LMFDB - Embedded newform 738.2.h.b.37.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [738,2,Mod(37,738)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(738, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 8])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("738.37"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 738 = 2 \cdot 3^{2} \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	738.h (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [4,-1,0,-1,-2,0,4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$5.89295966917$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 82)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			37.1
Root			$0.809017 + 0.587785i$ of defining polynomial
Character	$\chi$	$=$	738.37
Dual form			738.2.h.b.379.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.809017 + 0.587785i) q^{2} +(0.309017 - 0.951057i) q^{4} +(-0.500000 + 1.53884i) q^{5} +(2.11803 + 1.53884i) q^{7} +(0.309017 + 0.951057i) q^{8} +(-0.500000 - 1.53884i) q^{10} +(-0.927051 - 2.85317i) q^{11} +(-5.04508 + 3.66547i) q^{13} -2.61803 q^{14} +(-0.809017 - 0.587785i) q^{16} +(1.30902 + 4.02874i) q^{17} +(1.42705 + 1.03681i) q^{19} +(1.30902 + 0.951057i) q^{20} +(2.42705 + 1.76336i) q^{22} +(-1.30902 + 0.951057i) q^{23} +(1.92705 + 1.40008i) q^{25} +(1.92705 - 5.93085i) q^{26} +(2.11803 - 1.53884i) q^{28} +(0.163119 - 0.502029i) q^{29} +(-1.88197 - 5.79210i) q^{31} +1.00000 q^{32} +(-3.42705 - 2.48990i) q^{34} +(-3.42705 + 2.48990i) q^{35} +(0.454915 - 1.40008i) q^{37} -1.76393 q^{38} -1.61803 q^{40} +(-2.19098 + 6.01661i) q^{41} +(-7.85410 + 5.70634i) q^{43} -3.00000 q^{44} +(0.500000 - 1.53884i) q^{46} +(-1.23607 + 0.898056i) q^{47} +(-0.0450850 - 0.138757i) q^{49} -2.38197 q^{50} +(1.92705 + 5.93085i) q^{52} +(-3.66312 + 11.2739i) q^{53} +4.85410 q^{55} +(-0.809017 + 2.48990i) q^{56} +(0.163119 + 0.502029i) q^{58} +(-4.11803 + 2.99193i) q^{59} +(2.80902 + 2.04087i) q^{61} +(4.92705 + 3.57971i) q^{62} +(-0.809017 + 0.587785i) q^{64} +(-3.11803 - 9.59632i) q^{65} +(-4.76393 + 14.6619i) q^{67} +4.23607 q^{68} +(1.30902 - 4.02874i) q^{70} +(-1.19098 - 3.66547i) q^{71} -16.1803 q^{73} +(0.454915 + 1.40008i) q^{74} +(1.42705 - 1.03681i) q^{76} +(2.42705 - 7.46969i) q^{77} +14.0000 q^{79} +(1.30902 - 0.951057i) q^{80} +(-1.76393 - 6.15537i) q^{82} +16.0902 q^{83} -6.85410 q^{85} +(3.00000 - 9.23305i) q^{86} +(2.42705 - 1.76336i) q^{88} +(-5.04508 - 3.66547i) q^{89} -16.3262 q^{91} +(0.500000 + 1.53884i) q^{92} +(0.472136 - 1.45309i) q^{94} +(-2.30902 + 1.67760i) q^{95} +(1.69098 - 5.20431i) q^{97} +(0.118034 + 0.0857567i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - q^{2} - q^{4} - 2 q^{5} + 4 q^{7} - q^{8} - 2 q^{10} + 3 q^{11} - 9 q^{13} - 6 q^{14} - q^{16} + 3 q^{17} - q^{19} + 3 q^{20} + 3 q^{22} - 3 q^{23} + q^{25} + q^{26} + 4 q^{28} - 15 q^{29}+ \cdots - 4 q^{98}+O(q^{100}) $ 4 * q - q^2 - q^4 - 2 * q^5 + 4 * q^7 - q^8 - 2 * q^10 + 3 * q^11 - 9 * q^13 - 6 * q^14 - q^16 + 3 * q^17 - q^19 + 3 * q^20 + 3 * q^22 - 3 * q^23 + q^25 + q^26 + 4 * q^28 - 15 * q^29 - 12 * q^31 + 4 * q^32 - 7 * q^34 - 7 * q^35 + 13 * q^37 - 16 * q^38 - 2 * q^40 - 11 * q^41 - 18 * q^43 - 12 * q^44 + 2 * q^46 + 4 * q^47 + 11 * q^49 - 14 * q^50 + q^52 + q^53 + 6 * q^55 - q^56 - 15 * q^58 - 12 * q^59 + 9 * q^61 + 13 * q^62 - q^64 - 8 * q^65 - 28 * q^67 + 8 * q^68 + 3 * q^70 - 7 * q^71 - 20 * q^73 + 13 * q^74 - q^76 + 3 * q^77 + 56 * q^79 + 3 * q^80 - 16 * q^82 + 42 * q^83 - 14 * q^85 + 12 * q^86 + 3 * q^88 - 9 * q^89 - 34 * q^91 + 2 * q^92 - 16 * q^94 - 7 * q^95 + 9 * q^97 - 4 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/738\mathbb{Z}\right)^\times$.

$n$	$83$	$703$
$\chi(n)$	$1$	$e\left(\frac{4}{5}\right)$

Coefficient data

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

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

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

$2$	−0.809017	+	0.587785i	−0.572061	+	0.415627i
$2$	−0.809017	+	0.587785i	−0.572061	+	0.415627i
$3$		0			0
$3$		0			0
$4$	0.309017	−	0.951057i	0.154508	−	0.475528i
$5$	−0.500000	+	1.53884i	−0.223607	+	0.688191i	0.774823	+	0.632178i	$0.217839\pi$
$5$	−0.500000	+	1.53884i	−0.223607	+	0.688191i	−0.998430	+	0.0560130i	$0.982161\pi$
$6$		0			0
$7$	2.11803	+	1.53884i	0.800542	+	0.581628i	0.911073	−	0.412245i	$-0.135255\pi$
$7$	2.11803	+	1.53884i	0.800542	+	0.581628i	−0.110531	+	0.993873i	$0.535255\pi$
$8$	0.309017	+	0.951057i	0.109254	+	0.336249i
$9$		0			0
$10$	−0.500000	−	1.53884i	−0.158114	−	0.486624i
$11$	−0.927051	−	2.85317i	−0.279516	−	0.860263i	−0.987989	−	0.154525i	$-0.950615\pi$
$11$	−0.927051	−	2.85317i	−0.279516	−	0.860263i	0.708473	−	0.705738i	$-0.249385\pi$
$12$		0			0
$13$	−5.04508	+	3.66547i	−1.39925	+	1.01662i	−0.404478	+	0.914548i	$0.632547\pi$
$13$	−5.04508	+	3.66547i	−1.39925	+	1.01662i	−0.994777	+	0.102070i	$0.967453\pi$
$14$	−2.61803			−0.699699
$15$		0			0
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	1.30902	+	4.02874i	0.317483	+	0.977113i	0.974720	+	0.223429i	$0.0717251\pi$
$17$	1.30902	+	4.02874i	0.317483	+	0.977113i	−0.657237	+	0.753684i	$0.728275\pi$
$18$		0			0
$19$	1.42705	+	1.03681i	0.327388	+	0.237861i	0.739321	−	0.673353i	$-0.235146\pi$
$19$	1.42705	+	1.03681i	0.327388	+	0.237861i	−0.411934	+	0.911214i	$0.635146\pi$
$20$	1.30902	+	0.951057i	0.292705	+	0.212663i
$21$		0			0
$22$	2.42705	+	1.76336i	0.517449	+	0.375949i
$23$	−1.30902	+	0.951057i	−0.272949	+	0.198309i	−0.715836	−	0.698268i	$-0.753954\pi$
$23$	−1.30902	+	0.951057i	−0.272949	+	0.198309i	0.442887	+	0.896577i	$0.353954\pi$
$24$		0			0
$25$	1.92705	+	1.40008i	0.385410	+	0.280017i
$26$	1.92705	−	5.93085i	0.377926	−	1.16314i
$27$		0			0
$28$	2.11803	−	1.53884i	0.400271	−	0.290814i
$29$	0.163119	−	0.502029i	0.0302904	−	0.0932244i	−0.934768	−	0.355258i	$-0.884393\pi$
$29$	0.163119	−	0.502029i	0.0302904	−	0.0932244i	0.965059	+	0.262033i	$0.0843931\pi$
$30$		0			0
$31$	−1.88197	−	5.79210i	−0.338011	−	1.04029i	−0.965220	−	0.261440i	$-0.915803\pi$
$31$	−1.88197	−	5.79210i	−0.338011	−	1.04029i	0.627209	−	0.778851i	$-0.284197\pi$
$32$	1.00000			0.176777
$33$		0			0
$34$	−3.42705	−	2.48990i	−0.587734	−	0.427014i
$35$	−3.42705	+	2.48990i	−0.579277	+	0.420870i
$36$		0			0
$37$	0.454915	−	1.40008i	0.0747876	−	0.230172i	−0.906674	−	0.421832i	$-0.861387\pi$
$37$	0.454915	−	1.40008i	0.0747876	−	0.230172i	0.981461	+	0.191660i	$0.0613871\pi$
$38$	−1.76393			−0.286148
$39$		0			0
$40$	−1.61803			−0.255834
$41$	−2.19098	+	6.01661i	−0.342174	+	0.939637i
$41$	−2.19098	+	6.01661i	−0.342174	+	0.939637i
$42$		0			0
$43$	−7.85410	+	5.70634i	−1.19774	+	0.870209i	−0.994060	−	0.108829i	$-0.965290\pi$
$43$	−7.85410	+	5.70634i	−1.19774	+	0.870209i	−0.203679	+	0.979038i	$0.565290\pi$
$44$	−3.00000			−0.452267
$45$		0			0
$46$	0.500000	−	1.53884i	0.0737210	−	0.226890i
$47$	−1.23607	+	0.898056i	−0.180299	+	0.130995i	−0.674274	−	0.738481i	$-0.735543\pi$
$47$	−1.23607	+	0.898056i	−0.180299	+	0.130995i	0.493975	+	0.869476i	$0.335543\pi$
$48$		0			0
$49$	−0.0450850	−	0.138757i	−0.00644071	−	0.0198225i
$50$	−2.38197			−0.336861
$51$		0			0
$52$	1.92705	+	5.93085i	0.267234	+	0.822461i
$53$	−3.66312	+	11.2739i	−0.503168	+	1.54859i	0.300661	+	0.953731i	$0.402793\pi$
$53$	−3.66312	+	11.2739i	−0.503168	+	1.54859i	−0.803829	+	0.594861i	$0.797207\pi$
$54$		0			0
$55$	4.85410			0.654527
$56$	−0.809017	+	2.48990i	−0.108109	+	0.332727i
$57$		0			0
$58$	0.163119	+	0.502029i	0.0214186	+	0.0659196i
$59$	−4.11803	+	2.99193i	−0.536122	+	0.389516i	−0.822643	−	0.568558i	$-0.807501\pi$
