LMFDB - Embedded newform 880.2.bd.i.593.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [880,2,Mod(417,880)] 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("880.417"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(880, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 0, 1, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 880 = 2^{4} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	880.bd (of order $4$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [32,0,4,0,8,0,0,0,0,0,8,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(13)] == traces)

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

Self dual:	no
Analytic conductor:	$7.02683537787$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 440)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			593.3
Character	$\chi$	$=$	880.593
Dual form			880.2.bd.i.417.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.78145 - 1.78145i) q^{3} +(-0.300869 + 2.21573i) q^{5} +(-1.52953 - 1.52953i) q^{7} +3.34712i q^{9} +(-0.328917 + 3.30027i) q^{11} +(0.884324 - 0.884324i) q^{13} +(4.48320 - 3.41123i) q^{15} +(-0.303994 - 0.303994i) q^{17} +5.84773 q^{19} +5.44955i q^{21} +(-2.07794 - 2.07794i) q^{23} +(-4.81896 - 1.33329i) q^{25} +(0.618370 - 0.618370i) q^{27} +7.00868 q^{29} +4.58066 q^{31} +(6.46522 - 5.29332i) q^{33} +(3.84921 - 2.92884i) q^{35} +(4.10163 - 4.10163i) q^{37} -3.15076 q^{39} -2.46834i q^{41} +(8.48972 - 8.48972i) q^{43} +(-7.41632 - 1.00704i) q^{45} +(-7.49702 + 7.49702i) q^{47} -2.32109i q^{49} +1.08310i q^{51} +(4.04743 + 4.04743i) q^{53} +(-7.21357 - 1.72174i) q^{55} +(-10.4174 - 10.4174i) q^{57} -8.07502i q^{59} -2.60774i q^{61} +(5.11951 - 5.11951i) q^{63} +(1.69336 + 2.22549i) q^{65} +(-1.98917 + 1.98917i) q^{67} +7.40350i q^{69} -6.78733 q^{71} +(11.5640 - 11.5640i) q^{73} +(6.20953 + 10.9599i) q^{75} +(5.55095 - 4.54477i) q^{77} +7.60905 q^{79} +7.83816 q^{81} +(8.18822 - 8.18822i) q^{83} +(0.765033 - 0.582108i) q^{85} +(-12.4856 - 12.4856i) q^{87} -0.510584i q^{89} -2.70520 q^{91} +(-8.16021 - 8.16021i) q^{93} +(-1.75940 + 12.9570i) q^{95} +(1.60712 - 1.60712i) q^{97} +(-11.0464 - 1.10092i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 4 q^{3} + 8 q^{5} + 8 q^{11} - 24 q^{15} + 28 q^{23} + 4 q^{25} + 4 q^{27} - 24 q^{31} - 12 q^{33} + 4 q^{37} - 28 q^{45} - 8 q^{47} + 24 q^{53} - 12 q^{55} + 52 q^{67} - 48 q^{71} + 24 q^{75} + 56 q^{77}+ \cdots - 36 q^{97}+O(q^{100}) $ 32 * q + 4 * q^3 + 8 * q^5 + 8 * q^11 - 24 * q^15 + 28 * q^23 + 4 * q^25 + 4 * q^27 - 24 * q^31 - 12 * q^33 + 4 * q^37 - 28 * q^45 - 8 * q^47 + 24 * q^53 - 12 * q^55 + 52 * q^67 - 48 * q^71 + 24 * q^75 + 56 * q^77 - 24 * q^81 + 16 * q^91 - 76 * q^93 - 36 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/880\mathbb{Z}\right)^\times$.

$n$	$111$	$177$	$321$	$661$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$-1$	$1$

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
$3$	−1.78145	−	1.78145i	−1.02852	−	1.02852i	−0.999581	−	0.0289385i	$-0.990787\pi$
$3$	−1.78145	−	1.78145i	−1.02852	−	1.02852i	−0.0289385	−	0.999581i	$-0.509213\pi$
$4$		0			0
$5$	−0.300869	+	2.21573i	−0.134553	+	0.990906i
$5$	−0.300869	+	2.21573i	−0.134553	+	0.990906i
$6$		0			0
$7$	−1.52953	−	1.52953i	−0.578107	−	0.578107i	0.356274	−	0.934381i	$-0.384047\pi$
$7$	−1.52953	−	1.52953i	−0.578107	−	0.578107i	−0.934381	+	0.356274i	$0.884047\pi$
$8$		0			0
$9$			3.34712i			1.11571i
$10$		0			0
$11$	−0.328917	+	3.30027i	−0.0991722	+	0.995070i
$11$	−0.328917	+	3.30027i	−0.0991722	+	0.995070i
$12$		0			0
$13$	0.884324	−	0.884324i	0.245267	−	0.245267i	−0.573758	−	0.819025i	$-0.694515\pi$
$13$	0.884324	−	0.884324i	0.245267	−	0.245267i	0.819025	+	0.573758i	$0.194515\pi$
$14$		0			0
$15$	4.48320	−	3.41123i	1.15756	−	0.880777i
$16$		0			0
$17$	−0.303994	−	0.303994i	−0.0737294	−	0.0737294i	0.669280	−	0.743010i	$-0.266602\pi$
$17$	−0.303994	−	0.303994i	−0.0737294	−	0.0737294i	−0.743010	+	0.669280i	$0.766602\pi$
$18$		0			0
$19$	5.84773			1.34156			0.670781	−	0.741655i	$-0.265959\pi$
$19$	5.84773			1.34156			0.670781	+	0.741655i	$0.265959\pi$
$20$		0			0
$21$			5.44955i			1.18919i
$22$		0			0
$23$	−2.07794	−	2.07794i	−0.433281	−	0.433281i	0.456462	−	0.889743i	$-0.349117\pi$
$23$	−2.07794	−	2.07794i	−0.433281	−	0.433281i	−0.889743	+	0.456462i	$0.849117\pi$
$24$		0			0
$25$	−4.81896	−	1.33329i	−0.963791	−	0.266658i
$26$		0			0
$27$	0.618370	−	0.618370i	0.119005	−	0.119005i
$28$		0			0
$29$	7.00868			1.30148			0.650740	−	0.759301i	$-0.274459\pi$
$29$	7.00868			1.30148			0.650740	+	0.759301i	$0.274459\pi$
$30$		0			0
$31$	4.58066			0.822711			0.411356	−	0.911475i	$-0.365055\pi$
$31$	4.58066			0.822711			0.411356	+	0.911475i	$0.365055\pi$
$32$		0			0
$33$	6.46522	−	5.29332i	1.12545	−	0.921449i
$34$		0			0
$35$	3.84921	−	2.92884i	0.650636	−	0.495064i
$36$		0			0
$37$	4.10163	−	4.10163i	0.674303	−	0.674303i	−0.284402	−	0.958705i	$-0.591795\pi$
$37$	4.10163	−	4.10163i	0.674303	−	0.674303i	0.958705	+	0.284402i	$0.0917951\pi$
$38$		0			0
$39$	−3.15076			−0.504525
$40$		0			0
$41$		−	2.46834i		−	0.385490i	−0.981249	−	0.192745i	$-0.938261\pi$
$41$		−	2.46834i		−	0.385490i	0.981249	−	0.192745i	$-0.0617390\pi$
$42$		0			0
$43$	8.48972	−	8.48972i	1.29467	−	1.29467i	0.362806	−	0.931865i	$-0.381819\pi$
$43$	8.48972	−	8.48972i	1.29467	−	1.29467i	0.931865	−	0.362806i	$-0.118181\pi$
$44$		0			0
$45$	−7.41632	−	1.00704i	−1.10556	−	0.150121i
$46$		0			0
$47$	−7.49702	+	7.49702i	−1.09355	+	1.09355i	−0.0984072	+	0.995146i	$0.531375\pi$
$47$	−7.49702	+	7.49702i	−1.09355	+	1.09355i	−0.995146	+	0.0984072i	$0.968625\pi$
$48$		0			0
$49$		−	2.32109i		−	0.331585i
$50$		0			0
$51$			1.08310i			0.151664i
$52$		0			0
$53$	4.04743	+	4.04743i	0.555957	+	0.555957i	0.928154	−	0.372197i	$-0.121395\pi$
$53$	4.04743	+	4.04743i	0.555957	+	0.555957i	−0.372197	+	0.928154i	$0.621395\pi$
$54$		0			0
$55$	−7.21357	−	1.72174i	−0.972678	−	0.232160i
$56$		0			0
$57$	−10.4174	−	10.4174i	−1.37982	−	1.37982i
$58$		0			0
$59$		−	8.07502i		−	1.05128i	−0.850708	−	0.525639i	$-0.823826\pi$
$59$		−	8.07502i		−	1.05128i	0.850708	−	0.525639i	$-0.176174\pi$
$60$		0			0
$61$		−	2.60774i		−	0.333887i	−0.985966	−	0.166944i	$-0.946610\pi$
$61$		−	2.60774i		−	0.333887i	0.985966	−	0.166944i	$-0.0533898\pi$
$62$		0			0
$63$	5.11951	−	5.11951i	0.644997	−	0.644997i
$64$		0			0
$65$	1.69336	+	2.22549i	0.210036	+	0.276038i
