LMFDB - Embedded newform 539.2.q.f.361.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [539,2,Mod(214,539)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(539, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([20, 12]))

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

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

chi := DirichletCharacter("539.214");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 539 = 7^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	539.q (of order $15$, degree $8$, not 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:	$4.30393666895$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$4$ over $\Q(\zeta_{15})$
Twist minimal:	no (minimal twist has level 77)
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			361.3
Character	$\chi$	$=$	539.361
Dual form			539.2.q.f.324.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.37847 - 0.293003i) q^{2} +(-0.226135 - 2.15153i) q^{3} +(-0.0127572 + 0.00567988i) q^{4} +(1.22544 - 1.36099i) q^{5} +(-0.942126 - 2.89957i) q^{6} +(-2.29616 + 1.66826i) q^{8} +(-1.64350 + 0.349337i) q^{9} +O(q^{10})$	\(q+(1.37847 - 0.293003i) q^{2} +(-0.226135 - 2.15153i) q^{3} +(-0.0127572 + 0.00567988i) q^{4} +(1.22544 - 1.36099i) q^{5} +(-0.942126 - 2.89957i) q^{6} +(-2.29616 + 1.66826i) q^{8} +(-1.64350 + 0.349337i) q^{9} +(1.29046 - 2.23514i) q^{10} +(-0.972092 - 3.17097i) q^{11} +(0.0151053 + 0.0261631i) q^{12} +(1.43602 - 4.41961i) q^{13} +(-3.20531 - 2.32880i) q^{15} +(-2.65770 + 2.95168i) q^{16} +(-5.35068 - 1.13732i) q^{17} +(-2.16316 + 0.963102i) q^{18} +(5.29964 + 2.35955i) q^{19} +(-0.00790293 + 0.0243227i) q^{20} +(-2.26911 - 4.08626i) q^{22} +(0.359841 + 0.623263i) q^{23} +(4.10856 + 4.56301i) q^{24} +(0.172056 + 1.63701i) q^{25} +(0.684551 - 6.51307i) q^{26} +(-0.882303 - 2.71545i) q^{27} +(0.948551 + 0.689163i) q^{29} +(-5.10078 - 2.27101i) q^{30} +(0.875133 + 0.971933i) q^{31} +(0.0394969 - 0.0684106i) q^{32} +(-6.60261 + 2.80855i) q^{33} -7.70900 q^{34} +(0.0189823 - 0.0137915i) q^{36} +(-0.218960 + 2.08326i) q^{37} +(7.99676 + 1.69976i) q^{38} +(-9.83366 - 2.09021i) q^{39} +(-0.543325 + 5.16939i) q^{40} +(-0.741582 + 0.538791i) q^{41} +8.02379 q^{43} +(0.0304119 + 0.0349314i) q^{44} +(-1.53856 + 2.66487i) q^{45} +(0.678649 + 0.753716i) q^{46} +(-5.45920 - 2.43059i) q^{47} +(6.95163 + 5.05065i) q^{48} +(0.716823 + 2.20615i) q^{50} +(-1.23701 + 11.7693i) q^{51} +(0.00678326 + 0.0645384i) q^{52} +(6.78828 + 7.53915i) q^{53} +(-2.01186 - 3.48465i) q^{54} +(-5.50688 - 2.56282i) q^{55} +(3.87821 - 11.9359i) q^{57} +(1.50948 + 0.672063i) q^{58} +(7.01677 - 3.12407i) q^{59} +(0.0541182 + 0.0115032i) q^{60} +(4.19955 - 4.66407i) q^{61} +(1.49113 + 1.08337i) q^{62} +(2.48916 - 7.66083i) q^{64} +(-4.25528 - 7.37036i) q^{65} +(-8.27859 + 5.80610i) q^{66} +(7.73363 - 13.3950i) q^{67} +(0.0747196 - 0.0158821i) q^{68} +(1.25960 - 0.915151i) q^{69} +(4.29593 + 13.2215i) q^{71} +(3.19096 - 3.54392i) q^{72} +(-5.49463 + 2.44637i) q^{73} +(0.308573 + 2.93588i) q^{74} +(3.48316 - 0.740369i) q^{75} -0.0810106 q^{76} -14.1679 q^{78} +(15.2991 - 3.25193i) q^{79} +(0.760344 + 7.23419i) q^{80} +(-10.2477 + 4.56258i) q^{81} +(-0.864382 + 0.959993i) q^{82} +(1.35217 + 4.16157i) q^{83} +(-8.10479 + 5.88848i) q^{85} +(11.0606 - 2.35100i) q^{86} +(1.26825 - 2.19668i) q^{87} +(7.52209 + 5.65936i) q^{88} +(7.67186 + 13.2880i) q^{89} +(-1.34005 + 4.12425i) q^{90} +(-0.00813063 - 0.00590725i) q^{92} +(1.89325 - 2.10266i) q^{93} +(-8.23752 - 1.75094i) q^{94} +(9.70568 - 4.32125i) q^{95} +(-0.156119 - 0.0695087i) q^{96} +(-0.745114 + 2.29323i) q^{97} +(2.70537 + 4.87190i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 3 q^{2} - 2 q^{3} + 11 q^{4} - 5 q^{5} - 6 q^{6} - 10 q^{8} + 12 q^{9}+O(q^{10}) $ 32 * q + 3 * q^2 - 2 * q^3 + 11 * q^4 - 5 * q^5 - 6 * q^6 - 10 * q^8 + 12 * q^9	$ 32 q + 3 q^{2} - 2 q^{3} + 11 q^{4} - 5 q^{5} - 6 q^{6} - 10 q^{8} + 12 q^{9} + 12 q^{10} + 3 q^{11} + 18 q^{12} + 14 q^{13} - 36 q^{15} - 17 q^{16} - 5 q^{17} - 11 q^{18} + 19 q^{19} - 2 q^{20} - 66 q^{22} - 32 q^{23} - 35 q^{24} - 7 q^{25} - 27 q^{26} - 20 q^{27} + 6 q^{29} + 2 q^{30} - 7 q^{31} - 32 q^{32} - 26 q^{33} + 48 q^{34} + 104 q^{36} - 4 q^{37} - 5 q^{38} - 11 q^{39} - 10 q^{40} + 20 q^{41} - 16 q^{43} + 38 q^{44} + 70 q^{45} + 42 q^{46} - 23 q^{47} + 72 q^{48} + 104 q^{50} + 29 q^{51} + 33 q^{52} - 4 q^{53} + 60 q^{54} + 24 q^{55} - 22 q^{57} - 20 q^{58} + 17 q^{59} + 30 q^{60} - 7 q^{61} - 158 q^{62} + 14 q^{64} + 8 q^{65} + 8 q^{66} + 38 q^{67} - 2 q^{68} - 20 q^{69} - 28 q^{71} - 35 q^{73} + 29 q^{74} + 9 q^{75} - 104 q^{76} - 116 q^{78} - 15 q^{79} - 87 q^{80} + 14 q^{81} + 19 q^{82} - 10 q^{83} + 12 q^{85} + 52 q^{86} - 72 q^{87} - 55 q^{88} + 74 q^{89} + 28 q^{90} - 110 q^{92} - 32 q^{93} - 24 q^{94} - 32 q^{95} - 42 q^{96} - 40 q^{97} + 32 q^{99}+O(q^{100}) $ 32 * q + 3 * q^2 - 2 * q^3 + 11 * q^4 - 5 * q^5 - 6 * q^6 - 10 * q^8 + 12 * q^9 + 12 * q^10 + 3 * q^11 + 18 * q^12 + 14 * q^13 - 36 * q^15 - 17 * q^16 - 5 * q^17 - 11 * q^18 + 19 * q^19 - 2 * q^20 - 66 * q^22 - 32 * q^23 - 35 * q^24 - 7 * q^25 - 27 * q^26 - 20 * q^27 + 6 * q^29 + 2 * q^30 - 7 * q^31 - 32 * q^32 - 26 * q^33 + 48 * q^34 + 104 * q^36 - 4 * q^37 - 5 * q^38 - 11 * q^39 - 10 * q^40 + 20 * q^41 - 16 * q^43 + 38 * q^44 + 70 * q^45 + 42 * q^46 - 23 * q^47 + 72 * q^48 + 104 * q^50 + 29 * q^51 + 33 * q^52 - 4 * q^53 + 60 * q^54 + 24 * q^55 - 22 * q^57 - 20 * q^58 + 17 * q^59 + 30 * q^60 - 7 * q^61 - 158 * q^62 + 14 * q^64 + 8 * q^65 + 8 * q^66 + 38 * q^67 - 2 * q^68 - 20 * q^69 - 28 * q^71 - 35 * q^73 + 29 * q^74 + 9 * q^75 - 104 * q^76 - 116 * q^78 - 15 * q^79 - 87 * q^80 + 14 * q^81 + 19 * q^82 - 10 * q^83 + 12 * q^85 + 52 * q^86 - 72 * q^87 - 55 * q^88 + 74 * q^89 + 28 * q^90 - 110 * q^92 - 32 * q^93 - 24 * q^94 - 32 * q^95 - 42 * q^96 - 40 * q^97 + 32 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/539\mathbb{Z}\right)^\times$.

$n$	$199$	$442$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{3}{5}\right)$

Coefficient data

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

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

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

$2$	1.37847	−	0.293003i	0.974727	−	0.207185i	0.307097	−	0.951678i	$-0.400642\pi$
$2$	1.37847	−	0.293003i	0.974727	−	0.207185i	0.667630	+	0.744494i	$0.267309\pi$
$3$	−0.226135	−	2.15153i	−0.130559	−	1.24219i	−0.842014	−	0.539455i	$-0.818630\pi$
$3$	−0.226135	−	2.15153i	−0.130559	−	1.24219i	0.711455	−	0.702731i	$-0.248036\pi$
$4$	−0.0127572	+	0.00567988i	−0.00637861	+	0.00283994i
$5$	1.22544	−	1.36099i	0.548032	−	0.608651i	−0.403959	−	0.914777i	$-0.632366\pi$
$5$	1.22544	−	1.36099i	0.548032	−	0.608651i	0.951991	+	0.306126i	$0.0990329\pi$
$6$	−0.942126	−	2.89957i	−0.384621	−	1.18374i
$7$		0			0
$7$		0			0
$8$	−2.29616	+	1.66826i	−0.811817	+	0.589819i
$9$	−1.64350	+	0.349337i	−0.547834	+	0.116446i
$10$	1.29046	−	2.23514i	0.408078	−	0.706812i
$11$	−0.972092	−	3.17097i	−0.293097	−	0.956083i
$11$	−0.972092	−	3.17097i	−0.293097	−	0.956083i
$12$	0.0151053	+	0.0261631i	0.00436052	+	0.00755264i
$13$	1.43602	−	4.41961i	0.398280	−	1.22578i	−0.528097	−	0.849184i	$-0.677094\pi$
$13$	1.43602	−	4.41961i	0.398280	−	1.22578i	0.926377	−	0.376596i	$-0.122906\pi$
$14$		0			0
$15$	−3.20531	−	2.32880i	−0.827609	−	0.601293i
$16$	−2.65770	+	2.95168i	−0.664426	+	0.737920i
$17$	−5.35068	−	1.13732i	−1.29773	−	0.275841i	−0.493285	−	0.869868i	$-0.664204\pi$
$17$	−5.35068	−	1.13732i	−1.29773	−	0.275841i	−0.804445	+	0.594027i	$0.797537\pi$
$18$	−2.16316	+	0.963102i	−0.509862	+	0.227005i
$19$	5.29964	+	2.35955i	1.21582	+	0.541318i	0.911519	−	0.411258i	$-0.134910\pi$
$19$	5.29964	+	2.35955i	1.21582	+	0.541318i	0.304301	+	0.952576i	$0.401577\pi$
$20$	−0.00790293	+	0.0243227i	−0.00176715	+	0.00543873i
$21$		0			0
$22$	−2.26911	−	4.08626i	−0.483775	−	0.871194i
$23$	0.359841	+	0.623263i	0.0750321	+	0.129959i	0.901100	−	0.433611i	$-0.142761\pi$
$23$	0.359841	+	0.623263i	0.0750321	+	0.129959i	−0.826068	+	0.563570i	$0.809427\pi$
$24$	4.10856	+	4.56301i	0.838656	+	0.931421i
$25$	0.172056	+	1.63701i	0.0344113	+	0.327401i
$26$	0.684551	−	6.51307i	0.134252	−	1.27732i
$27$	−0.882303	−	2.71545i	−0.169799	−	0.522588i
$28$		0			0
$29$	0.948551	+	0.689163i	0.176142	+	0.127974i	0.672363	−	0.740222i	$-0.265280\pi$
$29$	0.948551	+	0.689163i	0.176142	+	0.127974i	−0.496221	+	0.868196i	$0.665280\pi$
$30$	−5.10078	−	2.27101i	−0.931271	−	0.414629i
$31$	0.875133	+	0.971933i	0.157178	+	0.174564i	0.816591	−	0.577217i	$-0.195861\pi$
$31$	0.875133	+	0.971933i	0.157178	+	0.174564i	−0.659412	+	0.751782i	$0.729195\pi$
$32$	0.0394969	−	0.0684106i	0.00698213	−	0.0120934i
$33$	−6.60261	+	2.80855i	−1.14937	+	0.488906i
$34$	−7.70900			−1.32208
$35$		0			0
$36$	0.0189823	−	0.0137915i	0.00316372	−	0.00229858i
$37$	−0.218960	+	2.08326i	−0.0359968	+	0.342486i	0.961670	+	0.274210i	$0.0884165\pi$
$37$	−0.218960	+	2.08326i	−0.0359968	+	0.342486i	−0.997666	+	0.0682759i	$0.978250\pi$
$38$	7.99676	+	1.69976i	1.29725	+	0.275738i
$39$	−9.83366	−	2.09021i	−1.57465	−	0.334701i
$40$	−0.543325	+	5.16939i	−0.0859073	+	0.817353i
$41$	−0.741582	+	0.538791i	−0.115816	+	0.0841449i	−0.644185	−	0.764869i	$-0.722803\pi$
$41$	−0.741582	+	0.538791i	−0.115816	+	0.0841449i	0.528370	+	0.849014i	$0.322803\pi$
$42$		0			0
$43$	8.02379			1.22362			0.611808	−	0.791006i	$-0.290442\pi$
$43$	8.02379			1.22362			0.611808	+	0.791006i	$0.290442\pi$
