LMFDB - Embedded newform 1860.2.s.a.1177.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1860,2,Mod(433,1860)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1860.433"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1860, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 0, 3, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1860 = 2^{2} \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1860.s (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$14.8521747760$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$32$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			1177.5
Character	$\chi$	$=$	1860.1177
Dual form			1860.2.s.a.433.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.707107 - 0.707107i) q^{3} +(1.82341 + 1.29429i) q^{5} +(2.05794 + 2.05794i) q^{7} +1.00000i q^{9} -1.00573i q^{11} +(-1.61989 - 1.61989i) q^{13} +(-0.374144 - 2.20454i) q^{15} +(3.86707 - 3.86707i) q^{17} -5.41335i q^{19} -2.91036i q^{21} +(-0.0230415 - 0.0230415i) q^{23} +(1.64963 + 4.72003i) q^{25} +(0.707107 - 0.707107i) q^{27} -1.52171 q^{29} +(4.36154 - 3.46078i) q^{31} +(-0.711157 + 0.711157i) q^{33} +(1.08889 + 6.41602i) q^{35} +(3.04683 - 3.04683i) q^{37} +2.29087i q^{39} +4.90469 q^{41} +(3.37048 + 3.37048i) q^{43} +(-1.29429 + 1.82341i) q^{45} +(-6.30613 - 6.30613i) q^{47} +1.47020i q^{49} -5.46886 q^{51} +(8.56616 + 8.56616i) q^{53} +(1.30170 - 1.83385i) q^{55} +(-3.82781 + 3.82781i) q^{57} +8.14662i q^{59} +14.6938i q^{61} +(-2.05794 + 2.05794i) q^{63} +(-0.857115 - 5.05033i) q^{65} +(5.16207 + 5.16207i) q^{67} +0.0325857i q^{69} +8.00050 q^{71} +(4.34589 + 4.34589i) q^{73} +(2.17110 - 4.50403i) q^{75} +(2.06972 - 2.06972i) q^{77} -3.07648 q^{79} -1.00000 q^{81} +(-10.8786 - 10.8786i) q^{83} +(12.0564 - 2.04614i) q^{85} +(1.07601 + 1.07601i) q^{87} -2.30653 q^{89} -6.66726i q^{91} +(-5.53121 - 0.636934i) q^{93} +(7.00643 - 9.87074i) q^{95} +(1.43316 + 1.43316i) q^{97} +1.00573 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 8 q^{7} + 16 q^{25} + 8 q^{31} - 8 q^{33} + 24 q^{35} + 16 q^{41} + 56 q^{47} + 8 q^{63} - 32 q^{67} - 16 q^{71} - 64 q^{81} - 32 q^{87} - 32 q^{95} + 64 q^{97}+O(q^{100}) $ 64 * q - 8 * q^7 + 16 * q^25 + 8 * q^31 - 8 * q^33 + 24 * q^35 + 16 * q^41 + 56 * q^47 + 8 * q^63 - 32 * q^67 - 16 * q^71 - 64 * q^81 - 32 * q^87 - 32 * q^95 + 64 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1860\mathbb{Z}\right)^\times$.

$n$	$931$	$1117$	$1241$	$1801$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$1$	$-1$

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
$3$	−0.707107	−	0.707107i	−0.408248	−	0.408248i
$3$	−0.707107	−	0.707107i	−0.408248	−	0.408248i
$4$		0			0
$5$	1.82341	+	1.29429i	0.815453	+	0.578824i
$5$	1.82341	+	1.29429i	0.815453	+	0.578824i
$6$		0			0
$7$	2.05794	+	2.05794i	0.777827	+	0.777827i	0.979461	−	0.201634i	$-0.0646252\pi$
$7$	2.05794	+	2.05794i	0.777827	+	0.777827i	−0.201634	+	0.979461i	$0.564625\pi$
$8$		0			0
$9$			1.00000i			0.333333i
$10$		0			0
$11$		−	1.00573i		−	0.303238i	−0.988439	−	0.151619i	$-0.951551\pi$
$11$		−	1.00573i		−	0.303238i	0.988439	−	0.151619i	$-0.0484487\pi$
$12$		0			0
$13$	−1.61989	−	1.61989i	−0.449277	−	0.449277i	0.445837	−	0.895114i	$-0.352906\pi$
$13$	−1.61989	−	1.61989i	−0.449277	−	0.449277i	−0.895114	+	0.445837i	$0.852906\pi$
$14$		0			0
$15$	−0.374144	−	2.20454i	−0.0966035	−	0.569211i
$16$		0			0
$17$	3.86707	−	3.86707i	0.937903	−	0.937903i	−0.0602790	−	0.998182i	$-0.519199\pi$
$17$	3.86707	−	3.86707i	0.937903	−	0.937903i	0.998182	+	0.0602790i	$0.0191990\pi$
$18$		0			0
$19$		−	5.41335i		−	1.24191i	−0.783848	−	0.620953i	$-0.786746\pi$
$19$		−	5.41335i		−	1.24191i	0.783848	−	0.620953i	$-0.213254\pi$
$20$		0			0
$21$		−	2.91036i		−	0.635093i
$22$		0			0
$23$	−0.0230415	−	0.0230415i	−0.00480449	−	0.00480449i	0.704700	−	0.709505i	$-0.251081\pi$
$23$	−0.0230415	−	0.0230415i	−0.00480449	−	0.00480449i	−0.709505	+	0.704700i	$0.751081\pi$
$24$		0			0
$25$	1.64963	+	4.72003i	0.329926	+	0.944007i
$26$		0			0
$27$	0.707107	−	0.707107i	0.136083	−	0.136083i
$28$		0			0
$29$	−1.52171			−0.282574			−0.141287	−	0.989969i	$-0.545124\pi$
$29$	−1.52171			−0.282574			−0.141287	+	0.989969i	$0.545124\pi$
$30$		0			0
$31$	4.36154	−	3.46078i	0.783355	−	0.621574i
$31$	4.36154	−	3.46078i	0.783355	−	0.621574i
$32$		0			0
$33$	−0.711157	+	0.711157i	−0.123796	+	0.123796i
$34$		0			0
$35$	1.08889	+	6.41602i	0.184057	+	1.08451i
$36$		0			0
$37$	3.04683	−	3.04683i	0.500895	−	0.500895i	−0.410821	−	0.911716i	$-0.634758\pi$
$37$	3.04683	−	3.04683i	0.500895	−	0.500895i	0.911716	+	0.410821i	$0.134758\pi$
$38$		0			0
$39$			2.29087i			0.366833i
$40$		0			0
$41$	4.90469			0.765984			0.382992	−	0.923752i	$-0.374894\pi$
$41$	4.90469			0.765984			0.382992	+	0.923752i	$0.374894\pi$
$42$		0			0
$43$	3.37048	+	3.37048i	0.513993	+	0.513993i	0.915748	−	0.401754i	$-0.131599\pi$
$43$	3.37048	+	3.37048i	0.513993	+	0.513993i	−0.401754	+	0.915748i	$0.631599\pi$
$44$		0			0
$45$	−1.29429	+	1.82341i	−0.192941	+	0.271818i
$46$		0			0
$47$	−6.30613	−	6.30613i	−0.919844	−	0.919844i	0.0771735	−	0.997018i	$-0.475410\pi$
$47$	−6.30613	−	6.30613i	−0.919844	−	0.919844i	−0.997018	+	0.0771735i	$0.975410\pi$
$48$		0			0
$49$			1.47020i			0.210029i
$50$		0			0
$51$	−5.46886			−0.765794
$52$		0			0
$53$	8.56616	+	8.56616i	1.17665	+	1.17665i	0.980592	+	0.196061i	$0.0628150\pi$
$53$	8.56616	+	8.56616i	1.17665	+	1.17665i	0.196061	+	0.980592i	$0.437185\pi$
$54$		0			0
$55$	1.30170	−	1.83385i	0.175521	−	0.247276i
$56$		0			0
$57$	−3.82781	+	3.82781i	−0.507006	+	0.507006i
$58$		0			0
$59$			8.14662i			1.06060i	0.847810	+	0.530300i	$0.177921\pi$
$59$			8.14662i			1.06060i	−0.847810	+	0.530300i	$0.822079\pi$
$60$		0			0
$61$			14.6938i			1.88135i	0.339313	+	0.940673i	$0.389805\pi$
$61$			14.6938i			1.88135i	−0.339313	+	0.940673i	$0.610195\pi$
$62$		0			0
$63$	−2.05794	+	2.05794i	−0.259276	+	0.259276i
$64$		0			0
$65$	−0.857115	−	5.05033i	−0.106312	−	0.626416i
$66$		0			0
$67$	5.16207	+	5.16207i	0.630647	+	0.630647i	0.948230	−	0.317583i	$-0.102871\pi$
$67$	5.16207	+	5.16207i	0.630647	+	0.630647i	−0.317583	+	0.948230i	$0.602871\pi$
$68$		0			0
$69$			0.0325857i			0.00392285i
$70$		0			0
$71$	8.00050			0.949485			0.474742	−	0.880125i	$-0.342541\pi$
