LMFDB - Embedded newform 539.2.f.e.344.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [539,2,Mod(148,539)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(539, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("539.148");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 539 = 7^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	539.f (of order $5$, degree $4$, 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:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 3 x^{15} + 14 x^{14} - 32 x^{13} + 86 x^{12} - 145 x^{11} + 245 x^{10} - 245 x^{9} + 640 x^{8} + \cdots + 25 $ x^16 - 3x^15 + 14x^14 - 32x^13 + 86x^12 - 145x^11 + 245x^10 - 245x^9 + 640x^8 - 1175x^7 + 2135x^6 - 2300x^5 + 1850x^4 - 925x^3 + 700x^2 - 200*x + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 5 $
Twist minimal:	no (minimal twist has level 77)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			344.3
Root			$0.183009 - 0.132964i$ of defining polynomial
Character	$\chi$	$=$	539.344
Dual form			539.2.f.e.246.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.183009 + 0.132964i) q^{2} +(0.0677147 + 0.208405i) q^{3} +(-0.602221 + 1.85345i) q^{4} +(-2.01892 - 1.46683i) q^{5} +(-0.0401026 - 0.0291363i) q^{6} +(-0.276036 - 0.849550i) q^{8} +(2.38820 - 1.73513i) q^{9} +0.564516 q^{10} +(-2.66598 - 1.97296i) q^{11} -0.427046 q^{12} +(4.15429 - 3.01827i) q^{13} +(0.168984 - 0.520079i) q^{15} +(-2.98979 - 2.17221i) q^{16} +(-1.16298 - 0.844956i) q^{17} +(-0.206353 + 0.635089i) q^{18} +(1.87526 + 5.77147i) q^{19} +(3.93453 - 2.85860i) q^{20} +(0.750229 + 0.00659095i) q^{22} +7.08292 q^{23} +(0.158358 - 0.115054i) q^{24} +(0.379361 + 1.16755i) q^{25} +(-0.358952 + 1.10474i) q^{26} +(1.05516 + 0.766622i) q^{27} +(2.01408 - 6.19869i) q^{29} +(0.0382260 + 0.117648i) q^{30} +(6.22049 - 4.51945i) q^{31} +2.62252 q^{32} +(0.230648 - 0.689200i) q^{33} +0.325184 q^{34} +(1.77775 + 5.47134i) q^{36} +(-1.23122 + 3.78932i) q^{37} +(-1.11058 - 0.806887i) q^{38} +(0.910328 + 0.661392i) q^{39} +(-0.688853 + 2.12007i) q^{40} +(-2.08556 - 6.41868i) q^{41} -0.802299 q^{43} +(5.26228 - 3.75309i) q^{44} -7.36674 q^{45} +(-1.29624 + 0.941771i) q^{46} +(-2.08655 - 6.42174i) q^{47} +(0.250246 - 0.770178i) q^{48} +(-0.224669 - 0.163231i) q^{50} +(0.0973416 - 0.299587i) q^{51} +(3.09240 + 9.51742i) q^{52} +(-5.32469 + 3.86861i) q^{53} -0.295037 q^{54} +(2.48840 + 7.89379i) q^{55} +(-1.07582 + 0.781627i) q^{57} +(0.455607 + 1.40221i) q^{58} +(-0.888810 + 2.73548i) q^{59} +(0.862172 + 0.626405i) q^{60} +(-0.691986 - 0.502757i) q^{61} +(-0.537482 + 1.65420i) q^{62} +(5.49964 - 3.99573i) q^{64} -12.8145 q^{65} +(0.0494280 + 0.156797i) q^{66} -1.64668 q^{67} +(2.26645 - 1.64667i) q^{68} +(0.479618 + 1.47611i) q^{69} +(-3.65738 - 2.65724i) q^{71} +(-2.13331 - 1.54994i) q^{72} +(4.58827 - 14.1212i) q^{73} +(-0.278517 - 0.857187i) q^{74} +(-0.217635 + 0.158121i) q^{75} -11.8264 q^{76} -0.254539 q^{78} +(-1.98444 + 1.44178i) q^{79} +(2.84989 + 8.77105i) q^{80} +(2.64832 - 8.15069i) q^{81} +(1.23513 + 0.897372i) q^{82} +(1.81851 + 1.32122i) q^{83} +(1.10856 + 3.41180i) q^{85} +(0.146828 - 0.106677i) q^{86} +1.42822 q^{87} +(-0.940224 + 2.80949i) q^{88} -1.73566 q^{89} +(1.34818 - 0.979509i) q^{90} +(-4.26549 + 13.1278i) q^{92} +(1.36309 + 0.990346i) q^{93} +(1.23572 + 0.897800i) q^{94} +(4.67976 - 14.4028i) q^{95} +(0.177584 + 0.546546i) q^{96} +(-9.77095 + 7.09901i) q^{97} +(-9.79024 - 0.0860098i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 3 q^{2} + 2 q^{3} - 11 q^{4} + 5 q^{5} - 3 q^{6} - 5 q^{8} - 12 q^{9} - 12 q^{10} - 3 q^{11} - 18 q^{12} + 7 q^{13} - 18 q^{15} + 17 q^{16} + 5 q^{17} + 11 q^{18} - 19 q^{19} - q^{20} - 33 q^{22}+ \cdots + 16 q^{99}+O(q^{100}) $ 16 * q - 3 * q^2 + 2 * q^3 - 11 * q^4 + 5 * q^5 - 3 * q^6 - 5 * q^8 - 12 * q^9 - 12 * q^10 - 3 * q^11 - 18 * q^12 + 7 * q^13 - 18 * q^15 + 17 * q^16 + 5 * q^17 + 11 * q^18 - 19 * q^19 - q^20 - 33 * q^22 + 32 * q^23 + 35 * q^24 + 7 * q^25 + 27 * q^26 - 10 * q^27 + 3 * q^29 - 2 * q^30 + 7 * q^31 + 32 * q^32 + 26 * q^33 + 24 * q^34 + 52 * q^36 + 4 * q^37 + 5 * q^38 + 11 * q^39 + 10 * q^40 + 10 * q^41 - 8 * q^43 - 38 * q^44 - 70 * q^45 - 42 * q^46 + 23 * q^47 + 36 * q^48 + 52 * q^50 - 29 * q^51 - 33 * q^52 + 4 * q^53 - 60 * q^54 + 12 * q^55 - 11 * q^57 + 20 * q^58 - 17 * q^59 - 30 * q^60 + 7 * q^61 - 79 * q^62 + 7 * q^64 - 8 * q^65 - 8 * q^66 - 38 * q^67 + 2 * q^68 - 10 * q^69 - 14 * q^71 + 35 * q^73 - 29 * q^74 - 9 * q^75 - 52 * q^76 - 58 * q^78 + 15 * q^79 + 87 * q^80 - 14 * q^81 - 19 * q^82 - 5 * q^83 + 6 * q^85 - 52 * q^86 + 72 * q^87 + 55 * q^88 - 74 * q^89 + 14 * q^90 - 55 * q^92 + 32 * q^93 + 24 * q^94 + 32 * q^95 + 42 * q^96 - 20 * q^97 + 16 * q^99

Character values

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

$n$	$199$	$442$
$\chi(n)$	$1$	$e\left(\frac{4}{5}\right)$

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 $

$2$	−0.183009	+	0.132964i	−0.129407	+	0.0940195i	−0.650606	−	0.759416i	$-0.725485\pi$
$2$	−0.183009	+	0.132964i	−0.129407	+	0.0940195i	0.521199	+	0.853435i	$0.325485\pi$
$3$	0.0677147	+	0.208405i	0.0390951	+	0.120322i	0.968699	−	0.248237i	$-0.0798511\pi$
$3$	0.0677147	+	0.208405i	0.0390951	+	0.120322i	−0.929604	+	0.368559i	$0.879851\pi$
$4$	−0.602221	+	1.85345i	−0.301111	+	0.926723i
$5$	−2.01892	−	1.46683i	−0.902889	−	0.655987i	0.0363174	−	0.999340i	$-0.488437\pi$
$5$	−2.01892	−	1.46683i	−0.902889	−	0.655987i	−0.939206	+	0.343353i	$0.888437\pi$
$6$	−0.0401026	−	0.0291363i	−0.0163718	−	0.0118948i
$7$		0			0
$7$		0			0
$8$	−0.276036	−	0.849550i	−0.0975933	−	0.300361i
$9$	2.38820	−	1.73513i	0.796068	−	0.578377i
$10$	0.564516			0.178516
$11$	−2.66598	−	1.97296i	−0.803822	−	0.594870i
$11$	−2.66598	−	1.97296i	−0.803822	−	0.594870i
$12$	−0.427046			−0.123278
$13$	4.15429	−	3.01827i	1.15219	−	0.837117i	0.163422	−	0.986556i	$-0.447747\pi$
$13$	4.15429	−	3.01827i	1.15219	−	0.837117i	0.988771	+	0.149439i	$0.0477468\pi$
$14$		0			0
$15$	0.168984	−	0.520079i	0.0436314	−	0.134284i
$16$	−2.98979	−	2.17221i	−0.747449	−	0.543053i
$17$	−1.16298	−	0.844956i	−0.282065	−	0.204932i	0.437753	−	0.899095i	$-0.355774\pi$
$17$	−1.16298	−	0.844956i	−0.282065	−	0.204932i	−0.719817	+	0.694163i	$0.755774\pi$
$18$	−0.206353	+	0.635089i	−0.0486378	+	0.149692i
$19$	1.87526	+	5.77147i	0.430215	+	1.32406i	0.897912	+	0.440176i	$0.145084\pi$
$19$	1.87526	+	5.77147i	0.430215	+	1.32406i	−0.467697	+	0.883889i	$0.654916\pi$
$20$	3.93453	−	2.85860i	0.879788	−	0.639203i
$21$		0			0
$22$	0.750229	+	0.00659095i	0.159949	+	0.00140520i
$23$	7.08292			1.47689			0.738446	−	0.674313i	$-0.235560\pi$
$23$	7.08292			1.47689			0.738446	+	0.674313i	$0.235560\pi$
$24$	0.158358	−	0.115054i	0.0323248	−	0.0234853i
$25$	0.379361	+	1.16755i	0.0758722	+	0.233511i
$26$	−0.358952	+	1.10474i	−0.0703962	+	0.216657i
$27$	1.05516	+	0.766622i	0.203067	+	0.147536i
$28$		0			0
$29$	2.01408	−	6.19869i	0.374004	−	1.15107i	−0.570143	−	0.821545i	$-0.693112\pi$
$29$	2.01408	−	6.19869i	0.374004	−	1.15107i	0.944148	−	0.329522i	$-0.106888\pi$
$30$	0.0382260	+	0.117648i	0.00697909	+	0.0214794i
$31$	6.22049	−	4.51945i	1.11723	−	0.811718i	0.133446	−	0.991056i	$-0.457396\pi$
$31$	6.22049	−	4.51945i	1.11723	−	0.811718i	0.983787	+	0.179338i	$0.0573957\pi$
$32$	2.62252			0.463601
$33$	0.230648	−	0.689200i	0.0401506	−	0.119974i
$34$	0.325184			0.0557687
$35$		0			0
$36$	1.77775	+	5.47134i	0.296291	+	0.911890i
$37$	−1.23122	+	3.78932i	−0.202412	+	0.622960i	0.797398	+	0.603454i	$0.206209\pi$
$37$	−1.23122	+	3.78932i	−0.202412	+	0.622960i	−0.999810	+	0.0195059i	$0.993791\pi$
$38$	−1.11058	−	0.806887i	−0.180161	−	0.130894i
$39$	0.910328	+	0.661392i	0.145769	+	0.105907i
$40$	−0.688853	+	2.12007i	−0.108917	+	0.335213i
$41$	−2.08556	−	6.41868i	−0.325709	−	1.00243i	−0.971120	−	0.238594i	$-0.923314\pi$
$41$	−2.08556	−	6.41868i	−0.325709	−	1.00243i	0.645410	−	0.763836i	$-0.276686\pi$
$42$		0			0
$43$	−0.802299			−0.122349			−0.0611747	−	0.998127i	$-0.519485\pi$
$43$	−0.802299			−0.122349			−0.0611747	+	0.998127i	$0.519485\pi$
$44$	5.26228	−	3.75309i	0.793319	−	0.565799i
$45$	−7.36674			−1.09817
$46$	−1.29624	+	0.941771i	−0.191120	+	0.138857i
$47$	−2.08655	−	6.42174i	−0.304355	−	0.936707i	−0.979917	−	0.199405i	$-0.936099\pi$
$47$	−2.08655	−	6.42174i	−0.304355	−	0.936707i	0.675563	−	0.737303i	$-0.263901\pi$
$48$	0.250246	−	0.770178i	0.0361199	−	0.111166i
$49$		0			0
$50$	−0.224669	−	0.163231i	−0.0317729	−	0.0230844i
$51$	0.0973416	−	0.299587i	0.0136306	−	0.0419505i
$52$	3.09240	+	9.51742i	0.428838	+	1.31983i
$53$	−5.32469	+	3.86861i	−0.731402	+	0.531394i	−0.890007	−	0.455948i	$-0.849300\pi$
$53$	−5.32469	+	3.86861i	−0.731402	+	0.531394i	0.158605	+	0.987342i	$0.449300\pi$
$54$	−0.295037			−0.0401495
$55$	2.48840	+	7.89379i	0.335535	+	1.06440i
$56$		0			0
