LMFDB - Embedded newform 1050.2.bc.f.943.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1050,2,Mod(157,1050)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1050, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 2]))

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

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

chi := DirichletCharacter("1050.157");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1050.bc (of order $12$, 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:	$8.38429221223$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{12})$
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} - 28x^{14} + 519x^{12} - 5404x^{10} + 40705x^{8} - 194544x^{6} + 672624x^{4} - 1306368x^{2} + 1679616 $ x^16 - 28x^14 + 519x^12 - 5404x^10 + 40705x^8 - 194544x^6 + 672624x^4 - 1306368*x^2 + 1679616
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			943.2
Root			$2.35727 + 1.36097i$ of defining polynomial
Character	$\chi$	$=$	1050.943
Dual form			1050.2.bc.f.157.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.258819 - 0.965926i) q^{2} +(0.965926 + 0.258819i) q^{3} +(-0.866025 + 0.500000i) q^{4} -1.00000i q^{6} +(2.46313 + 0.965926i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.866025 + 0.500000i) q^{9} +O(q^{10})$	\(q+(-0.258819 - 0.965926i) q^{2} +(0.965926 + 0.258819i) q^{3} +(-0.866025 + 0.500000i) q^{4} -1.00000i q^{6} +(2.46313 + 0.965926i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.866025 + 0.500000i) q^{9} +(1.92471 + 3.33369i) q^{11} +(-0.965926 + 0.258819i) q^{12} +(-4.42535 + 4.42535i) q^{13} +(0.295509 - 2.62920i) q^{14} +(0.500000 - 0.866025i) q^{16} +(0.364671 - 1.36097i) q^{17} +(0.258819 - 0.965926i) q^{18} +(-1.76317 + 3.05390i) q^{19} +(2.12920 + 1.57052i) q^{21} +(2.72194 - 2.72194i) q^{22} +(-1.36097 + 0.364671i) q^{23} +(0.500000 + 0.866025i) q^{24} +(5.41993 + 3.12920i) q^{26} +(0.707107 + 0.707107i) q^{27} +(-2.61609 + 0.395046i) q^{28} +6.66738i q^{29} +(-4.55390 + 2.62920i) q^{31} +(-0.965926 - 0.258819i) q^{32} +(0.996301 + 3.71825i) q^{33} -1.40898 q^{34} -1.00000 q^{36} +(-2.63283 - 9.82586i) q^{37} +(3.40619 + 0.912685i) q^{38} +(-5.41993 + 3.12920i) q^{39} -0.741607i q^{41} +(0.965926 - 2.46313i) q^{42} +(1.52070 + 1.52070i) q^{43} +(-3.33369 - 1.92471i) q^{44} +(0.704491 + 1.22021i) q^{46} +(5.07922 - 1.36097i) q^{47} +(0.707107 - 0.707107i) q^{48} +(5.13397 + 4.75839i) q^{49} +(0.704491 - 1.22021i) q^{51} +(1.61979 - 6.04514i) q^{52} +(2.54922 - 9.51380i) q^{53} +(0.500000 - 0.866025i) q^{54} +(1.05868 + 2.42471i) q^{56} +(-2.49350 + 2.49350i) q^{57} +(6.44019 - 1.72564i) q^{58} +(6.84941 + 11.8635i) q^{59} +(-0.857750 - 0.495222i) q^{61} +(3.71825 + 3.71825i) q^{62} +(1.65017 + 2.06808i) q^{63} +1.00000i q^{64} +(3.33369 - 1.92471i) q^{66} +(7.39689 + 1.98199i) q^{67} +(0.364671 + 1.36097i) q^{68} -1.40898 q^{69} +11.2584 q^{71} +(0.258819 + 0.965926i) q^{72} +(-10.2878 - 2.75660i) q^{73} +(-8.80963 + 5.08624i) q^{74} -3.52634i q^{76} +(1.52070 + 10.0704i) q^{77} +(4.42535 + 4.42535i) q^{78} +(2.72849 + 1.57529i) q^{79} +(0.500000 + 0.866025i) q^{81} +(-0.716337 + 0.191942i) q^{82} +(0.471906 - 0.471906i) q^{83} +(-2.62920 - 0.295509i) q^{84} +(1.07529 - 1.86246i) q^{86} +(-1.72564 + 6.44019i) q^{87} +(-0.996301 + 3.71825i) q^{88} +(6.97594 - 12.0827i) q^{89} +(-15.1748 + 6.62564i) q^{91} +(0.996301 - 0.996301i) q^{92} +(-5.07922 + 1.36097i) q^{93} +(-2.62920 - 4.55390i) q^{94} +(-0.866025 - 0.500000i) q^{96} +(6.98682 + 6.98682i) q^{97} +(3.26748 - 6.19060i) q^{98} +3.84941i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q+O(q^{10}) $ 16 * q	$ 16 q - 4 q^{11} + 8 q^{14} + 8 q^{16} - 4 q^{19} - 4 q^{21} + 8 q^{24} - 16 q^{34} - 16 q^{36} - 12 q^{44} + 8 q^{46} + 96 q^{49} + 8 q^{51} + 8 q^{54} - 4 q^{56} + 40 q^{59} - 24 q^{61} + 12 q^{66} - 16 q^{69} + 104 q^{71} - 48 q^{74} - 12 q^{79} + 8 q^{81} - 4 q^{84} + 52 q^{86} + 60 q^{89} - 52 q^{91} - 4 q^{94}+O(q^{100}) $ 16 * q - 4 * q^11 + 8 * q^14 + 8 * q^16 - 4 * q^19 - 4 * q^21 + 8 * q^24 - 16 * q^34 - 16 * q^36 - 12 * q^44 + 8 * q^46 + 96 * q^49 + 8 * q^51 + 8 * q^54 - 4 * q^56 + 40 * q^59 - 24 * q^61 + 12 * q^66 - 16 * q^69 + 104 * q^71 - 48 * q^74 - 12 * q^79 + 8 * q^81 - 4 * q^84 + 52 * q^86 + 60 * q^89 - 52 * q^91 - 4 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times$.

$n$	$127$	$451$	$701$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{5}{6}\right)$	$1$

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 $

$2$	−0.258819	−	0.965926i	−0.183013	−	0.683013i
$2$	−0.258819	−	0.965926i	−0.183013	−	0.683013i
$3$	0.965926	+	0.258819i	0.557678	+	0.149429i
$3$	0.965926	+	0.258819i	0.557678	+	0.149429i
$4$	−0.866025	+	0.500000i	−0.433013	+	0.250000i
$5$		0			0
$5$		0			0
$6$		−	1.00000i		−	0.408248i
$7$	2.46313	+	0.965926i	0.930974	+	0.365086i
$7$	2.46313	+	0.965926i	0.930974	+	0.365086i
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	0.866025	+	0.500000i	0.288675	+	0.166667i
$10$		0			0
$11$	1.92471	+	3.33369i	0.580321	+	1.00514i	0.995441	+	0.0953782i	$0.0304061\pi$
$11$	1.92471	+	3.33369i	0.580321	+	1.00514i	−0.415121	+	0.909766i	$0.636261\pi$
$12$	−0.965926	+	0.258819i	−0.278839	+	0.0747146i
$13$	−4.42535	+	4.42535i	−1.22737	+	1.22737i	−0.262417	+	0.964954i	$0.584520\pi$
$13$	−4.42535	+	4.42535i	−1.22737	+	1.22737i	−0.964954	+	0.262417i	$0.915480\pi$
$14$	0.295509	−	2.62920i	0.0789781	−	0.702682i
$15$		0			0
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	0.364671	−	1.36097i	0.0884458	−	0.330084i	−0.907499	−	0.420055i	$-0.862011\pi$
$17$	0.364671	−	1.36097i	0.0884458	−	0.330084i	0.995944	+	0.0899709i	$0.0286774\pi$
$18$	0.258819	−	0.965926i	0.0610042	−	0.227671i
$19$	−1.76317	+	3.05390i	−0.404499	+	0.700613i	−0.994263	−	0.106963i	$-0.965887\pi$
$19$	−1.76317	+	3.05390i	−0.404499	+	0.700613i	0.589764	+	0.807576i	$0.299221\pi$
$20$		0			0
$21$	2.12920	+	1.57052i	0.464629	+	0.342715i
$22$	2.72194	−	2.72194i	0.580321	−	0.580321i
$23$	−1.36097	+	0.364671i	−0.283782	+	0.0760392i	−0.397903	−	0.917428i	$-0.630262\pi$
$23$	−1.36097	+	0.364671i	−0.283782	+	0.0760392i	0.114120	+	0.993467i	$0.463595\pi$
$24$	0.500000	+	0.866025i	0.102062	+	0.176777i
$25$		0			0
$26$	5.41993	+	3.12920i	1.06294	+	0.613686i
$27$	0.707107	+	0.707107i	0.136083	+	0.136083i
$28$	−2.61609	+	0.395046i	−0.494395	+	0.0746568i
$29$			6.66738i			1.23810i	0.785351	+	0.619050i	$0.212482\pi$
$29$			6.66738i			1.23810i	−0.785351	+	0.619050i	$0.787518\pi$
$30$		0			0
$31$	−4.55390	+	2.62920i	−0.817905	+	0.472218i	−0.849693	−	0.527277i	$-0.823213\pi$
$31$	−4.55390	+	2.62920i	−0.817905	+	0.472218i	0.0317885	+	0.999495i	$0.489880\pi$
$32$	−0.965926	−	0.258819i	−0.170753	−	0.0457532i
$33$	0.996301	+	3.71825i	0.173434	+	0.647263i
$34$	−1.40898			−0.241638
$35$		0			0
$36$	−1.00000			−0.166667
$37$	−2.63283	−	9.82586i	−0.432835	−	1.61536i	−0.746195	−	0.665727i	$-0.768121\pi$
$37$	−2.63283	−	9.82586i	−0.432835	−	1.61536i	0.313360	−	0.949634i	$-0.398545\pi$
$38$	3.40619	+	0.912685i	0.552556	+	0.148057i
$39$	−5.41993	+	3.12920i	−0.867883	+	0.501072i
$40$		0			0
$41$		−	0.741607i		−	0.115820i	−0.998322	−	0.0579098i	$-0.981556\pi$
$41$		−	0.741607i		−	0.115820i	0.998322	−	0.0579098i	$-0.0184436\pi$
$42$	0.965926	−	2.46313i	0.149046	−	0.380069i
$43$	1.52070	+	1.52070i	0.231904	+	0.231904i	0.813487	−	0.581583i	$-0.197566\pi$
$43$	1.52070	+	1.52070i	0.231904	+	0.231904i	−0.581583	+	0.813487i	$0.697566\pi$
$44$	−3.33369	−	1.92471i	−0.502572	−	0.290160i
$45$		0			0
$46$	0.704491	+	1.22021i	0.103872	+	0.179911i
$47$	5.07922	−	1.36097i	0.740880	−	0.198518i	0.131411	−	0.991328i	$-0.458049\pi$
$47$	5.07922	−	1.36097i	0.740880	−	0.198518i	0.609469	+	0.792810i	$0.291383\pi$
$48$	0.707107	−	0.707107i	0.102062	−	0.102062i
$49$	5.13397	+	4.75839i	0.733425	+	0.679770i
$50$		0			0
$51$	0.704491	−	1.22021i	0.0986485	−	0.170864i
$52$	1.61979	−	6.04514i	0.224625	−	0.838311i
$53$	2.54922	−	9.51380i	0.350162	−	1.30682i	−0.536303	−	0.844025i	$-0.680180\pi$
$53$	2.54922	−	9.51380i	0.350162	−	1.30682i	0.886465	−	0.462796i	$-0.153154\pi$
$54$	0.500000	−	0.866025i	0.0680414	−	0.117851i
$55$		0			0
$56$	1.05868	+	2.42471i	0.141472	+	0.324015i
$57$	−2.49350	+	2.49350i	−0.330272	+	0.330272i
$58$	6.44019	−	1.72564i	0.845638	−	0.226588i
$59$	6.84941	+	11.8635i	0.891717	+	1.54450i	0.837815	+	0.545954i	$0.183832\pi$
