LMFDB - Embedded newform 324.3.o.a.5.13

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			5.13
Character	$\chi$	$=$	324.5
Dual form			324.3.o.a.65.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.79639 - 2.40271i) q^{3} +(3.71691 - 2.76713i) q^{5} +(-11.2502 + 7.39935i) q^{7} +(-2.54600 - 8.63237i) q^{9} +O(q^{10})$	\(q+(1.79639 - 2.40271i) q^{3} +(3.71691 - 2.76713i) q^{5} +(-11.2502 + 7.39935i) q^{7} +(-2.54600 - 8.63237i) q^{9} +(1.91360 - 16.3719i) q^{11} +(-2.42871 - 8.11244i) q^{13} +(0.0283820 - 13.9015i) q^{15} +(7.12098 + 1.25562i) q^{17} +(-4.78784 - 27.1532i) q^{19} +(-2.43116 + 40.3229i) q^{21} +(14.6741 - 22.3109i) q^{23} +(-1.01172 + 3.37939i) q^{25} +(-25.3147 - 9.38977i) q^{27} +(-25.2938 + 23.8635i) q^{29} +(-1.80475 + 30.9863i) q^{31} +(-35.8993 - 34.0081i) q^{33} +(-21.3408 + 58.6334i) q^{35} +(56.7073 - 20.6398i) q^{37} +(-23.8547 - 8.73760i) q^{39} +(2.43280 - 10.2648i) q^{41} +(-0.821893 - 1.90536i) q^{43} +(-33.3502 - 25.0406i) q^{45} +(-56.4374 + 3.28710i) q^{47} +(52.4078 - 121.495i) q^{49} +(15.8089 - 14.8541i) q^{51} +(84.7095 + 48.9071i) q^{53} +(-38.1906 - 66.1480i) q^{55} +(-73.8420 - 37.2738i) q^{57} +(3.79607 + 32.4774i) q^{59} +(52.0691 + 26.1501i) q^{61} +(92.5168 + 78.2768i) q^{63} +(-31.4755 - 23.4326i) q^{65} +(26.0663 - 27.6287i) q^{67} +(-27.2462 - 75.3367i) q^{69} +(30.2054 - 35.9974i) q^{71} +(-40.0293 + 33.5886i) q^{73} +(6.30225 + 8.50157i) q^{75} +(99.6131 + 198.346i) q^{77} +(-84.1023 + 19.9326i) q^{79} +(-68.0357 + 43.9561i) q^{81} +(15.1055 + 63.7352i) q^{83} +(29.9425 - 15.0377i) q^{85} +(11.8995 + 103.642i) q^{87} +(-19.5215 - 23.2648i) q^{89} +(87.3501 + 73.2954i) q^{91} +(71.2090 + 59.9996i) q^{93} +(-92.9325 - 87.6773i) q^{95} +(50.0317 - 67.2042i) q^{97} +(-146.200 + 25.1640i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	1.79639	−	2.40271i	0.598795	−	0.800902i
$3$	1.79639	−	2.40271i	0.598795	−	0.800902i
$4$		0			0
$5$	3.71691	−	2.76713i	0.743381	−	0.553427i	−0.157486	−	0.987521i	$-0.550339\pi$
$5$	3.71691	−	2.76713i	0.743381	−	0.553427i	0.900867	+	0.434095i	$0.142932\pi$
$6$		0			0
$7$	−11.2502	+	7.39935i	−1.60717	+	1.05705i	−0.653177	+	0.757205i	$0.726564\pi$
$7$	−11.2502	+	7.39935i	−1.60717	+	1.05705i	−0.953988	+	0.299844i	$0.903065\pi$
$8$		0			0
$9$	−2.54600	−	8.63237i	−0.282889	−	0.959153i
$10$		0			0
$11$	1.91360	−	16.3719i	0.173964	−	1.48836i	−0.570834	−	0.821065i	$-0.693380\pi$
$11$	1.91360	−	16.3719i	0.173964	−	1.48836i	0.744798	−	0.667290i	$-0.232546\pi$
$12$		0			0
$13$	−2.42871	−	8.11244i	−0.186824	−	0.624034i	−0.999165	−	0.0408522i	$-0.986993\pi$
$13$	−2.42871	−	8.11244i	−0.186824	−	0.624034i	0.812342	−	0.583182i	$-0.198192\pi$
$14$		0			0
$15$	0.0283820	−	13.9015i	0.00189214	−	0.926765i
$16$		0			0
$17$	7.12098	+	1.25562i	0.418881	+	0.0738601i	0.379116	−	0.925349i	$-0.376228\pi$
$17$	7.12098	+	1.25562i	0.418881	+	0.0738601i	0.0397649	+	0.999209i	$0.487339\pi$
$18$		0			0
$19$	−4.78784	−	27.1532i	−0.251992	−	1.42912i	−0.803678	−	0.595065i	$-0.797126\pi$
$19$	−4.78784	−	27.1532i	−0.251992	−	1.42912i	0.551686	−	0.834052i	$-0.313985\pi$
$20$		0			0
$21$	−2.43116	+	40.3229i	−0.115769	+	1.92014i
$22$		0			0
$23$	14.6741	−	22.3109i	0.638006	−	0.970041i	−0.361288	−	0.932454i	$-0.617663\pi$
$23$	14.6741	−	22.3109i	0.638006	−	0.970041i	0.999293	−	0.0375862i	$-0.0119669\pi$
$24$		0			0
$25$	−1.01172	+	3.37939i	−0.0404690	+	0.135176i
$26$		0			0
$27$	−25.3147	−	9.38977i	−0.937580	−	0.347769i
$28$		0			0
$29$	−25.2938	+	23.8635i	−0.872200	+	0.822878i	−0.985323	−	0.170703i	$-0.945396\pi$
$29$	−25.2938	+	23.8635i	−0.872200	+	0.822878i	0.113123	+	0.993581i	$0.463915\pi$
$30$		0			0
$31$	−1.80475	+	30.9863i	−0.0582177	+	0.999559i	0.835090	+	0.550113i	$0.185415\pi$
$31$	−1.80475	+	30.9863i	−0.0582177	+	0.999559i	−0.893308	+	0.449445i	$0.851622\pi$
$32$		0			0
$33$	−35.8993	−	34.0081i	−1.08786	−	1.03055i
$34$		0			0
$35$	−21.3408	+	58.6334i	−0.609737	+	1.67524i
$36$		0			0
$37$	56.7073	−	20.6398i	1.53263	−	0.557832i	0.568367	−	0.822775i	$-0.307576\pi$
$37$	56.7073	−	20.6398i	1.53263	−	0.557832i	0.964264	+	0.264943i	$0.0853533\pi$
$38$		0			0
$39$	−23.8547	−	8.73760i	−0.611659	−	0.224041i
$40$		0			0
$41$	2.43280	−	10.2648i	0.0593365	−	0.250361i	−0.935291	−	0.353880i	$-0.884862\pi$
$41$	2.43280	−	10.2648i	0.0593365	−	0.250361i	0.994627	+	0.103519i	$0.0330103\pi$
$42$		0			0
$43$	−0.821893	−	1.90536i	−0.0191138	−	0.0443108i	0.908392	−	0.418120i	$-0.137311\pi$
$43$	−0.821893	−	1.90536i	−0.0191138	−	0.0443108i	−0.927506	+	0.373809i	$0.878052\pi$
$44$		0			0
$45$	−33.3502	−	25.0406i	−0.741115	−	0.556457i
$46$		0			0
$47$	−56.4374	+	3.28710i	−1.20079	+	0.0699383i	−0.646852	−	0.762616i	$-0.723915\pi$
$47$	−56.4374	+	3.28710i	−1.20079	+	0.0699383i	−0.553943	+	0.832554i	$0.686878\pi$
$48$		0			0
$49$	52.4078	−	121.495i	1.06955	−	2.47949i
$50$		0			0
$51$	15.8089	−	14.8541i	0.309979	−	0.291256i
$52$		0			0
$53$	84.7095	+	48.9071i	1.59829	+	0.922775i	0.991816	+	0.127673i	$0.0407509\pi$
$53$	84.7095	+	48.9071i	1.59829	+	0.922775i	0.606476	+	0.795102i	$0.292582\pi$
$54$		0			0
$55$	−38.1906	−	66.1480i	−0.694374	−	1.20269i
$56$		0			0
$57$	−73.8420	−	37.2738i	−1.29547	−	0.653927i
$58$		0			0
$59$	3.79607	+	32.4774i	0.0643401	+	0.550465i	0.986513	+	0.163686i	$0.0523383\pi$
$59$	3.79607	+	32.4774i	0.0643401	+	0.550465i	−0.922172	+	0.386779i	$0.873588\pi$
$60$		0			0
$61$	52.0691	+	26.1501i	0.853592	+	0.428690i	0.821102	−	0.570782i	$-0.193360\pi$
$61$	52.0691	+	26.1501i	0.853592	+	0.428690i	0.0324906	+	0.999472i	$0.489656\pi$
$62$		0			0
$63$	92.5168	+	78.2768i	1.46852	+	1.24249i
$64$		0			0
$65$	−31.4755	−	23.4326i	−0.484238	−	0.360502i
$66$		0			0
$67$	26.0663	−	27.6287i	0.389049	−	0.412368i	−0.503014	−	0.864278i	$-0.667776\pi$
$67$	26.0663	−	27.6287i	0.389049	−	0.412368i	0.892064	+	0.451910i	$0.149257\pi$
$68$		0			0
$69$	−27.2462	−	75.3367i	−0.394873	−	1.09184i
$70$		0			0
$71$	30.2054	−	35.9974i	0.425429	−	0.507006i	−0.510169	−	0.860074i	$-0.670417\pi$
$71$	30.2054	−	35.9974i	0.425429	−	0.507006i	0.935598	+	0.353068i	$0.114862\pi$
$72$		0			0
$73$	−40.0293	+	33.5886i	−0.548346	+	0.460117i	−0.874381	−	0.485241i	$-0.838732\pi$
$73$	−40.0293	+	33.5886i	−0.548346	+	0.460117i	0.326034	+	0.945358i	$0.394288\pi$
$74$		0			0
$75$	6.30225	+	8.50157i	0.0840300	+	0.113354i
$76$		0			0
$77$	99.6131	+	198.346i	1.29368	+	2.57592i
$78$		0			0
$79$	−84.1023	+	19.9326i	−1.06459	+	0.252312i	−0.725344	−	0.688387i	$-0.758319\pi$
$79$	−84.1023	+	19.9326i	−1.06459	+	0.252312i	−0.339243	+	0.940699i	$0.610171\pi$
$80$		0			0
$81$	−68.0357	+	43.9561i	−0.839948	+	0.542668i
$82$		0			0
$83$	15.1055	+	63.7352i	0.181994	+	0.767894i	0.985089	+	0.172043i	$0.0550368\pi$
