LMFDB - Embedded newform 300.2.o.a.109.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [300,2,Mod(109,300)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(300, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 7]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("300.109");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 300 = 2^{2} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	300.o (of order $10$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$2.39551206064$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			109.6
Character	$\chi$	$=$	300.109
Dual form			300.2.o.a.289.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.951057 - 0.309017i) q^{3} +(2.23394 - 0.0974182i) q^{5} -1.31873i q^{7} +(0.809017 - 0.587785i) q^{9} +O(q^{10})$	\(q+(0.951057 - 0.309017i) q^{3} +(2.23394 - 0.0974182i) q^{5} -1.31873i q^{7} +(0.809017 - 0.587785i) q^{9} +(-1.25737 - 0.913532i) q^{11} +(1.42727 + 1.96447i) q^{13} +(2.09450 - 0.782977i) q^{15} +(-1.25004 - 0.406161i) q^{17} +(0.315522 - 0.971077i) q^{19} +(-0.407508 - 1.25418i) q^{21} +(-2.94350 + 4.05137i) q^{23} +(4.98102 - 0.435254i) q^{25} +(0.587785 - 0.809017i) q^{27} +(1.82443 + 5.61503i) q^{29} +(2.73547 - 8.41891i) q^{31} +(-1.47813 - 0.480272i) q^{33} +(-0.128468 - 2.94596i) q^{35} +(-2.95370 - 4.06542i) q^{37} +(1.96447 + 1.42727i) q^{39} +(-6.43499 + 4.67529i) q^{41} +6.84831i q^{43} +(1.75004 - 1.39189i) q^{45} +(-7.37336 + 2.39575i) q^{47} +5.26096 q^{49} -1.31436 q^{51} +(-3.75685 + 1.22067i) q^{53} +(-2.89789 - 1.91829i) q^{55} -1.02105i q^{57} +(-6.35355 + 4.61613i) q^{59} +(2.83287 + 2.05820i) q^{61} +(-0.775127 - 1.06687i) q^{63} +(3.37982 + 4.24947i) q^{65} +(-7.92426 - 2.57475i) q^{67} +(-1.54749 + 4.76268i) q^{69} +(-4.00454 - 12.3247i) q^{71} +(-7.47339 + 10.2862i) q^{73} +(4.60273 - 1.95317i) q^{75} +(-1.20470 + 1.65812i) q^{77} +(0.386585 + 1.18979i) q^{79} +(0.309017 - 0.951057i) q^{81} +(-7.80521 - 2.53607i) q^{83} +(-2.83208 - 0.785565i) q^{85} +(3.47028 + 4.77643i) q^{87} +(7.74667 + 5.62829i) q^{89} +(2.59059 - 1.88218i) q^{91} -8.85217i q^{93} +(0.610258 - 2.20007i) q^{95} +(-15.4769 + 5.02874i) q^{97} -1.55419 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 2 q^{5} + 6 q^{9}+O(q^{10}) $ 24 * q - 2 * q^5 + 6 * q^9	$ 24 q - 2 q^{5} + 6 q^{9} - 6 q^{11} + 4 q^{15} + 10 q^{17} + 10 q^{19} - 4 q^{21} + 40 q^{23} - 4 q^{25} + 4 q^{29} + 6 q^{31} + 10 q^{33} - 6 q^{35} - 10 q^{41} + 2 q^{45} - 40 q^{47} - 56 q^{49} + 16 q^{51} - 60 q^{53} - 62 q^{55} - 36 q^{59} - 12 q^{61} - 10 q^{63} + 20 q^{67} + 4 q^{69} + 40 q^{71} + 60 q^{73} + 8 q^{75} - 40 q^{77} + 8 q^{79} - 6 q^{81} - 50 q^{83} + 34 q^{85} - 20 q^{87} - 30 q^{91} - 60 q^{95} - 40 q^{97} - 4 q^{99}+O(q^{100}) $ 24 * q - 2 * q^5 + 6 * q^9 - 6 * q^11 + 4 * q^15 + 10 * q^17 + 10 * q^19 - 4 * q^21 + 40 * q^23 - 4 * q^25 + 4 * q^29 + 6 * q^31 + 10 * q^33 - 6 * q^35 - 10 * q^41 + 2 * q^45 - 40 * q^47 - 56 * q^49 + 16 * q^51 - 60 * q^53 - 62 * q^55 - 36 * q^59 - 12 * q^61 - 10 * q^63 + 20 * q^67 + 4 * q^69 + 40 * q^71 + 60 * q^73 + 8 * q^75 - 40 * q^77 + 8 * q^79 - 6 * q^81 - 50 * q^83 + 34 * q^85 - 20 * q^87 - 30 * q^91 - 60 * q^95 - 40 * q^97 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/300\mathbb{Z}\right)^\times$.

$n$	$101$	$151$	$277$
$\chi(n)$	$1$	$1$	$e\left(\frac{7}{10}\right)$

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			0
$2$		0			0
$3$	0.951057	−	0.309017i	0.549093	−	0.178411i
$3$	0.951057	−	0.309017i	0.549093	−	0.178411i
$4$		0			0
$5$	2.23394	−	0.0974182i	0.999051	−	0.0435667i
$5$	2.23394	−	0.0974182i	0.999051	−	0.0435667i
$6$		0			0
$7$		−	1.31873i		−	0.498431i	−0.968448	−	0.249216i	$-0.919827\pi$
$7$		−	1.31873i		−	0.498431i	0.968448	−	0.249216i	$-0.0801728\pi$
$8$		0			0
$9$	0.809017	−	0.587785i	0.269672	−	0.195928i
$10$		0			0
$11$	−1.25737	−	0.913532i	−0.379111	−	0.275440i	0.381868	−	0.924217i	$-0.375281\pi$
$11$	−1.25737	−	0.913532i	−0.379111	−	0.275440i	−0.760979	+	0.648777i	$0.775281\pi$
$12$		0			0
$13$	1.42727	+	1.96447i	0.395854	+	0.544846i	0.959697	−	0.281036i	$-0.0906780\pi$
$13$	1.42727	+	1.96447i	0.395854	+	0.544846i	−0.563844	+	0.825882i	$0.690678\pi$
$14$		0			0
$15$	2.09450	−	0.782977i	0.540799	−	0.202164i
$16$		0			0
$17$	−1.25004	−	0.406161i	−0.303178	−	0.0985085i	0.153477	−	0.988152i	$-0.450953\pi$
$17$	−1.25004	−	0.406161i	−0.303178	−	0.0985085i	−0.456655	+	0.889644i	$0.650953\pi$
$18$		0			0
$19$	0.315522	−	0.971077i	0.0723857	−	0.222780i	−0.908318	−	0.418280i	$-0.862633\pi$
$19$	0.315522	−	0.971077i	0.0723857	−	0.222780i	0.980704	+	0.195500i	$0.0626330\pi$
$20$		0			0
$21$	−0.407508	−	1.25418i	−0.0889256	−	0.273685i
$22$		0			0
$23$	−2.94350	+	4.05137i	−0.613761	+	0.844770i	−0.996880	−	0.0789291i	$-0.974850\pi$
$23$	−2.94350	+	4.05137i	−0.613761	+	0.844770i	0.383119	+	0.923699i	$0.374850\pi$
$24$		0			0
$25$	4.98102	−	0.435254i	0.996204	−	0.0870507i
$26$		0			0
$27$	0.587785	−	0.809017i	0.113119	−	0.155695i
$28$		0			0
$29$	1.82443	+	5.61503i	0.338789	+	1.04268i	0.964825	+	0.262891i	$0.0846760\pi$
$29$	1.82443	+	5.61503i	0.338789	+	1.04268i	−0.626037	+	0.779794i	$0.715324\pi$
$30$		0			0
$31$	2.73547	−	8.41891i	0.491305	−	1.51208i	−0.331332	−	0.943514i	$-0.607498\pi$
$31$	2.73547	−	8.41891i	0.491305	−	1.51208i	0.822637	−	0.568567i	$-0.192502\pi$
$32$		0			0
$33$	−1.47813	−	0.480272i	−0.257309	−	0.0836047i
$34$		0			0
$35$	−0.128468	−	2.94596i	−0.0217150	−	0.497958i
$36$		0			0
$37$	−2.95370	−	4.06542i	−0.485586	−	0.668352i	0.493981	−	0.869473i	$-0.335541\pi$
$37$	−2.95370	−	4.06542i	−0.485586	−	0.668352i	−0.979566	+	0.201121i	$0.935541\pi$
$38$		0			0
$39$	1.96447	+	1.42727i	0.314567	+	0.228546i
$40$		0			0
$41$	−6.43499	+	4.67529i	−1.00498	+	0.730158i	−0.963150	−	0.268967i	$-0.913318\pi$
$41$	−6.43499	+	4.67529i	−1.00498	+	0.730158i	−0.0418271	+	0.999125i	$0.513318\pi$
$42$		0			0
$43$			6.84831i			1.04436i	0.852836	+	0.522179i	$0.174881\pi$
$43$			6.84831i			1.04436i	−0.852836	+	0.522179i	$0.825119\pi$
$44$		0			0
$45$	1.75004	−	1.39189i	0.260880	−	0.207491i
$46$		0			0
$47$	−7.37336	+	2.39575i	−1.07552	+	0.349456i	−0.792633	−	0.609698i	$-0.791291\pi$
$47$	−7.37336	+	2.39575i	−1.07552	+	0.349456i	−0.282882	+	0.959155i	$0.591291\pi$
$48$		0			0
$49$	5.26096			0.751566
$50$		0			0
$51$	−1.31436			−0.184048
$52$		0			0
$53$	−3.75685	+	1.22067i	−0.516043	+	0.167673i	−0.555449	−	0.831551i	$-0.687454\pi$
$53$	−3.75685	+	1.22067i	−0.516043	+	0.167673i	0.0394057	+	0.999223i	$0.487454\pi$
$54$		0			0
$55$	−2.89789	−	1.91829i	−0.390751	−	0.258662i
$56$		0			0
$57$		−	1.02105i		−	0.135241i
$58$		0			0
$59$	−6.35355	+	4.61613i	−0.827162	+	0.600969i	−0.918755	−	0.394828i	$-0.870804\pi$
$59$	−6.35355	+	4.61613i	−0.827162	+	0.600969i	0.0915928	+	0.995797i	$0.470804\pi$
$60$		0			0
$61$	2.83287	+	2.05820i	0.362711	+	0.263525i	0.754182	−	0.656665i	$-0.228034\pi$
$61$	2.83287	+	2.05820i	0.362711	+	0.263525i	−0.391471	+	0.920191i	$0.628034\pi$
