LMFDB - Embedded newform 13.3.d.a.8.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [13,3,Mod(5,13)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(13, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([3])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("13.5"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$N$	$=$	$13$
Weight:	$k$	$=$	$3$
Character orbit:	$[\chi]$	$=$	13.d (of order $4$ , degree $2$ , minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$0.354224343668$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(i)$
Coefficient field:	$\Q(i, \sqrt{10})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$x^{4} + 25$ x^4 + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$1$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			8.2
Root			$1.58114 + 1.58114i$ of defining polynomial
Character	$\chi$	$=$	13.8
Dual form			13.3.d.a.5.2

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.581139 + 0.581139i) q^{2} -4.16228 q^{3} -3.32456i q^{4} +(3.58114 + 3.58114i) q^{5} +(-2.41886 - 2.41886i) q^{6} +(-4.58114 + 4.58114i) q^{7} +(4.25658 - 4.25658i) q^{8} +8.32456 q^{9} +4.16228i q^{10} +(5.32456 - 5.32456i) q^{11} +13.8377i q^{12} +(-5.90569 - 11.5811i) q^{13} -5.32456 q^{14} +(-14.9057 - 14.9057i) q^{15} -8.35089 q^{16} +21.9737i q^{17} +(4.83772 + 4.83772i) q^{18} +(3.16228 + 3.16228i) q^{19} +(11.9057 - 11.9057i) q^{20} +(19.0680 - 19.0680i) q^{21} +6.18861 q^{22} +8.51317i q^{23} +(-17.7171 + 17.7171i) q^{24} +0.649111i q^{25} +(3.29822 - 10.1623i) q^{26} +2.81139 q^{27} +(15.2302 + 15.2302i) q^{28} -5.81139 q^{29} -17.3246i q^{30} +(0.513167 + 0.513167i) q^{31} +(-21.8794 - 21.8794i) q^{32} +(-22.1623 + 22.1623i) q^{33} +(-12.7698 + 12.7698i) q^{34} -32.8114 q^{35} -27.6754i q^{36} +(24.2302 - 24.2302i) q^{37} +3.67544i q^{38} +(24.5811 + 48.2039i) q^{39} +30.4868 q^{40} +(4.83772 + 4.83772i) q^{41} +22.1623 q^{42} -30.4868i q^{43} +(-17.7018 - 17.7018i) q^{44} +(29.8114 + 29.8114i) q^{45} +(-4.94733 + 4.94733i) q^{46} +(-37.3662 + 37.3662i) q^{47} +34.7587 q^{48} +7.02633i q^{49} +(-0.377223 + 0.377223i) q^{50} -91.4605i q^{51} +(-38.5021 + 19.6338i) q^{52} -35.8114 q^{53} +(1.63381 + 1.63381i) q^{54} +38.1359 q^{55} +39.0000i q^{56} +(-13.1623 - 13.1623i) q^{57} +(-3.37722 - 3.37722i) q^{58} +(58.2719 - 58.2719i) q^{59} +(-49.5548 + 49.5548i) q^{60} -80.3246 q^{61} +0.596443i q^{62} +(-38.1359 + 38.1359i) q^{63} +7.97367i q^{64} +(20.3246 - 62.6228i) q^{65} -25.7587 q^{66} +(39.0833 + 39.0833i) q^{67} +73.0527 q^{68} -35.4342i q^{69} +(-19.0680 - 19.0680i) q^{70} +(91.5548 + 91.5548i) q^{71} +(35.4342 - 35.4342i) q^{72} +(31.6228 - 31.6228i) q^{73} +28.1623 q^{74} -2.70178i q^{75} +(10.5132 - 10.5132i) q^{76} +48.7851i q^{77} +(-13.7281 + 42.2982i) q^{78} -18.7851 q^{79} +(-29.9057 - 29.9057i) q^{80} -86.6228 q^{81} +5.62278i q^{82} +(-44.6228 - 44.6228i) q^{83} +(-63.3925 - 63.3925i) q^{84} +(-78.6907 + 78.6907i) q^{85} +(17.7171 - 17.7171i) q^{86} +24.1886 q^{87} -45.3288i q^{88} +(8.89039 - 8.89039i) q^{89} +34.6491i q^{90} +(80.1096 + 26.0000i) q^{91} +28.3025 q^{92} +(-2.13594 - 2.13594i) q^{93} -43.4299 q^{94} +22.6491i q^{95} +(91.0680 + 91.0680i) q^{96} +(-121.355 - 121.355i) q^{97} +(-4.08328 + 4.08328i) q^{98} +(44.3246 - 44.3246i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$4 q - 4 q^{2} - 4 q^{3} + 8 q^{5} - 16 q^{6} - 12 q^{7} + 36 q^{8} + 8 q^{9} - 4 q^{11} + 8 q^{13} + 4 q^{14} - 28 q^{15} - 84 q^{16} + 32 q^{18} + 16 q^{20} + 32 q^{21} + 88 q^{22} + 24 q^{24} - 88 q^{26}+ \cdots + 152 q^{99}+O(q^{100})$ 4 * q - 4 * q^2 - 4 * q^3 + 8 * q^5 - 16 * q^6 - 12 * q^7 + 36 * q^8 + 8 * q^9 - 4 * q^11 + 8 * q^13 + 4 * q^14 - 28 * q^15 - 84 * q^16 + 32 * q^18 + 16 * q^20 + 32 * q^21 + 88 * q^22 + 24 * q^24 - 88 * q^26 - 52 * q^27 + 4 * q^28 + 40 * q^29 + 40 * q^31 + 20 * q^32 - 76 * q^33 - 108 * q^34 - 68 * q^35 + 40 * q^37 + 92 * q^39 + 84 * q^40 + 32 * q^41 + 76 * q^42 - 172 * q^44 + 56 * q^45 + 132 * q^46 - 4 * q^47 - 76 * q^48 - 128 * q^50 + 80 * q^52 - 80 * q^53 + 152 * q^54 + 64 * q^55 - 40 * q^57 - 140 * q^58 + 56 * q^59 - 116 * q^60 - 296 * q^61 - 64 * q^63 + 56 * q^65 + 112 * q^66 - 84 * q^67 + 444 * q^68 - 32 * q^70 + 284 * q^71 - 48 * q^72 + 100 * q^74 + 80 * q^76 - 232 * q^78 + 64 * q^79 - 88 * q^80 - 220 * q^81 - 52 * q^83 - 184 * q^84 - 144 * q^85 - 24 * q^86 + 160 * q^87 + 200 * q^89 + 156 * q^91 - 456 * q^92 + 80 * q^93 - 452 * q^94 + 320 * q^96 - 68 * q^97 + 224 * q^98 + 152 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/13\mathbb{Z}\right)^\times$ .

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

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

$2$	0.581139	+	0.581139i	0.290569	+	0.290569i	0.837305	−	0.546736i	$-0.184130\pi$
$2$	0.581139	+	0.581139i	0.290569	+	0.290569i	−0.546736	+	0.837305i	$0.684130\pi$
$3$	−4.16228			−1.38743			−0.693713	−	0.720252i	$-0.744026\pi$
$3$	−4.16228			−1.38743			−0.693713	+	0.720252i	$0.744026\pi$
$4$		−	3.32456i		−	0.831139i
$5$	3.58114	+	3.58114i	0.716228	+	0.716228i	0.967831	−	0.251603i	$-0.0809577\pi$
$5$	3.58114	+	3.58114i	0.716228	+	0.716228i	−0.251603	+	0.967831i	$0.580958\pi$
$6$	−2.41886	−	2.41886i	−0.403144	−	0.403144i
$7$	−4.58114	+	4.58114i	−0.654448	+	0.654448i	−0.954061	−	0.299613i	$-0.903143\pi$
$7$	−4.58114	+	4.58114i	−0.654448	+	0.654448i	0.299613	+	0.954061i	$0.403143\pi$
$8$	4.25658	−	4.25658i	0.532073	−	0.532073i
$9$	8.32456			0.924951
$10$			4.16228i			0.416228i
$11$	5.32456	−	5.32456i	0.484050	−	0.484050i	−0.422372	−	0.906423i	$-0.638802\pi$
$11$	5.32456	−	5.32456i	0.484050	−	0.484050i	0.906423	+	0.422372i	$0.138802\pi$
$12$			13.8377i			1.15314i
$13$	−5.90569	−	11.5811i	−0.454284	−	0.890857i
$13$	−5.90569	−	11.5811i	−0.454284	−	0.890857i
$14$	−5.32456			−0.380325
$15$	−14.9057	−	14.9057i	−0.993713	−	0.993713i
$16$	−8.35089			−0.521931
$17$			21.9737i			1.29257i	0.763097	+	0.646284i	$0.223678\pi$
$17$			21.9737i			1.29257i	−0.763097	+	0.646284i	$0.776322\pi$
$18$	4.83772	+	4.83772i	0.268762	+	0.268762i
$19$	3.16228	+	3.16228i	0.166436	+	0.166436i	0.785411	−	0.618975i	$-0.212452\pi$
$19$	3.16228	+	3.16228i	0.166436	+	0.166436i	−0.618975	+	0.785411i	$0.712452\pi$
$20$	11.9057	−	11.9057i	0.595285	−	0.595285i
$21$	19.0680	−	19.0680i	0.907999	−	0.907999i
$22$	6.18861			0.281301
$23$			8.51317i			0.370138i	0.982726	+	0.185069i	$0.0592508\pi$
$23$			8.51317i			0.370138i	−0.982726	+	0.185069i	$0.940749\pi$
$24$	−17.7171	+	17.7171i	−0.738212	+	0.738212i
$25$			0.649111i			0.0259644i
$26$	3.29822	−	10.1623i	0.126855	−	0.390857i
$27$	2.81139			0.104125
$28$	15.2302	+	15.2302i	0.543937	+	0.543937i
$29$	−5.81139			−0.200393			−0.100196	−	0.994968i	$-0.531947\pi$
$29$	−5.81139			−0.200393			−0.100196	+	0.994968i	$0.531947\pi$
$30$		−	17.3246i		−	0.577485i
$31$	0.513167	+	0.513167i	0.0165538	+	0.0165538i	0.715335	−	0.698781i	$-0.246274\pi$
$31$	0.513167	+	0.513167i	0.0165538	+	0.0165538i	−0.698781	+	0.715335i	$0.746274\pi$
$32$	−21.8794	−	21.8794i	−0.683730	−	0.683730i
$33$	−22.1623	+	22.1623i	−0.671584	+	0.671584i
$34$	−12.7698	+	12.7698i	−0.375581	+	0.375581i
$35$	−32.8114			−0.937468
$36$		−	27.6754i		−	0.768762i
$37$	24.2302	−	24.2302i	0.654872	−	0.654872i	−0.299290	−	0.954162i	$-0.596750\pi$
$37$	24.2302	−	24.2302i	0.654872	−	0.654872i	0.954162	+	0.299290i	$0.0967499\pi$
$38$			3.67544i			0.0967222i
$39$	24.5811	+	48.2039i	0.630286	+	1.23600i
$40$	30.4868			0.762171
$41$	4.83772	+	4.83772i	0.117993	+	0.117993i	0.763638	−	0.645645i	$-0.223411\pi$
$41$	4.83772	+	4.83772i	0.117993	+	0.117993i	−0.645645	+	0.763638i	$0.723411\pi$
$42$	22.1623			0.527673
$43$		−	30.4868i		−	0.708996i	−0.935057	−	0.354498i	$-0.884652\pi$
$43$		−	30.4868i		−	0.708996i	0.935057	−	0.354498i	$-0.115348\pi$
$44$	−17.7018	−	17.7018i	−0.402313	−	0.402313i
$45$	29.8114	+	29.8114i	0.662475	+	0.662475i
$46$	−4.94733	+	4.94733i	−0.107551	+	0.107551i
$47$	−37.3662	+	37.3662i	−0.795025	+	0.795025i	−0.982306	−	0.187281i	$-0.940033\pi$
