LMFDB - Embedded newform 108.6.h.a.35.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [108,6,Mod(35,108)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(108, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 1]))

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

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

chi := DirichletCharacter("108.35");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 108 = 2^{2} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	108.h (of order $6$, 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:	$17.3214525398$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$28$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 36)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			35.13
Character	$\chi$	$=$	108.35
Dual form			108.6.h.a.71.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.253656 + 5.65116i) q^{2} +(-31.8713 - 2.86690i) q^{4} +(-84.3255 + 48.6853i) q^{5} +(-87.9661 - 50.7872i) q^{7} +(24.2857 - 179.383i) q^{8} +O(q^{10})$	\(q+(-0.253656 + 5.65116i) q^{2} +(-31.8713 - 2.86690i) q^{4} +(-84.3255 + 48.6853i) q^{5} +(-87.9661 - 50.7872i) q^{7} +(24.2857 - 179.383i) q^{8} +(-253.739 - 488.886i) q^{10} +(73.2291 - 126.837i) q^{11} +(402.832 + 697.726i) q^{13} +(309.320 - 484.228i) q^{14} +(1007.56 + 182.744i) q^{16} +1238.37i q^{17} -2616.12i q^{19} +(2827.14 - 1309.91i) q^{20} +(698.199 + 446.002i) q^{22} +(-84.5912 - 146.516i) q^{23} +(3178.02 - 5504.50i) q^{25} +(-4045.15 + 2099.49i) q^{26} +(2657.99 + 1870.85i) q^{28} +(-1952.82 - 1127.46i) q^{29} +(1787.03 - 1031.74i) q^{31} +(-1288.29 + 5647.54i) q^{32} +(-6998.21 - 314.119i) q^{34} +9890.37 q^{35} +445.632 q^{37} +(14784.1 + 663.594i) q^{38} +(6685.41 + 16308.9i) q^{40} +(1720.61 - 993.393i) q^{41} +(3464.26 + 2000.09i) q^{43} +(-2697.54 + 3832.51i) q^{44} +(849.444 - 440.874i) q^{46} +(3539.24 - 6130.14i) q^{47} +(-3244.81 - 5620.18i) q^{49} +(30300.7 + 19355.8i) q^{50} +(-10838.5 - 23392.3i) q^{52} +6234.98i q^{53} +14260.7i q^{55} +(-11246.7 + 14546.2i) q^{56} +(6866.81 - 10749.7i) q^{58} +(-16724.9 - 28968.4i) q^{59} +(14717.5 - 25491.5i) q^{61} +(5377.25 + 10360.5i) q^{62} +(-31588.4 - 8712.87i) q^{64} +(-67938.0 - 39224.1i) q^{65} +(23308.8 - 13457.4i) q^{67} +(3550.28 - 39468.4i) q^{68} +(-2508.75 + 55892.1i) q^{70} -36309.5 q^{71} -38203.0 q^{73} +(-113.037 + 2518.34i) q^{74} +(-7500.15 + 83379.1i) q^{76} +(-12883.4 + 7438.21i) q^{77} +(54553.0 + 31496.2i) q^{79} +(-93860.1 + 33643.5i) q^{80} +(5177.38 + 9975.41i) q^{82} +(39957.8 - 69208.9i) q^{83} +(-60290.3 - 104426. i) q^{85} +(-12181.6 + 19069.8i) q^{86} +(-20973.9 - 16216.4i) q^{88} -96604.3i q^{89} -81835.0i q^{91} +(2275.98 + 4912.18i) q^{92} +(33744.7 + 21555.8i) q^{94} +(127367. + 220605. i) q^{95} +(-8318.60 + 14408.2i) q^{97} +(32583.6 - 16911.4i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 3 q^{2} - q^{4} + 6 q^{5}+O(q^{10}) $ 56 * q + 3 * q^2 - q^4 + 6 * q^5	$ 56 q + 3 q^{2} - q^{4} + 6 q^{5} - 68 q^{10} - 2 q^{13} + 1518 q^{14} - q^{16} + 1242 q^{20} + 63 q^{22} + 12498 q^{25} - 2052 q^{28} + 11946 q^{29} + 7233 q^{32} + 6361 q^{34} - 8 q^{37} + 14877 q^{38} - 1526 q^{40} + 43536 q^{41} - 26880 q^{46} + 38414 q^{49} - 38631 q^{50} + 24988 q^{52} - 21186 q^{56} - 3314 q^{58} - 2 q^{61} - 106342 q^{64} - 35970 q^{65} - 31413 q^{68} + 10524 q^{70} + 53620 q^{73} + 20406 q^{74} + 26193 q^{76} - 26178 q^{77} - 151286 q^{82} + 6248 q^{85} - 279237 q^{86} - 122541 q^{88} - 435804 q^{92} + 63480 q^{94} - 58148 q^{97}+O(q^{100}) $ 56 * q + 3 * q^2 - q^4 + 6 * q^5 - 68 * q^10 - 2 * q^13 + 1518 * q^14 - q^16 + 1242 * q^20 + 63 * q^22 + 12498 * q^25 - 2052 * q^28 + 11946 * q^29 + 7233 * q^32 + 6361 * q^34 - 8 * q^37 + 14877 * q^38 - 1526 * q^40 + 43536 * q^41 - 26880 * q^46 + 38414 * q^49 - 38631 * q^50 + 24988 * q^52 - 21186 * q^56 - 3314 * q^58 - 2 * q^61 - 106342 * q^64 - 35970 * q^65 - 31413 * q^68 + 10524 * q^70 + 53620 * q^73 + 20406 * q^74 + 26193 * q^76 - 26178 * q^77 - 151286 * q^82 + 6248 * q^85 - 279237 * q^86 - 122541 * q^88 - 435804 * q^92 + 63480 * q^94 - 58148 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$29$	$55$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$

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 $

$2$	−0.253656	+	5.65116i	−0.0448405	+	0.998994i
$2$	−0.253656	+	5.65116i	−0.0448405	+	0.998994i
$3$		0			0
$3$		0			0
$4$	−31.8713	−	2.86690i	−0.995979	−	0.0895907i
$5$	−84.3255	+	48.6853i	−1.50846	+	0.870910i	−0.508508	+	0.861057i	$0.669803\pi$
$5$	−84.3255	+	48.6853i	−1.50846	+	0.870910i	−0.999951	+	0.00985262i	$0.996864\pi$
$6$		0			0
$7$	−87.9661	−	50.7872i	−0.678532	−	0.391750i	0.120770	−	0.992681i	$-0.461464\pi$
$7$	−87.9661	−	50.7872i	−0.678532	−	0.391750i	−0.799302	+	0.600930i	$0.794797\pi$
$8$	24.2857	−	179.383i	0.134161	−	0.990960i
$9$		0			0
$10$	−253.739	−	488.886i	−0.802394	−	1.54599i
$11$	73.2291	−	126.837i	0.182474	−	0.316055i	−0.760248	−	0.649633i	$-0.774923\pi$
$11$	73.2291	−	126.837i	0.182474	−	0.316055i	0.942723	+	0.333578i	$0.108256\pi$
