LMFDB - Embedded newform 324.3.j.a.307.14

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [324,3,Mod(19,324)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(324, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([9, 16])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("324.19"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 324 = 2^{2} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	324.j (of order $18$, degree $6$, not minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$8.82836056527$
Analytic rank:	$0$
Dimension:	$204$
Relative dimension:	$34$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 108)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			307.14
Character	$\chi$	$=$	324.307
Dual form			324.3.j.a.19.14

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.376263 + 1.96429i) q^{2} +(-3.71685 - 1.47818i) q^{4} +(1.26933 - 7.19876i) q^{5} +(2.67622 + 3.18940i) q^{7} +(4.30208 - 6.74478i) q^{8} +(13.6628 + 5.20197i) q^{10} +(-18.4141 + 3.24691i) q^{11} +(-15.1228 + 5.50426i) q^{13} +(-7.27185 + 4.05681i) q^{14} +(11.6300 + 10.9883i) q^{16} +(-7.49839 + 12.9876i) q^{17} +(-0.338254 + 0.195291i) q^{19} +(-15.3590 + 24.8804i) q^{20} +(0.550703 - 37.3923i) q^{22} +(-10.6620 + 12.7065i) q^{23} +(-26.7186 - 9.72476i) q^{25} +(-5.12179 - 31.7767i) q^{26} +(-5.23262 - 15.8104i) q^{28} +(-36.9589 - 13.4520i) q^{29} +(-14.0094 + 16.6957i) q^{31} +(-25.9602 + 18.7101i) q^{32} +(-22.6900 - 19.6158i) q^{34} +(26.3567 - 15.2170i) q^{35} +(5.57476 - 9.65577i) q^{37} +(-0.256335 - 0.737910i) q^{38} +(-43.0932 - 39.5310i) q^{40} +(56.8435 - 20.6894i) q^{41} +(24.4766 - 4.31589i) q^{43} +(73.2421 + 15.1511i) q^{44} +(-20.9475 - 25.7242i) q^{46} +(14.6599 + 17.4709i) q^{47} +(5.49867 - 31.1845i) q^{49} +(29.1554 - 48.8239i) q^{50} +(64.3456 + 1.89574i) q^{52} -51.2309 q^{53} +136.680i q^{55} +(33.0251 - 4.32947i) q^{56} +(40.3298 - 67.5365i) q^{58} +(-82.3895 - 14.5275i) q^{59} +(19.0252 - 15.9640i) q^{61} +(-27.5240 - 33.8005i) q^{62} +(-26.9841 - 58.0332i) q^{64} +(20.4279 + 115.852i) q^{65} +(-17.9869 - 49.4186i) q^{67} +(47.0684 - 37.1890i) q^{68} +(19.9736 + 57.4978i) q^{70} +(-75.5843 - 43.6386i) q^{71} +(17.8942 + 30.9937i) q^{73} +(16.8691 + 14.5835i) q^{74} +(1.54592 - 0.225868i) q^{76} +(-59.6359 - 50.0405i) q^{77} +(-3.59582 + 9.87943i) q^{79} +(93.8648 - 69.7734i) q^{80} +(19.2517 + 119.442i) q^{82} +(-34.4827 + 94.7405i) q^{83} +(83.9766 + 70.4647i) q^{85} +(-0.732011 + 49.7030i) q^{86} +(-57.3195 + 138.168i) q^{88} +(7.29925 + 12.6427i) q^{89} +(-58.0273 - 33.5021i) q^{91} +(58.4116 - 31.4678i) q^{92} +(-39.8339 + 22.2225i) q^{94} +(0.976496 + 2.68290i) q^{95} +(-1.45511 - 8.25233i) q^{97} +(59.1864 + 22.5346i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 204 q + 6 q^{2} - 6 q^{4} + 12 q^{5} + 3 q^{8} - 3 q^{10} - 12 q^{13} - 39 q^{14} - 6 q^{16} + 6 q^{17} + 69 q^{20} - 6 q^{22} - 12 q^{25} + 174 q^{26} - 12 q^{28} - 60 q^{29} + 96 q^{32} + 6 q^{34} - 6 q^{37}+ \cdots - 510 q^{98}+O(q^{100}) $ 204 * q + 6 * q^2 - 6 * q^4 + 12 * q^5 + 3 * q^8 - 3 * q^10 - 12 * q^13 - 39 * q^14 - 6 * q^16 + 6 * q^17 + 69 * q^20 - 6 * q^22 - 12 * q^25 + 174 * q^26 - 12 * q^28 - 60 * q^29 + 96 * q^32 + 6 * q^34 - 6 * q^37 - 72 * q^38 + 69 * q^40 + 192 * q^41 + 219 * q^44 - 3 * q^46 - 12 * q^49 + 165 * q^50 + 21 * q^52 + 24 * q^53 - 99 * q^56 - 141 * q^58 - 12 * q^61 - 294 * q^62 - 3 * q^64 + 156 * q^65 - 375 * q^68 - 165 * q^70 - 6 * q^73 - 447 * q^74 - 54 * q^76 - 132 * q^77 - 798 * q^80 - 12 * q^82 + 138 * q^85 - 606 * q^86 - 198 * q^88 + 114 * q^89 - 723 * q^92 - 357 * q^94 + 168 * q^97 - 510 * q^98

Character values

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

$n$	$163$	$245$
$\chi(n)$	$-1$	$e\left(\frac{1}{9}\right)$

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 $

$2$	−0.376263	+	1.96429i	−0.188132	+	0.982144i
$2$	−0.376263	+	1.96429i	−0.188132	+	0.982144i
$3$		0			0
$3$		0			0
$4$	−3.71685	−	1.47818i	−0.929213	−	0.369545i
$5$	1.26933	−	7.19876i	0.253867	−	1.43975i	−0.545097	−	0.838373i	$-0.683507\pi$
$5$	1.26933	−	7.19876i	0.253867	−	1.43975i	0.798964	−	0.601378i	$-0.205382\pi$
$6$		0			0
$7$	2.67622	+	3.18940i	0.382317	+	0.455628i	0.922544	−	0.385891i	$-0.126106\pi$
$7$	2.67622	+	3.18940i	0.382317	+	0.455628i	−0.540227	+	0.841519i	$0.681662\pi$
$8$	4.30208	−	6.74478i	0.537761	−	0.843098i
$9$		0			0
$10$	13.6628	+	5.20197i	1.36628	+	0.520197i
$11$	−18.4141	+	3.24691i	−1.67401	+	0.295173i	−0.928504	−	0.371323i	$-0.878904\pi$
$11$	−18.4141	+	3.24691i	−1.67401	+	0.295173i	−0.745508	+	0.666497i	$0.767793\pi$
$12$		0			0
$13$	−15.1228	+	5.50426i	−1.16330	+	0.423405i	−0.850274	−	0.526341i	$-0.823564\pi$
$13$	−15.1228	+	5.50426i	−1.16330	+	0.423405i	−0.313022	+	0.949746i	$0.601341\pi$
$14$	−7.27185	+	4.05681i	−0.519418	+	0.289772i
$15$		0			0
$16$	11.6300	+	10.9883i	0.726873	+	0.686772i
$17$	−7.49839	+	12.9876i	−0.441082	+	0.763976i	−0.997770	−	0.0667452i	$-0.978739\pi$
$17$	−7.49839	+	12.9876i	−0.441082	+	0.763976i	0.556688	+	0.830722i	$0.312072\pi$
$18$		0			0
$19$	−0.338254	+	0.195291i	−0.0178029	+	0.0102785i	−0.508875	−	0.860840i	$-0.669938\pi$
$19$	−0.338254	+	0.195291i	−0.0178029	+	0.0102785i	0.491072	+	0.871119i	$0.336605\pi$
$20$	−15.3590	+	24.8804i	−0.767949	+	1.24402i
$21$		0			0
$22$	0.550703	−	37.3923i	0.0250319	−	1.69965i
$23$	−10.6620	+	12.7065i	−0.463566	+	0.552456i	−0.946291	−	0.323316i	$-0.895202\pi$
$23$	−10.6620	+	12.7065i	−0.463566	+	0.552456i	0.482725	+	0.875772i	$0.339647\pi$
$24$		0			0
$25$	−26.7186	−	9.72476i	−1.06874	−	0.388990i
$26$	−5.12179	−	31.7767i	−0.196992	−	1.22218i
$27$		0			0
$28$	−5.23262	−	15.8104i	−0.186879	−	0.564659i
$29$	−36.9589	−	13.4520i	−1.27445	−	0.463861i	−0.385855	−	0.922560i	$-0.626093\pi$
$29$	−36.9589	−	13.4520i	−1.27445	−	0.463861i	−0.888592	+	0.458699i	$0.848316\pi$
$30$		0			0
$31$	−14.0094	+	16.6957i	−0.451916	+	0.538572i	−0.943111	−	0.332477i	$-0.892116\pi$
$31$	−14.0094	+	16.6957i	−0.451916	+	0.538572i	0.491196	+	0.871049i	$0.336560\pi$
$32$	−25.9602	+	18.7101i	−0.811256	+	0.584691i
$33$		0			0
$34$	−22.6900	−	19.6158i	−0.667353	−	0.576934i
$35$	26.3567	−	15.2170i	0.753049	−	0.434773i
$36$		0			0
$37$	5.57476	−	9.65577i	0.150669	−	0.260967i	−0.780804	−	0.624776i	$-0.785190\pi$
$37$	5.57476	−	9.65577i	0.150669	−	0.260967i	0.931474	+	0.363809i	$0.118524\pi$
$38$	−0.256335	−	0.737910i	−0.00674567	−	0.0194187i
$39$		0			0
$40$	−43.0932	−	39.5310i	−1.07733	−	0.988276i
$41$	56.8435	−	20.6894i	1.38643	−	0.504618i	0.462307	−	0.886720i	$-0.347022\pi$
$41$	56.8435	−	20.6894i	1.38643	−	0.504618i	0.924120	+	0.382101i	$0.124800\pi$
$42$		0			0
$43$	24.4766	−	4.31589i	0.569224	−	0.100369i	0.118374	−	0.992969i	$-0.462232\pi$
$43$	24.4766	−	4.31589i	0.569224	−	0.100369i	0.450850	+	0.892600i	$0.351121\pi$
$44$	73.2421	+	15.1511i	1.66459	+	0.344343i
$45$		0			0
$46$	−20.9475	−	25.7242i	−0.455380	−	0.559223i
$47$	14.6599	+	17.4709i	0.311912	+	0.371722i	0.899111	−	0.437720i	$-0.144214\pi$
$47$	14.6599	+	17.4709i	0.311912	+	0.371722i	−0.587199	+	0.809442i	$0.699769\pi$
$48$		0			0
$49$	5.49867	−	31.1845i	0.112218	−	0.636419i
$50$	29.1554	−	48.8239i	0.583109	−	0.976477i
$51$		0			0
$52$	64.3456	+	1.89574i	1.23742	+	0.0364565i
$53$	−51.2309			−0.966621			−0.483310	−	0.875449i	$-0.660566\pi$
$53$	−51.2309			−0.966621			−0.483310	+	0.875449i	$0.660566\pi$
$54$		0			0
$55$			136.680i			2.48510i
$56$	33.0251	−	4.32947i	0.589734	−	0.0773120i
$57$		0			0
$58$	40.3298	−	67.5365i	0.695342	−	1.16442i
$59$	−82.3895	−	14.5275i	−1.39643	−	0.246229i	−0.575755	−	0.817622i	$-0.695292\pi$
$59$	−82.3895	−	14.5275i	−1.39643	−	0.246229i	−0.820676	+	0.571394i	$0.806403\pi$
$60$		0			0
$61$	19.0252	−	15.9640i	0.311888	−	0.261705i	−0.473384	−	0.880856i	$-0.656968\pi$
$61$	19.0252	−	15.9640i	0.311888	−	0.261705i	0.785272	+	0.619151i	$0.212523\pi$