$71$	8.00050			0.949485			0.474742	+	0.880125i	$0.342541\pi$
$72$		0			0
$73$	4.34589	+	4.34589i	0.508648	+	0.508648i	0.914111	−	0.405463i	$-0.132890\pi$
$73$	4.34589	+	4.34589i	0.508648	+	0.508648i	−0.405463	+	0.914111i	$0.632890\pi$
$74$		0			0
$75$	2.17110	−	4.50403i	0.250697	−	0.520081i
$76$		0			0
$77$	2.06972	−	2.06972i	0.235867	−	0.235867i
$78$		0			0
$79$	−3.07648			−0.346131			−0.173066	−	0.984910i	$-0.555367\pi$
$79$	−3.07648			−0.346131			−0.173066	+	0.984910i	$0.555367\pi$
$80$		0			0
$81$	−1.00000			−0.111111
$82$		0			0
$83$	−10.8786	−	10.8786i	−1.19408	−	1.19408i	−0.975911	−	0.218167i	$-0.929992\pi$
$83$	−10.8786	−	10.8786i	−1.19408	−	1.19408i	−0.218167	−	0.975911i	$-0.570008\pi$
$84$		0			0
$85$	12.0564	−	2.04614i	1.30770	−	0.221935i
$86$		0			0
$87$	1.07601	+	1.07601i	0.115360	+	0.115360i
$88$		0			0
$89$	−2.30653			−0.244492			−0.122246	−	0.992500i	$-0.539010\pi$
$89$	−2.30653			−0.244492			−0.122246	+	0.992500i	$0.539010\pi$
$90$		0			0
$91$		−	6.66726i		−	0.698919i
$92$		0			0
$93$	−5.53121	−	0.636934i	−0.573560	−	0.0660469i
$94$		0			0
$95$	7.00643	−	9.87074i	0.718845	−	1.01272i
$96$		0			0
$97$	1.43316	+	1.43316i	0.145515	+	0.145515i	0.776111	−	0.630596i	$-0.217190\pi$
$97$	1.43316	+	1.43316i	0.145515	+	0.145515i	−0.630596	+	0.776111i	$0.717190\pi$
$98$		0			0
$99$	1.00573			0.101079
$100$		0			0
$101$	−15.2263			−1.51508			−0.757539	−	0.652790i	$-0.773598\pi$
$101$	−15.2263			−1.51508			−0.757539	+	0.652790i	$0.773598\pi$
$102$		0			0
$103$	3.32263	−	3.32263i	0.327388	−	0.327388i	−0.524204	−	0.851593i	$-0.675637\pi$
$103$	3.32263	−	3.32263i	0.327388	−	0.327388i	0.851593	+	0.524204i	$0.175637\pi$
$104$		0			0
$105$	3.76685	−	5.30678i	0.367607	−	0.517888i
$106$		0			0
$107$	−3.16896	−	3.16896i	−0.306355	−	0.306355i	0.537139	−	0.843494i	$-0.319505\pi$
$107$	−3.16896	−	3.16896i	−0.306355	−	0.306355i	−0.843494	+	0.537139i	$0.819505\pi$
$108$		0			0
$109$			7.07906i			0.678051i	0.940777	+	0.339025i	$0.110097\pi$
$109$			7.07906i			0.678051i	−0.940777	+	0.339025i	$0.889903\pi$
$110$		0			0
$111$	−4.30886			−0.408979
$112$		0			0
$113$	8.80829	−	8.80829i	0.828614	−	0.828614i	−0.158711	−	0.987325i	$-0.550734\pi$
$113$	8.80829	−	8.80829i	0.828614	−	0.828614i	0.987325	+	0.158711i	$0.0507339\pi$
$114$		0			0
$115$	−0.0121917	−	0.0718365i	−0.00113688	−	0.00669879i
$116$		0			0
$117$	1.61989	−	1.61989i	0.149759	−	0.149759i
$118$		0			0
$119$	15.9164			1.45905
$120$		0			0
$121$	9.98851			0.908047
$122$		0			0
$123$	−3.46814	−	3.46814i	−0.312712	−	0.312712i
$124$		0			0
$125$	−3.10113	+	10.7416i	−0.277374	+	0.960762i
$126$		0			0
$127$	1.63590	−	1.63590i	0.145163	−	0.145163i	−0.630790	−	0.775953i	$-0.717269\pi$
$127$	1.63590	−	1.63590i	0.145163	−	0.145163i	0.775953	+	0.630790i	$0.217269\pi$
$128$		0			0
$129$		−	4.76658i		−	0.419674i
$130$		0			0
$131$	−0.855356			−0.0747328			−0.0373664	−	0.999302i	$-0.511897\pi$
$131$	−0.855356			−0.0747328			−0.0373664	+	0.999302i	$0.511897\pi$
$132$		0			0
$133$	11.1403	−	11.1403i	0.965988	−	0.965988i
$134$		0			0
$135$	2.20454	−	0.374144i	0.189737	−	0.0322012i
$136$		0			0
$137$	14.3878	−	14.3878i	1.22924	−	1.22924i	0.264984	−	0.964253i	$-0.414633\pi$
$137$	14.3878	−	14.3878i	1.22924	−	1.22924i	0.964253	−	0.264984i	$-0.0853666\pi$
$138$		0			0
$139$	−3.22344			−0.273409			−0.136705	−	0.990612i	$-0.543651\pi$
$139$	−3.22344			−0.273409			−0.136705	+	0.990612i	$0.543651\pi$
$140$		0			0
$141$			8.91822i			0.751050i
$142$		0			0
$143$	−1.62917	+	1.62917i	−0.136238	+	0.136238i
$144$		0			0
$145$	−2.77469	−	1.96953i	−0.230425	−	0.163560i
$146$		0			0
$147$	1.03959	−	1.03959i	0.0857440	−	0.0857440i
$148$		0			0
$149$			0.502232i			0.0411444i	0.999788	+	0.0205722i	$0.00654880\pi$
$149$			0.502232i			0.0411444i	−0.999788	+	0.0205722i	$0.993451\pi$
$150$		0			0
$151$		−	11.4130i		−	0.928779i	−0.885631	−	0.464390i	$-0.846274\pi$
$151$		−	11.4130i		−	0.928779i	0.885631	−	0.464390i	$-0.153726\pi$
$152$		0			0
$153$	3.86707	+	3.86707i	0.312634	+	0.312634i
$154$		0			0
$155$	12.4321	−	0.665319i	0.998571	−	0.0534397i
$156$		0			0
$157$	13.7527	+	13.7527i	1.09759	+	1.09759i	0.994692	+	0.102895i	$0.0328105\pi$
$157$	13.7527	+	13.7527i	1.09759	+	1.09759i	0.102895	+	0.994692i	$0.467190\pi$
$158$		0			0
$159$		−	12.1144i		−	0.960733i
$160$		0			0
$161$		−	0.0948361i		−	0.00747413i
$162$		0			0
$163$	9.73756	−	9.73756i	0.762705	−	0.762705i	−0.214106	−	0.976811i	$-0.568684\pi$
$163$	9.73756	−	9.73756i	0.762705	−	0.762705i	0.976811	+	0.214106i	$0.0686837\pi$
$164$		0			0
$165$	−2.21717	+	0.376286i	−0.172606	+	0.0292939i
$166$		0			0
$167$	0.0310054	−	0.0310054i	0.00239927	−	0.00239927i	−0.705906	−	0.708305i	$-0.749460\pi$
$167$	0.0310054	−	0.0310054i	0.00239927	−	0.00239927i	0.708305	+	0.705906i	$0.249460\pi$
$168$		0			0
$169$		−	7.75191i		−	0.596301i
$170$		0			0
$171$	5.41335			0.413969
$172$		0			0
$173$	−7.68514	+	7.68514i	−0.584290	+	0.584290i	−0.936079	−	0.351789i	$-0.885573\pi$
$173$	−7.68514	+	7.68514i	−0.584290	+	0.584290i	0.351789	+	0.936079i	$0.385573\pi$
$174$		0			0
$175$	−6.31869	+	13.1084i	−0.477648	+	0.990899i
$176$		0			0
$177$	5.76053	−	5.76053i	0.432988	−	0.432988i
$178$		0			0
$179$	−15.3123			−1.14449			−0.572247	−	0.820081i	$-0.693928\pi$
$179$	−15.3123			−1.14449			−0.572247	+	0.820081i	$0.693928\pi$
$180$		0			0
$181$			25.4413i			1.89104i	0.325567	+	0.945519i	$0.394445\pi$
$181$			25.4413i			1.89104i	−0.325567	+	0.945519i	$0.605555\pi$
$182$		0			0
$183$	10.3901	−	10.3901i	0.768057	−	0.768057i
$184$		0			0
$185$	9.49908	−	1.61213i	0.698387	−	0.118526i
$186$		0			0
$187$	−3.88922	−	3.88922i	−0.284408	−	0.284408i
$188$		0			0
$189$	2.91036			0.211698
$190$		0			0
$191$	−1.36662			−0.0988853			−0.0494426	−	0.998777i	$-0.515745\pi$
$191$	−1.36662			−0.0988853			−0.0494426	+	0.998777i	$0.515745\pi$
$192$		0			0
$193$	−7.74265	+	7.74265i	−0.557328	+	0.557328i	−0.928546	−	0.371217i	$-0.878940\pi$
$193$	−7.74265	+	7.74265i	−0.557328	+	0.557328i	0.371217	+	0.928546i	$0.378940\pi$
$194$		0			0
$195$	−2.96505	+	4.17719i	−0.212332	+	0.299135i
$196$		0			0
$197$	4.97387	−	4.97387i	0.354374	−	0.354374i	−0.507360	−	0.861734i	$-0.669379\pi$
$197$	4.97387	−	4.97387i	0.354374	−	0.354374i	0.861734	+	0.507360i	$0.169379\pi$
$198$		0			0
