LMFDB - Embedded newform 120.3.u.b.73.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [120,3,Mod(73,120)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(120, base_ring=CyclotomicField(4))

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

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("120.73");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 120 = 2^{3} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	120.u (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$3.26976317232$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} + 8x^{6} + 269x^{4} - 1116x^{3} + 2312x^{2} + 680x + 100 $ x^8 - 4x^7 + 8x^6 + 269x^4 - 1116x^3 + 2312x^2 + 680x + 100
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2\cdot 5 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			73.2
Root			$-2.88489 + 2.88489i$ of defining polynomial
Character	$\chi$	$=$	120.73
Dual form			120.3.u.b.97.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.22474 - 1.22474i) q^{3} +(1.88489 + 4.63111i) q^{5} +(6.02356 - 6.02356i) q^{7} +3.00000i q^{9} +O(q^{10})$	\(q+(-1.22474 - 1.22474i) q^{3} +(1.88489 + 4.63111i) q^{5} +(6.02356 - 6.02356i) q^{7} +3.00000i q^{9} +17.0038 q^{11} +(0.124585 + 0.124585i) q^{13} +(3.36342 - 7.98044i) q^{15} +(10.7744 - 10.7744i) q^{17} -4.04713i q^{19} -14.7547 q^{21} +(1.85568 + 1.85568i) q^{23} +(-17.8944 + 17.4583i) q^{25} +(3.67423 - 3.67423i) q^{27} +54.4448i q^{29} -53.1995 q^{31} +(-20.8254 - 20.8254i) q^{33} +(39.2496 + 16.5420i) q^{35} +(21.2693 - 21.2693i) q^{37} -0.305169i q^{39} -52.1414 q^{41} +(-50.4554 - 50.4554i) q^{43} +(-13.8933 + 5.65467i) q^{45} +(13.4045 - 13.4045i) q^{47} -23.5667i q^{49} -26.3918 q^{51} +(12.4315 + 12.4315i) q^{53} +(32.0504 + 78.7466i) q^{55} +(-4.95670 + 4.95670i) q^{57} -8.79413i q^{59} +105.860 q^{61} +(18.0707 + 18.0707i) q^{63} +(-0.342137 + 0.811794i) q^{65} +(-46.8595 + 46.8595i) q^{67} -4.54547i q^{69} -56.8955 q^{71} +(-52.7296 - 52.7296i) q^{73} +(43.2980 + 0.534094i) q^{75} +(102.424 - 102.424i) q^{77} -15.2920i q^{79} -9.00000 q^{81} +(46.1914 + 46.1914i) q^{83} +(70.2060 + 29.5888i) q^{85} +(66.6810 - 66.6810i) q^{87} +0.948538i q^{89} +1.50089 q^{91} +(65.1558 + 65.1558i) q^{93} +(18.7427 - 7.62840i) q^{95} +(77.6693 - 77.6693i) q^{97} +51.0115i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 12 q^{5} + 4 q^{7}+O(q^{10}) $ 8 * q - 12 * q^5 + 4 * q^7	$ 8 q - 12 q^{5} + 4 q^{7} + 32 q^{11} - 4 q^{13} + 52 q^{17} - 24 q^{21} - 40 q^{23} - 84 q^{25} + 96 q^{31} + 60 q^{33} + 24 q^{35} - 60 q^{37} - 152 q^{41} - 88 q^{43} - 16 q^{47} - 168 q^{51} + 108 q^{53} + 116 q^{55} - 24 q^{57} + 264 q^{61} + 12 q^{63} + 164 q^{65} - 216 q^{67} - 240 q^{71} - 208 q^{73} + 120 q^{75} + 168 q^{77} - 72 q^{81} + 336 q^{83} - 12 q^{85} + 252 q^{87} + 592 q^{91} + 264 q^{93} - 128 q^{95} - 208 q^{97}+O(q^{100}) $ 8 * q - 12 * q^5 + 4 * q^7 + 32 * q^11 - 4 * q^13 + 52 * q^17 - 24 * q^21 - 40 * q^23 - 84 * q^25 + 96 * q^31 + 60 * q^33 + 24 * q^35 - 60 * q^37 - 152 * q^41 - 88 * q^43 - 16 * q^47 - 168 * q^51 + 108 * q^53 + 116 * q^55 - 24 * q^57 + 264 * q^61 + 12 * q^63 + 164 * q^65 - 216 * q^67 - 240 * q^71 - 208 * q^73 + 120 * q^75 + 168 * q^77 - 72 * q^81 + 336 * q^83 - 12 * q^85 + 252 * q^87 + 592 * q^91 + 264 * q^93 - 128 * q^95 - 208 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/120\mathbb{Z}\right)^\times$.

$n$	$31$	$41$	$61$	$97$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{3}{4}\right)$

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			0
$2$		0			0
$3$	−1.22474	−	1.22474i	−0.408248	−	0.408248i
$3$	−1.22474	−	1.22474i	−0.408248	−	0.408248i
$4$		0			0
$5$	1.88489	+	4.63111i	0.376978	+	0.926222i
$5$	1.88489	+	4.63111i	0.376978	+	0.926222i
$6$		0			0
$7$	6.02356	−	6.02356i	0.860509	−	0.860509i	−0.130888	−	0.991397i	$-0.541783\pi$
$7$	6.02356	−	6.02356i	0.860509	−	0.860509i	0.991397	+	0.130888i	$0.0417828\pi$
$8$		0			0
$9$			3.00000i			0.333333i
$10$		0			0
$11$	17.0038			1.54580			0.772901	−	0.634526i	$-0.218805\pi$
$11$	17.0038			1.54580			0.772901	+	0.634526i	$0.218805\pi$
$12$		0			0
$13$	0.124585	+	0.124585i	0.00958344	+	0.00958344i	0.711882	−	0.702299i	$-0.247843\pi$
$13$	0.124585	+	0.124585i	0.00958344	+	0.00958344i	−0.702299	+	0.711882i	$0.747843\pi$
$14$		0			0
$15$	3.36342	−	7.98044i	0.224228	−	0.532029i
$16$		0			0
$17$	10.7744	−	10.7744i	0.633788	−	0.633788i	−0.315228	−	0.949016i	$-0.602081\pi$
$17$	10.7744	−	10.7744i	0.633788	−	0.633788i	0.949016	+	0.315228i	$0.102081\pi$
$18$		0			0
$19$		−	4.04713i		−	0.213007i	−0.994312	−	0.106503i	$-0.966035\pi$
$19$		−	4.04713i		−	0.213007i	0.994312	−	0.106503i	$-0.0339655\pi$
$20$		0			0
$21$	−14.7547			−0.702603
$22$		0			0
$23$	1.85568	+	1.85568i	0.0806817	+	0.0806817i	0.746296	−	0.665614i	$-0.231830\pi$
$23$	1.85568	+	1.85568i	0.0806817	+	0.0806817i	−0.665614	+	0.746296i	$0.731830\pi$
$24$		0			0
$25$	−17.8944	+	17.4583i	−0.715775	+	0.698331i
$26$		0			0
$27$	3.67423	−	3.67423i	0.136083	−	0.136083i
$28$		0			0
$29$			54.4448i			1.87741i	0.344724	+	0.938704i	$0.387972\pi$
$29$			54.4448i			1.87741i	−0.344724	+	0.938704i	$0.612028\pi$
$30$		0			0
$31$	−53.1995			−1.71611			−0.858056	−	0.513556i	$-0.828328\pi$
$31$	−53.1995			−1.71611			−0.858056	+	0.513556i	$0.828328\pi$
$32$		0			0
$33$	−20.8254	−	20.8254i	−0.631071	−	0.631071i
$34$		0			0
$35$	39.2496	+	16.5420i	1.12142	+	0.472629i
$36$		0			0
$37$	21.2693	−	21.2693i	0.574846	−	0.574846i	−0.358633	−	0.933479i	$-0.616757\pi$
$37$	21.2693	−	21.2693i	0.574846	−	0.574846i	0.933479	+	0.358633i	$0.116757\pi$
$38$		0			0
$39$		−	0.305169i		−	0.00782484i
$40$		0			0
$41$	−52.1414			−1.27174			−0.635871	−	0.771796i	$-0.719359\pi$
$41$	−52.1414			−1.27174			−0.635871	+	0.771796i	$0.719359\pi$
$42$		0			0
$43$	−50.4554	−	50.4554i	−1.17338	−	1.17338i	−0.981398	−	0.191984i	$-0.938508\pi$
$43$	−50.4554	−	50.4554i	−1.17338	−	1.17338i	−0.191984	−	0.981398i	$-0.561492\pi$
$44$		0			0
$45$	−13.8933	+	5.65467i	−0.308741	+	0.125659i
$46$		0			0
$47$	13.4045	−	13.4045i	0.285201	−	0.285201i	−0.549978	−	0.835179i	$-0.685364\pi$
$47$	13.4045	−	13.4045i	0.285201	−	0.285201i	0.835179	+	0.549978i	$0.185364\pi$
$48$		0			0
$49$		−	23.5667i		−	0.480952i
$50$		0			0
$51$	−26.3918			−0.517486
$52$		0			0
$53$	12.4315	+	12.4315i	0.234556	+	0.234556i	0.814591	−	0.580035i	$-0.196961\pi$
$53$	12.4315	+	12.4315i	0.234556	+	0.234556i	−0.580035	+	0.814591i	$0.696961\pi$
$54$		0			0
$55$	32.0504	+	78.7466i	0.582734	+	1.43176i
$56$		0			0
$57$	−4.95670	+	4.95670i	−0.0869596	+	0.0869596i
$58$		0			0
