LMFDB - Embedded newform 378.4.l.a.143.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [378,4,Mod(143,378)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(378, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 1]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("378.143");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 378 = 2 \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	378.l (of order $6$, degree $2$, not 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:	$22.3027219822$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			143.9
Character	$\chi$	$=$	378.143
Dual form			378.4.l.a.341.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.00000i q^{2} -4.00000 q^{4} +(3.13500 - 5.42997i) q^{5} +(13.5626 + 12.6118i) q^{7} -8.00000i q^{8} +O(q^{10})$	\(q+2.00000i q^{2} -4.00000 q^{4} +(3.13500 - 5.42997i) q^{5} +(13.5626 + 12.6118i) q^{7} -8.00000i q^{8} +(10.8599 + 6.26999i) q^{10} +(-30.9743 + 17.8830i) q^{11} +(43.2237 - 24.9552i) q^{13} +(-25.2235 + 27.1251i) q^{14} +16.0000 q^{16} +(23.2809 - 40.3238i) q^{17} +(-14.3421 + 8.28040i) q^{19} +(-12.5400 + 21.7199i) q^{20} +(-35.7660 - 61.9486i) q^{22} +(42.8182 + 24.7211i) q^{23} +(42.8436 + 74.2073i) q^{25} +(49.9105 + 86.4475i) q^{26} +(-54.2503 - 50.4471i) q^{28} +(161.868 + 93.4545i) q^{29} -291.470i q^{31} +32.0000i q^{32} +(80.6475 + 46.5619i) q^{34} +(111.000 - 34.1066i) q^{35} +(198.915 + 344.531i) q^{37} +(-16.5608 - 28.6842i) q^{38} +(-43.4398 - 25.0800i) q^{40} +(97.2074 + 168.368i) q^{41} +(-115.723 + 200.439i) q^{43} +(123.897 - 71.5321i) q^{44} +(-49.4422 + 85.6363i) q^{46} +68.8983 q^{47} +(24.8868 + 342.096i) q^{49} +(-148.415 + 85.6872i) q^{50} +(-172.895 + 99.8210i) q^{52} +(446.076 + 257.542i) q^{53} +224.253i q^{55} +(100.894 - 108.501i) q^{56} +(-186.909 + 323.736i) q^{58} +211.598 q^{59} +161.574i q^{61} +582.940 q^{62} -64.0000 q^{64} -312.938i q^{65} -872.379 q^{67} +(-93.1238 + 161.295i) q^{68} +(68.2132 + 222.000i) q^{70} +61.8704i q^{71} +(-405.059 - 233.861i) q^{73} +(-689.062 + 397.830i) q^{74} +(57.3683 - 33.1216i) q^{76} +(-645.628 - 148.101i) q^{77} +972.318 q^{79} +(50.1600 - 86.8796i) q^{80} +(-336.736 + 194.415i) q^{82} +(51.1359 - 88.5699i) q^{83} +(-145.971 - 252.830i) q^{85} +(-400.878 - 231.447i) q^{86} +(143.064 + 247.794i) q^{88} +(242.765 + 420.481i) q^{89} +(900.955 + 206.670i) q^{91} +(-171.273 - 98.8843i) q^{92} +137.797i q^{94} +103.836i q^{95} +(-329.851 - 190.439i) q^{97} +(-684.192 + 49.7737i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 192 q^{4} - 12 q^{7}+O(q^{10}) $ 48 * q - 192 * q^4 - 12 * q^7	$ 48 q - 192 q^{4} - 12 q^{7} + 24 q^{11} + 72 q^{13} + 132 q^{14} + 768 q^{16} - 144 q^{17} - 408 q^{23} - 600 q^{25} - 120 q^{26} + 48 q^{28} - 42 q^{29} + 780 q^{35} - 168 q^{37} + 618 q^{41} - 42 q^{43} - 96 q^{44} - 252 q^{46} - 396 q^{47} - 42 q^{49} - 1464 q^{50} - 288 q^{52} + 36 q^{53} - 528 q^{56} - 252 q^{58} + 3000 q^{59} - 2952 q^{62} - 3072 q^{64} + 1176 q^{67} + 576 q^{68} - 324 q^{70} - 1260 q^{74} - 6420 q^{77} - 2460 q^{79} + 720 q^{85} + 1200 q^{86} + 4398 q^{89} - 90 q^{91} + 1632 q^{92} + 1584 q^{97} + 1104 q^{98}+O(q^{100}) $ 48 * q - 192 * q^4 - 12 * q^7 + 24 * q^11 + 72 * q^13 + 132 * q^14 + 768 * q^16 - 144 * q^17 - 408 * q^23 - 600 * q^25 - 120 * q^26 + 48 * q^28 - 42 * q^29 + 780 * q^35 - 168 * q^37 + 618 * q^41 - 42 * q^43 - 96 * q^44 - 252 * q^46 - 396 * q^47 - 42 * q^49 - 1464 * q^50 - 288 * q^52 + 36 * q^53 - 528 * q^56 - 252 * q^58 + 3000 * q^59 - 2952 * q^62 - 3072 * q^64 + 1176 * q^67 + 576 * q^68 - 324 * q^70 - 1260 * q^74 - 6420 * q^77 - 2460 * q^79 + 720 * q^85 + 1200 * q^86 + 4398 * q^89 - 90 * q^91 + 1632 * q^92 + 1584 * q^97 + 1104 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/378\mathbb{Z}\right)^\times$.

$n$	$29$	$325$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$			2.00000i			0.707107i
$2$			2.00000i			0.707107i
$3$		0			0
$3$		0			0
$4$	−4.00000			−0.500000
$5$	3.13500	−	5.42997i	0.280403	−	0.485672i	−0.691081	−	0.722777i	$-0.742865\pi$
$5$	3.13500	−	5.42997i	0.280403	−	0.485672i	0.971484	+	0.237105i	$0.0761987\pi$
$6$		0			0
$7$	13.5626	+	12.6118i	0.732310	+	0.680971i
$7$	13.5626	+	12.6118i	0.732310	+	0.680971i
$8$		−	8.00000i		−	0.353553i
$9$		0			0
$10$	10.8599	+	6.26999i	0.343422	+	0.198275i
$11$	−30.9743	+	17.8830i	−0.849009	+	0.490176i	−0.860316	−	0.509760i	$-0.829734\pi$
$11$	−30.9743	+	17.8830i	−0.849009	+	0.490176i	0.0113072	+	0.999936i	$0.496401\pi$
$12$		0			0
$13$	43.2237	−	24.9552i	0.922162	−	0.532411i	0.0378380	−	0.999284i	$-0.487953\pi$
$13$	43.2237	−	24.9552i	0.922162	−	0.532411i	0.884324	+	0.466873i	$0.154620\pi$
$14$	−25.2235	+	27.1251i	−0.481519	+	0.517821i
$15$		0			0
$16$	16.0000			0.250000
$17$	23.2809	−	40.3238i	0.332145	−	0.575291i	−0.650788	−	0.759260i	$-0.725561\pi$
$17$	23.2809	−	40.3238i	0.332145	−	0.575291i	0.982932	+	0.183969i	$0.0588945\pi$
$18$		0			0
$19$	−14.3421	+	8.28040i	−0.173174	+	0.0999818i	−0.584081	−	0.811695i	$-0.698545\pi$
$19$	−14.3421	+	8.28040i	−0.173174	+	0.0999818i	0.410908	+	0.911677i	$0.365212\pi$
$20$	−12.5400	+	21.7199i	−0.140201	+	0.242836i
$21$		0			0
$22$	−35.7660	−	61.9486i	−0.346607	−	0.600340i
$23$	42.8182	+	24.7211i	0.388183	+	0.224117i	0.681372	−	0.731937i	$-0.261383\pi$
$23$	42.8182	+	24.7211i	0.388183	+	0.224117i	−0.293190	+	0.956054i	$0.594717\pi$
$24$		0			0
$25$	42.8436	+	74.2073i	0.342749	+	0.593658i
$26$	49.9105	+	86.4475i	0.376471	+	0.652067i
$27$		0			0
$28$	−54.2503	−	50.4471i	−0.366155	−	0.340486i
$29$	161.868	+	93.4545i	1.03649	+	0.598416i	0.918836	−	0.394639i	$-0.129130\pi$
$29$	161.868	+	93.4545i	1.03649	+	0.598416i	0.117651	+	0.993055i	$0.462464\pi$
$30$		0			0
$31$		−	291.470i		−	1.68869i	−0.535796	−	0.844347i	$-0.679988\pi$
$31$		−	291.470i		−	1.68869i	0.535796	−	0.844347i	$-0.320012\pi$
$32$			32.0000i			0.176777i
$33$		0			0
$34$	80.6475	+	46.5619i	0.406792	+	0.234862i
$35$	111.000	−	34.1066i	0.536070	−	0.164716i
$36$		0			0
$37$	198.915	+	344.531i	0.883823	+	1.53083i	0.847057	+	0.531502i	$0.178372\pi$
$37$	198.915	+	344.531i	0.883823	+	1.53083i	0.0367654	+	0.999324i	$0.488295\pi$
$38$	−16.5608	−	28.6842i	−0.0706978	−	0.122452i
$39$		0			0
$40$	−43.4398	−	25.0800i	−0.171711	−	0.0991373i
$41$	97.2074	+	168.368i	0.370274	+	0.641334i	0.989608	−	0.143794i	$-0.0459303\pi$
$41$	97.2074	+	168.368i	0.370274	+	0.641334i	−0.619333	+	0.785128i	$0.712597\pi$
$42$		0			0
$43$	−115.723	+	200.439i	−0.410411	+	0.710852i	−0.994935	−	0.100524i	$-0.967948\pi$
$43$	−115.723	+	200.439i	−0.410411	+	0.710852i	0.584524	+	0.811377i	$0.301281\pi$
$44$	123.897	−	71.5321i	0.424505	−	0.245088i
$45$		0			0
$46$	−49.4422	+	85.6363i	−0.158475	+	0.274487i
$47$	68.8983			0.213827			0.106913	−	0.994268i	$-0.465903\pi$
$47$	68.8983			0.213827			0.106913	+	0.994268i	$0.465903\pi$
$48$		0			0
$49$	24.8868	+	342.096i	0.0725564	+	0.997364i
$50$	−148.415	+	85.6872i	−0.419780	+	0.242360i
$51$		0			0
$52$	−172.895	+	99.8210i	−0.461081	+	0.266205i
$53$	446.076	+	257.542i	1.15610	+	0.667474i	0.950366	−	0.311135i	$-0.100709\pi$
$53$	446.076	+	257.542i	1.15610	+	0.667474i	0.205732	+	0.978608i	$0.434042\pi$
$54$		0			0
$55$			224.253i			0.549786i
$56$	100.894	−	108.501i	0.240760	−	0.258911i
$57$		0			0
$58$	−186.909	+	323.736i	−0.423144	+	0.732907i
$59$	211.598			0.466910			0.233455	−	0.972368i	$-0.424997\pi$
$59$	211.598			0.466910			0.233455	+	0.972368i	$0.424997\pi$
