LMFDB - Embedded newform 324.3.o.a.5.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [324,3,Mod(5,324)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(324, base_ring=CyclotomicField(54))

chi = DirichletCharacter(H, H._module([0, 23]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("324.5");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 324 = 2^{2} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	324.o (of order $54$, degree $18$, 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:	$8.82836056527$
Analytic rank:	$0$
Dimension:	$324$
Relative dimension:	$18$ over $\Q(\zeta_{54})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{54}]$

Embedding invariants

Embedding label			5.17
Character	$\chi$	$=$	324.5
Dual form			324.3.o.a.65.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.94286 + 0.582717i) q^{3} +(5.13522 - 3.82303i) q^{5} +(3.31229 - 2.17853i) q^{7} +(8.32088 + 3.42971i) q^{9} +O(q^{10})$	\(q+(2.94286 + 0.582717i) q^{3} +(5.13522 - 3.82303i) q^{5} +(3.31229 - 2.17853i) q^{7} +(8.32088 + 3.42971i) q^{9} +(-0.480652 + 4.11224i) q^{11} +(-0.145678 - 0.486597i) q^{13} +(17.3400 - 8.25827i) q^{15} +(-19.6534 - 3.46543i) q^{17} +(-2.04833 - 11.6166i) q^{19} +(11.0171 - 4.48098i) q^{21} +(8.81970 - 13.4097i) q^{23} +(4.58486 - 15.3145i) q^{25} +(22.4887 + 14.9419i) q^{27} +(-10.8795 + 10.2643i) q^{29} +(-1.57896 + 27.1097i) q^{31} +(-3.81077 + 11.8217i) q^{33} +(8.68077 - 23.8502i) q^{35} +(11.6418 - 4.23727i) q^{37} +(-0.145161 - 1.51688i) q^{39} +(1.01794 - 4.29502i) q^{41} +(21.3640 + 49.5273i) q^{43} +(55.8415 - 14.1987i) q^{45} +(25.7996 - 1.50266i) q^{47} +(-13.1826 + 30.5607i) q^{49} +(-55.8180 - 21.6507i) q^{51} +(-5.12718 - 2.96018i) q^{53} +(13.2530 + 22.9548i) q^{55} +(0.741268 - 35.3798i) q^{57} +(-8.92774 - 76.3817i) q^{59} +(-13.5091 - 6.78452i) q^{61} +(35.0329 - 6.76707i) q^{63} +(-2.60836 - 1.94185i) q^{65} +(-68.4316 + 72.5333i) q^{67} +(33.7692 - 34.3235i) q^{69} +(5.41579 - 6.45429i) q^{71} +(-24.0192 + 20.1545i) q^{73} +(22.4166 - 42.3968i) q^{75} +(7.36658 + 14.6681i) q^{77} +(50.9936 - 12.0857i) q^{79} +(57.4741 + 57.0765i) q^{81} +(-14.7516 - 62.2420i) q^{83} +(-114.173 + 57.3399i) q^{85} +(-37.9982 + 23.8668i) q^{87} +(-108.213 - 128.963i) q^{89} +(-1.54259 - 1.29439i) q^{91} +(-20.4439 + 78.8599i) q^{93} +(-54.9294 - 51.8232i) q^{95} +(-42.4611 + 57.0351i) q^{97} +(-18.1033 + 32.5690i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 324 q+O(q^{10}) $ 324 * q	$ 324 q - 135 q^{21} - 81 q^{23} + 27 q^{27} + 81 q^{29} + 189 q^{33} + 243 q^{35} + 216 q^{41} + 432 q^{45} + 324 q^{47} + 126 q^{51} - 216 q^{57} - 378 q^{59} - 540 q^{63} - 108 q^{65} - 351 q^{67} + 504 q^{69} + 648 q^{71} + 450 q^{75} + 432 q^{77} - 54 q^{79} - 72 q^{81} - 216 q^{83} + 270 q^{85} - 1008 q^{87} - 648 q^{89} - 684 q^{93} - 432 q^{95} + 459 q^{97} - 252 q^{99}+O(q^{100}) $ 324 * q - 135 * q^21 - 81 * q^23 + 27 * q^27 + 81 * q^29 + 189 * q^33 + 243 * q^35 + 216 * q^41 + 432 * q^45 + 324 * q^47 + 126 * q^51 - 216 * q^57 - 378 * q^59 - 540 * q^63 - 108 * q^65 - 351 * q^67 + 504 * q^69 + 648 * q^71 + 450 * q^75 + 432 * q^77 - 54 * q^79 - 72 * q^81 - 216 * q^83 + 270 * q^85 - 1008 * q^87 - 648 * q^89 - 684 * q^93 - 432 * q^95 + 459 * q^97 - 252 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/324\mathbb{Z}\right)^\times$.

$n$	$163$	$245$
$\chi(n)$	$1$	$e\left(\frac{23}{54}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	2.94286	+	0.582717i	0.980954	+	0.194239i
$3$	2.94286	+	0.582717i	0.980954	+	0.194239i
$4$		0			0
$5$	5.13522	−	3.82303i	1.02704	−	0.764606i	0.0547818	−	0.998498i	$-0.482554\pi$
$5$	5.13522	−	3.82303i	1.02704	−	0.764606i	0.972263	+	0.233892i	$0.0751463\pi$
$6$		0			0
$7$	3.31229	−	2.17853i	0.473185	−	0.311218i	−0.290424	−	0.956898i	$-0.593796\pi$
$7$	3.31229	−	2.17853i	0.473185	−	0.311218i	0.763608	+	0.645680i	$0.223426\pi$
$8$		0			0
$9$	8.32088	+	3.42971i	0.924542	+	0.381079i
$10$		0			0
$11$	−0.480652	+	4.11224i	−0.0436956	+	0.373840i	0.953643	+	0.300939i	$0.0972999\pi$
$11$	−0.480652	+	4.11224i	−0.0436956	+	0.373840i	−0.997339	+	0.0729015i	$0.976774\pi$
$12$		0			0
$13$	−0.145678	−	0.486597i	−0.0112060	−	0.0374305i	0.952204	−	0.305464i	$-0.0988115\pi$
$13$	−0.145678	−	0.486597i	−0.0112060	−	0.0374305i	−0.963410	+	0.268033i	$0.913626\pi$
$14$		0			0
$15$	17.3400	−	8.25827i	1.15600	−	0.550552i
$16$		0			0
$17$	−19.6534	−	3.46543i	−1.15608	−	0.203849i	−0.437454	−	0.899241i	$-0.644120\pi$
$17$	−19.6534	−	3.46543i	−1.15608	−	0.203849i	−0.718631	+	0.695392i	$0.755231\pi$
$18$		0			0
$19$	−2.04833	−	11.6166i	−0.107807	−	0.611402i	−0.990062	−	0.140631i	$-0.955087\pi$
$19$	−2.04833	−	11.6166i	−0.107807	−	0.611402i	0.882255	−	0.470771i	$-0.156024\pi$
$20$		0			0
$21$	11.0171	−	4.48098i	0.524623	−	0.213380i
$22$		0			0
$23$	8.81970	−	13.4097i	0.383465	−	0.583030i	−0.591248	−	0.806490i	$-0.701365\pi$
$23$	8.81970	−	13.4097i	0.383465	−	0.583030i	0.974713	+	0.223459i	$0.0717350\pi$
$24$		0			0
$25$	4.58486	−	15.3145i	0.183394	−	0.612580i
$26$		0			0
$27$	22.4887	+	14.9419i	0.832913	+	0.553403i
$28$		0			0
$29$	−10.8795	+	10.2643i	−0.375157	+	0.353942i	−0.850608	−	0.525800i	$-0.823766\pi$
$29$	−10.8795	+	10.2643i	−0.375157	+	0.353942i	0.475452	+	0.879742i	$0.342285\pi$
$30$		0			0
$31$	−1.57896	+	27.1097i	−0.0509341	+	0.874505i	0.871990	+	0.489524i	$0.162829\pi$
$31$	−1.57896	+	27.1097i	−0.0509341	+	0.874505i	−0.922924	+	0.384982i	$0.874208\pi$
$32$		0			0
$33$	−3.81077	+	11.8217i	−0.115478	+	0.358233i
$34$		0			0
$35$	8.68077	−	23.8502i	0.248022	−	0.681435i
$36$		0			0
$37$	11.6418	−	4.23727i	0.314644	−	0.114521i	−0.179871	−	0.983690i	$-0.557568\pi$
$37$	11.6418	−	4.23727i	0.314644	−	0.114521i	0.494515	+	0.869169i	$0.335346\pi$
$38$		0			0
$39$	−0.145161	−	1.51688i	−0.00372207	−	0.0388943i
$40$		0			0
$41$	1.01794	−	4.29502i	0.0248278	−	0.104757i	−0.959220	−	0.282660i	$-0.908783\pi$
$41$	1.01794	−	4.29502i	0.0248278	−	0.104757i	0.984048	+	0.177903i	$0.0569314\pi$
$42$		0			0
$43$	21.3640	+	49.5273i	0.496837	+	1.15180i	0.963584	+	0.267407i	$0.0861667\pi$
$43$	21.3640	+	49.5273i	0.496837	+	1.15180i	−0.466747	+	0.884391i	$0.654574\pi$
$44$		0			0
$45$	55.8415	−	14.1987i	1.24092	−	0.315526i
$46$		0			0
$47$	25.7996	−	1.50266i	0.548929	−	0.0319715i	0.218560	−	0.975823i	$-0.429864\pi$
$47$	25.7996	−	1.50266i	0.548929	−	0.0319715i	0.330369	+	0.943852i	$0.392827\pi$
$48$		0			0
$49$	−13.1826	+	30.5607i	−0.269033	+	0.623689i
$50$		0			0
$51$	−55.8180	−	21.6507i	−1.09447	−	0.424523i
$52$		0			0
$53$	−5.12718	−	2.96018i	−0.0967393	−	0.0558524i	0.450850	−	0.892600i	$-0.351121\pi$
$53$	−5.12718	−	2.96018i	−0.0967393	−	0.0558524i	−0.547589	+	0.836747i	$0.684454\pi$
$54$		0			0
$55$	13.2530	+	22.9548i	0.240963	+	0.417360i
$56$		0			0
$57$	0.741268	−	35.3798i	0.0130047	−	0.620698i
$58$		0			0
$59$	−8.92774	−	76.3817i	−0.151318	−	1.29460i	−0.828999	−	0.559249i	$-0.811089\pi$
$59$	−8.92774	−	76.3817i	−0.151318	−	1.29460i	0.677682	−	0.735355i	$-0.262985\pi$
$60$		0			0
$61$	−13.5091	−	6.78452i	−0.221460	−	0.111222i	0.334610	−	0.942357i	$-0.391395\pi$
