LMFDB - Embedded newform 378.3.o.a.307.16

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [378,3,Mod(181,378)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(378, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([4, 3])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("378.181"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 378 = 2 \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	378.o (of order $6$, degree $2$, 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:	$10.2997539928$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			307.16
Character	$\chi$	$=$	378.307
Dual form			378.3.o.a.181.16

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.707107 + 1.22474i) q^{2} +(-1.00000 + 1.73205i) q^{4} +(8.58770 + 4.95811i) q^{5} +(-4.53080 + 5.33591i) q^{7} -2.82843 q^{8} +14.0237i q^{10} +(6.74260 + 11.6785i) q^{11} +(-10.5236 - 6.07580i) q^{13} +(-9.73888 - 1.77601i) q^{14} +(-2.00000 - 3.46410i) q^{16} -20.1850i q^{17} -4.66654i q^{19} +(-17.1754 + 9.91622i) q^{20} +(-9.53548 + 16.5159i) q^{22} +(0.0880089 - 0.152436i) q^{23} +(36.6657 + 63.5069i) q^{25} -17.1849i q^{26} +(-4.71127 - 13.1835i) q^{28} +(7.01783 + 12.1552i) q^{29} +(-0.0205898 - 0.0118875i) q^{31} +(2.82843 - 4.89898i) q^{32} +(24.7214 - 14.2729i) q^{34} +(-65.3651 + 23.3590i) q^{35} -2.42366 q^{37} +(5.71533 - 3.29975i) q^{38} +(-24.2897 - 14.0237i) q^{40} +(-9.48159 - 5.47420i) q^{41} +(-3.53303 - 6.11939i) q^{43} -26.9704 q^{44} +0.248927 q^{46} +(-39.7838 + 22.9692i) q^{47} +(-7.94379 - 48.3518i) q^{49} +(-51.8532 + 89.8124i) q^{50} +(21.0472 - 12.1516i) q^{52} +57.1896 q^{53} +133.722i q^{55} +(12.8150 - 15.0922i) q^{56} +(-9.92471 + 17.1901i) q^{58} +(41.9730 + 24.2331i) q^{59} +(34.2752 - 19.7888i) q^{61} -0.0336230i q^{62} +8.00000 q^{64} +(-60.2489 - 104.354i) q^{65} +(-45.1674 + 78.2322i) q^{67} +(34.9614 + 20.1850i) q^{68} +(-74.8289 - 63.5383i) q^{70} +80.6841 q^{71} -17.8424i q^{73} +(-1.71379 - 2.96837i) q^{74} +(8.08269 + 4.66654i) q^{76} +(-92.8649 - 16.9351i) q^{77} +(10.1791 + 17.6308i) q^{79} -39.6649i q^{80} -15.4834i q^{82} +(25.2325 - 14.5680i) q^{83} +(100.079 - 173.342i) q^{85} +(4.99646 - 8.65413i) q^{86} +(-19.0710 - 33.0319i) q^{88} -81.5430i q^{89} +(80.1001 - 28.6247i) q^{91} +(0.176018 + 0.304872i) q^{92} +(-56.2627 - 32.4833i) q^{94} +(23.1372 - 40.0749i) q^{95} +(94.2248 - 54.4007i) q^{97} +(53.6015 - 43.9190i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 32 q^{4} - 2 q^{7} + 12 q^{11} + 12 q^{14} - 64 q^{16} - 12 q^{23} + 80 q^{25} + 8 q^{28} + 48 q^{29} - 348 q^{35} - 88 q^{37} + 32 q^{43} - 48 q^{44} + 48 q^{46} + 50 q^{49} - 48 q^{50} + 864 q^{53}+ \cdots - 624 q^{98}+O(q^{100}) $ 32 * q - 32 * q^4 - 2 * q^7 + 12 * q^11 + 12 * q^14 - 64 * q^16 - 12 * q^23 + 80 * q^25 + 8 * q^28 + 48 * q^29 - 348 * q^35 - 88 * q^37 + 32 * q^43 - 48 * q^44 + 48 * q^46 + 50 * q^49 - 48 * q^50 + 864 * q^53 + 24 * q^56 + 48 * q^58 + 256 * q^64 - 120 * q^65 - 140 * q^67 - 108 * q^70 - 552 * q^71 - 144 * q^74 + 258 * q^77 - 176 * q^79 - 60 * q^85 - 96 * q^86 + 372 * q^91 - 24 * q^92 - 528 * q^95 - 624 * q^98

Character values

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

$n$	$29$	$325$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$

Coefficient data

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

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

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

$2$	0.707107	+	1.22474i	0.353553	+	0.612372i
$2$	0.707107	+	1.22474i	0.353553	+	0.612372i
$3$		0			0
$3$		0			0
$4$	−1.00000	+	1.73205i	−0.250000	+	0.433013i
$5$	8.58770	+	4.95811i	1.71754	+	0.991622i	0.923356	+	0.383946i	$0.125435\pi$
$5$	8.58770	+	4.95811i	1.71754	+	0.991622i	0.794185	+	0.607677i	$0.207898\pi$
$6$		0			0
$7$	−4.53080	+	5.33591i	−0.647256	+	0.762272i
$7$	−4.53080	+	5.33591i	−0.647256	+	0.762272i
$8$	−2.82843			−0.353553
$9$		0			0
$10$			14.0237i			1.40237i
$11$	6.74260	+	11.6785i	0.612964	+	1.06168i	0.990738	+	0.135787i	$0.0433562\pi$
$11$	6.74260	+	11.6785i	0.612964	+	1.06168i	−0.377774	+	0.925898i	$0.623310\pi$
$12$		0			0
$13$	−10.5236	−	6.07580i	−0.809507	−	0.467369i	0.0372779	−	0.999305i	$-0.488131\pi$
$13$	−10.5236	−	6.07580i	−0.809507	−	0.467369i	−0.846785	+	0.531936i	$0.821465\pi$
$14$	−9.73888	−	1.77601i	−0.695634	−	0.126858i
$15$		0			0
$16$	−2.00000	−	3.46410i	−0.125000	−	0.216506i
$17$		−	20.1850i		−	1.18735i	−0.804705	−	0.593675i	$-0.797676\pi$
$17$		−	20.1850i		−	1.18735i	0.804705	−	0.593675i	$-0.202324\pi$
$18$		0			0
$19$		−	4.66654i		−	0.245608i	−0.992431	−	0.122804i	$-0.960811\pi$
$19$		−	4.66654i		−	0.245608i	0.992431	−	0.122804i	$-0.0391886\pi$
$20$	−17.1754	+	9.91622i	−0.858770	+	0.495811i
$21$		0			0
$22$	−9.53548	+	16.5159i	−0.433431	+	0.750724i
$23$	0.0880089	−	0.152436i	0.00382647	−	0.00662765i	−0.864106	−	0.503310i	$-0.832115\pi$
$23$	0.0880089	−	0.152436i	0.00382647	−	0.00662765i	0.867932	+	0.496683i	$0.165449\pi$
$24$		0			0
$25$	36.6657	+	63.5069i	1.46663	+	2.54028i
$26$		−	17.1849i		−	0.660959i
$27$		0			0
$28$	−4.71127	−	13.1835i	−0.168259	−	0.470838i
$29$	7.01783	+	12.1552i	0.241994	+	0.419146i	0.961282	−	0.275566i	$-0.0888652\pi$
$29$	7.01783	+	12.1552i	0.241994	+	0.419146i	−0.719288	+	0.694712i	$0.755532\pi$
$30$		0			0
$31$	−0.0205898	−	0.0118875i	−0.000664188	−	0.000383469i	0.499668	−	0.866217i	$-0.333455\pi$
$31$	−0.0205898	−	0.0118875i	−0.000664188	−	0.000383469i	−0.500332	+	0.865834i	$0.666789\pi$
$32$	2.82843	−	4.89898i	0.0883883	−	0.153093i
$33$		0			0
$34$	24.7214	−	14.2729i	0.727100	−	0.419792i
$35$	−65.3651	+	23.3590i	−1.86758	+	0.667399i
$36$		0			0
$37$	−2.42366			−0.0655043			−0.0327522	−	0.999464i	$-0.510427\pi$
$37$	−2.42366			−0.0655043			−0.0327522	+	0.999464i	$0.510427\pi$
$38$	5.71533	−	3.29975i	0.150403	−	0.0868354i
$39$		0			0
$40$	−24.2897	−	14.0237i	−0.607242	−	0.350591i
$41$	−9.48159	−	5.47420i	−0.231258	−	0.133517i	0.379894	−	0.925030i	$-0.375960\pi$
$41$	−9.48159	−	5.47420i	−0.231258	−	0.133517i	−0.611152	+	0.791513i	$0.709294\pi$
$42$		0			0
$43$	−3.53303	−	6.11939i	−0.0821636	−	0.142311i	0.822015	−	0.569465i	$-0.192850\pi$
$43$	−3.53303	−	6.11939i	−0.0821636	−	0.142311i	−0.904179	+	0.427154i	$0.859516\pi$
$44$	−26.9704			−0.612964
$45$		0			0
$46$	0.248927			0.00541145
$47$	−39.7838	+	22.9692i	−0.846463	+	0.488706i	−0.859456	−	0.511210i	$-0.829197\pi$
$47$	−39.7838	+	22.9692i	−0.846463	+	0.488706i	0.0129929	+	0.999916i	$0.495864\pi$
$48$		0			0
$49$	−7.94379	−	48.3518i	−0.162118	−	0.986771i
$50$	−51.8532	+	89.8124i	−1.03706	+	1.79625i
$51$		0			0
$52$	21.0472	−	12.1516i	0.404753	−	0.233684i
$53$	57.1896			1.07905			0.539524	−	0.841970i	$-0.318604\pi$
$53$	57.1896			1.07905			0.539524	+	0.841970i	$0.318604\pi$
$54$		0			0
$55$			133.722i			2.43131i
$56$	12.8150	−	15.0922i	0.228840	−	0.269504i
$57$		0			0
$58$	−9.92471	+	17.1901i	−0.171116	+	0.296381i
$59$	41.9730	+	24.2331i	0.711406	+	0.410730i	0.811581	−	0.584239i	$-0.198607\pi$
$59$	41.9730	+	24.2331i	0.711406	+	0.410730i	−0.100175	+	0.994970i	$0.531940\pi$
$60$		0			0
$61$	34.2752	−	19.7888i	0.561888	−	0.324406i	−0.192015	−	0.981392i	$-0.561502\pi$
$61$	34.2752	−	19.7888i	0.561888	−	0.324406i	0.753903	+	0.656986i	$0.228169\pi$
$62$		−	0.0336230i		−	0.000542307i
$63$		0			0
$64$	8.00000			0.125000
