LMFDB - Embedded newform 680.2.cg.b.73.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [680,2,Mod(57,680)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(680, base_ring=CyclotomicField(16)) chi = DirichletCharacter(H, H._module([0, 0, 4, 15])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("680.57"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 680 = 2^{3} \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	680.cg (of order $16$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [112] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$5.42982733745$
Analytic rank:	$0$
Dimension:	$112$
Relative dimension:	$14$ over $\Q(\zeta_{16})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			73.4
Character	$\chi$	$=$	680.73
Dual form			680.2.cg.b.177.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.431185 + 2.16772i) q^{3} +(-1.72137 - 1.42720i) q^{5} +(3.13047 + 2.09171i) q^{7} +(-1.74143 - 0.721324i) q^{9} +(4.13611 + 2.76366i) q^{11} -4.22102i q^{13} +(3.83599 - 3.11604i) q^{15} +(3.83647 + 1.51046i) q^{17} +(-4.74204 + 1.96422i) q^{19} +(-5.88405 + 5.88405i) q^{21} +(-2.01280 + 0.400370i) q^{23} +(0.926199 + 4.91347i) q^{25} +(-1.36923 + 2.04920i) q^{27} +(-1.19633 + 6.01436i) q^{29} +(2.21798 - 1.48200i) q^{31} +(-7.77427 + 7.77427i) q^{33} +(-2.40339 - 8.06840i) q^{35} +(-4.75306 - 0.945443i) q^{37} +(9.14997 + 1.82004i) q^{39} +(1.48544 + 7.46784i) q^{41} +(10.7322 - 4.44543i) q^{43} +(1.96816 + 3.72703i) q^{45} -9.66773 q^{47} +(2.74578 + 6.62891i) q^{49} +(-4.92848 + 7.66509i) q^{51} +(2.23033 - 5.38449i) q^{53} +(-3.17546 - 10.6603i) q^{55} +(-2.21317 - 11.1263i) q^{57} +(-3.10699 + 7.50094i) q^{59} +(-7.48983 + 1.48982i) q^{61} +(-3.94269 - 5.90065i) q^{63} +(-6.02424 + 7.26592i) q^{65} +(-2.07300 - 2.07300i) q^{67} -4.53580i q^{69} +(8.82168 + 13.2026i) q^{71} +(1.28356 - 0.857646i) q^{73} +(-11.0504 - 0.110878i) q^{75} +(7.16718 + 17.3031i) q^{77} +(7.90124 - 11.8250i) q^{79} +(-7.85019 - 7.85019i) q^{81} +(-1.90214 - 0.787891i) q^{83} +(-4.44824 - 8.07547i) q^{85} +(-12.5216 - 5.18661i) q^{87} +(1.46520 + 1.46520i) q^{89} +(8.82915 - 13.2138i) q^{91} +(2.25620 + 5.44696i) q^{93} +(10.9661 + 3.38671i) q^{95} +(15.5723 - 10.4051i) q^{97} +(-5.20926 - 7.79621i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q + 16 q^{15} - 24 q^{27} - 8 q^{29} + 16 q^{31} - 48 q^{33} - 32 q^{35} - 16 q^{37} - 16 q^{41} + 48 q^{43} - 24 q^{45} - 16 q^{47} - 80 q^{49} + 32 q^{51} - 8 q^{53} + 24 q^{55} - 80 q^{59} - 24 q^{61}+ \cdots + 48 q^{99}+O(q^{100}) $ 112 * q + 16 * q^15 - 24 * q^27 - 8 * q^29 + 16 * q^31 - 48 * q^33 - 32 * q^35 - 16 * q^37 - 16 * q^41 + 48 * q^43 - 24 * q^45 - 16 * q^47 - 80 * q^49 + 32 * q^51 - 8 * q^53 + 24 * q^55 - 80 * q^59 - 24 * q^61 - 72 * q^63 + 16 * q^65 - 48 * q^67 - 40 * q^71 - 16 * q^73 + 16 * q^75 + 24 * q^77 + 40 * q^79 - 24 * q^83 + 16 * q^85 + 16 * q^87 - 16 * q^89 + 16 * q^93 - 8 * q^95 + 64 * q^97 + 48 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/680\mathbb{Z}\right)^\times$.

$n$	$137$	$241$	$341$	$511$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{5}{16}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.431185	+	2.16772i	−0.248945	+	1.25153i	0.630747	+	0.775988i	$0.282748\pi$
$3$	−0.431185	+	2.16772i	−0.248945	+	1.25153i	−0.879693	+	0.475543i	$0.842252\pi$
$4$		0			0
$5$	−1.72137	−	1.42720i	−0.769818	−	0.638263i
$5$	−1.72137	−	1.42720i	−0.769818	−	0.638263i
$6$		0			0
$7$	3.13047	+	2.09171i	1.18321	+	0.790592i	0.981986	−	0.188954i	$-0.0605096\pi$
$7$	3.13047	+	2.09171i	1.18321	+	0.790592i	0.201219	+	0.979546i	$0.435510\pi$
$8$		0			0
$9$	−1.74143	−	0.721324i	−0.580477	−	0.240441i
$10$		0			0
$11$	4.13611	+	2.76366i	1.24709	+	0.833276i	0.991063	−	0.133395i	$-0.0425878\pi$
$11$	4.13611	+	2.76366i	1.24709	+	0.833276i	0.256023	+	0.966671i	$0.417588\pi$
$12$		0			0
$13$		−	4.22102i		−	1.17070i	−0.810781	−	0.585350i	$-0.800957\pi$
$13$		−	4.22102i		−	1.17070i	0.810781	−	0.585350i	$-0.199043\pi$
$14$		0			0
$15$	3.83599	−	3.11604i	0.990449	−	0.804559i
$16$		0			0
$17$	3.83647	+	1.51046i	0.930481	+	0.366341i
$17$	3.83647	+	1.51046i	0.930481	+	0.366341i
$18$		0			0
$19$	−4.74204	+	1.96422i	−1.08790	+	0.450623i	−0.853274	−	0.521463i	$-0.825386\pi$
$19$	−4.74204	+	1.96422i	−1.08790	+	0.450623i	−0.234626	+	0.972086i	$0.575386\pi$
$20$		0			0
$21$	−5.88405	+	5.88405i	−1.28400	+	1.28400i
$22$		0			0
$23$	−2.01280	+	0.400370i	−0.419697	+	0.0834829i	−0.400421	−	0.916331i	$-0.631136\pi$
$23$	−2.01280	+	0.400370i	−0.419697	+	0.0834829i	−0.0192759	+	0.999814i	$0.506136\pi$
$24$		0			0
$25$	0.926199	+	4.91347i	0.185240	+	0.982693i
$26$		0			0
$27$	−1.36923	+	2.04920i	−0.263509	+	0.394369i
$28$		0			0
$29$	−1.19633	+	6.01436i	−0.222153	+	1.11684i	0.695216	+	0.718801i	$0.255309\pi$
$29$	−1.19633	+	6.01436i	−0.222153	+	1.11684i	−0.917369	+	0.398038i	$0.869691\pi$
$30$		0			0
$31$	2.21798	−	1.48200i	0.398360	−	0.266176i	−0.340214	−	0.940348i	$-0.610499\pi$
$31$	2.21798	−	1.48200i	0.398360	−	0.266176i	0.738574	+	0.674172i	$0.235499\pi$
$32$		0			0
$33$	−7.77427	+	7.77427i	−1.35333	+	1.35333i
$34$		0			0
$35$	−2.40339	−	8.06840i	−0.406247	−	1.36381i
$36$		0			0
$37$	−4.75306	−	0.945443i	−0.781399	−	0.155430i	−0.211756	−	0.977322i	$-0.567918\pi$
$37$	−4.75306	−	0.945443i	−0.781399	−	0.155430i	−0.569642	+	0.821893i	$0.692918\pi$
$38$		0			0
$39$	9.14997	+	1.82004i	1.46517	+	0.291440i
$40$		0			0
$41$	1.48544	+	7.46784i	0.231988	+	1.16628i	0.904592	+	0.426278i	$0.140175\pi$
$41$	1.48544	+	7.46784i	0.231988	+	1.16628i	−0.672605	+	0.740002i	$0.734825\pi$
$42$		0			0
$43$	10.7322	−	4.44543i	1.63665	−	0.677921i	0.640694	−	0.767796i	$-0.278647\pi$
$43$	10.7322	−	4.44543i	1.63665	−	0.677921i	0.995953	+	0.0898750i	$0.0286468\pi$
$44$		0			0
$45$	1.96816	+	3.72703i	0.293397	+	0.555593i
$46$		0			0
$47$	−9.66773			−1.41018			−0.705091	−	0.709116i	$-0.749094\pi$
$47$	−9.66773			−1.41018			−0.705091	+	0.709116i	$0.749094\pi$
$48$		0			0
$49$	2.74578	+	6.62891i	0.392255	+	0.946987i
$50$		0			0
$51$	−4.92848	+	7.66509i	−0.690125	+	1.07333i
$52$		0			0
$53$	2.23033	−	5.38449i	0.306359	−	0.739617i	−0.693458	−	0.720497i	$-0.743914\pi$
$53$	2.23033	−	5.38449i	0.306359	−	0.739617i	0.999817	−	0.0191197i	$-0.00608637\pi$
$54$		0			0
$55$	−3.17546	−	10.6603i	−0.428180	−	1.43744i
$56$		0			0
$57$	−2.21317	−	11.1263i	−0.293141	−	1.47372i
$58$		0			0
$59$	−3.10699	+	7.50094i	−0.404496	+	0.976539i	0.582065	+	0.813143i	$0.302245\pi$
$59$	−3.10699	+	7.50094i	−0.404496	+	0.976539i	−0.986560	+	0.163397i	$0.947755\pi$
$60$		0			0
$61$	−7.48983	+	1.48982i	−0.958974	+	0.190752i	−0.649674	−	0.760213i	$-0.725095\pi$
$61$	−7.48983	+	1.48982i	−0.958974	+	0.190752i	−0.309300	+	0.950965i	$0.600095\pi$
$62$		0			0
$63$	−3.94269	−	5.90065i	−0.496732	−	0.743412i
$64$		0			0
$65$	−6.02424	+	7.26592i	−0.747215	+	0.901226i
$66$		0			0