$59$	6.84941	+	11.8635i	0.891717	+	1.54450i	0.0539019	+	0.998546i	$0.482834\pi$
$60$		0			0
$61$	−0.857750	−	0.495222i	−0.109824	−	0.0634067i	0.444082	−	0.895986i	$-0.353530\pi$
$61$	−0.857750	−	0.495222i	−0.109824	−	0.0634067i	−0.553906	+	0.832579i	$0.686863\pi$
$62$	3.71825	+	3.71825i	0.472218	+	0.472218i
$63$	1.65017	+	2.06808i	0.207901	+	0.260553i
$64$			1.00000i			0.125000i
$65$		0			0
$66$	3.33369	−	1.92471i	0.410349	−	0.236915i
$67$	7.39689	+	1.98199i	0.903673	+	0.242139i	0.680593	−	0.732662i	$-0.261722\pi$
$67$	7.39689	+	1.98199i	0.903673	+	0.242139i	0.223080	+	0.974800i	$0.428389\pi$
$68$	0.364671	+	1.36097i	0.0442229	+	0.165042i
$69$	−1.40898			−0.169622
$70$		0			0
$71$	11.2584			1.33613			0.668063	−	0.744105i	$-0.267124\pi$
$71$	11.2584			1.33613			0.668063	+	0.744105i	$0.267124\pi$
$72$	0.258819	+	0.965926i	0.0305021	+	0.113835i
$73$	−10.2878	−	2.75660i	−1.20409	−	0.322636i	−0.399652	−	0.916667i	$-0.630869\pi$
$73$	−10.2878	−	2.75660i	−1.20409	−	0.322636i	−0.804442	+	0.594031i	$0.797536\pi$
$74$	−8.80963	+	5.08624i	−1.02410	+	0.591263i
$75$		0			0
$76$		−	3.52634i		−	0.404499i
$77$	1.52070	+	10.0704i	0.173299	+	1.14763i
$78$	4.42535	+	4.42535i	0.501072	+	0.501072i
$79$	2.72849	+	1.57529i	0.306979	+	0.177234i	0.645574	−	0.763698i	$-0.276618\pi$
$79$	2.72849	+	1.57529i	0.306979	+	0.177234i	−0.338595	+	0.940932i	$0.609952\pi$
$80$		0			0
$81$	0.500000	+	0.866025i	0.0555556	+	0.0962250i
$82$	−0.716337	+	0.191942i	−0.0791062	+	0.0211964i
$83$	0.471906	−	0.471906i	0.0517984	−	0.0517984i	−0.680733	−	0.732532i	$-0.738339\pi$
$83$	0.471906	−	0.471906i	0.0517984	−	0.0517984i	0.732532	+	0.680733i	$0.238339\pi$
$84$	−2.62920	−	0.295509i	−0.286869	−	0.0322427i
$85$		0			0
$86$	1.07529	−	1.86246i	0.115952	−	0.200835i
$87$	−1.72564	+	6.44019i	−0.185008	+	0.690461i
$88$	−0.996301	+	3.71825i	−0.106206	+	0.396366i
$89$	6.97594	−	12.0827i	0.739448	−	1.28076i	−0.213296	−	0.976988i	$-0.568420\pi$
$89$	6.97594	−	12.0827i	0.739448	−	1.28076i	0.952744	−	0.303774i	$-0.0982467\pi$
$90$		0			0
$91$	−15.1748	+	6.62564i	−1.59075	+	0.694555i
$92$	0.996301	−	0.996301i	0.103872	−	0.103872i
$93$	−5.07922	+	1.36097i	−0.526690	+	0.141126i
$94$	−2.62920	−	4.55390i	−0.271181	−	0.469699i
$95$		0			0
$96$	−0.866025	−	0.500000i	−0.0883883	−	0.0510310i
$97$	6.98682	+	6.98682i	0.709404	+	0.709404i	0.966410	−	0.257006i	$-0.0827359\pi$
$97$	6.98682	+	6.98682i	0.709404	+	0.709404i	−0.257006	+	0.966410i	$0.582736\pi$
$98$	3.26748	−	6.19060i	0.330066	−	0.625345i
$99$			3.84941i			0.386880i
$100$		0			0
$101$	12.4415	−	7.18310i	1.23797	−	0.714745i	0.269295	−	0.963058i	$-0.413209\pi$
$101$	12.4415	−	7.18310i	1.23797	−	0.714745i	0.968680	+	0.248313i	$0.0798761\pi$
$102$	−1.36097	−	0.364671i	−0.134756	−	0.0361079i
$103$	−3.97706	−	14.8426i	−0.391872	−	1.46249i	−0.827043	−	0.562138i	$-0.809979\pi$
$103$	−3.97706	−	14.8426i	−0.391872	−	1.46249i	0.435172	−	0.900348i	$-0.356688\pi$
$104$	−6.25839			−0.613686
$105$		0			0
$106$	−9.84941			−0.956659
$107$	−0.697125	−	2.60170i	−0.0673936	−	0.251516i	0.924008	−	0.382374i	$-0.124893\pi$
$107$	−0.697125	−	2.60170i	−0.0673936	−	0.251516i	−0.991401	+	0.130858i	$0.958227\pi$
$108$	−0.965926	−	0.258819i	−0.0929463	−	0.0249049i
$109$	−14.5503	+	8.40064i	−1.39367	+	0.804636i	−0.993719	−	0.111901i	$-0.964306\pi$
$109$	−14.5503	+	8.40064i	−1.39367	+	0.804636i	−0.399951	+	0.916537i	$0.630973\pi$
$110$		0			0
$111$		−	10.1725i		−	0.965529i
$112$	2.06808	−	1.65017i	0.195415	−	0.155926i
$113$	10.2109	+	10.2109i	0.960563	+	0.960563i	0.999251	−	0.0386883i	$-0.0123179\pi$
$113$	10.2109	+	10.2109i	0.960563	+	0.960563i	−0.0386883	+	0.999251i	$0.512318\pi$
$114$	3.05390	+	1.76317i	0.286024	+	0.165136i
$115$		0			0
$116$	−3.33369	−	5.77412i	−0.309525	−	0.536113i
$117$	−6.04514	+	1.61979i	−0.558874	+	0.149750i
$118$	9.68653	−	9.68653i	0.891717	−	0.891717i
$119$	2.21283	−	3.00000i	0.202850	−	0.275010i
$120$		0			0
$121$	−1.90898	+	3.30645i	−0.173544	+	0.300587i
$122$	−0.256346	+	0.956695i	−0.0232085	+	0.0866151i
$123$	0.191942	−	0.716337i	0.0173068	−	0.0645900i
$124$	2.62920	−	4.55390i	0.236109	−	0.408952i
$125$		0			0
$126$	1.57052	−	2.12920i	0.139913	−	0.189684i
$127$	14.5565	−	14.5565i	1.29168	−	1.29168i	0.357936	−	0.933746i	$-0.383481\pi$
$127$	14.5565	−	14.5565i	1.29168	−	1.29168i	0.933746	−	0.357936i	$-0.116519\pi$
$128$	0.965926	−	0.258819i	0.0853766	−	0.0228766i
$129$	1.07529	+	1.86246i	0.0946744	+	0.163981i
$130$		0			0
$131$	−5.66631	−	3.27145i	−0.495068	−	0.285828i	0.231607	−	0.972810i	$-0.425602\pi$
$131$	−5.66631	−	3.27145i	−0.495068	−	0.285828i	−0.726675	+	0.686982i	$0.758935\pi$
$132$	−2.72194	−	2.72194i	−0.236915	−	0.236915i
$133$	−7.29275	+	5.81905i	−0.632362	+	0.504576i
$134$		−	7.65782i		−	0.661535i
$135$		0			0
$136$	1.22021	−	0.704491i	0.104633	−	0.0604096i
$137$	−10.9950	−	2.94610i	−0.939367	−	0.251703i	−0.243523	−	0.969895i	$-0.578303\pi$
$137$	−10.9950	−	2.94610i	−0.939367	−	0.251703i	−0.695845	+	0.718192i	$0.744970\pi$
$138$	0.364671	+	1.36097i	0.0310429	+	0.115854i
$139$	−3.50510			−0.297299			−0.148650	−	0.988890i	$-0.547493\pi$
$139$	−3.50510			−0.297299			−0.148650	+	0.988890i	$0.547493\pi$
$140$		0			0
$141$	5.25839			0.442837
$142$	−2.91389	−	10.8748i	−0.244528	−	0.912591i
$143$	−23.2702	−	6.23524i	−1.94596	−	0.521417i
$144$	0.866025	−	0.500000i	0.0721688	−	0.0416667i
$145$		0			0
$146$			10.6507i			0.881458i
$147$	3.72748	+	5.92503i	0.307437	+	0.488688i
$148$	7.19303	+	7.19303i	0.591263	+	0.591263i
$149$	11.9713	+	6.91165i	0.980730	+	0.566225i	0.902490	−	0.430710i	$-0.141737\pi$
$149$	11.9713	+	6.91165i	0.980730	+	0.566225i	0.0782393	+	0.996935i	$0.475070\pi$
$150$		0			0
$151$	−2.97861	−	5.15910i	−0.242396	−	0.419842i	0.719001	−	0.695010i	$-0.244600\pi$
$151$	−2.97861	−	5.15910i	−0.242396	−	0.419842i	−0.961396	+	0.275168i	$0.911267\pi$
$152$	−3.40619	+	0.912685i	−0.276278	+	0.0740285i
$153$	0.996301	−	0.996301i	0.0805462	−	0.0805462i
$154$	9.33369	−	4.07529i	0.752130	−	0.328397i
$155$		0			0
$156$	3.12920	−	5.41993i	0.250536	−	0.433941i
$157$	−2.58387	+	9.64315i	−0.206216	+	0.769607i	0.782860	+	0.622198i	$0.213760\pi$
$157$	−2.58387	+	9.64315i	−0.206216	+	0.769607i	−0.989076	+	0.147409i	$0.952907\pi$
$158$	0.815432	−	3.04324i	0.0648723	−	0.242107i
$159$	4.92471	−	8.52984i	0.390555	−	0.676460i
$160$		0			0
$161$	−3.70449	−	0.416367i	−0.291955	−	0.0328143i
$162$	0.707107	−	0.707107i	0.0555556	−	0.0555556i
$163$	−1.32888	+	0.356071i	−0.104086	+	0.0278896i	−0.310486	−	0.950578i	$-0.600492\pi$
$163$	−1.32888	+	0.356071i	−0.104086	+	0.0278896i	0.206400	+	0.978468i	$0.433825\pi$
$164$	0.370803	+	0.642250i	0.0289549	+	0.0501513i
$165$		0			0
$166$	−0.577964	−	0.333688i	−0.0448587	−	0.0258992i
$167$	−7.69393	−	7.69393i	−0.595374	−	0.595374i	0.343704	−	0.939078i	$-0.388318\pi$
$167$	−7.69393	−	7.69393i	−0.595374	−	0.595374i	−0.939078	+	0.343704i	$0.888318\pi$
$168$	0.395046	+	2.61609i	0.0304785	+	0.201836i
$169$		−	26.1675i		−	2.01288i
$170$		0			0
$171$	−3.05390	+	1.76317i	−0.233538	+	0.134833i
$172$	−2.07731	−	0.556613i	−0.158393	−	0.0424414i
$173$	0.439687	+	1.64094i	0.0334288	+	0.124758i	0.980624	−	0.195900i	$-0.0627627\pi$
$173$	0.439687	+	1.64094i	0.0334288	+	0.124758i	−0.947195	+	0.320658i	$0.896096\pi$
$174$	6.66738			0.505452
$175$		0			0
$176$	3.84941			0.290160
$177$	3.54552	+	13.2320i	0.266497	+	0.994581i
$178$	−13.4765	−	3.61101i	−1.01010	−	0.270657i
$179$	11.9713	−	6.91165i	0.894779	−	0.516601i	0.0192766	−	0.999814i	$-0.493864\pi$
$179$	11.9713	−	6.91165i	0.894779	−	0.516601i	0.875503	+	0.483213i	$0.160530\pi$
$180$		0			0
$181$		−	3.36086i		−	0.249811i	−0.992169	−	0.124905i	$-0.960137\pi$
$181$		−	3.36086i		−	0.249811i	0.992169	−	0.124905i	$-0.0398627\pi$
$182$	10.3274	+	12.9429i	0.765517	+	0.959388i
$183$	−0.700350	−	0.700350i	−0.0517713	−	0.0517713i
$184$	−1.22021	−	0.704491i	−0.0899554	−	0.0519358i
$185$		0			0
$186$	2.62920	+	4.55390i	0.192782	+	0.333908i
$187$	5.23894	−	1.40377i	0.383109	−	0.102654i
$188$	−3.71825	+	3.71825i	−0.271181	+	0.271181i
$189$	1.05868	+	2.42471i	0.0770076	+	0.176371i
$190$		0			0
$191$	−0.370803	+	0.642250i	−0.0268304	+	0.0464716i	−0.879129	−	0.476584i	$-0.841875\pi$
$191$	−0.370803	+	0.642250i	−0.0268304	+	0.0464716i	0.852298	+	0.523056i	$0.175208\pi$
$192$	−0.258819	+	0.965926i	−0.0186787	+	0.0697097i
$193$	1.91759	−	7.15653i	0.138031	−	0.515138i	−0.861936	−	0.507017i	$-0.830748\pi$