$59$		−	8.79413i		−	0.149053i	−0.997219	−	0.0745265i	$-0.976255\pi$
$59$		−	8.79413i		−	0.149053i	0.997219	−	0.0745265i	$-0.0237445\pi$
$60$		0			0
$61$	105.860			1.73542			0.867708	−	0.497074i	$-0.165592\pi$
$61$	105.860			1.73542			0.867708	+	0.497074i	$0.165592\pi$
$62$		0			0
$63$	18.0707	+	18.0707i	0.286836	+	0.286836i
$64$		0			0
$65$	−0.342137	+	0.811794i	−0.00526364	+	0.0124891i
$66$		0			0
$67$	−46.8595	+	46.8595i	−0.699396	+	0.699396i	−0.964280	−	0.264885i	$-0.914666\pi$
$67$	−46.8595	+	46.8595i	−0.699396	+	0.699396i	0.264885	+	0.964280i	$0.414666\pi$
$68$		0			0
$69$		−	4.54547i		−	0.0658763i
$70$		0			0
$71$	−56.8955			−0.801346			−0.400673	−	0.916221i	$-0.631224\pi$
$71$	−56.8955			−0.801346			−0.400673	+	0.916221i	$0.631224\pi$
$72$		0			0
$73$	−52.7296	−	52.7296i	−0.722324	−	0.722324i	0.246754	−	0.969078i	$-0.420636\pi$
$73$	−52.7296	−	52.7296i	−0.722324	−	0.722324i	−0.969078	+	0.246754i	$0.920636\pi$
$74$		0			0
$75$	43.2980	+	0.534094i	0.577306	+	0.00712125i
$76$		0			0
$77$	102.424	−	102.424i	1.33018	−	1.33018i
$78$		0			0
$79$		−	15.2920i		−	0.193569i	−0.995305	−	0.0967846i	$-0.969144\pi$
$79$		−	15.2920i		−	0.193569i	0.995305	−	0.0967846i	$-0.0308558\pi$
$80$		0			0
$81$	−9.00000			−0.111111
$82$		0			0
$83$	46.1914	+	46.1914i	0.556523	+	0.556523i	0.928316	−	0.371792i	$-0.121257\pi$
$83$	46.1914	+	46.1914i	0.556523	+	0.556523i	−0.371792	+	0.928316i	$0.621257\pi$
$84$		0			0
$85$	70.2060	+	29.5888i	0.825953	+	0.348104i
$86$		0			0
$87$	66.6810	−	66.6810i	0.766449	−	0.766449i
$88$		0			0
$89$			0.948538i			0.0106577i	0.999986	+	0.00532886i	$0.00169624\pi$
$89$			0.948538i			0.0106577i	−0.999986	+	0.00532886i	$0.998304\pi$
$90$		0			0
$91$	1.50089			0.0164933
$92$		0			0
$93$	65.1558	+	65.1558i	0.700600	+	0.700600i
$94$		0			0
$95$	18.7427	−	7.62840i	0.197292	−	0.0802989i
$96$		0			0
$97$	77.6693	−	77.6693i	0.800715	−	0.800715i	−0.182492	−	0.983207i	$-0.558417\pi$
$97$	77.6693	−	77.6693i	0.800715	−	0.800715i	0.983207	+	0.182492i	$0.0584165\pi$
$98$		0			0
$99$			51.0115i			0.515268i
$100$		0			0
$101$	−49.6243			−0.491329			−0.245665	−	0.969355i	$-0.579006\pi$
$101$	−49.6243			−0.491329			−0.245665	+	0.969355i	$0.579006\pi$
$102$		0			0
$103$	18.7930	+	18.7930i	0.182457	+	0.182457i	0.792425	−	0.609969i	$-0.208818\pi$
$103$	18.7930	+	18.7930i	0.182457	+	0.182457i	−0.609969	+	0.792425i	$0.708818\pi$
$104$		0			0
$105$	−27.8109	−	68.3305i	−0.264866	−	0.650766i
$106$		0			0
$107$	−69.0004	+	69.0004i	−0.644863	+	0.644863i	−0.951747	−	0.306884i	$-0.900714\pi$
$107$	−69.0004	+	69.0004i	−0.644863	+	0.644863i	0.306884	+	0.951747i	$0.400714\pi$
$108$		0			0
$109$			130.003i			1.19268i	0.802730	+	0.596342i	$0.203380\pi$
$109$			130.003i			1.19268i	−0.802730	+	0.596342i	$0.796620\pi$
$110$		0			0
$111$	−52.0989			−0.469360
$112$		0			0
$113$	−157.585	−	157.585i	−1.39456	−	1.39456i	−0.814760	−	0.579799i	$-0.803131\pi$
$113$	−157.585	−	157.585i	−1.39456	−	1.39456i	−0.579799	−	0.814760i	$-0.696869\pi$
$114$		0			0
$115$	−5.09610	+	12.0916i	−0.0443139	+	0.105144i
$116$		0			0
$117$	−0.373754	+	0.373754i	−0.00319448	+	0.00319448i
$118$		0			0
$119$		−	129.801i		−	1.09076i
$120$		0			0
$121$	168.130			1.38951
$122$		0			0
$123$	63.8599	+	63.8599i	0.519186	+	0.519186i
$124$		0			0
$125$	−114.580	−	49.9638i	−0.916641	−	0.399711i
$126$		0			0
$127$	−106.268	+	106.268i	−0.836753	+	0.836753i	−0.988430	−	0.151677i	$-0.951533\pi$
$127$	−106.268	+	106.268i	−0.836753	+	0.836753i	0.151677	+	0.988430i	$0.451533\pi$
$128$		0			0
$129$			123.590i			0.958062i
$130$		0			0
$131$	−102.890			−0.785421			−0.392711	−	0.919662i	$-0.628463\pi$
$131$	−102.890			−0.785421			−0.392711	+	0.919662i	$0.628463\pi$
$132$		0			0
$133$	−24.3781	−	24.3781i	−0.183294	−	0.183294i
$134$		0			0
$135$	23.9413	+	10.0903i	0.177343	+	0.0747426i
$136$		0			0
$137$	−84.7079	+	84.7079i	−0.618306	+	0.618306i	−0.945097	−	0.326791i	$-0.894033\pi$
$137$	−84.7079	+	84.7079i	−0.618306	+	0.618306i	0.326791	+	0.945097i	$0.394033\pi$
$138$		0			0
$139$		−	244.050i		−	1.75575i	−0.478887	−	0.877877i	$-0.658960\pi$
$139$		−	244.050i		−	1.75575i	0.478887	−	0.877877i	$-0.341040\pi$
$140$		0			0
$141$	−32.8341			−0.232866
$142$		0			0
$143$	2.11842	+	2.11842i	0.0148141	+	0.0148141i
$144$		0			0
$145$	−252.140	+	102.623i	−1.73890	+	0.707742i
$146$		0			0
$147$	−28.8631	+	28.8631i	−0.196348	+	0.196348i
$148$		0			0
$149$			220.759i			1.48161i	0.671722	+	0.740803i	$0.265555\pi$
$149$			220.759i			1.48161i	−0.671722	+	0.740803i	$0.734445\pi$
$150$		0			0
$151$	217.984			1.44360			0.721802	−	0.692099i	$-0.243314\pi$
$151$	217.984			1.44360			0.721802	+	0.692099i	$0.243314\pi$
$152$		0			0
$153$	32.3232	+	32.3232i	0.211263	+	0.211263i
$154$		0			0
$155$	−100.275	−	246.373i	−0.646937	−	1.58950i
$156$		0			0
$157$	−185.043	+	185.043i	−1.17862	+	1.17862i	−0.198522	+	0.980096i	$0.563614\pi$
$157$	−185.043	+	185.043i	−1.17862	+	1.17862i	−0.980096	+	0.198522i	$0.936386\pi$
$158$		0			0
$159$		−	30.4508i		−	0.191514i
$160$		0			0
$161$	22.3556			0.138855
$162$		0			0
$163$	−15.5263	−	15.5263i	−0.0952533	−	0.0952533i	0.657874	−	0.753128i	$-0.271456\pi$
$163$	−15.5263	−	15.5263i	−0.0952533	−	0.0952533i	−0.753128	+	0.657874i	$0.771456\pi$
$164$		0			0
$165$	57.1910	−	135.698i	0.346612	−	0.822412i
$166$		0			0
$167$	−21.5448	+	21.5448i	−0.129011	+	0.129011i	−0.768664	−	0.639653i	$-0.779078\pi$
$167$	−21.5448	+	21.5448i	−0.129011	+	0.129011i	0.639653	+	0.768664i	$0.279078\pi$
$168$		0			0
$169$		−	168.969i		−	0.999816i
$170$		0			0
$171$	12.1414			0.0710023
$172$		0			0
$173$	86.5808	+	86.5808i	0.500467	+	0.500467i	0.911583	−	0.411116i	$-0.134861\pi$
$173$	86.5808	+	86.5808i	0.500467	+	0.500467i	−0.411116	+	0.911583i	$0.634861\pi$
$174$		0			0
$175$	−2.62679	+	212.949i	−0.0150102	+	1.21685i
$176$		0			0
$177$	−10.7706	+	10.7706i	−0.0608507	+	0.0608507i
$178$		0			0
$179$		−	45.4647i		−	0.253993i	−0.991903	−	0.126996i	$-0.959466\pi$
$179$		−	45.4647i		−	0.253993i	0.991903	−	0.126996i	$-0.0405336\pi$
$180$		0			0
$181$	13.4991			0.0745807			0.0372903	−	0.999304i	$-0.488127\pi$
$181$	13.4991			0.0745807			0.0372903	+	0.999304i	$0.488127\pi$
$182$		0			0
$183$	−129.652	−	129.652i	−0.708481	−	0.708481i
$184$		0			0
$185$	138.591	+	58.4101i	0.749139	+	0.315730i
$186$		0			0
$187$	183.206	−	183.206i	0.979711	−	0.979711i
$188$		0			0
$189$		−	44.2640i		−	0.234201i
$190$		0			0
$191$	67.6690			0.354288			0.177144	−	0.984185i	$-0.443314\pi$
$191$	67.6690			0.354288			0.177144	+	0.984185i	$0.443314\pi$
$192$		0			0
$193$	31.9967	+	31.9967i	0.165786	+	0.165786i	0.785124	−	0.619338i	$-0.212599\pi$
