LMFDB - Embedded newform 378.3.r.a.305.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [378,3,Mod(233,378)] 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([5, 2])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("378.233"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 378 = 2 \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	378.r (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			305.10
Character	$\chi$	$=$	378.305
Dual form			378.3.r.a.233.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.41421i q^{2} -2.00000 q^{4} +(-2.90307 - 1.67609i) q^{5} +(5.64984 + 4.13271i) q^{7} -2.82843i q^{8} +(2.37035 - 4.10556i) q^{10} +(-12.2880 + 7.09448i) q^{11} +(-8.31908 - 14.4091i) q^{13} +(-5.84453 + 7.99008i) q^{14} +4.00000 q^{16} +(-13.5532 - 7.82495i) q^{17} +(17.3162 + 29.9925i) q^{19} +(5.80614 + 3.35218i) q^{20} +(-10.0331 - 17.3779i) q^{22} +(-22.7453 - 13.1320i) q^{23} +(-6.88146 - 11.9190i) q^{25} +(20.3775 - 11.7650i) q^{26} +(-11.2997 - 8.26542i) q^{28} +(-18.2368 - 10.5290i) q^{29} -33.7477 q^{31} +5.65685i q^{32} +(11.0662 - 19.1671i) q^{34} +(-9.47510 - 21.4672i) q^{35} +(-31.9815 - 55.3936i) q^{37} +(-42.4158 + 24.4888i) q^{38} +(-4.74069 + 8.21112i) q^{40} +(-5.44200 + 3.14194i) q^{41} +(0.0742627 - 0.128627i) q^{43} +(24.5760 - 14.1890i) q^{44} +(18.5715 - 32.1667i) q^{46} -41.9794i q^{47} +(14.8414 + 46.6983i) q^{49} +(16.8561 - 9.73185i) q^{50} +(16.6382 + 28.8182i) q^{52} +(38.6074 + 22.2900i) q^{53} +47.5639 q^{55} +(11.6891 - 15.9802i) q^{56} +(14.8903 - 25.7907i) q^{58} +41.4581i q^{59} +15.9995 q^{61} -47.7264i q^{62} -8.00000 q^{64} +55.7741i q^{65} -85.3249 q^{67} +(27.1064 + 15.6499i) q^{68} +(30.3592 - 13.3998i) q^{70} +56.4376i q^{71} +(4.42855 - 7.67047i) q^{73} +(78.3383 - 45.2287i) q^{74} +(-34.6324 - 59.9850i) q^{76} +(-98.7447 - 10.7001i) q^{77} +29.1408 q^{79} +(-11.6123 - 6.70435i) q^{80} +(-4.44338 - 7.69616i) q^{82} +(48.8531 + 28.2054i) q^{83} +(26.2306 + 45.4328i) q^{85} +(0.181906 + 0.105023i) q^{86} +(20.0662 + 34.7557i) q^{88} +(5.43082 - 3.13549i) q^{89} +(12.5470 - 115.789i) q^{91} +(45.4906 + 26.2640i) q^{92} +59.3679 q^{94} -116.094i q^{95} +(-32.1934 + 55.7605i) q^{97} +(-66.0414 + 20.9889i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 64 q^{4} + 2 q^{7} + 36 q^{11} + 10 q^{13} - 36 q^{14} + 128 q^{16} + 54 q^{17} + 28 q^{19} + 126 q^{23} + 80 q^{25} + 72 q^{26} - 4 q^{28} - 36 q^{29} + 16 q^{31} + 90 q^{35} + 22 q^{37} - 72 q^{41}+ \cdots - 288 q^{98}+O(q^{100}) $ 32 * q - 64 * q^4 + 2 * q^7 + 36 * q^11 + 10 * q^13 - 36 * q^14 + 128 * q^16 + 54 * q^17 + 28 * q^19 + 126 * q^23 + 80 * q^25 + 72 * q^26 - 4 * q^28 - 36 * q^29 + 16 * q^31 + 90 * q^35 + 22 * q^37 - 72 * q^41 + 16 * q^43 - 72 * q^44 - 12 * q^46 + 2 * q^49 + 288 * q^50 - 20 * q^52 + 72 * q^53 - 24 * q^55 + 72 * q^56 - 24 * q^58 + 124 * q^61 - 256 * q^64 - 140 * q^67 - 108 * q^68 + 72 * q^70 + 196 * q^73 - 216 * q^74 - 56 * q^76 - 486 * q^77 + 76 * q^79 + 60 * q^85 + 144 * q^86 + 486 * q^89 - 122 * q^91 - 252 * q^92 - 336 * q^94 - 38 * q^97 - 288 * q^98

Character values

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

$n$	$29$	$325$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$			1.41421i			0.707107i
$2$			1.41421i			0.707107i
$3$		0			0
$3$		0			0
$4$	−2.00000			−0.500000
$5$	−2.90307	−	1.67609i	−0.580614	−	0.335218i	0.180763	−	0.983527i	$-0.442143\pi$
$5$	−2.90307	−	1.67609i	−0.580614	−	0.335218i	−0.761377	+	0.648309i	$0.775477\pi$
$6$		0			0
$7$	5.64984	+	4.13271i	0.807120	+	0.590387i
$7$	5.64984	+	4.13271i	0.807120	+	0.590387i
$8$		−	2.82843i		−	0.353553i
$9$		0			0
$10$	2.37035	−	4.10556i	0.237035	−	0.410556i
$11$	−12.2880	+	7.09448i	−1.11709	+	0.644953i	−0.940657	−	0.339360i	$-0.889790\pi$
$11$	−12.2880	+	7.09448i	−1.11709	+	0.644953i	−0.176434	+	0.984312i	$0.556456\pi$
$12$		0			0
$13$	−8.31908	−	14.4091i	−0.639930	−	1.10839i	−0.985448	−	0.169978i	$-0.945630\pi$
$13$	−8.31908	−	14.4091i	−0.639930	−	1.10839i	0.345518	−	0.938412i	$-0.387703\pi$
$14$	−5.84453	+	7.99008i	−0.417467	+	0.570720i
$15$		0			0
$16$	4.00000			0.250000
$17$	−13.5532	−	7.82495i	−0.797248	−	0.460291i	0.0452601	−	0.998975i	$-0.485588\pi$
$17$	−13.5532	−	7.82495i	−0.797248	−	0.460291i	−0.842508	+	0.538684i	$0.818922\pi$
$18$		0			0
$19$	17.3162	+	29.9925i	0.911378	+	1.57855i	0.812120	+	0.583491i	$0.198314\pi$
$19$	17.3162	+	29.9925i	0.911378	+	1.57855i	0.0992583	+	0.995062i	$0.468353\pi$
$20$	5.80614	+	3.35218i	0.290307	+	0.167609i
$21$		0			0
$22$	−10.0331	−	17.3779i	−0.456050	−	0.789903i
$23$	−22.7453	−	13.1320i	−0.988926	−	0.570956i	−0.0839727	−	0.996468i	$-0.526761\pi$
$23$	−22.7453	−	13.1320i	−0.988926	−	0.570956i	−0.904953	+	0.425512i	$0.860094\pi$
$24$		0			0
$25$	−6.88146	−	11.9190i	−0.275258	−	0.476761i
$26$	20.3775	−	11.7650i	0.783750	−	0.452499i
$27$		0			0
$28$	−11.2997	−	8.26542i	−0.403560	−	0.295194i
$29$	−18.2368	−	10.5290i	−0.628855	−	0.363069i	0.151454	−	0.988464i	$-0.451605\pi$
$29$	−18.2368	−	10.5290i	−0.628855	−	0.363069i	−0.780308	+	0.625395i	$0.784938\pi$
$30$		0			0
$31$	−33.7477			−1.08863			−0.544317	−	0.838879i	$-0.683211\pi$
$31$	−33.7477			−1.08863			−0.544317	+	0.838879i	$0.683211\pi$
$32$			5.65685i			0.176777i
$33$		0			0
$34$	11.0662	−	19.1671i	0.325475	−	0.563739i
$35$	−9.47510	−	21.4672i	−0.270717	−	0.613348i
$36$		0			0
$37$	−31.9815	−	55.3936i	−0.864365	−	1.49712i	−0.867677	−	0.497129i	$-0.834388\pi$
$37$	−31.9815	−	55.3936i	−0.864365	−	1.49712i	0.00331203	−	0.999995i	$-0.498946\pi$
$38$	−42.4158	+	24.4888i	−1.11621	+	0.644441i
$39$		0			0
$40$	−4.74069	+	8.21112i	−0.118517	+	0.205278i
$41$	−5.44200	+	3.14194i	−0.132732	+	0.0766328i	−0.564896	−	0.825162i	$-0.691084\pi$
$41$	−5.44200	+	3.14194i	−0.132732	+	0.0766328i	0.432164	+	0.901795i	$0.357750\pi$
$42$		0			0
$43$	0.0742627	−	0.128627i	0.00172704	−	0.00299132i	−0.865161	−	0.501495i	$-0.832784\pi$
$43$	0.0742627	−	0.128627i	0.00172704	−	0.00299132i	0.866888	+	0.498504i	$0.166117\pi$
$44$	24.5760	−	14.1890i	0.558545	−	0.322476i
$45$		0			0
$46$	18.5715	−	32.1667i	0.403727	−	0.699276i
$47$		−	41.9794i		−	0.893179i	−0.894739	−	0.446590i	$-0.852638\pi$
$47$		−	41.9794i		−	0.893179i	0.894739	−	0.446590i	$-0.147362\pi$
$48$		0			0
$49$	14.8414	+	46.6983i	0.302886	+	0.953027i
$50$	16.8561	−	9.73185i	0.337121	−	0.194637i
$51$		0			0
$52$	16.6382	+	28.8182i	0.319965	+	0.554195i
$53$	38.6074	+	22.2900i	0.728442	+	0.420566i	0.817852	−	0.575429i	$-0.195165\pi$
$53$	38.6074	+	22.2900i	0.728442	+	0.420566i	−0.0894100	+	0.995995i	$0.528498\pi$
$54$		0			0
$55$	47.5639			0.864798
$56$	11.6891	−	15.9802i	0.208733	−	0.285360i
$57$		0			0
$58$	14.8903	−	25.7907i	0.256729	−	0.444667i
$59$			41.4581i			0.702679i	0.936248	+	0.351340i	$0.114274\pi$
$59$			41.4581i			0.702679i	−0.936248	+	0.351340i	$0.885726\pi$
$60$		0			0
$61$	15.9995			0.262287			0.131144	−	0.991363i	$-0.458135\pi$
$61$	15.9995			0.262287			0.131144	+	0.991363i	$0.458135\pi$
$62$		−	47.7264i		−	0.769781i
$63$		0			0
$64$	−8.00000			−0.125000
$65$			55.7741i			0.858063i
$66$		0			0
$67$	−85.3249			−1.27351			−0.636753	−	0.771068i	$-0.719723\pi$
$67$	−85.3249			−1.27351			−0.636753	+	0.771068i	$0.719723\pi$
$68$	27.1064	+	15.6499i	0.398624	+	0.230146i
$69$		0			0