$193$	1.91759	−	7.15653i	0.138031	−	0.515138i	0.999967	−	0.00812132i	$-0.00258513\pi$
$194$	4.94043	−	8.55707i	0.354702	−	0.614362i
$195$		0			0
$196$	−6.82535	−	1.55390i	−0.487525	−	0.110993i
$197$	−12.5349	+	12.5349i	−0.893076	+	0.893076i	−0.994811	−	0.101735i	$-0.967561\pi$
$197$	−12.5349	+	12.5349i	−0.893076	+	0.893076i	0.101735	+	0.994811i	$0.467561\pi$
$198$	3.71825	−	0.996301i	0.264244	−	0.0708040i
$199$	0.350302	+	0.606741i	0.0248323	+	0.0430107i	0.878174	−	0.478340i	$-0.158762\pi$
$199$	0.350302	+	0.606741i	0.0248323	+	0.0430107i	−0.853342	+	0.521351i	$0.825428\pi$
$200$		0			0
$201$	6.63187	+	3.82891i	0.467776	+	0.270070i
$202$	−10.1584	−	10.1584i	−0.714745	−	0.714745i
$203$	−6.44019	+	16.4226i	−0.452013	+	1.15264i
$204$			1.40898i			0.0986485i
$205$		0			0
$206$	−13.3075	+	7.68310i	−0.927179	+	0.535307i
$207$	−1.36097	−	0.364671i	−0.0945941	−	0.0253464i
$208$	1.61979	+	6.04514i	0.112312	+	0.419155i
$209$	−13.5743			−0.938957
$210$		0			0
$211$	−15.4426			−1.06311			−0.531555	−	0.847024i	$-0.678392\pi$
$211$	−15.4426			−1.06311			−0.531555	+	0.847024i	$0.678392\pi$
$212$	2.54922	+	9.51380i	0.175081	+	0.653410i
$213$	10.8748	+	2.91389i	0.745127	+	0.199656i
$214$	−2.33262	+	1.34674i	−0.159455	+	0.0920614i
$215$		0			0
$216$			1.00000i			0.0680414i
$217$	−13.7564	+	2.07731i	−0.933848	+	0.141017i
$218$	11.8803	+	11.8803i	0.804636	+	0.804636i
$219$	−9.22377	−	5.32535i	−0.623285	−	0.359854i
$220$		0			0
$221$	4.40898	+	7.63658i	0.296580	+	0.513692i
$222$	−9.82586	+	2.63283i	−0.659469	+	0.176704i
$223$	1.17901	−	1.17901i	0.0789525	−	0.0789525i	−0.666528	−	0.745480i	$-0.732220\pi$
$223$	1.17901	−	1.17901i	0.0789525	−	0.0789525i	0.745480	+	0.666528i	$0.232220\pi$
$224$	−2.12920	−	1.57052i	−0.142263	−	0.104935i
$225$		0			0
$226$	7.22021	−	12.5058i	0.480282	−	0.831872i
$227$	−2.97938	+	11.1192i	−0.197749	+	0.738008i	0.793790	+	0.608192i	$0.208105\pi$
$227$	−2.97938	+	11.1192i	−0.197749	+	0.738008i	−0.991538	+	0.129815i	$0.958562\pi$
$228$	0.912685	−	3.40619i	0.0604440	−	0.225580i
$229$	7.80873	−	13.5251i	0.516016	−	0.893765i	−0.483811	−	0.875172i	$-0.660748\pi$
$229$	7.80873	−	13.5251i	0.516016	−	0.893765i	0.999827	−	0.0185931i	$-0.00591872\pi$
$230$		0			0
$231$	−1.13754	+	10.1209i	−0.0748443	+	0.665904i
$232$	−4.71455	+	4.71455i	−0.309525	+	0.309525i
$233$	28.7141	−	7.69393i	1.88113	−	0.504046i	0.881641	−	0.471920i	$-0.156439\pi$
$233$	28.7141	−	7.69393i	1.88113	−	0.504046i	0.999484	−	0.0321261i	$-0.0102278\pi$
$234$	3.12920	+	5.41993i	0.204562	+	0.354312i
$235$		0			0
$236$	−11.8635	−	6.84941i	−0.772250	−	0.445859i
$237$	2.22780	+	2.22780i	0.144711	+	0.144711i
$238$	−3.47050	−	1.36097i	−0.224959	−	0.0882187i
$239$		−	7.95188i		−	0.514364i	−0.966363	−	0.257182i	$-0.917206\pi$
$239$		−	7.95188i		−	0.514364i	0.966363	−	0.257182i	$-0.0827940\pi$
$240$		0			0
$241$	−9.81069	+	5.66420i	−0.631962	+	0.364863i	−0.781512	−	0.623891i	$-0.785551\pi$
$241$	−9.81069	+	5.66420i	−0.631962	+	0.364863i	0.149550	+	0.988754i	$0.452218\pi$
$242$	3.68787	+	0.988162i	0.237065	+	0.0635215i
$243$	0.258819	+	0.965926i	0.0166032	+	0.0619642i
$244$	0.990444			0.0634067
$245$		0			0
$246$	−0.741607			−0.0472831
$247$	−5.71194	−	21.3172i	−0.363442	−	1.35638i
$248$	−5.07922	−	1.36097i	−0.322531	−	0.0864218i
$249$	0.577964	−	0.333688i	0.0366270	−	0.0211466i
$250$		0			0
$251$		−	21.0336i		−	1.32763i	−0.747898	−	0.663814i	$-0.768937\pi$
$251$		−	21.0336i		−	1.32763i	0.747898	−	0.663814i	$-0.231063\pi$
$252$	−2.46313	−	0.965926i	−0.155162	−	0.0608476i
$253$	−3.83517	−	3.83517i	−0.241115	−	0.241115i
$254$	−17.8280	−	10.2930i	−1.11863	−	0.645841i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−25.0314	+	6.70715i	−1.56142	+	0.418380i	−0.933112	−	0.359587i	$-0.882918\pi$
$257$	−25.0314	+	6.70715i	−1.56142	+	0.418380i	−0.628305	+	0.777967i	$0.716251\pi$
$258$	1.52070	−	1.52070i	0.0946744	−	0.0946744i
$259$	3.00606	−	26.7454i	0.186787	−	1.66188i
$260$		0			0
$261$	−3.33369	+	5.77412i	−0.206350	+	0.357409i
$262$	−1.69343	+	6.31995i	−0.104620	+	0.390448i
$263$	4.29407	−	16.0257i	0.264784	−	0.988187i	−0.697599	−	0.716489i	$-0.745748\pi$
$263$	4.29407	−	16.0257i	0.264784	−	0.988187i	0.962383	−	0.271698i	$-0.0875852\pi$
$264$	−1.92471	+	3.33369i	−0.118457	+	0.205174i
$265$		0			0
$266$	7.50828	+	5.53818i	0.460362	+	0.339568i
$267$	9.86547	−	9.86547i	0.603757	−	0.603757i
$268$	−7.39689	+	1.98199i	−0.451837	+	0.121069i
$269$	13.6804	+	23.6952i	0.834110	+	1.44472i	0.894753	+	0.446562i	$0.147352\pi$
$269$	13.6804	+	23.6952i	0.834110	+	1.44472i	−0.0606421	+	0.998160i	$0.519315\pi$
$270$		0			0
$271$	−0.828972	−	0.478607i	−0.0503565	−	0.0290733i	0.474610	−	0.880196i	$-0.342589\pi$
$271$	−0.828972	−	0.478607i	−0.0503565	−	0.0290733i	−0.524967	+	0.851123i	$0.675922\pi$
$272$	−0.996301	−	0.996301i	−0.0604096	−	0.0604096i
$273$	−16.3725	+	2.47236i	−0.990911	+	0.149634i
$274$			11.3829i			0.687665i
$275$		0			0
$276$	1.22021	−	0.704491i	0.0734483	−	0.0424054i
$277$	−20.1045	−	5.38699i	−1.20796	−	0.323673i	−0.402001	−	0.915639i	$-0.631685\pi$
$277$	−20.1045	−	5.38699i	−1.20796	−	0.323673i	−0.805963	+	0.591966i	$0.798352\pi$
$278$	0.907188	+	3.38567i	0.0544095	+	0.203059i
$279$	−5.25839			−0.314812
$280$		0			0
$281$	2.89220			0.172534			0.0862670	−	0.996272i	$-0.472506\pi$
$281$	2.89220			0.172534			0.0862670	+	0.996272i	$0.472506\pi$
$282$	−1.36097	−	5.07922i	−0.0810447	−	0.302463i
$283$	−20.4714	−	5.48531i	−1.21690	−	0.326068i	−0.407435	−	0.913234i	$-0.633577\pi$
$283$	−20.4714	−	5.48531i	−1.21690	−	0.326068i	−0.809466	+	0.587167i	$0.800243\pi$
$284$	−9.75005	+	5.62920i	−0.578559	+	0.334031i
$285$		0			0
$286$			24.0911i			1.42454i
$287$	0.716337	−	1.82667i	0.0422841	−	0.107825i
$288$	−0.707107	−	0.707107i	−0.0416667	−	0.0416667i
$289$	13.0032	+	7.50738i	0.764892	+	0.441611i
$290$		0			0
$291$	4.94043	+	8.55707i	0.289613	+	0.501625i
$292$	10.2878	−	2.75660i	0.602047	−	0.161318i
$293$	−14.1436	+	14.1436i	−0.826280	+	0.826280i	−0.987000	−	0.160720i	$-0.948618\pi$
$293$	−14.1436	+	14.1436i	−0.826280	+	0.826280i	0.160720	+	0.987000i	$0.448618\pi$
$294$	4.75839	−	5.13397i	0.277515	−	0.299419i
$295$		0			0
$296$	5.08624	−	8.80963i	0.295632	−	0.512049i
$297$	−0.996301	+	3.71825i	−0.0578112	+	0.215754i
$298$	3.57773	−	13.3523i	0.207253	−	0.773477i
$299$	4.40898	−	7.63658i	0.254978	−	0.441635i
$300$		0			0
$301$	2.27679	+	5.21455i	0.131232	+	0.300561i
$302$	−4.21239	+	4.21239i	−0.242396	+	0.242396i
$303$	13.8767	−	3.71825i	0.797194	−	0.213608i
$304$	1.76317	+	3.05390i	0.101125	+	0.175153i
$305$		0			0
$306$	−1.22021	−	0.704491i	−0.0697550	−	0.0402731i
$307$	6.81363	+	6.81363i	0.388874	+	0.388874i	0.874286	−	0.485411i	$-0.161330\pi$
$307$	6.81363	+	6.81363i	0.388874	+	0.388874i	−0.485411	+	0.874286i	$0.661330\pi$
$308$	−6.35217	−	7.96089i	−0.361948	−	0.453614i
$309$		−	15.3662i		−	0.874152i
$310$		0			0
$311$	−17.8568	+	10.3096i	−1.01257	+	0.584605i	−0.911942	−	0.410319i	$-0.865417\pi$
$311$	−17.8568	+	10.3096i	−1.01257	+	0.584605i	−0.100624	+	0.994925i	$0.532084\pi$
$312$	−6.04514	−	1.61979i	−0.342239	−	0.0917026i
$313$	4.26240	+	15.9075i	0.240925	+	0.899145i	0.975388	+	0.220496i	$0.0707677\pi$
$313$	4.26240	+	15.9075i	0.240925	+	0.899145i	−0.734463	+	0.678649i	$0.762566\pi$
$314$	9.98332			0.563391
$315$		0			0
$316$	−3.15059			−0.177234
$317$	−6.87988	−	25.6761i	−0.386412	−	1.44211i	−0.835928	−	0.548838i	$-0.815070\pi$
$317$	−6.87988	−	25.6761i	−0.386412	−	1.44211i	0.449516	−	0.893272i	$-0.351596\pi$
$318$	−9.51380	−	2.54922i	−0.533507	−	0.142953i
$319$	−22.2269	+	12.8327i	−1.24447	+	0.718495i
$320$		0			0
$321$		−	2.69348i		−	0.150336i
$322$	0.556613	+	3.68603i	0.0310189	+	0.205414i
$323$	3.51330	+	3.51330i	0.195485	+	0.195485i
$324$	−0.866025	−	0.500000i	−0.0481125	−	0.0277778i
$325$		0			0
$326$	0.687877	+	1.19144i	0.0380980	+	0.0659876i
$327$	−16.2288	+	4.34849i	−0.897455	+	0.240472i
$328$	0.524395	−	0.524395i	0.0289549	−	0.0289549i
$329$	13.8253	+	1.55390i	0.762216	+	0.0856694i
$330$		0			0
$331$	−3.37347	+	5.84303i	−0.185423	+	0.321162i	−0.943719	−	0.330749i	$-0.892699\pi$
$331$	−3.37347	+	5.84303i	−0.185423	+	0.321162i	0.758296	+	0.651910i	$0.226032\pi$
$332$	−0.172729	+	0.644635i	−0.00947976	+	0.0353789i
$333$	2.63283	−	9.82586i	0.144278	−	0.538454i
$334$	−5.44043	+	9.42310i	−0.297687	+	0.515609i
$335$		0			0
$336$	2.42471	−	1.05868i	0.132279	−	0.0577557i
