LMFDB - Embedded newform 504.3.g.c.379.12

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [504,3,Mod(379,504)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("504.379"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(504, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1, 0, 0])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	504.g (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [24,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$13.7330053238$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			379.12
Character	$\chi$	$=$	504.379
Dual form			504.3.g.c.379.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.434362 + 1.95226i) q^{2} +(-3.62266 - 1.69598i) q^{4} +6.98187i q^{5} -2.64575i q^{7} +(4.88454 - 6.33572i) q^{8} +(-13.6304 - 3.03266i) q^{10} -10.2933 q^{11} -24.6510i q^{13} +(5.16520 + 1.14921i) q^{14} +(10.2473 + 12.2879i) q^{16} +3.19343 q^{17} -23.7405 q^{19} +(11.8411 - 25.2929i) q^{20} +(4.47101 - 20.0952i) q^{22} -4.46806i q^{23} -23.7465 q^{25} +(48.1253 + 10.7075i) q^{26} +(-4.48713 + 9.58466i) q^{28} -26.7443i q^{29} +30.9233i q^{31} +(-28.4402 + 14.6681i) q^{32} +(-1.38710 + 6.23441i) q^{34} +18.4723 q^{35} -39.9783i q^{37} +(10.3120 - 46.3477i) q^{38} +(44.2351 + 34.1032i) q^{40} +27.9614 q^{41} +36.0826 q^{43} +(37.2891 + 17.4572i) q^{44} +(8.72283 + 1.94076i) q^{46} -22.1841i q^{47} -7.00000 q^{49} +(10.3146 - 46.3594i) q^{50} +(-41.8075 + 89.3022i) q^{52} -90.1138i q^{53} -71.8664i q^{55} +(-16.7627 - 12.9233i) q^{56} +(52.2119 + 11.6167i) q^{58} +59.4672 q^{59} -85.5528i q^{61} +(-60.3705 - 13.4319i) q^{62} +(-16.2826 - 61.8941i) q^{64} +172.110 q^{65} -14.9028 q^{67} +(-11.5687 - 5.41598i) q^{68} +(-8.02365 + 36.0628i) q^{70} +91.2862i q^{71} -89.8637 q^{73} +(78.0481 + 17.3650i) q^{74} +(86.0037 + 40.2633i) q^{76} +27.2335i q^{77} -2.20766i q^{79} +(-85.7924 + 71.5455i) q^{80} +(-12.1453 + 54.5879i) q^{82} -141.857 q^{83} +22.2961i q^{85} +(-15.6729 + 70.4427i) q^{86} +(-50.2779 + 65.2154i) q^{88} -26.1571 q^{89} -65.2204 q^{91} +(-7.57773 + 16.1863i) q^{92} +(43.3092 + 9.63592i) q^{94} -165.753i q^{95} +121.525 q^{97} +(3.04053 - 13.6658i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 2 q^{4} + 12 q^{10} + 66 q^{16} - 64 q^{19} - 144 q^{22} - 168 q^{25} - 14 q^{28} + 12 q^{34} + 196 q^{40} + 224 q^{43} - 84 q^{46} - 168 q^{49} - 364 q^{52} + 348 q^{58} + 214 q^{64} - 32 q^{67}+ \cdots - 144 q^{97}+O(q^{100}) $ 24 * q - 2 * q^4 + 12 * q^10 + 66 * q^16 - 64 * q^19 - 144 * q^22 - 168 * q^25 - 14 * q^28 + 12 * q^34 + 196 * q^40 + 224 * q^43 - 84 * q^46 - 168 * q^49 - 364 * q^52 + 348 * q^58 + 214 * q^64 - 32 * q^67 - 84 * q^70 + 240 * q^73 + 416 * q^76 + 300 * q^82 - 120 * q^88 + 192 * q^94 - 144 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$1$	$-1$	$-1$	$1$

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 $

$2$	−0.434362	+	1.95226i	−0.217181	+	0.976131i
$2$	−0.434362	+	1.95226i	−0.217181	+	0.976131i
$3$		0			0
$3$		0			0
$4$	−3.62266	−	1.69598i	−0.905665	−	0.423994i
$5$			6.98187i			1.39637i	0.715916	+	0.698187i	$0.246010\pi$
$5$			6.98187i			1.39637i	−0.715916	+	0.698187i	$0.753990\pi$
$6$		0			0
$7$		−	2.64575i		−	0.377964i
$7$		−	2.64575i		−	0.377964i
$8$	4.88454	−	6.33572i	0.610567	−	0.791965i
$9$		0			0
$10$	−13.6304	−	3.03266i	−1.36304	−	0.303266i
$11$	−10.2933			−0.935753			−0.467877	−	0.883794i	$-0.654981\pi$
$11$	−10.2933			−0.935753			−0.467877	+	0.883794i	$0.654981\pi$
$12$		0			0
$13$		−	24.6510i		−	1.89623i	−0.317925	−	0.948116i	$-0.602986\pi$
$13$		−	24.6510i		−	1.89623i	0.317925	−	0.948116i	$-0.397014\pi$
$14$	5.16520	+	1.14921i	0.368943	+	0.0820866i
$15$		0			0
$16$	10.2473	+	12.2879i	0.640458	+	0.767993i
$17$	3.19343			0.187849			0.0939244	−	0.995579i	$-0.470059\pi$
$17$	3.19343			0.187849			0.0939244	+	0.995579i	$0.470059\pi$
$18$		0			0
$19$	−23.7405			−1.24950			−0.624750	−	0.780825i	$-0.714799\pi$
$19$	−23.7405			−1.24950			−0.624750	+	0.780825i	$0.714799\pi$
$20$	11.8411	−	25.2929i	0.592054	−	1.26465i
$21$		0			0
$22$	4.47101	−	20.0952i	0.203228	−	0.913418i
$23$		−	4.46806i		−	0.194264i	−0.995272	−	0.0971318i	$-0.969033\pi$
$23$		−	4.46806i		−	0.194264i	0.995272	−	0.0971318i	$-0.0309668\pi$
$24$		0			0
$25$	−23.7465			−0.949859
$26$	48.1253	+	10.7075i	1.85097	+	0.411825i
$27$		0			0
$28$	−4.48713	+	9.58466i	−0.160255	+	0.342309i
$29$		−	26.7443i		−	0.922217i	−0.887344	−	0.461109i	$-0.847452\pi$
$29$		−	26.7443i		−	0.922217i	0.887344	−	0.461109i	$-0.152548\pi$
$30$		0			0
$31$			30.9233i			0.997527i	0.866738	+	0.498763i	$0.166212\pi$
$31$			30.9233i			0.997527i	−0.866738	+	0.498763i	$0.833788\pi$
$32$	−28.4402	+	14.6681i	−0.888757	+	0.458378i
$33$		0			0
$34$	−1.38710	+	6.23441i	−0.0407972	+	0.183365i
$35$	18.4723			0.527780
$36$		0			0
$37$		−	39.9783i		−	1.08049i	−0.841506	−	0.540247i	$-0.818331\pi$
$37$		−	39.9783i		−	1.08049i	0.841506	−	0.540247i	$-0.181669\pi$
$38$	10.3120	−	46.3477i	0.271367	−	1.21968i
$39$		0			0
$40$	44.2351	+	34.1032i	1.10588	+	0.852580i
$41$	27.9614			0.681984			0.340992	−	0.940066i	$-0.389237\pi$
$41$	27.9614			0.681984			0.340992	+	0.940066i	$0.389237\pi$
$42$		0			0
$43$	36.0826			0.839130			0.419565	−	0.907725i	$-0.362183\pi$
$43$	36.0826			0.839130			0.419565	+	0.907725i	$0.362183\pi$
$44$	37.2891	+	17.4572i	0.847479	+	0.396754i
$45$		0			0
$46$	8.72283	+	1.94076i	0.189627	+	0.0421903i
$47$		−	22.1841i		−	0.472002i	−0.971753	−	0.236001i	$-0.924163\pi$
$47$		−	22.1841i		−	0.472002i	0.971753	−	0.236001i	$-0.0758369\pi$
$48$		0			0
$49$	−7.00000			−0.142857
$50$	10.3146	−	46.3594i	0.206291	−	0.927188i
$51$		0			0
$52$	−41.8075	+	89.3022i	−0.803991	+	1.71735i
$53$		−	90.1138i		−	1.70026i	−0.526572	−	0.850130i	$-0.676523\pi$
$53$		−	90.1138i		−	1.70026i	0.526572	−	0.850130i	$-0.323477\pi$
$54$		0			0
$55$		−	71.8664i		−	1.30666i
$56$	−16.7627	−	12.9233i	−0.299335	−	0.230773i
$57$		0			0
$58$	52.2119	+	11.6167i	0.900205	+	0.200288i
$59$	59.4672			1.00792			0.503959	−	0.863728i	$-0.331876\pi$
$59$	59.4672			1.00792			0.503959	+	0.863728i	$0.331876\pi$
$60$		0			0
$61$		−	85.5528i		−	1.40250i	−0.712913	−	0.701252i	$-0.752625\pi$
$61$		−	85.5528i		−	1.40250i	0.712913	−	0.701252i	$-0.247375\pi$
$62$	−60.3705	−	13.4319i	−0.973717	−	0.216644i
$63$		0			0
$64$	−16.2826	−	61.8941i	−0.254416	−	0.967095i
$65$	172.110			2.64785
$66$		0			0
$67$	−14.9028			−0.222429			−0.111215	−	0.993796i	$-0.535474\pi$
$67$	−14.9028			−0.222429			−0.111215	+	0.993796i	$0.535474\pi$
$68$	−11.5687	−	5.41598i	−0.170128	−	0.0796468i
$69$		0			0
$70$	−8.02365	+	36.0628i	−0.114624	+	0.515182i