$70$	30.3592	−	13.3998i	0.433702	−	0.191426i
$71$			56.4376i			0.794896i	0.917625	+	0.397448i	$0.130104\pi$
$71$			56.4376i			0.794896i	−0.917625	+	0.397448i	$0.869896\pi$
$72$		0			0
$73$	4.42855	−	7.67047i	0.0606650	−	0.105075i	−0.834098	−	0.551617i	$-0.814011\pi$
$73$	4.42855	−	7.67047i	0.0606650	−	0.105075i	0.894763	+	0.446542i	$0.147345\pi$
$74$	78.3383	−	45.2287i	1.05863	−	0.611198i
$75$		0			0
$76$	−34.6324	−	59.9850i	−0.455689	−	0.789276i
$77$	−98.7447	−	10.7001i	−1.28240	−	0.138962i
$78$		0			0
$79$	29.1408			0.368870			0.184435	−	0.982845i	$-0.440954\pi$
$79$	29.1408			0.368870			0.184435	+	0.982845i	$0.440954\pi$
$80$	−11.6123	−	6.70435i	−0.145153	−	0.0838044i
$81$		0			0
$82$	−4.44338	−	7.69616i	−0.0541875	−	0.0938556i
$83$	48.8531	+	28.2054i	0.588592	+	0.339824i	0.764540	−	0.644576i	$-0.222966\pi$
$83$	48.8531	+	28.2054i	0.588592	+	0.339824i	−0.175949	+	0.984399i	$0.556299\pi$
$84$		0			0
$85$	26.2306	+	45.4328i	0.308595	+	0.534503i
$86$	0.181906	+	0.105023i	0.00211518	+	0.00122120i
$87$		0			0
$88$	20.0662	+	34.7557i	0.228025	+	0.394951i
$89$	5.43082	−	3.13549i	0.0610205	−	0.0352302i	−0.469179	−	0.883103i	$-0.655450\pi$
$89$	5.43082	−	3.13549i	0.0610205	−	0.0352302i	0.530200	+	0.847873i	$0.322117\pi$
$90$		0			0
$91$	12.5470	−	115.789i	0.137879	−	1.27241i
$92$	45.4906	+	26.2640i	0.494463	+	0.285478i
$93$		0			0
$94$	59.3679			0.631573
$95$		−	116.094i		−	1.22204i
$96$		0			0
$97$	−32.1934	+	55.7605i	−0.331890	+	0.574851i	−0.982883	−	0.184233i	$-0.941020\pi$
$97$	−32.1934	+	55.7605i	−0.331890	+	0.574851i	0.650992	+	0.759084i	$0.274353\pi$
$98$	−66.0414	+	20.9889i	−0.673892	+	0.214173i
$99$		0			0
$100$	13.7629	+	23.8381i	0.137629	+	0.238381i
$101$	−80.7285	+	46.6086i	−0.799292	+	0.461472i	−0.843224	−	0.537563i	$-0.819345\pi$
$101$	−80.7285	+	46.6086i	−0.799292	+	0.461472i	0.0439314	+	0.999035i	$0.486012\pi$
$102$		0			0
$103$	−64.5523	+	111.808i	−0.626721	+	1.08551i	0.361484	+	0.932378i	$0.382270\pi$
$103$	−64.5523	+	111.808i	−0.626721	+	1.08551i	−0.988205	+	0.153135i	$0.951063\pi$
$104$	−40.7550	+	23.5299i	−0.391875	+	0.226249i
$105$		0			0
$106$	−31.5228	+	54.5991i	−0.297385	+	0.515086i
$107$	−92.8758	+	53.6219i	−0.867998	+	0.501139i	−0.866682	−	0.498860i	$-0.833752\pi$
$107$	−92.8758	+	53.6219i	−0.867998	+	0.501139i	−0.00131550	+	0.999999i	$0.500419\pi$
$108$		0			0
$109$	−16.5505	+	28.6662i	−0.151839	+	0.262993i	−0.931904	−	0.362706i	$-0.881853\pi$
$109$	−16.5505	+	28.6662i	−0.151839	+	0.262993i	0.780064	+	0.625699i	$0.215186\pi$
$110$			67.2655i			0.611505i
$111$		0			0
$112$	22.5994	+	16.5308i	0.201780	+	0.147597i
$113$	146.122	−	84.3635i	1.29311	−	0.746580i	0.313909	−	0.949453i	$-0.398361\pi$
$113$	146.122	−	84.3635i	1.29311	−	0.746580i	0.979205	+	0.202874i	$0.0650280\pi$
$114$		0			0
$115$	44.0208	+	76.2462i	0.382789	+	0.663011i
$116$	36.4736	+	21.0580i	0.314427	+	0.181535i
$117$		0			0
$118$	−58.6306			−0.496869
$119$	−44.2353	−	100.221i	−0.371725	−	0.842195i
$120$		0			0
$121$	40.1633	−	69.5649i	0.331928	−	0.574916i
$122$			22.6267i			0.185465i
$123$		0			0
$124$	67.4954			0.544317
$125$			129.940i			1.03952i
$126$		0			0
$127$	75.2845			0.592792			0.296396	−	0.955065i	$-0.404215\pi$
$127$	75.2845			0.592792			0.296396	+	0.955065i	$0.404215\pi$
$128$		−	11.3137i		−	0.0883883i
$129$		0			0
$130$	−78.8765			−0.606742
$131$	135.527	+	78.2467i	1.03456	+	0.597303i	0.918288	−	0.395914i	$-0.129572\pi$
$131$	135.527	+	78.2467i	1.03456	+	0.597303i	0.116272	+	0.993217i	$0.462906\pi$
$132$		0			0
$133$	−26.1166	+	241.016i	−0.196366	+	1.81215i
$134$		−	120.668i		−	0.900505i
$135$		0			0
$136$	−22.1323	+	38.3343i	−0.162738	+	0.281870i
$137$	71.6146	−	41.3467i	0.522734	−	0.301801i	−0.215318	−	0.976544i	$-0.569079\pi$
$137$	71.6146	−	41.3467i	0.522734	−	0.301801i	0.738053	+	0.674743i	$0.235746\pi$
$138$		0			0
$139$	50.4535	+	87.3880i	0.362975	+	0.628690i	0.988449	−	0.151554i	$-0.0484279\pi$
$139$	50.4535	+	87.3880i	0.362975	+	0.628690i	−0.625474	+	0.780245i	$0.715095\pi$
$140$	18.9502	+	42.9344i	0.135359	+	0.306674i
$141$		0			0
$142$	−79.8148			−0.562076
$143$	204.450	+	118.039i	1.42972	+	0.825449i
$144$		0			0
$145$	35.2951	+	61.1329i	0.243415	+	0.421606i
$146$	10.8477	+	6.26291i	0.0742992	+	0.0428967i
$147$		0			0
$148$	63.9630	+	110.787i	0.432182	+	0.748562i
$149$	−104.181	−	60.1490i	−0.699203	−	0.403685i	0.107848	−	0.994167i	$-0.465604\pi$
$149$	−104.181	−	60.1490i	−0.699203	−	0.403685i	−0.807050	+	0.590483i	$0.798937\pi$
$150$		0			0
$151$	−36.8571	−	63.8384i	−0.244087	−	0.422771i	0.717788	−	0.696262i	$-0.245155\pi$
$151$	−36.8571	−	63.8384i	−0.244087	−	0.422771i	−0.961875	+	0.273491i	$0.911822\pi$
$152$	84.8316	−	48.9776i	0.558103	−	0.322221i
$153$		0			0
$154$	15.1322	−	139.646i	0.0982608	−	0.906793i
$155$	97.9719	+	56.5641i	0.632077	+	0.364930i
$156$		0			0
$157$	−263.591			−1.67893			−0.839463	−	0.543417i	$-0.817130\pi$
$157$	−263.591			−1.67893			−0.839463	+	0.543417i	$0.817130\pi$
$158$			41.2113i			0.260831i
$159$		0			0
$160$	9.48139	−	16.4222i	0.0592587	−	0.102639i
$161$	−74.2365	−	168.193i	−0.461097	−	1.04468i
$162$		0			0
$163$	−36.3832	−	63.0176i	−0.223210	−	0.386611i	0.732571	−	0.680691i	$-0.238320\pi$
$163$	−36.3832	−	63.0176i	−0.223210	−	0.386611i	−0.955781	+	0.294080i	$0.904987\pi$
$164$	10.8840	−	6.28389i	0.0663659	−	0.0383164i
$165$		0			0
$166$	−39.8884	+	69.0887i	−0.240292	+	0.416197i
$167$	172.653	−	99.6811i	1.03385	−	0.596893i	0.115764	−	0.993277i	$-0.463068\pi$
$167$	172.653	−	99.6811i	1.03385	−	0.596893i	0.918085	+	0.396384i	$0.129735\pi$
$168$		0			0
$169$	−53.9143	+	93.3824i	−0.319020	+	0.552558i
$170$	−64.2516	+	37.0957i	−0.377951	+	0.218210i
$171$		0			0
$172$	−0.148525	+	0.257253i	−0.000863519	+	0.00149566i
$173$			249.497i			1.44218i	0.692841	+	0.721090i	$0.256359\pi$
$173$			249.497i			1.44218i	−0.692841	+	0.721090i	$0.743641\pi$
$174$		0			0
$175$	10.3788	−	95.7797i	0.0593072	−	0.547313i
$176$	−49.1520	+	28.3779i	−0.279273	+	0.161238i
$177$		0			0
$178$	4.43425	+	7.68034i	0.0249115	+	0.0431480i
$179$	−178.420	−	103.011i	−0.996760	−	0.575479i	−0.0894717	−	0.995989i	$-0.528518\pi$
$179$	−178.420	−	103.011i	−0.996760	−	0.575479i	−0.907288	+	0.420510i	$0.861851\pi$
$180$		0			0
$181$	−68.0662			−0.376056			−0.188028	−	0.982164i	$-0.560210\pi$
$181$	−68.0662			−0.376056			−0.188028	+	0.982164i	$0.560210\pi$
$182$	163.751	+	17.7442i	0.899730	+	0.0974955i
$183$		0			0
$184$	−37.1429	+	64.3334i	−0.201864	+	0.349638i
$185$			214.415i			1.15900i
$186$		0			0
$187$	222.056			1.18746
$188$			83.9588i			0.446590i
$189$		0			0
$190$	164.181			0.864113
$191$		−	258.142i		−	1.35153i	−0.737117	−	0.675765i	$-0.763813\pi$
$191$		−	258.142i		−	1.35153i	0.737117	−	0.675765i	$-0.236187\pi$
$192$		0			0
$193$	159.600			0.826945			0.413473	−	0.910516i	$-0.364316\pi$
$193$	159.600			0.826945			0.413473	+	0.910516i	$0.364316\pi$
$194$	−78.8573	−	45.5283i	−0.406481	−	0.234682i
$195$		0			0
$196$	−29.6828	−	93.3966i	−0.151443	−	0.476513i
$197$			173.797i			0.882219i	0.897453	+	0.441109i	$0.145415\pi$
$197$			173.797i			0.882219i	−0.897453	+	0.441109i	$0.854585\pi$
$198$		0			0
$199$	48.3082	−	83.6723i	0.242755	−	0.420464i	−0.718743	−	0.695276i	$-0.755282\pi$
$199$	48.3082	−	83.6723i	0.242755	−	0.420464i	0.961498	+	0.274812i	$0.0886156\pi$
