LMFDB - Embedded newform 675.2.ba.c.443.15

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [675,2,Mod(32,675)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(675, base_ring=CyclotomicField(36)) chi = DirichletCharacter(H, H._module([10, 9])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("675.32"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 675 = 3^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	675.ba (of order $36$, degree $12$, minimal)

Newform invariants

comment:select newform

sage:traces = [288] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$5.38990213644$
Analytic rank:	$0$
Dimension:	$288$
Relative dimension:	$24$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			443.15
Character	$\chi$	$=$	675.443
Dual form			675.2.ba.c.32.15

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.0632765 + 0.723253i) q^{2} +(1.46710 + 0.920668i) q^{3} +(1.45052 - 0.255767i) q^{4} +(-0.573043 + 1.11934i) q^{6} +(2.68947 + 3.84096i) q^{7} +(0.652582 + 2.43547i) q^{8} +(1.30474 + 2.70142i) q^{9} +(-0.808938 - 2.22254i) q^{11} +(2.36353 + 0.960217i) q^{12} +(-1.61947 - 0.141685i) q^{13} +(-2.60780 + 2.18821i) q^{14} +(1.04798 - 0.381434i) q^{16} +(1.54346 - 5.76028i) q^{17} +(-1.87125 + 1.11459i) q^{18} +(-5.87988 - 3.39475i) q^{19} +(0.409461 + 8.11116i) q^{21} +(1.55627 - 0.725702i) q^{22} +(-6.23184 - 4.36358i) q^{23} +(-1.28486 + 4.17388i) q^{24} -1.18025i q^{26} +(-0.572926 + 5.16447i) q^{27} +(4.88352 + 4.88352i) q^{28} +(-5.33663 - 4.47797i) q^{29} +(-0.379220 - 2.15066i) q^{31} +(2.47335 + 5.30412i) q^{32} +(0.859430 - 4.00544i) q^{33} +(4.26381 + 0.751824i) q^{34} +(2.58349 + 3.58476i) q^{36} +(4.82802 + 1.29366i) q^{37} +(2.08321 - 4.46745i) q^{38} +(-2.24547 - 1.69886i) q^{39} +(3.01626 + 3.59464i) q^{41} +(-5.84051 + 0.809389i) q^{42} +(2.94459 + 1.37309i) q^{43} +(-1.74184 - 3.01695i) q^{44} +(2.76165 - 4.78331i) q^{46} +(8.00447 - 5.60479i) q^{47} +(1.88866 + 0.405242i) q^{48} +(-5.12557 + 14.0824i) q^{49} +(7.56772 - 7.02987i) q^{51} +(-2.38532 + 0.208688i) q^{52} +(-1.85094 + 1.85094i) q^{53} +(-3.77147 - 0.0875810i) q^{54} +(-7.59943 + 9.05665i) q^{56} +(-5.50091 - 10.3938i) q^{57} +(2.90102 - 4.14309i) q^{58} +(4.22316 + 1.53710i) q^{59} +(0.391593 - 2.22083i) q^{61} +(1.53148 - 0.410358i) q^{62} +(-6.86696 + 12.2768i) q^{63} +(-1.74806 + 1.00925i) q^{64} +(2.95133 + 0.368136i) q^{66} +(-0.696469 + 7.96068i) q^{67} +(0.765543 - 8.75020i) q^{68} +(-5.12530 - 12.1393i) q^{69} +(-0.899200 + 0.519153i) q^{71} +(-5.72776 + 4.94055i) q^{72} +(-3.70095 + 0.991667i) q^{73} +(-0.630146 + 3.57374i) q^{74} +(-9.39718 - 3.42029i) q^{76} +(6.36106 - 9.08454i) q^{77} +(1.08662 - 1.73154i) q^{78} +(4.12821 - 4.91981i) q^{79} +(-5.59530 + 7.04930i) q^{81} +(-2.40897 + 2.40897i) q^{82} +(0.731354 - 0.0639852i) q^{83} +(2.66850 + 11.6607i) q^{84} +(-0.806766 + 2.21657i) q^{86} +(-3.70663 - 11.4829i) q^{87} +(4.88502 - 3.42053i) q^{88} +(0.0118115 - 0.0204581i) q^{89} +(-3.81130 - 6.60136i) q^{91} +(-10.1555 - 4.73559i) q^{92} +(1.42369 - 3.50436i) q^{93} +(4.56018 + 5.43461i) q^{94} +(-1.25469 + 10.0588i) q^{96} +(-1.30593 + 2.80057i) q^{97} +(-10.5095 - 2.81600i) q^{98} +(4.94855 - 5.08512i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 288 q + 24 q^{6} + 36 q^{11} + 48 q^{21} - 192 q^{36} - 180 q^{41} - 60 q^{51} - 288 q^{56} + 72 q^{61} + 144 q^{71} + 216 q^{76} + 24 q^{81} - 36 q^{91} - 168 q^{96}+O(q^{100}) $ 288 * q + 24 * q^6 + 36 * q^11 + 48 * q^21 - 192 * q^36 - 180 * q^41 - 60 * q^51 - 288 * q^56 + 72 * q^61 + 144 * q^71 + 216 * q^76 + 24 * q^81 - 36 * q^91 - 168 * q^96

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/675\mathbb{Z}\right)^\times$.

$n$	$326$	$352$
$\chi(n)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	0.0632765	+	0.723253i	0.0447432	+	0.511417i	0.985189	+	0.171473i	$0.0548526\pi$
$2$	0.0632765	+	0.723253i	0.0447432	+	0.511417i	−0.940446	+	0.339944i	$0.889592\pi$
$3$	1.46710	+	0.920668i	0.847028	+	0.531548i
$3$	1.46710	+	0.920668i	0.847028	+	0.531548i
$4$	1.45052	−	0.255767i	0.725262	−	0.127883i
$5$		0			0
$5$		0			0
$6$	−0.573043	+	1.11934i	−0.233944	+	0.456968i
$7$	2.68947	+	3.84096i	1.01652	+	1.45175i	0.887892	+	0.460053i	$0.152169\pi$
$7$	2.68947	+	3.84096i	1.01652	+	1.45175i	0.128631	+	0.991693i	$0.458942\pi$
$8$	0.652582	+	2.43547i	0.230722	+	0.861068i
$9$	1.30474	+	2.70142i	0.434914	+	0.900472i
$10$		0			0
$11$	−0.808938	−	2.22254i	−0.243904	−	0.670121i	−0.999880	−	0.0155209i	$-0.995059\pi$
$11$	−0.808938	−	2.22254i	−0.243904	−	0.670121i	0.755976	−	0.654600i	$-0.227163\pi$
$12$	2.36353	+	0.960217i	0.682294	+	0.277191i
$13$	−1.61947	−	0.141685i	−0.449160	−	0.0392964i	−0.139668	−	0.990198i	$-0.544603\pi$
$13$	−1.61947	−	0.141685i	−0.449160	−	0.0392964i	−0.309492	+	0.950902i	$0.600159\pi$
$14$	−2.60780	+	2.18821i	−0.696965	+	0.584823i
$15$		0			0
$16$	1.04798	−	0.381434i	0.261995	−	0.0953585i
$17$	1.54346	−	5.76028i	0.374345	−	1.39707i	−0.479955	−	0.877293i	$-0.659347\pi$
$17$	1.54346	−	5.76028i	0.374345	−	1.39707i	0.854300	−	0.519781i	$-0.173986\pi$
$18$	−1.87125	+	1.11459i	−0.441058	+	0.262712i
$19$	−5.87988	−	3.39475i	−1.34894	−	0.778810i	−0.360839	−	0.932628i	$-0.617510\pi$
$19$	−5.87988	−	3.39475i	−1.34894	−	0.778810i	−0.988099	+	0.153819i	$0.950843\pi$
$20$		0			0
$21$	0.409461	+	8.11116i	0.0893517	+	1.77000i
$22$	1.55627	−	0.725702i	0.331798	−	0.154720i
$23$	−6.23184	−	4.36358i	−1.29943	−	0.909870i	−0.300395	−	0.953815i	$-0.597119\pi$
$23$	−6.23184	−	4.36358i	−1.29943	−	0.909870i	−0.999034	+	0.0439446i	$0.986007\pi$
$24$	−1.28486	+	4.17388i	−0.262270	+	0.851989i
$25$		0			0
$26$		−	1.18025i		−	0.231466i
$27$	−0.572926	+	5.16447i	−0.110260	+	0.993903i
$28$	4.88352	+	4.88352i	0.922899	+	0.922899i
$29$	−5.33663	−	4.47797i	−0.990988	−	0.831538i	−0.00527757	−	0.999986i	$-0.501680\pi$
$29$	−5.33663	−	4.47797i	−0.990988	−	0.831538i	−0.985710	+	0.168448i	$0.946124\pi$
$30$		0			0
$31$	−0.379220	−	2.15066i	−0.0681099	−	0.386270i	−0.999739	−	0.0228591i	$-0.992723\pi$
$31$	−0.379220	−	2.15066i	−0.0681099	−	0.386270i	0.931629	−	0.363411i	$-0.118388\pi$
$32$	2.47335	+	5.30412i	0.437231	+	0.937644i
$33$	0.859430	−	4.00544i	0.149608	−	0.697258i
$34$	4.26381	+	0.751824i	0.731237	+	0.128937i
$35$		0			0
$36$	2.58349	+	3.58476i	0.430582	+	0.597460i
$37$	4.82802	+	1.29366i	0.793721	+	0.212677i	0.632825	−	0.774294i	$-0.281895\pi$
$37$	4.82802	+	1.29366i	0.793721	+	0.212677i	0.160896	+	0.986971i	$0.448562\pi$
$38$	2.08321	−	4.46745i	0.337941	−	0.724717i
$39$	−2.24547	−	1.69886i	−0.359563	−	0.272035i
$40$		0			0
$41$	3.01626	+	3.59464i	0.471060	+	0.561388i	0.948296	−	0.317388i	$-0.102806\pi$
$41$	3.01626	+	3.59464i	0.471060	+	0.561388i	−0.477236	+	0.878775i	$0.658361\pi$
$42$	−5.84051	+	0.809389i	−0.901211	+	0.124891i
$43$	2.94459	+	1.37309i	0.449047	+	0.209394i	0.633968	−	0.773360i	$-0.281425\pi$
$43$	2.94459	+	1.37309i	0.449047	+	0.209394i	−0.184921	+	0.982753i	$0.559203\pi$
$44$	−1.74184	−	3.01695i	−0.262592	−	0.454822i
$45$		0			0
$46$	2.76165	−	4.78331i	0.407183	−	0.705261i
$47$	8.00447	−	5.60479i	1.16757	−	0.817543i	0.181423	−	0.983405i	$-0.441930\pi$
$47$	8.00447	−	5.60479i	1.16757	−	0.817543i	0.986149	+	0.165862i	$0.0530407\pi$
$48$	1.88866	+	0.405242i	0.272605	+	0.0584917i
$49$	−5.12557	+	14.0824i	−0.732225	+	2.01177i
$50$		0			0
$51$	7.56772	−	7.02987i	1.05969	−	0.984379i
$52$	−2.38532	+	0.208688i	−0.330784	+	0.0289398i
$53$	−1.85094	+	1.85094i	−0.254246	+	0.254246i	−0.822709	−	0.568463i	$-0.807538\pi$
$53$	−1.85094	+	1.85094i	−0.254246	+	0.254246i	0.568463	+	0.822709i	$0.307538\pi$
$54$	−3.77147	−	0.0875810i	−0.513232	−	0.0119183i
$55$		0			0
$56$	−7.59943	+	9.05665i	−1.01552	+	1.21025i
$57$	−5.50091	−	10.3938i	−0.728614	−	1.37670i
$58$	2.90102	−	4.14309i	0.380923	−	0.544014i
$59$	4.22316	+	1.53710i	0.549808	+	0.200114i	0.601961	−	0.798525i	$-0.294386\pi$
$59$	4.22316	+	1.53710i	0.549808	+	0.200114i	−0.0521532	+	0.998639i	$0.516608\pi$
$60$		0			0
$61$	0.391593	−	2.22083i	0.0501383	−	0.284348i	−0.949422	−	0.314003i	$-0.898330\pi$
$61$	0.391593	−	2.22083i	0.0501383	−	0.284348i	0.999560	+	0.0296548i	$0.00944081\pi$
$62$	1.53148	−	0.410358i	0.194498	−	0.0521156i
$63$	−6.86696	+	12.2768i	−0.865156	+	1.54673i
$64$	−1.74806	+	1.00925i	−0.218508	+	0.126156i
$65$		0			0
$66$	2.95133	+	0.368136i	0.363284	+	0.0453144i
$67$	−0.696469	+	7.96068i	−0.0850873	+	0.972552i	0.826904	+	0.562343i	$0.190100\pi$
$67$	−0.696469	+	7.96068i	−0.0850873	+	0.972552i	−0.911992	+	0.410209i	$0.865456\pi$