$61$	−13.5091	−	6.78452i	−0.221460	−	0.111222i	−0.556071	+	0.831135i	$0.687692\pi$
$62$		0			0
$63$	35.0329	−	6.76707i	0.556078	−	0.107414i
$64$		0			0
$65$	−2.60836	−	1.94185i	−0.0401286	−	0.0298747i
$66$		0			0
$67$	−68.4316	+	72.5333i	−1.02137	+	1.08259i	−0.0248087	+	0.999692i	$0.507898\pi$
$67$	−68.4316	+	72.5333i	−1.02137	+	1.08259i	−0.996558	+	0.0828936i	$0.973584\pi$
$68$		0			0
$69$	33.7692	−	34.3235i	0.489409	−	0.497442i
$70$		0			0
$71$	5.41579	−	6.45429i	0.0762788	−	0.0909055i	−0.726555	−	0.687108i	$-0.758880\pi$
$71$	5.41579	−	6.45429i	0.0762788	−	0.0909055i	0.802834	+	0.596202i	$0.203324\pi$
$72$		0			0
$73$	−24.0192	+	20.1545i	−0.329031	+	0.276089i	−0.792305	−	0.610126i	$-0.791119\pi$
$73$	−24.0192	+	20.1545i	−0.329031	+	0.276089i	0.463274	+	0.886215i	$0.346675\pi$
$74$		0			0
$75$	22.4166	−	42.3968i	0.298888	−	0.565290i
$76$		0			0
$77$	7.36658	+	14.6681i	0.0956698	+	0.190494i
$78$		0			0
$79$	50.9936	−	12.0857i	0.645488	−	0.152983i	0.105183	−	0.994453i	$-0.466457\pi$
$79$	50.9936	−	12.0857i	0.645488	−	0.152983i	0.540305	+	0.841469i	$0.318309\pi$
$80$		0			0
$81$	57.4741	+	57.0765i	0.709557	+	0.704648i
$82$		0			0
$83$	−14.7516	−	62.2420i	−0.177730	−	0.749904i	−0.986767	−	0.162145i	$-0.948159\pi$
$83$	−14.7516	−	62.2420i	−0.177730	−	0.749904i	0.809036	−	0.587758i	$-0.199989\pi$
$84$		0			0
$85$	−114.173	+	57.3399i	−1.34321	+	0.674588i
$86$		0			0
$87$	−37.9982	+	23.8668i	−0.436761	+	0.274331i
$88$		0			0
$89$	−108.213	−	128.963i	−1.21587	−	1.44902i	−0.856751	−	0.515730i	$-0.827521\pi$
$89$	−108.213	−	128.963i	−1.21587	−	1.44902i	−0.359122	−	0.933291i	$-0.616924\pi$
$90$		0			0
$91$	−1.54259	−	1.29439i	−0.0169516	−	0.0142240i
$92$		0			0
$93$	−20.4439	+	78.8599i	−0.219827	+	0.847956i
$94$		0			0
$95$	−54.9294	−	51.8232i	−0.578204	−	0.545508i
$96$		0			0
$97$	−42.4611	+	57.0351i	−0.437743	+	0.587991i	−0.965175	−	0.261607i	$-0.915748\pi$
$97$	−42.4611	+	57.0351i	−0.437743	+	0.587991i	0.527432	+	0.849597i	$0.323155\pi$
$98$		0			0
$99$	−18.1033	+	32.5690i	−0.182861	+	0.328980i
$100$		0			0
$101$	−74.6109	+	148.563i	−0.738722	+	1.47092i	0.138261	+	0.990396i	$0.455849\pi$
$101$	−74.6109	+	148.563i	−0.738722	+	1.47092i	−0.876983	+	0.480521i	$0.840448\pi$
$102$		0			0
$103$	20.3945	−	2.38378i	0.198005	−	0.0231435i	−0.0165122	−	0.999864i	$-0.505256\pi$
$103$	20.3945	−	2.38378i	0.198005	−	0.0231435i	0.214517	+	0.976720i	$0.431182\pi$
$104$		0			0
$105$	39.4443	−	65.1295i	0.375660	−	0.620281i
$106$		0			0
$107$	87.2888	−	50.3962i	0.815783	−	0.470992i	−0.0331773	−	0.999449i	$-0.510563\pi$
$107$	87.2888	−	50.3962i	0.815783	−	0.470992i	0.848960	+	0.528457i	$0.177229\pi$
$108$		0			0
$109$	−107.068	+	185.447i	−0.982273	+	1.70135i	−0.328797	+	0.944401i	$0.606643\pi$
$109$	−107.068	+	185.447i	−0.982273	+	1.70135i	−0.653477	+	0.756947i	$0.726690\pi$
$110$		0			0
$111$	36.7294	−	5.68583i	0.330895	−	0.0512237i
$112$		0			0
$113$	−113.758	−	49.0703i	−1.00671	−	0.434250i	−0.172089	−	0.985081i	$-0.555052\pi$
$113$	−113.758	−	49.0703i	−1.00671	−	0.434250i	−0.834617	+	0.550831i	$0.814311\pi$
$114$		0			0
$115$	−5.97459	−	102.580i	−0.0519530	−	0.891998i
$116$		0			0
$117$	0.456722	−	4.54855i	0.00390360	−	0.0388765i
$118$		0			0
$119$	−72.6475	+	31.3371i	−0.610483	+	0.263337i
$120$		0			0
$121$	101.059	+	23.9514i	0.835198	+	0.197945i
$122$		0			0
$123$	5.49843	−	12.0465i	0.0447027	−	0.0979388i
$124$		0			0
$125$	19.7371	+	54.2273i	0.157897	+	0.433819i
$126$		0			0
$127$	−12.1409	−	4.41892i	−0.0955974	−	0.0347946i	0.293779	−	0.955873i	$-0.405087\pi$
$127$	−12.1409	−	4.41892i	−0.0955974	−	0.0347946i	−0.389376	+	0.921079i	$0.627309\pi$
$128$		0			0
$129$	34.0109	+	158.201i	0.263650	+	1.22637i
$130$		0			0
$131$	−95.9762	−	5.58998i	−0.732643	−	0.0426716i	−0.312233	−	0.950006i	$-0.601077\pi$
$131$	−95.9762	−	5.58998i	−0.732643	−	0.0426716i	−0.420410	+	0.907334i	$0.638114\pi$
$132$		0			0
$133$	−32.0918	−	34.0154i	−0.241292	−	0.255755i
$134$		0			0
$135$	172.608	−	9.24492i	1.27857	−	0.0684809i
$136$		0			0
$137$	−53.9684	−	16.1571i	−0.393930	−	0.117935i	0.0837109	−	0.996490i	$-0.473323\pi$
$137$	−53.9684	−	16.1571i	−0.393930	−	0.117935i	−0.477641	+	0.878555i	$0.658508\pi$
$138$		0			0
$139$	−166.507	−	109.514i	−1.19790	−	0.787868i	−0.215834	−	0.976430i	$-0.569247\pi$
$139$	−166.507	−	109.514i	−1.19790	−	0.787868i	−0.982061	+	0.188562i	$0.939617\pi$
$140$		0			0
$141$	76.8004	+	10.6118i	0.544684	+	0.0752608i
$142$		0			0
$143$	2.07102	−	0.365177i	0.0144827	−	0.00255369i
$144$		0			0
$145$	−16.6281	+	94.3024i	−0.114676	+	0.650361i
$146$		0			0
$147$	−56.6029	+	82.2543i	−0.385054	+	0.559553i
$148$		0			0
$149$	−261.088	+	78.1647i	−1.75227	+	0.524595i	−0.992135	−	0.125169i	$-0.960053\pi$
$149$	−261.088	+	78.1647i	−1.75227	+	0.524595i	−0.760135	+	0.649765i	$0.774867\pi$
$150$		0			0
$151$	−142.117	−	16.6110i	−0.941169	−	0.110007i	−0.368349	−	0.929688i	$-0.620077\pi$
$151$	−142.117	−	16.6110i	−0.941169	−	0.110007i	−0.572820	+	0.819681i	$0.694151\pi$
$152$		0			0
$153$	−151.648	−	96.2411i	−0.991167	−	0.629027i
$154$		0			0
$155$	95.5328	+	145.251i	0.616341	+	0.937100i
$156$		0			0
$157$	−94.2629	−	126.617i	−0.600400	−	0.806478i	0.393197	−	0.919454i	$-0.371369\pi$
$157$	−94.2629	−	126.617i	−0.600400	−	0.806478i	−0.993598	+	0.112976i	$0.963962\pi$
$158$		0			0
$159$	−13.3636	−	11.6991i	−0.0840481	−	0.0735792i
$160$		0			0
$161$		−	63.6308i		−	0.395222i
$162$		0			0
$163$	293.050			1.79785			0.898925	−	0.438102i	$-0.144349\pi$
$163$	293.050			1.79785			0.898925	+	0.438102i	$0.144349\pi$
$164$		0			0
$165$	25.6255	+	75.2756i	0.155306	+	0.456216i
$166$		0			0
$167$	1.80830	−	1.34623i	0.0108282	−	0.00806126i	−0.591731	−	0.806136i	$-0.701555\pi$
$167$	1.80830	−	1.34623i	0.0108282	−	0.00806126i	0.602559	+	0.798074i	$0.294148\pi$
$168$		0			0
$169$	140.982	−	92.7252i	0.834212	−	0.548670i
$170$		0			0
$171$	22.7978	−	103.686i	0.133321	−	0.606350i
$172$		0			0
$173$	0.815873	−	6.98024i	0.00471603	−	0.0403482i	−0.990675	−	0.136243i	$-0.956497\pi$
$173$	0.815873	−	6.98024i	0.00471603	−	0.0403482i	0.995391	+	0.0958949i	$0.0305713\pi$
$174$		0			0
$175$	−18.1767	−	60.7143i	−0.103867	−	0.346939i
$176$		0			0
$177$	18.2358	−	229.983i	0.103027	−	1.29934i
$178$		0			0
$179$	282.326	+	49.7817i	1.57724	+	0.278110i	0.892627	−	0.450796i	$-0.148860\pi$
$179$	282.326	+	49.7817i	1.57724	+	0.278110i	0.684614	+	0.728906i	$0.259971\pi$
$180$		0			0
$181$	37.9341	+	215.135i	0.209580	+	1.18859i	0.890067	+	0.455829i	$0.150657\pi$
$181$	37.9341	+	215.135i	0.209580	+	1.18859i	−0.680487	+	0.732760i	$0.738232\pi$
$182$		0			0
$183$	−35.8019	−	27.8379i	−0.195639	−	0.152120i
$184$		0			0
$185$	43.5841	−	66.2663i	0.235590	−	0.358196i
$186$		0			0
$187$	23.6972	−	79.1540i	0.126723	−	0.423283i
$188$		0			0
$189$	107.040	+	0.499714i	0.566351	+	0.00264399i
$190$		0			0
$191$	199.702	−	188.409i	1.04556	−	0.986437i	0.0456403	−	0.998958i	$-0.485467\pi$
$191$	199.702	−	188.409i	1.04556	−	0.986437i	0.999922	+	0.0125212i	$0.00398572\pi$
$192$		0			0
