LMFDB - Embedded newform 108.4.i.a.49.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [108,4,Mod(13,108)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(108, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 8]))

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

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

chi := DirichletCharacter("108.13");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 108 = 2^{2} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	108.i (of order $9$, degree $6$, 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:	$6.37220628062$
Analytic rank:	$0$
Dimension:	$54$
Relative dimension:	$9$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			49.3
Character	$\chi$	$=$	108.49
Dual form			108.4.i.a.97.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.72085 - 3.62702i) q^{3} +(-6.50317 + 2.36696i) q^{5} +(1.34685 + 7.63837i) q^{7} +(0.689498 + 26.9912i) q^{9} +O(q^{10})$	\(q+(-3.72085 - 3.62702i) q^{3} +(-6.50317 + 2.36696i) q^{5} +(1.34685 + 7.63837i) q^{7} +(0.689498 + 26.9912i) q^{9} +(13.7454 + 5.00292i) q^{11} +(40.8838 + 34.3056i) q^{13} +(32.7823 + 14.7800i) q^{15} +(-29.6006 + 51.2697i) q^{17} +(46.8884 + 81.2131i) q^{19} +(22.6931 - 33.3063i) q^{21} +(4.51998 - 25.6341i) q^{23} +(-59.0669 + 49.5630i) q^{25} +(95.3320 - 102.931i) q^{27} +(-172.381 + 144.645i) q^{29} +(4.27764 - 24.2597i) q^{31} +(-32.9990 - 68.4700i) q^{33} +(-26.8385 - 46.4856i) q^{35} +(-38.3554 + 66.4335i) q^{37} +(-27.6957 - 275.932i) q^{39} +(-305.098 - 256.008i) q^{41} +(282.678 + 102.886i) q^{43} +(-68.3710 - 173.896i) q^{45} +(-3.08562 - 17.4994i) q^{47} +(265.784 - 96.7374i) q^{49} +(296.096 - 83.4053i) q^{51} -242.682 q^{53} -101.230 q^{55} +(120.096 - 472.247i) q^{57} +(-211.368 + 76.9317i) q^{59} +(81.1159 + 460.031i) q^{61} +(-205.240 + 41.6197i) q^{63} +(-347.074 - 126.325i) q^{65} +(333.309 + 279.680i) q^{67} +(-109.793 + 78.9866i) q^{69} +(277.317 - 480.327i) q^{71} +(-226.923 - 393.043i) q^{73} +(399.545 + 29.8199i) q^{75} +(-19.7011 + 111.731i) q^{77} +(-537.292 + 450.842i) q^{79} +(-728.049 + 37.2208i) q^{81} +(-427.701 + 358.883i) q^{83} +(71.1442 - 403.479i) q^{85} +(1166.03 + 87.0265i) q^{87} +(578.094 + 1001.29i) q^{89} +(-206.974 + 358.490i) q^{91} +(-103.907 + 74.7517i) q^{93} +(-497.151 - 417.160i) q^{95} +(1388.22 + 505.270i) q^{97} +(-125.557 + 374.455i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 54 q + 12 q^{5} - 48 q^{9}+O(q^{10}) $ 54 * q + 12 * q^5 - 48 * q^9	$ 54 q + 12 q^{5} - 48 q^{9} - 87 q^{11} + 234 q^{15} + 204 q^{17} - 12 q^{21} + 96 q^{23} - 216 q^{25} + 27 q^{27} + 318 q^{29} - 54 q^{31} + 63 q^{33} + 6 q^{35} + 66 q^{39} + 867 q^{41} - 513 q^{43} - 306 q^{45} - 1548 q^{47} + 594 q^{49} - 1368 q^{51} - 1068 q^{53} - 1269 q^{57} - 1218 q^{59} - 54 q^{61} + 30 q^{63} + 96 q^{65} - 2997 q^{67} + 1476 q^{69} - 120 q^{71} - 216 q^{73} + 732 q^{75} + 3480 q^{77} + 2808 q^{79} + 3348 q^{81} + 4464 q^{83} + 2160 q^{85} + 4824 q^{87} + 4029 q^{89} + 270 q^{91} + 1164 q^{93} - 1650 q^{95} - 3483 q^{97} - 5076 q^{99}+O(q^{100}) $ 54 * q + 12 * q^5 - 48 * q^9 - 87 * q^11 + 234 * q^15 + 204 * q^17 - 12 * q^21 + 96 * q^23 - 216 * q^25 + 27 * q^27 + 318 * q^29 - 54 * q^31 + 63 * q^33 + 6 * q^35 + 66 * q^39 + 867 * q^41 - 513 * q^43 - 306 * q^45 - 1548 * q^47 + 594 * q^49 - 1368 * q^51 - 1068 * q^53 - 1269 * q^57 - 1218 * q^59 - 54 * q^61 + 30 * q^63 + 96 * q^65 - 2997 * q^67 + 1476 * q^69 - 120 * q^71 - 216 * q^73 + 732 * q^75 + 3480 * q^77 + 2808 * q^79 + 3348 * q^81 + 4464 * q^83 + 2160 * q^85 + 4824 * q^87 + 4029 * q^89 + 270 * q^91 + 1164 * q^93 - 1650 * q^95 - 3483 * q^97 - 5076 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/108\mathbb{Z}\right)^\times$.

$n$	$29$	$55$
$\chi(n)$	$e\left(\frac{7}{9}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−3.72085	−	3.62702i	−0.716079	−	0.698020i
$3$	−3.72085	−	3.62702i	−0.716079	−	0.698020i
$4$		0			0
$5$	−6.50317	+	2.36696i	−0.581661	+	0.211707i	−0.616058	−	0.787701i	$-0.711271\pi$
$5$	−6.50317	+	2.36696i	−0.581661	+	0.211707i	0.0343968	+	0.999408i	$0.489049\pi$
$6$		0			0
$7$	1.34685	+	7.63837i	0.0727231	+	0.412433i	0.999337	+	0.0364180i	$0.0115948\pi$
$7$	1.34685	+	7.63837i	0.0727231	+	0.412433i	−0.926614	+	0.376015i	$0.877294\pi$
$8$		0			0
$9$	0.689498	+	26.9912i	0.0255370	+	0.999674i
$10$		0			0
$11$	13.7454	+	5.00292i	0.376763	+	0.137131i	0.523459	−	0.852051i	$-0.324641\pi$
$11$	13.7454	+	5.00292i	0.376763	+	0.137131i	−0.146695	+	0.989182i	$0.546864\pi$
$12$		0			0
$13$	40.8838	+	34.3056i	0.872241	+	0.731897i	0.964569	−	0.263832i	$-0.0849864\pi$
$13$	40.8838	+	34.3056i	0.872241	+	0.731897i	−0.0923280	+	0.995729i	$0.529431\pi$
$14$		0			0
$15$	32.7823	+	14.7800i	0.564291	+	0.254412i
$16$		0			0
$17$	−29.6006	+	51.2697i	−0.422306	+	0.731455i	−0.996165	−	0.0874994i	$-0.972112\pi$
$17$	−29.6006	+	51.2697i	−0.422306	+	0.731455i	0.573859	+	0.818954i	$0.305446\pi$
$18$		0			0
$19$	46.8884	+	81.2131i	0.566155	+	0.980609i	0.996941	+	0.0781550i	$0.0249029\pi$
$19$	46.8884	+	81.2131i	0.566155	+	0.980609i	−0.430786	+	0.902454i	$0.641764\pi$
$20$		0			0
$21$	22.6931	−	33.3063i	0.235811	−	0.346097i
$22$		0			0
$23$	4.51998	−	25.6341i	0.0409774	−	0.232395i	−0.957440	−	0.288633i	$-0.906799\pi$
$23$	4.51998	−	25.6341i	0.0409774	−	0.232395i	0.998417	+	0.0562379i	$0.0179105\pi$
$24$		0			0
$25$	−59.0669	+	49.5630i	−0.472535	+	0.396504i
$26$		0			0
$27$	95.3320	−	102.931i	0.679506	−	0.733670i
$28$		0			0
$29$	−172.381	+	144.645i	−1.10380	+	0.926201i	−0.997675	−	0.0681509i	$-0.978290\pi$
$29$	−172.381	+	144.645i	−1.10380	+	0.926201i	−0.106129	+	0.994352i	$0.533846\pi$
$30$		0			0
$31$	4.27764	−	24.2597i	0.0247834	−	0.140554i	−0.969905	−	0.243482i	$-0.921710\pi$
$31$	4.27764	−	24.2597i	0.0247834	−	0.140554i	0.994689	+	0.102929i	$0.0328213\pi$
$32$		0			0
$33$	−32.9990	−	68.4700i	−0.174072	−	0.361185i
$34$		0			0
$35$	−26.8385	−	46.4856i	−0.129615	−	0.224500i
$36$		0			0
$37$	−38.3554	+	66.4335i	−0.170421	+	0.295178i	−0.938567	−	0.345096i	$-0.887846\pi$
$37$	−38.3554	+	66.4335i	−0.170421	+	0.295178i	0.768146	+	0.640275i	$0.221180\pi$
$38$		0			0
$39$	−27.6957	−	275.932i	−0.113714	−	1.13294i
$40$		0			0
$41$	−305.098	−	256.008i	−1.16215	−	0.975164i	−0.162222	−	0.986754i	$-0.551866\pi$
$41$	−305.098	−	256.008i	−1.16215	−	0.975164i	−0.999933	+	0.0115905i	$0.996311\pi$
$42$		0			0
$43$	282.678	+	102.886i	1.00251	+	0.364885i	0.790553	−	0.612394i	$-0.209793\pi$
$43$	282.678	+	102.886i	1.00251	+	0.364885i	0.211960	+	0.977278i	$0.432016\pi$
$44$		0			0
$45$	−68.3710	−	173.896i	−0.226492	−	0.576065i
$46$		0			0
$47$	−3.08562	−	17.4994i	−0.00957624	−	0.0543096i	0.979645	−	0.200737i	$-0.0643336\pi$
$47$	−3.08562	−	17.4994i	−0.00957624	−	0.0543096i	−0.989221	+	0.146427i	$0.953223\pi$
$48$		0			0
$49$	265.784	−	96.7374i	0.774880	−	0.282033i
$50$		0			0
$51$	296.096	−	83.4053i	0.812974	−	0.229001i
$52$		0			0
$53$	−242.682			−0.628960			−0.314480	−	0.949264i	$-0.601830\pi$
$53$	−242.682			−0.628960			−0.314480	+	0.949264i	$0.601830\pi$
$54$		0			0