$200$	−33.7121	+	19.4637i	−0.168561	+	0.0973185i
$201$		0			0
$202$	−65.9146	−	114.167i	−0.326310	−	0.565185i
$203$	−59.5216	−	134.855i	−0.293210	−	0.664308i
$204$		0			0
$205$	21.0647			0.102755
$206$	−158.120	−	91.2907i	−0.767574	−	0.443159i
$207$		0			0
$208$	−33.2763	−	57.6363i	−0.159982	−	0.277098i
$209$	−425.562	−	245.699i	−2.03618	−	1.17559i
$210$		0			0
$211$	8.68169	+	15.0371i	0.0411455	+	0.0712660i	0.885865	−	0.463944i	$-0.153566\pi$
$211$	8.68169	+	15.0371i	0.0411455	+	0.0712660i	−0.844719	+	0.535210i	$0.820233\pi$
$212$	−77.2148	−	44.5800i	−0.364221	−	0.210283i
$213$		0			0
$214$	−75.8328	−	131.346i	−0.354359	−	0.613767i
$215$	−0.431179	+	0.248942i	−0.00200549	+	0.00115787i
$216$		0			0
$217$	−190.669	−	139.469i	−0.878659	−	0.642716i
$218$	−40.5402	−	23.4059i	−0.185964	−	0.107366i
$219$		0			0
$220$	−95.1278			−0.432399
$221$			260.386i			1.17822i
$222$		0			0
$223$	147.273	−	255.085i	0.660418	−	1.14388i	−0.320088	−	0.947388i	$-0.603713\pi$
$223$	147.273	−	255.085i	0.660418	−	1.14388i	0.980506	−	0.196489i	$-0.0629541\pi$
$224$	−23.3781	+	31.9603i	−0.104367	+	0.142680i
$225$		0			0
$226$	119.308	+	206.648i	0.527912	+	0.914370i
$227$	194.224	−	112.135i	0.855612	−	0.493988i	−0.00692812	−	0.999976i	$-0.502205\pi$
$227$	194.224	−	112.135i	0.855612	−	0.493988i	0.862541	+	0.505988i	$0.168872\pi$
$228$		0			0
$229$	51.7349	−	89.6074i	0.225916	−	0.391299i	−0.730678	−	0.682723i	$-0.760796\pi$
$229$	51.7349	−	89.6074i	0.225916	−	0.391299i	0.956594	+	0.291424i	$0.0941290\pi$
$230$	−107.828	+	62.2548i	−0.468819	+	0.270673i
$231$		0			0
$232$	−29.7805	+	51.5814i	−0.128364	+	0.222334i
$233$	187.439	−	108.218i	0.804457	−	0.464454i	−0.0405700	−	0.999177i	$-0.512917\pi$
$233$	187.439	−	108.218i	0.804457	−	0.464454i	0.845027	+	0.534723i	$0.179584\pi$
$234$		0			0
$235$	−70.3612	+	121.869i	−0.299409	+	0.518592i
$236$		−	82.9162i		−	0.351340i
$237$		0			0
$238$	141.734	−	62.5581i	0.595522	−	0.262849i
$239$	387.074	−	223.477i	1.61956	−	0.935052i	0.632524	−	0.774541i	$-0.282019\pi$
$239$	387.074	−	223.477i	1.61956	−	0.935052i	0.987034	−	0.160511i	$-0.0513144\pi$
$240$		0			0
$241$	41.3755	+	71.6645i	0.171683	+	0.297363i	0.939008	−	0.343895i	$-0.111746\pi$
$241$	41.3755	+	71.6645i	0.171683	+	0.297363i	−0.767326	+	0.641258i	$0.778413\pi$
$242$	98.3796	+	56.7995i	0.406527	+	0.234709i
$243$		0			0
$244$	−31.9991			−0.131144
$245$	35.1848	−	160.444i	0.143611	−	0.654873i
$246$		0			0
$247$	288.110	−	499.020i	1.16644	−	2.02033i
$248$			95.4529i			0.384891i
$249$		0			0
$250$	−183.763			−0.735052
$251$			228.368i			0.909831i	0.890535	+	0.454916i	$0.150331\pi$
$251$			228.368i			0.909831i	−0.890535	+	0.454916i	$0.849669\pi$
$252$		0			0
$253$	372.659			1.47296
$254$			106.468i			0.419167i
$255$		0			0
$256$	16.0000			0.0625000
$257$	−66.3878	−	38.3290i	−0.258318	−	0.149140i	0.365249	−	0.930910i	$-0.380984\pi$
$257$	−66.3878	−	38.3290i	−0.258318	−	0.149140i	−0.623567	+	0.781770i	$0.714317\pi$
$258$		0			0
$259$	48.2352	−	445.135i	0.186236	−	1.71867i
$260$		−	111.548i		−	0.429031i
$261$		0			0
$262$	−110.658	+	191.665i	−0.422357	+	0.731544i
$263$	−306.958	+	177.222i	−1.16714	+	0.673849i	−0.953005	−	0.302955i	$-0.902027\pi$
$263$	−306.958	+	177.222i	−1.16714	+	0.673849i	−0.214136	+	0.976804i	$0.568694\pi$
$264$		0			0
$265$	−74.7200	−	129.419i	−0.281962	−	0.488373i
$266$	−340.848	−	36.9345i	−1.28138	−	0.138852i
$267$		0			0
$268$	170.650			0.636753
$269$	87.8658	+	50.7294i	0.326639	+	0.188585i	0.654348	−	0.756194i	$-0.272943\pi$
$269$	87.8658	+	50.7294i	0.326639	+	0.188585i	−0.327709	+	0.944779i	$0.606277\pi$
$270$		0			0
$271$	−37.9220	−	65.6829i	−0.139934	−	0.242372i	0.787538	−	0.616267i	$-0.211356\pi$
$271$	−37.9220	−	65.6829i	−0.139934	−	0.242372i	−0.927471	+	0.373894i	$0.878022\pi$
$272$	−54.2129	−	31.2998i	−0.199312	−	0.115073i
$273$		0			0
$274$	58.4731	+	101.278i	0.213405	+	0.369629i
$275$	169.119	+	97.6407i	0.614977	+	0.355057i
$276$		0			0
$277$	−134.061	−	232.200i	−0.483973	−	0.838266i	0.515857	−	0.856674i	$-0.327473\pi$
$277$	−134.061	−	232.200i	−0.483973	−	0.838266i	−0.999831	+	0.0184083i	$0.994140\pi$
$278$	−123.585	+	71.3520i	−0.444551	+	0.256662i
$279$		0			0
$280$	−60.7183	+	26.7996i	−0.216851	+	0.0957130i
$281$	−423.951	−	244.768i	−1.50872	−	0.871060i	−0.999948	−	0.0101594i	$-0.996766\pi$
$281$	−423.951	−	244.768i	−1.50872	−	0.871060i	−0.508773	−	0.860901i	$-0.669901\pi$
$282$		0			0
$283$	−523.237			−1.84889			−0.924446	−	0.381312i	$-0.875472\pi$
$283$	−523.237			−1.84889			−0.924446	+	0.381312i	$0.875472\pi$
$284$		−	112.875i		−	0.397448i
$285$		0			0
$286$	−166.933	+	289.136i	−0.583680	+	1.01096i
$287$	−43.7312	−	4.73875i	−0.152374	−	0.0165113i
$288$		0			0
$289$	−22.0403	−	38.1749i	−0.0762639	−	0.132093i
$290$	−86.4550	+	49.9148i	−0.298121	+	0.172120i
$291$		0			0
$292$	−8.85710	+	15.3409i	−0.0303325	+	0.0525375i
$293$	−64.1639	+	37.0450i	−0.218989	+	0.126434i	−0.605482	−	0.795859i	$-0.707020\pi$
$293$	−64.1639	+	37.0450i	−0.218989	+	0.126434i	0.386493	+	0.922292i	$0.373686\pi$
$294$		0			0
$295$	69.4874	−	120.356i	0.235551	−	0.407985i
$296$	−156.677	+	90.4573i	−0.529313	+	0.305599i
$297$		0			0
$298$	85.0636	−	147.334i	0.285448	−	0.494411i
$299$			436.985i			1.46149i
$300$		0			0
$301$	0.951149	−	0.419815i	0.00315996	−	0.00139473i
$302$	90.2811	−	52.1238i	0.298944	−	0.172596i
$303$		0			0
$304$	69.2647	+	119.970i	0.227844	+	0.394638i
$305$	−46.4477	−	26.8166i	−0.152288	−	0.0879233i
$306$		0			0
$307$	−159.112			−0.518280			−0.259140	−	0.965840i	$-0.583439\pi$
$307$	−159.112			−0.518280			−0.259140	+	0.965840i	$0.583439\pi$
$308$	197.489	+	21.4001i	0.641199	+	0.0694808i
$309$		0			0
$310$	−79.9937	+	138.553i	−0.258044	+	0.446946i
$311$			446.556i			1.43587i	0.696109	+	0.717936i	$0.254913\pi$
$311$			446.556i			1.43587i	−0.696109	+	0.717936i	$0.745087\pi$
$312$		0			0
$313$	−196.307			−0.627178			−0.313589	−	0.949559i	$-0.601531\pi$
$313$	−196.307			−0.627178			−0.313589	+	0.949559i	$0.601531\pi$
$314$		−	372.774i		−	1.18718i
$315$		0			0
$316$	−58.2815			−0.184435
$317$		−	340.779i		−	1.07501i	−0.843260	−	0.537506i	$-0.819367\pi$
$317$		−	340.779i		−	1.07501i	0.843260	−	0.537506i	$-0.180633\pi$
$318$		0			0
$319$	298.791			0.936650
$320$	23.2246	+	13.4087i	0.0725767	+	0.0419022i
$321$		0			0
$322$	237.861	−	104.986i	0.738700	−	0.326044i
$323$		−	541.993i		−	1.67800i
$324$		0			0
$325$	−114.495	+	198.311i	−0.352292	+	0.610187i
$326$	89.1204	−	51.4537i	0.273375	−	0.157833i
$327$		0			0
$328$	8.88676	+	15.3923i	0.0270938	+	0.0469278i
$329$	173.489	−	237.177i	0.527322	−	0.720903i
$330$		0			0
$331$	−563.578			−1.70265			−0.851326	−	0.524638i	$-0.824201\pi$
$331$	−563.578			−1.70265			−0.851326	+	0.524638i	$0.824201\pi$
$332$	−97.7062	−	56.4107i	−0.294296	−	0.169912i
$333$		0			0
$334$	140.970	+	244.168i	0.422067	+	0.731041i
$335$	247.704	+	143.012i	0.739416	+	0.426902i
$336$		0			0
$337$	303.340	+	525.401i	0.900119	+	1.55905i	0.827338	+	0.561704i	$0.189854\pi$
$337$	303.340	+	525.401i	0.900119	+	1.55905i	0.0727808	+	0.997348i	$0.476813\pi$
$338$	−132.063	−	76.2464i	−0.390718	−	0.225581i
$339$		0			0
$340$	−52.4612	−	90.8655i	−0.154298	−	0.267252i
$341$	414.692	−	239.422i	1.21610	−	0.702118i
$342$		0			0
