LMFDB - Embedded newform 72.7.m.a.41.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [72,7,Mod(41,72)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(72, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 5]))

N = Newforms(chi, 7, names="a")

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

chi := DirichletCharacter("72.41");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 72 = 2^{3} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	72.m (of order $6$, 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:	$16.5638940206$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			41.4
Character	$\chi$	$=$	72.41
Dual form			72.7.m.a.65.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-19.7087 - 18.4545i) q^{3} +(-11.9109 - 6.87674i) q^{5} +(174.223 + 301.763i) q^{7} +(47.8620 + 727.427i) q^{9} +O(q^{10})$	\(q+(-19.7087 - 18.4545i) q^{3} +(-11.9109 - 6.87674i) q^{5} +(174.223 + 301.763i) q^{7} +(47.8620 + 727.427i) q^{9} +(-126.778 + 73.1950i) q^{11} +(591.569 - 1024.63i) q^{13} +(107.840 + 355.340i) q^{15} -5874.21i q^{17} +7448.19 q^{19} +(2135.19 - 9162.55i) q^{21} +(4029.65 + 2326.52i) q^{23} +(-7717.92 - 13367.8i) q^{25} +(12481.0 - 15219.9i) q^{27} +(29689.1 - 17141.0i) q^{29} +(-3273.48 + 5669.83i) q^{31} +(3849.39 + 897.042i) q^{33} -4792.35i q^{35} +57924.0 q^{37} +(-30568.0 + 9276.91i) q^{39} +(-14891.9 - 8597.83i) q^{41} +(22614.2 + 39169.0i) q^{43} +(4432.25 - 8993.42i) q^{45} +(43037.6 - 24847.8i) q^{47} +(-1882.91 + 3261.29i) q^{49} +(-108406. + 115773. i) q^{51} -200622. i q^{53} +2013.37 q^{55} +(-146794. - 137453. i) q^{57} +(-12700.8 - 7332.84i) q^{59} +(131369. + 227538. i) q^{61} +(-211172. + 141178. i) q^{63} +(-14092.2 + 8136.13i) q^{65} +(-226222. + 391827. i) q^{67} +(-36484.2 - 120218. i) q^{69} +252831. i q^{71} -90978.2 q^{73} +(-94587.0 + 405892. i) q^{75} +(-44175.2 - 25504.5i) q^{77} +(323522. + 560356. i) q^{79} +(-526859. + 69632.3i) q^{81} +(589001. - 340060. i) q^{83} +(-40395.4 + 69966.9i) q^{85} +(-901460. - 210071. i) q^{87} -1.28071e6i q^{89} +412260. q^{91} +(169150. - 51334.3i) q^{93} +(-88714.4 - 51219.3i) q^{95} +(719696. + 1.24655e6i) q^{97} +(-59311.9 - 88718.2i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 10 q^{3} + 74 q^{9}+O(q^{10}) $ 36 * q + 10 * q^3 + 74 * q^9	$ 36 q + 10 q^{3} + 74 q^{9} + 1350 q^{11} + 7912 q^{15} + 9540 q^{19} + 3828 q^{21} + 30888 q^{23} + 56250 q^{25} + 11392 q^{27} + 38556 q^{29} + 27720 q^{31} + 33514 q^{33} + 134068 q^{39} + 179226 q^{41} + 15930 q^{43} - 185620 q^{45} + 187596 q^{47} - 198774 q^{49} - 158098 q^{51} - 197064 q^{55} - 244990 q^{57} - 408618 q^{59} + 17136 q^{61} - 417048 q^{63} - 125712 q^{65} + 27090 q^{67} - 848504 q^{69} - 534060 q^{73} - 1405714 q^{75} + 48168 q^{77} + 172620 q^{79} + 349010 q^{81} + 1801980 q^{83} - 791568 q^{85} + 28500 q^{87} + 538560 q^{91} - 1116448 q^{93} + 1832652 q^{95} + 770706 q^{97} - 614260 q^{99}+O(q^{100}) $ 36 * q + 10 * q^3 + 74 * q^9 + 1350 * q^11 + 7912 * q^15 + 9540 * q^19 + 3828 * q^21 + 30888 * q^23 + 56250 * q^25 + 11392 * q^27 + 38556 * q^29 + 27720 * q^31 + 33514 * q^33 + 134068 * q^39 + 179226 * q^41 + 15930 * q^43 - 185620 * q^45 + 187596 * q^47 - 198774 * q^49 - 158098 * q^51 - 197064 * q^55 - 244990 * q^57 - 408618 * q^59 + 17136 * q^61 - 417048 * q^63 - 125712 * q^65 + 27090 * q^67 - 848504 * q^69 - 534060 * q^73 - 1405714 * q^75 + 48168 * q^77 + 172620 * q^79 + 349010 * q^81 + 1801980 * q^83 - 791568 * q^85 + 28500 * q^87 + 538560 * q^91 - 1116448 * q^93 + 1832652 * q^95 + 770706 * q^97 - 614260 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/72\mathbb{Z}\right)^\times$.

$n$	$37$	$55$	$65$
$\chi(n)$	$1$	$1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−19.7087	−	18.4545i	−0.729950	−	0.683500i
$3$	−19.7087	−	18.4545i	−0.729950	−	0.683500i
$4$		0			0
$5$	−11.9109	−	6.87674i	−0.0952869	−	0.0550139i	0.451599	−	0.892221i	$-0.350854\pi$
$5$	−11.9109	−	6.87674i	−0.0952869	−	0.0550139i	−0.546886	+	0.837207i	$0.684187\pi$
$6$		0			0
$7$	174.223	+	301.763i	0.507939	+	0.879777i	0.999958	+	0.00919179i	$0.00292588\pi$
$7$	174.223	+	301.763i	0.507939	+	0.879777i	−0.492019	+	0.870585i	$0.663741\pi$
$8$		0			0
$9$	47.8620	+	727.427i	0.0656544	+	0.997842i
$10$		0			0
$11$	−126.778	+	73.1950i	−0.0952498	+	0.0549925i	−0.546868	−	0.837219i	$-0.684180\pi$
$11$	−126.778	+	73.1950i	−0.0952498	+	0.0549925i	0.451618	+	0.892211i	$0.350847\pi$
$12$		0			0
$13$	591.569	−	1024.63i	0.269262	−	0.466376i	−0.699409	−	0.714721i	$-0.746554\pi$
$13$	591.569	−	1024.63i	0.269262	−	0.466376i	0.968672	+	0.248346i	$0.0798868\pi$
$14$		0			0
$15$	107.840	+	355.340i	0.0319527	+	0.105286i
$16$		0			0
$17$		−	5874.21i		−	1.19565i	−0.801628	−	0.597823i	$-0.796033\pi$
$17$		−	5874.21i		−	1.19565i	0.801628	−	0.597823i	$-0.203967\pi$
$18$		0			0
$19$	7448.19			1.08590			0.542950	−	0.839765i	$-0.317307\pi$
$19$	7448.19			1.08590			0.542950	+	0.839765i	$0.317307\pi$
$20$		0			0
$21$	2135.19	−	9162.55i	0.230557	−	0.989370i
$22$		0			0
$23$	4029.65	+	2326.52i	0.331195	+	0.191216i	0.656372	−	0.754438i	$-0.272090\pi$
$23$	4029.65	+	2326.52i	0.331195	+	0.191216i	−0.325177	+	0.945653i	$0.605424\pi$
$24$		0			0
$25$	−7717.92	−	13367.8i	−0.493947	−	0.855541i
$26$		0			0
$27$	12481.0	−	15219.9i	0.634101	−	0.773250i
$28$		0			0
$29$	29689.1	−	17141.0i	1.21731	−	0.702816i	0.252971	−	0.967474i	$-0.418592\pi$
$29$	29689.1	−	17141.0i	1.21731	−	0.702816i	0.964343	+	0.264657i	$0.0852589\pi$
$30$		0			0
$31$	−3273.48	+	5669.83i	−0.109882	+	0.190320i	−0.915722	−	0.401812i	$-0.868380\pi$
$31$	−3273.48	+	5669.83i	−0.109882	+	0.190320i	0.805841	+	0.592133i	$0.201714\pi$
$32$		0			0
$33$	3849.39	+	897.042i	0.107115	+	0.0249615i
$34$		0			0
$35$		−	4792.35i		−	0.111775i
$36$		0			0
$37$	57924.0			1.14355			0.571773	−	0.820412i	$-0.306256\pi$
$37$	57924.0			1.14355			0.571773	+	0.820412i	$0.306256\pi$
$38$		0			0
$39$	−30568.0	+	9276.91i	−0.515316	+	0.156390i
$40$		0			0
$41$	−14891.9	−	8597.83i	−0.216072	−	0.124749i	0.388058	−	0.921635i	$-0.373146\pi$
$41$	−14891.9	−	8597.83i	−0.216072	−	0.124749i	−0.604130	+	0.796886i	$0.706479\pi$
$42$		0			0
$43$	22614.2	+	39169.0i	0.284431	+	0.492649i	0.972471	−	0.233024i	$-0.0748620\pi$
$43$	22614.2	+	39169.0i	0.284431	+	0.492649i	−0.688040	+	0.725673i	$0.741529\pi$
$44$		0			0
$45$	4432.25	−	8993.42i	0.0486392	−	0.0986932i
$46$		0			0
$47$	43037.6	−	24847.8i	0.414529	−	0.239328i	−0.278205	−	0.960522i	$-0.589739\pi$
$47$	43037.6	−	24847.8i	0.414529	−	0.239328i	0.692734	+	0.721193i	$0.256406\pi$
$48$		0			0
$49$	−1882.91	+	3261.29i	−0.0160045	+	0.0277205i
$50$		0			0
$51$	−108406.	+	115773.i	−0.817224	+	0.872762i
$52$		0			0
$53$		−	200622.i		−	1.34757i	−0.738928	−	0.673785i	$-0.764668\pi$
$53$		−	200622.i		−	1.34757i	0.738928	−	0.673785i	$-0.235332\pi$
$54$		0			0
$55$	2013.37			0.0121014
$56$		0			0
$57$	−146794.	−	137453.i	−0.792653	−	0.742214i
$58$		0			0
$59$	−12700.8	−	7332.84i	−0.0618410	−	0.0357039i	0.468761	−	0.883325i	$-0.344701\pi$
$59$	−12700.8	−	7332.84i	−0.0618410	−	0.0357039i	−0.530602	+	0.847621i	$0.678034\pi$
$60$		0			0
