LMFDB - Embedded newform 108.6.i.a.13.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [108,6,Mod(13,108)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(108, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 8]))

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

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

chi := DirichletCharacter("108.13");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 108 = 2^{2} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	108.i (of order $9$, degree $6$, 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:	$17.3214525398$
Analytic rank:	$0$
Dimension:	$90$
Relative dimension:	$15$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			13.6
Character	$\chi$	$=$	108.13
Dual form			108.6.i.a.25.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.93759 + 14.7858i) q^{3} +(-1.72634 - 1.44857i) q^{5} +(22.1444 + 8.05989i) q^{7} +(-194.240 - 146.012i) q^{9} +O(q^{10})$	\(q+(-4.93759 + 14.7858i) q^{3} +(-1.72634 - 1.44857i) q^{5} +(22.1444 + 8.05989i) q^{7} +(-194.240 - 146.012i) q^{9} +(-344.335 + 288.931i) q^{11} +(-134.905 + 765.083i) q^{13} +(29.9423 - 18.3729i) q^{15} +(1030.21 - 1784.37i) q^{17} +(-1026.25 - 1777.51i) q^{19} +(-228.512 + 287.626i) q^{21} +(-3211.06 + 1168.73i) q^{23} +(-541.769 - 3072.52i) q^{25} +(3117.99 - 2151.05i) q^{27} +(-828.537 - 4698.87i) q^{29} +(3658.82 - 1331.70i) q^{31} +(-2571.90 - 6517.89i) q^{33} +(-26.5534 - 45.9918i) q^{35} +(-3719.42 + 6442.23i) q^{37} +(-10646.3 - 5772.34i) q^{39} +(1794.85 - 10179.1i) q^{41} +(-8541.99 + 7167.58i) q^{43} +(123.816 + 533.439i) q^{45} +(-3222.13 - 1172.76i) q^{47} +(-12449.5 - 10446.4i) q^{49} +(21296.7 + 24043.0i) q^{51} -29567.7 q^{53} +1012.98 q^{55} +(31349.2 - 6397.28i) q^{57} +(-1055.53 - 885.698i) q^{59} +(23202.5 + 8445.03i) q^{61} +(-3124.49 - 4798.91i) q^{63} +(1341.17 - 1125.37i) q^{65} +(-9988.58 + 56648.1i) q^{67} +(-1425.74 - 53248.9i) q^{69} +(13632.6 - 23612.3i) q^{71} +(17105.2 + 29627.1i) q^{73} +(48104.8 + 7160.36i) q^{75} +(-9953.82 + 3622.89i) q^{77} +(6948.24 + 39405.4i) q^{79} +(16409.7 + 56723.1i) q^{81} +(-4329.71 - 24555.0i) q^{83} +(-4363.28 + 1588.11i) q^{85} +(73567.5 + 10950.5i) q^{87} +(-4003.50 - 6934.26i) q^{89} +(-9153.86 + 15854.9i) q^{91} +(1624.55 + 60674.0i) q^{93} +(-803.203 + 4555.19i) q^{95} +(-131553. + 110386. i) q^{97} +(109071. - 5844.96i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 90 q - 87 q^{5} + 330 q^{9}+O(q^{10}) $ 90 * q - 87 * q^5 + 330 * q^9	$ 90 q - 87 q^{5} + 330 q^{9} - 1257 q^{11} + 531 q^{15} - 3468 q^{17} + 12894 q^{21} + 8106 q^{23} + 4959 q^{25} - 17415 q^{27} + 3468 q^{29} - 6651 q^{31} + 33624 q^{33} - 8229 q^{35} - 10545 q^{39} + 68673 q^{41} + 9459 q^{43} - 53469 q^{45} - 57087 q^{47} - 5490 q^{49} + 42831 q^{51} - 4146 q^{53} + 24624 q^{57} + 5388 q^{59} + 70110 q^{61} - 98115 q^{63} - 172425 q^{65} - 15039 q^{67} + 251037 q^{69} + 67812 q^{71} - 27009 q^{73} - 75273 q^{75} + 23991 q^{77} - 216180 q^{79} + 177822 q^{81} - 76725 q^{83} - 53100 q^{85} - 201483 q^{87} - 98814 q^{89} - 90999 q^{91} + 21765 q^{93} - 143490 q^{95} - 71739 q^{97} + 13635 q^{99}+O(q^{100}) $ 90 * q - 87 * q^5 + 330 * q^9 - 1257 * q^11 + 531 * q^15 - 3468 * q^17 + 12894 * q^21 + 8106 * q^23 + 4959 * q^25 - 17415 * q^27 + 3468 * q^29 - 6651 * q^31 + 33624 * q^33 - 8229 * q^35 - 10545 * q^39 + 68673 * q^41 + 9459 * q^43 - 53469 * q^45 - 57087 * q^47 - 5490 * q^49 + 42831 * q^51 - 4146 * q^53 + 24624 * q^57 + 5388 * q^59 + 70110 * q^61 - 98115 * q^63 - 172425 * q^65 - 15039 * q^67 + 251037 * q^69 + 67812 * q^71 - 27009 * q^73 - 75273 * q^75 + 23991 * q^77 - 216180 * q^79 + 177822 * q^81 - 76725 * q^83 - 53100 * q^85 - 201483 * q^87 - 98814 * q^89 - 90999 * q^91 + 21765 * q^93 - 143490 * q^95 - 71739 * q^97 + 13635 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/108\mathbb{Z}\right)^\times$.

$n$	$29$	$55$
$\chi(n)$	$e\left(\frac{4}{9}\right)$	$1$

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
$3$	−4.93759	+	14.7858i	−0.316746	+	0.948510i
$3$	−4.93759	+	14.7858i	−0.316746	+	0.948510i
$4$		0			0
$5$	−1.72634	−	1.44857i	−0.0308817	−	0.0259128i	0.627216	−	0.778845i	$-0.284194\pi$
$5$	−1.72634	−	1.44857i	−0.0308817	−	0.0259128i	−0.658098	+	0.752932i	$0.728639\pi$
$6$		0			0
$7$	22.1444	+	8.05989i	0.170812	+	0.0621704i	0.426010	−	0.904718i	$-0.359919\pi$
$7$	22.1444	+	8.05989i	0.170812	+	0.0621704i	−0.255199	+	0.966889i	$0.582141\pi$
$8$		0			0
$9$	−194.240	−	146.012i	−0.799344	−	0.600874i
$10$		0			0
$11$	−344.335	+	288.931i	−0.858023	+	0.719967i	−0.961541	−	0.274661i	$-0.911434\pi$
$11$	−344.335	+	288.931i	−0.858023	+	0.719967i	0.103518	+	0.994628i	$0.466990\pi$
$12$		0			0
$13$	−134.905	+	765.083i	−0.221395	+	1.25560i	0.648062	+	0.761588i	$0.275580\pi$
$13$	−134.905	+	765.083i	−0.221395	+	1.25560i	−0.869457	+	0.494008i	$0.835531\pi$
$14$		0			0
$15$	29.9423	−	18.3729i	0.0343603	−	0.0210838i
$16$		0			0
$17$	1030.21	−	1784.37i	0.864575	−	1.49749i	−0.00289399	−	0.999996i	$-0.500921\pi$
$17$	1030.21	−	1784.37i	0.864575	−	1.49749i	0.867469	−	0.497492i	$-0.165745\pi$
$18$		0			0
$19$	−1026.25	−	1777.51i	−0.652181	−	1.12961i	−0.982592	−	0.185774i	$-0.940521\pi$
$19$	−1026.25	−	1777.51i	−0.652181	−	1.12961i	0.330411	−	0.943837i	$-0.392813\pi$
$20$		0			0
$21$	−228.512	+	287.626i	−0.113073	+	0.142325i
$22$		0			0
$23$	−3211.06	+	1168.73i	−1.26570	+	0.460676i	−0.885677	−	0.464303i	$-0.846305\pi$
$23$	−3211.06	+	1168.73i	−1.26570	+	0.460676i	−0.380019	+	0.924978i	$0.624083\pi$
$24$		0			0
$25$	−541.769	−	3072.52i	−0.173366	−	0.983207i
$26$		0			0
$27$	3117.99	−	2151.05i	0.823125	−	0.567861i
$28$		0			0
$29$	−828.537	−	4698.87i	−0.182943	−	1.03752i	−0.928569	−	0.371159i	$-0.878960\pi$
$29$	−828.537	−	4698.87i	−0.182943	−	1.03752i	0.745626	−	0.666365i	$-0.232151\pi$
$30$		0			0
$31$	3658.82	−	1331.70i	0.683812	−	0.248887i	0.0233287	−	0.999728i	$-0.492574\pi$
$31$	3658.82	−	1331.70i	0.683812	−	0.248887i	0.660484	+	0.750841i	$0.270351\pi$
$32$		0			0
$33$	−2571.90	−	6517.89i	−0.411120	−	1.04189i
$34$		0			0
$35$	−26.5534	−	45.9918i	−0.00366395	−	0.00634615i
$36$		0			0
$37$	−3719.42	+	6442.23i	−0.446654	+	0.773627i	−0.998166	−	0.0605397i	$-0.980718\pi$
$37$	−3719.42	+	6442.23i	−0.446654	+	0.773627i	0.551512	+	0.834167i	$0.314051\pi$
$38$		0			0
$39$	−10646.3	−	5772.34i	−1.12082	−	0.607701i
$40$		0			0
$41$	1794.85	−	10179.1i	0.166751	−	0.945694i	−0.780489	−	0.625170i	$-0.785030\pi$
$41$	1794.85	−	10179.1i	0.166751	−	0.945694i	0.947240	−	0.320524i	$-0.103859\pi$
$42$		0			0
$43$	−8541.99	+	7167.58i	−0.704511	+	0.591155i	−0.923053	−	0.384672i	$-0.874314\pi$
$43$	−8541.99	+	7167.58i	−0.704511	+	0.591155i	0.218542	+	0.975828i	$0.429870\pi$
$44$		0			0
$45$	123.816	+	533.439i	0.00911475	+	0.0392693i
$46$		0			0
$47$	−3222.13	−	1172.76i	−0.212764	−	0.0774399i	0.233439	−	0.972371i	$-0.425002\pi$
$47$	−3222.13	−	1172.76i	−0.212764	−	0.0774399i	−0.446204	+	0.894931i	$0.647224\pi$
$48$		0			0
$49$	−12449.5	−	10446.4i	−0.740733	−	0.621549i
$50$		0			0
$51$	21296.7	+	24043.0i	1.14653	+	1.29438i
$52$		0			0
$53$	−29567.7			−1.44586			−0.722932	−	0.690920i	$-0.757206\pi$
$53$	−29567.7			−1.44586			−0.722932	+	0.690920i	$0.757206\pi$
$54$		0			0
$55$	1012.98			0.0451536
$56$		0			0