$343$	−109.139	+	325.173i	−0.318189	+	0.948027i
$344$	−0.363811	−	0.210047i	−0.00105759	−	0.000610600i
$345$		0			0
$346$	−352.842			−1.01978
$347$		−	52.3842i		−	0.150963i	−0.997147	−	0.0754816i	$-0.975951\pi$
$347$		−	52.3842i		−	0.150963i	0.997147	−	0.0754816i	$-0.0240494\pi$
$348$		0			0
$349$	−4.33946	+	7.51616i	−0.0124340	+	0.0215363i	−0.872175	−	0.489193i	$-0.837291\pi$
$349$	−4.33946	+	7.51616i	−0.0124340	+	0.0215363i	0.859741	+	0.510729i	$0.170625\pi$
$350$	135.453	+	14.6778i	0.387008	+	0.0419365i
$351$		0			0
$352$	−40.1324	−	69.5114i	−0.114013	−	0.197476i
$353$	−103.990	+	60.0388i	−0.294590	+	0.170082i	−0.640010	−	0.768367i	$-0.721070\pi$
$353$	−103.990	+	60.0388i	−0.294590	+	0.170082i	0.345420	+	0.938448i	$0.387736\pi$
$354$		0			0
$355$	94.5944	−	163.842i	0.266463	−	0.461528i
$356$	−10.8616	+	6.27097i	−0.0305102	+	0.0176151i
$357$		0			0
$358$	145.679	−	252.324i	0.406925	−	0.704816i
$359$	−101.066	+	58.3503i	−0.281520	+	0.162536i	−0.634111	−	0.773242i	$-0.718634\pi$
$359$	−101.066	+	58.3503i	−0.281520	+	0.162536i	0.352591	+	0.935777i	$0.385301\pi$
$360$		0			0
$361$	−419.200	+	726.076i	−1.16122	+	2.01129i
$362$		−	96.2602i		−	0.265912i
$363$		0			0
$364$	−25.0940	+	231.579i	−0.0689397	+	0.636205i
$365$	−25.7128	+	14.8453i	−0.0704459	+	0.0406720i
$366$		0			0
$367$	−148.299	−	256.861i	−0.404085	−	0.699895i	0.590130	−	0.807308i	$-0.299077\pi$
$367$	−148.299	−	256.861i	−0.404085	−	0.699895i	−0.994214	+	0.107413i	$0.965743\pi$
$368$	−90.9812	−	52.5280i	−0.247231	−	0.142739i
$369$		0			0
$370$	−303.229			−0.819538
$371$	126.008	+	285.488i	0.339643	+	0.769510i
$372$		0			0
$373$	208.053	−	360.359i	0.557783	−	0.966109i	−0.439898	−	0.898048i	$-0.644985\pi$
$373$	208.053	−	360.359i	0.557783	−	0.966109i	0.997681	−	0.0680609i	$-0.0216812\pi$
$374$			314.034i			0.839664i
$375$		0			0
$376$	−118.736			−0.315787
$377$			350.367i			0.929355i
$378$		0			0
$379$	315.897			0.833501			0.416750	−	0.909021i	$-0.363169\pi$
$379$	315.897			0.833501			0.416750	+	0.909021i	$0.363169\pi$
$380$			232.188i			0.611020i
$381$		0			0
$382$	365.068			0.955676
$383$	−348.813	−	201.387i	−0.910740	−	0.525816i	−0.0300707	−	0.999548i	$-0.509573\pi$
$383$	−348.813	−	201.387i	−0.910740	−	0.525816i	−0.880669	+	0.473732i	$0.842907\pi$
$384$		0			0
$385$	268.729	+	196.568i	0.697996	+	0.510566i
$386$			225.709i			0.584739i
$387$		0			0
$388$	64.3867	−	111.521i	0.165945	−	0.287425i
$389$	−314.791	+	181.745i	−0.809232	+	0.467210i	−0.846689	−	0.532088i	$-0.821408\pi$
$389$	−314.791	+	181.745i	−0.809232	+	0.467210i	0.0374573	+	0.999298i	$0.488074\pi$
$390$		0			0
$391$	205.515	+	355.962i	0.525613	+	0.910388i
$392$	132.083	−	41.9779i	0.336946	−	0.107086i
$393$		0			0
$394$	−245.786			−0.623823
$395$	−84.5977	−	48.8425i	−0.214171	−	0.123652i
$396$		0			0
$397$	32.4146	+	56.1437i	0.0816489	+	0.141420i	0.903958	−	0.427621i	$-0.140648\pi$
$397$	32.4146	+	56.1437i	0.0816489	+	0.141420i	−0.822309	+	0.569041i	$0.807315\pi$
$398$	118.330	+	68.3181i	0.297313	+	0.171654i
$399$		0			0
$400$	−27.5258	−	47.6761i	−0.0688146	−	0.119190i
$401$	−430.383	−	248.482i	−1.07328	−	0.619656i	−0.144201	−	0.989548i	$-0.546061\pi$
$401$	−430.383	−	248.482i	−1.07328	−	0.619656i	−0.929074	+	0.369893i	$0.879394\pi$
$402$		0			0
$403$	280.750	+	486.273i	0.696650	+	1.20663i
$404$	161.457	−	93.2173i	0.399646	−	0.230736i
$405$		0			0
$406$	190.713	−	84.1762i	0.469737	−	0.207331i
$407$	785.977	+	453.784i	1.93115	+	1.11495i
$408$		0			0
$409$	493.994			1.20781			0.603905	−	0.797056i	$-0.293611\pi$
$409$	493.994			1.20781			0.603905	+	0.797056i	$0.293611\pi$
$410$			29.7900i			0.0726585i
$411$		0			0
$412$	129.105	−	223.616i	0.313361	−	0.542757i
$413$	−171.334	+	234.232i	−0.414853	+	0.567147i
$414$		0			0
$415$	−94.5493	−	163.764i	−0.227830	−	0.394613i
$416$	81.5100	−	47.0598i	0.195938	−	0.113125i
$417$		0			0
$418$	347.470	−	601.836i	0.831269	−	1.43980i
$419$	−229.187	+	132.321i	−0.546987	+	0.315803i	−0.747906	−	0.663805i	$-0.768940\pi$
$419$	−229.187	+	132.321i	−0.546987	+	0.315803i	0.200919	+	0.979608i	$0.435607\pi$
$420$		0			0
$421$	−41.2156	+	71.3876i	−0.0978994	+	0.169567i	−0.910815	−	0.412815i	$-0.864546\pi$
$421$	−41.2156	+	71.3876i	−0.0978994	+	0.169567i	0.812916	+	0.582382i	$0.197879\pi$
$422$	−21.2657	+	12.2778i	−0.0503927	+	0.0290942i
$423$		0			0
$424$	63.0456	−	109.198i	0.148693	−	0.257543i
$425$			215.388i			0.506796i
$426$		0			0
$427$	90.3948	+	66.1214i	0.211697	+	0.154851i
$428$	185.752	−	107.244i	0.433999	−	0.250569i
$429$		0			0
$430$	−0.352057	−	0.609780i	−0.000818736	−	0.00141809i
$431$	409.848	+	236.626i	0.950924	+	0.549016i	0.893368	−	0.449326i	$-0.148336\pi$
$431$	409.848	+	236.626i	0.950924	+	0.549016i	0.0575561	+	0.998342i	$0.481669\pi$
$432$		0			0
$433$	140.867			0.325328			0.162664	−	0.986681i	$-0.447991\pi$
$433$	140.867			0.325328			0.162664	+	0.986681i	$0.447991\pi$
$434$	197.239	−	269.647i	0.454469	−	0.621306i
$435$		0			0
$436$	33.1009	−	57.3325i	0.0759195	−	0.131497i
$437$		−	909.584i		−	2.08143i
$438$		0			0
$439$	−255.155			−0.581218			−0.290609	−	0.956842i	$-0.593858\pi$
$439$	−255.155			−0.581218			−0.290609	+	0.956842i	$0.593858\pi$
$440$		−	134.531i		−	0.305752i
$441$		0			0
$442$	−368.241			−0.833124
$443$		−	466.380i		−	1.05278i	−0.850244	−	0.526388i	$-0.823546\pi$
$443$		−	466.380i		−	1.05278i	0.850244	−	0.526388i	$-0.176454\pi$
$444$		0			0
$445$	−21.0214			−0.0472391
$446$	360.744	+	208.276i	0.808843	+	0.466986i
$447$		0			0
$448$	−45.1987	−	33.0617i	−0.100890	−	0.0737984i
$449$			383.226i			0.853509i	0.904367	+	0.426755i	$0.140343\pi$
$449$			383.226i			0.853509i	−0.904367	+	0.426755i	$0.859657\pi$
$450$		0			0
$451$	44.5809	−	77.2164i	0.0988490	−	0.171212i
$452$	−292.244	+	168.727i	−0.646557	+	0.373290i
$453$		0			0
$454$	158.583	+	274.674i	0.349302	+	0.605009i
$455$	−230.498	+	315.115i	−0.506589	+	0.692560i
$456$		0			0
$457$	−483.494			−1.05797			−0.528987	−	0.848630i	$-0.677428\pi$
$457$	−483.494			−1.05797			−0.528987	+	0.848630i	$0.677428\pi$
$458$	126.724	+	73.1641i	0.276690	+	0.159747i
$459$		0			0
$460$	−88.0416	−	152.492i	−0.191395	−	0.331505i
$461$	391.665	+	226.128i	0.849599	+	0.490516i	0.860516	−	0.509424i	$-0.170142\pi$
$461$	391.665	+	226.128i	0.849599	+	0.490516i	−0.0109166	+	0.999940i	$0.503475\pi$
$462$		0			0
$463$	−157.167	−	272.221i	−0.339454	−	0.587951i	0.644876	−	0.764287i	$-0.276909\pi$
$463$	−157.167	−	272.221i	−0.339454	−	0.587951i	−0.984330	+	0.176336i	$0.943575\pi$
$464$	−72.9471	−	42.1160i	−0.157214	−	0.0907673i
$465$		0			0
$466$	153.043	+	265.078i	0.328418	+	0.568837i
$467$	−258.779	+	149.406i	−0.554130	+	0.319927i	−0.750786	−	0.660545i	$-0.770325\pi$
$467$	−258.779	+	149.406i	−0.554130	+	0.319927i	0.196656	+	0.980473i	$0.436992\pi$
$468$		0			0
$469$	−482.072	−	352.623i	−1.02787	−	0.751862i
$470$	−172.349	−	99.5058i	−0.366700	−	0.211714i
$471$		0			0
$472$	117.261			0.248435
$473$			2.10742i			0.00445543i
$474$		0			0
$475$	238.321	−	412.784i	0.501729	−	0.869019i
$476$	88.4705	+	200.442i	0.185862	+	0.421098i
$477$		0			0
$478$	316.045	+	547.406i	0.661182	+	1.14520i
$479$	436.436	−	251.976i	0.911139	−	0.526047i	0.0303418	−	0.999540i	$-0.490340\pi$
$479$	436.436	−	251.976i	0.911139	−	0.526047i	0.880798	+	0.473493i	$0.157007\pi$
$480$		0			0