$62$		0			0
$63$	−0.775127	−	1.06687i	−0.0976568	−	0.134413i
$64$		0			0
$65$	3.37982	+	4.24947i	0.419215	+	0.527082i
$66$		0			0
$67$	−7.92426	−	2.57475i	−0.968102	−	0.314555i	−0.218052	−	0.975937i	$-0.569970\pi$
$67$	−7.92426	−	2.57475i	−0.968102	−	0.314555i	−0.750050	+	0.661382i	$0.769970\pi$
$68$		0			0
$69$	−1.54749	+	4.76268i	−0.186296	+	0.573359i
$70$		0			0
$71$	−4.00454	−	12.3247i	−0.475252	−	1.46267i	−0.845618	−	0.533788i	$-0.820768\pi$
$71$	−4.00454	−	12.3247i	−0.475252	−	1.46267i	0.370366	−	0.928886i	$-0.379232\pi$
$72$		0			0
$73$	−7.47339	+	10.2862i	−0.874694	+	1.20391i	0.103168	+	0.994664i	$0.467102\pi$
$73$	−7.47339	+	10.2862i	−0.874694	+	1.20391i	−0.977862	+	0.209249i	$0.932898\pi$
$74$		0			0
$75$	4.60273	−	1.95317i	0.531477	−	0.225533i
$76$		0			0
$77$	−1.20470	+	1.65812i	−0.137288	+	0.188961i
$78$		0			0
$79$	0.386585	+	1.18979i	0.0434942	+	0.133861i	0.970446	−	0.241320i	$-0.0775804\pi$
$79$	0.386585	+	1.18979i	0.0434942	+	0.133861i	−0.926951	+	0.375182i	$0.877580\pi$
$80$		0			0
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$		0			0
$83$	−7.80521	−	2.53607i	−0.856734	−	0.278370i	−0.152470	−	0.988308i	$-0.548723\pi$
$83$	−7.80521	−	2.53607i	−0.856734	−	0.278370i	−0.704264	+	0.709939i	$0.748723\pi$
$84$		0			0
$85$	−2.83208	−	0.785565i	−0.307182	−	0.0852065i
$86$		0			0
$87$	3.47028	+	4.77643i	0.372053	+	0.512087i
$88$		0			0
$89$	7.74667	+	5.62829i	0.821146	+	0.596597i	0.917040	−	0.398794i	$-0.130571\pi$
$89$	7.74667	+	5.62829i	0.821146	+	0.596597i	−0.0958948	+	0.995391i	$0.530571\pi$
$90$		0			0
$91$	2.59059	−	1.88218i	0.271568	−	0.197306i
$92$		0			0
$93$		−	8.85217i		−	0.917927i
$94$		0			0
$95$	0.610258	−	2.20007i	0.0626112	−	0.225722i
$96$		0			0
$97$	−15.4769	+	5.02874i	−1.57144	+	0.510591i	−0.959833	−	0.280573i	$-0.909476\pi$
$97$	−15.4769	+	5.02874i	−1.57144	+	0.510591i	−0.611604	+	0.791164i	$0.709476\pi$
$98$		0			0
$99$	−1.55419			−0.156202
$100$		0			0
$101$	5.63722			0.560925			0.280462	−	0.959865i	$-0.409512\pi$
$101$	5.63722			0.560925			0.280462	+	0.959865i	$0.409512\pi$
$102$		0			0
$103$	8.00179	−	2.59994i	0.788439	−	0.256179i	0.113000	−	0.993595i	$-0.463954\pi$
$103$	8.00179	−	2.59994i	0.788439	−	0.256179i	0.675439	+	0.737415i	$0.263954\pi$
$104$		0			0
$105$	−1.03253	−	2.76208i	−0.100765	−	0.269551i
$106$		0			0
$107$		−	2.06196i		−	0.199337i	−0.995021	−	0.0996687i	$-0.968222\pi$
$107$		−	2.06196i		−	0.199337i	0.995021	−	0.0996687i	$-0.0317783\pi$
$108$		0			0
$109$	11.3052	−	8.21372i	1.08284	−	0.786731i	0.104666	−	0.994507i	$-0.466623\pi$
$109$	11.3052	−	8.21372i	1.08284	−	0.786731i	0.978176	+	0.207776i	$0.0666226\pi$
$110$		0			0
$111$	−4.06542	−	2.95370i	−0.385873	−	0.280353i
$112$		0			0
$113$	3.50093	+	4.81862i	0.329340	+	0.453297i	0.941290	−	0.337599i	$-0.109615\pi$
$113$	3.50093	+	4.81862i	0.329340	+	0.453297i	−0.611950	+	0.790896i	$0.709615\pi$
$114$		0			0
$115$	−6.18093	+	9.33730i	−0.576375	+	0.870707i
$116$		0			0
$117$	2.30937	+	0.750360i	0.213502	+	0.0693708i
$118$		0			0
$119$	−0.535615	+	1.64845i	−0.0490997	+	0.151113i
$120$		0			0
$121$	−2.65275	−	8.16433i	−0.241159	−	0.742211i
$122$		0			0
$123$	−4.67529	+	6.43499i	−0.421557	+	0.580224i
$124$		0			0
$125$	11.0849	−	1.45757i	0.991465	−	0.130369i
$126$		0			0
$127$	−1.42406	+	1.96004i	−0.126364	+	0.173926i	−0.867512	−	0.497417i	$-0.834282\pi$
$127$	−1.42406	+	1.96004i	−0.126364	+	0.173926i	0.741147	+	0.671342i	$0.234282\pi$
$128$		0			0
$129$	2.11624	+	6.51313i	0.186325	+	0.573449i
$130$		0			0
$131$	3.37948	−	10.4010i	0.295267	−	0.908737i	−0.687865	−	0.725839i	$-0.741452\pi$
$131$	3.37948	−	10.4010i	0.295267	−	0.908737i	0.983132	−	0.182899i	$-0.0585481\pi$
$132$		0			0
$133$	−1.28058	−	0.416087i	−0.111041	−	0.0360793i
$134$		0			0
$135$	1.23427	−	1.86456i	0.106229	−	0.160476i
$136$		0			0
$137$	2.19602	+	3.02256i	0.187618	+	0.258235i	0.892456	−	0.451134i	$-0.148980\pi$
$137$	2.19602	+	3.02256i	0.187618	+	0.258235i	−0.704838	+	0.709368i	$0.748980\pi$
$138$		0			0
$139$	−1.73765	−	1.26247i	−0.147385	−	0.107082i	0.511649	−	0.859194i	$-0.329035\pi$
$139$	−1.73765	−	1.26247i	−0.147385	−	0.107082i	−0.659034	+	0.752113i	$0.729035\pi$
$140$		0			0
$141$	−6.27216	+	4.55699i	−0.528211	+	0.383768i
$142$		0			0
$143$		−	3.77392i		−	0.315591i
$144$		0			0
$145$	4.62269	+	12.3659i	0.383894	+	1.02693i
$146$		0			0
$147$	5.00347	−	1.62573i	0.412680	−	0.134088i
$148$		0			0
$149$	7.85344			0.643379			0.321690	−	0.946845i	$-0.395749\pi$
$149$	7.85344			0.643379			0.321690	+	0.946845i	$0.395749\pi$
$150$		0			0
$151$	22.5124			1.83203			0.916016	−	0.401141i	$-0.131386\pi$
$151$	22.5124			1.83203			0.916016	+	0.401141i	$0.131386\pi$
$152$		0			0
$153$	−1.25004	+	0.406161i	−0.101059	+	0.0328362i
$154$		0			0
$155$	5.29073	−	19.0739i	0.424962	−	1.53205i
$156$		0			0
$157$		−	19.4083i		−	1.54895i	−0.632602	−	0.774477i	$-0.718013\pi$
$157$		−	19.4083i		−	1.54895i	0.632602	−	0.774477i	$-0.281987\pi$
$158$		0			0
$159$	−3.19577	+	2.32186i	−0.253441	+	0.184136i
$160$		0			0
$161$	5.34265	+	3.88166i	0.421060	+	0.305918i
$162$		0			0
$163$	8.89817	+	12.2473i	0.696959	+	0.959281i	0.999980	+	0.00629741i	$0.00200454\pi$
$163$	8.89817	+	12.2473i	0.696959	+	0.959281i	−0.303022	+	0.952984i	$0.597995\pi$
$164$		0			0
$165$	−3.34884	−	0.928906i	−0.260707	−	0.0723152i
$166$		0			0
$167$	17.9807	+	5.84227i	1.39139	+	0.452089i	0.906395	−	0.422431i	$-0.138823\pi$
$167$	17.9807	+	5.84227i	1.39139	+	0.452089i	0.484990	+	0.874519i	$0.338823\pi$
$168$		0			0
$169$	2.19518	−	6.75608i	0.168860	−	0.519698i
$170$		0			0
$171$	−0.315522	−	0.971077i	−0.0241286	−	0.0742601i
$172$		0			0
$173$	14.1479	−	19.4729i	1.07564	−	1.48050i	0.211415	−	0.977396i	$-0.432193\pi$
$173$	14.1479	−	19.4729i	1.07564	−	1.48050i	0.864228	−	0.503100i	$-0.167807\pi$
$174$		0			0
$175$	−0.573980	−	6.56860i	−0.0433888	−	0.496539i
$176$		0			0
$177$	−4.61613	+	6.35355i	−0.346969	+	0.477562i
$178$		0			0
$179$	−0.461162	−	1.41931i	−0.0344689	−	0.106084i	0.932342	−	0.361578i	$-0.117762\pi$
$179$	−0.461162	−	1.41931i	−0.0344689	−	0.106084i	−0.966811	+	0.255494i	$0.917762\pi$
$180$		0			0
$181$	−0.809018	+	2.48990i	−0.0601338	+	0.185073i	−0.976611	−	0.215014i	$-0.931020\pi$
$181$	−0.809018	+	2.48990i	−0.0601338	+	0.185073i	0.916477	+	0.400087i	$0.131020\pi$
$182$		0			0
$183$	3.33023	+	1.08206i	0.246178	+	0.0799881i
$184$		0			0
$185$	−6.99446	−	8.79419i	−0.514243	−	0.646562i
$186$		0			0
$187$	1.20071	+	1.65264i	0.0878050	+	0.120853i
$188$		0			0
$189$	−1.06687	−	0.775127i	−0.0776035	−	0.0563822i
$190$		0			0
$191$	−16.6599	+	12.1041i	−1.20547	+	0.875824i	−0.994811	−	0.101736i	$-0.967560\pi$
$191$	−16.6599	+	12.1041i	−1.20547	+	0.875824i	−0.210657	+	0.977560i	$0.567560\pi$
$192$		0			0
$193$		−	5.15953i		−	0.371391i	−0.982607	−	0.185696i	$-0.940546\pi$
$193$		−	5.15953i		−	0.371391i	0.982607	−	0.185696i	$-0.0594539\pi$
$194$		0			0
$195$	4.52756	+	2.99707i	0.324225	+	0.214625i
$196$		0			0