$62$	−27.5240	−	33.8005i	−0.443936	−	0.545169i
$63$		0			0
$64$	−26.9841	−	58.0332i	−0.421627	−	0.906769i
$65$	20.4279	+	115.852i	0.314275	+	1.78234i
$66$		0			0
$67$	−17.9869	−	49.4186i	−0.268461	−	0.737592i	−0.998529	−	0.0542169i	$-0.982734\pi$
$67$	−17.9869	−	49.4186i	−0.268461	−	0.737592i	0.730068	−	0.683375i	$-0.239488\pi$
$68$	47.0684	−	37.1890i	0.692183	−	0.546897i
$69$		0			0
$70$	19.9736	+	57.4978i	0.285337	+	0.821397i
$71$	−75.5843	−	43.6386i	−1.06457	−	0.614628i	−0.137875	−	0.990450i	$-0.544027\pi$
$71$	−75.5843	−	43.6386i	−1.06457	−	0.614628i	−0.926692	+	0.375821i	$0.877361\pi$
$72$		0			0
$73$	17.8942	+	30.9937i	0.245127	+	0.424572i	0.962167	−	0.272460i	$-0.0878372\pi$
$73$	17.8942	+	30.9937i	0.245127	+	0.424572i	−0.717041	+	0.697031i	$0.754504\pi$
$74$	16.8691	+	14.5835i	0.227961	+	0.197075i
$75$		0			0
$76$	1.54592	−	0.225868i	0.0203410	−	0.00297195i
$77$	−59.6359	−	50.0405i	−0.774493	−	0.649877i
$78$		0			0
$79$	−3.59582	+	9.87943i	−0.0455167	+	0.125056i	−0.960368	−	0.278734i	$-0.910085\pi$
$79$	−3.59582	+	9.87943i	−0.0455167	+	0.125056i	0.914852	+	0.403790i	$0.132307\pi$
$80$	93.8648	−	69.7734i	1.17331	−	0.872168i
$81$		0			0
$82$	19.2517	+	119.442i	0.234777	+	1.45661i
$83$	−34.4827	+	94.7405i	−0.415455	+	1.14145i	0.538794	+	0.842438i	$0.318880\pi$
$83$	−34.4827	+	94.7405i	−0.415455	+	1.14145i	−0.954249	+	0.299015i	$0.903342\pi$
$84$		0			0
$85$	83.9766	+	70.4647i	0.987960	+	0.828997i
$86$	−0.732011	+	49.7030i	−0.00851176	+	0.577942i
$87$		0			0
$88$	−57.3195	+	138.168i	−0.651357	+	1.57009i
$89$	7.29925	+	12.6427i	0.0820141	+	0.142053i	0.904115	−	0.427289i	$-0.140531\pi$
$89$	7.29925	+	12.6427i	0.0820141	+	0.142053i	−0.822101	+	0.569342i	$0.807198\pi$
$90$		0			0
$91$	−58.0273	−	33.5021i	−0.637663	−	0.368155i
$92$	58.4116	−	31.4678i	0.634909	−	0.342041i
$93$		0			0
$94$	−39.8339	+	22.2225i	−0.423765	+	0.236410i
$95$	0.976496	+	2.68290i	0.0102789	+	0.0282411i
$96$		0			0
$97$	−1.45511	−	8.25233i	−0.0150011	−	0.0850755i	0.976388	−	0.216024i	$-0.0693089\pi$
$97$	−1.45511	−	8.25233i	−0.0150011	−	0.0850755i	−0.991389	+	0.130948i	$0.958198\pi$
$98$	59.1864	+	22.5346i	0.603943	+	0.229945i
$99$		0			0
$100$	84.9340	+	75.6403i	0.849340	+	0.756403i
$101$	110.882	−	93.0413i	1.09784	−	0.921201i	0.100567	−	0.994930i	$-0.467934\pi$
$101$	110.882	−	93.0413i	1.09784	−	0.921201i	0.997278	+	0.0737291i	$0.0234900\pi$
$102$		0			0
$103$	−3.58880	−	0.632802i	−0.0348427	−	0.00614371i	0.156200	−	0.987726i	$-0.450076\pi$
$103$	−3.58880	−	0.632802i	−0.0348427	−	0.00614371i	−0.191042	+	0.981582i	$0.561187\pi$
$104$	−27.9347	+	125.680i	−0.268603	+	1.20846i
$105$		0			0
$106$	19.2763	−	100.632i	0.181852	−	0.949361i
$107$			118.520i			1.10766i	0.832629	+	0.553831i	$0.186835\pi$
$107$			118.520i			1.10766i	−0.832629	+	0.553831i	$0.813165\pi$
$108$		0			0
$109$	−209.035			−1.91775			−0.958874	−	0.283830i	$-0.908395\pi$
$109$	−209.035			−1.91775			−0.958874	+	0.283830i	$0.908395\pi$
$110$	−268.479	−	51.4278i	−2.44072	−	0.467525i
$111$		0			0
$112$	−3.92181	+	66.4998i	−0.0350162	+	0.593748i
$113$	19.3433	−	109.701i	0.171180	−	0.970810i	−0.771281	−	0.636494i	$-0.780384\pi$
$113$	19.3433	−	109.701i	0.171180	−	0.970810i	0.942461	−	0.334315i	$-0.108505\pi$
$114$		0			0
$115$	77.9373	+	92.8820i	0.677715	+	0.807670i
$116$	117.487	+	104.631i	1.01281	+	0.901990i
$117$		0			0
$118$	59.5363	−	156.370i	0.504545	−	1.32517i
$119$	−61.4899	+	10.8423i	−0.516722	+	0.0911121i
$120$		0			0
$121$	214.835	−	78.1935i	1.77549	−	0.646227i
$122$	24.1995	+	43.3776i	0.198356	+	0.355554i
$123$		0			0
$124$	76.7501	−	41.3472i	0.618952	−	0.333445i
$125$	−12.5484	+	21.7345i	−0.100387	+	0.173876i
$126$		0			0
$127$	9.25406	−	5.34284i	0.0728666	−	0.0420696i	−0.463124	−	0.886293i	$-0.653272\pi$
$127$	9.25406	−	5.34284i	0.0728666	−	0.0420696i	0.535991	+	0.844224i	$0.319938\pi$
$128$	124.147	−	31.1688i	0.969899	−	0.243506i
$129$		0			0
$130$	−235.254	−	3.46474i	−1.80964	−	0.0266519i
$131$	41.0569	−	48.9297i	0.313411	−	0.373509i	−0.586226	−	0.810148i	$-0.699387\pi$
$131$	41.0569	−	48.9297i	0.313411	−	0.373509i	0.899637	+	0.436639i	$0.143831\pi$
$132$		0			0
$133$	−1.52810	−	0.556184i	−0.0114895	−	0.00418184i
$134$	103.840	−	16.7370i	0.774927	−	0.124903i
$135$		0			0
$136$	55.3398	+	106.449i	0.406910	+	0.782712i
$137$	179.780	+	65.4345i	1.31226	+	0.477624i	0.900971	−	0.433880i	$-0.142856\pi$
$137$	179.780	+	65.4345i	1.31226	+	0.477624i	0.411291	+	0.911504i	$0.365078\pi$
$138$		0			0
$139$	−89.1108	+	106.198i	−0.641085	+	0.764015i	−0.984541	−	0.175153i	$-0.943958\pi$
$139$	−89.1108	+	106.198i	−0.641085	+	0.764015i	0.343456	+	0.939169i	$0.388402\pi$
$140$	−120.457	+	17.5996i	−0.860411	+	0.125711i
$141$		0			0
$142$	114.158	−	132.050i	0.803932	−	0.929927i
$143$	260.602	−	150.459i	1.82239	−	1.05216i
$144$		0			0
$145$	−143.751	+	248.983i	−0.991384	+	1.71713i
$146$	−67.6135	+	23.4876i	−0.463106	+	0.160874i
$147$		0			0
$148$	−34.9935	+	27.6486i	−0.236443	+	0.186815i
$149$	−56.2932	+	20.4890i	−0.377806	+	0.137510i	−0.523941	−	0.851754i	$-0.675539\pi$
$149$	−56.2932	+	20.4890i	−0.377806	+	0.137510i	0.146135	+	0.989265i	$0.453317\pi$
$150$		0			0
$151$	69.7855	−	12.3051i	0.462156	−	0.0814905i	0.0622775	−	0.998059i	$-0.480164\pi$
$151$	69.7855	−	12.3051i	0.462156	−	0.0814905i	0.399878	+	0.916568i	$0.369052\pi$
$152$	−0.138002	+	3.12161i	−0.000907909	+	0.0205369i
$153$		0			0
$154$	120.733	−	98.3137i	0.783979	−	0.638401i
$155$	102.406	+	122.043i	0.660683	+	0.787372i
$156$		0			0
$157$	−11.9033	+	67.5070i	−0.0758172	+	0.429981i	0.923146	+	0.384450i	$0.125609\pi$
$157$	−11.9033	+	67.5070i	−0.0758172	+	0.429981i	−0.998963	+	0.0455306i	$0.985502\pi$
$158$	−18.0531	−	10.7805i	−0.114260	−	0.0682309i
$159$		0			0
$160$	101.737	+	210.631i	0.635858	+	1.31644i
$161$	−69.0599			−0.428944
$162$		0			0
$163$		−	166.784i		−	1.02321i	−0.859220	−	0.511606i	$-0.829051\pi$
$163$		−	166.784i		−	1.02321i	0.859220	−	0.511606i	$-0.170949\pi$
$164$	−241.862	−	7.12567i	−1.47477	−	0.0434492i
$165$		0			0
$166$	−173.123	−	103.381i	−1.04291	−	0.622780i
$167$	77.6761	+	13.6964i	0.465126	+	0.0820143i	0.401300	−	0.915947i	$-0.368559\pi$
$167$	77.6761	+	13.6964i	0.465126	+	0.0820143i	0.0638264	+	0.997961i	$0.479670\pi$
$168$		0			0
$169$	68.9419	−	57.8491i	0.407940	−	0.342302i
$170$	−170.010	+	138.441i	−1.00006	+	0.814358i
$171$		0			0
$172$	−97.3556	−	20.1393i	−0.566021	−	0.117089i
$173$	14.3748	+	81.5234i	0.0830912	+	0.471233i	0.997752	+	0.0670117i	$0.0213465\pi$
$173$	14.3748	+	81.5234i	0.0830912	+	0.471233i	−0.914661	+	0.404222i	$0.867542\pi$
$174$		0			0
$175$	−40.4887	−	111.242i	−0.231364	−	0.635667i
$176$	−249.834	−	164.579i	−1.41951	−	0.935110i
$177$		0			0
$178$	−27.5803	+	9.58086i	−0.154946	+	0.0538250i
$179$	−46.3255	−	26.7460i	−0.258801	−	0.149419i	0.364986	−	0.931013i	$-0.381074\pi$
$179$	−46.3255	−	26.7460i	−0.258801	−	0.149419i	−0.623788	+	0.781594i	$0.714407\pi$
$180$		0			0
$181$	32.4491	+	56.2035i	0.179277	+	0.310516i	0.941633	−	0.336641i	$-0.109291\pi$
$181$	32.4491	+	56.2035i	0.179277	+	0.310516i	−0.762356	+	0.647158i	$0.775958\pi$
$182$	87.6413	−	101.377i	0.481546	−	0.557015i
$183$		0			0
$184$	39.8336	+	126.577i	0.216487	+	0.687920i
$185$	−62.4333	−	52.3878i	−0.337477	−	0.283177i
$186$		0			0
$187$	95.9068	−	263.502i	0.512871	−	1.40910i
$188$	−28.6634	−	86.6068i	−0.152465	−	0.460675i
$189$		0			0
$190$	−5.63741	+	0.908641i	−0.0296706	+	0.00478232i
$191$	72.7756	−	199.949i	0.381024	−	1.04685i	−0.589902	−	0.807475i	$-0.700834\pi$
$191$	72.7756	−	199.949i	0.381024	−	1.04685i	0.970926	−	0.239380i	$-0.0769442\pi$
$192$		0			0
$193$	−11.4584	−	9.61478i	−0.0593702	−	0.0498175i	0.612620	−	0.790378i	$-0.290116\pi$
$193$	−11.4584	−	9.61478i	−0.0593702	−	0.0498175i	−0.671990	+	0.740560i	$0.734560\pi$
$194$	16.7574	+	0.246799i	0.0863786	+	0.00127216i