$12$		0			0
$13$	402.832	+	697.726i	0.661098	+	1.14506i	0.980327	+	0.197378i	$0.0632427\pi$
$13$	402.832	+	697.726i	0.661098	+	1.14506i	−0.319229	+	0.947678i	$0.603424\pi$
$14$	309.320	−	484.228i	0.421782	−	0.660283i
$15$		0			0
$16$	1007.56	+	182.744i	0.983947	+	0.178461i
$17$			1238.37i			1.03927i	0.854389	+	0.519633i	$0.173931\pi$
$17$			1238.37i			1.03927i	−0.854389	+	0.519633i	$0.826069\pi$
$18$		0			0
$19$		−	2616.12i		−	1.66254i	−0.555866	−	0.831272i	$-0.687613\pi$
$19$		−	2616.12i		−	1.66254i	0.555866	−	0.831272i	$-0.312387\pi$
$20$	2827.14	−	1309.91i	1.58042	−	0.732263i
$21$		0			0
$22$	698.199	+	446.002i	0.307555	+	0.196463i
$23$	−84.5912	−	146.516i	−0.0333431	−	0.0577519i	0.848872	−	0.528598i	$-0.177282\pi$
$23$	−84.5912	−	146.516i	−0.0333431	−	0.0577519i	−0.882215	+	0.470846i	$0.843949\pi$
$24$		0			0
$25$	3178.02	−	5504.50i	1.01697	−	1.76144i
$26$	−4045.15	+	2099.49i	−1.17355	+	0.609088i
$27$		0			0
$28$	2657.99	+	1870.85i	0.640706	+	0.450965i
$29$	−1952.82	−	1127.46i	−0.431189	−	0.248947i	0.268664	−	0.963234i	$-0.413418\pi$
$29$	−1952.82	−	1127.46i	−0.431189	−	0.248947i	−0.699853	+	0.714287i	$0.746751\pi$
$30$		0			0
$31$	1787.03	−	1031.74i	0.333985	−	0.192826i	−0.323624	−	0.946186i	$-0.604901\pi$
$31$	1787.03	−	1031.74i	0.333985	−	0.192826i	0.657609	+	0.753359i	$0.271568\pi$
$32$	−1288.29	+	5647.54i	−0.222402	+	0.974955i
$33$		0			0
$34$	−6998.21	−	314.119i	−1.03822	−	0.0466012i
$35$	9890.37			1.36472
$36$		0			0
$37$	445.632			0.0535146			0.0267573	−	0.999642i	$-0.491482\pi$
$37$	445.632			0.0535146			0.0267573	+	0.999642i	$0.491482\pi$
$38$	14784.1	+	663.594i	1.66087	+	0.0745492i
$39$		0			0
$40$	6685.41	+	16308.9i	0.660660	+	1.61166i
$41$	1720.61	−	993.393i	0.159853	−	0.0922914i	−0.417939	−	0.908475i	$-0.637248\pi$
$41$	1720.61	−	993.393i	0.159853	−	0.0922914i	0.577793	+	0.816184i	$0.303914\pi$
$42$		0			0
$43$	3464.26	+	2000.09i	0.285719	+	0.164960i	0.636010	−	0.771681i	$-0.280584\pi$
$43$	3464.26	+	2000.09i	0.285719	+	0.164960i	−0.350291	+	0.936641i	$0.613917\pi$
$44$	−2697.54	+	3832.51i	−0.210056	+	0.298436i
$45$		0			0
$46$	849.444	−	440.874i	0.0591889	−	0.0307199i
$47$	3539.24	−	6130.14i	0.233703	−	0.404786i	−0.725192	−	0.688547i	$-0.758249\pi$
$47$	3539.24	−	6130.14i	0.233703	−	0.404786i	0.958895	+	0.283761i	$0.0915822\pi$
$48$		0			0
$49$	−3244.81	−	5620.18i	−0.193063	−	0.334395i
$50$	30300.7	+	19355.8i	1.71407	+	1.09493i
$51$		0			0
$52$	−10838.5	−	23392.3i	−0.555853	−	1.19968i
$53$			6234.98i			0.304891i	0.988312	+	0.152446i	$0.0487149\pi$
$53$			6234.98i			0.304891i	−0.988312	+	0.152446i	$0.951285\pi$
$54$		0			0
$55$			14260.7i			0.635675i
$56$	−11246.7	+	14546.2i	−0.479241	+	0.619840i
$57$		0			0
$58$	6866.81	−	10749.7i	0.268031	−	0.419592i
$59$	−16724.9	−	28968.4i	−0.625509	−	1.08341i	−0.988442	−	0.151598i	$-0.951558\pi$
$59$	−16724.9	−	28968.4i	−0.625509	−	1.08341i	0.362933	−	0.931815i	$-0.381775\pi$
$60$		0			0
$61$	14717.5	−	25491.5i	0.506420	−	0.877145i	−0.493553	−	0.869716i	$-0.664302\pi$
$61$	14717.5	−	25491.5i	0.506420	−	0.877145i	0.999972	−	0.00742891i	$-0.00236472\pi$
$62$	5377.25	+	10360.5i	0.177656	+	0.342296i
$63$		0			0
$64$	−31588.4	−	8712.87i	−0.964002	−	0.265896i
$65$	−67938.0	−	39224.1i	−1.99448	−	1.15151i
$66$		0			0
$67$	23308.8	−	13457.4i	0.634357	−	0.366246i	−0.148081	−	0.988975i	$-0.547310\pi$
$67$	23308.8	−	13457.4i	0.634357	−	0.366246i	0.782437	+	0.622729i	$0.213976\pi$
$68$	3550.28	−	39468.4i	0.0931086	−	1.03509i
$69$		0			0
$70$	−2508.75	+	55892.1i	−0.0611945	+	1.36334i
$71$	−36309.5			−0.854819			−0.427409	−	0.904058i	$-0.640574\pi$
$71$	−36309.5			−0.854819			−0.427409	+	0.904058i	$0.640574\pi$
$72$		0			0
$73$	−38203.0			−0.839056			−0.419528	−	0.907742i	$-0.637804\pi$
$73$	−38203.0			−0.839056			−0.419528	+	0.907742i	$0.637804\pi$
$74$	−113.037	+	2518.34i	−0.00239962	+	0.0534608i
$75$		0			0
$76$	−7500.15	+	83379.1i	−0.148948	+	1.65586i
$77$	−12883.4	+	7438.21i	−0.247629	+	0.142969i
$78$		0			0
$79$	54553.0	+	31496.2i	0.983448	+	0.567794i	0.903309	−	0.428990i	$-0.141130\pi$
$79$	54553.0	+	31496.2i	0.983448	+	0.567794i	0.0801384	+	0.996784i	$0.474464\pi$
$80$	−93860.1	+	33643.5i	−1.63967	+	0.587728i
$81$		0			0
$82$	5177.38	+	9975.41i	0.0850307	+	0.163831i
$83$	39957.8	−	69208.9i	0.636658	−	1.10272i	−0.349503	−	0.936935i	$-0.613650\pi$
$83$	39957.8	−	69208.9i	0.636658	−	1.10272i	0.986161	−	0.165789i	$-0.0530170\pi$
$84$		0			0
$85$	−60290.3	−	104426.i	−0.905107	−	1.56769i
$86$	−12181.6	+	19069.8i	−0.177606	+	0.278035i
$87$		0			0
$88$	−20973.9	−	16216.4i	−0.288717	−	0.223227i
$89$		−	96604.3i		−	1.29277i	−0.763011	−	0.646385i	$-0.776280\pi$
$89$		−	96604.3i		−	1.29277i	0.763011	−	0.646385i	$-0.223720\pi$
$90$		0			0
$91$		−	81835.0i		−	1.03594i
$92$	2275.98	+	4912.18i	0.0280349	+	0.0605069i
$93$		0			0
$94$	33744.7	+	21555.8i	0.393900	+	0.251619i
$95$	127367.	+	220605.i	1.44793	+	2.50788i
$96$		0			0
$97$	−8318.60	+	14408.2i	−0.0897678	+	0.155482i	−0.907413	−	0.420240i	$-0.861946\pi$
$97$	−8318.60	+	14408.2i	−0.0897678	+	0.155482i	0.817645	+	0.575723i	$0.195279\pi$