$44$	0.0304119	+	0.0349314i	0.00458477	+	0.00526610i
$45$	−1.53856	+	2.66487i	−0.229356	+	0.397256i
$46$	0.678649	+	0.753716i	0.100061	+	0.111129i
$47$	−5.45920	−	2.43059i	−0.796306	−	0.354538i	−0.0320786	−	0.999485i	$-0.510213\pi$
$47$	−5.45920	−	2.43059i	−0.796306	−	0.354538i	−0.764227	+	0.644947i	$0.776879\pi$
$48$	6.95163	+	5.05065i	1.00338	+	0.728999i
$49$		0			0
$50$	0.716823	+	2.20615i	0.101374	+	0.311997i
$51$	−1.23701	+	11.7693i	−0.173216	+	1.64804i
$52$	0.00678326	+	0.0645384i	0.000940669	+	0.00894986i
$53$	6.78828	+	7.53915i	0.932443	+	1.03558i	0.999285	+	0.0378188i	$0.0120410\pi$
$53$	6.78828	+	7.53915i	0.932443	+	1.03558i	−0.0668420	+	0.997764i	$0.521292\pi$
$54$	−2.01186	−	3.48465i	−0.273780	−	0.474201i
$55$	−5.50688	−	2.56282i	−0.742547	−	0.345570i
$56$		0			0
$57$	3.87821	−	11.9359i	0.513682	−	1.58095i
$58$	1.50948	+	0.672063i	0.198204	+	0.0882462i
$59$	7.01677	−	3.12407i	0.913505	−	0.406719i	0.104503	−	0.994525i	$-0.466675\pi$
$59$	7.01677	−	3.12407i	0.913505	−	0.406719i	0.809002	+	0.587806i	$0.200008\pi$
$60$	0.0541182	+	0.0115032i	0.00698663	+	0.00148505i
$61$	4.19955	−	4.66407i	0.537697	−	0.597173i	−0.411674	−	0.911331i	$-0.635056\pi$
$61$	4.19955	−	4.66407i	0.537697	−	0.597173i	0.949371	+	0.314158i	$0.101722\pi$
$62$	1.49113	+	1.08337i	0.189373	+	0.137588i
$63$		0			0
$64$	2.48916	−	7.66083i	0.311144	−	0.957604i
$65$	−4.25528	−	7.37036i	−0.527802	−	0.914180i
$66$	−8.27859	+	5.80610i	−1.01902	+	0.714681i
$67$	7.73363	−	13.3950i	0.944814	−	1.63647i	0.188690	−	0.982037i	$-0.439576\pi$
$67$	7.73363	−	13.3950i	0.944814	−	1.63647i	0.756124	−	0.654429i	$-0.227091\pi$
$68$	0.0747196	−	0.0158821i	0.00906108	−	0.00192599i
$69$	1.25960	−	0.915151i	0.151638	−	0.110171i
$70$		0			0
$71$	4.29593	+	13.2215i	0.509833	+	1.56910i	0.792491	+	0.609883i	$0.208784\pi$
$71$	4.29593	+	13.2215i	0.509833	+	1.56910i	−0.282659	+	0.959221i	$0.591216\pi$
$72$	3.19096	−	3.54392i	0.376059	−	0.417655i
$73$	−5.49463	+	2.44637i	−0.643098	+	0.286326i	−0.702258	−	0.711923i	$-0.747825\pi$
$73$	−5.49463	+	2.44637i	−0.643098	+	0.286326i	0.0591596	+	0.998249i	$0.481158\pi$
$74$	0.308573	+	2.93588i	0.0358709	+	0.341289i
$75$	3.48316	−	0.740369i	0.402201	−	0.0854904i
$76$	−0.0810106			−0.00929255
$77$		0			0
$78$	−14.1679			−1.60420
$79$	15.2991	−	3.25193i	1.72129	−	0.365871i	0.761842	−	0.647762i	$-0.224295\pi$
$79$	15.2991	−	3.25193i	1.72129	−	0.365871i	0.959446	+	0.281891i	$0.0909617\pi$
$80$	0.760344	+	7.23419i	0.0850091	+	0.808807i
$81$	−10.2477	+	4.56258i	−1.13864	+	0.506953i
$82$	−0.864382	+	0.959993i	−0.0954550	+	0.106014i
$83$	1.35217	+	4.16157i	0.148420	+	0.456791i	0.997435	−	0.0715783i	$-0.0228036\pi$
$83$	1.35217	+	4.16157i	0.148420	+	0.456791i	−0.849015	+	0.528370i	$0.822804\pi$
$84$		0			0
$85$	−8.10479	+	5.88848i	−0.879088	+	0.638695i
$86$	11.0606	−	2.35100i	1.19269	−	0.253514i
$87$	1.26825	−	2.19668i	0.135971	−	0.235509i
$88$	7.52209	+	5.65936i	0.801857	+	0.603290i
$89$	7.67186	+	13.2880i	0.813215	+	1.40853i	0.910602	+	0.413283i	$0.135618\pi$
$89$	7.67186	+	13.2880i	0.813215	+	1.40853i	−0.0973874	+	0.995247i	$0.531049\pi$
$90$	−1.34005	+	4.12425i	−0.141254	+	0.434735i
$91$		0			0
$92$	−0.00813063	−	0.00590725i	−0.000847677	−	0.000615873i
$93$	1.89325	−	2.10266i	0.196320	−	0.218036i
$94$	−8.23752	−	1.75094i	−0.849635	−	0.180596i
$95$	9.70568	−	4.32125i	0.995782	−	0.443351i
$96$	−0.156119	−	0.0695087i	−0.0159338	−	0.00709420i
$97$	−0.745114	+	2.29323i	−0.0756549	+	0.232842i	−0.981731	−	0.190272i	$-0.939063\pi$
$97$	−0.745114	+	2.29323i	−0.0756549	+	0.232842i	0.906077	+	0.423114i	$0.139063\pi$
$98$		0			0
$99$	2.70537	+	4.87190i	0.271900	+	0.489645i
$100$	−0.0114930	−	0.0199064i	−0.00114930	−	0.00199064i
$101$	−7.95989	−	8.84035i	−0.792039	−	0.879648i	0.202996	−	0.979180i	$-0.434932\pi$
$101$	−7.95989	−	8.84035i	−0.792039	−	0.879648i	−0.995034	+	0.0995315i	$0.968266\pi$
$102$	1.74327	+	16.5861i	0.172610	+	1.64227i
$103$	0.0414261	−	0.394143i	0.00408183	−	0.0388360i	−0.992291	−	0.123927i	$-0.960451\pi$
$103$	0.0414261	−	0.394143i	0.00408183	−	0.0388360i	0.996373	+	0.0850905i	$0.0271179\pi$
$104$	4.07573	+	12.5438i	0.399658	+	1.23002i
$105$		0			0
$106$	11.5665	+	8.40352i	1.12343	+	0.816222i
$107$	−2.98670	−	1.32977i	−0.288735	−	0.128553i	0.257258	−	0.966343i	$-0.417181\pi$
$107$	−2.98670	−	1.32977i	−0.288735	−	0.128553i	−0.545993	+	0.837789i	$0.683848\pi$
$108$	0.0266791	+	0.0296302i	0.00256720	+	0.00285117i
$109$	1.42319	−	2.46504i	0.136317	−	0.236108i	−0.789783	−	0.613387i	$-0.789807\pi$
$109$	1.42319	−	2.46504i	0.136317	−	0.236108i	0.926100	+	0.377279i	$0.123140\pi$
$110$	−8.34199	−	1.91924i	−0.795378	−	0.182992i
$111$	4.53172			0.430132
$112$		0			0
$113$	−11.7668	+	8.54906i	−1.10692	+	0.804228i	−0.982177	−	0.187961i	$-0.939812\pi$
$113$	−11.7668	+	8.54906i	−1.10692	+	0.804228i	−0.124748	+	0.992188i	$0.539812\pi$
$114$	1.84875	−	17.5896i	0.173151	−	1.64742i
$115$	1.28921	+	0.274031i	0.120220	+	0.0255535i
$116$	−0.0160152	−	0.00340414i	−0.00148698	−	0.000316067i
$117$	−0.816165	+	7.76529i	−0.0754545	+	0.717902i
$118$	8.75705	−	6.36237i	0.806152	−	0.585704i
$119$		0			0
$120$	11.2450			1.02652
$121$	−9.11007	+	6.16495i	−0.828188	+	0.560450i
$122$	4.42237	−	7.65977i	0.400383	−	0.693483i
$123$	1.32692	+	1.47370i	0.119644	+	0.132879i
$124$	−0.0166847	−	0.00742852i	−0.00149833	−	0.000667100i
$125$	9.84690	+	7.15419i	0.880734	+	0.639890i
$126$		0			0
$127$	1.55524	+	4.78655i	0.138006	+	0.424737i	0.996045	−	0.0888458i	$-0.0283178\pi$
$127$	1.55524	+	4.78655i	0.138006	+	0.424737i	−0.858040	+	0.513583i	$0.828318\pi$
$128$	1.17007	−	11.1324i	0.103420	−	0.983979i
$129$	−1.81446	−	17.2634i	−0.159754	−	1.51996i
$130$	−8.02532	−	8.91302i	−0.703867	−	0.781724i
$131$	−0.0900265	−	0.155930i	−0.00786565	−	0.0136237i	0.862066	−	0.506796i	$-0.169170\pi$
$131$	−0.0900265	−	0.155930i	−0.00786565	−	0.0136237i	−0.869931	+	0.493173i	$0.835837\pi$
$132$	0.0682787	−	0.0733313i	0.00594290	−	0.00638267i
$133$		0			0
$134$	6.73581	−	20.7307i	0.581885	−	1.79086i
$135$	−4.77689	−	2.12681i	−0.411129	−	0.183047i
$136$	14.1834	−	6.31485i	1.21621	−	0.541494i
$137$	−8.14206	−	1.73065i	−0.695623	−	0.147859i	−0.153488	−	0.988151i	$-0.549051\pi$
$137$	−8.14206	−	1.73065i	−0.695623	−	0.147859i	−0.542135	+	0.840291i	$0.682384\pi$
$138$	1.46818	−	1.63058i	0.124980	−	0.138804i
$139$	−5.63172	−	4.09169i	−0.477677	−	0.347052i	0.322749	−	0.946485i	$-0.395393\pi$
$139$	−5.63172	−	4.09169i	−0.477677	−	0.347052i	−0.800425	+	0.599432i	$0.795393\pi$
$140$		0			0
$141$	−3.99497	+	12.2953i	−0.336438	+	1.03545i
$142$	9.79576	+	16.9667i	0.822042	+	1.42382i
$143$	−15.4104	−	0.257299i	−1.28868	−	0.0215164i
$144$	3.33681	−	5.77952i	0.278067	−	0.481627i
$145$	2.10033	−	0.446439i	0.174423	−	0.0370747i
$146$	−6.85740	+	4.98219i	−0.567523	+	0.412329i
$147$		0			0
$148$	−0.00903937	−	0.0278203i	−0.000743031	−	0.00228682i
$149$	−2.15079	+	2.38870i	−0.176200	+	0.195690i	−0.824775	−	0.565461i	$-0.808698\pi$
$149$	−2.15079	+	2.38870i	−0.176200	+	0.195690i	0.648575	+	0.761150i	$0.275365\pi$
$150$	4.58451	−	2.04115i	0.374324	−	0.166660i
$151$	−2.32754	−	22.1450i	−0.189412	−	1.80214i	−0.515597	−	0.856831i	$-0.672430\pi$
$151$	−2.32754	−	22.1450i	−0.189412	−	1.80214i	0.326185	−	0.945306i	$-0.394237\pi$
$152$	−16.1052	+	3.42326i	−1.30630	+	0.277663i
$153$	9.19115			0.743061
$154$		0			0
$155$	2.39521			0.192388
$156$	0.137322	−	0.0291888i	0.0109946	−	0.00233697i
$157$	1.38550	+	13.1822i	0.110575	+	1.05205i	0.899308	+	0.437316i	$0.144071\pi$
$157$	1.38550	+	13.1822i	0.110575	+	1.05205i	−0.788733	+	0.614736i	$0.789263\pi$
$158$	20.1366	−	8.96540i	1.60198	−	0.713249i
$159$	14.6856	−	16.3101i	1.16465	−	1.29347i
$160$	−0.0447049	−	0.137588i	−0.00353423	−	0.0108773i
$161$		0			0
$162$	−12.7893	+	9.29200i	−1.00483	+	0.730048i
$163$	−13.4186	+	2.85220i	−1.05102	+	0.223402i	−0.700869	−	0.713290i	$-0.747204\pi$
$163$	−13.4186	+	2.85220i	−1.05102	+	0.223402i	−0.350154	+	0.936692i	$0.613871\pi$
$164$	0.00640025	−	0.0110856i	0.000499776	−	0.000865637i
$165$	−4.26868	+	12.4278i	−0.332316	+	0.967499i
$166$	3.08329	+	5.34041i	0.239310	+	0.414496i
$167$	−2.87651	+	8.85300i	−0.222591	+	0.685066i	0.775936	+	0.630812i	$0.217278\pi$
$167$	−2.87651	+	8.85300i	−0.222591	+	0.685066i	−0.998527	+	0.0542539i	$0.982722\pi$
$168$		0			0
$169$	−6.95361	−	5.05209i	−0.534893	−	0.388623i
$170$	−9.44689	+	10.4918i	−0.724543	+	0.804687i
$171$	−9.53424	−	2.02657i	−0.729102	−	0.154975i
$172$	−0.102361	+	0.0455742i	−0.00780497	+	0.00347500i
$173$	−9.59742	−	4.27304i	−0.729678	−	0.324874i	0.00805375	−	0.999968i	$-0.497436\pi$
$173$	−9.59742	−	4.27304i	−0.729678	−	0.324874i	−0.737732	+	0.675094i	$0.764103\pi$
$174$	1.10462	−	3.39966i	0.0837409	−	0.257728i
$175$		0			0
$176$	11.9432	+	5.55819i	0.900254	+	0.418964i
$177$	−8.30826	−	14.3903i	−0.624487	−	1.08164i
$178$	14.4689	+	16.0693i	1.08449	+	1.20445i
$179$	0.870023	+	8.27771i	0.0650285	+	0.618705i	0.977699	+	0.210010i	$0.0673496\pi$
$179$	0.870023	+	8.27771i	0.0650285	+	0.618705i	−0.912671	+	0.408696i	$0.865984\pi$
$180$	0.00449165	−	0.0427352i	0.000334788	−	0.00318529i
$181$	4.57437	+	14.0785i	0.340010	+	1.04644i	0.964201	+	0.265172i	$0.0854286\pi$
$181$	4.57437	+	14.0785i	0.340010	+	1.04644i	−0.624191	+	0.781272i	$0.714571\pi$
$182$		0			0
$183$	−10.9845	−	7.98074i	−0.812001	−	0.589953i
$184$	−1.86602	−	0.830806i	−0.137565	−	0.0612478i
$185$	2.56697	+	2.85091i	0.188727	+	0.209603i
$186$	1.99370	−	3.45319i	0.146185	−	0.253200i
$187$	1.59494	+	18.0724i	0.116634	+	1.32159i