$60$		0			0
$61$			161.574i			0.339139i	0.985518	+	0.169569i	$0.0542377\pi$
$61$			161.574i			0.339139i	−0.985518	+	0.169569i	$0.945762\pi$
$62$	582.940			1.19409
$63$		0			0
$64$	−64.0000			−0.125000
$65$		−	312.938i		−	0.597157i
$66$		0			0
$67$	−872.379			−1.59072			−0.795359	−	0.606139i	$-0.792718\pi$
$67$	−872.379			−1.59072			−0.795359	+	0.606139i	$0.792718\pi$
$68$	−93.1238	+	161.295i	−0.166072	+	0.287646i
$69$		0			0
$70$	68.2132	+	222.000i	0.116472	+	0.379059i
$71$			61.8704i			0.103418i	0.998662	+	0.0517089i	$0.0164668\pi$
$71$			61.8704i			0.103418i	−0.998662	+	0.0517089i	$0.983533\pi$
$72$		0			0
$73$	−405.059	−	233.861i	−0.649433	−	0.374950i	0.138806	−	0.990320i	$-0.455673\pi$
$73$	−405.059	−	233.861i	−0.649433	−	0.374950i	−0.788239	+	0.615369i	$0.789007\pi$
$74$	−689.062	+	397.830i	−1.08246	+	0.624957i
$75$		0			0
$76$	57.3683	−	33.1216i	0.0865868	−	0.0499909i
$77$	−645.628	−	148.101i	−0.955534	−	0.219190i
$78$		0			0
$79$	972.318			1.38474			0.692369	−	0.721543i	$-0.256567\pi$
$79$	972.318			1.38474			0.692369	+	0.721543i	$0.256567\pi$
$80$	50.1600	−	86.8796i	0.0701007	−	0.121418i
$81$		0			0
$82$	−336.736	+	194.415i	−0.453492	+	0.261824i
$83$	51.1359	−	88.5699i	0.0676252	−	0.117130i	−0.830230	−	0.557421i	$-0.811791\pi$
$83$	51.1359	−	88.5699i	0.0676252	−	0.117130i	0.897855	+	0.440290i	$0.145124\pi$
$84$		0			0
$85$	−145.971	−	252.830i	−0.186268	−	0.322626i
$86$	−400.878	−	231.447i	−0.502649	−	0.290204i
$87$		0			0
$88$	143.064	+	247.794i	0.173303	+	0.300170i
$89$	242.765	+	420.481i	0.289135	+	0.500796i	0.973603	−	0.228246i	$-0.0732991\pi$
$89$	242.765	+	420.481i	0.289135	+	0.500796i	−0.684469	+	0.729042i	$0.739966\pi$
$90$		0			0
$91$	900.955	+	206.670i	1.03787	+	0.238076i
$92$	−171.273	−	98.8843i	−0.194091	−	0.112059i
$93$		0			0
$94$			137.797i			0.151198i
$95$			103.836i			0.112141i
$96$		0			0
$97$	−329.851	−	190.439i	−0.345271	−	0.199342i	0.317330	−	0.948315i	$-0.397214\pi$
$97$	−329.851	−	190.439i	−0.345271	−	0.199342i	−0.662600	+	0.748973i	$0.730547\pi$
$98$	−684.192	+	49.7737i	−0.705243	+	0.0513051i
$99$		0			0
$100$	−171.374	−	296.829i	−0.171374	−	0.296829i
$101$	727.915	+	1260.79i	0.717131	+	1.24211i	0.962132	+	0.272585i	$0.0878784\pi$
$101$	727.915	+	1260.79i	0.717131	+	1.24211i	−0.245001	+	0.969523i	$0.578788\pi$
$102$		0			0
$103$	−588.486	−	339.762i	−0.562963	−	0.325027i	0.191371	−	0.981518i	$-0.438707\pi$
$103$	−588.486	−	339.762i	−0.562963	−	0.325027i	−0.754334	+	0.656491i	$0.772040\pi$
$104$	−199.642	−	345.790i	−0.188236	−	0.326034i
$105$		0			0
$106$	−515.084	+	892.151i	−0.471975	+	0.817485i
$107$	−514.875	+	297.263i	−0.465185	+	0.268575i	−0.714222	−	0.699919i	$-0.753219\pi$
$107$	−514.875	+	297.263i	−0.465185	+	0.268575i	0.249037	+	0.968494i	$0.419886\pi$
$108$		0			0
$109$	1033.40	−	1789.90i	0.908091	−	1.57286i	0.0913778	−	0.995816i	$-0.470873\pi$
$109$	1033.40	−	1789.90i	0.908091	−	1.57286i	0.816713	−	0.577044i	$-0.195794\pi$
$110$	−448.506			−0.388758
$111$		0			0
$112$	217.001	+	201.788i	0.183078	+	0.170243i
$113$	454.747	−	262.548i	0.378575	−	0.218571i	−0.298623	−	0.954371i	$-0.596527\pi$
$113$	454.747	−	262.548i	0.378575	−	0.218571i	0.677198	+	0.735801i	$0.263194\pi$
$114$		0			0
$115$	268.470	−	155.001i	0.217695	−	0.125686i
$116$	−647.472	−	373.818i	−0.518244	−	0.299208i
$117$		0			0
$118$			423.196i			0.330156i
$119$	824.303	−	253.280i	0.634990	−	0.195111i
$120$		0			0
$121$	−25.8954	+	44.8522i	−0.0194556	+	0.0336981i
$122$	−323.149			−0.239807
$123$		0			0
$124$			1165.88i			0.844347i
$125$	1321.01			0.945236
$126$		0			0
$127$	940.079			0.656839			0.328419	−	0.944532i	$-0.393484\pi$
$127$	940.079			0.656839			0.328419	+	0.944532i	$0.393484\pi$
$128$		−	128.000i		−	0.0883883i
$129$		0			0
$130$	625.877			0.422254
$131$	1366.98	−	2367.67i	0.911704	−	1.57912i	0.100047	−	0.994983i	$-0.468101\pi$
$131$	1366.98	−	2367.67i	0.911704	−	1.57912i	0.811657	−	0.584135i	$-0.198566\pi$
$132$		0			0
$133$	−298.946	−	68.5753i	−0.194902	−	0.0447085i
$134$		−	1744.76i		−	1.12481i
$135$		0			0
$136$	−322.590	−	186.248i	−0.203396	−	0.117431i
$137$	−2508.79	+	1448.45i	−1.56453	+	0.903283i	−0.567743	+	0.823206i	$0.692183\pi$
$137$	−2508.79	+	1448.45i	−1.56453	+	0.903283i	−0.996789	+	0.0800767i	$0.974483\pi$
$138$		0			0
$139$	72.0482	−	41.5971i	0.0439644	−	0.0253829i	−0.477857	−	0.878438i	$-0.658586\pi$
$139$	72.0482	−	41.5971i	0.0439644	−	0.0253829i	0.521821	+	0.853055i	$0.325253\pi$
$140$	−444.001	+	136.426i	−0.268035	+	0.0823581i
$141$		0			0
$142$	−123.741			−0.0731275
$143$	−892.550	+	1545.94i	−0.521949	+	0.904043i
$144$		0			0
$145$	1014.91	−	585.959i	0.581268	−	0.335595i
$146$	467.722	−	810.118i	0.265130	−	0.459218i
$147$		0			0
$148$	−795.660	−	1378.12i	−0.441911	−	0.765413i
$149$	552.584	+	319.035i	0.303822	+	0.175412i	0.644159	−	0.764892i	$-0.277208\pi$
$149$	552.584	+	319.035i	0.303822	+	0.175412i	−0.340337	+	0.940304i	$0.610541\pi$
$150$		0			0
$151$	−428.203	−	741.670i	−0.230773	−	0.399710i	0.727263	−	0.686359i	$-0.240792\pi$
$151$	−428.203	−	741.670i	−0.230773	−	0.399710i	−0.958036	+	0.286649i	$0.907459\pi$
$152$	66.2432	+	114.737i	0.0353489	+	0.0612261i
$153$		0			0
$154$	296.201	−	1291.26i	0.154991	−	0.675664i
$155$	−1582.67	−	913.757i	−0.820151	−	0.473515i
$156$		0			0
$157$		−	2659.48i		−	1.35191i	−0.736945	−	0.675953i	$-0.763732\pi$
$157$		−	2659.48i		−	1.35191i	0.736945	−	0.675953i	$-0.236268\pi$
$158$			1944.64i			0.979158i
$159$		0			0
$160$	173.759	+	100.320i	0.0858554	+	0.0495687i
$161$	268.948	+	875.294i	0.131653	+	0.428465i
$162$		0			0
$163$	373.107	+	646.241i	0.179288	+	0.310537i	0.941637	−	0.336630i	$-0.109287\pi$
$163$	373.107	+	646.241i	0.179288	+	0.310537i	−0.762349	+	0.647167i	$0.775954\pi$
$164$	−388.830	−	673.473i	−0.185137	−	0.320667i
$165$		0			0
$166$	177.140	+	102.272i	0.0828236	+	0.0478182i
$167$	−1128.87	−	1955.26i	−0.523081	−	0.906002i	−0.999639	−	0.0268594i	$-0.991449\pi$
$167$	−1128.87	−	1955.26i	−0.523081	−	0.906002i	0.476559	−	0.879143i	$-0.341884\pi$
$168$		0			0
$169$	147.028	−	254.660i	0.0669221	−	0.115913i
$170$	505.660	−	291.943i	0.228131	−	0.131712i
$171$		0			0
$172$	462.894	−	801.756i	0.205205	−	0.355426i
$173$	3507.26			1.54134			0.770670	−	0.637234i	$-0.219922\pi$
$173$	3507.26			1.54134			0.770670	+	0.637234i	$0.219922\pi$
$174$		0			0
$175$	−354.815	+	1546.77i	−0.153266	+	0.668144i
$176$	−495.589	+	286.128i	−0.212252	+	0.122544i
$177$		0			0
$178$	−840.961	+	485.529i	−0.354116	+	0.204449i
$179$	−3695.90	−	2133.83i	−1.54326	−	0.891004i	−0.998630	−	0.0523310i	$-0.983335\pi$
$179$	−3695.90	−	2133.83i	−1.54326	−	0.891004i	−0.544635	−	0.838673i	$-0.683332\pi$
$180$		0			0
$181$		−	3644.08i		−	1.49648i	−0.663430	−	0.748238i	$-0.730900\pi$
$181$		−	3644.08i		−	1.49648i	0.663430	−	0.748238i	$-0.269100\pi$
$182$	−413.341	+	1801.91i	−0.168345	+	0.733881i
$183$		0			0
$184$	197.769	−	342.545i	0.0792375	−	0.137243i
$185$	2494.39			0.991305
$186$		0			0
$187$			1665.33i			0.651237i
$188$	−275.593			−0.106913
$189$		0			0
$190$	−207.672			−0.0792954
$191$		−	672.755i		−	0.254863i	−0.991847	−	0.127431i	$-0.959327\pi$
$191$		−	672.755i		−	0.254863i	0.991847	−	0.127431i	$-0.0406733\pi$
$192$		0			0
$193$	−2708.60			−1.01020			−0.505102	−	0.863060i	$-0.668545\pi$
$193$	−2708.60			−1.01020			−0.505102	+	0.863060i	$0.668545\pi$
$194$	380.879	−	659.701i	0.140956	−	0.244143i
$195$		0			0