$55$	−101.230			−0.248180
$56$		0			0
$57$	120.096	−	472.247i	0.279073	−	1.09738i
$58$		0			0
$59$	−211.368	+	76.9317i	−0.466403	+	0.169757i	−0.564522	−	0.825418i	$-0.690940\pi$
$59$	−211.368	+	76.9317i	−0.466403	+	0.169757i	0.0981193	+	0.995175i	$0.468717\pi$
$60$		0			0
$61$	81.1159	+	460.031i	0.170259	+	0.965589i	0.943475	+	0.331445i	$0.107536\pi$
$61$	81.1159	+	460.031i	0.170259	+	0.965589i	−0.773215	+	0.634144i	$0.781353\pi$
$62$		0			0
$63$	−205.240	+	41.6197i	−0.410441	+	0.0832316i
$64$		0			0
$65$	−347.074	−	126.325i	−0.662296	−	0.241056i
$66$		0			0
$67$	333.309	+	279.680i	0.607764	+	0.509975i	0.893931	−	0.448205i	$-0.147937\pi$
$67$	333.309	+	279.680i	0.607764	+	0.509975i	−0.286166	+	0.958180i	$0.592381\pi$
$68$		0			0
$69$	−109.793	+	78.9866i	−0.191559	+	0.137810i
$70$		0			0
$71$	277.317	−	480.327i	0.463541	−	0.802877i	−0.535593	−	0.844476i	$-0.679912\pi$
$71$	277.317	−	480.327i	0.463541	−	0.802877i	0.999134	+	0.0415991i	$0.0132452\pi$
$72$		0			0
$73$	−226.923	−	393.043i	−0.363827	−	0.630166i	0.624760	−	0.780817i	$-0.285197\pi$
$73$	−226.923	−	393.043i	−0.363827	−	0.630166i	−0.988587	+	0.150650i	$0.951863\pi$
$74$		0			0
$75$	399.545	+	29.8199i	0.615140	+	0.0459108i
$76$		0			0
$77$	−19.7011	+	111.731i	−0.0291578	+	0.165362i
$78$		0			0
$79$	−537.292	+	450.842i	−0.765191	+	0.642072i	−0.939473	−	0.342624i	$-0.888684\pi$
$79$	−537.292	+	450.842i	−0.765191	+	0.642072i	0.174281	+	0.984696i	$0.444240\pi$
$80$		0			0
$81$	−728.049	+	37.2208i	−0.998696	+	0.0510573i
$82$		0			0
$83$	−427.701	+	358.883i	−0.565617	+	0.474609i	−0.880188	−	0.474625i	$-0.842584\pi$
$83$	−427.701	+	358.883i	−0.565617	+	0.474609i	0.314571	+	0.949234i	$0.398139\pi$
$84$		0			0
$85$	71.1442	−	403.479i	0.0907844	−	0.514864i
$86$		0			0
$87$	1166.03	+	87.0265i	1.43692	+	0.107244i
$88$		0			0
$89$	578.094	+	1001.29i	0.688515	+	1.19254i	0.972318	+	0.233660i	$0.0750702\pi$
$89$	578.094	+	1001.29i	0.688515	+	1.19254i	−0.283804	+	0.958882i	$0.591596\pi$
$90$		0			0
$91$	−206.974	+	358.490i	−0.238426	+	0.412967i
$92$		0			0
$93$	−103.907	+	74.7517i	−0.115856	+	0.0833483i
$94$		0			0
$95$	−497.151	−	417.160i	−0.536912	−	0.450523i
$96$		0			0
$97$	1388.22	+	505.270i	1.45312	+	0.528891i	0.943460	−	0.331488i	$-0.107551\pi$
$97$	1388.22	+	505.270i	1.45312	+	0.528891i	0.509656	+	0.860378i	$0.329773\pi$
$98$		0			0
$99$	−125.557	+	374.455i	−0.127465	+	0.380142i
$100$		0			0
$101$	285.927	+	1621.57i	0.281691	+	1.59755i	0.716870	+	0.697207i	$0.245574\pi$
$101$	285.927	+	1621.57i	0.281691	+	1.59755i	−0.435178	+	0.900344i	$0.643315\pi$
$102$		0			0
$103$	495.107	−	180.204i	0.473634	−	0.172389i	−0.0941639	−	0.995557i	$-0.530018\pi$
$103$	495.107	−	180.204i	0.473634	−	0.172389i	0.567798	+	0.823168i	$0.307796\pi$
$104$		0			0
$105$	−68.7421	+	270.310i	−0.0638909	+	0.251234i
$106$		0			0
$107$	1997.93			1.80512			0.902559	−	0.430566i	$-0.141686\pi$
$107$	1997.93			1.80512			0.902559	+	0.430566i	$0.141686\pi$
$108$		0			0
$109$	−1268.88			−1.11502			−0.557509	−	0.830171i	$-0.688243\pi$
$109$	−1268.88			−1.11502			−0.557509	+	0.830171i	$0.688243\pi$
$110$		0			0
$111$	383.670	−	108.074i	0.328075	−	0.0924135i
$112$		0			0
$113$	216.017	−	78.6237i	0.179833	−	0.0654539i	−0.250534	−	0.968108i	$-0.580606\pi$
$113$	216.017	−	78.6237i	0.179833	−	0.0654539i	0.430367	+	0.902654i	$0.358384\pi$
$114$		0			0
$115$	31.2806	+	177.401i	0.0253647	+	0.143850i
$116$		0			0
$117$	−897.760	+	1127.16i	−0.709384	+	0.890647i
$118$		0			0
$119$	−431.484	−	157.047i	−0.332387	−	0.120979i
$120$		0			0
$121$	−855.698	−	718.016i	−0.642899	−	0.539456i
$122$		0			0
$123$	206.681	+	2059.16i	0.151511	+	1.50950i
$124$		0			0
$125$	699.341	−	1211.29i	0.500408	−	0.866732i
$126$		0			0
$127$	−923.845	−	1600.15i	−0.645496	−	1.11803i	−0.984187	−	0.177134i	$-0.943317\pi$
$127$	−923.845	−	1600.15i	−0.645496	−	1.11803i	0.338691	−	0.940898i	$-0.390016\pi$
$128$		0			0
$129$	−678.633	−	1408.10i	−0.463181	−	0.961059i
$130$		0			0
$131$	462.901	−	2625.24i	0.308732	−	1.75091i	−0.296665	−	0.954981i	$-0.595875\pi$
$131$	462.901	−	2625.24i	0.308732	−	1.75091i	0.605397	−	0.795924i	$-0.293014\pi$
$132$		0			0
$133$	−557.184	+	467.533i	−0.363263	+	0.304814i
$134$		0			0
$135$	−376.326	+	895.025i	−0.239919	+	0.570604i
$136$		0			0
$137$	−150.629	+	126.392i	−0.0939348	+	0.0788206i	−0.688546	−	0.725193i	$-0.741751\pi$
$137$	−150.629	+	126.392i	−0.0939348	+	0.0788206i	0.594611	+	0.804014i	$0.297306\pi$
$138$		0			0
$139$	236.445	−	1340.95i	0.144281	−	0.818257i	−0.823661	−	0.567082i	$-0.808072\pi$
$139$	236.445	−	1340.95i	0.144281	−	0.818257i	0.967942	−	0.251174i	$-0.0808168\pi$
$140$		0			0
$141$	−51.9895	+	76.3043i	−0.0310518	+	0.0455743i
$142$		0			0
$143$	390.337	+	676.083i	0.228263	+	0.395363i
$144$		0			0
$145$	778.653	−	1348.67i	0.445956	−	0.772419i
$146$		0			0
$147$	−1339.81	−	604.057i	−0.751740	−	0.338924i
$148$		0			0
$149$	−582.798	−	489.026i	−0.320434	−	0.268876i	0.468355	−	0.883541i	$-0.344847\pi$
$149$	−582.798	−	489.026i	−0.320434	−	0.268876i	−0.788789	+	0.614664i	$0.789291\pi$
$150$		0			0
$151$	−2128.86	−	774.842i	−1.14731	−	0.417588i	−0.302764	−	0.953066i	$-0.597909\pi$
$151$	−2128.86	−	774.842i	−1.14731	−	0.417588i	−0.844549	+	0.535478i	$0.820132\pi$
$152$		0			0
$153$	−1404.24	−	763.605i	−0.742001	−	0.403489i
$154$		0			0
$155$	29.6035	+	167.890i	0.0153407	+	0.0870016i
$156$		0			0
$157$	3067.14	−	1116.35i	1.55914	−	0.567480i	0.588599	−	0.808425i	$-0.299680\pi$
$157$	3067.14	−	1116.35i	1.55914	−	0.567480i	0.970539	+	0.240946i	$0.0774576\pi$
$158$		0			0
$159$	902.982	+	880.210i	0.450385	+	0.439026i
$160$		0			0
$161$	201.890			0.0988272
$162$		0			0
$163$	−3101.93			−1.49057			−0.745283	−	0.666749i	$-0.767685\pi$
$163$	−3101.93			−1.49057			−0.745283	+	0.666749i	$0.767685\pi$
$164$		0			0
$165$	376.664	+	367.164i	0.177716	+	0.173235i
$166$		0			0
$167$	875.969	−	318.826i	0.405895	−	0.147734i	−0.131001	−	0.991382i	$-0.541819\pi$
$167$	875.969	−	318.826i	0.405895	−	0.147734i	0.536896	+	0.843649i	$0.319597\pi$
$168$		0			0
$169$	113.107	+	641.464i	0.0514827	+	0.291973i
$170$		0			0
$171$	−2159.71	+	1321.57i	−0.965831	+	0.591012i
$172$		0			0
$173$	2953.58	+	1075.01i	1.29801	+	0.472439i	0.896349	−	0.443348i	$-0.146210\pi$
$173$	2953.58	+	1075.01i	1.29801	+	0.472439i	0.401665	+	0.915787i	$0.368432\pi$
$174$		0			0
$175$	−458.134	−	384.420i	−0.197895	−	0.166054i
$176$		0			0
$177$	1065.50	+	480.384i	0.452475	+	0.203999i
$178$		0			0
$179$	1491.37	−	2583.12i	0.622737	−	1.07861i	−0.366237	−	0.930522i	$-0.619354\pi$
$179$	1491.37	−	2583.12i	0.622737	−	1.07861i	0.988974	−	0.148090i	$-0.0473125\pi$
$180$		0			0
$181$	−475.603	−	823.768i	−0.195311	−	0.338289i	0.751691	−	0.659515i	$-0.229238\pi$
$181$	−475.603	−	823.768i	−0.195311	−	0.338289i	−0.947002	+	0.321226i	$0.895905\pi$
$182$		0			0
$183$	1366.72	−	2005.92i	0.552081	−	0.810282i
$184$		0			0
$185$	92.1862	−	522.814i	0.0366360	−	0.207773i
$186$		0			0
$187$	−663.370	+	556.634i	−0.259414	+	0.217674i
$188$		0			0
$189$	914.623	+	589.548i	0.352006	+	0.226896i
$190$		0			0