$68$	0.765543	−	8.75020i	0.0928357	−	1.06112i
$69$	−5.12530	−	12.1393i	−0.617014	−	1.46139i
$70$		0			0
$71$	−0.899200	+	0.519153i	−0.106715	+	0.0616121i	−0.552408	−	0.833574i	$-0.686291\pi$
$71$	−0.899200	+	0.519153i	−0.106715	+	0.0616121i	0.445692	+	0.895186i	$0.352958\pi$
$72$	−5.72776	+	4.94055i	−0.675023	+	0.582249i
$73$	−3.70095	+	0.991667i	−0.433163	+	0.116066i	−0.468811	−	0.883299i	$-0.655317\pi$
$73$	−3.70095	+	0.991667i	−0.433163	+	0.116066i	0.0356473	+	0.999364i	$0.488651\pi$
$74$	−0.630146	+	3.57374i	−0.0732530	+	0.415439i
$75$		0			0
$76$	−9.39718	−	3.42029i	−1.07793	−	0.392334i
$77$	6.36106	−	9.08454i	0.724911	−	1.03528i
$78$	1.08662	−	1.73154i	0.123035	−	0.196058i
$79$	4.12821	−	4.91981i	0.464460	−	0.553522i	−0.482072	−	0.876132i	$-0.660116\pi$
$79$	4.12821	−	4.91981i	0.464460	−	0.553522i	0.946532	+	0.322610i	$0.104560\pi$
$80$		0			0
$81$	−5.59530	+	7.04930i	−0.621700	+	0.783256i
$82$	−2.40897	+	2.40897i	−0.266027	+	0.266027i
$83$	0.731354	−	0.0639852i	0.0802766	−	0.00702329i	−0.0469467	−	0.998897i	$-0.514949\pi$
$83$	0.731354	−	0.0639852i	0.0802766	−	0.00702329i	0.127223	+	0.991874i	$0.459394\pi$
$84$	2.66850	+	11.6607i	0.291157	+	1.27229i
$85$		0			0
$86$	−0.806766	+	2.21657i	−0.0869958	+	0.239019i
$87$	−3.70663	−	11.4829i	−0.397393	−	1.23109i
$88$	4.88502	−	3.42053i	0.520745	−	0.364630i
$89$	0.0118115	−	0.0204581i	0.00125201	−	0.00216855i	−0.865399	−	0.501084i	$-0.832935\pi$
$89$	0.0118115	−	0.0204581i	0.00125201	−	0.00216855i	0.866651	+	0.498915i	$0.166268\pi$
$90$		0			0
$91$	−3.81130	−	6.60136i	−0.399533	−	0.692011i
$92$	−10.1555	−	4.73559i	−1.05878	−	0.493719i
$93$	1.42369	−	3.50436i	0.147630	−	0.363386i
$94$	4.56018	+	5.43461i	0.470346	+	0.560537i
$95$		0			0
$96$	−1.25469	+	10.0588i	−0.128056	+	1.02662i
$97$	−1.30593	+	2.80057i	−0.132597	+	0.284355i	−0.961385	−	0.275208i	$-0.911253\pi$
$97$	−1.30593	+	2.80057i	−0.132597	+	0.284355i	0.828788	+	0.559563i	$0.189031\pi$
$98$	−10.5095	−	2.81600i	−1.06162	−	0.284459i
$99$	4.94855	−	5.08512i	0.497348	−	0.511074i
$100$		0			0
$101$	−7.06992	−	1.24662i	−0.703484	−	0.124043i	−0.189547	−	0.981872i	$-0.560702\pi$
$101$	−7.06992	−	1.24662i	−0.703484	−	0.124043i	−0.513936	+	0.857828i	$0.671813\pi$
$102$	5.56324	+	5.02855i	0.550842	+	0.497901i
$103$	5.43656	+	11.6587i	0.535680	+	1.14877i	0.968893	+	0.247478i	$0.0796019\pi$
$103$	5.43656	+	11.6587i	0.535680	+	1.14877i	−0.433213	+	0.901291i	$0.642620\pi$
$104$	−0.711765	−	4.03662i	−0.0697943	−	0.395823i
$105$		0			0
$106$	−1.45582	−	1.22158i	−0.141401	−	0.118650i
$107$	−1.53529	−	1.53529i	−0.148422	−	0.148422i	0.628991	−	0.777413i	$-0.283468\pi$
$107$	−1.53529	−	1.53529i	−0.148422	−	0.148422i	−0.777413	+	0.628991i	$0.783468\pi$
$108$	0.489856	+	7.63772i	0.0471364	+	0.734940i
$109$		−	8.51427i		−	0.815519i	−0.913089	−	0.407760i	$-0.866310\pi$
$109$		−	8.51427i		−	0.815519i	0.913089	−	0.407760i	$-0.133690\pi$
$110$		0			0
$111$	5.89213	+	6.34293i	0.559256	+	0.602044i
$112$	4.28358	+	2.99940i	0.404761	+	0.283416i
$113$	−15.2119	+	7.09341i	−1.43101	+	0.667292i	−0.974902	−	0.222632i	$-0.928535\pi$
$113$	−15.2119	+	7.09341i	−1.43101	+	0.667292i	−0.456109	+	0.889924i	$0.650757\pi$
$114$	7.16931	−	4.63624i	0.671467	−	0.434224i
$115$		0			0
$116$	−8.88623	−	5.13047i	−0.825066	−	0.476352i
$117$	−1.73024	−	4.55972i	−0.159960	−	0.421546i
$118$	−0.844488	+	3.15167i	−0.0777415	+	0.290135i
$119$	26.2761	−	9.56371i	2.40873	−	0.876704i
$120$		0			0
$121$	4.14119	−	3.47487i	0.376472	−	0.315897i
$122$	1.63100	+	0.142694i	0.147664	+	0.0129189i
$123$	1.11567	+	8.05065i	0.100597	+	0.725902i
$124$	−1.10014	−	3.02260i	−0.0987951	−	0.271437i
$125$		0			0
$126$	−9.31377	−	4.18972i	−0.829737	−	0.373250i
$127$	1.01322	+	3.78140i	0.0899090	+	0.335545i	0.996198	−	0.0871125i	$-0.0277640\pi$
$127$	1.01322	+	3.78140i	0.0899090	+	0.335545i	−0.906289	+	0.422658i	$0.861097\pi$
$128$	5.87310	+	8.38765i	0.519113	+	0.741371i
$129$	3.05585	+	4.72544i	0.269052	+	0.416052i
$130$		0			0
$131$	1.77050	−	0.312187i	0.154689	−	0.0272759i	−0.0957672	−	0.995404i	$-0.530530\pi$
$131$	1.77050	−	0.312187i	0.154689	−	0.0272759i	0.250456	+	0.968128i	$0.419419\pi$
$132$	0.222167	−	6.02980i	0.0193371	−	0.524827i
$133$	−2.77465	−	31.7145i	−0.240593	−	2.74999i
$134$	−5.80166			−0.501187
$135$		0			0
$136$	15.0362			1.28935
$137$	1.55119	+	17.7302i	0.132527	+	1.51479i	0.713376	+	0.700781i	$0.247165\pi$
$137$	1.55119	+	17.7302i	0.132527	+	1.51479i	−0.580849	+	0.814011i	$0.697279\pi$
$138$	8.45544	−	4.47502i	0.719775	−	0.380939i
$139$	10.7147	−	1.88930i	0.908812	−	0.160248i	0.300348	−	0.953830i	$-0.402897\pi$
$139$	10.7147	−	1.88930i	0.908812	−	0.160248i	0.608464	+	0.793581i	$0.291786\pi$
$140$		0			0
$141$	16.9035	−	0.853308i	1.42353	−	0.0718615i
$142$	−0.432377	−	0.617499i	−0.0362843	−	0.0518194i
$143$	0.995148	+	3.71394i	0.0832185	+	0.310576i
$144$	2.39776	+	2.33336i	0.199813	+	0.194447i
$145$		0			0
$146$	−0.951409	−	2.61398i	−0.0787392	−	0.216334i
$147$	−20.4849	+	15.9413i	−1.68957	+	1.31481i
$148$	7.33403	+	0.641645i	0.602854	+	0.0527429i
$149$	2.11066	−	1.77106i	0.172912	−	0.145091i	−0.552225	−	0.833695i	$-0.686221\pi$
$149$	2.11066	−	1.77106i	0.172912	−	0.145091i	0.725137	+	0.688605i	$0.241776\pi$
$150$		0			0
$151$	11.9995	−	4.36746i	0.976505	−	0.355419i	0.196025	−	0.980599i	$-0.437197\pi$
$151$	11.9995	−	4.36746i	0.976505	−	0.355419i	0.780480	+	0.625180i	$0.214975\pi$
$152$	4.43071	−	16.5356i	0.359378	−	1.34122i
$153$	17.5747	−	3.34614i	1.42083	−	0.270520i
$154$	6.97293	+	4.02582i	0.561895	+	0.324410i
$155$		0			0
$156$	−3.69162	−	1.88992i	−0.295566	−	0.151315i
$157$	−8.54167	+	3.98305i	−0.681700	+	0.317882i	−0.732441	−	0.680830i	$-0.761619\pi$
$157$	−8.54167	+	3.98305i	−0.681700	+	0.317882i	0.0507417	+	0.998712i	$0.483841\pi$
$158$	3.81949	+	2.67443i	0.303862	+	0.212767i
$159$	−4.41960	+	1.01140i	−0.350497	+	0.0802095i
$160$		0			0
$161$		−	35.6720i		−	2.81134i
$162$	−5.45248	−	3.60076i	−0.428387	−	0.282903i
$163$	−14.5355	−	14.5355i	−1.13851	−	1.13851i	−0.988718	−	0.149787i	$-0.952141\pi$
$163$	−14.5355	−	14.5355i	−1.13851	−	1.13851i	−0.149787	−	0.988718i	$-0.547859\pi$
$164$	5.29454	+	4.44265i	0.413434	+	0.346913i
$165$		0			0
$166$	0.0925550	+	0.524906i	0.00718366	+	0.0407406i
$167$	−4.53222	−	9.71939i	−0.350714	−	0.752109i	0.649250	−	0.760575i	$-0.275083\pi$
$167$	−4.53222	−	9.71939i	−0.350714	−	0.752109i	−0.999964	+	0.00846620i	$0.997305\pi$
$168$	−19.4873	+	6.29042i	−1.50347	+	0.485316i
$169$	−10.1999	−	1.79852i	−0.784608	−	0.138348i
$170$		0			0
$171$	1.49891	−	20.3133i	0.114625	−	1.55340i
$172$	4.62240	+	1.23857i	0.352454	+	0.0944399i
$173$	−5.26315	+	11.2869i	−0.400150	+	0.858125i	0.598235	+	0.801321i	$0.295869\pi$
$173$	−5.26315	+	11.2869i	−0.400150	+	0.858125i	−0.998385	+	0.0568042i	$0.981909\pi$
$174$	8.07048	−	3.40743i	0.611822	−	0.258317i
$175$		0			0
$176$	−1.69550	−	2.02062i	−0.127803	−	0.152310i
$177$	4.78061	+	6.14320i	0.359333	+	0.461751i
$178$	0.0155437	+	0.00724817i	0.00116505	+	0.000543273i
$179$	−1.92319	−	3.33107i	−0.143746	−	0.248976i	0.785158	−	0.619295i	$-0.212582\pi$
$179$	−1.92319	−	3.33107i	−0.143746	−	0.248976i	−0.928904	+	0.370319i	$0.879248\pi$
$180$		0			0
$181$	7.10764	−	12.3108i	0.528307	−	0.915054i	−0.471149	−	0.882054i	$-0.656161\pi$
$181$	7.10764	−	12.3108i	0.528307	−	0.915054i	0.999455	−	0.0330001i	$-0.0105062\pi$
$182$	4.53329	−	3.17424i	0.336030	−	0.235291i
$183$	2.61915	−	2.89765i	0.193613	−	0.214200i
$184$	6.56058	−	18.0250i	0.483652	−	1.32882i
$185$		0			0
$186$	2.62463	+	0.807948i	0.192447	+	0.0592416i
$187$	−14.0510	+	1.22931i	−1.02751	+	0.0898957i
$188$	10.1772	−	10.1772i	0.742246	−	0.742246i
$189$	−21.3774	+	11.6891i	−1.55497	+	0.850256i
$190$		0			0
$191$	−16.4099	+	19.5565i	−1.18738	+	1.41506i	−0.300046	+	0.953925i	$0.597002\pi$
$191$	−16.4099	+	19.5565i	−1.18738	+	1.41506i	−0.887330	+	0.461135i	$0.847443\pi$
$192$	−3.49376	−	0.128727i	−0.252140	−	0.00929004i
$193$	−3.79769	+	5.42367i	−0.273364	+	0.390404i	−0.932236	−	0.361851i	$-0.882145\pi$
$193$	−3.79769	+	5.42367i	−0.273364	+	0.390404i	0.658872	+	0.752255i	$0.271034\pi$
$194$	−2.10816	−	0.767306i	−0.151357	−	0.0550894i
$195$		0			0
$196$	−3.83296	+	21.7378i	−0.273783	+	1.55270i
$197$	−19.1258	+	5.12475i	−1.36266	+	0.365123i	−0.864792	−	0.502131i	$-0.832550\pi$
$197$	−19.1258	+	5.12475i	−1.36266	+	0.365123i	−0.497866	+	0.867254i	$0.665883\pi$
$198$	3.99095	+	3.25729i	0.283625	+	0.231485i
$199$	1.14239	−	0.659562i	0.0809822	−	0.0467551i	−0.458962	−	0.888456i	$-0.651779\pi$