$71$			91.2862i			1.28572i	0.765983	+	0.642860i	$0.222252\pi$
$71$			91.2862i			1.28572i	−0.765983	+	0.642860i	$0.777748\pi$
$72$		0			0
$73$	−89.8637			−1.23101			−0.615505	−	0.788133i	$-0.711048\pi$
$73$	−89.8637			−1.23101			−0.615505	+	0.788133i	$0.711048\pi$
$74$	78.0481	+	17.3650i	1.05470	+	0.234663i
$75$		0			0
$76$	86.0037	+	40.2633i	1.13163	+	0.529780i
$77$			27.2335i			0.353682i
$78$		0			0
$79$		−	2.20766i		−	0.0279451i	−0.999902	−	0.0139725i	$-0.995552\pi$
$79$		−	2.20766i		−	0.0279451i	0.999902	−	0.0139725i	$-0.00444774\pi$
$80$	−85.7924	+	71.5455i	−1.07241	+	0.894319i
$81$		0			0
$82$	−12.1453	+	54.5879i	−0.148114	+	0.665706i
$83$	−141.857			−1.70913			−0.854563	−	0.519348i	$-0.826175\pi$
$83$	−141.857			−1.70913			−0.854563	+	0.519348i	$0.826175\pi$
$84$		0			0
$85$			22.2961i			0.262307i
$86$	−15.6729	+	70.4427i	−0.182243	+	0.819101i
$87$		0			0
$88$	−50.2779	+	65.2154i	−0.571340	+	0.741084i
$89$	−26.1571			−0.293900			−0.146950	−	0.989144i	$-0.546946\pi$
$89$	−26.1571			−0.293900			−0.146950	+	0.989144i	$0.546946\pi$
$90$		0			0
$91$	−65.2204			−0.716708
$92$	−7.57773	+	16.1863i	−0.0823666	+	0.175938i
$93$		0			0
$94$	43.3092	+	9.63592i	0.460736	+	0.102510i
$95$		−	165.753i		−	1.74477i
$96$		0			0
$97$	121.525			1.25284			0.626418	−	0.779487i	$-0.284520\pi$
$97$	121.525			1.25284			0.626418	+	0.779487i	$0.284520\pi$
$98$	3.04053	−	13.6658i	0.0310258	−	0.139447i
$99$		0			0
$100$	86.0254	+	40.2735i	0.860254	+	0.402735i
$101$			130.469i			1.29177i	0.763433	+	0.645887i	$0.223512\pi$
$101$			130.469i			1.29177i	−0.763433	+	0.645887i	$0.776488\pi$
$102$		0			0
$103$		−	78.8527i		−	0.765561i	−0.923839	−	0.382780i	$-0.874967\pi$
$103$		−	78.8527i		−	0.765561i	0.923839	−	0.382780i	$-0.125033\pi$
$104$	−156.182	−	120.409i	−1.50175	−	1.15778i
$105$		0			0
$106$	175.926	+	39.1420i	1.65968	+	0.369264i
$107$	−202.725			−1.89462			−0.947312	−	0.320313i	$-0.896212\pi$
$107$	−202.725			−1.89462			−0.947312	+	0.320313i	$0.896212\pi$
$108$		0			0
$109$			60.6394i			0.556325i	0.960534	+	0.278162i	$0.0897253\pi$
$109$			60.6394i			0.556325i	−0.960534	+	0.278162i	$0.910275\pi$
$110$	140.302	+	31.2160i	1.27547	+	0.283782i
$111$		0			0
$112$	32.5107	−	27.1119i	0.290274	−	0.242070i
$113$	134.568			1.19087			0.595433	−	0.803405i	$-0.296981\pi$
$113$	134.568			1.19087			0.595433	+	0.803405i	$0.296981\pi$
$114$		0			0
$115$	31.1954			0.271265
$116$	−45.3577	+	96.8855i	−0.391014	+	0.835220i
$117$		0			0
$118$	−25.8303	+	116.096i	−0.218900	+	0.983861i
$119$		−	8.44902i		−	0.0710002i
$120$		0			0
$121$	−15.0482			−0.124366
$122$	167.022	+	37.1609i	1.36903	+	0.304597i
$123$		0			0
$124$	52.4452	−	112.025i	0.422945	−	0.903425i
$125$			8.75187i			0.0700149i
$126$		0			0
$127$		−	234.380i		−	1.84551i	−0.385381	−	0.922757i	$-0.625930\pi$
$127$		−	234.380i		−	1.84551i	0.385381	−	0.922757i	$-0.374070\pi$
$128$	127.906	−	4.90357i	0.999266	−	0.0383091i
$129$		0			0
$130$	−74.7580	+	336.004i	−0.575062	+	2.58465i
$131$	−9.52941			−0.0727436			−0.0363718	−	0.999338i	$-0.511580\pi$
$131$	−9.52941			−0.0727436			−0.0363718	+	0.999338i	$0.511580\pi$
$132$		0			0
$133$			62.8114i			0.472266i
$134$	6.47319	−	29.0941i	0.0483074	−	0.217120i
$135$		0			0
$136$	15.5984	−	20.2327i	0.114694	−	0.148770i
$137$	−150.790			−1.10066			−0.550330	−	0.834947i	$-0.685498\pi$
$137$	−150.790			−1.10066			−0.550330	+	0.834947i	$0.685498\pi$
$138$		0			0
$139$	−29.9967			−0.215804			−0.107902	−	0.994162i	$-0.534413\pi$
$139$	−29.9967			−0.215804			−0.107902	+	0.994162i	$0.534413\pi$
$140$	−66.9188	−	31.3286i	−0.477992	−	0.223775i
$141$		0			0
$142$	−178.215	−	39.6512i	−1.25503	−	0.279234i
$143$			253.740i			1.77441i
$144$		0			0
$145$	186.725			1.28776
$146$	39.0333	−	175.438i	0.267352	−	1.20163i
$147$		0			0
$148$	−67.8022	+	144.828i	−0.458123	+	0.978566i
$149$			6.87752i			0.0461578i	0.999734	+	0.0230789i	$0.00734690\pi$
$149$			6.87752i			0.0461578i	−0.999734	+	0.0230789i	$0.992653\pi$
$150$		0			0
$151$		−	91.6177i		−	0.606740i	−0.952873	−	0.303370i	$-0.901888\pi$
$151$		−	91.6177i		−	0.606740i	0.952873	−	0.303370i	$-0.0981117\pi$
$152$	−115.961	+	150.413i	−0.762903	+	0.989559i
$153$		0			0
$154$	−53.1669	−	11.8292i	−0.345240	−	0.0768128i
$155$	−215.903			−1.39292
$156$		0			0
$157$		−	162.359i		−	1.03413i	−0.855946	−	0.517066i	$-0.827024\pi$
$157$		−	162.359i		−	1.03413i	0.855946	−	0.517066i	$-0.172976\pi$
$158$	4.30994	+	0.958924i	0.0272781	+	0.00606914i
$159$		0			0
$160$	−102.411	−	198.566i	−0.640067	−	1.24104i
$161$	−11.8214			−0.0734247
$162$		0			0
$163$	−293.979			−1.80355			−0.901776	−	0.432203i	$-0.857736\pi$
$163$	−293.979			−1.80355			−0.901776	+	0.432203i	$0.857736\pi$
$164$	−101.295	−	47.4218i	−0.617649	−	0.289157i
$165$		0			0
$166$	61.6174	−	276.943i	0.371189	−	1.66833i
$167$			126.717i			0.758787i	0.925235	+	0.379393i	$0.123867\pi$
$167$			126.717i			0.758787i	−0.925235	+	0.379393i	$0.876133\pi$
$168$		0			0
$169$	−438.672			−2.59569
$170$	−43.5279	−	9.68457i	−0.256046	−	0.0569681i
$171$		0			0
$172$	−130.715	−	61.1952i	−0.759971	−	0.355786i
$173$		−	188.667i		−	1.09056i	−0.838254	−	0.545281i	$-0.816423\pi$
$173$		−	188.667i		−	1.09056i	0.838254	−	0.545281i	$-0.183577\pi$
$174$		0			0
$175$			62.8273i			0.359013i
$176$	−105.479	−	126.483i	−0.599311	−	0.718652i
$177$		0			0
$178$	11.3616	−	51.0655i	0.0638294	−	0.286885i
$179$	−333.961			−1.86570			−0.932852	−	0.360259i	$-0.882688\pi$
$179$	−333.961			−1.86570			−0.932852	+	0.360259i	$0.882688\pi$
$180$		0			0
$181$		−	37.7402i		−	0.208509i	−0.994551	−	0.104255i	$-0.966754\pi$
$181$		−	37.7402i		−	0.208509i	0.994551	−	0.104255i	$-0.0332457\pi$
$182$	28.3293	−	127.327i	0.155655	−	0.699601i
$183$		0			0
$184$	−28.3084	−	21.8244i	−0.153850	−	0.118611i
$185$	279.123			1.50877
$186$		0			0
$187$	−32.8709			−0.175780
$188$	−37.6237	+	80.3655i	−0.200126	+	0.427476i
$189$		0			0
$190$	323.593	+	71.9967i	1.70312	+	0.378930i
$191$			161.558i			0.845853i	0.906164	+	0.422927i	$0.138997\pi$
$191$			161.558i			0.845853i	−0.906164	+	0.422927i	$0.861003\pi$
$192$		0			0
$193$	−40.4535			−0.209604			−0.104802	−	0.994493i	$-0.533421\pi$
$193$	−40.4535			−0.209604			−0.104802	+	0.994493i	$0.533421\pi$
$194$	−52.7858	+	237.249i	−0.272092	+	1.22293i
$195$		0			0
$196$	25.3586	+	11.8718i	0.129381	+	0.0605706i
$197$		−	38.7796i		−	0.196851i	−0.995144	−	0.0984253i	$-0.968619\pi$
$197$		−	38.7796i		−	0.196851i	0.995144	−	0.0984253i	$-0.0313806\pi$
$198$		0			0
$199$		−	66.2660i		−	0.332995i	−0.986042	−	0.166497i	$-0.946754\pi$