$199$	−8.43176			−0.597712			−0.298856	−	0.954298i	$-0.596605\pi$
$199$	−8.43176			−0.597712			−0.298856	+	0.954298i	$0.596605\pi$
$200$		0			0
$201$		−	7.30027i		−	0.514921i
$202$		0			0
$203$	−3.13157	−	3.13157i	−0.219793	−	0.219793i
$204$		0			0
$205$	8.94325	+	6.34809i	0.624624	+	0.443370i
$206$		0			0
$207$	0.0230415	−	0.0230415i	0.00160150	−	0.00160150i
$208$		0			0
$209$	−5.44435			−0.376593
$210$		0			0
$211$	3.58266			0.246641			0.123320	−	0.992367i	$-0.460646\pi$
$211$	3.58266			0.246641			0.123320	+	0.992367i	$0.460646\pi$
$212$		0			0
$213$	−5.65721	−	5.65721i	−0.387625	−	0.387625i
$214$		0			0
$215$	1.78338	+	10.5081i	0.121626	+	0.716649i
$216$		0			0
$217$	16.0978	+	1.85371i	1.09279	+	0.125838i
$218$		0			0
$219$		−	6.14602i		−	0.415310i
$220$		0			0
$221$	−12.5285			−0.842756
$222$		0			0
$223$	−14.9347	−	14.9347i	−1.00010	−	1.00010i	−1.00000		9.86711e-5i	$-0.999969\pi$
$223$	−14.9347	−	14.9347i	−1.00010	−	1.00010i	−9.86711e−5	−	1.00000i	$-0.500031\pi$
$224$		0			0
$225$	−4.72003	+	1.64963i	−0.314669	+	0.109975i
$226$		0			0
$227$	−8.48418	−	8.48418i	−0.563115	−	0.563115i	0.367076	−	0.930191i	$-0.380359\pi$
$227$	−8.48418	−	8.48418i	−0.563115	−	0.563115i	−0.930191	+	0.367076i	$0.880359\pi$
$228$		0			0
$229$	−0.256836			−0.0169722			−0.00848608	−	0.999964i	$-0.502701\pi$
$229$	−0.256836			−0.0169722			−0.00848608	+	0.999964i	$0.502701\pi$
$230$		0			0
$231$	−2.92703			−0.192584
$232$		0			0
$233$	−0.602617	+	0.602617i	−0.0394787	+	0.0394787i	−0.726571	−	0.687092i	$-0.758887\pi$
$233$	−0.602617	+	0.602617i	−0.0394787	+	0.0394787i	0.687092	+	0.726571i	$0.258887\pi$
$234$		0			0
$235$	−3.33669	−	19.6606i	−0.217662	−	1.28252i
$236$		0			0
$237$	2.17540	+	2.17540i	0.141307	+	0.141307i
$238$		0			0
$239$	−14.9826			−0.969145			−0.484573	−	0.874751i	$-0.661025\pi$
$239$	−14.9826			−0.969145			−0.484573	+	0.874751i	$0.661025\pi$
$240$		0			0
$241$			12.8347i			0.826757i	0.910559	+	0.413378i	$0.135651\pi$
$241$			12.8347i			0.826757i	−0.910559	+	0.413378i	$0.864349\pi$
$242$		0			0
$243$	0.707107	+	0.707107i	0.0453609	+	0.0453609i
$244$		0			0
$245$	−1.90287	+	2.68078i	−0.121570	+	0.171269i
$246$		0			0
$247$	−8.76903	+	8.76903i	−0.557960	+	0.557960i
$248$		0			0
$249$			15.3846i			0.974961i
$250$		0			0
$251$		−	6.10846i		−	0.385562i	−0.981242	−	0.192781i	$-0.938249\pi$
$251$		−	6.10846i		−	0.385562i	0.981242	−	0.192781i	$-0.0617507\pi$
$252$		0			0
$253$	−0.0231735	+	0.0231735i	−0.00145691	+	0.00145691i
$254$		0			0
$255$	−9.97197	−	7.07829i	−0.624469	−	0.443260i
$256$		0			0
$257$	−5.89894	−	5.89894i	−0.367966	−	0.367966i	0.498769	−	0.866735i	$-0.333786\pi$
$257$	−5.89894	−	5.89894i	−0.367966	−	0.367966i	−0.866735	+	0.498769i	$0.833786\pi$
$258$		0			0
$259$	12.5404			0.779220
$260$		0			0
$261$		−	1.52171i		−	0.0941912i
$262$		0			0
$263$	−3.53635	−	3.53635i	−0.218061	−	0.218061i	0.589620	−	0.807681i	$-0.299277\pi$
$263$	−3.53635	−	3.53635i	−0.218061	−	0.218061i	−0.807681	+	0.589620i	$0.799277\pi$
$264$		0			0
$265$	4.53252	+	26.7067i	0.278430	+	1.64058i
$266$		0			0
$267$	1.63096	+	1.63096i	0.0998133	+	0.0998133i
$268$		0			0
$269$	−6.24247			−0.380610			−0.190305	−	0.981725i	$-0.560948\pi$
$269$	−6.24247			−0.380610			−0.190305	+	0.981725i	$0.560948\pi$
$270$		0			0
$271$			24.9306i			1.51442i	0.653169	+	0.757212i	$0.273439\pi$
$271$			24.9306i			1.51442i	−0.653169	+	0.757212i	$0.726561\pi$
$272$		0			0
$273$	−4.71447	+	4.71447i	−0.285332	+	0.285332i
$274$		0			0
$275$	4.74707	−	1.65908i	0.286259	−	0.100046i
$276$		0			0
$277$	−6.42045	+	6.42045i	−0.385767	+	0.385767i	−0.873175	−	0.487407i	$-0.837943\pi$
$277$	−6.42045	+	6.42045i	−0.385767	+	0.385767i	0.487407	+	0.873175i	$0.337943\pi$
$278$		0			0
$279$	3.46078	+	4.36154i	0.207191	+	0.261118i
$280$		0			0
$281$	−23.7338			−1.41584			−0.707920	−	0.706293i	$-0.750366\pi$
$281$	−23.7338			−1.41584			−0.707920	+	0.706293i	$0.750366\pi$
$282$		0			0
$283$	17.2573	−	17.2573i	1.02584	−	1.02584i	0.0261852	−	0.999657i	$-0.491664\pi$
$283$	17.2573	−	17.2573i	1.02584	−	1.02584i	0.999657	−	0.0261852i	$-0.00833596\pi$
$284$		0			0
$285$	−11.9340	+	2.02537i	−0.706907	+	0.119972i
$286$		0			0
$287$	10.0935	+	10.0935i	0.595803	+	0.595803i
$288$		0			0
$289$		−	12.9085i		−	0.759323i
$290$		0			0
$291$		−	2.02679i		−	0.118813i
$292$		0			0
$293$	−15.7208	+	15.7208i	−0.918421	+	0.918421i	−0.996915	−	0.0784938i	$-0.974989\pi$
$293$	−15.7208	+	15.7208i	−0.918421	+	0.918421i	0.0784938	+	0.996915i	$0.474989\pi$
$294$		0			0
$295$	−10.5441	+	14.8546i	−0.613900	+	0.864869i
$296$		0			0
$297$	−0.711157	−	0.711157i	−0.0412655	−	0.0412655i
$298$		0			0
$299$			0.0746495i			0.00431709i
$300$		0			0
$301$			13.8725i			0.799595i
$302$		0			0
$303$	10.7667	+	10.7667i	0.618528	+	0.618528i
$304$		0			0
$305$	−19.0180	+	26.7928i	−1.08897	+	1.53415i
$306$		0			0
$307$	−2.85580	−	2.85580i	−0.162989	−	0.162989i	0.620900	−	0.783889i	$-0.286767\pi$
$307$	−2.85580	−	2.85580i	−0.162989	−	0.162989i	−0.783889	+	0.620900i	$0.786767\pi$
$308$		0			0
$309$	−4.69891			−0.267311
$310$		0			0
$311$	−8.54691			−0.484651			−0.242325	−	0.970195i	$-0.577910\pi$
$311$	−8.54691			−0.484651			−0.242325	+	0.970195i	$0.577910\pi$
$312$		0			0
$313$	6.85368	+	6.85368i	0.387393	+	0.387393i	0.873757	−	0.486363i	$-0.161677\pi$
$313$	6.85368	+	6.85368i	0.387393	+	0.387393i	−0.486363	+	0.873757i	$0.661677\pi$
$314$		0			0
$315$	−6.41602	+	1.08889i	−0.361502	+	0.0613522i
$316$		0			0
$317$	−5.83077	−	5.83077i	−0.327489	−	0.327489i	0.524142	−	0.851631i	$-0.324386\pi$
$317$	−5.83077	−	5.83077i	−0.327489	−	0.327489i	−0.851631	+	0.524142i	$0.824386\pi$
$318$		0			0
$319$			1.53042i			0.0856871i
$320$		0			0
$321$			4.48158i			0.250137i
$322$		0			0
$323$	−20.9338	−	20.9338i	−1.16479	−	1.16479i
$324$		0			0
$325$	4.97371	−	10.3182i	0.275892	−	0.572349i
$326$		0			0
$327$	5.00565	−	5.00565i	0.276813	−	0.276813i
$328$		0			0
$329$		−	25.9552i		−	1.43096i
$330$		0			0
$331$			33.1274i			1.82084i	0.413680	+	0.910422i	$0.364243\pi$
$331$			33.1274i			1.82084i	−0.413680	+	0.910422i	$0.635757\pi$
$332$		0			0
$333$	3.04683	+	3.04683i	0.166965	+	0.166965i
$334$		0			0
$335$	2.73135	+	16.0938i	0.149229	+	0.879296i
$336$		0			0
$337$	1.86151	−	1.86151i	0.101403	−	0.101403i	−0.654585	−	0.755988i	$-0.727157\pi$
