LMFDB - Embedded newform 144.6.i.b.97.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [144,6,Mod(49,144)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(144, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 2]))

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("144.49");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 144 = 2^{4} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	144.i (of order $3$, degree $2$, not 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:	$23.0952700531$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.47347183152.3
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} + 118x^{4} - 231x^{3} + 3700x^{2} - 3585x + 32331 $ x^6 - 3x^5 + 118x^4 - 231x^3 + 3700x^2 - 3585*x + 32331
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{4} $
Twist minimal:	no (minimal twist has level 18)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			97.2
Root			$0.500000 + 8.40123i$ of defining polynomial
Character	$\chi$	$=$	144.97
Dual form			144.6.i.b.49.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.43381 + 15.3973i) q^{3} +(-20.8014 - 36.0292i) q^{5} +(-101.661 + 176.082i) q^{7} +(-231.153 + 74.9483i) q^{9} +O(q^{10})$	\(q+(2.43381 + 15.3973i) q^{3} +(-20.8014 - 36.0292i) q^{5} +(-101.661 + 176.082i) q^{7} +(-231.153 + 74.9483i) q^{9} +(235.168 - 407.323i) q^{11} +(-241.506 - 418.300i) q^{13} +(504.125 - 407.974i) q^{15} +1259.86 q^{17} -1978.94 q^{19} +(-2958.60 - 1136.75i) q^{21} +(239.119 + 414.166i) q^{23} +(697.100 - 1207.41i) q^{25} +(-1716.58 - 3376.72i) q^{27} +(580.249 - 1005.02i) q^{29} +(-1186.50 - 2055.07i) q^{31} +(6844.02 + 2629.60i) q^{33} +8458.76 q^{35} +8185.10 q^{37} +(5852.91 - 4736.60i) q^{39} +(-8758.87 - 15170.8i) q^{41} +(11435.0 - 19806.1i) q^{43} +(7508.64 + 6769.22i) q^{45} +(-8685.43 + 15043.6i) q^{47} +(-12266.3 - 21245.9i) q^{49} +(3066.26 + 19398.4i) q^{51} -5390.58 q^{53} -19567.3 q^{55} +(-4816.38 - 30470.4i) q^{57} +(-22281.8 - 38593.2i) q^{59} +(-2084.17 + 3609.88i) q^{61} +(10302.2 - 48321.1i) q^{63} +(-10047.3 + 17402.5i) q^{65} +(1228.46 + 2127.76i) q^{67} +(-5795.07 + 4689.79i) q^{69} -2184.37 q^{71} +3037.34 q^{73} +(20287.5 + 7794.83i) q^{75} +(47814.7 + 82817.5i) q^{77} +(-25266.2 + 43762.3i) q^{79} +(47814.5 - 34649.1i) q^{81} +(-25913.9 + 44884.2i) q^{83} +(-26206.9 - 45391.7i) q^{85} +(16886.8 + 6488.23i) q^{87} -20154.7 q^{89} +98206.5 q^{91} +(28754.8 - 23270.5i) q^{93} +(41164.9 + 71299.6i) q^{95} +(-40214.4 + 69653.3i) q^{97} +(-23831.7 + 111779. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 9 q^{3} - 54 q^{5} + 132 q^{7} - 177 q^{9}+O(q^{10}) $ 6 * q - 9 * q^3 - 54 * q^5 + 132 * q^7 - 177 * q^9	$ 6 q - 9 q^{3} - 54 q^{5} + 132 q^{7} - 177 q^{9} + 315 q^{11} - 744 q^{13} - 2286 q^{15} + 2898 q^{17} - 2262 q^{19} - 11076 q^{21} + 3168 q^{23} - 2883 q^{25} - 18144 q^{27} - 5148 q^{29} + 8610 q^{31} + 17469 q^{33} - 2700 q^{35} + 39936 q^{37} + 49026 q^{39} + 5049 q^{41} + 31389 q^{43} + 2538 q^{45} - 12924 q^{47} - 52857 q^{49} - 36837 q^{51} - 96048 q^{53} - 126252 q^{55} - 17469 q^{57} - 62955 q^{59} - 75966 q^{61} - 49578 q^{63} + 108702 q^{65} + 32991 q^{67} - 29250 q^{69} + 129672 q^{71} - 8466 q^{73} + 105483 q^{75} + 88740 q^{77} - 89202 q^{79} + 123435 q^{81} - 32634 q^{83} + 71388 q^{85} + 151524 q^{87} + 66132 q^{89} + 301836 q^{91} + 57678 q^{93} + 82944 q^{95} + 46245 q^{97} - 282168 q^{99}+O(q^{100}) $ 6 * q - 9 * q^3 - 54 * q^5 + 132 * q^7 - 177 * q^9 + 315 * q^11 - 744 * q^13 - 2286 * q^15 + 2898 * q^17 - 2262 * q^19 - 11076 * q^21 + 3168 * q^23 - 2883 * q^25 - 18144 * q^27 - 5148 * q^29 + 8610 * q^31 + 17469 * q^33 - 2700 * q^35 + 39936 * q^37 + 49026 * q^39 + 5049 * q^41 + 31389 * q^43 + 2538 * q^45 - 12924 * q^47 - 52857 * q^49 - 36837 * q^51 - 96048 * q^53 - 126252 * q^55 - 17469 * q^57 - 62955 * q^59 - 75966 * q^61 - 49578 * q^63 + 108702 * q^65 + 32991 * q^67 - 29250 * q^69 + 129672 * q^71 - 8466 * q^73 + 105483 * q^75 + 88740 * q^77 - 89202 * q^79 + 123435 * q^81 - 32634 * q^83 + 71388 * q^85 + 151524 * q^87 + 66132 * q^89 + 301836 * q^91 + 57678 * q^93 + 82944 * q^95 + 46245 * q^97 - 282168 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/144\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	2.43381	+	15.3973i	0.156129	+	0.987737i
$3$	2.43381	+	15.3973i	0.156129	+	0.987737i
$4$		0			0
$5$	−20.8014	−	36.0292i	−0.372108	−	0.644509i	0.617782	−	0.786349i	$-0.288031\pi$
$5$	−20.8014	−	36.0292i	−0.372108	−	0.644509i	−0.989890	+	0.141840i	$0.954698\pi$
$6$		0			0
$7$	−101.661	+	176.082i	−0.784166	+	1.35822i	0.145330	+	0.989383i	$0.453576\pi$
$7$	−101.661	+	176.082i	−0.784166	+	1.35822i	−0.929496	+	0.368832i	$0.879758\pi$
$8$		0			0
$9$	−231.153	+	74.9483i	−0.951247	+	0.308429i
$10$		0			0
$11$	235.168	−	407.323i	0.585998	−	1.01498i	−0.408752	−	0.912646i	$-0.634036\pi$
$11$	235.168	−	407.323i	0.585998	−	1.01498i	0.994750	−	0.102333i	$-0.0326308\pi$
$12$		0			0
$13$	−241.506	−	418.300i	−0.396341	−	0.686482i	0.596931	−	0.802293i	$-0.296387\pi$
$13$	−241.506	−	418.300i	−0.396341	−	0.686482i	−0.993271	+	0.115811i	$0.963053\pi$
$14$		0			0
$15$	504.125	−	407.974i	0.578508	−	0.468171i
$16$		0			0
$17$	1259.86			1.05730			0.528652	−	0.848839i	$-0.322698\pi$
$17$	1259.86			1.05730			0.528652	+	0.848839i	$0.322698\pi$
$18$		0			0
$19$	−1978.94			−1.25762			−0.628810	−	0.777559i	$-0.716458\pi$
$19$	−1978.94			−1.25762			−0.628810	+	0.777559i	$0.716458\pi$
$20$		0			0
$21$	−2958.60	−	1136.75i	−1.46399	−	0.562492i
$22$		0			0
$23$	239.119	+	414.166i	0.0942529	+	0.163251i	0.909297	−	0.416149i	$-0.136620\pi$
$23$	239.119	+	414.166i	0.0942529	+	0.163251i	−0.815044	+	0.579400i	$0.803287\pi$
$24$		0			0
$25$	697.100	−	1207.41i	0.223072	−	0.386372i
$26$		0			0
$27$	−1716.58	−	3376.72i	−0.453164	−	0.891427i
$28$		0			0
$29$	580.249	−	1005.02i	0.128121	−	0.221912i	−0.794828	−	0.606835i	$-0.792439\pi$
$29$	580.249	−	1005.02i	0.128121	−	0.221912i	0.922949	+	0.384923i	$0.125772\pi$
$30$		0			0
$31$	−1186.50	−	2055.07i	−0.221749	−	0.384081i	0.733590	−	0.679592i	$-0.237843\pi$
$31$	−1186.50	−	2055.07i	−0.221749	−	0.384081i	−0.955339	+	0.295511i	$0.904510\pi$
$32$		0			0
$33$	6844.02	+	2629.60i	1.09402	+	0.420344i
$34$		0			0
$35$	8458.76			1.16718
$36$		0			0
$37$	8185.10			0.982923			0.491462	−	0.870899i	$-0.336463\pi$
$37$	8185.10			0.982923			0.491462	+	0.870899i	$0.336463\pi$
$38$		0			0
$39$	5852.91	−	4736.60i	0.616183	−	0.498660i
$40$		0			0
$41$	−8758.87	−	15170.8i	−0.813745	−	1.40945i	−0.910226	−	0.414113i	$-0.864092\pi$
$41$	−8758.87	−	15170.8i	−0.813745	−	1.40945i	0.0964809	−	0.995335i	$-0.469241\pi$
$42$		0			0
$43$	11435.0	−	19806.1i	0.943119	−	1.63353i	0.183644	−	0.982993i	$-0.441211\pi$
$43$	11435.0	−	19806.1i	0.943119	−	1.63353i	0.759475	−	0.650537i	$-0.225456\pi$
$44$		0			0
$45$	7508.64	+	6769.22i	0.552752	+	0.498319i
$46$		0			0
$47$	−8685.43	+	15043.6i	−0.573518	+	0.993362i	0.422683	+	0.906277i	$0.361088\pi$
$47$	−8685.43	+	15043.6i	−0.573518	+	0.993362i	−0.996201	+	0.0870843i	$0.972245\pi$
$48$		0			0