$67$	−2.07300	−	2.07300i	−0.253257	−	0.253257i	0.569047	−	0.822305i	$-0.307312\pi$
$67$	−2.07300	−	2.07300i	−0.253257	−	0.253257i	−0.822305	+	0.569047i	$0.807312\pi$
$68$		0			0
$69$		−	4.53580i		−	0.546046i
$70$		0			0
$71$	8.82168	+	13.2026i	1.04694	+	1.56686i	0.802003	+	0.597319i	$0.203768\pi$
$71$	8.82168	+	13.2026i	1.04694	+	1.56686i	0.244938	+	0.969539i	$0.421232\pi$
$72$		0			0
$73$	1.28356	−	0.857646i	0.150229	−	0.100380i	−0.478184	−	0.878260i	$-0.658705\pi$
$73$	1.28356	−	0.857646i	0.150229	−	0.100380i	0.628413	+	0.777880i	$0.283705\pi$
$74$		0			0
$75$	−11.0504	−	0.110878i	−1.27599	−	0.0128031i
$76$		0			0
$77$	7.16718	+	17.3031i	0.816776	+	1.97187i
$78$		0			0
$79$	7.90124	−	11.8250i	0.888959	−	1.33042i	−0.0543564	−	0.998522i	$-0.517311\pi$
$79$	7.90124	−	11.8250i	0.888959	−	1.33042i	0.943315	−	0.331899i	$-0.107689\pi$
$80$		0			0
$81$	−7.85019	−	7.85019i	−0.872243	−	0.872243i
$82$		0			0
$83$	−1.90214	−	0.787891i	−0.208787	−	0.0864823i	0.275839	−	0.961204i	$-0.411044\pi$
$83$	−1.90214	−	0.787891i	−0.208787	−	0.0864823i	−0.484626	+	0.874721i	$0.661044\pi$
$84$		0			0
$85$	−4.44824	−	8.07547i	−0.482479	−	0.875907i
$86$		0			0
$87$	−12.5216	−	5.18661i	−1.34245	−	0.556063i
$88$		0			0
$89$	1.46520	+	1.46520i	0.155311	+	0.155311i	0.780485	−	0.625174i	$-0.214972\pi$
$89$	1.46520	+	1.46520i	0.155311	+	0.155311i	−0.625174	+	0.780485i	$0.714972\pi$
$90$		0			0
$91$	8.82915	−	13.2138i	0.925547	−	1.38518i
$92$		0			0
$93$	2.25620	+	5.44696i	0.233957	+	0.564823i
$94$		0			0
$95$	10.9661	+	3.38671i	1.12510	+	0.347469i
$96$		0			0
$97$	15.5723	−	10.4051i	1.58113	−	1.05647i	0.618449	−	0.785825i	$-0.287762\pi$
$97$	15.5723	−	10.4051i	1.58113	−	1.05647i	0.962678	−	0.270650i	$-0.0872385\pi$
$98$		0			0
$99$	−5.20926	−	7.79621i	−0.523550	−	0.783548i
$100$		0			0
$101$		−	11.1001i		−	1.10450i	−0.833678	−	0.552251i	$-0.813769\pi$
$101$		−	11.1001i		−	1.10450i	0.833678	−	0.552251i	$-0.186231\pi$
$102$		0			0
$103$	2.83195	+	2.83195i	0.279040	+	0.279040i	0.832726	−	0.553685i	$-0.186779\pi$
$103$	2.83195	+	2.83195i	0.279040	+	0.279040i	−0.553685	+	0.832726i	$0.686779\pi$
$104$		0			0
$105$	18.5263	−	1.73088i	1.80798	−	0.168917i
$106$		0			0
$107$	−1.29146	−	1.93281i	−0.124850	−	0.186852i	0.763779	−	0.645478i	$-0.223342\pi$
$107$	−1.29146	−	1.93281i	−0.124850	−	0.186852i	−0.888629	+	0.458626i	$0.848342\pi$
$108$		0			0
$109$	7.71478	−	1.53457i	0.738942	−	0.146985i	0.188753	−	0.982025i	$-0.439556\pi$
$109$	7.71478	−	1.53457i	0.738942	−	0.146985i	0.550189	+	0.835040i	$0.314556\pi$
$110$		0			0
$111$	4.09890	−	9.89563i	0.389051	−	0.939251i
$112$		0			0
$113$	−1.05921	−	5.32501i	−0.0996421	−	0.500935i	−0.998086	−	0.0618458i	$-0.980301\pi$
$113$	−1.05921	−	5.32501i	−0.0996421	−	0.500935i	0.898444	−	0.439089i	$-0.144699\pi$
$114$		0			0
$115$	4.03616	+	2.18348i	0.376374	+	0.203610i
$116$		0			0
$117$	−3.04472	+	7.35061i	−0.281485	+	0.679564i
$118$		0			0
$119$	8.85050	+	12.7532i	0.811324	+	1.16909i
$120$		0			0
$121$	5.26009	+	12.6990i	0.478190	+	1.15445i
$122$		0			0
$123$	−16.8286			−1.51739
$124$		0			0
$125$	5.41817	−	9.77974i	0.484616	−	0.874727i
$126$		0			0
$127$	2.44564	−	1.01302i	0.217016	−	0.0898909i	−0.271527	−	0.962431i	$-0.587529\pi$
$127$	2.44564	−	1.01302i	0.217016	−	0.0898909i	0.488543	+	0.872540i	$0.337529\pi$
$128$		0			0
$129$	5.00885	+	25.1812i	0.441005	+	2.21708i
$130$		0			0
$131$	5.54329	+	1.10263i	0.484320	+	0.0963371i	0.431210	−	0.902252i	$-0.358087\pi$
$131$	5.54329	+	1.10263i	0.484320	+	0.0963371i	0.0531095	+	0.998589i	$0.483087\pi$
$132$		0			0
$133$	−18.9534	−	3.77006i	−1.64347	−	0.326906i
$134$		0			0
$135$	5.28157	−	1.57325i	0.454565	−	0.135404i
$136$		0			0
$137$	−9.72991	+	9.72991i	−0.831282	+	0.831282i	−0.987692	−	0.156410i	$-0.950008\pi$
$137$	−9.72991	+	9.72991i	−0.831282	+	0.831282i	0.156410	+	0.987692i	$0.450008\pi$
$138$		0			0
$139$	−1.64878	+	1.10168i	−0.139847	+	0.0934430i	−0.623526	−	0.781803i	$-0.714300\pi$
$139$	−1.64878	+	1.10168i	−0.139847	+	0.0934430i	0.483678	+	0.875246i	$0.339300\pi$
$140$		0			0
$141$	4.16858	−	20.9569i	0.351058	−	1.76489i
$142$		0			0
$143$	11.6655	−	17.4586i	0.975516	−	1.45996i
$144$		0			0
$145$	10.6430	−	8.64551i	0.883854	−	0.717970i
$146$		0			0
$147$	−15.5535	+	3.09379i	−1.28283	+	0.255171i
$148$		0			0
$149$	3.44678	−	3.44678i	0.282371	−	0.282371i	−0.551683	−	0.834054i	$-0.686014\pi$
$149$	3.44678	−	3.44678i	0.282371	−	0.282371i	0.834054	+	0.551683i	$0.186014\pi$
$150$		0			0
$151$	8.18343	−	3.38969i	0.665958	−	0.275849i	−0.0239850	−	0.999712i	$-0.507635\pi$
$151$	8.18343	−	3.38969i	0.665958	−	0.275849i	0.689943	+	0.723863i	$0.257635\pi$
$152$		0			0
$153$	−5.59142	−	5.39770i	−0.452039	−	0.436378i
$154$		0			0
$155$	−5.93306	−	0.614425i	−0.476555	−	0.0493518i
$156$		0			0
$157$			2.28334i			0.182230i	0.995840	+	0.0911152i	$0.0290432\pi$
$157$			2.28334i			0.182230i	−0.995840	+	0.0911152i	$0.970957\pi$
$158$		0			0
$159$	10.7104	+	7.15644i	0.849387	+	0.567542i
$160$		0			0
$161$	−7.13845	−	2.95684i	−0.562588	−	0.233032i
$162$		0			0
$163$	−8.02384	−	5.36136i	−0.628476	−	0.419934i	0.200128	−	0.979770i	$-0.435864\pi$
$163$	−8.02384	−	5.36136i	−0.628476	−	0.419934i	−0.828604	+	0.559836i	$0.810864\pi$
$164$		0			0
$165$	24.4778	−	2.28692i	1.90559	−	0.178037i
$166$		0			0
$167$	−3.05988	+	15.3831i	−0.236781	+	1.19038i	0.661155	+	0.750249i	$0.270067\pi$
$167$	−3.05988	+	15.3831i	−0.236781	+	1.19038i	−0.897935	+	0.440127i	$0.854933\pi$
$168$		0			0
$169$	−4.81701			−0.370539
$170$		0			0
$171$	9.67478			0.739849
$172$		0			0
$173$	2.83595	−	14.2573i	0.215613	−	1.08396i	−0.709626	−	0.704579i	$-0.751136\pi$
$173$	2.83595	−	14.2573i	0.215613	−	1.08396i	0.925240	−	0.379384i	$-0.123864\pi$
$174$		0			0
$175$	−7.37812	+	17.3188i	−0.557733	+	1.30918i
$176$		0			0
$177$	−14.9202	−	9.96937i	−1.12147	−	0.749344i
$178$		0			0
$179$	0.674495	+	0.279385i	0.0504142	+	0.0208822i	0.407748	−	0.913094i	$-0.366314\pi$
$179$	0.674495	+	0.279385i	0.0504142	+	0.0208822i	−0.357334	+	0.933977i	$0.616314\pi$
$180$		0			0
$181$	−11.2948	−	7.54697i	−0.839539	−	0.560962i	0.0598016	−	0.998210i	$-0.480953\pi$
$181$	−11.2948	−	7.54697i	−0.839539	−	0.560962i	−0.899341	+	0.437248i	$0.855953\pi$
$182$		0			0
$183$		−	16.8782i		−	1.24767i
$184$		0			0
$185$	6.83242	+	8.41103i	0.502330	+	0.618391i
$186$		0			0
$187$	11.6937	+	16.8502i	0.855126	+	1.23221i
$188$		0			0
$189$	−8.57267	+	3.55091i	−0.623570	+	0.258291i
$190$		0			0
$191$	9.58514	−	9.58514i	0.693556	−	0.693556i	−0.269456	−	0.963013i	$-0.586844\pi$
$191$	9.58514	−	9.58514i	0.693556	−	0.693556i	0.963013	+	0.269456i	$0.0868440\pi$
$192$		0			0
$193$	−0.0209589	+	0.00416899i	−0.00150866	+	0.000300091i	−0.195845	−	0.980635i	$-0.562745\pi$
$193$	−0.0209589	+	0.00416899i	−0.00150866	+	0.000300091i	0.194336	+	0.980935i	$0.437745\pi$
$194$		0			0
$195$	−13.1529	−	16.1918i	−0.941897	−	1.15952i
$196$		0			0
