LMFDB - Embedded newform 1860.2.s.a.1177.6

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			1177.6
Character	$\chi$	$=$	1860.1177
Dual form			1860.2.s.a.433.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.707107 - 0.707107i) q^{3} +(-0.193900 + 2.22765i) q^{5} +(-2.45774 - 2.45774i) q^{7} +1.00000i q^{9} -2.71402i q^{11} +(3.28292 + 3.28292i) q^{13} +(1.71229 - 1.43807i) q^{15} +(-1.47309 + 1.47309i) q^{17} -2.29182i q^{19} +3.47577i q^{21} +(1.10448 + 1.10448i) q^{23} +(-4.92481 - 0.863882i) q^{25} +(0.707107 - 0.707107i) q^{27} +1.82309 q^{29} +(-5.56269 - 0.237761i) q^{31} +(-1.91910 + 1.91910i) q^{33} +(5.95153 - 4.99842i) q^{35} +(-4.28242 + 4.28242i) q^{37} -4.64275i q^{39} +6.87600 q^{41} +(4.47584 + 4.47584i) q^{43} +(-2.22765 - 0.193900i) q^{45} +(-1.11839 - 1.11839i) q^{47} +5.08097i q^{49} +2.08327 q^{51} +(6.61030 + 6.61030i) q^{53} +(6.04587 + 0.526249i) q^{55} +(-1.62056 + 1.62056i) q^{57} +6.91537i q^{59} +9.59089i q^{61} +(2.45774 - 2.45774i) q^{63} +(-7.94974 + 6.67662i) q^{65} +(0.811325 + 0.811325i) q^{67} -1.56197i q^{69} -0.0283312 q^{71} +(6.32948 + 6.32948i) q^{73} +(2.87151 + 4.09322i) q^{75} +(-6.67036 + 6.67036i) q^{77} -8.59322 q^{79} -1.00000 q^{81} +(10.5286 + 10.5286i) q^{83} +(-2.99590 - 3.56717i) q^{85} +(-1.28912 - 1.28912i) q^{87} +1.53775 q^{89} -16.1371i q^{91} +(3.76529 + 4.10154i) q^{93} +(5.10537 + 0.444385i) q^{95} +(6.71200 + 6.71200i) q^{97} +2.71402 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	−0.193900	+	2.22765i	−0.0867148	+	0.996233i
$5$	−0.193900	+	2.22765i	−0.0867148	+	0.996233i
$6$		0			0
$7$	−2.45774	−	2.45774i	−0.928938	−	0.928938i	0.0686991	−	0.997637i	$-0.478115\pi$
$7$	−2.45774	−	2.45774i	−0.928938	−	0.928938i	−0.997637	+	0.0686991i	$0.978115\pi$
$8$		0			0
$9$			1.00000i			0.333333i
$10$		0			0
$11$		−	2.71402i		−	0.818308i	−0.912465	−	0.409154i	$-0.865824\pi$
$11$		−	2.71402i		−	0.818308i	0.912465	−	0.409154i	$-0.134176\pi$
$12$		0			0
$13$	3.28292	+	3.28292i	0.910518	+	0.910518i	0.996313	−	0.0857948i	$-0.0273429\pi$
$13$	3.28292	+	3.28292i	0.910518	+	0.910518i	−0.0857948	+	0.996313i	$0.527343\pi$
$14$		0			0
$15$	1.71229	−	1.43807i	0.442112	−	0.371309i
$16$		0			0
$17$	−1.47309	+	1.47309i	−0.357278	+	0.357278i	−0.862809	−	0.505531i	$-0.831297\pi$
$17$	−1.47309	+	1.47309i	−0.357278	+	0.357278i	0.505531	+	0.862809i	$0.331297\pi$
$18$		0			0
$19$		−	2.29182i		−	0.525780i	−0.964826	−	0.262890i	$-0.915324\pi$
$19$		−	2.29182i		−	0.525780i	0.964826	−	0.262890i	$-0.0846757\pi$
$20$		0			0
$21$			3.47577i			0.758475i
$22$		0			0
$23$	1.10448	+	1.10448i	0.230299	+	0.230299i	0.812818	−	0.582518i	$-0.197933\pi$
$23$	1.10448	+	1.10448i	0.230299	+	0.230299i	−0.582518	+	0.812818i	$0.697933\pi$
$24$		0			0
$25$	−4.92481	−	0.863882i	−0.984961	−	0.172776i
$26$		0			0
$27$	0.707107	−	0.707107i	0.136083	−	0.136083i
$28$		0			0
$29$	1.82309			0.338540			0.169270	−	0.985570i	$-0.445859\pi$
$29$	1.82309			0.338540			0.169270	+	0.985570i	$0.445859\pi$
$30$		0			0
$31$	−5.56269	−	0.237761i	−0.999088	−	0.0427032i
$31$	−5.56269	−	0.237761i	−0.999088	−	0.0427032i
$32$		0			0
$33$	−1.91910	+	1.91910i	−0.334073	+	0.334073i
$34$		0			0
$35$	5.95153	−	4.99842i	1.00599	−	0.844887i
$36$		0			0
$37$	−4.28242	+	4.28242i	−0.704025	+	0.704025i	−0.965272	−	0.261247i	$-0.915866\pi$
$37$	−4.28242	+	4.28242i	−0.704025	+	0.704025i	0.261247	+	0.965272i	$0.415866\pi$
$38$		0			0
$39$		−	4.64275i		−	0.743435i
$40$		0			0
$41$	6.87600			1.07385			0.536925	−	0.843630i	$-0.319586\pi$
$41$	6.87600			1.07385			0.536925	+	0.843630i	$0.319586\pi$
$42$		0			0
$43$	4.47584	+	4.47584i	0.682560	+	0.682560i	0.960576	−	0.278017i	$-0.0896770\pi$
$43$	4.47584	+	4.47584i	0.682560	+	0.682560i	−0.278017	+	0.960576i	$0.589677\pi$
$44$		0			0
$45$	−2.22765	−	0.193900i	−0.332078	−	0.0289049i
$46$		0			0
$47$	−1.11839	−	1.11839i	−0.163134	−	0.163134i	0.620819	−	0.783954i	$-0.286800\pi$
$47$	−1.11839	−	1.11839i	−0.163134	−	0.163134i	−0.783954	+	0.620819i	$0.786800\pi$
$48$		0			0
$49$			5.08097i			0.725853i
$50$		0			0
$51$	2.08327			0.291716
$52$		0			0
$53$	6.61030	+	6.61030i	0.907995	+	0.907995i	0.996110	−	0.0881152i	$-0.0280844\pi$
$53$	6.61030	+	6.61030i	0.907995	+	0.907995i	−0.0881152	+	0.996110i	$0.528084\pi$
$54$		0			0
$55$	6.04587	+	0.526249i	0.815225	+	0.0709594i
$56$		0			0
$57$	−1.62056	+	1.62056i	−0.214649	+	0.214649i
$58$		0			0
$59$			6.91537i			0.900304i	0.892952	+	0.450152i	$0.148630\pi$
$59$			6.91537i			0.900304i	−0.892952	+	0.450152i	$0.851370\pi$
$60$		0			0
$61$			9.59089i			1.22799i	0.789311	+	0.613994i	$0.210438\pi$
$61$			9.59089i			1.22799i	−0.789311	+	0.613994i	$0.789562\pi$
$62$		0			0
$63$	2.45774	−	2.45774i	0.309646	−	0.309646i
$64$		0			0
$65$	−7.94974	+	6.67662i	−0.986044	+	0.828133i
$66$		0			0
$67$	0.811325	+	0.811325i	0.0991191	+	0.0991191i	0.754927	−	0.655808i	$-0.227672\pi$
$67$	0.811325	+	0.811325i	0.0991191	+	0.0991191i	−0.655808	+	0.754927i	$0.727672\pi$
$68$		0			0
$69$		−	1.56197i		−	0.188039i
$70$		0			0
$71$	−0.0283312			−0.00336229			−0.00168115	−	0.999999i	$-0.500535\pi$
$71$	−0.0283312			−0.00336229			−0.00168115	+	0.999999i	$0.500535\pi$
$72$		0			0
$73$	6.32948	+	6.32948i	0.740809	+	0.740809i	0.972734	−	0.231925i	$-0.0745022\pi$
$73$	6.32948	+	6.32948i	0.740809	+	0.740809i	−0.231925	+	0.972734i	$0.574502\pi$
$74$		0			0
$75$	2.87151	+	4.09322i	0.331573	+	0.472644i
$76$		0			0
$77$	−6.67036	+	6.67036i	−0.760158	+	0.760158i
$78$		0			0
$79$	−8.59322			−0.966813			−0.483406	−	0.875396i	$-0.660601\pi$
$79$	−8.59322			−0.966813			−0.483406	+	0.875396i	$0.660601\pi$
$80$		0			0
$81$	−1.00000			−0.111111
$82$		0			0
$83$	10.5286	+	10.5286i	1.15566	+	1.15566i	0.985398	+	0.170265i	$0.0544623\pi$
$83$	10.5286	+	10.5286i	1.15566	+	1.15566i	0.170265	+	0.985398i	$0.445538\pi$
$84$		0			0
$85$	−2.99590	−	3.56717i	−0.324951	−	0.386913i
$86$		0			0
$87$	−1.28912	−	1.28912i	−0.138208	−	0.138208i
$88$		0			0
$89$	1.53775			0.163001			0.0815006	−	0.996673i	$-0.474029\pi$
$89$	1.53775			0.163001			0.0815006	+	0.996673i	$0.474029\pi$
$90$		0			0