$61$	131369.	+	227538.i	0.578766	+	1.00245i	0.995621	+	0.0934796i	$0.0297990\pi$
$61$	131369.	+	227538.i	0.578766	+	1.00245i	−0.416855	+	0.908973i	$0.636868\pi$
$62$		0			0
$63$	−211172.	+	141178.i	−0.844530	+	0.564604i
$64$		0			0
$65$	−14092.2	+	8136.13i	−0.0513143	+	0.0296263i
$66$		0			0
$67$	−226222.	+	391827.i	−0.752159	+	1.30278i	0.194615	+	0.980880i	$0.437654\pi$
$67$	−226222.	+	391827.i	−0.752159	+	1.30278i	−0.946774	+	0.321898i	$0.895679\pi$
$68$		0			0
$69$	−36484.2	−	120218.i	−0.111060	−	0.365950i
$70$		0			0
$71$			252831.i			0.706408i	0.935546	+	0.353204i	$0.114908\pi$
$71$			252831.i			0.706408i	−0.935546	+	0.353204i	$0.885092\pi$
$72$		0			0
$73$	−90978.2			−0.233867			−0.116933	−	0.993140i	$-0.537306\pi$
$73$	−90978.2			−0.233867			−0.116933	+	0.993140i	$0.537306\pi$
$74$		0			0
$75$	−94587.0	+	405892.i	−0.224206	+	0.962115i
$76$		0			0
$77$	−44175.2	−	25504.5i	−0.0967623	−	0.0558657i
$78$		0			0
$79$	323522.	+	560356.i	0.656178	+	1.13653i	0.981597	+	0.190964i	$0.0611614\pi$
$79$	323522.	+	560356.i	0.656178	+	1.13653i	−0.325419	+	0.945570i	$0.605505\pi$
$80$		0			0
$81$	−526859.	+	69632.3i	−0.991379	+	0.131025i
$82$		0			0
$83$	589001.	−	340060.i	1.03011	−	0.594732i	0.113091	−	0.993585i	$-0.463925\pi$
$83$	589001.	−	340060.i	1.03011	−	0.594732i	0.917015	+	0.398852i	$0.130591\pi$
$84$		0			0
$85$	−40395.4	+	69966.9i	−0.0657772	+	0.113929i
$86$		0			0
$87$	−901460.	−	210071.i	−1.36895	−	0.319014i
$88$		0			0
$89$		−	1.28071e6i		−	1.81669i	−0.418227	−	0.908343i	$-0.637348\pi$
$89$		−	1.28071e6i		−	1.81669i	0.418227	−	0.908343i	$-0.362652\pi$
$90$		0			0
$91$	412260.			0.547075
$92$		0			0
$93$	169150.	−	51334.3i	0.210292	−	0.0638203i
$94$		0			0
$95$	−88714.4	−	51219.3i	−0.103472	−	0.0597397i
$96$		0			0
$97$	719696.	+	1.24655e6i	0.788558	+	1.36582i	0.926850	+	0.375431i	$0.122505\pi$
$97$	719696.	+	1.24655e6i	0.788558	+	1.36582i	−0.138292	+	0.990391i	$0.544161\pi$
$98$		0			0
$99$	−59311.9	−	88718.2i	−0.0611274	−	0.0914338i
$100$		0			0
$101$	733738.	−	423624.i	0.712159	−	0.411165i	−0.0997010	−	0.995017i	$-0.531789\pi$
$101$	733738.	−	423624.i	0.712159	−	0.411165i	0.811860	+	0.583852i	$0.198455\pi$
$102$		0			0
$103$	940443.	−	1.62889e6i	0.860638	−	1.49067i	−0.0106753	−	0.999943i	$-0.503398\pi$
$103$	940443.	−	1.62889e6i	0.860638	−	1.49067i	0.871314	−	0.490726i	$-0.163269\pi$
$104$		0			0
$105$	−88440.5	+	94450.8i	−0.0763982	+	0.0815901i
$106$		0			0
$107$		−	1.47092e6i		−	1.20071i	−0.799733	−	0.600355i	$-0.795026\pi$
$107$		−	1.47092e6i		−	1.20071i	0.799733	−	0.600355i	$-0.204974\pi$
$108$		0			0
$109$	653410.			0.504553			0.252276	−	0.967655i	$-0.418821\pi$
$109$	653410.			0.504553			0.252276	+	0.967655i	$0.418821\pi$
$110$		0			0
$111$	−1.14160e6	−	1.06896e6i	−0.834732	−	0.781614i
$112$		0			0
$113$	−171444.	−	98983.3i	−0.118819	−	0.0686004i	0.439412	−	0.898285i	$-0.355187\pi$
$113$	−171444.	−	98983.3i	−0.118819	−	0.0686004i	−0.558232	+	0.829685i	$0.688520\pi$
$114$		0			0
$115$	−31997.7	−	55421.7i	−0.0210390	−	0.0364407i
$116$		0			0
$117$	773656.	+	381283.i	0.483048	+	0.238062i
$118$		0			0
$119$	1.77262e6	−	1.02342e6i	1.05190	−	0.607315i
$120$		0			0
$121$	−875065.	+	1.51566e6i	−0.493952	+	0.855549i
$122$		0			0
$123$	134830.	+	444274.i	0.0724556	+	0.238746i
$124$		0			0
$125$			427195.i			0.218724i
$126$		0			0
$127$	−691996.			−0.337826			−0.168913	−	0.985631i	$-0.554026\pi$
$127$	−691996.			−0.337826			−0.168913	+	0.985631i	$0.554026\pi$
$128$		0			0
$129$	277149.	−	1.18930e6i	0.129105	−	0.554018i
$130$		0			0
$131$	2.57045e6	+	1.48405e6i	1.14339	+	0.660138i	0.947269	−	0.320441i	$-0.103831\pi$
$131$	2.57045e6	+	1.48405e6i	1.14339	+	0.660138i	0.196124	+	0.980579i	$0.437164\pi$
$132$		0			0
$133$	1.29765e6	+	2.24759e6i	0.551572	+	0.955350i
$134$		0			0
$135$	−253323.	+	95453.2i	−0.102961	+	0.0387962i
$136$		0			0
$137$	−2.54787e6	+	1.47101e6i	−0.990868	+	0.572078i	−0.905534	−	0.424275i	$-0.860529\pi$
$137$	−2.54787e6	+	1.47101e6i	−0.990868	+	0.572078i	−0.0853343	+	0.996352i	$0.527196\pi$
$138$		0			0
$139$	692271.	−	1.19905e6i	0.257770	−	0.446470i	−0.707875	−	0.706338i	$-0.750346\pi$
$139$	692271.	−	1.19905e6i	0.257770	−	0.446470i	0.965644	+	0.259868i	$0.0836791\pi$
$140$		0			0
$141$	−1.30677e6	−	304522.i	−0.466166	−	0.108633i
$142$		0			0
$143$			173200.i			0.0592296i
$144$		0			0
$145$	−471497.			−0.154659
$146$		0			0
$147$	97295.2	−	29527.5i	0.0306295	−	0.00929556i
$148$		0			0
$149$	−4.13745e6	−	2.38876e6i	−1.25076	−	0.722126i	−0.279499	−	0.960146i	$-0.590168\pi$
$149$	−4.13745e6	−	2.38876e6i	−1.25076	−	0.722126i	−0.971260	+	0.238020i	$0.923502\pi$
$150$		0			0
$151$	−2.69352e6	−	4.66531e6i	−0.782328	−	1.35503i	−0.930583	−	0.366082i	$-0.880699\pi$
$151$	−2.69352e6	−	4.66531e6i	−0.782328	−	1.35503i	0.148255	−	0.988949i	$-0.452634\pi$
$152$		0			0
$153$	4.27306e6	−	281151.i	1.19307	−	0.0784994i
$154$		0			0
$155$	77980.0	−	45021.8i	0.0209405	−	0.0120900i
$156$		0			0
$157$	−1.14340e6	+	1.98042e6i	−0.295460	+	0.511751i	−0.975092	−	0.221802i	$-0.928806\pi$
$157$	−1.14340e6	+	1.98042e6i	−0.295460	+	0.511751i	0.679632	+	0.733553i	$0.262139\pi$
$158$		0			0
$159$	−3.70238e6	+	3.95399e6i	−0.921064	+	0.983659i
$160$		0			0
$161$			1.62133e6i			0.388503i
$162$		0			0
$163$	−847231.			−0.195632			−0.0978158	−	0.995205i	$-0.531186\pi$
$163$	−847231.			−0.195632			−0.0978158	+	0.995205i	$0.531186\pi$
$164$		0			0
$165$	−39680.9	−	37155.8i	−0.00883343	−	0.00827132i
$166$		0			0
$167$	299706.	+	173035.i	0.0643496	+	0.0371523i	0.531830	−	0.846851i	$-0.321505\pi$
$167$	299706.	+	173035.i	0.0643496	+	0.0371523i	−0.467480	+	0.884004i	$0.654838\pi$
$168$		0			0
$169$	1.71350e6	+	2.96786e6i	0.354996	+	0.614871i
$170$		0			0
$171$	356486.	+	5.41802e6i	0.0712941	+	1.08356i
$172$		0			0
$173$	−4.07747e6	+	2.35413e6i	−0.787504	+	0.454666i	−0.839083	−	0.544003i	$-0.816908\pi$
$173$	−4.07747e6	+	2.35413e6i	−0.787504	+	0.454666i	0.0515792	+	0.998669i	$0.483575\pi$
$174$		0			0
$175$	2.68928e6	−	4.65797e6i	0.501790	−	0.869126i
$176$		0			0
$177$	114993.	+	378908.i	0.0207372	+	0.0683305i
$178$		0			0
$179$			1.00696e7i			1.75571i	0.478923	+	0.877857i	$0.341027\pi$
$179$			1.00696e7i			1.75571i	−0.478923	+	0.877857i	$0.658973\pi$
$180$		0			0
$181$	−1.03185e7			−1.74013			−0.870064	−	0.492939i	$-0.835923\pi$
$181$	−1.03185e7			−1.74013			−0.870064	+	0.492939i	$0.835923\pi$
$182$		0			0
$183$	1.60999e6	−	6.90881e6i	0.262706	−	1.12733i
$184$		0			0
$185$	−689925.	−	398329.i	−0.108965	−	0.0629110i
$186$		0			0
$187$	429963.	+	744718.i	0.0657516	+	0.113885i
$188$		0			0
$189$	6.76728e6	+	1.11466e6i	1.00237	+	0.165103i
$190$		0			0
$191$	−6.37892e6	+	3.68287e6i	−0.915476	+	0.528550i	−0.882189	−	0.470895i	$-0.843931\pi$
$191$	−6.37892e6	+	3.68287e6i	−0.915476	+	0.528550i	−0.0332871	+	0.999446i	$0.510598\pi$
$192$		0			0
$193$	3.08328e6	−	5.34040e6i	0.428885	−	0.742851i	−0.567889	−	0.823105i	$-0.692240\pi$
$193$	3.08328e6	−	5.34040e6i	0.428885	−	0.742851i	0.996774	+	0.0802539i	$0.0255731\pi$
$194$		0			0
$195$	427887.	+	99712.4i	0.0577065	+	0.0134476i
$196$		0			0
$197$			1.92754e6i			0.252119i	0.992023	+	0.126059i	$0.0402330\pi$