$98$	32583.6	−	16911.4i	0.342716	−	0.177875i
$99$		0			0
$100$	−117069.	+	166324.i	−1.17069	+	1.66324i
$101$	−25178.9	−	14537.1i	−0.245603	−	0.141799i	0.372146	−	0.928174i	$-0.378622\pi$
$101$	−25178.9	−	14537.1i	−0.245603	−	0.141799i	−0.617749	+	0.786375i	$0.711955\pi$
$102$		0			0
$103$	−132194.	+	76322.2i	−1.22777	+	0.708855i	−0.966564	−	0.256427i	$-0.917455\pi$
$103$	−132194.	+	76322.2i	−1.22777	+	0.708855i	−0.261210	+	0.965282i	$0.584121\pi$
$104$	134943.	−	55316.5i	1.22340	−	0.501500i
$105$		0			0
$106$	−35234.9	−	1581.54i	−0.304585	−	0.0136715i
$107$	−160032.			−1.35129			−0.675645	−	0.737227i	$-0.736135\pi$
$107$	−160032.			−1.35129			−0.675645	+	0.737227i	$0.736135\pi$
$108$		0			0
$109$	136775.			1.10265			0.551327	−	0.834289i	$-0.314122\pi$
$109$	136775.			1.10265			0.551327	+	0.834289i	$0.314122\pi$
$110$	−80589.7	−	3617.32i	−0.635035	−	0.0285039i
$111$		0			0
$112$	−79350.2	−	67246.5i	−0.597727	−	0.506553i
$113$	−29144.4	+	16826.5i	−0.214713	+	0.123965i	−0.603500	−	0.797363i	$-0.706228\pi$
$113$	−29144.4	+	16826.5i	−0.214713	+	0.123965i	0.388787	+	0.921328i	$0.372894\pi$
$114$		0			0
$115$	14266.4	+	8236.70i	0.100593	+	0.0580776i
$116$	59006.6	+	41532.2i	0.407151	+	0.286576i
$117$		0			0
$118$	167947.	−	87167.2i	1.11037	−	0.576299i
$119$	62893.2	−	108934.i	0.407133	−	0.705175i
$120$		0			0
$121$	69800.5	+	120898.i	0.433406	+	0.750682i
$122$	140324.	+	89637.3i	0.853555	+	0.545242i
$123$		0			0
$124$	−59912.8	+	27759.7i	−0.349917	+	0.162129i
$125$			314609.i			1.80093i
$126$		0			0
$127$		−	7342.22i		−	0.0403941i	−0.999796	−	0.0201971i	$-0.993571\pi$
$127$		−	7342.22i		−	0.0403941i	0.999796	−	0.0201971i	$-0.00642936\pi$
$128$	57250.4	−	176301.i	0.308855	−	0.951109i
$129$		0			0
$130$	238894.	−	373980.i	1.23979	−	1.94084i
$131$	−104864.	−	181630.i	−0.533886	−	0.924718i	−0.999216	−	0.0395811i	$-0.987398\pi$
$131$	−104864.	−	181630.i	−0.533886	−	0.924718i	0.465330	−	0.885137i	$-0.345936\pi$
$132$		0			0
$133$	−132865.	+	230130.i	−0.651302	+	1.12809i
$134$	70137.3	+	135136.i	0.337433	+	0.650141i
$135$		0			0
$136$	222142.	+	30074.6i	1.02987	+	0.139429i
$137$	221740.	+	128022.i	1.00935	+	0.582749i	0.911002	−	0.412403i	$-0.135310\pi$
$137$	221740.	+	128022.i	1.00935	+	0.582749i	0.0983495	+	0.995152i	$0.468644\pi$
$138$		0			0
$139$	31429.4	−	18145.7i	0.137974	−	0.0796595i	−0.429424	−	0.903103i	$-0.641283\pi$
$139$	31429.4	−	18145.7i	0.137974	−	0.0796595i	0.567398	+	0.823444i	$0.307950\pi$
$140$	−315219.	−	28354.7i	−1.35923	−	0.122266i
$141$		0			0
$142$	9210.11	−	205191.i	0.0383305	−	0.853959i
$143$	117996.			0.482534
$144$		0			0
$145$	219563.			0.867241
$146$	9690.43	−	215892.i	0.0376236	−	0.838212i
$147$		0			0
$148$	−14202.9	−	1277.58i	−0.0532994	−	0.00479441i
$149$	411222.	−	237419.i	1.51744	−	0.876092i	0.517646	−	0.855595i	$-0.326808\pi$
$149$	411222.	−	237419.i	1.51744	−	0.876092i	0.999790	−	0.0204977i	$-0.00652507\pi$
$150$		0			0
$151$	103973.	+	60029.0i	0.371090	+	0.214249i	0.673935	−	0.738791i	$-0.264603\pi$
$151$	103973.	+	60029.0i	0.371090	+	0.214249i	−0.302844	+	0.953040i	$0.597936\pi$
$152$	−469287.	−	63534.2i	−1.64751	−	0.223048i
$153$		0			0
$154$	−38766.6	−	74692.7i	−0.131721	−	0.253791i
$155$	−100461.	+	174004.i	−0.335869	+	0.581742i
$156$		0			0
$157$	−111283.	−	192748.i	−0.360312	−	0.624079i	0.627700	−	0.778456i	$-0.283997\pi$
$157$	−111283.	−	192748.i	−0.360312	−	0.624079i	−0.988012	+	0.154376i	$0.950663\pi$
$158$	−191828.	+	300299.i	−0.611321	+	0.956998i
$159$		0			0
$160$	−166317.	−	538953.i	−0.513613	−	1.66437i
$161$			17184.6i			0.0522486i
$162$		0			0
$163$		−	489772.i		−	1.44386i	−0.691967	−	0.721929i	$-0.743255\pi$
$163$		−	489772.i		−	1.44386i	0.691967	−	0.721929i	$-0.256745\pi$
$164$	−57686.0	+	26727.9i	−0.167479	+	0.0775989i
$165$		0			0
$166$	380975.	+	243363.i	1.07307	+	0.685464i
$167$	−43035.4	−	74539.6i	−0.119408	−	0.206822i	0.800125	−	0.599833i	$-0.204766\pi$
$167$	−43035.4	−	74539.6i	−0.119408	−	0.206822i	−0.919533	+	0.393012i	$0.871433\pi$
$168$		0			0
$169$	−138901.	+	240584.i	−0.374102	+	0.647963i
$170$	605421.	−	314222.i	1.60670	−	0.833901i
$171$		0			0
$172$	−104676.	−	73677.2i	−0.269791	−	0.189894i
$173$	170126.	+	98222.4i	0.432171	+	0.249514i	0.700271	−	0.713877i	$-0.253062\pi$
$173$	170126.	+	98222.4i	0.432171	+	0.249514i	−0.268100	+	0.963391i	$0.586396\pi$
$174$		0			0
$175$	−559116.	+	322806.i	−1.38009	+	0.796795i
$176$	96961.4	−	114413.i	0.235949	−	0.278417i
$177$		0			0
$178$	545927.	+	24504.2i	1.29147	+	0.0579684i
$179$	348859.			0.813799			0.406900	−	0.913473i	$-0.366610\pi$
$179$	348859.			0.813799			0.406900	+	0.913473i	$0.366610\pi$
$180$		0			0
$181$	−35362.9			−0.0802326			−0.0401163	−	0.999195i	$-0.512773\pi$
$181$	−35362.9			−0.0802326			−0.0401163	+	0.999195i	$0.512773\pi$
$182$	462463.	+	20757.9i	1.03490	+	0.0464521i
$183$		0			0
$184$	−28336.8	+	11616.0i	−0.0617031	+	0.0252936i
$185$	−37578.1	+	21695.7i	−0.0807246	+	0.0466064i
$186$		0			0
$187$	157070.	+	90684.5i	0.328465	+	0.189640i
$188$	−130375.	+	185229.i	−0.269029	+	0.382221i