$59$	−4.11803	+	2.99193i	−0.536122	+	0.389516i	0.286521	+	0.958074i	$0.407501\pi$
$60$		0			0
$61$	2.80902	+	2.04087i	0.359658	+	0.261307i	0.752909	−	0.658124i	$-0.228650\pi$
$61$	2.80902	+	2.04087i	0.359658	+	0.261307i	−0.393252	+	0.919431i	$0.628650\pi$
$62$	4.92705	+	3.57971i	0.625736	+	0.454624i
$63$		0			0
$64$	−0.809017	+	0.587785i	−0.101127	+	0.0734732i
$65$	−3.11803	−	9.59632i	−0.386745	−	1.19028i
$66$		0			0
$67$	−4.76393	+	14.6619i	−0.582007	+	1.79123i	0.0289644	+	0.999580i	$0.490779\pi$
$67$	−4.76393	+	14.6619i	−0.582007	+	1.79123i	−0.610971	+	0.791653i	$0.709221\pi$
$68$	4.23607			0.513699
$69$		0			0
$70$	1.30902	−	4.02874i	0.156457	−	0.481527i
$71$	−1.19098	−	3.66547i	−0.141344	−	0.435011i	0.855179	−	0.518333i	$-0.173447\pi$
$71$	−1.19098	−	3.66547i	−0.141344	−	0.435011i	−0.996523	+	0.0833216i	$0.973447\pi$
$72$		0			0
$73$	−16.1803			−1.89377			−0.946883	−	0.321579i	$-0.895786\pi$
$73$	−16.1803			−1.89377			−0.946883	+	0.321579i	$0.895786\pi$
$74$	0.454915	+	1.40008i	0.0528828	+	0.162757i
$75$		0			0
$76$	1.42705	−	1.03681i	0.163694	−	0.118931i
$77$	2.42705	−	7.46969i	0.276588	−	0.851251i
$78$		0			0
$79$	14.0000			1.57512			0.787562	−	0.616236i	$-0.211343\pi$
$79$	14.0000			1.57512			0.787562	+	0.616236i	$0.211343\pi$
$80$	1.30902	−	0.951057i	0.146353	−	0.106331i
$81$		0			0
$82$	−1.76393	−	6.15537i	−0.194794	−	0.679747i
$83$	16.0902			1.76613			0.883063	−	0.469255i	$-0.155477\pi$
$83$	16.0902			1.76613			0.883063	+	0.469255i	$0.155477\pi$
$84$		0			0
$85$	−6.85410			−0.743432
$86$	3.00000	−	9.23305i	0.323498	−	0.995625i
$87$		0			0
$88$	2.42705	−	1.76336i	0.258725	−	0.187974i
$89$	−5.04508	−	3.66547i	−0.534778	−	0.388539i	0.287364	−	0.957821i	$-0.407221\pi$
$89$	−5.04508	−	3.66547i	−0.534778	−	0.388539i	−0.822142	+	0.569283i	$0.807221\pi$
$90$		0			0
$91$	−16.3262			−1.71145
$92$	0.500000	+	1.53884i	0.0521286	+	0.160435i
$93$		0			0
$94$	0.472136	−	1.45309i	0.0486971	−	0.149874i
$95$	−2.30902	+	1.67760i	−0.236900	+	0.172118i
$96$		0			0
$97$	1.69098	−	5.20431i	0.171693	−	0.528418i	−0.827774	−	0.561062i	$-0.810393\pi$
$97$	1.69098	−	5.20431i	0.171693	−	0.528418i	0.999467	+	0.0326444i	$0.0103929\pi$
$98$	0.118034	+	0.0857567i	0.0119232	+	0.00866274i
$99$		0			0
$100$	1.92705	−	1.40008i	0.192705	−	0.140008i
$101$	6.30902	+	4.58377i	0.627771	+	0.456102i	0.855627	−	0.517593i	$-0.173172\pi$
$101$	6.30902	+	4.58377i	0.627771	+	0.456102i	−0.227857	+	0.973695i	$0.573172\pi$
$102$		0			0
$103$	9.89919	+	7.19218i	0.975396	+	0.708667i	0.956675	−	0.291158i	$-0.0940406\pi$
$103$	9.89919	+	7.19218i	0.975396	+	0.708667i	0.0187209	+	0.999825i	$0.494041\pi$
$104$	−5.04508	−	3.66547i	−0.494711	−	0.359429i
$105$		0			0
$106$	−3.66312	−	11.2739i	−0.355794	−	1.09502i
$107$	−4.61803	−	3.35520i	−0.446442	−	0.324359i	0.341747	−	0.939792i	$-0.388981\pi$
$107$	−4.61803	−	3.35520i	−0.446442	−	0.324359i	−0.788189	+	0.615433i	$0.788981\pi$
$108$		0			0
$109$	7.47214			0.715701			0.357850	−	0.933779i	$-0.383510\pi$
$109$	7.47214			0.715701			0.357850	+	0.933779i	$0.383510\pi$
$110$	−3.92705	+	2.85317i	−0.374430	+	0.272039i
$111$		0			0
$112$	−0.809017	−	2.48990i	−0.0764449	−	0.235273i
$113$	−5.51722	−	16.9803i	−0.519016	−	1.59737i	−0.775853	−	0.630914i	$-0.782680\pi$
$113$	−5.51722	−	16.9803i	−0.519016	−	1.59737i	0.256837	−	0.966455i	$-0.417320\pi$
$114$		0			0
$115$	−0.809017	−	2.48990i	−0.0754412	−	0.232184i
$116$	−0.427051	−	0.310271i	−0.0396507	−	0.0288079i
$117$		0			0
$118$	1.57295	−	4.84104i	0.144802	−	0.445654i
$119$	−3.42705	+	10.5474i	−0.314157	+	0.966877i
$120$		0			0
$121$	1.61803	−	1.17557i	0.147094	−	0.106870i
$122$	−3.47214			−0.314352
$123$		0			0
$124$	−6.09017			−0.546913
$125$	−9.66312	+	7.02067i	−0.864296	+	0.627948i
$126$		0			0
$127$	2.10081	−	6.46564i	0.186417	−	0.573733i	−0.813553	−	0.581491i	$-0.802470\pi$
$127$	2.10081	−	6.46564i	0.186417	−	0.573733i	0.999970	+	0.00775835i	$0.00246958\pi$
$128$	0.309017	−	0.951057i	0.0273135	−	0.0840623i
$129$		0			0
$130$	8.16312	+	5.93085i	0.715953	+	0.520170i
$131$	2.82624	+	8.69827i	0.246930	+	0.759971i	0.995313	+	0.0967048i	$0.0308303\pi$
$131$	2.82624	+	8.69827i	0.246930	+	0.759971i	−0.748384	+	0.663266i	$0.769170\pi$
$132$		0			0
$133$	1.42705	+	4.39201i	0.123741	+	0.380836i
$134$	−4.76393	−	14.6619i	−0.411541	−	1.26659i
$135$		0			0
$136$	−3.42705	+	2.48990i	−0.293867	+	0.213507i
$137$	6.76393			0.577882			0.288941	−	0.957347i	$-0.406697\pi$
$137$	6.76393			0.577882			0.288941	+	0.957347i	$0.406697\pi$
$138$		0			0
$139$	−0.190983	−	0.138757i	−0.0161990	−	0.0117692i	0.579656	−	0.814861i	$-0.303187\pi$
$139$	−0.190983	−	0.138757i	−0.0161990	−	0.0117692i	−0.595855	+	0.803092i	$0.703187\pi$
$140$	1.30902	+	4.02874i	0.110632	+	0.340491i
$141$		0			0
$142$	3.11803	+	2.26538i	0.261660	+	0.190107i
$143$	15.1353	+	10.9964i	1.26567	+	0.919566i
$144$		0			0
$145$	0.690983	+	0.502029i	0.0573830	+	0.0416912i
$146$	13.0902	−	9.51057i	1.08335	−	0.787100i
$147$		0			0
$148$	−1.19098	−	0.865300i	−0.0978982	−	0.0711272i
$149$	3.52786	−	10.8576i	0.289014	−	0.889493i	−0.696153	−	0.717894i	$-0.745106\pi$
$149$	3.52786	−	10.8576i	0.289014	−	0.889493i	0.985167	−	0.171600i	$-0.0548936\pi$
$150$		0			0
$151$	12.3262	−	8.95554i	1.00310	−	0.728791i	0.0403454	−	0.999186i	$-0.487154\pi$
$151$	12.3262	−	8.95554i	1.00310	−	0.728791i	0.962750	+	0.270395i	$0.0871542\pi$
$152$	−0.545085	+	1.67760i	−0.0442122	+	0.136071i
$153$		0			0
$154$	2.42705	+	7.46969i	0.195577	+	0.601925i
$155$	9.85410			0.791501
$156$		0			0
$157$	−2.38197	−	1.73060i	−0.190102	−	0.138117i	0.488664	−	0.872472i	$-0.337485\pi$
$157$	−2.38197	−	1.73060i	−0.190102	−	0.138117i	−0.678765	+	0.734355i	$0.737485\pi$
$158$	−11.3262	+	8.22899i	−0.901067	+	0.654664i
$159$		0			0
$160$	−0.500000	+	1.53884i	−0.0395285	+	0.121656i
$161$	−4.23607			−0.333849
$162$		0			0
$163$	4.03444			0.316002			0.158001	−	0.987439i	$-0.449495\pi$
$163$	4.03444			0.316002			0.158001	+	0.987439i	$0.449495\pi$
$164$	5.04508	+	3.94298i	0.393955	+	0.307895i
$165$		0			0
$166$	−13.0172	+	9.45756i	−1.01033	+	0.734049i
$167$	24.0344			1.85984			0.929920	−	0.367761i	$-0.119875\pi$
$167$	24.0344			1.85984			0.929920	+	0.367761i	$0.119875\pi$
$168$		0			0
$169$	8.00000	−	24.6215i	0.615385	−	1.89396i
$170$	5.54508	−	4.02874i	0.425289	−	0.308990i
$171$		0			0
$172$	3.00000	+	9.23305i	0.228748	+	0.704014i
$173$	3.76393			0.286166			0.143083	−	0.989711i	$-0.454298\pi$
$173$	3.76393			0.286166			0.143083	+	0.989711i	$0.454298\pi$
$174$		0			0
$175$	1.92705	+	5.93085i	0.145671	+	0.448330i
$176$	−0.927051	+	2.85317i	−0.0698791	+	0.215066i
$177$		0			0
$178$	6.23607			0.467413
$179$	7.52786	−	23.1684i	0.562659	−	1.73169i	−0.112148	−	0.993692i	$-0.535773\pi$
$179$	7.52786	−	23.1684i	0.562659	−	1.73169i	0.674807	−	0.737995i	$-0.264227\pi$
$180$		0			0
$181$	1.86475	+	5.73910i	0.138605	+	0.426584i	0.996133	−	0.0878537i	$-0.0280008\pi$
$181$	1.86475	+	5.73910i	0.138605	+	0.426584i	−0.857528	+	0.514437i	$0.828001\pi$
$182$	13.2082	−	9.59632i	0.979057	−	0.711327i
$183$		0			0
$184$	−1.30902	−	0.951057i	−0.0965020	−	0.0701128i
$185$	1.92705	+	1.40008i	0.141680	+	0.102936i
$186$		0			0
$187$	10.2812	−	7.46969i	0.751832	−	0.546238i
$188$	0.472136	+	1.45309i	0.0344341	+	0.105977i
$189$		0			0
$190$	0.881966	−	2.71441i	0.0639845	−	0.196924i
$191$	−5.00000			−0.361787			−0.180894	−	0.983503i	$-0.557899\pi$
$191$	−5.00000			−0.361787			−0.180894	+	0.983503i	$0.557899\pi$
$192$		0			0
$193$	−3.73607	+	11.4984i	−0.268928	+	0.827675i	0.721834	+	0.692066i	$0.243299\pi$
