LMFDB - Embedded newform 232.2.m.d.25.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [232,2,Mod(25,232)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(232, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([0, 0, 8]))

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

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

chi := DirichletCharacter("232.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 232 = 2^{3} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	232.m (of order $7$, degree $6$, 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:	$1.85252932689$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$4$ over $\Q(\zeta_{7})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			25.1
Character	$\chi$	$=$	232.25
Dual form			232.2.m.d.65.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.49260 + 1.20038i) q^{3} +(-0.0857933 + 0.375885i) q^{5} +(-1.11973 + 0.539232i) q^{7} +(2.90171 - 3.63863i) q^{9} +O(q^{10})$	\(q+(-2.49260 + 1.20038i) q^{3} +(-0.0857933 + 0.375885i) q^{5} +(-1.11973 + 0.539232i) q^{7} +(2.90171 - 3.63863i) q^{9} +(-2.69274 - 3.37659i) q^{11} +(-2.73736 - 3.43254i) q^{13} +(-0.237354 - 1.03992i) q^{15} -3.23759 q^{17} +(-3.41620 - 1.64515i) q^{19} +(2.14375 - 2.68818i) q^{21} +(1.04422 + 4.57502i) q^{23} +(4.37092 + 2.10492i) q^{25} +(-1.01823 + 4.46114i) q^{27} +(-5.31473 - 0.868136i) q^{29} +(1.19782 - 5.24800i) q^{31} +(10.7651 + 5.18421i) q^{33} +(-0.106624 - 0.467151i) q^{35} +(-0.607148 + 0.761340i) q^{37} +(10.9435 + 5.27011i) q^{39} -6.85312 q^{41} +(2.80971 + 12.3102i) q^{43} +(1.11876 + 1.40288i) q^{45} +(-2.26323 - 2.83799i) q^{47} +(-3.40141 + 4.26524i) q^{49} +(8.07004 - 3.88633i) q^{51} +(-1.98407 + 8.69278i) q^{53} +(1.50023 - 0.722473i) q^{55} +10.4900 q^{57} -0.479557 q^{59} +(4.69633 - 2.26163i) q^{61} +(-1.28706 + 5.63896i) q^{63} +(1.52509 - 0.734444i) q^{65} +(-0.875730 + 1.09813i) q^{67} +(-8.09456 - 10.1503i) q^{69} +(-5.63489 - 7.06593i) q^{71} +(-1.99597 - 8.74490i) q^{73} -13.4217 q^{75} +(4.83590 + 2.32885i) q^{77} +(8.41539 - 10.5526i) q^{79} +(0.289815 + 1.26976i) q^{81} +(-15.3775 - 7.40539i) q^{83} +(0.277764 - 1.21696i) q^{85} +(14.2896 - 4.21575i) q^{87} +(-1.20736 + 5.28980i) q^{89} +(4.91603 + 2.36743i) q^{91} +(3.31387 + 14.5190i) q^{93} +(0.911476 - 1.14295i) q^{95} +(-13.2779 - 6.39431i) q^{97} -20.0997 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - q^{3} - 8 q^{5} + 5 q^{7} - 3 q^{9}+O(q^{10}) $ 24 * q - q^3 - 8 * q^5 + 5 * q^7 - 3 * q^9	$ 24 q - q^{3} - 8 q^{5} + 5 q^{7} - 3 q^{9} - 6 q^{11} + q^{13} - q^{15} - 16 q^{17} - 10 q^{19} - 5 q^{21} + 11 q^{23} + 10 q^{25} - 7 q^{27} - 2 q^{29} + 12 q^{31} + 13 q^{33} - 8 q^{35} + q^{37} + 34 q^{39} - 22 q^{41} + 3 q^{43} + 60 q^{45} + 9 q^{47} - 67 q^{49} - q^{51} + 19 q^{53} - 88 q^{55} - 2 q^{57} + 114 q^{59} - 11 q^{61} - 108 q^{63} + 8 q^{65} - 25 q^{67} - 84 q^{69} - 21 q^{71} + 30 q^{73} - 26 q^{75} - 22 q^{77} + 48 q^{79} + 16 q^{81} - 37 q^{83} + 8 q^{85} + 11 q^{87} - 5 q^{89} - 11 q^{91} - 18 q^{93} - 21 q^{95} + 35 q^{97} + 32 q^{99}+O(q^{100}) $ 24 * q - q^3 - 8 * q^5 + 5 * q^7 - 3 * q^9 - 6 * q^11 + q^13 - q^15 - 16 * q^17 - 10 * q^19 - 5 * q^21 + 11 * q^23 + 10 * q^25 - 7 * q^27 - 2 * q^29 + 12 * q^31 + 13 * q^33 - 8 * q^35 + q^37 + 34 * q^39 - 22 * q^41 + 3 * q^43 + 60 * q^45 + 9 * q^47 - 67 * q^49 - q^51 + 19 * q^53 - 88 * q^55 - 2 * q^57 + 114 * q^59 - 11 * q^61 - 108 * q^63 + 8 * q^65 - 25 * q^67 - 84 * q^69 - 21 * q^71 + 30 * q^73 - 26 * q^75 - 22 * q^77 + 48 * q^79 + 16 * q^81 - 37 * q^83 + 8 * q^85 + 11 * q^87 - 5 * q^89 - 11 * q^91 - 18 * q^93 - 21 * q^95 + 35 * q^97 + 32 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/232\mathbb{Z}\right)^\times$.

$n$	$89$	$117$	$175$
$\chi(n)$	$e\left(\frac{4}{7}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−2.49260	+	1.20038i	−1.43911	+	0.693037i	−0.980666	−	0.195688i	$-0.937306\pi$
$3$	−2.49260	+	1.20038i	−1.43911	+	0.693037i	−0.458440	+	0.888725i	$0.651592\pi$
$4$		0			0
$5$	−0.0857933	+	0.375885i	−0.0383680	+	0.168101i	−0.990482	−	0.137642i	$-0.956048\pi$
$5$	−0.0857933	+	0.375885i	−0.0383680	+	0.168101i	0.952114	+	0.305743i	$0.0989048\pi$
$6$		0			0
$7$	−1.11973	+	0.539232i	−0.423217	+	0.203810i	−0.633355	−	0.773861i	$-0.718323\pi$
$7$	−1.11973	+	0.539232i	−0.423217	+	0.203810i	0.210139	+	0.977672i	$0.432608\pi$
$8$		0			0
$9$	2.90171	−	3.63863i	0.967236	−	1.21288i
$10$		0			0
$11$	−2.69274	−	3.37659i	−0.811892	−	1.01808i	−0.999359	−	0.0358095i	$-0.988599\pi$
$11$	−2.69274	−	3.37659i	−0.811892	−	1.01808i	0.187467	−	0.982271i	$-0.439972\pi$
$12$		0			0
$13$	−2.73736	−	3.43254i	−0.759207	−	0.952015i	0.240620	−	0.970619i	$-0.422649\pi$
$13$	−2.73736	−	3.43254i	−0.759207	−	0.952015i	−0.999827	+	0.0186043i	$0.994078\pi$
$14$		0			0
$15$	−0.237354	−	1.03992i	−0.0612846	−	0.268506i
$16$		0			0
$17$	−3.23759			−0.785232			−0.392616	−	0.919703i	$-0.628430\pi$
$17$	−3.23759			−0.785232			−0.392616	+	0.919703i	$0.628430\pi$
$18$		0			0
$19$	−3.41620	−	1.64515i	−0.783729	−	0.377424i	−0.00116918	−	0.999999i	$-0.500372\pi$
$19$	−3.41620	−	1.64515i	−0.783729	−	0.377424i	−0.782560	+	0.622575i	$0.786086\pi$
$20$		0			0
$21$	2.14375	−	2.68818i	0.467806	−	0.586610i
$22$		0			0
$23$	1.04422	+	4.57502i	0.217735	+	0.953957i	0.959147	+	0.282908i	$0.0912991\pi$
$23$	1.04422	+	4.57502i	0.217735	+	0.953957i	−0.741413	+	0.671050i	$0.765844\pi$
$24$		0			0
$25$	4.37092	+	2.10492i	0.874183	+	0.420984i
$26$		0			0
$27$	−1.01823	+	4.46114i	−0.195958	+	0.858547i
$28$		0			0
$29$	−5.31473	−	0.868136i	−0.986920	−	0.161209i
$29$	−5.31473	−	0.868136i	−0.986920	−	0.161209i
$30$		0			0
$31$	1.19782	−	5.24800i	0.215135	−	0.942569i	−0.745882	−	0.666079i	$-0.767972\pi$
$31$	1.19782	−	5.24800i	0.215135	−	0.942569i	0.961017	−	0.276490i	$-0.0891713\pi$
$32$		0			0
$33$	10.7651	+	5.18421i	1.87397	+	0.902455i
$34$		0			0
$35$	−0.106624	−	0.467151i	−0.0180228	−	0.0789629i
$36$		0			0
$37$	−0.607148	+	0.761340i	−0.0998146	+	0.125164i	−0.829230	−	0.558907i	$-0.811221\pi$
$37$	−0.607148	+	0.761340i	−0.0998146	+	0.125164i	0.729415	+	0.684071i	$0.239792\pi$
$38$		0			0
$39$	10.9435	+	5.27011i	1.75236	+	0.843892i
$40$		0			0
$41$	−6.85312			−1.07028			−0.535139	−	0.844764i	$-0.679741\pi$
$41$	−6.85312			−1.07028			−0.535139	+	0.844764i	$0.679741\pi$
$42$		0			0
$43$	2.80971	+	12.3102i	0.428477	+	1.87728i	0.477750	+	0.878496i	$0.341452\pi$
$43$	2.80971	+	12.3102i	0.428477	+	1.87728i	−0.0492732	+	0.998785i	$0.515691\pi$
$44$		0			0
$45$	1.11876	+	1.40288i	0.166775	+	0.209129i
$46$		0			0
$47$	−2.26323	−	2.83799i	−0.330125	−	0.413964i	0.588873	−	0.808226i	$-0.299572\pi$
$47$	−2.26323	−	2.83799i	−0.330125	−	0.413964i	−0.918998	+	0.394262i	$0.871000\pi$
$48$		0			0
$49$	−3.40141	+	4.26524i	−0.485916	+	0.609320i
$50$		0			0
$51$	8.07004	−	3.88633i	1.13003	−	0.544195i
$52$		0			0
$53$	−1.98407	+	8.69278i	−0.272533	+	1.19405i	0.634479	+	0.772940i	$0.281215\pi$
$53$	−1.98407	+	8.69278i	−0.272533	+	1.19405i	−0.907012	+	0.421105i	$0.861642\pi$