$57$	−1.07582	+	0.781627i	−0.142495	+	0.103529i
$58$	0.455607	+	1.40221i	0.0598241	+	0.184120i
$59$	−0.888810	+	2.73548i	−0.115713	+	0.356129i	−0.992095	−	0.125488i	$-0.959950\pi$
$59$	−0.888810	+	2.73548i	−0.115713	+	0.356129i	0.876382	+	0.481617i	$0.159950\pi$
$60$	0.862172	+	0.626405i	0.111306	+	0.0808685i
$61$	−0.691986	−	0.502757i	−0.0885997	−	0.0643715i	0.542604	−	0.839989i	$-0.317439\pi$
$61$	−0.691986	−	0.502757i	−0.0885997	−	0.0643715i	−0.631203	+	0.775617i	$0.717439\pi$
$62$	−0.537482	+	1.65420i	−0.0682603	+	0.210084i
$63$		0			0
$64$	5.49964	−	3.99573i	0.687455	−	0.499466i
$65$	−12.8145			−1.58944
$66$	0.0494280	+	0.156797i	0.00608417	+	0.0193004i
$67$	−1.64668			−0.201174			−0.100587	−	0.994928i	$-0.532072\pi$
$67$	−1.64668			−0.201174			−0.100587	+	0.994928i	$0.532072\pi$
$68$	2.26645	−	1.64667i	0.274848	−	0.199689i
$69$	0.479618	+	1.47611i	0.0577393	+	0.177703i
$70$		0			0
$71$	−3.65738	−	2.65724i	−0.434051	−	0.315357i	0.349216	−	0.937042i	$-0.386448\pi$
$71$	−3.65738	−	2.65724i	−0.434051	−	0.315357i	−0.783267	+	0.621686i	$0.786448\pi$
$72$	−2.13331	−	1.54994i	−0.251413	−	0.182662i
$73$	4.58827	−	14.1212i	0.537016	−	1.65277i	−0.202236	−	0.979337i	$-0.564821\pi$
$73$	4.58827	−	14.1212i	0.537016	−	1.65277i	0.739252	−	0.673429i	$-0.235179\pi$
$74$	−0.278517	−	0.857187i	−0.0323769	−	0.0996459i
$75$	−0.217635	+	0.158121i	−0.0251303	+	0.0182583i
$76$	−11.8264			−1.35658
$77$		0			0
$78$	−0.254539			−0.0288209
$79$	−1.98444	+	1.44178i	−0.223267	+	0.162213i	−0.693796	−	0.720171i	$-0.744063\pi$
$79$	−1.98444	+	1.44178i	−0.223267	+	0.162213i	0.470529	+	0.882385i	$0.344063\pi$
$80$	2.84989	+	8.77105i	0.318627	+	0.980633i
$81$	2.64832	−	8.15069i	0.294258	−	0.905633i
$82$	1.23513	+	0.897372i	0.136397	+	0.0990982i
$83$	1.81851	+	1.32122i	0.199607	+	0.145023i	0.683099	−	0.730326i	$-0.260632\pi$
$83$	1.81851	+	1.32122i	0.199607	+	0.145023i	−0.483492	+	0.875349i	$0.660632\pi$
$84$		0			0
$85$	1.10856	+	3.41180i	0.120240	+	0.370061i
$86$	0.146828	−	0.106677i	0.0158328	−	0.0115032i
$87$	1.42822			0.153121
$88$	−0.940224	+	2.80949i	−0.100228	+	0.299492i
$89$	−1.73566			−0.183980			−0.0919898	−	0.995760i	$-0.529323\pi$
$89$	−1.73566			−0.183980			−0.0919898	+	0.995760i	$0.529323\pi$
$90$	1.34818	−	0.979509i	0.142111	−	0.103249i
$91$		0			0
$92$	−4.26549	+	13.1278i	−0.444708	+	1.36867i
$93$	1.36309	+	0.990346i	0.141346	+	0.102694i
$94$	1.23572	+	0.897800i	0.127454	+	0.0926010i
$95$	4.67976	−	14.4028i	0.480134	−	1.47770i
$96$	0.177584	+	0.546546i	0.0181245	+	0.0557816i
$97$	−9.77095	+	7.09901i	−0.992089	+	0.720795i	−0.960378	−	0.278702i	$-0.910096\pi$
$97$	−9.77095	+	7.09901i	−0.992089	+	0.720795i	−0.0317117	+	0.999497i	$0.510096\pi$
$98$		0			0
$99$	−9.79024	−	0.0860098i	−0.983956	−	0.00864431i
$100$	−2.39246			−0.239246
$101$	−2.98801	+	2.17091i	−0.297318	+	0.216014i	−0.726436	−	0.687234i	$-0.758825\pi$
$101$	−2.98801	+	2.17091i	−0.297318	+	0.216014i	0.429118	+	0.903249i	$0.358825\pi$
$102$	0.0220198	+	0.0677699i	0.00218028	+	0.00671022i
$103$	0.355853	−	1.09520i	0.0350632	−	0.107913i	−0.931993	−	0.362476i	$-0.881931\pi$
$103$	0.355853	−	1.09520i	0.0350632	−	0.107913i	0.967056	+	0.254563i	$0.0819315\pi$
$104$	−3.71090	−	2.69613i	−0.363884	−	0.264377i
$105$		0			0
$106$	0.460080	−	1.41598i	0.0446869	−	0.137532i
$107$	0.360665	+	1.11001i	0.0348668	+	0.107309i	0.966975	−	0.254870i	$-0.0820328\pi$
$107$	0.360665	+	1.11001i	0.0348668	+	0.107309i	−0.932108	+	0.362179i	$0.882033\pi$
$108$	−2.05633	+	1.49401i	−0.197871	+	0.143762i
$109$	9.30234			0.891003			0.445501	−	0.895281i	$-0.353025\pi$
$109$	9.30234			0.891003			0.445501	+	0.895281i	$0.353025\pi$
$110$	−1.50499	−	1.11377i	−0.143495	−	0.106194i
$111$	−0.873083			−0.0828694
$112$		0			0
$113$	1.01893	+	3.13595i	0.0958529	+	0.295005i	0.987475	−	0.157775i	$-0.0504322\pi$
$113$	1.01893	+	3.13595i	0.0958529	+	0.295005i	−0.891622	+	0.452780i	$0.850432\pi$
$114$	0.0929560	−	0.286089i	0.00870613	−	0.0267947i
$115$	−14.2999	−	10.3895i	−1.33347	−	0.968822i
$116$	10.2760	+	7.46596i	0.954104	+	0.693197i
$117$	4.68420	−	14.4165i	0.433054	−	1.33280i
$118$	−0.201059	−	0.618796i	−0.0185090	−	0.0569648i
$119$		0			0
$120$	−0.488478			−0.0445918
$121$	3.21486	+	10.5197i	0.292260	+	0.956339i
$122$	0.193488			0.0175176
$123$	1.19646	−	0.869279i	0.107881	−	0.0783802i
$124$	4.63045	+	14.2511i	0.415827	+	1.27978i
$125$	−2.90909	+	8.95326i	−0.260197	+	0.800804i
$126$		0			0
$127$	0.233972	+	0.169990i	0.0207616	+	0.0150842i	0.598118	−	0.801408i	$-0.295916\pi$
$127$	0.233972	+	0.169990i	0.0207616	+	0.0150842i	−0.577356	+	0.816492i	$0.695916\pi$
$128$	−2.09601	+	6.45084i	−0.185262	+	0.570179i
$129$	−0.0543275	−	0.167203i	−0.00478327	−	0.0147214i
$130$	2.34516	−	1.70386i	0.205684	−	0.149438i
$131$	16.5059			1.44212			0.721062	−	0.692871i	$-0.243654\pi$
$131$	16.5059			1.44212			0.721062	+	0.692871i	$0.243654\pi$
$132$	1.13849	+	0.842544i	0.0990932	+	0.0733341i
$133$		0			0
$134$	0.301357	−	0.218949i	0.0260333	−	0.0189143i
$135$	−1.00579	−	3.09550i	−0.0865645	−	0.266418i
$136$	−0.396808	+	1.22125i	−0.0340260	+	0.104721i
$137$	−7.54479	−	5.48161i	−0.644595	−	0.468326i	0.216831	−	0.976209i	$-0.430428\pi$
$137$	−7.54479	−	5.48161i	−0.644595	−	0.468326i	−0.861426	+	0.507883i	$0.830428\pi$
$138$	−0.284044	−	0.206370i	−0.0241794	−	0.0175674i
$139$	−1.49147	+	4.59026i	−0.126505	+	0.389341i	−0.994172	−	0.107804i	$-0.965618\pi$
$139$	−1.49147	+	4.59026i	−0.126505	+	0.389341i	0.867668	+	0.497145i	$0.165618\pi$
$140$		0			0
$141$	1.19703	−	0.869693i	0.100808	−	0.0732414i
$142$	1.02265			0.0858189
$143$	−17.0302	−	0.149614i	−1.42413	−	0.0125114i
$144$	−10.9093			−0.909109
$145$	−13.1587	+	9.56035i	−1.09277	+	0.793944i
$146$	1.03792	+	3.19438i	0.0858987	+	0.264369i
$147$		0			0
$148$	−6.28183	−	4.56401i	−0.516363	−	0.375160i
$149$	−0.745845	−	0.541888i	−0.0611020	−	0.0443932i	0.556815	−	0.830637i	$-0.312023\pi$
$149$	−0.745845	−	0.541888i	−0.0611020	−	0.0443932i	−0.617917	+	0.786243i	$0.712023\pi$
$150$	0.0188048	−	0.0578751i	0.00153540	−	0.00472549i
$151$	5.59210	+	17.2107i	0.455079	+	1.40059i	0.871043	+	0.491207i	$0.163444\pi$
$151$	5.59210	+	17.2107i	0.455079	+	1.40059i	−0.415964	+	0.909381i	$0.636556\pi$
$152$	4.38551	−	3.18626i	0.355712	−	0.258440i
$153$	−4.24355			−0.343070
$154$		0			0
$155$	−19.1880			−1.54121
$156$	−1.77407	+	1.28894i	−0.142039	+	0.103198i
$157$	3.79267	+	11.6726i	0.302688	+	0.931577i	0.980530	+	0.196369i	$0.0629152\pi$
$157$	3.79267	+	11.6726i	0.302688	+	0.931577i	−0.677842	+	0.735207i	$0.737085\pi$
$158$	0.171466	−	0.527718i	0.0136411	−	0.0419830i
$159$	−1.16680	−	0.847727i	−0.0925329	−	0.0672291i
$160$	−5.29467	−	3.84680i	−0.418580	−	0.304116i
$161$		0			0
$162$	0.599080	+	1.84378i	0.0470682	+	0.144861i
$163$	−6.55233	+	4.76055i	−0.513218	+	0.372875i	−0.814043	−	0.580804i	$-0.802738\pi$
$163$	−6.55233	+	4.76055i	−0.513218	+	0.372875i	0.300825	+	0.953679i	$0.402738\pi$
$164$	13.1526			1.02705
$165$	−1.47660	+	1.05312i	−0.114953	+	0.0819852i
$166$	−0.508478			−0.0394655
$167$	−10.5590	+	7.67154i	−0.817077	+	0.593641i	−0.915874	−	0.401466i	$-0.868501\pi$
$167$	−10.5590	+	7.67154i	−0.817077	+	0.593641i	0.0987965	+	0.995108i	$0.468501\pi$
$168$		0			0
$169$	4.13096	−	12.7138i	0.317766	−	0.977985i
$170$	−0.656522	−	0.476991i	−0.0503529	−	0.0365835i
$171$	14.4928	+	10.5296i	1.10829	+	0.805219i
$172$	0.483161	−	1.48702i	0.0368407	−	0.113384i
$173$	−1.82697	−	5.62283i	−0.138902	−	0.427496i	0.857275	−	0.514859i	$-0.172156\pi$
$173$	−1.82697	−	5.62283i	−0.138902	−	0.427496i	−0.996176	+	0.0873636i	$0.972156\pi$
$174$	−0.261376	+	0.189901i	−0.0198149	+	0.0143964i
$175$		0			0
$176$	3.68503	+	11.6898i	0.277770	+	0.881153i
$177$	−0.630271			−0.0473741
$178$	0.317641	−	0.230780i	0.0238082	−	0.0172977i
$179$	1.33961	+	4.12290i	0.100127	+	0.308160i	0.988556	−	0.150854i	$-0.0482025\pi$
$179$	1.33961	+	4.12290i	0.100127	+	0.308160i	−0.888429	+	0.459015i	$0.848202\pi$
$180$	4.43641	−	13.6539i	0.330670	−	1.01770i
$181$	8.76223	+	6.36613i	0.651291	+	0.473191i	0.863711	−	0.503988i	$-0.168134\pi$
$181$	8.76223	+	6.36613i	0.651291	+	0.473191i	−0.212420	+	0.977179i	$0.568134\pi$
$182$		0			0
$183$	0.0579192	−	0.178257i	0.00428151	−	0.0131771i
$184$	−1.95514	−	6.01730i	−0.144135	−	0.443601i
$185$	8.04404	−	5.84433i	0.591409	−	0.429684i
$186$	−0.381138			−0.0279464
$187$	1.43342	+	4.54715i	0.104822	+	0.332520i
$188$	13.1589			0.959713
$189$		0			0
$190$	1.05862	+	3.25808i	0.0768000	+	0.236366i
$191$	3.60178	−	11.0851i	0.260616	−	0.802093i	−0.732055	−	0.681245i	$-0.761439\pi$
$191$	3.60178	−	11.0851i	0.260616	−	0.802093i	0.992671	−	0.120848i	$-0.0385613\pi$
$192$	1.20513	+	0.875581i	0.0869731	+	0.0631896i
$193$	−18.1587	−	13.1931i	−1.30709	−	0.949659i	−0.307096	−	0.951679i	$-0.599357\pi$
$193$	−18.1587	−	13.1931i	−1.30709	−	0.949659i	−0.999998	+	0.00201912i	$0.999357\pi$