$66$		0			0
$67$	−1.98917	+	1.98917i	−0.243016	+	0.243016i	−0.818096	−	0.575081i	$-0.804971\pi$
$67$	−1.98917	+	1.98917i	−0.243016	+	0.243016i	0.575081	+	0.818096i	$0.304971\pi$
$68$		0			0
$69$			7.40350i			0.891277i
$70$		0			0
$71$	−6.78733			−0.805508			−0.402754	−	0.915308i	$-0.631947\pi$
$71$	−6.78733			−0.805508			−0.402754	+	0.915308i	$0.631947\pi$
$72$		0			0
$73$	11.5640	−	11.5640i	1.35346	−	1.35346i	0.471700	−	0.881759i	$-0.343641\pi$
$73$	11.5640	−	11.5640i	1.35346	−	1.35346i	0.881759	−	0.471700i	$-0.156359\pi$
$74$		0			0
$75$	6.20953	+	10.9599i	0.717015	+	1.26554i
$76$		0			0
$77$	5.55095	−	4.54477i	0.632589	−	0.517925i
$78$		0			0
$79$	7.60905			0.856086			0.428043	−	0.903758i	$-0.359203\pi$
$79$	7.60905			0.856086			0.428043	+	0.903758i	$0.359203\pi$
$80$		0			0
$81$	7.83816			0.870907
$82$		0			0
$83$	8.18822	−	8.18822i	0.898774	−	0.898774i	−0.0965539	−	0.995328i	$-0.530782\pi$
$83$	8.18822	−	8.18822i	0.898774	−	0.898774i	0.995328	+	0.0965539i	$0.0307820\pi$
$84$		0			0
$85$	0.765033	−	0.582108i	0.0829794	−	0.0631385i
$86$		0			0
$87$	−12.4856	−	12.4856i	−1.33860	−	1.33860i
$88$		0			0
$89$		−	0.510584i		−	0.0541218i	−0.999634	−	0.0270609i	$-0.991385\pi$
$89$		−	0.510584i		−	0.0541218i	0.999634	−	0.0270609i	$-0.00861480\pi$
$90$		0			0
$91$	−2.70520			−0.283582
$92$		0			0
$93$	−8.16021	−	8.16021i	−0.846175	−	0.846175i
$94$		0			0
$95$	−1.75940	+	12.9570i	−0.180511	+	1.32936i
$96$		0			0
$97$	1.60712	−	1.60712i	0.163178	−	0.163178i	−0.620795	−	0.783973i	$-0.713190\pi$
$97$	1.60712	−	1.60712i	0.163178	−	0.163178i	0.783973	+	0.620795i	$0.213190\pi$
$98$		0			0
$99$	−11.0464	−	1.10092i	−1.11021	−	0.110647i
$100$		0			0
$101$			18.1666i			1.80764i	0.427913	+	0.903820i	$0.359249\pi$
$101$			18.1666i			1.80764i	−0.427913	+	0.903820i	$0.640751\pi$
$102$		0			0
$103$	12.6439	+	12.6439i	1.24584	+	1.24584i	0.957540	+	0.288299i	$0.0930898\pi$
$103$	12.6439	+	12.6439i	1.24584	+	1.24584i	0.288299	+	0.957540i	$0.406910\pi$
$104$		0			0
$105$	−12.0748	−	1.63960i	−1.17837	−	0.160008i
$106$		0			0
$107$	8.57552	+	8.57552i	0.829027	+	0.829027i	0.987382	−	0.158355i	$-0.0506190\pi$
$107$	8.57552	+	8.57552i	0.829027	+	0.829027i	−0.158355	+	0.987382i	$0.550619\pi$
$108$		0			0
$109$	3.10511			0.297415			0.148708	−	0.988881i	$-0.452489\pi$
$109$	3.10511			0.297415			0.148708	+	0.988881i	$0.452489\pi$
$110$		0			0
$111$	−14.6137			−1.38707
$112$		0			0
$113$	−7.20515	−	7.20515i	−0.677803	−	0.677803i	0.281699	−	0.959503i	$-0.409102\pi$
$113$	−7.20515	−	7.20515i	−0.677803	−	0.677803i	−0.959503	+	0.281699i	$0.909102\pi$
$114$		0			0
$115$	5.22936	−	3.97898i	0.487640	−	0.371042i
$116$		0			0
$117$	2.95994	+	2.95994i	0.273646	+	0.273646i
$118$		0			0
$119$			0.929935i			0.0852470i
$120$		0			0
$121$	−10.7836	−	2.17103i	−0.980330	−	0.197367i
$122$		0			0
$123$	−4.39722	+	4.39722i	−0.396484	+	0.396484i
$124$		0			0
$125$	4.40409	−	10.2764i	0.393914	−	0.919147i
$126$		0			0
$127$	0.487942	+	0.487942i	0.0432978	+	0.0432978i	0.728424	−	0.685126i	$-0.240253\pi$
$127$	0.487942	+	0.487942i	0.0432978	+	0.0432978i	−0.685126	+	0.728424i	$0.740253\pi$
$128$		0			0
$129$	−30.2480			−2.66319
$130$		0			0
$131$			12.6997i			1.10958i	0.831990	+	0.554791i	$0.187202\pi$
$131$			12.6997i			1.10958i	−0.831990	+	0.554791i	$0.812798\pi$
$132$		0			0
$133$	−8.94427	−	8.94427i	−0.775567	−	0.775567i
$134$		0			0
$135$	1.18410	+	1.55619i	0.101911	+	0.133936i
$136$		0			0
$137$	10.4906	−	10.4906i	0.896274	−	0.896274i	−0.0988305	−	0.995104i	$-0.531510\pi$
$137$	10.4906	−	10.4906i	0.896274	−	0.896274i	0.995104	+	0.0988305i	$0.0315101\pi$
$138$		0			0
$139$	−12.5097			−1.06106			−0.530530	−	0.847666i	$-0.678007\pi$
$139$	−12.5097			−1.06106			−0.530530	+	0.847666i	$0.678007\pi$
$140$		0			0
$141$	26.7111			2.24948
$142$		0			0
$143$	2.62764	+	3.20938i	0.219735	+	0.268382i
$144$		0			0
$145$	−2.10869	+	15.5294i	−0.175117	+	1.28964i
$146$		0			0
$147$	−4.13491	+	4.13491i	−0.341041	+	0.341041i
$148$		0			0
$149$	8.41517			0.689398			0.344699	−	0.938713i	$-0.387981\pi$
$149$	8.41517			0.689398			0.344699	+	0.938713i	$0.387981\pi$
$150$		0			0
$151$			6.83507i			0.556230i	0.960548	+	0.278115i	$0.0897097\pi$
$151$			6.83507i			0.556230i	−0.960548	+	0.278115i	$0.910290\pi$
$152$		0			0
$153$	1.01750	−	1.01750i	0.0822603	−	0.0822603i
$154$		0			0
$155$	−1.37818	+	10.1495i	−0.110698	+	0.815230i
$156$		0			0
$157$	−13.0855	+	13.0855i	−1.04434	+	1.04434i	−0.0453663	+	0.998970i	$0.514445\pi$
$157$	−13.0855	+	13.0855i	−1.04434	+	1.04434i	−0.998970	+	0.0453663i	$0.985555\pi$
$158$		0			0
$159$		−	14.4206i		−	1.14363i
$160$		0			0
$161$			6.35654i			0.500966i
$162$		0			0
$163$	12.8355	+	12.8355i	1.00535	+	1.00535i	0.999986	+	0.00536615i	$0.00170811\pi$
$163$	12.8355	+	12.8355i	1.00535	+	1.00535i	0.00536615	+	0.999986i	$0.498292\pi$
$164$		0			0
$165$	9.78341	+	15.9178i	0.761637	+	1.23920i
$166$		0			0
$167$	−2.60268	−	2.60268i	−0.201402	−	0.201402i	0.599199	−	0.800600i	$-0.295486\pi$
$167$	−2.60268	−	2.60268i	−0.201402	−	0.201402i	−0.800600	+	0.599199i	$0.795486\pi$
$168$		0			0
$169$			11.4359i			0.879688i
$170$		0			0
$171$			19.5730i			1.49679i
$172$		0			0
$173$	−2.92391	+	2.92391i	−0.222301	+	0.222301i	−0.809467	−	0.587166i	$-0.800244\pi$
$173$	−2.92391	+	2.92391i	−0.222301	+	0.222301i	0.587166	+	0.809467i	$0.300244\pi$
$174$		0			0
$175$	5.33142	+	9.41003i	0.403018	+	0.711331i
$176$		0			0
$177$	−14.3852	+	14.3852i	−1.08126	+	1.08126i
$178$		0			0
$179$		−	3.79240i		−	0.283457i	−0.989906	−	0.141728i	$-0.954734\pi$
$179$		−	3.79240i		−	0.283457i	0.989906	−	0.141728i	$-0.0452660\pi$
$180$		0			0
$181$	−9.76096			−0.725526			−0.362763	−	0.931881i	$-0.618167\pi$
$181$	−9.76096			−0.725526			−0.362763	+	0.931881i	$0.618167\pi$
$182$		0			0
$183$	−4.64556	+	4.64556i	−0.343410	+	0.343410i
$184$		0			0
$185$	7.85406	+	10.3222i	0.577442	+	0.758900i
$186$		0			0
$187$	1.10325	−	0.903276i	0.0806779	−	0.0660540i
$188$		0			0
$189$	−1.89163			−0.137596
$190$		0			0
$191$	13.5188			0.978188			0.489094	−	0.872231i	$-0.337328\pi$
$191$	13.5188			0.978188			0.489094	+	0.872231i	$0.337328\pi$
$192$		0			0
$193$	−16.9973	+	16.9973i	−1.22350	+	1.22350i	−0.257114	+	0.966381i	$0.582772\pi$
$193$	−16.9973	+	16.9973i	−1.22350	+	1.22350i	−0.966381	+	0.257114i	$0.917228\pi$
$194$		0			0
$195$	0.947964	−	6.98124i	0.0678851	−	0.499937i
$196$		0			0