$199$		−	66.2660i		−	0.332995i	0.986042	−	0.166497i	$-0.0532458\pi$
$200$	−115.991	+	150.451i	−0.579953	+	0.752255i
$201$		0			0
$202$	−254.710	−	56.6708i	−1.26094	−	0.280548i
$203$	−70.7588			−0.348565
$204$		0			0
$205$			195.223i			0.952305i
$206$	153.941	+	34.2506i	0.747288	+	0.166265i
$207$		0			0
$208$	302.909	−	252.607i	1.45629	−	1.21446i
$209$	244.368			1.16922
$210$		0			0
$211$	327.671			1.55294			0.776472	−	0.630151i	$-0.217007\pi$
$211$	327.671			1.55294			0.776472	+	0.630151i	$0.217007\pi$
$212$	−152.831	+	326.452i	−0.720900	+	1.53987i
$213$		0			0
$214$	88.0558	−	395.772i	0.411476	−	1.84940i
$215$			251.924i			1.17174i
$216$		0			0
$217$	81.8155			0.377030
$218$	−118.384	−	26.3394i	−0.543046	−	0.120823i
$219$		0			0
$220$	−121.884	+	260.347i	−0.554017	+	1.18340i
$221$		−	78.7213i		−	0.356205i
$222$		0			0
$223$			42.2322i			0.189382i	0.995507	+	0.0946911i	$0.0301863\pi$
$223$			42.2322i			0.189382i	−0.995507	+	0.0946911i	$0.969814\pi$
$224$	38.8081	+	75.2458i	0.173251	+	0.335919i
$225$		0			0
$226$	−58.4511	+	262.712i	−0.258633	+	1.16244i
$227$	−39.0565			−0.172055			−0.0860275	−	0.996293i	$-0.527417\pi$
$227$	−39.0565			−0.172055			−0.0860275	+	0.996293i	$0.527417\pi$
$228$		0			0
$229$		−	88.1788i		−	0.385060i	−0.981291	−	0.192530i	$-0.938331\pi$
$229$		−	88.1788i		−	0.385060i	0.981291	−	0.192530i	$-0.0616693\pi$
$230$	−13.5501	+	60.9017i	−0.0589135	+	0.264790i
$231$		0			0
$232$	−169.444	−	130.633i	−0.730363	−	0.563075i
$233$	−14.4269			−0.0619180			−0.0309590	−	0.999521i	$-0.509856\pi$
$233$	−14.4269			−0.0619180			−0.0309590	+	0.999521i	$0.509856\pi$
$234$		0			0
$235$	154.886			0.659091
$236$	−215.429	−	100.855i	−0.912836	−	0.427351i
$237$		0			0
$238$	16.4947	+	3.66993i	0.0693055	+	0.0154199i
$239$		−	396.571i		−	1.65929i	−0.558289	−	0.829646i	$-0.688542\pi$
$239$		−	396.571i		−	1.65929i	0.558289	−	0.829646i	$-0.311458\pi$
$240$		0			0
$241$	−40.8615			−0.169550			−0.0847748	−	0.996400i	$-0.527017\pi$
$241$	−40.8615			−0.169550			−0.0847748	+	0.996400i	$0.527017\pi$
$242$	6.53637	−	29.3781i	0.0270098	−	0.121397i
$243$		0			0
$244$	−145.095	+	309.929i	−0.594654	+	1.27020i
$245$		−	48.8731i		−	0.199482i
$246$		0			0
$247$			585.227i			2.36934i
$248$	195.922	+	151.046i	0.790006	+	0.609057i
$249$		0			0
$250$	−17.0859	−	3.80147i	−0.0683438	−	0.0152059i
$251$	53.2343			0.212089			0.106044	−	0.994361i	$-0.466181\pi$
$251$	53.2343			0.212089			0.106044	+	0.994361i	$0.466181\pi$
$252$		0			0
$253$			45.9911i			0.181783i
$254$	457.572	+	101.806i	1.80147	+	0.400810i
$255$		0			0
$256$	−45.9844	+	251.836i	−0.179627	+	0.983735i
$257$	327.553			1.27452			0.637262	−	0.770647i	$-0.280067\pi$
$257$	327.553			1.27452			0.637262	+	0.770647i	$0.280067\pi$
$258$		0			0
$259$	−105.773			−0.408389
$260$	−623.496	−	291.895i	−2.39806	−	1.12267i
$261$		0			0
$262$	4.13921	−	18.6039i	0.0157985	−	0.0710073i
$263$		−	230.794i		−	0.877542i	−0.898599	−	0.438771i	$-0.855414\pi$
$263$		−	230.794i		−	0.877542i	0.898599	−	0.438771i	$-0.144586\pi$
$264$		0			0
$265$	629.163			2.37420
$266$	−122.624	−	27.2829i	−0.460994	−	0.102567i
$267$		0			0
$268$	53.9876	+	25.2747i	0.201446	+	0.0943086i
$269$			383.152i			1.42436i	0.701998	+	0.712179i	$0.252292\pi$
$269$			383.152i			1.42436i	−0.701998	+	0.712179i	$0.747708\pi$
$270$		0			0
$271$			187.455i			0.691715i	0.938287	+	0.345858i	$0.112412\pi$
$271$			187.455i			0.691715i	−0.938287	+	0.345858i	$0.887588\pi$
$272$	32.7241	+	39.2405i	0.120309	+	0.144267i
$273$		0			0
$274$	65.4976	−	294.383i	0.239042	−	1.07439i
$275$	244.429			0.888834
$276$		0			0
$277$		−	5.90998i		−	0.0213357i	−0.999943	−	0.0106678i	$-0.996604\pi$
$277$		−	5.90998i		−	0.0213357i	0.999943	−	0.0106678i	$-0.00339574\pi$
$278$	13.0294	−	58.5615i	0.0468685	−	0.210653i
$279$		0			0
$280$	90.2285	−	117.035i	0.322245	−	0.417983i
$281$	−327.587			−1.16579			−0.582896	−	0.812547i	$-0.698080\pi$
$281$	−327.587			−1.16579			−0.582896	+	0.812547i	$0.698080\pi$
$282$		0			0
$283$	532.270			1.88081			0.940406	−	0.340055i	$-0.110446\pi$
$283$	532.270			1.88081			0.940406	+	0.340055i	$0.110446\pi$
$284$	154.819	−	330.699i	0.545138	−	1.16443i
$285$		0			0
$286$	−495.367	−	110.215i	−1.73205	−	0.385367i
$287$		−	73.9788i		−	0.257766i
$288$		0			0
$289$	−278.802			−0.964713
$290$	−81.1062	+	364.537i	−0.279677	+	1.25702i
$291$		0			0
$292$	325.546	+	152.407i	1.11488	+	0.521941i
$293$		−	272.256i		−	0.929201i	−0.885520	−	0.464601i	$-0.846198\pi$
$293$		−	272.256i		−	0.929201i	0.885520	−	0.464601i	$-0.153802\pi$
$294$		0			0
$295$			415.192i			1.40743i
$296$	−253.291	−	195.275i	−0.855714	−	0.659714i
$297$		0			0
$298$	−13.4267	−	2.98733i	−0.0450561	−	0.0100246i
$299$	−110.142			−0.368369
$300$		0			0
$301$		−	95.4656i		−	0.317161i
$302$	178.862	+	39.7952i	0.592258	+	0.131772i
$303$		0			0
$304$	−243.277	−	291.720i	−0.800252	−	0.959607i
$305$	597.318			1.95842
$306$		0			0
$307$	223.209			0.727067			0.363533	−	0.931581i	$-0.381570\pi$
$307$	223.209			0.727067			0.363533	+	0.931581i	$0.381570\pi$
$308$	46.1873	−	98.6576i	0.149959	−	0.320317i
$309$		0			0
$310$	93.7798	−	421.499i	0.302516	−	1.35967i
$311$			20.4156i			0.0656451i	0.999461	+	0.0328226i	$0.0104496\pi$
$311$			20.4156i			0.0656451i	−0.999461	+	0.0328226i	$0.989550\pi$
$312$		0			0
$313$	332.605			1.06264			0.531318	−	0.847172i	$-0.321697\pi$
$313$	332.605			1.06264			0.531318	+	0.847172i	$0.321697\pi$
$314$	316.967	+	70.5224i	1.00945	+	0.224594i
$315$		0			0
$316$	−3.74414	+	7.99761i	−0.0118486	+	0.0253089i
$317$			327.477i			1.03305i	0.856272	+	0.516525i	$0.172775\pi$
$317$			327.477i			1.03305i	−0.856272	+	0.516525i	$0.827225\pi$
$318$		0			0
$319$			275.287i			0.862968i
$320$	432.136	−	113.683i	1.35043	−	0.355260i
$321$		0			0
$322$	5.13476	−	23.0784i	0.0159464	−	0.0716722i
$323$	−75.8136			−0.234717
$324$		0			0
$325$			585.375i			1.80115i
$326$	127.693	−	573.924i	0.391697	−	1.76050i
$327$		0			0
$328$	136.578	−	177.155i	0.416397	−	0.540108i
$329$	−58.6936			−0.178400
$330$		0			0
$331$	−320.023			−0.966836			−0.483418	−	0.875390i	$-0.660605\pi$
$331$	−320.023			−0.966836			−0.483418	+	0.875390i	$0.660605\pi$
$332$	513.901	+	240.587i	1.54790	+	0.724659i
$333$		0			0
$334$	−247.386	−	55.0412i	−0.740676	−	0.164794i
$335$		−	104.049i		−	0.310594i
$336$		0			0
$337$	−223.478			−0.663141			−0.331570	−	0.943431i	$-0.607578\pi$
$337$	−223.478			−0.663141			−0.331570	+	0.943431i	$0.607578\pi$
$338$	190.542	−	856.404i	0.563735	−	2.53374i
$339$		0			0
$340$	37.8137	−	80.7712i	0.111217	−	0.237562i
$341$		−	318.303i		−	0.933439i
$342$		0			0
$343$			18.5203i			0.0539949i
