LMFDB - Embedded newform 370.2.l.c.101.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [370,2,Mod(11,370)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(370, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 5]))

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

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

chi := DirichletCharacter("370.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 370 = 2 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	370.l (of order $6$, 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:	$2.95446487479$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	12.0.116304318664704.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2x^{11} + x^{10} + 6x^{9} - 9x^{8} - 2x^{7} + 18x^{6} - 4x^{5} - 36x^{4} + 48x^{3} + 16x^{2} - 64x + 64 $ x^12 - 2x^11 + x^10 + 6x^9 - 9x^8 - 2x^7 + 18x^6 - 4x^5 - 36x^4 + 48x^3 + 16x^2 - 64x + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			101.2
Root			$1.33544 + 0.465413i$ of defining polynomial
Character	$\chi$	$=$	370.101
Dual form			370.2.l.c.11.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(0.264658 + 0.458402i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.866025 + 0.500000i) q^{5} -0.529317i q^{6} +(-0.146963 - 0.254547i) q^{7} -1.00000i q^{8} +(1.35991 - 2.35544i) q^{9} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(0.264658 + 0.458402i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.866025 + 0.500000i) q^{5} -0.529317i q^{6} +(-0.146963 - 0.254547i) q^{7} -1.00000i q^{8} +(1.35991 - 2.35544i) q^{9} +1.00000 q^{10} +2.07238 q^{11} +(-0.264658 + 0.458402i) q^{12} +(-1.12057 + 0.646963i) q^{13} +0.293926i q^{14} +(-0.458402 - 0.264658i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(6.79903 + 3.92542i) q^{17} +(-2.35544 + 1.35991i) q^{18} +(4.85244 - 2.80156i) q^{19} +(-0.866025 - 0.500000i) q^{20} +(0.0777900 - 0.134736i) q^{21} +(-1.79474 - 1.03619i) q^{22} +7.41413i q^{23} +(0.458402 - 0.264658i) q^{24} +(0.500000 - 0.866025i) q^{25} +1.29393 q^{26} +3.02760 q^{27} +(0.146963 - 0.254547i) q^{28} -1.03418i q^{29} +(0.264658 + 0.458402i) q^{30} +2.80725i q^{31} +(0.866025 - 0.500000i) q^{32} +(0.548473 + 0.949984i) q^{33} +(-3.92542 - 6.79903i) q^{34} +(0.254547 + 0.146963i) q^{35} +2.71982 q^{36} +(1.74081 - 5.82834i) q^{37} -5.60311 q^{38} +(-0.593138 - 0.342448i) q^{39} +(0.500000 + 0.866025i) q^{40} +(0.350817 + 0.607633i) q^{41} +(-0.134736 + 0.0777900i) q^{42} -6.19378i q^{43} +(1.03619 + 1.79474i) q^{44} +2.71982i q^{45} +(3.70706 - 6.42082i) q^{46} -6.29968 q^{47} -0.529317 q^{48} +(3.45680 - 5.98736i) q^{49} +(-0.866025 + 0.500000i) q^{50} +4.15558i q^{51} +(-1.12057 - 0.646963i) q^{52} +(-2.25925 + 3.91314i) q^{53} +(-2.62198 - 1.51380i) q^{54} +(-1.79474 + 1.03619i) q^{55} +(-0.254547 + 0.146963i) q^{56} +(2.56848 + 1.48291i) q^{57} +(-0.517090 + 0.895626i) q^{58} +(6.73473 + 3.88830i) q^{59} -0.529317i q^{60} +(5.86730 - 3.38749i) q^{61} +(1.40363 - 2.43115i) q^{62} -0.799427 q^{63} -1.00000 q^{64} +(0.646963 - 1.12057i) q^{65} -1.09695i q^{66} +(1.89242 + 3.27776i) q^{67} +7.85084i q^{68} +(-3.39865 + 1.96221i) q^{69} +(-0.146963 - 0.254547i) q^{70} +(-5.25337 - 9.09911i) q^{71} +(-2.35544 - 1.35991i) q^{72} -16.3032 q^{73} +(-4.42176 + 4.17709i) q^{74} +0.529317 q^{75} +(4.85244 + 2.80156i) q^{76} +(-0.304564 - 0.527520i) q^{77} +(0.342448 + 0.593138i) q^{78} +(-7.66147 + 4.42335i) q^{79} -1.00000i q^{80} +(-3.27846 - 5.67845i) q^{81} -0.701634i q^{82} +(-6.41272 + 11.1071i) q^{83} +0.155580 q^{84} -7.85084 q^{85} +(-3.09689 + 5.36397i) q^{86} +(0.474070 - 0.273704i) q^{87} -2.07238i q^{88} +(-5.70748 - 3.29521i) q^{89} +(1.35991 - 2.35544i) q^{90} +(0.329365 + 0.190159i) q^{91} +(-6.42082 + 3.70706i) q^{92} +(-1.28685 + 0.742963i) q^{93} +(5.45568 + 3.14984i) q^{94} +(-2.80156 + 4.85244i) q^{95} +(0.458402 + 0.264658i) q^{96} -13.8888i q^{97} +(-5.98736 + 3.45680i) q^{98} +(2.81826 - 4.88137i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 4 q^{3} + 6 q^{4} + 2 q^{7} - 2 q^{9}+O(q^{10}) $ 12 * q + 4 * q^3 + 6 * q^4 + 2 * q^7 - 2 * q^9	$ 12 q + 4 q^{3} + 6 q^{4} + 2 q^{7} - 2 q^{9} + 12 q^{10} - 16 q^{11} - 4 q^{12} + 6 q^{13} - 6 q^{16} - 6 q^{17} + 18 q^{19} - 14 q^{21} + 6 q^{22} + 6 q^{25} + 8 q^{26} - 32 q^{27} - 2 q^{28} + 4 q^{30} - 10 q^{33} - 10 q^{34} - 6 q^{35} - 4 q^{36} - 26 q^{37} + 8 q^{38} + 18 q^{39} + 6 q^{40} + 4 q^{41} + 18 q^{42} - 8 q^{44} - 4 q^{46} - 20 q^{47} - 8 q^{48} + 2 q^{49} + 6 q^{52} - 2 q^{53} + 6 q^{55} + 6 q^{56} + 36 q^{57} + 8 q^{58} + 12 q^{59} + 24 q^{61} + 10 q^{62} - 16 q^{63} - 12 q^{64} + 4 q^{65} + 28 q^{67} - 6 q^{69} + 2 q^{70} - 40 q^{71} - 12 q^{73} + 14 q^{74} + 8 q^{75} + 18 q^{76} - 24 q^{77} - 10 q^{78} + 24 q^{79} - 6 q^{81} - 16 q^{83} - 28 q^{84} - 20 q^{85} - 16 q^{86} - 24 q^{87} + 6 q^{89} - 2 q^{90} - 18 q^{91} + 6 q^{92} + 78 q^{93} + 4 q^{95} - 12 q^{98} + 22 q^{99}+O(q^{100}) $ 12 * q + 4 * q^3 + 6 * q^4 + 2 * q^7 - 2 * q^9 + 12 * q^10 - 16 * q^11 - 4 * q^12 + 6 * q^13 - 6 * q^16 - 6 * q^17 + 18 * q^19 - 14 * q^21 + 6 * q^22 + 6 * q^25 + 8 * q^26 - 32 * q^27 - 2 * q^28 + 4 * q^30 - 10 * q^33 - 10 * q^34 - 6 * q^35 - 4 * q^36 - 26 * q^37 + 8 * q^38 + 18 * q^39 + 6 * q^40 + 4 * q^41 + 18 * q^42 - 8 * q^44 - 4 * q^46 - 20 * q^47 - 8 * q^48 + 2 * q^49 + 6 * q^52 - 2 * q^53 + 6 * q^55 + 6 * q^56 + 36 * q^57 + 8 * q^58 + 12 * q^59 + 24 * q^61 + 10 * q^62 - 16 * q^63 - 12 * q^64 + 4 * q^65 + 28 * q^67 - 6 * q^69 + 2 * q^70 - 40 * q^71 - 12 * q^73 + 14 * q^74 + 8 * q^75 + 18 * q^76 - 24 * q^77 - 10 * q^78 + 24 * q^79 - 6 * q^81 - 16 * q^83 - 28 * q^84 - 20 * q^85 - 16 * q^86 - 24 * q^87 + 6 * q^89 - 2 * q^90 - 18 * q^91 + 6 * q^92 + 78 * q^93 + 4 * q^95 - 12 * q^98 + 22 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/370\mathbb{Z}\right)^\times$.

$n$	$261$	$297$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$

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 $

$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$3$	0.264658	+	0.458402i	0.152801	+	0.264658i	0.932256	−	0.361799i	$-0.117837\pi$
$3$	0.264658	+	0.458402i	0.152801	+	0.264658i	−0.779455	+	0.626458i	$0.784504\pi$
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	−0.866025	+	0.500000i	−0.387298	+	0.223607i
$5$	−0.866025	+	0.500000i	−0.387298	+	0.223607i
$6$		−	0.529317i		−	0.216093i
$7$	−0.146963	−	0.254547i	−0.0555468	−	0.0962099i	0.836915	−	0.547333i	$-0.184357\pi$
$7$	−0.146963	−	0.254547i	−0.0555468	−	0.0962099i	−0.892462	+	0.451123i	$0.851024\pi$
$8$		−	1.00000i		−	0.353553i
$9$	1.35991	−	2.35544i	0.453304	−	0.785146i
$10$	1.00000			0.316228
$11$	2.07238			0.624847			0.312424	−	0.949943i	$-0.398859\pi$
$11$	2.07238			0.624847			0.312424	+	0.949943i	$0.398859\pi$
$12$	−0.264658	+	0.458402i	−0.0764003	+	0.132329i
$13$	−1.12057	+	0.646963i	−0.310791	+	0.179435i	−0.647280	−	0.762252i	$-0.724094\pi$
$13$	−1.12057	+	0.646963i	−0.310791	+	0.179435i	0.336489	+	0.941687i	$0.390760\pi$
$14$			0.293926i			0.0785550i
$15$	−0.458402	−	0.264658i	−0.118359	−	0.0683345i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	6.79903	+	3.92542i	1.64901	+	0.952054i	0.977468	+	0.211085i	$0.0676995\pi$
$17$	6.79903	+	3.92542i	1.64901	+	0.952054i	0.671538	+	0.740970i	$0.265634\pi$
$18$	−2.35544	+	1.35991i	−0.555182	+	0.320534i
$19$	4.85244	−	2.80156i	1.11323	−	0.642721i	0.173563	−	0.984823i	$-0.444472\pi$
$19$	4.85244	−	2.80156i	1.11323	−	0.642721i	0.939663	+	0.342102i	$0.111139\pi$
$20$	−0.866025	−	0.500000i	−0.193649	−	0.111803i
$21$	0.0777900	−	0.134736i	0.0169752	−	0.0294018i
$22$	−1.79474	−	1.03619i	−0.382639	−	0.220917i
$23$			7.41413i			1.54595i	0.634435	+	0.772976i	$0.281233\pi$
$23$			7.41413i			1.54595i	−0.634435	+	0.772976i	$0.718767\pi$
$24$	0.458402	−	0.264658i	0.0935708	−	0.0540231i
$25$	0.500000	−	0.866025i	0.100000	−	0.173205i
$26$	1.29393			0.253760
$27$	3.02760			0.582661
$28$	0.146963	−	0.254547i	0.0277734	−	0.0481049i
$29$		−	1.03418i		−	0.192042i	−0.995379	−	0.0960212i	$-0.969388\pi$
$29$		−	1.03418i		−	0.192042i	0.995379	−	0.0960212i	$-0.0306116\pi$
$30$	0.264658	+	0.458402i	0.0483198	+	0.0836923i
$31$			2.80725i			0.504197i	0.967702	+	0.252099i	$0.0811208\pi$
$31$			2.80725i			0.504197i	−0.967702	+	0.252099i	$0.918879\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$	0.548473	+	0.949984i	0.0954770	+	0.165371i
$34$	−3.92542	−	6.79903i	−0.673204	−	1.16602i
$35$	0.254547	+	0.146963i	0.0430264	+	0.0248413i
$36$	2.71982			0.453304
$37$	1.74081	−	5.82834i	0.286187	−	0.958174i
$37$	1.74081	−	5.82834i	0.286187	−	0.958174i
$38$	−5.60311			−0.908945
$39$	−0.593138	−	0.342448i	−0.0949781	−	0.0548356i
$40$	0.500000	+	0.866025i	0.0790569	+	0.136931i
$41$	0.350817	+	0.607633i	0.0547884	+	0.0948964i	0.892119	−	0.451801i	$-0.149218\pi$
$41$	0.350817	+	0.607633i	0.0547884	+	0.0948964i	−0.837330	+	0.546697i	$0.815885\pi$
$42$	−0.134736	+	0.0777900i	−0.0207902	+	0.0120033i
$43$		−	6.19378i		−	0.944543i	−0.881453	−	0.472272i	$-0.843434\pi$
$43$		−	6.19378i		−	0.944543i	0.881453	−	0.472272i	$-0.156566\pi$