$197$			1.92754e6i			0.252119i	−0.992023	+	0.126059i	$0.959767\pi$
$198$		0			0
$199$	−1.36601e7			−1.73338			−0.866689	−	0.498849i	$-0.833756\pi$
$199$	−1.36601e7			−1.73338			−0.866689	+	0.498849i	$0.833756\pi$
$200$		0			0
$201$	1.16895e7	−	3.54758e6i	1.43949	−	0.436862i
$202$		0			0
$203$	1.03450e7	+	5.97271e6i	1.23664	+	0.713976i
$204$		0			0
$205$	118250.	+	204815.i	0.0137259	+	0.0237739i
$206$		0			0
$207$	−1.49951e6	+	3.04263e6i	−0.169059	+	0.343035i
$208$		0			0
$209$	−944264.	+	545171.i	−0.103432	+	0.0597164i
$210$		0			0
$211$	7.93878e6	−	1.37504e7i	0.845097	−	1.46375i	−0.0404403	−	0.999182i	$-0.512876\pi$
$211$	7.93878e6	−	1.37504e7i	0.845097	−	1.46375i	0.885537	−	0.464569i	$-0.153791\pi$
$212$		0			0
$213$	4.66587e6	−	4.98296e6i	0.482830	−	0.515642i
$214$		0			0
$215$		−	622049.i		−	0.0625906i
$216$		0			0
$217$	−2.28126e6			−0.223253
$218$		0			0
$219$	1.79306e6	+	1.67896e6i	0.170711	+	0.159848i
$220$		0			0
$221$	−6.01888e6	−	3.47500e6i	−0.557620	−	0.321942i
$222$		0			0
$223$	−2.36926e6	−	4.10367e6i	−0.213647	−	0.370048i	0.739206	−	0.673479i	$-0.235201\pi$
$223$	−2.36926e6	−	4.10367e6i	−0.213647	−	0.370048i	−0.952853	+	0.303431i	$0.901868\pi$
$224$		0			0
$225$	9.35473e6	−	6.25404e6i	0.821266	−	0.549051i
$226$		0			0
$227$	3.33511e6	−	1.92552e6i	0.285123	−	0.164616i	−0.350617	−	0.936519i	$-0.614028\pi$
$227$	3.33511e6	−	1.92552e6i	0.285123	−	0.164616i	0.635740	+	0.771903i	$0.280695\pi$
$228$		0			0
$229$	7.67290e6	−	1.32899e7i	0.638930	−	1.10666i	−0.346738	−	0.937962i	$-0.612711\pi$
$229$	7.67290e6	−	1.32899e7i	0.638930	−	1.10666i	0.985668	−	0.168697i	$-0.0539559\pi$
$230$		0			0
$231$	399959.	+	1.31789e6i	0.0324474	+	0.106916i
$232$		0			0
$233$		−	1.02349e7i		−	0.809128i	−0.914510	−	0.404564i	$-0.867423\pi$
$233$		−	1.02349e7i		−	0.809128i	0.914510	−	0.404564i	$-0.132577\pi$
$234$		0			0
$235$	−683487.			−0.0526656
$236$		0			0
$237$	3.96492e6	−	1.70143e7i	0.297844	−	1.27811i
$238$		0			0
$239$	−6.90651e6	−	3.98748e6i	−0.505900	−	0.292082i	0.225247	−	0.974302i	$-0.427681\pi$
$239$	−6.90651e6	−	3.98748e6i	−0.505900	−	0.292082i	−0.731147	+	0.682220i	$0.761015\pi$
$240$		0			0
$241$	2.05887e6	+	3.56606e6i	0.147088	+	0.254764i	0.930150	−	0.367180i	$-0.119677\pi$
$241$	2.05887e6	+	3.56606e6i	0.147088	+	0.254764i	−0.783062	+	0.621944i	$0.786343\pi$
$242$		0			0
$243$	1.16687e7	+	8.35058e6i	0.813213	+	0.581966i
$244$		0			0
$245$	44854.1	−	25896.6i	0.00305003	−	0.00176094i
$246$		0			0
$247$	4.40612e6	−	7.63162e6i	0.292392	−	0.506438i
$248$		0			0
$249$	−1.78841e7	−	4.16761e6i	−1.15843	−	0.269953i
$250$		0			0
$251$			2.62166e7i			1.65789i	0.559331	+	0.828944i	$0.311058\pi$
$251$			2.62166e7i			1.65789i	−0.559331	+	0.828944i	$0.688942\pi$
$252$		0			0
$253$	−681159.			−0.0420617
$254$		0			0
$255$	2.08734e6	−	633476.i	0.125885	−	0.0382041i
$256$		0			0
$257$	−334472.	−	193108.i	−0.0197043	−	0.0113763i	0.490116	−	0.871657i	$-0.336955\pi$
$257$	−334472.	−	193108.i	−0.0197043	−	0.0113763i	−0.509820	+	0.860281i	$0.670288\pi$
$258$		0			0
$259$	1.00917e7	+	1.74794e7i	0.580852	+	1.00607i
$260$		0			0
$261$	1.38898e7	+	2.07762e7i	0.781222	+	1.16854i
$262$		0			0
$263$	1.76401e7	−	1.01845e7i	0.969690	−	0.559851i	0.0705479	−	0.997508i	$-0.477525\pi$
$263$	1.76401e7	−	1.01845e7i	0.969690	−	0.559851i	0.899142	+	0.437658i	$0.144192\pi$
$264$		0			0
$265$	−1.37963e6	+	2.38958e6i	−0.0741351	+	0.128406i
$266$		0			0
$267$	−2.36348e7	+	2.52410e7i	−1.24171	+	1.32609i
$268$		0			0
$269$		−	1.43063e7i		−	0.734971i	−0.930029	−	0.367485i	$-0.880219\pi$
$269$		−	1.43063e7i		−	0.734971i	0.930029	−	0.367485i	$-0.119781\pi$
$270$		0			0
$271$	−2.34991e7			−1.18071			−0.590356	−	0.807143i	$-0.701013\pi$
$271$	−2.34991e7			−1.18071			−0.590356	+	0.807143i	$0.701013\pi$
$272$		0			0
$273$	−8.12509e6	−	7.60806e6i	−0.399338	−	0.373926i
$274$		0			0
$275$	1.95692e6	+	1.12983e6i	0.0940967	+	0.0543268i
$276$		0			0
$277$	6.28412e6	+	1.08844e7i	0.295669	+	0.512113i	0.975140	−	0.221589i	$-0.0711242\pi$
$277$	6.28412e6	+	1.08844e7i	0.295669	+	0.512113i	−0.679471	+	0.733702i	$0.737791\pi$
$278$		0			0
$279$	−4.28107e6	−	2.10985e6i	−0.197124	−	0.0971491i
$280$		0			0
$281$	−3.57148e7	+	2.06199e7i	−1.60964	+	0.929327i	−0.620192	+	0.784450i	$0.712945\pi$
$281$	−3.57148e7	+	2.06199e7i	−1.60964	+	0.929327i	−0.989450	+	0.144877i	$0.953721\pi$
$282$		0			0
$283$	−2.65591e6	+	4.60016e6i	−0.117180	+	0.202962i	−0.918649	−	0.395075i	$-0.870719\pi$
$283$	−2.65591e6	+	4.60016e6i	−0.117180	+	0.202962i	0.801469	+	0.598036i	$0.204052\pi$
$284$		0			0
$285$	803215.	+	2.64664e6i	0.0346974	+	0.114330i
$286$		0			0
$287$		−	5.99177e6i		−	0.253460i
$288$		0			0
$289$	−1.03688e7			−0.429569
$290$		0			0
$291$	8.82023e6	−	3.78494e7i	0.357932	−	1.53596i
$292$		0			0
$293$	3.10900e7	+	1.79498e7i	1.23600	+	0.713603i	0.968273	−	0.249893i	$-0.0803955\pi$
$293$	3.10900e7	+	1.79498e7i	1.23600	+	0.713603i	0.267723	+	0.963496i	$0.413729\pi$
$294$		0			0
$295$	100852.	+	174681.i	0.00392843	+	0.00680424i
$296$		0			0
$297$	−468293.	+	2.84309e6i	−0.0178751	+	0.108523i
$298$		0			0
$299$	4.76763e6	−	2.75259e6i	0.178357	−	0.102974i
$300$		0			0
$301$	−7.87985e6	+	1.36483e7i	−0.288947	+	0.500471i
$302$		0			0
$303$	−2.22788e7	−	5.19172e6i	−0.800872	−	0.186631i
$304$		0			0
$305$		−	3.61356e6i		−	0.127361i
$306$		0			0
$307$	1.18219e7			0.408574			0.204287	−	0.978911i	$-0.434512\pi$
$307$	1.18219e7			0.408574			0.204287	+	0.978911i	$0.434512\pi$
$308$		0			0
$309$	−4.85953e7	+	1.47479e7i	−1.64710	+	0.499868i
$310$		0			0
$311$	−4.05781e7	−	2.34278e7i	−1.34899	−	0.778842i	−0.360888	−	0.932609i	$-0.617526\pi$
$311$	−4.05781e7	−	2.34278e7i	−1.34899	−	0.778842i	−0.988107	+	0.153767i	$0.950860\pi$
$312$		0			0
$313$	1.98876e7	+	3.44464e7i	0.648560	+	1.12334i	0.983467	+	0.181088i	$0.0579617\pi$
$313$	1.98876e7	+	3.44464e7i	0.648560	+	1.12334i	−0.334907	+	0.942251i	$0.608705\pi$
$314$		0			0
$315$	3.48609e6	−	229372.i	0.111534	−	0.00733851i
$316$		0			0
$317$	3.64631e7	−	2.10520e7i	1.14466	−	0.660869i	0.197079	−	0.980388i	$-0.436855\pi$
$317$	3.64631e7	−	2.10520e7i	1.14466	−	0.660869i	0.947580	+	0.319519i	$0.103521\pi$
$318$		0			0
$319$	−2.50927e6	+	4.34618e6i	−0.0772993	+	0.133886i
$320$		0			0
$321$	−2.71451e7	+	2.89899e7i	−0.820686	+	0.876459i
$322$		0			0
$323$		−	4.37522e7i		−	1.29835i
$324$		0			0
$325$	−1.82627e7			−0.532005
$326$		0			0
$327$	−1.28778e7	−	1.20584e7i	−0.368298	−	0.344862i
$328$		0			0
$329$	1.49963e7	+	8.65812e6i	0.421111	+	0.243128i
$330$		0			0
$331$	2.54769e7	+	4.41273e7i	0.702527	+	1.21681i	0.967577	+	0.252577i	$0.0812782\pi$
$331$	2.54769e7	+	4.41273e7i	0.702527	+	1.21681i	−0.265050	+	0.964235i	$0.585388\pi$
$332$		0			0
$333$	2.77236e6	+	4.21355e7i	0.0750788	+	1.14108i
$334$		0			0
$335$	5.38899e6	−	3.11133e6i	0.143342	−	0.0827584i
$336$		0			0
$337$	1.05221e7	−	1.82249e7i	0.274925	−	0.476184i	−0.695191	−	0.718825i	$-0.744680\pi$
$337$	1.05221e7	−	1.82249e7i	0.274925	−	0.476184i	0.970116	+	0.242641i	$0.0780137\pi$
$338$		0			0
$339$	1.55224e6	+	5.11475e6i	0.0398438	+	0.131288i
$340$		0			0