$344$	176.247	−	228.609i	0.512345	−	0.664562i
$345$		0			0
$346$	368.328	+	81.9497i	1.06453	+	0.236849i
$347$	−56.6497			−0.163256			−0.0816278	−	0.996663i	$-0.526012\pi$
$347$	−56.6497			−0.163256			−0.0816278	+	0.996663i	$0.526012\pi$
$348$		0			0
$349$		−	466.731i		−	1.33734i	−0.743560	−	0.668669i	$-0.766864\pi$
$349$		−	466.731i		−	1.33734i	0.743560	−	0.668669i	$-0.233136\pi$
$350$	−122.655	−	27.2898i	−0.350444	−	0.0779708i
$351$		0			0
$352$	292.744	−	150.983i	0.831658	−	0.428929i
$353$	594.614			1.68446			0.842230	−	0.539118i	$-0.181242\pi$
$353$	594.614			1.68446			0.842230	+	0.539118i	$0.181242\pi$
$354$		0			0
$355$	−637.348			−1.79535
$356$	94.7582	+	44.3618i	0.266175	+	0.124612i
$357$		0			0
$358$	145.060	−	651.980i	0.405195	−	1.82117i
$359$		−	453.751i		−	1.26393i	−0.774997	−	0.631965i	$-0.782248\pi$
$359$		−	453.751i		−	1.26393i	0.774997	−	0.631965i	$-0.217752\pi$
$360$		0			0
$361$	202.611			0.561248
$362$	73.6787	+	16.3929i	0.203532	+	0.0452842i
$363$		0			0
$364$	236.272	+	110.612i	0.649098	+	0.303880i
$365$		−	627.416i		−	1.71895i
$366$		0			0
$367$			213.287i			0.581165i	0.956850	+	0.290582i	$0.0938490\pi$
$367$			213.287i			0.581165i	−0.956850	+	0.290582i	$0.906151\pi$
$368$	54.9031	−	45.7857i	0.149193	−	0.124418i
$369$		0			0
$370$	−121.240	+	544.922i	−0.327677	+	1.47276i
$371$	−238.419			−0.642638
$372$		0			0
$373$			266.533i			0.714566i	0.933996	+	0.357283i	$0.116297\pi$
$373$			266.533i			0.714566i	−0.933996	+	0.357283i	$0.883703\pi$
$374$	14.2779	−	64.1726i	0.0381761	−	0.171585i
$375$		0			0
$376$	−140.552	−	108.359i	−0.373809	−	0.288189i
$377$	−659.274			−1.74874
$378$		0			0
$379$	79.5559			0.209910			0.104955	−	0.994477i	$-0.466530\pi$
$379$	79.5559			0.209910			0.104955	+	0.994477i	$0.466530\pi$
$380$	−281.113	+	600.467i	−0.739771	+	1.58018i
$381$		0			0
$382$	−315.404	−	70.1746i	−0.825664	−	0.183703i
$383$			628.831i			1.64186i	0.571032	+	0.820928i	$0.306543\pi$
$383$			628.831i			1.64186i	−0.571032	+	0.820928i	$0.693457\pi$
$384$		0			0
$385$	−190.141			−0.493872
$386$	17.5715	−	78.9759i	0.0455219	−	0.204601i
$387$		0			0
$388$	−440.244	−	206.104i	−1.13465	−	0.531195i
$389$			389.345i			1.00089i	0.865769	+	0.500443i	$0.166830\pi$
$389$			389.345i			1.00089i	−0.865769	+	0.500443i	$0.833170\pi$
$390$		0			0
$391$		−	14.2684i		−	0.0364922i
$392$	−34.1917	+	44.3500i	−0.0872238	+	0.113138i
$393$		0			0
$394$	75.7079	+	16.8444i	0.192152	+	0.0427522i
$395$	15.4136			0.0390218
$396$		0			0
$397$			288.463i			0.726608i	0.931671	+	0.363304i	$0.118351\pi$
$397$			288.463i			0.726608i	−0.931671	+	0.363304i	$0.881649\pi$
$398$	129.369	+	28.7834i	0.325047	+	0.0723201i
$399$		0			0
$400$	−243.338	−	291.794i	−0.608345	−	0.729485i
$401$	−326.512			−0.814246			−0.407123	−	0.913373i	$-0.633468\pi$
$401$	−326.512			−0.814246			−0.407123	+	0.913373i	$0.633468\pi$
$402$		0			0
$403$	762.292			1.89154
$404$	221.273	−	472.645i	0.547704	−	1.16991i
$405$		0			0
$406$	30.7349	−	138.140i	0.0757017	−	0.340246i
$407$			411.508i			1.01108i
$408$		0			0
$409$	48.4391			0.118433			0.0592166	−	0.998245i	$-0.481140\pi$
$409$	48.4391			0.118433			0.0592166	+	0.998245i	$0.481140\pi$
$410$	−381.126	−	84.7972i	−0.929575	−	0.206822i
$411$		0			0
$412$	−133.732	+	285.657i	−0.324593	+	0.693341i
$413$		−	157.335i		−	0.380957i
$414$		0			0
$415$		−	990.430i		−	2.38658i
$416$	361.583	+	701.081i	0.869191	+	1.68529i
$417$		0			0
$418$	−106.144	+	477.070i	−0.253933	+	1.14132i
$419$	389.884			0.930512			0.465256	−	0.885176i	$-0.345962\pi$
$419$	389.884			0.930512			0.465256	+	0.885176i	$0.345962\pi$
$420$		0			0
$421$			704.810i			1.67413i	0.547101	+	0.837066i	$0.315731\pi$
$421$			704.810i			1.67413i	−0.547101	+	0.837066i	$0.684269\pi$
$422$	−142.328	+	639.701i	−0.337270	+	1.51588i
$423$		0			0
$424$	−570.936	−	440.164i	−1.34655	−	1.03812i
$425$	−75.8327			−0.178430
$426$		0			0
$427$	−226.351			−0.530097
$428$	734.403	+	343.816i	1.71589	+	0.803309i
$429$		0			0
$430$	−491.822	−	109.426i	−1.14377	−	0.254479i
$431$			255.485i			0.592772i	0.955068	+	0.296386i	$0.0957815\pi$
$431$			255.485i			0.592772i	−0.955068	+	0.296386i	$0.904219\pi$
$432$		0			0
$433$	347.438			0.802397			0.401199	−	0.915991i	$-0.368594\pi$
$433$	347.438			0.802397			0.401199	+	0.915991i	$0.368594\pi$
$434$	−35.5375	+	159.725i	−0.0818836	+	0.368031i
$435$		0			0
$436$	102.843	−	219.676i	0.235878	−	0.503844i
$437$			106.074i			0.242732i
$438$		0			0
$439$			28.2038i			0.0642456i	0.999484	+	0.0321228i	$0.0102268\pi$
$439$			28.2038i			0.0642456i	−0.999484	+	0.0321228i	$0.989773\pi$
$440$	−455.325	−	351.034i	−1.03483	−	0.797804i
$441$		0			0
$442$	153.685	+	34.1935i	0.347703	+	0.0773608i
$443$	742.964			1.67712			0.838560	−	0.544809i	$-0.183398\pi$
$443$	742.964			1.67712			0.838560	+	0.544809i	$0.183398\pi$
$444$		0			0
$445$		−	182.625i		−	0.410394i
$446$	−82.4484	−	18.3441i	−0.184862	−	0.0411302i
$447$		0			0
$448$	−163.756	+	43.0798i	−0.365527	+	0.0961602i
$449$	−210.406			−0.468609			−0.234305	−	0.972163i	$-0.575281\pi$
$449$	−210.406			−0.468609			−0.234305	+	0.972163i	$0.575281\pi$
$450$		0			0
$451$	−287.814			−0.638169
$452$	−487.493	−	228.224i	−1.07853	−	0.504920i
$453$		0			0
$454$	16.9646	−	76.2485i	0.0373670	−	0.167948i
$455$		−	455.361i		−	1.00079i
$456$		0			0
$457$	481.714			1.05408			0.527040	−	0.849841i	$-0.323302\pi$
$457$	481.714			1.05408			0.527040	+	0.849841i	$0.323302\pi$
$458$	172.148	+	38.3015i	0.375869	+	0.0836277i
$459$		0			0
$460$	−113.010	−	52.9067i	−0.245675	−	0.115015i
$461$		−	338.772i		−	0.734862i	−0.930051	−	0.367431i	$-0.880237\pi$
$461$		−	338.772i		−	0.734862i	0.930051	−	0.367431i	$-0.119763\pi$
$462$		0			0
$463$			399.738i			0.863366i	0.902025	+	0.431683i	$0.142080\pi$
$463$			399.738i			0.863366i	−0.902025	+	0.431683i	$0.857920\pi$
$464$	328.631	−	274.058i	0.708256	−	0.590641i
$465$		0			0
$466$	6.26649	−	28.1651i	0.0134474	−	0.0604401i
$467$	−36.9575			−0.0791381			−0.0395690	−	0.999217i	$-0.512599\pi$
$467$	−36.9575			−0.0791381			−0.0395690	+	0.999217i	$0.512599\pi$
$468$		0			0
$469$			39.4290i			0.0840703i
$470$	−67.2767	+	302.379i	−0.143142	+	0.643360i
$471$		0			0
$472$	290.470	−	376.767i	0.615401	−	0.798236i
$473$	−371.409			−0.785219
$474$		0			0
$475$	563.753			1.18685
$476$	−14.3293	+	30.6079i	−0.0301036	+	0.0643024i
$477$		0			0
$478$	774.211	+	172.255i	1.61969	+	0.360367i
$479$		−	357.037i		−	0.745380i	−0.927956	−	0.372690i	$-0.878435\pi$
$479$		−	357.037i		−	0.745380i	0.927956	−	0.372690i	$-0.121565\pi$
$480$		0			0
$481$	−985.506			−2.04887
$482$	17.7486	−	79.7723i	0.0368229	−	0.165503i