$193$	31.9967	+	31.9967i	0.165786	+	0.165786i	−0.619338	+	0.785124i	$0.712599\pi$
$194$		0			0
$195$	1.41327	−	0.575210i	0.00724754	−	0.00294980i
$196$		0			0
$197$	122.056	−	122.056i	0.619575	−	0.619575i	−0.325848	−	0.945422i	$-0.605650\pi$
$197$	122.056	−	122.056i	0.619575	−	0.619575i	0.945422	+	0.325848i	$0.105650\pi$
$198$		0			0
$199$		−	4.36392i		−	0.0219292i	−0.999940	−	0.0109646i	$-0.996510\pi$
$199$		−	4.36392i		−	0.0219292i	0.999940	−	0.0109646i	$-0.00349022\pi$
$200$		0			0
$201$	114.782			0.571054
$202$		0			0
$203$	327.952	+	327.952i	1.61553	+	1.61553i
$204$		0			0
$205$	−98.2809	−	241.473i	−0.479419	−	1.17791i
$206$		0			0
$207$	−5.56704	+	5.56704i	−0.0268939	+	0.0268939i
$208$		0			0
$209$		−	68.8167i		−	0.329266i
$210$		0			0
$211$	183.096			0.867756			0.433878	−	0.900972i	$-0.357145\pi$
$211$	183.096			0.867756			0.433878	+	0.900972i	$0.357145\pi$
$212$		0			0
$213$	69.6825	+	69.6825i	0.327148	+	0.327148i
$214$		0			0
$215$	138.562	−	328.768i	0.644473	−	1.52915i
$216$		0			0
$217$	−320.451	+	320.451i	−1.47673	+	1.47673i
$218$		0			0
$219$			129.161i			0.589775i
$220$		0			0
$221$	2.68465			0.0121477
$222$		0			0
$223$	−5.03964	−	5.03964i	−0.0225993	−	0.0225993i	0.695717	−	0.718316i	$-0.255087\pi$
$223$	−5.03964	−	5.03964i	−0.0225993	−	0.0225993i	−0.718316	+	0.695717i	$0.755087\pi$
$224$		0			0
$225$	−52.3748	−	53.6831i	−0.232777	−	0.238592i
$226$		0			0
$227$	−226.475	+	226.475i	−0.997689	+	0.997689i	−0.999997	−	0.00230792i	$-0.999265\pi$
$227$	−226.475	+	226.475i	−0.997689	+	0.997689i	0.00230792	+	0.999997i	$0.499265\pi$
$228$		0			0
$229$		−	276.917i		−	1.20924i	−0.796513	−	0.604621i	$-0.793324\pi$
$229$		−	276.917i		−	1.20924i	0.796513	−	0.604621i	$-0.206676\pi$
$230$		0			0
$231$	−250.886			−1.08609
$232$		0			0
$233$	198.106	+	198.106i	0.850242	+	0.850242i	0.990163	−	0.139921i	$-0.0446847\pi$
$233$	198.106	+	198.106i	0.850242	+	0.850242i	−0.139921	+	0.990163i	$0.544685\pi$
$234$		0			0
$235$	87.3435	+	36.8116i	0.371675	+	0.156645i
$236$		0			0
$237$	−18.7288	+	18.7288i	−0.0790243	+	0.0790243i
$238$		0			0
$239$			230.183i			0.963111i	0.876416	+	0.481555i	$0.159928\pi$
$239$			230.183i			0.963111i	−0.876416	+	0.481555i	$0.840072\pi$
$240$		0			0
$241$	283.542			1.17652			0.588261	−	0.808671i	$-0.299813\pi$
$241$	283.542			1.17652			0.588261	+	0.808671i	$0.299813\pi$
$242$		0			0
$243$	11.0227	+	11.0227i	0.0453609	+	0.0453609i
$244$		0			0
$245$	109.140	−	44.4206i	0.445468	−	0.181308i
$246$		0			0
$247$	0.504210	−	0.504210i	0.00204134	−	0.00204134i
$248$		0			0
$249$		−	113.145i		−	0.454400i
$250$		0			0
$251$	202.731			0.807694			0.403847	−	0.914826i	$-0.367673\pi$
$251$	202.731			0.807694			0.403847	+	0.914826i	$0.367673\pi$
$252$		0			0
$253$	31.5536	+	31.5536i	0.124718	+	0.124718i
$254$		0			0
$255$	−49.7456	−	122.223i	−0.195081	−	0.479307i
$256$		0			0
$257$	202.151	−	202.151i	0.786580	−	0.786580i	−0.194352	−	0.980932i	$-0.562260\pi$
$257$	202.151	−	202.151i	0.786580	−	0.786580i	0.980932	+	0.194352i	$0.0622604\pi$
$258$		0			0
$259$		−	256.234i		−	0.989320i
$260$		0			0
$261$	−163.334			−0.625803
$262$		0			0
$263$	−34.3895	−	34.3895i	−0.130759	−	0.130759i	0.638699	−	0.769457i	$-0.279473\pi$
$263$	−34.3895	−	34.3895i	−0.130759	−	0.130759i	−0.769457	+	0.638699i	$0.779473\pi$
$264$		0			0
$265$	−34.1395	+	81.0035i	−0.128828	+	0.305674i
$266$		0			0
$267$	1.16172	−	1.16172i	0.00435100	−	0.00435100i
$268$		0			0
$269$		−	32.5471i		−	0.120993i	−0.998168	−	0.0604964i	$-0.980732\pi$
$269$		−	32.5471i		−	0.120993i	0.998168	−	0.0604964i	$-0.0192684\pi$
$270$		0			0
$271$	−91.9490			−0.339295			−0.169648	−	0.985505i	$-0.554263\pi$
$271$	−91.9490			−0.339295			−0.169648	+	0.985505i	$0.554263\pi$
$272$		0			0
$273$	−1.83820	−	1.83820i	−0.00673335	−	0.00673335i
$274$		0			0
$275$	−304.273	+	296.858i	−1.10645	+	1.07948i
$276$		0			0
$277$	27.6712	−	27.6712i	0.0998959	−	0.0998959i	−0.655393	−	0.755288i	$-0.727497\pi$
$277$	27.6712	−	27.6712i	0.0998959	−	0.0998959i	0.755288	+	0.655393i	$0.227497\pi$
$278$		0			0
$279$		−	159.598i		−	0.572038i
$280$		0			0
$281$	183.408			0.652697			0.326348	−	0.945250i	$-0.394182\pi$
$281$	183.408			0.652697			0.326348	+	0.945250i	$0.394182\pi$
$282$		0			0
$283$	−333.158	−	333.158i	−1.17724	−	1.17724i	−0.980445	−	0.196793i	$-0.936947\pi$
$283$	−333.158	−	333.158i	−1.17724	−	1.17724i	−0.196793	−	0.980445i	$-0.563053\pi$
$284$		0			0
$285$	−32.2979	−	13.6122i	−0.113326	−	0.0477620i
$286$		0			0
$287$	−314.077	+	314.077i	−1.09434	+	1.09434i
$288$		0			0
$289$			56.8248i			0.196626i
$290$		0			0
$291$	−190.250			−0.653781
$292$		0			0
$293$	−185.884	−	185.884i	−0.634417	−	0.634417i	0.314756	−	0.949173i	$-0.398077\pi$
$293$	−185.884	−	185.884i	−0.634417	−	0.634417i	−0.949173	+	0.314756i	$0.898077\pi$
$294$		0			0
$295$	40.7266	−	16.5760i	0.138056	−	0.0561898i
$296$		0			0
$297$	62.4761	−	62.4761i	0.210357	−	0.210357i
$298$		0			0
$299$			0.462378i			0.00154642i
$300$		0			0
$301$	−607.843			−2.01941
$302$		0			0
$303$	60.7770	+	60.7770i	0.200584	+	0.200584i
$304$		0			0
$305$	199.535	+	490.251i	0.654214	+	1.60738i
$306$		0			0
$307$	−184.175	+	184.175i	−0.599920	+	0.599920i	−0.940291	−	0.340371i	$-0.889447\pi$
$307$	−184.175	+	184.175i	−0.599920	+	0.599920i	0.340371	+	0.940291i	$0.389447\pi$
$308$		0			0
$309$		−	46.0333i		−	0.148975i
$310$		0			0
$311$	191.522			0.615826			0.307913	−	0.951415i	$-0.400369\pi$
$311$	191.522			0.615826			0.307913	+	0.951415i	$0.400369\pi$
$312$		0			0
$313$	−257.541	−	257.541i	−0.822815	−	0.822815i	0.163696	−	0.986511i	$-0.447658\pi$
$313$	−257.541	−	257.541i	−0.822815	−	0.822815i	−0.986511	+	0.163696i	$0.947658\pi$
$314$		0			0
$315$	−49.6261	+	117.749i	−0.157543	+	0.373805i
$316$		0			0
$317$	162.518	−	162.518i	0.512674	−	0.512674i	−0.402671	−	0.915345i	$-0.631918\pi$
$317$	162.518	−	162.518i	0.512674	−	0.512674i	0.915345	+	0.402671i	$0.131918\pi$
$318$		0			0
$319$			925.771i			2.90210i
$320$		0			0
$321$	169.016			0.526529
$322$		0			0
$323$	−43.6054	−	43.6054i	−0.135001	−	0.135001i
$324$		0			0
$325$	−4.40440	−	0.0543296i	−0.0135520	−	0.000167168i
$326$		0			0
$327$	159.220	−	159.220i	0.486911	−	0.486911i
$328$		0			0
$329$		−	161.485i		−	0.490837i
$330$		0			0
$331$	49.0405			0.148159			0.0740793	−	0.997252i	$-0.476398\pi$
$331$	49.0405			0.148159			0.0740793	+	0.997252i	$0.476398\pi$
$332$		0			0
$333$	63.8079	+	63.8079i	0.191615	+	0.191615i
$334$		0			0
$335$	−305.337	−	128.686i	−0.911453	−	0.384139i
$336$		0			0
$337$	−17.6580	+	17.6580i	−0.0523977	+	0.0523977i	−0.732820	−	0.680422i	$-0.761796\pi$
