$505$	6.61920			0.294550
$506$	−22.4855			−0.999604
$507$		0			0
$508$	6.95639			0.308640
$509$	14.7801	+	25.5999i	0.655118	+	1.13470i	0.981864	+	0.189585i	$0.0607144\pi$
$509$	14.7801	+	25.5999i	0.655118	+	1.13470i	−0.326746	+	0.945112i	$0.605952\pi$
$510$		0			0
$511$	24.1464	+	6.20946i	1.06818	+	0.274691i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	4.08461	+	7.07475i	0.180164	+	0.312054i
$515$	−3.05265	+	5.28735i	−0.134516	+	0.232988i
$516$		0			0
$517$	8.38361	−	14.5208i	0.368711	−	0.638626i
$518$	−7.56067	−	27.1188i	−0.332197	−	1.19153i
$519$		0			0
$520$	−0.664031			−0.0291197
$521$	19.4542	+	33.6957i	0.852306	+	1.47624i	0.879122	+	0.476596i	$0.158130\pi$
$521$	19.4542	+	33.6957i	0.852306	+	1.47624i	−0.0268165	+	0.999640i	$0.508537\pi$
$522$		0			0
$523$	9.81571	−	17.0013i	0.429211	−	0.743415i	−0.567592	−	0.823310i	$-0.692125\pi$
$523$	9.81571	−	17.0013i	0.429211	−	0.743415i	0.996803	+	0.0798944i	$0.0254583\pi$
$524$	−4.88725	−	8.46497i	−0.213501	−	0.369794i
$525$		0			0
$526$	−8.24002	+	14.2721i	−0.359282	+	0.622294i
$527$	3.14531	+	5.44784i	0.137012	+	0.237312i
$528$		0			0
$529$	5.41786	−	9.38402i	0.235559	−	0.408001i
$530$	3.27668	−	5.67538i	0.142330	−	0.246523i
$531$		0			0
$532$	3.94585	+	14.1531i	0.171074	+	0.613613i
$533$	0.339852	+	0.588640i	0.0147206	+	0.0254968i
$534$		0			0
$535$	−14.6484			−0.633304
$536$	−7.28641			−0.314725
$537$		0			0
$538$	−12.8752	−	22.3005i	−0.555089	−	0.961443i
$539$	39.5306	+	21.7710i	1.70271	+	0.937744i
$540$		0			0
$541$	−0.957774	+	1.65891i	−0.0411779	+	0.0713222i	−0.885880	−	0.463915i	$-0.846444\pi$
$541$	−0.957774	+	1.65891i	−0.0411779	+	0.0713222i	0.844702	+	0.535237i	$0.179778\pi$
$542$	10.3794	−	17.9777i	0.445834	−	0.772207i
$543$		0			0
$544$	0.411850	+	0.713345i	0.0176579	+	0.0305844i
$545$	0.492869	−	0.853674i	0.0211122	−	0.0365674i
$546$		0			0
$547$	0.366029	+	0.633981i	0.0156503	+	0.0271071i	0.873744	−	0.486385i	$-0.161685\pi$
$547$	0.366029	+	0.633981i	0.0156503	+	0.0271071i	−0.858094	+	0.513492i	$0.828351\pi$
$548$	−6.42809	+	11.1338i	−0.274594	+	0.475611i
$549$		0			0
$550$	3.22352	+	5.58330i	0.137451	+	0.238073i
$551$	22.5968			0.962657
$552$		0			0
$553$	−10.0092	+	10.2134i	−0.425636	+	0.434318i
$554$	−15.5538	+	26.9400i	−0.660819	+	1.14457i
$555$		0			0
$556$	−9.29552	+	16.1003i	−0.394218	+	0.682805i
$557$	2.32694	+	4.03038i	0.0985957	+	0.170773i	0.911104	−	0.412177i	$-0.135232\pi$
$557$	2.32694	+	4.03038i	0.0985957	+	0.170773i	−0.812508	+	0.582950i	$0.801898\pi$
$558$		0			0
$559$	−5.51153			−0.233113
$560$	2.56238	+	0.658939i	0.108280	+	0.0278452i
$561$		0			0
$562$	15.0816	+	26.1221i	0.636178	+	1.10189i
$563$	30.9455			1.30420			0.652100	−	0.758133i	$-0.273888\pi$
$563$	30.9455			1.30420			0.652100	+	0.758133i	$0.273888\pi$
$564$		0			0
$565$	−8.12816			−0.341954
$566$	−22.2721			−0.936166
$567$		0			0
$568$	3.44704			0.144634
$569$	21.2645			0.891453			0.445727	−	0.895169i	$-0.352945\pi$
$569$	21.2645			0.891453			0.445727	+	0.895169i	$0.352945\pi$
$570$		0			0
$571$	−3.81210			−0.159531			−0.0797656	−	0.996814i	$-0.525417\pi$
$571$	−3.81210			−0.159531			−0.0797656	+	0.996814i	$0.525417\pi$
$572$	2.14052	+	3.70748i	0.0894995	+	0.155018i
$573$		0			0
$574$	−0.727303	−	2.60871i	−0.0303570	−	0.108885i
$575$	3.48773			0.145448
$576$		0			0
$577$	−6.39547	−	11.0773i	−0.266247	−	0.461153i	0.701643	−	0.712529i	$-0.252450\pi$
$577$	−6.39547	−	11.0773i	−0.266247	−	0.461153i	−0.967890	+	0.251376i	$0.919117\pi$
$578$	−8.16076	+	14.1348i	−0.339443	+	0.587932i
$579$		0			0
$580$	2.03452	−	3.52389i	0.0844787	−	0.146321i