$191$	−2073.86	+	1740.18i	−0.785651	+	0.659240i	−0.944665	−	0.328037i	$-0.893613\pi$
$191$	−2073.86	+	1740.18i	−0.785651	+	0.659240i	0.159014	+	0.987276i	$0.449169\pi$
$192$		0			0
$193$	742.402	−	4210.37i	0.276887	−	1.57031i	−0.456015	−	0.889972i	$-0.650724\pi$
$193$	742.402	−	4210.37i	0.276887	−	1.57031i	0.732903	−	0.680334i	$-0.238165\pi$
$194$		0			0
$195$	833.231	+	1728.88i	0.305994	+	0.634911i
$196$		0			0
$197$	2280.07	+	3949.20i	0.824610	+	1.42827i	0.902217	+	0.431282i	$0.141939\pi$
$197$	2280.07	+	3949.20i	0.824610	+	1.42827i	−0.0776069	+	0.996984i	$0.524728\pi$
$198$		0			0
$199$	−1556.41	+	2695.78i	−0.554428	+	0.960297i	0.443520	+	0.896264i	$0.353730\pi$
$199$	−1556.41	+	2695.78i	−0.554428	+	0.960297i	−0.997948	+	0.0640327i	$0.979604\pi$
$200$		0			0
$201$	−225.792	−	2249.57i	−0.0792345	−	0.789414i
$202$		0			0
$203$	−1337.02	−	1121.89i	−0.462268	−	0.387889i
$204$		0			0
$205$	2590.07	+	942.707i	0.882429	+	0.321178i
$206$		0			0
$207$	695.011	+	104.325i	0.233365	+	0.0350294i
$208$		0			0
$209$	238.198	+	1350.89i	0.0788349	+	0.447095i
$210$		0			0
$211$	−1845.57	+	671.733i	−0.602153	+	0.219166i	−0.625066	−	0.780572i	$-0.714928\pi$
$211$	−1845.57	+	671.733i	−0.602153	+	0.219166i	0.0229132	+	0.999737i	$0.492706\pi$
$212$		0			0
$213$	−2774.01	+	781.393i	−0.892356	+	0.251362i
$214$		0			0
$215$	−2081.83			−0.660371
$216$		0			0
$217$	191.066			0.0597714
$218$		0			0
$219$	−581.224	+	2285.51i	−0.179340	+	0.705207i
$220$		0			0
$221$	−2969.02	+	1080.64i	−0.903702	+	0.328920i
$222$		0			0
$223$	737.919	+	4184.95i	0.221591	+	1.25670i	0.869096	+	0.494643i	$0.164701\pi$
$223$	737.919	+	4184.95i	0.221591	+	1.25670i	−0.647506	+	0.762061i	$0.724188\pi$
$224$		0			0
$225$	−1378.49	−	1560.11i	−0.408442	−	0.462255i
$226$		0			0
$227$	−1470.13	−	535.082i	−0.429849	−	0.156452i	0.118030	−	0.993010i	$-0.462342\pi$
$227$	−1470.13	−	535.082i	−0.429849	−	0.156452i	−0.547879	+	0.836558i	$0.684564\pi$
$228$		0			0
$229$	3409.84	+	2861.19i	0.983967	+	0.825647i	0.984683	−	0.174353i	$-0.0557834\pi$
$229$	3409.84	+	2861.19i	0.983967	+	0.825647i	−0.000715825		1.00000i	$0.500228\pi$
$230$		0			0
$231$	478.554	−	344.277i	0.136305	−	0.0980596i
$232$		0			0
$233$	1513.22	−	2620.97i	0.425469	−	0.736934i	−0.570995	−	0.820953i	$-0.693443\pi$
$233$	1513.22	−	2620.97i	0.425469	−	0.736934i	0.996464	+	0.0840197i	$0.0267759\pi$
$234$		0			0
$235$	61.4866	+	106.498i	0.0170679	+	0.0295624i
$236$		0			0
$237$	3634.40	+	271.252i	0.996116	+	0.0743448i
$238$		0			0
$239$	352.245	−	1997.68i	0.0953340	−	0.540666i	−0.899311	−	0.437311i	$-0.855931\pi$
$239$	352.245	−	1997.68i	0.0953340	−	0.540666i	0.994645	−	0.103355i	$-0.0329579\pi$
$240$		0			0
$241$	1684.85	−	1413.75i	0.450334	−	0.377875i	−0.389226	−	0.921142i	$-0.627257\pi$
$241$	1684.85	−	1413.75i	0.450334	−	0.377875i	0.839560	+	0.543267i	$0.182813\pi$
$242$		0			0
$243$	2843.96	+	2502.15i	0.750784	+	0.660548i
$244$		0			0
$245$	−1499.46	+	1258.20i	−0.391009	+	0.328096i
$246$		0			0
$247$	−869.087	+	4928.84i	−0.223881	+	1.26969i
$248$		0			0
$249$	2893.09	+	215.925i	0.736313	+	0.0549545i
$250$		0			0
$251$	1848.46	+	3201.63i	0.464836	+	0.805119i	0.999194	−	0.0401391i	$-0.0127801\pi$
$251$	1848.46	+	3201.63i	0.464836	+	0.805119i	−0.534359	+	0.845258i	$0.679447\pi$
$252$		0			0
$253$	190.374	−	329.738i	0.0473072	−	0.0819385i
$254$		0			0
$255$	−1728.14	+	1243.24i	−0.424394	+	0.305314i
$256$		0			0
$257$	2233.86	+	1874.44i	0.542197	+	0.454957i	0.872289	−	0.488992i	$-0.162635\pi$
$257$	2233.86	+	1874.44i	0.542197	+	0.454957i	−0.330091	+	0.943949i	$0.607080\pi$
$258$		0			0
$259$	−559.102	−	203.497i	−0.134135	−	0.0488211i
$260$		0			0
$261$	−4022.99	−	4553.03i	−0.954087	−	1.07979i
$262$		0			0
$263$	−270.803	−	1535.80i	−0.0634920	−	0.360081i	−0.999957	−	0.00931899i	$-0.997034\pi$
$263$	−270.803	−	1535.80i	−0.0634920	−	0.360081i	0.936465	−	0.350762i	$-0.114077\pi$
$264$		0			0
$265$	1578.20	−	574.417i	0.365841	−	0.133155i
$266$		0			0
$267$	1480.68	−	5822.40i	0.339387	−	1.33455i
$268$		0			0
$269$	−7131.45			−1.61640			−0.808201	−	0.588906i	$-0.799559\pi$
$269$	−7131.45			−1.61640			−0.808201	+	0.588906i	$0.799559\pi$
$270$		0			0
$271$	5551.33			1.24435			0.622175	−	0.782878i	$-0.286249\pi$
$271$	5551.33			1.24435			0.622175	+	0.782878i	$0.286249\pi$
$272$		0			0
$273$	2070.37	−	583.189i	0.458991	−	0.129290i
$274$		0			0
$275$	−1059.86	+	385.757i	−0.232407	+	0.0845891i
$276$		0			0
$277$	680.783	+	3860.91i	0.147669	+	0.837471i	0.965185	+	0.261567i	$0.0842391\pi$
$277$	680.783	+	3860.91i	0.147669	+	0.837471i	−0.817517	+	0.575905i	$0.804650\pi$
$278$		0			0
$279$	657.748	+	98.7316i	0.141141	+	0.0211860i
$280$		0			0
$281$	−5176.79	−	1884.20i	−1.09901	−	0.400006i	−0.272057	−	0.962281i	$-0.587704\pi$
$281$	−5176.79	−	1884.20i	−1.09901	−	0.400006i	−0.826950	+	0.562275i	$0.809926\pi$
$282$		0			0
$283$	−962.891	−	807.961i	−0.202254	−	0.169711i	0.536035	−	0.844196i	$-0.319922\pi$
$283$	−962.891	−	807.961i	−0.202254	−	0.169711i	−0.738289	+	0.674484i	$0.764366\pi$
$284$		0			0
$285$	336.783	+	3355.37i	0.0699975	+	0.697385i
$286$		0			0
$287$	1544.56	−	2675.26i	0.317674	−	0.550228i
$288$		0			0
$289$	704.111	+	1219.56i	0.143316	+	0.248230i
$290$		0			0
$291$	−3332.73	−	6915.13i	−0.671369	−	1.39303i
$292$		0			0
$293$	−1207.87	+	6850.17i	−0.240834	+	1.36584i	0.589137	+	0.808033i	$0.299468\pi$
$293$	−1207.87	+	6850.17i	−0.240834	+	1.36584i	−0.829971	+	0.557806i	$0.811643\pi$
$294$		0			0
$295$	1192.47	−	1000.60i	0.235350	−	0.197482i
$296$		0			0
$297$	1825.33	−	937.892i	0.356621	−	0.183239i
$298$		0			0
$299$	1064.19	−	892.959i	0.205831	−	0.172713i
$300$		0			0
$301$	−405.159	+	2297.77i	−0.0775847	+	0.440005i
$302$		0			0
$303$	4817.58	−	7070.70i	0.913409	−	1.34060i
$304$		0			0
$305$	−1616.38	−	2799.66i	−0.303455	−	0.525600i
$306$		0			0
$307$	1319.29	−	2285.08i	0.245263	−	0.424808i	−0.716942	−	0.697132i	$-0.754459\pi$
$307$	1319.29	−	2285.08i	0.245263	−	0.424808i	0.962206	+	0.272324i	$0.0877923\pi$
$308$		0			0
$309$	−2495.82	−	1125.25i	−0.459490	−	0.207162i
$310$		0			0
$311$	−4431.20	−	3718.22i	−0.807943	−	0.677945i	0.142173	−	0.989842i	$-0.454591\pi$
$311$	−4431.20	−	3718.22i	−0.807943	−	0.677945i	−0.950116	+	0.311897i	$0.899036\pi$
$312$		0			0
$313$	−1731.49	−	630.210i	−0.312682	−	0.113807i	0.180912	−	0.983499i	$-0.442095\pi$
$313$	−1731.49	−	630.210i	−0.312682	−	0.113807i	−0.493594	+	0.869692i	$0.664317\pi$
$314$		0			0
$315$	1236.20	−	756.455i	0.221117	−	0.135306i
$316$		0			0
$317$	−71.8687	−	407.588i	−0.0127336	−	0.0722158i	0.977779	−	0.209639i	$-0.0672290\pi$
$317$	−71.8687	−	407.588i	−0.0127336	−	0.0722158i	−0.990512	+	0.137424i	$0.956118\pi$
$318$		0			0
$319$	−3093.09	+	1125.79i	−0.542883	+	0.197593i
$320$		0			0
$321$	−7434.02	−	7246.54i	−1.29261	−	1.26001i
$322$		0			0
$323$	−5551.70			−0.956361
$324$		0			0
$325$	−4115.17			−0.702364
$326$		0			0
$327$	4721.33	+	4602.26i	0.798441	+	0.778305i
$328$		0			0
$329$	129.511	−	47.1381i	0.0217026	−	0.00789912i
$330$		0			0
$331$	−1439.06	−	8161.32i	−0.238967	−	1.35525i	−0.834097	−	0.551618i	$-0.814011\pi$