$47$	−37.3662	+	37.3662i	−0.795025	+	0.795025i	0.187281	+	0.982306i	$0.440033\pi$
$48$	34.7587			0.724140
$49$			7.02633i			0.143395i
$50$	−0.377223	+	0.377223i	−0.00754447	+	0.00754447i
$51$		−	91.4605i		−	1.79334i
$52$	−38.5021	+	19.6338i	−0.740426	+	0.377573i
$53$	−35.8114			−0.675687			−0.337843	−	0.941202i	$-0.609697\pi$
$53$	−35.8114			−0.675687			−0.337843	+	0.941202i	$0.609697\pi$
$54$	1.63381	+	1.63381i	0.0302557	+	0.0302557i
$55$	38.1359			0.693381
$56$			39.0000i			0.696429i
$57$	−13.1623	−	13.1623i	−0.230917	−	0.230917i
$58$	−3.37722	−	3.37722i	−0.0582280	−	0.0582280i
$59$	58.2719	−	58.2719i	0.987659	−	0.987659i	−0.0122657	−	0.999925i	$-0.503904\pi$
$59$	58.2719	−	58.2719i	0.987659	−	0.987659i	0.999925	+	0.0122657i	$0.00390438\pi$
$60$	−49.5548	+	49.5548i	−0.825913	+	0.825913i
$61$	−80.3246			−1.31680			−0.658398	−	0.752670i	$-0.728766\pi$
$61$	−80.3246			−1.31680			−0.658398	+	0.752670i	$0.728766\pi$
$62$			0.596443i			0.00962004i
$63$	−38.1359	+	38.1359i	−0.605332	+	0.605332i
$64$			7.97367i			0.124589i
$65$	20.3246	−	62.6228i	0.312685	−	0.963427i
$66$	−25.7587			−0.390284
$67$	39.0833	+	39.0833i	0.583332	+	0.583332i	0.935817	−	0.352485i	$-0.114663\pi$
$67$	39.0833	+	39.0833i	0.583332	+	0.583332i	−0.352485	+	0.935817i	$0.614663\pi$
$68$	73.0527			1.07430
$69$		−	35.4342i		−	0.513539i
$70$	−19.0680	−	19.0680i	−0.272400	−	0.272400i
$71$	91.5548	+	91.5548i	1.28950	+	1.28950i	0.935088	+	0.354417i	$0.115321\pi$
$71$	91.5548	+	91.5548i	1.28950	+	1.28950i	0.354417	+	0.935088i	$0.384679\pi$
$72$	35.4342	−	35.4342i	0.492141	−	0.492141i
$73$	31.6228	−	31.6228i	0.433189	−	0.433189i	−0.456523	−	0.889712i	$-0.650905\pi$
$73$	31.6228	−	31.6228i	0.433189	−	0.433189i	0.889712	+	0.456523i	$0.150905\pi$
$74$	28.1623			0.380571
$75$		−	2.70178i		−	0.0360237i
$76$	10.5132	−	10.5132i	0.138331	−	0.138331i
$77$			48.7851i			0.633572i
$78$	−13.7281	+	42.2982i	−0.176001	+	0.542285i
$79$	−18.7851			−0.237785			−0.118893	−	0.992907i	$-0.537934\pi$
$79$	−18.7851			−0.237785			−0.118893	+	0.992907i	$0.537934\pi$
$80$	−29.9057	−	29.9057i	−0.373821	−	0.373821i
$81$	−86.6228			−1.06942
$82$			5.62278i			0.0685704i
$83$	−44.6228	−	44.6228i	−0.537624	−	0.537624i	0.385207	−	0.922830i	$-0.374130\pi$
$83$	−44.6228	−	44.6228i	−0.537624	−	0.537624i	−0.922830	+	0.385207i	$0.874130\pi$
$84$	−63.3925	−	63.3925i	−0.754673	−	0.754673i
$85$	−78.6907	+	78.6907i	−0.925774	+	0.925774i
$86$	17.7171	−	17.7171i	0.206013	−	0.206013i
$87$	24.1886			0.278030
$88$		−	45.3288i		−	0.515100i
$89$	8.89039	−	8.89039i	0.0998920	−	0.0998920i	−0.655395	−	0.755287i	$-0.727498\pi$
$89$	8.89039	−	8.89039i	0.0998920	−	0.0998920i	0.755287	+	0.655395i	$0.227498\pi$
$90$			34.6491i			0.384990i
$91$	80.1096	+	26.0000i	0.880325	+	0.285714i
$92$	28.3025			0.307636
$93$	−2.13594	−	2.13594i	−0.0229671	−	0.0229671i
$94$	−43.4299			−0.462020
$95$			22.6491i			0.238412i
$96$	91.0680	+	91.0680i	0.948625	+	0.948625i
$97$	−121.355	−	121.355i	−1.25108	−	1.25108i	−0.955235	−	0.295850i	$-0.904397\pi$
$97$	−121.355	−	121.355i	−1.25108	−	1.25108i	−0.295850	−	0.955235i	$-0.595603\pi$
$98$	−4.08328	+	4.08328i	−0.0416661	+	0.0416661i
$99$	44.3246	−	44.3246i	0.447723	−	0.447723i
$100$	2.15800			0.0215800
$101$			104.921i			1.03882i	0.854525	+	0.519411i	$0.173849\pi$
$101$			104.921i			1.03882i	−0.854525	+	0.519411i	$0.826151\pi$
$102$	53.1512	−	53.1512i	0.521091	−	0.521091i
$103$		−	35.4342i		−	0.344021i	−0.985095	−	0.172011i	$-0.944974\pi$
$103$		−	35.4342i		−	0.344021i	0.985095	−	0.172011i	$-0.0550263\pi$
$104$	−74.4342	−	24.1580i	−0.715713	−	0.232289i
$105$	136.570			1.30067
$106$	−20.8114	−	20.8114i	−0.196334	−	0.196334i
$107$	−4.42989			−0.0414009			−0.0207004	−	0.999786i	$-0.506590\pi$
$107$	−4.42989			−0.0414009			−0.0207004	+	0.999786i	$0.506590\pi$
$108$		−	9.34662i		−	0.0865427i
$109$	120.774	+	120.774i	1.10802	+	1.10802i	0.993411	+	0.114608i	$0.0365611\pi$
$109$	120.774	+	120.774i	1.10802	+	1.10802i	0.114608	+	0.993411i	$0.463439\pi$
$110$	22.1623	+	22.1623i	0.201475	+	0.201475i
$111$	−100.853	+	100.853i	−0.908586	+	0.908586i
$112$	38.2566	−	38.2566i	0.341577	−	0.341577i
$113$	68.5438			0.606582			0.303291	−	0.952898i	$-0.401915\pi$
$113$	68.5438			0.606582			0.303291	+	0.952898i	$0.401915\pi$
$114$		−	15.2982i		−	0.134195i
$115$	−30.4868	+	30.4868i	−0.265103	+	0.265103i
$116$			19.3203i			0.166554i
$117$	−49.1623	−	96.4078i	−0.420190	−	0.823999i
$118$	67.7281			0.573967
$119$	−100.664	−	100.664i	−0.845919	−	0.845919i
$120$	−126.895			−1.05746
$121$			64.2982i			0.531390i
$122$	−46.6797	−	46.6797i	−0.382621	−	0.382621i
$123$	−20.1359	−	20.1359i	−0.163707	−	0.163707i
$124$	1.70605	−	1.70605i	0.0137585	−	0.0137585i
$125$	87.2039	−	87.2039i	0.697631	−	0.697631i
$126$	−44.3246			−0.351782
$127$		−	101.162i		−	0.796553i	−0.917265	−	0.398277i	$-0.869608\pi$
$127$		−	101.162i		−	0.796553i	0.917265	−	0.398277i	$-0.130392\pi$
$128$	−92.1512	+	92.1512i	−0.719932	+	0.719932i
$129$			126.895i			0.983680i
$130$	48.2039	−	24.5811i	0.370799	−	0.189086i
$131$	−257.732			−1.96742			−0.983711	−	0.179755i	$-0.942469\pi$
$131$	−257.732			−1.96742			−0.983711	+	0.179755i	$0.942469\pi$
$132$	73.6797	+	73.6797i	0.558180	+	0.558180i
$133$	−28.9737			−0.217847
$134$			45.4256i			0.338997i
$135$	10.0680	+	10.0680i	0.0745776	+	0.0745776i
$136$	93.5327	+	93.5327i	0.687741	+	0.687741i
$137$	175.272	−	175.272i	1.27936	−	1.27936i	0.338329	−	0.941028i	$-0.390138\pi$
$137$	175.272	−	175.272i	1.27936	−	1.27936i	0.941028	−	0.338329i	$-0.109862\pi$
$138$	20.5922	−	20.5922i	0.149219	−	0.149219i
$139$	135.460			0.974536			0.487268	−	0.873252i	$-0.337993\pi$
$139$	135.460			0.974536			0.487268	+	0.873252i	$0.337993\pi$
$140$			109.083i			0.779166i
$141$	155.528	−	155.528i	1.10304	−	1.10304i
$142$			106.412i			0.749381i
$143$	−93.1096	−	30.2192i	−0.651116	−	0.211323i
$144$	−69.5174			−0.482760
$145$	−20.8114	−	20.8114i	−0.143527	−	0.143527i
$146$	36.7544			0.251743
$147$		−	29.2456i		−	0.198949i
$148$	−80.5548	−	80.5548i	−0.544289	−	0.544289i
$149$	36.2192	+	36.2192i	0.243082	+	0.243082i	0.818124	−	0.575042i	$-0.195014\pi$
$149$	36.2192	+	36.2192i	0.243082	+	0.243082i	−0.575042	+	0.818124i	$0.695014\pi$
$150$	1.57011	−	1.57011i	0.0104674	−	0.0104674i
$151$	−75.1776	+	75.1776i	−0.497865	+	0.497865i	−0.910773	−	0.412908i	$-0.864513\pi$
$151$	−75.1776	+	75.1776i	−0.497865	+	0.497865i	0.412908	+	0.910773i	$0.364513\pi$
$152$	26.9210			0.177112
$153$			182.921i			1.19556i
$154$	−28.3509	+	28.3509i	−0.184097	+	0.184097i
$155$			3.67544i			0.0237125i
$156$	160.257	−	81.7214i	1.02729	−	0.523855i
$157$	55.4562			0.353224			0.176612	−	0.984281i	$-0.443486\pi$
$157$	55.4562			0.353224			0.176612	+	0.984281i	$0.443486\pi$
$158$	−10.9167	−	10.9167i	−0.0690932	−	0.0690932i
$159$	149.057			0.937465
$160$		−	156.706i		−	0.979413i
$161$	−39.0000	−	39.0000i	−0.242236	−	0.242236i
$162$	−50.3399	−	50.3399i	−0.310740	−	0.310740i
$163$	−45.4605	+	45.4605i	−0.278899	+	0.278899i	−0.832669	−	0.553771i	$-0.813188\pi$
$163$	−45.4605	+	45.4605i	−0.278899	+	0.278899i	0.553771	+	0.832669i	$0.313188\pi$
$164$	16.0833	−	16.0833i	0.0980688	−	0.0980688i
$165$	−158.732			−0.962014
$166$		−	51.8641i		−	0.312434i
$167$	−137.215	+	137.215i	−0.821646	+	0.821646i	−0.986344	−	0.164698i	$-0.947335\pi$
$167$	−137.215	+	137.215i	−0.821646	+	0.821646i	0.164698	+	0.986344i	$0.447335\pi$
$168$		−	162.329i		−	0.966243i
$169$	−99.2456	+	136.789i	−0.587252	+	0.809404i
$170$	−91.4605			−0.538003
$171$	26.3246	+	26.3246i	0.153945	+	0.153945i
$172$	−101.355			−0.589274
$173$			79.3815i			0.458853i	0.973326	+	0.229426i	$0.0736850\pi$
$173$			79.3815i			0.458853i	−0.973326	+	0.229426i	$0.926315\pi$
$174$	14.0569	+	14.0569i	0.0807870	+	0.0807870i
$175$	−2.97367	−	2.97367i	−0.0169924	−	0.0169924i
$176$	−44.4648	+	44.4648i	−0.252641	+	0.252641i
$177$	−242.544	+	242.544i	−1.37030	+	1.37030i
$178$	10.3331			0.0580511
$179$		−	318.329i		−	1.77837i	−0.457545	−	0.889187i	$-0.651271\pi$
$179$		−	318.329i		−	1.77837i	0.457545	−	0.889187i	$-0.348729\pi$
