LMFDB - Embedded newform 539.2.q.g.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.g.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	$0.181370\pi$
$3$	0.226135	+	2.15153i	0.130559	+	1.24219i	−0.711455	+	0.702731i	$0.751964\pi$
$4$	−0.0127572	+	0.00567988i	−0.00637861	+	0.00283994i
$5$	−1.22544	+	1.36099i	−0.548032	+	0.608651i	−0.951991	−	0.306126i	$-0.900967\pi$
$5$	−1.22544	+	1.36099i	−0.548032	+	0.608651i	0.403959	+	0.914777i	$0.367634\pi$
$6$	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	$0.322906\pi$
$13$	−1.43602	+	4.41961i	−0.398280	+	1.22578i	−0.926377	+	0.376596i	$0.877094\pi$
$14$		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	0.804445	−	0.594027i	$-0.202463\pi$
$17$	5.35068	+	1.13732i	1.29773	+	0.275841i	0.493285	+	0.869868i	$0.335796\pi$
$18$	−2.16316	+	0.963102i	−0.509862	+	0.227005i
$19$	−5.29964	−	2.35955i	−1.21582	−	0.541318i	−0.304301	−	0.952576i	$-0.598423\pi$
$19$	−5.29964	−	2.35955i	−1.21582	−	0.541318i	−0.911519	+	0.411258i	$0.865090\pi$
$20$	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	0.659412	−	0.751782i	$-0.270805\pi$
$31$	−0.875133	−	0.971933i	−0.157178	−	0.174564i	−0.816591	+	0.577217i	$0.804139\pi$
$32$	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	−0.528370	−	0.849014i	$-0.677197\pi$
$41$	0.741582	−	0.538791i	0.115816	−	0.0841449i	0.644185	+	0.764869i	$0.277197\pi$
$42$		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	0.764227	−	0.644947i	$-0.223121\pi$
$47$	5.45920	+	2.43059i	0.796306	+	0.354538i	0.0320786	+	0.999485i	$0.489787\pi$
$48$	−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	−0.809002	−	0.587806i	$-0.799992\pi$
$59$	−7.01677	+	3.12407i	−0.913505	+	0.406719i	−0.104503	+	0.994525i	$0.533325\pi$
$60$	0.0541182	+	0.0115032i	0.00698663	+	0.00148505i
$61$	−4.19955	+	4.66407i	−0.537697	+	0.597173i	−0.949371	−	0.314158i	$-0.898278\pi$
$61$	−4.19955	+	4.66407i	−0.537697	+	0.597173i	0.411674	+	0.911331i	$0.364944\pi$
$62$	−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	−0.0591596	−	0.998249i	$-0.518842\pi$
$73$	5.49463	−	2.44637i	0.643098	−	0.286326i	0.702258	+	0.711923i	$0.252175\pi$
$74$	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	0.849015	−	0.528370i	$-0.177196\pi$
$83$	−1.35217	−	4.16157i	−0.148420	−	0.456791i	−0.997435	+	0.0715783i	$0.977196\pi$
$84$		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	$-0.864382\pi$
$89$	−7.67186	−	13.2880i	−0.813215	−	1.40853i	0.0973874	−	0.995247i	$-0.468951\pi$
$90$	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	−0.906077	−	0.423114i	$-0.860937\pi$
$97$	0.745114	−	2.29323i	0.0756549	−	0.232842i	0.981731	+	0.190272i	$0.0609370\pi$
$98$		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	0.995034	−	0.0995315i	$-0.0317344\pi$
$101$	7.95989	+	8.84035i	0.792039	+	0.879648i	−0.202996	+	0.979180i	$0.565068\pi$
$102$	1.74327	+	16.5861i	0.172610	+	1.64227i
$103$	−0.0414261	+	0.394143i	−0.00408183	+	0.0388360i	−0.996373	−	0.0850905i	$-0.972882\pi$
$103$	−0.0414261	+	0.394143i	−0.00408183	+	0.0388360i	0.992291	+	0.123927i	$0.0395487\pi$
$104$	−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	0.869931	−	0.493173i	$-0.164163\pi$
$131$	0.0900265	+	0.155930i	0.00786565	+	0.0136237i	−0.862066	+	0.506796i	$0.830830\pi$
$132$	−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	0.800425	−	0.599432i	$-0.204607\pi$
$139$	5.63172	+	4.09169i	0.477677	+	0.347052i	−0.322749	+	0.946485i	$0.604607\pi$
$140$		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	$-0.855929\pi$