$197$	0.629917	−	0.942738i	0.0448798	−	0.0671673i	−0.808351	−	0.588701i	$-0.799640\pi$
$197$	0.629917	−	0.942738i	0.0448798	−	0.0671673i	0.853231	+	0.521533i	$0.174640\pi$
$198$		0			0
$199$	3.59154	−	18.0559i	0.254598	−	1.27995i	−0.615919	−	0.787809i	$-0.711215\pi$
$199$	3.59154	−	18.0559i	0.254598	−	1.27995i	0.870517	−	0.492139i	$-0.163785\pi$
$200$		0			0
$201$	5.38752	−	3.59983i	0.380007	−	0.253912i
$202$		0			0
$203$	−16.3254	+	16.3254i	−1.14582	+	1.14582i
$204$		0			0
$205$	8.10110	−	14.9749i	0.565806	−	1.04589i
$206$		0			0
$207$	3.79394	+	0.754662i	0.263697	+	0.0524526i
$208$		0			0
$209$	−25.0421	−	4.98118i	−1.73220	−	0.344555i
$210$		0			0
$211$	1.46364	+	7.35823i	0.100761	+	0.506561i	0.997898	+	0.0648078i	$0.0206434\pi$
$211$	1.46364	+	7.35823i	0.100761	+	0.506561i	−0.897136	+	0.441754i	$0.854357\pi$
$212$		0			0
$213$	−32.4232	+	13.4301i	−2.22160	+	0.920218i
$214$		0			0
$215$	−24.8186	−	7.66481i	−1.69261	−	0.522736i
$216$		0			0
$217$	10.0432			0.681778
$218$		0			0
$219$	1.30568	+	3.15219i	0.0882297	+	0.213005i
$220$		0			0
$221$	6.37569	−	16.1938i	0.428875	−	1.08931i
$222$		0			0
$223$	2.57584	−	6.21862i	0.172491	−	0.416430i	−0.813866	−	0.581053i	$-0.802641\pi$
$223$	2.57584	−	6.21862i	0.172491	−	0.416430i	0.986357	+	0.164623i	$0.0526409\pi$
$224$		0			0
$225$	1.93129	−	9.22455i	0.128753	−	0.614970i
$226$		0			0
$227$	−5.31351	−	26.7128i	−0.352670	−	1.77299i	−0.595937	−	0.803032i	$-0.703219\pi$
$227$	−5.31351	−	26.7128i	−0.352670	−	1.77299i	0.243267	−	0.969959i	$-0.421781\pi$
$228$		0			0
$229$	−10.5423	+	25.4513i	−0.696654	+	1.68187i	0.0342698	+	0.999413i	$0.489089\pi$
$229$	−10.5423	+	25.4513i	−0.696654	+	1.68187i	−0.730924	+	0.682459i	$0.760911\pi$
$230$		0			0
$231$	−40.5986	+	8.07557i	−2.67119	+	0.531333i
$232$		0			0
$233$	−6.42361	−	9.61362i	−0.420825	−	0.629809i	0.559118	−	0.829088i	$-0.311140\pi$
$233$	−6.42361	−	9.61362i	−0.420825	−	0.629809i	−0.979943	+	0.199279i	$0.936140\pi$
$234$		0			0
$235$	16.6417	+	13.7978i	1.08558	+	0.900068i
$236$		0			0
$237$	22.2264	+	22.2264i	1.44376	+	1.44376i
$238$		0			0
$239$		−	4.78935i		−	0.309797i	−0.987930	−	0.154899i	$-0.950495\pi$
$239$		−	4.78935i		−	0.309797i	0.987930	−	0.154899i	$-0.0495051\pi$
$240$		0			0
$241$	−10.1658	−	15.2143i	−0.654839	−	0.980036i	−0.999152	−	0.0411812i	$-0.986888\pi$
$241$	−10.1658	−	15.2143i	−0.654839	−	0.980036i	0.344312	−	0.938855i	$-0.388112\pi$
$242$		0			0
$243$	14.2543	−	9.52439i	0.914411	−	0.610990i
$244$		0			0
$245$	4.73428	−	15.3296i	0.302462	−	0.979369i
$246$		0			0
$247$	8.29101	+	20.0163i	0.527544	+	1.27360i
$248$		0			0
$249$	2.52810	−	3.78357i	0.160212	−	0.239774i
$250$		0			0
$251$	0.603647	+	0.603647i	0.0381019	+	0.0381019i	0.725901	−	0.687799i	$-0.241423\pi$
$251$	0.603647	+	0.603647i	0.0381019	+	0.0381019i	−0.687799	+	0.725901i	$0.741423\pi$
$252$		0			0
$253$	−9.43164	−	3.90671i	−0.592962	−	0.245613i
$254$		0			0
$255$	19.4233	−	6.16049i	1.21634	−	0.385785i
$256$		0			0
$257$	−10.4570	−	4.33143i	−0.652290	−	0.270187i	0.0319004	−	0.999491i	$-0.489844\pi$
$257$	−10.4570	−	4.33143i	−0.652290	−	0.270187i	−0.684190	+	0.729304i	$0.739844\pi$
$258$		0			0
$259$	−12.9017	−	12.9017i	−0.801673	−	0.801673i
$260$		0			0
$261$	6.42163	−	9.61065i	0.397489	−	0.594884i
$262$		0			0
$263$	1.94692	+	4.70029i	0.120052	+	0.289832i	0.972469	−	0.233030i	$-0.0748641\pi$
$263$	1.94692	+	4.70029i	0.120052	+	0.289832i	−0.852417	+	0.522863i	$0.824864\pi$
$264$		0			0
$265$	−11.5240	+	6.08555i	−0.707911	+	0.373833i
$266$		0			0
$267$	−3.80792	+	2.54437i	−0.233041	+	0.155713i
$268$		0			0
$269$	−7.51776	−	11.2511i	−0.458366	−	0.685993i	0.528243	−	0.849093i	$-0.322851\pi$
$269$	−7.51776	−	11.2511i	−0.458366	−	0.685993i	−0.986610	+	0.163100i	$0.947851\pi$
$270$		0			0
$271$			12.8673i			0.781631i	0.920469	+	0.390816i	$0.127807\pi$
$271$			12.8673i			0.781631i	−0.920469	+	0.390816i	$0.872193\pi$
$272$		0			0
$273$	24.8367	+	24.8367i	1.50318	+	1.50318i
$274$		0			0
$275$	−9.74830	+	22.8824i	−0.587845	+	1.37986i
$276$		0			0
$277$	0.772355	+	1.15591i	0.0464063	+	0.0694520i	0.853947	−	0.520360i	$-0.174202\pi$
$277$	0.772355	+	1.15591i	0.0464063	+	0.0694520i	−0.807541	+	0.589811i	$0.799202\pi$
$278$		0			0
$279$	−4.93146	+	0.980928i	−0.295239	+	0.0587266i
$280$		0			0
$281$	−0.796461	+	1.92283i	−0.0475129	+	0.114706i	−0.945854	−	0.324592i	$-0.894773\pi$
$281$	−0.796461	+	1.92283i	−0.0475129	+	0.114706i	0.898341	+	0.439298i	$0.144773\pi$
$282$		0			0
$283$	0.534584	+	2.68753i	0.0317777	+	0.159757i	0.993416	−	0.114564i	$-0.0365470\pi$
$283$	0.534584	+	2.68753i	0.0317777	+	0.159757i	−0.961638	+	0.274321i	$0.911547\pi$
$284$		0			0
$285$	−12.0699	+	22.3111i	−0.714956	+	1.32160i
$286$		0			0
$287$	−10.9704	+	26.4849i	−0.647563	+	1.56336i
$288$		0			0
$289$	12.4370	+	11.5897i	0.731589	+	0.681746i
$290$		0			0
$291$	15.8407	+	38.2428i	0.928598	+	2.24183i
$292$		0			0
$293$	25.5662			1.49360			0.746798	−	0.665051i	$-0.231590\pi$
$293$	25.5662			1.49360			0.746798	+	0.665051i	$0.231590\pi$
$294$		0			0
$295$	16.0536	−	8.47756i	0.934677	−	0.493583i
$296$		0			0
$297$	−11.3266	+	4.69163i	−0.657236	+	0.272236i
$298$		0			0
$299$	1.68997	+	8.49605i	0.0977334	+	0.491339i
$300$		0			0
$301$	42.8954	+	8.53242i	2.47245	+	0.491801i
$302$		0			0
$303$	24.0619	+	4.78620i	1.38232	+	0.274960i
$304$		0			0
$305$	15.0190	+	8.12496i	0.859986	+	0.465234i
$306$		0			0
$307$	16.3835	−	16.3835i	0.935056	−	0.935056i	−0.0629603	−	0.998016i	$-0.520054\pi$
$307$	16.3835	−	16.3835i	0.935056	−	0.935056i	0.998016	+	0.0629603i	$0.0200542\pi$
$308$		0			0
$309$	−7.35996	+	4.91777i	−0.418693	+	0.279762i
$310$		0			0
$311$	−4.38807	+	22.0603i	−0.248825	+	1.25093i	0.631058	+	0.775736i	$0.282621\pi$
$311$	−4.38807	+	22.0603i	−0.248825	+	1.25093i	−0.879883	+	0.475191i	$0.842379\pi$
$312$		0			0
$313$	−13.5266	+	20.2440i	−0.764570	+	1.14426i	0.221047	+	0.975263i	$0.429053\pi$
$313$	−13.5266	+	20.2440i	−0.764570	+	1.14426i	−0.985617	+	0.168996i	$0.945947\pi$
$314$		0			0
$315$	−1.63460	+	15.7842i	−0.0920993	+	0.889338i
$316$		0			0
$317$	16.9829	−	3.37811i	0.953856	−	0.189734i	0.306456	−	0.951885i	$-0.400857\pi$
$317$	16.9829	−	3.37811i	0.953856	−	0.189734i	0.647399	+	0.762151i	$0.275857\pi$
$318$		0			0
$319$	−21.5698	+	21.5698i	−1.20768	+	1.20768i
$320$		0			0
$321$	4.74665	−	1.96613i	0.264932	−	0.109738i
$322$		0			0
$323$	−21.1596	+	0.372996i	−1.17735	+	0.0207541i
$324$		0			0
$325$	20.7398	−	3.90951i	1.15044	−	0.216860i
$326$		0			0
$327$			17.3851i			0.961400i
$328$		0			0
$329$	−30.2645	−	20.2221i	−1.66854	−	1.11488i
$330$		0			0
$331$	−9.88196	−	4.09324i	−0.543162	−	0.224985i	0.0941952	−	0.995554i	$-0.469972\pi$
$331$	−9.88196	−	4.09324i	−0.543162	−	0.224985i	−0.637357	+	0.770569i	$0.719972\pi$
$332$		0			0
$333$	7.59516	+	5.07492i	0.416212	+	0.278104i
$334$		0			0
$335$	0.609805	+	6.52698i	0.0333172	+	0.356607i
$336$		0			0