$341$		−	958410.i		−	0.0241706i
$342$		0			0
$343$	3.96822e7			0.983361
$344$		0			0
$345$	−392148.	+	1.68279e6i	−0.00954977	+	0.0409801i
$346$		0			0
$347$	−2.19815e7	−	1.26910e7i	−0.526101	−	0.303745i	0.213326	−	0.976981i	$-0.431570\pi$
$347$	−2.19815e7	−	1.26910e7i	−0.526101	−	0.303745i	−0.739427	+	0.673236i	$0.764904\pi$
$348$		0			0
$349$	8.53217e6	+	1.47781e7i	0.200717	+	0.347651i	0.948760	−	0.315999i	$-0.102340\pi$
$349$	8.53217e6	+	1.47781e7i	0.200717	+	0.347651i	−0.748043	+	0.663650i	$0.769006\pi$
$350$		0			0
$351$	−8.21133e6	−	2.17920e7i	−0.189886	−	0.503937i
$352$		0			0
$353$	5.43603e6	−	3.13850e6i	0.123583	−	0.0713506i	−0.436934	−	0.899493i	$-0.643936\pi$
$353$	5.43603e6	−	3.13850e6i	0.123583	−	0.0713506i	0.560517	+	0.828143i	$0.310602\pi$
$354$		0			0
$355$	1.73865e6	−	3.01144e6i	0.0388623	−	0.0673114i
$356$		0			0
$357$	−5.38227e7	−	1.25426e7i	−1.18294	−	0.275665i
$358$		0			0
$359$		−	1.06102e7i		−	0.229319i	−0.993405	−	0.114660i	$-0.963422\pi$
$359$		−	1.06102e7i		−	0.229319i	0.993405	−	0.114660i	$-0.0365777\pi$
$360$		0			0
$361$	8.42970e6			0.179180
$362$		0			0
$363$	4.52171e7	−	1.37227e7i	0.945328	−	0.286892i
$364$		0			0
$365$	1.08363e6	+	625634.i	0.0222845	+	0.0128659i
$366$		0			0
$367$	3.08647e7	+	5.34592e7i	0.624401	+	1.08149i	0.988656	+	0.150195i	$0.0479901\pi$
$367$	3.08647e7	+	5.34592e7i	0.624401	+	1.08149i	−0.364256	+	0.931299i	$0.618677\pi$
$368$		0			0
$369$	5.54154e6	−	1.12443e7i	0.110294	−	0.223796i
$370$		0			0
$371$	6.05404e7	−	3.49530e7i	1.18556	−	0.684483i
$372$		0			0
$373$	2.71932e7	−	4.70999e7i	0.524002	−	0.907599i	−0.475607	−	0.879658i	$-0.657772\pi$
$373$	2.71932e7	−	4.70999e7i	0.524002	−	0.907599i	0.999610	−	0.0279410i	$-0.00889505\pi$
$374$		0			0
$375$	7.88367e6	−	8.41943e6i	0.149498	−	0.159657i
$376$		0			0
$377$		−	4.05603e7i		−	0.756968i
$378$		0			0
$379$	−5.28347e7			−0.970514			−0.485257	−	0.874372i	$-0.661274\pi$
$379$	−5.28347e7			−0.970514			−0.485257	+	0.874372i	$0.661274\pi$
$380$		0			0
$381$	1.36383e7	+	1.27705e7i	0.246596	+	0.230904i
$382$		0			0
$383$	4.48100e6	+	2.58710e6i	0.0797587	+	0.0460487i	0.539349	−	0.842082i	$-0.318670\pi$
$383$	4.48100e6	+	2.58710e6i	0.0797587	+	0.0460487i	−0.459590	+	0.888131i	$0.652004\pi$
$384$		0			0
$385$	350776.	+	607562.i	0.00614678	+	0.0106465i
$386$		0			0
$387$	−2.74102e7	+	1.83249e7i	−0.472912	+	0.316162i
$388$		0			0
$389$	3.79065e7	−	2.18853e7i	0.643969	−	0.371795i	−0.142173	−	0.989842i	$-0.545409\pi$
$389$	3.79065e7	−	2.18853e7i	0.643969	−	0.371795i	0.786142	+	0.618046i	$0.212076\pi$
$390$		0			0
$391$	1.36665e7	−	2.36710e7i	0.228626	−	0.395992i
$392$		0			0
$393$	−2.32727e7	−	7.66851e7i	−0.383415	−	1.26338i
$394$		0			0
$395$		−	8.89909e6i		−	0.144396i
$396$		0			0
$397$	−2.06308e7			−0.329719			−0.164860	−	0.986317i	$-0.552717\pi$
$397$	−2.06308e7			−0.329719			−0.164860	+	0.986317i	$0.552717\pi$
$398$		0			0
$399$	1.59033e7	−	6.82445e7i	0.250362	−	1.07436i
$400$		0			0
$401$	9.01853e7	+	5.20685e7i	1.39863	+	0.807499i	0.994249	−	0.107093i	$-0.0341541\pi$
$401$	9.01853e7	+	5.20685e7i	1.39863	+	0.807499i	0.404380	+	0.914591i	$0.367487\pi$
$402$		0			0
$403$	3.87298e6	+	6.70820e6i	0.0591739	+	0.102492i
$404$		0			0
$405$	6.75419e6	+	2.79370e6i	0.101674	+	0.0420546i
$406$		0			0
$407$	−7.34347e6	+	4.23975e6i	−0.108923	+	0.0628865i
$408$		0			0
$409$	2.29857e7	−	3.98125e7i	0.335961	−	0.581901i	−0.647708	−	0.761888i	$-0.724272\pi$
$409$	2.29857e7	−	3.98125e7i	0.335961	−	0.581901i	0.983669	+	0.179988i	$0.0576057\pi$
$410$		0			0
$411$	7.73620e7	+	1.80280e7i	1.11430	+	0.259670i
$412$		0			0
$413$		−	5.11020e6i		−	0.0725417i
$414$		0			0
$415$	−9.35402e6			−0.130874
$416$		0			0
$417$	−3.57716e7	+	1.08561e7i	−0.493321	+	0.149715i
$418$		0			0
$419$	−1.03911e8	−	5.99931e7i	−1.41260	−	0.815566i	−0.416968	−	0.908921i	$-0.636907\pi$
$419$	−1.03911e8	−	5.99931e7i	−1.41260	−	0.815566i	−0.995633	+	0.0933554i	$0.970241\pi$
$420$		0			0
$421$	−6.72752e7	−	1.16524e8i	−0.901589	−	1.56160i	−0.825432	−	0.564502i	$-0.809068\pi$
$421$	−6.72752e7	−	1.16524e8i	−0.901589	−	1.56160i	−0.0761568	−	0.997096i	$-0.524265\pi$
$422$		0			0
$423$	2.01348e7	+	3.01175e7i	0.266028	+	0.397921i
$424$		0			0
$425$	−7.85254e7	+	4.53367e7i	−1.02292	+	0.590586i
$426$		0			0
$427$	−4.57750e7	+	7.92847e7i	−0.587956	+	1.01837i
$428$		0			0
$429$	3.19632e6	−	3.41353e6i	0.0404835	−	0.0432347i
$430$		0			0
$431$			6.33408e7i			0.791137i	0.918436	+	0.395569i	$0.129452\pi$
$431$			6.33408e7i			0.791137i	−0.918436	+	0.395569i	$0.870548\pi$
$432$		0			0
$433$	1.05323e8			1.29736			0.648678	−	0.761063i	$-0.275322\pi$
$433$	1.05323e8			1.29736			0.648678	+	0.761063i	$0.275322\pi$
$434$		0			0
$435$	9.29256e6	+	8.70124e6i	0.112893	+	0.105709i
$436$		0			0
$437$	3.00136e7	+	1.73284e7i	0.359645	+	0.207641i
$438$		0			0
$439$	1.59455e7	+	2.76184e7i	0.188471	+	0.326441i	0.944741	−	0.327819i	$-0.106314\pi$
$439$	1.59455e7	+	2.76184e7i	0.188471	+	0.326441i	−0.756270	+	0.654260i	$0.772980\pi$
$440$		0			0
$441$	−2.46247e6	−	1.21359e6i	−0.0287115	−	0.0141500i
$442$		0			0
$443$	−7.88028e7	+	4.54968e7i	−0.906422	+	0.523323i	−0.879278	−	0.476308i	$-0.841975\pi$
$443$	−7.88028e7	+	4.54968e7i	−0.906422	+	0.523323i	−0.0271439	+	0.999632i	$0.508641\pi$
$444$		0			0
$445$	−8.80709e6	+	1.52543e7i	−0.0999430	+	0.173106i
$446$		0			0
$447$	3.74602e7	+	1.23434e8i	0.419418	+	1.38201i
$448$		0			0
$449$			3.63065e7i			0.401093i	0.979684	+	0.200547i	$0.0642718\pi$
$449$			3.63065e7i			0.401093i	−0.979684	+	0.200547i	$0.935728\pi$
$450$		0			0
$451$	2.51727e6			0.0274411
$452$		0			0
$453$	−3.30104e7	+	1.41654e8i	−0.355104	+	1.52383i
$454$		0			0
$455$	−4.91037e6	−	2.83501e6i	−0.0521291	−	0.0300968i
$456$		0			0
$457$	3.68907e6	+	6.38966e6i	0.0386517	+	0.0669467i	0.884704	−	0.466153i	$-0.154360\pi$
$457$	3.68907e6	+	6.38966e6i	0.0386517	+	0.0669467i	−0.846052	+	0.533100i	$0.821027\pi$
$458$		0			0
$459$	−8.94047e7	−	7.33161e7i	−0.924533	−	0.758161i
$460$		0			0
$461$	2.48677e6	−	1.43574e6i	0.0253824	−	0.0146545i	−0.487255	−	0.873260i	$-0.662002\pi$
$461$	2.48677e6	−	1.43574e6i	0.0253824	−	0.0146545i	0.512638	+	0.858605i	$0.328668\pi$
$462$		0			0
$463$	−5.05812e7	+	8.76092e7i	−0.509620	+	0.882687i	0.490318	+	0.871543i	$0.336881\pi$
$463$	−5.05812e7	+	8.76092e7i	−0.509620	+	0.882687i	−0.999938	+	0.0111436i	$0.996453\pi$
$464$		0			0
$465$	−2.36773e6	−	551764.i	−0.0235491	−	0.00548775i
$466$		0			0
$467$			1.24658e8i			1.22397i	0.790870	+	0.611984i	$0.209628\pi$
$467$			1.24658e8i			1.22397i	−0.790870	+	0.611984i	$0.790372\pi$
$468$		0			0
$469$	−1.57652e8			−1.52820
$470$		0			0
$471$	5.90825e7	−	1.79306e7i	0.565453	−	0.171606i
$472$		0			0
$473$	−5.73396e6	−	3.31050e6i	−0.0541840	−	0.0312831i
$474$		0			0
$475$	−5.74846e7	−	9.95662e7i	−0.536377	−	0.929033i
$476$		0			0
$477$	1.45938e8	−	9.60218e6i	1.34466	−	0.0884738i
$478$		0			0
$479$	−7.38687e7	+	4.26481e7i	−0.672131	+	0.388055i	−0.796883	−	0.604133i	$-0.793520\pi$
$479$	−7.38687e7	+	4.26481e7i	−0.672131	+	0.388055i	0.124753	+	0.992188i	$0.460186\pi$
$480$		0			0
$481$	3.42661e7	−	5.93506e7i	0.307914	−	0.533322i
$482$		0			0