$197$	9.99630	−	3.24799i	0.712207	−	0.231410i	0.0695657	−	0.997577i	$-0.477839\pi$
$197$	9.99630	−	3.24799i	0.712207	−	0.231410i	0.642641	+	0.766167i	$0.277839\pi$
$198$		0			0
$199$	−3.65216			−0.258895			−0.129447	−	0.991586i	$-0.541320\pi$
$199$	−3.65216			−0.258895			−0.129447	+	0.991586i	$0.541320\pi$
$200$		0			0
$201$	−8.33206			−0.587698
$202$		0			0
$203$	7.40468	−	2.40593i	0.519707	−	0.168863i
$204$		0			0
$205$	−13.9200	+	11.0712i	−0.972212	+	0.773249i
$206$		0			0
$207$			5.00777i			0.348064i
$208$		0			0
$209$	−1.28384	+	0.932763i	−0.0888049	+	0.0645206i
$210$		0			0
$211$	21.3259	+	15.4941i	1.46813	+	1.06666i	0.981150	+	0.193249i	$0.0619026\pi$
$211$	21.3259	+	15.4941i	1.46813	+	1.06666i	0.486983	+	0.873411i	$0.338097\pi$
$212$		0			0
$213$	−7.61709	−	10.4840i	−0.521914	−	0.718354i
$214$		0			0
$215$	0.667150	+	15.2988i	0.0454993	+	1.04337i
$216$		0			0
$217$	−11.1022	−	3.60733i	−0.753669	−	0.244882i
$218$		0			0
$219$	−3.92899	+	12.0922i	−0.265497	+	0.817115i
$220$		0			0
$221$	−0.986247	−	3.03536i	−0.0663422	−	0.204180i
$222$		0			0
$223$	−10.8706	+	14.9621i	−0.727950	+	1.00194i	0.271272	+	0.962503i	$0.412556\pi$
$223$	−10.8706	+	14.9621i	−0.727950	+	1.00194i	−0.999222	+	0.0394348i	$0.987444\pi$
$224$		0			0
$225$	3.77389	−	3.27990i	0.251593	−	0.218660i
$226$		0			0
$227$	10.9690	−	15.0976i	0.728039	−	1.00206i	−0.271179	−	0.962529i	$-0.587414\pi$
$227$	10.9690	−	15.0976i	0.728039	−	1.00206i	0.999218	−	0.0395311i	$-0.0125864\pi$
$228$		0			0
$229$	−8.63423	−	26.5734i	−0.570566	−	1.75602i	−0.650803	−	0.759247i	$-0.725568\pi$
$229$	−8.63423	−	26.5734i	−0.570566	−	1.75602i	0.0802368	−	0.996776i	$-0.474432\pi$
$230$		0			0
$231$	−0.633347	+	1.94924i	−0.0416712	+	0.128251i
$232$		0			0
$233$	−23.5456	−	7.65043i	−1.54252	−	0.501196i	−0.590452	−	0.807073i	$-0.701050\pi$
$233$	−23.5456	−	7.65043i	−1.54252	−	0.501196i	−0.952071	+	0.305877i	$0.901050\pi$
$234$		0			0
$235$	−16.2383	+	6.07028i	−1.05927	+	0.395981i
$236$		0			0
$237$	0.735329	+	1.01209i	0.0477647	+	0.0657425i
$238$		0			0
$239$	−9.47102	−	6.88110i	−0.612629	−	0.445101i	0.237710	−	0.971336i	$-0.423603\pi$
$239$	−9.47102	−	6.88110i	−0.612629	−	0.445101i	−0.850339	+	0.526235i	$0.823603\pi$
$240$		0			0
$241$	−24.1221	+	17.5257i	−1.55384	+	1.12893i	−0.612998	+	0.790084i	$0.710037\pi$
$241$	−24.1221	+	17.5257i	−1.55384	+	1.12893i	−0.940842	+	0.338846i	$0.889963\pi$
$242$		0			0
$243$		−	1.00000i		−	0.0641500i
$244$		0			0
$245$	11.7527	−	0.512514i	0.750853	−	0.0327433i
$246$		0			0
$247$	2.35799	−	0.766156i	0.150035	−	0.0487493i
$248$		0			0
$249$	−8.20689			−0.520090
$250$		0			0
$251$	−2.87297			−0.181340			−0.0906700	−	0.995881i	$-0.528901\pi$
$251$	−2.87297			−0.181340			−0.0906700	+	0.995881i	$0.528901\pi$
$252$		0			0
$253$	7.40212	−	2.40510i	0.465367	−	0.151207i
$254$		0			0
$255$	−2.93622	+	0.128043i	−0.183873	+	0.00801837i
$256$		0			0
$257$			8.11716i			0.506334i	0.967423	+	0.253167i	$0.0814723\pi$
$257$			8.11716i			0.506334i	−0.967423	+	0.253167i	$0.918528\pi$
$258$		0			0
$259$	−5.36118	+	3.89512i	−0.333127	+	0.242031i
$260$		0			0
$261$	4.77643	+	3.47028i	0.295654	+	0.214805i
$262$		0			0
$263$	13.1117	+	18.0467i	0.808501	+	1.11281i	0.991553	+	0.129703i	$0.0414025\pi$
$263$	13.1117	+	18.0467i	0.808501	+	1.11281i	−0.183051	+	0.983103i	$0.558597\pi$
$264$		0			0
$265$	−8.27368	+	3.09291i	−0.508248	+	0.189996i
$266$		0			0
$267$	9.10676	+	2.95897i	0.557325	+	0.181086i
$268$		0			0
$269$	2.53369	−	7.79789i	0.154482	−	0.475446i	−0.843626	−	0.536931i	$-0.819584\pi$
$269$	2.53369	−	7.79789i	0.154482	−	0.475446i	0.998108	+	0.0614851i	$0.0195837\pi$
$270$		0			0
$271$	−2.93158	−	9.02246i	−0.178081	−	0.548075i	0.821680	−	0.569949i	$-0.193037\pi$
$271$	−2.93158	−	9.02246i	−0.178081	−	0.548075i	−0.999761	+	0.0218733i	$0.993037\pi$
$272$		0			0
$273$	1.88218	−	2.59059i	0.113915	−	0.156790i
$274$		0			0
$275$	−6.66060	−	4.00305i	−0.401649	−	0.241393i
$276$		0			0
$277$	0.270190	−	0.371885i	0.0162341	−	0.0223444i	−0.800823	−	0.598901i	$-0.795604\pi$
$277$	0.270190	−	0.371885i	0.0162341	−	0.0223444i	0.817057	+	0.576557i	$0.195604\pi$
$278$		0			0
$279$	−2.73547	−	8.41891i	−0.163768	−	0.504027i
$280$		0			0
$281$	−4.71493	+	14.5111i	−0.281269	+	0.865658i	0.706223	+	0.707990i	$0.250398\pi$
$281$	−4.71493	+	14.5111i	−0.281269	+	0.865658i	−0.987492	+	0.157668i	$0.949602\pi$
$282$		0			0
$283$	10.1502	+	3.29800i	0.603366	+	0.196046i	0.594741	−	0.803917i	$-0.297255\pi$
$283$	10.1502	+	3.29800i	0.603366	+	0.196046i	0.00862506	+	0.999963i	$0.497255\pi$
$284$		0			0
$285$	−0.0994689	−	2.28097i	−0.00589203	−	0.135113i
$286$		0			0
$287$	6.16543	+	8.48598i	0.363934	+	0.500912i
$288$		0			0
$289$	−12.3557	−	8.97692i	−0.726804	−	0.528054i
$290$		0			0
$291$	−13.1654	+	9.56522i	−0.771770	+	0.560723i
$292$		0			0
$293$		−	30.8334i		−	1.80130i	−0.434541	−	0.900652i	$-0.643089\pi$
$293$		−	30.8334i		−	1.80130i	0.434541	−	0.900652i	$-0.356911\pi$
$294$		0			0
$295$	−13.7438	+	10.9311i	−0.800195	+	0.636435i
$296$		0			0
$297$	−1.47813	+	0.480272i	−0.0857696	+	0.0278682i
$298$		0			0
$299$	−12.1600			−0.703229
$300$		0			0
$301$	9.03104			0.520541
$302$		0			0
$303$	5.36132	−	1.74200i	0.308000	−	0.100075i
$304$		0			0
$305$	6.52897	+	4.32193i	0.373848	+	0.247473i
$306$		0			0
$307$			17.8634i			1.01952i	0.860318	+	0.509758i	$0.170265\pi$
$307$			17.8634i			1.01952i	−0.860318	+	0.509758i	$0.829735\pi$
$308$		0			0
$309$	6.80673	−	4.94538i	0.387221	−	0.281333i
$310$		0			0
$311$	9.75942	+	7.09063i	0.553406	+	0.402073i	0.829040	−	0.559190i	$-0.188888\pi$
$311$	9.75942	+	7.09063i	0.553406	+	0.402073i	−0.275634	+	0.961263i	$0.588888\pi$
$312$		0			0
$313$	11.0264	+	15.1766i	0.623250	+	0.857830i	0.997584	−	0.0694641i	$-0.0221289\pi$
$313$	11.0264	+	15.1766i	0.623250	+	0.857830i	−0.374335	+	0.927294i	$0.622129\pi$
$314$		0			0
$315$	−1.83552	−	2.30782i	−0.103420	−	0.130031i
$316$		0			0
$317$	−10.1912	−	3.31133i	−0.572395	−	0.185983i	0.00849553	−	0.999964i	$-0.497296\pi$
$317$	−10.1912	−	3.31133i	−0.572395	−	0.185983i	−0.580891	+	0.813981i	$0.697296\pi$
$318$		0			0
$319$	2.83552	−	8.72685i	0.158759	−	0.488610i
$320$		0			0
$321$	−0.637181	−	1.96104i	−0.0355640	−	0.109455i
$322$		0			0
$323$	−0.788827	+	1.08573i	−0.0438915	+	0.0604115i
$324$		0			0
$325$	7.96430	+	9.16383i	0.441780	+	0.508318i
$326$		0			0
$327$	8.21372	−	11.3052i	0.454219	−	0.625179i
$328$		0			0
$329$	3.15934	+	9.72344i	0.174180	+	0.536071i
$330$		0			0
$331$	0.671547	−	2.06681i	0.0369116	−	0.113602i	−0.930903	−	0.365266i	$-0.880978\pi$
$331$	0.671547	−	2.06681i	0.0369116	−	0.113602i	0.967815	+	0.251664i	$0.0809779\pi$
$332$		0			0
$333$	−4.77919	−	1.55285i	−0.261898	−	0.0850959i
$334$		0			0
$335$	−17.9532	−	4.97988i	−0.980887	−	0.272080i
$336$		0			0
$337$	−5.91844	−	8.14603i	−0.322398	−	0.443743i	0.616800	−	0.787120i	$-0.288429\pi$
$337$	−5.91844	−	8.14603i	−0.322398	−	0.443743i	−0.939197	+	0.343378i	$0.888429\pi$
$338$		0			0