$49$	−12266.3	−	21245.9i	−0.729833	−	1.26411i
$50$		0			0
$51$	3066.26	+	19398.4i	0.165076	+	1.04434i
$52$		0			0
$53$	−5390.58			−0.263600			−0.131800	−	0.991276i	$-0.542076\pi$
$53$	−5390.58			−0.263600			−0.131800	+	0.991276i	$0.542076\pi$
$54$		0			0
$55$	−19567.3			−0.872218
$56$		0			0
$57$	−4816.38	−	30470.4i	−0.196351	−	1.24220i
$58$		0			0
$59$	−22281.8	−	38593.2i	−0.833335	−	1.44338i	−0.895379	−	0.445306i	$-0.853095\pi$
$59$	−22281.8	−	38593.2i	−0.833335	−	1.44338i	0.0620431	−	0.998073i	$-0.480238\pi$
$60$		0			0
$61$	−2084.17	+	3609.88i	−0.0717147	+	0.124213i	−0.899653	−	0.436606i	$-0.856180\pi$
$61$	−2084.17	+	3609.88i	−0.0717147	+	0.124213i	0.827938	+	0.560819i	$0.189514\pi$
$62$		0			0
$63$	10302.2	−	48321.1i	0.327023	−	1.53386i
$64$		0			0
$65$	−10047.3	+	17402.5i	−0.294963	+	0.510891i
$66$		0			0
$67$	1228.46	+	2127.76i	0.0334330	+	0.0579076i	0.882258	−	0.470767i	$-0.156023\pi$
$67$	1228.46	+	2127.76i	0.0334330	+	0.0579076i	−0.848825	+	0.528674i	$0.822689\pi$
$68$		0			0
$69$	−5795.07	+	4689.79i	−0.146533	+	0.118585i
$70$		0			0
$71$	−2184.37			−0.0514256			−0.0257128	−	0.999669i	$-0.508186\pi$
$71$	−2184.37			−0.0514256			−0.0257128	+	0.999669i	$0.508186\pi$
$72$		0			0
$73$	3037.34			0.0667093			0.0333546	−	0.999444i	$-0.489381\pi$
$73$	3037.34			0.0667093			0.0333546	+	0.999444i	$0.489381\pi$
$74$		0			0
$75$	20287.5	+	7794.83i	0.416462	+	0.160012i
$76$		0			0
$77$	47814.7	+	82817.5i	0.919040	+	1.59182i
$78$		0			0
$79$	−25266.2	+	43762.3i	−0.455482	+	0.788918i	−0.998716	−	0.0506633i	$-0.983866\pi$
$79$	−25266.2	+	43762.3i	−0.455482	+	0.788918i	0.543234	+	0.839582i	$0.317200\pi$
$80$		0			0
$81$	47814.5	−	34649.1i	0.809743	−	0.586785i
$82$		0			0
$83$	−25913.9	+	44884.2i	−0.412893	+	0.715152i	−0.995205	−	0.0978135i	$-0.968815\pi$
$83$	−25913.9	+	44884.2i	−0.412893	+	0.715152i	0.582311	+	0.812966i	$0.302148\pi$
$84$		0			0
$85$	−26206.9	−	45391.7i	−0.393431	−	0.681442i
$86$		0			0
$87$	16886.8	+	6488.23i	0.239194	+	0.0919027i
$88$		0			0
$89$	−20154.7			−0.269713			−0.134857	−	0.990865i	$-0.543057\pi$
$89$	−20154.7			−0.269713			−0.134857	+	0.990865i	$0.543057\pi$
$90$		0			0
$91$	98206.5			1.24319
$92$		0			0
$93$	28754.8	−	23270.5i	0.344749	−	0.278996i
$94$		0			0
$95$	41164.9	+	71299.6i	0.467970	+	0.810547i
$96$		0			0
$97$	−40214.4	+	69653.3i	−0.433962	+	0.751644i	−0.997210	−	0.0746433i	$-0.976218\pi$
$97$	−40214.4	+	69653.3i	−0.433962	+	0.751644i	0.563248	+	0.826288i	$0.309552\pi$
$98$		0			0
$99$	−23831.7	+	111779.i	−0.244380	+	1.14623i
$100$		0			0
$101$	−28450.2	+	49277.2i	−0.277512	+	0.480665i	−0.970766	−	0.240028i	$-0.922843\pi$
$101$	−28450.2	+	49277.2i	−0.277512	+	0.480665i	0.693254	+	0.720694i	$0.256177\pi$
$102$		0			0
$103$	−98505.0	−	170616.i	−0.914882	−	1.58462i	−0.807074	−	0.590451i	$-0.798950\pi$
$103$	−98505.0	−	170616.i	−0.914882	−	1.58462i	−0.107808	−	0.994172i	$-0.534383\pi$
$104$		0			0
$105$	20587.0	+	130242.i	0.182230	+	1.15286i
$106$		0			0
$107$	23482.4			0.198282			0.0991411	−	0.995073i	$-0.468390\pi$
$107$	23482.4			0.198282			0.0991411	+	0.995073i	$0.468390\pi$
$108$		0			0
$109$	−118550.			−0.955727			−0.477863	−	0.878434i	$-0.658589\pi$
$109$	−118550.			−0.955727			−0.477863	+	0.878434i	$0.658589\pi$
$110$		0			0
$111$	19921.0	+	126028.i	0.153463	+	0.970869i
$112$		0			0
$113$	223.401	+	386.942i	0.00164585	+	0.00285069i	0.866847	−	0.498574i	$-0.166143\pi$
$113$	223.401	+	386.942i	0.00164585	+	0.00285069i	−0.865201	+	0.501425i	$0.832809\pi$
$114$		0			0
$115$	9948.04	−	17230.5i	0.0701444	−	0.121494i
$116$		0			0
$117$	87175.6	+	78590.9i	0.588749	+	0.530772i
$118$		0			0
$119$	−128078.	+	221838.i	−0.829102	+	1.43605i
$120$		0			0
$121$	−30082.4	−	52104.3i	−0.186788	−	0.323527i
$122$		0			0
$123$	212272.	−	171786.i	1.26511	−	1.02382i
$124$		0			0
$125$	−188012.			−1.07624
$126$		0			0
$127$	−193803.			−1.06623			−0.533116	−	0.846042i	$-0.678979\pi$
$127$	−193803.			−1.06623			−0.533116	+	0.846042i	$0.678979\pi$
$128$		0			0
$129$	332790.	+	127864.i	1.76075	+	0.676511i
$130$		0			0
$131$	48037.8	+	83203.8i	0.244571	+	0.423609i	0.962011	−	0.273011i	$-0.0880196\pi$
$131$	48037.8	+	83203.8i	0.244571	+	0.423609i	−0.717440	+	0.696620i	$0.754686\pi$
$132$		0			0
$133$	201181.	−	348455.i	0.986183	−	1.70812i
$134$		0			0
$135$	−85953.0	+	132088.i	−0.405907	+	0.623775i
$136$		0			0
$137$	−116089.	+	201071.i	−0.528431	+	0.915269i	0.471020	+	0.882123i	$0.343886\pi$
$137$	−116089.	+	201071.i	−0.528431	+	0.915269i	−0.999451	+	0.0331465i	$0.989447\pi$
$138$		0			0
$139$	−80284.0	−	139056.i	−0.352445	−	0.610453i	0.634232	−	0.773143i	$-0.281316\pi$
$139$	−80284.0	−	139056.i	−0.352445	−	0.610453i	−0.986677	+	0.162689i	$0.947983\pi$
$140$		0			0
$141$	−252770.	−	97118.8i	−1.07072	−	0.411392i
$142$		0			0
$143$	−227177.			−0.929020
$144$		0			0
$145$	−48280.1			−0.190699
$146$		0			0
$147$	297275.	−	240576.i	1.13466	−	0.918247i
$148$		0			0
$149$	139592.	+	241781.i	0.515105	+	0.892189i	0.999846	+	0.0175309i	$0.00558055\pi$
$149$	139592.	+	241781.i	0.515105	+	0.892189i	−0.484741	+	0.874658i	$0.661086\pi$
$150$		0			0
$151$	−14288.8	+	24749.0i	−0.0509981	+	0.0883314i	−0.890398	−	0.455184i	$-0.849574\pi$
$151$	−14288.8	+	24749.0i	−0.0509981	+	0.0883314i	0.839399	+	0.543515i	$0.182907\pi$
$152$		0			0
$153$	−291221.	+	94424.3i	−1.00576	+	0.326103i
$154$		0			0
$155$	−49361.6	+	85496.9i	−0.165029	+	0.285839i
$156$		0			0
$157$	62127.0	+	107607.i	0.201155	+	0.348411i	0.948901	−	0.315574i	$-0.102197\pi$
$157$	62127.0	+	107607.i	0.201155	+	0.348411i	−0.747746	+	0.663985i	$0.768864\pi$
$158$		0			0
$159$	−13119.7	−	83000.3i	−0.0411557	−	0.260367i
$160$		0			0
$161$	−97236.1			−0.295640
$162$		0			0
$163$	−163892.			−0.483159			−0.241579	−	0.970381i	$-0.577665\pi$
$163$	−163892.			−0.483159			−0.241579	+	0.970381i	$0.577665\pi$
$164$		0			0
$165$	−47623.2	−	301284.i	−0.136179	−	0.861521i
$166$		0			0
$167$	−81164.7	−	140581.i	−0.225204	−	0.390065i	0.731177	−	0.682188i	$-0.238972\pi$
$167$	−81164.7	−	140581.i	−0.225204	−	0.390065i	−0.956381	+	0.292123i	$0.905638\pi$
$168$		0			0
$169$	68996.6	−	119506.i	0.185828	−	0.321863i
$170$		0			0
$171$	457439.	−	148318.i	1.19631	−	0.387887i
$172$		0			0
$173$	192179.	−	332863.i	0.488191	−	0.845572i	−0.511716	−	0.859154i	$-0.670990\pi$
$173$	192179.	−	332863.i	0.488191	−	0.845572i	0.999908	+	0.0135821i	$0.00432345\pi$
$174$		0			0
$175$	141735.	+	245493.i	0.349851	+	0.605960i
$176$		0			0
$177$	540001.	−	437008.i	1.29557	−	1.04847i
$178$		0			0
$179$	511991.			1.19434			0.597172	−	0.802113i	$-0.296291\pi$
$179$	511991.			1.19434			0.597172	+	0.802113i	$0.296291\pi$
$180$		0			0
$181$	−285832.			−0.648507			−0.324254	−	0.945970i	$-0.605113\pi$
$181$	−285832.			−0.648507			−0.324254	+	0.945970i	$0.605113\pi$
$182$		0			0
$183$	−60654.9	−	23304.7i	−0.133887	−	0.0514419i
$184$		0			0
$185$	−170262.	−	294902.i	−0.365753	−	0.633503i
$186$		0			0
$187$	296279.	−	513170.i	0.619578	−	1.07314i
$188$		0			0
$189$	769087.	+	41021.1i	1.56611	+	0.0835321i
$190$		0			0
$191$	18626.1	−	32261.4i	0.0369436	−	0.0639882i	−0.846962	−	0.531653i	$-0.821571\pi$