$91$		−	16.1371i		−	1.69163i
$92$		0			0
$93$	3.76529	+	4.10154i	0.390442	+	0.425309i
$94$		0			0
$95$	5.10537	+	0.444385i	0.523800	+	0.0455929i
$96$		0			0
$97$	6.71200	+	6.71200i	0.681500	+	0.681500i	0.960338	−	0.278838i	$-0.0899493\pi$
$97$	6.71200	+	6.71200i	0.681500	+	0.681500i	−0.278838	+	0.960338i	$0.589949\pi$
$98$		0			0
$99$	2.71402			0.272769
$100$		0			0
$101$	−17.2493			−1.71637			−0.858186	−	0.513339i	$-0.828408\pi$
$101$	−17.2493			−1.71637			−0.858186	+	0.513339i	$0.828408\pi$
$102$		0			0
$103$	−12.4100	+	12.4100i	−1.22280	+	1.22280i	−0.256162	+	0.966634i	$0.582458\pi$
$103$	−12.4100	+	12.4100i	−1.22280	+	1.22280i	−0.966634	+	0.256162i	$0.917542\pi$
$104$		0			0
$105$	−7.74278	−	0.673952i	−0.755618	−	0.0657710i
$106$		0			0
$107$	8.58946	+	8.58946i	0.830375	+	0.830375i	0.987568	−	0.157193i	$-0.0502445\pi$
$107$	8.58946	+	8.58946i	0.830375	+	0.830375i	−0.157193	+	0.987568i	$0.550244\pi$
$108$		0			0
$109$		−	3.26217i		−	0.312460i	−0.987721	−	0.156230i	$-0.950066\pi$
$109$		−	3.26217i		−	0.312460i	0.987721	−	0.156230i	$-0.0499340\pi$
$110$		0			0
$111$	6.05625			0.574834
$112$		0			0
$113$	7.70976	−	7.70976i	0.725273	−	0.725273i	−0.244401	−	0.969674i	$-0.578591\pi$
$113$	7.70976	−	7.70976i	0.725273	−	0.725273i	0.969674	+	0.244401i	$0.0785914\pi$
$114$		0			0
$115$	−2.67454	+	2.24622i	−0.249402	+	0.209461i
$116$		0			0
$117$	−3.28292	+	3.28292i	−0.303506	+	0.303506i
$118$		0			0
$119$	7.24097			0.663778
$120$		0			0
$121$	3.63409			0.330372
$122$		0			0
$123$	−4.86206	−	4.86206i	−0.438398	−	0.438398i
$124$		0			0
$125$	2.87934	−	10.8032i	0.257536	−	0.966269i
$126$		0			0
$127$	−4.70529	+	4.70529i	−0.417527	+	0.417527i	−0.884350	−	0.466824i	$-0.845398\pi$
$127$	−4.70529	+	4.70529i	−0.417527	+	0.417527i	0.466824	+	0.884350i	$0.345398\pi$
$128$		0			0
$129$		−	6.32980i		−	0.557308i
$130$		0			0
$131$	1.20032			0.104872			0.0524361	−	0.998624i	$-0.483301\pi$
$131$	1.20032			0.104872			0.0524361	+	0.998624i	$0.483301\pi$
$132$		0			0
$133$	−5.63271	+	5.63271i	−0.488417	+	0.488417i
$134$		0			0
$135$	1.43807	+	1.71229i	0.123770	+	0.147371i
$136$		0			0
$137$	−4.78518	+	4.78518i	−0.408825	+	0.408825i	−0.881329	−	0.472504i	$-0.843350\pi$
$137$	−4.78518	+	4.78518i	−0.408825	+	0.408825i	0.472504	+	0.881329i	$0.343350\pi$
$138$		0			0
$139$	−2.07578			−0.176066			−0.0880328	−	0.996118i	$-0.528058\pi$
$139$	−2.07578			−0.176066			−0.0880328	+	0.996118i	$0.528058\pi$
$140$		0			0
$141$			1.58165i			0.133199i
$142$		0			0
$143$	8.90991	−	8.90991i	0.745084	−	0.745084i
$144$		0			0
$145$	−0.353498	+	4.06121i	−0.0293564	+	0.337265i
$146$		0			0
$147$	3.59279	−	3.59279i	0.296328	−	0.296328i
$148$		0			0
$149$		−	2.77646i		−	0.227457i	−0.993512	−	0.113728i	$-0.963721\pi$
$149$		−	2.77646i		−	0.227457i	0.993512	−	0.113728i	$-0.0362794\pi$
$150$		0			0
$151$			9.22131i			0.750419i	0.926940	+	0.375210i	$0.122429\pi$
$151$			9.22131i			0.750419i	−0.926940	+	0.375210i	$0.877571\pi$
$152$		0			0
$153$	−1.47309	−	1.47309i	−0.119093	−	0.119093i
$154$		0			0
$155$	1.60825	−	12.3456i	0.129178	−	0.991621i
$156$		0			0
$157$	10.7087	+	10.7087i	0.854645	+	0.854645i	0.990701	−	0.136056i	$-0.0434427\pi$
$157$	10.7087	+	10.7087i	0.854645	+	0.854645i	−0.136056	+	0.990701i	$0.543443\pi$
$158$		0			0
$159$		−	9.34838i		−	0.741375i
$160$		0			0
$161$		−	5.42903i		−	0.427868i
$162$		0			0
$163$	−11.6845	+	11.6845i	−0.915197	+	0.915197i	−0.996675	−	0.0814778i	$-0.974036\pi$
$163$	−11.6845	+	11.6845i	−0.915197	+	0.915197i	0.0814778	+	0.996675i	$0.474036\pi$
$164$		0			0
$165$	−3.90296	−	4.64719i	−0.303845	−	0.361783i
$166$		0			0
$167$	−8.18179	+	8.18179i	−0.633126	+	0.633126i	−0.948851	−	0.315725i	$-0.897752\pi$
$167$	−8.18179	+	8.18179i	−0.633126	+	0.633126i	0.315725	+	0.948851i	$0.397752\pi$
$168$		0			0
$169$			8.55512i			0.658086i
$170$		0			0
$171$	2.29182			0.175260
$172$		0			0
$173$	4.12255	−	4.12255i	0.313432	−	0.313432i	−0.532806	−	0.846238i	$-0.678862\pi$
$173$	4.12255	−	4.12255i	0.313432	−	0.313432i	0.846238	+	0.532806i	$0.178862\pi$
$174$		0			0
$175$	9.98069	+	14.2271i	0.754470	+	1.07547i
$176$		0			0
$177$	4.88990	−	4.88990i	0.367548	−	0.367548i
$178$		0			0
$179$	24.6854			1.84507			0.922537	−	0.385908i	$-0.126112\pi$
$179$	24.6854			1.84507			0.922537	+	0.385908i	$0.126112\pi$
$180$		0			0
$181$		−	11.9435i		−	0.887754i	−0.896088	−	0.443877i	$-0.853603\pi$
$181$		−	11.9435i		−	0.887754i	0.896088	−	0.443877i	$-0.146397\pi$
$182$		0			0
$183$	6.78178	−	6.78178i	0.501324	−	0.501324i
$184$		0			0
$185$	−8.70935	−	10.3701i	−0.640324	−	0.762423i
$186$		0			0
$187$	3.99801	+	3.99801i	0.292363	+	0.292363i
$188$		0			0
$189$	−3.47577			−0.252825
$190$		0			0
$191$	−20.6436			−1.49372			−0.746858	−	0.664984i	$-0.768438\pi$
$191$	−20.6436			−1.49372			−0.746858	+	0.664984i	$0.768438\pi$
$192$		0			0
$193$	−4.72497	+	4.72497i	−0.340111	+	0.340111i	−0.856409	−	0.516298i	$-0.827310\pi$
$193$	−4.72497	+	4.72497i	−0.340111	+	0.340111i	0.516298	+	0.856409i	$0.327310\pi$
$194$		0			0
$195$	10.3424	+	0.900230i	0.740634	+	0.0644668i
$196$		0			0
$197$	15.9430	−	15.9430i	1.13589	−	1.13589i	0.146710	−	0.989180i	$-0.453132\pi$
$197$	15.9430	−	15.9430i	1.13589	−	1.13589i	0.989180	−	0.146710i	$-0.0468684\pi$
$198$		0			0
$199$	18.6097			1.31921			0.659605	−	0.751613i	$-0.270724\pi$
$199$	18.6097			1.31921			0.659605	+	0.751613i	$0.270724\pi$
$200$		0			0
$201$		−	1.14739i		−	0.0809304i
$202$		0			0
$203$	−4.48069	−	4.48069i	−0.314483	−	0.314483i
$204$		0			0
$205$	−1.33326	+	15.3173i	−0.0931187	+	1.06981i
$206$		0			0
$207$	−1.10448	+	1.10448i	−0.0767664	+	0.0767664i
$208$		0			0
$209$	−6.22005			−0.430250
$210$		0			0
$211$	−15.1401			−1.04229			−0.521145	−	0.853468i	$-0.674495\pi$
$211$	−15.1401			−1.04229			−0.521145	+	0.853468i	$0.674495\pi$
$212$		0			0
$213$	0.0200332	+	0.0200332i	0.00137265	+	0.00137265i
$214$		0			0
$215$	−10.8385	+	9.10272i	−0.739177	+	0.620801i
$216$		0			0
$217$	13.0873	+	14.2560i	0.888422	+	0.967760i
$218$		0			0
$219$		−	8.95123i		−	0.604868i
$220$		0			0
$221$	−9.67210			−0.650616
$222$		0			0