$65$	−60.2489	−	104.354i	−0.926907	−	1.60545i
$66$		0			0
$67$	−45.1674	+	78.2322i	−0.674140	+	1.16764i	0.302580	+	0.953124i	$0.402152\pi$
$67$	−45.1674	+	78.2322i	−0.674140	+	1.16764i	−0.976720	+	0.214520i	$0.931181\pi$
$68$	34.9614	+	20.1850i	0.514138	+	0.296838i
$69$		0			0
$70$	−74.8289	−	63.5383i	−1.06898	−	0.907690i
$71$	80.6841			1.13640			0.568198	−	0.822892i	$-0.307641\pi$
$71$	80.6841			1.13640			0.568198	+	0.822892i	$0.307641\pi$
$72$		0			0
$73$		−	17.8424i		−	0.244417i	−0.992504	−	0.122208i	$-0.961002\pi$
$73$		−	17.8424i		−	0.244417i	0.992504	−	0.122208i	$-0.0389976\pi$
$74$	−1.71379	−	2.96837i	−0.0231593	−	0.0401130i
$75$		0			0
$76$	8.08269	+	4.66654i	0.106351	+	0.0614019i
$77$	−92.8649	−	16.9351i	−1.20604	−	0.219937i
$78$		0			0
$79$	10.1791	+	17.6308i	0.128850	+	0.223174i	0.923231	−	0.384245i	$-0.125538\pi$
$79$	10.1791	+	17.6308i	0.128850	+	0.223174i	−0.794381	+	0.607419i	$0.792205\pi$
$80$		−	39.6649i		−	0.495811i
$81$		0			0
$82$		−	15.4834i		−	0.188822i
$83$	25.2325	−	14.5680i	0.304006	−	0.175518i	−0.340235	−	0.940340i	$-0.610507\pi$
$83$	25.2325	−	14.5680i	0.304006	−	0.175518i	0.644241	+	0.764822i	$0.277173\pi$
$84$		0			0
$85$	100.079	−	173.342i	1.17740	−	2.03932i
$86$	4.99646	−	8.65413i	0.0580984	−	0.100629i
$87$		0			0
$88$	−19.0710	−	33.0319i	−0.216715	−	0.375362i
$89$		−	81.5430i		−	0.916213i	−0.888897	−	0.458107i	$-0.848528\pi$
$89$		−	81.5430i		−	0.916213i	0.888897	−	0.458107i	$-0.151472\pi$
$90$		0			0
$91$	80.1001	−	28.6247i	0.880221	−	0.314557i
$92$	0.176018	+	0.304872i	0.00191324	+	0.00331382i
$93$		0			0
$94$	−56.2627	−	32.4833i	−0.598540	−	0.345567i
$95$	23.1372	−	40.0749i	0.243550	−	0.421841i
$96$		0			0
$97$	94.2248	−	54.4007i	0.971390	−	0.560832i	0.0717301	−	0.997424i	$-0.477148\pi$
$97$	94.2248	−	54.4007i	0.971390	−	0.560832i	0.899660	+	0.436592i	$0.143815\pi$
$98$	53.6015	−	43.9190i	0.546954	−	0.448153i
$99$		0			0
$100$	−146.663			−1.46663
$101$	120.353	−	69.4857i	1.19161	−	0.687977i	0.232939	−	0.972491i	$-0.425166\pi$
$101$	120.353	−	69.4857i	1.19161	−	0.687977i	0.958672	+	0.284514i	$0.0918323\pi$
$102$		0			0
$103$	−66.0960	−	38.1606i	−0.641709	−	0.370491i	0.143563	−	0.989641i	$-0.454144\pi$
$103$	−66.0960	−	38.1606i	−0.641709	−	0.370491i	−0.785273	+	0.619150i	$0.787477\pi$
$104$	29.7652	+	17.1849i	0.286204	+	0.165240i
$105$		0			0
$106$	40.4391	+	70.0426i	0.381501	+	0.660779i
$107$	84.5769			0.790439			0.395219	−	0.918587i	$-0.370669\pi$
$107$	84.5769			0.790439			0.395219	+	0.918587i	$0.370669\pi$
$108$		0			0
$109$	−24.1111			−0.221203			−0.110601	−	0.993865i	$-0.535278\pi$
$109$	−24.1111			−0.221203			−0.110601	+	0.993865i	$0.535278\pi$
$110$	−163.776	+	94.5560i	−1.48887	+	0.859600i
$111$		0			0
$112$	27.5457	+	5.02332i	0.245944	+	0.0448511i
$113$	72.7392	−	125.988i	0.643710	−	1.11494i	−0.340888	−	0.940104i	$-0.610728\pi$
$113$	72.7392	−	125.988i	0.643710	−	1.11494i	0.984598	−	0.174835i	$-0.0559390\pi$
$114$		0			0
$115$	1.51159	−	0.872716i	0.0131442	−	0.00758883i
$116$	−28.0713			−0.241994
$117$		0			0
$118$			68.5415i			0.580861i
$119$	107.705	+	91.4539i	0.905084	+	0.768520i
$120$		0			0
$121$	−30.4254	+	52.6983i	−0.251450	+	0.435523i
$122$	48.4724	+	27.9856i	0.397315	+	0.229390i
$123$		0			0
$124$	0.0411797	−	0.0237751i	0.000332094	−	0.000191735i
$125$			479.266i			3.83413i
$126$		0			0
$127$	−155.852			−1.22718			−0.613590	−	0.789625i	$-0.710275\pi$
$127$	−155.852			−1.22718			−0.613590	+	0.789625i	$0.710275\pi$
$128$	5.65685	+	9.79796i	0.0441942	+	0.0765466i
$129$		0			0
$130$	85.2049	−	147.579i	0.655422	−	1.13522i
$131$	86.1056	+	49.7131i	0.657295	+	0.379489i	0.791245	−	0.611499i	$-0.209433\pi$
$131$	86.1056	+	49.7131i	0.657295	+	0.379489i	−0.133951	+	0.990988i	$0.542766\pi$
$132$		0			0
$133$	24.9002	+	21.1432i	0.187220	+	0.158971i
$134$	−127.753			−0.953377
$135$		0			0
$136$			57.0917i			0.419792i
$137$	−12.3339	−	21.3630i	−0.0900287	−	0.155934i	0.817494	−	0.575937i	$-0.195363\pi$
$137$	−12.3339	−	21.3630i	−0.0900287	−	0.155934i	−0.907523	+	0.420002i	$0.862029\pi$
$138$		0			0
$139$	98.5930	+	56.9227i	0.709302	+	0.409516i	0.810803	−	0.585320i	$-0.199031\pi$
$139$	98.5930	+	56.9227i	0.709302	+	0.409516i	−0.101500	+	0.994835i	$0.532364\pi$
$140$	24.9062	−	136.575i	0.177901	−	0.975534i
$141$		0			0
$142$	57.0523	+	98.8175i	0.401777	+	0.695898i
$143$		−	163.867i		−	1.14592i
$144$		0			0
$145$			139.181i			0.959867i
$146$	21.8524	−	12.6165i	0.149674	−	0.0864144i
$147$		0			0
$148$	2.42366	−	4.19790i	0.0163761	−	0.0283642i
$149$	85.7383	−	148.503i	0.575425	−	0.996665i	−0.420571	−	0.907260i	$-0.638170\pi$
$149$	85.7383	−	148.503i	0.575425	−	0.996665i	0.995995	−	0.0894051i	$-0.0284966\pi$
$150$		0			0
$151$	−118.787	−	205.745i	−0.786669	−	1.36255i	−0.927997	−	0.372588i	$-0.878471\pi$
$151$	−118.787	−	205.745i	−0.786669	−	1.36255i	0.141328	−	0.989963i	$-0.454863\pi$
$152$			13.1990i			0.0868354i
$153$		0			0
$154$	−44.9242	−	125.711i	−0.291715	−	0.816304i
$155$	−0.117880	−	0.204173i	−0.000760513	−	0.00131725i
$156$		0			0
$157$	67.7529	+	39.1171i	0.431547	+	0.249154i	0.700005	−	0.714137i	$-0.253181\pi$
$157$	67.7529	+	39.1171i	0.431547	+	0.249154i	−0.268458	+	0.963291i	$0.586514\pi$
$158$	−14.3955	+	24.9337i	−0.0911106	+	0.157808i
$159$		0			0
$160$	48.5794	−	28.0473i	0.303621	−	0.175296i
$161$	0.414633	+	1.16026i	0.00257536	+	0.00720660i
$162$		0			0
$163$	236.898			1.45336			0.726682	−	0.686974i	$-0.241061\pi$
$163$	236.898			1.45336			0.726682	+	0.686974i	$0.241061\pi$
$164$	18.9632	−	10.9484i	0.115629	−	0.0667585i
$165$		0			0
$166$	35.6842	+	20.6023i	0.214965	+	0.124110i
$167$	−200.478	−	115.746i	−1.20047	−	0.693089i	−0.239807	−	0.970821i	$-0.577084\pi$
$167$	−200.478	−	115.746i	−1.20047	−	0.693089i	−0.960659	+	0.277732i	$0.910417\pi$
$168$		0			0
$169$	−10.6694	−	18.4800i	−0.0631327	−	0.109349i
$170$	283.067			1.66510
$171$		0			0
$172$	14.1321			0.0821636
$173$	−110.666	+	63.8930i	−0.639688	+	0.369324i	−0.784494	−	0.620136i	$-0.787077\pi$
$173$	−110.666	+	63.8930i	−0.639688	+	0.369324i	0.144807	+	0.989460i	$0.453744\pi$
$174$		0			0
$175$	−504.992	−	92.0919i	−2.88567	−	0.526239i
$176$	26.9704	−	46.7141i	0.153241	−	0.265421i
$177$		0			0
$178$	99.8694	−	57.6596i	0.561064	−	0.323930i
$179$	−132.848			−0.742165			−0.371083	−	0.928600i	$-0.621013\pi$
$179$	−132.848			−0.742165			−0.371083	+	0.928600i	$0.621013\pi$
$180$		0			0
$181$			93.4546i			0.516323i	0.966102	+	0.258162i	$0.0831167\pi$
$181$			93.4546i			0.516323i	−0.966102	+	0.258162i	$0.916883\pi$
$182$	91.6973	+	77.8615i	0.503831	+	0.427810i
$183$		0			0
$184$	−0.248927	+	0.431154i	−0.00135286	+	0.00234323i
$185$	−20.8137	−	12.0168i	−0.112506	−	0.0649556i
$186$		0			0
$187$	235.731	−	136.099i	1.26059	−	0.727803i
$188$		−	91.8767i		−	0.488706i
$189$		0			0
$190$	65.4420			0.344432
$191$	146.456	+	253.668i	0.766783	+	1.32811i	0.939299	+	0.343100i	$0.111477\pi$
$191$	146.456	+	253.668i	0.766783	+	1.32811i	−0.172516	+	0.985007i	$0.555190\pi$
$192$		0			0
$193$	129.618	−	224.504i	0.671594	−	1.16323i	−0.305859	−	0.952077i	$-0.598943\pi$
$193$	129.618	−	224.504i	0.671594	−	1.16323i	0.977452	−	0.211157i	$-0.0677232\pi$
$194$	133.254	+	76.9342i	0.686876	+	0.396568i
$195$		0			0
$196$	91.6916	+	34.5927i	0.467814	+	0.176494i
$197$	−336.752			−1.70940			−0.854700	−	0.519123i	$-0.826259\pi$