$581$	−4.59776	−	1.18235i	−0.190747	−	0.0490523i
$582$		0			0
$583$	−42.2498			−1.74981
$584$	−4.71172	−	8.16093i	−0.194972	−	0.337702i
$585$		0			0
$586$	10.9592	−	18.9818i	0.452719	−	0.784133i
$587$	0.214025	+	0.370702i	0.00883376	+	0.0153005i	0.870408	−	0.492330i	$-0.163855\pi$
$587$	0.214025	+	0.370702i	0.00883376	+	0.0153005i	−0.861575	+	0.507631i	$0.830521\pi$
$588$		0			0
$589$	21.2056	−	36.7292i	0.873762	−	1.51340i
$590$	−1.45817	−	2.52562i	−0.0600318	−	0.103978i
$591$		0			0
$592$	−5.32042	+	9.21523i	−0.218668	+	0.378744i
$593$	1.28439	−	2.22463i	0.0527437	−	0.0913548i	−0.838448	−	0.544981i	$-0.816537\pi$
$593$	1.28439	−	2.22463i	0.0527437	−	0.0913548i	0.891192	+	0.453627i	$0.149870\pi$
$594$		0			0
$595$	−0.585266	−	2.09925i	−0.0239936	−	0.0860607i
$596$	−4.81823	−	8.34542i	−0.197363	−	0.341842i
$597$		0			0
$598$	2.31596			0.0947068
$599$	−22.4250			−0.916263			−0.458131	−	0.888885i	$-0.651481\pi$
$599$	−22.4250			−0.916263			−0.458131	+	0.888885i	$0.651481\pi$
$600$		0			0
$601$	10.5605	+	18.2913i	0.430772	+	0.746119i	0.996940	−	0.0781708i	$-0.0249080\pi$
$601$	10.5605	+	18.2913i	0.430772	+	0.746119i	−0.566168	+	0.824290i	$0.691575\pi$
$602$	21.2680	+	5.46926i	0.866820	+	0.222910i
$603$		0			0
$604$	−8.83973	+	15.3109i	−0.359684	+	0.622990i
$605$	15.2821	−	26.4694i	0.621307	−	1.07614i
$606$		0			0
$607$	8.80365	+	15.2484i	0.357329	+	0.618912i	0.987514	−	0.157533i	$-0.0503541\pi$
$607$	8.80365	+	15.2484i	0.357329	+	0.618912i	−0.630185	+	0.776445i	$0.717021\pi$
$608$	2.77668	−	4.80936i	0.112609	−	0.195045i
$609$		0			0
$610$	0.383753	+	0.664680i	0.0155377	+	0.0269121i
$611$	−0.863495	+	1.49562i	−0.0349333	+	0.0605062i
$612$		0			0
$613$	−5.45250	−	9.44400i	−0.220224	−	0.381440i	0.734652	−	0.678444i	$-0.237346\pi$
$613$	−5.45250	−	9.44400i	−0.220224	−	0.381440i	−0.954876	+	0.297005i	$0.904012\pi$
$614$	8.76843			0.353865
$615$		0			0
$616$	−4.58083	−	16.4306i	−0.184567	−	0.662009i
$617$	3.11423	−	5.39400i	0.125374	−	0.217154i	−0.796505	−	0.604632i	$-0.793320\pi$
$617$	3.11423	−	5.39400i	0.125374	−	0.217154i	0.921879	+	0.387478i	$0.126654\pi$
$618$		0			0
$619$	15.1300	−	26.2060i	0.608128	−	1.05331i	−0.383421	−	0.923574i	$-0.625254\pi$
$619$	15.1300	−	26.2060i	0.608128	−	1.05331i	0.991549	−	0.129734i	$-0.0414124\pi$
$620$	−3.81852	−	6.61386i	−0.153355	−	0.265619i
$621$		0			0
$622$	28.7971			1.15466
$623$	−2.93445	−	10.5254i	−0.117566	−	0.421690i
$624$		0			0
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−15.0040			−0.599678
$627$		0			0
$628$	−13.0284			−0.519888
$629$	8.76486			0.349478
$630$		0			0
$631$	−18.3294			−0.729681			−0.364841	−	0.931070i	$-0.618876\pi$
$631$	−18.3294			−0.729681			−0.364841	+	0.931070i	$0.618876\pi$
$632$	5.40500			0.214999
$633$		0			0
$634$	−23.7437			−0.942984
$635$	3.47820	+	6.02441i	0.138028	+	0.239072i
$636$		0			0
$637$	−4.07157	−	2.24237i	−0.161322	−	0.0888459i
$638$	−26.2332			−1.03858
$639$		0			0
$640$	−0.500000	−	0.866025i	−0.0197642	−	0.0342327i
$641$	16.0332	−	27.7703i	0.633273	−	1.09686i	−0.353605	−	0.935395i	$-0.615044\pi$
$641$	16.0332	−	27.7703i	0.633273	−	1.09686i	0.986878	−	0.161467i	$-0.0516225\pi$
$642$		0			0
$643$	10.2036	−	17.6732i	0.402391	−	0.696962i	−0.591623	−	0.806215i	$-0.701512\pi$
$643$	10.2036	−	17.6732i	0.402391	−	0.696962i	0.994014	+	0.109253i	$0.0348458\pi$
$644$	−8.93690	−	2.29820i	−0.352163	−	0.0905618i
$645$		0			0
$646$	−4.57431			−0.179974
$647$	−8.83588	−	15.3042i	−0.347374	−	0.601670i	0.638408	−	0.769698i	$-0.279593\pi$
$647$	−8.83588	−	15.3042i	−0.347374	−	0.601670i	−0.985782	+	0.168028i	$0.946260\pi$