$337$	−17.6580	+	17.6580i	−0.0523977	+	0.0523977i	0.680422	+	0.732820i	$0.261796\pi$
$338$		0			0
$339$			386.003i			1.13865i
$340$		0			0
$341$	−904.595			−2.65277
$342$		0			0
$343$	153.199	+	153.199i	0.446646	+	0.446646i
$344$		0			0
$345$	21.0506	−	8.56771i	0.0610161	−	0.0248339i
$346$		0			0
$347$	296.136	−	296.136i	0.853417	−	0.853417i	−0.137135	−	0.990552i	$-0.543789\pi$
$347$	296.136	−	296.136i	0.853417	−	0.853417i	0.990552	+	0.137135i	$0.0437894\pi$
$348$		0			0
$349$		−	217.733i		−	0.623877i	−0.950102	−	0.311939i	$-0.899022\pi$
$349$		−	217.733i		−	0.623877i	0.950102	−	0.311939i	$-0.100978\pi$
$350$		0			0
$351$	0.915507			0.00260828
$352$		0			0
$353$	70.0501	+	70.0501i	0.198442	+	0.198442i	0.799332	−	0.600890i	$-0.205187\pi$
$353$	70.0501	+	70.0501i	0.198442	+	0.198442i	−0.600890	+	0.799332i	$0.705187\pi$
$354$		0			0
$355$	−107.242	−	263.490i	−0.302090	−	0.742224i
$356$		0			0
$357$	−158.973	+	158.973i	−0.445301	+	0.445301i
$358$		0			0
$359$		−	265.093i		−	0.738422i	−0.929346	−	0.369211i	$-0.879628\pi$
$359$		−	265.093i		−	0.738422i	0.929346	−	0.369211i	$-0.120372\pi$
$360$		0			0
$361$	344.621			0.954628
$362$		0			0
$363$	−205.917	−	205.917i	−0.567263	−	0.567263i
$364$		0			0
$365$	144.807	−	343.586i	0.396732	−	0.941333i
$366$		0			0
$367$	473.377	−	473.377i	1.28986	−	1.28986i	0.354984	−	0.934872i	$-0.384486\pi$
$367$	473.377	−	473.377i	1.28986	−	1.28986i	0.934872	−	0.354984i	$-0.115514\pi$
$368$		0			0
$369$		−	156.424i		−	0.423914i
$370$		0			0
$371$	149.764			0.403675
$372$		0			0
$373$	201.623	+	201.623i	0.540544	+	0.540544i	0.923688	−	0.383144i	$-0.125159\pi$
$373$	201.623	+	201.623i	0.540544	+	0.540544i	−0.383144	+	0.923688i	$0.625159\pi$
$374$		0			0
$375$	79.1385	+	201.524i	0.211036	+	0.537398i
$376$		0			0
$377$	−6.78299	+	6.78299i	−0.0179920	+	0.0179920i
$378$		0			0
$379$			230.312i			0.607684i	0.952722	+	0.303842i	$0.0982695\pi$
$379$			230.312i			0.607684i	−0.952722	+	0.303842i	$0.901730\pi$
$380$		0			0
$381$	260.301			0.683206
$382$		0			0
$383$	−312.599	−	312.599i	−0.816185	−	0.816185i	0.169368	−	0.985553i	$-0.445827\pi$
$383$	−312.599	−	312.599i	−0.816185	−	0.816185i	−0.985553	+	0.169368i	$0.945827\pi$
$384$		0			0
$385$	667.393	+	281.278i	1.73349	+	0.730592i
$386$		0			0
$387$	151.366	−	151.366i	0.391127	−	0.391127i
$388$		0			0
$389$			555.109i			1.42702i	0.700647	+	0.713508i	$0.252895\pi$
$389$			555.109i			1.42702i	−0.700647	+	0.713508i	$0.747105\pi$
$390$		0			0
$391$	39.9876			0.102270
$392$		0			0
$393$	126.014	+	126.014i	0.320647	+	0.320647i
$394$		0			0
$395$	70.8188	−	28.8237i	0.179288	−	0.0729714i
$396$		0			0
$397$	221.888	−	221.888i	0.558911	−	0.558911i	−0.370086	−	0.928997i	$-0.620672\pi$
$397$	221.888	−	221.888i	0.558911	−	0.558911i	0.928997	+	0.370086i	$0.120672\pi$
$398$		0			0
$399$			59.7140i			0.149659i
$400$		0			0
$401$	−319.629			−0.797079			−0.398540	−	0.917151i	$-0.630483\pi$
$401$	−319.629			−0.797079			−0.398540	+	0.917151i	$0.630483\pi$
$402$		0			0
$403$	−6.62784	−	6.62784i	−0.0164463	−	0.0164463i
$404$		0			0
$405$	−16.9640	−	41.6800i	−0.0418865	−	0.102914i
$406$		0			0
$407$	361.659	−	361.659i	0.888598	−	0.888598i
$408$		0			0
$409$			40.1118i			0.0980730i	0.998797	+	0.0490365i	$0.0156151\pi$
$409$			40.1118i			0.0980730i	−0.998797	+	0.0490365i	$0.984385\pi$
$410$		0			0
$411$	207.491			0.504844
$412$		0			0
$413$	−52.9720	−	52.9720i	−0.128262	−	0.128262i
$414$		0			0
$415$	−126.852	+	300.984i	−0.305667	+	0.725262i
$416$		0			0
$417$	−298.899	+	298.899i	−0.716783	+	0.716783i
$418$		0			0
$419$			345.933i			0.825616i	0.910818	+	0.412808i	$0.135452\pi$
$419$			345.933i			0.825616i	−0.910818	+	0.412808i	$0.864548\pi$
$420$		0			0
$421$	−105.186			−0.249849			−0.124925	−	0.992166i	$-0.539869\pi$
$421$	−105.186			−0.249849			−0.124925	+	0.992166i	$0.539869\pi$
$422$		0			0
$423$	40.2134	+	40.2134i	0.0950672	+	0.0950672i
$424$		0			0
$425$	−4.69856	+	380.903i	−0.0110554	+	0.896243i
$426$		0			0
$427$	637.657	−	637.657i	1.49334	−	1.49334i
$428$		0			0
$429$		−	5.18904i		−	0.0120957i
$430$		0			0
$431$	147.504			0.342236			0.171118	−	0.985251i	$-0.445262\pi$
$431$	147.504			0.342236			0.171118	+	0.985251i	$0.445262\pi$
$432$		0			0
$433$	202.619	+	202.619i	0.467942	+	0.467942i	0.901247	−	0.433305i	$-0.142653\pi$
$433$	202.619	+	202.619i	0.467942	+	0.467942i	−0.433305	+	0.901247i	$0.642653\pi$
$434$		0			0
$435$	434.494	+	183.121i	0.998836	+	0.420967i
$436$		0			0
$437$	7.51017	−	7.51017i	0.0171857	−	0.0171857i
$438$		0			0
$439$		−	513.562i		−	1.16985i	−0.811089	−	0.584923i	$-0.801125\pi$
$439$		−	513.562i		−	1.16985i	0.811089	−	0.584923i	$-0.198875\pi$
$440$		0			0
$441$	70.7000			0.160317
$442$		0			0
$443$	−200.016	−	200.016i	−0.451503	−	0.451503i	0.444350	−	0.895853i	$-0.353435\pi$
$443$	−200.016	−	200.016i	−0.451503	−	0.451503i	−0.895853	+	0.444350i	$0.853435\pi$
$444$		0			0
$445$	−4.39278	+	1.78789i	−0.00987142	+	0.00401773i
$446$		0			0
$447$	270.374	−	270.374i	0.604863	−	0.604863i
$448$		0			0
$449$		−	387.201i		−	0.862363i	−0.902265	−	0.431182i	$-0.858097\pi$
$449$		−	387.201i		−	0.862363i	0.902265	−	0.431182i	$-0.141903\pi$
$450$		0			0
$451$	−886.603			−1.96586
$452$		0			0
$453$	−266.975	−	266.975i	−0.589349	−	0.589349i
$454$		0			0
$455$	2.82901	+	6.95078i	0.00621761	+	0.0152764i
$456$		0			0
$457$	−124.992	+	124.992i	−0.273505	+	0.273505i	−0.830509	−	0.557005i	$-0.811951\pi$
$457$	−124.992	+	124.992i	−0.273505	+	0.273505i	0.557005	+	0.830509i	$0.311951\pi$
$458$		0			0
$459$		−	79.1753i		−	0.172495i
$460$		0			0
$461$	−420.024			−0.911114			−0.455557	−	0.890207i	$-0.650560\pi$
$461$	−420.024			−0.911114			−0.455557	+	0.890207i	$0.650560\pi$
$462$		0			0
$463$	228.184	+	228.184i	0.492839	+	0.492839i	0.909200	−	0.416361i	$-0.136695\pi$
$463$	228.184	+	228.184i	0.492839	+	0.492839i	−0.416361	+	0.909200i	$0.636695\pi$
$464$		0			0
$465$	−178.932	+	424.555i	−0.384800	+	0.913022i
$466$		0			0
$467$	17.4129	−	17.4129i	0.0372867	−	0.0372867i	−0.688218	−	0.725504i	$-0.741607\pi$
$467$	17.4129	−	17.4129i	0.0372867	−	0.0372867i	0.725504	+	0.688218i	$0.241607\pi$
$468$		0			0
$469$			564.522i			1.20367i
$470$		0			0
$471$	453.261			0.962338
$472$		0			0
$473$	−857.935	−	857.935i	−1.81382	−	1.81382i
$474$		0			0
$475$	70.6559	+	72.4208i	0.148749	+	0.152465i
$476$		0			0
$477$	−37.2944	+	37.2944i	−0.0781854	+	0.0781854i
$478$		0			0
$479$		−	319.260i		−	0.666514i	−0.942836	−	0.333257i	$-0.891852\pi$
$479$		−	319.260i		−	0.666514i	0.942836	−	0.333257i	$-0.108148\pi$
$480$		0			0