$196$	−99.5473	−	1368.38i	−0.0362782	−	0.498682i
$197$		−	4148.15i		−	1.50022i	−0.661313	−	0.750110i	$-0.730001\pi$
$197$		−	4148.15i		−	1.50022i	0.661313	−	0.750110i	$-0.269999\pi$
$198$		0			0
$199$	856.708	+	494.621i	0.305178	+	0.176195i	0.644767	−	0.764379i	$-0.276955\pi$
$199$	856.708	+	494.621i	0.305178	+	0.176195i	−0.339589	+	0.940574i	$0.610288\pi$
$200$	593.658	−	342.749i	0.209890	−	0.121180i
$201$		0			0
$202$	−2521.57	+	1455.83i	−0.878303	+	0.507088i
$203$	1016.72	+	3308.93i	0.351526	+	1.14404i
$204$		0			0
$205$	1218.98			0.415304
$206$	679.525	−	1176.97i	0.229829	−	0.398075i
$207$		0			0
$208$	691.580	−	399.284i	0.230541	−	0.133103i
$209$	296.157	−	512.959i	0.0980173	−	0.169771i
$210$		0			0
$211$	−956.935	−	1657.46i	−0.312219	−	0.540778i	0.666624	−	0.745394i	$-0.267739\pi$
$211$	−956.935	−	1657.46i	−0.312219	−	0.540778i	−0.978842	+	0.204616i	$0.934405\pi$
$212$	−1784.30	−	1030.17i	−0.578049	−	0.333737i
$213$		0			0
$214$	−594.526	−	1029.75i	−0.189911	−	0.328936i
$215$	725.586	+	1256.75i	0.230161	+	0.398650i
$216$		0			0
$217$	3675.95	−	3953.08i	1.14995	−	1.23665i
$218$	3579.81	+	2066.80i	1.11218	+	0.642117i
$219$		0			0
$220$		−	897.011i		−	0.274893i
$221$		−	2323.93i		−	0.707349i
$222$		0			0
$223$	513.983	+	296.748i	0.154345	+	0.0891109i	0.575183	−	0.818025i	$-0.304931\pi$
$223$	513.983	+	296.748i	0.154345	+	0.0891109i	−0.420839	+	0.907136i	$0.638264\pi$
$224$	−403.576	+	434.002i	−0.120380	+	0.129455i
$225$		0			0
$226$	525.097	+	909.494i	0.154553	+	0.267693i
$227$	−2488.48	−	4310.17i	−0.727604	−	1.26025i	−0.957893	−	0.287124i	$-0.907301\pi$
$227$	−2488.48	−	4310.17i	−0.727604	−	1.26025i	0.230290	−	0.973122i	$-0.426033\pi$
$228$		0			0
$229$	1809.05	+	1044.45i	0.522031	+	0.301395i	0.737765	−	0.675057i	$-0.235881\pi$
$229$	1809.05	+	1044.45i	0.522031	+	0.301395i	−0.215734	+	0.976452i	$0.569214\pi$
$230$	310.002	+	536.939i	0.0888736	+	0.153934i
$231$		0			0
$232$	747.636	−	1294.94i	0.211572	−	0.366454i
$233$	100.786	−	58.1890i	0.0283379	−	0.0163609i	−0.485764	−	0.874090i	$-0.661459\pi$
$233$	100.786	−	58.1890i	0.0283379	−	0.0163609i	0.514102	+	0.857729i	$0.328125\pi$
$234$		0			0
$235$	215.996	−	374.116i	0.0599576	−	0.103850i
$236$	−846.392			−0.233455
$237$		0			0
$238$	506.561	+	1648.61i	0.137964	+	0.449005i
$239$	−1017.31	+	587.342i	−0.275331	+	0.158962i	−0.631308	−	0.775532i	$-0.717482\pi$
$239$	−1017.31	+	587.342i	−0.275331	+	0.158962i	0.355977	+	0.934495i	$0.384148\pi$
$240$		0			0
$241$	−1610.41	+	929.773i	−0.430439	+	0.248514i	−0.699534	−	0.714600i	$-0.746609\pi$
$241$	−1610.41	+	929.773i	−0.430439	+	0.248514i	0.269095	+	0.963114i	$0.413276\pi$
$242$	−89.7044	−	51.7909i	−0.0238282	−	0.0137572i
$243$		0			0
$244$		−	646.297i		−	0.169569i
$245$	1935.59	+	937.335i	0.504737	+	0.244425i
$246$		0			0
$247$	−413.279	+	715.820i	−0.106463	+	0.184399i
$248$	−2331.76			−0.597044
$249$		0			0
$250$			2642.01i			0.668383i
$251$	−5632.95			−1.41653			−0.708264	−	0.705948i	$-0.750521\pi$
$251$	−5632.95			−1.41653			−0.708264	+	0.705948i	$0.750521\pi$
$252$		0			0
$253$	−1768.35			−0.439428
$254$			1880.16i			0.464455i
$255$		0			0
$256$	256.000			0.0625000
$257$	−1602.62	+	2775.82i	−0.388983	+	0.673738i	−0.992313	−	0.123753i	$-0.960507\pi$
$257$	−1602.62	+	2775.82i	−0.388983	+	0.673738i	0.603330	+	0.797492i	$0.293840\pi$
$258$		0			0
$259$	−1647.34	+	7181.40i	−0.395216	+	1.72290i
$260$			1251.75i			0.298579i
$261$		0			0
$262$	4735.34	+	2733.95i	1.11660	+	0.644672i
$263$	−624.784	+	360.719i	−0.146486	+	0.0845738i	−0.571452	−	0.820636i	$-0.693620\pi$
$263$	−624.784	+	360.719i	−0.146486	+	0.0845738i	0.424966	+	0.905210i	$0.360286\pi$
$264$		0			0
$265$	2796.89	−	1614.79i	0.648346	−	0.374323i
$266$	137.151	−	597.892i	0.0316137	−	0.137816i
$267$		0			0
$268$	3489.52			0.795359
$269$	−3255.57	+	5638.81i	−0.737902	+	1.27808i	0.215537	+	0.976496i	$0.430850\pi$
$269$	−3255.57	+	5638.81i	−0.737902	+	1.27808i	−0.953438	+	0.301588i	$0.902483\pi$
$270$		0			0
$271$	−7040.66	+	4064.93i	−1.57819	+	0.911168i	−0.583078	+	0.812416i	$0.698152\pi$
$271$	−7040.66	+	4064.93i	−1.57819	+	0.911168i	−0.995112	+	0.0987520i	$0.968515\pi$
$272$	372.495	−	645.180i	0.0830361	−	0.143823i
$273$		0			0
$274$	−2896.91	−	5017.59i	−0.638717	−	1.10629i
$275$	−2654.10	−	1532.35i	−0.581994	−	0.336014i
$276$		0			0
$277$	217.552	+	376.811i	0.0471893	+	0.0817342i	0.888655	−	0.458576i	$-0.151640\pi$
$277$	217.552	+	376.811i	0.0471893	+	0.0817342i	−0.841466	+	0.540310i	$0.818307\pi$
$278$	83.1941	+	144.096i	0.0179484	+	0.0310875i
$279$		0			0
$280$	−272.853	−	888.001i	−0.0582360	−	0.189529i
$281$	−6468.65	−	3734.68i	−1.37326	−	0.792855i	−0.381927	−	0.924192i	$-0.624739\pi$
$281$	−6468.65	−	3734.68i	−1.37326	−	0.792855i	−0.991338	+	0.131338i	$0.958073\pi$
$282$		0			0
$283$			1772.40i			0.372290i	0.982522	+	0.186145i	$0.0595995\pi$
$283$			1772.40i			0.372290i	−0.982522	+	0.186145i	$0.940401\pi$
$284$		−	247.482i		−	0.0517089i
$285$		0			0
$286$	−3091.88	−	1785.10i	−0.639255	−	0.369074i
$287$	−805.037	+	3509.46i	−0.165574	+	0.721802i
$288$		0			0
$289$	1372.50	+	2377.23i	0.279360	+	0.483866i
$290$	1171.92	+	2029.82i	0.237302	+	0.411018i
$291$		0			0
$292$	1620.24	+	935.444i	0.324716	+	0.187475i
$293$	3227.59	+	5590.35i	0.643542	+	1.11465i	0.984636	+	0.174618i	$0.0558691\pi$
$293$	3227.59	+	5590.35i	0.643542	+	1.11465i	−0.341094	+	0.940029i	$0.610798\pi$
$294$		0			0
$295$	663.359	−	1148.97i	0.130923	−	0.226765i
$296$	2756.25	−	1591.32i	0.541229	−	0.312478i
$297$		0			0
$298$	−638.069	+	1105.17i	−0.124035	+	0.214834i
$299$	2467.68			0.477290
$300$		0			0
$301$	−4097.40	+	1258.99i	−0.784618	+	0.241086i
$302$	1483.34	−	856.407i	0.282638	−	0.163181i
$303$		0			0
$304$	−229.473	+	132.486i	−0.0432934	+	0.0249955i
$305$	877.344	+	506.535i	0.164710	+	0.0950954i
$306$		0			0
$307$			364.330i			0.0677310i	0.999426	+	0.0338655i	$0.0107818\pi$
$307$			364.330i			0.0677310i	−0.999426	+	0.0338655i	$0.989218\pi$
$308$	2582.51	+	592.403i	0.477767	+	0.109595i
$309$		0			0
$310$	1827.51	−	3165.35i	0.334825	−	0.579934i
$311$	9771.89			1.78171			0.890857	−	0.454284i	$-0.150105\pi$
$311$	9771.89			1.78171			0.890857	+	0.454284i	$0.150105\pi$
$312$		0			0
$313$			7750.01i			1.39954i	0.714367	+	0.699771i	$0.246715\pi$
$313$			7750.01i			1.39954i	−0.714367	+	0.699771i	$0.753285\pi$
$314$	5318.95			0.955942
$315$		0			0
$316$	−3889.27			−0.692369
$317$		−	9853.10i		−	1.74576i	−0.487937	−	0.872879i	$-0.662250\pi$
$317$		−	9853.10i		−	1.74576i	0.487937	−	0.872879i	$-0.337750\pi$
$318$		0			0
$319$	−6685.00			−1.17332
$320$	−200.640	+	347.518i	−0.0350503	+	0.0607090i
$321$		0			0
$322$	−1750.59	+	537.896i	−0.302970	+	0.0930925i
$323$			771.102i			0.132834i
$324$		0			0
$325$	3703.72	+	2138.34i	0.632140	+	0.364966i
$326$	−1292.48	+	746.215i	−0.219583	+	0.126776i
$327$		0			0
$328$	1346.95	−	777.660i	0.226746	−	0.130912i
$329$	934.439	+	868.929i	0.156587	+	0.145610i
$330$		0			0
$331$	6111.13			1.01480			0.507399	−	0.861711i	$-0.330607\pi$
$331$	6111.13			1.01480			0.507399	+	0.861711i	$0.330607\pi$
$332$	−204.543	+	354.280i	−0.0338126	+	0.0585651i
$333$		0			0
$334$	3910.51	−	2257.74i	0.640640	−	0.369874i
$335$	−2734.91	+	4737.00i	−0.446041	+	0.772566i
$336$		0			0
$337$	3140.28	+	5439.13i	0.507602	+	0.879193i	0.999961	+	0.00880090i	$0.00280145\pi$
$337$	3140.28	+	5439.13i	0.507602	+	0.879193i	−0.492359	+	0.870392i	$0.663865\pi$
$338$	509.320	+	294.056i	0.0819626	+	0.0473211i
