LMFDB - Embedded newform 312.4.m.a.181.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [312,4,Mod(181,312)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(312, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 0, 1]))

N = Newforms(chi, 4, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("312.181");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 312 = 2^{3} \cdot 3 \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	312.m (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$18.4085959218$
Analytic rank:	$0$
Dimension:	$84$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			181.10
Character	$\chi$	$=$	312.181
Dual form			312.4.m.a.181.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.56970 + 1.18180i) q^{2} -3.00000i q^{3} +(5.20671 - 6.07373i) q^{4} -8.43796 q^{5} +(3.54539 + 7.70910i) q^{6} +8.36709i q^{7} +(-6.20176 + 21.7609i) q^{8} -9.00000 q^{9} +O(q^{10})$	\(q+(-2.56970 + 1.18180i) q^{2} -3.00000i q^{3} +(5.20671 - 6.07373i) q^{4} -8.43796 q^{5} +(3.54539 + 7.70910i) q^{6} +8.36709i q^{7} +(-6.20176 + 21.7609i) q^{8} -9.00000 q^{9} +(21.6830 - 9.97196i) q^{10} +57.7885 q^{11} +(-18.2212 - 15.6201i) q^{12} +(-18.9697 - 42.8620i) q^{13} +(-9.88821 - 21.5009i) q^{14} +25.3139i q^{15} +(-9.78034 - 63.2483i) q^{16} -72.1970 q^{17} +(23.1273 - 10.6362i) q^{18} -144.199 q^{19} +(-43.9340 + 51.2499i) q^{20} +25.1013 q^{21} +(-148.499 + 68.2943i) q^{22} +168.461 q^{23} +(65.2828 + 18.6053i) q^{24} -53.8009 q^{25} +(99.4005 + 87.7242i) q^{26} +27.0000i q^{27} +(50.8194 + 43.5650i) q^{28} +96.0104i q^{29} +(-29.9159 - 65.0490i) q^{30} +59.3688i q^{31} +(99.8792 + 150.971i) q^{32} -173.366i q^{33} +(185.525 - 85.3222i) q^{34} -70.6012i q^{35} +(-46.8604 + 54.6636i) q^{36} +187.632 q^{37} +(370.547 - 170.413i) q^{38} +(-128.586 + 56.9090i) q^{39} +(52.3302 - 183.618i) q^{40} +211.432i q^{41} +(-64.5027 + 29.6646i) q^{42} +160.852i q^{43} +(300.888 - 350.992i) q^{44} +75.9416 q^{45} +(-432.893 + 199.086i) q^{46} +539.374i q^{47} +(-189.745 + 29.3410i) q^{48} +272.992 q^{49} +(138.252 - 63.5817i) q^{50} +216.591i q^{51} +(-359.102 - 107.953i) q^{52} +583.906i q^{53} +(-31.9085 - 69.3819i) q^{54} -487.617 q^{55} +(-182.076 - 51.8907i) q^{56} +432.596i q^{57} +(-113.465 - 246.718i) q^{58} +236.128 q^{59} +(153.750 + 131.802i) q^{60} +438.613i q^{61} +(-70.1619 - 152.560i) q^{62} -75.3038i q^{63} +(-435.076 - 269.912i) q^{64} +(160.065 + 361.668i) q^{65} +(204.883 + 445.497i) q^{66} -639.558 q^{67} +(-375.909 + 438.505i) q^{68} -505.382i q^{69} +(83.4363 + 181.424i) q^{70} +79.3300i q^{71} +(55.8159 - 195.848i) q^{72} -40.6482i q^{73} +(-482.158 + 221.743i) q^{74} +161.403i q^{75} +(-750.800 + 875.822i) q^{76} +483.522i q^{77} +(263.173 - 298.202i) q^{78} +807.497 q^{79} +(82.5261 + 533.686i) q^{80} +81.0000 q^{81} +(-249.870 - 543.317i) q^{82} -1390.02 q^{83} +(130.695 - 152.458i) q^{84} +609.195 q^{85} +(-190.094 - 413.340i) q^{86} +288.031 q^{87} +(-358.391 + 1257.53i) q^{88} -1051.90i q^{89} +(-195.147 + 89.7476i) q^{90} +(358.630 - 158.721i) q^{91} +(877.125 - 1023.18i) q^{92} +178.106 q^{93} +(-637.431 - 1386.03i) q^{94} +1216.74 q^{95} +(452.912 - 299.638i) q^{96} +1002.06i q^{97} +(-701.507 + 322.621i) q^{98} -520.097 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 84 q - 756 q^{9}+O(q^{10}) $ 84 * q - 756 * q^9	$ 84 q - 756 q^{9} - 36 q^{10} + 12 q^{12} - 208 q^{14} - 148 q^{16} - 104 q^{17} + 620 q^{22} + 2188 q^{25} + 444 q^{26} - 204 q^{30} - 40 q^{38} - 1924 q^{40} + 192 q^{42} + 624 q^{48} - 3396 q^{49} - 1292 q^{52} - 1616 q^{55} + 608 q^{56} - 2120 q^{62} - 2856 q^{64} + 696 q^{65} - 396 q^{66} - 2536 q^{68} - 3936 q^{74} - 156 q^{78} + 3160 q^{79} + 6804 q^{81} + 4276 q^{82} - 2088 q^{87} + 1780 q^{88} + 324 q^{90} + 4792 q^{92} - 860 q^{94} + 2480 q^{95}+O(q^{100}) $ 84 * q - 756 * q^9 - 36 * q^10 + 12 * q^12 - 208 * q^14 - 148 * q^16 - 104 * q^17 + 620 * q^22 + 2188 * q^25 + 444 * q^26 - 204 * q^30 - 40 * q^38 - 1924 * q^40 + 192 * q^42 + 624 * q^48 - 3396 * q^49 - 1292 * q^52 - 1616 * q^55 + 608 * q^56 - 2120 * q^62 - 2856 * q^64 + 696 * q^65 - 396 * q^66 - 2536 * q^68 - 3936 * q^74 - 156 * q^78 + 3160 * q^79 + 6804 * q^81 + 4276 * q^82 - 2088 * q^87 + 1780 * q^88 + 324 * q^90 + 4792 * q^92 - 860 * q^94 + 2480 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/312\mathbb{Z}\right)^\times$.

$n$	$79$	$145$	$157$	$209$
$\chi(n)$	$1$	$-1$	$-1$	$1$

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 $

$2$	−2.56970	+	1.18180i	−0.908526	+	0.417828i
$2$	−2.56970	+	1.18180i	−0.908526	+	0.417828i
$3$		−	3.00000i		−	0.577350i
$3$		−	3.00000i		−	0.577350i
$4$	5.20671	−	6.07373i	0.650839	−	0.759216i
$5$	−8.43796			−0.754714			−0.377357	−	0.926068i	$-0.623167\pi$
$5$	−8.43796			−0.754714			−0.377357	+	0.926068i	$0.623167\pi$
$6$	3.54539	+	7.70910i	0.241233	+	0.524538i
$7$			8.36709i			0.451781i	0.974153	+	0.225890i	$0.0725291\pi$
$7$			8.36709i			0.451781i	−0.974153	+	0.225890i	$0.927471\pi$
$8$	−6.20176	+	21.7609i	−0.274082	+	0.961706i
$9$	−9.00000			−0.333333
$10$	21.6830	−	9.97196i	0.685677	−	0.315341i
$11$	57.7885			1.58399			0.791995	−	0.610527i	$-0.209042\pi$
$11$	57.7885			1.58399			0.791995	+	0.610527i	$0.209042\pi$
$12$	−18.2212	−	15.6201i	−0.438334	−	0.375762i
$13$	−18.9697	−	42.8620i	−0.404711	−	0.914445i
$13$	−18.9697	−	42.8620i	−0.404711	−	0.914445i
$14$	−9.88821	−	21.5009i	−0.188767	−	0.410454i
$15$			25.3139i			0.435734i
$16$	−9.78034	−	63.2483i	−0.152818	−	0.988254i
$17$	−72.1970			−1.03002			−0.515010	−	0.857184i	$-0.672212\pi$
$17$	−72.1970			−1.03002			−0.515010	+	0.857184i	$0.672212\pi$
$18$	23.1273	−	10.6362i	0.302842	−	0.139276i
$19$	−144.199			−1.74113			−0.870563	−	0.492056i	$-0.836245\pi$
$19$	−144.199			−1.74113			−0.870563	+	0.492056i	$0.836245\pi$
$20$	−43.9340	+	51.2499i	−0.491197	+	0.572991i
$21$	25.1013			0.260836
$22$	−148.499	+	68.2943i	−1.43910	+	0.661836i
$23$	168.461			1.52724			0.763619	−	0.645668i	$-0.223421\pi$
$23$	168.461			1.52724			0.763619	+	0.645668i	$0.223421\pi$
$24$	65.2828	+	18.6053i	0.555241	+	0.158241i
$25$	−53.8009			−0.430407
$26$	99.4005	+	87.7242i	0.749771	+	0.661697i
$27$			27.0000i			0.192450i
$28$	50.8194	+	43.5650i	0.342999	+	0.294036i
$29$			96.0104i			0.614782i	0.951583	+	0.307391i	$0.0994560\pi$
$29$			96.0104i			0.614782i	−0.951583	+	0.307391i	$0.900544\pi$
$30$	−29.9159	−	65.0490i	−0.182062	−	0.395876i
$31$			59.3688i			0.343966i	0.985100	+	0.171983i	$0.0550174\pi$