$197$	−336.752			−1.70940			−0.854700	+	0.519123i	$0.826259\pi$
$198$		0			0
$199$		−	92.4947i		−	0.464797i	−0.972621	−	0.232399i	$-0.925343\pi$
$199$		−	92.4947i		−	0.464797i	0.972621	−	0.232399i	$-0.0746574\pi$
$200$	−103.706	−	179.625i	−0.518532	−	0.898124i
$201$		0			0
$202$	170.204	+	98.2676i	0.842596	+	0.486473i
$203$	−96.6556	−	17.6264i	−0.476136	−	0.0868296i
$204$		0			0
$205$	−54.2834	−	94.0215i	−0.264797	−	0.458642i
$206$		−	107.934i		−	0.523953i
$207$		0			0
$208$			48.6064i			0.233684i
$209$	54.4984	−	31.4647i	0.260758	−	0.150549i
$210$		0			0
$211$	−99.0672	+	171.589i	−0.469513	+	0.813220i	−0.999392	−	0.0348530i	$-0.988904\pi$
$211$	−99.0672	+	171.589i	−0.469513	+	0.813220i	0.529880	+	0.848073i	$0.322237\pi$
$212$	−57.1896	+	99.0552i	−0.269762	+	0.467242i
$213$		0			0
$214$	59.8049	+	103.585i	0.279462	+	0.484043i
$215$		−	70.0687i		−	0.325901i
$216$		0			0
$217$	0.156719	−	0.0560054i	0.000722208	−	0.000258089i
$218$	−17.0491	−	29.5299i	−0.0782069	−	0.135458i
$219$		0			0
$220$	−231.614	−	133.722i	−1.05279	−	0.607829i
$221$	−122.640	+	212.418i	−0.554930	+	0.961168i
$222$		0			0
$223$	−150.650	+	86.9779i	−0.675561	+	0.390036i	−0.798181	−	0.602418i	$-0.794204\pi$
$223$	−150.650	+	86.9779i	−0.675561	+	0.390036i	0.122619	+	0.992454i	$0.460871\pi$
$224$	13.3255	+	37.2885i	0.0594887	+	0.166466i
$225$		0			0
$226$	205.738			0.910343
$227$	178.543	−	103.082i	0.786535	−	0.454106i	−0.0522063	−	0.998636i	$-0.516625\pi$
$227$	178.543	−	103.082i	0.786535	−	0.454106i	0.838741	+	0.544530i	$0.183292\pi$
$228$		0			0
$229$	−17.2640	−	9.96735i	−0.0753884	−	0.0435255i	0.461832	−	0.886967i	$-0.347192\pi$
$229$	−17.2640	−	9.96735i	−0.0753884	−	0.0435255i	−0.537220	+	0.843442i	$0.680526\pi$
$230$	2.13771	+	1.23421i	0.00929438	+	0.00536611i
$231$		0			0
$232$	−19.8494	−	34.3802i	−0.0855579	−	0.148191i
$233$	−257.078			−1.10334			−0.551670	−	0.834062i	$-0.686009\pi$
$233$	−257.078			−1.10334			−0.551670	+	0.834062i	$0.686009\pi$
$234$		0			0
$235$	−455.535			−1.93845
$236$	−83.9459	+	48.4662i	−0.355703	+	0.205365i
$237$		0			0
$238$	−35.8487	+	196.579i	−0.150625	+	0.825961i
$239$	6.18007	−	10.7042i	0.0258580	−	0.0447874i	−0.852807	−	0.522227i	$-0.825102\pi$
$239$	6.18007	−	10.7042i	0.0258580	−	0.0447874i	0.878665	+	0.477439i	$0.158435\pi$
$240$		0			0
$241$	−257.287	+	148.544i	−1.06758	+	0.616367i	−0.927519	−	0.373776i	$-0.878063\pi$
$241$	−257.287	+	148.544i	−1.06758	+	0.616367i	−0.140060	+	0.990143i	$0.544730\pi$
$242$	−86.0560			−0.355603
$243$		0			0
$244$			79.1551i			0.324406i
$245$	171.515	−	454.617i	0.700060	−	1.85558i
$246$		0			0
$247$	−28.3530	+	49.1088i	−0.114789	+	0.198821i
$248$	0.0582368	+	0.0336230i	0.000234826	+	0.000135577i
$249$		0			0
$250$	−586.978	+	338.892i	−2.34791	+	1.35557i
$251$			349.874i			1.39392i	0.717111	+	0.696959i	$0.245464\pi$
$251$			349.874i			1.39392i	−0.717111	+	0.696959i	$0.754536\pi$
$252$		0			0
$253$	2.37364			0.00938196
$254$	−110.204	−	190.879i	−0.433874	−	0.751492i
$255$		0			0
$256$	−8.00000	+	13.8564i	−0.0312500	+	0.0541266i
$257$	−292.983	−	169.154i	−1.14001	−	0.658186i	−0.193578	−	0.981085i	$-0.562009\pi$
$257$	−292.983	−	169.154i	−1.14001	−	0.658186i	−0.946433	+	0.322899i	$0.895343\pi$
$258$		0			0
$259$	10.9811	−	12.9324i	0.0423981	−	0.0499321i
$260$	240.996			0.926907
$261$		0			0
$262$			140.610i			0.536679i
$263$	−32.7296	−	56.6894i	−0.124447	−	0.215549i	0.797069	−	0.603888i	$-0.206382\pi$
$263$	−32.7296	−	56.6894i	−0.124447	−	0.215549i	−0.921517	+	0.388339i	$0.873049\pi$
$264$		0			0
$265$	491.127	+	283.552i	1.85331	+	1.07001i
$266$	−8.28784	+	45.4469i	−0.0311573	+	0.170853i
$267$		0			0
$268$	−90.3347	−	156.464i	−0.337070	−	0.583822i
$269$		−	248.366i		−	0.923293i	−0.887064	−	0.461646i	$-0.847259\pi$
$269$		−	248.366i		−	0.923293i	0.887064	−	0.461646i	$-0.152741\pi$
$270$		0			0
$271$		−	59.5945i		−	0.219906i	−0.993937	−	0.109953i	$-0.964930\pi$
$271$		−	59.5945i		−	0.219906i	0.993937	−	0.109953i	$-0.0350700\pi$
$272$	−69.9227	+	40.3699i	−0.257069	+	0.148419i
$273$		0			0
$274$	17.4428	−	30.2118i	0.0636599	−	0.110262i
$275$	−494.445	+	856.404i	−1.79798	+	3.11420i
$276$		0			0
$277$	222.096	+	384.682i	0.801791	+	1.38874i	0.918436	+	0.395569i	$0.129453\pi$
$277$	222.096	+	384.682i	0.801791	+	1.38874i	−0.116645	+	0.993174i	$0.537214\pi$
$278$			161.002i			0.579143i
$279$		0			0
$280$	184.881	−	66.0692i	0.660288	−	0.235961i
$281$	231.769	+	401.435i	0.824799	+	1.42859i	0.902073	+	0.431584i	$0.142045\pi$
$281$	231.769	+	401.435i	0.824799	+	1.42859i	−0.0772735	+	0.997010i	$0.524621\pi$
$282$		0			0
$283$	−88.7084	−	51.2158i	−0.313457	−	0.180975i	0.335015	−	0.942213i	$-0.391259\pi$
$283$	−88.7084	−	51.2158i	−0.313457	−	0.180975i	−0.648472	+	0.761238i	$0.724592\pi$
$284$	−80.6841	+	139.749i	−0.284099	+	0.492074i
$285$		0			0
$286$	200.695	−	115.871i	0.701730	−	0.405144i
$287$	72.1689	−	25.7904i	0.251460	−	0.0898620i
$288$		0			0
$289$	−118.432			−0.409800
$290$	−170.461	+	98.4157i	−0.587796	+	0.339364i
$291$		0			0
$292$	30.9040	+	17.8424i	0.105836	+	0.0611042i
$293$	288.554	+	166.597i	0.984825	+	0.568589i	0.903723	−	0.428117i	$-0.140823\pi$
$293$	288.554	+	166.597i	0.984825	+	0.568589i	0.0811016	+	0.996706i	$0.474156\pi$
$294$		0			0
$295$	240.301	+	416.213i	0.814579	+	1.41089i
$296$	6.85515			0.0231593
$297$		0			0
$298$	242.504			0.813773
$299$	−1.85234	+	1.06945i	−0.00619511	+	0.00357675i
$300$		0			0
$301$	48.6600	+	8.87378i	0.161661	+	0.0294810i
$302$	167.990	−	290.968i	0.556259	−	0.963469i
$303$		0			0
$304$	−16.1654	+	9.33309i	−0.0531756	+	0.0307010i
$305$	392.460			1.28675
$306$		0			0
$307$		−	323.443i		−	1.05356i	−0.850002	−	0.526780i	$-0.823399\pi$
$307$		−	323.443i		−	1.05356i	0.850002	−	0.526780i	$-0.176601\pi$
$308$	122.197	−	143.912i	0.396745	−	0.467245i
$309$		0			0
$310$	0.166707	−	0.288745i	0.000537764	−	0.000931434i
$311$	−399.241	−	230.502i	−1.28373	−	0.741164i	−0.306205	−	0.951965i	$-0.599059\pi$
$311$	−399.241	−	230.502i	−1.28373	−	0.741164i	−0.977529	+	0.210801i	$0.932393\pi$
$312$		0			0
$313$	237.475	−	137.106i	0.758705	−	0.438039i	−0.0701256	−	0.997538i	$-0.522340\pi$
$313$	237.475	−	137.106i	0.758705	−	0.438039i	0.828831	+	0.559500i	$0.189007\pi$
$314$			110.640i			0.352357i
$315$		0			0
$316$	−40.7165			−0.128850
$317$	−212.280	−	367.679i	−0.669652	−	1.15987i	−0.978001	−	0.208598i	$-0.933110\pi$
$317$	−212.280	−	367.679i	−0.669652	−	1.15987i	0.308349	−	0.951273i	$-0.400223\pi$
$318$		0			0
$319$	−94.6369	+	163.916i	−0.296667	+	0.513843i
$320$	68.7016	+	39.6649i	0.214693	+	0.123953i
$321$		0			0
$322$	−1.12784	+	1.32825i	−0.00350260	+	0.00412500i
$323$	−94.1940			−0.291622
$324$		0			0
$325$		−	891.094i		−	2.74183i
$326$	167.512	+	290.140i	0.513842	+	0.890000i
$327$		0			0
$328$	26.8180	+	15.4834i	0.0817621	+	0.0472054i
$329$	57.6907	−	316.351i	0.175352	−	0.961553i
$330$		0			0
$331$	−123.513	−	213.931i	−0.373152	−	0.646318i	0.616897	−	0.787044i	$-0.288390\pi$
$331$	−123.513	−	213.931i	−0.373152	−	0.646318i	−0.990049	+	0.140726i	$0.955056\pi$
$332$			58.2720i			0.175518i
$333$		0			0
$334$		−	327.379i		−	0.980176i
$335$	−775.768	+	447.890i	−2.31572	+	1.33698i
$336$		0			0
$337$	−57.2883	+	99.2262i	−0.169995	+	0.294440i	−0.938418	−	0.345503i	$-0.887708\pi$
$337$	−57.2883	+	99.2262i	−0.169995	+	0.294440i	0.768423	+	0.639942i	$0.221042\pi$