$199$	1.14239	−	0.659562i	0.0809822	−	0.0467551i	0.539944	+	0.841701i	$0.318445\pi$
$200$		0			0
$201$	−8.35093	+	11.0379i	−0.589029	+	0.778551i
$202$	0.454261	−	5.19223i	0.0319617	−	0.365324i
$203$	2.84698	−	32.5411i	0.199819	−	2.28394i
$204$	9.17915	−	12.1326i	0.642669	−	0.849450i
$205$		0			0
$206$	−8.08822	+	4.66973i	−0.563533	+	0.325356i
$207$	3.65691	−	22.5282i	0.254173	−	1.56581i
$208$	−1.75122	+	0.469237i	−0.121425	+	0.0325357i
$209$	−2.78851	+	15.8144i	−0.192885	+	1.09391i
$210$		0			0
$211$	−10.2026	−	3.71343i	−0.702374	−	0.255643i	−0.0339496	−	0.999424i	$-0.510809\pi$
$211$	−10.2026	−	3.71343i	−0.702374	−	0.255643i	−0.668424	+	0.743780i	$0.733031\pi$
$212$	−2.21142	+	3.15824i	−0.151881	+	0.216909i
$213$	−1.79718	−	0.0662166i	−0.123141	−	0.00453709i
$214$	1.01326	−	1.20755i	0.0692647	−	0.0825465i
$215$		0			0
$216$	−12.9518	+	1.97490i	−0.881257	+	0.134375i
$217$	7.24070	−	7.24070i	0.491531	−	0.491531i
$218$	6.15797	−	0.538753i	0.417071	−	0.0364890i
$219$	−6.34264	−	1.95248i	−0.428596	−	0.131936i
$220$		0			0
$221$	−3.31573	+	9.10991i	−0.223040	+	0.612799i
$222$	−4.21471	+	4.66286i	−0.282873	+	0.312951i
$223$	18.7870	−	13.1548i	1.25807	−	0.880911i	0.261627	−	0.965169i	$-0.415741\pi$
$223$	18.7870	−	13.1548i	1.25807	−	0.880911i	0.996444	+	0.0842578i	$0.0268519\pi$
$224$	−13.7209	+	23.7653i	−0.916765	+	1.58788i
$225$		0			0
$226$	−6.09288	−	10.5532i	−0.405292	−	0.701987i
$227$	9.72553	+	4.53509i	0.645506	+	0.301005i	0.717665	−	0.696389i	$-0.245211\pi$
$227$	9.72553	+	4.53509i	0.645506	+	0.301005i	−0.0721585	+	0.997393i	$0.522989\pi$
$228$	−10.6376	−	13.6696i	−0.704493	−	0.905290i
$229$	7.42656	+	8.85063i	0.490761	+	0.584866i	0.953411	−	0.301675i	$-0.0975458\pi$
$229$	7.42656	+	8.85063i	0.490761	+	0.584866i	−0.462650	+	0.886541i	$0.653101\pi$
$230$		0			0
$231$	17.6961	−	7.47147i	1.16432	−	0.491586i
$232$	7.42336	−	15.9194i	0.487367	−	1.04516i
$233$	7.20963	+	1.93182i	0.472319	+	0.126557i	0.487124	−	0.873333i	$-0.338046\pi$
$233$	7.20963	+	1.93182i	0.472319	+	0.126557i	−0.0148049	+	0.999890i	$0.504713\pi$
$234$	3.18835	−	1.53992i	0.208429	−	0.100668i
$235$		0			0
$236$	6.51893	+	1.14946i	0.424346	+	0.0748237i
$237$	10.5860	−	3.41712i	0.687634	−	0.221966i
$238$	8.57965	+	18.3991i	0.556136	+	1.19264i
$239$	−5.16690	−	29.3030i	−0.334219	−	1.89545i	−0.434809	−	0.900523i	$-0.643184\pi$
$239$	−5.16690	−	29.3030i	−0.334219	−	1.89545i	0.100590	−	0.994928i	$-0.467927\pi$
$240$		0			0
$241$	13.1119	+	11.0022i	0.844614	+	0.708715i	0.958597	−	0.284768i	$-0.0919165\pi$
$241$	13.1119	+	11.0022i	0.844614	+	0.708715i	−0.113983	+	0.993483i	$0.536361\pi$
$242$	2.77525	+	2.77525i	0.178400	+	0.178400i
$243$	−14.6989	+	5.19059i	−0.942935	+	0.332976i
$244$		−	3.32153i		−	0.212639i
$245$		0			0
$246$	−5.75206	+	1.31633i	−0.366738	+	0.0839262i
$247$	9.04130	+	6.33078i	0.575284	+	0.402818i
$248$	4.99040	−	2.32706i	0.316891	−	0.147768i
$249$	1.13188	+	0.579462i	0.0717297	+	0.0367219i
$250$		0			0
$251$	8.52101	+	4.91961i	0.537841	+	0.310523i	0.744204	−	0.667953i	$-0.232829\pi$
$251$	8.52101	+	4.91961i	0.537841	+	0.310523i	−0.206362	+	0.978476i	$0.566163\pi$
$252$	−6.82069	+	19.5642i	−0.429663	+	1.23243i
$253$	−4.65706	+	17.3804i	−0.292787	+	1.09270i
$254$	−2.67080	+	0.972091i	−0.167581	+	0.0609944i
$255$		0			0
$256$	−8.78727	+	7.37340i	−0.549205	+	0.460837i
$257$	−0.0761136	−	0.00665907i	−0.00474783	−	0.000415382i	0.0847816	−	0.996400i	$-0.472981\pi$
$257$	−0.0761136	−	0.00665907i	−0.00474783	−	0.000415382i	−0.0895294	+	0.995984i	$0.528536\pi$
$258$	−3.22433	+	2.50916i	−0.200738	+	0.156213i
$259$	8.01589	+	22.0235i	0.498083	+	1.36847i
$260$		0			0
$261$	5.13393	−	20.2591i	0.317782	−	1.25400i
$262$	0.337821	+	1.26076i	0.0208706	+	0.0778903i
$263$	7.71569	+	11.0192i	0.475770	+	0.679470i	0.983264	−	0.182185i	$-0.0583170\pi$
$263$	7.71569	+	11.0192i	0.475770	+	0.679470i	−0.507494	+	0.861655i	$0.669428\pi$
$264$	10.3160	−	0.520762i	0.634904	−	0.0320507i
$265$		0			0
$266$	22.7620	−	4.01356i	1.39563	−	0.246087i
$267$	0.0361636	−	0.0191395i	0.00221318	−	0.00117132i
$268$	1.02583	+	11.7253i	0.0626625	+	0.716236i
$269$	−19.0909			−1.16399			−0.581996	−	0.813191i	$-0.697728\pi$
$269$	−19.0909			−1.16399			−0.581996	+	0.813191i	$0.697728\pi$
$270$		0			0
$271$	−16.1076			−0.978468			−0.489234	−	0.872153i	$-0.662724\pi$
$271$	−16.1076			−0.978468			−0.489234	+	0.872153i	$0.662724\pi$
$272$	−0.579647	−	6.62540i	−0.0351463	−	0.401724i
$273$	0.486121	−	13.1938i	0.0294214	−	0.798523i
$274$	−12.7253	+	2.24381i	−0.768761	+	0.135553i
$275$		0			0
$276$	−10.5392	−	16.2974i	−0.634385	−	0.980988i
$277$	4.21082	+	6.01367i	0.253004	+	0.361327i	0.925483	−	0.378789i	$-0.123659\pi$
$277$	4.21082	+	6.01367i	0.253004	+	0.361327i	−0.672479	+	0.740116i	$0.734771\pi$
$278$	2.04443	+	7.62992i	0.122617	+	0.457612i
$279$	5.31505	−	3.83049i	0.318204	−	0.229325i
$280$		0			0
$281$	5.52636	+	15.1836i	0.329675	+	0.905775i	0.988194	+	0.153210i	$0.0489612\pi$
$281$	5.52636	+	15.1836i	0.329675	+	0.905775i	−0.658518	+	0.752565i	$0.728817\pi$
$282$	1.68675	+	12.1715i	0.100444	+	0.724802i
$283$	10.5273	+	0.921022i	0.625785	+	0.0547491i	0.395638	−	0.918407i	$-0.370524\pi$
$283$	10.5273	+	0.921022i	0.625785	+	0.0547491i	0.230147	+	0.973156i	$0.426079\pi$
$284$	−1.17153	+	0.983029i	−0.0695174	+	0.0583321i
$285$		0			0
$286$	−2.62315	+	0.954750i	−0.155110	+	0.0564555i
$287$	−5.69471	+	21.2530i	−0.336148	+	1.25452i
$288$	−11.1015	+	13.6020i	−0.654165	+	0.801508i
$289$	−16.0762	−	9.28157i	−0.945656	−	0.545975i
$290$		0			0
$291$	−4.49432	+	2.90638i	−0.263462	+	0.170375i
$292$	−5.11468	+	2.38502i	−0.299314	+	0.139572i
$293$	7.71819	+	5.40433i	0.450901	+	0.315725i	0.776876	−	0.629654i	$-0.216803\pi$
$293$	7.71819	+	5.40433i	0.450901	+	0.315725i	−0.325974	+	0.945379i	$0.605692\pi$
$294$	−12.8258	−	13.8071i	−0.748016	−	0.805245i
$295$		0			0
$296$			12.6027i			0.732517i
$297$	11.9417	−	2.90439i	0.692928	−	0.168530i
$298$	1.41448	+	1.41448i	0.0819386	+	0.0819386i
$299$	9.47401	+	7.94964i	0.547896	+	0.459740i
$300$		0			0
$301$	2.64542	+	15.0029i	0.152480	+	0.864755i
$302$	3.91806	+	8.40232i	0.225459	+	0.483499i
$303$	−9.22453	−	8.33796i	−0.529936	−	0.479003i
$304$	−7.45688	−	1.31485i	−0.427682	−	0.0754118i
$305$		0			0
$306$	3.53218	+	12.4993i	0.201921	+	0.714535i
$307$	−26.0955	−	6.99226i	−1.48935	−	0.399069i	−0.579830	−	0.814737i	$-0.696881\pi$
$307$	−26.0955	−	6.99226i	−1.48935	−	0.399069i	−0.909516	+	0.415668i	$0.863548\pi$
$308$	6.90336	−	14.8043i	0.393355	−	0.843553i
$309$	−2.75787	+	22.1098i	−0.156890	+	1.25778i
$310$		0			0
$311$	5.82215	+	6.93856i	0.330144	+	0.393450i	0.905425	−	0.424505i	$-0.139552\pi$
$311$	5.82215	+	6.93856i	0.330144	+	0.393450i	−0.575282	+	0.817955i	$0.695108\pi$
$312$	2.67216	−	6.57741i	0.151281	−	0.372373i
$313$	−9.19503	−	4.28771i	−0.519734	−	0.242356i	0.145006	−	0.989431i	$-0.453680\pi$
$313$	−9.19503	−	4.28771i	−0.519734	−	0.242356i	−0.664740	+	0.747075i	$0.731458\pi$
$314$	−3.42124	−	5.92576i	−0.193072	−	0.334410i
$315$		0			0
$316$	4.72975	−	8.19217i	0.266069	−	0.460845i
$317$	−5.65260	+	3.95799i	−0.317481	+	0.222303i	−0.721444	−	0.692473i	$-0.756521\pi$
$317$	−5.65260	+	3.95799i	−0.317481	+	0.222303i	0.403963	+	0.914775i	$0.367632\pi$
$318$	−1.01116	−	3.13249i	−0.0567029	−	0.175661i
$319$	−5.63545	+	15.4833i	−0.315525	+	0.866897i
$320$		0			0
$321$	−0.838926	−	3.66591i	−0.0468243	−	0.204611i
$322$	25.7999	−	2.25720i	1.43777	−	0.125789i
$323$	−28.6301	+	28.6301i	−1.59302	+	1.59302i
$324$	−6.31314	+	11.6563i	−0.350730	+	0.647571i
$325$		0			0
$326$	9.59307	−	11.4326i	0.531311	−	0.633192i
$327$	7.83882	−	12.4913i	0.433487	−	0.690768i
$328$	−6.78626	+	9.69179i	−0.374709	+	0.535140i
$329$	43.0555	+	15.6709i	2.37373	+	0.863966i
$330$		0			0
$331$	−2.02614	+	11.4908i	−0.111367	+	0.631591i	0.877119	+	0.480274i	$0.159463\pi$
$331$	−2.02614	+	11.4908i	−0.111367	+	0.631591i	−0.988485	+	0.151318i	$0.951648\pi$
$332$	1.04448	−	0.279868i	0.0573234	−	0.0153598i
$333$	2.80459	+	14.7304i	0.153691	+	0.807220i
$334$	6.74280	−	3.89295i	0.368949	−	0.213013i
$335$		0			0
$336$	3.52298	+	8.34416i	0.192194	+	0.455211i
$337$	0.207325	−	2.36973i	0.0112937	−	0.129087i	−0.988455	−	0.151516i	$-0.951584\pi$
$337$	0.207325	−	2.36973i	0.0112937	−	0.129087i	0.999748	+	0.0224289i	$0.00713994\pi$
$338$	0.655370	−	7.49091i	0.0356474	−	0.407452i
$339$	−28.8479	−	3.59836i	−1.56680	−	0.195436i
$340$		0			0
$341$	−4.47317	+	2.58258i	−0.242236	+	0.139855i