$54$		0			0
$55$	1.50023	−	0.722473i	0.202291	−	0.0974182i
$56$		0			0
$57$	10.4900			1.38944
$58$		0			0
$59$	−0.479557			−0.0624330			−0.0312165	−	0.999513i	$-0.509938\pi$
$59$	−0.479557			−0.0624330			−0.0312165	+	0.999513i	$0.509938\pi$
$60$		0			0
$61$	4.69633	−	2.26163i	0.601303	−	0.289572i	−0.108362	−	0.994111i	$-0.534561\pi$
$61$	4.69633	−	2.26163i	0.601303	−	0.289572i	0.709665	+	0.704539i	$0.248846\pi$
$62$		0			0
$63$	−1.28706	+	5.63896i	−0.162154	+	0.710442i
$64$		0			0
$65$	1.52509	−	0.734444i	0.189164	−	0.0910965i
$66$		0			0
$67$	−0.875730	+	1.09813i	−0.106987	+	0.134158i	−0.832442	−	0.554112i	$-0.813058\pi$
$67$	−0.875730	+	1.09813i	−0.106987	+	0.134158i	0.725455	+	0.688270i	$0.241629\pi$
$68$		0			0
$69$	−8.09456	−	10.1503i	−0.974471	−	1.22195i
$70$		0			0
$71$	−5.63489	−	7.06593i	−0.668738	−	0.838571i	0.325525	−	0.945534i	$-0.394459\pi$
$71$	−5.63489	−	7.06593i	−0.668738	−	0.838571i	−0.994263	+	0.106962i	$0.965888\pi$
$72$		0			0
$73$	−1.99597	−	8.74490i	−0.233610	−	1.02351i	−0.946618	−	0.322357i	$-0.895525\pi$
$73$	−1.99597	−	8.74490i	−0.233610	−	1.02351i	0.713008	−	0.701156i	$-0.247332\pi$
$74$		0			0
$75$	−13.4217			−1.54980
$76$		0			0
$77$	4.83590	+	2.32885i	0.551102	+	0.265397i
$78$		0			0
$79$	8.41539	−	10.5526i	0.946805	−	1.18726i	−0.0353861	−	0.999374i	$-0.511266\pi$
$79$	8.41539	−	10.5526i	0.946805	−	1.18726i	0.982191	−	0.187883i	$-0.0601625\pi$
$80$		0			0
$81$	0.289815	+	1.26976i	0.0322017	+	0.141085i
$82$		0			0
$83$	−15.3775	−	7.40539i	−1.68789	−	0.812847i	−0.995852	−	0.0909907i	$-0.970997\pi$
$83$	−15.3775	−	7.40539i	−1.68789	−	0.812847i	−0.692043	−	0.721856i	$-0.743289\pi$
$84$		0			0
$85$	0.277764	−	1.21696i	0.0301277	−	0.131998i
$86$		0			0
$87$	14.2896	−	4.21575i	1.53201	−	0.451976i
$88$		0			0
$89$	−1.20736	+	5.28980i	−0.127980	+	0.560718i	0.869757	+	0.493481i	$0.164276\pi$
$89$	−1.20736	+	5.28980i	−0.127980	+	0.560718i	−0.997737	+	0.0672374i	$0.978582\pi$
$90$		0			0
$91$	4.91603	+	2.36743i	0.515339	+	0.248174i
$92$		0			0
$93$	3.31387	+	14.5190i	0.343633	+	1.50555i
$94$		0			0
$95$	0.911476	−	1.14295i	0.0935154	−	0.117265i
$96$		0			0
$97$	−13.2779	−	6.39431i	−1.34817	−	0.649244i	−0.386204	−	0.922414i	$-0.626214\pi$
$97$	−13.2779	−	6.39431i	−1.34817	−	0.649244i	−0.961966	+	0.273169i	$0.911928\pi$
$98$		0			0
$99$	−20.0997			−2.02010
$100$		0			0
$101$	1.36510	+	5.98090i	0.135833	+	0.595122i	0.996325	+	0.0856577i	$0.0272992\pi$
$101$	1.36510	+	5.98090i	0.135833	+	0.595122i	−0.860492	+	0.509464i	$0.829844\pi$
$102$		0			0
$103$	12.1626	+	15.2514i	1.19842	+	1.50277i	0.815273	+	0.579077i	$0.196587\pi$
$103$	12.1626	+	15.2514i	1.19842	+	1.50277i	0.383143	+	0.923689i	$0.374842\pi$
$104$		0			0
$105$	0.826528	+	1.03643i	0.0806609	+	0.101146i
$106$		0			0
$107$	4.48465	−	5.62358i	0.433548	−	0.543652i	−0.516282	−	0.856419i	$-0.672684\pi$
$107$	4.48465	−	5.62358i	0.433548	−	0.543652i	0.949830	+	0.312767i	$0.101256\pi$
$108$		0			0
$109$	15.8524	−	7.63410i	1.51838	−	0.731214i	0.525554	−	0.850760i	$-0.323858\pi$
$109$	15.8524	−	7.63410i	1.51838	−	0.731214i	0.992829	+	0.119546i	$0.0381438\pi$
$110$		0			0
$111$	0.599487	−	2.62653i	0.0569008	−	0.249299i
$112$		0			0
$113$	−14.5466	+	7.00529i	−1.36843	+	0.659002i	−0.966500	−	0.256668i	$-0.917375\pi$
$113$	−14.5466	+	7.00529i	−1.36843	+	0.659002i	−0.401932	+	0.915670i	$0.631661\pi$
$114$		0			0
$115$	−1.80927			−0.168715
$116$		0			0
$117$	−20.4327			−1.88901
$118$		0			0
$119$	3.62522	−	1.74581i	0.332323	−	0.160038i
$120$		0			0
$121$	−1.70278	+	7.46036i	−0.154798	+	0.678215i
$122$		0			0
$123$	17.0821	−	8.22632i	1.54024	−	0.741742i
$124$		0			0
$125$	−2.36814	+	2.96956i	−0.211813	+	0.265605i
$126$		0			0
$127$	−3.90841	−	4.90099i	−0.346815	−	0.434893i	0.577577	−	0.816336i	$-0.303998\pi$
$127$	−3.90841	−	4.90099i	−0.346815	−	0.434893i	−0.924392	+	0.381444i	$0.875427\pi$
$128$		0			0
$129$	−21.7803	−	27.3116i	−1.91765	−	2.40466i
$130$		0			0
$131$	1.47965	+	6.48279i	0.129278	+	0.566404i	0.997528	+	0.0702761i	$0.0223880\pi$
$131$	1.47965	+	6.48279i	0.129278	+	0.566404i	−0.868250	+	0.496128i	$0.834755\pi$
$132$		0			0
$133$	4.71232			0.408610
$134$		0			0
$135$	−1.58952	−	0.765473i	−0.136804	−	0.0658814i
$136$		0			0
$137$	1.01847	−	1.27712i	0.0870135	−	0.109111i	−0.736419	−	0.676526i	$-0.763485\pi$
$137$	1.01847	−	1.27712i	0.0870135	−	0.109111i	0.823432	+	0.567414i	$0.192056\pi$
$138$		0			0
$139$	−0.352686	−	1.54522i	−0.0299144	−	0.131064i	0.957766	−	0.287550i	$-0.0928406\pi$
$139$	−0.352686	−	1.54522i	−0.0299144	−	0.131064i	−0.987680	+	0.156486i	$0.949983\pi$
$140$		0			0
$141$	9.04799	+	4.35728i	0.761978	+	0.366949i
$142$		0			0
$143$	−4.21928	+	18.4859i	−0.352834	+	1.54587i
$144$		0			0
$145$	0.782288	−	1.92325i	0.0649655	−	0.159717i
$146$		0			0
$147$	3.35849	−	14.7145i	0.277004	−	1.21363i
$148$		0			0
$149$	−4.77392	−	2.29900i	−0.391095	−	0.188341i	0.227994	−	0.973663i	$-0.426783\pi$
$149$	−4.77392	−	2.29900i	−0.391095	−	0.188341i	−0.619088	+	0.785321i	$0.712498\pi$
$150$		0			0
$151$	0.176219	+	0.772066i	0.0143405	+	0.0628298i	0.981592	−	0.190990i	$-0.0611700\pi$
$151$	0.176219	+	0.772066i	0.0143405	+	0.0628298i	−0.967251	+	0.253820i	$0.918313\pi$
$152$		0			0
$153$	−9.39455	+	11.7804i	−0.759504	+	0.952388i
$154$		0			0
$155$	1.86988	+	0.900487i	0.150192	+	0.0723289i
$156$		0			0
$157$	−3.72631			−0.297392			−0.148696	−	0.988883i	$-0.547508\pi$
$157$	−3.72631			−0.297392			−0.148696	+	0.988883i	$0.547508\pi$
$158$		0			0
$159$	−5.48910	−	24.0493i	−0.435314	−	1.90723i
$160$		0			0
$161$	−3.63623	−	4.55969i	−0.286575	−	0.359354i
$162$		0			0
$163$	0.322571	+	0.404491i	0.0252657	+	0.0316822i	0.794304	−	0.607521i	$-0.207836\pi$
$163$	0.322571	+	0.404491i	0.0252657	+	0.0316822i	−0.769038	+	0.639203i	$0.779264\pi$
$164$		0			0
$165$	−2.87224	+	3.60168i	−0.223604	+	0.280390i
$166$		0			0
$167$	22.8684	−	11.0128i	1.76961	−	0.852198i	0.802982	−	0.596004i	$-0.203246\pi$
$167$	22.8684	−	11.0128i	1.76961	−	0.852198i	0.966625	−	0.256194i	$-0.0824686\pi$
$168$		0			0
$169$	−1.39642	+	6.11811i	−0.107417	+	0.470624i
$170$		0			0
$171$	−15.8989	+	7.65651i	−1.21582	+	0.585508i
$172$		0			0
$173$	13.0345			0.990996			0.495498	−	0.868609i	$-0.334986\pi$
$173$	13.0345			0.990996			0.495498	+	0.868609i	$0.334986\pi$
$174$		0			0
$175$	−6.02927			−0.455770
$176$		0			0
$177$	1.19535	−	0.575649i	0.0898477	−	0.0432684i
$178$		0			0
$179$	1.52987	−	6.70281i	0.114348	−	0.500991i	−0.885024	−	0.465546i	$-0.845858\pi$
$179$	1.52987	−	6.70281i	0.114348	−	0.500991i	0.999372	−	0.0354453i	$-0.0112849\pi$
$180$		0			0
$181$	19.6454	−	9.46073i	1.46023	−	0.703210i	0.475893	−	0.879503i	$-0.342125\pi$
$181$	19.6454	−	9.46073i	1.46023	−	0.703210i	0.984338	+	0.176293i	$0.0564106\pi$
$182$		0			0
$183$	−8.99128	+	11.2747i	−0.664654	+	0.833450i
$184$		0			0
$185$	−0.234087	−	0.293536i	−0.0172104	−	0.0215812i
$186$		0			0
$187$	8.71800	+	10.9320i	0.637523	+	0.799429i
$188$		0			0
$189$	−1.26545	−	5.54432i	−0.0920483	−	0.403290i