$195$		0			0
$196$	−66.5341	+	107.780i	−0.339460	+	0.549899i
$197$	34.4522	+	59.6729i	0.174884	+	0.302908i	0.940121	−	0.340840i	$-0.110712\pi$
$197$	34.4522	+	59.6729i	0.174884	+	0.302908i	−0.765237	+	0.643749i	$0.777378\pi$
$198$		0			0
$199$	−47.7506	−	27.5688i	−0.239953	−	0.138537i	0.375202	−	0.926943i	$-0.377573\pi$
$199$	−47.7506	−	27.5688i	−0.239953	−	0.138537i	−0.615155	+	0.788406i	$0.710907\pi$
$200$	−180.537	+	138.374i	−0.902685	+	0.691871i
$201$		0			0
$202$	141.039	+	252.813i	0.698213	+	1.25155i
$203$	−56.0067	−	153.877i	−0.275895	−	0.758015i
$204$		0			0
$205$	−76.7841	−	435.464i	−0.374557	−	2.12422i
$206$	2.59334	−	6.81133i	0.0125890	−	0.0330647i
$207$		0			0
$208$	−236.361	−	102.161i	−1.13635	−	0.491157i
$209$	5.59457	−	4.69440i	0.0267683	−	0.0224612i
$210$		0			0
$211$	162.329	+	28.6229i	0.769331	+	0.135654i	0.544519	−	0.838748i	$-0.316712\pi$
$211$	162.329	+	28.6229i	0.769331	+	0.135654i	0.224812	+	0.974402i	$0.427823\pi$
$212$	190.418	+	75.7285i	0.898197	+	0.357210i
$213$		0			0
$214$	−232.807	−	44.5947i	−1.08788	−	0.208387i
$215$		−	181.680i		−	0.845021i
$216$		0			0
$217$	−90.7415			−0.418164
$218$	78.6521	−	410.604i	0.360789	−	1.88351i
$219$		0			0
$220$	202.038	−	508.020i	0.918354	−	2.30918i
$221$	41.9098	−	237.683i	0.189637	−	1.07549i
$222$		0			0
$223$	−245.531	−	292.613i	−1.10104	−	1.31217i	−0.945967	−	0.324262i	$-0.894884\pi$
$223$	−245.531	−	292.613i	−1.10104	−	1.31217i	−0.155071	−	0.987903i	$-0.549561\pi$
$224$	−129.149	−	32.7250i	−0.576559	−	0.146094i
$225$		0			0
$226$	208.207	+	79.2725i	0.921270	+	0.350763i
$227$	157.728	−	27.8117i	0.694838	−	0.122519i	0.184935	−	0.982751i	$-0.440792\pi$
$227$	157.728	−	27.8117i	0.694838	−	0.122519i	0.509903	+	0.860232i	$0.329681\pi$
$228$		0			0
$229$	219.275	−	79.8096i	0.957533	−	0.348513i	0.184466	−	0.982839i	$-0.440944\pi$
$229$	219.275	−	79.8096i	0.957533	−	0.348513i	0.773066	+	0.634325i	$0.218722\pi$
$230$	−211.772	+	118.143i	−0.920748	+	0.513666i
$231$		0			0
$232$	−249.731	+	191.409i	−1.07643	+	0.825037i
$233$	−213.934	+	370.545i	−0.918172	+	1.59032i	−0.115982	+	0.993251i	$0.537002\pi$
$233$	−213.934	+	370.545i	−0.918172	+	1.59032i	−0.802190	+	0.597069i	$0.796332\pi$
$234$		0			0
$235$	144.377	−	83.3563i	0.614372	−	0.354708i
$236$	284.755	+	175.783i	1.20659	+	0.744843i
$237$		0			0
$238$	1.83895	−	124.864i	0.00772669	−	0.524637i
$239$	−29.7397	+	35.4424i	−0.124434	+	0.148295i	−0.824665	−	0.565622i	$-0.808636\pi$
$239$	−29.7397	+	35.4424i	−0.124434	+	0.148295i	0.700231	+	0.713917i	$0.253081\pi$
$240$		0			0
$241$	−240.056	−	87.3733i	−0.996083	−	0.362545i	−0.208010	−	0.978127i	$-0.566699\pi$
$241$	−240.056	−	87.3733i	−0.996083	−	0.362545i	−0.788073	+	0.615582i	$0.788921\pi$
$242$	72.7600	+	451.419i	0.300661	+	1.86537i
$243$		0			0
$244$	−94.3115	+	31.2133i	−0.386523	+	0.127923i
$245$	−217.510	−	79.1672i	−0.887797	−	0.323132i
$246$		0			0
$247$	4.04043	−	4.81520i	0.0163580	−	0.0194947i
$248$	52.3395	+	166.317i	0.211046	+	0.670632i
$249$		0			0
$250$	−37.9712	−	32.8265i	−0.151885	−	0.131306i
$251$	−411.736	+	237.716i	−1.64038	+	0.947076i	−0.659687	+	0.751541i	$0.729311\pi$
$251$	−411.736	+	237.716i	−1.64038	+	0.947076i	−0.980697	+	0.195535i	$0.937356\pi$
$252$		0			0
$253$	155.075	−	268.598i	0.612944	−	1.06165i
$254$	7.01290	+	20.1880i	0.0276098	+	0.0794801i
$255$		0			0
$256$	14.5125	+	255.588i	0.0566895	+	0.998392i
$257$	43.3069	−	15.7624i	0.168509	−	0.0613323i	−0.256388	−	0.966574i	$-0.582532\pi$
$257$	43.3069	−	15.7624i	0.168509	−	0.0613323i	0.424897	+	0.905242i	$0.360310\pi$
$258$		0			0
$259$	45.7154	−	8.06085i	0.176507	−	0.0311230i
$260$	95.3231	−	460.802i	0.366627	−	1.77232i
$261$		0			0
$262$	80.6638	+	99.0580i	0.307877	+	0.378084i
$263$	−102.839	−	122.559i	−0.391025	−	0.466005i	0.534237	−	0.845335i	$-0.320599\pi$
$263$	−102.839	−	122.559i	−0.391025	−	0.466005i	−0.925261	+	0.379330i	$0.876155\pi$
$264$		0			0
$265$	−65.0292	+	368.799i	−0.245393	+	1.39169i
$266$	1.66748	−	2.79236i	0.00626871	−	0.0104976i
$267$		0			0
$268$	−6.19492	+	210.270i	−0.0231154	+	0.784588i
$269$	−408.125			−1.51719			−0.758597	−	0.651560i	$-0.774115\pi$
$269$	−408.125			−1.51719			−0.758597	+	0.651560i	$0.774115\pi$
$270$		0			0
$271$		−	9.23489i		−	0.0340771i	−0.999855	−	0.0170385i	$-0.994576\pi$
$271$		−	9.23489i		−	0.0340771i	0.999855	−	0.0170385i	$-0.00542380\pi$
$272$	−229.918	+	68.6505i	−0.845288	+	0.252391i
$273$		0			0
$274$	−196.177	+	328.519i	−0.715974	+	1.19897i
$275$	523.574	+	92.3203i	1.90391	+	0.335710i
$276$		0			0
$277$	59.9164	−	50.2758i	0.216305	−	0.181501i	−0.528197	−	0.849122i	$-0.677132\pi$
$277$	59.9164	−	50.2758i	0.216305	−	0.181501i	0.744502	+	0.667621i	$0.232687\pi$
$278$	−175.075	−	214.998i	−0.629765	−	0.773373i
$279$		0			0
$280$	10.7531	−	243.235i	0.0384039	−	0.868697i
$281$	84.5660	+	479.598i	0.300947	+	1.70675i	0.641996	+	0.766708i	$0.278107\pi$
$281$	84.5660	+	479.598i	0.300947	+	1.70675i	−0.341049	+	0.940046i	$0.610782\pi$
$282$		0			0
$283$	−72.9296	−	200.373i	−0.257702	−	0.708030i	−0.999308	−	0.0371946i	$-0.988158\pi$
$283$	−72.9296	−	200.373i	−0.257702	−	0.708030i	0.741606	−	0.670836i	$-0.234064\pi$
$284$	216.430	+	273.925i	0.762077	+	0.964526i
$285$		0			0
$286$	197.489	+	568.510i	0.690521	+	1.98780i
$287$	218.112	+	125.927i	0.759973	+	0.438771i
$288$		0			0
$289$	32.0482	+	55.5091i	0.110893	+	0.192073i
$290$	−434.987	−	376.051i	−1.49995	−	1.29673i
$291$		0			0
$292$	−20.6959	−	141.650i	−0.0708765	−	0.485103i
$293$	125.729	+	105.500i	0.429111	+	0.360067i	0.831616	−	0.555351i	$-0.187416\pi$
$293$	125.729	+	105.500i	0.429111	+	0.360067i	−0.402505	+	0.915418i	$0.631861\pi$
$294$		0			0
$295$	−209.160	+	574.661i	−0.709016	+	1.94800i
$296$	−41.1430	−	79.1405i	−0.138996	−	0.267367i
$297$		0			0
$298$	−19.0653	−	118.285i	−0.0639775	−	0.396930i
$299$	91.3000	−	250.845i	0.305351	−	0.838946i
$300$		0			0
$301$	79.2699	+	66.5153i	0.263355	+	0.220981i
$302$	−2.08704	+	141.709i	−0.00691074	+	0.469234i
$303$		0			0
$304$	−6.07982	−	1.44562i	−0.0199994	−	0.00475534i
$305$	−90.7718	−	157.221i	−0.297613	−	0.515480i
$306$		0			0
$307$	−277.852	−	160.418i	−0.905056	−	0.522534i	−0.0262186	−	0.999656i	$-0.508347\pi$
$307$	−277.852	−	160.418i	−0.905056	−	0.522534i	−0.878837	+	0.477122i	$0.841680\pi$
$308$	147.689	+	274.146i	0.479510	+	0.890083i
$309$		0			0
$310$	−278.258	+	155.235i	−0.897608	+	0.500756i
$311$	141.775	+	389.525i	0.455870	+	1.25249i	0.928533	+	0.371249i	$0.121070\pi$
$311$	141.775	+	389.525i	0.455870	+	1.25249i	−0.472664	+	0.881243i	$0.656708\pi$
$312$		0			0
$313$	11.8062	+	66.9560i	0.0377193	+	0.213917i	0.997842	−	0.0656625i	$-0.0209161\pi$
$313$	11.8062	+	66.9560i	0.0377193	+	0.213917i	−0.960123	+	0.279579i	$0.909805\pi$
$314$	−128.124	−	48.7819i	−0.408039	−	0.155356i
$315$		0			0
$316$	27.9687	−	31.4051i	0.0885085	−	0.0993832i
$317$	423.973	−	355.755i	1.33745	−	1.12226i	0.355180	−	0.934798i	$-0.384419\pi$
$317$	423.973	−	355.755i	1.33745	−	1.12226i	0.982273	−	0.187458i	$-0.0600250\pi$
$318$		0			0
$319$	724.244	+	127.704i	2.27036	+	0.400325i
$320$	−452.019	+	120.589i	−1.41256	+	0.376839i
$321$		0			0
$322$	25.9847	−	135.654i	0.0806979	−	0.421284i
$323$		−	5.85748i		−	0.0181346i
$324$		0			0
$325$	457.588			1.40796
$326$	327.611	+	62.7545i	1.00494	+	0.192499i
$327$		0			0
$328$	105.001	−	472.405i	0.320124	−	1.44026i
$329$	−16.4887	+	93.5122i	−0.0501177	+	0.284232i
$330$		0			0
$331$	253.344	+	301.924i	0.765390	+	0.912157i	0.998176	−	0.0603714i	$-0.0192285\pi$
$331$	253.344	+	301.924i	0.765390	+	0.912157i	−0.232786	+	0.972528i	$0.574784\pi$
$332$	268.211	−	301.165i	0.807864	−	0.907123i
$333$		0			0
$334$	−56.1303	+	147.425i	−0.168055	+	0.441391i
$335$	−378.584	+	66.7546i	−1.13010	+	0.199267i
$336$		0			0
$337$	−495.696	+	180.418i	−1.47091	+	0.535366i	−0.948347	−	0.317236i	$-0.897245\pi$