$481$	−532.113	+	921.648i	−1.10626	+	1.91611i
$482$	−101.349	+	58.5138i	−0.210267	+	0.121398i
$483$		0			0
$484$	−80.3266	+	139.130i	−0.165964	+	0.287458i
$485$	186.919	−	107.918i	0.385400	−	0.222511i
$486$		0			0
$487$	146.436	−	253.634i	0.300690	−	0.520810i	−0.675603	−	0.737266i	$-0.736116\pi$
$487$	146.436	−	253.634i	0.300690	−	0.520810i	0.976292	+	0.216456i	$0.0694498\pi$
$488$		−	45.2535i		−	0.0927326i
$489$		0			0
$490$	226.902	+	49.7588i	0.463065	+	0.101549i
$491$	370.452	−	213.881i	0.754485	−	0.435602i	−0.0728274	−	0.997345i	$-0.523202\pi$
$491$	370.452	−	213.881i	0.754485	−	0.435602i	0.827312	+	0.561743i	$0.189869\pi$
$492$		0			0
$493$	164.778	+	285.404i	0.334235	+	0.578913i
$494$	705.721	+	407.448i	1.42859	+	0.824794i
$495$		0			0
$496$	−134.991			−0.272159
$497$	−233.240	+	318.864i	−0.469296	+	0.641577i
$498$		0			0
$499$	−103.195	+	178.740i	−0.206804	+	0.358196i	−0.950706	−	0.310093i	$-0.899640\pi$
$499$	−103.195	+	178.740i	−0.206804	+	0.358196i	0.743902	+	0.668289i	$0.232973\pi$
$500$		−	259.880i		−	0.519760i
$501$		0			0
$502$	−322.961			−0.643348
$503$		−	415.249i		−	0.825546i	−0.910834	−	0.412773i	$-0.864560\pi$
$503$		−	415.249i		−	0.825546i	0.910834	−	0.412773i	$-0.135440\pi$
$504$		0			0
$505$	312.481			0.618774
$506$			527.019i			1.04154i
$507$		0			0
$508$	−150.569			−0.296396
$509$	−333.324	−	192.445i	−0.654860	−	0.378084i	0.135455	−	0.990783i	$-0.456750\pi$
$509$	−333.324	−	192.445i	−0.654860	−	0.378084i	−0.790316	+	0.612700i	$0.790084\pi$
$510$		0			0
$511$	56.7204	−	25.0350i	0.110999	−	0.0489922i
$512$			22.6274i			0.0441942i
$513$		0			0
$514$	54.2054	−	93.8865i	0.105458	−	0.182659i
$515$	374.800	−	216.391i	0.727766	−	0.420176i
$516$		0			0
$517$	297.822	+	515.843i	0.576058	+	0.997762i
$518$	629.516	+	68.2149i	1.21528	+	0.131689i
$519$		0			0
$520$	157.753			0.303371
$521$	−191.141	−	110.355i	−0.366874	−	0.211815i	0.305218	−	0.952282i	$-0.401271\pi$
$521$	−191.141	−	110.355i	−0.366874	−	0.211815i	−0.672092	+	0.740468i	$0.734604\pi$
$522$		0			0
$523$	389.796	+	675.146i	0.745308	+	1.29091i	0.950051	+	0.312095i	$0.101031\pi$
$523$	389.796	+	675.146i	0.745308	+	1.29091i	−0.204743	+	0.978816i	$0.565636\pi$
$524$	−271.055	−	156.493i	−0.517280	−	0.298652i
$525$		0			0
$526$	−250.630	−	434.104i	−0.476483	−	0.825293i
$527$	457.390	+	264.074i	0.867912	+	0.501089i
$528$		0			0
$529$	80.3988	+	139.255i	0.151983	+	0.263242i
$530$	183.026	−	105.670i	0.345332	−	0.199377i
$531$		0			0
$532$	52.2333	−	482.031i	0.0981829	−	0.906074i
$533$	90.5450	+	52.2762i	0.169878	+	0.0980791i
$534$		0			0
$535$	359.500			0.671962
$536$			241.335i			0.450253i
$537$		0			0
$538$	−71.7422	+	124.261i	−0.133350	+	0.230969i
$539$	−513.672	−	468.537i	−0.953009	−	0.869270i
$540$		0			0
$541$	108.437	+	187.818i	0.200437	+	0.347168i	0.948669	−	0.316269i	$-0.102430\pi$
$541$	108.437	+	187.818i	0.200437	+	0.347168i	−0.748232	+	0.663437i	$0.769097\pi$
$542$	92.8896	−	53.6299i	0.171383	−	0.0989481i
$543$		0			0
$544$	44.2646	−	76.6686i	0.0813688	−	0.140935i
$545$	96.0943	−	55.4801i	0.176320	−	0.101798i
$546$		0			0
$547$	−330.752	+	572.879i	−0.604665	+	1.04731i	0.387440	+	0.921895i	$0.373360\pi$
$547$	−330.752	+	572.879i	−0.604665	+	1.04731i	−0.992104	+	0.125415i	$0.959974\pi$
$548$	−143.229	+	82.6934i	−0.261367	+	0.150900i
$549$		0			0
$550$	−138.085	+	239.170i	−0.251063	+	0.434854i
$551$		−	729.289i		−	1.32357i
$552$		0			0
$553$	164.641	+	120.430i	0.297723	+	0.217776i
$554$	328.380	−	189.590i	0.592744	−	0.342221i
$555$		0			0
$556$	−100.907	−	174.776i	−0.181487	−	0.314345i
$557$	−159.762	−	92.2387i	−0.286826	−	0.165599i	0.349684	−	0.936868i	$-0.386289\pi$
$557$	−159.762	−	92.2387i	−0.286826	−	0.165599i	−0.636510	+	0.771269i	$0.719622\pi$
$558$		0			0
$559$	−2.47119			−0.00442073
$560$	−37.9004	−	85.8687i	−0.0676793	−	0.153337i
$561$		0			0
$562$	346.154	−	599.557i	0.615933	−	1.06683i
$563$			1043.84i			1.85407i	0.374981	+	0.927033i	$0.377649\pi$
$563$			1043.84i			1.85407i	−0.374981	+	0.927033i	$0.622351\pi$
$564$		0			0
$565$	−565.603			−1.00107
$566$		−	739.968i		−	1.30736i
$567$		0			0
$568$	159.630			0.281038
$569$		−	75.8394i		−	0.133285i	−0.997777	−	0.0666427i	$-0.978771\pi$
$569$		−	75.8394i		−	0.133285i	0.997777	−	0.0666427i	$-0.0212288\pi$
$570$		0			0
$571$	−770.837			−1.34998			−0.674988	−	0.737829i	$-0.735851\pi$
$571$	−770.837			−1.34998			−0.674988	+	0.737829i	$0.735851\pi$
$572$	−408.900	−	236.078i	−0.714860	−	0.412724i
$573$		0			0
$574$	6.70160	−	61.8453i	0.0116753	−	0.107744i
$575$			361.469i			0.628642i
$576$		0			0
$577$	435.383	−	754.105i	0.754563	−	1.30694i	−0.191028	−	0.981585i	$-0.561182\pi$
$577$	435.383	−	754.105i	0.754563	−	1.30694i	0.945591	−	0.325357i	$-0.105484\pi$
$578$	53.9874	−	31.1697i	0.0934039	−	0.0539267i
$579$		0			0
$580$	−70.5902	−	122.266i	−0.121707	−	0.210803i
$581$	159.448	+	361.252i	0.274437	+	0.621775i
$582$		0			0
$583$	−632.544			−1.08498
$584$	−21.6954	−	12.5258i	−0.0371496	−	0.0214483i
$585$		0			0
$586$	−52.3896	−	90.7414i	−0.0894020	−	0.154849i
$587$	−520.453	−	300.484i	−0.886633	−	0.511898i	−0.0137932	−	0.999905i	$-0.504391\pi$
$587$	−520.453	−	300.484i	−0.886633	−	0.511898i	−0.872840	+	0.488007i	$0.837724\pi$
$588$		0			0
$589$	−584.381	−	1012.18i	−0.992158	−	1.71847i
$590$	170.209	+	98.2700i	0.288489	+	0.166559i
$591$		0			0
$592$	−127.926	−	221.574i	−0.216091	−	0.374281i
$593$	288.796	−	166.736i	0.487008	−	0.281174i	−0.236324	−	0.971674i	$-0.575943\pi$
$593$	288.796	−	166.736i	0.487008	−	0.281174i	0.723332	+	0.690500i	$0.242609\pi$
$594$		0			0
$595$	−39.5616	+	365.091i	−0.0664901	+	0.613599i
$596$	208.362	+	120.298i	0.349601	+	0.201842i
$597$		0			0
$598$	−617.990			−1.03343
$599$		−	410.366i		−	0.685086i	−0.939502	−	0.342543i	$-0.888712\pi$
$599$		−	410.366i		−	0.685086i	0.939502	−	0.342543i	$-0.111288\pi$
$600$		0			0
$601$	204.315	−	353.884i	0.339958	−	0.588825i	−0.644466	−	0.764633i	$-0.722920\pi$
$601$	204.315	−	353.884i	0.339958	−	0.588825i	0.984424	+	0.175808i	$0.0562538\pi$
$602$	0.593707	+	1.34513i	0.000986225	+	0.00223443i
$603$		0			0
$604$	73.7142	+	127.677i	0.122043	+	0.211385i
$605$	−233.194	+	134.634i	−0.385444	+	0.222536i
$606$		0			0
$607$	114.081	−	197.594i	0.187942	−	0.325526i	−0.756622	−	0.653853i	$-0.773152\pi$
$607$	114.081	−	197.594i	0.187942	−	0.325526i	0.944564	+	0.328327i	$0.106485\pi$
$608$	−169.663	+	97.9551i	−0.279051	+	0.161110i
$609$		0			0
$610$	37.9244	−	65.6870i	0.0621712	−	0.107684i
$611$	−604.885	+	349.230i	−0.989991	+	0.571572i
$612$		0			0
$613$	−59.5738	+	103.185i	−0.0971840	+	0.168328i	−0.910518	−	0.413469i	$-0.864317\pi$
$613$	−59.5738	+	103.185i	−0.0971840	+	0.168328i	0.813334	+	0.581797i	$0.197650\pi$
$614$		−	225.018i		−	0.366479i
$615$		0			0
$616$	−30.2643	+	279.292i	−0.0491304	+	0.453396i
$617$	−1004.18	+	579.761i	−1.62751	+	0.939645i	−0.642682	+	0.766133i	$0.722178\pi$
$617$	−1004.18	+	579.761i	−1.62751	+	0.939645i	−0.984832	+	0.173512i	$0.944488\pi$
$618$		0			0
$619$	382.915	+	663.228i	0.618603	+	1.07145i	0.989741	+	0.142873i	$0.0456342\pi$
$619$	382.915	+	663.228i	0.618603	+	1.07145i	−0.371138	+	0.928578i	$0.621032\pi$
$620$	−195.944	−	113.128i	−0.316038	−	0.182465i
$621$		0			0
$622$	−631.526			−1.01531
$623$	43.6413	+	4.72901i	0.0700503	+	0.00759071i