$83$	15.1055	+	63.7352i	0.181994	+	0.767894i	−0.803095	+	0.595851i	$0.796815\pi$
$84$		0			0
$85$	29.9425	−	15.0377i	0.352265	−	0.176914i
$86$		0			0
$87$	11.8995	+	103.642i	0.136776	+	1.19128i
$88$		0			0
$89$	−19.5215	−	23.2648i	−0.219343	−	0.261402i	0.645141	−	0.764064i	$-0.276799\pi$
$89$	−19.5215	−	23.2648i	−0.219343	−	0.261402i	−0.864483	+	0.502661i	$0.832354\pi$
$90$		0			0
$91$	87.3501	+	73.2954i	0.959891	+	0.805444i
$92$		0			0
$93$	71.2090	+	59.9996i	0.765688	+	0.645157i
$94$		0			0
$95$	−92.9325	−	87.6773i	−0.978237	−	0.922919i
$96$		0			0
$97$	50.0317	−	67.2042i	0.515790	−	0.692827i	−0.465568	−	0.885012i	$-0.654150\pi$
$97$	50.0317	−	67.2042i	0.515790	−	0.692827i	0.981359	+	0.192185i	$0.0615575\pi$
$98$		0			0
$99$	−146.200	+	25.1640i	−1.47677	+	0.254182i
$100$		0			0
$101$	50.5400	−	100.633i	0.500396	−	0.996370i	−0.491686	−	0.870773i	$-0.663619\pi$
$101$	50.5400	−	100.633i	0.500396	−	0.996370i	0.992081	−	0.125597i	$-0.0400846\pi$
$102$		0			0
$103$	124.552	−	14.5580i	1.20924	−	0.141340i	0.512516	−	0.858678i	$-0.328713\pi$
$103$	124.552	−	14.5580i	1.20924	−	0.141340i	0.696726	+	0.717337i	$0.254639\pi$
$104$		0			0
$105$	102.542	+	156.604i	0.976595	+	1.49146i
$106$		0			0
$107$	−6.43905	+	3.71758i	−0.0601780	+	0.0347438i	−0.529787	−	0.848131i	$-0.677728\pi$
$107$	−6.43905	+	3.71758i	−0.0601780	+	0.0347438i	0.469609	+	0.882874i	$0.344395\pi$
$108$		0			0
$109$	−26.6992	+	46.2444i	−0.244947	+	0.424261i	−0.962117	−	0.272638i	$-0.912104\pi$
$109$	−26.6992	+	46.2444i	−0.244947	+	0.424261i	0.717170	+	0.696899i	$0.245437\pi$
$110$		0			0
$111$	52.2769	−	173.328i	0.470963	−	1.56151i
$112$		0			0
$113$	111.149	+	47.9451i	0.983621	+	0.424293i	0.826285	−	0.563252i	$-0.190450\pi$
$113$	111.149	+	47.9451i	0.983621	+	0.424293i	0.157336	+	0.987545i	$0.449709\pi$
$114$		0			0
$115$	−7.19497	−	123.533i	−0.0625650	−	1.07420i
$116$		0			0
$117$	−63.8461	+	41.6198i	−0.545693	+	0.355725i
$118$		0			0
$119$	−89.4029	+	38.5647i	−0.751285	+	0.324073i
$120$		0			0
$121$	−146.639	−	34.7541i	−1.21189	−	0.287224i
$122$		0			0
$123$	−20.2930	−	24.2848i	−0.164984	−	0.197437i
$124$		0			0
$125$	45.2124	+	124.220i	0.361699	+	0.993759i
$126$		0			0
$127$	−112.050	−	40.7830i	−0.882286	−	0.321126i	−0.139154	−	0.990271i	$-0.544438\pi$
$127$	−112.050	−	40.7830i	−0.882286	−	0.321126i	−0.743132	+	0.669145i	$0.766660\pi$
$128$		0			0
$129$	−6.05446	−	1.44800i	−0.0469338	−	0.0112248i
$130$		0			0
$131$	148.842	+	8.66903i	1.13620	+	0.0661758i	0.615910	−	0.787817i	$-0.288789\pi$
$131$	148.842	+	8.66903i	1.13620	+	0.0661758i	0.520285	+	0.853993i	$0.325826\pi$
$132$		0			0
$133$	254.780	+	270.051i	1.91564	+	2.03046i
$134$		0			0
$135$	−120.075	+	35.1482i	−0.889444	+	0.260357i
$136$		0			0
$137$	225.265	+	67.4400i	1.64427	+	0.492263i	0.969362	−	0.245638i	$-0.0789973\pi$
$137$	225.265	+	67.4400i	1.64427	+	0.492263i	0.674910	+	0.737900i	$0.264183\pi$
$138$		0			0
$139$	−10.1774	−	6.69380i	−0.0732189	−	0.0481568i	0.512372	−	0.858764i	$-0.328767\pi$
$139$	−10.1774	−	6.69380i	−0.0732189	−	0.0481568i	−0.585591	+	0.810607i	$0.699137\pi$
$140$		0			0
$141$	−93.4853	+	141.507i	−0.663016	+	1.00360i
$142$		0			0
$143$	−137.464	+	24.2386i	−0.961285	+	0.169500i
$144$		0			0
$145$	−27.9813	+	158.690i	−0.192974	+	1.09441i
$146$		0			0
$147$	−197.772	−	344.172i	−1.34539	−	2.34131i
$148$		0			0
$149$	−100.188	+	29.9944i	−0.672406	+	0.201305i	−0.604764	−	0.796405i	$-0.706733\pi$
$149$	−100.188	+	29.9944i	−0.672406	+	0.201305i	−0.0676415	+	0.997710i	$0.521547\pi$
$150$		0			0
$151$	191.015	+	22.3265i	1.26500	+	0.147857i	0.722011	−	0.691882i	$-0.243218\pi$
$151$	191.015	+	22.3265i	1.26500	+	0.147857i	0.542990	+	0.839739i	$0.317292\pi$
$152$		0			0
$153$	−7.29104	−	64.6678i	−0.0476539	−	0.422665i
$154$		0			0
$155$	79.0352	+	120.167i	0.509904	+	0.775272i
$156$		0			0
$157$	−44.2432	−	59.4289i	−0.281804	−	0.378528i	0.638573	−	0.769561i	$-0.279525\pi$
$157$	−44.2432	−	59.4289i	−0.281804	−	0.378528i	−0.920377	+	0.391033i	$0.872118\pi$
$158$		0			0
$159$	269.680	−	115.676i	1.69610	−	0.727523i
$160$		0			0
$161$			359.581i			2.23342i
$162$		0			0
$163$	−139.937			−0.858507			−0.429253	−	0.903184i	$-0.641223\pi$
$163$	−139.937			−0.858507			−0.429253	+	0.903184i	$0.641223\pi$
$164$		0			0
$165$	−227.539	−	27.0665i	−1.37903	−	0.164040i
$166$		0			0
$167$	−76.0786	+	56.6384i	−0.455561	+	0.339152i	−0.800355	−	0.599526i	$-0.795356\pi$
$167$	−76.0786	+	56.6384i	−0.455561	+	0.339152i	0.344795	+	0.938678i	$0.387948\pi$
$168$		0			0
$169$	81.2843	−	53.4616i	0.480972	−	0.316341i
$170$		0			0
$171$	−222.207	+	110.463i	−1.29946	+	0.645980i
$172$		0			0
$173$	14.5318	−	124.327i	0.0839987	−	0.718654i	−0.883963	−	0.467557i	$-0.845134\pi$
$173$	14.5318	−	124.327i	0.0839987	−	0.718654i	0.967962	−	0.251098i	$-0.0807916\pi$
$174$		0			0
$175$	−13.6232	−	45.5048i	−0.0778471	−	0.260027i
$176$		0			0
$177$	84.8529	+	49.2211i	0.479395	+	0.278085i
$178$		0			0
$179$	−185.218	−	32.6590i	−1.03474	−	0.182452i	−0.369615	−	0.929185i	$-0.620510\pi$
$179$	−185.218	−	32.6590i	−1.03474	−	0.182452i	−0.665124	+	0.746733i	$0.731622\pi$
$180$		0			0
$181$	−4.20862	−	23.8683i	−0.0232521	−	0.131869i	0.970972	−	0.239193i	$-0.0768829\pi$
$181$	−4.20862	−	23.8683i	−0.0232521	−	0.131869i	−0.994224	+	0.107324i	$0.965772\pi$
$182$		0			0
$183$	156.367	−	78.1312i	0.854466	−	0.426947i
$184$		0			0
$185$	153.663	−	233.633i	0.830609	−	1.26288i
$186$		0			0
$187$	34.1836	−	114.181i	0.182800	−	0.610595i
$188$		0			0
$189$	354.272	−	81.6755i	1.87446	−	0.432146i
$190$		0			0
$191$	−23.8726	+	22.5227i	−0.124988	+	0.117920i	−0.746198	−	0.665724i	$-0.768123\pi$
$191$	−23.8726	+	22.5227i	−0.124988	+	0.117920i	0.621210	+	0.783644i	$0.286641\pi$
$192$		0			0
$193$	10.0665	−	172.835i	0.0521579	−	0.895517i	−0.866183	−	0.499727i	$-0.833434\pi$
$193$	10.0665	−	172.835i	0.0521579	−	0.895517i	0.918341	−	0.395790i	$-0.129529\pi$
$194$		0			0
$195$	−112.844	+	33.5323i	−0.578686	+	0.171961i
$196$		0			0
$197$	76.5999	−	210.457i	0.388832	−	1.06831i	−0.578696	−	0.815543i	$-0.696438\pi$
$197$	76.5999	−	210.457i	0.388832	−	1.06831i	0.967528	−	0.252764i	$-0.0813396\pi$
$198$		0			0
$199$	108.499	−	39.4904i	0.545221	−	0.198444i	−0.0547009	−	0.998503i	$-0.517421\pi$
$199$	108.499	−	39.4904i	0.545221	−	0.198444i	0.599922	+	0.800059i	$0.295198\pi$
$200$		0			0
$201$	−19.5585	−	112.261i	−0.0973059	−	0.558515i
$202$		0			0
$203$	107.985	−	455.625i	0.531947	−	2.24446i
$204$		0			0
$205$	−19.3615	−	44.8851i	−0.0944465	−	0.218952i
$206$		0			0
$207$	−229.957	−	69.8689i	−1.11090	−	0.337531i
$208$		0			0
$209$	−453.712	+	26.4257i	−2.17087	+	0.126439i
$210$		0			0
$211$	14.5403	−	33.7083i	0.0689115	−	0.159755i	−0.880279	−	0.474456i	$-0.842645\pi$
$211$	14.5403	−	33.7083i	0.0689115	−	0.159755i	0.949191	+	0.314701i	$0.101904\pi$