$338$	15.0888	−	26.1346i	0.0446415	−	0.0773214i
$339$		0			0
$340$	200.158	+	346.685i	0.588701	+	1.01966i
$341$		−	0.320612i		−	0.000940211i
$342$		0			0
$343$	293.992	+	176.685i	0.857121	+	0.515116i
$344$	9.99293	+	17.3083i	0.0290492	+	0.0503147i
$345$		0			0
$346$	−156.505	−	90.3584i	−0.452327	−	0.261151i
$347$	172.728	−	299.174i	0.497776	−	0.862173i	−0.502221	−	0.864739i	$-0.667484\pi$
$347$	172.728	−	299.174i	0.497776	−	0.862173i	0.999997	+	0.00256650i	$0.000816944\pi$
$348$		0			0
$349$	−584.225	+	337.302i	−1.67400	+	0.966483i	−0.708632	+	0.705578i	$0.750687\pi$
$349$	−584.225	+	337.302i	−1.67400	+	0.966483i	−0.965365	+	0.260905i	$0.915979\pi$
$350$	−244.294	−	683.605i	−0.697983	−	1.95316i
$351$		0			0
$352$	76.2838			0.216715
$353$	82.7699	−	47.7872i	0.234476	−	0.135375i	−0.378159	−	0.925740i	$-0.623443\pi$
$353$	82.7699	−	47.7872i	0.234476	−	0.135375i	0.612635	+	0.790366i	$0.290110\pi$
$354$		0			0
$355$	692.891	+	400.041i	1.95181	+	1.12688i
$356$	141.237	+	81.5430i	0.396732	+	0.229053i
$357$		0			0
$358$	−93.9374	−	162.704i	−0.262395	−	0.454482i
$359$	27.2256			0.0758374			0.0379187	−	0.999281i	$-0.487927\pi$
$359$	27.2256			0.0758374			0.0379187	+	0.999281i	$0.487927\pi$
$360$		0			0
$361$	339.223			0.939677
$362$	−114.458	+	66.0823i	−0.316182	+	0.182548i
$363$		0			0
$364$	−30.5207	+	167.362i	−0.0838480	+	0.459786i
$365$	88.4647	−	153.225i	0.242369	−	0.419796i
$366$		0			0
$367$	−130.761	+	75.4949i	−0.356297	+	0.205708i	−0.667455	−	0.744650i	$-0.732616\pi$
$367$	−130.761	+	75.4949i	−0.356297	+	0.205708i	0.311158	+	0.950358i	$0.399283\pi$
$368$	−0.704071			−0.00191324
$369$		0			0
$370$		−	33.9886i		−	0.0918610i
$371$	−259.114	+	305.158i	−0.698421	+	0.822529i
$372$		0			0
$373$	81.4304	−	141.042i	0.218312	−	0.378128i	−0.735980	−	0.677003i	$-0.763278\pi$
$373$	81.4304	−	141.042i	0.218312	−	0.378128i	0.954292	+	0.298876i	$0.0966116\pi$
$374$	333.373	+	192.473i	0.891373	+	0.514634i
$375$		0			0
$376$	112.525	−	64.9666i	0.299270	−	0.172784i
$377$		−	170.556i		−	0.452402i
$378$		0			0
$379$	−391.275			−1.03239			−0.516194	−	0.856472i	$-0.672651\pi$
$379$	−391.275			−1.03239			−0.516194	+	0.856472i	$0.672651\pi$
$380$	46.2745	+	80.1498i	0.121775	+	0.210920i
$381$		0			0
$382$	−207.119	+	358.741i	−0.542197	+	0.939113i
$383$	263.816	+	152.314i	0.688815	+	0.397687i	0.803168	−	0.595753i	$-0.203146\pi$
$383$	263.816	+	152.314i	0.688815	+	0.397687i	−0.114353	+	0.993440i	$0.536479\pi$
$384$		0			0
$385$	−713.530	−	605.868i	−1.85332	−	1.57368i
$386$	366.614			0.949777
$387$		0			0
$388$			217.603i			0.560832i
$389$	135.460	+	234.623i	0.348225	+	0.603144i	0.985934	−	0.167134i	$-0.0534511\pi$
$389$	135.460	+	234.623i	0.348225	+	0.603144i	−0.637709	+	0.770277i	$0.720118\pi$
$390$		0			0
$391$	−3.07691	−	1.77645i	−0.00786934	−	0.00454336i
$392$	22.4684	+	136.760i	0.0573174	+	0.348876i
$393$		0			0
$394$	−238.119	−	412.435i	−0.604364	−	1.04679i
$395$			201.877i			0.511081i
$396$		0			0
$397$			455.963i			1.14852i	0.818672	+	0.574261i	$0.194710\pi$
$397$			455.963i			1.14852i	−0.818672	+	0.574261i	$0.805290\pi$
$398$	113.282	−	65.4036i	0.284629	−	0.164331i
$399$		0			0
$400$	146.663	−	254.028i	0.366657	−	0.635069i
$401$	214.070	−	370.780i	0.533841	−	0.924640i	−0.465378	−	0.885112i	$-0.654081\pi$
$401$	214.070	−	370.780i	0.533841	−	0.924640i	0.999218	−	0.0395273i	$-0.0125852\pi$
$402$		0			0
$403$	0.144453	+	0.250199i	0.000358443	+	0.000620842i
$404$			277.943i			0.687977i
$405$		0			0
$406$	−46.7580	−	130.842i	−0.115167	−	0.322271i
$407$	−16.3418	−	28.3048i	−0.0401518	−	0.0695449i
$408$		0			0
$409$	−310.087	−	179.029i	−0.758159	−	0.437723i	0.0704753	−	0.997514i	$-0.477548\pi$
$409$	−310.087	−	179.029i	−0.758159	−	0.437723i	−0.828634	+	0.559790i	$0.810882\pi$
$410$	76.7683	−	132.967i	0.187240	−	0.324309i
$411$		0			0
$412$	132.192	−	76.3211i	0.320855	−	0.185245i
$413$	−319.476	+	114.169i	−0.773551	+	0.276437i
$414$		0			0
$415$	288.919			0.696191
$416$	−59.5304	+	34.3699i	−0.143102	+	0.0826199i
$417$		0			0
$418$	77.0724	+	44.4977i	0.184384	+	0.106454i
$419$	396.340	+	228.827i	0.945919	+	0.546127i	0.891811	−	0.452409i	$-0.149435\pi$
$419$	396.340	+	228.827i	0.945919	+	0.546127i	0.0541082	+	0.998535i	$0.482768\pi$
$420$		0			0
$421$	3.35845	+	5.81701i	0.00797732	+	0.0138171i	0.869987	−	0.493076i	$-0.164127\pi$
$421$	3.35845	+	5.81701i	0.00797732	+	0.0138171i	−0.862009	+	0.506893i	$0.830794\pi$
$422$	−280.204			−0.663991
$423$		0			0
$424$	−161.757			−0.381501
$425$	1281.88	−	740.096i	3.01620	−	1.74140i
$426$		0			0
$427$	−49.7027	+	272.548i	−0.116400	+	0.638286i
$428$	−84.5769	+	146.492i	−0.197610	+	0.342270i
$429$		0			0
$430$	85.8163	−	49.5460i	0.199573	−	0.115223i
$431$	399.366			0.926602			0.463301	−	0.886201i	$-0.346665\pi$
$431$	399.366			0.926602			0.463301	+	0.886201i	$0.346665\pi$
$432$		0			0
$433$			566.950i			1.30935i	0.755909	+	0.654677i	$0.227195\pi$
$433$			566.950i			1.30935i	−0.755909	+	0.654677i	$0.772805\pi$
$434$	0.179409	+	0.152339i	0.000413386	+	0.000351012i
$435$		0			0
$436$	24.1111	−	41.7616i	0.0553006	−	0.0957835i
$437$	−0.711349	−	0.410697i	−0.00162780	−	0.000939811i
$438$		0			0
$439$	−170.327	+	98.3382i	−0.387988	+	0.224005i	−0.681288	−	0.732015i	$-0.738580\pi$
$439$	−170.327	+	98.3382i	−0.387988	+	0.224005i	0.293300	+	0.956020i	$0.405247\pi$
$440$		−	378.224i		−	0.859600i
$441$		0			0
$442$	−346.877			−0.784790
$443$	−89.4345	−	154.905i	−0.201884	−	0.349673i	0.747252	−	0.664541i	$-0.231373\pi$
$443$	−89.4345	−	154.905i	−0.201884	−	0.349673i	−0.949135	+	0.314868i	$0.898040\pi$
$444$		0			0
$445$	404.299	−	700.267i	0.908538	−	1.57363i
$446$	−213.052	−	123.005i	−0.477694	−	0.275797i
$447$		0			0
$448$	−36.2464	+	42.6873i	−0.0809071	+	0.0952840i
$449$	−381.811			−0.850358			−0.425179	−	0.905109i	$-0.639789\pi$
$449$	−381.811			−0.850358			−0.425179	+	0.905109i	$0.639789\pi$
$450$		0			0
$451$		−	147.641i		−	0.327364i
$452$	145.478	+	251.976i	0.321855	+	0.557469i
$453$		0			0
$454$	252.499	+	145.780i	0.556164	+	0.321102i
$455$	829.800	+	151.325i	1.82374	+	0.332582i
$456$		0			0
$457$	−284.366	−	492.537i	−0.622245	−	1.07776i	−0.989067	−	0.147469i	$-0.952887\pi$
$457$	−284.366	−	492.537i	−0.622245	−	1.07776i	0.366821	−	0.930291i	$-0.380446\pi$
$458$		−	28.1919i		−	0.0615544i
$459$		0			0
$460$			3.49086i			0.00758883i
$461$	−315.707	+	182.273i	−0.684830	+	0.395387i	−0.801672	−	0.597764i	$-0.796056\pi$
$461$	−315.707	+	182.273i	−0.684830	+	0.395387i	0.116842	+	0.993150i	$0.462723\pi$
$462$		0			0
$463$	−59.3958	+	102.877i	−0.128285	+	0.222196i	−0.923012	−	0.384771i	$-0.874280\pi$
$463$	−59.3958	+	102.877i	−0.128285	+	0.222196i	0.794727	+	0.606967i	$0.207614\pi$
$464$	28.0713	−	48.6210i	0.0604985	−	0.104787i
$465$		0			0
$466$	−181.782	−	314.855i	−0.390090	−	0.675655i
$467$		−	401.009i		−	0.858692i	−0.903140	−	0.429346i	$-0.858744\pi$
$467$		−	401.009i		−	0.858692i	0.903140	−	0.429346i	$-0.141256\pi$
$468$		0			0
$469$	−212.795	−	595.463i	−0.453722	−	1.26964i
$470$	−322.112	−	557.914i	−0.685344	−	1.18705i
$471$		0			0
$472$	−118.717	−	68.5415i	−0.251520	−	0.145215i
$473$	47.6437	−	82.5213i	0.100727	−	0.174464i
$474$		0			0
$475$	296.358	−	171.102i	0.623911	−	0.360215i
$476$	−266.108	+	95.0967i	−0.559050	+	0.199783i
$477$		0			0
$478$	17.4799			0.0365688