$193$	−15.9478	+	273.813i	−0.0826312	+	1.41872i	0.661127	+	0.750274i	$0.270078\pi$
$193$	−15.9478	+	273.813i	−0.0826312	+	1.41872i	−0.743758	+	0.668449i	$0.766959\pi$
$194$		0			0
$195$	−6.54450	−	7.23454i	−0.0335615	−	0.0371002i
$196$		0			0
$197$	76.5284	−	210.260i	0.388469	−	1.06731i	−0.579222	−	0.815170i	$-0.696643\pi$
$197$	76.5284	−	210.260i	0.388469	−	1.06731i	0.967691	−	0.252140i	$-0.0811343\pi$
$198$		0			0
$199$	285.813	−	104.027i	1.43625	−	0.522751i	0.497532	−	0.867446i	$-0.334240\pi$
$199$	285.813	−	104.027i	1.43625	−	0.522751i	0.938715	+	0.344695i	$0.112018\pi$
$200$		0			0
$201$	−243.651	+	173.579i	−1.21219	+	0.863578i
$202$		0			0
$203$	−13.6751	+	57.6998i	−0.0673651	+	0.284236i
$204$		0			0
$205$	−11.1926	−	25.9475i	−0.0545983	−	0.126573i
$206$		0			0
$207$	119.379	−	81.3315i	0.576710	−	0.392906i
$208$		0			0
$209$	48.7550	−	2.83965i	0.233277	−	0.0135869i
$210$		0			0
$211$	102.122	−	236.746i	0.483991	−	1.12202i	−0.484908	−	0.874565i	$-0.661147\pi$
$211$	102.122	−	236.746i	0.483991	−	1.12202i	0.968900	−	0.247453i	$-0.0795937\pi$
$212$		0			0
$213$	19.6990	−	15.8382i	0.0924834	−	0.0743578i
$214$		0			0
$215$	299.053	+	172.658i	1.39095	+	0.803063i
$216$		0			0
$217$	53.8292	+	93.2350i	0.248061	+	0.429654i
$218$		0			0
$219$	−82.4297	+	45.3156i	−0.376391	+	0.206920i
$220$		0			0
$221$	1.17680	+	10.0681i	0.00532487	+	0.0455572i
$222$		0			0
$223$	−41.3364	−	20.7599i	−0.185365	−	0.0930937i	0.353696	−	0.935360i	$-0.384925\pi$
$223$	−41.3364	−	20.7599i	−0.185365	−	0.0930937i	−0.539061	+	0.842267i	$0.681221\pi$
$224$		0			0
$225$	90.6743	−	111.705i	0.402997	−	0.496468i
$226$		0			0
$227$	15.6789	+	11.6725i	0.0690698	+	0.0514206i	0.631140	−	0.775669i	$-0.282587\pi$
$227$	15.6789	+	11.6725i	0.0690698	+	0.0514206i	−0.562070	+	0.827090i	$0.689995\pi$
$228$		0			0
$229$	−56.5030	+	59.8896i	−0.246738	+	0.261527i	−0.838892	−	0.544298i	$-0.816796\pi$
$229$	−56.5030	+	59.8896i	−0.246738	+	0.261527i	0.592154	+	0.805825i	$0.298278\pi$
$230$		0			0
$231$	13.1315	+	47.4587i	0.0568463	+	0.205449i
$232$		0			0
$233$	129.196	−	153.970i	0.554491	−	0.660817i	−0.413880	−	0.910331i	$-0.635827\pi$
$233$	129.196	−	153.970i	0.554491	−	0.660817i	0.968371	+	0.249515i	$0.0802711\pi$
$234$		0			0
$235$	126.742	−	106.349i	0.539329	−	0.452550i
$236$		0			0
$237$	157.110	−	5.85173i	0.662910	−	0.0246908i
$238$		0			0
$239$	−24.7626	−	49.3063i	−0.103609	−	0.206303i	0.835855	−	0.548951i	$-0.184972\pi$
$239$	−24.7626	−	49.3063i	−0.103609	−	0.206303i	−0.939464	+	0.342648i	$0.888676\pi$
$240$		0			0
$241$	157.284	−	37.2771i	0.652632	−	0.154677i	0.109055	−	0.994036i	$-0.465218\pi$
$241$	157.284	−	37.2771i	0.652632	−	0.154677i	0.543577	+	0.839359i	$0.317070\pi$
$242$		0			0
$243$	135.879	+	201.459i	0.559173	+	0.829051i
$244$		0			0
$245$	49.1390	+	207.334i	0.200567	+	0.846260i
$246$		0			0
$247$	−5.35423	+	2.68899i	−0.0216770	+	0.0108866i
$248$		0			0
$249$	−7.14254	−	191.766i	−0.0286849	−	0.770143i
$250$		0			0
$251$	111.884	+	133.339i	0.445755	+	0.531230i	0.941399	−	0.337296i	$-0.109512\pi$
$251$	111.884	+	133.339i	0.445755	+	0.531230i	−0.495644	+	0.868526i	$0.665068\pi$
$252$		0			0
$253$	50.9047	+	42.7141i	0.201204	+	0.168831i
$254$		0			0
$255$	−369.409	+	102.213i	−1.44866	+	0.400835i
$256$		0			0
$257$	−60.6402	−	57.2111i	−0.235954	−	0.222611i	0.559178	−	0.829048i	$-0.311117\pi$
$257$	−60.6402	−	57.2111i	−0.235954	−	0.222611i	−0.795132	+	0.606437i	$0.792598\pi$
$258$		0			0
$259$	29.3301	−	39.3971i	0.113243	−	0.152112i
$260$		0			0
$261$	−125.731	+	48.0945i	−0.481728	+	0.184270i
$262$		0			0
$263$	−184.811	+	367.990i	−0.702705	+	1.39920i	0.204650	+	0.978835i	$0.434394\pi$
$263$	−184.811	+	367.990i	−0.702705	+	1.39920i	−0.907355	+	0.420365i	$0.861902\pi$
$264$		0			0
$265$	−37.6461	+	4.40019i	−0.142061	+	0.0166045i
$266$		0			0
$267$	−243.306	−	442.577i	−0.911259	−	1.65759i
$268$		0			0
$269$	106.187	−	61.3070i	0.394747	−	0.227907i	−0.289468	−	0.957188i	$-0.593478\pi$
$269$	106.187	−	61.3070i	0.394747	−	0.227907i	0.684215	+	0.729281i	$0.260145\pi$
$270$		0			0
$271$	−183.075	+	317.095i	−0.675553	+	1.17009i	0.300753	+	0.953702i	$0.402762\pi$
$271$	−183.075	+	317.095i	−0.675553	+	1.17009i	−0.976307	+	0.216391i	$0.930571\pi$
$272$		0			0
$273$	−3.78537	−	4.70810i	−0.0138658	−	0.0172458i
$274$		0			0
$275$	60.7732	+	26.2150i	0.220993	+	0.0953272i
$276$		0			0
$277$	−19.7624	−	339.308i	−0.0713445	−	1.22494i	−0.824026	−	0.566552i	$-0.808277\pi$
$277$	−19.7624	−	339.308i	−0.0713445	−	1.22494i	0.752681	−	0.658385i	$-0.228760\pi$
$278$		0			0
$279$	−106.117	+	220.161i	−0.380347	+	0.789107i
$280$		0			0
$281$	223.848	−	96.5584i	0.796610	−	0.343624i	0.0414302	−	0.999141i	$-0.486809\pi$
$281$	223.848	−	96.5584i	0.796610	−	0.343624i	0.755180	+	0.655517i	$0.227549\pi$
$282$		0			0
$283$	−323.938	−	76.7746i	−1.14466	−	0.271288i	−0.385822	−	0.922573i	$-0.626082\pi$
$283$	−323.938	−	76.7746i	−1.14466	−	0.271288i	−0.758834	+	0.651285i	$0.774230\pi$
$284$		0			0
$285$	−131.451	−	184.517i	−0.461233	−	0.647428i
$286$		0			0
$287$	−5.98511	−	16.4440i	−0.0208541	−	0.0572960i
$288$		0			0
$289$	102.677	+	37.3714i	0.355284	+	0.129313i
$290$		0			0
$291$	−158.192	+	143.104i	−0.543617	+	0.491765i
$292$		0			0
$293$	95.7610	+	5.57744i	0.326829	+	0.0190356i	0.220775	−	0.975325i	$-0.429141\pi$
$293$	95.7610	+	5.57744i	0.326829	+	0.0190356i	0.106054	+	0.994360i	$0.466178\pi$
$294$		0			0
$295$	−337.855	−	358.106i	−1.14527	−	1.21392i
$296$		0			0
$297$	−72.2539	+	85.2970i	−0.243279	+	0.287195i
$298$		0			0
$299$	−7.80995	−	2.33814i	−0.0261202	−	0.00781988i
$300$		0			0
$301$	178.660	+	117.507i	0.593556	+	0.390388i
$302$		0			0
$303$	−306.140	+	393.722i	−1.01036	+	1.29941i
$304$		0			0
$305$	−95.3096	+	16.8056i	−0.312490	+	0.0551005i
$306$		0			0
$307$	77.2135	−	437.900i	0.251510	−	1.42638i	−0.553365	−	0.832939i	$-0.686656\pi$
$307$	77.2135	−	437.900i	0.251510	−	1.42638i	0.804875	−	0.593445i	$-0.202232\pi$
$308$		0			0
$309$	61.4074	+	4.86911i	0.198729	+	0.0157576i
$310$		0			0
$311$	−278.336	+	83.3283i	−0.894970	+	0.267937i	−0.701077	−	0.713086i	$-0.747297\pi$
$311$	−278.336	+	83.3283i	−0.894970	+	0.267937i	−0.193894	+	0.981023i	$0.562112\pi$
$312$		0			0
$313$	246.796	+	28.8463i	0.788486	+	0.0921608i	0.500799	−	0.865564i	$-0.333040\pi$
$313$	246.796	+	28.8463i	0.788486	+	0.0921608i	0.287687	+	0.957725i	$0.407114\pi$
$314$		0			0
$315$	154.031	−	168.682i	0.488988	−	0.535500i
$316$		0			0
$317$	9.91703	+	15.0781i	0.0312840	+	0.0475650i	0.850791	−	0.525504i	$-0.176123\pi$
$317$	9.91703	+	15.0781i	0.0312840	+	0.0475650i	−0.819507	+	0.573069i	$0.805753\pi$
$318$		0			0
$319$	−36.9801	−	49.6729i	−0.115925	−	0.155714i
$320$		0			0
$321$	286.246	−	97.4444i	0.891731	−	0.303565i
$322$		0			0
$323$			235.405i			0.728809i
$324$		0			0
$325$	−8.11989			−0.0249843
$326$		0			0
$327$	−423.149	+	483.354i	−1.29403	+	1.47815i
$328$		0			0
$329$	82.1824	−	61.1825i	0.249794	−	0.185965i
$330$		0			0
$331$	332.686	−	218.811i	1.00509	−	0.661060i	0.0635591	−	0.997978i	$-0.479755\pi$
$331$	332.686	−	218.811i	1.00509	−	0.661060i	0.941534	+	0.336918i	$0.109384\pi$