$190$		0			0
$191$	−12.6291			−0.913809			−0.456905	−	0.889516i	$-0.651042\pi$
$191$	−12.6291			−0.913809			−0.456905	+	0.889516i	$0.651042\pi$
$192$		0			0
$193$	7.44152	+	3.58365i	0.535653	+	0.257957i	0.682096	−	0.731262i	$-0.261068\pi$
$193$	7.44152	+	3.58365i	0.535653	+	0.257957i	−0.146444	+	0.989219i	$0.546783\pi$
$194$		0			0
$195$	−2.91983	+	3.66135i	−0.209094	+	0.262195i
$196$		0			0
$197$	−5.67585	−	24.8675i	−0.404387	−	1.77174i	−0.609283	−	0.792953i	$-0.708543\pi$
$197$	−5.67585	−	24.8675i	−0.404387	−	1.77174i	0.204895	−	0.978784i	$-0.434315\pi$
$198$		0			0
$199$	−1.92918	−	0.929046i	−0.136756	−	0.0658583i	0.364254	−	0.931300i	$-0.381324\pi$
$199$	−1.92918	−	0.929046i	−0.136756	−	0.0658583i	−0.501010	+	0.865441i	$0.667038\pi$
$200$		0			0
$201$	0.864680	−	3.78841i	0.0609898	−	0.267214i
$202$		0			0
$203$	6.41917	−	1.89380i	0.450537	−	0.132918i
$204$		0			0
$205$	0.587952	−	2.57599i	0.0410644	−	0.179915i
$206$		0			0
$207$	19.6768	+	9.47585i	1.36763	+	0.658617i
$208$		0			0
$209$	3.64392	+	15.9651i	0.252055	+	1.10433i
$210$		0			0
$211$	−10.1683	+	12.7507i	−0.700017	+	0.877794i	−0.997025	−	0.0770811i	$-0.975440\pi$
$211$	−10.1683	+	12.7507i	−0.700017	+	0.877794i	0.297007	+	0.954875i	$0.404011\pi$
$212$		0			0
$213$	22.5273	+	10.8486i	1.54355	+	0.743333i
$214$		0			0
$215$	−4.86826			−0.332013
$216$		0			0
$217$	1.48866	+	6.52223i	0.101057	+	0.442758i
$218$		0			0
$219$	15.4723	+	19.4017i	1.04552	+	1.31104i
$220$		0			0
$221$	8.86245	+	11.1132i	0.596153	+	0.747552i
$222$		0			0
$223$	−4.60856	+	5.77895i	−0.308612	+	0.386987i	−0.911816	−	0.410600i	$-0.865319\pi$
$223$	−4.60856	+	5.77895i	−0.308612	+	0.386987i	0.603204	+	0.797587i	$0.293891\pi$
$224$		0			0
$225$	20.3421	−	9.79626i	1.35614	−	0.653084i
$226$		0			0
$227$	−6.19972	+	27.1627i	−0.411490	+	1.80285i	0.165621	+	0.986189i	$0.447037\pi$
$227$	−6.19972	+	27.1627i	−0.411490	+	1.80285i	−0.577111	+	0.816666i	$0.695820\pi$
$228$		0			0
$229$	−9.85742	+	4.74708i	−0.651397	+	0.313696i	−0.730240	−	0.683191i	$-0.760592\pi$
$229$	−9.85742	+	4.74708i	−0.651397	+	0.313696i	0.0788431	+	0.996887i	$0.474877\pi$
$230$		0			0
$231$	−14.8495			−0.977023
$232$		0			0
$233$	22.6821			1.48596			0.742978	−	0.669316i	$-0.233413\pi$
$233$	22.6821			1.48596			0.742978	+	0.669316i	$0.233413\pi$
$234$		0			0
$235$	1.26093	−	0.607232i	0.0822540	−	0.0396114i
$236$		0			0
$237$	−8.30920	+	36.4050i	−0.539741	+	2.36476i
$238$		0			0
$239$	−17.2072	+	8.28655i	−1.11304	+	0.536012i	−0.897736	−	0.440534i	$-0.854789\pi$
$239$	−17.2072	+	8.28655i	−1.11304	+	0.536012i	−0.215305	+	0.976547i	$0.569075\pi$
$240$		0			0
$241$	11.6239	−	14.5759i	0.748761	−	0.938916i	−0.250815	−	0.968035i	$-0.580699\pi$
$241$	11.6239	−	14.5759i	0.748761	−	0.938916i	0.999576	+	0.0291186i	$0.00927006\pi$
$242$		0			0
$243$	−10.8056	−	13.5498i	−0.693180	−	0.869220i
$244$		0			0
$245$	−1.31142	−	1.64447i	−0.0837836	−	0.105061i
$246$		0			0
$247$	3.70430	+	16.2296i	0.235699	+	1.03266i
$248$		0			0
$249$	47.2192			2.99239
$250$		0			0
$251$	1.76123	+	0.848164i	0.111168	+	0.0535356i	0.488641	−	0.872485i	$-0.337493\pi$
$251$	1.76123	+	0.848164i	0.111168	+	0.0535356i	−0.377473	+	0.926020i	$0.623207\pi$
$252$		0			0
$253$	12.6362	−	15.8452i	0.794428	−	0.996182i
$254$		0			0
$255$	0.768457	+	3.36683i	0.0481226	+	0.210839i
$256$		0			0
$257$	−15.0110	−	7.22890i	−0.936359	−	0.450926i	−0.0974753	−	0.995238i	$-0.531077\pi$
$257$	−15.0110	−	7.22890i	−0.936359	−	0.450926i	−0.838883	+	0.544311i	$0.816791\pi$
$258$		0			0
$259$	0.269301	−	1.17989i	0.0167336	−	0.0733145i
$260$		0			0
$261$	−18.5806	+	16.8192i	−1.15011	+	1.04108i
$262$		0			0
$263$	1.08952	−	4.77350i	0.0671827	−	0.294347i	−0.930164	−	0.367144i	$-0.880336\pi$
$263$	1.08952	−	4.77350i	0.0671827	−	0.294347i	0.997347	+	0.0727976i	$0.0231927\pi$
$264$		0			0
$265$	−3.09727	−	1.49157i	−0.190264	−	0.0916262i
$266$		0			0
$267$	−3.34027	−	14.6347i	−0.204421	−	0.895628i
$268$		0			0
$269$	6.47794	−	8.12308i	0.394967	−	0.495273i	−0.544094	−	0.839025i	$-0.683126\pi$
$269$	6.47794	−	8.12308i	0.394967	−	0.495273i	0.939061	+	0.343751i	$0.111698\pi$
$270$		0			0
$271$	3.50572	+	1.68827i	0.212957	+	0.102555i	0.537322	−	0.843377i	$-0.319436\pi$
$271$	3.50572	+	1.68827i	0.212957	+	0.102555i	−0.324364	+	0.945932i	$0.605150\pi$
$272$		0			0
$273$	−15.0955			−0.913622
$274$		0			0
$275$	−4.66228	−	20.4268i	−0.281146	−	1.23178i
$276$		0			0
$277$	−10.4374	−	13.0881i	−0.627122	−	0.786386i	0.362205	−	0.932099i	$-0.382024\pi$
$277$	−10.4374	−	13.0881i	−0.627122	−	0.786386i	−0.989327	+	0.145712i	$0.953453\pi$
$278$		0			0
$279$	−15.6198	−	19.5866i	−0.935132	−	1.17262i
$280$		0			0
$281$	−1.63133	+	2.04563i	−0.0973171	+	0.122032i	−0.828105	−	0.560572i	$-0.810581\pi$
$281$	−1.63133	+	2.04563i	−0.0973171	+	0.122032i	0.730788	+	0.682604i	$0.239153\pi$
$282$		0			0
$283$	−20.7856	+	10.0098i	−1.23558	+	0.595023i	−0.933609	−	0.358295i	$-0.883358\pi$
$283$	−20.7856	+	10.0098i	−1.23558	+	0.595023i	−0.301969	+	0.953318i	$0.597644\pi$
$284$		0			0
$285$	−0.899975	+	3.94305i	−0.0533099	+	0.233566i
$286$		0			0
$287$	7.67362	−	3.69542i	0.452960	−	0.218134i
$288$		0			0
$289$	−6.51799			−0.383411
$290$		0			0
$291$	40.7722			2.39011
$292$		0			0
$293$	2.46322	−	1.18622i	0.143903	−	0.0692999i	−0.360547	−	0.932741i	$-0.617410\pi$
$293$	2.46322	−	1.18622i	0.143903	−	0.0692999i	0.504449	+	0.863441i	$0.331696\pi$
$294$		0			0
$295$	0.0411428	−	0.180258i	0.00239543	−	0.0104951i
$296$		0			0
$297$	17.8053	−	8.57457i	1.03317	−	0.497547i
$298$		0			0
$299$	12.8455	−	16.1078i	0.742876	−	0.931537i
$300$		0			0
$301$	−9.78413	−	12.2689i	−0.563948	−	0.707169i
$302$		0			0
$303$	−10.5820	−	13.2694i	−0.607919	−	0.762306i
$304$		0			0
$305$	0.447200	+	1.95931i	0.0256066	+	0.112190i
$306$		0			0
$307$	−15.3288			−0.874859			−0.437429	−	0.899253i	$-0.644111\pi$
$307$	−15.3288			−0.874859			−0.437429	+	0.899253i	$0.644111\pi$
$308$		0			0
$309$	−48.6239	−	23.4161i	−2.76612	−	1.33209i
$310$		0			0
$311$	−7.57119	+	9.49397i	−0.429323	+	0.538354i	−0.948694	−	0.316195i	$-0.897595\pi$
$311$	−7.57119	+	9.49397i	−0.429323	+	0.538354i	0.519372	+	0.854548i	$0.326166\pi$
$312$		0			0
$313$	−0.947890	−	4.15298i	−0.0535779	−	0.234740i	0.941048	−	0.338273i	$-0.109843\pi$
$313$	−0.947890	−	4.15298i	−0.0535779	−	0.234740i	−0.994626	+	0.103532i	$0.966985\pi$
$314$		0			0
$315$	−2.00918	−	0.967570i	−0.113204	−	0.0545164i
$316$		0			0
$317$	4.69061	−	20.5509i	0.263451	−	1.15425i	−0.654028	−	0.756470i	$-0.726922\pi$
$317$	4.69061	−	20.5509i	0.263451	−	1.15425i	0.917479	−	0.397784i	$-0.130221\pi$
$318$		0			0
$319$	11.3798	+	20.2833i	0.637149	+	1.13565i
$320$		0			0
$321$	−4.42806	+	19.4006i	−0.247150	+	1.08284i
$322$		0			0
$323$	11.0603	+	5.32634i	0.615409	+	0.296365i
$324$		0			0
$325$	−4.73954	−	20.7653i	−0.262902	−	1.15185i
$326$		0			0
$327$	−30.3499	+	38.0576i	−1.67835	+	2.10459i
$328$		0			0
$329$	4.06453	+	1.95737i	0.224085	+	0.107914i
$330$		0			0
$331$	4.72121			0.259501			0.129751	−	0.991547i	$-0.458582\pi$