$339$	4.81862	+	3.50093i	0.261711	+	0.190144i
$340$		0			0
$341$	−11.1304	+	8.08674i	−0.602747	+	0.437922i
$342$		0			0
$343$		−	16.1688i		−	0.873035i
$344$		0			0
$345$	−2.99303	+	10.7903i	−0.161139	+	0.580931i
$346$		0			0
$347$	13.9570	−	4.53489i	0.749249	−	0.243446i	0.0905912	−	0.995888i	$-0.471124\pi$
$347$	13.9570	−	4.53489i	0.749249	−	0.243446i	0.658658	+	0.752442i	$0.271124\pi$
$348$		0			0
$349$	−18.5685			−0.993949			−0.496974	−	0.867765i	$-0.665556\pi$
$349$	−18.5685			−0.993949			−0.496974	+	0.867765i	$0.665556\pi$
$350$		0			0
$351$	2.42822			0.129609
$352$		0			0
$353$	17.5663	−	5.70763i	0.934959	−	0.303787i	0.198370	−	0.980127i	$-0.436435\pi$
$353$	17.5663	−	5.70763i	0.934959	−	0.303787i	0.736589	+	0.676340i	$0.236435\pi$
$354$		0			0
$355$	−10.1466	−	27.1426i	−0.538524	−	1.44058i
$356$		0			0
$357$			1.73329i			0.0917352i
$358$		0			0
$359$	−19.9550	+	14.4981i	−1.05318	+	0.765182i	−0.972815	−	0.231583i	$-0.925609\pi$
$359$	−19.9550	+	14.4981i	−1.05318	+	0.765182i	−0.0803676	+	0.996765i	$0.525609\pi$
$360$		0			0
$361$	14.5279	+	10.5551i	0.764626	+	0.555533i
$362$		0			0
$363$	−5.04583	−	6.94499i	−0.264837	−	0.364517i
$364$		0			0
$365$	−15.6931	+	23.7069i	−0.821413	+	1.24088i
$366$		0			0
$367$	12.4469	+	4.04423i	0.649721	+	0.211107i	0.615291	−	0.788300i	$-0.289038\pi$
$367$	12.4469	+	4.04423i	0.649721	+	0.211107i	0.0344301	+	0.999407i	$0.489038\pi$
$368$		0			0
$369$	−2.45795	+	7.56478i	−0.127956	+	0.393807i
$370$		0			0
$371$	1.60973	+	4.95425i	0.0835733	+	0.257212i
$372$		0			0
$373$	−0.174079	+	0.239599i	−0.00901348	+	0.0124060i	−0.813500	−	0.581565i	$-0.802441\pi$
$373$	−0.174079	+	0.239599i	−0.00901348	+	0.0124060i	0.804486	+	0.593971i	$0.202441\pi$
$374$		0			0
$375$	10.0920	−	4.81166i	0.521147	−	0.248473i
$376$		0			0
$377$	−8.42659	+	11.5982i	−0.433992	+	0.597338i
$378$		0			0
$379$	−2.41901	−	7.44495i	−0.124256	−	0.382421i	0.869509	−	0.493918i	$-0.164436\pi$
$379$	−2.41901	−	7.44495i	−0.124256	−	0.382421i	−0.993765	+	0.111496i	$0.964436\pi$
$380$		0			0
$381$	−0.748670	+	2.30417i	−0.0383555	+	0.118046i
$382$		0			0
$383$	−19.8293	−	6.44294i	−1.01323	−	0.329219i	−0.245090	−	0.969500i	$-0.578818\pi$
$383$	−19.8293	−	6.44294i	−1.01323	−	0.329219i	−0.768140	+	0.640282i	$0.778818\pi$
$384$		0			0
$385$	−2.52970	+	3.82152i	−0.128925	+	0.194763i
$386$		0			0
$387$	4.02534	+	5.54040i	0.204619	+	0.281634i
$388$		0			0
$389$	−22.6010	−	16.4206i	−1.14592	−	0.832558i	−0.157985	−	0.987441i	$-0.550500\pi$
$389$	−22.6010	−	16.4206i	−1.14592	−	0.832558i	−0.987933	+	0.154883i	$0.950500\pi$
$390$		0			0
$391$	5.32498	−	3.86883i	0.269296	−	0.195655i
$392$		0			0
$393$		−	10.9362i		−	0.551660i
$394$		0			0
$395$	0.979517	+	2.62026i	0.0492848	+	0.131839i
$396$		0			0
$397$	30.6358	−	9.95418i	1.53757	−	0.499586i	0.586863	−	0.809686i	$-0.300363\pi$
$397$	30.6358	−	9.95418i	1.53757	−	0.499586i	0.950704	+	0.310100i	$0.100363\pi$
$398$		0			0
$399$	−1.34649			−0.0674086
$400$		0			0
$401$	−10.3441			−0.516562			−0.258281	−	0.966070i	$-0.583156\pi$
$401$	−10.3441			−0.516562			−0.258281	+	0.966070i	$0.583156\pi$
$402$		0			0
$403$	20.4429	−	6.64232i	1.01834	−	0.330877i
$404$		0			0
$405$	0.597677	−	2.15471i	0.0296988	−	0.107068i
$406$		0			0
$407$			7.81004i			0.387129i
$408$		0			0
$409$	29.7399	−	21.6073i	1.47054	−	1.06841i	0.490087	−	0.871673i	$-0.336965\pi$
$409$	29.7399	−	21.6073i	1.47054	−	1.06841i	0.980456	−	0.196739i	$-0.0630351\pi$
$410$		0			0
$411$	3.02256	+	2.19602i	0.149092	+	0.108322i
$412$		0			0
$413$	6.08740	+	8.37859i	0.299542	+	0.412284i
$414$		0			0
$415$	−17.6835	−	4.90507i	−0.868048	−	0.240780i
$416$		0			0
$417$	−2.04272	−	0.663721i	−0.100033	−	0.0325026i
$418$		0			0
$419$	8.74262	−	26.9070i	0.427105	−	1.31449i	−0.473859	−	0.880601i	$-0.657139\pi$
$419$	8.74262	−	26.9070i	0.427105	−	1.31449i	0.900964	−	0.433894i	$-0.142861\pi$
$420$		0			0
$421$	0.392142	+	1.20689i	0.0191118	+	0.0588202i	0.960158	−	0.279459i	$-0.0901551\pi$
$421$	0.392142	+	1.20689i	0.0191118	+	0.0588202i	−0.941046	+	0.338279i	$0.890155\pi$
$422$		0			0
$423$	−4.55699	+	6.27216i	−0.221568	+	0.304963i
$424$		0			0
$425$	−6.40323	−	1.47901i	−0.310602	−	0.0717427i
$426$		0			0
$427$	2.71420	−	3.73577i	0.131349	−	0.180787i
$428$		0			0
$429$	−1.16621	−	3.58921i	−0.0563049	−	0.173289i
$430$		0			0
$431$	2.24011	−	6.89434i	0.107902	−	0.332089i	−0.882498	−	0.470315i	$-0.844140\pi$
$431$	2.24011	−	6.89434i	0.107902	−	0.332089i	0.990401	+	0.138226i	$0.0441402\pi$
$432$		0			0
$433$	3.64988	+	1.18592i	0.175402	+	0.0569916i	0.395401	−	0.918508i	$-0.370606\pi$
$433$	3.64988	+	1.18592i	0.175402	+	0.0569916i	−0.219999	+	0.975500i	$0.570606\pi$
$434$		0			0
$435$	8.21772	+	10.3322i	0.394010	+	0.495392i
$436$		0			0
$437$	3.00546	+	4.13666i	0.143771	+	0.197883i
$438$		0			0
$439$	25.5358	+	18.5528i	1.21876	+	0.885479i	0.995996	−	0.0893940i	$-0.0284930\pi$
$439$	25.5358	+	18.5528i	1.21876	+	0.885479i	0.222761	+	0.974873i	$0.428493\pi$
$440$		0			0
$441$	4.25621	−	3.09232i	0.202677	−	0.147253i
$442$		0			0
$443$			2.65284i			0.126040i	0.998012	+	0.0630200i	$0.0200732\pi$
$443$			2.65284i			0.126040i	−0.998012	+	0.0630200i	$0.979927\pi$
$444$		0			0
$445$	17.8539	+	11.8186i	0.846358	+	0.560256i
$446$		0			0
$447$	7.46907	−	2.42685i	0.353275	−	0.114786i
$448$		0			0
$449$	27.3646			1.29142			0.645709	−	0.763584i	$-0.276562\pi$
$449$	27.3646			1.29142			0.645709	+	0.763584i	$0.276562\pi$
$450$		0			0
$451$	12.3622			0.582113
$452$		0			0
$453$	21.4106	−	6.95671i	1.00596	−	0.326855i
$454$		0			0
$455$	5.60389	−	4.45705i	0.262714	−	0.208950i
$456$		0			0
$457$		−	1.66698i		−	0.0779781i	−0.999240	−	0.0389891i	$-0.987586\pi$
$457$		−	1.66698i		−	0.0779781i	0.999240	−	0.0389891i	$-0.0124138\pi$
$458$		0			0
$459$	−1.06334	+	0.772564i	−0.0496326	+	0.0360602i
$460$		0			0
$461$	27.8272	+	20.2176i	1.29604	+	0.941630i	0.999909	−	0.0135170i	$-0.00430273\pi$
$461$	27.8272	+	20.2176i	1.29604	+	0.941630i	0.296133	+	0.955147i	$0.404303\pi$
$462$		0			0
$463$	−20.7939	−	28.6204i	−0.966377	−	1.33010i	−0.943856	−	0.330357i	$-0.892831\pi$
$463$	−20.7939	−	28.6204i	−0.966377	−	1.33010i	−0.0225205	−	0.999746i	$-0.507169\pi$
$464$		0			0
$465$	−0.862362	−	19.7753i	−0.0399911	−	0.917055i
$466$		0			0
$467$	22.9613	+	7.46057i	1.06252	+	0.345234i	0.787571	−	0.616224i	$-0.211338\pi$
$467$	22.9613	+	7.46057i	1.06252	+	0.345234i	0.274951	+	0.961458i	$0.411338\pi$
$468$		0			0
$469$	−3.39538	+	10.4499i	−0.156784	+	0.482532i
$470$		0			0
$471$	−5.99751	−	18.4584i	−0.276351	−	0.850520i
$472$		0			0
$473$	6.25615	−	8.61086i	0.287658	−	0.395928i
$474$		0			0
$475$	1.14896	−	4.97428i	0.0527177	−	0.228236i
$476$		0			0
$477$	−2.32186	+	3.19577i	−0.106311	+	0.146324i
$478$		0			0
$479$	7.03656	+	21.6563i	0.321509	+	0.989502i	0.972992	+	0.230839i	$0.0741470\pi$
$479$	7.03656	+	21.6563i	0.321509	+	0.989502i	−0.651483	+	0.758663i	$0.725853\pi$
$480$		0			0
$481$	3.77067	−	11.6049i	0.171928	−	0.529139i
$482$		0			0