$332$		0			0
$333$	111.403	+	4.67022i	0.334543	+	0.0140247i
$334$		0			0
$335$	−74.1145	+	634.090i	−0.221237	+	1.89281i
$336$		0			0
$337$	−41.3165	−	138.007i	−0.122601	−	0.409516i	0.874551	−	0.484933i	$-0.161156\pi$
$337$	−41.3165	−	138.007i	−0.122601	−	0.409516i	−0.997152	+	0.0754177i	$0.975971\pi$
$338$		0			0
$339$	−306.179	−	210.696i	−0.903184	−	0.621521i
$340$		0			0
$341$	−110.723	−	19.5234i	−0.324700	−	0.0572533i
$342$		0			0
$343$	56.6458	+	321.254i	0.165148	+	0.936601i
$344$		0			0
$345$	42.1926	−	305.360i	0.122297	−	0.885100i
$346$		0			0
$347$	91.7987	−	139.573i	0.264550	−	0.402228i	−0.678646	−	0.734465i	$-0.737433\pi$
$347$	91.7987	−	139.573i	0.264550	−	0.402228i	0.943196	+	0.332237i	$0.107803\pi$
$348$		0			0
$349$	129.783	−	433.504i	0.371870	−	1.24213i	−0.543463	−	0.839433i	$-0.682887\pi$
$349$	129.783	−	433.504i	0.371870	−	1.24213i	0.915333	−	0.402698i	$-0.131928\pi$
$350$		0			0
$351$	3.99458	−	13.1196i	0.0113806	−	0.0373778i
$352$		0			0
$353$	−298.495	+	281.616i	−0.845596	+	0.797779i	−0.981202	−	0.192984i	$-0.938183\pi$
$353$	−298.495	+	281.616i	−0.845596	+	0.797779i	0.135606	+	0.990763i	$0.456702\pi$
$354$		0			0
$355$	3.13634	−	53.8490i	0.00883477	−	0.151687i
$356$		0			0
$357$	−232.052	+	49.8877i	−0.650006	+	0.139742i
$358$		0			0
$359$	−51.9954	+	142.856i	−0.144834	+	0.397928i	−0.990804	−	0.135302i	$-0.956800\pi$
$359$	−51.9954	+	142.856i	−0.144834	+	0.397928i	0.845971	+	0.533230i	$0.179022\pi$
$360$		0			0
$361$	208.478	−	75.8799i	0.577502	−	0.210194i
$362$		0			0
$363$	283.446	+	129.374i	0.780842	+	0.356403i
$364$		0			0
$365$	−46.2927	+	195.324i	−0.126829	+	0.535135i
$366$		0			0
$367$	−27.7762	−	64.3924i	−0.0756843	−	0.175456i	0.876173	−	0.481996i	$-0.160088\pi$
$367$	−27.7762	−	64.3924i	−0.0756843	−	0.175456i	−0.951858	+	0.306540i	$0.900829\pi$
$368$		0			0
$369$	23.2008	−	32.2471i	0.0628748	−	0.0873905i
$370$		0			0
$371$	−23.4316	+	1.36473i	−0.0631578	+	0.00367853i
$372$		0			0
$373$	−67.6896	+	156.922i	−0.181474	+	0.420703i	−0.984534	−	0.175195i	$-0.943944\pi$
$373$	−67.6896	+	156.922i	−0.181474	+	0.420703i	0.803060	+	0.595898i	$0.203204\pi$
$374$		0			0
$375$	26.4845	+	171.085i	0.0706253	+	0.456226i
$376$		0			0
$377$	6.57949	+	3.79867i	0.0174522	+	0.0100760i
$378$		0			0
$379$	−334.436	−	579.260i	−0.882417	−	1.52839i	−0.848646	−	0.528961i	$-0.822582\pi$
$379$	−334.436	−	579.260i	−0.882417	−	1.52839i	−0.0337710	−	0.999430i	$-0.510752\pi$
$380$		0			0
$381$	−33.1540	−	20.0790i	−0.0870182	−	0.0527007i
$382$		0			0
$383$	50.0181	+	427.932i	0.130595	+	1.11732i	0.886531	+	0.462669i	$0.153108\pi$
$383$	50.0181	+	427.932i	0.130595	+	1.11732i	−0.755935	+	0.654646i	$0.772818\pi$
$384$		0			0
$385$	93.9055	+	47.1611i	0.243910	+	0.122496i
$386$		0			0
$387$	7.90286	+	485.383i	0.0204208	+	1.25422i
$388$		0			0
$389$	427.571	+	318.315i	1.09915	+	0.818290i	0.984547	−	0.175121i	$-0.0560316\pi$
$389$	427.571	+	318.315i	1.09915	+	0.818290i	0.114607	+	0.993411i	$0.463439\pi$
$390$		0			0
$391$	−219.808	+	232.983i	−0.562168	+	0.595863i
$392$		0			0
$393$	−279.188	−	72.3775i	−0.710401	−	0.184167i
$394$		0			0
$395$	215.659	−	257.013i	0.545973	−	0.650665i
$396$		0			0
$397$	564.141	−	473.370i	1.42101	−	1.19237i	0.470212	−	0.882553i	$-0.344177\pi$
$397$	564.141	−	473.370i	1.42101	−	1.19237i	0.950797	−	0.309815i	$-0.100267\pi$
$398$		0			0
$399$	−74.6206	−	118.803i	−0.187019	−	0.297752i
$400$		0			0
$401$	−195.937	−	390.142i	−0.488621	−	0.972924i	−0.993933	−	0.109987i	$-0.964919\pi$
$401$	−195.937	−	390.142i	−0.488621	−	0.972924i	0.505312	−	0.862936i	$-0.331377\pi$
$402$		0			0
$403$	13.4215	−	3.18095i	0.0333040	−	0.00789318i
$404$		0			0
$405$	513.348	+	73.3748i	1.26752	+	0.181172i
$406$		0			0
$407$	11.8290	+	49.9106i	0.0290640	+	0.122630i
$408$		0			0
$409$	−200.565	+	100.727i	−0.490378	+	0.246277i	−0.676765	−	0.736199i	$-0.736619\pi$
$409$	−200.565	+	100.727i	−0.490378	+	0.246277i	0.186387	+	0.982476i	$0.440322\pi$
$410$		0			0
$411$	−149.407	−	78.9964i	−0.363520	−	0.192205i
$412$		0			0
$413$	−195.971	−	233.549i	−0.474506	−	0.565494i
$414$		0			0
$415$	−313.706	−	263.231i	−0.755918	−	0.634291i
$416$		0			0
$417$	−426.193	−	419.310i	−1.02205	−	1.00554i
$418$		0			0
$419$	−102.084	−	96.3112i	−0.243637	−	0.229860i	0.554731	−	0.832030i	$-0.312821\pi$
$419$	−102.084	−	96.3112i	−0.243637	−	0.229860i	−0.798368	+	0.602170i	$0.794303\pi$
$420$		0			0
$421$	30.6961	−	41.2320i	0.0729123	−	0.0979382i	−0.764171	−	0.645014i	$-0.776852\pi$
$421$	30.6961	−	41.2320i	0.0729123	−	0.0979382i	0.837083	+	0.547076i	$0.184259\pi$
$422$		0			0
$423$	219.829	+	75.9819i	0.519691	+	0.179626i
$424$		0			0
$425$	−143.179	+	285.094i	−0.336893	+	0.670809i
$426$		0			0
$427$	−59.5263	+	6.95763i	−0.139406	+	0.0162942i
$428$		0			0
$429$	6.30753	+	0.132154i	0.0147029	+	0.000308051i
$430$		0			0
$431$	−109.124	+	63.0028i	−0.253188	+	0.146178i	−0.621223	−	0.783634i	$-0.713364\pi$
$431$	−109.124	+	63.0028i	−0.253188	+	0.146178i	0.368035	+	0.929812i	$0.380031\pi$
$432$		0			0
$433$	−295.692	+	512.153i	−0.682891	+	1.18280i	0.291203	+	0.956661i	$0.405944\pi$
$433$	−295.692	+	512.153i	−0.682891	+	1.18280i	−0.974095	+	0.226141i	$0.927389\pi$
$434$		0			0
$435$	−103.886	+	267.829i	−0.238818	+	0.615700i
$436$		0			0
$437$	−173.841	−	74.9878i	−0.397806	−	0.171597i
$438$		0			0
$439$	29.9433	+	514.106i	0.0682079	+	1.17108i	0.842658	+	0.538449i	$0.180990\pi$
$439$	29.9433	+	514.106i	0.0682079	+	1.17108i	−0.774450	+	0.632635i	$0.781973\pi$
$440$		0			0
$441$	−214.506	+	209.080i	−0.486407	+	0.474104i
$442$		0			0
$443$	344.399	−	148.559i	0.777424	−	0.335348i	0.0298740	−	0.999554i	$-0.490489\pi$
$443$	344.399	−	148.559i	0.777424	−	0.335348i	0.747550	+	0.664206i	$0.231230\pi$
$444$		0			0
$445$	−1048.73	−	248.552i	−2.35669	−	0.558545i
$446$		0			0
$447$	−813.895	+	77.8874i	−1.82079	+	0.174245i
$448$		0			0
$449$	−195.608	−	537.429i	−0.435653	−	1.19695i	−0.942293	−	0.334789i	$-0.891335\pi$
$449$	−195.608	−	537.429i	−0.435653	−	1.19695i	0.506640	−	0.862158i	$-0.330887\pi$
$450$		0			0
$451$	17.1729	+	6.25042i	0.0380773	+	0.0138590i
$452$		0			0
$453$	−408.550	−	131.698i	−0.901876	−	0.290723i
$454$		0			0
$455$	−12.8700	−	0.749594i	−0.0282858	−	0.00164746i
$456$		0			0
$457$	127.422	+	135.059i	0.278823	+	0.295535i	0.851617	−	0.524164i	$-0.175622\pi$
$457$	127.422	+	135.059i	0.278823	+	0.295535i	−0.572795	+	0.819699i	$0.694141\pi$
$458$		0			0
$459$	−390.199	−	371.592i	−0.850108	−	0.809570i
$460$		0			0
$461$	−171.978	−	51.4870i	−0.373055	−	0.111685i	0.0947866	−	0.995498i	$-0.469783\pi$
$461$	−171.978	−	51.4870i	−0.373055	−	0.111685i	−0.467842	+	0.883812i	$0.654968\pi$
$462$		0			0
$463$	415.868	+	273.521i	0.898203	+	0.590757i	0.912471	−	0.409141i	$-0.134172\pi$
$463$	415.868	+	273.521i	0.898203	+	0.590757i	−0.0142686	+	0.999898i	$0.504542\pi$
$464$		0			0
$465$	196.500	+	483.121i	0.422581	+	1.03897i
$466$		0			0
$467$	−51.2883	+	9.04351i	−0.109825	+	0.0193651i	−0.228291	−	0.973593i	$-0.573314\pi$
$467$	−51.2883	+	9.04351i	−0.109825	+	0.0193651i	0.118466	+	0.992958i	$0.462202\pi$