$331$	4.72121			0.259501			0.129751	+	0.991547i	$0.458582\pi$
$332$		0			0
$333$	1.00846	+	4.41837i	0.0552635	+	0.242125i
$334$		0			0
$335$	−0.337639	−	0.423386i	−0.0184472	−	0.0231321i
$336$		0			0
$337$	−13.2237	−	16.5820i	−0.720343	−	0.903282i	0.278014	−	0.960577i	$-0.410324\pi$
$337$	−13.2237	−	16.5820i	−0.720343	−	0.903282i	−0.998357	+	0.0572952i	$0.981752\pi$
$338$		0			0
$339$	27.8500	−	34.9228i	1.51261	−	1.89675i
$340$		0			0
$341$	−20.9458	+	10.0870i	−1.13428	+	0.546239i
$342$		0			0
$343$	3.44455	−	15.0915i	0.185988	−	0.814867i
$344$		0			0
$345$	4.50979	−	2.17180i	0.242799	−	0.116926i
$346$		0			0
$347$	−13.9042			−0.746416			−0.373208	−	0.927748i	$-0.621742\pi$
$347$	−13.9042			−0.746416			−0.373208	+	0.927748i	$0.621742\pi$
$348$		0			0
$349$	−17.1560			−0.918339			−0.459170	−	0.888349i	$-0.651853\pi$
$349$	−17.1560			−0.918339			−0.459170	+	0.888349i	$0.651853\pi$
$350$		0			0
$351$	18.1003	−	8.71664i	0.966122	−	0.465260i
$352$		0			0
$353$	−4.86393	+	21.3103i	−0.258881	+	1.13423i	0.663569	+	0.748115i	$0.269041\pi$
$353$	−4.86393	+	21.3103i	−0.258881	+	1.13423i	−0.922450	+	0.386116i	$0.873816\pi$
$354$		0			0
$355$	3.13941	−	1.51186i	0.166623	−	0.0802413i
$356$		0			0
$357$	−6.94060	+	8.70324i	−0.367336	+	0.460624i
$358$		0			0
$359$	−8.41601	−	10.5533i	−0.444180	−	0.556984i	0.508459	−	0.861086i	$-0.330215\pi$
$359$	−8.41601	−	10.5533i	−0.444180	−	0.556984i	−0.952640	+	0.304102i	$0.901644\pi$
$360$		0			0
$361$	−2.88244	−	3.61447i	−0.151707	−	0.190235i
$362$		0			0
$363$	−4.71088	−	20.6397i	−0.247257	−	1.08330i
$364$		0			0
$365$	3.45832			0.181017
$366$		0			0
$367$	−6.33495	−	3.05075i	−0.330682	−	0.159248i	0.261174	−	0.965292i	$-0.415890\pi$
$367$	−6.33495	−	3.05075i	−0.330682	−	0.159248i	−0.591856	+	0.806044i	$0.701605\pi$
$368$		0			0
$369$	−19.8858	+	24.9360i	−1.03521	+	1.29811i
$370$		0			0
$371$	−2.46581	−	10.8034i	−0.128018	−	0.560885i
$372$		0			0
$373$	19.8105	+	9.54024i	1.02575	+	0.493975i	0.869599	−	0.493758i	$-0.164377\pi$
$373$	19.8105	+	9.54024i	1.02575	+	0.493975i	0.156150	+	0.987733i	$0.450092\pi$
$374$		0			0
$375$	2.33826	−	10.2446i	0.120747	−	0.529028i
$376$		0			0
$377$	11.5684	+	20.6194i	0.595803	+	1.06195i
$378$		0			0
$379$	−2.75929	+	12.0892i	−0.141735	+	0.620982i	0.853297	+	0.521425i	$0.174599\pi$
$379$	−2.75929	+	12.0892i	−0.141735	+	0.620982i	−0.995032	+	0.0995563i	$0.968258\pi$
$380$		0			0
$381$	15.6252	+	7.52468i	0.800501	+	0.385501i
$382$		0			0
$383$	−1.65775	−	7.26309i	−0.0847072	−	0.371126i	0.914752	−	0.404016i	$-0.132386\pi$
$383$	−1.65775	−	7.26309i	−0.0847072	−	0.371126i	−0.999459	+	0.0328899i	$0.989529\pi$
$384$		0			0
$385$	−1.29027	+	1.61794i	−0.0657581	+	0.0824580i
$386$		0			0
$387$	52.9450	+	25.4970i	2.69135	+	1.29608i
$388$		0			0
$389$	20.3307			1.03081			0.515405	−	0.856947i	$-0.327642\pi$
$389$	20.3307			1.03081			0.515405	+	0.856947i	$0.327642\pi$
$390$		0			0
$391$	−3.38075	−	14.8120i	−0.170972	−	0.749078i
$392$		0			0
$393$	−11.4700	−	14.3829i	−0.578583	−	0.725521i
$394$		0			0
$395$	3.24457	+	4.06856i	0.163252	+	0.204712i
$396$		0			0
$397$	−22.6380	+	28.3871i	−1.13617	+	1.42471i	−0.245888	+	0.969298i	$0.579079\pi$
$397$	−22.6380	+	28.3871i	−1.13617	+	1.42471i	−0.890281	+	0.455412i	$0.849492\pi$
$398$		0			0
$399$	−11.7460	+	5.65655i	−0.588033	+	0.283182i
$400$		0			0
$401$	2.84192	−	12.4513i	0.141919	−	0.621786i	−0.853070	−	0.521797i	$-0.825262\pi$
$401$	2.84192	−	12.4513i	0.141919	−	0.621786i	0.994989	−	0.0999893i	$-0.0318809\pi$
$402$		0			0
$403$	−21.2928	+	10.2541i	−1.06067	+	0.510793i
$404$		0			0
$405$	−0.502149			−0.0249520
$406$		0			0
$407$	4.20563			0.208465
$408$		0			0
$409$	−1.46703	+	0.706482i	−0.0725398	+	0.0349333i	−0.469802	−	0.882772i	$-0.655675\pi$
$409$	−1.46703	+	0.706482i	−0.0725398	+	0.0349333i	0.397262	+	0.917705i	$0.369960\pi$
$410$		0			0
$411$	−1.00562	+	4.40589i	−0.0496033	+	0.217326i
$412$		0			0
$413$	0.536973	−	0.258592i	0.0264227	−	0.0127245i
$414$		0			0
$415$	4.10286	−	5.14482i	0.201401	−	0.252549i
$416$		0			0
$417$	2.73395	+	3.42826i	0.133882	+	0.167883i
$418$		0			0
$419$	12.0710	+	15.1366i	0.589709	+	0.739472i	0.983735	−	0.179628i	$-0.0574894\pi$
$419$	12.0710	+	15.1366i	0.589709	+	0.739472i	−0.394026	+	0.919099i	$0.628918\pi$
$420$		0			0
$421$	5.84710	+	25.6178i	0.284970	+	1.24854i	0.891333	+	0.453349i	$0.149771\pi$
$421$	5.84710	+	25.6178i	0.284970	+	1.24854i	−0.606363	+	0.795188i	$0.707372\pi$
$422$		0			0
$423$	−16.8936			−0.821396
$424$		0			0
$425$	−14.1512	−	6.81488i	−0.686436	−	0.330570i
$426$		0			0
$427$	−4.03906	+	5.06481i	−0.195464	+	0.245104i
$428$		0			0
$429$	−11.6730	−	51.1427i	−0.563577	−	2.46919i
$430$		0			0
$431$	14.8498	+	7.15131i	0.715292	+	0.344466i	0.755881	−	0.654710i	$-0.227209\pi$
$431$	14.8498	+	7.15131i	0.715292	+	0.344466i	−0.0405887	+	0.999176i	$0.512923\pi$
$432$		0			0
$433$	5.17603	−	22.6777i	0.248744	−	1.08982i	−0.684057	−	0.729428i	$-0.739786\pi$
$433$	5.17603	−	22.6777i	0.248744	−	1.08982i	0.932801	−	0.360391i	$-0.117357\pi$
$434$		0			0
$435$	0.358684	+	5.73294i	0.0171976	+	0.274873i
$436$		0			0
$437$	3.95935	−	17.3471i	0.189402	−	0.829822i
$438$		0			0
$439$	−26.9608	−	12.9836i	−1.28677	−	0.619674i	−0.339646	−	0.940553i	$-0.610307\pi$
$439$	−26.9608	−	12.9836i	−1.28677	−	0.619674i	−0.947120	+	0.320879i	$0.896022\pi$
$440$		0			0
$441$	5.64970	+	24.7529i	0.269033	+	1.17871i
$442$		0			0
$443$	9.07555	−	11.3804i	0.431192	−	0.540698i	−0.518006	−	0.855377i	$-0.673325\pi$
$443$	9.07555	−	11.3804i	0.431192	−	0.540698i	0.949198	+	0.314679i	$0.101897\pi$
$444$		0			0
$445$	−1.88478	−	0.907660i	−0.0893469	−	0.0430272i
$446$		0			0
$447$	14.6592			0.693354
$448$		0			0
$449$	3.50431	+	15.3534i	0.165379	+	0.724572i	0.987805	+	0.155699i	$0.0497631\pi$
$449$	3.50431	+	15.3534i	0.165379	+	0.724572i	−0.822426	+	0.568872i	$0.807380\pi$
$450$		0			0
$451$	18.4537	+	23.1402i	0.868950	+	1.08963i
$452$		0			0
$453$	−1.36601	−	1.71293i	−0.0641809	−	0.0804803i
$454$		0			0
$455$	−1.31165	+	1.64475i	−0.0614909	+	0.0771071i
$456$		0			0
$457$	−21.5303	+	10.3684i	−1.00714	+	0.485015i	−0.863357	−	0.504594i	$-0.831642\pi$
$457$	−21.5303	+	10.3684i	−1.00714	+	0.485015i	−0.143787	+	0.989609i	$0.545928\pi$
$458$		0			0
$459$	3.29660	−	14.4434i	0.153872	−	0.674159i
$460$		0			0
$461$	3.98136	−	1.91732i	0.185431	−	0.0892986i	−0.338865	−	0.940835i	$-0.610043\pi$
$461$	3.98136	−	1.91732i	0.185431	−	0.0892986i	0.524296	+	0.851536i	$0.324329\pi$
$462$		0			0
$463$	−28.6300			−1.33055			−0.665275	−	0.746599i	$-0.731686\pi$
$463$	−28.6300			−1.33055			−0.665275	+	0.746599i	$0.731686\pi$
$464$		0			0
$465$	−5.74180			−0.266269
$466$		0			0
$467$	23.3452	−	11.2425i	1.08029	−	0.520240i	0.192880	−	0.981222i	$-0.438217\pi$
$467$	23.3452	−	11.2425i	1.08029	−	0.520240i	0.887409	+	0.460983i	$0.152503\pi$
$468$		0			0
$469$	0.388431	−	1.70183i	0.0179361	−	0.0785831i
$470$		0			0
$471$	9.28821	−	4.47297i	0.427978	−	0.206103i
$472$		0			0
$473$	34.0005	−	42.6353i	1.56335	−	1.96037i
$474$		0			0