$483$		0			0
$484$	54.5146	+	25.5214i	0.112634	+	0.0527302i
$485$			848.472i			1.74943i
$486$		0			0
$487$		−	511.946i		−	1.05122i	−0.850725	−	0.525612i	$-0.823837\pi$
$487$		−	511.946i		−	1.05122i	0.850725	−	0.525612i	$-0.176163\pi$
$488$	−542.038	−	417.886i	−1.11073	−	0.856323i
$489$		0			0
$490$	95.4131	+	21.2286i	0.194721	+	0.0433237i
$491$	280.026			0.570317			0.285158	−	0.958480i	$-0.407954\pi$
$491$	280.026			0.570317			0.285158	+	0.958480i	$0.407954\pi$
$492$		0			0
$493$		−	85.4060i		−	0.173237i
$494$	−1142.52	−	254.200i	−2.31279	−	0.514575i
$495$		0			0
$496$	−379.983	+	316.882i	−0.766094	+	0.638874i
$497$	241.520			0.485957
$498$		0			0
$499$	29.8727			0.0598651			0.0299326	−	0.999552i	$-0.490471\pi$
$499$	29.8727			0.0598651			0.0299326	+	0.999552i	$0.490471\pi$
$500$	14.8430	−	31.7050i	0.0296859	−	0.0634101i
$501$		0			0
$502$	−23.1229	+	103.927i	−0.0460616	+	0.207027i
$503$		−	756.842i		−	1.50466i	−0.658789	−	0.752328i	$-0.728931\pi$
$503$		−	756.842i		−	1.50466i	0.658789	−	0.752328i	$-0.271069\pi$
$504$		0			0
$505$	−910.919			−1.80380
$506$	−89.7866	−	19.9768i	−0.177444	−	0.0394797i
$507$		0			0
$508$	−397.504	+	849.081i	−0.782487	+	1.67142i
$509$			261.461i			0.513676i	0.966454	+	0.256838i	$0.0826808\pi$
$509$			261.461i			0.513676i	−0.966454	+	0.256838i	$0.917319\pi$
$510$		0			0
$511$			237.757i			0.465278i
$512$	−471.676	−	199.162i	−0.921243	−	0.388988i
$513$		0			0
$514$	−142.276	+	639.469i	−0.276802	+	1.24410i
$515$	550.539			1.06901
$516$		0			0
$517$			228.347i			0.441678i
$518$	45.9436	−	206.496i	0.0886942	−	0.398641i
$519$		0			0
$520$	840.678	−	1090.44i	1.61669	−	2.09700i
$521$	−178.719			−0.343030			−0.171515	−	0.985182i	$-0.554866\pi$
$521$	−178.719			−0.343030			−0.171515	+	0.985182i	$0.554866\pi$
$522$		0			0
$523$	−432.390			−0.826749			−0.413375	−	0.910561i	$-0.635650\pi$
$523$	−432.390			−0.826749			−0.413375	+	0.910561i	$0.635650\pi$
$524$	34.5218	+	16.1617i	0.0658813	+	0.0308428i
$525$		0			0
$526$	450.570	+	100.248i	0.856597	+	0.190585i
$527$			98.7515i			0.187384i
$528$		0			0
$529$	509.036			0.962262
$530$	−273.284	+	1228.29i	−0.515631	+	2.31753i
$531$		0			0
$532$	106.527	−	227.544i	0.200238	−	0.427715i
$533$		−	689.276i		−	1.29320i
$534$		0			0
$535$		−	1415.40i		−	2.64560i
$536$	−72.7930	+	94.4197i	−0.135808	+	0.176156i
$537$		0			0
$538$	−748.014	−	166.427i	−1.39036	−	0.309343i
$539$	72.0530			0.133679
$540$		0			0
$541$		−	591.883i		−	1.09405i	−0.837115	−	0.547027i	$-0.815760\pi$
$541$		−	591.883i		−	1.09405i	0.837115	−	0.547027i	$-0.184240\pi$
$542$	−365.961	−	81.4232i	−0.675205	−	0.150227i
$543$		0			0
$544$	−90.8219	+	46.8415i	−0.166952	+	0.0861057i
$545$	−423.376			−0.776837
$546$		0			0
$547$	−685.589			−1.25336			−0.626681	−	0.779276i	$-0.715587\pi$
$547$	−685.589			−1.25336			−0.626681	+	0.779276i	$0.715587\pi$
$548$	546.263	+	255.737i	0.996830	+	0.466673i
$549$		0			0
$550$	−106.171	+	477.190i	−0.193038	+	0.867619i
$551$			634.922i			1.15231i
$552$		0			0
$553$	−5.84092			−0.0105623
$554$	11.5378	+	2.56707i	0.0208264	+	0.00463369i
$555$		0			0
$556$	108.668	+	50.8738i	0.195446	+	0.0914996i
$557$			747.072i			1.34124i	0.741800	+	0.670621i	$0.233972\pi$
$557$			747.072i			1.34124i	−0.741800	+	0.670621i	$0.766028\pi$
$558$		0			0
$559$		−	889.473i		−	1.59119i
$560$	189.292	+	226.985i	0.338021	+	0.405331i
$561$		0			0
$562$	142.291	−	639.537i	0.253188	−	1.13797i
$563$	396.402			0.704089			0.352044	−	0.935983i	$-0.385487\pi$
$563$	396.402			0.704089			0.352044	+	0.935983i	$0.385487\pi$
$564$		0			0
$565$			939.535i			1.66289i
$566$	−231.197	+	1039.13i	−0.408476	+	1.83592i
$567$		0			0
$568$	578.363	+	445.890i	1.01825	+	0.785018i
$569$	553.486			0.972735			0.486368	−	0.873754i	$-0.338322\pi$
$569$	553.486			0.972735			0.486368	+	0.873754i	$0.338322\pi$
$570$		0			0
$571$	−377.714			−0.661495			−0.330748	−	0.943719i	$-0.607301\pi$
$571$	−377.714			−0.661495			−0.330748	+	0.943719i	$0.607301\pi$
$572$	430.337	−	919.214i	0.752337	−	1.60702i
$573$		0			0
$574$	144.426	+	32.1336i	0.251613	+	0.0559818i
$575$			106.101i			0.184523i
$576$		0			0
$577$	537.850			0.932149			0.466075	−	0.884745i	$-0.345668\pi$
$577$	537.850			0.932149			0.466075	+	0.884745i	$0.345668\pi$
$578$	121.101	−	544.295i	0.209517	−	0.941686i
$579$		0			0
$580$	−676.442	−	316.681i	−1.16628	−	0.546002i
$581$			375.320i			0.645989i
$582$		0			0
$583$			927.568i			1.59103i
$584$	−438.942	+	569.351i	−0.751614	+	0.974916i
$585$		0			0
$586$	531.515	+	118.258i	0.907023	+	0.201805i
$587$	−1090.47			−1.85770			−0.928848	−	0.370462i	$-0.879199\pi$
$587$	−1090.47			−1.85770			−0.928848	+	0.370462i	$0.879199\pi$
$588$		0			0
$589$		−	734.135i		−	1.24641i
$590$	−810.564	−	180.343i	−1.37384	−	0.305667i
$591$		0			0
$592$	491.249	−	409.671i	0.829812	−	0.692012i
$593$	−818.098			−1.37959			−0.689796	−	0.724004i	$-0.742300\pi$
$593$	−818.098			−1.37959			−0.689796	+	0.724004i	$0.742300\pi$
$594$		0			0
$595$	58.9899			0.0991428
$596$	11.6641	−	24.9149i	0.0195706	−	0.0418035i
$597$		0			0
$598$	47.8416	−	215.027i	0.0800026	−	0.359576i
$599$		−	599.646i		−	1.00108i	−0.865714	−	0.500540i	$-0.833135\pi$
$599$		−	599.646i		−	1.00108i	0.865714	−	0.500540i	$-0.166865\pi$
$600$		0			0
$601$	764.930			1.27276			0.636381	−	0.771375i	$-0.280431\pi$
$601$	764.930			1.27276			0.636381	+	0.771375i	$0.280431\pi$
$602$	186.374	+	41.4666i	0.309591	+	0.0688814i
$603$		0			0
$604$	−155.381	+	331.900i	−0.257254	+	0.549503i
$605$		−	105.065i		−	0.173661i
$606$		0			0
$607$			995.165i			1.63948i	0.572735	+	0.819740i	$0.305882\pi$
$607$			995.165i			1.63948i	−0.572735	+	0.819740i	$0.694118\pi$
$608$	675.185	−	348.228i	1.11050	−	0.572743i
$609$		0			0
$610$	−259.452	+	1166.12i	−0.425331	+	1.91168i
$611$	−546.861			−0.895025
$612$		0			0
$613$		−	720.164i		−	1.17482i	−0.809290	−	0.587410i	$-0.800148\pi$
$613$		−	720.164i		−	1.17482i	0.809290	−	0.587410i	$-0.199852\pi$
$614$	−96.9536	+	435.763i	−0.157905	+	0.709712i
$615$		0			0
$616$	172.544	+	133.023i	0.280103	+	0.215946i
$617$	−840.661			−1.36250			−0.681249	−	0.732052i	$-0.738563\pi$
$617$	−840.661			−1.36250			−0.681249	+	0.732052i	$0.738563\pi$
$618$		0			0
$619$	156.739			0.253213			0.126606	−	0.991953i	$-0.459592\pi$
$619$	156.739			0.253213			0.126606	+	0.991953i	$0.459592\pi$
$620$	782.142	+	366.166i	1.26152	+	0.590590i
$621$		0			0
$622$	−39.8567	−	8.86777i	−0.0640783	−	0.0142569i
$623$			69.2051i			0.111084i
$624$		0			0
$625$	−654.767			−1.04763
$626$	−144.471	+	649.332i	−0.230784	+	1.03727i
$627$		0			0