$157$	−1.38550	−	13.1822i	−0.110575	−	1.05205i	0.788733	−	0.614736i	$-0.210737\pi$
$158$	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	$-0.782722\pi$
$167$	2.87651	−	8.85300i	0.222591	−	0.685066i	0.998527	−	0.0542539i	$-0.0172780\pi$
$168$		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	0.737732	−	0.675094i	$-0.235897\pi$
$173$	9.59742	+	4.27304i	0.729678	+	0.324874i	−0.00805375	+	0.999968i	$0.502564\pi$
$174$	−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	$-0.914571\pi$
$181$	−4.57437	−	14.0785i	−0.340010	−	1.04644i	0.624191	−	0.781272i	$-0.285429\pi$
$182$		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	−0.779989	−	0.625794i	$-0.784775\pi$
$199$	2.14364	−	3.71290i	0.151959	−	0.263200i	0.931948	+	0.362593i	$0.118109\pi$
$200$	−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	−0.448412	−	0.893827i	$-0.648010\pi$
$223$	3.92893	−	2.85453i	0.263101	−	0.191154i	0.711513	+	0.702673i	$0.248010\pi$
$224$		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	−0.394661	−	0.918827i	$-0.629138\pi$
$227$	0.362809	−	0.161533i	0.0240805	−	0.0107213i	0.418742	+	0.908105i	$0.362471\pi$
$228$	0.0183193	+	0.174297i	0.00121323	+	0.0115431i
$229$	−2.14178	+	0.455250i	−0.141533	+	0.0300838i	−0.278133	−	0.960542i	$-0.589716\pi$
$229$	−2.14178	+	0.455250i	−0.141533	+	0.0300838i	0.136600	+	0.990626i	$0.456382\pi$
$230$	−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	$-0.590080\pi$
$241$	10.7421	−	18.6059i	0.691962	−	1.19851i	0.971194	−	0.238290i	$-0.0765869\pi$
$242$	−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	−0.955105	−	0.296268i	$-0.904258\pi$
$251$	−0.130968	+	0.403077i	−0.00826660	+	0.0254420i	0.946838	+	0.321710i	$0.104258\pi$
$252$		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	$0.216402\pi$
$257$	−1.82298	+	17.3445i	−0.113715	+	1.08192i	−0.891384	+	0.453249i	$0.850265\pi$
$258$	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	0.268077	−	0.963398i	$-0.413612\pi$
$269$	1.98664	+	0.422274i	0.121128	+	0.0257465i	−0.146949	+	0.989144i	$0.546945\pi$
$270$	−7.20797	−	1.53210i	−0.438663	−	0.0932407i
$271$	−0.794880	+	7.56278i	−0.0482855	+	0.459406i	0.943489	+	0.331405i	$0.107523\pi$
$271$	−0.794880	+	7.56278i	−0.0482855	+	0.459406i	−0.991774	+	0.128001i	$0.959144\pi$
$272$	−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	$0.342959\pi$
$283$	3.25461	+	30.9656i	0.193467	+	1.84071i	−0.280120	+	0.959965i	$0.590374\pi$
$284$	−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	0.986522	−	0.163632i	$-0.0523209\pi$
$293$	19.4409	+	14.1247i	1.13575	+	0.825171i	0.149229	+	0.988803i	$0.452321\pi$
$294$		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	$-0.549826\pi$
$307$	−5.46298			−0.311789			−0.155894	+	0.987774i	$0.549826\pi$
$308$		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	$-0.904504\pi$
$311$	−1.45174	−	13.8124i	−0.0823204	−	0.783227i	0.873013	−	0.487697i	$-0.162163\pi$
$312$	26.0667	−	11.6057i	1.47574	−	0.657041i
$313$	18.3667	−	20.3983i	1.03815	−	1.15298i	0.0501114	−	0.998744i	$-0.484042\pi$
$313$	18.3667	−	20.3983i	1.03815	−	1.15298i	0.988034	−	0.154234i	$-0.0492910\pi$
$314$	−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	−0.450307	−	0.892874i	$-0.648686\pi$
$349$	4.85185	−	3.52507i	0.259713	−	0.188693i	0.710021	+	0.704181i	$0.248686\pi$
$350$		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	$0.387613\pi$
$353$	−12.0191	+	20.8177i	−0.639712	+	1.10801i	−0.985496	+	0.169699i	$0.945720\pi$