$180$	99.1096	−	99.1096i	0.550609	−	0.550609i
$181$		−	238.144i		−	1.31572i	−0.753142	−	0.657858i	$-0.771463\pi$
$181$		−	238.144i		−	1.31572i	0.753142	−	0.657858i	$-0.228537\pi$
$182$	31.4452	+	61.6644i	0.172776	+	0.338815i
$183$	334.333			1.82696
$184$	36.2370	+	36.2370i	0.196940	+	0.196940i
$185$	173.544			0.938074
$186$		−	2.48256i		−	0.0133471i
$187$	117.000	+	117.000i	0.625668	+	0.625668i
$188$	124.226	+	124.226i	0.660776	+	0.660776i
$189$	−12.8794	+	12.8794i	−0.0681448	+	0.0681448i
$190$	−13.1623	+	13.1623i	−0.0692751	+	0.0692751i
$191$	−3.70605			−0.0194034			−0.00970171	−	0.999953i	$-0.503088\pi$
$191$	−3.70605			−0.0194034			−0.00970171	+	0.999953i	$0.503088\pi$
$192$		−	33.1886i		−	0.172857i
$193$	43.1359	−	43.1359i	0.223502	−	0.223502i	−0.586469	−	0.809972i	$-0.699483\pi$
$193$	43.1359	−	43.1359i	0.223502	−	0.223502i	0.809972	+	0.586469i	$0.199483\pi$
$194$		−	141.048i		−	0.727054i
$195$	−84.5964	+	260.653i	−0.433828	+	1.33668i
$196$	23.3594			0.119181
$197$	126.094	+	126.094i	0.640073	+	0.640073i	0.950573	−	0.310501i	$-0.100497\pi$
$197$	126.094	+	126.094i	0.640073	+	0.640073i	−0.310501	+	0.950573i	$0.600497\pi$
$198$	51.5174			0.260189
$199$		−	152.241i		−	0.765032i	−0.923949	−	0.382516i	$-0.875058\pi$
$199$		−	152.241i		−	0.765032i	0.923949	−	0.382516i	$-0.124942\pi$
$200$	2.76299	+	2.76299i	0.0138150	+	0.0138150i
$201$	−162.675	−	162.675i	−0.809331	−	0.809331i
$202$	−60.9737	+	60.9737i	−0.301850	+	0.301850i
$203$	26.6228	−	26.6228i	0.131147	−	0.131147i
$204$	−304.065			−1.49052
$205$			34.6491i			0.169020i
$206$	20.5922	−	20.5922i	0.0999620	−	0.0999620i
$207$			70.8683i			0.342359i
$208$	49.3178	+	96.7128i	0.237105	+	0.464965i
$209$	33.6754			0.161127
$210$	79.3662	+	79.3662i	0.377934	+	0.377934i
$211$	−47.5744			−0.225471			−0.112736	−	0.993625i	$-0.535961\pi$
$211$	−47.5744			−0.225471			−0.112736	+	0.993625i	$0.535961\pi$
$212$			119.057i			0.561589i
$213$	−381.077	−	381.077i	−1.78909	−	1.78909i
$214$	−2.57438	−	2.57438i	−0.0120298	−	0.0120298i
$215$	109.178	−	109.178i	0.507803	−	0.507803i
$216$	11.9669	−	11.9669i	0.0554024	−	0.0554024i
$217$	−4.70178			−0.0216672
$218$			140.373i			0.643913i
$219$	−131.623	+	131.623i	−0.601017	+	0.601017i
$220$		−	126.785i		−	0.576296i
$221$	254.480	−	129.770i	1.15149	−	0.587193i
$222$	−117.219			−0.528015
$223$	−38.2260	−	38.2260i	−0.171417	−	0.171417i	0.616185	−	0.787602i	$-0.288677\pi$
$223$	−38.2260	−	38.2260i	−0.171417	−	0.171417i	−0.787602	+	0.616185i	$0.788677\pi$
$224$	200.465			0.894932
$225$			5.40356i			0.0240158i
$226$	39.8334	+	39.8334i	0.176254	+	0.176254i
$227$	44.7324	+	44.7324i	0.197059	+	0.197059i	0.798738	−	0.601679i	$-0.205501\pi$
$227$	44.7324	+	44.7324i	0.197059	+	0.197059i	−0.601679	+	0.798738i	$0.705501\pi$
$228$	−43.7587	+	43.7587i	−0.191924	+	0.191924i
$229$	−167.634	+	167.634i	−0.732025	+	0.732025i	−0.971021	−	0.238995i	$-0.923182\pi$
$229$	−167.634	+	167.634i	−0.732025	+	0.732025i	0.238995	+	0.971021i	$0.423182\pi$
$230$	−35.4342			−0.154062
$231$		−	203.057i		−	0.879034i
$232$	−24.7367	+	24.7367i	−0.106624	+	0.106624i
$233$			292.789i			1.25661i	0.777969	+	0.628303i	$0.216250\pi$
$233$			292.789i			1.25661i	−0.777969	+	0.628303i	$0.783750\pi$
$234$	27.4562	−	84.5964i	0.117334	−	0.361523i
$235$	−267.627			−1.13884
$236$	−193.728	−	193.728i	−0.820882	−	0.820882i
$237$	78.1886			0.329910
$238$		−	117.000i		−	0.491597i
$239$	0.0153037	+	0.0153037i	6.40324e−5	+	6.40324e-5i	0.707139	−	0.707075i	$-0.249986\pi$
$239$	0.0153037	+	0.0153037i	6.40324e−5	+	6.40324e-5i	−0.707075	+	0.707139i	$0.749986\pi$
$240$	124.476	+	124.476i	0.518649	+	0.518649i
$241$	240.197	−	240.197i	0.996669	−	0.996669i	−0.00332576	−	0.999994i	$-0.501059\pi$
$241$	240.197	−	240.197i	0.996669	−	0.996669i	0.999994	+	0.00332576i	$0.00105862\pi$
$242$	−37.3662	+	37.3662i	−0.154406	+	0.154406i
$243$	335.246			1.37961
$244$			267.043i			1.09444i
$245$	−25.1623	+	25.1623i	−0.102703	+	0.102703i
$246$		−	23.4036i		−	0.0951364i
$247$	17.9473	−	55.2982i	0.0726613	−	0.223879i
$248$	4.36868			0.0176156
$249$	185.732	+	185.732i	0.745913	+	0.745913i
$250$	101.355			0.405421
$251$			131.842i			0.525267i	0.964896	+	0.262633i	$0.0845910\pi$
$251$			131.842i			0.525267i	−0.964896	+	0.262633i	$0.915409\pi$
$252$	126.785	+	126.785i	0.503115	+	0.503115i
$253$	45.3288	+	45.3288i	0.179165	+	0.179165i
$254$	58.7893	−	58.7893i	0.231454	−	0.231454i
$255$	327.533	−	327.533i	1.28444	−	1.28444i
$256$	−75.2107			−0.293792
$257$		−	156.579i		−	0.609255i	−0.952471	−	0.304628i	$-0.901468\pi$
$257$		−	156.579i		−	0.609255i	0.952471	−	0.304628i	$-0.0985320\pi$
$258$	−73.7434	+	73.7434i	−0.285827	+	0.285827i
$259$			222.004i			0.857159i
$260$	−208.193	−	67.5701i	−0.800742	−	0.259885i
$261$	−48.3772			−0.185353
$262$	−149.778	−	149.778i	−0.571673	−	0.571673i
$263$	−338.982			−1.28891			−0.644453	−	0.764644i	$-0.722915\pi$
$263$	−338.982			−1.28891			−0.644453	+	0.764644i	$0.722915\pi$
$264$			188.671i			0.714664i
$265$	−128.246	−	128.246i	−0.483945	−	0.483945i
$266$	−16.8377	−	16.8377i	−0.0632997	−	0.0632997i
$267$	−37.0043	+	37.0043i	−0.138593	+	0.138593i
$268$	129.935	−	129.935i	0.484830	−	0.484830i
$269$	−222.061			−0.825506			−0.412753	−	0.910843i	$-0.635433\pi$
$269$	−222.061			−0.825506			−0.412753	+	0.910843i	$0.635433\pi$
$270$			11.7018i			0.0433399i
$271$	39.0722	−	39.0722i	0.144178	−	0.144178i	−0.631333	−	0.775511i	$-0.717492\pi$
$271$	39.0722	−	39.0722i	0.144178	−	0.144178i	0.775511	+	0.631333i	$0.217492\pi$
$272$		−	183.500i		−	0.674631i
$273$	−333.438	−	108.219i	−1.22139	−	0.396407i
$274$	203.715			0.743484
$275$	3.45623	+	3.45623i	0.0125681	+	0.0125681i
$276$	−117.803			−0.426822
$277$			112.053i			0.404522i	0.979332	+	0.202261i	$0.0648290\pi$
$277$			112.053i			0.404522i	−0.979332	+	0.202261i	$0.935171\pi$
$278$	78.7214	+	78.7214i	0.283170	+	0.283170i
$279$	4.27189	+	4.27189i	0.0153114	+	0.0153114i
$280$	−139.664	+	139.664i	−0.498801	+	0.498801i
$281$	−174.846	+	174.846i	−0.622229	+	0.622229i	−0.946101	−	0.323872i	$-0.895015\pi$
$281$	−174.846	+	174.846i	−0.622229	+	0.622229i	0.323872	+	0.946101i	$0.395015\pi$
$282$	180.767			0.641019
$283$			271.201i			0.958309i	0.877731	+	0.479154i	$0.159057\pi$
$283$			271.201i			0.958309i	−0.877731	+	0.479154i	$0.840943\pi$
$284$	304.379	−	304.379i	1.07176	−	1.07176i
$285$		−	94.2719i		−	0.330779i
$286$	−36.5480	−	71.6712i	−0.127790	−	0.250599i
$287$	−44.3246			−0.154441
$288$	−182.136	−	182.136i	−0.632416	−	0.632416i
$289$	−193.842			−0.670734
$290$		−	24.1886i		−	0.0834090i
$291$	505.114	+	505.114i	1.73579	+	1.73579i
$292$	−105.132	−	105.132i	−0.360040	−	0.360040i
$293$	−240.156	+	240.156i	−0.819643	+	0.819643i	−0.986056	−	0.166413i	$-0.946782\pi$
$293$	−240.156	+	240.156i	−0.819643	+	0.819643i	0.166413	+	0.986056i	$0.446782\pi$
$294$	16.9957	−	16.9957i	0.0578086	−	0.0578086i
$295$	417.359			1.41478
$296$		−	206.276i		−	0.696879i
$297$	14.9694	−	14.9694i	0.0504020	−	0.0504020i
$298$			42.0968i			0.141264i
$299$	98.5922	−	50.2762i	0.329740	−	0.168148i
$300$	−8.98221			−0.0299407
$301$	139.664	+	139.664i	0.464001	+	0.464001i
$302$	−87.3772			−0.289329
$303$		−	436.710i		−	1.44129i
$304$	−26.4078	−	26.4078i	−0.0868679	−	0.0868679i
$305$	−287.653	−	287.653i	−0.943126	−	0.943126i
$306$	−106.302	+	106.302i	−0.347394	+	0.347394i
$307$	219.684	−	219.684i	0.715583	−	0.715583i	−0.252114	−	0.967697i	$-0.581126\pi$
$307$	219.684	−	219.684i	0.715583	−	0.715583i	0.967697	+	0.252114i	$0.0811259\pi$
$308$	162.189			0.526586
$309$			147.487i			0.477304i
$310$	−2.13594	+	2.13594i	−0.00689014	+	0.00689014i
$311$			341.684i			1.09866i	0.835605	+	0.549331i	$0.185117\pi$
$311$			341.684i			1.09866i	−0.835605	+	0.549331i	$0.814883\pi$
$312$	309.816	+	100.552i	0.992999	+	0.322283i
$313$	438.517			1.40101			0.700507	−	0.713645i	$-0.252957\pi$
$313$	438.517			1.40101			0.700507	+	0.713645i	$0.252957\pi$
$314$	32.2278	+	32.2278i	0.102636	+	0.102636i
$315$	−273.140			−0.867112
$316$			62.4520i			0.197633i