$31$			59.3688i			0.343966i	−0.985100	+	0.171983i	$0.944983\pi$
$32$	99.8792	+	150.971i	0.551760	+	0.834003i
$33$		−	173.366i		−	0.914517i
$34$	185.525	−	85.3222i	0.935800	−	0.430372i
$35$		−	70.6012i		−	0.340965i
$36$	−46.8604	+	54.6636i	−0.216946	+	0.253072i
$37$	187.632			0.833689			0.416845	−	0.908978i	$-0.363136\pi$
$37$	187.632			0.833689			0.416845	+	0.908978i	$0.363136\pi$
$38$	370.547	−	170.413i	1.58186	−	0.727492i
$39$	−128.586	+	56.9090i	−0.527955	+	0.233660i
$40$	52.3302	−	183.618i	0.206853	−	0.725813i
$41$			211.432i			0.805370i	0.915339	+	0.402685i	$0.131923\pi$
$41$			211.432i			0.805370i	−0.915339	+	0.402685i	$0.868077\pi$
$42$	−64.5027	+	29.6646i	−0.236976	+	0.108985i
$43$			160.852i			0.570456i	0.958460	+	0.285228i	$0.0920694\pi$
$43$			160.852i			0.570456i	−0.958460	+	0.285228i	$0.907931\pi$
$44$	300.888	−	350.992i	1.03092	−	1.20259i
$45$	75.9416			0.251571
$46$	−432.893	+	199.086i	−1.38753	+	0.638123i
$47$			539.374i			1.67395i	0.547239	+	0.836976i	$0.315679\pi$
$47$			539.374i			1.67395i	−0.547239	+	0.836976i	$0.684321\pi$
$48$	−189.745	+	29.3410i	−0.570569	+	0.0882294i
$49$	272.992			0.795894
$50$	138.252	−	63.5817i	0.391036	−	0.179836i
$51$			216.591i			0.594682i
$52$	−359.102	−	107.953i	−0.957663	−	0.287893i
$53$			583.906i			1.51332i	0.653811	+	0.756658i	$0.273169\pi$
$53$			583.906i			1.51332i	−0.653811	+	0.756658i	$0.726831\pi$
$54$	−31.9085	−	69.3819i	−0.0804111	−	0.174846i
$55$	−487.617			−1.19546
$56$	−182.076	−	51.8907i	−0.434480	−	0.123825i
$57$			432.596i			1.00524i
$58$	−113.465	−	246.718i	−0.256874	−	0.558546i
$59$	236.128			0.521038			0.260519	−	0.965469i	$-0.416106\pi$
$59$	236.128			0.521038			0.260519	+	0.965469i	$0.416106\pi$
$60$	153.750	+	131.802i	0.330816	+	0.283593i
$61$			438.613i			0.920634i	0.887755	+	0.460317i	$0.152264\pi$
$61$			438.613i			0.920634i	−0.887755	+	0.460317i	$0.847736\pi$
$62$	−70.1619	−	152.560i	−0.143719	−	0.312502i
$63$		−	75.3038i		−	0.150594i
$64$	−435.076	−	269.912i	−0.849758	−	0.527172i
$65$	160.065	+	361.668i	0.305441	+	0.690144i
$66$	204.883	+	445.497i	0.382111	+	0.830863i
$67$	−639.558			−1.16619			−0.583093	−	0.812405i	$-0.698158\pi$
$67$	−639.558			−1.16619			−0.583093	+	0.812405i	$0.698158\pi$
$68$	−375.909	+	438.505i	−0.670377	+	0.782008i
$69$		−	505.382i		−	0.881751i
$70$	83.4363	+	181.424i	0.142465	+	0.309776i
$71$			79.3300i			0.132602i	0.997800	+	0.0663009i	$0.0211197\pi$
$71$			79.3300i			0.132602i	−0.997800	+	0.0663009i	$0.978880\pi$
$72$	55.8159	−	195.848i	0.0913606	−	0.320569i
$73$		−	40.6482i		−	0.0651713i	−0.999469	−	0.0325857i	$-0.989626\pi$
$73$		−	40.6482i		−	0.0651713i	0.999469	−	0.0325857i	$-0.0103742\pi$
$74$	−482.158	+	221.743i	−0.757429	+	0.348339i
$75$			161.403i			0.248496i
$76$	−750.800	+	875.822i	−1.13319	+	1.32189i
$77$			483.522i			0.715616i
$78$	263.173	−	298.202i	0.382031	−	0.432881i
$79$	807.497			1.15001			0.575004	−	0.818151i	$-0.305001\pi$
$79$	807.497			1.15001			0.575004	+	0.818151i	$0.305001\pi$
$80$	82.5261	+	533.686i	0.115334	+	0.745849i
$81$	81.0000			0.111111
$82$	−249.870	−	543.317i	−0.336506	−	0.731699i
$83$	−1390.02			−1.83825			−0.919124	−	0.393969i	$-0.871102\pi$
$83$	−1390.02			−1.83825			−0.919124	+	0.393969i	$0.871102\pi$
$84$	130.695	−	152.458i	0.169762	−	0.198031i
$85$	609.195			0.777370
$86$	−190.094	−	413.340i	−0.238353	−	0.518275i
$87$	288.031			0.354945
$88$	−358.391	+	1257.53i	−0.434143	+	1.52333i
$89$		−	1051.90i		−	1.25282i	−0.779494	−	0.626409i	$-0.784524\pi$
$89$		−	1051.90i		−	1.25282i	0.779494	−	0.626409i	$-0.215476\pi$
$90$	−195.147	+	89.7476i	−0.228559	+	0.105114i
$91$	358.630	−	158.721i	0.413128	−	0.182840i
$92$	877.125	−	1023.18i	0.993985	−	1.15950i
$93$	178.106			0.198589
$94$	−637.431	−	1386.03i	−0.699425	−	1.52083i
$95$	1216.74			1.31405
$96$	452.912	−	299.638i	0.481512	−	0.318559i
$97$			1002.06i			1.04890i	0.851441	+	0.524450i	$0.175729\pi$
$97$			1002.06i			1.04890i	−0.851441	+	0.524450i	$0.824271\pi$
$98$	−701.507	+	322.621i	−0.723091	+	0.332547i
$99$	−520.097			−0.527997
$100$	−280.126	+	326.772i	−0.280126	+	0.326772i
$101$			709.387i			0.698878i	0.936959	+	0.349439i	$0.113628\pi$
$101$			709.387i			0.698878i	−0.936959	+	0.349439i	$0.886372\pi$
$102$	−255.967	−	556.574i	−0.248475	−	0.540284i
$103$	535.679			0.512446			0.256223	−	0.966618i	$-0.417522\pi$
$103$	535.679			0.512446			0.256223	+	0.966618i	$0.417522\pi$
$104$	1050.36	−	146.978i	0.990351	−	0.138580i
$105$	−211.804			−0.196856
$106$	−690.059	−	1500.46i	−0.632306	−	1.37489i
$107$			1877.42i			1.69623i	0.529810	+	0.848116i	$0.322263\pi$
$107$			1877.42i			1.69623i	−0.529810	+	0.848116i	$0.677737\pi$
$108$	163.991	+	140.581i	0.146111	+	0.125254i
$109$	−1084.63			−0.953110			−0.476555	−	0.879145i	$-0.658115\pi$
$109$	−1084.63			−0.953110			−0.476555	+	0.879145i	$0.658115\pi$
$110$	1253.03	−	576.265i	1.08611	−	0.499497i
$111$		−	562.896i		−	0.481331i
$112$	529.204	−	81.8330i	0.446474	−	0.0690401i
$113$	393.209			0.327345			0.163672	−	0.986515i	$-0.447666\pi$
$113$	393.209			0.327345			0.163672	+	0.986515i	$0.447666\pi$
$114$	−511.240	−	1111.64i	−0.420018	−	0.913287i
$115$	−1421.46			−1.15263
$116$	583.141	+	499.898i	0.466752	+	0.400124i
$117$	170.727	+	385.758i	0.134904	+	0.304815i
$118$	−606.778	+	279.055i	−0.473377	+	0.217705i
$119$		−	604.079i		−	0.465343i
$120$	−550.853	−	156.991i	−0.419048	−	0.119427i
$121$	2008.51			1.50903
$122$	−518.352	−	1127.10i	−0.384667	−	0.836419i
$123$	634.297			0.464980
$124$	360.590	+	309.116i	0.261144	+	0.223866i
$125$	1508.71			1.07955
$126$	88.9939	+	193.508i	0.0629223	+	0.136818i
$127$	−1119.16			−0.781966			−0.390983	−	0.920398i	$-0.627865\pi$
$127$	−1119.16			−0.781966			−0.390983	+	0.920398i	$0.627865\pi$
$128$	1437.00	+	179.421i	0.992295	+	0.123897i
$129$	482.555			0.329353
$130$	−838.738	−	740.213i	−0.565863	−	0.499392i
$131$		−	2927.91i		−	1.95277i	−0.216041	−	0.976384i	$-0.569314\pi$
$131$		−	2927.91i		−	1.95277i	0.216041	−	0.976384i	$-0.430686\pi$
$132$	−1052.98	−	902.664i	−0.694316	−	0.595203i
$133$		−	1206.52i		−	0.786607i
$134$	1643.47	−	755.828i	1.05951	−	0.487266i
$135$		−	227.825i		−	0.145245i
$136$	447.749	−	1571.07i	0.282310	−	0.990577i
$137$			366.021i			0.228257i	0.993466	+	0.114129i	$0.0364076\pi$
$137$			366.021i			0.228257i	−0.993466	+	0.114129i	$0.963592\pi$
$138$	597.259	+	1298.68i	0.368421	+	0.801093i
$139$		−	1679.55i		−	1.02488i	−0.858724	−	0.512439i	$-0.828742\pi$
$139$		−	1679.55i		−	1.02488i	0.858724	−	0.512439i	$-0.171258\pi$