$337$	6.46373	−	32.4954i	0.352102	−	1.77014i	−0.246553	−	0.969129i	$-0.579298\pi$
$337$	6.46373	−	32.4954i	0.352102	−	1.77014i	0.598655	−	0.801007i	$-0.295702\pi$
$338$		0			0
$339$	11.9998			0.651741
$340$		0			0
$341$	13.2696			0.718587
$342$		0			0
$343$	−0.128595	+	0.646493i	−0.00694350	+	0.0349073i
$344$		0			0
$345$	−6.47350	+	7.80777i	−0.348521	+	0.420356i
$346$		0			0
$347$	10.0397	+	6.70831i	0.538959	+	0.360121i	0.795062	−	0.606529i	$-0.207438\pi$
$347$	10.0397	+	6.70831i	0.538959	+	0.360121i	−0.256103	+	0.966650i	$0.582438\pi$
$348$		0			0
$349$	−16.1128	−	6.67412i	−0.862496	−	0.357258i	−0.0928128	−	0.995684i	$-0.529586\pi$
$349$	−16.1128	−	6.67412i	−0.862496	−	0.357258i	−0.769683	+	0.638426i	$0.779586\pi$
$350$		0			0
$351$	8.64971	+	5.77955i	0.461687	+	0.308490i
$352$		0			0
$353$		−	29.0008i		−	1.54356i	−0.635890	−	0.771779i	$-0.719367\pi$
$353$		−	29.0008i		−	1.54356i	0.635890	−	0.771779i	$-0.280633\pi$
$354$		0			0
$355$	3.65738	−	35.3168i	0.194114	−	1.87442i
$356$		0			0
$357$	−31.4616	+	13.6863i	−1.66512	+	0.724358i
$358$		0			0
$359$	9.94825	−	4.12070i	0.525049	−	0.217482i	−0.104384	−	0.994537i	$-0.533287\pi$
$359$	9.94825	−	4.12070i	0.525049	−	0.217482i	0.629433	+	0.777055i	$0.283287\pi$
$360$		0			0
$361$	5.19380	−	5.19380i	0.273358	−	0.273358i
$362$		0			0
$363$	−29.7959	+	5.92677i	−1.56388	+	0.311075i
$364$		0			0
$365$	−3.43350	−	0.355572i	−0.179718	−	0.0186115i
$366$		0			0
$367$	16.0032	−	23.9504i	0.835359	−	1.25020i	−0.130582	−	0.991438i	$-0.541684\pi$
$367$	16.0032	−	23.9504i	0.835359	−	1.25020i	0.965940	−	0.258765i	$-0.0833156\pi$
$368$		0			0
$369$	2.79993	−	14.0762i	0.145759	−	0.732778i
$370$		0			0
$371$	18.2448	−	12.1908i	0.947222	−	0.632913i
$372$		0			0
$373$	−14.6978	+	14.6978i	−0.761025	+	0.761025i	−0.976508	−	0.215483i	$-0.930868\pi$
$373$	−14.6978	+	14.6978i	−0.761025	+	0.761025i	0.215483	+	0.976508i	$0.430868\pi$
$374$		0			0
$375$	18.8635	+	15.9619i	0.974105	+	0.824271i
$376$		0			0
$377$	25.3867	+	5.04973i	1.30748	+	0.260075i
$378$		0			0
$379$	−2.25247	−	0.448044i	−0.115702	−	0.0230145i	0.136900	−	0.990585i	$-0.456286\pi$
$379$	−2.25247	−	0.448044i	−0.115702	−	0.0230145i	−0.252601	+	0.967570i	$0.581286\pi$
$380$		0			0
$381$	1.14141	+	5.73826i	0.0584762	+	0.293980i
$382$		0			0
$383$	−25.8533	+	10.7088i	−1.32104	+	0.547193i	−0.928086	−	0.372365i	$-0.878547\pi$
$383$	−25.8533	+	10.7088i	−1.32104	+	0.547193i	−0.392954	+	0.919558i	$0.628547\pi$
$384$		0			0
$385$	12.3577	−	40.0140i	0.629805	−	2.03930i
$386$		0			0
$387$	−21.8960			−1.11304
$388$		0			0
$389$	7.84714	+	18.9447i	0.397866	+	0.960533i	0.988171	+	0.153353i	$0.0490072\pi$
$389$	7.84714	+	18.9447i	0.397866	+	0.960533i	−0.590306	+	0.807180i	$0.700993\pi$
$390$		0			0
$391$	−8.32677	−	1.50424i	−0.421103	−	0.0760728i
$392$		0			0
$393$	−4.78037	+	11.5408i	−0.241138	+	0.582158i
$394$		0			0
$395$	−30.4776	+	9.07856i	−1.53350	+	0.456792i
$396$		0			0
$397$	−1.14401	−	5.75131i	−0.0574161	−	0.288650i	0.941400	−	0.337292i	$-0.109511\pi$
$397$	−1.14401	−	5.75131i	−0.0574161	−	0.288650i	−0.998816	+	0.0486414i	$0.984511\pi$
$398$		0			0
$399$	16.3448	−	39.4600i	0.818266	−	1.97547i
$400$		0			0
$401$	−9.58259	+	1.90610i	−0.478532	+	0.0951859i	−0.428462	−	0.903560i	$-0.640944\pi$
$401$	−9.58259	+	1.90610i	−0.478532	+	0.0951859i	−0.0500698	+	0.998746i	$0.515944\pi$
$402$		0			0
$403$	−6.25557	−	9.36212i	−0.311612	−	0.466360i
$404$		0			0
$405$	2.30925	+	24.7168i	0.114748	+	1.22819i
$406$		0			0
$407$	−17.0463	−	17.0463i	−0.844955	−	0.844955i
$408$		0			0
$409$		−	30.1989i		−	1.49324i	−0.665251	−	0.746619i	$-0.731676\pi$
$409$		−	30.1989i		−	1.49324i	0.665251	−	0.746619i	$-0.268324\pi$
$410$		0			0
$411$	−16.8963	−	25.2871i	−0.833432	−	1.24732i
$412$		0			0
$413$	−25.4161	+	16.9825i	−1.25065	+	0.835655i
$414$		0			0
$415$	2.14980	+	4.07098i	0.105529	+	0.199837i
$416$		0			0
$417$	−1.67719	−	4.04911i	−0.0821326	−	0.198286i
$418$		0			0
$419$	−20.6124	+	30.8486i	−1.00698	+	1.50705i	−0.152006	+	0.988380i	$0.548573\pi$
$419$	−20.6124	+	30.8486i	−1.00698	+	1.50705i	−0.854973	+	0.518672i	$0.826427\pi$
$420$		0			0
$421$	−1.65668	−	1.65668i	−0.0807415	−	0.0807415i	0.665583	−	0.746324i	$-0.268183\pi$
$421$	−1.65668	−	1.65668i	−0.0807415	−	0.0807415i	−0.746324	+	0.665583i	$0.768183\pi$
$422$		0			0
$423$	16.8357	+	6.97356i	0.818578	+	0.339066i
$424$		0			0
$425$	−3.86826	+	20.2494i	−0.187638	+	0.982238i
$426$		0			0
$427$	−26.5629	−	11.0027i	−1.28547	−	0.532459i
$428$		0			0
$429$	32.8153	+	32.8153i	1.58434	+	1.58434i
$430$		0			0
$431$	10.6826	−	15.9877i	0.514565	−	0.770101i	−0.479656	−	0.877457i	$-0.659238\pi$
$431$	10.6826	−	15.9877i	0.514565	−	0.770101i	0.994221	+	0.107356i	$0.0342385\pi$
$432$		0			0
$433$	0.644265	+	1.55539i	0.0309614	+	0.0747474i	0.938604	−	0.344996i	$-0.112120\pi$
$433$	0.644265	+	1.55539i	0.0309614	+	0.0747474i	−0.907643	+	0.419744i	$0.862120\pi$
$434$		0			0
$435$	14.1519	+	26.7988i	0.678531	+	1.28491i
$436$		0			0
$437$	8.75835	−	5.85214i	0.418969	−	0.279946i
$438$		0			0
$439$	7.18716	+	10.7563i	0.343025	+	0.513373i	0.962369	−	0.271747i	$-0.0876014\pi$
$439$	7.18716	+	10.7563i	0.343025	+	0.513373i	−0.619344	+	0.785120i	$0.712601\pi$
$440$		0			0
$441$		−	13.5244i		−	0.644018i
$442$		0			0
$443$	9.00393	+	9.00393i	0.427790	+	0.427790i	0.887875	−	0.460085i	$-0.152181\pi$
$443$	9.00393	+	9.00393i	0.427790	+	0.427790i	−0.460085	+	0.887875i	$0.652181\pi$
$444$		0			0
$445$	−0.431013	−	4.61329i	−0.0204320	−	0.218691i
$446$		0			0
$447$	5.98544	+	8.95784i	0.283102	+	0.423691i
$448$		0			0
$449$	32.7297	−	6.51034i	1.54461	−	0.307242i	0.652052	−	0.758174i	$-0.273908\pi$
$449$	32.7297	−	6.51034i	1.54461	−	0.307242i	0.892558	+	0.450932i	$0.148908\pi$
$450$		0			0
$451$	−14.4946	+	34.9931i	−0.682525	+	1.64776i
$452$		0			0
$453$	3.81930	+	19.2009i	0.179447	+	0.902139i
$454$		0			0
$455$	−34.0569	+	10.1447i	−1.59661	+	0.475593i
$456$		0			0
$457$	6.06926	−	14.6525i	0.283908	−	0.685415i	−0.716012	−	0.698088i	$-0.754034\pi$
$457$	6.06926	−	14.6525i	0.283908	−	0.685415i	0.999920	+	0.0126736i	$0.00403424\pi$
$458$		0			0
$459$	−8.34825	+	5.79352i	−0.389663	+	0.270419i
$460$		0			0
$461$	8.26564	+	19.9550i	0.384969	+	0.929398i	0.990988	+	0.133948i	$0.0427654\pi$
$461$	8.26564	+	19.9550i	0.384969	+	0.929398i	−0.606019	+	0.795450i	$0.707235\pi$
$462$		0			0
$463$	−20.4039			−0.948249			−0.474124	−	0.880458i	$-0.657235\pi$
$463$	−20.4039			−0.948249			−0.474124	+	0.880458i	$0.657235\pi$
$464$		0			0
$465$	3.89015	−	12.5963i	0.180401	−	0.584138i
$466$		0			0
$467$	11.5282	−	4.77516i	0.533464	−	0.220968i	−0.0996559	−	0.995022i	$-0.531774\pi$
$467$	11.5282	−	4.77516i	0.533464	−	0.220968i	0.633119	+	0.774054i	$0.281774\pi$
$468$		0			0
$469$	−2.15334	−	10.8256i	−0.0994321	−	0.499879i
$470$		0			0
$471$	−4.94963	−	0.984543i	−0.228067	−	0.0453654i
$472$		0			0
$473$	56.6753	+	11.2734i	2.60593	+	0.518353i