$483$	6.28066	+	2.04071i	0.285780	+	0.0928555i
$484$		0			0
$485$	−34.0846	+	12.7416i	−1.54770	+	0.578568i
$486$		0			0
$487$	−5.49973	−	7.56973i	−0.249217	−	0.343017i	0.666020	−	0.745934i	$-0.267996\pi$
$487$	−5.49973	−	7.56973i	−0.249217	−	0.343017i	−0.915237	+	0.402917i	$0.867996\pi$
$488$		0			0
$489$	12.2473	+	8.89817i	0.553841	+	0.402389i
$490$		0			0
$491$	−14.7363	+	10.7066i	−0.665042	+	0.483181i	−0.868362	−	0.495931i	$-0.834827\pi$
$491$	−14.7363	+	10.7066i	−0.665042	+	0.483181i	0.203320	+	0.979112i	$0.434827\pi$
$492$		0			0
$493$		−	7.76000i		−	0.349493i
$494$		0			0
$495$	−3.47198	+	0.151407i	−0.156054	+	0.00680523i
$496$		0			0
$497$	−16.2529	+	5.28089i	−0.729043	+	0.236880i
$498$		0			0
$499$	−6.14936			−0.275283			−0.137642	−	0.990482i	$-0.543952\pi$
$499$	−6.14936			−0.275283			−0.137642	+	0.990482i	$0.543952\pi$
$500$		0			0
$501$	18.9060			0.844657
$502$		0			0
$503$	−15.0653	+	4.89502i	−0.671730	+	0.218258i	−0.624971	−	0.780648i	$-0.714889\pi$
$503$	−15.0653	+	4.89502i	−0.671730	+	0.218258i	−0.0467590	+	0.998906i	$0.514889\pi$
$504$		0			0
$505$	12.5932	−	0.549168i	0.560392	−	0.0244377i
$506$		0			0
$507$		−	7.10376i		−	0.315489i
$508$		0			0
$509$	−4.09898	+	2.97808i	−0.181684	+	0.132001i	−0.674910	−	0.737900i	$-0.735818\pi$
$509$	−4.09898	+	2.97808i	−0.181684	+	0.132001i	0.493226	+	0.869901i	$0.335818\pi$
$510$		0			0
$511$	13.5647	+	9.85535i	0.600068	+	0.435975i
$512$		0			0
$513$	−0.600159	−	0.826047i	−0.0264976	−	0.0364709i
$514$		0			0
$515$	17.6223	−	6.58764i	0.776530	−	0.290286i
$516$		0			0
$517$	11.4596	+	3.72346i	0.503994	+	0.163758i
$518$		0			0
$519$	7.43798	−	22.8918i	0.326491	−	1.00484i
$520$		0			0
$521$	−11.2578	−	34.6481i	−0.493215	−	1.51796i	−0.819720	−	0.572764i	$-0.805871\pi$
$521$	−11.2578	−	34.6481i	−0.493215	−	1.51796i	0.326505	−	0.945195i	$-0.394129\pi$
$522$		0			0
$523$	−6.80572	+	9.36727i	−0.297593	+	0.409602i	−0.931462	−	0.363839i	$-0.881466\pi$
$523$	−6.80572	+	9.36727i	−0.297593	+	0.409602i	0.633869	+	0.773441i	$0.281466\pi$
$524$		0			0
$525$	−2.57570	−	6.06974i	−0.112413	−	0.264905i
$526$		0			0
$527$	−6.83887	+	9.41289i	−0.297906	+	0.410032i
$528$		0			0
$529$	−0.642075	−	1.97610i	−0.0279163	−	0.0859175i
$530$		0			0
$531$	−2.42684	+	7.46905i	−0.105316	+	0.324129i
$532$		0			0
$533$	−18.3689	−	5.96843i	−0.795647	−	0.258521i
$534$		0			0
$535$	−0.200873	−	4.60631i	−0.00868448	−	0.199148i
$536$		0			0
$537$	−0.877183	−	1.20734i	−0.0378532	−	0.0521005i
$538$		0			0
$539$	−6.61498	−	4.80606i	−0.284927	−	0.207012i
$540$		0			0
$541$	−17.2715	+	12.5485i	−0.742559	+	0.539500i	−0.893511	−	0.449041i	$-0.851766\pi$
$541$	−17.2715	+	12.5485i	−0.742559	+	0.539500i	0.150953	+	0.988541i	$0.451766\pi$
$542$		0			0
$543$			2.61804i			0.112351i
$544$		0			0
$545$	24.4550	−	19.4503i	1.04754	−	0.833160i
$546$		0			0
$547$	−24.1049	+	7.83217i	−1.03065	+	0.334879i	−0.775048	−	0.631902i	$-0.782274\pi$
$547$	−24.1049	+	7.83217i	−1.03065	+	0.334879i	−0.255604	+	0.966781i	$0.582274\pi$
$548$		0			0
$549$	3.50161			0.149445
$550$		0			0
$551$	6.02827			0.256813
$552$		0			0
$553$	1.56900	−	0.509800i	0.0667207	−	0.0216789i
$554$		0			0
$555$	−9.36968	−	6.20236i	−0.397721	−	0.263276i
$556$		0			0
$557$			0.953134i			0.0403856i	0.999796	+	0.0201928i	$0.00642800\pi$
$557$			0.953134i			0.0403856i	−0.999796	+	0.0201928i	$0.993572\pi$
$558$		0			0
$559$	−13.4533	+	9.77439i	−0.569014	+	0.413413i
$560$		0			0
$561$	1.65264	+	1.20071i	0.0697746	+	0.0506942i
$562$		0			0
$563$	17.9315	+	24.6806i	0.755723	+	1.04016i	0.997558	+	0.0698461i	$0.0222508\pi$
$563$	17.9315	+	24.6806i	0.755723	+	1.04016i	−0.241835	+	0.970317i	$0.577749\pi$
$564$		0			0
$565$	8.29030	+	10.4235i	0.348776	+	0.438519i
$566$		0			0
$567$	−1.25418	−	0.407508i	−0.0526707	−	0.0171137i
$568$		0			0
$569$	−9.81510	+	30.2078i	−0.411471	+	1.26638i	0.503899	+	0.863762i	$0.331898\pi$
$569$	−9.81510	+	30.2078i	−0.411471	+	1.26638i	−0.915370	+	0.402614i	$0.868102\pi$
$570$		0			0
$571$	−8.65796	−	26.6465i	−0.362324	−	1.11512i	−0.951640	−	0.307217i	$-0.900602\pi$
$571$	−8.65796	−	26.6465i	−0.362324	−	1.11512i	0.589315	−	0.807903i	$-0.299398\pi$
$572$		0			0
$573$	−12.1041	+	16.6599i	−0.505657	+	0.695977i
$574$		0			0
$575$	−12.8982	+	21.4611i	−0.537893	+	0.894991i
$576$		0			0
$577$	−3.33187	+	4.58593i	−0.138708	+	0.190915i	−0.872719	−	0.488222i	$-0.837646\pi$
$577$	−3.33187	+	4.58593i	−0.138708	+	0.190915i	0.734012	+	0.679137i	$0.237646\pi$
$578$		0			0
$579$	−1.59438	−	4.90701i	−0.0662603	−	0.203928i
$580$		0			0
$581$	−3.34438	+	10.2929i	−0.138748	+	0.427023i
$582$		0			0
$583$	5.83888	+	1.89717i	0.241822	+	0.0785726i
$584$		0			0
$585$	5.23211	+	1.45129i	0.216321	+	0.0600034i
$586$		0			0
$587$	−19.9949	−	27.5206i	−0.825278	−	1.13590i	−0.988784	−	0.149355i	$-0.952280\pi$
$587$	−19.9949	−	27.5206i	−0.825278	−	1.13590i	0.163506	−	0.986542i	$-0.447720\pi$
$588$		0			0
$589$	−7.31231	−	5.31270i	−0.301298	−	0.218906i
$590$		0			0
$591$	8.50336	−	6.17805i	0.349781	−	0.254131i
$592$		0			0
$593$			22.9225i			0.941313i	0.882316	+	0.470657i	$0.155983\pi$
$593$			22.9225i			0.941313i	−0.882316	+	0.470657i	$0.844017\pi$
$594$		0			0
$595$	−1.03594	+	3.73473i	−0.0424696	+	0.153109i
$596$		0			0
$597$	−3.47341	+	1.12858i	−0.142157	+	0.0461896i
$598$		0			0
$599$	17.7017			0.723270			0.361635	−	0.932320i	$-0.382219\pi$
$599$	17.7017			0.723270			0.361635	+	0.932320i	$0.382219\pi$
$600$		0			0
$601$	−28.8773			−1.17793			−0.588964	−	0.808159i	$-0.700464\pi$
$601$	−28.8773			−1.17793			−0.588964	+	0.808159i	$0.700464\pi$
$602$		0			0
$603$	−7.92426	+	2.57475i	−0.322701	+	0.104852i
$604$		0			0
$605$	−6.72145	−	17.9802i	−0.273266	−	0.731000i
$606$		0			0
$607$			11.5926i			0.470528i	0.971932	+	0.235264i	$0.0755954\pi$
$607$			11.5926i			0.470528i	−0.971932	+	0.235264i	$0.924405\pi$
$608$		0			0
$609$	6.29880	−	4.57634i	0.255240	−	0.185443i
$610$		0			0
$611$	−15.2302	−	11.0654i	−0.616146	−	0.447657i
$612$		0			0
$613$	−7.48123	−	10.2970i	−0.302164	−	0.415893i	0.630754	−	0.775983i	$-0.282746\pi$
$613$	−7.48123	−	10.2970i	−0.302164	−	0.415893i	−0.932917	+	0.360090i	$0.882746\pi$
$614$		0			0
$615$	−9.81746	+	14.8309i	−0.395878	+	0.598038i
$616$		0			0
$617$	−40.7643	−	13.2451i	−1.64111	−	0.533229i	−0.664323	−	0.747446i	$-0.731280\pi$
$617$	−40.7643	−	13.2451i	−1.64111	−	0.533229i	−0.976786	+	0.214217i	$0.931280\pi$
$618$		0			0
$619$	−4.30448	+	13.2478i	−0.173012	+	0.532475i	−0.999537	−	0.0304242i	$-0.990314\pi$
$619$	−4.30448	+	13.2478i	−0.173012	+	0.532475i	0.826525	+	0.562899i	$0.190314\pi$
$620$		0			0
$621$	1.54749	+	4.76268i	0.0620985	+	0.191120i
$622$		0			0
$623$	7.42216	−	10.2157i	0.297363	−	0.409285i
$624$		0			0
$625$	24.6211	−	4.33601i	0.984844	−	0.173441i
$626$		0			0
$627$	−0.932763	+	1.28384i	−0.0372510	+	0.0512715i
$628$		0			0
$629$	2.04102	+	6.28160i	0.0813806	+	0.250464i
$630$		0			0
$631$	−2.66089	+	8.18939i	−0.105928	+	0.326014i	−0.989947	−	0.141437i	$-0.954828\pi$
