LMFDB - Embedded newform 603.2.g.c.163.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [603,2,Mod(37,603)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(603, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("603.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 603 = 3^{2} \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	603.g (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.81497924188$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{5})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 2x^{2} + x + 1 $ x^4 - x^3 + 2*x^2 + x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			163.1
Root			$0.809017 - 1.40126i$ of defining polynomial
Character	$\chi$	$=$	603.163
Dual form			603.2.g.c.37.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.809017 + 1.40126i) q^{2} +(-0.309017 - 0.535233i) q^{4} -1.23607 q^{5} +(0.118034 + 0.204441i) q^{7} -2.23607 q^{8} +O(q^{10})$	\(q+(-0.809017 + 1.40126i) q^{2} +(-0.309017 - 0.535233i) q^{4} -1.23607 q^{5} +(0.118034 + 0.204441i) q^{7} -2.23607 q^{8} +(1.00000 - 1.73205i) q^{10} +(-2.50000 - 4.33013i) q^{11} +(-0.118034 + 0.204441i) q^{13} -0.381966 q^{14} +(2.42705 - 4.20378i) q^{16} +(1.11803 - 1.93649i) q^{17} +(0.881966 - 1.52761i) q^{19} +(0.381966 + 0.661585i) q^{20} +8.09017 q^{22} +(-0.881966 + 1.52761i) q^{23} -3.47214 q^{25} +(-0.190983 - 0.330792i) q^{26} +(0.0729490 - 0.126351i) q^{28} +(0.263932 + 0.457144i) q^{29} +(-3.35410 - 5.80948i) q^{31} +(1.69098 + 2.92887i) q^{32} +(1.80902 + 3.13331i) q^{34} +(-0.145898 - 0.252703i) q^{35} +(3.73607 - 6.47106i) q^{37} +(1.42705 + 2.47172i) q^{38} +2.76393 q^{40} +(-2.11803 - 3.66854i) q^{41} -0.763932 q^{43} +(-1.54508 + 2.67617i) q^{44} +(-1.42705 - 2.47172i) q^{46} +(0.881966 + 1.52761i) q^{47} +(3.47214 - 6.01392i) q^{49} +(2.80902 - 4.86536i) q^{50} +0.145898 q^{52} +9.70820 q^{53} +(3.09017 + 5.35233i) q^{55} +(-0.263932 - 0.457144i) q^{56} -0.854102 q^{58} -6.00000 q^{59} +(-6.35410 + 11.0056i) q^{61} +10.8541 q^{62} +4.23607 q^{64} +(0.145898 - 0.252703i) q^{65} +(-8.00000 - 1.73205i) q^{67} -1.38197 q^{68} +0.472136 q^{70} +(2.26393 + 3.92125i) q^{71} +(-1.35410 + 2.34537i) q^{73} +(6.04508 + 10.4704i) q^{74} -1.09017 q^{76} +(0.590170 - 1.02220i) q^{77} +(-4.73607 - 8.20311i) q^{79} +(-3.00000 + 5.19615i) q^{80} +6.85410 q^{82} +(5.50000 - 9.52628i) q^{83} +(-1.38197 + 2.39364i) q^{85} +(0.618034 - 1.07047i) q^{86} +(5.59017 + 9.68246i) q^{88} +2.00000 q^{89} -0.0557281 q^{91} +1.09017 q^{92} -2.85410 q^{94} +(-1.09017 + 1.88823i) q^{95} +(-4.50000 + 7.79423i) q^{97} +(5.61803 + 9.73072i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - q^{2} + q^{4} + 4 q^{5} - 4 q^{7}+O(q^{10}) $ 4 * q - q^2 + q^4 + 4 * q^5 - 4 * q^7	$ 4 q - q^{2} + q^{4} + 4 q^{5} - 4 q^{7} + 4 q^{10} - 10 q^{11} + 4 q^{13} - 6 q^{14} + 3 q^{16} + 8 q^{19} + 6 q^{20} + 10 q^{22} - 8 q^{23} + 4 q^{25} - 3 q^{26} + 7 q^{28} + 10 q^{29} + 9 q^{32} + 5 q^{34} - 14 q^{35} + 6 q^{37} - q^{38} + 20 q^{40} - 4 q^{41} - 12 q^{43} + 5 q^{44} + q^{46} + 8 q^{47} - 4 q^{49} + 9 q^{50} + 14 q^{52} + 12 q^{53} - 10 q^{55} - 10 q^{56} + 10 q^{58} - 24 q^{59} - 12 q^{61} + 30 q^{62} + 8 q^{64} + 14 q^{65} - 32 q^{67} - 10 q^{68} - 16 q^{70} + 18 q^{71} + 8 q^{73} + 13 q^{74} + 18 q^{76} - 20 q^{77} - 10 q^{79} - 12 q^{80} + 14 q^{82} + 22 q^{83} - 10 q^{85} - 2 q^{86} + 8 q^{89} - 36 q^{91} - 18 q^{92} + 2 q^{94} + 18 q^{95} - 18 q^{97} + 18 q^{98}+O(q^{100}) $ 4 * q - q^2 + q^4 + 4 * q^5 - 4 * q^7 + 4 * q^10 - 10 * q^11 + 4 * q^13 - 6 * q^14 + 3 * q^16 + 8 * q^19 + 6 * q^20 + 10 * q^22 - 8 * q^23 + 4 * q^25 - 3 * q^26 + 7 * q^28 + 10 * q^29 + 9 * q^32 + 5 * q^34 - 14 * q^35 + 6 * q^37 - q^38 + 20 * q^40 - 4 * q^41 - 12 * q^43 + 5 * q^44 + q^46 + 8 * q^47 - 4 * q^49 + 9 * q^50 + 14 * q^52 + 12 * q^53 - 10 * q^55 - 10 * q^56 + 10 * q^58 - 24 * q^59 - 12 * q^61 + 30 * q^62 + 8 * q^64 + 14 * q^65 - 32 * q^67 - 10 * q^68 - 16 * q^70 + 18 * q^71 + 8 * q^73 + 13 * q^74 + 18 * q^76 - 20 * q^77 - 10 * q^79 - 12 * q^80 + 14 * q^82 + 22 * q^83 - 10 * q^85 - 2 * q^86 + 8 * q^89 - 36 * q^91 - 18 * q^92 + 2 * q^94 + 18 * q^95 - 18 * q^97 + 18 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/603\mathbb{Z}\right)^\times$.

$n$	$136$	$470$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.809017	+	1.40126i	−0.572061	+	0.990839i	0.424293	+	0.905525i	$0.360523\pi$
$2$	−0.809017	+	1.40126i	−0.572061	+	0.990839i	−0.996354	+	0.0853143i	$0.972811\pi$
$3$		0			0
$3$		0			0
$4$	−0.309017	−	0.535233i	−0.154508	−	0.267617i
$5$	−1.23607			−0.552786			−0.276393	−	0.961045i	$-0.589139\pi$
$5$	−1.23607			−0.552786			−0.276393	+	0.961045i	$0.589139\pi$
$6$		0			0
$7$	0.118034	+	0.204441i	0.0446127	+	0.0772714i	0.887469	−	0.460866i	$-0.152461\pi$
$7$	0.118034	+	0.204441i	0.0446127	+	0.0772714i	−0.842857	+	0.538138i	$0.819128\pi$
$8$	−2.23607			−0.790569
$9$		0			0
$10$	1.00000	−	1.73205i	0.316228	−	0.547723i
$11$	−2.50000	−	4.33013i	−0.753778	−	1.30558i	−0.945979	−	0.324227i	$-0.894896\pi$
$11$	−2.50000	−	4.33013i	−0.753778	−	1.30558i	0.192201	−	0.981356i	$-0.438437\pi$
$12$		0			0
$13$	−0.118034	+	0.204441i	−0.0327367	+	0.0567017i	−0.881930	−	0.471381i	$-0.843756\pi$
$13$	−0.118034	+	0.204441i	−0.0327367	+	0.0567017i	0.849193	+	0.528083i	$0.177089\pi$
$14$	−0.381966			−0.102085
$15$		0			0
$16$	2.42705	−	4.20378i	0.606763	−	1.05094i
$17$	1.11803	−	1.93649i	0.271163	−	0.469668i	−0.697997	−	0.716101i	$-0.745925\pi$
$17$	1.11803	−	1.93649i	0.271163	−	0.469668i	0.969160	+	0.246433i	$0.0792584\pi$
$18$		0			0
$19$	0.881966	−	1.52761i	0.202337	−	0.350458i	−0.746944	−	0.664887i	$-0.768480\pi$
$19$	0.881966	−	1.52761i	0.202337	−	0.350458i	0.949281	+	0.314429i	$0.101813\pi$
$20$	0.381966	+	0.661585i	0.0854102	+	0.147935i
$21$		0			0
$22$	8.09017			1.72483
$23$	−0.881966	+	1.52761i	−0.183903	+	0.318529i	−0.943206	−	0.332208i	$-0.892206\pi$
$23$	−0.881966	+	1.52761i	−0.183903	+	0.318529i	0.759304	+	0.650737i	$0.225540\pi$
$24$		0			0
$25$	−3.47214			−0.694427
$26$	−0.190983	−	0.330792i	−0.0374548	−	0.0648737i
$27$		0			0
$28$	0.0729490	−	0.126351i	0.0137861	−	0.0238782i
$29$	0.263932	+	0.457144i	0.0490109	+	0.0848894i	0.889490	−	0.456954i	$-0.151060\pi$
$29$	0.263932	+	0.457144i	0.0490109	+	0.0848894i	−0.840479	+	0.541844i	$0.817726\pi$
$30$		0			0
$31$	−3.35410	−	5.80948i	−0.602414	−	1.04341i	−0.992454	−	0.122615i	$-0.960872\pi$
$31$	−3.35410	−	5.80948i	−0.602414	−	1.04341i	0.390040	−	0.920798i	$-0.372461\pi$
$32$	1.69098	+	2.92887i	0.298926	+	0.517756i
$33$		0			0
$34$	1.80902	+	3.13331i	0.310244	+	0.537358i
$35$	−0.145898	−	0.252703i	−0.0246613	−	0.0427146i
$36$		0			0
$37$	3.73607	−	6.47106i	0.614206	−	1.06384i	−0.376317	−	0.926491i	$-0.622810\pi$
$37$	3.73607	−	6.47106i	0.614206	−	1.06384i	0.990523	−	0.137345i	$-0.0438569\pi$
$38$	1.42705	+	2.47172i	0.231498	+	0.400967i
$39$		0			0
$40$	2.76393			0.437016
$41$	−2.11803	−	3.66854i	−0.330781	−	0.572930i	0.651884	−	0.758319i	$-0.273979\pi$
$41$	−2.11803	−	3.66854i	−0.330781	−	0.572930i	−0.982665	+	0.185389i	$0.940646\pi$
$42$		0			0
$43$	−0.763932			−0.116499			−0.0582493	−	0.998302i	$-0.518552\pi$
$43$	−0.763932			−0.116499			−0.0582493	+	0.998302i	$0.518552\pi$
$44$	−1.54508	+	2.67617i	−0.232930	+	0.403447i
$45$		0			0
$46$	−1.42705	−	2.47172i	−0.210407	−	0.364436i
$47$	0.881966	+	1.52761i	0.128648	+	0.222825i	0.923153	−	0.384433i	$-0.125603\pi$