$212$		0			0
$213$	−32.2307	−	137.240i	−0.151318	−	0.644319i
$214$		0			0
$215$	−8.32729	−	4.80776i	−0.0387316	−	0.0223617i
$216$		0			0
$217$	−208.975	−	361.955i	−0.963017	−	1.66799i
$218$		0			0
$219$	8.79546	+	156.517i	0.0401619	+	0.714688i
$220$		0			0
$221$	−7.10861	−	60.8181i	−0.0321657	−	0.275195i
$222$		0			0
$223$	38.5452	+	19.3581i	0.172848	+	0.0868076i	0.533120	−	0.846040i	$-0.321020\pi$
$223$	38.5452	+	19.3581i	0.172848	+	0.0868076i	−0.360271	+	0.932848i	$0.617316\pi$
$224$		0			0
$225$	31.7480	+	0.129638i	0.141102	+	0.000576168i
$226$		0			0
$227$	−78.7449	−	58.6234i	−0.346894	−	0.258253i	0.409584	−	0.912273i	$-0.365674\pi$
$227$	−78.7449	−	58.6234i	−0.346894	−	0.258253i	−0.756478	+	0.654020i	$0.773081\pi$
$228$		0			0
$229$	28.1941	−	29.8840i	0.123119	−	0.130498i	−0.662882	−	0.748724i	$-0.730667\pi$
$229$	28.1941	−	29.8840i	0.123119	−	0.130498i	0.786000	+	0.618226i	$0.212148\pi$
$230$		0			0
$231$	655.511	+	116.965i	2.83771	+	0.506340i
$232$		0			0
$233$	−71.7253	+	85.4789i	−0.307834	+	0.366862i	−0.897676	−	0.440657i	$-0.854746\pi$
$233$	−71.7253	+	85.4789i	−0.307834	+	0.366862i	0.589842	+	0.807519i	$0.299190\pi$
$234$		0			0
$235$	−200.676	+	168.388i	−0.853942	+	0.716543i
$236$		0			0
$237$	−103.188	+	237.880i	−0.435392	+	1.00371i
$238$		0			0
$239$	−109.557	−	218.145i	−0.458396	−	0.912741i	−0.997511	−	0.0705093i	$-0.977538\pi$
$239$	−109.557	−	218.145i	−0.458396	−	0.912741i	0.539115	−	0.842232i	$-0.318759\pi$
$240$		0			0
$241$	−15.6961	+	3.72005i	−0.0651291	+	0.0154359i	−0.263051	−	0.964782i	$-0.584729\pi$
$241$	−15.6961	+	3.72005i	−0.0651291	+	0.0154359i	0.197922	+	0.980218i	$0.436581\pi$
$242$		0			0
$243$	−16.6048	+	242.432i	−0.0683326	+	0.997663i
$244$		0			0
$245$	−141.398	−	596.605i	−0.577135	−	2.43512i
$246$		0			0
$247$	−208.651	+	104.788i	−0.844739	+	0.424244i
$248$		0			0
$249$	180.272	+	78.1988i	0.723985	+	0.314051i
$250$		0			0
$251$	100.874	+	120.217i	0.401888	+	0.478951i	0.928595	−	0.371096i	$-0.121018\pi$
$251$	100.874	+	120.217i	0.401888	+	0.478951i	−0.526707	+	0.850047i	$0.676573\pi$
$252$		0			0
$253$	−337.192	−	282.938i	−1.33277	−	1.11833i
$254$		0			0
$255$	17.6571	−	98.9565i	0.0692435	−	0.388065i
$256$		0			0
$257$	141.752	+	133.736i	0.551565	+	0.520375i	0.910787	−	0.412877i	$-0.135476\pi$
$257$	141.752	+	133.736i	0.551565	+	0.520375i	−0.359221	+	0.933252i	$0.616958\pi$
$258$		0			0
$259$	−485.246	+	651.798i	−1.87354	+	2.51659i
$260$		0			0
$261$	270.396	+	157.589i	1.03600	+	0.603790i
$262$		0			0
$263$	187.966	−	374.270i	0.714698	−	1.42308i	−0.183289	−	0.983059i	$-0.558675\pi$
$263$	187.966	−	374.270i	0.714698	−	1.42308i	0.897987	−	0.440021i	$-0.145029\pi$
$264$		0			0
$265$	450.190	−	52.6196i	1.69883	−	0.198565i
$266$		0			0
$267$	−90.9667	+	5.11187i	−0.340699	+	0.0191456i
$268$		0			0
$269$	−447.067	+	258.114i	−1.66196	+	0.959533i	−0.690182	+	0.723636i	$0.742470\pi$
$269$	−447.067	+	258.114i	−1.66196	+	0.959533i	−0.971778	+	0.235897i	$0.924197\pi$
$270$		0			0
$271$	−227.301	+	393.698i	−0.838751	+	1.45276i	0.0521890	+	0.998637i	$0.483380\pi$
$271$	−227.301	+	393.698i	−0.838751	+	1.45276i	−0.890940	+	0.454122i	$0.849953\pi$
$272$		0			0
$273$	333.022	−	78.2099i	1.21986	−	0.286483i
$274$		0			0
$275$	53.3911	+	23.0307i	0.194149	+	0.0837479i
$276$		0			0
$277$	20.0088	+	343.538i	0.0722340	+	1.24021i	0.818478	+	0.574538i	$0.194818\pi$
$277$	20.0088	+	343.538i	0.0722340	+	1.24021i	−0.746244	+	0.665672i	$0.768145\pi$
$278$		0			0
$279$	272.080	−	63.3120i	0.975198	−	0.226925i
$280$		0			0
$281$	−453.554	+	195.644i	−1.61407	+	0.696242i	−0.995956	−	0.0898466i	$-0.971362\pi$
$281$	−453.554	+	195.644i	−1.61407	+	0.696242i	−0.618114	+	0.786088i	$0.712103\pi$
$282$		0			0
$283$	207.740	+	49.2354i	0.734065	+	0.173977i	0.580613	−	0.814180i	$-0.302813\pi$
$283$	207.740	+	49.2354i	0.734065	+	0.173977i	0.153452	+	0.988156i	$0.450961\pi$
$284$		0			0
$285$	−377.606	+	65.7874i	−1.32493	+	0.230833i
$286$		0			0
$287$	48.5833	+	133.482i	0.169280	+	0.465092i
$288$		0			0
$289$	−222.439	−	80.9613i	−0.769686	−	0.280143i
$290$		0			0
$291$	−71.5958	−	240.936i	−0.246034	−	0.827959i
$292$		0			0
$293$	−17.1691	−	0.999987i	−0.0585977	−	0.00341292i	0.0288210	−	0.999585i	$-0.490825\pi$
$293$	−17.1691	−	0.999987i	−0.0585977	−	0.00341292i	−0.0874186	+	0.996172i	$0.527862\pi$
$294$		0			0
$295$	103.979	+	110.211i	0.352471	+	0.373598i
$296$		0			0
$297$	−202.171	+	396.481i	−0.680709	+	1.33495i
$298$		0			0
$299$	−216.635	−	64.8564i	−0.724533	−	0.216911i
$300$		0			0
$301$	23.3449	+	15.3542i	0.0775577	+	0.0510105i
$302$		0			0
$303$	−151.003	−	302.209i	−0.498360	−	0.997389i
$304$		0			0
$305$	265.897	−	46.8848i	0.871793	−	0.153721i
$306$		0			0
$307$	73.8829	−	419.011i	0.240661	−	1.36486i	−0.589697	−	0.807625i	$-0.700753\pi$
$307$	73.8829	−	419.011i	0.240661	−	1.36486i	0.830358	−	0.557231i	$-0.188136\pi$
$308$		0			0
$309$	188.765	−	325.414i	0.610888	−	1.05312i
$310$		0			0
$311$	232.488	−	69.6025i	0.747551	−	0.223802i	0.109703	−	0.993964i	$-0.465010\pi$
$311$	232.488	−	69.6025i	0.747551	−	0.223802i	0.637848	+	0.770162i	$0.279825\pi$
$312$		0			0
$313$	−415.450	−	48.5592i	−1.32732	−	0.155141i	−0.577285	−	0.816542i	$-0.695888\pi$
$313$	−415.450	−	48.5592i	−1.32732	−	0.155141i	−0.750032	+	0.661401i	$0.769962\pi$
$314$		0			0
$315$	560.479	+	34.9411i	1.77930	+	0.110924i
$316$		0			0
$317$	105.452	+	160.333i	0.332657	+	0.505781i	0.962624	−	0.270841i	$-0.0873019\pi$
$317$	105.452	+	160.333i	0.332657	+	0.505781i	−0.629967	+	0.776622i	$0.716931\pi$
$318$		0			0
$319$	342.288	+	459.773i	1.07300	+	1.44129i
$320$		0			0
$321$	−2.63474	+	22.1494i	−0.00820791	+	0.0690011i
$322$		0			0
$323$		−	199.369i		−	0.617242i
$324$		0			0
$325$	29.8723			0.0919148
$326$		0			0
$327$	63.1497	+	147.223i	0.193118	+	0.450224i
$328$		0			0
$329$	610.607	−	454.580i	1.85595	−	1.38170i
$330$		0			0
$331$	−167.796	+	110.361i	−0.506937	+	0.333418i	−0.777079	−	0.629403i	$-0.783300\pi$
$331$	−167.796	+	110.361i	−0.506937	+	0.333418i	0.270142	+	0.962820i	$0.412929\pi$
$332$		0			0
$333$	−322.547	−	436.970i	−0.968610	−	1.31222i
$334$		0			0
$335$	20.4338	−	174.822i	0.0609963	−	0.521857i
$336$		0			0
$337$	−123.616	−	412.907i	−0.366813	−	1.22524i	−0.919912	−	0.392126i	$-0.871740\pi$
$337$	−123.616	−	412.907i	−0.366813	−	1.22524i	0.553098	−	0.833116i	$-0.313445\pi$
$338$		0			0
$339$	314.865	−	180.931i	0.928805	−	0.533720i
$340$		0			0
$341$	503.851	+	88.8426i	1.47757	+	0.260536i
$342$		0			0
$343$	194.813	+	1104.84i	0.567969	+	3.22111i
$344$		0			0
$345$	−309.738	−	204.625i	−0.897792	−	0.593117i
$346$		0			0
$347$	17.3704	−	26.4104i	0.0500588	−	0.0761107i	−0.809591	−	0.586994i	$-0.800311\pi$