$189$		0			0
$190$	−1.27898e6	+	663811.i	−2.57028	+	1.33401i
$191$	−434850.	+	753182.i	−0.862494	+	1.49388i	0.00701997	+	0.999975i	$0.497765\pi$
$191$	−434850.	+	753182.i	−0.862494	+	1.49388i	−0.869514	+	0.493908i	$0.835568\pi$
$192$		0			0
$193$	426577.	+	738854.i	0.824336	+	1.42779i	0.902425	+	0.430846i	$0.141785\pi$
$193$	426577.	+	738854.i	0.824336	+	1.42779i	−0.0780890	+	0.996946i	$0.524882\pi$
$194$	−79313.2	−	50664.5i	−0.151301	−	0.0966495i
$195$		0			0
$196$	87303.9	+	188425.i	0.162328	+	0.350347i
$197$			259841.i			0.477026i	0.971139	+	0.238513i	$0.0766600\pi$
$197$			259841.i			0.477026i	−0.971139	+	0.238513i	$0.923340\pi$
$198$		0			0
$199$		−	264379.i		−	0.473255i	−0.971600	−	0.236627i	$-0.923958\pi$
$199$		−	264379.i		−	0.473255i	0.971600	−	0.236627i	$-0.0760420\pi$
$200$	−910232.	−	703763.i	−1.60908	−	1.24409i
$201$		0			0
$202$	88538.2	−	138603.i	0.152669	−	0.238998i
$203$	114521.	+	198357.i	0.195050	+	0.337837i
$204$		0			0
$205$	−96727.3	+	167537.i	−0.160755	+	0.278436i
$206$	−397777.	−	766409.i	−0.653089	−	1.25832i
$207$		0			0
$208$	278373.	+	776617.i	0.446138	+	1.24465i
$209$	−331819.	−	191576.i	−0.525455	−	0.303372i
$210$		0			0
$211$	−889657.	+	513644.i	−1.37568	+	0.794247i	−0.991636	−	0.129069i	$-0.958801\pi$
$211$	−889657.	+	513644.i	−1.37568	+	0.794247i	−0.384041	+	0.923316i	$0.625468\pi$
$212$	17875.1	−	198717.i	0.0273154	−	0.303665i
$213$		0			0
$214$	40593.2	−	904369.i	0.0605924	−	1.34993i
$215$	−389500.			−0.574661
$216$		0			0
$217$	−209597.			−0.302159
$218$	−34693.7	+	772936.i	−0.0494435	+	1.10155i
$219$		0			0
$220$	40884.1	−	454508.i	0.0569506	−	0.633119i
$221$	−864041.	+	498854.i	−1.19002	+	0.687057i
$222$		0			0
$223$	524934.	+	303071.i	0.706875	+	0.408115i	0.809903	−	0.586564i	$-0.199520\pi$
$223$	524934.	+	303071.i	0.706875	+	0.408115i	−0.103028	+	0.994678i	$0.532853\pi$
$224$	400149.	−	431364.i	0.532846	−	0.574412i
$225$		0			0
$226$	−87696.8	−	168968.i	−0.114212	−	0.220056i
$227$	85552.8	−	148182.i	0.110197	−	0.190867i	−0.805653	−	0.592388i	$-0.798185\pi$
$227$	85552.8	−	148182.i	0.110197	−	0.190867i	0.915850	+	0.401522i	$0.131519\pi$
$228$		0			0
$229$	−689040.	−	1.19345e6i	−0.868271	−	1.50389i	−0.863762	−	0.503900i	$-0.831898\pi$
$229$	−689040.	−	1.19345e6i	−0.868271	−	1.50389i	−0.00450932	−	0.999990i	$-0.501435\pi$
$230$	−50165.7	+	78532.4i	−0.0625298	+	0.0978879i
$231$		0			0
$232$	−249673.	+	322921.i	−0.304545	+	0.393892i
$233$		−	1.36894e6i		−	1.65194i	−0.563711	−	0.825972i	$-0.690627\pi$
$233$		−	1.36894e6i		−	1.65194i	0.563711	−	0.825972i	$-0.309373\pi$
$234$		0			0
$235$			689236.i			0.814138i
$236$	449995.	+	971209.i	0.525930	+	1.13510i
$237$		0			0
$238$	599652.	+	383052.i	0.686210	+	0.438344i
$239$	−155455.	−	269255.i	−0.176039	−	0.304908i	0.764481	−	0.644646i	$-0.222995\pi$
$239$	−155455.	−	269255.i	−0.176039	−	0.304908i	−0.940520	+	0.339737i	$0.889662\pi$
$240$		0			0
$241$	196168.	−	339774.i	0.217564	−	0.376832i	−0.736499	−	0.676439i	$-0.763522\pi$
$241$	196168.	−	339774.i	0.217564	−	0.376832i	0.954063	+	0.299607i	$0.0968557\pi$
$242$	−700920.	+	363788.i	−0.769361	+	0.399309i
$243$		0			0
$244$	−542149.	+	770255.i	−0.582967	+	0.828247i
$245$	547241.	+	315950.i	0.582456	+	0.336281i
$246$		0			0
$247$	1.82533e6	−	1.05386e6i	1.90371	−	1.09910i
$248$	−141677.	−	345619.i	−0.146275	−	0.356835i
$249$		0			0
$250$	−1.77791e6	−	79802.4i	−1.79912	−	0.0807544i
$251$	241581.			0.242035			0.121017	−	0.992650i	$-0.461384\pi$
$251$	241581.			0.242035			0.121017	+	0.992650i	$0.461384\pi$
$252$		0			0
$253$	−24778.1			−0.0243370
$254$	41492.1	+	1862.40i	0.0403535	+	0.00181129i
$255$		0			0
$256$	981785.	+	368252.i	0.936303	+	0.351192i
$257$	231851.	−	133859.i	0.218966	−	0.126420i	−0.386506	−	0.922287i	$-0.626318\pi$
$257$	231851.	−	133859.i	0.218966	−	0.126420i	0.605471	+	0.795867i	$0.292985\pi$
$258$		0			0
$259$	−39200.5	−	22632.4i	−0.0363113	−	0.0209644i
$260$	2.05282e6	+	1.44489e6i	1.88329	+	1.32557i
$261$		0			0
$262$	1.05302e6	−	546533.i	0.947728	−	0.491885i
$263$	829311.	−	1.43641e6i	0.739313	−	1.28053i	−0.213493	−	0.976945i	$-0.568484\pi$
$263$	829311.	−	1.43641e6i	0.739313	−	1.28053i	0.952805	−	0.303582i	$-0.0981827\pi$
$264$		0			0
$265$	−303552.	−	525767.i	−0.265533	−	0.459916i
$266$	−1.26680e6	−	809218.i	−1.09775	−	0.701231i
$267$		0			0
$268$	−781464.	+	362080.i	−0.664618	+	0.307941i
$269$		−	1.42634e6i		−	1.20183i	−0.799312	−	0.600916i	$-0.794803\pi$
$269$		−	1.42634e6i		−	1.20183i	0.799312	−	0.600916i	$-0.205197\pi$
$270$		0			0
$271$		−	1.91215e6i		−	1.58161i	−0.612068	−	0.790805i	$-0.709662\pi$
$271$		−	1.91215e6i		−	1.58161i	0.612068	−	0.790805i	$-0.290338\pi$
$272$	−226304.	+	1.24773e6i	−0.185468	+	1.02258i
$273$		0			0
$274$	−779716.	+	1.22061e6i	−0.627423	+	0.982205i
$275$	−465447.	−	806179.i	−0.371141	−	0.642835i
$276$		0			0
$277$	169154.	−	292983.i	0.132459	−	0.229426i	−0.792165	−	0.610307i	$-0.791046\pi$
$277$	169154.	−	292983.i	0.132459	−	0.229426i	0.924624	+	0.380881i	$0.124379\pi$
$278$	94572.4	+	182215.i	0.0733926	+	0.141408i