$44$	1.03619	+	1.79474i	0.156212	+	0.270567i
$45$			2.71982i			0.405447i
$46$	3.70706	−	6.42082i	0.546577	−	0.946699i
$47$	−6.29968			−0.918903			−0.459451	−	0.888203i	$-0.651954\pi$
$47$	−6.29968			−0.918903			−0.459451	+	0.888203i	$0.651954\pi$
$48$	−0.529317			−0.0764003
$49$	3.45680	−	5.98736i	0.493829	−	0.855337i
$50$	−0.866025	+	0.500000i	−0.122474	+	0.0707107i
$51$			4.15558i			0.581898i
$52$	−1.12057	−	0.646963i	−0.155395	−	0.0897176i
$53$	−2.25925	+	3.91314i	−0.310332	+	0.537511i	−0.978434	−	0.206559i	$-0.933774\pi$
$53$	−2.25925	+	3.91314i	−0.310332	+	0.537511i	0.668102	+	0.744070i	$0.267107\pi$
$54$	−2.62198	−	1.51380i	−0.356806	−	0.206002i
$55$	−1.79474	+	1.03619i	−0.242002	+	0.139720i
$56$	−0.254547	+	0.146963i	−0.0340153	+	0.0196388i
$57$	2.56848	+	1.48291i	0.340203	+	0.196416i
$58$	−0.517090	+	0.895626i	−0.0678972	+	0.117601i
$59$	6.73473	+	3.88830i	0.876787	+	0.506213i	0.869598	−	0.493761i	$-0.164378\pi$
$59$	6.73473	+	3.88830i	0.876787	+	0.506213i	0.00718926	+	0.999974i	$0.497712\pi$
$60$		−	0.529317i		−	0.0683345i
$61$	5.86730	−	3.38749i	0.751231	−	0.433723i	−0.0749078	−	0.997190i	$-0.523866\pi$
$61$	5.86730	−	3.38749i	0.751231	−	0.433723i	0.826138	+	0.563467i	$0.190533\pi$
$62$	1.40363	−	2.43115i	0.178261	−	0.308757i
$63$	−0.799427			−0.100718
$64$	−1.00000			−0.125000
$65$	0.646963	−	1.12057i	0.0802459	−	0.138990i
$66$		−	1.09695i		−	0.135025i
$67$	1.89242	+	3.27776i	0.231195	+	0.400442i	0.958160	−	0.286233i	$-0.0924030\pi$
$67$	1.89242	+	3.27776i	0.231195	+	0.400442i	−0.726965	+	0.686675i	$0.759070\pi$
$68$			7.85084i			0.952054i
$69$	−3.39865	+	1.96221i	−0.409149	+	0.236222i
$70$	−0.146963	−	0.254547i	−0.0175654	−	0.0304242i
$71$	−5.25337	−	9.09911i	−0.623461	−	1.07987i	−0.988836	−	0.149005i	$-0.952393\pi$
$71$	−5.25337	−	9.09911i	−0.623461	−	1.07987i	0.365376	−	0.930860i	$-0.380940\pi$
$72$	−2.35544	−	1.35991i	−0.277591	−	0.160267i
$73$	−16.3032			−1.90814			−0.954071	−	0.299581i	$-0.903153\pi$
$73$	−16.3032			−1.90814			−0.954071	+	0.299581i	$0.903153\pi$
$74$	−4.42176	+	4.17709i	−0.514019	+	0.485577i
$75$	0.529317			0.0611202
$76$	4.85244	+	2.80156i	0.556613	+	0.321361i
$77$	−0.304564	−	0.527520i	−0.0347082	−	0.0601164i
$78$	0.342448	+	0.593138i	0.0387746	+	0.0671596i
$79$	−7.66147	+	4.42335i	−0.861983	+	0.497666i	−0.864676	−	0.502330i	$-0.832476\pi$
$79$	−7.66147	+	4.42335i	−0.861983	+	0.497666i	0.00269286	+	0.999996i	$0.499143\pi$
$80$		−	1.00000i		−	0.111803i
$81$	−3.27846	−	5.67845i	−0.364273	−	0.630939i
$82$		−	0.701634i		−	0.0774826i
$83$	−6.41272	+	11.1071i	−0.703887	+	1.21917i	0.263205	+	0.964740i	$0.415221\pi$
$83$	−6.41272	+	11.1071i	−0.703887	+	1.21917i	−0.967092	+	0.254428i	$0.918113\pi$
$84$	0.155580			0.0169752
$85$	−7.85084			−0.851543
$86$	−3.09689	+	5.36397i	−0.333946	+	0.578412i
$87$	0.474070	−	0.273704i	0.0508256	−	0.0293442i
$88$		−	2.07238i		−	0.220917i
$89$	−5.70748	−	3.29521i	−0.604992	−	0.349292i	0.166011	−	0.986124i	$-0.446911\pi$
$89$	−5.70748	−	3.29521i	−0.604992	−	0.349292i	−0.771003	+	0.636832i	$0.780245\pi$
$90$	1.35991	−	2.35544i	0.143347	−	0.248285i
$91$	0.329365	+	0.190159i	0.0345269	+	0.0199341i
$92$	−6.42082	+	3.70706i	−0.669417	+	0.386488i
$93$	−1.28685	+	0.742963i	−0.133440	+	0.0770416i
$94$	5.45568	+	3.14984i	0.562711	+	0.324881i
$95$	−2.80156	+	4.85244i	−0.287434	+	0.497850i
$96$	0.458402	+	0.264658i	0.0467854	+	0.0270116i
$97$		−	13.8888i		−	1.41019i	−0.709111	−	0.705097i	$-0.750903\pi$
$97$		−	13.8888i		−	1.41019i	0.709111	−	0.705097i	$-0.249097\pi$
$98$	−5.98736	+	3.45680i	−0.604815	+	0.349190i
$99$	2.81826	−	4.88137i	0.283246	−	0.490596i
$100$	1.00000			0.100000
$101$	−5.67653			−0.564836			−0.282418	−	0.959291i	$-0.591136\pi$
$101$	−5.67653			−0.564836			−0.282418	+	0.959291i	$0.591136\pi$
$102$	2.07779	−	3.59884i	0.205732	−	0.356338i
$103$			14.2166i			1.40080i	0.713749	+	0.700402i	$0.246996\pi$
$103$			14.2166i			1.40080i	−0.713749	+	0.700402i	$0.753004\pi$
$104$	0.646963	+	1.12057i	0.0634399	+	0.109881i
$105$			0.155580i			0.0151830i
$106$	3.91314	−	2.25925i	0.380078	−	0.219438i
$107$	2.45517	+	4.25247i	0.237350	+	0.411102i	0.959953	−	0.280161i	$-0.0903879\pi$
$107$	2.45517	+	4.25247i	0.237350	+	0.411102i	−0.722603	+	0.691263i	$0.757055\pi$
$108$	1.51380	+	2.62198i	0.145665	+	0.252300i
$109$	9.97600	+	5.75965i	0.955528	+	0.551674i	0.894794	−	0.446480i	$-0.147322\pi$
$109$	9.97600	+	5.75965i	0.955528	+	0.551674i	0.0607341	+	0.998154i	$0.480656\pi$
$110$	2.07238			0.197594
$111$	3.13244	−	0.744531i	0.297318	−	0.0706677i
$112$	0.293926			0.0277734
$113$	−9.13677	−	5.27512i	−0.859515	−	0.496241i	0.00433475	−	0.999991i	$-0.498620\pi$
$113$	−9.13677	−	5.27512i	−0.859515	−	0.496241i	−0.863850	+	0.503749i	$0.831954\pi$
$114$	−1.48291	−	2.56848i	−0.138887	−	0.240560i
$115$	−3.70706	−	6.42082i	−0.345686	−	0.598745i
$116$	0.895626	−	0.517090i	0.0831568	−	0.0480106i
$117$			3.51925i			0.325355i
$118$	−3.88830	−	6.73473i	−0.357947	−	0.619982i
$119$		−	2.30757i		−	0.211534i
$120$	−0.264658	+	0.458402i	−0.0241599	+	0.0418461i
$121$	−6.70523			−0.609566
$122$	−6.77497			−0.613377
$123$	−0.185693	+	0.321630i	−0.0167434	+	0.0290004i
$124$	−2.43115	+	1.40363i	−0.218324	+	0.126049i
$125$			1.00000i			0.0894427i
$126$	0.692324	+	0.399713i	0.0616771	+	0.0356093i
$127$	−0.321465	+	0.556793i	−0.0285254	+	0.0494074i	−0.879936	−	0.475093i	$-0.842414\pi$
$127$	−0.321465	+	0.556793i	−0.0285254	+	0.0494074i	0.851410	+	0.524500i	$0.175748\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$	2.83924	−	1.63924i	0.249981	−	0.144327i
$130$	−1.12057	+	0.646963i	−0.0982807	+	0.0567424i
$131$	11.5810	+	6.68631i	1.01184	+	0.584186i	0.911730	−	0.410791i	$-0.134747\pi$
$131$	11.5810	+	6.68631i	1.01184	+	0.584186i	0.100110	+	0.994976i	$0.468081\pi$
$132$	−0.548473	+	0.949984i	−0.0477385	+	0.0826855i
$133$	−1.42626	−	0.823450i	−0.123672	−	0.0714022i
$134$		−	3.78483i		−	0.326960i
$135$	−2.62198	+	1.51380i	−0.225664	+	0.130287i
$136$	3.92542	−	6.79903i	0.336602	−	0.583012i
$137$	0.919043			0.0785192			0.0392596	−	0.999229i	$-0.487500\pi$
$137$	0.919043			0.0785192			0.0392596	+	0.999229i	$0.487500\pi$
$138$	3.92442			0.334069
$139$	−7.25419	+	12.5646i	−0.615292	+	1.06572i	0.375041	+	0.927008i	$0.377629\pi$
$139$	−7.25419	+	12.5646i	−0.615292	+	1.06572i	−0.990333	+	0.138709i	$0.955705\pi$
$140$			0.293926i			0.0248413i
$141$	−1.66726	−	2.88778i	−0.140409	−	0.243195i
$142$			10.5067i			0.881706i
$143$	−2.32226	+	1.34076i	−0.194197	+	0.112120i
$144$	1.35991	+	2.35544i	0.113326	+	0.196286i
$145$	0.517090	+	0.895626i	0.0429420	+	0.0743777i
$146$	14.1190	+	8.15159i	1.16849	+	0.674630i
$147$	3.65949			0.301829
$148$	5.91790	−	1.40659i	0.486448	−	0.115621i
$149$	9.98664			0.818137			0.409069	−	0.912504i	$-0.365854\pi$
$149$	9.98664			0.818137			0.409069	+	0.912504i	$0.365854\pi$
$150$	−0.458402	−	0.264658i	−0.0374283	−	0.0216093i
$151$	−9.35117	−	16.1967i	−0.760987	−	1.31807i	−0.942342	−	0.334651i	$-0.891382\pi$
$151$	−9.35117	−	16.1967i	−0.760987	−	1.31807i	0.181355	−	0.983418i	$-0.441952\pi$
$152$	−2.80156	−	4.85244i	−0.227236	−	0.393585i
$153$	18.4922	−	10.6765i	1.49500	−	0.863140i
$154$			0.609127i			0.0490849i
$155$	−1.40363	−	2.43115i	−0.112742	−	0.195275i
$156$		−	0.684896i		−	0.0548356i
$157$	11.0557	−	19.1491i	0.882345	−	1.52827i	0.0336179	−	0.999435i	$-0.489297\pi$
$157$	11.0557	−	19.1491i	0.882345	−	1.52827i	0.848727	−	0.528831i	$-0.177370\pi$
$158$	8.84671			0.703806
$159$	−2.39172			−0.189676
$160$	−0.500000	+	0.866025i	−0.0395285	+	0.0684653i
$161$	1.88725	−	1.08960i	0.148736	−	0.0858727i
$162$			6.55691i			0.515160i
$163$	−4.40218	−	2.54160i	−0.344805	−	0.199073i	0.317590	−	0.948228i	$-0.397127\pi$
$163$	−4.40218	−	2.54160i	−0.344805	−	0.199073i	−0.662395	+	0.749155i	$0.730460\pi$
$164$	−0.350817	+	0.607633i	−0.0273942	+	0.0474482i
$165$	−0.949984	−	0.548473i	−0.0739561	−	0.0426986i
$166$	11.1071	−	6.41272i	0.862082	−	0.497723i
$167$	2.12819	−	1.22871i	0.164684	−	0.0950805i	−0.415393	−	0.909642i	$-0.636356\pi$
$167$	2.12819	−	1.22871i	0.164684	−	0.0950805i	0.580077	+	0.814562i	$0.303022\pi$
$168$	−0.134736	−	0.0777900i	−0.0103951	−	0.00600163i
$169$	−5.66288	+	9.80839i	−0.435606	+	0.754492i
$170$	6.79903	+	3.92542i	0.521462	+	0.301066i
$171$		−	15.2395i		−	1.16539i
$172$	5.36397	−	3.09689i	0.408999	−	0.236136i
$173$	11.0751	−	19.1826i	0.842023	−	1.45843i	−0.0461585	−	0.998934i	$-0.514698\pi$
$173$	11.0751	−	19.1826i	0.842023	−	1.45843i	0.888182	−	0.459493i	$-0.151969\pi$
$174$	−0.547408			−0.0414989
$175$	−0.293926			−0.0222187
$176$	−1.03619	+	1.79474i	−0.0781059	+	0.135283i
$177$			4.11628i			0.309399i
$178$	3.29521	+	5.70748i	0.246987	+	0.427794i
$179$			3.33164i			0.249019i	0.992218	+	0.124509i	$0.0397357\pi$
$179$			3.33164i			0.249019i	−0.992218	+	0.124509i	$0.960264\pi$
$180$	−2.35544	+	1.35991i	−0.175564	+	0.101362i
$181$	−0.432718	−	0.749490i	−0.0321637	−	0.0557091i	0.849495	−	0.527596i	$-0.176906\pi$
$181$	−0.432718	−	0.749490i	−0.0321637	−	0.0557091i	−0.881659	+	0.471887i	$0.843573\pi$