$468$		0			0
$469$	−68.6497	+	389.332i	−0.146375	+	0.830131i
$470$		0			0
$471$	−203.621	−	427.545i	−0.432316	−	0.907739i
$472$		0			0
$473$	−213.937	+	64.0485i	−0.452298	+	0.135409i
$474$		0			0
$475$	−187.294	−	21.8916i	−0.394304	−	0.0460875i
$476$		0			0
$477$	−32.5101	−	42.2161i	−0.0681554	−	0.0885033i
$478$		0			0
$479$	−0.741567	−	1.12750i	−0.00154816	−	0.00235386i	0.834713	−	0.550685i	$-0.185634\pi$
$479$	−0.741567	−	1.12750i	−0.00154816	−	0.00235386i	−0.836261	+	0.548332i	$0.815263\pi$
$480$		0			0
$481$	−3.75779	−	5.04759i	−0.00781246	−	0.0104940i
$482$		0			0
$483$	37.0787	−	187.257i	0.0767676	−	0.387695i
$484$		0			0
$485$			455.218i			0.938594i
$486$		0			0
$487$	168.122			0.345220			0.172610	−	0.984990i	$-0.444780\pi$
$487$	168.122			0.345220			0.172610	+	0.984990i	$0.444780\pi$
$488$		0			0
$489$	862.405	+	170.765i	1.76361	+	0.349213i
$490$		0			0
$491$	437.109	−	325.415i	0.890241	−	0.662760i	−0.0516545	−	0.998665i	$-0.516449\pi$
$491$	437.109	−	325.415i	0.890241	−	0.662760i	0.941896	+	0.335905i	$0.109042\pi$
$492$		0			0
$493$	249.391	−	164.027i	0.505863	−	0.332712i
$494$		0			0
$495$	31.5480	+	236.458i	0.0637333	+	0.477693i
$496$		0			0
$497$	3.87783	−	33.1770i	0.00780248	−	0.0667544i
$498$		0			0
$499$	117.013	+	390.852i	0.234496	+	0.783270i	0.991528	+	0.129893i	$0.0414632\pi$
$499$	117.013	+	390.852i	0.234496	+	0.783270i	−0.757033	+	0.653377i	$0.773352\pi$
$500$		0			0
$501$	6.10606	−	2.90804i	0.0121877	−	0.00580448i
$502$		0			0
$503$	664.772	+	117.217i	1.32161	+	0.233036i	0.789559	−	0.613674i	$-0.210309\pi$
$503$	664.772	+	117.217i	1.32161	+	0.233036i	0.532054	+	0.846710i	$0.321420\pi$
$504$		0			0
$505$	184.816	+	1048.14i	0.365972	+	2.07553i
$506$		0			0
$507$	468.923	−	190.725i	0.924897	−	0.376184i
$508$		0			0
$509$	331.048	−	503.335i	0.650390	−	0.988870i	−0.348284	−	0.937389i	$-0.613236\pi$
$509$	331.048	−	503.335i	0.650390	−	0.988870i	0.998674	−	0.0514806i	$-0.0163940\pi$
$510$		0			0
$511$	−35.6515	+	119.084i	−0.0697681	+	0.233042i
$512$		0			0
$513$	127.510	−	291.849i	0.248558	−	0.568906i
$514$		0			0
$515$	95.6172	−	90.2102i	0.185664	−	0.175165i
$516$		0			0
$517$	−6.22136	+	106.817i	−0.0120336	+	0.206609i
$518$		0			0
$519$	6.46850	−	20.0665i	0.0124634	−	0.0386637i
$520$		0			0
$521$	67.7865	−	186.242i	0.130108	−	0.357470i	−0.857484	−	0.514511i	$-0.827973\pi$
$521$	67.7865	−	186.242i	0.130108	−	0.357470i	0.987592	+	0.157041i	$0.0501956\pi$
$522$		0			0
$523$	−56.8108	+	20.6774i	−0.108625	+	0.0395362i	−0.395761	−	0.918354i	$-0.629519\pi$
$523$	−56.8108	+	20.6774i	−0.108625	+	0.0395362i	0.287136	+	0.957890i	$0.407297\pi$
$524$		0			0
$525$	−18.1122	−	189.266i	−0.0344994	−	0.360506i
$526$		0			0
$527$	124.979	−	527.326i	0.237151	−	1.00062i
$528$		0			0
$529$	107.493	+	249.197i	0.203201	+	0.471073i
$530$		0			0
$531$	187.681	−	666.182i	0.353447	−	1.25458i
$532$		0			0
$533$	−2.23823	+	0.130362i	−0.00419931	+	0.000244582i
$534$		0			0
$535$	255.581	−	592.503i	0.477721	−	1.10748i
$536$		0			0
$537$	801.838	+	311.017i	1.49318	+	0.579175i
$538$		0			0
$539$	−119.337	−	68.8992i	−0.221404	−	0.127828i
$540$		0			0
$541$	−438.908	−	760.211i	−0.811290	−	1.40520i	−0.911961	−	0.410277i	$-0.865432\pi$
$541$	−438.908	−	760.211i	−0.811290	−	1.40520i	0.100671	−	0.994920i	$-0.467901\pi$
$542$		0			0
$543$	−13.7279	+	655.217i	−0.0252817	+	1.20666i
$544$		0			0
$545$	159.152	+	1361.63i	0.292022	+	2.49841i
$546$		0			0
$547$	857.245	+	430.525i	1.56718	+	0.787065i	0.999349	−	0.0360826i	$-0.0114880\pi$
$547$	857.245	+	430.525i	1.56718	+	0.787065i	0.567827	+	0.823148i	$0.307784\pi$
$548$		0			0
$549$	−89.1386	−	102.785i	−0.162365	−	0.187223i
$550$		0			0
$551$	141.522	+	105.359i	0.256845	+	0.191214i
$552$		0			0
$553$	142.577	−	151.122i	0.257824	−	0.273277i
$554$		0			0
$555$	166.876	−	169.616i	0.300678	−	0.305614i
$556$		0			0
$557$	405.425	−	483.167i	0.727872	−	0.867445i	−0.267498	−	0.963558i	$-0.586197\pi$
$557$	405.425	−	483.167i	0.727872	−	0.867445i	0.995370	+	0.0961139i	$0.0306413\pi$
$558$		0			0
$559$	20.9876	−	17.6107i	0.0375449	−	0.0315039i
$560$		0			0
$561$	115.862	−	219.131i	0.206527	−	0.390607i
$562$		0			0
$563$	−348.907	−	694.732i	−0.619729	−	1.23398i	−0.956318	−	0.292330i	$-0.905570\pi$
$563$	−348.907	−	694.732i	−0.619729	−	1.23398i	0.336589	−	0.941652i	$-0.390727\pi$
$564$		0			0
$565$	−771.769	+	182.913i	−1.36596	+	0.323739i
$566$		0			0
$567$	314.714	+	63.8448i	0.555051	+	0.112601i
$568$		0			0
$569$	−121.231	−	511.512i	−0.213059	−	0.898967i	−0.969536	−	0.244947i	$-0.921229\pi$
$569$	−121.231	−	511.512i	−0.213059	−	0.898967i	0.756477	−	0.654020i	$-0.226919\pi$
$570$		0			0
$571$	322.100	−	161.765i	0.564098	−	0.283301i	−0.143810	−	0.989605i	$-0.545935\pi$
$571$	322.100	−	161.765i	0.564098	−	0.283301i	0.707908	+	0.706305i	$0.249639\pi$
$572$		0			0
$573$	697.486	−	438.093i	1.21725	−	0.764560i
$574$		0			0
$575$	−164.926	−	196.551i	−0.286827	−	0.341827i
$576$		0			0
$577$	−185.271	−	155.461i	−0.321094	−	0.269430i	0.467965	−	0.883747i	$-0.344987\pi$
$577$	−185.271	−	155.461i	−0.321094	−	0.269430i	−0.789059	+	0.614317i	$0.789432\pi$
$578$		0			0
$579$	−206.488	+	796.502i	−0.356629	+	1.37565i
$580$		0			0
$581$	−184.458	−	174.027i	−0.317483	−	0.299530i
$582$		0			0
$583$	14.6374	−	19.6614i	0.0251070	−	0.0337245i
$584$		0			0
$585$	−15.0439	−	25.1039i	−0.0257160	−	0.0429126i
$586$		0			0
$587$	−83.9334	+	167.125i	−0.142987	+	0.284711i	−0.953715	−	0.300713i	$-0.902775\pi$
$587$	−83.9334	+	167.125i	−0.142987	+	0.284711i	0.810728	+	0.585424i	$0.199072\pi$
$588$		0			0
$589$	318.158	−	37.1873i	0.540166	−	0.0631363i
$590$		0			0
$591$	347.735	−	574.172i	0.588384	−	0.971526i
$592$		0			0
$593$	−381.562	+	220.295i	−0.643444	+	0.371493i	−0.785940	−	0.618303i	$-0.787821\pi$
$593$	−381.562	+	220.295i	−0.643444	+	0.371493i	0.142496	+	0.989795i	$0.454487\pi$
$594$		0			0
$595$	−253.258	+	438.656i	−0.425644	+	0.737237i
$596$		0			0
$597$	901.727	−	139.590i	1.51043	−	0.233820i
$598$		0			0
$599$	741.144	+	319.698i	1.23730	+	0.533720i	0.911337	−	0.411662i	$-0.135052\pi$
$599$	741.144	+	319.698i	1.23730	+	0.533720i	0.325965	+	0.945382i	$0.394311\pi$
$600$		0			0
$601$	−18.2648	−	313.595i	−0.0303907	−	0.521789i	−0.978810	−	0.204770i	$-0.934355\pi$
$601$	−18.2648	−	313.595i	−0.0303907	−	0.521789i	0.948419	−	0.317019i	$-0.102682\pi$
$602$		0			0
$603$	−818.179	+	368.840i	−1.35685	+	0.611675i
$604$		0			0
$605$	610.527	−	263.356i	1.00914	−	0.435299i
$606$		0			0
$607$	−32.7866	−	7.77056i	−0.0540141	−	0.0128016i	0.203520	−	0.979071i	$-0.434762\pi$
$607$	−32.7866	−	7.77056i	−0.0540141	−	0.0128016i	−0.257534	+	0.966269i	$0.582910\pi$
$608$		0			0
$609$	−73.8666	+	161.834i	−0.121292	+	0.265737i
$610$		0			0
$611$	−4.48962	−	12.3351i	−0.00734798	−	0.0201884i
$612$		0			0
$613$	774.586	+	281.926i	1.26360	+	0.459912i	0.884975	−	0.465639i	$-0.154175\pi$
$613$	774.586	+	281.926i	1.26360	+	0.459912i	0.378623	+	0.925551i	$0.376398\pi$
$614$		0			0
$615$	−17.8184	−	82.8820i	−0.0289730	−	0.134768i
$616$		0			0
$617$	−825.427	−	48.0757i	−1.33781	−	0.0779184i	−0.625741	−	0.780031i	$-0.715203\pi$