$475$	−11.4690	−	14.3817i	−0.526233	−	0.659875i
$476$		0			0
$477$	25.8726	+	32.4432i	1.18463	+	1.48547i
$478$		0			0
$479$	1.49722	+	6.55975i	0.0684097	+	0.299723i	0.997546	−	0.0700150i	$-0.0223047\pi$
$479$	1.49722	+	6.55975i	0.0684097	+	0.299723i	−0.929136	+	0.369738i	$0.879448\pi$
$480$		0			0
$481$	4.27531			0.194937
$482$		0			0
$483$	14.5370	+	7.00067i	0.661458	+	0.318541i
$484$		0			0
$485$	3.54269	−	4.44239i	0.160865	−	0.201718i
$486$		0			0
$487$	−5.50826	−	24.1333i	−0.249603	−	1.09358i	−0.931959	−	0.362563i	$-0.881902\pi$
$487$	−5.50826	−	24.1333i	−0.249603	−	1.09358i	0.682356	−	0.731020i	$-0.260955\pi$
$488$		0			0
$489$	−1.28958	−	0.621030i	−0.0583169	−	0.0280839i
$490$		0			0
$491$	3.41952	−	14.9819i	0.154321	−	0.676124i	−0.837279	−	0.546777i	$-0.815855\pi$
$491$	3.41952	−	14.9819i	0.154321	−	0.676124i	0.991599	−	0.129347i	$-0.0412881\pi$
$492$		0			0
$493$	17.2069	+	2.81067i	0.774961	+	0.126586i
$494$		0			0
$495$	1.72442	−	7.55518i	0.0775070	−	0.339580i
$496$		0			0
$497$	10.1197	+	4.87339i	0.453931	+	0.218602i
$498$		0			0
$499$	2.91456	+	12.7695i	0.130474	+	0.571643i	0.997326	+	0.0730780i	$0.0232822\pi$
$499$	2.91456	+	12.7695i	0.130474	+	0.571643i	−0.866853	+	0.498565i	$0.833861\pi$
$500$		0			0
$501$	−43.7823	+	54.9012i	−1.95605	+	2.45281i
$502$		0			0
$503$	8.16582	+	3.93245i	0.364096	+	0.175339i	0.606982	−	0.794715i	$-0.292380\pi$
$503$	8.16582	+	3.93245i	0.364096	+	0.175339i	−0.242886	+	0.970055i	$0.578094\pi$
$504$		0			0
$505$	−2.36525			−0.105252
$506$		0			0
$507$	−3.86331	−	16.9263i	−0.171576	−	0.751722i
$508$		0			0
$509$	−3.02513	−	3.79339i	−0.134087	−	0.168139i	0.710255	−	0.703944i	$-0.248580\pi$
$509$	−3.02513	−	3.79339i	−0.134087	−	0.168139i	−0.844342	+	0.535805i	$0.820008\pi$
$510$		0			0
$511$	6.95046	+	8.71560i	0.307470	+	0.385555i
$512$		0			0
$513$	10.8177	−	13.5650i	0.477614	−	0.598909i
$514$		0			0
$515$	−6.77625	+	3.26327i	−0.298597	+	0.143797i
$516$		0			0
$517$	−3.48847	+	15.2840i	−0.153423	+	0.672188i
$518$		0			0
$519$	−32.4899	+	15.6463i	−1.42615	+	0.686797i
$520$		0			0
$521$	−25.5713			−1.12030			−0.560150	−	0.828391i	$-0.689257\pi$
$521$	−25.5713			−1.12030			−0.560150	+	0.828391i	$0.689257\pi$
$522$		0			0
$523$	13.8459			0.605439			0.302719	−	0.953080i	$-0.402105\pi$
$523$	13.8459			0.605439			0.302719	+	0.953080i	$0.402105\pi$
$524$		0			0
$525$	15.0286	−	7.23738i	0.655901	−	0.315865i
$526$		0			0
$527$	−3.87806	+	16.9909i	−0.168931	+	0.740135i
$528$		0			0
$529$	0.881876	−	0.424689i	0.0383424	−	0.0184647i
$530$		0			0
$531$	−1.39154	+	1.74493i	−0.0603875	+	0.0757235i
$532$		0			0
$533$	18.7595	+	23.5236i	0.812562	+	1.01892i
$534$		0			0
$535$	1.72907	+	2.16818i	0.0747540	+	0.0937386i
$536$		0			0
$537$	4.23252	+	18.5439i	0.182647	+	0.800227i
$538$		0			0
$539$	23.5611			1.01485
$540$		0			0
$541$	25.8496	+	12.4485i	1.11136	+	0.535202i	0.897213	−	0.441599i	$-0.145589\pi$
$541$	25.8496	+	12.4485i	1.11136	+	0.535202i	0.214147	+	0.976801i	$0.431303\pi$
$542$		0			0
$543$	−37.6118	+	47.1637i	−1.61408	+	2.02399i
$544$		0			0
$545$	1.50952	+	6.61363i	0.0646606	+	0.283297i
$546$		0			0
$547$	−11.4293	−	5.50404i	−0.488680	−	0.235336i	0.173283	−	0.984872i	$-0.444562\pi$
$547$	−11.4293	−	5.50404i	−0.488680	−	0.235336i	−0.661963	+	0.749536i	$0.730277\pi$
$548$		0			0
$549$	5.39813	−	23.6508i	0.230387	−	1.00939i
$550$		0			0
$551$	16.7279	+	11.7093i	0.712634	+	0.498832i
$552$		0			0
$553$	−3.73265	+	16.3538i	−0.158729	+	0.695436i
$554$		0			0
$555$	0.935840	+	0.450677i	0.0397242	+	0.0191302i
$556$		0			0
$557$	−1.65014	−	7.22972i	−0.0699185	−	0.306333i	0.927862	−	0.372924i	$-0.121645\pi$
$557$	−1.65014	−	7.22972i	−0.0699185	−	0.306333i	−0.997780	+	0.0665911i	$0.978788\pi$
$558$		0			0
$559$	34.5639	−	43.3418i	1.46190	−	1.83316i
$560$		0			0
$561$	−34.8531	−	16.7844i	−1.47150	−	0.708636i
$562$		0			0
$563$	21.1847			0.892828			0.446414	−	0.894826i	$-0.352701\pi$
$563$	21.1847			0.892828			0.446414	+	0.894826i	$0.352701\pi$
$564$		0			0
$565$	−1.38518	−	6.06887i	−0.0582750	−	0.255319i
$566$		0			0
$567$	−1.00921	−	1.26551i	−0.0423828	−	0.0531464i
$568$		0			0
$569$	5.04098	+	6.32119i	0.211329	+	0.264998i	0.876187	−	0.481972i	$-0.160079\pi$
$569$	5.04098	+	6.32119i	0.211329	+	0.264998i	−0.664858	+	0.746970i	$0.731508\pi$
$570$		0			0
$571$	−4.48746	+	5.62709i	−0.187794	+	0.235487i	−0.866812	−	0.498636i	$-0.833835\pi$
$571$	−4.48746	+	5.62709i	−0.187794	+	0.235487i	0.679017	+	0.734122i	$0.262406\pi$
$572$		0			0
$573$	31.4793	−	15.1597i	1.31507	−	0.633304i
$574$		0			0
$575$	−5.06587	+	22.1950i	−0.211261	+	0.925596i
$576$		0			0
$577$	17.9872	−	8.66219i	0.748818	−	0.360612i	−0.0202362	−	0.999795i	$-0.506442\pi$
$577$	17.9872	−	8.66219i	0.748818	−	0.360612i	0.769054	+	0.639183i	$0.220728\pi$
$578$		0			0
$579$	−22.8505			−0.949635
$580$		0			0
$581$	21.2118			0.880012
$582$		0			0
$583$	34.6946	−	16.7080i	1.43690	−	0.691976i
$584$		0			0
$585$	1.75299	−	7.68037i	0.0724774	−	0.317544i
$586$		0			0
$587$	−0.676730	+	0.325896i	−0.0279316	+	0.0134512i	−0.447797	−	0.894135i	$-0.647791\pi$
$587$	−0.676730	+	0.325896i	−0.0279316	+	0.0134512i	0.419866	+	0.907586i	$0.362077\pi$
$588$		0			0
$589$	−12.7258	+	15.9576i	−0.524356	+	0.657521i
$590$		0			0
$591$	43.9980	+	55.1717i	1.80984	+	2.26946i
$592$		0			0
$593$	−27.0071	−	33.8658i	−1.10905	−	1.39070i	−0.911941	−	0.410321i	$-0.865417\pi$
$593$	−27.0071	−	33.8658i	−1.10905	−	1.39070i	−0.197108	−	0.980382i	$-0.563155\pi$
$594$		0			0
$595$	0.345206	+	1.51244i	0.0141521	+	0.0620042i
$596$		0			0
$597$	5.92390			0.242449
$598$		0			0
$599$	4.46369	+	2.14960i	0.182381	+	0.0878303i	0.522846	−	0.852427i	$-0.324870\pi$
$599$	4.46369	+	2.14960i	0.182381	+	0.0878303i	−0.340465	+	0.940257i	$0.610584\pi$
$600$		0			0
$601$	−28.8591	+	36.1882i	−1.17719	+	1.47615i	−0.330705	+	0.943734i	$0.607286\pi$
$601$	−28.8591	+	36.1882i	−1.17719	+	1.47615i	−0.846484	+	0.532414i	$0.821285\pi$
$602$		0			0
$603$	1.45458	+	6.37291i	0.0592349	+	0.259525i
$604$		0			0
$605$	−2.65815	−	1.28010i	−0.108069	−	0.0520434i
$606$		0			0
$607$	5.90692	−	25.8799i	0.239755	−	1.05043i	−0.701482	−	0.712687i	$-0.747478\pi$
$607$	5.90692	−	25.8799i	0.239755	−	1.05043i	0.941237	−	0.337747i	$-0.109665\pi$
$608$		0			0
$609$	−13.7272	+	12.4259i	−0.556253	+	0.503523i
$610$		0			0
$611$	−3.54627	+	15.5372i	−0.143467	+	0.628569i
$612$		0			0
$613$	−38.6837	−	18.6291i	−1.56242	−	0.752421i	−0.565060	−	0.825050i	$-0.691147\pi$
$613$	−38.6837	−	18.6291i	−1.56242	−	0.752421i	−0.997359	+	0.0726285i	$0.976861\pi$
$614$		0			0
$615$	1.62662	+	7.12668i	0.0655916	+	0.287376i
$616$		0			0
$617$	−15.7081	+	19.6974i	−0.632386	+	0.792987i	−0.990028	−	0.140872i	$-0.955009\pi$
$617$	−15.7081	+	19.6974i	−0.632386	+	0.792987i	0.357642	+	0.933859i	$0.383581\pi$
$618$		0			0
$619$	4.73330	+	2.27944i	0.190247	+	0.0916183i	0.526582	−	0.850124i	$-0.323473\pi$
$619$	4.73330	+	2.27944i	0.190247	+	0.0916183i	−0.336335	+	0.941742i	$0.609187\pi$
$620$		0			0
$621$	−21.4731			−0.861684
