LMFDB - Embedded newform 656.2.u.b.529.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [656,2,Mod(305,656)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(656, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 0, 4])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("656.305"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 656 = 2^{4} \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	656.u (of order $5$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [4,0,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$5.23818637260$
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:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 82)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			529.1
Root			$0.809017 + 0.587785i$ of defining polynomial
Character	$\chi$	$=$	656.529
Dual form			656.2.u.b.625.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+0.618034 q^{3} +(0.500000 - 1.53884i) q^{5} +(-2.11803 - 1.53884i) q^{7} -2.61803 q^{9} +(-0.927051 - 2.85317i) q^{11} +(-5.04508 + 3.66547i) q^{13} +(0.309017 - 0.951057i) q^{15} +(-1.30902 - 4.02874i) q^{17} +(-1.42705 - 1.03681i) q^{19} +(-1.30902 - 0.951057i) q^{21} +(-1.30902 + 0.951057i) q^{23} +(1.92705 + 1.40008i) q^{25} -3.47214 q^{27} +(-0.163119 + 0.502029i) q^{29} +(1.88197 + 5.79210i) q^{31} +(-0.572949 - 1.76336i) q^{33} +(-3.42705 + 2.48990i) q^{35} +(0.454915 - 1.40008i) q^{37} +(-3.11803 + 2.26538i) q^{39} +(2.19098 - 6.01661i) q^{41} +(7.85410 - 5.70634i) q^{43} +(-1.30902 + 4.02874i) q^{45} +(-1.23607 + 0.898056i) q^{47} +(-0.0450850 - 0.138757i) q^{49} +(-0.809017 - 2.48990i) q^{51} +(3.66312 - 11.2739i) q^{53} -4.85410 q^{55} +(-0.881966 - 0.640786i) q^{57} +(-4.11803 + 2.99193i) q^{59} +(2.80902 + 2.04087i) q^{61} +(5.54508 + 4.02874i) q^{63} +(3.11803 + 9.59632i) q^{65} +(4.76393 - 14.6619i) q^{67} +(-0.809017 + 0.587785i) q^{69} +(-1.19098 - 3.66547i) q^{71} -16.1803 q^{73} +(1.19098 + 0.865300i) q^{75} +(-2.42705 + 7.46969i) q^{77} -14.0000 q^{79} +5.70820 q^{81} +16.0902 q^{83} -6.85410 q^{85} +(-0.100813 + 0.310271i) q^{87} +(5.04508 + 3.66547i) q^{89} +16.3262 q^{91} +(1.16312 + 3.57971i) q^{93} +(-2.30902 + 1.67760i) q^{95} +(1.69098 - 5.20431i) q^{97} +(2.42705 + 7.46969i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{3} + 2 q^{5} - 4 q^{7} - 6 q^{9} + 3 q^{11} - 9 q^{13} - q^{15} - 3 q^{17} + q^{19} - 3 q^{21} - 3 q^{23} + q^{25} + 4 q^{27} + 15 q^{29} + 12 q^{31} - 9 q^{33} - 7 q^{35} + 13 q^{37} - 8 q^{39}+ \cdots + 3 q^{99}+O(q^{100}) $ 4 * q - 2 * q^3 + 2 * q^5 - 4 * q^7 - 6 * q^9 + 3 * q^11 - 9 * q^13 - q^15 - 3 * q^17 + q^19 - 3 * q^21 - 3 * q^23 + q^25 + 4 * q^27 + 15 * q^29 + 12 * q^31 - 9 * q^33 - 7 * q^35 + 13 * q^37 - 8 * q^39 + 11 * q^41 + 18 * q^43 - 3 * q^45 + 4 * q^47 + 11 * q^49 - q^51 - q^53 - 6 * q^55 - 8 * q^57 - 12 * q^59 + 9 * q^61 + 11 * q^63 + 8 * q^65 + 28 * q^67 - q^69 - 7 * q^71 - 20 * q^73 + 7 * q^75 - 3 * q^77 - 56 * q^79 - 4 * q^81 + 42 * q^83 - 14 * q^85 - 25 * q^87 + 9 * q^89 + 34 * q^91 - 11 * q^93 - 7 * q^95 + 9 * q^97 + 3 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/656\mathbb{Z}\right)^\times$.

$n$	$129$	$165$	$575$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.618034			0.356822			0.178411	−	0.983956i	$-0.442904\pi$
$3$	0.618034			0.356822			0.178411	+	0.983956i	$0.442904\pi$
$4$		0			0
$5$	0.500000	−	1.53884i	0.223607	−	0.688191i	−0.774823	−	0.632178i	$-0.782161\pi$
$5$	0.500000	−	1.53884i	0.223607	−	0.688191i	0.998430	−	0.0560130i	$-0.0178388\pi$
$6$		0			0
$7$	−2.11803	−	1.53884i	−0.800542	−	0.581628i	0.110531	−	0.993873i	$-0.464745\pi$
$7$	−2.11803	−	1.53884i	−0.800542	−	0.581628i	−0.911073	+	0.412245i	$0.864745\pi$
$8$		0			0
$9$	−2.61803			−0.872678
$10$		0			0
$11$	−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	$0.967453\pi$
$14$		0			0
$15$	0.309017	−	0.951057i	0.0797878	−	0.245562i
$16$		0			0
$17$	−1.30902	−	4.02874i	−0.317483	−	0.977113i	−0.974720	−	0.223429i	$-0.928275\pi$
$17$	−1.30902	−	4.02874i	−0.317483	−	0.977113i	0.657237	−	0.753684i	$-0.271725\pi$
$18$		0			0
$19$	−1.42705	−	1.03681i	−0.327388	−	0.237861i	0.411934	−	0.911214i	$-0.364854\pi$
$19$	−1.42705	−	1.03681i	−0.327388	−	0.237861i	−0.739321	+	0.673353i	$0.764854\pi$
$20$		0			0
$21$	−1.30902	−	0.951057i	−0.285651	−	0.207538i
$22$		0			0
$23$	−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
$26$		0			0
$27$	−3.47214			−0.668213
$28$		0			0
$29$	−0.163119	+	0.502029i	−0.0302904	+	0.0932244i	−0.965059	−	0.262033i	$-0.915607\pi$
$29$	−0.163119	+	0.502029i	−0.0302904	+	0.0932244i	0.934768	+	0.355258i	$0.115607\pi$
$30$		0			0
$31$	1.88197	+	5.79210i	0.338011	+	1.04029i	0.965220	+	0.261440i	$0.0841973\pi$
$31$	1.88197	+	5.79210i	0.338011	+	1.04029i	−0.627209	+	0.778851i	$0.715803\pi$
$32$		0			0
$33$	−0.572949	−	1.76336i	−0.0997376	−	0.306961i
$34$		0			0
$35$	−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	$0.0613871\pi$
$38$		0			0
$39$	−3.11803	+	2.26538i	−0.499285	+	0.362752i
$40$		0			0
$41$	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	0.203679	−	0.979038i	$-0.434710\pi$
$43$	7.85410	−	5.70634i	1.19774	−	0.870209i	0.994060	+	0.108829i	$0.0347102\pi$
$44$		0			0
$45$	−1.30902	+	4.02874i	−0.195137	+	0.600569i
$46$		0			0
$47$	−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
$50$		0			0