$140$	−428.812	−	367.600i	−0.258866	−	0.221913i
$141$	1618.12			0.966457
$142$	−93.7519	−	203.854i	−0.0554048	−	0.120472i
$143$	−1096.23	−	2476.93i	−0.641058	−	1.44847i
$144$	88.0231	+	569.235i	0.0509393	+	0.329418i
$145$		−	810.132i		−	0.463985i
$146$	48.0379	+	104.454i	0.0272304	+	0.0592099i
$147$		−	818.975i		−	0.459510i
$148$	976.945	−	1139.63i	0.542597	−	0.632950i
$149$	−693.976			−0.381562			−0.190781	−	0.981633i	$-0.561102\pi$
$149$	−693.976			−0.381562			−0.190781	+	0.981633i	$0.561102\pi$
$150$	−190.745	−	414.756i	−0.103829	−	0.225765i
$151$			1464.84i			0.789448i	0.918800	+	0.394724i	$0.129160\pi$
$151$			1464.84i			0.789448i	−0.918800	+	0.394724i	$0.870840\pi$
$152$	894.285	−	3137.89i	0.477211	−	1.67445i
$153$	649.773			0.343340
$154$	−571.425	−	1242.51i	−0.299005	−	0.650156i
$155$		−	500.951i		−	0.259596i
$156$	−323.860	+	1077.31i	−0.166215	+	0.552907i
$157$			3120.49i			1.58625i	0.609056	+	0.793127i	$0.291549\pi$
$157$			3120.49i			1.58625i	−0.609056	+	0.793127i	$0.708451\pi$
$158$	−2075.03	+	954.298i	−1.04481	+	0.480506i
$159$	1751.72			0.873713
$160$	−842.776	−	1273.88i	−0.416421	−	0.629434i
$161$			1409.53i			0.689976i
$162$	−208.146	+	95.7256i	−0.100947	+	0.0464254i
$163$	−2488.19			−1.19565			−0.597824	−	0.801628i	$-0.703968\pi$
$163$	−2488.19			−1.19565			−0.597824	+	0.801628i	$0.703968\pi$
$164$	1284.18	+	1100.87i	0.611450	+	0.524166i
$165$			1462.85i			0.690199i
$166$	3571.93	−	1642.72i	1.67010	−	0.768072i
$167$		−	2905.66i		−	1.34639i	−0.739466	−	0.673194i	$-0.764922\pi$
$167$		−	2905.66i		−	1.34639i	0.739466	−	0.673194i	$-0.235078\pi$
$168$	−155.672	+	546.227i	−0.0714903	+	0.250847i
$169$	−1477.30	+	1626.16i	−0.672419	+	0.740171i
$170$	−1565.45	+	719.945i	−0.706261	+	0.324808i
$171$	1297.79			0.580376
$172$	976.968	+	837.507i	0.433100	+	0.371275i
$173$			2339.59i			1.02818i	0.857735	+	0.514092i	$0.171871\pi$
$173$			2339.59i			1.02818i	−0.857735	+	0.514092i	$0.828129\pi$
$174$	−740.154	+	340.395i	−0.322476	+	0.148306i
$175$		−	450.157i		−	0.194449i
$176$	−565.192	−	3655.02i	−0.242062	−	1.56539i
$177$		−	708.384i		−	0.300822i
$178$	1243.13	+	2703.06i	0.523463	+	1.13822i
$179$			4222.06i			1.76297i	0.472214	+	0.881484i	$0.343455\pi$
$179$			4222.06i			1.76297i	−0.472214	+	0.881484i	$0.656545\pi$
$180$	395.406	−	461.249i	0.163732	−	0.190997i
$181$		−	3070.52i		−	1.26094i	−0.776215	−	0.630469i	$-0.782863\pi$
$181$		−	3070.52i		−	1.26094i	0.776215	−	0.630469i	$-0.217137\pi$
$182$	−733.996	+	831.694i	−0.298942	+	0.338732i
$183$	1315.84			0.531528
$184$	−1044.75	+	3665.86i	−0.418588	+	1.46875i
$185$	−1583.23			−0.629197
$186$	−457.680	+	210.486i	−0.180423	+	0.0829761i
$187$	−4172.16			−1.63154
$188$	3276.01	+	2808.36i	1.27089	+	1.08947i
$189$	−225.911			−0.0869452
$190$	−3126.66	+	1437.94i	−1.19385	+	0.549049i
$191$	−623.978			−0.236385			−0.118192	−	0.992991i	$-0.537710\pi$
$191$	−623.978			−0.236385			−0.118192	+	0.992991i	$0.537710\pi$
$192$	−809.737	+	1305.23i	−0.304363	+	0.490608i
$193$		−	197.490i		−	0.0736560i	−0.999322	−	0.0368280i	$-0.988275\pi$
$193$		−	197.490i		−	0.0736560i	0.999322	−	0.0368280i	$-0.0117254\pi$
$194$	−1184.23	−	2574.98i	−0.438260	−	0.952953i
$195$	1085.00	−	480.196i	0.398455	−	0.176346i
$196$	1421.39	−	1658.08i	0.517999	−	0.604256i
$197$	3571.39			1.29163			0.645815	−	0.763494i	$-0.276518\pi$
$197$	3571.39			1.29163			0.645815	+	0.763494i	$0.276518\pi$
$198$	1336.49	−	614.649i	0.479699	−	0.220612i
$199$	2395.86			0.853458			0.426729	−	0.904379i	$-0.359666\pi$
$199$	2395.86			0.853458			0.426729	+	0.904379i	$0.359666\pi$
$200$	333.660	−	1170.76i	0.117967	−	0.413925i
$201$			1918.67i			0.673298i
$202$	−838.352	−	1822.91i	−0.292011	−	0.634949i
$203$	−803.328			−0.277747
$204$	1315.51	+	1127.73i	0.451492	+	0.387042i
$205$		−	1784.06i		−	0.607824i
$206$	−1376.53	+	633.064i	−0.465571	+	0.214115i
$207$	−1516.14			−0.509079
$208$	−2525.42	+	1619.00i	−0.841857	+	0.539701i
$209$	−8333.02			−2.75793
$210$	544.271	−	250.309i	0.178849	−	0.0822521i
$211$		−	197.614i		−	0.0644754i	−0.999480	−	0.0322377i	$-0.989737\pi$
$211$		−	197.614i		−	0.0644754i	0.999480	−	0.0322377i	$-0.0102633\pi$
$212$	3546.49	+	3040.23i	1.14893	+	0.984924i
$213$	237.990			0.0765577
$214$	−2218.73	−	4824.40i	−0.708734	−	1.54107i
$215$		−	1357.26i		−	0.430531i
$216$	−587.545	−	167.448i	−0.185080	−	0.0527471i
$217$	−496.744			−0.155397
$218$	2787.18	−	1281.82i	0.865925	−	0.398236i
$219$	−121.945			−0.0376267
$220$	−2538.88	+	2961.65i	−0.778051	+	0.907612i
$221$	1369.55	+	3094.51i	0.416860	+	0.941897i
$222$	665.229	+	1446.47i	0.201114	+	0.437302i
$223$		−	2694.89i		−	0.809252i	−0.914482	−	0.404626i	$-0.867402\pi$
$223$		−	2694.89i		−	0.809252i	0.914482	−	0.404626i	$-0.132598\pi$
$224$	−1263.19	+	835.698i	−0.376786	+	0.249274i
$225$	484.208			0.143469
$226$	−1010.43	+	464.693i	−0.297401	+	0.136774i
$227$	−825.056			−0.241237			−0.120619	−	0.992699i	$-0.538488\pi$
$227$	−825.056			−0.241237			−0.120619	+	0.992699i	$0.538488\pi$
$228$	2627.47	+	2252.40i	0.763194	+	0.654249i
$229$	838.916			0.242084			0.121042	−	0.992647i	$-0.461376\pi$
$229$	838.916			0.242084			0.121042	+	0.992647i	$0.461376\pi$
$230$	3652.73	−	1679.88i	1.04719	−	0.481600i
$231$	1450.57			0.413161
$232$	−2089.28	−	595.434i	−0.591240	−	0.168501i
$233$	486.416			0.136765			0.0683824	−	0.997659i	$-0.478216\pi$
$233$	486.416			0.136765			0.0683824	+	0.997659i	$0.478216\pi$
$234$	−894.605	−	789.518i	−0.249924	−	0.220566i
$235$		−	4551.21i		−	1.26336i
$236$	1229.45	−	1434.18i	0.339112	−	0.395581i
$237$		−	2422.49i		−	0.663957i
$238$	713.899	+	1552.30i	0.194434	+	0.422776i
$239$			690.902i			0.186990i	0.995620	+	0.0934952i	$0.0298040\pi$
$239$			690.902i			0.186990i	−0.995620	+	0.0934952i	$0.970196\pi$
$240$	1601.06	−	247.578i	0.430616	−	0.0665880i
$241$			1005.08i			0.268643i	0.990938	+	0.134322i	$0.0428855\pi$
$241$			1005.08i			0.268643i	−0.990938	+	0.134322i	$0.957114\pi$
$242$	−5161.28	+	2373.66i	−1.37099	+	0.630514i
$243$		−	243.000i		−	0.0641500i
$244$	2664.02	+	2283.73i	0.698960	+	0.599184i
$245$	−2303.49			−0.600673
$246$	−1629.95	+	749.610i	−0.422447	+	0.194282i
$247$	2735.40	+	6180.64i	0.704653	+	1.59216i
$248$	−1291.92	−	368.191i	−0.330794	−	0.0942748i
$249$			4170.06i			1.06131i
$250$	−3876.94	+	1782.99i	−0.980797	+	0.451066i
$251$			2502.31i			0.629262i	0.949214	+	0.314631i	$0.101881\pi$
$251$			2502.31i			0.629262i	−0.949214	+	0.314631i	$0.898119\pi$
$252$	−457.375	−	392.085i	−0.114333	−	0.0980121i
$253$	9735.09			2.41913