$57$	31349.2	−	6397.28i	1.27802	−	0.260800i
$58$		0			0
$59$	−1055.53	−	885.698i	−0.0394768	−	0.0331250i	0.622836	−	0.782353i	$-0.285980\pi$
$59$	−1055.53	−	885.698i	−0.0394768	−	0.0331250i	−0.662313	+	0.749228i	$0.730425\pi$
$60$		0			0
$61$	23202.5	+	8445.03i	0.798382	+	0.290587i	0.708816	−	0.705394i	$-0.249230\pi$
$61$	23202.5	+	8445.03i	0.798382	+	0.290587i	0.0895660	+	0.995981i	$0.471452\pi$
$62$		0			0
$63$	−3124.49	−	4798.91i	−0.0991807	−	0.152332i
$64$		0			0
$65$	1341.17	−	1125.37i	0.0393732	−	0.0330380i
$66$		0			0
$67$	−9988.58	+	56648.1i	−0.271842	+	1.54169i	0.476975	+	0.878917i	$0.341733\pi$
$67$	−9988.58	+	56648.1i	−0.271842	+	1.54169i	−0.748817	+	0.662777i	$0.769378\pi$
$68$		0			0
$69$	−1425.74	−	53248.9i	−0.0360510	−	1.34644i
$70$		0			0
$71$	13632.6	−	23612.3i	0.320946	−	0.555894i	−0.659738	−	0.751496i	$-0.729333\pi$
$71$	13632.6	−	23612.3i	0.320946	−	0.555894i	0.980683	+	0.195602i	$0.0626660\pi$
$72$		0			0
$73$	17105.2	+	29627.1i	0.375683	+	0.650701i	0.990429	−	0.138024i	$-0.0440750\pi$
$73$	17105.2	+	29627.1i	0.375683	+	0.650701i	−0.614746	+	0.788725i	$0.710742\pi$
$74$		0			0
$75$	48104.8	+	7160.36i	0.987495	+	0.146988i
$76$		0			0
$77$	−9953.82	+	3622.89i	−0.191321	+	0.0696352i
$78$		0			0
$79$	6948.24	+	39405.4i	0.125258	+	0.710376i	0.981154	+	0.193227i	$0.0618955\pi$
$79$	6948.24	+	39405.4i	0.125258	+	0.710376i	−0.855896	+	0.517149i	$0.826993\pi$
$80$		0			0
$81$	16409.7	+	56723.1i	0.277900	+	0.960610i
$82$		0			0
$83$	−4329.71	−	24555.0i	−0.0689864	−	0.391242i	−0.999677	−	0.0254329i	$-0.991904\pi$
$83$	−4329.71	−	24555.0i	−0.0689864	−	0.391242i	0.930690	−	0.365809i	$-0.119208\pi$
$84$		0			0
$85$	−4363.28	+	1588.11i	−0.0655037	+	0.0238414i
$86$		0			0
$87$	73567.5	+	10950.5i	1.04205	+	0.155108i
$88$		0			0
$89$	−4003.50	−	6934.26i	−0.0535753	−	0.0927952i	0.837994	−	0.545679i	$-0.183728\pi$
$89$	−4003.50	−	6934.26i	−0.0535753	−	0.0927952i	−0.891569	+	0.452884i	$0.850395\pi$
$90$		0			0
$91$	−9153.86	+	15854.9i	−0.115878	+	0.200706i
$92$		0			0
$93$	1624.55	+	60674.0i	0.0194771	+	0.727437i
$94$		0			0
$95$	−803.203	+	4555.19i	−0.00913096	+	0.0517842i
$96$		0			0
$97$	−131553.	+	110386.i	−1.41962	+	1.19120i	−0.468074	+	0.883689i	$0.655052\pi$
$97$	−131553.	+	110386.i	−1.41962	+	1.19120i	−0.951544	+	0.307512i	$0.900503\pi$
$98$		0			0
$99$	109071.	−	5844.96i	1.11846	−	0.0599368i
$100$		0			0
$101$	−71568.2	−	26048.7i	−0.698098	−	0.254087i	−0.0314995	−	0.999504i	$-0.510028\pi$
$101$	−71568.2	−	26048.7i	−0.698098	−	0.254087i	−0.666599	+	0.745417i	$0.732250\pi$
$102$		0			0
$103$	142841.	+	119858.i	1.32666	+	1.11320i	0.984846	+	0.173434i	$0.0554863\pi$
$103$	142841.	+	119858.i	1.32666	+	1.11320i	0.341816	+	0.939767i	$0.388958\pi$
$104$		0			0
$105$	811.136	−	165.525i	0.00717993	−	0.00146518i
$106$		0			0
$107$	−106085.			−0.895769			−0.447885	−	0.894091i	$-0.647822\pi$
$107$	−106085.			−0.895769			−0.447885	+	0.894091i	$0.647822\pi$
$108$		0			0
$109$	−102126.			−0.823324			−0.411662	−	0.911337i	$-0.635052\pi$
$109$	−102126.			−0.823324			−0.411662	+	0.911337i	$0.635052\pi$
$110$		0			0
$111$	−76888.6	−	86803.7i	−0.592318	−	0.668700i
$112$		0			0
$113$	−95902.2	−	80471.5i	−0.706533	−	0.592852i	0.217091	−	0.976151i	$-0.430343\pi$
$113$	−95902.2	−	80471.5i	−0.706533	−	0.592852i	−0.923624	+	0.383300i	$0.874788\pi$
$114$		0			0
$115$	7236.39	+	2633.83i	0.0510243	+	0.0185713i
$116$		0			0
$117$	137916.	−	128912.i	0.931427	−	0.870622i
$118$		0			0
$119$	37195.1	−	31210.4i	0.240779	−	0.202038i
$120$		0			0
$121$	7118.95	−	40373.5i	0.0442031	−	0.250688i
$122$		0			0
$123$	141644.	+	76798.6i	0.844182	+	0.457710i
$124$		0			0
$125$	−7036.71	+	12187.9i	−0.0402805	+	0.0697678i
$126$		0			0
$127$	−4465.45	−	7734.39i	−0.0245672	−	0.0425517i	0.853480	−	0.521125i	$-0.174487\pi$
$127$	−4465.45	−	7734.39i	−0.0245672	−	0.0425517i	−0.878048	+	0.478573i	$0.841154\pi$
$128$		0			0
$129$	−63801.7	−	161691.i	−0.337565	−	0.855483i
$130$		0			0
$131$	38473.1	−	14003.1i	0.195875	−	0.0712926i	−0.242220	−	0.970221i	$-0.577876\pi$
$131$	38473.1	−	14003.1i	0.195875	−	0.0712926i	0.438095	+	0.898929i	$0.355653\pi$
$132$		0			0
$133$	−8399.04	−	47633.3i	−0.0411719	−	0.233497i
$134$		0			0
$135$	−8498.68	−	803.184i	−0.0401344	−	0.00379298i
$136$		0			0
$137$	−67046.5	−	380240.i	−0.305193	−	1.73084i	−0.622594	−	0.782545i	$-0.713921\pi$
$137$	−67046.5	−	380240.i	−0.305193	−	1.73084i	0.317401	−	0.948292i	$-0.397190\pi$
$138$		0			0
$139$	−164921.	+	60026.3i	−0.724001	+	0.263515i	−0.677623	−	0.735409i	$-0.736990\pi$
$139$	−164921.	+	60026.3i	−0.724001	+	0.263515i	−0.0463775	+	0.998924i	$0.514768\pi$
$140$		0			0
$141$	33249.8	−	41851.3i	0.140845	−	0.177280i
$142$		0			0
$143$	−174604.	−	302423.i	−0.714025	−	1.23673i
$144$		0			0
$145$	−5376.31	+	9312.04i	−0.0212356	+	0.0367811i
$146$		0			0
$147$	215929.	−	132496.i	0.824170	−	0.505720i
$148$		0			0
$149$	−21734.4	+	123262.i	−0.0802014	+	0.454844i	0.918088	+	0.396377i	$0.129733\pi$
$149$	−21734.4	+	123262.i	−0.0802014	+	0.454844i	−0.998289	+	0.0584677i	$0.981379\pi$
$150$		0			0
$151$	−32463.9	+	27240.4i	−0.115867	+	0.0972236i	−0.698880	−	0.715239i	$-0.746318\pi$
$151$	−32463.9	+	27240.4i	−0.115867	+	0.0972236i	0.583014	+	0.812462i	$0.301873\pi$
$152$		0			0
$153$	−460649.	+	196174.i	−1.59089	+	0.677506i
$154$		0			0
$155$	−8245.44	−	3001.09i	−0.0275667	−	0.0100335i
$156$		0			0
$157$	5716.09	+	4796.37i	0.0185076	+	0.0155297i	0.651995	−	0.758224i	$-0.273933\pi$
$157$	5716.09	+	4796.37i	0.0185076	+	0.0155297i	−0.633487	+	0.773753i	$0.718377\pi$
$158$		0			0
$159$	145993.	−	437182.i	0.457972	−	1.37142i
$160$		0			0
$161$	−80526.8			−0.244836
$162$		0			0
$163$	107065.			0.315630			0.157815	−	0.987469i	$-0.449555\pi$
$163$	107065.			0.315630			0.157815	+	0.987469i	$0.449555\pi$
$164$		0			0
$165$	−5001.66	+	14977.7i	−0.0143022	+	0.0428287i
$166$		0			0
$167$	307666.	+	258162.i	0.853667	+	0.716312i	0.960594	−	0.277955i	$-0.0896567\pi$
$167$	307666.	+	258162.i	0.853667	+	0.716312i	−0.106927	+	0.994267i	$0.534101\pi$
$168$		0			0
$169$	−218251.	−	79436.9i	−0.587813	−	0.213947i
$170$		0			0
$171$	−60200.3	+	495110.i	−0.157437	+	1.29483i
$172$		0			0
$173$	75076.8	−	62996.9i	0.190717	−	0.160031i	−0.542429	−	0.840102i	$-0.682495\pi$
$173$	75076.8	−	62996.9i	0.190717	−	0.160031i	0.733147	+	0.680071i	$0.238051\pi$
$174$		0			0
$175$	12767.1	−	72405.6i	0.0315134	−	0.178722i
$176$		0			0
$177$	18307.5	−	11233.7i	0.0439235	−	0.0269519i
$178$		0			0
$179$	−315185.	+	545916.i	−0.735246	+	1.27348i	0.219370	+	0.975642i	$0.429600\pi$
$179$	−315185.	+	545916.i	−0.735246	+	1.27348i	−0.954616	+	0.297841i	$0.903733\pi$
$180$		0			0
$181$	−362286.	−	627497.i	−0.821968	−	1.42369i	−0.904215	−	0.427078i	$-0.859543\pi$
$181$	−362286.	−	627497.i	−0.821968	−	1.42369i	0.0822473	−	0.996612i	$-0.473790\pi$
$182$		0			0
$183$	−239431.	+	301370.i	−0.528509	+	0.665231i
$184$		0			0
$185$	15753.0	−	5733.63i	0.0338403	−	0.0123169i
$186$		0			0
$187$	160824.	+	912080.i	0.336316	+	1.90734i
$188$		0			0
$189$	86383.2	−	22503.0i	0.175904	−	0.0458233i
$190$		0			0
$191$	35979.1	+	204047.i	0.0713619	+	0.404713i	0.999475	+	0.0324139i	$0.0103195\pi$
$191$	35979.1	+	204047.i	0.0713619	+	0.404713i	−0.928113	+	0.372300i	$0.878569\pi$
$192$		0			0
$193$	842965.	−	306814.i	1.62898	−	0.592901i	0.643918	−	0.765094i	$-0.277308\pi$