$354$	−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	−0.137644	−	0.990482i	$-0.543953\pi$
$367$	9.69981	−	4.31863i	0.506326	−	0.225431i	0.643970	+	0.765051i	$0.277286\pi$
$368$	−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	0.195562	−	0.980691i	$-0.437347\pi$
$383$	15.1299	−	3.21595i	0.773100	−	0.164328i	0.577538	+	0.816364i	$0.304013\pi$
$384$	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	0.999613	−	0.0278101i	$-0.00885338\pi$
$397$	9.47870	+	16.4176i	0.475722	+	0.823975i	−0.523891	+	0.851785i	$0.675520\pi$
$398$	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	0.830221	−	0.557435i	$-0.188214\pi$
$409$	3.82345	+	4.24638i	0.189058	+	0.209970i	−0.641163	+	0.767405i	$0.721548\pi$
$410$	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	$-0.731220\pi$
$419$	−27.1909			−1.32836			−0.664181	+	0.747571i	$0.731220\pi$
$420$		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	0.124200	−	0.992257i	$-0.460364\pi$
$433$	−16.2539	−	11.8092i	−0.781113	−	0.567512i	−0.905313	+	0.424745i	$0.860364\pi$
$434$		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	$-0.946103\pi$
$439$	−13.3841	−	23.1819i	−0.638788	−	1.10641i	0.346912	−	0.937898i	$-0.387230\pi$
$440$	−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	$-0.431671\pi$
$461$	9.14737			0.426035			0.213018	+	0.977048i	$0.431671\pi$
$462$		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	−0.973348	−	0.229331i	$-0.926346\pi$
$467$	−13.9068	+	15.4451i	−0.643531	+	0.714714i	0.329817	+	0.944045i	$0.393013\pi$
$468$	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	0.720473	−	0.693483i	$-0.243925\pi$
$479$	24.0001	+	5.10138i	1.09659	+	0.233088i	0.376120	+	0.926571i	$0.377258\pi$
$480$	−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	−0.100193	−	0.994968i	$-0.531946\pi$
$503$	18.2812	−	13.2820i	0.815117	−	0.592217i	0.915310	+	0.402751i	$0.131946\pi$
$504$		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	−0.0767809	−	0.997048i	$-0.524464\pi$
$509$	−19.6080	−	8.73004i	−0.869108	−	0.386952i	−0.792328	+	0.610096i	$0.791131\pi$
$510$	−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	0.430462	−	0.902609i	$-0.358351\pi$
$521$	31.7106	−	14.1185i	1.38927	−	0.618541i	0.958804	+	0.284067i	$0.0916840\pi$
$522$	−2.71561	−	0.577220i	−0.118859	−	0.0252642i
$523$	13.2007	−	14.6609i	0.577226	−	0.641075i	−0.381849	−	0.924225i	$-0.624713\pi$
$523$	13.2007	−	14.6609i	0.577226	−	0.641075i	0.959076	+	0.283150i	$0.0913793\pi$
$524$	−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	0.221579	−	0.975142i	$-0.428879\pi$
$563$	−18.3031	−	20.3276i	−0.771383	−	0.856707i	−0.992962	+	0.118435i	$0.962212\pi$
$564$	−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	−0.564755	−	0.825259i	$-0.691029\pi$
$577$	−34.0218	−	7.23156i	−1.41635	−	0.301054i	−0.851592	+	0.524205i	$0.824363\pi$
$578$	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	0.802618	−	0.596493i	$-0.203440\pi$
$587$	11.7105	+	8.50816i	0.483343	+	0.351169i	−0.319276	+	0.947662i	$0.603440\pi$
$588$		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	0.978053	−	0.208356i	$-0.0668114\pi$
$593$	7.51453	+	13.0155i	0.308585	+	0.534484i	−0.669468	+	0.742841i	$0.733478\pi$
$594$	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	0.129581	−	0.991569i	$-0.458637\pi$
$601$	−18.9605	−	13.7756i	−0.773415	−	0.561919i	−0.902995	+	0.429650i	$0.858637\pi$
$602$		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	0.323334	−	0.946285i	$-0.395196\pi$