$648$		0			0
$649$	−9.40086	+	16.2828i	−0.369016	+	0.639154i
$650$	−0.332016	−	0.575068i	−0.0130227	−	0.0225560i
$651$		0			0
$652$	−4.56357	+	7.90433i	−0.178723	+	0.309557i
$653$	−8.41493	−	14.5751i	−0.329302	−	0.570367i	0.653072	−	0.757296i	$-0.273480\pi$
$653$	−8.41493	−	14.5751i	−0.329302	−	0.570367i	−0.982373	+	0.186929i	$0.940147\pi$
$654$		0			0
$655$	4.88725	−	8.46497i	0.190961	−	0.330754i
$656$	−0.511800	+	0.886464i	−0.0199824	+	0.0346106i
$657$		0			0
$658$	4.81622	−	4.91445i	0.187756	−	0.191585i
$659$	10.8307	+	18.7593i	0.421904	+	0.730760i	0.996126	−	0.0879404i	$-0.0280285\pi$
$659$	10.8307	+	18.7593i	0.421904	+	0.730760i	−0.574221	+	0.818700i	$0.694695\pi$
$660$		0			0
$661$	−26.9171			−1.04696			−0.523478	−	0.852039i	$-0.675366\pi$
$661$	−26.9171			−1.04696			−0.523478	+	0.852039i	$0.675366\pi$
$662$	3.51509			0.136618
$663$		0			0
$664$	0.897166	+	1.55394i	0.0348168	+	0.0603045i
$665$	−10.2840	+	10.4937i	−0.398796	+	0.406930i
$666$		0			0
$667$	−7.09585	+	12.2904i	−0.274752	+	0.475885i
$668$	−2.33645	+	4.04686i	−0.0904001	+	0.156578i
$669$		0			0
$670$	−3.64320	−	6.31021i	−0.140749	−	0.243785i
$671$	2.47407	−	4.28522i	0.0955104	−	0.165429i
$672$		0			0
$673$	−6.59897	−	11.4298i	−0.254372	−	0.440585i	0.710353	−	0.703846i	$-0.248535\pi$
$673$	−6.59897	−	11.4298i	−0.254372	−	0.440585i	−0.964725	+	0.263261i	$0.915202\pi$
$674$	−16.6235	+	28.7927i	−0.640312	+	1.10905i
$675$		0			0
$676$	6.27953	+	10.8765i	0.241520	+	0.418326i
$677$	38.1698			1.46698			0.733492	−	0.679698i	$-0.237889\pi$
$677$	38.1698			1.46698			0.733492	+	0.679698i	$0.237889\pi$
$678$		0			0
$679$	−46.0538	−	11.8431i	−1.76738	−	0.454497i
$680$	−0.411850	+	0.713345i	−0.0157937	+	0.0273555i
$681$		0			0
$682$	−24.6181	+	42.6398i	−0.942676	+	1.63276i
$683$	−10.2925	−	17.8271i	−0.393830	−	0.682134i	0.599121	−	0.800659i	$-0.295517\pi$
$683$	−10.2925	−	17.8271i	−0.393830	−	0.682134i	−0.992951	+	0.118525i	$0.962184\pi$
$684$		0			0
$685$	−12.8562			−0.491209
$686$	13.4863	+	12.6933i	0.514910	+	0.484631i
$687$		0			0
$688$	−4.15005	−	7.18810i	−0.158219	−	0.274044i
$689$	4.35164			0.165784
$690$		0			0
$691$	−21.6237			−0.822605			−0.411303	−	0.911499i	$-0.634926\pi$
$691$	−21.6237			−0.822605			−0.411303	+	0.911499i	$0.634926\pi$
$692$	25.6473			0.974966
$693$		0			0
$694$	5.36573			0.203680
$695$	−18.5910			−0.705198
$696$		0			0
$697$	0.843140			0.0319362
$698$	−2.39917	−	4.15548i	−0.0908097	−	0.157287i
$699$		0			0
$700$	0.710533	+	2.54856i	0.0268556	+	0.0963264i
$701$	−27.0870			−1.02306			−0.511530	−	0.859265i	$-0.670921\pi$
$701$	−27.0870			−1.02306			−0.511530	+	0.859265i	$0.670921\pi$
$702$		0			0
$703$	−29.5462	−	51.1756i	−1.11436	−	1.93012i
$704$	−3.22352	+	5.58330i	−0.121491	+	0.210428i
$705$		0			0
$706$	16.2100	−	28.0765i	0.610071	−	1.05667i
$707$	−4.70316	−	16.8694i	−0.176881	−	0.634439i
$708$		0			0
$709$	−11.6415			−0.437208			−0.218604	−	0.975814i	$-0.570150\pi$
$709$	−11.6415			−0.437208			−0.218604	+	0.975814i	$0.570150\pi$
$710$	1.72352	+	2.98522i	0.0646825	+	0.112033i
$711$		0			0
$712$	−2.06497	+	3.57663i	−0.0773879	+	0.134040i
$713$	13.3180	+	23.0674i	0.498761	+	0.863880i
$714$		0			0
$715$	−2.14052	+	3.70748i	−0.0800508	+	0.138652i
$716$	2.98463	+	5.16954i	0.111541	+	0.193195i
$717$		0			0
$718$	−5.80951	+	10.0624i	−0.216809	+	0.375524i
$719$	−10.0296	+	17.3718i	−0.374040	+	0.647857i	−0.990183	−	0.139778i	$-0.955361\pi$
$719$	−10.0296	+	17.3718i	−0.374040	+	0.647857i	0.616142	+	0.787635i	$0.288695\pi$
$720$		0			0
$721$	15.6441	+	4.02302i	0.582617	+	0.149825i