$617$	−825.427	−	48.0757i	−1.33781	−	0.0779184i	−0.712066	+	0.702112i	$0.752240\pi$
$618$		0			0
$619$	−724.278	−	767.690i	−1.17008	−	1.24021i	−0.965226	−	0.261417i	$-0.915810\pi$
$619$	−724.278	−	767.690i	−1.17008	−	1.24021i	−0.204852	−	0.978793i	$-0.565671\pi$
$620$		0			0
$621$	398.709	−	169.783i	0.642044	−	0.273403i
$622$		0			0
$623$	−639.381	−	191.418i	−1.02629	−	0.307252i
$624$		0			0
$625$	642.571	+	422.626i	1.02811	+	0.676201i
$626$		0			0
$627$	145.134	+	20.0536i	0.231474	+	0.0319835i
$628$		0			0
$629$	−243.486	+	42.9331i	−0.387099	+	0.0682561i
$630$		0			0
$631$	18.2014	−	103.225i	0.0288453	−	0.163590i	−0.966982	−	0.254843i	$-0.917976\pi$
$631$	18.2014	−	103.225i	0.0288453	−	0.163590i	0.995828	+	0.0912533i	$0.0290873\pi$
$632$		0			0
$633$	438.487	−	637.202i	0.692713	−	1.00664i
$634$		0			0
$635$	−79.2397	+	23.7228i	−0.124787	+	0.0373588i
$636$		0			0
$637$	16.7912	+	1.96261i	0.0263598	+	0.00308101i
$638$		0			0
$639$	67.2005	−	35.1308i	0.105165	−	0.0549777i
$640$		0			0
$641$	−473.763	−	720.322i	−0.739101	−	1.12375i	−0.987885	−	0.155189i	$-0.950401\pi$
$641$	−473.763	−	720.322i	−0.739101	−	1.12375i	0.248784	−	0.968559i	$-0.419969\pi$
$642$		0			0
$643$	338.275	+	454.382i	0.526088	+	0.706659i	0.983155	−	0.182773i	$-0.0585074\pi$
$643$	338.275	+	454.382i	0.526088	+	0.706659i	−0.457067	+	0.889432i	$0.651100\pi$
$644$		0			0
$645$	779.462	+	682.374i	1.20847	+	1.05794i
$646$		0			0
$647$		−	99.8467i		−	0.154323i	−0.997019	−	0.0771613i	$-0.975414\pi$
$647$		−	99.8467i		−	0.154323i	0.997019	−	0.0771613i	$-0.0245856\pi$
$648$		0			0
$649$	318.391			0.490587
$650$		0			0
$651$	104.082	+	305.745i	0.159881	+	0.469654i
$652$		0			0
$653$	−358.868	+	267.167i	−0.549568	+	0.409138i	−0.835810	−	0.549019i	$-0.815001\pi$
$653$	−358.868	+	267.167i	−0.549568	+	0.409138i	0.286242	+	0.958157i	$0.407594\pi$
$654$		0			0
$655$	−514.230	+	338.214i	−0.785084	+	0.516358i
$656$		0			0
$657$	−268.985	+	85.3244i	−0.409415	+	0.129870i
$658$		0			0
$659$	92.8145	−	794.079i	0.140841	−	1.20498i	−0.719219	−	0.694784i	$-0.755500\pi$
$659$	92.8145	−	794.079i	0.140841	−	1.20498i	0.860060	−	0.510192i	$-0.170426\pi$
$660$		0			0
$661$	−273.529	−	913.651i	−0.413811	−	1.38223i	−0.870311	−	0.492502i	$-0.836082\pi$
$661$	−273.529	−	913.651i	−0.413811	−	1.38223i	0.456500	−	0.889723i	$-0.349103\pi$
$662$		0			0
$663$	−2.40372	+	30.3149i	−0.00362553	+	0.0457238i
$664$		0			0
$665$	−294.841	−	51.9884i	−0.443369	−	0.0781780i
$666$		0			0
$667$	41.6871	+	236.419i	0.0624995	+	0.354452i
$668$		0			0
$669$	−109.550	−	85.1809i	−0.163752	−	0.127326i
$670$		0			0
$671$	34.3927	−	52.2916i	0.0512560	−	0.0779309i
$672$		0			0
$673$	−23.9476	+	79.9905i	−0.0355833	+	0.118857i	−0.973936	−	0.226823i	$-0.927166\pi$
$673$	−23.9476	+	79.9905i	−0.0355833	+	0.118857i	0.938353	+	0.345679i	$0.112351\pi$
$674$		0			0
$675$	331.935	−	275.896i	0.491755	−	0.408735i
$676$		0			0
$677$	442.155	−	417.152i	0.653109	−	0.616177i	−0.286641	−	0.958038i	$-0.592539\pi$
$677$	442.155	−	417.152i	0.653109	−	0.616177i	0.939751	+	0.341861i	$0.111057\pi$
$678$		0			0
$679$	−16.3908	+	281.420i	−0.0241397	+	0.414462i
$680$		0			0
$681$	39.3390	+	43.4868i	0.0577665	+	0.0638573i
$682$		0			0
$683$	−394.613	+	1084.19i	−0.577764	+	1.58739i	0.214177	+	0.976795i	$0.431293\pi$
$683$	−394.613	+	1084.19i	−0.577764	+	1.58739i	−0.791941	+	0.610598i	$0.790929\pi$
$684$		0			0
$685$	−338.909	+	123.353i	−0.494757	+	0.180077i
$686$		0			0
$687$	−201.179	+	143.322i	−0.292837	+	0.208620i
$688$		0			0
$689$	−0.693499	+	2.92610i	−0.00100653	+	0.00424688i
$690$		0			0
$691$	124.496	+	288.613i	0.180167	+	0.417675i	0.984236	−	0.176862i	$-0.0565947\pi$
$691$	124.496	+	288.613i	0.180167	+	0.417675i	−0.804068	+	0.594537i	$0.797335\pi$
$692$		0			0
$693$	10.9892	+	147.316i	0.0158574	+	0.212578i
$694$		0			0
$695$	−1273.73	+	74.1861i	−1.83270	+	0.106743i
$696$		0			0
$697$	−34.8901	+	80.8843i	−0.0500575	+	0.116046i
$698$		0			0
$699$	469.928	−	377.828i	0.672287	−	0.540527i
$700$		0			0
$701$	332.684	+	192.075i	0.474585	+	0.274002i	0.718157	−	0.695881i	$-0.244986\pi$
$701$	332.684	+	192.075i	0.474585	+	0.274002i	−0.243572	+	0.969883i	$0.578319\pi$
$702$		0			0
$703$	−73.0691	−	126.559i	−0.103939	−	0.180028i
$704$		0			0
$705$	434.956	−	239.117i	0.616960	−	0.339173i
$706$		0			0
$707$	76.5147	+	654.625i	0.108224	+	0.925919i
$708$		0			0
$709$	330.680	+	166.074i	0.466404	+	0.234237i	0.666450	−	0.745550i	$-0.267813\pi$
$709$	330.680	+	166.074i	0.466404	+	0.234237i	−0.200046	+	0.979786i	$0.564109\pi$
$710$		0			0
$711$	465.762	+	74.3296i	0.655080	+	0.104542i
$712$		0			0
$713$	349.606	+	260.272i	0.490332	+	0.365038i
$714$		0			0
$715$	9.23908	−	9.79286i	0.0129218	−	0.0136963i
$716$		0			0
$717$	−44.1412	−	159.531i	−0.0615637	−	0.222498i
$718$		0			0
$719$	552.176	−	658.057i	0.767977	−	0.915239i	−0.230347	−	0.973109i	$-0.573986\pi$
$719$	552.176	−	658.057i	0.767977	−	0.915239i	0.998324	+	0.0578691i	$0.0184306\pi$
$720$		0			0
$721$	62.3595	−	52.3258i	0.0864903	−	0.0725740i
$722$		0			0
$723$	484.588	−	18.0490i	0.670246	−	0.0249641i
$724$		0			0
$725$	107.312	+	213.675i	0.148016	+	0.294724i
$726$		0			0
$727$	−1152.88	+	273.237i	−1.58580	+	0.375842i	−0.926578	−	0.376103i	$-0.877264\pi$
$727$	−1152.88	+	273.237i	−1.58580	+	0.375842i	−0.659226	+	0.751945i	$0.729116\pi$
$728$		0			0
$729$	282.480	+	672.046i	0.387489	+	0.921874i
$730$		0			0
$731$	−248.242	−	1047.42i	−0.339593	−	1.43286i
$732$		0			0
$733$	−492.368	+	247.277i	−0.671717	+	0.337349i	−0.751755	−	0.659443i	$-0.770792\pi$
$733$	−492.368	+	247.277i	−0.671717	+	0.337349i	0.0800379	+	0.996792i	$0.474496\pi$
$734$		0			0
$735$	23.7924	+	638.789i	0.0323707	+	0.869100i
$736$		0			0
$737$	−265.382	−	316.271i	−0.360085	−	0.429132i
$738$		0			0
$739$	−983.763	−	825.475i	−1.33121	−	1.11702i	−0.983794	−	0.179305i	$-0.942615\pi$
$739$	−983.763	−	825.475i	−1.33121	−	1.11702i	−0.347415	−	0.937712i	$-0.612940\pi$
$740$		0			0
$741$	−17.3237	+	4.79334i	−0.0233788	+	0.00646874i
$742$		0			0
$743$	357.739	+	337.510i	0.481480	+	0.454253i	0.888305	−	0.459253i	$-0.151883\pi$
$743$	357.739	+	337.510i	0.481480	+	0.454253i	−0.406826	+	0.913506i	$0.633364\pi$
$744$		0			0
$745$	−1041.92	+	1399.54i	−1.39855	+	1.87858i
$746$		0			0
$747$	90.7256	−	568.502i	0.121453	−	0.761047i
$748$		0			0
$749$	179.336	−	357.088i	0.239434	−	0.476753i
$750$		0			0
$751$	904.358	−	105.704i	1.20420	−	0.140751i	0.509772	−	0.860309i	$-0.329730\pi$
$751$	904.358	−	105.704i	1.20420	−	0.140751i	0.694432	+	0.719558i	$0.255656\pi$
$752$		0			0
$753$	251.562	+	457.595i	0.334080	+	0.607695i
$754$		0			0
$755$	−793.304	+	458.015i	−1.05073	+	0.606642i
$756$		0			0
$757$	−339.653	+	588.297i	−0.448683	+	0.777142i	−0.998301	−	0.0582742i	$-0.981440\pi$
$757$	−339.653	+	588.297i	−0.448683	+	0.777142i	0.549617	+	0.835417i	$0.314774\pi$
$758$		0			0
$759$	124.915	+	155.365i	0.164579	+	0.204697i
$760$		0			0
$761$	−574.668	−	247.887i	−0.755148	−	0.325739i	−0.0165300	−	0.999863i	$-0.505262\pi$