$481$	5.29966			0.0110180
$482$		0			0
$483$	−27.3799	−	27.3799i	−0.0566872	−	0.0566872i
$484$		0			0
$485$	506.094	+	213.297i	1.04349	+	0.439788i
$486$		0			0
$487$	−276.414	+	276.414i	−0.567586	+	0.567586i	−0.931452	−	0.363865i	$-0.881457\pi$
$487$	−276.414	+	276.414i	−0.567586	+	0.567586i	0.363865	+	0.931452i	$0.381457\pi$
$488$		0			0
$489$			38.0315i			0.0777740i
$490$		0			0
$491$	42.5613			0.0866829			0.0433414	−	0.999060i	$-0.486200\pi$
$491$	42.5613			0.0866829			0.0433414	+	0.999060i	$0.486200\pi$
$492$		0			0
$493$	586.610	+	586.610i	1.18988	+	1.18988i
$494$		0			0
$495$	−236.240	+	96.1511i	−0.477252	+	0.194245i
$496$		0			0
$497$	−342.714	+	342.714i	−0.689565	+	0.689565i
$498$		0			0
$499$			669.280i			1.34124i	0.741800	+	0.670621i	$0.233972\pi$
$499$			669.280i			1.34124i	−0.741800	+	0.670621i	$0.766028\pi$
$500$		0			0
$501$	52.7739			0.105337
$502$		0			0
$503$	−3.01493	−	3.01493i	−0.00599389	−	0.00599389i	0.704103	−	0.710097i	$-0.251349\pi$
$503$	−3.01493	−	3.01493i	−0.00599389	−	0.00599389i	−0.710097	+	0.704103i	$0.751349\pi$
$504$		0			0
$505$	−93.5363	−	229.815i	−0.185220	−	0.455080i
$506$		0			0
$507$	−206.944	+	206.944i	−0.408173	+	0.408173i
$508$		0			0
$509$		−	506.628i		−	0.995339i	−0.867367	−	0.497670i	$-0.834189\pi$
$509$		−	506.628i		−	0.995339i	0.867367	−	0.497670i	$-0.165811\pi$
$510$		0			0
$511$	−635.241			−1.24313
$512$		0			0
$513$	−14.8701	−	14.8701i	−0.0289865	−	0.0289865i
$514$		0			0
$515$	−51.6098	+	122.455i	−0.100213	+	0.237778i
$516$		0			0
$517$	227.927	−	227.927i	0.440865	−	0.440865i
$518$		0			0
$519$		−	212.079i		−	0.408630i
$520$		0			0
$521$	399.589			0.766966			0.383483	−	0.923548i	$-0.374725\pi$
$521$	399.589			0.766966			0.383483	+	0.923548i	$0.374725\pi$
$522$		0			0
$523$	−404.156	−	404.156i	−0.772764	−	0.772764i	0.205824	−	0.978589i	$-0.434012\pi$
$523$	−404.156	−	404.156i	−0.772764	−	0.772764i	−0.978589	+	0.205824i	$0.934012\pi$
$524$		0			0
$525$	264.025	−	257.591i	0.502905	−	0.490650i
$526$		0			0
$527$	−573.192	+	573.192i	−1.08765	+	1.08765i
$528$		0			0
$529$		−	522.113i		−	0.986981i
$530$		0			0
$531$	26.3824			0.0496844
$532$		0			0
$533$	−6.49602	−	6.49602i	−0.0121877	−	0.0121877i
$534$		0			0
$535$	−449.607	−	189.490i	−0.840386	−	0.354187i
$536$		0			0
$537$	−55.6826	+	55.6826i	−0.103692	+	0.103692i
$538$		0			0
$539$		−	400.723i		−	0.743457i
$540$		0			0
$541$	−766.639			−1.41708			−0.708538	−	0.705672i	$-0.750645\pi$
$541$	−766.639			−1.41708			−0.708538	+	0.705672i	$0.750645\pi$
$542$		0			0
$543$	−16.5330	−	16.5330i	−0.0304474	−	0.0304474i
$544$		0			0
$545$	−602.056	+	245.041i	−1.10469	+	0.449616i
$546$		0			0
$547$	−192.460	+	192.460i	−0.351846	+	0.351846i	−0.860796	−	0.508950i	$-0.830034\pi$
$547$	−192.460	+	192.460i	−0.351846	+	0.351846i	0.508950	+	0.860796i	$0.330034\pi$
$548$		0			0
$549$			317.581i			0.578472i
$550$		0			0
$551$	220.345			0.399901
$552$		0			0
$553$	−92.1121	−	92.1121i	−0.166568	−	0.166568i
$554$		0			0
$555$	−98.2008	−	241.276i	−0.176938	−	0.434731i
$556$		0			0
$557$	−162.407	+	162.407i	−0.291574	+	0.291574i	−0.837702	−	0.546128i	$-0.816101\pi$
$557$	−162.407	+	162.407i	−0.291574	+	0.291574i	0.546128	+	0.837702i	$0.316101\pi$
$558$		0			0
$559$		−	12.5719i		−	0.0224901i
$560$		0			0
$561$	−448.761			−0.799931
$562$		0			0
$563$	687.682	+	687.682i	1.22146	+	1.22146i	0.967113	+	0.254346i	$0.0818603\pi$
$563$	687.682	+	687.682i	1.22146	+	1.22146i	0.254346	+	0.967113i	$0.418140\pi$
$564$		0			0
$565$	432.763	−	1026.82i	0.765953	−	1.81739i
$566$		0			0
$567$	−54.2121	+	54.2121i	−0.0956121	+	0.0956121i
$568$		0			0
$569$			452.621i			0.795468i	0.917501	+	0.397734i	$0.130203\pi$
$569$			452.621i			0.795468i	−0.917501	+	0.397734i	$0.869797\pi$
$570$		0			0
$571$	8.52498			0.0149299			0.00746496	−	0.999972i	$-0.497624\pi$
$571$	8.52498			0.0149299			0.00746496	+	0.999972i	$0.497624\pi$
$572$		0			0
$573$	−82.8772	−	82.8772i	−0.144637	−	0.144637i
$574$		0			0
$575$	−65.6032	−	0.809236i	−0.114092	−	0.00140737i
$576$		0			0
$577$	271.812	−	271.812i	0.471078	−	0.471078i	−0.431186	−	0.902263i	$-0.641905\pi$
$577$	271.812	−	271.812i	0.471078	−	0.471078i	0.902263	+	0.431186i	$0.141905\pi$
$578$		0			0
$579$		−	78.3755i		−	0.135364i
$580$		0			0
$581$	556.474			0.957787
$582$		0			0
$583$	211.383	+	211.383i	0.362577	+	0.362577i
$584$		0			0
$585$	−2.43538	−	1.02641i	−0.00416305	−	0.00175455i
$586$		0			0
$587$	160.042	−	160.042i	0.272644	−	0.272644i	−0.557519	−	0.830164i	$-0.688247\pi$
$587$	160.042	−	160.042i	0.272644	−	0.272644i	0.830164	+	0.557519i	$0.188247\pi$
$588$		0			0
$589$			215.305i			0.365544i
$590$		0			0
$591$	−298.975			−0.505881
$592$		0			0
$593$	−25.3238	−	25.3238i	−0.0427045	−	0.0427045i	0.685432	−	0.728137i	$-0.259613\pi$
$593$	−25.3238	−	25.3238i	−0.0427045	−	0.0427045i	−0.728137	+	0.685432i	$0.759613\pi$
$594$		0			0
$595$	601.121	−	244.660i	1.01029	−	0.411193i
$596$		0			0
$597$	−5.34469	+	5.34469i	−0.00895257	+	0.00895257i
$598$		0			0
$599$			1017.30i			1.69832i	0.528132	+	0.849162i	$0.322893\pi$
$599$			1017.30i			1.69832i	−0.528132	+	0.849162i	$0.677107\pi$
$600$		0			0
$601$	−322.485			−0.536580			−0.268290	−	0.963338i	$-0.586459\pi$
$601$	−322.485			−0.536580			−0.268290	+	0.963338i	$0.586459\pi$
$602$		0			0
$603$	−140.579	−	140.579i	−0.233132	−	0.233132i
$604$		0			0
$605$	316.907	+	778.629i	0.523813	+	1.28699i
$606$		0			0
$607$	−151.189	+	151.189i	−0.249076	+	0.249076i	−0.820591	−	0.571515i	$-0.806356\pi$
$607$	−151.189	+	151.189i	−0.249076	+	0.249076i	0.571515	+	0.820591i	$0.306356\pi$
$608$		0			0
$609$		−	803.315i		−	1.31907i
$610$		0			0
$611$	3.33998			0.00546642
$612$		0			0
$613$	397.727	+	397.727i	0.648821	+	0.648821i	0.952708	−	0.303887i	$-0.0982847\pi$
$613$	397.727	+	397.727i	0.648821	+	0.648821i	−0.303887	+	0.952708i	$0.598285\pi$
$614$		0			0
$615$	−175.373	+	416.111i	−0.285160	+	0.676604i
$616$		0			0
$617$	657.460	−	657.460i	1.06557	−	1.06557i	0.0678812	−	0.997693i	$-0.478376\pi$
$617$	657.460	−	657.460i	1.06557	−	1.06557i	0.997693	−	0.0678812i	$-0.0216239\pi$
$618$		0			0
$619$			984.228i			1.59003i	0.606590	+	0.795015i	$0.292537\pi$
$619$			984.228i			1.59003i	−0.606590	+	0.795015i	$0.707463\pi$
$620$		0			0
$621$	13.6364			0.0219588
$622$		0			0
$623$	5.71358	+	5.71358i	0.00917107	+	0.00917107i
$624$		0			0
$625$	15.4168	−	624.810i	0.0246669	−	0.999696i
$626$		0			0
$627$	−84.2829	+	84.2829i	−0.134422	+	0.134422i
$628$		0			0
$629$		−	458.328i		−	0.728661i
$630$		0			0
$631$	−242.533			−0.384362			−0.192181	−	0.981359i	$-0.561556\pi$