$279$		0			0
$280$	240195.	−	1.77416e6i	0.183091	−	1.35238i
$281$	−817291.	−	471863.i	−0.617463	−	0.356492i	0.158418	−	0.987372i	$-0.449361\pi$
$281$	−817291.	−	471863.i	−0.617463	−	0.356492i	−0.775881	+	0.630880i	$0.782694\pi$
$282$		0			0
$283$	−1.92014e6	+	1.10859e6i	−1.42517	+	0.822821i	−0.996734	−	0.0807515i	$-0.974268\pi$
$283$	−1.92014e6	+	1.10859e6i	−1.42517	+	0.822821i	−0.428434	+	0.903573i	$0.640935\pi$
$284$	1.15723e6	+	104096.i	0.851381	+	0.0765838i
$285$		0			0
$286$	−29930.4	+	666816.i	−0.0216370	+	0.482049i
$287$	−201807.			−0.144621
$288$		0			0
$289$	−113695.			−0.0800752
$290$	−55693.5	+	1.24079e6i	−0.0388875	+	0.866369i
$291$		0			0
$292$	1.21758e6	+	109524.i	0.835682	+	0.0751716i
$293$	−1.18621e6	+	684857.i	−0.807219	+	0.466048i	−0.845989	−	0.533200i	$-0.820989\pi$
$293$	−1.18621e6	+	684857.i	−0.807219	+	0.466048i	0.0387699	+	0.999248i	$0.487656\pi$
$294$		0			0
$295$	2.82067e6	+	1.62851e6i	1.88711	+	1.08952i
$296$	10822.5	−	79938.8i	0.00717956	−	0.0530308i
$297$		0			0
$298$	1.23739e6	+	2.38410e6i	0.807169	+	1.55519i
$299$	68152.1	−	118043.i	0.0440861	−	0.0763593i
$300$		0			0
$301$	−203158.	−	351880.i	−0.129246	−	0.223861i
$302$	−365607.	+	572343.i	−0.230673	+	0.361110i
$303$		0			0
$304$	478079.	−	2.63590e6i	0.296699	−	1.63586i
$305$			2.86611e6i			1.76418i
$306$		0			0
$307$		−	809224.i		−	0.490030i	−0.969519	−	0.245015i	$-0.921207\pi$
$307$		−	809224.i		−	0.490030i	0.969519	−	0.245015i	$-0.0787929\pi$
$308$	431934.	−	200130.i	0.259442	−	0.120209i
$309$		0			0
$310$	−957843.	−	611860.i	−0.566096	−	0.361616i
$311$	35523.7	+	61528.8i	0.0208265	+	0.0360726i	0.876251	−	0.481855i	$-0.160037\pi$
$311$	35523.7	+	61528.8i	0.0208265	+	0.0360726i	−0.855424	+	0.517928i	$0.826704\pi$
$312$		0			0
$313$	893740.	−	1.54800e6i	0.515644	−	0.893122i	−0.484191	−	0.874963i	$-0.660886\pi$
$313$	893740.	−	1.54800e6i	0.515644	−	0.893122i	0.999835	−	0.0181599i	$-0.00578080\pi$
$314$	1.11748e6	−	579986.i	0.639608	−	0.331966i
$315$		0			0
$316$	−1.64838e6	−	1.16022e6i	−0.928624	−	0.653618i
$317$	287153.	+	165788.i	0.160496	+	0.0926627i	0.578097	−	0.815968i	$-0.303796\pi$
$317$	287153.	+	165788.i	0.160496	+	0.0926627i	−0.417601	+	0.908631i	$0.637129\pi$
$318$		0			0
$319$	−286007.	+	165126.i	−0.157362	+	0.0908529i
$320$	3.08790e6	−	803175.i	1.68573	−	0.438466i
$321$		0			0
$322$	−97113.0	−	4358.98i	−0.0521961	−	0.00234285i
$323$	3.23971e6			1.72783
$324$		0			0
$325$	5.12084e6			2.68926
$326$	2.76778e6	+	124234.i	1.44241	+	0.0647433i
$327$		0			0
$328$	−136412.	−	332773.i	−0.0700110	−	0.170790i
$329$	−622666.	+	359496.i	−0.317150	+	0.183107i
$330$		0			0
$331$	−2.05838e6	−	1.18840e6i	−1.03265	−	0.596203i	−0.114910	−	0.993376i	$-0.536658\pi$
$331$	−2.05838e6	−	1.18840e6i	−1.03265	−	0.596203i	−0.917744	+	0.397173i	$0.869991\pi$
$332$	−1.47192e6	+	2.09122e6i	−0.732891	+	1.04125i
$333$		0			0
$334$	432152.	−	224293.i	0.211968	−	0.110014i
$335$	−1.31035e6	+	2.26960e6i	−0.637934	+	1.10493i
$336$		0			0
$337$	−62983.9	−	109091.i	−0.0302103	−	0.0523257i	0.850525	−	0.525935i	$-0.176284\pi$
$337$	−62983.9	−	109091.i	−0.0302103	−	0.0523257i	−0.880735	+	0.473609i	$0.842951\pi$
$338$	−1.32435e6	−	845980.i	−0.630536	−	0.402780i
$339$		0			0
$340$	1.62215e6	+	3.50104e6i	0.761017	+	1.64248i
$341$		−	302214.i		−	0.140743i
$342$		0			0
$343$			2.36634e6i			1.08603i
$344$	442914.	−	572855.i	0.201801	−	0.261005i
$345$		0			0
$346$	−598224.	+	936496.i	−0.268642	+	0.420548i
$347$	−577346.	−	999992.i	−0.257402	−	0.445834i	0.708143	−	0.706069i	$-0.249533\pi$
$347$	−577346.	−	999992.i	−0.257402	−	0.445834i	−0.965545	+	0.260235i	$0.916200\pi$
$348$		0			0
$349$	−1.82275e6	+	3.15709e6i	−0.801056	+	1.38747i	0.117865	+	0.993030i	$0.462395\pi$
$349$	−1.82275e6	+	3.15709e6i	−0.801056	+	1.38747i	−0.918922	+	0.394440i	$0.870938\pi$
$350$	−1.68241e6	−	3.24154e6i	−0.734110	−	1.41443i
$351$		0			0
$352$	621974.	+	576967.i	0.267557	+	0.248196i
$353$	−990369.	−	571790.i	−0.423020	−	0.244230i	0.273349	−	0.961915i	$-0.411869\pi$
$353$	−990369.	−	571790.i	−0.423020	−	0.244230i	−0.696368	+	0.717685i	$0.745202\pi$
$354$		0			0
$355$	3.06181e6	−	1.76774e6i	1.28946	−	0.744470i
$356$	−276955.	+	3.07891e6i	−0.115820	+	1.28757i
$357$		0			0
$358$	−88490.1	+	1.97146e6i	−0.0364911	+	0.812981i
$359$	−111222.			−0.0455466			−0.0227733	−	0.999741i	$-0.507250\pi$
$359$	−111222.			−0.0455466			−0.0227733	+	0.999741i	$0.507250\pi$
$360$		0			0
$361$	−4.36797e6			−1.76405
$362$	8970.00	−	199841.i	0.00359767	−	0.0801519i
$363$		0			0
$364$	−234613.	+	2.60819e6i	−0.0928108	+	1.03178i
$365$	3.22149e6	−	1.85993e6i	1.26568	−	0.730742i
$366$		0			0
$367$	−3.77385e6	−	2.17883e6i	−1.46258	−	0.844421i	−0.463450	−	0.886123i	$-0.653388\pi$
$367$	−3.77385e6	−	2.17883e6i	−1.46258	−	0.844421i	−0.999130	+	0.0417025i	$0.986722\pi$
$368$	−58455.9	−	163083.i	−0.0225014	−	0.0627752i
$369$		0			0
$370$	−113074.	−	217863.i	−0.0429398	−	0.0827333i
$371$	316657.	−	548466.i	0.119441	−	0.206878i
$372$		0			0
$373$	−1.34963e6	−	2.33763e6i	−0.502277	−	0.869970i	−0.999997	−	0.00263144i	$-0.999162\pi$