$339$		0			0
$340$	583.885	+	1011.32i	0.0931342	+	0.161313i
$341$	5212.36	+	9028.07i	0.827757	+	1.43372i
$342$		0			0
$343$	−3976.90	+	4953.57i	−0.626043	+	0.779789i
$344$	1603.51	+	925.788i	0.251324	+	0.145102i
$345$		0			0
$346$			7014.52i			1.08989i
$347$			4806.84i			0.743644i	0.928304	+	0.371822i	$0.121267\pi$
$347$			4806.84i			0.743644i	−0.928304	+	0.371822i	$0.878733\pi$
$348$		0			0
$349$	−6460.22	−	3729.81i	−0.990853	−	0.572069i	−0.0853238	−	0.996353i	$-0.527192\pi$
$349$	−6460.22	−	3729.81i	−0.990853	−	0.572069i	−0.905529	+	0.424284i	$0.860526\pi$
$350$	−3093.55	−	709.630i	−0.472449	−	0.108375i
$351$		0			0
$352$	−572.257	−	991.177i	−0.0866516	−	0.150085i
$353$	−4952.28	−	8577.60i	−0.746695	−	1.29331i	−0.949399	−	0.314073i	$-0.898306\pi$
$353$	−4952.28	−	8577.60i	−0.746695	−	1.29331i	0.202704	−	0.979240i	$-0.435027\pi$
$354$		0			0
$355$	335.955	+	193.964i	0.0502271	+	0.0289986i
$356$	−971.059	−	1681.92i	−0.144567	−	0.250398i
$357$		0			0
$358$	4267.66	−	7391.80i	0.630035	−	1.09125i
$359$	7597.13	−	4386.20i	1.11688	−	0.644833i	0.176280	−	0.984340i	$-0.443594\pi$
$359$	7597.13	−	4386.20i	1.11688	−	0.644833i	0.940603	+	0.339507i	$0.110260\pi$
$360$		0			0
$361$	−3292.37	+	5702.55i	−0.480007	+	0.831397i
$362$	7288.16			1.05817
$363$		0			0
$364$	−3603.82	−	826.681i	−0.518933	−	0.119038i
$365$	−2539.72	+	1466.31i	−0.364205	+	0.210274i
$366$		0			0
$367$	3110.46	−	1795.83i	0.442411	−	0.255426i	−0.262209	−	0.965011i	$-0.584451\pi$
$367$	3110.46	−	1795.83i	0.442411	−	0.255426i	0.704620	+	0.709585i	$0.251118\pi$
$368$	685.091	+	395.537i	0.0970457	+	0.0560294i
$369$		0			0
$370$			4988.79i			0.700958i
$371$	2801.88	+	9118.73i	0.392092	+	1.27607i
$372$		0			0
$373$	3377.44	−	5849.90i	0.468840	−	0.812055i	−0.530525	−	0.847669i	$-0.678005\pi$
$373$	3377.44	−	5849.90i	0.468840	−	0.812055i	0.999366	+	0.0356140i	$0.0113387\pi$
$374$	−3330.67			−0.460494
$375$		0			0
$376$		−	551.187i		−	0.0755991i
$377$	9328.72			1.27441
$378$		0			0
$379$	−6355.80			−0.861412			−0.430706	−	0.902492i	$-0.641735\pi$
$379$	−6355.80			−0.861412			−0.430706	+	0.902492i	$0.641735\pi$
$380$		−	415.345i		−	0.0560704i
$381$		0			0
$382$	1345.51			0.180215
$383$	−2536.01	+	4392.49i	−0.338339	+	0.586020i	−0.984120	−	0.177502i	$-0.943198\pi$
$383$	−2536.01	+	4392.49i	−0.338339	+	0.586020i	0.645781	+	0.763522i	$0.276532\pi$
$384$		0			0
$385$	−2828.22	+	3041.45i	−0.374389	+	0.402614i
$386$		−	5417.20i		−	0.714322i
$387$		0			0
$388$	1319.40	+	761.757i	0.172635	+	0.0996711i
$389$	5660.81	−	3268.27i	0.737827	−	0.425984i	−0.0834519	−	0.996512i	$-0.526595\pi$
$389$	5660.81	−	3268.27i	0.737827	−	0.425984i	0.821279	+	0.570527i	$0.193261\pi$
$390$		0			0
$391$	1993.69	−	1151.06i	0.257866	−	0.148879i
$392$	2736.77	−	199.095i	0.352622	−	0.0256525i
$393$		0			0
$394$	8296.29			1.06082
$395$	3048.22	−	5279.66i	0.388284	−	0.672528i
$396$		0			0
$397$	1416.31	−	817.704i	0.179049	−	0.103374i	−0.407797	−	0.913073i	$-0.633703\pi$
$397$	1416.31	−	817.704i	0.179049	−	0.103374i	0.586846	+	0.809699i	$0.300370\pi$
$398$	−989.241	+	1713.42i	−0.124588	+	0.215793i
$399$		0			0
$400$	685.497	+	1187.32i	0.0856872	+	0.148415i
$401$	−1705.06	−	984.415i	−0.212335	−	0.122592i	0.390061	−	0.920789i	$-0.372454\pi$
$401$	−1705.06	−	984.415i	−0.212335	−	0.122592i	−0.602396	+	0.798197i	$0.705787\pi$
$402$		0			0
$403$	−7273.70	−	12598.4i	−0.899079	−	1.55725i
$404$	−2911.66	−	5043.14i	−0.358566	−	0.621054i
$405$		0			0
$406$	−6617.85	+	2033.44i	−0.808962	+	0.248566i
$407$	−12322.5	−	7114.40i	−1.50075	−	0.866457i
$408$		0			0
$409$		−	10183.7i		−	1.23117i	−0.788069	−	0.615587i	$-0.788919\pi$
$409$		−	10183.7i		−	1.23117i	0.788069	−	0.615587i	$-0.211081\pi$
$410$			2437.96i			0.293664i
$411$		0			0
$412$	2353.94	+	1359.05i	0.281482	+	0.162513i
$413$	2869.81	+	2668.62i	0.341923	+	0.317953i
$414$		0			0
$415$	−320.622	−	555.333i	−0.0379246	−	0.0656873i
$416$	798.568	+	1383.16i	0.0941178	+	0.163017i
$417$		0			0
$418$	1025.92	+	592.314i	0.120046	+	0.0693087i
$419$	−382.680	−	662.820i	−0.0446184	−	0.0772814i	0.842854	−	0.538143i	$-0.180874\pi$
$419$	−382.680	−	662.820i	−0.0446184	−	0.0772814i	−0.887472	+	0.460861i	$0.847541\pi$
$420$		0			0
$421$	1465.65	−	2538.59i	0.169671	−	0.293879i	−0.768633	−	0.639690i	$-0.779063\pi$
$421$	1465.65	−	2538.59i	0.169671	−	0.293879i	0.938304	+	0.345811i	$0.112396\pi$
$422$	3314.92	−	1913.87i	0.382388	−	0.220772i
$423$		0			0
$424$	2060.34	−	3568.61i	0.235988	−	0.408742i
$425$	3989.76			0.455368
$426$		0			0
$427$	−2037.74	+	2191.36i	−0.230944	+	0.248355i
$428$	2059.50	−	1189.05i	0.232593	−	0.134287i
$429$		0			0
$430$	−2513.50	+	1451.17i	−0.281888	+	0.162748i
$431$	−11353.3	−	6554.82i	−1.26884	−	0.732563i	−0.294069	−	0.955784i	$-0.595010\pi$
$431$	−11353.3	−	6554.82i	−1.26884	−	0.732563i	−0.974768	+	0.223221i	$0.928343\pi$
$432$		0			0
$433$			2018.08i			0.223979i	0.993709	+	0.111990i	$0.0357223\pi$
$433$			2018.08i			0.223979i	−0.993709	+	0.111990i	$0.964278\pi$
$434$	7906.16	+	7351.90i	0.874442	+	0.813139i
$435$		0			0
$436$	−4133.61	+	7159.62i	−0.454046	+	0.786430i
$437$	−818.802			−0.0896307
$438$		0			0
$439$			7290.56i			0.792618i	0.918117	+	0.396309i	$0.129709\pi$
$439$			7290.56i			0.792618i	−0.918117	+	0.396309i	$0.870291\pi$
$440$	1794.02			0.194379
$441$		0			0
$442$	4647.85			0.500171
$443$			4425.69i			0.474652i	0.971430	+	0.237326i	$0.0762709\pi$
$443$			4425.69i			0.474652i	−0.971430	+	0.237326i	$0.923729\pi$
$444$		0			0
$445$	3044.27			0.324297
$446$	−593.496	+	1027.97i	−0.0630109	+	0.109138i
$447$		0			0
$448$	−868.005	−	807.153i	−0.0915388	−	0.0851214i
$449$			9769.16i			1.02680i	0.858148	+	0.513402i	$0.171615\pi$
$449$			9769.16i			1.02680i	−0.858148	+	0.513402i	$0.828385\pi$
$450$		0			0
$451$	−6021.86	−	3476.72i	−0.628733	−	0.362999i
$452$	−1818.99	+	1050.19i	−0.189288	+	0.109285i
$453$		0			0
$454$	8620.34	−	4976.95i	0.891129	−	0.514494i
$455$	3946.71	−	4244.25i	0.406647	−	0.437304i
$456$		0			0
$457$	6422.39			0.657389			0.328695	−	0.944436i	$-0.393391\pi$
$457$	6422.39			0.657389			0.328695	+	0.944436i	$0.393391\pi$
$458$	−2088.91	+	3618.09i	−0.213118	+	0.369132i
$459$		0			0
$460$	−1073.88	+	620.004i	−0.108847	+	0.0628431i
$461$	−8118.36	+	14061.4i	−0.820195	+	1.42062i	0.0853423	+	0.996352i	$0.472802\pi$
$461$	−8118.36	+	14061.4i	−0.820195	+	1.42062i	−0.905537	+	0.424267i	$0.860532\pi$
$462$		0			0
$463$	8360.59	+	14481.0i	0.839200	+	1.45354i	0.890564	+	0.454857i	$0.150310\pi$
$463$	8360.59	+	14481.0i	0.839200	+	1.45354i	−0.0513644	+	0.998680i	$0.516357\pi$
$464$	2589.89	+	1495.27i	0.259122	+	0.149604i
$465$		0			0
$466$	116.378	+	201.573i	0.0115689	+	0.0200379i
$467$	483.053	+	836.673i	0.0478652	+	0.0829049i	0.888965	−	0.457974i	$-0.151425\pi$
$467$	483.053	+	836.673i	0.0478652	+	0.0829049i	−0.841100	+	0.540879i	$0.818092\pi$
$468$		0			0
$469$	−11831.7	−	11002.2i	−1.16490	−	1.08323i
$470$	748.232	+	431.992i	0.0734327	+	0.0423964i
$471$		0			0
$472$		−	1692.78i		−	0.165078i
$473$		−	8277.94i		−	0.804694i
$474$		0			0
$475$	−1228.93	−	709.524i	−0.118710	−	0.0685373i
$476$	−3297.21	+	1013.12i	−0.317495	+	0.0975554i
$477$		0			0
$478$	−1174.68	−	2034.61i	−0.112403	−	0.194688i
$479$	−1040.50	−	1802.20i	−0.0992521	−	0.171910i	0.812123	−	0.583486i	$-0.198312\pi$
$479$	−1040.50	−	1802.20i	−0.0992521	−	0.171910i	−0.911375	+	0.411576i	$0.864978\pi$
$480$		0			0
$481$	17195.7	+	9927.95i	1.63006	+	0.941113i