$51$	−0.809017	−	2.48990i	−0.113285	−	0.348655i
$52$		0			0
$53$	3.66312	−	11.2739i	0.503168	−	1.54859i	−0.300661	−	0.953731i	$-0.597207\pi$
$53$	3.66312	−	11.2739i	0.503168	−	1.54859i	0.803829	−	0.594861i	$-0.202793\pi$
$54$		0			0
$55$	−4.85410			−0.654527
$56$		0			0
$57$	−0.881966	−	0.640786i	−0.116819	−	0.0848742i
$58$		0			0
$59$	−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	$0.628650\pi$
$62$		0			0
$63$	5.54508	+	4.02874i	0.698615	+	0.507574i
$64$		0			0
$65$	3.11803	+	9.59632i	0.386745	+	1.19028i
$66$		0			0
$67$	4.76393	−	14.6619i	0.582007	−	1.79123i	−0.0289644	−	0.999580i	$-0.509221\pi$
$67$	4.76393	−	14.6619i	0.582007	−	1.79123i	0.610971	−	0.791653i	$-0.290779\pi$
$68$		0			0
$69$	−0.809017	+	0.587785i	−0.0973942	+	0.0707610i
$70$		0			0
$71$	−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			0
$75$	1.19098	+	0.865300i	0.137523	+	0.0999162i
$76$		0			0
$77$	−2.42705	+	7.46969i	−0.276588	+	0.851251i
$78$		0			0
$79$	−14.0000			−1.57512			−0.787562	−	0.616236i	$-0.788657\pi$
$79$	−14.0000			−1.57512			−0.787562	+	0.616236i	$0.788657\pi$
$80$		0			0
$81$	5.70820			0.634245
$82$		0			0
$83$	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
$86$		0			0
$87$	−0.100813	+	0.310271i	−0.0108083	+	0.0332645i
$88$		0			0
$89$	5.04508	+	3.66547i	0.534778	+	0.388539i	0.822142	−	0.569283i	$-0.192779\pi$
$89$	5.04508	+	3.66547i	0.534778	+	0.388539i	−0.287364	+	0.957821i	$0.592779\pi$
$90$		0			0
$91$	16.3262			1.71145
$92$		0			0
$93$	1.16312	+	3.57971i	0.120610	+	0.371199i
$94$		0			0
$95$	−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			0
$99$	2.42705	+	7.46969i	0.243928	+	0.750733i
$100$		0			0
$101$	−6.30902	−	4.58377i	−0.627771	−	0.456102i	0.227857	−	0.973695i	$-0.426828\pi$
$101$	−6.30902	−	4.58377i	−0.627771	−	0.456102i	−0.855627	+	0.517593i	$0.826828\pi$
$102$		0			0
$103$	−9.89919	−	7.19218i	−0.975396	−	0.708667i	−0.0187209	−	0.999825i	$-0.505959\pi$
$103$	−9.89919	−	7.19218i	−0.975396	−	0.708667i	−0.956675	+	0.291158i	$0.905959\pi$
$104$		0			0
$105$	−2.11803	+	1.53884i	−0.206699	+	0.150176i
$106$		0			0
$107$	−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	$0.383510\pi$
$110$		0			0
$111$	0.281153	−	0.865300i	0.0266859	−	0.0821306i
$112$		0			0
$113$	5.51722	+	16.9803i	0.519016	+	1.59737i	0.775853	+	0.630914i	$0.217320\pi$
$113$	5.51722	+	16.9803i	0.519016	+	1.59737i	−0.256837	+	0.966455i	$0.582680\pi$
$114$		0			0
$115$	0.809017	+	2.48990i	0.0754412	+	0.232184i
$116$		0			0
$117$	13.2082	−	9.59632i	1.22110	−	0.887180i
$118$		0			0
$119$	−3.42705	+	10.5474i	−0.314157	+	0.966877i
$120$		0			0
$121$	1.61803	−	1.17557i	0.147094	−	0.106870i
$122$		0			0
$123$	1.35410	−	3.71847i	0.122095	−	0.335283i
$124$		0			0
$125$	9.66312	−	7.02067i	0.864296	−	0.627948i
$126$		0			0
$127$	−2.10081	+	6.46564i	−0.186417	+	0.573733i	−0.999970	−	0.00775835i	$-0.997530\pi$
$127$	−2.10081	+	6.46564i	−0.186417	+	0.573733i	0.813553	+	0.581491i	$0.197530\pi$
$128$		0			0
$129$	4.85410	−	3.52671i	0.427380	−	0.310510i
$130$		0			0
$131$	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
$134$		0			0
$135$	−1.73607	+	5.34307i	−0.149417	+	0.459858i
$136$		0			0
$137$	−6.76393			−0.577882			−0.288941	−	0.957347i	$-0.593303\pi$
$137$	−6.76393			−0.577882			−0.288941	+	0.957347i	$0.593303\pi$
$138$		0			0
$139$	0.190983	+	0.138757i	0.0161990	+	0.0117692i	0.595855	−	0.803092i	$-0.296813\pi$
$139$	0.190983	+	0.138757i	0.0161990	+	0.0117692i	−0.579656	+	0.814861i	$0.696813\pi$
$140$		0			0
$141$	−0.763932	+	0.555029i	−0.0643347	+	0.0467419i
$142$		0			0
$143$	15.1353	+	10.9964i	1.26567	+	0.919566i
$144$		0			0
$145$	0.690983	+	0.502029i	0.0573830	+	0.0416912i
$146$		0			0
$147$	−0.0278640	−	0.0857567i	−0.00229819	−	0.00707309i
$148$		0			0
$149$	−3.52786	+	10.8576i	−0.289014	+	0.889493i	0.696153	+	0.717894i	$0.254894\pi$
$149$	−3.52786	+	10.8576i	−0.289014	+	0.889493i	−0.985167	+	0.171600i	$0.945106\pi$
$150$		0			0
$151$	−12.3262	+	8.95554i	−1.00310	+	0.728791i	−0.962750	−	0.270395i	$-0.912846\pi$
$151$	−12.3262	+	8.95554i	−1.00310	+	0.728791i	−0.0403454	+	0.999186i	$0.512846\pi$
$152$		0			0
$153$	3.42705	+	10.5474i	0.277061	+	0.852705i
$154$		0			0
$155$	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	$0.737485\pi$
$158$		0			0
$159$	2.26393	−	6.96767i	0.179541	−	0.552572i
$160$		0			0
$161$	4.23607			0.333849
$162$		0			0
$163$	−4.03444			−0.316002			−0.158001	−	0.987439i	$-0.550505\pi$
$163$	−4.03444			−0.316002			−0.158001	+	0.987439i	$0.550505\pi$
$164$		0			0
$165$	−3.00000			−0.233550
$166$		0			0
$167$	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
$170$		0			0
$171$	3.73607	+	2.71441i	0.285704	+	0.207576i
$172$		0			0
$173$	−3.76393			−0.286166			−0.143083	−	0.989711i	$-0.545702\pi$
$173$	−3.76393			−0.286166			−0.143083	+	0.989711i	$0.545702\pi$
$174$		0			0
$175$	−1.92705	−	5.93085i	−0.145671	−	0.448330i
$176$		0			0
$177$	−2.54508	+	1.84911i	−0.191300	+	0.138988i
$178$		0			0
$179$	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	$0.828001\pi$
$182$		0			0
$183$	1.73607	+	1.26133i	0.128334	+	0.0932400i
$184$		0			0
$185$	−1.92705	−	1.40008i	−0.141680	−	0.102936i
$186$		0			0
$187$	−10.2812	+	7.46969i	−0.751832	+	0.546238i
$188$		0			0
$189$	7.35410	+	5.34307i	0.534932	+	0.388651i
$190$		0			0
$191$	−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	$0.956701\pi$