$194$	0.844259	−	2.59836i	0.0606143	−	0.186552i
$195$	−0.867729	−	2.67060i	−0.0621394	−	0.191245i
$196$		0			0
$197$	24.1022			1.71721			0.858604	−	0.512639i	$-0.171332\pi$
$197$	24.1022			1.71721			0.858604	+	0.512639i	$0.171332\pi$
$198$	1.80314	−	1.28601i	0.128143	−	0.0913925i
$199$	−18.7205			−1.32706			−0.663531	−	0.748148i	$-0.730943\pi$
$199$	−18.7205			−1.32706			−0.663531	+	0.748148i	$0.730943\pi$
$200$	0.887178	−	0.644573i	0.0627330	−	0.0455782i
$201$	−0.111505	−	0.343176i	−0.00786493	−	0.0242058i
$202$	0.258179	−	0.794593i	0.0181654	−	0.0559074i
$203$		0			0
$204$	0.496647	+	0.360835i	0.0347722	+	0.0252635i
$205$	−5.20455	+	16.0180i	−0.363502	+	1.11874i
$206$	0.0804979	+	0.247747i	0.00560855	+	0.0172614i
$207$	16.9155	−	12.2898i	1.17571	−	0.854200i
$208$	−18.9768			−1.31580
$209$	6.38746	−	19.0864i	0.441830	−	1.32023i
$210$		0			0
$211$	6.12131	−	4.44739i	0.421408	−	0.306171i	−0.356796	−	0.934182i	$-0.616131\pi$
$211$	6.12131	−	4.44739i	0.421408	−	0.306171i	0.778204	+	0.628011i	$0.216131\pi$
$212$	−3.96362	−	12.1988i	−0.272223	−	0.837815i
$213$	0.306123	−	0.942149i	0.0209752	−	0.0645550i
$214$	−0.213596	−	0.155187i	−0.0146011	−	0.0106083i
$215$	1.61978	+	1.17684i	0.110468	+	0.0802596i
$216$	0.360021	−	1.10803i	0.0244963	−	0.0753919i
$217$		0			0
$218$	−1.70241	+	1.23687i	−0.115302	+	0.0837717i
$219$	3.25362			0.219859
$220$	−16.1293	−	0.141700i	−1.08744	−	0.00955340i
$221$	−7.38167			−0.496545
$222$	0.159782	−	0.116088i	0.0107239	−	0.00779134i
$223$	−5.41533	−	16.6667i	−0.362637	−	1.11608i	−0.951447	−	0.307811i	$-0.900403\pi$
$223$	−5.41533	−	16.6667i	−0.362637	−	1.11608i	0.588810	−	0.808271i	$-0.299597\pi$
$224$		0			0
$225$	2.93185	+	2.13011i	0.195457	+	0.142008i
$226$	−0.603440	−	0.438425i	−0.0401403	−	0.0291636i
$227$	7.93471	−	24.4205i	0.526645	−	1.62085i	−0.234394	−	0.972142i	$-0.575311\pi$
$227$	7.93471	−	24.4205i	0.526645	−	1.62085i	0.761039	−	0.648706i	$-0.224689\pi$
$228$	−0.800823	−	2.46468i	−0.0530358	−	0.163227i
$229$	−16.0484	+	11.6598i	−1.06051	+	0.770503i	−0.974182	−	0.225764i	$-0.927512\pi$
$229$	−16.0484	+	11.6598i	−1.06051	+	0.770503i	−0.0863246	+	0.996267i	$0.527512\pi$
$230$	3.99842			0.263648
$231$		0			0
$232$	−5.82205			−0.382236
$233$	16.3539	−	11.8818i	1.07138	−	0.778405i	0.0952219	−	0.995456i	$-0.469644\pi$
$233$	16.3539	−	11.8818i	1.07138	−	0.778405i	0.976160	+	0.217051i	$0.0696439\pi$
$234$	1.05962	+	3.26117i	0.0692695	+	0.213189i
$235$	−5.20704	+	16.0256i	−0.339670	+	1.04540i
$236$	−4.53480	−	3.29472i	−0.295190	−	0.214468i
$237$	−0.434850	−	0.315937i	−0.0282465	−	0.0205223i
$238$		0			0
$239$	5.28431	+	16.2634i	0.341814	+	1.05199i	0.963267	+	0.268544i	$0.0865424\pi$
$239$	5.28431	+	16.2634i	0.341814	+	1.05199i	−0.621454	+	0.783451i	$0.713458\pi$
$240$	−1.63495	+	1.18786i	−0.105535	+	0.0766760i
$241$	24.1529			1.55582			0.777912	−	0.628373i	$-0.216279\pi$
$241$	24.1529			1.55582			0.777912	+	0.628373i	$0.216279\pi$
$242$	−1.98709	−	1.49774i	−0.127735	−	0.0962786i
$243$	5.79074			0.371476
$244$	1.34856	−	0.979787i	0.0863328	−	0.0627245i
$245$		0			0
$246$	−0.103380	+	0.318171i	−0.00659128	+	0.0202859i
$247$	25.2102	+	18.3163i	1.60409	+	1.16544i
$248$	−5.55658	−	4.03709i	−0.352843	−	0.256356i
$249$	−0.152209	+	0.468452i	−0.00964586	+	0.0296869i
$250$	−0.658069	−	2.02533i	−0.0416200	−	0.128093i
$251$	9.62305	−	6.99156i	0.607402	−	0.441303i	−0.241097	−	0.970501i	$-0.577507\pi$
$251$	9.62305	−	6.99156i	0.607402	−	0.441303i	0.848498	+	0.529198i	$0.177507\pi$
$252$		0			0
$253$	−18.8829	−	13.9743i	−1.18716	−	0.878558i
$254$	−0.0654215			−0.00410491
$255$	−0.635968	+	0.462058i	−0.0398259	+	0.0289352i
$256$	3.72721	+	11.4712i	0.232951	+	0.716949i
$257$	−7.09531	+	21.8371i	−0.442593	+	1.36216i	0.442509	+	0.896764i	$0.354089\pi$
$257$	−7.09531	+	21.8371i	−0.442593	+	1.36216i	−0.885102	+	0.465397i	$0.845911\pi$
$258$	0.0321743	+	0.0233760i	0.00200308	+	0.00145533i
$259$		0			0
$260$	7.71715	−	23.7509i	0.478597	−	1.47297i
$261$	−5.94552	−	18.2984i	−0.368018	−	1.13264i
$262$	−3.02072	+	2.19468i	−0.186621	+	0.135588i
$263$	1.93774			0.119486			0.0597432	−	0.998214i	$-0.480972\pi$
$263$	1.93774			0.119486			0.0597432	+	0.998214i	$0.480972\pi$
$264$	−0.649177	−	0.00570319i	−0.0399541	−	0.000351007i
$265$	16.4247			1.00896
$266$		0			0
$267$	−0.117530	−	0.361720i	−0.00719271	−	0.0221369i
$268$	0.991666	−	3.05203i	0.0605756	−	0.186433i
$269$	5.81421	+	4.22427i	0.354499	+	0.257558i	0.750754	−	0.660582i	$-0.229690\pi$
$269$	5.81421	+	4.22427i	0.354499	+	0.257558i	−0.396255	+	0.918140i	$0.629690\pi$
$270$	0.595657	+	0.432770i	0.0362505	+	0.0263376i
$271$	−0.368071	+	1.13281i	−0.0223587	+	0.0688130i	−0.961613	−	0.274408i	$-0.911518\pi$
$271$	−0.368071	+	1.13281i	−0.0223587	+	0.0688130i	0.939255	+	0.343221i	$0.111518\pi$
$272$	1.64165	+	5.05249i	0.0995398	+	0.306352i
$273$		0			0
$274$	2.10962			0.127447
$275$	1.29217	−	3.86113i	0.0779207	−	0.232835i
$276$	−3.02473			−0.182067
$277$	−8.36543	+	6.07784i	−0.502630	+	0.365182i	−0.810021	−	0.586401i	$-0.800544\pi$
$277$	−8.36543	+	6.07784i	−0.502630	+	0.365182i	0.307391	+	0.951583i	$0.400544\pi$
$278$	−0.337387	−	1.03837i	−0.0202351	−	0.0622773i
$279$	7.01396	−	21.5867i	0.419915	−	1.29236i
$280$		0			0
$281$	10.6396	+	7.73015i	0.634707	+	0.461142i	0.858028	−	0.513603i	$-0.171690\pi$
$281$	10.6396	+	7.73015i	0.634707	+	0.461142i	−0.223321	+	0.974745i	$0.571690\pi$
$282$	−0.103429	+	0.318323i	−0.00615913	+	0.0189559i
$283$	−0.0927146	−	0.285346i	−0.00551131	−	0.0169621i	0.948263	−	0.317486i	$-0.102839\pi$
$283$	−0.0927146	−	0.285346i	−0.00551131	−	0.0169621i	−0.953774	+	0.300524i	$0.902839\pi$
$284$	7.12761	−	5.17851i	0.422946	−	0.307288i
$285$	3.31850			0.196571
$286$	3.13656	−	2.23701i	0.185469	−	0.132277i
$287$		0			0
$288$	6.26312	−	4.55042i	0.369058	−	0.268136i
$289$	−4.61471	−	14.2026i	−0.271454	−	0.835448i
$290$	1.13698	−	3.49926i	0.0667656	−	0.205483i
$291$	−2.14110	−	1.55560i	−0.125514	−	0.0911910i
$292$	23.4098	+	17.0082i	1.36995	+	0.995330i
$293$	−4.98880	+	15.3539i	−0.291449	+	0.896987i	0.692942	+	0.720993i	$0.256314\pi$
$293$	−4.98880	+	15.3539i	−0.291449	+	0.896987i	−0.984391	+	0.175994i	$0.943686\pi$
$294$		0			0
$295$	5.80692	−	4.21898i	0.338092	−	0.245638i
$296$	3.55908			0.206867
$297$	−1.30053	−	4.12559i	−0.0754644	−	0.239391i
$298$	0.208548			0.0120808
$299$	29.4245	−	21.3782i	1.70166	−	1.23633i
$300$	−0.162005	−	0.498599i	−0.00935334	−	0.0287866i
$301$		0			0
$302$	−3.31180	−	2.40617i	−0.190573	−	0.138459i
$303$	−0.654761	−	0.475711i	−0.0376150	−	0.0273289i
$304$	6.93020	−	21.3290i	0.397474	−	1.22330i
$305$	0.659605	+	2.03005i	0.0377688	+	0.116241i
$306$	0.776607	−	0.564238i	0.0443956	−	0.0322553i
$307$	28.6376			1.63443			0.817217	−	0.576330i	$-0.195516\pi$
$307$	28.6376			1.63443			0.817217	+	0.576330i	$0.195516\pi$
$308$		0			0
$309$	0.252341			0.0143552
$310$	3.51157	−	2.55130i	0.199444	−	0.144904i
$311$	9.83377	+	30.2652i	0.557622	+	1.71618i	0.688916	+	0.724841i	$0.258087\pi$
$311$	9.83377	+	30.2652i	0.557622	+	1.71618i	−0.131294	+	0.991343i	$0.541913\pi$
$312$	0.310603	−	0.955937i	0.0175844	−	0.0541193i
$313$	0.0276872	+	0.0201159i	0.00156497	+	0.00113702i	0.588567	−	0.808448i	$-0.299692\pi$
$313$	0.0276872	+	0.0201159i	0.00156497	+	0.00113702i	−0.587002	+	0.809585i	$0.699692\pi$
$314$	−2.24613	−	1.63191i	−0.126756	−	0.0920938i
$315$		0			0
$316$	−1.47719	−	4.54633i	−0.0830985	−	0.255751i
$317$	−18.1134	+	13.1602i	−1.01735	+	0.739149i	−0.965738	−	0.259518i	$-0.916436\pi$
$317$	−18.1134	+	13.1602i	−1.01735	+	0.739149i	−0.0516132	+	0.998667i	$0.516436\pi$
$318$	0.326251			0.0182952
$319$	−17.5992	+	12.5519i	−0.985368	+	0.702770i
$320$	−16.9644			−0.948339
$321$	−0.206909	+	0.150328i	−0.0115486	+	0.00839052i
$322$		0			0
$323$	2.69574	−	8.29662i	0.149995	−	0.461636i
$324$	13.5120	+	9.81704i	0.750666	+	0.545391i
$325$	5.09997	+	3.70534i	0.282895	+	0.205535i
$326$	0.566155	−	1.74244i	0.0313564	−	0.0965051i
$327$	0.629906	+	1.93865i	0.0348339	+	0.107208i
$328$	−4.87730	+	3.54357i	−0.269304	+	0.195661i
$329$		0			0
$330$	0.130204	−	0.389064i	0.00716751	−	0.0214173i
$331$	10.7577			0.591297			0.295648	−	0.955297i	$-0.404464\pi$
$331$	10.7577			0.591297			0.295648	+	0.955297i	$0.404464\pi$
$332$	−3.54396	+	2.57484i	−0.194500	+	0.141313i
$333$	3.63455	+	11.1860i	0.199172	+	0.612989i
$334$	0.912348	−	2.80792i	0.0499215	−	0.153642i
$335$	3.32452	+	2.41540i	0.181638	+	0.131968i
$336$		0			0
$337$	2.31915	−	7.13761i	0.126332	−	0.388810i	−0.867809	−	0.496897i	$-0.834473\pi$
$337$	2.31915	−	7.13761i	0.126332	−	0.388810i	0.994141	+	0.108087i	$0.0344726\pi$
$338$	0.934471	+	2.87601i	0.0508285	+	0.156434i
$339$	−0.584549	+	0.424700i	−0.0317483	+	0.0230665i
$340$	−6.99118			−0.379150
$341$	−25.5004	−	0.224027i	−1.38092	−	0.0121318i