$337$	1.86151	−	1.86151i	0.101403	−	0.101403i	0.755988	+	0.654585i	$0.227157\pi$
$338$		0			0
$339$	−12.4568			−0.676560
$340$		0			0
$341$	−3.48060	−	4.38652i	−0.188485	−	0.237543i
$342$		0			0
$343$	11.3800	−	11.3800i	0.614461	−	0.614461i
$344$		0			0
$345$	−0.0421753	+	0.0594170i	−0.00227064	+	0.00319890i
$346$		0			0
$347$	7.41622	−	7.41622i	0.398123	−	0.398123i	−0.479447	−	0.877571i	$-0.659163\pi$
$347$	7.41622	−	7.41622i	0.398123	−	0.398123i	0.877571	+	0.479447i	$0.159163\pi$
$348$		0			0
$349$		−	24.5437i		−	1.31379i	−0.753980	−	0.656897i	$-0.771869\pi$
$349$		−	24.5437i		−	1.31379i	0.753980	−	0.656897i	$-0.228131\pi$
$350$		0			0
$351$	−2.29087			−0.122278
$352$		0			0
$353$	−18.6975	−	18.6975i	−0.995167	−	0.995167i	0.00482173	−	0.999988i	$-0.498465\pi$
$353$	−18.6975	−	18.6975i	−0.995167	−	0.995167i	−0.999988	+	0.00482173i	$0.998465\pi$
$354$		0			0
$355$	14.5882	+	10.3550i	0.774260	+	0.549584i
$356$		0			0
$357$	−11.2546	−	11.2546i	−0.595655	−	0.595655i
$358$		0			0
$359$			9.13969i			0.482374i	0.970479	+	0.241187i	$0.0775367\pi$
$359$			9.13969i			0.482374i	−0.970479	+	0.241187i	$0.922463\pi$
$360$		0			0
$361$	−10.3043			−0.542332
$362$		0			0
$363$	−7.06295	−	7.06295i	−0.370708	−	0.370708i
$364$		0			0
$365$	2.29950	+	13.5492i	0.120361	+	0.709197i
$366$		0			0
$367$	−5.07571	+	5.07571i	−0.264950	+	0.264950i	−0.827062	−	0.562111i	$-0.809989\pi$
$367$	−5.07571	+	5.07571i	−0.264950	+	0.264950i	0.562111	+	0.827062i	$0.309989\pi$
$368$		0			0
$369$			4.90469i			0.255328i
$370$		0			0
$371$			35.2572i			1.83046i
$372$		0			0
$373$	25.4369	−	25.4369i	1.31707	−	1.31707i	0.400994	−	0.916081i	$-0.368665\pi$
$373$	25.4369	−	25.4369i	1.31707	−	1.31707i	0.916081	−	0.400994i	$-0.131335\pi$
$374$		0			0
$375$	9.78832	−	5.40266i	0.505467	−	0.278992i
$376$		0			0
$377$	2.46500	+	2.46500i	0.126954	+	0.126954i
$378$		0			0
$379$			7.06419i			0.362863i	0.983404	+	0.181431i	$0.0580731\pi$
$379$			7.06419i			0.362863i	−0.983404	+	0.181431i	$0.941927\pi$
$380$		0			0
$381$	−2.31351			−0.118525
$382$		0			0
$383$	−15.4749	−	15.4749i	−0.790733	−	0.790733i	0.190880	−	0.981613i	$-0.438866\pi$
$383$	−15.4749	−	15.4749i	−0.790733	−	0.790733i	−0.981613	+	0.190880i	$0.938866\pi$
$384$		0			0
$385$	6.45277	−	1.09513i	0.328863	−	0.0558130i
$386$		0			0
$387$	−3.37048	+	3.37048i	−0.171331	+	0.171331i
$388$		0			0
$389$	−34.3348			−1.74084			−0.870422	−	0.492307i	$-0.836154\pi$
$389$	−34.3348			−1.74084			−0.870422	+	0.492307i	$0.836154\pi$
$390$		0			0
$391$	−0.178207			−0.00901229
$392$		0			0
$393$	0.604828	+	0.604828i	0.0305095	+	0.0305095i
$394$		0			0
$395$	−5.60968	−	3.98186i	−0.282254	−	0.200349i
$396$		0			0
$397$	−5.22595	−	5.22595i	−0.262283	−	0.262283i	0.563698	−	0.825981i	$-0.309378\pi$
$397$	−5.22595	−	5.22595i	−0.262283	−	0.262283i	−0.825981	+	0.563698i	$0.809378\pi$
$398$		0			0
$399$	−15.7548			−0.788726
$400$		0			0
$401$			19.4750i			0.972535i	0.873810	+	0.486268i	$0.161642\pi$
$401$			19.4750i			0.972535i	−0.873810	+	0.486268i	$0.838358\pi$
$402$		0			0
$403$	−12.6713	−	1.45913i	−0.631202	−	0.0726846i
$404$		0			0
$405$	−1.82341	−	1.29429i	−0.0906059	−	0.0643137i
$406$		0			0
$407$	−3.06428	−	3.06428i	−0.151891	−	0.151891i
$408$		0			0
$409$	−15.9313			−0.787753			−0.393876	−	0.919163i	$-0.628866\pi$
$409$	−15.9313			−0.787753			−0.393876	+	0.919163i	$0.628866\pi$
$410$		0			0
$411$	−20.3475			−1.00367
$412$		0			0
$413$	−16.7652	+	16.7652i	−0.824963	+	0.824963i
$414$		0			0
$415$	−5.75606	−	33.9161i	−0.282554	−	1.66488i
$416$		0			0
$417$	2.27932	+	2.27932i	0.111619	+	0.111619i
$418$		0			0
$419$		−	31.2344i		−	1.52590i	−0.646457	−	0.762951i	$-0.723750\pi$
$419$		−	31.2344i		−	1.52590i	0.646457	−	0.762951i	$-0.276250\pi$
$420$		0			0
$421$	−0.248101			−0.0120917			−0.00604585	−	0.999982i	$-0.501924\pi$
$421$	−0.248101			−0.0120917			−0.00604585	+	0.999982i	$0.501924\pi$
$422$		0			0
$423$	6.30613	−	6.30613i	0.306615	−	0.306615i
$424$		0			0
$425$	24.6320	+	11.8735i	1.19483	+	0.575947i
$426$		0			0
$427$	−30.2389	+	30.2389i	−1.46336	+	1.46336i
$428$		0			0
$429$	2.30399			0.111238
$430$		0			0
$431$	−25.3748			−1.22226			−0.611130	−	0.791530i	$-0.709285\pi$
$431$	−25.3748			−1.22226			−0.611130	+	0.791530i	$0.709285\pi$
$432$		0			0
$433$	4.14491	+	4.14491i	0.199192	+	0.199192i	0.799653	−	0.600462i	$-0.205017\pi$
$433$	4.14491	+	4.14491i	0.199192	+	0.199192i	−0.600462	+	0.799653i	$0.705017\pi$
$434$		0			0
$435$	0.569336	+	3.35467i	0.0272976	+	0.160844i
$436$		0			0
$437$	−0.124732	+	0.124732i	−0.00596673	+	0.00596673i
$438$		0			0
$439$			40.2522i			1.92113i	0.278054	+	0.960565i	$0.410311\pi$
$439$			40.2522i			1.92113i	−0.278054	+	0.960565i	$0.589689\pi$
$440$		0			0
$441$	−1.47020			−0.0700097
$442$		0			0
$443$	7.45632	−	7.45632i	0.354260	−	0.354260i	−0.507432	−	0.861692i	$-0.669405\pi$
$443$	7.45632	−	7.45632i	0.354260	−	0.354260i	0.861692	+	0.507432i	$0.169405\pi$
$444$		0			0
$445$	−4.20575	−	2.98532i	−0.199371	−	0.141518i
$446$		0			0
$447$	0.355132	−	0.355132i	0.0167972	−	0.0167972i
$448$		0			0
$449$	33.2207			1.56778			0.783891	−	0.620898i	$-0.213232\pi$
$449$	33.2207			1.56778			0.783891	+	0.620898i	$0.213232\pi$
$450$		0			0
$451$		−	4.93278i		−	0.232276i
$452$		0			0
$453$	−8.07023	+	8.07023i	−0.379173	+	0.379173i
$454$		0			0
$455$	8.62936	−	12.1571i	0.404551	−	0.569935i
$456$		0			0
$457$	16.0114	−	16.0114i	0.748981	−	0.748981i	−0.225307	−	0.974288i	$-0.572338\pi$
$457$	16.0114	−	16.0114i	0.748981	−	0.748981i	0.974288	+	0.225307i	$0.0723384\pi$
$458$		0			0
$459$		−	5.46886i		−	0.255265i
$460$		0			0
$461$			3.24594i			0.151178i	0.997139	+	0.0755892i	$0.0240838\pi$
$461$			3.24594i			0.151178i	−0.997139	+	0.0755892i	$0.975916\pi$
$462$		0			0
$463$	26.3184	+	26.3184i	1.22312	+	1.22312i	0.966517	+	0.256602i	$0.0826028\pi$
$463$	26.3184	+	26.3184i	1.22312	+	1.22312i	0.256602	+	0.966517i	$0.417397\pi$
$464$		0			0
$465$	−9.26128	−	8.32038i	−0.429482	−	0.385848i
$466$		0			0
$467$	−6.57118	−	6.57118i	−0.304078	−	0.304078i	0.538529	−	0.842607i	$-0.318980\pi$
$467$	−6.57118	−	6.57118i	−0.304078	−	0.304078i	−0.842607	+	0.538529i	$0.818980\pi$
$468$		0			0
$469$			21.2464i			0.981068i
$470$		0			0
$471$		−	19.4493i		−	0.896176i
$472$		0			0
$473$	3.38978	−	3.38978i	0.155862	−	0.155862i