$631$	−2.66089	+	8.18939i	−0.105928	+	0.326014i	0.884019	+	0.467451i	$0.154828\pi$
$632$		0			0
$633$	25.0701	+	8.14575i	0.996445	+	0.323765i
$634$		0			0
$635$	−2.99032	+	4.51736i	−0.118667	+	0.179266i
$636$		0			0
$637$	7.50882	+	10.3350i	0.297510	+	0.409488i
$638$		0			0
$639$	−10.4840	−	7.61709i	−0.414742	−	0.301327i
$640$		0			0
$641$	17.0591	−	12.3942i	0.673794	−	0.489540i	−0.197499	−	0.980303i	$-0.563282\pi$
$641$	17.0591	−	12.3942i	0.673794	−	0.489540i	0.871293	+	0.490763i	$0.163282\pi$
$642$		0			0
$643$		−	12.2412i		−	0.482747i	−0.970432	−	0.241374i	$-0.922402\pi$
$643$		−	12.2412i		−	0.482747i	0.970432	−	0.241374i	$-0.0775979\pi$
$644$		0			0
$645$	5.36207	+	14.3438i	0.211131	+	0.564787i
$646$		0			0
$647$	10.7461	−	3.49162i	0.422472	−	0.137270i	−0.0900623	−	0.995936i	$-0.528707\pi$
$647$	10.7461	−	3.49162i	0.422472	−	0.137270i	0.512535	+	0.858667i	$0.328707\pi$
$648$		0			0
$649$	12.2057			0.479117
$650$		0			0
$651$	−11.6736			−0.457524
$652$		0			0
$653$	−20.2319	+	6.57373i	−0.791734	+	0.257250i	−0.676842	−	0.736128i	$-0.736652\pi$
$653$	−20.2319	+	6.57373i	−0.791734	+	0.257250i	−0.114892	+	0.993378i	$0.536652\pi$
$654$		0			0
$655$	6.53633	−	23.5644i	0.255396	−	0.920738i
$656$		0			0
$657$			12.7145i			0.496039i
$658$		0			0
$659$	−14.9986	+	10.8971i	−0.584263	+	0.424492i	−0.840258	−	0.542186i	$-0.817597\pi$
$659$	−14.9986	+	10.8971i	−0.584263	+	0.424492i	0.255995	+	0.966678i	$0.417597\pi$
$660$		0			0
$661$	−16.0800	−	11.6828i	−0.625441	−	0.454409i	0.229377	−	0.973338i	$-0.426331\pi$
$661$	−16.0800	−	11.6828i	−0.625441	−	0.454409i	−0.854818	+	0.518928i	$0.826331\pi$
$662$		0			0
$663$	−1.87595	−	2.58203i	−0.0728560	−	0.100278i
$664$		0			0
$665$	−2.90129	−	0.804763i	−0.112507	−	0.0312074i
$666$		0			0
$667$	−28.1188	−	9.13635i	−1.08876	−	0.353761i
$668$		0			0
$669$	−5.71502	+	17.5890i	−0.220955	+	0.680031i
$670$		0			0
$671$	−1.68173	−	5.17583i	−0.0649224	−	0.199811i
$672$		0			0
$673$	−25.6055	+	35.2430i	−0.987021	+	1.35852i	−0.0540603	+	0.998538i	$0.517216\pi$
$673$	−25.6055	+	35.2430i	−0.987021	+	1.35852i	−0.932960	+	0.359980i	$0.882784\pi$
$674$		0			0
$675$	2.57564	−	4.28557i	0.0991365	−	0.164951i
$676$		0			0
$677$	−2.73904	+	3.76996i	−0.105270	+	0.144891i	−0.858402	−	0.512978i	$-0.828542\pi$
$677$	−2.73904	+	3.76996i	−0.105270	+	0.144891i	0.753132	+	0.657870i	$0.228542\pi$
$678$		0			0
$679$	6.63152	+	20.4097i	0.254494	+	0.783253i
$680$		0			0
$681$	5.76675	−	17.7482i	0.220982	−	0.680114i
$682$		0			0
$683$	−37.0242	−	12.0299i	−1.41669	−	0.460311i	−0.502141	−	0.864786i	$-0.667454\pi$
$683$	−37.0242	−	12.0299i	−1.41669	−	0.460311i	−0.914549	+	0.404475i	$0.867454\pi$
$684$		0			0
$685$	5.20024	+	6.53830i	0.198691	+	0.249816i
$686$		0			0
$687$	−16.4233	−	22.6047i	−0.626588	−	0.862424i
$688$		0			0
$689$	−7.76002	−	5.63798i	−0.295633	−	0.214790i
$690$		0			0
$691$	7.81060	−	5.67473i	0.297129	−	0.215877i	−0.429225	−	0.903198i	$-0.641213\pi$
$691$	7.81060	−	5.67473i	0.297129	−	0.215877i	0.726354	+	0.687321i	$0.241213\pi$
$692$		0			0
$693$			2.04956i			0.0778562i
$694$		0			0
$695$	−4.00479	−	2.65102i	−0.151910	−	0.100559i
$696$		0			0
$697$	9.94289	−	3.23064i	0.376614	−	0.122369i
$698$		0			0
$699$	−24.7573			−0.936407
$700$		0			0
$701$	18.6430			0.704135			0.352068	−	0.935975i	$-0.385479\pi$
$701$	18.6430			0.704135			0.352068	+	0.935975i	$0.385479\pi$
$702$		0			0
$703$	−4.87980	+	1.58554i	−0.184045	+	0.0597999i
$704$		0			0
$705$	−13.5677	+	10.7911i	−0.510990	+	0.406416i
$706$		0			0
$707$		−	7.43395i		−	0.279582i
$708$		0			0
$709$	−9.85935	+	7.16324i	−0.370276	+	0.269021i	−0.757325	−	0.653038i	$-0.773494\pi$
$709$	−9.85935	+	7.16324i	−0.370276	+	0.269021i	0.387050	+	0.922059i	$0.373494\pi$
$710$		0			0
$711$	1.01209	+	0.735329i	0.0379565	+	0.0275770i
$712$		0			0
$713$	26.0563	+	35.8634i	0.975817	+	1.34310i
$714$		0			0
$715$	−0.367649	−	8.43073i	−0.0137493	−	0.315291i
$716$		0			0
$717$	−11.1338	−	3.61761i	−0.415801	−	0.135102i
$718$		0			0
$719$	13.2311	−	40.7210i	0.493435	−	1.51864i	−0.325947	−	0.945388i	$-0.605683\pi$
$719$	13.2311	−	40.7210i	0.493435	−	1.51864i	0.819382	−	0.573248i	$-0.194317\pi$
$720$		0			0
$721$	−3.42860	−	10.5522i	−0.127688	−	0.392983i
$722$		0			0
$723$	−17.5257	+	24.1221i	−0.651788	+	0.897110i
$724$		0			0
$725$	11.5315	+	27.1745i	0.428269	+	1.00923i
$726$		0			0
$727$	0.631037	−	0.868548i	0.0234039	−	0.0322126i	−0.797155	−	0.603775i	$-0.793663\pi$
$727$	0.631037	−	0.868548i	0.0234039	−	0.0322126i	0.820559	+	0.571562i	$0.193663\pi$
$728$		0			0
$729$	−0.309017	−	0.951057i	−0.0114451	−	0.0352243i
$730$		0			0
$731$	2.78152	−	8.56063i	0.102878	−	0.316626i
$732$		0			0
$733$	0.773538	+	0.251338i	0.0285713	+	0.00928337i	0.323268	−	0.946308i	$-0.395219\pi$
$733$	0.773538	+	0.251338i	0.0285713	+	0.00928337i	−0.294696	+	0.955591i	$0.595219\pi$
$734$		0			0
$735$	11.0191	−	4.11921i	0.406446	−	0.151940i
$736$		0			0
$737$	7.61160	+	10.4765i	0.280377	+	0.385906i
$738$		0			0
$739$	30.6000	+	22.2322i	1.12564	+	0.817824i	0.985054	−	0.172244i	$-0.0551018\pi$
$739$	30.6000	+	22.2322i	1.12564	+	0.817824i	0.140585	+	0.990069i	$0.455102\pi$
$740$		0			0
$741$	2.00582	−	1.45732i	0.0736857	−	0.0535358i
$742$		0			0
$743$			45.7517i			1.67847i	0.543772	+	0.839233i	$0.316996\pi$
$743$			45.7517i			1.67847i	−0.543772	+	0.839233i	$0.683004\pi$
$744$		0			0
$745$	17.5442	−	0.765068i	0.642768	−	0.0280299i
$746$		0			0
$747$	−7.80521	+	2.53607i	−0.285578	+	0.0927899i
$748$		0			0
$749$	−2.71916			−0.0993560
$750$		0			0
$751$	−39.1925			−1.43016			−0.715078	−	0.699045i	$-0.753609\pi$
$751$	−39.1925			−1.43016			−0.715078	+	0.699045i	$0.753609\pi$
$752$		0			0
$753$	−2.73235	+	0.887796i	−0.0995725	+	0.0323531i
$754$		0			0
$755$	50.2915	−	2.19312i	1.83029	−	0.0798157i
$756$		0			0
$757$		−	4.48615i		−	0.163052i	−0.996671	−	0.0815259i	$-0.974021\pi$
$757$		−	4.48615i		−	0.163052i	0.996671	−	0.0815259i	$-0.0259793\pi$
$758$		0			0
$759$	6.29662	−	4.57476i	0.228553	−	0.166053i
$760$		0			0
$761$	−17.2776	−	12.5529i	−0.626312	−	0.455043i	0.228808	−	0.973471i	$-0.426517\pi$
$761$	−17.2776	−	12.5529i	−0.626312	−	0.455043i	−0.855121	+	0.518429i	$0.826517\pi$
$762$		0			0
$763$	−10.8316	−	14.9085i	−0.392131	−	0.539723i
$764$		0			0
$765$	−2.75294	+	1.02912i	−0.0995328	+	0.0372078i
$766$		0			0
$767$	−18.1365	−	5.89290i	−0.654870	−	0.212780i
$768$		0			0
$769$	−7.94179	+	24.4423i	−0.286388	+	0.881413i	0.699591	+	0.714544i	$0.253366\pi$
$769$	−7.94179	+	24.4423i	−0.286388	+	0.881413i	−0.985979	+	0.166869i	$0.946634\pi$
$770$		0			0
$771$	2.50834	+	7.71988i	0.0903357	+	0.278025i
$772$		0			0
$773$	17.4223	−	23.9797i	0.626636	−	0.862490i	−0.371179	−	0.928561i	$-0.621046\pi$
$773$	17.4223	−	23.9797i	0.626636	−	0.862490i	0.997815	+	0.0660712i	$0.0210465\pi$
$774$		0			0
$775$	9.96107	−	43.1254i	0.357812	−	1.54911i
$776$		0			0
$777$	−3.89512	+	5.36118i	−0.139737	+	0.192331i
$778$		0			0
$779$	2.50969	+	7.72403i	0.0899189	+	0.276742i