$47$	0.881966	+	1.52761i	0.128648	+	0.222825i	−0.794505	+	0.607258i	$0.792270\pi$
$48$		0			0
$49$	3.47214	−	6.01392i	0.496019	−	0.859131i
$50$	2.80902	−	4.86536i	0.397255	−	0.688066i
$51$		0			0
$52$	0.145898			0.0202324
$53$	9.70820			1.33352			0.666762	−	0.745271i	$-0.267680\pi$
$53$	9.70820			1.33352			0.666762	+	0.745271i	$0.267680\pi$
$54$		0			0
$55$	3.09017	+	5.35233i	0.416678	+	0.721708i
$56$	−0.263932	−	0.457144i	−0.0352694	−	0.0610884i
$57$		0			0
$58$	−0.854102			−0.112149
$59$	−6.00000			−0.781133			−0.390567	−	0.920575i	$-0.627721\pi$
$59$	−6.00000			−0.781133			−0.390567	+	0.920575i	$0.627721\pi$
$60$		0			0
$61$	−6.35410	+	11.0056i	−0.813559	+	1.40913i	0.0967983	+	0.995304i	$0.469140\pi$
$61$	−6.35410	+	11.0056i	−0.813559	+	1.40913i	−0.910358	+	0.413822i	$0.864194\pi$
$62$	10.8541			1.37847
$63$		0			0
$64$	4.23607			0.529508
$65$	0.145898	−	0.252703i	0.0180964	−	0.0313439i
$66$		0			0
$67$	−8.00000	−	1.73205i	−0.977356	−	0.211604i
$67$	−8.00000	−	1.73205i	−0.977356	−	0.211604i
$68$	−1.38197			−0.167588
$69$		0			0
$70$	0.472136			0.0564310
$71$	2.26393	+	3.92125i	0.268679	+	0.465366i	0.968521	−	0.248932i	$-0.0800795\pi$
$71$	2.26393	+	3.92125i	0.268679	+	0.465366i	−0.699842	+	0.714298i	$0.746746\pi$
$72$		0			0
$73$	−1.35410	+	2.34537i	−0.158486	+	0.274505i	−0.934323	−	0.356428i	$-0.883994\pi$
$73$	−1.35410	+	2.34537i	−0.158486	+	0.274505i	0.775837	+	0.630933i	$0.217328\pi$
$74$	6.04508	+	10.4704i	0.702727	+	1.21716i
$75$		0			0
$76$	−1.09017			−0.125051
$77$	0.590170	−	1.02220i	0.0672561	−	0.116491i
$78$		0			0
$79$	−4.73607	−	8.20311i	−0.532849	−	0.922922i	−0.999264	−	0.0383559i	$-0.987788\pi$
$79$	−4.73607	−	8.20311i	−0.532849	−	0.922922i	0.466415	−	0.884566i	$-0.345545\pi$
$80$	−3.00000	+	5.19615i	−0.335410	+	0.580948i
$81$		0			0
$82$	6.85410			0.756909
$83$	5.50000	−	9.52628i	0.603703	−	1.04565i	−0.388552	−	0.921427i	$-0.627024\pi$
$83$	5.50000	−	9.52628i	0.603703	−	1.04565i	0.992255	−	0.124218i	$-0.0396422\pi$
$84$		0			0
$85$	−1.38197	+	2.39364i	−0.149895	+	0.259626i
$86$	0.618034	−	1.07047i	0.0666443	−	0.115431i
$87$		0			0
$88$	5.59017	+	9.68246i	0.595914	+	1.03215i
$89$	2.00000			0.212000			0.106000	−	0.994366i	$-0.466196\pi$
$89$	2.00000			0.212000			0.106000	+	0.994366i	$0.466196\pi$
$90$		0			0
$91$	−0.0557281			−0.00584189
$92$	1.09017			0.113658
$93$		0			0
$94$	−2.85410			−0.294378
$95$	−1.09017	+	1.88823i	−0.111849	+	0.193728i
$96$		0			0
$97$	−4.50000	+	7.79423i	−0.456906	+	0.791384i	−0.998796	−	0.0490655i	$-0.984376\pi$
$97$	−4.50000	+	7.79423i	−0.456906	+	0.791384i	0.541890	+	0.840450i	$0.317709\pi$
$98$	5.61803	+	9.73072i	0.567507	+	0.982951i
$99$		0			0
$100$	1.07295	+	1.85840i	0.107295	+	0.185840i
$101$	−5.73607	−	9.93516i	−0.570760	−	0.988585i	−0.996488	−	0.0837343i	$-0.973315\pi$
$101$	−5.73607	−	9.93516i	−0.570760	−	0.988585i	0.425728	−	0.904851i	$-0.360018\pi$
$102$		0			0
$103$	0.736068	+	1.27491i	0.0725269	+	0.125620i	0.900008	−	0.435873i	$-0.143560\pi$
$103$	0.736068	+	1.27491i	0.0725269	+	0.125620i	−0.827481	+	0.561493i	$0.810227\pi$
$104$	0.263932	−	0.457144i	0.0258807	−	0.0448266i
$105$		0			0
$106$	−7.85410	+	13.6037i	−0.762858	+	1.32131i
$107$	1.70820			0.165138			0.0825692	−	0.996585i	$-0.473687\pi$
$107$	1.70820			0.165138			0.0825692	+	0.996585i	$0.473687\pi$
$108$		0			0
$109$	−8.94427			−0.856706			−0.428353	−	0.903612i	$-0.640906\pi$
$109$	−8.94427			−0.856706			−0.428353	+	0.903612i	$0.640906\pi$
$110$	−10.0000			−0.953463
$111$		0			0
$112$	1.14590			0.108277
$113$	−1.35410	−	2.34537i	−0.127383	−	0.220634i	0.795279	−	0.606244i	$-0.207324\pi$
$113$	−1.35410	−	2.34537i	−0.127383	−	0.220634i	−0.922662	+	0.385610i	$0.873991\pi$
$114$		0			0
$115$	1.09017	−	1.88823i	0.101659	−	0.176078i
$116$	0.163119	−	0.282530i	0.0151452	−	0.0262323i
$117$		0			0
$118$	4.85410	−	8.40755i	0.446856	−	0.773978i
$119$	0.527864			0.0483892
$120$		0			0
$121$	−7.00000	+	12.1244i	−0.636364	+	1.10221i
$122$	−10.2812	−	17.8075i	−0.930812	−	1.61221i
$123$		0			0
$124$	−2.07295	+	3.59045i	−0.186156	+	0.322432i
$125$	10.4721			0.936656
$126$		0			0
$127$	−5.59017	−	9.68246i	−0.496047	−	0.859179i	0.503942	−	0.863737i	$-0.331882\pi$
$127$	−5.59017	−	9.68246i	−0.496047	−	0.859179i	−0.999990	+	0.00455811i	$0.998549\pi$
$128$	−6.80902	+	11.7936i	−0.601838	+	1.04241i
$129$		0			0
$130$	0.236068	+	0.408882i	0.0207045	+	0.0358613i
$131$	−10.4721			−0.914955			−0.457477	−	0.889221i	$-0.651247\pi$
$131$	−10.4721			−0.914955			−0.457477	+	0.889221i	$0.651247\pi$
$132$		0			0
$133$	0.416408			0.0361071
$134$	8.89919	−	9.80881i	0.768773	−	0.847352i
$135$		0			0
$136$	−2.50000	+	4.33013i	−0.214373	+	0.371305i
$137$	−19.8885			−1.69919			−0.849596	−	0.527433i	$-0.823154\pi$
$137$	−19.8885			−1.69919			−0.849596	+	0.527433i	$0.823154\pi$
$138$		0			0
$139$	−8.94427			−0.758643			−0.379322	−	0.925265i	$-0.623843\pi$
$139$	−8.94427			−0.758643			−0.379322	+	0.925265i	$0.623843\pi$
$140$	−0.0901699	+	0.156179i	−0.00762075	+	0.0131995i
$141$		0			0
$142$	−7.32624			−0.614804
$143$	1.18034			0.0987050
$144$		0			0
$145$	−0.326238	−	0.565061i	−0.0270926	−	0.0469257i
$146$	−2.19098	−	3.79489i	−0.181327	−	0.314068i
$147$		0			0
$148$	−4.61803			−0.379600
$149$	−16.4721			−1.34945			−0.674725	−	0.738069i	$-0.735738\pi$
$149$	−16.4721			−1.34945			−0.674725	+	0.738069i	$0.735738\pi$
$150$		0			0
$151$	−1.88197	+	3.25966i	−0.153152	+	0.265267i	−0.932385	−	0.361468i	$-0.882276\pi$
$151$	−1.88197	+	3.25966i	−0.153152	+	0.265267i	0.779232	+	0.626735i	$0.215609\pi$
$152$	−1.97214	+	3.41584i	−0.159961	+	0.277061i
$153$		0			0
$154$	0.954915	+	1.65396i	0.0769492	+	0.133280i
$155$	4.14590	+	7.18091i	0.333007	+	0.576784i
$156$		0			0
$157$	−1.35410	+	2.34537i	−0.108069	+	0.187181i	−0.914988	−	0.403481i	$-0.867800\pi$
$157$	−1.35410	+	2.34537i	−0.108069	+	0.187181i	0.806919	+	0.590662i	$0.201133\pi$
$158$	15.3262			1.21929
$159$		0			0
$160$	−2.09017	−	3.62028i	−0.165242	−	0.286208i
$161$	−0.416408			−0.0328175
$162$		0			0
$163$	−3.26393	−	5.65330i	−0.255651	−	0.442800i	0.709421	−	0.704785i	$-0.248956\pi$
$163$	−3.26393	−	5.65330i	−0.255651	−	0.442800i	−0.965072	+	0.261984i	$0.915623\pi$
$164$	−1.30902	+	2.26728i	−0.102217	+	0.177045i
$165$		0			0
$166$	8.89919	+	15.4138i	0.690711	+	1.19635i
$167$	7.35410	+	12.7377i	0.569077	+	0.985671i	0.996657	+	0.0816936i	$0.0260329\pi$
$167$	7.35410	+	12.7377i	0.569077	+	0.985671i	−0.427580	+	0.903978i	$0.640634\pi$
$168$		0			0
$169$	6.47214	+	11.2101i	0.497857	+	0.862313i
$170$	−2.23607	−	3.87298i	−0.171499	−	0.297044i
$171$		0			0
$172$	0.236068	+	0.408882i	0.0180000	+	0.0311769i
$173$	5.35410	−	9.27358i	0.407065	−	0.705057i	−0.587495	−	0.809228i	$-0.699886\pi$
$173$	5.35410	−	9.27358i	0.407065	−	0.705057i	0.994559	+	0.104171i	$0.0332190\pi$
$174$		0			0
$175$	−0.409830	−	0.709846i	−0.0309802	−	0.0536594i
$176$	−24.2705			−1.82946
$177$		0			0
$178$	−1.61803	+	2.80252i	−0.121277	+	0.210058i
$179$		0			0			−	1.00000i	$-0.5\pi$
$179$		0			0				1.00000i	$0.5\pi$
$180$		0			0
$181$	0.500000	+	0.866025i	0.0371647	+	0.0643712i	0.884009	−	0.467469i	$-0.154834\pi$
$181$	0.500000	+	0.866025i	0.0371647	+	0.0643712i	−0.846845	+	0.531840i	$0.821501\pi$
$182$	0.0450850	−	0.0780895i	0.00334192	−	0.00578838i
$183$		0			0
$184$	1.97214	−	3.41584i	0.145388	−	0.251819i
$185$	−4.61803	+	7.99867i	−0.339525	+	0.588074i
$186$		0			0
$187$	−11.1803			−0.817587