$474$		0			0
$475$	25.5512	−	8.93003i	1.17237	−	0.409738i
$476$		0			0
$477$	−8.56616	+	8.56616i	−0.392218	+	0.392218i
$478$		0			0
$479$		−	22.4929i		−	1.02773i	−0.857872	−	0.513863i	$-0.828214\pi$
$479$		−	22.4929i		−	1.02773i	0.857872	−	0.513863i	$-0.171786\pi$
$480$		0			0
$481$	−9.87105			−0.450081
$482$		0			0
$483$	−0.0670592	+	0.0670592i	−0.00305130	+	0.00305130i
$484$		0			0
$485$	0.758310	+	4.46815i	0.0344331	+	0.202888i
$486$		0			0
$487$	−14.5479	+	14.5479i	−0.659229	+	0.659229i	−0.955198	−	0.295969i	$-0.904358\pi$
$487$	−14.5479	+	14.5479i	−0.659229	+	0.659229i	0.295969	+	0.955198i	$0.404358\pi$
$488$		0			0
$489$	−13.7710			−0.622746
$490$		0			0
$491$			34.8516i			1.57283i	0.617699	+	0.786415i	$0.288065\pi$
$491$			34.8516i			1.57283i	−0.617699	+	0.786415i	$0.711935\pi$
$492$		0			0
$493$	−5.88454	+	5.88454i	−0.265027	+	0.265027i
$494$		0			0
$495$	1.83385	+	1.30170i	0.0824255	+	0.0585071i
$496$		0			0
$497$	16.4645	+	16.4645i	0.738535	+	0.738535i
$498$		0			0
$499$	−16.5368			−0.740288			−0.370144	−	0.928974i	$-0.620692\pi$
$499$	−16.5368			−0.740288			−0.370144	+	0.928974i	$0.620692\pi$
$500$		0			0
$501$	−0.0438483			−0.00195900
$502$		0			0
$503$	16.4932	−	16.4932i	0.735395	−	0.735395i	−0.236288	−	0.971683i	$-0.575931\pi$
$503$	16.4932	−	16.4932i	0.735395	−	0.735395i	0.971683	+	0.236288i	$0.0759309\pi$
$504$		0			0
$505$	−27.7638	−	19.7073i	−1.23547	−	0.876963i
$506$		0			0
$507$	−5.48143	+	5.48143i	−0.243439	+	0.243439i
$508$		0			0
$509$	32.2747			1.43055			0.715276	−	0.698842i	$-0.246301\pi$
$509$	32.2747			1.43055			0.715276	+	0.698842i	$0.246301\pi$
$510$		0			0
$511$			17.8871i			0.791281i
$512$		0			0
$513$	−3.82781	−	3.82781i	−0.169002	−	0.169002i
$514$		0			0
$515$	10.3589	−	1.75807i	0.456470	−	0.0774696i
$516$		0			0
$517$	−6.34225	+	6.34225i	−0.278932	+	0.278932i
$518$		0			0
$519$	10.8684			0.477071
$520$		0			0
$521$	−2.33345			−0.102230			−0.0511152	−	0.998693i	$-0.516278\pi$
$521$	−2.33345			−0.102230			−0.0511152	+	0.998693i	$0.516278\pi$
$522$		0			0
$523$	1.66581	+	1.66581i	0.0728409	+	0.0728409i	0.742589	−	0.669748i	$-0.233598\pi$
$523$	1.66581	+	1.66581i	0.0728409	+	0.0728409i	−0.669748	+	0.742589i	$0.733598\pi$
$524$		0			0
$525$	13.7370	−	4.80103i	0.599532	−	0.209534i
$526$		0			0
$527$	3.48330	−	30.2495i	0.151735	−	1.31769i
$528$		0			0
$529$		−	22.9989i		−	0.999954i
$530$		0			0
$531$	−8.14662			−0.353533
$532$		0			0
$533$	−7.94506	−	7.94506i	−0.344139	−	0.344139i
$534$		0			0
$535$	−1.67675	−	9.87984i	−0.0724924	−	0.427143i
$536$		0			0
$537$	10.8274	+	10.8274i	0.467238	+	0.467238i
$538$		0			0
$539$	1.47862			0.0636888
$540$		0			0
$541$	−14.2584			−0.613016			−0.306508	−	0.951868i	$-0.599161\pi$
$541$	−14.2584			−0.613016			−0.306508	+	0.951868i	$0.599161\pi$
$542$		0			0
$543$	17.9897	−	17.9897i	0.772013	−	0.772013i
$544$		0			0
$545$	−9.16235	+	12.9080i	−0.392472	+	0.552918i
$546$		0			0
$547$	15.0238	+	15.0238i	0.642373	+	0.642373i	0.951138	−	0.308765i	$-0.0999158\pi$
$547$	15.0238	+	15.0238i	0.642373	+	0.642373i	−0.308765	+	0.951138i	$0.599916\pi$
$548$		0			0
$549$	−14.6938			−0.627116
$550$		0			0
$551$			8.23752i			0.350930i
$552$		0			0
$553$	−6.33120	−	6.33120i	−0.269230	−	0.269230i
$554$		0			0
$555$	−7.85682	−	5.57692i	−0.333503	−	0.236727i
$556$		0			0
$557$	−26.2534	+	26.2534i	−1.11239	+	1.11239i	−0.119567	+	0.992826i	$0.538151\pi$
$557$	−26.2534	+	26.2534i	−1.11239	+	1.11239i	−0.992826	+	0.119567i	$0.961849\pi$
$558$		0			0
$559$		−	10.9196i		−	0.461850i
$560$		0			0
$561$			5.50019i			0.232218i
$562$		0			0
$563$	10.9502	−	10.9502i	0.461496	−	0.461496i	−0.437650	−	0.899146i	$-0.644189\pi$
$563$	10.9502	−	10.9502i	0.461496	−	0.461496i	0.899146	+	0.437650i	$0.144189\pi$
$564$		0			0
$565$	27.4616	−	4.66063i	1.15532	−	0.196074i
$566$		0			0
$567$	−2.05794	−	2.05794i	−0.0864252	−	0.0864252i
$568$		0			0
$569$	−16.0944			−0.674711			−0.337355	−	0.941377i	$-0.609532\pi$
$569$	−16.0944			−0.674711			−0.337355	+	0.941377i	$0.609532\pi$
$570$		0			0
$571$		−	16.1373i		−	0.675323i	−0.941268	−	0.337662i	$-0.890364\pi$
$571$		−	16.1373i		−	0.675323i	0.941268	−	0.337662i	$-0.109636\pi$
$572$		0			0
$573$	0.966348	+	0.966348i	0.0403698	+	0.0403698i
$574$		0			0
$575$	0.0707468	−	0.146767i	0.00295034	−	0.00612060i
$576$		0			0
$577$	−31.9071	−	31.9071i	−1.32831	−	1.32831i	−0.906844	−	0.421466i	$-0.861516\pi$
$577$	−31.9071	−	31.9071i	−1.32831	−	1.32831i	−0.421466	−	0.906844i	$-0.638484\pi$
$578$		0			0
$579$	10.9498			0.455057
$580$		0			0
$581$		−	44.7748i		−	1.85757i
$582$		0			0
$583$	8.61522	−	8.61522i	0.356806	−	0.356806i
$584$		0			0
$585$	5.05033	−	0.857115i	0.208805	−	0.0354373i
$586$		0			0
$587$	15.1930	−	15.1930i	0.627081	−	0.627081i	−0.320251	−	0.947333i	$-0.603767\pi$
$587$	15.1930	−	15.1930i	0.627081	−	0.627081i	0.947333	+	0.320251i	$0.103767\pi$
$588$		0			0
$589$	−18.7344	−	23.6105i	−0.771937	−	0.972854i
$590$		0			0
$591$	−7.03412			−0.289345
$592$		0			0
$593$	4.50648	−	4.50648i	0.185059	−	0.185059i	−0.608497	−	0.793556i	$-0.708227\pi$
$593$	4.50648	−	4.50648i	0.185059	−	0.185059i	0.793556	+	0.608497i	$0.208227\pi$
$594$		0			0
$595$	29.0220	+	20.6004i	1.18979	+	0.844533i
$596$		0			0
$597$	5.96216	+	5.96216i	0.244015	+	0.244015i
$598$		0			0
$599$		−	1.14017i		−	0.0465859i	−0.999729	−	0.0232930i	$-0.992585\pi$
$599$		−	1.14017i		−	0.0465859i	0.999729	−	0.0232930i	$-0.00741505\pi$
$600$		0			0
$601$		−	16.8924i		−	0.689055i	−0.938776	−	0.344528i	$-0.888039\pi$
$601$		−	16.8924i		−	0.689055i	0.938776	−	0.344528i	$-0.111961\pi$
$602$		0			0
$603$	−5.16207	+	5.16207i	−0.210216	+	0.210216i
$604$		0			0
$605$	18.2131	+	12.9280i	0.740469	+	0.525599i
$606$		0			0
$607$	24.4029	+	24.4029i	0.990483	+	0.990483i	0.999955	−	0.00947208i	$-0.00301510\pi$
$607$	24.4029	+	24.4029i	0.990483	+	0.990483i	−0.00947208	+	0.999955i	$0.503015\pi$
$608$		0			0
$609$			4.42871i			0.179461i
$610$		0			0
$611$			20.4305i			0.826529i
$612$		0			0
$613$	26.8537	+	26.8537i	1.08461	+	1.08461i	0.996073	+	0.0885364i	$0.0282189\pi$
$613$	26.8537	+	26.8537i	1.08461	+	1.08461i	0.0885364	+	0.996073i	$0.471781\pi$
$614$		0			0
$615$	−1.83506	−	10.8126i	−0.0739967	−	0.436007i
$616$		0			0
$617$	14.8475	+	14.8475i	0.597739	+	0.597739i	0.939710	−	0.341971i	$-0.111095\pi$