$193$	842965.	−	306814.i	1.62898	−	0.592901i	0.985063	+	0.172194i	$0.0550855\pi$
$194$		0			0
$195$	10017.4	+	25386.9i	0.0188656	+	0.0478105i
$196$		0			0
$197$	−35511.0	−	61506.8i	−0.0651924	−	0.112917i	0.831587	−	0.555395i	$-0.187433\pi$
$197$	−35511.0	−	61506.8i	−0.0651924	−	0.112917i	−0.896779	+	0.442478i	$0.854099\pi$
$198$		0			0
$199$	274639.	−	475688.i	0.491620	−	0.851510i	−0.508334	−	0.861160i	$-0.669738\pi$
$199$	274639.	−	475688.i	0.491620	−	0.851510i	0.999953	+	0.00964980i	$0.00307168\pi$
$200$		0			0
$201$	−788268.	−	427394.i	−1.37621	−	0.746171i
$202$		0			0
$203$	19524.9	−	110731.i	0.0332544	−	0.188595i
$204$		0			0
$205$	−17843.7	+	14972.7i	−0.0296552	+	0.0248837i
$206$		0			0
$207$	794368.	+	241840.i	1.28853	+	0.392286i
$208$		0			0
$209$	866951.	+	315545.i	1.37287	+	0.499683i
$210$		0			0
$211$	356558.	+	299188.i	0.551345	+	0.462634i	0.875396	−	0.483406i	$-0.160600\pi$
$211$	356558.	+	299188.i	0.551345	+	0.462634i	−0.324051	+	0.946040i	$0.605045\pi$
$212$		0			0
$213$	281815.	+	318156.i	0.425613	+	0.480498i
$214$		0			0
$215$	25129.2			0.0370750
$216$		0			0
$217$	91755.6			0.132277
$218$		0			0
$219$	−522519.	+	106628.i	−0.736193	+	0.150232i
$220$		0			0
$221$	1.22621e6	+	1.02891e6i	1.68883	+	1.41709i
$222$		0			0
$223$	−897497.	−	326662.i	−1.20857	−	0.439883i	−0.342361	−	0.939568i	$-0.611227\pi$
$223$	−897497.	−	326662.i	−1.20857	−	0.439883i	−0.866207	+	0.499686i	$0.833449\pi$
$224$		0			0
$225$	−343393.	+	675913.i	−0.452205	+	0.890092i
$226$		0			0
$227$	793520.	−	665843.i	1.02210	−	0.857644i	0.0322101	−	0.999481i	$-0.489745\pi$
$227$	793520.	−	665843.i	1.02210	−	0.857644i	0.989890	+	0.141837i	$0.0453010\pi$
$228$		0			0
$229$	−68621.9	+	389174.i	−0.0864717	+	0.490405i	0.910558	+	0.413382i	$0.135653\pi$
$229$	−68621.9	+	389174.i	−0.0864717	+	0.490405i	−0.997029	+	0.0770231i	$0.975458\pi$
$230$		0			0
$231$	−4419.58	−	165064.i	−0.00544943	−	0.203527i
$232$		0			0
$233$	−94879.5	+	164336.i	−0.114494	+	0.198309i	−0.917577	−	0.397557i	$-0.869858\pi$
$233$	−94879.5	+	164336.i	−0.114494	+	0.198309i	0.803083	+	0.595867i	$0.203191\pi$
$234$		0			0
$235$	3863.67	+	6692.08i	0.00456384	+	0.00790481i
$236$		0			0
$237$	−616949.	−	91832.3i	−0.713474	−	0.106200i
$238$		0			0
$239$	−527506.	+	191997.i	−0.597356	+	0.217420i	−0.622962	−	0.782252i	$-0.714071\pi$
$239$	−527506.	+	191997.i	−0.597356	+	0.217420i	0.0256059	+	0.999672i	$0.491848\pi$
$240$		0			0
$241$	−117928.	−	668804.i	−0.130790	−	0.741747i	−0.977699	−	0.210010i	$-0.932650\pi$
$241$	−117928.	−	668804.i	−0.130790	−	0.741747i	0.846909	−	0.531738i	$-0.178461\pi$
$242$		0			0
$243$	−919721.	−	37444.0i	−0.999172	−	0.0406786i
$244$		0			0
$245$	6359.76	+	36068.0i	0.00676902	+	0.0383890i
$246$		0			0
$247$	1.49839e6	−	545370.i	1.56273	−	0.568786i
$248$		0			0
$249$	384444.	+	57224.2i	0.392948	+	0.0584900i
$250$		0			0
$251$	490804.	+	850097.i	0.491727	+	0.851695i	0.999955	−	0.00952707i	$-0.00303261\pi$
$251$	490804.	+	850097.i	0.491727	+	0.851695i	−0.508228	+	0.861223i	$0.669699\pi$
$252$		0			0
$253$	767997.	−	1.33021e6i	0.754325	−	1.30653i
$254$		0			0
$255$	−1937.34	−	72356.1i	−0.00186575	−	0.0696826i
$256$		0			0
$257$	−348743.	+	1.97782e6i	−0.329362	+	1.86790i	0.147699	+	0.989032i	$0.452813\pi$
$257$	−348743.	+	1.97782e6i	−0.329362	+	1.86790i	−0.477061	+	0.878870i	$0.658298\pi$
$258$		0			0
$259$	−134288.	+	112681.i	−0.124391	+	0.104376i
$260$		0			0
$261$	−525158.	+	1.03369e6i	−0.477187	+	0.939264i
$262$		0			0
$263$	−1.28969e6	−	469407.i	−1.14973	−	0.418466i	−0.304309	−	0.952573i	$-0.598426\pi$
$263$	−1.28969e6	−	469407.i	−1.14973	−	0.418466i	−0.845417	+	0.534107i	$0.820648\pi$
$264$		0			0
$265$	51043.9	+	42830.9i	0.0446508	+	0.0374664i
$266$		0			0
$267$	122296.	−	24956.5i	0.104987	−	0.0214242i
$268$		0			0
$269$	−1.42935e6			−1.20436			−0.602182	−	0.798359i	$-0.705702\pi$
$269$	−1.42935e6			−1.20436			−0.602182	+	0.798359i	$0.705702\pi$
$270$		0			0
$271$	−1.81679e6			−1.50274			−0.751368	−	0.659884i	$-0.770606\pi$
$271$	−1.81679e6			−1.50274			−0.751368	+	0.659884i	$0.770606\pi$
$272$		0			0
$273$	−189230.	−	213632.i	−0.153668	−	0.173484i
$274$		0			0
$275$	1.07430e6	+	901442.i	0.856628	+	0.718797i
$276$		0			0
$277$	805433.	+	293154.i	0.630710	+	0.229560i	0.637541	−	0.770417i	$-0.279952\pi$
$277$	805433.	+	293154.i	0.630710	+	0.229560i	−0.00683002	+	0.999977i	$0.502174\pi$
$278$		0			0
$279$	−905136.	−	275563.i	−0.696151	−	0.211939i
$280$		0			0
$281$	927555.	−	778311.i	0.700768	−	0.588014i	−0.221224	−	0.975223i	$-0.571005\pi$
$281$	927555.	−	778311.i	0.700768	−	0.588014i	0.921992	+	0.387209i	$0.126561\pi$
$282$		0			0
$283$	88901.8	−	504187.i	0.0659849	−	0.374219i	−0.933877	−	0.357595i	$-0.883597\pi$
$283$	88901.8	−	504187.i	0.0659849	−	0.374219i	0.999862	−	0.0166243i	$-0.00529191\pi$
$284$		0			0
$285$	−63386.3	−	34367.7i	−0.0462257	−	0.0250633i
$286$		0			0
$287$	121788.	−	210944.i	0.0872773	−	0.151169i
$288$		0			0
$289$	−1.41273e6	−	2.44692e6i	−0.994979	−	1.72335i
$290$		0			0
$291$	−982594.	−	2.49016e6i	−0.680208	−	1.72383i
$292$		0			0
$293$	2.73115e6	−	994057.i	1.85856	−	0.676460i	0.878504	−	0.477735i	$-0.158542\pi$
$293$	2.73115e6	−	994057.i	1.85856	−	0.676460i	0.980055	−	0.198725i	$-0.0636802\pi$
$294$		0			0
$295$	539.214	+	3058.03i	0.000360750	+	0.00204591i
$296$		0			0
$297$	−452126.	+	1.64157e6i	−0.297419	+	1.07986i
$298$		0			0
$299$	−460989.	−	2.61440e6i	−0.298203	−	1.69119i
$300$		0			0
$301$	−246927.	+	89874.0i	−0.157091	+	0.0571765i
$302$		0			0
$303$	738525.	−	929576.i	0.462124	−	0.581672i
$304$		0			0
$305$	−27822.2	−	48189.5i	−0.0171255	−	0.0296622i
$306$		0			0
$307$	689459.	−	1.19418e6i	0.417506	−	0.723142i	−0.578182	−	0.815908i	$-0.696238\pi$
$307$	689459.	−	1.19418e6i	0.417506	−	0.723142i	0.995688	+	0.0927663i	$0.0295710\pi$
$308$		0			0
$309$	−2.47749e6	+	1.52021e6i	−1.47610	+	0.905749i
$310$		0			0
$311$	111820.	−	634160.i	0.0655566	−	0.371790i	−0.934325	−	0.356422i	$-0.883997\pi$
$311$	111820.	−	634160.i	0.0655566	−	0.371790i	0.999882	−	0.0153687i	$-0.00489219\pi$
$312$		0			0
$313$	−2.10595e6	+	1.76710e6i	−1.21503	+	1.01953i	−0.215960	+	0.976402i	$0.569288\pi$
$313$	−2.10595e6	+	1.76710e6i	−1.21503	+	1.01953i	−0.999070	+	0.0431291i	$0.986267\pi$
$314$		0			0
$315$	−1557.64	+	12810.6i	−0.000884483	+	0.00727433i
$316$		0			0
$317$	2.23869e6	+	814817.i	1.25126	+	0.455420i	0.880826	−	0.473441i	$-0.156988\pi$
$317$	2.23869e6	+	814817.i	1.25126	+	0.455420i	0.370430	+	0.928861i	$0.379210\pi$
$318$		0			0
$319$	1.64294e6	+	1.37859e6i	0.903952	+	0.758506i
$320$		0			0
$321$	523806.	−	1.56856e6i	0.283732	−	0.849646i
$322$		0			0
$323$	−4.22900e6			−2.25544
$324$		0			0
$325$	2.42382e6			1.27289
$326$		0			0
$327$	504257.	−	1.51002e6i	0.260785	−	0.780932i
$328$		0			0
$329$	−61899.8	−	51940.1i	−0.0315282	−	0.0264553i
$330$		0			0
$331$	−1.14824e6	−	417925.i	−0.576053	−	0.209666i	0.0375313	−	0.999295i	$-0.488051\pi$
$331$	−1.14824e6	−	417925.i	−0.576053	−	0.209666i	−0.613584	+	0.789629i	$0.710273\pi$
$332$		0			0
$333$	1.66311e6	−	708260.i	0.821883	−	0.350011i
$334$		0			0
$335$	99302.5	−	83324.7i	0.0483446	−	0.0405660i
$336$		0			0
$337$	566168.	−	3.21090e6i	0.271563	−	1.54011i	−0.478109	−	0.878301i	$-0.658678\pi$