$337$	−495.696	+	180.418i	−1.47091	+	0.535366i	−0.522560	+	0.852602i	$0.675023\pi$
$338$	87.6920	+	157.188i	0.259444	+	0.465054i
$339$		0			0
$340$	−207.969	−	386.039i	−0.611674	−	1.13541i
$341$	203.761	−	352.925i	0.597540	−	1.03497i
$342$		0			0
$343$	290.853	−	167.924i	0.847968	−	0.489574i
$344$	76.1908	−	183.657i	0.221485	−	0.533886i
$345$		0			0
$346$	−165.544	−	2.43808i	−0.478451	−	0.00704648i
$347$	105.358	−	125.560i	0.303624	−	0.361845i	−0.592561	−	0.805526i	$-0.701883\pi$
$347$	105.358	−	125.560i	0.303624	−	0.361845i	0.896185	+	0.443681i	$0.146328\pi$
$348$		0			0
$349$	111.453	+	40.5656i	0.319350	+	0.116234i	0.496721	−	0.867910i	$-0.334537\pi$
$349$	111.453	+	40.5656i	0.319350	+	0.116234i	−0.177371	+	0.984144i	$0.556759\pi$
$350$	233.745	−	37.6752i	0.667843	−	0.107643i
$351$		0			0
$352$	417.285	−	428.820i	1.18547	−	1.21824i
$353$	−405.217	−	147.487i	−1.14792	−	0.417810i	−0.303154	−	0.952941i	$-0.598040\pi$
$353$	−405.217	−	147.487i	−1.14792	−	0.417810i	−0.844769	+	0.535132i	$0.820262\pi$
$354$		0			0
$355$	−410.086	+	488.721i	−1.15517	+	1.37668i
$356$	−8.44210	−	57.7806i	−0.0237138	−	0.162305i
$357$		0			0
$358$	69.9674	−	80.9330i	0.195440	−	0.226070i
$359$	−276.576	+	159.681i	−0.770407	+	0.444795i	−0.833020	−	0.553243i	$-0.813390\pi$
$359$	−276.576	+	159.681i	−0.770407	+	0.444795i	0.0626127	+	0.998038i	$0.480057\pi$
$360$		0			0
$361$	−180.424	+	312.503i	−0.499789	+	0.865659i
$362$	−122.609	+	42.5920i	−0.338699	+	0.117658i
$363$		0			0
$364$	166.157	+	210.297i	0.456475	+	0.577739i
$365$	245.830	−	89.4748i	0.673507	−	0.245136i
$366$		0			0
$367$	−605.049	+	106.686i	−1.64863	+	0.290699i	−0.919329	−	0.393490i	$-0.871268\pi$
$367$	−605.049	+	106.686i	−1.64863	+	0.290699i	−0.729305	+	0.684188i	$0.760157\pi$
$368$	−263.622	+	30.6183i	−0.716365	+	0.0832018i
$369$		0			0
$370$	126.396	−	102.925i	0.341611	−	0.278177i
$371$	−137.105	−	163.396i	−0.369556	−	0.440419i
$372$		0			0
$373$	104.221	−	591.065i	0.279412	−	1.58462i	−0.445177	−	0.895442i	$-0.646859\pi$
$373$	104.221	−	591.065i	0.279412	−	1.58462i	0.724589	−	0.689181i	$-0.242030\pi$
$374$	481.507	+	287.535i	1.28745	+	0.768810i
$375$		0			0
$376$	180.906	−	23.7161i	0.481132	−	0.0630747i
$377$	632.967			1.67896
$378$		0			0
$379$			14.1542i			0.0373462i	0.999826	+	0.0186731i	$0.00594418\pi$
$379$			14.1542i			0.0373462i	−0.999826	+	0.0186731i	$0.994056\pi$
$380$	0.336317	−	11.4154i	0.000885046	−	0.0300405i
$381$		0			0
$382$	365.375	+	218.186i	0.956479	+	0.571167i
$383$	−357.007	−	62.9499i	−0.932133	−	0.164360i	−0.313095	−	0.949722i	$-0.601366\pi$
$383$	−357.007	−	62.9499i	−0.932133	−	0.164360i	−0.619037	+	0.785362i	$0.712477\pi$
$384$		0			0
$385$	−435.927	+	365.786i	−1.13228	+	0.950095i
$386$	23.1976	−	18.8900i	0.0600974	−	0.0489378i
$387$		0			0
$388$	−6.79000	+	32.8236i	−0.0175000	+	0.0845969i
$389$	67.1581	+	380.873i	0.172643	+	0.979107i	0.940829	+	0.338881i	$0.110048\pi$
$389$	67.1581	+	380.873i	0.172643	+	0.979107i	−0.768186	+	0.640226i	$0.778841\pi$
$390$		0			0
$391$	−85.0789	−	233.752i	−0.217593	−	0.597832i
$392$	−186.677	−	171.246i	−0.476217	−	0.436852i
$393$		0			0
$394$	−130.178	+	45.2212i	−0.330401	+	0.114775i
$395$	66.5553	+	38.4257i	0.168494	+	0.0972803i
$396$		0			0
$397$	75.4765	+	130.729i	0.190117	+	0.329293i	0.945289	−	0.326234i	$-0.105780\pi$
$397$	75.4765	+	130.729i	0.190117	+	0.329293i	−0.755172	+	0.655527i	$0.772447\pi$
$398$	72.1199	−	83.4228i	0.181206	−	0.209605i
$399$		0			0
$400$	−203.877	−	406.692i	−0.509693	−	1.01673i
$401$	172.496	+	144.741i	0.430164	+	0.360951i	0.832014	−	0.554755i	$-0.187188\pi$
$401$	172.496	+	144.741i	0.430164	+	0.360951i	−0.401850	+	0.915706i	$0.631633\pi$
$402$		0			0
$403$	119.964	−	329.598i	0.297677	−	0.817862i
$404$	−549.665	+	181.917i	−1.36056	+	0.450289i
$405$		0			0
$406$	323.332	−	52.1149i	0.796385	−	0.128362i
$407$	−71.3030	+	195.903i	−0.175192	+	0.481335i
$408$		0			0
$409$	−74.9861	−	62.9208i	−0.183340	−	0.153841i	0.546499	−	0.837460i	$-0.315960\pi$
$409$	−74.9861	−	62.9208i	−0.183340	−	0.153841i	−0.729839	+	0.683619i	$0.760405\pi$
$410$	884.269	+	13.0232i	2.15675	+	0.0317640i
$411$		0			0
$412$	12.4036	+	7.65692i	0.0301059	+	0.0185848i
$413$	−174.158	−	301.651i	−0.421691	−	0.730391i
$414$		0			0
$415$	638.244	+	368.490i	1.53794	+	0.887928i
$416$	289.607	−	425.842i	0.696170	−	1.02366i
$417$		0			0
$418$	7.11612	+	12.7557i	0.0170242	+	0.0305159i
$419$	18.1404	+	49.8403i	0.0432945	+	0.118951i	0.959456	−	0.281859i	$-0.0909511\pi$
$419$	18.1404	+	49.8403i	0.0432945	+	0.118951i	−0.916161	+	0.400810i	$0.868729\pi$
$420$		0			0
$421$	69.5196	+	394.265i	0.165130	+	0.936497i	0.948931	+	0.315485i	$0.102167\pi$
$421$	69.5196	+	394.265i	0.165130	+	0.936497i	−0.783801	+	0.621012i	$0.786722\pi$
$422$	−117.302	+	308.091i	−0.277967	+	0.730073i
$423$		0			0
$424$	−220.400	+	345.541i	−0.519811	+	0.814956i
$425$	326.648	−	274.090i	0.768583	−	0.644917i
$426$		0			0
$427$	101.831	+	17.9556i	0.238481	+	0.0420506i
$428$	175.194	−	440.521i	0.409331	−	1.02925i
$429$		0			0
$430$	356.871	+	68.3594i	0.829932	+	0.158975i
$431$		−	445.360i		−	1.03332i	−0.856191	−	0.516659i	$-0.827175\pi$
$431$		−	445.360i		−	1.03332i	0.856191	−	0.516659i	$-0.172825\pi$
$432$		0			0
$433$	−52.1504			−0.120440			−0.0602199	−	0.998185i	$-0.519180\pi$
$433$	−52.1504			−0.120440			−0.0602199	+	0.998185i	$0.519180\pi$
$434$	34.1427	−	178.242i	0.0786698	−	0.410697i
$435$		0			0
$436$	776.951	+	308.991i	1.78200	+	0.708694i
$437$	1.12501	−	6.38022i	0.00257438	−	0.0146001i
$438$		0			0
$439$	−307.416	−	366.365i	−0.700265	−	0.834543i	0.292291	−	0.956329i	$-0.405582\pi$
$439$	−307.416	−	366.365i	−0.700265	−	0.834543i	−0.992556	+	0.121786i	$0.961138\pi$
$440$	921.878	+	588.010i	2.09518	+	1.33639i
$441$		0			0
$442$	451.108	+	171.754i	1.02061	+	0.388584i
$443$	−64.2664	+	11.3319i	−0.145071	+	0.0255799i	−0.245712	−	0.969343i	$-0.579022\pi$
$443$	−64.2664	+	11.3319i	−0.145071	+	0.0255799i	0.100641	+	0.994923i	$0.467911\pi$
$444$		0			0
$445$	100.277	−	36.4978i	0.225341	−	0.0820174i
$446$	667.161	−	372.195i	1.49588	−	0.834517i
$447$		0			0
$448$	112.875	−	241.373i	0.251954	−	0.538779i
$449$	107.513	−	186.218i	0.239450	−	0.414740i	−0.721106	−	0.692824i	$-0.756366\pi$
$449$	107.513	−	186.218i	0.239450	−	0.414740i	0.960557	+	0.278084i	$0.0896994\pi$
$450$		0			0
$451$	−979.548	+	565.542i	−2.17195	+	1.25397i
$452$	−234.055	+	379.151i	−0.517820	+	0.838830i
$453$		0			0
$454$	−4.71711	+	320.288i	−0.0103901	+	0.705481i
$455$	−314.830	+	375.199i	−0.691933	+	0.824614i
$456$		0			0
$457$	731.479	+	266.237i	1.60061	+	0.582575i	0.979552	−	0.201189i	$-0.0644806\pi$
$457$	731.479	+	266.237i	1.60061	+	0.582575i	0.621059	+	0.783764i	$0.286703\pi$
$458$	74.2638	+	460.749i	0.162148	+	1.00600i
$459$		0			0
$460$	−152.385	−	460.434i	−0.331272	−	1.00094i
$461$	41.6290	+	15.1517i	0.0903015	+	0.0328670i	0.386776	−	0.922174i	$-0.373589\pi$
$461$	41.6290	+	15.1517i	0.0903015	+	0.0328670i	−0.296474	+	0.955041i	$0.595811\pi$
$462$		0			0
$463$	−525.356	+	626.094i	−1.13468	+	1.35226i	−0.207234	+	0.978291i	$0.566446\pi$
$463$	−525.356	+	626.094i	−1.13468	+	1.35226i	−0.927443	+	0.373964i	$0.877998\pi$
$464$	−282.017	−	562.564i	−0.607795	−	1.21242i
$465$		0			0
$466$	−647.361	−	559.650i	−1.38919	−	1.20097i
$467$	−392.786	+	226.775i	−0.841084	+	0.485600i	−0.857632	−	0.514263i	$-0.828065\pi$
$467$	−392.786	+	226.775i	−0.841084	+	0.485600i	0.0165487	+	0.999863i	$0.494732\pi$
$468$		0			0
$469$	109.479	−	189.623i	0.233430	−	0.404313i
$470$	109.412	+	314.963i	0.232791	+	0.670133i
$471$		0			0
$472$	−452.431	+	493.200i	−0.958540	+	1.04492i
$473$	−436.702	+	158.947i	−0.923261	+	0.336039i
$474$		0			0
$475$	10.9368	−	1.92846i	0.0230249	−	0.00405991i
$476$	244.576	+	50.5938i	0.513815	+	0.106290i
$477$		0			0
$478$	−58.4291	−	71.7530i	−0.122237	−	0.150111i