$194$		0			0
$195$	1.92705	+	5.93085i	0.137999	+	0.424717i
$196$		0			0
$197$	−0.982779	−	3.02468i	−0.0700201	−	0.215500i	0.909923	−	0.414777i	$-0.136140\pi$
$197$	−0.982779	−	3.02468i	−0.0700201	−	0.215500i	−0.979943	+	0.199277i	$0.936140\pi$
$198$		0			0
$199$	5.28115	−	3.83698i	0.374371	−	0.271996i	−0.384650	−	0.923062i	$-0.625678\pi$
$199$	5.28115	−	3.83698i	0.374371	−	0.271996i	0.759021	+	0.651066i	$0.225678\pi$
$200$		0			0
$201$	2.94427	−	9.06154i	0.207673	−	0.639152i
$202$		0			0
$203$	1.11803	−	0.812299i	0.0784706	−	0.0570122i
$204$		0			0
$205$	−8.16312	−	6.37988i	−0.570137	−	0.445590i
$206$		0			0
$207$	3.42705	−	2.48990i	0.238197	−	0.173060i
$208$		0			0
$209$	−1.63525	+	5.03280i	−0.113113	+	0.348126i
$210$		0			0
$211$	5.04508	−	3.66547i	0.347318	−	0.252341i	−0.400425	−	0.916330i	$-0.631138\pi$
$211$	5.04508	−	3.66547i	0.347318	−	0.252341i	0.747743	+	0.663988i	$0.231138\pi$
$212$		0			0
$213$	−0.736068	−	2.26538i	−0.0504345	−	0.155222i
$214$		0			0
$215$	−4.85410	−	14.9394i	−0.331047	−	1.01886i
$216$		0			0
$217$	4.92705	−	15.1639i	0.334470	−	1.02939i
$218$		0			0
$219$	−10.0000			−0.675737
$220$		0			0
$221$	21.3713	+	15.5272i	1.43759	+	1.04447i
$222$		0			0
$223$	−20.7984	+	15.1109i	−1.39276	+	1.01190i	−0.397206	+	0.917729i	$0.630020\pi$
$223$	−20.7984	+	15.1109i	−1.39276	+	1.01190i	−0.995556	+	0.0941715i	$0.969980\pi$
$224$		0			0
$225$	−5.04508	−	3.66547i	−0.336339	−	0.244365i
$226$		0			0
$227$	−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	$0.785900\pi$
$230$		0			0
$231$	−1.50000	+	4.61653i	−0.0986928	+	0.303745i
$232$		0			0
$233$	−10.7533	+	7.81272i	−0.704471	+	0.511828i	−0.881385	−	0.472398i	$-0.843389\pi$
$233$	−10.7533	+	7.81272i	−0.704471	+	0.511828i	0.176914	+	0.984226i	$0.443389\pi$
$234$		0			0
$235$	0.763932	+	2.35114i	0.0498334	+	0.153372i
$236$		0			0
$237$	−8.65248			−0.562039
$238$		0			0
$239$	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			0
$243$	13.9443			0.894525
$244$		0			0
$245$	−0.236068			−0.0150818
$246$		0			0
$247$	11.0000			0.699913
$248$		0			0
$249$	9.94427			0.630193
$250$		0			0
$251$	−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
$254$		0			0
$255$	−4.23607			−0.265273
$256$		0			0
$257$	−1.47214	−	4.53077i	−0.0918293	−	0.282622i	0.894585	−	0.446898i	$-0.147471\pi$
$257$	−1.47214	−	4.53077i	−0.0918293	−	0.282622i	−0.986414	+	0.164276i	$0.947471\pi$
$258$		0			0
$259$	−3.11803	+	2.26538i	−0.193745	+	0.140764i
$260$		0			0
$261$	0.427051	−	1.31433i	0.0264338	−	0.0813548i
$262$		0			0
$263$	−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
$266$		0			0
$267$	3.11803	+	2.26538i	0.190821	+	0.138639i
$268$		0			0
$269$	4.89919	−	3.55947i	0.298709	−	0.217025i	−0.428328	−	0.903623i	$-0.640897\pi$
$269$	4.89919	−	3.55947i	0.298709	−	0.217025i	0.727036	+	0.686599i	$0.240897\pi$
$270$		0			0
$271$	−21.1353	−	15.3557i	−1.28388	−	0.932790i	−0.284213	−	0.958761i	$-0.591732\pi$
$271$	−21.1353	−	15.3557i	−1.28388	−	0.932790i	−0.999663	+	0.0259713i	$0.991732\pi$
$272$		0			0
$273$	10.0902			0.610685
$274$		0			0
$275$	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			0
$279$	−4.92705	−	15.1639i	−0.294975	−	0.907839i
$280$		0			0
$281$	−8.04508	+	5.84510i	−0.479930	+	0.348689i	−0.801298	−	0.598265i	$-0.795857\pi$
$281$	−8.04508	+	5.84510i	−0.479930	+	0.348689i	0.321369	+	0.946954i	$0.395857\pi$
$282$		0			0
$283$	5.40983	−	16.6497i	0.321581	−	0.989725i	−0.651379	−	0.758752i	$-0.725809\pi$
$283$	5.40983	−	16.6497i	0.321581	−	0.989725i	0.972960	−	0.230972i	$-0.0741907\pi$
$284$		0			0
$285$	−1.42705	+	1.03681i	−0.0845312	+	0.0614155i
$286$		0			0
$287$	−13.8992	+	9.37181i	−0.820443	+	0.553200i
$288$		0			0
$289$	−0.763932	+	0.555029i	−0.0449372	+	0.0326488i
$290$		0			0
$291$	1.04508	−	3.21644i	0.0612640	−	0.188551i
$292$		0			0
$293$	5.50000	−	3.99598i	0.321313	−	0.233448i	−0.415422	−	0.909629i	$-0.636366\pi$
$293$	5.50000	−	3.99598i	0.321313	−	0.233448i	0.736736	+	0.676181i	$0.236366\pi$
$294$		0			0
$295$	2.54508	+	7.83297i	0.148181	+	0.456053i
$296$		0			0
$297$	3.21885	+	9.90659i	0.186776	+	0.574839i
$298$		0			0
$299$	3.11803	−	9.59632i	0.180321	−	0.554970i
$300$		0			0
$301$	−25.4164			−1.46498
$302$		0			0
$303$	−3.89919	−	2.83293i	−0.224002	−	0.162747i
$304$		0			0
$305$	4.54508	−	3.30220i	0.260251	−	0.189083i
$306$		0			0
$307$	−18.1803	−	13.2088i	−1.03761	−	0.753865i	−0.0677899	−	0.997700i	$-0.521595\pi$
$307$	−18.1803	−	13.2088i	−1.03761	−	0.753865i	−0.969817	+	0.243834i	$0.921595\pi$
$308$		0			0
$309$	−6.11803	−	4.44501i	−0.348043	−	0.252868i
$310$		0			0
$311$	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	$0.0793686\pi$
$314$		0			0
$315$	8.97214	−	6.51864i	0.505523	−	0.367284i
$316$		0			0
$317$	−4.19098	−	12.8985i	−0.235389	−	0.724453i	−0.997070	−	0.0765002i	$-0.975625\pi$
$317$	−4.19098	−	12.8985i	−0.235389	−	0.724453i	0.761681	−	0.647953i	$-0.224375\pi$
$318$		0			0
$319$	1.58359			0.0886641
$320$		0			0
$321$	−2.85410	−	2.07363i	−0.159300	−	0.115739i
$322$		0			0
$323$	−2.30902	+	7.10642i	−0.128477	+	0.395412i
$324$		0			0
$325$	−14.8541			−0.823957
$326$		0			0
$327$	4.61803			0.255378
$328$		0			0
$329$	4.00000			0.220527
$330$		0			0
$331$	10.0902			0.554606			0.277303	−	0.960783i	$-0.410559\pi$
$331$	10.0902			0.554606			0.277303	+	0.960783i	$0.410559\pi$