$337$	−2.19755	+	2.19755i	−0.119708	+	0.119708i	−0.764423	−	0.644715i	$-0.776976\pi$
$337$	−2.19755	+	2.19755i	−0.119708	+	0.119708i	0.644715	+	0.764423i	$0.276976\pi$
$338$	−25.2758	+	6.77264i	−1.37482	+	0.368383i
$339$	7.22021	+	12.5058i	0.392148	+	0.679221i
$340$		0			0
$341$	−17.5298	−	10.1209i	−0.949294	−	0.548075i
$342$	2.49350	+	2.49350i	0.134833	+	0.134833i
$343$	8.04937	+	16.6796i	0.434625	+	0.900611i
$344$			2.15059i			0.115952i
$345$		0			0
$346$	1.47122	−	0.849411i	0.0790934	−	0.0456646i
$347$	12.7957	+	3.42859i	0.686908	+	0.184056i	0.585359	−	0.810774i	$-0.300954\pi$
$347$	12.7957	+	3.42859i	0.686908	+	0.184056i	0.101549	+	0.994831i	$0.467620\pi$
$348$	−1.72564	−	6.44019i	−0.0925042	−	0.345230i
$349$	−18.1788			−0.973090			−0.486545	−	0.873655i	$-0.661743\pi$
$349$	−18.1788			−0.973090			−0.486545	+	0.873655i	$0.661743\pi$
$350$		0			0
$351$	−6.25839			−0.334048
$352$	−0.996301	−	3.71825i	−0.0531030	−	0.198183i
$353$	21.0687	+	5.64535i	1.12138	+	0.300472i	0.771440	−	0.636302i	$-0.219537\pi$
$353$	21.0687	+	5.64535i	1.12138	+	0.300472i	0.349936	+	0.936774i	$0.386203\pi$
$354$	11.8635	−	6.84941i	0.630539	−	0.364042i
$355$		0			0
$356$			13.9519i			0.739448i
$357$	2.91389	−	2.32505i	0.154219	−	0.123055i
$358$	−9.77455	−	9.77455i	−0.516601	−	0.516601i
$359$	−24.7752	−	14.3040i	−1.30758	−	0.754934i	−0.325892	−	0.945407i	$-0.605664\pi$
$359$	−24.7752	−	14.3040i	−1.30758	−	0.754934i	−0.981692	+	0.190473i	$0.938998\pi$
$360$		0			0
$361$	3.28246	+	5.68538i	0.172761	+	0.299230i
$362$	−3.24634	+	0.869854i	−0.170624	+	0.0457185i
$363$	−2.69971	+	2.69971i	−0.141698	+	0.141698i
$364$	9.82891	−	13.3253i	0.515175	−	0.698438i
$365$		0			0
$366$	−0.495222	+	0.857750i	−0.0258857	+	0.0448353i
$367$	−8.40733	+	31.3766i	−0.438859	+	1.63784i	0.292800	+	0.956174i	$0.405413\pi$
$367$	−8.40733	+	31.3766i	−0.438859	+	1.63784i	−0.731659	+	0.681671i	$0.761254\pi$
$368$	−0.364671	+	1.36097i	−0.0190098	+	0.0709456i
$369$	0.370803	−	0.642250i	0.0193033	−	0.0334342i
$370$		0			0
$371$	15.4687	−	20.9713i	0.803093	−	1.08878i
$372$	3.71825	−	3.71825i	0.192782	−	0.192782i
$373$	21.3172	−	5.71194i	1.10377	−	0.295753i	0.339468	−	0.940618i	$-0.389753\pi$
$373$	21.3172	−	5.71194i	1.10377	−	0.295753i	0.764297	+	0.644865i	$0.223086\pi$
$374$	−2.71188	−	4.69711i	−0.140228	−	0.242882i
$375$		0			0
$376$	4.55390	+	2.62920i	0.234850	+	0.135590i
$377$	−29.5055	−	29.5055i	−1.51961	−	1.51961i
$378$	2.06808	−	1.65017i	0.106371	−	0.0848754i
$379$		−	15.8588i		−	0.814614i	−0.913291	−	0.407307i	$-0.866468\pi$
$379$		−	15.8588i		−	0.814614i	0.913291	−	0.407307i	$-0.133532\pi$
$380$		0			0
$381$	17.8280	−	10.2930i	0.913357	−	0.527327i
$382$	0.716337	+	0.191942i	0.0366510	+	0.00982061i
$383$	−4.59325	−	17.1422i	−0.234704	−	0.875927i	−0.978282	−	0.207278i	$-0.933540\pi$
$383$	−4.59325	−	17.1422i	−0.234704	−	0.875927i	0.743578	−	0.668649i	$-0.233127\pi$
$384$	1.00000			0.0510310
$385$		0			0
$386$	−7.40898			−0.377107
$387$	0.556613	+	2.07731i	0.0282942	+	0.105596i
$388$	−9.54418	−	2.55735i	−0.484532	−	0.129830i
$389$	−30.2340	+	17.4556i	−1.53292	+	0.885034i	−0.533700	+	0.845674i	$0.679199\pi$
$389$	−30.2340	+	17.4556i	−1.53292	+	0.885034i	−0.999225	+	0.0393604i	$0.987468\pi$
$390$		0			0
$391$			1.98523i			0.100397i
$392$	0.265576	+	6.99496i	0.0134136	+	0.353299i
$393$	−4.62652	−	4.62652i	−0.233377	−	0.233377i
$394$	15.3521	+	8.86353i	0.773427	+	0.446538i
$395$		0			0
$396$	−1.92471	−	3.33369i	−0.0967201	−	0.167524i
$397$	34.8886	−	9.34838i	1.75101	−	0.469182i	0.766169	−	0.642640i	$-0.222161\pi$
$397$	34.8886	−	9.34838i	1.75101	−	0.469182i	0.984841	+	0.173458i	$0.0554941\pi$
$398$	0.495402	−	0.495402i	0.0248323	−	0.0248323i
$399$	−8.55034	+	3.73327i	−0.428052	+	0.186897i
$400$		0			0
$401$	−0.741607	+	1.28450i	−0.0370341	+	0.0641449i	−0.883948	−	0.467585i	$-0.845124\pi$
$401$	−0.741607	+	1.28450i	−0.0370341	+	0.0641449i	0.846914	+	0.531729i	$0.178458\pi$
$402$	1.98199	−	7.39689i	0.0988526	−	0.368923i
$403$	8.51750	−	31.7877i	0.424287	−	1.58346i
$404$	−7.18310	+	12.4415i	−0.357373	+	0.618987i
$405$		0			0
$406$	17.5298	+	1.97027i	0.869991	+	0.0977828i
$407$	27.6889	−	27.6889i	1.37249	−	1.37249i
$408$	1.36097	−	0.364671i	0.0673782	−	0.0180539i
$409$	1.51216	+	2.61914i	0.0747716	+	0.129508i	0.900987	−	0.433846i	$-0.142844\pi$
$409$	1.51216	+	2.61914i	0.0747716	+	0.129508i	−0.826215	+	0.563354i	$0.809511\pi$
$410$		0			0
$411$	−9.85786	−	5.69144i	−0.486252	−	0.280738i
$412$	10.8655	+	10.8655i	0.535307	+	0.535307i
$413$	5.41167	+	35.8374i	0.266291	+	1.76344i
$414$			1.40898i			0.0692477i
$415$		0			0
$416$	5.41993	−	3.12920i	0.265734	−	0.153421i
$417$	−3.38567	−	0.907188i	−0.165797	−	0.0444252i
$418$	3.51330	+	13.1118i	0.171841	+	0.641319i
$419$	14.8547			0.725702			0.362851	−	0.931847i	$-0.381803\pi$
$419$	14.8547			0.725702			0.362851	+	0.931847i	$0.381803\pi$
$420$		0			0
$421$	27.2920			1.33013			0.665065	−	0.746786i	$-0.268404\pi$
$421$	27.2920			1.33013			0.665065	+	0.746786i	$0.268404\pi$
$422$	3.99683	+	14.9164i	0.194563	+	0.726117i
$423$	5.07922	+	1.36097i	0.246960	+	0.0661727i
$424$	8.52984	−	4.92471i	0.414246	−	0.239165i
$425$		0			0
$426$		−	11.2584i		−	0.545471i
$427$	−1.63440	−	2.04832i	−0.0790940	−	0.0991250i
$428$	1.90458	+	1.90458i	0.0920614	+	0.0920614i
$429$	−20.8635	−	12.0456i	−1.00730	−	0.581565i
$430$		0			0
$431$	−18.5242	−	32.0848i	−0.892278	−	1.54547i	−0.837138	−	0.546992i	$-0.815773\pi$
$431$	−18.5242	−	32.0848i	−0.892278	−	1.54547i	−0.0551401	−	0.998479i	$-0.517561\pi$
$432$	0.965926	−	0.258819i	0.0464731	−	0.0124524i
$433$	7.65990	−	7.65990i	0.368111	−	0.368111i	−0.498677	−	0.866788i	$-0.666181\pi$
$433$	7.65990	−	7.65990i	0.368111	−	0.368111i	0.866788	+	0.498677i	$0.166181\pi$
$434$	5.56696	+	12.7501i	0.267222	+	0.612022i
$435$		0			0
$436$	8.40064	−	14.5503i	0.402318	−	0.696835i
$437$	1.28596	−	4.79925i	0.0615156	−	0.229579i
$438$	−2.75660	+	10.2878i	−0.131716	+	0.491569i
$439$	−10.1375	+	17.5586i	−0.483835	+	0.838027i	−0.999828	−	0.0185660i	$-0.994090\pi$
$439$	−10.1375	+	17.5586i	−0.483835	+	0.838027i	0.515992	+	0.856593i	$0.327423\pi$
$440$		0			0
$441$	2.06696	+	6.68788i	0.0984265	+	0.318470i
$442$	6.23524	−	6.23524i	0.296580	−	0.296580i
$443$	6.79186	−	1.81987i	0.322691	−	0.0864647i	−0.0938374	−	0.995588i	$-0.529913\pi$
$443$	6.79186	−	1.81987i	0.322691	−	0.0864647i	0.416528	+	0.909123i	$0.363247\pi$
$444$	5.08624	+	8.80963i	0.241382	+	0.418086i
$445$		0			0
$446$	−1.44399	−	0.833688i	−0.0683749	−	0.0394763i
$447$	9.77455	+	9.77455i	0.462320	+	0.462320i
$448$	−0.965926	+	2.46313i	−0.0456357	+	0.116372i
$449$		−	4.46654i		−	0.210789i	−0.994430	−	0.105394i	$-0.966389\pi$
$449$		−	4.46654i		−	0.210789i	0.994430	−	0.105394i	$-0.0336105\pi$
$450$		0			0
$451$	2.47229	−	1.42737i	0.116415	−	0.0672125i
$452$	−13.9484	−	3.73746i	−0.656077	−	0.175795i
$453$	−1.54184	−	5.75423i	−0.0724420	−	0.270357i
$454$	11.5114			0.540259
$455$		0			0
$456$	−3.52634			−0.165136
$457$	6.28043	+	23.4389i	0.293786	+	1.09643i	0.942176	+	0.335117i	$0.108776\pi$
$457$	6.28043	+	23.4389i	0.293786	+	1.09643i	−0.648390	+	0.761308i	$0.724557\pi$
$458$	−15.0853	−	4.04210i	−0.704891	−	0.188875i
$459$	1.22021	−	0.704491i	0.0569547	−	0.0328828i
$460$		0			0
$461$			8.81796i			0.410694i	0.978689	+	0.205347i	$0.0658322\pi$
$461$			8.81796i			0.410694i	−0.978689	+	0.205347i	$0.934168\pi$
$462$	10.0704	−	1.52070i	0.468518	−	0.0707492i
$463$	1.05131	+	1.05131i	0.0488583	+	0.0488583i	0.731114	−	0.682256i	$-0.239001\pi$
$463$	1.05131	+	1.05131i	0.0488583	+	0.0488583i	−0.682256	+	0.731114i	$0.739001\pi$
$464$	5.77412	+	3.33369i	0.268057	+	0.154763i
$465$		0			0
$466$	−14.8635	−	25.7444i	−0.688540	−	1.19259i
$467$	35.7465	−	9.57824i	1.65415	−	0.443228i	0.693379	−	0.720573i	$-0.256121\pi$
$467$	35.7465	−	9.57824i	1.65415	−	0.443228i	0.960770	+	0.277345i	$0.0894546\pi$
$468$	4.42535	−	4.42535i	0.204562	−	0.204562i
$469$	16.3050	+	12.0267i	0.752895	+	0.555343i
$470$		0			0
$471$	−4.99166	+	8.64581i	−0.230004	+	0.398378i
$472$	−3.54552	+	13.2320i	−0.163196	+	0.609054i
$473$	−2.14263	+	7.99642i	−0.0985184	+	0.367676i
$474$	1.57529	−	2.72849i	0.0723557	−	0.125324i
$475$		0			0
$476$	−0.416367	+	3.70449i	−0.0190841	+	0.169795i
$477$	6.96459	−	6.96459i	0.318886	−	0.318886i
$478$	−7.68092	+	2.05810i	−0.351317	+	0.0941352i
$479$	0.778723	+	1.34879i	0.0355807	+	0.0616277i	0.883267	−	0.468870i	$-0.155339\pi$