$479$	394.817	+	470.525i	0.824253	+	0.982307i	0.999998	−	0.00212887i	$-0.000677642\pi$
$479$	394.817	+	470.525i	0.824253	+	0.982307i	−0.175744	+	0.984436i	$0.556233\pi$
$480$		0			0
$481$	−31.1583	+	176.708i	−0.0647782	+	0.367376i
$482$	261.951	−	438.664i	0.543466	−	0.910091i
$483$		0			0
$484$	−914.093	−	26.9308i	−1.88862	−	0.0556422i
$485$	−61.2535			−0.126296
$486$		0			0
$487$		−	660.590i		−	1.35645i	−0.734856	−	0.678224i	$-0.762750\pi$
$487$		−	660.590i		−	1.35645i	0.734856	−	0.678224i	$-0.237250\pi$
$488$	−25.8259	−	196.999i	−0.0529220	−	0.403687i
$489$		0			0
$490$	237.348	−	397.465i	0.484384	−	0.811153i
$491$	−711.257	−	125.414i	−1.44859	−	0.255425i	−0.606638	−	0.794978i	$-0.707482\pi$
$491$	−711.257	−	125.414i	−1.44859	−	0.255425i	−0.841952	+	0.539553i	$0.818593\pi$
$492$		0			0
$493$	451.841	−	379.140i	0.916514	−	0.769047i
$494$	7.93817	+	9.74835i	0.0160692	+	0.0197335i
$495$		0			0
$496$	−346.387	+	40.2310i	−0.698361	+	0.0811108i
$497$	−63.0995	−	357.855i	−0.126961	−	0.720030i
$498$		0			0
$499$	−79.8454	−	219.374i	−0.160011	−	0.439626i	0.833616	−	0.552344i	$-0.186267\pi$
$499$	−79.8454	−	219.374i	−0.160011	−	0.439626i	−0.993627	+	0.112718i	$0.964044\pi$
$500$	78.7679	−	62.2350i	0.157536	−	0.124470i
$501$		0			0
$502$	−312.021	−	898.212i	−0.621557	−	1.78927i
$503$	225.781	+	130.355i	0.448870	+	0.259155i	0.707353	−	0.706861i	$-0.249889\pi$
$503$	225.781	+	130.355i	0.448870	+	0.259155i	−0.258483	+	0.966016i	$0.583223\pi$
$504$		0			0
$505$	−529.035	−	916.315i	−1.04759	−	1.81449i
$506$	469.254	+	405.675i	0.927379	+	0.801729i
$507$		0			0
$508$	−42.2936	+	6.17936i	−0.0832552	+	0.0121641i
$509$	−590.919	−	495.840i	−1.16094	−	0.974145i	−0.161022	−	0.986951i	$-0.551479\pi$
$509$	−590.919	−	495.840i	−1.16094	−	0.974145i	−0.999918	+	0.0128062i	$0.995924\pi$
$510$		0			0
$511$	−50.9623	+	140.018i	−0.0997306	+	0.274008i
$512$	−507.509	−	67.6618i	−0.991229	−	0.132152i
$513$		0			0
$514$	14.6671	+	90.9980i	0.0285352	+	0.177039i
$515$	−9.11078	+	25.0316i	−0.0176908	+	0.0486051i
$516$		0			0
$517$	−326.675	−	274.113i	−0.631867	−	0.530199i
$518$	−1.36719	+	92.8311i	−0.00263936	+	0.179211i
$519$		0			0
$520$	869.282	+	360.625i	1.67170	+	0.693510i
$521$	213.733	+	370.196i	0.410236	+	0.710550i	0.994915	−	0.100715i	$-0.0321130\pi$
$521$	213.733	+	370.196i	0.410236	+	0.710550i	−0.584679	+	0.811264i	$0.698780\pi$
$522$		0			0
$523$	699.824	+	404.044i	1.33810	+	0.772550i	0.986525	−	0.163611i	$-0.0523143\pi$
$523$	699.824	+	404.044i	1.33810	+	0.772550i	0.351571	+	0.936161i	$0.385648\pi$
$524$	−224.929	+	121.175i	−0.429254	+	0.231250i
$525$		0			0
$526$	279.436	−	155.892i	0.531248	−	0.296372i
$527$	−111.790	−	307.139i	−0.212125	−	0.582807i
$528$		0			0
$529$	44.0835	+	250.010i	0.0833336	+	0.472608i
$530$	−699.959	−	266.502i	−1.32068	−	0.502833i
$531$		0			0
$532$	4.85760	+	4.32607i	0.00913082	+	0.00813170i
$533$	−745.756	+	625.764i	−1.39917	+	1.17404i
$534$		0			0
$535$	853.196	+	150.441i	1.59476	+	0.281199i
$536$	−410.699	−	91.2854i	−0.766230	−	0.170309i
$537$		0			0
$538$	153.563	−	801.675i	0.285432	−	1.49010i
$539$			592.090i			1.09850i
$540$		0			0
$541$	−374.121			−0.691535			−0.345768	−	0.938320i	$-0.612381\pi$
$541$	−374.121			−0.691535			−0.345768	+	0.938320i	$0.612381\pi$
$542$	18.1400	+	3.47475i	0.0334686	+	0.00641098i
$543$		0			0
$544$	−48.3394	−	477.456i	−0.0888592	−	0.877677i
$545$	−265.335	+	1504.79i	−0.486853	+	2.76108i
$546$		0			0
$547$	630.498	+	751.399i	1.15265	+	1.37367i	0.915559	+	0.402184i	$0.131749\pi$
$547$	630.498	+	751.399i	1.15265	+	1.37367i	0.237089	+	0.971488i	$0.423807\pi$
$548$	−571.491	−	508.957i	−1.04287	−	0.928754i
$549$		0			0
$550$	−378.346	+	993.714i	−0.687901	+	1.80675i
$551$	15.1286	−	2.66758i	0.0274566	−	0.00484134i
$552$		0			0
$553$	−41.1326	+	14.9710i	−0.0743808	+	0.0270724i
$554$	76.2119	+	136.610i	0.137567	+	0.246589i
$555$		0			0
$556$	488.192	−	263.001i	0.878043	−	0.473023i
$557$	37.0277	−	64.1338i	0.0664770	−	0.115141i	−0.830871	−	0.556465i	$-0.812157\pi$
$557$	37.0277	−	64.1338i	0.0664770	−	0.115141i	0.897348	+	0.441323i	$0.145491\pi$
$558$		0			0
$559$	−346.400	+	199.994i	−0.619678	+	0.357771i
$560$	473.738	+	112.643i	0.845961	+	0.201148i
$561$		0			0
$562$	−973.887	−	14.3431i	−1.73290	−	0.0255216i
$563$	394.263	−	469.864i	0.700290	−	0.834573i	−0.292270	−	0.956336i	$-0.594410\pi$
$563$	394.263	−	469.864i	0.700290	−	0.834573i	0.992559	+	0.121763i	$0.0388549\pi$
$564$		0			0
$565$	−765.161	−	278.496i	−1.35427	−	0.492913i
$566$	421.030	−	67.8619i	0.743869	−	0.119897i
$567$		0			0
$568$	−619.503	+	322.063i	−1.09067	+	0.567012i
$569$	−128.189	−	46.6569i	−0.225288	−	0.0819980i	0.226910	−	0.973916i	$-0.427138\pi$
$569$	−128.189	−	46.6569i	−0.225288	−	0.0819980i	−0.452198	+	0.891918i	$0.649360\pi$
$570$		0			0
$571$	28.1385	−	33.5342i	0.0492794	−	0.0587289i	−0.740842	−	0.671680i	$-0.765573\pi$
$571$	28.1385	−	33.5342i	0.0492794	−	0.0587289i	0.790121	+	0.612951i	$0.210018\pi$
$572$	−1191.02	+	174.016i	−2.08221	+	0.304224i
$573$		0			0
$574$	−329.425	+	381.054i	−0.573911	+	0.663856i
$575$	408.441	−	235.814i	0.710333	−	0.410111i
$576$		0			0
$577$	−73.2045	+	126.794i	−0.126871	+	0.219747i	−0.922463	−	0.386086i	$-0.873827\pi$
$577$	−73.2045	+	126.794i	−0.126871	+	0.219747i	0.795592	+	0.605833i	$0.207160\pi$
$578$	−121.094	+	42.0658i	−0.209506	+	0.0727782i
$579$		0			0
$580$	902.342	−	712.945i	1.55576	−	1.22922i
$581$	−394.448	+	143.567i	−0.678913	+	0.247104i
$582$		0			0
$583$	943.372	−	166.342i	1.61813	−	0.285321i
$584$	286.028	+	12.6449i	0.489775	+	0.0216523i
$585$		0			0
$586$	−254.539	+	207.273i	−0.434367	+	0.353708i
$587$	−439.369	−	523.619i	−0.748499	−	0.892026i	0.248564	−	0.968616i	$-0.420041\pi$
$587$	−439.369	−	523.619i	−0.748499	−	0.892026i	−0.997063	+	0.0765892i	$0.975597\pi$
$588$		0			0
$589$	1.47820	−	8.38331i	0.00250969	−	0.0142331i
$590$	−1050.10	−	627.074i	−1.77983	−	1.06284i
$591$		0			0
$592$	170.935	−	51.0389i	0.288742	−	0.0862144i
$593$	339.967			0.573301			0.286650	−	0.958035i	$-0.407458\pi$
$593$	339.967			0.573301			0.286650	+	0.958035i	$0.407458\pi$
$594$		0			0
$595$			456.414i			0.767082i
$596$	239.520	+	7.05668i	0.401879	+	0.0118401i
$597$		0			0
$598$	458.378	+	273.723i	0.766519	+	0.457731i
$599$	113.226	+	19.9649i	0.189026	+	0.0333303i	0.267359	−	0.963597i	$-0.413849\pi$
$599$	113.226	+	19.9649i	0.189026	+	0.0333303i	−0.0783338	+	0.996927i	$0.524960\pi$
$600$		0			0
$601$	−41.4690	+	34.7966i	−0.0689999	+	0.0578978i	−0.676635	−	0.736318i	$-0.736563\pi$
$601$	−41.4690	+	34.7966i	−0.0689999	+	0.0578978i	0.607635	+	0.794216i	$0.292118\pi$
$602$	−160.482	+	130.682i	−0.266581	+	0.217079i
$603$		0			0
$604$	−277.571	−	57.4194i	−0.459555	−	0.0950652i
$605$	−290.199	−	1645.80i	−0.479667	−	2.72033i
$606$		0			0
$607$	−221.274	−	607.945i	−0.364537	−	1.00156i	−0.977406	−	0.211372i	$-0.932207\pi$
$607$	−221.274	−	607.945i	−0.364537	−	1.00156i	0.612869	−	0.790185i	$-0.290015\pi$
$608$	5.12723	−	11.3986i	0.00843295	−	0.0187477i
$609$		0			0
$610$	342.982	−	119.145i	0.562266	−	0.195320i
$611$	−317.864	−	183.519i	−0.520235	−	0.300358i
$612$		0			0
$613$	107.603	+	186.374i	0.175535	+	0.304035i	0.940346	−	0.340219i	$-0.110501\pi$
$613$	107.603	+	186.374i	0.175535	+	0.304035i	−0.764811	+	0.644254i	$0.777168\pi$
$614$	419.653	−	485.422i	0.683473	−	0.790590i
$615$		0			0
$616$	−594.071	+	186.953i	−0.964401	+	0.303495i
$617$	246.443	+	206.791i	0.399422	+	0.335155i	0.820270	−	0.571976i	$-0.193823\pi$
$617$	246.443	+	206.791i	0.399422	+	0.335155i	−0.420848	+	0.907131i	$0.638267\pi$
$618$		0			0
$619$	−129.813	+	356.659i	−0.209715	+	0.576186i	−0.999298	−	0.0374568i	$-0.988074\pi$
$619$	−129.813	+	356.659i	−0.209715	+	0.576186i	0.789584	+	0.613643i	$0.210297\pi$
$620$	−200.227	−	604.989i	−0.322946	−	0.975788i
$621$		0			0
$622$	−818.484	+	131.924i	−1.31589	+	0.212096i
