LMFDB - Embedded newform 72.7.m.a.41.16

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			41.16
Character	$\chi$	$=$	72.41
Dual form			72.7.m.a.65.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(24.3041 - 11.7607i) q^{3} +(76.0344 + 43.8985i) q^{5} +(-287.890 - 498.640i) q^{7} +(452.374 - 571.663i) q^{9} +O(q^{10})$	\(q+(24.3041 - 11.7607i) q^{3} +(76.0344 + 43.8985i) q^{5} +(-287.890 - 498.640i) q^{7} +(452.374 - 571.663i) q^{9} +(-759.950 + 438.757i) q^{11} +(1457.18 - 2523.90i) q^{13} +(2364.22 + 172.697i) q^{15} +1890.02i q^{17} +1611.84 q^{19} +(-12861.2 - 8733.21i) q^{21} +(-7093.22 - 4095.27i) q^{23} +(-3958.35 - 6856.06i) q^{25} +(4271.40 - 19213.9i) q^{27} +(39159.7 - 22608.9i) q^{29} +(-8297.21 + 14371.2i) q^{31} +(-13309.8 + 19601.1i) q^{33} -50551.7i q^{35} +37329.6 q^{37} +(5732.54 - 78478.4i) q^{39} +(-8256.57 - 4766.93i) q^{41} +(-68804.6 - 119173. i) q^{43} +(59491.1 - 23607.5i) q^{45} +(4808.78 - 2776.35i) q^{47} +(-106937. + 185220. i) q^{49} +(22227.8 + 45935.1i) q^{51} +266280. i q^{53} -77043.1 q^{55} +(39174.4 - 18956.3i) q^{57} +(215319. + 124314. i) q^{59} +(182387. + 315903. i) q^{61} +(-415288. - 60995.9i) q^{63} +(221591. - 127936. i) q^{65} +(-130531. + 226087. i) q^{67} +(-220557. - 16110.9i) q^{69} -131448. i q^{71} -159473. q^{73} +(-176836. - 120077. i) q^{75} +(437564. + 252628. i) q^{77} +(443525. + 768208. i) q^{79} +(-122156. - 517211. i) q^{81} +(492235. - 284192. i) q^{83} +(-82968.9 + 143706. i) q^{85} +(685845. - 1.01003e6i) q^{87} +837943. i q^{89} -1.67803e6 q^{91} +(-32641.3 + 446859. i) q^{93} +(122556. + 70757.5i) q^{95} +(-430032. - 744838. i) q^{97} +(-92960.4 + 632917. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	24.3041	−	11.7607i	0.900150	−	0.435580i
$3$	24.3041	−	11.7607i	0.900150	−	0.435580i
$4$		0			0
$5$	76.0344	+	43.8985i	0.608275	+	0.351188i	0.772290	−	0.635270i	$-0.219111\pi$
$5$	76.0344	+	43.8985i	0.608275	+	0.351188i	−0.164015	+	0.986458i	$0.552445\pi$
$6$		0			0
$7$	−287.890	−	498.640i	−0.839330	−	1.45376i	−0.890456	−	0.455070i	$-0.849614\pi$
$7$	−287.890	−	498.640i	−0.839330	−	1.45376i	0.0511261	−	0.998692i	$-0.483719\pi$
$8$		0			0
$9$	452.374	−	571.663i	0.620541	−	0.784174i
$10$		0			0
$11$	−759.950	+	438.757i	−0.570961	+	0.329645i	−0.757533	−	0.652797i	$-0.773596\pi$
$11$	−759.950	+	438.757i	−0.570961	+	0.329645i	0.186572	+	0.982441i	$0.440262\pi$
$12$		0			0
$13$	1457.18	−	2523.90i	0.663257	−	1.14879i	−0.316498	−	0.948593i	$-0.602507\pi$
$13$	1457.18	−	2523.90i	0.663257	−	1.14879i	0.979755	−	0.200201i	$-0.0641596\pi$
$14$		0			0
$15$	2364.22	+	172.697i	0.700509	+	0.0511695i
$16$		0			0
$17$			1890.02i			0.384697i	0.981327	+	0.192349i	$0.0616105\pi$
$17$			1890.02i			0.384697i	−0.981327	+	0.192349i	$0.938390\pi$
$18$		0			0
$19$	1611.84			0.234997			0.117498	−	0.993073i	$-0.462512\pi$
$19$	1611.84			0.234997			0.117498	+	0.993073i	$0.462512\pi$
$20$		0			0
$21$	−12861.2	−	8733.21i	−1.38875	−	0.943009i
$22$		0			0
$23$	−7093.22	−	4095.27i	−0.582989	−	0.336589i	0.179332	−	0.983789i	$-0.442607\pi$
$23$	−7093.22	−	4095.27i	−0.582989	−	0.336589i	−0.762320	+	0.647200i	$0.775940\pi$
$24$		0			0
$25$	−3958.35	−	6856.06i	−0.253334	−	0.438788i
$26$		0			0
$27$	4271.40	−	19213.9i	0.217010	−	0.976169i
$28$		0			0
$29$	39159.7	−	22608.9i	1.60563	−	0.927011i	0.615298	−	0.788294i	$-0.289036\pi$
$29$	39159.7	−	22608.9i	1.60563	−	0.927011i	0.990332	−	0.138717i	$-0.0442977\pi$
$30$		0			0
$31$	−8297.21	+	14371.2i	−0.278514	+	0.482400i	−0.971016	−	0.239016i	$-0.923175\pi$
$31$	−8297.21	+	14371.2i	−0.278514	+	0.482400i	0.692502	+	0.721416i	$0.256509\pi$
$32$		0			0
$33$	−13309.8	+	19601.1i	−0.370364	+	0.545429i
$34$		0			0
$35$		−	50551.7i		−	1.17905i
$36$		0			0
$37$	37329.6			0.736968			0.368484	−	0.929634i	$-0.379877\pi$
$37$	37329.6			0.736968			0.368484	+	0.929634i	$0.379877\pi$
$38$		0			0
$39$	5732.54	−	78478.4i	0.0966393	−	1.32299i
$40$		0			0
$41$	−8256.57	−	4766.93i	−0.119798	−	0.0691652i	0.438904	−	0.898534i	$-0.355367\pi$
$41$	−8256.57	−	4766.93i	−0.119798	−	0.0691652i	−0.558701	+	0.829369i	$0.688700\pi$
$42$		0			0
$43$	−68804.6	−	119173.i	−0.865391	−	1.49890i	−0.866658	−	0.498902i	$-0.833737\pi$
$43$	−68804.6	−	119173.i	−0.865391	−	1.49890i	0.00126735	−	0.999999i	$-0.499597\pi$
$44$		0			0
$45$	59491.1	−	23607.5i	0.652852	−	0.259067i
$46$		0			0
$47$	4808.78	−	2776.35i	0.0463171	−	0.0267412i	−0.476663	−	0.879086i	$-0.658154\pi$
$47$	4808.78	−	2776.35i	0.0463171	−	0.0267412i	0.522980	+	0.852345i	$0.324820\pi$
$48$		0			0
$49$	−106937.	+	185220.i	−0.908949	+	1.57435i
$50$		0			0
$51$	22227.8	+	45935.1i	0.167566	+	0.346285i
$52$		0			0
$53$			266280.i			1.78859i	0.447480	+	0.894294i	$0.352322\pi$
$53$			266280.i			1.78859i	−0.447480	+	0.894294i	$0.647678\pi$
$54$		0			0
$55$	−77043.1			−0.463069
$56$		0			0
$57$	39174.4	−	18956.3i	0.211533	−	0.102360i
$58$		0			0
$59$	215319.	+	124314.i	1.04840	+	0.605293i	0.922201	−	0.386712i	$-0.126389\pi$
$59$	215319.	+	124314.i	1.04840	+	0.605293i	0.126198	+	0.992005i	$0.459723\pi$
$60$		0			0
$61$	182387.	+	315903.i	0.803533	+	1.39176i	0.917277	+	0.398250i	$0.130382\pi$
$61$	182387.	+	315903.i	0.803533	+	1.39176i	−0.113744	+	0.993510i	$0.536284\pi$
$62$		0			0
$63$	−415288.	−	60995.9i	−1.66084	−	0.243938i
$64$		0			0
$65$	221591.	−	127936.i	0.806885	−	0.465855i
$66$		0			0
$67$	−130531.	+	226087.i	−0.434001	+	0.751712i	−0.997214	−	0.0746004i	$-0.976232\pi$
$67$	−130531.	+	226087.i	−0.434001	+	0.751712i	0.563213	+	0.826312i	$0.309565\pi$
$68$		0			0
$69$	−220557.	−	16110.9i	−0.671388	−	0.0490424i
$70$		0			0
$71$		−	131448.i		−	0.367266i	−0.982995	−	0.183633i	$-0.941214\pi$
$71$		−	131448.i		−	0.367266i	0.982995	−	0.183633i	$-0.0587857\pi$
$72$		0			0
$73$	−159473.			−0.409939			−0.204969	−	0.978768i	$-0.565709\pi$
$73$	−159473.			−0.409939			−0.204969	+	0.978768i	$0.565709\pi$
$74$		0			0
$75$	−176836.	−	120077.i	−0.419166	−	0.284628i
$76$		0			0
$77$	437564.	+	252628.i	0.958450	+	0.553361i
$78$		0			0
$79$	443525.	+	768208.i	0.899574	+	1.55811i	0.828039	+	0.560671i	$0.189457\pi$
$79$	443525.	+	768208.i	0.899574	+	1.55811i	0.0715356	+	0.997438i	$0.477210\pi$
$80$		0			0
$81$	−122156.	−	517211.i	−0.229858	−	0.973224i
$82$		0			0
$83$	492235.	−	284192.i	0.860872	−	0.497025i	−0.00343214	−	0.999994i	$-0.501092\pi$
$83$	492235.	−	284192.i	0.860872	−	0.497025i	0.864304	+	0.502969i	$0.167759\pi$
$84$		0			0
$85$	−82968.9	+	143706.i	−0.135101	+	0.234002i
$86$		0			0
$87$	685845.	−	1.01003e6i	1.04152	−	1.53383i
$88$		0			0
$89$			837943.i			1.18862i	0.804234	+	0.594312i	$0.202576\pi$
$89$			837943.i			1.18862i	−0.804234	+	0.594312i	$0.797424\pi$
$90$		0			0