$761$	−574.668	−	247.887i	−0.755148	−	0.325739i	−0.738618	+	0.674124i	$0.764521\pi$
$762$		0			0
$763$	49.3615	+	847.505i	0.0646940	+	1.11075i
$764$		0			0
$765$	−1146.68	+	85.5376i	−1.49893	+	0.111814i
$766$		0			0
$767$	−35.8665	+	15.4713i	−0.0467621	+	0.0201712i
$768$		0			0
$769$	−533.194	−	126.369i	−0.693360	−	0.164329i	−0.131198	−	0.991356i	$-0.541882\pi$
$769$	−533.194	−	126.369i	−0.693360	−	0.164329i	−0.562162	+	0.827027i	$0.690030\pi$
$770$		0			0
$771$	−145.118	−	203.700i	−0.188220	−	0.264203i
$772$		0			0
$773$	59.2640	+	162.826i	0.0766675	+	0.210642i	0.972106	−	0.234544i	$-0.0753597\pi$
$773$	59.2640	+	162.826i	0.0766675	+	0.210642i	−0.895438	+	0.445186i	$0.853137\pi$
$774$		0			0
$775$	407.931	+	148.475i	0.526363	+	0.191581i
$776$		0			0
$777$	109.272	−	98.8492i	0.140633	−	0.127219i
$778$		0			0
$779$	−51.9788	−	3.02742i	−0.0667250	−	0.00388629i
$780$		0			0
$781$	23.9385	+	25.3733i	0.0306511	+	0.0324882i
$782$		0			0
$783$	−398.035	+	68.2698i	−0.508346	+	0.0871901i
$784$		0			0
$785$	−968.121	−	289.837i	−1.23328	−	0.369219i
$786$		0			0
$787$	265.276	+	174.475i	0.337073	+	0.221696i	0.706749	−	0.707464i	$-0.250161\pi$
$787$	265.276	+	174.475i	0.337073	+	0.221696i	−0.369676	+	0.929161i	$0.620531\pi$
$788$		0			0
$789$	−758.308	+	975.250i	−0.961100	+	1.23606i
$790$		0			0
$791$	−483.700	+	85.2894i	−0.611504	+	0.107825i
$792$		0			0
$793$	−1.33335	+	7.56183i	−0.00168141	+	0.00953572i
$794$		0			0
$795$	−113.351	−	8.98784i	−0.142580	−	0.0113055i
$796$		0			0
$797$	−1067.33	+	319.537i	−1.33918	+	0.400925i	−0.874703	−	0.484659i	$-0.838944\pi$
$797$	−1067.33	+	319.537i	−1.33918	+	0.400925i	−0.464479	+	0.885584i	$0.653758\pi$
$798$		0			0
$799$	−512.259	−	59.8745i	−0.641125	−	0.0749368i
$800$		0			0
$801$	−458.119	−	1444.22i	−0.571934	−	1.80303i
$802$		0			0
$803$	−71.3354	−	108.460i	−0.0888361	−	0.135069i
$804$		0			0
$805$	−243.263	−	326.758i	−0.302189	−	0.405911i
$806$		0			0
$807$	348.218	−	118.541i	0.431497	−	0.146891i
$808$		0			0
$809$			1431.28i			1.76920i	0.466348	+	0.884601i	$0.345569\pi$
$809$			1431.28i			1.76920i	−0.466348	+	0.884601i	$0.654431\pi$
$810$		0			0
$811$	−1142.93			−1.40929			−0.704645	−	0.709560i	$-0.748894\pi$
$811$	−1142.93			−1.40929			−0.704645	+	0.709560i	$0.748894\pi$
$812$		0			0
$813$	−723.541	+	826.487i	−0.889965	+	1.01659i
$814$		0			0
$815$	1504.87	−	1120.34i	1.84647	−	1.37465i
$816$		0			0
$817$	531.581	−	349.626i	0.650649	−	0.427939i
$818$		0			0
$819$	−8.39634	−	16.0611i	−0.0102519	−	0.0196106i
$820$		0			0
$821$	174.943	−	1496.74i	0.213086	−	1.82307i	−0.287958	−	0.957643i	$-0.592976\pi$
$821$	174.943	−	1496.74i	0.213086	−	1.82307i	0.501044	−	0.865422i	$-0.332950\pi$
$822$		0			0
$823$	115.596	+	386.117i	0.140457	+	0.469158i	0.999054	−	0.0434930i	$-0.0138486\pi$
$823$	115.596	+	386.117i	0.140457	+	0.469158i	−0.858597	+	0.512651i	$0.828663\pi$
$824$		0			0
$825$	163.571	+	112.561i	0.198268	+	0.136437i
$826$		0			0
$827$	50.4134	+	8.88925i	0.0609594	+	0.0107488i	0.204045	−	0.978962i	$-0.434591\pi$
$827$	50.4134	+	8.88925i	0.0609594	+	0.0107488i	−0.143085	+	0.989710i	$0.545702\pi$
$828$		0			0
$829$	−17.6454	−	100.072i	−0.0212851	−	0.120714i	0.972314	−	0.233679i	$-0.0750764\pi$
$829$	−17.6454	−	100.072i	−0.0212851	−	0.120714i	−0.993599	+	0.112965i	$0.963965\pi$
$830$		0			0
$831$	139.562	−	1010.05i	0.167945	−	1.21547i
$832$		0			0
$833$	364.990	−	554.940i	0.438163	−	0.666195i
$834$		0			0
$835$	4.13935	−	13.8264i	0.00495730	−	0.0165585i
$836$		0			0
$837$	−440.578	+	586.068i	−0.526378	+	0.700200i
$838$		0			0
$839$	−314.348	+	296.572i	−0.374669	+	0.353482i	−0.850426	−	0.526095i	$-0.823656\pi$
$839$	−314.348	+	296.572i	−0.374669	+	0.353482i	0.475757	+	0.879577i	$0.342174\pi$
$840$		0			0
$841$	−35.8916	+	616.235i	−0.0426773	+	0.732741i
$842$		0			0
$843$	715.019	−	153.718i	0.848184	−	0.182347i
$844$		0			0
$845$	369.482	−	1015.14i	0.437257	−	1.20135i
$846$		0			0
$847$	386.916	−	140.826i	0.456807	−	0.166264i
$848$		0			0
$849$	−908.566	−	414.701i	−1.07016	−	0.488458i
$850$		0			0
$851$	45.8567	−	193.485i	0.0538857	−	0.227361i
$852$		0			0
$853$	426.425	+	988.563i	0.499912	+	1.15893i	0.962237	+	0.272215i	$0.0877561\pi$
$853$	426.425	+	988.563i	0.499912	+	1.15893i	−0.462325	+	0.886711i	$0.652985\pi$
$854$		0			0
$855$	−279.322	−	619.607i	−0.326693	−	0.724686i
$856$		0			0
$857$	733.392	−	42.7152i	0.855766	−	0.0498427i	0.375350	−	0.926883i	$-0.377523\pi$
$857$	733.392	−	42.7152i	0.855766	−	0.0498427i	0.480416	+	0.877041i	$0.340486\pi$
$858$		0			0
$859$	211.618	−	490.585i	0.246354	−	0.571112i	−0.749508	−	0.661996i	$-0.769710\pi$
$859$	211.618	−	490.585i	0.246354	−	0.571112i	0.995862	+	0.0908833i	$0.0289690\pi$
$860$		0			0
$861$	−8.03119	−	51.8799i	−0.00932775	−	0.0602555i
$862$		0			0
$863$	−329.493	−	190.233i	−0.381800	−	0.220432i	0.296801	−	0.954939i	$-0.404080\pi$
$863$	−329.493	−	190.233i	−0.381800	−	0.220432i	−0.678601	+	0.734507i	$0.737413\pi$
$864$		0			0
$865$	−22.4960	−	38.9642i	−0.0260069	−	0.0450453i
$866$		0			0
$867$	280.388	+	169.811i	0.323400	+	0.195860i
$868$		0			0
$869$	25.1891	+	215.507i	0.0289864	+	0.247994i
$870$		0			0
$871$	45.2634	+	22.7321i	0.0519672	+	0.0260989i
$872$		0			0
$873$	−548.928	+	328.953i	−0.628783	+	0.376808i
$874$		0			0
$875$	183.511	+	136.619i	0.209727	+	0.156136i
$876$		0			0
$877$	−335.350	+	355.450i	−0.382383	+	0.405303i	−0.889765	−	0.456419i	$-0.849132\pi$
$877$	−335.350	+	355.450i	−0.382383	+	0.405303i	0.507382	+	0.861721i	$0.330613\pi$
$878$		0			0
$879$	278.561	+	72.2152i	0.316907	+	0.0821561i
$880$		0			0
$881$	−508.509	+	606.018i	−0.577195	+	0.687875i	−0.973091	−	0.230421i	$-0.925990\pi$
$881$	−508.509	+	606.018i	−0.577195	+	0.687875i	0.395896	+	0.918295i	$0.370434\pi$
$882$		0			0
$883$	73.3227	−	61.5250i	0.0830382	−	0.0696773i	−0.600324	−	0.799757i	$-0.704962\pi$
$883$	73.3227	−	61.5250i	0.0830382	−	0.0696773i	0.683362	+	0.730080i	$0.260517\pi$
$884$		0			0
$885$	−785.588	−	1250.73i	−0.887670	−	1.41325i
$886$		0			0
$887$	333.966	+	664.980i	0.376511	+	0.749696i	0.999470	−	0.0325592i	$-0.0103657\pi$
$887$	333.966	+	664.980i	0.376511	+	0.749696i	−0.622958	+	0.782255i	$0.714069\pi$
$888$		0			0
$889$	−49.8409	+	11.8125i	−0.0560640	+	0.0132874i
$890$		0			0
$891$	−262.337	+	208.914i	−0.294430	+	0.234471i
$892$		0			0
$893$	−70.3020	−	296.627i	−0.0787256	−	0.332169i
$894$		0			0
$895$	1640.12	−	823.701i	1.83254	−	0.920337i
$896$		0			0
$897$	−21.6211	−	11.4318i	−0.0241038	−	0.0127445i
$898$		0			0
$899$	−261.084	−	311.148i	−0.290416	−	0.346104i
$900$		0			0
$901$	90.5084	+	75.9456i	0.100453	+	0.0842903i
$902$		0			0
$903$	457.300	+	449.915i	0.506423	+	0.498245i
$904$		0			0
$905$	1017.27	+	959.742i	1.12405	+	1.06049i
$906$		0			0
$907$	−536.683	+	720.891i	−0.591712	+	0.794808i	−0.992614	−	0.121313i	$-0.961289\pi$
$907$	−536.683	+	720.891i	−0.591712	+	0.794808i	0.400902	+	0.916121i	$0.368697\pi$
$908$		0			0
$909$	−1130.36	+	980.278i	−1.24352	+	1.07841i
$910$		0			0
$911$	−344.049	+	685.058i	−0.377661	+	0.751984i	−0.999515	−	0.0311488i	$-0.990083\pi$
$911$	−344.049	+	685.058i	−0.377661	+	0.751984i	0.621854	+	0.783133i	$0.286380\pi$
