LMFDB - Embedded newform 288.4.i.c.193.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [288,4,Mod(97,288)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(288, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 4]))

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

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

chi := DirichletCharacter("288.97");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 288 = 2^{5} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	288.i (of order $3$, degree $2$, 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:	$16.9925500817$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 11x^{14} + 37x^{12} - 702x^{10} - 15606x^{8} - 56862x^{6} + 242757x^{4} + 5845851x^{2} + 43046721 $ x^16 + 11x^14 + 37x^12 - 702x^10 - 15606x^8 - 56862x^6 + 242757x^4 + 5845851*x^2 + 43046721
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{16}\cdot 3^{12} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			193.3
Root			$0.0690752 - 2.99920i$ of defining polynomial
Character	$\chi$	$=$	288.193
Dual form			288.4.i.c.97.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.70100 - 4.43899i) q^{3} +(-9.12890 + 15.8117i) q^{5} +(13.5144 + 23.4077i) q^{7} +(-12.4092 + 23.9794i) q^{9} +O(q^{10})$	\(q+(-2.70100 - 4.43899i) q^{3} +(-9.12890 + 15.8117i) q^{5} +(13.5144 + 23.4077i) q^{7} +(-12.4092 + 23.9794i) q^{9} +(-22.5332 - 39.0287i) q^{11} +(24.1911 - 41.9002i) q^{13} +(94.8451 - 2.18439i) q^{15} -91.4583 q^{17} +40.1599 q^{19} +(67.4038 - 123.214i) q^{21} +(46.6039 - 80.7203i) q^{23} +(-104.173 - 180.434i) q^{25} +(139.961 - 9.68413i) q^{27} +(-79.3032 - 137.357i) q^{29} +(-137.448 + 238.068i) q^{31} +(-112.385 + 205.441i) q^{33} -493.487 q^{35} -142.786 q^{37} +(-251.334 + 5.78853i) q^{39} +(160.370 - 277.769i) q^{41} +(-75.9700 - 131.584i) q^{43} +(-265.873 - 415.116i) q^{45} +(-69.1137 - 119.708i) q^{47} +(-193.779 + 335.636i) q^{49} +(247.029 + 405.982i) q^{51} -426.814 q^{53} +822.813 q^{55} +(-108.472 - 178.269i) q^{57} +(86.2700 - 149.424i) q^{59} +(34.3040 + 59.4162i) q^{61} +(-729.005 + 33.5975i) q^{63} +(441.676 + 765.005i) q^{65} +(376.136 - 651.487i) q^{67} +(-484.193 + 11.1515i) q^{69} +691.923 q^{71} -190.062 q^{73} +(-519.570 + 949.776i) q^{75} +(609.047 - 1054.90i) q^{77} +(-444.863 - 770.525i) q^{79} +(-421.024 - 595.130i) q^{81} +(-186.838 - 323.613i) q^{83} +(834.914 - 1446.11i) q^{85} +(-395.529 + 723.027i) q^{87} -1269.84 q^{89} +1307.71 q^{91} +(1428.03 - 32.8891i) q^{93} +(-366.616 + 634.997i) q^{95} +(540.178 + 935.615i) q^{97} +(1215.50 - 56.0186i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 10 q^{5} - 6 q^{9}+O(q^{10}) $ 16 * q - 10 * q^5 - 6 * q^9	$ 16 q - 10 q^{5} - 6 q^{9} + 78 q^{13} - 188 q^{17} + 66 q^{21} - 238 q^{25} - 314 q^{29} - 336 q^{33} - 320 q^{37} + 368 q^{41} + 402 q^{45} + 14 q^{49} + 112 q^{53} - 1146 q^{57} + 482 q^{61} + 846 q^{65} - 642 q^{69} - 3204 q^{73} + 822 q^{77} + 954 q^{81} + 3248 q^{85} - 3832 q^{89} - 1602 q^{93} + 3864 q^{97}+O(q^{100}) $ 16 * q - 10 * q^5 - 6 * q^9 + 78 * q^13 - 188 * q^17 + 66 * q^21 - 238 * q^25 - 314 * q^29 - 336 * q^33 - 320 * q^37 + 368 * q^41 + 402 * q^45 + 14 * q^49 + 112 * q^53 - 1146 * q^57 + 482 * q^61 + 846 * q^65 - 642 * q^69 - 3204 * q^73 + 822 * q^77 + 954 * q^81 + 3248 * q^85 - 3832 * q^89 - 1602 * q^93 + 3864 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/288\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−2.70100	−	4.43899i	−0.519808	−	0.854283i
$3$	−2.70100	−	4.43899i	−0.519808	−	0.854283i
$4$		0			0
$5$	−9.12890	+	15.8117i	−0.816513	+	1.41424i	0.0917229	+	0.995785i	$0.470763\pi$
$5$	−9.12890	+	15.8117i	−0.816513	+	1.41424i	−0.908236	+	0.418458i	$0.862571\pi$
$6$		0			0
$7$	13.5144	+	23.4077i	0.729710	+	1.26390i	0.957006	+	0.290069i	$0.0936784\pi$
$7$	13.5144	+	23.4077i	0.729710	+	1.26390i	−0.227295	+	0.973826i	$0.572988\pi$
$8$		0			0
$9$	−12.4092	+	23.9794i	−0.459600	+	0.888126i
$10$		0			0
$11$	−22.5332	−	39.0287i	−0.617638	−	1.06978i	−0.989916	−	0.141659i	$-0.954756\pi$
$11$	−22.5332	−	39.0287i	−0.617638	−	1.06978i	0.372278	−	0.928121i	$-0.378577\pi$
$12$		0			0
$13$	24.1911	−	41.9002i	0.516107	−	0.893924i	−0.483718	−	0.875224i	$-0.660714\pi$
$13$	24.1911	−	41.9002i	0.516107	−	0.893924i	0.999825	−	0.0187002i	$-0.00595280\pi$
$14$		0			0
$15$	94.8451	−	2.18439i	1.63259	−	0.0376006i
$16$		0			0
$17$	−91.4583			−1.30482			−0.652409	−	0.757867i	$-0.726241\pi$
$17$	−91.4583			−1.30482			−0.652409	+	0.757867i	$0.726241\pi$
$18$		0			0
$19$	40.1599			0.484911			0.242456	−	0.970162i	$-0.422047\pi$
$19$	40.1599			0.484911			0.242456	+	0.970162i	$0.422047\pi$
$20$		0			0
$21$	67.4038	−	123.214i	0.700416	−	1.28036i
$22$		0			0
$23$	46.6039	−	80.7203i	0.422503	−	0.731798i	−0.573680	−	0.819079i	$-0.694485\pi$
$23$	46.6039	−	80.7203i	0.422503	−	0.731798i	0.996184	+	0.0872819i	$0.0278181\pi$
$24$		0			0
$25$	−104.173	−	180.434i	−0.833388	−	1.44347i
$26$		0			0
$27$	139.961	−	9.68413i	0.997615	−	0.0690264i
$28$		0			0
$29$	−79.3032	−	137.357i	−0.507801	−	0.879537i	−0.999959	−	0.00903146i	$-0.997125\pi$
$29$	−79.3032	−	137.357i	−0.507801	−	0.879537i	0.492158	−	0.870506i	$-0.336208\pi$
$30$		0			0
$31$	−137.448	+	238.068i	−0.796337	+	1.37930i	0.125649	+	0.992075i	$0.459899\pi$
$31$	−137.448	+	238.068i	−0.796337	+	1.37930i	−0.921986	+	0.387222i	$0.873435\pi$
$32$		0			0
$33$	−112.385	+	205.441i	−0.592842	+	1.08372i
$34$		0			0
$35$	−493.487			−2.38327
$36$		0			0
$37$	−142.786			−0.634429			−0.317214	−	0.948354i	$-0.602748\pi$
$37$	−142.786			−0.634429			−0.317214	+	0.948354i	$0.602748\pi$
$38$		0			0
$39$	−251.334	+	5.78853i	−1.03194	+	0.0237668i
$40$		0			0
$41$	160.370	−	277.769i	0.610867	−	1.05805i	−0.380227	−	0.924893i	$-0.624154\pi$
$41$	160.370	−	277.769i	0.610867	−	1.05805i	0.991095	−	0.133160i	$-0.0425125\pi$
$42$		0			0
$43$	−75.9700	−	131.584i	−0.269426	−	0.466659i	0.699288	−	0.714840i	$-0.253501\pi$
$43$	−75.9700	−	131.584i	−0.269426	−	0.466659i	−0.968714	+	0.248181i	$0.920167\pi$
$44$		0			0
$45$	−265.873	−	415.116i	−0.880756	−	1.37515i
$46$		0			0
$47$	−69.1137	−	119.708i	−0.214495	−	0.371516i	0.738621	−	0.674121i	$-0.235477\pi$
$47$	−69.1137	−	119.708i	−0.214495	−	0.371516i	−0.953116	+	0.302604i	$0.902144\pi$
$48$		0			0
$49$	−193.779	+	335.636i	−0.564954	+	0.978529i
$50$		0			0
$51$	247.029	+	405.982i	0.678254	+	1.11468i
$52$		0			0
$53$	−426.814			−1.10618			−0.553089	−	0.833122i	$-0.686551\pi$
$53$	−426.814			−1.10618			−0.553089	+	0.833122i	$0.686551\pi$
$54$		0			0
$55$	822.813			2.01724
$56$		0			0
$57$	−108.472	−	178.269i	−0.252061	−	0.414252i
$58$		0			0
$59$	86.2700	−	149.424i	0.190363	−	0.329718i	−0.755008	−	0.655716i	$-0.772367\pi$