$342$	14.7865	−	0.201261i	0.799562	−	0.0108829i
$343$	−36.1708	+	9.69193i	−1.95304	+	0.523315i
$344$	−1.42252	+	8.06752i	−0.0766972	+	0.434971i
$345$		0			0
$346$	−8.49630	−	3.09240i	−0.456764	−	0.166248i
$347$	6.70944	−	9.58207i	0.360181	−	0.514392i	−0.597637	−	0.801767i	$-0.703894\pi$
$347$	6.70944	−	9.58207i	0.360181	−	0.514392i	0.957818	+	0.287375i	$0.0927824\pi$
$348$	−8.31350	−	15.7082i	−0.445650	−	0.842046i
$349$	15.6352	−	18.6334i	0.836935	−	0.997421i	−0.163007	−	0.986625i	$-0.552119\pi$
$349$	15.6352	−	18.6334i	0.836935	−	0.997421i	0.999942	−	0.0107955i	$-0.00343640\pi$
$350$		0			0
$351$	1.65956	−	8.28252i	0.0885809	−	0.442088i
$352$	9.78782	−	9.78782i	0.521692	−	0.521692i
$353$	31.5344	−	2.75891i	1.67841	−	0.146842i	0.792241	−	0.610208i	$-0.208914\pi$
$353$	31.5344	−	2.75891i	1.67841	−	0.146842i	0.886167	+	0.463366i	$0.153359\pi$
$354$	−4.14059	+	3.84631i	−0.220070	+	0.204429i
$355$		0			0
$356$	0.0119003	−	0.0326959i	0.000630716	−	0.00173288i
$357$	47.3546	+	10.1607i	2.50627	+	0.537759i
$358$	2.28751	−	1.60173i	0.120899	−	0.0846543i
$359$	10.9060	−	18.8897i	0.575596	−	0.996962i	−0.420381	−	0.907348i	$-0.638103\pi$
$359$	10.9060	−	18.8897i	0.575596	−	0.996962i	0.995977	−	0.0896137i	$-0.0285632\pi$
$360$		0			0
$361$	13.5487	+	23.4670i	0.713089	+	1.23511i
$362$	9.35357	+	4.36164i	0.491612	+	0.229243i
$363$	9.27472	−	1.28531i	0.486797	−	0.0674612i
$364$	−7.21679	−	8.60063i	−0.378262	−	0.450796i
$365$		0			0
$366$	2.26146	+	1.71096i	0.118209	+	0.0894332i
$367$	3.57482	−	7.66622i	0.186604	−	0.400173i	−0.790643	−	0.612277i	$-0.790254\pi$
$367$	3.57482	−	7.66622i	0.186604	−	0.400173i	0.977247	+	0.212104i	$0.0680315\pi$
$368$	−8.19528	−	2.19592i	−0.427208	−	0.114470i
$369$	−5.77517	+	12.8382i	−0.300643	+	0.668332i
$370$		0			0
$371$	−12.0874	−	2.13133i	−0.627546	−	0.110653i
$372$	1.16880	−	5.44730i	0.0605996	−	0.282429i
$373$	−14.2517	−	30.5630i	−0.737927	−	1.58249i	−0.810920	−	0.585158i	$-0.801033\pi$
$373$	−14.2517	−	30.5630i	−0.737927	−	1.58249i	0.0729923	−	0.997333i	$-0.476745\pi$
$374$	−1.77820	−	10.0847i	−0.0919484	−	0.521465i
$375$		0			0
$376$	18.8739	+	15.8370i	0.973345	+	0.816733i
$377$	8.00804	+	8.00804i	0.412435	+	0.412435i
$378$	−9.80686	−	14.7216i	−0.504410	−	0.757198i
$379$			4.83051i			0.248126i	0.992274	+	0.124063i	$0.0395926\pi$
$379$			4.83051i			0.248126i	−0.992274	+	0.124063i	$0.960407\pi$
$380$		0			0
$381$	−1.99492	+	6.48052i	−0.102203	+	0.332007i
$382$	−15.1827	−	10.6310i	−0.776813	−	0.543930i
$383$	−22.4867	+	10.4857i	−1.14902	+	0.535795i	−0.901368	−	0.433055i	$-0.857436\pi$
$383$	−22.4867	+	10.4857i	−1.14902	+	0.535795i	−0.247649	+	0.968850i	$0.579658\pi$
$384$	0.894156	+	17.7127i	0.0456297	+	0.903895i
$385$		0			0
$386$	−4.16299	−	2.40350i	−0.211891	−	0.122335i
$387$	0.132655	+	9.74610i	0.00674325	+	0.495422i
$388$	−1.17799	+	4.39631i	−0.0598033	+	0.223189i
$389$	−35.9511	+	13.0851i	−1.82279	+	0.663443i	−0.828099	+	0.560583i	$0.810577\pi$
$389$	−35.9511	+	13.0851i	−1.82279	+	0.663443i	−0.994696	+	0.102860i	$0.967201\pi$
$390$		0			0
$391$	−34.7541	+	29.1622i	−1.75759	+	1.47479i
$392$	−37.6421	−	3.29326i	−1.90121	−	0.166335i
$393$	2.88491	+	1.17203i	0.145525	+	0.0591212i
$394$	−4.91670	−	13.5085i	−0.247700	−	0.680550i
$395$		0			0
$396$	5.87739	−	8.64176i	0.295350	−	0.434265i
$397$	−5.54075	−	20.6784i	−0.278082	−	1.03782i	−0.953747	−	0.300609i	$-0.902810\pi$
$397$	−5.54075	−	20.6784i	−0.278082	−	1.03782i	0.675665	−	0.737209i	$-0.263857\pi$
$398$	0.549317	+	0.784506i	0.0275348	+	0.0393237i
$399$	25.1278	−	49.0827i	1.25796	−	2.45721i
$400$		0			0
$401$	34.5128	−	6.08555i	1.72349	−	0.303898i	0.777690	−	0.628648i	$-0.216392\pi$
$401$	34.5128	−	6.08555i	1.72349	−	0.303898i	0.945800	+	0.324751i	$0.105280\pi$
$402$	−8.51159	−	5.34140i	−0.424519	−	0.266405i
$403$	0.309418	+	3.53666i	0.0154132	+	0.176174i
$404$	−10.5739			−0.526073
$405$		0			0
$406$	23.7156			1.17699
$407$	−1.03035	−	11.7770i	−0.0510725	−	0.583762i
$408$	22.0596	+	13.8434i	1.09211	+	0.685349i
$409$	−31.2192	+	5.50478i	−1.54369	+	0.272194i	−0.879693	−	0.475542i	$-0.842252\pi$
$409$	−31.2192	+	5.50478i	−1.54369	+	0.272194i	−0.663996	+	0.747736i	$0.731141\pi$
$410$		0			0
$411$	−14.0479	+	27.4400i	−0.692930	+	1.35352i
$412$	10.8678	+	15.5208i	0.535417	+	0.764655i
$413$	5.45409	+	20.3549i	0.268378	+	1.00160i
$414$	16.5250	+	1.21937i	0.812157	+	0.0599288i
$415$		0			0
$416$	−3.25400	−	8.94028i	−0.159540	−	0.438333i
$417$	17.4590	+	7.09294i	0.854969	+	0.347343i
$418$	−11.6143	−	1.01612i	−0.568073	−	0.0496999i
$419$	−21.7068	+	18.2142i	−1.06045	+	0.889821i	−0.994153	−	0.107979i	$-0.965562\pi$
$419$	−21.7068	+	18.2142i	−1.06045	+	0.889821i	−0.0662941	+	0.997800i	$0.521118\pi$
$420$		0			0
$421$	−7.16992	+	2.60964i	−0.349441	+	0.127186i	−0.510776	−	0.859714i	$-0.670642\pi$
$421$	−7.16992	+	2.60964i	−0.349441	+	0.127186i	0.161336	+	0.986900i	$0.448420\pi$
$422$	2.04017	−	7.61401i	0.0993138	−	0.370644i
$423$	25.5846	+	14.3106i	1.24397	+	0.695805i
$424$	−5.71578	−	3.30001i	−0.277583	−	0.160263i
$425$		0			0
$426$	−0.0658278	−	1.30401i	−0.00318937	−	0.0631793i
$427$	9.58330	−	4.46876i	0.463768	−	0.216259i
$428$	−2.61965	−	1.83430i	−0.126626	−	0.0886642i
$429$	−1.95933	+	6.36491i	−0.0945974	+	0.307301i
$430$		0			0
$431$		−	20.7923i		−	1.00153i	−0.865583	−	0.500765i	$-0.833052\pi$
$431$		−	20.7923i		−	1.00153i	0.865583	−	0.500765i	$-0.166948\pi$
$432$	1.36949	+	5.63080i	0.0658896	+	0.270912i
$433$	7.85031	+	7.85031i	0.377262	+	0.377262i	0.870113	−	0.492852i	$-0.164045\pi$
$433$	7.85031	+	7.85031i	0.377262	+	0.377262i	−0.492852	+	0.870113i	$0.664045\pi$
$434$	5.69503	+	4.77870i	0.273370	+	0.229385i
$435$		0			0
$436$	−2.17767	−	12.3502i	−0.104291	−	0.591465i
$437$	21.8292	+	46.8129i	1.04423	+	2.23937i
$438$	1.01079	−	4.71088i	0.0482976	−	0.225095i
$439$	9.06380	+	1.59819i	0.432591	+	0.0762775i	0.385704	−	0.922623i	$-0.373959\pi$
$439$	9.06380	+	1.59819i	0.432591	+	0.0762775i	0.0468875	+	0.998900i	$0.485070\pi$
$440$		0			0
$441$	−44.7300	+	4.52758i	−2.13000	+	0.215599i
$442$	−6.79858	−	1.82167i	−0.323375	−	0.0866482i
$443$	0.656035	−	1.40687i	0.0311692	−	0.0668425i	−0.890107	−	0.455752i	$-0.849370\pi$
$443$	0.656035	−	1.40687i	0.0311692	−	0.0668425i	0.921276	+	0.388910i	$0.127148\pi$
$444$	10.1690	+	7.69356i	0.482599	+	0.365120i
$445$		0			0
$446$	10.7030	+	12.7554i	0.506803	+	0.603985i
$447$	4.72710	−	0.655091i	0.223584	−	0.0309847i
$448$	−8.57783	−	3.99991i	−0.405264	−	0.188978i
$449$	1.66148	+	2.87776i	0.0784099	+	0.135810i	0.902564	−	0.430556i	$-0.141682\pi$
$449$	1.66148	+	2.87776i	0.0784099	+	0.135810i	−0.824154	+	0.566366i	$0.808349\pi$
$450$		0			0
$451$	5.54925	−	9.61159i	0.261304	−	0.452592i
$452$	−20.2509	+	14.1798i	−0.952523	+	0.666964i
$453$	21.6254	+	4.64007i	1.01605	+	0.218009i
$454$	−2.66462	+	7.32099i	−0.125057	+	0.343591i
$455$		0			0
$456$	21.7241	−	20.1801i	1.01732	−	0.945021i
$457$	−17.1702	+	1.50219i	−0.803186	+	0.0702697i	−0.481353	−	0.876527i	$-0.659855\pi$
$457$	−17.1702	+	1.50219i	−0.803186	+	0.0702697i	−0.321833	+	0.946796i	$0.604299\pi$
$458$	−5.93132	+	5.93132i	−0.277152	+	0.277152i
$459$	28.8645	+	11.2714i	1.34728	+	0.526103i
$460$		0			0
$461$	8.39687	−	10.0070i	0.391081	−	0.466072i	−0.534198	−	0.845359i	$-0.679386\pi$
$461$	8.39687	−	10.0070i	0.391081	−	0.466072i	0.925279	+	0.379287i	$0.123831\pi$
$462$	6.52351	+	12.3260i	0.303501	+	0.573458i
$463$	0.780347	−	1.11445i	0.0362658	−	0.0517929i	−0.800610	−	0.599186i	$-0.795491\pi$
$463$	0.780347	−	1.11445i	0.0362658	−	0.0517929i	0.836876	+	0.547393i	$0.184380\pi$
$464$	−7.30074	−	2.65725i	−0.338928	−	0.123360i
$465$		0			0
$466$	−0.940992	+	5.33663i	−0.0435906	+	0.247215i
$467$	−0.117944	+	0.0316030i	−0.00545780	+	0.00146241i	−0.261547	−	0.965191i	$-0.584233\pi$
$467$	−0.117944	+	0.0316030i	−0.00545780	+	0.00146241i	0.256089	+	0.966653i	$0.417566\pi$
$468$	−3.67597	−	6.17145i	−0.169922	−	0.285275i
$469$	−32.4498	+	18.7349i	−1.49839	+	0.865096i
$470$		0			0
$471$	−16.1985	−	2.02053i	−0.746388	−	0.0931011i
$472$	−0.987611	+	11.2884i	−0.0454585	+	0.519593i
$473$	0.669745	−	7.65522i	0.0307949	−	0.351987i
$474$	3.14129	+	7.44013i	0.144284	+	0.341737i
$475$		0			0
$476$	35.6680	−	20.5929i	1.63484	−	0.943876i
$477$	−7.41514	−	2.58516i	−0.339516	−	0.118366i
$478$	20.8665	−	5.59117i	0.954412	−	0.255734i
$479$	4.54350	−	25.7675i	0.207598	−	1.17735i	−0.685701	−	0.727883i	$-0.740504\pi$
$479$	4.54350	−	25.7675i	0.207598	−	1.17735i	0.893299	−	0.449463i	$-0.148385\pi$
$480$		0			0