$188$	0.545085	−	0.944115i	0.0397544	−	0.0688567i
$189$		0			0
$190$	−1.76393	−	3.05522i	−0.127969	−	0.221649i
$191$	−4.20820	+	7.28882i	−0.304495	+	0.527401i	−0.977149	−	0.212557i	$-0.931821\pi$
$191$	−4.20820	+	7.28882i	−0.304495	+	0.527401i	0.672654	+	0.739957i	$0.265154\pi$
$192$		0			0
$193$	9.88854			0.711793			0.355896	−	0.934525i	$-0.384176\pi$
$193$	9.88854			0.711793			0.355896	+	0.934525i	$0.384176\pi$
$194$	−7.28115	−	12.6113i	−0.522756	−	0.905441i
$195$		0			0
$196$	−4.29180			−0.306557
$197$	−0.0278640	−	0.0482619i	−0.00198523	−	0.00343852i	0.865031	−	0.501718i	$-0.167299\pi$
$197$	−0.0278640	−	0.0482619i	−0.00198523	−	0.00343852i	−0.867016	+	0.498280i	$0.833965\pi$
$198$		0			0
$199$	3.02786	−	5.24441i	0.214640	−	0.371767i	−0.738521	−	0.674230i	$-0.764476\pi$
$199$	3.02786	−	5.24441i	0.214640	−	0.371767i	0.953161	+	0.302463i	$0.0978090\pi$
$200$	7.76393			0.548993
$201$		0			0
$202$	18.5623			1.30604
$203$	−0.0623059	+	0.107917i	−0.00437302	+	0.00757429i
$204$		0			0
$205$	2.61803	+	4.53457i	0.182851	+	0.316708i
$206$	−2.38197			−0.165959
$207$		0			0
$208$	0.572949	+	0.992377i	0.0397269	+	0.0688090i
$209$	−8.81966			−0.610069
$210$		0			0
$211$	2.73607	−	4.73901i	0.188359	−	0.326247i	−0.756344	−	0.654174i	$-0.773017\pi$
$211$	2.73607	−	4.73901i	0.188359	−	0.326247i	0.944703	+	0.327927i	$0.106350\pi$
$212$	−3.00000	−	5.19615i	−0.206041	−	0.356873i
$213$		0			0
$214$	−1.38197	+	2.39364i	−0.0944693	+	0.163626i
$215$	0.944272			0.0643988
$216$		0			0
$217$	0.791796	−	1.37143i	0.0537506	−	0.0930988i
$218$	7.23607	−	12.5332i	0.490088	−	0.848858i
$219$		0			0
$220$	1.90983	−	3.30792i	0.128761	−	0.223020i
$221$	0.263932	+	0.457144i	0.0177540	+	0.0307508i
$222$		0			0
$223$	−21.4164			−1.43415			−0.717074	−	0.696997i	$-0.754519\pi$
$223$	−21.4164			−1.43415			−0.717074	+	0.696997i	$0.754519\pi$
$224$	−0.399187	+	0.691412i	−0.0266718	+	0.0461969i
$225$		0			0
$226$	4.38197			0.291484
$227$	−3.35410	−	5.80948i	−0.222620	−	0.385588i	0.732983	−	0.680247i	$-0.238127\pi$
$227$	−3.35410	−	5.80948i	−0.222620	−	0.385588i	−0.955603	+	0.294658i	$0.904794\pi$
$228$		0			0
$229$	6.20820	−	10.7529i	0.410250	−	0.710573i	−0.584667	−	0.811273i	$-0.698775\pi$
$229$	6.20820	−	10.7529i	0.410250	−	0.710573i	0.994917	+	0.100700i	$0.0321082\pi$
$230$	1.76393	+	3.05522i	0.116310	+	0.201455i
$231$		0			0
$232$	−0.590170	−	1.02220i	−0.0387466	−	0.0671110i
$233$	11.0623	+	19.1605i	0.724716	+	1.25524i	0.959091	+	0.283098i	$0.0913623\pi$
$233$	11.0623	+	19.1605i	0.724716	+	1.25524i	−0.234375	+	0.972146i	$0.575304\pi$
$234$		0			0
$235$	−1.09017	−	1.88823i	−0.0711148	−	0.123175i
$236$	1.85410	+	3.21140i	0.120692	+	0.209044i
$237$		0			0
$238$	−0.427051	+	0.739674i	−0.0276816	+	0.0479459i
$239$	3.40983	+	5.90600i	0.220564	+	0.382027i	0.954979	−	0.296673i	$-0.0958770\pi$
$239$	3.40983	+	5.90600i	0.220564	+	0.382027i	−0.734416	+	0.678700i	$0.762544\pi$
$240$		0			0
$241$	−16.1803			−1.04227			−0.521134	−	0.853475i	$-0.674491\pi$
$241$	−16.1803			−1.04227			−0.521134	+	0.853475i	$0.674491\pi$
$242$	−11.3262	−	19.6176i	−0.728078	−	1.26107i
$243$		0			0
$244$	7.85410			0.502807
$245$	−4.29180	+	7.43361i	−0.274193	+	0.474916i
$246$		0			0
$247$	0.208204	+	0.360620i	0.0132477	+	0.0229457i
$248$	7.50000	+	12.9904i	0.476250	+	0.824890i
$249$		0			0
$250$	−8.47214	+	14.6742i	−0.535825	+	0.928076i
$251$	10.6803	−	18.4989i	0.674137	−	1.16764i	−0.302583	−	0.953123i	$-0.597849\pi$
$251$	10.6803	−	18.4989i	0.674137	−	1.16764i	0.976720	−	0.214517i	$-0.0688176\pi$
$252$		0			0
$253$	8.81966			0.554487
$254$	18.0902			1.13508
$255$		0			0
$256$	−6.78115	−	11.7453i	−0.423822	−	0.734081i
$257$	10.2984	+	17.8373i	0.642395	+	1.11266i	0.984897	+	0.173143i	$0.0553924\pi$
$257$	10.2984	+	17.8373i	0.642395	+	1.11266i	−0.342502	+	0.939517i	$0.611274\pi$
$258$		0			0
$259$	1.76393			0.109605
$260$	−0.180340			−0.0111842
$261$		0			0
$262$	8.47214	−	14.6742i	0.523410	−	0.906573i
$263$	27.1246			1.67258			0.836288	−	0.548291i	$-0.184721\pi$
$263$	27.1246			1.67258			0.836288	+	0.548291i	$0.184721\pi$
$264$		0			0
$265$	−12.0000			−0.737154
$266$	−0.336881	+	0.583495i	−0.0206555	+	0.0357764i
$267$		0			0
$268$	1.54508	+	4.81710i	0.0943811	+	0.294251i
$269$	7.88854			0.480973			0.240487	−	0.970652i	$-0.422693\pi$
$269$	7.88854			0.480973			0.240487	+	0.970652i	$0.422693\pi$
$270$		0			0
$271$	20.3607			1.23682			0.618412	−	0.785854i	$-0.287776\pi$
$271$	20.3607			1.23682			0.618412	+	0.785854i	$0.287776\pi$
$272$	−5.42705	−	9.39993i	−0.329063	−	0.569954i
$273$		0			0
$274$	16.0902	−	27.8690i	0.972043	−	1.68363i
$275$	8.68034	+	15.0348i	0.523444	+	0.906632i
$276$		0			0
$277$	28.6525			1.72156			0.860780	−	0.508977i	$-0.169976\pi$
$277$	28.6525			1.72156			0.860780	+	0.508977i	$0.169976\pi$
$278$	7.23607	−	12.5332i	0.433991	−	0.751694i
$279$		0			0
$280$	0.326238	+	0.565061i	0.0194964	+	0.0337688i
$281$	−6.50000	+	11.2583i	−0.387757	+	0.671616i	−0.992148	−	0.125073i	$-0.960084\pi$
$281$	−6.50000	+	11.2583i	−0.387757	+	0.671616i	0.604390	+	0.796689i	$0.293417\pi$
$282$		0			0
$283$	6.29180			0.374008			0.187004	−	0.982359i	$-0.440122\pi$
$283$	6.29180			0.374008			0.187004	+	0.982359i	$0.440122\pi$
$284$	1.39919	−	2.42346i	0.0830265	−	0.143806i
$285$		0			0
$286$	−0.954915	+	1.65396i	−0.0564653	+	0.0978008i
$287$	0.500000	−	0.866025i	0.0295141	−	0.0511199i
$288$		0			0
$289$	6.00000	+	10.3923i	0.352941	+	0.611312i
$290$	1.05573			0.0619945
$291$		0			0
$292$	1.67376			0.0979495
$293$	20.6525			1.20653			0.603265	−	0.797541i	$-0.293866\pi$
$293$	20.6525			1.20653			0.603265	+	0.797541i	$0.293866\pi$
$294$		0			0
$295$	7.41641			0.431800
$296$	−8.35410	+	14.4697i	−0.485572	+	0.841036i
$297$		0			0
$298$	13.3262	−	23.0817i	0.771968	−	1.33709i
$299$	−0.208204	−	0.360620i	−0.0120407	−	0.0208552i
$300$		0			0
$301$	−0.0901699	−	0.156179i	−0.00519731	−	0.00900200i
$302$	−3.04508	−	5.27424i	−0.175225	−	0.303499i
$303$		0			0
$304$	−4.28115	−	7.41517i	−0.245541	−	0.425289i
$305$	7.85410	−	13.6037i	0.449725	−	0.778946i
$306$		0			0
$307$	17.4443	−	30.2144i	0.995597	−	1.72442i	0.416622	−	0.909080i	$-0.363214\pi$
$307$	17.4443	−	30.2144i	0.995597	−	1.72442i	0.578975	−	0.815345i	$-0.303453\pi$
$308$	−0.729490			−0.0415666
$309$		0			0
$310$	−13.4164			−0.762001
$311$	9.05573			0.513503			0.256752	−	0.966477i	$-0.417348\pi$
$311$	9.05573			0.513503			0.256752	+	0.966477i	$0.417348\pi$
$312$		0			0
$313$	−14.6525			−0.828207			−0.414103	−	0.910230i	$-0.635905\pi$
$313$	−14.6525			−0.828207			−0.414103	+	0.910230i	$0.635905\pi$
$314$	−2.19098	−	3.79489i	−0.123644	−	0.214158i
$315$		0			0
$316$	−2.92705	+	5.06980i	−0.164659	+	0.285199i
$317$	7.64590	−	13.2431i	0.429436	−	0.743806i	−0.567387	−	0.823451i	$-0.692046\pi$
$317$	7.64590	−	13.2431i	0.429436	−	0.743806i	0.996823	+	0.0796457i	$0.0253789\pi$
$318$		0			0
$319$	1.31966	−	2.28572i	0.0738868	−	0.127976i
$320$	−5.23607			−0.292705
$321$		0			0
$322$	0.336881	−	0.583495i	0.0187736	−	0.0325169i
$323$	−1.97214	−	3.41584i	−0.109733	−	0.190062i
$324$		0			0
$325$	0.409830	−	0.709846i	0.0227333	−	0.0393752i
$326$	10.5623			0.584992
$327$		0			0
$328$	4.73607	+	8.20311i	0.261506	+	0.452941i
$329$	−0.208204	+	0.360620i	−0.0114787	+	0.0198816i
$330$		0			0
$331$	−9.73607	−	16.8634i	−0.535143	−	0.926894i	−0.999156	−	0.0410663i	$-0.986925\pi$
$331$	−9.73607	−	16.8634i	−0.535143	−	0.926894i	0.464014	−	0.885828i	$-0.346409\pi$