$337$	566168.	−	3.21090e6i	0.271563	−	1.54011i	0.749672	−	0.661810i	$-0.230211\pi$
$338$		0			0
$339$	1.66336e6	−	1.02066e6i	0.786117	−	0.482370i
$340$		0			0
$341$	−875088.	+	1.51570e6i	−0.407536	+	0.705873i
$342$		0			0
$343$	−389522.	−	674673.i	−0.178771	−	0.309641i
$344$		0			0
$345$	−74673.6	+	93991.1i	−0.0337769	+	0.0425147i
$346$		0			0
$347$	−3.06226e6	+	1.11457e6i	−1.36527	+	0.496918i	−0.917680	−	0.397321i	$-0.869940\pi$
$347$	−3.06226e6	+	1.11457e6i	−1.36527	+	0.496918i	−0.447590	+	0.894239i	$0.647718\pi$
$348$		0			0
$349$	188281.	+	1.06779e6i	0.0827452	+	0.469271i	0.997820	+	0.0659882i	$0.0210200\pi$
$349$	188281.	+	1.06779e6i	0.0827452	+	0.469271i	−0.915075	+	0.403283i	$0.867869\pi$
$350$		0			0
$351$	1.22510e6	+	2.67571e6i	0.530768	+	1.15923i
$352$		0			0
$353$	166397.	+	943683.i	0.0710736	+	0.403078i	0.999502	+	0.0315661i	$0.0100495\pi$
$353$	166397.	+	943683.i	0.0710736	+	0.403078i	−0.928428	+	0.371512i	$0.878839\pi$
$354$		0			0
$355$	−57738.5	+	21015.1i	−0.0243162	+	0.00885036i
$356$		0			0
$357$	277817.	+	704064.i	0.115369	+	0.292376i
$358$		0			0
$359$	−1.70689e6	−	2.95642e6i	−0.698987	−	1.21068i	−0.968818	−	0.247773i	$-0.920301\pi$
$359$	−1.70689e6	−	2.95642e6i	−0.698987	−	1.21068i	0.269831	−	0.962908i	$-0.413032\pi$
$360$		0			0
$361$	−868321.	+	1.50398e6i	−0.350681	+	0.607397i
$362$		0			0
$363$	561805.	+	304607.i	0.223779	+	0.121332i
$364$		0			0
$365$	13387.5	−	75924.6i	0.00525980	−	0.0298298i
$366$		0			0
$367$	−3.65292e6	+	3.06517e6i	−1.41571	+	1.18793i	−0.462125	+	0.886815i	$0.652913\pi$
$367$	−3.65292e6	+	3.06517e6i	−1.41571	+	1.18793i	−0.953589	+	0.301110i	$0.902643\pi$
$368$		0			0
$369$	−1.83491e6	+	1.71513e6i	−0.701535	+	0.655738i
$370$		0			0
$371$	−654757.	−	238312.i	−0.246971	−	0.0898899i
$372$		0			0
$373$	2.89694e6	+	2.43083e6i	1.07812	+	0.904652i	0.995764	−	0.0919504i	$-0.0293101\pi$
$373$	2.89694e6	+	2.43083e6i	1.07812	+	0.904652i	0.0823590	+	0.996603i	$0.473755\pi$
$374$		0			0
$375$	−145464.	−	164222.i	−0.0534168	−	0.0603052i
$376$		0			0
$377$	3.70680e6			1.34321
$378$		0			0
$379$	−544357.			−0.194664			−0.0973321	−	0.995252i	$-0.531031\pi$
$379$	−544357.			−0.194664			−0.0973321	+	0.995252i	$0.531031\pi$
$380$		0			0
$381$	136408.	−	27836.1i	0.0481423	−	0.00982418i
$382$		0			0
$383$	2.43672e6	+	2.04465e6i	0.848807	+	0.712233i	0.959526	−	0.281618i	$-0.0908712\pi$
$383$	2.43672e6	+	2.04465e6i	0.848807	+	0.712233i	−0.110720	+	0.993852i	$0.535316\pi$
$384$		0			0
$385$	22431.7	+	8164.47i	0.00771277	+	0.00280722i
$386$		0			0
$387$	2.70576e6	−	144997.i	0.918357	−	0.0492133i
$388$		0			0
$389$	2.41786e6	−	2.02883e6i	0.810136	−	0.679785i	−0.140504	−	0.990080i	$-0.544872\pi$
$389$	2.41786e6	−	2.02883e6i	0.810136	−	0.679785i	0.950640	+	0.310295i	$0.100428\pi$
$390$		0			0
$391$	−1.22261e6	+	6.93377e6i	−0.404433	+	2.29365i
$392$		0			0
$393$	17082.4	+	637997.i	0.00557913	+	0.208371i
$394$		0			0
$395$	45086.6	−	78092.2i	0.0145397	−	0.0251834i
$396$		0			0
$397$	−499021.	−	864329.i	−0.158907	−	0.275235i	0.775568	−	0.631264i	$-0.217464\pi$
$397$	−499021.	−	864329.i	−0.158907	−	0.275235i	−0.934475	+	0.356030i	$0.884130\pi$
$398$		0			0
$399$	745769.	+	111007.i	0.234516	+	0.0349075i
$400$		0			0
$401$	−2.83690e6	+	1.03255e6i	−0.881013	+	0.320663i	−0.742619	−	0.669714i	$-0.766416\pi$
$401$	−2.83690e6	+	1.03255e6i	−0.881013	+	0.320663i	−0.138395	+	0.990377i	$0.544194\pi$
$402$		0			0
$403$	525270.	+	2.97895e6i	0.161109	+	0.913695i
$404$		0			0
$405$	53838.7	−	121694.i	0.0163101	−	0.0368665i
$406$		0			0
$407$	−580634.	−	3.29294e6i	−0.173747	−	0.985366i
$408$		0			0
$409$	1.50413e6	−	547457.i	0.444606	−	0.161824i	−0.110008	−	0.993931i	$-0.535088\pi$
$409$	1.50413e6	−	547457.i	0.444606	−	0.161824i	0.554615	+	0.832107i	$0.312866\pi$
$410$		0			0
$411$	5.95320e6	+	886129.i	1.73839	+	0.258757i
$412$		0			0
$413$	−16235.5	−	28120.7i	−0.00468371	−	0.00811242i
$414$		0			0
$415$	−28095.2	+	48662.2i	−0.00800776	+	0.0138699i
$416$		0			0
$417$	−73226.4	−	2.73488e6i	−0.0206218	−	0.770189i
$418$		0			0
$419$	245348.	−	1.39144e6i	0.0682728	−	0.387194i	−0.931455	−	0.363857i	$-0.881460\pi$
$419$	245348.	−	1.39144e6i	0.0682728	−	0.387194i	0.999728	−	0.0233374i	$-0.00742920\pi$
$420$		0			0
$421$	2.71600e6	−	2.27900e6i	0.746836	−	0.626669i	−0.187828	−	0.982202i	$-0.560145\pi$
$421$	2.71600e6	−	2.27900e6i	0.746836	−	0.626669i	0.934664	+	0.355532i	$0.115700\pi$
$422$		0			0
$423$	454631.	+	698269.i	0.123540	+	0.189746i
$424$		0			0
$425$	−6.04066e6	−	2.19862e6i	−1.62223	−	0.590443i
$426$		0			0
$427$	445739.	+	374019.i	0.118307	+	0.0992714i
$428$		0			0
$429$	5.33368e6	−	1.08842e6i	1.39921	−	0.285531i
$430$		0			0
$431$	−5.23153e6			−1.35655			−0.678275	−	0.734808i	$-0.737272\pi$
$431$	−5.23153e6			−1.35655			−0.678275	+	0.734808i	$0.737272\pi$
$432$		0			0
$433$	−5.49690e6			−1.40896			−0.704479	−	0.709724i	$-0.748819\pi$
$433$	−5.49690e6			−1.40896			−0.704479	+	0.709724i	$0.748819\pi$
$434$		0			0
$435$	−111140.	−	125472.i	−0.0281610	−	0.0317925i
$436$		0			0
$437$	5.37279e6	+	4.50830e6i	1.34585	+	1.12930i
$438$		0			0
$439$	4.03723e6	+	1.46943e6i	0.999820	+	0.363905i	0.789515	−	0.613731i	$-0.210332\pi$
$439$	4.03723e6	+	1.46943e6i	0.999820	+	0.363905i	0.210305	+	0.977636i	$0.432554\pi$
$440$		0			0
$441$	892896.	+	3.84689e6i	0.218627	+	0.941918i
$442$		0			0
$443$	−50413.4	+	42301.8i	−0.0122050	+	0.0102412i	−0.648870	−	0.760900i	$-0.724758\pi$
$443$	−50413.4	+	42301.8i	−0.0122050	+	0.0102412i	0.636665	+	0.771141i	$0.280314\pi$
$444$		0			0
$445$	−3133.38	+	17770.3i	−0.000750089	+	0.00425396i
$446$		0			0
$447$	−1.71521e6	−	929977.i	−0.406021	−	0.220142i
$448$		0			0
$449$	−539666.	+	934729.i	−0.126331	+	0.218811i	−0.922252	−	0.386588i	$-0.873653\pi$
$449$	−539666.	+	934729.i	−0.126331	+	0.218811i	0.795922	+	0.605400i	$0.206987\pi$
$450$		0			0
$451$	2.32303e6	+	4.02361e6i	0.537792	+	0.931482i
$452$		0			0
$453$	−242479.	−	614507.i	−0.0555173	−	0.140696i
$454$		0			0
$455$	38769.7	−	14111.0i	0.00877939	−	0.00319544i
$456$		0			0
$457$	101240.	+	574162.i	0.0226758	+	0.128601i	0.994044	−	0.108977i	$-0.0347576\pi$
$457$	101240.	+	574162.i	0.0226758	+	0.128601i	−0.971368	+	0.237578i	$0.923646\pi$
$458$		0			0
$459$	−626101.	−	7.77969e6i	−0.138712	−	1.72358i
$460$		0			0
$461$	−450174.	−	2.55306e6i	−0.0986571	−	0.559512i	−0.993565	−	0.113262i	$-0.963870\pi$
$461$	−450174.	−	2.55306e6i	−0.0986571	−	0.559512i	0.894908	−	0.446250i	$-0.147241\pi$
$462$		0			0
$463$	540890.	−	196868.i	0.117262	−	0.0426798i	−0.282723	−	0.959202i	$-0.591238\pi$
$463$	540890.	−	196868.i	0.117262	−	0.0426798i	0.399985	+	0.916522i	$0.369015\pi$
$464$		0			0
$465$	85086.2	−	107097.i	0.0182485	−	0.0229692i
$466$		0			0
$467$	−1.89590e6	−	3.28380e6i	−0.402276	−	0.696762i	0.591724	−	0.806140i	$-0.298447\pi$
$467$	−1.89590e6	−	3.28380e6i	−0.402276	−	0.696762i	−0.994000	+	0.109378i	$0.965114\pi$
$468$		0			0
$469$	−677768.	+	1.17393e6i	−0.142282	+	0.246439i
$470$		0			0
$471$	−99141.9	+	60834.5i	−0.0205923	+	0.0126357i
$472$		0			0
$473$	870366.	−	4.93609e6i	0.178875	−	1.01445i
$474$		0			0
$475$	−4.90546e6	+	4.11617e6i	−0.997576	+	0.837066i
$476$		0			0
$477$	5.74324e6	+	4.31725e6i	1.15574	+	0.868782i
$478$		0			0
$479$	2.24322e6	+	816464.i	0.446717	+	0.162592i	0.555576	−	0.831465i	$-0.312498\pi$