$722$	5.91994	+	10.2536i	0.220317	+	0.381601i
$723$		0			0
$724$	−5.42323			−0.201553
$725$	4.06903			0.151120
$726$		0			0
$727$	22.3086	+	38.6397i	0.827381	+	1.43307i	0.900086	+	0.435712i	$0.143503\pi$
$727$	22.3086	+	38.6397i	0.827381	+	1.43307i	−0.0727056	+	0.997353i	$0.523163\pi$
$728$	0.471816	+	1.69232i	0.0174867	+	0.0627216i
$729$		0			0
$730$	4.71172	−	8.16093i	0.174388	−	0.302050i
$731$	−3.41840	+	5.92084i	−0.126434	+	0.218990i
$732$		0			0
$733$	14.3012	+	24.7703i	0.528225	+	0.914913i	0.999458	+	0.0329046i	$0.0104757\pi$
$733$	14.3012	+	24.7703i	0.528225	+	0.914913i	−0.471233	+	0.882009i	$0.656191\pi$
$734$	−8.36773	+	14.4933i	−0.308859	+	0.534959i
$735$		0			0
$736$	1.74387	+	3.02046i	0.0642797	+	0.111336i
$737$	−23.4879	+	40.6822i	−0.865187	+	1.49855i
$738$		0			0
$739$	15.3554	+	26.5963i	0.564858	+	0.978362i	0.997063	+	0.0765870i	$0.0244023\pi$
$739$	15.3554	+	26.5963i	0.564858	+	0.978362i	−0.432205	+	0.901775i	$0.642264\pi$
$740$	−10.6408			−0.391165
$741$		0			0
$742$	−16.7922	−	4.31827i	−0.616462	−	0.158529i
$743$	14.6908	−	25.4452i	0.538953	−	0.933493i	−0.460008	−	0.887915i	$-0.652154\pi$
$743$	14.6908	−	25.4452i	0.538953	−	0.933493i	0.998961	−	0.0455786i	$-0.0145131\pi$
$744$		0			0
$745$	4.81823	−	8.34542i	0.176526	−	0.305753i
$746$	−6.07788	−	10.5272i	−0.222527	−	0.385428i
$747$		0			0
$748$	5.31042			0.194168
$749$	10.4082	+	37.3322i	0.380306	+	1.36409i
$750$		0			0
$751$	−24.0333	−	41.6269i	−0.876987	−	1.51899i	−0.854631	−	0.519236i	$-0.826217\pi$
$751$	−24.0333	−	41.6269i	−0.876987	−	1.51899i	−0.0223556	−	0.999750i	$-0.507117\pi$
$752$	−2.60076			−0.0948401
$753$		0			0
$754$	2.70197			0.0983998
$755$	−17.6795			−0.643422
$756$		0			0
$757$	−34.8053			−1.26502			−0.632510	−	0.774553i	$-0.717975\pi$
$757$	−34.8053			−1.26502			−0.632510	+	0.774553i	$0.717975\pi$
$758$	18.5422			0.673483
$759$		0			0
$760$	5.55337			0.201442
$761$	4.22209	+	7.31287i	0.153050	+	0.265091i	0.932347	−	0.361564i	$-0.117757\pi$
$761$	4.22209	+	7.31287i	0.153050	+	0.265091i	−0.779297	+	0.626655i	$0.784424\pi$
$762$		0			0
$763$	−2.52584	−	0.649540i	−0.0914414	−	0.0235149i
$764$	−4.97914			−0.180139
$765$		0			0
$766$	−4.16276	−	7.21011i	−0.150407	−	0.260512i
$767$	0.968269	−	1.67709i	0.0349622	−	0.0605562i
$768$		0			0
$769$	−17.1205	+	29.6535i	−0.617380	+	1.06933i	0.372582	+	0.927999i	$0.378473\pi$
$769$	−17.1205	+	29.6535i	−0.617380	+	1.06933i	−0.989962	+	0.141334i	$0.954861\pi$
$770$	11.9389	−	12.1824i	0.430249	−	0.439025i
$771$		0			0
$772$	−23.4191			−0.842873
$773$	5.43968	+	9.42179i	0.195652	+	0.338878i	0.947114	−	0.320898i	$-0.103985\pi$
$773$	5.43968	+	9.42179i	0.195652	+	0.338878i	−0.751462	+	0.659776i	$0.770651\pi$
$774$		0			0
$775$	3.81852	−	6.61386i	0.137165	−	0.237577i
$776$	8.98652	+	15.5651i	0.322597	+	0.558755i
$777$		0			0
$778$	6.54784	−	11.3412i	0.234751	−	0.406601i
$779$	−2.84222	−	4.92286i	−0.101833	−	0.176380i
$780$		0			0
$781$	11.1116	−	19.2458i	0.397604	−	0.688670i
$782$	1.43642	−	2.48796i	0.0513664	−	0.0889692i
$783$		0			0
$784$	−0.141315	−	6.99857i	−0.00504697	−	0.249949i
$785$	−6.51418	−	11.2829i	−0.232501	−	0.402704i
$786$		0			0
$787$	39.1930			1.39708			0.698540	−	0.715571i	$-0.253834\pi$
$787$	39.1930			1.39708			0.698540	+	0.715571i	$0.253834\pi$
$788$	11.5441			0.411240
$789$		0			0
$790$	2.70250	+	4.68087i	0.0961507	+	0.166538i
$791$	5.77533	+	20.7151i	0.205347	+	0.736544i
$792$		0			0
$793$	−0.254824	+	0.441368i	−0.00904907	+	0.0156734i
$794$	−13.2600	+	22.9670i	−0.470581	+	0.815069i
$795$		0			0
$796$	8.07725	+	13.9902i	0.286291	+	0.495870i