$191$	18626.1	−	32261.4i	0.0369436	−	0.0639882i	0.883906	+	0.467665i	$0.154904\pi$
$192$		0			0
$193$	−289378.	−	501217.i	−0.559206	−	0.968573i	−0.997563	−	0.0697722i	$-0.977773\pi$
$193$	−289378.	−	501217.i	−0.559206	−	0.968573i	0.438357	−	0.898801i	$-0.355561\pi$
$194$		0			0
$195$	−292404.	−	112347.i	−0.550678	−	0.211581i
$196$		0			0
$197$	234386.			0.430294			0.215147	−	0.976582i	$-0.430977\pi$
$197$	234386.			0.430294			0.215147	+	0.976582i	$0.430977\pi$
$198$		0			0
$199$	−200551.			−0.358997			−0.179499	−	0.983758i	$-0.557448\pi$
$199$	−200551.			−0.358997			−0.179499	+	0.983758i	$0.557448\pi$
$200$		0			0
$201$	−29771.9	+	24093.6i	−0.0519776	+	0.0420640i
$202$		0			0
$203$	117977.	+	204342.i	0.200936	+	0.348031i
$204$		0			0
$205$	−364394.	+	631149.i	−0.605601	+	1.04893i
$206$		0			0
$207$	−86314.2	−	77814.3i	−0.140009	−	0.126222i
$208$		0			0
$209$	−465384.	+	806069.i	−0.736963	+	1.27646i
$210$		0			0
$211$	−269826.	−	467352.i	−0.417232	−	0.722667i	0.578428	−	0.815733i	$-0.303666\pi$
$211$	−269826.	−	467352.i	−0.417232	−	0.722667i	−0.995660	+	0.0930667i	$0.970333\pi$
$212$		0			0
$213$	−5316.34	−	33633.3i	−0.00802905	−	0.0507950i
$214$		0			0
$215$	−951461.			−1.40377
$216$		0			0
$217$	482480.			0.695553
$218$		0			0
$219$	7392.32	+	46766.8i	0.0104153	+	0.0658912i
$220$		0			0
$221$	−304263.	−	526999.i	−0.419053	−	0.725821i
$222$		0			0
$223$	442584.	−	766578.i	0.595983	−	1.03227i	−0.397424	−	0.917635i	$-0.630096\pi$
$223$	442584.	−	766578.i	0.595983	−	1.03227i	0.993407	−	0.114638i	$-0.0365708\pi$
$224$		0			0
$225$	−70643.3	+	331344.i	−0.0930282	+	0.436337i
$226$		0			0
$227$	159067.	−	275512.i	0.204887	−	0.354875i	−0.745210	−	0.666830i	$-0.767651\pi$
$227$	159067.	−	275512.i	0.204887	−	0.354875i	0.950097	+	0.311955i	$0.100984\pi$
$228$		0			0
$229$	−246934.	−	427703.i	−0.311166	−	0.538956i	0.667449	−	0.744656i	$-0.267386\pi$
$229$	−246934.	−	427703.i	−0.311166	−	0.538956i	−0.978615	+	0.205700i	$0.934053\pi$
$230$		0			0
$231$	−1.15879e6	+	937779.i	−1.42881	+	1.15630i
$232$		0			0
$233$	1.16189e6			1.40208			0.701041	−	0.713121i	$-0.252719\pi$
$233$	1.16189e6			1.40208			0.701041	+	0.713121i	$0.252719\pi$
$234$		0			0
$235$	722678.			0.853641
$236$		0			0
$237$	−735313.	−	282521.i	−0.850358	−	0.326723i
$238$		0			0
$239$	−579263.	−	1.00331e6i	−0.655965	−	1.13617i	−0.981651	−	0.190687i	$-0.938928\pi$
$239$	−579263.	−	1.00331e6i	−0.655965	−	1.13617i	0.325685	−	0.945478i	$-0.394405\pi$
$240$		0			0
$241$	410557.	−	711106.i	0.455335	−	0.788663i	−0.543372	−	0.839492i	$-0.682853\pi$
$241$	410557.	−	711106.i	0.455335	−	0.788663i	0.998707	+	0.0508285i	$0.0161862\pi$
$242$		0			0
$243$	649873.	+	651885.i	0.706013	+	0.708198i
$244$		0			0
$245$	−510314.	+	883889.i	−0.543153	+	0.940768i
$246$		0			0
$247$	477926.	+	827792.i	0.498446	+	0.863334i
$248$		0			0
$249$	−754165.	−	289764.i	−0.770847	−	0.296174i
$250$		0			0
$251$	852357.			0.853959			0.426980	−	0.904261i	$-0.359578\pi$
$251$	852357.			0.853959			0.426980	+	0.904261i	$0.359578\pi$
$252$		0			0
$253$	224933.			0.220928
$254$		0			0
$255$	635126.	−	513990.i	0.611659	−	0.494999i
$256$		0			0
$257$	−650171.	−	1.12613e6i	−0.614037	−	1.06354i	−0.990553	−	0.137133i	$-0.956211\pi$
$257$	−650171.	−	1.12613e6i	−0.614037	−	1.06354i	0.376515	−	0.926410i	$-0.377122\pi$
$258$		0			0
$259$	−832103.	+	1.44124e6i	−0.770775	+	1.33502i
$260$		0			0
$261$	−58801.8	+	275803.i	−0.0534305	+	0.250609i
$262$		0			0
$263$	−572288.	+	991232.i	−0.510182	+	0.883662i	0.489748	+	0.871864i	$0.337089\pi$
$263$	−572288.	+	991232.i	−0.510182	+	0.883662i	−0.999930	+	0.0117977i	$0.996245\pi$
$264$		0			0
$265$	112132.	+	194218.i	0.0980876	+	0.169893i
$266$		0			0
$267$	−49052.9	−	310329.i	−0.0421101	−	0.266406i
$268$		0			0
$269$	1.54095e6			1.29840			0.649199	−	0.760619i	$-0.275104\pi$
$269$	1.54095e6			1.29840			0.649199	+	0.760619i	$0.275104\pi$
$270$		0			0
$271$	−1.42397e6			−1.17782			−0.588908	−	0.808200i	$-0.700442\pi$
$271$	−1.42397e6			−1.17782			−0.588908	+	0.808200i	$0.700442\pi$
$272$		0			0
$273$	239016.	+	1.51211e6i	0.194098	+	1.22794i
$274$		0			0
$275$	−327871.	−	567889.i	−0.261440	−	0.452827i
$276$		0			0
$277$	−798009.	+	1.38219e6i	−0.624897	+	1.08235i	0.363664	+	0.931530i	$0.381526\pi$
$277$	−798009.	+	1.38219e6i	−0.624897	+	1.08235i	−0.988561	+	0.150823i	$0.951808\pi$
$278$		0			0
$279$	428286.	+	386110.i	0.329400	+	0.296962i
$280$		0			0
$281$	−200767.	+	347738.i	−0.151679	+	0.262716i	−0.931845	−	0.362857i	$-0.881801\pi$
$281$	−200767.	+	347738.i	−0.151679	+	0.262716i	0.780166	+	0.625573i	$0.215135\pi$
$282$		0			0
$283$	535582.	+	927656.i	0.397521	+	0.688527i	0.993419	−	0.114533i	$-0.0365372\pi$
$283$	535582.	+	927656.i	0.397521	+	0.688527i	−0.595898	+	0.803060i	$0.703204\pi$
$284$		0			0
$285$	−997634.	+	807358.i	−0.727544	+	0.588781i
$286$		0			0
$287$	3.56173e6			2.55244
$288$		0			0
$289$	167390.			0.117892
$290$		0			0
$291$	−1.17035e6	−	449669.i	−0.810181	−	0.311287i
$292$		0			0
$293$	358830.	+	621511.i	0.244185	+	0.422941i	0.961902	−	0.273394i	$-0.0881462\pi$
$293$	358830.	+	621511.i	0.244185	+	0.422941i	−0.717717	+	0.696335i	$0.754813\pi$
$294$		0			0
$295$	−926986.	+	1.60559e6i	−0.620181	+	1.07418i
$296$		0			0
$297$	−1.77910e6	−	94892.7i	−1.17033	−	0.0624226i
$298$		0			0
$299$	115497.	−	200047.i	0.0747125	−	0.129406i
$300$		0			0
$301$	2.32499e6	+	4.02700e6i	1.47912	+	2.56192i
$302$		0			0
$303$	−827978.	−	318125.i	−0.518098	−	0.199063i
$304$		0			0
$305$	173415.			0.106742
$306$		0			0
$307$	2.25621e6			1.36626			0.683131	−	0.730296i	$-0.260618\pi$
$307$	2.25621e6			1.36626			0.683131	+	0.730296i	$0.260618\pi$
$308$		0			0
$309$	2.38728e6	−	1.93196e6i	1.42235	−	1.15107i
$310$		0			0
$311$	897190.	+	1.55398e6i	0.525997	+	0.911054i	0.999541	+	0.0302837i	$0.00964107\pi$
$311$	897190.	+	1.55398e6i	0.525997	+	0.911054i	−0.473544	+	0.880770i	$0.657026\pi$
$312$		0			0
$313$	281895.	−	488257.i	0.162640	−	0.281701i	−0.773175	−	0.634193i	$-0.781332\pi$
$313$	281895.	−	488257.i	0.162640	−	0.281701i	0.935815	+	0.352492i	$0.114666\pi$
$314$		0			0
$315$	−1.95527e6	+	633969.i	−1.11027	+	0.359991i
$316$		0			0
$317$	1.59153e6	−	2.75662e6i	0.889544	−	1.54074i	0.0491288	−	0.998792i	$-0.484356\pi$
$317$	1.59153e6	−	2.75662e6i	0.889544	−	1.54074i	0.840415	−	0.541943i	$-0.182311\pi$
$318$		0			0
$319$	−272912.	−	472698.i	−0.150157	−	0.260080i
$320$		0			0
$321$	57151.9	+	361566.i	0.0309576	+	0.195851i
$322$		0			0
$323$	−2.49319e6			−1.32969
$324$		0			0
$325$	−673414.			−0.353650
$326$		0			0
$327$	−288528.	−	1.82534e6i	−0.149217	−	0.944006i
$328$		0			0
$329$	−1.76593e6	−	3.05869e6i	−0.899466	−	1.55792i
$330$		0			0
$331$	−3762.47	+	6516.79i	−0.00188757	+	0.00326937i	−0.866968	−	0.498364i	$-0.833934\pi$
$331$	−3762.47	+	6516.79i	−0.00188757	+	0.00326937i	0.865080	+	0.501634i	$0.167267\pi$
$332$		0			0
$333$	−1.89201e6	+	613459.i	−0.935003	+	0.303162i
$334$		0			0
$335$	51107.6	−	88520.9i	0.0248813	−	0.0430957i
$336$		0			0
$337$	734831.	+	1.27277e6i	0.352463	+	0.610483i	0.986680	−	0.162671i	$-0.0520111\pi$