$317$	153.140	+	153.140i	0.483092	+	0.483092i	0.906118	−	0.423026i	$-0.139032\pi$
$317$	153.140	+	153.140i	0.483092	+	0.483092i	−0.423026	+	0.906118i	$0.639032\pi$
$318$	86.6228	+	86.6228i	0.272399	+	0.272399i
$319$	−30.9431	+	30.9431i	−0.0970002	+	0.0970002i
$320$	−28.5548	+	28.5548i	−0.0892338	+	0.0892338i
$321$	18.4384			0.0574406
$322$		−	45.3288i		−	0.140773i
$323$	−69.4868	+	69.4868i	−0.215130	+	0.215130i
$324$			287.982i			0.888834i
$325$	7.51744	−	3.83345i	0.0231306	−	0.0117952i
$326$	−52.8377			−0.162079
$327$	−502.695	−	502.695i	−1.53729	−	1.53729i
$328$	41.1843			0.125562
$329$		−	342.359i		−	1.04061i
$330$	−92.2456	−	92.2456i	−0.279532	−	0.279532i
$331$	−195.982	−	195.982i	−0.592091	−	0.592091i	0.346105	−	0.938196i	$-0.387504\pi$
$331$	−195.982	−	195.982i	−0.592091	−	0.592091i	−0.938196	+	0.346105i	$0.887504\pi$
$332$	−148.351	+	148.351i	−0.446840	+	0.446840i
$333$	201.706	−	201.706i	0.605724	−	0.605724i
$334$	−159.482			−0.477491
$335$			279.925i			0.835598i
$336$	−159.235	+	159.235i	−0.473912	+	0.473912i
$337$		−	7.32456i		−	0.0217346i	−0.999941	−	0.0108673i	$-0.996541\pi$
$337$		−	7.32456i		−	0.0217346i	0.999941	−	0.0108673i	$-0.00345923\pi$
$338$	−137.169	+	21.8181i	−0.405826	+	0.0645507i
$339$	−285.298			−0.841588
$340$	261.612	+	261.612i	0.769446	+	0.769446i
$341$	5.46477			0.0160257
$342$			30.5964i			0.0894633i
$343$	−256.664	−	256.664i	−0.748293	−	0.748293i
$344$	−129.770	−	129.770i	−0.377238	−	0.377238i
$345$	126.895	−	126.895i	0.367811	−	0.367811i
$346$	−46.1317	+	46.1317i	−0.133329	+	0.133329i
$347$	−154.759			−0.445991			−0.222995	−	0.974820i	$-0.571583\pi$
$347$	−154.759			−0.445991			−0.222995	+	0.974820i	$0.571583\pi$
$348$		−	80.4164i		−	0.231082i
$349$	220.419	−	220.419i	0.631573	−	0.631573i	−0.316890	−	0.948462i	$-0.602639\pi$
$349$	220.419	−	220.419i	0.631573	−	0.631573i	0.948462	+	0.316890i	$0.102639\pi$
$350$		−	3.45623i		−	0.00987493i
$351$	−16.6032	−	32.5591i	−0.0473026	−	0.0927609i
$352$	−232.996			−0.661920
$353$	331.680	+	331.680i	0.939603	+	0.939603i	0.998277	−	0.0586746i	$-0.0186874\pi$
$353$	331.680	+	331.680i	0.939603	+	0.939603i	−0.0586746	+	0.998277i	$0.518687\pi$
$354$	−281.903			−0.796337
$355$			655.741i			1.84716i
$356$	−29.5566	−	29.5566i	−0.0830241	−	0.0830241i
$357$	418.993	+	418.993i	1.17365	+	1.17365i
$358$	184.993	−	184.993i	0.516741	−	0.516741i
$359$	132.785	−	132.785i	0.369875	−	0.369875i	−0.497557	−	0.867431i	$-0.665769\pi$
$359$	132.785	−	132.785i	0.369875	−	0.369875i	0.867431	+	0.497557i	$0.165769\pi$
$360$	253.789			0.704970
$361$		−	341.000i		−	0.944598i
$362$	138.395	−	138.395i	0.382307	−	0.382307i
$363$		−	267.627i		−	0.737265i
$364$	86.4384	−	266.329i	0.237468	−	0.731673i
$365$	226.491			0.620524
$366$	194.294	+	194.294i	0.530858	+	0.530858i
$367$	282.416			0.769527			0.384763	−	0.923015i	$-0.374283\pi$
$367$	282.416			0.769527			0.384763	+	0.923015i	$0.374283\pi$
$368$		−	71.0925i		−	0.193186i
$369$	40.2719	+	40.2719i	0.109138	+	0.109138i
$370$	100.853	+	100.853i	0.272576	+	0.272576i
$371$	164.057	−	164.057i	0.442202	−	0.442202i
$372$	−7.10106	+	7.10106i	−0.0190889	+	0.0190889i
$373$	−648.877			−1.73962			−0.869808	−	0.493390i	$-0.835758\pi$
$373$	−648.877			−1.73962			−0.869808	+	0.493390i	$0.835758\pi$
$374$			135.986i			0.363600i
$375$	−362.967	+	362.967i	−0.967912	+	0.967912i
$376$			318.105i			0.846023i
$377$	34.3203	+	67.3025i	0.0910352	+	0.178521i
$378$	−14.9694			−0.0396016
$379$	−429.302	−	429.302i	−1.13272	−	1.13272i	−0.989722	−	0.143002i	$-0.954325\pi$
$379$	−429.302	−	429.302i	−1.13272	−	1.13272i	−0.143002	−	0.989722i	$-0.545675\pi$
$380$	75.2982			0.198153
$381$			421.065i			1.10516i
$382$	−2.15373	−	2.15373i	−0.00563804	−	0.00563804i
$383$	132.739	+	132.739i	0.346577	+	0.346577i	0.858833	−	0.512256i	$-0.171190\pi$
$383$	132.739	+	132.739i	0.346577	+	0.346577i	−0.512256	+	0.858833i	$0.671190\pi$
$384$	383.559	−	383.559i	0.998852	−	0.998852i
$385$	−174.706	+	174.706i	−0.453782	+	0.453782i
$386$	50.1359			0.129886
$387$		−	253.789i		−	0.655786i
$388$	−403.452	+	403.452i	−1.03982	+	1.03982i
$389$		−	510.342i		−	1.31193i	−0.754790	−	0.655966i	$-0.772261\pi$
$389$		−	510.342i		−	1.31193i	0.754790	−	0.655966i	$-0.227739\pi$
$390$	−200.638	+	102.314i	−0.514457	+	0.262342i
$391$	−187.065			−0.478428
$392$	29.9082	+	29.9082i	0.0762964	+	0.0762964i
$393$	1072.75			2.72965
$394$			146.557i			0.371971i
$395$	−67.2719	−	67.2719i	−0.170309	−	0.170309i
$396$	−147.359	−	147.359i	−0.372120	−	0.372120i
$397$	−142.061	+	142.061i	−0.357837	+	0.357837i	−0.863015	−	0.505178i	$-0.831427\pi$
$397$	−142.061	+	142.061i	−0.357837	+	0.357837i	0.505178	+	0.863015i	$0.331427\pi$
$398$	88.4733	−	88.4733i	0.222295	−	0.222295i
$399$	120.596			0.302247
$400$		−	5.42065i		−	0.0135516i
$401$	144.298	−	144.298i	0.359846	−	0.359846i	−0.503910	−	0.863756i	$-0.668106\pi$
$401$	144.298	−	144.298i	0.359846	−	0.359846i	0.863756	+	0.503910i	$0.168106\pi$
$402$		−	189.074i		−	0.470333i
$403$	2.91245	−	8.97367i	0.00722693	−	0.0222672i
$404$	348.816			0.863405
$405$	−310.208	−	310.208i	−0.765946	−	0.765946i
$406$	30.9431			0.0762144
$407$		−	258.031i		−	0.633982i
$408$	−389.309	−	389.309i	−0.954189	−	0.954189i
$409$	91.8598	+	91.8598i	0.224596	+	0.224596i	0.810431	−	0.585835i	$-0.199233\pi$
$409$	91.8598	+	91.8598i	0.224596	+	0.224596i	−0.585835	+	0.810431i	$0.699233\pi$
$410$	−20.1359	+	20.1359i	−0.0491121	+	0.0491121i
$411$	−729.530	+	729.530i	−1.77501	+	1.77501i
$412$	−117.803			−0.285929
$413$			533.903i			1.29274i
$414$	−41.1843	+	41.1843i	−0.0994791	+	0.0994791i
$415$		−	319.601i		−	0.770122i
$416$	−124.175	+	382.601i	−0.298498	+	0.919713i
$417$	−563.824			−1.35210
$418$	19.5701	+	19.5701i	0.0468184	+	0.0468184i
$419$	−83.2327			−0.198646			−0.0993231	−	0.995055i	$-0.531668\pi$
$419$	−83.2327			−0.198646			−0.0993231	+	0.995055i	$0.531668\pi$
$420$		−	454.035i		−	1.08104i
$421$	68.3135	+	68.3135i	0.162265	+	0.162265i	0.783569	−	0.621304i	$-0.213397\pi$
$421$	68.3135	+	68.3135i	0.162265	+	0.162265i	−0.621304	+	0.783569i	$0.713397\pi$
$422$	−27.6473	−	27.6473i	−0.0655150	−	0.0655150i
$423$	−311.057	+	311.057i	−0.735359	+	0.735359i
$424$	−152.434	+	152.434i	−0.359515	+	0.359515i
$425$	−14.2633			−0.0335608
$426$		−	442.917i		−	1.03971i
$427$	367.978	−	367.978i	0.861775	−	0.861775i
$428$			14.7274i			0.0344099i
$429$	387.548	+	125.781i	0.903375	+	0.293195i
$430$	126.895			0.295104
$431$	469.963	+	469.963i	1.09040	+	1.09040i	0.995485	+	0.0949152i	$0.0302580\pi$
$431$	469.963	+	469.963i	1.09040	+	1.09040i	0.0949152	+	0.995485i	$0.469742\pi$
$432$	−23.4776			−0.0543463
$433$		−	122.140i		−	0.282079i	−0.990004	−	0.141040i	$-0.954956\pi$
$433$		−	122.140i		−	0.282079i	0.990004	−	0.141040i	$-0.0450445\pi$
$434$	−2.73239	−	2.73239i	−0.00629582	−	0.00629582i
$435$	86.6228	+	86.6228i	0.199133	+	0.199133i
$436$	401.520	−	401.520i	0.920917	−	0.920917i
$437$	−26.9210	+	26.9210i	−0.0616041	+	0.0616041i
$438$	−152.982			−0.349274
$439$			31.2897i			0.0712749i	0.999365	+	0.0356374i	$0.0113462\pi$
$439$			31.2897i			0.0712749i	−0.999365	+	0.0356374i	$0.988654\pi$
$440$	162.329	−	162.329i	0.368929	−	0.368929i
$441$			58.4911i			0.132633i
$442$	223.302	+	72.4740i	0.505209	+	0.163968i
$443$	567.372			1.28075			0.640375	−	0.768062i	$-0.278779\pi$
$443$	567.372			1.28075			0.640375	+	0.768062i	$0.278779\pi$
$444$	335.291	+	335.291i	0.755161	+	0.755161i
$445$	63.6754			0.143091
$446$		−	44.4292i		−	0.0996170i
$447$	−150.754	−	150.754i	−0.337258	−	0.337258i
$448$	−36.5285	−	36.5285i	−0.0815368	−	0.0815368i
$449$	−530.873	+	530.873i	−1.18234	+	1.18234i	−0.203209	+	0.979135i	$0.565137\pi$
$449$	−530.873	+	530.873i	−1.18234	+	1.18234i	−0.979135	+	0.203209i	$0.934863\pi$
$450$	−3.14022	+	3.14022i	−0.00697826	+	0.00697826i
$451$	51.5174			0.114229
$452$		−	227.878i		−	0.504154i
$453$	312.910	−	312.910i	0.690750	−	0.690750i
$454$			51.9915i			0.114519i
$455$	193.774	+	379.993i	0.425877	+	0.835150i
$456$	−112.053			−0.245730