$197$	7.79758	+	7.79758i	0.555555	+	0.555555i	0.928039	−	0.372484i	$-0.121494\pi$
$197$	7.79758	+	7.79758i	0.555555	+	0.555555i	−0.372484	+	0.928039i	$0.621494\pi$
$198$		0			0
$199$		−	18.7501i		−	1.32916i	−0.747217	−	0.664580i	$-0.768610\pi$
$199$		−	18.7501i		−	1.32916i	0.747217	−	0.664580i	$-0.231390\pi$
$200$		0			0
$201$	7.08720			0.499892
$202$		0			0
$203$	−10.7200	−	10.7200i	−0.752394	−	0.752394i
$204$		0			0
$205$	5.46918	+	0.742646i	0.381984	+	0.0518686i
$206$		0			0
$207$	6.95512	−	6.95512i	0.483414	−	0.483414i
$208$		0			0
$209$	−1.92342	+	19.2991i	−0.133046	+	1.33495i
$210$		0			0
$211$		−	10.6204i		−	0.731139i	−0.930784	−	0.365569i	$-0.880874\pi$
$211$		−	10.6204i		−	0.731139i	0.930784	−	0.365569i	$-0.119126\pi$
$212$		0			0
$213$	12.0913	+	12.0913i	0.828481	+	0.828481i
$214$		0			0
$215$	16.2567	+	21.3653i	1.10870	+	1.45710i
$216$		0			0
$217$	−7.00625	−	7.00625i	−0.475615	−	0.475615i
$218$		0			0
$219$	−41.2012			−2.78412
$220$		0			0
$221$	−0.537659			−0.0361669
$222$		0			0
$223$	−2.61503	−	2.61503i	−0.175115	−	0.175115i	0.614107	−	0.789223i	$-0.289516\pi$
$223$	−2.61503	−	2.61503i	−0.175115	−	0.175115i	−0.789223	+	0.614107i	$0.789516\pi$
$224$		0			0
$225$	4.46268	−	16.1296i	0.297512	−	1.07531i
$226$		0			0
$227$	−12.0556	−	12.0556i	−0.800158	−	0.800158i	0.182962	−	0.983120i	$-0.441432\pi$
$227$	−12.0556	−	12.0556i	−0.800158	−	0.800158i	−0.983120	+	0.182962i	$0.941432\pi$
$228$		0			0
$229$			10.9190i			0.721550i	0.932653	+	0.360775i	$0.117488\pi$
$229$			10.9190i			0.721550i	−0.932653	+	0.360775i	$0.882512\pi$
$230$		0			0
$231$	−17.9850	−	1.79245i	−1.18333	−	0.117934i
$232$		0			0
$233$	14.2452	−	14.2452i	0.933235	−	0.933235i	−0.0646717	−	0.997907i	$-0.520600\pi$
$233$	14.2452	−	14.2452i	0.933235	−	0.933235i	0.997907	+	0.0646717i	$0.0206000\pi$
$234$		0			0
$235$	−14.3558	−	18.8670i	−0.936469	−	1.23075i
$236$		0			0
$237$	−13.5551	−	13.5551i	−0.880501	−	0.880501i
$238$		0			0
$239$	20.0592			1.29752			0.648762	−	0.760991i	$-0.275287\pi$
$239$	20.0592			1.29752			0.648762	+	0.760991i	$0.275287\pi$
$240$		0			0
$241$		−	9.03519i		−	0.582008i	−0.956722	−	0.291004i	$-0.906011\pi$
$241$		−	9.03519i		−	0.582008i	0.956722	−	0.291004i	$-0.0939893\pi$
$242$		0			0
$243$	−15.8184	−	15.8184i	−1.01475	−	1.01475i
$244$		0			0
$245$	5.14292	+	0.698344i	0.328569	+	0.0446156i
$246$		0			0
$247$	5.17129	−	5.17129i	0.329042	−	0.329042i
$248$		0			0
$249$	−29.1738			−1.84881
$250$		0			0
$251$	13.7921			0.870549			0.435275	−	0.900298i	$-0.356651\pi$
$251$	13.7921			0.870549			0.435275	+	0.900298i	$0.356651\pi$
$252$		0			0
$253$	7.54126	−	6.17431i	0.474115	−	0.388176i
$254$		0			0
$255$	−2.39986	−	0.325871i	−0.150285	−	0.0204068i
$256$		0			0
$257$	4.02455	−	4.02455i	0.251045	−	0.251045i	−0.570354	−	0.821399i	$-0.693194\pi$
$257$	4.02455	−	4.02455i	0.251045	−	0.251045i	0.821399	+	0.570354i	$0.193194\pi$
$258$		0			0
$259$	−12.5471			−0.779639
$260$		0			0
$261$			23.4589i			1.45207i
$262$		0			0
$263$	−13.0080	+	13.0080i	−0.802110	+	0.802110i	−0.983425	−	0.181315i	$-0.941965\pi$
$263$	−13.0080	+	13.0080i	−0.802110	+	0.802110i	0.181315	+	0.983425i	$0.441965\pi$
$264$		0			0
$265$	−10.1858	+	7.75028i	−0.625707	+	0.476096i
$266$		0			0
$267$	−0.909578	+	0.909578i	−0.0556653	+	0.0556653i
$268$		0			0
$269$			19.8989i			1.21326i	0.794984	+	0.606630i	$0.207479\pi$
$269$			19.8989i			1.21326i	−0.794984	+	0.606630i	$0.792521\pi$
$270$		0			0
$271$		−	30.9084i		−	1.87755i	−0.344531	−	0.938775i	$-0.611962\pi$
$271$		−	30.9084i		−	1.87755i	0.344531	−	0.938775i	$-0.388038\pi$
$272$		0			0
$273$	4.81917	+	4.81917i	0.291669	+	0.291669i
$274$		0			0
$275$	5.98526	−	15.4653i	0.360925	−	0.932595i
$276$		0			0
$277$	−11.5217	−	11.5217i	−0.692270	−	0.692270i	0.270461	−	0.962731i	$-0.412824\pi$
$277$	−11.5217	−	11.5217i	−0.692270	−	0.692270i	−0.962731	+	0.270461i	$0.912824\pi$
$278$		0			0
$279$			15.3320i			0.917904i
$280$		0			0
$281$		−	21.2994i		−	1.27062i	−0.772259	−	0.635308i	$-0.780873\pi$
$281$		−	21.2994i		−	1.27062i	0.772259	−	0.635308i	$-0.219127\pi$
$282$		0			0
$283$	−0.816018	+	0.816018i	−0.0485072	+	0.0485072i	−0.730944	−	0.682437i	$-0.760920\pi$
$283$	−0.816018	+	0.816018i	−0.0485072	+	0.0485072i	0.682437	+	0.730944i	$0.260920\pi$
$284$		0			0
$285$	26.2166	−	19.9480i	1.55293	−	1.18162i
$286$		0			0
$287$	−3.77539	+	3.77539i	−0.222854	+	0.222854i
$288$		0			0
$289$		−	16.8152i		−	0.989128i
$290$		0			0
$291$	−5.72599			−0.335663
$292$		0			0
$293$	−12.7346	+	12.7346i	−0.743961	+	0.743961i	−0.973338	−	0.229377i	$-0.926331\pi$
$293$	−12.7346	+	12.7346i	−0.743961	+	0.743961i	0.229377	+	0.973338i	$0.426331\pi$
$294$		0			0
$295$	17.8921	+	2.42952i	1.04172	+	0.141452i
$296$		0			0
$297$	1.83740	+	2.24418i	0.106617	+	0.130221i
$298$		0			0
$299$	−3.67515			−0.212540
$300$		0			0
$301$	−25.9705			−1.49692
$302$		0			0
$303$	32.3628	−	32.3628i	1.85919	−	1.85919i
$304$		0			0
$305$	5.77807	+	0.784588i	0.330851	+	0.0449254i
$306$		0			0
$307$	−6.67492	−	6.67492i	−0.380958	−	0.380958i	0.490489	−	0.871447i	$-0.336818\pi$
$307$	−6.67492	−	6.67492i	−0.380958	−	0.380958i	−0.871447	+	0.490489i	$0.836818\pi$
$308$		0			0
$309$		−	45.0489i		−	2.56274i
$310$		0			0
$311$	12.4220			0.704386			0.352193	−	0.935927i	$-0.385436\pi$
$311$	12.4220			0.704386			0.352193	+	0.935927i	$0.385436\pi$
$312$		0			0
$313$	−13.2894	−	13.2894i	−0.751162	−	0.751162i	0.223534	−	0.974696i	$-0.428241\pi$
$313$	−13.2894	−	13.2894i	−0.751162	−	0.751162i	−0.974696	+	0.223534i	$0.928241\pi$
$314$		0			0
$315$	9.80317	+	12.8838i	0.552346	+	0.725918i
$316$		0			0
$317$	−2.84585	+	2.84585i	−0.159839	+	0.159839i	−0.782495	−	0.622656i	$-0.786053\pi$
$317$	−2.84585	+	2.84585i	−0.159839	+	0.159839i	0.622656	+	0.782495i	$0.286053\pi$
$318$		0			0
$319$	−2.30527	+	23.1306i	−0.129071	+	1.29506i
$320$		0			0
$321$		−	30.5537i		−	1.70534i
$322$		0			0
$323$	−1.77768	−	1.77768i	−0.0989126	−	0.0989126i
$324$		0			0
$325$	−5.44058	+	3.08246i	−0.301789	+	0.170984i
$326$		0			0
$327$	−5.53159	−	5.53159i	−0.305898	−	0.305898i
$328$		0			0
$329$	22.9338			1.26438
$330$		0			0
$331$	23.7666			1.30633			0.653165	−	0.757216i	$-0.273441\pi$
$331$	23.7666			1.30633			0.653165	+	0.757216i	$0.273441\pi$
$332$		0			0
$333$	13.7286	+	13.7286i	0.752324	+	0.752324i
$334$		0			0
$335$	−3.80899	−	5.00595i	−0.208107	−	0.273504i
$336$		0			0