$223$	17.6458	+	17.6458i	1.18165	+	1.18165i	0.979317	+	0.202330i	$0.0648513\pi$
$223$	17.6458	+	17.6458i	1.18165	+	1.18165i	0.202330	+	0.979317i	$0.435149\pi$
$224$		0			0
$225$	0.863882	−	4.92481i	0.0575921	−	0.328320i
$226$		0			0
$227$	−1.13568	−	1.13568i	−0.0753776	−	0.0753776i	0.668413	−	0.743790i	$-0.266974\pi$
$227$	−1.13568	−	1.13568i	−0.0753776	−	0.0753776i	−0.743790	+	0.668413i	$0.766974\pi$
$228$		0			0
$229$	1.59282			0.105256			0.0526282	−	0.998614i	$-0.483240\pi$
$229$	1.59282			0.105256			0.0526282	+	0.998614i	$0.483240\pi$
$230$		0			0
$231$	9.43331			0.620666
$232$		0			0
$233$	7.52086	−	7.52086i	0.492708	−	0.492708i	−0.416450	−	0.909158i	$-0.636726\pi$
$233$	7.52086	−	7.52086i	0.492708	−	0.492708i	0.909158	+	0.416450i	$0.136726\pi$
$234$		0			0
$235$	2.70824	−	2.27453i	0.176666	−	0.148374i
$236$		0			0
$237$	6.07632	+	6.07632i	0.394700	+	0.394700i
$238$		0			0
$239$	4.96761			0.321328			0.160664	−	0.987009i	$-0.448636\pi$
$239$	4.96761			0.321328			0.160664	+	0.987009i	$0.448636\pi$
$240$		0			0
$241$			3.16154i			0.203653i	0.994802	+	0.101826i	$0.0324686\pi$
$241$			3.16154i			0.203653i	−0.994802	+	0.101826i	$0.967531\pi$
$242$		0			0
$243$	0.707107	+	0.707107i	0.0453609	+	0.0453609i
$244$		0			0
$245$	−11.3186	−	0.985201i	−0.723119	−	0.0629422i
$246$		0			0
$247$	7.52387	−	7.52387i	0.478732	−	0.478732i
$248$		0			0
$249$		−	14.8897i		−	0.943595i
$250$		0			0
$251$		−	20.1749i		−	1.27343i	−0.771099	−	0.636715i	$-0.780293\pi$
$251$		−	20.1749i		−	1.27343i	0.771099	−	0.636715i	$-0.219707\pi$
$252$		0			0
$253$	2.99757	−	2.99757i	0.188456	−	0.188456i
$254$		0			0
$255$	−0.403947	+	4.64079i	−0.0252961	+	0.290617i
$256$		0			0
$257$	−2.75948	−	2.75948i	−0.172132	−	0.172132i	0.615784	−	0.787915i	$-0.288840\pi$
$257$	−2.75948	−	2.75948i	−0.172132	−	0.172132i	−0.787915	+	0.615784i	$0.788840\pi$
$258$		0			0
$259$	21.0501			1.30799
$260$		0			0
$261$			1.82309i			0.112847i
$262$		0			0
$263$	−15.0096	−	15.0096i	−0.925534	−	0.925534i	0.0718793	−	0.997413i	$-0.477100\pi$
$263$	−15.0096	−	15.0096i	−0.925534	−	0.925534i	−0.997413	+	0.0718793i	$0.977100\pi$
$264$		0			0
$265$	−16.0072	+	13.4437i	−0.983311	+	0.825838i
$266$		0			0
$267$	−1.08735	−	1.08735i	−0.0665450	−	0.0665450i
$268$		0			0
$269$	6.88799			0.419968			0.209984	−	0.977705i	$-0.432659\pi$
$269$	6.88799			0.419968			0.209984	+	0.977705i	$0.432659\pi$
$270$		0			0
$271$			0.519309i			0.0315458i	0.999876	+	0.0157729i	$0.00502088\pi$
$271$			0.519309i			0.0315458i	−0.999876	+	0.0157729i	$0.994979\pi$
$272$		0			0
$273$	−11.4107	+	11.4107i	−0.690605	+	0.690605i
$274$		0			0
$275$	−2.34459	+	13.3660i	−0.141384	+	0.806001i
$276$		0			0
$277$	−4.28182	+	4.28182i	−0.257270	+	0.257270i	−0.823943	−	0.566673i	$-0.808230\pi$
$277$	−4.28182	+	4.28182i	−0.257270	+	0.257270i	0.566673	+	0.823943i	$0.308230\pi$
$278$		0			0
$279$	0.237761	−	5.56269i	0.0142344	−	0.333029i
$280$		0			0
$281$	−11.5724			−0.690353			−0.345176	−	0.938538i	$-0.612181\pi$
$281$	−11.5724			−0.690353			−0.345176	+	0.938538i	$0.612181\pi$
$282$		0			0
$283$	−2.45482	+	2.45482i	−0.145924	+	0.145924i	−0.776294	−	0.630371i	$-0.782903\pi$
$283$	−2.45482	+	2.45482i	−0.145924	+	0.145924i	0.630371	+	0.776294i	$0.282903\pi$
$284$		0			0
$285$	−3.29581	−	3.92427i	−0.195227	−	0.232454i
$286$		0			0
$287$	−16.8994	−	16.8994i	−0.997541	−	0.997541i
$288$		0			0
$289$			12.6600i			0.744705i
$290$		0			0
$291$		−	9.49220i		−	0.556442i
$292$		0			0
$293$	10.3416	−	10.3416i	0.604163	−	0.604163i	−0.337251	−	0.941415i	$-0.609497\pi$
$293$	10.3416	−	10.3416i	0.604163	−	0.604163i	0.941415	+	0.337251i	$0.109497\pi$
$294$		0			0
$295$	−15.4050	−	1.34089i	−0.896913	−	0.0780697i
$296$		0			0
$297$	−1.91910	−	1.91910i	−0.111358	−	0.111358i
$298$		0			0
$299$			7.25181i			0.419383i
$300$		0			0
$301$		−	22.0009i		−	1.26811i
$302$		0			0
$303$	12.1971	+	12.1971i	0.700706	+	0.700706i
$304$		0			0
$305$	−21.3651	−	1.85968i	−1.22336	−	0.106485i
$306$		0			0
$307$	−20.9033	−	20.9033i	−1.19301	−	1.19301i	−0.976217	−	0.216795i	$-0.930440\pi$
$307$	−20.9033	−	20.9033i	−1.19301	−	1.19301i	−0.216795	−	0.976217i	$-0.569560\pi$
$308$		0			0
$309$	17.5504			0.998409
$310$		0			0
$311$	20.4650			1.16046			0.580232	−	0.814452i	$-0.302962\pi$
$311$	20.4650			1.16046			0.580232	+	0.814452i	$0.302962\pi$
$312$		0			0
$313$	−20.4512	−	20.4512i	−1.15597	−	1.15597i	−0.985334	−	0.170637i	$-0.945418\pi$
$313$	−20.4512	−	20.4512i	−1.15597	−	1.15597i	−0.170637	−	0.985334i	$-0.554582\pi$
$314$		0			0
$315$	4.99842	+	5.95153i	0.281629	+	0.335331i
$316$		0			0
$317$	−15.9401	−	15.9401i	−0.895286	−	0.895286i	0.0997288	−	0.995015i	$-0.468202\pi$
$317$	−15.9401	−	15.9401i	−0.895286	−	0.895286i	−0.995015	+	0.0997288i	$0.968202\pi$
$318$		0			0
$319$		−	4.94791i		−	0.277030i
$320$		0			0
$321$		−	12.1473i		−	0.677998i
$322$		0			0
$323$	3.37607	+	3.37607i	0.187850	+	0.187850i
$324$		0			0
$325$	−13.3317	−	19.0038i	−0.739509	−	1.05414i
$326$		0			0
$327$	−2.30670	+	2.30670i	−0.127561	+	0.127561i
$328$		0			0
$329$			5.49744i			0.303083i
$330$		0			0
$331$		−	17.8576i		−	0.981545i	−0.871288	−	0.490772i	$-0.836715\pi$
$331$		−	17.8576i		−	0.981545i	0.871288	−	0.490772i	$-0.163285\pi$
$332$		0			0
$333$	−4.28242	−	4.28242i	−0.234675	−	0.234675i
$334$		0			0
$335$	−1.96466	+	1.65003i	−0.107341	+	0.0901507i
$336$		0			0
$337$	−10.9905	+	10.9905i	−0.598691	+	0.598691i	−0.939964	−	0.341273i	$-0.889142\pi$
$337$	−10.9905	+	10.9905i	−0.598691	+	0.598691i	0.341273	+	0.939964i	$0.389142\pi$
$338$		0			0
$339$	−10.9032			−0.592183
$340$		0			0
$341$	−0.645289	+	15.0972i	−0.0349444	+	0.817561i
$342$		0			0
$343$	−4.71647	+	4.71647i	−0.254666	+	0.254666i
$344$		0			0
$345$	3.47951	+	0.302865i	0.187330	+	0.0163057i
$346$		0			0
$347$	−0.520869	+	0.520869i	−0.0279617	+	0.0279617i	−0.720949	−	0.692988i	$-0.756294\pi$
$347$	−0.520869	+	0.520869i	−0.0279617	+	0.0279617i	0.692988	+	0.720949i	$0.256294\pi$
$348$		0			0
$349$			15.6728i			0.838947i	0.907768	+	0.419474i	$0.137785\pi$
$349$			15.6728i			0.838947i	−0.907768	+	0.419474i	$0.862215\pi$
$350$		0			0
$351$	4.64275			0.247812