$347$	17.3704	−	26.4104i	0.0500588	−	0.0761107i	0.859650	+	0.510883i	$0.170682\pi$
$348$		0			0
$349$	88.5359	−	295.731i	0.253685	−	0.847365i	−0.732365	−	0.680912i	$-0.761583\pi$
$349$	88.5359	−	295.731i	0.253685	−	0.847365i	0.986049	−	0.166453i	$-0.0532314\pi$
$350$		0			0
$351$	−14.6921	+	228.169i	−0.0418578	+	0.650053i
$352$		0			0
$353$	−45.4576	+	42.8871i	−0.128775	+	0.121493i	−0.747935	−	0.663772i	$-0.768955\pi$
$353$	−45.4576	+	42.8871i	−0.128775	+	0.121493i	0.619160	+	0.785265i	$0.287473\pi$
$354$		0			0
$355$	12.6610	−	217.381i	0.0356649	−	0.612342i
$356$		0			0
$357$	−67.9425	+	284.086i	−0.190315	+	0.795759i
$358$		0			0
$359$	41.4175	−	113.794i	0.115369	−	0.316974i	−0.868547	−	0.495607i	$-0.834945\pi$
$359$	41.4175	−	113.794i	0.115369	−	0.316974i	0.983916	+	0.178634i	$0.0571677\pi$
$360$		0			0
$361$	−375.145	+	136.541i	−1.03918	+	0.378231i
$362$		0			0
$363$	−346.924	+	289.899i	−0.955713	+	0.798619i
$364$		0			0
$365$	−55.8410	+	235.612i	−0.152989	+	0.645512i
$366$		0			0
$367$	−7.43648	−	17.2397i	−0.0202629	−	0.0469747i	0.907784	−	0.419438i	$-0.137773\pi$
$367$	−7.43648	−	17.2397i	−0.0202629	−	0.0469747i	−0.928047	+	0.372463i	$0.878513\pi$
$368$		0			0
$369$	−94.8033	+	5.13333i	−0.256920	+	0.0139115i
$370$		0			0
$371$	−1314.88	+	76.5828i	−3.54414	+	0.206423i
$372$		0			0
$373$	−30.9455	+	71.7396i	−0.0829637	+	0.192331i	−0.954648	−	0.297736i	$-0.903769\pi$
$373$	−30.9455	+	71.7396i	−0.0829637	+	0.192331i	0.871685	+	0.490067i	$0.163028\pi$
$374$		0			0
$375$	379.683	+	114.515i	1.01249	+	0.305373i
$376$		0			0
$377$	255.022	+	147.237i	0.676451	+	0.390549i
$378$		0			0
$379$	18.2372	+	31.5877i	0.0481192	+	0.0833450i	0.889082	−	0.457748i	$-0.151344\pi$
$379$	18.2372	+	31.5877i	0.0481192	+	0.0833450i	−0.840963	+	0.541093i	$0.818011\pi$
$380$		0			0
$381$	−299.275	+	195.962i	−0.785499	+	0.514336i
$382$		0			0
$383$	73.0294	+	624.807i	0.190677	+	1.63135i	0.662082	+	0.749432i	$0.269673\pi$
$383$	73.0294	+	624.807i	0.190677	+	1.63135i	−0.471405	+	0.881917i	$0.656253\pi$
$384$		0			0
$385$	919.102	+	461.590i	2.38728	+	1.19894i
$386$		0			0
$387$	−14.3553	+	11.9459i	−0.0370937	+	0.0308681i
$388$		0			0
$389$	530.209	+	394.726i	1.36301	+	1.01472i	0.996438	+	0.0843281i	$0.0268744\pi$
$389$	530.209	+	394.726i	1.36301	+	1.01472i	0.366567	+	0.930392i	$0.380533\pi$
$390$		0			0
$391$	132.508	−	140.451i	0.338896	−	0.359209i
$392$		0			0
$393$	288.206	−	342.050i	0.733348	−	0.870356i
$394$		0			0
$395$	−257.444	+	306.810i	−0.651757	+	0.776734i
$396$		0			0
$397$	492.338	−	413.121i	1.24015	−	1.04061i	0.242633	−	0.970118i	$-0.421989\pi$
$397$	492.338	−	413.121i	1.24015	−	1.04061i	0.997513	−	0.0704877i	$-0.0224555\pi$
$398$		0			0
$399$	1106.54	−	127.046i	2.77327	−	0.318411i
$400$		0			0
$401$	−116.928	−	232.823i	−0.291592	−	0.580607i	0.699369	−	0.714761i	$-0.253465\pi$
$401$	−116.928	−	232.823i	−0.291592	−	0.580607i	−0.990960	+	0.134154i	$0.957168\pi$
$402$		0			0
$403$	255.758	−	60.6157i	0.634635	−	0.150411i
$404$		0			0
$405$	−131.250	+	351.645i	−0.324074	+	0.868258i
$406$		0			0
$407$	−229.397	−	967.903i	−0.563630	−	2.37814i
$408$		0			0
$409$	32.5580	−	16.3512i	0.0796038	−	0.0399785i	−0.408552	−	0.912735i	$-0.633966\pi$
$409$	32.5580	−	16.3512i	0.0796038	−	0.0399785i	0.488156	+	0.872757i	$0.337670\pi$
$410$		0			0
$411$	566.702	−	420.098i	1.37884	−	1.02214i
$412$		0			0
$413$	−283.018	−	337.288i	−0.685274	−	0.816678i
$414$		0			0
$415$	232.509	+	195.099i	0.560264	+	0.470117i
$416$		0			0
$417$	−34.3658	+	12.4287i	−0.0824120	+	0.0298051i
$418$		0			0
$419$	−60.6464	−	57.2169i	−0.144741	−	0.136556i	0.610466	−	0.792042i	$-0.290982\pi$
$419$	−60.6464	−	57.2169i	−0.144741	−	0.136556i	−0.755207	+	0.655487i	$0.772464\pi$
$420$		0			0
$421$	−215.859	+	289.949i	−0.512730	+	0.688715i	−0.980809	−	0.194971i	$-0.937539\pi$
$421$	−215.859	+	289.949i	−0.512730	+	0.688715i	0.468079	+	0.883686i	$0.344946\pi$
$422$		0			0
$423$	172.065	+	478.819i	0.406773	+	1.13196i
$424$		0			0
$425$	−11.4477	+	22.7943i	−0.0269358	+	0.0536336i
$426$		0			0
$427$	−779.280	+	91.0847i	−1.82501	+	0.213313i
$428$		0			0
$429$	−188.700	+	373.827i	−0.439859	+	0.871391i
$430$		0			0
$431$	−38.3743	+	22.1554i	−0.0890356	+	0.0514047i	−0.543857	−	0.839178i	$-0.683037\pi$
$431$	−38.3743	+	22.1554i	−0.0890356	+	0.0514047i	0.454821	+	0.890583i	$0.349703\pi$
$432$		0			0
$433$	−133.413	+	231.079i	−0.308114	+	0.533669i	−0.977950	−	0.208840i	$-0.933031\pi$
$433$	−133.413	+	231.079i	−0.308114	+	0.533669i	0.669836	+	0.742509i	$0.266364\pi$
$434$		0			0
$435$	331.019	+	352.298i	0.760964	+	0.809881i
$436$		0			0
$437$	−676.071	−	291.629i	−1.54707	−	0.667342i
$438$		0			0
$439$	45.9938	+	789.684i	0.104770	+	1.79882i	0.485603	+	0.874180i	$0.338600\pi$
$439$	45.9938	+	789.684i	0.104770	+	1.79882i	−0.380833	+	0.924644i	$0.624363\pi$
$440$		0			0
$441$	−1182.22	−	143.077i	−2.68077	−	0.324439i
$442$		0			0
$443$	705.829	−	304.465i	1.59329	−	0.687279i	0.599692	−	0.800231i	$-0.295290\pi$
$443$	705.829	−	304.465i	1.59329	−	0.687279i	0.993601	+	0.112951i	$0.0360305\pi$
$444$		0			0
$445$	−136.936	−	32.4545i	−0.307722	−	0.0729315i
$446$		0			0
$447$	−107.909	+	294.605i	−0.241407	+	0.659072i
$448$		0			0
$449$	188.737	+	518.551i	0.420350	+	1.15490i	0.951507	+	0.307628i	$0.0995352\pi$
$449$	188.737	+	518.551i	0.420350	+	1.15490i	−0.531157	+	0.847273i	$0.678243\pi$
$450$		0			0
$451$	−163.399	−	59.4722i	−0.362303	−	0.131867i
$452$		0			0
$453$	396.781	−	418.846i	0.875895	−	0.924606i
$454$		0			0
$455$	527.490	+	30.7228i	1.15932	+	0.0675226i
$456$		0			0
$457$	−369.227	−	391.358i	−0.807937	−	0.856363i	0.184022	−	0.982922i	$-0.441088\pi$
$457$	−369.227	−	391.358i	−0.807937	−	0.856363i	−0.991959	+	0.126559i	$0.959607\pi$
$458$		0			0
$459$	−168.475	−	98.6500i	−0.367048	−	0.214924i
$460$		0			0
$461$	305.067	+	91.3311i	0.661751	+	0.198115i	0.600029	−	0.799978i	$-0.295156\pi$
$461$	305.067	+	91.3311i	0.661751	+	0.198115i	0.0617218	+	0.998093i	$0.480341\pi$
$462$		0			0
$463$	−667.860	−	439.258i	−1.44246	−	0.948722i	−0.998615	−	0.0526193i	$-0.983243\pi$
$463$	−667.860	−	439.258i	−1.44246	−	0.948722i	−0.443847	−	0.896103i	$-0.646387\pi$
$464$		0			0
$465$	430.704	+	25.9681i	0.926245	+	0.0558454i
$466$		0			0
$467$	33.9358	−	5.98380i	0.0726678	−	0.0128133i	−0.137196	−	0.990544i	$-0.543809\pi$
$467$	33.9358	−	5.98380i	0.0726678	−	0.0128133i	0.209864	+	0.977731i	$0.432698\pi$
$468$		0			0
$469$	−88.8160	+	503.701i	−0.189373	+	1.07399i
$470$		0			0
$471$	−222.268	−	0.453795i	−0.471907	−	0.000963472i
$472$		0			0
$473$	−32.7672	+	9.80985i	−0.0692752	+	0.0207396i
$474$		0			0
$475$	96.6054	+	11.2916i	0.203380	+	0.0237717i
$476$		0			0
$477$	206.513	−	855.762i	0.432942	−	1.79405i
$478$		0			0
$479$	32.0070	+	48.6642i	0.0668204	+	0.101595i	0.867352	−	0.497695i	$-0.165820\pi$