$91$	−1.67803e6			−2.22676
$92$		0			0
$93$	−32641.3	+	446859.i	−0.0405806	+	0.555548i
$94$		0			0
$95$	122556.	+	70757.5i	0.142943	+	0.0825281i
$96$		0			0
$97$	−430032.	−	744838.i	−0.471179	−	0.816106i	0.528278	−	0.849072i	$-0.322838\pi$
$97$	−430032.	−	744838.i	−0.471179	−	0.816106i	−0.999456	+	0.0329659i	$0.989505\pi$
$98$		0			0
$99$	−92960.4	+	632917.i	−0.0958059	+	0.652291i
$100$		0			0
$101$	391471.	−	226016.i	0.379958	−	0.219369i	−0.297842	−	0.954615i	$-0.596267\pi$
$101$	391471.	−	226016.i	0.379958	−	0.219369i	0.677800	+	0.735247i	$0.262934\pi$
$102$		0			0
$103$	−475439.	+	823485.i	−0.435094	+	0.753605i	−0.997303	−	0.0733900i	$-0.976618\pi$
$103$	−475439.	+	823485.i	−0.435094	+	0.753605i	0.562209	+	0.826995i	$0.309952\pi$
$104$		0			0
$105$	−594521.	−	1.22861e6i	−0.513570	−	1.06132i
$106$		0			0
$107$		−	1.76186e6i		−	1.43821i	−0.694903	−	0.719103i	$-0.744553\pi$
$107$		−	1.76186e6i		−	1.43821i	0.694903	−	0.719103i	$-0.255447\pi$
$108$		0			0
$109$	993465.			0.767137			0.383569	−	0.923512i	$-0.374695\pi$
$109$	993465.			0.767137			0.383569	+	0.923512i	$0.374695\pi$
$110$		0			0
$111$	907262.	−	439021.i	0.663382	−	0.321008i
$112$		0			0
$113$	890215.	+	513966.i	0.616964	+	0.356204i	0.775686	−	0.631119i	$-0.217404\pi$
$113$	890215.	+	513966.i	0.616964	+	0.356204i	−0.158722	+	0.987323i	$0.550737\pi$
$114$		0			0
$115$	−359553.	−	622763.i	−0.236412	−	0.409477i
$116$		0			0
$117$	−783633.	−	1.97476e6i	−0.489277	−	1.23298i
$118$		0			0
$119$	942439.	−	544118.i	0.559258	−	0.322888i
$120$		0			0
$121$	−500765.	+	867350.i	−0.282669	+	0.489597i
$122$		0			0
$123$	−256730.	−	18753.2i	−0.137963	−	0.0100777i
$124$		0			0
$125$		−	2.06689e6i		−	1.05825i
$126$		0			0
$127$	1.65197e6			0.806475			0.403237	−	0.915095i	$-0.367885\pi$
$127$	1.65197e6			0.806475			0.403237	+	0.915095i	$0.367885\pi$
$128$		0			0
$129$	−3.07379e6	−	2.08720e6i	−1.43187	−	0.972290i
$130$		0			0
$131$	1.75032e6	+	1.01055e6i	0.778581	+	0.449514i	0.835927	−	0.548841i	$-0.184931\pi$
$131$	1.75032e6	+	1.01055e6i	0.778581	+	0.449514i	−0.0573463	+	0.998354i	$0.518264\pi$
$132$		0			0
$133$	−464034.	−	803730.i	−0.197240	−	0.341630i
$134$		0			0
$135$	1.16824e6	−	1.27341e6i	0.474820	−	0.517568i
$136$		0			0
$137$	−1.25537e6	+	724786.i	−0.488212	+	0.281870i	−0.723833	−	0.689976i	$-0.757621\pi$
$137$	−1.25537e6	+	724786.i	−0.488212	+	0.281870i	0.235620	+	0.971845i	$0.424288\pi$
$138$		0			0
$139$	−1.48038e6	+	2.56409e6i	−0.551224	+	0.954748i	0.446963	+	0.894552i	$0.352506\pi$
$139$	−1.48038e6	+	2.56409e6i	−0.551224	+	0.954748i	−0.998187	+	0.0601950i	$0.980828\pi$
$140$		0			0
$141$	84221.2	−	124031.i	0.0300444	−	0.0442459i
$142$		0			0
$143$			2.55738e6i			0.874556i
$144$		0			0
$145$	3.96998e6			1.30222
$146$		0			0
$147$	−420691.	+	5.75925e6i	−0.132438	+	1.81307i
$148$		0			0
$149$	−1.03415e6	−	597065.i	−0.312625	−	0.180494i	0.335476	−	0.942049i	$-0.391103\pi$
$149$	−1.03415e6	−	597065.i	−0.312625	−	0.180494i	−0.648100	+	0.761555i	$0.724436\pi$
$150$		0			0
$151$	−720995.	−	1.24880e6i	−0.209412	−	0.362712i	0.742117	−	0.670270i	$-0.233822\pi$
$151$	−720995.	−	1.24880e6i	−0.209412	−	0.362712i	−0.951529	+	0.307558i	$0.900488\pi$
$152$		0			0
$153$	1.08045e6	+	854996.i	0.301670	+	0.238720i
$154$		0			0
$155$	−1.26175e6	+	728470.i	−0.338826	+	0.195621i
$156$		0			0
$157$	740950.	−	1.28336e6i	0.191465	−	0.331627i	−0.754271	−	0.656563i	$-0.772009\pi$
$157$	740950.	−	1.28336e6i	0.191465	−	0.331627i	0.945736	+	0.324936i	$0.105343\pi$
$158$		0			0
$159$	3.13162e6	+	6.47168e6i	0.779073	+	1.61000i
$160$		0			0
$161$			4.71596e6i			1.13004i
$162$		0			0
$163$	−2.88701e6			−0.666632			−0.333316	−	0.942815i	$-0.608168\pi$
$163$	−2.88701e6			−0.666632			−0.333316	+	0.942815i	$0.608168\pi$
$164$		0			0
$165$	−1.87246e6	+	906077.i	−0.416831	+	0.201703i
$166$		0			0
$167$	−4.36313e6	−	2.51905e6i	−0.936804	−	0.540864i	−0.0478470	−	0.998855i	$-0.515236\pi$
$167$	−4.36313e6	−	2.51905e6i	−0.936804	−	0.540864i	−0.888957	+	0.457991i	$0.848569\pi$
$168$		0			0
$169$	−1.83332e6	−	3.17540e6i	−0.379819	−	0.657866i
$170$		0			0
$171$	729157.	−	921432.i	0.145825	−	0.184279i
$172$		0			0
$173$	−8.39067e6	+	4.84436e6i	−1.62054	+	0.935617i	−0.633759	+	0.773531i	$0.718489\pi$
$173$	−8.39067e6	+	4.84436e6i	−1.62054	+	0.935617i	−0.986777	+	0.162086i	$0.948178\pi$
$174$		0			0
$175$	−2.27914e6	+	3.94758e6i	−0.425262	+	0.736575i
$176$		0			0
$177$	6.69514e6	+	489055.i	1.20737	+	0.0881937i
$178$		0			0
$179$		−	3.68196e6i		−	0.641977i	−0.947083	−	0.320989i	$-0.895985\pi$
$179$		−	3.68196e6i		−	0.641977i	0.947083	−	0.320989i	$-0.104015\pi$
$180$		0			0
$181$	7.80619e6			1.31645			0.658223	−	0.752823i	$-0.271308\pi$
$181$	7.80619e6			1.31645			0.658223	+	0.752823i	$0.271308\pi$
$182$		0			0
$183$	8.14796e6	+	5.53274e6i	1.32952	+	0.902791i
$184$		0			0
$185$	2.83834e6	+	1.63871e6i	0.448279	+	0.258814i
$186$		0			0
$187$	−829259.	−	1.43632e6i	−0.126813	−	0.219647i
$188$		0			0
$189$	−1.08105e7	+	3.40161e6i	−1.60126	+	0.503848i
$190$		0			0
$191$	1.06026e7	−	6.12141e6i	1.52164	−	0.878519i	0.521967	−	0.852966i	$-0.325198\pi$
$191$	1.06026e7	−	6.12141e6i	1.52164	−	0.878519i	0.999673	−	0.0255536i	$-0.00813484\pi$
$192$		0			0
$193$	3.82405e6	−	6.62344e6i	0.531926	−	0.921323i	−0.467379	−	0.884057i	$-0.654802\pi$
$193$	3.82405e6	−	6.62344e6i	0.531926	−	0.921323i	0.999305	−	0.0372661i	$-0.0118649\pi$
$194$		0			0
$195$	3.88095e6	−	5.71541e6i	0.523401	−	0.770803i
$196$		0			0
$197$			3.78222e6i			0.494707i	0.968925	+	0.247354i	$0.0795609\pi$
$197$			3.78222e6i			0.494707i	−0.968925	+	0.247354i	$0.920439\pi$
$198$		0			0
$199$	6.66157e6			0.845312			0.422656	−	0.906290i	$-0.361098\pi$
$199$	6.66157e6			0.845312			0.422656	+	0.906290i	$0.361098\pi$
$200$		0			0
$201$	−513512.	+	7.02997e6i	−0.0632357	+	0.865695i
$202$		0			0
$203$	−2.25474e7	−	1.30177e7i	−2.69531	−	1.55614i
$204$		0			0
$205$	−418522.	−	724902.i	−0.0485799	−	0.0841429i
$206$		0			0
$207$	−5.54991e6	+	2.20234e6i	−0.625712	+	0.248298i
$208$		0			0
$209$	−1.22492e6	+	707208.i	−0.134174	+	0.0774655i
$210$		0			0
$211$	−92905.6	+	160917.i	−0.00988996	+	0.0171299i	−0.870928	−	0.491411i	$-0.836481\pi$
$211$	−92905.6	+	160917.i	−0.00988996	+	0.0171299i	0.861038	+	0.508541i	$0.169815\pi$
$212$		0			0
$213$	−1.54592e6	−	3.19473e6i	−0.159973	−	0.330594i
$214$		0			0
$215$		−	1.20817e7i		−	1.21566i
$216$		0			0
$217$	9.55474e6			0.935060
$218$		0			0
$219$	−3.87585e6	+	1.87551e6i	−0.369007	+	0.178561i
$220$		0			0
$221$	4.77022e6	+	2.75409e6i	0.441938	+	0.255153i
$222$		0			0
$223$	−1.00170e7	−	1.73499e7i	−0.903279	−	1.56453i	−0.823211	−	0.567736i	$-0.807820\pi$
