LMFDB - Embedded newform 675.2.ba.c.518.10

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			518.10
Character	$\chi$	$=$	675.518
Dual form			675.2.ba.c.632.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.723253 - 0.0632765i) q^{2} +(0.920668 + 1.46710i) q^{3} +(-1.45052 - 0.255767i) q^{4} +(-0.573043 - 1.11934i) q^{6} +(-3.84096 - 2.68947i) q^{7} +(2.43547 + 0.652582i) q^{8} +(-1.30474 + 2.70142i) q^{9} +(-0.808938 + 2.22254i) q^{11} +(-0.960217 - 2.36353i) q^{12} +(-0.141685 - 1.61947i) q^{13} +(2.60780 + 2.18821i) q^{14} +(1.04798 + 0.381434i) q^{16} +(5.76028 - 1.54346i) q^{17} +(1.11459 - 1.87125i) q^{18} +(5.87988 - 3.39475i) q^{19} +(0.409461 - 8.11116i) q^{21} +(0.725702 - 1.55627i) q^{22} +(-4.36358 - 6.23184i) q^{23} +(1.28486 + 4.17388i) q^{24} +1.18025i q^{26} +(-5.16447 + 0.572926i) q^{27} +(4.88352 + 4.88352i) q^{28} +(5.33663 - 4.47797i) q^{29} +(-0.379220 + 2.15066i) q^{31} +(-5.30412 - 2.47335i) q^{32} +(-4.00544 + 0.859430i) q^{33} +(-4.26381 + 0.751824i) q^{34} +(2.58349 - 3.58476i) q^{36} +(-1.29366 - 4.82802i) q^{37} +(-4.46745 + 2.08321i) q^{38} +(2.24547 - 1.69886i) q^{39} +(3.01626 - 3.59464i) q^{41} +(-0.809389 + 5.84051i) q^{42} +(1.37309 + 2.94459i) q^{43} +(1.74184 - 3.01695i) q^{44} +(2.76165 + 4.78331i) q^{46} +(5.60479 - 8.00447i) q^{47} +(0.405242 + 1.88866i) q^{48} +(5.12557 + 14.0824i) q^{49} +(7.56772 + 7.02987i) q^{51} +(-0.208688 + 2.38532i) q^{52} +(1.85094 - 1.85094i) q^{53} +(3.77147 - 0.0875810i) q^{54} +(-7.59943 - 9.05665i) q^{56} +(10.3938 + 5.50091i) q^{57} +(-4.14309 + 2.90102i) q^{58} +(-4.22316 + 1.53710i) q^{59} +(0.391593 + 2.22083i) q^{61} +(0.410358 - 1.53148i) q^{62} +(12.2768 - 6.86696i) q^{63} +(1.74806 + 1.00925i) q^{64} +(2.95133 - 0.368136i) q^{66} +(-7.96068 + 0.696469i) q^{67} +(-8.75020 + 0.765543i) q^{68} +(5.12530 - 12.1393i) q^{69} +(-0.899200 - 0.519153i) q^{71} +(-4.94055 + 5.72776i) q^{72} +(0.991667 - 3.70095i) q^{73} +(0.630146 + 3.57374i) q^{74} +(-9.39718 + 3.42029i) q^{76} +(9.08454 - 6.36106i) q^{77} +(-1.73154 + 1.08662i) q^{78} +(-4.12821 - 4.91981i) q^{79} +(-5.59530 - 7.04930i) q^{81} +(-2.40897 + 2.40897i) q^{82} +(-0.0639852 + 0.731354i) q^{83} +(-2.66850 + 11.6607i) q^{84} +(-0.806766 - 2.21657i) q^{86} +(11.4829 + 3.70663i) q^{87} +(-3.42053 + 4.88502i) q^{88} +(-0.0118115 - 0.0204581i) q^{89} +(-3.81130 + 6.60136i) q^{91} +(4.73559 + 10.1555i) q^{92} +(-3.50436 + 1.42369i) q^{93} +(-4.56018 + 5.43461i) q^{94} +(-1.25469 - 10.0588i) q^{96} +(-2.80057 + 1.30593i) q^{97} +(-2.81600 - 10.5095i) 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 $\left(\mathbb{Z}/675\mathbb{Z}\right)^\times$.

$n$	$326$	$352$
$\chi(n)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−0.723253	−	0.0632765i	−0.511417	−	0.0447432i	−0.171473	−	0.985189i	$-0.554853\pi$
$2$	−0.723253	−	0.0632765i	−0.511417	−	0.0447432i	−0.339944	+	0.940446i	$0.610408\pi$
$3$	0.920668	+	1.46710i	0.531548	+	0.847028i
$3$	0.920668	+	1.46710i	0.531548	+	0.847028i
$4$	−1.45052	−	0.255767i	−0.725262	−	0.127883i
$5$		0			0
$5$		0			0
$6$	−0.573043	−	1.11934i	−0.233944	−	0.456968i
$7$	−3.84096	−	2.68947i	−1.45175	−	1.01652i	−0.991693	−	0.128631i	$-0.958942\pi$
$7$	−3.84096	−	2.68947i	−1.45175	−	1.01652i	−0.460053	−	0.887892i	$-0.652169\pi$
$8$	2.43547	+	0.652582i	0.861068	+	0.230722i
$9$	−1.30474	+	2.70142i	−0.434914	+	0.900472i
$10$		0			0
$11$	−0.808938	+	2.22254i	−0.243904	+	0.670121i	0.755976	+	0.654600i	$0.227163\pi$
$11$	−0.808938	+	2.22254i	−0.243904	+	0.670121i	−0.999880	+	0.0155209i	$0.995059\pi$
$12$	−0.960217	−	2.36353i	−0.277191	−	0.682294i
$13$	−0.141685	−	1.61947i	−0.0392964	−	0.449160i	−0.990198	−	0.139668i	$-0.955397\pi$
$13$	−0.141685	−	1.61947i	−0.0392964	−	0.449160i	0.950902	−	0.309492i	$-0.100159\pi$
$14$	2.60780	+	2.18821i	0.696965	+	0.584823i
$15$		0			0
$16$	1.04798	+	0.381434i	0.261995	+	0.0953585i
$17$	5.76028	−	1.54346i	1.39707	−	0.374345i	0.519781	−	0.854300i	$-0.326014\pi$
$17$	5.76028	−	1.54346i	1.39707	−	0.374345i	0.877293	+	0.479955i	$0.159347\pi$
$18$	1.11459	−	1.87125i	0.262712	−	0.441058i
$19$	5.87988	−	3.39475i	1.34894	−	0.778810i	0.360839	−	0.932628i	$-0.382490\pi$
$19$	5.87988	−	3.39475i	1.34894	−	0.778810i	0.988099	+	0.153819i	$0.0491571\pi$
$20$		0			0
$21$	0.409461	−	8.11116i	0.0893517	−	1.77000i
$22$	0.725702	−	1.55627i	0.154720	−	0.331798i
$23$	−4.36358	−	6.23184i	−0.909870	−	1.29943i	−0.953815	−	0.300395i	$-0.902881\pi$
$23$	−4.36358	−	6.23184i	−0.909870	−	1.29943i	0.0439446	−	0.999034i	$-0.486007\pi$
$24$	1.28486	+	4.17388i	0.262270	+	0.851989i
$25$		0			0
$26$			1.18025i			0.231466i
$27$	−5.16447	+	0.572926i	−0.993903	+	0.110260i
$28$	4.88352	+	4.88352i	0.922899	+	0.922899i
$29$	5.33663	−	4.47797i	0.990988	−	0.831538i	0.00527757	−	0.999986i	$-0.498320\pi$
$29$	5.33663	−	4.47797i	0.990988	−	0.831538i	0.985710	+	0.168448i	$0.0538756\pi$
$30$		0			0
$31$	−0.379220	+	2.15066i	−0.0681099	+	0.386270i	0.931629	+	0.363411i	$0.118388\pi$
$31$	−0.379220	+	2.15066i	−0.0681099	+	0.386270i	−0.999739	+	0.0228591i	$0.992723\pi$
$32$	−5.30412	−	2.47335i	−0.937644	−	0.437231i
$33$	−4.00544	+	0.859430i	−0.697258	+	0.149608i
$34$	−4.26381	+	0.751824i	−0.731237	+	0.128937i
$35$		0			0
$36$	2.58349	−	3.58476i	0.430582	−	0.597460i
$37$	−1.29366	−	4.82802i	−0.212677	−	0.793721i	−0.986971	−	0.160896i	$-0.948562\pi$
$37$	−1.29366	−	4.82802i	−0.212677	−	0.793721i	0.774294	−	0.632825i	$-0.218105\pi$
$38$	−4.46745	+	2.08321i	−0.724717	+	0.337941i
$39$	2.24547	−	1.69886i	0.359563	−	0.272035i
$40$		0			0
$41$	3.01626	−	3.59464i	0.471060	−	0.561388i	−0.477236	−	0.878775i	$-0.658361\pi$
$41$	3.01626	−	3.59464i	0.471060	−	0.561388i	0.948296	+	0.317388i	$0.102806\pi$
$42$	−0.809389	+	5.84051i	−0.124891	+	0.901211i
$43$	1.37309	+	2.94459i	0.209394	+	0.449047i	0.982753	−	0.184921i	$-0.0592030\pi$
$43$	1.37309	+	2.94459i	0.209394	+	0.449047i	−0.773360	+	0.633968i	$0.781425\pi$
$44$	1.74184	−	3.01695i	0.262592	−	0.454822i
$45$		0			0
$46$	2.76165	+	4.78331i	0.407183	+	0.705261i
$47$	5.60479	−	8.00447i	0.817543	−	1.16757i	−0.165862	−	0.986149i	$-0.553041\pi$
$47$	5.60479	−	8.00447i	0.817543	−	1.16757i	0.983405	−	0.181423i	$-0.0580704\pi$
$48$	0.405242	+	1.88866i	0.0584917	+	0.272605i
$49$	5.12557	+	14.0824i	0.732225	+	2.01177i
$50$		0			0
$51$	7.56772	+	7.02987i	1.05969	+	0.984379i
$52$	−0.208688	+	2.38532i	−0.0289398	+	0.330784i
$53$	1.85094	−	1.85094i	0.254246	−	0.254246i	−0.568463	−	0.822709i	$-0.692462\pi$
$53$	1.85094	−	1.85094i	0.254246	−	0.254246i	0.822709	+	0.568463i	$0.192462\pi$
$54$	3.77147	−	0.0875810i	0.513232	−	0.0119183i
$55$		0			0
$56$	−7.59943	−	9.05665i	−1.01552	−	1.21025i
$57$	10.3938	+	5.50091i	1.37670	+	0.728614i
$58$	−4.14309	+	2.90102i	−0.544014	+	0.380923i
$59$	−4.22316	+	1.53710i	−0.549808	+	0.200114i	−0.601961	−	0.798525i	$-0.705614\pi$
$59$	−4.22316	+	1.53710i	−0.549808	+	0.200114i	0.0521532	+	0.998639i	$0.483392\pi$
$60$		0			0
$61$	0.391593	+	2.22083i	0.0501383	+	0.284348i	0.999560	−	0.0296548i	$-0.00944081\pi$
$61$	0.391593	+	2.22083i	0.0501383	+	0.284348i	−0.949422	+	0.314003i	$0.898330\pi$
$62$	0.410358	−	1.53148i	0.0521156	−	0.194498i
$63$	12.2768	−	6.86696i	1.54673	−	0.865156i
$64$	1.74806	+	1.00925i	0.218508	+	0.126156i
$65$		0			0
$66$	2.95133	−	0.368136i	0.363284	−	0.0453144i
$67$	−7.96068	+	0.696469i	−0.972552	+	0.0850873i	−0.562343	−	0.826904i	$-0.690100\pi$
$67$	−7.96068	+	0.696469i	−0.972552	+	0.0850873i	−0.410209	+	0.911992i	$0.634544\pi$
$68$	−8.75020	+	0.765543i	−1.06112	+	0.0928357i
$69$	5.12530	−	12.1393i	0.617014	−	1.46139i
$70$		0			0
$71$	−0.899200	−	0.519153i	−0.106715	−	0.0616121i	0.445692	−	0.895186i	$-0.352958\pi$
$71$	−0.899200	−	0.519153i	−0.106715	−	0.0616121i	−0.552408	+	0.833574i	$0.686291\pi$
$72$	−4.94055	+	5.72776i	−0.582249	+	0.675023i
$73$	0.991667	−	3.70095i	0.116066	−	0.433163i	−0.883299	−	0.468811i	$-0.844683\pi$
$73$	0.991667	−	3.70095i	0.116066	−	0.433163i	0.999364	+	0.0356473i	$0.0113493\pi$