$479$	0.778723	+	1.34879i	0.0355807	+	0.0616277i	−0.847687	+	0.530497i	$0.822005\pi$
$480$		0			0
$481$	55.1341	+	31.8317i	2.51390	+	1.45140i
$482$	8.01039	+	8.01039i	0.364863	+	0.364863i
$483$	−3.47050	−	1.36097i	−0.157913	−	0.0619264i
$484$		−	3.81796i		−	0.173544i
$485$		0			0
$486$	0.866025	−	0.500000i	0.0392837	−	0.0226805i
$487$	−7.56068	−	2.02588i	−0.342607	−	0.0918013i	0.0834127	−	0.996515i	$-0.473418\pi$
$487$	−7.56068	−	2.02588i	−0.342607	−	0.0918013i	−0.426020	+	0.904714i	$0.640085\pi$
$488$	−0.256346	−	0.956695i	−0.0116042	−	0.0433076i
$489$	−1.37575			−0.0622137
$490$		0			0
$491$	43.8776			1.98017			0.990085	−	0.140468i	$-0.0448608\pi$
$491$	43.8776			1.98017			0.990085	+	0.140468i	$0.0448608\pi$
$492$	0.191942	+	0.716337i	0.00865341	+	0.0322950i
$493$	9.07411	+	2.43140i	0.408677	+	0.109505i
$494$	−19.1125	+	11.0346i	−0.859913	+	0.496471i
$495$		0			0
$496$			5.25839i			0.236109i
$497$	27.7308	+	10.8748i	1.24390	+	0.487800i
$498$	−0.471906	−	0.471906i	−0.0211466	−	0.0211466i
$499$	29.9024	+	17.2642i	1.33862	+	0.772850i	0.986602	−	0.163144i	$-0.0521636\pi$
$499$	29.9024	+	17.2642i	1.33862	+	0.772850i	0.352014	+	0.935995i	$0.385497\pi$
$500$		0			0
$501$	−5.44043	−	9.42310i	−0.243060	−	0.420993i
$502$	−20.3169	+	5.44389i	−0.906786	+	0.242973i
$503$	16.9300	−	16.9300i	0.754872	−	0.754872i	−0.220512	−	0.975384i	$-0.570773\pi$
$503$	16.9300	−	16.9300i	0.754872	−	0.754872i	0.975384	+	0.220512i	$0.0707728\pi$
$504$	−0.295509	+	2.62920i	−0.0131630	+	0.117114i
$505$		0			0
$506$	−2.71188	+	4.69711i	−0.120558	+	0.208812i
$507$	6.77264	−	25.2758i	0.300784	−	1.12254i
$508$	−5.32805	+	19.8846i	−0.236394	+	0.882235i
$509$	5.10674	−	8.84514i	0.226352	−	0.392054i	−0.730372	−	0.683050i	$-0.760653\pi$
$509$	5.10674	−	8.84514i	0.226352	−	0.392054i	0.956724	+	0.290996i	$0.0939866\pi$
$510$		0			0
$511$	−22.6774	−	16.7271i	−1.00319	−	0.739963i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	−3.40619	+	0.912685i	−0.150387	+	0.0402960i
$514$	12.9572	+	22.4426i	0.571518	+	0.989899i
$515$		0			0
$516$	−1.86246	−	1.07529i	−0.0819904	−	0.0473372i
$517$	14.3131	+	14.3131i	0.629487	+	0.629487i
$518$	−26.6121	+	4.01860i	−1.16927	+	0.176567i
$519$			1.69882i			0.0745700i
$520$		0			0
$521$	−15.0251	+	8.67476i	−0.658263	+	0.380048i	−0.791615	−	0.611021i	$-0.790759\pi$
$521$	−15.0251	+	8.67476i	−0.658263	+	0.380048i	0.133352	+	0.991069i	$0.457426\pi$
$522$	6.44019	+	1.72564i	0.281879	+	0.0755294i
$523$	10.9108	+	40.7197i	0.477097	+	1.78055i	0.613281	+	0.789865i	$0.289849\pi$
$523$	10.9108	+	40.7197i	0.477097	+	1.78055i	−0.136184	+	0.990684i	$0.543484\pi$
$524$	6.54289			0.285828
$525$		0			0
$526$	−16.5910			−0.723403
$527$	1.91759	+	7.15653i	0.0835313	+	0.311743i
$528$	3.71825	+	0.996301i	0.161816	+	0.0433584i
$529$	−18.1993	+	10.5074i	−0.791275	+	0.456843i
$530$		0			0
$531$			13.6988i			0.594478i
$532$	3.40619	−	8.68582i	0.147677	−	0.376578i
$533$	3.28187	+	3.28187i	0.142154	+	0.142154i
$534$	−12.0827	−	6.97594i	−0.522869	−	0.301878i
$535$		0			0
$536$	3.82891	+	6.63187i	0.165384	+	0.286453i
$537$	13.3523	−	3.57773i	0.576194	−	0.154391i
$538$	19.3470	−	19.3470i	0.834110	−	0.834110i
$539$	−5.98161	+	26.2736i	−0.257646	+	1.13168i
$540$		0			0
$541$	11.3709	−	19.6950i	0.488874	−	0.846754i	−0.511044	−	0.859554i	$-0.670741\pi$
$541$	11.3709	−	19.6950i	0.488874	−	0.846754i	0.999918	+	0.0128002i	$0.00407455\pi$
$542$	−0.247745	+	0.924599i	−0.0106416	+	0.0397149i
$543$	0.869854	−	3.24634i	0.0373290	−	0.139314i
$544$	−0.704491	+	1.22021i	−0.0302048	+	0.0523163i
$545$		0			0
$546$	6.62564	+	15.1748i	0.283551	+	0.649420i
$547$	12.2324	−	12.2324i	0.523021	−	0.523021i	−0.395462	−	0.918483i	$-0.629415\pi$
$547$	12.2324	−	12.2324i	0.523021	−	0.523021i	0.918483	+	0.395462i	$0.129415\pi$
$548$	10.9950	−	2.94610i	0.469684	−	0.125851i
$549$	−0.495222	−	0.857750i	−0.0211356	−	0.0366079i
$550$		0			0
$551$	−20.3615	−	11.7557i	−0.867430	−	0.500811i
$552$	−0.996301	−	0.996301i	−0.0424054	−	0.0424054i
$553$	5.19900	+	6.51567i	0.221084	+	0.277074i
$554$			20.8137i			0.884291i
$555$		0			0
$556$	3.03551	−	1.75255i	0.128734	−	0.0743248i
$557$	34.7179	+	9.30265i	1.47105	+	0.394166i	0.903290	−	0.429031i	$-0.141145\pi$
$557$	34.7179	+	9.30265i	1.47105	+	0.394166i	0.567757	+	0.823196i	$0.307811\pi$
$558$	1.36097	+	5.07922i	0.0576146	+	0.215020i
$559$	−13.4592			−0.569265
$560$		0			0
$561$	5.42375			0.228991
$562$	−0.748555	−	2.79365i	−0.0315759	−	0.117843i
$563$	−31.9435	−	8.55924i	−1.34626	−	0.360729i	−0.487506	−	0.873120i	$-0.662093\pi$
$563$	−31.9435	−	8.55924i	−1.34626	−	0.360729i	−0.858752	+	0.512391i	$0.828760\pi$
$564$	−4.55390	+	2.62920i	−0.191754	+	0.110709i
$565$		0			0
$566$			21.1936i			0.890833i
$567$	0.395046	+	2.61609i	0.0165904	+	0.109866i
$568$	7.96089	+	7.96089i	0.334031	+	0.334031i
$569$	−14.4472	−	8.34107i	−0.605656	−	0.349676i	0.165607	−	0.986192i	$-0.447042\pi$
$569$	−14.4472	−	8.34107i	−0.605656	−	0.349676i	−0.771264	+	0.636516i	$0.780375\pi$
$570$		0			0
$571$	−1.21754	−	2.10885i	−0.0509527	−	0.0882526i	0.839424	−	0.543477i	$-0.182892\pi$
$571$	−1.21754	−	2.10885i	−0.0509527	−	0.0882526i	−0.890377	+	0.455224i	$0.849559\pi$
$572$	23.2702	−	6.23524i	0.972978	−	0.260709i
$573$	−0.524395	+	0.524395i	−0.0219069	+	0.0219069i
$574$	−1.94983	−	0.219151i	−0.0813843	−	0.00914720i
$575$		0			0
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	0.464598	−	1.73390i	0.0193415	−	0.0721834i	−0.955581	−	0.294730i	$-0.904770\pi$
$577$	0.464598	−	1.73390i	0.0193415	−	0.0721834i	0.974922	+	0.222547i	$0.0714370\pi$
$578$	3.88611	−	14.5032i	0.161641	−	0.603252i
$579$	3.70449	−	6.41637i	0.153953	−	0.266655i
$580$		0			0
$581$	1.61819	−	0.706537i	0.0671338	−	0.0293121i
$582$	6.98682	−	6.98682i	0.289613	−	0.289613i
$583$	36.6225	−	9.81298i	1.51675	−	0.406412i
$584$	−5.32535	−	9.22377i	−0.220365	−	0.381683i
$585$		0			0
$586$	17.3223	+	10.0011i	0.715580	+	0.413140i
$587$	−28.3042	−	28.3042i	−1.16824	−	1.16824i	−0.982622	−	0.185619i	$-0.940571\pi$
$587$	−28.3042	−	28.3042i	−1.16824	−	1.16824i	−0.185619	−	0.982622i	$-0.559429\pi$
$588$	−6.19060	−	3.26748i	−0.255296	−	0.134749i
$589$		−	18.5429i		−	0.764047i
$590$		0			0
$591$	−15.3521	+	8.86353i	−0.631500	+	0.364597i
$592$	−9.82586	−	2.63283i	−0.403840	−	0.108209i
$593$	0.710130	+	2.65024i	0.0291616	+	0.108832i	0.978973	−	0.203992i	$-0.0653916\pi$
$593$	0.710130	+	2.65024i	0.0291616	+	0.108832i	−0.949811	+	0.312824i	$0.898725\pi$
$594$	3.84941			0.157943
$595$		0			0
$596$	−13.8233			−0.566225
$597$	0.181330	+	0.676732i	0.00742133	+	0.0276968i
$598$	−8.51750	−	2.28226i	−0.348306	−	0.0933284i
$599$	27.3558	−	15.7939i	1.11773	−	0.645321i	0.176909	−	0.984227i	$-0.443390\pi$
$599$	27.3558	−	15.7939i	1.11773	−	0.645321i	0.940820	+	0.338906i	$0.110057\pi$
$600$		0			0
$601$		−	4.59089i		−	0.187266i	−0.995607	−	0.0936332i	$-0.970152\pi$
$601$		−	4.59089i		−	0.187266i	0.995607	−	0.0936332i	$-0.0298481\pi$
$602$	4.44759	−	3.54883i	0.181270	−	0.144640i
$603$	5.41490	+	5.41490i	0.220512	+	0.220512i
$604$	5.15910	+	2.97861i	0.209921	+	0.121198i
$605$		0			0
$606$	−7.18310	−	12.4415i	−0.291793	−	0.505401i
$607$	16.4732	−	4.41399i	0.668628	−	0.179158i	0.0914911	−	0.995806i	$-0.470837\pi$
$607$	16.4732	−	4.41399i	0.668628	−	0.179158i	0.577137	+	0.816648i	$0.304170\pi$
$608$	2.49350	−	2.49350i	0.101125	−	0.101125i
$609$	−10.4712	+	14.1962i	−0.424315	+	0.575257i
$610$		0			0
$611$	−16.4545	+	28.5001i	−0.665680	+	1.15299i
$612$	−0.364671	+	1.36097i	−0.0147410	+	0.0550140i
$613$	−2.92689	+	10.9233i	−0.118216	+	0.441188i	−0.999507	−	0.0313851i	$-0.990008\pi$
$613$	−2.92689	+	10.9233i	−0.118216	+	0.441188i	0.881291	+	0.472573i	$0.156675\pi$
$614$	4.81796	−	8.34496i	0.194437	−	0.336775i
$615$		0			0
$616$	−6.04556	+	8.19615i	−0.243583	+	0.330232i
$617$	−3.28476	+	3.28476i	−0.132240	+	0.132240i	−0.770128	−	0.637889i	$-0.779808\pi$
$617$	−3.28476	+	3.28476i	−0.132240	+	0.132240i	0.637889	+	0.770128i	$0.279808\pi$
$618$	−14.8426	+	3.97706i	−0.597057	+	0.159981i
$619$	−12.8766	−	22.3029i	−0.517554	−	0.896429i	−0.999792	−	0.0203891i	$-0.993510\pi$
$619$	−12.8766	−	22.3029i	−0.517554	−	0.896429i	0.482239	−	0.876040i	$-0.339824\pi$
$620$		0			0
$621$	−1.22021	−	0.704491i	−0.0489655	−	0.0282703i
$622$	14.5800	+	14.5800i	0.584605	+	0.584605i
$623$	28.8536	−	23.0229i	1.15599	−	0.922394i
$624$			6.25839i			0.250536i
$625$		0			0