$59$	86.2700	−	149.424i	0.190363	−	0.329718i	0.945370	+	0.325998i	$0.105700\pi$
$60$		0			0
$61$	34.3040	+	59.4162i	0.0720029	+	0.124713i	0.899779	−	0.436346i	$-0.143728\pi$
$61$	34.3040	+	59.4162i	0.0720029	+	0.124713i	−0.827776	+	0.561059i	$0.810394\pi$
$62$		0			0
$63$	−729.005	+	33.5975i	−1.45787	+	0.0671887i
$64$		0			0
$65$	441.676	+	765.005i	0.842817	+	1.45980i
$66$		0			0
$67$	376.136	−	651.487i	0.685856	−	1.18794i	−0.287311	−	0.957837i	$-0.592761\pi$
$67$	376.136	−	651.487i	0.685856	−	1.18794i	0.973167	−	0.230100i	$-0.0739053\pi$
$68$		0			0
$69$	−484.193	+	11.1515i	−0.844783	+	0.0194563i
$70$		0			0
$71$	691.923			1.15657			0.578283	−	0.815837i	$-0.303723\pi$
$71$	691.923			1.15657			0.578283	+	0.815837i	$0.303723\pi$
$72$		0			0
$73$	−190.062			−0.304726			−0.152363	−	0.988325i	$-0.548688\pi$
$73$	−190.062			−0.304726			−0.152363	+	0.988325i	$0.548688\pi$
$74$		0			0
$75$	−519.570	+	949.776i	−0.799931	+	1.46228i
$76$		0			0
$77$	609.047	−	1054.90i	0.901394	−	1.56126i
$78$		0			0
$79$	−444.863	−	770.525i	−0.633557	−	1.09735i	−0.986819	−	0.161828i	$-0.948261\pi$
$79$	−444.863	−	770.525i	−0.633557	−	1.09735i	0.353262	−	0.935524i	$-0.385072\pi$
$80$		0			0
$81$	−421.024	−	595.130i	−0.577536	−	0.816365i
$82$		0			0
$83$	−186.838	−	323.613i	−0.247086	−	0.427965i	0.715630	−	0.698479i	$-0.246140\pi$
$83$	−186.838	−	323.613i	−0.247086	−	0.427965i	−0.962716	+	0.270514i	$0.912806\pi$
$84$		0			0
$85$	834.914	−	1446.11i	1.06540	−	1.84533i
$86$		0			0
$87$	−395.529	+	723.027i	−0.487415	+	0.890996i
$88$		0			0
$89$	−1269.84			−1.51240			−0.756198	−	0.654343i	$-0.772945\pi$
$89$	−1269.84			−1.51240			−0.756198	+	0.654343i	$0.772945\pi$
$90$		0			0
$91$	1307.71			1.50644
$92$		0			0
$93$	1428.03	−	32.8891i	1.59225	−	0.0366714i
$94$		0			0
$95$	−366.616	+	634.997i	−0.395937	+	0.685782i
$96$		0			0
$97$	540.178	+	935.615i	0.565430	+	0.979354i	0.997010	+	0.0772788i	$0.0246231\pi$
$97$	540.178	+	935.615i	0.565430	+	0.979354i	−0.431579	+	0.902075i	$0.642044\pi$
$98$		0			0
$99$	1215.50	−	56.0186i	1.23397	−	0.0568696i
$100$		0			0
$101$	289.126	+	500.782i	0.284843	+	0.493363i	0.972571	−	0.232606i	$-0.0747252\pi$
$101$	289.126	+	500.782i	0.284843	+	0.493363i	−0.687728	+	0.725968i	$0.741392\pi$
$102$		0			0
$103$	981.509	−	1700.02i	0.938941	−	1.62629i	0.171490	−	0.985186i	$-0.445142\pi$
$103$	981.509	−	1700.02i	0.938941	−	1.62629i	0.767451	−	0.641108i	$-0.221525\pi$
$104$		0			0
$105$	1332.91	+	2190.58i	1.23884	+	2.03599i
$106$		0			0
$107$	−1366.26			−1.23441			−0.617204	−	0.786803i	$-0.711735\pi$
$107$	−1366.26			−1.23441			−0.617204	+	0.786803i	$0.711735\pi$
$108$		0			0
$109$	−1059.40			−0.930940			−0.465470	−	0.885064i	$-0.654115\pi$
$109$	−1059.40			−0.930940			−0.465470	+	0.885064i	$0.654115\pi$
$110$		0			0
$111$	385.665	+	633.825i	0.329781	+	0.541982i
$112$		0			0
$113$	−668.800	+	1158.40i	−0.556774	+	0.964361i	0.440989	+	0.897512i	$0.354628\pi$
$113$	−668.800	+	1158.40i	−0.556774	+	0.964361i	−0.997763	+	0.0668484i	$0.978706\pi$
$114$		0			0
$115$	850.884	+	1473.77i	0.689959	+	1.19504i
$116$		0			0
$117$	704.549	+	1100.03i	0.556715	+	0.869216i
$118$		0			0
$119$	−1236.01	−	2140.83i	−0.952139	−	1.64915i
$120$		0			0
$121$	−349.991	+	606.202i	−0.262953	+	0.455449i
$122$		0			0
$123$	−1666.17	+	38.3739i	−1.22141	+	0.0281305i
$124$		0			0
$125$	1521.73			1.08886
$126$		0			0
$127$	672.023			0.469546			0.234773	−	0.972050i	$-0.424565\pi$
$127$	672.023			0.469546			0.234773	+	0.972050i	$0.424565\pi$
$128$		0			0
$129$	−378.904	+	692.638i	−0.258610	+	0.472739i
$130$		0			0
$131$	636.306	−	1102.11i	0.424384	−	0.735054i	−0.571979	−	0.820268i	$-0.693824\pi$
$131$	636.306	−	1102.11i	0.424384	−	0.735054i	0.996363	+	0.0852141i	$0.0271574\pi$
$132$		0			0
$133$	542.738	+	940.050i	0.353845	+	0.612877i
$134$		0			0
$135$	−1124.57	+	2301.44i	−0.716946	+	1.46723i
$136$		0			0
$137$	206.210	+	357.167i	0.128597	+	0.222736i	0.923133	−	0.384481i	$-0.125619\pi$
$137$	206.210	+	357.167i	0.128597	+	0.222736i	−0.794536	+	0.607216i	$0.792286\pi$
$138$		0			0
$139$	−960.619	+	1663.84i	−0.586177	+	1.01529i	0.408551	+	0.912736i	$0.366034\pi$
$139$	−960.619	+	1663.84i	−0.586177	+	1.01529i	−0.994728	+	0.102553i	$0.967299\pi$
$140$		0			0
$141$	−344.708	+	630.127i	−0.205884	+	0.376356i
$142$		0			0
$143$	−2180.41			−1.27507
$144$		0			0
$145$	2895.80			1.65851
$146$		0			0
$147$	2013.28	−	46.3682i	1.12961	−	0.0260162i
$148$		0			0
$149$	−422.760	+	732.242i	−0.232442	+	0.402601i	−0.958526	−	0.285005i	$-0.908005\pi$
$149$	−422.760	+	732.242i	−0.232442	+	0.402601i	0.726084	+	0.687606i	$0.241338\pi$
$150$		0			0
$151$	872.752	+	1511.65i	0.470355	+	0.814679i	0.999425	−	0.0338994i	$-0.0107926\pi$
$151$	872.752	+	1511.65i	0.470355	+	0.814679i	−0.529070	+	0.848578i	$0.677459\pi$
$152$		0			0
$153$	1134.92	−	2193.12i	0.599694	−	1.15884i
$154$		0			0
$155$	−2509.50	−	4346.59i	−1.30044	−	2.25243i
$156$		0			0
$157$	−14.2899	+	24.7508i	−0.00726406	+	0.0125817i	−0.869635	−	0.493696i	$-0.835646\pi$
$157$	−14.2899	+	24.7508i	−0.00726406	+	0.0125817i	0.862371	+	0.506278i	$0.168979\pi$
$158$		0			0
$159$	1152.83	+	1894.62i	0.575000	+	0.944990i
$160$		0			0
$161$	2519.30			1.23322
$162$		0			0
$163$	−1420.03			−0.682362			−0.341181	−	0.939998i	$-0.610827\pi$
$163$	−1420.03			−0.682362			−0.341181	+	0.939998i	$0.610827\pi$
$164$		0			0
$165$	−2222.42	−	3652.46i	−1.04858	−	1.72329i
$166$		0			0
$167$	−455.054	+	788.176i	−0.210857	+	0.365215i	−0.951983	−	0.306151i	$-0.900959\pi$
$167$	−455.054	+	788.176i	−0.210857	+	0.365215i	0.741126	+	0.671366i	$0.234292\pi$
$168$		0			0
$169$	−71.9160	−	124.562i	−0.0327337	−	0.0566965i
$170$		0			0
$171$	−498.352	+	963.011i	−0.222865	+	0.430663i
$172$		0			0
$173$	−10.6595	−	18.4628i	−0.00468454	−	0.00811387i	0.863674	−	0.504051i	$-0.168158\pi$
$173$	−10.6595	−	18.4628i	−0.00468454	−	0.00811387i	−0.868358	+	0.495938i	$0.834824\pi$
$174$		0			0
$175$	2815.69	−	4876.92i	1.21626	−	2.10663i
$176$		0			0
$177$	−896.307	+	20.6430i	−0.380624	+	0.00876623i
$178$		0			0
$179$	−3415.94			−1.42636			−0.713182	−	0.700978i	$-0.752747\pi$
$179$	−3415.94			−1.42636			−0.713182	+	0.700978i	$0.752747\pi$
$180$		0			0
$181$	−1579.83			−0.648772			−0.324386	−	0.945925i	$-0.605158\pi$
$181$	−1579.83			−0.648772			−0.324386	+	0.945925i	$0.605158\pi$
$182$		0			0
$183$	171.093	−	312.758i	0.0691123	−	0.126337i
$184$		0			0
$185$	1303.48	−	2257.69i	0.518020	−	0.897236i
$186$		0			0
$187$	2060.85	+	3569.50i	0.805905	+	1.39587i
$188$		0			0
$189$	2118.18	+	3145.30i	0.815212	+	1.21051i
$190$		0			0
$191$	2140.39	+	3707.26i	0.810854	+	1.40444i	0.912267	+	0.409596i	$0.134330\pi$
