LMFDB - Embedded newform 546.2.z.b.131.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(131,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 5, 0]))

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

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

chi := DirichletCharacter("546.131");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.z (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:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			131.8
Character	$\chi$	$=$	546.131
Dual form			546.2.z.b.521.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(1.62906 + 0.588348i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-1.04730 + 1.81398i) q^{5} +(-1.11664 - 1.32406i) q^{6} +(1.84957 - 1.89185i) q^{7} -1.00000i q^{8} +(2.30769 + 1.91691i) q^{9} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(1.62906 + 0.588348i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-1.04730 + 1.81398i) q^{5} +(-1.11664 - 1.32406i) q^{6} +(1.84957 - 1.89185i) q^{7} -1.00000i q^{8} +(2.30769 + 1.91691i) q^{9} +(1.81398 - 1.04730i) q^{10} +(1.67306 - 0.965940i) q^{11} +(0.305007 + 1.70498i) q^{12} -1.00000i q^{13} +(-2.54770 + 0.713604i) q^{14} +(-2.77337 + 2.33891i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-0.345960 - 0.599220i) q^{17} +(-1.04007 - 2.81394i) q^{18} +(2.08687 + 1.20485i) q^{19} -2.09460 q^{20} +(4.12613 - 1.99375i) q^{21} -1.93188 q^{22} +(3.14870 + 1.81790i) q^{23} +(0.588348 - 1.62906i) q^{24} +(0.306322 + 0.530566i) q^{25} +(-0.500000 + 0.866025i) q^{26} +(2.63157 + 4.48050i) q^{27} +(2.56317 + 0.655850i) q^{28} +3.88157i q^{29} +(3.57126 - 0.638869i) q^{30} +(0.817770 - 0.472140i) q^{31} +(0.866025 - 0.500000i) q^{32} +(3.29383 - 0.589238i) q^{33} +0.691920i q^{34} +(1.49472 + 5.33641i) q^{35} +(-0.506247 + 2.95698i) q^{36} +(-3.57753 + 6.19647i) q^{37} +(-1.20485 - 2.08687i) q^{38} +(0.588348 - 1.62906i) q^{39} +(1.81398 + 1.04730i) q^{40} -8.66067 q^{41} +(-4.57021 - 0.336428i) q^{42} +8.01907 q^{43} +(1.67306 + 0.965940i) q^{44} +(-5.89408 + 2.17852i) q^{45} +(-1.81790 - 3.14870i) q^{46} +(2.19759 - 3.80633i) q^{47} +(-1.32406 + 1.11664i) q^{48} +(-0.158181 - 6.99821i) q^{49} -0.612645i q^{50} +(-0.211041 - 1.17971i) q^{51} +(0.866025 - 0.500000i) q^{52} +(-4.81192 + 2.77816i) q^{53} +(-0.0387561 - 5.19601i) q^{54} +4.04652i q^{55} +(-1.89185 - 1.84957i) q^{56} +(2.69076 + 3.19058i) q^{57} +(1.94079 - 3.36154i) q^{58} +(-5.21237 - 9.02810i) q^{59} +(-3.41224 - 1.23235i) q^{60} +(2.92469 + 1.68857i) q^{61} -0.944280 q^{62} +(7.89475 - 0.820344i) q^{63} -1.00000 q^{64} +(1.81398 + 1.04730i) q^{65} +(-3.14716 - 1.13662i) q^{66} +(-4.98074 - 8.62689i) q^{67} +(0.345960 - 0.599220i) q^{68} +(4.05987 + 4.81401i) q^{69} +(1.37375 - 5.36883i) q^{70} -3.58456i q^{71} +(1.91691 - 2.30769i) q^{72} +(7.46660 - 4.31085i) q^{73} +(6.19647 - 3.57753i) q^{74} +(0.186861 + 1.04455i) q^{75} +2.40970i q^{76} +(1.26702 - 4.95175i) q^{77} +(-1.32406 + 1.11664i) q^{78} +(-8.33482 + 14.4363i) q^{79} +(-1.04730 - 1.81398i) q^{80} +(1.65090 + 8.84729i) q^{81} +(7.50036 + 4.33034i) q^{82} +12.5850 q^{83} +(3.78970 + 2.57646i) q^{84} +1.44930 q^{85} +(-6.94472 - 4.00954i) q^{86} +(-2.28372 + 6.32333i) q^{87} +(-0.965940 - 1.67306i) q^{88} +(7.45988 - 12.9209i) q^{89} +(6.19369 + 1.06039i) q^{90} +(-1.89185 - 1.84957i) q^{91} +3.63581i q^{92} +(1.60998 - 0.288012i) q^{93} +(-3.80633 + 2.19759i) q^{94} +(-4.37115 + 2.52369i) q^{95} +(1.70498 - 0.305007i) q^{96} -2.33951i q^{97} +(-3.36212 + 6.13972i) q^{98} +(5.71253 + 0.978010i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 16 q^{4} + 2 q^{7} + 2 q^{9}+O(q^{10}) $ 32 * q + 16 * q^4 + 2 * q^7 + 2 * q^9	$ 32 q + 16 q^{4} + 2 q^{7} + 2 q^{9} + 6 q^{10} + 24 q^{11} - 4 q^{14} - 12 q^{15} - 16 q^{16} - 4 q^{17} - 24 q^{18} + 4 q^{21} - 12 q^{22} - 6 q^{24} - 18 q^{25} - 16 q^{26} + 6 q^{27} - 2 q^{28} - 8 q^{30} - 6 q^{31} + 14 q^{33} - 48 q^{35} + 4 q^{36} - 16 q^{38} - 6 q^{39} + 6 q^{40} - 16 q^{41} + 14 q^{42} + 32 q^{43} + 24 q^{44} + 20 q^{45} + 16 q^{46} - 20 q^{47} - 26 q^{49} - 46 q^{51} + 60 q^{53} + 6 q^{54} - 8 q^{56} - 8 q^{57} - 10 q^{58} - 8 q^{59} - 6 q^{60} + 36 q^{61} - 36 q^{62} + 84 q^{63} - 32 q^{64} + 6 q^{65} + 36 q^{66} + 4 q^{68} + 36 q^{69} - 18 q^{70} - 24 q^{72} - 48 q^{73} + 84 q^{74} - 2 q^{75} - 52 q^{77} + 18 q^{79} - 74 q^{81} - 24 q^{83} + 8 q^{84} - 32 q^{85} + 24 q^{86} + 14 q^{87} - 6 q^{88} + 20 q^{89} + 6 q^{90} - 8 q^{91} - 40 q^{93} + 72 q^{95} - 6 q^{96} - 32 q^{98}+O(q^{100}) $ 32 * q + 16 * q^4 + 2 * q^7 + 2 * q^9 + 6 * q^10 + 24 * q^11 - 4 * q^14 - 12 * q^15 - 16 * q^16 - 4 * q^17 - 24 * q^18 + 4 * q^21 - 12 * q^22 - 6 * q^24 - 18 * q^25 - 16 * q^26 + 6 * q^27 - 2 * q^28 - 8 * q^30 - 6 * q^31 + 14 * q^33 - 48 * q^35 + 4 * q^36 - 16 * q^38 - 6 * q^39 + 6 * q^40 - 16 * q^41 + 14 * q^42 + 32 * q^43 + 24 * q^44 + 20 * q^45 + 16 * q^46 - 20 * q^47 - 26 * q^49 - 46 * q^51 + 60 * q^53 + 6 * q^54 - 8 * q^56 - 8 * q^57 - 10 * q^58 - 8 * q^59 - 6 * q^60 + 36 * q^61 - 36 * q^62 + 84 * q^63 - 32 * q^64 + 6 * q^65 + 36 * q^66 + 4 * q^68 + 36 * q^69 - 18 * q^70 - 24 * q^72 - 48 * q^73 + 84 * q^74 - 2 * q^75 - 52 * q^77 + 18 * q^79 - 74 * q^81 - 24 * q^83 + 8 * q^84 - 32 * q^85 + 24 * q^86 + 14 * q^87 - 6 * q^88 + 20 * q^89 + 6 * q^90 - 8 * q^91 - 40 * q^93 + 72 * q^95 - 6 * q^96 - 32 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$3$	1.62906	+	0.588348i	0.940540	+	0.339683i
$3$	1.62906	+	0.588348i	0.940540	+	0.339683i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	−1.04730	+	1.81398i	−0.468367	+	0.811236i	−0.999346	−	0.0361491i	$-0.988491\pi$
$5$	−1.04730	+	1.81398i	−0.468367	+	0.811236i	0.530979	+	0.847385i	$0.321824\pi$
$6$	−1.11664	−	1.32406i	−0.455865	−	0.540544i
$7$	1.84957	−	1.89185i	0.699072	−	0.715052i
$7$	1.84957	−	1.89185i	0.699072	−	0.715052i
$8$		−	1.00000i		−	0.353553i
$9$	2.30769	+	1.91691i	0.769231	+	0.638971i
$10$	1.81398	−	1.04730i	0.573630	−	0.331186i
$11$	1.67306	−	0.965940i	0.504446	−	0.291242i	−0.226102	−	0.974104i	$-0.572598\pi$
$11$	1.67306	−	0.965940i	0.504446	−	0.291242i	0.730548	+	0.682862i	$0.239265\pi$
$12$	0.305007	+	1.70498i	0.0880480	+	0.492186i
$13$		−	1.00000i		−	0.277350i
$13$		−	1.00000i		−	0.277350i
$14$	−2.54770	+	0.713604i	−0.680901	+	0.190719i
$15$	−2.77337	+	2.33891i	−0.716081	+	0.603903i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−0.345960	−	0.599220i	−0.0839076	−	0.145332i	0.821018	−	0.570903i	$-0.193407\pi$
$17$	−0.345960	−	0.599220i	−0.0839076	−	0.145332i	−0.904925	+	0.425571i	$0.860073\pi$
$18$	−1.04007	−	2.81394i	−0.245146	−	0.663252i
$19$	2.08687	+	1.20485i	0.478760	+	0.276412i	0.719900	−	0.694078i	$-0.244188\pi$
$19$	2.08687	+	1.20485i	0.478760	+	0.276412i	−0.241140	+	0.970490i	$0.577521\pi$
$20$	−2.09460			−0.468367
$21$	4.12613	−	1.99375i	0.900396	−	0.435072i
$22$	−1.93188			−0.411878
$23$	3.14870	+	1.81790i	0.656550	+	0.379059i	0.790961	−	0.611866i	$-0.209581\pi$
$23$	3.14870	+	1.81790i	0.656550	+	0.379059i	−0.134411	+	0.990926i	$0.542914\pi$
$24$	0.588348	−	1.62906i	0.120096	−	0.332531i
$25$	0.306322	+	0.530566i	0.0612645	+	0.106113i
$26$	−0.500000	+	0.866025i	−0.0980581	+	0.169842i
$27$	2.63157	+	4.48050i	0.506445	+	0.862272i
$28$	2.56317	+	0.655850i	0.484394	+	0.123944i
$29$			3.88157i			0.720790i	0.932800	+	0.360395i	$0.117358\pi$
$29$			3.88157i			0.720790i	−0.932800	+	0.360395i	$0.882642\pi$
$30$	3.57126	−	0.638869i	0.652020	−	0.116641i
$31$	0.817770	−	0.472140i	0.146876	−	0.0847988i	−0.424761	−	0.905305i	$-0.639642\pi$
$31$	0.817770	−	0.472140i	0.146876	−	0.0847988i	0.571637	+	0.820507i	$0.306309\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$	3.29383	−	0.589238i	0.573381	−	0.102573i
$34$			0.691920i			0.118663i
$35$	1.49472	+	5.33641i	0.252653	+	0.902019i
$36$	−0.506247	+	2.95698i	−0.0843746	+	0.492830i
$37$	−3.57753	+	6.19647i	−0.588142	+	1.01869i	0.406333	+	0.913725i	$0.366807\pi$
$37$	−3.57753	+	6.19647i	−0.588142	+	1.01869i	−0.994476	+	0.104968i	$0.966526\pi$
$38$	−1.20485	−	2.08687i	−0.195453	−	0.338534i
$39$	0.588348	−	1.62906i	0.0942111	−	0.260859i
$40$	1.81398	+	1.04730i	0.286815	+	0.165593i
$41$	−8.66067			−1.35257			−0.676285	−	0.736640i	$-0.736411\pi$
$41$	−8.66067			−1.35257			−0.676285	+	0.736640i	$0.736411\pi$
$42$	−4.57021	−	0.336428i	−0.705199	−	0.0519119i
$43$	8.01907			1.22290			0.611449	−	0.791284i	$-0.290587\pi$
$43$	8.01907			1.22290			0.611449	+	0.791284i	$0.290587\pi$
$44$	1.67306	+	0.965940i	0.252223	+	0.145621i
$45$	−5.89408	+	2.17852i	−0.878638	+	0.324755i
$46$	−1.81790	−	3.14870i	−0.268035	−	0.464251i
$47$	2.19759	−	3.80633i	0.320551	−	0.555210i	−0.660051	−	0.751221i	$-0.729465\pi$
$47$	2.19759	−	3.80633i	0.320551	−	0.555210i	0.980602	+	0.196010i	$0.0627987\pi$
$48$	−1.32406	+	1.11664i	−0.191111	+	0.161173i
$49$	−0.158181	−	6.99821i	−0.0225973	−	0.999745i
$50$		−	0.612645i		−	0.0866410i
$51$	−0.211041	−	1.17971i	−0.0295516	−	0.165193i
$52$	0.866025	−	0.500000i	0.120096	−	0.0693375i
$53$	−4.81192	+	2.77816i	−0.660968	+	0.381610i	−0.792646	−	0.609683i	$-0.791297\pi$
$53$	−4.81192	+	2.77816i	−0.660968	+	0.381610i	0.131678	+	0.991293i	$0.457964\pi$
$54$	−0.0387561	−	5.19601i	−0.00527404	−	0.707087i
$55$			4.04652i			0.545633i