$780$		0			0
$781$	−6.22383	+	19.1550i	−0.222706	+	0.685420i
$782$		0			0
$783$	5.61503	+	1.82443i	0.200665	+	0.0651999i
$784$		0			0
$785$	−1.89073	−	43.3572i	−0.0674829	−	1.54748i
$786$		0			0
$787$	−4.72360	−	6.50148i	−0.168378	−	0.231753i	0.716486	−	0.697601i	$-0.245749\pi$
$787$	−4.72360	−	6.50148i	−0.168378	−	0.231753i	−0.884865	+	0.465848i	$0.845749\pi$
$788$		0			0
$789$	18.0467	+	13.1117i	0.642479	+	0.466789i
$790$		0			0
$791$	6.35443	−	4.61676i	0.225938	−	0.164153i
$792$		0			0
$793$			8.50268i			0.301939i
$794$		0			0
$795$	−6.91298	+	5.49824i	−0.245178	+	0.195002i
$796$		0			0
$797$	15.6232	−	5.07628i	0.553401	−	0.179811i	−0.0189486	−	0.999820i	$-0.506032\pi$
$797$	15.6232	−	5.07628i	0.553401	−	0.179811i	0.572350	+	0.820009i	$0.306032\pi$
$798$		0			0
$799$	10.1900			0.360497
$800$		0			0
$801$	9.57541			0.338331
$802$		0			0
$803$	18.7936	−	6.10642i	0.663213	−	0.215491i
$804$		0			0
$805$	12.3133	+	8.15095i	0.433988	+	0.287283i
$806$		0			0
$807$		−	8.19918i		−	0.288625i
$808$		0			0
$809$	39.2743	−	28.5344i	1.38081	−	1.00322i	0.384006	−	0.923330i	$-0.374544\pi$
$809$	39.2743	−	28.5344i	1.38081	−	1.00322i	0.996804	−	0.0798870i	$-0.0254560\pi$
$810$		0			0
$811$	−17.2584	−	12.5390i	−0.606024	−	0.440302i	0.241988	−	0.970279i	$-0.422201\pi$
$811$	−17.2584	−	12.5390i	−0.606024	−	0.440302i	−0.848012	+	0.529977i	$0.822201\pi$
$812$		0			0
$813$	−5.57619	−	7.67496i	−0.195565	−	0.269173i
$814$		0			0
$815$	21.0711	+	26.4929i	0.738090	+	0.928006i
$816$		0			0
$817$	6.65024	+	2.16079i	0.232662	+	0.0755966i
$818$		0			0
$819$	0.989519	−	3.04543i	0.0345766	−	0.106416i
$820$		0			0
$821$	0.922371	+	2.83877i	0.0321910	+	0.0990736i	0.965861	−	0.259061i	$-0.0834130\pi$
$821$	0.922371	+	2.83877i	0.0321910	+	0.0990736i	−0.933670	+	0.358134i	$0.883413\pi$
$822$		0			0
$823$	−2.01233	+	2.76974i	−0.0701455	+	0.0965469i	−0.842648	−	0.538464i	$-0.819005\pi$
$823$	−2.01233	+	2.76974i	−0.0701455	+	0.0965469i	0.772503	+	0.635011i	$0.219005\pi$
$824$		0			0
$825$	−7.57162	−	1.74889i	−0.263610	−	0.0608884i
$826$		0			0
$827$	4.58186	−	6.30639i	0.159327	−	0.219295i	−0.721889	−	0.692009i	$-0.756726\pi$
$827$	4.58186	−	6.30639i	0.159327	−	0.219295i	0.881216	+	0.472715i	$0.156726\pi$
$828$		0			0
$829$	6.65047	+	20.4680i	0.230980	+	0.710884i	0.997629	+	0.0688179i	$0.0219227\pi$
$829$	6.65047	+	20.4680i	0.230980	+	0.710884i	−0.766649	+	0.642067i	$0.778077\pi$
$830$		0			0
$831$	0.142047	−	0.437177i	0.00492757	−	0.0151655i
$832$		0			0
$833$	−6.57639	−	2.13680i	−0.227858	−	0.0740357i
$834$		0			0
$835$	40.7370	+	11.2997i	1.40976	+	0.391041i
$836$		0			0
$837$	−5.20317	−	7.16155i	−0.179848	−	0.247540i
$838$		0			0
$839$	3.31004	+	2.40488i	0.114275	+	0.0830258i	0.643455	−	0.765484i	$-0.277500\pi$
$839$	3.31004	+	2.40488i	0.114275	+	0.0830258i	−0.529180	+	0.848510i	$0.677500\pi$
$840$		0			0
$841$	−4.73850	+	3.44272i	−0.163397	+	0.118715i
$842$		0			0
$843$			15.2578i			0.525508i
$844$		0			0
$845$	4.24575	−	15.3066i	0.146058	−	0.526562i
$846$		0			0
$847$	−10.7665	+	3.49825i	−0.369941	+	0.120201i
$848$		0			0
$849$	10.6725			0.366281
$850$		0			0
$851$	25.1648			0.862637
$852$		0			0
$853$	−23.8815	+	7.75958i	−0.817688	+	0.265683i	−0.687850	−	0.725852i	$-0.741446\pi$
$853$	−23.8815	+	7.75958i	−0.817688	+	0.265683i	−0.129837	+	0.991535i	$0.541446\pi$
$854$		0			0
$855$	−0.799459	−	2.13859i	−0.0273409	−	0.0731384i
$856$		0			0
$857$		−	35.8315i		−	1.22398i	−0.790865	−	0.611991i	$-0.790369\pi$
$857$		−	35.8315i		−	1.22398i	0.790865	−	0.611991i	$-0.209631\pi$
$858$		0			0
$859$	−23.2363	+	16.8821i	−0.792811	+	0.576011i	−0.908796	−	0.417240i	$-0.862997\pi$
$859$	−23.2363	+	16.8821i	−0.792811	+	0.576011i	0.115985	+	0.993251i	$0.462997\pi$
$860$		0			0
$861$	8.48598	+	6.16543i	0.289202	+	0.210117i
$862$		0			0
$863$	12.3598	+	17.0119i	0.420734	+	0.579090i	0.965795	−	0.259306i	$-0.0834937\pi$
$863$	12.3598	+	17.0119i	0.420734	+	0.579090i	−0.545062	+	0.838396i	$0.683494\pi$
$864$		0			0
$865$	29.7086	−	44.8796i	1.01012	−	1.52595i
$866$		0			0
$867$	−14.5250	−	4.71945i	−0.493293	−	0.160281i
$868$		0			0
$869$	0.600828	−	1.84916i	0.0203817	−	0.0627284i
$870$		0			0
$871$	−6.25204	−	19.2418i	−0.211842	−	0.651984i
$872$		0			0
$873$	−9.56522	+	13.1654i	−0.323734	+	0.445581i
$874$		0			0
$875$	−1.92214	−	14.6180i	−0.0649802	−	0.494177i
$876$		0			0
$877$	4.13682	−	5.69384i	0.139690	−	0.192267i	−0.733440	−	0.679754i	$-0.762086\pi$
$877$	4.13682	−	5.69384i	0.139690	−	0.192267i	0.873130	+	0.487487i	$0.162086\pi$
$878$		0			0
$879$	−9.52803	−	29.3243i	−0.321373	−	0.989083i
$880$		0			0
$881$	15.1220	−	46.5406i	0.509472	−	1.56799i	−0.283649	−	0.958928i	$-0.591545\pi$
$881$	15.1220	−	46.5406i	0.509472	−	1.56799i	0.793121	−	0.609064i	$-0.208455\pi$
$882$		0			0
$883$	−8.09007	−	2.62862i	−0.272252	−	0.0884602i	0.169709	−	0.985494i	$-0.445717\pi$
$883$	−8.09007	−	2.62862i	−0.272252	−	0.0884602i	−0.441961	+	0.897034i	$0.645717\pi$
$884$		0			0
$885$	−9.69322	+	14.6432i	−0.325834	+	0.492225i
$886$		0			0
$887$	−19.7983	−	27.2500i	−0.664761	−	0.914966i	0.334866	−	0.942266i	$-0.391309\pi$
$887$	−19.7983	−	27.2500i	−0.664761	−	0.914966i	−0.999627	+	0.0273002i	$0.991309\pi$
$888$		0			0
$889$	2.58476	+	1.87794i	0.0866901	+	0.0629840i
$890$		0			0
$891$	−1.25737	+	0.913532i	−0.0421235	+	0.0306045i
$892$		0			0
$893$			7.91602i			0.264899i
$894$		0			0
$895$	−1.16848	−	3.12574i	−0.0390579	−	0.104482i
$896$		0			0
$897$	−11.5648	+	3.75764i	−0.386138	+	0.125464i
$898$		0			0
$899$	52.2631			1.74307
$900$		0			0
$901$	5.19199			0.172970
$902$		0			0
$903$	8.58903	−	2.79075i	0.285825	−	0.0928702i
$904$		0			0
$905$	−1.56474	+	5.64112i	−0.0520137	+	0.187517i
$906$		0			0
$907$			42.2382i			1.40250i	0.712918	+	0.701248i	$0.247373\pi$
$907$			42.2382i			1.40250i	−0.712918	+	0.701248i	$0.752627\pi$
$908$		0			0
$909$	4.56061	−	3.31348i	0.151266	−	0.109901i
$910$		0			0
$911$	30.4371	+	22.1138i	1.00843	+	0.732664i	0.963878	−	0.266343i	$-0.0858153\pi$
$911$	30.4371	+	22.1138i	1.00843	+	0.732664i	0.0445478	+	0.999007i	$0.485815\pi$
$912$		0			0
$913$	7.49726	+	10.3191i	0.248123	+	0.341512i
$914$		0			0
$915$	7.54497	+	2.09283i	0.249429	+	0.0691869i
$916$		0			0
$917$	−13.7160	−	4.45661i	−0.452943	−	0.147170i
$918$		0			0
$919$	−11.7537	+	36.1742i	−0.387719	+	1.19328i	0.546769	+	0.837283i	$0.315857\pi$
$919$	−11.7537	+	36.1742i	−0.387719	+	1.19328i	−0.934488	+	0.355993i	$0.884143\pi$
$920$		0			0
$921$	5.52009	+	16.9891i	0.181893	+	0.559809i
$922$		0			0
$923$	18.4960	−	25.4575i	0.608802	−	0.837944i
$924$		0			0
$925$	−16.4819	−	18.9643i	−0.541923	−	0.623544i
$926$		0			0
$927$	4.94538	−	6.80673i	0.162427	−	0.223562i
$928$		0			0
$929$	7.91592	+	24.3627i	0.259713	+	0.799314i	0.992864	+	0.119249i	$0.0380486\pi$
$929$	7.91592	+	24.3627i	0.259713	+	0.799314i	−0.733152	+	0.680065i	$0.761951\pi$
$930$		0			0
$931$	1.65995	−	5.10880i	0.0544027	−	0.167434i
$932$		0			0
$933$	11.4729	+	3.72777i	0.375605	+	0.122042i