$223$	−1.00170e7	−	1.73499e7i	−0.903279	−	1.56453i	−0.0800680	−	0.996789i	$-0.525514\pi$
$224$		0			0
$225$	−5.71001e6	−	838664.i	−0.501290	−	0.0736275i
$226$		0			0
$227$	−1.15408e7	+	6.66311e6i	−0.986643	+	0.569639i	−0.904269	−	0.426963i	$-0.859583\pi$
$227$	−1.15408e7	+	6.66311e6i	−0.986643	+	0.569639i	−0.0823738	+	0.996602i	$0.526250\pi$
$228$		0			0
$229$	6.90639e6	−	1.19622e7i	0.575102	−	0.996106i	−0.420929	−	0.907094i	$-0.638296\pi$
$229$	6.90639e6	−	1.19622e7i	0.575102	−	0.996106i	0.996031	−	0.0890118i	$-0.0283709\pi$
$230$		0			0
$231$	1.36056e7	+	993840.i	1.10378	+	0.0806270i
$232$		0			0
$233$			8.46088e6i			0.668879i	0.942417	+	0.334440i	$0.108547\pi$
$233$			8.46088e6i			0.668879i	−0.942417	+	0.334440i	$0.891453\pi$
$234$		0			0
$235$	487510.			0.0375647
$236$		0			0
$237$	1.98141e7	+	1.34544e7i	1.48843	+	1.01070i
$238$		0			0
$239$	8.35612e6	+	4.82441e6i	0.612084	+	0.353387i	0.773781	−	0.633454i	$-0.218363\pi$
$239$	8.35612e6	+	4.82441e6i	0.612084	+	0.353387i	−0.161697	+	0.986841i	$0.551697\pi$
$240$		0			0
$241$	−1.28100e6	−	2.21875e6i	−0.0915160	−	0.158510i	0.816633	−	0.577157i	$-0.195838\pi$
$241$	−1.28100e6	−	2.21875e6i	−0.0915160	−	0.158510i	−0.908149	+	0.418647i	$0.862505\pi$
$242$		0			0
$243$	−9.05163e6	−	1.11337e7i	−0.630824	−	0.775926i
$244$		0			0
$245$	−1.62618e7	+	9.38873e6i	−1.10578	+	0.638423i
$246$		0			0
$247$	2.34874e6	−	4.06814e6i	0.155863	−	0.269963i
$248$		0			0
$249$	8.62103e6	−	1.26960e7i	0.558420	−	0.822375i
$250$		0			0
$251$			6.55408e6i			0.414468i	0.978291	+	0.207234i	$0.0664461\pi$
$251$			6.55408e6i			0.414468i	−0.978291	+	0.207234i	$0.933554\pi$
$252$		0			0
$253$	7.18732e6			0.443819
$254$		0			0
$255$	−326401.	+	4.46842e6i	−0.0196848	+	0.269484i
$256$		0			0
$257$	−1.66112e7	−	9.59050e6i	−0.978594	−	0.564991i	−0.0767484	−	0.997050i	$-0.524454\pi$
$257$	−1.66112e7	−	9.59050e6i	−0.978594	−	0.564991i	−0.901845	+	0.432059i	$0.857787\pi$
$258$		0			0
$259$	−1.07468e7	−	1.86141e7i	−0.618559	−	1.07138i
$260$		0			0
$261$	4.79019e6	−	3.26138e7i	0.269421	−	1.83434i
$262$		0			0
$263$	1.90102e7	−	1.09755e7i	1.04501	−	0.603336i	0.123760	−	0.992312i	$-0.460505\pi$
$263$	1.90102e7	−	1.09755e7i	1.04501	−	0.603336i	0.921248	+	0.388977i	$0.127171\pi$
$264$		0			0
$265$	−1.16893e7	+	2.02464e7i	−0.628130	+	1.08795i
$266$		0			0
$267$	9.85476e6	+	2.03654e7i	0.517741	+	1.06994i
$268$		0			0
$269$		−	2.94632e7i		−	1.51364i	−0.653624	−	0.756820i	$-0.726752\pi$
$269$		−	2.94632e7i		−	1.51364i	0.653624	−	0.756820i	$-0.273248\pi$
$270$		0			0
$271$	1.02226e7			0.513633			0.256816	−	0.966460i	$-0.417326\pi$
$271$	1.02226e7			0.513633			0.256816	+	0.966460i	$0.417326\pi$
$272$		0			0
$273$	−4.07828e7	+	1.97347e7i	−2.00442	+	0.969933i
$274$		0			0
$275$	6.01629e6	+	3.47351e6i	0.289288	+	0.167021i
$276$		0			0
$277$	1.95145e6	+	3.38001e6i	0.0918159	+	0.159030i	0.908275	−	0.418373i	$-0.137400\pi$
$277$	1.95145e6	+	3.38001e6i	0.0918159	+	0.159030i	−0.816459	+	0.577403i	$0.804066\pi$
$278$		0			0
$279$	4.46203e6	+	1.12444e7i	0.205457	+	0.517753i
$280$		0			0
$281$	2.21074e7	−	1.27637e7i	0.996364	−	0.575251i	0.0891933	−	0.996014i	$-0.471571\pi$
$281$	2.21074e7	−	1.27637e7i	0.996364	−	0.575251i	0.907170	+	0.420763i	$0.138238\pi$
$282$		0			0
$283$	−2.15887e7	+	3.73928e7i	−0.952507	+	1.64979i	−0.212533	+	0.977154i	$0.568171\pi$
$283$	−2.15887e7	+	3.73928e7i	−0.952507	+	1.64979i	−0.739973	+	0.672636i	$0.765162\pi$
$284$		0			0
$285$	3.81075e6	+	278361.i	0.164618	+	0.0120247i
$286$		0			0
$287$			5.48941e6i			0.232210i
$288$		0			0
$289$	2.05654e7			0.852008
$290$		0			0
$291$	−1.92113e7	−	1.30451e7i	−0.779611	−	0.529382i
$292$		0			0
$293$	3.54435e7	+	2.04633e7i	1.40908	+	0.813530i	0.995299	−	0.0968486i	$-0.0308763\pi$
$293$	3.54435e7	+	2.04633e7i	1.40908	+	0.813530i	0.413776	+	0.910379i	$0.364210\pi$
$294$		0			0
$295$	1.09144e7	+	1.89044e7i	0.425143	+	0.736369i
$296$		0			0
$297$	5.18421e6	+	1.64757e7i	0.197885	+	0.628891i
$298$		0			0
$299$	−2.06721e7	+	1.19351e7i	−0.773342	+	0.446489i
$300$		0			0
$301$	−3.96164e7	+	6.86175e7i	−1.45270	+	2.51614i
$302$		0			0
$303$	6.85623e6	−	1.00970e7i	0.246466	−	0.362966i
$304$		0			0
$305$			3.20260e7i			1.12876i
$306$		0			0
$307$	1.13791e7			0.393270			0.196635	−	0.980477i	$-0.436999\pi$
$307$	1.13791e7			0.393270			0.196635	+	0.980477i	$0.436999\pi$
$308$		0			0
$309$	−1.87038e6	+	2.56055e7i	−0.0633950	+	0.867876i
$310$		0			0
$311$	2.74028e7	+	1.58210e7i	0.910990	+	0.525960i	0.880750	−	0.473582i	$-0.157039\pi$
$311$	2.74028e7	+	1.58210e7i	0.910990	+	0.525960i	0.0302406	+	0.999543i	$0.490373\pi$
$312$		0			0
$313$	−2.35641e7	−	4.08142e7i	−0.768454	−	1.33100i	−0.938401	−	0.345548i	$-0.887693\pi$
$313$	−2.35641e7	−	4.08142e7i	−0.768454	−	1.33100i	0.169947	−	0.985453i	$-0.445640\pi$
$314$		0			0
$315$	−2.88986e7	−	2.28683e7i	−0.924580	−	0.731648i
$316$		0			0
$317$	1.19540e7	−	6.90163e6i	0.375262	−	0.216658i	−0.300493	−	0.953784i	$-0.597151\pi$
$317$	1.19540e7	−	6.90163e6i	0.375262	−	0.216658i	0.675755	+	0.737126i	$0.263818\pi$
$318$		0			0
$319$	−1.98396e7	+	3.43632e7i	−0.611169	+	1.05858i
$320$		0			0
$321$	−2.07207e7	−	4.28205e7i	−0.626453	−	1.29460i
$322$		0			0
$323$			3.04642e6i			0.0904027i
$324$		0			0
$325$	−2.30720e7			−0.672103
$326$		0			0
$327$	2.41452e7	−	1.16838e7i	0.690539	−	0.334149i
$328$		0			0
$329$	−2.76880e6	−	1.59857e6i	−0.0777507	−	0.0448894i
$330$		0			0
$331$	2.46345e6	+	4.26682e6i	0.0679297	+	0.117658i	0.897990	−	0.440016i	$-0.145027\pi$
$331$	2.46345e6	+	4.26682e6i	0.0679297	+	0.117658i	−0.830060	+	0.557674i	$0.811694\pi$
$332$		0			0
$333$	1.68870e7	−	2.13400e7i	0.457319	−	0.577911i
$334$		0			0
$335$	−1.98498e7	+	1.14603e7i	−0.527984	+	0.304832i
$336$		0			0
$337$	1.66064e7	−	2.87632e7i	0.433897	−	0.751532i	−0.563308	−	0.826247i	$-0.690471\pi$
$337$	1.66064e7	−	2.87632e7i	0.433897	−	0.751532i	0.997205	+	0.0747152i	$0.0238048\pi$
$338$		0			0
$339$	2.76804e7	+	2.02195e6i	0.710515	+	0.0519004i
$340$		0			0
$341$		−	1.45618e7i		−	0.367243i
$342$		0			0
$343$	5.54044e7			1.37297
$344$		0			0
$345$	−1.60627e7	−	1.09071e7i	−0.391166	−	0.265615i
$346$		0			0
$347$	2.58654e7	+	1.49334e7i	0.619058	+	0.357413i	0.776502	−	0.630115i	$-0.216992\pi$
$347$	2.58654e7	+	1.49334e7i	0.619058	+	0.357413i	−0.157444	+	0.987528i	$0.550325\pi$
$348$		0			0
$349$	−1.27156e7	−	2.20241e7i	−0.299130	−	0.518109i	0.676807	−	0.736161i	$-0.263363\pi$
$349$	−1.27156e7	−	2.20241e7i	−0.299130	−	0.518109i	−0.975937	+	0.218051i	$0.930030\pi$
$350$		0			0
$351$	−4.22699e7	−	3.87787e7i	−0.977485	−	0.896751i
$352$		0			0
$353$	2.08239e7	−	1.20227e7i	0.473411	−	0.273324i	−0.244256	−	0.969711i	$-0.578544\pi$