$617$	14.8475	+	14.8475i	0.597739	+	0.597739i	−0.341971	+	0.939710i	$0.611095\pi$
$618$		0			0
$619$	2.38578			0.0958927			0.0479463	−	0.998850i	$-0.484732\pi$
$619$	2.38578			0.0958927			0.0479463	+	0.998850i	$0.484732\pi$
$620$		0			0
$621$	−0.0325857			−0.00130762
$622$		0			0
$623$	−4.74669	−	4.74669i	−0.190172	−	0.190172i
$624$		0			0
$625$	−19.5574	+	15.5726i	−0.782297	+	0.622906i
$626$		0			0
$627$	3.84974	+	3.84974i	0.153744	+	0.153744i
$628$		0			0
$629$		−	23.5646i		−	0.939582i
$630$		0			0
$631$		−	38.9538i		−	1.55072i	−0.631517	−	0.775362i	$-0.717567\pi$
$631$		−	38.9538i		−	1.55072i	0.631517	−	0.775362i	$-0.282433\pi$
$632$		0			0
$633$	−2.53332	−	2.53332i	−0.100691	−	0.100691i
$634$		0			0
$635$	5.10024	−	0.865586i	0.202397	−	0.0343497i
$636$		0			0
$637$	2.38157	−	2.38157i	0.0943612	−	0.0943612i
$638$		0			0
$639$			8.00050i			0.316495i
$640$		0			0
$641$			37.0561i			1.46363i	0.681503	+	0.731815i	$0.261326\pi$
$641$			37.0561i			1.46363i	−0.681503	+	0.731815i	$0.738674\pi$
$642$		0			0
$643$	−24.3651	−	24.3651i	−0.960865	−	0.960865i	0.0383974	−	0.999263i	$-0.487775\pi$
$643$	−24.3651	−	24.3651i	−0.960865	−	0.960865i	−0.999263	+	0.0383974i	$0.987775\pi$
$644$		0			0
$645$	6.16933	−	8.69141i	0.242917	−	0.342224i
$646$		0			0
$647$	−7.68973	+	7.68973i	−0.302315	+	0.302315i	−0.841919	−	0.539604i	$-0.818574\pi$
$647$	−7.68973	+	7.68973i	−0.302315	+	0.302315i	0.539604	+	0.841919i	$0.318574\pi$
$648$		0			0
$649$	8.19328			0.321614
$650$		0			0
$651$	−10.0721	−	12.6937i	−0.394757	−	0.497503i
$652$		0			0
$653$	−31.2791	+	31.2791i	−1.22405	+	1.22405i	−0.257865	+	0.966181i	$0.583019\pi$
$653$	−31.2791	+	31.2791i	−1.22405	+	1.22405i	−0.966181	+	0.257865i	$0.916981\pi$
$654$		0			0
$655$	−1.55966	−	1.10708i	−0.0609411	−	0.0432571i
$656$		0			0
$657$	−4.34589	+	4.34589i	−0.169549	+	0.169549i
$658$		0			0
$659$		−	15.1979i		−	0.592025i	−0.955184	−	0.296012i	$-0.904343\pi$
$659$		−	15.1979i		−	0.592025i	0.955184	−	0.296012i	$-0.0956569\pi$
$660$		0			0
$661$	−41.9891			−1.63319			−0.816593	−	0.577214i	$-0.804140\pi$
$661$	−41.9891			−1.63319			−0.816593	+	0.577214i	$0.804140\pi$
$662$		0			0
$663$	8.85896	+	8.85896i	0.344054	+	0.344054i
$664$		0			0
$665$	34.7321	−	5.89455i	1.34685	−	0.228581i
$666$		0			0
$667$	0.0350624	+	0.0350624i	0.00135762	+	0.00135762i
$668$		0			0
$669$			21.1208i			0.816577i
$670$		0			0
$671$	14.7779			0.570496
$672$		0			0
$673$	−7.16198	−	7.16198i	−0.276074	−	0.276074i	0.555465	−	0.831540i	$-0.312540\pi$
$673$	−7.16198	−	7.16198i	−0.276074	−	0.276074i	−0.831540	+	0.555465i	$0.812540\pi$
$674$		0			0
$675$	4.50403	+	2.17110i	0.173360	+	0.0835657i
$676$		0			0
$677$	−15.4002	+	15.4002i	−0.591878	+	0.591878i	−0.938138	−	0.346261i	$-0.887451\pi$
$677$	−15.4002	+	15.4002i	−0.591878	+	0.591878i	0.346261	+	0.938138i	$0.387451\pi$
$678$		0			0
$679$			5.89869i			0.226371i
$680$		0			0
$681$			11.9984i			0.459781i
$682$		0			0
$683$	−26.5875	+	26.5875i	−1.01734	+	1.01734i	−0.0174967	+	0.999847i	$0.505570\pi$
$683$	−26.5875	+	26.5875i	−1.01734	+	1.01734i	−0.999847	+	0.0174967i	$0.994430\pi$
$684$		0			0
$685$	44.8569	−	7.61288i	1.71390	−	0.290873i
$686$		0			0
$687$	0.181610	+	0.181610i	0.00692886	+	0.00692886i
$688$		0			0
$689$		−	27.7525i		−	1.05729i
$690$		0			0
$691$	−34.2311			−1.30221			−0.651107	−	0.758986i	$-0.725695\pi$
$691$	−34.2311			−1.30221			−0.651107	+	0.758986i	$0.725695\pi$
$692$		0			0
$693$	2.06972	+	2.06972i	0.0786223	+	0.0786223i
$694$		0			0
$695$	−5.87765	−	4.17207i	−0.222952	−	0.158256i
$696$		0			0
$697$	18.9668	−	18.9668i	0.718419	−	0.718419i
$698$		0			0
$699$	0.852229			0.0322342
$700$		0			0
$701$	40.8969			1.54466			0.772328	−	0.635224i	$-0.219092\pi$
$701$	40.8969			1.54466			0.772328	+	0.635224i	$0.219092\pi$
$702$		0			0
$703$	−16.4935	−	16.4935i	−0.622065	−	0.622065i
$704$		0			0
$705$	−11.5428	+	16.2616i	−0.434725	+	0.612446i
$706$		0			0
$707$	−31.3348	−	31.3348i	−1.17847	−	1.17847i
$708$		0			0
$709$	−12.4592			−0.467914			−0.233957	−	0.972247i	$-0.575168\pi$
$709$	−12.4592			−0.467914			−0.233957	+	0.972247i	$0.575168\pi$
$710$		0			0
$711$		−	3.07648i		−	0.115377i
$712$		0			0
$713$	−0.180238	−	0.0207549i	−0.00674997	−	0.000777277i
$714$		0			0
$715$	−5.07925	+	0.862024i	−0.189953	+	0.0322379i
$716$		0			0
$717$	10.5943	+	10.5943i	0.395652	+	0.395652i
$718$		0			0
$719$	15.7212			0.586303			0.293152	−	0.956066i	$-0.405296\pi$
$719$	15.7212			0.586303			0.293152	+	0.956066i	$0.405296\pi$
$720$		0			0
$721$	13.6755			0.509303
$722$		0			0
$723$	9.07552	−	9.07552i	0.337522	−	0.337522i
$724$		0			0
$725$	−2.51025	−	7.18250i	−0.0932285	−	0.266751i
$726$		0			0
$727$	19.8045	+	19.8045i	0.734509	+	0.734509i	0.971510	−	0.237000i	$-0.0761643\pi$
$727$	19.8045	+	19.8045i	0.734509	+	0.734509i	−0.237000	+	0.971510i	$0.576164\pi$
$728$		0			0
$729$		−	1.00000i		−	0.0370370i
$730$		0			0
$731$	26.0678			0.964151
$732$		0			0
$733$	−35.2165	+	35.2165i	−1.30075	+	1.30075i	−0.372864	+	0.927886i	$0.621624\pi$
$733$	−35.2165	+	35.2165i	−1.30075	+	1.30075i	−0.927886	+	0.372864i	$0.878376\pi$
$734$		0			0
$735$	3.24113	−	0.550067i	0.119551	−	0.0202895i
$736$		0			0
$737$	5.19163	−	5.19163i	0.191236	−	0.191236i
$738$		0			0
$739$	−41.5683			−1.52912			−0.764558	−	0.644555i	$-0.777043\pi$
$739$	−41.5683			−1.52912			−0.764558	+	0.644555i	$0.777043\pi$
$740$		0			0
$741$	12.4013			0.455572
$742$		0			0
$743$	34.8299	+	34.8299i	1.27779	+	1.27779i	0.941904	+	0.335881i	$0.109034\pi$
$743$	34.8299	+	34.8299i	1.27779	+	1.27779i	0.335881	+	0.941904i	$0.390966\pi$
$744$		0			0
$745$	−0.650033	+	0.915774i	−0.0238154	+	0.0335514i
$746$		0			0
$747$	10.8786	−	10.8786i	0.398026	−	0.398026i
$748$		0			0
$749$		−	13.0430i		−	0.476582i
$750$		0			0
$751$	−6.71692			−0.245104			−0.122552	−	0.992462i	$-0.539108\pi$
$751$	−6.71692			−0.245104			−0.122552	+	0.992462i	$0.539108\pi$
$752$		0			0
$753$	−4.31933	+	4.31933i	−0.157405	+	0.157405i
$754$		0			0
$755$	14.7718	−	20.8106i	0.537599	−	0.757376i
$756$		0			0
$757$	13.6338	−	13.6338i	0.495528	−	0.495528i	−0.414515	−	0.910043i	$-0.636049\pi$
$757$	13.6338	−	13.6338i	0.495528	−	0.495528i	0.910043	+	0.414515i	$0.136049\pi$
$758$		0			0
$759$	0.0327723			0.00118956
$760$		0			0