$332$		0			0
$333$	−1.19098	+	3.66547i	−0.0652655	+	0.200866i
$334$		0			0
$335$	−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	$0.759997\pi$
$338$		0			0
$339$	3.40983	+	10.4944i	0.185197	+	0.569976i
$340$		0			0
$341$	14.7812	−	10.7391i	0.800444	−	0.581557i
$342$		0			0
$343$	−5.78115	+	17.7926i	−0.312153	+	0.960708i
$344$		0			0
$345$	0.500000	+	1.53884i	0.0269191	+	0.0828485i
$346$		0			0
$347$	−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	$0.754638\pi$
$350$		0			0
$351$	17.5172	−	12.7270i	0.935000	−	0.679317i
$352$		0			0
$353$	−6.16312	−	4.47777i	−0.328030	−	0.238328i	0.411564	−	0.911381i	$-0.364983\pi$
$353$	−6.16312	−	4.47777i	−0.328030	−	0.238328i	−0.739594	+	0.673053i	$0.764983\pi$
$354$		0			0
$355$	−6.23607			−0.330976
$356$		0			0
$357$	−2.11803	+	6.51864i	−0.112098	+	0.345003i
$358$		0			0
$359$	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
$362$		0			0
$363$	1.00000	−	0.726543i	0.0524864	−	0.0381336i
$364$		0			0
$365$	−8.09017	+	24.8990i	−0.423459	+	1.30327i
$366$		0			0
$367$	7.42705	−	5.39607i	0.387689	−	0.281672i	−0.376819	−	0.926287i	$-0.622982\pi$
$367$	7.42705	−	5.39607i	0.387689	−	0.281672i	0.764508	+	0.644614i	$0.222982\pi$
$368$		0			0
$369$	−5.73607	+	15.7517i	−0.298608	+	0.820000i
$370$		0			0
$371$	−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	$-0.126025\pi$
$374$		0			0
$375$	5.97214	−	4.33901i	0.308400	−	0.224066i
$376$		0			0
$377$	−1.01722	−	3.13068i	−0.0523895	−	0.161238i
$378$		0			0
$379$	4.64590	+	14.2986i	0.238644	+	0.734470i	0.996617	+	0.0821845i	$0.0261897\pi$
$379$	4.64590	+	14.2986i	0.238644	+	0.734470i	−0.757973	+	0.652285i	$0.773810\pi$
$380$		0			0
$381$	−1.29837	+	3.99598i	−0.0665177	+	0.204720i
$382$		0			0
$383$	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
$386$		0			0
$387$	−20.5623	+	14.9394i	−1.04524	+	0.759412i
$388$		0			0
$389$	−30.3156	−	22.0256i	−1.53706	−	1.11674i	−0.952145	−	0.305647i	$-0.901127\pi$
$389$	−30.3156	−	22.0256i	−1.53706	−	1.11674i	−0.584917	−	0.811093i	$-0.698873\pi$
$390$		0			0
$391$	5.54508	+	4.02874i	0.280427	+	0.203742i
$392$		0			0
$393$	1.74671	+	5.37582i	0.0881099	+	0.271174i
$394$		0			0
$395$	−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	$0.0687301\pi$
$398$		0			0
$399$	0.881966	+	2.71441i	0.0441535	+	0.135891i
$400$		0			0
$401$	24.8885			1.24287			0.621437	−	0.783464i	$-0.286549\pi$
$401$	24.8885			1.24287			0.621437	+	0.783464i	$0.286549\pi$
$402$		0			0
$403$	−30.7254	−	22.3233i	−1.53054	−	1.11200i
$404$		0			0
$405$	2.85410	−	8.78402i	0.141821	−	0.436482i
$406$		0			0
$407$	−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	$0.502129\pi$
$410$		0			0
$411$	−4.18034			−0.206201
$412$		0			0
$413$	13.3262			0.655741
$414$		0			0
$415$	8.04508	−	24.7602i	0.394918	−	1.21543i
$416$		0			0
$417$	0.118034	+	0.0857567i	0.00578015	+	0.00419952i
$418$		0			0
$419$	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	$-0.331016\pi$
$422$		0			0
$423$	3.23607	−	2.35114i	0.157343	−	0.114316i
$424$		0			0
$425$	3.11803	−	9.59632i	0.151247	−	0.465490i
$426$		0			0
$427$	−2.80902	−	8.64527i	−0.135938	−	0.418374i
$428$		0			0
$429$	9.35410	+	6.79615i	0.451620	+	0.328121i
$430$		0			0
$431$	−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	$0.235615\pi$
$434$		0			0
$435$	0.427051	+	0.310271i	0.0204755	+	0.0148763i
$436$		0			0
$437$	2.85410			0.136530
$438$		0			0
$439$	7.16312	−	22.0458i	0.341877	−	1.05219i	−0.621357	−	0.783527i	$-0.713419\pi$
$439$	7.16312	−	22.0458i	0.341877	−	1.05219i	0.963234	−	0.268662i	$-0.0865815\pi$
$440$		0			0
$441$	0.118034	+	0.363271i	0.00562067	+	0.0172986i
$442$		0			0
$443$	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
$446$		0			0
$447$	−2.18034	+	6.71040i	−0.103127	+	0.317391i
$448$		0			0
$449$	−5.57295	+	4.04898i	−0.263004	+	0.191083i	−0.711470	−	0.702716i	$-0.751970\pi$
$449$	−5.57295	+	4.04898i	−0.263004	+	0.191083i	0.448466	+	0.893800i	$0.351970\pi$
$450$		0			0
$451$	−19.1976	−	0.673542i	−0.903978	−	0.0317159i
$452$		0			0
$453$	−7.61803	+	5.53483i	−0.357926	+	0.260049i
$454$		0			0
$455$	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	$0.219420\pi$
$458$		0			0
$459$	4.54508	+	13.9883i	0.212146	+	0.652919i
$460$		0			0
$461$	9.60081	+	29.5483i	0.447154	+	1.37620i	0.880104	+	0.474782i	$0.157473\pi$
$461$	9.60081	+	29.5483i	0.447154	+	1.37620i	−0.432949	+	0.901418i	$0.642527\pi$
$462$		0			0
$463$	5.30902	−	16.3395i	0.246731	−	0.759360i	−0.748616	−	0.663004i	$-0.769281\pi$
$463$	5.30902	−	16.3395i	0.246731	−	0.759360i	0.995347	−	0.0963559i	$-0.0307187\pi$
$464$		0			0
$465$	6.09017			0.282425
$466$		0			0
$467$	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
$470$		0			0
$471$	−1.47214	−	1.06957i	−0.0678324	−	0.0492832i
$472$		0			0
$473$	−23.5623	−	17.1190i	−1.08340	−	0.787133i
$474$		0			0
$475$	−1.29837	−	3.99598i	−0.0595735	−	0.183348i
$476$		0			0
$477$	−9.59017	+	29.5155i	−0.439104	+	1.35142i
$478$		0			0
$479$	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
$482$		0			0
$483$	2.61803			0.119125
$484$		0			0
$485$	−7.16312	−	5.20431i	−0.325260	−	0.236316i
$486$		0			0
$487$	3.87132	−	11.9147i	0.175426	−	0.539907i	−0.824226	−	0.566261i	$-0.808390\pi$
$487$	3.87132	−	11.9147i	0.175426	−	0.539907i	0.999653	+	0.0263537i	$0.00838960\pi$
$488$		0			0