$482$	−1859.55	−	3220.83i	−0.175726	−	0.304367i
$483$		0			0
$484$	103.582	−	179.409i	0.00972781	−	0.0168491i
$485$	−2068.16	+	1194.05i	−0.193630	+	0.111792i
$486$		0			0
$487$	−5242.01	+	9079.43i	−0.487758	+	0.844822i	−0.999901	−	0.0140783i	$-0.995519\pi$
$487$	−5242.01	+	9079.43i	−0.487758	+	0.844822i	0.512143	+	0.858900i	$0.328852\pi$
$488$	1292.59			0.119904
$489$		0			0
$490$	−1874.67	+	3871.18i	−0.172835	+	0.356903i
$491$	−1977.10	+	1141.48i	−0.181722	+	0.104917i	−0.588101	−	0.808787i	$-0.700124\pi$
$491$	−1977.10	+	1141.48i	−0.181722	+	0.104917i	0.406380	+	0.913704i	$0.366791\pi$
$492$		0			0
$493$	7536.88	−	4351.42i	0.688527	−	0.397521i
$494$	−1431.64	−	826.558i	−0.130390	−	0.0752806i
$495$		0			0
$496$		−	4663.52i		−	0.422174i
$497$	−780.295	+	839.122i	−0.0704246	+	0.0757340i
$498$		0			0
$499$	6596.35	−	11425.2i	0.591770	−	1.02497i	−0.402225	−	0.915541i	$-0.631763\pi$
$499$	6596.35	−	11425.2i	0.591770	−	1.02497i	0.993994	−	0.109434i	$-0.0349038\pi$
$500$	−5284.03			−0.472618
$501$		0			0
$502$		−	11265.9i		−	1.00164i
$503$	−20871.3			−1.85011			−0.925054	−	0.379837i	$-0.875980\pi$
$503$	−20871.3			−1.85011			−0.925054	+	0.379837i	$0.875980\pi$
$504$		0			0
$505$	9128.04			0.804342
$506$		−	3536.70i		−	0.310722i
$507$		0			0
$508$	−3760.32			−0.328419
$509$	9448.24	−	16364.8i	0.822762	−	1.42507i	−0.0808554	−	0.996726i	$-0.525765\pi$
$509$	9448.24	−	16364.8i	0.822762	−	1.42507i	0.903618	−	0.428340i	$-0.140901\pi$
$510$		0			0
$511$	−2544.24	−	8280.27i	−0.220256	−	0.716825i
$512$			512.000i			0.0441942i
$513$		0			0
$514$	−5551.64	−	3205.24i	−0.476405	−	0.275053i
$515$	−3689.80	+	2130.31i	−0.315713	+	0.182277i
$516$		0			0
$517$	−2134.08	+	1232.11i	−0.181541	+	0.104813i
$518$	−14362.8	−	3294.69i	−1.21827	−	0.279460i
$519$		0			0
$520$	−2503.51			−0.211127
$521$	3809.21	−	6597.74i	0.320316	−	0.554803i	−0.660237	−	0.751057i	$-0.729544\pi$
$521$	3809.21	−	6597.74i	0.320316	−	0.554803i	0.980553	+	0.196254i	$0.0628777\pi$
$522$		0			0
$523$	7284.36	−	4205.63i	0.609030	−	0.351624i	−0.163556	−	0.986534i	$-0.552296\pi$
$523$	7284.36	−	4205.63i	0.609030	−	0.351624i	0.772586	+	0.634910i	$0.218963\pi$
$524$	−5467.90	+	9470.68i	−0.455852	+	0.789559i
$525$		0			0
$526$	−721.438	−	1249.57i	−0.0598027	−	0.103581i
$527$	−11753.2	−	6785.69i	−0.971491	−	0.560891i
$528$		0			0
$529$	−4861.24	−	8419.91i	−0.399543	−	0.692028i
$530$	3229.57	+	5593.78i	0.264686	+	0.458450i
$531$		0			0
$532$	1195.78	+	274.301i	0.0974508	+	0.0223543i
$533$	8403.34	+	4851.67i	0.682906	+	0.394276i
$534$		0			0
$535$			3727.68i			0.301237i
$536$			6979.03i			0.562404i
$537$		0			0
$538$	−11277.6	−	6511.14i	−0.903741	−	0.521775i
$539$	−6888.56	−	10151.1i	−0.550485	−	0.811206i
$540$		0			0
$541$	−3902.20	−	6758.80i	−0.310108	−	0.537123i	0.668277	−	0.743912i	$-0.267032\pi$
$541$	−3902.20	−	6758.80i	−0.310108	−	0.537123i	−0.978386	+	0.206789i	$0.933699\pi$
$542$	−8129.85	−	14081.3i	−0.644293	−	1.11595i
$543$		0			0
$544$	1290.36	+	744.990i	0.101698	+	0.0587154i
$545$	−6479.42	−	11222.7i	−0.509262	−	0.882068i
$546$		0			0
$547$	4523.73	−	7835.34i	0.353603	−	0.612459i	−0.633275	−	0.773927i	$-0.718290\pi$
$547$	4523.73	−	7835.34i	0.353603	−	0.612459i	0.986878	+	0.161468i	$0.0516230\pi$
$548$	10035.2	−	5793.81i	0.782266	−	0.451641i
$549$		0			0
$550$	3064.69	−	5308.20i	0.237598	−	0.411532i
$551$	−3095.37			−0.239323
$552$		0			0
$553$	13187.1	+	12262.6i	1.01406	+	0.942967i
$554$	−753.622	+	435.104i	−0.0577948	+	0.0333678i
$555$		0			0
$556$	−288.193	+	166.388i	−0.0219822	+	0.0126914i
$557$	−12259.3	−	7077.91i	−0.932573	−	0.538421i	−0.0449485	−	0.998989i	$-0.514312\pi$
$557$	−12259.3	−	7077.91i	−0.932573	−	0.538421i	−0.887624	+	0.460568i	$0.847646\pi$
$558$		0			0
$559$			11551.6i			0.874028i
$560$	1776.00	−	545.705i	0.134018	−	0.0411790i
$561$		0			0
$562$	7469.36	−	12937.3i	0.560633	−	0.971045i
$563$	3146.02			0.235504			0.117752	−	0.993043i	$-0.462431\pi$
$563$	3146.02			0.235504			0.117752	+	0.993043i	$0.462431\pi$
$564$		0			0
$565$		−	3292.35i		−	0.245151i
$566$	−3544.80			−0.263249
$567$		0			0
$568$	494.963			0.0365637
$569$		−	13230.2i		−	0.974761i	−0.873190	−	0.487380i	$-0.837953\pi$
$569$		−	13230.2i		−	0.974761i	0.873190	−	0.487380i	$-0.162047\pi$
$570$		0			0
$571$	−23753.7			−1.74091			−0.870455	−	0.492248i	$-0.836175\pi$
$571$	−23753.7			−1.74091			−0.870455	+	0.492248i	$0.836175\pi$
$572$	3570.20	−	6183.77i	0.260975	−	0.452022i
$573$		0			0
$574$	−7018.93	−	1610.07i	−0.510391	−	0.117079i
$575$			4236.56i			0.307264i
$576$		0			0
$577$	10226.8	+	5904.42i	0.737860	+	0.426004i	0.821291	−	0.570510i	$-0.193254\pi$
$577$	10226.8	+	5904.42i	0.737860	+	0.426004i	−0.0834307	+	0.996514i	$0.526588\pi$
$578$	−4754.46	+	2744.99i	−0.342145	+	0.197537i
$579$		0			0
$580$	−4059.65	+	2343.84i	−0.290634	+	0.167798i
$581$	1810.56	−	556.323i	0.129285	−	0.0397249i
$582$		0			0
$583$	−18422.5			−1.30872
$584$	−1870.89	+	3240.47i	−0.132565	+	0.229609i
$585$		0			0
$586$	−11180.7	+	6455.18i	−0.788175	+	0.455053i
$587$	−204.871	+	354.847i	−0.0144053	+	0.0249508i	−0.873138	−	0.487473i	$-0.837919\pi$
$587$	−204.871	+	354.847i	−0.0144053	+	0.0249508i	0.858733	+	0.512424i	$0.171252\pi$
$588$		0			0
$589$	2413.49	+	4180.29i	0.168839	+	0.292437i
$590$	2297.94	+	1326.72i	0.160347	+	0.0925765i
$591$		0			0
$592$	3182.64	+	5512.50i	0.220956	+	0.382706i
$593$	7449.99	+	12903.8i	0.515910	+	0.893582i	0.999829	+	0.0184697i	$0.00587943\pi$
$593$	7449.99	+	12903.8i	0.515910	+	0.893582i	−0.483919	+	0.875113i	$0.660787\pi$
$594$		0			0
$595$	1208.88	−	5269.98i	0.0832930	−	0.363106i
$596$	−2210.34	−	1276.14i	−0.151911	−	0.0877058i
$597$		0			0
$598$			4935.36i			0.337495i
$599$			4608.04i			0.314323i	0.987573	+	0.157162i	$0.0502344\pi$
$599$			4608.04i			0.314323i	−0.987573	+	0.157162i	$0.949766\pi$
$600$		0			0
$601$	−22121.3	−	12771.7i	−1.50141	−	0.866838i	−0.999999	−	0.00162759i	$-0.999482\pi$
$601$	−22121.3	−	12771.7i	−1.50141	−	0.866838i	−0.501409	−	0.865210i	$-0.667185\pi$
$602$	−2517.98	−	8194.79i	−0.170474	−	0.554809i
$603$		0			0
$604$	1712.81	+	2966.68i	0.115386	+	0.199855i
$605$	162.364	+	281.223i	0.0109108	+	0.0188981i
$606$		0			0
$607$	−4080.31	−	2355.77i	−0.272841	−	0.157525i	0.357337	−	0.933976i	$-0.383685\pi$
$607$	−4080.31	−	2355.77i	−0.272841	−	0.157525i	−0.630178	+	0.776451i	$0.717018\pi$
$608$	−264.973	−	458.947i	−0.0176745	−	0.0306131i
$609$		0			0
$610$	−1013.07	+	1754.69i	−0.0672426	+	0.116468i
$611$	2978.04	−	1719.37i	0.197183	−	0.113844i
$612$		0			0
$613$	10757.0	−	18631.8i	0.708765	−	1.22762i	−0.256550	−	0.966531i	$-0.582586\pi$
$613$	10757.0	−	18631.8i	0.708765	−	1.22762i	0.965315	−	0.261087i	$-0.0840808\pi$
$614$	−728.660			−0.0478931
$615$		0			0
$616$	−1184.81	+	5165.02i	−0.0774954	+	0.337832i
$617$	2340.83	−	1351.48i	0.152736	−	0.0881824i	−0.421684	−	0.906743i	$-0.638561\pi$
$617$	2340.83	−	1351.48i	0.152736	−	0.0881824i	0.574420	+	0.818560i	$0.305227\pi$
$618$		0			0
$619$	4762.17	−	2749.44i	0.309221	−	0.178529i	−0.337357	−	0.941377i	$-0.609533\pi$
$619$	4762.17	−	2749.44i	0.309221	−	0.178529i	0.646578	+	0.762848i	$0.276200\pi$
$620$	6330.70	+	3655.03i	0.410076	+	0.236757i
$621$		0			0
$622$			19543.8i			1.25986i
$623$	−2010.49	+	8764.49i	−0.129291	+	0.563631i
$624$		0			0
$625$	−1214.09	+	2102.87i	−0.0777020	+	0.134584i
$626$	−15500.0			−0.989626
$627$		0			0
$628$			10637.9i			0.675953i