$373$	−1.34963e6	−	2.33763e6i	−0.502277	−	0.869970i	0.497719	−	0.867338i	$-0.334171\pi$
$374$	−552315.	+	864626.i	−0.204177	+	0.319631i
$375$		0			0
$376$	−1.01369e6	−	783753.i	−0.369773	−	0.285897i
$377$		−	1.81671e6i		−	0.658313i
$378$		0			0
$379$		−	2.05325e6i		−	0.734249i	−0.930172	−	0.367125i	$-0.880342\pi$
$379$		−	2.05325e6i		−	0.734249i	0.930172	−	0.367125i	$-0.119658\pi$
$380$	−3.42689e6	−	7.39613e6i	−1.21742	−	2.62752i
$381$		0			0
$382$	−4.14606e6	−	2.64846e6i	−1.45371	−	0.928613i
$383$	2.72270e6	+	4.71586e6i	0.948426	+	1.64272i	0.748741	+	0.662862i	$0.230658\pi$
$383$	2.72270e6	+	4.71586e6i	0.948426	+	1.64272i	0.199685	+	0.979860i	$0.436008\pi$
$384$		0			0
$385$	724263.	−	1.25446e6i	0.249026	−	0.431326i
$386$	−4.28359e6	+	2.22324e6i	−1.46332	+	0.759484i
$387$		0			0
$388$	306432.	−	435361.i	0.103337	−	0.146815i
$389$	−2.51571e6	−	1.45244e6i	−0.842919	−	0.486660i	0.0153362	−	0.999882i	$-0.495118\pi$
$389$	−2.51571e6	−	1.45244e6i	−0.842919	−	0.486660i	−0.858255	+	0.513223i	$0.828451\pi$
$390$		0			0
$391$	181441.	−	104755.i	0.0600196	−	0.0346523i
$392$	−1.08697e6	+	445574.i	−0.357274	+	0.146455i
$393$		0			0
$394$	−1.46841e6	−	65910.3i	−0.476547	−	0.0213901i
$395$	−6.13361e6			−1.97799
$396$		0			0
$397$	−1.59810e6			−0.508896			−0.254448	−	0.967086i	$-0.581894\pi$
$397$	−1.59810e6			−0.508896			−0.254448	+	0.967086i	$0.581894\pi$
$398$	1.49405e6	+	67061.4i	0.472779	+	0.0212210i
$399$		0			0
$400$	4.20797e6	−	4.96536e6i	1.31499	−	1.55167i
$401$	1.48732e6	−	858705.i	0.461895	−	0.266675i	−0.250945	−	0.968001i	$-0.580741\pi$
$401$	1.48732e6	−	858705.i	0.461895	−	0.266675i	0.712841	+	0.701326i	$0.247408\pi$
$402$		0			0
$403$	1.43974e6	+	831237.i	0.441594	+	0.254954i
$404$	760810.	+	535501.i	0.231912	+	0.163233i
$405$		0			0
$406$	−1.15000e6	+	596864.i	−0.346243	+	0.179705i
$407$	32633.2	−	56522.4i	0.00976504	−	0.0169135i
$408$		0			0
$409$	2.74998e6	+	4.76310e6i	0.812870	+	1.40793i	0.910847	+	0.412744i	$0.135430\pi$
$409$	2.74998e6	+	4.76310e6i	0.812870	+	1.40793i	−0.0979768	+	0.995189i	$0.531237\pi$
$410$	−922242.	−	589119.i	−0.270947	−	0.173079i
$411$		0			0
$412$	4.43200e6	−	2.05350e6i	1.28634	−	0.596008i
$413$			3.39765e6i			0.980174i
$414$		0			0
$415$			7.78143e6i			2.21789i
$416$	−4.45940e6	+	1.37614e6i	−1.26341	+	0.389878i
$417$		0			0
$418$	1.16679e6	−	1.82657e6i	0.326628	−	0.511323i
$419$	−3.22137e6	−	5.57958e6i	−0.896408	−	1.55262i	−0.832052	−	0.554698i	$-0.812834\pi$
$419$	−3.22137e6	−	5.57958e6i	−0.896408	−	1.55262i	−0.0643564	−	0.997927i	$-0.520499\pi$
$420$		0			0
$421$	−1.68713e6	+	2.92220e6i	−0.463921	+	0.803535i	−0.999152	−	0.0411706i	$-0.986891\pi$
$421$	−1.68713e6	+	2.92220e6i	−0.463921	+	0.803535i	0.535231	+	0.844706i	$0.320225\pi$
$422$	−2.67702e6	−	5.15789e6i	−0.731762	−	1.40991i
$423$		0			0
$424$	1.11845e6	+	151421.i	0.302135	+	0.0409044i
$425$	6.81659e6	+	3.93556e6i	1.83060	+	1.05690i
$426$		0			0
$427$	−2.58929e6	+	1.49493e6i	−0.687244	+	0.396780i
$428$	5.10044e6	+	458797.i	1.34586	+	0.121063i
$429$		0			0
$430$	98799.1	−	2.20113e6i	0.0257681	−	0.574083i
$431$	−1.69209e6			−0.438763			−0.219382	−	0.975639i	$-0.570404\pi$
$431$	−1.69209e6			−0.438763			−0.219382	+	0.975639i	$0.570404\pi$
$432$		0			0
$433$	−3.34335e6			−0.856964			−0.428482	−	0.903550i	$-0.640951\pi$
$433$	−3.34335e6			−0.856964			−0.428482	+	0.903550i	$0.640951\pi$
$434$	53165.5	−	1.18447e6i	0.0135490	−	0.301855i
$435$		0			0
$436$	−4.35919e6	−	392120.i	−1.09822	−	0.0987876i
$437$	−383304.	+	221300.i	−0.0960150	+	0.0554343i
$438$		0			0
$439$	4.12524e6	+	2.38171e6i	1.02162	+	0.589831i	0.914572	−	0.404424i	$-0.132528\pi$
$439$	4.12524e6	+	2.38171e6i	1.02162	+	0.589831i	0.107045	+	0.994254i	$0.465861\pi$
$440$	2.55813e6	+	346332.i	0.629928	+	0.0852826i
$441$		0			0
$442$	−2.59994e6	−	5.00937e6i	−0.633005	−	1.21963i
$443$	2.19145e6	−	3.79571e6i	0.530546	−	0.918932i	−0.468819	−	0.883294i	$-0.655320\pi$
$443$	2.19145e6	−	3.79571e6i	0.530546	−	0.918932i	0.999365	−	0.0356380i	$-0.0113463\pi$
$444$		0			0
$445$	4.70321e6	+	8.14620e6i	1.12589	+	1.95009i
$446$	−1.84586e6	+	2.88961e6i	−0.439401	+	0.687864i
$447$		0			0
$448$	2.33621e6	+	2.37073e6i	0.549941	+	0.558067i
$449$			2.64215e6i			0.618502i	0.950981	+	0.309251i	$0.100078\pi$
$449$			2.64215e6i			0.618502i	−0.950981	+	0.309251i	$0.899922\pi$
$450$		0			0
$451$		−	290981.i		−	0.0673633i
$452$	977110.	−	452729.i	0.224956	−	0.104230i
$453$		0			0
$454$	815699.	+	521060.i	0.185733	+	0.118645i
$455$	3.98416e6	+	6.90077e6i	0.902212	+	1.56268i
$456$		0			0
$457$	1.74172e6	−	3.01674e6i	0.390110	−	0.675690i	−0.602354	−	0.798229i	$-0.705770\pi$
$457$	1.74172e6	−	3.01674e6i	0.390110	−	0.675690i	0.992464	+	0.122539i	$0.0391037\pi$
$458$	6.91917e6	−	3.59115e6i	1.54131	−	0.799963i
$459$		0			0
$460$	−431075.	−	303415.i	−0.0949856	−	0.0668563i
$461$	−2.93883e6	−	1.69673e6i	−0.644054	−	0.371845i	0.142121	−	0.989849i	$-0.454608\pi$
$461$	−2.93883e6	−	1.69673e6i	−0.644054	−	0.371845i	−0.786174	+	0.618005i	$0.787941\pi$
$462$		0			0