$622$		0			0
$623$	−1.50051	−	6.57418i	−0.0601168	−	0.263389i
$624$		0			0
$625$	14.2108	+	17.8198i	0.568432	+	0.712791i
$626$		0			0
$627$	−28.2469	−	35.4205i	−1.12807	−	1.41456i
$628$		0			0
$629$	1.96570	−	2.46491i	0.0783776	−	0.0982824i
$630$		0			0
$631$	6.32111	−	3.04408i	0.251639	−	0.121183i	−0.303812	−	0.952732i	$-0.598260\pi$
$631$	6.32111	−	3.04408i	0.251639	−	0.121183i	0.555452	+	0.831549i	$0.312545\pi$
$632$		0			0
$633$	10.0400	−	43.9883i	0.399056	−	1.74838i
$634$		0			0
$635$	2.17753	−	1.04864i	0.0864125	−	0.0416141i
$636$		0			0
$637$	23.9515			0.948992
$638$		0			0
$639$	−42.0611			−1.66391
$640$		0			0
$641$	−21.2886	+	10.2520i	−0.840848	+	0.404931i	−0.804172	−	0.594396i	$-0.797391\pi$
$641$	−21.2886	+	10.2520i	−0.840848	+	0.404931i	−0.0366754	+	0.999327i	$0.511677\pi$
$642$		0			0
$643$	−2.71261	+	11.8847i	−0.106975	+	0.468688i	0.892857	+	0.450341i	$0.148698\pi$
$643$	−2.71261	+	11.8847i	−0.106975	+	0.468688i	−0.999832	+	0.0183471i	$0.994160\pi$
$644$		0			0
$645$	12.1346	−	5.84374i	0.477801	−	0.230097i
$646$		0			0
$647$	−13.0903	+	16.4147i	−0.514631	+	0.645327i	−0.969459	−	0.245252i	$-0.921129\pi$
$647$	−13.0903	+	16.4147i	−0.514631	+	0.645327i	0.454828	+	0.890579i	$0.349701\pi$
$648$		0			0
$649$	1.29132	+	1.61927i	0.0506889	+	0.0635618i
$650$		0			0
$651$	−11.5397	−	14.4704i	−0.452278	−	0.567139i
$652$		0			0
$653$	7.36904	+	32.2859i	0.288373	+	1.26344i	0.886758	+	0.462235i	$0.152952\pi$
$653$	7.36904	+	32.2859i	0.288373	+	1.26344i	−0.598385	+	0.801209i	$0.704191\pi$
$654$		0			0
$655$	−2.56373			−0.100173
$656$		0			0
$657$	−37.6111	−	18.1126i	−1.46735	−	0.706638i
$658$		0			0
$659$	17.5622	−	22.0223i	0.684127	−	0.857869i	−0.311600	−	0.950213i	$-0.600865\pi$
$659$	17.5622	−	22.0223i	0.684127	−	0.857869i	0.995727	+	0.0923447i	$0.0294362\pi$
$660$		0			0
$661$	−7.79277	−	34.1424i	−0.303104	−	1.32798i	−0.865414	−	0.501058i	$-0.832944\pi$
$661$	−7.79277	−	34.1424i	−0.303104	−	1.32798i	0.562310	−	0.826927i	$-0.309913\pi$
$662$		0			0
$663$	−35.4306	−	17.0625i	−1.37601	−	0.662651i
$664$		0			0
$665$	−0.404286	+	1.77129i	−0.0156775	+	0.0686878i
$666$		0			0
$667$	−1.57800	−	25.2215i	−0.0611003	−	0.976581i
$668$		0			0
$669$	4.55041	−	19.9366i	0.175929	−	0.770795i
$670$		0			0
$671$	−20.2826	−	9.76758i	−0.783001	−	0.377073i
$672$		0			0
$673$	3.24473	+	14.2161i	0.125075	+	0.547990i	0.998172	+	0.0604429i	$0.0192513\pi$
$673$	3.24473	+	14.2161i	0.125075	+	0.547990i	−0.873096	+	0.487548i	$0.837892\pi$
$674$		0			0
$675$	−13.8409	+	17.3560i	−0.532738	+	0.668032i
$676$		0			0
$677$	−10.4265	−	5.02115i	−0.400724	−	0.192979i	0.222657	−	0.974897i	$-0.428527\pi$
$677$	−10.4265	−	5.02115i	−0.400724	−	0.192979i	−0.623381	+	0.781918i	$0.714241\pi$
$678$		0			0
$679$	18.3157			0.702891
$680$		0			0
$681$	−17.1520	−	75.1480i	−0.657268	−	2.87968i
$682$		0			0
$683$	−16.6389	−	20.8645i	−0.636668	−	0.798356i	0.353914	−	0.935278i	$-0.384851\pi$
$683$	−16.6389	−	20.8645i	−0.636668	−	0.798356i	−0.990582	+	0.136922i	$0.956279\pi$
$684$		0			0
$685$	0.392672	+	0.492395i	0.0150032	+	0.0188134i
$686$		0			0
$687$	18.8724	−	23.6652i	0.720026	−	0.902884i
$688$		0			0
$689$	35.2694	−	16.9849i	1.34366	−	0.647072i
$690$		0			0
$691$	−3.73629	+	16.3698i	−0.142135	+	0.622736i	0.852802	+	0.522235i	$0.174902\pi$
$691$	−3.73629	+	16.3698i	−0.142135	+	0.622736i	−0.994937	+	0.100501i	$0.967956\pi$
$692$		0			0
$693$	22.5062	−	10.8384i	0.854939	−	0.411717i
$694$		0			0
$695$	0.611083			0.0231797
$696$		0			0
$697$	22.1876			0.840416
$698$		0			0
$699$	−56.5376	+	27.2271i	−2.13845	+	1.02982i
$700$		0			0
$701$	5.47847	−	24.0028i	0.206919	−	0.906572i	−0.759684	−	0.650293i	$-0.774646\pi$
$701$	5.47847	−	24.0028i	0.206919	−	0.906572i	0.966603	−	0.256279i	$-0.0824966\pi$
$702$		0			0
$703$	3.32666	−	1.60203i	0.125467	−	0.0604219i
$704$		0			0
$705$	−2.41409	+	3.02718i	−0.0909200	+	0.114010i
$706$		0			0
$707$	−4.75363	−	5.96086i	−0.178779	−	0.224181i
$708$		0			0
$709$	16.6918	+	20.9308i	0.626873	+	0.786073i	0.989293	−	0.145941i	$-0.0466211\pi$
$709$	16.6918	+	20.9308i	0.626873	+	0.786073i	−0.362421	+	0.932015i	$0.618050\pi$
$710$		0			0
$711$	−13.9778	−	61.2409i	−0.524210	−	2.29671i
$712$		0			0
$713$	25.2605			0.946013
$714$		0			0
$715$	−6.58658	−	3.17193i	−0.246324	−	0.118623i
$716$		0			0
$717$	32.9438	−	41.3102i	1.23031	−	1.54276i
$718$		0			0
$719$	2.17372	+	9.52369i	0.0810661	+	0.355174i	0.999150	−	0.0412113i	$-0.0131217\pi$
$719$	2.17372	+	9.52369i	0.0810661	+	0.355174i	−0.918084	+	0.396385i	$0.870265\pi$
$720$		0			0
$721$	−21.8428	−	10.5189i	−0.813469	−	0.391746i
$722$		0			0
$723$	−11.4772	+	50.2850i	−0.426842	+	1.87012i
$724$		0			0
$725$	−21.4029	−	14.9816i	−0.794883	−	0.556404i
$726$		0			0
$727$	−0.566976	+	2.48409i	−0.0210280	+	0.0921296i	−0.984353	−	0.176208i	$-0.943617\pi$
$727$	−0.566976	+	2.48409i	−0.0210280	+	0.0921296i	0.963325	+	0.268337i	$0.0864741\pi$
$728$		0			0
$729$	39.6787	+	19.1082i	1.46958	+	0.707712i
$730$		0			0
$731$	−9.09671	−	39.8553i	−0.336454	−	1.47410i
$732$		0			0
$733$	−24.9774	+	31.3207i	−0.922562	+	1.15686i	0.0647236	+	0.997903i	$0.479383\pi$
$733$	−24.9774	+	31.3207i	−0.922562	+	1.15686i	−0.987286	+	0.158953i	$0.949188\pi$
$734$		0			0
$735$	5.24283	+	2.52482i	0.193385	+	0.0931292i
$736$		0			0
$737$	6.06605			0.223446
$738$		0			0
$739$	2.21949	+	9.72422i	0.0816452	+	0.357711i	0.999204	−	0.0398887i	$-0.0127004\pi$
$739$	2.21949	+	9.72422i	0.0816452	+	0.357711i	−0.917559	+	0.397600i	$0.869843\pi$
$740$		0			0
$741$	−28.7150	−	36.0074i	−1.05487	−	1.32277i
$742$		0			0
$743$	−2.08080	−	2.60924i	−0.0763371	−	0.0957237i	0.742197	−	0.670182i	$-0.233784\pi$
$743$	−2.08080	−	2.60924i	−0.0763371	−	0.0957237i	−0.818534	+	0.574459i	$0.805213\pi$
$744$		0			0
$745$	1.27373	−	1.59721i	0.0466659	−	0.0585171i
$746$		0			0
$747$	−71.5663	+	34.4645i	−2.61848	+	1.26099i
$748$		0			0
$749$	−1.98917	+	8.71513i	−0.0726828	+	0.318444i
$750$		0			0
$751$	−32.5880	+	15.6936i	−1.18915	+	0.572667i	−0.920566	−	0.390588i	$-0.872272\pi$
$751$	−32.5880	+	15.6936i	−1.18915	+	0.572667i	−0.268589	+	0.963255i	$0.586557\pi$
$752$		0			0
$753$	−5.40817			−0.197085
$754$		0			0
$755$	−0.305327			−0.0111120
$756$		0			0
$757$	36.8376	−	17.7401i	1.33889	−	0.644774i	0.379061	−	0.925372i	$-0.376247\pi$
$757$	36.8376	−	17.7401i	1.33889	−	0.644774i	0.959825	+	0.280598i	$0.0905327\pi$
$758$		0			0
$759$	−12.4767	+	54.6641i	−0.452876	+	1.98418i
$760$		0			0
$761$	−12.6501	+	6.09196i	−0.458565	+	0.220833i	−0.648881	−	0.760890i	$-0.724763\pi$
$761$	−12.6501	+	6.09196i	−0.458565	+	0.220833i	0.190316	+	0.981723i	$0.439049\pi$
$762$		0			0
$763$	−13.6338	+	17.0962i	−0.493576	+	0.618924i
$764$		0			0
$765$	−3.62209	−	4.54195i	−0.130957	−	0.164215i
$766$		0			0
$767$	1.31272	+	1.64610i	0.0473996	+	0.0594372i
$768$		0			0
$769$	6.59597	+	28.8988i	0.237857	+	1.04212i	0.942932	+	0.332986i	$0.108056\pi$
$769$	6.59597	+	28.8988i	0.237857	+	1.04212i	−0.705075	+	0.709133i	$0.749087\pi$
$770$		0			0
$771$	46.0938			1.66003
$772$		0			0