$74$	0.630146	+	3.57374i	0.0732530	+	0.415439i
$75$		0			0
$76$	−9.39718	+	3.42029i	−1.07793	+	0.392334i
$77$	9.08454	−	6.36106i	1.03528	−	0.724911i
$78$	−1.73154	+	1.08662i	−0.196058	+	0.123035i
$79$	−4.12821	−	4.91981i	−0.464460	−	0.553522i	0.482072	−	0.876132i	$-0.339884\pi$
$79$	−4.12821	−	4.91981i	−0.464460	−	0.553522i	−0.946532	+	0.322610i	$0.895440\pi$
$80$		0			0
$81$	−5.59530	−	7.04930i	−0.621700	−	0.783256i
$82$	−2.40897	+	2.40897i	−0.266027	+	0.266027i
$83$	−0.0639852	+	0.731354i	−0.00702329	+	0.0802766i	−0.998897	−	0.0469467i	$-0.985051\pi$
$83$	−0.0639852	+	0.731354i	−0.00702329	+	0.0802766i	0.991874	+	0.127223i	$0.0406065\pi$
$84$	−2.66850	+	11.6607i	−0.291157	+	1.27229i
$85$		0			0
$86$	−0.806766	−	2.21657i	−0.0869958	−	0.239019i
$87$	11.4829	+	3.70663i	1.23109	+	0.397393i
$88$	−3.42053	+	4.88502i	−0.364630	+	0.520745i
$89$	−0.0118115	−	0.0204581i	−0.00125201	−	0.00216855i	0.865399	−	0.501084i	$-0.167065\pi$
$89$	−0.0118115	−	0.0204581i	−0.00125201	−	0.00216855i	−0.866651	+	0.498915i	$0.833732\pi$
$90$		0			0
$91$	−3.81130	+	6.60136i	−0.399533	+	0.692011i
$92$	4.73559	+	10.1555i	0.493719	+	1.05878i
$93$	−3.50436	+	1.42369i	−0.363386	+	0.147630i
$94$	−4.56018	+	5.43461i	−0.470346	+	0.560537i
$95$		0			0
$96$	−1.25469	−	10.0588i	−0.128056	−	1.02662i
$97$	−2.80057	+	1.30593i	−0.284355	+	0.132597i	−0.559563	−	0.828788i	$-0.689031\pi$
$97$	−2.80057	+	1.30593i	−0.284355	+	0.132597i	0.275208	+	0.961385i	$0.411253\pi$
$98$	−2.81600	−	10.5095i	−0.284459	−	1.06162i
$99$	−4.94855	−	5.08512i	−0.497348	−	0.511074i
$100$		0			0
$101$	−7.06992	+	1.24662i	−0.703484	+	0.124043i	−0.513936	−	0.857828i	$-0.671813\pi$
$101$	−7.06992	+	1.24662i	−0.703484	+	0.124043i	−0.189547	+	0.981872i	$0.560702\pi$
$102$	−5.02855	−	5.56324i	−0.497901	−	0.550842i
$103$	11.6587	+	5.43656i	1.14877	+	0.535680i	0.901291	−	0.433213i	$-0.142620\pi$
$103$	11.6587	+	5.43656i	1.14877	+	0.535680i	0.247478	+	0.968893i	$0.420398\pi$
$104$	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	0.777413	−	0.628991i	$-0.216532\pi$
$107$	1.53529	+	1.53529i	0.148422	+	0.148422i	−0.628991	+	0.777413i	$0.716532\pi$
$108$	7.63772	+	0.489856i	0.734940	+	0.0471364i
$109$		−	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
$112$	−2.99940	−	4.28358i	−0.283416	−	0.404761i
$113$	7.09341	−	15.2119i	0.667292	−	1.43101i	−0.222632	−	0.974902i	$-0.571465\pi$
$113$	7.09341	−	15.2119i	0.667292	−	1.43101i	0.889924	−	0.456109i	$-0.150757\pi$
$114$	−7.16931	−	4.63624i	−0.671467	−	0.434224i
$115$		0			0
$116$	−8.88623	+	5.13047i	−0.825066	+	0.476352i
$117$	4.55972	+	1.73024i	0.421546	+	0.159960i
$118$	3.15167	−	0.844488i	0.290135	−	0.0777415i
$119$	−26.2761	−	9.56371i	−2.40873	−	0.876704i
$120$		0			0
$121$	4.14119	+	3.47487i	0.376472	+	0.315897i
$122$	−0.142694	−	1.63100i	−0.0129189	−	0.147664i
$123$	8.05065	+	1.11567i	0.725902	+	0.100597i
$124$	1.10014	−	3.02260i	0.0987951	−	0.271437i
$125$		0			0
$126$	−9.31377	+	4.18972i	−0.829737	+	0.373250i
$127$	−3.78140	−	1.01322i	−0.335545	−	0.0899090i	0.0871125	−	0.996198i	$-0.472236\pi$
$127$	−3.78140	−	1.01322i	−0.335545	−	0.0899090i	−0.422658	+	0.906289i	$0.638903\pi$
$128$	8.38765	+	5.87310i	0.741371	+	0.519113i
$129$	−3.05585	+	4.72544i	−0.269052	+	0.416052i
$130$		0			0
$131$	1.77050	+	0.312187i	0.154689	+	0.0272759i	0.250456	−	0.968128i	$-0.419419\pi$
$131$	1.77050	+	0.312187i	0.154689	+	0.0272759i	−0.0957672	+	0.995404i	$0.530530\pi$
$132$	6.02980	−	0.222167i	0.524827	−	0.0193371i
$133$	−31.7145	−	2.77465i	−2.74999	−	0.240593i
$134$	5.80166			0.501187
$135$		0			0
$136$	15.0362			1.28935
$137$	−17.7302	−	1.55119i	−1.51479	−	0.132527i	−0.700781	−	0.713376i	$-0.747165\pi$
$137$	−17.7302	−	1.55119i	−1.51479	−	0.132527i	−0.814011	+	0.580849i	$0.802721\pi$
$138$	−4.47502	+	8.45544i	−0.380939	+	0.719775i
$139$	−10.7147	−	1.88930i	−0.908812	−	0.160248i	−0.300348	−	0.953830i	$-0.597103\pi$
$139$	−10.7147	−	1.88930i	−0.908812	−	0.160248i	−0.608464	+	0.793581i	$0.708214\pi$
$140$		0			0
$141$	16.9035	+	0.853308i	1.42353	+	0.0718615i
$142$	0.617499	+	0.432377i	0.0518194	+	0.0362843i
$143$	3.71394	+	0.995148i	0.310576	+	0.0832185i
$144$	−2.39776	+	2.33336i	−0.199813	+	0.194447i
$145$		0			0
$146$	−0.951409	+	2.61398i	−0.0787392	+	0.216334i
$147$	−15.9413	+	20.4849i	−1.31481	+	1.68957i
$148$	0.641645	+	7.33403i	0.0527429	+	0.602854i
$149$	−2.11066	−	1.77106i	−0.172912	−	0.145091i	0.552225	−	0.833695i	$-0.313779\pi$
$149$	−2.11066	−	1.77106i	−0.172912	−	0.145091i	−0.725137	+	0.688605i	$0.758224\pi$
$150$		0			0
$151$	11.9995	+	4.36746i	0.976505	+	0.355419i	0.780480	−	0.625180i	$-0.214975\pi$
$151$	11.9995	+	4.36746i	0.976505	+	0.355419i	0.196025	+	0.980599i	$0.437197\pi$
$152$	16.5356	−	4.43071i	1.34122	−	0.359378i
$153$	−3.34614	+	17.5747i	−0.270520	+	1.42083i
$154$	−6.97293	+	4.02582i	−0.561895	+	0.324410i
$155$		0			0
$156$	−3.69162	+	1.88992i	−0.295566	+	0.151315i
$157$	−3.98305	+	8.54167i	−0.317882	+	0.681700i	−0.998712	−	0.0507417i	$-0.983841\pi$
$157$	−3.98305	+	8.54167i	−0.317882	+	0.681700i	0.680830	+	0.732441i	$0.261619\pi$
$158$	2.67443	+	3.81949i	0.212767	+	0.303862i
$159$	4.41960	+	1.01140i	0.350497	+	0.0802095i
$160$		0			0
$161$			35.6720i			2.81134i
$162$	3.60076	+	5.45248i	0.282903	+	0.428387i
$163$	−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
$167$	9.71939	+	4.53222i	0.752109	+	0.350714i	0.760575	−	0.649250i	$-0.224917\pi$
$167$	9.71939	+	4.53222i	0.752109	+	0.350714i	−0.00846620	+	0.999964i	$0.502695\pi$
$168$	6.29042	−	19.4873i	0.485316	−	1.50347i
$169$	10.1999	−	1.79852i	0.784608	−	0.138348i
$170$		0			0
$171$	1.49891	+	20.3133i	0.114625	+	1.55340i
$172$	−1.23857	−	4.62240i	−0.0944399	−	0.352454i
$173$	11.2869	−	5.26315i	0.858125	−	0.400150i	0.0568042	−	0.998385i	$-0.481909\pi$
$173$	11.2869	−	5.26315i	0.858125	−	0.400150i	0.801321	+	0.598235i	$0.204131\pi$
$174$	−8.07048	−	3.40743i	−0.611822	−	0.258317i
$175$		0			0
$176$	−1.69550	+	2.02062i	−0.127803	+	0.152310i
$177$	−6.14320	−	4.78061i	−0.461751	−	0.359333i
$178$	0.00724817	+	0.0155437i	0.000543273	+	0.00116505i
$179$	1.92319	−	3.33107i	0.143746	−	0.248976i	−0.785158	−	0.619295i	$-0.787418\pi$
$179$	1.92319	−	3.33107i	0.143746	−	0.248976i	0.928904	+	0.370319i	$0.120752\pi$
$180$		0			0
$181$	7.10764	+	12.3108i	0.528307	+	0.915054i	0.999455	+	0.0330001i	$0.0105062\pi$
$181$	7.10764	+	12.3108i	0.528307	+	0.915054i	−0.471149	+	0.882054i	$0.656161\pi$
$182$	3.17424	−	4.53329i	0.235291	−	0.336030i
$183$	−2.89765	+	2.61915i	−0.214200	+	0.193613i
$184$	−6.56058	−	18.0250i	−0.483652	−	1.32882i
$185$		0			0
$186$	2.62463	−	0.807948i	0.192447	−	0.0592416i
$187$	−1.22931	+	14.0510i	−0.0898957	+	1.02751i
$188$	−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	−0.887330	−	0.461135i	$-0.847443\pi$
$191$	−16.4099	−	19.5565i	−1.18738	−	1.41506i	−0.300046	−	0.953925i	$-0.597002\pi$
$192$	0.128727	+	3.49376i	0.00929004	+	0.252140i
$193$	5.42367	−	3.79769i	0.390404	−	0.273364i	−0.361851	−	0.932236i	$-0.617855\pi$
$193$	5.42367	−	3.79769i	0.390404	−	0.273364i	0.752255	+	0.658872i	$0.228966\pi$
$194$	2.10816	−	0.767306i	0.151357	−	0.0550894i
$195$		0			0
$196$	−3.83296	−	21.7378i	−0.273783	−	1.55270i
$197$	−5.12475	+	19.1258i	−0.365123	+	1.36266i	0.502131	+	0.864792i	$0.332550\pi$
$197$	−5.12475	+	19.1258i	−0.365123	+	1.36266i	−0.867254	+	0.497866i	$0.834117\pi$
$198$	3.25729	+	3.99095i	0.231485	+	0.283625i
$199$	−1.14239	−	0.659562i	−0.0809822	−	0.0467551i	0.458962	−	0.888456i	$-0.348221\pi$
$199$	−1.14239	−	0.659562i	−0.0809822	−	0.0467551i	−0.539944	+	0.841701i	$0.681555\pi$
$200$		0			0
$201$	−8.35093	−	11.0379i	−0.589029	−	0.778551i
$202$	5.19223	−	0.454261i	0.365324	−	0.0319617i
$203$	−32.5411	+	2.84698i	−2.28394	+	0.199819i
$204$	−9.17915	−	12.1326i	−0.642669	−	0.849450i
$205$		0			0
$206$	−8.08822	−	4.66973i	−0.563533	−	0.325356i
$207$	22.5282	−	3.65691i	1.56581	−	0.254173i
$208$	0.469237	−	1.75122i	0.0325357	−	0.121425i