$188$	0.0834496			0.00608619
$189$		0			0
$190$	12.1129	−	8.80052i	0.878760	−	0.638457i
$191$	1.00418	−	9.55413i	0.0726599	−	0.691313i	−0.896191	−	0.443668i	$-0.853677\pi$
$191$	1.00418	−	9.55413i	0.0726599	−	0.691313i	0.968851	−	0.247644i	$-0.0796565\pi$
$192$	−17.0454	−	3.62311i	−1.23015	−	0.261475i
$193$	1.45530	+	0.309333i	0.104755	+	0.0222663i	0.259991	−	0.965611i	$-0.416281\pi$
$193$	1.45530	+	0.309333i	0.104755	+	0.0222663i	−0.155236	+	0.987877i	$0.549614\pi$
$194$	−0.355196	+	3.37947i	−0.0255016	+	0.242632i
$195$	−14.8953	+	10.8221i	−1.06667	+	0.774983i
$196$		0			0
$197$	−14.0434			−1.00055			−0.500274	−	0.865867i	$-0.666767\pi$
$197$	−14.0434			−1.00055			−0.500274	+	0.865867i	$0.666767\pi$
$198$	5.15676	+	5.92310i	0.366475	+	0.420936i
$199$	−2.14364	+	3.71290i	−0.151959	+	0.263200i	−0.931948	−	0.362593i	$-0.881891\pi$
$199$	−2.14364	+	3.71290i	−0.151959	+	0.263200i	0.779989	+	0.625794i	$0.215225\pi$
$200$	−3.12602	−	3.47180i	−0.221043	−	0.245493i
$201$	−30.5687	−	13.6101i	−2.15615	−	0.959979i
$202$	−13.5627	−	9.85391i	−0.954271	−	0.693318i
$203$		0			0
$204$	−0.0510676	−	0.157170i	−0.00357545	−	0.0110041i
$205$	−0.175475	+	1.66954i	−0.0122557	+	0.116605i
$206$	−0.0583804	−	0.555453i	−0.00406756	−	0.0387002i
$207$	−0.809128	−	0.898628i	−0.0562383	−	0.0624590i
$208$	9.22877	+	15.9847i	0.639900	+	1.10834i
$209$	2.33032	−	19.0987i	0.161192	−	1.32108i
$210$		0			0
$211$	−0.449704	+	1.38405i	−0.0309589	+	0.0952816i	−0.965342	−	0.260988i	$-0.915952\pi$
$211$	−0.449704	+	1.38405i	−0.0309589	+	0.0952816i	0.934383	+	0.356270i	$0.115952\pi$
$212$	−0.129421	−	0.0576220i	−0.00888868	−	0.00395749i
$213$	27.4750	−	12.2327i	1.88256	−	0.838168i
$214$	−4.50671	−	0.957931i	−0.308072	−	0.0654828i
$215$	9.83265	−	10.9203i	0.670581	−	0.744756i
$216$	6.55599	+	4.76320i	0.446079	+	0.324095i
$217$		0			0
$218$	1.23957	−	3.81499i	0.0839540	−	0.258384i
$219$	6.50596	+	11.2687i	0.439632	+	0.761465i
$220$	0.0848089	+	0.00141601i	0.00571782	+	9.54673e-5i
$221$	−12.7102	+	22.0147i	−0.854980	+	1.48087i
$222$	6.24685	−	1.32781i	0.419261	−	0.0891166i
$223$	−3.92893	+	2.85453i	−0.263101	+	0.191154i	−0.711513	−	0.702673i	$-0.751990\pi$
$223$	−3.92893	+	2.85453i	−0.263101	+	0.191154i	0.448412	+	0.893827i	$0.351990\pi$
$224$		0			0
$225$	−0.854642	−	2.63032i	−0.0569761	−	0.175354i
$226$	−13.7153	+	15.2323i	−0.912325	+	1.01324i
$227$	−0.362809	+	0.161533i	−0.0240805	+	0.0107213i	−0.418742	−	0.908105i	$-0.637529\pi$
$227$	−0.362809	+	0.161533i	−0.0240805	+	0.0107213i	0.394661	+	0.918827i	$0.370862\pi$
$228$	0.0183193	+	0.174297i	0.00121323	+	0.0115431i
$229$	2.14178	−	0.455250i	0.141533	−	0.0300838i	−0.136600	−	0.990626i	$-0.543618\pi$
$229$	2.14178	−	0.455250i	0.141533	−	0.0300838i	0.278133	+	0.960542i	$0.410284\pi$
$230$	1.85744			0.122476
$231$		0			0
$232$	−3.32773			−0.218476
$233$	1.23262	−	0.262001i	0.0807515	−	0.0171643i	−0.167359	−	0.985896i	$-0.553524\pi$
$233$	1.23262	−	0.262001i	0.0807515	−	0.0171643i	0.248110	+	0.968732i	$0.420190\pi$
$234$	1.15020	+	10.9434i	0.0751906	+	0.715391i
$235$	−9.99790	+	4.45135i	−0.652191	+	0.290374i
$236$	−0.0717701	+	0.0797088i	−0.00467184	+	0.00518860i
$237$	−10.4563	−	32.1812i	−0.679210	−	2.09039i
$238$		0			0
$239$	9.02997	−	6.56066i	0.584100	−	0.424374i	−0.256100	−	0.966650i	$-0.582438\pi$
$239$	9.02997	−	6.56066i	0.584100	−	0.424374i	0.840200	+	0.542277i	$0.182438\pi$
$240$	15.3926	−	3.27181i	0.993591	−	0.211194i
$241$	−10.7421	+	18.6059i	−0.691962	+	1.19851i	0.279232	+	0.960224i	$0.409920\pi$
$241$	−10.7421	+	18.6059i	−0.691962	+	1.19851i	−0.971194	+	0.238290i	$0.923413\pi$
$242$	−10.7516	+	11.1675i	−0.691141	+	0.717873i
$243$	7.85110	+	13.5985i	0.503648	+	0.872344i
$244$	−0.0270832	+	0.0833535i	−0.00173382	+	0.00533616i
$245$		0			0
$246$	2.26092	+	1.64266i	0.144151	+	0.104732i
$247$	18.0387	−	20.0340i	1.14777	−	1.27473i
$248$	−3.63089	−	0.771769i	−0.230562	−	0.0490074i
$249$	8.64796	−	3.85032i	0.548042	−	0.244004i
$250$	15.6699	+	6.97668i	0.991050	+	0.441244i
$251$	0.130968	−	0.403077i	0.00826660	−	0.0254420i	−0.946838	−	0.321710i	$-0.895742\pi$
$251$	0.130968	−	0.403077i	0.00826660	−	0.0254420i	0.955105	+	0.296268i	$0.0957423\pi$
$252$		0			0
$253$	1.62655	−	1.74691i	0.102260	−	0.109828i
$254$	3.54633	+	6.14243i	0.222517	+	0.385410i
$255$	14.5020	+	16.1061i	0.908151	+	1.00860i
$256$	0.0350308	+	0.333296i	0.00218943	+	0.0208310i
$257$	1.82298	−	17.3445i	0.113715	−	1.08192i	−0.777670	−	0.628673i	$-0.783598\pi$
$257$	1.82298	−	17.3445i	0.113715	−	1.08192i	0.891384	−	0.453249i	$-0.149735\pi$
$258$	−7.55942	−	23.2655i	−0.470629	−	1.44845i
$259$		0			0
$260$	0.0961483	+	0.0698558i	0.00596286	+	0.00433227i
$261$	−1.79970	−	0.801276i	−0.111398	−	0.0495977i
$262$	−0.169787	−	0.188568i	−0.0104895	−	0.0116498i
$263$	−0.757596	+	1.31219i	−0.0467153	+	0.0809133i	−0.888438	−	0.458997i	$-0.848209\pi$
$263$	−0.757596	+	1.31219i	−0.0467153	+	0.0809133i	0.841722	+	0.539911i	$0.181542\pi$
$264$	10.4753	−	17.4638i	0.644709	−	1.07482i
$265$	18.5793			1.14132
$266$		0			0
$267$	26.8548	−	19.5111i	1.64348	−	1.19406i
$268$	−0.0225774	+	0.214810i	−0.00137913	+	0.0131216i
$269$	−1.98664	−	0.422274i	−0.121128	−	0.0257465i	0.146949	−	0.989144i	$-0.453055\pi$
$269$	−1.98664	−	0.422274i	−0.121128	−	0.0257465i	−0.268077	+	0.963398i	$0.586388\pi$
$270$	−7.20797	−	1.53210i	−0.438663	−	0.0932407i
$271$	0.794880	−	7.56278i	0.0482855	−	0.459406i	−0.943489	−	0.331405i	$-0.892477\pi$
$271$	0.794880	−	7.56278i	0.0482855	−	0.459406i	0.991774	−	0.128001i	$-0.0408561\pi$
$272$	17.5775	−	12.7708i	1.06579	−	0.774344i
$273$		0			0
$274$	−11.7307			−0.708676
$275$	5.02364	−	2.13691i	0.302937	−	0.128860i
$276$	−0.0108710	+	0.0188291i	−0.000654358	+	0.00113338i
$277$	9.65342	+	10.7212i	0.580018	+	0.644175i	0.959728	−	0.280930i	$-0.0906430\pi$
$277$	9.65342	+	10.7212i	0.580018	+	0.644175i	−0.379710	+	0.925105i	$0.623976\pi$
$278$	−8.96205	−	3.99016i	−0.537508	−	0.239314i
$279$	−1.77781	−	1.29166i	−0.106435	−	0.0773295i
$280$		0			0
$281$	5.48494	+	16.8809i	0.327204	+	1.00703i	0.970436	+	0.241359i	$0.0775933\pi$
$281$	5.48494	+	16.8809i	0.327204	+	1.00703i	−0.643232	+	0.765672i	$0.722407\pi$
$282$	−1.90441	+	18.1192i	−0.113406	+	1.07898i
$283$	−3.25461	−	30.9656i	−0.193467	−	1.84071i	−0.473587	−	0.880747i	$-0.657041\pi$
$283$	−3.25461	−	30.9656i	−0.193467	−	1.84071i	0.280120	−	0.959965i	$-0.409626\pi$
$284$	−0.129901	−	0.144269i	−0.00770818	−	0.00856080i
$285$	−11.4921	−	19.9049i	−0.680733	−	1.17906i
$286$	−21.3182	+	4.16062i	−1.26057	+	0.246022i
$287$		0			0
$288$	−0.0410148	+	0.126231i	−0.00241682	+	0.00743821i
$289$	11.8060	+	5.25635i	0.694469	+	0.309197i
$290$	2.76444	−	1.23081i	0.162333	−	0.0722755i
$291$	5.10244	+	1.08456i	0.299110	+	0.0635779i
$292$	0.0562012	−	0.0624177i	0.00328892	−	0.00365272i
$293$	−19.4409	−	14.1247i	−1.13575	−	0.825171i	−0.149229	−	0.988803i	$-0.547679\pi$
$293$	−19.4409	−	14.1247i	−1.13575	−	0.825171i	−0.986522	+	0.163632i	$0.947679\pi$
$294$		0			0
$295$	4.34679	−	13.3781i	0.253080	−	0.778901i
$296$	−2.97266	−	5.14880i	−0.172782	−	0.299268i
$297$	−7.75292	+	5.43742i	−0.449870	+	0.315511i
$298$	−2.26491	+	3.92295i	−0.131203	+	0.227250i
$299$	3.27132	−	0.695341i	0.189185	−	0.0402126i
$300$	−0.0402302	+	0.0292290i	−0.00232269	+	0.00168754i
$301$		0			0
$302$	−9.69701	−	29.8443i	−0.558000	−	1.71735i
$303$	−17.2203	+	19.1251i	−0.989279	+	1.09871i
$304$	−21.0495	+	9.37184i	−1.20727	+	0.537512i
$305$	−1.20145	−	11.4310i	−0.0687949	−	0.654540i
$306$	12.6697	−	2.69304i	0.724281	−	0.153951i
$307$	5.46298			0.311789			0.155894	−	0.987774i	$-0.450174\pi$
$307$	5.46298			0.311789			0.155894	+	0.987774i	$0.450174\pi$
$308$		0			0
$309$	−0.857378			−0.0487745
$310$	3.30172	−	0.701803i	0.187525	−	0.0398597i
$311$	1.45174	+	13.8124i	0.0823204	+	0.783227i	0.955334	+	0.295530i	$0.0954962\pi$
$311$	1.45174	+	13.8124i	0.0823204	+	0.783227i	−0.873013	+	0.487697i	$0.837837\pi$
$312$	26.0667	−	11.6057i	1.47574	−	0.657041i
$313$	−18.3667	+	20.3983i	−1.03815	+	1.15298i	−0.0501114	+	0.998744i	$0.515958\pi$
$313$	−18.3667	+	20.3983i	−1.03815	+	1.15298i	−0.988034	+	0.154234i	$0.950709\pi$
$314$	5.77229	+	17.7653i	0.325749	+	1.00255i
$315$		0			0
$316$	−0.176704	+	0.128383i	−0.00994038	+	0.00722211i
$317$	−7.65469	+	1.62706i	−0.429930	+	0.0913845i	−0.417794	−	0.908542i	$-0.637197\pi$
$317$	−7.65469	+	1.62706i	−0.429930	+	0.0913845i	−0.0121365	+	0.999926i	$0.503863\pi$
$318$	15.4648	−	26.7859i	0.867226	−	1.50208i
$319$	1.26323	−	3.67776i	0.0707275	−	0.205915i
$320$	−7.37598	−	12.7756i	−0.412330	−	0.714176i
$321$	−2.18563	+	6.72669i	−0.121990	+	0.375447i
$322$		0			0
$323$	−25.6731	−	18.6526i	−1.42849	−	1.03786i
$324$	0.104817	−	0.116412i	0.00582319	−	0.00646731i
$325$	7.48201	+	1.59035i	0.415027	+	0.0882168i
$326$	−17.6614	+	7.86337i	−0.978175	+	0.435512i
$327$	−5.62544	−	2.50461i	−0.311088	−	0.138505i
$328$	0.803950	−	2.47430i	0.0443907	−	0.136621i
$329$		0			0
$330$	−2.24288	+	18.3820i	−0.123467	+	1.01190i
$331$	14.0731	+	24.3753i	0.773527	+	1.33979i	0.935619	+	0.353012i	$0.114843\pi$
$331$	14.0731	+	24.3753i	0.773527	+	1.33979i	−0.162092	+	0.986776i	$0.551824\pi$
$332$	−0.0408872	−	0.0454098i	−0.00224398	−	0.00249219i
$333$	−0.367900	−	3.50034i	−0.0201608	−	0.191817i
$334$	−1.37124	+	13.0464i	−0.0750307	+	0.713869i
$335$	−8.75338	−	26.9401i	−0.478248	−	1.47190i
$336$		0			0
$337$	20.2084	+	14.6823i	1.10082	+	0.799793i	0.981194	−	0.193025i	$-0.0618300\pi$