$254$	2875.91	−	1322.62i	0.710437	−	0.326728i
$255$		−	1827.59i		−	0.448815i
$256$	−3904.69	+	1237.18i	−0.953293	+	0.302046i
$257$	−1805.64			−0.438259			−0.219130	−	0.975696i	$-0.570322\pi$
$257$	−1805.64			−0.438259			−0.219130	+	0.975696i	$0.570322\pi$
$258$	−1240.02	+	570.282i	−0.299226	+	0.137613i
$259$			1569.93i			0.376645i
$260$	3030.09	+	910.907i	0.722761	+	0.217277i
$261$		−	864.094i		−	0.204927i
$262$	3460.20	+	7523.85i	0.815922	+	1.77414i
$263$	−7806.91			−1.83040			−0.915199	−	0.403002i	$-0.867967\pi$
$263$	−7806.91			−1.83040			−0.915199	+	0.403002i	$0.867967\pi$
$264$	3772.60	+	1075.17i	0.879497	+	0.250653i
$265$		−	4926.98i		−	1.14212i
$266$	1425.86	+	3100.40i	0.328667	+	0.714653i
$267$	−3155.69			−0.723315
$268$	−3329.99	+	3884.50i	−0.758999	+	0.885387i
$269$		−	5945.63i		−	1.34763i	−0.738902	−	0.673813i	$-0.764655\pi$
$269$		−	5945.63i		−	1.34763i	0.738902	−	0.673813i	$-0.235345\pi$
$270$	269.243	+	585.441i	0.0606874	+	0.131959i
$271$		−	1898.73i		−	0.425608i	−0.977095	−	0.212804i	$-0.931740\pi$
$271$		−	1898.73i		−	0.425608i	0.977095	−	0.212804i	$-0.0682596\pi$
$272$	706.111	+	4566.34i	0.157405	+	1.01792i
$273$	−476.163	−	1075.89i	−0.105563	−	0.238520i
$274$	−432.562	−	940.563i	−0.0953724	−	0.207378i
$275$	−3109.07			−0.681761
$276$	−3069.55	−	2631.38i	−0.669439	−	0.573878i
$277$			2881.71i			0.625073i	0.949906	+	0.312536i	$0.101179\pi$
$277$			2881.71i			0.625073i	−0.949906	+	0.312536i	$0.898821\pi$
$278$	1984.89	+	4315.95i	0.428223	+	0.931128i
$279$		−	534.319i		−	0.114655i
$280$	1536.35	+	437.852i	0.327908	+	0.0934523i
$281$			2630.79i			0.558505i	0.960218	+	0.279252i	$0.0900866\pi$
$281$			2630.79i			0.558505i	−0.960218	+	0.279252i	$0.909913\pi$
$282$	−4158.09	+	1912.29i	−0.878051	+	0.403813i
$283$		−	6320.15i		−	1.32754i	−0.747937	−	0.663770i	$-0.768955\pi$
$283$		−	6320.15i		−	1.32754i	0.747937	−	0.663770i	$-0.231045\pi$
$284$	481.829	+	413.048i	0.100673	+	0.0863024i
$285$		−	3650.22i		−	0.758669i
$286$	5744.21	+	5069.45i	1.18763	+	1.04812i
$287$	−1769.07			−0.363850
$288$	−898.913	−	1358.74i	−0.183920	−	0.278001i
$289$	299.405			0.0609414
$290$	957.411	+	2081.79i	0.193866	+	0.421542i
$291$	3006.17			0.605583
$292$	−246.886	−	211.643i	−0.0494791	−	0.0424160i
$293$	−4914.81			−0.979953			−0.489976	−	0.871736i	$-0.662995\pi$
$293$	−4914.81			−0.979953			−0.489976	+	0.871736i	$0.662995\pi$
$294$	967.863	+	2104.52i	0.191996	+	0.417477i
$295$	−1992.44			−0.393235
$296$	−1163.65	+	4083.05i	−0.228499	+	0.801764i
$297$			1560.29i			0.304839i
$298$	1783.31	−	820.139i	0.346659	−	0.159427i
$299$	−3195.64	−	7220.56i	−0.618089	−	1.39657i
$300$	980.316	+	840.377i	0.188662	+	0.161731i
$301$	−1345.86			−0.257721
$302$	−1731.14	−	3764.19i	−0.329854	−	0.717234i
$303$	2128.16			0.403497
$304$	1410.31	+	9120.31i	0.266075	+	1.72068i
$305$		−	3701.00i		−	0.694815i
$306$	−1669.72	+	767.900i	−0.311933	+	0.143457i
$307$	34.9320			0.00649405			0.00324702	−	0.999995i	$-0.498966\pi$
$307$	34.9320			0.00649405			0.00324702	+	0.999995i	$0.498966\pi$
$308$	2936.78	+	2517.56i	0.543307	+	0.465751i
$309$		−	1607.04i		−	0.295861i
$310$	592.023	+	1287.29i	0.108467	+	0.235850i
$311$	−6754.52			−1.23155			−0.615777	−	0.787920i	$-0.711158\pi$
$311$	−6754.52			−1.23155			−0.615777	+	0.787920i	$0.711158\pi$
$312$	−440.933	−	3151.09i	−0.0800093	−	0.571780i
$313$	3933.85			0.710397			0.355199	−	0.934791i	$-0.384413\pi$
$313$	3933.85			0.710397			0.355199	+	0.934791i	$0.384413\pi$
$314$	−3687.78	−	8018.71i	−0.662782	−	1.44115i
$315$			635.411i			0.113655i
$316$	4204.40	−	4904.52i	0.748469	−	0.873104i
$317$	4978.06			0.882005			0.441003	−	0.897506i	$-0.354623\pi$
$317$	4978.06			0.882005			0.441003	+	0.897506i	$0.354623\pi$
$318$	−4501.39	+	2070.18i	−0.793791	+	0.365062i
$319$			5548.30i			0.973809i
$320$	3671.16	+	2277.51i	0.641324	+	0.397864i
$321$	5632.25			0.979320
$322$	−1665.77	−	3622.06i	−0.288292	−	0.626861i
$323$	10410.7			1.79340
$324$	421.744	−	491.972i	0.0723154	−	0.0843573i
$325$	1020.58	+	2306.01i	0.174190	+	0.393583i
$326$	6393.91	−	2940.54i	1.08628	−	0.499575i
$327$			3253.90i			0.550278i
$328$	−4600.96	−	1311.25i	−0.774529	−	0.220737i
$329$	−4512.99			−0.756259
$330$	−1728.79	−	3759.09i	−0.288385	−	0.627064i
$331$	9305.29			1.54521			0.772606	−	0.634886i	$-0.218953\pi$
$331$	9305.29			1.54521			0.772606	+	0.634886i	$0.218953\pi$
$332$	−7237.43	+	8442.60i	−1.19640	+	1.39563i
$333$	−1688.69			−0.277896
$334$	3433.90	+	7466.68i	0.562560	+	1.22323i
$335$	5396.57			0.880137
$336$	−245.499	−	1587.61i	−0.0398603	−	0.257772i
$337$	−9088.98			−1.46916			−0.734582	−	0.678520i	$-0.762622\pi$
$337$	−9088.98			−1.46916			−0.734582	+	0.678520i	$0.762622\pi$
$338$	1874.44	−	5924.61i	0.301645	−	0.953420i
$339$		−	1179.63i		−	0.188993i
$340$	3171.90	−	3700.09i	0.505943	−	0.590192i
$341$			3430.83i			0.544839i
$342$	−3334.92	+	1533.72i	−0.527286	+	0.242497i
$343$			5154.06i			0.811350i
$344$	−3500.28	−	997.563i	−0.548612	−	0.156352i
$345$			4264.39i			0.665470i
$346$	−2764.92	−	6012.05i	−0.429605	−	0.934132i
$347$			3.22515i			0.000498948i	1.00000		0.000249474i	$7.94101e-5\pi$
$347$			3.22515i			0.000498948i	−1.00000		0.000249474i	$0.999921\pi$
$348$	1499.69	−	1749.42i	0.231012	−	0.269480i
$349$	12260.0			1.88041			0.940207	−	0.340604i	$-0.110632\pi$
$349$	12260.0			1.88041			0.940207	+	0.340604i	$0.110632\pi$
$350$	531.994	+	1156.77i	0.0812465	+	0.176662i
$351$	1157.27	−	512.181i	0.175985	−	0.0778866i
$352$	5771.87	+	8724.37i	0.873982	+	1.32105i
$353$			8026.84i			1.21027i	0.796123	+	0.605135i	$0.206881\pi$
$353$			8026.84i			1.21027i	−0.796123	+	0.605135i	$0.793119\pi$
$354$	837.166	+	1820.33i	0.125692	+	0.273304i
$355$		−	669.383i		−	0.100076i
$356$	−6388.94	−	5476.92i	−0.951160	−	0.815383i
$357$	−1812.24			−0.268666
$358$	−4989.61	−	10849.4i	−0.736618	−	1.60170i
$359$		−	5963.70i		−	0.876747i	−0.898793	−	0.438374i	$-0.855555\pi$
$359$		−	5963.70i		−	0.876747i	0.898793	−	0.438374i	$-0.144445\pi$
$360$	−470.972	+	1652.56i	−0.0689511	+	0.241938i
$361$	13934.2			2.03152
$362$	3628.73	+	7890.30i	0.526855	+	1.14559i
$363$		−	6025.54i		−	0.871236i
$364$	903.256	−	3004.64i	0.130065	−	0.432653i
$365$			342.988i			0.0491857i
$366$	−3381.31	+	1555.06i	−0.482907	+	0.222088i
$367$	−9542.35			−1.35724			−0.678619	−	0.734490i	$-0.737421\pi$
$367$	−9542.35			−1.35724			−0.678619	+	0.734490i	$0.737421\pi$
$368$	−1647.60	−	10654.8i	−0.233389	−	1.50930i
$369$		−	1902.89i		−	0.268457i
$370$	4068.43	−	1871.06i	0.571642	−	0.262896i