$761$		−	5.06818i		−	0.183721i	−0.995772	−	0.0918607i	$-0.970719\pi$
$761$		−	5.06818i		−	0.183721i	0.995772	−	0.0918607i	$-0.0292814\pi$
$762$		0			0
$763$	−14.5683	+	14.5683i	−0.527406	+	0.527406i
$764$		0			0
$765$	2.04614	+	12.0564i	0.0739784	+	0.435898i
$766$		0			0
$767$	13.1966	−	13.1966i	0.476503	−	0.476503i
$768$		0			0
$769$			3.43119i			0.123732i	0.998084	+	0.0618659i	$0.0197051\pi$
$769$			3.43119i			0.123732i	−0.998084	+	0.0618659i	$0.980295\pi$
$770$		0			0
$771$			8.34236i			0.300443i
$772$		0			0
$773$	−21.6945	−	21.6945i	−0.780299	−	0.780299i	0.199582	−	0.979881i	$-0.436041\pi$
$773$	−21.6945	−	21.6945i	−0.780299	−	0.780299i	−0.979881	+	0.199582i	$0.936041\pi$
$774$		0			0
$775$	23.5299	+	14.8776i	0.845220	+	0.534419i
$776$		0			0
$777$	−8.86737	−	8.86737i	−0.318115	−	0.318115i
$778$		0			0
$779$		−	26.5508i		−	0.951281i
$780$		0			0
$781$		−	8.04632i		−	0.287920i
$782$		0			0
$783$	−1.07601	+	1.07601i	−0.0384534	+	0.0384534i
$784$		0			0
$785$	7.27683	+	42.8768i	0.259721	+	1.53034i
$786$		0			0
$787$	−23.1426	+	23.1426i	−0.824945	+	0.824945i	−0.986812	−	0.161868i	$-0.948248\pi$
$787$	−23.1426	+	23.1426i	−0.824945	+	0.824945i	0.161868	+	0.986812i	$0.448248\pi$
$788$		0			0
$789$			5.00115i			0.178046i
$790$		0			0
$791$	36.2538			1.28904
$792$		0			0
$793$	23.8023	−	23.8023i	0.845245	−	0.845245i
$794$		0			0
$795$	15.6795	−	22.0895i	0.556095	−	0.783432i
$796$		0			0
$797$	27.6350	−	27.6350i	0.978881	−	0.978881i	−0.0209005	−	0.999782i	$-0.506653\pi$
$797$	27.6350	−	27.6350i	0.978881	−	0.978881i	0.999782	+	0.0209005i	$0.00665330\pi$
$798$		0			0
$799$	−48.7725			−1.72545
$800$		0			0
$801$		−	2.30653i		−	0.0814973i
$802$		0			0
$803$	4.37078	−	4.37078i	0.154242	−	0.154242i
$804$		0			0
$805$	0.122745	−	0.172925i	0.00432620	−	0.00609480i
$806$		0			0
$807$	4.41409	+	4.41409i	0.155383	+	0.155383i
$808$		0			0
$809$	34.4248			1.21031			0.605155	−	0.796108i	$-0.293111\pi$
$809$	34.4248			1.21031			0.605155	+	0.796108i	$0.293111\pi$
$810$		0			0
$811$	−21.3123			−0.748377			−0.374189	−	0.927353i	$-0.622079\pi$
$811$	−21.3123			−0.748377			−0.374189	+	0.927353i	$0.622079\pi$
$812$		0			0
$813$	17.6286	−	17.6286i	0.618261	−	0.618261i
$814$		0			0
$815$	30.3588	−	5.15233i	1.06342	−	0.180478i
$816$		0			0
$817$	18.2456	−	18.2456i	0.638332	−	0.638332i
$818$		0			0
$819$	6.66726			0.232973
$820$		0			0
$821$		−	10.5414i		−	0.367898i	−0.982936	−	0.183949i	$-0.941112\pi$
$821$		−	10.5414i		−	0.367898i	0.982936	−	0.183949i	$-0.0588881\pi$
$822$		0			0
$823$	15.6469	+	15.6469i	0.545416	+	0.545416i	0.925111	−	0.379696i	$-0.123971\pi$
$823$	15.6469	+	15.6469i	0.545416	+	0.545416i	−0.379696	+	0.925111i	$0.623971\pi$
$824$		0			0
$825$	−4.52983	−	2.18354i	−0.157708	−	0.0760210i
$826$		0			0
$827$	−27.3164	+	27.3164i	−0.949884	+	0.949884i	−0.998803	−	0.0489188i	$-0.984422\pi$
$827$	−27.3164	+	27.3164i	−0.949884	+	0.949884i	0.0489188	+	0.998803i	$0.484422\pi$
$828$		0			0
$829$	31.3754			1.08971			0.544856	−	0.838530i	$-0.316584\pi$
$829$	31.3754			1.08971			0.544856	+	0.838530i	$0.316584\pi$
$830$		0			0
$831$	9.07988			0.314978
$832$		0			0
$833$	5.68538	+	5.68538i	0.196987	+	0.196987i
$834$		0			0
$835$	0.0966656	−	0.0164056i	0.00334525	−	0.000567738i
$836$		0			0
$837$	0.636934	−	5.53121i	0.0220156	−	0.191187i
$838$		0			0
$839$			32.4564i			1.12052i	0.828317	+	0.560259i	$0.189298\pi$
$839$			32.4564i			1.12052i	−0.828317	+	0.560259i	$0.810702\pi$
$840$		0			0
$841$	−26.6844			−0.920152
$842$		0			0
$843$	16.7823	+	16.7823i	0.578014	+	0.578014i
$844$		0			0
$845$	10.0332	−	14.1349i	0.345153	−	0.486255i
$846$		0			0
$847$	20.5557	+	20.5557i	0.706303	+	0.706303i
$848$		0			0
$849$	−24.4056			−0.837597
$850$		0			0
$851$	−0.140407			−0.00481310
$852$		0			0
$853$	−15.7877	+	15.7877i	−0.540560	+	0.540560i	−0.923693	−	0.383133i	$-0.874845\pi$
$853$	−15.7877	+	15.7877i	−0.540560	+	0.540560i	0.383133	+	0.923693i	$0.374845\pi$
$854$		0			0
$855$	9.87074	+	7.00643i	0.337572	+	0.239615i
$856$		0			0
$857$	18.8453	+	18.8453i	0.643744	+	0.643744i	0.951474	−	0.307730i	$-0.0995692\pi$
$857$	18.8453	+	18.8453i	0.643744	+	0.643744i	−0.307730	+	0.951474i	$0.599569\pi$
$858$		0			0
$859$	7.88204			0.268932			0.134466	−	0.990918i	$-0.457068\pi$
$859$	7.88204			0.268932			0.134466	+	0.990918i	$0.457068\pi$
$860$		0			0
$861$		−	14.2744i		−	0.486471i
$862$		0			0
$863$	−16.9278	−	16.9278i	−0.576229	−	0.576229i	0.357633	−	0.933862i	$-0.383584\pi$
$863$	−16.9278	−	16.9278i	−0.576229	−	0.576229i	−0.933862	+	0.357633i	$0.883584\pi$
$864$		0			0
$865$	−23.9599	+	4.06635i	−0.814662	+	0.138260i
$866$		0			0
$867$	−9.12768	+	9.12768i	−0.309992	+	0.309992i
$868$		0			0
$869$			3.09410i			0.104960i
$870$		0			0
$871$		−	16.7240i		−	0.566670i
$872$		0			0
$873$	−1.43316	+	1.43316i	−0.0485050	+	0.0485050i
$874$		0			0
$875$	−28.4876	+	15.7237i	−0.963055	+	0.531558i
$876$		0			0
$877$	21.8245	+	21.8245i	0.736962	+	0.736962i	0.971989	−	0.235027i	$-0.0755178\pi$
$877$	21.8245	+	21.8245i	0.736962	+	0.736962i	−0.235027	+	0.971989i	$0.575518\pi$
$878$		0			0
$879$	22.2326			0.749887
$880$		0			0
$881$			6.39498i			0.215452i	0.994181	+	0.107726i	$0.0343570\pi$
$881$			6.39498i			0.215452i	−0.994181	+	0.107726i	$0.965643\pi$
$882$		0			0
$883$	−35.5788	−	35.5788i	−1.19732	−	1.19732i	−0.974965	−	0.222358i	$-0.928625\pi$
$883$	−35.5788	−	35.5788i	−1.19732	−	1.19732i	−0.222358	−	0.974965i	$-0.571375\pi$
$884$		0			0
$885$	17.9596	−	3.04801i	0.603705	−	0.102458i
$886$		0			0
$887$	−5.71681	−	5.71681i	−0.191952	−	0.191952i	0.604587	−	0.796539i	$-0.293338\pi$
$887$	−5.71681	−	5.71681i	−0.191952	−	0.191952i	−0.796539	+	0.604587i	$0.793338\pi$
$888$		0			0
$889$	6.73316			0.225823
$890$		0			0
$891$			1.00573i			0.0336931i
$892$		0			0
$893$	−34.1373	+	34.1373i	−1.14236	+	1.14236i
$894$		0			0
$895$	−27.9206	−	19.8185i	−0.933281	−	0.662460i
$896$		0			0
$897$	0.0527852	−	0.0527852i	0.00176245	−	0.00176245i
$898$		0			0
$899$	−6.63698	+	5.26629i	−0.221356	+	0.175640i
$900$		0			0
$901$	66.2519			2.20717
$902$		0			0
$903$	9.80931	−	9.80931i	0.326433	−	0.326433i
$904$		0			0
$905$	−32.9284	+	46.3899i	−1.09458	+	1.54205i
$906$		0			0
$907$	7.41057	+	7.41057i	0.246064	+	0.246064i	0.819353	−	0.573289i	$-0.194333\pi$
$907$	7.41057	+	7.41057i	0.246064	+	0.246064i	−0.573289	+	0.819353i	$0.694333\pi$