$337$	20.2084	+	14.6823i	1.10082	+	0.799793i	0.119628	+	0.992819i	$0.461830\pi$
$338$	−11.0656	−	4.92674i	−0.601891	−	0.267979i
$339$	21.0544	+	23.3833i	1.14352	+	1.27001i
$340$	0.0699488	−	0.121155i	0.00379350	−	0.00657054i
$341$	2.23126	−	3.71983i	0.120829	−	0.201440i
$342$	−13.7365			−0.742783
$343$		0			0
$344$	−18.4239	+	13.3858i	−0.993352	+	0.721713i
$345$	0.298050	−	2.83575i	0.0160464	−	0.152672i
$346$	−14.4818	−	3.07820i	−0.778545	−	0.165485i
$347$	−20.1980	−	4.29322i	−1.08429	−	0.230472i	−0.369088	−	0.929395i	$-0.620330\pi$
$347$	−20.1980	−	4.29322i	−1.08429	−	0.230472i	−0.715197	+	0.698923i	$0.753663\pi$
$348$	−0.00370251	+	0.0352271i	−0.000198476	+	0.00188837i
$349$	−4.85185	+	3.52507i	−0.259713	+	0.188693i	−0.710021	−	0.704181i	$-0.751314\pi$
$349$	−4.85185	+	3.52507i	−0.259713	+	0.188693i	0.450307	+	0.892874i	$0.351314\pi$
$350$		0			0
$351$	−13.2682			−0.708206
$352$	−0.255322	−	0.0587419i	−0.0136087	−	0.00313095i
$353$	12.0191	−	20.8177i	0.639712	−	1.10801i	−0.345784	−	0.938314i	$-0.612387\pi$
$353$	12.0191	−	20.8177i	0.639712	−	1.10801i	0.985496	−	0.169699i	$-0.0542796\pi$
$354$	−15.6691	−	17.4023i	−0.832804	−	0.924922i
$355$	23.2587	+	10.3554i	1.23444	+	0.549609i
$356$	−0.173346	−	0.125943i	−0.00918732	−	0.00667498i
$357$		0			0
$358$	3.62470	+	11.1557i	0.191571	+	0.589596i
$359$	1.14460	−	10.8901i	0.0604096	−	0.574759i	−0.921891	−	0.387449i	$-0.873356\pi$
$359$	1.14460	−	10.8901i	0.0604096	−	0.574759i	0.982301	−	0.187310i	$-0.0599770\pi$
$360$	−0.912905	−	8.68571i	−0.0481143	−	0.457777i
$361$	9.80520	+	10.8898i	0.516063	+	0.573146i
$362$	10.4307	+	18.0664i	0.548224	+	0.949551i
$363$	15.3242	+	18.2065i	0.804311	+	0.955593i
$364$		0			0
$365$	−3.40385	+	10.4760i	−0.178166	+	0.548338i
$366$	−17.4803	−	7.78272i	−0.913709	−	0.406809i
$367$	−9.69981	+	4.31863i	−0.506326	+	0.225431i	−0.643970	−	0.765051i	$-0.722714\pi$
$367$	−9.69981	+	4.31863i	−0.506326	+	0.225431i	0.137644	+	0.990482i	$0.456047\pi$
$368$	−2.79602	−	0.594313i	−0.145753	−	0.0309807i
$369$	1.03057	−	1.14456i	0.0536494	−	0.0595837i
$370$	4.37382	+	3.17777i	0.227384	+	0.165204i
$371$		0			0
$372$	−0.0122097	+	0.0375775i	−0.000633042	+	0.00194830i
$373$	−18.3018	−	31.6996i	−0.947631	−	1.64135i	−0.750395	−	0.660989i	$-0.770137\pi$
$373$	−18.3018	−	31.6996i	−0.947631	−	1.64135i	−0.197236	−	0.980356i	$-0.563196\pi$
$374$	7.49386	+	24.4450i	0.387498	+	1.26402i
$375$	13.1657	−	22.8037i	0.679875	−	1.17758i
$376$	16.5901	−	3.52633i	0.855568	−	0.181857i
$377$	4.40797	−	3.20258i	0.227022	−	0.164941i
$378$		0			0
$379$	−3.91147	−	12.0383i	−0.200919	−	0.618364i	−0.999856	−	0.0169501i	$-0.994604\pi$
$379$	−3.91147	−	12.0383i	−0.200919	−	0.618364i	0.798938	−	0.601414i	$-0.205396\pi$
$380$	−0.0992734	+	0.110254i	−0.00509262	+	0.00565592i
$381$	9.94670	−	4.42856i	0.509585	−	0.226882i
$382$	−1.41516	−	13.4643i	−0.0724058	−	0.688895i
$383$	−15.1299	+	3.21595i	−0.773100	+	0.164328i	−0.577538	−	0.816364i	$-0.695987\pi$
$383$	−15.1299	+	3.21595i	−0.773100	+	0.164328i	−0.195562	+	0.980691i	$0.562653\pi$
$384$	−24.2164			−1.23579
$385$		0			0
$386$	2.09672			0.106720
$387$	−13.1871	+	2.80301i	−0.670338	+	0.142485i
$388$	−0.00351966	−	0.0334873i	−0.000178684	−	0.00170006i
$389$	−11.6139	+	5.17082i	−0.588846	+	0.262171i	−0.679457	−	0.733715i	$-0.737785\pi$
$389$	−11.6139	+	5.17082i	−0.588846	+	0.262171i	0.0906110	+	0.995886i	$0.471118\pi$
$390$	−17.3618	+	19.2823i	−0.879150	+	0.976395i
$391$	−1.21654	−	3.74414i	−0.0615232	−	0.189349i
$392$		0			0
$393$	−0.315131	+	0.228956i	−0.0158963	+	0.0115493i
$394$	−19.3584	+	4.11475i	−0.975261	+	0.207298i
$395$	14.3223	−	24.8070i	0.720633	−	1.24817i
$396$	−0.0621848	−	0.0467857i	−0.00312491	−	0.00235107i
$397$	−9.47870	−	16.4176i	−0.475722	−	0.823975i	0.523891	−	0.851785i	$-0.324480\pi$
$397$	−9.47870	−	16.4176i	−0.475722	−	0.823975i	−0.999613	+	0.0278101i	$0.991147\pi$
$398$	−1.86706	+	5.74622i	−0.0935873	+	0.288032i
$399$		0			0
$400$	−5.28919	−	3.84282i	−0.264460	−	0.192141i
$401$	−5.80945	+	6.45205i	−0.290110	+	0.322200i	−0.870528	−	0.492119i	$-0.836223\pi$
$401$	−5.80945	+	6.45205i	−0.290110	+	0.322200i	0.580418	+	0.814319i	$0.302889\pi$
$402$	−46.1259	−	9.80436i	−2.30055	−	0.488997i
$403$	5.55228	−	2.47203i	0.276579	−	0.123141i
$404$	0.151758	+	0.0675671i	0.00755025	+	0.00336159i
$405$	−6.34833	+	19.5381i	−0.315451	+	0.970858i
$406$		0			0
$407$	6.81881	−	1.33081i	0.337996	−	0.0659658i
$408$	−16.7939	−	29.0880i	−0.831424	−	1.44007i
$409$	−3.82345	−	4.24638i	−0.189058	−	0.209970i	0.641163	−	0.767405i	$-0.278452\pi$
$409$	−3.82345	−	4.24638i	−0.189058	−	0.209970i	−0.830221	+	0.557435i	$0.811786\pi$
$410$	0.247292	+	2.35282i	0.0122129	+	0.116198i
$411$	−1.88234	+	17.9092i	−0.0928488	+	0.883397i
$412$	0.00171020	+	0.00526346i	8.42556e−5	+	0.000259312i
$413$		0			0
$414$	−1.37866	−	1.00166i	−0.0677575	−	0.0492287i
$415$	7.32084	+	3.25945i	0.359366	+	0.160000i
$416$	−0.245630	−	0.272800i	−0.0120430	−	0.0133751i
$417$	−7.52986	+	13.0421i	−0.368739	+	0.638674i
$418$	−2.38369	−	27.0098i	−0.116590	−	1.32109i
$419$	27.1909			1.32836			0.664181	−	0.747571i	$-0.268780\pi$
$419$	27.1909			1.32836			0.664181	+	0.747571i	$0.268780\pi$
$420$		0			0
$421$	19.3881	−	14.0863i	0.944921	−	0.686525i	−0.00467947	−	0.999989i	$-0.501490\pi$
$421$	19.3881	−	14.0863i	0.944921	−	0.686525i	0.949600	+	0.313464i	$0.101490\pi$
$422$	−0.214374	+	2.03963i	−0.0104356	+	0.0992878i
$423$	9.82129	+	2.08758i	0.477528	+	0.101502i
$424$	−28.1643	−	5.98651i	−1.36778	−	0.290730i
$425$	0.941185	−	8.95478i	0.0456542	−	0.434370i
$426$	34.2893	−	24.9126i	1.66132	−	1.20702i
$427$		0			0
$428$	0.0456549			0.00220681
$429$	2.93124	+	33.2141i	0.141522	+	1.60359i
$430$	10.3544	−	17.9343i	0.499331	−	0.864867i
$431$	11.0227	+	12.2419i	0.530945	+	0.589674i	0.947627	−	0.319378i	$-0.103474\pi$
$431$	11.0227	+	12.2419i	0.530945	+	0.589674i	−0.416683	+	0.909052i	$0.636807\pi$
$432$	10.3600	+	4.61258i	0.498447	+	0.221923i
$433$	16.2539	+	11.8092i	0.781113	+	0.567512i	0.905313	−	0.424745i	$-0.139636\pi$
$433$	16.2539	+	11.8092i	0.781113	+	0.567512i	−0.124200	+	0.992257i	$0.539636\pi$
$434$		0			0
$435$	−1.43548	−	4.41797i	−0.0688262	−	0.211825i
$436$	−0.00415484	+	0.0395306i	−0.000198981	+	0.00189317i
$437$	0.436407	+	4.15213i	0.0208762	+	0.198623i
$438$	12.2700	+	13.6273i	0.586285	+	0.651136i
$439$	13.3841	+	23.1819i	0.638788	+	1.10641i	0.985699	+	0.168515i	$0.0538970\pi$
$439$	13.3841	+	23.1819i	0.638788	+	1.10641i	−0.346912	+	0.937898i	$0.612770\pi$
$440$	16.9201	−	3.30226i	0.806636	−	0.157429i
$441$		0			0
$442$	−11.0703	+	34.0708i	−0.526559	+	1.62058i
$443$	23.9489	+	10.6627i	1.13785	+	0.506602i	0.887158	−	0.461466i	$-0.152676\pi$
$443$	23.9489	+	10.6627i	1.13785	+	0.506602i	0.250689	+	0.968068i	$0.419343\pi$
$444$	−0.0578121	+	0.0257396i	−0.00274364	+	0.00122155i
$445$	27.4862	+	5.84237i	1.30297	+	0.276955i
$446$	−4.57953	+	5.08609i	−0.216847	+	0.240833i
$447$	5.62573	+	4.08733i	0.266088	+	0.193324i
$448$		0			0
$449$	3.01211	−	9.27033i	0.142150	−	0.437494i	−0.854483	−	0.519479i	$-0.826126\pi$
$449$	3.01211	−	9.27033i	0.142150	−	0.437494i	0.996634	+	0.0819851i	$0.0261260\pi$
$450$	−1.94879	−	3.37541i	−0.0918669	−	0.159118i
$451$	2.42937	+	1.82778i	0.114395	+	0.0860667i
$452$	0.101554	−	0.175896i	0.00477668	−	0.00827345i
$453$	−47.1194	+	10.0155i	−2.21386	+	0.470571i
$454$	−0.452792	+	0.328973i	−0.0212506	+	0.0154395i
$455$		0			0
$456$	11.0072	+	33.8767i	0.515459	+	1.58642i
$457$	7.95282	−	8.83250i	0.372017	−	0.413167i	−0.527845	−	0.849341i	$-0.677000\pi$
$457$	7.95282	−	8.83250i	0.372017	−	0.413167i	0.899863	+	0.436173i	$0.143667\pi$
$458$	2.81900	−	1.25510i	0.131723	−	0.0586469i
$459$	1.63258	+	15.5329i	0.0762022	+	0.725016i
$460$	−0.0180033	+	0.00382671i	−0.000839406	+	0.000178421i
$461$	−9.14737			−0.426035			−0.213018	−	0.977048i	$-0.568329\pi$
$461$	−9.14737			−0.426035			−0.213018	+	0.977048i	$0.568329\pi$
$462$		0			0
$463$	38.9342			1.80943			0.904713	−	0.426021i	$-0.140085\pi$
$463$	38.9342			1.80943			0.904713	+	0.426021i	$0.140085\pi$
$464$	−4.55516	+	0.968228i	−0.211468	+	0.0449489i
$465$	−0.541640	−	5.15336i	−0.0251179	−	0.238981i
$466$	1.62236	−	0.722322i	0.0751545	−	0.0334609i
$467$	13.9068	−	15.4451i	0.643531	−	0.714714i	−0.329817	−	0.944045i	$-0.606987\pi$
$467$	13.9068	−	15.4451i	0.643531	−	0.714714i	0.973348	+	0.229331i	$0.0736538\pi$
$468$	−0.0336939	−	0.103699i	−0.00155750	−	0.00479350i
$469$		0			0
$470$	−12.4776	+	9.06548i	−0.575547	+	0.418159i
$471$	28.0485	−	5.96190i	1.29241	−	0.274710i
$472$	−10.8999	+	18.8792i	−0.501708	+	0.868984i
$473$	−7.79986	−	25.4432i	−0.358638	−	1.16988i
$474$	−23.8429	−	41.2971i	−1.09514	−	1.89684i
$475$	−2.95076	+	9.08152i	−0.135390	+	0.416689i
$476$		0			0
$477$	−13.7903	−	10.0192i	−0.631413	−	0.458748i
$478$	10.5253	−	11.6895i	0.481414	−	0.534665i
$479$	−24.0001	−	5.10138i	−1.09659	−	0.233088i	−0.376120	−	0.926571i	$-0.622742\pi$
$479$	−24.0001	−	5.10138i	−1.09659	−	0.233088i	−0.720473	+	0.693483i	$0.756075\pi$
$480$	−0.285914	+	0.127297i	−0.0130501	+	0.00581030i
$481$	8.89279	+	3.95932i	0.405476	+	0.180530i
$482$	−9.35614	+	28.7952i	−0.426161	+	1.31159i
$483$		0			0
$484$	0.0812030	−	0.130392i	0.00369105	−	0.00592690i
$485$	2.20796	+	3.82429i	0.100258	+	0.173652i
$486$	14.8069	+	16.4448i	0.671656	+	0.745949i
$487$	1.29315	+	12.3035i	0.0585984	+	0.557527i	0.983953	+	0.178425i	$0.0571002\pi$
$487$	1.29315	+	12.3035i	0.0585984	+	0.557527i	−0.925355	+	0.379102i	$0.876233\pi$
$488$	−1.86196	+	17.7154i	−0.0842872	+	0.801939i