$193$	−3.73607	+	11.4984i	−0.268928	+	0.827675i	−0.990762	+	0.135610i	$0.956701\pi$
$194$	1.69098	+	5.20431i	0.121406	+	0.373648i
$195$		0			0
$196$	−0.145898			−0.0104213
$197$	0.982779	+	3.02468i	0.0700201	+	0.215500i	0.979943	−	0.199277i	$-0.0638595\pi$
$197$	0.982779	+	3.02468i	0.0700201	+	0.215500i	−0.909923	+	0.414777i	$0.863860\pi$
$198$		0			0
$199$	−5.28115	+	3.83698i	−0.374371	+	0.271996i	−0.759021	−	0.651066i	$-0.774322\pi$
$199$	−5.28115	+	3.83698i	−0.374371	+	0.271996i	0.384650	+	0.923062i	$0.374322\pi$
$200$	−0.736068	+	2.26538i	−0.0520479	+	0.160187i
$201$		0			0
$202$	−7.79837			−0.548692
$203$	1.11803	−	0.812299i	0.0784706	−	0.0570122i
$204$		0			0
$205$	−8.16312	−	6.37988i	−0.570137	−	0.445590i
$206$	−12.2361			−0.852527
$207$		0			0
$208$	6.23607			0.432394
$209$	1.63525	−	5.03280i	0.113113	−	0.348126i
$210$		0			0
$211$	−5.04508	+	3.66547i	−0.347318	+	0.252341i	−0.747743	−	0.663988i	$-0.768862\pi$
$211$	−5.04508	+	3.66547i	−0.347318	+	0.252341i	0.400425	+	0.916330i	$0.368862\pi$
$212$	9.59017	+	6.96767i	0.658656	+	0.478541i
$213$		0			0
$214$	5.70820			0.390205
$215$	−4.85410	−	14.9394i	−0.331047	−	1.01886i
$216$		0			0
$217$	4.92705	−	15.1639i	0.334470	−	1.02939i
$218$	−6.04508	+	4.39201i	−0.409425	+	0.297465i
$219$		0			0
$220$	1.50000	−	4.61653i	0.101130	−	0.311246i
$221$	−21.3713	−	15.5272i	−1.43759	−	1.04447i
$222$		0			0
$223$	20.7984	−	15.1109i	1.39276	−	1.01190i	0.397206	−	0.917729i	$-0.369980\pi$
$223$	20.7984	−	15.1109i	1.39276	−	1.01190i	0.995556	−	0.0941715i	$-0.0300202\pi$
$224$	2.11803	+	1.53884i	0.141517	+	0.102818i
$225$		0			0
$226$	14.4443	+	10.4944i	0.960819	+	0.698076i
$227$	−15.0902	−	10.9637i	−1.00157	−	0.727683i	−0.0391456	−	0.999234i	$-0.512464\pi$
$227$	−15.0902	−	10.9637i	−1.00157	−	0.727683i	−0.962424	+	0.271550i	$0.912464\pi$
$228$		0			0
$229$	3.28115	+	10.0984i	0.216825	+	0.667318i	0.999019	+	0.0442832i	$0.0141004\pi$
$229$	3.28115	+	10.0984i	0.216825	+	0.667318i	−0.782194	+	0.623035i	$0.785900\pi$
$230$	2.11803	+	1.53884i	0.139659	+	0.101468i
$231$		0			0
$232$	0.527864			0.0346560
$233$	10.7533	−	7.81272i	0.704471	−	0.511828i	−0.176914	−	0.984226i	$-0.556611\pi$
$233$	10.7533	−	7.81272i	0.704471	−	0.511828i	0.881385	+	0.472398i	$0.156611\pi$
$234$		0			0
$235$	−0.763932	−	2.35114i	−0.0498334	−	0.153372i
$236$	1.57295	+	4.84104i	0.102390	+	0.315125i
$237$		0			0
$238$	−3.42705	−	10.5474i	−0.222143	−	0.683685i
$239$	20.4443	+	14.8536i	1.32243	+	0.960802i	0.999899	+	0.0142429i	$0.00453381\pi$
$239$	20.4443	+	14.8536i	1.32243	+	0.960802i	0.322531	+	0.946559i	$0.395466\pi$
$240$		0			0
$241$	−4.72542	+	14.5434i	−0.304391	+	0.936820i	0.675512	+	0.737349i	$0.263923\pi$
$241$	−4.72542	+	14.5434i	−0.304391	+	0.936820i	−0.979904	+	0.199472i	$0.936077\pi$
$242$	−0.618034	+	1.90211i	−0.0397287	+	0.122272i
$243$		0			0
$244$	2.80902	−	2.04087i	0.179829	−	0.130653i
$245$	0.236068			0.0150818
$246$		0			0
$247$	−11.0000			−0.699913
$248$	4.92705	−	3.57971i	0.312868	−	0.227312i
$249$		0			0
$250$	3.69098	−	11.3597i	0.233438	−	0.718449i
$251$	−5.42705	+	16.7027i	−0.342552	+	1.05427i	0.620329	+	0.784342i	$0.286999\pi$
$251$	−5.42705	+	16.7027i	−0.342552	+	1.05427i	−0.962881	+	0.269926i	$0.913001\pi$
$252$		0			0
$253$	3.92705	+	2.85317i	0.246892	+	0.179377i
$254$	2.10081	+	6.46564i	0.131817	+	0.405690i
$255$		0			0
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	1.47214	+	4.53077i	0.0918293	+	0.282622i	0.986414	−	0.164276i	$-0.0525288\pi$
$257$	1.47214	+	4.53077i	0.0918293	+	0.282622i	−0.894585	+	0.446898i	$0.852529\pi$
$258$		0			0
$259$	3.11803	−	2.26538i	0.193745	−	0.140764i
$260$	−10.0902			−0.625766
$261$		0			0
$262$	−7.39919	−	5.37582i	−0.457123	−	0.332120i
$263$	−0.0278640	−	0.0857567i	−0.00171817	−	0.00528799i	0.950194	−	0.311660i	$-0.100885\pi$
$263$	−0.0278640	−	0.0857567i	−0.00171817	−	0.00528799i	−0.951912	+	0.306372i	$0.900885\pi$
$264$		0			0
$265$	−15.5172	−	11.2739i	−0.953215	−	0.692551i
$266$	−3.73607	−	2.71441i	−0.229073	−	0.166431i
$267$		0			0
$268$	12.4721	+	9.06154i	0.761857	+	0.553521i
$269$	−4.89919	+	3.55947i	−0.298709	+	0.217025i	−0.727036	−	0.686599i	$-0.759103\pi$
$269$	−4.89919	+	3.55947i	−0.298709	+	0.217025i	0.428328	+	0.903623i	$0.359103\pi$
$270$		0			0
$271$	21.1353	+	15.3557i	1.28388	+	0.932790i	0.999663	−	0.0259713i	$-0.00826784\pi$
$271$	21.1353	+	15.3557i	1.28388	+	0.932790i	0.284213	+	0.958761i	$0.408268\pi$
$272$	1.30902	−	4.02874i	0.0793708	−	0.244278i
$273$		0			0
$274$	−5.47214	+	3.97574i	−0.330584	+	0.240183i
$275$	2.20820	−	6.79615i	0.133160	−	0.409823i
$276$		0			0
$277$	−4.82624	−	14.8536i	−0.289981	−	0.892468i	−0.984861	−	0.173343i	$-0.944543\pi$
$277$	−4.82624	−	14.8536i	−0.289981	−	0.892468i	0.694881	−	0.719125i	$-0.255457\pi$
$278$	0.236068			0.0141584
$279$		0			0
$280$	−3.42705	−	2.48990i	−0.204805	−	0.148800i
$281$	8.04508	−	5.84510i	0.479930	−	0.348689i	−0.321369	−	0.946954i	$-0.604143\pi$
$281$	8.04508	−	5.84510i	0.479930	−	0.348689i	0.801298	+	0.598265i	$0.204143\pi$
$282$		0			0
$283$	−5.40983	+	16.6497i	−0.321581	+	0.989725i	0.651379	+	0.758752i	$0.274191\pi$
$283$	−5.40983	+	16.6497i	−0.321581	+	0.989725i	−0.972960	+	0.230972i	$0.925809\pi$
$284$	−3.85410			−0.228699
$285$		0			0
$286$	−18.7082			−1.10624
$287$	−13.8992	+	9.37181i	−0.820443	+	0.553200i
$288$		0			0
$289$	−0.763932	+	0.555029i	−0.0449372	+	0.0326488i
$290$	−0.854102			−0.0501546
$291$		0			0
$292$	−5.00000	+	15.3884i	−0.292603	+	0.900539i
$293$	−5.50000	+	3.99598i	−0.321313	+	0.233448i	−0.736736	−	0.676181i	$-0.763634\pi$
$293$	−5.50000	+	3.99598i	−0.321313	+	0.233448i	0.415422	+	0.909629i	$0.363634\pi$
$294$		0			0
$295$	−2.54508	−	7.83297i	−0.148181	−	0.456053i
$296$	1.47214			0.0855662
$297$		0			0
$298$	3.52786	+	10.8576i	0.204364	+	0.628967i
$299$	3.11803	−	9.59632i	0.180321	−	0.554970i
$300$		0			0
$301$	−25.4164			−1.46498
$302$	−4.70820	+	14.4904i	−0.270927	+	0.833827i
$303$		0			0
$304$	−0.545085	−	1.67760i	−0.0312628	−	0.0962169i
$305$	−4.54508	+	3.30220i	−0.260251	+	0.189083i
$306$		0			0
$307$	18.1803	+	13.2088i	1.03761	+	0.753865i	0.969817	−	0.243834i	$-0.0784053\pi$
$307$	18.1803	+	13.2088i	1.03761	+	0.753865i	0.0677899	+	0.997700i	$0.478405\pi$
$308$	−6.35410	−	4.61653i	−0.362059	−	0.263051i
$309$		0			0
$310$	−7.97214	+	5.79210i	−0.452787	+	0.328969i
$311$	1.40983	+	4.33901i	0.0799441	+	0.246043i	0.983038	−	0.183399i	$-0.0587102\pi$
$311$	1.40983	+	4.33901i	0.0799441	+	0.246043i	−0.903094	+	0.429442i	$0.858710\pi$
$312$		0			0
$313$	0.708204	−	2.17963i	0.0400301	−	0.123200i	−0.929044	−	0.369968i	$-0.879369\pi$
$313$	0.708204	−	2.17963i	0.0400301	−	0.123200i	0.969075	+	0.246768i	$0.0793686\pi$
$314$	2.94427			0.166155
$315$		0			0
$316$	4.32624	−	13.3148i	0.243370	−	0.749016i
$317$	4.19098	+	12.8985i	0.235389	+	0.724453i	0.997070	+	0.0765002i	$0.0243746\pi$
$317$	4.19098	+	12.8985i	0.235389	+	0.724453i	−0.761681	+	0.647953i	$0.775625\pi$
$318$		0			0
$319$	−1.58359			−0.0886641
$320$	−0.500000	−	1.53884i	−0.0279508	−	0.0860239i
$321$		0			0
$322$	3.42705	−	2.48990i	0.190982	−	0.138757i
$323$	−2.30902	+	7.10642i	−0.128477	+	0.395412i
$324$		0			0
$325$	−14.8541			−0.823957
$326$	−3.26393	+	2.37139i	−0.180772	+	0.131339i
$327$		0			0
$328$	−6.39919	−	0.224514i	−0.353336	−	0.0123967i
$329$	−4.00000			−0.220527
$330$		0			0
$331$	−10.0902			−0.554606			−0.277303	−	0.960783i	$-0.589441\pi$
$331$	−10.0902			−0.554606			−0.277303	+	0.960783i	$0.589441\pi$
$332$	4.97214	−	15.3027i	0.272881	−	0.839843i
$333$		0			0
$334$	−19.4443	+	14.1271i	−1.06394	+	0.773000i
$335$	−20.1803	−	14.6619i	−1.10257	−	0.801064i