$479$	2.24322e6	+	816464.i	0.446717	+	0.162592i	−0.108860	+	0.994057i	$0.534720\pi$
$480$		0			0
$481$	−4.42707e6	−	3.71475e6i	−0.872476	−	0.732095i
$482$		0			0
$483$	397608.	−	1.19065e6i	0.0775510	−	0.232230i
$484$		0			0
$485$	387008.			0.0747077
$486$		0			0
$487$	2.74296e6			0.524080			0.262040	−	0.965057i	$-0.415605\pi$
$487$	2.74296e6			0.524080			0.262040	+	0.965057i	$0.415605\pi$
$488$		0			0
$489$	−528642.	+	1.58304e6i	−0.0999747	+	0.299378i
$490$		0			0
$491$	−5.34164e6	−	4.48216e6i	−0.999932	−	0.839043i	−0.0129571	−	0.999916i	$-0.504124\pi$
$491$	−5.34164e6	−	4.48216e6i	−0.999932	−	0.839043i	−0.986975	+	0.160873i	$0.948569\pi$
$492$		0			0
$493$	−9.23809e6	−	3.36239e6i	−1.71185	−	0.623062i
$494$		0			0
$495$	−196761.	−	147907.i	−0.0360933	−	0.0271317i
$496$		0			0
$497$	492196.	−	413002.i	0.0893815	−	0.0750000i
$498$		0			0
$499$	−132228.	+	749904.i	−0.0237724	+	0.134820i	−0.994384	−	0.105831i	$-0.966250\pi$
$499$	−132228.	+	749904.i	−0.0237724	+	0.134820i	0.970612	+	0.240651i	$0.0773609\pi$
$500$		0			0
$501$	−5.33627e6	+	3.27439e6i	−0.949825	+	0.582823i
$502$		0			0
$503$	−2.88001e6	+	4.98833e6i	−0.507545	+	0.879094i	0.492417	+	0.870359i	$0.336114\pi$
$503$	−2.88001e6	+	4.98833e6i	−0.507545	+	0.879094i	−0.999962	+	0.00873422i	$0.997220\pi$
$504$		0			0
$505$	85817.7	+	148641.i	0.0149744	+	0.0259364i
$506$		0			0
$507$	2.25217e6	−	2.83479e6i	0.389118	−	0.489780i
$508$		0			0
$509$	−7.92662e6	+	2.88505e6i	−1.35611	+	0.493582i	−0.914848	−	0.403798i	$-0.867690\pi$
$509$	−7.92662e6	+	2.88505e6i	−1.35611	+	0.493582i	−0.441258	+	0.897380i	$0.645468\pi$
$510$		0			0
$511$	139993.	+	793938.i	0.0237166	+	0.134504i
$512$		0			0
$513$	−7.02336e6	−	3.33476e6i	−1.17829	−	0.559463i
$514$		0			0
$515$	−72969.6	−	413831.i	−0.0121234	−	0.0687551i
$516$		0			0
$517$	1.44834e6	−	527152.i	0.238311	−	0.0867381i
$518$		0			0
$519$	560762.	+	1.42112e6i	0.0913819	+	0.231587i
$520$		0			0
$521$	−2.16858e6	−	3.75609e6i	−0.350011	−	0.606236i	0.636240	−	0.771491i	$-0.280489\pi$
$521$	−2.16858e6	−	3.75609e6i	−0.350011	−	0.606236i	−0.986251	+	0.165255i	$0.947155\pi$
$522$		0			0
$523$	1.53337e6	−	2.65587e6i	0.245127	−	0.424573i	−0.717040	−	0.697032i	$-0.754504\pi$
$523$	1.53337e6	−	2.65587e6i	0.245127	−	0.424573i	0.962167	+	0.272459i	$0.0878369\pi$
$524$		0			0
$525$	1.00754e6	+	546280.i	0.159538	+	0.0865003i
$526$		0			0
$527$	1.39309e6	−	7.90063e6i	0.218501	−	1.23918i
$528$		0			0
$529$	4.01447e6	−	3.36854e6i	0.623720	−	0.523363i
$530$		0			0
$531$	75704.4	+	326159.i	0.0116516	+	0.0501988i
$532$		0			0
$533$	7.54573e6	+	2.74642e6i	1.15049	+	0.418745i
$534$		0			0
$535$	183140.	+	153672.i	0.0276629	+	0.0232119i
$536$		0			0
$537$	−6.51556e6	−	7.35577e6i	−0.975025	−	1.10076i
$538$		0			0
$539$	7.30507e6			1.08306
$540$		0			0
$541$	3.73625e6			0.548836			0.274418	−	0.961611i	$-0.411515\pi$
$541$	3.73625e6			0.548836			0.274418	+	0.961611i	$0.411515\pi$
$542$		0			0
$543$	1.10669e7	−	2.25837e6i	1.61074	−	0.328696i
$544$		0			0
$545$	176305.	+	147937.i	0.0254257	+	0.0213347i
$546$		0			0
$547$	240558.	+	87556.0i	0.0343757	+	0.0125117i	0.359151	−	0.933280i	$-0.383066\pi$
$547$	240558.	+	87556.0i	0.0343757	+	0.0125117i	−0.324775	+	0.945791i	$0.605289\pi$
$548$		0			0
$549$	−3.27379e6	−	5.02822e6i	−0.463575	−	0.712006i
$550$		0			0
$551$	−7.50202e6	+	6.29494e6i	−1.05269	+	0.883309i
$552$		0			0
$553$	−163739.	+	928610.i	−0.0227687	+	0.129128i
$554$		0			0
$555$	6994.48	+	261232.i	0.000963880	+	0.0359992i
$556$		0			0
$557$	5.83904e6	−	1.01135e7i	0.797450	−	1.38122i	−0.123822	−	0.992304i	$-0.539515\pi$
$557$	5.83904e6	−	1.01135e7i	0.797450	−	1.38122i	0.921272	−	0.388920i	$-0.127152\pi$
$558$		0			0
$559$	−4.33144e6	−	7.50227e6i	−0.586277	−	1.01546i
$560$		0			0
$561$	−1.42799e7	−	2.12556e6i	−1.91566	−	0.285145i
$562$		0			0
$563$	3.88807e6	−	1.41514e6i	0.516968	−	0.188161i	−0.0703422	−	0.997523i	$-0.522409\pi$
$563$	3.88807e6	−	1.41514e6i	0.516968	−	0.188161i	0.587310	+	0.809362i	$0.300187\pi$
$564$		0			0
$565$	48991.1	+	277843.i	0.00645649	+	0.0366166i
$566$		0			0
$567$	−93798.7	+	1.38836e6i	−0.0122529	+	0.181361i
$568$		0			0
$569$	1.70006e6	+	9.64151e6i	0.220132	+	1.24843i	0.871776	+	0.489905i	$0.162969\pi$
$569$	1.70006e6	+	9.64151e6i	0.220132	+	1.24843i	−0.651644	+	0.758525i	$0.725920\pi$
$570$		0			0
$571$	−3.10032e6	+	1.12842e6i	−0.397939	+	0.144838i	−0.533235	−	0.845967i	$-0.679024\pi$
$571$	−3.10032e6	+	1.12842e6i	−0.397939	+	0.144838i	0.135296	+	0.990805i	$0.456802\pi$
$572$		0			0
$573$	−3.19466e6	−	475522.i	−0.406478	−	0.0605040i
$574$		0			0
$575$	5.33061e6	+	9.23289e6i	0.672368	+	1.16458i
$576$		0			0
$577$	1.72140e6	−	2.98154e6i	0.215249	−	0.372822i	−0.738101	−	0.674691i	$-0.764277\pi$
$577$	1.72140e6	−	2.98154e6i	0.215249	−	0.372822i	0.953350	+	0.301869i	$0.0976104\pi$
$578$		0			0
$579$	374284.	+	1.39788e7i	0.0463985	+	1.73290i
$580$		0			0
$581$	102032.	−	578652.i	0.0125400	−	0.0711176i
$582$		0			0
$583$	1.01812e7	−	8.54301e6i	1.24058	−	1.04097i
$584$		0			0
$585$	−424828.	+	22765.9i	−0.0513244	+	0.00275039i
$586$		0			0
$587$	−8.09107e6	−	2.94491e6i	−0.969194	−	0.352758i	−0.191564	−	0.981480i	$-0.561356\pi$
$587$	−8.09107e6	−	2.94491e6i	−0.969194	−	0.352758i	−0.777630	+	0.628722i	$0.783578\pi$
$588$		0			0
$589$	−6.12198e6	−	5.13695e6i	−0.727115	−	0.610122i
$590$		0			0
$591$	1.08477e6	−	221363.i	0.127752	−	0.0260698i
$592$		0			0
$593$	−4.36237e6			−0.509432			−0.254716	−	0.967016i	$-0.581982\pi$
$593$	−4.36237e6			−0.509432			−0.254716	+	0.967016i	$0.581982\pi$
$594$		0			0
$595$	−109422.			−0.0126710
$596$		0			0
$597$	5.67739e6	+	6.40951e6i	0.651948	+	0.736019i
$598$		0			0
$599$	1.24010e7	+	1.04056e7i	1.41217	+	1.18495i	0.955379	+	0.295382i	$0.0954470\pi$
$599$	1.24010e7	+	1.04056e7i	1.41217	+	1.18495i	0.456795	+	0.889572i	$0.348997\pi$
$600$		0			0
$601$	5.51950e6	+	2.00893e6i	0.623324	+	0.226871i	0.634323	−	0.773068i	$-0.281279\pi$
$601$	5.51950e6	+	2.00893e6i	0.623324	+	0.226871i	−0.0109990	+	0.999940i	$0.503501\pi$
$602$		0			0
$603$	1.02115e7	−	9.54489e6i	1.14366	−	1.06900i
$604$		0			0
$605$	−70773.7	+	59386.2i	−0.00786111	+	0.00659625i
$606$		0			0
$607$	1.50642e6	−	8.54334e6i	0.165949	−	0.941143i	−0.782132	−	0.623113i	$-0.785868\pi$
$607$	1.50642e6	−	8.54334e6i	0.165949	−	0.941143i	0.948081	−	0.318030i	$-0.103021\pi$
$608$		0			0
$609$	1.54085e6	+	835437.i	0.168351	+	0.0912789i
$610$		0			0
$611$	1.33194e6	−	2.30699e6i	0.144338	−	0.250001i
$612$		0			0
$613$	3.37158e6	+	5.83975e6i	0.362395	+	0.627687i	0.988355	−	0.152169i	$-0.0486257\pi$
$613$	3.37158e6	+	5.83975e6i	0.362395	+	0.627687i	−0.625959	+	0.779856i	$0.715292\pi$
$614$		0			0
$615$	−133278.	−	337763.i	−0.0142092	−	0.0360101i
$616$		0			0
$617$	−9.56213e6	+	3.48033e6i	−1.01121	+	0.368051i	−0.793898	−	0.608051i	$-0.791952\pi$
$617$	−9.56213e6	+	3.48033e6i	−1.01121	+	0.368051i	−0.217313	+	0.976102i	$0.569729\pi$
$618$		0			0
$619$	−674865.	−	3.82735e6i	−0.0707930	−	0.401487i	−0.999527	−	0.0307413i	$-0.990213\pi$
$619$	−674865.	−	3.82735e6i	−0.0707930	−	0.401487i	0.928734	−	0.370746i	$-0.120898\pi$
$620$		0			0
$621$	−7.49807e6	+	1.05513e7i	−0.780226	+	1.09793i
$622$		0			0
$623$	−32765.5	−	185823.i	−0.00338218	−	0.0191813i
$624$		0			0
$625$	−9.13197e6	+	3.32377e6i	−0.935114	+	0.340354i
$626$		0			0