$209$	2.78851	+	15.8144i	0.192885	+	1.09391i
$210$		0			0
$211$	−10.2026	+	3.71343i	−0.702374	+	0.255643i	−0.668424	−	0.743780i	$-0.733031\pi$
$211$	−10.2026	+	3.71343i	−0.702374	+	0.255643i	−0.0339496	+	0.999424i	$0.510809\pi$
$212$	−3.15824	+	2.21142i	−0.216909	+	0.151881i
$213$	−0.0662166	−	1.79718i	−0.00453709	−	0.123141i
$214$	−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
$218$	−0.538753	+	6.15797i	−0.0364890	+	0.417071i
$219$	6.34264	−	1.95248i	0.428596	−	0.131936i
$220$		0			0
$221$	−3.31573	−	9.10991i	−0.223040	−	0.612799i
$222$	−4.66286	+	4.21471i	−0.312951	+	0.282873i
$223$	−13.1548	+	18.7870i	−0.880911	+	1.25807i	0.0842578	+	0.996444i	$0.473148\pi$
$223$	−13.1548	+	18.7870i	−0.880911	+	1.25807i	−0.965169	+	0.261627i	$0.915741\pi$
$224$	13.7209	+	23.7653i	0.916765	+	1.58788i
$225$		0			0
$226$	−6.09288	+	10.5532i	−0.405292	+	0.701987i
$227$	−4.53509	−	9.72553i	−0.301005	−	0.645506i	0.696389	−	0.717665i	$-0.254789\pi$
$227$	−4.53509	−	9.72553i	−0.301005	−	0.645506i	−0.997393	+	0.0721585i	$0.977011\pi$
$228$	−13.6696	−	10.6376i	−0.905290	−	0.704493i
$229$	−7.42656	+	8.85063i	−0.490761	+	0.584866i	−0.953411	−	0.301675i	$-0.902454\pi$
$229$	−7.42656	+	8.85063i	−0.490761	+	0.584866i	0.462650	+	0.886541i	$0.346899\pi$
$230$		0			0
$231$	17.6961	+	7.47147i	1.16432	+	0.491586i
$232$	15.9194	−	7.42336i	1.04516	−	0.487367i
$233$	1.93182	+	7.20963i	0.126557	+	0.472319i	0.999890	−	0.0148049i	$-0.00471272\pi$
$233$	1.93182	+	7.20963i	0.126557	+	0.472319i	−0.873333	+	0.487124i	$0.838046\pi$
$234$	−3.18835	−	1.53992i	−0.208429	−	0.100668i
$235$		0			0
$236$	6.51893	−	1.14946i	0.424346	−	0.0748237i
$237$	3.41712	−	10.5860i	0.221966	−	0.687634i
$238$	18.3991	+	8.57965i	1.19264	+	0.556136i
$239$	5.16690	−	29.3030i	0.334219	−	1.89545i	−0.100590	−	0.994928i	$-0.532073\pi$
$239$	5.16690	−	29.3030i	0.334219	−	1.89545i	0.434809	−	0.900523i	$-0.356816\pi$
$240$		0			0
$241$	13.1119	−	11.0022i	0.844614	−	0.708715i	−0.113983	−	0.993483i	$-0.536361\pi$
$241$	13.1119	−	11.0022i	0.844614	−	0.708715i	0.958597	+	0.284768i	$0.0919165\pi$
$242$	−2.77525	−	2.77525i	−0.178400	−	0.178400i
$243$	5.19059	−	14.6989i	0.332976	−	0.942935i
$244$		−	3.32153i		−	0.212639i
$245$		0			0
$246$	−5.75206	−	1.31633i	−0.366738	−	0.0839262i
$247$	−6.33078	−	9.04130i	−0.402818	−	0.575284i
$248$	−2.32706	+	4.99040i	−0.147768	+	0.316891i
$249$	−1.13188	+	0.579462i	−0.0717297	+	0.0367219i
$250$		0			0
$251$	8.52101	−	4.91961i	0.537841	−	0.310523i	−0.206362	−	0.978476i	$-0.566163\pi$
$251$	8.52101	−	4.91961i	0.537841	−	0.310523i	0.744204	+	0.667953i	$0.232829\pi$
$252$	−19.5642	+	6.82069i	−1.23243	+	0.429663i
$253$	17.3804	−	4.65706i	1.09270	−	0.292787i
$254$	2.67080	+	0.972091i	0.167581	+	0.0609944i
$255$		0			0
$256$	−8.78727	−	7.37340i	−0.549205	−	0.460837i
$257$	0.00665907	+	0.0761136i	0.000415382	+	0.00474783i	0.996400	−	0.0847816i	$-0.0270192\pi$
$257$	0.00665907	+	0.0761136i	0.000415382	+	0.00474783i	−0.995984	+	0.0895294i	$0.971464\pi$
$258$	2.50916	−	3.22433i	0.156213	−	0.200738i
$259$	−8.01589	+	22.0235i	−0.498083	+	1.36847i
$260$		0			0
$261$	5.13393	+	20.2591i	0.317782	+	1.25400i
$262$	−1.26076	−	0.337821i	−0.0778903	−	0.0208706i
$263$	11.0192	+	7.71569i	0.679470	+	0.475770i	0.861655	−	0.507494i	$-0.169428\pi$
$263$	11.0192	+	7.71569i	0.679470	+	0.475770i	−0.182185	+	0.983264i	$0.558317\pi$
$264$	−10.3160	−	0.520762i	−0.634904	−	0.0320507i
$265$		0			0
$266$	22.7620	+	4.01356i	1.39563	+	0.246087i
$267$	0.0191395	−	0.0361636i	0.00117132	−	0.00221318i
$268$	11.7253	+	1.02583i	0.716236	+	0.0626625i
$269$	19.0909			1.16399			0.581996	−	0.813191i	$-0.302272\pi$
$269$	19.0909			1.16399			0.581996	+	0.813191i	$0.302272\pi$
$270$		0			0
$271$	−16.1076			−0.978468			−0.489234	−	0.872153i	$-0.662724\pi$
$271$	−16.1076			−0.978468			−0.489234	+	0.872153i	$0.662724\pi$
$272$	6.62540	+	0.579647i	0.401724	+	0.0351463i
$273$	−13.1938	+	0.486121i	−0.798523	+	0.0294214i
$274$	12.7253	+	2.24381i	0.768761	+	0.135553i
$275$		0			0
$276$	−10.5392	+	16.2974i	−0.634385	+	0.980988i
$277$	−6.01367	−	4.21082i	−0.361327	−	0.253004i	0.378789	−	0.925483i	$-0.376341\pi$
$277$	−6.01367	−	4.21082i	−0.361327	−	0.253004i	−0.740116	+	0.672479i	$0.765229\pi$
$278$	7.62992	+	2.04443i	0.457612	+	0.122617i
$279$	−5.31505	−	3.83049i	−0.318204	−	0.229325i
$280$		0			0
$281$	5.52636	−	15.1836i	0.329675	−	0.905775i	−0.658518	−	0.752565i	$-0.728817\pi$
$281$	5.52636	−	15.1836i	0.329675	−	0.905775i	0.988194	−	0.153210i	$-0.0489612\pi$
$282$	−12.1715	−	1.68675i	−0.724802	−	0.100444i
$283$	0.921022	+	10.5273i	0.0547491	+	0.625785i	0.973156	+	0.230147i	$0.0739208\pi$
$283$	0.921022	+	10.5273i	0.0547491	+	0.625785i	−0.918407	+	0.395638i	$0.870524\pi$
$284$	1.17153	+	0.983029i	0.0695174	+	0.0583321i
$285$		0			0
$286$	−2.62315	−	0.954750i	−0.155110	−	0.0564555i
$287$	−21.2530	+	5.69471i	−1.25452	+	0.336148i
$288$	13.6020	−	11.1015i	0.801508	−	0.654165i
$289$	16.0762	−	9.28157i	0.945656	−	0.545975i
$290$		0			0
$291$	−4.49432	−	2.90638i	−0.263462	−	0.170375i
$292$	−2.38502	+	5.11468i	−0.139572	+	0.299314i
$293$	5.40433	+	7.71819i	0.315725	+	0.450901i	0.945379	−	0.325974i	$-0.105692\pi$
$293$	5.40433	+	7.71819i	0.315725	+	0.450901i	−0.629654	+	0.776876i	$0.716803\pi$
$294$	12.8258	−	13.8071i	0.748016	−	0.805245i
$295$		0			0
$296$		−	12.6027i		−	0.732517i
$297$	2.90439	−	11.9417i	0.168530	−	0.692928i
$298$	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
$302$	−8.40232	−	3.91806i	−0.483499	−	0.225459i
$303$	−8.33796	−	9.22453i	−0.479003	−	0.529936i
$304$	7.45688	−	1.31485i	0.427682	−	0.0754118i
$305$		0			0
$306$	3.53218	−	12.4993i	0.201921	−	0.714535i
$307$	6.99226	+	26.0955i	0.399069	+	1.48935i	0.814737	+	0.579830i	$0.196881\pi$
$307$	6.99226	+	26.0955i	0.399069	+	1.48935i	−0.415668	+	0.909516i	$0.636452\pi$
$308$	−14.8043	+	6.90336i	−0.843553	+	0.393355i
$309$	2.75787	+	22.1098i	0.156890	+	1.25778i
$310$		0			0
$311$	5.82215	−	6.93856i	0.330144	−	0.393450i	−0.575282	−	0.817955i	$-0.695108\pi$
$311$	5.82215	−	6.93856i	0.330144	−	0.393450i	0.905425	+	0.424505i	$0.139552\pi$
$312$	6.57741	−	2.67216i	0.372373	−	0.151281i
$313$	−4.28771	−	9.19503i	−0.242356	−	0.519734i	0.747075	−	0.664740i	$-0.231458\pi$
$313$	−4.28771	−	9.19503i	−0.242356	−	0.519734i	−0.989431	+	0.145006i	$0.953680\pi$
$314$	3.42124	−	5.92576i	0.193072	−	0.334410i
$315$		0			0
$316$	4.72975	+	8.19217i	0.266069	+	0.460845i
$317$	−3.95799	+	5.65260i	−0.222303	+	0.317481i	−0.914775	−	0.403963i	$-0.867632\pi$
$317$	−3.95799	+	5.65260i	−0.222303	+	0.317481i	0.692473	+	0.721444i	$0.256521\pi$
$318$	−3.13249	−	1.01116i	−0.175661	−	0.0567029i
$319$	5.63545	+	15.4833i	0.315525	+	0.866897i
$320$		0			0
$321$	−0.838926	+	3.66591i	−0.0468243	+	0.204611i
$322$	2.25720	−	25.7999i	0.125789	−	1.43777i
$323$	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
$327$	12.4913	−	7.83882i	0.690768	−	0.433487i
$328$	9.69179	−	6.78626i	0.535140	−	0.374709i
$329$	−43.0555	+	15.6709i	−2.37373	+	0.863966i
$330$		0			0
$331$	−2.02614	−	11.4908i	−0.111367	−	0.631591i	−0.988485	−	0.151318i	$-0.951648\pi$
$331$	−2.02614	−	11.4908i	−0.111367	−	0.631591i	0.877119	−	0.480274i	$-0.159463\pi$
$332$	0.279868	−	1.04448i	0.0153598	−	0.0573234i
$333$	14.7304	+	2.80459i	0.807220	+	0.153691i
$334$	−6.74280	−	3.89295i	−0.368949	−	0.213013i
$335$		0			0
$336$	3.52298	−	8.34416i	0.192194	−	0.455211i
$337$	2.36973	−	0.207325i	0.129087	−	0.0112937i	−0.0224289	−	0.999748i	$-0.507140\pi$
$337$	2.36973	−	0.207325i	0.129087	−	0.0112937i	0.151516	+	0.988455i	$0.451584\pi$
$338$	−7.49091	+	0.655370i	−0.407452	+	0.0356474i
$339$	28.8479	−	3.59836i	1.56680	−	0.195436i
$340$		0			0
$341$	−4.47317	−	2.58258i	−0.242236	−	0.139855i
$342$	0.201261	−	14.7865i	0.0108829	−	0.799562i
$343$	9.69193	−	36.1708i	0.523315	−	1.95304i
$344$	1.42252	+	8.06752i	0.0766972	+	0.434971i
$345$		0			0
$346$	−8.49630	+	3.09240i	−0.456764	+	0.166248i
$347$	9.58207	−	6.70944i	0.514392	−	0.360181i	−0.287375	−	0.957818i	$-0.592782\pi$