$629$	18523.7			1.17423
$630$		0			0
$631$	4581.49			0.289043			0.144521	−	0.989502i	$-0.453836\pi$
$631$	4581.49			0.289043			0.144521	+	0.989502i	$0.453836\pi$
$632$		−	7778.55i		−	0.489579i
$633$		0			0
$634$	19706.2			1.23444
$635$	2947.14	−	5104.60i	0.184179	−	0.319008i
$636$		0			0
$637$	9612.79	+	14165.6i	0.597916	+	0.881102i
$638$		−	13370.0i		−	0.829660i
$639$		0			0
$640$	−695.037	−	401.280i	−0.0429277	−	0.0247843i
$641$	9061.68	−	5231.76i	0.558370	−	0.322375i	−0.194121	−	0.980978i	$-0.562186\pi$
$641$	9061.68	−	5231.76i	0.558370	−	0.322375i	0.752491	+	0.658603i	$0.228852\pi$
$642$		0			0
$643$	8065.14	−	4656.41i	0.494647	−	0.285585i	−0.231853	−	0.972751i	$-0.574479\pi$
$643$	8065.14	−	4656.41i	0.494647	−	0.285585i	0.726500	+	0.687166i	$0.241146\pi$
$644$	−1075.79	−	3501.18i	−0.0658263	−	0.214232i
$645$		0			0
$646$	−1542.20			−0.0939276
$647$	1518.40	−	2629.95i	0.0922636	−	0.159805i	−0.816200	−	0.577770i	$-0.803923\pi$
$647$	1518.40	−	2629.95i	0.0922636	−	0.159805i	0.908463	+	0.417965i	$0.137256\pi$
$648$		0			0
$649$	−6554.10	+	3784.01i	−0.396411	+	0.228868i
$650$	−4276.69	+	7407.44i	−0.258070	+	0.446990i
$651$		0			0
$652$	−1492.43	−	2584.96i	−0.0896442	−	0.155268i
$653$	9204.11	+	5313.99i	0.551584	+	0.318457i	0.749761	−	0.661709i	$-0.230169\pi$
$653$	9204.11	+	5313.99i	0.551584	+	0.318457i	−0.198177	+	0.980166i	$0.563502\pi$
$654$		0			0
$655$	−8570.93	−	14845.3i	−0.511288	−	0.885577i
$656$	1555.32	+	2693.89i	0.0925686	+	0.160334i
$657$		0			0
$658$	−1737.86	+	1868.88i	−0.102962	+	0.110724i
$659$	19703.4	+	11375.8i	1.16470	+	0.672439i	0.952426	−	0.304771i	$-0.0985801\pi$
$659$	19703.4	+	11375.8i	1.16470	+	0.672439i	0.212273	+	0.977210i	$0.431913\pi$
$660$		0			0
$661$		−	24890.5i		−	1.46464i	−0.680959	−	0.732322i	$-0.738437\pi$
$661$		−	24890.5i		−	1.46464i	0.680959	−	0.732322i	$-0.261563\pi$
$662$			12222.3i			0.717570i
$663$		0			0
$664$	−708.559	−	409.087i	−0.0414118	−	0.0239091i
$665$	−1309.56	+	1408.29i	−0.0763646	+	0.0821218i
$666$		0			0
$667$	4620.59	+	8003.10i	0.268231	+	0.464590i
$668$	4515.47	+	7821.03i	0.261540	+	0.453001i
$669$		0			0
$670$	−9473.99	−	5469.81i	−0.546287	−	0.315399i
$671$	−2889.44	−	5004.65i	−0.166238	−	0.287932i
$672$		0			0
$673$	14456.0	−	25038.4i	0.827988	−	1.43412i	−0.0716260	−	0.997432i	$-0.522819\pi$
$673$	14456.0	−	25038.4i	0.827988	−	1.43412i	0.899614	−	0.436686i	$-0.143848\pi$
$674$	−10878.3	+	6280.56i	−0.621683	+	0.358929i
$675$		0			0
$676$	−588.112	+	1018.64i	−0.0334611	+	0.0579563i
$677$	2841.36			0.161303			0.0806516	−	0.996742i	$-0.474300\pi$
$677$	2841.36			0.161303			0.0806516	+	0.996742i	$0.474300\pi$
$678$		0			0
$679$	−2071.85	−	6742.85i	−0.117099	−	0.381100i
$680$	−2022.64	+	1167.77i	−0.114066	+	0.0658558i
$681$		0			0
$682$	−18056.1	+	10424.7i	−1.01379	+	0.585313i
$683$	−4541.45	−	2622.01i	−0.254427	−	0.146894i	0.367362	−	0.930078i	$-0.380261\pi$
$683$	−4541.45	−	2622.01i	−0.254427	−	0.146894i	−0.621790	+	0.783184i	$0.713594\pi$
$684$		0			0
$685$			18163.6i			1.01313i
$686$	−9907.14	−	7953.81i	−0.551394	−	0.442679i
$687$		0			0
$688$	−1851.58	+	3207.02i	−0.102603	+	0.177713i
$689$	25708.1			1.42148
$690$		0			0
$691$			27479.2i			1.51282i	0.654098	+	0.756410i	$0.273049\pi$
$691$			27479.2i			1.51282i	−0.654098	+	0.756410i	$0.726951\pi$
$692$	−14029.0			−0.770670
$693$		0			0
$694$	−9613.67			−0.525836
$695$		−	521.627i		−	0.0284697i
$696$		0			0
$697$	9052.32			0.491939
$698$	7459.62	−	12920.4i	0.404514	−	0.700639i
$699$		0			0
$700$	1419.26	−	6187.10i	0.0766329	−	0.334072i
$701$			21986.6i			1.18462i	0.805709	+	0.592312i	$0.201785\pi$
$701$			21986.6i			1.18462i	−0.805709	+	0.592312i	$0.798215\pi$
$702$		0			0
$703$	−5705.71	−	3294.19i	−0.306110	−	0.176732i
$704$	1982.35	−	1144.51i	0.106126	−	0.0612720i
$705$		0			0
$706$	17155.2	−	9904.56i	0.914510	−	0.527993i
$707$	−6028.33	+	26279.8i	−0.320677	+	1.39795i
$708$		0			0
$709$	14584.1			0.772522			0.386261	−	0.922390i	$-0.373766\pi$
$709$	14584.1			0.772522			0.386261	+	0.922390i	$0.373766\pi$
$710$	−387.927	+	671.910i	−0.0205051	+	0.0355159i
$711$		0			0
$712$	3363.85	−	1942.12i	0.177058	−	0.102225i
$713$	7205.45	−	12480.2i	0.378466	−	0.655522i
$714$		0			0
$715$	5596.28	+	9693.05i	0.292712	+	0.506992i
$716$	14783.6	+	8535.31i	0.771632	+	0.445502i
$717$		0			0
$718$	8772.41	+	15194.3i	0.455966	+	0.789756i
$719$	1290.42	+	2235.08i	0.0669327	+	0.115931i	0.897550	−	0.440913i	$-0.145345\pi$
$719$	1290.42	+	2235.08i	0.0669327	+	0.115931i	−0.830617	+	0.556844i	$0.812012\pi$
$720$		0			0
$721$	−3696.38	−	12029.9i	−0.190930	−	0.621382i
$722$	−11405.1	−	6584.74i	−0.587886	−	0.339416i
$723$		0			0
$724$			14576.3i			0.748238i
$725$			16015.7i			0.820426i
$726$		0			0
$727$	18588.7	+	10732.2i	0.948304	+	0.547503i	0.892554	−	0.450941i	$-0.148912\pi$
$727$	18588.7	+	10732.2i	0.948304	+	0.547503i	0.0557500	+	0.998445i	$0.482245\pi$
$728$	1653.36	−	7207.64i	0.0841727	−	0.366941i
$729$		0			0
$730$	−2932.61	−	5079.44i	−0.148686	−	0.257532i
$731$	5388.30	+	9332.81i	0.272631	+	0.472211i
$732$		0			0
$733$	−7251.06	−	4186.40i	−0.365381	−	0.210953i	0.306058	−	0.952013i	$-0.400990\pi$
$733$	−7251.06	−	4186.40i	−0.365381	−	0.210953i	−0.671438	+	0.741060i	$0.734323\pi$
$734$	3591.65	+	6220.93i	0.180614	+	0.312832i
$735$		0			0
$736$	−791.074	+	1370.18i	−0.0396187	+	0.0686217i
$737$	27021.3	−	15600.8i	1.35053	−	0.779731i
$738$		0			0
$739$	−1215.39	+	2105.11i	−0.0604989	+	0.104787i	−0.894689	−	0.446691i	$-0.852602\pi$
$739$	−1215.39	+	2105.11i	−0.0604989	+	0.104787i	0.834190	+	0.551478i	$0.185936\pi$
$740$	−9977.57			−0.495652
$741$		0			0
$742$	−18237.5	+	5603.75i	−0.902316	+	0.277251i
$743$	6627.55	−	3826.42i	0.327243	−	0.188934i	−0.327374	−	0.944895i	$-0.606164\pi$
$743$	6627.55	−	3826.42i	0.327243	−	0.188934i	0.654616	+	0.755961i	$0.272830\pi$
$744$		0			0
$745$	3464.70	−	2000.35i	0.170385	−	0.0983718i
$746$	11699.8	+	6754.89i	0.574210	+	0.331520i
$747$		0			0
$748$		−	6661.33i		−	0.325618i
$749$	−10732.0	−	2461.83i	−0.523552	−	0.120098i
$750$		0			0
$751$	−6293.03	+	10899.8i	−0.305773	+	0.529615i	−0.977433	−	0.211245i	$-0.932248\pi$
$751$	−6293.03	+	10899.8i	−0.305773	+	0.529615i	0.671660	+	0.740860i	$0.265582\pi$
$752$	1102.37			0.0534567
$753$		0			0
$754$			18657.4i			0.901146i
$755$	−5369.67			−0.258837
$756$		0			0
$757$	−34119.4			−1.63817			−0.819083	−	0.573676i	$-0.805517\pi$
$757$	−34119.4			−1.63817			−0.819083	+	0.573676i	$0.805517\pi$
$758$		−	12711.6i		−	0.609111i
$759$		0			0
$760$	830.689			0.0396477
$761$	−10597.4	+	18355.2i	−0.504801	+	0.874341i	0.495183	+	0.868788i	$0.335101\pi$
$761$	−10597.4	+	18355.2i	−0.504801	+	0.874341i	−0.999985	+	0.00555279i	$0.998232\pi$
$762$		0			0
$763$	36589.4	−	11242.7i	1.73608	−	0.533437i
$764$			2691.02i			0.127431i
$765$		0			0
$766$	−8784.98	−	5072.01i	−0.414379	−	0.239242i
$767$	9146.06	−	5280.48i	0.430567	−	0.248588i
$768$		0			0
$769$	−26557.2	+	15332.8i	−1.24535	+	0.719006i	−0.970179	−	0.242388i	$-0.922069\pi$
$769$	−26557.2	+	15332.8i	−1.24535	+	0.719006i	−0.275175	+	0.961394i	$0.588736\pi$
$770$	−6082.89	−	5656.45i	−0.284691	−	0.264733i
$771$		0			0
$772$	10834.4			0.505102
$773$	−14614.1	+	25312.3i	−0.679988	+	1.17777i	0.294996	+	0.955499i	$0.404682\pi$
$773$	−14614.1	+	25312.3i	−0.679988	+	1.17777i	−0.974984	+	0.222276i	$0.928652\pi$
$774$		0			0
$775$	21629.2	−	12487.6i	1.00251	−	0.578798i
$776$	−1523.51	+	2638.80i	−0.0704781	+	0.122072i