$627$	−8.94623e6	+	1.12606e7i	−0.908806	+	1.14391i
$628$		0			0
$629$	7.66356e6	+	1.32737e7i	0.772332	+	1.33772i
$630$		0			0
$631$	−8.84479e6	+	1.53196e7i	−0.884329	+	1.53170i	−0.0378489	+	0.999283i	$0.512051\pi$
$631$	−8.84479e6	+	1.53196e7i	−0.884329	+	1.53170i	−0.846480	+	0.532420i	$0.821283\pi$
$632$		0			0
$633$	−6.18427e6	+	3.79473e6i	−0.613450	+	0.376419i
$634$		0			0
$635$	−3494.93	+	19820.7i	−0.000343957	+	0.00195068i
$636$		0			0
$637$	9.67183e6	−	8.11563e6i	0.944409	−	0.792453i
$638$		0			0
$639$	−6.09568e6	+	2.59594e6i	−0.590568	+	0.251502i
$640$		0			0
$641$	1.13591e7	+	4.13436e6i	1.09194	+	0.397432i	0.824338	−	0.566098i	$-0.191548\pi$
$641$	1.13591e7	+	4.13436e6i	1.09194	+	0.397432i	0.267599	+	0.963531i	$0.413770\pi$
$642$		0			0
$643$	1.23303e7	+	1.03463e7i	1.17610	+	0.986867i	0.999997	+	0.00249508i	$0.000794211\pi$
$643$	1.23303e7	+	1.03463e7i	1.17610	+	0.986867i	0.176105	+	0.984371i	$0.443650\pi$
$644$		0			0
$645$	−124077.	+	371555.i	−0.0117434	+	0.0351661i
$646$		0			0
$647$	1.34513e7			1.26329			0.631647	−	0.775256i	$-0.282379\pi$
$647$	1.34513e7			1.26329			0.631647	+	0.775256i	$0.282379\pi$
$648$		0			0
$649$	619362.			0.0577209
$650$		0			0
$651$	−453051.	+	1.35668e6i	−0.0418981	+	0.125466i
$652$		0			0
$653$	3.44135e6	+	2.88763e6i	0.315824	+	0.265008i	0.786894	−	0.617088i	$-0.211688\pi$
$653$	3.44135e6	+	2.88763e6i	0.315824	+	0.265008i	−0.471070	+	0.882096i	$0.656132\pi$
$654$		0			0
$655$	−86702.1	−	31557.0i	−0.00789635	−	0.00287404i
$656$		0			0
$657$	1.00340e6	−	8.25235e6i	0.0906903	−	0.745872i
$658$		0			0
$659$	−542202.	+	454961.i	−0.0486348	+	0.0408095i	−0.666781	−	0.745254i	$-0.732328\pi$
$659$	−542202.	+	454961.i	−0.0486348	+	0.0408095i	0.618146	+	0.786063i	$0.287884\pi$
$660$		0			0
$661$	2.80682e6	−	1.59182e7i	0.249868	−	1.41707i	−0.559043	−	0.829139i	$-0.688831\pi$
$661$	2.80682e6	−	1.59182e7i	0.249868	−	1.41707i	0.808910	−	0.587932i	$-0.200058\pi$
$662$		0			0
$663$	−2.12679e7	+	1.30502e7i	−1.87906	+	1.15301i
$664$		0			0
$665$	−54500.7	+	94398.0i	−0.00477912	+	0.00827768i
$666$		0			0
$667$	8.15220e6	+	1.41200e7i	0.709513	+	1.22891i
$668$		0			0
$669$	9.26144e6	−	1.16573e7i	0.800043	−	1.00701i
$670$		0			0
$671$	−1.04295e7	+	3.79601e6i	−0.894243	+	0.325478i
$672$		0			0
$673$	−2.78349e6	−	1.57860e7i	−0.236893	−	1.34349i	−0.838590	−	0.544764i	$-0.816619\pi$
$673$	−2.78349e6	−	1.57860e7i	−0.236893	−	1.34349i	0.601696	−	0.798725i	$-0.294492\pi$
$674$		0			0
$675$	−8.29839e6	−	8.41473e6i	−0.701027	−	0.710854i
$676$		0			0
$677$	2.14497e6	+	1.21647e7i	0.179866	+	1.02007i	0.932376	+	0.361490i	$0.117732\pi$
$677$	2.14497e6	+	1.21647e7i	0.179866	+	1.02007i	−0.752510	+	0.658581i	$0.771157\pi$
$678$		0			0
$679$	−3.80286e6	+	1.38413e6i	−0.316545	+	0.115213i
$680$		0			0
$681$	5.92695e6	+	1.50205e7i	0.489738	+	1.24113i
$682$		0			0
$683$	9.69093e6	+	1.67852e7i	0.794902	+	1.37681i	0.922901	+	0.385037i	$0.125811\pi$
$683$	9.69093e6	+	1.67852e7i	0.794902	+	1.37681i	−0.127999	+	0.991774i	$0.540855\pi$
$684$		0			0
$685$	−435060.	+	753545.i	−0.0354260	+	0.0613597i
$686$		0			0
$687$	−5.41543e6	−	2.93621e6i	−0.437765	−	0.237353i
$688$		0			0
$689$	3.98882e6	−	2.26217e7i	0.320108	−	1.81542i
$690$		0			0
$691$	−1.94162e6	+	1.62921e6i	−0.154692	+	0.129802i	−0.716849	−	0.697229i	$-0.754416\pi$
$691$	−1.94162e6	+	1.62921e6i	−0.154692	+	0.129802i	0.562157	+	0.827031i	$0.309972\pi$
$692$		0			0
$693$	2.46242e6	+	749669.i	0.194773	+	0.0592975i
$694$		0			0
$695$	371662.	+	135274.i	0.0291868	+	0.0106231i
$696$		0			0
$697$	−1.63143e7	−	1.36893e7i	−1.27200	−	1.06733i
$698$		0			0
$699$	−1.96137e6	−	2.21429e6i	−0.151833	−	0.171412i
$700$		0			0
$701$	1.05085e7			0.807695			0.403847	−	0.914826i	$-0.367673\pi$
$701$	1.05085e7			0.807695			0.403847	+	0.914826i	$0.367673\pi$
$702$		0			0
$703$	1.52682e7			1.16520
$704$		0			0
$705$	−118025.	+	24084.8i	−0.00894338	+	0.00182503i
$706$		0			0
$707$	−1.37488e6	−	1.15366e6i	−0.103447	−	0.0868021i
$708$		0			0
$709$	1.74966e7	+	6.36824e6i	1.30719	+	0.475777i	0.899331	−	0.437269i	$-0.144054\pi$
$709$	1.74966e7	+	6.36824e6i	1.30719	+	0.475777i	0.407856	+	0.913046i	$0.366276\pi$
$710$		0			0
$711$	4.40405e6	−	8.66866e6i	0.326722	−	0.643099i
$712$		0			0
$713$	−1.01923e7	+	8.55236e6i	−0.750842	+	0.630031i
$714$		0			0
$715$	−136655.	+	775011.i	−0.00999681	+	0.0566947i
$716$		0			0
$717$	−234217.	−	8.74761e6i	−0.0170146	−	0.635465i
$718$		0			0
$719$	4.16215e6	−	7.20905e6i	0.300258	−	0.520063i	−0.675936	−	0.736960i	$-0.736260\pi$
$719$	4.16215e6	−	7.20905e6i	0.300258	−	0.520063i	0.976194	+	0.216897i	$0.0695937\pi$
$720$		0			0
$721$	2.19708e6	+	3.80546e6i	0.157401	+	0.272627i
$722$		0			0
$723$	1.04711e7	+	1.55861e6i	0.744982	+	0.110890i
$724$		0			0
$725$	−1.39885e7	+	5.09140e6i	−0.988385	+	0.359743i
$726$		0			0
$727$	−3.98082e6	−	2.25764e7i	−0.279342	−	1.58423i	−0.724821	−	0.688937i	$-0.758078\pi$
$727$	−3.98082e6	−	2.25764e7i	−0.279342	−	1.58423i	0.445479	−	0.895293i	$-0.353033\pi$
$728$		0			0
$729$	5.09484e6	−	1.34139e7i	0.355068	−	0.934840i
$730$		0			0
$731$	3.98961e6	+	2.26262e7i	0.276145	+	1.56609i
$732$		0			0
$733$	−1.97837e6	+	720068.i	−0.136003	+	0.0495010i	−0.409125	−	0.912478i	$-0.634166\pi$
$733$	−1.97837e6	+	720068.i	−0.136003	+	0.0495010i	0.273122	+	0.961979i	$0.411944\pi$
$734$		0			0
$735$	−564696.	−	84054.6i	−0.0385564	−	0.00573909i
$736$		0			0
$737$	−1.29280e7	−	2.23919e7i	−0.876721	−	1.51853i
$738$		0			0
$739$	1.06584e7	−	1.84610e7i	0.717931	−	1.24349i	−0.243887	−	0.969804i	$-0.578423\pi$
$739$	1.06584e7	−	1.84610e7i	0.717931	−	1.24349i	0.961818	−	0.273690i	$-0.0882441\pi$
$740$		0			0
$741$	665298.	+	2.48477e7i	0.0445114	+	1.66242i
$742$		0			0
$743$	4.90603e6	−	2.78235e7i	0.326031	−	1.84901i	−0.176302	−	0.984336i	$-0.556413\pi$
$743$	4.90603e6	−	2.78235e7i	0.326031	−	1.84901i	0.502332	−	0.864675i	$-0.332475\pi$
$744$		0			0
$745$	216075.	−	181308.i	0.0142631	−	0.0119681i
$746$		0			0
$747$	−2.74433e6	+	5.40177e6i	−0.179943	+	0.354189i
$748$		0			0
$749$	−2.34919e6	−	855036.i	−0.153008	−	0.0556903i
$750$		0			0
$751$	−1.82337e7	−	1.52999e7i	−1.17971	−	0.989892i	−0.999981	−	0.00617487i	$-0.998034\pi$
$751$	−1.82337e7	−	1.52999e7i	−1.17971	−	0.989892i	−0.179726	−	0.983717i	$-0.557521\pi$
$752$		0			0
$753$	−1.49928e7	+	3.05951e6i	−0.963595	+	0.196636i
$754$		0			0
$755$	95503.5			0.00609750
$756$		0			0
$757$	−1.55654e7			−0.987233			−0.493616	−	0.869680i	$-0.664325\pi$
$757$	−1.55654e7			−0.987233			−0.493616	+	0.869680i	$0.664325\pi$
$758$		0			0
$759$	1.58762e7	+	1.79235e7i	1.00033	+	1.12932i
$760$		0			0
$761$	1.14679e7	+	9.62272e6i	0.717831	+	0.602332i	0.926784	−	0.375594i	$-0.122561\pi$
$761$	1.14679e7	+	9.62272e6i	0.717831	+	0.602332i	−0.208953	+	0.977926i	$0.567006\pi$
$762$		0			0
$763$	−2.26152e6	−	823125.i	−0.140634	−	0.0511864i
$764$		0			0
$765$	1.07941e6	+	328619.i	0.0666857	+	0.0203020i
$766$		0			0
$767$	820028.	−	688085.i	0.0503316	−	0.0422332i
$768$		0			0
$769$	−3.38956e6	+	1.92232e7i	−0.206694	+	1.17222i	0.688058	+	0.725656i	$0.258463\pi$
$769$	−3.38956e6	+	1.92232e7i	−0.206694	+	1.17222i	−0.894752	+	0.446564i	$0.852648\pi$
$770$		0			0
$771$	−2.75217e7	−	1.49221e7i	−1.66740	−	0.904054i
$772$		0			0
$773$	5.72135e6	−	9.90967e6i	0.344390	−	0.596500i	−0.640853	−	0.767664i	$-0.721419\pi$