$353$	2.08239e7	−	1.20227e7i	0.473411	−	0.273324i	0.717666	+	0.696387i	$0.245210\pi$
$354$		0			0
$355$	5.77038e6	−	9.99460e6i	0.128979	−	0.223399i
$356$		0			0
$357$	1.65059e7	−	2.43080e7i	0.362773	−	0.534249i
$358$		0			0
$359$			6.34043e7i			1.37036i	0.728372	+	0.685182i	$0.240277\pi$
$359$			6.34043e7i			1.37036i	−0.728372	+	0.685182i	$0.759723\pi$
$360$		0			0
$361$	−4.44478e7			−0.944776
$362$		0			0
$363$	−1.97001e6	+	2.69694e7i	−0.0411860	+	0.563835i
$364$		0			0
$365$	−1.21254e7	−	7.00063e6i	−0.249356	−	0.143966i
$366$		0			0
$367$	2.48912e6	+	4.31128e6i	0.0503555	+	0.0872183i	0.890104	−	0.455757i	$-0.150631\pi$
$367$	2.48912e6	+	4.31128e6i	0.0503555	+	0.0872183i	−0.839749	+	0.542975i	$0.817298\pi$
$368$		0			0
$369$	−6.46014e6	+	2.56354e6i	−0.128577	+	0.0510224i
$370$		0			0
$371$	1.32778e8	−	7.66593e7i	2.60018	−	1.50122i
$372$		0			0
$373$	−8.20797e6	+	1.42166e7i	−0.158165	+	0.273949i	−0.934207	−	0.356732i	$-0.883891\pi$
$373$	−8.20797e6	+	1.42166e7i	−0.158165	+	0.273949i	0.776042	+	0.630681i	$0.217224\pi$
$374$		0			0
$375$	−2.43080e7	−	5.02338e7i	−0.460951	−	0.952581i
$376$		0			0
$377$		−	1.31780e8i		−	2.45939i
$378$		0			0
$379$	−5.40621e7			−0.993060			−0.496530	−	0.868020i	$-0.665393\pi$
$379$	−5.40621e7			−0.993060			−0.496530	+	0.868020i	$0.665393\pi$
$380$		0			0
$381$	4.01496e7	−	1.94282e7i	0.725949	−	0.351284i
$382$		0			0
$383$	−2.73475e7	−	1.57891e7i	−0.486767	−	0.281035i	0.236465	−	0.971640i	$-0.424011\pi$
$383$	−2.73475e7	−	1.57891e7i	−0.486767	−	0.281035i	−0.723232	+	0.690605i	$0.757344\pi$
$384$		0			0
$385$	2.21799e7	+	3.84168e7i	0.388667	+	0.673192i
$386$		0			0
$387$	−9.92523e7	−	1.45778e7i	−1.71241	−	0.251512i
$388$		0			0
$389$	−5.31062e7	+	3.06609e7i	−0.902186	+	0.520877i	−0.877909	−	0.478828i	$-0.841062\pi$
$389$	−5.31062e7	+	3.06609e7i	−0.902186	+	0.520877i	−0.0242774	+	0.999705i	$0.507728\pi$
$390$		0			0
$391$	7.74014e6	−	1.34063e7i	0.129485	−	0.224274i
$392$		0			0
$393$	5.44246e7	+	3.97551e6i	0.896639	+	0.0654960i
$394$		0			0
$395$			7.78803e7i			1.26368i
$396$		0			0
$397$	−5.04695e7			−0.806598			−0.403299	−	0.915068i	$-0.632137\pi$
$397$	−5.04695e7			−0.806598			−0.403299	+	0.915068i	$0.632137\pi$
$398$		0			0
$399$	−2.07303e7	−	1.40766e7i	−0.326352	−	0.221604i
$400$		0			0
$401$	6.65382e7	+	3.84158e7i	1.03190	+	0.595768i	0.917529	−	0.397670i	$-0.130181\pi$
$401$	6.65382e7	+	3.84158e7i	1.03190	+	0.595768i	0.114372	+	0.993438i	$0.463514\pi$
$402$		0			0
$403$	2.41810e7	+	4.18827e7i	0.369453	+	0.639911i
$404$		0			0
$405$	1.34167e7	−	4.46883e7i	0.201967	−	0.672711i
$406$		0			0
$407$	−2.83686e7	+	1.63786e7i	−0.420780	+	0.242938i
$408$		0			0
$409$	−3.49336e7	+	6.05068e7i	−0.510592	+	0.884370i	0.489333	+	0.872097i	$0.337240\pi$
$409$	−3.49336e7	+	6.05068e7i	−0.510592	+	0.884370i	−0.999925	+	0.0122735i	$0.996093\pi$
$410$		0			0
$411$	−2.19865e7	+	3.23792e7i	−0.316688	+	0.466380i
$412$		0			0
$413$		−	1.43156e8i		−	2.03216i
$414$		0			0
$415$	4.99024e7			0.698196
$416$		0			0
$417$	−5.82382e6	+	7.97279e7i	−0.0803156	+	1.09952i
$418$		0			0
$419$	−7.63774e7	−	4.40965e7i	−1.03830	−	0.599463i	−0.118949	−	0.992900i	$-0.537952\pi$
$419$	−7.63774e7	−	4.40965e7i	−1.03830	−	0.599463i	−0.919351	+	0.393437i	$0.871286\pi$
$420$		0			0
$421$	1.87269e7	+	3.24359e7i	0.250968	+	0.434690i	0.963793	−	0.266653i	$-0.0859177\pi$
$421$	1.87269e7	+	3.24359e7i	0.250968	+	0.434690i	−0.712824	+	0.701343i	$0.752584\pi$
$422$		0			0
$423$	588231.	−	4.00495e6i	0.00777190	−	0.0529147i
$424$		0			0
$425$	1.29581e7	−	7.48135e6i	0.168801	−	0.0974571i
$426$		0			0
$427$	1.05015e8	−	1.81891e8i	1.34886	−	2.33629i
$428$		0			0
$429$	3.00765e7	+	6.21548e7i	0.380939	+	0.787232i
$430$		0			0
$431$			6.23855e7i			0.779205i	0.920983	+	0.389603i	$0.127388\pi$
$431$			6.23855e7i			0.779205i	−0.920983	+	0.389603i	$0.872612\pi$
$432$		0			0
$433$	1.16020e6			0.0142912			0.00714560	−	0.999974i	$-0.497725\pi$
$433$	1.16020e6			0.0142912			0.00714560	+	0.999974i	$0.497725\pi$
$434$		0			0
$435$	9.64866e7	−	4.66895e7i	1.17219	−	0.567220i
$436$		0			0
$437$	−1.14332e7	−	6.60094e6i	−0.137001	−	0.0790973i
$438$		0			0
$439$	−5.61813e7	−	9.73088e7i	−0.664046	−	1.15016i	−0.979543	−	0.201234i	$-0.935505\pi$
$439$	−5.61813e7	−	9.73088e7i	−0.664046	−	1.15016i	0.315497	−	0.948926i	$-0.397829\pi$
$440$		0			0
$441$	5.75080e7	+	1.44921e8i	0.670521	+	1.68972i
$442$		0			0
$443$	−7.64250e6	+	4.41240e6i	−0.0879072	+	0.0507532i	−0.543309	−	0.839533i	$-0.682829\pi$
$443$	−7.64250e6	+	4.41240e6i	−0.0879072	+	0.0507532i	0.455402	+	0.890286i	$0.349496\pi$
$444$		0			0
$445$	−3.67844e7	+	6.37125e7i	−0.417430	+	0.723011i
$446$		0			0
$447$	−3.21558e7	−	2.34886e6i	−0.360029	−	0.0262987i
$448$		0			0
$449$			1.56529e8i			1.72924i	0.502429	+	0.864619i	$0.332440\pi$
$449$			1.56529e8i			1.72924i	−0.502429	+	0.864619i	$0.667560\pi$
$450$		0			0
$451$	8.36611e6			0.0911998
$452$		0			0
$453$	−3.22098e7	−	2.18715e7i	−0.346492	−	0.235280i
$454$		0			0
$455$	−1.27588e8	−	7.36628e7i	−1.35449	−	0.782013i
$456$		0			0
$457$	−4.05022e7	−	7.01519e7i	−0.424356	−	0.735006i	0.572004	−	0.820251i	$-0.306166\pi$
$457$	−4.05022e7	−	7.01519e7i	−0.424356	−	0.735006i	−0.996360	+	0.0852445i	$0.972833\pi$
$458$		0			0
$459$	3.63147e7	+	8.07302e6i	0.375530	+	0.0834830i
$460$		0			0
$461$	−1.07723e8	+	6.21942e7i	−1.09953	+	0.634815i	−0.936098	−	0.351740i	$-0.885590\pi$
$461$	−1.07723e8	+	6.21942e7i	−1.09953	+	0.634815i	−0.163434	+	0.986554i	$0.552257\pi$
$462$		0			0
$463$	−1.03335e7	+	1.78981e7i	−0.104113	+	0.180329i	−0.913375	−	0.407118i	$-0.866534\pi$
$463$	−1.03335e7	+	1.78981e7i	−0.104113	+	0.180329i	0.809263	+	0.587447i	$0.199867\pi$
$464$		0			0
$465$	−2.20983e7	+	3.25437e7i	−0.219786	+	0.323674i
$466$		0			0
$467$			1.51409e8i			1.48663i	0.668944	+	0.743313i	$0.266747\pi$
$467$			1.51409e8i			1.48663i	−0.668944	+	0.743313i	$0.733253\pi$
$468$		0			0
$469$	1.50315e8			1.45708
$470$		0			0
$471$	2.91491e6	−	3.99050e7i	0.0278973	−	0.381913i
$472$		0			0
$473$	1.04576e8	+	6.03771e7i	0.988210	+	0.570543i
$474$		0			0
$475$	−6.38024e6	−	1.10509e7i	−0.0595328	−	0.103114i
$476$		0			0
$477$	1.52222e8	+	1.20458e8i	1.40256	+	1.10989i
$478$		0			0
$479$	−2.30356e7	+	1.32996e7i	−0.209601	+	0.121013i	−0.601126	−	0.799154i	$-0.705281\pi$
$479$	−2.30356e7	+	1.32996e7i	−0.209601	+	0.121013i	0.391525	+	0.920167i	$0.371948\pi$
$480$		0			0
$481$	5.43958e7	−	9.42163e7i	0.488799	−	0.846625i
$482$		0			0
$483$	5.54627e7	+	1.14617e8i	0.492220	+	1.01720i
$484$		0			0
$485$		−	7.55110e7i		−	0.661889i
$486$		0			0
$487$	1.40740e7			0.121851			0.0609257	−	0.998142i	$-0.480595\pi$
$487$	1.40740e7			0.121851			0.0609257	+	0.998142i	$0.480595\pi$
$488$		0			0