$777$		0			0
$778$	6536.54	+	11321.6i	0.301216	+	0.521722i
$779$	−2788.31	−	1609.83i	−0.128244	−	0.0740414i
$780$		0			0
$781$	−1106.43	−	1916.39i	−0.0506929	−	0.0878027i
$782$	2302.12	+	3987.39i	0.105273	+	0.182339i
$783$		0			0
$784$	398.189	+	5473.54i	0.0181391	+	0.249341i
$785$	−14440.9	−	8337.45i	−0.656582	−	0.379078i
$786$		0			0
$787$		−	32507.2i		−	1.47237i	−0.676780	−	0.736185i	$-0.736625\pi$
$787$		−	32507.2i		−	1.47237i	0.676780	−	0.736185i	$-0.263375\pi$
$788$			16592.6i			0.750110i
$789$		0			0
$790$	10559.3	+	6096.43i	0.475549	+	0.274559i
$791$	9478.74	+	2174.33i	0.426075	+	0.0977375i
$792$		0			0
$793$	4032.13	+	6983.85i	0.180561	+	0.312741i
$794$	1635.41	+	2832.61i	0.0730963	+	0.126607i
$795$		0			0
$796$	−3426.83	−	1978.48i	−0.152589	−	0.0880973i
$797$	−6381.72	−	11053.5i	−0.283629	−	0.491259i	0.688647	−	0.725097i	$-0.258205\pi$
$797$	−6381.72	−	11053.5i	−0.283629	−	0.491259i	−0.972276	+	0.233837i	$0.924872\pi$
$798$		0			0
$799$	1604.02	−	2778.24i	0.0710214	−	0.123013i
$800$	−2374.63	+	1370.99i	−0.104945	+	0.0605900i
$801$		0			0
$802$	1968.83	−	3410.11i	0.0866855	−	0.150144i
$803$	16728.6			0.735166
$804$		0			0
$805$	5595.98	+	1283.66i	0.245009	+	0.0562027i
$806$	25196.8	−	14547.4i	1.10114	−	0.635745i
$807$		0			0
$808$	10086.3	−	5823.32i	0.439151	−	0.253544i
$809$	−12991.2	−	7500.45i	−0.564580	−	0.325960i	0.190402	−	0.981706i	$-0.439021\pi$
$809$	−12991.2	−	7500.45i	−0.564580	−	0.325960i	−0.754982	+	0.655746i	$0.772354\pi$
$810$		0			0
$811$			38700.3i			1.67565i	0.545939	+	0.837825i	$0.316173\pi$
$811$			38700.3i			1.67565i	−0.545939	+	0.837825i	$0.683827\pi$
$812$	−4066.88	−	13235.7i	−0.175763	−	0.572022i
$813$		0			0
$814$	14228.8	−	24645.0i	0.612677	−	1.06119i
$815$	4678.76			0.201092
$816$		0			0
$817$		−	3832.95i		−	0.164135i
$818$	20367.4			0.870572
$819$		0			0
$820$	−4875.92			−0.207652
$821$			33564.7i			1.42682i	0.700748	+	0.713409i	$0.252850\pi$
$821$			33564.7i			1.42682i	−0.700748	+	0.713409i	$0.747150\pi$
$822$		0			0
$823$	12731.9			0.539254			0.269627	−	0.962965i	$-0.413100\pi$
$823$	12731.9			0.539254			0.269627	+	0.962965i	$0.413100\pi$
$824$	−2718.10	+	4707.88i	−0.114914	+	0.199038i
$825$		0			0
$826$	−5337.25	+	5739.63i	−0.224826	+	0.241776i
$827$		−	7857.63i		−	0.330395i	−0.986261	−	0.165197i	$-0.947174\pi$
$827$		−	7857.63i		−	0.330395i	0.986261	−	0.165197i	$-0.0528261\pi$
$828$		0			0
$829$	2882.83	+	1664.41i	0.120778	+	0.0697312i	0.559172	−	0.829052i	$-0.311119\pi$
$829$	2882.83	+	1664.41i	0.120778	+	0.0697312i	−0.438394	+	0.898783i	$0.644453\pi$
$830$	1110.67	−	641.243i	0.0464479	−	0.0268167i
$831$		0			0
$832$	−2766.32	+	1597.14i	−0.115270	+	0.0665513i
$833$	14374.0	+	6960.78i	0.597874	+	0.289528i
$834$		0			0
$835$	−14156.0			−0.586693
$836$	−1184.63	+	2051.84i	−0.0490087	+	0.0848855i
$837$		0			0
$838$	1325.64	−	765.359i	0.0546462	−	0.0315500i
$839$	20884.5	−	36173.0i	0.859372	−	1.48848i	−0.0131565	−	0.999913i	$-0.504188\pi$
$839$	20884.5	−	36173.0i	0.859372	−	1.48848i	0.872529	−	0.488563i	$-0.162479\pi$
$840$		0			0
$841$	5273.00	+	9133.10i	0.216204	+	0.374476i
$842$	5077.18	+	2931.31i	0.207804	+	0.119976i
$843$		0			0
$844$	3827.74	+	6629.84i	0.156109	+	0.270389i
$845$	−921.864	−	1596.72i	−0.0375303	−	0.0650044i
$846$		0			0
$847$	−916.874	+	281.724i	−0.0371950	+	0.0114288i
$848$	7137.21	+	4120.67i	0.289025	+	0.166868i
$849$		0			0
$850$			7979.51i			0.321994i
$851$			19669.6i			0.792320i
$852$		0			0
$853$	−979.976	−	565.789i	−0.0393362	−	0.0227107i	0.480203	−	0.877157i	$-0.340563\pi$
$853$	−979.976	−	565.789i	−0.0393362	−	0.0227107i	−0.519539	+	0.854447i	$0.673896\pi$
$854$	−4382.73	−	4075.47i	−0.175613	−	0.163302i
$855$		0			0
$856$	2378.11	+	4119.00i	0.0949556	+	0.164468i
$857$	5323.91	+	9221.27i	0.212207	+	0.367553i	0.952405	−	0.304836i	$-0.0986017\pi$
$857$	5323.91	+	9221.27i	0.212207	+	0.367553i	−0.740198	+	0.672389i	$0.765268\pi$
$858$		0			0
$859$	−19637.3	−	11337.6i	−0.779995	−	0.450330i	0.0564337	−	0.998406i	$-0.482027\pi$
$859$	−19637.3	−	11337.6i	−0.779995	−	0.450330i	−0.836428	+	0.548076i	$0.815360\pi$
$860$	−2902.34	−	5027.00i	−0.115080	−	0.199325i
$861$		0			0
$862$	13109.6	−	22706.6i	0.518000	−	0.897203i
$863$	−24026.8	+	13871.9i	−0.947718	+	0.547165i	−0.892371	−	0.451302i	$-0.850960\pi$
$863$	−24026.8	+	13871.9i	−0.947718	+	0.547165i	−0.0553469	+	0.998467i	$0.517626\pi$
$864$		0			0
$865$	10995.2	−	19044.3i	0.432196	−	0.748585i
$866$	−4036.17			−0.158377
$867$		0			0
$868$	−14703.8	+	15812.3i	−0.574976	+	0.618324i
$869$	−30116.9	+	17388.0i	−1.17566	+	0.678765i
$870$		0			0
$871$	−37707.5	+	21770.4i	−1.46690	+	0.846915i
$872$	−14319.2	−	8267.21i	−0.556090	−	0.321059i
$873$		0			0
$874$		−	1637.60i		−	0.0633785i
$875$	17916.3	+	16660.2i	0.692206	+	0.643678i
$876$		0			0
$877$	−6175.13	+	10695.6i	−0.237764	+	0.411820i	−0.960072	−	0.279752i	$-0.909748\pi$
$877$	−6175.13	+	10695.6i	−0.237764	+	0.411820i	0.722308	+	0.691571i	$0.243081\pi$
$878$	−14581.1			−0.560466
$879$		0			0
$880$			3588.05i			0.137447i
$881$	8091.04			0.309415			0.154707	−	0.987960i	$-0.450557\pi$
$881$	8091.04			0.309415			0.154707	+	0.987960i	$0.450557\pi$
$882$		0			0
$883$	−26466.7			−1.00869			−0.504347	−	0.863501i	$-0.668267\pi$
$883$	−26466.7			−1.00869			−0.504347	+	0.863501i	$0.668267\pi$
$884$			9295.70i			0.353675i
$885$		0			0
$886$	−8851.37			−0.335629
$887$	−10029.3	+	17371.2i	−0.379651	+	0.657576i	−0.991011	−	0.133777i	$-0.957289\pi$
$887$	−10029.3	+	17371.2i	−0.379651	+	0.657576i	0.611360	+	0.791353i	$0.290623\pi$
$888$		0			0
$889$	12749.9	+	11856.1i	0.481010	+	0.447288i
$890$			6088.53i			0.229312i
$891$		0			0
$892$	−2055.93	−	1186.99i	−0.0771723	−	0.0445554i
$893$	−988.145	+	570.506i	−0.0370291	+	0.0213788i
$894$		0			0
$895$	−23173.3	+	13379.1i	−0.865471	+	0.499680i
$896$	1614.31	−	1736.01i	0.0601899	−	0.0647277i
$897$		0			0
$898$	−19538.3			−0.726060
$899$	27239.2	−	47179.7i	1.01054	−	1.75031i
$900$		0			0
$901$	20770.1	−	11991.6i	0.767983	−	0.443395i
$902$	6953.45	−	12043.7i	0.256679	−	0.444581i
$903$		0			0
$904$	−2100.39	−	3637.98i	−0.0772764	−	0.133847i
$905$	−19787.3	−	11424.2i	−0.726796	−	0.419616i
$906$		0			0
$907$	23167.2	+	40126.8i	0.848132	+	1.46901i	0.882873	+	0.469611i	$0.155606\pi$
$907$	23167.2	+	40126.8i	0.848132	+	1.46901i	−0.0347412	+	0.999396i	$0.511061\pi$
$908$	9953.91	+	17240.7i	0.363802	+	0.630123i
$909$		0			0
$910$	8488.50	+	7893.41i	0.309221	+	0.287543i
$911$	13019.7	+	7516.95i	0.473505	+	0.273378i	0.717706	−	0.696346i	$-0.245192\pi$
$911$	13019.7	+	7516.95i	0.473505	+	0.273378i	−0.244201	+	0.969725i	$0.578526\pi$
$912$		0			0
$913$			3657.85i			0.132593i
$914$			12844.8i			0.464844i
$915$		0			0
$916$	−7236.18	−	4177.81i	−0.261016	−	0.150697i
$917$	48400.2	−	14871.7i	1.74298	−	0.535560i
$918$		0			0
$919$	19964.7	+	34579.9i	0.716622	+	1.24123i	0.962330	+	0.271883i	$0.0876462\pi$
$919$	19964.7	+	34579.9i	0.716622	+	1.24123i	−0.245708	+	0.969344i	$0.579020\pi$
$920$	−1240.01	−	2147.76i	−0.0444368	−	0.0769668i
$921$		0			0
$922$	−28122.8	−	16236.7i	−1.00453	−	0.579965i
$923$	1543.99	+	2674.27i	0.0550608	+	0.0953681i
$924$		0			0
$925$	−17044.5	+	29521.9i	−0.605858	+	1.04938i
$926$	−28961.9	+	16721.2i	−1.02781	+	0.593404i
$927$		0			0
$928$	−2990.55	+	5179.78i	−0.105786	+	0.183227i
$929$	−44135.3			−1.55870			−0.779350	−	0.626589i	$-0.784450\pi$
$929$	−44135.3			−1.55870			−0.779350	+	0.626589i	$0.784450\pi$