$628$	−275.356	+	588.170i	−0.438466	+	0.936577i
$629$		−	127.668i		−	0.202970i
$630$		0			0
$631$		−	383.162i		−	0.607230i	−0.952795	−	0.303615i	$-0.901806\pi$
$631$		−	383.162i		−	0.607230i	0.952795	−	0.303615i	$-0.0981937\pi$
$632$	−13.9871	−	10.7834i	−0.0221315	−	0.0170623i
$633$		0			0
$634$	−639.321	−	142.243i	−1.00839	−	0.224359i
$635$	1636.41			2.57703
$636$		0			0
$637$			172.557i			0.270890i
$638$	−537.432	−	119.574i	−0.842370	−	0.187420i
$639$		0			0
$640$	34.2360	+	893.023i	0.0534938	+	1.39535i
$641$	−829.167			−1.29355			−0.646776	−	0.762680i	$-0.723883\pi$
$641$	−829.167			−1.29355			−0.646776	+	0.762680i	$0.723883\pi$
$642$		0			0
$643$	1020.04			1.58637			0.793187	−	0.608979i	$-0.208420\pi$
$643$	1020.04			1.58637			0.793187	+	0.608979i	$0.208420\pi$
$644$	42.8249	+	20.0488i	0.0664982	+	0.0311317i
$645$		0			0
$646$	32.9305	−	148.008i	0.0509760	−	0.229115i
$647$			356.439i			0.550910i	0.961314	+	0.275455i	$0.0888286\pi$
$647$			356.439i			0.550910i	−0.961314	+	0.275455i	$0.911171\pi$
$648$		0			0
$649$	−612.113			−0.943163
$650$	−1142.81	−	254.264i	−1.75816	−	0.391176i
$651$		0			0
$652$	1064.99	+	498.581i	1.63341	+	0.764695i
$653$			239.538i			0.366827i	0.983036	+	0.183414i	$0.0587147\pi$
$653$			239.538i			0.366827i	−0.983036	+	0.183414i	$0.941285\pi$
$654$		0			0
$655$		−	66.5331i		−	0.101577i
$656$	286.529	+	343.586i	0.436782	+	0.523759i
$657$		0			0
$658$	25.4943	−	114.585i	0.0387451	−	0.174142i
$659$	64.0319			0.0971653			0.0485827	−	0.998819i	$-0.484530\pi$
$659$	64.0319			0.0971653			0.0485827	+	0.998819i	$0.484530\pi$
$660$		0			0
$661$		−	983.021i		−	1.48717i	−0.668640	−	0.743586i	$-0.733123\pi$
$661$		−	983.021i		−	1.48717i	0.668640	−	0.743586i	$-0.266877\pi$
$662$	139.006	−	624.768i	0.209978	−	0.943759i
$663$		0			0
$664$	−692.908	+	898.769i	−1.04354	+	1.35357i
$665$	−438.541			−0.659460
$666$		0			0
$667$	−119.495			−0.179153
$668$	214.910	−	459.054i	0.321721	−	0.687207i
$669$		0			0
$670$	203.131	+	45.1949i	0.303181	+	0.0674551i
$671$			880.620i			1.31240i
$672$		0			0
$673$	652.090			0.968931			0.484465	−	0.874810i	$-0.339014\pi$
$673$	652.090			0.968931			0.484465	+	0.874810i	$0.339014\pi$
$674$	97.0704	−	436.289i	0.144021	−	0.647312i
$675$		0			0
$676$	1589.16	+	743.978i	2.35083	+	1.10056i
$677$		−	828.016i		−	1.22307i	−0.791219	−	0.611534i	$-0.790553\pi$
$677$		−	828.016i		−	1.22307i	0.791219	−	0.611534i	$-0.209447\pi$
$678$		0			0
$679$		−	321.525i		−	0.473528i
$680$	141.262	+	108.906i	0.207738	+	0.160156i
$681$		0			0
$682$	621.411	+	138.259i	0.911159	+	0.202725i
$683$	−143.799			−0.210541			−0.105270	−	0.994444i	$-0.533571\pi$
$683$	−143.799			−0.210541			−0.105270	+	0.994444i	$0.533571\pi$
$684$		0			0
$685$		−	1052.80i		−	1.53693i
$686$	−36.1564	−	8.04449i	−0.0527061	−	0.0117267i
$687$		0			0
$688$	369.750	+	443.379i	0.537428	+	0.644446i
$689$	−2221.40			−3.22409
$690$		0			0
$691$	373.712			0.540828			0.270414	−	0.962744i	$-0.412839\pi$
$691$	373.712			0.540828			0.270414	+	0.962744i	$0.412839\pi$
$692$	−319.975	+	683.477i	−0.462391	+	0.987683i
$693$		0			0
$694$	24.6064	−	110.595i	0.0354560	−	0.159359i
$695$		−	209.433i		−	0.301343i
$696$		0			0
$697$	89.2926			0.128110
$698$	911.182	+	202.730i	1.30542	+	0.290444i
$699$		0			0
$700$	106.554	−	227.602i	0.152219	−	0.325146i
$701$			518.085i			0.739066i	0.929218	+	0.369533i	$0.120482\pi$
$701$			518.085i			0.739066i	−0.929218	+	0.369533i	$0.879518\pi$
$702$		0			0
$703$			949.104i			1.35008i
$704$	167.602	+	637.093i	0.238071	+	0.904962i
$705$		0			0
$706$	−258.278	+	1160.84i	−0.365832	+	1.64425i
$707$	345.189			0.488245
$708$		0			0
$709$			733.222i			1.03416i	0.855936	+	0.517082i	$0.172982\pi$
$709$			733.222i			1.03416i	−0.855936	+	0.517082i	$0.827018\pi$
$710$	276.839	−	1244.27i	0.389915	−	1.75249i
$711$		0			0
$712$	−127.765	+	165.724i	−0.179445	+	0.232758i
$713$	138.167			0.193783
$714$		0			0
$715$	−1771.58			−2.47773
$716$	1209.83	+	566.390i	1.68970	+	0.791048i
$717$		0			0
$718$	885.841	+	197.092i	1.23376	+	0.274501i
$719$			885.412i			1.23145i	0.787962	+	0.615724i	$0.211137\pi$
$719$			885.412i			1.23145i	−0.787962	+	0.615724i	$0.788863\pi$
$720$		0			0
$721$	−208.625			−0.289355
$722$	−88.0063	+	395.549i	−0.121892	+	0.547852i
$723$		0			0
$724$	−64.0064	+	136.720i	−0.0884067	+	0.188840i
$725$			635.083i			0.875977i
$726$		0			0
$727$			813.477i			1.11895i	0.828847	+	0.559476i	$0.188997\pi$
$727$			813.477i			1.11895i	−0.828847	+	0.559476i	$0.811003\pi$
$728$	−318.572	+	413.218i	−0.437598	+	0.567608i
$729$		0			0
$730$	1224.88	+	272.526i	1.67792	+	0.373323i
$731$	115.227			0.157630
$732$		0			0
$733$		−	564.027i		−	0.769477i	−0.923026	−	0.384739i	$-0.874292\pi$
$733$		−	564.027i		−	0.769477i	0.923026	−	0.384739i	$-0.125708\pi$
$734$	−416.393	−	92.6439i	−0.567293	−	0.126218i
$735$		0			0
$736$	65.5380	+	127.073i	0.0890462	+	0.172653i
$737$	153.398			0.208139
$738$		0			0
$739$	287.625			0.389208			0.194604	−	0.980882i	$-0.437658\pi$
$739$	287.625			0.389208			0.194604	+	0.980882i	$0.437658\pi$
$740$	−1011.17	−	473.386i	−1.36644	−	0.639711i
$741$		0			0
$742$	103.560	−	465.456i	0.139569	−	0.627299i
$743$			630.568i			0.848679i	0.905503	+	0.424339i	$0.139494\pi$
$743$			630.568i			0.848679i	−0.905503	+	0.424339i	$0.860506\pi$
$744$		0			0
$745$	−48.0179			−0.0644536
$746$	−520.343	−	115.772i	−0.697510	−	0.155190i
$747$		0			0
$748$	119.080	+	55.7482i	0.159198	+	0.0745297i
$749$			536.359i			0.716100i
$750$		0			0
$751$		−	637.535i		−	0.848914i	−0.905448	−	0.424457i	$-0.860465\pi$
$751$		−	637.535i		−	0.848914i	0.905448	−	0.424457i	$-0.139535\pi$
$752$	272.596	−	227.328i	0.362494	−	0.302298i
$753$		0			0
$754$	286.363	−	1287.08i	0.379792	−	1.70700i
$755$	639.663			0.847235
$756$		0			0
$757$		−	133.159i		−	0.175904i	−0.996125	−	0.0879520i	$-0.971968\pi$
$757$		−	133.159i		−	0.175904i	0.996125	−	0.0879520i	$-0.0280322\pi$
$758$	−34.5560	+	155.314i	−0.0455884	+	0.204900i
$759$		0			0
$760$	−1050.16	−	809.626i	−1.38179	−	1.06530i
$761$	−331.848			−0.436069			−0.218034	−	0.975941i	$-0.569964\pi$
$761$	−331.848			−0.436069			−0.218034	+	0.975941i	$0.569964\pi$
$762$		0			0
$763$	160.437			0.210271
$764$	273.998	−	585.270i	0.358637	−	0.766060i
$765$		0			0
$766$	−1227.64	−	273.140i	−1.60267	−	0.356579i
$767$		−	1465.93i		−	1.91125i
$768$		0			0
$769$	−256.591			−0.333669			−0.166834	−	0.985985i	$-0.553355\pi$
$769$	−256.591			−0.333669			−0.166834	+	0.985985i	$0.553355\pi$
$770$	82.5898	−	371.204i	0.107259	−	0.482084i
$771$		0			0
$772$	146.549	+	68.6082i	0.189831	+	0.0888707i