$336$		0			0
$337$	−26.7639			−1.45792			−0.728962	−	0.684554i	$-0.759997\pi$
$337$	−26.7639			−1.45792			−0.728962	+	0.684554i	$0.759997\pi$
$338$	8.00000	+	24.6215i	0.435143	+	1.33923i
$339$		0			0
$340$	−2.11803	+	6.51864i	−0.114867	+	0.353523i
$341$	−14.7812	+	10.7391i	−0.800444	+	0.581557i
$342$		0			0
$343$	5.78115	−	17.7926i	0.312153	−	0.960708i
$344$	−7.85410	−	5.70634i	−0.423465	−	0.307665i
$345$		0			0
$346$	−3.04508	+	2.21238i	−0.163705	+	0.118938i
$347$	−23.2533	−	16.8945i	−1.24830	−	0.906944i	−0.250180	−	0.968199i	$-0.580490\pi$
$347$	−23.2533	−	16.8945i	−1.24830	−	0.906944i	−0.998122	+	0.0612549i	$0.980490\pi$
$348$		0			0
$349$	−5.16312	−	3.75123i	−0.276375	−	0.200798i	0.440960	−	0.897527i	$-0.354638\pi$
$349$	−5.16312	−	3.75123i	−0.276375	−	0.200798i	−0.717335	+	0.696729i	$0.754638\pi$
$350$	−5.04508	−	3.66547i	−0.269671	−	0.195928i
$351$		0			0
$352$	−0.927051	−	2.85317i	−0.0494120	−	0.152074i
$353$	6.16312	+	4.47777i	0.328030	+	0.238328i	0.739594	−	0.673053i	$-0.235017\pi$
$353$	6.16312	+	4.47777i	0.328030	+	0.238328i	−0.411564	+	0.911381i	$0.635017\pi$
$354$		0			0
$355$	6.23607			0.330976
$356$	−5.04508	+	3.66547i	−0.267389	+	0.194269i
$357$		0			0
$358$	7.52786	+	23.1684i	0.397860	+	1.22449i
$359$	3.47214	+	10.6861i	0.183252	+	0.563993i	0.999914	−	0.0131242i	$-0.00417769\pi$
$359$	3.47214	+	10.6861i	0.183252	+	0.563993i	−0.816662	+	0.577117i	$0.804178\pi$
$360$		0			0
$361$	−4.90983	−	15.1109i	−0.258412	−	0.795311i
$362$	−4.88197	−	3.54696i	−0.256590	−	0.186424i
$363$		0			0
$364$	−5.04508	+	15.5272i	−0.264434	+	0.813845i
$365$	8.09017	−	24.8990i	0.423459	−	1.30327i
$366$		0			0
$367$	−7.42705	+	5.39607i	−0.387689	+	0.281672i	−0.764508	−	0.644614i	$-0.777018\pi$
$367$	−7.42705	+	5.39607i	−0.387689	+	0.281672i	0.376819	+	0.926287i	$0.377018\pi$
$368$	1.61803			0.0843459
$369$		0			0
$370$	−2.38197			−0.123833
$371$	−25.1074	+	18.2416i	−1.30351	+	0.947056i
$372$		0			0
$373$	7.78115	−	23.9479i	0.402893	−	1.23998i	−0.519749	−	0.854319i	$-0.673975\pi$
$373$	7.78115	−	23.9479i	0.402893	−	1.23998i	0.922642	−	0.385658i	$-0.126025\pi$
$374$	−3.92705	+	12.0862i	−0.203063	+	0.624964i
$375$		0			0
$376$	−1.23607	−	0.898056i	−0.0637453	−	0.0463137i
$377$	1.01722	+	3.13068i	0.0523895	+	0.161238i
$378$		0			0
$379$	−4.64590	−	14.2986i	−0.238644	−	0.734470i	−0.996617	−	0.0821845i	$-0.973810\pi$
$379$	−4.64590	−	14.2986i	−0.238644	−	0.734470i	0.757973	−	0.652285i	$-0.226190\pi$
$380$	0.881966	+	2.71441i	0.0452439	+	0.139246i
$381$		0			0
$382$	4.04508	−	2.93893i	0.206965	−	0.150369i
$383$	3.18034			0.162508			0.0812539	−	0.996693i	$-0.474108\pi$
$383$	3.18034			0.162508			0.0812539	+	0.996693i	$0.474108\pi$
$384$		0			0
$385$	10.2812	+	7.46969i	0.523976	+	0.380691i
$386$	−3.73607	−	11.4984i	−0.190161	−	0.585255i
$387$		0			0
$388$	−4.42705	−	3.21644i	−0.224749	−	0.163290i
$389$	30.3156	+	22.0256i	1.53706	+	1.11674i	0.952145	+	0.305647i	$0.0988729\pi$
$389$	30.3156	+	22.0256i	1.53706	+	1.11674i	0.584917	+	0.811093i	$0.301127\pi$
$390$		0			0
$391$	−5.54508	−	4.02874i	−0.280427	−	0.203742i
$392$	0.118034	−	0.0857567i	0.00596162	−	0.00433137i
$393$		0			0
$394$	−2.57295	−	1.86936i	−0.129623	−	0.0941768i
$395$	−7.00000	+	21.5438i	−0.352208	+	1.08399i
$396$		0			0
$397$	21.4164	−	15.5599i	1.07486	−	0.780931i	0.0980794	−	0.995179i	$-0.468730\pi$
$397$	21.4164	−	15.5599i	1.07486	−	0.780931i	0.976779	+	0.214248i	$0.0687301\pi$
$398$	2.01722	−	6.20837i	0.101114	−	0.311197i
$399$		0			0
$400$	−0.736068	−	2.26538i	−0.0368034	−	0.113269i
$401$	−24.8885			−1.24287			−0.621437	−	0.783464i	$-0.713451\pi$
$401$	−24.8885			−1.24287			−0.621437	+	0.783464i	$0.713451\pi$
$402$		0			0
$403$	30.7254	+	22.3233i	1.53054	+	1.11200i
$404$	6.30902	−	4.58377i	0.313885	−	0.228051i
$405$		0			0
$406$	−0.427051	+	1.31433i	−0.0211942	+	0.0652290i
$407$	−4.41641			−0.218913
$408$		0			0
$409$	−0.270510			−0.0133759			−0.00668793	−	0.999978i	$-0.502129\pi$
$409$	−0.270510			−0.0133759			−0.00668793	+	0.999978i	$0.502129\pi$
$410$	10.3541	+	0.363271i	0.511353	+	0.0179407i
$411$		0			0
$412$	9.89919	−	7.19218i	0.487698	−	0.354333i
$413$	−13.3262			−0.655741
$414$		0			0
$415$	−8.04508	+	24.7602i	−0.394918	+	1.21543i
$416$	−5.04508	+	3.66547i	−0.247356	+	0.179714i
$417$		0			0
$418$	1.63525	+	5.03280i	0.0799829	+	0.246162i
$419$	17.9787			0.878318			0.439159	−	0.898409i	$-0.355277\pi$
$419$	17.9787			0.878318			0.439159	+	0.898409i	$0.355277\pi$
$420$		0			0
$421$	−8.41641	−	25.9030i	−0.410191	−	1.26244i	−0.916483	−	0.400075i	$-0.868984\pi$
$421$	−8.41641	−	25.9030i	−0.410191	−	1.26244i	0.506292	−	0.862362i	$-0.331016\pi$
$422$	1.92705	−	5.93085i	0.0938074	−	0.288709i
$423$		0			0
$424$	−11.8541			−0.575686
$425$	−3.11803	+	9.59632i	−0.151247	+	0.465490i
$426$		0			0
$427$	2.80902	+	8.64527i	0.135938	+	0.418374i
$428$	−4.61803	+	3.35520i	−0.223221	+	0.162180i
$429$		0			0
$430$	12.7082	+	9.23305i	0.612844	+	0.445257i
$431$	−9.51722	−	6.91467i	−0.458428	−	0.333068i	0.334486	−	0.942401i	$-0.391437\pi$
$431$	−9.51722	−	6.91467i	−0.458428	−	0.333068i	−0.792914	+	0.609333i	$0.791437\pi$
$432$		0			0
$433$	6.76393	−	4.91428i	0.325054	−	0.236165i	−0.413275	−	0.910606i	$-0.635615\pi$
$433$	6.76393	−	4.91428i	0.325054	−	0.236165i	0.738329	+	0.674441i	$0.235615\pi$
$434$	4.92705	+	15.1639i	0.236506	+	0.727891i
$435$		0			0
$436$	2.30902	−	7.10642i	0.110582	−	0.340336i
$437$	−2.85410			−0.136530
$438$		0			0
$439$	−7.16312	+	22.0458i	−0.341877	+	1.05219i	0.621357	+	0.783527i	$0.286581\pi$
$439$	−7.16312	+	22.0458i	−0.341877	+	1.05219i	−0.963234	+	0.268662i	$0.913419\pi$
$440$	1.50000	+	4.61653i	0.0715097	+	0.220084i
$441$		0			0
$442$	26.4164			1.25650
$443$	7.19756	+	22.1518i	0.341966	+	1.05246i	0.963188	+	0.268829i	$0.0866368\pi$
$443$	7.19756	+	22.1518i	0.341966	+	1.05246i	−0.621221	+	0.783635i	$0.713363\pi$
$444$		0			0
$445$	8.16312	−	5.93085i	0.386969	−	0.281149i
$446$	−7.94427	+	24.4500i	−0.376172	+	1.15774i
$447$		0			0
$448$	−2.61803			−0.123690
$449$	5.57295	−	4.04898i	0.263004	−	0.191083i	−0.448466	−	0.893800i	$-0.648030\pi$
$449$	5.57295	−	4.04898i	0.263004	−	0.191083i	0.711470	+	0.702716i	$0.248030\pi$
$450$		0			0
$451$	19.1976	+	0.673542i	0.903978	+	0.0317159i
$452$	−17.8541			−0.839786
$453$		0			0
$454$	18.6525			0.875404
$455$	8.16312	−	25.1235i	0.382693	−	1.17781i
$456$		0			0
$457$	8.66312	−	6.29412i	0.405244	−	0.294427i	−0.366430	−	0.930446i	$-0.619420\pi$
$457$	8.66312	−	6.29412i	0.405244	−	0.294427i	0.771673	+	0.636019i	$0.219420\pi$
$458$	−8.59017	−	6.24112i	−0.401392	−	0.291629i
$459$		0			0
$460$	−2.61803			−0.122066
$461$	−9.60081	−	29.5483i	−0.447154	−	1.37620i	−0.880104	−	0.474782i	$-0.842527\pi$
$461$	−9.60081	−	29.5483i	−0.447154	−	1.37620i	0.432949	−	0.901418i	$-0.357473\pi$
$462$		0			0
$463$	−5.30902	+	16.3395i	−0.246731	+	0.759360i	0.748616	+	0.663004i	$0.230719\pi$
$463$	−5.30902	+	16.3395i	−0.246731	+	0.759360i	−0.995347	+	0.0963559i	$0.969281\pi$
$464$	−0.427051	+	0.310271i	−0.0198253	+	0.0144040i
$465$		0			0
$466$	−4.10739	+	12.6412i	−0.190271	+	0.585595i
$467$	22.6525	+	16.4580i	1.04823	+	0.761585i	0.971875	−	0.235496i	$-0.0756714\pi$
$467$	22.6525	+	16.4580i	1.04823	+	0.761585i	0.0763562	+	0.997081i	$0.475671\pi$
$468$		0			0
$469$	−32.6525	+	23.7234i	−1.50775	+	1.09545i
$470$	2.00000	+	1.45309i	0.0922531	+	0.0670258i
$471$		0			0
$472$	−4.11803	−	2.99193i	−0.189548	−	0.137715i
$473$	23.5623	+	17.1190i	1.08340	+	0.787133i
$474$		0			0
$475$	1.29837	+	3.99598i	0.0595735	+	0.183348i
$476$	8.97214	+	6.51864i	0.411237	+	0.298781i