$371$	−4885.60			−0.683686
$372$	927.348	−	1081.77i	0.129249	−	0.150772i
$373$		−	7120.07i		−	0.988373i	−0.869356	−	0.494186i	$-0.835466\pi$
$373$		−	7120.07i		−	0.988373i	0.869356	−	0.494186i	$-0.164534\pi$
$374$	10721.2	−	4930.64i	1.48230	−	0.681705i
$375$		−	4526.14i		−	0.623277i
$376$	−11737.3	−	3345.07i	−1.60985	−	0.458800i
$377$	4115.20	−	1821.29i	0.562184	−	0.248809i
$378$	580.525	−	266.982i	0.0789920	−	0.0363282i
$379$	−1748.05			−0.236917			−0.118458	−	0.992959i	$-0.537795\pi$
$379$	−1748.05			−0.236917			−0.118458	+	0.992959i	$0.537795\pi$
$380$	6335.22	−	7390.15i	0.855236	−	0.997650i
$381$			3357.49i			0.451468i
$382$	1603.44	−	737.416i	0.214762	−	0.0987682i
$383$		−	5565.09i		−	0.742462i	−0.928541	−	0.371231i	$-0.878936\pi$
$383$		−	5565.09i		−	0.742462i	0.928541	−	0.371231i	$-0.121064\pi$
$384$	538.264	−	4310.99i	0.0715317	−	0.572902i
$385$		−	4079.94i		−	0.540085i
$386$	233.393	+	507.489i	0.0307756	+	0.0669184i
$387$		−	1447.66i		−	0.190152i
$388$	6086.21	+	5217.41i	0.796342	+	0.682665i
$389$		−	561.404i		−	0.0731731i	−0.999330	−	0.0365865i	$-0.988352\pi$
$389$		−	561.404i		−	0.0731731i	0.999330	−	0.0365865i	$-0.0116485\pi$
$390$	−2220.64	+	2516.21i	−0.288324	+	0.326701i
$391$	−12162.3			−1.57308
$392$	−1693.03	+	5940.56i	−0.218140	+	0.765417i
$393$	−8783.73			−1.12743
$394$	−9177.40	+	4220.66i	−1.17348	+	0.539680i
$395$	−6813.63			−0.867926
$396$	−2707.99	+	3158.93i	−0.343641	+	0.400864i
$397$	−5649.99			−0.714269			−0.357134	−	0.934053i	$-0.616246\pi$
$397$	−5649.99			−0.714269			−0.357134	+	0.934053i	$0.616246\pi$
$398$	−6156.65	+	2831.42i	−0.775389	+	0.356599i
$399$	−3619.57			−0.454148
$400$	526.191	+	3402.81i	0.0657739	+	0.425352i
$401$		−	5458.35i		−	0.679743i	−0.940472	−	0.339871i	$-0.889616\pi$
$401$		−	5458.35i		−	0.679743i	0.940472	−	0.339871i	$-0.110384\pi$
$402$	−2267.48	−	4930.42i	−0.281323	−	0.611709i
$403$	2544.66	−	1126.21i	0.314538	−	0.139207i
$404$	4308.62	+	3693.57i	0.530599	+	0.454857i
$405$	−683.475			−0.0838571
$406$	2064.31	−	949.371i	0.252340	−	0.116050i
$407$	10843.0			1.32056
$408$	−4713.22	−	1343.25i	−0.571910	−	0.162992i
$409$		−	12750.8i		−	1.54154i	−0.637116	−	0.770768i	$-0.719873\pi$
$409$		−	12750.8i		−	1.54154i	0.637116	−	0.770768i	$-0.280127\pi$
$410$	2108.39	+	4584.49i	0.253966	+	0.552224i
$411$	1098.06			0.131784
$412$	2789.12	−	3253.57i	0.333520	−	0.389058i
$413$			1975.71i			0.235395i
$414$	3896.04	−	1791.78i	0.462512	−	0.212708i
$415$	11728.9			1.38735
$416$	4576.23	−	7144.89i	0.539347	−	0.842084i
$417$	−5038.66			−0.591713
$418$	21413.4	−	9847.94i	2.50565	−	1.15234i
$419$			4624.93i			0.539242i	0.962966	+	0.269621i	$0.0868985\pi$
$419$			4624.93i			0.539242i	−0.962966	+	0.269621i	$0.913102\pi$
$420$	−1102.80	+	1286.44i	−0.128122	+	0.149456i
$421$	1108.40			0.128314			0.0641568	−	0.997940i	$-0.479564\pi$
$421$	1108.40			0.128314			0.0641568	+	0.997940i	$0.479564\pi$
$422$	233.540	+	507.808i	0.0269396	+	0.0585775i
$423$		−	4854.37i		−	0.557984i
$424$	−12706.3	−	3621.25i	−1.45536	−	0.414772i
$425$	3884.26			0.443328
$426$	−611.562	+	281.256i	−0.0695547	+	0.0319880i
$427$	−3669.92			−0.415924
$428$	11402.9	+	9775.17i	1.28781	+	1.10397i
$429$	−7430.80	+	3288.69i	−0.836276	+	0.370115i
$430$	1604.00	+	3487.75i	0.179888	+	0.391149i
$431$			2059.16i			0.230130i	0.993358	+	0.115065i	$0.0367077\pi$
$431$			2059.16i			0.230130i	−0.993358	+	0.115065i	$0.963292\pi$
$432$	1707.70	−	264.069i	0.190190	−	0.0294098i
$433$	8396.61			0.931906			0.465953	−	0.884809i	$-0.345712\pi$
$433$	8396.61			0.931906			0.465953	+	0.884809i	$0.345712\pi$
$434$	1276.48	−	587.051i	0.141182	−	0.0649293i
$435$	−2430.40			−0.267882
$436$	−5647.37	+	6587.76i	−0.620321	+	0.723616i
$437$	−24291.8			−2.65911
$438$	313.361	−	144.114i	0.0341848	−	0.0157215i
$439$	−827.173			−0.0899290			−0.0449645	−	0.998989i	$-0.514317\pi$
$439$	−827.173			−0.0899290			−0.0449645	+	0.998989i	$0.514317\pi$
$440$	3024.09	−	10611.0i	0.327654	−	1.14968i
$441$	−2456.93			−0.265298
$442$	−7176.42	−	6333.42i	−0.772279	−	0.681561i
$443$			14728.4i			1.57961i	0.613358	+	0.789805i	$0.289818\pi$
$443$			14728.4i			1.57961i	−0.613358	+	0.789805i	$0.710182\pi$
$444$	−3418.88	−	2930.84i	−0.365434	−	0.313269i
$445$			8875.86i			0.945520i
$446$	3184.81	+	6925.06i	0.338129	+	0.735227i
$447$			2081.93i			0.220295i
$448$	2258.38	−	3640.32i	0.238166	−	0.383904i
$449$		−	1124.15i		−	0.118156i	−0.998253	−	0.0590781i	$-0.981184\pi$
$449$		−	1124.15i		−	0.118156i	0.998253	−	0.0590781i	$-0.0188161\pi$
$450$	−1244.27	+	572.236i	−0.130345	+	0.0599454i
$451$			12218.4i			1.27570i
$452$	2047.32	−	2388.24i	0.213049	−	0.248525i
$453$	4394.51			0.455788
$454$	2120.15	−	975.049i	0.219170	−	0.100796i
$455$	−3026.11	+	1339.28i	−0.311794	+	0.137992i
$456$	−9413.68	−	2682.86i	−0.966746	−	0.275518i
$457$		−	17029.0i		−	1.74307i	−0.490334	−	0.871535i	$-0.663125\pi$
$457$		−	17029.0i		−	1.74307i	0.490334	−	0.871535i	$-0.336875\pi$
$458$	−2155.76	+	991.429i	−0.219939	+	0.101149i
$459$		−	1949.32i		−	0.198227i
$460$	−7401.15	+	8633.58i	−0.750174	+	0.875093i
$461$	−7086.48			−0.715944			−0.357972	−	0.933732i	$-0.616532\pi$
$461$	−7086.48			−0.715944			−0.357972	+	0.933732i	$0.616532\pi$
$462$	−3727.52	+	1714.27i	−0.375368	+	0.172630i
$463$			9841.61i			0.987859i	0.869502	+	0.493929i	$0.164440\pi$
$463$			9841.61i			0.987859i	−0.869502	+	0.493929i	$0.835560\pi$
$464$	6072.49	−	939.015i	0.607561	−	0.0939497i
$465$	−1502.85			−0.149878
$466$	−1249.94	+	574.845i	−0.124254	+	0.0571442i
$467$			13523.9i			1.34007i	0.742331	+	0.670034i	$0.233720\pi$
$467$			13523.9i			1.34007i	−0.742331	+	0.670034i	$0.766280\pi$
$468$	3231.92	+	971.581i	0.319221	+	0.0959644i
$469$		−	5351.24i		−	0.526860i
$470$	5378.61	+	11695.3i	0.527866	+	1.14779i
$471$	9361.46			0.915825
$472$	−1464.41	+	5138.37i	−0.142807	+	0.501086i
$473$			9295.37i			0.903598i
$474$	2862.89	+	6225.08i	0.277420	+	0.603222i
$475$	7758.01			0.749393
$476$	−3669.01	−	3145.26i	−0.353296	−	0.302863i
$477$		−	5255.16i		−	0.504438i
$478$	−816.506	−	1775.41i	−0.0781299	−	0.169886i
$479$			8823.16i			0.841630i	0.907147	+	0.420815i	$0.138256\pi$
$479$			8823.16i			0.841630i	−0.907147	+	0.420815i	$0.861744\pi$
$480$	−3821.65	+	2528.33i	−0.363404	+	0.240421i
$481$	−3559.32	−	8042.28i	−0.337403	−	0.762363i
$482$	−1187.80	−	2582.76i	−0.112247	−	0.244069i
$483$	4228.58			0.398358
$484$	10457.7	−	12199.2i	0.982132	−	1.14568i
$485$		−	8455.30i		−	0.791619i
$486$	287.177	+	624.437i	0.0268037	+	0.0582820i