$352$		0			0
$353$	−5.62429	−	5.62429i	−0.299351	−	0.299351i	0.541409	−	0.840760i	$-0.317891\pi$
$353$	−5.62429	−	5.62429i	−0.299351	−	0.299351i	−0.840760	+	0.541409i	$0.817891\pi$
$354$		0			0
$355$	0.00549342	−	0.0631118i	0.000291560	−	0.00334963i
$356$		0			0
$357$	−5.12014	−	5.12014i	−0.270986	−	0.270986i
$358$		0			0
$359$			5.19621i			0.274245i	0.990554	+	0.137123i	$0.0437854\pi$
$359$			5.19621i			0.274245i	−0.990554	+	0.137123i	$0.956215\pi$
$360$		0			0
$361$	13.7475			0.723555
$362$		0			0
$363$	−2.56969	−	2.56969i	−0.134874	−	0.134874i
$364$		0			0
$365$	−15.3271	+	12.8725i	−0.802258	+	0.673780i
$366$		0			0
$367$	−8.10340	+	8.10340i	−0.422994	+	0.422994i	−0.886233	−	0.463239i	$-0.846687\pi$
$367$	−8.10340	+	8.10340i	−0.422994	+	0.422994i	0.463239	+	0.886233i	$0.346687\pi$
$368$		0			0
$369$			6.87600i			0.357950i
$370$		0			0
$371$		−	32.4928i		−	1.68694i
$372$		0			0
$373$	−19.1745	+	19.1745i	−0.992820	+	0.992820i	−0.999974	−	0.00715443i	$-0.997723\pi$
$373$	−19.1745	+	19.1745i	−0.992820	+	0.992820i	0.00715443	+	0.999974i	$0.497723\pi$
$374$		0			0
$375$	−9.67503	+	5.60302i	−0.499616	+	0.289339i
$376$		0			0
$377$	5.98507	+	5.98507i	0.308247	+	0.308247i
$378$		0			0
$379$		−	33.6200i		−	1.72695i	−0.504396	−	0.863473i	$-0.668285\pi$
$379$		−	33.6200i		−	1.72695i	0.504396	−	0.863473i	$-0.331715\pi$
$380$		0			0
$381$	6.65428			0.340909
$382$		0			0
$383$	5.51918	+	5.51918i	0.282017	+	0.282017i	0.833913	−	0.551896i	$-0.186095\pi$
$383$	5.51918	+	5.51918i	0.282017	+	0.282017i	−0.551896	+	0.833913i	$0.686095\pi$
$384$		0			0
$385$	−13.5658	−	16.1526i	−0.691377	−	0.823211i
$386$		0			0
$387$	−4.47584	+	4.47584i	−0.227520	+	0.227520i
$388$		0			0
$389$	−28.8415			−1.46232			−0.731160	−	0.682206i	$-0.761021\pi$
$389$	−28.8415			−1.46232			−0.731160	+	0.682206i	$0.761021\pi$
$390$		0			0
$391$	−3.25400			−0.164562
$392$		0			0
$393$	−0.848752	−	0.848752i	−0.0428139	−	0.0428139i
$394$		0			0
$395$	1.66623	−	19.1426i	0.0838370	−	0.963171i
$396$		0			0
$397$	−10.1875	−	10.1875i	−0.511297	−	0.511297i	0.403627	−	0.914924i	$-0.367749\pi$
$397$	−10.1875	−	10.1875i	−0.511297	−	0.511297i	−0.914924	+	0.403627i	$0.867749\pi$
$398$		0			0
$399$	7.96585			0.398791
$400$		0			0
$401$		−	29.9852i		−	1.49739i	−0.662916	−	0.748694i	$-0.730681\pi$
$401$		−	29.9852i		−	1.49739i	0.662916	−	0.748694i	$-0.269319\pi$
$402$		0			0
$403$	−17.4813	−	19.0424i	−0.870805	−	0.948569i
$404$		0			0
$405$	0.193900	−	2.22765i	0.00963498	−	0.110693i
$406$		0			0
$407$	11.6226	+	11.6226i	0.576109	+	0.576109i
$408$		0			0
$409$	24.5560			1.21422			0.607108	−	0.794620i	$-0.292330\pi$
$409$	24.5560			1.21422			0.607108	+	0.794620i	$0.292330\pi$
$410$		0			0
$411$	6.76726			0.333804
$412$		0			0
$413$	16.9962	−	16.9962i	0.836327	−	0.836327i
$414$		0			0
$415$	−25.4955	+	21.4125i	−1.25152	+	1.05110i
$416$		0			0
$417$	1.46780	+	1.46780i	0.0718785	+	0.0718785i
$418$		0			0
$419$			6.12061i			0.299011i	0.988761	+	0.149506i	$0.0477682\pi$
$419$			6.12061i			0.299011i	−0.988761	+	0.149506i	$0.952232\pi$
$420$		0			0
$421$	4.79546			0.233717			0.116858	−	0.993149i	$-0.462718\pi$
$421$	4.79546			0.233717			0.116858	+	0.993149i	$0.462718\pi$
$422$		0			0
$423$	1.11839	−	1.11839i	0.0543781	−	0.0543781i
$424$		0			0
$425$	8.52728	−	5.98212i	0.413634	−	0.290176i
$426$		0			0
$427$	23.5719	−	23.5719i	1.14072	−	1.14072i
$428$		0			0
$429$	−12.6005			−0.608359
$430$		0			0
$431$	23.2078			1.11788			0.558941	−	0.829207i	$-0.311208\pi$
$431$	23.2078			1.11788			0.558941	+	0.829207i	$0.311208\pi$
$432$		0			0
$433$	−22.0504	−	22.0504i	−1.05967	−	1.05967i	−0.998103	−	0.0615709i	$-0.980389\pi$
$433$	−22.0504	−	22.0504i	−1.05967	−	1.05967i	−0.0615709	−	0.998103i	$-0.519611\pi$
$434$		0			0
$435$	3.12167	−	2.62175i	0.149673	−	0.125703i
$436$		0			0
$437$	2.53126	−	2.53126i	0.121087	−	0.121087i
$438$		0			0
$439$			21.0653i			1.00539i	0.864463	+	0.502696i	$0.167659\pi$
$439$			21.0653i			1.00539i	−0.864463	+	0.502696i	$0.832341\pi$
$440$		0			0
$441$	−5.08097			−0.241951
$442$		0			0
$443$	−17.4338	+	17.4338i	−0.828306	+	0.828306i	−0.987282	−	0.158976i	$-0.949181\pi$
$443$	−17.4338	+	17.4338i	−0.828306	+	0.828306i	0.158976	+	0.987282i	$0.449181\pi$
$444$		0			0
$445$	−0.298170	+	3.42556i	−0.0141346	+	0.162387i
$446$		0			0
$447$	−1.96326	+	1.96326i	−0.0928589	+	0.0928589i
$448$		0			0
$449$	−18.2055			−0.859172			−0.429586	−	0.903026i	$-0.641340\pi$
$449$	−18.2055			−0.859172			−0.429586	+	0.903026i	$0.641340\pi$
$450$		0			0
$451$		−	18.6616i		−	0.878740i
$452$		0			0
$453$	6.52045	−	6.52045i	0.306357	−	0.306357i
$454$		0			0
$455$	35.9478	+	3.12899i	1.68526	+	0.146689i
$456$		0			0
$457$	−9.67798	+	9.67798i	−0.452717	+	0.452717i	−0.896255	−	0.443539i	$-0.853723\pi$
$457$	−9.67798	+	9.67798i	−0.452717	+	0.452717i	0.443539	+	0.896255i	$0.353723\pi$
$458$		0			0
$459$			2.08327i			0.0972387i
$460$		0			0
$461$			10.8514i			0.505399i	0.967545	+	0.252700i	$0.0813185\pi$
$461$			10.8514i			0.505399i	−0.967545	+	0.252700i	$0.918682\pi$
$462$		0			0
$463$	0.429617	+	0.429617i	0.0199660	+	0.0199660i	0.717019	−	0.697053i	$-0.245506\pi$
$463$	0.429617	+	0.429617i	0.0199660	+	0.0199660i	−0.697053	+	0.717019i	$0.745506\pi$
$464$		0			0
$465$	−9.86686	+	7.59244i	−0.457564	+	0.352091i
$466$		0			0
$467$	16.3811	+	16.3811i	0.758026	+	0.758026i	0.975963	−	0.217937i	$-0.0699328\pi$
$467$	16.3811	+	16.3811i	0.758026	+	0.758026i	−0.217937	+	0.975963i	$0.569933\pi$
$468$		0			0
$469$		−	3.98805i		−	0.184151i
$470$		0			0
$471$		−	15.1444i		−	0.697815i
$472$		0			0
$473$	12.1475	−	12.1475i	0.558544	−	0.558544i
$474$		0			0
$475$	−1.97986	+	11.2868i	−0.0908424	+	0.517873i
$476$		0			0
$477$	−6.61030	+	6.61030i	−0.302665	+	0.302665i
$478$		0			0
$479$			22.1802i			1.01344i	0.862110	+	0.506720i	$0.169142\pi$
$479$			22.1802i			1.01344i	−0.862110	+	0.506720i	$0.830858\pi$
$480$		0			0
$481$	−28.1177			−1.28206
$482$		0			0
$483$	−3.83891	+	3.83891i	−0.174676	+	0.174676i
$484$		0			0
$485$	−16.2534	+	13.6505i	−0.738029	+	0.619837i
$486$		0			0