$489$	−2.49342			−0.112756
$490$		0			0
$491$	−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
$494$		0			0
$495$	12.7082			0.571191
$496$		0			0
$497$	−3.11803	+	9.59632i	−0.139863	+	0.430454i
$498$		0			0
$499$	27.2533	+	19.8007i	1.22002	+	0.886400i	0.996102	−	0.0882071i	$-0.0281137\pi$
$499$	27.2533	+	19.8007i	1.22002	+	0.886400i	0.223923	+	0.974607i	$0.428114\pi$
$500$		0			0
$501$	14.8541			0.663632
$502$		0			0
$503$	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
$506$		0			0
$507$	4.94427	−	15.2169i	0.219583	−	0.675806i
$508$		0			0
$509$	9.92705	+	30.5523i	0.440009	+	1.35421i	0.887866	+	0.460103i	$0.152187\pi$
$509$	9.92705	+	30.5523i	0.440009	+	1.35421i	−0.447857	+	0.894105i	$0.647813\pi$
$510$		0			0
$511$	34.2705	+	24.8990i	1.51604	+	1.10147i
$512$		0			0
$513$	4.95492	+	3.59996i	0.218765	+	0.158942i
$514$		0			0
$515$	−16.0172	+	11.6372i	−0.705803	+	0.512796i
$516$		0			0
$517$	3.70820	+	2.69417i	0.163087	+	0.118489i
$518$		0			0
$519$	−2.32624			−0.102111
$520$		0			0
$521$	2.29837	−	7.07367i	0.100694	−	0.309903i	−0.888002	−	0.459840i	$-0.847907\pi$
$521$	2.29837	−	7.07367i	0.100694	−	0.309903i	0.988696	+	0.149937i	$0.0479069\pi$
$522$		0			0
$523$	4.91641	+	15.1311i	0.214980	+	0.661639i	0.999155	+	0.0410998i	$0.0130862\pi$
$523$	4.91641	+	15.1311i	0.214980	+	0.661639i	−0.784176	+	0.620539i	$0.786914\pi$
$524$		0			0
$525$	−1.19098	−	3.66547i	−0.0519788	−	0.159974i
$526$		0			0
$527$	20.8713	−	15.1639i	0.909169	−	0.660550i
$528$		0			0
$529$	−6.29837	+	19.3844i	−0.273842	+	0.842800i
$530$		0			0
$531$	10.7812	−	7.83297i	0.467862	−	0.339922i
$532$		0			0
$533$	11.0000	+	38.3853i	0.476463	+	1.66265i
$534$		0			0
$535$	−7.47214	+	5.42882i	−0.323049	+	0.234709i
$536$		0			0
$537$	4.65248	−	14.3188i	0.200769	−	0.617904i
$538$		0			0
$539$	−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	$0.734669\pi$
$542$		0			0
$543$	1.15248	+	3.54696i	0.0494575	+	0.152214i
$544$		0			0
$545$	3.73607	−	11.4984i	0.160036	−	0.492539i
$546$		0			0
$547$	−9.00000			−0.384812			−0.192406	−	0.981315i	$-0.561629\pi$
$547$	−9.00000			−0.384812			−0.192406	+	0.981315i	$0.561629\pi$
$548$		0			0
$549$	−7.35410	−	5.34307i	−0.313865	−	0.228037i
$550$		0			0
$551$	0.753289	−	0.547296i	0.0320912	−	0.0233156i
$552$		0			0
$553$	29.6525	+	21.5438i	1.26095	+	0.916135i
$554$		0			0
$555$	−1.19098	−	0.865300i	−0.0505544	−	0.0367299i
$556$		0			0
$557$	0.343459	+	1.05706i	0.0145528	+	0.0447890i	0.958069	−	0.286537i	$-0.0925041\pi$
$557$	0.343459	+	1.05706i	0.0145528	+	0.0447890i	−0.943516	+	0.331326i	$0.892504\pi$
$558$		0			0
$559$	−18.7082	+	57.5779i	−0.791273	+	2.43529i
$560$		0			0
$561$	−6.35410	+	4.61653i	−0.268270	+	0.194910i
$562$		0			0
$563$	−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
$566$		0			0
$567$	−12.0902	−	8.78402i	−0.507739	−	0.368894i
$568$		0			0
$569$	12.0517	−	37.0912i	0.505232	−	1.55494i	−0.295148	−	0.955451i	$-0.595369\pi$
$569$	12.0517	−	37.0912i	0.505232	−	1.55494i	0.800380	−	0.599493i	$-0.204631\pi$
$570$		0			0
$571$	6.12461			0.256307			0.128154	−	0.991754i	$-0.459095\pi$
$571$	6.12461			0.256307			0.128154	+	0.991754i	$0.459095\pi$
$572$		0			0
$573$	−3.09017			−0.129094
$574$		0			0
$575$	−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			0
$579$	−2.30902	+	7.10642i	−0.0959595	+	0.295333i
$580$		0			0
$581$	−34.0795	−	24.7602i	−1.41386	−	1.02723i
$582$		0			0
$583$	−35.5623			−1.47284
$584$		0			0
$585$	−8.16312	−	25.1235i	−0.337503	−	1.03873i
$586$		0			0
$587$	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
$590$		0			0
$591$	−0.607391	−	1.86936i	−0.0249847	−	0.0768951i
$592$		0			0
$593$	6.76393	+	4.91428i	0.277761	+	0.201805i	0.717940	−	0.696105i	$-0.245085\pi$
$593$	6.76393	+	4.91428i	0.277761	+	0.201805i	−0.440179	+	0.897910i	$0.645085\pi$
$594$		0			0
$595$	14.5172	+	10.5474i	0.595148	+	0.432400i
$596$		0			0
$597$	3.26393	−	2.37139i	0.133584	−	0.0970543i
$598$		0			0
$599$	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	$0.687035\pi$
$602$		0			0
$603$	−12.4721	+	38.3853i	−0.507905	+	1.56317i
$604$		0			0
$605$	−1.00000	−	3.07768i	−0.0406558	−	0.125126i
$606$		0			0
$607$	−12.2188	−	37.6057i	−0.495948	−	1.52637i	−0.815475	−	0.578793i	$-0.803524\pi$
$607$	−12.2188	−	37.6057i	−0.495948	−	1.52637i	0.319527	−	0.947577i	$-0.396476\pi$
$608$		0			0
$609$	0.690983	−	0.502029i	0.0280000	−	0.0203432i
$610$		0			0
$611$	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	$0.138528\pi$
$614$		0			0
$615$	−5.04508	−	3.94298i	−0.203437	−	0.158996i
$616$		0			0
$617$	12.8541	−	9.33905i	0.517487	−	0.375976i	−0.298170	−	0.954513i	$-0.596376\pi$
$617$	12.8541	−	9.33905i	0.517487	−	0.375976i	0.815656	+	0.578537i	$0.196376\pi$
$618$		0			0
$619$	−0.0729490	+	0.224514i	−0.00293207	+	0.00902398i	−0.952512	−	0.304502i	$-0.901510\pi$
$619$	−0.0729490	+	0.224514i	−0.00293207	+	0.00902398i	0.949580	+	0.313526i	$0.101510\pi$
$620$		0			0
$621$	4.54508	−	3.30220i	0.182388	−	0.132513i
$622$		0			0
$623$	−5.04508	−	15.5272i	−0.202127	−	0.622083i
$624$		0			0
$625$	−2.29180	−	7.05342i	−0.0916718	−	0.282137i
$626$		0			0
$627$	−1.01064	+	3.11044i	−0.0403612	+	0.124219i
$628$		0			0
$629$	−6.23607			−0.248648
$630$		0			0
$631$	6.47214	+	4.70228i	0.257652	+	0.187195i	0.709111	−	0.705097i	$-0.249096\pi$