$481$	−7.63553	−	2.77910i	−0.348150	−	0.126716i
$482$	−7.12771	+	10.1794i	−0.324658	+	0.463660i
$483$	32.8420	−	52.3342i	1.49436	−	2.38129i
$484$	5.11814	−	6.09956i	0.232643	−	0.277253i
$485$		0			0
$486$	−4.68420	−	10.3026i	−0.212480	−	0.467335i
$487$	−9.16515	+	9.16515i	−0.415313	+	0.415313i	−0.883584	−	0.468272i	$-0.844877\pi$
$487$	−9.16515	+	9.16515i	−0.415313	+	0.415313i	0.468272	+	0.883584i	$0.344877\pi$
$488$	5.66431	−	0.495563i	0.256411	−	0.0224331i
$489$	−7.94259	−	34.7073i	−0.359176	−	1.56952i
$490$		0			0
$491$	8.42964	−	23.1603i	0.380424	−	1.04521i	−0.590753	−	0.806852i	$-0.701169\pi$
$491$	8.42964	−	23.1603i	0.380424	−	1.04521i	0.971178	−	0.238356i	$-0.0766084\pi$
$492$	3.67740	+	11.3923i	0.165790	+	0.513605i
$493$	−34.0313	+	23.8289i	−1.53269	+	1.07320i
$494$	−4.00666	+	6.93974i	−0.180268	+	0.312233i
$495$		0			0
$496$	−1.21775	−	2.10921i	−0.0546787	−	0.0947062i
$497$	−4.41241	−	2.05754i	−0.197924	−	0.0922933i
$498$	−0.347477	+	0.855299i	−0.0155708	+	0.0383269i
$499$	4.55089	+	5.42354i	0.203726	+	0.242791i	0.858227	−	0.513270i	$-0.171566\pi$
$499$	4.55089	+	5.42354i	0.203726	+	0.242791i	−0.654502	+	0.756061i	$0.727122\pi$
$500$		0			0
$501$	2.29912	−	18.4319i	0.102717	−	0.823479i
$502$	−3.01894	+	6.47414i	−0.134742	+	0.288955i
$503$	3.54336	+	0.949440i	0.157990	+	0.0423334i	0.336947	−	0.941524i	$-0.390606\pi$
$503$	3.54336	+	0.949440i	0.157990	+	0.0423334i	−0.178957	+	0.983857i	$0.557272\pi$
$504$	−34.3811	−	8.71264i	−1.53145	−	0.388092i
$505$		0			0
$506$	−12.8651	−	2.26846i	−0.571924	−	0.100846i
$507$	−13.3084	−	12.0293i	−0.591047	−	0.534241i
$508$	2.43686	+	5.22586i	0.108118	+	0.231860i
$509$	0.686733	+	3.89466i	0.0304389	+	0.172628i	0.996237	−	0.0866661i	$-0.0276213\pi$
$509$	0.686733	+	3.89466i	0.0304389	+	0.172628i	−0.965799	+	0.259294i	$0.916510\pi$
$510$		0			0
$511$	−13.7625	−	11.5481i	−0.608819	−	0.510859i
$512$	8.59188	+	8.59188i	0.379711	+	0.379711i
$513$	20.9008	−	28.4215i	0.922794	−	1.25484i
$514$		−	0.0554707i		−	0.00244671i
$515$		0			0
$516$	5.64119	+	6.07279i	0.248340	+	0.267340i
$517$	−18.9320	−	13.2563i	−0.832628	−	0.583012i
$518$	−15.4213	+	7.19108i	−0.677574	+	0.315958i
$519$	−18.1130	+	11.7133i	−0.795073	+	0.514157i
$520$		0			0
$521$	16.1589	+	9.32937i	0.707936	+	0.408727i	0.810296	−	0.586020i	$-0.199306\pi$
$521$	16.1589	+	9.32937i	0.707936	+	0.408727i	−0.102360	+	0.994747i	$0.532639\pi$
$522$	14.9773	+	2.43121i	0.655538	+	0.106411i
$523$	9.40272	−	35.0914i	0.411152	−	1.53444i	−0.381268	−	0.924465i	$-0.624512\pi$
$523$	9.40272	−	35.0914i	0.411152	−	1.53444i	0.792420	−	0.609976i	$-0.208821\pi$
$524$	2.48830	−	0.905668i	0.108702	−	0.0395643i
$525$		0			0
$526$	−7.48142	+	6.27765i	−0.326205	+	0.273719i
$527$	−12.9737	−	1.13506i	−0.565145	−	0.0494438i
$528$	−0.627145	−	4.52544i	−0.0272930	−	0.196945i
$529$	11.9285	+	32.7734i	0.518633	+	1.42493i
$530$		0			0
$531$	1.35777	+	13.4140i	0.0589223	+	0.582119i
$532$	−12.1362	−	45.2929i	−0.526171	−	1.96370i
$533$	−4.37542	−	6.24875i	−0.189521	−	0.270664i
$534$	0.0161310	+	0.0249444i	0.000698057	+	0.00107945i
$535$		0			0
$536$	−19.8425	+	3.49876i	−0.857065	+	0.151124i
$537$	0.245298	−	6.65762i	0.0105854	−	0.287297i
$538$	−1.20800	−	13.8076i	−0.0520808	−	0.595286i
$539$	35.4450			1.52672
$540$		0			0
$541$	−22.9374			−0.986154			−0.493077	−	0.869986i	$-0.664128\pi$
$541$	−22.9374			−0.986154			−0.493077	+	0.869986i	$0.664128\pi$
$542$	−1.01923	−	11.6499i	−0.0437798	−	0.500406i
$543$	21.7617	−	11.5173i	0.933885	−	0.494256i
$544$	34.3707	−	6.06049i	1.47363	−	0.259841i
$545$		0			0
$546$	9.57320	−	0.483266i	0.409695	−	0.0206819i
$547$	−8.76004	−	12.5106i	−0.374552	−	0.534916i	0.586982	−	0.809600i	$-0.300316\pi$
$547$	−8.76004	−	12.5106i	−0.374552	−	0.534916i	−0.961535	+	0.274684i	$0.911427\pi$
$548$	6.78483	+	25.3213i	0.289834	+	1.08167i
$549$	6.51032	−	1.83976i	0.277854	−	0.0785189i
$550$		0			0
$551$	16.1772	+	44.4465i	0.689172	+	1.89348i
$552$	26.2201	−	20.4044i	1.11600	−	0.868467i
$553$	29.9995	+	2.62461i	1.27571	+	0.111610i
$554$	−4.08296	+	3.42601i	−0.173469	+	0.145557i
$555$		0			0
$556$	15.0588	−	5.48094i	0.638634	−	0.232444i
$557$	−1.82503	+	6.81110i	−0.0773290	+	0.288596i	−0.993751	−	0.111617i	$-0.964397\pi$
$557$	−1.82503	+	6.81110i	−0.0773290	+	0.288596i	0.916422	+	0.400213i	$0.131064\pi$
$558$	3.10673	+	3.60175i	0.131518	+	0.152474i
$559$	−4.57413	−	2.64088i	−0.193465	−	0.111697i
$560$		0			0
$561$	−21.7460	−	11.1328i	−0.918116	−	0.470028i
$562$	−10.6319	+	4.95772i	−0.448478	+	0.209129i
$563$	25.5845	+	17.9144i	1.07826	+	0.755004i	0.970965	−	0.239224i	$-0.0768929\pi$
$563$	25.5845	+	17.9144i	1.07826	+	0.755004i	0.107293	+	0.994227i	$0.465782\pi$
$564$	24.3007	−	5.56109i	1.02324	−	0.234164i
$565$		0			0
$566$			7.67220i			0.322487i
$567$	−42.1244	−	2.53244i	−1.76906	−	0.106353i
$568$	−1.85118	−	1.85118i	−0.0776739	−	0.0776739i
$569$	24.7601	+	20.7762i	1.03800	+	0.870984i	0.991781	−	0.127948i	$-0.0408389\pi$
$569$	24.7601	+	20.7762i	1.03800	+	0.870984i	0.0462172	+	0.998931i	$0.485283\pi$
$570$		0			0
$571$	−7.28419	−	41.3107i	−0.304834	−	1.72880i	−0.624286	−	0.781196i	$-0.714610\pi$
$571$	−7.28419	−	41.3107i	−0.304834	−	1.72880i	0.319453	−	0.947602i	$-0.396501\pi$
$572$	2.39339	+	5.13264i	0.100073	+	0.214606i
$573$	−42.0799	+	13.5832i	−1.75791	+	0.567448i
$574$	−15.7316	−	2.77391i	−0.656625	−	0.115781i
$575$		0			0
$576$	−5.00716	−	3.40544i	−0.208632	−	0.141894i
$577$	15.0234	+	4.02551i	0.625433	+	0.167584i	0.557596	−	0.830112i	$-0.311724\pi$
$577$	15.0234	+	4.02551i	0.625433	+	0.167584i	0.0678366	+	0.997696i	$0.478390\pi$
$578$	5.69568	−	12.2144i	0.236909	−	0.508054i
$579$	−10.5650	+	4.46063i	−0.439065	+	0.185377i
$580$		0			0
$581$	2.21272	+	2.63701i	0.0917990	+	0.109402i
$582$	−2.38643	−	3.06662i	−0.0989209	−	0.127116i
$583$	5.61107	+	2.61649i	0.232387	+	0.108364i
$584$	−4.83034	−	8.36640i	−0.199881	−	0.346204i
$585$		0			0
$586$	−3.42032	+	5.92417i	−0.141292	+	0.244725i
$587$	−21.6287	+	15.1446i	−0.892712	+	0.625084i	−0.927300	−	0.374318i	$-0.877877\pi$
$587$	−21.6287	+	15.1446i	−0.892712	+	0.625084i	0.0345884	+	0.999402i	$0.488988\pi$
$588$	−25.6366	+	28.3626i	−1.05724	+	1.16965i
$589$	−5.07120	+	13.9330i	−0.208955	+	0.574099i
$590$		0			0
$591$	−32.7776	−	10.0900i	−1.34829	−	0.415048i
$592$	5.55312	−	0.485835i	0.228232	−	0.0199677i
$593$	2.61058	−	2.61058i	0.107204	−	0.107204i	−0.651470	−	0.758674i	$-0.725847\pi$
$593$	2.61058	−	2.61058i	0.107204	−	0.107204i	0.758674	+	0.651470i	$0.225847\pi$
$594$	2.85624	+	8.45309i	0.117193	+	0.346835i
$595$		0			0
$596$	2.60859	−	3.10880i	0.106852	−	0.127341i
$597$	2.28324	+	0.0841254i	0.0934468	+	0.00344302i
$598$	−5.15012	+	7.35514i	−0.210604	+	0.300774i
$599$	24.1321	+	8.78335i	0.986010	+	0.358878i	0.784174	−	0.620541i	$-0.213087\pi$
$599$	24.1321	+	8.78335i	0.986010	+	0.358878i	0.201836	+	0.979419i	$0.435309\pi$
$600$		0			0
$601$	−7.14602	+	40.5271i	−0.291492	+	1.65313i	0.389636	+	0.920969i	$0.372601\pi$
$601$	−7.14602	+	40.5271i	−0.291492	+	1.65313i	−0.681128	+	0.732165i	$0.738510\pi$
$602$	−10.6835	+	2.86264i	−0.435428	+	0.116673i
$603$	−22.4138	+	8.50518i	−0.912761	+	0.346358i
$604$	16.2885	−	9.40418i	0.662770	−	0.382650i
$605$		0			0
$606$	5.44676	−	7.19927i	0.221259	−	0.292450i
$607$	0.744689	−	8.51183i	0.0302260	−	0.345485i	−0.965990	−	0.258578i	$-0.916746\pi$
$607$	0.744689	−	8.51183i	0.0302260	−	0.345485i	0.996216	−	0.0869069i	$-0.0276983\pi$
$608$	3.46315	−	39.5840i	0.140449	−	1.60534i
$609$	34.1364	−	45.1198i	1.38328	−	1.82835i
$610$		0			0
$611$	−13.7571	+	7.94266i	−0.556553	+	0.321326i
$612$	24.6368	−	9.34869i	0.995882	−	0.377899i
$613$	−9.00556	+	2.41303i	−0.363731	+	0.0974614i	−0.436056	−	0.899920i	$-0.643625\pi$
$613$	−9.00556	+	2.41303i	−0.363731	+	0.0974614i	0.0723246	+	0.997381i	$0.476958\pi$
$614$	3.40594	−	19.3161i	0.137453	−	0.779533i
$615$		0			0
$616$	26.2762	+	9.56376i	1.05870	+	0.385335i
$617$	26.0142	−	37.1521i	1.04729	−	1.49569i	0.189372	−	0.981905i	$-0.439355\pi$
$617$	26.0142	−	37.1521i	1.04729	−	1.49569i	0.857920	−	0.513783i	$-0.171756\pi$
$618$	−16.1655	−	0.595612i	−0.650270	−	0.0239590i
$619$	15.0061	−	17.8836i	0.603147	−	0.718803i	−0.374928	−	0.927054i	$-0.622333\pi$
$619$	15.0061	−	17.8836i	0.603147	−	0.718803i	0.978075	+	0.208251i	$0.0667770\pi$
$620$		0			0
$621$	26.1060	−	29.6842i	1.04760	−	1.19118i
$622$	−4.64993	+	4.64993i	−0.186445	+	0.186445i
$623$	0.110345	−	0.00965394i	0.00442088	−	0.000386777i
$624$	−3.00121	−	0.923872i	−0.120145	−	0.0369845i
$625$		0			0