$337$	734831.	+	1.27277e6i	0.352463	+	0.610483i	−0.634218	+	0.773154i	$0.718678\pi$
$338$		0			0
$339$	−5414.14	+	4381.51i	−0.00255876	+	0.00207074i
$340$		0			0
$341$	−1.11610e6			−0.519779
$342$		0			0
$343$	1.57078e6			0.720909
$344$		0			0
$345$	289515.	+	111237.i	0.130955	+	0.0503155i
$346$		0			0
$347$	−1.31149e6	−	2.27156e6i	−0.584709	−	1.01275i	−0.994912	−	0.100751i	$-0.967875\pi$
$347$	−1.31149e6	−	2.27156e6i	−0.584709	−	1.01275i	0.410203	−	0.911994i	$-0.365458\pi$
$348$		0			0
$349$	−582327.	+	1.00862e6i	−0.255919	+	0.443265i	−0.965145	−	0.261716i	$-0.915711\pi$
$349$	−582327.	+	1.00862e6i	−0.255919	+	0.443265i	0.709225	+	0.704982i	$0.249045\pi$
$350$		0			0
$351$	−997918.	+	1.53354e6i	−0.432341	+	0.664398i
$352$		0			0
$353$	−1.57339e6	+	2.72518e6i	−0.672045	+	1.16402i	0.305278	+	0.952263i	$0.401251\pi$
$353$	−1.57339e6	+	2.72518e6i	−0.672045	+	1.16402i	−0.977323	+	0.211753i	$0.932083\pi$
$354$		0			0
$355$	45438.0	+	78700.9i	0.0191359	+	0.0331443i
$356$		0			0
$357$	−3.72742e6	−	1.43215e6i	−1.54788	−	0.594726i
$358$		0			0
$359$	720847.			0.295194			0.147597	−	0.989048i	$-0.452846\pi$
$359$	720847.			0.295194			0.147597	+	0.989048i	$0.452846\pi$
$360$		0			0
$361$	1.44012e6			0.581607
$362$		0			0
$363$	729050.	−	590000.i	0.290396	−	0.235009i
$364$		0			0
$365$	−63181.1	−	109433.i	−0.0248230	−	0.0429947i
$366$		0			0
$367$	41258.2	−	71461.4i	0.0159899	−	0.0276953i	−0.857920	−	0.513784i	$-0.828243\pi$
$367$	41258.2	−	71461.4i	0.0159899	−	0.0276953i	0.873910	+	0.486088i	$0.161577\pi$
$368$		0			0
$369$	3.16166e6	+	2.85032e6i	1.20879	+	1.08975i
$370$		0			0
$371$	548010.	−	949181.i	0.206706	−	0.358026i
$372$		0			0
$373$	−2.65152e6	−	4.59256e6i	−0.986784	−	1.70916i	−0.633724	−	0.773560i	$-0.718474\pi$
$373$	−2.65152e6	−	4.59256e6i	−0.986784	−	1.70916i	−0.353060	−	0.935601i	$-0.614859\pi$
$374$		0			0
$375$	−457586.	−	2.89487e6i	−0.168033	−	1.06304i
$376$		0			0
$377$	−560534.			−0.203118
$378$		0			0
$379$	49534.8			0.0177138			0.00885691	−	0.999961i	$-0.497181\pi$
$379$	49534.8			0.0177138			0.00885691	+	0.999961i	$0.497181\pi$
$380$		0			0
$381$	−471681.	−	2.98404e6i	−0.166470	−	1.05316i
$382$		0			0
$383$	−1.92179e6	−	3.32863e6i	−0.669434	−	1.15949i	−0.978063	−	0.208311i	$-0.933203\pi$
$383$	−1.92179e6	−	3.32863e6i	−0.669434	−	1.15949i	0.308628	−	0.951183i	$-0.400130\pi$
$384$		0			0
$385$	1.98923e6	−	3.44545e6i	0.683963	−	1.18466i
$386$		0			0
$387$	−1.15881e6	+	5.43527e6i	−0.393311	+	1.84478i
$388$		0			0
$389$	1.96659e6	−	3.40623e6i	0.658930	−	1.14130i	−0.321963	−	0.946752i	$-0.604343\pi$
$389$	1.96659e6	−	3.40623e6i	0.658930	−	1.14130i	0.980893	−	0.194548i	$-0.0623240\pi$
$390$		0			0
$391$	301257.	+	521792.i	0.0996540	+	0.172606i
$392$		0			0
$393$	−1.16420e6	+	942154.i	−0.380229	+	0.307709i
$394$		0			0
$395$	2.10229e6			0.677953
$396$		0			0
$397$	1.48840e6			0.473960			0.236980	−	0.971514i	$-0.423842\pi$
$397$	1.48840e6			0.473960			0.236980	+	0.971514i	$0.423842\pi$
$398$		0			0
$399$	5.85490e6	+	2.24956e6i	1.84114	+	0.707402i
$400$		0			0
$401$	1.84020e6	+	3.18731e6i	0.571483	+	0.989837i	0.996414	+	0.0846115i	$0.0269649\pi$
$401$	1.84020e6	+	3.18731e6i	0.571483	+	0.989837i	−0.424931	+	0.905226i	$0.639702\pi$
$402$		0			0
$403$	−573091.	+	992622.i	−0.175776	+	0.304454i
$404$		0			0
$405$	−2.24299e6	−	1.00197e6i	−0.679500	−	0.303540i
$406$		0			0
$407$	1.92487e6	−	3.33398e6i	0.575991	−	0.997646i
$408$		0			0
$409$	−290013.	−	502318.i	−0.0857254	−	0.148481i	0.819975	−	0.572400i	$-0.193987\pi$
$409$	−290013.	−	502318.i	−0.0857254	−	0.148481i	−0.905700	+	0.423919i	$0.860654\pi$
$410$		0			0
$411$	−3.37849e6	−	1.29808e6i	−0.986549	−	0.379050i
$412$		0			0
$413$	9.06073e6			2.61389
$414$		0			0
$415$	2.15619e6			0.614563
$416$		0			0
$417$	1.94569e6	−	1.57459e6i	0.547940	−	0.443433i
$418$		0			0
$419$	−759450.	−	1.31541e6i	−0.211331	−	0.366037i	0.740800	−	0.671726i	$-0.234447\pi$
$419$	−759450.	−	1.31541e6i	−0.211331	−	0.366037i	−0.952131	+	0.305689i	$0.901113\pi$
$420$		0			0
$421$	−2.70128e6	+	4.67875e6i	−0.742787	+	1.28654i	0.208435	+	0.978036i	$0.433163\pi$
$421$	−2.70128e6	+	4.67875e6i	−0.742787	+	1.28654i	−0.951222	+	0.308508i	$0.900170\pi$
$422$		0			0
$423$	880172.	−	4.12834e6i	0.239175	−	1.12182i
$424$		0			0
$425$	878248.	−	1.52117e6i	0.235855	−	0.408513i
$426$		0			0
$427$	−423756.	−	733967.i	−0.112472	−	0.194808i
$428$		0			0
$429$	−552908.	−	3.49792e6i	−0.145047	−	0.917627i
$430$		0			0
$431$	3.04614e6			0.789871			0.394935	−	0.918709i	$-0.370767\pi$
$431$	3.04614e6			0.789871			0.394935	+	0.918709i	$0.370767\pi$
$432$		0			0
$433$	−1.07293e6			−0.275011			−0.137505	−	0.990501i	$-0.543908\pi$
$433$	−1.07293e6			−0.275011			−0.137505	+	0.990501i	$0.543908\pi$
$434$		0			0
$435$	−117505.	−	743383.i	−0.0297737	−	0.188360i
$436$		0			0
$437$	−473203.	−	819612.i	−0.118534	−	0.205307i
$438$		0			0
$439$	3.81738e6	−	6.61190e6i	0.945376	−	1.63744i	0.190380	−	0.981710i	$-0.439028\pi$
$439$	3.81738e6	−	6.61190e6i	0.945376	−	1.63744i	0.754996	−	0.655729i	$-0.227639\pi$
$440$		0			0
$441$	4.42774e6	+	3.99171e6i	1.08414	+	0.977378i
$442$		0			0
$443$	−3.30067e6	+	5.71693e6i	−0.799085	+	1.38406i	0.121127	+	0.992637i	$0.461349\pi$
$443$	−3.30067e6	+	5.71693e6i	−0.799085	+	1.38406i	−0.920213	+	0.391419i	$0.871984\pi$
$444$		0			0
$445$	419248.	+	726159.i	0.100362	+	0.173833i
$446$		0			0
$447$	−3.38303e6	+	2.73779e6i	−0.800824	+	0.648085i
$448$		0			0
$449$	−5.52311e6			−1.29291			−0.646454	−	0.762953i	$-0.723749\pi$
$449$	−5.52311e6			−1.29291			−0.646454	+	0.762953i	$0.723749\pi$
$450$		0			0
$451$	−8.23922e6			−1.90741
$452$		0			0
$453$	−415844.	−	159775.i	−0.0952104	−	0.0365816i
$454$		0			0
$455$	−2.04284e6	−	3.53830e6i	−0.462600	−	0.801246i
$456$		0			0
$457$	−706717.	+	1.22407e6i	−0.158291	+	0.274167i	−0.934252	−	0.356613i	$-0.883932\pi$
$457$	−706717.	+	1.22407e6i	−0.158291	+	0.274167i	0.775962	+	0.630780i	$0.217265\pi$
$458$		0			0
$459$	−2.16266e6	−	4.25420e6i	−0.479132	−	0.942509i
$460$		0			0
$461$	−4.25416e6	+	7.36841e6i	−0.932312	+	1.61481i	−0.152953	+	0.988234i	$0.548878\pi$
$461$	−4.25416e6	+	7.36841e6i	−0.932312	+	1.61481i	−0.779359	+	0.626578i	$0.784455\pi$
$462$		0			0
$463$	2.04077e6	+	3.53472e6i	0.442427	+	0.766307i	0.997869	−	0.0652489i	$-0.0207841\pi$
$463$	2.04077e6	+	3.53472e6i	0.442427	+	0.766307i	−0.555442	+	0.831555i	$0.687451\pi$
$464$		0			0
$465$	−1.43656e6	−	551952.i	−0.308099	−	0.118377i
$466$		0			0
$467$	5.38239e6			1.14204			0.571022	−	0.820935i	$-0.306547\pi$
$467$	5.38239e6			1.14204			0.571022	+	0.820935i	$0.306547\pi$
$468$		0			0
$469$	−499545.			−0.104868
$470$		0			0
$471$	−1.50565e6	+	1.21848e6i	−0.312732	+	0.253085i
$472$		0			0
$473$	−5.37831e6	−	9.31550e6i	−1.10533	−	1.91449i
$474$		0			0
$475$	−1.37952e6	+	2.38940e6i	−0.280540	+	0.485909i
$476$		0			0
$477$	1.24605e6	−	404014.i	0.250749	−	0.0813019i
$478$		0			0
$479$	−4.29153e6	+	7.43315e6i	−0.854621	+	1.48025i	0.0223760	+	0.999750i	$0.492877\pi$
$479$	−4.29153e6	+	7.43315e6i	−0.854621	+	1.48025i	−0.876997	+	0.480497i	$0.840456\pi$