$191$	2140.39	+	3707.26i	0.810854	+	1.40444i	−0.101413	+	0.994844i	$0.532336\pi$
$192$		0			0
$193$	142.629	−	247.040i	0.0531950	−	0.0921365i	−0.838202	−	0.545360i	$-0.816393\pi$
$193$	142.629	−	247.040i	0.0531950	−	0.0921365i	0.891397	+	0.453224i	$0.149726\pi$
$194$		0			0
$195$	2202.88	−	4026.87i	0.808982	−	1.47882i
$196$		0			0
$197$	−608.803			−0.220180			−0.110090	−	0.993922i	$-0.535114\pi$
$197$	−608.803			−0.220180			−0.110090	+	0.993922i	$0.535114\pi$
$198$		0			0
$199$	2415.88			0.860588			0.430294	−	0.902689i	$-0.358410\pi$
$199$	2415.88			0.860588			0.430294	+	0.902689i	$0.358410\pi$
$200$		0			0
$201$	−3907.88	+	90.0032i	−1.37135	+	0.0315838i
$202$		0			0
$203$	2143.47	−	3712.61i	0.741095	−	1.28361i
$204$		0			0
$205$	2928.00	+	5071.44i	0.997563	+	1.72783i
$206$		0			0
$207$	1357.31	+	2119.21i	0.455746	+	0.711570i
$208$		0			0
$209$	−904.932	−	1567.39i	−0.299500	−	0.518749i
$210$		0			0
$211$	−135.514	+	234.718i	−0.0442142	+	0.0765812i	−0.887286	−	0.461220i	$-0.847412\pi$
$211$	−135.514	+	234.718i	−0.0442142	+	0.0765812i	0.843071	+	0.537802i	$0.180745\pi$
$212$		0			0
$213$	−1868.88	−	3071.44i	−0.601191	−	0.988034i
$214$		0			0
$215$	2774.09			0.879959
$216$		0			0
$217$	−7430.14			−2.32438
$218$		0			0
$219$	513.356	+	843.681i	0.158399	+	0.260323i
$220$		0			0
$221$	−2212.48	+	3832.12i	−0.673426	+	1.16641i
$222$		0			0
$223$	−3171.14	−	5492.58i	−0.952266	−	1.64937i	−0.740503	−	0.672053i	$-0.765413\pi$
$223$	−3171.14	−	5492.58i	−0.952266	−	1.64937i	−0.211763	−	0.977321i	$-0.567921\pi$
$224$		0			0
$225$	5619.40	−	258.980i	1.66501	−	0.0767349i
$226$		0			0
$227$	1229.67	+	2129.85i	0.359543	+	0.622746i	0.987884	−	0.155191i	$-0.0495994\pi$
$227$	1229.67	+	2129.85i	0.359543	+	0.622746i	−0.628342	+	0.777937i	$0.716266\pi$
$228$		0			0
$229$	2032.05	−	3519.62i	0.586383	−	1.01565i	−0.408318	−	0.912840i	$-0.633885\pi$
$229$	2032.05	−	3519.62i	0.586383	−	1.01565i	0.994701	−	0.102806i	$-0.0327820\pi$
$230$		0			0
$231$	−6327.72	+	145.735i	−1.80231	+	0.0415093i
$232$		0			0
$233$	−191.711			−0.0539030			−0.0269515	−	0.999637i	$-0.508580\pi$
$233$	−191.711			−0.0539030			−0.0269515	+	0.999637i	$0.508580\pi$
$234$		0			0
$235$	2523.73			0.700552
$236$		0			0
$237$	−2218.77	+	4055.93i	−0.608122	+	1.11165i
$238$		0			0
$239$	49.8484	−	86.3400i	0.0134913	−	0.0233677i	−0.859201	−	0.511638i	$-0.829039\pi$
$239$	49.8484	−	86.3400i	0.0134913	−	0.0233677i	0.872692	+	0.488271i	$0.162372\pi$
$240$		0			0
$241$	−3116.51	−	5397.95i	−0.832995	−	1.44279i	−0.895653	−	0.444754i	$-0.853291\pi$
$241$	−3116.51	−	5397.95i	−0.832995	−	1.44279i	0.0626578	−	0.998035i	$-0.480042\pi$
$242$		0			0
$243$	−1504.59	+	3476.37i	−0.397199	+	0.917732i
$244$		0			0
$245$	−3537.98	−	6127.96i	−0.922585	−	1.59796i
$246$		0			0
$247$	971.512	−	1682.71i	0.250266	−	0.433474i
$248$		0			0
$249$	−931.863	+	1703.45i	−0.237166	+	0.433541i
$250$		0			0
$251$	648.526			0.163086			0.0815431	−	0.996670i	$-0.474015\pi$
$251$	648.526			0.163086			0.0815431	+	0.996670i	$0.474015\pi$
$252$		0			0
$253$	−4200.54			−1.04382
$254$		0			0
$255$	−8674.38	+	199.781i	−2.13024	+	0.0490619i
$256$		0			0
$257$	−649.384	+	1124.77i	−0.157617	+	0.273000i	−0.934009	−	0.357250i	$-0.883714\pi$
$257$	−649.384	+	1124.77i	−0.157617	+	0.273000i	0.776392	+	0.630250i	$0.217048\pi$
$258$		0			0
$259$	−1929.67	−	3342.29i	−0.462949	−	0.801852i
$260$		0			0
$261$	4277.83	−	197.152i	1.01453	−	0.0467562i
$262$		0			0
$263$	1214.29	+	2103.21i	0.284701	+	0.493116i	0.972537	−	0.232750i	$-0.0747725\pi$
$263$	1214.29	+	2103.21i	0.284701	+	0.493116i	−0.687836	+	0.725866i	$0.741439\pi$
$264$		0			0
$265$	3896.34	−	6748.67i	0.903209	−	1.56440i
$266$		0			0
$267$	3429.85	+	5636.82i	0.786155	+	1.29201i
$268$		0			0
$269$	−1342.70			−0.304333			−0.152167	−	0.988355i	$-0.548625\pi$
$269$	−1342.70			−0.304333			−0.152167	+	0.988355i	$0.548625\pi$
$270$		0			0
$271$	−5293.43			−1.18654			−0.593272	−	0.805002i	$-0.702164\pi$
$271$	−5293.43			−1.18654			−0.593272	+	0.805002i	$0.702164\pi$
$272$		0			0
$273$	−3532.13	−	5804.92i	−0.783057	−	1.28692i
$274$		0			0
$275$	−4694.73	+	8131.50i	−1.02946	+	1.78308i
$276$		0			0
$277$	344.082	+	595.967i	0.0746349	+	0.129271i	0.900927	−	0.433970i	$-0.142888\pi$
$277$	344.082	+	595.967i	0.0746349	+	0.129271i	−0.826293	+	0.563241i	$0.809554\pi$
$278$		0			0
$279$	−4003.10	−	6250.16i	−0.858993	−	1.34117i
$280$		0			0
$281$	−3565.29	−	6175.26i	−0.756894	−	1.31098i	−0.944427	−	0.328720i	$-0.893383\pi$
$281$	−3565.29	−	6175.26i	−0.756894	−	1.31098i	0.187534	−	0.982258i	$-0.439951\pi$
$282$		0			0
$283$	−2196.18	+	3803.90i	−0.461305	+	0.799004i	−0.999026	−	0.0441187i	$-0.985952\pi$
$283$	−2196.18	+	3803.90i	−0.461305	+	0.799004i	0.537721	+	0.843123i	$0.319285\pi$
$284$		0			0
$285$	3808.97	−	87.7251i	0.791663	−	0.0182329i
$286$		0			0
$287$	8669.23			1.78303
$288$		0			0
$289$	3451.63			0.702549
$290$		0			0
$291$	2694.16	−	4924.94i	0.542731	−	0.992113i
$292$		0			0
$293$	−2858.52	+	4951.10i	−0.569954	+	0.987188i	0.426616	+	0.904433i	$0.359705\pi$
$293$	−2858.52	+	4951.10i	−0.569954	+	0.987188i	−0.996570	+	0.0827558i	$0.973628\pi$
$294$		0			0
$295$	1575.10	+	2728.15i	0.310867	+	0.538438i
$296$		0			0
$297$	−3531.74	−	5244.29i	−0.690008	−	1.02460i
$298$		0			0
$299$	−2254.80	−	3905.42i	−0.436114	−	0.755372i
$300$		0			0
$301$	2053.38	−	3556.56i	0.393206	−	0.681052i
$302$		0			0
$303$	1442.03	−	2636.04i	0.273408	−	0.499791i
$304$		0			0
$305$	−1252.63			−0.235165
$306$		0			0
$307$	−1068.51			−0.198642			−0.0993208	−	0.995055i	$-0.531667\pi$
$307$	−1068.51			−0.198642			−0.0993208	+	0.995055i	$0.531667\pi$
$308$		0			0
$309$	−10197.4	+	234.859i	−1.87738	+	0.0432384i
$310$		0			0
$311$	2262.87	−	3919.40i	0.412590	−	0.714627i	−0.582582	−	0.812772i	$-0.697958\pi$
$311$	2262.87	−	3919.40i	0.412590	−	0.714627i	0.995172	+	0.0981448i	$0.0312908\pi$
$312$		0			0
$313$	3858.86	+	6683.74i	0.696855	+	1.20699i	0.969551	+	0.244889i	$0.0787514\pi$
$313$	3858.86	+	6683.74i	0.696855	+	1.20699i	−0.272696	+	0.962100i	$0.587915\pi$
$314$		0			0
$315$	6123.78	−	11833.5i	1.09535	−	2.11665i
$316$		0			0
$317$	3054.49	+	5290.53i	0.541190	+	0.937368i	0.998836	+	0.0482340i	$0.0153593\pi$
$317$	3054.49	+	5290.53i	0.541190	+	0.937368i	−0.457646	+	0.889134i	$0.651307\pi$
$318$		0			0
$319$	−3573.91	+	6190.19i	−0.627274	+	1.08647i
$320$		0			0
$321$	3690.28	+	6064.82i	0.641655	+	1.05453i
$322$		0			0
$323$	−3672.96			−0.632721
$324$		0			0
$325$	−10080.3			−1.72047
$326$		0			0
$327$	2861.45	+	4702.68i	0.483910	+	0.795286i
$328$		0			0
$329$	1868.06	−	3235.58i	0.313038	−	0.542198i
$330$		0			0
$331$	−1439.02	−	2492.46i	−0.238960	−	0.413891i	0.721456	−	0.692460i	$-0.243473\pi$