$182$	−0.190159	−	0.329365i	−0.0140955	−	0.0244142i
$183$	3.10566	+	1.79305i	0.229577	+	0.132546i
$184$	7.41413			0.546577
$185$	1.40659	+	5.91790i	0.103414	+	0.435092i
$186$	1.48593			0.108953
$187$	14.0902	+	8.13497i	1.03038	+	0.594888i
$188$	−3.14984	−	5.45568i	−0.229726	−	0.397897i
$189$	−0.444945	−	0.770667i	−0.0323650	−	0.0560578i
$190$	4.85244	−	2.80156i	0.352033	−	0.203246i
$191$			21.3827i			1.54720i	0.633674	+	0.773600i	$0.281546\pi$
$191$			21.3827i			1.54720i	−0.633674	+	0.773600i	$0.718454\pi$
$192$	−0.264658	−	0.458402i	−0.0191001	−	0.0330823i
$193$		−	1.73377i		−	0.124799i	−0.998051	−	0.0623997i	$-0.980125\pi$
$193$		−	1.73377i		−	0.124799i	0.998051	−	0.0623997i	$-0.0198754\pi$
$194$	−6.94440	+	12.0281i	−0.498579	+	0.863564i
$195$	0.684896			0.0490465
$196$	6.91361			0.493829
$197$	−2.02386	+	3.50543i	−0.144194	+	0.249752i	−0.929072	−	0.369899i	$-0.879392\pi$
$197$	−2.02386	+	3.50543i	−0.144194	+	0.249752i	0.784878	+	0.619650i	$0.212726\pi$
$198$	−4.88137	+	2.81826i	−0.346904	+	0.200285i
$199$		−	6.89498i		−	0.488772i	−0.969678	−	0.244386i	$-0.921414\pi$
$199$		−	6.89498i		−	0.488772i	0.969678	−	0.244386i	$-0.0785864\pi$
$200$	−0.866025	−	0.500000i	−0.0612372	−	0.0353553i
$201$	−1.00169	+	1.73497i	−0.0706536	+	0.122376i
$202$	4.91602	+	2.83827i	0.345890	+	0.199700i
$203$	−0.263248	+	0.151986i	−0.0184764	+	0.0106673i
$204$	−3.59884	+	2.07779i	−0.251969	+	0.145474i
$205$	−0.607633	−	0.350817i	−0.0424389	−	0.0245021i
$206$	7.10830	−	12.3119i	0.495259	−	0.857813i
$207$	17.4635	+	10.0826i	1.21380	+	0.700787i
$208$		−	1.29393i		−	0.0897176i
$209$	10.0561	−	5.80590i	0.695596	−	0.401602i
$210$	0.0777900	−	0.134736i	0.00536802	−	0.00929768i
$211$	−13.1121			−0.902676			−0.451338	−	0.892353i	$-0.649053\pi$
$211$	−13.1121			−0.902676			−0.451338	+	0.892353i	$0.649053\pi$
$212$	−4.51850			−0.310332
$213$	2.78070	−	4.81631i	0.190530	−	0.330008i
$214$		−	4.91033i		−	0.335663i
$215$	3.09689	+	5.36397i	0.211206	+	0.365820i
$216$		−	3.02760i		−	0.206002i
$217$	0.714579	−	0.412562i	0.0485088	−	0.0280066i
$218$	−5.75965	−	9.97600i	−0.390093	−	0.675660i
$219$	−4.31477	−	7.47340i	−0.291565	−	0.505006i
$220$	−1.79474	−	1.03619i	−0.121001	−	0.0698600i
$221$	−10.1584			−0.683328
$222$	−3.08504	−	0.921438i	−0.207054	−	0.0618429i
$223$	10.4348			0.698769			0.349385	−	0.936979i	$-0.386391\pi$
$223$	10.4348			0.698769			0.349385	+	0.936979i	$0.386391\pi$
$224$	−0.254547	−	0.146963i	−0.0170077	−	0.00981938i
$225$	−1.35991	−	2.35544i	−0.0906608	−	0.157029i
$226$	5.27512	+	9.13677i	0.350896	+	0.607769i
$227$	3.21149	−	1.85416i	0.213154	−	0.123065i	−0.389622	−	0.920975i	$-0.627394\pi$
$227$	3.21149	−	1.85416i	0.213154	−	0.123065i	0.602776	+	0.797910i	$0.294061\pi$
$228$			2.96582i			0.196416i
$229$	−2.16173	−	3.74423i	−0.142851	−	0.247426i	0.785718	−	0.618585i	$-0.212294\pi$
$229$	−2.16173	−	3.74423i	−0.142851	−	0.247426i	−0.928569	+	0.371159i	$0.878960\pi$
$230$			7.41413i			0.488873i
$231$	0.161211	−	0.279225i	0.0106069	−	0.0183717i
$232$	−1.03418			−0.0678972
$233$	−17.6328			−1.15517			−0.577583	−	0.816332i	$-0.696004\pi$
$233$	−17.6328			−1.15517			−0.577583	+	0.816332i	$0.696004\pi$
$234$	1.75963	−	3.04776i	0.115030	−	0.199238i
$235$	5.45568	−	3.14984i	0.355890	−	0.205473i
$236$			7.77659i			0.506213i
$237$	−4.05534	−	2.34135i	−0.263423	−	0.152087i
$238$	−1.15378	+	1.99841i	−0.0747886	+	0.129538i
$239$	−14.5079	−	8.37612i	−0.938436	−	0.541806i	−0.0489662	−	0.998800i	$-0.515593\pi$
$239$	−14.5079	−	8.37612i	−0.938436	−	0.541806i	−0.889470	+	0.456994i	$0.848926\pi$
$240$	0.458402	−	0.264658i	0.0295897	−	0.0170836i
$241$	17.7379	−	10.2410i	1.14260	−	0.659681i	0.195527	−	0.980698i	$-0.437358\pi$
$241$	17.7379	−	10.2410i	1.14260	−	0.659681i	0.947073	+	0.321018i	$0.104025\pi$
$242$	5.80690	+	3.35261i	0.373282	+	0.215514i
$243$	6.27674	−	10.8716i	0.402653	−	0.697415i
$244$	5.86730	+	3.38749i	0.375615	+	0.216862i
$245$			6.91361i			0.441694i
$246$	0.321630	−	0.185693i	0.0205064	−	0.0118394i
$247$	−3.62501	+	6.27870i	−0.230654	+	0.399504i
$248$	2.80725			0.178261
$249$	−6.78871			−0.430217
$250$	0.500000	−	0.866025i	0.0316228	−	0.0547723i
$251$			23.3671i			1.47492i	0.675391	+	0.737460i	$0.263975\pi$
$251$			23.3671i			1.47492i	−0.675391	+	0.737460i	$0.736025\pi$
$252$	−0.399713	−	0.692324i	−0.0251796	−	0.0436123i
$253$			15.3649i			0.965984i
$254$	0.556793	−	0.321465i	0.0349363	−	0.0201705i
$255$	−2.07779	−	3.59884i	−0.130116	−	0.225368i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−20.9800	−	12.1128i	−1.30870	−	0.755578i	−0.326820	−	0.945087i	$-0.605977\pi$
$257$	−20.9800	−	12.1128i	−1.30870	−	0.755578i	−0.981879	+	0.189509i	$0.939310\pi$
$258$	−3.27847			−0.204109
$259$	−1.73942	+	0.413433i	−0.108083	+	0.0256895i
$260$	1.29393			0.0802459
$261$	−2.43594	−	1.40639i	−0.150781	−	0.0870535i
$262$	−6.68631	−	11.5810i	−0.413082	−	0.715478i
$263$	8.86167	+	15.3489i	0.546434	+	0.946451i	0.998515	+	0.0544746i	$0.0173484\pi$
$263$	8.86167	+	15.3489i	0.546434	+	0.946451i	−0.452081	+	0.891977i	$0.649318\pi$
$264$	0.949984	−	0.548473i	0.0584675	−	0.0337562i
$265$		−	4.51850i		−	0.277569i
$266$	0.823450	+	1.42626i	0.0504890	+	0.0874495i
$267$		−	3.48842i		−	0.213488i
$268$	−1.89242	+	3.27776i	−0.115598	+	0.200221i
$269$	3.23020			0.196949			0.0984745	−	0.995140i	$-0.468604\pi$
$269$	3.23020			0.196949			0.0984745	+	0.995140i	$0.468604\pi$
$270$	3.02760			0.184254
$271$	−11.3821	+	19.7143i	−0.691412	+	1.19756i	0.279964	+	0.960011i	$0.409678\pi$
$271$	−11.3821	+	19.7143i	−0.691412	+	1.19756i	−0.971375	+	0.237549i	$0.923656\pi$
$272$	−6.79903	+	3.92542i	−0.412252	+	0.238014i
$273$			0.201309i			0.0121838i
$274$	−0.795915	−	0.459522i	−0.0480830	−	0.0277607i
$275$	1.03619	−	1.79474i	0.0624847	−	0.108227i
$276$	−3.39865	−	1.96221i	−0.204575	−	0.118111i
$277$	−11.7917	+	6.80792i	−0.708493	+	0.409048i	−0.810503	−	0.585735i	$-0.800806\pi$
$277$	−11.7917	+	6.80792i	−0.708493	+	0.409048i	0.102010	+	0.994783i	$0.467473\pi$
$278$	12.5646	−	7.25419i	0.753576	−	0.435077i
$279$	6.61231	+	3.81762i	0.395868	+	0.228555i
$280$	0.146963	−	0.254547i	0.00878272	−	0.0152121i
$281$	−21.1680	−	12.2213i	−1.26278	−	0.729064i	−0.289166	−	0.957279i	$-0.593378\pi$
$281$	−21.1680	−	12.2213i	−1.26278	−	0.729064i	−0.973611	+	0.228215i	$0.926711\pi$
$282$			3.33453i			0.198568i
$283$	11.2864	−	6.51619i	0.670905	−	0.387347i	−0.125514	−	0.992092i	$-0.540058\pi$
$283$	11.2864	−	6.51619i	0.670905	−	0.387347i	0.796419	+	0.604745i	$0.206725\pi$
$284$	5.25337	−	9.09911i	0.311730	−	0.539933i
$285$	−2.96582			−0.175680
$286$	2.68151			0.158561
$287$	0.103114	−	0.178599i	0.00608664	−	0.0105424i
$288$		−	2.71982i		−	0.160267i
$289$	22.3178	+	38.6556i	1.31281	+	2.27386i
$290$		−	1.03418i		−	0.0607291i
$291$	6.36665	−	3.67579i	0.373220	−	0.215478i
$292$	−8.15159	−	14.1190i	−0.477036	−	0.826250i
$293$	−9.64331	−	16.7027i	−0.563368	−	0.975782i	−0.997199	−	0.0747880i	$-0.976172\pi$
$293$	−9.64331	−	16.7027i	−0.563368	−	0.975782i	0.433831	−	0.900994i	$-0.357161\pi$
$294$	−3.16921	−	1.82974i	−0.184832	−	0.106713i
$295$	−7.77659			−0.452771
$296$	−5.82834	−	1.74081i	−0.338766	−	0.101182i
$297$	6.27434			0.364074
$298$	−8.64868	−	4.99332i	−0.501005	−	0.289255i
$299$	−4.79667	−	8.30807i	−0.277398	−	0.480468i
$300$	0.264658	+	0.458402i	0.0152801	+	0.0264658i
$301$	−1.57661	+	0.910257i	−0.0908744	+	0.0524663i
$302$			18.7023i			1.07620i
$303$	−1.50234	−	2.60213i	−0.0863072	−	0.149489i
$304$			5.60311i			0.321361i
$305$	−3.38749	+	5.86730i	−0.193967	+	0.335961i
$306$	−21.3529			−1.22066
$307$	−11.2230			−0.640530			−0.320265	−	0.947328i	$-0.603772\pi$
$307$	−11.2230			−0.640530			−0.320265	+	0.947328i	$0.603772\pi$
$308$	0.304564	−	0.527520i	0.0173541	−	0.0300582i
$309$	−6.51691	+	3.76254i	−0.370734	+	0.214044i
$310$			2.80725i			0.159441i
$311$	6.95849	+	4.01749i	0.394580	+	0.227811i	0.684143	−	0.729348i	$-0.260177\pi$
$311$	6.95849	+	4.01749i	0.394580	+	0.227811i	−0.289563	+	0.957159i	$0.593510\pi$
$312$	−0.342448	+	0.593138i	−0.0193873	+	0.0335798i
$313$	3.86597	+	2.23202i	0.218517	+	0.126161i	0.605264	−	0.796025i	$-0.293068\pi$
$313$	3.86597	+	2.23202i	0.218517	+	0.126161i	−0.386746	+	0.922186i	$0.626401\pi$
$314$	−19.1491	+	11.0557i	−1.08065	+	0.623912i
$315$	0.692324	−	0.399713i	0.0390080	−	0.0225213i
$316$	−7.66147	−	4.42335i	−0.430991	−	0.248833i
$317$	0.797443	−	1.38121i	0.0447888	−	0.0775765i	−0.842762	−	0.538287i	$-0.819072\pi$
$317$	0.797443	−	1.38121i	0.0447888	−	0.0775765i	0.887551	+	0.460710i	$0.152405\pi$
$318$	2.07129	+	1.19586i	0.116152	+	0.0670605i
$319$		−	2.14322i		−	0.119997i
$320$	0.866025	−	0.500000i	0.0484123	−	0.0279508i
$321$	−1.29956	+	2.25090i	−0.0725344	+	0.125633i
$322$	−2.17921			−0.121442
$323$	43.9891			2.44762
$324$	3.27846	−	5.67845i	0.182137	−	0.315470i
$325$			1.29393i			0.0717741i
$326$	2.54160	+	4.40218i	0.140766	+	0.243814i
$327$			6.09735i			0.337184i
$328$	0.607633	−	0.350817i	0.0335509	−	0.0193706i
$329$	0.925820	+	1.60357i	0.0510421	+	0.0884075i
$330$	0.548473	+	0.949984i	0.0301925	+	0.0522949i