$457$	232.092	+	232.092i	0.507860	+	0.507860i	0.913869	−	0.406009i	$-0.133080\pi$
$457$	232.092	+	232.092i	0.507860	+	0.507860i	−0.406009	+	0.913869i	$0.633080\pi$
$458$	−194.837			−0.425408
$459$			61.7765i			0.134589i
$460$	101.355	+	101.355i	0.220337	+	0.220337i
$461$	−209.748	−	209.748i	−0.454984	−	0.454984i	0.442021	−	0.897005i	$-0.354262\pi$
$461$	−209.748	−	209.748i	−0.454984	−	0.454984i	−0.897005	+	0.442021i	$0.854262\pi$
$462$	118.004	−	118.004i	0.255421	−	0.255421i
$463$	127.645	−	127.645i	0.275691	−	0.275691i	−0.555695	−	0.831386i	$-0.687548\pi$
$463$	127.645	−	127.645i	0.275691	−	0.275691i	0.831386	+	0.555695i	$0.187548\pi$
$464$	48.5303			0.104591
$465$		−	15.2982i		−	0.0328994i
$466$	−170.151	+	170.151i	−0.365131	+	0.365131i
$467$		−	687.737i		−	1.47267i	−0.676617	−	0.736335i	$-0.736555\pi$
$467$		−	687.737i		−	1.47267i	0.676617	−	0.736335i	$-0.263445\pi$
$468$	−320.513	+	163.443i	−0.684857	+	0.349237i
$469$	−358.092			−0.763522
$470$	−155.528	−	155.528i	−0.330912	−	0.330912i
$471$	−230.824			−0.490073
$472$		−	496.078i		−	1.05101i
$473$	−162.329	−	162.329i	−0.343190	−	0.343190i
$474$	45.4384	+	45.4384i	0.0958617	+	0.0958617i
$475$	−2.05267	+	2.05267i	−0.00432141	+	0.00432141i
$476$	−334.664	+	334.664i	−0.703077	+	0.703077i
$477$	−298.114			−0.624977
$478$			0.0177872i			3.72117e-5i
$479$	−318.642	+	318.642i	−0.665224	+	0.665224i	−0.956607	−	0.291383i	$-0.905885\pi$
$479$	−318.642	+	318.642i	−0.665224	+	0.665224i	0.291383	+	0.956607i	$0.405885\pi$
$480$			652.254i			1.35886i
$481$	−423.710	−	137.517i	−0.880895	−	0.285899i
$482$	279.176			0.579203
$483$	162.329	+	162.329i	0.336085	+	0.336085i
$484$	213.763			0.441659
$485$		−	869.179i		−	1.79212i
$486$	194.824	+	194.824i	0.400873	+	0.400873i
$487$	557.065	+	557.065i	1.14387	+	1.14387i	0.987736	+	0.156136i	$0.0499038\pi$
$487$	557.065	+	557.065i	1.14387	+	1.14387i	0.156136	+	0.987736i	$0.450096\pi$
$488$	−341.908	+	341.908i	−0.700632	+	0.700632i
$489$	189.219	−	189.219i	0.386951	−	0.386951i
$490$	−29.2456			−0.0596848
$491$		−	400.698i		−	0.816085i	−0.912963	−	0.408042i	$-0.866212\pi$
$491$		−	400.698i		−	0.816085i	0.912963	−	0.408042i	$-0.133788\pi$
$492$	−66.9431	+	66.9431i	−0.136063	+	0.136063i
$493$		−	127.698i		−	0.259021i
$494$	42.5658	−	21.7061i	0.0861657	−	0.0439394i
$495$	317.465			0.641343
$496$	−4.28540	−	4.28540i	−0.00863992	−	0.00863992i
$497$	−838.851			−1.68783
$498$			215.873i			0.433479i
$499$	102.671	+	102.671i	0.205754	+	0.205754i	0.802460	−	0.596706i	$-0.203524\pi$
$499$	102.671	+	102.671i	0.205754	+	0.205754i	−0.596706	+	0.802460i	$0.703524\pi$
$500$	−289.914	−	289.914i	−0.579828	−	0.579828i
$501$	571.127	−	571.127i	1.13997	−	1.13997i
$502$	−76.6185	+	76.6185i	−0.152627	+	0.152627i
$503$	−46.2719			−0.0919918			−0.0459959	−	0.998942i	$-0.514646\pi$
$503$	−46.2719			−0.0919918			−0.0459959	+	0.998942i	$0.514646\pi$
$504$			324.658i			0.644162i
$505$	−375.737	+	375.737i	−0.744033	+	0.744033i
$506$			52.6847i			0.104120i
$507$	413.088	−	569.355i	0.814768	−	1.12299i
$508$	−336.320			−0.662046
$509$	−372.280	−	372.280i	−0.731396	−	0.731396i	0.239500	−	0.970896i	$-0.423016\pi$
$509$	−372.280	−	372.280i	−0.731396	−	0.731396i	−0.970896	+	0.239500i	$0.923016\pi$
$510$	380.684			0.746439
$511$			289.737i			0.566999i
$512$	324.897	+	324.897i	0.634565	+	0.634565i
$513$	8.89039	+	8.89039i	0.0173302	+	0.0173302i
$514$	90.9939	−	90.9939i	0.177031	−	0.177031i
$515$	126.895	−	126.895i	0.246397	−	0.246397i
$516$	421.868			0.817574
$517$			397.917i			0.769665i
$518$	−129.015	+	129.015i	−0.249064	+	0.249064i
$519$		−	330.408i		−	0.636624i
$520$	−180.046	−	353.072i	−0.346242	−	0.678985i
$521$	27.1224			0.0520584			0.0260292	−	0.999661i	$-0.491714\pi$
$521$	27.1224			0.0520584			0.0260292	+	0.999661i	$0.491714\pi$
$522$	−28.1139	−	28.1139i	−0.0538580	−	0.0538580i
$523$	473.851			0.906024			0.453012	−	0.891504i	$-0.350349\pi$
$523$	473.851			0.906024			0.453012	+	0.891504i	$0.350349\pi$
$524$			856.846i			1.63520i
$525$	12.3772	+	12.3772i	0.0235757	+	0.0235757i
$526$	−196.996	−	196.996i	−0.374517	−	0.374517i
$527$	−11.2762	+	11.2762i	−0.0213969	+	0.0213969i
$528$	185.075	−	185.075i	0.350520	−	0.350520i
$529$	456.526			0.862998
$530$		−	149.057i		−	0.281240i
$531$	485.088	−	485.088i	0.913536	−	0.913536i
$532$			96.3246i			0.181061i
$533$	27.4562	−	84.5964i	0.0515126	−	0.158718i
$534$	−43.0092			−0.0805416
$535$	−15.8641	−	15.8641i	−0.0296524	−	0.0296524i
$536$	332.722			0.620751
$537$			1324.97i			2.46736i
$538$	−129.048	−	129.048i	−0.239867	−	0.239867i
$539$	37.4121	+	37.4121i	0.0694102	+	0.0694102i
$540$	33.4715	−	33.4715i	0.0619843	−	0.0619843i
$541$	531.379	−	531.379i	0.982216	−	0.982216i	−0.0176283	−	0.999845i	$-0.505612\pi$
$541$	531.379	−	531.379i	0.982216	−	0.982216i	0.999845	+	0.0176283i	$0.00561156\pi$
$542$	45.4128			0.0837874
$543$			991.223i			1.82546i
$544$	480.770	−	480.770i	0.883768	−	0.883768i
$545$			865.017i			1.58719i
$546$	−130.884	−	256.664i	−0.239714	−	0.470081i
$547$	−716.223			−1.30937			−0.654683	−	0.755903i	$-0.727198\pi$
$547$	−716.223			−1.30937			−0.654683	+	0.755903i	$0.727198\pi$
$548$	−582.701	−	582.701i	−1.06332	−	1.06332i
$549$	−668.666			−1.21797
$550$			4.01709i			0.00730381i
$551$	−18.3772	−	18.3772i	−0.0333525	−	0.0333525i
$552$	−150.828	−	150.828i	−0.273240	−	0.273240i
$553$	86.0569	−	86.0569i	0.155618	−	0.155618i
$554$	−65.1182	+	65.1182i	−0.117542	+	0.117542i
$555$	−722.337			−1.30151
$556$		−	450.346i		−	0.809975i
$557$	−248.577	+	248.577i	−0.446278	+	0.446278i	−0.894115	−	0.447837i	$-0.852194\pi$
$557$	−248.577	+	248.577i	−0.446278	+	0.446278i	0.447837	+	0.894115i	$0.352194\pi$
$558$			4.96512i			0.00889806i
$559$	−353.072	+	180.046i	−0.631614	+	0.322086i
$560$	274.004			0.489293
$561$	−486.986	−	486.986i	−0.868069	−	0.868069i
$562$	−203.220			−0.361601
$563$		−	708.329i		−	1.25813i	−0.777352	−	0.629066i	$-0.783437\pi$
$563$		−	708.329i		−	1.25813i	0.777352	−	0.629066i	$-0.216563\pi$
$564$	−517.063	−	517.063i	−0.916778	−	0.916778i
$565$	245.465	+	245.465i	0.434451	+	0.434451i
$566$	−157.606	+	157.606i	−0.278455	+	0.278455i
$567$	396.831	−	396.831i	0.699878	−	0.699878i
$568$	779.421			1.37222
$569$		−	349.394i		−	0.614050i	−0.951701	−	0.307025i	$-0.900667\pi$
$569$		−	349.394i		−	0.614050i	0.951701	−	0.307025i	$-0.0993335\pi$
$570$	54.7851	−	54.7851i	0.0961141	−	0.0961141i
$571$			906.285i			1.58719i	0.608447	+	0.793594i	$0.291793\pi$
$571$			906.285i			1.58719i	−0.608447	+	0.793594i	$0.708207\pi$
$572$	−100.465	+	309.548i	−0.175639	+	0.541168i
$573$	15.4256			0.0269208
$574$	−25.7587	−	25.7587i	−0.0448758	−	0.0448758i
$575$	−5.52599			−0.00961041
$576$			66.3772i			0.115238i
$577$	357.842	+	357.842i	0.620177	+	0.620177i	0.945577	−	0.325400i	$-0.105499\pi$
$577$	357.842	+	357.842i	0.620177	+	0.620177i	−0.325400	+	0.945577i	$0.605499\pi$
$578$	−112.649	−	112.649i	−0.194895	−	0.194895i
$579$	−179.544	+	179.544i	−0.310093	+	0.310093i
$580$	−69.1886	+	69.1886i	−0.119291	+	0.119291i
$581$	408.846			0.703694
$582$			587.083i			1.00873i
$583$	−190.680	+	190.680i	−0.327066	+	0.327066i
$584$		−	269.210i		−	0.460976i
$585$	169.193	−	521.307i	0.289219	−	0.891123i
$586$	−279.127			−0.476327
$587$	405.311	+	405.311i	0.690479	+	0.690479i	0.962337	−	0.271858i	$-0.0876383\pi$
$587$	405.311	+	405.311i	0.690479	+	0.690479i	−0.271858	+	0.962337i	$0.587638\pi$
$588$	−97.2285			−0.165355
$589$			3.24555i			0.00551028i
$590$	242.544	+	242.544i	0.411091	+	0.411091i
$591$	−524.840	−	524.840i	−0.888053	−	0.888053i
$592$	−202.344	+	202.344i	−0.341798	+	0.341798i
$593$	550.285	−	550.285i	0.927967	−	0.927967i	−0.0696070	−	0.997574i	$-0.522175\pi$
$593$	550.285	−	550.285i	0.927967	−	0.927967i	0.997574	+	0.0696070i	$0.0221745\pi$
$594$	17.3986			0.0292906
$595$		−	720.986i		−	1.21174i
$596$	120.413	−	120.413i	0.202035	−	0.202035i
$597$			633.670i			1.06142i
$598$	86.5132	+	28.0783i	0.144671	+	0.0469537i
$599$	235.228			0.392702			0.196351	−	0.980534i	$-0.437091\pi$