$331$	−1439.02	−	2492.46i	−0.238960	−	0.413891i	−0.960416	+	0.278569i	$0.910140\pi$
$332$		0			0
$333$	1771.86	−	3423.92i	0.291583	−	0.563453i
$334$		0			0
$335$	6867.41	+	11894.7i	1.12002	+	1.93993i
$336$		0			0
$337$	921.233	−	1595.62i	0.148910	−	0.257920i	−0.781915	−	0.623385i	$-0.785757\pi$
$337$	921.233	−	1595.62i	0.148910	−	0.257920i	0.930825	+	0.365465i	$0.119090\pi$
$338$		0			0
$339$	6948.54	−	160.033i	1.11325	−	0.0256395i
$340$		0			0
$341$	12388.6			1.96739
$342$		0			0
$343$	−1204.37			−0.189591
$344$		0			0
$345$	4243.83	−	7757.73i	0.662261	−	1.21061i
$346$		0			0
$347$	−2046.79	+	3545.15i	−0.316650	+	0.548455i	−0.979787	−	0.200044i	$-0.935892\pi$
$347$	−2046.79	+	3545.15i	−0.316650	+	0.548455i	0.663137	+	0.748498i	$0.269225\pi$
$348$		0			0
$349$	2981.94	+	5164.87i	0.457362	+	0.792175i	0.998821	−	0.0485526i	$-0.0154609\pi$
$349$	2981.94	+	5164.87i	0.457362	+	0.792175i	−0.541458	+	0.840728i	$0.682128\pi$
$350$		0			0
$351$	2980.05	−	6098.68i	0.453172	−	0.927417i
$352$		0			0
$353$	4826.27	+	8359.35i	0.727695	+	1.26041i	0.957855	+	0.287252i	$0.0927418\pi$
$353$	4826.27	+	8359.35i	0.727695	+	1.26041i	−0.230160	+	0.973153i	$0.573925\pi$
$354$		0			0
$355$	−6316.49	+	10940.5i	−0.944351	+	1.63566i
$356$		0			0
$357$	−6164.64	+	11269.0i	−0.913915	+	1.67064i
$358$		0			0
$359$	−1896.77			−0.278851			−0.139425	−	0.990233i	$-0.544526\pi$
$359$	−1896.77			−0.278851			−0.139425	+	0.990233i	$0.544526\pi$
$360$		0			0
$361$	−5246.18			−0.764861
$362$		0			0
$363$	3636.25	−	83.7471i	0.525767	−	0.0121090i
$364$		0			0
$365$	1735.05	−	3005.20i	0.248813	−	0.430957i
$366$		0			0
$367$	−3263.53	−	5652.60i	−0.464182	−	0.803987i	0.534982	−	0.844863i	$-0.320318\pi$
$367$	−3263.53	−	5652.60i	−0.464182	−	0.803987i	−0.999164	+	0.0408763i	$0.986985\pi$
$368$		0			0
$369$	4670.67	+	7292.46i	0.658930	+	1.02881i
$370$		0			0
$371$	−5768.15	−	9990.73i	−0.807190	−	1.39809i
$372$		0			0
$373$	−6473.57	+	11212.6i	−0.898629	+	1.55647i	−0.0693816	+	0.997590i	$0.522103\pi$
$373$	−6473.57	+	11212.6i	−0.898629	+	1.55647i	−0.829248	+	0.558881i	$0.811231\pi$
$374$		0			0
$375$	−4110.20	−	6754.95i	−0.565999	−	0.930197i
$376$		0			0
$377$	−7673.72			−1.04832
$378$		0			0
$379$	−8745.65			−1.18531			−0.592657	−	0.805455i	$-0.701921\pi$
$379$	−8745.65			−1.18531			−0.592657	+	0.805455i	$0.701921\pi$
$380$		0			0
$381$	−1815.13	−	2983.10i	−0.244074	−	0.401126i
$382$		0			0
$383$	2080.22	−	3603.05i	0.277531	−	0.480698i	−0.693239	−	0.720707i	$-0.743817\pi$
$383$	2080.22	−	3603.05i	0.277531	−	0.480698i	0.970771	+	0.240009i	$0.0771505\pi$
$384$		0			0
$385$	11119.8	+	19260.1i	1.47200	+	2.54958i
$386$		0			0
$387$	4098.03	−	188.865i	0.538280	−	0.0248076i
$388$		0			0
$389$	−3033.78	−	5254.66i	−0.395421	−	0.684888i	0.597734	−	0.801694i	$-0.296068\pi$
$389$	−3033.78	−	5254.66i	−0.395421	−	0.684888i	−0.993155	+	0.116806i	$0.962734\pi$
$390$		0			0
$391$	−4262.31	+	7382.54i	−0.551290	+	0.954862i
$392$		0			0
$393$	−6610.93	+	152.257i	−0.848543	+	0.0195429i
$394$		0			0
$395$	16244.4			2.06923
$396$		0			0
$397$	7668.73			0.969477			0.484739	−	0.874659i	$-0.338915\pi$
$397$	7668.73			0.969477			0.484739	+	0.874659i	$0.338915\pi$
$398$		0			0
$399$	2706.93	−	4948.28i	0.339640	−	0.620862i
$400$		0			0
$401$	5271.09	−	9129.79i	0.656423	−	1.13696i	−0.325112	−	0.945675i	$-0.605402\pi$
$401$	5271.09	−	9129.79i	0.656423	−	1.13696i	0.981535	−	0.191282i	$-0.0612645\pi$
$402$		0			0
$403$	6650.05	+	11518.2i	0.821991	+	1.42373i
$404$		0			0
$405$	13253.5	−	1224.22i	1.62610	−	0.150203i
$406$		0			0
$407$	3217.43	+	5572.75i	0.391847	+	0.678700i
$408$		0			0
$409$	5376.24	−	9311.91i	0.649970	−	1.12578i	−0.333159	−	0.942870i	$-0.608115\pi$
$409$	5376.24	−	9311.91i	0.649970	−	1.12578i	0.983130	−	0.182911i	$-0.0585519\pi$
$410$		0			0
$411$	1028.48	−	1880.07i	0.123434	−	0.225638i
$412$		0			0
$413$	4663.56			0.555638
$414$		0			0
$415$	6822.49			0.806995
$416$		0			0
$417$	9980.39	−	229.860i	1.17204	−	0.0269935i
$418$		0			0
$419$	3676.86	−	6368.51i	0.428702	−	0.742534i	−0.568056	−	0.822990i	$-0.692304\pi$
$419$	3676.86	−	6368.51i	0.428702	−	0.742534i	0.996758	+	0.0804557i	$0.0256376\pi$
$420$		0			0
$421$	−5528.64	−	9575.89i	−0.640023	−	1.10855i	−0.985427	−	0.170098i	$-0.945592\pi$
$421$	−5528.64	−	9575.89i	−0.640023	−	1.10855i	0.345405	−	0.938454i	$-0.387742\pi$
$422$		0			0
$423$	3728.18	−	171.820i	0.428535	−	0.0197498i
$424$		0			0
$425$	9527.53	+	16502.2i	1.08742	+	1.88347i
$426$		0			0
$427$	−927.197	+	1605.95i	−0.105082	+	0.182008i
$428$		0			0
$429$	5889.29	+	9678.81i	0.662791	+	1.08927i
$430$		0			0
$431$	4274.92			0.477763			0.238882	−	0.971049i	$-0.423219\pi$
$431$	4274.92			0.477763			0.238882	+	0.971049i	$0.423219\pi$
$432$		0			0
$433$	−13431.7			−1.49073			−0.745364	−	0.666658i	$-0.767724\pi$
$433$	−13431.7			−1.49073			−0.745364	+	0.666658i	$0.767724\pi$
$434$		0			0
$435$	−7821.56	−	12854.4i	−0.862104	−	1.41683i
$436$		0			0
$437$	1871.61	−	3241.72i	0.204877	−	0.354857i
$438$		0			0
$439$	−3642.60	−	6309.17i	−0.396018	−	0.685923i	0.597213	−	0.802083i	$-0.296275\pi$
$439$	−3642.60	−	6309.17i	−0.396018	−	0.685923i	−0.993230	+	0.116160i	$0.962941\pi$
$440$		0			0
$441$	−5643.70	−	8811.68i	−0.609405	−	0.951482i
$442$		0			0
$443$	5658.08	+	9800.08i	0.606825	+	1.05105i	0.991760	+	0.128108i	$0.0408903\pi$
$443$	5658.08	+	9800.08i	0.606825	+	1.05105i	−0.384936	+	0.922943i	$0.625776\pi$
$444$		0			0
$445$	11592.3	−	20078.4i	1.23489	−	2.13889i
$446$		0			0
$447$	4392.29	−	101.159i	0.464761	−	0.0107040i
$448$		0			0
$449$	−11389.3			−1.19709			−0.598544	−	0.801090i	$-0.704254\pi$
$449$	−11389.3			−1.19709			−0.598544	+	0.801090i	$0.704254\pi$
$450$		0			0
$451$	−14454.6			−1.50918
$452$		0			0
$453$	4352.90	−	7957.11i	0.451472	−	0.825292i
$454$		0			0
$455$	−11938.0	+	20677.2i	−1.23002	+	2.13047i
$456$		0			0
$457$	−315.133	−	545.826i	−0.0322567	−	0.0558702i	0.849446	−	0.527675i	$-0.176936\pi$
$457$	−315.133	−	545.826i	−0.0322567	−	0.0558702i	−0.881703	+	0.471805i	$0.843603\pi$
$458$		0			0
$459$	−12800.6	+	885.695i	−1.30171	+	0.0900669i
$460$		0			0
$461$	2497.13	+	4325.16i	0.252284	+	0.436969i	0.964154	−	0.265342i	$-0.0854849\pi$
$461$	2497.13	+	4325.16i	0.252284	+	0.436969i	−0.711870	+	0.702311i	$0.752152\pi$
$462$		0			0
$463$	1631.05	−	2825.06i	0.163718	−	0.283567i	−0.772482	−	0.635037i	$-0.780985\pi$
$463$	1631.05	−	2825.06i	0.163718	−	0.283567i	0.936199	+	0.351470i	$0.114318\pi$
$464$		0			0
$465$	−12516.3	+	22879.8i	−1.24823	+	2.28177i
$466$		0			0
$467$	−8445.84			−0.836888			−0.418444	−	0.908243i	$-0.637424\pi$
$467$	−8445.84			−0.836888			−0.418444	+	0.908243i	$0.637424\pi$
$468$		0			0
$469$	20333.0			2.00190
$470$		0			0