$483$	2.99209e7	−	3.19543e7i	0.265542	−	0.283588i
$484$		0			0
$485$		−	1.97966e7i		−	0.173527i
$486$		0			0
$487$	−2.27758e6			−0.0197191			−0.00985954	−	0.999951i	$-0.503138\pi$
$487$	−2.27758e6			−0.0197191			−0.00985954	+	0.999951i	$0.503138\pi$
$488$		0			0
$489$	1.66978e7	+	1.56352e7i	0.142801	+	0.133714i
$490$		0			0
$491$	−7.70339e7	−	4.44755e7i	−0.650785	−	0.375731i	0.137972	−	0.990436i	$-0.455942\pi$
$491$	−7.70339e7	−	4.44755e7i	−0.650785	−	0.375731i	−0.788757	+	0.614705i	$0.789275\pi$
$492$		0			0
$493$	−1.00690e8	−	1.74400e8i	−0.840320	−	1.45548i
$494$		0			0
$495$	96364.1	+	1.46458e6i	0.000794511	+	0.0120753i
$496$		0			0
$497$	−7.62952e7	+	4.40490e7i	−0.621481	+	0.358812i
$498$		0			0
$499$	−1.63413e7	+	2.83039e7i	−0.131518	+	0.227795i	−0.924262	−	0.381759i	$-0.875318\pi$
$499$	−1.63413e7	+	2.83039e7i	−0.131518	+	0.227795i	0.792744	+	0.609555i	$0.208652\pi$
$500$		0			0
$501$	−2.71352e6	−	8.94122e6i	−0.0215784	−	0.0711023i
$502$		0			0
$503$			1.66285e8i			1.30662i	0.757092	+	0.653309i	$0.226620\pi$
$503$			1.66285e8i			1.30662i	−0.757092	+	0.653309i	$0.773380\pi$
$504$		0			0
$505$	−1.16526e7			−0.0904792
$506$		0			0
$507$	2.09998e7	−	9.01143e7i	0.161135	−	0.691465i
$508$		0			0
$509$	8.70764e7	+	5.02736e7i	0.660309	+	0.381230i	0.792395	−	0.610009i	$-0.208834\pi$
$509$	8.70764e7	+	5.02736e7i	0.660309	+	0.381230i	−0.132086	+	0.991238i	$0.542167\pi$
$510$		0			0
$511$	−1.58505e7	−	2.74539e7i	−0.118790	−	0.205751i
$512$		0			0
$513$	9.29610e7	−	1.13361e8i	0.688571	−	0.839673i
$514$		0			0
$515$	−2.24030e7	+	1.29344e7i	−0.164015	+	0.0946942i
$516$		0			0
$517$	−3.63747e6	+	6.30028e6i	−0.0263225	+	0.0455920i
$518$		0			0
$519$	1.23806e8	+	2.88510e7i	0.885603	+	0.206376i
$520$		0			0
$521$			6.25786e7i			0.442499i	0.975217	+	0.221250i	$0.0710136\pi$
$521$			6.25786e7i			0.442499i	−0.975217	+	0.221250i	$0.928986\pi$
$522$		0			0
$523$	9.85991e7			0.689236			0.344618	−	0.938743i	$-0.388008\pi$
$523$	9.85991e7			0.689236			0.344618	+	0.938743i	$0.388008\pi$
$524$		0			0
$525$	−1.38963e8	+	4.21730e7i	−0.960330	+	0.291445i
$526$		0			0
$527$	3.33058e7	+	1.92291e7i	0.227556	+	0.131379i
$528$		0			0
$529$	−6.31926e7	−	1.09453e8i	−0.426873	−	0.739366i
$530$		0			0
$531$	4.72622e6	−	9.58991e6i	0.0315668	−	0.0640517i
$532$		0			0
$533$	−1.76192e7	+	1.01724e7i	−0.116360	+	0.0671804i
$534$		0			0
$535$	−1.01151e7	+	1.75200e7i	−0.0660558	+	0.114412i
$536$		0			0
$537$	1.85830e8	−	1.98459e8i	1.20003	−	1.28158i
$538$		0			0
$539$		−	551278.i		−	0.00352050i
$540$		0			0
$541$	1.15378e8			0.728669			0.364334	−	0.931268i	$-0.381296\pi$
$541$	1.15378e8			0.728669			0.364334	+	0.931268i	$0.381296\pi$
$542$		0			0
$543$	2.03364e8	+	1.90423e8i	1.27021	+	1.18938i
$544$		0			0
$545$	−7.78268e6	−	4.49333e6i	−0.0480773	−	0.0277574i
$546$		0			0
$547$	−1.39534e8	−	2.41680e8i	−0.852548	−	1.47666i	−0.878901	−	0.477004i	$-0.841723\pi$
$547$	−1.39534e8	−	2.41680e8i	−0.852548	−	1.47666i	0.0263533	−	0.999653i	$-0.491611\pi$
$548$		0			0
$549$	−1.59230e8	+	1.06452e8i	−0.962291	+	0.643333i
$550$		0			0
$551$	2.21130e8	−	1.27669e8i	1.32188	−	0.763189i
$552$		0			0
$553$	−1.12730e8	+	1.95254e8i	−0.666597	+	1.15458i
$554$		0			0
$555$	6.24654e6	+	2.05828e7i	0.0365393	+	0.120399i
$556$		0			0
$557$		−	2.31085e8i		−	1.33723i	−0.743608	−	0.668616i	$-0.766887\pi$
$557$		−	2.31085e8i		−	1.33723i	0.743608	−	0.668616i	$-0.233113\pi$
$558$		0			0
$559$	5.35116e7			0.306346
$560$		0			0
$561$	5.26941e6	−	2.26121e7i	0.0298451	−	0.128072i
$562$		0			0
$563$	1.40012e6	+	808357.i	0.00784583	+	0.00452979i	0.503918	−	0.863752i	$-0.331891\pi$
$563$	1.40012e6	+	808357.i	0.00784583	+	0.00452979i	−0.496072	+	0.868281i	$0.665225\pi$
$564$		0			0
$565$	1.36137e6	+	2.35795e6i	0.00754796	+	0.0130734i
$566$		0			0
$567$	−1.12804e8	−	1.46855e8i	−0.618833	−	0.805639i
$568$		0			0
$569$	−3.12079e8	+	1.80179e8i	−1.69406	+	0.978063i	−0.742873	+	0.669432i	$0.766538\pi$
$569$	−3.12079e8	+	1.80179e8i	−1.69406	+	0.978063i	−0.951182	+	0.308631i	$0.900129\pi$
$570$		0			0
$571$	1.04629e8	−	1.81222e8i	0.562008	−	0.973426i	−0.435314	−	0.900279i	$-0.643363\pi$
$571$	1.04629e8	−	1.81222e8i	0.562008	−	0.973426i	0.997321	−	0.0731467i	$-0.0233041\pi$
$572$		0			0
$573$	1.93685e8	+	4.51354e7i	1.02952	+	0.239913i
$574$		0			0
$575$		−	7.18236e7i		−	0.377801i
$576$		0			0
$577$	3.35380e8			1.74586			0.872932	−	0.487842i	$-0.162216\pi$
$577$	3.35380e8			1.74586			0.872932	+	0.487842i	$0.162216\pi$
$578$		0			0
$579$	−1.59322e8	+	4.83516e7i	−0.820804	+	0.249101i
$580$		0			0
$581$	2.05235e8	+	1.18493e8i	1.04646	+	0.604176i
$582$		0			0
$583$	1.46845e7	+	2.54344e7i	0.0741062	+	0.128356i
$584$		0			0
$585$	−6.59293e6	−	9.86164e6i	−0.0329314	−	0.0492585i
$586$		0			0
$587$	1.86161e8	−	1.07480e8i	0.920394	−	0.531390i	0.0366334	−	0.999329i	$-0.488337\pi$
$587$	1.86161e8	−	1.07480e8i	0.920394	−	0.531390i	0.883761	+	0.467939i	$0.155003\pi$
$588$		0			0
$589$	−2.43815e7	+	4.22300e7i	−0.119320	+	0.206669i
$590$		0			0
$591$	3.55718e7	−	3.79892e7i	0.172323	−	0.184034i
$592$		0			0
$593$			6.69362e7i			0.320994i	0.987036	+	0.160497i	$0.0513097\pi$
$593$			6.69362e7i			0.320994i	−0.987036	+	0.160497i	$0.948690\pi$
$594$		0			0
$595$	−2.81513e7			−0.133643
$596$		0			0
$597$	2.69221e8	+	2.52090e8i	1.26528	+	1.18476i
$598$		0			0
$599$	−1.45227e8	−	8.38469e7i	−0.675721	−	0.390128i	0.122520	−	0.992466i	$-0.460902\pi$
$599$	−1.45227e8	−	8.38469e7i	−0.675721	−	0.390128i	−0.798241	+	0.602338i	$0.794236\pi$
$600$		0			0
$601$	1.78113e8	+	3.08500e8i	0.820486	+	1.42112i	0.905321	+	0.424729i	$0.139630\pi$
$601$	1.78113e8	+	3.08500e8i	0.820486	+	1.42112i	−0.0848347	+	0.996395i	$0.527036\pi$
$602$		0			0
$603$	−2.95853e8	−	1.45806e8i	−1.34935	−	0.665003i
$604$		0			0
$605$	2.08456e7	−	1.20352e7i	0.0941343	−	0.0543484i
$606$		0			0
$607$	9.53839e7	−	1.65210e8i	0.426490	−	0.738703i	−0.570068	−	0.821597i	$-0.693083\pi$
$607$	9.53839e7	−	1.65210e8i	0.426490	−	0.738703i	0.996558	+	0.0828946i	$0.0264165\pi$
$608$		0			0
$609$	−9.36634e7	−	3.08627e8i	−0.414685	−	1.36641i
$610$		0			0
$611$		−	5.87967e7i		−	0.257768i
$612$		0			0
$613$	−1.55345e8			−0.674398			−0.337199	−	0.941433i	$-0.609480\pi$
$613$	−1.55345e8			−0.674398			−0.337199	+	0.941433i	$0.609480\pi$
$614$		0			0
$615$	1.44921e6	−	6.21888e6i	0.00623027	−	0.0267354i
$616$		0			0
$617$	−2.99628e8	−	1.72990e8i	−1.27564	−	0.736489i	−0.299593	−	0.954067i	$-0.596851\pi$
$617$	−2.99628e8	−	1.72990e8i	−1.27564	−	0.736489i	−0.976043	+	0.217578i	$0.930184\pi$
$618$		0			0
$619$	−1.02237e8	−	1.77079e8i	−0.431057	−	0.746612i	0.565908	−	0.824468i	$-0.308526\pi$
$619$	−1.02237e8	−	1.77079e8i	−0.431057	−	0.746612i	−0.996965	+	0.0778566i	$0.975192\pi$
$620$		0			0
$621$	8.57035e7	−	3.22935e7i	0.357869	−	0.134847i
$622$		0			0
$623$	3.86470e8	−	2.23129e8i	1.59828	−	0.922766i
$624$		0			0
$625$	−1.17655e8	+	2.03784e8i	−0.481914	+	0.834700i
$626$		0			0
$627$	2.86710e7	+	6.68134e6i	0.116316	+	0.0271057i
$628$		0			0
$629$		−	3.40258e8i		−	1.36728i
$630$		0			0
$631$	8.55193e7			0.340390			0.170195	−	0.985410i	$-0.445560\pi$