$797$	−4.92224	+	8.52558i	−0.174355	+	0.301991i	−0.939938	−	0.341346i	$-0.889117\pi$
$797$	−4.92224	+	8.52558i	−0.174355	+	0.301991i	0.765583	+	0.643337i	$0.222451\pi$
$798$		0			0
$799$	1.07113	+	1.85524i	0.0378937	+	0.0656338i
$800$	0.500000	−	0.866025i	0.0176777	−	0.0306186i
$801$		0			0
$802$	14.6317	+	25.3429i	0.516663	+	0.894887i
$803$	−60.7532			−2.14393
$804$		0			0
$805$	−2.47815	−	8.88868i	−0.0873433	−	0.313285i
$806$	2.53561	−	4.39181i	0.0893132	−	0.154695i
$807$		0			0
$808$	−3.30960	+	5.73239i	−0.116431	+	0.201665i
$809$	−23.6574	−	40.9759i	−0.831751	−	1.44064i	−0.896648	−	0.442744i	$-0.854005\pi$
$809$	−23.6574	−	40.9759i	−0.831751	−	1.44064i	0.0648970	−	0.997892i	$-0.479328\pi$
$810$		0			0
$811$	−46.7680			−1.64225			−0.821124	−	0.570750i	$-0.806652\pi$
$811$	−46.7680			−1.64225			−0.821124	+	0.570750i	$0.806652\pi$
$812$	−10.4264	−	2.68124i	−0.365895	−	0.0940932i
$813$		0			0
$814$	34.3009	+	59.4109i	1.20225	+	2.08235i
$815$	−9.12713			−0.319709
$816$		0			0
$817$	46.0935			1.61261
$818$	−14.1459			−0.494600
$819$		0			0
$820$	−1.02360			−0.0357457
$821$	26.4273			0.922319			0.461159	−	0.887317i	$-0.347434\pi$
$821$	26.4273			0.922319			0.461159	+	0.887317i	$0.347434\pi$
$822$		0			0
$823$	2.27855			0.0794252			0.0397126	−	0.999211i	$-0.487356\pi$
$823$	2.27855			0.0794252			0.0397126	+	0.999211i	$0.487356\pi$
$824$	−3.05265	−	5.28735i	−0.106344	−	0.184193i
$825$		0			0
$826$	−5.40061	+	5.51076i	−0.187911	+	0.191744i
$827$	−49.2996			−1.71431			−0.857157	−	0.515055i	$-0.827771\pi$
$827$	−49.2996			−1.71431			−0.857157	+	0.515055i	$0.827771\pi$
$828$		0			0
$829$	−3.70244	−	6.41282i	−0.128591	−	0.222726i	0.794540	−	0.607212i	$-0.207712\pi$
$829$	−3.70244	−	6.41282i	−0.128591	−	0.222726i	−0.923131	+	0.384486i	$0.874379\pi$
$830$	−0.897166	+	1.55394i	−0.0311411	+	0.0539380i
$831$		0			0
$832$	0.332016	−	0.575068i	0.0115106	−	0.0199369i
$833$	−4.93420	+	2.98317i	−0.170960	+	0.103361i
$834$		0			0
$835$	−4.67291			−0.161713
$836$	−17.9014	−	31.0061i	−0.619132	−	1.07237i
$837$		0			0
$838$	−16.6209	+	28.7882i	−0.574158	+	0.994471i
$839$	−20.2441	−	35.0638i	−0.698904	−	1.21054i	−0.968847	−	0.247660i	$-0.920338\pi$
$839$	−20.2441	−	35.0638i	−0.698904	−	1.21054i	0.269943	−	0.962876i	$-0.412995\pi$
$840$		0			0
$841$	6.22148	−	10.7759i	0.214534	−	0.371584i
$842$	−9.58351	−	16.5991i	−0.330270	−	0.572044i
$843$		0			0
$844$	13.0581	−	22.6172i	0.449477	−	0.778517i
$845$	−6.27953	+	10.8765i	−0.216022	+	0.374162i
$846$		0			0
$847$	−78.3173	−	20.1400i	−2.69102	−	0.692018i
$848$	3.27668	+	5.67538i	0.112522	+	0.194893i
$849$		0			0
$850$	−0.823700			−0.0282527
$851$	37.1124			1.27220
$852$		0			0
$853$	−27.6859	−	47.9534i	−0.947947	−	1.64189i	−0.749741	−	0.661732i	$-0.769822\pi$
$853$	−27.6859	−	47.9534i	−0.947947	−	1.64189i	−0.198206	−	0.980160i	$-0.563512\pi$
$854$	1.42131	−	1.45029i	0.0486361	−	0.0496280i
$855$		0			0
$856$	7.32418	−	12.6859i	0.250335	−	0.433594i
$857$	−15.4437	+	26.7493i	−0.527547	+	0.913739i	0.471937	+	0.881632i	$0.343555\pi$
$857$	−15.4437	+	26.7493i	−0.527547	+	0.913739i	−0.999484	+	0.0321065i	$0.989778\pi$
$858$		0			0
$859$	−10.2344	−	17.7266i	−0.349195	−	0.604823i	0.636912	−	0.770936i	$-0.280211\pi$
$859$	−10.2344	−	17.7266i	−0.349195	−	0.604823i	−0.986107	+	0.166114i	$0.946878\pi$
$860$	4.15005	−	7.18810i	0.141516	−	0.245112i
$861$		0			0
$862$	9.77141	+	16.9246i	0.332815	+	0.576453i
$863$	−5.65435	+	9.79362i	−0.192476	+	0.333379i	−0.946070	−	0.323961i	$-0.894985\pi$
$863$	−5.65435	+	9.79362i	−0.192476	+	0.333379i	0.753594	+	0.657340i	$0.228319\pi$
$864$		0			0