$471$	148.466	−	3.41934i	0.0145243	−	0.000334511i
$472$		0			0
$473$	−3423.69	+	5930.01i	−0.332815	+	0.576453i
$474$		0			0
$475$	−4183.60	−	7246.21i	−0.404119	−	0.699955i
$476$		0			0
$477$	5296.42	−	10234.8i	0.508399	−	0.982426i
$478$		0			0
$479$	1050.40	+	1819.35i	0.100197	+	0.173546i	0.911766	−	0.410711i	$-0.134719\pi$
$479$	1050.40	+	1819.35i	0.100197	+	0.173546i	−0.811569	+	0.584257i	$0.801386\pi$
$480$		0			0
$481$	−3454.15	+	5982.76i	−0.327433	+	0.567131i
$482$		0			0
$483$	−6804.62	−	11183.1i	−0.641038	−	1.05352i
$484$		0			0
$485$	−19724.9			−1.84672
$486$		0			0
$487$	−14117.2			−1.31357			−0.656786	−	0.754077i	$-0.728084\pi$
$487$	−14117.2			−1.31357			−0.656786	+	0.754077i	$0.728084\pi$
$488$		0			0
$489$	3835.49	+	6303.48i	0.354697	+	0.582931i
$490$		0			0
$491$	−2085.78	+	3612.68i	−0.191711	+	0.332053i	−0.945817	−	0.324699i	$-0.894737\pi$
$491$	−2085.78	+	3612.68i	−0.191711	+	0.332053i	0.754107	+	0.656752i	$0.228070\pi$
$492$		0			0
$493$	7252.94	+	12562.5i	0.662588	+	1.14764i
$494$		0			0
$495$	−10210.5	+	19730.6i	−0.927122	+	1.79156i
$496$		0			0
$497$	9350.94	+	16196.3i	0.843957	+	1.46178i
$498$		0			0
$499$	6611.49	−	11451.4i	0.593128	−	1.02733i	−0.400680	−	0.916218i	$-0.631226\pi$
$499$	6611.49	−	11451.4i	0.593128	−	1.02733i	0.993808	−	0.111110i	$-0.0354405\pi$
$500$		0			0
$501$	4727.80	−	108.887i	0.421602	−	0.00970999i
$502$		0			0
$503$	2048.22			0.181562			0.0907810	−	0.995871i	$-0.471064\pi$
$503$	2048.22			0.181562			0.0907810	+	0.995871i	$0.471064\pi$
$504$		0			0
$505$	−10557.6			−0.930313
$506$		0			0
$507$	−358.684	+	655.676i	−0.0314196	+	0.0574351i
$508$		0			0
$509$	−3833.94	+	6640.59i	−0.333864	+	0.578269i	−0.983266	−	0.182176i	$-0.941686\pi$
$509$	−3833.94	+	6640.59i	−0.333864	+	0.578269i	0.649402	+	0.760445i	$0.275019\pi$
$510$		0			0
$511$	−2568.57	−	4448.90i	−0.222362	−	0.385142i
$512$		0			0
$513$	5620.84	−	388.914i	0.483755	−	0.0334717i
$514$		0			0
$515$	17920.2	+	31038.7i	1.53332	+	2.65578i
$516$		0			0
$517$	−3114.70	+	5394.83i	−0.264960	+	0.458925i
$518$		0			0
$519$	−53.1647	+	97.1853i	−0.00449648	+	0.00821958i
$520$		0			0
$521$	−4477.20			−0.376487			−0.188243	−	0.982122i	$-0.560279\pi$
$521$	−4477.20			−0.376487			−0.188243	+	0.982122i	$0.560279\pi$
$522$		0			0
$523$	−9507.51			−0.794903			−0.397452	−	0.917623i	$-0.630105\pi$
$523$	−9507.51			−0.794903			−0.397452	+	0.917623i	$0.630105\pi$
$524$		0			0
$525$	−29253.7	+	673.748i	−2.43188	+	0.0560091i
$526$		0			0
$527$	12570.8	−	21773.3i	1.03908	−	1.79973i
$528$		0			0
$529$	1739.66	+	3013.17i	0.142982	+	0.247651i
$530$		0			0
$531$	2512.56	+	3922.94i	0.205340	+	0.320604i
$532$		0			0
$533$	−7759.04	−	13439.0i	−0.630546	−	1.09214i
$534$		0			0
$535$	12472.5	−	21603.0i	1.00791	−	1.74575i
$536$		0			0
$537$	9226.45	+	15163.3i	0.741435	+	1.21852i
$538$		0			0
$539$	17465.9			1.39575
$540$		0			0
$541$	−19412.5			−1.54271			−0.771356	−	0.636403i	$-0.780421\pi$
$541$	−19412.5			−1.54271			−0.771356	+	0.636403i	$0.780421\pi$
$542$		0			0
$543$	4267.11	+	7012.83i	0.337236	+	0.554235i
$544$		0			0
$545$	9671.18	−	16751.0i	0.760125	−	1.31657i
$546$		0			0
$547$	11170.2	+	19347.4i	0.873134	+	1.51231i	0.858738	+	0.512415i	$0.171249\pi$
$547$	11170.2	+	19347.4i	0.873134	+	1.51231i	0.0143957	+	0.999896i	$0.495418\pi$
$548$		0			0
$549$	−1850.45	+	85.2814i	−0.143853	+	0.00662973i
$550$		0			0
$551$	−3184.81	−	5516.25i	−0.246239	−	0.426498i
$552$		0			0
$553$	12024.1	−	20826.4i	0.924625	−	1.60150i
$554$		0			0
$555$	−13542.6	+	311.901i	−1.03576	+	0.0238549i
$556$		0			0
$557$	9779.43			0.743928			0.371964	−	0.928247i	$-0.378685\pi$
$557$	9779.43			0.743928			0.371964	+	0.928247i	$0.378685\pi$
$558$		0			0
$559$	−7351.18			−0.556211
$560$		0			0
$561$	10278.6	−	18789.3i	0.773551	−	1.41405i
$562$		0			0
$563$	11560.4	−	20023.2i	0.865385	−	1.49889i	−0.00127960	−	0.999999i	$-0.500407\pi$
$563$	11560.4	−	20023.2i	0.865385	−	1.49889i	0.866664	−	0.498891i	$-0.166259\pi$
$564$		0			0
$565$	−12210.8	−	21149.8i	−0.909227	−	1.57483i
$566$		0			0
$567$	8240.72	−	17898.0i	0.610366	−	1.32566i
$568$		0			0
$569$	−10571.5	−	18310.3i	−0.778873	−	1.34905i	−0.932592	−	0.360933i	$-0.882458\pi$
$569$	−10571.5	−	18310.3i	−0.778873	−	1.34905i	0.153719	−	0.988115i	$-0.450875\pi$
$570$		0			0
$571$	1551.21	−	2686.77i	0.113688	−	0.196914i	−0.803566	−	0.595215i	$-0.797067\pi$
$571$	1551.21	−	2686.77i	0.113688	−	0.196914i	0.917255	+	0.398301i	$0.130400\pi$
$572$		0			0
$573$	10675.3	−	19514.5i	0.778302	−	1.42274i
$574$		0			0
$575$	−19419.6			−1.40844
$576$		0			0
$577$	−12927.7			−0.932735			−0.466367	−	0.884591i	$-0.654438\pi$
$577$	−12927.7			−0.932735			−0.466367	+	0.884591i	$0.654438\pi$
$578$		0			0
$579$	−1481.85	+	34.1287i	−0.106362	+	0.00244964i
$580$		0			0
$581$	5050.01	−	8746.87i	0.360602	−	0.624581i
$582$		0			0
$583$	9617.50	+	16658.0i	0.683218	+	1.18337i
$584$		0			0
$585$	−23825.2	+	1098.03i	−1.68385	+	0.0776031i
$586$		0			0
$587$	−5459.85	−	9456.73i	−0.383905	−	0.664942i	0.607712	−	0.794158i	$-0.292088\pi$
$587$	−5459.85	−	9456.73i	−0.383905	−	0.664942i	−0.991617	+	0.129215i	$0.958754\pi$
$588$		0			0
$589$	−5519.92	+	9560.78i	−0.386153	+	0.668837i
$590$		0			0
$591$	1644.38	+	2702.47i	0.114451	+	0.188096i
$592$		0			0
$593$	14962.0			1.03611			0.518056	−	0.855346i	$-0.326656\pi$
$593$	14962.0			1.03611			0.518056	+	0.855346i	$0.326656\pi$
$594$		0			0
$595$	45133.5			3.10974
$596$		0			0
$597$	−6525.29	−	10724.0i	−0.447340	−	0.735186i
$598$		0			0
$599$	−11609.3	+	20107.9i	−0.791893	+	1.37160i	0.132901	+	0.991129i	$0.457571\pi$
$599$	−11609.3	+	20107.9i	−0.791893	+	1.37160i	−0.924794	+	0.380469i	$0.875762\pi$
$600$		0			0
$601$	11805.3	+	20447.4i	0.801246	+	1.38780i	0.918797	+	0.394731i	$0.129162\pi$
$601$	11805.3	+	20447.4i	0.801246	+	1.38780i	−0.117551	+	0.993067i	$0.537504\pi$
$602$		0			0
$603$	10954.7	+	17103.9i	0.739819	+	1.15510i
$604$		0			0
$605$	−6390.06	−	11067.9i	−0.429410	−	0.743760i
$606$		0			0
$607$	−4942.09	+	8559.95i	−0.330466	+	0.572385i	−0.982603	−	0.185717i	$-0.940539\pi$
$607$	−4942.09	+	8559.95i	−0.330466	+	0.572385i	0.652137	+	0.758101i	$0.273873\pi$
$608$		0			0
$609$	−22269.7	+	512.898i	−1.48180	+	0.0341275i
$610$		0			0
$611$	−6687.73			−0.442810
$612$		0			0
$613$	−14005.3			−0.922785			−0.461393	−	0.887196i	$-0.652650\pi$
$613$	−14005.3			−0.922785			−0.461393	+	0.887196i	$0.652650\pi$
$614$		0			0
$615$	14603.5	−	26695.3i	0.957515	−	1.75034i
$616$		0			0
$617$	−2548.89	+	4414.81i	−0.166312	+	0.288061i	−0.937120	−	0.349006i	$-0.886519\pi$
$617$	−2548.89	+	4414.81i	−0.166312	+	0.288061i	0.770808	+	0.637067i	$0.219853\pi$
$618$		0			0
$619$	−13628.3	−	23604.9i	−0.884925	−	1.53274i	−0.845800	−	0.533501i	$-0.820876\pi$