$631$	8.55193e7			0.340390			0.170195	+	0.985410i	$0.445560\pi$
$632$		0			0
$633$	−4.10219e8	+	1.24495e8i	−1.61735	+	0.490841i
$634$		0			0
$635$	8.24227e6	+	4.75868e6i	0.0321904	+	0.0185851i
$636$		0			0
$637$	2.22774e6	+	3.85856e6i	0.00861879	+	0.0149282i
$638$		0			0
$639$	−1.83916e8	+	1.21010e7i	−0.704884	+	0.0463787i
$640$		0			0
$641$	−8.54208e7	+	4.93177e7i	−0.324332	+	0.187253i	−0.653322	−	0.757080i	$-0.726625\pi$
$641$	−8.54208e7	+	4.93177e7i	−0.324332	+	0.187253i	0.328990	+	0.944333i	$0.393292\pi$
$642$		0			0
$643$	−6.60822e7	+	1.14458e8i	−0.248572	+	0.430539i	−0.963130	−	0.269038i	$-0.913294\pi$
$643$	−6.60822e7	+	1.14458e8i	−0.248572	+	0.430539i	0.714558	+	0.699576i	$0.246628\pi$
$644$		0			0
$645$	−1.14796e7	+	1.22598e7i	−0.0427807	+	0.0456880i
$646$		0			0
$647$			4.53195e8i			1.67329i	0.547742	+	0.836647i	$0.315487\pi$
$647$			4.53195e8i			1.67329i	−0.547742	+	0.836647i	$0.684513\pi$
$648$		0			0
$649$	2.14691e6			0.00785380
$650$		0			0
$651$	4.49606e7	+	4.20996e7i	0.162963	+	0.152593i
$652$		0			0
$653$	3.30549e8	+	1.90842e8i	1.18712	+	0.685386i	0.957652	−	0.287929i	$-0.0929668\pi$
$653$	3.30549e8	+	1.90842e8i	1.18712	+	0.685386i	0.229472	+	0.973315i	$0.426300\pi$
$654$		0			0
$655$	−2.04109e7	−	3.53527e7i	−0.0726336	−	0.125805i
$656$		0			0
$657$	−4.35440e6	−	6.61800e7i	−0.0153544	−	0.233362i
$658$		0			0
$659$	−6.45319e7	+	3.72575e7i	−0.225485	+	0.130184i	−0.608488	−	0.793563i	$-0.708223\pi$
$659$	−6.45319e7	+	3.72575e7i	−0.225485	+	0.130184i	0.383002	+	0.923747i	$0.374890\pi$
$660$		0			0
$661$	−2.54030e8	+	4.39992e8i	−0.879590	+	1.52349i	−0.0277976	+	0.999614i	$0.508849\pi$
$661$	−2.54030e8	+	4.39992e8i	−0.879590	+	1.52349i	−0.851792	+	0.523880i	$0.824484\pi$
$662$		0			0
$663$	5.44945e7	+	1.79563e8i	0.186987	+	0.616136i
$664$		0			0
$665$		−	3.56943e7i		−	0.121376i
$666$		0			0
$667$	1.59515e8			0.537558
$668$		0			0
$669$	−2.90364e7	+	1.24601e8i	−0.0969761	+	0.416144i
$670$		0			0
$671$	−3.33093e7	−	1.92311e7i	−0.110255	−	0.0636556i
$672$		0			0
$673$	1.91532e8	+	3.31743e8i	0.628342	+	1.08832i	0.987884	+	0.155192i	$0.0495997\pi$
$673$	1.91532e8	+	3.31743e8i	0.628342	+	1.08832i	−0.359542	+	0.933129i	$0.617067\pi$
$674$		0			0
$675$	−2.99784e8	−	4.93783e7i	−0.974760	−	0.160555i
$676$		0			0
$677$	−4.68507e7	+	2.70493e7i	−0.150991	+	0.0871745i	−0.573592	−	0.819141i	$-0.694450\pi$
$677$	−4.68507e7	+	2.70493e7i	−0.150991	+	0.0871745i	0.422601	+	0.906316i	$0.361117\pi$
$678$		0			0
$679$	−2.50775e8	+	4.34356e8i	−0.801079	+	1.38751i
$680$		0			0
$681$	−1.01265e8	−	2.35983e7i	−0.320640	−	0.0747203i
$682$		0			0
$683$		−	5.83173e7i		−	0.183035i	−0.995803	−	0.0915177i	$-0.970828\pi$
$683$		−	5.83173e7i		−	0.183035i	0.995803	−	0.0915177i	$-0.0291718\pi$
$684$		0			0
$685$	4.04631e7			0.125889
$686$		0			0
$687$	−3.96480e8	+	1.20325e8i	−1.22279	+	0.371097i
$688$		0			0
$689$	−2.05563e8	−	1.18682e8i	−0.628474	−	0.362850i
$690$		0			0
$691$	1.67618e8	+	2.90324e8i	0.508028	+	0.879930i	0.999957	+	0.00929488i	$0.00295870\pi$
$691$	1.67618e8	+	2.90324e8i	0.508028	+	0.879930i	−0.491929	+	0.870635i	$0.663708\pi$
$692$		0			0
$693$	1.64384e7	−	3.33549e7i	0.0493923	−	0.100221i
$694$		0			0
$695$	−1.64911e7	+	9.52114e6i	−0.0491241	+	0.0283618i
$696$		0			0
$697$	−5.05055e7	+	8.74780e7i	−0.149156	+	0.258345i
$698$		0			0
$699$	−1.88881e8	+	2.01717e8i	−0.553040	+	0.590623i
$700$		0			0
$701$		−	5.62607e8i		−	1.63324i	−0.577173	−	0.816622i	$-0.695844\pi$
$701$		−	5.62607e8i		−	1.63324i	0.577173	−	0.816622i	$-0.304156\pi$
$702$		0			0
$703$	4.31429e8			1.24178
$704$		0			0
$705$	1.34706e7	+	1.26134e7i	0.0384432	+	0.0359969i
$706$		0			0
$707$	2.55668e8	+	1.47610e8i	0.723467	+	0.417694i
$708$		0			0
$709$	−1.55645e8	−	2.69586e8i	−0.436715	−	0.756412i	0.560719	−	0.828006i	$-0.310525\pi$
$709$	−1.55645e8	−	2.69586e8i	−0.436715	−	0.756412i	−0.997434	+	0.0715942i	$0.977191\pi$
$710$		0			0
$711$	−3.92134e8	+	2.62158e8i	−1.09100	+	0.729381i
$712$		0			0
$713$	−2.63820e7	+	1.52316e7i	−0.0727844	+	0.0420221i
$714$		0			0
$715$	1.19105e6	−	2.06296e6i	0.00325845	−	0.00564381i
$716$		0			0
$717$	6.25311e7	+	2.06044e8i	0.169644	+	0.558988i
$718$		0			0
$719$		−	1.52803e8i		−	0.411098i	−0.978647	−	0.205549i	$-0.934102\pi$
$719$		−	1.52803e8i		−	0.411098i	0.978647	−	0.205549i	$-0.0658979\pi$
$720$		0			0
$721$	6.55388e8			1.74861
$722$		0			0
$723$	2.52324e7	−	1.08278e8i	0.0667643	−	0.286500i
$724$		0			0
$725$	−4.58276e8	−	2.64586e8i	−1.20258	−	0.694308i
$726$		0			0
$727$	−2.37170e8	−	4.10790e8i	−0.617243	−	1.06910i	−0.989986	−	0.141162i	$-0.954916\pi$
$727$	−2.37170e8	−	4.10790e8i	−0.617243	−	1.06910i	0.372743	−	0.927935i	$-0.378417\pi$
$728$		0			0
$729$	−7.58690e7	−	3.79919e8i	−0.195831	−	0.980638i
$730$		0			0
$731$	2.30087e8	−	1.32841e8i	0.589033	−	0.340079i
$732$		0			0
$733$	2.01674e7	−	3.49309e7i	0.0512080	−	0.0886948i	−0.839285	−	0.543691i	$-0.817026\pi$
$733$	2.01674e7	−	3.49309e7i	0.0512080	−	0.0886948i	0.890493	+	0.454997i	$0.150360\pi$
$734$		0			0
$735$	−1.36192e6	−	317375.i	−0.00342997	−	0.000799302i
$736$		0			0
$737$		−	6.62332e7i		−	0.165452i
$738$		0			0
$739$	−1.15717e8			−0.286724			−0.143362	−	0.989670i	$-0.545791\pi$
$739$	−1.15717e8			−0.286724			−0.143362	+	0.989670i	$0.545791\pi$
$740$		0			0
$741$	−2.27677e8	+	6.90962e7i	−0.559582	+	0.169824i
$742$		0			0
$743$	2.79803e8	+	1.61544e8i	0.682160	+	0.393845i	0.800668	−	0.599108i	$-0.204478\pi$
$743$	2.79803e8	+	1.61544e8i	0.682160	+	0.393845i	−0.118509	+	0.992953i	$0.537811\pi$
$744$		0			0
$745$	3.28537e7	+	5.69043e7i	0.0794540	+	0.137618i
$746$		0			0
$747$	2.75560e8	+	4.12180e8i	0.661080	+	0.988837i
$748$		0			0
$749$	4.43870e8	−	2.56269e8i	1.05636	−	0.609888i
$750$		0			0
$751$	5.00962e6	−	8.67691e6i	0.0118273	−	0.0204854i	−0.860051	−	0.510208i	$-0.829569\pi$
$751$	5.00962e6	−	8.67691e6i	0.0118273	−	0.0204854i	0.871878	+	0.489722i	$0.162902\pi$
$752$		0			0
$753$	4.83815e8	−	5.16694e8i	1.13317	−	1.21018i
$754$		0			0
$755$			7.40904e7i			0.172156i
$756$		0			0
$757$	−2.09015e8			−0.481825			−0.240913	−	0.970547i	$-0.577447\pi$
$757$	−2.09015e8			−0.481825			−0.240913	+	0.970547i	$0.577447\pi$
$758$		0			0
$759$	1.34247e7	+	1.25705e7i	0.0307029	+	0.0287492i
$760$		0			0
$761$	−9.92162e7	−	5.72825e7i	−0.225127	−	0.129977i	0.383195	−	0.923668i	$-0.374824\pi$
$761$	−9.92162e7	−	5.72825e7i	−0.225127	−	0.129977i	−0.608322	+	0.793690i	$0.708157\pi$
$762$		0			0
$763$	1.13839e8	+	1.97175e8i	0.256282	+	0.443894i
$764$		0			0
$765$	−5.28292e7	−	2.60360e7i	−0.118002	−	0.0581553i
$766$		0			0
$767$	−1.50269e7	+	8.67576e6i	−0.0333029	+	0.0192274i
$768$		0			0
$769$	8.90668e7	−	1.54268e8i	0.195856	−	0.339233i	−0.751325	−	0.659933i	$-0.770585\pi$
$769$	8.90668e7	−	1.54268e8i	0.195856	−	0.339233i	0.947181	+	0.320700i	$0.103918\pi$
$770$		0			0
$771$	3.02829e6	+	9.97841e6i	0.00660746	+	0.0217720i
$772$		0			0
$773$		−	6.46379e7i		−	0.139942i	−0.997549	−	0.0699711i	$-0.977709\pi$
$773$		−	6.46379e7i		−	0.139942i	0.997549	−	0.0699711i	$-0.0222907\pi$
$774$		0			0
$775$	1.01058e8			0.217103
$776$		0			0
$777$	1.23679e8	−	5.30732e8i	0.263653	−	1.13139i
$778$		0			0