$56$	−1.89185	−	1.84957i	−0.252809	−	0.247159i
$57$	2.69076	+	3.19058i	0.356400	+	0.422603i
$58$	1.94079	−	3.36154i	0.254838	−	0.441392i
$59$	−5.21237	−	9.02810i	−0.678593	−	1.17536i	−0.975405	−	0.220422i	$-0.929257\pi$
$59$	−5.21237	−	9.02810i	−0.678593	−	1.17536i	0.296811	−	0.954936i	$-0.404077\pi$
$60$	−3.41224	−	1.23235i	−0.440518	−	0.159096i
$61$	2.92469	+	1.68857i	0.374469	+	0.216200i	0.675409	−	0.737443i	$-0.263967\pi$
$61$	2.92469	+	1.68857i	0.374469	+	0.216200i	−0.300940	+	0.953643i	$0.597300\pi$
$62$	−0.944280			−0.119924
$63$	7.89475	−	0.820344i	0.994645	−	0.103354i
$64$	−1.00000			−0.125000
$65$	1.81398	+	1.04730i	0.224996	+	0.129902i
$66$	−3.14716	−	1.13662i	−0.387388	−	0.139908i
$67$	−4.98074	−	8.62689i	−0.608494	−	1.05394i	−0.991489	−	0.130192i	$-0.958441\pi$
$67$	−4.98074	−	8.62689i	−0.608494	−	1.05394i	0.382995	−	0.923751i	$-0.374893\pi$
$68$	0.345960	−	0.599220i	0.0419538	−	0.0726661i
$69$	4.05987	+	4.81401i	0.488752	+	0.579539i
$70$	1.37375	−	5.36883i	0.164194	−	0.641698i
$71$		−	3.58456i		−	0.425409i	−0.977117	−	0.212705i	$-0.931773\pi$
$71$		−	3.58456i		−	0.425409i	0.977117	−	0.212705i	$-0.0682272\pi$
$72$	1.91691	−	2.30769i	0.225910	−	0.271964i
$73$	7.46660	−	4.31085i	0.873900	−	0.504546i	0.00525772	−	0.999986i	$-0.498326\pi$
$73$	7.46660	−	4.31085i	0.873900	−	0.504546i	0.868642	+	0.495440i	$0.164993\pi$
$74$	6.19647	−	3.57753i	0.720324	−	0.415880i
$75$	0.186861	+	1.04455i	0.0215769	+	0.120614i
$76$			2.40970i			0.276412i
$77$	1.26702	−	4.95175i	0.144391	−	0.564304i
$78$	−1.32406	+	1.11664i	−0.149920	+	0.126434i
$79$	−8.33482	+	14.4363i	−0.937741	+	1.62421i	−0.168069	+	0.985775i	$0.553753\pi$
$79$	−8.33482	+	14.4363i	−0.937741	+	1.62421i	−0.769672	+	0.638439i	$0.779580\pi$
$80$	−1.04730	−	1.81398i	−0.117092	−	0.202809i
$81$	1.65090	+	8.84729i	0.183433	+	0.983032i
$82$	7.50036	+	4.33034i	0.828277	+	0.478206i
$83$	12.5850			1.38138			0.690691	−	0.723150i	$-0.257306\pi$
$83$	12.5850			1.38138			0.690691	+	0.723150i	$0.257306\pi$
$84$	3.78970	+	2.57646i	0.413491	+	0.281115i
$85$	1.44930			0.157198
$86$	−6.94472	−	4.00954i	−0.748868	−	0.432359i
$87$	−2.28372	+	6.32333i	−0.244840	+	0.677932i
$88$	−0.965940	−	1.67306i	−0.102970	−	0.178349i
$89$	7.45988	−	12.9209i	0.790746	−	1.36961i	−0.134760	−	0.990878i	$-0.543026\pi$
$89$	7.45988	−	12.9209i	0.790746	−	1.36961i	0.925506	−	0.378734i	$-0.123640\pi$
$90$	6.19369	+	1.06039i	0.652872	+	0.111775i
$91$	−1.89185	−	1.84957i	−0.198320	−	0.193888i
$92$			3.63581i			0.379059i
$93$	1.60998	−	0.288012i	0.166947	−	0.0298655i
$94$	−3.80633	+	2.19759i	−0.392593	+	0.226664i
$95$	−4.37115	+	2.52369i	−0.448471	+	0.258925i
$96$	1.70498	−	0.305007i	0.174014	−	0.0311297i
$97$		−	2.33951i		−	0.237541i	−0.992922	−	0.118770i	$-0.962105\pi$
$97$		−	2.33951i		−	0.237541i	0.992922	−	0.118770i	$-0.0378952\pi$
$98$	−3.36212	+	6.13972i	−0.339625	+	0.620205i
$99$	5.71253	+	0.978010i	0.574131	+	0.0982937i
$100$	−0.306322	+	0.530566i	−0.0306322	+	0.0530566i
$101$	−7.51343	−	13.0136i	−0.747615	−	1.29491i	−0.948963	−	0.315387i	$-0.897866\pi$
$101$	−7.51343	−	13.0136i	−0.747615	−	1.29491i	0.201349	−	0.979520i	$-0.435468\pi$
$102$	−0.407090	+	1.12718i	−0.0403079	+	0.111608i
$103$	−16.1762	−	9.33933i	−1.59389	−	0.920231i	−0.992631	−	0.121174i	$-0.961334\pi$
$103$	−16.1762	−	9.33933i	−1.59389	−	0.920231i	−0.601256	−	0.799057i	$-0.705333\pi$
$104$	−1.00000			−0.0980581
$105$	−0.704682	+	9.57277i	−0.0687699	+	0.934206i
$106$	5.55632			0.539678
$107$	−1.30018	−	0.750662i	−0.125694	−	0.0725692i	0.435835	−	0.900027i	$-0.356453\pi$
$107$	−1.30018	−	0.750662i	−0.125694	−	0.0725692i	−0.561528	+	0.827457i	$0.689786\pi$
$108$	−2.56444	+	4.51925i	−0.246763	+	0.434865i
$109$	−1.87726	−	3.25151i	−0.179809	−	0.311438i	0.762006	−	0.647570i	$-0.224215\pi$
$109$	−1.87726	−	3.25151i	−0.179809	−	0.311438i	−0.941815	+	0.336132i	$0.890881\pi$
$110$	2.02326	−	3.50439i	0.192910	−	0.334130i
$111$	−9.47370	+	7.98960i	−0.899204	+	0.758339i
$112$	0.713604	+	2.54770i	0.0674292	+	0.240735i
$113$		−	8.66137i		−	0.814793i	−0.913251	−	0.407396i	$-0.866437\pi$
$113$		−	8.66137i		−	0.814793i	0.913251	−	0.407396i	$-0.133563\pi$
$114$	−0.734978	−	4.10851i	−0.0688370	−	0.384797i
$115$	−6.59528	+	3.80778i	−0.615013	+	0.355078i
$116$	−3.36154	+	1.94079i	−0.312111	+	0.180197i
$117$	1.91691	−	2.30769i	0.177219	−	0.213346i
$118$			10.4247i			0.959676i
$119$	−1.77351	−	0.453796i	−0.162578	−	0.0415994i
$120$	2.33891	+	2.77337i	0.213512	+	0.253173i
$121$	−3.63392	+	6.29413i	−0.330356	+	0.572194i
$122$	−1.68857	−	2.92469i	−0.152876	−	0.264789i
$123$	−14.1088	−	5.09549i	−1.27215	−	0.459445i
$124$	0.817770	+	0.472140i	0.0734379	+	0.0423994i
$125$	−11.7563			−1.05151
$126$	−7.24722	−	3.23693i	−0.645634	−	0.288369i
$127$	−2.17602			−0.193091			−0.0965454	−	0.995329i	$-0.530779\pi$
$127$	−2.17602			−0.193091			−0.0965454	+	0.995329i	$0.530779\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$	13.0636	+	4.71800i	1.15018	+	0.415397i
$130$	−1.04730	−	1.81398i	−0.0918544	−	0.159096i
$131$	−3.27646	+	5.67499i	−0.286265	+	0.495826i	−0.972915	−	0.231162i	$-0.925747\pi$
$131$	−3.27646	+	5.67499i	−0.286265	+	0.495826i	0.686650	+	0.726988i	$0.259081\pi$
$132$	2.15721	+	2.55792i	0.187761	+	0.222638i
$133$	6.13920	−	1.71957i	0.532336	−	0.149106i
$134$			9.96148i			0.860541i
$135$	−10.8836	+	0.0811787i	−0.936708	+	0.00698675i
$136$	−0.599220	+	0.345960i	−0.0513827	+	0.0296658i
$137$	−12.3253	+	7.11601i	−1.05302	+	0.607962i	−0.923494	−	0.383614i	$-0.874679\pi$
$137$	−12.3253	+	7.11601i	−1.05302	+	0.607962i	−0.129527	+	0.991576i	$0.541346\pi$
$138$	−1.10895	−	6.19899i	−0.0944000	−	0.527693i
$139$			8.44011i			0.715881i	0.933744	+	0.357940i	$0.116521\pi$
$139$			8.44011i			0.715881i	−0.933744	+	0.357940i	$0.883479\pi$
$140$	−3.87411	+	3.96267i	−0.327422	+	0.334907i
$141$	5.81945	−	4.90781i	0.490086	−	0.413312i
$142$	−1.79228	+	3.10432i	−0.150405	+	0.260509i
$143$	−0.965940	−	1.67306i	−0.0807760	−	0.139908i
$144$	−2.81394	+	1.04007i	−0.234495	+	0.0866721i
$145$	−7.04109	−	4.06517i	−0.584731	−	0.337594i
$146$	−8.62169			−0.713536
$147$	3.85970	−	11.4936i	0.318342	−	0.947976i
$148$	−7.15506			−0.588142
$149$	0.0334409	+	0.0193071i	0.00273959	+	0.00158170i	0.501369	−	0.865233i	$-0.332830\pi$
$149$	0.0334409	+	0.0193071i	0.00273959	+	0.00158170i	−0.498630	+	0.866815i	$0.666163\pi$
$150$	0.360448	−	0.998037i	0.0294305	−	0.0814894i
$151$	−10.4122	−	18.0344i	−0.847329	−	1.46762i	−0.883583	−	0.468274i	$-0.844876\pi$
$151$	−10.4122	−	18.0344i	−0.847329	−	1.46762i	0.0362546	−	0.999343i	$-0.488457\pi$
$152$	1.20485	−	2.08687i	0.0977264	−	0.169267i
$153$	0.350283	−	2.04599i	0.0283187	−	0.165409i
$154$	−3.57315	+	3.65483i	−0.287933	+	0.294514i
$155$			1.97789i			0.158868i
$156$	1.70498	−	0.305007i	0.136508	−	0.0244201i
$157$	3.98152	−	2.29873i	0.317760	−	0.183459i	−0.332634	−	0.943056i	$-0.607937\pi$
$157$	3.98152	−	2.29873i	0.317760	−	0.183459i	0.650394	+	0.759597i	$0.274604\pi$
$158$	14.4363	−	8.33482i	1.14849	−	0.663083i
$159$	−9.47344	+	1.69472i	−0.751293	+	0.134400i
$160$			2.09460i			0.165593i
$161$	9.26294	−	2.59453i	0.730022	−	0.204477i
$162$	2.99392	−	8.48743i	0.235225	−	0.666835i
$163$	−9.93799	+	17.2131i	−0.778404	+	1.34823i	0.154458	+	0.987999i	$0.450637\pi$
$163$	−9.93799	+	17.2131i	−0.778404	+	1.34823i	−0.932862	+	0.360235i	$0.882696\pi$
$164$	−4.33034	−	7.50036i	−0.338143	−	0.585680i
$165$	−2.38076	+	6.59204i	−0.185342	+	0.513189i
$166$	−10.8989	−	6.29250i	−0.845921	−	0.488393i
$167$	−5.36254			−0.414965			−0.207483	−	0.978239i	$-0.566527\pi$
$167$	−5.36254			−0.414965			−0.207483	+	0.978239i	$0.566527\pi$
$168$	−1.99375	−	4.12613i	−0.153821	−	0.318338i
$169$	−1.00000			−0.0769231
$170$	−1.25513	−	0.724648i	−0.0962639	−	0.0555780i
$171$	2.50625	+	6.78077i	0.191658	+	0.518538i
$172$	4.00954	+	6.94472i	0.305724	+	0.529530i
$173$	−0.0694333	+	0.120262i	−0.00527892	+	0.00914335i	−0.868653	−	0.495421i	$-0.835014\pi$
$173$	−0.0694333	+	0.120262i	−0.00527892	+	0.00914335i	0.863374	+	0.504565i	$0.168347\pi$
$174$	5.13942	−	4.33430i	0.389618	−	0.328583i
$175$	1.57031	+	0.401803i	0.118705	+	0.0303735i
$176$			1.93188i			0.145621i
$177$	−3.17962	−	17.7740i	−0.238995	−	1.33598i
$178$	−12.9209	+	7.45988i	−0.968462	+	0.559142i
$179$	12.4682	−	7.19850i	0.931914	−	0.538041i	0.0444976	−	0.999009i	$-0.485831\pi$
$179$	12.4682	−	7.19850i	0.931914	−	0.538041i	0.887416	+	0.460969i	$0.152498\pi$
$180$	−4.83370	−	4.01517i	−0.360283	−	0.299273i
$181$		−	9.27914i		−	0.689713i	−0.938655	−	0.344856i	$-0.887928\pi$
$181$		−	9.27914i		−	0.689713i	0.938655	−	0.344856i	$-0.112072\pi$
$182$	0.713604	+	2.54770i	0.0528958	+	0.188848i
$183$	3.77104	+	4.47153i	0.278764	+	0.330545i
$184$	1.81790	−	3.14870i	0.134018	−	0.232125i
$185$	−7.49350	−	12.9791i	−0.550933	−	0.954244i
$186$	−1.53829	−	0.555565i	−0.112793	−	0.0407360i
$187$	−1.15762	−	0.668353i	−0.0846537	−	0.0488748i
$188$	4.39517			0.320551
$189$	13.3437	+	3.30847i	0.970611	+	0.240655i
$190$	5.04737			0.366175
$191$	−2.93538	−	1.69474i	−0.212397	−	0.122627i	0.390028	−	0.920803i	$-0.372465\pi$
$191$	−2.93538	−	1.69474i	−0.212397	−	0.122627i	−0.602425	+	0.798176i	$0.705799\pi$
$192$	−1.62906	−	0.588348i	−0.117568	−	0.0424603i
$193$	−6.28558	−	10.8869i	−0.452446	−	0.783659i	0.546091	−	0.837726i	$-0.316115\pi$