$480$		0			0
$481$	−1.97675e6	−	3.42383e6i	−0.389573	−	0.674760i
$482$		0			0
$483$	−236655.	−	1.49717e6i	−0.0461580	−	0.292014i
$484$		0			0
$485$	3.34607e6			0.645922
$486$		0			0
$487$	3.96670e6			0.757891			0.378946	−	0.925419i	$-0.376287\pi$
$487$	3.96670e6			0.757891			0.378946	+	0.925419i	$0.376287\pi$
$488$		0			0
$489$	−398884.	−	2.52350e6i	−0.0754352	−	0.477234i
$490$		0			0
$491$	2.88205e6	+	4.99185e6i	0.539507	+	0.934454i	0.998931	+	0.0462362i	$0.0147227\pi$
$491$	2.88205e6	+	4.99185e6i	0.539507	+	0.934454i	−0.459424	+	0.888217i	$0.651944\pi$
$492$		0			0
$493$	731033.	−	1.26619e6i	0.135463	−	0.234628i
$494$		0			0
$495$	4.52305e6	−	1.46654e6i	0.829695	−	0.269017i
$496$		0			0
$497$	222064.	−	384627.i	0.0403262	−	0.0698471i
$498$		0			0
$499$	−2.32003e6	−	4.01841e6i	−0.417102	−	0.722442i	0.578544	−	0.815651i	$-0.303621\pi$
$499$	−2.32003e6	−	4.01841e6i	−0.417102	−	0.722442i	−0.995647	+	0.0932088i	$0.970288\pi$
$500$		0			0
$501$	1.96703e6	−	1.59187e6i	0.350120	−	0.283343i
$502$		0			0
$503$	2.73360e6			0.481743			0.240872	−	0.970557i	$-0.422567\pi$
$503$	2.73360e6			0.481743			0.240872	+	0.970557i	$0.422567\pi$
$504$		0			0
$505$	2.36722e6			0.413057
$506$		0			0
$507$	2.00799e6	+	771506.i	0.346929	+	0.133297i
$508$		0			0
$509$	2.97841e6	+	5.15877e6i	0.509555	+	0.882574i	0.999939	+	0.0110680i	$0.00352313\pi$
$509$	2.97841e6	+	5.15877e6i	0.509555	+	0.882574i	−0.490384	+	0.871506i	$0.663144\pi$
$510$		0			0
$511$	−308778.	+	534820.i	−0.0523112	+	0.0906056i
$512$		0			0
$513$	3.39702e6	+	6.68234e6i	0.569908	+	1.12108i
$514$		0			0
$515$	−4.09809e6	+	7.09810e6i	−0.680869	+	1.17930i
$516$		0			0
$517$	4.08507e6	+	7.07555e6i	0.672161	+	1.16422i
$518$		0			0
$519$	5.59292e6	+	2.14890e6i	0.911424	+	0.350186i
$520$		0			0
$521$	−1.11813e7			−1.80468			−0.902339	−	0.431027i	$-0.858151\pi$
$521$	−1.11813e7			−1.80468			−0.902339	+	0.431027i	$0.858151\pi$
$522$		0			0
$523$	−4.60970e6			−0.736917			−0.368458	−	0.929644i	$-0.620114\pi$
$523$	−4.60970e6			−0.736917			−0.368458	+	0.929644i	$0.620114\pi$
$524$		0			0
$525$	−3.43497e6	+	2.77982e6i	−0.543907	+	0.440169i
$526$		0			0
$527$	−1.49482e6	−	2.58910e6i	−0.234456	−	0.406090i
$528$		0			0
$529$	3.10382e6	−	5.37597e6i	0.482233	−	0.835252i
$530$		0			0
$531$	8.04299e6	+	7.25095e6i	1.23789	+	1.11599i
$532$		0			0
$533$	−4.23063e6	+	7.32767e6i	−0.645041	+	1.11724i
$534$		0			0
$535$	−488468.	−	846052.i	−0.0737823	−	0.127795i
$536$		0			0
$537$	1.24609e6	+	7.88327e6i	0.186472	+	1.17970i
$538$		0			0
$539$	−1.15386e7			−1.71072
$540$		0			0
$541$	−8.65572e6			−1.27148			−0.635741	−	0.771902i	$-0.719305\pi$
$541$	−8.65572e6			−1.27148			−0.635741	+	0.771902i	$0.719305\pi$
$542$		0			0
$543$	−695662.	−	4.40104e6i	−0.101251	−	0.640554i
$544$		0			0
$545$	2.46600e6	+	4.27124e6i	0.355633	+	0.615975i
$546$		0			0
$547$	581626.	−	1.00741e6i	0.0831143	−	0.143958i	−0.821472	−	0.570249i	$-0.806847\pi$
$547$	581626.	−	1.00741e6i	0.0831143	−	0.143958i	0.904586	+	0.426291i	$0.140180\pi$
$548$		0			0
$549$	211207.	−	990641.i	0.0299073	−	0.140277i
$550$		0			0
$551$	−1.14828e6	+	1.98888e6i	−0.161127	+	0.279081i
$552$		0			0
$553$	−5.13715e6	−	8.89781e6i	−0.714347	−	1.23729i
$554$		0			0
$555$	4.12631e6	−	3.33931e6i	0.568629	−	0.460176i
$556$		0			0
$557$	1.23037e7			1.68034			0.840168	−	0.542326i	$-0.182456\pi$
$557$	1.23037e7			1.68034			0.840168	+	0.542326i	$0.182456\pi$
$558$		0			0
$559$	−1.10465e7			−1.49519
$560$		0			0
$561$	8.62251e6	+	3.31293e6i	1.15672	+	0.444432i
$562$		0			0
$563$	−2.76949e6	−	4.79690e6i	−0.368239	−	0.637808i	0.621052	−	0.783770i	$-0.286706\pi$
$563$	−2.76949e6	−	4.79690e6i	−0.368239	−	0.637808i	−0.989290	+	0.145962i	$0.953372\pi$
$564$		0			0
$565$	9294.13	−	16097.9i	0.00122486	−	0.00212152i
$566$		0			0
$567$	1.24020e6	+	1.19417e7i	0.162007	+	1.55994i
$568$		0			0
$569$	−6.91495e6	+	1.19770e7i	−0.895382	+	1.55085i	−0.0620514	+	0.998073i	$0.519764\pi$
$569$	−6.91495e6	+	1.19770e7i	−0.895382	+	1.55085i	−0.833331	+	0.552775i	$0.813569\pi$
$570$		0			0
$571$	990947.	+	1.71637e6i	0.127192	+	0.220303i	0.922588	−	0.385787i	$-0.126070\pi$
$571$	990947.	+	1.71637e6i	0.127192	+	0.220303i	−0.795396	+	0.606091i	$0.792737\pi$
$572$		0			0
$573$	542071.	+	208274.i	0.0689715	+	0.0265001i
$574$		0			0
$575$	666760.			0.0841007
$576$		0			0
$577$	9.36673e6			1.17125			0.585623	−	0.810583i	$-0.300850\pi$
$577$	9.36673e6			1.17125			0.585623	+	0.810583i	$0.300850\pi$
$578$		0			0
$579$	7.01309e6	−	5.67550e6i	0.869387	−	0.703571i
$580$		0			0
$581$	−5.26886e6	−	9.12593e6i	−0.647554	−	1.12160i
$582$		0			0
$583$	−1.26769e6	+	2.19570e6i	−0.154469	+	0.267549i
$584$		0			0
$585$	1.01818e6	−	4.77567e6i	0.123009	−	0.576958i
$586$		0			0
$587$	−929269.	+	1.60954e6i	−0.111313	+	0.192800i	−0.916300	−	0.400493i	$-0.868839\pi$
$587$	−929269.	+	1.60954e6i	−0.111313	+	0.192800i	0.804987	+	0.593293i	$0.202172\pi$
$588$		0			0
$589$	2.34801e6	+	4.06687e6i	0.278876	+	0.483028i
$590$		0			0
$591$	570451.	+	3.60890e6i	0.0671815	+	0.425017i
$592$		0			0
$593$	1.50844e6			0.176154			0.0880770	−	0.996114i	$-0.471928\pi$
$593$	1.50844e6			0.176154			0.0880770	+	0.996114i	$0.471928\pi$
$594$		0			0
$595$	1.06568e7			1.23406
$596$		0			0
$597$	−488103.	−	3.08793e6i	−0.0560500	−	0.354595i
$598$		0			0
$599$	6.50791e6	+	1.12720e7i	0.741096	+	1.28362i	0.951997	+	0.306108i	$0.0990268\pi$
$599$	6.50791e6	+	1.12720e7i	0.741096	+	1.28362i	−0.210901	+	0.977507i	$0.567640\pi$
$600$		0			0
$601$	6.92629e6	−	1.19967e7i	0.782194	−	1.35480i	−0.148467	−	0.988917i	$-0.547434\pi$
$601$	6.92629e6	−	1.19967e7i	0.782194	−	1.35480i	0.930661	−	0.365882i	$-0.119233\pi$
$602$		0			0
$603$	−443435.	−	399767.i	−0.0496634	−	0.0447727i
$604$		0			0
$605$	−1.25152e6	+	2.16769e6i	−0.139011	+	0.240773i
$606$		0			0
$607$	−4.75435e6	−	8.23478e6i	−0.523745	−	0.907153i	−0.999618	−	0.0276388i	$-0.991201\pi$
$607$	−4.75435e6	−	8.23478e6i	−0.523745	−	0.907153i	0.475873	−	0.879514i	$-0.342132\pi$
$608$		0			0
$609$	−2.85919e6	+	2.31386e6i	−0.312391	+	0.252810i
$610$		0			0
$611$	8.39032e6			0.909234
$612$		0			0
$613$	−1.65462e7			−1.77848			−0.889238	−	0.457445i	$-0.848765\pi$
$613$	−1.65462e7			−1.77848			−0.889238	+	0.457445i	$0.848765\pi$
$614$		0			0
$615$	−1.06049e7	−	4.07458e6i	−1.13062	−	0.434405i
$616$		0			0
$617$	2.75765e6	+	4.77638e6i	0.291626	+	0.505111i	0.974194	−	0.225711i	$-0.0724705\pi$
$617$	2.75765e6	+	4.77638e6i	0.291626	+	0.505111i	−0.682569	+	0.730822i	$0.739137\pi$
$618$		0			0
$619$	1.24124e6	−	2.14989e6i	0.130205	−	0.225522i	−0.793550	−	0.608505i	$-0.791770\pi$
$619$	1.24124e6	−	2.14989e6i	0.130205	−	0.225522i	0.923756	+	0.382982i	$0.125103\pi$
$620$		0			0
$621$	988056.	−	1.51839e6i	0.102814	−	0.157999i
$622$		0			0
$623$	2.04895e6	−	3.54888e6i	0.211500	−	0.366329i
$624$		0			0
$625$	1.73248e6	+	3.00074e6i	0.177406	+	0.307276i
$626$		0			0
$627$	−1.35439e7	−	5.20383e6i	−1.37587	−	0.528633i
$628$		0			0
$629$	1.03121e7			1.03925
$630$		0			0
$631$	9.16852e6			0.916697			0.458349	−	0.888772i	$-0.348441\pi$