$487$			8482.21i			0.789252i	0.918842	+	0.394626i	$0.129126\pi$
$487$			8482.21i			0.789252i	−0.918842	+	0.394626i	$0.870874\pi$
$488$	−9544.63	−	2720.17i	−0.885379	−	0.252329i
$489$			7464.58i			0.690307i
$490$	5919.28	−	2722.26i	0.545727	−	0.250978i
$491$		−	6293.37i		−	0.578444i	−0.957262	−	0.289222i	$-0.906603\pi$
$491$		−	6293.37i		−	0.578444i	0.957262	−	0.289222i	$-0.0933965\pi$
$492$	3302.60	−	3852.54i	0.302627	−	0.353021i
$493$		−	6931.66i		−	0.633238i
$494$	−14333.4	−	12649.7i	−1.30545	−	1.15210i
$495$	4388.55			0.398487
$496$	3754.97	−	580.647i	0.339926	−	0.0525642i
$497$	−663.761			−0.0599069
$498$	−4928.17	−	10715.8i	−0.443447	−	0.964230i
$499$	503.304			0.0451523			0.0225761	−	0.999745i	$-0.492813\pi$
$499$	503.304			0.0451523			0.0225761	+	0.999745i	$0.492813\pi$
$500$	7855.44	−	9163.52i	0.702612	−	0.819610i
$501$	−8716.99			−0.777338
$502$	−2957.23	−	6430.20i	−0.262923	−	0.571701i
$503$	4401.21			0.390139			0.195070	−	0.980789i	$-0.437507\pi$
$503$	4401.21			0.390139			0.195070	+	0.980789i	$0.437507\pi$
$504$	1638.68	+	467.017i	0.144827	+	0.0412749i
$505$		−	5985.78i		−	0.527453i
$506$	−25016.2	+	11504.9i	−2.19784	+	1.01078i
$507$	4878.47	+	4431.91i	0.427338	+	0.388221i
$508$	−5827.16	+	6797.49i	−0.508934	+	0.593681i
$509$	4188.23			0.364715			0.182358	−	0.983232i	$-0.441627\pi$
$509$	4188.23			0.364715			0.182358	+	0.983232i	$0.441627\pi$
$510$	2159.84	+	4696.35i	0.187528	+	0.407760i
$511$	340.107			0.0294431
$512$	8571.78	−	7793.73i	0.739888	−	0.672730i
$513$		−	3893.36i		−	0.335080i
$514$	4639.95	−	2133.90i	0.398170	−	0.183117i
$515$	−4520.03			−0.386750
$516$	2512.52	−	2930.91i	0.214356	−	0.250050i
$517$			31169.6i			2.65153i
$518$	−1855.34	−	4034.26i	−0.157373	−	0.342191i
$519$	7018.77			0.593622
$520$	−8862.92	+	1240.19i	−0.747432	+	0.104588i
$521$	280.072			0.0235512			0.0117756	−	0.999931i	$-0.496252\pi$
$521$	280.072			0.0235512			0.0117756	+	0.999931i	$0.496252\pi$
$522$	1021.18	+	2220.46i	0.0856245	+	0.186182i
$523$			10351.8i			0.865493i	0.901516	+	0.432747i	$0.142456\pi$
$523$			10351.8i			0.865493i	−0.901516	+	0.432747i	$0.857544\pi$
$524$	−17783.3	−	15244.8i	−1.48257	−	1.27094i
$525$	−1350.47			−0.112265
$526$	20061.4	−	9226.19i	1.66296	−	0.764793i
$527$		−	4286.25i		−	0.354292i
$528$	−10965.1	+	1695.57i	−0.903776	+	0.139755i
$529$	16212.0			1.33245
$530$	5822.69	+	12660.8i	0.477210	+	1.03765i
$531$	−2125.15			−0.173679
$532$	−7328.09	−	6282.01i	−0.597205	−	0.511954i
$533$	9062.41	−	4010.80i	0.736466	−	0.325942i
$534$	8109.18	−	3729.39i	0.657151	−	0.302222i
$535$		−	15841.6i		−	1.28017i
$536$	3966.39	−	13917.4i	0.319630	−	1.12153i
$537$	12666.2			1.01785
$538$	7026.53	+	15278.5i	0.563076	+	1.22435i
$539$	15775.8			1.26069
$540$	−1383.75	−	1186.22i	−0.110272	−	0.0945309i
$541$	−16992.5			−1.35040			−0.675199	−	0.737635i	$-0.735942\pi$
$541$	−16992.5			−1.35040			−0.675199	+	0.737635i	$0.735942\pi$
$542$	2243.92	+	4879.17i	0.177831	+	0.386676i
$543$	−9211.55			−0.728002
$544$	−7210.98	−	10899.6i	−0.568324	−	0.859040i
$545$	9152.09			0.719325
$546$	2495.08	+	2201.99i	0.195567	+	0.172594i
$547$			162.426i			0.0126963i	0.999980	+	0.00634813i	$0.00202069\pi$
$547$			162.426i			0.0126963i	−0.999980	+	0.00634813i	$0.997979\pi$
$548$	2223.11	+	1905.76i	0.173297	+	0.148559i
$549$		−	3947.52i		−	0.306878i
$550$	7989.38	−	3674.29i	0.619397	−	0.284859i
$551$		−	13844.6i		−	1.07041i
$552$	10997.6	+	3134.26i	0.847985	+	0.241672i
$553$			6756.41i			0.519551i
$554$	−3405.60	−	7405.13i	−0.261173	−	0.567895i
$555$			4749.69i			0.363267i
$556$	−10201.2	−	8744.95i	−0.778103	−	0.667030i
$557$	135.037			0.0102723			0.00513617	−	0.999987i	$-0.498365\pi$
$557$	135.037			0.0102723			0.00513617	+	0.999987i	$0.498365\pi$
$558$	631.457	+	1373.04i	0.0479063	+	0.104167i
$559$	6894.42	−	3051.30i	0.521651	−	0.230870i
$560$	−4465.40	+	690.504i	−0.336960	+	0.0521056i
$561$			12516.5i			0.941971i
$562$	−3109.06	−	6760.34i	−0.233359	−	0.507416i
$563$			15659.2i			1.17221i	0.810234	+	0.586106i	$0.199340\pi$
$563$			15659.2i			1.17221i	−0.810234	+	0.586106i	$0.800660\pi$
$564$	8425.09	−	9828.03i	0.629008	−	0.733750i
$565$	−3317.88			−0.247052
$566$	7469.14	+	16240.9i	0.554684	+	1.20610i
$567$			677.734i			0.0501978i
$568$	−1726.29	−	491.986i	−0.127524	−	0.0363438i
$569$	−13692.7			−1.00884			−0.504418	−	0.863460i	$-0.668293\pi$
$569$	−13692.7			−1.00884			−0.504418	+	0.863460i	$0.668293\pi$
$570$	4313.82	+	9379.97i	0.316993	+	0.689270i
$571$		−	23805.8i		−	1.74473i	−0.488856	−	0.872365i	$-0.662586\pi$
$571$		−	23805.8i		−	1.74473i	0.488856	−	0.872365i	$-0.337414\pi$
$572$	−20752.0	−	6238.47i	−1.51693	−	0.456020i
$573$			1871.93i			0.136477i
$574$	4545.98	−	2090.69i	0.330567	−	0.152027i
$575$	−9063.32			−0.657333
$576$	3915.69	+	2429.21i	0.283253	+	0.175724i
$577$			10653.4i			0.768642i	0.923200	+	0.384321i	$0.125564\pi$
$577$			10653.4i			0.768642i	−0.923200	+	0.384321i	$0.874436\pi$
$578$	−769.381	+	353.836i	−0.0553669	+	0.0254631i
$579$	−592.469			−0.0425253
$580$	−4920.52	−	4218.12i	−0.352265	−	0.301979i
$581$		−	11630.4i		−	0.830484i
$582$	−7724.94	+	3552.68i	−0.550188	+	0.253030i
$583$			33743.1i			2.39708i
$584$	884.542	+	252.090i	0.0626757	+	0.0178623i
$585$	−1440.59	−	3255.01i	−0.101814	−	0.230048i
$586$	12629.6	−	5808.31i	0.890313	−	0.409452i
$587$	15680.9			1.10259			0.551294	−	0.834311i	$-0.314134\pi$
$587$	15680.9			1.10259			0.551294	+	0.834311i	$0.314134\pi$
$588$	−4974.23	−	4264.17i	−0.348867	−	0.299067i
$589$		−	8560.89i		−	0.598888i
$590$	5119.97	−	2354.66i	0.357264	−	0.164305i
$591$		−	10714.2i		−	0.745723i
$592$	−1835.11	−	11867.4i	−0.127403	−	0.823897i
$593$		−	7750.92i		−	0.536749i	−0.963315	−	0.268375i	$-0.913514\pi$
$593$		−	7750.92i		−	0.536749i	0.963315	−	0.268375i	$-0.0864865\pi$
$594$	−1843.95	−	4009.48i	−0.127370	−	0.276954i
$595$			5097.19i			0.351201i
$596$	−3613.33	+	4215.02i	−0.248335	+	0.289688i
$597$		−	7187.59i		−	0.492744i
$598$	16745.1	+	14778.1i	1.14508	+	1.01057i
$599$	5641.89			0.384844			0.192422	−	0.981312i	$-0.438366\pi$
$599$	5641.89			0.384844			0.192422	+	0.981312i	$0.438366\pi$
$600$	−3512.27	−	1000.98i	−0.238980	−	0.0681081i
$601$	10995.2			0.746264			0.373132	−	0.927778i	$-0.378284\pi$
$601$	10995.2			0.746264			0.373132	+	0.927778i	$0.378284\pi$
$602$	3458.45	−	1590.53i	0.234146	−	0.107683i
$603$	5756.02			0.388729
$604$	8897.01	+	7626.97i	0.599361	+	0.513803i
$605$	−16947.8			−1.13888
$606$	−5468.73	+	2515.06i	−0.366588	+	0.168593i