$331$	−18.1749	−	10.4933i	−0.998982	−	0.576762i	−0.0910350	−	0.995848i	$-0.529018\pi$
$331$	−18.1749	−	10.4933i	−0.998982	−	0.576762i	−0.907947	+	0.419085i	$0.862351\pi$
$332$	−12.8254			−0.703887
$333$	−11.3609	−	12.0264i	−0.622576	−	0.659042i
$334$	−2.45742			−0.134464
$335$	−3.27776	−	1.89242i	−0.179083	−	0.103394i
$336$	0.0777900	+	0.134736i	0.00424379	+	0.00735046i
$337$	8.87719	+	15.3758i	0.483572	+	0.837571i	0.999822	−	0.0188671i	$-0.00600596\pi$
$337$	8.87719	+	15.3758i	0.483572	+	0.837571i	−0.516250	+	0.856438i	$0.672673\pi$
$338$	9.80839	−	5.66288i	0.533506	−	0.308020i
$339$		−	5.58441i		−	0.303304i
$340$	−3.92542	−	6.79903i	−0.212886	−	0.368729i
$341$			5.81770i			0.315046i
$342$	−7.61974	+	13.1978i	−0.412028	+	0.713654i
$343$	−4.08957			−0.220816
$344$	−6.19378			−0.333946
$345$	1.96221	−	3.39865i	0.105642	−	0.182977i
$346$	−19.1826	+	11.0751i	−1.03126	+	0.595400i
$347$			0.477201i			0.0256175i	0.999918	+	0.0128088i	$0.00407726\pi$
$347$			0.477201i			0.0256175i	−0.999918	+	0.0128088i	$0.995923\pi$
$348$	0.474070	+	0.273704i	0.0254128	+	0.0146721i
$349$	−14.7960	+	25.6274i	−0.792011	+	1.37180i	0.132709	+	0.991155i	$0.457633\pi$
$349$	−14.7960	+	25.6274i	−0.792011	+	1.37180i	−0.924720	+	0.380648i	$0.875701\pi$
$350$	0.254547	+	0.146963i	0.0136061	+	0.00785550i
$351$	−3.39264	+	1.95874i	−0.181086	+	0.104550i
$352$	1.79474	−	1.03619i	0.0956598	−	0.0552292i
$353$	0.136506	+	0.0788118i	0.00726548	+	0.00419473i	0.503628	−	0.863920i	$-0.331998\pi$
$353$	0.136506	+	0.0788118i	0.00726548	+	0.00419473i	−0.496363	+	0.868115i	$0.665331\pi$
$354$	2.05814	−	3.56480i	0.109389	−	0.189467i
$355$	9.09911	+	5.25337i	0.482931	+	0.278820i
$356$		−	6.59043i		−	0.349292i
$357$	1.05779	−	0.610716i	0.0559843	−	0.0323225i
$358$	1.66582	−	2.88529i	0.0880414	−	0.152492i
$359$	−23.3175			−1.23065			−0.615324	−	0.788274i	$-0.710975\pi$
$359$	−23.3175			−1.23065			−0.615324	+	0.788274i	$0.710975\pi$
$360$	2.71982			0.143347
$361$	6.19744	−	10.7343i	0.326181	−	0.564962i
$362$			0.865436i			0.0454863i
$363$	−1.77459	−	3.07369i	−0.0931420	−	0.161327i
$364$			0.380318i			0.0199341i
$365$	14.1190	−	8.15159i	0.739020	−	0.426674i
$366$	−1.79305	−	3.10566i	−0.0937244	−	0.162335i
$367$	−16.8183	−	29.1302i	−0.877910	−	1.52059i	−0.853630	−	0.520880i	$-0.825604\pi$
$367$	−16.8183	−	29.1302i	−0.877910	−	1.52059i	−0.0242803	−	0.999705i	$-0.507729\pi$
$368$	−6.42082	−	3.70706i	−0.334709	−	0.193244i
$369$	1.90832			0.0993433
$370$	1.74081	−	5.82834i	0.0905003	−	0.303001i
$371$	1.32811			0.0689518
$372$	−1.28685	−	0.742963i	−0.0667200	−	0.0385208i
$373$	4.57346	+	7.92146i	0.236805	+	0.410158i	0.959796	−	0.280700i	$-0.0905665\pi$
$373$	4.57346	+	7.92146i	0.236805	+	0.410158i	−0.722991	+	0.690858i	$0.757233\pi$
$374$	−8.13497	−	14.0902i	−0.420650	−	0.728586i
$375$	−0.458402	+	0.264658i	−0.0236718	+	0.0136669i
$376$			6.29968i			0.324881i
$377$	0.669076	+	1.15887i	0.0344592	+	0.0596850i
$378$			0.889890i			0.0457710i
$379$	15.3698	−	26.6212i	0.789491	−	1.36744i	−0.136787	−	0.990600i	$-0.543678\pi$
$379$	15.3698	−	26.6212i	0.789491	−	1.36744i	0.926279	−	0.376839i	$-0.122989\pi$
$380$	−5.60311			−0.287434
$381$	−0.340313			−0.0174348
$382$	10.6914	−	18.5180i	0.547018	−	0.947462i
$383$	2.52908	−	1.46016i	0.129230	−	0.0746109i	−0.433991	−	0.900917i	$-0.642895\pi$
$383$	2.52908	−	1.46016i	0.129230	−	0.0746109i	0.563221	+	0.826306i	$0.309562\pi$
$384$			0.529317i			0.0270116i
$385$	0.527520	+	0.304564i	0.0268849	+	0.0155220i
$386$	−0.866885	+	1.50149i	−0.0441233	+	0.0764237i
$387$	−14.5891	−	8.42300i	−0.741604	−	0.428165i
$388$	12.0281	−	6.94440i	0.610632	−	0.352549i
$389$	−0.963419	+	0.556230i	−0.0488473	+	0.0282020i	−0.524225	−	0.851580i	$-0.675645\pi$
$389$	−0.963419	+	0.556230i	−0.0488473	+	0.0282020i	0.475377	+	0.879782i	$0.342311\pi$
$390$	−0.593138	−	0.342448i	−0.0300347	−	0.0173405i
$391$	−29.1036	+	50.4089i	−1.47183	+	2.54929i
$392$	−5.98736	−	3.45680i	−0.302407	−	0.174595i
$393$			7.07835i			0.357055i
$394$	3.50543	−	2.02386i	0.176601	−	0.101961i
$395$	4.42335	−	7.66147i	0.222563	−	0.385491i
$396$	5.63652			0.283246
$397$	20.9531			1.05160			0.525802	−	0.850607i	$-0.323765\pi$
$397$	20.9531			1.05160			0.525802	+	0.850607i	$0.323765\pi$
$398$	−3.44749	+	5.97122i	−0.172807	+	0.299310i
$399$		−	0.871732i		−	0.0436412i
$400$	0.500000	+	0.866025i	0.0250000	+	0.0433013i
$401$			17.8082i			0.889297i	0.895705	+	0.444649i	$0.146671\pi$
$401$			17.8082i			0.889297i	−0.895705	+	0.444649i	$0.853329\pi$
$402$	1.73497	−	1.00169i	0.0865326	−	0.0499596i
$403$	−1.81619	−	3.14573i	−0.0904708	−	0.156700i
$404$	−2.83827	−	4.91602i	−0.141209	−	0.244581i
$405$	5.67845	+	3.27846i	0.282165	+	0.162908i
$406$	0.303972			0.0150859
$407$	3.60762	−	12.0786i	0.178823	−	0.598712i
$408$	4.15558			0.205732
$409$	17.6665	+	10.1997i	0.873550	+	0.504345i	0.868526	−	0.495643i	$-0.165067\pi$
$409$	17.6665	+	10.1997i	0.873550	+	0.504345i	0.00502392	+	0.999987i	$0.498401\pi$
$410$	0.350817	+	0.607633i	0.0173256	+	0.0300089i
$411$	0.243232	+	0.421291i	0.0119978	+	0.0207807i
$412$	−12.3119	+	7.10830i	−0.606566	+	0.350201i
$413$		−	2.28574i		−	0.112474i
$414$	−10.0826	−	17.4635i	−0.495531	−	0.858285i
$415$		−	12.8254i		−	0.629576i
$416$	−0.646963	+	1.12057i	−0.0317200	+	0.0549406i
$417$	−7.67952			−0.376068
$418$	−11.6118			−0.567952
$419$	16.9775	−	29.4059i	0.829405	−	1.43657i	−0.0691009	−	0.997610i	$-0.522013\pi$
$419$	16.9775	−	29.4059i	0.829405	−	1.43657i	0.898506	−	0.438962i	$-0.144654\pi$
$420$	−0.134736	+	0.0777900i	−0.00657445	+	0.00379576i
$421$			3.88522i			0.189354i	0.995508	+	0.0946769i	$0.0301818\pi$
$421$			3.88522i			0.189354i	−0.995508	+	0.0946769i	$0.969818\pi$
$422$	11.3554	+	6.55606i	0.552774	+	0.319144i
$423$	−8.56701	+	14.8385i	−0.416542	+	0.721473i
$424$	3.91314	+	2.25925i	0.190039	+	0.109719i
$425$	6.79903	−	3.92542i	0.329801	−	0.190411i
$426$	−4.81631	+	2.78070i	−0.233351	+	0.134725i
$427$	−1.72455	−	0.995670i	−0.0834569	−	0.0481839i
$428$	−2.45517	+	4.25247i	−0.118675	+	0.205551i
$429$	−1.22921	−	0.709684i	−0.0593468	−	0.0342639i
$430$		−	6.19378i		−	0.298691i
$431$	7.10406	−	4.10153i	0.342190	−	0.197564i	−0.319050	−	0.947738i	$-0.603364\pi$
$431$	7.10406	−	4.10153i	0.342190	−	0.197564i	0.661240	+	0.750174i	$0.270030\pi$
$432$	−1.51380	+	2.62198i	−0.0728327	+	0.126150i
$433$	−5.99021			−0.287871			−0.143935	−	0.989587i	$-0.545976\pi$
$433$	−5.99021			−0.287871			−0.143935	+	0.989587i	$0.545976\pi$
$434$	−0.825125			−0.0396072
$435$	−0.273704	+	0.474070i	−0.0131231	+	0.0227299i
$436$			11.5193i			0.551674i
$437$	20.7711	+	35.9766i	0.993616	+	1.72099i
$438$			8.62954i			0.412335i
$439$	−6.59052	+	3.80504i	−0.314548	+	0.181605i	−0.648960	−	0.760822i	$-0.724796\pi$
$439$	−6.59052	+	3.80504i	−0.314548	+	0.181605i	0.334412	+	0.942427i	$0.391462\pi$
$440$	1.03619	+	1.79474i	0.0493985	+	0.0855607i
$441$	−9.40190	−	16.2846i	−0.447709	−	0.775455i
$442$	8.79744	+	5.07920i	0.418451	+	0.241593i
$443$	2.38816			0.113465			0.0567324	−	0.998389i	$-0.481932\pi$
$443$	2.38816			0.113465			0.0567324	+	0.998389i	$0.481932\pi$
$444$	2.21100	+	2.34051i	0.104930	+	0.111076i
$445$	6.59043			0.312416
$446$	−9.03684	−	5.21742i	−0.427907	−	0.247052i
$447$	2.64305	+	4.57789i	0.125012	+	0.216527i
$448$	0.146963	+	0.254547i	0.00694335	+	0.0120262i
$449$	17.5884	−	10.1547i	0.830047	−	0.479228i	−0.0238217	−	0.999716i	$-0.507583\pi$
$449$	17.5884	−	10.1547i	0.830047	−	0.479228i	0.853869	+	0.520488i	$0.174250\pi$
$450$			2.71982i			0.128214i
$451$	0.727028	+	1.25925i	0.0342344	+	0.0592957i
$452$		−	10.5502i		−	0.496241i
$453$	4.94973	−	8.57318i	0.232558	−	0.402803i
$454$	−3.70831			−0.174040
$455$	−0.380318			−0.0178296
$456$	1.48291	−	2.56848i	0.0694436	−	0.120280i
$457$	−13.3729	+	7.72086i	−0.625559	+	0.361167i	−0.779030	−	0.626987i	$-0.784288\pi$
$457$	−13.3729	+	7.72086i	−0.625559	+	0.361167i	0.153471	+	0.988153i	$0.450955\pi$
$458$			4.32347i			0.202022i
$459$	20.5847	+	11.8846i	0.960812	+	0.554725i
$460$	3.70706	−	6.42082i	0.172843	−	0.299372i
$461$	−14.4941	−	8.36819i	−0.675059	−	0.389746i	0.122932	−	0.992415i	$-0.460770\pi$
$461$	−14.4941	−	8.36819i	−0.675059	−	0.389746i	−0.797991	+	0.602670i	$0.794104\pi$
$462$	−0.279225	+	0.161211i	−0.0129907	+	0.00750019i
$463$	27.7820	−	16.0400i	1.29114	−	0.745440i	0.312283	−	0.949989i	$-0.398906\pi$
$463$	27.7820	−	16.0400i	1.29114	−	0.745440i	0.978856	+	0.204549i	$0.0655728\pi$
$464$	0.895626	+	0.517090i	0.0415784	+	0.0240053i
$465$	0.742963	−	1.28685i	0.0344541	−	0.0596762i
$466$	15.2705	+	8.81642i	0.707392	+	0.408413i
$467$		−	3.15769i		−	0.146121i	−0.997328	−	0.0730603i	$-0.976723\pi$
$467$		−	3.15769i		−	0.146121i	0.997328	−	0.0730603i	$-0.0232766\pi$
$468$	−3.04776	+	1.75963i	−0.140883	+	0.0813387i
$469$	0.556230	−	0.963419i	0.0256843	−	0.0444865i
$470$	−6.29968			−0.290583
$471$	11.7040			0.539291
$472$	3.88830	−	6.73473i	0.178973	−	0.309991i
$473$		−	12.8359i		−	0.590195i
$474$	2.34135	+	4.05534i	0.107542	+	0.186268i
$475$		−	5.60311i		−	0.257088i