$912$		0			0
$913$	263.045	−	30.7455i	0.288110	−	0.0336753i
$914$		0			0
$915$	−290.276	−	6.08179i	−0.317241	−	0.00664677i
$916$		0			0
$917$	−330.079	+	190.571i	−0.359956	+	0.207820i
$918$		0			0
$919$	−375.385	+	650.186i	−0.408471	+	0.707493i	−0.994719	−	0.102639i	$-0.967271\pi$
$919$	−375.385	+	650.186i	−0.408471	+	0.707493i	0.586247	+	0.810132i	$0.300605\pi$
$920$		0			0
$921$	482.400	−	1243.69i	0.523779	−	1.35036i
$922$		0			0
$923$	−3.92960	−	1.69506i	−0.00425742	−	0.00183647i
$924$		0			0
$925$	−11.5156	−	197.716i	−0.0124493	−	0.213747i
$926$		0			0
$927$	177.876	+	50.1122i	0.191884	+	0.0540585i
$928$		0			0
$929$	893.466	−	385.404i	0.961750	−	0.414859i	0.143455	−	0.989657i	$-0.454179\pi$
$929$	893.466	−	385.404i	0.961750	−	0.414859i	0.818295	+	0.574798i	$0.194919\pi$
$930$		0			0
$931$	382.015	+	90.5393i	0.410328	+	0.0972495i
$932$		0			0
$933$	−867.661	+	83.0327i	−0.929969	+	0.0889953i
$934$		0			0
$935$	−180.918	−	497.068i	−0.193495	−	0.531624i
$936$		0			0
$937$	−762.745	−	277.616i	−0.814028	−	0.296282i	−0.0987416	−	0.995113i	$-0.531482\pi$
$937$	−762.745	−	277.616i	−0.814028	−	0.296282i	−0.715287	+	0.698831i	$0.753704\pi$
$938$		0			0
$939$	709.478	+	228.703i	0.755567	+	0.243560i
$940$		0			0
$941$	1455.15	+	84.7527i	1.54638	+	0.0900666i	0.809973	−	0.586467i	$-0.199482\pi$
$941$	1455.15	+	84.7527i	1.54638	+	0.0900666i	0.736411	+	0.676534i	$0.236519\pi$
$942$		0			0
$943$	−48.6170	−	51.5310i	−0.0515557	−	0.0546458i
$944$		0			0
$945$	551.586	−	406.652i	0.583689	−	0.430320i
$946$		0			0
$947$	−159.191	−	47.6585i	−0.168100	−	0.0503258i	0.201647	−	0.979458i	$-0.435371\pi$
$947$	−159.191	−	47.6585i	−0.168100	−	0.0503258i	−0.369747	+	0.929132i	$0.620556\pi$
$948$		0			0
$949$	13.3062	+	8.75162i	0.0140213	+	0.00922194i
$950$		0			0
$951$	20.3982	+	50.1517i	0.0214492	+	0.0527357i
$952$		0			0
$953$	−1637.72	+	288.774i	−1.71849	+	0.303016i	−0.944091	−	0.329684i	$-0.893058\pi$
$953$	−1637.72	+	288.774i	−1.71849	+	0.303016i	−0.774397	+	0.632700i	$0.781947\pi$
$954$		0			0
$955$	305.221	−	1730.99i	0.319603	−	1.81256i
$956$		0			0
$957$	−79.8821	−	167.729i	−0.0834713	−	0.175266i
$958$		0			0
$959$	−213.958	+	64.0548i	−0.223105	+	0.0667933i
$960$		0			0
$961$	222.061	+	25.9552i	0.231073	+	0.0270085i
$962$		0			0
$963$	899.164	−	119.965i	0.933711	−	0.124575i
$964$		0			0
$965$	964.902	+	1467.06i	0.999898	+	1.52027i
$966$		0			0
$967$	336.840	+	452.455i	0.348335	+	0.467896i	0.941416	−	0.337247i	$-0.109496\pi$
$967$	336.840	+	452.455i	0.348335	+	0.467896i	−0.593081	+	0.805143i	$0.702088\pi$
$968$		0			0
$969$	−137.175	+	692.765i	−0.141563	+	0.714928i
$970$		0			0
$971$			636.315i			0.655320i	0.944796	+	0.327660i	$0.106260\pi$
$971$			636.315i			0.655320i	−0.944796	+	0.327660i	$0.893740\pi$
$972$		0			0
$973$	−790.100			−0.812025
$974$		0			0
$975$	−23.8957	−	4.73160i	−0.0245084	−	0.00485292i
$976$		0			0
$977$	59.0656	−	43.9727i	0.0604561	−	0.0450079i	−0.566506	−	0.824057i	$-0.691705\pi$
$977$	59.0656	−	43.9727i	0.0604561	−	0.0450079i	0.626962	+	0.779049i	$0.284298\pi$
$978$		0			0
$979$	582.339	−	383.010i	0.594831	−	0.391226i
$980$		0			0
$981$	−1526.93	+	1175.87i	−1.55650	+	1.19864i
$982$		0			0
$983$	−132.979	+	1137.71i	−0.135279	+	1.15739i	0.739600	+	0.673046i	$0.235015\pi$
$983$	−132.979	+	1137.71i	−0.135279	+	1.15739i	−0.874879	+	0.484341i	$0.839059\pi$
$984$		0			0
$985$	−410.840	−	1372.30i	−0.417097	−	1.39320i
$986$		0			0
$987$	277.504	−	132.163i	0.281159	−	0.133903i
$988$		0			0
$989$	852.570	+	150.331i	0.862053	+	0.152003i
$990$		0			0
$991$	−298.518	−	1692.98i	−0.301229	−	1.70836i	−0.640743	−	0.767756i	$-0.721373\pi$
$991$	−298.518	−	1692.98i	−0.301229	−	1.70836i	0.339513	−	0.940601i	$-0.389738\pi$
$992$		0			0
$993$	1106.55	−	450.069i	1.11435	−	0.453241i
$994$		0			0
$995$	1070.01	−	1626.88i	1.07539	−	1.63505i
$996$		0			0
$997$	256.748	−	857.599i	0.257521	−	0.860180i	−0.727257	−	0.686365i	$-0.759205\pi$
$997$	256.748	−	857.599i	0.257521	−	0.860180i	0.984778	−	0.173815i	$-0.0556095\pi$
$998$		0			0
$999$	325.122	+	78.6601i	0.325447	+	0.0787388i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	324.3.o.a.5.17	✓	324
81.65	odd	54	inner	324.3.o.a.65.17	yes	324

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
324.3.o.a.5.17	✓	324	1.1	even	1	trivial
324.3.o.a.65.17	yes	324	81.65	odd	54	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 324 = 2^{2} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	324.o (of order \(54\), degree \(18\), minimal)

\(f(q)\)	\(=\)	\(q+(2.94286 + 0.582717i) q^{3} +(5.13522 - 3.82303i) q^{5} +(3.31229 - 2.17853i) q^{7} +(8.32088 + 3.42971i) q^{9} +O(q^{10})\)	\(q+(2.94286 + 0.582717i) q^{3} +(5.13522 - 3.82303i) q^{5} +(3.31229 - 2.17853i) q^{7} +(8.32088 + 3.42971i) q^{9} +(-0.480652 + 4.11224i) q^{11} +(-0.145678 - 0.486597i) q^{13} +(17.3400 - 8.25827i) q^{15} +(-19.6534 - 3.46543i) q^{17} +(-2.04833 - 11.6166i) q^{19} +(11.0171 - 4.48098i) q^{21} +(8.81970 - 13.4097i) q^{23} +(4.58486 - 15.3145i) q^{25} +(22.4887 + 14.9419i) q^{27} +(-10.8795 + 10.2643i) q^{29} +(-1.57896 + 27.1097i) q^{31} +(-3.81077 + 11.8217i) q^{33} +(8.68077 - 23.8502i) q^{35} +(11.6418 - 4.23727i) q^{37} +(-0.145161 - 1.51688i) q^{39} +(1.01794 - 4.29502i) q^{41} +(21.3640 + 49.5273i) q^{43} +(55.8415 - 14.1987i) q^{45} +(25.7996 - 1.50266i) q^{47} +(-13.1826 + 30.5607i) q^{49} +(-55.8180 - 21.6507i) q^{51} +(-5.12718 - 2.96018i) q^{53} +(13.2530 + 22.9548i) q^{55} +(0.741268 - 35.3798i) q^{57} +(-8.92774 - 76.3817i) q^{59} +(-13.5091 - 6.78452i) q^{61} +(35.0329 - 6.76707i) q^{63} +(-2.60836 - 1.94185i) q^{65} +(-68.4316 + 72.5333i) q^{67} +(33.7692 - 34.3235i) q^{69} +(5.41579 - 6.45429i) q^{71} +(-24.0192 + 20.1545i) q^{73} +(22.4166 - 42.3968i) q^{75} +(7.36658 + 14.6681i) q^{77} +(50.9936 - 12.0857i) q^{79} +(57.4741 + 57.0765i) q^{81} +(-14.7516 - 62.2420i) q^{83} +(-114.173 + 57.3399i) q^{85} +(-37.9982 + 23.8668i) q^{87} +(-108.213 - 128.963i) q^{89} +(-1.54259 - 1.29439i) q^{91} +(-20.4439 + 78.8599i) q^{93} +(-54.9294 - 51.8232i) q^{95} +(-42.4611 + 57.0351i) q^{97} +(-18.1033 + 32.5690i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 324 q+O(q^{10}) \) 324 * q	\( 324 q - 135 q^{21} - 81 q^{23} + 27 q^{27} + 81 q^{29} + 189 q^{33} + 243 q^{35} + 216 q^{41} + 432 q^{45} + 324 q^{47} + 126 q^{51} - 216 q^{57} - 378 q^{59} - 540 q^{63} - 108 q^{65} - 351 q^{67} + 504 q^{69} + 648 q^{71} + 450 q^{75} + 432 q^{77} - 54 q^{79} - 72 q^{81} - 216 q^{83} + 270 q^{85} - 1008 q^{87} - 648 q^{89} - 684 q^{93} - 432 q^{95} + 459 q^{97} - 252 q^{99}+O(q^{100}) \) 324 * q - 135 * q^21 - 81 * q^23 + 27 * q^27 + 81 * q^29 + 189 * q^33 + 243 * q^35 + 216 * q^41 + 432 * q^45 + 324 * q^47 + 126 * q^51 - 216 * q^57 - 378 * q^59 - 540 * q^63 - 108 * q^65 - 351 * q^67 + 504 * q^69 + 648 * q^71 + 450 * q^75 + 432 * q^77 - 54 * q^79 - 72 * q^81 - 216 * q^83 + 270 * q^85 - 1008 * q^87 - 648 * q^89 - 684 * q^93 - 432 * q^95 + 459 * q^97 - 252 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more