$773$	5.72135e6	−	9.90967e6i	0.344390	−	0.596500i	0.985243	+	0.171163i	$0.0547526\pi$
$774$		0			0
$775$	−6.07392e6	−	1.05203e7i	−0.363258	−	0.629181i
$776$		0			0
$777$	−1.00302e6	−	2.54193e6i	−0.0596015	−	0.151046i
$778$		0			0
$779$	−1.99355e7	+	7.25592e6i	−1.17702	+	0.428400i
$780$		0			0
$781$	2.12816e6	+	1.20694e7i	0.124847	+	0.708040i
$782$		0			0
$783$	−1.26909e7	−	1.28688e7i	−0.739755	−	0.750125i
$784$		0			0
$785$	−2920.03	−	16560.3i	−0.000169127	−	0.000959168i
$786$		0			0
$787$	−5.23803e6	+	1.90649e6i	−0.301461	+	0.109723i	−0.488322	−	0.872664i	$-0.662391\pi$
$787$	−5.23803e6	+	1.90649e6i	−0.301461	+	0.109723i	0.186861	+	0.982386i	$0.440169\pi$
$788$		0			0
$789$	1.33085e7	−	1.67513e7i	0.761091	−	0.957979i
$790$		0			0
$791$	−1.47510e6	−	2.55495e6i	−0.0838263	−	0.145191i
$792$		0			0
$793$	−9.59127e6	+	1.66126e7i	−0.541618	+	0.938110i
$794$		0			0
$795$	−885323.	+	543244.i	−0.0496803	+	0.0304844i
$796$		0			0
$797$	4.37758e6	−	2.48265e7i	0.244112	−	1.38443i	−0.578435	−	0.815729i	$-0.696336\pi$
$797$	4.37758e6	−	2.48265e7i	0.244112	−	1.38443i	0.822547	−	0.568698i	$-0.192553\pi$
$798$		0			0
$799$	−5.41211e6	+	4.54130e6i	−0.299916	+	0.251659i
$800$		0			0
$801$	−234847.	+	1.93148e6i	−0.0129332	+	0.106367i
$802$		0			0
$803$	−1.44501e7	−	5.25940e6i	−0.790827	−	0.287838i
$804$		0			0
$805$	139017.	+	116649.i	0.00756097	+	0.00634440i
$806$		0			0
$807$	7.05754e6	−	2.11341e7i	0.381478	−	1.14235i
$808$		0			0
$809$	2.08622e7			1.12070			0.560350	−	0.828256i	$-0.310667\pi$
$809$	2.08622e7			1.12070			0.560350	+	0.828256i	$0.310667\pi$
$810$		0			0
$811$	−2.46839e6			−0.131784			−0.0658919	−	0.997827i	$-0.520989\pi$
$811$	−2.46839e6			−0.131784			−0.0658919	+	0.997827i	$0.520989\pi$
$812$		0			0
$813$	8.97058e6	−	2.68628e7i	0.475986	−	1.42536i
$814$		0			0
$815$	−184831.	−	155091.i	−0.00974720	−	0.00817887i
$816$		0			0
$817$	2.15067e7	+	7.82779e6i	1.12724	+	0.410284i
$818$		0			0
$819$	4.09307e6	−	1.74309e6i	0.213226	−	0.0908053i
$820$		0			0
$821$	−1.56241e7	+	1.31102e7i	−0.808980	+	0.678815i	−0.950364	−	0.311140i	$-0.899289\pi$
$821$	−1.56241e7	+	1.31102e7i	−0.808980	+	0.678815i	0.141384	+	0.989955i	$0.454845\pi$
$822$		0			0
$823$	−1.11629e6	+	6.33081e6i	−0.0574485	+	0.325806i	−0.999965	−	0.00835274i	$-0.997341\pi$
$823$	−1.11629e6	+	6.33081e6i	−0.0574485	+	0.325806i	0.942517	+	0.334159i	$0.108452\pi$
$824$		0			0
$825$	−1.86330e7	+	1.14334e7i	−0.953120	+	0.584845i
$826$		0			0
$827$	−9.44914e6	+	1.63664e7i	−0.480428	+	0.832126i	−0.999748	−	0.0224538i	$-0.992852\pi$
$827$	−9.44914e6	+	1.63664e7i	−0.480428	+	0.832126i	0.519320	+	0.854580i	$0.326185\pi$
$828$		0			0
$829$	1.90497e7	+	3.29950e7i	0.962724	+	1.66749i	0.715610	+	0.698500i	$0.246149\pi$
$829$	1.90497e7	+	3.29950e7i	0.962724	+	1.66749i	0.247114	+	0.968986i	$0.420518\pi$
$830$		0			0
$831$	−8.31141e6	+	1.04615e7i	−0.417515	+	0.525523i
$832$		0			0
$833$	−3.14658e7	+	1.14526e7i	−1.57118	+	0.571863i
$834$		0			0
$835$	−157170.	−	891353.i	−0.00780104	−	0.0442419i
$836$		0			0
$837$	8.54361e6	−	1.20226e7i	0.421529	−	0.593175i
$838$		0			0
$839$	−4.93598e6	−	2.79933e7i	−0.242085	−	1.37293i	−0.827166	−	0.561958i	$-0.810048\pi$
$839$	−4.93598e6	−	2.79933e7i	−0.242085	−	1.37293i	0.585081	−	0.810975i	$-0.301063\pi$
$840$		0			0
$841$	−2.11871e6	+	771146.i	−0.103295	+	0.0375964i
$842$		0			0
$843$	6.92808e6	+	1.75576e7i	0.335772	+	0.850936i
$844$		0			0
$845$	261706.	+	453287.i	0.0126087	+	0.0218390i
$846$		0			0
$847$	483051.	−	836668.i	0.0231358	−	0.0400723i
$848$		0			0
$849$	7.01586e6	+	3.80395e6i	0.334050	+	0.181120i
$850$		0			0
$851$	4.41407e6	−	2.50334e7i	0.208937	−	1.18494i
$852$		0			0
$853$	1.38736e7	−	1.16413e7i	0.652853	−	0.547809i	−0.255082	−	0.966919i	$-0.582103\pi$
$853$	1.38736e7	−	1.16413e7i	0.652853	−	0.547809i	0.907935	+	0.419111i	$0.137658\pi$
$854$		0			0
$855$	821129.	−	767525.i	0.0384146	−	0.0359068i
$856$		0			0
$857$	−9.39812e6	−	3.42064e6i	−0.437108	−	0.159094i	0.114087	−	0.993471i	$-0.463606\pi$
$857$	−9.39812e6	−	3.42064e6i	−0.437108	−	0.159094i	−0.551195	+	0.834376i	$0.685828\pi$
$858$		0			0
$859$	−1.11111e7	−	9.32332e6i	−0.513776	−	0.431109i	0.348679	−	0.937242i	$-0.386630\pi$
$859$	−1.11111e7	−	9.32332e6i	−0.513776	−	0.431109i	−0.862456	+	0.506133i	$0.831075\pi$
$860$		0			0
$861$	2.51763e6	+	2.84229e6i	0.115740	+	0.130666i
$862$		0			0
$863$	6.74026e6			0.308070			0.154035	−	0.988065i	$-0.450773\pi$
$863$	6.74026e6			0.308070			0.154035	+	0.988065i	$0.450773\pi$
$864$		0			0
$865$	−220864.			−0.0100365
$866$		0			0
$867$	4.31551e7	−	8.80647e6i	1.94978	−	0.397882i
$868$		0			0
$869$	−1.37780e7	−	1.15611e7i	−0.618922	−	0.519337i
$870$		0			0
$871$	−4.19929e7	−	1.52842e7i	−1.87556	−	0.682648i
$872$		0			0
$873$	4.16707e7	−	2.23307e6i	1.85053	−	0.0991668i
$874$		0			0
$875$	−254057.	+	213179.i	−0.0112179	+	0.00941292i
$876$		0			0
$877$	997805.	−	5.65883e6i	0.0438073	−	0.248444i	−0.955038	−	0.296483i	$-0.904186\pi$
$877$	997805.	−	5.65883e6i	0.0438073	−	0.248444i	0.998845	+	0.0480394i	$0.0152973\pi$
$878$		0			0
$879$	1.21265e6	+	4.52905e7i	0.0529377	+	1.97713i
$880$		0			0
$881$	−1.73439e6	+	3.00406e6i	−0.0752850	+	0.130397i	−0.901210	−	0.433382i	$-0.857320\pi$
$881$	−1.73439e6	+	3.00406e6i	−0.0752850	+	0.130397i	0.825925	+	0.563780i	$0.190653\pi$
$882$		0			0
$883$	−628505.	−	1.08860e6i	−0.0271273	−	0.0469859i	0.852143	−	0.523309i	$-0.175303\pi$
$883$	−628505.	−	1.08860e6i	−0.0271273	−	0.0469859i	−0.879270	+	0.476323i	$0.841969\pi$
$884$		0			0
$885$	−47877.9	−	7126.59i	−0.00205484	−	0.000305861i
$886$		0			0
$887$	2.60272e7	−	9.47313e6i	1.11076	−	0.404282i	0.279485	−	0.960150i	$-0.409836\pi$
$887$	2.60272e7	−	9.47313e6i	1.11076	−	0.404282i	0.831271	+	0.555868i	$0.187614\pi$
$888$		0			0
$889$	−36546.3	−	207264.i	−0.00155092	−	0.00879569i
$890$		0			0
$891$	−2.20395e7	−	1.47904e7i	−0.930052	−	0.624147i
$892$		0			0
$893$	1.22211e6	+	6.93093e6i	0.0512840	+	0.290846i
$894$		0			0
$895$	1.33491e6	−	485869.i	0.0557052	−	0.0202750i
$896$		0			0
$897$	4.09322e7	+	6.09272e6i	1.69857	+	0.252831i
$898$		0			0
$899$	−9.28896e6	−	1.60889e7i	−0.383326	−	0.663939i
$900$		0			0
$901$	−3.04608e7	+	5.27597e7i	−1.25006	+	2.16516i
$902$		0			0
$903$	−109638.	−	4.09477e6i	−0.00447446	−	0.167113i
$904$		0			0
$905$	−283546.	+	1.60807e6i	−0.0115081	+	0.0652655i
$906$		0			0
$907$	1.24503e7	−	1.04471e7i	0.502531	−	0.421673i	−0.355961	−	0.934501i	$-0.615846\pi$
$907$	1.24503e7	−	1.04471e7i	0.502531	−	0.421673i	0.858492	+	0.512827i	$0.171402\pi$
$908$		0			0
$909$	1.00980e7	+	1.55096e7i	0.405346	+	0.622572i
$910$		0			0
$911$	1.28245e7	+	4.66775e6i	0.511971	+	0.186342i	0.585071	−	0.810982i	$-0.301067\pi$
$911$	1.28245e7	+	4.66775e6i	0.511971	+	0.186342i	−0.0730993	+	0.997325i	$0.523289\pi$
$912$		0			0
$913$	8.58557e6	+	7.20415e6i	0.340873	+	0.286026i
$914$		0			0
$915$	849896.	−	173434.i	0.0335593	−	0.00684829i
$916$		0			0
$917$	964824.			0.0378900
$918$		0			0
$919$	2.53414e7			0.989788			0.494894	−	0.868953i	$-0.335207\pi$
$919$	2.53414e7			0.989788			0.494894	+	0.868953i	$0.335207\pi$
$920$		0			0
$921$	1.42526e7	+	1.60906e7i	0.553664	+	0.625061i
$922$		0			0
$923$	1.62263e7	+	1.36154e7i	0.626923	+	0.526051i
$924$		0			0
$925$	2.18090e7	+	7.93781e6i	0.838071	+	0.305033i
$926$		0			0