$474$		0			0
$475$	−14.0432	−	21.4806i	−0.644346	−	0.985598i
$476$		0			0
$477$	−7.76793	+	7.76793i	−0.355669	+	0.355669i
$478$		0			0
$479$	9.63578	−	6.43842i	0.440270	−	0.294179i	−0.315610	−	0.948889i	$-0.602209\pi$
$479$	9.63578	−	6.43842i	0.440270	−	0.294179i	0.755880	+	0.654710i	$0.227209\pi$
$480$		0			0
$481$	−3.99073	+	20.0628i	−0.181962	+	0.914784i
$482$		0			0
$483$	9.48758	−	14.1992i	0.431700	−	0.646085i
$484$		0			0
$485$	−41.6557	−	4.31384i	−1.89149	−	0.195881i
$486$		0			0
$487$	1.60789	−	0.319829i	0.0728605	−	0.0144929i	−0.158525	−	0.987355i	$-0.550674\pi$
$487$	1.60789	−	0.319829i	0.0728605	−	0.0144929i	0.231386	+	0.972862i	$0.425674\pi$
$488$		0			0
$489$	15.0817	−	15.0817i	0.682017	−	0.682017i
$490$		0			0
$491$	−15.5833	+	6.45480i	−0.703263	+	0.291301i	−0.705514	−	0.708696i	$-0.749284\pi$
$491$	−15.5833	+	6.45480i	−0.703263	+	0.291301i	0.00225034	+	0.999997i	$0.499284\pi$
$492$		0			0
$493$	−13.6741	+	21.2669i	−0.615852	+	0.957813i
$494$		0			0
$495$	−2.15971	+	20.8548i	−0.0970717	+	0.937353i
$496$		0			0
$497$			59.7827i			2.68162i
$498$		0			0
$499$	24.7200	+	16.5174i	1.10662	+	0.739421i	0.968006	−	0.250926i	$-0.0807350\pi$
$499$	24.7200	+	16.5174i	1.10662	+	0.739421i	0.138615	+	0.990346i	$0.455735\pi$
$500$		0			0
$501$	−32.0267	−	13.2659i	−1.43085	−	0.592677i
$502$		0			0
$503$	−14.2451	−	9.51824i	−0.635155	−	0.424397i	0.195871	−	0.980630i	$-0.437246\pi$
$503$	−14.2451	−	9.51824i	−0.635155	−	0.424397i	−0.831027	+	0.556232i	$0.812246\pi$
$504$		0			0
$505$	−15.8421	+	19.1073i	−0.704963	+	0.850265i
$506$		0			0
$507$	2.07702	−	10.4419i	0.0922439	−	0.463741i
$508$		0			0
$509$	15.4508			0.684844			0.342422	−	0.939546i	$-0.388753\pi$
$509$	15.4508			0.684844			0.342422	+	0.939546i	$0.388753\pi$
$510$		0			0
$511$	5.81208			0.257111
$512$		0			0
$513$	2.46788	−	12.4069i	0.108960	−	0.547776i
$514$		0			0
$515$	−0.833062	−	8.91658i	−0.0367091	−	0.392912i
$516$		0			0
$517$	−39.9868	−	26.7183i	−1.75862	−	1.17507i
$518$		0			0
$519$	29.6829	+	12.2951i	1.30294	+	0.539694i
$520$		0			0
$521$	−28.4273	−	18.9945i	−1.24542	−	0.832165i	−0.254562	−	0.967056i	$-0.581931\pi$
$521$	−28.4273	−	18.9945i	−1.24542	−	0.832165i	−0.990860	+	0.134892i	$0.956931\pi$
$522$		0			0
$523$		−	28.1308i		−	1.23007i	−0.788498	−	0.615037i	$-0.789141\pi$
$523$		−	28.1308i		−	1.23007i	0.788498	−	0.615037i	$-0.210859\pi$
$524$		0			0
$525$	−34.3609	−	23.4613i	−1.49963	−	1.02393i
$526$		0			0
$527$	10.7477	−	2.33550i	0.468178	−	0.101736i
$528$		0			0
$529$	−17.3582	+	7.18999i	−0.754703	+	0.312608i
$530$		0			0
$531$	10.8212	−	10.8212i	0.469601	−	0.469601i
$532$		0			0
$533$	31.5219	−	6.27009i	1.36536	−	0.271588i
$534$		0			0
$535$	−0.535428	+	5.17025i	−0.0231486	+	0.223530i
$536$		0			0
$537$	−0.896460	+	1.34165i	−0.0386851	+	0.0578964i
$538$		0			0
$539$	−6.96319	+	35.0063i	−0.299926	+	1.50783i
$540$		0			0
$541$	2.27314	−	1.51886i	0.0977300	−	0.0653011i	−0.505745	−	0.862683i	$-0.668782\pi$
$541$	2.27314	−	1.51886i	0.0977300	−	0.0653011i	0.603475	+	0.797382i	$0.293782\pi$
$542$		0			0
$543$	21.2299	−	21.2299i	0.911061	−	0.911061i
$544$		0			0
$545$	−15.4701	−	8.36899i	−0.662666	−	0.358488i
$546$		0			0
$547$	19.7797	+	3.93443i	0.845719	+	0.168224i	0.598886	−	0.800834i	$-0.295610\pi$
$547$	19.7797	+	3.93443i	0.845719	+	0.168224i	0.246833	+	0.969058i	$0.420610\pi$
$548$		0			0
$549$	14.1177	+	2.80818i	0.602527	+	0.119850i
$550$		0			0
$551$	−6.14047	−	30.8702i	−0.261593	−	1.31512i
$552$		0			0
$553$	49.4691	−	20.4908i	2.10364	−	0.871357i
$554$		0			0
$555$	−21.1788	+	11.1840i	−0.898988	+	0.474736i
$556$		0			0
$557$	−6.48647			−0.274840			−0.137420	−	0.990513i	$-0.543881\pi$
$557$	−6.48647			−0.274840			−0.137420	+	0.990513i	$0.543881\pi$
$558$		0			0
$559$	−18.7642	−	45.3009i	−0.793643	−	1.91602i
$560$		0			0
$561$	−41.5685	+	18.0830i	−1.75502	+	0.763466i
$562$		0			0
$563$	11.1043	−	26.8081i	0.467990	−	1.12983i	−0.497049	−	0.867722i	$-0.665583\pi$
$563$	11.1043	−	26.8081i	0.467990	−	1.12983i	0.965039	−	0.262106i	$-0.0844169\pi$
$564$		0			0
$565$	−5.77657	+	10.6780i	−0.243022	+	0.449227i
$566$		0			0
$567$	−8.15443	−	40.9951i	−0.342454	−	1.72163i
$568$		0			0
$569$	3.01560	−	7.28029i	0.126420	−	0.305206i	−0.847979	−	0.530030i	$-0.822181\pi$
$569$	3.01560	−	7.28029i	0.126420	−	0.305206i	0.974399	+	0.224824i	$0.0721807\pi$
$570$		0			0
$571$	0.516009	−	0.102641i	0.0215943	−	0.00429538i	−0.184281	−	0.982874i	$-0.558996\pi$
$571$	0.516009	−	0.102641i	0.0215943	−	0.00429538i	0.205876	+	0.978578i	$0.433996\pi$
$572$		0			0
$573$	16.6449	+	24.9108i	0.695350	+	1.04066i
$574$		0			0
$575$	−3.83145	−	9.51898i	−0.159783	−	0.396969i
$576$		0			0
$577$	−28.9945	−	28.9945i	−1.20706	−	1.20706i	−0.971975	−	0.235082i	$-0.924464\pi$
$577$	−28.9945	−	28.9945i	−1.20706	−	1.20706i	−0.235082	−	0.971975i	$-0.575536\pi$
$578$		0			0
$579$		−	0.0472306i		−	0.00196284i
$580$		0			0
$581$	−4.30654	−	6.44519i	−0.178665	−	0.267392i
$582$		0			0
$583$	24.1058	−	16.1070i	0.998361	−	0.667084i
$584$		0			0
$585$	15.7319	−	8.30766i	0.650433	−	0.343480i
$586$		0			0
$587$	18.5209	+	44.7134i	0.764439	+	1.84552i	0.427698	+	0.903922i	$0.359325\pi$
$587$	18.5209	+	44.7134i	0.764439	+	1.84552i	0.336741	+	0.941597i	$0.390675\pi$
$588$		0			0
$589$	−7.60676	+	11.3843i	−0.313431	+	0.469083i
$590$		0			0
$591$	1.77198	+	1.77198i	0.0728894	+	0.0728894i
$592$		0			0
$593$	21.9084	+	9.07476i	0.899671	+	0.372656i	0.784093	−	0.620643i	$-0.213128\pi$
$593$	21.9084	+	9.07476i	0.899671	+	0.372656i	0.115577	+	0.993299i	$0.463128\pi$
$594$		0			0
$595$	2.96648	−	34.5844i	0.121614	−	1.41782i
$596$		0			0
$597$	37.5914	+	15.5709i	1.53851	+	0.637273i
$598$		0			0
$599$	−19.6018	−	19.6018i	−0.800910	−	0.800910i	0.182328	−	0.983238i	$-0.441637\pi$
$599$	−19.6018	−	19.6018i	−0.800910	−	0.800910i	−0.983238	+	0.182328i	$0.941637\pi$
$600$		0			0
$601$	−12.2916	+	18.3957i	−0.501385	+	0.750376i	−0.992700	−	0.120606i	$-0.961516\pi$
$601$	−12.2916	+	18.3957i	−0.501385	+	0.750376i	0.491315	+	0.870982i	$0.336516\pi$
$602$		0			0
$603$	2.11468	+	5.10529i	0.0861165	+	0.207904i
$604$		0			0
$605$	9.06945	−	29.3668i	0.368726	−	1.19393i
$606$		0			0
$607$	8.06548	−	5.38918i	0.327368	−	0.218740i	−0.381015	−	0.924569i	$-0.624425\pi$
$607$	8.06548	−	5.38918i	0.327368	−	0.218740i	0.708382	+	0.705829i	$0.249425\pi$
$608$		0			0
$609$	−28.3495	−	42.4280i	−1.14878	−	1.71927i
$610$		0			0
$611$			40.8077i			1.65090i
$612$		0			0
$613$	−8.57142	−	8.57142i	−0.346196	−	0.346196i	0.512494	−	0.858691i	$-0.328722\pi$
$613$	−8.57142	−	8.57142i	−0.346196	−	0.346196i	−0.858691	+	0.512494i	$0.828722\pi$
$614$		0			0
$615$	28.9683	+	24.0178i	1.16811	+	0.968493i
$616$		0			0
$617$	3.32528	+	4.97663i	0.133871	+	0.200352i	0.892348	−	0.451347i	$-0.149056\pi$
$617$	3.32528	+	4.97663i	0.133871	+	0.200352i	−0.758478	+	0.651699i	$0.774056\pi$
$618$		0			0