$332$	−6.79837			−0.373109
$333$		0			0
$334$	−23.7984			−1.30219
$335$	9.88854	+	2.14093i	0.540269	+	0.116972i
$336$		0			0
$337$	−9.20820	+	15.9491i	−0.501603	+	0.868802i	0.498395	+	0.866950i	$0.333923\pi$
$337$	−9.20820	+	15.9491i	−0.501603	+	0.868802i	−0.999998	+	0.00185178i	$0.999411\pi$
$338$	−20.9443			−1.13922
$339$		0			0
$340$	1.70820			0.0926404
$341$	−16.7705	+	29.0474i	−0.908174	+	1.57300i
$342$		0			0
$343$	3.29180			0.177740
$344$	1.70820			0.0921002
$345$		0			0
$346$	8.66312	+	15.0050i	0.465732	+	0.806672i
$347$	−2.88197	−	4.99171i	−0.154712	−	0.267969i	0.778242	−	0.627964i	$-0.216112\pi$
$347$	−2.88197	−	4.99171i	−0.154712	−	0.267969i	−0.932954	+	0.359995i	$0.882778\pi$
$348$		0			0
$349$	30.0689			1.60955			0.804775	−	0.593580i	$-0.202286\pi$
$349$	30.0689			1.60955			0.804775	+	0.593580i	$0.202286\pi$
$350$	1.32624			0.0708904
$351$		0			0
$352$	8.45492	−	14.6443i	0.450648	−	0.780546i
$353$	7.73607	−	13.3993i	0.411749	−	0.713171i	−0.583332	−	0.812234i	$-0.698251\pi$
$353$	7.73607	−	13.3993i	0.411749	−	0.713171i	0.995081	+	0.0990632i	$0.0315846\pi$
$354$		0			0
$355$	−2.79837	−	4.84693i	−0.148522	−	0.257248i
$356$	−0.618034	−	1.07047i	−0.0327557	−	0.0567346i
$357$		0			0
$358$		0			0
$359$	−32.6525			−1.72333			−0.861666	−	0.507476i	$-0.830579\pi$
$359$	−32.6525			−1.72333			−0.861666	+	0.507476i	$0.830579\pi$
$360$		0			0
$361$	7.94427	+	13.7599i	0.418120	+	0.724204i
$362$	−1.61803			−0.0850420
$363$		0			0
$364$	0.0172209	+	0.0298275i	0.000902622	+	0.00156339i
$365$	1.67376	−	2.89904i	0.0876087	−	0.151743i
$366$		0			0
$367$	−12.6803	−	21.9630i	−0.661908	−	1.14646i	−0.980114	−	0.198437i	$-0.936413\pi$
$367$	−12.6803	−	21.9630i	−0.661908	−	1.14646i	0.318205	−	0.948022i	$-0.396920\pi$
$368$	4.28115	+	7.41517i	0.223171	+	0.386543i
$369$		0			0
$370$	−7.47214	−	12.9421i	−0.388458	−	0.672829i
$371$	1.14590	+	1.98475i	0.0594921	+	0.103043i
$372$		0			0
$373$	2.73607	+	4.73901i	0.141668	+	0.245377i	0.928125	−	0.372269i	$-0.121420\pi$
$373$	2.73607	+	4.73901i	0.141668	+	0.245377i	−0.786457	+	0.617645i	$0.788087\pi$
$374$	9.04508	−	15.6665i	0.467710	−	0.810098i
$375$		0			0
$376$	−1.97214	−	3.41584i	−0.101705	−	0.176158i
$377$	−0.124612			−0.00641783
$378$		0			0
$379$	12.7361	−	22.0595i	0.654208	−	1.13312i	−0.327884	−	0.944718i	$-0.606335\pi$
$379$	12.7361	−	22.0595i	0.654208	−	1.13312i	0.982092	−	0.188403i	$-0.0603312\pi$
$380$	1.34752			0.0691265
$381$		0			0
$382$	−6.80902	−	11.7936i	−0.348380	−	0.603411i
$383$	−8.73607	+	15.1313i	−0.446392	+	0.773174i	−0.998148	−	0.0608317i	$-0.980625\pi$
$383$	−8.73607	+	15.1313i	−0.446392	+	0.773174i	0.551756	+	0.834006i	$0.313958\pi$
$384$		0			0
$385$	−0.729490	+	1.26351i	−0.0371783	+	0.0643946i
$386$	−8.00000	+	13.8564i	−0.407189	+	0.705273i
$387$		0			0
$388$	5.56231			0.282383
$389$	−2.50000	+	4.33013i	−0.126755	+	0.219546i	−0.922418	−	0.386194i	$-0.873790\pi$
$389$	−2.50000	+	4.33013i	−0.126755	+	0.219546i	0.795663	+	0.605740i	$0.207123\pi$
$390$		0			0
$391$	1.97214	+	3.41584i	0.0997352	+	0.172746i
$392$	−7.76393	+	13.4475i	−0.392138	+	0.679203i
$393$		0			0
$394$	0.0901699			0.00454270
$395$	5.85410	+	10.1396i	0.294552	+	0.510179i
$396$		0			0
$397$	27.8885			1.39969			0.699843	−	0.714297i	$-0.253253\pi$
$397$	27.8885			1.39969			0.699843	+	0.714297i	$0.253253\pi$
$398$	4.89919	+	8.48564i	0.245574	+	0.425347i
$399$		0			0
$400$	−8.42705	+	14.5961i	−0.421353	+	0.729804i
$401$	8.94427			0.446656			0.223328	−	0.974743i	$-0.428308\pi$
$401$	8.94427			0.446656			0.223328	+	0.974743i	$0.428308\pi$
$402$		0			0
$403$	1.58359			0.0788843
$404$	−3.54508	+	6.14027i	−0.176375	+	0.305490i
$405$		0			0
$406$	−0.100813	−	0.174613i	−0.00500327	−	0.00866591i
$407$	−37.3607			−1.85190
$408$		0			0
$409$	0.0278640	+	0.0482619i	0.00137779	+	0.00238640i	0.866713	−	0.498806i	$-0.166228\pi$
$409$	0.0278640	+	0.0482619i	0.00137779	+	0.00238640i	−0.865336	+	0.501193i	$0.832895\pi$
$410$	−8.47214			−0.418409
$411$		0			0
$412$	0.454915	−	0.787936i	0.0224121	−	0.0388188i
$413$	−0.708204	−	1.22665i	−0.0348484	−	0.0603593i
$414$		0			0
$415$	−6.79837	+	11.7751i	−0.333719	+	0.578018i
$416$	−0.798374			−0.0391435
$417$		0			0
$418$	7.13525	−	12.3586i	0.348997	−	0.604480i
$419$	12.8262	−	22.2157i	0.626603	−	1.08531i	−0.361626	−	0.932323i	$-0.617778\pi$
$419$	12.8262	−	22.2157i	0.626603	−	1.08531i	0.988229	−	0.152984i	$-0.0488884\pi$
$420$		0			0
$421$	−9.59017	+	16.6107i	−0.467396	+	0.809554i	−0.999306	−	0.0372469i	$-0.988141\pi$
$421$	−9.59017	+	16.6107i	−0.467396	+	0.809554i	0.531910	+	0.846801i	$0.321475\pi$
$422$	4.42705	+	7.66788i	0.215505	+	0.373266i
$423$		0			0
$424$	−21.7082			−1.05424
$425$	−3.88197	+	6.72376i	−0.188303	+	0.326150i
$426$		0			0
$427$	−3.00000			−0.145180
$428$	−0.527864	−	0.914287i	−0.0255153	−	0.0441937i
$429$		0			0
$430$	−0.763932	+	1.32317i	−0.0368401	+	0.0638089i
$431$	−16.5344	−	28.6385i	−0.796436	−	1.37947i	−0.921923	−	0.387372i	$-0.873383\pi$
$431$	−16.5344	−	28.6385i	−0.796436	−	1.37947i	0.125487	−	0.992095i	$-0.459951\pi$
$432$		0			0
$433$	16.1180	+	27.9173i	0.774583	+	1.34162i	0.935028	+	0.354573i	$0.115374\pi$
$433$	16.1180	+	27.9173i	0.774583	+	1.34162i	−0.160445	+	0.987045i	$0.551293\pi$
$434$	1.28115	+	2.21902i	0.0614973	+	0.106516i
$435$		0			0
$436$	2.76393	+	4.78727i	0.132368	+	0.229269i
$437$	1.55573	+	2.69460i	0.0744206	+	0.128900i
$438$		0			0
$439$	−7.29837	+	12.6412i	−0.348332	+	0.603329i	−0.985953	−	0.167021i	$-0.946585\pi$
$439$	−7.29837	+	12.6412i	−0.348332	+	0.603329i	0.637621	+	0.770350i	$0.279919\pi$
$440$	−6.90983	−	11.9682i	−0.329413	−	0.570560i
$441$		0			0
$442$	−0.854102			−0.0406255
$443$	−7.20820	−	12.4850i	−0.342472	−	0.593179i	0.642419	−	0.766354i	$-0.277931\pi$
$443$	−7.20820	−	12.4850i	−0.342472	−	0.593179i	−0.984891	+	0.173174i	$0.944598\pi$
$444$		0			0
$445$	−2.47214			−0.117190
$446$	17.3262	−	30.0099i	0.820421	−	1.42101i
$447$		0			0
$448$	0.500000	+	0.866025i	0.0236228	+	0.0409159i
$449$	−8.59017	−	14.8786i	−0.405395	−	0.702165i	0.588972	−	0.808153i	$-0.299533\pi$
$449$	−8.59017	−	14.8786i	−0.405395	−	0.702165i	−0.994367	+	0.105988i	$0.966199\pi$
$450$		0			0
$451$	−10.5902	+	18.3427i	−0.498672	+	0.863725i
$452$	−0.836881	+	1.44952i	−0.0393636	+	0.0681797i
$453$		0			0
$454$	10.8541			0.509408
$455$	0.0688837			0.00322932
$456$		0			0
$457$	−0.354102	−	0.613323i	−0.0165642	−	0.0286900i	0.857624	−	0.514276i	$-0.171939\pi$
$457$	−0.354102	−	0.613323i	−0.0165642	−	0.0286900i	−0.874189	+	0.485586i	$0.838606\pi$
$458$	10.0451	+	17.3986i	0.469376	+	0.812983i
$459$		0			0
$460$	−1.34752			−0.0628286
$461$	−34.4721			−1.60553			−0.802764	−	0.596297i	$-0.796638\pi$
$461$	−34.4721			−1.60553			−0.802764	+	0.596297i	$0.796638\pi$
$462$		0			0
$463$	2.59017	−	4.48631i	0.120375	−	0.208496i	−0.799540	−	0.600612i	$-0.794924\pi$
$463$	2.59017	−	4.48631i	0.120375	−	0.208496i	0.919916	+	0.392116i	$0.128257\pi$
$464$	2.56231			0.118952
$465$		0			0
$466$	−35.7984			−1.65833
$467$	−19.0623	+	33.0169i	−0.882098	+	1.52784i	−0.0330946	+	0.999452i	$0.510536\pi$
$467$	−19.0623	+	33.0169i	−0.882098	+	1.52784i	−0.849004	+	0.528387i	$0.822797\pi$
$468$		0			0
$469$	−0.590170	−	1.83997i	−0.0272515	−	0.0849618i
$470$	3.52786			0.162728
$471$		0			0
$472$	13.4164			0.617540
$473$	1.90983	+	3.30792i	0.0878141	+	0.152098i
$474$		0			0