$623$	−20.7881	+	57.1148i	−0.0333677	+	0.0916771i
$624$		0			0
$625$	−403.996	−	338.993i	−0.646394	−	0.542389i
$626$	−135.963	−	2.00242i	−0.217193	−	0.00319876i
$627$		0			0
$628$	144.030	−	233.318i	0.229348	−	0.371526i
$629$	83.6035	+	144.806i	0.132915	+	0.230216i
$630$		0			0
$631$	−789.534	−	455.838i	−1.25124	−	0.722405i	−0.279887	−	0.960033i	$-0.590297\pi$
$631$	−789.534	−	455.838i	−1.25124	−	0.722405i	−0.971356	+	0.237628i	$0.923630\pi$
$632$	51.1651	+	66.7551i	0.0809574	+	0.105625i
$633$		0			0
$634$	539.280	+	966.662i	0.850600	+	1.52470i
$635$	−26.7153	−	73.3996i	−0.0420713	−	0.115590i
$636$		0			0
$637$	88.4923	+	501.865i	0.138920	+	0.787857i
$638$	−523.353	+	1374.57i	−0.820303	+	2.15450i
$639$		0			0
$640$	−66.7925	−	933.268i	−0.104363	−	1.45823i
$641$	−415.837	+	348.929i	−0.648732	+	0.544351i	−0.906686	−	0.421807i	$-0.861396\pi$
$641$	−415.837	+	348.929i	−0.648732	+	0.544351i	0.257954	+	0.966157i	$0.416952\pi$
$642$		0			0
$643$	−330.645	−	58.3017i	−0.514223	−	0.0906714i	−0.0894857	−	0.995988i	$-0.528522\pi$
$643$	−330.645	−	58.3017i	−0.514223	−	0.0906714i	−0.424737	+	0.905317i	$0.639633\pi$
$644$	256.686	+	102.083i	0.398580	+	0.158514i
$645$		0			0
$646$	11.5058	+	2.20396i	0.0178108	+	0.00341170i
$647$		−	1.27262i		−	0.00196696i	−1.00000		0.000983479i	$-0.999687\pi$
$647$		−	1.27262i		−	0.00196696i	1.00000		0.000983479i	$-0.000313051\pi$
$648$		0			0
$649$	1564.30			2.41032
$650$	−172.174	+	898.835i	−0.264883	+	1.38282i
$651$		0			0
$652$	−246.536	+	619.910i	−0.378123	+	0.950782i
$653$	67.8083	−	384.560i	0.103841	−	0.588913i	−0.887836	−	0.460161i	$-0.847792\pi$
$653$	67.8083	−	384.560i	0.103841	−	0.588913i	0.991677	−	0.128752i	$-0.0410972\pi$
$654$		0			0
$655$	−300.118	−	357.667i	−0.458196	−	0.546056i
$656$	888.430	+	384.000i	1.35431	+	0.585366i
$657$		0			0
$658$	−177.481	−	67.5738i	−0.269728	−	0.102696i
$659$	226.021	−	39.8536i	0.342975	−	0.0604758i	0.000492450	−	1.00000i	$-0.499843\pi$
$659$	226.021	−	39.8536i	0.342975	−	0.0604758i	0.342483	+	0.939524i	$0.388732\pi$
$660$		0			0
$661$	128.136	−	46.6376i	0.193851	−	0.0705561i	−0.243270	−	0.969959i	$-0.578220\pi$
$661$	128.136	−	46.6376i	0.193851	−	0.0705561i	0.437121	+	0.899402i	$0.355998\pi$
$662$	−688.389	+	384.038i	−1.03986	+	0.580118i
$663$		0			0
$664$	490.656	+	640.160i	0.738940	+	0.964097i
$665$	−5.94351	+	10.2945i	−0.00893761	+	0.0154804i
$666$		0			0
$667$	564.984	−	326.194i	0.847052	−	0.489046i
$668$	−268.465	−	165.727i	−0.401893	−	0.248094i
$669$		0			0
$670$	11.3221	−	768.766i	0.0168987	−	1.14741i
$671$	−298.499	+	355.737i	−0.444856	+	0.530159i
$672$		0			0
$673$	−353.816	−	128.779i	−0.525730	−	0.191350i	0.0655006	−	0.997853i	$-0.479136\pi$
$673$	−353.816	−	128.779i	−0.525730	−	0.191350i	−0.591231	+	0.806502i	$0.701358\pi$
$674$	−167.882	−	1041.57i	−0.249082	−	1.54536i
$675$		0			0
$676$	−341.758	+	113.108i	−0.505559	+	0.167320i
$677$	−458.210	−	166.775i	−0.676824	−	0.246344i	−0.0193408	−	0.999813i	$-0.506157\pi$
$677$	−458.210	−	166.775i	−0.676824	−	0.246344i	−0.657483	+	0.753469i	$0.728379\pi$
$678$		0			0
$679$	22.4257	−	26.7260i	0.0330276	−	0.0393608i
$680$	836.544	−	263.258i	1.23021	−	0.387145i
$681$		0			0
$682$	616.577	+	533.038i	0.904073	+	0.781581i
$683$	1052.67	−	607.762i	1.54125	−	0.889842i	0.542491	−	0.840061i	$-0.317481\pi$
$683$	1052.67	−	607.762i	1.54125	−	0.889842i	0.998760	−	0.0497805i	$-0.0158522\pi$
$684$		0			0
$685$	699.248	−	1211.13i	1.02080	−	1.76808i
$686$	220.414	+	634.502i	0.321303	+	0.924931i
$687$		0			0
$688$	332.087	+	218.764i	0.482684	+	0.317971i
$689$	774.757	−	281.988i	1.12447	−	0.409272i
$690$		0			0
$691$	72.6934	−	12.8178i	0.105200	−	0.0185496i	−0.120800	−	0.992677i	$-0.538546\pi$
$691$	72.6934	−	12.8178i	0.105200	−	0.0185496i	0.226000	+	0.974127i	$0.427435\pi$
$692$	67.0773	−	324.259i	0.0969325	−	0.468582i
$693$		0			0
$694$	206.994	+	254.196i	0.298263	+	0.366277i
$695$	651.383	+	776.288i	0.937242	+	1.11696i
$696$		0			0
$697$	−157.530	+	893.398i	−0.226012	+	1.28178i
$698$	−121.618	+	203.663i	−0.174238	+	0.291780i
$699$		0			0
$700$	−13.9448	+	473.318i	−0.0199211	+	0.676169i
$701$	807.939			1.15255			0.576276	−	0.817255i	$-0.304505\pi$
$701$	807.939			1.15255			0.576276	+	0.817255i	$0.304505\pi$
$702$		0			0
$703$			4.35481i			0.00619461i
$704$	685.318	+	981.016i	0.973463	+	1.39349i
$705$		0			0
$706$	442.175	−	740.469i	0.626310	−	1.04882i
$707$	593.491	+	104.649i	0.839450	+	0.148018i
$708$		0			0
$709$	−375.128	+	314.770i	−0.529094	+	0.443963i	−0.867788	−	0.496934i	$-0.834459\pi$
$709$	−375.128	+	314.770i	−0.529094	+	0.443963i	0.338694	+	0.940896i	$0.390015\pi$
$710$	−805.688	−	989.414i	−1.13477	−	1.39354i
$711$		0			0
$712$	116.674	+	5.15801i	0.163868	+	0.00724439i
$713$	−62.7760	−	356.020i	−0.0880449	−	0.499327i
$714$		0			0
$715$	−752.324	−	2066.99i	−1.05220	−	2.89090i
$716$	132.649	+	167.888i	0.185265	+	0.234481i
$717$		0			0
$718$	−209.595	−	603.357i	−0.291914	−	0.840331i
$719$	−370.164	−	213.715i	−0.514832	−	0.297239i	0.219985	−	0.975503i	$-0.429399\pi$
$719$	−370.164	−	213.715i	−0.514832	−	0.297239i	−0.734818	+	0.678265i	$0.762732\pi$
$720$		0			0
$721$	−7.58616	−	13.1396i	−0.0105217	−	0.0182242i
$722$	−545.959	−	471.988i	−0.756176	−	0.653722i
$723$		0			0
$724$	−37.5296	−	256.865i	−0.0518365	−	0.354787i
$725$	856.673	+	718.834i	1.18162	+	0.991495i
$726$		0			0
$727$	405.970	−	1115.39i	0.558418	−	1.53424i	−0.263514	−	0.964656i	$-0.584882\pi$
$727$	405.970	−	1115.39i	0.558418	−	1.53424i	0.821932	−	0.569585i	$-0.192896\pi$
$728$	−475.603	+	247.253i	−0.653301	+	0.339633i
$729$		0			0
$730$	83.2574	+	516.547i	0.114051	+	0.707599i
$731$	−127.482	+	350.255i	−0.174394	+	0.479145i
$732$		0			0
$733$	−714.992	−	599.950i	−0.975432	−	0.818485i	0.00796157	−	0.999968i	$-0.497466\pi$
$733$	−714.992	−	599.950i	−0.975432	−	0.818485i	−0.983394	+	0.181483i	$0.941910\pi$
$734$	18.0949	−	1228.63i	0.0246525	−	1.67389i
$735$		0			0
$736$	39.0483	−	529.350i	0.0530548	−	0.719226i
$737$	491.671	+	851.599i	0.667125	+	1.15549i
$738$		0			0
$739$	−168.234	−	97.1298i	−0.227651	−	0.131434i	0.381837	−	0.924230i	$-0.375292\pi$
$739$	−168.234	−	97.1298i	−0.227651	−	0.131434i	−0.609488	+	0.792795i	$0.708625\pi$
$740$	154.617	+	287.005i	0.208942	+	0.387845i
$741$		0			0
$742$	372.544	−	207.834i	0.502080	−	0.280100i
$743$	−237.223	−	651.765i	−0.319277	−	0.877207i	−0.990692	−	0.136125i	$-0.956535\pi$
$743$	−237.223	−	651.765i	−0.319277	−	0.877207i	0.671414	−	0.741082i	$-0.265687\pi$
$744$		0			0
$745$	76.0407	+	431.248i	0.102068	+	0.578857i
$746$	1121.81	+	427.115i	1.50376	+	0.572541i
$747$		0			0
$748$	−745.975	+	837.630i	−0.997292	+	1.11983i
$749$	−378.007	+	317.185i	−0.504682	+	0.423479i
$750$		0			0
$751$	−826.362	−	145.710i	−1.10035	−	0.194021i	−0.406152	−	0.913806i	$-0.633129\pi$
$751$	−826.362	−	145.710i	−1.10035	−	0.194021i	−0.694198	+	0.719785i	$0.744241\pi$
$752$	−21.4830	+	364.274i	−0.0285678	+	0.484407i
$753$		0			0
$754$	−238.163	+	1243.33i	−0.315865	+	1.64898i
$755$		−	517.988i		−	0.686077i
$756$		0			0
$757$	−851.184			−1.12442			−0.562209	−	0.826995i	$-0.690048\pi$
$757$	−851.184			−1.12442			−0.562209	+	0.826995i	$0.690048\pi$
$758$	−27.8029	−	5.32571i	−0.0366793	−	0.00702600i
$759$		0			0
$760$	22.2965	+	4.95581i	0.0293376	+	0.00652081i
$761$	110.424	−	626.247i	0.145104	−	0.822926i	−0.822179	−	0.569228i	$-0.807242\pi$
$761$	110.424	−	626.247i	0.145104	−	0.822926i	0.967284	−	0.253698i	$-0.0816468\pi$
$762$		0			0
$763$	−559.423	−	666.694i	−0.733188	−	0.873780i
$764$	−566.057	+	635.606i	−0.740912	+	0.831946i
$765$		0			0
$766$	257.980	−	677.578i	0.336789	−	0.884567i
$767$	1325.93	−	233.796i	1.72872	−	0.304819i
$768$		0			0
$769$	−233.035	+	84.8179i	−0.303037	+	0.110296i	−0.489063	−	0.872248i	$-0.662661\pi$
$769$	−233.035	+	84.8179i	−0.303037	+	0.110296i	0.186026	+	0.982545i	$0.440439\pi$