$477$		0			0
$478$	−25.2705			−1.15585
$479$	21.5623	−	15.6659i	0.985207	−	0.715795i	0.0263407	−	0.999653i	$-0.491615\pi$
$479$	21.5623	−	15.6659i	0.985207	−	0.715795i	0.958866	+	0.283858i	$0.0916145\pi$
$480$		0			0
$481$	2.83688	+	8.73102i	0.129351	+	0.398100i
$482$	−4.72542	−	14.5434i	−0.215237	−	0.662432i
$483$		0			0
$484$	−0.618034	−	1.90211i	−0.0280925	−	0.0864597i
$485$	7.16312	+	5.20431i	0.325260	+	0.236316i
$486$		0			0
$487$	−3.87132	+	11.9147i	−0.175426	+	0.539907i	−0.999653	−	0.0263537i	$-0.991610\pi$
$487$	−3.87132	+	11.9147i	−0.175426	+	0.539907i	0.824226	+	0.566261i	$0.191610\pi$
$488$	−1.07295	+	3.30220i	−0.0485701	+	0.149483i
$489$		0			0
$490$	−0.190983	+	0.138757i	−0.00862773	+	0.00626841i
$491$	−26.4721			−1.19467			−0.597335	−	0.801992i	$-0.703774\pi$
$491$	−26.4721			−1.19467			−0.597335	+	0.801992i	$0.703774\pi$
$492$		0			0
$493$	2.23607			0.100707
$494$	8.89919	−	6.46564i	0.400393	−	0.290903i
$495$		0			0
$496$	−1.88197	+	5.79210i	−0.0845028	+	0.260073i
$497$	3.11803	−	9.59632i	0.139863	−	0.430454i
$498$		0			0
$499$	−27.2533	−	19.8007i	−1.22002	−	0.886400i	−0.223923	−	0.974607i	$-0.571886\pi$
$499$	−27.2533	−	19.8007i	−1.22002	−	0.886400i	−0.996102	+	0.0882071i	$0.971886\pi$
$500$	3.69098	+	11.3597i	0.165066	+	0.508020i
$501$		0			0
$502$	−5.42705	−	16.7027i	−0.242221	−	0.745480i
$503$	1.27458	+	3.92274i	0.0568305	+	0.174906i	0.975442	−	0.220255i	$-0.0706888\pi$
$503$	1.27458	+	3.92274i	0.0568305	+	0.174906i	−0.918612	+	0.395161i	$0.870689\pi$
$504$		0			0
$505$	−10.2082	+	7.41669i	−0.454259	+	0.330039i
$506$	−4.85410			−0.215791
$507$		0			0
$508$	−5.50000	−	3.99598i	−0.244023	−	0.177293i
$509$	−9.92705	−	30.5523i	−0.440009	−	1.35421i	−0.887866	−	0.460103i	$-0.847813\pi$
$509$	−9.92705	−	30.5523i	−0.440009	−	1.35421i	0.447857	−	0.894105i	$-0.352187\pi$
$510$		0			0
$511$	−34.2705	−	24.8990i	−1.51604	−	1.10147i
$512$	−0.809017	−	0.587785i	−0.0357538	−	0.0259767i
$513$		0			0
$514$	−3.85410	−	2.80017i	−0.169997	−	0.123510i
$515$	−16.0172	+	11.6372i	−0.705803	+	0.512796i
$516$		0			0
$517$	3.70820	+	2.69417i	0.163087	+	0.118489i
$518$	−1.19098	+	3.66547i	−0.0523288	+	0.161051i
$519$		0			0
$520$	8.16312	−	5.93085i	0.357976	−	0.260085i
$521$	−2.29837	+	7.07367i	−0.100694	+	0.309903i	−0.988696	−	0.149937i	$-0.952093\pi$
$521$	−2.29837	+	7.07367i	−0.100694	+	0.309903i	0.888002	+	0.459840i	$0.152093\pi$
$522$		0			0
$523$	−4.91641	−	15.1311i	−0.214980	−	0.661639i	−0.999155	−	0.0410998i	$-0.986914\pi$
$523$	−4.91641	−	15.1311i	−0.214980	−	0.661639i	0.784176	−	0.620539i	$-0.213086\pi$
$524$	9.14590			0.399540
$525$		0			0
$526$	0.0729490	+	0.0530006i	0.00318073	+	0.00231093i
$527$	20.8713	−	15.1639i	0.909169	−	0.660550i
$528$		0			0
$529$	−6.29837	+	19.3844i	−0.273842	+	0.842800i
$530$	19.1803			0.833141
$531$		0			0
$532$	4.61803			0.200217
$533$	−11.0000	−	38.3853i	−0.476463	−	1.66265i
$534$		0			0
$535$	7.47214	−	5.42882i	0.323049	−	0.234709i
$536$	−15.4164			−0.665887
$537$		0			0
$538$	1.87132	−	5.75934i	0.0806785	−	0.248303i
$539$	−0.354102	+	0.257270i	−0.0152523	+	0.0110814i
$540$		0			0
$541$	7.13525	+	21.9601i	0.306769	+	0.944137i	0.979011	+	0.203806i	$0.0653311\pi$
$541$	7.13525	+	21.9601i	0.306769	+	0.944137i	−0.672243	+	0.740331i	$0.734669\pi$
$542$	−26.1246			−1.12215
$543$		0			0
$544$	1.30902	+	4.02874i	0.0561236	+	0.172731i
$545$	−3.73607	+	11.4984i	−0.160036	+	0.492539i
$546$		0			0
$547$	9.00000			0.384812			0.192406	−	0.981315i	$-0.438371\pi$
$547$	9.00000			0.384812			0.192406	+	0.981315i	$0.438371\pi$
$548$	2.09017	−	6.43288i	0.0892876	−	0.274799i
$549$		0			0
$550$	2.20820	+	6.79615i	0.0941581	+	0.289789i
$551$	0.753289	−	0.547296i	0.0320912	−	0.0233156i
$552$		0			0
$553$	29.6525	+	21.5438i	1.26095	+	0.916135i
$554$	12.6353	+	9.18005i	0.536821	+	0.390023i
$555$		0			0
$556$	−0.190983	+	0.138757i	−0.00809948	+	0.00588462i
$557$	−0.343459	−	1.05706i	−0.0145528	−	0.0447890i	0.943516	−	0.331326i	$-0.107496\pi$
$557$	−0.343459	−	1.05706i	−0.0145528	−	0.0447890i	−0.958069	+	0.286537i	$0.907496\pi$
$558$		0			0
$559$	18.7082	−	57.5779i	0.791273	−	2.43529i
$560$	4.23607			0.179007
$561$		0			0
$562$	−3.07295	+	9.45756i	−0.129625	+	0.398943i
$563$	−2.85410	−	8.78402i	−0.120286	−	0.370202i	0.872727	−	0.488209i	$-0.162350\pi$
$563$	−2.85410	−	8.78402i	−0.120286	−	0.370202i	−0.993013	+	0.118007i	$0.962350\pi$
$564$		0			0
$565$	28.8885			1.21535
$566$	−5.40983	−	16.6497i	−0.227392	−	0.699841i
$567$		0			0
$568$	3.11803	−	2.26538i	0.130830	−	0.0950534i
$569$	−12.0517	+	37.0912i	−0.505232	+	1.55494i	0.295148	+	0.955451i	$0.404631\pi$
$569$	−12.0517	+	37.0912i	−0.505232	+	1.55494i	−0.800380	+	0.599493i	$0.795369\pi$
$570$		0			0
$571$	−6.12461			−0.256307			−0.128154	−	0.991754i	$-0.540905\pi$
$571$	−6.12461			−0.256307			−0.128154	+	0.991754i	$0.540905\pi$
$572$	15.1353	−	10.9964i	0.632837	−	0.459783i
$573$		0			0
$574$	5.73607	−	15.7517i	0.239419	−	0.657463i
$575$	−3.85410			−0.160727
$576$		0			0
$577$	13.4721			0.560852			0.280426	−	0.959876i	$-0.409524\pi$
$577$	13.4721			0.560852			0.280426	+	0.959876i	$0.409524\pi$
$578$	0.291796	−	0.898056i	0.0121371	−	0.0373542i
$579$		0			0
$580$	0.690983	−	0.502029i	0.0286915	−	0.0208456i
$581$	34.0795	+	24.7602i	1.41386	+	1.02723i
$582$		0			0
$583$	35.5623			1.47284
$584$	−5.00000	−	15.3884i	−0.206901	−	0.636777i
$585$		0			0
$586$	2.10081	−	6.46564i	0.0867838	−	0.267093i
$587$	9.73607	−	7.07367i	0.401851	−	0.291962i	−0.368444	−	0.929650i	$-0.620109\pi$
$587$	9.73607	−	7.07367i	0.401851	−	0.291962i	0.770294	+	0.637689i	$0.220109\pi$
$588$		0			0
$589$	3.31966	−	10.2169i	0.136784	−	0.420979i
$590$	6.66312	+	4.84104i	0.274316	+	0.199302i
$591$		0			0
$592$	−1.19098	+	0.865300i	−0.0489491	+	0.0355636i
$593$	−6.76393	−	4.91428i	−0.277761	−	0.201805i	0.440179	−	0.897910i	$-0.354915\pi$
$593$	−6.76393	−	4.91428i	−0.277761	−	0.201805i	−0.717940	+	0.696105i	$0.754915\pi$
$594$		0			0
$595$	−14.5172	−	10.5474i	−0.595148	−	0.432400i
$596$	−9.23607	−	6.71040i	−0.378324	−	0.274869i
$597$		0			0
$598$	3.11803	+	9.59632i	0.127506	+	0.392423i
$599$	19.7984	+	14.3844i	0.808940	+	0.587729i	0.913523	−	0.406787i	$-0.133351\pi$
$599$	19.7984	+	14.3844i	0.808940	+	0.587729i	−0.104583	+	0.994516i	$0.533351\pi$
$600$		0			0
$601$	−27.1803			−1.10871			−0.554355	−	0.832281i	$-0.687035\pi$
$601$	−27.1803			−1.10871			−0.554355	+	0.832281i	$0.687035\pi$
$602$	20.5623	−	14.9394i	0.838057	−	0.608884i
$603$		0			0
$604$	−4.70820	−	14.4904i	−0.191574	−	0.589604i
$605$	1.00000	+	3.07768i	0.0406558	+	0.125126i
$606$		0			0
$607$	12.2188	+	37.6057i	0.495948	+	1.52637i	0.815475	+	0.578793i	$0.196476\pi$
$607$	12.2188	+	37.6057i	0.495948	+	1.52637i	−0.319527	+	0.947577i	$0.603524\pi$
$608$	1.42705	+	1.03681i	0.0578746	+	0.0420483i
$609$		0			0
$610$	1.73607	−	5.34307i	0.0702913	−	0.216334i
$611$	2.94427	−	9.06154i	0.119112	−	0.366591i
$612$		0			0
$613$	19.4615	−	14.1396i	0.786042	−	0.571093i	−0.120744	−	0.992684i	$-0.538528\pi$
$613$	19.4615	−	14.1396i	0.786042	−	0.571093i	0.906786	+	0.421591i	$0.138528\pi$
$614$	−22.4721			−0.906902
$615$		0			0
$616$	7.85410			0.316451
$617$	−12.8541	+	9.33905i	−0.517487	+	0.375976i	−0.815656	−	0.578537i	$-0.803624\pi$
$617$	−12.8541	+	9.33905i	−0.517487	+	0.375976i	0.298170	+	0.954513i	$0.403624\pi$
$618$		0			0
$619$	0.0729490	−	0.224514i	0.00293207	−	0.00902398i	−0.949580	−	0.313526i	$-0.898490\pi$
$619$	0.0729490	−	0.224514i	0.00293207	−	0.00902398i	0.952512	+	0.304502i	$0.0984899\pi$
$620$	3.04508	−	9.37181i	0.122294	−	0.376381i
$621$		0			0