$927$	−1.02448e7	−	4.41378e7i	−0.391564	−	1.68699i
$928$		0			0
$929$	1.16269e7	−	9.75616e6i	0.442004	−	0.370885i	−0.394455	−	0.918915i	$-0.629066\pi$
$929$	1.16269e7	−	9.75616e6i	0.442004	−	0.370885i	0.836459	+	0.548030i	$0.184622\pi$
$930$		0			0
$931$	−5.79229e6	+	3.28497e7i	−0.219016	+	1.24210i
$932$		0			0
$933$	8.82445e6	+	4.78456e6i	0.331882	+	0.179944i
$934$		0			0
$935$	1.04358e6	−	1.80753e6i	0.0390387	−	0.0676170i
$936$		0			0
$937$	1.60766e7	+	2.78454e7i	0.598197	+	1.03611i	0.993087	+	0.117379i	$0.0374491\pi$
$937$	1.60766e7	+	2.78454e7i	0.598197	+	1.03611i	−0.394891	+	0.918728i	$0.629218\pi$
$938$		0			0
$939$	−1.57297e7	−	3.98634e7i	−0.582180	−	1.47540i
$940$		0			0
$941$	−4.86899e7	+	1.77217e7i	−1.79252	+	0.652425i	−0.793484	+	0.608592i	$0.791735\pi$
$941$	−4.86899e7	+	1.77217e7i	−1.79252	+	0.652425i	−0.999039	+	0.0438332i	$0.986043\pi$
$942$		0			0
$943$	6.13327e6	+	3.47835e7i	0.224602	+	1.27378i
$944$		0			0
$945$	−181724.	−	86284.3i	−0.00661962	−	0.00314306i
$946$		0			0
$947$	1.82887e6	+	1.03721e7i	0.0662688	+	0.375829i	0.999848	+	0.0174568i	$0.00555696\pi$
$947$	1.82887e6	+	1.03721e7i	0.0662688	+	0.375829i	−0.933579	+	0.358372i	$0.883332\pi$
$948$		0			0
$949$	−2.49747e7	+	9.09006e6i	−0.900192	+	0.327643i
$950$		0			0
$951$	−2.31015e7	+	2.90776e7i	−0.828301	+	1.04258i
$952$		0			0
$953$	−3.88326e6	−	6.72601e6i	−0.138505	−	0.239897i	0.788426	−	0.615130i	$-0.210896\pi$
$953$	−3.88326e6	−	6.72601e6i	−0.138505	−	0.239897i	−0.926931	+	0.375232i	$0.877563\pi$
$954$		0			0
$955$	233465.	−	404374.i	0.00828350	−	0.0143474i
$956$		0			0
$957$	−2.84958e7	+	1.74853e7i	−1.00577	+	0.617154i
$958$		0			0
$959$	1.57999e6	−	8.96055e6i	0.0554762	−	0.314621i
$960$		0			0
$961$	−1.03177e7	+	8.65755e6i	−0.360390	+	0.302403i
$962$		0			0
$963$	2.06061e7	+	1.54898e7i	0.716027	+	0.538245i
$964$		0			0
$965$	−1.89969e6	−	691430.i	−0.0656695	−	0.0239017i
$966$		0			0
$967$	2.56650e7	+	2.15355e7i	0.882623	+	0.740608i	0.966717	−	0.255850i	$-0.0823552\pi$
$967$	2.56650e7	+	2.15355e7i	0.882623	+	0.740608i	−0.0840940	+	0.996458i	$0.526800\pi$
$968$		0			0
$969$	2.08810e7	−	6.25291e7i	0.714402	−	2.13931i
$970$		0			0
$971$	−2.25758e7			−0.768413			−0.384207	−	0.923247i	$-0.625525\pi$
$971$	−2.25758e7			−0.768413			−0.384207	+	0.923247i	$0.625525\pi$
$972$		0			0
$973$	−4.13587e6			−0.140051
$974$		0			0
$975$	−1.19678e7	+	3.58382e7i	−0.403184	+	1.20735i
$976$		0			0
$977$	4.94037e6	+	4.14546e6i	0.165586	+	0.138943i	0.721815	−	0.692086i	$-0.243308\pi$
$977$	4.94037e6	+	4.14546e6i	0.165586	+	0.138943i	−0.556229	+	0.831029i	$0.687752\pi$
$978$		0			0
$979$	3.38207e6	+	1.23097e6i	0.112778	+	0.0410479i
$980$		0			0
$981$	1.98370e7	+	1.49117e7i	0.658119	+	0.494714i
$982$		0			0
$983$	−2.23932e7	+	1.87902e7i	−0.739151	+	0.620221i	−0.932609	−	0.360887i	$-0.882474\pi$
$983$	−2.23932e7	+	1.87902e7i	−0.739151	+	0.620221i	0.193459	+	0.981108i	$0.438029\pi$
$984$		0			0
$985$	−27793.0	+	157622.i	−0.000912735	+	0.00517638i
$986$		0			0
$987$	1.07361e6	−	658780.i	0.0350796	−	0.0215252i
$988$		0			0
$989$	1.90519e7	−	3.29989e7i	0.619366	−	1.07277i
$990$		0			0
$991$	−2.83838e7	−	4.91621e7i	−0.918092	−	1.59018i	−0.802311	−	0.596907i	$-0.796396\pi$
$991$	−2.83838e7	−	4.91621e7i	−0.918092	−	1.59018i	−0.115781	−	0.993275i	$-0.536937\pi$
$992$		0			0
$993$	1.18489e7	−	1.49141e7i	0.381333	−	0.479981i
$994$		0			0
$995$	−1.16319e6	+	423366.i	−0.0372471	+	0.0135568i
$996$		0			0
$997$	2.64606e6	+	1.50065e7i	0.0843065	+	0.478126i	0.997504	+	0.0706089i	$0.0224942\pi$
$997$	2.64606e6	+	1.50065e7i	0.0843065	+	0.478126i	−0.913198	+	0.407517i	$0.866395\pi$
$998$		0			0
$999$	2.26045e6	+	2.80875e7i	0.0716608	+	0.890429i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	108.6.i.a.13.6	✓	90
3.2	odd	2		324.6.i.a.253.9		90
27.2	odd	18		324.6.i.a.73.9		90
27.25	even	9	inner	108.6.i.a.25.6	yes	90

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.6.i.a.13.6	✓	90	1.1	even	1	trivial
108.6.i.a.25.6	yes	90	27.25	even	9	inner
324.6.i.a.73.9		90	27.2	odd	18
324.6.i.a.253.9		90	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:	\( N \)	\(=\)	\( 108 = 2^{2} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	108.i (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-4.93759 + 14.7858i) q^{3} +(-1.72634 - 1.44857i) q^{5} +(22.1444 + 8.05989i) q^{7} +(-194.240 - 146.012i) q^{9} +O(q^{10})\)	\(q+(-4.93759 + 14.7858i) q^{3} +(-1.72634 - 1.44857i) q^{5} +(22.1444 + 8.05989i) q^{7} +(-194.240 - 146.012i) q^{9} +(-344.335 + 288.931i) q^{11} +(-134.905 + 765.083i) q^{13} +(29.9423 - 18.3729i) q^{15} +(1030.21 - 1784.37i) q^{17} +(-1026.25 - 1777.51i) q^{19} +(-228.512 + 287.626i) q^{21} +(-3211.06 + 1168.73i) q^{23} +(-541.769 - 3072.52i) q^{25} +(3117.99 - 2151.05i) q^{27} +(-828.537 - 4698.87i) q^{29} +(3658.82 - 1331.70i) q^{31} +(-2571.90 - 6517.89i) q^{33} +(-26.5534 - 45.9918i) q^{35} +(-3719.42 + 6442.23i) q^{37} +(-10646.3 - 5772.34i) q^{39} +(1794.85 - 10179.1i) q^{41} +(-8541.99 + 7167.58i) q^{43} +(123.816 + 533.439i) q^{45} +(-3222.13 - 1172.76i) q^{47} +(-12449.5 - 10446.4i) q^{49} +(21296.7 + 24043.0i) q^{51} -29567.7 q^{53} +1012.98 q^{55} +(31349.2 - 6397.28i) q^{57} +(-1055.53 - 885.698i) q^{59} +(23202.5 + 8445.03i) q^{61} +(-3124.49 - 4798.91i) q^{63} +(1341.17 - 1125.37i) q^{65} +(-9988.58 + 56648.1i) q^{67} +(-1425.74 - 53248.9i) q^{69} +(13632.6 - 23612.3i) q^{71} +(17105.2 + 29627.1i) q^{73} +(48104.8 + 7160.36i) q^{75} +(-9953.82 + 3622.89i) q^{77} +(6948.24 + 39405.4i) q^{79} +(16409.7 + 56723.1i) q^{81} +(-4329.71 - 24555.0i) q^{83} +(-4363.28 + 1588.11i) q^{85} +(73567.5 + 10950.5i) q^{87} +(-4003.50 - 6934.26i) q^{89} +(-9153.86 + 15854.9i) q^{91} +(1624.55 + 60674.0i) q^{93} +(-803.203 + 4555.19i) q^{95} +(-131553. + 110386. i) q^{97} +(109071. - 5844.96i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 90 q - 87 q^{5} + 330 q^{9}+O(q^{10}) \) 90 * q - 87 * q^5 + 330 * q^9	\( 90 q - 87 q^{5} + 330 q^{9} - 1257 q^{11} + 531 q^{15} - 3468 q^{17} + 12894 q^{21} + 8106 q^{23} + 4959 q^{25} - 17415 q^{27} + 3468 q^{29} - 6651 q^{31} + 33624 q^{33} - 8229 q^{35} - 10545 q^{39} + 68673 q^{41} + 9459 q^{43} - 53469 q^{45} - 57087 q^{47} - 5490 q^{49} + 42831 q^{51} - 4146 q^{53} + 24624 q^{57} + 5388 q^{59} + 70110 q^{61} - 98115 q^{63} - 172425 q^{65} - 15039 q^{67} + 251037 q^{69} + 67812 q^{71} - 27009 q^{73} - 75273 q^{75} + 23991 q^{77} - 216180 q^{79} + 177822 q^{81} - 76725 q^{83} - 53100 q^{85} - 201483 q^{87} - 98814 q^{89} - 90999 q^{91} + 21765 q^{93} - 143490 q^{95} - 71739 q^{97} + 13635 q^{99}+O(q^{100}) \) 90 * q - 87 * q^5 + 330 * q^9 - 1257 * q^11 + 531 * q^15 - 3468 * q^17 + 12894 * q^21 + 8106 * q^23 + 4959 * q^25 - 17415 * q^27 + 3468 * q^29 - 6651 * q^31 + 33624 * q^33 - 8229 * q^35 - 10545 * q^39 + 68673 * q^41 + 9459 * q^43 - 53469 * q^45 - 57087 * q^47 - 5490 * q^49 + 42831 * q^51 - 4146 * q^53 + 24624 * q^57 + 5388 * q^59 + 70110 * q^61 - 98115 * q^63 - 172425 * q^65 - 15039 * q^67 + 251037 * q^69 + 67812 * q^71 - 27009 * q^73 - 75273 * q^75 + 23991 * q^77 - 216180 * q^79 + 177822 * q^81 - 76725 * q^83 - 53100 * q^85 - 201483 * q^87 - 98814 * q^89 - 90999 * q^91 + 21765 * q^93 - 143490 * q^95 - 71739 * q^97 + 13635 * q^99

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