$487$	19.7412	−	19.7412i	0.894558	−	0.894558i	−0.100390	−	0.994948i	$-0.532009\pi$
$487$	19.7412	−	19.7412i	0.894558	−	0.894558i	0.994948	+	0.100390i	$0.0320091\pi$
$488$		0			0
$489$	16.5243			0.747255
$490$		0			0
$491$			5.14521i			0.232200i	0.993238	+	0.116100i	$0.0370393\pi$
$491$			5.14521i			0.232200i	−0.993238	+	0.116100i	$0.962961\pi$
$492$		0			0
$493$	−2.68559	+	2.68559i	−0.120953	+	0.120953i
$494$		0			0
$495$	−0.526249	+	6.04587i	−0.0236531	+	0.271742i
$496$		0			0
$497$	0.0696306	+	0.0696306i	0.00312336	+	0.00312336i
$498$		0			0
$499$	−28.2886			−1.26637			−0.633186	−	0.773999i	$-0.718253\pi$
$499$	−28.2886			−1.26637			−0.633186	+	0.773999i	$0.718253\pi$
$500$		0			0
$501$	11.5708			0.516945
$502$		0			0
$503$	12.7296	−	12.7296i	0.567586	−	0.567586i	−0.363866	−	0.931451i	$-0.618543\pi$
$503$	12.7296	−	12.7296i	0.567586	−	0.567586i	0.931451	+	0.363866i	$0.118543\pi$
$504$		0			0
$505$	3.34465	−	38.4254i	0.148835	−	1.70991i
$506$		0			0
$507$	6.04938	−	6.04938i	0.268663	−	0.268663i
$508$		0			0
$509$	−3.78823			−0.167910			−0.0839551	−	0.996470i	$-0.526755\pi$
$509$	−3.78823			−0.167910			−0.0839551	+	0.996470i	$0.526755\pi$
$510$		0			0
$511$		−	31.1124i		−	1.37633i
$512$		0			0
$513$	−1.62056	−	1.62056i	−0.0715496	−	0.0715496i
$514$		0			0
$515$	−25.2388	−	30.0514i	−1.11216	−	1.32422i
$516$		0			0
$517$	−3.03534	+	3.03534i	−0.133494	+	0.133494i
$518$		0			0
$519$	−5.83017			−0.255916
$520$		0			0
$521$	14.7857			0.647775			0.323888	−	0.946096i	$-0.395010\pi$
$521$	14.7857			0.647775			0.323888	+	0.946096i	$0.395010\pi$
$522$		0			0
$523$	31.9997	+	31.9997i	1.39925	+	1.39925i	0.802222	+	0.597025i	$0.203651\pi$
$523$	31.9997	+	31.9997i	1.39925	+	1.39925i	0.597025	+	0.802222i	$0.296349\pi$
$524$		0			0
$525$	3.00265	−	17.1175i	0.131047	−	0.747068i
$526$		0			0
$527$	8.54461	−	7.84412i	0.372209	−	0.341695i
$528$		0			0
$529$		−	20.5603i		−	0.893924i
$530$		0			0
$531$	−6.91537			−0.300101
$532$		0			0
$533$	22.5733	+	22.5733i	0.977760	+	0.977760i
$534$		0			0
$535$	−20.7998	+	17.4688i	−0.899253	+	0.755241i
$536$		0			0
$537$	−17.4552	−	17.4552i	−0.753248	−	0.753248i
$538$		0			0
$539$	13.7899			0.593971
$540$		0			0
$541$	22.6350			0.973155			0.486578	−	0.873637i	$-0.338245\pi$
$541$	22.6350			0.973155			0.486578	+	0.873637i	$0.338245\pi$
$542$		0			0
$543$	−8.44533	+	8.44533i	−0.362424	+	0.362424i
$544$		0			0
$545$	7.26696	+	0.632536i	0.311283	+	0.0270949i
$546$		0			0
$547$	−26.8240	−	26.8240i	−1.14691	−	1.14691i	−0.987157	−	0.159756i	$-0.948929\pi$
$547$	−26.8240	−	26.8240i	−1.14691	−	1.14691i	−0.159756	−	0.987157i	$-0.551071\pi$
$548$		0			0
$549$	−9.59089			−0.409329
$550$		0			0
$551$		−	4.17821i		−	0.177998i
$552$		0			0
$553$	21.1199	+	21.1199i	0.898110	+	0.898110i
$554$		0			0
$555$	−1.17431	+	13.4912i	−0.0498466	+	0.572669i
$556$		0			0
$557$	−18.2347	+	18.2347i	−0.772629	+	0.772629i	−0.978565	−	0.205936i	$-0.933976\pi$
$557$	−18.2347	+	18.2347i	−0.772629	+	0.772629i	0.205936	+	0.978565i	$0.433976\pi$
$558$		0			0
$559$			29.3877i			1.24297i
$560$		0			0
$561$		−	5.65404i		−	0.238714i
$562$		0			0
$563$	2.15091	−	2.15091i	0.0906500	−	0.0906500i	−0.660328	−	0.750978i	$-0.729583\pi$
$563$	2.15091	−	2.15091i	0.0906500	−	0.0906500i	0.750978	+	0.660328i	$0.229583\pi$
$564$		0			0
$565$	15.6797	+	18.6695i	0.659649	+	0.785433i
$566$		0			0
$567$	2.45774	+	2.45774i	0.103215	+	0.103215i
$568$		0			0
$569$	36.5551			1.53247			0.766236	−	0.642560i	$-0.222128\pi$
$569$	36.5551			1.53247			0.766236	+	0.642560i	$0.222128\pi$
$570$		0			0
$571$		−	34.3953i		−	1.43940i	−0.694287	−	0.719698i	$-0.744280\pi$
$571$		−	34.3953i		−	1.43940i	0.694287	−	0.719698i	$-0.255720\pi$
$572$		0			0
$573$	14.5972	+	14.5972i	0.609807	+	0.609807i
$574$		0			0
$575$	−4.48519	−	6.39347i	−0.187046	−	0.266626i
$576$		0			0
$577$	−7.37304	−	7.37304i	−0.306944	−	0.306944i	0.536779	−	0.843723i	$-0.319641\pi$
$577$	−7.37304	−	7.37304i	−0.306944	−	0.306944i	−0.843723	+	0.536779i	$0.819641\pi$
$578$		0			0
$579$	6.68212			0.277699
$580$		0			0
$581$		−	51.7531i		−	2.14708i
$582$		0			0
$583$	17.9405	−	17.9405i	0.743020	−	0.743020i
$584$		0			0
$585$	−6.67662	−	7.94974i	−0.276044	−	0.328681i
$586$		0			0
$587$	27.3712	−	27.3712i	1.12973	−	1.12973i	0.139511	−	0.990220i	$-0.455447\pi$
$587$	27.3712	−	27.3712i	1.12973	−	1.12973i	0.990220	−	0.139511i	$-0.0445532\pi$
$588$		0			0
$589$	−0.544907	+	12.7487i	−0.0224525	+	0.525301i
$590$		0			0
$591$	−22.5468			−0.927450
$592$		0			0
$593$	−2.03712	+	2.03712i	−0.0836543	+	0.0836543i	−0.747696	−	0.664041i	$-0.768840\pi$
$593$	−2.03712	+	2.03712i	−0.0836543	+	0.0836543i	0.664041	+	0.747696i	$0.268840\pi$
$594$		0			0
$595$	−1.40402	+	16.1303i	−0.0575594	+	0.661278i
$596$		0			0
$597$	−13.1591	−	13.1591i	−0.538565	−	0.538565i
$598$		0			0
$599$		−	2.98220i		−	0.121850i	−0.998142	−	0.0609248i	$-0.980595\pi$
$599$		−	2.98220i		−	0.121850i	0.998142	−	0.0609248i	$-0.0194050\pi$
$600$		0			0
$601$			24.8250i			1.01263i	0.862348	+	0.506316i	$0.168993\pi$
$601$			24.8250i			1.01263i	−0.862348	+	0.506316i	$0.831007\pi$
$602$		0			0
$603$	−0.811325	+	0.811325i	−0.0330397	+	0.0330397i
$604$		0			0
$605$	−0.704652	+	8.09547i	−0.0286482	+	0.329128i
$606$		0			0
$607$	24.9052	+	24.9052i	1.01087	+	1.01087i	0.999940	+	0.0109324i	$0.00347996\pi$
$607$	24.9052	+	24.9052i	1.01087	+	1.01087i	0.0109324	+	0.999940i	$0.496520\pi$
$608$		0			0
$609$			6.33665i			0.256774i
$610$		0			0
$611$		−	7.34319i		−	0.297073i
$612$		0			0
$613$	4.49504	+	4.49504i	0.181553	+	0.181553i	0.792032	−	0.610479i	$-0.209023\pi$
$613$	4.49504	+	4.49504i	0.181553	+	0.181553i	−0.610479	+	0.792032i	$0.709023\pi$
$614$		0			0
$615$	11.7737	−	9.88820i	0.474762	−	0.398731i
$616$		0			0
$617$	33.3878	+	33.3878i	1.34414	+	1.34414i	0.891889	+	0.452255i	$0.149380\pi$
$617$	33.3878	+	33.3878i	1.34414	+	1.34414i	0.452255	+	0.891889i	$0.350620\pi$
$618$		0			0
$619$	31.3769			1.26114			0.630571	−	0.776131i	$-0.282821\pi$
$619$	31.3769			1.26114			0.630571	+	0.776131i	$0.282821\pi$
$620$		0			0
$621$	1.56197			0.0626795
$622$		0			0
$623$	−3.77939	−	3.77939i	−0.151418	−	0.151418i