$619$	−13628.3	−	23604.9i	−0.884925	−	1.53274i	−0.0391253	−	0.999234i	$-0.512457\pi$
$620$		0			0
$621$	5741.04	−	11749.0i	0.370982	−	0.759216i
$622$		0			0
$623$	−17161.2	−	29724.1i	−1.10361	−	1.91151i
$624$		0			0
$625$	−870.044	+	1506.96i	−0.0556828	+	0.0964455i
$626$		0			0
$627$	−4513.39	+	8250.50i	−0.287476	+	0.525507i
$628$		0			0
$629$	13059.0			0.827814
$630$		0			0
$631$	10155.9			0.640729			0.320364	−	0.947294i	$-0.396195\pi$
$631$	10155.9			0.640729			0.320364	+	0.947294i	$0.396195\pi$
$632$		0			0
$633$	1407.93	−	32.4264i	0.0884050	−	0.00203607i
$634$		0			0
$635$	−6134.83	+	10625.8i	−0.383391	+	0.664052i
$636$		0			0
$637$	9375.46	+	16238.8i	0.583154	+	1.01005i
$638$		0			0
$639$	−8586.20	+	16591.9i	−0.531557	+	1.02718i
$640$		0			0
$641$	−6884.56	−	11924.4i	−0.424218	−	0.734768i	0.572129	−	0.820164i	$-0.306118\pi$
$641$	−6884.56	−	11924.4i	−0.424218	−	0.734768i	−0.996347	+	0.0853962i	$0.972784\pi$
$642$		0			0
$643$	−6150.22	+	10652.5i	−0.377202	+	0.653334i	−0.990654	−	0.136398i	$-0.956447\pi$
$643$	−6150.22	+	10652.5i	−0.377202	+	0.653334i	0.613452	+	0.789732i	$0.289781\pi$
$644$		0			0
$645$	−7492.81	−	12314.1i	−0.457410	−	0.751734i
$646$		0			0
$647$	−2182.01			−0.132587			−0.0662934	−	0.997800i	$-0.521117\pi$
$647$	−2182.01			−0.132587			−0.0662934	+	0.997800i	$0.521117\pi$
$648$		0			0
$649$	−7775.76			−0.470301
$650$		0			0
$651$	20068.8	+	32982.3i	1.20823	+	1.98568i
$652$		0			0
$653$	−5523.47	+	9566.92i	−0.331011	+	0.573327i	−0.982710	−	0.185150i	$-0.940723\pi$
$653$	−5523.47	+	9566.92i	−0.331011	+	0.573327i	0.651700	+	0.758477i	$0.274056\pi$
$654$		0			0
$655$	11617.5	+	20122.2i	0.693030	+	1.20036i
$656$		0			0
$657$	2358.51	−	4557.56i	0.140052	−	0.270635i
$658$		0			0
$659$	−15188.6	−	26307.5i	−0.897822	−	1.55507i	−0.830273	−	0.557357i	$-0.811815\pi$
$659$	−15188.6	−	26307.5i	−0.897822	−	1.55507i	−0.0675494	−	0.997716i	$-0.521518\pi$
$660$		0			0
$661$	14462.4	−	25049.6i	0.851016	−	1.47400i	−0.0292770	−	0.999571i	$-0.509321\pi$
$661$	14462.4	−	25049.6i	0.851016	−	1.47400i	0.880293	−	0.474431i	$-0.157346\pi$
$662$		0			0
$663$	22986.6	−	529.409i	1.34650	−	0.0310114i
$664$		0			0
$665$	−19818.4			−1.15568
$666$		0			0
$667$	−14783.3			−0.858191
$668$		0			0
$669$	−15816.2	+	28912.1i	−0.914037	+	1.67086i
$670$		0			0
$671$	1545.96	−	2677.68i	0.0889434	−	0.154055i
$672$		0			0
$673$	−15078.3	−	26116.3i	−0.863631	−	1.49585i	−0.868400	−	0.495865i	$-0.834851\pi$
$673$	−15078.3	−	26116.3i	−0.863631	−	1.49585i	0.00476838	−	0.999989i	$-0.498482\pi$
$674$		0			0
$675$	−16327.6	−	24244.9i	−0.931038	−	1.38250i
$676$		0			0
$677$	1898.08	+	3287.57i	0.107753	+	0.186634i	0.914860	−	0.403772i	$-0.132301\pi$
$677$	1898.08	+	3287.57i	0.107753	+	0.186634i	−0.807106	+	0.590406i	$0.798968\pi$
$678$		0			0
$679$	−14600.4	+	25288.6i	−0.825200	+	1.42929i
$680$		0			0
$681$	6133.05	−	11211.2i	0.345108	−	0.630859i
$682$		0			0
$683$	−23752.6			−1.33070			−0.665351	−	0.746530i	$-0.731718\pi$
$683$	−23752.6			−1.33070			−0.665351	+	0.746530i	$0.731718\pi$
$684$		0			0
$685$	−7529.89			−0.420004
$686$		0			0
$687$	−21112.1	+	486.237i	−1.17246	+	0.0270030i
$688$		0			0
$689$	−10325.1	+	17883.6i	−0.570907	+	0.988840i
$690$		0			0
$691$	−6734.28	−	11664.1i	−0.370744	−	0.642148i	0.618936	−	0.785441i	$-0.287564\pi$
$691$	−6734.28	−	11664.1i	−0.370744	−	0.642148i	−0.989680	+	0.143294i	$0.954231\pi$
$692$		0			0
$693$	17738.1	+	27695.0i	0.972315	+	1.51811i
$694$		0			0
$695$	−17538.8	−	30378.0i	−0.957243	−	1.65799i
$696$		0			0
$697$	−14667.2	+	25404.3i	−0.797071	+	1.38057i
$698$		0			0
$699$	517.811	+	851.001i	0.0280192	+	0.0460484i
$700$		0			0
$701$	17822.2			0.960253			0.480126	−	0.877199i	$-0.340591\pi$
$701$	17822.2			0.960253			0.480126	+	0.877199i	$0.340591\pi$
$702$		0			0
$703$	−5734.27			−0.307642
$704$		0			0
$705$	−6816.58	−	11202.8i	−0.364152	−	0.598470i
$706$		0			0
$707$	−7814.75	+	13535.6i	−0.415706	+	0.720024i
$708$		0			0
$709$	4283.54	+	7419.31i	0.226900	+	0.393002i	0.956888	−	0.290458i	$-0.0938077\pi$
$709$	4283.54	+	7419.31i	0.226900	+	0.393002i	−0.729988	+	0.683460i	$0.760474\pi$
$710$		0			0
$711$	23997.1	−	1105.95i	1.26577	−	0.0583353i
$712$		0			0
$713$	12811.3	+	22189.7i	0.672911	+	1.16552i
$714$		0			0
$715$	19904.7	−	34476.0i	1.04111	−	1.80326i
$716$		0			0
$717$	−517.903	+	11.9279i	−0.0269755	+	0.000621278i
$718$		0			0
$719$	19619.6			1.01765			0.508823	−	0.860871i	$-0.330081\pi$
$719$	19619.6			1.01765			0.508823	+	0.860871i	$0.330081\pi$
$720$		0			0
$721$	53058.1			2.74062
$722$		0			0
$723$	−15543.7	+	28414.0i	−0.799554	+	1.46159i
$724$		0			0
$725$	−16522.6	+	28617.9i	−0.846391	+	1.46599i
$726$		0			0
$727$	9008.06	+	15602.4i	0.459547	+	0.795958i	0.998937	−	0.0460976i	$-0.0146785\pi$
$727$	9008.06	+	15602.4i	0.459547	+	0.795958i	−0.539390	+	0.842056i	$0.681345\pi$
$728$		0			0
$729$	19495.4	−	2710.81i	0.990471	−	0.137723i
$730$		0			0
$731$	6948.09	+	12034.4i	0.351552	+	0.608905i
$732$		0			0
$733$	5225.39	−	9050.65i	0.263307	−	0.456062i	−0.703811	−	0.710387i	$-0.748520\pi$
$733$	5225.39	−	9050.65i	0.263307	−	0.456062i	0.967119	+	0.254325i	$0.0818533\pi$
$734$		0			0
$735$	−17645.9	+	32256.7i	−0.885547	+	1.61878i
$736$		0			0
$737$	−33902.2			−1.69444
$738$		0			0
$739$	23104.4			1.15008			0.575041	−	0.818125i	$-0.304986\pi$
$739$	23104.4			1.15008			0.575041	+	0.818125i	$0.304986\pi$
$740$		0			0
$741$	−10093.6	+	232.467i	−0.500400	+	0.0115248i
$742$		0			0
$743$	6107.32	−	10578.2i	0.301556	−	0.522310i	−0.674933	−	0.737879i	$-0.735827\pi$
$743$	6107.32	−	10578.2i	0.301556	−	0.522310i	0.976489	+	0.215569i	$0.0691608\pi$
$744$		0			0
$745$	−7718.66	−	13369.1i	−0.379584	−	0.657458i
$746$		0			0
$747$	10078.5	−	464.488i	0.493647	−	0.0227506i
$748$		0			0
$749$	−18464.3	−	31981.0i	−0.900760	−	1.56016i
$750$		0			0
$751$	−1747.19	+	3026.23i	−0.0848947	+	0.147042i	−0.905346	−	0.424674i	$-0.860389\pi$
$751$	−1747.19	+	3026.23i	−0.0848947	+	0.147042i	0.820452	+	0.571716i	$0.193722\pi$
$752$		0			0
$753$	−1751.67	−	2878.80i	−0.0847735	−	0.139322i
$754$		0			0
$755$	−31869.1			−1.53620
$756$		0			0
$757$	15198.3			0.729712			0.364856	−	0.931064i	$-0.381118\pi$
$757$	15198.3			0.729712			0.364856	+	0.931064i	$0.381118\pi$
$758$		0			0
$759$	11345.7	+	18646.1i	0.542584	+	0.891715i
$760$		0			0
$761$	11621.0	−	20128.2i	0.553563	−	0.958799i	−0.444451	−	0.895803i	$-0.646601\pi$
$761$	11621.0	−	20128.2i	0.553563	−	0.958799i	0.998014	−	0.0629961i	$-0.0200656\pi$
$762$		0			0
$763$	−14317.2	−	24798.2i	−0.679316	−	1.17661i
$764$		0			0
$765$	24316.3	+	37965.8i	1.14923	+	1.79432i
$766$		0			0
$767$	−4173.93	−	7229.46i	−0.196495	−	0.340340i