$479$	−103.679	+	59.8591i	−0.216449	+	0.124967i	−0.604305	−	0.796753i	$-0.706549\pi$
$479$	−103.679	+	59.8591i	−0.216449	+	0.124967i	0.387856	+	0.921720i	$0.373216\pi$
$480$		0			0
$481$	25.5056	+	14.7257i	0.0530262	+	0.0306147i
$482$	−363.858	−	210.074i	−0.754893	−	0.435837i
$483$		0			0
$484$	−60.8508	−	105.397i	−0.125725	−	0.217762i
$485$	1078.90			2.22453
$486$		0			0
$487$	−570.074			−1.17058			−0.585291	−	0.810823i	$-0.699020\pi$
$487$	−570.074			−1.17058			−0.585291	+	0.810823i	$0.699020\pi$
$488$	−96.9448	+	55.9711i	−0.198657	+	0.114695i
$489$		0			0
$490$	678.069	−	111.401i	1.38381	−	0.227349i
$491$	141.060	−	244.323i	0.287291	−	0.497602i	−0.685871	−	0.727723i	$-0.740579\pi$
$491$	141.060	−	244.323i	0.287291	−	0.497602i	0.973162	+	0.230121i	$0.0739121\pi$
$492$		0			0
$493$	245.353	−	141.655i	0.497673	−	0.287332i
$494$	−80.1943			−0.162337
$495$		0			0
$496$			0.0951003i			0.000191735i
$497$	−365.563	+	430.523i	−0.735540	+	0.866243i
$498$		0			0
$499$	30.1314	−	52.1891i	0.0603835	−	0.104587i	−0.834253	−	0.551381i	$-0.814101\pi$
$499$	30.1314	−	52.1891i	0.0603835	−	0.104587i	0.894637	+	0.446794i	$0.147434\pi$
$500$	−830.113	−	479.266i	−1.66023	−	0.958532i
$501$		0			0
$502$	−428.506	+	247.398i	−0.853597	+	0.492825i
$503$		−	3.37300i		−	0.00670576i	−0.999994	−	0.00335288i	$-0.998933\pi$
$503$		−	3.37300i		−	0.00670576i	0.999994	−	0.00335288i	$-0.00106726\pi$
$504$		0			0
$505$	1378.07			2.72885
$506$	1.67841	+	2.90710i	0.00331702	+	0.00574525i
$507$		0			0
$508$	155.852	−	269.943i	0.306795	−	0.531385i
$509$	−11.9659	−	6.90849i	−0.0235086	−	0.0135727i	0.488200	−	0.872732i	$-0.337654\pi$
$509$	−11.9659	−	6.90849i	−0.0235086	−	0.0135727i	−0.511708	+	0.859159i	$0.670987\pi$
$510$		0			0
$511$	95.2055	+	80.8404i	0.186312	+	0.158200i
$512$	−22.6274			−0.0441942
$513$		0			0
$514$		−	478.439i		−	0.930816i
$515$	−378.409	−	655.423i	−0.734774	−	1.27267i
$516$		0			0
$517$	−536.492	−	309.744i	−1.03770	−	0.599118i
$518$	23.6037	+	4.30445i	0.0455671	+	0.00830975i
$519$		0			0
$520$	170.410	+	295.158i	0.327711	+	0.567612i
$521$			163.277i			0.313391i	0.987647	+	0.156695i	$0.0500841\pi$
$521$			163.277i			0.313391i	−0.987647	+	0.156695i	$0.949916\pi$
$522$		0			0
$523$		−	953.671i		−	1.82346i	−0.410787	−	0.911731i	$-0.634746\pi$
$523$		−	953.671i		−	1.82346i	0.410787	−	0.911731i	$-0.365254\pi$
$524$	−172.211	+	99.4262i	−0.328647	+	0.189745i
$525$		0			0
$526$	46.2867	−	80.1709i	0.0879975	−	0.152416i
$527$	−0.239949	+	0.415605i	−0.000455312	+	0.000788624i
$528$		0			0
$529$	264.485	+	458.101i	0.499971	+	0.865975i
$530$			802.007i			1.51322i
$531$		0			0
$532$	−61.5213	+	21.9853i	−0.115641	+	0.0413258i
$533$	66.5202	+	115.216i	0.124803	+	0.216166i
$534$		0			0
$535$	726.321	+	419.342i	1.35761	+	0.783817i
$536$	127.753	−	221.274i	0.238344	−	0.412825i
$537$		0			0
$538$	304.185	−	175.621i	0.565399	−	0.326433i
$539$	511.116	−	418.789i	0.948267	−	0.776974i
$540$		0			0
$541$	296.567			0.548183			0.274092	−	0.961704i	$-0.411623\pi$
$541$	296.567			0.548183			0.274092	+	0.961704i	$0.411623\pi$
$542$	72.9881	−	42.1397i	0.134664	−	0.0777485i
$543$		0			0
$544$	−98.8857	−	57.0917i	−0.181775	−	0.104948i
$545$	−207.059	−	119.545i	−0.379924	−	0.219349i
$546$		0			0
$547$	−205.972	−	356.754i	−0.376548	−	0.652201i	0.614009	−	0.789299i	$-0.289556\pi$
$547$	−205.972	−	356.754i	−0.376548	−	0.652201i	−0.990557	+	0.137098i	$0.956223\pi$
$548$	49.3357			0.0900287
$549$		0			0
$550$	−1398.50			−2.54273
$551$	56.7230	−	32.7490i	0.102945	−	0.0594356i
$552$		0			0
$553$	−140.196	−	25.5665i	−0.253519	−	0.0462324i
$554$	−314.091	+	544.022i	−0.566952	+	0.981989i
$555$		0			0
$556$	−197.186	+	113.845i	−0.354651	+	0.204758i
$557$	−558.037			−1.00186			−0.500931	−	0.865487i	$-0.667009\pi$
$557$	−558.037			−1.00186			−0.500931	+	0.865487i	$0.667009\pi$
$558$		0			0
$559$			85.8639i			0.153603i
$560$	211.648	+	179.713i	0.377943	+	0.320917i
$561$		0			0
$562$	−327.770	+	567.715i	−0.583221	+	1.01017i
$563$	251.341	+	145.112i	0.446432	+	0.257748i	0.706322	−	0.707891i	$-0.250353\pi$
$563$	251.341	+	145.112i	0.446432	+	0.257748i	−0.259890	+	0.965638i	$0.583686\pi$
$564$		0			0
$565$	1249.33	−	721.298i	2.21120	−	1.27663i
$566$		−	144.860i		−	0.255937i
$567$		0			0
$568$	−228.209			−0.401777
$569$	−321.956	−	557.644i	−0.565828	−	0.980043i	−0.996972	−	0.0777596i	$-0.975223\pi$
$569$	−321.956	−	557.644i	−0.565828	−	0.980043i	0.431144	−	0.902283i	$-0.358110\pi$
$570$		0			0
$571$	542.172	−	939.070i	0.949514	−	1.64461i	0.203063	−	0.979166i	$-0.434910\pi$
$571$	542.172	−	939.070i	0.949514	−	1.64461i	0.746451	−	0.665441i	$-0.231756\pi$
$572$	283.825	+	163.867i	0.496198	+	0.286480i
$573$		0			0
$574$	82.6178	+	70.1520i	0.143933	+	0.122216i
$575$	12.9076			0.0224481
$576$		0			0
$577$			650.622i			1.12759i	0.825913	+	0.563797i	$0.190660\pi$
$577$			650.622i			1.12759i	−0.825913	+	0.563797i	$0.809340\pi$
$578$	−83.7443	−	145.049i	−0.144886	−	0.250950i
$579$		0			0
$580$	−241.068	−	139.181i	−0.415635	−	0.239967i
$581$	−36.5899	+	200.643i	−0.0629774	+	0.345341i
$582$		0			0
$583$	385.607	+	667.890i	0.661418	+	1.14561i
$584$			50.4660i			0.0864144i
$585$		0			0
$586$			471.206i			0.804106i
$587$	199.425	−	115.138i	0.339736	−	0.196147i	−0.320419	−	0.947276i	$-0.603824\pi$
$587$	199.425	−	115.138i	0.339736	−	0.196147i	0.660155	+	0.751129i	$0.270490\pi$
$588$		0			0
$589$	−0.0554737	+	0.0960833i	−9.41829e−5	+	0.000163130i
$590$	−339.837	+	588.614i	−0.575994	+	0.997651i
$591$		0			0
$592$	4.84732	+	8.39581i	0.00818804	+	0.0141821i
$593$			715.009i			1.20575i	0.797836	+	0.602875i	$0.205978\pi$
$593$			715.009i			1.20575i	−0.797836	+	0.602875i	$0.794022\pi$
$594$		0			0
$595$	471.500	+	1319.39i	0.792437	+	2.21747i
$596$	171.477	+	297.006i	0.287712	+	0.498332i
$597$		0			0
$598$	−2.61960	−	1.51243i	−0.00438060	−	0.00252914i
$599$	−433.990	+	751.692i	−0.724523	+	1.25491i	0.234646	+	0.972081i	$0.424607\pi$
$599$	−433.990	+	751.692i	−0.724523	+	1.25491i	−0.959170	+	0.282831i	$0.908727\pi$
$600$		0			0
$601$	−242.032	+	139.737i	−0.402716	+	0.232508i	−0.687655	−	0.726037i	$-0.741360\pi$
$601$	−242.032	+	139.737i	−0.402716	+	0.232508i	0.284939	+	0.958546i	$0.408027\pi$
$602$	23.5397	+	65.8707i	0.0391024	+	0.109420i
$603$		0			0
$604$	475.148			0.786669
$605$	−522.568	+	301.705i	−0.863749	+	0.498686i
$606$		0			0
$607$	−381.944	−	220.515i	−0.629232	−	0.363287i	0.151223	−	0.988500i	$-0.451679\pi$
$607$	−381.944	−	220.515i	−0.629232	−	0.363287i	−0.780454	+	0.625213i	$0.785012\pi$
$608$	−22.8613	−	13.1990i	−0.0376008	−	0.0217089i
$609$		0			0
$610$	277.511	+	480.663i	0.454936	+	0.787973i
$611$	558.224			0.913623
$612$		0			0
$613$	−249.504			−0.407022			−0.203511	−	0.979073i	$-0.565235\pi$
$613$	−249.504			−0.407022			−0.203511	+	0.979073i	$0.565235\pi$
$614$	396.135	−	228.709i	0.645171	−	0.372490i
$615$		0			0
$616$	262.662	+	47.8998i	0.426399	+	0.0777594i
$617$	−276.294	+	478.555i	−0.447802	+	0.775616i	−0.998243	−	0.0592581i	$-0.981127\pi$
$617$	−276.294	+	478.555i	−0.447802	+	0.775616i	0.550440	+	0.834874i	$0.314460\pi$
$618$		0			0
$619$	−855.461	+	493.901i	−1.38201	+	0.797901i	−0.992397	−	0.123079i	$-0.960723\pi$
$619$	−855.461	+	493.901i	−1.38201	+	0.797901i	−0.389609	+	0.920980i	$0.627390\pi$
$620$	0.471518			0.000760513
$621$		0			0
$622$		−	651.958i		−	1.04816i
$623$	435.106	+	369.455i	0.698404	+	0.593025i