$599$	235.228			0.392702			0.196351	+	0.980534i	$0.437091\pi$
$600$	−11.5003	−	11.5003i	−0.0191672	−	0.0191672i
$601$	−559.298			−0.930612			−0.465306	−	0.885150i	$-0.654056\pi$
$601$	−559.298			−0.930612			−0.465306	+	0.885150i	$0.654056\pi$
$602$			162.329i			0.269649i
$603$	325.351	+	325.351i	0.539554	+	0.539554i
$604$	249.932	+	249.932i	0.413795	+	0.413795i
$605$	−230.261	+	230.261i	−0.380596	+	0.380596i
$606$	253.789	−	253.789i	0.418794	−	0.418794i
$607$	−507.912			−0.836757			−0.418379	−	0.908273i	$-0.637402\pi$
$607$	−507.912			−0.836757			−0.418379	+	0.908273i	$0.637402\pi$
$608$		−	138.377i		−	0.227594i
$609$	−110.811	+	110.811i	−0.181956	+	0.181956i
$610$		−	334.333i		−	0.548087i
$611$	653.416	+	212.070i	1.06942	+	0.347086i
$612$	608.131			0.993678
$613$	−231.540	−	231.540i	−0.377715	−	0.377715i	0.492562	−	0.870277i	$-0.336060\pi$
$613$	−231.540	−	231.540i	−0.377715	−	0.377715i	−0.870277	+	0.492562i	$0.836060\pi$
$614$	255.334			0.415853
$615$		−	144.219i		−	0.234503i
$616$	207.658	+	207.658i	0.337107	+	0.337107i
$617$	−271.412	−	271.412i	−0.439890	−	0.439890i	0.452085	−	0.891975i	$-0.350680\pi$
$617$	−271.412	−	271.412i	−0.439890	−	0.439890i	−0.891975	+	0.452085i	$0.850680\pi$
$618$	−85.7103	+	85.7103i	−0.138690	+	0.138690i
$619$	−235.048	+	235.048i	−0.379723	+	0.379723i	−0.871002	−	0.491279i	$-0.836529\pi$
$619$	−235.048	+	235.048i	−0.379723	+	0.379723i	0.491279	+	0.871002i	$0.336529\pi$
$620$	12.2192			0.0197084
$621$			23.9338i			0.0385408i
$622$	−198.566	+	198.566i	−0.319238	+	0.319238i
$623$			81.4562i			0.130748i
$624$	−205.274	−	402.546i	−0.328965	−	0.645105i
$625$	640.806			1.02529
$626$	254.840	+	254.840i	0.407092	+	0.407092i
$627$	−140.167			−0.223551
$628$		−	184.367i		−	0.293578i
$629$	532.427	+	532.427i	0.846466	+	0.846466i
$630$	−158.732	−	158.732i	−0.251956	−	0.251956i
$631$	−95.4630	+	95.4630i	−0.151288	+	0.151288i	−0.778693	−	0.627405i	$-0.784117\pi$
$631$	−95.4630	+	95.4630i	−0.151288	+	0.151288i	0.627405	+	0.778693i	$0.284117\pi$
$632$	−79.9602	+	79.9602i	−0.126519	+	0.126519i
$633$	198.018			0.312824
$634$			177.991i			0.280744i
$635$	362.276	−	362.276i	0.570514	−	0.570514i
$636$		−	495.548i		−	0.779164i
$637$	81.3729	−	41.4954i	0.127744	−	0.0651419i
$638$	−35.9644			−0.0563706
$639$	762.153	+	762.153i	1.19273	+	1.19273i
$640$	−660.013			−1.03127
$641$		−	904.710i		−	1.41140i	−0.708508	−	0.705702i	$-0.750632\pi$
$641$		−	904.710i		−	1.41140i	0.708508	−	0.705702i	$-0.249368\pi$
$642$	10.7153	+	10.7153i	0.0166905	+	0.0166905i
$643$	−108.312	−	108.312i	−0.168447	−	0.168447i	0.617849	−	0.786297i	$-0.288004\pi$
$643$	−108.312	−	108.312i	−0.168447	−	0.168447i	−0.786297	+	0.617849i	$0.788004\pi$
$644$	−129.658	+	129.658i	−0.201332	+	0.201332i
$645$	−454.427	+	454.427i	−0.704539	+	0.704539i
$646$	−80.7630			−0.125020
$647$			306.474i			0.473685i	0.971548	+	0.236842i	$0.0761125\pi$
$647$			306.474i			0.473685i	−0.971548	+	0.236842i	$0.923888\pi$
$648$	−368.717	+	368.717i	−0.569008	+	0.569008i
$649$		−	620.544i		−	0.956154i
$650$	6.59644	+	2.14091i	0.0101484	+	0.00329371i
$651$	19.5701			0.0300616
$652$	151.136	+	151.136i	0.231804	+	0.231804i
$653$	−1009.69			−1.54624			−0.773118	−	0.634262i	$-0.781304\pi$
$653$	−1009.69			−1.54624			−0.773118	+	0.634262i	$0.781304\pi$
$654$		−	584.271i		−	0.893381i
$655$	−922.975	−	922.975i	−1.40912	−	1.40912i
$656$	−40.3993	−	40.3993i	−0.0615843	−	0.0615843i
$657$	263.246	−	263.246i	0.400678	−	0.400678i
$658$	198.958	−	198.958i	0.302368	−	0.302368i
$659$	−211.009			−0.320196			−0.160098	−	0.987101i	$-0.551181\pi$
$659$	−211.009			−0.320196			−0.160098	+	0.987101i	$0.551181\pi$
$660$			527.715i			0.799568i
$661$	−61.5922	+	61.5922i	−0.0931803	+	0.0931803i	−0.752160	−	0.658980i	$-0.770988\pi$
$661$	−61.5922	+	61.5922i	−0.0931803	+	0.0931803i	0.658980	+	0.752160i	$0.270988\pi$
$662$		−	227.786i		−	0.344087i
$663$	−1059.22	+	540.138i	−1.59761	+	0.814687i
$664$	−379.881			−0.572110
$665$	−103.759	−	103.759i	−0.156028	−	0.156028i
$666$	234.438			0.352010
$667$		−	49.4733i		−	0.0741729i
$668$	456.179	+	456.179i	0.682902	+	0.682902i
$669$	159.107	+	159.107i	0.237828	+	0.237828i
$670$	−162.675	+	162.675i	−0.242799	+	0.242799i
$671$	−427.693	+	427.693i	−0.637396	+	0.637396i
$672$	−834.390			−1.24165
$673$			105.500i			0.156760i	0.996924	+	0.0783801i	$0.0249748\pi$
$673$			105.500i			0.156760i	−0.996924	+	0.0783801i	$0.975025\pi$
$674$	4.25658	−	4.25658i	0.00631541	−	0.00631541i
$675$			1.82490i			0.00270356i
$676$	454.764	+	329.947i	0.672727	+	0.488088i
$677$	−215.969			−0.319009			−0.159505	−	0.987197i	$-0.550990\pi$
$677$	−215.969			−0.319009			−0.159505	+	0.987197i	$0.550990\pi$
$678$	−165.798	−	165.798i	−0.244540	−	0.244540i
$679$	1111.89			1.63754
$680$			669.907i			0.985158i
$681$	−186.189	−	186.189i	−0.273405	−	0.273405i
$682$	3.17579	+	3.17579i	0.00465659	+	0.00465659i
$683$	672.956	−	672.956i	0.985294	−	0.985294i	−0.0145993	−	0.999893i	$-0.504647\pi$
$683$	672.956	−	672.956i	0.985294	−	0.985294i	0.999893	+	0.0145993i	$0.00464727\pi$
$684$	87.5174	−	87.5174i	0.127949	−	0.127949i
$685$	1255.35			1.83262
$686$		−	298.315i		−	0.434862i
$687$	697.738	−	697.738i	1.01563	−	1.01563i
$688$			254.592i			0.370047i
$689$	211.491	+	414.737i	0.306954	+	0.601940i
$690$	147.487			0.213749
$691$	−563.105	−	563.105i	−0.814913	−	0.814913i	0.170453	−	0.985366i	$-0.445477\pi$
$691$	−563.105	−	563.105i	−0.814913	−	0.814913i	−0.985366	+	0.170453i	$0.945477\pi$
$692$	263.908			0.381370
$693$			406.114i			0.586023i
$694$	−89.9363	−	89.9363i	−0.129591	−	0.129591i
$695$	485.103	+	485.103i	0.697990	+	0.697990i
$696$	102.961	−	102.961i	0.147932	−	0.147932i
$697$	−106.302	+	106.302i	−0.152514	+	0.152514i
$698$	256.188			0.367031
$699$		−	1218.67i		−	1.74345i
$700$	−9.88612	+	9.88612i	−0.0141230	+	0.0141230i
$701$		−	179.934i		−	0.256682i	−0.991730	−	0.128341i	$-0.959035\pi$
$701$		−	179.934i		−	0.256682i	0.991730	−	0.128341i	$-0.0409651\pi$
$702$	9.27258	−	28.5701i	0.0132088	−	0.0406982i
$703$	153.246			0.217988
$704$	42.4562	+	42.4562i	0.0603071	+	0.0603071i
$705$	1113.94			1.58005
$706$			385.504i			0.546040i
$707$	−480.658	−	480.658i	−0.679855	−	0.679855i
$708$	806.350	+	806.350i	1.13891	+	1.13891i
$709$	−291.315	+	291.315i	−0.410882	+	0.410882i	−0.882046	−	0.471164i	$-0.843834\pi$
$709$	−291.315	+	291.315i	−0.410882	+	0.410882i	0.471164	+	0.882046i	$0.343834\pi$
$710$	−381.077	+	381.077i	−0.536727	+	0.536727i
$711$	−156.377			−0.219940
$712$		−	75.6854i		−	0.106300i
$713$	−4.36868	+	4.36868i	−0.00612718	+	0.00612718i
$714$			486.986i			0.682054i
$715$	−225.219	−	441.658i	−0.314992	−	0.617703i
$716$	−1058.30			−1.47808
$717$	−0.0636984	−	0.0636984i	−8.88401e−5	−	8.88401e-5i
$718$	154.333			0.214949
$719$			487.565i			0.678116i	0.940766	+	0.339058i	$0.110108\pi$
$719$			487.565i			0.678116i	−0.940766	+	0.339058i	$0.889892\pi$
$720$	−248.952	−	248.952i	−0.345766	−	0.345766i
$721$	162.329	+	162.329i	0.225144	+	0.225144i
$722$	198.168	−	198.168i	0.274471	−	0.274471i
$723$	−999.767	+	999.767i	−1.38280	+	1.38280i
$724$	−791.725			−1.09354
$725$		−	3.77223i		−	0.00520308i
$726$	155.528	−	155.528i	0.214227	−	0.214227i
$727$		−	277.337i		−	0.381482i	−0.981640	−	0.190741i	$-0.938911\pi$
$727$		−	277.337i		−	0.381482i	0.981640	−	0.190741i	$-0.0610891\pi$
$728$	451.664	−	230.322i	0.620418	−	0.316376i
$729$	−615.780			−0.844691
$730$	131.623	+	131.623i	0.180305	+	0.180305i
$731$	669.907			0.916426
$732$		−	1111.51i		−	1.51845i
$733$	−235.559	−	235.559i	−0.321363	−	0.321363i	0.527927	−	0.849290i	$-0.322970\pi$
$733$	−235.559	−	235.559i	−0.321363	−	0.321363i	−0.849290	+	0.527927i	$0.822970\pi$
$734$	164.123	+	164.123i	0.223601	+	0.223601i
$735$	104.732	−	104.732i	0.142493	−	0.142493i
$736$	186.263	−	186.263i	0.253074	−	0.253074i
$737$	416.202			0.564725
$738$			46.8071i			0.0634243i
$739$	−667.732	+	667.732i	−0.903561	+	0.903561i	−0.995742	−	0.0921811i	$-0.970616\pi$
$739$	−667.732	+	667.732i	−0.903561	+	0.903561i	0.0921811	+	0.995742i	$0.470616\pi$