$337$	9.10416	+	9.10416i	0.495935	+	0.495935i	0.910170	−	0.414235i	$-0.135951\pi$
$337$	9.10416	+	9.10416i	0.495935	+	0.495935i	−0.414235	+	0.910170i	$0.635951\pi$
$338$		0			0
$339$			25.6712i			1.39427i
$340$		0			0
$341$	−1.50666	+	15.1174i	−0.0815901	+	0.818656i
$342$		0			0
$343$	−14.2569	+	14.2569i	−0.769798	+	0.769798i
$344$		0			0
$345$	−16.4042	−	2.22748i	−0.883172	−	0.119924i
$346$		0			0
$347$	3.85348	+	3.85348i	0.206866	+	0.206866i	0.802934	−	0.596068i	$-0.203271\pi$
$347$	3.85348	+	3.85348i	0.206866	+	0.206866i	−0.596068	+	0.802934i	$0.703271\pi$
$348$		0			0
$349$	−31.9890			−1.71233			−0.856165	−	0.516702i	$-0.827160\pi$
$349$	−31.9890			−1.71233			−0.856165	+	0.516702i	$0.827160\pi$
$350$		0			0
$351$		−	1.09368i		−	0.0583763i
$352$		0			0
$353$	2.82326	+	2.82326i	0.150267	+	0.150267i	0.778237	−	0.627970i	$-0.216114\pi$
$353$	2.82326	+	2.82326i	0.150267	+	0.150267i	−0.627970	+	0.778237i	$0.716114\pi$
$354$		0			0
$355$	2.04210	−	15.0389i	0.108383	−	0.798183i
$356$		0			0
$357$	1.65663	−	1.65663i	0.0876782	−	0.0876782i
$358$		0			0
$359$	23.6416			1.24776			0.623879	−	0.781521i	$-0.285556\pi$
$359$	23.6416			1.24776			0.623879	+	0.781521i	$0.285556\pi$
$360$		0			0
$361$	15.1960			0.799790
$362$		0			0
$363$	15.3429	+	23.0781i	0.805293	+	1.21128i
$364$		0			0
$365$	22.1434	+	29.1019i	1.15904	+	1.52326i
$366$		0			0
$367$	11.8905	−	11.8905i	0.620680	−	0.620680i	−0.325025	−	0.945705i	$-0.605373\pi$
$367$	11.8905	−	11.8905i	0.620680	−	0.620680i	0.945705	+	0.325025i	$0.105373\pi$
$368$		0			0
$369$	8.26182			0.430093
$370$		0			0
$371$		−	12.3813i		−	0.642805i
$372$		0			0
$373$	1.89470	−	1.89470i	0.0981037	−	0.0981037i	−0.656352	−	0.754455i	$-0.727901\pi$
$373$	1.89470	−	1.89470i	0.0981037	−	0.0981037i	0.754455	+	0.656352i	$0.227901\pi$
$374$		0			0
$375$	−26.1525	+	10.4612i	−1.35051	+	0.540213i
$376$		0			0
$377$	6.19795	−	6.19795i	0.319210	−	0.319210i
$378$		0			0
$379$			28.9628i			1.48772i	0.668336	+	0.743859i	$0.267007\pi$
$379$			28.9628i			1.48772i	−0.668336	+	0.743859i	$0.732993\pi$
$380$		0			0
$381$		−	1.73849i		−	0.0890654i
$382$		0			0
$383$	−16.6202	−	16.6202i	−0.849251	−	0.849251i	0.140789	−	0.990040i	$-0.455036\pi$
$383$	−16.6202	−	16.6202i	−0.849251	−	0.849251i	−0.990040	+	0.140789i	$0.955036\pi$
$384$		0			0
$385$	8.39990	+	13.6668i	0.428099	+	0.696525i
$386$		0			0
$387$	28.4161	+	28.4161i	1.44447	+	1.44447i
$388$		0			0
$389$		−	28.2986i		−	1.43479i	−0.696665	−	0.717397i	$-0.745333\pi$
$389$		−	28.2986i		−	1.43479i	0.696665	−	0.717397i	$-0.254667\pi$
$390$		0			0
$391$			1.26337i			0.0638912i
$392$		0			0
$393$	22.6239	−	22.6239i	1.14123	−	1.14123i
$394$		0			0
$395$	−2.28933	+	16.8596i	−0.115189	+	0.848301i
$396$		0			0
$397$	19.7234	−	19.7234i	0.989888	−	0.989888i	−0.0100613	−	0.999949i	$-0.503203\pi$
$397$	19.7234	−	19.7234i	0.989888	−	0.989888i	0.999949	+	0.0100613i	$0.00320266\pi$
$398$		0			0
$399$			31.8675i			1.59537i
$400$		0			0
$401$	−38.0099			−1.89812			−0.949061	−	0.315092i	$-0.897965\pi$
$401$	−38.0099			−1.89812			−0.949061	+	0.315092i	$0.897965\pi$
$402$		0			0
$403$	4.05079	−	4.05079i	0.201784	−	0.201784i
$404$		0			0
$405$	−2.35826	+	17.3673i	−0.117183	+	0.862987i
$406$		0			0
$407$	12.1874	+	14.8856i	0.604107	+	0.737851i
$408$		0			0
$409$	−2.46478			−0.121876			−0.0609378	−	0.998142i	$-0.519409\pi$
$409$	−2.46478			−0.121876			−0.0609378	+	0.998142i	$0.519409\pi$
$410$		0			0
$411$	−37.3770			−1.84367
$412$		0			0
$413$	−12.3510	+	12.3510i	−0.607751	+	0.607751i
$414$		0			0
$415$	15.6793	+	20.6065i	0.769669	+	1.01153i
$416$		0			0
$417$	22.2854	+	22.2854i	1.09132	+	1.09132i
$418$		0			0
$419$		−	25.4043i		−	1.24108i	−0.784175	−	0.620540i	$-0.786913\pi$
$419$		−	25.4043i		−	1.24108i	0.784175	−	0.620540i	$-0.213087\pi$
$420$		0			0
$421$	7.18265			0.350061			0.175031	−	0.984563i	$-0.443998\pi$
$421$	7.18265			0.350061			0.175031	+	0.984563i	$0.443998\pi$
$422$		0			0
$423$	−25.0934	−	25.0934i	−1.22008	−	1.22008i
$424$		0			0
$425$	1.05962	+	1.87025i	0.0513992	+	0.0907203i
$426$		0			0
$427$	−3.98861	+	3.98861i	−0.193023	+	0.193023i
$428$		0			0
$429$	1.03634	−	10.3984i	0.0500348	−	0.502038i
$430$		0			0
$431$		−	3.08421i		−	0.148561i	−0.997237	−	0.0742806i	$-0.976334\pi$
$431$		−	3.08421i		−	0.148561i	0.997237	−	0.0742806i	$-0.0236660\pi$
$432$		0			0
$433$	11.3329	+	11.3329i	0.544624	+	0.544624i	0.924881	−	0.380257i	$-0.124164\pi$
$433$	11.3329	+	11.3329i	0.544624	+	0.544624i	−0.380257	+	0.924881i	$0.624164\pi$
$434$		0			0
$435$	31.4213	−	23.9082i	1.50654	−	1.14631i
$436$		0			0
$437$	−12.1513	−	12.1513i	−0.581274	−	0.581274i
$438$		0			0
$439$	−4.53785			−0.216580			−0.108290	−	0.994119i	$-0.534537\pi$
$439$	−4.53785			−0.216580			−0.108290	+	0.994119i	$0.534537\pi$
$440$		0			0
$441$	7.76896			0.369951
$442$		0			0
$443$	5.92742	+	5.92742i	0.281620	+	0.281620i	0.833755	−	0.552135i	$-0.186187\pi$
$443$	5.92742	+	5.92742i	0.281620	+	0.281620i	−0.552135	+	0.833755i	$0.686187\pi$
$444$		0			0
$445$	1.13132	+	0.153619i	0.0536296	+	0.00728222i
$446$		0			0
$447$	−14.9912	−	14.9912i	−0.709059	−	0.709059i
$448$		0			0
$449$		−	20.5293i		−	0.968837i	−0.874836	−	0.484419i	$-0.839031\pi$
$449$		−	20.5293i		−	0.968837i	0.874836	−	0.484419i	$-0.160969\pi$
$450$		0			0
$451$	8.14620	+	0.811878i	0.383589	+	0.0382299i
$452$		0			0
$453$	12.1763	−	12.1763i	0.572094	−	0.572094i
$454$		0			0
$455$	0.813909	−	5.99400i	0.0381566	−	0.281003i
$456$		0			0
$457$	22.7956	+	22.7956i	1.06633	+	1.06633i	0.997638	+	0.0686971i	$0.0218842\pi$
$457$	22.7956	+	22.7956i	1.06633	+	1.06633i	0.0686971	+	0.997638i	$0.478116\pi$
$458$		0			0
$459$	−0.375962			−0.0175484
$460$		0			0
$461$		−	19.3522i		−	0.901323i	−0.892695	−	0.450662i	$-0.851188\pi$
$461$		−	19.3522i		−	0.901323i	0.892695	−	0.450662i	$-0.148812\pi$
$462$		0			0
$463$	−4.69686	−	4.69686i	−0.218281	−	0.218281i	0.589492	−	0.807774i	$-0.299328\pi$
$463$	−4.69686	−	4.69686i	−0.218281	−	0.218281i	−0.807774	+	0.589492i	$0.799328\pi$
$464$		0			0
$465$	20.5360	−	15.6257i	0.952335	−	0.724625i
$466$		0			0
$467$	−3.61995	+	3.61995i	−0.167511	+	0.167511i	−0.785885	−	0.618373i	$-0.787792\pi$
$467$	−3.61995	+	3.61995i	−0.167511	+	0.167511i	0.618373	+	0.785885i	$0.287792\pi$
$468$		0			0
$469$	6.08497			0.280978
$470$		0			0
$471$	46.6223			2.14824
$472$		0			0
$473$	25.2260	+	30.8108i	1.15989	+	1.41668i
$474$		0			0