$631$	6.47214	+	4.70228i	0.257652	+	0.187195i	−0.451459	+	0.892292i	$0.649096\pi$
$632$		0			0
$633$	3.11803	−	2.26538i	0.123931	−	0.0900409i
$634$		0			0
$635$	8.89919	+	6.46564i	0.353153	+	0.256581i
$636$		0			0
$637$	0.736068	+	0.534785i	0.0291641	+	0.0211889i
$638$		0			0
$639$	3.11803	+	9.59632i	0.123348	+	0.379625i
$640$		0			0
$641$	−1.48278	+	4.56352i	−0.0585663	+	0.180248i	−0.976060	−	0.217502i	$-0.930209\pi$
$641$	−1.48278	+	4.56352i	−0.0585663	+	0.180248i	0.917494	+	0.397751i	$0.130209\pi$
$642$		0			0
$643$	5.76393	−	4.18774i	0.227307	−	0.165148i	−0.468303	−	0.883568i	$-0.655134\pi$
$643$	5.76393	−	4.18774i	0.227307	−	0.165148i	0.695610	+	0.718420i	$0.255134\pi$
$644$		0			0
$645$	−3.00000	−	9.23305i	−0.118125	−	0.363551i
$646$		0			0
$647$	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
$650$		0			0
$651$	3.04508	−	9.37181i	0.119346	−	0.367310i
$652$		0			0
$653$	27.8328			1.08918			0.544591	−	0.838702i	$-0.316685\pi$
$653$	27.8328			1.08918			0.544591	+	0.838702i	$0.316685\pi$
$654$		0			0
$655$	14.7984			0.578220
$656$		0			0
$657$	42.3607			1.65265
$658$		0			0
$659$	−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	$0.112252\pi$
$662$		0			0
$663$	13.2082	+	9.59632i	0.512964	+	0.372690i
$664$		0			0
$665$	7.47214			0.289757
$666$		0			0
$667$	−0.263932	−	0.812299i	−0.0102195	−	0.0314524i
$668$		0			0
$669$	−12.8541	+	9.33905i	−0.496968	+	0.361069i
$670$		0			0
$671$	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	$0.988692\pi$
$674$		0			0
$675$	−6.69098	−	4.86128i	−0.257536	−	0.187111i
$676$		0			0
$677$	−25.9894	−	18.8824i	−0.998852	−	0.725709i	−0.0370104	−	0.999315i	$-0.511783\pi$
$677$	−25.9894	−	18.8824i	−0.998852	−	0.725709i	−0.961842	+	0.273606i	$0.911783\pi$
$678$		0			0
$679$	−11.5902	+	8.42075i	−0.444790	+	0.323159i
$680$		0			0
$681$	−9.32624	−	6.77591i	−0.357382	−	0.259653i
$682$		0			0
$683$	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
$686$		0			0
$687$	2.02786	+	6.24112i	0.0773678	+	0.238114i
$688$		0			0
$689$	22.8435	+	70.3049i	0.870266	+	2.67840i
$690$		0			0
$691$	−2.90983	+	2.11412i	−0.110695	+	0.0804247i	−0.641756	−	0.766909i	$-0.721794\pi$
$691$	−2.90983	+	2.11412i	−0.110695	+	0.0804247i	0.531061	+	0.847334i	$0.321794\pi$
$692$		0			0
$693$	6.35410	−	19.5559i	0.241372	−	0.742868i
$694$		0			0
$695$	0.309017	−	0.224514i	0.0117217	−	0.00851630i
$696$		0			0
$697$	−27.1074	−	0.951057i	−1.02677	−	0.0360238i
$698$		0			0
$699$	−6.64590	+	4.82853i	−0.251371	+	0.182632i
$700$		0			0
$701$	11.1697	−	34.3768i	0.421874	−	1.29839i	−0.484083	−	0.875022i	$-0.660847\pi$
$701$	11.1697	−	34.3768i	0.421874	−	1.29839i	0.905956	−	0.423371i	$-0.139153\pi$
$702$		0			0
$703$	−2.10081	+	1.52633i	−0.0792337	+	0.0575666i
$704$		0			0
$705$	0.472136	+	1.45309i	0.0177817	+	0.0547263i
$706$		0			0
$707$	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	$0.921869\pi$
$710$		0			0
$711$	36.6525			1.37458
$712$		0			0
$713$	−7.97214	−	5.79210i	−0.298559	−	0.216916i
$714$		0			0
$715$	24.4894	−	17.7926i	0.915850	−	0.665404i
$716$		0			0
$717$	12.6353	+	9.18005i	0.471872	+	0.342835i
$718$		0			0
$719$	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
$722$		0			0
$723$	−2.92047	+	8.98829i	−0.108614	+	0.334278i
$724$		0			0
$725$	−1.01722	+	0.739054i	−0.0377786	+	0.0274478i
$726$		0			0
$727$	3.00000	+	9.23305i	0.111264	+	0.342435i	0.991149	−	0.132751i	$-0.0423809\pi$
$727$	3.00000	+	9.23305i	0.111264	+	0.342435i	−0.879886	+	0.475186i	$0.842381\pi$
$728$		0			0
$729$	−8.50658			−0.315058
$730$		0			0
$731$	−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	$-0.00333035\pi$
$734$		0			0
$735$	−0.145898			−0.00538153
$736$		0			0
$737$	−46.2492			−1.70361
$738$		0			0
$739$	19.8328			0.729562			0.364781	−	0.931093i	$-0.381144\pi$
$739$	19.8328			0.729562			0.364781	+	0.931093i	$0.381144\pi$
$740$		0			0
$741$	6.79837			0.249745
$742$		0			0
$743$	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
$746$		0			0
$747$	−42.1246			−1.54126
$748$		0			0
$749$	4.61803	+	14.2128i	0.168739	+	0.519326i
$750$		0			0
$751$	6.02786	−	4.37950i	0.219960	−	0.159810i	−0.472349	−	0.881412i	$-0.656594\pi$
$751$	6.02786	−	4.37950i	0.219960	−	0.159810i	0.692309	+	0.721602i	$0.256594\pi$
$752$		0			0
$753$	−3.35410	+	10.3229i	−0.122230	+	0.376186i
$754$		0			0
$755$	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	$0.620065\pi$
$758$		0			0
$759$	2.42705	+	1.76336i	0.0880964	+	0.0640058i
$760$		0			0
$761$	−0.427051	+	0.310271i	−0.0154806	+	0.0112473i	−0.595499	−	0.803356i	$-0.703045\pi$
$761$	−0.427051	+	0.310271i	−0.0154806	+	0.0112473i	0.580018	+	0.814604i	$0.303045\pi$
$762$		0			0
$763$	−15.8262	−	11.4984i	−0.572948	−	0.416271i
$764$		0			0
$765$	17.9443			0.648777
$766$		0			0
$767$	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	$0.725606\pi$
$770$		0			0
$771$	−0.909830	−	2.80017i	−0.0327667	−	0.100846i
$772$		0			0
$773$	−12.2812	+	8.92278i	−0.441722	+	0.320930i	−0.786319	−	0.617821i	$-0.788016\pi$
$773$	−12.2812	+	8.92278i	−0.441722	+	0.320930i	0.344597	+	0.938751i	$0.388016\pi$
$774$		0			0
$775$	−4.48278	+	13.7966i	−0.161026	+	0.495588i
$776$		0			0
$777$	−1.92705	+	1.40008i	−0.0691326	+	0.0502278i
$778$		0			0
$779$	−9.36475	+	6.31437i	−0.335527	+	0.226236i
$780$		0			0
$781$	−9.35410	+	6.79615i	−0.334716	+	0.243185i
$782$		0			0