$347$	9.58207	−	6.70944i	0.514392	−	0.360181i	0.801767	+	0.597637i	$0.203894\pi$
$348$	−15.7082	−	8.31350i	−0.842046	−	0.445650i
$349$	−15.6352	−	18.6334i	−0.836935	−	0.997421i	−0.999942	−	0.0107955i	$-0.996564\pi$
$349$	−15.6352	−	18.6334i	−0.836935	−	0.997421i	0.163007	−	0.986625i	$-0.447881\pi$
$350$		0			0
$351$	1.65956	+	8.28252i	0.0885809	+	0.442088i
$352$	9.78782	−	9.78782i	0.521692	−	0.521692i
$353$	−2.75891	+	31.5344i	−0.146842	+	1.67841i	0.463366	+	0.886167i	$0.346641\pi$
$353$	−2.75891	+	31.5344i	−0.146842	+	1.67841i	−0.610208	+	0.792241i	$0.708914\pi$
$354$	4.14059	+	3.84631i	0.220070	+	0.204429i
$355$		0			0
$356$	0.0119003	+	0.0326959i	0.000630716	+	0.00173288i
$357$	−10.1607	−	47.3546i	−0.537759	−	2.50627i
$358$	−1.60173	+	2.28751i	−0.0846543	+	0.120899i
$359$	−10.9060	−	18.8897i	−0.575596	−	0.996962i	−0.995977	−	0.0896137i	$-0.971437\pi$
$359$	−10.9060	−	18.8897i	−0.575596	−	0.996962i	0.420381	−	0.907348i	$-0.361897\pi$
$360$		0			0
$361$	13.5487	−	23.4670i	0.713089	−	1.23511i
$362$	−4.36164	−	9.35357i	−0.229243	−	0.491612i
$363$	−1.28531	+	9.27472i	−0.0674612	+	0.486797i
$364$	7.21679	−	8.60063i	0.378262	−	0.450796i
$365$		0			0
$366$	2.26146	−	1.71096i	0.118209	−	0.0894332i
$367$	7.66622	−	3.57482i	0.400173	−	0.186604i	−0.212104	−	0.977247i	$-0.568031\pi$
$367$	7.66622	−	3.57482i	0.400173	−	0.186604i	0.612277	+	0.790643i	$0.290254\pi$
$368$	−2.19592	−	8.19528i	−0.114470	−	0.427208i
$369$	5.77517	+	12.8382i	0.300643	+	0.668332i
$370$		0			0
$371$	−12.0874	+	2.13133i	−0.627546	+	0.110653i
$372$	5.44730	−	1.16880i	0.282429	−	0.0605996i
$373$	−30.5630	−	14.2517i	−1.58249	−	0.737927i	−0.585158	−	0.810920i	$-0.698967\pi$
$373$	−30.5630	−	14.2517i	−1.58249	−	0.737927i	−0.997333	+	0.0729923i	$0.976745\pi$
$374$	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
$378$	−14.7216	−	9.80686i	−0.757198	−	0.504410i
$379$			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
$382$	10.6310	+	15.1827i	0.543930	+	0.776813i
$383$	10.4857	−	22.4867i	0.535795	−	1.14902i	−0.433055	−	0.901368i	$-0.642564\pi$
$383$	10.4857	−	22.4867i	0.535795	−	1.14902i	0.968850	−	0.247649i	$-0.0796579\pi$
$384$	−0.894156	+	17.7127i	−0.0456297	+	0.903895i
$385$		0			0
$386$	−4.16299	+	2.40350i	−0.211891	+	0.122335i
$387$	−9.74610	−	0.132655i	−0.495422	−	0.00674325i
$388$	4.39631	−	1.17799i	0.223189	−	0.0598033i
$389$	35.9511	+	13.0851i	1.82279	+	0.663443i	0.994696	+	0.102860i	$0.0327995\pi$
$389$	35.9511	+	13.0851i	1.82279	+	0.663443i	0.828099	+	0.560583i	$0.189423\pi$
$390$		0			0
$391$	−34.7541	−	29.1622i	−1.75759	−	1.47479i
$392$	3.29326	+	37.6421i	0.166335	+	1.90121i
$393$	1.17203	+	2.88491i	0.0591212	+	0.145525i
$394$	4.91670	−	13.5085i	0.247700	−	0.680550i
$395$		0			0
$396$	5.87739	+	8.64176i	0.295350	+	0.434265i
$397$	20.6784	+	5.54075i	1.03782	+	0.278082i	0.737209	−	0.675665i	$-0.236143\pi$
$397$	20.6784	+	5.54075i	1.03782	+	0.278082i	0.300609	+	0.953747i	$0.402810\pi$
$398$	0.784506	+	0.549317i	0.0393237	+	0.0275348i
$399$	−25.1278	−	49.0827i	−1.25796	−	2.45721i
$400$		0			0
$401$	34.5128	+	6.08555i	1.72349	+	0.303898i	0.945800	−	0.324751i	$-0.105280\pi$
$401$	34.5128	+	6.08555i	1.72349	+	0.303898i	0.777690	+	0.628648i	$0.216392\pi$
$402$	5.34140	+	8.51159i	0.266405	+	0.424519i
$403$	3.53666	+	0.309418i	0.176174	+	0.0154132i
$404$	10.5739			0.526073
$405$		0			0
$406$	23.7156			1.17699
$407$	11.7770	+	1.03035i	0.583762	+	0.0510725i
$408$	13.8434	+	22.0596i	0.685349	+	1.09211i
$409$	31.2192	+	5.50478i	1.54369	+	0.272194i	0.879693	−	0.475542i	$-0.157748\pi$
$409$	31.2192	+	5.50478i	1.54369	+	0.272194i	0.663996	+	0.747736i	$0.268859\pi$
$410$		0			0
$411$	−14.0479	−	27.4400i	−0.692930	−	1.35352i
$412$	−15.5208	−	10.8678i	−0.764655	−	0.535417i
$413$	20.3549	+	5.45409i	1.00160	+	0.268378i
$414$	−16.5250	+	1.21937i	−0.812157	+	0.0599288i
$415$		0			0
$416$	−3.25400	+	8.94028i	−0.159540	+	0.438333i
$417$	−7.09294	−	17.4590i	−0.347343	−	0.854969i
$418$	−1.01612	−	11.6143i	−0.0496999	−	0.568073i
$419$	21.7068	+	18.2142i	1.06045	+	0.889821i	0.994153	−	0.107979i	$-0.0344380\pi$
$419$	21.7068	+	18.2142i	1.06045	+	0.889821i	0.0662941	+	0.997800i	$0.478882\pi$
$420$		0			0
$421$	−7.16992	−	2.60964i	−0.349441	−	0.127186i	0.161336	−	0.986900i	$-0.448420\pi$
$421$	−7.16992	−	2.60964i	−0.349441	−	0.127186i	−0.510776	+	0.859714i	$0.670642\pi$
$422$	7.61401	−	2.04017i	0.370644	−	0.0993138i
$423$	14.3106	+	25.5846i	0.695805	+	1.24397i
$424$	5.71578	−	3.30001i	0.277583	−	0.160263i
$425$		0			0
$426$	−0.0658278	+	1.30401i	−0.00318937	+	0.0631793i
$427$	4.46876	−	9.58330i	0.216259	−	0.463768i
$428$	−1.83430	−	2.61965i	−0.0886642	−	0.126626i
$429$	1.95933	+	6.36491i	0.0945974	+	0.307301i
$430$		0			0
$431$			20.7923i			1.00153i	0.865583	+	0.500765i	$0.166948\pi$
$431$			20.7923i			1.00153i	−0.865583	+	0.500765i	$0.833052\pi$
$432$	−5.63080	−	1.36949i	−0.270912	−	0.0658896i
$433$	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
$437$	−46.8129	−	21.8292i	−2.23937	−	1.04423i
$438$	−4.71088	+	1.01079i	−0.225095	+	0.0482976i
$439$	−9.06380	+	1.59819i	−0.432591	+	0.0762775i	−0.385704	−	0.922623i	$-0.626041\pi$
$439$	−9.06380	+	1.59819i	−0.432591	+	0.0762775i	−0.0468875	+	0.998900i	$0.514930\pi$
$440$		0			0
$441$	−44.7300	−	4.52758i	−2.13000	−	0.215599i
$442$	1.82167	+	6.79858i	0.0866482	+	0.323375i
$443$	−1.40687	+	0.656035i	−0.0668425	+	0.0311692i	−0.455752	−	0.890107i	$-0.650630\pi$
$443$	−1.40687	+	0.656035i	−0.0668425	+	0.0311692i	0.388910	+	0.921276i	$0.372852\pi$
$444$	−10.1690	+	7.69356i	−0.482599	+	0.365120i
$445$		0			0
$446$	10.7030	−	12.7554i	0.506803	−	0.603985i
$447$	0.655091	−	4.72710i	0.0309847	−	0.223584i
$448$	−3.99991	−	8.57783i	−0.188978	−	0.405264i
$449$	−1.66148	+	2.87776i	−0.0784099	+	0.135810i	−0.902564	−	0.430556i	$-0.858318\pi$
$449$	−1.66148	+	2.87776i	−0.0784099	+	0.135810i	0.824154	+	0.566366i	$0.191651\pi$
$450$		0			0
$451$	5.54925	+	9.61159i	0.261304	+	0.452592i
$452$	−14.1798	+	20.2509i	−0.666964	+	0.952523i
$453$	4.64007	+	21.6254i	0.218009	+	1.01605i
$454$	2.66462	+	7.32099i	0.125057	+	0.343591i
$455$		0			0
$456$	21.7241	+	20.1801i	1.01732	+	0.945021i
$457$	−1.50219	+	17.1702i	−0.0702697	+	0.803186i	0.876527	+	0.481353i	$0.159855\pi$
$457$	−1.50219	+	17.1702i	−0.0702697	+	0.803186i	−0.946796	+	0.321833i	$0.895701\pi$
$458$	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	0.925279	−	0.379287i	$-0.123831\pi$
$461$	8.39687	+	10.0070i	0.391081	+	0.466072i	−0.534198	+	0.845359i	$0.679386\pi$
$462$	−12.3260	−	6.52351i	−0.573458	−	0.303501i
$463$	−1.11445	+	0.780347i	−0.0517929	+	0.0362658i	−0.599186	−	0.800610i	$-0.704509\pi$
$463$	−1.11445	+	0.780347i	−0.0517929	+	0.0362658i	0.547393	+	0.836876i	$0.315620\pi$
$464$	7.30074	−	2.65725i	0.338928	−	0.123360i
$465$		0			0
$466$	−0.940992	−	5.33663i	−0.0435906	−	0.247215i
$467$	−0.0316030	+	0.117944i	−0.00146241	+	0.00545780i	−0.966653	−	0.256089i	$-0.917566\pi$
$467$	−0.0316030	+	0.117944i	−0.00146241	+	0.00545780i	0.965191	+	0.261547i	$0.0842326\pi$
$468$	−6.17145	−	3.67597i	−0.285275	−	0.169922i
$469$	32.4498	+	18.7349i	1.49839	+	0.865096i
$470$		0			0
$471$	−16.1985	+	2.02053i	−0.746388	+	0.0931011i
$472$	−11.2884	+	0.987611i	−0.519593	+	0.0454585i
$473$	−7.65522	+	0.669745i	−0.351987	+	0.0307949i
$474$	−3.14129	+	7.44013i	−0.144284	+	0.341737i
$475$		0			0
$476$	35.6680	+	20.5929i	1.63484	+	0.943876i
$477$	2.58516	+	7.41514i	0.118366	+	0.339516i
$478$	−5.59117	+	20.8665i	−0.255734	+	0.954412i
$479$	−4.54350	−	25.7675i	−0.207598	−	1.17735i	−0.893299	−	0.449463i	$-0.851615\pi$
$479$	−4.54350	−	25.7675i	−0.207598	−	1.17735i	0.685701	−	0.727883i	$-0.259496\pi$
$480$		0			0
$481$	−7.63553	+	2.77910i	−0.348150	+	0.126716i
$482$	−10.1794	+	7.12771i	−0.463660	+	0.324658i
$483$	−52.3342	+	32.8420i	−2.38129	+	1.49436i
$484$	−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	$0.344877\pi$
$488$	−0.495563	+	5.66431i	−0.0224331	+	0.256411i