$607$	24.7261	−	5.25570i	1.00360	−	0.213322i	0.680269	+	0.732963i	$0.261863\pi$
$608$	−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	$-0.661305\pi$
$619$	−4.78656	−	45.5411i	−0.192388	−	1.83045i	0.292953	−	0.956127i	$-0.405362\pi$
$620$	−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	$-0.663848\pi$
$643$	−15.3575	−	47.2657i	−0.605642	−	1.86398i	−0.113330	−	0.993557i	$-0.536152\pi$
$644$		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	0.580770	−	0.814067i	$-0.302751\pi$
$647$	−7.36491	−	8.17956i	−0.289545	−	0.321572i	−0.870315	+	0.492496i	$0.836085\pi$
$648$	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	−0.993184	−	0.116555i	$-0.962815\pi$
$661$	−10.1722	+	17.6187i	−0.395652	+	0.685290i	0.597532	+	0.801845i	$0.296148\pi$
$662$	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	−0.697890	−	0.716205i	$-0.745877\pi$
$677$	2.27257	−	2.52394i	0.0873418	−	0.0970029i	0.785231	+	0.619203i	$0.212544\pi$
$678$	−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	−0.329675	−	0.944095i	$-0.606939\pi$
$691$	−6.48892	+	1.37926i	−0.246850	+	0.0524696i	0.0828248	+	0.996564i	$0.473606\pi$
$692$	−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	−0.990193	−	0.139703i	$-0.955385\pi$
$719$	0.198634	−	1.88988i	0.00740781	−	0.0704806i	0.997601	+	0.0692225i	$0.0220518\pi$
$720$	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	$-0.582503\pi$
$727$	−13.8211			−0.512595			−0.256298	+	0.966598i	$0.582503\pi$
$728$		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	$0.385002\pi$
$733$	−5.05650	+	48.1094i	−0.186766	+	1.77696i	−0.540235	+	0.841514i	$0.681665\pi$
$734$	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	0.474724	−	0.880135i	$-0.342548\pi$
$761$	34.9349	−	7.42564i	1.26639	−	0.269179i	0.791665	+	0.610956i	$0.209215\pi$
$762$	−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	$-0.469521\pi$
$769$	5.30246			0.191212			0.0956058	+	0.995419i	$0.469521\pi$
$770$		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	$0.321091\pi$
$773$	5.21505	+	49.6179i	0.187572	+	1.78463i	−0.345356	+	0.938472i	$0.612242\pi$
$774$	−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	−0.465203	−	0.885204i	$-0.654019\pi$
$787$	−35.0734	−	7.45508i	−1.25023	−	0.265745i	−0.785029	+	0.619459i	$0.787352\pi$
$788$	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	0.998749	−	0.0499962i	$-0.0159209\pi$
$797$	4.55530	+	14.0198i	0.161357	+	0.496606i	−0.837392	+	0.546602i	$0.815921\pi$
$798$		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	−0.608392	−	0.793637i	$-0.708185\pi$
$811$	−1.18472	+	0.860750i	−0.0416012	+	0.0302250i	0.566790	+	0.823862i	$0.308185\pi$
$812$		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	−0.696639	−	0.717422i	$-0.745322\pi$
$829$	−18.1286	+	8.07138i	−0.629633	+	0.280331i	0.0670059	+	0.997753i	$0.478655\pi$
$830$	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	−0.471039	−	0.882112i	$-0.656121\pi$
$839$	6.44019	−	4.67907i	0.222340	−	0.161539i	0.693379	+	0.720573i	$0.256121\pi$
$840$		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	$0.0982473\pi$
$853$	10.5292	+	32.4055i	0.360513	+	1.10954i	−0.592231	+	0.805768i	$0.701753\pi$
$854$		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	−0.996373	−	0.0850904i	$-0.972882\pi$
$857$	−12.4269	+	21.5241i	−0.424496	+	0.735249i	0.571877	+	0.820339i	$0.306215\pi$
$858$	13.7725	+	44.9259i	0.470185	+	1.53374i
$859$	−1.02827	−	1.78102i	−0.0350841	−	0.0607675i	0.847950	−	0.530076i	$-0.177837\pi$