$475$	−28.1800	−	7.79673i	−1.29299	−	0.357738i
$476$		0			0
$477$	−13.5472	+	13.5472i	−0.620284	+	0.620284i
$478$		0			0
$479$	−19.7177			−0.900925			−0.450463	−	0.892795i	$-0.648741\pi$
$479$	−19.7177			−0.900925			−0.450463	+	0.892795i	$0.648741\pi$
$480$		0			0
$481$		−	7.25433i		−	0.330769i
$482$		0			0
$483$	11.3239	−	11.3239i	0.515253	−	0.515253i
$484$		0			0
$485$	3.07741	+	4.04447i	0.139738	+	0.183650i
$486$		0			0
$487$	−11.1464	+	11.1464i	−0.505091	+	0.505091i	−0.913016	−	0.407925i	$-0.866253\pi$
$487$	−11.1464	+	11.1464i	−0.505091	+	0.505091i	0.407925	+	0.913016i	$0.366253\pi$
$488$		0			0
$489$		−	45.7315i		−	2.06805i
$490$		0			0
$491$			5.12509i			0.231292i	0.993290	+	0.115646i	$0.0368938\pi$
$491$			5.12509i			0.231292i	−0.993290	+	0.115646i	$0.963106\pi$
$492$		0			0
$493$	−2.13060	−	2.13060i	−0.0959573	−	0.0959573i
$494$		0			0
$495$	5.76287	−	24.1447i	0.259022	−	1.08522i
$496$		0			0
$497$	10.3814	+	10.3814i	0.465670	+	0.465670i
$498$		0			0
$499$			13.1043i			0.586629i	0.956016	+	0.293314i	$0.0947583\pi$
$499$			13.1043i			0.586629i	−0.956016	+	0.293314i	$0.905242\pi$
$500$		0			0
$501$			9.27309i			0.414291i
$502$		0			0
$503$	−12.0287	+	12.0287i	−0.536334	+	0.536334i	−0.922450	−	0.386116i	$-0.873816\pi$
$503$	−12.0287	+	12.0287i	−0.536334	+	0.536334i	0.386116	+	0.922450i	$0.373816\pi$
$504$		0			0
$505$	−40.2523	−	5.46575i	−1.79120	−	0.243223i
$506$		0			0
$507$	20.3725	−	20.3725i	0.904776	−	0.904776i
$508$		0			0
$509$			33.3415i			1.47783i	0.673796	+	0.738917i	$0.264663\pi$
$509$			33.3415i			1.47783i	−0.673796	+	0.738917i	$0.735337\pi$
$510$		0			0
$511$	−35.3748			−1.56489
$512$		0			0
$513$	3.61606	−	3.61606i	0.159653	−	0.159653i
$514$		0			0
$515$	−31.8197	+	24.2114i	−1.40214	+	1.06688i
$516$		0			0
$517$	−22.2763	−	27.2081i	−0.979712	−	1.19661i
$518$		0			0
$519$	10.4176			0.457281
$520$		0			0
$521$	−27.1194			−1.18812			−0.594061	−	0.804420i	$-0.702476\pi$
$521$	−27.1194			−1.18812			−0.594061	+	0.804420i	$0.702476\pi$
$522$		0			0
$523$	16.8930	−	16.8930i	0.738678	−	0.738678i	−0.233644	−	0.972322i	$-0.575065\pi$
$523$	16.8930	−	16.8930i	0.738678	−	0.738678i	0.972322	+	0.233644i	$0.0750652\pi$
$524$		0			0
$525$	7.26583	−	26.2611i	0.317107	−	1.14613i
$526$		0			0
$527$	−1.39249	−	1.39249i	−0.0606580	−	0.0606580i
$528$		0			0
$529$		−	14.3643i		−	0.624535i
$530$		0			0
$531$	27.0280			1.17292
$532$		0			0
$533$	−2.18281	−	2.18281i	−0.0945481	−	0.0945481i
$534$		0			0
$535$	−21.5812	+	16.4210i	−0.933036	+	0.709941i
$536$		0			0
$537$	−6.75596	+	6.75596i	−0.291541	+	0.291541i
$538$		0			0
$539$	7.66024	+	0.763446i	0.329950	+	0.0328840i
$540$		0			0
$541$		−	19.5896i		−	0.842221i	−0.907009	−	0.421110i	$-0.861640\pi$
$541$		−	19.5896i		−	0.842221i	0.907009	−	0.421110i	$-0.138360\pi$
$542$		0			0
$543$	17.3886	+	17.3886i	0.746218	+	0.746218i
$544$		0			0
$545$	−0.934230	+	6.88010i	−0.0400180	+	0.294711i
$546$		0			0
$547$	5.45521	+	5.45521i	0.233248	+	0.233248i	0.814047	−	0.580799i	$-0.197260\pi$
$547$	5.45521	+	5.45521i	0.233248	+	0.233248i	−0.580799	+	0.814047i	$0.697260\pi$
$548$		0			0
$549$	8.72842			0.372520
$550$		0			0
$551$	40.9849			1.74602
$552$		0			0
$553$	−11.6383	−	11.6383i	−0.494909	−	0.494909i
$554$		0			0
$555$	4.39679	−	32.3800i	0.186634	−	1.37445i
$556$		0			0
$557$	1.93073	+	1.93073i	0.0818074	+	0.0818074i	0.746826	−	0.665019i	$-0.231577\pi$
$557$	1.93073	+	1.93073i	0.0818074	+	0.0818074i	−0.665019	+	0.746826i	$0.731577\pi$
$558$		0			0
$559$		−	15.0153i		−	0.635081i
$560$		0			0
$561$	−3.57453	−	0.356250i	−0.150917	−	0.0150409i
$562$		0			0
$563$	7.11122	−	7.11122i	0.299702	−	0.299702i	−0.541195	−	0.840897i	$-0.682028\pi$
$563$	7.11122	−	7.11122i	0.299702	−	0.299702i	0.840897	+	0.541195i	$0.182028\pi$
$564$		0			0
$565$	18.1325	−	13.7969i	0.762840	−	0.580440i
$566$		0			0
$567$	−11.9887	−	11.9887i	−0.503477	−	0.503477i
$568$		0			0
$569$	−7.48123			−0.313630			−0.156815	−	0.987628i	$-0.550123\pi$
$569$	−7.48123			−0.313630			−0.156815	+	0.987628i	$0.550123\pi$
$570$		0			0
$571$		−	20.8881i		−	0.874139i	−0.899428	−	0.437069i	$-0.856016\pi$
$571$		−	20.8881i		−	0.874139i	0.899428	−	0.437069i	$-0.143984\pi$
$572$		0			0
$573$	−24.0831	−	24.0831i	−1.00609	−	1.00609i
$574$		0			0
$575$	7.24302	+	12.7840i	0.302055	+	0.533131i
$576$		0			0
$577$	−25.4516	+	25.4516i	−1.05956	+	1.05956i	−0.0614540	+	0.998110i	$0.519574\pi$
$577$	−25.4516	+	25.4516i	−1.05956	+	1.05956i	−0.998110	+	0.0614540i	$0.980426\pi$
$578$		0			0
$579$	60.5598			2.51678
$580$		0			0
$581$	−25.0482			−1.03917
$582$		0			0
$583$	−14.6889	+	12.0264i	−0.608352	+	0.498081i
$584$		0			0
$585$	−7.44899	+	5.66788i	−0.307978	+	0.234338i
$586$		0			0
$587$	−13.3887	+	13.3887i	−0.552612	+	0.552612i	−0.927194	−	0.374582i	$-0.877786\pi$
$587$	−13.3887	+	13.3887i	−0.552612	+	0.552612i	0.374582	+	0.927194i	$0.377786\pi$
$588$		0			0
$589$	26.7865			1.10372
$590$		0			0
$591$		−	27.7820i		−	1.14280i
$592$		0			0
$593$	7.54934	−	7.54934i	0.310014	−	0.310014i	−0.534901	−	0.844915i	$-0.679651\pi$
$593$	7.54934	−	7.54934i	0.310014	−	0.310014i	0.844915	+	0.534901i	$0.179651\pi$
$594$		0			0
$595$	−2.06049	−	0.279788i	−0.0844718	−	0.0114702i
$596$		0			0
$597$	−33.4024	+	33.4024i	−1.36707	+	1.36707i
$598$		0			0
$599$		−	0.363805i		−	0.0148647i	−0.999972	−	0.00743234i	$-0.997634\pi$
$599$		−	0.363805i		−	0.0148647i	0.999972	−	0.00743234i	$-0.00236581\pi$
$600$		0			0
$601$			12.7778i			0.521216i	0.965445	+	0.260608i	$0.0839230\pi$
$601$			12.7778i			0.521216i	−0.965445	+	0.260608i	$0.916077\pi$
$602$		0			0
$603$	−6.65798	−	6.65798i	−0.271134	−	0.271134i
$604$		0			0
$605$	8.05489	−	23.2405i	0.327478	−	0.944859i
$606$		0			0
$607$	−3.09163	−	3.09163i	−0.125486	−	0.125486i	0.641575	−	0.767060i	$-0.278281\pi$
$607$	−3.09163	−	3.09163i	−0.125486	−	0.125486i	−0.767060	+	0.641575i	$0.778281\pi$
$608$		0			0
$609$			38.1941i			1.54770i
$610$		0			0
$611$			13.2596i			0.536426i
$612$		0			0
$613$	13.4790	−	13.4790i	0.544411	−	0.544411i	−0.380408	−	0.924819i	$-0.624216\pi$
$613$	13.4790	−	13.4790i	0.544411	−	0.544411i	0.924819	+	0.380408i	$0.124216\pi$
$614$		0			0
$615$	−8.42008	−	11.0661i	−0.339530	−	0.446226i
$616$		0			0
$617$	−1.48032	+	1.48032i	−0.0595952	+	0.0595952i	−0.736276	−	0.676681i	$-0.763418\pi$
$617$	−1.48032	+	1.48032i	−0.0595952	+	0.0595952i	0.676681	+	0.736276i	$0.263418\pi$
$618$		0			0