$631$	9.16852e6			0.916697			0.458349	+	0.888772i	$0.348441\pi$
$632$		0			0
$633$	6.53925e6	−	5.29204e6i	0.648662	−	0.524945i
$634$		0			0
$635$	4.03138e6	+	6.98256e6i	0.396753	+	0.687196i
$636$		0			0
$637$	−5.92476e6	+	1.02620e7i	−0.578525	+	1.00204i
$638$		0			0
$639$	504923.	−	163715.i	0.0489185	−	0.0158612i
$640$		0			0
$641$	994072.	−	1.72178e6i	0.0955593	−	0.165514i	−0.814283	−	0.580469i	$-0.802869\pi$
$641$	994072.	−	1.72178e6i	0.0955593	−	0.165514i	0.909842	+	0.414955i	$0.136203\pi$
$642$		0			0
$643$	−2.62237e6	−	4.54208e6i	−0.250130	−	0.433239i	0.713431	−	0.700725i	$-0.247140\pi$
$643$	−2.62237e6	−	4.54208e6i	−0.250130	−	0.433239i	−0.963562	+	0.267487i	$0.913807\pi$
$644$		0			0
$645$	−2.31568e6	−	1.46499e7i	−0.219169	−	1.38655i
$646$		0			0
$647$	−9.94212e6			−0.933723			−0.466862	−	0.884330i	$-0.654615\pi$
$647$	−9.94212e6			−0.933723			−0.466862	+	0.884330i	$0.654615\pi$
$648$		0			0
$649$	−2.09598e7			−1.95333
$650$		0			0
$651$	1.17427e6	+	7.42889e6i	0.108596	+	0.687023i
$652$		0			0
$653$	1.21132e6	+	2.09806e6i	0.111167	+	0.192547i	0.916241	−	0.400628i	$-0.131208\pi$
$653$	1.21132e6	+	2.09806e6i	0.111167	+	0.192547i	−0.805074	+	0.593174i	$0.797875\pi$
$654$		0			0
$655$	1.99851e6	−	3.46152e6i	0.182013	−	0.315256i
$656$		0			0
$657$	−702091.	+	227643.i	−0.0634570	+	0.0205751i
$658$		0			0
$659$	7.70304e6	−	1.33421e7i	0.690953	−	1.19677i	−0.280573	−	0.959833i	$-0.590524\pi$
$659$	7.70304e6	−	1.33421e7i	0.690953	−	1.19677i	0.971526	−	0.236933i	$-0.0761422\pi$
$660$		0			0
$661$	−3.40975e6	−	5.90586e6i	−0.303542	−	0.525751i	0.673393	−	0.739284i	$-0.264836\pi$
$661$	−3.40975e6	−	5.90586e6i	−0.303542	−	0.525751i	−0.976936	+	0.213534i	$0.931503\pi$
$662$		0			0
$663$	7.37384e6	−	5.96745e6i	0.651493	−	0.527236i
$664$		0			0
$665$	−1.67394e7			−1.46786
$666$		0			0
$667$	554995.			0.0483030
$668$		0			0
$669$	1.28804e7	+	4.94889e6i	1.11266	+	0.427506i
$670$		0			0
$671$	980259.	+	1.69786e6i	0.0840494	+	0.145578i
$672$		0			0
$673$	114441.	−	198218.i	0.00973969	−	0.0168696i	−0.861114	−	0.508411i	$-0.830233\pi$
$673$	114441.	−	198218.i	0.00973969	−	0.0168696i	0.870854	+	0.491541i	$0.163566\pi$
$674$		0			0
$675$	−5.27373e6	−	281287.i	−0.445511	−	0.0237624i
$676$		0			0
$677$	1.00487e7	−	1.74048e7i	0.842629	−	1.45948i	−0.0450356	−	0.998985i	$-0.514340\pi$
$677$	1.00487e7	−	1.74048e7i	0.842629	−	1.45948i	0.887665	−	0.460491i	$-0.152327\pi$
$678$		0			0
$679$	−8.17644e6	−	1.41620e7i	−0.680597	−	1.17883i
$680$		0			0
$681$	4.62928e6	+	1.77865e6i	0.382512	+	0.146968i
$682$		0			0
$683$	−1.34916e7			−1.10665			−0.553325	−	0.832965i	$-0.686641\pi$
$683$	−1.34916e7			−1.10665			−0.553325	+	0.832965i	$0.686641\pi$
$684$		0			0
$685$	9.65924e6			0.786533
$686$		0			0
$687$	5.98447e6	−	4.84307e6i	0.483764	−	0.391497i
$688$		0			0
$689$	1.30185e6	+	2.25488e6i	0.104475	+	0.180957i
$690$		0			0
$691$	2.16664e6	−	3.75273e6i	0.172620	−	0.298987i	−0.766715	−	0.641988i	$-0.778110\pi$
$691$	2.16664e6	−	3.75273e6i	0.172620	−	0.298987i	0.939335	+	0.343001i	$0.111443\pi$
$692$		0			0
$693$	−1.72595e7	−	1.55599e7i	−1.36520	−	1.23076i
$694$		0			0
$695$	−3.34005e6	+	5.78513e6i	−0.262295	+	0.454309i
$696$		0			0
$697$	−1.10349e7	−	1.91131e7i	−0.860376	−	1.49021i
$698$		0			0
$699$	2.82781e6	+	1.78899e7i	0.218906	+	1.38489i
$700$		0			0
$701$	−4.00999e6			−0.308211			−0.154106	−	0.988054i	$-0.549250\pi$
$701$	−4.00999e6			−0.308211			−0.154106	+	0.988054i	$0.549250\pi$
$702$		0			0
$703$	−1.61978e7			−1.23614
$704$		0			0
$705$	1.75886e6	+	1.11273e7i	0.133278	+	0.843172i
$706$		0			0
$707$	−5.78454e6	−	1.00191e7i	−0.435231	−	0.753843i
$708$		0			0
$709$	−2.57127e6	+	4.45358e6i	−0.192102	+	0.332731i	−0.945947	−	0.324322i	$-0.894864\pi$
$709$	−2.57127e6	+	4.45358e6i	−0.192102	+	0.332731i	0.753844	+	0.657053i	$0.228197\pi$
$710$		0			0
$711$	2.56044e6	−	1.20094e7i	0.189951	−	0.890940i
$712$		0			0
$713$	567428.	−	982813.i	0.0418010	−	0.0724014i
$714$		0			0
$715$	4.72562e6	+	8.18501e6i	0.345695	+	0.598762i
$716$		0			0
$717$	1.40385e7	−	1.13610e7i	1.01982	−	0.825310i
$718$		0			0
$719$	1.15318e6			0.0831906			0.0415953	−	0.999135i	$-0.486756\pi$
$719$	1.15318e6			0.0831906			0.0415953	+	0.999135i	$0.486756\pi$
$720$		0			0
$721$	4.00564e7			2.86968
$722$		0			0
$723$	1.19483e7	+	4.59077e6i	0.850083	+	0.326618i
$724$		0			0
$725$	−808984.	−	1.40120e6i	−0.0571603	−	0.0990046i
$726$		0			0
$727$	−9.27449e6	+	1.60639e7i	−0.650810	+	1.12724i	0.332117	+	0.943238i	$0.392237\pi$
$727$	−9.27449e6	+	1.60639e7i	−0.650810	+	1.12724i	−0.982927	+	0.183997i	$0.941096\pi$
$728$		0			0
$729$	−8.45558e6	+	1.15929e7i	−0.589284	+	0.807926i
$730$		0			0
$731$	1.44065e7	−	2.49529e7i	0.997163	−	1.72714i
$732$		0			0
$733$	2.05765e6	+	3.56395e6i	0.141453	+	0.245003i	0.928044	−	0.372471i	$-0.121489\pi$
$733$	2.05765e6	+	3.56395e6i	0.141453	+	0.245003i	−0.786591	+	0.617474i	$0.788156\pi$
$734$		0			0
$735$	−1.48515e7	−	5.70623e6i	−1.01403	−	0.389610i
$736$		0			0
$737$	1.15558e6			0.0783666
$738$		0			0
$739$	2.27852e7			1.53477			0.767384	−	0.641188i	$-0.221558\pi$
$739$	2.27852e7			1.53477			0.767384	+	0.641188i	$0.221558\pi$
$740$		0			0
$741$	−1.15826e7	+	9.37345e6i	−0.774924	+	0.627125i
$742$		0			0
$743$	−1.05194e7	−	1.82202e7i	−0.699068	−	1.21082i	−0.968790	−	0.247884i	$-0.920265\pi$
$743$	−1.05194e7	−	1.82202e7i	−0.699068	−	1.21082i	0.269721	−	0.962938i	$-0.413068\pi$
$744$		0			0
$745$	5.80745e6	−	1.00588e7i	0.383349	−	0.663980i
$746$		0			0
$747$	2.62609e6	−	1.23173e7i	0.172190	−	0.807635i
$748$		0			0
$749$	−2.38724e6	+	4.13482e6i	−0.155486	+	0.269310i
$750$		0			0
$751$	1.03484e7	+	1.79240e7i	0.669537	+	1.15967i	0.978034	+	0.208446i	$0.0668406\pi$
$751$	1.03484e7	+	1.79240e7i	0.669537	+	1.15967i	−0.308497	+	0.951225i	$0.599826\pi$
$752$		0			0
$753$	2.07448e6	+	1.31240e7i	0.133328	+	0.843487i
$754$		0			0
$755$	1.18891e6			0.0759072
$756$		0			0
$757$	1.22154e7			0.774761			0.387380	−	0.921920i	$-0.373380\pi$
$757$	1.22154e7			0.774761			0.387380	+	0.921920i	$0.373380\pi$
$758$		0			0
$759$	547444.	+	3.46335e6i	0.0344933	+	0.218219i
$760$		0			0
$761$	−642893.	−	1.11352e6i	−0.0402417	−	0.0697007i	0.845203	−	0.534445i	$-0.179479\pi$
$761$	−642893.	−	1.11352e6i	−0.0402417	−	0.0697007i	−0.885445	+	0.464745i	$0.846146\pi$
$762$		0			0
$763$	1.20518e7	−	2.08744e7i	0.749449	−	1.29808i
$764$		0			0
$765$	9.45984e6	+	8.52827e6i	0.584427	+	0.526874i
$766$		0			0
$767$	−1.07623e7	+	1.86409e7i	−0.660570	+	1.14414i
$768$		0			0
$769$	5.43009e6	+	9.40520e6i	0.331125	+	0.573525i	0.982733	−	0.185031i	$-0.0592386\pi$
$769$	5.43009e6	+	9.40520e6i	0.331125	+	0.573525i	−0.651608	+	0.758556i	$0.725905\pi$
$770$		0			0
$771$	1.57569e7	−	1.27517e7i	0.954632	−	0.772557i
$772$		0			0
$773$	−7.80047e6			−0.469540			−0.234770	−	0.972051i	$-0.575434\pi$
$773$	−7.80047e6			−0.469540			−0.234770	+	0.972051i	$0.575434\pi$
$774$		0			0
$775$	−3.30842e6			−0.197864
$776$		0			0
$777$	−2.42164e7	−	9.30441e6i	−1.43899	−	0.552887i
$778$		0			0
$779$	1.73333e7	+	3.00222e7i	1.02338	+	1.77255i
$780$		0			0