$859$	−1.02827	−	1.78102i	−0.0350841	−	0.0607675i	−0.883034	+	0.469308i	$0.844503\pi$
$860$	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	$-0.465330\pi$
$881$	6.45292			0.217404			0.108702	+	0.994074i	$0.465330\pi$
$882$		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	$0.204800\pi$
$887$	−3.19407	+	30.3896i	−0.107246	+	1.02038i	−0.907309	+	0.420465i	$0.861867\pi$
$888$	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	−0.965008	−	0.262219i	$-0.915546\pi$
$929$	−18.3900	+	20.4241i	−0.603355	+	0.670093i	0.361654	+	0.932313i	$0.382212\pi$
$930$	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	−0.993765	−	0.111495i	$-0.964436\pi$
$937$	−3.80357	+	11.7062i	−0.124257	+	0.382425i	0.869508	+	0.493919i	$0.164436\pi$
$938$		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	0.184573	−	0.982819i	$-0.440910\pi$
$941$	−1.42823	−	0.303580i	−0.0465590	−	0.00989642i	−0.231132	+	0.972922i	$0.574243\pi$
$942$	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	0.905521	−	0.424301i	$-0.139480\pi$
$971$	37.2720	+	16.5946i	1.19612	+	0.532545i	0.290595	+	0.956846i	$0.406147\pi$
$972$	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	−0.390549	−	0.920582i	$-0.627715\pi$
$983$	1.01110	−	0.450172i	0.0322492	−	0.0143583i	0.422798	+	0.906224i	$0.361048\pi$
$984$	−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	0.348786	−	0.937202i	$-0.386594\pi$
$997$	40.3737	−	17.9755i	1.27865	−	0.569290i	0.929861	+	0.367912i	$0.119927\pi$
$998$	−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.g.361.3		32
7.2	even	3	inner	539.2.q.g.471.2		32
7.3	odd	6		539.2.f.e.295.2		16
7.4	even	3		77.2.f.b.64.2	✓	16
7.5	odd	6		539.2.q.f.471.2		32
7.6	odd	2		539.2.q.f.361.3		32
11.5	even	5	inner	539.2.q.g.214.2		32
21.11	odd	6		693.2.m.i.64.3		16
77.4	even	15		847.2.a.p.1.3		8
77.5	odd	30		539.2.q.f.324.3		32
77.16	even	15	inner	539.2.q.g.324.3		32
77.18	odd	30		847.2.a.o.1.6		8
77.25	even	15		847.2.f.w.323.3		16
77.27	odd	10		539.2.q.f.214.2		32
77.32	odd	6		847.2.f.x.372.3		16
77.38	odd	30		539.2.f.e.148.2		16
77.39	odd	30		847.2.f.x.148.3		16
77.46	odd	30		847.2.f.v.729.2		16
77.53	even	15		847.2.f.w.729.3		16
77.59	odd	30		5929.2.a.bt.1.3		8
77.60	even	15		77.2.f.b.71.2	yes	16
77.73	even	30		5929.2.a.bs.1.6		8
77.74	odd	30		847.2.f.v.323.2		16
231.95	even	30		7623.2.a.cw.1.3		8
231.137	odd	30		693.2.m.i.379.3		16
231.158	odd	30		7623.2.a.ct.1.6		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.2.f.b.64.2	✓	16	7.4	even	3
77.2.f.b.71.2	yes	16	77.60	even	15
539.2.f.e.148.2		16	77.38	odd	30
539.2.f.e.295.2		16	7.3	odd	6
539.2.q.f.214.2		32	77.27	odd	10
539.2.q.f.324.3		32	77.5	odd	30
539.2.q.f.361.3		32	7.6	odd	2
539.2.q.f.471.2		32	7.5	odd	6
539.2.q.g.214.2		32	11.5	even	5	inner
539.2.q.g.324.3		32	77.16	even	15	inner
539.2.q.g.361.3		32	1.1	even	1	trivial
539.2.q.g.471.2		32	7.2	even	3	inner
693.2.m.i.64.3		16	21.11	odd	6
693.2.m.i.379.3		16	231.137	odd	30
847.2.a.o.1.6		8	77.18	odd	30
847.2.a.p.1.3		8	77.4	even	15
847.2.f.v.323.2		16	77.74	odd	30
847.2.f.v.729.2		16	77.46	odd	30
847.2.f.w.323.3		16	77.25	even	15
847.2.f.w.729.3		16	77.53	even	15
847.2.f.x.148.3		16	77.39	odd	30
847.2.f.x.372.3		16	77.32	odd	6
5929.2.a.bs.1.6		8	77.73	even	30
5929.2.a.bt.1.3		8	77.59	odd	30
7623.2.a.ct.1.6		8	231.158	odd	30
7623.2.a.cw.1.3		8	231.95	even	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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