$773$			889.126i			1.15023i	0.818073	+	0.575114i	$0.195042\pi$
$773$			889.126i			1.15023i	−0.818073	+	0.575114i	$0.804958\pi$
$774$		0			0
$775$		−	734.321i		−	0.947510i
$776$	593.594	−	769.949i	0.764940	−	0.992202i
$777$		0			0
$778$	−760.103	−	169.116i	−0.976997	−	0.217373i
$779$	−663.816			−0.852139
$780$		0			0
$781$		−	939.635i		−	1.20312i
$782$	27.8558	+	6.19766i	0.0356212	+	0.00792540i
$783$		0			0
$784$	−71.7313	−	86.0152i	−0.0914940	−	0.109713i
$785$	1133.57			1.44403
$786$		0			0
$787$	237.130			0.301309			0.150654	−	0.988586i	$-0.451862\pi$
$787$	237.130			0.301309			0.150654	+	0.988586i	$0.451862\pi$
$788$	−65.7692	+	140.485i	−0.0834635	+	0.178281i
$789$		0			0
$790$	−6.69508	+	30.0914i	−0.00847478	+	0.0380904i
$791$		−	356.033i		−	0.450105i
$792$		0			0
$793$	−2108.96			−2.65947
$794$	−563.156	−	125.297i	−0.709265	−	0.157805i
$795$		0			0
$796$	−112.386	+	240.059i	−0.141188	+	0.301582i
$797$			54.0956i			0.0678740i	0.999424	+	0.0339370i	$0.0108046\pi$
$797$			54.0956i			0.0678740i	−0.999424	+	0.0339370i	$0.989195\pi$
$798$		0			0
$799$		−	70.8434i		−	0.0886650i
$800$	675.356	−	348.316i	0.844195	−	0.435395i
$801$		0			0
$802$	141.824	−	637.438i	0.176839	−	0.794811i
$803$	924.993			1.15192
$804$		0			0
$805$		−	82.5354i		−	0.102528i
$806$	−331.110	+	1488.19i	−0.410807	+	1.84639i
$807$		0			0
$808$	826.616	+	637.281i	1.02304	+	0.788714i
$809$	381.017			0.470973			0.235487	−	0.971878i	$-0.424332\pi$
$809$	381.017			0.470973			0.235487	+	0.971878i	$0.424332\pi$
$810$		0			0
$811$	821.965			1.01352			0.506760	−	0.862087i	$-0.330843\pi$
$811$	821.965			1.01352			0.506760	+	0.862087i	$0.330843\pi$
$812$	256.335	+	120.005i	0.315683	+	0.147790i
$813$		0			0
$814$	−803.372	−	178.743i	−0.986944	−	0.219586i
$815$		−	2052.52i		−	2.51843i
$816$		0			0
$817$	−856.618			−1.04849
$818$	−21.0401	+	94.5659i	−0.0257214	+	0.115606i
$819$		0			0
$820$	331.093	−	707.225i	0.403772	−	0.862469i
$821$		−	118.925i		−	0.144853i	−0.997374	−	0.0724266i	$-0.976926\pi$
$821$		−	118.925i		−	0.144853i	0.997374	−	0.0724266i	$-0.0230743\pi$
$822$		0			0
$823$		−	1154.09i		−	1.40229i	−0.713018	−	0.701145i	$-0.752672\pi$
$823$		−	1154.09i		−	1.40229i	0.713018	−	0.701145i	$-0.247328\pi$
$824$	−499.589	−	385.159i	−0.606297	−	0.467426i
$825$		0			0
$826$	307.160	+	68.3404i	0.371864	+	0.0827366i
$827$	1111.06			1.34348			0.671741	−	0.740786i	$-0.265547\pi$
$827$	1111.06			1.34348			0.671741	+	0.740786i	$0.265547\pi$
$828$		0			0
$829$		−	1108.39i		−	1.33702i	−0.743704	−	0.668509i	$-0.766933\pi$
$829$		−	1108.39i		−	1.33702i	0.743704	−	0.668509i	$-0.233067\pi$
$830$	1933.58	+	430.205i	2.32961	+	0.518319i
$831$		0			0
$832$	−1525.75	+	401.383i	−1.83384	+	0.482432i
$833$	−22.3540			−0.0268355
$834$		0			0
$835$	−884.724			−1.05955
$836$	−885.261	−	414.442i	−1.05892	−	0.495744i
$837$		0			0
$838$	−169.351	+	761.157i	−0.202089	+	0.908301i
$839$			374.127i			0.445920i	0.974828	+	0.222960i	$0.0715719\pi$
$839$			374.127i			0.445920i	−0.974828	+	0.222960i	$0.928428\pi$
$840$		0			0
$841$	125.743			0.149516
$842$	−1375.97	−	306.142i	−1.63417	−	0.363590i
$843$		0			0
$844$	−1187.04	−	555.723i	−1.40645	−	0.658439i
$845$		−	3062.75i		−	3.62456i
$846$		0			0
$847$			39.8139i			0.0470058i
$848$	1107.31	−	923.426i	1.30579	−	1.08895i
$849$		0			0
$850$	32.9388	−	148.045i	0.0387516	−	0.174171i
$851$	−178.626			−0.209901
$852$		0			0
$853$			559.108i			0.655461i	0.944771	+	0.327730i	$0.106284\pi$
$853$			559.108i			0.655461i	−0.944771	+	0.327730i	$0.893716\pi$
$854$	98.3184	−	441.897i	0.115127	−	0.517444i
$855$		0			0
$856$	−990.216	+	1284.41i	−1.15679	+	1.50048i
$857$	1449.03			1.69081			0.845406	−	0.534124i	$-0.179358\pi$
$857$	1449.03			1.69081			0.845406	+	0.534124i	$0.179358\pi$
$858$		0			0
$859$	324.702			0.378000			0.189000	−	0.981977i	$-0.439475\pi$
$859$	324.702			0.378000			0.189000	+	0.981977i	$0.439475\pi$
$860$	427.257	−	912.635i	0.496811	−	1.06120i
$861$		0			0
$862$	−498.773	−	110.973i	−0.578623	−	0.128739i
$863$		−	1427.85i		−	1.65452i	−0.561816	−	0.827262i	$-0.689897\pi$
$863$		−	1427.85i		−	1.65452i	0.561816	−	0.827262i	$-0.310103\pi$
$864$		0			0
$865$	1317.25			1.52283
$866$	−150.914	+	678.290i	−0.174265	+	0.783245i
$867$		0			0
$868$	−296.390	−	138.757i	−0.341463	−	0.159858i
$869$			22.7241i			0.0261497i
$870$		0			0
$871$			367.368i			0.421777i
$872$	384.194	+	296.195i	0.440590	+	0.339674i
$873$		0			0
$874$	−207.084	−	46.0745i	−0.236939	−	0.0527168i
$875$	23.1553			0.0264632
$876$		0			0
$877$		−	676.175i		−	0.771009i	−0.922706	−	0.385505i	$-0.874027\pi$
$877$		−	676.175i		−	0.771009i	0.922706	−	0.385505i	$-0.125973\pi$
$878$	−55.0613	−	12.2507i	−0.0627122	−	0.0139529i
$879$		0			0
$880$	883.086	−	736.439i	1.00351	−	0.836862i
$881$	558.769			0.634244			0.317122	−	0.948385i	$-0.397283\pi$
$881$	558.769			0.634244			0.317122	+	0.948385i	$0.397283\pi$
$882$		0			0
$883$	−1192.56			−1.35058			−0.675290	−	0.737552i	$-0.735981\pi$
$883$	−1192.56			−1.35058			−0.675290	+	0.737552i	$0.735981\pi$
$884$	−133.509	+	285.180i	−0.151029	+	0.322602i
$885$		0			0
$886$	−322.715	+	1450.46i	−0.364238	+	1.63709i
$887$			173.161i			0.195221i	0.995225	+	0.0976103i	$0.0311199\pi$
$887$			173.161i			0.195221i	−0.995225	+	0.0976103i	$0.968880\pi$
$888$		0			0
$889$	−620.112			−0.697539
$890$	356.532	+	79.3254i	0.400598	+	0.0891296i
$891$		0			0
$892$	71.6248	−	152.993i	0.0802969	−	0.171517i
$893$			526.661i			0.589766i
$894$		0			0
$895$		−	2331.67i		−	2.60522i
$896$	−12.9736	−	338.408i	−0.0144795	−	0.377687i
$897$		0			0
$898$	91.3921	−	410.767i	0.101773	−	0.457424i
$899$	827.023			0.919936
$900$		0			0
$901$		−	287.772i		−	0.319392i
$902$	125.015	−	561.889i	0.138598	−	0.622937i
$903$		0			0
$904$	657.301	−	852.583i	0.727103	−	0.943123i
$905$	263.497			0.291157
$906$		0			0
$907$	813.148			0.896525			0.448262	−	0.893902i	$-0.352043\pi$
$907$	813.148			0.896525			0.448262	+	0.893902i	$0.352043\pi$
$908$	141.488	+	66.2388i	0.155824	+	0.0729503i
$909$		0			0
$910$	888.984	+	197.791i	0.976905	+	0.217353i
$911$		−	90.1970i		−	0.0990088i	−0.998774	−	0.0495044i	$-0.984236\pi$
$911$		−	90.1970i		−	0.0990088i	0.998774	−	0.0495044i	$-0.0157642\pi$
$912$		0			0
$913$	1460.18			1.59932
$914$	−209.238	+	940.433i	−0.228926	+	1.02892i
$915$		0			0
$916$	−149.549	+	319.442i	−0.163263	+	0.348736i
$917$			25.2124i			0.0274945i
$918$		0			0
$919$			1408.38i			1.53251i	0.642536	+	0.766255i	$0.277882\pi$
$919$			1408.38i			1.53251i	−0.642536	+	0.766255i	$0.722118\pi$
$920$	152.375	−	197.645i	0.165625	−	0.214832i
$921$		0			0
$922$	661.371	+	147.149i	0.717322	+	0.159598i