$619$	17.1024	−	3.40188i	0.687404	−	0.136733i	0.160983	−	0.986957i	$-0.448534\pi$
$619$	17.1024	−	3.40188i	0.687404	−	0.136733i	0.526421	+	0.850224i	$0.323534\pi$
$620$		0			0
$621$	1.93554	−	4.67282i	0.0776707	−	0.187514i
$622$		0			0
$623$	1.52199	+	7.65156i	0.0609772	+	0.306553i
$624$		0			0
$625$	−23.2843	+	9.10170i	−0.931372	+	0.364068i
$626$		0			0
$627$	21.5956	−	52.1363i	0.862444	−	2.08212i
$628$		0			0
$629$	−16.8069	−	10.8065i	−0.670136	−	0.430883i
$630$		0			0
$631$	8.37564	+	20.2206i	0.333429	+	0.804969i	0.998315	+	0.0580241i	$0.0184800\pi$
$631$	8.37564	+	20.2206i	0.333429	+	0.804969i	−0.664886	+	0.746945i	$0.731520\pi$
$632$		0			0
$633$	−16.5816			−0.659061
$634$		0			0
$635$	−5.65563	−	1.74665i	−0.224437	−	0.0693136i
$636$		0			0
$637$	27.9807	−	11.5900i	1.10864	−	0.459213i
$638$		0			0
$639$	−5.83901	−	29.3547i	−0.230988	−	1.16125i
$640$		0			0
$641$	−24.3704	−	4.84757i	−0.962572	−	0.191467i	−0.311300	−	0.950312i	$-0.600764\pi$
$641$	−24.3704	−	4.84757i	−0.962572	−	0.191467i	−0.651272	+	0.758844i	$0.725764\pi$
$642$		0			0
$643$	4.24024	+	0.843436i	0.167219	+	0.0332619i	0.277989	−	0.960584i	$-0.410332\pi$
$643$	4.24024	+	0.843436i	0.167219	+	0.0332619i	−0.110771	+	0.993846i	$0.535332\pi$
$644$		0			0
$645$	27.3165	−	50.4947i	1.07559	−	1.98823i
$646$		0			0
$647$	10.2178	−	10.2178i	0.401703	−	0.401703i	−0.477130	−	0.878833i	$-0.658323\pi$
$647$	10.2178	−	10.2178i	0.401703	−	0.401703i	0.878833	+	0.477130i	$0.158323\pi$
$648$		0			0
$649$	−33.5810	+	22.4381i	−1.31817	+	0.880771i
$650$		0			0
$651$	−4.33049	+	21.7709i	−0.169725	+	0.853267i
$652$		0			0
$653$	−5.70697	+	8.54109i	−0.223331	+	0.334239i	−0.926167	−	0.377113i	$-0.876917\pi$
$653$	−5.70697	+	8.54109i	−0.223331	+	0.334239i	0.702836	+	0.711352i	$0.251917\pi$
$654$		0			0
$655$	−7.96836	−	9.80941i	−0.311349	−	0.383285i
$656$		0			0
$657$	−2.85387	+	0.567670i	−0.111340	+	0.0221469i
$658$		0			0
$659$	−10.2670	+	10.2670i	−0.399946	+	0.399946i	−0.878214	−	0.478268i	$-0.841265\pi$
$659$	−10.2670	+	10.2670i	−0.399946	+	0.399946i	0.478268	+	0.878214i	$0.341265\pi$
$660$		0			0
$661$	30.6283	−	12.6867i	1.19130	−	0.493454i	0.303124	−	0.952951i	$-0.401970\pi$
$661$	30.6283	−	12.6867i	1.19130	−	0.493454i	0.888179	+	0.459497i	$0.151970\pi$
$662$		0			0
$663$	32.3545	+	20.8032i	1.25654	+	0.807930i
$664$		0			0
$665$	27.2451	+	33.5399i	1.05652	+	1.30062i
$666$		0			0
$667$		−	12.5846i		−	0.487280i
$668$		0			0
$669$	12.3695	+	8.26506i	0.478234	+	0.319546i
$670$		0			0
$671$	−35.0961	−	14.5373i	−1.35487	−	0.561206i
$672$		0			0
$673$	20.7230	+	13.8467i	0.798812	+	0.533749i	0.886680	−	0.462383i	$-0.153005\pi$
$673$	20.7230	+	13.8467i	0.798812	+	0.533749i	−0.0878682	+	0.996132i	$0.528005\pi$
$674$		0			0
$675$	−11.3369	−	4.82971i	−0.436356	−	0.185895i
$676$		0			0
$677$	1.35850	−	6.82965i	0.0522114	−	0.262485i	−0.945859	−	0.324578i	$-0.894778\pi$
$677$	1.35850	−	6.82965i	0.0522114	−	0.262485i	0.998070	+	0.0620934i	$0.0197777\pi$
$678$		0			0
$679$	70.5129			2.70604
$680$		0			0
$681$	60.1969			2.30675
$682$		0			0
$683$	0.507559	−	2.55167i	0.0194212	−	0.0976370i	−0.969859	−	0.243667i	$-0.921650\pi$
$683$	0.507559	−	2.55167i	0.0194212	−	0.0976370i	0.989280	+	0.146030i	$0.0466496\pi$
$684$		0			0
$685$	30.6353	−	2.86220i	1.17051	−	0.109359i
$686$		0			0
$687$	−50.6256	−	33.8269i	−1.93149	−	1.29058i
$688$		0			0
$689$	−22.7281	−	9.41427i	−0.865870	−	0.358655i
$690$		0			0
$691$	2.45452	+	1.64005i	0.0933742	+	0.0623906i	0.601381	−	0.798963i	$-0.294617\pi$
$691$	2.45452	+	1.64005i	0.0933742	+	0.0623906i	−0.508007	+	0.861353i	$0.669617\pi$
$692$		0			0
$693$		−	35.3020i		−	1.34101i
$694$		0			0
$695$	4.41046	+	0.456745i	0.167298	+	0.0173253i
$696$		0			0
$697$	−5.58101	+	30.8938i	−0.211396	+	1.17019i
$698$		0			0
$699$	23.6094	−	9.77932i	0.892988	−	0.369888i
$700$		0			0
$701$	−15.2365	+	15.2365i	−0.575476	+	0.575476i	−0.933653	−	0.358178i	$-0.883398\pi$
$701$	−15.2365	+	15.2365i	−0.575476	+	0.575476i	0.358178	+	0.933653i	$0.383398\pi$
$702$		0			0
$703$	24.3963	−	4.85272i	0.920124	−	0.183024i
$704$		0			0
$705$	−37.0853	+	30.1250i	−1.39671	+	1.13457i
$706$		0			0
$707$	23.2182	−	34.7485i	0.873211	−	1.30685i
$708$		0			0
$709$	1.66529	−	8.37197i	0.0625412	−	0.314416i	−0.936833	−	0.349776i	$-0.886258\pi$
$709$	1.66529	−	8.37197i	0.0625412	−	0.314416i	0.999375	+	0.0353598i	$0.0112577\pi$
$710$		0			0
$711$	−22.2891	+	14.8931i	−0.835908	+	0.558536i
$712$		0			0
$713$	−3.87098	+	3.87098i	−0.144969	+	0.144969i
$714$		0			0
$715$	−44.9975	+	13.4037i	−1.68281	+	0.501270i
$716$		0			0
$717$	10.3819	+	2.06510i	0.387721	+	0.0771224i
$718$		0			0
$719$	−7.74145	−	1.53987i	−0.288707	−	0.0574275i	0.0486120	−	0.998818i	$-0.484520\pi$
$719$	−7.74145	−	1.53987i	−0.288707	−	0.0574275i	−0.337319	+	0.941390i	$0.609520\pi$
$720$		0			0
$721$	2.94171	+	14.7890i	0.109555	+	0.550769i
$722$		0			0
$723$	37.3635	−	15.4765i	1.38956	−	0.575577i
$724$		0			0
$725$	−30.6594	−	0.307634i	−1.13866	−	0.0114252i
$726$		0			0
$727$	−39.7517			−1.47431			−0.737154	−	0.675725i	$-0.763831\pi$
$727$	−39.7517			−1.47431			−0.737154	+	0.675725i	$0.763831\pi$
$728$		0			0
$729$	1.75447	+	4.23567i	0.0649804	+	0.156877i
$730$		0			0
$731$	47.8885	−	0.844166i	1.77122	−	0.0312226i
$732$		0			0
$733$	5.84955	−	14.1221i	0.216058	−	0.521610i	−0.778275	−	0.627924i	$-0.783905\pi$
$733$	5.84955	−	14.1221i	0.216058	−	0.521610i	0.994333	+	0.106314i	$0.0339048\pi$
$734$		0			0
$735$	31.1888	+	16.8725i	1.15041	+	0.622350i
$736$		0			0
$737$	−2.84509	−	14.3032i	−0.104800	−	0.526867i
$738$		0			0
$739$	3.77380	−	9.11077i	0.138822	−	0.335145i	−0.839145	−	0.543908i	$-0.816944\pi$
$739$	3.77380	−	9.11077i	0.138822	−	0.335145i	0.977966	+	0.208763i	$0.0669439\pi$
$740$		0			0
$741$	−46.9645	+	9.34182i	−1.72528	+	0.343180i
$742$		0			0
$743$	26.9503	+	40.3339i	0.988710	+	1.47971i	0.873772	+	0.486336i	$0.161667\pi$
$743$	26.9503	+	40.3339i	0.988710	+	1.47971i	0.114938	+	0.993373i	$0.463333\pi$
$744$		0			0
$745$	−10.8524	+	1.01392i	−0.397602	+	0.0371473i
$746$		0			0
$747$	2.74412	+	2.74412i	0.100402	+	0.100402i
$748$		0			0
$749$		−	8.75197i		−	0.319790i
$750$		0			0
$751$	−20.6000	−	30.8300i	−0.751704	−	1.12500i	−0.988170	−	0.153364i	$-0.950989\pi$
$751$	−20.6000	−	30.8300i	−0.751704	−	1.12500i	0.236466	−	0.971640i	$-0.424011\pi$
$752$		0			0
$753$	−1.56882	+	1.04825i	−0.0571710	+	0.0382004i
$754$		0			0
$755$	−18.9244	−	5.84450i	−0.688731	−	0.212703i
$756$		0			0
$757$	−10.2412	−	24.7244i	−0.372223	−	0.898625i	−0.993373	−	0.114934i	$-0.963334\pi$
$757$	−10.2412	−	24.7244i	−0.372223	−	0.898625i	0.621151	−	0.783691i	$-0.286666\pi$
$758$		0			0
$759$	12.5354	−	18.7606i	0.455007	−	0.680966i
$760$		0			0
$761$	−24.4640	−	24.4640i	−0.886818	−	0.886818i	0.107398	−	0.994216i	$-0.465748\pi$
$761$	−24.4640	−	24.4640i	−0.886818	−	0.886818i	−0.994216	+	0.107398i	$0.965748\pi$
$762$		0			0