$770$	−554.486	−	993.919i	−0.720112	−	1.29080i
$771$		0			0
$772$	28.3770	+	52.6744i	0.0367578	+	0.0682310i
$773$	346.850	−	600.761i	0.448706	−	0.777181i	−0.549596	−	0.835430i	$-0.685218\pi$
$773$	346.850	−	600.761i	0.448706	−	0.777181i	0.998302	+	0.0582491i	$0.0185518\pi$
$774$		0			0
$775$	536.673	−	309.848i	0.692481	−	0.399804i
$776$	−61.9201	−	25.6878i	−0.0797940	−	0.0331029i
$777$		0			0
$778$	−773.413	−	11.3906i	−0.994104	−	0.0146409i
$779$	−15.1871	+	18.0993i	−0.0194957	+	0.0232340i
$780$		0			0
$781$	1533.51	+	558.152i	1.96352	+	0.714663i
$782$	491.169	−	79.1669i	0.628093	−	0.101236i
$783$		0			0
$784$	406.616	−	302.254i	0.518643	−	0.385528i
$785$	470.857	+	171.378i	0.599818	+	0.218316i
$786$		0			0
$787$	−140.899	+	167.917i	−0.179033	+	0.213363i	−0.848096	−	0.529843i	$-0.822251\pi$
$787$	−140.899	+	167.917i	−0.179033	+	0.213363i	0.669063	+	0.743205i	$0.266695\pi$
$788$	−39.8463	−	272.722i	−0.0505664	−	0.346094i
$789$		0			0
$790$	−100.521	+	116.276i	−0.127242	+	0.147184i
$791$	401.648	−	231.892i	0.507773	−	0.293163i
$792$		0			0
$793$	−199.845	+	346.141i	−0.252011	+	0.436496i
$794$	−285.189	+	99.0690i	−0.359180	+	0.124772i
$795$		0			0
$796$	136.730	+	173.053i	0.171772	+	0.217404i
$797$	−416.664	+	151.653i	−0.522791	+	0.190280i	−0.589917	−	0.807464i	$-0.700839\pi$
$797$	−416.664	+	151.653i	−0.522791	+	0.190280i	0.0671257	+	0.997745i	$0.478617\pi$
$798$		0			0
$799$	−336.831	+	59.3924i	−0.421566	+	0.0743334i
$800$	875.571	−	247.450i	1.09446	−	0.309313i
$801$		0			0
$802$	−349.217	+	284.371i	−0.435433	+	0.354577i
$803$	−430.140	−	512.621i	−0.535667	−	0.638383i
$804$		0			0
$805$	−87.6602	+	497.146i	−0.108895	+	0.617572i
$806$	602.288	+	359.660i	0.747255	+	0.446228i
$807$		0			0
$808$	−150.518	−	1148.15i	−0.186285	−	1.42098i
$809$	−244.622			−0.302376			−0.151188	−	0.988505i	$-0.548310\pi$
$809$	−244.622			−0.302376			−0.151188	+	0.988505i	$0.548310\pi$
$810$		0			0
$811$			1469.40i			1.81184i	0.423453	+	0.905918i	$0.360818\pi$
$811$			1469.40i			1.81184i	−0.423453	+	0.905918i	$0.639182\pi$
$812$	−19.2894	+	654.726i	−0.0237554	+	0.806313i
$813$		0			0
$814$	−357.982	−	213.771i	−0.439781	−	0.262618i
$815$	−1200.63	−	211.704i	−1.47317	−	0.259760i
$816$		0			0
$817$	−7.43647	+	6.23994i	−0.00910216	+	0.00763762i
$818$	151.809	−	123.619i	0.185586	−	0.151124i
$819$		0			0
$820$	−358.299	+	1732.06i	−0.436950	+	2.11227i
$821$	−29.3718	−	166.576i	−0.0357757	−	0.202894i	0.961681	−	0.274171i	$-0.0884036\pi$
$821$	−29.3718	−	166.576i	−0.0357757	−	0.202894i	−0.997457	+	0.0712774i	$0.977292\pi$
$822$		0			0
$823$	307.283	+	844.254i	0.373370	+	1.02583i	0.974049	+	0.226335i	$0.0726745\pi$
$823$	307.283	+	844.254i	0.373370	+	1.02583i	−0.600680	+	0.799490i	$0.705103\pi$
$824$	−19.7074	+	21.4833i	−0.0239168	+	0.0260720i
$825$		0			0
$826$	658.059	−	228.597i	0.796682	−	0.276752i
$827$	1161.59	+	670.645i	1.40459	+	0.810938i	0.994859	−	0.101271i	$-0.0322909\pi$
$827$	1161.59	+	670.645i	1.40459	+	0.810938i	0.409726	+	0.912209i	$0.365624\pi$
$828$		0			0
$829$	557.477	+	965.578i	0.672469	+	1.16475i	0.977202	+	0.212313i	$0.0680995\pi$
$829$	557.477	+	965.578i	0.672469	+	1.16475i	−0.304733	+	0.952438i	$0.598567\pi$
$830$	−963.969	+	1115.05i	−1.16141	+	1.34343i
$831$		0			0
$832$	727.507	+	729.100i	0.874408	+	0.876322i
$833$	363.781	+	305.248i	0.436712	+	0.366445i
$834$		0			0
$835$	197.194	−	541.786i	0.236160	−	0.648845i
$836$	−27.7333	+	9.17861i	−0.0331738	+	0.0109792i
$837$		0			0
$838$	−104.726	+	16.8798i	−0.124972	+	0.0201430i
$839$	−152.747	+	419.670i	−0.182059	+	0.500203i	−0.996828	−	0.0795824i	$-0.974641\pi$
$839$	−152.747	+	419.670i	−0.182059	+	0.500203i	0.814769	+	0.579785i	$0.196864\pi$
$840$		0			0
$841$	540.765	+	453.756i	0.643003	+	0.539543i
$842$	−800.608	−	11.7911i	−0.950841	−	0.0140037i
$843$		0			0
$844$	−561.042	−	346.338i	−0.664742	−	0.410353i
$845$	−328.931	−	569.726i	−0.389268	−	0.674232i
$846$		0			0
$847$	824.335	+	475.930i	0.973241	+	0.561901i
$848$	−595.814	−	562.943i	−0.702611	−	0.663848i
$849$		0			0
$850$	415.486	+	744.760i	0.488807	+	0.876188i
$851$	63.2528	+	173.786i	0.0743276	+	0.204213i
$852$		0			0
$853$	−7.00887	−	39.7493i	−0.00821673	−	0.0465994i	0.980424	−	0.196899i	$-0.0630872\pi$
$853$	−7.00887	−	39.7493i	−0.00821673	−	0.0465994i	−0.988640	+	0.150300i	$0.951976\pi$
$854$	−73.5853	+	193.270i	−0.0861655	+	0.226311i
$855$		0			0
$856$	799.391	+	509.883i	0.933868	+	0.595657i
$857$	−166.999	+	140.129i	−0.194865	+	0.163511i	−0.735000	−	0.678067i	$-0.762818\pi$
$857$	−166.999	+	140.129i	−0.194865	+	0.163511i	0.540135	+	0.841579i	$0.318373\pi$
$858$		0			0
$859$	1612.96	+	284.408i	1.87772	+	0.331093i	0.991282	−	0.131757i	$-0.0420618\pi$
$859$	1612.96	+	284.408i	1.87772	+	0.331093i	0.886437	+	0.462849i	$0.153173\pi$
$860$	−268.555	+	675.276i	−0.312273	+	0.785204i
$861$		0			0
$862$	874.816	+	167.573i	1.01487	+	0.194400i
$863$			859.974i			0.996494i	0.867035	+	0.498247i	$0.166023\pi$
$863$			859.974i			0.996494i	−0.867035	+	0.498247i	$0.833977\pi$
$864$		0			0
$865$	605.113			0.699553
$866$	19.6223	−	102.438i	0.0226585	−	0.118289i
$867$		0			0
$868$	337.273	+	134.132i	0.388563	+	0.154530i
$869$	34.1363	−	193.596i	0.0392822	−	0.222781i
$870$		0			0
$871$	544.027	+	648.346i	0.624600	+	0.744369i
$872$	−899.285	+	1409.89i	−1.03129	+	1.61685i
$873$		0			0
$874$	12.1093	+	4.61048i	0.0138550	+	0.00527515i
$875$	−102.902	+	18.1444i	−0.117602	+	0.0207365i
$876$		0			0
$877$	−356.422	+	129.727i	−0.406411	+	0.147921i	−0.537133	−	0.843498i	$-0.680493\pi$
$877$	−356.422	+	129.727i	−0.406411	+	0.147921i	0.130722	+	0.991419i	$0.458270\pi$
$878$	835.315	−	466.005i	0.951384	−	0.530757i
$879$		0			0
$880$	−1501.89	+	1589.59i	−1.70669	+	1.80635i
$881$	41.1847	−	71.3340i	0.0467477	−	0.0809693i	−0.841705	−	0.539938i	$-0.818448\pi$
$881$	41.1847	−	71.3340i	0.0467477	−	0.0809693i	0.888452	+	0.458969i	$0.151781\pi$
$882$		0			0
$883$	−328.446	+	189.629i	−0.371967	+	0.214755i	−0.674317	−	0.738442i	$-0.735562\pi$
$883$	−328.446	+	189.629i	−0.371967	+	0.214755i	0.302351	+	0.953197i	$0.402229\pi$
$884$	−507.110	+	821.481i	−0.573654	+	0.929277i
$885$		0			0
$886$	1.92198	−	130.501i	0.00216928	−	0.147293i
$887$	257.770	−	307.198i	0.290609	−	0.346334i	−0.600911	−	0.799316i	$-0.705195\pi$
$887$	257.770	−	307.198i	0.290609	−	0.346334i	0.891520	+	0.452982i	$0.149640\pi$
$888$		0			0
$889$	41.8063	+	15.2163i	0.0470262	+	0.0171162i
$890$	33.9616	+	210.705i	0.0381591	+	0.236747i
$891$		0			0
$892$	480.069	+	1450.54i	0.538194	+	1.62616i
$893$	−8.37069	−	3.04668i	−0.00937367	−	0.00341174i
$894$		0			0
$895$	−251.341	+	299.536i	−0.280827	+	0.334677i
$896$	431.655	+	312.540i	0.481758	+	0.348817i
$897$		0			0
$898$	325.333	+	281.254i	0.362286	+	0.313201i
$899$	742.362	−	428.603i	0.825765	−	0.476755i
$900$		0			0
$901$	384.150	−	665.367i	0.426359	−	0.738476i
$902$	−742.319	−	2136.91i	−0.822970	−	2.36908i
$903$		0			0
$904$	−656.696	−	602.412i	−0.726433	−	0.666385i
$905$	445.784	−	162.252i	0.492579	−	0.179284i
$906$		0			0
$907$	−131.754	+	23.2317i	−0.145263	+	0.0256138i	−0.245807	−	0.969319i	$-0.579053\pi$
$907$	−131.754	+	23.2317i	−0.145263	+	0.0256138i	0.100544	+	0.994933i	$0.467942\pi$
$908$	−627.363	−	129.779i	−0.690929	−	0.142928i
$909$		0			0
$910$	−618.540	−	759.590i	−0.679715	−	0.834714i
$911$	264.618	+	315.359i	0.290469	+	0.346168i	0.891469	−	0.453081i	$-0.149675\pi$
$911$	264.618	+	315.359i	0.290469	+	0.346168i	−0.601000	+	0.799249i	$0.705231\pi$
$912$		0			0
$913$	327.356	−	1856.53i	0.358550	−	2.03344i
$914$	−798.194	+	1336.66i	−0.873298	+	1.46243i
$915$		0			0
$916$	−932.985	−	27.4874i	−1.01854	−	0.0300081i
$917$	265.934			0.290004
$918$		0			0
$919$		−	651.417i		−	0.708832i	−0.935088	−	0.354416i	$-0.884680\pi$
$919$		−	651.417i		−	0.708832i	0.935088	−	0.354416i	$-0.115320\pi$
$920$	961.762	−	126.083i	1.04539	−	0.137047i