$619$		−	2.93096i		−	0.117805i	−0.998264	−	0.0589025i	$-0.981240\pi$
$619$		−	2.93096i		−	0.117805i	0.998264	−	0.0589025i	$-0.0187601\pi$
$620$		0			0
$621$	−2.56988			−0.103126
$622$		0			0
$623$	−0.780952	+	0.780952i	−0.0312882	+	0.0312882i
$624$		0			0
$625$	21.4447	+	12.8501i	0.857787	+	0.514005i
$626$		0			0
$627$	37.8069	−	30.9539i	1.50986	−	1.23618i
$628$		0			0
$629$	−2.49374			−0.0994319
$630$		0			0
$631$	−44.5685			−1.77424			−0.887122	−	0.461535i	$-0.847299\pi$
$631$	−44.5685			−1.77424			−0.887122	+	0.461535i	$0.847299\pi$
$632$		0			0
$633$	−18.9197	+	18.9197i	−0.751991	+	0.751991i
$634$		0			0
$635$	−1.22796	+	0.934343i	−0.0487299	+	0.0370783i
$636$		0			0
$637$	−2.05260	−	2.05260i	−0.0813269	−	0.0813269i
$638$		0			0
$639$		−	22.7180i		−	0.898710i
$640$		0			0
$641$	27.6637			1.09265			0.546325	−	0.837574i	$-0.316026\pi$
$641$	27.6637			1.09265			0.546325	+	0.837574i	$0.316026\pi$
$642$		0			0
$643$	−3.11829	−	3.11829i	−0.122973	−	0.122973i	0.642942	−	0.765915i	$-0.277714\pi$
$643$	−3.11829	−	3.11829i	−0.122973	−	0.122973i	−0.765915	+	0.642942i	$0.777714\pi$
$644$		0			0
$645$	9.10068	−	67.0215i	0.358339	−	2.63897i
$646$		0			0
$647$	−21.1385	+	21.1385i	−0.831040	+	0.831040i	−0.987659	−	0.156619i	$-0.949940\pi$
$647$	−21.1385	+	21.1385i	−0.831040	+	0.831040i	0.156619	+	0.987659i	$0.449940\pi$
$648$		0			0
$649$	26.6498	+	2.65601i	1.04609	+	0.104257i
$650$		0			0
$651$			24.9625i			0.978359i
$652$		0			0
$653$	2.05913	+	2.05913i	0.0805801	+	0.0805801i	0.746248	−	0.665668i	$-0.231853\pi$
$653$	2.05913	+	2.05913i	0.0805801	+	0.0805801i	−0.665668	+	0.746248i	$0.731853\pi$
$654$		0			0
$655$	−28.1392	−	3.82095i	−1.09949	−	0.149297i
$656$		0			0
$657$	38.7059	+	38.7059i	1.51006	+	1.51006i
$658$		0			0
$659$	28.9414			1.12740			0.563698	−	0.825981i	$-0.309378\pi$
$659$	28.9414			1.12740			0.563698	+	0.825981i	$0.309378\pi$
$660$		0			0
$661$	41.6833			1.62129			0.810647	−	0.585536i	$-0.199116\pi$
$661$	41.6833			1.62129			0.810647	+	0.585536i	$0.199116\pi$
$662$		0			0
$663$	0.957812	+	0.957812i	0.0371983	+	0.0371983i
$664$		0			0
$665$	22.5092	−	17.1271i	0.872868	−	0.664159i
$666$		0			0
$667$	−14.5636	−	14.5636i	−0.563907	−	0.563907i
$668$		0			0
$669$			9.31707i			0.360219i
$670$		0			0
$671$	8.60627	+	0.857731i	0.332241	+	0.0331123i
$672$		0			0
$673$	−10.2229	+	10.2229i	−0.394062	+	0.394062i	−0.876133	−	0.482070i	$-0.839885\pi$
$673$	−10.2229	+	10.2229i	−0.394062	+	0.394062i	0.482070	+	0.876133i	$0.339885\pi$
$674$		0			0
$675$	−3.80436	+	2.15543i	−0.146430	+	0.0829626i
$676$		0			0
$677$	−33.5097	−	33.5097i	−1.28788	−	1.28788i	−0.936070	−	0.351815i	$-0.885565\pi$
$677$	−33.5097	−	33.5097i	−1.28788	−	1.28788i	−0.351815	−	0.936070i	$-0.614435\pi$
$678$		0			0
$679$	−4.91626			−0.188669
$680$		0			0
$681$			42.9529i			1.64596i
$682$		0			0
$683$	−5.04385	−	5.04385i	−0.192998	−	0.192998i	0.603992	−	0.796990i	$-0.293576\pi$
$683$	−5.04385	−	5.04385i	−0.192998	−	0.192998i	−0.796990	+	0.603992i	$0.793576\pi$
$684$		0			0
$685$	20.0881	+	26.4007i	0.767528	+	1.00872i
$686$		0			0
$687$	19.4517	−	19.4517i	0.742128	−	0.742128i
$688$		0			0
$689$	7.15848			0.272716
$690$		0			0
$691$	−37.0145			−1.40810			−0.704049	−	0.710151i	$-0.748626\pi$
$691$	−37.0145			−1.40810			−0.704049	+	0.710151i	$0.748626\pi$
$692$		0			0
$693$	15.2119	+	18.5797i	0.577852	+	0.705783i
$694$		0			0
$695$	3.76378	−	27.7182i	0.142768	−	1.05141i
$696$		0			0
$697$	−0.750361	+	0.750361i	−0.0284219	+	0.0284219i
$698$		0			0
$699$	−50.7542			−1.91970
$700$		0			0
$701$			42.0327i			1.58755i	0.608209	+	0.793777i	$0.291888\pi$
$701$			42.0327i			1.58755i	−0.608209	+	0.793777i	$0.708112\pi$
$702$		0			0
$703$	23.9852	−	23.9852i	0.904620	−	0.904620i
$704$		0			0
$705$	−8.03654	+	59.1847i	−0.302674	+	2.22903i
$706$		0			0
$707$	27.7862	−	27.7862i	1.04501	−	1.04501i
$708$		0			0
$709$			24.3303i			0.913744i	0.889532	+	0.456872i	$0.151030\pi$
$709$			24.3303i			0.913744i	−0.889532	+	0.456872i	$0.848970\pi$
$710$		0			0
$711$			25.4684i			0.955139i
$712$		0			0
$713$	−9.51836	−	9.51836i	−0.356465	−	0.356465i
$714$		0			0
$715$	−7.90171	+	4.85656i	−0.295507	+	0.181625i
$716$		0			0
$717$	−35.7345	−	35.7345i	−1.33453	−	1.33453i
$718$		0			0
$719$		−	29.3291i		−	1.09379i	−0.837201	−	0.546895i	$-0.815810\pi$
$719$		−	29.3291i		−	1.09379i	0.837201	−	0.546895i	$-0.184190\pi$
$720$		0			0
$721$		−	38.6784i		−	1.44046i
$722$		0			0
$723$	−16.0957	+	16.0957i	−0.598606	+	0.598606i
$724$		0			0
$725$	−33.7745	−	9.34460i	−1.25435	−	0.347050i
$726$		0			0
$727$	−1.38305	+	1.38305i	−0.0512946	+	0.0512946i	−0.732289	−	0.680994i	$-0.761548\pi$
$727$	−1.38305	+	1.38305i	−0.0512946	+	0.0512946i	0.680994	+	0.732289i	$0.261548\pi$
$728$		0			0
$729$			32.8448i			1.21647i
$730$		0			0
$731$	−5.16165			−0.190911
$732$		0			0
$733$	−5.36112	+	5.36112i	−0.198017	+	0.198017i	−0.799150	−	0.601132i	$-0.794717\pi$
$733$	−5.36112	+	5.36112i	−0.198017	+	0.198017i	0.601132	+	0.799150i	$0.294717\pi$
$734$		0			0
$735$	−7.91779	−	10.4059i	−0.292052	−	0.383828i
$736$		0			0
$737$	−5.91053	−	7.21907i	−0.217717	−	0.265918i
$738$		0			0
$739$	26.5663			0.977258			0.488629	−	0.872492i	$-0.337497\pi$
$739$	26.5663			0.977258			0.488629	+	0.872492i	$0.337497\pi$
$740$		0			0
$741$	−18.4248			−0.676851
$742$		0			0
$743$	−32.8436	+	32.8436i	−1.20491	+	1.20491i	−0.232261	+	0.972654i	$0.574612\pi$
$743$	−32.8436	+	32.8436i	−1.20491	+	1.20491i	−0.972654	+	0.232261i	$0.925388\pi$
$744$		0			0
$745$	−2.53186	+	18.6458i	−0.0927602	+	0.683129i
$746$		0			0
$747$	27.4069	+	27.4069i	1.00277	+	1.00277i
$748$		0			0
$749$		−	26.2330i		−	0.958533i
$750$		0			0
$751$	17.8712			0.652130			0.326065	−	0.945347i	$-0.394277\pi$
$751$	17.8712			0.652130			0.326065	+	0.945347i	$0.394277\pi$
$752$		0			0
$753$	−24.5699	−	24.5699i	−0.895377	−	0.895377i
$754$		0			0
$755$	−15.1447	−	2.05646i	−0.551172	−	0.0748422i
$756$		0			0
$757$	−15.8663	+	15.8663i	−0.576671	+	0.576671i	−0.933985	−	0.357313i	$-0.883693\pi$
$757$	−15.8663	+	15.8663i	−0.576671	+	0.576671i	0.357313	+	0.933985i	$0.383693\pi$
$758$		0			0
$759$	−24.4336	−	2.43514i	−0.886883	−	0.0883899i
$760$		0			0
$761$			30.6777i			1.11206i	0.831161	+	0.556032i	$0.187677\pi$
$761$			30.6777i			1.11206i	−0.831161	+	0.556032i	$0.812323\pi$
$762$		0			0
$763$	−4.74935	−	4.74935i	−0.171938	−	0.171938i
$764$		0			0