$489$	−7.01662e7	+	3.39532e7i	−0.600069	+	0.290371i
$490$		0			0
$491$	−5.23514e7	−	3.02251e7i	−0.442267	−	0.255343i	0.262292	−	0.964989i	$-0.415522\pi$
$491$	−5.23514e7	−	3.02251e7i	−0.442267	−	0.255343i	−0.704559	+	0.709646i	$0.748855\pi$
$492$		0			0
$493$	4.27312e7	+	7.40126e7i	0.356619	+	0.617682i
$494$		0			0
$495$	−3.48523e7	+	4.40427e7i	−0.287353	+	0.363127i
$496$		0			0
$497$	−6.55455e7	+	3.78427e7i	−0.533917	+	0.308257i
$498$		0			0
$499$	−3.06506e7	+	5.30884e7i	−0.246682	+	0.427266i	−0.962603	−	0.270915i	$-0.912674\pi$
$499$	−3.06506e7	+	5.30884e7i	−0.246682	+	0.427266i	0.715921	+	0.698181i	$0.246007\pi$
$500$		0			0
$501$	−1.35667e8	−	9.90999e6i	−1.07885	−	0.0788061i
$502$		0			0
$503$		−	7.29236e7i		−	0.573012i	−0.958078	−	0.286506i	$-0.907506\pi$
$503$		−	7.29236e7i		−	0.573012i	0.958078	−	0.286506i	$-0.0924939\pi$
$504$		0			0
$505$	3.96870e7			0.308158
$506$		0			0
$507$	−8.19017e7	−	5.56140e7i	−0.628448	−	0.426737i
$508$		0			0
$509$	−1.07611e8	−	6.21291e7i	−0.816022	−	0.471131i	0.0330205	−	0.999455i	$-0.489487\pi$
$509$	−1.07611e8	−	6.21291e7i	−0.816022	−	0.471131i	−0.849043	+	0.528324i	$0.822821\pi$
$510$		0			0
$511$	4.59108e7	+	7.95198e7i	0.344074	+	0.595953i
$512$		0			0
$513$	6.88483e6	−	3.09699e7i	0.0509966	−	0.229397i
$514$		0			0
$515$	−7.22994e7	+	4.17421e7i	−0.529314	+	0.305599i
$516$		0			0
$517$	−2.43629e6	+	4.21977e6i	−0.0176302	+	0.0305364i
$518$		0			0
$519$	−1.46955e8	+	2.16417e8i	−1.05119	+	1.54807i
$520$		0			0
$521$		−	1.09934e8i		−	0.777357i	−0.921373	−	0.388679i	$-0.872932\pi$
$521$		−	1.09934e8i		−	0.777357i	0.921373	−	0.388679i	$-0.127068\pi$
$522$		0			0
$523$	1.58005e8			1.10450			0.552248	−	0.833680i	$-0.313770\pi$
$523$	1.58005e8			1.10450			0.552248	+	0.833680i	$0.313770\pi$
$524$		0			0
$525$	−8.96616e6	+	1.22746e8i	−0.0619624	+	0.848264i
$526$		0			0
$527$	−2.71618e7	−	1.56819e7i	−0.185578	−	0.107144i
$528$		0			0
$529$	−4.04754e7	−	7.01055e7i	−0.273416	−	0.473571i
$530$		0			0
$531$	1.68471e8	−	6.68532e7i	1.12523	−	0.446518i
$532$		0			0
$533$	−2.40625e7	+	1.38925e7i	−0.158913	+	0.0917486i
$534$		0			0
$535$	7.73432e7	−	1.33962e8i	0.505081	−	0.874825i
$536$		0			0
$537$	−4.33022e7	−	8.94865e7i	−0.279632	−	0.577876i
$538$		0			0
$539$		−	1.87677e8i		−	1.19852i
$540$		0			0
$541$	−2.44811e8			−1.54611			−0.773053	−	0.634342i	$-0.781271\pi$
$541$	−2.44811e8			−1.54611			−0.773053	+	0.634342i	$0.781271\pi$
$542$		0			0
$543$	1.89722e8	−	9.18058e7i	1.18500	−	0.573417i
$544$		0			0
$545$	7.55375e7	+	4.36116e7i	0.466631	+	0.269409i
$546$		0			0
$547$	7.03155e7	+	1.21790e8i	0.429624	+	0.744131i	0.996840	−	0.0794382i	$-0.0253126\pi$
$547$	7.03155e7	+	1.21790e8i	0.429624	+	0.744131i	−0.567215	+	0.823570i	$0.691979\pi$
$548$		0			0
$549$	2.63097e8	+	3.86427e7i	1.59001	+	0.233534i
$550$		0			0
$551$	6.31194e7	−	3.64420e7i	0.377318	−	0.217845i
$552$		0			0
$553$	2.55373e8	−	4.42319e8i	1.51008	−	2.61553i
$554$		0			0
$555$	8.82554e7	+	6.44672e6i	0.516253	+	0.0377103i
$556$		0			0
$557$		−	1.60943e8i		−	0.931335i	−0.884960	−	0.465668i	$-0.845814\pi$
$557$		−	1.60943e8i		−	0.931335i	0.884960	−	0.465668i	$-0.154186\pi$
$558$		0			0
$559$	−4.01042e8			−2.29591
$560$		0			0
$561$	−3.70464e7	−	2.51557e7i	−0.209825	−	0.142478i
$562$		0			0
$563$	1.48787e8	+	8.59020e7i	0.833756	+	0.481369i	0.855137	−	0.518402i	$-0.173473\pi$
$563$	1.48787e8	+	8.59020e7i	0.833756	+	0.481369i	−0.0213812	+	0.999771i	$0.506806\pi$
$564$		0			0
$565$	4.51246e7	+	7.81582e7i	0.250189	+	0.433340i
$566$		0			0
$567$	−2.22735e8	+	2.09812e8i	−1.22191	+	1.15102i
$568$		0			0
$569$	−3.86686e7	+	2.23254e7i	−0.209905	+	0.121189i	−0.601267	−	0.799048i	$-0.705337\pi$
$569$	−3.86686e7	+	2.23254e7i	−0.209905	+	0.121189i	0.391362	+	0.920237i	$0.372004\pi$
$570$		0			0
$571$	1.20675e8	−	2.09016e8i	0.648201	−	1.12272i	−0.335351	−	0.942093i	$-0.608855\pi$
$571$	1.20675e8	−	2.09016e8i	0.648201	−	1.12272i	0.983552	−	0.180624i	$-0.0578117\pi$
$572$		0			0
$573$	1.85694e8	−	2.73468e8i	0.987040	−	1.45359i
$574$		0			0
$575$			6.48421e7i			0.341078i
$576$		0			0
$577$	−2.31508e8			−1.20514			−0.602572	−	0.798065i	$-0.705857\pi$
$577$	−2.31508e8			−1.20514			−0.602572	+	0.798065i	$0.705857\pi$
$578$		0			0
$579$	1.50438e7	−	2.05950e8i	0.0775038	−	1.06103i
$580$		0			0
$581$	−2.83419e8	−	1.63632e8i	−1.44511	−	0.834335i
$582$		0			0
$583$	−1.16832e8	−	2.02359e8i	−0.589599	−	1.02121i
$584$		0			0
$585$	2.71060e7	−	1.84550e8i	0.135393	−	0.921821i
$586$		0			0
$587$	−2.57665e7	+	1.48763e7i	−0.127392	+	0.0735496i	−0.562342	−	0.826905i	$-0.690099\pi$
$587$	−2.57665e7	+	1.48763e7i	−0.127392	+	0.0735496i	0.434950	+	0.900455i	$0.356766\pi$
$588$		0			0
$589$	−1.33738e7	+	2.31641e7i	−0.0654499	+	0.113363i
$590$		0			0
$591$	4.44814e7	+	9.19233e7i	0.215484	+	0.445311i
$592$		0			0
$593$			1.95353e8i			0.936819i	0.883511	+	0.468410i	$0.155173\pi$
$593$			1.95353e8i			0.936819i	−0.883511	+	0.468410i	$0.844827\pi$
$594$		0			0
$595$	9.55437e7			0.453577
$596$		0			0
$597$	1.61903e8	−	7.83444e7i	0.760908	−	0.368201i
$598$		0			0
$599$	−1.00264e8	−	5.78877e7i	−0.466516	−	0.269343i	0.248264	−	0.968692i	$-0.420140\pi$
$599$	−1.00264e8	−	5.78877e7i	−0.466516	−	0.269343i	−0.714780	+	0.699349i	$0.753473\pi$
$600$		0			0
$601$	1.60850e7	+	2.78600e7i	0.0740964	+	0.128339i	0.900693	−	0.434456i	$-0.143059\pi$
$601$	1.60850e7	+	2.78600e7i	0.0740964	+	0.128339i	−0.826597	+	0.562795i	$0.809726\pi$
$602$		0			0
$603$	7.01966e7	+	1.76896e8i	0.320158	+	0.806800i
$604$		0			0
$605$	−7.61507e7	+	4.39656e7i	−0.343881	+	0.198540i
$606$		0			0
$607$	−7.96688e7	+	1.37990e8i	−0.356223	+	0.616997i	−0.987326	−	0.158702i	$-0.949269\pi$
$607$	−7.96688e7	+	1.37990e8i	−0.356223	+	0.616997i	0.631103	+	0.775699i	$0.282602\pi$
$608$		0			0
$609$	−7.01090e8	−	5.12119e7i	−3.10400	−	0.226735i
$610$		0			0
$611$		−	1.61825e7i		−	0.0709451i
$612$		0			0
$613$	2.06622e8			0.897007			0.448504	−	0.893781i	$-0.351957\pi$
$613$	2.06622e8			0.897007			0.448504	+	0.893781i	$0.351957\pi$
$614$		0			0
$615$	−1.86971e7	−	1.26960e7i	−0.0803802	−	0.0545808i
$616$		0			0
$617$	3.16493e8	+	1.82727e8i	1.34744	+	0.777943i	0.987886	−	0.155183i	$-0.0495967\pi$
$617$	3.16493e8	+	1.82727e8i	1.34744	+	0.777943i	0.359551	+	0.933126i	$0.382930\pi$
$618$		0			0
$619$	2.21094e8	+	3.82946e8i	0.932190	+	1.61460i	0.779569	+	0.626316i	$0.215438\pi$
$619$	2.21094e8	+	3.82946e8i	0.932190	+	1.61460i	0.152621	+	0.988285i	$0.451229\pi$
$620$		0			0
$621$	−1.08984e8	+	1.18796e8i	−0.455082	+	0.496053i
$622$		0			0
$623$	4.17832e8	−	2.41236e8i	1.72798	−	0.997648i
$624$		0			0
$625$	2.88841e7	−	5.00287e7i	0.118309	−	0.204917i
$626$		0			0
$627$	−2.14533e7	+	3.15939e7i	−0.0870345	+	0.128174i