$489$	9.17101	+	28.2255i	0.414727	+	1.27640i
$490$		0			0
$491$	−13.3691	−	9.71320i	−0.603338	−	0.438350i	0.243724	−	0.969845i	$-0.421631\pi$
$491$	−13.3691	−	9.71320i	−0.603338	−	0.438350i	−0.847062	+	0.531494i	$0.821631\pi$
$492$	−0.0252982	−	0.0112635i	−0.00114053	−	0.000507798i
$493$	−4.29159	−	4.76630i	−0.193284	−	0.214663i
$494$	18.9958	−	32.9017i	0.854661	−	1.48032i
$495$	9.94585	+	2.28824i	0.447033	+	0.102849i
$496$	−5.19468			−0.233248
$497$		0			0
$498$	10.7928	−	7.84144i	0.483638	−	0.351383i
$499$	1.43632	−	13.6657i	0.0642985	−	0.611760i	−0.914165	−	0.405342i	$-0.867153\pi$
$499$	1.43632	−	13.6657i	0.0642985	−	0.611760i	0.978464	−	0.206418i	$-0.0661807\pi$
$500$	−0.166254	−	0.0353384i	−0.00743510	−	0.00158038i
$501$	19.6980	+	4.18693i	0.880041	+	0.187058i
$502$	0.0624323	−	0.594004i	0.00278649	−	0.0265117i
$503$	−18.2812	+	13.2820i	−0.815117	+	0.592217i	−0.915310	−	0.402751i	$-0.868054\pi$
$503$	−18.2812	+	13.2820i	−0.815117	+	0.592217i	0.100193	+	0.994968i	$0.468054\pi$
$504$		0			0
$505$	−21.7859			−0.969461
$506$	1.73030	−	2.88466i	0.0769212	−	0.128239i
$507$	−9.29728	+	16.1034i	−0.412907	+	0.715175i
$508$	−0.0470276	−	0.0522294i	−0.00208651	−	0.00231731i
$509$	19.6080	+	8.73004i	0.869108	+	0.386952i	0.792328	−	0.610096i	$-0.208869\pi$
$509$	19.6080	+	8.73004i	0.869108	+	0.386952i	0.0767809	+	0.997048i	$0.475536\pi$
$510$	24.7098	+	17.9527i	1.09417	+	0.794958i
$511$		0			0
$512$	7.06408	+	21.7410i	0.312191	+	0.960825i
$513$	1.73135	−	16.4727i	0.0764411	−	0.727289i
$514$	−2.56907	−	24.4431i	−0.113317	−	1.07814i
$515$	−0.485657	−	0.539377i	−0.0214006	−	0.0237678i
$516$	0.121202	+	0.209927i	0.00533560	+	0.00924154i
$517$	−2.40048	+	19.6737i	−0.105573	+	0.865248i
$518$		0			0
$519$	−7.02327	+	21.6154i	−0.308287	+	0.948811i
$520$	22.0665	+	9.82464i	0.967680	+	0.430839i
$521$	−31.7106	+	14.1185i	−1.38927	+	0.618541i	−0.958804	−	0.284067i	$-0.908316\pi$
$521$	−31.7106	+	14.1185i	−1.38927	+	0.618541i	−0.430462	+	0.902609i	$0.641649\pi$
$522$	−2.71561	−	0.577220i	−0.118859	−	0.0252642i
$523$	−13.2007	+	14.6609i	−0.577226	+	0.641075i	−0.959076	−	0.283150i	$-0.908621\pi$
$523$	−13.2007	+	14.6609i	−0.577226	+	0.641075i	0.381849	+	0.924225i	$0.375287\pi$
$524$	0.00203415	+	0.00147790i	8.88624e−5	+	6.45623e-5i
$525$		0			0
$526$	−0.659847	+	2.03080i	−0.0287707	+	0.0885471i
$527$	−3.57715	−	6.19581i	−0.155823	−	0.269894i
$528$	9.25783	−	26.9531i	0.402895	−	1.17298i
$529$	11.2410	−	19.4700i	0.488740	−	0.846523i
$530$	25.6110	−	5.44379i	1.11247	−	0.236463i
$531$	−10.4407	+	7.58562i	−0.453088	+	0.329188i
$532$		0			0
$533$	1.31632	+	4.05122i	0.0570162	+	0.175478i
$534$	31.3017	−	34.7641i	1.35456	−	1.50439i
$535$	−5.46981	+	2.43531i	−0.236480	+	0.105288i
$536$	4.58874	+	43.6590i	0.198203	+	1.88578i
$537$	17.6130	−	3.74376i	0.760057	−	0.161555i
$538$	−2.86226			−0.123401
$539$		0			0
$540$	0.0730199			0.00314227
$541$	5.42816	−	1.15379i	0.233375	−	0.0496053i	−0.0897397	−	0.995965i	$-0.528603\pi$
$541$	5.42816	−	1.15379i	0.233375	−	0.0496053i	0.323114	+	0.946360i	$0.395270\pi$
$542$	−1.12020	−	10.6580i	−0.0481167	−	0.457800i
$543$	29.2558	−	13.0255i	1.25549	−	0.558978i
$544$	−0.289140	+	0.321122i	−0.0123968	+	0.0137680i
$545$	−1.61085	−	4.95770i	−0.0690014	−	0.212364i
$546$		0			0
$547$	6.83353	−	4.96485i	0.292181	−	0.212282i	−0.432032	−	0.901858i	$-0.642203\pi$
$547$	6.83353	−	4.96485i	0.292181	−	0.212282i	0.724213	+	0.689576i	$0.242203\pi$
$548$	0.113700	−	0.0241676i	0.00485702	−	0.00103239i
$549$	−5.27263	+	9.13246i	−0.225030	+	0.389764i
$550$	6.29883	−	4.41761i	0.268583	−	0.188367i
$551$	3.40086	+	5.89047i	0.144882	+	0.250942i
$552$	−1.36553	+	4.20267i	−0.0581209	+	0.178878i
$553$		0			0
$554$	16.4483	+	11.9504i	0.698822	+	0.507724i
$555$	5.55333	−	6.16760i	0.235726	−	0.261800i
$556$	0.0950854	+	0.0202110i	0.00403252	+	0.000857139i
$557$	−11.1302	+	4.95547i	−0.471600	+	0.209970i	−0.628754	−	0.777604i	$-0.716435\pi$
$557$	−11.1302	+	4.95547i	−0.471600	+	0.209970i	0.157154	+	0.987574i	$0.449768\pi$
$558$	−2.82913	−	1.25961i	−0.119766	−	0.0533235i
$559$	11.5223	−	35.4620i	0.487342	−	1.49988i
$560$		0			0
$561$	38.5226	−	7.51837i	1.62643	−	0.317426i
$562$	12.5070	+	21.6628i	0.527576	+	0.913789i
$563$	18.3031	+	20.3276i	0.771383	+	0.856707i	0.992962	−	0.118435i	$-0.0377878\pi$
$563$	18.3031	+	20.3276i	0.771383	+	0.856707i	−0.221579	+	0.975142i	$0.571121\pi$
$564$	−0.0188709	−	0.179544i	−0.000794607	−	0.00756018i
$565$	−2.78429	+	26.4907i	−0.117136	+	1.11447i
$566$	−13.5594	−	41.7316i	−0.569944	−	1.75411i
$567$		0			0
$568$	−31.9211	−	23.1920i	−1.33938	−	0.973115i
$569$	6.51836	+	2.90216i	0.273264	+	0.121665i	0.538794	−	0.842438i	$-0.318880\pi$
$569$	6.51836	+	2.90216i	0.273264	+	0.121665i	−0.265530	+	0.964103i	$0.585547\pi$
$570$	−21.6737	−	24.0711i	−0.907812	−	1.00823i
$571$	−16.2420	+	28.1319i	−0.679705	+	1.17728i	0.295365	+	0.955385i	$0.404559\pi$
$571$	−16.2420	+	28.1319i	−0.679705	+	1.17728i	−0.975070	+	0.221899i	$0.928775\pi$
$572$	0.198055	−	0.0842468i	0.00828110	−	0.00352253i
$573$	−20.7831			−0.868226
$574$		0			0
$575$	−0.958373	+	0.696299i	−0.0399669	+	0.0290377i
$576$	−1.41472	+	13.4601i	−0.0589466	+	0.560839i
$577$	34.0218	+	7.23156i	1.41635	+	0.301054i	0.851592	−	0.524205i	$-0.175637\pi$
$577$	34.0218	+	7.23156i	1.41635	+	0.301054i	0.564755	+	0.825259i	$0.308971\pi$
$578$	17.8143	+	3.78655i	0.740978	+	0.157500i
$579$	0.336445	−	3.20106i	0.0139822	−	0.133032i
$580$	−0.0242587	+	0.0176249i	−0.00100729	+	0.000731836i
$581$		0			0
$582$	7.35135			0.304723
$583$	17.3076	−	28.8542i	0.716806	−	1.19502i
$584$	8.53540	−	14.7837i	0.353197	−	0.611756i
$585$	9.56829	+	10.6267i	0.395600	+	0.439359i
$586$	−30.9373	−	13.7742i	−1.27801	−	0.569006i
$587$	−11.7105	−	8.50816i	−0.483343	−	0.351169i	0.319276	−	0.947662i	$-0.396560\pi$
$587$	−11.7105	−	8.50816i	−0.483343	−	0.351169i	−0.802618	+	0.596493i	$0.796560\pi$
$588$		0			0
$589$	2.34456	+	7.21581i	0.0966059	+	0.297322i
$590$	2.07212	−	19.7149i	0.0853078	−	0.811650i
$591$	3.17570	+	30.2147i	0.130631	+	1.24287i
$592$	−5.56720	−	6.18300i	−0.228810	−	0.254120i
$593$	−7.51453	−	13.0155i	−0.308585	−	0.534484i	0.669468	−	0.742841i	$-0.266522\pi$
$593$	−7.51453	−	13.0155i	−0.308585	−	0.534484i	−0.978053	+	0.208356i	$0.933189\pi$
$594$	−9.09400	+	9.76696i	−0.373131	+	0.400743i
$595$		0			0
$596$	0.0138706	−	0.0426894i	0.000568163	−	0.00174863i
$597$	8.47316	+	3.77250i	0.346784	+	0.154398i
$598$	4.30569	−	1.91702i	0.176073	−	0.0783926i
$599$	−1.72198	−	0.366019i	−0.0703583	−	0.0149551i	0.172598	−	0.984992i	$-0.444784\pi$
$599$	−1.72198	−	0.366019i	−0.0703583	−	0.0149551i	−0.242956	+	0.970037i	$0.578117\pi$
$600$	−6.76278	+	7.51083i	−0.276089	+	0.306628i
$601$	18.9605	+	13.7756i	0.773415	+	0.561919i	0.902995	−	0.429650i	$-0.141363\pi$
$601$	18.9605	+	13.7756i	0.773415	+	0.561919i	−0.129581	+	0.991569i	$0.541363\pi$
$602$		0			0
$603$	−8.03085	+	24.7164i	−0.327042	+	1.00653i
$604$	0.155474	+	0.269289i	0.00632615	+	0.0109572i
$605$	−2.77342	+	19.9534i	−0.112755	+	0.811222i
$606$	−18.1340	+	31.4089i	−0.736642	+	1.27590i
$607$	−24.7261	+	5.25570i	−1.00360	+	0.213322i	−0.680269	−	0.732963i	$-0.738137\pi$
$607$	−24.7261	+	5.25570i	−1.00360	+	0.213322i	−0.323334	+	0.946285i	$0.604804\pi$
$608$	0.370738	−	0.269357i	0.0150354	−	0.0109239i
$609$		0			0
$610$	−5.00550	−	15.4053i	−0.202667	−	0.623744i
$611$	−18.5818	+	20.6372i	−0.751739	+	0.834890i
$612$	−0.117254	+	0.0522046i	−0.00473969	+	0.00211025i
$613$	−0.121352	−	1.15458i	−0.00490134	−	0.0466331i	0.991798	−	0.127816i	$-0.0407968\pi$
$613$	−0.121352	−	1.15458i	−0.00490134	−	0.0466331i	−0.996699	+	0.0811832i	$0.974130\pi$
$614$	7.53056	−	1.60067i	0.303909	−	0.0645978i
$615$	3.63174			0.146446
$616$		0			0
$617$	12.9711			0.522197			0.261098	−	0.965312i	$-0.415915\pi$
$617$	12.9711			0.522197			0.261098	+	0.965312i	$0.415915\pi$
$618$	−1.18187	+	0.251214i	−0.0475418	+	0.0101053i
$619$	4.78656	+	45.5411i	0.192388	+	1.83045i	0.485342	+	0.874325i	$0.338695\pi$
$619$	4.78656	+	45.5411i	0.192388	+	1.83045i	−0.292953	+	0.956127i	$0.594638\pi$
$620$	−0.0305562	+	0.0136045i	−0.00122717	+	0.000546369i
$621$	1.37495	−	1.52704i	0.0551749	−	0.0612779i
$622$	6.04824	+	18.6146i	0.242512	+	0.746377i
$623$		0			0
$624$	32.3046	−	23.4707i	1.29322	−	0.939578i
$625$	13.7532	−	2.92334i	0.550129	−	0.116934i
$626$	−19.3412	+	33.4999i	−0.773029	+	1.33893i
$627$	−41.6184	−	0.694879i	−1.66208	−	0.0277508i
$628$	−0.0925483	−	0.160298i	−0.00369308	−	0.00639660i
$629$	3.54092	−	10.8978i	0.141186	−	0.434525i
$630$		0			0
$631$	10.2103	+	7.41824i	0.406467	+	0.295316i	0.772170	−	0.635416i	$-0.219171\pi$
$631$	10.2103	+	7.41824i	0.406467	+	0.295316i	−0.365703	+	0.930732i	$0.619171\pi$
$632$	−29.7043	+	32.9899i	−1.18157	+	1.31227i
$633$	3.07951	+	0.654570i	0.122400	+	0.0260168i
$634$	−10.0750	+	4.48570i	−0.400131	+	0.178150i
$635$	8.42027	+	3.74895i	0.334148	+	0.148772i
$636$	−0.0947088	+	0.291484i	−0.00375545	+	0.0115581i
$637$		0			0
$638$	0.663738	−	5.43981i	0.0262776	−	0.215364i
$639$	−11.6791	−	20.2288i	−0.462019	−	0.800240i
$640$	−13.7173	−	15.2346i	−0.542222	−	0.602199i
$641$	−2.92227	−	27.8036i	−0.115423	−	1.09818i	−0.886914	−	0.461935i	$-0.847155\pi$
$641$	−2.92227	−	27.8036i	−0.115423	−	1.09818i	0.771491	−	0.636240i	$-0.219511\pi$
$642$	−1.04189	+	9.91295i	−0.0411202	+	0.391233i
$643$	15.3575	+	47.2657i	0.605642	+	1.86398i	0.492313	+	0.870418i	$0.336152\pi$
$643$	15.3575	+	47.2657i	0.605642	+	1.86398i	0.113330	+	0.993557i	$0.463848\pi$