$779$	−1.10918e8	−	6.40383e7i	−0.234632	−	0.135465i
$780$		0			0
$781$	−1.85060e7	−	3.20533e7i	−0.0388471	−	0.0672852i
$782$		0			0
$783$	1.09666e8	−	6.65801e8i	0.228447	−	1.38694i
$784$		0			0
$785$	2.72377e7	−	1.57257e7i	0.0563069	−	0.0325088i
$786$		0			0
$787$	2.71231e7	−	4.69785e7i	0.0556435	−	0.0963774i	−0.836862	−	0.547414i	$-0.815612\pi$
$787$	2.71231e7	−	4.69785e7i	0.0556435	−	0.0963774i	0.892505	+	0.451037i	$0.148946\pi$
$788$		0			0
$789$	−5.35612e8	−	1.24816e8i	−1.09048	−	0.254120i
$790$		0			0
$791$		−	6.89808e7i		−	0.139379i
$792$		0			0
$793$	3.10855e8			0.623360
$794$		0			0
$795$	7.12892e7	−	2.16351e7i	0.141880	−	0.0430584i
$796$		0			0
$797$	3.78686e8	+	2.18634e8i	0.748005	+	0.431861i	0.824972	−	0.565173i	$-0.191191\pi$
$797$	3.78686e8	+	2.18634e8i	0.748005	+	0.431861i	−0.0769679	+	0.997034i	$0.524524\pi$
$798$		0			0
$799$	−1.45961e8	−	2.52812e8i	−0.286152	−	0.495630i
$800$		0			0
$801$	9.31621e8	−	6.12972e7i	1.81277	−	0.119273i
$802$		0			0
$803$	1.15340e7	−	6.65915e6i	0.0222758	−	0.0128609i
$804$		0			0
$805$	1.11495e7	−	1.93115e7i	0.0213731	−	0.0370193i
$806$		0			0
$807$	−2.64016e8	+	2.81958e8i	−0.502353	+	0.536492i
$808$		0			0
$809$			6.33456e8i			1.19638i	0.801353	+	0.598192i	$0.204114\pi$
$809$			6.33456e8i			1.19638i	−0.801353	+	0.598192i	$0.795886\pi$
$810$		0			0
$811$	−5.19424e8			−0.973776			−0.486888	−	0.873464i	$-0.661868\pi$
$811$	−5.19424e8			−0.973776			−0.486888	+	0.873464i	$0.661868\pi$
$812$		0			0
$813$	4.63136e8	+	4.33665e8i	0.861861	+	0.807017i
$814$		0			0
$815$	1.00913e7	+	5.82619e6i	0.0186411	+	0.0107625i
$816$		0			0
$817$	1.68435e8	+	2.91738e8i	0.308864	+	0.534968i
$818$		0			0
$819$	1.97316e7	+	2.99889e8i	0.0359179	+	0.545895i
$820$		0			0
$821$	1.22135e8	−	7.05146e7i	0.220704	−	0.127423i	−0.385572	−	0.922678i	$-0.625996\pi$
$821$	1.22135e8	−	7.05146e7i	0.220704	−	0.127423i	0.606276	+	0.795254i	$0.292663\pi$
$822$		0			0
$823$	3.53973e8	−	6.13099e8i	0.634995	−	1.09984i	−0.351521	−	0.936180i	$-0.614336\pi$
$823$	3.53973e8	−	6.13099e8i	0.634995	−	1.09984i	0.986516	−	0.163664i	$-0.0523311\pi$
$824$		0			0
$825$	−1.77178e7	−	5.83813e7i	−0.0315535	−	0.103971i
$826$		0			0
$827$			3.18849e7i			0.0563726i	0.999603	+	0.0281863i	$0.00897316\pi$
$827$			3.18849e7i			0.0563726i	−0.999603	+	0.0281863i	$0.991027\pi$
$828$		0			0
$829$	−7.36305e8			−1.29239			−0.646196	−	0.763171i	$-0.723641\pi$
$829$	−7.36305e8			−1.29239			−0.646196	+	0.763171i	$0.723641\pi$
$830$		0			0
$831$	7.70151e7	−	3.30488e8i	0.134206	−	0.575907i
$832$		0			0
$833$	1.91575e7	+	1.10606e7i	0.0331439	+	0.0191357i
$834$		0			0
$835$	−2.37984e6	−	4.12200e6i	−0.00408778	−	0.00708025i
$836$		0			0
$837$	4.54378e7	+	1.20587e8i	0.0774892	+	0.205648i
$838$		0			0
$839$	−4.52044e8	+	2.60988e8i	−0.765411	+	0.441910i	−0.831235	−	0.555921i	$-0.812366\pi$
$839$	−4.52044e8	+	2.60988e8i	−0.765411	+	0.441910i	0.0658240	+	0.997831i	$0.479032\pi$
$840$		0			0
$841$	2.90215e8	−	5.02668e8i	0.487902	−	0.845071i
$842$		0			0
$843$	1.08442e9	+	2.52708e8i	1.81015	+	0.421828i
$844$		0			0
$845$		−	4.71331e7i		−	0.0781188i
$846$		0			0
$847$	−6.09827e8			−1.00359
$848$		0			0
$849$	1.37238e8	−	4.16496e7i	0.224260	−	0.0680593i
$850$		0			0
$851$	2.33414e8	+	1.34761e8i	0.378737	+	0.218664i
$852$		0			0
$853$	−2.40439e8	−	4.16453e8i	−0.387399	−	0.670994i	0.604700	−	0.796453i	$-0.293293\pi$
$853$	−2.40439e8	−	4.16453e8i	−0.387399	−	0.670994i	−0.992099	+	0.125459i	$0.959960\pi$
$854$		0			0
$855$	3.30123e7	−	6.69847e7i	0.0528174	−	0.107171i
$856$		0			0
$857$	−9.61064e8	+	5.54871e8i	−1.52690	+	0.881555i	−0.527408	+	0.849612i	$0.676836\pi$
$857$	−9.61064e8	+	5.54871e8i	−1.52690	+	0.881555i	−0.999490	+	0.0319423i	$0.989831\pi$
$858$		0			0
$859$	−6.56703e7	+	1.13744e8i	−0.103607	+	0.179453i	−0.913168	−	0.407583i	$-0.866372\pi$
$859$	−6.56703e7	+	1.13744e8i	−0.103607	+	0.179453i	0.809561	+	0.587036i	$0.199705\pi$
$860$		0			0
$861$	−1.10575e8	+	1.18090e8i	−0.173240	+	0.185013i
$862$		0			0
$863$			2.23845e8i			0.348269i	0.984722	+	0.174134i	$0.0557127\pi$
$863$			2.23845e8i			0.348269i	−0.984722	+	0.174134i	$0.944287\pi$
$864$		0			0
$865$	6.47550e7			0.100052
$866$		0			0
$867$	2.04354e8	+	1.91350e8i	0.313564	+	0.293611i
$868$		0			0
$869$	−8.20305e7	−	4.73603e7i	−0.125002	−	0.0721698i
$870$		0			0
$871$	2.67651e8	+	4.63586e8i	0.405056	+	0.701578i
$872$		0			0
$873$	−8.72328e8	+	5.83189e8i	−1.31110	+	0.876529i
$874$		0			0
$875$	−1.28912e8	+	7.44272e7i	−0.192428	+	0.111098i
$876$		0			0
$877$	3.59421e8	−	6.22536e8i	0.532850	−	0.922924i	−0.466414	−	0.884567i	$-0.654454\pi$
$877$	3.59421e8	−	6.22536e8i	0.532850	−	0.922924i	0.999264	−	0.0383570i	$-0.0122124\pi$
$878$		0			0
$879$	−2.81486e8	−	9.27516e8i	−0.414468	−	1.36570i
$880$		0			0
$881$			2.83002e7i			0.0413868i	0.999786	+	0.0206934i	$0.00658738\pi$
$881$			2.83002e7i			0.0413868i	−0.999786	+	0.0206934i	$0.993413\pi$
$882$		0			0
$883$	6.58209e8			0.956052			0.478026	−	0.878346i	$-0.341353\pi$
$883$	6.58209e8			0.956052			0.478026	+	0.878346i	$0.341353\pi$
$884$		0			0
$885$	1.23599e6	−	5.30390e6i	0.00178314	−	0.00765183i
$886$		0			0
$887$	−8.79763e8	−	5.07931e8i	−1.26065	−	0.727837i	−0.287450	−	0.957796i	$-0.592808\pi$
$887$	−8.79763e8	−	5.07931e8i	−1.26065	−	0.727837i	−0.973200	+	0.229958i	$0.926141\pi$
$888$		0			0
$889$	−1.20562e8	−	2.08819e8i	−0.171595	−	0.297211i
$890$		0			0
$891$	6.16972e7	−	4.73913e7i	0.0872233	−	0.0669986i
$892$		0			0
$893$	3.20553e8	−	1.85071e8i	0.450137	−	0.259887i
$894$		0			0
$895$	6.92461e7	−	1.19938e8i	0.0965887	−	0.167297i
$896$		0			0
$897$	−1.44761e8	−	3.37344e7i	−0.200574	−	0.0467408i
$898$		0			0
$899$			2.24443e8i			0.308906i
$900$		0			0
$901$	−1.17850e9			−1.61122
$902$		0			0
$903$	4.07174e8	−	1.23571e8i	0.552989	−	0.167824i
$904$		0			0
$905$	1.22902e8	+	7.09577e7i	0.165811	+	0.0957313i
$906$		0			0
$907$	1.13812e8	+	1.97128e8i	0.152533	+	0.264196i	0.932158	−	0.362051i	$-0.117923\pi$
$907$	1.13812e8	+	1.97128e8i	0.152533	+	0.264196i	−0.779625	+	0.626247i	$0.784590\pi$
$908$		0			0
$909$	3.43274e8	+	5.13465e8i	0.457034	+	0.683628i
$910$		0			0
$911$	−6.03068e8	+	3.48182e8i	−0.797648	+	0.460522i	−0.842648	−	0.538465i	$-0.819004\pi$
$911$	−6.03068e8	+	3.48182e8i	−0.797648	+	0.460522i	0.0450002	+	0.998987i	$0.485671\pi$
$912$		0			0
$913$	−4.97814e7	+	8.62240e7i	−0.0654116	+	0.113296i
$914$		0			0
$915$	−6.66865e7	+	7.12184e7i	−0.0870512	+	0.0929671i
$916$		0			0
$917$			1.03422e9i			1.34124i
$918$		0			0
$919$	−1.12576e9			−1.45043			−0.725217	−	0.688521i	$-0.758260\pi$
$919$	−1.12576e9			−1.45043			−0.725217	+	0.688521i	$0.758260\pi$
$920$		0			0
$921$	−2.32993e8	−	2.18167e8i	−0.298239	−	0.279261i
$922$		0			0
$923$	2.59058e8	+	1.49567e8i	0.329452	+	0.190209i
$924$		0			0
$925$	−4.47053e8	−	7.74319e8i	−0.564851	−	0.978351i
$926$		0			0
$927$	1.22991e9	+	6.06141e8i	1.54396	+	0.760913i
$928$		0			0
$929$	−3.85596e8	+	2.22624e8i	−0.480934	+	0.277667i	−0.720805	−	0.693137i	$-0.756228\pi$
$929$	−3.85596e8	+	2.22624e8i	−0.480934	+	0.277667i	0.239872	+	0.970805i	$0.422895\pi$
$930$		0			0
$931$	−1.40243e7	+	2.42907e7i	−0.0173793	+	0.0301018i