$331$	−1439.06	−	8161.32i	−0.238967	−	1.35525i	0.595131	−	0.803629i	$-0.297100\pi$
$332$		0			0
$333$	−1819.57	−	989.452i	−0.299434	−	0.162828i
$334$		0			0
$335$	−2829.56	−	1029.87i	−0.461478	−	0.167964i
$336$		0			0
$337$	−992.442	−	832.758i	−0.160421	−	0.134609i	0.559044	−	0.829138i	$-0.311168\pi$
$337$	−992.442	−	832.758i	−0.160421	−	0.134609i	−0.719465	+	0.694529i	$0.755613\pi$
$338$		0			0
$339$	−1088.94	−	490.949i	−0.174463	−	0.0786570i
$340$		0			0
$341$	180.167	−	312.059i	0.0286117	−	0.0495570i
$342$		0			0
$343$	2427.08	+	4203.82i	0.382069	+	0.661763i
$344$		0			0
$345$	527.047	−	773.540i	0.0822471	−	0.120713i
$346$		0			0
$347$	229.552	−	1301.85i	0.0355129	−	0.201404i	−0.961889	−	0.273440i	$-0.911839\pi$
$347$	229.552	−	1301.85i	0.0355129	−	0.201404i	0.997402	+	0.0720360i	$0.0229497\pi$
$348$		0			0
$349$	1971.21	−	1654.04i	0.302339	−	0.253693i	−0.478978	−	0.877827i	$-0.658993\pi$
$349$	1971.21	−	1654.04i	0.302339	−	0.253693i	0.781317	+	0.624134i	$0.214548\pi$
$350$		0			0
$351$	7428.65	−	937.795i	1.12966	−	0.142609i
$352$		0			0
$353$	7466.29	−	6264.96i	1.12575	−	0.944618i	0.126872	−	0.991919i	$-0.459506\pi$
$353$	7466.29	−	6264.96i	1.12575	−	0.944618i	0.998881	+	0.0473007i	$0.0150619\pi$
$354$		0			0
$355$	−666.523	+	3780.04i	−0.0996490	+	0.565137i
$356$		0			0
$357$	1035.88	+	2149.35i	0.153570	+	0.318644i
$358$		0			0
$359$	5633.32	+	9757.19i	0.828176	+	1.43444i	0.899468	+	0.436987i	$0.143954\pi$
$359$	5633.32	+	9757.19i	0.828176	+	1.43444i	−0.0712921	+	0.997455i	$0.522712\pi$
$360$		0			0
$361$	−967.548	+	1675.84i	−0.141063	+	0.244328i
$362$		0			0
$363$	579.671	+	5775.26i	0.0838150	+	0.835049i
$364$		0			0
$365$	2406.04	+	2018.90i	0.345035	+	0.289518i
$366$		0			0
$367$	−721.883	−	262.744i	−0.102676	−	0.0373709i	0.290171	−	0.956975i	$-0.406288\pi$
$367$	−721.883	−	262.744i	−0.102676	−	0.0373709i	−0.392847	+	0.919604i	$0.628510\pi$
$368$		0			0
$369$	6699.59	−	8411.48i	0.945168	−	1.18668i
$370$		0			0
$371$	−326.856	−	1853.69i	−0.0457399	−	0.259404i
$372$		0			0
$373$	−3384.75	+	1231.95i	−0.469854	+	0.171013i	−0.566086	−	0.824346i	$-0.691543\pi$
$373$	−3384.75	+	1231.95i	−0.469854	+	0.171013i	0.0962323	+	0.995359i	$0.469321\pi$
$374$		0			0
$375$	−6995.53	+	1970.53i	−0.963327	+	0.271353i
$376$		0			0
$377$	−12009.7			−1.64067
$378$		0			0
$379$	11322.2			1.53451			0.767257	−	0.641340i	$-0.221621\pi$
$379$	11322.2			1.53451			0.767257	+	0.641340i	$0.221621\pi$
$380$		0			0
$381$	−2366.27	+	9304.71i	−0.318182	+	1.25117i
$382$		0			0
$383$	6956.61	−	2532.00i	0.928110	−	0.337805i	0.166650	−	0.986016i	$-0.446705\pi$
$383$	6956.61	−	2532.00i	0.928110	−	0.337805i	0.761460	+	0.648212i	$0.224483\pi$
$384$		0			0
$385$	−136.342	−	773.235i	−0.0180484	−	0.102358i
$386$		0			0
$387$	−2582.12	+	7700.76i	−0.339165	+	1.01150i
$388$		0			0
$389$	6863.75	+	2498.20i	0.894617	+	0.325614i	0.748094	−	0.663593i	$-0.230969\pi$
$389$	6863.75	+	2498.20i	0.894617	+	0.325614i	0.146523	+	0.989207i	$0.453192\pi$
$390$		0			0
$391$	1180.46	+	990.522i	0.152681	+	0.128115i
$392$		0			0
$393$	−11244.2	+	8089.19i	−1.44324	+	1.03828i
$394$		0			0
$395$	2426.98	−	4203.65i	0.309151	−	0.535465i
$396$		0			0
$397$	4660.31	+	8071.90i	0.589155	+	1.02045i	0.994343	+	0.106213i	$0.0338725\pi$
$397$	4660.31	+	8071.90i	0.589155	+	1.02045i	−0.405189	+	0.914233i	$0.632794\pi$
$398$		0			0
$399$	3768.95	+	281.294i	0.472891	+	0.0352941i
$400$		0			0
$401$	−1648.21	+	9347.46i	−0.205256	+	1.16406i	0.691781	+	0.722108i	$0.256827\pi$
$401$	−1648.21	+	9347.46i	−0.205256	+	1.16406i	−0.897037	+	0.441956i	$0.854285\pi$
$402$		0			0
$403$	1007.13	−	845.082i	0.124488	−	0.104458i
$404$		0			0
$405$	4646.53	−	1965.32i	0.570093	−	0.241129i
$406$		0			0
$407$	−859.572	+	721.267i	−0.104687	+	0.0878424i
$408$		0			0
$409$	727.417	−	4125.39i	0.0879424	−	0.498746i	−0.908740	−	0.417362i	$-0.862955\pi$
$409$	727.417	−	4125.39i	0.0879424	−	0.498746i	0.996683	−	0.0813844i	$-0.0259341\pi$
$410$		0			0
$411$	1018.89	+	76.0448i	0.122283	+	0.00912656i
$412$		0			0
$413$	−872.313	−	1510.89i	−0.103932	−	0.180015i
$414$		0			0
$415$	1931.95	−	3346.23i	0.228519	−	0.395807i
$416$		0			0
$417$	−5743.42	+	4131.88i	−0.674476	+	0.485225i
$418$		0			0
$419$	12673.7	+	10634.5i	1.47769	+	1.23993i	0.908611	+	0.417643i	$0.137144\pi$
$419$	12673.7	+	10634.5i	1.47769	+	1.23993i	0.569077	+	0.822284i	$0.307301\pi$
$420$		0			0
$421$	−6440.45	−	2344.13i	−0.745578	−	0.271368i	−0.0588342	−	0.998268i	$-0.518738\pi$
$421$	−6440.45	−	2344.13i	−0.745578	−	0.271368i	−0.686744	+	0.726900i	$0.740961\pi$
$422$		0			0
$423$	470.202	−	95.3503i	0.0540473	−	0.0109600i
$424$		0			0
$425$	−792.666	−	4495.43i	−0.0904705	−	0.513084i
$426$		0			0
$427$	−3404.63	+	1239.19i	−0.385859	+	0.140441i
$428$		0			0
$429$	999.779	−	3931.36i	0.112517	−	0.442443i
$430$		0			0
$431$	−16248.1			−1.81588			−0.907938	−	0.419104i	$-0.862344\pi$
$431$	−16248.1			−1.81588			−0.907938	+	0.419104i	$0.862344\pi$
$432$		0			0
$433$	−6251.26			−0.693803			−0.346901	−	0.937902i	$-0.612766\pi$
$433$	−6251.26			−0.693803			−0.346901	+	0.937902i	$0.612766\pi$
$434$		0			0
$435$	−7788.89	+	2194.00i	−0.858503	+	0.241826i
$436$		0			0
$437$	2293.76	−	834.860i	0.251088	−	0.0913885i
$438$		0			0
$439$	−2321.71	−	13167.1i	−0.252412	−	1.43150i	−0.802629	−	0.596479i	$-0.796566\pi$
$439$	−2321.71	−	13167.1i	−0.252412	−	1.43150i	0.550216	−	0.835022i	$-0.314545\pi$
$440$		0			0
$441$	2794.32	+	7107.13i	0.301729	+	0.767425i
$442$		0			0
$443$	13255.0	+	4824.43i	1.42159	+	0.517417i	0.934509	−	0.355940i	$-0.115839\pi$
$443$	13255.0	+	4824.43i	1.42159	+	0.517417i	0.487081	+	0.873357i	$0.338061\pi$
$444$		0			0
$445$	−6129.45	−	5143.22i	−0.652952	−	0.547892i
$446$		0			0
$447$	394.802	+	3933.41i	0.0417752	+	0.416206i
$448$		0			0
$449$	6125.14	−	10609.0i	0.643793	−	1.11508i	−0.340786	−	0.940141i	$-0.610693\pi$
$449$	6125.14	−	10609.0i	0.643793	−	1.11508i	0.984579	−	0.174941i	$-0.0559736\pi$
$450$		0			0
$451$	−2912.91	−	5045.32i	−0.304133	−	0.526773i
$452$		0			0
$453$	5110.82	+	10604.5i	0.530082	+	1.09987i
$454$		0			0
$455$	497.457	−	2821.22i	0.0512553	−	0.290683i
$456$		0			0
$457$	−3161.89	+	2653.14i	−0.323648	+	0.271573i	−0.790106	−	0.612971i	$-0.789974\pi$
$457$	−3161.89	+	2653.14i	−0.323648	+	0.271573i	0.466458	+	0.884544i	$0.345530\pi$
$458$		0			0
$459$	2455.37	+	7934.46i	0.249688	+	0.806861i
$460$		0			0
$461$	11312.5	−	9492.29i	1.14289	−	0.959002i	0.143364	−	0.989670i	$-0.454208\pi$
$461$	11312.5	−	9492.29i	1.14289	−	0.959002i	0.999530	+	0.0306683i	$0.00976354\pi$
$462$		0			0
$463$	−1803.16	+	10226.2i	−0.180993	+	1.02646i	0.750003	+	0.661434i	$0.230052\pi$
$463$	−1803.16	+	10226.2i	−0.180993	+	1.02646i	−0.930996	+	0.365029i	$0.881059\pi$
$464$		0			0
$465$	498.789	−	732.066i	0.0497436	−	0.0730081i
$466$		0			0
$467$	9089.22	+	15743.0i	0.900640	+	1.55995i	0.826665	+	0.562694i	$0.190235\pi$
$467$	9089.22	+	15743.0i	0.900640	+	1.55995i	0.0739745	+	0.997260i	$0.476432\pi$
$468$		0			0
$469$	−1687.38	+	2922.63i	−0.166132	+	0.287749i
$470$		0			0
$471$	−15461.4	−	6970.81i	−1.51258	−	0.681949i
$472$		0			0