$479$	32.0070	+	48.6642i	0.0668204	+	0.101595i	−0.800532	+	0.599290i	$0.795450\pi$
$480$		0			0
$481$	−305.164	−	409.907i	−0.634437	−	0.852197i
$482$		0			0
$483$	863.967	+	645.945i	1.78875	+	1.33736i
$484$		0			0
$485$		−	388.236i		−	0.800486i
$486$		0			0
$487$	−0.915727			−0.00188034			−0.000940171	−	1.00000i	$-0.500299\pi$
$487$	−0.915727			−0.00188034			−0.000940171		1.00000i	$0.500299\pi$
$488$		0			0
$489$	−251.380	+	336.227i	−0.514070	+	0.687580i
$490$		0			0
$491$	−392.619	+	292.294i	−0.799630	+	0.595303i	−0.917504	−	0.397726i	$-0.869800\pi$
$491$	−392.619	+	292.294i	−0.799630	+	0.595303i	0.117874	+	0.993029i	$0.462392\pi$
$492$		0			0
$493$	−210.080	+	138.172i	−0.426126	+	0.280268i
$494$		0			0
$495$	−473.781	+	498.088i	−0.957133	+	1.00624i
$496$		0			0
$497$	−73.4584	+	628.477i	−0.147804	+	1.26454i
$498$		0			0
$499$	−82.6675	−	276.129i	−0.165666	−	0.553364i	−0.999998	−	0.00210100i	$-0.999331\pi$
$499$	−82.6675	−	276.129i	−0.165666	−	0.553364i	0.834331	−	0.551263i	$-0.185854\pi$
$500$		0			0
$501$	−0.580931	+	284.539i	−0.00115954	+	0.567942i
$502$		0			0
$503$	158.317	+	27.9155i	0.314745	+	0.0554981i	0.328789	−	0.944403i	$-0.393359\pi$
$503$	158.317	+	27.9155i	0.314745	+	0.0554981i	−0.0140440	+	0.999901i	$0.504470\pi$
$504$		0			0
$505$	−90.6136	−	513.895i	−0.179433	−	1.01761i
$506$		0			0
$507$	17.5655	−	291.340i	0.0346460	−	0.574635i
$508$		0			0
$509$	−84.6111	+	128.645i	−0.166230	+	0.252740i	−0.908991	−	0.416817i	$-0.863146\pi$
$509$	−84.6111	+	128.645i	−0.166230	+	0.252740i	0.742761	+	0.669557i	$0.233516\pi$
$510$		0			0
$511$	201.802	−	674.067i	0.394917	−	1.31911i
$512$		0			0
$513$	−133.760	+	732.331i	−0.260740	+	1.42755i
$514$		0			0
$515$	422.664	−	398.763i	0.820706	−	0.774296i
$516$		0			0
$517$	−54.1825	+	930.277i	−0.104802	+	1.79938i
$518$		0			0
$519$	−272.617	−	258.255i	−0.525274	−	0.497601i
$520$		0			0
$521$	25.1808	−	69.1837i	0.0483317	−	0.132790i	−0.913178	−	0.407560i	$-0.866380\pi$
$521$	25.1808	−	69.1837i	0.0483317	−	0.132790i	0.961510	+	0.274770i	$0.0886018\pi$
$522$		0			0
$523$	546.695	−	198.981i	1.04531	−	0.380460i	0.238417	−	0.971163i	$-0.423371\pi$
$523$	546.695	−	198.981i	1.04531	−	0.380460i	0.806889	+	0.590702i	$0.201149\pi$
$524$		0			0
$525$	−133.807	−	49.0115i	−0.254871	−	0.0933552i
$526$		0			0
$527$	−51.7586	+	218.387i	−0.0982137	+	0.414396i
$528$		0			0
$529$	−72.9214	−	169.051i	−0.137848	−	0.319567i
$530$		0			0
$531$	270.693	−	115.457i	0.509779	−	0.217433i
$532$		0			0
$533$	−89.1810	+	5.19420i	−0.167319	+	0.00974522i
$534$		0			0
$535$	−13.6463	+	31.6356i	−0.0255070	+	0.0591320i
$536$		0			0
$537$	−411.193	+	386.357i	−0.765723	+	0.719474i
$538$		0			0
$539$	−1888.82	−	1090.51i	−3.50430	−	2.02321i
$540$		0			0
$541$	−286.094	−	495.530i	−0.528825	−	0.915952i	−0.999435	−	0.0336108i	$-0.989299\pi$
$541$	−286.094	−	495.530i	−0.528825	−	0.915952i	0.470610	−	0.882341i	$-0.344034\pi$
$542$		0			0
$543$	−64.9088	−	32.7646i	−0.119537	−	0.0603399i
$544$		0			0
$545$	28.7260	+	245.767i	0.0527082	+	0.450948i
$546$		0			0
$547$	106.033	+	53.2519i	0.193845	+	0.0973526i	0.543074	−	0.839685i	$-0.317260\pi$
$547$	106.033	+	53.2519i	0.193845	+	0.0973526i	−0.349229	+	0.937037i	$0.613557\pi$
$548$		0			0
$549$	93.1693	−	516.058i	0.169707	−	0.939997i
$550$		0			0
$551$	769.073	+	572.553i	1.39578	+	1.03912i
$552$		0			0
$553$	798.676	−	846.547i	1.44426	−	1.53083i
$554$		0			0
$555$	−285.314	−	788.901i	−0.514079	−	1.42144i
$556$		0			0
$557$	403.795	−	481.224i	0.724946	−	0.863957i	−0.270155	−	0.962817i	$-0.587075\pi$
$557$	403.795	−	481.224i	0.724946	−	0.863957i	0.995101	+	0.0988598i	$0.0315195\pi$
$558$		0			0
$559$	−13.4610	+	11.2951i	−0.0240805	+	0.0202059i
$560$		0			0
$561$	−212.937	−	287.247i	−0.379567	−	0.512026i
$562$		0			0
$563$	311.967	+	621.178i	0.554116	+	1.10334i	0.980081	+	0.198596i	$0.0636382\pi$
$563$	311.967	+	621.178i	0.554116	+	1.10334i	−0.425965	+	0.904739i	$0.640065\pi$
$564$		0			0
$565$	545.801	−	129.357i	0.966020	−	0.228951i
$566$		0			0
$567$	440.167	−	997.933i	0.776308	−	1.76002i
$568$		0			0
$569$	105.497	+	445.128i	0.185408	+	0.782299i	0.983669	+	0.179987i	$0.0576056\pi$
$569$	105.497	+	445.128i	0.185408	+	0.782299i	−0.798261	+	0.602312i	$0.794246\pi$
$570$		0			0
$571$	111.171	−	55.8322i	0.194695	−	0.0977797i	−0.348781	−	0.937204i	$-0.613404\pi$
$571$	111.171	−	55.8322i	0.194695	−	0.0977797i	0.543476	+	0.839425i	$0.317108\pi$
$572$		0			0
$573$	11.2309	+	97.8183i	0.0196002	+	0.170713i
$574$		0			0
$575$	60.5513	+	72.1622i	0.105307	+	0.125499i
$576$		0			0
$577$	−446.685	−	374.813i	−0.774150	−	0.649589i	0.167618	−	0.985852i	$-0.446392\pi$
$577$	−446.685	−	374.813i	−0.774150	−	0.649589i	−0.941768	+	0.336263i	$0.890837\pi$
$578$		0			0
$579$	−397.188	−	334.665i	−0.685990	−	0.578005i
$580$		0			0
$581$	−641.538	−	605.260i	−1.10420	−	1.04176i
$582$		0			0
$583$	962.802	−	1293.27i	1.65146	−	2.21830i
$584$		0			0
$585$	−122.143	+	331.368i	−0.208791	+	0.566440i
$586$		0			0
$587$	156.721	−	312.056i	0.266986	−	0.531612i	−0.719693	−	0.694292i	$-0.755718\pi$
$587$	156.721	−	312.056i	0.266986	−	0.531612i	0.986679	+	0.162680i	$0.0520138\pi$
$588$		0			0
$589$	850.019	−	99.3530i	1.44316	−	0.168681i
$590$		0			0
$591$	−368.062	−	562.108i	−0.622779	−	0.951113i
$592$		0			0
$593$	−438.175	+	252.980i	−0.738911	+	0.426611i	−0.821673	−	0.569959i	$-0.806959\pi$
$593$	−438.175	+	252.980i	−0.738911	+	0.426611i	0.0827619	+	0.996569i	$0.473626\pi$
$594$		0			0
$595$	−225.589	+	390.731i	−0.379141	+	0.656691i
$596$		0			0
$597$	100.022	−	331.631i	0.167541	−	0.555496i
$598$		0			0
$599$	−67.0686	−	28.9306i	−0.111968	−	0.0482981i	0.339359	−	0.940657i	$-0.389790\pi$
$599$	−67.0686	−	28.9306i	−0.111968	−	0.0482981i	−0.451327	+	0.892359i	$0.649049\pi$
$600$		0			0
$601$	25.1863	+	432.432i	0.0419073	+	0.719521i	0.952185	+	0.305522i	$0.0988311\pi$
$601$	25.1863	+	432.432i	0.0419073	+	0.719521i	−0.910278	+	0.413999i	$0.864132\pi$
$602$		0			0
$603$	−304.866	−	154.671i	−0.505582	−	0.256503i
$604$		0			0
$605$	−641.212	+	276.592i	−1.05986	+	0.457177i
$606$		0			0
$607$	15.9101	+	3.77075i	0.0262110	+	0.00621212i	0.243700	−	0.969851i	$-0.421639\pi$
$607$	15.9101	+	3.77075i	0.0262110	+	0.00621212i	−0.217489	+	0.976063i	$0.569787\pi$
$608$		0			0
$609$	−900.751	−	1077.94i	−1.47907	−	1.77001i
$610$		0			0
$611$	163.736	+	449.861i	0.267981	+	0.736271i
$612$		0			0
$613$	599.505	+	218.202i	0.977985	+	0.355958i	0.781057	−	0.624460i	$-0.214681\pi$
$613$	599.505	+	218.202i	0.977985	+	0.355958i	0.196929	+	0.980418i	$0.436903\pi$
$614$		0			0
$615$	−142.627	−	34.1108i	−0.231913	−	0.0554647i
$616$		0			0
$617$	514.198	+	29.9487i	0.833385	+	0.0485391i	0.469530	−	0.882917i	$-0.344423\pi$