$624$		0			0
$625$	−1459.61	+	2528.12i	−2.33538	+	4.04499i
$626$	335.840	+	193.897i	0.536485	+	0.309740i
$627$		0			0
$628$	−135.506	+	78.2343i	−0.215774	+	0.124577i
$629$			48.9215i			0.0777766i
$630$		0			0
$631$	−236.443			−0.374712			−0.187356	−	0.982292i	$-0.559992\pi$
$631$	−236.443			−0.374712			−0.187356	+	0.982292i	$0.559992\pi$
$632$	−28.7909	−	49.8674i	−0.0455553	−	0.0789041i
$633$		0			0
$634$	300.209	−	519.977i	0.473516	−	0.820153i
$635$	−1338.41	−	772.731i	−2.10773	−	1.21690i
$636$		0			0
$637$	−210.178	+	557.099i	−0.329950	+	0.874567i
$638$	−267.674			−0.419551
$639$		0			0
$640$			112.189i			0.175296i
$641$	−122.793	−	212.685i	−0.191565	−	0.331801i	0.754204	−	0.656640i	$-0.228023\pi$
$641$	−122.793	−	212.685i	−0.191565	−	0.331801i	−0.945769	+	0.324839i	$0.894690\pi$
$642$		0			0
$643$	−1004.04	−	579.685i	−1.56150	−	0.901532i	−0.997106	−	0.0760269i	$-0.975777\pi$
$643$	−1004.04	−	579.685i	−1.56150	−	0.901532i	−0.564394	−	0.825505i	$-0.690890\pi$
$644$	−2.42427	−	0.442097i	−0.00376439	−	0.000686486i
$645$		0			0
$646$	−66.6052	−	115.364i	−0.103104	−	0.178581i
$647$		−	78.1821i		−	0.120838i	−0.998173	−	0.0604189i	$-0.980756\pi$
$647$		−	78.1821i		−	0.120838i	0.998173	−	0.0604189i	$-0.0192437\pi$
$648$		0			0
$649$			653.577i			1.00705i
$650$	1091.36	−	630.099i	1.67902	−	0.969383i
$651$		0			0
$652$	−236.898	+	410.320i	−0.363341	+	0.629325i
$653$	615.100	−	1065.38i	0.941960	−	1.63152i	0.180233	−	0.983624i	$-0.442315\pi$
$653$	615.100	−	1065.38i	0.941960	−	1.63152i	0.761727	−	0.647898i	$-0.224352\pi$
$654$		0			0
$655$	492.966	+	853.843i	0.752620	+	1.30358i
$656$			43.7936i			0.0667585i
$657$		0			0
$658$	428.243	−	153.037i	0.650825	−	0.232580i
$659$	−59.0656	−	102.305i	−0.0896291	−	0.155242i	0.817725	−	0.575609i	$-0.195235\pi$
$659$	−59.0656	−	102.305i	−0.0896291	−	0.155242i	−0.907354	+	0.420367i	$0.861901\pi$
$660$		0			0
$661$	558.811	+	322.629i	0.845402	+	0.488093i	0.859097	−	0.511813i	$-0.171026\pi$
$661$	558.811	+	322.629i	0.845402	+	0.488093i	−0.0136948	+	0.999906i	$0.504359\pi$
$662$	174.674	−	302.545i	0.263858	−	0.457016i
$663$		0			0
$664$	−71.3683	+	41.2045i	−0.107482	+	0.0620550i
$665$	109.006	+	305.029i	0.163918	+	0.458691i
$666$		0			0
$667$	2.47053			0.00370394
$668$	400.955	−	231.492i	0.600233	−	0.346545i
$669$		0			0
$670$	−1097.10	−	633.412i	−1.63746	−	0.945390i
$671$	462.208	+	266.856i	0.688834	+	0.397699i
$672$		0			0
$673$	−429.109	−	743.239i	−0.637607	−	1.10437i	−0.985956	−	0.167002i	$-0.946591\pi$
$673$	−429.109	−	743.239i	−0.637607	−	1.10437i	0.348350	−	0.937365i	$-0.386742\pi$
$674$	−162.036			−0.240409
$675$		0			0
$676$	42.6777			0.0631327
$677$	−88.6309	+	51.1710i	−0.130917	+	0.0755850i	−0.564028	−	0.825756i	$-0.690749\pi$
$677$	−88.6309	+	51.1710i	−0.130917	+	0.0755850i	0.433111	+	0.901341i	$0.357416\pi$
$678$		0			0
$679$	−136.636	+	749.253i	−0.201231	+	1.10347i
$680$	−283.067	+	490.286i	−0.416275	+	0.721009i
$681$		0			0
$682$	0.392668	−	0.226707i	0.000575759	−	0.000332415i
$683$	−1031.39			−1.51009			−0.755044	−	0.655674i	$-0.772384\pi$
$683$	−1031.39			−1.51009			−0.755044	+	0.655674i	$0.772384\pi$
$684$		0			0
$685$		−	244.612i		−	0.357098i
$686$	−8.50975	+	485.001i	−0.0124049	+	0.706998i
$687$		0			0
$688$	−14.1321	+	24.4776i	−0.0205409	+	0.0355779i
$689$	−601.839	−	347.472i	−0.873497	−	0.504314i
$690$		0			0
$691$	−791.470	+	456.956i	−1.14540	+	0.661296i	−0.947762	−	0.318979i	$-0.896660\pi$
$691$	−791.470	+	456.956i	−1.14540	+	0.661296i	−0.197637	+	0.980275i	$0.563327\pi$
$692$		−	255.572i		−	0.369324i
$693$		0			0
$694$	488.549			0.703961
$695$	564.458	+	977.670i	0.812170	+	1.40672i
$696$		0			0
$697$	−110.496	+	191.385i	−0.158531	+	0.274584i
$698$	−826.219	−	477.018i	−1.18369	−	0.683406i
$699$		0			0
$700$	664.500	−	782.580i	0.949285	−	1.11797i
$701$	194.138			0.276945			0.138472	−	0.990366i	$-0.455781\pi$
$701$	194.138			0.276945			0.138472	+	0.990366i	$0.455781\pi$
$702$		0			0
$703$			11.3101i			0.0160884i
$704$	53.9408	+	93.4282i	0.0766205	+	0.132711i
$705$		0			0
$706$	117.054	+	67.5813i	0.165799	+	0.0957243i
$707$	−174.524	+	957.016i	−0.246852	+	1.35363i
$708$		0			0
$709$	217.583	+	376.864i	0.306886	+	0.531543i	0.977680	−	0.210102i	$-0.0673795\pi$
$709$	217.583	+	376.864i	0.306886	+	0.531543i	−0.670793	+	0.741645i	$0.734046\pi$
$710$			1131.49i			1.59364i
$711$		0			0
$712$			230.638i			0.323930i
$713$	−0.00362417	+	0.00209242i	−5.08299e−6	+	2.93467e-6i
$714$		0			0
$715$	812.469	−	1407.24i	1.13632	−	1.96817i
$716$	132.848	−	230.099i	0.185541	−	0.321367i
$717$		0			0
$718$	19.2514	+	33.3445i	0.0268126	+	0.0464408i
$719$		−	922.050i		−	1.28241i	−0.767371	−	0.641203i	$-0.778436\pi$
$719$		−	922.050i		−	1.28241i	0.767371	−	0.641203i	$-0.221564\pi$
$720$		0			0
$721$	503.089	−	179.785i	0.697765	−	0.249354i
$722$	239.867	+	415.462i	0.332226	+	0.575432i
$723$		0			0
$724$	−161.868	−	93.4546i	−0.223575	−	0.129081i
$725$	−514.628	+	891.362i	−0.709832	+	1.22946i
$726$		0			0
$727$	451.861	−	260.882i	0.621542	−	0.358847i	−0.155927	−	0.987769i	$-0.549837\pi$
$727$	451.861	−	260.882i	0.621542	−	0.358847i	0.777469	+	0.628921i	$0.216503\pi$
$728$	−226.557	+	80.9628i	−0.311205	+	0.111213i
$729$		0			0
$730$	250.216			0.342762
$731$	−123.520	+	71.3141i	−0.168974	+	0.0975569i
$732$		0			0
$733$	132.926	+	76.7450i	0.181346	+	0.104700i	0.587925	−	0.808916i	$-0.299945\pi$
$733$	132.926	+	76.7450i	0.181346	+	0.104700i	−0.406579	+	0.913616i	$0.633278\pi$
$734$	−184.924	−	106.766i	−0.251940	−	0.145458i
$735$		0			0
$736$	−0.497853	−	0.862307i	−0.000676431	−	0.00117161i
$737$	−1218.18			−1.65289
$738$		0			0
$739$	−316.707			−0.428561			−0.214280	−	0.976772i	$-0.568741\pi$
$739$	−316.707			−0.428561			−0.214280	+	0.976772i	$0.568741\pi$
$740$	41.6273	−	24.0336i	0.0562532	−	0.0324778i
$741$		0			0
$742$	−556.962	−	101.569i	−0.750623	−	0.136886i
$743$	658.244	−	1140.11i	0.885927	−	1.53447i	0.0412793	−	0.999148i	$-0.486857\pi$
$743$	658.244	−	1140.11i	0.885927	−	1.53447i	0.844648	−	0.535323i	$-0.179810\pi$
$744$		0			0
$745$	1472.59	−	850.200i	1.97663	−	1.14121i
$746$	230.320			0.308740
$747$		0			0
$748$			544.396i			0.727803i
$749$	−383.201	+	451.295i	−0.511616	+	0.602529i
$750$		0			0
$751$	423.985	−	734.364i	0.564561	−	0.977848i	−0.432530	−	0.901620i	$-0.642379\pi$
$751$	423.985	−	734.364i	0.564561	−	0.977848i	0.997090	−	0.0762280i	$-0.0242877\pi$
$752$	159.135	+	91.8767i	0.211616	+	0.122176i
$753$		0			0
$754$	208.887	−	120.601i	0.277039	−	0.159948i
$755$		−	2355.84i		−	3.12031i
$756$		0			0
$757$	−1170.49			−1.54622			−0.773112	−	0.634269i	$-0.781301\pi$
$757$	−1170.49			−1.54622			−0.773112	+	0.634269i	$0.781301\pi$
$758$	−276.673	−	479.212i	−0.365004	−	0.632205i
$759$		0			0
$760$	−65.4420	+	113.349i	−0.0861079	+	0.149143i
$761$	240.508	+	138.858i	0.316043	+	0.182467i	0.649627	−	0.760253i	$-0.274925\pi$
$761$	240.508	+	138.858i	0.316043	+	0.182467i	−0.333585	+	0.942720i	$0.608258\pi$
$762$		0			0
$763$	109.242	−	128.654i	0.143175	−	0.168617i
$764$	−585.822			−0.766783
$765$		0			0
$766$			430.810i			0.562415i
$767$	−294.471	−	510.038i	−0.383925	−	0.664978i
$768$		0			0
$769$	−460.984	−	266.149i	−0.599459	−	0.346098i	0.169370	−	0.985553i	$-0.445827\pi$
$769$	−460.984	−	266.149i	−0.599459	−	0.346098i	−0.768829	+	0.639455i	$0.779160\pi$