$622$	−3.69098	−	2.68166i	−0.147995	−	0.107525i
$623$	−5.04508	−	15.5272i	−0.202127	−	0.622083i
$624$		0			0
$625$	−2.29180	−	7.05342i	−0.0916718	−	0.282137i
$626$	0.708204	+	2.17963i	0.0283055	+	0.0871154i
$627$		0			0
$628$	−2.38197	+	1.73060i	−0.0950508	+	0.0690584i
$629$	6.23607			0.248648
$630$		0			0
$631$	−6.47214	−	4.70228i	−0.257652	−	0.187195i	0.451459	−	0.892292i	$-0.350904\pi$
$631$	−6.47214	−	4.70228i	−0.257652	−	0.187195i	−0.709111	+	0.705097i	$0.750904\pi$
$632$	4.32624	+	13.3148i	0.172089	+	0.529634i
$633$		0			0
$634$	−10.9721	−	7.97172i	−0.435759	−	0.316598i
$635$	8.89919	+	6.46564i	0.353153	+	0.256581i
$636$		0			0
$637$	0.736068	+	0.534785i	0.0291641	+	0.0211889i
$638$	1.28115	−	0.930812i	0.0507213	−	0.0368512i
$639$		0			0
$640$	1.30902	+	0.951057i	0.0517434	+	0.0375938i
$641$	1.48278	−	4.56352i	0.0585663	−	0.180248i	−0.917494	−	0.397751i	$-0.869791\pi$
$641$	1.48278	−	4.56352i	0.0585663	−	0.180248i	0.976060	+	0.217502i	$0.0697909\pi$
$642$		0			0
$643$	−5.76393	+	4.18774i	−0.227307	+	0.165148i	−0.695610	−	0.718420i	$-0.744866\pi$
$643$	−5.76393	+	4.18774i	−0.227307	+	0.165148i	0.468303	+	0.883568i	$0.344866\pi$
$644$	−1.30902	+	4.02874i	−0.0515825	+	0.158755i
$645$		0			0
$646$	−2.30902	−	7.10642i	−0.0908471	−	0.279598i
$647$	18.3820			0.722670			0.361335	−	0.932436i	$-0.382321\pi$
$647$	18.3820			0.722670			0.361335	+	0.932436i	$0.382321\pi$
$648$		0			0
$649$	12.3541	+	8.97578i	0.484941	+	0.352330i
$650$	12.0172	−	8.73102i	0.471354	−	0.342459i
$651$		0			0
$652$	1.24671	−	3.83698i	0.0488250	−	0.150268i
$653$	−27.8328			−1.08918			−0.544591	−	0.838702i	$-0.683315\pi$
$653$	−27.8328			−1.08918			−0.544591	+	0.838702i	$0.683315\pi$
$654$		0			0
$655$	−14.7984			−0.578220
$656$	5.30902	−	3.57971i	0.207282	−	0.139764i
$657$		0			0
$658$	3.23607	−	2.35114i	0.126155	−	0.0916570i
$659$	−20.6525			−0.804506			−0.402253	−	0.915528i	$-0.631773\pi$
$659$	−20.6525			−0.804506			−0.402253	+	0.915528i	$0.631773\pi$
$660$		0			0
$661$	−0.611456	+	1.88187i	−0.0237829	+	0.0731962i	−0.962244	−	0.272190i	$-0.912252\pi$
$661$	−0.611456	+	1.88187i	−0.0237829	+	0.0731962i	0.938461	+	0.345386i	$0.112252\pi$
$662$	8.16312	−	5.93085i	0.317269	−	0.230509i
$663$		0			0
$664$	4.97214	+	15.3027i	0.192956	+	0.593858i
$665$	−7.47214			−0.289757
$666$		0			0
$667$	0.263932	+	0.812299i	0.0102195	+	0.0314524i
$668$	7.42705	−	22.8581i	0.287361	−	0.884407i
$669$		0			0
$670$	24.9443			0.963681
$671$	3.21885	−	9.90659i	0.124262	−	0.382440i
$672$		0			0
$673$	−4.40983	−	13.5721i	−0.169986	−	0.523165i	0.829383	−	0.558681i	$-0.188692\pi$
$673$	−4.40983	−	13.5721i	−0.169986	−	0.523165i	−0.999369	+	0.0355165i	$0.988692\pi$
$674$	21.6525	−	15.7314i	0.834022	−	0.605953i
$675$		0			0
$676$	−20.9443	−	15.2169i	−0.805549	−	0.585266i
$677$	25.9894	+	18.8824i	0.998852	+	0.725709i	0.961842	−	0.273606i	$-0.0882165\pi$
$677$	25.9894	+	18.8824i	0.998852	+	0.725709i	0.0370104	+	0.999315i	$0.488217\pi$
$678$		0			0
$679$	11.5902	−	8.42075i	0.444790	−	0.323159i
$680$	−2.11803	−	6.51864i	−0.0812229	−	0.249978i
$681$		0			0
$682$	5.64590	−	17.3763i	0.216193	−	0.665372i
$683$	13.2016			0.505146			0.252573	−	0.967578i	$-0.418723\pi$
$683$	13.2016			0.505146			0.252573	+	0.967578i	$0.418723\pi$
$684$		0			0
$685$	−3.38197	+	10.4086i	−0.129218	+	0.397693i
$686$	5.78115	+	17.7926i	0.220725	+	0.679323i
$687$		0			0
$688$	9.70820			0.370122
$689$	−22.8435	−	70.3049i	−0.870266	−	2.67840i
$690$		0			0
$691$	2.90983	−	2.11412i	0.110695	−	0.0804247i	−0.531061	−	0.847334i	$-0.678206\pi$
$691$	2.90983	−	2.11412i	0.110695	−	0.0804247i	0.641756	+	0.766909i	$0.278206\pi$
$692$	1.16312	−	3.57971i	0.0442151	−	0.136080i
$693$		0			0
$694$	28.7426			1.09106
$695$	0.309017	−	0.224514i	0.0117217	−	0.00851630i
$696$		0			0
$697$	−27.1074	−	0.951057i	−1.02677	−	0.0360238i
$698$	6.38197			0.241561
$699$		0			0
$700$	6.23607			0.235701
$701$	−11.1697	+	34.3768i	−0.421874	+	1.29839i	0.484083	+	0.875022i	$0.339153\pi$
$701$	−11.1697	+	34.3768i	−0.421874	+	1.29839i	−0.905956	+	0.423371i	$0.860847\pi$
$702$		0			0
$703$	2.10081	−	1.52633i	0.0792337	−	0.0575666i
$704$	2.42705	+	1.76336i	0.0914729	+	0.0664590i
$705$		0			0
$706$	−7.61803			−0.286708
$707$	6.30902	+	19.4172i	0.237275	+	0.730257i
$708$		0			0
$709$	−8.73607	+	26.8869i	−0.328090	+	1.00976i	0.641937	+	0.766758i	$0.278131\pi$
$709$	−8.73607	+	26.8869i	−0.328090	+	1.00976i	−0.970026	+	0.242999i	$0.921869\pi$
$710$	−5.04508	+	3.66547i	−0.189339	+	0.137563i
$711$		0			0
$712$	1.92705	−	5.93085i	0.0722193	−	0.222268i
$713$	7.97214	+	5.79210i	0.298559	+	0.216916i
$714$		0			0
$715$	−24.4894	+	17.7926i	−0.915850	+	0.665404i
$716$	−19.7082	−	14.3188i	−0.736530	−	0.535120i
$717$		0			0
$718$	−9.09017	−	6.60440i	−0.339242	−	0.246474i
$719$	30.1074	+	21.8743i	1.12282	+	0.815774i	0.984634	−	0.174633i	$-0.0558739\pi$
$719$	30.1074	+	21.8743i	1.12282	+	0.815774i	0.138183	+	0.990407i	$0.455874\pi$
$720$		0			0
$721$	9.89919	+	30.4666i	0.368665	+	1.13463i
$722$	12.8541	+	9.33905i	0.478380	+	0.347564i
$723$		0			0
$724$	6.03444			0.224268
$725$	1.01722	−	0.739054i	0.0377786	−	0.0274478i
$726$		0			0
$727$	−3.00000	−	9.23305i	−0.111264	−	0.342435i	0.879886	−	0.475186i	$-0.157619\pi$
$727$	−3.00000	−	9.23305i	−0.111264	−	0.342435i	−0.991149	+	0.132751i	$0.957619\pi$
$728$	−5.04508	−	15.5272i	−0.186983	−	0.575475i
$729$		0			0
$730$	8.09017	+	24.8990i	0.299431	+	0.921553i
$731$	−33.2705	−	24.1724i	−1.23055	−	0.894050i
$732$		0			0
$733$	5.33688	−	16.4252i	0.197122	−	0.606680i	−0.802823	−	0.596217i	$-0.796670\pi$
$733$	5.33688	−	16.4252i	0.197122	−	0.606680i	0.999945	−	0.0104624i	$-0.00333035\pi$
$734$	2.83688	−	8.73102i	0.104711	−	0.322268i
$735$		0			0
$736$	−1.30902	+	0.951057i	−0.0482510	+	0.0350564i
$737$	46.2492			1.70361
$738$		0			0
$739$	−19.8328			−0.729562			−0.364781	−	0.931093i	$-0.618856\pi$
$739$	−19.8328			−0.729562			−0.364781	+	0.931093i	$0.618856\pi$
$740$	1.92705	−	1.40008i	0.0708398	−	0.0514681i
$741$		0			0
$742$	9.59017	−	29.5155i	0.352066	−	1.08355i
$743$	9.23607	−	28.4257i	0.338838	−	1.04284i	−0.625962	−	0.779854i	$-0.715293\pi$
$743$	9.23607	−	28.4257i	0.338838	−	1.04284i	0.964800	−	0.262984i	$-0.0847066\pi$
$744$		0			0
$745$	14.9443	+	10.8576i	0.547516	+	0.397793i
$746$	7.78115	+	23.9479i	0.284888	+	0.876796i
$747$		0			0
$748$	−3.92705	−	12.0862i	−0.143587	−	0.441916i
$749$	−4.61803	−	14.2128i	−0.168739	−	0.519326i
$750$		0			0
$751$	−6.02786	+	4.37950i	−0.219960	+	0.159810i	−0.692309	−	0.721602i	$-0.743406\pi$
$751$	−6.02786	+	4.37950i	−0.219960	+	0.159810i	0.472349	+	0.881412i	$0.343406\pi$
$752$	1.52786			0.0557155
$753$		0			0
$754$	−2.66312	−	1.93487i	−0.0969851	−	0.0704638i
$755$	7.61803	+	23.4459i	0.277249	+	0.853284i
$756$		0			0
$757$	11.0623	+	8.03724i	0.402066	+	0.292118i	0.770382	−	0.637582i	$-0.220065\pi$
$757$	11.0623	+	8.03724i	0.402066	+	0.292118i	−0.368316	+	0.929701i	$0.620065\pi$
$758$	12.1631	+	8.83702i	0.441784	+	0.320975i
$759$		0			0
$760$	−2.30902	−	1.67760i	−0.0837568	−	0.0608529i
$761$	0.427051	−	0.310271i	0.0154806	−	0.0112473i	−0.580018	−	0.814604i	$-0.696955\pi$
$761$	0.427051	−	0.310271i	0.0154806	−	0.0112473i	0.595499	+	0.803356i	$0.296955\pi$
$762$		0			0
$763$	15.8262	+	11.4984i	0.572948	+	0.416271i
$764$	−1.54508	+	4.75528i	−0.0558992	+	0.172040i
$765$		0			0
$766$	−2.57295	+	1.86936i	−0.0929644	+	0.0675426i
$767$	9.80902	−	30.1891i	0.354183	−	1.09006i
$768$		0			0
$769$	8.92705	+	27.4746i	0.321918	+	0.990761i	0.972813	+	0.231593i	$0.0743938\pi$