$193$	−6.28558	−	10.8869i	−0.452446	−	0.783659i	−0.998537	+	0.0540663i	$0.982782\pi$
$194$	−1.16975	+	2.02607i	−0.0839833	+	0.145463i
$195$	2.33891	+	2.77337i	0.167493	+	0.198605i
$196$	5.98154	−	3.63610i	0.427253	−	0.259721i
$197$			12.0271i			0.856894i	0.903567	+	0.428447i	$0.140939\pi$
$197$			12.0271i			0.856894i	−0.903567	+	0.428447i	$0.859061\pi$
$198$	−4.45819	−	3.70324i	−0.316830	−	0.263178i
$199$	−13.0591	+	7.53965i	−0.925732	+	0.534472i	−0.885459	−	0.464717i	$-0.846156\pi$
$199$	−13.0591	+	7.53965i	−0.925732	+	0.534472i	−0.0402727	+	0.999189i	$0.512823\pi$
$200$	0.530566	−	0.306322i	0.0375167	−	0.0216603i
$201$	−3.03832	−	16.9842i	−0.214307	−	1.19797i
$202$			15.0269i			1.05729i
$203$	7.34335	+	7.17924i	0.515402	+	0.503884i
$204$	0.916141	−	0.772623i	0.0641427	−	0.0540944i
$205$	9.07033	−	15.7103i	0.633499	−	1.09725i
$206$	9.33933	+	16.1762i	0.650702	+	1.12705i
$207$	3.78148	+	10.2309i	0.262831	+	0.711100i
$208$	0.866025	+	0.500000i	0.0600481	+	0.0346688i
$209$	4.65526			0.322011
$210$	5.39666	−	7.93792i	0.372405	−	0.547768i
$211$	11.0298			0.759324			0.379662	−	0.925125i	$-0.376040\pi$
$211$	11.0298			0.759324			0.379662	+	0.925125i	$0.376040\pi$
$212$	−4.81192	−	2.77816i	−0.330484	−	0.190805i
$213$	2.10897	−	5.83948i	0.144504	−	0.400114i
$214$	0.750662	+	1.30018i	0.0513142	+	0.0888788i
$215$	−8.39838	+	14.5464i	−0.572765	+	0.992058i
$216$	4.48050	−	2.63157i	0.304859	−	0.179056i
$217$	0.619306	−	2.42035i	0.0420412	−	0.164304i
$218$			3.75452i			0.254288i
$219$	14.6998	−	2.62968i	0.993324	−	0.177697i
$220$	−3.50439	+	2.02326i	−0.236266	+	0.136408i
$221$	−0.599220	+	0.345960i	−0.0403079	+	0.0232718i
$222$	12.1993	−	2.18235i	0.818761	−	0.146470i
$223$		−	14.2894i		−	0.956889i	−0.878118	−	0.478444i	$-0.841201\pi$
$223$		−	14.2894i		−	0.956889i	0.878118	−	0.478444i	$-0.158799\pi$
$224$	0.655850	−	2.56317i	0.0438209	−	0.171259i
$225$	−0.310150	+	1.81158i	−0.0206767	+	0.120772i
$226$	−4.33068	+	7.50096i	−0.288073	+	0.498957i
$227$	10.4107	+	18.0319i	0.690983	+	1.19682i	0.971516	+	0.236973i	$0.0761553\pi$
$227$	10.4107	+	18.0319i	0.690983	+	1.19682i	−0.280534	+	0.959844i	$0.590511\pi$
$228$	−1.41774	+	3.92556i	−0.0938924	+	0.259977i
$229$	−0.284143	−	0.164050i	−0.0187767	−	0.0108407i	0.490582	−	0.871395i	$-0.336784\pi$
$229$	−0.284143	−	0.164050i	−0.0187767	−	0.0108407i	−0.509359	+	0.860554i	$0.670117\pi$
$230$	7.61557			0.502156
$231$	4.97741	−	7.32126i	0.327490	−	0.481703i
$232$	3.88157			0.254838
$233$	7.80411	+	4.50571i	0.511264	+	0.295179i	0.733353	−	0.679848i	$-0.237954\pi$
$233$	7.80411	+	4.50571i	0.511264	+	0.295179i	−0.222089	+	0.975026i	$0.571287\pi$
$234$	−2.81394	+	1.04007i	−0.183953	+	0.0679912i
$235$	4.60307	+	7.97275i	0.300271	+	0.520085i
$236$	5.21237	−	9.02810i	0.339297	−	0.587679i
$237$	−22.0715	+	18.6139i	−1.43370	+	1.20910i
$238$	1.30901	+	1.27975i	0.0848504	+	0.0829542i
$239$			28.2160i			1.82514i	0.408922	+	0.912569i	$0.365905\pi$
$239$			28.2160i			1.82514i	−0.408922	+	0.912569i	$0.634095\pi$
$240$	−0.638869	−	3.57126i	−0.0412388	−	0.230524i
$241$	9.92924	−	5.73265i	0.639599	−	0.369272i	−0.144861	−	0.989452i	$-0.546274\pi$
$241$	9.92924	−	5.73265i	0.639599	−	0.369272i	0.784460	+	0.620180i	$0.212940\pi$
$242$	6.29413	−	3.63392i	0.404602	−	0.233597i
$243$	−2.51586	+	15.3841i	−0.161393	+	0.986890i
$244$			3.37715i			0.216200i
$245$	12.8603	+	7.04230i	0.821612	+	0.449916i
$246$	9.67082	+	11.4672i	0.616589	+	0.731123i
$247$	1.20485	−	2.08687i	0.0766629	−	0.132784i
$248$	−0.472140	−	0.817770i	−0.0299809	−	0.0519285i
$249$	20.5018	+	7.40436i	1.29925	+	0.469232i
$250$	10.1812	+	5.87813i	0.643917	+	0.371765i
$251$	−25.7601			−1.62596			−0.812982	−	0.582289i	$-0.802157\pi$
$251$	−25.7601			−1.62596			−0.812982	+	0.582289i	$0.802157\pi$
$252$	4.65781	+	6.42688i	0.293415	+	0.404855i
$253$	7.02395			0.441592
$254$	1.88449	+	1.08801i	0.118244	+	0.0682679i
$255$	2.36100	+	0.852691i	0.147851	+	0.0533976i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	6.89377	−	11.9404i	0.430021	−	0.744819i	−0.566853	−	0.823819i	$-0.691839\pi$
$257$	6.89377	−	11.9404i	0.430021	−	0.744819i	0.996875	+	0.0789999i	$0.0251727\pi$
$258$	−8.95439	−	10.6177i	−0.557476	−	0.661029i
$259$	5.10588	+	18.2289i	0.317264	+	1.13269i
$260$			2.09460i			0.129902i
$261$	−7.44063	+	8.95748i	−0.460564	+	0.554454i
$262$	5.67499	−	3.27646i	0.350602	−	0.202420i
$263$	18.5720	−	10.7225i	1.14520	−	0.661180i	0.197484	−	0.980306i	$-0.436723\pi$
$263$	18.5720	−	10.7225i	1.14520	−	0.661180i	0.947712	+	0.319126i	$0.103389\pi$
$264$	−0.589238	−	3.29383i	−0.0362651	−	0.202721i
$265$		−	11.6383i		−	0.714934i
$266$	−6.17649	−	1.58041i	−0.378705	−	0.0969009i
$267$	19.7546	−	16.6599i	1.20896	−	1.01957i
$268$	4.98074	−	8.62689i	0.304247	−	0.526971i
$269$	−4.76794	−	8.25831i	−0.290706	−	0.503518i	0.683271	−	0.730165i	$-0.260557\pi$
$269$	−4.76794	−	8.25831i	−0.290706	−	0.503518i	−0.973977	+	0.226647i	$0.927224\pi$
$270$	9.46603	+	5.37148i	0.576084	+	0.326898i
$271$	−22.0755	−	12.7453i	−1.34099	−	0.774221i	−0.354038	−	0.935231i	$-0.615192\pi$
$271$	−22.0755	−	12.7453i	−1.34099	−	0.774221i	−0.986953	+	0.161010i	$0.948525\pi$
$272$	0.691920			0.0419538
$273$	−1.99375	−	4.12613i	−0.120667	−	0.249725i
$274$	14.2320			0.859788
$275$	1.02499	+	0.591778i	0.0618092	+	0.0356856i
$276$	−2.13912	+	5.92296i	−0.128760	+	0.356520i
$277$	9.72968	+	16.8523i	0.584600	+	1.01256i	0.994925	+	0.100618i	$0.0320819\pi$
$277$	9.72968	+	16.8523i	0.584600	+	1.01256i	−0.410325	+	0.911939i	$0.634585\pi$
$278$	4.22006	−	7.30935i	0.253102	−	0.438386i
$279$	2.79221	+	0.478039i	0.167165	+	0.0286195i
$280$	5.33641	−	1.49472i	0.318912	−	0.0893263i
$281$		−	8.66815i		−	0.517099i	−0.965998	−	0.258549i	$-0.916756\pi$
$281$		−	8.66815i		−	0.517099i	0.965998	−	0.258549i	$-0.0832445\pi$
$282$	−7.49370	+	1.34056i	−0.446243	+	0.0798292i
$283$	19.9498	−	11.5180i	1.18589	−	0.684676i	0.228523	−	0.973539i	$-0.426610\pi$
$283$	19.9498	−	11.5180i	1.18589	−	0.684676i	0.957371	+	0.288862i	$0.0932770\pi$
$284$	3.10432	−	1.79228i	0.184208	−	0.106352i
$285$	−8.60569	+	1.53949i	−0.509757	+	0.0911913i
$286$			1.93188i			0.114235i
$287$	−16.0185	+	16.3847i	−0.945544	+	0.967157i
$288$	2.95698	+	0.506247i	0.174242	+	0.0298309i
$289$	8.26062	−	14.3078i	0.485919	−	0.841636i
$290$	4.06517	+	7.04109i	0.238715	+	0.413467i
$291$	1.37644	−	3.81120i	0.0806885	−	0.223417i
$292$	7.46660	+	4.31085i	0.436950	+	0.252273i
$293$	−18.2447			−1.06587			−0.532934	−	0.846157i	$-0.678911\pi$
$293$	−18.2447			−1.06587			−0.532934	+	0.846157i	$0.678911\pi$
$294$	−9.08939	+	8.02390i	−0.530104	+	0.467963i
$295$	21.8357			1.27132
$296$	6.19647	+	3.57753i	0.360162	+	0.207940i
$297$	8.73066	+	4.95419i	0.506604	+	0.287471i
$298$	−0.0193071	−	0.0334409i	−0.00111843	−	0.00193718i
$299$	1.81790	−	3.14870i	0.105132	−	0.182094i
$300$	−0.811176	+	0.684101i	−0.0468333	+	0.0394966i
$301$	14.8318	−	15.1709i	0.854893	−	0.874434i
$302$			20.8243i			1.19830i
$303$	−4.58331	−	25.6206i	−0.263304	−	1.47186i
$304$	−2.08687	+	1.20485i	−0.119690	+	0.0691030i
$305$	−6.12607	+	3.53689i	−0.350778	+	0.202522i
$306$	−1.32635	+	1.59674i	−0.0758224	+	0.0912795i
$307$			21.8510i			1.24710i	0.781783	+	0.623551i	$0.214311\pi$
$307$			21.8510i			1.24710i	−0.781783	+	0.623551i	$0.785689\pi$
$308$	4.92185	−	1.37860i	0.280448	−	0.0785529i
$309$	−20.8573	−	24.7316i	−1.18653	−	1.40693i
$310$	0.988945	−	1.71290i	0.0561683	−	0.0972863i
$311$	−1.41409	−	2.44927i	−0.0801856	−	0.138885i	0.823144	−	0.567833i	$-0.192218\pi$
$311$	−1.41409	−	2.44927i	−0.0801856	−	0.138885i	−0.903330	+	0.428947i	$0.858885\pi$
$312$	−1.62906	−	0.588348i	−0.0922275	−	0.0333086i
$313$	−8.58082	−	4.95414i	−0.485017	−	0.280025i	0.237488	−	0.971390i	$-0.423676\pi$
$313$	−8.58082	−	4.95414i	−0.485017	−	0.280025i	−0.722505	+	0.691366i	$0.757009\pi$
$314$	−4.59746			−0.259450
$315$	−6.78009	+	15.1800i	−0.382015	+	0.855299i
$316$	−16.6696			−0.937741
$317$	15.2159	+	8.78492i	0.854612	+	0.493410i	0.862204	−	0.506561i	$-0.169083\pi$
$317$	15.2159	+	8.78492i	0.854612	+	0.493410i	−0.00759227	+	0.999971i	$0.502417\pi$
$318$	9.05160	+	3.26905i	0.507589	+	0.183319i
$319$	3.74937	+	6.49410i	0.209924	+	0.363600i
$320$	1.04730	−	1.81398i	0.0585459	−	0.101404i
$321$	−1.67643	−	1.98784i	−0.0935693	−	0.110950i
$322$	−9.31921	−	2.38455i	−0.519339	−	0.132886i
$323$		−	1.66732i		−	0.0927723i
$324$	−6.83653	+	5.85337i	−0.379807	+	0.325187i
$325$	0.530566	−	0.306322i	0.0294305	−	0.0169917i
$326$	17.2131	−	9.93799i	0.953346	−	0.550414i
$327$	−1.14516	−	6.40140i	−0.0633273	−	0.353998i
$328$			8.66067i			0.478206i
$329$	−3.13641	−	11.1976i	−0.172916	−	0.617342i
$330$	5.35782	−	4.51849i	0.294938	−	0.248735i
$331$	7.70234	−	13.3408i	0.423359	−	0.733279i	−0.572907	−	0.819621i	$-0.694184\pi$
$331$	7.70234	−	13.3408i	0.423359	−	0.733279i	0.996266	+	0.0863414i	$0.0275176\pi$
$332$	6.29250	+	10.8989i	0.345346	+	0.598156i
$333$	−20.1339	+	7.44173i	−1.10333	+	0.407804i
$334$	4.64409	+	2.68127i	0.254113	+	0.146712i
$335$	20.8653			1.13999
$336$	−0.336428	+	4.57021i	−0.0183536	+	0.249325i
$337$	14.4566			0.787501			0.393750	−	0.919217i	$-0.371177\pi$
$337$	14.4566			0.787501			0.393750	+	0.919217i	$0.371177\pi$
$338$	0.866025	+	0.500000i	0.0471056	+	0.0271964i