$476$	1.99841	−	1.15378i	0.0915970	−	0.0528836i
$477$	6.14477	+	10.6430i	0.281350	+	0.487312i
$478$	8.37612	+	14.5079i	0.383115	+	0.663574i
$479$	−7.75108	−	4.47509i	−0.354156	−	0.204472i	0.312358	−	0.949964i	$-0.398881\pi$
$479$	−7.75108	−	4.47509i	−0.354156	−	0.204472i	−0.666514	+	0.745492i	$0.732214\pi$
$480$	−0.529317			−0.0241599
$481$	1.82002	+	7.65732i	0.0829858	+	0.349144i
$482$	−20.4820			−0.932929
$483$	0.998951	+	0.576745i	0.0454538	+	0.0262428i
$484$	−3.35261	−	5.80690i	−0.152392	−	0.263950i
$485$	6.94440	+	12.0281i	0.315329	+	0.546166i
$486$	−10.8716	+	6.27674i	−0.493147	+	0.284719i
$487$		−	2.23943i		−	0.101478i	−0.998712	−	0.0507391i	$-0.983842\pi$
$487$		−	2.23943i		−	0.101478i	0.998712	−	0.0507391i	$-0.0161577\pi$
$488$	−3.38749	−	5.86730i	−0.153344	−	0.265600i
$489$		−	2.69062i		−	0.121674i
$490$	3.45680	−	5.98736i	0.156162	−	0.270481i
$491$	1.22439			0.0552558			0.0276279	−	0.999618i	$-0.491205\pi$
$491$	1.22439			0.0552558			0.0276279	+	0.999618i	$0.491205\pi$
$492$	−0.371387			−0.0167434
$493$	4.05959	−	7.03141i	0.182835	−	0.316679i
$494$	6.27870	−	3.62501i	0.282492	−	0.163097i
$495$			5.63652i			0.253343i
$496$	−2.43115	−	1.40363i	−0.109162	−	0.0630247i
$497$	−1.54410	+	2.67446i	−0.0692625	+	0.119966i
$498$	5.87920	+	3.39436i	0.263453	+	0.152105i
$499$	−25.5769	+	14.7668i	−1.14498	+	0.661053i	−0.947659	−	0.319286i	$-0.896557\pi$
$499$	−25.5769	+	14.7668i	−1.14498	+	0.661053i	−0.197320	+	0.980339i	$0.563224\pi$
$500$	−0.866025	+	0.500000i	−0.0387298	+	0.0223607i
$501$	1.12649	+	0.650377i	0.0503277	+	0.0290567i
$502$	11.6836	−	20.2365i	0.521463	−	0.903200i
$503$	12.8878	+	7.44076i	0.574637	+	0.331767i	0.758999	−	0.651091i	$-0.225689\pi$
$503$	12.8878	+	7.44076i	0.574637	+	0.331767i	−0.184362	+	0.982858i	$0.559022\pi$
$504$			0.799427i			0.0356093i
$505$	4.91602	−	2.83827i	0.218760	−	0.126301i
$506$	7.68246	−	13.3064i	0.341527	−	0.591542i
$507$	−5.99491			−0.266243
$508$	−0.642930			−0.0285254
$509$	2.20692	−	3.82250i	0.0978202	−	0.169430i	−0.812962	−	0.582317i	$-0.802146\pi$
$509$	2.20692	−	3.82250i	0.0978202	−	0.169430i	0.910782	+	0.412887i	$0.135480\pi$
$510$			4.15558i			0.184012i
$511$	2.39596	+	4.14993i	0.105991	+	0.183582i
$512$			1.00000i			0.0441942i
$513$	14.6912	−	8.48199i	0.648634	−	0.374489i
$514$	12.1128	+	20.9800i	0.534274	+	0.925390i
$515$	−7.10830	−	12.3119i	−0.313229	−	0.542529i
$516$	2.83924	+	1.63924i	0.124991	+	0.0721633i
$517$	−13.0554			−0.574174
$518$	1.71310	+	0.511669i	0.0752694	+	0.0224814i
$519$	11.7245			0.514646
$520$	−1.12057	−	0.646963i	−0.0491404	−	0.0283712i
$521$	3.16732	+	5.48595i	0.138763	+	0.240344i	0.927029	−	0.374991i	$-0.122354\pi$
$521$	3.16732	+	5.48595i	0.138763	+	0.240344i	−0.788266	+	0.615335i	$0.789021\pi$
$522$	1.40639	+	2.43594i	0.0615562	+	0.106618i
$523$	−19.8971	+	11.4876i	−0.870039	+	0.502317i	−0.867361	−	0.497679i	$-0.834186\pi$
$523$	−19.8971	+	11.4876i	−0.870039	+	0.502317i	−0.00267771	+	0.999996i	$0.500852\pi$
$524$			13.3726i			0.584186i
$525$	−0.0777900	−	0.134736i	−0.00339503	−	0.00588037i
$526$		−	17.7233i		−	0.772774i
$527$	−11.0196	+	19.0866i	−0.480023	+	0.831425i
$528$	−1.09695			−0.0477385
$529$	−31.9693			−1.38997
$530$	−2.25925	+	3.91314i	−0.0981356	+	0.169976i
$531$	18.3173	−	10.5755i	0.794902	−	0.458937i
$532$		−	1.64690i		−	0.0714022i
$533$	−0.786232	−	0.453932i	−0.0340555	−	0.0196620i
$534$	−1.74421	+	3.02106i	−0.0754794	+	0.130734i
$535$	−4.25247	−	2.45517i	−0.183850	−	0.106146i
$536$	3.27776	−	1.89242i	0.141578	−	0.0817399i
$537$	−1.52723	+	0.881747i	−0.0659049	+	0.0380502i
$538$	−2.79744	−	1.61510i	−0.120606	−	0.0696320i
$539$	7.16382	−	12.4081i	0.308568	−	0.534455i
$540$	−2.62198	−	1.51380i	−0.112832	−	0.0651435i
$541$			17.4720i			0.751182i	0.926786	+	0.375591i	$0.122560\pi$
$541$			17.4720i			0.751182i	−0.926786	+	0.375591i	$0.877440\pi$
$542$	19.7143	−	11.3821i	0.846803	−	0.488902i
$543$	0.229045	−	0.396717i	0.00982925	−	0.0170248i
$544$	7.85084			0.336602
$545$	−11.5193			−0.493432
$546$	0.100654	−	0.174339i	0.00430761	−	0.00746100i
$547$		−	0.472193i		−	0.0201895i	−0.999949	−	0.0100948i	$-0.996787\pi$
$547$		−	0.472193i		−	0.0201895i	0.999949	−	0.0100948i	$-0.00321331\pi$
$548$	0.459522	+	0.795915i	0.0196298	+	0.0339998i
$549$		−	18.4267i		−	0.786434i
$550$	−1.79474	+	1.03619i	−0.0765278	+	0.0441834i
$551$	−2.89731	−	5.01829i	−0.123430	−	0.213786i
$552$	1.96221	+	3.39865i	0.0835172	+	0.144656i
$553$	2.25191	+	1.30014i	0.0957608	+	0.0552875i
$554$	13.6158			0.578482
$555$	−2.34051	+	2.21100i	−0.0993490	+	0.0938519i
$556$	−14.5084			−0.615292
$557$	−1.48312	−	0.856281i	−0.0628419	−	0.0362818i	0.468250	−	0.883596i	$-0.344885\pi$
$557$	−1.48312	−	0.856281i	−0.0628419	−	0.0362818i	−0.531092	+	0.847314i	$0.678218\pi$
$558$	−3.81762	−	6.61231i	−0.161613	−	0.279921i
$559$	4.00715	+	6.94059i	0.169484	+	0.293555i
$560$	−0.254547	+	0.146963i	−0.0107566	+	0.00621032i
$561$			8.61195i			0.363597i
$562$	12.2213	+	21.1680i	0.515526	+	0.892918i
$563$			16.9156i			0.712907i	0.934313	+	0.356454i	$0.116014\pi$
$563$			16.9156i			0.712907i	−0.934313	+	0.356454i	$0.883986\pi$
$564$	1.66726	−	2.88778i	0.0702044	−	0.121598i
$565$	10.5502			0.443852
$566$	−13.0324			−0.547792
$567$	−0.963624	+	1.66905i	−0.0404684	+	0.0700933i
$568$	−9.09911	+	5.25337i	−0.381790	+	0.220427i
$569$			33.6655i			1.41133i	0.708545	+	0.705666i	$0.249352\pi$
$569$			33.6655i			1.41133i	−0.708545	+	0.705666i	$0.750648\pi$
$570$	2.56848	+	1.48291i	0.107582	+	0.0621123i
$571$	4.80744	−	8.32674i	0.201185	−	0.348463i	−0.747725	−	0.664008i	$-0.768854\pi$
$571$	4.80744	−	8.32674i	0.201185	−	0.348463i	0.948911	+	0.315545i	$0.102187\pi$
$572$	−2.32226	−	1.34076i	−0.0970984	−	0.0560598i
$573$	−9.80187	+	5.65912i	−0.409479	+	0.236413i
$574$	−0.178599	+	0.103114i	−0.00745459	+	0.00430391i
$575$	6.42082	+	3.70706i	0.267767	+	0.154595i
$576$	−1.35991	+	2.35544i	−0.0566630	+	0.0981432i
$577$	−10.0336	−	5.79289i	−0.417704	−	0.241161i	0.276391	−	0.961045i	$-0.410862\pi$
$577$	−10.0336	−	5.79289i	−0.417704	−	0.241161i	−0.694094	+	0.719884i	$0.744195\pi$
$578$		−	44.6357i		−	1.85660i
$579$	0.794763	−	0.458856i	0.0330292	−	0.0190694i
$580$	−0.517090	+	0.895626i	−0.0214710	+	0.0371888i
$581$	3.76973			0.156395
$582$	−7.35157			−0.304733
$583$	−4.68203	+	8.10952i	−0.193910	+	0.335862i
$584$			16.3032i			0.674630i
$585$	−1.75963	−	3.04776i	−0.0727516	−	0.126009i
$586$			19.2866i			0.796723i
$587$	17.6687	−	10.2010i	0.729266	−	0.421042i	−0.0888876	−	0.996042i	$-0.528331\pi$
$587$	17.6687	−	10.2010i	0.729266	−	0.421042i	0.818154	+	0.575000i	$0.194998\pi$
$588$	1.82974	+	3.16921i	0.0754574	+	0.130696i
$589$	7.86468	+	13.6220i	0.324058	+	0.561286i
$590$	6.73473	+	3.88830i	0.277264	+	0.160079i
$591$	−2.14253			−0.0881318
$592$	4.17709	+	4.42176i	0.171677	+	0.181733i
$593$	37.4255			1.53688			0.768440	−	0.639922i	$-0.221033\pi$
$593$	37.4255			1.53688			0.768440	+	0.639922i	$0.221033\pi$
$594$	−5.43374	−	3.13717i	−0.222949	−	0.128720i
$595$	1.15378	+	1.99841i	0.0473005	+	0.0819269i
$596$	4.99332	+	8.64868i	0.204534	+	0.354264i
$597$	3.16067	−	1.82481i	0.129358	−	0.0746846i
$598$			9.59333i			0.392301i
$599$	−19.7501	−	34.2081i	−0.806966	−	1.39771i	−0.914956	−	0.403554i	$-0.867775\pi$
$599$	−19.7501	−	34.2081i	−0.806966	−	1.39771i	0.107990	−	0.994152i	$-0.465559\pi$
$600$		−	0.529317i		−	0.0216093i
$601$	−0.565496	+	0.979468i	−0.0230671	+	0.0399534i	−0.877329	−	0.479890i	$-0.840676\pi$
$601$	−0.565496	+	0.979468i	−0.0230671	+	0.0399534i	0.854261	+	0.519844i	$0.174010\pi$
$602$	1.82051			0.0741986
$603$	10.2941			0.419207
$604$	9.35117	−	16.1967i	0.380494	−	0.659034i
$605$	5.80690	−	3.35261i	0.236084	−	0.136303i
$606$			3.00468i			0.122057i
$607$	−26.2681	−	15.1659i	−1.06619	−	0.615566i	−0.139053	−	0.990285i	$-0.544406\pi$
$607$	−26.2681	−	15.1659i	−1.06619	−	0.615566i	−0.927138	+	0.374719i	$0.877739\pi$
$608$	2.80156	−	4.85244i	0.113618	−	0.196792i
$609$	−0.139341	−	0.0804488i	−0.00564640	−	0.00325995i
$610$	5.86730	−	3.38749i	0.237560	−	0.137155i
$611$	7.05925	−	4.07566i	0.285587	−	0.164884i
$612$	18.4922	+	10.6765i	0.747501	+	0.431570i
$613$	6.71892	−	11.6375i	0.271375	−	0.470035i	−0.697839	−	0.716254i	$-0.745855\pi$
$613$	6.71892	−	11.6375i	0.271375	−	0.470035i	0.969214	+	0.246220i	$0.0791884\pi$
$614$	9.71939	+	5.61149i	0.392243	+	0.226461i
$615$		−	0.371387i		−	0.0149758i
$616$	−0.527520	+	0.304564i	−0.0212544	+	0.0122712i
$617$	16.6727	−	28.8779i	0.671216	−	1.16258i	−0.306343	−	0.951921i	$-0.599105\pi$
$617$	16.6727	−	28.8779i	0.671216	−	1.16258i	0.977559	−	0.210660i	$-0.0675612\pi$
$618$	7.52508			0.302703
$619$	2.31285			0.0929613			0.0464807	−	0.998919i	$-0.485199\pi$
$619$	2.31285			0.0929613			0.0464807	+	0.998919i	$0.485199\pi$
$620$	1.40363	−	2.43115i	0.0563710	−	0.0976374i
$621$			22.4470i			0.900767i
$622$	−4.01749	−	6.95849i	−0.161087	−	0.279010i
$623$			1.93710i			0.0776082i
$624$	0.593138	−	0.342448i	0.0237445	−	0.0137089i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−2.23202	−	3.86597i	−0.0892093	−	0.154515i