$923$	2250.30			2.43802
$924$		0			0
$925$			949.344i			1.02632i
$926$	−780.394	−	173.631i	−0.842758	−	0.187506i
$927$		0			0
$928$	392.288	+	760.614i	0.422724	+	0.819627i
$929$	−1438.63			−1.54858			−0.774292	−	0.632829i	$-0.781894\pi$
$929$	−1438.63			−1.54858			−0.774292	+	0.632829i	$0.781894\pi$
$930$		0			0
$931$	166.183			0.178500
$932$	52.2637	+	24.4677i	0.0560769	+	0.0262529i
$933$		0			0
$934$	16.0529	−	72.1507i	0.0171873	−	0.0772492i
$935$		−	229.500i		−	0.245455i
$936$		0			0
$937$	−371.801			−0.396799			−0.198399	−	0.980121i	$-0.563574\pi$
$937$	−371.801			−0.396799			−0.198399	+	0.980121i	$0.563574\pi$
$938$	−76.9757	−	17.1264i	−0.0820637	−	0.0182585i
$939$		0			0
$940$	−561.101	−	262.684i	−0.596916	−	0.279451i
$941$			737.684i			0.783936i	0.919979	+	0.391968i	$0.128206\pi$
$941$			737.684i			0.783936i	−0.919979	+	0.391968i	$0.871794\pi$
$942$		0			0
$943$		−	124.933i		−	0.132485i
$944$	609.380	+	730.726i	0.645529	+	0.774074i
$945$		0			0
$946$	161.326	−	725.087i	0.170535	−	0.766477i
$947$	−906.635			−0.957376			−0.478688	−	0.877985i	$-0.658888\pi$
$947$	−906.635			−0.957376			−0.478688	+	0.877985i	$0.658888\pi$
$948$		0			0
$949$			2215.23i			2.33428i
$950$	−244.873	+	1100.59i	−0.257761	+	1.15852i
$951$		0			0
$952$	−53.5306	−	41.2695i	−0.0562296	−	0.0433504i
$953$	480.032			0.503706			0.251853	−	0.967765i	$-0.418960\pi$
$953$	480.032			0.503706			0.251853	+	0.967765i	$0.418960\pi$
$954$		0			0
$955$	−1127.98			−1.18113
$956$	−672.575	+	1436.64i	−0.703530	+	1.50276i
$957$		0			0
$958$	697.030	+	155.083i	0.727589	+	0.161882i
$959$			398.954i			0.416011i
$960$		0			0
$961$	4.74730			0.00493996
$962$	428.066	−	1923.97i	0.444975	−	1.99996i
$963$		0			0
$964$	148.027	+	69.3000i	0.153555	+	0.0718880i
$965$		−	282.441i		−	0.292685i
$966$		0			0
$967$			1445.24i			1.49456i	0.664509	+	0.747280i	$0.268641\pi$
$967$			1445.24i			1.49456i	−0.664509	+	0.747280i	$0.731359\pi$
$968$	−73.5036	+	95.3413i	−0.0759335	+	0.0984931i
$969$		0			0
$970$	−1656.44	−	368.544i	−1.70767	−	0.379942i
$971$	−1767.08			−1.81986			−0.909928	−	0.414766i	$-0.863864\pi$
$971$	−1767.08			−1.81986			−0.909928	+	0.414766i	$0.863864\pi$
$972$		0			0
$973$			79.3639i			0.0815662i
$974$	999.453	+	222.370i	1.02613	+	0.228306i
$975$		0			0
$976$	1051.26	−	876.688i	1.07711	−	0.898246i
$977$	225.446			0.230753			0.115376	−	0.993322i	$-0.463193\pi$
$977$	225.446			0.230753			0.115376	+	0.993322i	$0.463193\pi$
$978$		0			0
$979$	269.242			0.275018
$980$	−82.8876	+	177.051i	−0.0845792	+	0.180664i
$981$		0			0
$982$	−121.632	+	546.684i	−0.123862	+	0.556704i
$983$		−	198.843i		−	0.202282i	−0.994872	−	0.101141i	$-0.967751\pi$
$983$		−	198.843i		−	0.202282i	0.994872	−	0.101141i	$-0.0322493\pi$
$984$		0			0
$985$	270.754			0.274877
$986$	166.735	+	37.0971i	0.169102	+	0.0376238i
$987$		0			0
$988$	992.531	−	2120.08i	1.00459	−	2.14583i
$989$		−	161.219i		−	0.163013i
$990$		0			0
$991$			32.6795i			0.0329763i	0.999864	+	0.0164882i	$0.00524858\pi$
$991$			32.6795i			0.0329763i	−0.999864	+	0.0164882i	$0.994751\pi$
$992$	−453.586	−	879.467i	−0.457244	−	0.886559i
$993$		0			0
$994$	−104.907	+	471.511i	−0.105540	+	0.474358i
$995$	462.661			0.464985
$996$		0			0
$997$			1241.41i			1.24515i	0.782560	+	0.622575i	$0.213914\pi$
$997$			1241.41i			1.24515i	−0.782560	+	0.622575i	$0.786086\pi$
$998$	−12.9755	+	58.3193i	−0.0130016	+	0.0584362i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.3.g.c.379.12	yes	24
3.2	odd	2	inner	504.3.g.c.379.13	yes	24
4.3	odd	2		2016.3.g.c.1135.20		24
8.3	odd	2	inner	504.3.g.c.379.11	✓	24
8.5	even	2		2016.3.g.c.1135.19		24
12.11	even	2		2016.3.g.c.1135.5		24
24.5	odd	2		2016.3.g.c.1135.6		24
24.11	even	2	inner	504.3.g.c.379.14	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.3.g.c.379.11	✓	24	8.3	odd	2	inner
504.3.g.c.379.12	yes	24	1.1	even	1	trivial
504.3.g.c.379.13	yes	24	3.2	odd	2	inner
504.3.g.c.379.14	yes	24	24.11	even	2	inner
2016.3.g.c.1135.5		24	12.11	even	2
2016.3.g.c.1135.6		24	24.5	odd	2
2016.3.g.c.1135.19		24	8.5	even	2
2016.3.g.c.1135.20		24	4.3	odd	2

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:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	504.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.434362 + 1.95226i) q^{2} +(-3.62266 - 1.69598i) q^{4} +6.98187i q^{5} -2.64575i q^{7} +(4.88454 - 6.33572i) q^{8} +(-13.6304 - 3.03266i) q^{10} -10.2933 q^{11} -24.6510i q^{13} +(5.16520 + 1.14921i) q^{14} +(10.2473 + 12.2879i) q^{16} +3.19343 q^{17} -23.7405 q^{19} +(11.8411 - 25.2929i) q^{20} +(4.47101 - 20.0952i) q^{22} -4.46806i q^{23} -23.7465 q^{25} +(48.1253 + 10.7075i) q^{26} +(-4.48713 + 9.58466i) q^{28} -26.7443i q^{29} +30.9233i q^{31} +(-28.4402 + 14.6681i) q^{32} +(-1.38710 + 6.23441i) q^{34} +18.4723 q^{35} -39.9783i q^{37} +(10.3120 - 46.3477i) q^{38} +(44.2351 + 34.1032i) q^{40} +27.9614 q^{41} +36.0826 q^{43} +(37.2891 + 17.4572i) q^{44} +(8.72283 + 1.94076i) q^{46} -22.1841i q^{47} -7.00000 q^{49} +(10.3146 - 46.3594i) q^{50} +(-41.8075 + 89.3022i) q^{52} -90.1138i q^{53} -71.8664i q^{55} +(-16.7627 - 12.9233i) q^{56} +(52.2119 + 11.6167i) q^{58} +59.4672 q^{59} -85.5528i q^{61} +(-60.3705 - 13.4319i) q^{62} +(-16.2826 - 61.8941i) q^{64} +172.110 q^{65} -14.9028 q^{67} +(-11.5687 - 5.41598i) q^{68} +(-8.02365 + 36.0628i) q^{70} +91.2862i q^{71} -89.8637 q^{73} +(78.0481 + 17.3650i) q^{74} +(86.0037 + 40.2633i) q^{76} +27.2335i q^{77} -2.20766i q^{79} +(-85.7924 + 71.5455i) q^{80} +(-12.1453 + 54.5879i) q^{82} -141.857 q^{83} +22.2961i q^{85} +(-15.6729 + 70.4427i) q^{86} +(-50.2779 + 65.2154i) q^{88} -26.1571 q^{89} -65.2204 q^{91} +(-7.57773 + 16.1863i) q^{92} +(43.3092 + 9.63592i) q^{94} -165.753i q^{95} +121.525 q^{97} +(3.04053 - 13.6658i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 2 q^{4} + 12 q^{10} + 66 q^{16} - 64 q^{19} - 144 q^{22} - 168 q^{25} - 14 q^{28} + 12 q^{34} + 196 q^{40} + 224 q^{43} - 84 q^{46} - 168 q^{49} - 364 q^{52} + 348 q^{58} + 214 q^{64} - 32 q^{67}+ \cdots - 144 q^{97}+O(q^{100}) \) 24 * q - 2 * q^4 + 12 * q^10 + 66 * q^16 - 64 * q^19 - 144 * q^22 - 168 * q^25 - 14 * q^28 + 12 * q^34 + 196 * q^40 + 224 * q^43 - 84 * q^46 - 168 * q^49 - 364 * q^52 + 348 * q^58 + 214 * q^64 - 32 * q^67 - 84 * q^70 + 240 * q^73 + 416 * q^76 + 300 * q^82 - 120 * q^88 + 192 * q^94 - 144 * q^97

Introduction

L-functions

Modular forms

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Representations

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Database

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