$473$	3370.80	+	2828.43i	0.327673	+	0.274950i
$474$		0			0
$475$	−6794.72	−	2473.07i	−0.656343	−	0.238889i
$476$		0			0
$477$	−167.329	−	6550.26i	−0.0160617	−	0.628755i
$478$		0			0
$479$	−878.825	−	4984.07i	−0.0838300	−	0.475423i	−0.997603	−	0.0691981i	$-0.977956\pi$
$479$	−878.825	−	4984.07i	−0.0838300	−	0.475423i	0.913773	−	0.406225i	$-0.133155\pi$
$480$		0			0
$481$	−3847.16	+	1400.25i	−0.364689	+	0.132736i
$482$		0			0
$483$	−751.204	−	732.259i	−0.0707681	−	0.0689834i
$484$		0			0
$485$	−10223.8			−0.957191
$486$		0			0
$487$	16549.8			1.53993			0.769963	−	0.638089i	$-0.220275\pi$
$487$	16549.8			1.53993			0.769963	+	0.638089i	$0.220275\pi$
$488$		0			0
$489$	11541.8	+	11250.8i	1.06736	+	1.04044i
$490$		0			0
$491$	1518.20	−	552.579i	0.139542	−	0.0507893i	−0.271305	−	0.962493i	$-0.587455\pi$
$491$	1518.20	−	552.579i	0.139542	−	0.0507893i	0.410847	+	0.911704i	$0.365233\pi$
$492$		0			0
$493$	−2313.32	−	13119.5i	−0.211332	−	1.19852i
$494$		0			0
$495$	−69.7982	−	2732.33i	−0.00633777	−	0.248099i
$496$		0			0
$497$	4042.41	+	1471.32i	0.364843	+	0.132792i
$498$		0			0
$499$	−4436.72	−	3722.85i	−0.398026	−	0.333983i	0.421704	−	0.906733i	$-0.361432\pi$
$499$	−4436.72	−	3722.85i	−0.398026	−	0.333983i	−0.819730	+	0.572750i	$0.805876\pi$
$500$		0			0
$501$	−4415.74	−	1990.85i	−0.393774	−	0.177534i
$502$		0			0
$503$	2966.70	−	5138.47i	0.262979	−	0.455493i	−0.704053	−	0.710147i	$-0.748628\pi$
$503$	2966.70	−	5138.47i	0.262979	−	0.455493i	0.967032	+	0.254654i	$0.0819617\pi$
$504$		0			0
$505$	−5697.64	−	9868.59i	−0.502062	−	0.869597i
$506$		0			0
$507$	1905.74	−	2797.04i	0.166937	−	0.245011i
$508$		0			0
$509$	−1327.68	+	7529.66i	−0.115616	+	0.655690i	0.870828	+	0.491589i	$0.163584\pi$
$509$	−1327.68	+	7529.66i	−0.115616	+	0.655690i	−0.986443	+	0.164102i	$0.947528\pi$
$510$		0			0
$511$	2696.57	−	2262.69i	0.233443	−	0.195882i
$512$		0			0
$513$	12829.3	+	2915.93i	1.10415	+	0.250958i
$514$		0			0
$515$	−2793.23	+	2343.79i	−0.238998	+	0.200544i
$516$		0			0
$517$	45.1350	−	255.974i	0.00383953	−	0.0217751i
$518$		0			0
$519$	−7090.74	−	14712.7i	−0.599709	−	1.24434i
$520$		0			0
$521$	294.488	+	510.068i	0.0247635	+	0.0428916i	0.878142	−	0.478401i	$-0.158783\pi$
$521$	294.488	+	510.068i	0.0247635	+	0.0428916i	−0.853378	+	0.521292i	$0.825450\pi$
$522$		0			0
$523$	4872.57	−	8439.54i	0.407386	−	0.705613i	−0.587210	−	0.809434i	$-0.699774\pi$
$523$	4872.57	−	8439.54i	0.407386	−	0.705613i	0.994596	+	0.103822i	$0.0331071\pi$
$524$		0			0
$525$	310.352	+	3092.03i	0.0257997	+	0.257043i
$526$		0			0
$527$	1117.17	+	937.415i	0.0923426	+	0.0774847i
$528$		0			0
$529$	10796.6	+	3929.63i	0.887365	+	0.322974i
$530$		0			0
$531$	−2222.22	−	5652.03i	−0.181612	−	0.461916i
$532$		0			0
$533$	−3691.08	−	20933.2i	−0.299960	−	1.70115i
$534$		0			0
$535$	−12992.9	+	4729.03i	−1.04997	+	0.382157i
$536$		0			0
$537$	−14918.2	+	4202.20i	−1.19882	+	0.337688i
$538$		0			0
$539$	4137.28			0.330622
$540$		0			0
$541$	−4636.36			−0.368452			−0.184226	−	0.982884i	$-0.558978\pi$
$541$	−4636.36			−0.368452			−0.184226	+	0.982884i	$0.558978\pi$
$542$		0			0
$543$	−1218.17	+	4790.14i	−0.0962741	+	0.378572i
$544$		0			0
$545$	8251.77	−	3003.40i	0.648563	−	0.236058i
$546$		0			0
$547$	−3576.84	−	20285.3i	−0.279588	−	1.58562i	−0.723999	−	0.689801i	$-0.757698\pi$
$547$	−3576.84	−	20285.3i	−0.279588	−	1.58562i	0.444411	−	0.895823i	$-0.353413\pi$
$548$		0			0
$549$	−12360.9	+	2506.60i	−0.960926	+	0.194862i
$550$		0			0
$551$	−19829.7	−	7217.42i	−1.53317	−	0.558027i
$552$		0			0
$553$	−4167.35	−	3496.82i	−0.320459	−	0.268897i
$554$		0			0
$555$	−2239.27	+	1610.95i	−0.171264	+	0.123209i
$556$		0			0
$557$	2376.10	−	4115.53i	0.180752	−	0.313071i	−0.761385	−	0.648300i	$-0.775480\pi$
$557$	2376.10	−	4115.53i	0.180752	−	0.313071i	0.942137	+	0.335229i	$0.108814\pi$
$558$		0			0
$559$	8027.38	+	13903.8i	0.607374	+	1.05200i
$560$		0			0
$561$	4487.22	+	334.903i	0.337702	+	0.0252043i
$562$		0			0
$563$	1868.80	−	10598.5i	0.139894	−	0.793379i	−0.831432	−	0.555627i	$-0.812478\pi$
$563$	1868.80	−	10598.5i	0.139894	−	0.793379i	0.971326	−	0.237752i	$-0.0764106\pi$
$564$		0			0
$565$	−1218.69	+	1022.61i	−0.0907449	+	0.0761440i
$566$		0			0
$567$	−1264.88	−	5510.98i	−0.0936859	−	0.408182i
$568$		0			0
$569$	2744.52	−	2302.93i	0.202208	−	0.169673i	−0.536061	−	0.844180i	$-0.680088\pi$
$569$	2744.52	−	2302.93i	0.202208	−	0.169673i	0.738269	+	0.674507i	$0.235644\pi$
$570$		0			0
$571$	588.801	−	3339.25i	0.0431533	−	0.244735i	−0.955599	−	0.294670i	$-0.904790\pi$
$571$	588.801	−	3339.25i	0.0431533	−	0.244735i	0.998752	+	0.0499351i	$0.0159015\pi$
$572$		0			0
$573$	14028.2	+	1046.99i	1.02275	+	0.0763327i
$574$		0			0
$575$	1003.52	+	1738.15i	0.0727821	+	0.126062i
$576$		0			0
$577$	−1802.55	+	3122.12i	−0.130054	+	0.225261i	−0.923697	−	0.383123i	$-0.874848\pi$
$577$	−1802.55	+	3122.12i	−0.130054	+	0.225261i	0.793643	+	0.608384i	$0.208182\pi$
$578$		0			0
$579$	−18033.4	+	12973.5i	−1.29438	+	0.931189i
$580$		0			0
$581$	−3317.33	−	2783.57i	−0.236878	−	0.198764i
$582$		0			0
$583$	−3335.76	−	1214.12i	−0.236969	−	0.0862497i
$584$		0			0
$585$	3170.35	−	9455.05i	0.224064	−	0.668236i
$586$		0			0
$587$	3392.97	+	19242.5i	0.238574	+	1.35302i	0.834955	+	0.550318i	$0.185494\pi$
$587$	3392.97	+	19242.5i	0.238574	+	1.35302i	−0.596381	+	0.802702i	$0.703395\pi$
$588$		0			0
$589$	2170.78	−	790.099i	0.151860	−	0.0552724i
$590$		0			0
$591$	5840.00	−	22964.2i	0.406473	−	1.59835i
$592$		0			0
$593$	−9718.65			−0.673013			−0.336507	−	0.941681i	$-0.609245\pi$
$593$	−9718.65			−0.673013			−0.336507	+	0.941681i	$0.609245\pi$
$594$		0			0
$595$	3177.74			0.218949
$596$		0			0
$597$	15568.8	−	4385.49i	1.06732	−	0.300647i
$598$		0			0
$599$	−23413.0	+	8521.62i	−1.59704	+	0.581275i	−0.978819	−	0.204728i	$-0.934369\pi$
$599$	−23413.0	+	8521.62i	−1.59704	+	0.581275i	−0.618222	+	0.786003i	$0.712147\pi$
$600$		0			0
$601$	4759.65	+	26993.3i	0.323045	+	1.83208i	0.523069	+	0.852290i	$0.324787\pi$
$601$	4759.65	+	26993.3i	0.323045	+	1.83208i	−0.200024	+	0.979791i	$0.564102\pi$
$602$		0			0
$603$	−7319.07	+	9189.26i	−0.494288	+	0.620589i
$604$		0			0
$605$	7264.26	+	2643.98i	0.488156	+	0.177674i
$606$		0			0
$607$	19958.2	+	16746.9i	1.33456	+	1.11983i	0.982988	+	0.183671i	$0.0587979\pi$
$607$	19958.2	+	16746.9i	1.33456	+	1.11983i	0.351574	+	0.936160i	$0.385646\pi$
$608$		0			0
$609$	905.731	+	9023.79i	0.0602661	+	0.600431i
$610$		0			0
$611$	474.175	−	821.296i	0.0313962	−	0.0543798i
$612$		0			0
$613$	−694.965	−	1203.72i	−0.0457902	−	0.0793109i	0.842222	−	0.539131i	$-0.181247\pi$
$613$	−694.965	−	1203.72i	−0.0457902	−	0.0793109i	−0.888012	+	0.459820i	$0.847914\pi$
$614$		0			0
$615$	−6218.04	−	12901.9i	−0.407700	−	0.845942i
$616$		0			0
$617$	−1604.15	+	9097.57i	−0.104669	+	0.593605i	0.886684	+	0.462377i	$0.153003\pi$
$617$	−1604.15	+	9097.57i	−0.104669	+	0.593605i	−0.991352	+	0.131228i	$0.958108\pi$
$618$		0			0
$619$	5940.36	−	4984.55i	0.385724	−	0.323661i	−0.429221	−	0.903200i	$-0.641212\pi$
$619$	5940.36	−	4984.55i	0.385724	−	0.323661i	0.814945	+	0.579539i	$0.196767\pi$