$773$	35.1868	+	16.9451i	1.26558	+	0.609471i	0.941645	−	0.336608i	$-0.109280\pi$
$773$	35.1868	+	16.9451i	1.26558	+	0.609471i	0.323935	+	0.946079i	$0.394994\pi$
$774$		0			0
$775$	16.2822	−	20.4172i	0.584874	−	0.733409i
$776$		0			0
$777$	0.745044	+	3.26425i	0.0267283	+	0.117104i
$778$		0			0
$779$	23.4116	+	11.2744i	0.838808	+	0.403949i
$780$		0			0
$781$	−8.68545	+	38.0534i	−0.310790	+	1.36166i
$782$		0			0
$783$	9.28448	−	22.8258i	0.331800	−	0.815728i
$784$		0			0
$785$	0.319692	−	1.40066i	0.0114103	−	0.0499918i
$786$		0			0
$787$	−30.7250	−	14.7964i	−1.09523	−	0.527434i	−0.203073	−	0.979164i	$-0.565093\pi$
$787$	−30.7250	−	14.7964i	−1.09523	−	0.527434i	−0.892155	+	0.451729i	$0.850807\pi$
$788$		0			0
$789$	3.01425	+	13.2063i	0.107310	+	0.470156i
$790$		0			0
$791$	12.5108	−	15.6880i	0.444832	−	0.557801i
$792$		0			0
$793$	−20.6187	−	9.92942i	−0.732190	−	0.352604i
$794$		0			0
$795$	9.51071			0.337310
$796$		0			0
$797$	6.19992	+	27.1636i	0.219612	+	0.962185i	0.957765	+	0.287551i	$0.0928411\pi$
$797$	6.19992	+	27.1636i	0.219612	+	0.962185i	−0.738153	+	0.674633i	$0.764302\pi$
$798$		0			0
$799$	7.32740	+	9.18827i	0.259225	+	0.325058i
$800$		0			0
$801$	15.7442	+	19.7426i	0.556294	+	0.697571i
$802$		0			0
$803$	−24.1533	+	30.2873i	−0.852352	+	1.06882i
$804$		0			0
$805$	2.02589	−	0.975615i	0.0714031	−	0.0343859i
$806$		0			0
$807$	−6.39620	+	28.0236i	−0.225157	+	0.986477i
$808$		0			0
$809$	16.4983	−	7.94518i	0.580051	−	0.279338i	−0.120764	−	0.992681i	$-0.538534\pi$
$809$	16.4983	−	7.94518i	0.580051	−	0.279338i	0.700815	+	0.713344i	$0.252820\pi$
$810$		0			0
$811$	48.7533			1.71196			0.855980	−	0.517009i	$-0.172955\pi$
$811$	48.7533			1.71196			0.855980	+	0.517009i	$0.172955\pi$
$812$		0			0
$813$	−10.7649			−0.377542
$814$		0			0
$815$	−0.179716	+	0.0865469i	−0.00629519	+	0.00303161i
$816$		0			0
$817$	10.6536	−	46.6763i	0.372721	−	1.63300i
$818$		0			0
$819$	22.8791	−	11.0180i	0.799460	−	0.384999i
$820$		0			0
$821$	−9.07390	+	11.3783i	−0.316681	+	0.397106i	−0.914540	−	0.404496i	$-0.867447\pi$
$821$	−9.07390	+	11.3783i	−0.316681	+	0.397106i	0.597859	+	0.801602i	$0.296018\pi$
$822$		0			0
$823$	−8.92440	−	11.1908i	−0.311085	−	0.390088i	0.601569	−	0.798821i	$-0.294542\pi$
$823$	−8.92440	−	11.1908i	−0.311085	−	0.390088i	−0.912654	+	0.408732i	$0.865971\pi$
$824$		0			0
$825$	36.1411	+	45.3195i	1.25827	+	1.57782i
$826$		0			0
$827$	3.53943	+	15.5073i	0.123078	+	0.539240i	0.998443	+	0.0557779i	$0.0177639\pi$
$827$	3.53943	+	15.5073i	0.123078	+	0.539240i	−0.875365	+	0.483462i	$0.839379\pi$
$828$		0			0
$829$	−35.5681			−1.23533			−0.617666	−	0.786441i	$-0.711922\pi$
$829$	−35.5681			−1.23533			−0.617666	+	0.786441i	$0.711922\pi$
$830$		0			0
$831$	41.7269	+	20.0946i	1.44749	+	0.697075i
$832$		0			0
$833$	11.0124	−	13.8091i	0.381557	−	0.478457i
$834$		0			0
$835$	2.17760	+	9.54071i	0.0753591	+	0.330170i
$836$		0			0
$837$	22.1924	+	10.6873i	0.767082	+	0.369407i
$838$		0			0
$839$	2.88960	−	12.6601i	0.0997600	−	0.437077i	−0.900239	−	0.435397i	$-0.856608\pi$
$839$	2.88960	−	12.6601i	0.0997600	−	0.437077i	0.999999	−	0.00168008i	$-0.000534787\pi$
$840$		0			0
$841$	27.4927	+	9.22782i	0.948023	+	0.318201i
$842$		0			0
$843$	1.61075	−	7.05715i	0.0554771	−	0.243061i
$844$		0			0
$845$	−2.17991	−	1.04979i	−0.0749910	−	0.0361138i
$846$		0			0
$847$	−2.11622	−	9.27176i	−0.0727141	−	0.318581i
$848$		0			0
$849$	39.7948	−	49.9011i	1.36575	−	1.71260i
$850$		0			0
$851$	−4.11714	−	1.98271i	−0.141134	−	0.0679664i
$852$		0			0
$853$	−3.28244			−0.112389			−0.0561943	−	0.998420i	$-0.517897\pi$
$853$	−3.28244			−0.112389			−0.0561943	+	0.998420i	$0.517897\pi$
$854$		0			0
$855$	−1.51395	−	6.63304i	−0.0517759	−	0.226845i
$856$		0			0
$857$	1.72221	+	2.15959i	0.0588297	+	0.0737701i	0.810376	−	0.585910i	$-0.199263\pi$
$857$	1.72221	+	2.15959i	0.0588297	+	0.0737701i	−0.751546	+	0.659681i	$0.770692\pi$
$858$		0			0
$859$	13.5750	+	17.0226i	0.463174	+	0.580802i	0.957485	−	0.288483i	$-0.0931510\pi$
$859$	13.5750	+	17.0226i	0.463174	+	0.580802i	−0.494311	+	0.869285i	$0.664580\pi$
$860$		0			0
$861$	−14.6914	+	18.4224i	−0.500682	+	0.627835i
$862$		0			0
$863$	−20.3051	+	9.77842i	−0.691194	+	0.332861i	−0.746291	−	0.665620i	$-0.768167\pi$
$863$	−20.3051	+	9.77842i	−0.691194	+	0.332861i	0.0550973	+	0.998481i	$0.482453\pi$
$864$		0			0
$865$	−1.11827	+	4.89948i	−0.0380225	+	0.166587i
$866$		0			0
$867$	16.2468	−	7.82403i	0.551769	−	0.265718i
$868$		0			0
$869$	−58.2922			−1.97743
$870$		0			0
$871$	6.16656			0.208946
$872$		0			0
$873$	−61.7952	+	29.7590i	−2.09145	+	1.00719i
$874$		0			0
$875$	1.05039	−	4.60207i	0.0355097	−	0.155578i
$876$		0			0
$877$	−12.1910	+	5.87086i	−0.411660	+	0.198245i	−0.628239	−	0.778020i	$-0.716224\pi$
$877$	−12.1910	+	5.87086i	−0.411660	+	0.198245i	0.216580	+	0.976265i	$0.430510\pi$
$878$		0			0
$879$	−4.71592	+	5.91358i	−0.159064	+	0.199460i
$880$		0			0
$881$	−28.7883	−	36.0994i	−0.969902	−	1.21622i	−0.976341	−	0.216239i	$-0.930621\pi$
$881$	−28.7883	−	36.0994i	−0.969902	−	1.21622i	0.00643896	−	0.999979i	$-0.497950\pi$
$882$		0			0
$883$	−30.7765	−	38.5925i	−1.03571	−	1.29874i	−0.953262	−	0.302145i	$-0.902297\pi$
$883$	−30.7765	−	38.5925i	−1.03571	−	1.29874i	−0.0824485	−	0.996595i	$-0.526274\pi$
$884$		0			0
$885$	0.113825	+	0.498700i	0.00382619	+	0.0167636i
$886$		0			0
$887$	−11.5191			−0.386772			−0.193386	−	0.981123i	$-0.561947\pi$
$887$	−11.5191			−0.386772			−0.193386	+	0.981123i	$0.561947\pi$
$888$		0			0
$889$	7.01912	+	3.38023i	0.235414	+	0.113369i
$890$		0			0
$891$	3.50707	−	4.39773i	0.117491	−	0.147329i
$892$		0			0
$893$	3.06268	+	13.4185i	0.102489	+	0.449033i
$894$		0			0
$895$	2.38823	+	1.15011i	0.0798299	+	0.0384440i
$896$		0			0
$897$	−12.6834	+	55.5698i	−0.423488	+	1.85542i
$898$		0			0
$899$	−10.9221	+	26.8518i	−0.364272	+	0.895559i
$900$		0			0
$901$	6.42362	−	28.1437i	0.214002	−	0.937602i
$902$		0			0
$903$	39.1153	+	18.8369i	1.30167	+	0.626854i
$904$		0			0
$905$	1.87070	+	8.19608i	0.0621842	+	0.272447i
$906$		0			0
$907$	20.5121	−	25.7213i	0.681092	−	0.854063i	−0.314362	−	0.949303i	$-0.601791\pi$
$907$	20.5121	−	25.7213i	0.681092	−	0.854063i	0.995454	+	0.0952404i	$0.0303620\pi$
$908$		0			0
$909$	25.7234	+	12.3877i	0.853191	+	0.410875i
$910$		0			0
$911$	6.81813			0.225895			0.112947	−	0.993601i	$-0.463971\pi$
$911$	6.81813			0.225895			0.112947	+	0.993601i	$0.463971\pi$
$912$		0			0
$913$	16.4025	+	71.8642i	0.542844	+	2.37836i
$914$		0			0
$915$	−3.46660	−	4.34698i	−0.114602	−	0.143707i
$916$		0			0
$917$	−5.15253	−	6.46107i	−0.170152	−	0.213363i
$918$		0			0
$919$	33.6724	−	42.2238i	1.11075	−	1.39284i	0.200041	−	0.979788i	$-0.435893\pi$
$919$	33.6724	−	42.2238i	1.11075	−	1.39284i	0.910709	−	0.413049i	$-0.135536\pi$
$920$		0			0
$921$	38.2086	−	18.4003i	1.25901	−	0.606310i
$922$		0			0
$923$	−8.82936	+	38.6840i	−0.290622	+	1.27330i
$924$		0			0
$925$	−4.25636	+	2.04975i	−0.139948	+	0.0673955i
$926$		0			0
$927$	90.7865			2.98182
$928$		0			0