$626$	14.2623	−	8.23433i	0.570035	−	0.329110i
$627$	−13.1118	−	3.51330i	−0.523635	−	0.140308i
$628$	−2.58387	−	9.64315i	−0.103108	−	0.384804i
$629$	−14.3328			−0.571488
$630$		0			0
$631$	35.5189			1.41399			0.706993	−	0.707221i	$-0.250051\pi$
$631$	35.5189			1.41399			0.706993	+	0.707221i	$0.250051\pi$
$632$	0.815432	+	3.04324i	0.0324362	+	0.121053i
$633$	−14.9164	−	3.99683i	−0.592872	−	0.158860i
$634$	−23.0205	+	13.2909i	−0.914262	+	0.527849i
$635$		0			0
$636$			9.84941i			0.390555i
$637$	−43.7772	+	1.66208i	−1.73452	+	0.0658540i
$638$	18.1482	+	18.1482i	0.718495	+	0.718495i
$639$	9.75005	+	5.62920i	0.385706	+	0.222688i
$640$		0			0
$641$	6.14492	+	10.6433i	0.242710	+	0.420386i	0.961485	−	0.274857i	$-0.0886304\pi$
$641$	6.14492	+	10.6433i	0.242710	+	0.420386i	−0.718775	+	0.695242i	$0.755297\pi$
$642$	−2.60170	+	0.697125i	−0.102681	+	0.0275133i
$643$	−25.5136	+	25.5136i	−1.00616	+	1.00616i	−0.00617772	+	0.999981i	$0.501966\pi$
$643$	−25.5136	+	25.5136i	−1.00616	+	1.00616i	−0.999981	+	0.00617772i	$0.998034\pi$
$644$	3.41637	−	1.49166i	0.134624	−	0.0587797i
$645$		0			0
$646$	2.48428	−	4.30289i	0.0977426	−	0.169295i
$647$	8.44686	−	31.5241i	0.332080	−	1.23934i	−0.574920	−	0.818210i	$-0.694967\pi$
$647$	8.44686	−	31.5241i	0.332080	−	1.23934i	0.907000	−	0.421130i	$-0.138367\pi$
$648$	−0.258819	+	0.965926i	−0.0101674	+	0.0379452i
$649$	−26.3662	+	45.6676i	−1.03496	+	1.79261i
$650$		0			0
$651$	−13.8253	−	1.55390i	−0.541858	−	0.0609022i
$652$	0.972804	−	0.972804i	0.0380980	−	0.0380980i
$653$	−18.0668	+	4.84099i	−0.707010	+	0.189443i	−0.594368	−	0.804193i	$-0.702598\pi$
$653$	−18.0668	+	4.84099i	−0.707010	+	0.189443i	−0.112642	+	0.993636i	$0.535931\pi$
$654$	8.40064	+	14.5503i	0.328491	+	0.568963i
$655$		0			0
$656$	−0.642250	−	0.370803i	−0.0250757	−	0.0144774i
$657$	−7.53118	−	7.53118i	−0.293819	−	0.293819i
$658$	−2.07731	−	13.7564i	−0.0809820	−	0.536282i
$659$		−	43.5871i		−	1.69791i	−0.528462	−	0.848957i	$-0.677231\pi$
$659$		−	43.5871i		−	1.69791i	0.528462	−	0.848957i	$-0.322769\pi$
$660$		0			0
$661$	21.3300	−	12.3149i	0.829642	−	0.478994i	−0.0240879	−	0.999710i	$-0.507668\pi$
$661$	21.3300	−	12.3149i	0.829642	−	0.478994i	0.853730	+	0.520716i	$0.174335\pi$
$662$	6.51705	+	1.74624i	0.253292	+	0.0678695i
$663$	2.28226	+	8.51750i	0.0886355	+	0.330792i
$664$	0.667375			0.0258992
$665$		0			0
$666$	−10.1725			−0.394176
$667$	−2.43140	−	9.07411i	−0.0941442	−	0.351351i
$668$	10.5101	+	2.81617i	0.406648	+	0.108961i
$669$	1.44399	−	0.833688i	0.0558279	−	0.0322322i
$670$		0			0
$671$		−	3.81263i		−	0.147185i
$672$	−1.65017	−	2.06808i	−0.0636565	−	0.0797779i
$673$	−11.4796	−	11.4796i	−0.442506	−	0.442506i	0.450348	−	0.892853i	$-0.351300\pi$
$673$	−11.4796	−	11.4796i	−0.442506	−	0.442506i	−0.892853	+	0.450348i	$0.851300\pi$
$674$	2.69144	+	1.55390i	0.103670	+	0.0598541i
$675$		0			0
$676$	13.0837	+	22.6617i	0.503221	+	0.871604i
$677$	−16.0065	+	4.28892i	−0.615179	+	0.164837i	−0.552935	−	0.833224i	$-0.686492\pi$
$677$	−16.0065	+	4.28892i	−0.615179	+	0.164837i	−0.0622438	+	0.998061i	$0.519826\pi$
$678$	10.2109	−	10.2109i	0.392148	−	0.392148i
$679$	10.4607	+	23.9582i	0.401444	+	0.919430i
$680$		0			0
$681$	−5.75572	+	9.96921i	−0.220560	+	0.382021i
$682$	−5.23894	+	19.5520i	−0.200609	+	0.748685i
$683$	3.60132	−	13.4403i	0.137801	−	0.514279i	−0.862170	−	0.506619i	$-0.830895\pi$
$683$	3.60132	−	13.4403i	0.137801	−	0.514279i	0.999971	−	0.00765999i	$-0.00243827\pi$
$684$	1.76317	−	3.05390i	0.0674165	−	0.116769i
$685$		0			0
$686$	14.0279	−	12.0921i	0.535587	−	0.461678i
$687$	11.0432	−	11.0432i	0.421325	−	0.421325i
$688$	2.07731	−	0.556613i	0.0791967	−	0.0212207i
$689$	30.8207	+	53.3831i	1.17418	+	2.03373i
$690$		0			0
$691$	4.05178	+	2.33929i	0.154137	+	0.0889909i	0.575085	−	0.818094i	$-0.304969\pi$
$691$	4.05178	+	2.33929i	0.154137	+	0.0889909i	−0.420948	+	0.907085i	$0.638302\pi$
$692$	−1.20125	−	1.20125i	−0.0456646	−	0.0456646i
$693$	−3.71825	+	9.48158i	−0.141244	+	0.360176i
$694$		−	13.2471i		−	0.502851i
$695$		0			0
$696$	−5.77412	+	3.33369i	−0.218867	+	0.126363i
$697$	−1.00931	−	0.270443i	−0.0382302	−	0.0102438i
$698$	4.70503	+	17.5594i	0.178088	+	0.664633i
$699$	29.7271			1.12438
$700$		0			0
$701$	27.2732			1.03009			0.515047	−	0.857162i	$-0.327775\pi$
$701$	27.2732			1.03009			0.515047	+	0.857162i	$0.327775\pi$
$702$	1.61979	+	6.04514i	0.0611351	+	0.228159i
$703$	34.6493	+	9.28426i	1.30682	+	0.350163i
$704$	−3.33369	+	1.92471i	−0.125643	+	0.0725401i
$705$		0			0
$706$		−	21.8120i		−	0.820904i
$707$	37.5833	−	5.67532i	1.41347	−	0.213442i
$708$	−9.68653	−	9.68653i	−0.364042	−	0.364042i
$709$	−22.7497	−	13.1345i	−0.854382	−	0.493278i	0.00774478	−	0.999970i	$-0.497535\pi$
$709$	−22.7497	−	13.1345i	−0.854382	−	0.493278i	−0.862127	+	0.506692i	$0.830868\pi$
$710$		0			0
$711$	1.57529	+	2.72849i	0.0590782	+	0.102326i
$712$	13.4765	−	3.61101i	0.505052	−	0.135328i
$713$	5.23894	−	5.23894i	0.196200	−	0.196200i
$714$	−3.00000	−	2.21283i	−0.112272	−	0.0828131i
$715$		0			0
$716$	−6.91165	+	11.9713i	−0.258301	+	0.447390i
$717$	2.05810	−	7.68092i	0.0768610	−	0.286849i
$718$	−7.40427	+	27.6331i	−0.276325	+	1.03126i
$719$	−10.2929	+	17.8279i	−0.383862	+	0.664869i	−0.991611	−	0.129261i	$-0.958740\pi$
$719$	−10.2929	+	17.8279i	−0.383862	+	0.664869i	0.607748	+	0.794130i	$0.292073\pi$
$720$		0			0
$721$	4.54085	−	40.4008i	0.169110	−	1.50460i
$722$	4.64209	−	4.64209i	0.172761	−	0.172761i
$723$	−10.9424	+	2.93201i	−0.406952	+	0.109043i
$724$	1.68043	+	2.91059i	0.0624527	+	0.108171i
$725$		0			0
$726$	3.30645	+	1.90898i	0.122714	+	0.0708490i
$727$	−7.63477	−	7.63477i	−0.283158	−	0.283158i	0.551209	−	0.834367i	$-0.314167\pi$
$727$	−7.63477	−	7.63477i	−0.283158	−	0.283158i	−0.834367	+	0.551209i	$0.814167\pi$
$728$	−15.4152	−	6.04514i	−0.571326	−	0.224048i
$729$			1.00000i			0.0370370i
$730$		0			0
$731$	2.62418	−	1.51507i	0.0970588	−	0.0560369i
$732$	0.956695	+	0.256346i	0.0353605	+	0.00947481i
$733$	3.65082	+	13.6250i	0.134846	+	0.503252i	0.999998	+	0.00174331i	$0.000554912\pi$
$733$	3.65082	+	13.6250i	0.134846	+	0.503252i	−0.865152	+	0.501509i	$0.832778\pi$
$734$	32.4834			1.19899
$735$		0			0
$736$	1.40898			0.0519358
$737$	7.62949	+	28.4737i	0.281036	+	1.04884i
$738$	−0.716337	−	0.191942i	−0.0263687	−	0.00706548i
$739$	17.0208	−	9.82696i	0.626120	−	0.361490i	−0.153128	−	0.988206i	$-0.548935\pi$
$739$	17.0208	−	9.82696i	0.626120	−	0.361490i	0.779248	+	0.626716i	$0.215601\pi$
$740$		0			0
$741$		−	22.0692i		−	0.810734i
$742$	−24.2603	−	9.51380i	−0.890625	−	0.349263i
$743$	−20.7983	−	20.7983i	−0.763016	−	0.763016i	0.213851	−	0.976866i	$-0.431399\pi$
$743$	−20.7983	−	20.7983i	−0.763016	−	0.763016i	−0.976866	+	0.213851i	$0.931399\pi$
$744$	−4.55390	−	2.62920i	−0.166954	−	0.0963910i
$745$		0			0
$746$	−11.0346	−	19.1125i	−0.404006	−	0.699759i
$747$	0.644635	−	0.172729i	0.0235860	−	0.00631984i
$748$	−3.83517	+	3.83517i	−0.140228	+	0.140228i
$749$	0.795948	−	7.08170i	0.0290833	−	0.258760i
$750$		0			0
$751$	11.9305	−	20.6642i	0.435350	−	0.754048i	−0.561975	−	0.827155i	$-0.689958\pi$
$751$	11.9305	−	20.6642i	0.435350	−	0.754048i	0.997324	+	0.0731070i	$0.0232915\pi$
$752$	1.36097	−	5.07922i	0.0496296	−	0.185220i
$753$	5.44389	−	20.3169i	0.198386	−	0.740388i
$754$	−20.8635	+	36.1367i	−0.759805	+	1.31602i
$755$		0			0
$756$	−2.12920	−	1.57052i	−0.0774381	−	0.0571191i
$757$	−30.3903	+	30.3903i	−1.10455	+	1.10455i	−0.110699	+	0.993854i	$0.535309\pi$
$757$	−30.3903	+	30.3903i	−1.10455	+	1.10455i	−0.993854	+	0.110699i	$0.964691\pi$
$758$	−15.3185	+	4.10457i	−0.556392	+	0.149085i
$759$	−2.71188	−	4.69711i	−0.0984349	−	0.170494i
$760$		0			0
$761$	0.111347	+	0.0642865i	0.00403634	+	0.00233038i	0.502017	−	0.864858i	$-0.332592\pi$
$761$	0.111347	+	0.0642865i	0.00403634	+	0.00233038i	−0.497980	+	0.867188i	$0.665925\pi$
$762$	−14.5565	−	14.5565i	−0.527327	−	0.527327i
$763$	−43.9537	+	6.63729i	−1.59123	+	0.240286i
$764$		−	0.741607i		−	0.0268304i
$765$		0			0
$766$	−15.3693	+	8.87347i	−0.555316	+	0.320612i
$767$	−82.8113	−	22.1892i	−2.99014	−	0.801207i
$768$	−0.258819	−	0.965926i	−0.00933933	−	0.0348548i
$769$	−27.3976			−0.987984			−0.493992	−	0.869466i	$-0.664463\pi$
$769$	−27.3976			−0.987984			−0.493992	+	0.869466i	$0.664463\pi$
$770$		0			0
$771$	−25.9144			−0.933285
$772$	1.91759	+	7.15653i	0.0690154	+	0.257569i
$773$	−4.67901	−	1.25374i	−0.168292	−	0.0450938i	0.173689	−	0.984801i	$-0.444431\pi$