$475$	−3.06231	+	5.30407i	−0.140508	+	0.243367i
$476$	−0.163119	−	0.282530i	−0.00747655	−	0.0129498i
$477$		0			0
$478$	−11.0344			−0.504704
$479$	10.9721	−	19.0043i	0.501330	−	0.868328i	−0.498669	−	0.866792i	$-0.666178\pi$
$479$	10.9721	−	19.0043i	0.501330	−	0.868328i	0.999999	−	0.00153607i	$-0.000488947\pi$
$480$		0			0
$481$	0.881966	+	1.52761i	0.0402142	+	0.0696530i
$482$	13.0902	−	22.6728i	0.596241	−	1.03272i
$483$		0			0
$484$	8.65248			0.393294
$485$	5.56231	−	9.63420i	0.252571	−	0.437466i
$486$		0			0
$487$	18.2082	−	31.5375i	0.825092	−	1.42910i	−0.0767561	−	0.997050i	$-0.524456\pi$
$487$	18.2082	−	31.5375i	0.825092	−	1.42910i	0.901849	−	0.432052i	$-0.142210\pi$
$488$	14.2082	−	24.6093i	0.643175	−	1.11401i
$489$		0			0
$490$	−6.94427	−	12.0278i	−0.313710	−	0.543362i
$491$	−31.7082			−1.43097			−0.715486	−	0.698627i	$-0.753795\pi$
$491$	−31.7082			−1.43097			−0.715486	+	0.698627i	$0.753795\pi$
$492$		0			0
$493$	1.18034			0.0531598
$494$	−0.673762			−0.0303140
$495$		0			0
$496$	−32.5623			−1.46209
$497$	−0.534442	+	0.925680i	−0.0239730	+	0.0415224i
$498$		0			0
$499$	10.5902	−	18.3427i	0.474081	−	0.821133i	−0.525479	−	0.850807i	$-0.676114\pi$
$499$	10.5902	−	18.3427i	0.474081	−	0.821133i	0.999560	+	0.0296743i	$0.00944701\pi$
$500$	−3.23607	−	5.60503i	−0.144721	−	0.250665i
$501$		0			0
$502$	17.2812	+	29.9318i	0.771296	+	1.33592i
$503$	−7.20820	−	12.4850i	−0.321398	−	0.556678i	0.659379	−	0.751811i	$-0.270819\pi$
$503$	−7.20820	−	12.4850i	−0.321398	−	0.556678i	−0.980777	+	0.195133i	$0.937486\pi$
$504$		0			0
$505$	7.09017	+	12.2805i	0.315508	+	0.546477i
$506$	−7.13525	+	12.3586i	−0.317201	+	0.549408i
$507$		0			0
$508$	−3.45492	+	5.98409i	−0.153287	+	0.265501i
$509$	29.7082			1.31679			0.658396	−	0.752671i	$-0.271235\pi$
$509$	29.7082			1.31679			0.658396	+	0.752671i	$0.271235\pi$
$510$		0			0
$511$	−0.639320			−0.0282819
$512$	−5.29180			−0.233867
$513$		0			0
$514$	−33.3262			−1.46996
$515$	−0.909830	−	1.57587i	−0.0400919	−	0.0694412i
$516$		0			0
$517$	4.40983	−	7.63805i	0.193944	−	0.335921i
$518$	−1.42705	+	2.47172i	−0.0627010	+	0.108601i
$519$		0			0
$520$	−0.326238	+	0.565061i	−0.0143065	+	0.0247795i
$521$	−4.47214			−0.195928			−0.0979639	−	0.995190i	$-0.531233\pi$
$521$	−4.47214			−0.195928			−0.0979639	+	0.995190i	$0.531233\pi$
$522$		0			0
$523$	−13.1180	+	22.7211i	−0.573612	+	0.993524i	0.422579	+	0.906326i	$0.361125\pi$
$523$	−13.1180	+	22.7211i	−0.573612	+	0.993524i	−0.996191	+	0.0871985i	$0.972209\pi$
$524$	3.23607	+	5.60503i	0.141368	+	0.244857i
$525$		0			0
$526$	−21.9443	+	38.0086i	−0.956816	+	1.65725i
$527$	−15.0000			−0.653410
$528$		0			0
$529$	9.94427	+	17.2240i	0.432360	+	0.748869i
$530$	9.70820	−	16.8151i	0.421697	−	0.730401i
$531$		0			0
$532$	−0.128677	−	0.222875i	−0.00557886	−	0.00966287i
$533$	1.00000			0.0433148
$534$		0			0
$535$	−2.11146			−0.0912862
$536$	17.8885	+	3.87298i	0.772667	+	0.167287i
$537$		0			0
$538$	−6.38197	+	11.0539i	−0.275146	+	0.476567i
$539$	−34.7214			−1.49555
$540$		0			0
$541$	−11.1246			−0.478284			−0.239142	−	0.970985i	$-0.576866\pi$
$541$	−11.1246			−0.478284			−0.239142	+	0.970985i	$0.576866\pi$
$542$	−16.4721	+	28.5306i	−0.707539	+	1.22549i
$543$		0			0
$544$	7.56231			0.324231
$545$	11.0557			0.473575
$546$		0			0
$547$	22.9164	+	39.6924i	0.979835	+	1.69712i	0.662957	+	0.748657i	$0.269301\pi$
$547$	22.9164	+	39.6924i	0.979835	+	1.69712i	0.316878	+	0.948466i	$0.397366\pi$
$548$	6.14590	+	10.6450i	0.262540	+	0.454732i
$549$		0			0
$550$	−28.0902			−1.19777
$551$	0.931116			0.0396669
$552$		0			0
$553$	1.11803	−	1.93649i	0.0475436	−	0.0823480i
$554$	−23.1803	+	40.1495i	−0.984838	+	1.70579i
$555$		0			0
$556$	2.76393	+	4.78727i	0.117217	+	0.203026i
$557$	7.68034	+	13.3027i	0.325426	+	0.563655i	0.981599	−	0.190956i	$-0.0611588\pi$
$557$	7.68034	+	13.3027i	0.325426	+	0.563655i	−0.656172	+	0.754611i	$0.727825\pi$
$558$		0			0
$559$	0.0901699	−	0.156179i	0.00381378	−	0.00660566i
$560$	−1.41641			−0.0598542
$561$		0			0
$562$	−10.5172	−	18.2164i	−0.443642	−	0.768411i
$563$	44.5410			1.87718			0.938590	−	0.345034i	$-0.112133\pi$
$563$	44.5410			1.87718			0.938590	+	0.345034i	$0.112133\pi$
$564$		0			0
$565$	1.67376	+	2.89904i	0.0704157	+	0.121964i
$566$	−5.09017	+	8.81643i	−0.213956	+	0.370582i
$567$		0			0
$568$	−5.06231	−	8.76817i	−0.212410	−	0.367904i
$569$	12.2082	+	21.1452i	0.511795	+	0.886454i	0.999907	+	0.0136731i	$0.00435243\pi$
$569$	12.2082	+	21.1452i	0.511795	+	0.886454i	−0.488112	+	0.872781i	$0.662314\pi$
$570$		0			0
$571$	−9.88197	−	17.1161i	−0.413547	−	0.716285i	0.581727	−	0.813384i	$-0.302377\pi$
$571$	−9.88197	−	17.1161i	−0.413547	−	0.716285i	−0.995275	+	0.0970987i	$0.969044\pi$
$572$	−0.364745	−	0.631757i	−0.0152508	−	0.0264151i
$573$		0			0
$574$	0.809017	+	1.40126i	0.0337677	+	0.0584874i
$575$	3.06231	−	5.30407i	0.127707	−	0.221195i
$576$		0			0
$577$	4.73607	+	8.20311i	0.197165	+	0.341500i	0.947608	−	0.319435i	$-0.103493\pi$
$577$	4.73607	+	8.20311i	0.197165	+	0.341500i	−0.750443	+	0.660935i	$0.770160\pi$
$578$	−19.4164			−0.807616
$579$		0			0
$580$	−0.201626	+	0.349227i	−0.00837207	+	0.0145008i
$581$	2.59675			0.107731
$582$		0			0
$583$	−24.2705	−	42.0378i	−1.00518	−	1.74103i
$584$	3.02786	−	5.24441i	0.125294	−	0.217015i
$585$		0			0
$586$	−16.7082	+	28.9395i	−0.690210	+	1.19548i
$587$	5.82624	−	10.0913i	0.240475	−	0.416514i	−0.720375	−	0.693585i	$-0.756030\pi$
$587$	5.82624	−	10.0913i	0.240475	−	0.416514i	0.960850	+	0.277071i	$0.0893636\pi$
$588$		0			0
$589$	−11.8328			−0.487563
$590$	−6.00000	+	10.3923i	−0.247016	+	0.427844i
$591$		0			0
$592$	−18.1353	−	31.4112i	−0.745354	−	1.29099i
$593$	−6.68034	+	11.5707i	−0.274329	+	0.475151i	−0.969966	−	0.243242i	$-0.921789\pi$
$593$	−6.68034	+	11.5707i	−0.274329	+	0.475151i	0.695637	+	0.718394i	$0.255122\pi$
$594$		0			0
$595$	−0.652476			−0.0267489
$596$	5.09017	+	8.81643i	0.208501	+	0.361135i
$597$		0			0
$598$	0.673762			0.0275522
$599$	−8.64590	−	14.9751i	−0.353262	−	0.611867i	0.633557	−	0.773696i	$-0.281594\pi$
$599$	−8.64590	−	14.9751i	−0.353262	−	0.611867i	−0.986819	+	0.161829i	$0.948261\pi$
$600$		0			0
$601$	−12.6459	+	21.9033i	−0.515837	+	0.893456i	0.483994	+	0.875071i	$0.339186\pi$
$601$	−12.6459	+	21.9033i	−0.515837	+	0.893456i	−0.999831	+	0.0183845i	$0.994148\pi$
$602$	0.291796			0.0118927
$603$		0			0
$604$	2.32624			0.0946533
$605$	8.65248	−	14.9865i	0.351773	−	0.609289i
$606$		0			0
$607$	12.2082	+	21.1452i	0.495516	+	0.858258i	0.999987	−	0.00517029i	$-0.00164576\pi$
$607$	12.2082	+	21.1452i	0.495516	+	0.858258i	−0.504471	+	0.863429i	$0.668312\pi$
$608$	5.96556			0.241935
$609$		0			0
$610$	12.7082	+	22.0113i	0.514540	+	0.891210i
$611$	−0.416408			−0.0168461
$612$		0			0
$613$	15.6803	−	27.1591i	0.633323	−	1.09695i	−0.353545	−	0.935418i	$-0.615024\pi$
$613$	15.6803	−	27.1591i	0.633323	−	1.09695i	0.986868	−	0.161530i	$-0.0516428\pi$
$614$	28.2254	+	48.8879i	1.13909	+	1.97295i
$615$		0			0
$616$	−1.31966	+	2.28572i	−0.0531706	+	0.0920942i
$617$	15.7082			0.632388			0.316194	−	0.948694i	$-0.397595\pi$
$617$	15.7082			0.632388			0.316194	+	0.948694i	$0.397595\pi$
$618$		0			0
$619$	11.6459	−	20.1713i	0.468088	−	0.810752i	−0.531247	−	0.847217i	$-0.678276\pi$
$619$	11.6459	−	20.1713i	0.468088	−	0.810752i	0.999335	+	0.0364646i	$0.0116096\pi$
$620$	2.56231	−	4.43804i	0.102905	−	0.178236i
$621$		0			0
$622$	−7.32624	+	12.6894i	−0.293755	+	0.508799i