$865$	12.8237	+	22.2112i	0.436018	+	0.755205i
$866$	−20.6650			−0.702225
$867$		0			0
$868$	−14.1426	+	14.4311i	−0.480032	+	0.489823i
$869$	17.4231	−	30.1777i	0.591039	−	1.02371i
$870$		0			0
$871$	2.41920	−	4.19018i	0.0819715	−	0.141979i
$872$	0.492869	+	0.853674i	0.0166906	+	0.0289090i
$873$		0			0
$874$	−19.3687			−0.655154
$875$	−1.85185	+	1.88962i	−0.0626039	+	0.0638808i
$876$		0			0
$877$	−12.0717	−	20.9088i	−0.407633	−	0.706040i	0.586991	−	0.809593i	$-0.300312\pi$
$877$	−12.0717	−	20.9088i	−0.407633	−	0.706040i	−0.994624	+	0.103553i	$0.966979\pi$
$878$	−17.5808			−0.593325
$879$		0			0
$880$	−6.44704			−0.217330
$881$	−22.1574			−0.746502			−0.373251	−	0.927730i	$-0.621757\pi$
$881$	−22.1574			−0.746502			−0.373251	+	0.927730i	$0.621757\pi$
$882$		0			0
$883$	15.5148			0.522115			0.261057	−	0.965323i	$-0.415929\pi$
$883$	15.5148			0.522115			0.261057	+	0.965323i	$0.415929\pi$
$884$	−0.546963			−0.0183963
$885$		0			0
$886$	16.3960			0.550833
$887$	24.8136	+	42.9784i	0.833159	+	1.44307i	0.895521	+	0.445020i	$0.146803\pi$
$887$	24.8136	+	42.9784i	0.833159	+	1.44307i	−0.0623617	+	0.998054i	$0.519863\pi$
$888$		0			0
$889$	12.8822	−	13.1449i	0.432055	−	0.440867i
$890$	−4.12993			−0.138436
$891$		0			0
$892$	−0.452684	−	0.784071i	−0.0151570	−	0.0262526i
$893$	7.22150	−	12.5080i	0.241658	−	0.418564i
$894$		0			0
$895$	−2.98463	+	5.16954i	−0.0997653	+	0.172799i
$896$	−1.85185	+	1.88962i	−0.0618659	+	0.0631277i
$897$		0			0
$898$	−33.5534			−1.11969
$899$	15.5377	+	26.9120i	0.518210	+	0.897567i
$900$		0			0
$901$	2.69900	−	4.67481i	0.0899169	−	0.155741i
$902$	3.29960	+	5.71507i	0.109865	+	0.190291i
$903$		0			0
$904$	4.06408	−	7.03919i	0.135169	−	0.234120i
$905$	−2.71161	−	4.69665i	−0.0901371	−	0.156122i
$906$		0			0
$907$	−5.91561	+	10.2461i	−0.196424	+	0.340217i	−0.947367	−	0.320151i	$-0.896266\pi$
$907$	−5.91561	+	10.2461i	−0.196424	+	0.340217i	0.750942	+	0.660368i	$0.229600\pi$
$908$	−10.7112	+	18.5524i	−0.355464	+	0.615682i
$909$		0			0
$910$	−1.22969	+	1.25477i	−0.0407637	+	0.0415951i
$911$	−6.74673	−	11.6857i	−0.223529	−	0.387164i	0.732348	−	0.680931i	$-0.238424\pi$
$911$	−6.74673	−	11.6857i	−0.223529	−	0.387164i	−0.955877	+	0.293767i	$0.905091\pi$
$912$		0			0
$913$	11.5681			0.382849
$914$	−19.5171			−0.645568
$915$		0			0
$916$	7.96073	+	13.7884i	0.263030	+	0.455581i
$917$	−25.0460	−	6.44080i	−0.827093	−	0.212694i
$918$		0			0
$919$	−5.38406	+	9.32547i	−0.177604	+	0.307619i	−0.941059	−	0.338242i	$-0.890168\pi$
$919$	−5.38406	+	9.32547i	−0.177604	+	0.307619i	0.763455	+	0.645861i	$0.223501\pi$
$920$	−1.74387	+	3.02046i	−0.0574936	+	0.0995818i
$921$		0			0
$922$	−15.2287	−	26.3769i	−0.501531	−	0.868678i
$923$	−1.14447	+	1.98228i	−0.0376707	+	0.0652475i
$924$		0			0
$925$	−5.32042	−	9.21523i	−0.174934	−	0.302995i
$926$	7.56973	−	13.1112i	0.248757	−	0.430859i
$927$		0			0
$928$	2.03452	+	3.52389i	0.0667863	+	0.115677i
$929$	18.3053			0.600576			0.300288	−	0.953849i	$-0.402917\pi$
$929$	18.3053			0.600576			0.300288	+	0.953849i	$0.402917\pi$
$930$		0			0
$931$	34.0510	+	18.7532i	1.11598	+	0.614611i
$932$	3.45390	−	5.98232i	0.113136	−	0.195957i
$933$		0			0
$934$	0.118683	−	0.205565i	0.00388343	−	0.00672629i
$935$	2.65521	+	4.59896i	0.0868347	+	0.150402i
$936$		0			0
$937$	24.6739			0.806061			0.403030	−	0.915187i	$-0.367957\pi$
$937$	24.6739			0.806061			0.403030	+	0.915187i	$0.367957\pi$
$938$	−13.4933	+	13.7685i	−0.440573	+	0.449558i
$939$		0			0
$940$	−1.30038	−	2.25233i	−0.0424138	−	0.0734629i
$941$	−35.5744			−1.15969			−0.579846	−	0.814726i	$-0.696887\pi$