$628$		0			0
$629$			7.05537e7i			0.283510i
$630$		0			0
$631$	−2.30153e8			−0.916070			−0.458035	−	0.888934i	$-0.651447\pi$
$631$	−2.30153e8			−0.916070			−0.458035	+	0.888934i	$0.651447\pi$
$632$		0			0
$633$	−365492.	+	5.00357e6i	−0.00144101	+	0.0197274i
$634$		0			0
$635$	1.25606e8	+	7.25189e7i	0.490559	+	0.283224i
$636$		0			0
$637$	3.11652e8	+	5.39797e8i	1.20573	+	2.08839i
$638$		0			0
$639$	−7.51442e7	−	5.94639e7i	−0.288000	−	0.227903i
$640$		0			0
$641$	−2.21604e8	+	1.27943e8i	−0.841401	+	0.485783i	−0.857740	−	0.514083i	$-0.828132\pi$
$641$	−2.21604e8	+	1.27943e8i	−0.841401	+	0.485783i	0.0163389	+	0.999867i	$0.494799\pi$
$642$		0			0
$643$	−1.73173e8	+	2.99945e8i	−0.651400	+	1.12826i	0.331384	+	0.943496i	$0.392485\pi$
$643$	−1.73173e8	+	2.99945e8i	−0.651400	+	1.12826i	−0.982783	+	0.184762i	$0.940849\pi$
$644$		0			0
$645$	−1.42088e8	−	2.93634e8i	−0.529516	−	1.09428i
$646$		0			0
$647$			2.55648e8i			0.943907i	0.881623	+	0.471954i	$0.156451\pi$
$647$			2.55648e8i			0.943907i	−0.881623	+	0.471954i	$0.843549\pi$
$648$		0			0
$649$	−2.18175e8			−0.798127
$650$		0			0
$651$	2.32219e8	−	1.12370e8i	0.841695	−	0.407293i
$652$		0			0
$653$	1.92519e8	+	1.11151e8i	0.691407	+	0.399184i	0.804139	−	0.594442i	$-0.202627\pi$
$653$	1.92519e8	+	1.11151e8i	0.691407	+	0.399184i	−0.112732	+	0.993625i	$0.535960\pi$
$654$		0			0
$655$	8.87230e7	+	1.53673e8i	0.315728	+	0.546856i
$656$		0			0
$657$	−7.21416e7	+	9.11649e7i	−0.254384	+	0.321463i
$658$		0			0
$659$	3.13159e8	−	1.80802e8i	1.09423	−	0.631754i	0.159531	−	0.987193i	$-0.449002\pi$
$659$	3.13159e8	−	1.80802e8i	1.09423	−	0.631754i	0.934699	+	0.355439i	$0.115669\pi$
$660$		0			0
$661$	9.59201e7	−	1.66138e8i	0.332128	−	0.575262i	−0.650801	−	0.759248i	$-0.725567\pi$
$661$	9.59201e7	−	1.66138e8i	0.332128	−	0.575262i	0.982929	+	0.183986i	$0.0589002\pi$
$662$		0			0
$663$	1.48326e8	+	1.08346e7i	0.508950	+	0.0371769i
$664$		0			0
$665$		−	8.14815e7i		−	0.277073i
$666$		0			0
$667$	−3.70358e8			−1.24809
$668$		0			0
$669$	−4.47499e8	−	3.03867e8i	−1.49456	−	1.01486i
$670$		0			0
$671$	−2.77210e8	−	1.60047e8i	−0.917573	−	0.529761i
$672$		0			0
$673$	−1.09354e8	−	1.89406e8i	−0.358747	−	0.621368i	0.629005	−	0.777401i	$-0.283463\pi$
$673$	−1.09354e8	−	1.89406e8i	−0.358747	−	0.621368i	−0.987752	+	0.156034i	$0.950129\pi$
$674$		0			0
$675$	−1.48640e8	+	4.67705e7i	−0.483307	+	0.152076i
$676$		0			0
$677$	4.12742e8	−	2.38296e8i	1.33019	−	0.767983i	0.344858	−	0.938655i	$-0.387927\pi$
$677$	4.12742e8	−	2.38296e8i	1.33019	−	0.767983i	0.985328	+	0.170672i	$0.0545938\pi$
$678$		0			0
$679$	−2.47604e8	+	4.28863e8i	−0.790949	+	1.36996i
$680$		0			0
$681$	−2.02127e8	+	2.97668e8i	−0.640004	+	0.942522i
$682$		0			0
$683$		−	4.59479e7i		−	0.144213i	−0.997397	−	0.0721064i	$-0.977028\pi$
$683$		−	4.59479e7i		−	0.144213i	0.997397	−	0.0721064i	$-0.0229721\pi$
$684$		0			0
$685$	−1.27268e8			−0.395957
$686$		0			0
$687$	2.71698e7	−	3.71954e8i	0.0837947	−	1.14715i
$688$		0			0
$689$	6.72064e8	+	3.88016e8i	2.05472	+	1.18629i
$690$		0			0
$691$	−9.37101e7	−	1.62311e8i	−0.284022	−	0.491941i	0.688349	−	0.725379i	$-0.258336\pi$
$691$	−9.37101e7	−	1.62311e8i	−0.284022	−	0.491941i	−0.972372	+	0.233438i	$0.925002\pi$
$692$		0			0
$693$	3.42361e8	−	1.35857e8i	1.02869	−	0.408208i
$694$		0			0
$695$	−2.25119e8	+	1.29973e8i	−0.670591	+	0.387166i
$696$		0			0
$697$	9.00959e6	−	1.56051e7i	0.0266077	−	0.0460858i
$698$		0			0
$699$	9.95055e7	+	2.05634e8i	0.291350	+	0.602092i
$700$		0			0
$701$			5.20746e8i			1.51172i	0.654733	+	0.755860i	$0.272781\pi$
$701$			5.20746e8i			1.51172i	−0.654733	+	0.755860i	$0.727219\pi$
$702$		0			0
$703$	6.01696e7			0.173185
$704$		0			0
$705$	1.18485e7	−	5.73344e6i	0.0338139	−	0.0163624i
$706$		0			0
$707$	−2.25401e8	−	1.30135e8i	−0.637819	−	0.368245i
$708$		0			0
$709$	7.76030e7	+	1.34412e8i	0.217741	+	0.377138i	0.954117	−	0.299434i	$-0.0967979\pi$
$709$	7.76030e7	+	1.34412e8i	0.217741	+	0.377138i	−0.736376	+	0.676572i	$0.763465\pi$
$710$		0			0
$711$	6.39796e8	+	9.39706e7i	1.78005	+	0.261447i
$712$		0			0
$713$	1.17708e8	−	6.79587e7i	0.324741	−	0.187489i
$714$		0			0
$715$	−1.12265e8	+	1.94449e8i	−0.307134	+	0.531971i
$716$		0			0
$717$	2.59826e8	+	1.89793e7i	0.704896	+	0.0514899i
$718$		0			0
$719$			6.10488e7i			0.164244i	0.996622	+	0.0821221i	$0.0261698\pi$
$719$			6.10488e7i			0.164244i	−0.996622	+	0.0821221i	$0.973830\pi$
$720$		0			0
$721$	5.47497e8			1.46075
$722$		0			0
$723$	−5.72274e7	−	3.88593e7i	−0.151422	−	0.102821i
$724$		0			0
$725$	−3.10016e8	−	1.78988e8i	−0.813522	−	0.469687i
$726$		0			0
$727$	1.47057e8	+	2.54710e8i	0.382721	+	0.662892i	0.991450	−	0.130486i	$-0.0416538\pi$
$727$	1.47057e8	+	2.54710e8i	0.382721	+	0.662892i	−0.608729	+	0.793378i	$0.708321\pi$
$728$		0			0
$729$	−3.50931e8	−	1.64141e8i	−0.905814	−	0.423676i
$730$		0			0
$731$	2.25239e8	−	1.30042e8i	0.576623	−	0.332914i
$732$		0			0
$733$	−2.60891e8	+	4.51877e8i	−0.662441	+	1.14738i	0.317531	+	0.948248i	$0.397146\pi$
$733$	−2.60891e8	+	4.51877e8i	−0.662441	+	1.14738i	−0.979972	+	0.199134i	$0.936187\pi$
$734$		0			0
$735$	−2.84809e8	+	4.19433e8i	−0.717285	+	1.05633i
$736$		0			0
$737$		−	2.29086e8i		−	0.572264i
$738$		0			0
$739$	−7.70011e8			−1.90793			−0.953967	−	0.299910i	$-0.903043\pi$
$739$	−7.70011e8			−1.90793			−0.953967	+	0.299910i	$0.903043\pi$
$740$		0			0
$741$	9.23997e6	−	1.26495e8i	0.0227099	−	0.310898i
$742$		0			0
$743$	8.00801e7	+	4.62343e7i	0.195235	+	0.112719i	0.594431	−	0.804147i	$-0.297377\pi$
$743$	8.00801e7	+	4.62343e7i	0.195235	+	0.112719i	−0.399196	+	0.916866i	$0.630711\pi$
$744$		0			0
$745$	−5.24205e7	−	9.07950e7i	−0.126775	−	0.219580i
$746$		0			0
$747$	6.02124e7	−	4.09954e8i	0.144452	−	0.983498i
$748$		0			0
$749$	−8.78537e8	+	5.07223e8i	−2.09081	+	1.20713i
$750$		0			0
$751$	3.21456e8	−	5.56778e8i	0.758930	−	1.31451i	−0.184466	−	0.982839i	$-0.559056\pi$
$751$	3.21456e8	−	5.56778e8i	0.758930	−	1.31451i	0.943397	−	0.331667i	$-0.107611\pi$
$752$		0			0
$753$	7.70803e7	+	1.59291e8i	0.180534	+	0.373083i
$754$		0			0
$755$		−	1.26602e8i		−	0.294172i
$756$		0			0
$757$	−4.03164e8			−0.929381			−0.464691	−	0.885473i	$-0.653834\pi$
$757$	−4.03164e8			−0.929381			−0.464691	+	0.885473i	$0.653834\pi$
$758$		0			0
$759$	1.74681e8	−	8.45276e7i	0.399503	−	0.193318i
$760$		0			0
$761$	5.11804e8	+	2.95490e8i	1.16131	+	0.670485i	0.951618	−	0.307282i	$-0.0994196\pi$
$761$	5.11804e8	+	2.95490e8i	1.16131	+	0.670485i	0.209695	+	0.977767i	$0.432753\pi$
$762$		0			0
$763$	−2.86009e8	−	4.95382e8i	−0.643881	−	1.11523i
$764$		0			0
$765$	4.46186e7	+	1.12439e8i	0.0996625	+	0.251150i
$766$		0			0
$767$	6.27515e8	−	3.62296e8i	1.39071	−	0.802930i