$740$		−	576.956i		−	0.779670i
$741$	−74.7018	+	230.167i	−0.100812	+	0.310616i
$742$	190.680			0.256981
$743$	335.358	+	335.358i	0.451356	+	0.451356i	0.895804	−	0.444448i	$-0.146600\pi$
$743$	335.358	+	335.358i	0.451356	+	0.451356i	−0.444448	+	0.895804i	$0.646600\pi$
$744$	−18.1836			−0.0244404
$745$			259.412i			0.348204i
$746$	−377.088	−	377.088i	−0.505479	−	0.505479i
$747$	−371.465	−	371.465i	−0.497275	−	0.497275i
$748$	388.973	−	388.973i	0.520017	−	0.520017i
$749$	20.2939	−	20.2939i	0.0270947	−	0.0270947i
$750$	−421.868			−0.562491
$751$			1300.24i			1.73134i	0.500615	+	0.865670i	$0.333107\pi$
$751$			1300.24i			1.73134i	−0.500615	+	0.865670i	$0.666893\pi$
$752$	312.041	−	312.041i	0.414948	−	0.414948i
$753$		−	548.763i		−	0.728769i
$754$	−19.1672	+	59.0569i	−0.0254207	+	0.0783249i
$755$	−538.443			−0.713169
$756$	42.8181	+	42.8181i	0.0566378	+	0.0566378i
$757$	1155.45			1.52636			0.763178	−	0.646188i	$-0.223638\pi$
$757$	1155.45			1.52636			0.763178	+	0.646188i	$0.223638\pi$
$758$		−	498.969i		−	0.658270i
$759$	−188.671	−	188.671i	−0.248579	−	0.248579i
$760$	96.4078	+	96.4078i	0.126852	+	0.126852i
$761$	−205.412	+	205.412i	−0.269924	+	0.269924i	−0.829069	−	0.559146i	$-0.811129\pi$
$761$	−205.412	+	205.412i	−0.269924	+	0.269924i	0.559146	+	0.829069i	$0.311129\pi$
$762$	−244.698	+	244.698i	−0.321125	+	0.321125i
$763$	−1106.57			−1.45028
$764$			12.3210i			0.0161269i
$765$	−655.065	+	655.065i	−0.856295	+	0.856295i
$766$			154.280i			0.201410i
$767$	−1018.99	−	330.719i	−1.32854	−	0.431185i
$768$	313.048			0.407614
$769$	62.0527	+	62.0527i	0.0806927	+	0.0806927i	0.746301	−	0.665608i	$-0.231828\pi$
$769$	62.0527	+	62.0527i	0.0806927	+	0.0806927i	−0.665608	+	0.746301i	$0.731828\pi$
$770$	−203.057			−0.263710
$771$			651.724i			0.845297i
$772$	−143.408	−	143.408i	−0.185761	−	0.185761i
$773$	−318.813	−	318.813i	−0.412436	−	0.412436i	0.470150	−	0.882586i	$-0.344200\pi$
$773$	−318.813	−	318.813i	−0.412436	−	0.412436i	−0.882586	+	0.470150i	$0.844200\pi$
$774$	147.487	−	147.487i	0.190551	−	0.190551i
$775$	−0.333102	+	0.333102i	−0.000429809	+	0.000429809i
$776$	−1033.12			−1.33134
$777$		−	924.043i		−	1.18925i
$778$	296.579	−	296.579i	0.381207	−	0.381207i
$779$			30.5964i			0.0392766i
$780$	866.557	+	281.246i	1.11097	+	0.360571i
$781$	974.977			1.24837
$782$	−108.711	−	108.711i	−0.139017	−	0.139017i
$783$	−16.3381			−0.0208660
$784$		−	58.6761i		−	0.0748420i
$785$	198.596	+	198.596i	0.252989	+	0.252989i
$786$	623.419	+	623.419i	0.793154	+	0.793154i
$787$	634.566	−	634.566i	0.806310	−	0.806310i	−0.177763	−	0.984073i	$-0.556886\pi$
$787$	634.566	−	634.566i	0.806310	−	0.806310i	0.984073	+	0.177763i	$0.0568862\pi$
$788$	419.207	−	419.207i	0.531989	−	0.531989i
$789$	1410.94			1.78826
$790$		−	78.1886i		−	0.0989729i
$791$	−314.009	+	314.009i	−0.396977	+	0.396977i
$792$		−	377.342i		−	0.476442i
$793$	474.372	+	930.250i	0.598200	+	1.17308i
$794$	−165.115			−0.207953
$795$	533.794	+	533.794i	0.671438	+	0.671438i
$796$	−506.135			−0.635847
$797$			407.026i			0.510698i	0.966849	+	0.255349i	$0.0821904\pi$
$797$			407.026i			0.510698i	−0.966849	+	0.255349i	$0.917810\pi$
$798$	70.0833	+	70.0833i	0.0878237	+	0.0878237i
$799$	−821.072	−	821.072i	−1.02762	−	1.02762i
$800$	14.2021	−	14.2021i	0.0177527	−	0.0177527i
$801$	74.0085	−	74.0085i	0.0923952	−	0.0923952i
$802$	167.715			0.209120
$803$		−	336.754i		−	0.419370i
$804$	−540.824	+	540.824i	−0.672666	+	0.672666i
$805$		−	279.329i		−	0.346992i
$806$	6.90748	−	3.52241i	0.00857008	−	0.00437023i
$807$	924.280			1.14533
$808$	446.605	+	446.605i	0.552729	+	0.552729i
$809$	−647.641			−0.800545			−0.400272	−	0.916396i	$-0.631084\pi$
$809$	−647.641			−0.800545			−0.400272	+	0.916396i	$0.631084\pi$
$810$		−	360.548i		−	0.445121i
$811$	850.386	+	850.386i	1.04856	+	1.04856i	0.998759	+	0.0498055i	$0.0158601\pi$
$811$	850.386	+	850.386i	1.04856	+	1.04856i	0.0498055	+	0.998759i	$0.484140\pi$
$812$	−88.5089	−	88.5089i	−0.109001	−	0.109001i
$813$	−162.630	+	162.630i	−0.200036	+	0.200036i
$814$	149.952	−	149.952i	0.184216	−	0.184216i
$815$	−325.601			−0.399510
$816$			763.777i			0.936001i
$817$	96.4078	−	96.4078i	0.118002	−	0.118002i
$818$			106.767i			0.130521i
$819$	666.877	+	216.438i	0.814257	+	0.264272i
$820$	115.193			0.140479
$821$	330.186	+	330.186i	0.402176	+	0.402176i	0.878999	−	0.476824i	$-0.158212\pi$
$821$	330.186	+	330.186i	0.402176	+	0.402176i	−0.476824	+	0.878999i	$0.658212\pi$
$822$	−847.917			−1.03153
$823$		−	507.579i		−	0.616742i	−0.951266	−	0.308371i	$-0.900216\pi$
$823$		−	507.579i		−	0.616742i	0.951266	−	0.308371i	$-0.0997838\pi$
$824$	−150.828	−	150.828i	−0.183044	−	0.183044i
$825$	−14.3858	−	14.3858i	−0.0174373	−	0.0174373i
$826$	−310.272	+	310.272i	−0.375632	+	0.375632i
$827$	−488.452	+	488.452i	−0.590631	+	0.590631i	−0.937802	−	0.347171i	$-0.887142\pi$
$827$	−488.452	+	488.452i	−0.590631	+	0.590631i	0.347171	+	0.937802i	$0.387142\pi$
$828$	235.606			0.284548
$829$		−	1391.89i		−	1.67900i	−0.543361	−	0.839499i	$-0.682848\pi$
$829$		−	1391.89i		−	1.67900i	0.543361	−	0.839499i	$-0.317152\pi$
$830$	185.732	−	185.732i	0.223774	−	0.223774i
$831$		−	466.394i		−	0.561245i
$832$	92.3441	−	47.0900i	0.110991	−	0.0565986i
$833$	−154.394			−0.185347
$834$	−327.660	−	327.660i	−0.392878	−	0.392878i
$835$	−982.772			−1.17697
$836$		−	111.956i		−	0.133919i
$837$	1.44271	+	1.44271i	0.00172367	+	0.00172367i
$838$	−48.3698	−	48.3698i	−0.0577205	−	0.0577205i
$839$	−128.794	+	128.794i	−0.153508	+	0.153508i	−0.779683	−	0.626174i	$-0.784620\pi$
$839$	−128.794	+	128.794i	−0.153508	+	0.153508i	0.626174	+	0.779683i	$0.284620\pi$
$840$	581.322	−	581.322i	0.692050	−	0.692050i
$841$	−807.228			−0.959843
$842$			79.3993i			0.0942984i
$843$	727.759	−	727.759i	0.863296	−	0.863296i
$844$			158.164i			0.187398i
$845$	−845.274	+	134.449i	−1.00032	+	0.159112i
$846$	−361.535			−0.427346
$847$	−294.559	−	294.559i	−0.347768	−	0.347768i
$848$	299.057			0.352661
$849$		−	1128.82i		−	1.32958i
$850$	−8.28898	−	8.28898i	−0.00975174	−	0.00975174i
$851$	206.276	+	206.276i	0.242393	+	0.242393i
$852$	−1266.91	+	1266.91i	−1.48698	+	1.48698i
$853$	−485.546	+	485.546i	−0.569221	+	0.569221i	−0.931910	−	0.362689i	$-0.881859\pi$
$853$	−485.546	+	485.546i	−0.569221	+	0.569221i	0.362689	+	0.931910i	$0.381859\pi$
$854$	427.693			0.500811
$855$			188.544i			0.220519i
$856$	−18.8562	+	18.8562i	−0.0220283	+	0.0220283i
$857$			1245.24i			1.45302i	0.687157	+	0.726509i	$0.258859\pi$
$857$			1245.24i			1.45302i	−0.687157	+	0.726509i	$0.741141\pi$
$858$	152.123	+	298.315i	0.177300	+	0.347687i
$859$	1194.94			1.39108			0.695540	−	0.718487i	$-0.255165\pi$
$859$	1194.94			1.39108			0.695540	+	0.718487i	$0.255165\pi$
$860$	−362.967	−	362.967i	−0.422055	−	0.422055i
$861$	184.491			0.214275
$862$			546.227i			0.633674i
$863$	−604.195	−	604.195i	−0.700111	−	0.700111i	0.264324	−	0.964434i	$-0.414851\pi$
$863$	−604.195	−	604.195i	−0.700111	−	0.700111i	−0.964434	+	0.264324i	$0.914851\pi$
$864$	−61.5114	−	61.5114i	−0.0711937	−	0.0711937i
$865$	−284.276	+	284.276i	−0.328643	+	0.328643i
$866$	70.9804	−	70.9804i	0.0819635	−	0.0819635i
$867$	806.824			0.930593
$868$			15.6313i			0.0180084i
$869$	−100.022	+	100.022i	−0.115100	+	0.115100i
$870$			100.680i			0.115724i
$871$	221.815	−	683.443i	0.254667	−	0.784664i
$872$	1028.17			1.17909
$873$	−1010.23	−	1010.23i	−1.15719	−	1.15719i
$874$	−31.2897			−0.0358005
$875$			798.986i			0.913127i
$876$	437.587	+	437.587i	0.499529	+	0.499529i
$877$	−1065.53	−	1065.53i	−1.21497	−	1.21497i	−0.969370	−	0.245603i	$-0.921014\pi$
$877$	−1065.53	−	1065.53i	−1.21497	−	1.21497i	−0.245603	−	0.969370i	$-0.578986\pi$
$878$	−18.1836	+	18.1836i	−0.0207103	+	0.0207103i
$879$	999.594	−	999.594i	1.13719	−	1.13719i
$880$	−318.469			−0.361897
$881$			821.315i			0.932253i	0.884718	+	0.466126i	$0.154351\pi$
$881$			821.315i			0.932253i	−0.884718	+	0.466126i	$0.845649\pi$
$882$	−33.9915	+	33.9915i	−0.0385391	+	0.0385391i
$883$			1091.97i			1.23666i	0.785920	+	0.618329i	$0.212190\pi$