$763$	27.3607	+	11.3332i	0.990525	+	0.410289i
$764$		0			0
$765$	1.92127	+	17.2715i	0.0694636	+	0.624452i
$766$		0			0
$767$	31.6616	+	13.1147i	1.14323	+	0.473543i
$768$		0			0
$769$	−1.53054	−	1.53054i	−0.0551927	−	0.0551927i	0.678972	−	0.734164i	$-0.262426\pi$
$769$	−1.53054	−	1.53054i	−0.0551927	−	0.0551927i	−0.734164	+	0.678972i	$0.762426\pi$
$770$		0			0
$771$	13.8982	−	20.8001i	0.500532	−	0.749099i
$772$		0			0
$773$	−14.7877	−	35.7006i	−0.531876	−	1.28406i	−0.930279	−	0.366852i	$-0.880436\pi$
$773$	−14.7877	−	35.7006i	−0.531876	−	1.28406i	0.398404	−	0.917210i	$-0.369564\pi$
$774$		0			0
$775$	9.33607	+	9.52532i	0.335361	+	0.342160i
$776$		0			0
$777$	33.5303	−	22.4042i	1.20289	−	0.803747i
$778$		0			0
$779$	−21.7125	−	32.4951i	−0.777931	−	1.16426i
$780$		0			0
$781$			78.9876i			2.82640i
$782$		0			0
$783$	−10.6866	−	10.6866i	−0.381907	−	0.381907i
$784$		0			0
$785$	3.25878	−	3.93046i	0.116311	−	0.140284i
$786$		0			0
$787$	13.3000	+	19.9049i	0.474094	+	0.709532i	0.989033	−	0.147695i	$-0.0471854\pi$
$787$	13.3000	+	19.9049i	0.474094	+	0.709532i	−0.514939	+	0.857227i	$0.672185\pi$
$788$		0			0
$789$	−11.0284	+	2.19368i	−0.392621	+	0.0780971i
$790$		0			0
$791$	7.82256	−	18.8853i	0.278138	−	0.671485i
$792$		0			0
$793$	6.28856	+	31.6147i	0.223313	+	1.12267i
$794$		0			0
$795$	−8.22278	−	27.6047i	−0.291632	−	0.979037i
$796$		0			0
$797$	−4.06933	+	9.82424i	−0.144143	+	0.347992i	−0.979419	−	0.201839i	$-0.935308\pi$
$797$	−4.06933	+	9.82424i	−0.144143	+	0.347992i	0.835276	+	0.549832i	$0.185308\pi$
$798$		0			0
$799$	−37.0899	−	14.6027i	−1.31215	−	0.516607i
$800$		0			0
$801$	−1.49466	−	3.60844i	−0.0528114	−	0.127498i
$802$		0			0
$803$	7.67919			0.270993
$804$		0			0
$805$	8.06787	+	15.2778i	0.284355	+	0.538472i
$806$		0			0
$807$	27.6308	−	11.4450i	0.972650	−	0.402885i
$808$		0			0
$809$	5.55402	+	27.9219i	0.195269	+	0.981683i	0.946760	+	0.321940i	$0.104335\pi$
$809$	5.55402	+	27.9219i	0.195269	+	0.981683i	−0.751491	+	0.659743i	$0.770665\pi$
$810$		0			0
$811$	16.0616	+	3.19486i	0.564000	+	0.112187i	0.468853	−	0.883276i	$-0.344668\pi$
$811$	16.0616	+	3.19486i	0.564000	+	0.112187i	0.0951480	+	0.995463i	$0.469668\pi$
$812$		0			0
$813$	−27.8926	−	5.54818i	−0.978235	−	0.194583i
$814$		0			0
$815$	6.16023	+	20.6805i	0.215784	+	0.724406i
$816$		0			0
$817$	−42.1608	+	42.1608i	−1.47502	+	1.47502i
$818$		0			0
$819$	−24.9068	+	16.6422i	−0.870313	+	0.581524i
$820$		0			0
$821$	2.42265	−	12.1795i	0.0845510	−	0.425067i	−0.915205	−	0.402988i	$-0.867972\pi$
$821$	2.42265	−	12.1795i	0.0845510	−	0.425067i	0.999756	−	0.0220786i	$-0.00702841\pi$
$822$		0			0
$823$	−23.7568	+	35.5545i	−0.828109	+	1.23935i	0.140331	+	0.990105i	$0.455183\pi$
$823$	−23.7568	+	35.5545i	−0.828109	+	1.23935i	−0.968440	+	0.249248i	$0.919817\pi$
$824$		0			0
$825$	−45.3991	−	30.9981i	−1.58059	−	1.07921i
$826$		0			0
$827$	12.8080	−	2.54767i	0.445379	−	0.0885913i	0.0326943	−	0.999465i	$-0.489591\pi$
$827$	12.8080	−	2.54767i	0.445379	−	0.0885913i	0.412684	+	0.910874i	$0.364591\pi$
$828$		0			0
$829$	23.4532	−	23.4532i	0.814564	−	0.814564i	−0.170750	−	0.985314i	$-0.554619\pi$
$829$	23.4532	−	23.4532i	0.814564	−	0.814564i	0.985314	+	0.170750i	$0.0546191\pi$
$830$		0			0
$831$	−2.83871	+	1.17583i	−0.0984739	+	0.0407892i
$832$		0			0
$833$	0.521412	+	29.5790i	0.0180658	+	1.02485i
$834$		0			0
$835$	27.2219	−	22.1128i	0.942052	−	0.765245i
$836$		0			0
$837$			6.57428i			0.227240i
$838$		0			0
$839$	−43.4456	−	29.0294i	−1.49991	−	1.00221i	−0.989858	−	0.142064i	$-0.954626\pi$
$839$	−43.4456	−	29.0294i	−1.49991	−	1.00221i	−0.510052	−	0.860144i	$-0.670374\pi$
$840$		0			0
$841$	−7.94881	−	3.29250i	−0.274097	−	0.113535i
$842$		0			0
$843$	−3.82472	−	2.55560i	−0.131730	−	0.0880194i
$844$		0			0
$845$	8.29183	+	6.87484i	0.285248	+	0.236502i
$846$		0			0
$847$	−10.0961	+	50.7563i	−0.346905	+	1.74401i
$848$		0			0
$849$	−6.05631			−0.207852
$850$		0			0
$851$	9.94547			0.340926
$852$		0			0
$853$	−2.69182	+	13.5327i	−0.0921661	+	0.463350i	0.906947	+	0.421245i	$0.138407\pi$
$853$	−2.69182	+	13.5327i	−0.0921661	+	0.463350i	−0.999113	+	0.0421057i	$0.986593\pi$
$854$		0			0
$855$	−16.6538	−	13.8078i	−0.569549	−	0.472218i
$856$		0			0
$857$	27.3707	+	18.2885i	0.934967	+	0.624725i	0.926927	−	0.375243i	$-0.122441\pi$
$857$	27.3707	+	18.2885i	0.934967	+	0.624725i	0.00804031	+	0.999968i	$0.497441\pi$
$858$		0			0
$859$	26.7649	+	11.0864i	0.913208	+	0.378263i	0.789284	−	0.614029i	$-0.210452\pi$
$859$	26.7649	+	11.0864i	0.913208	+	0.378263i	0.123924	+	0.992292i	$0.460452\pi$
$860$		0			0
$861$	−52.6815	−	35.2007i	−1.79538	−	1.19964i
$862$		0			0
$863$			3.33874i			0.113652i	0.998384	+	0.0568261i	$0.0180981\pi$
$863$			3.33874i			0.113652i	−0.998384	+	0.0568261i	$0.981902\pi$
$864$		0			0
$865$	−25.2297	+	20.4945i	−0.857836	+	0.696835i
$866$		0			0
$867$	−30.4858	+	21.9626i	−1.03535	+	0.745889i
$868$		0			0
$869$	65.3608	−	27.0733i	2.21721	−	0.918400i
$870$		0			0
$871$	−8.75018	+	8.75018i	−0.296488	+	0.296488i
$872$		0			0
$873$	−34.6235	+	6.88704i	−1.17183	+	0.233091i
$874$		0			0
$875$	37.4178	−	19.2819i	1.26495	−	0.651848i
$876$		0			0
$877$	16.6480	−	24.9155i	0.562163	−	0.841337i	−0.436121	−	0.899888i	$-0.643648\pi$
$877$	16.6480	−	24.9155i	0.562163	−	0.841337i	0.998284	+	0.0585510i	$0.0186480\pi$
$878$		0			0
$879$	−11.0238	+	55.4204i	−0.371823	+	1.86928i
$880$		0			0
$881$	47.7394	−	31.8984i	1.60838	−	1.07469i	0.663050	−	0.748575i	$-0.269262\pi$
$881$	47.7394	−	31.8984i	1.60838	−	1.07469i	0.945332	−	0.326111i	$-0.105738\pi$
$882$		0			0
$883$	−38.6932	+	38.6932i	−1.30213	+	1.30213i	−0.375175	+	0.926954i	$0.622417\pi$
$883$	−38.6932	+	38.6932i	−1.30213	+	1.30213i	−0.926954	+	0.375175i	$0.877583\pi$
$884$		0			0
$885$	11.4549	+	38.4551i	0.385051	+	1.29265i
$886$		0			0
$887$	−41.9896	−	8.35225i	−1.40987	−	0.280441i	−0.569296	−	0.822133i	$-0.692784\pi$
$887$	−41.9896	−	8.35225i	−1.40987	−	0.280441i	−0.840577	+	0.541691i	$0.817784\pi$
$888$		0			0
$889$	9.77495	+	1.94436i	0.327841	+	0.0652117i
$890$		0			0
$891$	−10.7740	−	54.1646i	−0.360943	−	1.81458i
$892$		0			0
$893$	45.8448	−	18.9895i	1.53414	−	0.635460i
$894$		0			0
$895$	−0.762315	−	1.44356i	−0.0254814	−	0.0482530i
$896$		0			0
$897$	−19.1457			−0.639257
$898$		0			0
$899$	6.25987	+	15.1127i	0.208778	+	0.504036i
$900$		0			0
$901$	16.6897	−	17.2886i	0.556013	−	0.575968i
$902$		0			0
$903$	−36.9917	+	89.3059i	−1.23101	+	2.97192i
$904$		0			0
$905$	8.67152	+	29.1111i	0.288251	+	0.967686i
$906$		0			0
$907$	7.38614	+	37.1327i	0.245253	+	1.23297i	0.885441	+	0.464752i	$0.153856\pi$
$907$	7.38614	+	37.1327i	0.245253	+	1.23297i	−0.640188	+	0.768218i	$0.721144\pi$
$908$		0			0
$909$	−8.00677	+	19.3301i	−0.265568	+	0.641138i
$910$		0			0
$911$	−7.17540	+	1.42728i	−0.237732	+	0.0472877i	−0.312518	−	0.949912i	$-0.601172\pi$
$911$	−7.17540	+	1.42728i	−0.237732	+	0.0472877i	0.0747865	+	0.997200i	$0.476172\pi$