$624$		0			0
$625$	45.7547	−	79.2494i	0.0732075	−	0.126799i
$626$		−	277.620i		−	0.443482i
$627$		0			0
$628$	527.183			0.839463
$629$			1001.01i			1.59144i
$630$		0			0
$631$	−562.217			−0.890994			−0.445497	−	0.895283i	$-0.646973\pi$
$631$	−562.217			−0.890994			−0.445497	+	0.895283i	$0.646973\pi$
$632$		−	82.4225i		−	0.130415i
$633$		0			0
$634$	481.934			0.760148
$635$	−218.556	−	126.184i	−0.344183	−	0.198714i
$636$		0			0
$637$	549.413	−	602.338i	0.862500	−	0.945586i
$638$			422.555i			0.662312i
$639$		0			0
$640$	−18.9628	+	32.8445i	−0.0296293	+	0.0513195i
$641$	−608.106	+	351.090i	−0.948684	+	0.547723i	−0.892672	−	0.450707i	$-0.851172\pi$
$641$	−608.106	+	351.090i	−0.948684	+	0.547723i	−0.0560121	+	0.998430i	$0.517839\pi$
$642$		0			0
$643$	110.674	+	191.694i	0.172122	+	0.298124i	0.939161	−	0.343476i	$-0.111604\pi$
$643$	110.674	+	191.694i	0.172122	+	0.298124i	−0.767040	+	0.641600i	$0.778271\pi$
$644$	148.473	+	336.387i	0.230548	+	0.522340i
$645$		0			0
$646$	766.494			1.18652
$647$	−501.744	−	289.682i	−0.775494	−	0.447731i	0.0593372	−	0.998238i	$-0.481101\pi$
$647$	−501.744	−	289.682i	−0.775494	−	0.447731i	−0.834831	+	0.550507i	$0.814435\pi$
$648$		0			0
$649$	−294.124	−	509.437i	−0.453195	−	0.784957i
$650$	−280.454	−	161.920i	−0.431468	−	0.249108i
$651$		0			0
$652$	72.7665	+	126.035i	0.111605	+	0.193306i
$653$	926.464	+	534.894i	1.41878	+	0.819134i	0.996192	−	0.0871874i	$-0.0277879\pi$
$653$	926.464	+	534.894i	1.41878	+	0.819134i	0.422589	+	0.906321i	$0.361121\pi$
$654$		0			0
$655$	−262.297	−	454.311i	−0.400453	−	0.693605i
$656$	−21.7680	+	12.5678i	−0.0331830	+	0.0191582i
$657$		0			0
$658$	335.419	+	245.350i	0.509755	+	0.372873i
$659$	−740.124	−	427.311i	−1.12310	−	0.648423i	−0.180911	−	0.983499i	$-0.557905\pi$
$659$	−740.124	−	427.311i	−1.12310	−	0.648423i	−0.942191	+	0.335076i	$0.891238\pi$
$660$		0			0
$661$	−1180.67			−1.78619			−0.893094	−	0.449870i	$-0.851470\pi$
$661$	−1180.67			−1.78619			−0.893094	+	0.449870i	$0.851470\pi$
$662$		−	797.019i		−	1.20396i
$663$		0			0
$664$	79.7768	−	138.177i	0.120146	−	0.208099i
$665$	479.782	−	655.911i	0.721477	−	0.986333i
$666$		0			0
$667$	276.534	+	478.971i	0.414594	+	0.718097i
$668$	−345.305	+	199.362i	−0.516924	+	0.298446i
$669$		0			0
$670$	−202.250	+	350.307i	−0.301865	+	0.522846i
$671$	−196.602	+	113.508i	−0.292999	+	0.169163i
$672$		0			0
$673$	232.243	−	402.257i	0.345086	−	0.597707i	−0.640283	−	0.768139i	$-0.721183\pi$
$673$	232.243	−	402.257i	0.345086	−	0.597707i	0.985369	+	0.170432i	$0.0545163\pi$
$674$	−743.029	+	428.988i	−1.10242	+	0.636480i
$675$		0			0
$676$	107.829	−	186.765i	0.159510	−	0.276279i
$677$			182.958i			0.270248i	0.990829	+	0.135124i	$0.0431433\pi$
$677$			182.958i			0.270248i	−0.990829	+	0.135124i	$0.956857\pi$
$678$		0			0
$679$	−412.330	+	181.992i	−0.607260	+	0.268030i
$680$	128.503	−	74.1914i	0.188975	−	0.109105i
$681$		0			0
$682$	338.594	+	586.462i	0.496472	+	0.859916i
$683$	−878.043	−	506.938i	−1.28557	−	0.742223i	−0.307708	−	0.951481i	$-0.599562\pi$
$683$	−878.043	−	506.938i	−1.28557	−	0.742223i	−0.977861	+	0.209258i	$0.932895\pi$
$684$		0			0
$685$	−277.203			−0.404676
$686$	−459.865	−	154.346i	−0.670356	−	0.224994i
$687$		0			0
$688$	0.297051	−	0.514507i	0.000431760	−	0.000747830i
$689$		−	741.730i		−	1.07653i
$690$		0			0
$691$	1002.41			1.45066			0.725331	−	0.688400i	$-0.241687\pi$
$691$	1002.41			1.45066			0.725331	+	0.688400i	$0.241687\pi$
$692$		−	498.995i		−	0.721090i
$693$		0			0
$694$	74.0825			0.106747
$695$		−	338.258i		−	0.486702i
$696$		0			0
$697$	98.3422			0.141094
$698$	−10.6295	−	6.13692i	−0.0152285	−	0.00879215i
$699$		0			0
$700$	−20.7575	+	191.559i	−0.0296536	+	0.273656i
$701$			77.0590i			0.109927i	0.998488	+	0.0549636i	$0.0175043\pi$
$701$			77.0590i			0.109927i	−0.998488	+	0.0549636i	$0.982496\pi$
$702$		0			0
$703$	1107.59	−	1918.41i	1.57553	−	2.72889i
$704$	98.3040	−	56.7558i	0.139636	−	0.0806191i
$705$		0			0
$706$	−84.9077	−	147.064i	−0.120266	−	0.208306i
$707$	−648.723	−	70.2962i	−0.917572	−	0.0994288i
$708$		0			0
$709$	906.235			1.27819			0.639093	−	0.769129i	$-0.279310\pi$
$709$	906.235			1.27819			0.639093	+	0.769129i	$0.279310\pi$
$710$	231.708	+	133.777i	0.326349	+	0.188418i
$711$		0			0
$712$	−8.86850	−	15.3607i	−0.0124558	−	0.0215740i
$713$	767.601	+	443.175i	1.07658	+	0.621563i
$714$		0			0
$715$	−395.688	−	685.352i	−0.553410	−	0.958534i
$716$	356.840	+	206.022i	0.498380	+	0.287740i
$717$		0			0
$718$	−82.5198	−	142.928i	−0.114930	−	0.199065i
$719$	−20.7034	+	11.9531i	−0.0287947	+	0.0166246i	−0.514328	−	0.857593i	$-0.671959\pi$
$719$	−20.7034	+	11.9531i	−0.0287947	+	0.0166246i	0.485534	+	0.874218i	$0.338625\pi$
$720$		0			0
$721$	−826.780	+	364.921i	−1.14671	+	0.506131i
$722$	−1026.83	−	592.838i	−1.42220	−	0.821106i
$723$		0			0
$724$	136.132			0.188028
$725$			289.820i			0.399751i
$726$		0			0
$727$	185.455	−	321.217i	0.255096	−	0.441839i	−0.709826	−	0.704377i	$-0.751226\pi$
$727$	185.455	−	321.217i	0.255096	−	0.441839i	0.964921	+	0.262539i	$0.0845597\pi$
$728$	−327.502	−	35.4883i	−0.449865	−	0.0487477i
$729$		0			0
$730$	−20.9944	−	36.3633i	−0.0287594	−	0.0498128i
$731$	−2.01300	+	1.16220i	−0.00275376	+	0.00158988i
$732$		0			0
$733$	309.948	−	536.846i	0.422849	−	0.732396i	−0.573368	−	0.819298i	$-0.694363\pi$
$733$	309.948	−	536.846i	0.422849	−	0.732396i	0.996217	+	0.0869020i	$0.0276967\pi$
$734$	363.257	−	209.726i	0.494900	−	0.285731i
$735$		0			0
$736$	74.2858	−	128.667i	0.100932	−	0.174819i
$737$	1048.47	−	605.336i	1.42262	−	0.821352i
$738$		0			0
$739$	−304.105	+	526.725i	−0.411508	+	0.712754i	−0.995055	−	0.0993262i	$-0.968331\pi$
$739$	−304.105	+	526.725i	−0.411508	+	0.712754i	0.583546	+	0.812080i	$0.301665\pi$
$740$		−	428.830i		−	0.579501i
$741$		0			0
$742$	−403.741	+	178.202i	−0.544126	+	0.240164i
$743$	−723.866	+	417.924i	−0.974248	+	0.562482i	−0.900529	−	0.434797i	$-0.856820\pi$
$743$	−723.866	+	417.924i	−0.974248	+	0.562482i	−0.0737195	+	0.997279i	$0.523487\pi$
$744$		0			0
$745$	201.630	+	349.234i	0.270645	+	0.468770i
$746$	509.624	+	294.232i	0.683142	+	0.394412i
$747$		0			0
$748$	−444.112			−0.593732
$749$	−746.337	−	80.8737i	−0.996445	−	0.107976i
$750$		0			0
$751$	−521.619	+	903.470i	−0.694566	+	1.20302i	0.275761	+	0.961226i	$0.411070\pi$
$751$	−521.619	+	903.470i	−0.694566	+	1.20302i	−0.970327	+	0.241797i	$0.922263\pi$
$752$		−	167.918i		−	0.223295i
$753$		0			0
$754$	−495.494			−0.657153
$755$			247.103i			0.327289i
$756$		0			0
$757$	441.367			0.583047			0.291524	−	0.956564i	$-0.405838\pi$
$757$	441.367			0.583047			0.291524	+	0.956564i	$0.405838\pi$
$758$			446.745i			0.589374i
$759$		0			0
$760$	−328.363			−0.432056
$761$	257.357	+	148.585i	0.338182	+	0.195249i	0.659468	−	0.751733i	$-0.270782\pi$
$761$	257.357	+	148.585i	0.338182	+	0.195249i	−0.321286	+	0.946982i	$0.604115\pi$
$762$		0			0
$763$	−211.977	+	93.5615i	−0.277820	+	0.122623i
$764$			516.285i			0.675765i
$765$		0			0
$766$	284.805	−	493.297i	0.371808	−	0.643990i
$767$	597.373	−	344.893i	0.778843	−	0.449665i
$768$		0			0
$769$	−79.6447	−	137.949i	−0.103569	−	0.179387i	0.809584	−	0.587005i	$-0.199693\pi$
$769$	−79.6447	−	137.949i	−0.103569	−	0.179387i	−0.913153	+	0.407618i	$0.866360\pi$
$770$	−277.989	+	380.039i	−0.361024	+	0.493558i