$941$	−35.5744			−1.15969			−0.579846	+	0.814726i	$0.696887\pi$
$942$		0			0
$943$	3.57005			0.116257
$944$	2.91633			0.0949186
$945$		0			0
$946$	−53.5111			−1.73979
$947$	10.4955			0.341059			0.170530	−	0.985353i	$-0.445452\pi$
$947$	10.4955			0.341059			0.170530	+	0.985353i	$0.445452\pi$
$948$		0			0
$949$	6.25746			0.203126
$950$	2.77668	+	4.80936i	0.0900875	+	0.156036i
$951$		0			0
$952$	2.11063	+	0.542768i	0.0684060	+	0.0175912i
$953$	5.72697			0.185515			0.0927574	−	0.995689i	$-0.470432\pi$
$953$	5.72697			0.185515			0.0927574	+	0.995689i	$0.470432\pi$
$954$		0			0
$955$	−2.48957	−	4.31206i	−0.0805605	−	0.139535i
$956$	−7.95013	+	13.7700i	−0.257125	+	0.445354i
$957$		0			0
$958$	6.76029	−	11.7092i	0.218415	−	0.378306i
$959$	9.13474	+	32.7647i	0.294976	+	1.05803i
$960$		0			0
$961$	27.3243			0.881428
$962$	−3.53292	−	6.11920i	−0.113906	−	0.197291i
$963$		0			0
$964$	−4.67555	+	8.09830i	−0.150589	+	0.260829i
$965$	−11.7096	−	20.2816i	−0.376944	−	0.652887i
$966$		0			0
$967$	−25.0249	+	43.3445i	−0.804748	+	1.39386i	0.111713	+	0.993740i	$0.464366\pi$
$967$	−25.0249	+	43.3445i	−0.804748	+	1.39386i	−0.916461	+	0.400124i	$0.868967\pi$
$968$	15.2821	+	26.4694i	0.491186	+	0.850760i
$969$		0			0
$970$	−8.98652	+	15.5651i	−0.288540	+	0.499765i
$971$	0.713412	−	1.23567i	0.0228945	−	0.0396544i	−0.854351	−	0.519696i	$-0.826045\pi$
$971$	0.713412	−	1.23567i	0.0228945	−	0.0396544i	0.877246	+	0.480042i	$0.159378\pi$
$972$		0			0
$973$	13.2096	+	47.3803i	0.423479	+	1.51894i
$974$	−19.3582	−	33.5294i	−0.620276	−	1.07435i
$975$		0			0
$976$	−0.767506			−0.0245673
$977$	−56.7098			−1.81431			−0.907154	−	0.420799i	$-0.861750\pi$
$977$	−56.7098			−1.81431			−0.907154	+	0.420799i	$0.861750\pi$
$978$		0			0
$979$	13.3129	+	23.0586i	0.425482	+	0.736957i
$980$	5.99028	−	3.62167i	0.191353	−	0.115690i
$981$		0			0
$982$	5.10089	−	8.83500i	0.162776	−	0.281936i
$983$	−14.4756	+	25.0724i	−0.461699	+	0.799686i	−0.999046	−	0.0436753i	$-0.986093\pi$
$983$	−14.4756	+	25.0724i	−0.461699	+	0.799686i	0.537347	+	0.843361i	$0.319427\pi$
$984$		0			0
$985$	5.77203	+	9.99744i	0.183912	+	0.318545i
$986$	1.67583	−	2.90263i	0.0533694	−	0.0924384i
$987$		0			0
$988$	1.84380	+	3.19356i	0.0586592	+	0.101601i
$989$	−14.4743	+	25.0702i	−0.460255	+	0.797185i
$990$		0			0
$991$	12.3215	+	21.3414i	0.391404	+	0.677931i	0.992635	−	0.121144i	$-0.0386562\pi$
$991$	12.3215	+	21.3414i	0.391404	+	0.677931i	−0.601231	+	0.799075i	$0.705323\pi$
$992$	7.63703			0.242476
$993$		0			0
$994$	6.38339	−	6.51358i	0.202469	−	0.206598i
$995$	−8.07725	+	13.9902i	−0.256066	+	0.443519i
$996$		0			0
$997$	−12.7388	+	22.0642i	−0.403441	+	0.698780i	−0.994139	−	0.108113i	$-0.965519\pi$
$997$	−12.7388	+	22.0642i	−0.403441	+	0.698780i	0.590698	+	0.806893i	$0.298853\pi$
$998$	−5.34312	−	9.25456i	−0.169134	−	0.292948i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1890.2.i.g.1171.5		12
3.2	odd	2		630.2.i.g.121.5	✓	12
7.4	even	3		1890.2.l.g.361.2		12
9.2	odd	6		630.2.l.g.331.4	yes	12
9.7	even	3		1890.2.l.g.1801.2		12
21.11	odd	6		630.2.l.g.571.4	yes	12
63.11	odd	6		630.2.i.g.151.5	yes	12
63.25	even	3	inner	1890.2.i.g.991.5		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.i.g.121.5	✓	12	3.2	odd	2
630.2.i.g.151.5	yes	12	63.11	odd	6
630.2.l.g.331.4	yes	12	9.2	odd	6
630.2.l.g.571.4	yes	12	21.11	odd	6
1890.2.i.g.991.5		12	63.25	even	3	inner
1890.2.i.g.1171.5		12	1.1	even	1	trivial
1890.2.l.g.361.2		12	7.4	even	3
1890.2.l.g.1801.2		12	9.7	even	3