$623$	0.236068	+	0.408882i	0.00945786	+	0.0163815i
$624$		0			0
$625$	4.41641			0.176656
$626$	11.8541	−	20.5319i	0.473785	−	0.820620i
$627$		0			0
$628$	1.67376			0.0667904
$629$	−8.35410	−	14.4697i	−0.333100	−	0.576946i
$630$		0			0
$631$	−4.55573	+	7.89075i	−0.181361	+	0.314126i	−0.942344	−	0.334645i	$-0.891383\pi$
$631$	−4.55573	+	7.89075i	−0.181361	+	0.314126i	0.760983	+	0.648771i	$0.224717\pi$
$632$	10.5902	+	18.3427i	0.421254	+	0.729634i
$633$		0			0
$634$	12.3713	+	21.4278i	0.491328	+	0.851005i
$635$	6.90983	+	11.9682i	0.274208	+	0.474943i
$636$		0			0
$637$	0.819660	+	1.41969i	0.0324761	+	0.0562503i
$638$	2.13525	+	3.69837i	0.0845356	+	0.146420i
$639$		0			0
$640$	8.41641	−	14.5776i	0.332688	−	0.576232i
$641$	−24.5902	−	42.5914i	−0.971253	−	1.68226i	−0.691783	−	0.722106i	$-0.743174\pi$
$641$	−24.5902	−	42.5914i	−0.971253	−	1.68226i	−0.279471	−	0.960154i	$-0.590159\pi$
$642$		0			0
$643$	−8.29180			−0.326997			−0.163498	−	0.986544i	$-0.552278\pi$
$643$	−8.29180			−0.326997			−0.163498	+	0.986544i	$0.552278\pi$
$644$	0.128677	+	0.222875i	0.00507059	+	0.00878252i
$645$		0			0
$646$	6.38197			0.251095
$647$	14.8820	−	25.7763i	0.585070	−	1.01337i	−0.409796	−	0.912177i	$-0.634400\pi$
$647$	14.8820	−	25.7763i	0.585070	−	1.01337i	0.994867	−	0.101195i	$-0.0322665\pi$
$648$		0			0
$649$	15.0000	+	25.9808i	0.588802	+	1.01983i
$650$	0.663119	+	1.14856i	0.0260097	+	0.0450501i
$651$		0			0
$652$	−2.01722	+	3.49393i	−0.0790005	+	0.136833i
$653$	12.1180	−	20.9891i	0.474215	−	0.821365i	−0.525349	−	0.850887i	$-0.676065\pi$
$653$	12.1180	−	20.9891i	0.474215	−	0.821365i	0.999564	+	0.0295219i	$0.00939849\pi$
$654$		0			0
$655$	12.9443			0.505775
$656$	−20.5623			−0.802823
$657$		0			0
$658$	−0.336881	−	0.583495i	−0.0131330	−	0.0227470i
$659$	22.3885	+	38.7781i	0.872134	+	1.51058i	0.859785	+	0.510656i	$0.170598\pi$
$659$	22.3885	+	38.7781i	0.872134	+	1.51058i	0.0123490	+	0.999924i	$0.496069\pi$
$660$		0			0
$661$	−36.3607			−1.41427			−0.707133	−	0.707080i	$-0.750012\pi$
$661$	−36.3607			−1.41427			−0.707133	+	0.707080i	$0.750012\pi$
$662$	31.5066			1.22454
$663$		0			0
$664$	−12.2984	+	21.3014i	−0.477269	+	0.826655i
$665$	−0.514708			−0.0199595
$666$		0			0
$667$	−0.931116			−0.0360530
$668$	4.54508	−	7.87232i	0.175855	−	0.304589i
$669$		0			0
$670$	−11.0000	+	12.1244i	−0.424967	+	0.468405i
$671$	63.5410			2.45297
$672$		0			0
$673$	−18.3607			−0.707752			−0.353876	−	0.935292i	$-0.615137\pi$
$673$	−18.3607			−0.707752			−0.353876	+	0.935292i	$0.615137\pi$
$674$	−14.8992	−	25.8061i	−0.573895	−	0.994016i
$675$		0			0
$676$	4.00000	−	6.92820i	0.153846	−	0.266469i
$677$	−2.73607	−	4.73901i	−0.105156	−	0.182135i	0.808646	−	0.588295i	$-0.200201\pi$
$677$	−2.73607	−	4.73901i	−0.105156	−	0.182135i	−0.913802	+	0.406160i	$0.866867\pi$
$678$		0			0
$679$	−2.12461			−0.0815351
$680$	3.09017	−	5.35233i	0.118503	−	0.205253i
$681$		0			0
$682$	−27.1353	−	46.9996i	−1.03906	−	1.79971i
$683$	0.881966	−	1.52761i	0.0337475	−	0.0584524i	−0.848658	−	0.528941i	$-0.822589\pi$
$683$	0.881966	−	1.52761i	0.0337475	−	0.0584524i	0.882406	+	0.470489i	$0.155922\pi$
$684$		0			0
$685$	24.5836			0.939291
$686$	−2.66312	+	4.61266i	−0.101678	+	0.176112i
$687$		0			0
$688$	−1.85410	+	3.21140i	−0.0706870	+	0.122433i
$689$	−1.14590	+	1.98475i	−0.0436552	+	0.0756131i
$690$		0			0
$691$	18.4443	+	31.9464i	0.701653	+	1.21530i	0.967886	+	0.251390i	$0.0808877\pi$
$691$	18.4443	+	31.9464i	0.701653	+	1.21530i	−0.266233	+	0.963909i	$0.585779\pi$
$692$	−6.61803			−0.251580
$693$		0			0
$694$	9.32624			0.354019
$695$	11.0557			0.419368
$696$		0			0
$697$	−9.47214			−0.358783
$698$	−24.3262	+	42.1343i	−0.920762	+	1.59481i
$699$		0			0
$700$	−0.253289	+	0.438709i	−0.00957342	+	0.0165817i
$701$	−16.7361	−	28.9877i	−0.632113	−	1.09485i	−0.987119	−	0.159987i	$-0.948855\pi$
$701$	−16.7361	−	28.9877i	−0.632113	−	1.09485i	0.355007	−	0.934864i	$-0.384479\pi$
$702$		0			0
$703$	−6.59017	−	11.4145i	−0.248553	−	0.430506i
$704$	−10.5902	−	18.3427i	−0.399132	−	0.691317i
$705$		0			0
$706$	12.5172	+	21.6805i	0.471092	+	0.815955i
$707$	1.35410	−	2.34537i	0.0509262	−	0.0882068i
$708$		0			0
$709$	−7.06231	+	12.2323i	−0.265230	+	0.459393i	−0.967624	−	0.252396i	$-0.918781\pi$
$709$	−7.06231	+	12.2323i	−0.265230	+	0.459393i	0.702394	+	0.711789i	$0.252115\pi$
$710$	9.05573			0.339855
$711$		0			0
$712$	−4.47214			−0.167600
$713$	11.8328			0.443142
$714$		0			0
$715$	−1.45898			−0.0545628
$716$		0			0
$717$		0			0
$718$	26.4164	−	45.7546i	0.985852	−	1.70755i
$719$	17.3541	−	30.0582i	0.647199	−	1.12098i	−0.336590	−	0.941651i	$-0.609274\pi$
$719$	17.3541	−	30.0582i	0.647199	−	1.12098i	0.983789	−	0.179330i	$-0.0573930\pi$
$720$		0			0
$721$	−0.173762	+	0.300965i	−0.00647124	+	0.0112085i
$722$	−25.7082			−0.956760
$723$		0			0
$724$	0.309017	−	0.535233i	0.0114845	−	0.0198918i
$725$	−0.916408	−	1.58726i	−0.0340345	−	0.0589495i
$726$		0			0
$727$	19.6803	−	34.0873i	0.729903	−	1.26423i	−0.227020	−	0.973890i	$-0.572898\pi$
$727$	19.6803	−	34.0873i	0.729903	−	1.26423i	0.956924	−	0.290340i	$-0.0937683\pi$
$728$	0.124612			0.00461842
$729$		0			0
$730$	2.70820	+	4.69075i	0.100235	+	0.173612i
$731$	−0.854102	+	1.47935i	−0.0315901	+	0.0547157i
$732$		0			0
$733$	5.68034	+	9.83864i	0.209808	+	0.363398i	0.951654	−	0.307172i	$-0.0993827\pi$
$733$	5.68034	+	9.83864i	0.209808	+	0.363398i	−0.741846	+	0.670570i	$0.766049\pi$
$734$	41.0344			1.51461
$735$		0			0
$736$	−5.96556			−0.219893
$737$	12.5000	+	38.9711i	0.460443	+	1.43552i
$738$		0			0
$739$	2.35410	−	4.07742i	0.0865970	−	0.149990i	−0.819474	−	0.573117i	$-0.805734\pi$
$739$	2.35410	−	4.07742i	0.0865970	−	0.149990i	0.906071	+	0.423126i	$0.139067\pi$
$740$	5.70820			0.209838
$741$		0			0
$742$	−3.70820			−0.136132
$743$	−17.5902	+	30.4671i	−0.645321	+	1.11773i	0.338907	+	0.940820i	$0.389943\pi$
$743$	−17.5902	+	30.4671i	−0.645321	+	1.11773i	−0.984227	+	0.176908i	$0.943390\pi$
$744$		0			0
$745$	20.3607			0.745958
$746$	−8.85410			−0.324172
$747$		0			0
$748$	3.45492	+	5.98409i	0.126324	+	0.218800i
$749$	0.201626	+	0.349227i	0.00736726	+	0.0127605i
$750$		0			0
$751$	−38.6525			−1.41045			−0.705224	−	0.708984i	$-0.749154\pi$
$751$	−38.6525			−1.41045			−0.705224	+	0.708984i	$0.749154\pi$
$752$	8.56231			0.312235
$753$		0			0
$754$	0.100813	−	0.174613i	0.00367140	−	0.00635904i
$755$	2.32624	−	4.02916i	0.0846605	−	0.146636i
$756$		0			0
$757$	15.6803	+	27.1591i	0.569912	+	0.987116i	0.996574	+	0.0827050i	$0.0263559\pi$
$757$	15.6803	+	27.1591i	0.569912	+	0.987116i	−0.426662	+	0.904411i	$0.640311\pi$
$758$	20.6074	+	35.6930i	0.748494	+	1.29643i
$759$		0			0
$760$	2.43769	−	4.22221i	0.0884245	−	0.153156i
$761$	−36.7639			−1.33269			−0.666346	−	0.745643i	$-0.732143\pi$
$761$	−36.7639			−1.33269			−0.666346	+	0.745643i	$0.732143\pi$
$762$		0			0
$763$	−1.05573	−	1.82857i	−0.0382199	−	0.0661988i
$764$	5.20163			0.188188
$765$		0			0
$766$	−14.1353	−	24.4830i	−0.510728	−	0.884606i
$767$	0.708204	−	1.22665i	0.0255718	−	0.0442916i
$768$		0			0
$769$	7.29837	+	12.6412i	0.263186	+	0.455852i	0.967087	−	0.254447i	$-0.0818933\pi$
$769$	7.29837	+	12.6412i	0.263186	+	0.455852i	−0.703901	+	0.710298i	$0.748560\pi$
$770$	−1.18034	−	2.04441i	−0.0425365	−	0.0736754i
$771$		0			0
$772$	−3.05573	−	5.29268i	−0.109978	−	0.190488i
$773$	2.88197	+	4.99171i	0.103657	+	0.179539i	0.913189	−	0.407537i	$-0.133612\pi$