$912$		0			0
$913$	−5.68999	−	8.51568i	−0.188311	−	0.281828i
$914$		0			0
$915$	−24.0886	+	29.0536i	−0.796344	+	0.960481i
$916$		0			0
$917$	15.0467	+	15.0467i	0.496886	+	0.496886i
$918$		0			0
$919$		−	5.35520i		−	0.176652i	−0.996092	−	0.0883258i	$-0.971848\pi$
$919$		−	5.35520i		−	0.176652i	0.996092	−	0.0883258i	$-0.0281517\pi$
$920$		0			0
$921$	28.4504	+	42.5791i	0.937474	+	1.40303i
$922$		0			0
$923$	55.7284	−	37.2365i	1.83432	−	1.22565i
$924$		0			0
$925$	0.243119	−	24.2297i	0.00799369	−	0.796667i
$926$		0			0
$927$	−2.88889	−	6.97440i	−0.0948836	−	0.229069i
$928$		0			0
$929$	−10.4696	+	15.6689i	−0.343497	+	0.514079i	−0.962490	−	0.271317i	$-0.912541\pi$
$929$	−10.4696	+	15.6689i	−0.343497	+	0.514079i	0.618993	+	0.785396i	$0.287541\pi$
$930$		0			0
$931$	−26.0412	−	26.0412i	−0.853467	−	0.853467i
$932$		0			0
$933$	−45.9284	−	19.0242i	−1.50363	−	0.622824i
$934$		0			0
$935$	3.91945	−	45.6945i	0.128180	−	1.49437i
$936$		0			0
$937$	52.0704	+	21.5683i	1.70107	+	0.704605i	0.999964	−	0.00845667i	$-0.00269187\pi$
$937$	52.0704	+	21.5683i	1.70107	+	0.704605i	0.701102	+	0.713061i	$0.252692\pi$
$938$		0			0
$939$	−38.0508	−	38.0508i	−1.24174	−	1.24174i
$940$		0			0
$941$	−19.1537	+	28.6655i	−0.624391	+	0.934468i	0.375579	+	0.926790i	$0.377444\pi$
$941$	−19.1537	+	28.6655i	−0.624391	+	0.934468i	−0.999971	+	0.00767738i	$0.997556\pi$
$942$		0			0
$943$	−5.97979	−	14.4365i	−0.194729	−	0.470117i
$944$		0			0
$945$	19.8246	+	6.12249i	0.644893	+	0.199165i
$946$		0			0
$947$	−13.9631	+	9.32986i	−0.453740	+	0.303180i	−0.761359	−	0.648330i	$-0.775468\pi$
$947$	−13.9631	+	9.32986i	−0.453740	+	0.303180i	0.307619	+	0.951510i	$0.400468\pi$
$948$		0			0
$949$	−3.62014	−	5.41792i	−0.117515	−	0.175873i
$950$		0			0
$951$			38.2707i			1.24101i
$952$		0			0
$953$	−14.4629	−	14.4629i	−0.468498	−	0.468498i	0.432929	−	0.901428i	$-0.357480\pi$
$953$	−14.4629	−	14.4629i	−0.468498	−	0.468498i	−0.901428	+	0.432929i	$0.857480\pi$
$954$		0			0
$955$	−30.1794	+	2.81962i	−0.976584	+	0.0912407i
$956$		0			0
$957$	−37.4567	−	56.0578i	−1.21080	−	1.81209i
$958$		0			0
$959$	−50.8113	+	10.1070i	−1.64078	+	0.326372i
$960$		0			0
$961$	−9.14011	+	22.0662i	−0.294842	+	0.711812i
$962$		0			0
$963$	0.854810	+	4.29742i	0.0275459	+	0.138482i
$964$		0			0
$965$	0.0420280	+	0.0227362i	0.00135293	+	0.000731905i
$966$		0			0
$967$	−1.93646	+	4.67502i	−0.0622723	+	0.150339i	−0.951953	−	0.306245i	$-0.900927\pi$
$967$	−1.93646	+	4.67502i	−0.0622723	+	0.150339i	0.889680	+	0.456584i	$0.150927\pi$
$968$		0			0
$969$	8.31516	−	46.0288i	0.267121	−	1.47866i
$970$		0			0
$971$	−10.8652	−	26.2309i	−0.348680	−	0.841789i	−0.996776	−	0.0802300i	$-0.974435\pi$
$971$	−10.8652	−	26.2309i	−0.348680	−	0.841789i	0.648096	−	0.761559i	$-0.275565\pi$
$972$		0			0
$973$	−7.46583			−0.239344
$974$		0			0
$975$	−0.468020	+	46.6438i	−0.0149886	+	1.49380i
$976$		0			0
$977$	14.6161	−	6.05420i	0.467611	−	0.193691i	−0.136421	−	0.990651i	$-0.543560\pi$
$977$	14.6161	−	6.05420i	0.467611	−	0.193691i	0.604032	+	0.796960i	$0.293560\pi$
$978$		0			0
$979$	2.01092	+	10.1096i	0.0642693	+	0.323104i
$980$		0			0
$981$	−14.5417	−	2.89252i	−0.464280	−	0.0923510i
$982$		0			0
$983$	−17.9953	−	3.57948i	−0.573960	−	0.114168i	−0.100428	−	0.994944i	$-0.532021\pi$
$983$	−17.9953	−	3.57948i	−0.573960	−	0.114168i	−0.473532	+	0.880776i	$0.657021\pi$
$984$		0			0
$985$	−2.42979	+	0.723779i	−0.0774197	+	0.0230615i
$986$		0			0
$987$	56.8853	−	56.8853i	1.81068	−	1.81068i
$988$		0			0
$989$	−19.8219	+	13.2446i	−0.630301	+	0.421153i
$990$		0			0
$991$	−6.86263	+	34.5008i	−0.217999	+	1.09595i	0.704427	+	0.709777i	$0.251204\pi$
$991$	−6.86263	+	34.5008i	−0.217999	+	1.09595i	−0.922425	+	0.386176i	$0.873796\pi$
$992$		0			0
$993$	13.1339	−	19.6563i	0.416793	−	0.623775i
$994$		0			0
$995$	−31.9517	+	25.9549i	−1.01294	+	0.822827i
$996$		0			0
$997$	−55.4992	+	11.0395i	−1.75768	+	0.349624i	−0.965447	−	0.260600i	$-0.916080\pi$
$997$	−55.4992	+	11.0395i	−1.75768	+	0.349624i	−0.792229	+	0.610223i	$0.791080\pi$
$998$		0			0
$999$	8.44544	−	8.44544i	0.267202	−	0.267202i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	680.2.cg.b.73.4	✓	112
5.2	odd	4		680.2.cq.b.617.11	yes	112
17.7	odd	16		680.2.cq.b.313.11	yes	112
85.7	even	16	inner	680.2.cg.b.177.4	yes	112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
680.2.cg.b.73.4	✓	112	1.1	even	1	trivial
680.2.cg.b.177.4	yes	112	85.7	even	16	inner
680.2.cq.b.313.11	yes	112	17.7	odd	16
680.2.cq.b.617.11	yes	112	5.2	odd	4

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 680 = 2^{3} \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	680.cg (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.431185 + 2.16772i) q^{3} +(-1.72137 - 1.42720i) q^{5} +(3.13047 + 2.09171i) q^{7} +(-1.74143 - 0.721324i) q^{9} +(4.13611 + 2.76366i) q^{11} -4.22102i q^{13} +(3.83599 - 3.11604i) q^{15} +(3.83647 + 1.51046i) q^{17} +(-4.74204 + 1.96422i) q^{19} +(-5.88405 + 5.88405i) q^{21} +(-2.01280 + 0.400370i) q^{23} +(0.926199 + 4.91347i) q^{25} +(-1.36923 + 2.04920i) q^{27} +(-1.19633 + 6.01436i) q^{29} +(2.21798 - 1.48200i) q^{31} +(-7.77427 + 7.77427i) q^{33} +(-2.40339 - 8.06840i) q^{35} +(-4.75306 - 0.945443i) q^{37} +(9.14997 + 1.82004i) q^{39} +(1.48544 + 7.46784i) q^{41} +(10.7322 - 4.44543i) q^{43} +(1.96816 + 3.72703i) q^{45} -9.66773 q^{47} +(2.74578 + 6.62891i) q^{49} +(-4.92848 + 7.66509i) q^{51} +(2.23033 - 5.38449i) q^{53} +(-3.17546 - 10.6603i) q^{55} +(-2.21317 - 11.1263i) q^{57} +(-3.10699 + 7.50094i) q^{59} +(-7.48983 + 1.48982i) q^{61} +(-3.94269 - 5.90065i) q^{63} +(-6.02424 + 7.26592i) q^{65} +(-2.07300 - 2.07300i) q^{67} -4.53580i q^{69} +(8.82168 + 13.2026i) q^{71} +(1.28356 - 0.857646i) q^{73} +(-11.0504 - 0.110878i) q^{75} +(7.16718 + 17.3031i) q^{77} +(7.90124 - 11.8250i) q^{79} +(-7.85019 - 7.85019i) q^{81} +(-1.90214 - 0.787891i) q^{83} +(-4.44824 - 8.07547i) q^{85} +(-12.5216 - 5.18661i) q^{87} +(1.46520 + 1.46520i) q^{89} +(8.82915 - 13.2138i) q^{91} +(2.25620 + 5.44696i) q^{93} +(10.9661 + 3.38671i) q^{95} +(15.5723 - 10.4051i) q^{97} +(-5.20926 - 7.79621i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q + 16 q^{15} - 24 q^{27} - 8 q^{29} + 16 q^{31} - 48 q^{33} - 32 q^{35} - 16 q^{37} - 16 q^{41} + 48 q^{43} - 24 q^{45} - 16 q^{47} - 80 q^{49} + 32 q^{51} - 8 q^{53} + 24 q^{55} - 80 q^{59} - 24 q^{61}+ \cdots + 48 q^{99}+O(q^{100}) \) 112 * q + 16 * q^15 - 24 * q^27 - 8 * q^29 + 16 * q^31 - 48 * q^33 - 32 * q^35 - 16 * q^37 - 16 * q^41 + 48 * q^43 - 24 * q^45 - 16 * q^47 - 80 * q^49 + 32 * q^51 - 8 * q^53 + 24 * q^55 - 80 * q^59 - 24 * q^61 - 72 * q^63 + 16 * q^65 - 48 * q^67 - 40 * q^71 - 16 * q^73 + 16 * q^75 + 24 * q^77 + 40 * q^79 - 24 * q^83 + 16 * q^85 + 16 * q^87 - 16 * q^89 + 16 * q^93 - 8 * q^95 + 64 * q^97 + 48 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more