$631$	−242.533			−0.384362			−0.192181	+	0.981359i	$0.561556\pi$
$632$		0			0
$633$	−224.246	−	224.246i	−0.354260	−	0.354260i
$634$		0			0
$635$	−692.440	−	291.834i	−1.09046	−	0.459581i
$636$		0			0
$637$	2.93604	−	2.93604i	0.00460917	−	0.00460917i
$638$		0			0
$639$		−	170.687i		−	0.267115i
$640$		0			0
$641$	761.727			1.18834			0.594171	−	0.804339i	$-0.297480\pi$
$641$	761.727			1.18834			0.594171	+	0.804339i	$0.297480\pi$
$642$		0			0
$643$	11.3113	+	11.3113i	0.0175914	+	0.0175914i	0.715848	−	0.698256i	$-0.246040\pi$
$643$	11.3113	+	11.3113i	0.0175914	+	0.0175914i	−0.698256	+	0.715848i	$0.746040\pi$
$644$		0			0
$645$	−572.359	+	232.954i	−0.887379	+	0.361169i
$646$		0			0
$647$	−290.292	+	290.292i	−0.448674	+	0.448674i	−0.894914	−	0.446240i	$-0.852763\pi$
$647$	−290.292	+	290.292i	−0.448674	+	0.448674i	0.446240	+	0.894914i	$0.352763\pi$
$648$		0			0
$649$		−	149.534i		−	0.230407i
$650$		0			0
$651$	784.940			1.20575
$652$		0			0
$653$	791.306	+	791.306i	1.21180	+	1.21180i	0.970434	+	0.241368i	$0.0775961\pi$
$653$	791.306	+	791.306i	1.21180	+	1.21180i	0.241368	+	0.970434i	$0.422404\pi$
$654$		0			0
$655$	−193.937	−	476.496i	−0.296087	−	0.727474i
$656$		0			0
$657$	158.189	−	158.189i	0.240775	−	0.240775i
$658$		0			0
$659$		−	1153.66i		−	1.75062i	−0.483559	−	0.875312i	$-0.660656\pi$
$659$		−	1153.66i		−	1.75062i	0.483559	−	0.875312i	$-0.339344\pi$
$660$		0			0
$661$	1250.76			1.89222			0.946111	−	0.323842i	$-0.104975\pi$
$661$	1250.76			1.89222			0.946111	+	0.323842i	$0.104975\pi$
$662$		0			0
$663$	−3.28801	−	3.28801i	−0.00495929	−	0.00495929i
$664$		0			0
$665$	66.9477	−	158.848i	0.100673	−	0.238869i
$666$		0			0
$667$	−101.032	+	101.032i	−0.151472	+	0.151472i
$668$		0			0
$669$			12.3445i			0.0184522i
$670$		0			0
$671$	1800.03			2.68261
$672$		0			0
$673$	−320.198	−	320.198i	−0.475778	−	0.475778i	0.428001	−	0.903778i	$-0.359218\pi$
$673$	−320.198	−	320.198i	−0.475778	−	0.475778i	−0.903778	+	0.428001i	$0.859218\pi$
$674$		0			0
$675$	−1.60228	+	129.894i	−0.00237375	+	0.192435i
$676$		0			0
$677$	105.922	−	105.922i	0.156457	−	0.156457i	−0.624538	−	0.780995i	$-0.714713\pi$
$677$	105.922	−	105.922i	0.156457	−	0.156457i	0.780995	+	0.624538i	$0.214713\pi$
$678$		0			0
$679$		−	935.692i		−	1.37804i
$680$		0			0
$681$	554.749			0.814610
$682$		0			0
$683$	467.606	+	467.606i	0.684636	+	0.684636i	0.961041	−	0.276405i	$-0.0891432\pi$
$683$	467.606	+	467.606i	0.684636	+	0.684636i	−0.276405	+	0.961041i	$0.589143\pi$
$684$		0			0
$685$	−551.957	−	232.626i	−0.805776	−	0.339601i
$686$		0			0
$687$	−339.152	+	339.152i	−0.493671	+	0.493671i
$688$		0			0
$689$			3.09754i			0.00449571i
$690$		0			0
$691$	47.2980			0.0684487			0.0342243	−	0.999414i	$-0.489104\pi$
$691$	47.2980			0.0684487			0.0342243	+	0.999414i	$0.489104\pi$
$692$		0			0
$693$	307.271	+	307.271i	0.443392	+	0.443392i
$694$		0			0
$695$	1130.22	−	460.007i	1.62622	−	0.661881i
$696$		0			0
$697$	−561.792	+	561.792i	−0.806014	+	0.806014i
$698$		0			0
$699$		−	485.260i		−	0.694220i
$700$		0			0
$701$	444.721			0.634409			0.317204	−	0.948357i	$-0.397256\pi$
$701$	444.721			0.634409			0.317204	+	0.948357i	$0.397256\pi$
$702$		0			0
$703$	−86.0796	−	86.0796i	−0.122446	−	0.122446i
$704$		0			0
$705$	−61.8887	−	152.058i	−0.0877854	−	0.215686i
$706$		0			0
$707$	−298.915	+	298.915i	−0.422793	+	0.422793i
$708$		0			0
$709$			996.549i			1.40557i	0.711403	+	0.702785i	$0.248060\pi$
$709$			996.549i			1.40557i	−0.711403	+	0.702785i	$0.751940\pi$
$710$		0			0
$711$	45.8759			0.0645231
$712$		0			0
$713$	−98.7212	−	98.7212i	−0.138459	−	0.138459i
$714$		0			0
$715$	−5.81764	+	13.8036i	−0.00813655	+	0.0193057i
$716$		0			0
$717$	281.916	−	281.916i	0.393188	−	0.393188i
$718$		0			0
$719$			319.778i			0.444753i	0.974961	+	0.222377i	$0.0713814\pi$
$719$			319.778i			0.444753i	−0.974961	+	0.222377i	$0.928619\pi$
$720$		0			0
$721$	226.402			0.314011
$722$		0			0
$723$	−347.266	−	347.266i	−0.480313	−	0.480313i
$724$		0			0
$725$	−950.513	−	974.256i	−1.31105	−	1.34380i
$726$		0			0
$727$	−116.716	+	116.716i	−0.160545	+	0.160545i	−0.782808	−	0.622263i	$-0.786213\pi$
$727$	−116.716	+	116.716i	−0.160545	+	0.160545i	0.622263	+	0.782808i	$0.286213\pi$
$728$		0			0
$729$		−	27.0000i		−	0.0370370i
$730$		0			0
$731$	−1087.25			−1.48735
$732$		0			0
$733$	−121.699	−	121.699i	−0.166028	−	0.166028i	0.619203	−	0.785231i	$-0.287456\pi$
$733$	−121.699	−	121.699i	−0.166028	−	0.166028i	−0.785231	+	0.619203i	$0.787456\pi$
$734$		0			0
$735$	−188.072	−	79.2645i	−0.255881	−	0.107843i
$736$		0			0
$737$	−796.791	+	796.791i	−1.08113	+	1.08113i
$738$		0			0
$739$		−	498.476i		−	0.674528i	−0.941410	−	0.337264i	$-0.890499\pi$
$739$		−	498.476i		−	0.674528i	0.941410	−	0.337264i	$-0.109501\pi$
$740$		0			0
$741$	−1.23506			−0.00166674
$742$		0			0
$743$	13.9317	+	13.9317i	0.0187507	+	0.0187507i	0.716420	−	0.697669i	$-0.245779\pi$
$743$	13.9317	+	13.9317i	0.0187507	+	0.0187507i	−0.697669	+	0.716420i	$0.745779\pi$
$744$		0			0
$745$	−1022.36	+	416.108i	−1.37230	+	0.558534i
$746$		0			0
$747$	−138.574	+	138.574i	−0.185508	+	0.185508i
$748$		0			0
$749$			831.257i			1.10982i
$750$		0			0
$751$	−148.692			−0.197992			−0.0989962	−	0.995088i	$-0.531563\pi$
$751$	−148.692			−0.197992			−0.0989962	+	0.995088i	$0.531563\pi$
$752$		0			0
$753$	−248.294	−	248.294i	−0.329740	−	0.329740i
$754$		0			0
$755$	410.877	+	1009.51i	0.544208	+	1.33710i
$756$		0			0
$757$	243.978	−	243.978i	0.322296	−	0.322296i	−0.527352	−	0.849647i	$-0.676815\pi$
$757$	243.978	−	243.978i	0.322296	−	0.322296i	0.849647	+	0.527352i	$0.176815\pi$
$758$		0			0
$759$		−	77.2903i		−	0.101832i
$760$		0			0
$761$	838.059			1.10126			0.550630	−	0.834749i	$-0.314387\pi$
$761$	838.059			1.10126			0.550630	+	0.834749i	$0.314387\pi$
$762$		0			0
$763$	783.079	+	783.079i	1.02632	+	1.02632i
$764$		0			0
$765$	−88.7665	+	210.618i	−0.116035	+	0.275318i
$766$		0			0
$767$	1.09561	−	1.09561i	0.00142844	−	0.00142844i
$768$		0			0
$769$		−	48.7943i		−	0.0634516i	−0.999497	−	0.0317258i	$-0.989900\pi$
$769$		−	48.7943i		−	0.0634516i	0.999497	−	0.0317258i	$-0.0101003\pi$
$770$		0			0
$771$	−495.167			−0.642240
$772$		0			0
$773$	349.857	+	349.857i	0.452596	+	0.452596i	0.896215	−	0.443619i	$-0.146306\pi$
$773$	349.857	+	349.857i	0.452596	+	0.452596i	−0.443619	+	0.896215i	$0.646306\pi$
$774$		0			0
$775$	951.971	−	928.772i	1.22835	−	1.19842i
$776$		0			0
$777$	−313.821	+	313.821i	−0.403888	+	0.403888i
$778$		0			0
$779$			211.023i			0.270889i
$780$		0			0
$781$	−967.442			−1.23872
$782$		0			0
$783$	200.043	+	200.043i	0.255483	+	0.255483i
$784$		0			0