$644$		0			0
$645$	−25.7188	−	18.6858i	−1.01268	−	0.735752i
$646$	−40.8549	−	18.1898i	−1.60741	−	0.715667i
$647$	7.36491	+	8.17956i	0.289545	+	0.321572i	0.870315	−	0.492496i	$-0.163915\pi$
$647$	7.36491	+	8.17956i	0.289545	+	0.321572i	−0.580770	+	0.814067i	$0.697249\pi$
$648$	15.9189	−	27.5723i	0.625352	−	1.08314i
$649$	−16.7273	−	19.2131i	−0.656602	−	0.754178i
$650$	10.7797			0.422816
$651$		0			0
$652$	0.154983	−	0.112602i	0.00606962	−	0.00440984i
$653$	−3.02468	+	28.7779i	−0.118365	+	1.12617i	0.760581	+	0.649244i	$0.224914\pi$
$653$	−3.02468	+	28.7779i	−0.118365	+	1.12617i	−0.878945	+	0.476922i	$0.841752\pi$
$654$	−8.48838	−	1.80426i	−0.331922	−	0.0705521i
$655$	−0.322541	−	0.0685582i	−0.0126027	−	0.00267879i
$656$	0.380567	−	3.62086i	0.0148587	−	0.141371i
$657$	8.17583	−	5.94009i	0.318969	−	0.231745i
$658$		0			0
$659$	10.8405			0.422288			0.211144	−	0.977455i	$-0.432281\pi$
$659$	10.8405			0.422288			0.211144	+	0.977455i	$0.432281\pi$
$660$	−0.0161317	−	0.182789i	−0.000627925	−	0.00711506i
$661$	10.1722	−	17.6187i	0.395652	−	0.685290i	−0.597532	−	0.801845i	$-0.703852\pi$
$661$	10.1722	−	17.6187i	0.395652	−	0.685290i	0.993184	+	0.116555i	$0.0371852\pi$
$662$	26.5414	+	29.4772i	1.03156	+	1.14566i
$663$	50.2395	+	22.3681i	1.95114	+	0.868704i
$664$	−10.0474	−	7.29986i	−0.389915	−	0.283289i
$665$		0			0
$666$	−1.53275	−	4.71732i	−0.0593929	−	0.182792i
$667$	−0.0882020	+	0.839186i	−0.00341520	+	0.0324934i
$668$	−0.0135877	−	0.129278i	−0.000525722	−	0.00500191i
$669$	7.03009	+	7.80770i	0.271799	+	0.301863i
$670$	−19.9598	−	34.5715i	−0.771116	−	1.33561i
$671$	−18.8720	−	8.78272i	−0.728544	−	0.339053i
$672$		0			0
$673$	−3.73255	+	11.4876i	−0.143879	+	0.442815i	−0.996865	−	0.0791188i	$-0.974789\pi$
$673$	−3.73255	+	11.4876i	−0.143879	+	0.442815i	0.852986	+	0.521934i	$0.174789\pi$
$674$	32.1586	+	14.3180i	1.23870	+	0.551507i
$675$	4.29340	−	1.91155i	0.165253	−	0.0735754i
$676$	0.117404	+	0.0249550i	0.00451554	+	0.000959807i
$677$	−2.27257	+	2.52394i	−0.0873418	+	0.0970029i	−0.785231	−	0.619203i	$-0.787456\pi$
$677$	−2.27257	+	2.52394i	−0.0873418	+	0.0970029i	0.697890	+	0.716205i	$0.254123\pi$
$678$	35.8743	+	26.0642i	1.37775	+	1.00099i
$679$		0			0
$680$	8.78642	−	27.0418i	0.336944	−	1.03701i
$681$	0.429587	+	0.744066i	0.0164618	+	0.0285127i
$682$	1.98581	−	5.78144i	0.0760405	−	0.221383i
$683$	2.37821	−	4.11919i	0.0909999	−	0.157616i	−0.816932	−	0.576734i	$-0.804327\pi$
$683$	2.37821	−	4.11919i	0.0909999	−	0.157616i	0.907932	+	0.419117i	$0.137660\pi$
$684$	0.133141	−	0.0283000i	0.00509077	−	0.00108208i
$685$	−12.3330	+	8.96042i	−0.471218	+	0.342360i
$686$		0			0
$687$	−1.46382	−	4.50516i	−0.0558481	−	0.171883i
$688$	−21.3249	+	23.6837i	−0.813003	+	0.902931i
$689$	43.0683	−	19.1752i	1.64077	−	0.730518i
$690$	−0.420032	−	3.99633i	−0.0159903	−	0.152138i
$691$	6.48892	−	1.37926i	0.246850	−	0.0524696i	−0.0828248	−	0.996564i	$-0.526394\pi$
$691$	6.48892	−	1.37926i	0.246850	−	0.0524696i	0.329675	+	0.944095i	$0.393061\pi$
$692$	0.146707			0.00557695
$693$		0			0
$694$	−29.1003			−1.10463
$695$	−12.4700	+	2.65059i	−0.473016	+	0.100543i
$696$	0.752517	+	7.15972i	0.0285241	+	0.271388i
$697$	4.58074	−	2.03948i	0.173508	−	0.0772507i
$698$	−5.65527	+	6.28082i	−0.214055	+	0.237733i
$699$	−0.842441	−	2.59277i	−0.0318641	−	0.0980675i
$700$		0			0
$701$	−2.45134	+	1.78101i	−0.0925860	+	0.0672677i	−0.633115	−	0.774058i	$-0.718224\pi$
$701$	−2.45134	+	1.78101i	−0.0925860	+	0.0672677i	0.540529	+	0.841325i	$0.318224\pi$
$702$	−18.2899	+	3.88764i	−0.690307	+	0.146729i
$703$	−6.07597	+	10.5239i	−0.229160	+	0.396916i
$704$	−26.7119	−	0.445995i	−1.00674	−	0.0168091i
$705$	11.8381	+	20.5042i	0.445848	+	0.772232i
$706$	10.4683	−	32.2182i	0.393981	−	1.21255i
$707$		0			0
$708$	0.187726	+	0.136391i	0.00705516	+	0.00512587i
$709$	−9.13835	+	10.1492i	−0.343198	+	0.381160i	−0.889891	−	0.456173i	$-0.849220\pi$
$709$	−9.13835	+	10.1492i	−0.343198	+	0.381160i	0.546693	+	0.837333i	$0.315886\pi$
$710$	35.0956	+	7.45979i	1.31711	+	0.279961i
$711$	−24.0081	+	10.6891i	−0.900376	+	0.400873i
$712$	−39.7838	−	17.7129i	−1.49096	−	0.663818i
$713$	−0.290862	+	0.895180i	−0.0108928	+	0.0335247i
$714$		0			0
$715$	−19.2346	+	20.6580i	−0.719335	+	0.772566i
$716$	−0.0581155	−	0.100659i	−0.00217188	−	0.00376180i
$717$	−16.1574	−	17.9447i	−0.603411	−	0.670155i
$718$	−1.61305	−	15.3471i	−0.0601984	−	0.572749i
$719$	−0.198634	+	1.88988i	−0.00740781	+	0.0704806i	−0.997601	−	0.0692225i	$-0.977948\pi$
$719$	−0.198634	+	1.88988i	−0.00740781	+	0.0704806i	0.990193	+	0.139703i	$0.0446148\pi$
$720$	−3.77680	−	11.6238i	−0.140753	−	0.433193i
$721$		0			0
$722$	16.7069	+	12.1383i	0.621768	+	0.451741i
$723$	42.4604	+	18.9046i	1.57912	+	0.703069i
$724$	−0.138320	−	0.153620i	−0.00514063	−	0.00570924i
$725$	−0.964960	+	1.67136i	−0.0358377	+	0.0620727i
$726$	26.4585	+	20.6071i	0.981967	+	0.764801i
$727$	13.8211			0.512595			0.256298	−	0.966598i	$-0.417497\pi$
$727$	13.8211			0.512595			0.256298	+	0.966598i	$0.417497\pi$
$728$		0			0
$729$	0.256684	−	0.186492i	0.00950682	−	0.00690711i
$730$	−1.62262	+	15.4382i	−0.0600558	+	0.571393i
$731$	−42.9327	−	9.12563i	−1.58792	−	0.337524i
$732$	0.185462	+	0.0394212i	0.00685487	+	0.00145705i
$733$	5.05650	−	48.1094i	0.186766	−	1.77696i	−0.353469	−	0.935446i	$-0.614998\pi$
$733$	5.05650	−	48.1094i	0.186766	−	1.77696i	0.540235	−	0.841514i	$-0.318335\pi$
$734$	−12.1055	+	8.79519i	−0.446824	+	0.324636i
$735$		0			0
$736$	0.0568504			0.00209553
$737$	−49.9931	−	11.5019i	−1.84152	−	0.423677i
$738$	1.08525	−	1.87971i	0.0399487	−	0.0691931i
$739$	15.5292	+	17.2470i	0.571253	+	0.634440i	0.957665	−	0.287886i	$-0.0929524\pi$
$739$	15.5292	+	17.2470i	0.571253	+	0.634440i	−0.386412	+	0.922326i	$0.626286\pi$
$740$	−0.0489402	−	0.0217896i	−0.00179908	−	0.000801001i
$741$	−47.1829	−	34.2804i	−1.73331	−	1.25932i
$742$		0			0
$743$	−13.8536	−	42.6369i	−0.508238	−	1.56420i	−0.795257	−	0.606272i	$-0.792664\pi$
$743$	−13.8536	−	42.6369i	−0.508238	−	1.56420i	0.287019	−	0.957925i	$-0.407336\pi$
$744$	−0.839413	+	7.98648i	−0.0307744	+	0.292799i
$745$	0.615322	+	5.85440i	0.0225437	+	0.214489i
$746$	−34.5166	−	38.3346i	−1.26374	−	1.40353i
$747$	−3.67609	−	6.36717i	−0.134501	−	0.232963i
$748$	−0.122996	−	0.221495i	−0.00449718	−	0.00809864i
$749$		0			0
$750$	11.4670	−	35.2919i	0.418717	−	1.28868i
$751$	−37.6249	−	16.7517i	−1.37295	−	0.611278i	−0.418112	−	0.908396i	$-0.637308\pi$
$751$	−37.6249	−	16.7517i	−1.37295	−	0.611278i	−0.954841	+	0.297118i	$0.903975\pi$
$752$	21.6833	−	9.65401i	0.790707	−	0.352045i
$753$	−0.896848	−	0.190631i	−0.0326829	−	0.00694697i
$754$	5.13790	−	5.70621i	0.187111	−	0.207808i
$755$	−32.9913	−	23.9696i	−1.20068	−	0.872343i
$756$		0			0
$757$	−6.76401	+	20.8175i	−0.245842	+	0.756624i	0.749655	+	0.661829i	$0.230219\pi$
$757$	−6.76401	+	20.8175i	−0.245842	+	0.756624i	−0.995497	+	0.0947948i	$0.969781\pi$
$758$	−8.91910	−	15.4483i	−0.323956	−	0.561109i
$759$	−4.12636	−	3.10453i	−0.149777	−	0.112687i
$760$	−15.0769	+	26.1139i	−0.546896	+	0.947251i
$761$	−34.9349	+	7.42564i	−1.26639	+	0.269179i	−0.791665	−	0.610956i	$-0.790785\pi$
$761$	−34.9349	+	7.42564i	−1.26639	+	0.269179i	−0.474724	+	0.880135i	$0.657452\pi$
$762$	12.4137	−	9.01906i	0.449700	−	0.326726i
$763$		0			0
$764$	0.0414558	+	0.127588i	0.00149982	+	0.00461596i
$765$	11.2632	−	12.5090i	0.407221	−	0.452265i
$766$	−19.9138	+	8.86620i	−0.719516	+	0.320349i
$767$	−3.73095	−	35.4976i	−0.134717	−	1.28174i
$768$	0.709175	−	0.150740i	0.0255901	−	0.00543935i
$769$	−5.30246			−0.191212			−0.0956058	−	0.995419i	$-0.530479\pi$
$769$	−5.30246			−0.191212			−0.0956058	+	0.995419i	$0.530479\pi$
$770$		0			0
$771$	−37.7295			−1.35880
$772$	−0.0203225	+	0.00431968i	−0.000731423	+	0.000155469i
$773$	−5.21505	−	49.6179i	−0.187572	−	1.78463i	−0.532929	−	0.846160i	$-0.678909\pi$
$773$	−5.21505	−	49.6179i	−0.187572	−	1.78463i	0.345356	−	0.938472i	$-0.387758\pi$
$774$	−17.3568	+	7.72773i	−0.623876	+	0.277768i
$775$	−1.44049	+	1.59983i	−0.0517439	+	0.0574674i
$776$	−2.11479	−	6.50867i	−0.0759167	−	0.233648i
$777$		0			0
$778$	−14.4943	+	10.5307i	−0.519646	+	0.377545i
$779$	−5.20142	+	1.10560i	−0.186360	+	0.0396121i
$780$	0.128554	−	0.222663i	0.00460298	−	0.00797260i
$781$	37.7489	−	26.4748i	1.35076	−	0.947342i
$782$	−2.77401	−	4.80473i	−0.0991986	−	0.171817i
$783$	1.03448	−	3.18379i	0.0369692	−	0.113779i
$784$		0			0
$785$	19.6386	+	14.2683i	0.700931	+	0.509256i
$786$	−0.367314	+	0.407944i	−0.0131017	+	0.0145509i
$787$	35.0734	+	7.45508i	1.25023	+	0.265745i	0.785029	−	0.619459i	$-0.212648\pi$
$787$	35.0734	+	7.45508i	1.25023	+	0.265745i	0.465203	+	0.885204i	$0.345981\pi$
$788$	0.179154	−	0.0797646i	0.00638211	−	0.00284150i
$789$	2.99454	+	1.33326i	0.106609	+	0.0474652i
$790$	12.4744	−	38.3922i	0.443818	−	1.36593i
$791$		0			0
$792$	−14.3396	−	6.67342i	−0.509535	−	0.237130i
$793$	−14.5828	−	25.2581i	−0.517849	−	0.896940i
$794$	−17.8765	−	19.8539i	−0.634414	−	0.704588i
$795$	−4.20143	−	39.9739i	−0.149009	−	1.41773i
$796$	0.00625810	−	0.0595419i	0.000221813	−	0.00211041i
$797$	−4.55530	−	14.0198i	−0.161357	−	0.496606i	0.837392	−	0.546602i	$-0.184079\pi$
$797$	−4.55530	−	14.0198i	−0.161357	−	0.496606i	−0.998749	+	0.0499962i	$0.984079\pi$
$798$		0			0
$799$	26.4460	+	19.2142i	0.935593	+	0.679748i
$800$	0.118784	+	0.0528862i	0.00419966	+	0.00186981i
$801$	−17.2507	−	19.1589i	−0.609524	−	0.676945i
$802$	−6.11769	+	10.5962i	−0.216023	+	0.374163i
$803$	13.0986	+	15.0452i	0.462241	+	0.530934i