$768$		0			0
$769$	−4.79612e7	+	8.30713e7i	−0.105466	+	0.182672i	−0.913928	−	0.405876i	$-0.866967\pi$
$769$	−4.79612e7	+	8.30713e7i	−0.105466	+	0.182672i	0.808463	+	0.588547i	$0.200300\pi$
$770$		0			0
$771$	−5.16511e8	−	3.77291e7i	−1.12698	−	0.0823216i
$772$		0			0
$773$		−	3.56838e8i		−	0.772562i	−0.922381	−	0.386281i	$-0.873760\pi$
$773$		−	3.56838e8i		−	0.772562i	0.922381	−	0.386281i	$-0.126240\pi$
$774$		0			0
$775$	1.31373e8			0.282229
$776$		0			0
$777$	−4.80105e8	−	3.26007e8i	−1.02347	−	0.694967i
$778$		0			0
$779$	−1.33083e7	−	7.68356e6i	−0.0281521	−	0.0162536i
$780$		0			0
$781$	5.76739e7	+	9.98942e7i	0.121067	+	0.209694i
$782$		0			0
$783$	−2.67139e8	−	8.48984e8i	−0.556483	−	1.76854i
$784$		0			0
$785$	1.12675e8	−	6.50531e7i	0.232927	−	0.134480i
$786$		0			0
$787$	2.17872e8	−	3.77366e8i	0.446969	−	0.774174i	−0.551218	−	0.834362i	$-0.685837\pi$
$787$	2.17872e8	−	3.77366e8i	0.446969	−	0.774174i	0.998187	+	0.0601877i	$0.0191699\pi$
$788$		0			0
$789$	3.32945e8	−	4.90323e8i	0.677863	−	0.998277i
$790$		0			0
$791$		−	5.91863e8i		−	1.19589i
$792$		0			0
$793$	1.06308e9			2.13180
$794$		0			0
$795$	−4.59857e7	+	6.29543e8i	−0.0915212	+	1.25292i
$796$		0			0
$797$	−1.33162e8	−	7.68814e7i	−0.263031	−	0.151861i	0.362685	−	0.931912i	$-0.381860\pi$
$797$	−1.33162e8	−	7.68814e7i	−0.263031	−	0.151861i	−0.625716	+	0.780051i	$0.715193\pi$
$798$		0			0
$799$	5.24736e6	+	9.08869e6i	0.0102873	+	0.0178181i
$800$		0			0
$801$	4.79021e8	+	3.79064e8i	0.932089	+	0.737590i
$802$		0			0
$803$	1.21192e8	−	6.99700e7i	0.234059	−	0.135134i
$804$		0			0
$805$	−2.07023e8	+	3.58575e8i	−0.396855	+	0.687372i
$806$		0			0
$807$	−3.46506e8	−	7.16074e8i	−0.659311	−	1.36250i
$808$		0			0
$809$			2.51654e8i			0.475289i	0.971352	+	0.237644i	$0.0763753\pi$
$809$			2.51654e8i			0.475289i	−0.971352	+	0.237644i	$0.923625\pi$
$810$		0			0
$811$	3.75903e8			0.704714			0.352357	−	0.935866i	$-0.385380\pi$
$811$	3.75903e8			0.704714			0.352357	+	0.935866i	$0.385380\pi$
$812$		0			0
$813$	2.48450e8	−	1.20224e8i	0.462347	−	0.223728i
$814$		0			0
$815$	−2.19512e8	−	1.26736e8i	−0.405496	−	0.234113i
$816$		0			0
$817$	−1.10902e8	−	1.92089e8i	−0.203364	−	0.352237i
$818$		0			0
$819$	−7.59095e8	+	9.59265e8i	−1.38180	+	1.74617i
$820$		0			0
$821$	1.59605e8	−	9.21482e7i	0.288415	−	0.166517i	−0.348812	−	0.937193i	$-0.613415\pi$
$821$	1.59605e8	−	9.21482e7i	0.288415	−	0.166517i	0.637227	+	0.770676i	$0.280081\pi$
$822$		0			0
$823$	4.00649e7	−	6.93945e7i	0.0718729	−	0.124487i	−0.827849	−	0.560951i	$-0.810436\pi$
$823$	4.00649e7	−	6.93945e7i	0.0718729	−	0.124487i	0.899722	+	0.436463i	$0.143769\pi$
$824$		0			0
$825$	1.87071e8	+	1.36648e7i	0.333154	+	0.0243356i
$826$		0			0
$827$		−	2.59013e8i		−	0.457937i	−0.973434	−	0.228968i	$-0.926465\pi$
$827$		−	2.59013e8i		−	0.457937i	0.973434	−	0.228968i	$-0.0735352\pi$
$828$		0			0
$829$	9.97649e7			0.175111			0.0875556	−	0.996160i	$-0.472094\pi$
$829$	9.97649e7			0.175111			0.0875556	+	0.996160i	$0.472094\pi$
$830$		0			0
$831$	8.71792e7	+	5.91976e7i	0.151918	+	0.103158i
$832$		0			0
$833$	−3.50070e8	−	2.02113e8i	−0.605647	−	0.349670i
$834$		0			0
$835$	−2.21165e8	−	3.83069e8i	−0.379890	−	0.657988i
$836$		0			0
$837$	2.40687e8	+	2.20807e8i	0.410464	+	0.376562i
$838$		0			0
$839$	−5.71895e8	+	3.30183e8i	−0.968345	+	0.559074i	−0.898731	−	0.438500i	$-0.855510\pi$
$839$	−5.71895e8	+	3.30183e8i	−0.968345	+	0.559074i	−0.0696137	+	0.997574i	$0.522177\pi$
$840$		0			0
$841$	7.24911e8	−	1.25558e9i	1.21870	−	2.11085i
$842$		0			0
$843$	3.87189e8	−	5.70206e8i	0.646309	−	0.951808i
$844$		0			0
$845$		−	3.21919e8i		−	0.533552i
$846$		0			0
$847$	5.76661e8			0.949009
$848$		0			0
$849$	−8.49304e7	+	1.16269e9i	−0.138784	+	1.89995i
$850$		0			0
$851$	−2.64787e8	−	1.52875e8i	−0.429644	−	0.248055i
$852$		0			0
$853$	−8.38761e7	−	1.45278e8i	−0.135142	−	0.234073i	0.790510	−	0.612450i	$-0.209816\pi$
$853$	−8.38761e7	−	1.45278e8i	−0.135142	−	0.234073i	−0.925652	+	0.378376i	$0.876482\pi$
$854$		0			0
$855$	9.58904e7	−	3.80516e7i	0.153418	−	0.0608800i
$856$		0			0
$857$	−4.64968e8	+	2.68449e8i	−0.738721	+	0.426501i	−0.821604	−	0.570059i	$-0.806920\pi$
$857$	−4.64968e8	+	2.68449e8i	−0.738721	+	0.426501i	0.0828833	+	0.996559i	$0.473587\pi$
$858$		0			0
$859$	−8.13119e7	+	1.40836e8i	−0.128285	+	0.222196i	−0.923012	−	0.384771i	$-0.874280\pi$
$859$	−8.13119e7	+	1.40836e8i	−0.128285	+	0.222196i	0.794727	+	0.606966i	$0.207614\pi$
$860$		0			0
$861$	6.45591e7	+	1.33415e8i	0.101146	+	0.209024i
$862$		0			0
$863$			8.63859e8i			1.34403i	0.740536	+	0.672017i	$0.234572\pi$
$863$			8.63859e8i			1.34403i	−0.740536	+	0.672017i	$0.765428\pi$
$864$		0			0
$865$	−8.50640e8			−1.31431
$866$		0			0
$867$	4.99823e8	−	2.41862e8i	0.766935	−	0.371117i
$868$		0			0
$869$	−6.74114e8	−	3.89200e8i	−1.02724	−	0.593080i
$870$		0			0
$871$	3.80414e8	+	6.58897e8i	0.575708	+	0.997156i
$872$		0			0
$873$	−6.20332e8	−	9.11119e7i	−0.932355	−	0.136941i
$874$		0			0
$875$	−1.03063e9	+	5.95037e8i	−1.53844	+	0.888218i
$876$		0			0
$877$	−5.41609e7	+	9.38095e7i	−0.0802948	+	0.139075i	−0.903377	−	0.428848i	$-0.858920\pi$
$877$	−5.41609e7	+	9.38095e7i	−0.0802948	+	0.139075i	0.823082	+	0.567923i	$0.192253\pi$
$878$		0			0
$879$	1.10208e9	+	8.05030e7i	1.62274	+	0.118535i
$880$		0			0
$881$			4.63041e8i			0.677160i	0.940938	+	0.338580i	$0.109947\pi$
$881$			4.63041e8i			0.677160i	−0.940938	+	0.338580i	$0.890053\pi$
$882$		0			0
$883$	−1.17767e8			−0.171057			−0.0855285	−	0.996336i	$-0.527258\pi$
$883$	−1.17767e8			−0.171057			−0.0855285	+	0.996336i	$0.527258\pi$
$884$		0			0
$885$	4.87592e8	+	3.31092e8i	0.703440	+	0.477659i
$886$		0			0
$887$	3.67818e8	+	2.12360e8i	0.527063	+	0.304300i	0.739820	−	0.672805i	$-0.234911\pi$
$887$	3.67818e8	+	2.12360e8i	0.527063	+	0.304300i	−0.212757	+	0.977105i	$0.568244\pi$
$888$		0			0
$889$	−4.75586e8	−	8.23739e8i	−0.676898	−	1.17242i
$890$		0			0
$891$	3.19763e8	+	3.39458e8i	0.452058	+	0.479902i
$892$		0			0
$893$	7.75101e6	−	4.47505e6i	0.0108844	−	0.00628410i
$894$		0			0
$895$	1.61632e8	−	2.79955e8i	0.225455	−	0.390499i
$896$		0			0
$897$	−3.62053e8	+	5.33188e8i	−0.501643	+	0.738760i
$898$		0			0
$899$			7.50362e8i			1.03274i
$900$		0			0
$901$	−5.03273e8			−0.688065
$902$		0			0
$903$	−1.55851e8	+	2.13360e9i	−0.211664	+	2.89767i
$904$		0			0
$905$	5.93539e8	+	3.42680e8i	0.800762	+	0.462320i
$906$		0			0
$907$	1.24860e8	+	2.16264e8i	0.167341	+	0.289842i	0.937484	−	0.348028i	$-0.113149\pi$
$907$	1.24860e8	+	2.16264e8i	0.167341	+	0.289842i	−0.770143	+	0.637871i	$0.779815\pi$
$908$		0			0
$909$	4.78864e7	−	3.26033e8i	0.0637560	−	0.434080i
$910$		0			0
$911$	−3.40817e8	+	1.96771e8i	−0.450781	+	0.260259i	−0.708160	−	0.706052i	$-0.750475\pi$