$908$		0			0
$909$		−	15.2263i		−	0.505026i
$910$		0			0
$911$		−	1.86609i		−	0.0618262i	−0.999522	−	0.0309131i	$-0.990158\pi$
$911$		−	1.86609i		−	0.0618262i	0.999522	−	0.0309131i	$-0.00984152\pi$
$912$		0			0
$913$	−10.9409	+	10.9409i	−0.362090	+	0.362090i
$914$		0			0
$915$	32.3931	−	5.49759i	1.07088	−	0.181745i
$916$		0			0
$917$	−1.76027	−	1.76027i	−0.0581292	−	0.0581292i
$918$		0			0
$919$			39.2561i			1.29494i	0.762091	+	0.647470i	$0.224173\pi$
$919$			39.2561i			1.29494i	−0.762091	+	0.647470i	$0.775827\pi$
$920$		0			0
$921$			4.03871i			0.133080i
$922$		0			0
$923$	−12.9599	−	12.9599i	−0.426581	−	0.426581i
$924$		0			0
$925$	19.4073	+	9.35498i	0.638107	+	0.307590i
$926$		0			0
$927$	3.32263	+	3.32263i	0.109129	+	0.109129i
$928$		0			0
$929$	11.4743			0.376460			0.188230	−	0.982125i	$-0.439725\pi$
$929$	11.4743			0.376460			0.188230	+	0.982125i	$0.439725\pi$
$930$		0			0
$931$	7.95872			0.260836
$932$		0			0
$933$	6.04358	+	6.04358i	0.197858	+	0.197858i
$934$		0			0
$935$	−2.05786	−	12.1254i	−0.0672992	−	0.396543i
$936$		0			0
$937$	−8.72571	−	8.72571i	−0.285056	−	0.285056i	0.550065	−	0.835122i	$-0.314603\pi$
$937$	−8.72571	−	8.72571i	−0.285056	−	0.285056i	−0.835122	+	0.550065i	$0.814603\pi$
$938$		0			0
$939$		−	9.69257i		−	0.316305i
$940$		0			0
$941$			26.3576i			0.859232i	0.903012	+	0.429616i	$0.141351\pi$
$941$			26.3576i			0.859232i	−0.903012	+	0.429616i	$0.858649\pi$
$942$		0			0
$943$	−0.113012	−	0.113012i	−0.00368017	−	0.00368017i
$944$		0			0
$945$	5.30678	+	3.76685i	0.172629	+	0.122536i
$946$		0			0
$947$	−7.52696	+	7.52696i	−0.244593	+	0.244593i	−0.818747	−	0.574154i	$-0.805331\pi$
$947$	−7.52696	+	7.52696i	−0.244593	+	0.244593i	0.574154	+	0.818747i	$0.305331\pi$
$948$		0			0
$949$		−	14.0797i		−	0.457048i
$950$		0			0
$951$			8.24595i			0.267393i
$952$		0			0
$953$	−4.76002	−	4.76002i	−0.154192	−	0.154192i	0.625795	−	0.779987i	$-0.284775\pi$
$953$	−4.76002	−	4.76002i	−0.154192	−	0.154192i	−0.779987	+	0.625795i	$0.784775\pi$
$954$		0			0
$955$	−2.49191	−	1.76880i	−0.0806363	−	0.0572371i
$956$		0			0
$957$	1.08217	−	1.08217i	0.0349816	−	0.0349816i
$958$		0			0
$959$	59.2185			1.91227
$960$		0			0
$961$	7.04603	−	30.1886i	0.227291	−	0.973827i
$962$		0			0
$963$	3.16896	−	3.16896i	0.102118	−	0.102118i
$964$		0			0
$965$	−24.1392	+	4.09679i	−0.777070	+	0.131880i
$966$		0			0
$967$	33.6415	−	33.6415i	1.08184	−	1.08184i	0.0855009	−	0.996338i	$-0.472751\pi$
$967$	33.6415	−	33.6415i	1.08184	−	1.08184i	0.996338	−	0.0855009i	$-0.0272490\pi$
$968$		0			0
$969$			29.6049i			0.951045i
$970$		0			0
$971$	−36.8940			−1.18399			−0.591993	−	0.805943i	$-0.701659\pi$
$971$	−36.8940			−1.18399			−0.591993	+	0.805943i	$0.701659\pi$
$972$		0			0
$973$	−6.63364	−	6.63364i	−0.212665	−	0.212665i
$974$		0			0
$975$	−10.8130	+	3.77909i	−0.346293	+	0.121028i
$976$		0			0
$977$	0.644193	+	0.644193i	0.0206096	+	0.0206096i	0.717336	−	0.696727i	$-0.245361\pi$
$977$	0.644193	+	0.644193i	0.0206096	+	0.0206096i	−0.696727	+	0.717336i	$0.745361\pi$
$978$		0			0
$979$			2.31974i			0.0741392i
$980$		0			0
$981$	−7.07906			−0.226017
$982$		0			0
$983$	−14.1590	−	14.1590i	−0.451602	−	0.451602i	0.444284	−	0.895886i	$-0.353458\pi$
$983$	−14.1590	−	14.1590i	−0.451602	−	0.451602i	−0.895886	+	0.444284i	$0.853458\pi$
$984$		0			0
$985$	15.5070	−	2.63177i	0.494095	−	0.0838551i
$986$		0			0
$987$	−18.3531	+	18.3531i	−0.584187	+	0.584187i
$988$		0			0
$989$		−	0.155322i		−	0.00493895i
$990$		0			0
$991$		−	25.3764i		−	0.806106i	−0.915177	−	0.403053i	$-0.867949\pi$
$991$		−	25.3764i		−	0.806106i	0.915177	−	0.403053i	$-0.132051\pi$
$992$		0			0
$993$	23.4246	−	23.4246i	0.743357	−	0.743357i
$994$		0			0
$995$	−15.3745	−	10.9131i	−0.487406	−	0.345970i
$996$		0			0
$997$	−15.0638	−	15.0638i	−0.477076	−	0.477076i	0.427119	−	0.904195i	$-0.359529\pi$
$997$	−15.0638	−	15.0638i	−0.477076	−	0.477076i	−0.904195	+	0.427119i	$0.859529\pi$
$998$		0			0
$999$		−	4.30886i		−	0.136326i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1860.2.s.a.1177.5	yes	64
5.3	odd	4	inner	1860.2.s.a.433.26	yes	64
31.30	odd	2	inner	1860.2.s.a.1177.26	yes	64
155.123	even	4	inner	1860.2.s.a.433.5	✓	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1860.2.s.a.433.5	✓	64	155.123	even	4	inner
1860.2.s.a.433.26	yes	64	5.3	odd	4	inner
1860.2.s.a.1177.5	yes	64	1.1	even	1	trivial
1860.2.s.a.1177.26	yes	64	31.30	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1860 = 2^{2} \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1860.s (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 0.707107i) q^{3} +(1.82341 + 1.29429i) q^{5} +(2.05794 + 2.05794i) q^{7} +1.00000i q^{9} -1.00573i q^{11} +(-1.61989 - 1.61989i) q^{13} +(-0.374144 - 2.20454i) q^{15} +(3.86707 - 3.86707i) q^{17} -5.41335i q^{19} -2.91036i q^{21} +(-0.0230415 - 0.0230415i) q^{23} +(1.64963 + 4.72003i) q^{25} +(0.707107 - 0.707107i) q^{27} -1.52171 q^{29} +(4.36154 - 3.46078i) q^{31} +(-0.711157 + 0.711157i) q^{33} +(1.08889 + 6.41602i) q^{35} +(3.04683 - 3.04683i) q^{37} +2.29087i q^{39} +4.90469 q^{41} +(3.37048 + 3.37048i) q^{43} +(-1.29429 + 1.82341i) q^{45} +(-6.30613 - 6.30613i) q^{47} +1.47020i q^{49} -5.46886 q^{51} +(8.56616 + 8.56616i) q^{53} +(1.30170 - 1.83385i) q^{55} +(-3.82781 + 3.82781i) q^{57} +8.14662i q^{59} +14.6938i q^{61} +(-2.05794 + 2.05794i) q^{63} +(-0.857115 - 5.05033i) q^{65} +(5.16207 + 5.16207i) q^{67} +0.0325857i q^{69} +8.00050 q^{71} +(4.34589 + 4.34589i) q^{73} +(2.17110 - 4.50403i) q^{75} +(2.06972 - 2.06972i) q^{77} -3.07648 q^{79} -1.00000 q^{81} +(-10.8786 - 10.8786i) q^{83} +(12.0564 - 2.04614i) q^{85} +(1.07601 + 1.07601i) q^{87} -2.30653 q^{89} -6.66726i q^{91} +(-5.53121 - 0.636934i) q^{93} +(7.00643 - 9.87074i) q^{95} +(1.43316 + 1.43316i) q^{97} +1.00573 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 8 q^{7} + 16 q^{25} + 8 q^{31} - 8 q^{33} + 24 q^{35} + 16 q^{41} + 56 q^{47} + 8 q^{63} - 32 q^{67} - 16 q^{71} - 64 q^{81} - 32 q^{87} - 32 q^{95} + 64 q^{97}+O(q^{100}) \) 64 * q - 8 * q^7 + 16 * q^25 + 8 * q^31 - 8 * q^33 + 24 * q^35 + 16 * q^41 + 56 * q^47 + 8 * q^63 - 32 * q^67 - 16 * q^71 - 64 * q^81 - 32 * q^87 - 32 * q^95 + 64 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more