$771$		0			0
$772$	−319.201			−0.413473
$773$	−767.592	−	443.170i	−0.993004	−	0.573311i	−0.0868334	−	0.996223i	$-0.527675\pi$
$773$	−767.592	−	443.170i	−0.993004	−	0.573311i	−0.906171	+	0.422912i	$0.861008\pi$
$774$		0			0
$775$	232.233	+	402.240i	0.299656	+	0.519019i
$776$	157.715	+	91.0566i	0.203241	+	0.117341i
$777$		0			0
$778$	−257.026	−	445.182i	−0.330367	−	0.572213i
$779$	−188.469	−	108.813i	−0.241938	−	0.139683i
$780$		0			0
$781$	−400.396	−	693.505i	−0.512670	−	0.887971i
$782$	−503.406	+	290.641i	−0.643741	+	0.371664i
$783$		0			0
$784$	59.3657	+	186.793i	0.0757215	+	0.238257i
$785$	765.224	+	441.802i	0.974808	+	0.562805i
$786$		0			0
$787$	989.314			1.25707			0.628535	−	0.777781i	$-0.283655\pi$
$787$	989.314			1.25707			0.628535	+	0.777781i	$0.283655\pi$
$788$		−	347.594i		−	0.441109i
$789$		0			0
$790$	69.0737	−	119.639i	0.0874351	−	0.151442i
$791$	1174.22	+	127.239i	1.48447	+	0.160858i
$792$		0			0
$793$	−133.101	−	230.538i	−0.167845	−	0.290717i
$794$	−79.3992	+	45.8412i	−0.0999991	+	0.0577345i
$795$		0			0
$796$	−96.6164	+	167.345i	−0.121377	+	0.210232i
$797$	1020.06	−	588.934i	1.27988	−	0.738939i	0.303054	−	0.952973i	$-0.401994\pi$
$797$	1020.06	−	588.934i	1.27988	−	0.738939i	0.976826	+	0.214034i	$0.0686605\pi$
$798$		0			0
$799$	−328.487	+	568.956i	−0.411123	+	0.712085i
$800$	67.4242	−	38.9274i	0.0842803	−	0.0486592i
$801$		0			0
$802$	351.407	−	608.654i	0.438163	−	0.758920i
$803$			125.673i			0.156504i
$804$		0			0
$805$	−66.3931	+	612.704i	−0.0824759	+	0.761123i
$806$	−687.694	+	397.040i	−0.853218	+	0.492606i
$807$		0			0
$808$	131.829	+	228.335i	0.163155	+	0.282592i
$809$	−240.690	−	138.963i	−0.297516	−	0.171771i	0.343810	−	0.939039i	$-0.388282\pi$
$809$	−240.690	−	138.963i	−0.297516	−	0.171771i	−0.641326	+	0.767268i	$0.721616\pi$
$810$		0			0
$811$	−594.387			−0.732906			−0.366453	−	0.930437i	$-0.619428\pi$
$811$	−594.387			−0.732906			−0.366453	+	0.930437i	$0.619428\pi$
$812$	119.043	+	269.709i	0.146605	+	0.332154i
$813$		0			0
$814$	−641.748	+	1111.54i	−0.788388	+	1.36553i
$815$			243.926i			0.299296i
$816$		0			0
$817$	5.14378			0.00629594
$818$			698.613i			0.854050i
$819$		0			0
$820$	−42.1294			−0.0513773
$821$			135.048i			0.164492i	0.996612	+	0.0822460i	$0.0262093\pi$
$821$			135.048i			0.164492i	−0.996612	+	0.0822460i	$0.973791\pi$
$822$		0			0
$823$	383.153			0.465557			0.232778	−	0.972530i	$-0.425218\pi$
$823$	383.153			0.465557			0.232778	+	0.972530i	$0.425218\pi$
$824$	316.240	+	182.581i	0.383787	+	0.221579i
$825$		0			0
$826$	−331.253	−	242.303i	−0.401033	−	0.293345i
$827$		−	1194.80i		−	1.44474i	−0.691504	−	0.722372i	$-0.743052\pi$
$827$		−	1194.80i		−	1.44474i	0.691504	−	0.722372i	$-0.256948\pi$
$828$		0			0
$829$	484.580	−	839.318i	0.584536	−	1.01245i	−0.410397	−	0.911907i	$-0.634610\pi$
$829$	484.580	−	839.318i	0.584536	−	1.01245i	0.994933	−	0.100539i	$-0.0320567\pi$
$830$	231.598	−	133.713i	0.279033	−	0.161100i
$831$		0			0
$832$	66.5527	+	115.273i	0.0799912	+	0.138549i
$833$	164.263	−	749.046i	0.197195	−	0.899214i
$834$		0			0
$835$	−668.297			−0.800356
$836$	851.125	+	491.397i	1.01809	+	0.587796i
$837$		0			0
$838$	−187.131	−	324.120i	−0.223306	−	0.386778i
$839$	766.287	+	442.416i	0.913334	+	0.527314i	0.881502	−	0.472180i	$-0.156533\pi$
$839$	766.287	+	442.416i	0.913334	+	0.527314i	0.0318317	+	0.999493i	$0.489866\pi$
$840$		0			0
$841$	−198.780	−	344.297i	−0.236361	−	0.409390i
$842$	−100.957	−	58.2877i	−0.119902	−	0.0692253i
$843$		0			0
$844$	−17.3634	−	30.0743i	−0.0205727	−	0.0356330i
$845$	313.034	−	180.730i	0.370455	−	0.213882i
$846$		0			0
$847$	514.408	−	227.047i	0.607329	−	0.268061i
$848$	154.430	+	89.1600i	0.182110	+	0.105142i
$849$		0			0
$850$	−304.605			−0.358359
$851$			1679.92i			1.97406i
$852$		0			0
$853$	−91.3479	+	158.219i	−0.107090	+	0.185486i	−0.914590	−	0.404382i	$-0.867487\pi$
$853$	−91.3479	+	158.219i	−0.107090	+	0.185486i	0.807500	+	0.589867i	$0.200820\pi$
$854$	−93.5098	+	127.838i	−0.109496	+	0.149693i
$855$		0			0
$856$	151.666	+	262.692i	0.177179	+	0.306884i
$857$	1043.89	−	602.693i	1.21808	−	0.703259i	0.253573	−	0.967316i	$-0.418394\pi$
$857$	1043.89	−	602.693i	1.21808	−	0.703259i	0.964507	+	0.264058i	$0.0850610\pi$
$858$		0			0
$859$	518.743	−	898.489i	0.603892	−	1.04597i	−0.388334	−	0.921519i	$-0.626949\pi$
$859$	518.743	−	898.489i	0.603892	−	1.04597i	0.992226	−	0.124452i	$-0.0397174\pi$
$860$	0.862359	−	0.497883i	0.00100274	−	0.000578934i
$861$		0			0
$862$	−334.640	+	579.613i	−0.388213	+	0.672405i
$863$	908.692	−	524.634i	1.05295	−	0.607919i	0.129473	−	0.991583i	$-0.458671\pi$
$863$	908.692	−	524.634i	1.05295	−	0.607919i	0.923473	+	0.383664i	$0.125338\pi$
$864$		0			0
$865$	418.179	−	724.308i	0.483444	−	0.837350i
$866$			199.216i			0.230042i
$867$		0			0
$868$	381.338	+	278.939i	0.439330	+	0.321358i
$869$	−358.082	+	206.739i	−0.412062	+	0.237904i
$870$		0			0
$871$	709.825	+	1229.45i	0.814955	+	1.41154i
$872$	81.0804	+	46.8118i	0.0929821	+	0.0536832i
$873$		0			0
$874$	1286.35			1.47179
$875$	−537.005	+	734.141i	−0.613720	+	0.839018i
$876$		0			0
$877$	532.536	−	922.379i	0.607224	−	1.05174i	−0.384471	−	0.923137i	$-0.625616\pi$
$877$	532.536	−	922.379i	0.607224	−	1.05174i	0.991696	−	0.128606i	$-0.0410504\pi$
$878$		−	360.843i		−	0.410983i
$879$		0			0
$880$	190.256			0.216200
$881$		−	963.331i		−	1.09345i	−0.837312	−	0.546726i	$-0.815874\pi$
$881$		−	963.331i		−	1.09345i	0.837312	−	0.546726i	$-0.184126\pi$
$882$		0			0
$883$	−1212.68			−1.37336			−0.686681	−	0.726959i	$-0.740933\pi$
$883$	−1212.68			−1.37336			−0.686681	+	0.726959i	$0.740933\pi$
$884$		−	520.771i		−	0.589108i
$885$		0			0
$886$	659.561			0.744426
$887$	−404.747	−	233.681i	−0.456310	−	0.263450i	0.254182	−	0.967157i	$-0.418194\pi$
$887$	−404.747	−	233.681i	−0.456310	−	0.263450i	−0.710491	+	0.703706i	$0.751527\pi$
$888$		0			0
$889$	425.346	+	311.129i	0.478454	+	0.349977i
$890$		−	29.7288i		−	0.0334031i
$891$		0			0
$892$	−294.546	+	510.169i	−0.330209	+	0.571939i
$893$	1259.07	−	726.923i	1.40993	−	0.814024i
$894$		0			0
$895$	345.310	+	598.095i	0.385822	+	0.668263i
$896$	46.7563	−	63.9207i	0.0521833	−	0.0713400i
$897$		0			0
$898$	−541.963			−0.603522
$899$	615.449	+	355.330i	0.684593	+	0.395250i
$900$		0			0
$901$	−348.836	−	604.202i	−0.387166	−	0.670591i
$902$	109.200	+	63.0469i	0.121065	+	0.0698968i
$903$		0			0
$904$	−238.616	−	413.295i	−0.263956	−	0.457185i
$905$	197.601	+	114.085i	0.218344	+	0.126061i
$906$		0			0
$907$	525.571	+	910.316i	0.579461	+	1.00366i	0.995541	+	0.0943280i	$0.0300702\pi$
$907$	525.571	+	910.316i	0.579461	+	1.00366i	−0.416080	+	0.909328i	$0.636596\pi$
$908$	−388.448	+	224.271i	−0.427806	+	0.246994i
$909$		0			0
$910$	−445.639	−	325.973i	−0.489714	−	0.358213i
$911$	−1182.79	−	682.886i	−1.29835	−	0.749601i	−0.318228	−	0.948014i	$-0.603088\pi$
$911$	−1182.79	−	682.886i	−1.29835	−	0.749601i	−0.980118	+	0.198413i	$0.936421\pi$
$912$		0			0
$913$	−800.409			−0.876681
$914$		−	683.764i		−	0.748101i
$915$		0			0
$916$	−103.470	+	179.215i	−0.112958	+	0.195649i
$917$	442.337	+	1002.18i	0.482374	+	1.09289i
$918$		0			0
$919$	87.7536	+	151.994i	0.0954881	+	0.165390i	0.909812	−	0.415020i	$-0.136225\pi$
$919$	87.7536	+	151.994i	0.0954881	+	0.165390i	−0.814324	+	0.580410i	$0.802892\pi$