$342$	−4.05236			−0.219126
$343$		0			0
$344$	0.221463	+	0.681593i	0.0119405	+	0.0367490i
$345$	1.19690	−	3.68368i	0.0644389	−	0.198322i
$346$	1.08198	+	0.786107i	0.0581678	+	0.0422614i
$347$	22.3950	+	16.2710i	1.20223	+	0.873471i	0.994502	−	0.104716i	$-0.0333934\pi$
$347$	22.3950	+	16.2710i	1.20223	+	0.873471i	0.207727	+	0.978187i	$0.433393\pi$
$348$	−0.860103	+	2.64712i	−0.0461063	+	0.141901i
$349$	3.41788	+	10.5192i	0.182955	+	0.563078i	0.999907	−	0.0136278i	$-0.00433799\pi$
$349$	3.41788	+	10.5192i	0.182955	+	0.563078i	−0.816952	+	0.576706i	$0.804338\pi$
$350$		0			0
$351$	6.69733			0.357477
$352$	−6.99159	−	5.17413i	−0.372653	−	0.275782i
$353$	−31.9202			−1.69894			−0.849469	−	0.527638i	$-0.823078\pi$
$353$	−31.9202			−1.69894			−0.849469	+	0.527638i	$0.823078\pi$
$354$	0.115345	−	0.0838032i	0.00613053	−	0.00445409i
$355$	3.48623	+	10.7295i	0.185030	+	0.569464i
$356$	1.04525	−	3.21695i	0.0553982	−	0.170498i
$357$		0			0
$358$	−0.793358	−	0.576408i	−0.0419303	−	0.0304641i
$359$	1.10574	−	3.40313i	0.0583590	−	0.179610i	−0.917628	−	0.397441i	$-0.869898\pi$
$359$	1.10574	−	3.40313i	0.0583590	−	0.179610i	0.975986	+	0.217831i	$0.0698982\pi$
$360$	2.03348	+	6.25842i	0.107174	+	0.329847i
$361$	−14.4219	+	10.4781i	−0.759046	+	0.551479i
$362$	−2.45003			−0.128771
$363$	−1.97467	+	1.38233i	−0.103643	+	0.0725536i
$364$		0			0
$365$	−29.9768	+	21.7794i	−1.56906	+	1.13999i
$366$	0.0131020	+	0.0403238i	0.000684852	+	0.00210776i
$367$	−0.708875	+	2.18169i	−0.0370030	+	0.113883i	−0.967852	−	0.251521i	$-0.919069\pi$
$367$	−0.708875	+	2.18169i	−0.0370030	+	0.113883i	0.930849	+	0.365404i	$0.119069\pi$
$368$	−21.1765	−	15.3856i	−1.10390	−	0.802031i
$369$	−16.1180	−	11.7104i	−0.839069	−	0.609619i
$370$	−0.695045	+	2.13913i	−0.0361337	+	0.111208i
$371$		0			0
$372$	−2.65644	+	1.93001i	−0.137730	+	0.100067i
$373$	7.96856			0.412596			0.206298	−	0.978489i	$-0.433858\pi$
$373$	7.96856			0.412596			0.206298	+	0.978489i	$0.433858\pi$
$374$	−0.866934	−	0.641576i	−0.0448281	−	0.0331751i
$375$	−2.06289			−0.106527
$376$	−4.87963	+	3.54526i	−0.251648	+	0.182833i
$377$	−10.3423	−	31.8302i	−0.532653	−	1.63934i
$378$		0			0
$379$	9.40174	+	6.83077i	0.482935	+	0.350873i	0.802461	−	0.596705i	$-0.203524\pi$
$379$	9.40174	+	6.83077i	0.482935	+	0.350873i	−0.319526	+	0.947578i	$0.603524\pi$
$380$	23.8766	+	17.3474i	1.22484	+	0.889902i
$381$	−0.0195835	+	0.0602717i	−0.00100329	+	0.00308781i
$382$	0.814764	+	2.50759i	0.0416869	+	0.128299i
$383$	10.1762	−	7.39343i	0.519979	−	0.377787i	−0.296617	−	0.954996i	$-0.595859\pi$
$383$	10.1762	−	7.39343i	0.519979	−	0.377787i	0.816596	+	0.577210i	$0.195859\pi$
$384$	−1.48632			−0.0758482
$385$		0			0
$386$	5.07741			0.258433
$387$	−1.91605	+	1.39209i	−0.0973984	+	0.0707641i
$388$	−7.27336	−	22.3851i	−0.369249	−	1.13643i
$389$	−0.135440	+	0.416842i	−0.00686709	+	0.0211347i	−0.954431	−	0.298431i	$-0.903537\pi$
$389$	−0.135440	+	0.416842i	−0.00686709	+	0.0211347i	0.947564	+	0.319565i	$0.103537\pi$
$390$	0.513894	+	0.373366i	0.0260221	+	0.0189061i
$391$	−8.23731	−	5.98476i	−0.416579	−	0.302662i
$392$		0			0
$393$	1.11769	+	3.43990i	0.0563800	+	0.173520i
$394$	−4.41091	+	3.20471i	−0.222218	+	0.161451i
$395$	6.12128			0.307995
$396$	6.05530	−	18.0939i	0.304290	−	0.909252i
$397$	−16.8147			−0.843905			−0.421952	−	0.906618i	$-0.638655\pi$
$397$	−16.8147			−0.843905			−0.421952	+	0.906618i	$0.638655\pi$
$398$	3.42602	−	2.48915i	0.171731	−	0.124770i
$399$		0			0
$400$	1.40196	−	4.31480i	0.0700981	−	0.215740i
$401$	−29.8211	−	21.6663i	−1.48919	−	1.08196i	−0.974446	−	0.224621i	$-0.927886\pi$
$401$	−29.8211	−	21.6663i	−1.48919	−	1.08196i	−0.514747	−	0.857342i	$-0.672114\pi$
$402$	0.0660362	+	0.0479781i	0.00329359	+	0.00239293i
$403$	12.2008	−	37.5502i	0.607766	−	1.87051i
$404$	−2.22423	−	6.84548i	−0.110660	−	0.340575i
$405$	−17.3024	+	12.5710i	−0.859766	+	0.624656i
$406$		0			0
$407$	10.7586	−	7.67308i	0.533283	−	0.380340i
$408$	−0.281384			−0.0139306
$409$	13.1659	−	9.56556i	0.651010	−	0.472986i	−0.212605	−	0.977138i	$-0.568195\pi$
$409$	13.1659	−	9.56556i	0.651010	−	0.472986i	0.863615	+	0.504152i	$0.168195\pi$
$410$	−1.17733	−	3.62345i	−0.0581441	−	0.178949i
$411$	0.631499	−	1.94356i	0.0311496	−	0.0958685i
$412$	1.81559	+	1.31911i	0.0894479	+	0.0649877i
$413$		0			0
$414$	−1.46158	+	4.49828i	−0.0718328	+	0.221079i
$415$	−1.73341	−	5.33489i	−0.0850898	−	0.261879i
$416$	10.8947	−	7.91548i	0.534158	−	0.388088i
$417$	−1.05763			−0.0517922
$418$	1.36884	+	4.34228i	0.0669520	+	0.212388i
$419$	−5.56352			−0.271796			−0.135898	−	0.990723i	$-0.543392\pi$
$419$	−5.56352			−0.271796			−0.135898	+	0.990723i	$0.543392\pi$
$420$		0			0
$421$	6.64120	+	20.4395i	0.323672	+	0.996161i	0.972036	+	0.234831i	$0.0754536\pi$
$421$	6.64120	+	20.4395i	0.323672	+	0.996161i	−0.648364	+	0.761331i	$0.724546\pi$
$422$	−0.528912	+	1.62782i	−0.0257470	+	0.0792412i
$423$	−16.1257	−	11.7160i	−0.784057	−	0.569651i
$424$	4.75638	+	3.45571i	0.230990	+	0.167824i
$425$	0.545341	−	1.67839i	0.0264529	−	0.0814137i
$426$	0.0692485	+	0.213125i	0.00335510	+	0.0103259i
$427$		0			0
$428$	−2.27455			−0.109944
$429$	−1.12201	−	3.55930i	−0.0541713	−	0.171844i
$430$	−0.452910			−0.0218413
$431$	22.4249	−	16.2927i	1.08017	−	0.784791i	0.102459	−	0.994737i	$-0.467329\pi$
$431$	22.4249	−	16.2927i	1.08017	−	0.784791i	0.977713	+	0.209947i	$0.0673290\pi$
$432$	−1.48946	−	4.58408i	−0.0716616	−	0.220552i
$433$	−2.87019	+	8.83352i	−0.137932	+	0.424512i	−0.996035	−	0.0889667i	$-0.971644\pi$
$433$	−2.87019	+	8.83352i	−0.137932	+	0.424512i	0.858102	+	0.513479i	$0.171644\pi$
$434$		0			0
$435$	−2.88346	−	2.09496i	−0.138251	−	0.100445i
$436$	−5.60207	+	17.2414i	−0.268290	+	0.825713i
$437$	13.2823	+	40.8788i	0.635380	+	1.95550i
$438$	−0.595442	+	0.432614i	−0.0284513	+	0.0206711i
$439$	14.7118			0.702156			0.351078	−	0.936346i	$-0.385815\pi$
$439$	14.7118			0.702156			0.351078	+	0.936346i	$0.385815\pi$
$440$	6.01928	−	4.29298i	0.286958	−	0.204660i
$441$		0			0
$442$	1.35091	−	0.981494i	0.0642563	−	0.0466849i
$443$	0.755067	+	2.32386i	0.0358743	+	0.110410i	0.967390	−	0.253291i	$-0.0815130\pi$
$443$	0.755067	+	2.32386i	0.0358743	+	0.110410i	−0.931516	+	0.363701i	$0.881513\pi$
$444$	0.525789	−	1.61821i	0.0249528	−	0.0767970i
$445$	3.50416	+	2.54592i	0.166113	+	0.120688i
$446$	3.20712	+	2.33011i	0.151861	+	0.110334i
$447$	0.0624272	−	0.192131i	0.00295271	−	0.00908750i
$448$		0			0
$449$	−3.85849	+	2.80335i	−0.182093	+	0.132298i	−0.675098	−	0.737728i	$-0.735899\pi$
$449$	−3.85849	+	2.80335i	−0.182093	+	0.132298i	0.493005	+	0.870027i	$0.335899\pi$
$450$	−0.819782			−0.0386449
$451$	−7.10376	+	21.2268i	−0.334503	+	0.999530i
$452$	−6.42593			−0.302250
$453$	−3.20812	+	2.33084i	−0.150731	+	0.109512i
$454$	1.79492	+	5.52420i	0.0842398	+	0.259264i
$455$		0			0
$456$	0.960995	+	0.698203i	0.0450027	+	0.0326964i
$457$	−25.1503	−	18.2728i	−1.17648	−	0.854764i	−0.184712	−	0.982793i	$-0.559135\pi$
$457$	−25.1503	−	18.2728i	−1.17648	−	0.854764i	−0.991770	+	0.128028i	$0.959135\pi$
$458$	1.38666	−	4.26770i	0.0647944	−	0.199417i
$459$	−0.579376	−	1.78313i	−0.0270429	−	0.0832296i
$460$	27.8680	−	20.2473i	1.29935	−	0.944034i
$461$	−29.7215			−1.38427			−0.692134	−	0.721769i	$-0.743329\pi$
$461$	−29.7215			−1.38427			−0.692134	+	0.721769i	$0.743329\pi$
$462$		0			0
$463$	−25.4553			−1.18301			−0.591505	−	0.806302i	$-0.701466\pi$
$463$	−25.4553			−1.18301			−0.591505	+	0.806302i	$0.701466\pi$
$464$	−19.4865	+	14.1578i	−0.904640	+	0.657259i
$465$	−1.29931	−	3.99886i	−0.0602540	−	0.185443i
$466$	−1.41306	+	4.34896i	−0.0654589	+	0.201462i
$467$	−2.57665	−	1.87204i	−0.119233	−	0.0866279i	0.526571	−	0.850131i	$-0.323478\pi$
$467$	−2.57665	−	1.87204i	−0.119233	−	0.0866279i	−0.645804	+	0.763503i	$0.723478\pi$
$468$	23.8992	+	17.3638i	1.10474	+	0.802643i
$469$		0			0
$470$	−1.17789	−	3.62517i	−0.0543320	−	0.167217i
$471$	−2.17581	+	1.58082i	−0.100256	+	0.0728402i
$472$	2.56927			0.118260
$473$	2.13891	+	1.58290i	0.0983472	+	0.0727820i
$474$	0.121590			0.00558479
$475$	−6.02709	+	4.37894i	−0.276542	+	0.200920i
$476$		0			0
$477$	−6.00389	+	18.4781i	−0.274899	+	0.846052i
$478$	−3.12952	−	2.27373i	−0.143141	−	0.103998i
$479$	2.61599	+	1.90062i	0.119527	+	0.0868418i	0.645943	−	0.763386i	$-0.276464\pi$
$479$	2.61599	+	1.90062i	0.119527	+	0.0868418i	−0.526416	+	0.850227i	$0.676464\pi$
$480$	0.443164	−	1.36392i	0.0202276	−	0.0622541i
$481$	6.32232	+	19.4581i	0.288273	+	0.887213i
$482$	−4.42019	+	3.21146i	−0.201334	+	0.146278i
$483$		0			0
$484$	−21.4338	−	0.376632i	−0.974264	−	0.0171196i
$485$	30.1398			1.36858
$486$	−1.05976	+	0.769958i	−0.0480715	+	0.0349260i
$487$	3.05029	+	9.38784i	0.138222	+	0.425404i	0.996077	−	0.0884878i	$-0.0282034\pi$
$487$	3.05029	+	9.38784i	0.138222	+	0.425404i	−0.857855	+	0.513891i	$0.828203\pi$