$626$	2.51927	−	6.92165i	0.100690	−	0.276645i
$627$	−18.6508	+	20.6340i	−0.744843	+	0.824042i
$628$	−11.3712	+	7.96218i	−0.453759	+	0.317726i
$629$	14.9037	−	25.8140i	0.594251	−	1.02927i
$630$		0			0
$631$	−15.4086	−	26.6885i	−0.613407	−	1.06245i	−0.990662	−	0.136343i	$-0.956465\pi$
$631$	−15.4086	−	26.6885i	−0.613407	−	1.06245i	0.377255	−	0.926110i	$-0.376868\pi$
$632$	14.6760	+	6.84355i	0.583781	+	0.272222i
$633$	−11.5493	−	14.8411i	−0.459044	−	0.589882i
$634$	−3.22031	−	3.83781i	−0.127895	−	0.152419i
$635$		0			0
$636$	−6.15205	+	2.59745i	−0.243945	+	0.102996i
$637$	10.2960	−	22.0798i	0.407941	−	0.874833i
$638$	−11.5549	−	3.09613i	−0.457464	−	0.122577i
$639$	−2.57567	−	1.75175i	−0.101892	−	0.0692982i
$640$		0			0
$641$	12.3888	+	2.18449i	0.489330	+	0.0862820i	0.412869	−	0.910791i	$-0.364527\pi$
$641$	12.3888	+	2.18449i	0.489330	+	0.0862820i	0.0764610	+	0.997073i	$0.475638\pi$
$642$	2.59830	−	0.838722i	0.102547	−	0.0331017i
$643$	16.1067	+	34.5408i	0.635185	+	1.36216i	0.915526	+	0.402258i	$0.131774\pi$
$643$	16.1067	+	34.5408i	0.635185	+	1.36216i	−0.280342	+	0.959900i	$0.590448\pi$
$644$	−9.12369	−	51.7430i	−0.359524	−	2.03896i
$645$		0			0
$646$	−22.5184	−	18.8952i	−0.885976	−	0.743422i
$647$	−16.5718	−	16.5718i	−0.651504	−	0.651504i	0.301851	−	0.953355i	$-0.402396\pi$
$647$	−16.5718	−	16.5718i	−0.651504	−	0.651504i	−0.953355	+	0.301851i	$0.902396\pi$
$648$	−20.8197	−	9.02693i	−0.817876	−	0.354611i
$649$		−	10.6295i		−	0.417246i
$650$		0			0
$651$	17.2891	−	3.95652i	0.677613	−	0.155068i
$652$	−24.8017	−	17.3664i	−0.971311	−	0.680119i
$653$	−5.39065	+	2.51370i	−0.210952	+	0.0983687i	−0.525223	−	0.850965i	$-0.676018\pi$
$653$	−5.39065	+	2.51370i	−0.210952	+	0.0983687i	0.314270	+	0.949334i	$0.398240\pi$
$654$	9.53035	+	4.87905i	0.372666	+	0.190786i
$655$		0			0
$656$	4.53210	+	2.61661i	0.176949	+	0.102161i
$657$	−7.50769	−	8.70394i	−0.292903	−	0.339573i
$658$	−8.60965	+	32.1316i	−0.335639	+	1.25262i
$659$	−34.7751	+	12.6571i	−1.35465	+	0.493051i	−0.914395	−	0.404824i	$-0.867333\pi$
$659$	−34.7751	+	12.6571i	−1.35465	+	0.493051i	−0.440251	+	0.897875i	$0.645111\pi$
$660$		0			0
$661$	13.5431	−	11.3640i	0.526766	−	0.442009i	−0.340217	−	0.940347i	$-0.610500\pi$
$661$	13.5431	−	11.3640i	0.526766	−	0.442009i	0.866983	+	0.498338i	$0.166056\pi$
$662$	−8.43896	−	0.738314i	−0.327990	−	0.0286954i
$663$	−13.2517	+	10.3124i	−0.514653	+	0.400501i
$664$	0.633102	+	1.73943i	0.0245691	+	0.0675031i
$665$		0			0
$666$	−10.4763	+	2.96052i	−0.405950	+	0.114718i
$667$	13.7171	+	51.1928i	0.531128	+	1.98219i
$668$	−9.06000	−	12.9390i	−0.350542	−	0.500626i
$669$	39.6736	−	2.00277i	1.53387	−	0.0774315i
$670$		0			0
$671$	−5.25266	+	0.926186i	−0.202777	+	0.0357550i
$672$	−42.0098	+	22.2336i	−1.62056	+	0.857678i
$673$	3.10515	+	35.4920i	0.119695	+	1.36812i	0.784049	+	0.620699i	$0.213151\pi$
$673$	3.10515	+	35.4920i	0.119695	+	1.36812i	−0.664354	+	0.747418i	$0.731293\pi$
$674$	1.72703			0.0665229
$675$		0			0
$676$	−15.2552			−0.586739
$677$	1.24538	+	14.2347i	0.0478637	+	0.547084i	0.981835	+	0.189737i	$0.0607634\pi$
$677$	1.24538	+	14.2347i	0.0478637	+	0.547084i	−0.933971	+	0.357348i	$0.883681\pi$
$678$	0.777131	−	21.0921i	0.0298455	−	0.810035i
$679$	−14.2691	+	2.51603i	−0.547599	+	0.0965564i
$680$		0			0
$681$	10.0930	+	15.6074i	0.386764	+	0.598077i
$682$	−2.15091	−	3.07182i	−0.0823625	−	0.117626i
$683$	−12.9972	−	48.5064i	−0.497326	−	1.85604i	−0.516594	−	0.856230i	$-0.672800\pi$
$683$	−12.9972	−	48.5064i	−0.497326	−	1.85604i	0.0192684	−	0.999814i	$-0.493866\pi$
$684$	−3.02125	−	29.8483i	−0.115521	−	1.14128i
$685$		0			0
$686$	−9.29847	−	25.5473i	−0.355017	−	0.975402i
$687$	2.74699	+	19.8221i	0.104804	+	0.756261i
$688$	3.60962	+	0.315801i	0.137616	+	0.0120398i
$689$	3.25978	−	2.73528i	0.124188	−	0.104206i
$690$		0			0
$691$	−0.280238	+	0.101998i	−0.0106608	+	0.00388020i	−0.347345	−	0.937737i	$-0.612917\pi$
$691$	−0.280238	+	0.101998i	−0.0106608	+	0.00388020i	0.336684	+	0.941618i	$0.390695\pi$
$692$	−4.74753	+	17.7180i	−0.180474	+	0.673538i
$693$	32.8407	+	5.33090i	1.24751	+	0.202504i
$694$	7.35481	+	4.24630i	0.279185	+	0.161187i
$695$		0			0
$696$	25.5473	−	16.5209i	0.968367	−	0.626223i
$697$	25.3616	−	11.8263i	0.960639	−	0.447953i
$698$	14.4660	+	10.1292i	0.547545	+	0.383395i
$699$	8.79867	+	9.47184i	0.332796	+	0.358258i
$700$		0			0
$701$			1.73681i			0.0655983i	0.999462	+	0.0327991i	$0.0104422\pi$
$701$			1.73681i			0.0655983i	−0.999462	+	0.0327991i	$0.989558\pi$
$702$	6.09537	+	0.676196i	0.230055	+	0.0255214i
$703$	−23.9965	−	23.9965i	−0.905046	−	0.905046i
$704$	3.65716	+	3.06872i	0.137835	+	0.115657i
$705$		0			0
$706$	3.99077	+	22.6328i	0.150195	+	0.851797i
$707$	−14.2261	−	30.5080i	−0.535028	−	1.14737i
$708$	8.50562	+	7.68814i	0.319661	+	0.288938i
$709$	28.4425	+	5.01519i	1.06818	+	0.188349i	0.679984	−	0.733227i	$-0.261987\pi$
$709$	28.4425	+	5.01519i	1.06818	+	0.188349i	0.388198	+	0.921576i	$0.373098\pi$
$710$		0			0
$711$	18.6767	+	4.73294i	0.700431	+	0.177499i
$712$	0.0575329	+	0.0154159i	0.00215614	+	0.000577735i
$713$	−7.02136	+	15.0574i	−0.262952	+	0.563902i
$714$	−4.35230	+	34.8923i	−0.162881	+	1.30581i
$715$		0			0
$716$	−3.64161	−	4.33991i	−0.136094	−	0.162190i
$717$	19.3979	−	47.7473i	0.724430	−	1.78315i
$718$	14.3521	+	6.69252i	0.535617	+	0.249762i
$719$	21.8672	+	37.8751i	0.815509	+	1.41250i	0.908962	+	0.416880i	$0.136876\pi$
$719$	21.8672	+	37.8751i	0.815509	+	1.41250i	−0.0934526	+	0.995624i	$0.529790\pi$
$720$		0			0
$721$	−30.1593	+	52.2374i	−1.12319	+	1.94542i
$722$	−16.1153	+	11.2840i	−0.599749	+	0.419949i
$723$	9.10707	+	28.2130i	0.338696	+	1.04925i
$724$	7.16111	−	19.6750i	0.266141	−	0.731215i
$725$		0			0
$726$	1.51648	+	6.62664i	0.0562817	+	0.245938i
$727$	−36.4355	+	3.18769i	−1.35132	+	0.118225i	−0.739704	−	0.672932i	$-0.765035\pi$
$727$	−36.4355	+	3.18769i	−1.35132	+	0.118225i	−0.611613	+	0.791157i	$0.709479\pi$
$728$	13.5902	−	13.5902i	0.503687	−	0.503687i
$729$	−26.3435	−	5.91772i	−0.975686	−	0.219175i
$730$		0			0
$731$	12.4542	−	14.8424i	0.460637	−	0.548966i
$732$	3.05802	−	4.87300i	0.113028	−	0.180111i
$733$	3.41756	−	4.88078i	0.126231	−	0.180276i	−0.751062	−	0.660231i	$-0.770458\pi$
$733$	3.41756	−	4.88078i	0.126231	−	0.180276i	0.877293	+	0.479955i	$0.159347\pi$
$734$	5.77082	+	2.10041i	0.213005	+	0.0775274i
$735$		0			0
$736$	7.73142	−	43.8471i	0.284984	−	1.61623i
$737$	18.2563	−	4.89177i	0.672480	−	0.180191i
$738$	−9.65073	−	3.36455i	−0.355248	−	0.123851i
$739$	12.8145	−	7.39844i	0.471388	−	0.272156i	−0.245433	−	0.969414i	$-0.578930\pi$
$739$	12.8145	−	7.39844i	0.471388	−	0.272156i	0.716821	+	0.697258i	$0.245597\pi$
$740$		0			0
$741$	7.43590	+	17.6119i	0.273165	+	0.646989i
$742$	0.776647	−	8.87711i	0.0285116	−	0.325889i
$743$	−0.372968	+	4.26304i	−0.0136829	+	0.156396i	−0.999962	−	0.00868886i	$-0.997234\pi$
$743$	−0.372968	+	4.26304i	−0.0136829	+	0.156396i	0.986279	+	0.165085i	$0.0527898\pi$
$744$	9.46384	+	1.18048i	0.346961	+	0.0432784i
$745$		0			0
$746$	21.2030	−	12.2415i	0.776296	−	0.448194i
$747$	1.12708	+	1.89221i	0.0412377	+	0.0692323i
$748$	−20.0669	+	5.37692i	−0.733720	+	0.196600i
$749$	1.76787	−	10.0261i	0.0645966	−	0.366346i
$750$		0			0
$751$	19.0790	+	6.94420i	0.696204	+	0.253397i	0.665789	−	0.746140i	$-0.268095\pi$
$751$	19.0790	+	6.94420i	0.696204	+	0.253397i	0.0304146	+	0.999537i	$0.490317\pi$
$752$	6.25068	−	8.92689i	0.227939	−	0.325530i
$753$	7.97182	+	15.0626i	0.290509	+	0.548910i
$754$	−5.28512	+	6.29857i	−0.192473	+	0.229380i
$755$		0			0
$756$	−28.0187	+	22.4229i	−1.01903	+	0.815514i
$757$	−25.0622	+	25.0622i	−0.910900	+	0.910900i	−0.996343	−	0.0854434i	$-0.972769\pi$
$757$	−25.0622	+	25.0622i	−0.910900	+	0.910900i	0.0854434	+	0.996343i	$0.472769\pi$
$758$	−3.49368	+	0.305657i	−0.126896	+	0.0111020i
$759$	−22.8339	+	21.2111i	−0.828819	+	0.769914i
$760$		0			0
$761$	−11.5003	+	31.5969i	−0.416887	+	1.14539i	0.536570	+	0.843856i	$0.319720\pi$
$761$	−11.5003	+	31.5969i	−0.416887	+	1.14539i	−0.953456	+	0.301531i	$0.902502\pi$
$762$	−4.81329	−	1.03277i	−0.174367	−	0.0374132i
$763$	32.7029	−	22.8988i	1.18393	−	0.828994i
$764$	−18.8010	+	32.5643i	−0.680196	+	1.17813i
$765$		0			0
$766$	−9.00671	−	15.6001i	−0.325426	−	0.563654i
$767$	−6.62148	−	3.08765i	−0.239088	−	0.111488i
$768$	−19.6802	+	2.72732i	−0.710149	+	0.0984138i
$769$	−0.789841	−	0.941295i	−0.0284824	−	0.0339440i	0.751615	−	0.659602i	$-0.229275\pi$
$769$	−0.789841	−	0.941295i	−0.0284824	−	0.0339440i	−0.780098	+	0.625658i	$0.784831\pi$