$883$			1091.97i			1.23666i	−0.785920	+	0.618329i	$0.787810\pi$
$884$	−431.427	−	846.033i	−0.488039	−	0.957051i
$885$	−1737.17			−1.96290
$886$	329.722	+	329.722i	0.372147	+	0.372147i
$887$	1478.73			1.66711			0.833555	−	0.552436i	$-0.186302\pi$
$887$	1478.73			1.66711			0.833555	+	0.552436i	$0.186302\pi$
$888$			858.579i			0.966868i
$889$	463.438	+	463.438i	0.521303	+	0.521303i
$890$	37.0043	+	37.0043i	0.0415778	+	0.0415778i
$891$	−461.228	+	461.228i	−0.517652	+	0.517652i
$892$	−127.084	+	127.084i	−0.142471	+	0.142471i
$893$	−236.325			−0.264641
$894$		−	175.219i		−	0.195994i
$895$	1139.98	−	1139.98i	1.27372	−	1.27372i
$896$		−	844.315i		−	0.942316i
$897$	−410.368	+	209.263i	−0.457489	+	0.233292i
$898$	−617.021			−0.687106
$899$	−2.98221	−	2.98221i	−0.00331726	−	0.00331726i
$900$	17.9644			0.0199605
$901$		−	786.907i		−	0.873371i
$902$	29.9388	+	29.9388i	0.0331916	+	0.0331916i
$903$	−581.322	−	581.322i	−0.643768	−	0.643768i
$904$	291.762	−	291.762i	0.322746	−	0.322746i
$905$	852.828	−	852.828i	0.942352	−	0.942352i
$906$	363.688			0.401422
$907$			1460.57i			1.61033i	0.593048	+	0.805167i	$0.297925\pi$
$907$			1460.57i			1.61033i	−0.593048	+	0.805167i	$0.702075\pi$
$908$	148.715	−	148.715i	0.163783	−	0.163783i
$909$			873.421i			0.960859i
$910$	−108.219	+	333.438i	−0.118922	+	0.366416i
$911$	287.689			0.315795			0.157897	−	0.987456i	$-0.449528\pi$
$911$	287.689			0.315795			0.157897	+	0.987456i	$0.449528\pi$
$912$	109.917	+	109.917i	0.120523	+	0.120523i
$913$	−475.193			−0.520474
$914$			269.755i			0.295137i
$915$	1197.29	+	1197.29i	1.30852	+	1.30852i
$916$	557.308	+	557.308i	0.608415	+	0.608415i
$917$	1180.71	−	1180.71i	1.28758	−	1.28758i
$918$	−35.9007	+	35.9007i	−0.0391075	+	0.0391075i
$919$	1696.20			1.84570			0.922851	−	0.385156i	$-0.125852\pi$
$919$	1696.20			1.84570			0.922851	+	0.385156i	$0.125852\pi$
$920$			259.540i			0.282108i
$921$	−914.386	+	914.386i	−0.992818	+	0.992818i
$922$		−	243.785i		−	0.264409i
$923$	519.614	−	1601.00i	0.562962	−	1.73457i
$924$	−675.074			−0.730600
$925$	15.7281	+	15.7281i	0.0170034	+	0.0170034i
$926$	148.359			0.160215
$927$		−	294.974i		−	0.318202i
$928$	127.149	+	127.149i	0.137015	+	0.137015i
$929$	912.403	+	912.403i	0.982134	+	0.982134i	0.999843	−	0.0177088i	$-0.00563717\pi$
$929$	912.403	+	912.403i	0.982134	+	0.982134i	−0.0177088	+	0.999843i	$0.505637\pi$
$930$	8.89039	−	8.89039i	0.00955956	−	0.00955956i
$931$	−22.2192	+	22.2192i	−0.0238660	+	0.0238660i
$932$	973.394			1.04441
$933$		−	1422.18i		−	1.52431i
$934$	399.670	−	399.670i	0.427913	−	0.427913i
$935$			837.986i			0.896242i
$936$	−619.631	−	201.105i	−0.661999	−	0.214855i
$937$	−1041.30			−1.11131			−0.555655	−	0.831413i	$-0.687533\pi$
$937$	−1041.30			−1.11131			−0.555655	+	0.831413i	$0.687533\pi$
$938$	−208.101	−	208.101i	−0.221856	−	0.221856i
$939$	−1825.23			−1.94380
$940$			889.741i			0.946533i
$941$	−502.392	−	502.392i	−0.533891	−	0.533891i	0.387837	−	0.921728i	$-0.373222\pi$
$941$	−502.392	−	502.392i	−0.533891	−	0.533891i	−0.921728	+	0.387837i	$0.873222\pi$
$942$	−134.141	−	134.141i	−0.142400	−	0.142400i
$943$	−41.1843	+	41.1843i	−0.0436737	+	0.0436737i
$944$	−486.622	+	486.622i	−0.515489	+	0.515489i
$945$	−92.2456			−0.0976143
$946$		−	188.671i		−	0.199441i
$947$	−683.569	+	683.569i	−0.721826	+	0.721826i	−0.968977	−	0.247151i	$-0.920506\pi$
$947$	−683.569	+	683.569i	−0.721826	+	0.721826i	0.247151	+	0.968977i	$0.420506\pi$
$948$		−	259.942i		−	0.274201i
$949$	−552.982	−	179.473i	−0.582700	−	0.189118i
$950$	−2.38577			−0.00251134
$951$	−637.412	−	637.412i	−0.670255	−	0.670255i
$952$	−856.973			−0.900182
$953$			694.290i			0.728531i	0.931295	+	0.364265i	$0.118680\pi$
$953$			694.290i			0.728531i	−0.931295	+	0.364265i	$0.881320\pi$
$954$	−173.246	−	173.246i	−0.181599	−	0.181599i
$955$	−13.2719	−	13.2719i	−0.0138973	−	0.0138973i
$956$	0.0508781	−	0.0508781i	5.32198e−5	−	5.32198e-5i
$957$	128.794	−	128.794i	0.134581	−	0.134581i
$958$	−370.351			−0.386588
$959$			1605.89i			1.67455i
$960$	118.853	−	118.853i	0.123805	−	0.123805i
$961$		−	960.473i		−	0.999452i
$962$	−166.318	−	326.151i	−0.172888	−	0.339035i
$963$	−36.8769			−0.0382937
$964$	−798.549	−	798.549i	−0.828370	−	0.828370i
$965$	308.952			0.320157
$966$			188.671i			0.195312i
$967$	−616.081	−	616.081i	−0.637106	−	0.637106i	0.312735	−	0.949841i	$-0.398755\pi$
$967$	−616.081	−	616.081i	−0.637106	−	0.637106i	−0.949841	+	0.312735i	$0.898755\pi$
$968$	273.691	+	273.691i	0.282738	+	0.282738i
$969$	289.223	−	289.223i	0.298476	−	0.298476i
$970$	505.114	−	505.114i	0.520736	−	0.520736i
$971$	−473.890			−0.488044			−0.244022	−	0.969770i	$-0.578467\pi$
$971$	−473.890			−0.488044			−0.244022	+	0.969770i	$0.578467\pi$
$972$		−	1114.54i		−	1.14665i
$973$	−620.563	+	620.563i	−0.637784	+	0.637784i
$974$			647.465i			0.664748i
$975$	−31.2897	+	15.9559i	−0.0320920	+	0.0163650i
$976$	670.781			0.687276
$977$	9.56087	+	9.56087i	0.00978594	+	0.00978594i	0.711983	−	0.702197i	$-0.247797\pi$
$977$	9.56087	+	9.56087i	0.00978594	+	0.00978594i	−0.702197	+	0.711983i	$0.747797\pi$
$978$	219.925			0.224872
$979$		−	94.6748i		−	0.0967056i
$980$	83.6534	+	83.6534i	0.0853606	+	0.0853606i
$981$	1005.39	+	1005.39i	1.02486	+	1.02486i
$982$	232.861	−	232.861i	0.237129	−	0.237129i
$983$	695.475	−	695.475i	0.707503	−	0.707503i	−0.258507	−	0.966009i	$-0.583230\pi$
$983$	695.475	−	695.475i	0.707503	−	0.707503i	0.966009	+	0.258507i	$0.0832304\pi$
$984$	−171.421			−0.174208
$985$			903.122i			0.916876i
$986$	74.2100	−	74.2100i	0.0752637	−	0.0752637i
$987$			1425.00i			1.44376i
$988$	−183.842	−	59.6669i	−0.186075	−	0.0603916i
$989$	259.540			0.262426
$990$	184.491	+	184.491i	0.186355	+	0.186355i
$991$	−1625.34			−1.64010			−0.820051	−	0.572291i	$-0.806055\pi$
$991$	−1625.34			−1.64010			−0.820051	+	0.572291i	$0.806055\pi$
$992$		−	22.4555i		−	0.0226366i
$993$	815.732	+	815.732i	0.821483	+	0.821483i
$994$	−487.489	−	487.489i	−0.490431	−	0.490431i
$995$	545.197	−	545.197i	0.547937	−	0.547937i
$996$	617.478	−	617.478i	0.619957	−	0.619957i
$997$	−31.3986			−0.0314931			−0.0157465	−	0.999876i	$-0.505012\pi$
$997$	−31.3986			−0.0314931			−0.0157465	+	0.999876i	$0.505012\pi$
$998$			119.332i			0.119572i
$999$	68.1206	−	68.1206i	0.0681888	−	0.0681888i

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	13.3.d.a.8.2	yes	4
3.2	odd	2		117.3.j.a.73.1		4
4.3	odd	2		208.3.t.c.177.2		4
5.2	odd	4		325.3.g.b.99.1		4
5.3	odd	4		325.3.g.a.99.2		4
5.4	even	2		325.3.j.a.151.1		4
13.2	odd	12		169.3.f.f.19.2		8
13.3	even	3		169.3.f.f.150.1		8
13.4	even	6		169.3.f.d.89.1		8
13.5	odd	4	inner	13.3.d.a.5.2	✓	4
13.6	odd	12		169.3.f.f.80.1		8
13.7	odd	12		169.3.f.d.80.2		8
13.8	odd	4		169.3.d.d.70.1		4
13.9	even	3		169.3.f.f.89.2		8
13.10	even	6		169.3.f.d.150.2		8
13.11	odd	12		169.3.f.d.19.1		8
13.12	even	2		169.3.d.d.99.1		4
39.5	even	4		117.3.j.a.109.1		4
52.31	even	4		208.3.t.c.161.2		4
65.18	even	4		325.3.g.b.174.1		4
65.44	odd	4		325.3.j.a.226.1		4
65.57	even	4		325.3.g.a.174.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
13.3.d.a.5.2	✓	4	13.5	odd	4	inner
13.3.d.a.8.2	yes	4	1.1	even	1	trivial
117.3.j.a.73.1		4	3.2	odd	2
117.3.j.a.109.1		4	39.5	even	4
169.3.d.d.70.1		4	13.8	odd	4
169.3.d.d.99.1		4	13.12	even	2
169.3.f.d.19.1		8	13.11	odd	12
169.3.f.d.80.2		8	13.7	odd	12
169.3.f.d.89.1		8	13.4	even	6
169.3.f.d.150.2		8	13.10	even	6
169.3.f.f.19.2		8	13.2	odd	12
169.3.f.f.80.1		8	13.6	odd	12
169.3.f.f.89.2		8	13.9	even	3
169.3.f.f.150.1		8	13.3	even	3
208.3.t.c.161.2		4	52.31	even	4
208.3.t.c.177.2		4	4.3	odd	2
325.3.g.a.99.2		4	5.3	odd	4
325.3.g.a.174.2		4	65.57	even	4
325.3.g.b.99.1		4	5.2	odd	4
325.3.g.b.174.1		4	65.18	even	4
325.3.j.a.151.1		4	5.4	even	2
325.3.j.a.226.1		4	65.44	odd	4

Overview	Random
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Classical	Maass
Hilbert	Bianchi

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	13.3.d.a.8.2

Level	$13$
Weight	$3$
Character	13.8
Analytic conductor	$0.354$
Analytic rank	$0$
Dimension	$4$
Inner twists	$2$