$768$		0			0
$769$	5230.37	−	9059.27i	0.245269	−	0.424819i	−0.716938	−	0.697137i	$-0.754457\pi$
$769$	5230.37	−	9059.27i	0.245269	−	0.424819i	0.962207	+	0.272318i	$0.0877903\pi$
$770$		0			0
$771$	6746.81	−	155.387i	0.315150	−	0.00725827i
$772$		0			0
$773$	28918.0			1.34555			0.672773	−	0.739849i	$-0.265103\pi$
$773$	28918.0			1.34555			0.672773	+	0.739849i	$0.265103\pi$
$774$		0			0
$775$	57273.9			2.65463
$776$		0			0
$777$	−9624.33	+	17593.3i	−0.444364	+	0.812299i
$778$		0			0
$779$	6440.44	−	11155.2i	0.296217	−	0.513062i
$780$		0			0
$781$	−15591.2	−	27004.8i	−0.714339	−	1.23727i
$782$		0			0
$783$	−12429.6	−	18456.7i	−0.567301	−	0.842388i
$784$		0			0
$785$	−260.902	−	451.895i	−0.0118624	−	0.0205463i
$786$		0			0
$787$	21622.8	−	37451.8i	0.979376	−	1.69633i	0.314712	−	0.949187i	$-0.398092\pi$
$787$	21622.8	−	37451.8i	0.979376	−	1.69633i	0.664665	−	0.747142i	$-0.268574\pi$
$788$		0			0
$789$	6056.32	−	11071.0i	0.273271	−	0.499540i
$790$		0			0
$791$	−36153.8			−1.62513
$792$		0			0
$793$	3319.40			0.148645
$794$		0			0
$795$	−40481.3	+	932.331i	−1.80594	+	0.0415929i
$796$		0			0
$797$	−9265.02	+	16047.5i	−0.411774	+	0.713213i	−0.995084	−	0.0990365i	$-0.968424\pi$
$797$	−9265.02	+	16047.5i	−0.411774	+	0.713213i	0.583310	+	0.812250i	$0.301757\pi$
$798$		0			0
$799$	6321.02	+	10948.3i	0.279877	+	0.484761i
$800$		0			0
$801$	15757.7	−	30450.1i	0.695097	−	1.34320i
$802$		0			0
$803$	4282.70	+	7417.85i	0.188211	+	0.325990i
$804$		0			0
$805$	−22998.4	+	39834.4i	−1.00694	+	1.74407i
$806$		0			0
$807$	3626.63	+	5960.21i	0.158195	+	0.259987i
$808$		0			0
$809$	38233.9			1.66160			0.830799	−	0.556573i	$-0.187884\pi$
$809$	38233.9			1.66160			0.830799	+	0.556573i	$0.187884\pi$
$810$		0			0
$811$	27394.6			1.18613			0.593066	−	0.805154i	$-0.297917\pi$
$811$	27394.6			1.18613			0.593066	+	0.805154i	$0.297917\pi$
$812$		0			0
$813$	14297.6	+	23497.5i	0.616774	+	1.01364i
$814$		0			0
$815$	12963.3	−	22453.0i	0.557158	−	0.965026i
$816$		0			0
$817$	−3050.95	−	5284.40i	−0.130648	−	0.226288i
$818$		0			0
$819$	−16227.7	+	31358.2i	−0.692357	+	1.33790i
$820$		0			0
$821$	5139.96	+	8902.67i	0.218497	+	0.378447i	0.954349	−	0.298695i	$-0.0965514\pi$
$821$	5139.96	+	8902.67i	0.218497	+	0.378447i	−0.735852	+	0.677143i	$0.763218\pi$
$822$		0			0
$823$	−15392.3	+	26660.2i	−0.651933	+	1.12918i	0.330721	+	0.943729i	$0.392708\pi$
$823$	−15392.3	+	26660.2i	−0.651933	+	1.12918i	−0.982653	+	0.185452i	$0.940625\pi$
$824$		0			0
$825$	48776.1	−	1123.37i	2.05838	−	0.0474070i
$826$		0			0
$827$	30714.2			1.29146			0.645730	−	0.763566i	$-0.276553\pi$
$827$	30714.2			1.29146			0.645730	+	0.763566i	$0.276553\pi$
$828$		0			0
$829$	−5205.36			−0.218081			−0.109041	−	0.994037i	$-0.534778\pi$
$829$	−5205.36			−0.218081			−0.109041	+	0.994037i	$0.534778\pi$
$830$		0			0
$831$	1716.12	−	3137.08i	0.0716386	−	0.130956i
$832$		0			0
$833$	17722.7	−	30696.7i	0.737162	−	1.27680i
$834$		0			0
$835$	−8308.27	−	14390.3i	−0.344335	−	0.596405i
$836$		0			0
$837$	−16932.0	+	34651.4i	−0.699230	+	1.43098i
$838$		0			0
$839$	−4152.30	−	7191.99i	−0.170862	−	0.295942i	0.767859	−	0.640618i	$-0.221322\pi$
$839$	−4152.30	−	7191.99i	−0.170862	−	0.295942i	−0.938721	+	0.344677i	$0.887989\pi$
$840$		0			0
$841$	−383.490	+	664.224i	−0.0157239	+	0.0272346i
$842$		0			0
$843$	−17782.0	+	32505.6i	−0.726508	+	1.32806i
$844$		0			0
$845$	2626.05			0.106910
$846$		0			0
$847$	−18919.7			−0.767519
$848$		0			0
$849$	22817.3	−	525.510i	0.922366	−	0.0212432i
$850$		0			0
$851$	−6654.38	+	11525.7i	−0.268048	+	0.464274i
$852$		0			0
$853$	24038.2	+	41635.5i	0.964893	+	1.67124i	0.709902	+	0.704301i	$0.248739\pi$
$853$	24038.2	+	41635.5i	0.964893	+	1.67124i	0.254991	+	0.966943i	$0.417927\pi$
$854$		0			0
$855$	−10677.4	−	16671.0i	−0.427089	−	0.666827i
$856$		0			0
$857$	6421.81	+	11122.9i	0.255968	+	0.443350i	0.965158	−	0.261668i	$-0.0842724\pi$
$857$	6421.81	+	11122.9i	0.255968	+	0.443350i	−0.709190	+	0.705018i	$0.750939\pi$
$858$		0			0
$859$	6551.37	−	11347.3i	0.260221	−	0.450716i	−0.706080	−	0.708132i	$-0.749538\pi$
$859$	6551.37	−	11347.3i	0.260221	−	0.450716i	0.966300	+	0.257417i	$0.0828713\pi$
$860$		0			0
$861$	−23415.6	−	38482.6i	−0.926830	−	1.52321i
$862$		0			0
$863$	12014.9			0.473918			0.236959	−	0.971520i	$-0.423849\pi$
$863$	12014.9			0.473918			0.236959	+	0.971520i	$0.423849\pi$
$864$		0			0
$865$	389.237			0.0153000
$866$		0			0
$867$	−9322.84	−	15321.7i	−0.365191	−	0.600176i
$868$		0			0
$869$	−20048.4	+	34724.8i	−0.782617	+	1.35553i
$870$		0			0
$871$	−18198.3	−	31520.3i	−0.707951	−	1.22621i
$872$		0			0
$873$	−29138.7	+	1342.91i	−1.12966	+	0.0520625i
$874$		0			0
$875$	20565.3	+	35620.2i	0.794554	+	1.37621i
$876$		0			0
$877$	−7943.52	+	13758.6i	−0.305854	+	0.529754i	−0.977451	−	0.211162i	$-0.932275\pi$
$877$	−7943.52	+	13758.6i	−0.305854	+	0.529754i	0.671597	+	0.740916i	$0.265608\pi$
$878$		0			0
$879$	29698.7	−	683.996i	1.13960	−	0.0262464i
$880$		0			0
$881$	−10124.1			−0.387164			−0.193582	−	0.981084i	$-0.562010\pi$
$881$	−10124.1			−0.387164			−0.193582	+	0.981084i	$0.562010\pi$
$882$		0			0
$883$	52412.2			1.99752			0.998760	−	0.0497824i	$-0.0158528\pi$
$883$	52412.2			1.99752			0.998760	+	0.0497824i	$0.0158528\pi$
$884$		0			0
$885$	7855.89	−	14360.6i	0.298387	−	0.545453i
$886$		0			0
$887$	−4697.76	+	8136.75i	−0.177830	+	0.308011i	−0.941137	−	0.338025i	$-0.890241\pi$
$887$	−4697.76	+	8136.75i	−0.177830	+	0.308011i	0.763307	+	0.646036i	$0.223574\pi$
$888$		0			0
$889$	9082.00	+	15730.5i	0.342633	+	0.593457i
$890$		0			0
$891$	−13740.1	+	29842.2i	−0.516623	+	1.12205i
$892$		0			0
$893$	−2775.60	−	4807.48i	−0.104011	−	0.180152i
$894$		0			0
$895$	31183.8	−	54011.8i	1.16465	−	2.01723i
$896$		0			0
$897$	−11245.9	+	20557.5i	−0.418606	+	0.765214i
$898$		0			0
$899$	43600.4			1.61752
$900$		0			0
$901$	39035.7			1.44336
$902$		0			0
$903$	−21333.7	+	491.340i	−0.786203	+	0.0181072i
$904$		0			0
$905$	14422.1	−	24979.8i	0.529731	−	0.917520i
$906$		0			0
$907$	3990.12	+	6911.09i	0.146075	+	0.253009i	0.929773	−	0.368132i	$-0.120003\pi$
$907$	3990.12	+	6911.09i	0.146075	+	0.253009i	−0.783699	+	0.621141i	$0.786669\pi$
$908$		0			0
$909$	−15596.3	+	718.782i	−0.569082	+	0.0262272i
$910$		0			0
$911$	3415.59	+	5915.97i	0.124219	+	0.215153i	0.921427	−	0.388551i	$-0.127024\pi$
$911$	3415.59	+	5915.97i	0.124219	+	0.215153i	−0.797208	+	0.603704i	$0.793691\pi$
$912$		0			0
$913$	−8420.11	+	14584.1i	−0.305219	+	0.528655i
$914$		0			0
$915$	3383.35	+	5560.41i	0.122241	+	0.200898i
$916$		0			0
$917$	34397.2			1.23871
$918$		0			0
$919$	5048.92			0.181228			0.0906140	−	0.995886i	$-0.471117\pi$
$919$	5048.92			0.181228			0.0906140	+	0.995886i	$0.471117\pi$