$627$	5.32287	+	3.07316i	0.212575	+	0.122730i
$628$	22.1115			0.882345
$629$	34.7145	−	32.7937i	1.38416	−	1.30757i
$630$	−0.799427			−0.0318499
$631$	−19.6379	−	11.3379i	−0.781772	−	0.451356i	0.0552858	−	0.998471i	$-0.482393\pi$
$631$	−19.6379	−	11.3379i	−0.781772	−	0.451356i	−0.837058	+	0.547114i	$0.815726\pi$
$632$	4.42335	+	7.66147i	0.175952	+	0.304757i
$633$	−3.47023	−	6.01062i	−0.137929	−	0.238901i
$634$	−1.38121	+	0.797443i	−0.0548549	+	0.0316705i
$635$		−	0.642930i		−	0.0255139i
$636$	−1.19586	−	2.07129i	−0.0474189	−	0.0821320i
$637$			8.94570i			0.354441i
$638$	−1.07161	+	1.85608i	−0.0424254	+	0.0734829i
$639$	−28.5765			−1.13047
$640$	−1.00000			−0.0395285
$641$	9.02568	−	15.6329i	0.356493	−	0.617464i	−0.630879	−	0.775881i	$-0.717306\pi$
$641$	9.02568	−	15.6329i	0.356493	−	0.617464i	0.987372	+	0.158417i	$0.0506390\pi$
$642$	2.25090	−	1.29956i	0.0888361	−	0.0512895i
$643$			44.2564i			1.74530i	0.488344	+	0.872651i	$0.337601\pi$
$643$			44.2564i			1.74530i	−0.488344	+	0.872651i	$0.662399\pi$
$644$	1.88725	+	1.08960i	0.0743679	+	0.0429364i
$645$	−1.63924	+	2.83924i	−0.0645449	+	0.111795i
$646$	−38.0957	−	21.9946i	−1.49886	−	0.865365i
$647$	−6.60035	+	3.81071i	−0.259487	+	0.149815i	−0.624100	−	0.781344i	$-0.714534\pi$
$647$	−6.60035	+	3.81071i	−0.259487	+	0.149815i	0.364614	+	0.931159i	$0.381201\pi$
$648$	−5.67845	+	3.27846i	−0.223071	+	0.128790i
$649$	13.9569	+	8.05804i	0.547858	+	0.316306i
$650$	0.646963	−	1.12057i	0.0253760	−	0.0439525i
$651$	0.378238	+	0.218376i	0.0148243	+	0.00855883i
$652$		−	5.08320i		−	0.199073i
$653$	−34.9924	+	20.2029i	−1.36936	+	0.790600i	−0.990846	−	0.134997i	$-0.956898\pi$
$653$	−34.9924	+	20.2029i	−1.36936	+	0.790600i	−0.378513	+	0.925596i	$0.623564\pi$
$654$	3.04868	−	5.28046i	0.119213	−	0.206482i
$655$	−13.3726			−0.522511
$656$	−0.701634			−0.0273942
$657$	−22.1709	+	38.4011i	−0.864968	+	1.49817i
$658$		−	1.85164i		−	0.0721844i
$659$	−8.14641	−	14.1100i	−0.317339	−	0.549647i	0.662593	−	0.748980i	$-0.269456\pi$
$659$	−8.14641	−	14.1100i	−0.317339	−	0.549647i	−0.979932	+	0.199332i	$0.936123\pi$
$660$		−	1.09695i		−	0.0426986i
$661$	21.9968	−	12.6999i	0.855577	−	0.493968i	−0.00695147	−	0.999976i	$-0.502213\pi$
$661$	21.9968	−	12.6999i	0.855577	−	0.493968i	0.862529	+	0.506008i	$0.168879\pi$
$662$	10.4933	+	18.1749i	0.407833	+	0.706387i
$663$	−2.68851	−	4.65663i	−0.104413	−	0.180849i
$664$	11.1071	+	6.41272i	0.431041	+	0.248862i
$665$	1.64690			0.0638641
$666$	3.82567	+	16.0956i	0.148242	+	0.623693i
$667$	7.66754			0.296888
$668$	2.12819	+	1.22871i	0.0823421	+	0.0475403i
$669$	2.76167	+	4.78335i	0.106772	+	0.184935i
$670$	1.89242	+	3.27776i	0.0731104	+	0.126631i
$671$	12.1593	−	7.02017i	0.469404	−	0.271011i
$672$		−	0.155580i		−	0.00600163i
$673$	1.21059	+	2.09680i	0.0466648	+	0.0808259i	0.888414	−	0.459042i	$-0.151807\pi$
$673$	1.21059	+	2.09680i	0.0466648	+	0.0808259i	−0.841750	+	0.539868i	$0.818474\pi$
$674$		−	17.7544i		−	0.683873i
$675$	1.51380	−	2.62198i	0.0582661	−	0.100920i
$676$	−11.3258			−0.435606
$677$	−44.6540			−1.71619			−0.858097	−	0.513487i	$-0.828353\pi$
$677$	−44.6540			−1.71619			−0.858097	+	0.513487i	$0.828353\pi$
$678$	−2.79221	+	4.83624i	−0.107234	+	0.185735i
$679$	−3.53536	+	2.04114i	−0.135675	+	0.0783318i
$680$			7.85084i			0.301066i
$681$	1.69990	+	0.981436i	0.0651402	+	0.0376087i
$682$	2.90885	−	5.03828i	0.111386	−	0.192926i
$683$	−15.4702	−	8.93174i	−0.591952	−	0.341764i	0.173917	−	0.984760i	$-0.444358\pi$
$683$	−15.4702	−	8.93174i	−0.591952	−	0.341764i	−0.765869	+	0.642997i	$0.777691\pi$
$684$	13.1978	−	7.61974i	0.504630	−	0.291348i
$685$	−0.795915	+	0.459522i	−0.0304103	+	0.0175574i
$686$	3.54167	+	2.04479i	0.135222	+	0.0780703i
$687$	1.14424	−	1.98189i	0.0436556	−	0.0756136i
$688$	5.36397	+	3.09689i	0.204500	+	0.118068i
$689$		−	5.84661i		−	0.222738i
$690$	−3.39865	+	1.96221i	−0.129384	+	0.0747001i
$691$	26.1342	−	45.2658i	0.994193	−	1.72199i	0.403899	−	0.914803i	$-0.367655\pi$
$691$	26.1342	−	45.2658i	0.994193	−	1.72199i	0.590293	−	0.807189i	$-0.299012\pi$
$692$	22.1502			0.842023
$693$	−1.65672			−0.0629335
$694$	0.238601	−	0.413268i	0.00905716	−	0.0156875i
$695$		−	14.5084i		−	0.550334i
$696$	−0.273704	−	0.474070i	−0.0103747	−	0.0179696i
$697$			5.50842i			0.208646i
$698$	25.6274	−	14.7960i	0.970012	−	0.560036i
$699$	−4.66668	−	8.08292i	−0.176510	−	0.305724i
$700$	−0.146963	−	0.254547i	−0.00555468	−	0.00962099i
$701$	2.10679	+	1.21636i	0.0795723	+	0.0459411i	0.539258	−	0.842140i	$-0.318705\pi$
$701$	2.10679	+	1.21636i	0.0795723	+	0.0459411i	−0.459686	+	0.888082i	$0.652038\pi$
$702$	3.91749			0.147856
$703$	−7.88127	−	33.1586i	−0.297248	−	1.25060i
$704$	−2.07238			−0.0781059
$705$	2.88778	+	1.66726i	0.108760	+	0.0627927i
$706$	−0.0788118	−	0.136506i	−0.00296612	−	0.00513747i
$707$	0.834240	+	1.44495i	0.0313748	+	0.0543428i
$708$	−3.56480	+	2.05814i	−0.133974	+	0.0773496i
$709$			31.6637i			1.18915i	0.804039	+	0.594577i	$0.202681\pi$
$709$			31.6637i			1.18915i	−0.804039	+	0.594577i	$0.797319\pi$
$710$	−5.25337	−	9.09911i	−0.197156	−	0.341483i
$711$			24.0615i			0.902376i
$712$	−3.29521	+	5.70748i	−0.123493	+	0.213897i
$713$	−20.8133			−0.779465
$714$	−1.22143			−0.0457110
$715$	1.34076	−	2.32226i	0.0501414	−	0.0868475i
$716$	−2.88529	+	1.66582i	−0.107828	+	0.0622547i
$717$		−	8.86724i		−	0.331153i
$718$	20.1935	+	11.6587i	0.753615	+	0.435100i
$719$	23.8782	−	41.3582i	0.890505	−	1.54240i	0.0512341	−	0.998687i	$-0.483685\pi$
$719$	23.8782	−	41.3582i	0.890505	−	1.54240i	0.839271	−	0.543713i	$-0.182982\pi$
$720$	−2.35544	−	1.35991i	−0.0877819	−	0.0506809i
$721$	3.61880	−	2.08931i	0.134771	−	0.0778101i
$722$	−10.7343	+	6.19744i	−0.399488	+	0.230645i
$723$	9.38898	+	5.42073i	0.349180	+	0.201599i
$724$	0.432718	−	0.749490i	0.0160818	−	0.0278546i
$725$	−0.895626	−	0.517090i	−0.0332627	−	0.0192042i
$726$			3.54919i			0.131723i
$727$	17.3168	−	9.99783i	0.642243	−	0.370799i	−0.143235	−	0.989689i	$-0.545750\pi$
$727$	17.3168	−	9.99783i	0.642243	−	0.370799i	0.785478	+	0.618890i	$0.212417\pi$
$728$	0.190159	−	0.329365i	0.00704777	−	0.0122071i
$729$	−13.0260			−0.482444
$730$	−16.3032			−0.603407
$731$	24.3132	−	42.1117i	0.899256	−	1.55756i
$732$			3.58611i			0.132546i
$733$	−2.79666	−	4.84396i	−0.103297	−	0.178916i	0.809744	−	0.586783i	$-0.199606\pi$
$733$	−2.79666	−	4.84396i	−0.103297	−	0.178916i	−0.913041	+	0.407867i	$0.866273\pi$
$734$			33.6367i			1.24155i
$735$	−3.16921	+	1.82974i	−0.116898	+	0.0674911i
$736$	3.70706	+	6.42082i	0.136644	+	0.236675i
$737$	3.92181	+	6.79277i	0.144462	+	0.250215i
$738$	−1.65266	−	0.954161i	−0.0608351	−	0.0351232i
$739$	−28.4656			−1.04712			−0.523562	−	0.851988i	$-0.675397\pi$
$739$	−28.4656			−1.04712			−0.523562	+	0.851988i	$0.675397\pi$
$740$	−4.42176	+	4.17709i	−0.162547	+	0.153553i
$741$	−3.83755			−0.140976
$742$	−1.15017	−	0.664053i	−0.0422242	−	0.0243781i
$743$	−25.7826	−	44.6568i	−0.945873	−	1.63830i	−0.753994	−	0.656881i	$-0.771875\pi$
$743$	−25.7826	−	44.6568i	−0.945873	−	1.63830i	−0.191879	−	0.981419i	$-0.561458\pi$
$744$	0.742963	+	1.28685i	0.0272383	+	0.0471782i
$745$	−8.64868	+	4.99332i	−0.316863	+	0.182941i
$746$		−	9.14692i		−	0.334892i
$747$	17.4415	+	30.2095i	0.638150	+	1.10531i
$748$			16.2699i			0.594888i
$749$	0.721637	−	1.24991i	0.0263680	−	0.0456708i
$750$	0.529317			0.0193279
$751$	22.0718			0.805410			0.402705	−	0.915330i	$-0.368070\pi$
$751$	22.0718			0.805410			0.402705	+	0.915330i	$0.368070\pi$
$752$	3.14984	−	5.45568i	0.114863	−	0.198948i
$753$	−10.7115	+	6.18430i	−0.390350	+	0.225369i
$754$		−	1.33815i		−	0.0487326i
$755$	16.1967	+	9.35117i	0.589458	+	0.340324i
$756$	0.444945	−	0.770667i	0.0161825	−	0.0280289i
$757$	−37.3920	−	21.5883i	−1.35904	−	0.784640i	−0.369543	−	0.929214i	$-0.620486\pi$
$757$	−37.3920	−	21.5883i	−1.35904	−	0.784640i	−0.989494	+	0.144573i	$0.953819\pi$
$758$	−26.6212	+	15.3698i	−0.966926	+	0.558255i
$759$	−7.04330	+	4.06645i	−0.255656	+	0.147603i
$760$	4.85244	+	2.80156i	0.176016	+	0.101623i
$761$	−13.5716	+	23.5068i	−0.491971	+	0.852119i	−0.999957	−	0.00924617i	$-0.997057\pi$
$761$	−13.5716	+	23.5068i	−0.491971	+	0.852119i	0.507986	+	0.861365i	$0.330390\pi$
$762$	0.294720	+	0.170157i	0.0106766	+	0.00616413i
$763$		−	3.38582i		−	0.122575i
$764$	−18.5180	+	10.6914i	−0.669957	+	0.386800i
$765$	−10.6765	+	18.4922i	−0.386008	+	0.668585i
$766$	−2.92033			−0.105516
$767$	−10.0623			−0.363330
$768$	0.264658	−	0.458402i	0.00955003	−	0.0165411i
$769$			39.3635i			1.41948i	0.704462	+	0.709742i	$0.251189\pi$
$769$			39.3635i			1.41948i	−0.704462	+	0.709742i	$0.748811\pi$
$770$	−0.304564	−	0.527520i	−0.0109757	−	0.0190105i
$771$		−	12.8230i		−	0.461811i
$772$	1.50149	−	0.866885i	0.0540397	−	0.0311999i
$773$	−3.15764	−	5.46920i	−0.113573	−	0.196713i	0.803636	−	0.595122i	$-0.202896\pi$
$773$	−3.15764	−	5.46920i	−0.113573	−	0.196713i	−0.917208	+	0.398408i	$0.869563\pi$
$774$	8.42300	+	14.5891i	0.302758	+	0.524393i
$775$	2.43115	+	1.40363i	0.0873296	+	0.0504197i
$776$	−13.8888			−0.498579
$777$	−0.649871	−	0.687936i	−0.0233140	−	0.0246796i