$489$	7.94259	−	34.7073i	0.359176	−	1.56952i
$490$		0			0
$491$	8.42964	+	23.1603i	0.380424	+	1.04521i	0.971178	+	0.238356i	$0.0766084\pi$
$491$	8.42964	+	23.1603i	0.380424	+	1.04521i	−0.590753	+	0.806852i	$0.701169\pi$
$492$	−11.3923	−	3.67740i	−0.513605	−	0.165790i
$493$	23.8289	−	34.0313i	1.07320	−	1.53269i
$494$	4.00666	+	6.93974i	0.180268	+	0.312233i
$495$		0			0
$496$	−1.21775	+	2.10921i	−0.0546787	+	0.0947062i
$497$	2.05754	+	4.41241i	0.0922933	+	0.197924i
$498$	0.855299	−	0.347477i	0.0383269	−	0.0155708i
$499$	−4.55089	+	5.42354i	−0.203726	+	0.242791i	−0.858227	−	0.513270i	$-0.828434\pi$
$499$	−4.55089	+	5.42354i	−0.203726	+	0.242791i	0.654502	+	0.756061i	$0.272878\pi$
$500$		0			0
$501$	2.29912	+	18.4319i	0.102717	+	0.823479i
$502$	−6.47414	+	3.01894i	−0.288955	+	0.134742i
$503$	0.949440	+	3.54336i	0.0423334	+	0.157990i	0.983857	−	0.178957i	$-0.0572722\pi$
$503$	0.949440	+	3.54336i	0.0423334	+	0.157990i	−0.941524	+	0.336947i	$0.890606\pi$
$504$	34.3811	−	8.71264i	1.53145	−	0.388092i
$505$		0			0
$506$	−12.8651	+	2.26846i	−0.571924	+	0.100846i
$507$	12.0293	+	13.3084i	0.534241	+	0.591047i
$508$	5.22586	+	2.43686i	0.231860	+	0.108118i
$509$	−0.686733	+	3.89466i	−0.0304389	+	0.172628i	−0.996237	−	0.0866661i	$-0.972379\pi$
$509$	−0.686733	+	3.89466i	−0.0304389	+	0.172628i	0.965799	+	0.259294i	$0.0834898\pi$
$510$		0			0
$511$	−13.7625	+	11.5481i	−0.608819	+	0.510859i
$512$	−8.59188	−	8.59188i	−0.379711	−	0.379711i
$513$	−28.4215	+	20.9008i	−1.25484	+	0.922794i
$514$		−	0.0554707i		−	0.00244671i
$515$		0			0
$516$	5.64119	−	6.07279i	0.248340	−	0.267340i
$517$	13.2563	+	18.9320i	0.583012	+	0.832628i
$518$	7.19108	−	15.4213i	0.315958	−	0.677574i
$519$	18.1130	+	11.7133i	0.795073	+	0.514157i
$520$		0			0
$521$	16.1589	−	9.32937i	0.707936	−	0.408727i	−0.102360	−	0.994747i	$-0.532639\pi$
$521$	16.1589	−	9.32937i	0.707936	−	0.408727i	0.810296	+	0.586020i	$0.199306\pi$
$522$	−2.43121	−	14.9773i	−0.106411	−	0.655538i
$523$	−35.0914	+	9.40272i	−1.53444	+	0.411152i	−0.924465	−	0.381268i	$-0.875488\pi$
$523$	−35.0914	+	9.40272i	−1.53444	+	0.411152i	−0.609976	+	0.792420i	$0.708821\pi$
$524$	−2.48830	−	0.905668i	−0.108702	−	0.0395643i
$525$		0			0
$526$	−7.48142	−	6.27765i	−0.326205	−	0.273719i
$527$	1.13506	+	12.9737i	0.0494438	+	0.565145i
$528$	−4.52544	−	0.627145i	−0.196945	−	0.0272930i
$529$	−11.9285	+	32.7734i	−0.518633	+	1.42493i
$530$		0			0
$531$	1.35777	−	13.4140i	0.0589223	−	0.582119i
$532$	45.2929	+	12.1362i	1.96370	+	0.526171i
$533$	−6.24875	−	4.37542i	−0.270664	−	0.189521i
$534$	−0.0161310	+	0.0249444i	−0.000698057	+	0.00107945i
$535$		0			0
$536$	−19.8425	−	3.49876i	−0.857065	−	0.151124i
$537$	6.65762	−	0.245298i	0.287297	−	0.0105854i
$538$	−13.8076	−	1.20800i	−0.595286	−	0.0520808i
$539$	−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	$0.664128\pi$
$542$	11.6499	+	1.01923i	0.500406	+	0.0437798i
$543$	−11.5173	+	21.7617i	−0.494256	+	0.933885i
$544$	−34.3707	−	6.06049i	−1.47363	−	0.259841i
$545$		0			0
$546$	9.57320	+	0.483266i	0.409695	+	0.0206819i
$547$	12.5106	+	8.76004i	0.534916	+	0.374552i	0.809600	−	0.586982i	$-0.199684\pi$
$547$	12.5106	+	8.76004i	0.534916	+	0.374552i	−0.274684	+	0.961535i	$0.588573\pi$
$548$	25.3213	+	6.78483i	1.08167	+	0.289834i
$549$	−6.51032	−	1.83976i	−0.277854	−	0.0785189i
$550$		0			0
$551$	16.1772	−	44.4465i	0.689172	−	1.89348i
$552$	20.4044	−	26.2201i	0.868467	−	1.11600i
$553$	2.62461	+	29.9995i	0.111610	+	1.27571i
$554$	4.08296	+	3.42601i	0.173469	+	0.145557i
$555$		0			0
$556$	15.0588	+	5.48094i	0.638634	+	0.232444i
$557$	−6.81110	+	1.82503i	−0.288596	+	0.0773290i	−0.400213	−	0.916422i	$-0.631064\pi$
$557$	−6.81110	+	1.82503i	−0.288596	+	0.0773290i	0.111617	+	0.993751i	$0.464397\pi$
$558$	3.60175	+	3.10673i	0.152474	+	0.131518i
$559$	4.57413	−	2.64088i	0.193465	−	0.111697i
$560$		0			0
$561$	−21.7460	+	11.1328i	−0.918116	+	0.470028i
$562$	−4.95772	+	10.6319i	−0.209129	+	0.448478i
$563$	17.9144	+	25.5845i	0.755004	+	1.07826i	0.994227	+	0.107293i	$0.0342182\pi$
$563$	17.9144	+	25.5845i	0.755004	+	1.07826i	−0.239224	+	0.970965i	$0.576893\pi$
$564$	−24.3007	−	5.56109i	−1.02324	−	0.234164i
$565$		0			0
$566$		−	7.67220i		−	0.322487i
$567$	2.53244	+	42.1244i	0.106353	+	1.76906i
$568$	−1.85118	−	1.85118i	−0.0776739	−	0.0776739i
$569$	−24.7601	+	20.7762i	−1.03800	+	0.870984i	−0.991781	−	0.127948i	$-0.959161\pi$
$569$	−24.7601	+	20.7762i	−1.03800	+	0.870984i	−0.0462172	+	0.998931i	$0.514717\pi$
$570$		0			0
$571$	−7.28419	+	41.3107i	−0.304834	+	1.72880i	0.319453	+	0.947602i	$0.396501\pi$
$571$	−7.28419	+	41.3107i	−0.304834	+	1.72880i	−0.624286	+	0.781196i	$0.714610\pi$
$572$	−5.13264	−	2.39339i	−0.214606	−	0.100073i
$573$	13.5832	−	42.0799i	0.567448	−	1.75791i
$574$	15.7316	−	2.77391i	0.656625	−	0.115781i
$575$		0			0
$576$	−5.00716	+	3.40544i	−0.208632	+	0.141894i
$577$	−4.02551	−	15.0234i	−0.167584	−	0.625433i	−0.997696	−	0.0678366i	$-0.978390\pi$
$577$	−4.02551	−	15.0234i	−0.167584	−	0.625433i	0.830112	−	0.557596i	$-0.188276\pi$
$578$	−12.2144	+	5.69568i	−0.508054	+	0.236909i
$579$	10.5650	+	4.46063i	0.439065	+	0.185377i
$580$		0			0
$581$	2.21272	−	2.63701i	0.0917990	−	0.109402i
$582$	3.06662	+	2.38643i	0.127116	+	0.0989209i
$583$	2.61649	+	5.61107i	0.108364	+	0.232387i
$584$	4.83034	−	8.36640i	0.199881	−	0.346204i
$585$		0			0
$586$	−3.42032	−	5.92417i	−0.141292	−	0.244725i
$587$	−15.1446	+	21.6287i	−0.625084	+	0.892712i	−0.999402	−	0.0345884i	$-0.988988\pi$
$587$	−15.1446	+	21.6287i	−0.625084	+	0.892712i	0.374318	+	0.927300i	$0.377877\pi$
$588$	28.3626	−	25.6366i	1.16965	−	1.05724i
$589$	5.07120	+	13.9330i	0.208955	+	0.574099i
$590$		0			0
$591$	−32.7776	+	10.0900i	−1.34829	+	0.415048i
$592$	0.485835	−	5.55312i	0.0199677	−	0.228232i
$593$	−2.61058	+	2.61058i	−0.107204	+	0.107204i	−0.758674	−	0.651470i	$-0.774153\pi$
$593$	−2.61058	+	2.61058i	−0.107204	+	0.107204i	0.651470	+	0.758674i	$0.274153\pi$
$594$	−2.85624	+	8.45309i	−0.117193	+	0.346835i
$595$		0			0
$596$	2.60859	+	3.10880i	0.106852	+	0.127341i
$597$	−0.0841254	−	2.28324i	−0.00344302	−	0.0934468i
$598$	7.35514	−	5.15012i	0.300774	−	0.210604i
$599$	−24.1321	+	8.78335i	−0.986010	+	0.358878i	−0.784174	−	0.620541i	$-0.786913\pi$
$599$	−24.1321	+	8.78335i	−0.986010	+	0.358878i	−0.201836	+	0.979419i	$0.564691\pi$
$600$		0			0
$601$	−7.14602	−	40.5271i	−0.291492	−	1.65313i	−0.681128	−	0.732165i	$-0.738510\pi$
$601$	−7.14602	−	40.5271i	−0.291492	−	1.65313i	0.389636	−	0.920969i	$-0.372601\pi$
$602$	−2.86264	+	10.6835i	−0.116673	+	0.435428i
$603$	8.50518	−	22.4138i	0.346358	−	0.912761i
$604$	−16.2885	−	9.40418i	−0.662770	−	0.382650i
$605$		0			0
$606$	5.44676	+	7.19927i	0.221259	+	0.292450i
$607$	8.51183	−	0.744689i	0.345485	−	0.0302260i	0.0869069	−	0.996216i	$-0.472302\pi$
$607$	8.51183	−	0.744689i	0.345485	−	0.0302260i	0.258578	+	0.965990i	$0.416746\pi$
$608$	−39.5840	+	3.46315i	−1.60534	+	0.140449i
$609$	−34.1364	−	45.1198i	−1.38328	−	1.82835i
$610$		0			0
$611$	−13.7571	−	7.94266i	−0.556553	−	0.321326i
$612$	9.34869	−	24.6368i	0.377899	−	0.995882i
$613$	2.41303	−	9.00556i	0.0974614	−	0.363731i	−0.899920	−	0.436056i	$-0.856375\pi$
$613$	2.41303	−	9.00556i	0.0974614	−	0.363731i	0.997381	+	0.0723246i	$0.0230418\pi$
$614$	−3.40594	−	19.3161i	−0.137453	−	0.779533i
$615$		0			0
$616$	26.2762	−	9.56376i	1.05870	−	0.385335i
$617$	37.1521	−	26.0142i	1.49569	−	1.04729i	0.513783	−	0.857920i	$-0.328244\pi$
$617$	37.1521	−	26.0142i	1.49569	−	1.04729i	0.981905	−	0.189372i	$-0.0606453\pi$
$618$	−0.595612	−	16.1655i	−0.0239590	−	0.650270i
$619$	−15.0061	−	17.8836i	−0.603147	−	0.718803i	0.374928	−	0.927054i	$-0.377667\pi$
$619$	−15.0061	−	17.8836i	−0.603147	−	0.718803i	−0.978075	+	0.208251i	$0.933223\pi$
$620$		0			0
$621$	26.1060	+	29.6842i	1.04760	+	1.19118i
$622$	−4.64993	+	4.64993i	−0.186445	+	0.186445i
$623$	−0.00965394	+	0.110345i	−0.000386777	+	0.00442088i
$624$	3.00121	−	0.923872i	0.120145	−	0.0369845i