$769$	8.92705	+	27.4746i	0.321918	+	0.990761i	−0.650895	+	0.759168i	$0.725606\pi$
$770$	−12.7082			−0.457972
$771$		0			0
$772$	9.78115	+	7.10642i	0.352031	+	0.255766i
$773$	12.2812	−	8.92278i	0.441722	−	0.320930i	−0.344597	−	0.938751i	$-0.611984\pi$
$773$	12.2812	−	8.92278i	0.441722	−	0.320930i	0.786319	+	0.617821i	$0.211984\pi$
$774$		0			0
$775$	4.48278	−	13.7966i	0.161026	−	0.495588i
$776$	5.47214			0.196438
$777$		0			0
$778$	−37.4721			−1.34344
$779$	−9.36475	+	6.31437i	−0.335527	+	0.226236i
$780$		0			0
$781$	−9.35410	+	6.79615i	−0.334716	+	0.243185i
$782$	6.85410			0.245102
$783$		0			0
$784$	−0.0450850	+	0.138757i	−0.00161018	+	0.00495562i
$785$	3.85410	−	2.80017i	0.137559	−	0.0999423i
$786$		0			0
$787$	−3.95492	−	12.1720i	−0.140977	−	0.433884i	0.855494	−	0.517812i	$-0.173253\pi$
$787$	−3.95492	−	12.1720i	−0.140977	−	0.433884i	−0.996472	+	0.0839281i	$0.973253\pi$
$788$	3.18034			0.113295
$789$		0			0
$790$	−7.00000	−	21.5438i	−0.249049	−	0.766493i
$791$	14.4443	−	44.4549i	0.513579	−	1.58063i
$792$		0			0
$793$	−21.6525			−0.768902
$794$	−8.18034	+	25.1765i	−0.290309	+	0.893480i
$795$		0			0
$796$	2.01722	+	6.20837i	0.0714985	+	0.220050i
$797$	−18.4164	+	13.3803i	−0.652343	+	0.473955i	−0.864068	−	0.503374i	$-0.832092\pi$
$797$	−18.4164	+	13.3803i	−0.652343	+	0.473955i	0.211726	+	0.977329i	$0.432092\pi$
$798$		0			0
$799$	−5.23607	−	3.80423i	−0.185239	−	0.134584i
$800$	1.92705	+	1.40008i	0.0681315	+	0.0495005i
$801$		0			0
$802$	20.1353	−	14.6291i	0.711001	−	0.516572i
$803$	15.0000	+	46.1653i	0.529339	+	1.62914i
$804$		0			0
$805$	2.11803	−	6.51864i	0.0746509	−	0.229752i
$806$	−37.9787			−1.33774
$807$		0			0
$808$	−2.40983	+	7.41669i	−0.0847775	+	0.260918i
$809$	9.45492	+	29.0992i	0.332417	+	1.02307i	0.967980	+	0.251026i	$0.0807679\pi$
$809$	9.45492	+	29.0992i	0.332417	+	1.02307i	−0.635563	+	0.772049i	$0.719232\pi$
$810$		0			0
$811$	19.0689			0.669599			0.334800	−	0.942289i	$-0.391331\pi$
$811$	19.0689			0.669599			0.334800	+	0.942289i	$0.391331\pi$
$812$	−0.427051	−	1.31433i	−0.0149866	−	0.0461239i
$813$		0			0
$814$	3.57295	−	2.59590i	0.125232	−	0.0909862i
$815$	−2.01722	+	6.20837i	−0.0706602	+	0.217470i
$816$		0			0
$817$	−17.1246			−0.599114
$818$	0.218847	−	0.159002i	0.00765181	−	0.00555936i
$819$		0			0
$820$	−8.59017	+	5.79210i	−0.299982	+	0.202269i
$821$	−10.4377			−0.364278			−0.182139	−	0.983273i	$-0.558302\pi$
$821$	−10.4377			−0.364278			−0.182139	+	0.983273i	$0.558302\pi$
$822$		0			0
$823$	1.43769			0.0501149			0.0250574	−	0.999686i	$-0.492023\pi$
$823$	1.43769			0.0501149			0.0250574	+	0.999686i	$0.492023\pi$
$824$	−3.78115	+	11.6372i	−0.131723	+	0.405401i
$825$		0			0
$826$	10.7812	−	7.83297i	0.375124	−	0.272544i
$827$	−9.51722	−	6.91467i	−0.330946	−	0.240446i	0.409886	−	0.912137i	$-0.365569\pi$
$827$	−9.51722	−	6.91467i	−0.330946	−	0.240446i	−0.740832	+	0.671690i	$0.765569\pi$
$828$		0			0
$829$	10.2918			0.357449			0.178724	−	0.983899i	$-0.442803\pi$
$829$	10.2918			0.357449			0.178724	+	0.983899i	$0.442803\pi$
$830$	−8.04508	−	24.7602i	−0.279249	−	0.859440i
$831$		0			0
$832$	1.92705	−	5.93085i	0.0668085	−	0.205615i
$833$	0.500000	−	0.363271i	0.0173240	−	0.0125866i
$834$		0			0
$835$	−12.0172	+	36.9852i	−0.415873	+	1.27993i
$836$	−4.28115	−	3.11044i	−0.148067	−	0.107577i
$837$		0			0
$838$	−14.5451	+	10.5676i	−0.502452	+	0.365052i
$839$	−18.6074	−	13.5191i	−0.642398	−	0.466730i	0.218275	−	0.975887i	$-0.429957\pi$
$839$	−18.6074	−	13.5191i	−0.642398	−	0.466730i	−0.860673	+	0.509158i	$0.829957\pi$
$840$		0			0
$841$	23.2361	+	16.8820i	0.801244	+	0.582138i
$842$	22.0344	+	16.0090i	0.759357	+	0.551705i
$843$		0			0
$844$	1.92705	+	5.93085i	0.0663318	+	0.204148i
$845$	33.8885	+	24.6215i	1.16580	+	0.847004i
$846$		0			0
$847$	5.23607			0.179913
$848$	9.59017	−	6.96767i	0.329328	−	0.239271i
$849$		0			0
$850$	−3.11803	−	9.59632i	−0.106948	−	0.329151i
$851$	0.736068	+	2.26538i	0.0252321	+	0.0776564i
$852$		0			0
$853$	4.19098	+	12.8985i	0.143497	+	0.441637i	0.996815	−	0.0797538i	$-0.0254134\pi$
$853$	4.19098	+	12.8985i	0.143497	+	0.441637i	−0.853318	+	0.521391i	$0.825413\pi$
$854$	−7.35410	−	5.34307i	−0.251652	−	0.182836i
$855$		0			0
$856$	1.76393	−	5.42882i	0.0602900	−	0.185553i
$857$	−5.60081	+	17.2375i	−0.191320	+	0.588823i	0.808680	+	0.588249i	$0.200183\pi$
$857$	−5.60081	+	17.2375i	−0.191320	+	0.588823i	−1.00000		0.000573603i	$0.999817\pi$
$858$		0			0
$859$	3.61803	−	2.62866i	0.123446	−	0.0896886i	−0.524349	−	0.851503i	$-0.675691\pi$
$859$	3.61803	−	2.62866i	0.123446	−	0.0896886i	0.647795	+	0.761815i	$0.275691\pi$
$860$	−15.7082			−0.535645
$861$		0			0
$862$	11.7639			0.400681
$863$	−2.38197	+	1.73060i	−0.0810831	+	0.0589103i	−0.627588	−	0.778545i	$-0.715958\pi$
$863$	−2.38197	+	1.73060i	−0.0810831	+	0.0589103i	0.546505	+	0.837456i	$0.315958\pi$
$864$		0			0
$865$	−1.88197	+	5.79210i	−0.0639888	+	0.196937i
$866$	−2.58359	+	7.95148i	−0.0877940	+	0.270202i
$867$		0			0
$868$	−12.8992	−	9.37181i	−0.437827	−	0.318100i
$869$	−12.9787	−	39.9444i	−0.440273	−	1.35502i
$870$		0			0
$871$	−29.7082	−	91.4325i	−1.00662	−	3.09807i
$872$	2.30902	+	7.10642i	0.0781932	+	0.240654i
$873$		0			0
$874$	2.30902	−	1.67760i	0.0781037	−	0.0567456i
$875$	−31.2705			−1.05714
$876$		0			0
$877$	−29.3435	−	21.3193i	−0.990858	−	0.719901i	−0.0307493	−	0.999527i	$-0.509789\pi$
$877$	−29.3435	−	21.3193i	−0.990858	−	0.719901i	−0.960109	+	0.279627i	$0.909789\pi$
$878$	−7.16312	−	22.0458i	−0.241744	−	0.744010i
$879$		0			0
$880$	−3.92705	−	2.85317i	−0.132381	−	0.0961803i
$881$	−37.0344	−	26.9071i	−1.24772	−	0.906523i	−0.249635	−	0.968340i	$-0.580310\pi$
$881$	−37.0344	−	26.9071i	−1.24772	−	0.906523i	−0.998088	+	0.0618170i	$0.980310\pi$
$882$		0			0
$883$	0.600813	+	0.436516i	0.0202190	+	0.0146899i	0.597849	−	0.801609i	$-0.296022\pi$
$883$	0.600813	+	0.436516i	0.0202190	+	0.0146899i	−0.577630	+	0.816299i	$0.696022\pi$
$884$	−21.3713	+	15.5272i	−0.718795	+	0.522235i
$885$		0			0
$886$	−18.8435	−	13.6906i	−0.633058	−	0.459944i
$887$	3.97871	−	12.2452i	0.133592	−	0.411154i	−0.861776	−	0.507289i	$-0.830648\pi$
$887$	3.97871	−	12.2452i	0.133592	−	0.411154i	0.995368	+	0.0961343i	$0.0306478\pi$
$888$		0			0
$889$	14.3992	−	10.4616i	0.482933	−	0.350872i
$890$	−3.11803	+	9.59632i	−0.104517	+	0.321669i
$891$		0			0
$892$	−7.94427	−	24.4500i	−0.265994	−	0.818645i
$893$	−2.69505			−0.0901864
$894$		0			0
$895$	31.8885	+	23.1684i	1.06592	+	0.774434i
$896$	2.11803	−	1.53884i	0.0707585	−	0.0514091i
$897$		0			0
$898$	−2.12868	+	6.55139i	−0.0710349	+	0.218623i
$899$	−3.21478			−0.107219
$900$		0			0
$901$	−50.2148			−1.67290
$902$	−15.9271	+	10.7391i	−0.530313	+	0.357574i
$903$		0			0
$904$	14.4443	−	10.4944i	0.480409	−	0.349038i
$905$	−9.76393			−0.324564
$906$		0			0
$907$	−12.2639	+	37.7445i	−0.407217	+	1.25329i	0.511812	+	0.859097i	$0.328974\pi$
$907$	−12.2639	+	37.7445i	−0.407217	+	1.25329i	−0.919030	+	0.394188i	$0.871026\pi$
$908$	−15.0902	+	10.9637i	−0.500785	+	0.363842i
$909$		0			0
$910$	8.16312	+	25.1235i	0.270605	+	0.832836i
$911$	−42.4853			−1.40760			−0.703800	−	0.710398i	$-0.748515\pi$
$911$	−42.4853			−1.40760			−0.703800	+	0.710398i	$0.748515\pi$
$912$		0			0
$913$	−14.9164	−	45.9080i	−0.493661	−	1.51933i
$914$	−3.30902	+	10.1841i	−0.109453	+	0.336860i
$915$		0			0
$916$	10.6180			0.350830
$917$	−7.39919	+	22.7724i	−0.244343	+	0.752009i
$918$		0			0
$919$	10.6525	+	32.7849i	0.351393	+	1.08148i	0.958072	+	0.286529i	$0.0925014\pi$
$919$	10.6525	+	32.7849i	0.351393	+	1.08148i	−0.606679	+	0.794947i	$0.707499\pi$
$920$	2.11803	−	1.53884i	0.0698295	−	0.0507341i
$921$		0			0