$773$	2.88197	+	4.99171i	0.103657	+	0.179539i	−0.809532	+	0.587076i	$0.800279\pi$
$774$		0			0
$775$	11.6459	+	20.1713i	0.418333	+	0.724574i
$776$	10.0623	−	17.4284i	0.361216	−	0.625644i
$777$		0			0
$778$	−4.04508	−	7.00629i	−0.145023	−	0.251188i
$779$	−7.47214			−0.267717
$780$		0			0
$781$	11.3197	−	19.6062i	0.405049	−	0.701566i
$782$	−6.38197			−0.228219
$783$		0			0
$784$	−16.8541	−	29.1922i	−0.601932	−	1.04258i
$785$	1.67376	−	2.89904i	0.0597391	−	0.103471i
$786$		0			0
$787$	6.26393	−	10.8494i	0.223285	−	0.386741i	−0.732518	−	0.680747i	$-0.761655\pi$
$787$	6.26393	−	10.8494i	0.223285	−	0.386741i	0.955804	+	0.294006i	$0.0949886\pi$
$788$	−0.0172209	+	0.0298275i	−0.000613470	+	0.00106256i
$789$		0			0
$790$	−18.9443			−0.674007
$791$	0.319660	−	0.553668i	0.0113658	−	0.0196862i
$792$		0			0
$793$	−1.50000	−	2.59808i	−0.0532666	−	0.0922604i
$794$	−22.5623	+	39.0791i	−0.800706	+	1.38686i
$795$		0			0
$796$	−3.74265			−0.132655
$797$	6.40983	+	11.1022i	0.227048	+	0.393258i	0.956932	−	0.290313i	$-0.0937593\pi$
$797$	6.40983	+	11.1022i	0.227048	+	0.393258i	−0.729884	+	0.683571i	$0.760426\pi$
$798$		0			0
$799$	3.94427			0.139538
$800$	−5.87132	−	10.1694i	−0.207583	−	0.359544i
$801$		0			0
$802$	−7.23607	+	12.5332i	−0.255514	+	0.442564i
$803$	13.5410			0.477852
$804$		0			0
$805$	0.514708			0.0181411
$806$	−1.28115	+	2.21902i	−0.0451267	+	0.0781617i
$807$		0			0
$808$	12.8262	+	22.2157i	0.451225	+	0.781545i
$809$	−45.5967			−1.60310			−0.801548	−	0.597930i	$-0.795990\pi$
$809$	−45.5967			−1.60310			−0.801548	+	0.597930i	$0.795990\pi$
$810$		0			0
$811$	15.9164	+	27.5680i	0.558901	+	0.968044i	0.997589	+	0.0694049i	$0.0221100\pi$
$811$	15.9164	+	27.5680i	0.558901	+	0.968044i	−0.438688	+	0.898639i	$0.644557\pi$
$812$	0.0770143			0.00270267
$813$		0			0
$814$	30.2254	−	52.3520i	1.05940	−	1.83494i
$815$	4.03444	+	6.98786i	0.141320	+	0.244774i
$816$		0			0
$817$	−0.673762	+	1.16699i	−0.0235720	+	0.0408278i
$818$	−0.0901699			−0.00315272
$819$		0			0
$820$	1.61803	−	2.80252i	0.0565042	−	0.0978681i
$821$	−2.68034	+	4.64248i	−0.0935445	+	0.162024i	−0.909000	−	0.416796i	$-0.863153\pi$
$821$	−2.68034	+	4.64248i	−0.0935445	+	0.162024i	0.815456	+	0.578819i	$0.196486\pi$
$822$		0			0
$823$	10.2082	−	17.6811i	0.355836	−	0.616325i	−0.631425	−	0.775437i	$-0.717530\pi$
$823$	10.2082	−	17.6811i	0.355836	−	0.616325i	0.987261	+	0.159112i	$0.0508630\pi$
$824$	−1.64590	−	2.85078i	−0.0573376	−	0.0993116i
$825$		0			0
$826$	2.29180			0.0797418
$827$	−3.40983	+	5.90600i	−0.118571	+	0.205372i	−0.919202	−	0.393787i	$-0.871165\pi$
$827$	−3.40983	+	5.90600i	−0.118571	+	0.205372i	0.800630	+	0.599159i	$0.204498\pi$
$828$		0			0
$829$	14.5836			0.506509			0.253255	−	0.967400i	$-0.418499\pi$
$829$	14.5836			0.506509			0.253255	+	0.967400i	$0.418499\pi$
$830$	−11.0000	−	19.0526i	−0.381816	−	0.661324i
$831$		0			0
$832$	−0.500000	+	0.866025i	−0.0173344	+	0.0300240i
$833$	−7.76393	−	13.4475i	−0.269004	−	0.465929i
$834$		0			0
$835$	−9.09017	−	15.7446i	−0.314578	−	0.544866i
$836$	2.72542	+	4.72057i	0.0942608	+	0.163264i
$837$		0			0
$838$	20.7533	+	35.9458i	0.716910	+	1.24173i
$839$	−22.5344	−	39.0308i	−0.777975	−	1.34749i	−0.933107	−	0.359599i	$-0.882913\pi$
$839$	−22.5344	−	39.0308i	−0.777975	−	1.34749i	0.155132	−	0.987894i	$-0.450420\pi$
$840$		0			0
$841$	14.3607	−	24.8734i	0.495196	−	0.857704i
$842$	−15.5172	−	26.8766i	−0.534759	−	0.926229i
$843$		0			0
$844$	−3.38197			−0.116412
$845$	−8.00000	−	13.8564i	−0.275208	−	0.476675i
$846$		0			0
$847$	−3.30495			−0.113559
$848$	23.5623	−	40.8111i	0.809133	−	1.40146i
$849$		0			0
$850$	−6.28115	−	10.8793i	−0.215442	−	0.373156i
$851$	6.59017	+	11.4145i	0.225908	+	0.391284i
$852$		0			0
$853$	16.0623	−	27.8207i	0.549963	−	0.952564i	−0.448314	−	0.893876i	$-0.647975\pi$
$853$	16.0623	−	27.8207i	0.549963	−	0.952564i	0.998276	−	0.0586873i	$-0.0186915\pi$
$854$	2.42705	−	4.20378i	0.0830520	−	0.143850i
$855$		0			0
$856$	−3.81966			−0.130553
$857$	2.29180			0.0782863			0.0391431	−	0.999234i	$-0.487537\pi$
$857$	2.29180			0.0782863			0.0391431	+	0.999234i	$0.487537\pi$
$858$		0			0
$859$	7.02786	+	12.1726i	0.239788	+	0.415324i	0.960653	−	0.277751i	$-0.0895889\pi$
$859$	7.02786	+	12.1726i	0.239788	+	0.415324i	−0.720866	+	0.693075i	$0.756256\pi$
$860$	−0.291796	−	0.505406i	−0.00995016	−	0.0172342i
$861$		0			0
$862$	53.5066			1.82244
$863$	−55.1935			−1.87881			−0.939404	−	0.342811i	$-0.888621\pi$
$863$	−55.1935			−1.87881			−0.939404	+	0.342811i	$0.888621\pi$
$864$		0			0
$865$	−6.61803	+	11.4628i	−0.225020	+	0.389746i
$866$	−52.1591			−1.77244
$867$		0			0
$868$	−0.978714			−0.0332197
$869$	−23.6803	+	41.0156i	−0.803301	+	1.39136i
$870$		0			0
$871$	1.29837	−	1.43109i	0.0439937	−	0.0484905i
$872$	20.0000			0.677285
$873$		0			0
$874$	−5.03444			−0.170293
$875$	1.23607	+	2.14093i	0.0417867	+	0.0723767i
$876$		0			0
$877$	13.4098	−	23.2265i	0.452818	−	0.784303i	−0.545742	−	0.837953i	$-0.683752\pi$
$877$	13.4098	−	23.2265i	0.452818	−	0.784303i	0.998560	+	0.0536498i	$0.0170855\pi$
$878$	−11.8090	−	20.4538i	−0.398535	−	0.690283i
$879$		0			0
$880$	30.0000			1.01130
$881$	12.5902	−	21.8068i	0.424174	−	0.734690i	−0.572169	−	0.820136i	$-0.693898\pi$
$881$	12.5902	−	21.8068i	0.424174	−	0.734690i	0.996343	+	0.0854453i	$0.0272313\pi$
$882$		0			0
$883$	−12.2639	−	21.2418i	−0.412714	−	0.714842i	0.582471	−	0.812851i	$-0.302086\pi$
$883$	−12.2639	−	21.2418i	−0.412714	−	0.714842i	−0.995185	+	0.0980093i	$0.968752\pi$
$884$	0.163119	−	0.282530i	0.00548628	−	0.00950252i
$885$		0			0
$886$	23.3262			0.783660
$887$	−25.6803	+	44.4797i	−0.862261	+	1.49348i	0.00747951	+	0.999972i	$0.497619\pi$
$887$	−25.6803	+	44.4797i	−0.862261	+	1.49348i	−0.869741	+	0.493509i	$0.835714\pi$
$888$		0			0
$889$	1.31966	−	2.28572i	0.0442600	−	0.0766605i
$890$	2.00000	−	3.46410i	0.0670402	−	0.116117i
$891$		0			0
$892$	6.61803	+	11.4628i	0.221588	+	0.383802i
$893$	3.11146			0.104121
$894$		0			0
$895$		0			0
$896$	−3.21478			−0.107398
$897$		0			0
$898$	27.7984			0.927644
$899$	1.77051	−	3.06661i	0.0590498	−	0.102277i
$900$		0			0
$901$	10.8541	−	18.7999i	0.361603	−	0.626314i
$902$	−17.1353	−	29.6791i	−0.570542	−	0.988207i
$903$		0			0
$904$	3.02786	+	5.24441i	0.100705	+	0.174427i
$905$	−0.618034	−	1.07047i	−0.0205441	−	0.0355835i
$906$		0			0
$907$	−25.7361	−	44.5762i	−0.854552	−	1.48013i	−0.877060	−	0.480381i	$-0.840498\pi$
$907$	−25.7361	−	44.5762i	−0.854552	−	1.48013i	0.0225078	−	0.999747i	$-0.492835\pi$
$908$	−2.07295	+	3.59045i	−0.0687932	+	0.119153i
$909$		0			0
$910$	−0.0557281	+	0.0965239i	−0.00184737	+	0.00319974i
$911$	30.2492			1.00220			0.501101	−	0.865389i	$-0.332929\pi$
$911$	30.2492			1.00220			0.501101	+	0.865389i	$0.332929\pi$
$912$		0			0
$913$	−55.0000			−1.82023
$914$	1.14590			0.0379029
$915$		0			0
$916$	−7.67376			−0.253548
$917$	−1.23607	−	2.14093i	−0.0408186	−	0.0706998i
$918$		0			0
$919$	10.2639	−	17.7777i	0.338576	−	0.586431i	−0.645589	−	0.763685i	$-0.723388\pi$
$919$	10.2639	−	17.7777i	0.338576	−	0.586431i	0.984165	+	0.177254i	$0.0567215\pi$
$920$	−2.43769	+	4.22221i	−0.0803684	+	0.139202i
$921$		0			0
$922$	27.8885	−	48.3044i	0.918460	−	1.59082i
$923$	−1.06888			−0.0351827
$924$		0			0
$925$	−12.9721	+	22.4684i	−0.426521	+	0.738756i
$926$	4.19098	+	7.25900i	0.137724	+	0.238545i
$927$		0			0
$928$	−0.892609	+	1.54604i	−0.0293013	+	0.0507514i
$929$	21.0557			0.690816			0.345408	−	0.938453i	$-0.387741\pi$