$625$		0			0
$626$	2.51927	+	6.92165i	0.100690	+	0.276645i
$627$	−20.6340	+	18.6508i	−0.824042	+	0.744843i
$628$	7.96218	−	11.3712i	0.317726	−	0.453759i
$629$	−14.9037	−	25.8140i	−0.594251	−	1.02927i
$630$		0			0
$631$	−15.4086	+	26.6885i	−0.613407	+	1.06245i	0.377255	+	0.926110i	$0.376868\pi$
$631$	−15.4086	+	26.6885i	−0.613407	+	1.06245i	−0.990662	+	0.136343i	$0.956465\pi$
$632$	−6.84355	−	14.6760i	−0.272222	−	0.583781i
$633$	−14.8411	−	11.5493i	−0.589882	−	0.459044i
$634$	3.22031	−	3.83781i	0.127895	−	0.152419i
$635$		0			0
$636$	−6.15205	−	2.59745i	−0.243945	−	0.102996i
$637$	22.0798	−	10.2960i	0.874833	−	0.407941i
$638$	−3.09613	−	11.5549i	−0.122577	−	0.457464i
$639$	2.57567	−	1.75175i	0.101892	−	0.0692982i
$640$		0			0
$641$	12.3888	−	2.18449i	0.489330	−	0.0862820i	0.0764610	−	0.997073i	$-0.475638\pi$
$641$	12.3888	−	2.18449i	0.489330	−	0.0862820i	0.412869	+	0.910791i	$0.364527\pi$
$642$	0.838722	−	2.59830i	0.0331017	−	0.102547i
$643$	34.5408	+	16.1067i	1.36216	+	0.635185i	0.959900	−	0.280342i	$-0.0904478\pi$
$643$	34.5408	+	16.1067i	1.36216	+	0.635185i	0.402258	+	0.915526i	$0.368226\pi$
$644$	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	0.953355	−	0.301851i	$-0.0976045\pi$
$647$	16.5718	+	16.5718i	0.651504	+	0.651504i	−0.301851	+	0.953355i	$0.597604\pi$
$648$	−9.02693	−	20.8197i	−0.354611	−	0.817876i
$649$		−	10.6295i		−	0.417246i
$650$		0			0
$651$	17.2891	+	3.95652i	0.677613	+	0.155068i
$652$	17.3664	+	24.8017i	0.680119	+	0.971311i
$653$	2.51370	−	5.39065i	0.0983687	−	0.210952i	−0.850965	−	0.525223i	$-0.823982\pi$
$653$	2.51370	−	5.39065i	0.0983687	−	0.210952i	0.949334	+	0.314270i	$0.101760\pi$
$654$	−9.53035	+	4.87905i	−0.372666	+	0.190786i
$655$		0			0
$656$	4.53210	−	2.61661i	0.176949	−	0.102161i
$657$	8.70394	+	7.50769i	0.339573	+	0.292903i
$658$	32.1316	−	8.60965i	1.25262	−	0.335639i
$659$	34.7751	+	12.6571i	1.35465	+	0.493051i	0.914395	−	0.404824i	$-0.132667\pi$
$659$	34.7751	+	12.6571i	1.35465	+	0.493051i	0.440251	+	0.897875i	$0.354889\pi$
$660$		0			0
$661$	13.5431	+	11.3640i	0.526766	+	0.442009i	0.866983	−	0.498338i	$-0.166056\pi$
$661$	13.5431	+	11.3640i	0.526766	+	0.442009i	−0.340217	+	0.940347i	$0.610500\pi$
$662$	0.738314	+	8.43896i	0.0286954	+	0.327990i
$663$	10.3124	−	13.2517i	0.400501	−	0.514653i
$664$	−0.633102	+	1.73943i	−0.0245691	+	0.0675031i
$665$		0			0
$666$	−10.4763	−	2.96052i	−0.405950	−	0.114718i
$667$	−51.1928	−	13.7171i	−1.98219	−	0.531128i
$668$	−12.9390	−	9.06000i	−0.500626	−	0.350542i
$669$	−39.6736	−	2.00277i	−1.53387	−	0.0774315i
$670$		0			0
$671$	−5.25266	−	0.926186i	−0.202777	−	0.0357550i
$672$	−22.2336	+	42.0098i	−0.857678	+	1.62056i
$673$	35.4920	+	3.10515i	1.36812	+	0.119695i	0.747418	−	0.664354i	$-0.231293\pi$
$673$	35.4920	+	3.10515i	1.36812	+	0.119695i	0.620699	+	0.784049i	$0.286849\pi$
$674$	−1.72703			−0.0665229
$675$		0			0
$676$	−15.2552			−0.586739
$677$	−14.2347	−	1.24538i	−0.547084	−	0.0478637i	−0.189737	−	0.981835i	$-0.560763\pi$
$677$	−14.2347	−	1.24538i	−0.547084	−	0.0478637i	−0.357348	+	0.933971i	$0.616319\pi$
$678$	−21.0921	+	0.777131i	−0.810035	+	0.0298455i
$679$	14.2691	+	2.51603i	0.547599	+	0.0965564i
$680$		0			0
$681$	10.0930	−	15.6074i	0.386764	−	0.598077i
$682$	3.07182	+	2.15091i	0.117626	+	0.0823625i
$683$	−48.5064	−	12.9972i	−1.85604	−	0.497326i	−0.856230	−	0.516594i	$-0.827200\pi$
$683$	−48.5064	−	12.9972i	−1.85604	−	0.497326i	−0.999814	+	0.0192684i	$0.993866\pi$
$684$	3.02125	−	29.8483i	0.115521	−	1.14128i
$685$		0			0
$686$	−9.29847	+	25.5473i	−0.355017	+	0.975402i
$687$	−19.8221	−	2.74699i	−0.756261	−	0.104804i
$688$	0.315801	+	3.60962i	0.0120398	+	0.137616i
$689$	−3.25978	−	2.73528i	−0.124188	−	0.104206i
$690$		0			0
$691$	−0.280238	−	0.101998i	−0.0106608	−	0.00388020i	0.336684	−	0.941618i	$-0.390695\pi$
$691$	−0.280238	−	0.101998i	−0.0106608	−	0.00388020i	−0.347345	+	0.937737i	$0.612917\pi$
$692$	−17.7180	+	4.74753i	−0.673538	+	0.180474i
$693$	5.33090	+	32.8407i	0.202504	+	1.24751i
$694$	−7.35481	+	4.24630i	−0.279185	+	0.161187i
$695$		0			0
$696$	25.5473	+	16.5209i	0.968367	+	0.626223i
$697$	11.8263	−	25.3616i	0.447953	−	0.960639i
$698$	10.1292	+	14.4660i	0.383395	+	0.547545i
$699$	−8.79867	+	9.47184i	−0.332796	+	0.358258i
$700$		0			0
$701$		−	1.73681i		−	0.0655983i	−0.999462	−	0.0327991i	$-0.989558\pi$
$701$		−	1.73681i		−	0.0655983i	0.999462	−	0.0327991i	$-0.0104422\pi$
$702$	−0.676196	−	6.09537i	−0.0255214	−	0.230055i
$703$	−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
$707$	30.5080	+	14.2261i	1.14737	+	0.535028i
$708$	7.68814	+	8.50562i	0.288938	+	0.319661i
$709$	−28.4425	+	5.01519i	−1.06818	+	0.188349i	−0.679984	−	0.733227i	$-0.738013\pi$
$709$	−28.4425	+	5.01519i	−1.06818	+	0.188349i	−0.388198	+	0.921576i	$0.626902\pi$
$710$		0			0
$711$	18.6767	−	4.73294i	0.700431	−	0.177499i
$712$	−0.0154159	−	0.0575329i	−0.000577735	−	0.00215614i
$713$	15.0574	−	7.02136i	0.563902	−	0.262952i
$714$	4.35230	+	34.8923i	0.162881	+	1.30581i
$715$		0			0
$716$	−3.64161	+	4.33991i	−0.136094	+	0.162190i
$717$	47.7473	−	19.3979i	1.78315	−	0.724430i
$718$	6.69252	+	14.3521i	0.249762	+	0.535617i
$719$	−21.8672	+	37.8751i	−0.815509	+	1.41250i	0.0934526	+	0.995624i	$0.470210\pi$
$719$	−21.8672	+	37.8751i	−0.815509	+	1.41250i	−0.908962	+	0.416880i	$0.863124\pi$
$720$		0			0
$721$	−30.1593	−	52.2374i	−1.12319	−	1.94542i
$722$	−11.2840	+	16.1153i	−0.419949	+	0.599749i
$723$	28.2130	+	9.10707i	1.04925	+	0.338696i
$724$	−7.16111	−	19.6750i	−0.266141	−	0.731215i
$725$		0			0
$726$	1.51648	−	6.62664i	0.0562817	−	0.245938i
$727$	−3.18769	+	36.4355i	−0.118225	+	1.35132i	0.672932	+	0.739704i	$0.265035\pi$
$727$	−3.18769	+	36.4355i	−0.118225	+	1.35132i	−0.791157	+	0.611613i	$0.790521\pi$
$728$	−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
$732$	4.87300	−	3.05802i	0.180111	−	0.113028i
$733$	−4.88078	+	3.41756i	−0.180276	+	0.126231i	−0.660231	−	0.751062i	$-0.729542\pi$
$733$	−4.88078	+	3.41756i	−0.180276	+	0.126231i	0.479955	+	0.877293i	$0.340653\pi$
$734$	−5.77082	+	2.10041i	−0.213005	+	0.0775274i
$735$		0			0
$736$	7.73142	+	43.8471i	0.284984	+	1.61623i
$737$	4.89177	−	18.2563i	0.180191	−	0.672480i
$738$	−3.36455	−	9.65073i	−0.123851	−	0.355248i
$739$	−12.8145	−	7.39844i	−0.471388	−	0.272156i	0.245433	−	0.969414i	$-0.421070\pi$
$739$	−12.8145	−	7.39844i	−0.471388	−	0.272156i	−0.716821	+	0.697258i	$0.754403\pi$
$740$		0			0
$741$	7.43590	−	17.6119i	0.273165	−	0.646989i
$742$	8.87711	−	0.776647i	0.325889	−	0.0285116i
$743$	4.26304	−	0.372968i	0.156396	−	0.0136829i	−0.00868886	−	0.999962i	$-0.502766\pi$
$743$	4.26304	−	0.372968i	0.156396	−	0.0136829i	0.165085	+	0.986279i	$0.447210\pi$
$744$	−9.46384	+	1.18048i	−0.346961	+	0.0432784i
$745$		0			0
$746$	21.2030	+	12.2415i	0.776296	+	0.448194i
$747$	−1.89221	−	1.12708i	−0.0692323	−	0.0412377i
$748$	5.37692	−	20.0669i	0.196600	−	0.733720i
$749$	−1.76787	−	10.0261i	−0.0645966	−	0.366346i
$750$		0			0
$751$	19.0790	−	6.94420i	0.696204	−	0.253397i	0.0304146	−	0.999537i	$-0.490317\pi$
$751$	19.0790	−	6.94420i	0.696204	−	0.253397i	0.665789	+	0.746140i	$0.268095\pi$
$752$	8.92689	−	6.25068i	0.325530	−	0.227939i
$753$	15.0626	+	7.97182i	0.548910	+	0.290509i
$754$	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	$0.472769\pi$
$758$	0.305657	−	3.49368i	0.0111020	−	0.126896i
$759$	22.8339	+	21.2111i	0.828819	+	0.769914i
$760$		0			0
$761$	−11.5003	−	31.5969i	−0.416887	−	1.14539i	−0.953456	−	0.301531i	$-0.902502\pi$
$761$	−11.5003	−	31.5969i	−0.416887	−	1.14539i	0.536570	−	0.843856i	$-0.319720\pi$
$762$	1.03277	+	4.81329i	0.0374132	+	0.174367i
$763$	−22.8988	+	32.7029i	−0.828994	+	1.18393i
$764$	18.8010	+	32.5643i	0.680196	+	1.17813i
$765$		0			0
$766$	−9.00671	+	15.6001i	−0.325426	+	0.563654i
$767$	3.08765	+	6.62148i	0.111488	+	0.239088i
$768$	2.72732	−	19.6802i	0.0984138	−	0.710149i
$769$	0.789841	−	0.941295i	0.0284824	−	0.0339440i	−0.751615	−	0.659602i	$-0.770725\pi$