$922$	25.1353	+	18.2618i	0.827786	+	0.601421i
$923$	19.4443	+	14.1271i	0.640016	+	0.464999i
$924$		0			0
$925$	2.83688	−	2.06111i	0.0932761	−	0.0677690i
$926$	−5.30902	−	16.3395i	−0.174465	−	0.536948i
$927$		0			0
$928$	0.163119	−	0.502029i	0.00535464	−	0.0164799i
$929$	27.8328			0.913165			0.456583	−	0.889681i	$-0.349073\pi$
$929$	27.8328			0.913165			0.456583	+	0.889681i	$0.349073\pi$
$930$		0			0
$931$	0.0795268	−	0.244758i	0.00260639	−	0.00802163i
$932$	−4.10739	−	12.6412i	−0.134542	−	0.414078i
$933$		0			0
$934$	−28.0000			−0.916188
$935$	6.35410	+	19.5559i	0.207801	+	0.639547i
$936$		0			0
$937$	−36.0238	+	26.1728i	−1.17685	+	0.855029i	−0.991812	−	0.127703i	$-0.959239\pi$
$937$	−36.0238	+	26.1728i	−1.17685	+	0.855029i	−0.185034	+	0.982732i	$0.559239\pi$
$938$	12.4721	−	38.3853i	0.407230	−	1.25332i
$939$		0			0
$940$	−2.47214			−0.0806322
$941$	24.4164	−	17.7396i	0.795952	−	0.578293i	−0.113772	−	0.993507i	$-0.536293\pi$
$941$	24.4164	−	17.7396i	0.795952	−	0.578293i	0.909724	+	0.415214i	$0.136293\pi$
$942$		0			0
$943$	−2.85410	−	9.95959i	−0.0929423	−	0.324329i
$944$	5.09017			0.165671
$945$		0			0
$946$	−29.1246			−0.946923
$947$	0.0172209	−	0.0530006i	0.000559605	−	0.00172229i	−0.950776	−	0.309878i	$-0.899712\pi$
$947$	0.0172209	−	0.0530006i	0.000559605	−	0.00172229i	0.951336	+	0.308156i	$0.0997118\pi$
$948$		0			0
$949$	81.6312	−	59.3085i	2.64986	−	1.92524i
$950$	−3.39919	−	2.46965i	−0.110284	−	0.0801262i
$951$		0			0
$952$	−11.0902			−0.359434
$953$	−12.2254	−	37.6260i	−0.396020	−	1.21883i	−0.928164	−	0.372171i	$-0.878613\pi$
$953$	−12.2254	−	37.6260i	−0.396020	−	1.21883i	0.532144	−	0.846654i	$-0.321387\pi$
$954$		0			0
$955$	2.50000	−	7.69421i	0.0808981	−	0.248979i
$956$	20.4443	−	14.8536i	0.661215	−	0.480401i
$957$		0			0
$958$	−8.23607	+	25.3480i	−0.266095	+	0.818957i
$959$	14.3262	+	10.4086i	0.462618	+	0.336112i
$960$		0			0
$961$	−4.92705	+	3.57971i	−0.158937	+	0.115475i
$962$	−7.42705	−	5.39607i	−0.239458	−	0.173976i
$963$		0			0
$964$	12.3713	+	8.98829i	0.398453	+	0.289493i
$965$	−15.8262	−	11.4984i	−0.509465	−	0.370148i
$966$		0			0
$967$	9.26393	+	28.5115i	0.297908	+	0.916866i	0.982229	+	0.187686i	$0.0600986\pi$
$967$	9.26393	+	28.5115i	0.297908	+	0.916866i	−0.684321	+	0.729181i	$0.739901\pi$
$968$	1.61803	+	1.17557i	0.0520056	+	0.0377843i
$969$		0			0
$970$	−8.85410			−0.284288
$971$	−9.92705	+	7.21242i	−0.318574	+	0.231458i	−0.735567	−	0.677452i	$-0.763084\pi$
$971$	−9.92705	+	7.21242i	−0.318574	+	0.231458i	0.416993	+	0.908910i	$0.363084\pi$
$972$		0			0
$973$	−0.190983	−	0.587785i	−0.00612263	−	0.0188435i
$974$	−3.87132	−	11.9147i	−0.124045	−	0.381772i
$975$		0			0
$976$	−1.07295	−	3.30220i	−0.0343443	−	0.105701i
$977$	46.4058	+	33.7158i	1.48465	+	1.07866i	0.976021	+	0.217678i	$0.0698484\pi$
$977$	46.4058	+	33.7158i	1.48465	+	1.07866i	0.508631	+	0.860984i	$0.330152\pi$
$978$		0			0
$979$	−5.78115	+	17.7926i	−0.184766	+	0.568653i
$980$	0.0729490	−	0.224514i	0.00233027	−	0.00717184i
$981$		0			0
$982$	21.4164	−	15.5599i	0.683425	−	0.496537i
$983$	−47.8115			−1.52495			−0.762475	−	0.647017i	$-0.776016\pi$
$983$	−47.8115			−1.52495			−0.762475	+	0.647017i	$0.776016\pi$
$984$		0			0
$985$	−5.14590			−0.163962
$986$	−1.80902	+	1.31433i	−0.0576108	+	0.0418567i
$987$		0			0
$988$	−3.39919	+	10.4616i	−0.108143	+	0.332829i
$989$	4.85410	−	14.9394i	0.154351	−	0.475045i
$990$		0			0
$991$	−5.82624	−	4.23301i	−0.185077	−	0.134466i	0.491389	−	0.870940i	$-0.336489\pi$
$991$	−5.82624	−	4.23301i	−0.185077	−	0.134466i	−0.676466	+	0.736474i	$0.736489\pi$
$992$	−1.88197	−	5.79210i	−0.0597525	−	0.183899i
$993$		0			0
$994$	3.11803	+	9.59632i	0.0988980	+	0.304377i
$995$	−3.26393	−	10.0453i	−0.103474	−	0.318459i
$996$		0			0
$997$	−10.4549	+	7.59594i	−0.331110	+	0.240566i	−0.740902	−	0.671614i	$-0.765602\pi$
$997$	−10.4549	+	7.59594i	−0.331110	+	0.240566i	0.409791	+	0.912179i	$0.365602\pi$
$998$	33.6869			1.06634
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	738.2.h.b.37.1		4
3.2	odd	2		82.2.d.b.37.1	✓	4
12.11	even	2		656.2.u.b.529.1		4
41.10	even	5	inner	738.2.h.b.379.1		4
123.92	odd	10		82.2.d.b.51.1	yes	4
123.98	odd	10		3362.2.a.h.1.1		2
123.107	odd	10		3362.2.a.e.1.2		2
492.215	even	10		656.2.u.b.625.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
82.2.d.b.37.1	✓	4	3.2	odd	2
82.2.d.b.51.1	yes	4	123.92	odd	10
656.2.u.b.529.1		4	12.11	even	2
656.2.u.b.625.1		4	492.215	even	10
738.2.h.b.37.1		4	1.1	even	1	trivial
738.2.h.b.379.1		4	41.10	even	5	inner
3362.2.a.e.1.2		2	123.107	odd	10
3362.2.a.h.1.1		2	123.98	odd	10

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 738 = 2 \cdot 3^{2} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	738.h (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.809017 + 0.587785i) q^{2} +(0.309017 - 0.951057i) q^{4} +(-0.500000 + 1.53884i) q^{5} +(2.11803 + 1.53884i) q^{7} +(0.309017 + 0.951057i) q^{8} +(-0.500000 - 1.53884i) q^{10} +(-0.927051 - 2.85317i) q^{11} +(-5.04508 + 3.66547i) q^{13} -2.61803 q^{14} +(-0.809017 - 0.587785i) q^{16} +(1.30902 + 4.02874i) q^{17} +(1.42705 + 1.03681i) q^{19} +(1.30902 + 0.951057i) q^{20} +(2.42705 + 1.76336i) q^{22} +(-1.30902 + 0.951057i) q^{23} +(1.92705 + 1.40008i) q^{25} +(1.92705 - 5.93085i) q^{26} +(2.11803 - 1.53884i) q^{28} +(0.163119 - 0.502029i) q^{29} +(-1.88197 - 5.79210i) q^{31} +1.00000 q^{32} +(-3.42705 - 2.48990i) q^{34} +(-3.42705 + 2.48990i) q^{35} +(0.454915 - 1.40008i) q^{37} -1.76393 q^{38} -1.61803 q^{40} +(-2.19098 + 6.01661i) q^{41} +(-7.85410 + 5.70634i) q^{43} -3.00000 q^{44} +(0.500000 - 1.53884i) q^{46} +(-1.23607 + 0.898056i) q^{47} +(-0.0450850 - 0.138757i) q^{49} -2.38197 q^{50} +(1.92705 + 5.93085i) q^{52} +(-3.66312 + 11.2739i) q^{53} +4.85410 q^{55} +(-0.809017 + 2.48990i) q^{56} +(0.163119 + 0.502029i) q^{58} +(-4.11803 + 2.99193i) q^{59} +(2.80902 + 2.04087i) q^{61} +(4.92705 + 3.57971i) q^{62} +(-0.809017 + 0.587785i) q^{64} +(-3.11803 - 9.59632i) q^{65} +(-4.76393 + 14.6619i) q^{67} +4.23607 q^{68} +(1.30902 - 4.02874i) q^{70} +(-1.19098 - 3.66547i) q^{71} -16.1803 q^{73} +(0.454915 + 1.40008i) q^{74} +(1.42705 - 1.03681i) q^{76} +(2.42705 - 7.46969i) q^{77} +14.0000 q^{79} +(1.30902 - 0.951057i) q^{80} +(-1.76393 - 6.15537i) q^{82} +16.0902 q^{83} -6.85410 q^{85} +(3.00000 - 9.23305i) q^{86} +(2.42705 - 1.76336i) q^{88} +(-5.04508 - 3.66547i) q^{89} -16.3262 q^{91} +(0.500000 + 1.53884i) q^{92} +(0.472136 - 1.45309i) q^{94} +(-2.30902 + 1.67760i) q^{95} +(1.69098 - 5.20431i) q^{97} +(0.118034 + 0.0857567i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - q^{2} - q^{4} - 2 q^{5} + 4 q^{7} - q^{8} - 2 q^{10} + 3 q^{11} - 9 q^{13} - 6 q^{14} - q^{16} + 3 q^{17} - q^{19} + 3 q^{20} + 3 q^{22} - 3 q^{23} + q^{25} + q^{26} + 4 q^{28} - 15 q^{29}+ \cdots - 4 q^{98}+O(q^{100}) \) 4 * q - q^2 - q^4 - 2 * q^5 + 4 * q^7 - q^8 - 2 * q^10 + 3 * q^11 - 9 * q^13 - 6 * q^14 - q^16 + 3 * q^17 - q^19 + 3 * q^20 + 3 * q^22 - 3 * q^23 + q^25 + q^26 + 4 * q^28 - 15 * q^29 - 12 * q^31 + 4 * q^32 - 7 * q^34 - 7 * q^35 + 13 * q^37 - 16 * q^38 - 2 * q^40 - 11 * q^41 - 18 * q^43 - 12 * q^44 + 2 * q^46 + 4 * q^47 + 11 * q^49 - 14 * q^50 + q^52 + q^53 + 6 * q^55 - q^56 - 15 * q^58 - 12 * q^59 + 9 * q^61 + 13 * q^62 - q^64 - 8 * q^65 - 28 * q^67 + 8 * q^68 + 3 * q^70 - 7 * q^71 - 20 * q^73 + 13 * q^74 - q^76 + 3 * q^77 + 56 * q^79 + 3 * q^80 - 16 * q^82 + 42 * q^83 - 14 * q^85 + 12 * q^86 + 3 * q^88 - 9 * q^89 - 34 * q^91 + 2 * q^92 - 16 * q^94 - 7 * q^95 + 9 * q^97 - 4 * q^98

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