$804$	0.467275			0.0164795
$805$		0			0
$806$	6.92934	−	5.03446i	0.244076	−	0.177331i
$807$	−0.459286	+	4.36982i	−0.0161676	+	0.153825i
$808$	33.0252	+	7.01973i	1.16182	+	0.246953i
$809$	26.3864	+	5.60859i	0.927695	+	0.197188i	0.646895	−	0.762579i	$-0.276067\pi$
$809$	26.3864	+	5.60859i	0.927695	+	0.197188i	0.280800	+	0.959766i	$0.409400\pi$
$810$	−3.02625	+	28.7929i	−0.106332	+	1.01168i
$811$	1.18472	−	0.860750i	0.0416012	−	0.0302250i	−0.566790	−	0.823862i	$-0.691815\pi$
$811$	1.18472	−	0.860750i	0.0416012	−	0.0302250i	0.608392	+	0.793637i	$0.291815\pi$
$812$		0			0
$813$	−16.4513			−0.576972
$814$	9.00961	−	3.83242i	0.315787	−	0.134326i
$815$	−12.5618	+	21.7577i	−0.440021	+	0.762138i
$816$	−31.4517	−	34.9306i	−1.10103	−	1.22282i
$817$	42.5232	+	18.9325i	1.48770	+	0.662366i
$818$	−6.51473	−	4.73323i	−0.227782	−	0.165493i
$819$		0			0
$820$	−0.00724418	−	0.0222953i	−0.000252978	−	0.000778586i
$821$	−3.20157	+	30.4609i	−0.111736	+	1.06309i	0.784687	+	0.619892i	$0.212824\pi$
$821$	−3.20157	+	30.4609i	−0.111736	+	1.06309i	−0.896423	+	0.443200i	$0.853843\pi$
$822$	2.65272	+	25.2389i	0.0925241	+	0.880308i
$823$	−16.4163	−	18.2322i	−0.572237	−	0.635534i	0.385661	−	0.922640i	$-0.373973\pi$
$823$	−16.4163	−	18.2322i	−0.572237	−	0.635534i	−0.957899	+	0.287107i	$0.907307\pi$
$824$	0.562412	+	0.974126i	0.0195925	+	0.0339353i
$825$	−5.73364	−	10.3253i	−0.199620	−	0.359480i
$826$		0			0
$827$	−2.02927	+	6.24545i	−0.0705646	+	0.217176i	−0.980119	−	0.198408i	$-0.936423\pi$
$827$	−2.02927	+	6.24545i	−0.0705646	+	0.217176i	0.909555	+	0.415584i	$0.136423\pi$
$828$	0.0154263	+	0.00686824i	0.000536102	+	0.000238688i
$829$	18.1286	−	8.07138i	0.629633	−	0.280331i	−0.0670059	−	0.997753i	$-0.521345\pi$
$829$	18.1286	−	8.07138i	0.629633	−	0.280331i	0.696639	+	0.717422i	$0.254678\pi$
$830$	11.0466	+	2.34803i	0.383433	+	0.0815012i
$831$	20.8840	−	23.1941i	0.724459	−	0.804593i
$832$	−30.2834	−	22.0022i	−1.04989	−	0.762789i
$833$		0			0
$834$	−6.55832	+	20.1844i	−0.227096	+	0.698930i
$835$	8.52382	+	14.7637i	0.294979	+	0.510918i
$836$	0.0787498	+	0.256882i	0.00272362	+	0.00888445i
$837$	1.86710	−	3.23392i	0.0645365	−	0.111781i
$838$	37.4819	−	7.96702i	1.29479	−	0.275216i
$839$	−6.44019	+	4.67907i	−0.222340	+	0.161539i	−0.693379	−	0.720573i	$-0.743879\pi$
$839$	−6.44019	+	4.67907i	−0.222340	+	0.161539i	0.471039	+	0.882112i	$0.343879\pi$
$840$		0			0
$841$	−8.53669	−	26.2732i	−0.294369	−	0.905973i
$842$	22.5987	−	25.0984i	0.778802	−	0.864947i
$843$	35.0795	−	15.6184i	1.20820	−	0.537926i
$844$	−0.00212424	−	0.0202108i	−7.31195e−5	−	0.000695686i
$845$	−15.3970	+	3.27274i	−0.529674	+	0.112586i
$846$	14.1500			0.486489
$847$		0			0
$848$	−40.2944			−1.38372
$849$	−65.8874	+	14.0048i	−2.26125	+	0.480643i
$850$	−1.32638	−	12.6197i	−0.0454945	−	0.432851i
$851$	−1.37721	+	0.613174i	−0.0472102	+	0.0210194i
$852$	−0.281025	+	0.312109i	−0.00962774	+	0.0106927i
$853$	−10.5292	−	32.4055i	−0.360513	−	1.10954i	−0.952744	−	0.303776i	$-0.901753\pi$
$853$	−10.5292	−	32.4055i	−0.360513	−	1.10954i	0.592231	−	0.805768i	$-0.298247\pi$
$854$		0			0
$855$	−14.4417	+	10.4925i	−0.493897	+	0.358837i
$856$	9.07636	−	1.92924i	0.310223	−	0.0659400i
$857$	12.4269	−	21.5241i	0.424496	−	0.735249i	−0.571877	−	0.820339i	$-0.693785\pi$
$857$	12.4269	−	21.5241i	0.424496	−	0.735249i	0.996373	+	0.0850904i	$0.0271179\pi$
$858$	13.7725	+	44.9259i	0.470185	+	1.53374i
$859$	1.02827	+	1.78102i	0.0350841	+	0.0607675i	0.883034	−	0.469308i	$-0.155497\pi$
$859$	1.02827	+	1.78102i	0.0350841	+	0.0607675i	−0.847950	+	0.530076i	$0.822163\pi$
$860$	−0.0634115	+	0.195160i	−0.00216231	+	0.00665491i
$861$		0			0
$862$	18.7814	+	13.6455i	0.639697	+	0.464767i
$863$	−0.173623	+	0.192828i	−0.00591020	+	0.00656394i	−0.746093	−	0.665842i	$-0.768072\pi$
$863$	−0.173623	+	0.192828i	−0.00591020	+	0.00656394i	0.740182	+	0.672406i	$0.234739\pi$
$864$	−0.220614	−	0.0468929i	−0.00750543	−	0.00159533i
$865$	−17.5766	+	7.82560i	−0.597621	+	0.266078i
$866$	25.8657	+	11.5161i	0.878951	+	0.391334i
$867$	8.63946	−	26.5895i	0.293412	−	0.903028i
$868$		0			0
$869$	−25.1840	−	45.3519i	−0.854307	−	1.53846i
$870$	−3.27325	−	5.66944i	−0.110974	−	0.192212i
$871$	−48.0953	−	53.4152i	−1.62965	−	1.80991i
$872$	0.844449	+	8.03440i	0.0285967	+	0.272079i
$873$	0.423488	−	4.02921i	0.0143329	−	0.136368i
$874$	1.81816	+	5.59573i	0.0615003	+	0.189278i
$875$		0			0
$876$	−0.147003	−	0.106804i	−0.00496676	−	0.00360856i
$877$	16.9855	+	7.56245i	0.573561	+	0.255366i	0.672956	−	0.739682i	$-0.265024\pi$
$877$	16.9855	+	7.56245i	0.573561	+	0.255366i	−0.0993955	+	0.995048i	$0.531691\pi$
$878$	25.2420	+	28.0340i	0.851875	+	0.946103i
$879$	−25.9933	+	45.0218i	−0.876734	+	1.51855i
$880$	22.2003	−	9.44333i	0.748371	−	0.318335i
$881$	−6.45292			−0.217404			−0.108702	−	0.994074i	$-0.534670\pi$
$881$	−6.45292			−0.217404			−0.108702	+	0.994074i	$0.534670\pi$
$882$		0			0
$883$	0.225301	−	0.163691i	0.00758198	−	0.00550863i	−0.583988	−	0.811762i	$-0.698508\pi$
$883$	0.225301	−	0.163691i	0.00758198	−	0.00550863i	0.591570	+	0.806254i	$0.298508\pi$
$884$	0.0371059	−	0.353039i	0.00124801	−	0.0118740i
$885$	−29.7663	−	6.32701i	−1.00058	−	0.212680i
$886$	36.1371	+	7.68118i	1.21405	+	0.258054i
$887$	3.19407	−	30.3896i	0.107246	−	1.02038i	−0.800062	−	0.599917i	$-0.795200\pi$
$887$	3.19407	−	30.3896i	0.107246	−	1.02038i	0.907309	−	0.420465i	$-0.138133\pi$
$888$	−10.4056	+	7.56009i	−0.349188	+	0.253700i
$889$		0			0
$890$	39.6008			1.32742
$891$	24.4295	+	28.0599i	0.818419	+	0.940043i
$892$	0.0339088	−	0.0587318i	0.00113535	−	0.00196649i
$893$	−23.1967	−	25.7625i	−0.776247	−	0.862109i
$894$	8.95251	+	3.98591i	0.299417	+	0.133309i
$895$	12.3320	+	8.95972i	0.412213	+	0.299491i
$896$		0			0
$897$	−2.23581	−	6.88111i	−0.0746514	−	0.229753i
$898$	1.43588	−	13.6615i	0.0479158	−	0.455889i
$899$	0.160288	+	1.52504i	0.00534590	+	0.0508628i
$900$	0.0258427	+	0.0287013i	0.000861425	+	0.000956709i
$901$	−27.7475	−	48.0600i	−0.924402	−	1.60111i
$902$	3.88437	+	1.80773i	0.129335	+	0.0601907i
$903$		0			0
$904$	12.7564	−	39.2601i	0.424271	−	1.30577i
$905$	24.7662	+	11.0266i	0.823255	+	0.366537i
$906$	−62.0181	+	27.6122i	−2.06041	+	0.917355i
$907$	−31.2368	−	6.63959i	−1.03720	−	0.220464i	−0.342317	−	0.939585i	$-0.611212\pi$
$907$	−31.2368	−	6.63959i	−1.03720	−	0.220464i	−0.694885	+	0.719121i	$0.744545\pi$
$908$	0.00371094	−	0.00412142i	0.000123152	−	0.000136774i
$909$	16.1704	+	11.7484i	0.536337	+	0.389671i
$910$		0			0
$911$	0.865378	−	2.66336i	0.0286713	−	0.0882411i	−0.935697	−	0.352805i	$-0.885228\pi$
$911$	0.865378	−	2.66336i	0.0286713	−	0.0882411i	0.964368	+	0.264564i	$0.0852280\pi$
$912$	24.9238	+	43.1693i	0.825310	+	1.42948i
$913$	11.8818	−	8.33313i	0.393229	−	0.275786i
$914$	8.37479	−	14.5056i	0.277013	−	0.479801i
$915$	−24.3225	+	5.16992i	−0.804078	+	0.170912i
$916$	−0.0247374	+	0.0179728i	−0.000817348	+	0.000593838i
$917$		0			0
$918$	6.80167	+	20.9334i	0.224488	+	0.690904i
$919$	−10.5949	+	11.7669i	−0.349494	+	0.388153i	−0.892102	−	0.451833i	$-0.850770\pi$
$919$	−10.5949	+	11.7669i	−0.349494	+	0.388153i	0.542608	+	0.839986i	$0.317437\pi$
$920$	−3.41740	+	1.52153i	−0.112668	+	0.0501632i
$921$	−1.23537	−	11.7538i	−0.0407068	−	0.387300i
$922$	−12.6094	+	2.68021i	−0.415268	+	0.0882679i
$923$	64.6030			2.12643
$924$		0			0
$925$	−3.44799			−0.113369
$926$	53.6697	−	11.4079i	1.76370	−	0.374885i
$927$	0.0696048	+	0.662246i	0.00228612	+	0.0217510i
$928$	0.0846109	−	0.0376712i	0.00277749	−	0.00123662i
$929$	18.3900	−	20.4241i	0.603355	−	0.670093i	−0.361654	−	0.932313i	$-0.617788\pi$
$929$	18.3900	−	20.4241i	0.603355	−	0.670093i	0.965008	+	0.262219i	$0.0844544\pi$
$930$	−2.25659	−	6.94506i	−0.0739964	−	0.227737i
$931$		0			0
$932$	−0.0142366	+	0.0103435i	−0.000466337	+	0.000338814i
$933$	29.3894	−	6.24691i	0.962166	−	0.204515i
$934$	14.6447	−	25.3654i	0.479189	−	0.829980i
$935$	26.5508	+	19.9759i	0.868303	+	0.653282i
$936$	−11.0805	−	19.1920i	−0.362177	−	0.627309i
$937$	3.80357	−	11.7062i	0.124257	−	0.382425i	−0.869508	−	0.493919i	$-0.835564\pi$
$937$	3.80357	−	11.7062i	0.124257	−	0.382425i	0.993765	+	0.111495i	$0.0355638\pi$
$938$		0			0
$939$	48.0408	+	34.9037i	1.56775	+	1.13904i
$940$	0.102262	−	0.113574i	0.00333543	−	0.00370437i
$941$	1.42823	+	0.303580i	0.0465590	+	0.00989642i	0.231132	−	0.972922i	$-0.425757\pi$
$941$	1.42823	+	0.303580i	0.0465590	+	0.00989642i	−0.184573	+	0.982819i	$0.559090\pi$
$942$	36.9172	−	16.4366i	1.20283	−	0.535534i
$943$	−0.602660	−	0.268322i	−0.0196253	−	0.00873775i
$944$	−9.42725	+	29.0141i	−0.306831	+	0.944328i
$945$		0			0
$946$	−18.2068	−	32.7873i	−0.591955	−	1.06601i
$947$	−5.53568	−	9.58807i	−0.179885	−	0.311571i	0.761956	−	0.647629i	$-0.224239\pi$
$947$	−5.53568	−	9.58807i	−0.179885	−	0.311571i	−0.941841	+	0.336059i	$0.890906\pi$
$948$	0.316179	+	0.351152i	0.0102690	+	0.0114049i
$949$	2.92160	+	27.7972i	0.0948392	+	0.902335i
$950$	−1.40663	+	13.3832i	−0.0456371	+	0.434208i
$951$	5.23165	+	16.1014i	0.169648	+	0.522123i
$952$		0			0
$953$	11.9924	+	8.71296i	0.388471	+	0.282240i	0.764828	−	0.644234i	$-0.222824\pi$
$953$	11.9924	+	8.71296i	0.388471	+	0.282240i	−0.376358	+	0.926474i	$0.622824\pi$
$954$	−21.9451	−	9.77061i	−0.710500	−	0.316335i
$955$	−11.7725	−	13.0747i	−0.380948	−	0.423086i
$956$	−0.0779335	+	0.134985i	−0.00252055	+	0.00436572i
$957$	−8.19846	−	1.88622i	−0.265019	−	0.0609727i
$958$	−34.5782			−1.11717
$959$		0			0
$960$	−25.8191	+	18.7586i	−0.833306	+	0.605432i