$920$	215.657	−	124.510i	0.234410	−	0.135336i
$921$		0			0
$922$	−319.793	+	553.898i	−0.346847	+	0.600757i
$923$	813.214	−	469.509i	0.881055	−	0.508677i
$924$		0			0
$925$	−440.158	+	762.377i	−0.475847	+	0.824191i
$926$	384.979	−	222.268i	0.415744	−	0.240030i
$927$		0			0
$928$	59.5611	−	103.163i	0.0641822	−	0.111167i
$929$			1052.24i			1.13266i	0.824179	+	0.566329i	$0.191637\pi$
$929$			1052.24i			1.13266i	−0.824179	+	0.566329i	$0.808363\pi$
$930$		0			0
$931$	−1143.60	+	1253.77i	−1.22836	+	1.34669i
$932$	−374.877	+	216.435i	−0.402229	+	0.232227i
$933$		0			0
$934$	−211.292	−	365.969i	−0.226223	−	0.391829i
$935$	−644.644	−	372.185i	−0.689458	−	0.398059i
$936$		0			0
$937$	1548.61			1.65274			0.826368	−	0.563131i	$-0.190403\pi$
$937$	1548.61			1.65274			0.826368	+	0.563131i	$0.190403\pi$
$938$	498.685	−	681.753i	0.531647	−	0.726816i
$939$		0			0
$940$	140.722	−	243.738i	0.149705	−	0.259296i
$941$		−	572.102i		−	0.607972i	−0.952677	−	0.303986i	$-0.901682\pi$
$941$		−	572.102i		−	0.607972i	0.952677	−	0.303986i	$-0.0983176\pi$
$942$		0			0
$943$	165.040			0.175016
$944$			165.832i			0.175670i
$945$		0			0
$946$	−2.98034			−0.00315047
$947$			959.484i			1.01318i	0.862186	+	0.506591i	$0.169095\pi$
$947$			959.484i			1.01318i	−0.862186	+	0.506591i	$0.830905\pi$
$948$		0			0
$949$	−147.366			−0.155285
$950$	583.765	+	337.037i	0.614490	+	0.354776i
$951$		0			0
$952$	−283.468	+	125.116i	−0.297761	+	0.131425i
$953$			1308.52i			1.37305i	0.727104	+	0.686527i	$0.240866\pi$
$953$			1308.52i			1.37305i	−0.727104	+	0.686527i	$0.759134\pi$
$954$		0			0
$955$	−432.669	+	749.405i	−0.453057	+	0.784717i
$956$	−774.149	+	446.955i	−0.809779	+	0.467526i
$957$		0			0
$958$	356.348	+	617.213i	0.371971	+	0.644273i
$959$	575.485	+	62.3600i	0.600089	+	0.0650261i
$960$		0			0
$961$	177.906			0.185126
$962$	−1303.41	−	752.522i	−1.35489	−	0.782247i
$963$		0			0
$964$	−82.7511	−	143.329i	−0.0858413	−	0.148682i
$965$	−463.331	−	267.504i	−0.480136	−	0.277207i
$966$		0			0
$967$	85.8474	+	148.692i	0.0887770	+	0.153766i	0.906994	−	0.421143i	$-0.138371\pi$
$967$	85.8474	+	148.692i	0.0887770	+	0.153766i	−0.818217	+	0.574909i	$0.805037\pi$
$968$	−196.759	−	113.599i	−0.203264	−	0.117354i
$969$		0			0
$970$	152.619	+	264.344i	0.157339	+	0.272519i
$971$	−803.642	+	463.983i	−0.827644	+	0.477840i	−0.853045	−	0.521837i	$-0.825247\pi$
$971$	−803.642	+	463.983i	−0.827644	+	0.477840i	0.0254013	+	0.999677i	$0.491914\pi$
$972$		0			0
$973$	−76.0950	+	702.238i	−0.0782066	+	0.721724i
$974$	358.693	+	207.092i	0.368268	+	0.212620i
$975$		0			0
$976$	63.9981			0.0655718
$977$		−	1422.61i		−	1.45610i	−0.685523	−	0.728051i	$-0.740426\pi$
$977$		−	1422.61i		−	1.45610i	0.685523	−	0.728051i	$-0.259574\pi$
$978$		0			0
$979$	−44.4893	+	77.0577i	−0.0454436	+	0.0787107i
$980$	−70.3696	+	320.888i	−0.0718057	+	0.327437i
$981$		0			0
$982$	302.473	+	523.898i	0.308017	+	0.533501i
$983$	244.614	−	141.228i	0.248844	−	0.143670i	−0.370391	−	0.928876i	$-0.620776\pi$
$983$	244.614	−	141.228i	0.248844	−	0.143670i	0.619235	+	0.785206i	$0.287443\pi$
$984$		0			0
$985$	291.299	−	504.545i	0.295735	−	0.512228i
$986$	−403.622	+	233.031i	−0.409353	+	0.236340i
$987$		0			0
$988$	−576.219	+	998.041i	−0.583218	+	1.01016i
$989$	−3.37825	+	1.95043i	−0.00341583	+	0.00197213i
$990$		0			0
$991$	587.805	−	1018.11i	0.593143	−	1.02735i	−0.400663	−	0.916226i	$-0.631220\pi$
$991$	587.805	−	1018.11i	0.593143	−	1.02735i	0.993806	−	0.111129i	$-0.0354465\pi$
$992$		−	190.906i		−	0.192445i
$993$		0			0
$994$	−450.941	−	329.852i	−0.453663	−	0.331843i
$995$	−280.484	+	161.938i	−0.281894	+	0.162751i
$996$		0			0
$997$	357.930	+	619.953i	0.359007	+	0.621818i	0.987795	−	0.155758i	$-0.0497821\pi$
$997$	357.930	+	619.953i	0.359007	+	0.621818i	−0.628788	+	0.777577i	$0.716449\pi$
$998$	−252.776	−	145.940i	−0.253283	−	0.146233i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	378.3.r.a.305.10		32
3.2	odd	2		126.3.r.a.11.1	yes	32
7.2	even	3		378.3.i.a.359.15		32
9.4	even	3		126.3.i.a.95.6	yes	32
9.5	odd	6		378.3.i.a.179.10		32
21.2	odd	6		126.3.i.a.65.6	✓	32
63.23	odd	6	inner	378.3.r.a.233.2		32
63.58	even	3		126.3.r.a.23.9	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.3.i.a.65.6	✓	32	21.2	odd	6
126.3.i.a.95.6	yes	32	9.4	even	3
126.3.r.a.11.1	yes	32	3.2	odd	2
126.3.r.a.23.9	yes	32	63.58	even	3
378.3.i.a.179.10		32	9.5	odd	6
378.3.i.a.359.15		32	7.2	even	3
378.3.r.a.233.2		32	63.23	odd	6	inner
378.3.r.a.305.10		32	1.1	even	1	trivial

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.r (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+1.41421i q^{2} -2.00000 q^{4} +(-2.90307 - 1.67609i) q^{5} +(5.64984 + 4.13271i) q^{7} -2.82843i q^{8} +(2.37035 - 4.10556i) q^{10} +(-12.2880 + 7.09448i) q^{11} +(-8.31908 - 14.4091i) q^{13} +(-5.84453 + 7.99008i) q^{14} +4.00000 q^{16} +(-13.5532 - 7.82495i) q^{17} +(17.3162 + 29.9925i) q^{19} +(5.80614 + 3.35218i) q^{20} +(-10.0331 - 17.3779i) q^{22} +(-22.7453 - 13.1320i) q^{23} +(-6.88146 - 11.9190i) q^{25} +(20.3775 - 11.7650i) q^{26} +(-11.2997 - 8.26542i) q^{28} +(-18.2368 - 10.5290i) q^{29} -33.7477 q^{31} +5.65685i q^{32} +(11.0662 - 19.1671i) q^{34} +(-9.47510 - 21.4672i) q^{35} +(-31.9815 - 55.3936i) q^{37} +(-42.4158 + 24.4888i) q^{38} +(-4.74069 + 8.21112i) q^{40} +(-5.44200 + 3.14194i) q^{41} +(0.0742627 - 0.128627i) q^{43} +(24.5760 - 14.1890i) q^{44} +(18.5715 - 32.1667i) q^{46} -41.9794i q^{47} +(14.8414 + 46.6983i) q^{49} +(16.8561 - 9.73185i) q^{50} +(16.6382 + 28.8182i) q^{52} +(38.6074 + 22.2900i) q^{53} +47.5639 q^{55} +(11.6891 - 15.9802i) q^{56} +(14.8903 - 25.7907i) q^{58} +41.4581i q^{59} +15.9995 q^{61} -47.7264i q^{62} -8.00000 q^{64} +55.7741i q^{65} -85.3249 q^{67} +(27.1064 + 15.6499i) q^{68} +(30.3592 - 13.3998i) q^{70} +56.4376i q^{71} +(4.42855 - 7.67047i) q^{73} +(78.3383 - 45.2287i) q^{74} +(-34.6324 - 59.9850i) q^{76} +(-98.7447 - 10.7001i) q^{77} +29.1408 q^{79} +(-11.6123 - 6.70435i) q^{80} +(-4.44338 - 7.69616i) q^{82} +(48.8531 + 28.2054i) q^{83} +(26.2306 + 45.4328i) q^{85} +(0.181906 + 0.105023i) q^{86} +(20.0662 + 34.7557i) q^{88} +(5.43082 - 3.13549i) q^{89} +(12.5470 - 115.789i) q^{91} +(45.4906 + 26.2640i) q^{92} +59.3679 q^{94} -116.094i q^{95} +(-32.1934 + 55.7605i) q^{97} +(-66.0414 + 20.9889i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 64 q^{4} + 2 q^{7} + 36 q^{11} + 10 q^{13} - 36 q^{14} + 128 q^{16} + 54 q^{17} + 28 q^{19} + 126 q^{23} + 80 q^{25} + 72 q^{26} - 4 q^{28} - 36 q^{29} + 16 q^{31} + 90 q^{35} + 22 q^{37} - 72 q^{41}+ \cdots - 288 q^{98}+O(q^{100}) \) 32 * q - 64 * q^4 + 2 * q^7 + 36 * q^11 + 10 * q^13 - 36 * q^14 + 128 * q^16 + 54 * q^17 + 28 * q^19 + 126 * q^23 + 80 * q^25 + 72 * q^26 - 4 * q^28 - 36 * q^29 + 16 * q^31 + 90 * q^35 + 22 * q^37 - 72 * q^41 + 16 * q^43 - 72 * q^44 - 12 * q^46 + 2 * q^49 + 288 * q^50 - 20 * q^52 + 72 * q^53 - 24 * q^55 + 72 * q^56 - 24 * q^58 + 124 * q^61 - 256 * q^64 - 140 * q^67 - 108 * q^68 + 72 * q^70 + 196 * q^73 - 216 * q^74 - 56 * q^76 - 486 * q^77 + 76 * q^79 + 60 * q^85 + 144 * q^86 + 486 * q^89 - 122 * q^91 - 252 * q^92 - 336 * q^94 - 38 * q^97 - 288 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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