$765$	1.94838	+	2.56065i	0.0704439	+	0.0925806i
$766$		0			0
$767$	−7.14093	−	7.14093i	−0.257844	−	0.257844i
$768$		0			0
$769$	−40.6433			−1.46564			−0.732818	−	0.680425i	$-0.761795\pi$
$769$	−40.6433			−1.46564			−0.732818	+	0.680425i	$0.761795\pi$
$770$		0			0
$771$	−14.3391			−0.516409
$772$		0			0
$773$	8.53506	+	8.53506i	0.306985	+	0.306985i	0.843739	−	0.536754i	$-0.180350\pi$
$773$	8.53506	+	8.53506i	0.306985	+	0.306985i	−0.536754	+	0.843739i	$0.680350\pi$
$774$		0			0
$775$	−22.0740	−	6.10735i	−0.792922	−	0.219383i
$776$		0			0
$777$	22.3520	+	22.3520i	0.801874	+	0.801874i
$778$		0			0
$779$		−	14.4342i		−	0.517159i
$780$		0			0
$781$	2.23247	−	22.4001i	0.0798840	−	0.801537i
$782$		0			0
$783$	4.33396	−	4.33396i	0.154883	−	0.154883i
$784$		0			0
$785$	−25.0570	−	32.9310i	−0.894322	−	1.17536i
$786$		0			0
$787$	9.42078	+	9.42078i	0.335814	+	0.335814i	0.854789	−	0.518975i	$-0.173686\pi$
$787$	9.42078	+	9.42078i	0.335814	+	0.335814i	−0.518975	+	0.854789i	$0.673686\pi$
$788$		0			0
$789$	46.3463			1.64997
$790$		0			0
$791$			22.0409i			0.783686i
$792$		0			0
$793$	−2.30609	−	2.30609i	−0.0818917	−	0.0818917i
$794$		0			0
$795$	31.9521	+	4.33870i	1.13323	+	0.153878i
$796$		0			0
$797$	−6.06738	+	6.06738i	−0.214918	+	0.214918i	−0.806353	−	0.591435i	$-0.798562\pi$
$797$	−6.06738	+	6.06738i	−0.214918	+	0.214918i	0.591435	+	0.806353i	$0.298562\pi$
$798$		0			0
$799$	4.55810			0.161254
$800$		0			0
$801$	1.70898			0.0603839
$802$		0			0
$803$	34.3607	+	41.9678i	1.21256	+	1.48101i
$804$		0			0
$805$	−14.0844	−	1.91249i	−0.496410	−	0.0674062i
$806$		0			0
$807$	35.4489	−	35.4489i	1.24786	−	1.24786i
$808$		0			0
$809$	52.1858			1.83475			0.917377	−	0.398019i	$-0.130302\pi$
$809$	52.1858			1.83475			0.917377	+	0.398019i	$0.130302\pi$
$810$		0			0
$811$			6.09021i			0.213856i	0.994267	+	0.106928i	$0.0341015\pi$
$811$			6.09021i			0.213856i	−0.994267	+	0.106928i	$0.965899\pi$
$812$		0			0
$813$	−55.0617	+	55.0617i	−1.93110	+	1.93110i
$814$		0			0
$815$	−32.3018	+	24.5782i	−1.13148	+	0.860937i
$816$		0			0
$817$	49.6456	−	49.6456i	1.73688	−	1.73688i
$818$		0			0
$819$		−	9.05461i		−	0.316394i
$820$		0			0
$821$			33.0669i			1.15404i	0.816729	+	0.577021i	$0.195785\pi$
$821$			33.0669i			1.15404i	−0.816729	+	0.577021i	$0.804215\pi$
$822$		0			0
$823$	14.1917	+	14.1917i	0.494690	+	0.494690i	0.909780	−	0.415090i	$-0.136250\pi$
$823$	14.1917	+	14.1917i	0.494690	+	0.494690i	−0.415090	+	0.909780i	$0.636250\pi$
$824$		0			0
$825$	−38.2131	+	16.8883i	−1.33041	+	0.587974i
$826$		0			0
$827$	−37.1038	−	37.1038i	−1.29023	−	1.29023i	−0.934646	−	0.355579i	$-0.884284\pi$
$827$	−37.1038	−	37.1038i	−1.29023	−	1.29023i	−0.355579	−	0.934646i	$-0.615716\pi$
$828$		0			0
$829$		−	35.7655i		−	1.24219i	−0.783736	−	0.621094i	$-0.786688\pi$
$829$		−	35.7655i		−	1.24219i	0.783736	−	0.621094i	$-0.213312\pi$
$830$		0			0
$831$			41.0505i			1.42403i
$832$		0			0
$833$	−0.705598	+	0.705598i	−0.0244475	+	0.0244475i
$834$		0			0
$835$	6.54992	−	4.98379i	0.226669	−	0.172471i
$836$		0			0
$837$	2.83254	−	2.83254i	0.0979071	−	0.0979071i
$838$		0			0
$839$			29.0915i			1.00435i	0.864766	+	0.502174i	$0.167466\pi$
$839$			29.0915i			1.00435i	−0.864766	+	0.502174i	$0.832534\pi$
$840$		0			0
$841$	20.1216			0.693848
$842$		0			0
$843$	−37.9438	+	37.9438i	−1.30685	+	1.30685i
$844$		0			0
$845$	−25.3390	−	3.44072i	−0.871688	−	0.118364i
$846$		0			0
$847$	13.1732	+	19.8145i	0.452636	+	0.680835i
$848$		0			0
$849$	2.90739			0.0997812
$850$		0			0
$851$	−17.0459			−0.584326
$852$		0			0
$853$	0.511025	−	0.511025i	0.0174972	−	0.0174972i	−0.698304	−	0.715801i	$-0.746062\pi$
$853$	0.511025	−	0.511025i	0.0174972	−	0.0174972i	0.715801	+	0.698304i	$0.246062\pi$
$854$		0			0
$855$	−43.3687	−	5.88892i	−1.48318	−	0.201397i
$856$		0			0
$857$	−6.01074	−	6.01074i	−0.205323	−	0.205323i	0.596953	−	0.802276i	$-0.296378\pi$
$857$	−6.01074	−	6.01074i	−0.205323	−	0.205323i	−0.802276	+	0.596953i	$0.796378\pi$
$858$		0			0
$859$		−	14.9147i		−	0.508882i	−0.967088	−	0.254441i	$-0.918109\pi$
$859$		−	14.9147i		−	0.508882i	0.967088	−	0.254441i	$-0.0818915\pi$
$860$		0			0
$861$	13.4513			0.458420
$862$		0			0
$863$	19.1426	+	19.1426i	0.651622	+	0.651622i	0.953383	−	0.301762i	$-0.0975747\pi$
$863$	19.1426	+	19.1426i	0.651622	+	0.651622i	−0.301762	+	0.953383i	$0.597575\pi$
$864$		0			0
$865$	−5.59889	−	7.35832i	−0.190368	−	0.250190i
$866$		0			0
$867$	−29.9554	+	29.9554i	−1.01734	+	1.01734i
$868$		0			0
$869$	−2.50275	+	25.1120i	−0.0848999	+	0.851865i
$870$		0			0
$871$			3.51814i			0.119208i
$872$		0			0
$873$	5.37920	+	5.37920i	0.182058	+	0.182058i
$874$		0			0
$875$	−22.4542	+	8.98183i	−0.759090	+	0.303641i
$876$		0			0
$877$	9.69384	+	9.69384i	0.327338	+	0.327338i	0.851573	−	0.524236i	$-0.175649\pi$
$877$	9.69384	+	9.69384i	0.327338	+	0.327338i	−0.524236	+	0.851573i	$0.675649\pi$
$878$		0			0
$879$	45.3719			1.53036
$880$		0			0
$881$	−18.8905			−0.636436			−0.318218	−	0.948018i	$-0.603084\pi$
$881$	−18.8905			−0.636436			−0.318218	+	0.948018i	$0.603084\pi$
$882$		0			0
$883$	−21.2111	−	21.2111i	−0.713809	−	0.713809i	0.253521	−	0.967330i	$-0.418411\pi$
$883$	−21.2111	−	21.2111i	−0.713809	−	0.713809i	−0.967330	+	0.253521i	$0.918411\pi$
$884$		0			0
$885$	−27.5458	−	36.2019i	−0.925941	−	1.21691i
$886$		0			0
$887$	6.10008	+	6.10008i	0.204821	+	0.204821i	0.802062	−	0.597241i	$-0.203736\pi$
$887$	6.10008	+	6.10008i	0.204821	+	0.204821i	−0.597241	+	0.802062i	$0.703736\pi$
$888$		0			0
$889$		−	1.49264i		−	0.0500616i
$890$		0			0
$891$	−2.57810	+	25.8681i	−0.0863697	+	0.866613i
$892$		0			0
$893$	−43.8406	+	43.8406i	−1.46707	+	1.46707i
$894$		0			0
$895$	8.40294	+	1.14101i	0.280879	+	0.0381399i
$896$		0			0
$897$	6.54709	+	6.54709i	0.218601	+	0.218601i
$898$		0			0
$899$	32.1044			1.07074
$900$		0			0
$901$		−	2.46079i		−	0.0819808i
$902$		0			0
$903$	46.2652	+	46.2652i	1.53961	+	1.53961i
$904$		0			0
$905$	2.93677	−	21.6277i	0.0976215	−	0.718929i
$906$		0			0
$907$	−29.1109	+	29.1109i	−0.966613	+	0.966613i	−0.999460	−	0.0328475i	$-0.989542\pi$
$907$	−29.1109	+	29.1109i	−0.966613	+	0.966613i	0.0328475	+	0.999460i	$0.489542\pi$
$908$		0			0
$909$	−60.8056			−2.01679
$910$		0			0
$911$	29.3410			0.972111			0.486055	−	0.873928i	$-0.338435\pi$
$911$	29.3410			0.972111			0.486055	+	0.873928i	$0.338435\pi$
$912$		0			0
$913$	24.3301	+	29.7166i	0.805210	+	0.983477i
$914$		0			0