$769$	0.789841	−	0.941295i	0.0284824	−	0.0339440i	0.780098	+	0.625658i	$0.215169\pi$
$770$		0			0
$771$	−0.105535	+	0.0798448i	−0.00380075	+	0.00287554i
$772$	−8.83848	+	4.12145i	−0.318104	+	0.148334i
$773$	0.759923	+	2.83607i	0.0273325	+	0.102006i	0.978245	−	0.207455i	$-0.0665180\pi$
$773$	0.759923	+	2.83607i	0.0273325	+	0.102006i	−0.950912	+	0.309461i	$0.899851\pi$
$774$	7.04050	+	0.712642i	0.253066	+	0.0256154i
$775$		0			0
$776$	−7.67293	+	1.35294i	−0.275442	+	0.0485679i
$777$	−39.6905	+	8.51622i	−1.42389	+	0.305518i
$778$	−25.1738	−	11.7387i	−0.902524	−	0.420854i
$779$	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
$783$	−24.9953	+	26.1838i	−0.893261	+	0.935734i
$784$			16.7132i			0.596899i
$785$		0			0
$786$	−0.665130	−	2.16068i	−0.0237244	−	0.0770690i
$787$	−26.2314	−	37.4623i	−0.935048	−	1.33539i	−0.942072	−	0.335411i	$-0.891125\pi$
$787$	−26.2314	−	37.4623i	−0.935048	−	1.33539i	0.00702395	−	0.999975i	$-0.497764\pi$
$788$	12.3253	−	26.4317i	0.439071	−	0.941591i
$789$	−1.17468	+	23.2697i	−0.0418199	+	0.828425i
$790$		0			0
$791$	−68.1573	+	39.3506i	−2.42339	+	1.39915i
$792$	−8.73357	−	15.6140i	−0.310334	−	0.554818i
$793$	3.54108	−	0.948830i	0.125748	−	0.0336940i
$794$	−14.6051	−	5.31582i	−0.518316	−	0.188651i
$795$		0			0
$796$	1.48838	+	1.24890i	0.0527541	+	0.0442660i
$797$	−2.09208	−	23.9126i	−0.0741053	−	0.847027i	−0.938740	−	0.344626i	$-0.888006\pi$
$797$	−2.09208	−	23.9126i	−0.0741053	−	0.847027i	0.864635	−	0.502401i	$-0.167550\pi$
$798$	15.0680	+	37.0892i	0.533401	+	1.31294i
$799$	19.9306	−	54.7588i	0.705093	−	1.93723i
$800$		0			0
$801$	0.0706766	−	0.00521520i	0.00249724	−	0.000184270i
$802$	−24.5765	−	6.58524i	−0.867825	−	0.232533i
$803$	7.42331	+	5.19786i	0.261963	+	0.183428i
$804$	9.29011	+	18.1466i	0.327637	+	0.639980i
$805$		0			0
$806$	−2.53832	−	0.447574i	−0.0894085	−	0.0157651i
$807$	17.5764	+	28.0082i	0.618718	+	0.985935i
$808$	−18.0321	−	1.57760i	−0.634367	−	0.0554999i
$809$	−6.88614			−0.242104			−0.121052	−	0.992646i	$-0.538627\pi$
$809$	−6.88614			−0.242104			−0.121052	+	0.992646i	$0.538627\pi$
$810$		0			0
$811$	51.9012			1.82250			0.911248	−	0.411858i	$-0.135120\pi$
$811$	51.9012			1.82250			0.911248	+	0.411858i	$0.135120\pi$
$812$	47.9298	+	4.19332i	1.68201	+	0.147157i
$813$	−14.8298	−	23.6314i	−0.520103	−	0.828790i
$814$	−8.45252	−	1.49041i	−0.296261	−	0.0522388i
$815$		0			0
$816$	5.24939	+	10.2538i	0.183766	+	0.358953i
$817$	18.0698	+	12.6526i	0.632181	+	0.442658i
$818$	−22.2310	−	5.95679i	−0.777290	−	0.208274i
$819$	−12.8603	−	18.9090i	−0.449374	−	0.660733i
$820$		0			0
$821$	1.56336	−	4.29529i	0.0545616	−	0.149907i	−0.909418	−	0.415884i	$-0.863472\pi$
$821$	1.56336	−	4.29529i	0.0545616	−	0.149907i	0.963979	+	0.265977i	$0.0856946\pi$
$822$	8.42386	+	20.7350i	0.293816	+	0.723216i
$823$	−0.775592	−	8.86506i	−0.0270354	−	0.309016i	−0.997657	−	0.0684071i	$-0.978208\pi$
$823$	−0.775592	−	8.86506i	−0.0270354	−	0.309016i	0.970622	−	0.240609i	$-0.0773472\pi$
$824$	24.8467	+	20.8488i	0.865575	+	0.726304i
$825$		0			0
$826$	−14.3767	−	5.23268i	−0.500228	−	0.182068i
$827$	−3.74729	+	1.00408i	−0.130306	+	0.0349154i	−0.323383	−	0.946268i	$-0.604820\pi$
$827$	−3.74729	+	1.00408i	−0.130306	+	0.0349154i	0.193077	+	0.981184i	$0.438153\pi$
$828$	−33.6129	−	0.457510i	−1.16813	−	0.0158996i
$829$	−23.2961	+	13.4500i	−0.809106	+	0.467138i	−0.846645	−	0.532157i	$-0.821381\pi$
$829$	−23.2961	+	13.4500i	−0.809106	+	0.467138i	0.0375391	+	0.999295i	$0.488048\pi$
$830$		0			0
$831$	0.641081	−	12.6994i	0.0222389	−	0.440537i
$832$	1.38677	−	2.97393i	0.0480774	−	0.103102i
$833$	51.2604	+	73.2075i	1.77607	+	2.53649i
$834$	4.02525	+	13.0761i	0.139383	+	0.452787i
$835$		0			0
$836$		−	23.6524i		−	0.818035i
$837$	0.726300	−	11.3243i	0.0251046	−	0.391425i
$838$	−14.5470	−	14.5470i	−0.502518	−	0.502518i
$839$	19.6667	−	16.5023i	0.678970	−	0.569724i	−0.236735	−	0.971574i	$-0.576077\pi$
$839$	19.6667	−	16.5023i	0.678970	−	0.569724i	0.915705	+	0.401850i	$0.131633\pi$
$840$		0			0
$841$	3.39167	−	19.2351i	0.116954	−	0.663280i
$842$	5.02054	+	2.34112i	0.173019	+	0.0806802i
$843$	27.3637	−	5.87131i	0.942455	−	0.202219i
$844$	15.7488	−	2.77695i	0.542097	−	0.0955864i
$845$		0			0
$846$	−8.73129	−	19.4097i	−0.300188	−	0.667319i
$847$	−6.56058	−	24.4844i	−0.225424	−	0.841295i
$848$	2.64576	−	1.23374i	0.0908557	−	0.0423667i
$849$	−14.5966	+	11.0434i	−0.500956	+	0.379009i
$850$		0			0
$851$	−24.4424	+	29.1294i	−0.837876	+	0.998542i
$852$	−0.363610	+	2.62379i	−0.0124571	+	0.0898895i
$853$	2.16662	+	4.64633i	0.0741837	+	0.159087i	0.939902	−	0.341444i	$-0.110916\pi$
$853$	2.16662	+	4.64633i	0.0741837	+	0.159087i	−0.865719	+	0.500531i	$0.833138\pi$
$854$	−3.83845	+	6.64838i	−0.131349	+	0.227503i
$855$		0			0
$856$	2.73725	+	4.74105i	0.0935572	+	0.162046i
$857$	−0.221145	+	0.315828i	−0.00755418	+	0.0107885i	−0.822911	−	0.568170i	$-0.807652\pi$
$857$	−0.221145	+	0.315828i	−0.00755418	+	0.0107885i	0.815357	+	0.578958i	$0.196541\pi$
$858$	−1.01434	−	4.72742i	−0.0346291	−	0.161392i
$859$	−14.9871	−	41.1768i	−0.511354	−	1.40493i	−0.879826	−	0.475295i	$-0.842341\pi$
$859$	−14.9871	−	41.1768i	−0.511354	−	1.40493i	0.368472	−	0.929639i	$-0.379881\pi$
$860$		0			0
$861$	−27.9216	−	25.9372i	−0.951566	−	0.883937i
$862$	1.31566	−	15.0381i	0.0448117	−	0.512200i
$863$	−1.22824	+	1.22824i	−0.0418098	+	0.0418098i	−0.727703	−	0.685893i	$-0.759412\pi$
$863$	−1.22824	+	1.22824i	−0.0418098	+	0.0418098i	0.685893	+	0.727703i	$0.259412\pi$
$864$	28.8100	+	9.73468i	0.980136	+	0.331180i
$865$		0			0
$866$	−5.18102	−	6.17450i	−0.176058	−	0.209818i
$867$	28.4178	+	15.0400i	0.965118	+	0.510786i
$868$	−12.3547	+	8.65089i	−0.419347	+	0.293630i
$869$	14.2739	−	5.19529i	0.484210	−	0.176238i
$870$		0			0
$871$	2.25582	+	12.7934i	0.0764355	+	0.433487i
$872$	5.55626	−	20.7362i	0.188159	−	0.702217i
$873$	0.126167	−	9.26941i	0.00427011	−	0.313722i
$874$	32.4763	+	18.7502i	1.09853	+	0.634236i
$875$		0			0
$876$	−9.69954	+	1.20988i	−0.327717	+	0.0408779i
$877$	25.7918	−	2.25649i	0.870926	−	0.0761961i	0.357075	−	0.934076i	$-0.383774\pi$
$877$	25.7918	−	2.25649i	0.870926	−	0.0761961i	0.513851	+	0.857880i	$0.328218\pi$
$878$	6.65655	−	0.582372i	0.224648	−	0.0196541i
$879$	−6.34773	+	15.0346i	−0.214104	+	0.507103i
$880$		0			0
$881$	−9.98167	−	5.76292i	−0.336291	−	0.194158i	0.322340	−	0.946624i	$-0.395531\pi$
$881$	−9.98167	−	5.76292i	−0.336291	−	0.194158i	−0.658631	+	0.752466i	$0.728864\pi$
$882$	32.0646	+	6.10494i	1.07967	+	0.205564i
$883$	−9.45962	+	35.3038i	−0.318342	+	1.18807i	0.602496	+	0.798122i	$0.294173\pi$
$883$	−9.45962	+	35.3038i	−0.318342	+	1.18807i	−0.920838	+	0.389945i	$0.872494\pi$
$884$	2.47954	+	14.0622i	0.0833961	+	0.472963i
$885$		0			0
$886$	1.05904	−	0.385458i	0.0355790	−	0.0129497i
$887$	20.5727	−	14.4052i	0.690763	−	0.483678i	−0.174718	−	0.984618i	$-0.555901\pi$
$887$	20.5727	−	14.4052i	0.690763	−	0.483678i	0.865482	+	0.500941i	$0.167013\pi$
$888$	18.4894	−	11.6029i	0.620463	−	0.389368i
$889$	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
$893$	5.78232	−	66.0922i	0.193498	−	2.21169i
$894$	−0.772911	+	3.37744i	−0.0258500	+	0.112959i
$895$		0			0
$896$	−16.4211	−	45.1166i	−0.548591	−	1.50724i
$897$	−20.3853	−	6.58031i	−0.680646	−	0.219710i
$898$	1.38376	−	1.97622i	0.0461768	−	0.0659473i
$899$	7.60684	+	13.1754i	0.253702	+	0.439425i
$900$		0			0
$901$	7.80507	−	13.5188i	0.260024	−	0.450376i
$902$	−3.40533	−	7.30275i	−0.113385	−	0.243155i
$903$	24.4463	−	9.93163i	0.813522	−	0.330504i
$904$	27.2027	−	32.4190i	0.904750	−	1.07824i
$905$		0			0
$906$	−1.98757	−	15.9342i	−0.0660324	−	0.529380i
$907$	−2.13753	+	0.996748i	−0.0709756	+	0.0330965i	−0.457782	−	0.889064i	$-0.651356\pi$
$907$	−2.13753	+	0.996748i	−0.0709756	+	0.0330965i	0.386806	+	0.922161i	$0.373578\pi$
$908$	4.09079	+	15.2670i	0.135758	+	0.506655i
$909$	5.85679	−	20.7253i	0.194257	−	0.687415i
$910$		0			0
$911$	−28.9448	+	5.10374i	−0.958983	+	0.169095i	−0.631167	−	0.775647i	$-0.717424\pi$