$617$	514.198	+	29.9487i	0.833385	+	0.0485391i	0.363855	+	0.931456i	$0.381460\pi$
$618$		0			0
$619$	−639.927	−	678.283i	−1.03381	−	1.09577i	−0.995332	−	0.0965120i	$-0.969231\pi$
$619$	−639.927	−	678.283i	−1.03381	−	1.09577i	−0.0384753	−	0.999260i	$-0.512250\pi$
$620$		0			0
$621$	−580.965	+	427.007i	−0.935532	+	0.687612i
$622$		0			0
$623$	391.764	+	117.287i	0.628835	+	0.188261i
$624$		0			0
$625$	438.102	+	288.144i	0.700963	+	0.461030i
$626$		0			0
$627$	−751.548	+	1137.61i	−1.19864	+	1.81437i
$628$		0			0
$629$	429.728	−	75.7726i	0.683192	−	0.120465i
$630$		0			0
$631$	119.749	−	679.130i	0.189776	−	1.07628i	−0.729887	−	0.683568i	$-0.760427\pi$
$631$	119.749	−	679.130i	0.189776	−	1.07628i	0.919663	−	0.392707i	$-0.128461\pi$
$632$		0			0
$633$	−54.8711	−	95.4892i	−0.0866842	−	0.150852i
$634$		0			0
$635$	−529.332	+	158.472i	−0.833594	+	0.249562i
$636$		0			0
$637$	−1112.90	−	130.080i	−1.74710	−	0.204207i
$638$		0			0
$639$	−387.646	−	169.095i	−0.606645	−	0.264624i
$640$		0			0
$641$	−376.007	−	571.691i	−0.586595	−	0.891874i	0.413229	−	0.910627i	$-0.364401\pi$
$641$	−376.007	−	571.691i	−0.586595	−	0.891874i	−0.999824	+	0.0187529i	$0.994030\pi$
$642$		0			0
$643$	63.9461	+	85.8945i	0.0994495	+	0.133584i	0.849062	−	0.528293i	$-0.177168\pi$
$643$	63.9461	+	85.8945i	0.0994495	+	0.133584i	−0.749613	+	0.661877i	$0.769760\pi$
$644$		0			0
$645$	−26.5107	+	11.3714i	−0.0411018	+	0.0176301i
$646$		0			0
$647$			1195.08i			1.84710i	0.383472	+	0.923552i	$0.374728\pi$
$647$			1195.08i			1.84710i	−0.383472	+	0.923552i	$0.625272\pi$
$648$		0			0
$649$	538.982			0.830480
$650$		0			0
$651$	−1245.07	−	148.105i	−1.91255	−	0.227504i
$652$		0			0
$653$	18.8944	−	14.0663i	0.0289347	−	0.0215411i	−0.582594	−	0.812763i	$-0.697962\pi$
$653$	18.8944	−	14.0663i	0.0289347	−	0.0215411i	0.611529	+	0.791222i	$0.290555\pi$
$654$		0			0
$655$	577.218	−	379.642i	0.881249	−	0.579607i
$656$		0			0
$657$	391.864	+	260.031i	0.596444	+	0.395786i
$658$		0			0
$659$	−66.9814	+	573.062i	−0.101641	+	0.869594i	0.842194	+	0.539175i	$0.181264\pi$
$659$	−66.9814	+	573.062i	−0.101641	+	0.869594i	−0.943835	+	0.330418i	$0.892810\pi$
$660$		0			0
$661$	−146.130	−	488.108i	−0.221074	−	0.738438i	−0.994517	−	0.104573i	$-0.966653\pi$
$661$	−146.130	−	488.108i	−0.221074	−	0.738438i	0.773443	−	0.633865i	$-0.218533\pi$
$662$		0			0
$663$	−158.898	−	92.1728i	−0.239665	−	0.139024i
$664$		0			0
$665$	1694.26	+	298.744i	2.54776	+	0.449239i
$666$		0			0
$667$	161.252	+	914.504i	0.241757	+	1.37107i
$668$		0			0
$669$	115.754	−	57.8381i	0.173025	−	0.0864546i
$670$		0			0
$671$	527.767	−	802.430i	0.786537	−	1.19587i
$672$		0			0
$673$	33.1411	−	110.699i	0.0492438	−	0.164486i	−0.929831	−	0.367987i	$-0.880047\pi$
$673$	33.1411	−	110.699i	0.0492438	−	0.164486i	0.979075	+	0.203502i	$0.0652322\pi$
$674$		0			0
$675$	57.3432	−	76.0484i	0.0849529	−	0.112664i
$676$		0			0
$677$	−464.821	+	438.536i	−0.686589	+	0.647763i	−0.948297	−	0.317384i	$-0.897196\pi$
$677$	−464.821	+	438.536i	−0.686589	+	0.647763i	0.261708	+	0.965147i	$0.415714\pi$
$678$		0			0
$679$	−65.5971	+	1126.26i	−0.0966084	+	1.65870i
$680$		0			0
$681$	−282.311	+	83.8907i	−0.414554	+	0.123188i
$682$		0			0
$683$	−89.7019	+	246.454i	−0.131335	+	0.360840i	−0.987877	−	0.155237i	$-0.950386\pi$
$683$	−89.7019	+	246.454i	−0.131335	+	0.360840i	0.856542	+	0.516077i	$0.172608\pi$
$684$		0			0
$685$	1023.90	−	372.671i	1.49475	−	0.544045i
$686$		0			0
$687$	−21.1551	−	121.426i	−0.0307934	−	0.176747i
$688$		0			0
$689$	191.021	−	805.982i	0.277244	−	1.16978i
$690$		0			0
$691$	280.082	+	649.304i	0.405329	+	0.939658i	0.991576	+	0.129526i	$0.0413454\pi$
$691$	280.082	+	649.304i	0.405329	+	0.939658i	−0.586247	+	0.810132i	$0.699395\pi$
$692$		0			0
$693$	1458.58	−	1364.89i	2.10473	−	1.96953i
$694$		0			0
$695$	−56.3512	+	3.28208i	−0.0810808	+	0.00472242i
$696$		0			0
$697$	30.2126	−	70.0406i	0.0433466	−	0.100489i
$698$		0			0
$699$	76.5345	+	325.888i	0.109491	+	0.466220i
$700$		0			0
$701$	584.498	+	337.460i	0.833805	+	0.481398i	0.855154	−	0.518374i	$-0.173463\pi$
$701$	584.498	+	337.460i	0.833805	+	0.481398i	−0.0213484	+	0.999772i	$0.506796\pi$
$702$		0			0
$703$	−831.942	−	1440.97i	−1.18342	−	2.04974i
$704$		0			0
$705$	44.0937	+	784.656i	0.0625443	+	1.11299i
$706$		0			0
$707$	176.038	+	1506.10i	0.248993	+	2.13027i
$708$		0			0
$709$	−745.357	−	374.332i	−1.05128	−	0.527972i	−0.162691	−	0.986677i	$-0.552017\pi$
$709$	−745.357	−	374.332i	−1.05128	−	0.527972i	−0.888589	+	0.458705i	$0.848314\pi$
$710$		0			0
$711$	386.191	+	675.254i	0.543165	+	0.949725i
$712$		0			0
$713$	664.851	+	494.963i	0.932469	+	0.694198i
$714$		0			0
$715$	−443.868	+	470.473i	−0.620795	+	0.658004i
$716$		0			0
$717$	−720.945	−	128.640i	−1.00550	−	0.179415i
$718$		0			0
$719$	211.913	−	252.548i	0.294733	−	0.351249i	−0.598274	−	0.801291i	$-0.704147\pi$
$719$	211.913	−	252.548i	0.294733	−	0.351249i	0.893007	+	0.450042i	$0.148591\pi$
$720$		0			0
$721$	−1293.51	+	1085.38i	−1.79405	+	1.50539i
$722$		0			0
$723$	−19.2581	+	44.3958i	−0.0266364	+	0.0614050i
$724$		0			0
$725$	−55.0537	−	109.621i	−0.0759362	−	0.151201i
$726$		0			0
$727$	46.1779	−	10.9444i	0.0635184	−	0.0150541i	−0.198734	−	0.980054i	$-0.563683\pi$
$727$	46.1779	−	10.9444i	0.0635184	−	0.0150541i	0.262252	+	0.964999i	$0.415535\pi$
$728$		0			0
$729$	552.664	+	475.398i	0.758113	+	0.652123i
$730$		0			0
$731$	−3.46027	−	14.6000i	−0.00473362	−	0.0199727i
$732$		0			0
$733$	−955.818	+	480.030i	−1.30398	+	0.654884i	−0.958915	−	0.283694i	$-0.908440\pi$
$733$	−955.818	+	480.030i	−1.30398	+	0.654884i	−0.345066	+	0.938578i	$0.612144\pi$
$734$		0			0
$735$	−1687.47	−	731.994i	−2.29588	−	0.995911i
$736$		0			0
$737$	−402.453	−	479.625i	−0.546070	−	0.650781i
$738$		0			0
$739$	454.068	+	381.009i	0.614436	+	0.515573i	0.896049	−	0.443955i	$-0.146425\pi$
$739$	454.068	+	381.009i	0.614436	+	0.515573i	−0.281613	+	0.959528i	$0.590869\pi$
$740$		0			0
$741$	−123.041	+	689.566i	−0.166048	+	0.930589i
$742$		0			0
$743$	636.114	+	600.142i	0.856142	+	0.807729i	0.982888	−	0.184207i	$-0.0589716\pi$
$743$	636.114	+	600.142i	0.856142	+	0.807729i	−0.126745	+	0.991935i	$0.540453\pi$
$744$		0			0
$745$	−289.392	+	388.721i	−0.388446	+	0.521774i
$746$		0			0
$747$	511.727	−	292.666i	0.685043	−	0.391789i
$748$		0			0
$749$	44.9326	−	89.4681i	0.0599901	−	0.119450i
$750$		0			0
$751$	496.523	−	58.0352i	0.661149	−	0.0772772i	0.221100	−	0.975251i	$-0.429035\pi$
$751$	496.523	−	58.0352i	0.661149	−	0.0772772i	0.440049	+	0.897974i	$0.354961\pi$
$752$		0			0
$753$	470.054	−	26.4147i	0.624242	−	0.0350793i
$754$		0			0
$755$	771.765	−	445.579i	1.02221	−	0.590171i
$756$		0			0
$757$	601.768	−	1042.29i	0.794939	−	1.37687i	−0.127940	−	0.991782i	$-0.540836\pi$