$785$	−1205.74	−	508.169i	−1.53598	−	0.647349i
$786$		0			0
$787$	−504.294	+	504.294i	−0.640780	+	0.640780i	−0.950747	−	0.309967i	$-0.899682\pi$
$787$	−504.294	+	504.294i	−0.640780	+	0.640780i	0.309967	+	0.950747i	$0.399682\pi$
$788$		0			0
$789$			84.2367i			0.106764i
$790$		0			0
$791$	−1898.45			−2.40006
$792$		0			0
$793$	13.1886	+	13.1886i	0.0166313	+	0.0166313i
$794$		0			0
$795$	141.021	−	57.3964i	0.177385	−	0.0721967i
$796$		0			0
$797$	−275.451	+	275.451i	−0.345610	+	0.345610i	−0.858471	−	0.512862i	$-0.828585\pi$
$797$	−275.451	+	275.451i	−0.345610	+	0.345610i	0.512862	+	0.858471i	$0.328585\pi$
$798$		0			0
$799$		−	288.850i		−	0.361514i
$800$		0			0
$801$	−2.84561			−0.00355258
$802$		0			0
$803$	−896.606	−	896.606i	−1.11657	−	1.11657i
$804$		0			0
$805$	42.1379	+	103.531i	0.0523452	+	0.128610i
$806$		0			0
$807$	−39.8619	+	39.8619i	−0.0493951	+	0.0493951i
$808$		0			0
$809$		−	472.171i		−	0.583648i	−0.956472	−	0.291824i	$-0.905738\pi$
$809$		−	472.171i		−	0.583648i	0.956472	−	0.291824i	$-0.0942621\pi$
$810$		0			0
$811$	1383.85			1.70636			0.853178	−	0.521620i	$-0.174672\pi$
$811$	1383.85			1.70636			0.853178	+	0.521620i	$0.174672\pi$
$812$		0			0
$813$	112.614	+	112.614i	0.138517	+	0.138517i
$814$		0			0
$815$	42.6386	−	101.169i	0.0523173	−	0.124134i
$816$		0			0
$817$	−204.200	+	204.200i	−0.249938	+	0.249938i
$818$		0			0
$819$			4.50266i			0.00549776i
$820$		0			0
$821$	−280.480			−0.341632			−0.170816	−	0.985303i	$-0.554640\pi$
$821$	−280.480			−0.341632			−0.170816	+	0.985303i	$0.554640\pi$
$822$		0			0
$823$	256.396	+	256.396i	0.311539	+	0.311539i	0.845505	−	0.533967i	$-0.179299\pi$
$823$	256.396	+	256.396i	0.311539	+	0.311539i	−0.533967	+	0.845505i	$0.679299\pi$
$824$		0			0
$825$	736.231	+	9.08164i	0.892402	+	0.0110081i
$826$		0			0
$827$	325.679	−	325.679i	0.393808	−	0.393808i	−0.482234	−	0.876042i	$-0.660175\pi$
$827$	325.679	−	325.679i	0.393808	−	0.393808i	0.876042	+	0.482234i	$0.160175\pi$
$828$		0			0
$829$			5.87954i			0.00709232i	0.999994	+	0.00354616i	$0.00112878\pi$
$829$			5.87954i			0.00709232i	−0.999994	+	0.00354616i	$0.998871\pi$
$830$		0			0
$831$	−67.7803			−0.0815647
$832$		0			0
$833$	−253.916	−	253.916i	−0.304822	−	0.304822i
$834$		0			0
$835$	−140.386	−	59.1669i	−0.168127	−	0.0708585i
$836$		0			0
$837$	−195.467	+	195.467i	−0.233533	+	0.233533i
$838$		0			0
$839$		−	141.023i		−	0.168085i	−0.996462	−	0.0840424i	$-0.973217\pi$
$839$		−	141.023i		−	0.168085i	0.996462	−	0.0840424i	$-0.0267831\pi$
$840$		0			0
$841$	−2123.24			−2.52466
$842$		0			0
$843$	−224.628	−	224.628i	−0.266462	−	0.266462i
$844$		0			0
$845$	782.514	−	318.488i	0.926052	−	0.376909i
$846$		0			0
$847$	1012.74	−	1012.74i	1.19568	−	1.19568i
$848$		0			0
$849$			816.068i			0.961211i
$850$		0			0
$851$	78.9380			0.0927591
$852$		0			0
$853$	−322.940	−	322.940i	−0.378593	−	0.378593i	0.492002	−	0.870594i	$-0.336265\pi$
$853$	−322.940	−	322.940i	−0.378593	−	0.378593i	−0.870594	+	0.492002i	$0.836265\pi$
$854$		0			0
$855$	22.8852	+	56.2281i	0.0267663	+	0.0657639i
$856$		0			0
$857$	277.382	−	277.382i	0.323667	−	0.323667i	−0.526505	−	0.850172i	$-0.676498\pi$
$857$	277.382	−	277.382i	0.323667	−	0.323667i	0.850172	+	0.526505i	$0.176498\pi$
$858$		0			0
$859$		−	530.257i		−	0.617295i	−0.951176	−	0.308648i	$-0.900124\pi$
$859$		−	530.257i		−	0.617295i	0.951176	−	0.308648i	$-0.0998764\pi$
$860$		0			0
$861$	769.328			0.893529
$862$		0			0
$863$	−725.484	−	725.484i	−0.840653	−	0.840653i	0.148291	−	0.988944i	$-0.452623\pi$
$863$	−725.484	−	725.484i	−0.840653	−	0.840653i	−0.988944	+	0.148291i	$0.952623\pi$
$864$		0			0
$865$	−237.770	+	564.161i	−0.274878	+	0.652209i
$866$		0			0
$867$	69.5959	−	69.5959i	0.0802721	−	0.0802721i
$868$		0			0
$869$		−	260.022i		−	0.299220i
$870$		0			0
$871$	−11.6760			−0.0134052
$872$		0			0
$873$	233.008	+	233.008i	0.266905	+	0.266905i
$874$		0			0
$875$	−991.141	+	389.221i	−1.13273	+	0.444824i
$876$		0			0
$877$	114.761	−	114.761i	0.130856	−	0.130856i	−0.638645	−	0.769501i	$-0.720505\pi$
$877$	114.761	−	114.761i	0.130856	−	0.130856i	0.769501	+	0.638645i	$0.220505\pi$
$878$		0			0
$879$			455.321i			0.517999i
$880$		0			0
$881$	−582.431			−0.661102			−0.330551	−	0.943788i	$-0.607235\pi$
$881$	−582.431			−0.661102			−0.330551	+	0.943788i	$0.607235\pi$
$882$		0			0
$883$	1140.67	+	1140.67i	1.29182	+	1.29182i	0.933663	+	0.358153i	$0.116594\pi$
$883$	1140.67	+	1140.67i	1.29182	+	1.29182i	0.358153	+	0.933663i	$0.383406\pi$
$884$		0			0
$885$	−70.1810	−	29.5783i	−0.0793006	−	0.0334218i
$886$		0			0
$887$	−910.472	+	910.472i	−1.02646	+	1.02646i	−0.0268221	+	0.999640i	$0.508539\pi$
$887$	−910.472	+	910.472i	−1.02646	+	1.02646i	−0.999640	+	0.0268221i	$0.991461\pi$
$888$		0			0
$889$			1280.22i			1.44007i
$890$		0			0
$891$	−153.034			−0.171756
$892$		0			0
$893$	−54.2496	−	54.2496i	−0.0607498	−	0.0607498i
$894$		0			0
$895$	210.552	−	85.6960i	0.235253	−	0.0957497i
$896$		0			0
$897$	0.566296	−	0.566296i	0.000631322	−	0.000631322i
$898$		0			0
$899$		−	2896.44i		−	3.22184i
$900$		0			0
$901$	267.883			0.297318
$902$		0			0
$903$	744.453	+	744.453i	0.824421	+	0.824421i
$904$		0			0
$905$	25.4443	+	62.5158i	0.0281153	+	0.0690783i
$906$		0			0
$907$	−928.527	+	928.527i	−1.02373	+	1.02373i	−0.0240232	+	0.999711i	$0.507648\pi$
$907$	−928.527	+	928.527i	−1.02373	+	1.02373i	−0.999711	+	0.0240232i	$0.992352\pi$
$908$		0			0
$909$		−	148.873i		−	0.163776i
$910$		0			0
$911$	751.939			0.825400			0.412700	−	0.910867i	$-0.364586\pi$
$911$	751.939			0.825400			0.412700	+	0.910867i	$0.364586\pi$
$912$		0			0
$913$	785.431	+	785.431i	0.860275	+	0.860275i
$914$		0			0
$915$	356.053	−	844.813i	0.389129	−	0.923292i
$916$		0			0
$917$	−619.766	+	619.766i	−0.675862	+	0.675862i
$918$		0			0
$919$		−	612.491i		−	0.666476i	−0.942843	−	0.333238i	$-0.891859\pi$
$919$		−	612.491i		−	0.666476i	0.942843	−	0.333238i	$-0.108141\pi$
$920$		0			0
$921$	451.136			0.489833
$922$		0			0
$923$	−7.08831	−	7.08831i	−0.00767965	−	0.00767965i
$924$		0			0
$925$	−9.27524	+	751.926i	−0.0100273	+	0.812893i
$926$		0			0
$927$	−56.3791	+	56.3791i	−0.0608189	+	0.0608189i
$928$		0			0
$929$			487.299i			0.524541i	0.964994	+	0.262271i	$0.0844713\pi$
$929$			487.299i			0.524541i	−0.964994	+	0.262271i	$0.915529\pi$
$930$		0			0
$931$	−95.3773			−0.102446
$932$		0			0
$933$	−234.565	−	234.565i	−0.251410	−	0.251410i
$934$		0			0
$935$	1193.77	+	503.124i	1.27676	+	0.538100i
$936$		0			0
$937$	943.521	−	943.521i	1.00696	−	1.00696i	0.00698356	−	0.999976i	$-0.497777\pi$