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:	\( N \)	\(=\)	\( 1890 = 2 \cdot 3^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1890.i (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{4} +(0.500000 + 0.866025i) q^{5} +(1.85185 - 1.88962i) q^{7} -1.00000 q^{8} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{4} +(0.500000 + 0.866025i) q^{5} +(1.85185 - 1.88962i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{10} +(-3.22352 + 5.58330i) q^{11} +(0.332016 - 0.575068i) q^{13} +(-1.85185 + 1.88962i) q^{14} +1.00000 q^{16} +(-0.411850 - 0.713345i) q^{17} +(-2.77668 + 4.80936i) q^{19} +(0.500000 + 0.866025i) q^{20} +(3.22352 - 5.58330i) q^{22} +(-1.74387 - 3.02046i) q^{23} +(-0.500000 + 0.866025i) q^{25} +(-0.332016 + 0.575068i) q^{26} +(1.85185 - 1.88962i) q^{28} +(-2.03452 - 3.52389i) q^{29} -7.63703 q^{31} -1.00000 q^{32} +(0.411850 + 0.713345i) q^{34} +(2.56238 + 0.658939i) q^{35} +(-5.32042 + 9.21523i) q^{37} +(2.77668 - 4.80936i) q^{38} +(-0.500000 - 0.866025i) q^{40} +(-0.511800 + 0.886464i) q^{41} +(-4.15005 - 7.18810i) q^{43} +(-3.22352 + 5.58330i) q^{44} +(1.74387 + 3.02046i) q^{46} -2.60076 q^{47} +(-0.141315 - 6.99857i) q^{49} +(0.500000 - 0.866025i) q^{50} +(0.332016 - 0.575068i) q^{52} +(3.27668 + 5.67538i) q^{53} -6.44704 q^{55} +(-1.85185 + 1.88962i) q^{56} +(2.03452 + 3.52389i) q^{58} +2.91633 q^{59} -0.767506 q^{61} +7.63703 q^{62} +1.00000 q^{64} +0.664031 q^{65} +7.28641 q^{67} +(-0.411850 - 0.713345i) q^{68} +(-2.56238 - 0.658939i) q^{70} -3.44704 q^{71} +(4.71172 + 8.16093i) q^{73} +(5.32042 - 9.21523i) q^{74} +(-2.77668 + 4.80936i) q^{76} +(4.58083 + 16.4306i) q^{77} -5.40500 q^{79} +(0.500000 + 0.866025i) q^{80} +(0.511800 - 0.886464i) q^{82} +(-0.897166 - 1.55394i) q^{83} +(0.411850 - 0.713345i) q^{85} +(4.15005 + 7.18810i) q^{86} +(3.22352 - 5.58330i) q^{88} +(2.06497 - 3.57663i) q^{89} +(-0.471816 - 1.69232i) q^{91} +(-1.74387 - 3.02046i) q^{92} +2.60076 q^{94} -5.55337 q^{95} +(-8.98652 - 15.5651i) q^{97} +(0.141315 + 6.99857i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 12 q^{2} + 12 q^{4} + 6 q^{5} + 4 q^{7} - 12 q^{8}+O(q^{10}) \) 12 * q - 12 * q^2 + 12 * q^4 + 6 * q^5 + 4 * q^7 - 12 * q^8	\( 12 q - 12 q^{2} + 12 q^{4} + 6 q^{5} + 4 q^{7} - 12 q^{8} - 6 q^{10} - 3 q^{11} - 2 q^{13} - 4 q^{14} + 12 q^{16} - q^{17} + 8 q^{19} + 6 q^{20} + 3 q^{22} - 11 q^{23} - 6 q^{25} + 2 q^{26} + 4 q^{28} - 13 q^{29} - 42 q^{31} - 12 q^{32} + q^{34} - 4 q^{35} + 18 q^{37} - 8 q^{38} - 6 q^{40} - 5 q^{41} - 11 q^{43} - 3 q^{44} + 11 q^{46} - 46 q^{47} + 6 q^{50} - 2 q^{52} - 2 q^{53} - 6 q^{55} - 4 q^{56} + 13 q^{58} + 2 q^{59} + 2 q^{61} + 42 q^{62} + 12 q^{64} - 4 q^{65} - 4 q^{67} - q^{68} + 4 q^{70} + 30 q^{71} + 22 q^{73} - 18 q^{74} + 8 q^{76} + 31 q^{77} - 54 q^{79} + 6 q^{80} + 5 q^{82} - 6 q^{83} + q^{85} + 11 q^{86} + 3 q^{88} + 18 q^{89} + 14 q^{91} - 11 q^{92} + 46 q^{94} + 16 q^{95} - 4 q^{97}+O(q^{100}) \) 12 * q - 12 * q^2 + 12 * q^4 + 6 * q^5 + 4 * q^7 - 12 * q^8 - 6 * q^10 - 3 * q^11 - 2 * q^13 - 4 * q^14 + 12 * q^16 - q^17 + 8 * q^19 + 6 * q^20 + 3 * q^22 - 11 * q^23 - 6 * q^25 + 2 * q^26 + 4 * q^28 - 13 * q^29 - 42 * q^31 - 12 * q^32 + q^34 - 4 * q^35 + 18 * q^37 - 8 * q^38 - 6 * q^40 - 5 * q^41 - 11 * q^43 - 3 * q^44 + 11 * q^46 - 46 * q^47 + 6 * q^50 - 2 * q^52 - 2 * q^53 - 6 * q^55 - 4 * q^56 + 13 * q^58 + 2 * q^59 + 2 * q^61 + 42 * q^62 + 12 * q^64 - 4 * q^65 - 4 * q^67 - q^68 + 4 * q^70 + 30 * q^71 + 22 * q^73 - 18 * q^74 + 8 * q^76 + 31 * q^77 - 54 * q^79 + 6 * q^80 + 5 * q^82 - 6 * q^83 + q^85 + 11 * q^86 + 3 * q^88 + 18 * q^89 + 14 * q^91 - 11 * q^92 + 46 * q^94 + 16 * q^95 - 4 * q^97

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