$961$	3.06159	−	29.1290i	0.0987608	−	0.939646i
$962$	13.4186	+	2.85220i	0.432632	+	0.0919587i
$963$	5.37319	+	1.14211i	0.173148	+	0.0368038i
$964$	0.0313604	−	0.298374i	0.00101005	−	0.00960998i
$965$	2.20437	−	1.60157i	0.0709612	−	0.0515563i
$966$		0			0
$967$	16.5193			0.531224			0.265612	−	0.964080i	$-0.414426\pi$
$967$	16.5193			0.531224			0.265612	+	0.964080i	$0.414426\pi$
$968$	10.6335	−	29.3537i	0.341773	−	0.943464i
$969$	−34.3260	+	59.4544i	−1.10271	+	1.90995i
$970$	4.16414	+	4.62474i	0.133702	+	0.148491i
$971$	−37.2720	−	16.5946i	−1.19612	−	0.532545i	−0.290595	−	0.956846i	$-0.593853\pi$
$971$	−37.2720	−	16.5946i	−1.19612	−	0.532545i	−0.905521	+	0.424301i	$0.860520\pi$
$972$	−0.177396	−	0.128886i	−0.00568998	−	0.00413401i
$973$		0			0
$974$	5.38755	+	16.5812i	0.172628	+	0.531296i
$975$	1.72974	−	16.4574i	0.0553961	−	0.527059i
$976$	2.60568	+	24.7914i	0.0834059	+	0.793554i
$977$	32.8640	+	36.4992i	1.05141	+	1.16771i	0.985463	+	0.169889i	$0.0543410\pi$
$977$	32.8640	+	36.4992i	1.05141	+	1.16771i	0.0659495	+	0.997823i	$0.478992\pi$
$978$	20.9121	+	36.2209i	0.668696	+	1.15822i
$979$	34.6782	−	37.2444i	1.10832	−	1.19034i
$980$		0			0
$981$	−1.47789	+	4.54847i	−0.0471853	+	0.145222i
$982$	−21.2749	−	9.47219i	−0.678909	−	0.302270i
$983$	−1.01110	+	0.450172i	−0.0322492	+	0.0143583i	−0.422798	−	0.906224i	$-0.638952\pi$
$983$	−1.01110	+	0.450172i	−0.0322492	+	0.0143583i	0.390549	+	0.920582i	$0.372285\pi$
$984$	−5.50534	−	1.17020i	−0.175504	−	0.0373045i
$985$	−17.2093	+	19.1128i	−0.548333	+	0.608985i
$986$	−7.31238	−	5.31275i	−0.232874	−	0.169193i
$987$		0			0
$988$	−0.116333	+	0.358036i	−0.00370104	+	0.0113906i
$989$	2.88729	+	5.00093i	0.0918105	+	0.159020i
$990$	14.3805	+	0.240104i	0.457043	+	0.00763100i
$991$	−20.8926	+	36.1870i	−0.663674	+	1.14952i	0.315969	+	0.948769i	$0.397670\pi$
$991$	−20.8926	+	36.1870i	−0.663674	+	1.14952i	−0.979643	+	0.200747i	$0.935663\pi$
$992$	0.101056	−	0.0214800i	0.00320852	−	0.000681991i
$993$	49.2618	−	35.7908i	1.56328	−	1.13579i
$994$		0			0
$995$	2.42630	+	7.46739i	0.0769189	+	0.236732i
$996$	−0.0884546	+	0.0982387i	−0.00280279	+	0.00311281i
$997$	−40.3737	+	17.9755i	−1.27865	+	0.569290i	−0.929861	−	0.367912i	$-0.880073\pi$
$997$	−40.3737	+	17.9755i	−1.27865	+	0.569290i	−0.348786	+	0.937202i	$0.613406\pi$
$998$	−2.02416	−	19.2586i	−0.0640737	−	0.609620i
$999$	5.85018	−	1.24349i	0.185092	−	0.0393424i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	539.2.q.f.361.3		32
7.2	even	3	inner	539.2.q.f.471.2		32
7.3	odd	6		77.2.f.b.64.2	✓	16
7.4	even	3		539.2.f.e.295.2		16
7.5	odd	6		539.2.q.g.471.2		32
7.6	odd	2		539.2.q.g.361.3		32
11.5	even	5	inner	539.2.q.f.214.2		32
21.17	even	6		693.2.m.i.64.3		16
77.3	odd	30		847.2.f.w.323.3		16
77.4	even	15		5929.2.a.bt.1.3		8
77.5	odd	30		539.2.q.g.324.3		32
77.10	even	6		847.2.f.x.372.3		16
77.16	even	15	inner	539.2.q.f.324.3		32
77.17	even	30		847.2.f.x.148.3		16
77.18	odd	30		5929.2.a.bs.1.6		8
77.24	even	30		847.2.f.v.729.2		16
77.27	odd	10		539.2.q.g.214.2		32
77.31	odd	30		847.2.f.w.729.3		16
77.38	odd	30		77.2.f.b.71.2	yes	16
77.52	even	30		847.2.f.v.323.2		16
77.59	odd	30		847.2.a.p.1.3		8
77.60	even	15		539.2.f.e.148.2		16
77.73	even	30		847.2.a.o.1.6		8
231.38	even	30		693.2.m.i.379.3		16
231.59	even	30		7623.2.a.ct.1.6		8
231.227	odd	30		7623.2.a.cw.1.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.2.f.b.64.2	✓	16	7.3	odd	6
77.2.f.b.71.2	yes	16	77.38	odd	30
539.2.f.e.148.2		16	77.60	even	15
539.2.f.e.295.2		16	7.4	even	3
539.2.q.f.214.2		32	11.5	even	5	inner
539.2.q.f.324.3		32	77.16	even	15	inner
539.2.q.f.361.3		32	1.1	even	1	trivial
539.2.q.f.471.2		32	7.2	even	3	inner
539.2.q.g.214.2		32	77.27	odd	10
539.2.q.g.324.3		32	77.5	odd	30
539.2.q.g.361.3		32	7.6	odd	2
539.2.q.g.471.2		32	7.5	odd	6
693.2.m.i.64.3		16	21.17	even	6
693.2.m.i.379.3		16	231.38	even	30
847.2.a.o.1.6		8	77.73	even	30
847.2.a.p.1.3		8	77.59	odd	30
847.2.f.v.323.2		16	77.52	even	30
847.2.f.v.729.2		16	77.24	even	30
847.2.f.w.323.3		16	77.3	odd	30
847.2.f.w.729.3		16	77.31	odd	30
847.2.f.x.148.3		16	77.17	even	30
847.2.f.x.372.3		16	77.10	even	6
5929.2.a.bs.1.6		8	77.18	odd	30
5929.2.a.bt.1.3		8	77.4	even	15
7623.2.a.ct.1.6		8	231.59	even	30
7623.2.a.cw.1.3		8	231.227	odd	30

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:	\( N \)	\(=\)	\( 539 = 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	539.q (of order \(15\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.37847 - 0.293003i) q^{2} +(-0.226135 - 2.15153i) q^{3} +(-0.0127572 + 0.00567988i) q^{4} +(1.22544 - 1.36099i) q^{5} +(-0.942126 - 2.89957i) q^{6} +(-2.29616 + 1.66826i) q^{8} +(-1.64350 + 0.349337i) q^{9} +O(q^{10})\)	\(q+(1.37847 - 0.293003i) q^{2} +(-0.226135 - 2.15153i) q^{3} +(-0.0127572 + 0.00567988i) q^{4} +(1.22544 - 1.36099i) q^{5} +(-0.942126 - 2.89957i) q^{6} +(-2.29616 + 1.66826i) q^{8} +(-1.64350 + 0.349337i) q^{9} +(1.29046 - 2.23514i) q^{10} +(-0.972092 - 3.17097i) q^{11} +(0.0151053 + 0.0261631i) q^{12} +(1.43602 - 4.41961i) q^{13} +(-3.20531 - 2.32880i) q^{15} +(-2.65770 + 2.95168i) q^{16} +(-5.35068 - 1.13732i) q^{17} +(-2.16316 + 0.963102i) q^{18} +(5.29964 + 2.35955i) q^{19} +(-0.00790293 + 0.0243227i) q^{20} +(-2.26911 - 4.08626i) q^{22} +(0.359841 + 0.623263i) q^{23} +(4.10856 + 4.56301i) q^{24} +(0.172056 + 1.63701i) q^{25} +(0.684551 - 6.51307i) q^{26} +(-0.882303 - 2.71545i) q^{27} +(0.948551 + 0.689163i) q^{29} +(-5.10078 - 2.27101i) q^{30} +(0.875133 + 0.971933i) q^{31} +(0.0394969 - 0.0684106i) q^{32} +(-6.60261 + 2.80855i) q^{33} -7.70900 q^{34} +(0.0189823 - 0.0137915i) q^{36} +(-0.218960 + 2.08326i) q^{37} +(7.99676 + 1.69976i) q^{38} +(-9.83366 - 2.09021i) q^{39} +(-0.543325 + 5.16939i) q^{40} +(-0.741582 + 0.538791i) q^{41} +8.02379 q^{43} +(0.0304119 + 0.0349314i) q^{44} +(-1.53856 + 2.66487i) q^{45} +(0.678649 + 0.753716i) q^{46} +(-5.45920 - 2.43059i) q^{47} +(6.95163 + 5.05065i) q^{48} +(0.716823 + 2.20615i) q^{50} +(-1.23701 + 11.7693i) q^{51} +(0.00678326 + 0.0645384i) q^{52} +(6.78828 + 7.53915i) q^{53} +(-2.01186 - 3.48465i) q^{54} +(-5.50688 - 2.56282i) q^{55} +(3.87821 - 11.9359i) q^{57} +(1.50948 + 0.672063i) q^{58} +(7.01677 - 3.12407i) q^{59} +(0.0541182 + 0.0115032i) q^{60} +(4.19955 - 4.66407i) q^{61} +(1.49113 + 1.08337i) q^{62} +(2.48916 - 7.66083i) q^{64} +(-4.25528 - 7.37036i) q^{65} +(-8.27859 + 5.80610i) q^{66} +(7.73363 - 13.3950i) q^{67} +(0.0747196 - 0.0158821i) q^{68} +(1.25960 - 0.915151i) q^{69} +(4.29593 + 13.2215i) q^{71} +(3.19096 - 3.54392i) q^{72} +(-5.49463 + 2.44637i) q^{73} +(0.308573 + 2.93588i) q^{74} +(3.48316 - 0.740369i) q^{75} -0.0810106 q^{76} -14.1679 q^{78} +(15.2991 - 3.25193i) q^{79} +(0.760344 + 7.23419i) q^{80} +(-10.2477 + 4.56258i) q^{81} +(-0.864382 + 0.959993i) q^{82} +(1.35217 + 4.16157i) q^{83} +(-8.10479 + 5.88848i) q^{85} +(11.0606 - 2.35100i) q^{86} +(1.26825 - 2.19668i) q^{87} +(7.52209 + 5.65936i) q^{88} +(7.67186 + 13.2880i) q^{89} +(-1.34005 + 4.12425i) q^{90} +(-0.00813063 - 0.00590725i) q^{92} +(1.89325 - 2.10266i) q^{93} +(-8.23752 - 1.75094i) q^{94} +(9.70568 - 4.32125i) q^{95} +(-0.156119 - 0.0695087i) q^{96} +(-0.745114 + 2.29323i) q^{97} +(2.70537 + 4.87190i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 3 q^{2} - 2 q^{3} + 11 q^{4} - 5 q^{5} - 6 q^{6} - 10 q^{8} + 12 q^{9}+O(q^{10}) \) 32 * q + 3 * q^2 - 2 * q^3 + 11 * q^4 - 5 * q^5 - 6 * q^6 - 10 * q^8 + 12 * q^9	\( 32 q + 3 q^{2} - 2 q^{3} + 11 q^{4} - 5 q^{5} - 6 q^{6} - 10 q^{8} + 12 q^{9} + 12 q^{10} + 3 q^{11} + 18 q^{12} + 14 q^{13} - 36 q^{15} - 17 q^{16} - 5 q^{17} - 11 q^{18} + 19 q^{19} - 2 q^{20} - 66 q^{22} - 32 q^{23} - 35 q^{24} - 7 q^{25} - 27 q^{26} - 20 q^{27} + 6 q^{29} + 2 q^{30} - 7 q^{31} - 32 q^{32} - 26 q^{33} + 48 q^{34} + 104 q^{36} - 4 q^{37} - 5 q^{38} - 11 q^{39} - 10 q^{40} + 20 q^{41} - 16 q^{43} + 38 q^{44} + 70 q^{45} + 42 q^{46} - 23 q^{47} + 72 q^{48} + 104 q^{50} + 29 q^{51} + 33 q^{52} - 4 q^{53} + 60 q^{54} + 24 q^{55} - 22 q^{57} - 20 q^{58} + 17 q^{59} + 30 q^{60} - 7 q^{61} - 158 q^{62} + 14 q^{64} + 8 q^{65} + 8 q^{66} + 38 q^{67} - 2 q^{68} - 20 q^{69} - 28 q^{71} - 35 q^{73} + 29 q^{74} + 9 q^{75} - 104 q^{76} - 116 q^{78} - 15 q^{79} - 87 q^{80} + 14 q^{81} + 19 q^{82} - 10 q^{83} + 12 q^{85} + 52 q^{86} - 72 q^{87} - 55 q^{88} + 74 q^{89} + 28 q^{90} - 110 q^{92} - 32 q^{93} - 24 q^{94} - 32 q^{95} - 42 q^{96} - 40 q^{97} + 32 q^{99}+O(q^{100}) \) 32 * q + 3 * q^2 - 2 * q^3 + 11 * q^4 - 5 * q^5 - 6 * q^6 - 10 * q^8 + 12 * q^9 + 12 * q^10 + 3 * q^11 + 18 * q^12 + 14 * q^13 - 36 * q^15 - 17 * q^16 - 5 * q^17 - 11 * q^18 + 19 * q^19 - 2 * q^20 - 66 * q^22 - 32 * q^23 - 35 * q^24 - 7 * q^25 - 27 * q^26 - 20 * q^27 + 6 * q^29 + 2 * q^30 - 7 * q^31 - 32 * q^32 - 26 * q^33 + 48 * q^34 + 104 * q^36 - 4 * q^37 - 5 * q^38 - 11 * q^39 - 10 * q^40 + 20 * q^41 - 16 * q^43 + 38 * q^44 + 70 * q^45 + 42 * q^46 - 23 * q^47 + 72 * q^48 + 104 * q^50 + 29 * q^51 + 33 * q^52 - 4 * q^53 + 60 * q^54 + 24 * q^55 - 22 * q^57 - 20 * q^58 + 17 * q^59 + 30 * q^60 - 7 * q^61 - 158 * q^62 + 14 * q^64 + 8 * q^65 + 8 * q^66 + 38 * q^67 - 2 * q^68 - 20 * q^69 - 28 * q^71 - 35 * q^73 + 29 * q^74 + 9 * q^75 - 104 * q^76 - 116 * q^78 - 15 * q^79 - 87 * q^80 + 14 * q^81 + 19 * q^82 - 10 * q^83 + 12 * q^85 + 52 * q^86 - 72 * q^87 - 55 * q^88 + 74 * q^89 + 28 * q^90 - 110 * q^92 - 32 * q^93 - 24 * q^94 - 32 * q^95 - 42 * q^96 - 40 * q^97 + 32 * q^99

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