$620$		0			0
$621$	−2207.65	−	2909.00i	−0.142657	−	0.187977i
$622$		0			0
$623$	−6869.59	+	5764.27i	−0.441773	+	0.370691i
$624$		0			0
$625$	−7.17646	+	40.6997i	−0.000459293	+	0.00260478i
$626$		0			0
$627$	4013.39	−	5890.40i	0.255629	−	0.375183i
$628$		0			0
$629$	−2270.68	−	3932.94i	−0.143940	−	0.249311i
$630$		0			0
$631$	−1569.14	+	2717.83i	−0.0989958	+	0.171466i	−0.911269	−	0.411811i	$-0.864896\pi$
$631$	−1569.14	+	2717.83i	−0.0989958	+	0.171466i	0.812273	+	0.583277i	$0.198230\pi$
$632$		0			0
$633$	9303.48	+	4194.50i	0.584171	+	0.263375i
$634$		0			0
$635$	9795.40	+	8219.32i	0.612155	+	0.513659i
$636$		0			0
$637$	14184.9	+	5162.88i	0.882301	+	0.321131i
$638$		0			0
$639$	13155.8	+	7153.92i	0.814453	+	0.442887i
$640$		0			0
$641$	1044.51	+	5923.70i	0.0643613	+	0.365011i	0.999930	+	0.0118653i	$0.00377692\pi$
$641$	1044.51	+	5923.70i	0.0643613	+	0.365011i	−0.935568	+	0.353146i	$0.885112\pi$
$642$		0			0
$643$	−3903.59	+	1420.79i	−0.239413	+	0.0871393i	−0.458940	−	0.888467i	$-0.651771\pi$
$643$	−3903.59	+	1420.79i	−0.239413	+	0.0871393i	0.219527	+	0.975606i	$0.429549\pi$
$644$		0			0
$645$	7746.19	+	7550.84i	0.472878	+	0.460952i
$646$		0			0
$647$	−3878.14			−0.235650			−0.117825	−	0.993034i	$-0.537592\pi$
$647$	−3878.14			−0.235650			−0.117825	+	0.993034i	$0.537592\pi$
$648$		0			0
$649$	−3290.22			−0.199002
$650$		0			0
$651$	−710.928	−	692.999i	−0.0428010	−	0.0417216i
$652$		0			0
$653$	3094.96	−	1126.48i	0.185475	−	0.0675075i	−0.247613	−	0.968859i	$-0.579646\pi$
$653$	3094.96	−	1126.48i	0.185475	−	0.0675075i	0.433088	+	0.901352i	$0.357424\pi$
$654$		0			0
$655$	3203.52	+	18168.1i	0.191102	+	1.08379i
$656$		0			0
$657$	10452.2	−	6395.93i	0.620670	−	0.379801i
$658$		0			0
$659$	−14236.8	−	5181.76i	−0.841556	−	0.306301i	−0.114963	−	0.993370i	$-0.536675\pi$
$659$	−14236.8	−	5181.76i	−0.841556	−	0.306301i	−0.726593	+	0.687068i	$0.758897\pi$
$660$		0			0
$661$	3706.41	+	3110.04i	0.218098	+	0.183006i	0.745290	−	0.666740i	$-0.232311\pi$
$661$	3706.41	+	3110.04i	0.218098	+	0.183006i	−0.527193	+	0.849746i	$0.676755\pi$
$662$		0			0
$663$	14966.8	+	6747.81i	0.876714	+	0.395269i
$664$		0			0
$665$	2516.83	−	4359.28i	0.146765	−	0.254204i
$666$		0			0
$667$	2928.68	+	5072.62i	0.170013	+	0.294471i
$668$		0			0
$669$	12433.2	−	18248.0i	0.718527	−	1.05457i
$670$		0			0
$671$	−1186.53	+	6729.13i	−0.0682643	+	0.387146i
$672$		0			0
$673$	−15159.9	+	12720.6i	−0.868305	+	0.728595i	−0.963741	−	0.266841i	$-0.914020\pi$
$673$	−15159.9	+	12720.6i	−0.868305	+	0.728595i	0.0954352	+	0.995436i	$0.469576\pi$
$674$		0			0
$675$	−529.390	+	10804.8i	−0.0301870	+	0.616111i
$676$		0			0
$677$	6219.26	−	5218.58i	0.353066	−	0.296257i	−0.448954	−	0.893555i	$-0.648203\pi$
$677$	6219.26	−	5218.58i	0.353066	−	0.296257i	0.802020	+	0.597298i	$0.203759\pi$
$678$		0			0
$679$	−1989.72	+	11284.2i	−0.112457	+	0.637775i
$680$		0			0
$681$	3529.37	+	7323.13i	0.198599	+	0.412075i
$682$		0			0
$683$	9569.27	+	16574.5i	0.536102	+	0.928557i	0.999109	+	0.0422019i	$0.0134373\pi$
$683$	9569.27	+	16574.5i	0.536102	+	0.928557i	−0.463007	+	0.886355i	$0.653229\pi$
$684$		0			0
$685$	680.397	−	1178.48i	0.0379513	−	0.0657336i
$686$		0			0
$687$	−2309.91	−	23013.6i	−0.128280	−	1.27806i
$688$		0			0
$689$	−9921.75	−	8325.33i	−0.548604	−	0.460334i
$690$		0			0
$691$	101.637	+	36.9930i	0.00559547	+	0.00203658i	0.344816	−	0.938670i	$-0.387941\pi$
$691$	101.637	+	36.9930i	0.00559547	+	0.00203658i	−0.339221	+	0.940707i	$0.610163\pi$
$692$		0			0
$693$	−3029.33	−	454.719i	−0.166053	−	0.0249255i
$694$		0			0
$695$	1636.33	+	9280.06i	0.0893085	+	0.506493i
$696$		0			0
$697$	22156.5	−	8064.32i	1.20407	−	0.438247i
$698$		0			0
$699$	−15136.8	+	4263.78i	−0.819063	+	0.230717i
$700$		0			0
$701$	−27394.8			−1.47601			−0.738007	−	0.674793i	$-0.764233\pi$
$701$	−27394.8			−1.47601			−0.738007	+	0.674793i	$0.764233\pi$
$702$		0			0
$703$	−7193.70			−0.385939
$704$		0			0
$705$	157.487	−	619.277i	0.00841321	−	0.0330827i
$706$		0			0
$707$	−12001.1	+	4368.04i	−0.638398	+	0.232358i
$708$		0			0
$709$	2265.35	+	12847.4i	0.119996	+	0.680529i	0.984155	+	0.177310i	$0.0567397\pi$
$709$	2265.35	+	12847.4i	0.119996	+	0.680529i	−0.864159	+	0.503218i	$0.832149\pi$
$710$		0			0
$711$	−12539.2	−	14191.3i	−0.661403	−	0.748545i
$712$		0			0
$713$	−602.540	−	219.307i	−0.0316484	−	0.0115191i
$714$		0			0
$715$	−4138.69	−	3472.77i	−0.216473	−	0.181642i
$716$		0			0
$717$	−8556.27	+	6155.47i	−0.445662	+	0.320614i
$718$		0			0
$719$	−7365.93	+	12758.2i	−0.382063	+	0.661752i	−0.991357	−	0.131192i	$-0.958119\pi$
$719$	−7365.93	+	12758.2i	−0.382063	+	0.661752i	0.609294	+	0.792944i	$0.291453\pi$
$720$		0			0
$721$	2043.30	+	3539.10i	0.105543	+	0.182806i
$722$		0			0
$723$	−11396.8	−	850.594i	−0.586238	−	0.0437537i
$724$		0			0
$725$	3012.97	−	17087.4i	0.154343	−	0.875325i
$726$		0			0
$727$	616.890	−	517.632i	0.0314707	−	0.0264070i	−0.626917	−	0.779086i	$-0.715683\pi$
$727$	616.890	−	517.632i	0.0314707	−	0.0264070i	0.658387	+	0.752679i	$0.271239\pi$
$728$		0			0
$729$	−1506.62	−	19625.3i	−0.0765443	−	0.997066i
$730$		0			0
$731$	−13642.4	+	11447.3i	−0.690263	+	0.579200i
$732$		0			0
$733$	314.266	−	1782.29i	0.0158358	−	0.0898095i	−0.975866	−	0.218372i	$-0.929925\pi$
$733$	314.266	−	1782.29i	0.0158358	−	0.0898095i	0.991701	+	0.128563i	$0.0410364\pi$
$734$		0			0
$735$	10142.8	+	757.005i	0.509010	+	0.0379898i
$736$		0			0
$737$	3182.26	+	5511.83i	0.159050	+	0.275483i
$738$		0			0
$739$	−2005.53	+	3473.68i	−0.0998303	+	0.172911i	−0.911614	−	0.411047i	$-0.865163\pi$
$739$	−2005.53	+	3473.68i	−0.0998303	+	0.172911i	0.811784	+	0.583958i	$0.198497\pi$
$740$		0			0
$741$	21110.7	−	15187.3i	1.04659	−	0.752927i
$742$		0			0
$743$	−20551.0	−	17244.3i	−1.01473	−	0.851456i	−0.0257705	−	0.999668i	$-0.508204\pi$
$743$	−20551.0	−	17244.3i	−1.01473	−	0.851456i	−0.988956	+	0.148211i	$0.952648\pi$
$744$		0			0
$745$	4947.54	+	1800.76i	0.243307	+	0.0885566i
$746$		0			0
$747$	−9981.59	−	11296.7i	−0.488899	−	0.553313i
$748$		0			0
$749$	2690.92	+	15261.0i	0.131274	+	0.744490i
$750$		0			0
$751$	33872.2	−	12328.5i	1.64582	−	0.599031i	0.657780	−	0.753210i	$-0.271496\pi$
$751$	33872.2	−	12328.5i	1.64582	−	0.599031i	0.988043	+	0.154179i	$0.0492734\pi$
$752$		0			0
$753$	4734.50	−	18617.2i	0.229130	−	0.900993i
$754$		0			0
$755$	15678.4			0.755754
$756$		0			0
$757$	−20176.1			−0.968708			−0.484354	−	0.874872i	$-0.660945\pi$
$757$	−20176.1			−0.968708			−0.484354	+	0.874872i	$0.660945\pi$
$758$		0			0
$759$	−1904.32	+	536.416i	−0.0910704	+	0.0256530i
$760$		0			0
$761$	−3112.67	+	1132.92i	−0.148271	+	0.0539662i	−0.415090	−	0.909781i	$-0.636250\pi$
$761$	−3112.67	+	1132.92i	−0.148271	+	0.0539662i	0.266819	+	0.963747i	$0.414028\pi$
$762$		0			0
$763$	−1709.00	−	9692.20i	−0.0810876	−	0.459871i
$764$		0			0
$765$	10939.4	+	1642.07i	0.517014	+	0.0776067i
$766$		0			0
$767$	−11280.7	−	4105.84i	−0.531060	−	0.193290i
$768$		0			0
$769$	−872.027	−	731.718i	−0.0408922	−	0.0343126i	0.622113	−	0.782928i	$-0.286275\pi$
$769$	−872.027	−	731.718i	−0.0408922	−	0.0343126i	−0.663005	+	0.748615i	$0.730719\pi$