$770$		0			0
$771$	−0.105535	−	0.0798448i	−0.00380075	−	0.00287554i
$772$	−4.12145	+	8.83848i	−0.148334	+	0.318104i
$773$	2.83607	+	0.759923i	0.102006	+	0.0273325i	0.309461	−	0.950912i	$-0.399851\pi$
$773$	2.83607	+	0.759923i	0.102006	+	0.0273325i	−0.207455	+	0.978245i	$0.566518\pi$
$774$	−7.04050	+	0.712642i	−0.253066	+	0.0256154i
$775$		0			0
$776$	−7.67293	−	1.35294i	−0.275442	−	0.0485679i
$777$	−8.51622	+	39.6905i	−0.305518	+	1.42389i
$778$	−11.7387	−	25.1738i	−0.420854	−	0.902524i
$779$	−5.53234	−	31.3755i	−0.198217	−	1.12414i
$780$		0			0
$781$	1.88123	+	1.57854i	0.0673159	+	0.0564847i
$782$	−23.2907	−	23.2907i	−0.832875	−	0.832875i
$783$	26.1838	−	24.9953i	0.935734	−	0.893261i
$784$			16.7132i			0.596899i
$785$		0			0
$786$	−0.665130	+	2.16068i	−0.0237244	+	0.0770690i
$787$	37.4623	+	26.2314i	1.33539	+	0.935048i	0.999975	−	0.00702395i	$-0.00223581\pi$
$787$	37.4623	+	26.2314i	1.33539	+	0.935048i	0.335411	+	0.942072i	$0.391125\pi$
$788$	−26.4317	+	12.3253i	−0.941591	+	0.439071i
$789$	1.17468	+	23.2697i	0.0418199	+	0.828425i
$790$		0			0
$791$	−68.1573	−	39.3506i	−2.42339	−	1.39915i
$792$	15.6140	+	8.73357i	0.554818	+	0.310334i
$793$	−0.948830	+	3.54108i	−0.0336940	+	0.125748i
$794$	14.6051	−	5.31582i	0.518316	−	0.188651i
$795$		0			0
$796$	1.48838	−	1.24890i	0.0527541	−	0.0442660i
$797$	23.9126	+	2.09208i	0.847027	+	0.0741053i	0.502401	−	0.864635i	$-0.332450\pi$
$797$	23.9126	+	2.09208i	0.847027	+	0.0741053i	0.344626	+	0.938740i	$0.388006\pi$
$798$	37.0892	+	15.0680i	1.31294	+	0.533401i
$799$	−19.9306	−	54.7588i	−0.705093	−	1.93723i
$800$		0			0
$801$	0.0706766	+	0.00521520i	0.00249724	+	0.000184270i
$802$	6.58524	+	24.5765i	0.232533	+	0.867825i
$803$	5.19786	+	7.42331i	0.183428	+	0.261963i
$804$	−9.29011	+	18.1466i	−0.327637	+	0.639980i
$805$		0			0
$806$	−2.53832	+	0.447574i	−0.0894085	+	0.0157651i
$807$	−28.0082	−	17.5764i	−0.985935	−	0.618718i
$808$	−1.57760	−	18.0321i	−0.0554999	−	0.634367i
$809$	6.88614			0.242104			0.121052	−	0.992646i	$-0.461373\pi$
$809$	6.88614			0.242104			0.121052	+	0.992646i	$0.461373\pi$
$810$		0			0
$811$	51.9012			1.82250			0.911248	−	0.411858i	$-0.135120\pi$
$811$	51.9012			1.82250			0.911248	+	0.411858i	$0.135120\pi$
$812$	−4.19332	−	47.9298i	−0.147157	−	1.68201i
$813$	−23.6314	−	14.8298i	−0.828790	−	0.520103i
$814$	8.45252	−	1.49041i	0.296261	−	0.0522388i
$815$		0			0
$816$	5.24939	−	10.2538i	0.183766	−	0.358953i
$817$	−12.6526	−	18.0698i	−0.442658	−	0.632181i
$818$	−5.95679	−	22.2310i	−0.208274	−	0.777290i
$819$	12.8603	−	18.9090i	0.449374	−	0.660733i
$820$		0			0
$821$	1.56336	+	4.29529i	0.0545616	+	0.149907i	0.963979	−	0.265977i	$-0.0856946\pi$
$821$	1.56336	+	4.29529i	0.0545616	+	0.149907i	−0.909418	+	0.415884i	$0.863472\pi$
$822$	−20.7350	−	8.42386i	−0.723216	−	0.293816i
$823$	−8.86506	−	0.775592i	−0.309016	−	0.0270354i	−0.0684071	−	0.997657i	$-0.521792\pi$
$823$	−8.86506	−	0.775592i	−0.309016	−	0.0270354i	−0.240609	+	0.970622i	$0.577347\pi$
$824$	−24.8467	+	20.8488i	−0.865575	+	0.726304i
$825$		0			0
$826$	−14.3767	+	5.23268i	−0.500228	+	0.182068i
$827$	−1.00408	+	3.74729i	−0.0349154	+	0.130306i	−0.981184	−	0.193077i	$-0.938153\pi$
$827$	−1.00408	+	3.74729i	−0.0349154	+	0.130306i	0.946268	+	0.323383i	$0.104820\pi$
$828$	−0.457510	−	33.6129i	−0.0158996	−	1.16813i
$829$	23.2961	+	13.4500i	0.809106	+	0.467138i	0.846645	−	0.532157i	$-0.178619\pi$
$829$	23.2961	+	13.4500i	0.809106	+	0.467138i	−0.0375391	+	0.999295i	$0.511952\pi$
$830$		0			0
$831$	0.641081	+	12.6994i	0.0222389	+	0.440537i
$832$	2.97393	−	1.38677i	0.103102	−	0.0480774i
$833$	73.2075	+	51.2604i	2.53649	+	1.77607i
$834$	−4.02525	+	13.0761i	−0.139383	+	0.452787i
$835$		0			0
$836$			23.6524i			0.818035i
$837$	11.3243	−	0.726300i	0.391425	−	0.0251046i
$838$	−14.5470	−	14.5470i	−0.502518	−	0.502518i
$839$	−19.6667	−	16.5023i	−0.678970	−	0.569724i	0.236735	−	0.971574i	$-0.423923\pi$
$839$	−19.6667	−	16.5023i	−0.678970	−	0.569724i	−0.915705	+	0.401850i	$0.868367\pi$
$840$		0			0
$841$	3.39167	+	19.2351i	0.116954	+	0.663280i
$842$	−2.34112	−	5.02054i	−0.0806802	−	0.173019i
$843$	−5.87131	+	27.3637i	−0.202219	+	0.942455i
$844$	−15.7488	−	2.77695i	−0.542097	−	0.0955864i
$845$		0			0
$846$	−8.73129	+	19.4097i	−0.300188	+	0.667319i
$847$	24.4844	+	6.56058i	0.841295	+	0.225424i
$848$	−1.23374	+	2.64576i	−0.0423667	+	0.0908557i
$849$	14.5966	+	11.0434i	0.500956	+	0.379009i
$850$		0			0
$851$	−24.4424	−	29.1294i	−0.837876	−	0.998542i
$852$	−2.62379	+	0.363610i	−0.0898895	+	0.0124571i
$853$	4.64633	+	2.16662i	0.159087	+	0.0741837i	0.500531	−	0.865719i	$-0.333138\pi$
$853$	4.64633	+	2.16662i	0.159087	+	0.0741837i	−0.341444	+	0.939902i	$0.610916\pi$
$854$	3.83845	+	6.64838i	0.131349	+	0.227503i
$855$		0			0
$856$	2.73725	−	4.74105i	0.0935572	−	0.162046i
$857$	−0.315828	+	0.221145i	−0.0107885	+	0.00755418i	−0.578958	−	0.815357i	$-0.696541\pi$
$857$	−0.315828	+	0.221145i	−0.0107885	+	0.00755418i	0.568170	+	0.822911i	$0.307652\pi$
$858$	−4.72742	−	1.01434i	−0.161392	−	0.0346291i
$859$	14.9871	−	41.1768i	0.511354	−	1.40493i	−0.368472	−	0.929639i	$-0.620119\pi$
$859$	14.9871	−	41.1768i	0.511354	−	1.40493i	0.879826	−	0.475295i	$-0.157659\pi$
$860$		0			0
$861$	−27.9216	+	25.9372i	−0.951566	+	0.883937i
$862$	15.0381	−	1.31566i	0.512200	−	0.0448117i
$863$	1.22824	−	1.22824i	0.0418098	−	0.0418098i	−0.685893	−	0.727703i	$-0.740588\pi$
$863$	1.22824	−	1.22824i	0.0418098	−	0.0418098i	0.727703	+	0.685893i	$0.240588\pi$
$864$	−28.8100	+	9.73468i	−0.980136	+	0.331180i
$865$		0			0
$866$	−5.18102	+	6.17450i	−0.176058	+	0.209818i
$867$	−15.0400	−	28.4178i	−0.510786	−	0.965118i
$868$	8.65089	−	12.3547i	0.293630	−	0.419347i
$869$	−14.2739	−	5.19529i	−0.484210	−	0.176238i
$870$		0			0
$871$	2.25582	−	12.7934i	0.0764355	−	0.433487i
$872$	20.7362	−	5.55626i	0.702217	−	0.188159i
$873$	−9.26941	+	0.126167i	−0.313722	+	0.00427011i
$874$	−32.4763	+	18.7502i	−1.09853	+	0.634236i
$875$		0			0
$876$	−9.69954	−	1.20988i	−0.327717	−	0.0408779i
$877$	2.25649	−	25.7918i	0.0761961	−	0.870926i	−0.857880	−	0.513851i	$-0.828218\pi$
$877$	2.25649	−	25.7918i	0.0761961	−	0.870926i	0.934076	−	0.357075i	$-0.116226\pi$
$878$	−0.582372	+	6.65655i	−0.0196541	+	0.224648i
$879$	6.34773	+	15.0346i	0.214104	+	0.507103i
$880$		0			0
$881$	−9.98167	+	5.76292i	−0.336291	+	0.194158i	−0.658631	−	0.752466i	$-0.728864\pi$
$881$	−9.98167	+	5.76292i	−0.336291	+	0.194158i	0.322340	+	0.946624i	$0.395531\pi$
$882$	−6.10494	−	32.0646i	−0.205564	−	1.07967i
$883$	35.3038	−	9.45962i	1.18807	−	0.318342i	0.389945	−	0.920838i	$-0.372494\pi$
$883$	35.3038	−	9.45962i	1.18807	−	0.318342i	0.798122	+	0.602496i	$0.205827\pi$
$884$	−2.47954	+	14.0622i	−0.0833961	+	0.472963i
$885$		0			0
$886$	1.05904	+	0.385458i	0.0355790	+	0.0129497i
$887$	14.4052	−	20.5727i	0.483678	−	0.690763i	−0.500941	−	0.865482i	$-0.667013\pi$
$887$	14.4052	−	20.5727i	0.483678	−	0.690763i	0.984618	+	0.174718i	$0.0559014\pi$
$888$	−11.6029	+	18.4894i	−0.389368	+	0.620463i
$889$	−11.7992	+	14.0617i	−0.395731	+	0.471614i
$890$		0			0
$891$	20.1936	+	6.73332i	0.676511	+	0.225575i
$892$	23.8865	−	23.8865i	0.799778	−	0.799778i
$893$	−66.0922	+	5.78232i	−2.21169	+	0.193498i
$894$	0.772911	+	3.37744i	0.0258500	+	0.112959i
$895$		0			0
$896$	−16.4211	+	45.1166i	−0.548591	+	1.50724i
$897$	6.58031	+	20.3853i	0.219710	+	0.680646i
$898$	−1.97622	+	1.38376i	−0.0659473	+	0.0461768i
$899$	−7.60684	+	13.1754i	−0.253702	+	0.439425i
$900$		0			0
$901$	7.80507	+	13.5188i	0.260024	+	0.450376i
$902$	7.30275	+	3.40533i	0.243155	+	0.113385i
$903$	−9.93163	+	24.4463i	−0.330504	+	0.813522i
$904$	−27.2027	−	32.4190i	−0.904750	−	1.07824i
$905$		0			0
$906$	−1.98757	+	15.9342i	−0.0660324	+	0.529380i
$907$	−0.996748	+	2.13753i	−0.0330965	+	0.0709756i	−0.922161	−	0.386806i	$-0.873578\pi$
$907$	−0.996748	+	2.13753i	−0.0330965	+	0.0709756i	0.889064	+	0.457782i	$0.151356\pi$
$908$	15.2670	+	4.09079i	0.506655	+	0.135758i
$909$	−5.85679	−	20.7253i	−0.194257	−	0.687415i
$910$		0			0
$911$	−28.9448	−	5.10374i	−0.958983	−	0.169095i	−0.327816	−	0.944742i	$-0.606313\pi$
$911$	−28.9448	−	5.10374i	−0.958983	−	0.169095i	−0.631167	+	0.775647i	$0.717424\pi$
$912$	−9.72942	−	8.79432i	−0.322173	−	0.291209i
$913$	−0.733830	−	1.57370i	−0.0242862	−	0.0520820i
$914$	−2.17293	−	12.3233i	−0.0718743	−	0.407619i
$915$		0			0
$916$	13.0361	+	10.9386i	0.430725	+	0.361421i
$917$	5.96079	+	5.96079i	0.196843	+	0.196843i
$918$	−6.32562	+	21.5896i	−0.208777	+	0.712562i