$339$	5.09590	−	14.1099i	0.276771	−	0.766345i
$340$	0.724648	+	1.25513i	0.0392996	+	0.0680689i
$341$	0.912118	−	1.57983i	0.0493939	−	0.0855528i
$342$	1.21991	−	7.12544i	0.0659650	−	0.385300i
$343$	−13.5321	−	12.6444i	−0.730666	−	0.682735i
$344$		−	8.01907i		−	0.432359i
$345$	−12.9844	+	2.32280i	−0.699058	+	0.125056i
$346$	0.120262	−	0.0694333i	0.00646533	−	0.00373276i
$347$	10.8790	−	6.28099i	0.584015	−	0.337181i	−0.178712	−	0.983901i	$-0.557193\pi$
$347$	10.8790	−	6.28099i	0.584015	−	0.337181i	0.762727	+	0.646720i	$0.223860\pi$
$348$	−6.61802	+	1.18391i	−0.354763	+	0.0634642i
$349$		−	17.7010i		−	0.947514i	−0.880656	−	0.473757i	$-0.842897\pi$
$349$		−	17.7010i		−	0.947514i	0.880656	−	0.473757i	$-0.157103\pi$
$350$	−1.15903	−	1.13313i	−0.0619528	−	0.0605683i
$351$	4.48050	−	2.63157i	0.239151	−	0.140463i
$352$	0.965940	−	1.67306i	0.0514848	−	0.0891743i
$353$	−0.222657	−	0.385653i	−0.0118508	−	0.0205263i	0.860039	−	0.510228i	$-0.170439\pi$
$353$	−0.222657	−	0.385653i	−0.0118508	−	0.0205263i	−0.871890	+	0.489702i	$0.837106\pi$
$354$	−6.13338	+	16.9826i	−0.325985	+	0.902613i
$355$	6.50231	+	3.75411i	0.345107	+	0.199248i
$356$	14.9198			0.790746
$357$	−2.62217	−	1.78270i	−0.138780	−	0.0943507i
$358$	−14.3970			−0.760905
$359$	17.9004	+	10.3348i	0.944745	+	0.545449i	0.891445	−	0.453130i	$-0.149692\pi$
$359$	17.9004	+	10.3348i	0.944745	+	0.545449i	0.0533007	+	0.998579i	$0.483026\pi$
$360$	2.17852	+	5.89408i	0.114818	+	0.310646i
$361$	−6.59666	−	11.4258i	−0.347193	−	0.601355i
$362$	−4.63957	+	8.03597i	−0.243850	+	0.422361i
$363$	−9.62302	+	8.11553i	−0.505078	+	0.425955i
$364$	0.655850	−	2.56317i	0.0343759	−	0.134347i
$365$			18.0590i			0.945252i
$366$	−1.03005	−	5.75798i	−0.0538418	−	0.300974i
$367$	−17.2106	+	9.93654i	−0.898385	+	0.518683i	−0.876676	−	0.481081i	$-0.840244\pi$
$367$	−17.2106	+	9.93654i	−0.898385	+	0.518683i	−0.0217093	+	0.999764i	$0.506911\pi$
$368$	−3.14870	+	1.81790i	−0.164137	+	0.0947648i
$369$	−19.9862	−	16.6017i	−1.04044	−	0.864252i
$370$			14.9870i			0.779137i
$371$	−3.64412	+	14.2418i	−0.189193	+	0.739399i
$372$	1.05442	+	1.25028i	0.0546690	+	0.0648239i
$373$	7.64212	−	13.2365i	0.395694	−	0.685362i	−0.597496	−	0.801872i	$-0.703838\pi$
$373$	7.64212	−	13.2365i	0.395694	−	0.685362i	0.993189	+	0.116510i	$0.0371708\pi$
$374$	0.668353	+	1.15762i	0.0345597	+	0.0598592i
$375$	−19.1517	−	6.91677i	−0.988989	−	0.357180i
$376$	−3.80633	−	2.19759i	−0.196297	−	0.113332i
$377$	3.88157			0.199911
$378$	−9.90174	−	9.53706i	−0.509291	−	0.490533i
$379$	−23.8814			−1.22670			−0.613352	−	0.789810i	$-0.710179\pi$
$379$	−23.8814			−1.22670			−0.613352	+	0.789810i	$0.710179\pi$
$380$	−4.37115	−	2.52369i	−0.224235	−	0.129462i
$381$	−3.54488	−	1.28026i	−0.181610	−	0.0655896i
$382$	1.69474	+	2.93538i	0.0867106	+	0.150187i
$383$	−18.7955	+	32.5547i	−0.960404	+	1.66347i	−0.238916	+	0.971040i	$0.576792\pi$
$383$	−18.7955	+	32.5547i	−0.960404	+	1.66347i	−0.721488	+	0.692427i	$0.756541\pi$
$384$	1.11664	+	1.32406i	0.0569831	+	0.0675679i
$385$	7.65540	+	7.48432i	0.390155	+	0.381436i
$386$			12.5712i			0.639855i
$387$	18.5056	+	15.3719i	0.940691	+	0.781395i
$388$	2.02607	−	1.16975i	0.102858	−	0.0593852i
$389$	25.5296	−	14.7395i	1.29440	−	0.747322i	0.314969	−	0.949102i	$-0.398006\pi$
$389$	25.5296	−	14.7395i	1.29440	−	0.747322i	0.979431	+	0.201780i	$0.0646725\pi$
$390$	−0.638869	−	3.57126i	−0.0323504	−	0.180838i
$391$		−	2.51569i		−	0.127224i
$392$	−6.99821	+	0.158181i	−0.353463	+	0.00798935i
$393$	−8.67642	+	7.31722i	−0.437668	+	0.369105i
$394$	6.01354	−	10.4158i	0.302958	−	0.524739i
$395$	−17.4581	−	30.2384i	−0.878414	−	1.52146i
$396$	2.00928	+	5.43620i	0.100970	+	0.273179i
$397$	16.3264	+	9.42604i	0.819398	+	0.473079i	0.850209	−	0.526446i	$-0.176476\pi$
$397$	16.3264	+	9.42604i	0.819398	+	0.473079i	−0.0308110	+	0.999525i	$0.509809\pi$
$398$	15.0793			0.755857
$399$	11.0129	+	0.810691i	0.551332	+	0.0405853i
$400$	−0.612645			−0.0306322
$401$	9.99593	+	5.77115i	0.499173	+	0.288198i	0.728372	−	0.685182i	$-0.240277\pi$
$401$	9.99593	+	5.77115i	0.499173	+	0.288198i	−0.229199	+	0.973380i	$0.573611\pi$
$402$	−5.86081	+	16.2279i	−0.292311	+	0.809373i
$403$	−0.472140	−	0.817770i	−0.0235190	−	0.0407360i
$404$	7.51343	−	13.0136i	0.373807	−	0.647453i
$405$	−17.7778	−	6.27108i	−0.883385	−	0.311612i
$406$	−2.76991	−	9.88908i	−0.137468	−	0.490787i
$407$			13.8227i			0.685167i
$408$	−1.17971	+	0.211041i	−0.0584045	+	0.0104481i
$409$	−20.8221	+	12.0217i	−1.02959	+	0.594433i	−0.916867	−	0.399194i	$-0.869290\pi$
$409$	−20.8221	+	12.0217i	−1.02959	+	0.594433i	−0.112721	+	0.993627i	$0.535957\pi$
$410$	−15.7103	+	9.07033i	−0.775875	+	0.447952i
$411$	−24.2654	+	4.34087i	−1.19692	+	0.214119i
$412$		−	18.6787i		−	0.920231i
$413$	−26.7204	−	6.83707i	−1.31483	−	0.336430i
$414$	1.84062	−	10.7510i	0.0904615	−	0.528383i
$415$	−13.1803	+	22.8289i	−0.646994	+	1.12063i
$416$	−0.500000	−	0.866025i	−0.0245145	−	0.0424604i
$417$	−4.96572	+	13.7495i	−0.243172	+	0.673315i
$418$	−4.03158	−	2.32763i	−0.197191	−	0.113848i
$419$	3.63647			0.177653			0.0888267	−	0.996047i	$-0.471688\pi$
$419$	3.63647			0.177653			0.0888267	+	0.996047i	$0.471688\pi$
$420$	−8.64260	+	4.17611i	−0.421716	+	0.203773i
$421$	−0.0321368			−0.00156625			−0.000783127	−	1.00000i	$-0.500249\pi$
$421$	−0.0321368			−0.00156625			−0.000783127		1.00000i	$0.500249\pi$
$422$	−9.55210	−	5.51491i	−0.464989	−	0.268461i
$423$	12.3678	−	4.57127i	0.601341	−	0.222263i
$424$	2.77816	+	4.81192i	0.134919	+	0.233687i
$425$	0.211951	−	0.367109i	0.0102811	−	0.0178074i
$426$	−4.74616	+	4.00265i	−0.229952	+	0.193929i
$427$	8.60395	−	2.40994i	0.416374	−	0.116625i
$428$		−	1.50132i		−	0.0725692i
$429$	−0.589238	−	3.29383i	−0.0284487	−	0.159027i
$430$	14.5464	−	8.39838i	0.701491	−	0.405006i
$431$	14.3401	−	8.27924i	0.690737	−	0.398797i	−0.113151	−	0.993578i	$-0.536094\pi$
$431$	14.3401	−	8.27924i	0.690737	−	0.398797i	0.803888	+	0.594781i	$0.202761\pi$
$432$	−5.19601	+	0.0387561i	−0.249993	+	0.00186466i
$433$			23.5650i			1.13246i	0.824247	+	0.566231i	$0.191599\pi$
$433$			23.5650i			1.13246i	−0.824247	+	0.566231i	$0.808401\pi$
$434$	−1.74651	+	1.78643i	−0.0838352	+	0.0857516i
$435$	−9.07864	−	10.7650i	−0.435288	−	0.516144i
$436$	1.87726	−	3.25151i	0.0899045	−	0.155719i
$437$	4.38061	+	7.58744i	0.209553	+	0.362957i
$438$	−14.0453	−	5.07255i	−0.671110	−	0.242376i
$439$	−1.10437	−	0.637611i	−0.0527089	−	0.0304315i	0.473414	−	0.880840i	$-0.343021\pi$
$439$	−1.10437	−	0.637611i	−0.0527089	−	0.0304315i	−0.526123	+	0.850409i	$0.676355\pi$
$440$	4.04652			0.192910
$441$	13.0499	−	16.4529i	0.621425	−	0.783474i
$442$	0.691920			0.0329113
$443$	5.80498	+	3.35151i	0.275803	+	0.159235i	0.631522	−	0.775358i	$-0.282431\pi$
$443$	5.80498	+	3.35151i	0.275803	+	0.159235i	−0.355719	+	0.934593i	$0.615764\pi$
$444$	−11.6560	−	4.20967i	−0.553172	−	0.199782i
$445$	15.6255	+	27.0641i	0.740719	+	1.28296i
$446$	−7.14470	+	12.3750i	−0.338311	+	0.585972i
$447$	0.0431181	+	0.0511275i	0.00203942	+	0.00241825i
$448$	−1.84957	+	1.89185i	−0.0873840	+	0.0893814i
$449$			11.4423i			0.539997i	0.962861	+	0.269998i	$0.0870232\pi$
$449$			11.4423i			0.539997i	−0.962861	+	0.269998i	$0.912977\pi$
$450$	1.17439	−	1.41380i	0.0553611	−	0.0666470i
$451$	−14.4898	+	8.36569i	−0.682298	+	0.393925i
$452$	7.50096	−	4.33068i	0.352816	−	0.203698i
$453$	−6.35157	−	35.5051i	−0.298423	−	1.66818i
$454$		−	20.8214i		−	0.977197i
$455$	5.33641	−	1.49472i	0.250175	−	0.0700733i
$456$	3.19058	−	2.69076i	0.149413	−	0.126007i
$457$	−15.9902	+	27.6958i	−0.747989	+	1.29556i	0.200796	+	0.979633i	$0.435647\pi$
$457$	−15.9902	+	27.6958i	−0.747989	+	1.29556i	−0.948785	+	0.315922i	$0.897686\pi$
$458$	0.164050	+	0.284143i	0.00766554	+	0.0132771i
$459$	1.77439	−	3.12696i	0.0828213	−	0.145954i
$460$	−6.59528	−	3.80778i	−0.307506	−	0.177539i
$461$	7.66318			0.356910			0.178455	−	0.983948i	$-0.442890\pi$
$461$	7.66318			0.356910			0.178455	+	0.983948i	$0.442890\pi$
$462$	−7.97119	+	3.85169i	−0.370853	+	0.179197i
$463$	−33.6757			−1.56504			−0.782522	−	0.622623i	$-0.786067\pi$
$463$	−33.6757			−1.56504			−0.782522	+	0.622623i	$0.786067\pi$
$464$	−3.36154	−	1.94079i	−0.156056	−	0.0900987i
$465$	−1.16369	+	3.22211i	−0.0539647	+	0.149422i
$466$	−4.50571	−	7.80411i	−0.208723	−	0.361519i
$467$	−9.89478	+	17.1383i	−0.457876	+	0.793064i	−0.998848	−	0.0479760i	$-0.984723\pi$
$467$	−9.89478	+	17.1383i	−0.457876	+	0.793064i	0.540973	+	0.841040i	$0.318056\pi$
$468$	2.95698	+	0.506247i	0.136686	+	0.0234013i
$469$	−25.5330	−	6.53324i	−1.17900	−	0.301677i
$470$		−	9.20613i		−	0.424647i
$471$	7.83860	−	1.40226i	0.361184	−	0.0646127i
$472$	−9.02810	+	5.21237i	−0.415552	+	0.239919i
$473$	13.4164	−	7.74595i	0.616885	−	0.356159i
$474$	28.4215	−	5.08436i	1.30544	−	0.233533i
$475$			1.47629i			0.0677370i
$476$	−0.493757	−	1.76280i	−0.0226313	−	0.0807980i
$477$	−16.4299	−	2.81287i	−0.752275	−	0.128793i
$478$	14.1080	−	24.4357i	0.645284	−	1.11766i
$479$	−10.3981	−	18.0101i	−0.475102	−	0.822900i	0.524492	−	0.851416i	$-0.324255\pi$
$479$	−10.3981	−	18.0101i	−0.475102	−	0.822900i	−0.999593	+	0.0285153i	$0.990922\pi$
$480$	−1.23235	+	3.41224i	−0.0562490	+	0.155747i
$481$	6.19647	+	3.57753i	0.282534	+	0.163121i
$482$	−11.4653			−0.522230
$483$	16.6164	+	1.22319i	0.756073	+	0.0556569i