$607$	−1343.46			−0.0898344			−0.0449172	−	0.998991i	$-0.514302\pi$
$607$	−1343.46			−0.0898344			−0.0449172	+	0.998991i	$0.514302\pi$
$608$	−14402.4	−	21769.7i	−0.960684	−	1.45210i
$609$			2409.98i			0.160357i
$610$	4373.83	+	9510.45i	0.290313	+	0.631257i
$611$	23118.7	−	10231.7i	1.53074	−	0.677467i
$612$	3383.18	−	3946.54i	0.223459	−	0.260669i
$613$	9486.08			0.625023			0.312511	−	0.949914i	$-0.398830\pi$
$613$	9486.08			0.625023			0.312511	+	0.949914i	$0.398830\pi$
$614$	−89.7647	+	41.2825i	−0.00590001	+	0.00271340i
$615$	−5352.17			−0.350927
$616$	−10521.9	−	2998.69i	−0.688213	−	0.196137i
$617$			23208.1i			1.51430i	0.653242	+	0.757149i	$0.273408\pi$
$617$			23208.1i			1.51430i	−0.653242	+	0.757149i	$0.726592\pi$
$618$	1899.19	+	4129.60i	0.123619	+	0.268797i
$619$	−15457.5			−1.00370			−0.501849	−	0.864955i	$-0.667347\pi$
$619$	−15457.5			−1.00370			−0.501849	+	0.864955i	$0.667347\pi$
$620$	−3042.64	−	2608.31i	−0.197089	−	0.168955i
$621$			4548.43i			0.293917i
$622$	17357.1	−	7982.47i	1.11890	−	0.514579i
$623$	8801.32			0.565999
$624$	4857.01	+	7576.26i	0.311596	+	0.486046i
$625$	−6005.36			−0.384343
$626$	−10108.8	+	4649.01i	−0.645415	+	0.296824i
$627$			24999.1i			1.59229i
$628$	18953.0	+	16247.5i	1.20431	+	1.03240i
$629$	−13546.5			−0.858717
$630$	−750.927	−	1632.81i	−0.0474883	−	0.103259i
$631$			16138.7i			1.01818i	0.860713	+	0.509091i	$0.170018\pi$
$631$			16138.7i			1.01818i	−0.860713	+	0.509091i	$0.829982\pi$
$632$	−5007.91	+	17571.9i	−0.315196	+	1.10597i
$633$	−592.842			−0.0372249
$634$	−12792.1	+	5883.06i	−0.801325	+	0.368527i
$635$	9443.45			0.590161
$636$	9120.69	−	10639.5i	0.568646	−	0.663337i
$637$	−5178.56	−	11701.0i	−0.322107	−	0.727801i
$638$	−6556.97	−	14257.5i	−0.406885	−	0.884731i
$639$		−	713.970i		−	0.0442006i
$640$	−12125.3	−	1513.95i	−0.748899	−	0.0935065i
$641$	−4067.71			−0.250647			−0.125324	−	0.992116i	$-0.539997\pi$
$641$	−4067.71			−0.250647			−0.125324	+	0.992116i	$0.539997\pi$
$642$	−14473.2	+	6656.18i	−0.889738	+	0.409188i
$643$	14570.0			0.893603			0.446801	−	0.894633i	$-0.352563\pi$
$643$	14570.0			0.893603			0.446801	+	0.894633i	$0.352563\pi$
$644$	8561.07	+	7338.99i	0.523841	+	0.449063i
$645$	−4071.78			−0.248567
$646$	−26752.4	+	12303.3i	−1.62935	+	0.749332i
$647$	19304.6			1.17302			0.586509	−	0.809943i	$-0.300502\pi$
$647$	19304.6			1.17302			0.586509	+	0.809943i	$0.300502\pi$
$648$	−502.343	+	1762.64i	−0.0304535	+	0.106856i
$649$	13645.5			0.825319
$650$	−5347.84	−	4719.64i	−0.322707	−	0.284799i
$651$			1490.23i			0.0897186i
$652$	−12955.3	+	15112.6i	−0.778173	+	0.907754i
$653$			1649.08i			0.0988260i	0.998778	+	0.0494130i	$0.0157351\pi$
$653$			1649.08i			0.0988260i	−0.998778	+	0.0494130i	$0.984265\pi$
$654$	−3845.45	−	8361.54i	−0.229922	−	0.499942i
$655$			24705.6i			1.47378i
$656$	13372.7	−	2067.88i	0.795910	−	0.123075i
$657$			365.834i			0.0217238i
$658$	11597.0	−	5333.44i	0.687081	−	0.315987i
$659$		−	16643.2i		−	0.983803i	−0.870651	−	0.491902i	$-0.836302\pi$
$659$		−	16643.2i		−	0.983803i	0.870651	−	0.491902i	$-0.163698\pi$
$660$	8884.96	+	7616.64i	0.524010	+	0.449208i
$661$	−5394.04			−0.317403			−0.158702	−	0.987327i	$-0.550731\pi$
$661$	−5394.04			−0.317403			−0.158702	+	0.987327i	$0.550731\pi$
$662$	−23911.8	+	10997.0i	−1.40387	+	0.645634i
$663$	9283.52	−	4108.66i	0.543804	−	0.240674i
$664$	8620.58	−	30248.1i	0.503830	−	1.76785i
$665$			10180.6i			0.593663i
$666$	4339.42	−	1995.69i	0.252476	−	0.116113i
$667$			16174.0i			0.938918i
$668$	−17648.2	−	15128.9i	−1.02220	−	0.876282i
$669$	−8084.67			−0.467222
$670$	−13867.6	+	6377.65i	−0.799627	+	0.367746i
$671$			25346.8i			1.45827i
$672$	2507.10	+	3789.56i	0.143919	+	0.217538i
$673$	−29896.5			−1.71237			−0.856186	−	0.516668i	$-0.827172\pi$
$673$	−29896.5			−1.71237			−0.856186	+	0.516668i	$0.827172\pi$
$674$	23356.0	−	10741.3i	1.33477	−	0.613859i
$675$		−	1452.62i		−	0.0828319i
$676$	2184.94	+	17439.7i	0.124314	+	0.992243i
$677$			5527.06i			0.313770i	0.987617	+	0.156885i	$0.0501452\pi$
$677$			5527.06i			0.313770i	−0.987617	+	0.156885i	$0.949855\pi$
$678$	1394.08	+	3031.28i	0.0789665	+	0.171705i
$679$	−8384.29			−0.473873
$680$	−3778.08	+	13256.7i	−0.213063	+	0.747602i
$681$			2475.17i			0.139278i
$682$	−4054.55	−	8816.21i	−0.227649	−	0.495000i
$683$	−1482.94			−0.0830790			−0.0415395	−	0.999137i	$-0.513226\pi$
$683$	−1482.94			−0.0830790			−0.0415395	+	0.999137i	$0.513226\pi$
$684$	6757.20	−	7882.40i	0.377731	−	0.440630i
$685$		−	3088.47i		−	0.172269i
$686$	−6091.05	−	13244.4i	−0.339005	−	0.737133i
$687$		−	2516.75i		−	0.139767i
$688$	10173.6	−	1573.18i	0.563756	−	0.0871759i
$689$	25027.4	−	11076.5i	1.38384	−	0.612455i
$690$	−5039.64	−	10958.2i	−0.278052	−	0.604596i
$691$	−18752.3			−1.03237			−0.516187	−	0.856476i	$-0.672649\pi$
$691$	−18752.3			−1.03237			−0.516187	+	0.856476i	$0.672649\pi$
$692$	14210.0	+	12181.6i	0.780614	+	0.669182i
$693$		−	4351.70i		−	0.238539i
$694$	−3.81147	−	8.28766i	−0.000208475	−	0.000453307i
$695$			14172.0i			0.773489i
$696$	−1786.30	+	6267.83i	−0.0972839	+	0.341353i
$697$		−	15264.8i		−	0.829547i
$698$	−31504.6	+	14488.9i	−1.70840	+	0.785690i
$699$		−	1459.25i		−	0.0789612i
$700$	−2734.13	−	2343.84i	−0.147629	−	0.126555i
$701$			30930.9i			1.66654i	0.552867	+	0.833269i	$0.313534\pi$
$701$			30930.9i			1.66654i	−0.552867	+	0.833269i	$0.686466\pi$
$702$	−2368.55	+	2683.81i	−0.127344	+	0.144294i
$703$	−27056.3			−1.45156
$704$	−25142.4	−	15597.8i	−1.34601	−	0.835036i
$705$	−13653.6			−0.729399
$706$	−9486.10	−	20626.6i	−0.505686	−	1.09956i
$707$	−5935.51			−0.315739
$708$	−4302.53	−	3688.35i	−0.228389	−	0.195786i
$709$	15172.9			0.803711			0.401855	−	0.915703i	$-0.368365\pi$
$709$	15172.9			0.803711			0.401855	+	0.915703i	$0.368365\pi$
$710$	791.075	+	1720.11i	0.0418148	+	0.0909221i
$711$	−7267.48			−0.383336
$712$	22890.3	+	6523.62i	1.20484	+	0.343375i
$713$			10001.3i			0.525318i
$714$	4656.90	−	2141.70i	0.244090	−	0.112256i
$715$	9249.93	+	20900.2i	0.483815	+	1.09318i
$716$	25643.6	+	21983.0i	1.33847	+	1.14741i
$717$	2072.71			0.107959
$718$	7047.89	+	15324.9i	0.366330	+	0.796547i
$719$	−7513.99			−0.389742			−0.194871	−	0.980829i	$-0.562429\pi$
$719$	−7513.99			−0.389742			−0.194871	+	0.980829i	$0.562429\pi$
$720$	−742.735	−	4803.18i	−0.0384446	−	0.248616i
$721$			4482.07i			0.231513i
$722$	−35806.7	+	16467.4i	−1.84569	+	0.848828i
$723$	3015.25			0.155101
$724$	−18649.5	−	15987.3i	−0.957324	−	0.820667i
$725$		−	5165.44i		−	0.264607i
$726$	7120.97	+	15483.8i	0.364027	+	0.791541i