$624$		0			0
$625$	23.5074	+	8.50890i	0.940297	+	0.340356i
$626$		0			0
$627$	4.39824	+	4.39824i	0.175649	+	0.175649i
$628$		0			0
$629$		−	12.6168i		−	0.503065i
$630$		0			0
$631$			2.43763i			0.0970405i	0.998822	+	0.0485203i	$0.0154505\pi$
$631$			2.43763i			0.0970405i	−0.998822	+	0.0485203i	$0.984549\pi$
$632$		0			0
$633$	10.7057	+	10.7057i	0.425513	+	0.425513i
$634$		0			0
$635$	−9.56935	−	11.3941i	−0.379748	−	0.452160i
$636$		0			0
$637$	−16.6804	+	16.6804i	−0.660902	+	0.660902i
$638$		0			0
$639$		−	0.0283312i		−	0.00112076i
$640$		0			0
$641$			39.3713i			1.55507i	0.628839	+	0.777536i	$0.283531\pi$
$641$			39.3713i			1.55507i	−0.628839	+	0.777536i	$0.716469\pi$
$642$		0			0
$643$	15.6177	+	15.6177i	0.615900	+	0.615900i	0.944477	−	0.328577i	$-0.106569\pi$
$643$	15.6177	+	15.6177i	0.615900	+	0.615900i	−0.328577	+	0.944477i	$0.606569\pi$
$644$		0			0
$645$	14.1005	+	1.22735i	0.555208	+	0.0483268i
$646$		0			0
$647$	−12.3506	+	12.3506i	−0.485552	+	0.485552i	−0.906899	−	0.421347i	$-0.861557\pi$
$647$	−12.3506	+	12.3506i	−0.485552	+	0.485552i	0.421347	+	0.906899i	$0.361557\pi$
$648$		0			0
$649$	18.7684			0.736726
$650$		0			0
$651$	0.826403	−	19.3346i	0.0323893	−	0.757783i
$652$		0			0
$653$	25.1500	−	25.1500i	0.984197	−	0.984197i	−0.0156799	−	0.999877i	$-0.504991\pi$
$653$	25.1500	−	25.1500i	0.984197	−	0.984197i	0.999877	+	0.0156799i	$0.00499128\pi$
$654$		0			0
$655$	−0.232742	+	2.67388i	−0.00909397	+	0.104477i
$656$		0			0
$657$	−6.32948	+	6.32948i	−0.246936	+	0.246936i
$658$		0			0
$659$			3.45652i			0.134647i	0.997731	+	0.0673235i	$0.0214460\pi$
$659$			3.45652i			0.134647i	−0.997731	+	0.0673235i	$0.978554\pi$
$660$		0			0
$661$	−6.24130			−0.242758			−0.121379	−	0.992606i	$-0.538732\pi$
$661$	−6.24130			−0.242758			−0.121379	+	0.992606i	$0.538732\pi$
$662$		0			0
$663$	6.83921	+	6.83921i	0.265613	+	0.265613i
$664$		0			0
$665$	−11.4555	−	13.6399i	−0.444225	−	0.528931i
$666$		0			0
$667$	2.01356	+	2.01356i	0.0779655	+	0.0779655i
$668$		0			0
$669$		−	24.9549i		−	0.964811i
$670$		0			0
$671$	26.0299			1.00487
$672$		0			0
$673$	3.18098	+	3.18098i	0.122618	+	0.122618i	0.765753	−	0.643135i	$-0.222367\pi$
$673$	3.18098	+	3.18098i	0.122618	+	0.122618i	−0.643135	+	0.765753i	$0.722367\pi$
$674$		0			0
$675$	−4.09322	+	2.87151i	−0.157548	+	0.110524i
$676$		0			0
$677$	−12.6823	+	12.6823i	−0.487420	+	0.487420i	−0.907491	−	0.420071i	$-0.862005\pi$
$677$	−12.6823	+	12.6823i	−0.487420	+	0.487420i	0.420071	+	0.907491i	$0.362005\pi$
$678$		0			0
$679$		−	32.9927i		−	1.26614i
$680$		0			0
$681$			1.60609i			0.0615455i
$682$		0			0
$683$	0.960792	−	0.960792i	0.0367637	−	0.0367637i	−0.688486	−	0.725250i	$-0.741724\pi$
$683$	0.960792	−	0.960792i	0.0367637	−	0.0367637i	0.725250	+	0.688486i	$0.241724\pi$
$684$		0			0
$685$	−9.73183	−	11.5875i	−0.371834	−	0.442736i
$686$		0			0
$687$	−1.12629	−	1.12629i	−0.0429707	−	0.0429707i
$688$		0			0
$689$			43.4022i			1.65349i
$690$		0			0
$691$	−22.9351			−0.872491			−0.436246	−	0.899828i	$-0.643692\pi$
$691$	−22.9351			−0.872491			−0.436246	+	0.899828i	$0.643692\pi$
$692$		0			0
$693$	−6.67036	−	6.67036i	−0.253386	−	0.253386i
$694$		0			0
$695$	0.402495	−	4.62411i	0.0152675	−	0.175402i
$696$		0			0
$697$	−10.1290	+	10.1290i	−0.383663	+	0.383663i
$698$		0			0
$699$	−10.6361			−0.402294
$700$		0			0
$701$	−37.0859			−1.40072			−0.700358	−	0.713791i	$-0.746976\pi$
$701$	−37.0859			−1.40072			−0.700358	+	0.713791i	$0.746976\pi$
$702$		0			0
$703$	9.81455	+	9.81455i	0.370163	+	0.370163i
$704$		0			0
$705$	−3.52335	−	0.306681i	−0.132697	−	0.0115503i
$706$		0			0
$707$	42.3944	+	42.3944i	1.59440	+	1.59440i
$708$		0			0
$709$	22.6828			0.851869			0.425934	−	0.904754i	$-0.359945\pi$
$709$	22.6828			0.851869			0.425934	+	0.904754i	$0.359945\pi$
$710$		0			0
$711$		−	8.59322i		−	0.322271i
$712$		0			0
$713$	−5.88125	−	6.40646i	−0.220255	−	0.239924i
$714$		0			0
$715$	18.1205	+	21.5758i	0.677668	+	0.806887i
$716$		0			0
$717$	−3.51263	−	3.51263i	−0.131182	−	0.131182i
$718$		0			0
$719$	−33.4001			−1.24561			−0.622807	−	0.782375i	$-0.714008\pi$
$719$	−33.4001			−1.24561			−0.622807	+	0.782375i	$0.714008\pi$
$720$		0			0
$721$	61.0012			2.27180
$722$		0			0
$723$	2.23555	−	2.23555i	0.0831409	−	0.0831409i
$724$		0			0
$725$	−8.97838	−	1.57494i	−0.333449	−	0.0584917i
$726$		0			0
$727$	−18.8699	−	18.8699i	−0.699844	−	0.699844i	0.264533	−	0.964377i	$-0.414782\pi$
$727$	−18.8699	−	18.8699i	−0.699844	−	0.699844i	−0.964377	+	0.264533i	$0.914782\pi$
$728$		0			0
$729$		−	1.00000i		−	0.0370370i
$730$		0			0
$731$	−13.1867			−0.487727
$732$		0			0
$733$	−3.21816	+	3.21816i	−0.118865	+	0.118865i	−0.764037	−	0.645172i	$-0.776786\pi$
$733$	−3.21816	+	3.21816i	−0.118865	+	0.118865i	0.645172	+	0.764037i	$0.276786\pi$
$734$		0			0
$735$	7.30682	+	8.70010i	0.269516	+	0.320908i
$736$		0			0
$737$	2.20195	−	2.20195i	0.0811100	−	0.0811100i
$738$		0			0
$739$	−38.6988			−1.42356			−0.711779	−	0.702403i	$-0.752110\pi$
$739$	−38.6988			−1.42356			−0.711779	+	0.702403i	$0.752110\pi$
$740$		0			0
$741$	−10.6404			−0.390883
$742$		0			0
$743$	13.9023	+	13.9023i	0.510027	+	0.510027i	0.914535	−	0.404507i	$-0.132557\pi$
$743$	13.9023	+	13.9023i	0.510027	+	0.510027i	−0.404507	+	0.914535i	$0.632557\pi$
$744$		0			0
$745$	6.18498	+	0.538357i	0.226600	+	0.0197239i
$746$		0			0
$747$	−10.5286	+	10.5286i	−0.385221	+	0.385221i
$748$		0			0
$749$		−	42.2213i		−	1.54273i
$750$		0			0
$751$	2.50907			0.0915573			0.0457787	−	0.998952i	$-0.485423\pi$
$751$	2.50907			0.0915573			0.0457787	+	0.998952i	$0.485423\pi$
$752$		0			0
$753$	−14.2658	+	14.2658i	−0.519875	+	0.519875i
$754$		0			0
$755$	−20.5418	−	1.78801i	−0.747593	−	0.0650725i
$756$		0			0
$757$	−18.0869	+	18.0869i	−0.657380	+	0.657380i	−0.954759	−	0.297380i	$-0.903887\pi$
$757$	−18.0869	+	18.0869i	−0.657380	+	0.657380i	0.297380	+	0.954759i	$0.403887\pi$
$758$		0			0
$759$	−4.23921			−0.153873
$760$		0			0
$761$			28.1268i			1.01960i	0.860294	+	0.509799i	$0.170280\pi$
$761$			28.1268i			1.01960i	−0.860294	+	0.509799i	$0.829720\pi$
$762$		0			0