$484$	−7.26784			−0.330356
$485$	4.24381	+	2.45017i	0.192702	+	0.111256i
$486$	9.87085	−	12.0651i	0.447751	−	0.547283i
$487$	2.80203	+	4.85326i	0.126972	+	0.219922i	0.922502	−	0.385992i	$-0.126141\pi$
$487$	2.80203	+	4.85326i	0.126972	+	0.219922i	−0.795530	+	0.605914i	$0.792807\pi$
$488$	1.68857	−	2.92469i	0.0764381	−	0.132395i
$489$	−26.3169	+	22.1942i	−1.19009	+	1.00366i
$490$	−7.61617	−	12.5289i	−0.344063	−	0.566000i
$491$		−	19.4106i		−	0.875989i	−0.898978	−	0.437994i	$-0.855689\pi$
$491$		−	19.4106i		−	0.875989i	0.898978	−	0.437994i	$-0.144311\pi$
$492$	−2.64157	−	14.7663i	−0.119091	−	0.665717i
$493$	2.32592	−	1.34287i	0.104754	−	0.0604798i
$494$	−2.08687	+	1.20485i	−0.0938925	+	0.0542089i
$495$	−7.75682	+	9.33813i	−0.348643	+	0.419718i
$496$			0.944280i			0.0423994i
$497$	−6.78145	−	6.62990i	−0.304189	−	0.297391i
$498$	−14.0529	−	16.6632i	−0.629724	−	0.746698i
$499$	−12.1481	+	21.0412i	−0.543825	+	0.941932i	0.454855	+	0.890565i	$0.349691\pi$
$499$	−12.1481	+	21.0412i	−0.543825	+	0.941932i	−0.998680	+	0.0513667i	$0.983642\pi$
$500$	−5.87813	−	10.1812i	−0.262878	−	0.455318i
$501$	−8.73591	−	3.15504i	−0.390292	−	0.140957i
$502$	22.3089	+	12.8801i	0.995695	+	0.574865i
$503$	7.56087			0.337123			0.168561	−	0.985691i	$-0.446088\pi$
$503$	7.56087			0.337123			0.168561	+	0.985691i	$0.446088\pi$
$504$	−0.820344	−	7.89475i	−0.0365410	−	0.351660i
$505$	31.4753			1.40063
$506$	−6.08292	−	3.51197i	−0.270419	−	0.156126i
$507$	−1.62906	−	0.588348i	−0.0723492	−	0.0261294i
$508$	−1.08801	−	1.88449i	−0.0482727	−	0.0836108i
$509$	−17.0560	+	29.5418i	−0.755992	+	1.30942i	0.188888	+	0.981999i	$0.439512\pi$
$509$	−17.0560	+	29.5418i	−0.755992	+	1.30942i	−0.944880	+	0.327417i	$0.893822\pi$
$510$	−1.61834	−	1.91895i	−0.0716612	−	0.0849725i
$511$	5.65454	−	22.0989i	0.250142	−	0.977598i
$512$			1.00000i			0.0441942i
$513$	0.0933909	+	12.5208i	0.00412331	+	0.552809i
$514$	−11.9404	+	6.89377i	−0.526666	+	0.304071i
$515$	33.8827	−	19.5622i	1.49305	−	0.862012i
$516$	2.44588	+	13.6724i	0.107674	+	0.601893i
$517$		−	8.49095i		−	0.373431i
$518$	4.69265	−	18.3397i	0.206183	−	0.805799i
$519$	−0.183867	+	0.155063i	−0.00807087	+	0.00680653i
$520$	1.04730	−	1.81398i	0.0459272	−	0.0795482i
$521$	−16.1589	−	27.9881i	−0.707935	−	1.22618i	−0.965622	−	0.259951i	$-0.916294\pi$
$521$	−16.1589	−	27.9881i	−0.707935	−	1.22618i	0.257687	−	0.966229i	$-0.417040\pi$
$522$	10.9225	−	4.03709i	0.478066	−	0.176699i
$523$	24.1399	+	13.9372i	1.05556	+	0.609430i	0.924202	−	0.381904i	$-0.124732\pi$
$523$	24.1399	+	13.9372i	1.05556	+	0.609430i	0.131362	+	0.991334i	$0.458065\pi$
$524$	−6.55291			−0.286265
$525$	2.32174	+	1.57845i	0.101329	+	0.0688894i
$526$	−21.4451			−0.935049
$527$	−0.565831	−	0.326683i	−0.0246480	−	0.0142305i
$528$	−1.13662	+	3.14716i	−0.0494649	+	0.136962i
$529$	−4.89045	−	8.47051i	−0.212628	−	0.368283i
$530$	−5.81914	+	10.0791i	−0.252767	+	0.437806i
$531$	5.27750	−	30.8257i	0.229024	−	1.33772i
$532$	4.55880	+	4.45692i	0.197649	+	0.193232i
$533$			8.66067i			0.375135i
$534$	−25.4380	+	4.55064i	−1.10081	+	0.196925i
$535$	2.72337	−	1.57234i	0.117741	−	0.0679781i
$536$	−8.62689	+	4.98074i	−0.372625	+	0.215135i
$537$	24.5466	−	4.39119i	1.05927	−	0.189494i
$538$			9.53588i			0.411121i
$539$	−7.02450	−	11.5556i	−0.302567	−	0.497736i
$540$	−5.51209	−	9.38486i	−0.237202	−	0.403860i
$541$	−15.0677	+	26.0980i	−0.647810	+	1.12204i	0.335835	+	0.941921i	$0.390982\pi$
$541$	−15.0677	+	26.0980i	−0.647810	+	1.12204i	−0.983645	+	0.180119i	$0.942352\pi$
$542$	12.7453	+	22.0755i	0.547457	+	0.948224i
$543$	5.45936	−	15.1163i	0.234284	−	0.648703i
$544$	−0.599220	−	0.345960i	−0.0256914	−	0.0148329i
$545$	7.86423			0.336866
$546$	−0.336428	+	4.57021i	−0.0143978	+	0.195587i
$547$	−7.84538			−0.335444			−0.167722	−	0.985834i	$-0.553641\pi$
$547$	−7.84538			−0.335444			−0.167722	+	0.985834i	$0.553641\pi$
$548$	−12.3253	−	7.11601i	−0.526511	−	0.303981i
$549$	3.51245	+	9.50309i	0.149908	+	0.405582i
$550$	−0.591778	−	1.02499i	−0.0252335	−	0.0437057i
$551$	−4.67672	+	8.10032i	−0.199235	+	0.345085i
$552$	4.81401	−	4.05987i	0.204898	−	0.172800i
$553$	11.8955	+	42.4692i	0.505849	+	1.80598i
$554$		−	19.4594i		−	0.826749i
$555$	−4.57115	−	25.5526i	−0.194034	−	1.08465i
$556$	−7.30935	+	4.22006i	−0.309986	+	0.178970i
$557$	−10.8446	+	6.26115i	−0.459502	+	0.265294i	−0.711835	−	0.702347i	$-0.752136\pi$
$557$	−10.8446	+	6.26115i	−0.459502	+	0.265294i	0.252333	+	0.967640i	$0.418802\pi$
$558$	−2.17911	−	1.81010i	−0.0922490	−	0.0766277i
$559$		−	8.01907i		−	0.339171i
$560$	−5.36883	−	1.37375i	−0.226874	−	0.0580513i
$561$	−1.49262	−	1.76987i	−0.0630183	−	0.0747242i
$562$	−4.33408	+	7.50684i	−0.182822	+	0.316657i
$563$	6.12663	+	10.6116i	0.258207	+	0.447227i	0.965762	−	0.259431i	$-0.0835351\pi$
$563$	6.12663	+	10.6116i	0.258207	+	0.447227i	−0.707555	+	0.706658i	$0.750202\pi$
$564$	7.16001	+	2.58589i	0.301491	+	0.108886i
$565$	15.7115	+	9.07106i	0.660989	+	0.381622i
$566$	−23.0361			−0.968278
$567$	19.7912	+	13.2404i	0.831152	+	0.556046i
$568$	−3.58456			−0.150405
$569$	34.2211	+	19.7576i	1.43462	+	0.828281i	0.997469	−	0.0711052i	$-0.0226526\pi$
$569$	34.2211	+	19.7576i	1.43462	+	0.828281i	0.437155	+	0.899386i	$0.355986\pi$
$570$	8.22249	+	2.96961i	0.344402	+	0.124383i
$571$	16.5630	+	28.6880i	0.693141	+	1.20056i	0.970803	+	0.239877i	$0.0771071\pi$
$571$	16.5630	+	28.6880i	0.693141	+	1.20056i	−0.277662	+	0.960679i	$0.589560\pi$
$572$	0.965940	−	1.67306i	0.0403880	−	0.0699541i
$573$	−3.78482	−	4.48787i	−0.158113	−	0.187483i
$574$	22.0648	−	6.18029i	0.920967	−	0.257960i
$575$			2.22746i			0.0928915i
$576$	−2.30769	−	1.91691i	−0.0961539	−	0.0798713i
$577$	23.3130	−	13.4597i	0.970531	−	0.560337i	0.0711331	−	0.997467i	$-0.477338\pi$
$577$	23.3130	−	13.4597i	0.970531	−	0.560337i	0.899398	+	0.437130i	$0.144005\pi$
$578$	−14.3078	+	8.26062i	−0.595127	+	0.343597i
$579$	−3.83430	−	21.4336i	−0.159348	−	0.890751i
$580$		−	8.13035i		−	0.337594i
$581$	23.2768	−	23.8089i	0.965686	−	0.987760i
$582$	−3.09764	+	2.61238i	−0.128401	+	0.108286i
$583$	−5.36708	+	9.29605i	−0.222282	+	0.385003i
$584$	−4.31085	−	7.46660i	−0.178384	−	0.308970i
$585$	2.17852	+	5.89408i	0.0900708	+	0.243690i
$586$	15.8004	+	9.12237i	0.652709	+	0.376842i
$587$	22.5994			0.932778			0.466389	−	0.884580i	$-0.345555\pi$
$587$	22.5994			0.932778			0.466389	+	0.884580i	$0.345555\pi$
$588$	11.8836	−	2.40420i	0.490071	−	0.0991476i
$589$	2.27544			0.0937577
$590$	−18.9103	−	10.9178i	−0.778523	−	0.449481i
$591$	−7.07611	+	19.5929i	−0.291072	+	0.805944i
$592$	−3.57753	−	6.19647i	−0.147036	−	0.254673i
$593$	16.5789	−	28.7155i	0.680814	−	1.17920i	−0.293919	−	0.955830i	$-0.594960\pi$
$593$	16.5789	−	28.7155i	0.680814	−	1.17920i	0.974733	−	0.223374i	$-0.0717071\pi$
$594$	−5.08387	−	8.65579i	−0.208594	−	0.355151i
$595$	2.68058	−	2.74185i	0.109893	−	0.112405i
$596$			0.0386143i			0.00158170i
$597$	−25.7100	+	4.59930i	−1.05224	+	0.188237i
$598$	−3.14870	+	1.81790i	−0.128760	+	0.0743396i
$599$	−39.7724	+	22.9626i	−1.62506	+	0.938227i	−0.639518	+	0.768776i	$0.720866\pi$
$599$	−39.7724	+	22.9626i	−1.62506	+	0.938227i	−0.985539	+	0.169451i	$0.945801\pi$
$600$	1.04455	−	0.186861i	0.0426436	−	0.00762858i
$601$		−	17.7850i		−	0.725466i	−0.931893	−	0.362733i	$-0.881844\pi$
$601$		−	17.7850i		−	0.725466i	0.931893	−	0.362733i	$-0.118156\pi$
$602$	−20.4302	+	5.72244i	−0.832672	+	0.233229i
$603$	5.04297	−	29.4559i	0.205366	−	1.19954i
$604$	10.4122	−	18.0344i	0.423664	−	0.733808i
$605$	−7.61161	−	13.1837i	−0.309456	−	0.535993i
$606$	−8.84102	+	24.4797i	−0.359142	+	0.994420i
$607$	23.5234	+	13.5812i	0.954785	+	0.551245i	0.894564	−	0.446940i	$-0.147486\pi$
$607$	23.5234	+	13.5812i	0.954785	+	0.551245i	0.0602210	+	0.998185i	$0.480819\pi$
$608$	2.40970			0.0977264
$609$	7.73889	+	16.0159i	0.313595	+	0.648996i
$610$	7.07377			0.286409
$611$	−3.80633	−	2.19759i	−0.153988	−	0.0889048i
$612$	1.94702	−	0.719642i	0.0787037	−	0.0290898i
$613$	−11.4277	−	19.7933i	−0.461559	−	0.799444i	0.537480	−	0.843277i	$-0.319376\pi$
$613$	−11.4277	−	19.7933i	−0.461559	−	0.799444i	−0.999039	+	0.0438328i	$0.986043\pi$
$614$	10.9255	−	18.9235i	0.440917	−	0.763691i
$615$	24.0192	−	20.2565i	0.968549	−	0.816822i
$616$	−4.95175	−	1.26702i	−0.199512	−	0.0510499i
$617$			31.8388i			1.28178i	0.767632	+	0.640891i	$0.221435\pi$
$617$			31.8388i			1.28178i	−0.767632	+	0.640891i	$0.778565\pi$
$618$	5.69713	+	31.8468i	0.229172	+	1.28107i
$619$	−25.4744	+	14.7077i	−1.02390	+	0.591151i	−0.915232	−	0.402926i	$-0.867993\pi$
$619$	−25.4744	+	14.7077i	−1.02390	+	0.591151i	−0.108672	+	0.994078i	$0.534660\pi$
$620$	−1.71290	+	0.988945i	−0.0687918	+	0.0397170i
$621$	0.140910	+	18.8917i	0.00565452	+	0.758097i
$622$			2.82818i			0.113400i
$623$	−10.6468	−	38.0111i	−0.426555	−	1.52288i
$624$	1.11664	+	1.32406i	0.0447012	+	0.0530047i
$625$	10.7807	−	18.6728i	0.431229	−	0.746910i
$626$	4.95414	+	8.58082i	0.198007	+	0.342959i
$627$	7.58372	+	2.73891i	0.302864	+	0.109382i
$628$	3.98152	+	2.29873i	0.158880	+	0.0917294i
$629$	4.95073			0.197399
$630$	13.4618	−	9.75626i	0.536329	−	0.388699i
$631$	20.0601			0.798581			0.399291	−	0.916824i	$-0.369256\pi$
$631$	20.0601			0.798581			0.399291	+	0.916824i	$0.369256\pi$
$632$	14.4363	+	8.33482i	0.574247	+	0.331541i