$773$	−4.67901	−	1.25374i	−0.168292	−	0.0450938i	−0.341981	+	0.939707i	$0.611098\pi$
$774$	1.86246	−	1.07529i	0.0669449	−	0.0386507i
$775$		0			0
$776$			9.88086i			0.354702i
$777$	9.82586	−	25.0561i	0.352501	−	0.898882i
$778$	24.6860	+	24.6860i	0.885034	+	0.885034i
$779$	2.26479	+	1.30758i	0.0811447	+	0.0468489i
$780$		0			0
$781$	21.6691	+	37.5320i	0.775381	+	1.34300i
$782$	1.91759	−	0.513816i	0.0685727	−	0.0183740i
$783$	−4.71455	+	4.71455i	−0.168484	+	0.168484i
$784$	6.68788	−	2.06696i	0.238853	−	0.0738199i
$785$		0			0
$786$	−3.27145	+	5.66631i	−0.116689	+	0.202111i
$787$	−13.5953	+	50.7385i	−0.484621	+	1.80863i	0.0971384	+	0.995271i	$0.469031\pi$
$787$	−13.5953	+	50.7385i	−0.484621	+	1.80863i	−0.581760	+	0.813361i	$0.697636\pi$
$788$	4.58810	−	17.1230i	0.163444	−	0.609982i
$789$	8.29551	−	14.3682i	0.295328	−	0.511523i
$790$		0			0
$791$	15.2878	+	35.0138i	0.543571	+	1.24495i
$792$	−2.72194	+	2.72194i	−0.0967201	+	0.0967201i
$793$	5.98738	−	1.60431i	0.212618	−	0.0569708i
$794$	−18.0597	−	31.2803i	−0.640914	−	1.11010i
$795$		0			0
$796$	−0.606741	−	0.350302i	−0.0215054	−	0.0124161i
$797$	8.85221	+	8.85221i	0.313561	+	0.313561i	0.846288	−	0.532726i	$-0.178832\pi$
$797$	8.85221	+	8.85221i	0.313561	+	0.313561i	−0.532726	+	0.846288i	$0.678832\pi$
$798$	5.81905	+	7.29275i	0.205992	+	0.258161i
$799$		−	7.40898i		−	0.262111i
$800$		0			0
$801$	12.0827	−	6.97594i	0.426920	−	0.246483i
$802$	1.43267	+	0.383884i	0.0505895	+	0.0135554i
$803$	−10.6113	−	39.6019i	−0.374465	−	1.39752i
$804$	−7.65782			−0.270070
$805$		0			0
$806$	−32.9091			−1.15917
$807$	7.08151	+	26.4286i	0.249281	+	0.930329i
$808$	13.8767	+	3.71825i	0.488180	+	0.130807i
$809$	17.1675	−	9.91165i	0.603577	−	0.348475i	−0.166871	−	0.985979i	$-0.553366\pi$
$809$	17.1675	−	9.91165i	0.603577	−	0.348475i	0.770447	+	0.637504i	$0.220033\pi$
$810$		0			0
$811$		−	7.73982i		−	0.271782i	−0.990724	−	0.135891i	$-0.956610\pi$
$811$		−	7.73982i		−	0.271782i	0.990724	−	0.135891i	$-0.0433897\pi$
$812$	−2.63392	−	17.4425i	−0.0924326	−	0.612111i
$813$	−0.676853	−	0.676853i	−0.0237383	−	0.0237383i
$814$	−33.9119	−	19.5790i	−1.18861	−	0.686245i
$815$		0			0
$816$	−0.704491	−	1.22021i	−0.0246621	−	0.0427160i
$817$	−7.32530	+	1.96281i	−0.256280	+	0.0686700i
$818$	2.13852	−	2.13852i	0.0747716	−	0.0747716i
$819$	−16.4545	−	1.84941i	−0.574968	−	0.0646236i
$820$		0			0
$821$	−18.9844	+	32.8819i	−0.662560	+	1.14759i	0.317381	+	0.948298i	$0.397197\pi$
$821$	−18.9844	+	32.8819i	−0.662560	+	1.14759i	−0.979941	+	0.199289i	$0.936137\pi$
$822$	−2.94610	+	10.9950i	−0.102757	+	0.383495i
$823$	9.28104	−	34.6373i	0.323517	−	1.20738i	−0.592278	−	0.805734i	$-0.701771\pi$
$823$	9.28104	−	34.6373i	0.323517	−	1.20738i	0.915795	−	0.401647i	$-0.131562\pi$
$824$	7.68310	−	13.3075i	0.267653	−	0.463589i
$825$		0			0
$826$	33.2156	−	14.5027i	1.15572	−	0.504612i
$827$	−16.9966	+	16.9966i	−0.591029	+	0.591029i	−0.937909	−	0.346881i	$-0.887241\pi$
$827$	−16.9966	+	16.9966i	−0.591029	+	0.591029i	0.346881	+	0.937909i	$0.387241\pi$
$828$	1.36097	−	0.364671i	0.0472971	−	0.0126732i
$829$	−12.8699	−	22.2913i	−0.446991	−	0.774210i	0.551198	−	0.834374i	$-0.314171\pi$
$829$	−12.8699	−	22.2913i	−0.446991	−	0.774210i	−0.998188	+	0.0601642i	$0.980838\pi$
$830$		0			0
$831$	−18.0252	−	10.4069i	−0.625288	−	0.361010i
$832$	−4.42535	−	4.42535i	−0.153421	−	0.153421i
$833$	8.34825	−	5.25195i	0.289250	−	0.181969i
$834$			3.50510i			0.121372i
$835$		0			0
$836$	11.7557	−	6.78717i	0.406580	−	0.234739i
$837$	−5.07922	−	1.36097i	−0.175563	−	0.0470421i
$838$	−3.84469	−	14.3486i	−0.132813	−	0.495664i
$839$	−39.3234			−1.35759			−0.678797	−	0.734326i	$-0.737499\pi$
$839$	−39.3234			−1.35759			−0.678797	+	0.734326i	$0.737499\pi$
$840$		0			0
$841$	−15.4539			−0.532893
$842$	−7.06368	−	26.3620i	−0.243431	−	0.908495i
$843$	2.79365	+	0.748555i	0.0962183	+	0.0257816i
$844$	13.3736	−	7.72128i	0.460340	−	0.265777i
$845$		0			0
$846$		−	5.25839i		−	0.180787i
$847$	−7.89585	+	6.30028i	−0.271305	+	0.216480i
$848$	−6.96459	−	6.96459i	−0.239165	−	0.239165i
$849$	−18.3542	−	10.5968i	−0.629914	−	0.363681i
$850$		0			0
$851$	7.16642	+	12.4126i	0.245662	+	0.425499i
$852$	−10.8748	+	2.91389i	−0.372564	+	0.0998281i
$853$	11.4032	−	11.4032i	0.390439	−	0.390439i	−0.484405	−	0.874844i	$-0.660964\pi$
$853$	11.4032	−	11.4032i	0.390439	−	0.390439i	0.874844	+	0.484405i	$0.160964\pi$
$854$	−1.55551	+	2.10885i	−0.0532284	+	0.0721634i
$855$		0			0
$856$	1.34674	−	2.33262i	0.0460307	−	0.0797275i
$857$	0.673539	−	2.51368i	0.0230077	−	0.0858658i	−0.953467	−	0.301496i	$-0.902514\pi$
$857$	0.673539	−	2.51368i	0.0230077	−	0.0858658i	0.976475	+	0.215630i	$0.0691806\pi$
$858$	−6.23524	+	23.2702i	−0.212868	+	0.794433i
$859$	−11.6663	+	20.2066i	−0.398049	+	0.689442i	−0.993485	−	0.113961i	$-0.963646\pi$
$859$	−11.6663	+	20.2066i	−0.398049	+	0.689442i	0.595436	+	0.803403i	$0.296979\pi$
$860$		0			0
$861$	1.16471	−	1.57903i	0.0396931	−	0.0538131i
$862$	−26.1971	+	26.1971i	−0.892278	+	0.892278i
$863$	−40.2335	+	10.7805i	−1.36957	+	0.366974i	−0.867320	−	0.497751i	$-0.834159\pi$
$863$	−40.2335	+	10.7805i	−1.36957	+	0.366974i	−0.502246	+	0.864725i	$0.667493\pi$
$864$	−0.500000	−	0.866025i	−0.0170103	−	0.0294628i
$865$		0			0
$866$	−9.38142	−	5.41637i	−0.318794	−	0.184056i
$867$	10.6170	+	10.6170i	0.360574	+	0.360574i
$868$	10.8748	−	8.67722i	0.369114	−	0.294524i
$869$			12.1279i			0.411411i
$870$		0			0
$871$	−41.5048	+	23.9628i	−1.40634	+	0.811949i
$872$	−16.2288	−	4.34849i	−0.549576	−	0.147259i
$873$	2.55735	+	9.54418i	0.0865533	+	0.323021i
$874$	−4.96855			−0.168064
$875$		0			0
$876$	10.6507			0.359854
$877$	−10.1242	−	37.7842i	−0.341871	−	1.27588i	−0.896225	−	0.443600i	$-0.853701\pi$
$877$	−10.1242	−	37.7842i	−0.341871	−	1.27588i	0.554354	−	0.832281i	$-0.312965\pi$
$878$	19.5841	+	5.24754i	0.660931	+	0.177096i
$879$	−17.3223	+	10.0011i	−0.584268	+	0.337327i
$880$		0			0
$881$			11.2584i			0.379305i	0.981851	+	0.189652i	$0.0607361\pi$
$881$			11.2584i			0.379305i	−0.981851	+	0.189652i	$0.939264\pi$
$882$	5.92503	−	3.72748i	0.199506	−	0.125511i
$883$	16.2037	+	16.2037i	0.545297	+	0.545297i	0.925077	−	0.379780i	$-0.124000\pi$
$883$	16.2037	+	16.2037i	0.545297	+	0.545297i	−0.379780	+	0.925077i	$0.624000\pi$
$884$	−7.63658	−	4.40898i	−0.256846	−	0.148290i
$885$		0			0
$886$	−3.51572	−	6.08941i	−0.118113	−	0.204578i
$887$	12.6721	−	3.39548i	0.425488	−	0.114009i	−0.0397194	−	0.999211i	$-0.512646\pi$
$887$	12.6721	−	3.39548i	0.425488	−	0.114009i	0.465207	+	0.885202i	$0.345980\pi$
$888$	7.19303	−	7.19303i	0.241382	−	0.241382i
$889$	49.9150	−	21.7940i	1.67410	−	0.730948i
$890$		0			0
$891$	−1.92471	+	3.33369i	−0.0644801	+	0.111683i
$892$	−0.431548	+	1.61056i	−0.0144493	+	0.0539256i
$893$	−4.79925	+	17.9111i	−0.160601	+	0.599371i
$894$	6.91165	−	11.9713i	0.231160	−	0.400381i
$895$		0			0
$896$	2.62920	+	0.295509i	0.0878353	+	0.00987226i
$897$	6.23524	−	6.23524i	0.208189	−	0.208189i
$898$	−4.31434	+	1.15602i	−0.143971	+	0.0385770i
$899$	−17.5298	−	30.3626i	−0.584653	−	1.01265i
$900$		0			0
$901$	−12.0184	−	6.93882i	−0.400391	−	0.231166i
$902$	−2.01861	−	2.01861i	−0.0672125	−	0.0672125i
$903$	0.849583	+	5.62614i	0.0282723	+	0.187226i
$904$			14.4404i			0.480282i
$905$		0			0
$906$	−5.15910	+	2.97861i	−0.171400	+	0.0989576i
$907$	9.85808	+	2.64146i	0.327332	+	0.0877084i	0.418743	−	0.908105i	$-0.362471\pi$
$907$	9.85808	+	2.64146i	0.327332	+	0.0877084i	−0.0914106	+	0.995813i	$0.529138\pi$
$908$	−2.97938	−	11.1192i	−0.0988743	−	0.369004i
$909$	14.3662			0.476497
$910$		0			0
$911$	1.10568			0.0366328			0.0183164	−	0.999832i	$-0.494169\pi$
$911$	1.10568			0.0366328			0.0183164	+	0.999832i	$0.494169\pi$
$912$	0.912685	+	3.40619i	0.0302220	+	0.112790i
$913$	2.48147	+	0.664907i	0.0821245	+	0.0220052i
$914$	21.0147	−	12.1329i	0.695106	−	0.401320i
$915$		0			0
$916$			15.6175i			0.516016i
$917$	−10.7969	−	13.5312i	−0.356544	−	0.446840i
$918$	−0.996301	−	0.996301i	−0.0328828	−	0.0328828i
$919$	35.1784	+	20.3103i	1.16043	+	0.669974i	0.951407	−	0.307937i	$-0.0996385\pi$
$919$	35.1784	+	20.3103i	1.16043	+	0.669974i	0.209023	+	0.977911i	$0.432972\pi$
$920$		0			0
$921$	4.81796	+	8.34496i	0.158757	+	0.274976i
$922$	8.51750	−	2.28226i	0.280509	−	0.0751621i
$923$	−49.8224	+	49.8224i	−1.63992	+	1.63992i
$924$	−4.07529	−	9.33369i	−0.134067	−	0.307056i
$925$		0			0
$926$	0.743385	−	1.28758i	0.0244291	−	0.0423125i