$488$	−0.236105	+	0.726655i	−0.0106880	+	0.0328941i
$489$	−1.43581	−	1.04318i	−0.0649296	−	0.0471741i
$490$		0			0
$491$	1.30591	−	4.01917i	0.0589348	−	0.181383i	−0.917255	−	0.398300i	$-0.869600\pi$
$491$	1.30591	−	4.01917i	0.0589348	−	0.181383i	0.976190	+	0.216918i	$0.0696003\pi$
$492$	0.890628	+	2.74107i	0.0401526	+	0.123577i
$493$	−7.57995	+	5.50716i	−0.341384	+	0.248030i
$494$	−7.04910			−0.317154
$495$	19.6396	+	14.5343i	0.882733	+	0.653267i
$496$	−28.4152			−1.27588
$497$		0			0
$498$	−0.0344314	−	0.105969i	−0.00154291	−	0.00474859i
$499$	−6.30249	+	19.3971i	−0.282138	+	0.868332i	0.705104	+	0.709104i	$0.250900\pi$
$499$	−6.30249	+	19.3971i	−0.282138	+	0.868332i	−0.987242	+	0.159228i	$0.949100\pi$
$500$	−14.8425	−	10.7837i	−0.663776	−	0.482261i
$501$	−2.31378	−	1.68106i	−0.103372	−	0.0751042i
$502$	−0.831480	+	2.55903i	−0.0371108	+	0.114215i
$503$	7.40382	+	22.7866i	0.330120	+	1.01600i	0.969076	+	0.246762i	$0.0793665\pi$
$503$	7.40382	+	22.7866i	0.330120	+	1.01600i	−0.638956	+	0.769243i	$0.720634\pi$
$504$		0			0
$505$	9.21692			0.410147
$506$	5.31381	+	0.0466832i	0.236228	+	0.00207532i
$507$	2.92934			0.130097
$508$	−0.455971	+	0.331282i	−0.0202304	+	0.0146983i
$509$	−1.14133	−	3.51264i	−0.0505884	−	0.155695i	0.922571	−	0.385828i	$-0.126084\pi$
$509$	−1.14133	−	3.51264i	−0.0505884	−	0.155695i	−0.973159	+	0.230132i	$0.926084\pi$
$510$	0.0549509	−	0.169121i	0.00243327	−	0.00748882i
$511$		0			0
$512$	−13.1822	−	9.57742i	−0.582576	−	0.423266i
$513$	−2.44582	+	7.52746i	−0.107986	+	0.332346i
$514$	−1.60504	−	4.93980i	−0.0707952	−	0.217885i
$515$	−2.32491	+	1.68915i	−0.102448	+	0.0744328i
$516$	0.342618			0.0150829
$517$	−7.10714	+	21.2369i	−0.312572	+	0.933997i
$518$		0			0
$519$	1.04811	−	0.761497i	0.0460069	−	0.0334260i
$520$	3.53725	+	10.8865i	0.155119	+	0.477406i
$521$	0.0736294	−	0.226608i	0.00322576	−	0.00992787i	−0.949431	−	0.313977i	$-0.898339\pi$
$521$	0.0736294	−	0.226608i	0.00322576	−	0.00992787i	0.952656	+	0.304049i	$0.0983386\pi$
$522$	3.52111	+	2.55823i	0.154115	+	0.111971i
$523$	−17.7914	−	12.9262i	−0.777966	−	0.565225i	0.126402	−	0.991979i	$-0.459657\pi$
$523$	−17.7914	−	12.9262i	−0.777966	−	0.565225i	−0.904368	+	0.426754i	$0.859657\pi$
$524$	−9.94018	+	30.5927i	−0.434239	+	1.33645i
$525$		0			0
$526$	−0.354624	+	0.257649i	−0.0154623	+	0.0112340i
$527$	−11.0531			−0.481479
$528$	−2.18668	+	1.55955i	−0.0951630	+	0.0678707i
$529$	27.1678			1.18121
$530$	−3.00587	+	2.18389i	−0.130567	+	0.0948622i
$531$	2.62375	+	8.07508i	0.113861	+	0.350429i
$532$		0			0
$533$	−28.0373	−	20.3703i	−1.21443	−	0.882336i
$534$	0.0696046	+	0.0505707i	0.00301208	+	0.00218841i
$535$	0.900048	−	2.77006i	0.0389125	−	0.119760i
$536$	0.454542	+	1.39894i	0.0196332	+	0.0604249i
$537$	−0.768521	+	0.558363i	−0.0331641	+	0.0240951i
$538$	−1.62573			−0.0700900
$539$		0			0
$540$	6.34305			0.272961
$541$	−23.1629	+	16.8288i	−0.995851	+	0.723528i	−0.961195	−	0.275871i	$-0.911034\pi$
$541$	−23.1629	+	16.8288i	−0.995851	+	0.723528i	−0.0346561	+	0.999399i	$0.511034\pi$
$542$	−0.0832618	−	0.256253i	−0.00357640	−	0.0110070i
$543$	−0.733399	+	2.25717i	−0.0314731	+	0.0968644i
$544$	−3.04995	−	2.21592i	−0.130765	−	0.0950066i
$545$	−18.7807	−	13.6450i	−0.804477	−	0.584486i
$546$		0			0
$547$	1.98033	+	6.09482i	0.0846727	+	0.260596i	0.984425	−	0.175805i	$-0.0562529\pi$
$547$	1.98033	+	6.09482i	0.0846727	+	0.260596i	−0.899752	+	0.436401i	$0.856253\pi$
$548$	14.7035	−	10.6827i	0.628103	−	0.456343i
$549$	−2.52495			−0.107762
$550$	0.276913	+	0.878433i	0.0118076	+	0.0374565i
$551$	39.5524			1.68499
$552$	1.12164	−	0.814919i	0.0477402	−	0.0346853i
$553$		0			0
$554$	0.722815	−	2.22460i	0.0307095	−	0.0945141i
$555$	1.76269	+	1.28067i	0.0748218	+	0.0543612i
$556$	−7.60961	−	5.52871i	−0.322719	−	0.234469i
$557$	−6.95884	+	21.4171i	−0.294855	+	0.907471i	0.688415	+	0.725317i	$0.258307\pi$
$557$	−6.95884	+	21.4171i	−0.294855	+	0.907471i	−0.983270	+	0.182154i	$0.941693\pi$
$558$	1.58664	+	4.88317i	0.0671677	+	0.206721i
$559$	−3.33298	+	2.42155i	−0.140970	+	0.102421i
$560$		0			0
$561$	−0.850583	+	0.606640i	−0.0359116	+	0.0256124i
$562$	−2.97498			−0.125492
$563$	−24.1303	+	17.5317i	−1.01697	+	0.738873i	−0.965660	−	0.259810i	$-0.916340\pi$
$563$	−24.1303	+	17.5317i	−1.01697	+	0.738873i	−0.0513116	+	0.998683i	$0.516340\pi$
$564$	0.891053	+	2.74238i	0.0375201	+	0.115475i
$565$	2.54277	−	7.82583i	0.106975	−	0.329235i
$566$	0.0549082	+	0.0398932i	0.00230797	+	0.00167684i
$567$		0			0
$568$	−1.24789	+	3.84062i	−0.0523604	+	0.161149i
$569$	9.04690	+	27.8435i	0.379266	+	1.16726i	0.940555	+	0.339640i	$0.110305\pi$
$569$	9.04690	+	27.8435i	0.379266	+	1.16726i	−0.561290	+	0.827619i	$0.689695\pi$
$570$	−0.607316	+	0.441241i	−0.0254376	+	0.0184815i
$571$	37.9252			1.58712			0.793559	−	0.608493i	$-0.208226\pi$
$571$	37.9252			1.58712			0.793559	+	0.608493i	$0.208226\pi$
$572$	10.5332	−	31.4744i	0.440416	−	1.31601i
$573$	2.55409			0.106699
$574$		0			0
$575$	2.68699	+	8.26969i	0.112055	+	0.344870i
$576$	6.20116	−	19.0852i	0.258382	−	0.795217i
$577$	7.09721	+	5.15642i	0.295461	+	0.214665i	0.725633	−	0.688082i	$-0.241547\pi$
$577$	7.09721	+	5.15642i	0.295461	+	0.214665i	−0.430172	+	0.902747i	$0.641547\pi$
$578$	2.73297	+	1.98562i	0.113676	+	0.0825908i
$579$	1.51989	−	4.67773i	0.0631643	−	0.194400i
$580$	−9.79515	−	30.1464i	−0.406721	−	1.25176i
$581$		0			0
$582$	0.598679			0.0248161
$583$	21.8281	+	0.191765i	0.904027	+	0.00794211i
$584$	−13.2632			−0.548836
$585$	−30.6036	+	22.2348i	−1.26530	+	0.919296i
$586$	−1.12852	−	3.47324i	−0.0466189	−	0.143478i
$587$	−2.83372	+	8.72130i	−0.116960	+	0.359966i	−0.992351	−	0.123450i	$-0.960604\pi$
$587$	−2.83372	+	8.72130i	−0.116960	+	0.359966i	0.875391	+	0.483416i	$0.160604\pi$
$588$		0			0
$589$	37.7489	+	27.4262i	1.55542	+	1.13008i
$590$	−0.501747	+	1.54422i	−0.0206566	+	0.0635745i
$591$	1.63207	+	5.02300i	0.0671345	+	0.206619i
$592$	11.9123	−	8.65480i	0.489593	−	0.355710i
$593$	−7.25596			−0.297967			−0.148983	−	0.988840i	$-0.547600\pi$
$593$	−7.25596			−0.297967			−0.148983	+	0.988840i	$0.547600\pi$
$594$	0.786562	+	0.582097i	0.0322730	+	0.0238837i
$595$		0			0
$596$	1.45352	−	1.05605i	0.0595386	−	0.0432573i
$597$	−1.26766	−	3.90144i	−0.0518817	−	0.159675i
$598$	−2.54243	+	7.82479i	−0.103968	+	0.319979i
$599$	16.1949	+	11.7663i	0.661708	+	0.480759i	0.867239	−	0.497892i	$-0.165892\pi$
$599$	16.1949	+	11.7663i	0.661708	+	0.480759i	−0.205532	+	0.978650i	$0.565892\pi$
$600$	0.194407	+	0.141245i	0.00793663	+	0.00576630i
$601$	3.48280	−	10.7189i	0.142066	−	0.437235i	−0.854556	−	0.519360i	$-0.826171\pi$
$601$	3.48280	−	10.7189i	0.142066	−	0.437235i	0.996622	+	0.0821246i	$0.0261705\pi$
$602$		0			0
$603$	−3.93261	+	2.85721i	−0.160148	+	0.116354i
$604$	−35.2668			−1.43499
$605$	8.94012	−	25.9542i	0.363468	−	1.05519i
$606$	0.183079			0.00743709
$607$	−10.9428	+	7.95040i	−0.444154	+	0.322697i	−0.787283	−	0.616591i	$-0.788513\pi$
$607$	−10.9428	+	7.95040i	−0.444154	+	0.322697i	0.343129	+	0.939288i	$0.388513\pi$
$608$	4.91792	+	15.1358i	0.199448	+	0.613838i
$609$		0			0
$610$	−0.390637	−	0.283814i	−0.0158164	−	0.0114913i
$611$	−28.0507	−	20.3800i	−1.13481	−	0.824487i
$612$	2.55555	−	7.86519i	0.103302	−	0.317931i
$613$	−9.51673	−	29.2895i	−0.384377	−	1.18299i	−0.936931	−	0.349514i	$-0.886347\pi$
$613$	−9.51673	−	29.2895i	−0.384377	−	1.18299i	0.552554	−	0.833477i	$-0.313653\pi$
$614$	−5.24093	+	3.80776i	−0.211507	+	0.153669i
$615$	−3.69064			−0.148821
$616$		0			0
$617$	23.6896			0.953707			0.476853	−	0.878983i	$-0.341777\pi$
$617$	23.6896			0.953707			0.476853	+	0.878983i	$0.341777\pi$
$618$	−0.0461807	+	0.0335522i	−0.00185766	+	0.00134967i
$619$	10.0393	+	30.8977i	0.403513	+	1.24188i	0.922131	+	0.386878i	$0.126447\pi$
$619$	10.0393	+	30.8977i	0.403513	+	1.24188i	−0.518618	+	0.855006i	$0.673553\pi$
$620$	11.5554	−	35.5639i	0.464076	−	1.42828i
$621$	7.47365	+	5.42992i	0.299907	+	0.217895i
$622$	−5.82385	−	4.23127i	−0.233515	−	0.169659i
$623$		0			0
$624$	−1.28501	−	3.95485i	−0.0514415	−	0.158321i
$625$	23.9721	−	17.4167i	0.958882	−	0.696669i
$626$	−0.00774169			−0.000309420
$627$	4.41022	+	0.0387449i	0.176127	+	0.00154732i
$628$	−23.9186			−0.954456
$629$	4.63370	−	3.36658i	0.184758	−	0.134234i
$630$		0			0
$631$	−4.67646	+	14.3927i	−0.186167	+	0.572962i	−0.999967	−	0.00818299i	$-0.997395\pi$
$631$	−4.67646	+	14.3927i	−0.186167	+	0.572962i	0.813800	+	0.581145i	$0.197395\pi$
$632$	1.77264	+	1.28790i	0.0705119	+	0.0512299i
$633$	1.34136	+	0.974555i	0.0533143	+	0.0387351i
$634$	1.56509	−	4.81686i	0.0621577	−	0.191302i
$635$	−0.223023	−	0.686395i	−0.00885041	−	0.0272387i
$636$	2.27388	−	1.65207i	0.0901654	−	0.0655090i
$637$		0			0
$638$	1.55187	−	4.63716i	0.0614393	−	0.183587i
$639$	−13.3452			−0.527929
$640$	13.6940	−	9.94925i	0.541302	−	0.393279i