$633$	17.9683	+	6.48937i	0.714174	+	0.257929i
$634$	−8.78492	−	15.2159i	−0.348894	−	0.604302i
$635$	2.27895	−	3.94726i	0.0904374	−	0.156642i
$636$	−6.20439	−	7.35688i	−0.246020	−	0.291719i
$637$	−6.99821	+	0.158181i	−0.277279	+	0.00626736i
$638$		−	7.49874i		−	0.296878i
$639$	6.87129	−	8.27207i	0.271824	−	0.327238i
$640$	−1.81398	+	1.04730i	−0.0717038	+	0.0413982i
$641$	39.6565	−	22.8957i	1.56634	−	0.904326i	0.569749	−	0.821819i	$-0.307040\pi$
$641$	39.6565	−	22.8957i	1.56634	−	0.904326i	0.996590	−	0.0825076i	$-0.0262929\pi$
$642$	0.457915	+	2.55973i	0.0180725	+	0.101025i
$643$			21.5260i			0.848904i	0.905450	+	0.424452i	$0.139533\pi$
$643$			21.5260i			0.848904i	−0.905450	+	0.424452i	$0.860467\pi$
$644$	6.87840	+	6.72468i	0.271047	+	0.264990i
$645$	−22.2398	+	18.7559i	−0.875693	+	0.738512i
$646$	−0.833662	+	1.44394i	−0.0328000	+	0.0568112i
$647$	7.06767	+	12.2416i	0.277859	+	0.481265i	0.970852	−	0.239678i	$-0.0770419\pi$
$647$	7.06767	+	12.2416i	0.277859	+	0.481265i	−0.692994	+	0.720944i	$0.743709\pi$
$648$	8.84729	−	1.65090i	0.347554	−	0.0648535i
$649$	−17.4412	−	10.0697i	−0.684627	−	0.395270i
$650$	−0.612645			−0.0240299
$651$	2.43290	−	3.57854i	0.0953528	−	0.140254i
$652$	−19.8760			−0.778404
$653$	−14.0019	−	8.08399i	−0.547936	−	0.316351i	0.200353	−	0.979724i	$-0.435791\pi$
$653$	−14.0019	−	8.08399i	−0.547936	−	0.316351i	−0.748289	+	0.663373i	$0.769124\pi$
$654$	−2.20896	+	6.11635i	−0.0863773	+	0.239168i
$655$	−6.86287	−	11.8868i	−0.268155	−	0.464457i
$656$	4.33034	−	7.50036i	0.169071	−	0.292840i
$657$	25.4941	+	4.36471i	0.994621	+	0.170284i
$658$	−2.88258	+	11.2656i	−0.112374	+	0.439178i
$659$		−	42.0011i		−	1.63613i	−0.575126	−	0.818065i	$-0.695047\pi$
$659$		−	42.0011i		−	1.63613i	0.575126	−	0.818065i	$-0.304953\pi$
$660$	−6.89925	+	1.23422i	−0.268553	+	0.0480419i
$661$	4.44931	−	2.56881i	0.173058	−	0.0999152i	−0.410969	−	0.911649i	$-0.634810\pi$
$661$	4.44931	−	2.56881i	0.173058	−	0.0999152i	0.584027	+	0.811734i	$0.301476\pi$
$662$	−13.3408	+	7.70234i	−0.518507	+	0.299360i
$663$	−1.17971	+	0.211041i	−0.0458162	+	0.00819614i
$664$		−	12.5850i		−	0.488393i
$665$	−3.31032	+	12.9373i	−0.128369	+	0.501687i
$666$	21.1574	+	3.62223i	0.819831	+	0.140359i
$667$	−7.05633	+	12.2219i	−0.273222	+	0.473235i
$668$	−2.68127	−	4.64409i	−0.103741	−	0.179685i
$669$	8.40714	−	23.2783i	0.325039	−	0.899992i
$670$	−18.0699	−	10.4327i	−0.698101	−	0.403049i
$671$	6.52424			0.251866
$672$	2.57646	−	3.78970i	0.0993891	−	0.146191i
$673$	−37.9013			−1.46099			−0.730494	−	0.682919i	$-0.760710\pi$
$673$	−37.9013			−1.46099			−0.730494	+	0.682919i	$0.760710\pi$
$674$	−12.5198	−	7.22830i	−0.482244	−	0.278424i
$675$	−1.57109	+	2.76870i	−0.0604713	+	0.106567i
$676$	−0.500000	−	0.866025i	−0.0192308	−	0.0333087i
$677$	−13.4434	+	23.2847i	−0.516672	+	0.894902i	0.483141	+	0.875543i	$0.339496\pi$
$677$	−13.4434	+	23.2847i	−0.516672	+	0.894902i	−0.999813	+	0.0193592i	$0.993837\pi$
$678$	−11.4681	+	9.67160i	−0.440431	+	0.371435i
$679$	−4.42599	−	4.32708i	−0.169854	−	0.166058i
$680$		−	1.44930i		−	0.0555780i
$681$	6.35068	+	35.5002i	0.243359	+	1.36037i
$682$	−1.57983	+	0.912118i	−0.0604950	+	0.0349268i
$683$	8.54705	−	4.93464i	0.327044	−	0.188819i	−0.327484	−	0.944857i	$-0.606201\pi$
$683$	8.54705	−	4.93464i	0.327044	−	0.188819i	0.654528	+	0.756038i	$0.272867\pi$
$684$	−4.61919	+	5.56086i	−0.176619	+	0.212625i
$685$		−	29.8104i		−	1.13900i
$686$	5.39695	+	17.7165i	0.206056	+	0.676418i
$687$	−0.366368	−	0.434422i	−0.0139778	−	0.0165742i
$688$	−4.00954	+	6.94472i	−0.152862	+	0.264765i
$689$	2.77816	+	4.81192i	0.105840	+	0.183319i
$690$	12.4062	+	4.48060i	0.472298	+	0.170574i
$691$	10.7402	+	6.20088i	0.408578	+	0.235893i	0.690179	−	0.723639i	$-0.257532\pi$
$691$	10.7402	+	6.20088i	0.408578	+	0.235893i	−0.281601	+	0.959532i	$0.590865\pi$
$692$	−0.138867			−0.00527892
$693$	12.4160	−	8.99834i	0.471644	−	0.341819i
$694$	−12.5620			−0.476846
$695$	−15.3102	−	8.83933i	−0.580748	−	0.335295i
$696$	6.32333	+	2.28372i	0.239685	+	0.0865640i
$697$	2.99625	+	5.18965i	0.113491	+	0.196572i
$698$	−8.85051	+	15.3295i	−0.334997	+	0.580232i
$699$	10.0625	+	11.9316i	0.380598	+	0.451295i
$700$	0.437186	+	1.56083i	0.0165241	+	0.0589940i
$701$			2.73572i			0.103327i	0.998665	+	0.0516634i	$0.0164523\pi$
$701$			2.73572i			0.103327i	−0.998665	+	0.0516634i	$0.983548\pi$
$702$	−5.19601	+	0.0387561i	−0.196111	+	0.00146276i
$703$	−14.9317	+	8.62079i	−0.563158	+	0.325139i
$704$	−1.67306	+	0.965940i	−0.0630557	+	0.0364052i
$705$	2.80794	+	15.6963i	0.105753	+	0.591157i
$706$			0.445314i			0.0167596i
$707$	−38.5165	−	9.85538i	−1.44856	−	0.370650i
$708$	13.8029	−	11.6406i	0.518746	−	0.437482i
$709$	4.28476	−	7.42143i	0.160918	−	0.278718i	−0.774280	−	0.632843i	$-0.781888\pi$
$709$	4.28476	−	7.42143i	0.160918	−	0.278718i	0.935198	+	0.354125i	$0.115221\pi$
$710$	−3.75411	−	6.50231i	−0.140889	−	0.244028i
$711$	−46.9074	+	17.3375i	−1.75916	+	0.650208i
$712$	−12.9209	−	7.45988i	−0.484231	−	0.279571i
$713$	3.43322			0.128575
$714$	1.37952	+	2.85495i	0.0516271	+	0.106844i
$715$	4.04652			0.151331
$716$	12.4682	+	7.19850i	0.465957	+	0.269020i
$717$	−16.6008	+	45.9656i	−0.619968	+	1.71662i
$718$	−10.3348	−	17.9004i	−0.385691	−	0.668036i
$719$	−12.6631	+	21.9332i	−0.472255	+	0.817969i	−0.999496	−	0.0317464i	$-0.989893\pi$
$719$	−12.6631	+	21.9332i	−0.472255	+	0.817969i	0.527241	+	0.849716i	$0.323226\pi$
$720$	1.06039	−	6.19369i	0.0395183	−	0.230825i
$721$	−47.5876	+	13.3292i	−1.77225	+	0.496404i
$722$			13.1933i			0.491005i
$723$	19.5482	−	3.49700i	0.727004	−	0.130055i
$724$	8.03597	−	4.63957i	0.298654	−	0.172428i
$725$	−2.05943	+	1.18901i	−0.0764853	+	0.0441588i
$726$	12.3915	−	2.21674i	0.459893	−	0.0822711i
$727$		−	48.9569i		−	1.81571i	−0.419284	−	0.907855i	$-0.637719\pi$
$727$		−	48.9569i		−	1.81571i	0.419284	−	0.907855i	$-0.362281\pi$
$728$	−1.84957	+	1.89185i	−0.0685496	+	0.0701166i
$729$	−13.1497	+	23.5815i	−0.487026	+	0.873387i
$730$	9.02951	−	15.6396i	0.334197	−	0.578846i
$731$	−2.77428	−	4.80519i	−0.102610	−	0.177726i
$732$	−1.98694	+	5.50158i	−0.0734393	+	0.203344i
$733$	43.4681	+	25.0963i	1.60553	+	0.926954i	0.990353	+	0.138566i	$0.0442494\pi$
$733$	43.4681	+	25.0963i	1.60553	+	0.926954i	0.615179	+	0.788388i	$0.289084\pi$
$734$	19.8731			0.733528
$735$	16.8069	+	19.0387i	0.619931	+	0.702251i
$736$	3.63581			0.134018
$737$	−16.6661	−	9.62219i	−0.613905	−	0.354438i
$738$	9.00767	+	24.3706i	0.331577	+	0.897095i
$739$	−8.36739	−	14.4927i	−0.307799	−	0.533124i	0.670081	−	0.742288i	$-0.266259\pi$
$739$	−8.36739	−	14.4927i	−0.307799	−	0.533124i	−0.977881	+	0.209164i	$0.932926\pi$
$740$	7.49350	−	12.9791i	0.275467	−	0.477122i
$741$	3.19058	−	2.69076i	0.117209	−	0.0988477i
$742$	10.2768	−	10.5117i	0.377274	−	0.385898i
$743$			6.98714i			0.256333i	0.991753	+	0.128167i	$0.0409092\pi$
$743$			6.98714i			0.256333i	−0.991753	+	0.128167i	$0.959091\pi$
$744$	−0.288012	−	1.60998i	−0.0105590	−	0.0590248i
$745$	−0.0700454	+	0.0404408i	−0.00256627	+	0.00148163i
$746$	−13.2365	+	7.64212i	−0.484624	+	0.279798i
$747$	29.0423	+	24.1243i	1.06260	+	0.882663i
$748$		−	1.33671i		−	0.0488748i
$749$	−3.82492	+	1.07135i	−0.139760	+	0.0391463i
$750$	13.1275	+	15.5659i	0.479347	+	0.568388i
$751$	0.680716	−	1.17903i	0.0248397	−	0.0430236i	−0.853338	−	0.521358i	$-0.825426\pi$
$751$	0.680716	−	1.17903i	0.0248397	−	0.0430236i	0.878178	+	0.478334i	$0.158759\pi$
$752$	2.19759	+	3.80633i	0.0801377	+	0.138803i
$753$	−41.9648	−	15.1559i	−1.52928	−	0.552312i
$754$	−3.36154	−	1.94079i	−0.122420	−	0.0706793i
$755$	43.6186			1.58744
$756$	3.80663	+	13.2102i	0.138446	+	0.480451i
$757$	−17.6138			−0.640186			−0.320093	−	0.947386i	$-0.603714\pi$
$757$	−17.6138			−0.640186			−0.320093	+	0.947386i	$0.603714\pi$
$758$	20.6819	+	11.9407i	0.751200	+	0.433705i
$759$	11.4425	+	4.13252i	0.415335	+	0.150001i
$760$	2.52369	+	4.37115i	0.0915437	+	0.158558i
$761$	−10.6541	+	18.4534i	−0.386210	+	0.668935i	−0.991936	−	0.126738i	$-0.959549\pi$
$761$	−10.6541	+	18.4534i	−0.386210	+	0.668935i	0.605727	+	0.795673i	$0.292883\pi$
$762$	2.42983	+	2.88118i	0.0880233	+	0.104374i
$763$	−9.62349	−	2.46240i	−0.348394	−	0.0891450i
$764$		−	3.38949i		−	0.122627i
$765$	3.34453	+	2.77817i	0.120922	+	0.100445i
$766$	32.5547	−	18.7955i	1.17625	−	0.679108i
$767$	−9.02810	+	5.21237i	−0.325986	+	0.188208i
$768$	−0.305007	−	1.70498i	−0.0110060	−	0.0615233i
$769$		−	49.2139i		−	1.77470i	−0.461099	−	0.887349i	$-0.652545\pi$
$769$		−	49.2139i		−	1.77470i	0.461099	−	0.887349i	$-0.347455\pi$
$770$	−2.88761	−	10.3093i	−0.104062	−	0.371522i
$771$	18.2555	−	15.3957i	0.657454	−	0.554461i
$772$	6.28558	−	10.8869i	0.226223	−	0.391830i
$773$	14.9637	+	25.9179i	0.538208	+	0.932203i	0.999001	+	0.0446955i	$0.0142317\pi$
$773$	14.9637	+	25.9179i	0.538208	+	0.932203i	−0.460793	+	0.887508i	$0.652435\pi$
$774$	−8.34036	−	22.5652i	−0.299788	−	0.811089i
$775$	0.501003	+	0.289254i	0.0179965	+	0.0103903i
$776$	−2.33951			−0.0839833
$777$	−2.40716	+	32.7001i	−0.0863564	+	1.17311i
$778$	−29.4790			−1.05687
$779$	−18.0737	−	10.4348i	−0.647556	−	0.373867i
$780$	−1.23235	+	3.41224i	−0.0441254	+	0.122178i
$781$	−3.46247	−	5.99718i	−0.123897	−	0.214596i
$782$	−1.25784	+	2.17865i	−0.0449804	+	0.0779084i
$783$	−17.3914	+	10.2146i	−0.621517	+	0.365041i