$921$		0			0
$922$	−45.4258	+	76.0702i	−0.0492687	+	0.0825057i
$923$	1383.25	+	243.904i	1.49864	+	0.264251i
$924$		0			0
$925$	−242.850	+	203.775i	−0.262540	+	0.220297i
$926$	−1032.16	−	1267.53i	−1.11464	−	1.36882i
$927$		0			0
$928$	1211.15	−	342.290i	1.30512	−	0.368847i
$929$	155.604	+	882.473i	0.167496	+	0.949917i	0.946454	+	0.322840i	$0.104638\pi$
$929$	155.604	+	882.473i	0.167496	+	0.949917i	−0.778958	+	0.627077i	$0.784251\pi$
$930$		0			0
$931$	4.23011	+	11.6221i	0.00454362	+	0.0124835i
$932$	1342.89	−	1061.03i	1.44087	−	1.13844i
$933$		0			0
$934$	−297.661	−	856.872i	−0.318694	−	0.917422i
$935$	−1775.15	−	1024.88i	−1.89855	−	1.09613i
$936$		0			0
$937$	−442.521	−	766.469i	−0.472275	−	0.818003i	0.527222	−	0.849727i	$-0.323234\pi$
$937$	−442.521	−	766.469i	−0.472275	−	0.818003i	−0.999497	+	0.0317240i	$0.989900\pi$
$938$	331.280	+	286.396i	0.353177	+	0.305326i
$939$		0			0
$940$	−659.845	+	96.4074i	−0.701963	+	0.102561i
$941$	−127.082	−	106.635i	−0.135050	−	0.113321i	0.572760	−	0.819723i	$-0.305873\pi$
$941$	−127.082	−	106.635i	−0.135050	−	0.113321i	−0.707811	+	0.706402i	$0.750317\pi$
$942$		0			0
$943$	−343.177	+	942.872i	−0.363921	+	0.999864i
$944$	−798.554	−	1074.28i	−0.845926	−	1.13801i
$945$		0			0
$946$	−147.902	−	917.615i	−0.156344	−	0.969994i
$947$	140.590	−	386.269i	0.148459	−	0.407887i	−0.843065	−	0.537811i	$-0.819251\pi$
$947$	140.590	−	386.269i	0.148459	−	0.407887i	0.991524	+	0.129924i	$0.0414735\pi$
$948$		0			0
$949$	−441.209	−	370.219i	−0.464920	−	0.390114i
$950$	−0.327083	+	22.2087i	−0.000344298	+	0.0233776i
$951$		0			0
$952$	−191.406	+	461.381i	−0.201056	+	0.484644i
$953$	−673.325	−	1166.23i	−0.706532	−	1.22375i	−0.966136	−	0.258034i	$-0.916925\pi$
$953$	−673.325	−	1166.23i	−0.706532	−	1.22375i	0.259604	−	0.965715i	$-0.416408\pi$
$954$		0			0
$955$	−1347.01	−	777.696i	−1.41048	−	0.814342i
$956$	162.928	−	87.7736i	0.170427	−	0.0918134i
$957$		0			0
$958$	−1072.80	+	598.494i	−1.11983	+	0.624732i
$959$	272.434	+	748.506i	0.284081	+	0.780507i
$960$		0			0
$961$	84.3912	+	478.606i	0.0878160	+	0.498029i
$962$	−335.381	−	127.693i	−0.348629	−	0.132737i
$963$		0			0
$964$	763.099	+	679.599i	0.791597	+	0.704979i
$965$	−83.7591	+	70.2822i	−0.0867970	+	0.0728313i
$966$		0			0
$967$	714.553	+	125.995i	0.738938	+	0.130295i	0.530433	−	0.847727i	$-0.322029\pi$
$967$	714.553	+	125.995i	0.738938	+	0.130295i	0.208505	+	0.978021i	$0.433140\pi$
$968$	396.840	−	1785.41i	0.409958	−	1.84443i
$969$		0			0
$970$	23.0475	−	120.320i	0.0237603	−	0.124041i
$971$			1795.99i			1.84963i	0.380419	+	0.924814i	$0.375780\pi$
$971$			1795.99i			1.84963i	−0.380419	+	0.924814i	$0.624220\pi$
$972$		0			0
$973$	−577.188			−0.593205
$974$	1297.59	+	248.556i	1.33223	+	0.255191i
$975$		0			0
$976$	396.681	+	23.3942i	0.406435	+	0.0239694i
$977$	−132.058	+	748.936i	−0.135166	+	0.766567i	0.839577	+	0.543240i	$0.182803\pi$
$977$	−132.058	+	748.936i	−0.135166	+	0.766567i	−0.974744	+	0.223327i	$0.928308\pi$
$978$		0			0
$979$	−175.459	−	209.104i	−0.179223	−	0.213589i
$980$	691.430	+	615.772i	0.705540	+	0.628339i
$981$		0			0
$982$	513.969	−	1349.93i	0.523390	−	1.37467i
$983$	−994.218	+	175.308i	−1.01141	+	0.178339i	−0.654711	−	0.755879i	$-0.727210\pi$
$983$	−994.218	+	175.308i	−1.01141	+	0.178339i	−0.356701	+	0.934219i	$0.616099\pi$
$984$		0			0
$985$	473.302	−	172.268i	0.480510	−	0.174891i
$986$	574.728	+	1030.20i	0.582889	+	1.04483i
$987$		0			0
$988$	−22.1354	+	11.9249i	−0.0224043	+	0.0120697i
$989$	−206.130	+	357.028i	−0.208423	+	0.360999i
$990$		0			0
$991$	892.014	−	515.005i	0.900115	−	0.519682i	0.0228778	−	0.999738i	$-0.492717\pi$
$991$	892.014	−	515.005i	0.900115	−	0.519682i	0.877238	+	0.480056i	$0.159384\pi$
$992$	51.3077	−	695.542i	0.0517215	−	0.701151i
$993$		0			0
$994$	726.672	+	10.7022i	0.731058	+	0.0107668i
$995$	−259.073	+	308.751i	−0.260375	+	0.310302i
$996$		0			0
$997$	707.962	+	257.677i	0.710092	+	0.258452i	0.671714	−	0.740811i	$-0.265559\pi$
$997$	707.962	+	257.677i	0.710092	+	0.258452i	0.0383783	+	0.999263i	$0.487781\pi$
$998$	460.956	−	74.2972i	0.461879	−	0.0744461i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	324.3.j.a.307.14		204
3.2	odd	2		108.3.j.a.31.21	yes	204
4.3	odd	2	inner	324.3.j.a.307.21		204
12.11	even	2		108.3.j.a.31.14	yes	204
27.7	even	9	inner	324.3.j.a.19.21		204
27.20	odd	18		108.3.j.a.7.14	✓	204
108.7	odd	18	inner	324.3.j.a.19.14		204
108.47	even	18		108.3.j.a.7.21	yes	204

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.3.j.a.7.14	✓	204	27.20	odd	18
108.3.j.a.7.21	yes	204	108.47	even	18
108.3.j.a.31.14	yes	204	12.11	even	2
108.3.j.a.31.21	yes	204	3.2	odd	2
324.3.j.a.19.14		204	108.7	odd	18	inner
324.3.j.a.19.21		204	27.7	even	9	inner
324.3.j.a.307.14		204	1.1	even	1	trivial
324.3.j.a.307.21		204	4.3	odd	2	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 324 = 2^{2} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	324.j (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.376263 + 1.96429i) q^{2} +(-3.71685 - 1.47818i) q^{4} +(1.26933 - 7.19876i) q^{5} +(2.67622 + 3.18940i) q^{7} +(4.30208 - 6.74478i) q^{8} +(13.6628 + 5.20197i) q^{10} +(-18.4141 + 3.24691i) q^{11} +(-15.1228 + 5.50426i) q^{13} +(-7.27185 + 4.05681i) q^{14} +(11.6300 + 10.9883i) q^{16} +(-7.49839 + 12.9876i) q^{17} +(-0.338254 + 0.195291i) q^{19} +(-15.3590 + 24.8804i) q^{20} +(0.550703 - 37.3923i) q^{22} +(-10.6620 + 12.7065i) q^{23} +(-26.7186 - 9.72476i) q^{25} +(-5.12179 - 31.7767i) q^{26} +(-5.23262 - 15.8104i) q^{28} +(-36.9589 - 13.4520i) q^{29} +(-14.0094 + 16.6957i) q^{31} +(-25.9602 + 18.7101i) q^{32} +(-22.6900 - 19.6158i) q^{34} +(26.3567 - 15.2170i) q^{35} +(5.57476 - 9.65577i) q^{37} +(-0.256335 - 0.737910i) q^{38} +(-43.0932 - 39.5310i) q^{40} +(56.8435 - 20.6894i) q^{41} +(24.4766 - 4.31589i) q^{43} +(73.2421 + 15.1511i) q^{44} +(-20.9475 - 25.7242i) q^{46} +(14.6599 + 17.4709i) q^{47} +(5.49867 - 31.1845i) q^{49} +(29.1554 - 48.8239i) q^{50} +(64.3456 + 1.89574i) q^{52} -51.2309 q^{53} +136.680i q^{55} +(33.0251 - 4.32947i) q^{56} +(40.3298 - 67.5365i) q^{58} +(-82.3895 - 14.5275i) q^{59} +(19.0252 - 15.9640i) q^{61} +(-27.5240 - 33.8005i) q^{62} +(-26.9841 - 58.0332i) q^{64} +(20.4279 + 115.852i) q^{65} +(-17.9869 - 49.4186i) q^{67} +(47.0684 - 37.1890i) q^{68} +(19.9736 + 57.4978i) q^{70} +(-75.5843 - 43.6386i) q^{71} +(17.8942 + 30.9937i) q^{73} +(16.8691 + 14.5835i) q^{74} +(1.54592 - 0.225868i) q^{76} +(-59.6359 - 50.0405i) q^{77} +(-3.59582 + 9.87943i) q^{79} +(93.8648 - 69.7734i) q^{80} +(19.2517 + 119.442i) q^{82} +(-34.4827 + 94.7405i) q^{83} +(83.9766 + 70.4647i) q^{85} +(-0.732011 + 49.7030i) q^{86} +(-57.3195 + 138.168i) q^{88} +(7.29925 + 12.6427i) q^{89} +(-58.0273 - 33.5021i) q^{91} +(58.4116 - 31.4678i) q^{92} +(-39.8339 + 22.2225i) q^{94} +(0.976496 + 2.68290i) q^{95} +(-1.45511 - 8.25233i) q^{97} +(59.1864 + 22.5346i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 204 q + 6 q^{2} - 6 q^{4} + 12 q^{5} + 3 q^{8} - 3 q^{10} - 12 q^{13} - 39 q^{14} - 6 q^{16} + 6 q^{17} + 69 q^{20} - 6 q^{22} - 12 q^{25} + 174 q^{26} - 12 q^{28} - 60 q^{29} + 96 q^{32} + 6 q^{34} - 6 q^{37}+ \cdots - 510 q^{98}+O(q^{100}) \) 204 * q + 6 * q^2 - 6 * q^4 + 12 * q^5 + 3 * q^8 - 3 * q^10 - 12 * q^13 - 39 * q^14 - 6 * q^16 + 6 * q^17 + 69 * q^20 - 6 * q^22 - 12 * q^25 + 174 * q^26 - 12 * q^28 - 60 * q^29 + 96 * q^32 + 6 * q^34 - 6 * q^37 - 72 * q^38 + 69 * q^40 + 192 * q^41 + 219 * q^44 - 3 * q^46 - 12 * q^49 + 165 * q^50 + 21 * q^52 + 24 * q^53 - 99 * q^56 - 141 * q^58 - 12 * q^61 - 294 * q^62 - 3 * q^64 + 156 * q^65 - 375 * q^68 - 165 * q^70 - 6 * q^73 - 447 * q^74 - 54 * q^76 - 132 * q^77 - 798 * q^80 - 12 * q^82 + 138 * q^85 - 606 * q^86 - 198 * q^88 + 114 * q^89 - 723 * q^92 - 357 * q^94 + 168 * q^97 - 510 * q^98

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