$911$	−3.40817e8	+	1.96771e8i	−0.450781	+	0.260259i	0.257379	+	0.966311i	$0.417141\pi$
$912$		0			0
$913$	−2.49383e8	+	4.31944e8i	−0.327683	+	0.567564i
$914$		0			0
$915$	3.76647e8	+	7.78362e8i	0.491667	+	1.01606i
$916$		0			0
$917$		−	1.16371e9i		−	1.50916i
$918$		0			0
$919$	6.11123e8			0.787376			0.393688	−	0.919244i	$-0.371199\pi$
$919$	6.11123e8			0.787376			0.393688	+	0.919244i	$0.371199\pi$
$920$		0			0
$921$	2.76557e8	−	1.33825e8i	0.354002	−	0.171301i
$922$		0			0
$923$	−3.31763e8	−	1.91543e8i	−0.421913	−	0.243591i
$924$		0			0
$925$	−1.47764e8	−	2.55934e8i	−0.186699	−	0.323373i
$926$		0			0
$927$	2.55679e8	+	6.44314e8i	0.320964	+	0.808832i
$928$		0			0
$929$	2.57534e8	−	1.48687e8i	0.321208	−	0.185450i	−0.330723	−	0.943728i	$-0.607292\pi$
$929$	2.57534e8	−	1.48687e8i	0.321208	−	0.185450i	0.651931	+	0.758278i	$0.273959\pi$
$930$		0			0
$931$	−1.72366e8	+	2.98546e8i	−0.213600	+	0.369966i
$932$		0			0
$933$	8.52064e8	+	6.22400e7i	1.04913	+	0.0766346i
$934$		0			0
$935$		−	1.45613e8i		−	0.178141i
$936$		0			0
$937$	5.69735e8			0.692555			0.346277	−	0.938132i	$-0.387446\pi$
$937$	5.69735e8			0.692555			0.346277	+	0.938132i	$0.387446\pi$
$938$		0			0
$939$	−1.05271e9	−	7.14822e8i	−1.27148	−	0.863378i
$940$		0			0
$941$	−9.05792e8	−	5.22959e8i	−1.08708	−	0.627623i	−0.154279	−	0.988027i	$-0.549306\pi$
$941$	−9.05792e8	−	5.22959e8i	−1.08708	−	0.627623i	−0.932796	+	0.360404i	$0.882639\pi$
$942$		0			0
$943$	3.90438e7	+	6.76259e7i	0.0465604	+	0.0806450i
$944$		0			0
$945$	−9.71298e8	−	2.15927e8i	−1.15095	−	0.255865i
$946$		0			0
$947$	−5.90999e8	+	3.41213e8i	−0.695884	+	0.401769i	−0.805812	−	0.592171i	$-0.798271\pi$
$947$	−5.90999e8	+	3.41213e8i	−0.695884	+	0.401769i	0.109929	+	0.993939i	$0.464938\pi$
$948$		0			0
$949$	−2.32380e8	+	4.02495e8i	−0.271895	+	0.470936i
$950$		0			0
$951$	2.09362e8	−	3.08324e8i	0.243420	−	0.358481i
$952$		0			0
$953$		−	5.91815e8i		−	0.683765i	−0.939743	−	0.341883i	$-0.888935\pi$
$953$		−	5.91815e8i		−	0.683765i	0.939743	−	0.341883i	$-0.111065\pi$
$954$		0			0
$955$	1.07488e9			1.23410
$956$		0			0
$957$	−7.80492e7	+	1.06849e9i	−0.0890498	+	1.21909i
$958$		0			0
$959$	7.22815e8	+	4.17317e8i	0.819542	+	0.473163i
$960$		0			0
$961$	3.06064e8	+	5.30119e8i	0.344860	+	0.597315i
$962$		0			0
$963$	−1.00719e9	−	7.97022e8i	−1.12780	−	0.892466i
$964$		0			0
$965$	5.81518e8	−	3.35740e8i	0.647115	−	0.373612i
$966$		0			0
$967$	2.97079e8	−	5.14556e8i	0.328543	−	0.569054i	−0.653680	−	0.756771i	$-0.726776\pi$
$967$	2.97079e8	−	5.14556e8i	0.328543	−	0.569054i	0.982223	+	0.187718i	$0.0601090\pi$
$968$		0			0
$969$	3.58278e7	+	7.40402e7i	0.0393776	+	0.0813760i
$970$		0			0
$971$		−	2.20535e8i		−	0.240891i	−0.992720	−	0.120445i	$-0.961568\pi$
$971$		−	2.20535e8i		−	0.240891i	0.992720	−	0.120445i	$-0.0384322\pi$
$972$		0			0
$973$	1.70474e9			1.85063
$974$		0			0
$975$	−5.60744e8	+	2.71342e8i	−0.604994	+	0.292754i
$976$		0			0
$977$	−1.24747e9	−	7.20227e8i	−1.33766	−	0.772299i	−0.351201	−	0.936300i	$-0.614227\pi$
$977$	−1.24747e9	−	7.20227e8i	−1.33766	−	0.772299i	−0.986460	+	0.164001i	$0.947560\pi$
$978$		0			0
$979$	−3.67654e8	−	6.36795e8i	−0.391824	−	0.678659i
$980$		0			0
$981$	4.49418e8	−	5.67927e8i	0.476040	−	0.601569i
$982$		0			0
$983$	4.41757e8	−	2.55048e8i	0.465074	−	0.268511i	−0.249101	−	0.968477i	$-0.580135\pi$
$983$	4.41757e8	−	2.55048e8i	0.465074	−	0.268511i	0.714176	+	0.699967i	$0.246802\pi$
$984$		0			0
$985$	−1.66034e8	+	2.87579e8i	−0.173735	+	0.300918i
$986$		0			0
$987$	−8.60933e7	−	6.28879e6i	−0.0895402	−	0.00654057i
$988$		0			0
$989$			1.12710e9i			1.16512i
$990$		0			0
$991$	4.62284e8			0.474993			0.237497	−	0.971388i	$-0.423673\pi$
$991$	4.62284e8			0.474993			0.237497	+	0.971388i	$0.423673\pi$
$992$		0			0
$993$	1.10052e8	+	7.47292e7i	0.112396	+	0.0763207i
$994$		0			0
$995$	5.06508e8	+	2.92433e8i	0.514182	+	0.296863i
$996$		0			0
$997$	−1.01379e8	−	1.75594e8i	−0.102297	−	0.177184i	0.810334	−	0.585969i	$-0.199286\pi$
$997$	−1.01379e8	−	1.75594e8i	−0.102297	−	0.177184i	−0.912631	+	0.408785i	$0.865953\pi$
$998$		0			0
$999$	1.59450e8	−	7.17250e8i	0.159929	−	0.719406i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	72.7.m.a.41.16	✓	36
3.2	odd	2		216.7.m.a.17.6		36
4.3	odd	2		144.7.q.d.113.3		36
9.2	odd	6	inner	72.7.m.a.65.16	yes	36
9.4	even	3		648.7.e.c.161.13		36
9.5	odd	6		648.7.e.c.161.24		36
9.7	even	3		216.7.m.a.89.6		36
12.11	even	2		432.7.q.d.17.6		36
36.7	odd	6		432.7.q.d.305.6		36
36.11	even	6		144.7.q.d.65.3		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
72.7.m.a.41.16	✓	36	1.1	even	1	trivial
72.7.m.a.65.16	yes	36	9.2	odd	6	inner
144.7.q.d.65.3		36	36.11	even	6
144.7.q.d.113.3		36	4.3	odd	2
216.7.m.a.17.6		36	3.2	odd	2
216.7.m.a.89.6		36	9.7	even	3
432.7.q.d.17.6		36	12.11	even	2
432.7.q.d.305.6		36	36.7	odd	6
648.7.e.c.161.13		36	9.4	even	3
648.7.e.c.161.24		36	9.5	odd	6

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)

\(f(q)\)	\(=\)	\(q+(24.3041 - 11.7607i) q^{3} +(76.0344 + 43.8985i) q^{5} +(-287.890 - 498.640i) q^{7} +(452.374 - 571.663i) q^{9} +O(q^{10})\)	\(q+(24.3041 - 11.7607i) q^{3} +(76.0344 + 43.8985i) q^{5} +(-287.890 - 498.640i) q^{7} +(452.374 - 571.663i) q^{9} +(-759.950 + 438.757i) q^{11} +(1457.18 - 2523.90i) q^{13} +(2364.22 + 172.697i) q^{15} +1890.02i q^{17} +1611.84 q^{19} +(-12861.2 - 8733.21i) q^{21} +(-7093.22 - 4095.27i) q^{23} +(-3958.35 - 6856.06i) q^{25} +(4271.40 - 19213.9i) q^{27} +(39159.7 - 22608.9i) q^{29} +(-8297.21 + 14371.2i) q^{31} +(-13309.8 + 19601.1i) q^{33} -50551.7i q^{35} +37329.6 q^{37} +(5732.54 - 78478.4i) q^{39} +(-8256.57 - 4766.93i) q^{41} +(-68804.6 - 119173. i) q^{43} +(59491.1 - 23607.5i) q^{45} +(4808.78 - 2776.35i) q^{47} +(-106937. + 185220. i) q^{49} +(22227.8 + 45935.1i) q^{51} +266280. i q^{53} -77043.1 q^{55} +(39174.4 - 18956.3i) q^{57} +(215319. + 124314. i) q^{59} +(182387. + 315903. i) q^{61} +(-415288. - 60995.9i) q^{63} +(221591. - 127936. i) q^{65} +(-130531. + 226087. i) q^{67} +(-220557. - 16110.9i) q^{69} -131448. i q^{71} -159473. q^{73} +(-176836. - 120077. i) q^{75} +(437564. + 252628. i) q^{77} +(443525. + 768208. i) q^{79} +(-122156. - 517211. i) q^{81} +(492235. - 284192. i) q^{83} +(-82968.9 + 143706. i) q^{85} +(685845. - 1.01003e6i) q^{87} +837943. i q^{89} -1.67803e6 q^{91} +(-32641.3 + 446859. i) q^{93} +(122556. + 70757.5i) q^{95} +(-430032. - 744838. i) q^{97} +(-92960.4 + 632917. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 10 q^{3} + 74 q^{9}+O(q^{10}) \) 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

Properties

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