$770$		0			0
$771$	−1513.28	−	15076.8i	−0.0706865	−	0.704250i
$772$		0			0
$773$	20299.3	−	35159.4i	0.944521	−	1.63596i	0.187814	−	0.982205i	$-0.439860\pi$
$773$	20299.3	−	35159.4i	0.944521	−	1.63596i	0.756707	−	0.653754i	$-0.226807\pi$
$774$		0			0
$775$	949.716	+	1644.96i	0.0440191	+	0.0762434i
$776$		0			0
$777$	1342.25	+	2785.05i	0.0619730	+	0.128589i
$778$		0			0
$779$	6485.62	−	36781.8i	0.298295	−	1.69171i
$780$		0			0
$781$	6214.87	−	5214.89i	0.284744	−	0.238929i
$782$		0			0
$783$	−1544.97	+	31532.6i	−0.0705144	+	1.43919i
$784$		0			0
$785$	−17303.8	+	14519.6i	−0.786750	+	0.660161i
$786$		0			0
$787$	4660.94	−	26433.5i	0.211111	−	1.19727i	−0.676418	−	0.736518i	$-0.736469\pi$
$787$	4660.94	−	26433.5i	0.211111	−	1.19727i	0.887529	−	0.460752i	$-0.152420\pi$
$788$		0			0
$789$	−4562.75	+	6696.69i	−0.205879	+	0.302165i
$790$		0			0
$791$	891.499	+	1544.12i	0.0400734	+	0.0694091i
$792$		0			0
$793$	−12465.3	+	21590.5i	−0.558204	+	0.966838i
$794$		0			0
$795$	−7955.67	−	3586.83i	−0.354916	−	0.160015i
$796$		0			0
$797$	−23016.9	−	19313.5i	−1.02296	−	0.858368i	−0.0329662	−	0.999456i	$-0.510495\pi$
$797$	−23016.9	−	19313.5i	−1.02296	−	0.858368i	−0.989997	+	0.141088i	$0.954940\pi$
$798$		0			0
$799$	988.525	+	359.794i	0.0437691	+	0.0159306i
$800$		0			0
$801$	−26627.3	+	16293.8i	−1.17457	+	0.718744i
$802$		0			0
$803$	−1152.79	−	6537.81i	−0.0506615	−	0.287315i
$804$		0			0
$805$	−1312.93	+	477.866i	−0.0574839	+	0.0209224i
$806$		0			0
$807$	26535.1	+	25865.9i	1.15747	+	1.12828i
$808$		0			0
$809$	21235.4			0.922865			0.461432	−	0.887175i	$-0.347336\pi$
$809$	21235.4			0.922865			0.461432	+	0.887175i	$0.347336\pi$
$810$		0			0
$811$	16153.8			0.699427			0.349714	−	0.936857i	$-0.386279\pi$
$811$	16153.8			0.699427			0.349714	+	0.936857i	$0.386279\pi$
$812$		0			0
$813$	−20655.7	−	20134.7i	−0.891053	−	0.868581i
$814$		0			0
$815$	20172.4	−	7342.15i	0.867004	−	0.315564i
$816$		0			0
$817$	4898.61	+	27781.4i	0.209768	+	1.18965i
$818$		0			0
$819$	−9818.78	−	5339.31i	−0.418921	−	0.227803i
$820$		0			0
$821$	20735.6	+	7547.15i	0.881459	+	0.320825i	0.742798	−	0.669515i	$-0.233498\pi$
$821$	20735.6	+	7547.15i	0.881459	+	0.320825i	0.138661	+	0.990340i	$0.455720\pi$
$822$		0			0
$823$	−12610.1	−	10581.1i	−0.534094	−	0.448158i	0.335418	−	0.942069i	$-0.391122\pi$
$823$	−12610.1	−	10581.1i	−0.534094	−	0.448158i	−0.869512	+	0.493911i	$0.835567\pi$
$824$		0			0
$825$	5342.72	+	2408.78i	0.225466	+	0.101652i
$826$		0			0
$827$	3411.08	−	5908.16i	0.143428	−	0.248424i	−0.785357	−	0.619043i	$-0.787521\pi$
$827$	3411.08	−	5908.16i	0.143428	−	0.248424i	0.928785	+	0.370618i	$0.120854\pi$
$828$		0			0
$829$	−16850.1	−	29185.1i	−0.705943	−	1.22273i	−0.966350	−	0.257230i	$-0.917190\pi$
$829$	−16850.1	−	29185.1i	−0.705943	−	1.22273i	0.260408	−	0.965499i	$-0.416143\pi$
$830$		0			0
$831$	11470.5	−	16835.1i	0.478829	−	0.702771i
$832$		0			0
$833$	−2907.66	+	16490.2i	−0.120942	+	0.685894i
$834$		0			0
$835$	−4941.92	+	4146.76i	−0.204817	+	0.171862i
$836$		0			0
$837$	−2089.28	−	2753.03i	−0.0862797	−	0.113690i
$838$		0			0
$839$	−17763.1	+	14905.0i	−0.730931	+	0.613324i	−0.930385	−	0.366583i	$-0.880527\pi$
$839$	−17763.1	+	14905.0i	−0.730931	+	0.613324i	0.199454	+	0.979907i	$0.436083\pi$
$840$		0			0
$841$	4557.96	−	25849.5i	0.186886	−	1.05988i
$842$		0			0
$843$	12428.0	+	25787.1i	0.507764	+	1.05356i
$844$		0			0
$845$	−2253.88	−	3903.83i	−0.0917582	−	0.158930i
$846$		0			0
$847$	4331.97	−	7503.20i	0.175736	−	0.304384i
$848$		0			0
$849$	652.286	+	6498.73i	0.0263680	+	0.262704i
$850$		0			0
$851$	1529.60	+	1283.48i	0.0616144	+	0.0517007i
$852$		0			0
$853$	−27893.1	−	10152.3i	−1.11963	−	0.407511i	−0.285111	−	0.958495i	$-0.592030\pi$
$853$	−27893.1	−	10152.3i	−1.11963	−	0.407511i	−0.834516	+	0.550984i	$0.814253\pi$
$854$		0			0
$855$	10916.9	−	13706.3i	0.436665	−	0.548242i
$856$		0			0
$857$	−1789.08	−	10146.4i	−0.0713114	−	0.404427i	−0.999479	−	0.0322654i	$-0.989728\pi$
$857$	−1789.08	−	10146.4i	−0.0713114	−	0.404427i	0.928168	−	0.372162i	$-0.121383\pi$
$858$		0			0
$859$	−955.259	+	347.686i	−0.0379430	+	0.0138101i	−0.360922	−	0.932596i	$-0.617538\pi$
$859$	−955.259	+	347.686i	−0.0379430	+	0.0138101i	0.322979	+	0.946406i	$0.395316\pi$
$860$		0			0
$861$	−15450.3	+	4352.09i	−0.611550	+	0.172264i
$862$		0			0
$863$	43831.8			1.72891			0.864456	−	0.502709i	$-0.167663\pi$
$863$	43831.8			1.72891			0.864456	+	0.502709i	$0.167663\pi$
$864$		0			0
$865$	−21752.1			−0.855023
$866$		0			0
$867$	1803.46	−	7091.61i	0.0706443	−	0.277790i
$868$		0			0
$869$	−9640.83	+	3508.97i	−0.376344	+	0.136978i
$870$		0			0
$871$	4032.38	+	22868.7i	0.156868	+	0.889642i
$872$		0			0
$873$	−12680.7	+	37818.0i	−0.491610	+	1.46615i
$874$		0			0
$875$	10194.2	+	3710.39i	0.393860	+	0.143353i
$876$		0			0
$877$	6970.64	+	5849.06i	0.268394	+	0.225210i	0.767045	−	0.641594i	$-0.221726\pi$
$877$	6970.64	+	5849.06i	0.268394	+	0.225210i	−0.498650	+	0.866803i	$0.666171\pi$
$878$		0			0
$879$	29340.0	−	21107.5i	1.12584	−	0.809941i
$880$		0			0
$881$	−17753.9	+	30750.6i	−0.678937	+	1.17595i	0.296365	+	0.955075i	$0.404226\pi$
$881$	−17753.9	+	30750.6i	−0.678937	+	1.17595i	−0.975301	+	0.220878i	$0.929108\pi$
$882$		0			0
$883$	−23165.8	−	40124.3i	−0.882889	−	1.52921i	−0.848114	−	0.529814i	$-0.822262\pi$
$883$	−23165.8	−	40124.3i	−0.882889	−	1.52921i	−0.0347750	−	0.999395i	$-0.511071\pi$
$884$		0			0
$885$	−8066.19	−	602.017i	−0.306375	−	0.0228662i
$886$		0			0
$887$	3331.76	−	18895.3i	0.126121	−	0.715268i	−0.854515	−	0.519427i	$-0.826145\pi$
$887$	3331.76	−	18895.3i	0.126121	−	0.715268i	0.980636	−	0.195841i	$-0.0627436\pi$
$888$		0			0
$889$	10978.2	−	9211.82i	0.414171	−	0.347530i
$890$		0			0
$891$	−10193.5	−	3130.76i	−0.383273	−	0.117715i
$892$		0			0
$893$	1276.50	−	1071.11i	0.0478348	−	0.0401382i
$894$		0			0
$895$	−3584.46	+	20328.5i	−0.133872	+	0.759224i
$896$		0			0
$897$	−7198.46	−	537.255i	−0.267948	−	0.0199982i
$898$		0			0
$899$	2771.65	+	4800.64i	0.102825	+	0.178098i
$900$		0			0
$901$	7183.51	−	12442.2i	0.265613	−	0.460056i
$902$		0			0
$903$	9841.60	−	7080.16i	0.362689	−	0.260922i
$904$		0			0
$905$	5042.75	+	4231.37i	0.185223	+	0.155420i
$906$		0			0
$907$	−2377.37	−	865.291i	−0.0870333	−	0.0316775i	0.298137	−	0.954523i	$-0.403635\pi$
$907$	−2377.37	−	865.291i	−0.0870333	−	0.0316775i	−0.385170	+	0.922846i	$0.625857\pi$
$908$		0			0
$909$	−43571.1	+	8835.59i	−1.58984	+	0.322396i
$910$		0			0
$911$	2356.17	+	13362.5i	0.0856898	+	0.485971i	0.997206	+	0.0747059i	$0.0238018\pi$
$911$	2356.17	+	13362.5i	0.0856898	+	0.485971i	−0.911516	+	0.411265i	$0.865087\pi$
$912$		0			0
$913$	−7674.38	+	2793.25i	−0.278187	+	0.101252i
$914$		0			0
$915$	−4140.08	+	16279.8i	−0.149581	+	0.588189i
$916$		0			0
$917$	20676.0			0.744583
$918$		0			0
$919$	−34243.4			−1.22915			−0.614574	−	0.788859i	$-0.710672\pi$
$919$	−34243.4			−1.22915			−0.614574	+	0.788859i	$0.710672\pi$
$920$		0			0
$921$	−13196.9	+	3717.35i	−0.472152	+	0.132998i
$922$		0			0
$923$	27815.7	−	10124.1i	0.991943	−	0.361038i
$924$		0			0