$463$	−167674.	+	96806.8i	−0.0363508	+	0.0209871i	−0.518065	−	0.855341i	$-0.673348\pi$
$463$	−167674.	+	96806.8i	−0.0363508	+	0.0209871i	0.481714	+	0.876328i	$0.340014\pi$
$464$	−1.76155e6	−	1.49285e6i	−0.379840	−	0.321901i
$465$		0			0
$466$	7.73612e6	+	347240.i	1.65028	+	0.0740739i
$467$	−3.24407e6			−0.688332			−0.344166	−	0.938909i	$-0.611838\pi$
$467$	−3.24407e6			−0.688332			−0.344166	+	0.938909i	$0.611838\pi$
$468$		0			0
$469$	−2.73385e6			−0.573908
$470$	−3.89498e6	−	174829.i	−0.813319	−	0.0365063i
$471$		0			0
$472$	−5.60261e6	+	2.29664e6i	−1.15754	+	0.474503i
$473$	507369.	−	292930.i	0.104273	−	0.0602020i
$474$		0			0
$475$	−1.44004e7	−	8.31408e6i	−2.92847	−	1.69075i
$476$	−2.31679e6	+	3.29157e6i	−0.468673	+	0.665864i
$477$		0			0
$478$	1.56104e6	−	810201.i	0.312495	−	0.162190i
$479$	−4.10699e6	+	7.11352e6i	−0.817871	+	1.41659i	0.0893767	+	0.995998i	$0.471513\pi$
$479$	−4.10699e6	+	7.11352e6i	−0.817871	+	1.41659i	−0.907248	+	0.420596i	$0.861821\pi$
$480$		0			0
$481$	179515.	+	310929.i	0.0353784	+	0.0612772i
$482$	1.87036e6	+	1.19477e6i	0.366697	+	0.234242i
$483$		0			0
$484$	−1.87803e6	−	4.05329e6i	−0.364409	−	0.786492i
$485$		−	1.61997e6i		−	0.312719i
$486$		0			0
$487$			1.63906e6i			0.313165i	0.987665	+	0.156583i	$0.0500477\pi$
$487$			1.63906e6i			0.313165i	−0.987665	+	0.156583i	$0.949952\pi$
$488$	−4.21532e6	−	3.25915e6i	−0.801273	−	0.619520i
$489$		0			0
$490$	−1.92429e6	+	3.01240e6i	−0.362060	+	0.566791i
$491$	2.03219e6	+	3.51985e6i	0.380417	+	0.658902i	0.991122	−	0.132957i	$-0.0424471\pi$
$491$	2.03219e6	+	3.51985e6i	0.380417	+	0.658902i	−0.610705	+	0.791858i	$0.709114\pi$
$492$		0			0
$493$	1.39621e6	−	2.41831e6i	0.258722	−	0.448120i
$494$	5.49251e6	+	1.05826e7i	1.01264	+	1.95107i
$495$		0			0
$496$	1.98908e6	−	712974.i	0.363036	−	0.130128i
$497$	3.19400e6	+	1.84406e6i	0.580022	+	0.334876i
$498$		0			0
$499$	2.92199e6	−	1.68701e6i	0.525325	−	0.303296i	−0.213786	−	0.976881i	$-0.568579\pi$
$499$	2.92199e6	−	1.68701e6i	0.525325	−	0.303296i	0.739111	+	0.673584i	$0.235246\pi$
$500$	901954.	−	1.00270e7i	0.161346	−	1.79369i
$501$		0			0
$502$	−61278.3	+	1.36521e6i	−0.0108529	+	0.241791i
$503$	7.37612e6			1.29989			0.649947	−	0.759979i	$-0.274791\pi$
$503$	7.37612e6			1.29989			0.649947	+	0.759979i	$0.274791\pi$
$504$		0			0
$505$	2.83097e6			0.493977
$506$	6285.12	−	140025.i	0.00109128	−	0.0243125i
$507$		0			0
$508$	−21049.4	+	234006.i	−0.00361894	+	0.0402317i
$509$	5.72270e6	−	3.30400e6i	0.979054	−	0.565257i	0.0770693	−	0.997026i	$-0.475444\pi$
$509$	5.72270e6	−	3.30400e6i	0.979054	−	0.565257i	0.901984	+	0.431769i	$0.142110\pi$
$510$		0			0
$511$	3.36057e6	+	1.94023e6i	0.569326	+	0.328700i
$512$	−2.33009e6	+	5.45482e6i	−0.392823	+	0.919614i
$513$		0			0
$514$	697650.	+	1.34418e6i	0.116474	+	0.224414i
$515$	7.43154e6	−	1.28718e7i	1.23470	−	2.13856i
$516$		0			0
$517$	−518350.	−	897809.i	−0.0852898	−	0.147726i
$518$	137843.	−	215788.i	0.0225715	−	0.0353348i
$519$		0			0
$520$	−8.68604e6	+	1.12343e7i	−1.40868	+	1.82196i
$521$			1.91733e6i			0.309459i	0.987957	+	0.154730i	$0.0494506\pi$
$521$			1.91733e6i			0.309459i	−0.987957	+	0.154730i	$0.950549\pi$
$522$		0			0
$523$		−	5.16891e6i		−	0.826313i	−0.910660	−	0.413157i	$-0.864426\pi$
$523$		−	5.16891e6i		−	0.826313i	0.910660	−	0.413157i	$-0.135574\pi$
$524$	2.82144e6	+	6.08943e6i	0.448893	+	0.968831i
$525$		0			0
$526$	7.90702e6	+	5.05093e6i	1.24609	+	0.795988i
$527$	1.27767e6	+	2.21300e6i	0.200398	+	0.347100i
$528$		0			0
$529$	3.20386e6	−	5.54925e6i	0.497776	−	0.862174i
$530$	3.04819e6	−	1.58206e6i	0.471360	−	0.244643i
$531$		0			0
$532$	4.89435e6	−	6.95362e6i	0.749750	−	1.06520i
$533$	1.38623e6	+	800342.i	0.211358	+	0.122027i
$534$		0			0
$535$	1.34948e7	−	7.79123e6i	2.03837	−	1.17685i
$536$	−1.84795e6	−	4.50803e6i	−0.277829	−	0.677758i
$537$		0			0
$538$	8.06051e6	+	361801.i	1.20062	+	0.0538907i
$539$	−950459.			−0.140916
$540$		0			0
$541$	3.10786e6			0.456528			0.228264	−	0.973599i	$-0.426695\pi$
$541$	3.10786e6			0.456528			0.228264	+	0.973599i	$0.426695\pi$
$542$	1.08059e7	+	485029.i	1.58002	+	0.0709201i
$543$		0			0
$544$	−6.99373e6	−	1.59538e6i	−1.01324	−	0.231135i
$545$	−1.15336e7	+	6.65892e6i	−1.66331	+	0.960313i
$546$		0			0
$547$	−3.78249e6	−	2.18382e6i	−0.540517	−	0.312068i	0.204772	−	0.978810i	$-0.434355\pi$
$547$	−3.78249e6	−	2.18382e6i	−0.540517	−	0.312068i	−0.745288	+	0.666742i	$0.767688\pi$
$548$	−6.70011e6	−	4.71592e6i	−0.953083	−	0.670834i
$549$		0			0
$550$	4.67391e6	−	2.42583e6i	0.658831	−	0.341943i
$551$	−2.94957e6	+	5.10881e6i	−0.413885	+	0.716870i
$552$		0			0
$553$	−3.19921e6	−	5.54120e6i	−0.444867	−	0.770532i
$554$	1.61279e6	+	1.03023e6i	0.223256	+	0.142614i
$555$		0			0
$556$	−1.05372e6	+	488224.i	−0.144556	+	0.0669780i
$557$		−	4.46009e6i		−	0.609124i	−0.952493	−	0.304562i	$-0.901490\pi$
$557$		−	4.46009e6i		−	0.609124i	0.952493	−	0.304562i	$-0.0985100\pi$
$558$		0			0
$559$			3.22281e6i			0.436219i
$560$	9.96516e6	+	1.80741e6i	1.34281	+	0.243549i
$561$		0			0
$562$	2.87389e6	−	4.49896e6i	0.383821	−	0.600857i