$641$	−5.11431	−	15.7402i	−0.202003	−	0.621701i	−0.999823	−	0.0188056i	$-0.994014\pi$
$641$	−5.11431	−	15.7402i	−0.202003	−	0.621701i	0.797820	−	0.602895i	$-0.205986\pi$
$642$	0.0178780	−	0.0550229i	0.000705589	−	0.00217158i
$643$	1.61403	+	1.17266i	0.0636513	+	0.0462454i	0.619156	−	0.785268i	$-0.287475\pi$
$643$	1.61403	+	1.17266i	0.0636513	+	0.0462454i	−0.555505	+	0.831513i	$0.687475\pi$
$644$		0			0
$645$	−0.135575	+	0.417258i	−0.00533828	+	0.0164295i
$646$	0.609806	+	1.87679i	0.0239925	+	0.0738413i
$647$	32.7261	−	23.7769i	1.28660	−	0.934767i	0.286866	−	0.957971i	$-0.407387\pi$
$647$	32.7261	−	23.7769i	1.28660	−	0.934767i	0.999731	+	0.0232039i	$0.00738670\pi$
$648$	−7.65545			−0.300735
$649$	7.76653	−	5.53913i	0.304863	−	0.217430i
$650$	−1.42602			−0.0559329
$651$		0			0
$652$	−4.87747	−	15.0113i	−0.191016	−	0.587888i
$653$	−12.8198	+	39.4552i	−0.501676	+	1.54400i	0.304611	+	0.952477i	$0.401473\pi$
$653$	−12.8198	+	39.4552i	−0.501676	+	1.54400i	−0.806288	+	0.591524i	$0.798527\pi$
$654$	−0.373048	−	0.271036i	−0.0145873	−	0.0105983i
$655$	−33.3240	−	24.2113i	−1.30208	−	0.946015i
$656$	−7.70736	+	23.7208i	−0.300922	+	0.926142i
$657$	−13.5445	−	41.6856i	−0.528421	−	1.62631i
$658$		0			0
$659$	−51.1359			−1.99197			−0.995985	−	0.0895158i	$-0.971468\pi$
$659$	−51.1359			−1.99197			−0.995985	+	0.0895158i	$0.971468\pi$
$660$	−1.06266	−	3.37101i	−0.0413639	−	0.131216i
$661$	42.8840			1.66800			0.833998	−	0.551768i	$-0.186046\pi$
$661$	42.8840			1.66800			0.833998	+	0.551768i	$0.186046\pi$
$662$	−1.96875	+	1.43038i	−0.0765178	+	0.0555934i
$663$	−0.499848	−	1.53837i	−0.0194125	−	0.0597455i
$664$	0.620472	−	1.90962i	0.0240790	−	0.0741075i
$665$		0			0
$666$	−2.15249	−	1.56387i	−0.0834072	−	0.0605988i
$667$	14.2655	−	43.9048i	0.552364	−	1.70000i
$668$	−7.85995	−	24.1904i	−0.304111	−	0.935956i
$669$	3.10671	−	2.25716i	0.120112	−	0.0872668i
$670$	−0.929577			−0.0359127
$671$	0.852898	+	2.70560i	0.0329258	+	0.104448i
$672$		0			0
$673$	20.2313	−	14.6989i	0.779858	−	0.566600i	−0.125078	−	0.992147i	$-0.539918\pi$
$673$	20.2313	−	14.6989i	0.779858	−	0.566600i	0.904936	+	0.425547i	$0.139918\pi$
$674$	0.524618	+	1.61461i	0.0202075	+	0.0621923i
$675$	−0.494784	+	1.52279i	−0.0190442	+	0.0586121i
$676$	21.0766	+	15.3130i	0.810638	+	0.588963i
$677$	−8.02456	−	5.83018i	−0.308409	−	0.224072i	0.422805	−	0.906221i	$-0.361046\pi$
$677$	−8.02456	−	5.83018i	−0.308409	−	0.224072i	−0.731213	+	0.682149i	$0.761046\pi$
$678$	0.0505080	−	0.155448i	0.00193975	−	0.00596993i
$679$		0			0
$680$	2.59249	−	1.88356i	0.0994175	−	0.0722310i
$681$	5.62665			0.215614
$682$	4.69658	−	3.34963i	0.179841	−	0.128264i
$683$	−39.8980			−1.52666			−0.763328	−	0.646011i	$-0.776436\pi$
$683$	−39.8980			−1.52666			−0.763328	+	0.646011i	$0.776436\pi$
$684$	−28.2439	+	20.5204i	−1.07993	+	0.784617i
$685$	7.19174	+	22.1339i	0.274782	+	0.845692i
$686$		0			0
$687$	−3.51667	−	2.55501i	−0.134169	−	0.0974798i
$688$	2.39871	+	1.74276i	0.0914499	+	0.0664422i
$689$	−10.4438	+	32.1427i	−0.397877	+	1.22454i
$690$	0.270752	+	0.833289i	0.0103074	+	0.0317228i
$691$	−5.35084	+	3.88762i	−0.203556	+	0.147892i	−0.684893	−	0.728643i	$-0.740151\pi$
$691$	−5.35084	+	3.88762i	−0.203556	+	0.147892i	0.481338	+	0.876535i	$0.340151\pi$
$692$	11.5218			0.437995
$693$		0			0
$694$	−6.26194			−0.237700
$695$	9.74430	−	7.07965i	0.369622	−	0.268546i
$696$	−0.394239	−	1.21334i	−0.0149436	−	0.0459916i
$697$	−2.99804	+	9.22701i	−0.113559	+	0.349498i
$698$	−2.02417	−	1.47065i	−0.0766159	−	0.0556647i
$699$	3.58363	+	2.60366i	0.135545	+	0.0984795i
$700$		0			0
$701$	4.51215	+	13.8870i	0.170421	+	0.524503i	0.999395	−	0.0347848i	$-0.0110746\pi$
$701$	4.51215	+	13.8870i	0.170421	+	0.524503i	−0.828973	+	0.559288i	$0.811075\pi$
$702$	−1.22567	+	0.890502i	−0.0462600	+	0.0336098i
$703$	−24.1788			−0.911920
$704$	−22.5453	−	0.198066i	−0.849709	−	0.00746491i
$705$	−3.69240			−0.139064
$706$	5.84167	−	4.24422i	0.219854	−	0.159733i
$707$		0			0
$708$	0.379563	−	1.16817i	0.0142648	−	0.0439027i
$709$	3.35261	+	2.43582i	0.125910	+	0.0914790i	0.648958	−	0.760824i	$-0.275205\pi$
$709$	3.35261	+	2.43582i	0.125910	+	0.0914790i	−0.523048	+	0.852303i	$0.675205\pi$
$710$	−2.06465	−	1.50006i	−0.0774849	−	0.0562961i
$711$	−2.23757	+	6.88654i	−0.0839155	+	0.258265i
$712$	0.479104	+	1.47453i	0.0179552	+	0.0552604i
$713$	44.0593	−	32.0109i	1.65003	−	1.19882i
$714$		0			0
$715$	34.1631	+	25.2824i	1.27763	+	0.945510i
$716$	−8.44832			−0.315729
$717$	−3.03155	+	2.20255i	−0.113215	+	0.0822557i
$718$	0.250132	+	0.769827i	0.00933484	+	0.0287297i
$719$	−5.26017	+	16.1891i	−0.196171	+	0.603753i	0.803790	+	0.594914i	$0.202814\pi$
$719$	−5.26017	+	16.1891i	−0.196171	+	0.603753i	−0.999961	+	0.00883941i	$0.997186\pi$
$720$	22.0250	+	16.0021i	0.820825	+	0.596364i
$721$		0			0
$722$	1.24612	−	3.83517i	0.0463759	−	0.142730i
$723$	1.63551	+	5.03357i	0.0608252	+	0.187201i
$724$	−17.0761	+	12.4065i	−0.634627	+	0.461084i
$725$	8.00136			0.297163
$726$	0.177581	−	0.515538i	0.00659066	−	0.0191334i
$727$	21.6199			0.801837			0.400918	−	0.916114i	$-0.368691\pi$
$727$	21.6199			0.801837			0.400918	+	0.916114i	$0.368691\pi$
$728$		0			0
$729$	−7.55284	−	23.2453i	−0.279735	−	0.860936i
$730$	2.59015	−	7.97166i	0.0958657	−	0.295044i
$731$	0.933059	+	0.677907i	0.0345104	+	0.0250733i
$732$	0.295510	+	0.214700i	0.0109224	+	0.00793555i
$733$	14.9047	−	45.8719i	0.550517	−	1.69432i	−0.156981	−	0.987602i	$-0.550176\pi$
$733$	14.9047	−	45.8719i	0.550517	−	1.69432i	0.707498	−	0.706715i	$-0.249824\pi$
$734$	−0.160355	−	0.493523i	−0.00591883	−	0.0182163i
$735$		0			0
$736$	18.5751			0.684688
$737$	4.39001	+	3.24883i	0.161708	+	0.119672i
$738$	4.50679			0.165897
$739$	6.60439	−	4.79837i	0.242946	−	0.176511i	−0.459649	−	0.888101i	$-0.652025\pi$
$739$	6.60439	−	4.79837i	0.242946	−	0.176511i	0.702595	+	0.711590i	$0.252025\pi$
$740$	5.98787	+	18.4288i	0.220118	+	0.677455i
$741$	−2.11010	+	6.49421i	−0.0775163	+	0.238571i
$742$		0			0
$743$	−15.8254	−	11.4978i	−0.580577	−	0.421814i	0.258355	−	0.966050i	$-0.416820\pi$
$743$	−15.8254	−	11.4978i	−0.580577	−	0.421814i	−0.838932	+	0.544236i	$0.816820\pi$
$744$	0.465086	−	1.43139i	0.0170509	−	0.0524772i
$745$	0.710943	+	2.18806i	0.0260469	+	0.0801642i
$746$	−1.45832	+	1.05953i	−0.0533927	+	0.0387921i
$747$	6.63546			0.242779
$748$	−9.29113	−	0.0816249i	−0.339717	−	0.00298450i
$749$		0			0
$750$	0.377527	−	0.274289i	0.0137853	−	0.0100156i
$751$	0.344955	+	1.06166i	0.0125876	+	0.0387406i	0.957153	−	0.289583i	$-0.0935165\pi$
$751$	0.344955	+	1.06166i	0.0125876	+	0.0387406i	−0.944565	+	0.328323i	$0.893516\pi$
$752$	−7.71103	+	23.7321i	−0.281192	+	0.865421i
$753$	2.10869	+	1.53206i	0.0768451	+	0.0558312i
$754$	6.12498	+	4.45006i	0.223059	+	0.162062i
$755$	13.9552	−	42.9497i	0.507882	−	1.56310i
$756$		0			0
$757$	21.5015	−	15.6218i	0.781485	−	0.567782i	−0.123939	−	0.992290i	$-0.539553\pi$
$757$	21.5015	−	15.6218i	0.781485	−	0.567782i	0.905424	+	0.424508i	$0.139553\pi$
$758$	−2.62885			−0.0954840
$759$	1.63366	−	4.88155i	0.0592981	−	0.177189i
$760$	−13.5277			−0.490701
$761$	5.09683	−	3.70306i	0.184760	−	0.134236i	−0.491561	−	0.870843i	$-0.663573\pi$
$761$	5.09683	−	3.70306i	0.184760	−	0.134236i	0.676321	+	0.736607i	$0.263573\pi$
$762$	−0.00443000	−	0.0136341i	−0.000160482	−	0.000493913i
$763$		0			0
$764$	18.3766	+	13.3514i	0.664844	+	0.483037i
$765$	8.56739	+	6.22457i	0.309755	+	0.225050i
$766$	−0.879273	+	2.70613i	−0.0317694	+	0.0977763i
$767$	4.56403	+	14.0466i	0.164797	+	0.507195i
$768$	−2.13826	+	1.55354i	−0.0771578	+	0.0560584i
$769$	−13.1916			−0.475700			−0.237850	−	0.971302i	$-0.576443\pi$
$769$	−13.1916			−0.475700			−0.237850	+	0.971302i	$0.576443\pi$
$770$		0			0
$771$	−5.03141			−0.181202
$772$	35.3883	−	25.7111i	1.27365	−	0.925362i
$773$	−14.1585	−	43.5753i	−0.509245	−	1.56729i	−0.793515	−	0.608550i	$-0.791751\pi$
$773$	−14.1585	−	43.5753i	−0.509245	−	1.56729i	0.284270	−	0.958744i	$-0.408249\pi$
$774$	0.165557	−	0.509531i	0.00595081	−	0.0183147i
$775$	7.63652	+	5.54825i	0.274312	+	0.199299i
$776$	8.72809	+	6.34133i	0.313320	+	0.227640i
$777$		0			0
$778$	−0.0306381	−	0.0942944i	−0.00109843	−	0.00338062i
$779$	33.1342	−	24.0734i	1.18716	−	0.862520i
$780$	5.47237			0.195942
$781$	4.50786	+	14.3000i	0.161304	+	0.511695i
$782$	2.30326			0.0823643
$783$	6.87723	−	4.99660i	0.245772	−	0.178564i
$784$		0			0
$785$	9.46469	−	29.1293i	0.337809	−	1.03967i
$786$	−0.661929	−	0.480919i	−0.0236102	−	0.0171538i
$787$	−15.2483	−	11.0785i	−0.543543	−	0.394907i	0.281856	−	0.959457i	$-0.409050\pi$
$787$	−15.2483	−	11.0785i	−0.543543	−	0.394907i	−0.825399	+	0.564549i	$0.809050\pi$
$788$	−14.5148	+	44.6721i	−0.517070	+	1.59138i
$789$	0.131214	+	0.403834i	0.00467133	+	0.0143769i
$790$	−1.12025	+	0.813909i	−0.0398567	+	0.0289576i
$791$		0			0