$915$	−8.89562	−	11.6910i	−0.294080	−	0.386494i
$916$		0			0
$917$	19.4246	−	19.4246i	0.641457	−	0.641457i
$918$		0			0
$919$	−12.4710			−0.411379			−0.205690	−	0.978617i	$-0.565944\pi$
$919$	−12.4710			−0.411379			−0.205690	+	0.978617i	$0.565944\pi$
$920$		0			0
$921$			23.7820i			0.783645i
$922$		0			0
$923$	−6.00220	+	6.00220i	−0.197565	+	0.197565i
$924$		0			0
$925$	−25.2342	+	14.2969i	−0.829696	+	0.470079i
$926$		0			0
$927$	−42.3206	+	42.3206i	−1.38999	+	1.38999i
$928$		0			0
$929$		−	7.26158i		−	0.238245i	−0.992880	−	0.119122i	$-0.961992\pi$
$929$		−	7.26158i		−	0.238245i	0.992880	−	0.119122i	$-0.0380081\pi$
$930$		0			0
$931$		−	13.5731i		−	0.444841i
$932$		0			0
$933$	−22.1291	−	22.1291i	−0.724475	−	0.724475i
$934$		0			0
$935$	1.66948	+	2.71628i	0.0545980	+	0.0888320i
$936$		0			0
$937$	35.9743	+	35.9743i	1.17523	+	1.17523i	0.980945	+	0.194285i	$0.0622387\pi$
$937$	35.9743	+	35.9743i	1.17523	+	1.17523i	0.194285	+	0.980945i	$0.437761\pi$
$938$		0			0
$939$			47.3488i			1.54517i
$940$		0			0
$941$		−	20.1138i		−	0.655692i	−0.944731	−	0.327846i	$-0.893677\pi$
$941$		−	20.1138i		−	0.655692i	0.944731	−	0.327846i	$-0.106323\pi$
$942$		0			0
$943$	−5.12907	+	5.12907i	−0.167025	+	0.167025i
$944$		0			0
$945$	0.569132	−	4.19134i	0.0185138	−	0.136344i
$946$		0			0
$947$	−23.3109	+	23.3109i	−0.757502	+	0.757502i	−0.975867	−	0.218365i	$-0.929928\pi$
$947$	−23.3109	+	23.3109i	−0.757502	+	0.757502i	0.218365	+	0.975867i	$0.429928\pi$
$948$		0			0
$949$		−	20.4526i		−	0.663919i
$950$		0			0
$951$	10.1395			0.328795
$952$		0			0
$953$	33.1105	−	33.1105i	1.07255	−	1.07255i	0.0754003	−	0.997153i	$-0.475977\pi$
$953$	33.1105	−	33.1105i	1.07255	−	1.07255i	0.997153	−	0.0754003i	$-0.0240235\pi$
$954$		0			0
$955$	−4.06739	+	29.9541i	−0.131618	+	0.969293i
$956$		0			0
$957$	45.3126	−	37.0992i	1.46475	−	1.19925i
$958$		0			0
$959$	−32.0914			−1.03628
$960$		0			0
$961$	−10.0175			−0.323146
$962$		0			0
$963$	−28.7033	+	28.7033i	−0.924950	+	0.924950i
$964$		0			0
$965$	−32.5476	−	42.7756i	−1.04775	−	1.37699i
$966$		0			0
$967$	15.4800	+	15.4800i	0.497803	+	0.497803i	0.910754	−	0.412950i	$-0.135502\pi$
$967$	15.4800	+	15.4800i	0.497803	+	0.497803i	−0.412950	+	0.910754i	$0.635502\pi$
$968$		0			0
$969$			6.33368i			0.203467i
$970$		0			0
$971$	49.5123			1.58892			0.794462	−	0.607313i	$-0.207753\pi$
$971$	49.5123			1.58892			0.794462	+	0.607313i	$0.207753\pi$
$972$		0			0
$973$	19.1339	+	19.1339i	0.613406	+	0.613406i
$974$		0			0
$975$	15.1834	+	4.20087i	0.486257	+	0.134536i
$976$		0			0
$977$	−23.4655	+	23.4655i	−0.750727	+	0.750727i	−0.974615	−	0.223888i	$-0.928125\pi$
$977$	−23.4655	+	23.4655i	−0.750727	+	0.750727i	0.223888	+	0.974615i	$0.428125\pi$
$978$		0			0
$979$	1.68507	+	0.167940i	0.0538549	+	0.00536737i
$980$		0			0
$981$			10.3932i			0.331828i
$982$		0			0
$983$	−36.6594	−	36.6594i	−1.16925	−	1.16925i	−0.982385	−	0.186869i	$-0.940166\pi$
$983$	−36.6594	−	36.6594i	−1.16925	−	1.16925i	−0.186869	−	0.982385i	$-0.559834\pi$
$984$		0			0
$985$	−19.6234	+	14.9313i	−0.625254	+	0.475752i
$986$		0			0
$987$	−40.8554	−	40.8554i	−1.30044	−	1.30044i
$988$		0			0
$989$	−35.2823			−1.12191
$990$		0			0
$991$	−15.1739			−0.482014			−0.241007	−	0.970523i	$-0.577478\pi$
$991$	−15.1739			−0.482014			−0.241007	+	0.970523i	$0.577478\pi$
$992$		0			0
$993$	−42.3389	−	42.3389i	−1.34359	−	1.34359i
$994$		0			0
$995$	41.5453	+	5.64132i	1.31707	+	0.178842i
$996$		0			0
$997$	1.83464	+	1.83464i	0.0581037	+	0.0581037i	0.735562	−	0.677458i	$-0.236918\pi$
$997$	1.83464	+	1.83464i	0.0581037	+	0.0581037i	−0.677458	+	0.735562i	$0.736918\pi$
$998$		0			0
$999$		−	5.07264i		−	0.160491i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	880.2.bd.i.593.3		32
4.3	odd	2		440.2.v.b.153.14	yes	32
5.2	odd	4	inner	880.2.bd.i.417.4		32
11.10	odd	2	inner	880.2.bd.i.593.4		32
20.7	even	4		440.2.v.b.417.13	yes	32
44.43	even	2		440.2.v.b.153.13	✓	32
55.32	even	4	inner	880.2.bd.i.417.3		32
220.87	odd	4		440.2.v.b.417.14	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
440.2.v.b.153.13	✓	32	44.43	even	2
440.2.v.b.153.14	yes	32	4.3	odd	2
440.2.v.b.417.13	yes	32	20.7	even	4
440.2.v.b.417.14	yes	32	220.87	odd	4
880.2.bd.i.417.3		32	55.32	even	4	inner
880.2.bd.i.417.4		32	5.2	odd	4	inner
880.2.bd.i.593.3		32	1.1	even	1	trivial
880.2.bd.i.593.4		32	11.10	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:	\( N \)	\(=\)	\( 880 = 2^{4} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	880.bd (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.78145 - 1.78145i) q^{3} +(-0.300869 + 2.21573i) q^{5} +(-1.52953 - 1.52953i) q^{7} +3.34712i q^{9} +(-0.328917 + 3.30027i) q^{11} +(0.884324 - 0.884324i) q^{13} +(4.48320 - 3.41123i) q^{15} +(-0.303994 - 0.303994i) q^{17} +5.84773 q^{19} +5.44955i q^{21} +(-2.07794 - 2.07794i) q^{23} +(-4.81896 - 1.33329i) q^{25} +(0.618370 - 0.618370i) q^{27} +7.00868 q^{29} +4.58066 q^{31} +(6.46522 - 5.29332i) q^{33} +(3.84921 - 2.92884i) q^{35} +(4.10163 - 4.10163i) q^{37} -3.15076 q^{39} -2.46834i q^{41} +(8.48972 - 8.48972i) q^{43} +(-7.41632 - 1.00704i) q^{45} +(-7.49702 + 7.49702i) q^{47} -2.32109i q^{49} +1.08310i q^{51} +(4.04743 + 4.04743i) q^{53} +(-7.21357 - 1.72174i) q^{55} +(-10.4174 - 10.4174i) q^{57} -8.07502i q^{59} -2.60774i q^{61} +(5.11951 - 5.11951i) q^{63} +(1.69336 + 2.22549i) q^{65} +(-1.98917 + 1.98917i) q^{67} +7.40350i q^{69} -6.78733 q^{71} +(11.5640 - 11.5640i) q^{73} +(6.20953 + 10.9599i) q^{75} +(5.55095 - 4.54477i) q^{77} +7.60905 q^{79} +7.83816 q^{81} +(8.18822 - 8.18822i) q^{83} +(0.765033 - 0.582108i) q^{85} +(-12.4856 - 12.4856i) q^{87} -0.510584i q^{89} -2.70520 q^{91} +(-8.16021 - 8.16021i) q^{93} +(-1.75940 + 12.9570i) q^{95} +(1.60712 - 1.60712i) q^{97} +(-11.0464 - 1.10092i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 4 q^{3} + 8 q^{5} + 8 q^{11} - 24 q^{15} + 28 q^{23} + 4 q^{25} + 4 q^{27} - 24 q^{31} - 12 q^{33} + 4 q^{37} - 28 q^{45} - 8 q^{47} + 24 q^{53} - 12 q^{55} + 52 q^{67} - 48 q^{71} + 24 q^{75} + 56 q^{77}+ \cdots - 36 q^{97}+O(q^{100}) \) 32 * q + 4 * q^3 + 8 * q^5 + 8 * q^11 - 24 * q^15 + 28 * q^23 + 4 * q^25 + 4 * q^27 - 24 * q^31 - 12 * q^33 + 4 * q^37 - 28 * q^45 - 8 * q^47 + 24 * q^53 - 12 * q^55 + 52 * q^67 - 48 * q^71 + 24 * q^75 + 56 * q^77 - 24 * q^81 + 16 * q^91 - 76 * q^93 - 36 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more