$934$		0			0
$935$	2.84333	+	3.57494i	0.0929868	+	0.116913i
$936$		0			0
$937$	22.3315	+	30.7367i	0.729538	+	1.00412i	0.999153	+	0.0411552i	$0.0131038\pi$
$937$	22.3315	+	30.7367i	0.729538	+	1.00412i	−0.269614	+	0.962968i	$0.586896\pi$
$938$		0			0
$939$	15.1766	+	11.0264i	0.495268	+	0.359833i
$940$		0			0
$941$	30.3522	−	22.0522i	0.989454	−	0.718881i	0.0296528	−	0.999560i	$-0.490560\pi$
$941$	30.3522	−	22.0522i	0.989454	−	0.718881i	0.959802	+	0.280680i	$0.0905598\pi$
$942$		0			0
$943$		−	39.8323i		−	1.29712i
$944$		0			0
$945$	−2.45884	−	1.62766i	−0.0799862	−	0.0529477i
$946$		0			0
$947$	−33.4391	+	10.8650i	−1.08663	+	0.353066i	−0.796942	−	0.604056i	$-0.793550\pi$
$947$	−33.4391	+	10.8650i	−1.08663	+	0.353066i	−0.289684	+	0.957122i	$0.593550\pi$
$948$		0			0
$949$	−30.8735			−1.00220
$950$		0			0
$951$	−10.7157			−0.347480
$952$		0			0
$953$	−49.5641	+	16.1044i	−1.60554	+	0.521671i	−0.968469	−	0.249134i	$-0.919854\pi$
$953$	−49.5641	+	16.1044i	−1.60554	+	0.521671i	−0.637071	+	0.770805i	$0.719854\pi$
$954$		0			0
$955$	−36.0381	+	28.6629i	−1.16617	+	0.927511i
$956$		0			0
$957$		−	9.17595i		−	0.296616i
$958$		0			0
$959$	3.98593	−	2.89594i	0.128712	−	0.0935149i
$960$		0			0
$961$	−38.3157	−	27.8380i	−1.23599	−	0.898001i
$962$		0			0
$963$	−1.21199	−	1.66816i	−0.0390559	−	0.0537558i
$964$		0			0
$965$	−0.502632	−	11.5261i	−0.0161803	−	0.371039i
$966$		0			0
$967$	39.7277	+	12.9083i	1.27756	+	0.415103i	0.867719	−	0.497055i	$-0.165585\pi$
$967$	39.7277	+	12.9083i	1.27756	+	0.415103i	0.409838	+	0.912158i	$0.365585\pi$
$968$		0			0
$969$	−0.414711	+	1.27635i	−0.0133224	+	0.0410022i
$970$		0			0
$971$	0.141561	+	0.435679i	0.00454289	+	0.0139816i	0.953302	−	0.302018i	$-0.0976602\pi$
$971$	0.141561	+	0.435679i	0.00454289	+	0.0139816i	−0.948759	+	0.315999i	$0.897660\pi$
$972$		0			0
$973$	−1.66486	+	2.29148i	−0.0533728	+	0.0734614i
$974$		0			0
$975$	10.4063	+	6.25422i	0.333268	+	0.200295i
$976$		0			0
$977$	−2.29079	+	3.15300i	−0.0732888	+	0.100873i	−0.844088	−	0.536205i	$-0.819857\pi$
$977$	−2.29079	+	3.15300i	−0.0732888	+	0.100873i	0.770799	+	0.637079i	$0.219857\pi$
$978$		0			0
$979$	−4.59881	−	14.1537i	−0.146979	−	0.452353i
$980$		0			0
$981$	4.31821	−	13.2901i	0.137870	−	0.424319i
$982$		0			0
$983$	53.5388	+	17.3958i	1.70762	+	0.554841i	0.989935	−	0.141523i	$-0.0452000\pi$
$983$	53.5388	+	17.3958i	1.70762	+	0.554841i	0.717689	+	0.696364i	$0.245200\pi$
$984$		0			0
$985$	22.0148	−	8.22966i	0.701449	−	0.262219i
$986$		0			0
$987$	6.00942	+	8.27125i	0.191282	+	0.263277i
$988$		0			0
$989$	−27.7451	−	20.1580i	−0.882242	−	0.640986i
$990$		0			0
$991$	−17.5804	+	12.7729i	−0.558460	+	0.405745i	−0.830895	−	0.556429i	$-0.812171\pi$
$991$	−17.5804	+	12.7729i	−0.558460	+	0.405745i	0.272435	+	0.962174i	$0.412171\pi$
$992$		0			0
$993$		−	2.17317i		−	0.0689636i
$994$		0			0
$995$	−8.15872	+	0.355786i	−0.258649	+	0.0112792i
$996$		0			0
$997$	36.6447	−	11.9066i	1.16055	−	0.377085i	0.335441	−	0.942061i	$-0.391115\pi$
$997$	36.6447	−	11.9066i	1.16055	−	0.377085i	0.825107	+	0.564976i	$0.191115\pi$
$998$		0			0
$999$	−5.02514			−0.158988

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	300.2.o.a.109.6	✓	24
3.2	odd	2		900.2.w.c.109.1		24
5.2	odd	4		1500.2.m.d.1201.5		24
5.3	odd	4		1500.2.m.c.1201.2		24
5.4	even	2		1500.2.o.c.49.2		24
25.2	odd	20		1500.2.m.d.301.5		24
25.6	even	5		7500.2.d.g.1249.4		24
25.8	odd	20		7500.2.a.n.1.4		12
25.11	even	5		1500.2.o.c.949.2		24
25.14	even	10	inner	300.2.o.a.289.6	yes	24
25.17	odd	20		7500.2.a.m.1.9		12
25.19	even	10		7500.2.d.g.1249.21		24
25.23	odd	20		1500.2.m.c.301.2		24
75.14	odd	10		900.2.w.c.289.1		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
300.2.o.a.109.6	✓	24	1.1	even	1	trivial
300.2.o.a.289.6	yes	24	25.14	even	10	inner
900.2.w.c.109.1		24	3.2	odd	2
900.2.w.c.289.1		24	75.14	odd	10
1500.2.m.c.301.2		24	25.23	odd	20
1500.2.m.c.1201.2		24	5.3	odd	4
1500.2.m.d.301.5		24	25.2	odd	20
1500.2.m.d.1201.5		24	5.2	odd	4
1500.2.o.c.49.2		24	5.4	even	2
1500.2.o.c.949.2		24	25.11	even	5
7500.2.a.m.1.9		12	25.17	odd	20
7500.2.a.n.1.4		12	25.8	odd	20
7500.2.d.g.1249.4		24	25.6	even	5
7500.2.d.g.1249.21		24	25.19	even	10

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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	300.o (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.951057 - 0.309017i) q^{3} +(2.23394 - 0.0974182i) q^{5} -1.31873i q^{7} +(0.809017 - 0.587785i) q^{9} +O(q^{10})\)	\(q+(0.951057 - 0.309017i) q^{3} +(2.23394 - 0.0974182i) q^{5} -1.31873i q^{7} +(0.809017 - 0.587785i) q^{9} +(-1.25737 - 0.913532i) q^{11} +(1.42727 + 1.96447i) q^{13} +(2.09450 - 0.782977i) q^{15} +(-1.25004 - 0.406161i) q^{17} +(0.315522 - 0.971077i) q^{19} +(-0.407508 - 1.25418i) q^{21} +(-2.94350 + 4.05137i) q^{23} +(4.98102 - 0.435254i) q^{25} +(0.587785 - 0.809017i) q^{27} +(1.82443 + 5.61503i) q^{29} +(2.73547 - 8.41891i) q^{31} +(-1.47813 - 0.480272i) q^{33} +(-0.128468 - 2.94596i) q^{35} +(-2.95370 - 4.06542i) q^{37} +(1.96447 + 1.42727i) q^{39} +(-6.43499 + 4.67529i) q^{41} +6.84831i q^{43} +(1.75004 - 1.39189i) q^{45} +(-7.37336 + 2.39575i) q^{47} +5.26096 q^{49} -1.31436 q^{51} +(-3.75685 + 1.22067i) q^{53} +(-2.89789 - 1.91829i) q^{55} -1.02105i q^{57} +(-6.35355 + 4.61613i) q^{59} +(2.83287 + 2.05820i) q^{61} +(-0.775127 - 1.06687i) q^{63} +(3.37982 + 4.24947i) q^{65} +(-7.92426 - 2.57475i) q^{67} +(-1.54749 + 4.76268i) q^{69} +(-4.00454 - 12.3247i) q^{71} +(-7.47339 + 10.2862i) q^{73} +(4.60273 - 1.95317i) q^{75} +(-1.20470 + 1.65812i) q^{77} +(0.386585 + 1.18979i) q^{79} +(0.309017 - 0.951057i) q^{81} +(-7.80521 - 2.53607i) q^{83} +(-2.83208 - 0.785565i) q^{85} +(3.47028 + 4.77643i) q^{87} +(7.74667 + 5.62829i) q^{89} +(2.59059 - 1.88218i) q^{91} -8.85217i q^{93} +(0.610258 - 2.20007i) q^{95} +(-15.4769 + 5.02874i) q^{97} -1.55419 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 2 q^{5} + 6 q^{9}+O(q^{10}) \) 24 * q - 2 * q^5 + 6 * q^9	\( 24 q - 2 q^{5} + 6 q^{9} - 6 q^{11} + 4 q^{15} + 10 q^{17} + 10 q^{19} - 4 q^{21} + 40 q^{23} - 4 q^{25} + 4 q^{29} + 6 q^{31} + 10 q^{33} - 6 q^{35} - 10 q^{41} + 2 q^{45} - 40 q^{47} - 56 q^{49} + 16 q^{51} - 60 q^{53} - 62 q^{55} - 36 q^{59} - 12 q^{61} - 10 q^{63} + 20 q^{67} + 4 q^{69} + 40 q^{71} + 60 q^{73} + 8 q^{75} - 40 q^{77} + 8 q^{79} - 6 q^{81} - 50 q^{83} + 34 q^{85} - 20 q^{87} - 30 q^{91} - 60 q^{95} - 40 q^{97} - 4 q^{99}+O(q^{100}) \) 24 * q - 2 * q^5 + 6 * q^9 - 6 * q^11 + 4 * q^15 + 10 * q^17 + 10 * q^19 - 4 * q^21 + 40 * q^23 - 4 * q^25 + 4 * q^29 + 6 * q^31 + 10 * q^33 - 6 * q^35 - 10 * q^41 + 2 * q^45 - 40 * q^47 - 56 * q^49 + 16 * q^51 - 60 * q^53 - 62 * q^55 - 36 * q^59 - 12 * q^61 - 10 * q^63 + 20 * q^67 + 4 * q^69 + 40 * q^71 + 60 * q^73 + 8 * q^75 - 40 * q^77 + 8 * q^79 - 6 * q^81 - 50 * q^83 + 34 * q^85 - 20 * q^87 - 30 * q^91 - 60 * q^95 - 40 * q^97 - 4 * q^99

Introduction

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