$781$	−513693.	+	889742.i	−0.0301353	+	0.0521959i
$782$		0			0
$783$	−4.38972e6	−	234137.i	−0.255878	−	0.0136479i
$784$		0			0
$785$	2.58466e6	−	4.47676e6i	0.149703	−	0.259293i
$786$		0			0
$787$	2.36760e6	+	4.10081e6i	0.136261	+	0.236011i	0.926079	−	0.377331i	$-0.123158\pi$
$787$	2.36760e6	+	4.10081e6i	0.136261	+	0.236011i	−0.789817	+	0.613342i	$0.789825\pi$
$788$		0			0
$789$	−1.66551e7	−	6.39921e6i	−0.952479	−	0.365960i
$790$		0			0
$791$	−90844.4			−0.00516246
$792$		0			0
$793$	2.01335e6			0.113694
$794$		0			0
$795$	−2.71752e6	+	2.19922e6i	−0.152495	+	0.123410i
$796$		0			0
$797$	2.59183e6	+	4.48918e6i	0.144531	+	0.250335i	0.929198	−	0.369583i	$-0.120499\pi$
$797$	2.59183e6	+	4.48918e6i	0.144531	+	0.250335i	−0.784667	+	0.619918i	$0.787166\pi$
$798$		0			0
$799$	−1.09424e7	+	1.89528e7i	−0.606383	+	1.05029i
$800$		0			0
$801$	4.65883e6	−	1.51056e6i	0.256564	−	0.0831874i
$802$		0			0
$803$	714285.	−	1.23718e6i	0.0390915	−	0.0677085i
$804$		0			0
$805$	2.02265e6	+	3.50333e6i	0.110010	+	0.190542i
$806$		0			0
$807$	3.75039e6	+	2.37265e7i	0.202718	+	1.28248i
$808$		0			0
$809$	7.85790e6			0.422119			0.211060	−	0.977473i	$-0.432309\pi$
$809$	7.85790e6			0.422119			0.211060	+	0.977473i	$0.432309\pi$
$810$		0			0
$811$	−2.34495e7			−1.25193			−0.625967	−	0.779849i	$-0.715296\pi$
$811$	−2.34495e7			−1.25193			−0.625967	+	0.779849i	$0.715296\pi$
$812$		0			0
$813$	−3.46567e6	−	2.19253e7i	−0.183891	−	1.16337i
$814$		0			0
$815$	3.40920e6	+	5.90491e6i	0.179787	+	0.311400i
$816$		0			0
$817$	−2.26293e7	+	3.91951e7i	−1.18608	+	2.05436i
$818$		0			0
$819$	−2.27007e7	+	7.36041e6i	−1.18258	+	0.383435i
$820$		0			0
$821$	1.29037e7	−	2.23499e7i	0.668125	−	1.15723i	−0.310303	−	0.950638i	$-0.600430\pi$
$821$	1.29037e7	−	2.23499e7i	0.668125	−	1.15723i	0.978428	−	0.206589i	$-0.0662362\pi$
$822$		0			0
$823$	5.93578e6	+	1.02811e7i	0.305477	+	0.529101i	0.977367	−	0.211549i	$-0.0678509\pi$
$823$	5.93578e6	+	1.02811e7i	0.305477	+	0.529101i	−0.671891	+	0.740650i	$0.734518\pi$
$824$		0			0
$825$	7.94598e6	−	6.43046e6i	0.406455	−	0.328933i
$826$		0			0
$827$	4.70487e6			0.239213			0.119606	−	0.992821i	$-0.461837\pi$
$827$	4.70487e6			0.239213			0.119606	+	0.992821i	$0.461837\pi$
$828$		0			0
$829$	−1.00951e7			−0.510183			−0.255091	−	0.966917i	$-0.582106\pi$
$829$	−1.00951e7			−0.510183			−0.255091	+	0.966917i	$0.582106\pi$
$830$		0			0
$831$	−2.32242e7	−	8.92318e6i	−1.16664	−	0.448247i
$832$		0			0
$833$	−1.54538e7	−	2.67668e7i	−0.771656	−	1.33655i
$834$		0			0
$835$	−3.37669e6	+	5.84859e6i	−0.167600	+	0.290292i
$836$		0			0
$837$	−4.90268e6	+	7.53417e6i	−0.241891	+	0.371725i
$838$		0			0
$839$	3.68716e6	−	6.38634e6i	0.180837	−	0.313218i	−0.761329	−	0.648366i	$-0.775453\pi$
$839$	3.68716e6	−	6.38634e6i	0.180837	−	0.313218i	0.942166	+	0.335147i	$0.108786\pi$
$840$		0			0
$841$	9.58220e6	+	1.65968e7i	0.467170	+	0.809162i
$842$		0			0
$843$	−5.84286e6	−	2.24493e6i	−0.283176	−	0.108801i
$844$		0			0
$845$	−5.74092e6			−0.276592
$846$		0			0
$847$	1.22328e7			0.585892
$848$		0			0
$849$	−1.29799e7	+	1.05043e7i	−0.618019	+	0.500145i
$850$		0			0
$851$	1.95721e6	+	3.38999e6i	0.0926434	+	0.160463i
$852$		0			0
$853$	−1.15979e7	+	2.00882e7i	−0.545769	+	0.945299i	0.452790	+	0.891617i	$0.350429\pi$
$853$	−1.15979e7	+	2.00882e7i	−0.545769	+	0.945299i	−0.998558	+	0.0536815i	$0.982904\pi$
$854$		0			0
$855$	−1.48592e7	−	1.33959e7i	−0.695151	−	0.626695i
$856$		0			0
$857$	−4.71610e6	+	8.16852e6i	−0.219346	+	0.379919i	−0.954608	−	0.297864i	$-0.903726\pi$
$857$	−4.71610e6	+	8.16852e6i	−0.219346	+	0.379919i	0.735262	+	0.677783i	$0.237059\pi$
$858$		0			0
$859$	7.97110e6	+	1.38064e7i	0.368583	+	0.638405i	0.989344	−	0.145595i	$-0.0465097\pi$
$859$	7.97110e6	+	1.38064e7i	0.368583	+	0.638405i	−0.620761	+	0.784000i	$0.713176\pi$
$860$		0			0
$861$	8.66859e6	+	5.48410e7i	0.398511	+	2.52114i
$862$		0			0
$863$	2.89248e7			1.32203			0.661017	−	0.750371i	$-0.270125\pi$
$863$	2.89248e7			1.32203			0.661017	+	0.750371i	$0.270125\pi$
$864$		0			0
$865$	−1.59904e7			−0.726639
$866$		0			0
$867$	407396.	+	2.57735e6i	0.0184064	+	0.116446i
$868$		0			0
$869$	1.18836e7	+	2.05830e7i	0.533824	+	0.924610i
$870$		0			0
$871$	593361.	−	1.02773e6i	0.0265017	−	0.0459023i
$872$		0			0
$873$	4.07528e6	−	1.91146e7i	0.180976	−	0.848846i
$874$		0			0
$875$	1.91134e7	−	3.31054e7i	0.843953	−	1.46177i
$876$		0			0
$877$	8.40397e6	+	1.45561e7i	0.368965	+	0.639066i	0.989404	−	0.145188i	$-0.0463788\pi$
$877$	8.40397e6	+	1.45561e7i	0.368965	+	0.639066i	−0.620439	+	0.784255i	$0.713046\pi$
$878$		0			0
$879$	−8.69627e6	+	7.03765e6i	−0.379630	+	0.307224i
$880$		0			0
$881$	2.56183e7			1.11202			0.556008	−	0.831177i	$-0.312332\pi$
$881$	2.56183e7			1.11202			0.556008	+	0.831177i	$0.312332\pi$
$882$		0			0
$883$	−1.53830e7			−0.663955			−0.331978	−	0.943287i	$-0.607716\pi$
$883$	−1.53830e7			−0.663955			−0.331978	+	0.943287i	$0.607716\pi$
$884$		0			0
$885$	−2.69778e7	−	1.03654e7i	−1.15784	−	0.444864i
$886$		0			0
$887$	−8.93554e6	−	1.54768e7i	−0.381340	−	0.660500i	0.609914	−	0.792467i	$-0.291204\pi$
$887$	−8.93554e6	−	1.54768e7i	−0.381340	−	0.660500i	−0.991254	+	0.131968i	$0.957870\pi$
$888$		0			0
$889$	1.97022e7	−	3.41252e7i	0.836103	−	1.44817i
$890$		0			0
$891$	−2.86891e6	−	2.76243e7i	−0.121066	−	1.16573i
$892$		0			0
$893$	1.71880e7	−	2.97705e7i	0.721267	−	1.24927i
$894$		0			0
$895$	−1.06501e7	−	1.84466e7i	−0.444424	−	0.769766i
$896$		0			0
$897$	3.36128e6	+	1.29147e6i	0.139484	+	0.0535923i
$898$		0			0
$899$	−2.75385e6			−0.113643
$900$		0			0
$901$	−6.79137e6			−0.278705
$902$		0			0
$903$	−5.63463e7	+	4.55995e7i	−2.29957	+	1.86097i
$904$		0			0
$905$	5.94572e6	+	1.02983e7i	0.241314	+	0.417969i
$906$		0			0
$907$	−2.54251e6	+	4.40375e6i	−0.102623	+	0.177748i	−0.912764	−	0.408486i	$-0.866057\pi$
$907$	−2.54251e6	+	4.40375e6i	−0.102623	+	0.177748i	0.810142	+	0.586234i	$0.199390\pi$
$908$		0			0
$909$	2.88311e6	−	1.35229e7i	0.115732	−	0.542824i
$910$		0			0
$911$	−2.52606e6	+	4.37526e6i	−0.100843	+	0.174666i	−0.912032	−	0.410118i	$-0.865487\pi$
$911$	−2.52606e6	+	4.37526e6i	−0.100843	+	0.174666i	0.811189	+	0.584784i	$0.198821\pi$
$912$		0			0
$913$	1.21882e7	+	2.11107e7i	0.483910	+	0.838156i
$914$		0			0
$915$	422059.	+	2.67012e6i	0.0166656	+	0.105433i
$916$		0			0
$917$	−1.95342e7			−0.767136
$918$		0			0
$919$	3.46731e7			1.35426			0.677132	−	0.735861i	$-0.263223\pi$
$919$	3.46731e7			1.35426			0.677132	+	0.735861i	$0.263223\pi$
$920$		0			0
$921$	5.49120e6	+	3.47395e7i	0.213313	+	1.34951i
$922$		0			0
$923$	527537.	+	913720.i	0.0203821	+	0.0353028i
$924$		0			0
$925$	5.70583e6	−	9.88279e6i	0.219263	−	0.379774i
$926$		0			0
$927$	3.55571e7	+	3.20556e7i	1.35902	+	1.22519i
$928$		0			0
$929$	8.00390e6	−	1.38632e7i	0.304272	−	0.527015i	−0.672827	−	0.739800i	$-0.734920\pi$
$929$	8.00390e6	−	1.38632e7i	0.304272	−	0.527015i	0.977099	+	0.212785i	$0.0682534\pi$
$930$		0			0
$931$	2.42743e7	+	4.20444e7i	0.917852	+	1.58977i
$932$		0			0
$933$	−2.17435e7	+	1.75964e7i	−0.817758	+	0.661789i
$934$		0			0
$935$	−2.46521e7			−0.922199
$936$		0			0