$783$	0.566371	−	1.74311i	0.0202405	−	0.0622937i
$784$		0			0
$785$	−3.85410	+	2.80017i	−0.137559	+	0.0999423i
$786$		0			0
$787$	3.95492	+	12.1720i	0.140977	+	0.433884i	0.996472	−	0.0839281i	$-0.0267466\pi$
$787$	3.95492	+	12.1720i	0.140977	+	0.433884i	−0.855494	+	0.517812i	$0.826747\pi$
$788$		0			0
$789$	−0.0172209	−	0.0530006i	−0.000613081	−	0.00188687i
$790$		0			0
$791$	14.4443	−	44.4549i	0.513579	−	1.58063i
$792$		0			0
$793$	−21.6525			−0.768902
$794$		0			0
$795$	−9.59017	−	6.96767i	−0.340128	−	0.247118i
$796$		0			0
$797$	18.4164	−	13.3803i	0.652343	−	0.473955i	−0.211726	−	0.977329i	$-0.567908\pi$
$797$	18.4164	−	13.3803i	0.652343	−	0.473955i	0.864068	+	0.503374i	$0.167908\pi$
$798$		0			0
$799$	5.23607	+	3.80423i	0.185239	+	0.134584i
$800$		0			0
$801$	−13.2082	−	9.59632i	−0.466689	−	0.339069i
$802$		0			0
$803$	15.0000	+	46.1653i	0.529339	+	1.62914i
$804$		0			0
$805$	2.11803	−	6.51864i	0.0746509	−	0.229752i
$806$		0			0
$807$	3.02786	−	2.19987i	0.106586	−	0.0774392i
$808$		0			0
$809$	−9.45492	−	29.0992i	−0.332417	−	1.02307i	−0.967980	−	0.251026i	$-0.919232\pi$
$809$	−9.45492	−	29.0992i	−0.332417	−	1.02307i	0.635563	−	0.772049i	$-0.280768\pi$
$810$		0			0
$811$	−19.0689			−0.669599			−0.334800	−	0.942289i	$-0.608669\pi$
$811$	−19.0689			−0.669599			−0.334800	+	0.942289i	$0.608669\pi$
$812$		0			0
$813$	−13.0623	−	9.49032i	−0.458115	−	0.332840i
$814$		0			0
$815$	−2.01722	+	6.20837i	−0.0706602	+	0.217470i
$816$		0			0
$817$	−17.1246			−0.599114
$818$		0			0
$819$	−42.7426			−1.49355
$820$		0			0
$821$	10.4377			0.364278			0.182139	−	0.983273i	$-0.441698\pi$
$821$	10.4377			0.364278			0.182139	+	0.983273i	$0.441698\pi$
$822$		0			0
$823$	−1.43769			−0.0501149			−0.0250574	−	0.999686i	$-0.507977\pi$
$823$	−1.43769			−0.0501149			−0.0250574	+	0.999686i	$0.507977\pi$
$824$		0			0
$825$	1.36475	−	4.20025i	0.0475143	−	0.146234i
$826$		0			0
$827$	−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	$0.442803\pi$
$830$		0			0
$831$	−2.98278	−	9.18005i	−0.103471	−	0.318452i
$832$		0			0
$833$	−0.500000	+	0.363271i	−0.0173240	+	0.0125866i
$834$		0			0
$835$	12.0172	−	36.9852i	0.415873	−	1.27993i
$836$		0			0
$837$	−6.53444	−	20.1109i	−0.225863	−	0.695136i
$838$		0			0
$839$	−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
$842$		0			0
$843$	−4.97214	+	3.61247i	−0.171249	+	0.124420i
$844$		0			0
$845$	−33.8885	−	24.6215i	−1.16580	−	0.847004i
$846$		0			0
$847$	−5.23607			−0.179913
$848$		0			0
$849$	3.34346	−	10.2901i	0.114747	−	0.353156i
$850$		0			0
$851$	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	$0.825413\pi$
$854$		0			0
$855$	6.04508	−	4.39201i	0.206738	−	0.150204i
$856$		0			0
$857$	5.60081	−	17.2375i	0.191320	−	0.588823i	−0.808680	−	0.588249i	$-0.799817\pi$
$857$	5.60081	−	17.2375i	0.191320	−	0.588823i	1.00000		0.000573603i	$-0.000182584\pi$
$858$		0			0
$859$	−3.61803	+	2.62866i	−0.123446	+	0.0896886i	−0.647795	−	0.761815i	$-0.724309\pi$
$859$	−3.61803	+	2.62866i	−0.123446	+	0.0896886i	0.524349	+	0.851503i	$0.324309\pi$
$860$		0			0
$861$	−8.59017	+	5.79210i	−0.292752	+	0.197394i
$862$		0			0
$863$	−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
$866$		0			0
$867$	−0.472136	+	0.343027i	−0.0160346	+	0.0116498i
$868$		0			0
$869$	12.9787	+	39.9444i	0.440273	+	1.35502i
$870$		0			0
$871$	29.7082	+	91.4325i	1.00662	+	3.09807i
$872$		0			0
$873$	−4.42705	+	13.6251i	−0.149833	+	0.461138i
$874$		0			0
$875$	−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	$0.909789\pi$
$878$		0			0
$879$	3.39919	−	2.46965i	0.114652	−	0.0832994i
$880$		0			0
$881$	37.0344	+	26.9071i	1.24772	+	0.906523i	0.998088	−	0.0618170i	$-0.0196895\pi$
$881$	37.0344	+	26.9071i	1.24772	+	0.906523i	0.249635	+	0.968340i	$0.419690\pi$
$882$		0			0
$883$	−0.600813	−	0.436516i	−0.0202190	−	0.0146899i	0.577630	−	0.816299i	$-0.303978\pi$
$883$	−0.600813	−	0.436516i	−0.0202190	−	0.0146899i	−0.597849	+	0.801609i	$0.703978\pi$
$884$		0			0
$885$	1.57295	+	4.84104i	0.0528741	+	0.162730i
$886$		0			0
$887$	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
$890$		0			0
$891$	−5.29180	−	16.2865i	−0.177282	−	0.545617i
$892$		0			0
$893$	2.69505			0.0901864
$894$		0			0
$895$	−31.8885	−	23.1684i	−1.06592	−	0.774434i
$896$		0			0
$897$	1.92705	−	5.93085i	0.0643424	−	0.198025i
$898$		0			0
$899$	−3.21478			−0.107219
$900$		0			0
$901$	−50.2148			−1.67290
$902$		0			0
$903$	−15.7082			−0.522736
$904$		0			0
$905$	9.76393			0.324564
$906$		0			0
$907$	12.2639	−	37.7445i	0.407217	−	1.25329i	−0.511812	−	0.859097i	$-0.671026\pi$
$907$	12.2639	−	37.7445i	0.407217	−	1.25329i	0.919030	−	0.394188i	$-0.128974\pi$
$908$		0			0
$909$	16.5172	+	12.0005i	0.547842	+	0.398030i
$910$		0			0
$911$	−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
$914$		0			0
$915$	2.80902	−	2.04087i	0.0928632	−	0.0674691i
$916$		0			0
$917$	7.39919	−	22.7724i	0.244343	−	0.752009i
$918$		0			0
$919$	−10.6525	−	32.7849i	−0.351393	−	1.08148i	−0.958072	−	0.286529i	$-0.907499\pi$
$919$	−10.6525	−	32.7849i	−0.351393	−	1.08148i	0.606679	−	0.794947i	$-0.292501\pi$
$920$		0			0
$921$	−11.2361	−	8.16348i	−0.370241	−	0.268996i
$922$		0			0
$923$	19.4443	+	14.1271i	0.640016	+	0.464999i
$924$		0			0
$925$	2.83688	−	2.06111i	0.0932761	−	0.0677690i
$926$		0			0
$927$	25.9164	+	18.8294i	0.851207	+	0.618438i
$928$		0			0