$757$	601.768	−	1042.29i	0.794939	−	1.37687i	0.922878	−	0.385092i	$-0.125830\pi$
$758$		0			0
$759$	−1285.54	+	301.909i	−1.69373	+	0.397772i
$760$		0			0
$761$	−443.909	−	191.484i	−0.583323	−	0.251621i	0.0839060	−	0.996474i	$-0.473260\pi$
$761$	−443.909	−	191.484i	−0.583323	−	0.251621i	−0.667229	+	0.744853i	$0.732520\pi$
$762$		0			0
$763$	−41.8079	−	717.814i	−0.0547941	−	0.940779i
$764$		0			0
$765$	−206.044	−	220.189i	−0.269339	−	0.287828i
$766$		0			0
$767$	254.252	−	109.673i	0.331489	−	0.142990i
$768$		0			0
$769$	490.723	+	116.303i	0.638131	+	0.151240i	0.536931	−	0.843626i	$-0.319584\pi$
$769$	490.723	+	116.303i	0.638131	+	0.151240i	0.101200	+	0.994866i	$0.467732\pi$
$770$		0			0
$771$	575.971	−	100.347i	0.747044	−	0.130152i
$772$		0			0
$773$	−265.125	−	728.426i	−0.342982	−	0.942336i	−0.984524	−	0.175248i	$-0.943927\pi$
$773$	−265.125	−	728.426i	−0.342982	−	0.942336i	0.641542	−	0.767088i	$-0.278295\pi$
$774$		0			0
$775$	−102.889	−	37.4486i	−0.132760	−	0.0483207i
$776$		0			0
$777$	694.392	+	2336.78i	0.893683	+	3.00744i
$778$		0			0
$779$	−290.370	−	16.9121i	−0.372747	−	0.0217100i
$780$		0			0
$781$	−531.545	−	563.405i	−0.680596	−	0.721389i
$782$		0			0
$783$	864.376	−	366.593i	1.10393	−	0.468190i
$784$		0			0
$785$	−328.896	−	98.4649i	−0.418975	−	0.125433i
$786$		0			0
$787$	867.399	+	570.497i	1.10216	+	0.724901i	0.964104	−	0.265523i	$-0.0855447\pi$
$787$	867.399	+	570.497i	1.10216	+	0.724901i	0.138055	+	0.990425i	$0.455915\pi$
$788$		0			0
$789$	−561.603	−	1123.96i	−0.711791	−	1.42454i
$790$		0			0
$791$	−1605.21	+	283.042i	−2.02934	+	0.357827i
$792$		0			0
$793$	85.6806	−	485.919i	0.108046	−	0.612760i
$794$		0			0
$795$	682.284	−	1176.20i	0.858219	−	1.47950i
$796$		0			0
$797$	−660.675	+	197.793i	−0.828952	+	0.248172i	−0.673047	−	0.739600i	$-0.735015\pi$
$797$	−660.675	+	197.793i	−0.828952	+	0.248172i	−0.155906	+	0.987772i	$0.549830\pi$
$798$		0			0
$799$	−406.017	−	47.4566i	−0.508156	−	0.0593949i
$800$		0			0
$801$	−151.129	+	227.749i	−0.188675	+	0.284331i
$802$		0			0
$803$	473.309	+	719.631i	0.589425	+	0.896178i
$804$		0			0
$805$	995.007	+	1336.53i	1.23603	+	1.66028i
$806$		0			0
$807$	−182.932	+	1537.84i	−0.226681	+	1.90563i
$808$		0			0
$809$			775.545i			0.958647i	0.877638	+	0.479323i	$0.159118\pi$
$809$			775.545i			0.958647i	−0.877638	+	0.479323i	$0.840882\pi$
$810$		0			0
$811$	−234.115			−0.288675			−0.144337	−	0.989529i	$-0.546105\pi$
$811$	−234.115			−0.288675			−0.144337	+	0.989529i	$0.546105\pi$
$812$		0			0
$813$	537.619	+	1253.37i	0.661278	+	1.54166i
$814$		0			0
$815$	−520.131	+	387.223i	−0.638198	+	0.475121i
$816$		0			0
$817$	−47.8016	+	31.4396i	−0.0585087	+	0.0384818i
$818$		0			0
$819$	410.320	−	940.649i	0.501001	−	1.14853i
$820$		0			0
$821$	−122.666	+	1049.47i	−0.149410	+	1.27828i	0.685571	+	0.728006i	$0.259553\pi$
$821$	−122.666	+	1049.47i	−0.149410	+	1.27828i	−0.834981	+	0.550279i	$0.814521\pi$
$822$		0			0
$823$	−122.758	−	410.039i	−0.149159	−	0.498224i	0.850454	−	0.526049i	$-0.176327\pi$
$823$	−122.758	−	410.039i	−0.149159	−	0.498224i	−0.999613	+	0.0278247i	$0.991142\pi$
$824$		0			0
$825$	151.247	−	86.9112i	0.183330	−	0.105347i
$826$		0			0
$827$	−389.962	−	68.7608i	−0.471538	−	0.0831449i	−0.0671705	−	0.997742i	$-0.521397\pi$
$827$	−389.962	−	68.7608i	−0.471538	−	0.0831449i	−0.404367	+	0.914597i	$0.632508\pi$
$828$		0			0
$829$	106.391	+	603.371i	0.128336	+	0.727829i	0.979270	+	0.202557i	$0.0649253\pi$
$829$	106.391	+	603.371i	0.128336	+	0.727829i	−0.850934	+	0.525272i	$0.823964\pi$
$830$		0			0
$831$	861.365	+	569.051i	1.03654	+	0.684779i
$832$		0			0
$833$	525.747	−	799.359i	0.631149	−	0.959615i
$834$		0			0
$835$	−126.051	+	421.039i	−0.150959	+	0.504239i
$836$		0			0
$837$	336.641	−	767.462i	0.402199	−	0.916920i
$838$		0			0
$839$	664.996	−	627.392i	0.792606	−	0.747785i	−0.179138	−	0.983824i	$-0.557331\pi$
$839$	664.996	−	627.392i	0.792606	−	0.747785i	0.971744	+	0.236039i	$0.0758493\pi$
$840$		0			0
$841$	21.4113	−	367.618i	0.0254594	−	0.437121i
$842$		0			0
$843$	−344.682	+	1441.21i	−0.408875	+	1.70962i
$844$		0			0
$845$	154.191	−	423.636i	0.182474	−	0.501345i
$846$		0			0
$847$	1906.87	−	694.044i	2.25132	−	0.819414i
$848$		0			0
$849$	491.480	−	410.694i	0.578893	−	0.483738i
$850$		0			0
$851$	371.638	−	1568.06i	0.436708	−	1.84261i
$852$		0			0
$853$	37.3844	+	86.6668i	0.0438270	+	0.101602i	0.938723	−	0.344672i	$-0.112010\pi$
$853$	37.3844	+	86.6668i	0.0438270	+	0.101602i	−0.894896	+	0.446274i	$0.852751\pi$
$854$		0			0
$855$	−520.257	+	1025.45i	−0.608488	+	1.19936i
$856$		0			0
$857$	1149.00	−	66.9217i	1.34073	−	0.0780884i	0.627277	−	0.778796i	$-0.284169\pi$
$857$	1149.00	−	66.9217i	1.34073	−	0.0780884i	0.713448	+	0.700708i	$0.247132\pi$
$858$		0			0
$859$	−171.154	+	396.780i	−0.199248	+	0.461909i	−0.988320	−	0.152392i	$-0.951303\pi$
$859$	−171.154	+	396.780i	−0.199248	+	0.461909i	0.789072	+	0.614301i	$0.210562\pi$
$860$		0			0
$861$	407.991	+	123.053i	0.473857	+	0.142918i
$862$		0			0
$863$	1142.84	+	659.821i	1.32427	+	0.764567i	0.984407	−	0.175908i	$-0.0562862\pi$
$863$	1142.84	+	659.821i	1.32427	+	0.764567i	0.339862	+	0.940475i	$0.389619\pi$
$864$		0			0
$865$	−290.017	−	502.324i	−0.335280	−	0.580721i
$866$		0			0
$867$	−594.113	+	389.019i	−0.685252	+	0.448695i
$868$		0			0
$869$	165.397	+	1415.06i	0.190330	+	1.62838i
$870$		0			0
$871$	−287.443	−	144.359i	−0.330015	−	0.165740i
$872$		0			0
$873$	−707.512	−	260.790i	−0.810438	−	0.298729i
$874$		0			0
$875$	−1427.79	−	1062.95i	−1.63176	−	1.21480i
$876$		0			0
$877$	−312.136	+	330.844i	−0.355913	+	0.377246i	−0.880448	−	0.474143i	$-0.842758\pi$
$877$	−312.136	+	330.844i	−0.355913	+	0.377246i	0.524535	+	0.851389i	$0.324239\pi$
$878$		0			0
$879$	−33.2450	+	39.4560i	−0.0378214	+	0.0448874i
$880$		0			0
$881$	−186.661	+	222.454i	−0.211874	+	0.252501i	−0.861506	−	0.507747i	$-0.830478\pi$
$881$	−186.661	+	222.454i	−0.211874	+	0.252501i	0.649632	+	0.760248i	$0.274923\pi$
$882$		0			0
$883$	947.604	−	795.134i	1.07316	−	0.900491i	0.0778284	−	0.996967i	$-0.475201\pi$
$883$	947.604	−	795.134i	1.07316	−	0.900491i	0.995335	+	0.0964754i	$0.0307569\pi$
$884$		0			0
$885$	451.592	−	51.8491i	0.510273	−	0.0585866i
$886$		0			0
$887$	222.210	+	442.457i	0.250519	+	0.498824i	0.983381	−	0.181553i	$-0.0581124\pi$
$887$	222.210	+	442.457i	0.250519	+	0.498824i	−0.732862	+	0.680377i	$0.761816\pi$
$888$		0			0
$889$	1562.35	−	370.284i	1.75742	−	0.416517i
$890$		0			0
$891$	589.451	+	1197.99i	0.661562	+	1.34454i
$892$		0			0
$893$	359.469	+	1516.72i	0.402541	+	1.69845i
$894$		0			0
$895$	−778.811	+	391.133i	−0.870180	+	0.437021i
$896$		0			0
$897$	−544.991	+	404.004i	−0.607571	+	0.450395i
$898$		0			0
$899$	−693.792	−	826.829i	−0.771738	−	0.919721i
$900$		0			0