$792$	2.62938	+	8.34104i	0.0934311	+	0.296386i
$793$	−4.39217			−0.155970
$794$	3.07724	−	2.23574i	0.109207	−	0.0793435i
$795$	1.11220	+	3.42299i	0.0394455	+	0.121401i
$796$	11.2739	−	34.6975i	0.399593	−	1.22982i
$797$	−22.7830	−	16.5528i	−0.807016	−	0.586331i	0.105948	−	0.994372i	$-0.466212\pi$
$797$	−22.7830	−	16.5528i	−0.807016	−	0.586331i	−0.912964	+	0.408040i	$0.866212\pi$
$798$		0			0
$799$	−2.99947	+	9.23141i	−0.106114	+	0.326584i
$800$	0.994884	+	3.06194i	0.0351744	+	0.108256i
$801$	−4.14511	+	3.01160i	−0.146460	+	0.106410i
$802$	8.33835			0.294437
$803$	−40.0928	+	28.5944i	−1.41485	+	1.00907i
$804$	0.703208			0.0248002
$805$		0			0
$806$	2.75996	+	8.49429i	0.0972155	+	0.299199i
$807$	−0.486649	+	1.49775i	−0.0171309	+	0.0527234i
$808$	2.66910	+	1.93921i	0.0938985	+	0.0682213i
$809$	5.29544	+	3.84736i	0.186178	+	0.135266i	0.676970	−	0.736011i	$-0.263293\pi$
$809$	5.29544	+	3.84736i	0.186178	+	0.135266i	−0.490792	+	0.871277i	$0.663293\pi$
$810$	1.49502	−	4.60119i	0.0525296	−	0.161670i
$811$	−5.81096	−	17.8843i	−0.204050	−	0.628002i	−0.999751	−	0.0223122i	$-0.992897\pi$
$811$	−5.81096	−	17.8843i	−0.204050	−	0.628002i	0.795701	−	0.605690i	$-0.207103\pi$
$812$		0			0
$813$	−0.261006			−0.00915387
$814$	−0.948675	+	2.83474i	−0.0332511	+	0.0993576i
$815$	20.2116			0.707980
$816$	−0.941797	+	0.684256i	−0.0329695	+	0.0239537i
$817$	−1.50452	−	4.63044i	−0.0526365	−	0.161999i
$818$	−1.13760	+	3.50116i	−0.0397751	+	0.122415i
$819$		0			0
$820$	−26.5542	−	19.2927i	−0.927311	−	0.673731i
$821$	−3.58089	+	11.0208i	−0.124974	+	0.384630i	−0.993896	−	0.110318i	$-0.964813\pi$
$821$	−3.58089	+	11.0208i	−0.124974	+	0.384630i	0.868922	+	0.494948i	$0.164813\pi$
$822$	0.142852	+	0.439654i	0.00498255	+	0.0153347i
$823$	−9.98844	+	7.25702i	−0.348175	+	0.252964i	−0.748103	−	0.663583i	$-0.769035\pi$
$823$	−9.98844	+	7.25702i	−0.348175	+	0.252964i	0.399928	+	0.916547i	$0.369035\pi$
$824$	−1.02866			−0.0358349
$825$	0.892177	+	0.00783800i	0.0310616	+	0.000272884i
$826$		0			0
$827$	3.63717	−	2.64256i	0.126477	−	0.0918907i	−0.522748	−	0.852487i	$-0.675093\pi$
$827$	3.63717	−	2.64256i	0.126477	−	0.0918907i	0.649225	+	0.760596i	$0.275093\pi$
$828$	12.5916	+	38.7531i	0.437590	+	1.34676i
$829$	6.13796	−	18.8907i	0.213180	−	0.656101i	−0.786098	−	0.618102i	$-0.787902\pi$
$829$	6.13796	−	18.8907i	0.213180	−	0.656101i	0.999278	−	0.0379987i	$-0.0120983\pi$
$830$	1.02658	+	0.745851i	0.0356330	+	0.0258889i
$831$	−1.83311	−	1.33183i	−0.0635900	−	0.0462008i
$832$	10.7869	−	33.1988i	0.373970	−	1.15096i
$833$		0			0
$834$	0.193555	−	0.140626i	0.00670226	−	0.00486947i
$835$	32.5706			1.12715
$836$	31.5290	+	23.3331i	1.09045	+	0.806991i
$837$	10.0284			0.346631
$838$	1.01817	−	0.739747i	0.0351722	−	0.0255541i
$839$	13.5513	+	41.7065i	0.467842	+	1.43987i	0.855373	+	0.518012i	$0.173328\pi$
$839$	13.5513	+	41.7065i	0.467842	+	1.43987i	−0.387532	+	0.921856i	$0.626672\pi$
$840$		0			0
$841$	−10.9057	−	7.92348i	−0.376060	−	0.273224i
$842$	−3.93311	−	2.85757i	−0.135544	−	0.0984785i
$843$	−0.890538	+	2.74079i	−0.0306717	+	0.0943979i
$844$	4.55662	+	14.0238i	0.156845	+	0.482720i
$845$	−26.9891	+	19.6087i	−0.928453	+	0.674561i
$846$	4.50894			0.155021
$847$		0			0
$848$	24.3232			0.835261
$849$	0.0531893	−	0.0386443i	0.00182545	−	0.00132627i
$850$	0.123362	+	0.379670i	0.00423129	+	0.0130226i
$851$	−8.72066	+	26.8394i	−0.298940	+	0.920044i
$852$	1.56187	+	1.13476i	0.0535088	+	0.0388764i
$853$	31.6655	+	23.0063i	1.08421	+	0.787721i	0.978411	−	0.206667i	$-0.0662616\pi$
$853$	31.6655	+	23.0063i	1.08421	+	0.787721i	0.105794	+	0.994388i	$0.466262\pi$
$854$		0			0
$855$	−13.8146	−	42.5169i	−0.472449	−	1.45405i
$856$	0.843455	−	0.612806i	0.0288287	−	0.0209453i
$857$	−35.0524			−1.19737			−0.598684	−	0.800986i	$-0.704309\pi$
$857$	−35.0524			−1.19737			−0.598684	+	0.800986i	$0.704309\pi$
$858$	0.678595	+	0.502195i	0.0231669	+	0.0171447i
$859$	32.5206			1.10959			0.554794	−	0.831988i	$-0.312797\pi$
$859$	32.5206			1.10959			0.554794	+	0.831988i	$0.312797\pi$
$860$	−3.15667	+	2.29345i	−0.107642	+	0.0782061i
$861$		0			0
$862$	−1.93763	+	5.96341i	−0.0659959	+	0.203114i
$863$	−10.2696	−	7.46132i	−0.349582	−	0.253986i	0.399111	−	0.916902i	$-0.369319\pi$
$863$	−10.2696	−	7.46132i	−0.349582	−	0.253986i	−0.748694	+	0.662916i	$0.769319\pi$
$864$	2.76719	+	2.01048i	0.0941418	+	0.0683981i
$865$	−4.55924	+	14.0319i	−0.155019	+	0.477099i
$866$	−0.649269	−	1.99824i	−0.0220630	−	0.0679031i
$867$	2.64741	−	1.92345i	0.0899107	−	0.0653239i
$868$		0			0
$869$	8.13505	+	0.0714685i	0.275963	+	0.00242440i
$870$	0.806251			0.0273345
$871$	−6.84079	+	4.97012i	−0.231791	+	0.168406i
$872$	−2.56778	−	7.90281i	−0.0869559	−	0.267623i
$873$	−11.0173	+	33.9078i	−0.372879	+	1.14760i
$874$	−7.86619	−	5.71512i	−0.266078	−	0.193317i
$875$		0			0
$876$	−1.95940	+	6.03041i	−0.0662020	+	0.203749i
$877$	−8.69388	−	26.7570i	−0.293571	−	0.903520i	−0.983698	−	0.179831i	$-0.942445\pi$
$877$	−8.69388	−	26.7570i	−0.293571	−	0.903520i	0.690126	−	0.723689i	$-0.257555\pi$
$878$	−2.69239	+	1.95614i	−0.0908638	+	0.0660164i
$879$	−3.53765			−0.119322
$880$	9.70720	−	29.0061i	0.327230	−	0.977797i
$881$	36.7964			1.23970			0.619850	−	0.784720i	$-0.287193\pi$
$881$	36.7964			1.23970			0.619850	+	0.784720i	$0.287193\pi$
$882$		0			0
$883$	−0.705855	−	2.17240i	−0.0237539	−	0.0731070i	0.938477	−	0.345342i	$-0.112237\pi$
$883$	−0.705855	−	2.17240i	−0.0237539	−	0.0731070i	−0.962231	+	0.272235i	$0.912237\pi$
$884$	4.44540	−	13.6815i	0.149515	−	0.460159i
$885$	1.27247	+	0.924502i	0.0427735	+	0.0310768i
$886$	−0.447173	−	0.324890i	−0.0150231	−	0.0109149i
$887$	−13.0614	+	40.1989i	−0.438560	+	1.34975i	0.450835	+	0.892607i	$0.351126\pi$
$887$	−13.0614	+	40.1989i	−0.438560	+	1.34975i	−0.889395	+	0.457140i	$0.848874\pi$
$888$	0.241002	+	0.741728i	0.00808750	+	0.0248908i
$889$		0			0
$890$	−0.979808			−0.0328432
$891$	−23.1413	+	16.5045i	−0.775264	+	0.552922i
$892$	34.1520			1.14349
$893$	33.1500	−	24.0849i	1.10932	−	0.805971i
$894$	0.0141217	+	0.0434623i	0.000472302	+	0.00145360i
$895$	3.34304	−	10.2888i	0.111745	−	0.343917i
$896$		0			0
$897$	6.44778	+	4.68459i	0.215285	+	0.156414i
$898$	0.333393	−	1.02608i	0.0111255	−	0.0342406i
$899$	−15.4861	−	47.6614i	−0.516491	−	1.58960i
$900$	−5.71367	+	4.15123i	−0.190456	+	0.138374i
$901$	9.46132			0.315202
$902$	−1.52234	−	4.82923i	−0.0506884	−	0.160796i
$903$		0			0
$904$	2.38288	−	1.73127i	0.0792535	−	0.0575810i
$905$	−8.35220	−	25.7054i	−0.277636	−	0.854477i
$906$	0.277198	−	0.853128i	0.00920929	−	0.0283433i
$907$	−31.9793	−	23.2343i	−1.06185	−	0.771483i	−0.0874240	−	0.996171i	$-0.527864\pi$
$907$	−31.9793	−	23.2343i	−1.06185	−	0.771483i	−0.974431	+	0.224689i	$0.927864\pi$
$908$	40.4837	+	29.4131i	1.34350	+	0.976108i
$909$	−3.36915	+	10.3692i	−0.111748	+	0.343924i
$910$		0			0
$911$	28.5013	−	20.7074i	0.944291	−	0.686067i	−0.00515893	−	0.999987i	$-0.501642\pi$
$911$	28.5013	−	20.7074i	0.944291	−	0.686067i	0.949450	+	0.313919i	$0.101642\pi$
$912$	4.91433			0.162730
$913$	−2.24138	−	7.11019i	−0.0741788	−	0.235313i
$914$	7.03234			0.232609
$915$	−0.378408	+	0.274929i	−0.0125098	+	0.00908888i
$916$	−11.9462	−	36.7666i	−0.394713	−	1.21480i
$917$		0			0
$918$	0.343123	+	0.249293i	0.0113247	+	0.00822791i
$919$	32.0455	+	23.2824i	1.05708	+	0.768017i	0.973547	−	0.228488i	$-0.0733780\pi$
$919$	32.0455	+	23.2824i	1.05708	+	0.768017i	0.0835379	+	0.996505i	$0.473378\pi$
$920$	−4.87909	+	15.0163i	−0.160859	+	0.495073i
$921$	1.93919	+	5.96821i	0.0638984	+	0.196659i
$922$	5.43930	−	3.95188i	0.179134	−	0.130148i
$923$	−23.2141			−0.764101
$924$		0			0
$925$	−4.89131			−0.160825
$926$	4.65855	−	3.38463i	0.153089	−	0.111226i
$927$	−1.05047	−	3.23302i	−0.0345020	−	0.106186i
$928$	5.28196	−	16.2562i	0.173389	−	0.533636i
$929$	2.11685	+	1.53798i	0.0694516	+	0.0504595i	0.621969	−	0.783042i	$-0.286333\pi$
$929$	2.11685	+	1.53798i	0.0694516	+	0.0504595i	−0.552518	+	0.833501i	$0.686333\pi$
$930$	0.769488	+	0.559066i	0.0252325	+	0.0183325i
$931$		0			0
$932$	12.1736	+	37.4666i	0.398761	+	1.22726i
$933$	−5.64152	+	4.09881i	−0.184695	+	0.134189i
$934$	0.720463			0.0235743
$935$	3.77594	−	11.2829i	0.123487	−	0.368991i
$936$	−13.5405			−0.442586
$937$	43.5575	−	31.6464i	1.42296	−	1.03384i	0.431689	−	0.902022i	$-0.357918\pi$
$937$	43.5575	−	31.6464i	1.42296	−	1.03384i	0.991274	−	0.131820i	$-0.0420822\pi$
$938$		0			0
$939$	−0.00231742	+	0.00713228i	−7.56261e−5	+	0.000232753i
$940$	−26.5668	−	19.3019i	−0.866514	−	0.629559i
$941$	23.9854	+	17.4264i	0.781902	+	0.568085i	0.905549	−	0.424241i	$-0.139459\pi$
$941$	23.9854	+	17.4264i	0.781902	+	0.568085i	−0.123647	+	0.992326i	$0.539459\pi$
$942$	0.188001	−	0.578607i	0.00612540	−	0.0188520i
$943$	−14.7718	−	45.4630i	−0.481037	−	1.48048i
$944$	8.59940	−	6.24783i	0.279887	−	0.203349i
$945$		0			0