$727$	9581.83			0.488818			0.244409	−	0.969672i	$-0.421406\pi$
$727$	9581.83			0.488818			0.244409	+	0.969672i	$0.421406\pi$
$728$	1229.77	+	8788.48i	0.0626078	+	0.447421i
$729$	−729.000			−0.0370370
$730$	−405.342	−	881.375i	−0.0205512	−	0.0446865i
$731$		−	11613.0i		−	0.587582i
$732$	6851.19	−	7992.05i	0.345939	−	0.403545i
$733$	1242.65			0.0626170			0.0313085	−	0.999510i	$-0.490033\pi$
$733$	1242.65			0.0626170			0.0313085	+	0.999510i	$0.490033\pi$
$734$	24521.0	−	11277.1i	1.23309	−	0.567093i
$735$			6910.48i			0.346798i
$736$	16825.7	+	25432.6i	0.842668	+	1.27372i
$737$	−36959.1			−1.84723
$738$	2248.83	+	4889.85i	0.112169	+	0.243900i
$739$	−7607.91			−0.378703			−0.189351	−	0.981909i	$-0.560639\pi$
$739$	−7607.91			−0.378703			−0.189351	+	0.981909i	$0.560639\pi$
$740$	−8243.42	+	9616.11i	−0.409506	+	0.477696i
$741$	18541.9	−	8206.19i	0.919236	−	0.406831i
$742$	12554.5	−	5773.79i	0.621147	−	0.285664i
$743$		−	23962.7i		−	1.18318i	−0.806238	−	0.591591i	$-0.798500\pi$
$743$		−	23962.7i		−	1.18318i	0.806238	−	0.591591i	$-0.201500\pi$
$744$	−1104.57	+	3875.76i	−0.0544296	+	0.190984i
$745$	5855.74			0.287970
$746$	8414.48	+	18296.4i	0.412970	+	0.897962i
$747$	12510.2			0.612749
$748$	−21723.2	+	25340.5i	−1.06187	+	1.23869i
$749$	−15708.5			−0.766325
$750$	5348.98	+	11630.8i	0.260423	+	0.566264i
$751$	−14661.3			−0.712383			−0.356192	−	0.934413i	$-0.615925\pi$
$751$	−14661.3			−0.712383			−0.356192	+	0.934413i	$0.615925\pi$
$752$	34114.5	−	5275.26i	1.65429	−	0.255810i
$753$	7506.94			0.363304
$754$	−8422.43	+	9543.49i	−0.406800	+	0.460946i
$755$		−	12360.2i		−	0.595807i
$756$	−1176.26	+	1372.12i	−0.0565873	+	0.0660102i
$757$			6391.51i			0.306874i	0.988158	+	0.153437i	$0.0490342\pi$
$757$			6391.51i			0.306874i	−0.988158	+	0.153437i	$0.950966\pi$
$758$	4491.97	−	2065.84i	0.215245	−	0.0989906i
$759$		−	29205.3i		−	1.39668i
$760$	−7545.94	+	26477.4i	−0.360158	+	1.26373i
$761$			3654.75i			0.174093i	0.996204	+	0.0870464i	$0.0277428\pi$
$761$			3654.75i			0.174093i	−0.996204	+	0.0870464i	$0.972257\pi$
$762$	−3967.87	−	8627.74i	−0.188636	−	0.410171i
$763$		−	9075.22i		−	0.430597i
$764$	−3248.87	+	3789.87i	−0.153848	+	0.179467i
$765$	−5482.76			−0.259123
$766$	6576.81	+	14300.6i	0.310222	+	0.674546i
$767$	−4479.27	−	10120.9i	−0.210870	−	0.476461i
$768$	3711.54	+	11714.1i	0.174386	+	0.550384i
$769$		−	13844.0i		−	0.649188i	−0.945853	−	0.324594i	$-0.894772\pi$
$769$		−	13844.0i		−	0.649188i	0.945853	−	0.324594i	$-0.105228\pi$
$770$	4821.66	+	10484.2i	0.225663	+	0.490682i
$771$			5416.91i			0.253029i
$772$	−1199.50	−	1028.27i	−0.0559208	−	0.0479382i
$773$	9330.55			0.434148			0.217074	−	0.976155

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 312 = 2^{3} \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	312.m (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.56970 + 1.18180i) q^{2} -3.00000i q^{3} +(5.20671 - 6.07373i) q^{4} -8.43796 q^{5} +(3.54539 + 7.70910i) q^{6} +8.36709i q^{7} +(-6.20176 + 21.7609i) q^{8} -9.00000 q^{9} +O(q^{10})\)	\(q+(-2.56970 + 1.18180i) q^{2} -3.00000i q^{3} +(5.20671 - 6.07373i) q^{4} -8.43796 q^{5} +(3.54539 + 7.70910i) q^{6} +8.36709i q^{7} +(-6.20176 + 21.7609i) q^{8} -9.00000 q^{9} +(21.6830 - 9.97196i) q^{10} +57.7885 q^{11} +(-18.2212 - 15.6201i) q^{12} +(-18.9697 - 42.8620i) q^{13} +(-9.88821 - 21.5009i) q^{14} +25.3139i q^{15} +(-9.78034 - 63.2483i) q^{16} -72.1970 q^{17} +(23.1273 - 10.6362i) q^{18} -144.199 q^{19} +(-43.9340 + 51.2499i) q^{20} +25.1013 q^{21} +(-148.499 + 68.2943i) q^{22} +168.461 q^{23} +(65.2828 + 18.6053i) q^{24} -53.8009 q^{25} +(99.4005 + 87.7242i) q^{26} +27.0000i q^{27} +(50.8194 + 43.5650i) q^{28} +96.0104i q^{29} +(-29.9159 - 65.0490i) q^{30} +59.3688i q^{31} +(99.8792 + 150.971i) q^{32} -173.366i q^{33} +(185.525 - 85.3222i) q^{34} -70.6012i q^{35} +(-46.8604 + 54.6636i) q^{36} +187.632 q^{37} +(370.547 - 170.413i) q^{38} +(-128.586 + 56.9090i) q^{39} +(52.3302 - 183.618i) q^{40} +211.432i q^{41} +(-64.5027 + 29.6646i) q^{42} +160.852i q^{43} +(300.888 - 350.992i) q^{44} +75.9416 q^{45} +(-432.893 + 199.086i) q^{46} +539.374i q^{47} +(-189.745 + 29.3410i) q^{48} +272.992 q^{49} +(138.252 - 63.5817i) q^{50} +216.591i q^{51} +(-359.102 - 107.953i) q^{52} +583.906i q^{53} +(-31.9085 - 69.3819i) q^{54} -487.617 q^{55} +(-182.076 - 51.8907i) q^{56} +432.596i q^{57} +(-113.465 - 246.718i) q^{58} +236.128 q^{59} +(153.750 + 131.802i) q^{60} +438.613i q^{61} +(-70.1619 - 152.560i) q^{62} -75.3038i q^{63} +(-435.076 - 269.912i) q^{64} +(160.065 + 361.668i) q^{65} +(204.883 + 445.497i) q^{66} -639.558 q^{67} +(-375.909 + 438.505i) q^{68} -505.382i q^{69} +(83.4363 + 181.424i) q^{70} +79.3300i q^{71} +(55.8159 - 195.848i) q^{72} -40.6482i q^{73} +(-482.158 + 221.743i) q^{74} +161.403i q^{75} +(-750.800 + 875.822i) q^{76} +483.522i q^{77} +(263.173 - 298.202i) q^{78} +807.497 q^{79} +(82.5261 + 533.686i) q^{80} +81.0000 q^{81} +(-249.870 - 543.317i) q^{82} -1390.02 q^{83} +(130.695 - 152.458i) q^{84} +609.195 q^{85} +(-190.094 - 413.340i) q^{86} +288.031 q^{87} +(-358.391 + 1257.53i) q^{88} -1051.90i q^{89} +(-195.147 + 89.7476i) q^{90} +(358.630 - 158.721i) q^{91} +(877.125 - 1023.18i) q^{92} +178.106 q^{93} +(-637.431 - 1386.03i) q^{94} +1216.74 q^{95} +(452.912 - 299.638i) q^{96} +1002.06i q^{97} +(-701.507 + 322.621i) q^{98} -520.097 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q - 756 q^{9}+O(q^{10}) \) 84 * q - 756 * q^9	\( 84 q - 756 q^{9} - 36 q^{10} + 12 q^{12} - 208 q^{14} - 148 q^{16} - 104 q^{17} + 620 q^{22} + 2188 q^{25} + 444 q^{26} - 204 q^{30} - 40 q^{38} - 1924 q^{40} + 192 q^{42} + 624 q^{48} - 3396 q^{49} - 1292 q^{52} - 1616 q^{55} + 608 q^{56} - 2120 q^{62} - 2856 q^{64} + 696 q^{65} - 396 q^{66} - 2536 q^{68} - 3936 q^{74} - 156 q^{78} + 3160 q^{79} + 6804 q^{81} + 4276 q^{82} - 2088 q^{87} + 1780 q^{88} + 324 q^{90} + 4792 q^{92} - 860 q^{94} + 2480 q^{95}+O(q^{100}) \) 84 * q - 756 * q^9 - 36 * q^10 + 12 * q^12 - 208 * q^14 - 148 * q^16 - 104 * q^17 + 620 * q^22 + 2188 * q^25 + 444 * q^26 - 204 * q^30 - 40 * q^38 - 1924 * q^40 + 192 * q^42 + 624 * q^48 - 3396 * q^49 - 1292 * q^52 - 1616 * q^55 + 608 * q^56 - 2120 * q^62 - 2856 * q^64 + 696 * q^65 - 396 * q^66 - 2536 * q^68 - 3936 * q^74 - 156 * q^78 + 3160 * q^79 + 6804 * q^81 + 4276 * q^82 - 2088 * q^87 + 1780 * q^88 + 324 * q^90 + 4792 * q^92 - 860 * q^94 + 2480 * q^95

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