$778$	1.11246			0.0398836
$779$	3.40464	+	1.96567i	0.121984	+	0.0704274i
$780$	0.342448	+	0.593138i	0.0122616	+	0.0212377i
$781$	−10.8870	−	18.8568i	−0.389567	−	0.674751i
$782$	50.4089	−	29.1036i	1.80262	−	1.04074i
$783$		−	3.13108i		−	0.111896i
$784$	3.45680	+	5.98736i	0.123457	+	0.213834i
$785$			22.1115i			0.789193i
$786$	3.53917	−	6.13003i	0.126238	−	0.218651i
$787$	−7.11304			−0.253553			−0.126776	−	0.991931i	$-0.540463\pi$
$787$	−7.11304			−0.253553			−0.126776	+	0.991931i	$0.540463\pi$
$788$	−4.04772			−0.144194
$789$	−4.69063	+	8.12441i	−0.166991	+	0.289237i
$790$	−7.66147	+	4.42335i	−0.272583	+	0.157376i
$791$			3.10099i			0.110258i
$792$	−4.88137	−	2.81826i	−0.173452	−	0.100142i
$793$	−4.38316	+	7.59185i	−0.155650	+	0.269595i
$794$	−18.1459	−	10.4765i	−0.643974	−	0.371798i
$795$	2.07129	−	1.19586i	0.0734610	−	0.0424128i
$796$	5.97122	−	3.44749i	0.211644	−	0.122193i
$797$	13.2242	+	7.63500i	0.468425	+	0.270446i	0.715580	−	0.698530i	$-0.246162\pi$
$797$	13.2242	+	7.63500i	0.468425	+	0.270446i	−0.247155	+	0.968976i	$0.579496\pi$
$798$	−0.435866	+	0.754942i	−0.0154295	+	0.0267247i
$799$	−42.8317	−	24.7289i	−1.51528	−	0.874845i
$800$		−	1.00000i		−	0.0353553i
$801$	−15.5233	+	8.96240i	−0.548490	+	0.316671i
$802$	8.90408	−	15.4223i	0.314414	−	0.544581i
$803$	−33.7864			−1.19230
$804$	−2.00337			−0.0706536
$805$	−1.08960	+	1.88725i	−0.0384034	+	0.0665167i
$806$			3.63238i			0.127945i
$807$	0.854900	+	1.48073i	0.0300939	+	0.0521242i
$808$			5.67653i			0.199700i
$809$	−27.1501	+	15.6751i	−0.954546	+	0.551108i	−0.894490	−	0.447087i	$-0.852461\pi$
$809$	−27.1501	+	15.6751i	−0.954546	+	0.551108i	−0.0600562	+	0.998195i	$0.519128\pi$
$810$	−3.27846	−	5.67845i	−0.115193	−	0.199521i
$811$	−5.96198	−	10.3265i	−0.209354	−	0.362611i	0.742158	−	0.670225i	$-0.233803\pi$
$811$	−5.96198	−	10.3265i	−0.209354	−	0.362611i	−0.951511	+	0.307615i	$0.900469\pi$
$812$	−0.263248	−	0.151986i	−0.00923818	−	0.00533367i
$813$	−12.0494			−0.422592
$814$	−9.16357	+	8.65653i	−0.321183	+	0.303411i
$815$	5.08320			0.178057
$816$	−3.59884	−	2.07779i	−0.125985	−	0.0727372i
$817$	−17.3522	−	30.0550i	−0.607078	−	1.05149i
$818$	−10.1997	−	17.6665i	−0.356625	−	0.617693i
$819$	0.895816	−	0.517200i	0.0313023	−	0.0180724i
$820$		−	0.701634i		−	0.0245021i
$821$	−8.94205	−	15.4881i	−0.312080	−	0.540538i	0.666733	−	0.745297i	$-0.267692\pi$
$821$	−8.94205	−	15.4881i	−0.312080	−	0.540538i	−0.978812	+	0.204759i	$0.934359\pi$
$822$		−	0.486465i		−	0.0169674i
$823$	−10.4526	+	18.1044i	−0.364355	+	0.631081i	−0.988672	−	0.150090i	$-0.952044\pi$
$823$	−10.4526	+	18.1044i	−0.364355	+	0.631081i	0.624318	+	0.781170i	$0.285377\pi$
$824$	14.2166			0.495259
$825$	1.09695			0.0381908
$826$	−1.14287	+	1.97951i	−0.0397656	+	0.0688760i
$827$	−42.1622	+	24.3423i	−1.46612	+	0.846466i	−0.999282	−	0.0378762i	$-0.987941\pi$
$827$	−42.1622	+	24.3423i	−1.46612	+	0.846466i	−0.466839	+	0.884342i	$0.654607\pi$
$828$			20.1651i			0.700787i
$829$	−15.8644	−	9.15930i	−0.550992	−	0.318116i	0.198530	−	0.980095i	$-0.436383\pi$
$829$	−15.8644	−	9.15930i	−0.550992	−	0.318116i	−0.749522	+	0.661979i	$0.769717\pi$
$830$	−6.41272	+	11.1071i	−0.222589	+	0.385535i
$831$	−6.24153	−	3.60355i	−0.216516	−	0.125006i
$832$	1.12057	−	0.646963i	0.0388489	−	0.0224294i
$833$	47.0058	−	27.1388i	1.62865	−	0.940304i
$834$	6.65066	+	3.83976i	0.230294	+	0.132960i
$835$	−1.22871	+	2.12819i	−0.0425213	+	0.0736490i
$836$	10.0561	+	5.80590i	0.347798	+	0.200801i
$837$			8.49923i			0.293776i
$838$	−29.4059	+	16.9775i	−1.01581	+	0.586478i
$839$	−2.84077	+	4.92036i	−0.0980743	+	0.169870i	−0.910888	−	0.412655i	$-0.864602\pi$
$839$	−2.84077	+	4.92036i	−0.0980743	+	0.169870i	0.812813	+	0.582524i	$0.197935\pi$
$840$	0.155580			0.00536802
$841$	27.9305			0.963120
$842$	1.94261	−	3.36470i	0.0669467	−	0.115955i
$843$		−	12.9379i		−	0.445606i
$844$	−6.55606	−	11.3554i	−0.225669	−	0.390870i
$845$		−	11.3258i		−	0.389618i
$846$	14.8385	−	8.56701i	0.510158	−	0.294540i
$847$	0.985420	+	1.70680i	0.0338594	+	0.0586463i
$848$	−2.25925	−	3.91314i	−0.0775830	−	0.134378i
$849$	5.97406	+	3.44913i	0.205029	+	0.118374i
$850$	−7.85084			−0.269282
$851$	43.2121	+	12.9066i	1.48129	+	0.442432i
$852$	5.56139			0.190530
$853$	3.35293	+	1.93582i	0.114802	+	0.0662811i	0.556302	−	0.830980i	$-0.312220\pi$
$853$	3.35293	+	1.93582i	0.114802	+	0.0662811i	−0.441499	+	0.897262i	$0.645553\pi$
$854$	0.995670	+	1.72455i	0.0340711	+	0.0590129i
$855$	7.61974	+	13.1978i	0.260590	+	0.451354i
$856$	4.25247	−	2.45517i	0.145346	−	0.0839158i
$857$		−	35.5171i		−	1.21324i	−0.794992	−	0.606620i	$-0.792525\pi$
$857$		−	35.5171i		−	1.21324i	0.794992	−	0.606620i	$-0.207475\pi$
$858$	0.709684	+	1.22921i	0.0242282	+	0.0419645i
$859$			21.1005i			0.719941i	0.932964	+	0.359970i	$0.117213\pi$
$859$			21.1005i			0.719941i	−0.932964	+	0.359970i	$0.882787\pi$
$860$	−3.09689	+	5.36397i	−0.105603	+	0.182910i
$861$	0.109160			0.00372017
$862$	−8.20306			−0.279397
$863$	−13.4887	+	23.3630i	−0.459159	+	0.795287i	−0.998917	−	0.0465333i	$-0.985183\pi$
$863$	−13.4887	+	23.3630i	−0.459159	+	0.795287i	0.539757	+	0.841821i	$0.318516\pi$
$864$	2.62198	−	1.51380i	0.0892015	−	0.0515005i
$865$			22.1502i			0.753128i
$866$	5.18767	+	2.99510i	0.176284	+	0.101778i
$867$	−11.8132	+	20.4611i	−0.401198	+	0.694894i
$868$	0.714579	+	0.412562i	0.0242544	+	0.0140033i
$869$	−15.8775	+	9.16688i	−0.538607	+	0.310965i
$870$	0.474070	−	0.273704i	0.0160725	−	0.00927944i
$871$	−4.24118	−	2.44865i	−0.143707	−	0.0829692i
$872$	5.75965	−	9.97600i	0.195046	−	0.337830i
$873$	−32.7142	−	18.8875i	−1.10721	−	0.639247i
$874$		−	41.5422i		−	1.40519i
$875$	0.254547	−	0.146963i	0.00860527	−	0.00496826i
$876$	4.31477	−	7.47340i	0.145783	−	0.252503i
$877$	34.2467			1.15643			0.578214	−	0.815885i	$-0.303750\pi$
$877$	34.2467			1.15643			0.578214	+	0.815885i	$0.303750\pi$
$878$	7.61008			0.256828
$879$	5.10436	−	8.84102i	0.172166	−	0.298200i
$880$		−	2.07238i		−	0.0698600i
$881$	25.7860	+	44.6627i	0.868752	+	1.50472i	0.863273	+	0.504738i	$0.168411\pi$
$881$	25.7860	+	44.6627i	0.868752	+	1.50472i	0.00547959	+	0.999985i	$0.498256\pi$
$882$			18.8038i			0.633157i
$883$	7.72184	−	4.45821i	0.259861	−	0.150031i	−0.364410	−	0.931238i	$-0.618729\pi$
$883$	7.72184	−	4.45821i	0.259861	−	0.150031i	0.624271	+	0.781208i	$0.285396\pi$
$884$	−5.07920	−	8.79744i	−0.170832	−	0.295890i
$885$	−2.05814	−	3.56480i	−0.0691836	−	0.119830i
$886$	−2.06821	−	1.19408i	−0.0694828	−	0.0401159i
$887$	0.0210689			0.000707423			0.000353712	−	1.00000i	$-0.499887\pi$
$887$	0.0210689			0.000707423			0.000353712		1.00000i	$0.499887\pi$
$888$	−0.744531	−	3.13244i	−0.0249848	−	0.105118i
$889$	0.188974			0.00633798
$890$	−5.70748	−	3.29521i	−0.191315	−	0.110456i
$891$	−6.79422	−	11.7679i	−0.227615	−	0.394241i
$892$	5.21742	+	9.03684i	0.174692	+	0.302576i
$893$	−30.5688	+	17.6489i	−1.02295	+	0.590598i
$894$		−	5.28609i		−	0.176793i
$895$	−1.66582	−	2.88529i	−0.0556823	−	0.0964445i
$896$		−	0.293926i		−	0.00981938i
$897$	2.53896	−	4.39760i	0.0847732	−	0.146832i
$898$	−20.3093			−0.677731
$899$	2.90320			0.0968272
$900$	1.35991	−	2.35544i	0.0453304	−	0.0785146i
$901$	−30.7214	+	17.7370i	−1.02348	+	0.590906i
$902$		−	1.45406i		−	0.0484147i
$903$	−0.834527	−	0.481814i	−0.0277713	−	0.0160338i
$904$	−5.27512	+	9.13677i	−0.175448	+	0.303884i
$905$	0.749490	+	0.432718i	0.0249139	+	0.0143840i
$906$	−8.57318	+	4.94973i	−0.284825	+	0.164444i
$907$	36.3626	−	20.9940i	1.20740	−	0.697093i	0.245210	−	0.969470i	$-0.421143\pi$
$907$	36.3626	−	20.9940i	1.20740	−	0.697093i	0.962191	+	0.272376i	$0.0878096\pi$
$908$	3.21149	+	1.85416i	0.106577	+	0.0615324i
$909$	−7.71958	+	13.3707i	−0.256042	+	0.443478i
$910$	0.329365	+	0.190159i	0.0109184	+	0.00630372i
$911$			57.8238i			1.91579i	0.287122	+	0.957894i	$0.407302\pi$
$911$			57.8238i			1.91579i	−0.287122	+	0.957894i	$0.592698\pi$
$912$	−2.56848	+	1.48291i	−0.0850507	+	0.0491041i
$913$	−13.2896	+	23.0183i	−0.439822	+	0.761793i
$914$	15.4417			0.510767
$915$	−3.58611			−0.118553
$916$	2.16173	−	3.74423i	0.0714257	−	0.123713i
$917$		−	3.93056i		−	0.129799i
$918$	−11.8846	−	20.5847i	−0.392250	−	0.679397i
$919$			48.5545i			1.60166i	0.598889	+	0.800832i	$0.295609\pi$
$919$			48.5545i			1.60166i	−0.598889	+	0.800832i	$0.704391\pi$
$920$	−6.42082	+	3.70706i	−0.211688	+	0.122218i
$921$	−2.97026	−	5.14464i	−0.0978733	−	0.169521i
$922$	8.36819	+	14.4941i	0.275592	+	0.477339i
$923$	11.7736	+	6.79748i	0.387532	+	0.223742i
$924$	0.322421			0.0106069
$925$	−4.17709	−	4.42176i	−0.137342	−	0.145386i
$926$	−32.0799			−1.05421
$927$	33.4863	+	19.3333i	1.09983	+	0.634990i
$928$	−0.517090	−	0.895626i	−0.0169743	−	0.0294004i
$929$	−7.16413	−	12.4086i	−0.235047	−	0.407114i	0.724239	−	0.689549i	$-0.242191\pi$
$929$	−7.16413	−	12.4086i	−0.235047	−	0.407114i	−0.959286	+	0.282435i	$0.908858\pi$
$930$	−1.28685	+	0.742963i	−0.0421974	+	0.0243627i
$931$		−	38.7377i		−	1.26958i
$932$	−8.81642	−	15.2705i	−0.288792	−	0.500202i
$933$			4.25304i			0.139238i
$934$	−1.57885	+	2.73464i	−0.0516614	+	0.0894802i