$932$		0			0
$933$	3.67391e8	+	1.21058e9i	0.452360	+	1.49055i
$934$		0			0
$935$		−	1.18270e7i		−	0.0144690i
$936$		0			0
$937$	−1.03280e9			−1.25545			−0.627723	−	0.778437i	$-0.716013\pi$
$937$	−1.03280e9			−1.25545			−0.627723	+	0.778437i	$0.716013\pi$
$938$		0			0
$939$	2.43733e8	−	1.04591e9i	0.294386	−	1.26327i
$940$		0			0
$941$	1.12302e9	+	6.48373e8i	1.34777	+	0.778137i	0.987934	−	0.154877i	$-0.0494982\pi$
$941$	1.12302e9	+	6.48373e8i	1.34777	+	0.778137i	0.359839	+	0.933014i	$0.382832\pi$
$942$		0			0
$943$	−4.00060e7	−	6.92925e7i	−0.0477079	−	0.0826326i
$944$		0			0
$945$	−7.29390e7	−	5.98134e7i	−0.0864300	−	0.0708766i
$946$		0			0
$947$	−9.61228e8	+	5.54965e8i	−1.13182	+	0.653455i	−0.944391	−	0.328823i	$-0.893348\pi$
$947$	−9.61228e8	+	5.54965e8i	−1.13182	+	0.653455i	−0.187426	+	0.982279i	$0.560015\pi$
$948$		0			0
$949$	−5.38199e7	+	9.32188e7i	−0.0629715	+	0.109070i
$950$		0			0
$951$	−1.10714e9	−	2.58003e8i	−1.28725	−	0.299973i
$952$		0			0
$953$			8.44814e8i			0.976073i	0.872823	+	0.488037i	$0.162287\pi$
$953$			8.44814e8i			0.976073i	−0.872823	+	0.488037i	$0.837713\pi$
$954$		0			0
$955$	1.01305e8			0.116311
$956$		0			0
$957$	1.29661e8	−	3.93501e7i	0.147936	−	0.0448962i
$958$		0			0
$959$	−8.87796e8	−	5.12569e8i	−1.00660	−	0.581162i
$960$		0			0
$961$	4.22320e8	+	7.31481e8i	0.475852	+	0.824200i
$962$		0			0
$963$	1.06999e9	−	7.04013e7i	1.19812	−	0.0788319i
$964$		0			0
$965$	−7.34491e7	+	4.24058e7i	−0.0817343	+	0.0471893i
$966$		0			0
$967$	2.58758e8	−	4.48183e8i	0.286164	−	0.495650i	−0.686727	−	0.726916i	$-0.740953\pi$
$967$	2.58758e8	−	4.48183e8i	0.286164	−	0.495650i	0.972891	+	0.231265i	$0.0742865\pi$
$968$		0			0
$969$	−8.07426e8	+	8.62298e8i	−0.887425	+	0.947733i
$970$		0			0
$971$			5.77306e8i			0.630591i	0.948993	+	0.315296i	$0.102104\pi$
$971$			5.77306e8i			0.630591i	−0.948993	+	0.315296i	$0.897896\pi$
$972$		0			0
$973$	4.82438e8			0.523725
$974$		0			0
$975$	3.59934e8	+	3.37030e8i	0.388337	+	0.363626i
$976$		0			0
$977$	1.31559e8	+	7.59559e7i	0.141071	+	0.0814475i	0.568874	−	0.822424i	$-0.307379\pi$
$977$	1.31559e8	+	7.59559e7i	0.141071	+	0.0814475i	−0.427803	+	0.903872i	$0.640712\pi$
$978$		0			0
$979$	9.37414e7	+	1.62365e8i	0.0999041	+	0.173039i
$980$		0			0
$981$	3.12735e7	+	4.75308e8i	0.0331261	+	0.503464i
$982$		0			0
$983$	9.87276e8	−	5.70004e8i	1.03939	−	0.600091i	0.119729	−	0.992807i	$-0.461798\pi$
$983$	9.87276e8	−	5.70004e8i	1.03939	−	0.600091i	0.919660	+	0.392715i	$0.128464\pi$
$984$		0			0
$985$	1.32552e7	−	2.29587e7i	0.0138700	−	0.0240236i
$986$		0			0
$987$	−1.35776e8	−	4.47389e8i	−0.141212	−	0.465301i
$988$		0			0
$989$			2.10450e8i			0.217550i
$990$		0			0
$991$	−1.01159e9			−1.03940			−0.519699	−	0.854350i	$-0.673956\pi$
$991$	−1.01159e9			−1.03940			−0.519699	+	0.854350i	$0.673956\pi$
$992$		0			0
$993$	3.12232e8	−	1.33985e9i	0.318882	−	1.36839i
$994$		0			0
$995$	1.62703e8	+	9.39366e7i	0.165168	+	0.0953599i
$996$		0			0
$997$	3.35954e8	+	5.81889e8i	0.338996	+	0.587158i	0.984244	−	0.176815i	$-0.0565795\pi$
$997$	3.35954e8	+	5.81889e8i	0.338996	+	0.587158i	−0.645248	+	0.763973i	$0.723246\pi$
$998$		0			0
$999$	7.22951e8	−	8.81597e8i	0.725124	−	0.884247i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	72.7.m.a.41.4	✓	36
3.2	odd	2		216.7.m.a.17.11		36
4.3	odd	2		144.7.q.d.113.15		36
9.2	odd	6	inner	72.7.m.a.65.4	yes	36
9.4	even	3		648.7.e.c.161.20		36
9.5	odd	6		648.7.e.c.161.17		36
9.7	even	3		216.7.m.a.89.11		36
12.11	even	2		432.7.q.d.17.11		36
36.7	odd	6		432.7.q.d.305.11		36
36.11	even	6		144.7.q.d.65.15		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
72.7.m.a.41.4	✓	36	1.1	even	1	trivial
72.7.m.a.65.4	yes	36	9.2	odd	6	inner
144.7.q.d.65.15		36	36.11	even	6
144.7.q.d.113.15		36	4.3	odd	2
216.7.m.a.17.11		36	3.2	odd	2
216.7.m.a.89.11		36	9.7	even	3
432.7.q.d.17.11		36	12.11	even	2
432.7.q.d.305.11		36	36.7	odd	6
648.7.e.c.161.17		36	9.5	odd	6
648.7.e.c.161.20		36	9.4	even	3

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:	\( N \)	\(=\)	\( 72 = 2^{3} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	72.m (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-19.7087 - 18.4545i) q^{3} +(-11.9109 - 6.87674i) q^{5} +(174.223 + 301.763i) q^{7} +(47.8620 + 727.427i) q^{9} +O(q^{10})\)	\(q+(-19.7087 - 18.4545i) q^{3} +(-11.9109 - 6.87674i) q^{5} +(174.223 + 301.763i) q^{7} +(47.8620 + 727.427i) q^{9} +(-126.778 + 73.1950i) q^{11} +(591.569 - 1024.63i) q^{13} +(107.840 + 355.340i) q^{15} -5874.21i q^{17} +7448.19 q^{19} +(2135.19 - 9162.55i) q^{21} +(4029.65 + 2326.52i) q^{23} +(-7717.92 - 13367.8i) q^{25} +(12481.0 - 15219.9i) q^{27} +(29689.1 - 17141.0i) q^{29} +(-3273.48 + 5669.83i) q^{31} +(3849.39 + 897.042i) q^{33} -4792.35i q^{35} +57924.0 q^{37} +(-30568.0 + 9276.91i) q^{39} +(-14891.9 - 8597.83i) q^{41} +(22614.2 + 39169.0i) q^{43} +(4432.25 - 8993.42i) q^{45} +(43037.6 - 24847.8i) q^{47} +(-1882.91 + 3261.29i) q^{49} +(-108406. + 115773. i) q^{51} -200622. i q^{53} +2013.37 q^{55} +(-146794. - 137453. i) q^{57} +(-12700.8 - 7332.84i) q^{59} +(131369. + 227538. i) q^{61} +(-211172. + 141178. i) q^{63} +(-14092.2 + 8136.13i) q^{65} +(-226222. + 391827. i) q^{67} +(-36484.2 - 120218. i) q^{69} +252831. i q^{71} -90978.2 q^{73} +(-94587.0 + 405892. i) q^{75} +(-44175.2 - 25504.5i) q^{77} +(323522. + 560356. i) q^{79} +(-526859. + 69632.3i) q^{81} +(589001. - 340060. i) q^{83} +(-40395.4 + 69966.9i) q^{85} +(-901460. - 210071. i) q^{87} -1.28071e6i q^{89} +412260. q^{91} +(169150. - 51334.3i) q^{93} +(-88714.4 - 51219.3i) q^{95} +(719696. + 1.24655e6i) q^{97} +(-59311.9 - 88718.2i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 10 q^{3} + 74 q^{9}+O(q^{10}) \) 36 * q + 10 * q^3 + 74 * q^9	\( 36 q + 10 q^{3} + 74 q^{9} + 1350 q^{11} + 7912 q^{15} + 9540 q^{19} + 3828 q^{21} + 30888 q^{23} + 56250 q^{25} + 11392 q^{27} + 38556 q^{29} + 27720 q^{31} + 33514 q^{33} + 134068 q^{39} + 179226 q^{41} + 15930 q^{43} - 185620 q^{45} + 187596 q^{47} - 198774 q^{49} - 158098 q^{51} - 197064 q^{55} - 244990 q^{57} - 408618 q^{59} + 17136 q^{61} - 417048 q^{63} - 125712 q^{65} + 27090 q^{67} - 848504 q^{69} - 534060 q^{73} - 1405714 q^{75} + 48168 q^{77} + 172620 q^{79} + 349010 q^{81} + 1801980 q^{83} - 791568 q^{85} + 28500 q^{87} + 538560 q^{91} - 1116448 q^{93} + 1832652 q^{95} + 770706 q^{97} - 614260 q^{99}+O(q^{100}) \) 36 * q + 10 * q^3 + 74 * q^9 + 1350 * q^11 + 7912 * q^15 + 9540 * q^19 + 3828 * q^21 + 30888 * q^23 + 56250 * q^25 + 11392 * q^27 + 38556 * q^29 + 27720 * q^31 + 33514 * q^33 + 134068 * q^39 + 179226 * q^41 + 15930 * q^43 - 185620 * q^45 + 187596 * q^47 - 198774 * q^49 - 158098 * q^51 - 197064 * q^55 - 244990 * q^57 - 408618 * q^59 + 17136 * q^61 - 417048 * q^63 - 125712 * q^65 + 27090 * q^67 - 848504 * q^69 - 534060 * q^73 - 1405714 * q^75 + 48168 * q^77 + 172620 * q^79 + 349010 * q^81 + 1801980 * q^83 - 791568 * q^85 + 28500 * q^87 + 538560 * q^91 - 1116448 * q^93 + 1832652 * q^95 + 770706 * q^97 - 614260 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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