$929$	−27.8328			−0.913165			−0.456583	−	0.889681i	$-0.650927\pi$
$929$	−27.8328			−0.913165			−0.456583	+	0.889681i	$0.650927\pi$
$930$		0			0
$931$	−0.0795268	+	0.244758i	−0.00260639	+	0.00802163i
$932$		0			0
$933$	0.871323	+	2.68166i	0.0285258	+	0.0877935i
$934$		0			0
$935$	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	$0.559239\pi$
$938$		0			0
$939$	0.437694	−	1.34708i	0.0142836	−	0.0439604i
$940$		0			0
$941$	−24.4164	+	17.7396i	−0.795952	+	0.578293i	−0.909724	−	0.415214i	$-0.863707\pi$
$941$	−24.4164	+	17.7396i	−0.795952	+	0.578293i	0.113772	+	0.993507i	$0.463707\pi$
$942$		0			0
$943$	2.85410	+	9.95959i	0.0929423	+	0.324329i
$944$		0			0
$945$	11.8992	−	8.64527i	0.387081	−	0.281231i
$946$		0			0
$947$	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
$950$		0			0
$951$	−2.59017	−	7.97172i	−0.0839920	−	0.258501i
$952$		0			0
$953$	12.2254	+	37.6260i	0.396020	+	1.21883i	0.928164	+	0.372171i	$0.121387\pi$
$953$	12.2254	+	37.6260i	0.396020	+	1.21883i	−0.532144	+	0.846654i	$0.678613\pi$
$954$		0			0
$955$	−2.50000	+	7.69421i	−0.0808981	+	0.248979i
$956$		0			0
$957$	0.978714			0.0316373
$958$		0			0
$959$	14.3262	+	10.4086i	0.462618	+	0.336112i
$960$		0			0
$961$	−4.92705	+	3.57971i	−0.158937	+	0.115475i
$962$		0			0
$963$	12.0902	+	8.78402i	0.389600	+	0.283061i
$964$		0			0
$965$	15.8262	+	11.4984i	0.509465	+	0.370148i
$966$		0			0
$967$	−9.26393	−	28.5115i	−0.297908	−	0.916866i	−0.982229	−	0.187686i	$-0.939901\pi$
$967$	−9.26393	−	28.5115i	−0.297908	−	0.916866i	0.684321	−	0.729181i	$-0.260099\pi$
$968$		0			0
$969$	−1.42705	+	4.39201i	−0.0458435	+	0.141092i
$970$		0			0
$971$	−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
$974$		0			0
$975$	−9.18034			−0.294006
$976$		0			0
$977$	−46.4058	−	33.7158i	−1.48465	−	1.07866i	−0.976021	−	0.217678i	$-0.930152\pi$
$977$	−46.4058	−	33.7158i	−1.48465	−	1.07866i	−0.508631	−	0.860984i	$-0.669848\pi$
$978$		0			0
$979$	5.78115	−	17.7926i	0.184766	−	0.568653i
$980$		0			0
$981$	−19.5623			−0.624576
$982$		0			0
$983$	−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
$986$		0			0
$987$	2.47214			0.0786890
$988$		0			0
$989$	−4.85410	+	14.9394i	−0.154351	+	0.475045i
$990$		0			0
$991$	5.82624	+	4.23301i	0.185077	+	0.134466i	0.676466	−	0.736474i	$-0.263511\pi$
$991$	5.82624	+	4.23301i	0.185077	+	0.134466i	−0.491389	+	0.870940i	$0.663511\pi$
$992$		0			0
$993$	6.23607			0.197896
$994$		0			0
$995$	−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	$0.365602\pi$
$998$		0			0
$999$	−1.57953	+	4.86128i	−0.0499740	+	0.153804i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
82.2.d.b.37.1	✓	4	4.3	odd	2
82.2.d.b.51.1	yes	4	164.51	odd	10
656.2.u.b.529.1		4	1.1	even	1	trivial
656.2.u.b.625.1		4	41.10	even	5	inner
738.2.h.b.37.1		4	12.11	even	2
738.2.h.b.379.1		4	492.215	even	10
3362.2.a.e.1.2		2	164.107	odd	10
3362.2.a.h.1.1		2	164.139	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:	\( N \)	\(=\)	\( 656 = 2^{4} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	656.u (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+0.618034 q^{3} +(0.500000 - 1.53884i) q^{5} +(-2.11803 - 1.53884i) q^{7} -2.61803 q^{9} +(-0.927051 - 2.85317i) q^{11} +(-5.04508 + 3.66547i) q^{13} +(0.309017 - 0.951057i) q^{15} +(-1.30902 - 4.02874i) q^{17} +(-1.42705 - 1.03681i) q^{19} +(-1.30902 - 0.951057i) q^{21} +(-1.30902 + 0.951057i) q^{23} +(1.92705 + 1.40008i) q^{25} -3.47214 q^{27} +(-0.163119 + 0.502029i) q^{29} +(1.88197 + 5.79210i) q^{31} +(-0.572949 - 1.76336i) q^{33} +(-3.42705 + 2.48990i) q^{35} +(0.454915 - 1.40008i) q^{37} +(-3.11803 + 2.26538i) q^{39} +(2.19098 - 6.01661i) q^{41} +(7.85410 - 5.70634i) q^{43} +(-1.30902 + 4.02874i) q^{45} +(-1.23607 + 0.898056i) q^{47} +(-0.0450850 - 0.138757i) q^{49} +(-0.809017 - 2.48990i) q^{51} +(3.66312 - 11.2739i) q^{53} -4.85410 q^{55} +(-0.881966 - 0.640786i) q^{57} +(-4.11803 + 2.99193i) q^{59} +(2.80902 + 2.04087i) q^{61} +(5.54508 + 4.02874i) q^{63} +(3.11803 + 9.59632i) q^{65} +(4.76393 - 14.6619i) q^{67} +(-0.809017 + 0.587785i) q^{69} +(-1.19098 - 3.66547i) q^{71} -16.1803 q^{73} +(1.19098 + 0.865300i) q^{75} +(-2.42705 + 7.46969i) q^{77} -14.0000 q^{79} +5.70820 q^{81} +16.0902 q^{83} -6.85410 q^{85} +(-0.100813 + 0.310271i) q^{87} +(5.04508 + 3.66547i) q^{89} +16.3262 q^{91} +(1.16312 + 3.57971i) q^{93} +(-2.30902 + 1.67760i) q^{95} +(1.69098 - 5.20431i) q^{97} +(2.42705 + 7.46969i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{3} + 2 q^{5} - 4 q^{7} - 6 q^{9} + 3 q^{11} - 9 q^{13} - q^{15} - 3 q^{17} + q^{19} - 3 q^{21} - 3 q^{23} + q^{25} + 4 q^{27} + 15 q^{29} + 12 q^{31} - 9 q^{33} - 7 q^{35} + 13 q^{37} - 8 q^{39}+ \cdots + 3 q^{99}+O(q^{100}) \) 4 * q - 2 * q^3 + 2 * q^5 - 4 * q^7 - 6 * q^9 + 3 * q^11 - 9 * q^13 - q^15 - 3 * q^17 + q^19 - 3 * q^21 - 3 * q^23 + q^25 + 4 * q^27 + 15 * q^29 + 12 * q^31 - 9 * q^33 - 7 * q^35 + 13 * q^37 - 8 * q^39 + 11 * q^41 + 18 * q^43 - 3 * q^45 + 4 * q^47 + 11 * q^49 - q^51 - q^53 - 6 * q^55 - 8 * q^57 - 12 * q^59 + 9 * q^61 + 11 * q^63 + 8 * q^65 + 28 * q^67 - q^69 - 7 * q^71 - 20 * q^73 + 7 * q^75 - 3 * q^77 - 56 * q^79 - 4 * q^81 + 42 * q^83 - 14 * q^85 - 25 * q^87 + 9 * q^89 + 34 * q^91 - 11 * q^93 - 7 * q^95 + 9 * q^97 + 3 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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