$763$	−8.01757	+	8.01757i	−0.290256	+	0.290256i
$764$		0			0
$765$	3.56717	−	2.99590i	0.128971	−	0.108317i
$766$		0			0
$767$	−22.7026	+	22.7026i	−0.819743	+	0.819743i
$768$		0			0
$769$		−	16.6524i		−	0.600501i	−0.953860	−	0.300250i	$-0.902930\pi$
$769$		−	16.6524i		−	0.600501i	0.953860	−	0.300250i	$-0.0970702\pi$
$770$		0			0
$771$			3.90250i			0.140545i
$772$		0			0
$773$	−13.7715	−	13.7715i	−0.495327	−	0.495327i	0.414653	−	0.909980i	$-0.363903\pi$
$773$	−13.7715	−	13.7715i	−0.495327	−	0.495327i	−0.909980	+	0.414653i	$0.863903\pi$
$774$		0			0
$775$	27.1897	+	5.97643i	0.976685	+	0.214680i
$776$		0			0
$777$	−14.8847	−	14.8847i	−0.533986	−	0.533986i
$778$		0			0
$779$		−	15.7586i		−	0.564609i
$780$		0			0
$781$			0.0768914i			0.00275139i
$782$		0			0
$783$	1.28912	−	1.28912i	0.0460695	−	0.0460695i
$784$		0			0
$785$	−25.9315	+	21.7787i	−0.925536	+	0.777316i
$786$		0			0
$787$	−11.6362	+	11.6362i	−0.414785	+	0.414785i	−0.883402	−	0.468617i	$-0.844753\pi$
$787$	−11.6362	+	11.6362i	−0.414785	+	0.414785i	0.468617	+	0.883402i	$0.344753\pi$
$788$		0			0
$789$			21.2268i			0.755695i
$790$		0			0
$791$	−37.8972			−1.34747
$792$		0			0
$793$	−31.4861	+	31.4861i	−1.11810	+	1.11810i
$794$		0			0
$795$	20.8249	+	1.81265i	0.738582	+	0.0642882i
$796$		0			0
$797$	−20.8720	+	20.8720i	−0.739325	+	0.739325i	−0.972447	−	0.233122i	$-0.925106\pi$
$797$	−20.8720	+	20.8720i	−0.739325	+	0.739325i	0.233122	+	0.972447i	$0.425106\pi$
$798$		0			0
$799$	3.29500			0.116569
$800$		0			0
$801$			1.53775i			0.0543337i
$802$		0			0
$803$	17.1783	−	17.1783i	0.606210	−	0.606210i
$804$		0			0
$805$	12.0940	+	1.05269i	0.426256	+	0.0371025i
$806$		0			0
$807$	−4.87055	−	4.87055i	−0.171451	−	0.171451i
$808$		0			0
$809$	−6.34366			−0.223031			−0.111516	−	0.993763i	$-0.535571\pi$
$809$	−6.34366			−0.223031			−0.111516	+	0.993763i	$0.535571\pi$
$810$		0			0
$811$	9.60582			0.337306			0.168653	−	0.985675i	$-0.446058\pi$
$811$	9.60582			0.337306			0.168653	+	0.985675i	$0.446058\pi$
$812$		0			0
$813$	0.367207	−	0.367207i	0.0128785	−	0.0128785i
$814$		0			0
$815$	−23.7632	−	28.2944i	−0.832389	−	0.991111i
$816$		0			0
$817$	10.2578	−	10.2578i	0.358876	−	0.358876i
$818$		0			0
$819$	16.1371			0.563877
$820$		0			0
$821$		−	28.2280i		−	0.985165i	−0.870266	−	0.492582i	$-0.836053\pi$
$821$		−	28.2280i		−	0.985165i	0.870266	−	0.492582i	$-0.163947\pi$
$822$		0			0
$823$	4.99027	+	4.99027i	0.173950	+	0.173950i	0.788712	−	0.614762i	$-0.210748\pi$
$823$	4.99027	+	4.99027i	0.173950	+	0.173950i	−0.614762	+	0.788712i	$0.710748\pi$
$824$		0			0
$825$	11.1091	−	7.79333i	0.386769	−	0.271329i
$826$		0			0
$827$	2.78262	−	2.78262i	0.0967613	−	0.0967613i	−0.657069	−	0.753830i	$-0.728204\pi$
$827$	2.78262	−	2.78262i	0.0967613	−	0.0967613i	0.753830	+	0.657069i	$0.228204\pi$
$828$		0			0
$829$	−20.5748			−0.714592			−0.357296	−	0.933991i	$-0.616301\pi$
$829$	−20.5748			−0.714592			−0.357296	+	0.933991i	$0.616301\pi$
$830$		0			0
$831$	6.05541			0.210060
$832$		0			0
$833$	−7.48475	−	7.48475i	−0.259331	−	0.259331i
$834$		0			0
$835$	−16.6397	−	19.8126i	−0.575840	−	0.685643i
$836$		0			0
$837$	−4.10154	+	3.76529i	−0.141770	+	0.130147i
$838$		0			0
$839$		−	7.71418i		−	0.266323i	−0.991094	−	0.133161i	$-0.957487\pi$
$839$		−	7.71418i		−	0.266323i	0.991094	−	0.133161i	$-0.0425129\pi$
$840$		0			0
$841$	−25.6763			−0.885391
$842$		0			0
$843$	8.18294	+	8.18294i	0.281835	+	0.281835i
$844$		0			0
$845$	−19.0578	−	1.65884i	−0.655607	−	0.0570658i
$846$		0			0
$847$	−8.93166	−	8.93166i	−0.306895	−	0.306895i
$848$		0			0
$849$	3.47164			0.119146
$850$		0			0
$851$	−9.45966			−0.324273
$852$		0			0
$853$	16.6770	−	16.6770i	0.571010	−	0.571010i	−0.361401	−	0.932411i	$-0.617701\pi$
$853$	16.6770	−	16.6770i	0.571010	−	0.571010i	0.932411	+	0.361401i	$0.117701\pi$
$854$		0			0
$855$	−0.444385	+	5.10537i	−0.0151976	+	0.174600i
$856$		0			0
$857$	−7.21107	−	7.21107i	−0.246326	−	0.246326i	0.573135	−	0.819461i	$-0.305727\pi$
$857$	−7.21107	−	7.21107i	−0.246326	−	0.246326i	−0.819461	+	0.573135i	$0.805727\pi$
$858$		0			0
$859$	−39.8826			−1.36078			−0.680388	−	0.732852i	$-0.738189\pi$
$859$	−39.8826			−1.36078			−0.680388	+	0.732852i	$0.738189\pi$
$860$		0			0
$861$			23.8994i			0.814489i
$862$		0			0
$863$	39.8690	+	39.8690i	1.35716	+	1.35716i	0.877403	+	0.479753i	$0.159274\pi$
$863$	39.8690	+	39.8690i	1.35716	+	1.35716i	0.479753	+	0.877403i	$0.340726\pi$
$864$		0			0
$865$	8.38422	+	9.98294i	0.285072	+	0.339430i
$866$		0			0
$867$	8.95196	−	8.95196i	0.304025	−	0.304025i
$868$		0			0
$869$			23.3222i			0.791151i
$870$		0			0
$871$			5.32703i			0.180500i
$872$		0			0
$873$	−6.71200	+	6.71200i	−0.227167	+	0.227167i
$874$		0			0
$875$	−33.6282	+	19.4748i	−1.13684	+	0.658369i
$876$		0			0
$877$	−5.28546	−	5.28546i	−0.178477	−	0.178477i	0.612214	−	0.790692i	$-0.290279\pi$
$877$	−5.28546	−	5.28546i	−0.178477	−	0.178477i	−0.790692	+	0.612214i	$0.790279\pi$
$878$		0			0
$879$	−14.6252			−0.493297
$880$		0			0
$881$			43.1286i			1.45304i	0.687145	+	0.726520i	$0.258864\pi$
$881$			43.1286i			1.45304i	−0.687145	+	0.726520i	$0.741136\pi$
$882$		0			0
$883$	−15.3005	−	15.3005i	−0.514903	−	0.514903i	0.401122	−	0.916025i	$-0.368620\pi$
$883$	−15.3005	−	15.3005i	−0.514903	−	0.514903i	−0.916025	+	0.401122i	$0.868620\pi$
$884$		0			0
$885$	9.94481	+	11.8411i	0.334291	+	0.398035i
$886$		0			0
$887$	−13.0433	−	13.0433i	−0.437952	−	0.437952i	0.453370	−	0.891322i	$-0.350222\pi$
$887$	−13.0433	−	13.0433i	−0.437952	−	0.437952i	−0.891322	+	0.453370i	$0.850222\pi$
$888$		0			0
$889$	23.1287			0.775713
$890$		0			0
$891$			2.71402i			0.0909231i
$892$		0			0
$893$	−2.56316	+	2.56316i	−0.0857728	+	0.0857728i
$894$		0			0
$895$	−4.78651	+	54.9903i	−0.159995	+	1.83812i
$896$		0			0
$897$	5.12781	−	5.12781i	0.171213	−	0.171213i
$898$		0			0
$899$	−10.1413	−	0.433461i	−0.338231	−	0.0144567i
$900$		0			0
$901$	−19.4752			−0.648813
$902$		0			0
$903$	−15.5570	+	15.5570i	−0.517705	+	0.517705i
$904$		0			0
$905$	26.6059	+	2.31585i	0.884410	+	0.0769814i
$906$		0			0
$907$	−20.0717	−	20.0717i	−0.666469	−	0.666469i	0.290428	−	0.956897i	$-0.406202\pi$