$937$	943.521	−	943.521i	1.00696	−	1.00696i	0.999976	−	0.00698356i	$-0.00222296\pi$
$938$		0			0
$939$			630.844i			0.671826i
$940$		0			0
$941$	243.515			0.258784			0.129392	−	0.991594i	$-0.458698\pi$
$941$	243.515			0.258784			0.129392	+	0.991594i	$0.458698\pi$
$942$		0			0
$943$	−96.7577	−	96.7577i	−0.102606	−	0.102606i
$944$		0			0
$945$	204.991	−	83.4328i	0.216922	−	0.0882887i
$946$		0			0
$947$	792.978	−	792.978i	0.837358	−	0.837358i	−0.151153	−	0.988510i	$-0.548299\pi$
$947$	792.978	−	792.978i	0.837358	−	0.837358i	0.988510	+	0.151153i	$0.0482985\pi$
$948$		0			0
$949$		−	13.1386i		−	0.0138447i
$950$		0			0
$951$	−398.085			−0.418596
$952$		0			0
$953$	−77.6634	−	77.6634i	−0.0814936	−	0.0814936i	0.665185	−	0.746679i	$-0.268353\pi$
$953$	−77.6634	−	77.6634i	−0.0814936	−	0.0814936i	−0.746679	+	0.665185i	$0.768353\pi$
$954$		0			0
$955$	127.549	+	313.383i	0.133559	+	0.328149i
$956$		0			0
$957$	1133.83	−	1133.83i	1.18478	−	1.18478i
$958$		0			0
$959$			1020.49i			1.06412i
$960$		0			0
$961$	1869.19			1.94504
$962$		0			0
$963$	−207.001	−	207.001i	−0.214954	−	0.214954i
$964$		0			0
$965$	−87.8699	+	208.490i	−0.0910569	+	0.216052i
$966$		0			0
$967$	294.078	−	294.078i	0.304113	−	0.304113i	−0.538507	−	0.842621i	$-0.681012\pi$
$967$	294.078	−	294.078i	0.304113	−	0.304113i	0.842621	+	0.538507i	$0.181012\pi$
$968$		0			0
$969$			106.811i			0.110228i
$970$		0			0
$971$	−322.263			−0.331888			−0.165944	−	0.986135i	$-0.553067\pi$
$971$	−322.263			−0.331888			−0.165944	+	0.986135i	$0.553067\pi$
$972$		0			0
$973$	−1470.05	−	1470.05i	−1.51084	−	1.51084i
$974$		0			0
$975$	5.32773	+	5.46081i	0.00546433	+	0.00560083i
$976$		0			0
$977$	739.522	−	739.522i	0.756932	−	0.756932i	−0.218831	−	0.975763i	$-0.570224\pi$
$977$	739.522	−	739.522i	0.756932	−	0.756932i	0.975763	+	0.218831i	$0.0702243\pi$
$978$		0			0
$979$			16.1288i			0.0164747i
$980$		0			0
$981$	−390.008			−0.397561
$982$		0			0
$983$	−767.218	−	767.218i	−0.780486	−	0.780486i	0.199427	−	0.979913i	$-0.436092\pi$
$983$	−767.218	−	767.218i	−0.780486	−	0.780486i	−0.979913	+	0.199427i	$0.936092\pi$
$984$		0			0
$985$	795.319	+	335.193i	0.807430	+	0.340298i
$986$		0			0
$987$	−197.778	+	197.778i	−0.200383	+	0.200383i
$988$		0			0
$989$		−	187.258i		−	0.189341i
$990$		0			0
$991$	908.418			0.916668			0.458334	−	0.888780i	$-0.348446\pi$
$991$	908.418			0.916668			0.458334	+	0.888780i	$0.348446\pi$
$992$		0			0
$993$	−60.0621	−	60.0621i	−0.0604855	−	0.0604855i
$994$		0			0
$995$	20.2098	−	8.22551i	0.0203113	−	0.00826685i
$996$		0			0
$997$	−397.062	+	397.062i	−0.398257	+	0.398257i	−0.877618	−	0.479361i	$-0.840868\pi$
$997$	−397.062	+	397.062i	−0.398257	+	0.398257i	0.479361	+	0.877618i	$0.340868\pi$
$998$		0			0
$999$		−	156.297i		−	0.156453i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	120.3.u.b.73.2	✓	8
3.2	odd	2		360.3.v.f.73.1		8
4.3	odd	2		240.3.bg.e.193.4		8
5.2	odd	4	inner	120.3.u.b.97.2	yes	8
5.3	odd	4		600.3.u.h.457.3		8
5.4	even	2		600.3.u.h.193.3		8
8.3	odd	2		960.3.bg.k.193.1		8
8.5	even	2		960.3.bg.l.193.3		8
12.11	even	2		720.3.bh.o.433.1		8
15.2	even	4		360.3.v.f.217.1		8
15.8	even	4		1800.3.v.t.1657.2		8
15.14	odd	2		1800.3.v.t.793.2		8
20.3	even	4		1200.3.bg.q.1057.2		8
20.7	even	4		240.3.bg.e.97.4		8
20.19	odd	2		1200.3.bg.q.193.2		8
40.27	even	4		960.3.bg.k.577.1		8
40.37	odd	4		960.3.bg.l.577.3		8
60.47	odd	4		720.3.bh.o.577.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
120.3.u.b.73.2	✓	8	1.1	even	1	trivial
120.3.u.b.97.2	yes	8	5.2	odd	4	inner
240.3.bg.e.97.4		8	20.7	even	4
240.3.bg.e.193.4		8	4.3	odd	2
360.3.v.f.73.1		8	3.2	odd	2
360.3.v.f.217.1		8	15.2	even	4
600.3.u.h.193.3		8	5.4	even	2
600.3.u.h.457.3		8	5.3	odd	4
720.3.bh.o.433.1		8	12.11	even	2
720.3.bh.o.577.1		8	60.47	odd	4
960.3.bg.k.193.1		8	8.3	odd	2
960.3.bg.k.577.1		8	40.27	even	4
960.3.bg.l.193.3		8	8.5	even	2
960.3.bg.l.577.3		8	40.37	odd	4
1200.3.bg.q.193.2		8	20.19	odd	2
1200.3.bg.q.1057.2		8	20.3	even	4
1800.3.v.t.793.2		8	15.14	odd	2
1800.3.v.t.1657.2		8	15.8	even	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 120 = 2^{3} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	120.u (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.22474 - 1.22474i) q^{3} +(1.88489 + 4.63111i) q^{5} +(6.02356 - 6.02356i) q^{7} +3.00000i q^{9} +O(q^{10})\)	\(q+(-1.22474 - 1.22474i) q^{3} +(1.88489 + 4.63111i) q^{5} +(6.02356 - 6.02356i) q^{7} +3.00000i q^{9} +17.0038 q^{11} +(0.124585 + 0.124585i) q^{13} +(3.36342 - 7.98044i) q^{15} +(10.7744 - 10.7744i) q^{17} -4.04713i q^{19} -14.7547 q^{21} +(1.85568 + 1.85568i) q^{23} +(-17.8944 + 17.4583i) q^{25} +(3.67423 - 3.67423i) q^{27} +54.4448i q^{29} -53.1995 q^{31} +(-20.8254 - 20.8254i) q^{33} +(39.2496 + 16.5420i) q^{35} +(21.2693 - 21.2693i) q^{37} -0.305169i q^{39} -52.1414 q^{41} +(-50.4554 - 50.4554i) q^{43} +(-13.8933 + 5.65467i) q^{45} +(13.4045 - 13.4045i) q^{47} -23.5667i q^{49} -26.3918 q^{51} +(12.4315 + 12.4315i) q^{53} +(32.0504 + 78.7466i) q^{55} +(-4.95670 + 4.95670i) q^{57} -8.79413i q^{59} +105.860 q^{61} +(18.0707 + 18.0707i) q^{63} +(-0.342137 + 0.811794i) q^{65} +(-46.8595 + 46.8595i) q^{67} -4.54547i q^{69} -56.8955 q^{71} +(-52.7296 - 52.7296i) q^{73} +(43.2980 + 0.534094i) q^{75} +(102.424 - 102.424i) q^{77} -15.2920i q^{79} -9.00000 q^{81} +(46.1914 + 46.1914i) q^{83} +(70.2060 + 29.5888i) q^{85} +(66.6810 - 66.6810i) q^{87} +0.948538i q^{89} +1.50089 q^{91} +(65.1558 + 65.1558i) q^{93} +(18.7427 - 7.62840i) q^{95} +(77.6693 - 77.6693i) q^{97} +51.0115i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 12 q^{5} + 4 q^{7}+O(q^{10}) \) 8 * q - 12 * q^5 + 4 * q^7	\( 8 q - 12 q^{5} + 4 q^{7} + 32 q^{11} - 4 q^{13} + 52 q^{17} - 24 q^{21} - 40 q^{23} - 84 q^{25} + 96 q^{31} + 60 q^{33} + 24 q^{35} - 60 q^{37} - 152 q^{41} - 88 q^{43} - 16 q^{47} - 168 q^{51} + 108 q^{53} + 116 q^{55} - 24 q^{57} + 264 q^{61} + 12 q^{63} + 164 q^{65} - 216 q^{67} - 240 q^{71} - 208 q^{73} + 120 q^{75} + 168 q^{77} - 72 q^{81} + 336 q^{83} - 12 q^{85} + 252 q^{87} + 592 q^{91} + 264 q^{93} - 128 q^{95} - 208 q^{97}+O(q^{100}) \) 8 * q - 12 * q^5 + 4 * q^7 + 32 * q^11 - 4 * q^13 + 52 * q^17 - 24 * q^21 - 40 * q^23 - 84 * q^25 + 96 * q^31 + 60 * q^33 + 24 * q^35 - 60 * q^37 - 152 * q^41 - 88 * q^43 - 16 * q^47 - 168 * q^51 + 108 * q^53 + 116 * q^55 - 24 * q^57 + 264 * q^61 + 12 * q^63 + 164 * q^65 - 216 * q^67 - 240 * q^71 - 208 * q^73 + 120 * q^75 + 168 * q^77 - 72 * q^81 + 336 * q^83 - 12 * q^85 + 252 * q^87 + 592 * q^91 + 264 * q^93 - 128 * q^95 - 208 * q^97

Introduction

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