$927$	3.97706	−	14.8426i	0.130624	−	0.487495i
$928$	1.72564	−	6.44019i	0.0566470	−	0.211410i
$929$	9.48534	−	16.4291i	0.311204	−	0.539021i	−0.667419	−	0.744682i	$-0.732601\pi$
$929$	9.48534	−	16.4291i	0.311204	−	0.539021i	0.978623	+	0.205661i	$0.0659345\pi$
$930$		0			0
$931$	−23.5837	+	7.28879i	−0.772926	+	0.238881i
$932$	−21.0202	+	21.0202i	−0.688540	+	0.688540i
$933$	−19.9167	+	5.33665i	−0.652042	+	0.174714i
$934$	−18.5037	−	32.0494i	−0.605461	−	1.04869i
$935$		0			0
$936$	−5.41993	−	3.12920i	−0.177156	−	0.102281i
$937$	−1.26931	−	1.26931i	−0.0414664	−	0.0414664i	0.686070	−	0.727536i	$-0.259335\pi$
$937$	−1.26931	−	1.26931i	−0.0414664	−	0.0414664i	−0.727536	+	0.686070i	$0.759335\pi$
$938$	7.39689	−	18.8622i	0.241517	−	0.615872i
$939$			16.4687i			0.537434i
$940$		0			0
$941$	−44.9611	+	25.9583i	−1.46569	+	0.846216i	−0.999265	−	0.0383456i	$-0.987791\pi$
$941$	−44.9611	+	25.9583i	−1.46569	+	0.846216i	−0.466424	+	0.884561i	$0.654458\pi$
$942$	9.64315	+	2.58387i	0.314191	+	0.0841872i
$943$	0.270443	+	1.00931i	0.00880683	+	0.0328675i
$944$	13.6988			0.445859
$945$		0			0
$946$	8.27850			0.269157
$947$	7.12325	+	26.5843i	0.231475	+	0.863875i	0.979706	+	0.200437i	$0.0642364\pi$
$947$	7.12325	+	26.5843i	0.231475	+	0.863875i	−0.748232	+	0.663437i	$0.769097\pi$
$948$	−3.04324	−	0.815432i	−0.0988397	−	0.0264840i
$949$	57.7260	−	33.3281i	1.87387	−	1.08188i
$950$		0			0
$951$		−	26.5818i		−	0.861974i
$952$	3.68603	−	0.556613i	0.119465	−	0.0180399i
$953$	−24.6409	−	24.6409i	−0.798197	−	0.798197i	0.184614	−	0.982811i	$-0.440897\pi$
$953$	−24.6409	−	24.6409i	−0.798197	−	0.798197i	−0.982811	+	0.184614i	$0.940897\pi$
$954$	−8.52984	−	4.92471i	−0.276164	−	0.159443i
$955$		0			0
$956$	3.97594	+	6.88653i	0.128591	+	0.222726i
$957$	−24.7909	+	6.64271i	−0.801377	+	0.214728i
$958$	1.10128	−	1.10128i	0.0355807	−	0.0355807i
$959$	−24.2364	−	17.8770i	−0.782633	−	0.577278i
$960$		0			0
$961$	−1.67465	+	2.90058i	−0.0540210	+	0.0935671i
$962$	16.4773	−	61.4941i	0.531249	−	1.98265i
$963$	0.697125	−	2.60170i	0.0224645	−	0.0838388i
$964$	5.66420	−	9.81069i	0.182432	−	0.315981i
$965$		0			0
$966$	−0.416367	+	3.70449i	−0.0133964	+	0.119190i
$967$	−36.8801	+	36.8801i	−1.18598	+	1.18598i	−0.207814	+	0.978168i	$0.566635\pi$
$967$	−36.8801	+	36.8801i	−1.18598	+	1.18598i	−0.978168	+	0.207814i	$0.933365\pi$
$968$	−3.68787	+	0.988162i	−0.118533	+	0.0317607i
$969$	2.48428	+	4.30289i	0.0798065	+	0.138229i
$970$		0			0
$971$	43.6973	+	25.2287i	1.40231	+	0.809626i	0.994630	−	0.103497i	$-0.0330031\pi$
$971$	43.6973	+	25.2287i	1.40231	+	0.809626i	0.407684	+	0.913123i	$0.366336\pi$
$972$	−0.707107	−	0.707107i	−0.0226805	−	0.0226805i
$973$	−8.63351	−	3.38567i	−0.276778	−	0.108540i
$974$			7.82739i			0.250806i
$975$		0			0
$976$	−0.857750	+	0.495222i	−0.0274559	+	0.0158517i
$977$	34.6339	+	9.28012i	1.10804	+	0.296897i	0.766033	−	0.642801i	$-0.222228\pi$
$977$	34.6339	+	9.28012i	1.10804	+	0.296897i	0.342003	+	0.939699i	$0.388895\pi$
$978$	0.356071	+	1.32888i	0.0113859	+	0.0424928i
$979$	53.7065			1.71647
$980$		0			0
$981$	−16.8013			−0.536424
$982$	−11.3564	−	42.3826i	−0.362396	−	1.35248i
$983$	4.21948	+	1.13061i	0.134580	+	0.0360607i	0.325480	−	0.945549i	$-0.394474\pi$
$983$	4.21948	+	1.13061i	0.134580	+	0.0360607i	−0.190900	+	0.981609i	$0.561141\pi$
$984$	0.642250	−	0.370803i	0.0204742	−	0.0118208i
$985$		0			0
$986$		−	9.39421i		−	0.299173i
$987$	12.9521	+	5.07922i	0.412269	+	0.161673i
$988$	15.6053	+	15.6053i	0.496471	+	0.496471i
$989$	−2.62418	−	1.51507i	−0.0834441	−	0.0481765i
$990$		0			0
$991$	−11.3772	−	19.7059i	−0.361409	−	0.625978i	0.626784	−	0.779193i	$-0.284371\pi$
$991$	−11.3772	−	19.7059i	−0.361409	−	0.625978i	−0.988193	+	0.153214i	$0.951037\pi$
$992$	5.07922	−	1.36097i	0.161265	−	0.0432109i
$993$	−4.77081	+	4.77081i	−0.151397	+	0.151397i
$994$	3.32696	−	29.6005i	0.105525	−	0.938872i
$995$		0			0
$996$	−0.333688	+	0.577964i	−0.0105733	+	0.0183135i
$997$	−7.11948	+	26.5703i	−0.225476	+	0.841489i	0.756737	+	0.653720i	$0.226792\pi$
$997$	−7.11948	+	26.5703i	−0.225476	+	0.841489i	−0.982213	+	0.187769i	$0.939874\pi$
$998$	8.93659	−	33.3518i	0.282883	−	1.05573i
$999$	5.08624	−	8.80963i	0.160922	−	0.278724i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1050.2.bc.f.943.2	yes	16
5.2	odd	4		1050.2.bc.e.607.4	yes	16
5.3	odd	4		1050.2.bc.e.607.1	yes	16
5.4	even	2	inner	1050.2.bc.f.943.3	yes	16
7.3	odd	6		1050.2.bc.e.493.3	yes	16
35.3	even	12	inner	1050.2.bc.f.157.3	yes	16
35.17	even	12	inner	1050.2.bc.f.157.2	yes	16
35.24	odd	6		1050.2.bc.e.493.2	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1050.2.bc.e.493.2	✓	16	35.24	odd	6
1050.2.bc.e.493.3	yes	16	7.3	odd	6
1050.2.bc.e.607.1	yes	16	5.3	odd	4
1050.2.bc.e.607.4	yes	16	5.2	odd	4
1050.2.bc.f.157.2	yes	16	35.17	even	12	inner
1050.2.bc.f.157.3	yes	16	35.3	even	12	inner
1050.2.bc.f.943.2	yes	16	1.1	even	1	trivial
1050.2.bc.f.943.3	yes	16	5.4	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1050.bc (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.258819 - 0.965926i) q^{2} +(0.965926 + 0.258819i) q^{3} +(-0.866025 + 0.500000i) q^{4} -1.00000i q^{6} +(2.46313 + 0.965926i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.866025 + 0.500000i) q^{9} +O(q^{10})\)	\(q+(-0.258819 - 0.965926i) q^{2} +(0.965926 + 0.258819i) q^{3} +(-0.866025 + 0.500000i) q^{4} -1.00000i q^{6} +(2.46313 + 0.965926i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.866025 + 0.500000i) q^{9} +(1.92471 + 3.33369i) q^{11} +(-0.965926 + 0.258819i) q^{12} +(-4.42535 + 4.42535i) q^{13} +(0.295509 - 2.62920i) q^{14} +(0.500000 - 0.866025i) q^{16} +(0.364671 - 1.36097i) q^{17} +(0.258819 - 0.965926i) q^{18} +(-1.76317 + 3.05390i) q^{19} +(2.12920 + 1.57052i) q^{21} +(2.72194 - 2.72194i) q^{22} +(-1.36097 + 0.364671i) q^{23} +(0.500000 + 0.866025i) q^{24} +(5.41993 + 3.12920i) q^{26} +(0.707107 + 0.707107i) q^{27} +(-2.61609 + 0.395046i) q^{28} +6.66738i q^{29} +(-4.55390 + 2.62920i) q^{31} +(-0.965926 - 0.258819i) q^{32} +(0.996301 + 3.71825i) q^{33} -1.40898 q^{34} -1.00000 q^{36} +(-2.63283 - 9.82586i) q^{37} +(3.40619 + 0.912685i) q^{38} +(-5.41993 + 3.12920i) q^{39} -0.741607i q^{41} +(0.965926 - 2.46313i) q^{42} +(1.52070 + 1.52070i) q^{43} +(-3.33369 - 1.92471i) q^{44} +(0.704491 + 1.22021i) q^{46} +(5.07922 - 1.36097i) q^{47} +(0.707107 - 0.707107i) q^{48} +(5.13397 + 4.75839i) q^{49} +(0.704491 - 1.22021i) q^{51} +(1.61979 - 6.04514i) q^{52} +(2.54922 - 9.51380i) q^{53} +(0.500000 - 0.866025i) q^{54} +(1.05868 + 2.42471i) q^{56} +(-2.49350 + 2.49350i) q^{57} +(6.44019 - 1.72564i) q^{58} +(6.84941 + 11.8635i) q^{59} +(-0.857750 - 0.495222i) q^{61} +(3.71825 + 3.71825i) q^{62} +(1.65017 + 2.06808i) q^{63} +1.00000i q^{64} +(3.33369 - 1.92471i) q^{66} +(7.39689 + 1.98199i) q^{67} +(0.364671 + 1.36097i) q^{68} -1.40898 q^{69} +11.2584 q^{71} +(0.258819 + 0.965926i) q^{72} +(-10.2878 - 2.75660i) q^{73} +(-8.80963 + 5.08624i) q^{74} -3.52634i q^{76} +(1.52070 + 10.0704i) q^{77} +(4.42535 + 4.42535i) q^{78} +(2.72849 + 1.57529i) q^{79} +(0.500000 + 0.866025i) q^{81} +(-0.716337 + 0.191942i) q^{82} +(0.471906 - 0.471906i) q^{83} +(-2.62920 - 0.295509i) q^{84} +(1.07529 - 1.86246i) q^{86} +(-1.72564 + 6.44019i) q^{87} +(-0.996301 + 3.71825i) q^{88} +(6.97594 - 12.0827i) q^{89} +(-15.1748 + 6.62564i) q^{91} +(0.996301 - 0.996301i) q^{92} +(-5.07922 + 1.36097i) q^{93} +(-2.62920 - 4.55390i) q^{94} +(-0.866025 - 0.500000i) q^{96} +(6.98682 + 6.98682i) q^{97} +(3.26748 - 6.19060i) q^{98} +3.84941i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q+O(q^{10}) \) 16 * q	\( 16 q - 4 q^{11} + 8 q^{14} + 8 q^{16} - 4 q^{19} - 4 q^{21} + 8 q^{24} - 16 q^{34} - 16 q^{36} - 12 q^{44} + 8 q^{46} + 96 q^{49} + 8 q^{51} + 8 q^{54} - 4 q^{56} + 40 q^{59} - 24 q^{61} + 12 q^{66} - 16 q^{69} + 104 q^{71} - 48 q^{74} - 12 q^{79} + 8 q^{81} - 4 q^{84} + 52 q^{86} + 60 q^{89} - 52 q^{91} - 4 q^{94}+O(q^{100}) \) 16 * q - 4 * q^11 + 8 * q^14 + 8 * q^16 - 4 * q^19 - 4 * q^21 + 8 * q^24 - 16 * q^34 - 16 * q^36 - 12 * q^44 + 8 * q^46 + 96 * q^49 + 8 * q^51 + 8 * q^54 - 4 * q^56 + 40 * q^59 - 24 * q^61 + 12 * q^66 - 16 * q^69 + 104 * q^71 - 48 * q^74 - 12 * q^79 + 8 * q^81 - 4 * q^84 + 52 * q^86 + 60 * q^89 - 52 * q^91 - 4 * q^94

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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