$907$	−20.0717	−	20.0717i	−0.666469	−	0.666469i	−0.956897	+	0.290428i	$0.906202\pi$
$908$		0			0
$909$		−	17.2493i		−	0.572124i
$910$		0			0
$911$			46.5773i			1.54317i	0.636124	+	0.771587i	$0.280537\pi$
$911$			46.5773i			1.54317i	−0.636124	+	0.771587i	$0.719463\pi$
$912$		0			0
$913$	28.5748	−	28.5748i	0.945688	−	0.945688i
$914$		0			0
$915$	13.7924	+	16.4224i	0.455963	+	0.542908i
$916$		0			0
$917$	−2.95007	−	2.95007i	−0.0974198	−	0.0974198i
$918$		0			0
$919$		−	27.9401i		−	0.921657i	−0.887489	−	0.460829i	$-0.847552\pi$
$919$		−	27.9401i		−	0.921657i	0.887489	−	0.460829i	$-0.152448\pi$
$920$		0			0
$921$			29.5617i			0.974090i
$922$		0			0
$923$	−0.0930089	−	0.0930089i	−0.00306143	−	0.00306143i
$924$		0			0
$925$	24.7896	−	17.3906i	0.815076	−	0.571799i
$926$		0			0
$927$	−12.4100	−	12.4100i	−0.407599	−	0.407599i
$928$		0			0
$929$	29.1875			0.957610			0.478805	−	0.877921i	$-0.341070\pi$
$929$	29.1875			0.957610			0.478805	+	0.877921i	$0.341070\pi$
$930$		0			0
$931$	11.6447			0.381639
$932$		0			0
$933$	−14.4709	−	14.4709i	−0.473757	−	0.473757i
$934$		0			0
$935$	−9.68136	+	8.13093i	−0.316614	+	0.265910i
$936$		0			0
$937$	−16.6491	−	16.6491i	−0.543904	−	0.543904i	0.380767	−	0.924671i	$-0.375660\pi$
$937$	−16.6491	−	16.6491i	−0.543904	−	0.543904i	−0.924671	+	0.380767i	$0.875660\pi$
$938$		0			0
$939$			28.9224i			0.943846i
$940$		0			0
$941$		−	50.4724i		−	1.64535i	−0.568510	−	0.822676i	$-0.692480\pi$
$941$		−	50.4724i		−	1.64535i	0.568510	−	0.822676i	$-0.307520\pi$
$942$		0			0
$943$	7.59438	+	7.59438i	0.247307	+	0.247307i
$944$		0			0
$945$	0.673952	−	7.74278i	0.0219237	−	0.251873i
$946$		0			0
$947$	−16.7599	+	16.7599i	−0.544623	+	0.544623i	−0.924881	−	0.380257i	$-0.875835\pi$
$947$	−16.7599	+	16.7599i	−0.544623	+	0.544623i	0.380257	+	0.924881i	$0.375835\pi$
$948$		0			0
$949$			41.5583i			1.34904i
$950$		0			0
$951$			22.5427i			0.730998i
$952$		0			0
$953$	0.879612	+	0.879612i	0.0284934	+	0.0284934i	0.721210	−	0.692717i	$-0.243586\pi$
$953$	0.879612	+	0.879612i	0.0284934	+	0.0284934i	−0.692717	+	0.721210i	$0.743586\pi$
$954$		0			0
$955$	4.00279	−	45.9865i	0.129527	−	1.48809i
$956$		0			0
$957$	−3.49870	+	3.49870i	−0.113097	+	0.113097i
$958$		0			0
$959$	23.5214			0.759547
$960$		0			0
$961$	30.8869	+	2.64518i	0.996353	+	0.0853285i
$962$		0			0
$963$	−8.58946	+	8.58946i	−0.276792	+	0.276792i
$964$		0			0
$965$	−9.60939	−	11.4417i	−0.309337	−	0.368322i
$966$		0			0
$967$	−8.43463	+	8.43463i	−0.271239	+	0.271239i	−0.829599	−	0.558360i	$-0.811431\pi$
$967$	−8.43463	+	8.43463i	−0.271239	+	0.271239i	0.558360	+	0.829599i	$0.311431\pi$
$968$		0			0
$969$		−	4.77449i		−	0.153379i
$970$		0			0
$971$	51.3283			1.64720			0.823602	−	0.567169i	$-0.191961\pi$
$971$	51.3283			1.64720			0.823602	+	0.567169i	$0.191961\pi$
$972$		0			0
$973$	5.10174	+	5.10174i	0.163554	+	0.163554i
$974$		0			0
$975$	−4.01079	+	22.8646i	−0.128448	+	0.732254i
$976$		0			0
$977$	36.1004	+	36.1004i	1.15495	+	1.15495i	0.985546	+	0.169408i	$0.0541854\pi$
$977$	36.1004	+	36.1004i	1.15495	+	1.15495i	0.169408	+	0.985546i	$0.445815\pi$
$978$		0			0
$979$		−	4.17349i		−	0.133385i
$980$		0			0
$981$	3.26217			0.104153
$982$		0			0
$983$	15.2871	+	15.2871i	0.487582	+	0.487582i	0.907542	−	0.419961i	$-0.137956\pi$
$983$	15.2871	+	15.2871i	0.487582	+	0.487582i	−0.419961	+	0.907542i	$0.637956\pi$
$984$		0			0
$985$	32.4239	+	38.6066i	1.03311	+	1.23011i
$986$		0			0
$987$	3.88727	−	3.88727i	0.123733	−	0.123733i
$988$		0			0
$989$			9.88693i			0.314386i
$990$		0			0
$991$			43.2592i			1.37417i	0.726575	+	0.687087i	$0.241111\pi$
$991$			43.2592i			1.37417i	−0.726575	+	0.687087i	$0.758889\pi$
$992$		0			0
$993$	−12.6273	+	12.6273i	−0.400714	+	0.400714i
$994$		0			0
$995$	−3.60843	+	41.4559i	−0.114395	+	1.31424i
$996$		0			0
$997$	33.8119	+	33.8119i	1.07083	+	1.07083i	0.997292	+	0.0735423i	$0.0234304\pi$
$997$	33.8119	+	33.8119i	1.07083	+	1.07083i	0.0735423	+	0.997292i	$0.476570\pi$
$998$		0			0
$999$			6.05625i			0.191611i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1860.2.s.a.1177.6	yes	64
5.3	odd	4	inner	1860.2.s.a.433.18	yes	64
31.30	odd	2	inner	1860.2.s.a.1177.18	yes	64
155.123	even	4	inner	1860.2.s.a.433.6	✓	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1860.2.s.a.433.6	✓	64	155.123	even	4	inner
1860.2.s.a.433.18	yes	64	5.3	odd	4	inner
1860.2.s.a.1177.6	yes	64	1.1	even	1	trivial
1860.2.s.a.1177.18	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)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 0.707107i) q^{3} +(-0.193900 + 2.22765i) q^{5} +(-2.45774 - 2.45774i) q^{7} +1.00000i q^{9} -2.71402i q^{11} +(3.28292 + 3.28292i) q^{13} +(1.71229 - 1.43807i) q^{15} +(-1.47309 + 1.47309i) q^{17} -2.29182i q^{19} +3.47577i q^{21} +(1.10448 + 1.10448i) q^{23} +(-4.92481 - 0.863882i) q^{25} +(0.707107 - 0.707107i) q^{27} +1.82309 q^{29} +(-5.56269 - 0.237761i) q^{31} +(-1.91910 + 1.91910i) q^{33} +(5.95153 - 4.99842i) q^{35} +(-4.28242 + 4.28242i) q^{37} -4.64275i q^{39} +6.87600 q^{41} +(4.47584 + 4.47584i) q^{43} +(-2.22765 - 0.193900i) q^{45} +(-1.11839 - 1.11839i) q^{47} +5.08097i q^{49} +2.08327 q^{51} +(6.61030 + 6.61030i) q^{53} +(6.04587 + 0.526249i) q^{55} +(-1.62056 + 1.62056i) q^{57} +6.91537i q^{59} +9.59089i q^{61} +(2.45774 - 2.45774i) q^{63} +(-7.94974 + 6.67662i) q^{65} +(0.811325 + 0.811325i) q^{67} -1.56197i q^{69} -0.0283312 q^{71} +(6.32948 + 6.32948i) q^{73} +(2.87151 + 4.09322i) q^{75} +(-6.67036 + 6.67036i) q^{77} -8.59322 q^{79} -1.00000 q^{81} +(10.5286 + 10.5286i) q^{83} +(-2.99590 - 3.56717i) q^{85} +(-1.28912 - 1.28912i) q^{87} +1.53775 q^{89} -16.1371i q^{91} +(3.76529 + 4.10154i) q^{93} +(5.10537 + 0.444385i) q^{95} +(6.71200 + 6.71200i) q^{97} +2.71402 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 8 q^{7} + 16 q^{25} + 8 q^{31} - 8 q^{33} + 24 q^{35} + 16 q^{41} + 56 q^{47} + 8 q^{63} - 32 q^{67} - 16 q^{71} - 64 q^{81} - 32 q^{87} - 32 q^{95} + 64 q^{97}+O(q^{100}) \) 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

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