$770$	237.492	−	1302.31i	0.308432	−	1.69131i
$771$		0			0
$772$	259.235	+	449.008i	0.335797	+	0.581617i
$773$			323.697i			0.418755i	0.977835	+	0.209377i	$0.0671437\pi$
$773$			323.697i			0.418755i	−0.977835	+	0.209377i	$0.932856\pi$
$774$		0			0
$775$		−	1.74346i		−	0.00224963i
$776$	−266.508	+	153.868i	−0.343438	+	0.198284i
$777$		0			0
$778$	−191.569	+	331.807i	−0.246232	+	0.426487i
$779$	−25.5456	+	44.2462i	−0.0327928	+	0.0567988i
$780$		0			0
$781$	544.021	+	942.272i	0.696570	+	1.20649i
$782$		−	5.02457i		−	0.00642529i
$783$		0			0
$784$	−151.608	+	124.222i	−0.193377	+	0.158446i
$785$	387.894	+	671.853i	0.494133	+	0.855863i
$786$		0			0
$787$	−943.069	−	544.481i	−1.19831	−	0.691844i	−0.238131	−	0.971233i	$-0.576535\pi$
$787$	−943.069	−	544.481i	−1.19831	−	0.691844i	−0.960178	+	0.279389i	$0.909868\pi$
$788$	336.752	−	583.271i	0.427350	−	0.740192i
$789$		0			0
$790$	−247.248	+	142.749i	−0.312972	+	0.180695i
$791$	342.694	+	958.956i	0.433241	+	1.21233i
$792$		0			0
$793$	−480.930			−0.606470
$794$	−558.438	+	322.415i	−0.703323	+	0.406064i
$795$		0			0
$796$	160.205	+	92.4947i	0.201263	+	0.116199i
$797$	−1.86876	−	1.07893i	−0.00234475	−	0.00135374i	0.498827	−	0.866701i	$-0.333764\pi$
$797$	−1.86876	−	1.07893i	−0.00234475	−	0.00135374i	−0.501172	+	0.865348i	$0.667098\pi$
$798$		0			0
$799$	463.631	+	803.033i	0.580265	+	1.00505i
$800$	414.826			0.518532
$801$		0			0
$802$	605.482			0.754965
$803$	208.373	−	120.304i	0.259494	−	0.149819i
$804$		0			0
$805$	−2.19197	+	12.0198i	−0.00272294	+	0.0149314i
$806$	−0.204287	+	0.353835i	−0.000253458	+	0.000439001i
$807$		0			0
$808$	−340.409	+	196.535i	−0.421298	+	0.243237i
$809$	137.194			0.169585			0.0847924	−	0.996399i	$-0.472977\pi$
$809$	137.194			0.169585			0.0847924	+	0.996399i	$0.472977\pi$
$810$		0			0
$811$		−	724.583i		−	0.893444i	−0.894673	−	0.446722i	$-0.852591\pi$
$811$		−	724.583i		−	0.893444i	0.894673	−	0.446722i	$-0.147409\pi$
$812$	127.185	−	149.786i	0.156632	−	0.184465i
$813$		0			0
$814$	23.1108	−	40.0290i	0.0283916	−	0.0491757i
$815$	2034.41	+	1174.57i	2.49621	+	1.44119i
$816$		0			0
$817$	−28.5564	+	16.4871i	−0.0349528	+	0.0201800i
$818$		−	506.370i		−	0.619034i
$819$		0			0
$820$	217.133			0.264797
$821$	557.777	+	966.098i	0.679387	+	1.17673i	0.975166	+	0.221477i	$0.0710877\pi$
$821$	557.777	+	966.098i	0.679387	+	1.17673i	−0.295778	+	0.955257i	$0.595579\pi$
$822$		0			0
$823$	255.274	−	442.148i	0.310175	−	0.537239i	−0.668225	−	0.743959i	$-0.732946\pi$
$823$	255.274	−	442.148i	0.310175	−	0.537239i	0.978400	+	0.206720i	$0.0662790\pi$
$824$	186.948	+	107.934i	0.226878	+	0.130988i
$825$		0			0
$826$	−365.731	−	310.548i	−0.442774	−	0.375966i
$827$	−1088.29			−1.31594			−0.657972	−	0.753042i	$-0.728585\pi$
$827$	−1088.29			−1.31594			−0.657972	+	0.753042i	$0.728585\pi$
$828$		0			0
$829$			1155.53i			1.39388i	0.717128	+	0.696942i	$0.245456\pi$
$829$			1155.53i			1.39388i	−0.717128	+	0.696942i	$0.754544\pi$
$830$	204.297	+	353.852i	0.246141	+	0.426328i
$831$		0			0
$832$	−84.1887	−	48.6064i	−0.101188	−	0.0584211i
$833$	−975.979	+	160.345i	−1.17164	+	0.192491i
$834$		0			0
$835$	−1147.76	−	1987.98i	−1.37457	−	2.38082i
$836$			125.859i			0.150549i
$837$		0			0
$838$			647.221i			0.772340i
$839$	162.598	−	93.8762i	0.193800	−	0.111891i	−0.399960	−	0.916533i	$-0.630976\pi$
$839$	162.598	−	93.8762i	0.193800	−	0.111891i	0.593760	+	0.804642i	$0.297643\pi$
$840$		0			0
$841$	322.000	−	557.721i	0.382878	−	0.663164i
$842$	−4.74957	+	8.22649i	−0.00564082	+	0.00977018i
$843$		0			0
$844$	−198.134	−	343.179i	−0.234756	−	0.406610i
$845$		−	211.601i		−	0.250415i
$846$		0			0
$847$	−143.342	−	401.112i	−0.169235	−	0.473568i
$848$	−114.379	−	198.110i	−0.134881	−	0.233621i
$849$		0			0
$850$	1812.86	+	1046.65i	2.13277	+	1.23136i
$851$	−0.213304	+	0.369453i	−0.000250651	+	0.000434139i
$852$		0			0
$853$	−659.061	+	380.509i	−0.772639	+	0.446083i	−0.833815	−	0.552044i	$-0.813848\pi$
$853$	−659.061	+	380.509i	−0.772639	+	0.446083i	0.0611763	+	0.998127i	$0.480515\pi$
$854$	−368.947	+	131.847i	−0.432022	+	0.154388i
$855$		0			0
$856$	−239.220			−0.279462
$857$	779.492	−	450.040i	0.909558	−	0.525134i	0.0292694	−	0.999572i	$-0.490682\pi$
$857$	779.492	−	450.040i	0.909558	−	0.525134i	0.880289	+	0.474438i	$0.157349\pi$
$858$		0			0
$859$	1001.95	+	578.477i	1.16642	+	0.673431i	0.952833	−	0.303494i	$-0.0981531\pi$
$859$	1001.95	+	578.477i	1.16642	+	0.673431i	0.213584	+	0.976925i	$0.431486\pi$
$860$	121.363	+	70.0687i	0.141119	+	0.0814752i
$861$		0			0
$862$	282.394	+	489.121i	0.327603	+	0.567426i
$863$	−512.272			−0.593594			−0.296797	−	0.954941i	$-0.595918\pi$
$863$	−512.272			−0.593594			−0.296797	+	0.954941i	$0.595918\pi$
$864$		0			0
$865$	−1267.15			−1.46492
$866$	−694.369	+	400.894i	−0.801812	+	0.462926i
$867$		0			0
$868$	−0.0597150	+	0.327451i	−6.87960e−5	+	0.000377247i
$869$	−137.268	+	237.755i	−0.157961	+	0.273596i
$870$		0			0
$871$	950.645	−	548.855i	1.09144	−	0.630144i
$872$	68.1964			0.0782069
$873$		0			0
$874$		−	1.16163i		−	0.00132909i
$875$	−2557.32	−	2171.45i	−2.92265	−	2.48166i
$876$		0			0
$877$	644.224	−	1115.83i	0.734577	−	1.27233i	−0.220331	−	0.975425i	$-0.570714\pi$
$877$	644.224	−	1115.83i	0.734577	−	1.27233i	0.954909	−	0.296900i	$-0.0959528\pi$
$878$	−240.878	−	139.071i	−0.274349	−	0.158395i
$879$		0			0
$880$	463.228	−	267.445i	0.526395	−	0.303914i
$881$			1247.46i			1.41596i	0.706235	+	0.707978i	$0.250392\pi$
$881$			1247.46i			1.41596i	−0.706235	+	0.707978i	$0.749608\pi$
$882$		0			0
$883$	−936.870			−1.06101			−0.530504	−	0.847682i	$-0.677997\pi$
$883$	−936.870			−1.06101			−0.530504	+	0.847682i	$0.677997\pi$
$884$	−245.279	−	424.836i	−0.277465	−	0.480584i
$885$		0			0
$886$	126.479	−	219.069i	0.142753	−	0.247256i
$887$	1251.49	+	722.546i	1.41092	+	0.814595i	0.995475	−	0.0950234i	$-0.0302926\pi$
$887$	1251.49	+	722.546i	1.41092	+	0.814595i	0.415445	+	0.909618i	$0.363626\pi$
$888$		0			0
$889$	706.133	−	831.611i	0.794301	−	0.935446i
$890$	1143.53			1.28487
$891$		0			0
$892$		−	347.912i		−	0.390036i
$893$	107.187	+	185.653i	0.120030	+	0.207898i
$894$		0			0
$895$	−1140.86	−	658.673i	−1.27470	−	0.735948i
$896$	−77.9110	−	14.2081i	−0.0869543	−	0.0158573i
$897$		0			0
$898$	−269.981	−	467.621i	−0.300647	−	0.520736i
$899$		−	0.333699i		−	0.000371189i
$900$		0			0
$901$		−	1154.37i		−	1.28121i
$902$	180.823	−	104.398i	0.200469	−	0.115741i
$903$		0			0
$904$	−205.738	+	356.348i	−0.227586	+	0.394190i
$905$	−463.358	+	802.560i	−0.511998	+	0.886806i
$906$		0			0
$907$	20.3747	+	35.2899i	0.0224638	+	0.0389084i	0.877039	−	0.480420i	$-0.159516\pi$
$907$	20.3747	+	35.2899i	0.0224638	+	0.0389084i	−0.854575	+	0.519328i	$0.826182\pi$
$908$			412.328i			0.454106i
$909$		0			0
$910$	401.423	+	1123.30i	0.441124	+	1.23439i
$911$	96.3670	+	166.913i	0.105782	+	0.183219i	0.914057	−	0.405585i	$-0.132932\pi$
$911$	96.3670	+	166.913i	0.105782	+	0.183219i	−0.808276	+	0.588804i	$0.799599\pi$
$912$		0			0
$913$	340.266	+	196.452i	0.372690	+	0.215172i
$914$	402.154	−	696.552i	0.439994	−	0.762092i
$915$		0			0
$916$	34.5279	−	19.9347i	0.0376942	−	0.0217628i
$917$	−655.391	+	234.212i	−0.714713	+	0.255411i
$918$		0			0
$919$	851.690			0.926757			0.463378	−	0.886161i	$-0.346637\pi$
$919$	851.690			0.926757			0.463378	+	0.886161i	$0.346637\pi$
$920$	−4.27542	+	2.46841i	−0.00464719	+	0.00268306i