$929$	21.0557			0.690816			0.345408	+	0.938453i	$0.387741\pi$
$930$		0			0
$931$	−6.12461	−	10.6081i	−0.200726	−	0.347668i
$932$	6.83688	−	11.8418i	0.223949	−	0.387892i
$933$		0			0
$934$	−30.8435	−	53.4224i	−1.00923	−	1.74804i
$935$	13.8197			0.451951
$936$		0			0
$937$	−54.7214			−1.78767			−0.893834	−	0.448397i	$-0.851995\pi$
$937$	−54.7214			−1.78767			−0.893834	+	0.448397i	$0.851995\pi$
$938$	3.05573	+	0.661585i	0.0997731	+	0.0216015i
$939$		0			0
$940$	−0.673762	+	1.16699i	−0.0219757	+	0.0380630i
$941$	−29.3050			−0.955314			−0.477657	−	0.878546i	$-0.658514\pi$
$941$	−29.3050			−0.955314			−0.477657	+	0.878546i	$0.658514\pi$
$942$		0			0
$943$	7.47214			0.243326
$944$	−14.5623	+	25.2227i	−0.473963	+	0.820927i
$945$		0			0
$946$	−6.18034			−0.200940
$947$	−30.7639			−0.999693			−0.499847	−	0.866114i	$-0.666610\pi$
$947$	−30.7639			−0.999693			−0.499847	+	0.866114i	$0.666610\pi$
$948$		0			0
$949$	−0.319660	−	0.553668i	−0.0103766	−	0.0179728i
$950$	−4.95492	−	8.58216i	−0.160759	−	0.278442i
$951$		0			0
$952$	−1.18034			−0.0382550
$953$	−44.2492			−1.43337			−0.716686	−	0.697396i	$-0.754342\pi$
$953$	−44.2492			−1.43337			−0.716686	+	0.697396i	$0.754342\pi$
$954$		0			0
$955$	5.20163	−	9.00948i	0.168321	−	0.291540i
$956$	2.10739	−	3.65011i	0.0681579	−	0.118053i
$957$		0			0
$958$	17.7533	+	30.7496i	0.573583	+	0.993474i
$959$	−2.34752	−	4.06603i	−0.0758055	−	0.131299i
$960$		0			0
$961$	−7.00000	+	12.1244i	−0.225806	+	0.391108i
$962$	−2.85410			−0.0920199
$963$		0			0
$964$	5.00000	+	8.66025i	0.161039	+	0.278928i
$965$	−12.2229			−0.393469
$966$		0			0
$967$	−3.97214	−	6.87994i	−0.127735	−	0.221244i	0.795064	−	0.606526i	$-0.207437\pi$
$967$	−3.97214	−	6.87994i	−0.127735	−	0.221244i	−0.922799	+	0.385282i	$0.874104\pi$
$968$	15.6525	−	27.1109i	0.503090	−	0.871377i
$969$		0			0
$970$	9.00000	+	15.5885i	0.288973	+	0.500515i
$971$	28.2426	+	48.9177i	0.906350	+	1.56984i	0.819095	+	0.573658i	$0.194476\pi$
$971$	28.2426	+	48.9177i	0.906350	+	1.56984i	0.0872544	+	0.996186i	$0.472191\pi$
$972$		0			0
$973$	−1.05573	−	1.82857i	−0.0338451	−	0.0586214i
$974$	29.4615	+	51.0288i	0.944007	+	1.63507i
$975$		0			0
$976$	30.8435	+	53.4224i	0.987275	+	1.71001i
$977$	14.9721	−	25.9325i	0.479001	−	0.829654i	−0.520709	−	0.853734i	$-0.674332\pi$
$977$	14.9721	−	25.9325i	0.479001	−	0.829654i	0.999710	+	0.0240801i	$0.00766566\pi$
$978$		0			0
$979$	−5.00000	−	8.66025i	−0.159801	−	0.276783i
$980$	5.30495			0.169460
$981$		0			0
$982$	25.6525	−	44.4314i	0.818603	−	1.41786i
$983$	1.05573			0.0336725			0.0168362	−	0.999858i	$-0.494641\pi$
$983$	1.05573			0.0336725			0.0168362	+	0.999858i	$0.494641\pi$
$984$		0			0
$985$	0.0344419	+	0.0596550i	0.00109741	+	0.00190077i
$986$	−0.954915	+	1.65396i	−0.0304107	+	0.0526729i
$987$		0			0
$988$	0.128677	−	0.222875i	0.00409376	−	0.00709061i
$989$	0.673762	−	1.16699i	0.0214244	−	0.0371081i
$990$		0			0
$991$	−38.0000			−1.20711			−0.603555	−	0.797321i	$-0.706250\pi$
$991$	−38.0000			−1.20711			−0.603555	+	0.797321i	$0.706250\pi$
$992$	11.3435	−	19.6474i	0.360155	−	0.623807i
$993$		0			0
$994$	−0.864745	−	1.49778i	−0.0274280	−	0.0475068i
$995$	−3.74265	+	6.48245i	−0.118650	+	0.205508i
$996$		0			0
$997$	51.4164			1.62837			0.814187	−	0.580603i	$-0.197183\pi$
$997$	51.4164			1.62837			0.814187	+	0.580603i	$0.197183\pi$
$998$	17.1353	+	29.6791i	0.542407	+	0.939477i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	603.2.g.c.163.1	yes	4
3.2	odd	2		603.2.g.d.163.2	yes	4
67.37	even	3	inner	603.2.g.c.37.1	✓	4
201.104	odd	6		603.2.g.d.37.2	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
603.2.g.c.37.1	✓	4	67.37	even	3	inner
603.2.g.c.163.1	yes	4	1.1	even	1	trivial
603.2.g.d.37.2	yes	4	201.104	odd	6
603.2.g.d.163.2	yes	4	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 603 = 3^{2} \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	603.g (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.809017 + 1.40126i) q^{2} +(-0.309017 - 0.535233i) q^{4} -1.23607 q^{5} +(0.118034 + 0.204441i) q^{7} -2.23607 q^{8} +O(q^{10})\)	\(q+(-0.809017 + 1.40126i) q^{2} +(-0.309017 - 0.535233i) q^{4} -1.23607 q^{5} +(0.118034 + 0.204441i) q^{7} -2.23607 q^{8} +(1.00000 - 1.73205i) q^{10} +(-2.50000 - 4.33013i) q^{11} +(-0.118034 + 0.204441i) q^{13} -0.381966 q^{14} +(2.42705 - 4.20378i) q^{16} +(1.11803 - 1.93649i) q^{17} +(0.881966 - 1.52761i) q^{19} +(0.381966 + 0.661585i) q^{20} +8.09017 q^{22} +(-0.881966 + 1.52761i) q^{23} -3.47214 q^{25} +(-0.190983 - 0.330792i) q^{26} +(0.0729490 - 0.126351i) q^{28} +(0.263932 + 0.457144i) q^{29} +(-3.35410 - 5.80948i) q^{31} +(1.69098 + 2.92887i) q^{32} +(1.80902 + 3.13331i) q^{34} +(-0.145898 - 0.252703i) q^{35} +(3.73607 - 6.47106i) q^{37} +(1.42705 + 2.47172i) q^{38} +2.76393 q^{40} +(-2.11803 - 3.66854i) q^{41} -0.763932 q^{43} +(-1.54508 + 2.67617i) q^{44} +(-1.42705 - 2.47172i) q^{46} +(0.881966 + 1.52761i) q^{47} +(3.47214 - 6.01392i) q^{49} +(2.80902 - 4.86536i) q^{50} +0.145898 q^{52} +9.70820 q^{53} +(3.09017 + 5.35233i) q^{55} +(-0.263932 - 0.457144i) q^{56} -0.854102 q^{58} -6.00000 q^{59} +(-6.35410 + 11.0056i) q^{61} +10.8541 q^{62} +4.23607 q^{64} +(0.145898 - 0.252703i) q^{65} +(-8.00000 - 1.73205i) q^{67} -1.38197 q^{68} +0.472136 q^{70} +(2.26393 + 3.92125i) q^{71} +(-1.35410 + 2.34537i) q^{73} +(6.04508 + 10.4704i) q^{74} -1.09017 q^{76} +(0.590170 - 1.02220i) q^{77} +(-4.73607 - 8.20311i) q^{79} +(-3.00000 + 5.19615i) q^{80} +6.85410 q^{82} +(5.50000 - 9.52628i) q^{83} +(-1.38197 + 2.39364i) q^{85} +(0.618034 - 1.07047i) q^{86} +(5.59017 + 9.68246i) q^{88} +2.00000 q^{89} -0.0557281 q^{91} +1.09017 q^{92} -2.85410 q^{94} +(-1.09017 + 1.88823i) q^{95} +(-4.50000 + 7.79423i) q^{97} +(5.61803 + 9.73072i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - q^{2} + q^{4} + 4 q^{5} - 4 q^{7}+O(q^{10}) \) 4 * q - q^2 + q^4 + 4 * q^5 - 4 * q^7	\( 4 q - q^{2} + q^{4} + 4 q^{5} - 4 q^{7} + 4 q^{10} - 10 q^{11} + 4 q^{13} - 6 q^{14} + 3 q^{16} + 8 q^{19} + 6 q^{20} + 10 q^{22} - 8 q^{23} + 4 q^{25} - 3 q^{26} + 7 q^{28} + 10 q^{29} + 9 q^{32} + 5 q^{34} - 14 q^{35} + 6 q^{37} - q^{38} + 20 q^{40} - 4 q^{41} - 12 q^{43} + 5 q^{44} + q^{46} + 8 q^{47} - 4 q^{49} + 9 q^{50} + 14 q^{52} + 12 q^{53} - 10 q^{55} - 10 q^{56} + 10 q^{58} - 24 q^{59} - 12 q^{61} + 30 q^{62} + 8 q^{64} + 14 q^{65} - 32 q^{67} - 10 q^{68} - 16 q^{70} + 18 q^{71} + 8 q^{73} + 13 q^{74} + 18 q^{76} - 20 q^{77} - 10 q^{79} - 12 q^{80} + 14 q^{82} + 22 q^{83} - 10 q^{85} - 2 q^{86} + 8 q^{89} - 36 q^{91} - 18 q^{92} + 2 q^{94} + 18 q^{95} - 18 q^{97} + 18 q^{98}+O(q^{100}) \) 4 * q - q^2 + q^4 + 4 * q^5 - 4 * q^7 + 4 * q^10 - 10 * q^11 + 4 * q^13 - 6 * q^14 + 3 * q^16 + 8 * q^19 + 6 * q^20 + 10 * q^22 - 8 * q^23 + 4 * q^25 - 3 * q^26 + 7 * q^28 + 10 * q^29 + 9 * q^32 + 5 * q^34 - 14 * q^35 + 6 * q^37 - q^38 + 20 * q^40 - 4 * q^41 - 12 * q^43 + 5 * q^44 + q^46 + 8 * q^47 - 4 * q^49 + 9 * q^50 + 14 * q^52 + 12 * q^53 - 10 * q^55 - 10 * q^56 + 10 * q^58 - 24 * q^59 - 12 * q^61 + 30 * q^62 + 8 * q^64 + 14 * q^65 - 32 * q^67 - 10 * q^68 - 16 * q^70 + 18 * q^71 + 8 * q^73 + 13 * q^74 + 18 * q^76 - 20 * q^77 - 10 * q^79 - 12 * q^80 + 14 * q^82 + 22 * q^83 - 10 * q^85 - 2 * q^86 + 8 * q^89 - 36 * q^91 - 18 * q^92 + 2 * q^94 + 18 * q^95 - 18 * q^97 + 18 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

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