$901$	541.806	+	454.629i	0.601339	+	0.504583i
$902$		0			0
$903$	78.8279	−	28.5089i	0.0872956	−	0.0315713i
$904$		0			0
$905$	−81.6898	−	77.0703i	−0.0902650	−	0.0851606i
$906$		0			0
$907$	75.7548	−	101.756i	0.0835223	−	0.112190i	−0.758398	−	0.651792i	$-0.774018\pi$
$907$	75.7548	−	101.756i	0.0835223	−	0.112190i	0.841921	+	0.539602i	$0.181425\pi$
$908$		0			0
$909$	−997.380	−	180.067i	−1.09723	−	0.198094i
$910$		0			0
$911$	−464.635	+	925.165i	−0.510028	+	1.01555i	0.480340	+	0.877083i	$0.340513\pi$
$911$	−464.635	+	925.165i	−0.510028	+	1.01555i	−0.990367	+	0.138466i	$0.955783\pi$
$912$		0			0
$913$	1072.37	−	125.342i	1.17456	−	0.137286i
$914$		0			0
$915$	365.003	−	723.095i	0.398910	−	0.790268i
$916$		0			0
$917$	−1738.64	+	1003.80i	−1.89600	+	1.09466i
$918$		0			0
$919$	391.929	−	678.841i	0.426473	−	0.738674i	−0.570083	−	0.821587i	$-0.693089\pi$
$919$	391.929	−	678.841i	0.426473	−	0.738674i	0.996557	+	0.0829131i	$0.0264224\pi$
$920$		0			0
$921$	−874.037	−	930.223i	−0.949009	−	1.01001i
$922$		0			0
$923$	−365.387	−	157.613i	−0.395869	−	0.170761i
$924$		0			0
$925$	12.3778	+	212.518i	0.0133814	+	0.229749i
$926$		0			0
$927$	−442.780	−	1038.11i	−0.477648	−	1.11986i
$928$		0			0
$929$	344.313	−	148.522i	0.370628	−	0.159873i	−0.202616	−	0.979258i	$-0.564944\pi$
$929$	344.313	−	148.522i	0.370628	−	0.159873i	0.573243	+	0.819385i	$0.305685\pi$
$930$		0			0
$931$	−3549.90	−	841.342i	−3.81300	−	0.903697i
$932$		0			0
$933$	250.404	−	683.635i	0.268386	−	0.732727i
$934$		0			0
$935$	−188.898	−	518.992i	−0.202029	−	0.555071i
$936$		0			0
$937$	568.400	+	206.881i	0.606617	+	0.220791i	0.627022	−	0.779001i	$-0.284273\pi$
$937$	568.400	+	206.881i	0.606617	+	0.220791i	−0.0204052	+	0.999792i	$0.506496\pi$
$938$		0			0
$939$	−862.982	+	910.975i	−0.919044	+	0.970154i
$940$		0			0
$941$	−461.955	−	26.9058i	−0.490919	−	0.0285928i	−0.189100	−	0.981958i	$-0.560557\pi$
$941$	−461.955	−	26.9058i	−0.490919	−	0.0285928i	−0.301820	+	0.953365i	$0.597594\pi$
$942$		0			0
$943$	−193.318	−	204.905i	−0.205003	−	0.217290i
$944$		0			0
$945$	1090.79	−	1283.90i	1.15427	−	1.35862i
$946$		0			0
$947$	1759.21	+	526.674i	1.85767	+	0.556150i	0.999052	+	0.0435359i	$0.0138623\pi$
$947$	1759.21	+	526.674i	1.85767	+	0.556150i	0.858619	+	0.512614i	$0.171323\pi$
$948$		0			0
$949$	369.705	+	243.159i	0.389573	+	0.256226i
$950$		0			0
$951$	574.665	+	34.6478i	0.604275	+	0.0364330i
$952$		0			0
$953$	1510.30	−	266.307i	1.58479	−	0.279441i	0.689282	−	0.724493i	$-0.257926\pi$
$953$	1510.30	−	266.307i	1.58479	−	0.279441i	0.895504	+	0.445053i	$0.146815\pi$
$954$		0			0
$955$	−26.4091	+	149.773i	−0.0276535	+	0.156831i
$956$		0			0
$957$	1719.58	+	3.51079i	1.79685	+	0.00366854i
$958$		0			0
$959$	−3033.28	+	908.105i	−3.16296	+	0.946929i
$960$		0			0
$961$	−2.39258	−	0.279653i	−0.00248968	−	0.000291002i
$962$		0			0
$963$	48.4854	+	46.1193i	0.0503483	+	0.0478912i
$964$		0			0
$965$	−440.841	−	670.266i	−0.456830	−	0.694576i
$966$		0			0
$967$	362.257	+	486.596i	0.374620	+	0.503202i	0.948952	−	0.315421i	$-0.102146\pi$
$967$	362.257	+	486.596i	0.374620	+	0.503202i	−0.574332	+	0.818622i	$0.694738\pi$
$968$		0			0
$969$	−479.026	−	358.144i	−0.494351	−	0.369602i
$970$		0			0
$971$		−	1173.89i		−	1.20895i	−0.796625	−	0.604473i	$-0.793384\pi$
$971$		−	1173.89i		−	1.20895i	0.796625	−	0.604473i	$-0.206616\pi$
$972$		0			0
$973$	164.027			0.168579
$974$		0			0
$975$	53.6622	−	71.7744i	0.0550381	−	0.0736148i
$976$		0			0
$977$	−972.096	+	723.699i	−0.994980	+	0.740735i	−0.965920	−	0.258842i	$-0.916659\pi$
$977$	−972.096	+	723.699i	−0.994980	+	0.740735i	−0.0290608	+	0.999578i	$0.509252\pi$
$978$		0			0
$979$	−418.246	+	275.085i	−0.427217	+	0.280985i
$980$		0			0
$981$	467.176	+	112.739i	0.476224	+	0.114923i
$982$		0			0
$983$	7.66016	−	65.5369i	0.00779264	−	0.0666703i	−0.988782	−	0.149363i	$-0.952278\pi$
$983$	7.66016	−	65.5369i	0.00779264	−	0.0666703i	0.996575	+	0.0826924i	$0.0263519\pi$
$984$		0			0
$985$	−297.647	−	994.209i	−0.302179	−	1.00935i
$986$		0			0
$987$	4.66255	−	2283.71i	0.00472396	−	2.31379i
$988$		0			0
$989$	−54.5710	−	9.62234i	−0.0551779	−	0.00972936i
$990$		0			0
$991$	241.647	+	1370.45i	0.243841	+	1.38289i	0.823168	+	0.567797i	$0.192204\pi$
$991$	241.647	+	1370.45i	0.243841	+	1.38289i	−0.579327	+	0.815095i	$0.696685\pi$
$992$		0			0
$993$	−36.2607	+	601.417i	−0.0365163	+	0.605656i
$994$		0			0
$995$	294.005	−	447.013i	0.295483	−	0.449259i
$996$		0			0
$997$	−381.900	+	1275.64i	−0.383049	+	1.27947i	0.521554	+	0.853218i	$0.325353\pi$
$997$	−381.900	+	1275.64i	−0.383049	+	1.27947i	−0.904603	+	0.426255i	$0.859833\pi$
$998$		0			0
$999$	−1629.33	−	9.97971i	−1.63096	−	0.00998970i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	324.3.o.a.5.13	✓	324
81.65	odd	54	inner	324.3.o.a.65.13	yes	324

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
324.3.o.a.5.13	✓	324	1.1	even	1	trivial
324.3.o.a.65.13	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)

\(f(q)\)	\(=\)	\(q+(1.79639 - 2.40271i) q^{3} +(3.71691 - 2.76713i) q^{5} +(-11.2502 + 7.39935i) q^{7} +(-2.54600 - 8.63237i) q^{9} +O(q^{10})\)	\(q+(1.79639 - 2.40271i) q^{3} +(3.71691 - 2.76713i) q^{5} +(-11.2502 + 7.39935i) q^{7} +(-2.54600 - 8.63237i) q^{9} +(1.91360 - 16.3719i) q^{11} +(-2.42871 - 8.11244i) q^{13} +(0.0283820 - 13.9015i) q^{15} +(7.12098 + 1.25562i) q^{17} +(-4.78784 - 27.1532i) q^{19} +(-2.43116 + 40.3229i) q^{21} +(14.6741 - 22.3109i) q^{23} +(-1.01172 + 3.37939i) q^{25} +(-25.3147 - 9.38977i) q^{27} +(-25.2938 + 23.8635i) q^{29} +(-1.80475 + 30.9863i) q^{31} +(-35.8993 - 34.0081i) q^{33} +(-21.3408 + 58.6334i) q^{35} +(56.7073 - 20.6398i) q^{37} +(-23.8547 - 8.73760i) q^{39} +(2.43280 - 10.2648i) q^{41} +(-0.821893 - 1.90536i) q^{43} +(-33.3502 - 25.0406i) q^{45} +(-56.4374 + 3.28710i) q^{47} +(52.4078 - 121.495i) q^{49} +(15.8089 - 14.8541i) q^{51} +(84.7095 + 48.9071i) q^{53} +(-38.1906 - 66.1480i) q^{55} +(-73.8420 - 37.2738i) q^{57} +(3.79607 + 32.4774i) q^{59} +(52.0691 + 26.1501i) q^{61} +(92.5168 + 78.2768i) q^{63} +(-31.4755 - 23.4326i) q^{65} +(26.0663 - 27.6287i) q^{67} +(-27.2462 - 75.3367i) q^{69} +(30.2054 - 35.9974i) q^{71} +(-40.0293 + 33.5886i) q^{73} +(6.30225 + 8.50157i) q^{75} +(99.6131 + 198.346i) q^{77} +(-84.1023 + 19.9326i) q^{79} +(-68.0357 + 43.9561i) q^{81} +(15.1055 + 63.7352i) q^{83} +(29.9425 - 15.0377i) q^{85} +(11.8995 + 103.642i) q^{87} +(-19.5215 - 23.2648i) q^{89} +(87.3501 + 73.2954i) q^{91} +(71.2090 + 59.9996i) q^{93} +(-92.9325 - 87.6773i) q^{95} +(50.0317 - 67.2042i) q^{97} +(-146.200 + 25.1640i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 324 q+O(q^{10}) \) 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

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