$784$	6.13972	+	3.36212i	0.219276	+	0.120076i
$785$			9.62985i			0.343704i
$786$	11.1726	−	1.99869i	0.398514	−	0.0712908i
$787$	17.6377	−	10.1831i	0.628715	−	0.362989i	−0.151539	−	0.988451i	$-0.548423\pi$
$787$	17.6377	−	10.1831i	0.628715	−	0.362989i	0.780254	+	0.625462i	$0.215090\pi$
$788$	−10.4158	+	6.01354i	−0.371046	+	0.214224i
$789$	36.5635	−	6.54090i	1.30169	−	0.232862i
$790$			34.9163i			1.24226i
$791$	−16.3860	−	16.0198i	−0.582619	−	0.569599i
$792$	0.978010	−	5.71253i	0.0347521	−	0.202986i
$793$	1.68857	−	2.92469i	0.0599630	−	0.103859i
$794$	−9.42604	−	16.3264i	−0.334518	−	0.579402i
$795$	6.84736	−	18.9595i	0.242851	−	0.672424i
$796$	−13.0591	−	7.53965i	−0.462866	−	0.267236i
$797$	−14.7873			−0.523792			−0.261896	−	0.965096i	$-0.584348\pi$
$797$	−14.7873			−0.523792			−0.261896	+	0.965096i	$0.584348\pi$
$798$	−9.13207	−	6.20851i	−0.323272	−	0.219779i
$799$	−3.04111			−0.107587
$800$	0.530566	+	0.306322i	0.0187583	+	0.0108301i
$801$	41.9833	−	15.5175i	1.48341	−	0.548285i
$802$	−5.77115	−	9.99593i	−0.203786	−	0.352968i
$803$	8.32804	−	14.4246i	0.293890	−	0.509033i
$804$	13.1896	−	11.1233i	0.465160	−	0.392290i
$805$	−4.99467	+	19.5200i	−0.176039	+	0.687991i
$806$			0.944280i			0.0332608i
$807$	−2.90851	−	16.2585i	−0.102385	−	0.572327i
$808$	−13.0136	+	7.51343i	−0.457819	+	0.264322i
$809$	−35.4312	+	20.4562i	−1.24569	+	0.719202i	−0.970248	−	0.242115i	$-0.922159\pi$
$809$	−35.4312	+	20.4562i	−1.24569	+	0.719202i	−0.275446	+	0.961317i	$0.588826\pi$
$810$	12.2605	+	14.3198i	0.430789	+	0.503147i
$811$		−	15.0715i		−	0.529231i	−0.964354	−	0.264616i	$-0.914755\pi$
$811$		−	15.0715i		−	0.529231i	0.964354	−	0.264616i	$-0.0852451\pi$
$812$	−2.54573	+	9.94915i	−0.0893377	+	0.349147i
$813$	−28.4637	−	33.7510i	−0.998266	−	1.18370i
$814$	6.91136	−	11.9708i	0.242243	−	0.419577i
$815$	−20.8161	−	36.0546i	−0.729157	−	1.26294i
$816$	1.12718	+	0.407090i	0.0394592	+	0.0142510i
$817$	16.7347	+	9.66180i	0.585474	+	0.338024i
$818$	24.0433			0.840655
$819$	−0.820344	−	7.89475i	−0.0286651	−	0.275865i
$820$	18.1407			0.633499
$821$	14.4930	+	8.36756i	0.505811	+	0.292030i	0.731110	−	0.682260i	$-0.239003\pi$
$821$	14.4930	+	8.36756i	0.505811	+	0.292030i	−0.225299	+	0.974290i	$0.572336\pi$
$822$	23.1849	+	8.37338i	0.808665	+	0.292055i
$823$	26.3860	+	45.7019i	0.919757	+	1.59307i	0.799783	+	0.600290i	$0.204948\pi$
$823$	26.3860	+	45.7019i	0.919757	+	1.59307i	0.119975	+	0.992777i	$0.461719\pi$
$824$	−9.33933	+	16.1762i	−0.325351	+	0.563524i
$825$	1.32160	+	1.56709i	0.0460123	+	0.0545592i
$826$	19.7220	+	19.2813i	0.686218	+	0.670882i
$827$		−	35.5394i		−	1.23583i	−0.786246	−	0.617913i	$-0.787978\pi$
$827$		−	35.5394i		−	1.23583i	0.786246	−	0.617913i	$-0.212022\pi$
$828$	−6.96952	+	8.39033i	−0.242208	+	0.291584i
$829$	23.3896	−	13.5040i	0.812354	−	0.469013i	−0.0354185	−	0.999373i	$-0.511276\pi$
$829$	23.3896	−	13.5040i	0.812354	−	0.469013i	0.847773	+	0.530360i	$0.177943\pi$
$830$	22.8289	−	13.1803i	0.792403	−	0.457494i
$831$	5.93525	+	33.1779i	0.205892	+	1.15093i
$832$			1.00000i			0.0346688i
$833$	−4.13875	+	2.51589i	−0.143399	+	0.0871703i
$834$	11.1752	−	9.42453i	0.386965	−	0.326345i
$835$	5.61619	−	9.72752i	0.194356	−	0.336635i
$836$	2.32763	+	4.03158i	0.0805028	+	0.139435i
$837$	4.26744	+	2.42155i	0.147504	+	0.0837010i
$838$	−3.14928	−	1.81824i	−0.108790	−	0.0628099i
$839$	12.4473			0.429730			0.214865	−	0.976644i	$-0.431069\pi$
$839$	12.4473			0.429730			0.214865	+	0.976644i	$0.431069\pi$
$840$	9.57277	+	0.704682i	0.330292	+	0.0243138i
$841$	13.9334			0.480462
$842$	0.0278313	+	0.0160684i	0.000959130	+	0.000553754i
$843$	5.09989	−	14.1210i	0.175650	−	0.486352i
$844$	5.51491	+	9.55210i	0.189831	+	0.328797i
$845$	1.04730	−	1.81398i	0.0360282	−	0.0624027i
$846$	−12.9964	−	2.22504i	−0.446826	−	0.0764986i
$847$	5.18636	+	18.5163i	0.178205	+	0.636226i
$848$		−	5.55632i		−	0.190805i
$849$	39.2761	−	7.02617i	1.34795	−	0.241138i
$850$	−0.367109	+	0.211951i	−0.0125917	+	0.00726984i
$851$	−22.5292	+	13.0072i	−0.772290	+	0.445882i
$852$	6.11162	−	1.09332i	0.209381	−	0.0374564i
$853$			37.5892i			1.28703i	0.765433	+	0.643515i	$0.222525\pi$
$853$			37.5892i			1.28703i	−0.765433	+	0.643515i	$0.777475\pi$
$854$	−8.65621	−	2.21490i	−0.296209	−	0.0757924i
$855$	−14.9250	−	2.55522i	−0.510423	−	0.0873866i
$856$	−0.750662	+	1.30018i	−0.0256571	+	0.0444394i
$857$	6.33608	+	10.9744i	0.216436	+	0.374879i	0.953716	−	0.300709i	$-0.0972233\pi$
$857$	6.33608	+	10.9744i	0.216436	+	0.374879i	−0.737280	+	0.675588i	$0.763890\pi$
$858$	−1.13662	+	3.14716i	−0.0388035	+	0.107442i
$859$	−10.2996	−	5.94647i	−0.351417	−	0.202891i	0.313892	−	0.949459i	$-0.398367\pi$
$859$	−10.2996	−	5.94647i	−0.351417	−	0.202891i	−0.665309	+	0.746568i	$0.731700\pi$
$860$	−16.7968			−0.572765
$861$	−35.7351	+	17.2672i	−1.21785	+	0.588465i
$862$	−16.5585			−0.563984
$863$	−14.3740	−	8.29886i	−0.489298	−	0.282496i	0.234985	−	0.971999i	$-0.424496\pi$
$863$	−14.3740	−	8.29886i	−0.489298	−	0.282496i	−0.724283	+	0.689502i	$0.757829\pi$
$864$	4.51925	+	2.56444i	0.153748	+	0.0872440i
$865$	−0.145435	−	0.251901i	−0.00494494	−	0.00856489i
$866$	11.7825	−	20.4079i	0.400385	−	0.693488i
$867$	21.8751	−	18.4482i	0.742916	−	0.626534i
$868$	2.40574	−	0.673841i	0.0816561	−	0.0228717i
$869$			32.2038i			1.09244i
$870$	2.47982	+	13.8621i	0.0840736	+	0.469970i
$871$	−8.62689	+	4.98074i	−0.292311	+	0.168766i
$872$	−3.25151	+	1.87726i	−0.110110	+	0.0635721i
$873$	4.48462	−	5.39886i	0.151782	−	0.182724i
$874$		−	8.76123i		−	0.296353i
$875$	−21.7440	+	22.2411i	−0.735082	+	0.751885i
$876$	9.62729	+	11.4156i	0.325276	+	0.385697i
$877$	18.9926	−	32.8962i	0.641336	−	1.11083i	−0.343799	−	0.939043i	$-0.611714\pi$
$877$	18.9926	−	32.8962i	0.641336	−	1.11083i	0.985135	−	0.171783i	$-0.0549528\pi$
$878$	0.637611	+	1.10437i	0.0215183	+	0.0372708i
$879$	−29.7218	−	10.7343i	−1.00249	−	0.362057i
$880$	−3.50439	−	2.02326i	−0.118133	−	0.0682041i
$881$	−52.5629			−1.77089			−0.885444	−	0.464746i	$-0.846146\pi$
$881$	−52.5629			−1.77089			−0.885444	+	0.464746i	$0.846146\pi$
$882$	−19.5280	+	7.72371i	−0.657543	+	0.260071i
$883$	21.4529			0.721948			0.360974	−	0.932576i	$-0.382444\pi$
$883$	21.4529			0.721948			0.360974	+	0.932576i	$0.382444\pi$
$884$	−0.599220	−	0.345960i	−0.0201540	−	0.0116359i
$885$	35.5717	+	12.8470i	1.19573	+	0.431847i
$886$	−3.35151	−	5.80498i	−0.112596	−	0.195022i
$887$	5.84800	−	10.1290i	0.196357	−	0.340099i	−0.750988	−	0.660316i	$-0.770422\pi$
$887$	5.84800	−	10.1290i	0.196357	−	0.340099i	0.947344	+	0.320217i	$0.103756\pi$
$888$	7.98960	+	9.47370i	0.268113	+	0.317917i
$889$	−4.02471	+	4.11671i	−0.134984	+	0.138070i
$890$		−	31.2510i		−	1.04753i
$891$	11.3080	+	13.2074i	0.378832	+	0.442463i
$892$	12.3750	−	7.14470i	0.414345	−	0.239222i
$893$	9.17213	−	5.29553i	0.306934	−	0.177208i
$894$	−0.0117776	−	0.0658367i	−0.000393903	−	0.00220191i
$895$			30.1560i			1.00800i
$896$	2.54770	−	0.713604i	0.0851126	−	0.0238398i
$897$	4.81401	−	4.05987i	0.160735	−	0.135555i
$898$	5.72116	−	9.90935i	0.190918	−	0.330679i
$899$	1.83265	+	3.17423i	0.0611221	+	0.105867i
$900$	−1.72395	+	0.637191i	−0.0574649	+	0.0212397i
$901$	3.32946	+	1.92227i	0.110920	+	0.0640400i
$902$	16.7314			0.557094
$903$	33.0877	−	15.9880i	1.10109	−	0.532048i
$904$	−8.66137			−0.288073
$905$	16.8322	+	9.71805i	0.559520	+	0.323039i
$906$	−12.2519	+	33.9241i	−0.407043	+	1.12705i
$907$	25.5815	+	44.3084i	0.849419	+	1.47124i	0.881727	+	0.471759i	$0.156381\pi$
$907$	25.5815	+	44.3084i	0.849419	+	1.47124i	−0.0323084	+	0.999478i	$0.510286\pi$
$908$	−10.4107	+	18.0319i	−0.345491	+	0.598409i
$909$	7.60731	−	44.4341i	0.252319	−	1.47379i
$910$	−5.36883	−	1.37375i	−0.177975	−	0.0455392i
$911$		−	43.0375i		−	1.42589i	−0.701218	−	0.712947i	$-0.747360\pi$
$911$		−	43.0375i		−	1.42589i	0.701218	−	0.712947i	$-0.252640\pi$
$912$	−4.10851	+	0.734978i	−0.136046	+	0.0243375i
$913$	21.0554	−	12.1564i	0.696833	−	0.402317i
$914$	27.6958	−	15.9902i	0.916096	−	0.528908i
$915$	−12.0607	+	2.15755i	−0.398714	+	0.0713265i
$916$		−	0.328100i		−	0.0108407i
$917$	4.67618	+	16.6949i	0.154421	+	0.551313i
$918$	−3.10015	+	1.82083i	−0.102320	+	0.0600965i
$919$	−18.7861	+	32.5385i	−0.619696	+	1.07335i	0.369845	+	0.929094i	$0.379411\pi$
$919$	−18.7861	+	32.5385i	−0.619696	+	1.07335i	−0.989541	+	0.144252i	$0.953922\pi$
$920$	3.80778	+	6.59528i	0.125539	+	0.217440i
$921$	−12.8560	+	35.5967i	−0.423619	+	1.17295i
$922$	−6.63651	−	3.83159i	−0.218562	−	0.126187i
$923$	−3.58456			−0.117987
$924$	8.82910	+	0.649938i	0.290456	+	0.0213814i
$925$	−4.38351			−0.144129
$926$	29.1640	+	16.8379i	0.958390	+	0.553327i
$927$	−19.4270	−	52.5606i	−0.638067	−	1.72632i
$928$	1.94079	+	3.36154i	0.0637094	+	0.110348i
$929$	1.73163	−	2.99926i	0.0568128	−	0.0984026i	−0.836220	−	0.548394i	$-0.815240\pi$
$929$	1.73163	−	2.99926i	0.0568128	−	0.0984026i	0.893033	+	0.449991i	$0.148573\pi$
$930$	2.61884	−	2.20858i	0.0858750	−	0.0724223i
$931$	8.10171	−	14.7949i	0.265523	−	0.484884i
$932$			9.01141i			0.295179i
$933$	−0.862614	−	4.82199i	−0.0282407	−	0.157865i
$934$	17.1383	−	9.89478i	0.560781	−	0.323767i
$935$	2.42476	−	1.39993i	0.0792980	−	0.0457827i
$936$	−2.30769	−	1.91691i	−0.0754293	−	0.0626562i
$937$		−	26.4458i		−	0.863948i	−0.901886	−	0.431974i	$-0.857817\pi$