$930$		0			0
$931$	−3189.62	−	4700.29i	−0.112283	−	0.165463i
$932$	−403.145	+	232.756i	−0.0141689	+	0.00818045i
$933$		0			0
$934$	−1673.35	+	966.107i	−0.0586226	+	0.0338458i
$935$	9042.72	+	5220.82i	0.316287	+	0.182608i
$936$		0			0
$937$		−	14789.5i		−	0.515636i	−0.966193	−	0.257818i	$-0.916996\pi$
$937$		−	14789.5i		−	0.515636i	0.966193	−	0.257818i	$-0.0830035\pi$
$938$	22004.5	−	23663.4i	0.765961	−	0.823708i
$939$		0			0
$940$	−863.984	+	1496.46i	−0.0299788	+	0.0519248i
$941$	36891.3			1.27802			0.639012	−	0.769196i	$-0.279343\pi$
$941$	36891.3			1.27802			0.639012	+	0.769196i	$0.279343\pi$
$942$		0			0
$943$			9612.29i			0.331940i
$944$	3385.57			0.116728
$945$		0			0
$946$	16555.9			0.569004
$947$		−	44743.3i		−	1.53533i	−0.640848	−	0.767667i	$-0.721417\pi$
$947$		−	44743.3i		−	1.53533i	0.640848	−	0.767667i	$-0.278583\pi$
$948$		0			0
$949$	−23344.2			−0.798510
$950$	1419.05	−	2457.86i	0.0484632	−	0.0839407i
$951$		0			0
$952$	−2026.24	−	6594.43i	−0.0689821	−	0.224503i
$953$			17728.3i			0.602597i	0.953530	+	0.301299i	$0.0974201\pi$
$953$			17728.3i			0.602597i	−0.953530	+	0.301299i	$0.902580\pi$
$954$		0			0
$955$	−3653.04	−	2109.08i	−0.123780	−	0.0714642i
$956$	4069.23	−	2349.37i	0.137665	−	0.0794812i
$957$		0			0
$958$	3604.41	−	2081.00i	0.121559	−	0.0701818i
$959$	−52293.3	−	11995.6i	−1.76083	−	0.403918i
$960$		0			0
$961$	−55163.7			−1.85169
$962$	−19855.9	+	34391.4i	−0.665467	+	1.15262i
$963$		0			0
$964$	6441.65	−	3719.09i	0.215220	−	0.124257i
$965$	−8491.46	+	14707.6i	−0.283264	+	0.490627i
$966$		0			0
$967$	14428.3	+	24990.6i	0.479818	+	0.831069i	0.999732	−	0.0231497i	$-0.00736945\pi$
$967$	14428.3	+	24990.6i	0.479818	+	0.831069i	−0.519914	+	0.854218i	$0.674036\pi$
$968$	358.818	+	207.163i	0.0119141	+	0.00687860i
$969$		0			0
$970$	−2388.11	−	4136.32i	−0.0790490	−	0.136917i
$971$	−26753.0	−	46337.6i	−0.884188	−	1.53146i	−0.846642	−	0.532163i	$-0.821379\pi$
$971$	−26753.0	−	46337.6i	−0.884188	−	1.53146i	−0.0375456	−	0.999295i	$-0.511954\pi$
$972$		0			0
$973$	1501.77	+	344.492i	0.0494806	+	0.0113504i
$974$	−18158.9	−	10484.0i	−0.597379	−	0.344897i
$975$		0			0
$976$			2585.19i			0.0847847i
$977$		−	53958.2i		−	1.76691i	−0.468513	−	0.883457i	$-0.655210\pi$
$977$		−	53958.2i		−	1.76691i	0.468513	−	0.883457i	$-0.344790\pi$
$978$		0			0
$979$	−15038.9	−	8682.73i	−0.490956	−	0.283454i
$980$	−7742.37	−	3749.34i	−0.252368	−	0.122213i
$981$		0			0
$982$	−2282.96	−	3954.21i	−0.0741876	−	0.128497i
$983$	−1195.74	−	2071.08i	−0.0387976	−	0.0671995i	0.845975	−	0.533223i	$-0.179019\pi$
$983$	−1195.74	−	2071.08i	−0.0387976	−	0.0671995i	−0.884772	+	0.466024i	$0.845686\pi$
$984$		0			0
$985$	−22524.3	−	13004.4i	−0.728614	−	0.420666i
$986$	8702.84	+	15073.8i	0.281090	+	0.486862i
$987$		0			0
$988$	1653.12	−	2863.28i	0.0532314	−	0.0921995i
$989$	−9910.13	+	5721.62i	−0.318629	+	0.183960i
$990$		0			0
$991$	5843.94	−	10122.0i	0.187325	−	0.324456i	−0.757033	−	0.653377i	$-0.773352\pi$
$991$	5843.94	−	10122.0i	0.187325	−	0.324456i	0.944357	+	0.328921i	$0.106685\pi$
$992$	9327.04			0.298522
$993$		0			0
$994$	−1678.24	−	1560.59i	−0.0535520	−	0.0497977i
$995$	5371.56	−	3101.27i	0.171145	−	0.0988109i
$996$		0			0
$997$	−8317.75	+	4802.26i	−0.264218	+	0.152547i	−0.626257	−	0.779616i	$-0.715414\pi$
$997$	−8317.75	+	4802.26i	−0.264218	+	0.152547i	0.362039	+	0.932163i	$0.382081\pi$
$998$	22850.4	+	13192.7i	0.724767	+	0.418444i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	378.4.l.a.143.9		48
3.2	odd	2		126.4.l.a.101.12	yes	48
7.5	odd	6		378.4.t.a.89.18		48
9.4	even	3		126.4.t.a.59.9	yes	48
9.5	odd	6		378.4.t.a.17.18		48
21.5	even	6		126.4.t.a.47.9	yes	48
63.5	even	6	inner	378.4.l.a.341.9		48
63.40	odd	6		126.4.l.a.5.24	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.4.l.a.5.24	✓	48	63.40	odd	6
126.4.l.a.101.12	yes	48	3.2	odd	2
126.4.t.a.47.9	yes	48	21.5	even	6
126.4.t.a.59.9	yes	48	9.4	even	3
378.4.l.a.143.9		48	1.1	even	1	trivial
378.4.l.a.341.9		48	63.5	even	6	inner
378.4.t.a.17.18		48	9.5	odd	6
378.4.t.a.89.18		48	7.5	odd	6

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:	\( N \)	\(=\)	\( 378 = 2 \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	378.l (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+2.00000i q^{2} -4.00000 q^{4} +(3.13500 - 5.42997i) q^{5} +(13.5626 + 12.6118i) q^{7} -8.00000i q^{8} +O(q^{10})\)	\(q+2.00000i q^{2} -4.00000 q^{4} +(3.13500 - 5.42997i) q^{5} +(13.5626 + 12.6118i) q^{7} -8.00000i q^{8} +(10.8599 + 6.26999i) q^{10} +(-30.9743 + 17.8830i) q^{11} +(43.2237 - 24.9552i) q^{13} +(-25.2235 + 27.1251i) q^{14} +16.0000 q^{16} +(23.2809 - 40.3238i) q^{17} +(-14.3421 + 8.28040i) q^{19} +(-12.5400 + 21.7199i) q^{20} +(-35.7660 - 61.9486i) q^{22} +(42.8182 + 24.7211i) q^{23} +(42.8436 + 74.2073i) q^{25} +(49.9105 + 86.4475i) q^{26} +(-54.2503 - 50.4471i) q^{28} +(161.868 + 93.4545i) q^{29} -291.470i q^{31} +32.0000i q^{32} +(80.6475 + 46.5619i) q^{34} +(111.000 - 34.1066i) q^{35} +(198.915 + 344.531i) q^{37} +(-16.5608 - 28.6842i) q^{38} +(-43.4398 - 25.0800i) q^{40} +(97.2074 + 168.368i) q^{41} +(-115.723 + 200.439i) q^{43} +(123.897 - 71.5321i) q^{44} +(-49.4422 + 85.6363i) q^{46} +68.8983 q^{47} +(24.8868 + 342.096i) q^{49} +(-148.415 + 85.6872i) q^{50} +(-172.895 + 99.8210i) q^{52} +(446.076 + 257.542i) q^{53} +224.253i q^{55} +(100.894 - 108.501i) q^{56} +(-186.909 + 323.736i) q^{58} +211.598 q^{59} +161.574i q^{61} +582.940 q^{62} -64.0000 q^{64} -312.938i q^{65} -872.379 q^{67} +(-93.1238 + 161.295i) q^{68} +(68.2132 + 222.000i) q^{70} +61.8704i q^{71} +(-405.059 - 233.861i) q^{73} +(-689.062 + 397.830i) q^{74} +(57.3683 - 33.1216i) q^{76} +(-645.628 - 148.101i) q^{77} +972.318 q^{79} +(50.1600 - 86.8796i) q^{80} +(-336.736 + 194.415i) q^{82} +(51.1359 - 88.5699i) q^{83} +(-145.971 - 252.830i) q^{85} +(-400.878 - 231.447i) q^{86} +(143.064 + 247.794i) q^{88} +(242.765 + 420.481i) q^{89} +(900.955 + 206.670i) q^{91} +(-171.273 - 98.8843i) q^{92} +137.797i q^{94} +103.836i q^{95} +(-329.851 - 190.439i) q^{97} +(-684.192 + 49.7737i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 192 q^{4} - 12 q^{7}+O(q^{10}) \) 48 * q - 192 * q^4 - 12 * q^7	\( 48 q - 192 q^{4} - 12 q^{7} + 24 q^{11} + 72 q^{13} + 132 q^{14} + 768 q^{16} - 144 q^{17} - 408 q^{23} - 600 q^{25} - 120 q^{26} + 48 q^{28} - 42 q^{29} + 780 q^{35} - 168 q^{37} + 618 q^{41} - 42 q^{43} - 96 q^{44} - 252 q^{46} - 396 q^{47} - 42 q^{49} - 1464 q^{50} - 288 q^{52} + 36 q^{53} - 528 q^{56} - 252 q^{58} + 3000 q^{59} - 2952 q^{62} - 3072 q^{64} + 1176 q^{67} + 576 q^{68} - 324 q^{70} - 1260 q^{74} - 6420 q^{77} - 2460 q^{79} + 720 q^{85} + 1200 q^{86} + 4398 q^{89} - 90 q^{91} + 1632 q^{92} + 1584 q^{97} + 1104 q^{98}+O(q^{100}) \) 48 * q - 192 * q^4 - 12 * q^7 + 24 * q^11 + 72 * q^13 + 132 * q^14 + 768 * q^16 - 144 * q^17 - 408 * q^23 - 600 * q^25 - 120 * q^26 + 48 * q^28 - 42 * q^29 + 780 * q^35 - 168 * q^37 + 618 * q^41 - 42 * q^43 - 96 * q^44 - 252 * q^46 - 396 * q^47 - 42 * q^49 - 1464 * q^50 - 288 * q^52 + 36 * q^53 - 528 * q^56 - 252 * q^58 + 3000 * q^59 - 2952 * q^62 - 3072 * q^64 + 1176 * q^67 + 576 * q^68 - 324 * q^70 - 1260 * q^74 - 6420 * q^77 - 2460 * q^79 + 720 * q^85 + 1200 * q^86 + 4398 * q^89 - 90 * q^91 + 1632 * q^92 + 1584 * q^97 + 1104 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

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