$929$	36.8689			1.20963			0.604816	−	0.796366i	$-0.293247\pi$
$929$	36.8689			1.20963			0.604816	+	0.796366i	$0.293247\pi$
$930$		0			0
$931$	18.6369	−	8.97504i	0.610798	−	0.294145i
$932$		0			0
$933$	7.47565	−	32.7530i	0.244742	−	1.07228i
$934$		0			0
$935$	−4.85713	+	2.33907i	−0.158845	+	0.0764958i
$936$		0			0
$937$	13.9331	−	17.4715i	0.455174	−	0.570770i	−0.500297	−	0.865854i	$-0.666776\pi$
$937$	13.9331	−	17.4715i	0.455174	−	0.570770i	0.955472	+	0.295083i	$0.0953474\pi$
$938$		0			0
$939$	7.34785	+	9.21391i	0.239788	+	0.300684i
$940$		0			0
$941$	−12.3009	−	15.4248i	−0.400998	−	0.502835i	0.539805	−	0.841790i	$-0.318498\pi$
$941$	−12.3009	−	15.4248i	−0.400998	−	0.502835i	−0.940803	+	0.338955i	$0.889927\pi$
$942$		0			0
$943$	−7.15616	−	31.3532i	−0.233037	−	1.02100i
$944$		0			0
$945$	2.19259			0.0713251
$946$		0			0
$947$	−53.3193	−	25.6772i	−1.73265	−	0.834398i	−0.985487	−	0.169752i	$-0.945703\pi$
$947$	−53.3193	−	25.6772i	−1.73265	−	0.834398i	−0.747158	−	0.664646i	$-0.768582\pi$
$948$		0			0
$949$	−24.5535	+	30.7891i	−0.797041	+	0.999458i
$950$		0			0
$951$	12.9770	+	56.8558i	0.420807	+	1.84368i
$952$		0			0
$953$	−20.3457	−	9.79796i	−0.659061	−	0.317387i	0.0742904	−	0.997237i	$-0.476331\pi$
$953$	−20.3457	−	9.79796i	−0.659061	−	0.317387i	−0.733352	+	0.679849i	$0.762045\pi$
$954$		0			0
$955$	1.08349	−	4.74709i	0.0350610	−	0.153612i
$956$		0			0
$957$	−52.7131	−	36.8982i	−1.70397	−	1.19275i
$958$		0			0
$959$	−0.451742	+	1.97921i	−0.0145875	+	0.0639120i
$960$		0			0
$961$	1.82330	+	0.878056i	0.0588162	+	0.0283244i
$962$		0			0
$963$	−7.44894	−	32.6360i	−0.240039	−	1.05168i
$964$		0			0
$965$	−1.98547	+	2.48971i	−0.0639147	+	0.0801465i
$966$		0			0
$967$	−7.21451	−	3.47433i	−0.232003	−	0.111727i	0.314271	−	0.949333i	$-0.398240\pi$
$967$	−7.21451	−	3.47433i	−0.232003	−	0.111727i	−0.546274	+	0.837607i	$0.683954\pi$
$968$		0			0
$969$	−33.9624			−1.09103
$970$		0			0
$971$	−3.23087	−	14.1554i	−0.103684	−	0.454268i	−0.999942	−	0.0107362i	$-0.996582\pi$
$971$	−3.23087	−	14.1554i	−0.103684	−	0.454268i	0.896259	−	0.443532i	$-0.146275\pi$
$972$		0			0
$973$	1.22814	+	1.54004i	0.0393724	+	0.0493715i
$974$		0			0
$975$	36.7399	+	46.0704i	1.17662	+	1.47543i
$976$		0			0
$977$	−13.5052	+	16.9350i	−0.432070	+	0.541799i	−0.949434	−	0.313967i	$-0.898342\pi$
$977$	−13.5052	+	16.9350i	−0.432070	+	0.541799i	0.517364	+	0.855766i	$0.326913\pi$
$978$		0			0
$979$	21.1126	−	10.1673i	0.674762	−	0.324948i
$980$		0			0
$981$	18.2213	−	79.8328i	0.581762	−	2.54887i
$982$		0			0
$983$	−8.15480	+	3.92714i	−0.260098	+	0.125256i	−0.559389	−	0.828905i	$-0.688964\pi$
$983$	−8.15480	+	3.92714i	−0.260098	+	0.125256i	0.299291	+	0.954162i	$0.403250\pi$
$984$		0			0
$985$	9.83428			0.313346
$986$		0			0
$987$	−12.4808			−0.397270
$988$		0			0
$989$	−53.3852	+	25.7090i	−1.69755	+	0.817498i
$990$		0			0
$991$	13.0266	−	57.0733i	0.413804	−	1.81299i	−0.151914	−	0.988394i	$-0.548544\pi$
$991$	13.0266	−	57.0733i	0.413804	−	1.81299i	0.565718	−	0.824599i	$-0.308599\pi$
$992$		0			0
$993$	−11.7681	+	5.66722i	−0.373450	+	0.179844i
$994$		0			0
$995$	0.514726	−	0.645446i	0.0163179	−	0.0204620i
$996$		0			0
$997$	4.68915	+	5.88001i	0.148507	+	0.186222i	0.850521	−	0.525942i	$-0.176287\pi$
$997$	4.68915	+	5.88001i	0.148507	+	0.186222i	−0.702014	+	0.712163i	$0.747716\pi$
$998$		0			0
$999$	−2.77823	−	3.48379i	−0.0878994	−	0.110222i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	232.2.m.d.25.1	✓	24
4.3	odd	2		464.2.u.i.257.4		24
29.6	even	14		6728.2.a.bb.1.1		12
29.7	even	7	inner	232.2.m.d.65.1	yes	24
29.23	even	7		6728.2.a.z.1.12		12
116.7	odd	14		464.2.u.i.65.4		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
232.2.m.d.25.1	✓	24	1.1	even	1	trivial
232.2.m.d.65.1	yes	24	29.7	even	7	inner
464.2.u.i.65.4		24	116.7	odd	14
464.2.u.i.257.4		24	4.3	odd	2
6728.2.a.z.1.12		12	29.23	even	7
6728.2.a.bb.1.1		12	29.6	even	14

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:	\( N \)	\(=\)	\( 232 = 2^{3} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	232.m (of order \(7\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.49260 + 1.20038i) q^{3} +(-0.0857933 + 0.375885i) q^{5} +(-1.11973 + 0.539232i) q^{7} +(2.90171 - 3.63863i) q^{9} +O(q^{10})\)	\(q+(-2.49260 + 1.20038i) q^{3} +(-0.0857933 + 0.375885i) q^{5} +(-1.11973 + 0.539232i) q^{7} +(2.90171 - 3.63863i) q^{9} +(-2.69274 - 3.37659i) q^{11} +(-2.73736 - 3.43254i) q^{13} +(-0.237354 - 1.03992i) q^{15} -3.23759 q^{17} +(-3.41620 - 1.64515i) q^{19} +(2.14375 - 2.68818i) q^{21} +(1.04422 + 4.57502i) q^{23} +(4.37092 + 2.10492i) q^{25} +(-1.01823 + 4.46114i) q^{27} +(-5.31473 - 0.868136i) q^{29} +(1.19782 - 5.24800i) q^{31} +(10.7651 + 5.18421i) q^{33} +(-0.106624 - 0.467151i) q^{35} +(-0.607148 + 0.761340i) q^{37} +(10.9435 + 5.27011i) q^{39} -6.85312 q^{41} +(2.80971 + 12.3102i) q^{43} +(1.11876 + 1.40288i) q^{45} +(-2.26323 - 2.83799i) q^{47} +(-3.40141 + 4.26524i) q^{49} +(8.07004 - 3.88633i) q^{51} +(-1.98407 + 8.69278i) q^{53} +(1.50023 - 0.722473i) q^{55} +10.4900 q^{57} -0.479557 q^{59} +(4.69633 - 2.26163i) q^{61} +(-1.28706 + 5.63896i) q^{63} +(1.52509 - 0.734444i) q^{65} +(-0.875730 + 1.09813i) q^{67} +(-8.09456 - 10.1503i) q^{69} +(-5.63489 - 7.06593i) q^{71} +(-1.99597 - 8.74490i) q^{73} -13.4217 q^{75} +(4.83590 + 2.32885i) q^{77} +(8.41539 - 10.5526i) q^{79} +(0.289815 + 1.26976i) q^{81} +(-15.3775 - 7.40539i) q^{83} +(0.277764 - 1.21696i) q^{85} +(14.2896 - 4.21575i) q^{87} +(-1.20736 + 5.28980i) q^{89} +(4.91603 + 2.36743i) q^{91} +(3.31387 + 14.5190i) q^{93} +(0.911476 - 1.14295i) q^{95} +(-13.2779 - 6.39431i) q^{97} -20.0997 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - q^{3} - 8 q^{5} + 5 q^{7} - 3 q^{9}+O(q^{10}) \) 24 * q - q^3 - 8 * q^5 + 5 * q^7 - 3 * q^9	\( 24 q - q^{3} - 8 q^{5} + 5 q^{7} - 3 q^{9} - 6 q^{11} + q^{13} - q^{15} - 16 q^{17} - 10 q^{19} - 5 q^{21} + 11 q^{23} + 10 q^{25} - 7 q^{27} - 2 q^{29} + 12 q^{31} + 13 q^{33} - 8 q^{35} + q^{37} + 34 q^{39} - 22 q^{41} + 3 q^{43} + 60 q^{45} + 9 q^{47} - 67 q^{49} - q^{51} + 19 q^{53} - 88 q^{55} - 2 q^{57} + 114 q^{59} - 11 q^{61} - 108 q^{63} + 8 q^{65} - 25 q^{67} - 84 q^{69} - 21 q^{71} + 30 q^{73} - 26 q^{75} - 22 q^{77} + 48 q^{79} + 16 q^{81} - 37 q^{83} + 8 q^{85} + 11 q^{87} - 5 q^{89} - 11 q^{91} - 18 q^{93} - 21 q^{95} + 35 q^{97} + 32 q^{99}+O(q^{100}) \) 24 * q - q^3 - 8 * q^5 + 5 * q^7 - 3 * q^9 - 6 * q^11 + q^13 - q^15 - 16 * q^17 - 10 * q^19 - 5 * q^21 + 11 * q^23 + 10 * q^25 - 7 * q^27 - 2 * q^29 + 12 * q^31 + 13 * q^33 - 8 * q^35 + q^37 + 34 * q^39 - 22 * q^41 + 3 * q^43 + 60 * q^45 + 9 * q^47 - 67 * q^49 - q^51 + 19 * q^53 - 88 * q^55 - 2 * q^57 + 114 * q^59 - 11 * q^61 - 108 * q^63 + 8 * q^65 - 25 * q^67 - 84 * q^69 - 21 * q^71 + 30 * q^73 - 26 * q^75 - 22 * q^77 + 48 * q^79 + 16 * q^81 - 37 * q^83 + 8 * q^85 + 11 * q^87 - 5 * q^89 - 11 * q^91 - 18 * q^93 - 21 * q^95 + 35 * q^97 + 32 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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