$911$	−28.9448	+	5.10374i	−0.958983	+	0.169095i	−0.327816	+	0.944742i	$0.606313\pi$
$912$	8.79432	+	9.72942i	0.291209	+	0.322173i
$913$	−1.57370	−	0.733830i	−0.0520820	−	0.0242862i
$914$	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
$918$	21.5896	−	6.32562i	0.712562	−	0.208777i
$919$			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
$922$	−5.43986	−	7.76892i	−0.179152	−	0.255856i
$923$	−0.713349	+	1.52978i	−0.0234802	+	0.0503533i
$924$	−23.7577	−	15.3636i	−0.781572	−	0.505426i
$925$		0			0
$926$	0.855408	−	0.493870i	0.0281105	−	0.0162296i
$927$	−29.8981	+	24.4018i	−0.981981	+	0.801460i
$928$	−39.3817	+	10.5523i	−1.29277	+	0.346396i
$929$	12.8079	+	4.66169i	0.420213	+	0.152945i	0.543468	−	0.839430i	$-0.317111\pi$
$929$	12.8079	+	4.66169i	0.420213	+	0.152945i	−0.123255	+	0.992375i	$0.539333\pi$
$930$		0			0
$931$	77.9440	+	65.4028i	2.55451	+	2.14349i
$932$	−0.958162	−	10.9518i	−0.0313856	−	0.358740i
$933$	15.5398	+	2.15354i	0.508750	+	0.0705036i
$934$	0.0303201	−	0.0833037i	0.000992103	−	0.00272578i
$935$		0			0
$936$	9.97593	+	7.18952i	0.326073	+	0.234997i
$937$	−12.7253	−	3.40972i	−0.415716	−	0.111391i	0.0448974	−	0.998992i	$-0.485704\pi$
$937$	−12.7253	−	3.40972i	−0.415716	−	0.111391i	−0.460613	+	0.887601i	$0.652371\pi$
$938$	−22.2839	−	15.6034i	−0.727596	−	0.509468i
$939$	9.54243	−	14.7561i	0.311406	−	0.481546i
$940$		0			0
$941$	28.4137	+	5.01010i	0.926260	+	0.163325i	0.616378	−	0.787450i	$-0.288599\pi$
$941$	28.4137	+	5.01010i	0.926260	+	0.163325i	0.309882	+	0.950775i	$0.399710\pi$
$942$	11.8435	−	0.436370i	0.385882	−	0.0142177i
$943$	−35.5629	−	3.11135i	−1.15809	−	0.101320i
$944$	−5.01209			−0.163130
$945$		0			0
$946$	5.57904			0.181390
$947$	−45.6685	−	3.99548i	−1.48403	−	0.129835i	−0.683860	−	0.729613i	$-0.739700\pi$
$947$	−45.6685	−	3.99548i	−1.48403	−	0.129835i	−0.800167	+	0.599778i	$0.795256\pi$
$948$	−7.66417	+	14.4813i	−0.248921	+	0.470329i
$949$	−6.13407	−	1.08160i	−0.199120	−	0.0351103i
$950$		0			0
$951$	−11.9369	−	0.602589i	−0.387080	−	0.0195403i
$952$	−57.7535	−	40.4394i	−1.87180	−	1.31065i
$953$	−15.2502	−	4.08629i	−0.494003	−	0.132368i	0.00321227	−	0.999995i	$-0.498978\pi$
$953$	−15.2502	−	4.08629i	−0.494003	−	0.132368i	−0.497216	+	0.867627i	$0.665644\pi$
$954$	−1.40052	−	5.52661i	−0.0453435	−	0.178930i
$955$		0			0
$956$	−14.9894	+	41.1831i	−0.484793	+	1.33196i
$957$	−17.5271	+	22.5227i	−0.566570	+	0.728056i
$958$	1.65563	+	18.9239i	0.0534909	+	0.611404i
$959$	63.9290	+	53.6428i	2.06438	+	1.73222i
$960$		0			0
$961$	24.6489	+	8.97148i	0.795127	+	0.289402i
$962$	5.69827	−	1.52685i	0.183720	−	0.0492275i
$963$	−6.15061	+	2.14430i	−0.198201	+	0.0690991i
$964$	−21.8332	+	12.6054i	−0.703199	+	0.405992i
$965$		0			0
$966$	39.9290	−	20.4416i	1.28469	−	0.657697i
$967$	3.92572	−	8.41873i	0.126243	−	0.270728i	−0.833021	−	0.553242i	$-0.813391\pi$
$967$	3.92572	−	8.41873i	0.126243	−	0.270728i	0.959263	+	0.282514i	$0.0911683\pi$
$968$	7.81810	+	11.1654i	0.251283	+	0.358869i
$969$	68.3620	+	15.6443i	2.19610	+	0.502567i
$970$		0			0
$971$		−	46.4051i		−	1.48921i	−0.667506	−	0.744605i	$-0.732638\pi$
$971$		−	46.4051i		−	1.48921i	0.667506	−	0.744605i	$-0.267362\pi$
$972$	−11.2886	+	19.9935i	−0.362081	+	0.641293i
$973$	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
$977$	−39.9638	−	18.6354i	−1.27856	−	0.596201i	−0.339708	−	0.940531i	$-0.610328\pi$
$977$	−39.9638	−	18.6354i	−1.27856	−	0.596201i	−0.938849	+	0.344330i	$0.888106\pi$
$978$	−7.94066	+	24.5996i	−0.253914	+	0.786607i
$979$	0.0550236	−	0.00970214i	0.00175856	−	0.000310082i
$980$		0			0
$981$	23.0006	+	11.1089i	0.734352	+	0.354681i
$982$	−4.63127	−	17.2841i	−0.147790	−	0.551559i
$983$	16.6857	−	7.78065i	0.532190	−	0.248164i	−0.137897	−	0.990447i	$-0.544034\pi$
$983$	16.6857	−	7.78065i	0.532190	−	0.248164i	0.670087	+	0.742282i	$0.266257\pi$
$984$	18.8790	+	7.97089i	0.601841	+	0.254103i
$985$		0			0
$986$	−19.3877	+	23.1054i	−0.617431	+	0.735826i
$987$	−62.6306	−	48.7389i	−1.99355	−	1.55137i
$988$	6.87049	+	14.7338i	0.218580	+	0.468745i
$989$	12.3587	−	21.4059i	0.392983	−	0.680667i
$990$		0			0
$991$	15.5919	+	27.0059i	0.495292	+	0.857871i	0.999985	−	0.00542792i	$-0.00172777\pi$
$991$	15.5919	+	27.0059i	0.495292	+	0.857871i	−0.504693	+	0.863299i	$0.668394\pi$
$992$	7.33077	−	10.4694i	0.232752	−	0.332404i
$993$	14.9927	−	13.5517i	0.475779	−	0.430052i
$994$	−1.20892	−	3.32149i	−0.0383447	−	0.105351i
$995$		0			0
$996$	1.79002	−	0.551028i	0.0567190	−	0.0174600i
$997$	−2.86290	+	32.7231i	−0.0906689	+	1.03635i	0.805488	+	0.592612i	$0.201903\pi$
$997$	−2.86290	+	32.7231i	−0.0906689	+	1.03635i	−0.896157	+	0.443738i	$0.853652\pi$
$998$	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.518.10	yes	288
5.2	odd	4	inner	675.2.ba.c.32.15	yes	288
5.3	odd	4	inner	675.2.ba.c.32.10	✓	288
5.4	even	2	inner	675.2.ba.c.518.15	yes	288
27.11	odd	18	inner	675.2.ba.c.443.15	yes	288
135.38	even	36	inner	675.2.ba.c.632.15	yes	288
135.92	even	36	inner	675.2.ba.c.632.10	yes	288
135.119	odd	18	inner	675.2.ba.c.443.10	yes	288

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
675.2.ba.c.32.10	✓	288	5.3	odd	4	inner
675.2.ba.c.32.15	yes	288	5.2	odd	4	inner
675.2.ba.c.443.10	yes	288	135.119	odd	18	inner
675.2.ba.c.443.15	yes	288	27.11	odd	18	inner
675.2.ba.c.518.10	yes	288	1.1	even	1	trivial
675.2.ba.c.518.15	yes	288	5.4	even	2	inner
675.2.ba.c.632.10	yes	288	135.92	even	36	inner
675.2.ba.c.632.15	yes	288	135.38	even	36	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+(-0.723253 - 0.0632765i) q^{2} +(0.920668 + 1.46710i) q^{3} +(-1.45052 - 0.255767i) q^{4} +(-0.573043 - 1.11934i) q^{6} +(-3.84096 - 2.68947i) q^{7} +(2.43547 + 0.652582i) q^{8} +(-1.30474 + 2.70142i) q^{9} +(-0.808938 + 2.22254i) q^{11} +(-0.960217 - 2.36353i) q^{12} +(-0.141685 - 1.61947i) q^{13} +(2.60780 + 2.18821i) q^{14} +(1.04798 + 0.381434i) q^{16} +(5.76028 - 1.54346i) q^{17} +(1.11459 - 1.87125i) q^{18} +(5.87988 - 3.39475i) q^{19} +(0.409461 - 8.11116i) q^{21} +(0.725702 - 1.55627i) q^{22} +(-4.36358 - 6.23184i) q^{23} +(1.28486 + 4.17388i) q^{24} +1.18025i q^{26} +(-5.16447 + 0.572926i) q^{27} +(4.88352 + 4.88352i) q^{28} +(5.33663 - 4.47797i) q^{29} +(-0.379220 + 2.15066i) q^{31} +(-5.30412 - 2.47335i) q^{32} +(-4.00544 + 0.859430i) q^{33} +(-4.26381 + 0.751824i) q^{34} +(2.58349 - 3.58476i) q^{36} +(-1.29366 - 4.82802i) q^{37} +(-4.46745 + 2.08321i) q^{38} +(2.24547 - 1.69886i) q^{39} +(3.01626 - 3.59464i) q^{41} +(-0.809389 + 5.84051i) q^{42} +(1.37309 + 2.94459i) q^{43} +(1.74184 - 3.01695i) q^{44} +(2.76165 + 4.78331i) q^{46} +(5.60479 - 8.00447i) q^{47} +(0.405242 + 1.88866i) q^{48} +(5.12557 + 14.0824i) q^{49} +(7.56772 + 7.02987i) q^{51} +(-0.208688 + 2.38532i) q^{52} +(1.85094 - 1.85094i) q^{53} +(3.77147 - 0.0875810i) q^{54} +(-7.59943 - 9.05665i) q^{56} +(10.3938 + 5.50091i) q^{57} +(-4.14309 + 2.90102i) q^{58} +(-4.22316 + 1.53710i) q^{59} +(0.391593 + 2.22083i) q^{61} +(0.410358 - 1.53148i) q^{62} +(12.2768 - 6.86696i) q^{63} +(1.74806 + 1.00925i) q^{64} +(2.95133 - 0.368136i) q^{66} +(-7.96068 + 0.696469i) q^{67} +(-8.75020 + 0.765543i) q^{68} +(5.12530 - 12.1393i) q^{69} +(-0.899200 - 0.519153i) q^{71} +(-4.94055 + 5.72776i) q^{72} +(0.991667 - 3.70095i) q^{73} +(0.630146 + 3.57374i) q^{74} +(-9.39718 + 3.42029i) q^{76} +(9.08454 - 6.36106i) q^{77} +(-1.73154 + 1.08662i) q^{78} +(-4.12821 - 4.91981i) q^{79} +(-5.59530 - 7.04930i) q^{81} +(-2.40897 + 2.40897i) q^{82} +(-0.0639852 + 0.731354i) q^{83} +(-2.66850 + 11.6607i) q^{84} +(-0.806766 - 2.21657i) q^{86} +(11.4829 + 3.70663i) q^{87} +(-3.42053 + 4.88502i) q^{88} +(-0.0118115 - 0.0204581i) q^{89} +(-3.81130 + 6.60136i) q^{91} +(4.73559 + 10.1555i) q^{92} +(-3.50436 + 1.42369i) q^{93} +(-4.56018 + 5.43461i) q^{94} +(-1.25469 - 10.0588i) q^{96} +(-2.80057 + 1.30593i) q^{97} +(-2.81600 - 10.5095i) 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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