$946$	−0.601908	−	0.00528791i	−0.0195697	−	0.000171925i
$947$	−15.7861			−0.512980			−0.256490	−	0.966547i	$-0.582566\pi$
$947$	−15.7861			−0.512980			−0.256490	+	0.966547i	$0.582566\pi$
$948$	0.847448	−	0.615707i	0.0275238	−	0.0199972i
$949$	−23.5607	−	72.5123i	−0.764812	−	2.35385i
$950$	0.520771	−	1.60277i	0.0168961	−	0.0520007i
$951$	−3.96919	−	2.88378i	−0.128710	−	0.0935131i
$952$		0			0
$953$	−10.8502	+	33.3934i	−0.351472	+	1.08172i	0.606555	+	0.795041i	$0.292551\pi$
$953$	−10.8502	+	33.3934i	−0.351472	+	1.08172i	−0.958027	+	0.286678i	$0.907449\pi$
$954$	−1.35815	−	4.17995i	−0.0439716	−	0.135331i
$955$	−23.5318	+	17.0968i	−0.761470	+	0.553240i
$956$	−33.3257			−1.07783
$957$	−3.80759	−	2.81782i	−0.123082	−	0.0910870i
$958$	−0.731463			−0.0236325
$959$		0			0
$960$	−1.14874	−	3.53546i	−0.0370754	−	0.114106i
$961$	8.68955	−	26.7437i	0.280308	−	0.862700i
$962$	−3.74426	−	2.72036i	−0.120720	−	0.0877080i
$963$	2.78736	+	2.02514i	0.0898214	+	0.0652591i
$964$	−14.5454	+	44.7661i	−0.468475	+	1.44182i
$965$	17.3090	+	53.2716i	0.557196	+	1.71487i
$966$		0			0
$967$	−49.2820			−1.58480			−0.792401	−	0.610001i	$-0.791169\pi$
$967$	−49.2820			−1.58480			−0.792401	+	0.610001i	$0.791169\pi$
$968$	8.04962	−	5.63500i	0.258725	−	0.181116i
$969$	1.91160			0.0614093
$970$	−5.51585	+	4.00750i	−0.177103	+	0.128673i
$971$	−11.5394	−	35.5148i	−0.370318	−	1.13972i	−0.946583	−	0.322460i	$-0.895490\pi$
$971$	−11.5394	−	35.5148i	−0.370318	−	1.13972i	0.576265	−	0.817263i	$-0.304510\pi$
$972$	−3.48730	+	10.7328i	−0.111855	+	0.344255i
$973$		0			0
$974$	−1.80647	−	1.31248i	−0.0578831	−	0.0420545i
$975$	−0.426867	+	1.31376i	−0.0136707	+	0.0420741i
$976$	0.976800	+	3.00628i	0.0312666	+	0.0962287i
$977$	−32.3999	+	23.5399i	−1.03656	+	0.753108i	−0.969612	−	0.244648i	$-0.921328\pi$
$977$	−32.3999	+	23.5399i	−1.03656	+	0.753108i	−0.0669524	+	0.997756i	$0.521328\pi$
$978$	0.401470			0.0128376
$979$	4.62723	+	3.42439i	0.147887	+	0.109444i
$980$		0			0
$981$	22.2159	−	16.1408i	0.709299	−	0.515336i
$982$	0.295411	+	0.909181i	0.00942694	+	0.0290131i
$983$	16.0817	−	49.4944i	0.512926	−	1.57862i	−0.274098	−	0.961702i	$-0.588379\pi$
$983$	16.0817	−	49.4944i	0.512926	−	1.57862i	0.787024	−	0.616923i	$-0.211621\pi$
$984$	−1.06876	−	0.776500i	−0.0340709	−	0.0247539i
$985$	−48.6604	−	35.3538i	−1.55045	−	1.12647i
$986$	0.654946	−	2.01572i	0.0208577	−	0.0641935i
$987$		0			0
$988$	−49.1304	+	35.6953i	−1.56305	+	1.13562i
$989$	−5.68262			−0.180697
$990$	−5.52674	−	0.0485539i	−0.175651	−	0.00154314i
$991$	45.4828			1.44481			0.722404	−	0.691471i	$-0.243037\pi$
$991$	45.4828			1.44481			0.722404	+	0.691471i	$0.243037\pi$
$992$	16.3134	−	11.8524i	0.517951	−	0.376313i
$993$	0.728455	+	2.24195i	0.0231168	+	0.0711463i
$994$		0			0
$995$	37.7953	+	27.4599i	1.19819	+	0.870536i
$996$	−0.776586	−	0.564223i	−0.0246071	−	0.0178781i
$997$	−8.63992	+	26.5909i	−0.273629	+	0.842143i	0.715950	+	0.698152i	$0.245994\pi$
$997$	−8.63992	+	26.5909i	−0.273629	+	0.842143i	−0.989579	+	0.143992i	$0.954006\pi$
$998$	−1.42569	−	4.38783i	−0.0451296	−	0.138894i
$999$	−4.20412	+	3.05447i	−0.133012	+	0.0966392i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	539.2.f.e.344.3		16
7.2	even	3		539.2.q.f.410.2		32
7.3	odd	6		539.2.q.g.520.3		32
7.4	even	3		539.2.q.f.520.3		32
7.5	odd	6		539.2.q.g.410.2		32
7.6	odd	2		77.2.f.b.36.3	yes	16
11.2	odd	10		5929.2.a.bs.1.5		8
11.4	even	5	inner	539.2.f.e.246.3		16
11.9	even	5		5929.2.a.bt.1.4		8
21.20	even	2		693.2.m.i.190.2		16
77.4	even	15		539.2.q.f.422.2		32
77.6	even	10		847.2.f.v.372.3		16
77.13	even	10		847.2.a.o.1.5		8
77.20	odd	10		847.2.a.p.1.4		8
77.26	odd	30		539.2.q.g.312.3		32
77.27	odd	10		847.2.f.w.372.2		16
77.37	even	15		539.2.q.f.312.3		32
77.41	even	10		847.2.f.v.148.3		16
77.48	odd	10		77.2.f.b.15.3	✓	16
77.59	odd	30		539.2.q.g.422.2		32
77.62	even	10		847.2.f.x.323.2		16
77.69	odd	10		847.2.f.w.148.2		16
77.76	even	2		847.2.f.x.729.2		16
231.20	even	10		7623.2.a.ct.1.5		8
231.125	even	10		693.2.m.i.631.2		16
231.167	odd	10		7623.2.a.cw.1.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.2.f.b.15.3	✓	16	77.48	odd	10
77.2.f.b.36.3	yes	16	7.6	odd	2
539.2.f.e.246.3		16	11.4	even	5	inner
539.2.f.e.344.3		16	1.1	even	1	trivial
539.2.q.f.312.3		32	77.37	even	15
539.2.q.f.410.2		32	7.2	even	3
539.2.q.f.422.2		32	77.4	even	15
539.2.q.f.520.3		32	7.4	even	3
539.2.q.g.312.3		32	77.26	odd	30
539.2.q.g.410.2		32	7.5	odd	6
539.2.q.g.422.2		32	77.59	odd	30
539.2.q.g.520.3		32	7.3	odd	6
693.2.m.i.190.2		16	21.20	even	2
693.2.m.i.631.2		16	231.125	even	10
847.2.a.o.1.5		8	77.13	even	10
847.2.a.p.1.4		8	77.20	odd	10
847.2.f.v.148.3		16	77.41	even	10
847.2.f.v.372.3		16	77.6	even	10
847.2.f.w.148.2		16	77.69	odd	10
847.2.f.w.372.2		16	77.27	odd	10
847.2.f.x.323.2		16	77.62	even	10
847.2.f.x.729.2		16	77.76	even	2
5929.2.a.bs.1.5		8	11.2	odd	10
5929.2.a.bt.1.4		8	11.9	even	5
7623.2.a.ct.1.5		8	231.20	even	10
7623.2.a.cw.1.4		8	231.167	odd	10

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.f (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.183009 + 0.132964i) q^{2} +(0.0677147 + 0.208405i) q^{3} +(-0.602221 + 1.85345i) q^{4} +(-2.01892 - 1.46683i) q^{5} +(-0.0401026 - 0.0291363i) q^{6} +(-0.276036 - 0.849550i) q^{8} +(2.38820 - 1.73513i) q^{9} +0.564516 q^{10} +(-2.66598 - 1.97296i) q^{11} -0.427046 q^{12} +(4.15429 - 3.01827i) q^{13} +(0.168984 - 0.520079i) q^{15} +(-2.98979 - 2.17221i) q^{16} +(-1.16298 - 0.844956i) q^{17} +(-0.206353 + 0.635089i) q^{18} +(1.87526 + 5.77147i) q^{19} +(3.93453 - 2.85860i) q^{20} +(0.750229 + 0.00659095i) q^{22} +7.08292 q^{23} +(0.158358 - 0.115054i) q^{24} +(0.379361 + 1.16755i) q^{25} +(-0.358952 + 1.10474i) q^{26} +(1.05516 + 0.766622i) q^{27} +(2.01408 - 6.19869i) q^{29} +(0.0382260 + 0.117648i) q^{30} +(6.22049 - 4.51945i) q^{31} +2.62252 q^{32} +(0.230648 - 0.689200i) q^{33} +0.325184 q^{34} +(1.77775 + 5.47134i) q^{36} +(-1.23122 + 3.78932i) q^{37} +(-1.11058 - 0.806887i) q^{38} +(0.910328 + 0.661392i) q^{39} +(-0.688853 + 2.12007i) q^{40} +(-2.08556 - 6.41868i) q^{41} -0.802299 q^{43} +(5.26228 - 3.75309i) q^{44} -7.36674 q^{45} +(-1.29624 + 0.941771i) q^{46} +(-2.08655 - 6.42174i) q^{47} +(0.250246 - 0.770178i) q^{48} +(-0.224669 - 0.163231i) q^{50} +(0.0973416 - 0.299587i) q^{51} +(3.09240 + 9.51742i) q^{52} +(-5.32469 + 3.86861i) q^{53} -0.295037 q^{54} +(2.48840 + 7.89379i) q^{55} +(-1.07582 + 0.781627i) q^{57} +(0.455607 + 1.40221i) q^{58} +(-0.888810 + 2.73548i) q^{59} +(0.862172 + 0.626405i) q^{60} +(-0.691986 - 0.502757i) q^{61} +(-0.537482 + 1.65420i) q^{62} +(5.49964 - 3.99573i) q^{64} -12.8145 q^{65} +(0.0494280 + 0.156797i) q^{66} -1.64668 q^{67} +(2.26645 - 1.64667i) q^{68} +(0.479618 + 1.47611i) q^{69} +(-3.65738 - 2.65724i) q^{71} +(-2.13331 - 1.54994i) q^{72} +(4.58827 - 14.1212i) q^{73} +(-0.278517 - 0.857187i) q^{74} +(-0.217635 + 0.158121i) q^{75} -11.8264 q^{76} -0.254539 q^{78} +(-1.98444 + 1.44178i) q^{79} +(2.84989 + 8.77105i) q^{80} +(2.64832 - 8.15069i) q^{81} +(1.23513 + 0.897372i) q^{82} +(1.81851 + 1.32122i) q^{83} +(1.10856 + 3.41180i) q^{85} +(0.146828 - 0.106677i) q^{86} +1.42822 q^{87} +(-0.940224 + 2.80949i) q^{88} -1.73566 q^{89} +(1.34818 - 0.979509i) q^{90} +(-4.26549 + 13.1278i) q^{92} +(1.36309 + 0.990346i) q^{93} +(1.23572 + 0.897800i) q^{94} +(4.67976 - 14.4028i) q^{95} +(0.177584 + 0.546546i) q^{96} +(-9.77095 + 7.09901i) q^{97} +(-9.79024 - 0.0860098i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 3 q^{2} + 2 q^{3} - 11 q^{4} + 5 q^{5} - 3 q^{6} - 5 q^{8} - 12 q^{9} - 12 q^{10} - 3 q^{11} - 18 q^{12} + 7 q^{13} - 18 q^{15} + 17 q^{16} + 5 q^{17} + 11 q^{18} - 19 q^{19} - q^{20} - 33 q^{22}+ \cdots + 16 q^{99}+O(q^{100}) \) 16 * q - 3 * q^2 + 2 * q^3 - 11 * q^4 + 5 * q^5 - 3 * q^6 - 5 * q^8 - 12 * q^9 - 12 * q^10 - 3 * q^11 - 18 * q^12 + 7 * q^13 - 18 * q^15 + 17 * q^16 + 5 * q^17 + 11 * q^18 - 19 * q^19 - q^20 - 33 * q^22 + 32 * q^23 + 35 * q^24 + 7 * q^25 + 27 * q^26 - 10 * q^27 + 3 * q^29 - 2 * q^30 + 7 * q^31 + 32 * q^32 + 26 * q^33 + 24 * q^34 + 52 * q^36 + 4 * q^37 + 5 * q^38 + 11 * q^39 + 10 * q^40 + 10 * q^41 - 8 * q^43 - 38 * q^44 - 70 * q^45 - 42 * q^46 + 23 * q^47 + 36 * q^48 + 52 * q^50 - 29 * q^51 - 33 * q^52 + 4 * q^53 - 60 * q^54 + 12 * q^55 - 11 * q^57 + 20 * q^58 - 17 * q^59 - 30 * q^60 + 7 * q^61 - 79 * q^62 + 7 * q^64 - 8 * q^65 - 8 * q^66 - 38 * q^67 + 2 * q^68 - 10 * q^69 - 14 * q^71 + 35 * q^73 - 29 * q^74 - 9 * q^75 - 52 * q^76 - 58 * q^78 + 15 * q^79 + 87 * q^80 - 14 * q^81 - 19 * q^82 - 5 * q^83 + 6 * q^85 - 52 * q^86 + 72 * q^87 + 55 * q^88 - 74 * q^89 + 14 * q^90 - 55 * q^92 + 32 * q^93 + 24 * q^94 + 32 * q^95 + 42 * q^96 - 20 * q^97 + 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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