$925$	−1027.11	−	5825.03i	−0.0365093	−	0.207055i
$926$		0			0
$927$	5205.30	+	13239.3i	0.184428	+	0.469077i
$928$		0			0
$929$	6133.04	+	2232.25i	0.216597	+	0.0788349i	0.448040	−	0.894014i	$-0.352122\pi$
$929$	6133.04	+	2232.25i	0.216597	+	0.0788349i	−0.231443	+	0.972849i	$0.574345\pi$
$930$		0			0
$931$	20318.5	+	17049.3i	0.715267	+	0.600180i
$932$		0			0
$933$	3001.81	+	29907.0i	0.105332	+	1.04942i
$934$		0			0
$935$	2996.48	−	5190.05i	0.104808	−	0.181533i
$936$		0			0
$937$	−4402.77	−	7625.83i	−0.153503	−	0.265875i	0.779010	−	0.627012i	$-0.215722\pi$
$937$	−4402.77	−	7625.83i	−0.153503	−	0.265875i	−0.932513	+	0.361137i	$0.882389\pi$
$938$		0			0
$939$	4156.83	+	8625.06i	0.144465	+	0.299753i
$940$		0			0
$941$	−7494.30	+	42502.3i	−0.259625	+	1.47241i	0.524291	+	0.851539i	$0.324331\pi$
$941$	−7494.30	+	42502.3i	−0.259625	+	1.47241i	−0.783916	+	0.620867i	$0.786781\pi$
$942$		0			0
$943$	−7941.57	+	6663.77i	−0.274245	+	0.230119i
$944$		0			0
$945$	−7343.38	−	1669.05i	−0.252783	−	0.0574543i
$946$		0			0
$947$	5003.21	−	4198.19i	0.171682	−	0.144058i	−0.552898	−	0.833249i	$-0.686478\pi$
$947$	5003.21	−	4198.19i	0.171682	−	0.144058i	0.724580	+	0.689191i	$0.242034\pi$
$948$		0			0
$949$	4206.07	−	23853.8i	0.143872	−	0.815941i
$950$		0			0
$951$	−1210.91	+	1777.24i	−0.0412898	+	0.0606005i
$952$		0			0
$953$	573.765	+	993.790i	0.0195027	+	0.0337797i	0.875612	−	0.483015i	$-0.160458\pi$
$953$	573.765	+	993.790i	0.0195027	+	0.0337797i	−0.856109	+	0.516795i	$0.827125\pi$
$954$		0			0
$955$	9367.74	−	16225.4i	0.317417	−	0.549782i
$956$		0			0
$957$	15592.2	+	7029.78i	0.526671	+	0.237451i
$958$		0			0
$959$	−1168.31	−	980.324i	−0.0393395	−	0.0330097i
$960$		0			0
$961$	27424.1	+	9981.57i	0.920551	+	0.335053i
$962$		0			0
$963$	1377.57	+	53926.6i	0.0460973	+	1.80453i
$964$		0			0
$965$	5137.81	+	29138.0i	0.171391	+	0.972004i
$966$		0			0
$967$	−4869.23	+	1772.25i	−0.161927	+	0.0589368i	−0.421712	−	0.906730i	$-0.638571\pi$
$967$	−4869.23	+	1772.25i	−0.161927	+	0.0589368i	0.259785	+	0.965667i	$0.416348\pi$
$968$		0			0
$969$	20657.1	+	20136.1i	0.684830	+	0.667559i
$970$		0			0
$971$	59813.0			1.97682			0.988409	−	0.151812i	$-0.0485108\pi$
$971$	59813.0			1.97682			0.988409	+	0.151812i	$0.0485108\pi$
$972$		0			0
$973$	10561.1			0.347969
$974$		0			0
$975$	15311.9	+	14925.8i	0.502948	+	0.490264i
$976$		0			0
$977$	17492.6	−	6366.79i	0.572813	−	0.208487i	−0.0393403	−	0.999226i	$-0.512526\pi$
$977$	17492.6	−	6366.79i	0.572813	−	0.208487i	0.612154	+	0.790739i	$0.290303\pi$
$978$		0			0
$979$	2936.77	+	16655.3i	0.0958730	+	0.543723i
$980$		0			0
$981$	−874.894	−	34248.7i	−0.0284742	−	1.11466i
$982$		0			0
$983$	2809.40	+	1022.54i	0.0911555	+	0.0331779i	0.387195	−	0.921998i	$-0.373444\pi$
$983$	2809.40	+	1022.54i	0.0911555	+	0.0331779i	−0.296040	+	0.955176i	$0.595666\pi$
$984$		0			0
$985$	−24175.3	−	20285.4i	−0.782018	−	0.656191i
$986$		0			0
$987$	−652.862	−	294.344i	−0.0210545	−	0.00949249i
$988$		0			0
$989$	3915.10	−	6781.15i	0.125878	−	0.218026i
$990$		0			0
$991$	11105.6	+	19235.4i	0.355984	+	0.616583i	0.987286	−	0.158954i	$-0.0508123\pi$
$991$	11105.6	+	19235.4i	0.355984	+	0.616583i	−0.631302	+	0.775537i	$0.717479\pi$
$992$		0			0
$993$	−24246.7	+	35586.6i	−0.774870	+	1.13727i
$994$		0			0
$995$	3740.80	−	21215.1i	0.119187	−	0.675944i
$996$		0			0
$997$	−17248.2	+	14473.0i	−0.547901	+	0.459744i	−0.874230	−	0.485513i	$-0.838633\pi$
$997$	−17248.2	+	14473.0i	−0.547901	+	0.459744i	0.326328	+	0.945256i	$0.394188\pi$
$998$		0			0
$999$	3181.58	+	10281.2i	0.100761	+	0.325608i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	108.4.i.a.49.3	✓	54
3.2	odd	2		324.4.i.a.37.7		54
27.11	odd	18		324.4.i.a.289.7		54
27.16	even	9	inner	108.4.i.a.97.3	yes	54

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.4.i.a.49.3	✓	54	1.1	even	1	trivial
108.4.i.a.97.3	yes	54	27.16	even	9	inner
324.4.i.a.37.7		54	3.2	odd	2
324.4.i.a.289.7		54	27.11	odd	18

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:	\( N \)	\(=\)	\( 108 = 2^{2} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	108.i (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.72085 - 3.62702i) q^{3} +(-6.50317 + 2.36696i) q^{5} +(1.34685 + 7.63837i) q^{7} +(0.689498 + 26.9912i) q^{9} +O(q^{10})\)	\(q+(-3.72085 - 3.62702i) q^{3} +(-6.50317 + 2.36696i) q^{5} +(1.34685 + 7.63837i) q^{7} +(0.689498 + 26.9912i) q^{9} +(13.7454 + 5.00292i) q^{11} +(40.8838 + 34.3056i) q^{13} +(32.7823 + 14.7800i) q^{15} +(-29.6006 + 51.2697i) q^{17} +(46.8884 + 81.2131i) q^{19} +(22.6931 - 33.3063i) q^{21} +(4.51998 - 25.6341i) q^{23} +(-59.0669 + 49.5630i) q^{25} +(95.3320 - 102.931i) q^{27} +(-172.381 + 144.645i) q^{29} +(4.27764 - 24.2597i) q^{31} +(-32.9990 - 68.4700i) q^{33} +(-26.8385 - 46.4856i) q^{35} +(-38.3554 + 66.4335i) q^{37} +(-27.6957 - 275.932i) q^{39} +(-305.098 - 256.008i) q^{41} +(282.678 + 102.886i) q^{43} +(-68.3710 - 173.896i) q^{45} +(-3.08562 - 17.4994i) q^{47} +(265.784 - 96.7374i) q^{49} +(296.096 - 83.4053i) q^{51} -242.682 q^{53} -101.230 q^{55} +(120.096 - 472.247i) q^{57} +(-211.368 + 76.9317i) q^{59} +(81.1159 + 460.031i) q^{61} +(-205.240 + 41.6197i) q^{63} +(-347.074 - 126.325i) q^{65} +(333.309 + 279.680i) q^{67} +(-109.793 + 78.9866i) q^{69} +(277.317 - 480.327i) q^{71} +(-226.923 - 393.043i) q^{73} +(399.545 + 29.8199i) q^{75} +(-19.7011 + 111.731i) q^{77} +(-537.292 + 450.842i) q^{79} +(-728.049 + 37.2208i) q^{81} +(-427.701 + 358.883i) q^{83} +(71.1442 - 403.479i) q^{85} +(1166.03 + 87.0265i) q^{87} +(578.094 + 1001.29i) q^{89} +(-206.974 + 358.490i) q^{91} +(-103.907 + 74.7517i) q^{93} +(-497.151 - 417.160i) q^{95} +(1388.22 + 505.270i) q^{97} +(-125.557 + 374.455i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 54 q + 12 q^{5} - 48 q^{9}+O(q^{10}) \) 54 * q + 12 * q^5 - 48 * q^9	\( 54 q + 12 q^{5} - 48 q^{9} - 87 q^{11} + 234 q^{15} + 204 q^{17} - 12 q^{21} + 96 q^{23} - 216 q^{25} + 27 q^{27} + 318 q^{29} - 54 q^{31} + 63 q^{33} + 6 q^{35} + 66 q^{39} + 867 q^{41} - 513 q^{43} - 306 q^{45} - 1548 q^{47} + 594 q^{49} - 1368 q^{51} - 1068 q^{53} - 1269 q^{57} - 1218 q^{59} - 54 q^{61} + 30 q^{63} + 96 q^{65} - 2997 q^{67} + 1476 q^{69} - 120 q^{71} - 216 q^{73} + 732 q^{75} + 3480 q^{77} + 2808 q^{79} + 3348 q^{81} + 4464 q^{83} + 2160 q^{85} + 4824 q^{87} + 4029 q^{89} + 270 q^{91} + 1164 q^{93} - 1650 q^{95} - 3483 q^{97} - 5076 q^{99}+O(q^{100}) \) 54 * q + 12 * q^5 - 48 * q^9 - 87 * q^11 + 234 * q^15 + 204 * q^17 - 12 * q^21 + 96 * q^23 - 216 * q^25 + 27 * q^27 + 318 * q^29 - 54 * q^31 + 63 * q^33 + 6 * q^35 + 66 * q^39 + 867 * q^41 - 513 * q^43 - 306 * q^45 - 1548 * q^47 + 594 * q^49 - 1368 * q^51 - 1068 * q^53 - 1269 * q^57 - 1218 * q^59 - 54 * q^61 + 30 * q^63 + 96 * q^65 - 2997 * q^67 + 1476 * q^69 - 120 * q^71 - 216 * q^73 + 732 * q^75 + 3480 * q^77 + 2808 * q^79 + 3348 * q^81 + 4464 * q^83 + 2160 * q^85 + 4824 * q^87 + 4029 * q^89 + 270 * q^91 + 1164 * q^93 - 1650 * q^95 - 3483 * q^97 - 5076 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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