$935$	−16.2699			−0.532084
$936$	3.51925			0.115030
$937$	22.6527	−	39.2357i	0.740032	−	1.28177i	−0.212448	−	0.977172i	$-0.568144\pi$
$937$	22.6527	−	39.2357i	0.740032	−	1.28177i	0.952480	−	0.304601i	$-0.0985230\pi$
$938$	−0.963419	+	0.556230i	−0.0314567	+	0.0181616i
$939$			2.36289i			0.0771099i
$940$	5.45568	+	3.14984i	0.177945	+	0.102736i
$941$	29.4606	−	51.0273i	0.960389	−	1.66344i	0.238865	−	0.971053i	$-0.423225\pi$
$941$	29.4606	−	51.0273i	0.960389	−	1.66344i	0.721524	−	0.692389i	$-0.243442\pi$
$942$	−10.1359	−	5.85199i	−0.330247	−	0.190668i
$943$	−4.50507	+	2.60100i	−0.146705	+	0.0847003i
$944$	−6.73473	+	3.88830i	−0.219197	+	0.126553i
$945$	0.770667	+	0.444945i	0.0250698	+	0.0144741i
$946$	−6.41795	+	11.1162i	−0.208665	+	0.361419i
$947$	−42.6958	−	24.6504i	−1.38743	−	0.801032i	−0.394403	−	0.918938i	$-0.629049\pi$
$947$	−42.6958	−	24.6504i	−1.38743	−	0.801032i	−0.993025	+	0.117906i	$0.962382\pi$
$948$		−	4.68271i		−	0.152087i
$949$	18.2689	−	10.5475i	0.593033	−	0.342388i
$950$	−2.80156	+	4.85244i	−0.0908945	+	0.157434i
$951$	0.844199			0.0273750
$952$	−2.30757			−0.0747886
$953$	−20.1558	+	34.9109i	−0.652910	+	1.13087i	0.329503	+	0.944154i	$0.393119\pi$
$953$	−20.1558	+	34.9109i	−0.652910	+	1.13087i	−0.982413	+	0.186719i	$0.940215\pi$
$954$		−	12.2895i		−	0.397888i
$955$	−10.6914	−	18.5180i	−0.345964	−	0.599228i
$956$		−	16.7522i		−	0.541806i
$957$	0.982454	−	0.567220i	0.0317582	−	0.0183356i
$958$	4.47509	+	7.75108i	0.144583	+	0.250426i
$959$	−0.135065	−	0.233940i	−0.00436149	−	0.00755432i
$960$	0.458402	+	0.264658i	0.0147948	+	0.00854181i
$961$	23.1193			0.745785
$962$	2.25248	−	7.54145i	0.0726227	−	0.243146i
$963$	13.3552			0.430366
$964$	17.7379	+	10.2410i	0.571300	+	0.329840i
$965$	0.866885	+	1.50149i	0.0279060	+	0.0483346i
$966$	−0.576745	−	0.998951i	−0.0185565	−	0.0321407i
$967$	10.4073	−	6.00868i	0.334678	−	0.193226i	−0.323238	−	0.946318i	$-0.604772\pi$
$967$	10.4073	−	6.00868i	0.334678	−	0.193226i	0.657916	+	0.753091i	$0.271438\pi$
$968$			6.70523i			0.215514i
$969$	11.6421	+	20.1647i	0.373998	+	0.647783i
$970$		−	13.8888i		−	0.445943i
$971$	21.2413	−	36.7911i	0.681667	−	1.18068i	−0.292805	−	0.956172i	$-0.594589\pi$
$971$	21.2413	−	36.7911i	0.681667	−	1.18068i	0.974472	−	0.224509i	$-0.0720779\pi$
$972$	12.5535			0.402653
$973$	4.26439			0.136710
$974$	−1.11971	+	1.93940i	−0.0358780	+	0.0621424i
$975$	−0.593138	+	0.342448i	−0.0189956	+	0.0109671i
$976$			6.77497i			0.216862i
$977$	−9.63104	−	5.56048i	−0.308124	−	0.177896i	0.337963	−	0.941160i	$-0.390262\pi$
$977$	−9.63104	−	5.56048i	−0.308124	−	0.177896i	−0.646087	+	0.763264i	$0.723596\pi$
$978$	−1.34531	+	2.33015i	−0.0430183	+	0.0745098i
$979$	−11.8281	−	6.82895i	−0.378027	−	0.218254i
$980$	−5.98736	+	3.45680i	−0.191259	+	0.110424i
$981$	27.1330	−	15.6652i	0.866289	−	0.500152i
$982$	−1.06035	−	0.612194i	−0.0338371	−	0.0195359i
$983$	4.62076	−	8.00339i	0.147379	−	0.255269i	−0.782879	−	0.622174i	$-0.786250\pi$
$983$	4.62076	−	8.00339i	0.147379	−	0.255269i	0.930258	+	0.366906i	$0.119583\pi$
$984$	0.321630	+	0.185693i	0.0102532	+	0.00591969i
$985$		−	4.04772i		−	0.128971i
$986$	−7.03141	+	4.05959i	−0.223926	+	0.129284i
$987$	−0.490052	+	0.848795i	−0.0155985	+	0.0270174i
$988$	−7.25001			−0.230654
$989$	45.9215			1.46022
$990$	2.81826	−	4.88137i	0.0895701	−	0.155140i
$991$			19.3657i			0.615173i	0.951520	+	0.307586i	$0.0995213\pi$
$991$			19.3657i			0.615173i	−0.951520	+	0.307586i	$0.900479\pi$
$992$	1.40363	+	2.43115i	0.0445652	+	0.0771892i
$993$		−	11.1085i		−	0.352518i
$994$	2.67446	−	1.54410i	0.0848289	−	0.0489760i
$995$	3.44749	+	5.97122i	0.109293	+	0.189301i
$996$	−3.39436	−	5.87920i	−0.107554	−	0.186290i
$997$	−39.6963	−	22.9187i	−1.25720	−	0.725842i	−0.284667	−	0.958626i	$-0.591883\pi$
$997$	−39.6963	−	22.9187i	−1.25720	−	0.725842i	−0.972528	+	0.232784i	$0.925217\pi$
$998$	29.5336			0.934871
$999$	5.27046	−	17.6459i	0.166750	−	0.558291i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	370.2.l.c.101.2	yes	12
37.11	even	6	inner	370.2.l.c.11.2	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
370.2.l.c.11.2	✓	12	37.11	even	6	inner
370.2.l.c.101.2	yes	12	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 370 = 2 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	370.l (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.264658 + 0.458402i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.866025 + 0.500000i) q^{5} -0.529317i q^{6} +(-0.146963 - 0.254547i) q^{7} -1.00000i q^{8} +(1.35991 - 2.35544i) q^{9} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.264658 + 0.458402i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.866025 + 0.500000i) q^{5} -0.529317i q^{6} +(-0.146963 - 0.254547i) q^{7} -1.00000i q^{8} +(1.35991 - 2.35544i) q^{9} +1.00000 q^{10} +2.07238 q^{11} +(-0.264658 + 0.458402i) q^{12} +(-1.12057 + 0.646963i) q^{13} +0.293926i q^{14} +(-0.458402 - 0.264658i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(6.79903 + 3.92542i) q^{17} +(-2.35544 + 1.35991i) q^{18} +(4.85244 - 2.80156i) q^{19} +(-0.866025 - 0.500000i) q^{20} +(0.0777900 - 0.134736i) q^{21} +(-1.79474 - 1.03619i) q^{22} +7.41413i q^{23} +(0.458402 - 0.264658i) q^{24} +(0.500000 - 0.866025i) q^{25} +1.29393 q^{26} +3.02760 q^{27} +(0.146963 - 0.254547i) q^{28} -1.03418i q^{29} +(0.264658 + 0.458402i) q^{30} +2.80725i q^{31} +(0.866025 - 0.500000i) q^{32} +(0.548473 + 0.949984i) q^{33} +(-3.92542 - 6.79903i) q^{34} +(0.254547 + 0.146963i) q^{35} +2.71982 q^{36} +(1.74081 - 5.82834i) q^{37} -5.60311 q^{38} +(-0.593138 - 0.342448i) q^{39} +(0.500000 + 0.866025i) q^{40} +(0.350817 + 0.607633i) q^{41} +(-0.134736 + 0.0777900i) q^{42} -6.19378i q^{43} +(1.03619 + 1.79474i) q^{44} +2.71982i q^{45} +(3.70706 - 6.42082i) q^{46} -6.29968 q^{47} -0.529317 q^{48} +(3.45680 - 5.98736i) q^{49} +(-0.866025 + 0.500000i) q^{50} +4.15558i q^{51} +(-1.12057 - 0.646963i) q^{52} +(-2.25925 + 3.91314i) q^{53} +(-2.62198 - 1.51380i) q^{54} +(-1.79474 + 1.03619i) q^{55} +(-0.254547 + 0.146963i) q^{56} +(2.56848 + 1.48291i) q^{57} +(-0.517090 + 0.895626i) q^{58} +(6.73473 + 3.88830i) q^{59} -0.529317i q^{60} +(5.86730 - 3.38749i) q^{61} +(1.40363 - 2.43115i) q^{62} -0.799427 q^{63} -1.00000 q^{64} +(0.646963 - 1.12057i) q^{65} -1.09695i q^{66} +(1.89242 + 3.27776i) q^{67} +7.85084i q^{68} +(-3.39865 + 1.96221i) q^{69} +(-0.146963 - 0.254547i) q^{70} +(-5.25337 - 9.09911i) q^{71} +(-2.35544 - 1.35991i) q^{72} -16.3032 q^{73} +(-4.42176 + 4.17709i) q^{74} +0.529317 q^{75} +(4.85244 + 2.80156i) q^{76} +(-0.304564 - 0.527520i) q^{77} +(0.342448 + 0.593138i) q^{78} +(-7.66147 + 4.42335i) q^{79} -1.00000i q^{80} +(-3.27846 - 5.67845i) q^{81} -0.701634i q^{82} +(-6.41272 + 11.1071i) q^{83} +0.155580 q^{84} -7.85084 q^{85} +(-3.09689 + 5.36397i) q^{86} +(0.474070 - 0.273704i) q^{87} -2.07238i q^{88} +(-5.70748 - 3.29521i) q^{89} +(1.35991 - 2.35544i) q^{90} +(0.329365 + 0.190159i) q^{91} +(-6.42082 + 3.70706i) q^{92} +(-1.28685 + 0.742963i) q^{93} +(5.45568 + 3.14984i) q^{94} +(-2.80156 + 4.85244i) q^{95} +(0.458402 + 0.264658i) q^{96} -13.8888i q^{97} +(-5.98736 + 3.45680i) q^{98} +(2.81826 - 4.88137i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 4 q^{3} + 6 q^{4} + 2 q^{7} - 2 q^{9}+O(q^{10}) \) 12 * q + 4 * q^3 + 6 * q^4 + 2 * q^7 - 2 * q^9	\( 12 q + 4 q^{3} + 6 q^{4} + 2 q^{7} - 2 q^{9} + 12 q^{10} - 16 q^{11} - 4 q^{12} + 6 q^{13} - 6 q^{16} - 6 q^{17} + 18 q^{19} - 14 q^{21} + 6 q^{22} + 6 q^{25} + 8 q^{26} - 32 q^{27} - 2 q^{28} + 4 q^{30} - 10 q^{33} - 10 q^{34} - 6 q^{35} - 4 q^{36} - 26 q^{37} + 8 q^{38} + 18 q^{39} + 6 q^{40} + 4 q^{41} + 18 q^{42} - 8 q^{44} - 4 q^{46} - 20 q^{47} - 8 q^{48} + 2 q^{49} + 6 q^{52} - 2 q^{53} + 6 q^{55} + 6 q^{56} + 36 q^{57} + 8 q^{58} + 12 q^{59} + 24 q^{61} + 10 q^{62} - 16 q^{63} - 12 q^{64} + 4 q^{65} + 28 q^{67} - 6 q^{69} + 2 q^{70} - 40 q^{71} - 12 q^{73} + 14 q^{74} + 8 q^{75} + 18 q^{76} - 24 q^{77} - 10 q^{78} + 24 q^{79} - 6 q^{81} - 16 q^{83} - 28 q^{84} - 20 q^{85} - 16 q^{86} - 24 q^{87} + 6 q^{89} - 2 q^{90} - 18 q^{91} + 6 q^{92} + 78 q^{93} + 4 q^{95} - 12 q^{98} + 22 q^{99}+O(q^{100}) \) 12 * q + 4 * q^3 + 6 * q^4 + 2 * q^7 - 2 * q^9 + 12 * q^10 - 16 * q^11 - 4 * q^12 + 6 * q^13 - 6 * q^16 - 6 * q^17 + 18 * q^19 - 14 * q^21 + 6 * q^22 + 6 * q^25 + 8 * q^26 - 32 * q^27 - 2 * q^28 + 4 * q^30 - 10 * q^33 - 10 * q^34 - 6 * q^35 - 4 * q^36 - 26 * q^37 + 8 * q^38 + 18 * q^39 + 6 * q^40 + 4 * q^41 + 18 * q^42 - 8 * q^44 - 4 * q^46 - 20 * q^47 - 8 * q^48 + 2 * q^49 + 6 * q^52 - 2 * q^53 + 6 * q^55 + 6 * q^56 + 36 * q^57 + 8 * q^58 + 12 * q^59 + 24 * q^61 + 10 * q^62 - 16 * q^63 - 12 * q^64 + 4 * q^65 + 28 * q^67 - 6 * q^69 + 2 * q^70 - 40 * q^71 - 12 * q^73 + 14 * q^74 + 8 * q^75 + 18 * q^76 - 24 * q^77 - 10 * q^78 + 24 * q^79 - 6 * q^81 - 16 * q^83 - 28 * q^84 - 20 * q^85 - 16 * q^86 - 24 * q^87 + 6 * q^89 - 2 * q^90 - 18 * q^91 + 6 * q^92 + 78 * q^93 + 4 * q^95 - 12 * q^98 + 22 * q^99

Introduction

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