$919$			44.6781i			1.47380i	0.676004	+	0.736898i	$0.263710\pi$
$919$			44.6781i			1.47380i	−0.676004	+	0.736898i	$0.736290\pi$
$920$		0			0
$921$	−31.8470	−	34.2836i	−1.04939	−	1.12968i
$922$	7.76892	+	5.43986i	0.255856	+	0.179152i
$923$	1.52978	−	0.713349i	0.0503533	−	0.0234802i
$924$	23.7577	−	15.3636i	0.781572	−	0.505426i
$925$		0			0
$926$	0.855408	+	0.493870i	0.0281105	+	0.0162296i
$927$	−24.4018	+	29.8981i	−0.801460	+	0.981981i
$928$	10.5523	−	39.3817i	0.346396	−	1.29277i
$929$	−12.8079	+	4.66169i	−0.420213	+	0.152945i	−0.543468	−	0.839430i	$-0.682889\pi$
$929$	−12.8079	+	4.66169i	−0.420213	+	0.152945i	0.123255	+	0.992375i	$0.460667\pi$
$930$		0			0
$931$	77.9440	−	65.4028i	2.55451	−	2.14349i
$932$	10.9518	+	0.958162i	0.358740	+	0.0313856i
$933$	2.15354	+	15.5398i	0.0705036	+	0.508750i
$934$	−0.0303201	−	0.0833037i	−0.000992103	−	0.00272578i
$935$		0			0
$936$	9.97593	−	7.18952i	0.326073	−	0.234997i
$937$	3.40972	+	12.7253i	0.111391	+	0.415716i	0.998992	−	0.0448974i	$-0.0142961\pi$
$937$	3.40972	+	12.7253i	0.111391	+	0.415716i	−0.887601	+	0.460613i	$0.847629\pi$
$938$	−15.6034	−	22.2839i	−0.509468	−	0.727596i
$939$	−9.54243	−	14.7561i	−0.311406	−	0.481546i
$940$		0			0
$941$	28.4137	−	5.01010i	0.926260	−	0.163325i	0.309882	−	0.950775i	$-0.399710\pi$
$941$	28.4137	−	5.01010i	0.926260	−	0.163325i	0.616378	+	0.787450i	$0.288599\pi$
$942$	0.436370	−	11.8435i	0.0142177	−	0.385882i
$943$	−3.11135	−	35.5629i	−0.101320	−	1.15809i
$944$	5.01209			0.163130
$945$		0			0
$946$	5.57904			0.181390
$947$	3.99548	+	45.6685i	0.129835	+	1.48403i	0.729613	+	0.683860i	$0.239700\pi$
$947$	3.99548	+	45.6685i	0.129835	+	1.48403i	−0.599778	+	0.800167i	$0.704744\pi$
$948$	14.4813	−	7.66417i	0.470329	−	0.248921i
$949$	6.13407	−	1.08160i	0.199120	−	0.0351103i
$950$		0			0
$951$	−11.9369	+	0.602589i	−0.387080	+	0.0195403i
$952$	40.4394	+	57.7535i	1.31065	+	1.87180i
$953$	−4.08629	−	15.2502i	−0.132368	−	0.494003i	0.867627	−	0.497216i	$-0.165644\pi$
$953$	−4.08629	−	15.2502i	−0.132368	−	0.494003i	−0.999995	+	0.00321227i	$0.998978\pi$
$954$	1.40052	−	5.52661i	0.0453435	−	0.178930i
$955$		0			0
$956$	−14.9894	−	41.1831i	−0.484793	−	1.33196i
$957$	−22.5227	+	17.5271i	−0.728056	+	0.566570i
$958$	18.9239	+	1.65563i	0.611404	+	0.0534909i
$959$	−63.9290	+	53.6428i	−2.06438	+	1.73222i
$960$		0			0
$961$	24.6489	−	8.97148i	0.795127	−	0.289402i
$962$	1.52685	−	5.69827i	0.0492275	−	0.183720i
$963$	2.14430	−	6.15061i	0.0690991	−	0.198201i
$964$	21.8332	+	12.6054i	0.703199	+	0.405992i
$965$		0			0
$966$	39.9290	+	20.4416i	1.28469	+	0.657697i
$967$	8.41873	−	3.92572i	0.270728	−	0.126243i	−0.282514	−	0.959263i	$-0.591168\pi$
$967$	8.41873	−	3.92572i	0.270728	−	0.126243i	0.553242	+	0.833021i	$0.313391\pi$
$968$	11.1654	+	7.81810i	0.358869	+	0.251283i
$969$	−68.3620	+	15.6443i	−2.19610	+	0.502567i
$970$		0			0
$971$			46.4051i			1.48921i	0.667506	+	0.744605i	$0.267362\pi$
$971$			46.4051i			1.48921i	−0.667506	+	0.744605i	$0.732638\pi$
$972$	−19.9935	+	11.2886i	−0.641293	+	0.362081i
$973$	36.0737	+	36.0737i	1.15647	+	1.15647i
$974$	−7.20866	−	6.04879i	−0.230981	−	0.193816i
$975$		0			0
$976$	−0.436719	−	2.47676i	−0.0139790	−	0.0792791i
$977$	18.6354	+	39.9638i	0.596201	+	1.27856i	0.940531	+	0.339708i	$0.110328\pi$
$977$	18.6354	+	39.9638i	0.596201	+	1.27856i	−0.344330	+	0.938849i	$0.611894\pi$
$978$	24.5996	−	7.94066i	0.786607	−	0.253914i
$979$	−0.0550236	−	0.00970214i	−0.00175856	−	0.000310082i
$980$		0			0
$981$	23.0006	−	11.1089i	0.734352	−	0.354681i
$982$	17.2841	+	4.63127i	0.551559	+	0.147790i
$983$	−7.78065	+	16.6857i	−0.248164	+	0.532190i	−0.990447	−	0.137897i	$-0.955966\pi$
$983$	−7.78065	+	16.6857i	−0.248164	+	0.532190i	0.742282	+	0.670087i	$0.233743\pi$
$984$	−18.8790	+	7.97089i	−0.601841	+	0.254103i
$985$		0			0
$986$	−19.3877	−	23.1054i	−0.617431	−	0.735826i
$987$	48.7389	+	62.6306i	1.55137	+	1.99355i
$988$	14.7338	+	6.87049i	0.468745	+	0.218580i
$989$	−12.3587	−	21.4059i	−0.392983	−	0.680667i
$990$		0			0
$991$	15.5919	−	27.0059i	0.495292	−	0.857871i	−0.504693	−	0.863299i	$-0.668394\pi$
$991$	15.5919	−	27.0059i	0.495292	−	0.857871i	0.999985	+	0.00542792i	$0.00172777\pi$
$992$	10.4694	−	7.33077i	0.332404	−	0.232752i
$993$	−13.5517	+	14.9927i	−0.430052	+	0.475779i
$994$	1.20892	−	3.32149i	0.0383447	−	0.105351i
$995$		0			0
$996$	1.79002	+	0.551028i	0.0567190	+	0.0174600i
$997$	−32.7231	+	2.86290i	−1.03635	+	0.0906689i	−0.592612	−	0.805488i	$-0.701903\pi$
$997$	−32.7231	+	2.86290i	−1.03635	+	0.0906689i	−0.443738	+	0.896157i	$0.646348\pi$
$998$	−3.63463	+	3.63463i	−0.115052	+	0.115052i
$999$	−9.44718	+	24.1930i	−0.298896	+	0.765432i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	675.2.ba.c.443.15	yes	288
5.2	odd	4	inner	675.2.ba.c.632.10	yes	288
5.3	odd	4	inner	675.2.ba.c.632.15	yes	288
5.4	even	2	inner	675.2.ba.c.443.10	yes	288
27.5	odd	18	inner	675.2.ba.c.518.10	yes	288
135.32	even	36	inner	675.2.ba.c.32.15	yes	288
135.59	odd	18	inner	675.2.ba.c.518.15	yes	288
135.113	even	36	inner	675.2.ba.c.32.10	✓	288

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
675.2.ba.c.32.10	✓	288	135.113	even	36	inner
675.2.ba.c.32.15	yes	288	135.32	even	36	inner
675.2.ba.c.443.10	yes	288	5.4	even	2	inner
675.2.ba.c.443.15	yes	288	1.1	even	1	trivial
675.2.ba.c.518.10	yes	288	27.5	odd	18	inner
675.2.ba.c.518.15	yes	288	135.59	odd	18	inner
675.2.ba.c.632.10	yes	288	5.2	odd	4	inner
675.2.ba.c.632.15	yes	288	5.3	odd	4	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:	\( N \)	\(=\)	\( 675 = 3^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	675.ba (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0632765 + 0.723253i) q^{2} +(1.46710 + 0.920668i) q^{3} +(1.45052 - 0.255767i) q^{4} +(-0.573043 + 1.11934i) q^{6} +(2.68947 + 3.84096i) q^{7} +(0.652582 + 2.43547i) q^{8} +(1.30474 + 2.70142i) q^{9} +(-0.808938 - 2.22254i) q^{11} +(2.36353 + 0.960217i) q^{12} +(-1.61947 - 0.141685i) q^{13} +(-2.60780 + 2.18821i) q^{14} +(1.04798 - 0.381434i) q^{16} +(1.54346 - 5.76028i) q^{17} +(-1.87125 + 1.11459i) q^{18} +(-5.87988 - 3.39475i) q^{19} +(0.409461 + 8.11116i) q^{21} +(1.55627 - 0.725702i) q^{22} +(-6.23184 - 4.36358i) q^{23} +(-1.28486 + 4.17388i) q^{24} -1.18025i q^{26} +(-0.572926 + 5.16447i) q^{27} +(4.88352 + 4.88352i) q^{28} +(-5.33663 - 4.47797i) q^{29} +(-0.379220 - 2.15066i) q^{31} +(2.47335 + 5.30412i) q^{32} +(0.859430 - 4.00544i) q^{33} +(4.26381 + 0.751824i) q^{34} +(2.58349 + 3.58476i) q^{36} +(4.82802 + 1.29366i) q^{37} +(2.08321 - 4.46745i) q^{38} +(-2.24547 - 1.69886i) q^{39} +(3.01626 + 3.59464i) q^{41} +(-5.84051 + 0.809389i) q^{42} +(2.94459 + 1.37309i) q^{43} +(-1.74184 - 3.01695i) q^{44} +(2.76165 - 4.78331i) q^{46} +(8.00447 - 5.60479i) q^{47} +(1.88866 + 0.405242i) q^{48} +(-5.12557 + 14.0824i) q^{49} +(7.56772 - 7.02987i) q^{51} +(-2.38532 + 0.208688i) q^{52} +(-1.85094 + 1.85094i) q^{53} +(-3.77147 - 0.0875810i) q^{54} +(-7.59943 + 9.05665i) q^{56} +(-5.50091 - 10.3938i) q^{57} +(2.90102 - 4.14309i) q^{58} +(4.22316 + 1.53710i) q^{59} +(0.391593 - 2.22083i) q^{61} +(1.53148 - 0.410358i) q^{62} +(-6.86696 + 12.2768i) q^{63} +(-1.74806 + 1.00925i) q^{64} +(2.95133 + 0.368136i) q^{66} +(-0.696469 + 7.96068i) q^{67} +(0.765543 - 8.75020i) q^{68} +(-5.12530 - 12.1393i) q^{69} +(-0.899200 + 0.519153i) q^{71} +(-5.72776 + 4.94055i) q^{72} +(-3.70095 + 0.991667i) q^{73} +(-0.630146 + 3.57374i) q^{74} +(-9.39718 - 3.42029i) q^{76} +(6.36106 - 9.08454i) q^{77} +(1.08662 - 1.73154i) q^{78} +(4.12821 - 4.91981i) q^{79} +(-5.59530 + 7.04930i) q^{81} +(-2.40897 + 2.40897i) q^{82} +(0.731354 - 0.0639852i) q^{83} +(2.66850 + 11.6607i) q^{84} +(-0.806766 + 2.21657i) q^{86} +(-3.70663 - 11.4829i) q^{87} +(4.88502 - 3.42053i) q^{88} +(0.0118115 - 0.0204581i) q^{89} +(-3.81130 - 6.60136i) q^{91} +(-10.1555 - 4.73559i) q^{92} +(1.42369 - 3.50436i) q^{93} +(4.56018 + 5.43461i) q^{94} +(-1.25469 + 10.0588i) q^{96} +(-1.30593 + 2.80057i) q^{97} +(-10.5095 - 2.81600i) q^{98} +(4.94855 - 5.08512i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 288 q + 24 q^{6} + 36 q^{11} + 48 q^{21} - 192 q^{36} - 180 q^{41} - 60 q^{51} - 288 q^{56} + 72 q^{61} + 144 q^{71} + 216 q^{76} + 24 q^{81} - 36 q^{91} - 168 q^{96}+O(q^{100}) \) 288 * q + 24 * q^6 + 36 * q^11 + 48 * q^21 - 192 * q^36 - 180 * q^41 - 60 * q^51 - 288 * q^56 + 72 * q^61 + 144 * q^71 + 216 * q^76 + 24 * q^81 - 36 * q^91 - 168 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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