$920$		0			0
$921$	2886.04	+	4743.09i	0.103255	+	0.169696i
$922$		0			0
$923$	16738.4	−	28991.7i	0.596912	−	1.03388i
$924$		0			0
$925$	14874.5	+	25763.4i	0.528725	+	0.915779i
$926$		0			0
$927$	28585.8	+	44631.9i	1.01282	+	1.58134i
$928$		0			0
$929$	22918.9	+	39696.6i	0.809412	+	1.40194i	0.913272	+	0.407350i	$0.133547\pi$
$929$	22918.9	+	39696.6i	0.809412	+	1.40194i	−0.103860	+	0.994592i	$0.533119\pi$
$930$		0			0
$931$	−7782.16	+	13479.1i	−0.273953	+	0.474500i
$932$		0			0
$933$	−23510.2	+	541.467i	−0.824962	+	0.0189998i
$934$		0			0
$935$	−75253.1			−2.63213
$936$		0			0
$937$	17955.1			0.626007			0.313004	−	0.949752i	$-0.398665\pi$
$937$	17955.1			0.626007			0.313004	+	0.949752i	$0.398665\pi$
$938$		0			0
$939$	19246.3	−	35182.2i	0.668880	−	1.22271i
$940$		0			0
$941$	−14348.6	+	24852.6i	−0.497080	+	0.860968i	−0.999994	−	0.00336865i	$-0.998928\pi$
$941$	−14348.6	+	24852.6i	−0.497080	+	0.860968i	0.502915	+	0.864336i	$0.332261\pi$
$942$		0			0
$943$	−14947.7	−	25890.2i	−0.516187	−	0.894063i
$944$		0			0
$945$	−69069.2	+	4778.99i	−2.37759	+	0.164509i
$946$		0			0
$947$	−11223.0	−	19438.9i	−0.385110	−	0.667031i	0.606674	−	0.794951i	$-0.292503\pi$
$947$	−11223.0	−	19438.9i	−0.385110	−	0.667031i	−0.991784	+	0.127920i	$0.959170\pi$
$948$		0			0
$949$	−4597.79	+	7963.61i	−0.157272	+	0.272402i
$950$		0			0
$951$	15234.4	−	27848.6i	0.519463	−	0.949581i
$952$		0			0
$953$	23371.1			0.794401			0.397200	−	0.917732i	$-0.369982\pi$
$953$	23371.1			0.794401			0.397200	+	0.917732i	$0.369982\pi$
$954$		0			0
$955$	−78157.5			−2.64829
$956$		0			0
$957$	37131.3	−	855.178i	1.25422	−	0.0288861i
$958$		0			0
$959$	−5573.63	+	9653.81i	−0.187677	+	0.325065i
$960$		0			0
$961$	−22888.6	−	39644.2i	−0.768306	−	1.33075i
$962$		0			0
$963$	16954.2	−	32762.2i	0.567334	−	1.09631i
$964$		0			0
$965$	2604.08	+	4510.41i	0.0868689	+	0.150461i
$966$		0			0
$967$	−8475.74	+	14680.4i	−0.281863	+	0.488201i	−0.971844	−	0.235627i	$-0.924286\pi$
$967$	−8475.74	+	14680.4i	−0.281863	+	0.488201i	0.689981	+	0.723828i	$0.257619\pi$
$968$		0			0
$969$	9920.66	+	16304.2i	0.328893	+	0.540523i
$970$		0			0
$971$	2100.40			0.0694182			0.0347091	−	0.999397i	$-0.488950\pi$
$971$	2100.40			0.0694182			0.0347091	+	0.999397i	$0.488950\pi$
$972$		0			0
$973$	−51928.8			−1.71096
$974$		0			0
$975$	27226.8	+	44746.2i	0.894314	+	1.46977i
$976$		0			0
$977$	−2205.45	+	3819.94i	−0.0722195	+	0.125088i	−0.899874	−	0.436150i	$-0.856342\pi$
$977$	−2205.45	+	3819.94i	−0.0722195	+	0.125088i	0.827654	+	0.561238i	$0.189675\pi$
$978$		0			0
$979$	28613.7	+	49560.3i	0.934113	+	1.61793i
$980$		0			0
$981$	13146.3	−	25403.9i	0.427860	−	0.826792i
$982$		0			0
$983$	−4379.54	−	7585.59i	−0.142101	−	0.246127i	0.786186	−	0.617989i	$-0.212053\pi$
$983$	−4379.54	−	7585.59i	−0.142101	−	0.246127i	−0.928288	+	0.371863i	$0.878719\pi$
$984$		0			0
$985$	5557.70	−	9626.21i	0.179780	−	0.311388i
$986$		0			0
$987$	−19408.3	+	446.997i	−0.625911	+	0.0144155i
$988$		0			0
$989$	−14162.0			−0.455334
$990$		0			0
$991$	−24705.7			−0.791928			−0.395964	−	0.918266i	$-0.629590\pi$
$991$	−24705.7			−0.791928			−0.395964	+	0.918266i	$0.629590\pi$
$992$		0			0
$993$	−7177.19	+	13119.9i	−0.229367	+	0.419283i
$994$		0			0
$995$	−22054.3	+	38199.2i	−0.702682	+	1.21708i
$996$		0			0
$997$	−4882.26	−	8456.32i	−0.155088	−	0.268620i	0.778003	−	0.628260i	$-0.216233\pi$
$997$	−4882.26	−	8456.32i	−0.155088	−	0.268620i	−0.933091	+	0.359640i	$0.882899\pi$
$998$		0			0
$999$	−19984.5	+	1382.76i	−0.632916	+	0.0437923i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	288.4.i.c.193.3	yes	16
3.2	odd	2		864.4.i.c.577.8		16
4.3	odd	2	inner	288.4.i.c.193.6	yes	16
9.2	odd	6		864.4.i.c.289.8		16
9.7	even	3	inner	288.4.i.c.97.3	✓	16
12.11	even	2		864.4.i.c.577.7		16
36.7	odd	6	inner	288.4.i.c.97.6	yes	16
36.11	even	6		864.4.i.c.289.7		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
288.4.i.c.97.3	✓	16	9.7	even	3	inner
288.4.i.c.97.6	yes	16	36.7	odd	6	inner
288.4.i.c.193.3	yes	16	1.1	even	1	trivial
288.4.i.c.193.6	yes	16	4.3	odd	2	inner
864.4.i.c.289.7		16	36.11	even	6
864.4.i.c.289.8		16	9.2	odd	6
864.4.i.c.577.7		16	12.11	even	2
864.4.i.c.577.8		16	3.2	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 288 = 2^{5} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	288.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.70100 - 4.43899i) q^{3} +(-9.12890 + 15.8117i) q^{5} +(13.5144 + 23.4077i) q^{7} +(-12.4092 + 23.9794i) q^{9} +O(q^{10})\)	\(q+(-2.70100 - 4.43899i) q^{3} +(-9.12890 + 15.8117i) q^{5} +(13.5144 + 23.4077i) q^{7} +(-12.4092 + 23.9794i) q^{9} +(-22.5332 - 39.0287i) q^{11} +(24.1911 - 41.9002i) q^{13} +(94.8451 - 2.18439i) q^{15} -91.4583 q^{17} +40.1599 q^{19} +(67.4038 - 123.214i) q^{21} +(46.6039 - 80.7203i) q^{23} +(-104.173 - 180.434i) q^{25} +(139.961 - 9.68413i) q^{27} +(-79.3032 - 137.357i) q^{29} +(-137.448 + 238.068i) q^{31} +(-112.385 + 205.441i) q^{33} -493.487 q^{35} -142.786 q^{37} +(-251.334 + 5.78853i) q^{39} +(160.370 - 277.769i) q^{41} +(-75.9700 - 131.584i) q^{43} +(-265.873 - 415.116i) q^{45} +(-69.1137 - 119.708i) q^{47} +(-193.779 + 335.636i) q^{49} +(247.029 + 405.982i) q^{51} -426.814 q^{53} +822.813 q^{55} +(-108.472 - 178.269i) q^{57} +(86.2700 - 149.424i) q^{59} +(34.3040 + 59.4162i) q^{61} +(-729.005 + 33.5975i) q^{63} +(441.676 + 765.005i) q^{65} +(376.136 - 651.487i) q^{67} +(-484.193 + 11.1515i) q^{69} +691.923 q^{71} -190.062 q^{73} +(-519.570 + 949.776i) q^{75} +(609.047 - 1054.90i) q^{77} +(-444.863 - 770.525i) q^{79} +(-421.024 - 595.130i) q^{81} +(-186.838 - 323.613i) q^{83} +(834.914 - 1446.11i) q^{85} +(-395.529 + 723.027i) q^{87} -1269.84 q^{89} +1307.71 q^{91} +(1428.03 - 32.8891i) q^{93} +(-366.616 + 634.997i) q^{95} +(540.178 + 935.615i) q^{97} +(1215.50 - 56.0186i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 10 q^{5} - 6 q^{9}+O(q^{10}) \) 16 * q - 10 * q^5 - 6 * q^9	\( 16 q - 10 q^{5} - 6 q^{9} + 78 q^{13} - 188 q^{17} + 66 q^{21} - 238 q^{25} - 314 q^{29} - 336 q^{33} - 320 q^{37} + 368 q^{41} + 402 q^{45} + 14 q^{49} + 112 q^{53} - 1146 q^{57} + 482 q^{61} + 846 q^{65} - 642 q^{69} - 3204 q^{73} + 822 q^{77} + 954 q^{81} + 3248 q^{85} - 3832 q^{89} - 1602 q^{93} + 3864 q^{97}+O(q^{100}) \) 16 * q - 10 * q^5 - 6 * q^9 + 78 * q^13 - 188 * q^17 + 66 * q^21 - 238 * q^25 - 314 * q^29 - 336 * q^33 - 320 * q^37 + 368 * q^41 + 402 * q^45 + 14 * q^49 + 112 * q^53 - 1146 * q^57 + 482 * q^61 + 846 * q^65 - 642 * q^69 - 3204 * q^73 + 822 * q^77 + 954 * q^81 + 3248 * q^85 - 3832 * q^89 - 1602 * q^93 + 3864 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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