$937$	−1.90843e7			−0.710112			−0.355056	−	0.934845i	$-0.615538\pi$
$937$	−1.90843e7			−0.710112			−0.355056	+	0.934845i	$0.615538\pi$
$938$		0			0
$939$	8.20392e6	+	3.15210e6i	0.303639	+	0.116664i
$940$		0			0
$941$	2.57109e7	+	4.45326e7i	0.946550	+	1.63947i	0.752617	+	0.658458i	$0.228791\pi$
$941$	2.57109e7	+	4.45326e7i	0.946550	+	1.63947i	0.193933	+	0.981015i	$0.437876\pi$
$942$		0			0
$943$	4.18882e6	−	7.25526e6i	0.153396	−	0.265689i
$944$		0			0
$945$	−1.45202e7	−	2.85629e7i	−0.528923	−	1.04045i
$946$		0			0
$947$	−2.11813e7	+	3.66871e7i	−0.767498	+	1.32935i	0.171418	+	0.985198i	$0.445165\pi$
$947$	−2.11813e7	+	3.66871e7i	−0.767498	+	1.32935i	−0.938916	+	0.344147i	$0.888168\pi$
$948$		0			0
$949$	−733535.	−	1.27052e6i	−0.0264396	−	0.0457948i
$950$		0			0
$951$	4.63179e7	+	1.77962e7i	1.66072	+	0.638081i
$952$		0			0
$953$	−3.48928e7			−1.24452			−0.622262	−	0.782809i	$-0.713786\pi$
$953$	−3.48928e7			−1.24452			−0.622262	+	0.782809i	$0.713786\pi$
$954$		0			0
$955$	−1.54980e6			−0.0549880
$956$		0			0
$957$	6.61405e6	−	5.35257e6i	0.233446	−	0.188922i
$958$		0			0
$959$	−2.36033e7	−	4.08821e7i	−0.828755	−	1.43545i
$960$		0			0
$961$	1.14990e7	−	1.99169e7i	0.401655	−	0.695686i
$962$		0			0
$963$	−5.42804e6	+	1.75997e6i	−0.188615	+	0.0611560i
$964$		0			0
$965$	−1.20389e7	+	2.08521e7i	−0.416170	+	0.720827i
$966$		0			0
$967$	3.66580e6	+	6.34935e6i	0.126067	+	0.218355i	0.922150	−	0.386833i	$-0.126431\pi$
$967$	3.66580e6	+	6.34935e6i	0.126067	+	0.218355i	−0.796082	+	0.605188i	$0.793098\pi$
$968$		0			0
$969$	−6.06796e6	−	3.83884e7i	−0.207603	−	1.31338i
$970$		0			0
$971$	−3.45114e6			−0.117467			−0.0587334	−	0.998274i	$-0.518706\pi$
$971$	−3.45114e6			−0.117467			−0.0587334	+	0.998274i	$0.518706\pi$
$972$		0			0
$973$	3.26469e7			1.10550
$974$		0			0
$975$	−1.63896e6	−	1.03688e7i	−0.0552151	−	0.349313i
$976$		0			0
$977$	1.14779e7	+	1.98803e7i	0.384704	+	0.666326i	0.991728	−	0.128357i	$-0.0409704\pi$
$977$	1.14779e7	+	1.98803e7i	0.384704	+	0.666326i	−0.607024	+	0.794683i	$0.707637\pi$
$978$		0			0
$979$	−4.73975e6	+	8.20949e6i	−0.158052	+	0.273753i
$980$		0			0
$981$	2.74031e7	−	8.88509e6i	0.909133	−	0.294774i
$982$		0			0
$983$	2.52879e7	−	4.38000e7i	0.834698	−	1.44574i	−0.0595772	−	0.998224i	$-0.518975\pi$
$983$	2.52879e7	−	4.38000e7i	0.834698	−	1.44574i	0.894276	−	0.447516i	$-0.147691\pi$
$984$		0			0
$985$	−4.87556e6	−	8.44471e6i	−0.160116	−	0.277328i
$986$		0			0
$987$	4.27976e7	−	3.46349e7i	1.39838	−	1.13167i
$988$		0			0
$989$	1.09373e7			0.355567
$990$		0			0
$991$	3.58604e7			1.15993			0.579964	−	0.814642i	$-0.303067\pi$
$991$	3.58604e7			1.15993			0.579964	+	0.814642i	$0.303067\pi$
$992$		0			0
$993$	−109498.	−	42071.2i	−0.00352398	−	0.00135398i
$994$		0			0
$995$	4.17174e6	+	7.22567e6i	0.133586	+	0.231377i
$996$		0			0
$997$	1.75536e7	−	3.04037e7i	0.559279	−	0.968699i	−0.438278	−	0.898839i	$-0.644411\pi$
$997$	1.75536e7	−	3.04037e7i	0.559279	−	0.968699i	0.997557	−	0.0698599i	$-0.0222552\pi$
$998$		0			0
$999$	−1.40504e7	−	2.76388e7i	−0.445426	−	0.876204i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	144.6.i.b.97.2		6
3.2	odd	2		432.6.i.b.289.2		6
4.3	odd	2		18.6.c.b.7.2	✓	6
9.4	even	3	inner	144.6.i.b.49.2		6
9.5	odd	6		432.6.i.b.145.2		6
12.11	even	2		54.6.c.b.19.2		6
36.7	odd	6		162.6.a.j.1.2		3
36.11	even	6		162.6.a.i.1.2		3
36.23	even	6		54.6.c.b.37.2		6
36.31	odd	6		18.6.c.b.13.2	yes	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
18.6.c.b.7.2	✓	6	4.3	odd	2
18.6.c.b.13.2	yes	6	36.31	odd	6
54.6.c.b.19.2		6	12.11	even	2
54.6.c.b.37.2		6	36.23	even	6
144.6.i.b.49.2		6	9.4	even	3	inner
144.6.i.b.97.2		6	1.1	even	1	trivial
162.6.a.i.1.2		3	36.11	even	6
162.6.a.j.1.2		3	36.7	odd	6
432.6.i.b.145.2		6	9.5	odd	6
432.6.i.b.289.2		6	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 144 = 2^{4} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	144.i (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.43381 + 15.3973i) q^{3} +(-20.8014 - 36.0292i) q^{5} +(-101.661 + 176.082i) q^{7} +(-231.153 + 74.9483i) q^{9} +O(q^{10})\)	\(q+(2.43381 + 15.3973i) q^{3} +(-20.8014 - 36.0292i) q^{5} +(-101.661 + 176.082i) q^{7} +(-231.153 + 74.9483i) q^{9} +(235.168 - 407.323i) q^{11} +(-241.506 - 418.300i) q^{13} +(504.125 - 407.974i) q^{15} +1259.86 q^{17} -1978.94 q^{19} +(-2958.60 - 1136.75i) q^{21} +(239.119 + 414.166i) q^{23} +(697.100 - 1207.41i) q^{25} +(-1716.58 - 3376.72i) q^{27} +(580.249 - 1005.02i) q^{29} +(-1186.50 - 2055.07i) q^{31} +(6844.02 + 2629.60i) q^{33} +8458.76 q^{35} +8185.10 q^{37} +(5852.91 - 4736.60i) q^{39} +(-8758.87 - 15170.8i) q^{41} +(11435.0 - 19806.1i) q^{43} +(7508.64 + 6769.22i) q^{45} +(-8685.43 + 15043.6i) q^{47} +(-12266.3 - 21245.9i) q^{49} +(3066.26 + 19398.4i) q^{51} -5390.58 q^{53} -19567.3 q^{55} +(-4816.38 - 30470.4i) q^{57} +(-22281.8 - 38593.2i) q^{59} +(-2084.17 + 3609.88i) q^{61} +(10302.2 - 48321.1i) q^{63} +(-10047.3 + 17402.5i) q^{65} +(1228.46 + 2127.76i) q^{67} +(-5795.07 + 4689.79i) q^{69} -2184.37 q^{71} +3037.34 q^{73} +(20287.5 + 7794.83i) q^{75} +(47814.7 + 82817.5i) q^{77} +(-25266.2 + 43762.3i) q^{79} +(47814.5 - 34649.1i) q^{81} +(-25913.9 + 44884.2i) q^{83} +(-26206.9 - 45391.7i) q^{85} +(16886.8 + 6488.23i) q^{87} -20154.7 q^{89} +98206.5 q^{91} +(28754.8 - 23270.5i) q^{93} +(41164.9 + 71299.6i) q^{95} +(-40214.4 + 69653.3i) q^{97} +(-23831.7 + 111779. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 9 q^{3} - 54 q^{5} + 132 q^{7} - 177 q^{9}+O(q^{10}) \) 6 * q - 9 * q^3 - 54 * q^5 + 132 * q^7 - 177 * q^9	\( 6 q - 9 q^{3} - 54 q^{5} + 132 q^{7} - 177 q^{9} + 315 q^{11} - 744 q^{13} - 2286 q^{15} + 2898 q^{17} - 2262 q^{19} - 11076 q^{21} + 3168 q^{23} - 2883 q^{25} - 18144 q^{27} - 5148 q^{29} + 8610 q^{31} + 17469 q^{33} - 2700 q^{35} + 39936 q^{37} + 49026 q^{39} + 5049 q^{41} + 31389 q^{43} + 2538 q^{45} - 12924 q^{47} - 52857 q^{49} - 36837 q^{51} - 96048 q^{53} - 126252 q^{55} - 17469 q^{57} - 62955 q^{59} - 75966 q^{61} - 49578 q^{63} + 108702 q^{65} + 32991 q^{67} - 29250 q^{69} + 129672 q^{71} - 8466 q^{73} + 105483 q^{75} + 88740 q^{77} - 89202 q^{79} + 123435 q^{81} - 32634 q^{83} + 71388 q^{85} + 151524 q^{87} + 66132 q^{89} + 301836 q^{91} + 57678 q^{93} + 82944 q^{95} + 46245 q^{97} - 282168 q^{99}+O(q^{100}) \) 6 * q - 9 * q^3 - 54 * q^5 + 132 * q^7 - 177 * q^9 + 315 * q^11 - 744 * q^13 - 2286 * q^15 + 2898 * q^17 - 2262 * q^19 - 11076 * q^21 + 3168 * q^23 - 2883 * q^25 - 18144 * q^27 - 5148 * q^29 + 8610 * q^31 + 17469 * q^33 - 2700 * q^35 + 39936 * q^37 + 49026 * q^39 + 5049 * q^41 + 31389 * q^43 + 2538 * q^45 - 12924 * q^47 - 52857 * q^49 - 36837 * q^51 - 96048 * q^53 - 126252 * q^55 - 17469 * q^57 - 62955 * q^59 - 75966 * q^61 - 49578 * q^63 + 108702 * q^65 + 32991 * q^67 - 29250 * q^69 + 129672 * q^71 - 8466 * q^73 + 105483 * q^75 + 88740 * q^77 - 89202 * q^79 + 123435 * q^81 - 32634 * q^83 + 71388 * q^85 + 151524 * q^87 + 66132 * q^89 + 301836 * q^91 + 57678 * q^93 + 82944 * q^95 + 46245 * q^97 - 282168 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more