$921$		0			0
$922$	−446.477	−	257.773i	−0.484248	−	0.279581i
$923$	−849.086	−	490.220i	−0.919920	−	0.531116i
$924$		0			0
$925$	−88.8653	−	153.919i	−0.0960706	−	0.166399i
$926$	−167.997			−0.181422
$927$		0			0
$928$	79.3977			0.0855579
$929$	−1301.36	+	751.342i	−1.40082	+	0.808764i	−0.994477	−	0.104957i	$-0.966530\pi$
$929$	−1301.36	+	751.342i	−1.40082	+	0.808764i	−0.406343	+	0.913721i	$0.633196\pi$
$930$		0			0
$931$	−225.636	+	37.0701i	−0.242359	+	0.0398175i
$932$	257.078	−	445.273i	0.275835	−	0.477760i
$933$		0			0
$934$	491.134	−	283.556i	0.525840	−	0.303594i
$935$	2699.18			2.88682
$936$		0			0
$937$		−	1330.62i		−	1.42009i	−0.704158	−	0.710043i	$-0.748675\pi$
$937$		−	1330.62i		−	1.42009i	0.704158	−	0.710043i	$-0.251325\pi$
$938$	578.821	−	681.676i	0.617080	−	0.726733i
$939$		0			0
$940$	455.535	−	789.009i	0.484611	−	0.839372i
$941$	−1089.81	−	629.201i	−1.15814	−	0.668651i	−0.207281	−	0.978282i	$-0.566461\pi$
$941$	−1089.81	−	629.201i	−1.15814	−	0.668651i	−0.950857	+	0.309631i	$0.899795\pi$
$942$		0			0
$943$	−1.66893	+	0.963556i	−0.00176981	+	0.00102180i
$944$		−	193.865i		−	0.205365i
$945$		0			0
$946$	134.757			0.142449
$947$	−671.501	−	1163.07i	−0.709083	−	1.22817i	−0.965198	−	0.261521i	$-0.915776\pi$
$947$	−671.501	−	1163.07i	−0.709083	−	1.22817i	0.256115	−	0.966646i	$-0.417557\pi$
$948$		0			0
$949$	−108.407	+	187.766i	−0.114233	+	0.197857i
$950$	419.113	+	241.975i	0.441172	+	0.254711i
$951$		0			0
$952$	−304.636	−	258.671i	−0.319996	−	0.271713i
$953$	1593.34			1.67192			0.835961	−	0.548789i	$-0.184911\pi$
$953$	1593.34			1.67192			0.835961	+	0.548789i	$0.184911\pi$
$954$		0			0
$955$			2904.57i			3.04144i
$956$	12.3601	+	21.4084i	0.0129290	+	0.0223937i
$957$		0			0
$958$	−146.624	−	84.6536i	−0.153053	−	0.0883649i
$959$	169.873	+	30.9786i	0.177136	+	0.0323031i
$960$		0			0
$961$	−480.500	−	832.250i	−0.500000	−	0.866025i
$962$			41.6505i			0.0432957i
$963$		0			0
$964$		−	594.178i		−	0.616367i
$965$	2226.23	−	1285.32i	2.30698	−	1.33193i
$966$		0			0
$967$	−819.205	+	1418.91i	−0.847162	+	1.46733i	0.0365690	+	0.999331i	$0.488357\pi$
$967$	−819.205	+	1418.91i	−0.847162	+	1.46733i	−0.883731	+	0.467996i	$0.844976\pi$
$968$	86.0560	−	149.053i	0.0889008	−	0.153981i
$969$		0			0
$970$	762.897	+	1321.38i	0.786492	+	1.36224i
$971$		−	1718.35i		−	1.76967i	−0.465902	−	0.884836i	$-0.654270\pi$
$971$		−	1718.35i		−	1.76967i	0.465902	−	0.884836i	$-0.345730\pi$
$972$		0			0
$973$	−750.439	+	268.178i	−0.771263	+	0.275620i
$974$	−403.103	−	698.195i	−0.413863	−	0.716832i
$975$		0			0
$976$	−137.101	−	79.1551i	−0.140472	−	0.0811016i
$977$	179.274	−	310.512i	0.183495	−	0.317822i	−0.759573	−	0.650422i	$-0.774592\pi$
$977$	179.274	−	310.512i	0.183495	−	0.317822i	0.943068	+	0.332599i	$0.107926\pi$
$978$		0			0
$979$	952.302	−	549.812i	0.972730	−	0.561606i
$980$	615.905	+	751.689i	0.628475	+	0.767030i
$981$		0			0
$982$	398.977			0.406290
$983$	−924.703	+	533.877i	−0.940694	+	0.543110i	−0.890178	−	0.455613i	$-0.849420\pi$
$983$	−924.703	+	533.877i	−0.940694	+	0.543110i	−0.0505165	+	0.998723i	$0.516087\pi$
$984$		0			0
$985$	−2891.92	−	1669.65i	−2.93596	−	1.69508i
$986$	346.981	+	200.330i	0.351908	+	0.203174i
$987$		0			0
$988$	−56.7059	−	98.2176i	−0.0573947	−	0.0994105i
$989$	−1.24375			−0.00125759
$990$		0			0
$991$	431.606			0.435526			0.217763	−	0.976002i	$-0.430124\pi$
$991$	431.606			0.435526			0.217763	+	0.976002i	$0.430124\pi$
$992$	−0.116474	+	0.0672461i	−0.000117413	+	6.77884e-5i
$993$		0			0
$994$	−785.773	−	143.296i	−0.790516	−	0.144161i
$995$	458.599	−	794.317i	0.460903	−	0.798308i
$996$		0			0
$997$	−123.674	+	71.4033i	−0.124046	+	0.0716181i	−0.560739	−	0.827993i	$-0.689483\pi$
$997$	−123.674	+	71.4033i	−0.124046	+	0.0716181i	0.436693	+	0.899611i	$0.356150\pi$
$998$	85.2244			0.0853952
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	378.3.o.a.307.16		32
3.2	odd	2		126.3.o.a.13.5	yes	32
7.6	odd	2	inner	378.3.o.a.307.9		32
9.2	odd	6		126.3.o.a.97.4	yes	32
9.4	even	3		1134.3.c.d.811.1		16
9.5	odd	6		1134.3.c.e.811.16		16
9.7	even	3	inner	378.3.o.a.181.9		32
21.20	even	2		126.3.o.a.13.4	✓	32
63.13	odd	6		1134.3.c.d.811.8		16
63.20	even	6		126.3.o.a.97.5	yes	32
63.34	odd	6	inner	378.3.o.a.181.16		32
63.41	even	6		1134.3.c.e.811.9		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.3.o.a.13.4	✓	32	21.20	even	2
126.3.o.a.13.5	yes	32	3.2	odd	2
126.3.o.a.97.4	yes	32	9.2	odd	6
126.3.o.a.97.5	yes	32	63.20	even	6
378.3.o.a.181.9		32	9.7	even	3	inner
378.3.o.a.181.16		32	63.34	odd	6	inner
378.3.o.a.307.9		32	7.6	odd	2	inner
378.3.o.a.307.16		32	1.1	even	1	trivial
1134.3.c.d.811.1		16	9.4	even	3
1134.3.c.d.811.8		16	63.13	odd	6
1134.3.c.e.811.9		16	63.41	even	6
1134.3.c.e.811.16		16	9.5	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.707107 + 1.22474i) q^{2} +(-1.00000 + 1.73205i) q^{4} +(8.58770 + 4.95811i) q^{5} +(-4.53080 + 5.33591i) q^{7} -2.82843 q^{8} +14.0237i q^{10} +(6.74260 + 11.6785i) q^{11} +(-10.5236 - 6.07580i) q^{13} +(-9.73888 - 1.77601i) q^{14} +(-2.00000 - 3.46410i) q^{16} -20.1850i q^{17} -4.66654i q^{19} +(-17.1754 + 9.91622i) q^{20} +(-9.53548 + 16.5159i) q^{22} +(0.0880089 - 0.152436i) q^{23} +(36.6657 + 63.5069i) q^{25} -17.1849i q^{26} +(-4.71127 - 13.1835i) q^{28} +(7.01783 + 12.1552i) q^{29} +(-0.0205898 - 0.0118875i) q^{31} +(2.82843 - 4.89898i) q^{32} +(24.7214 - 14.2729i) q^{34} +(-65.3651 + 23.3590i) q^{35} -2.42366 q^{37} +(5.71533 - 3.29975i) q^{38} +(-24.2897 - 14.0237i) q^{40} +(-9.48159 - 5.47420i) q^{41} +(-3.53303 - 6.11939i) q^{43} -26.9704 q^{44} +0.248927 q^{46} +(-39.7838 + 22.9692i) q^{47} +(-7.94379 - 48.3518i) q^{49} +(-51.8532 + 89.8124i) q^{50} +(21.0472 - 12.1516i) q^{52} +57.1896 q^{53} +133.722i q^{55} +(12.8150 - 15.0922i) q^{56} +(-9.92471 + 17.1901i) q^{58} +(41.9730 + 24.2331i) q^{59} +(34.2752 - 19.7888i) q^{61} -0.0336230i q^{62} +8.00000 q^{64} +(-60.2489 - 104.354i) q^{65} +(-45.1674 + 78.2322i) q^{67} +(34.9614 + 20.1850i) q^{68} +(-74.8289 - 63.5383i) q^{70} +80.6841 q^{71} -17.8424i q^{73} +(-1.71379 - 2.96837i) q^{74} +(8.08269 + 4.66654i) q^{76} +(-92.8649 - 16.9351i) q^{77} +(10.1791 + 17.6308i) q^{79} -39.6649i q^{80} -15.4834i q^{82} +(25.2325 - 14.5680i) q^{83} +(100.079 - 173.342i) q^{85} +(4.99646 - 8.65413i) q^{86} +(-19.0710 - 33.0319i) q^{88} -81.5430i q^{89} +(80.1001 - 28.6247i) q^{91} +(0.176018 + 0.304872i) q^{92} +(-56.2627 - 32.4833i) q^{94} +(23.1372 - 40.0749i) q^{95} +(94.2248 - 54.4007i) q^{97} +(53.6015 - 43.9190i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 32 q^{4} - 2 q^{7} + 12 q^{11} + 12 q^{14} - 64 q^{16} - 12 q^{23} + 80 q^{25} + 8 q^{28} + 48 q^{29} - 348 q^{35} - 88 q^{37} + 32 q^{43} - 48 q^{44} + 48 q^{46} + 50 q^{49} - 48 q^{50} + 864 q^{53}+ \cdots - 624 q^{98}+O(q^{100}) \) 32 * q - 32 * q^4 - 2 * q^7 + 12 * q^11 + 12 * q^14 - 64 * q^16 - 12 * q^23 + 80 * q^25 + 8 * q^28 + 48 * q^29 - 348 * q^35 - 88 * q^37 + 32 * q^43 - 48 * q^44 + 48 * q^46 + 50 * q^49 - 48 * q^50 + 864 * q^53 + 24 * q^56 + 48 * q^58 + 256 * q^64 - 120 * q^65 - 140 * q^67 - 108 * q^70 - 552 * q^71 - 144 * q^74 + 258 * q^77 - 176 * q^79 - 60 * q^85 - 96 * q^86 + 372 * q^91 - 24 * q^92 - 528 * q^95 - 624 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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