$937$		−	26.4458i		−	0.863948i	0.901886	−	0.431974i	$-0.142183\pi$
$938$	18.8456	+	18.4244i	0.615331	+	0.601580i
$939$	−11.0639	−	13.1191i	−0.361058	−	0.428126i
$940$	−4.60307	+	7.97275i	−0.150135	+	0.260042i
$941$	−16.9152	−	29.2979i	−0.551418	−	0.955084i	−0.998173	−	0.0604278i	$-0.980754\pi$
$941$	−16.9152	−	29.2979i	−0.551418	−	0.955084i	0.446754	−	0.894657i	$-0.352580\pi$
$942$	−7.48956	−	2.70491i	−0.244023	−	0.0881307i
$943$	−27.2699	−	15.7443i	−0.888030	−	0.512704i
$944$	10.4247			0.339297
$945$	−19.9763	+	20.7402i	−0.649830	+	0.674679i
$946$	−15.4919			−0.503685
$947$	0.430364	+	0.248471i	0.0139849	+	0.00807421i	0.506976	−	0.861960i	$-0.330763\pi$
$947$	0.430364	+	0.248471i	0.0139849	+	0.00807421i	−0.492991	+	0.870034i	$0.664097\pi$
$948$	−27.1559	−	9.80755i	−0.881983	−	0.318534i
$949$	−4.31085	−	7.46660i	−0.139936	−	0.242376i
$950$	0.738147	−	1.27851i	0.0239486	−	0.0414803i
$951$	19.6191	+	23.2635i	0.636194	+	0.754369i
$952$	−0.453796	+	1.77351i	−0.0147076	+	0.0574798i
$953$			41.4342i			1.34219i	0.741373	+	0.671093i	$0.234175\pi$
$953$			41.4342i			1.34219i	−0.741373	+	0.671093i	$0.765825\pi$
$954$	12.8223	+	10.6510i	0.415137	+	0.344838i
$955$	6.14846	−	3.54981i	0.198959	−	0.114869i
$956$	−24.4357	+	14.1080i	−0.790308	+	0.456285i
$957$	2.28717	+	12.7852i	0.0739337	+	0.413288i
$958$			20.7962i			0.671895i
$959$	−9.33408	+	36.4792i	−0.301413	+	1.17797i
$960$	2.77337	−	2.33891i	0.0895101	−	0.0754879i
$961$	−15.0542	+	26.0746i	−0.485618	+	0.841116i
$962$	−3.57753	−	6.19647i	−0.115344	−	0.199782i
$963$	−1.56147	−	4.22464i	−0.0503178	−	0.136137i
$964$	9.92924	+	5.73265i	0.319799	+	0.184636i
$965$	26.3316			0.847643
$966$	−13.7786	−	9.36751i	−0.443320	−	0.301395i
$967$	53.6640			1.72572			0.862859	−	0.505444i	$-0.168671\pi$
$967$	53.6640			1.72572			0.862859	+	0.505444i	$0.168671\pi$
$968$	6.29413	+	3.63392i	0.202301	+	0.116799i
$969$	0.980966	−	2.71617i	0.0315132	−	0.0872561i
$970$	−2.45017	−	4.24381i	−0.0786701	−	0.136261i
$971$	26.9806	−	46.7317i	0.865848	−	1.49969i	−0.000355104	−	1.00000i	$-0.500113\pi$
$971$	26.9806	−	46.7317i	0.865848	−	1.49969i	0.866203	−	0.499692i	$-0.166554\pi$
$972$	−14.5810	+	5.51325i	−0.467684	+	0.176837i
$973$	15.9674	+	15.6106i	0.511892	+	0.500452i
$974$		−	5.60406i		−	0.179566i
$975$	1.04455	−	0.186861i	0.0334524	−	0.00598435i
$976$	−2.92469	+	1.68857i	−0.0936172	+	0.0540499i
$977$	−52.5754	+	30.3544i	−1.68203	+	0.971123i	−0.721728	+	0.692177i	$0.756652\pi$
$977$	−52.5754	+	30.3544i	−1.68203	+	0.971123i	−0.960307	+	0.278946i	$0.910015\pi$
$978$	33.8882	−	6.06232i	1.08363	−	0.193852i
$979$		−	28.8232i		−	0.921194i
$980$	0.331326	+	14.6585i	0.0105838	+	0.468248i
$981$	1.90072	−	11.1020i	0.0606852	−	0.354461i
$982$	−9.70531	+	16.8101i	−0.309709	+	0.536431i
$983$	9.30310	+	16.1134i	0.296723	+	0.513939i	0.975384	−	0.220512i	$-0.0707729\pi$
$983$	9.30310	+	16.1134i	0.296723	+	0.513939i	−0.678661	+	0.734451i	$0.737440\pi$
$984$	−5.09549	+	14.1088i	−0.162438	+	0.449772i
$985$	−21.8169	−	12.5960i	−0.695143	−	0.401341i
$986$	−2.68574			−0.0855313
$987$	1.47866	−	20.0869i	0.0470662	−	0.639372i
$988$	2.40970			0.0766629
$989$	25.2497	+	14.5779i	0.802893	+	0.463550i
$990$	11.3867	−	4.20865i	0.361892	−	0.133760i
$991$	−13.6603	−	23.6603i	−0.433934	−	0.751596i	0.563274	−	0.826270i	$-0.309542\pi$
$991$	−13.6603	−	23.6603i	−0.433934	−	0.751596i	−0.997208	+	0.0746745i	$0.976208\pi$
$992$	0.472140	−	0.817770i	0.0149905	−	0.0259642i
$993$	20.3967	−	17.2014i	0.647268	−	0.545871i
$994$	2.55796	+	9.13238i	0.0811334	+	0.289662i
$995$		−	31.5851i		−	1.00132i
$996$	3.83852	+	21.4572i	0.121628	+	0.679898i
$997$	−24.8479	+	14.3459i	−0.786940	+	0.454340i	−0.838884	−	0.544310i	$-0.816792\pi$
$997$	−24.8479	+	14.3459i	−0.786940	+	0.454340i	0.0519442	+	0.998650i	$0.483458\pi$
$998$	21.0412	−	12.1481i	0.666047	−	0.384542i
$999$	−37.1778	+	0.277303i	−1.17625	+	0.00877346i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.z.b.131.8	yes	32
3.2	odd	2		546.2.z.a.131.13	✓	32
7.3	odd	6		546.2.z.a.521.13	yes	32
21.17	even	6	inner	546.2.z.b.521.8	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.z.a.131.13	✓	32	3.2	odd	2
546.2.z.a.521.13	yes	32	7.3	odd	6
546.2.z.b.131.8	yes	32	1.1	even	1	trivial
546.2.z.b.521.8	yes	32	21.17	even	6	inner

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:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.z (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(1.62906 + 0.588348i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-1.04730 + 1.81398i) q^{5} +(-1.11664 - 1.32406i) q^{6} +(1.84957 - 1.89185i) q^{7} -1.00000i q^{8} +(2.30769 + 1.91691i) q^{9} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(1.62906 + 0.588348i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-1.04730 + 1.81398i) q^{5} +(-1.11664 - 1.32406i) q^{6} +(1.84957 - 1.89185i) q^{7} -1.00000i q^{8} +(2.30769 + 1.91691i) q^{9} +(1.81398 - 1.04730i) q^{10} +(1.67306 - 0.965940i) q^{11} +(0.305007 + 1.70498i) q^{12} -1.00000i q^{13} +(-2.54770 + 0.713604i) q^{14} +(-2.77337 + 2.33891i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-0.345960 - 0.599220i) q^{17} +(-1.04007 - 2.81394i) q^{18} +(2.08687 + 1.20485i) q^{19} -2.09460 q^{20} +(4.12613 - 1.99375i) q^{21} -1.93188 q^{22} +(3.14870 + 1.81790i) q^{23} +(0.588348 - 1.62906i) q^{24} +(0.306322 + 0.530566i) q^{25} +(-0.500000 + 0.866025i) q^{26} +(2.63157 + 4.48050i) q^{27} +(2.56317 + 0.655850i) q^{28} +3.88157i q^{29} +(3.57126 - 0.638869i) q^{30} +(0.817770 - 0.472140i) q^{31} +(0.866025 - 0.500000i) q^{32} +(3.29383 - 0.589238i) q^{33} +0.691920i q^{34} +(1.49472 + 5.33641i) q^{35} +(-0.506247 + 2.95698i) q^{36} +(-3.57753 + 6.19647i) q^{37} +(-1.20485 - 2.08687i) q^{38} +(0.588348 - 1.62906i) q^{39} +(1.81398 + 1.04730i) q^{40} -8.66067 q^{41} +(-4.57021 - 0.336428i) q^{42} +8.01907 q^{43} +(1.67306 + 0.965940i) q^{44} +(-5.89408 + 2.17852i) q^{45} +(-1.81790 - 3.14870i) q^{46} +(2.19759 - 3.80633i) q^{47} +(-1.32406 + 1.11664i) q^{48} +(-0.158181 - 6.99821i) q^{49} -0.612645i q^{50} +(-0.211041 - 1.17971i) q^{51} +(0.866025 - 0.500000i) q^{52} +(-4.81192 + 2.77816i) q^{53} +(-0.0387561 - 5.19601i) q^{54} +4.04652i q^{55} +(-1.89185 - 1.84957i) q^{56} +(2.69076 + 3.19058i) q^{57} +(1.94079 - 3.36154i) q^{58} +(-5.21237 - 9.02810i) q^{59} +(-3.41224 - 1.23235i) q^{60} +(2.92469 + 1.68857i) q^{61} -0.944280 q^{62} +(7.89475 - 0.820344i) q^{63} -1.00000 q^{64} +(1.81398 + 1.04730i) q^{65} +(-3.14716 - 1.13662i) q^{66} +(-4.98074 - 8.62689i) q^{67} +(0.345960 - 0.599220i) q^{68} +(4.05987 + 4.81401i) q^{69} +(1.37375 - 5.36883i) q^{70} -3.58456i q^{71} +(1.91691 - 2.30769i) q^{72} +(7.46660 - 4.31085i) q^{73} +(6.19647 - 3.57753i) q^{74} +(0.186861 + 1.04455i) q^{75} +2.40970i q^{76} +(1.26702 - 4.95175i) q^{77} +(-1.32406 + 1.11664i) q^{78} +(-8.33482 + 14.4363i) q^{79} +(-1.04730 - 1.81398i) q^{80} +(1.65090 + 8.84729i) q^{81} +(7.50036 + 4.33034i) q^{82} +12.5850 q^{83} +(3.78970 + 2.57646i) q^{84} +1.44930 q^{85} +(-6.94472 - 4.00954i) q^{86} +(-2.28372 + 6.32333i) q^{87} +(-0.965940 - 1.67306i) q^{88} +(7.45988 - 12.9209i) q^{89} +(6.19369 + 1.06039i) q^{90} +(-1.89185 - 1.84957i) q^{91} +3.63581i q^{92} +(1.60998 - 0.288012i) q^{93} +(-3.80633 + 2.19759i) q^{94} +(-4.37115 + 2.52369i) q^{95} +(1.70498 - 0.305007i) q^{96} -2.33951i q^{97} +(-3.36212 + 6.13972i) q^{98} +(5.71253 + 0.978010i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 16 q^{4} + 2 q^{7} + 2 q^{9}+O(q^{10}) \) 32 * q + 16 * q^4 + 2 * q^7 + 2 * q^9	\( 32 q + 16 q^{4} + 2 q^{7} + 2 q^{9} + 6 q^{10} + 24 q^{11} - 4 q^{14} - 12 q^{15} - 16 q^{16} - 4 q^{17} - 24 q^{18} + 4 q^{21} - 12 q^{22} - 6 q^{24} - 18 q^{25} - 16 q^{26} + 6 q^{27} - 2 q^{28} - 8 q^{30} - 6 q^{31} + 14 q^{33} - 48 q^{35} + 4 q^{36} - 16 q^{38} - 6 q^{39} + 6 q^{40} - 16 q^{41} + 14 q^{42} + 32 q^{43} + 24 q^{44} + 20 q^{45} + 16 q^{46} - 20 q^{47} - 26 q^{49} - 46 q^{51} + 60 q^{53} + 6 q^{54} - 8 q^{56} - 8 q^{57} - 10 q^{58} - 8 q^{59} - 6 q^{60} + 36 q^{61} - 36 q^{62} + 84 q^{63} - 32 q^{64} + 6 q^{65} + 36 q^{66} + 4 q^{68} + 36 q^{69} - 18 q^{70} - 24 q^{72} - 48 q^{73} + 84 q^{74} - 2 q^{75} - 52 q^{77} + 18 q^{79} - 74 q^{81} - 24 q^{83} + 8 q^{84} - 32 q^{85} + 24 q^{86} + 14 q^{87} - 6 q^{88} + 20 q^{89} + 6 q^{90} - 8 q^{91} - 40 q^{93} + 72 q^{95} - 6 q^{96} - 32 q^{98}+O(q^{100}) \) 32 * q + 16 * q^4 + 2 * q^7 + 2 * q^9 + 6 * q^10 + 24 * q^11 - 4 * q^14 - 12 * q^15 - 16 * q^16 - 4 * q^17 - 24 * q^18 + 4 * q^21 - 12 * q^22 - 6 * q^24 - 18 * q^25 - 16 * q^26 + 6 * q^27 - 2 * q^28 - 8 * q^30 - 6 * q^31 + 14 * q^33 - 48 * q^35 + 4 * q^36 - 16 * q^38 - 6 * q^39 + 6 * q^40 - 16 * q^41 + 14 * q^42 + 32 * q^43 + 24 * q^44 + 20 * q^45 + 16 * q^46 - 20 * q^47 - 26 * q^49 - 46 * q^51 + 60 * q^53 + 6 * q^54 - 8 * q^56 - 8 * q^57 - 10 * q^58 - 8 * q^59 - 6 * q^60 + 36 * q^61 - 36 * q^62 + 84 * q^63 - 32 * q^64 + 6 * q^65 + 36 * q^66 + 4 * q^68 + 36 * q^69 - 18 * q^70 - 24 * q^72 - 48 * q^73 + 84 * q^74 - 2 * q^75 - 52 * q^77 + 18 * q^79 - 74 * q^81 - 24 * q^83 + 8 * q^84 - 32 * q^85 + 24 * q^86 + 14 * q^87 - 6 * q^88 + 20 * q^89 + 6 * q^90 - 8 * q^91 - 40 * q^93 + 72 * q^95 - 6 * q^96 - 32 * q^98

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