$563$	−5.22200e6	−	9.04476e6i	−0.694330	−	1.20261i	−0.970406	−	0.241478i	$-0.922368\pi$
$563$	−5.22200e6	−	9.04476e6i	−0.694330	−	1.20261i	0.276077	−	0.961136i	$-0.410966\pi$
$564$		0			0
$565$	1.63841e6	−	2.83781e6i	0.215924	−	0.373992i
$566$	−5.77778e6	−	1.11322e7i	−0.758089	−	1.46063i
$567$		0			0
$568$	−881801.	+	6.51330e6i	−0.114683	+	0.847091i
$569$	−2.55116e6	−	1.47291e6i	−0.330337	−	0.190720i	0.325654	−	0.945489i	$-0.394416\pi$
$569$	−2.55116e6	−	1.47291e6i	−0.330337	−	0.190720i	−0.655991	+	0.754769i	$0.727749\pi$
$570$		0			0
$571$	−199833.	+	115373.i	−0.0256493	+	0.0148086i	−0.512770	−	0.858526i	$-0.671381\pi$
$571$	−199833.	+	115373.i	−0.0256493	+	0.0148086i	0.487121	+	0.873335i	$0.338047\pi$
$572$	−3.76069e6	−	338284.i	−0.480594	−	0.0432306i
$573$		0			0
$574$	51189.5	−	1.14044e6i	0.00648487	−	0.144475i
$575$	−1.07533e6			−0.135635
$576$		0			0
$577$	4.42964e6			0.553897			0.276949	−	0.960885i	$-0.410677\pi$
$577$	4.42964e6			0.553897			0.276949	+	0.960885i	$0.410677\pi$
$578$	28839.5	−	642511.i	0.00359061	−	0.0799947i
$579$		0			0
$580$	−6.99777e6	−	629467.i	−0.863754	−	0.0776967i
$581$	−7.02986e6	+	4.05869e6i	−0.863985	+	0.498822i
$582$		0			0
$583$	790822.	+	456582.i	0.0963624	+	0.0556349i
$584$	−927787.	+	6.85297e6i	−0.112568	+	0.831470i
$585$		0			0
$586$	−3.56935e6	−	6.87717e6i	−0.429383	−	0.827305i
$587$	509131.	−	881841.i	0.0609866	−	0.105632i	−0.833920	−	0.551885i	$-0.813909\pi$
$587$	509131.	−	881841.i	0.0609866	−	0.105632i	0.894907	+	0.446253i	$0.147242\pi$
$588$		0			0
$589$	−2.69915e6	−	4.67507e6i	−0.320582	−	0.555265i
$590$	−9.91848e6	+	1.55270e7i	−1.17305	+	1.83636i
$591$		0			0
$592$	449002.	+	81436.6i	0.0526555	+	0.00955026i
$593$		−	1.12943e6i		−	0.131893i	−0.997823	−	0.0659466i	$-0.978993\pi$
$593$		−	1.12943e6i		−	0.131893i	0.997823	−	0.0659466i	$-0.0210067\pi$
$594$		0			0
$595$			1.22479e7i			1.41831i
$596$	−1.37868e7	+	6.38792e6i	−1.58982	+	0.736621i
$597$		0			0
$598$	649793.	+	415081.i	0.0743057	+	0.0474657i
$599$	−6.98600e6	−	1.21001e7i	−0.795539	−	1.37791i	−0.922496	−	0.386006i	$-0.873855\pi$
$599$	−6.98600e6	−	1.21001e7i	−0.795539	−	1.37791i	0.126958	−	0.991908i	$-0.459479\pi$
$600$		0			0
$601$	−7.90974e6	+	1.37001e7i	−0.893256	+	1.54717i	−0.0573087	+	0.998357i	$0.518252\pi$
$601$	−7.90974e6	+	1.37001e7i	−0.893256	+	1.54717i	−0.835948	+	0.548809i	$0.815081\pi$
$602$	2.04007e6	−	1.05882e6i	0.229432	−	0.119078i
$603$		0			0
$604$	−3.14167e6	−	2.21128e6i	−0.350403	−	0.246634i
$605$	−1.17719e7	−	6.79652e6i	−1.30755	−	0.754915i
$606$		0			0
$607$	−4.40500e6	+	2.54323e6i	−0.485259	+	0.280165i	−0.722606	−	0.691261i	$-0.757056\pi$
$607$	−4.40500e6	+	2.54323e6i	−0.485259	+	0.280165i	0.237346	+	0.971425i	$0.423722\pi$
$608$	1.47746e7	+	3.37032e6i	1.62091	+	0.369753i
$609$		0			0
$610$	−1.61969e7	−	727007.i	−1.76241	−	0.0791068i
$611$	5.70288e6			0.618004
$612$		0			0
$613$	−2.62634e6			−0.282293			−0.141147	−	0.989989i	$-0.545079\pi$
$613$	−2.62634e6			−0.282293			−0.141147	+	0.989989i	$0.545079\pi$
$614$	4.57306e6	+	205264.i	0.489537	+	0.0219732i
$615$		0			0
$616$	1.02141e6	+	2.49169e6i	0.108454	+	0.264571i
$617$	8.21879e6	−	4.74512e6i	0.869150	−	0.501804i	0.00208438	−	0.999998i	$-0.499337\pi$
$617$	8.21879e6	−	4.74512e6i	0.869150	−	0.501804i	0.867066	+	0.498194i	$0.166003\pi$
$618$		0			0
$619$	2.66128e6	+	1.53649e6i	0.279167	+	0.161177i	0.633046	−	0.774114i	$-0.281804\pi$
$619$	2.66128e6	+	1.53649e6i	0.279167	+	0.161177i	−0.353879	+	0.935291i	$0.615138\pi$
$620$	3.70069e6	−	5.25773e6i	0.386637	−	0.549312i
$621$		0			0
$622$	−356720.	+	185143.i	−0.0369702	+	0.0191881i
$623$	−4.90627e6	+	8.49790e6i	−0.506443	+	0.877186i
$624$		0			0
$625$	−5.38553e6	−	9.32800e6i	−0.551478	−	0.955188i
$626$	8.52132e6	+	5.44333e6i	0.869102	+	0.555174i
$627$		0			0
$628$	2.99414e6	+	6.46216e6i	0.302952	+	0.653850i
$629$			551856.i			0.0556159i
$630$		0			0
$631$		−	2.80779e6i		−	0.280731i	−0.990100	−	0.140366i	$-0.955172\pi$
$631$		−	2.80779e6i		−	0.280731i	0.990100	−	0.140366i	$-0.0448278\pi$
$632$	6.97474e6	−	9.02097e6i	0.694601	−	0.898381i
$633$		0			0
$634$	−1.00973e6	+	1.58070e6i	−0.0997662	+	0.156180i
$635$	357459.	+	619137.i	0.0351796	+	0.0609329i
$636$		0			0
$637$	2.61423e6	−	4.52798e6i	0.255267	−	0.442136i
$638$	−860607.	−	1.65816e6i	−0.0837053	−	0.161277i
$639$		0			0
$640$	3.75561e6	+	1.76539e7i	0.362436	+	1.70369i
$641$	−8.96448e6	−	5.17564e6i	−0.861747	−	0.497530i	0.00284982	−	0.999996i	$-0.499093\pi$
$641$	−8.96448e6	−	5.17564e6i	−0.861747	−	0.497530i	−0.864597	+	0.502466i	$0.832426\pi$
$642$		0			0
$643$	−4.22376e6	+	2.43859e6i	−0.402876	+	0.232601i	−0.687724	−	0.725972i	$-0.741390\pi$
$643$	−4.22376e6	+	2.43859e6i	−0.402876	+	0.232601i	0.284848	+	0.958573i	$0.408057\pi$
$644$	49266.6	−	547696.i	0.00468099	−	0.0520385i
$645$		0			0
$646$	−821772.	+	1.83081e7i	−0.0774765	+	1.72609i
$647$	9.58644e6			0.900319			0.450160	−	0.892948i	$-0.351367\pi$
$647$	9.58644e6			0.900319			0.450160	+	0.892948i	$0.351367\pi$
$648$		0			0
$649$	−4.89900e6			−0.456557
$650$	−1.29893e6	+	2.89387e7i	−0.120588	+	2.68656i
$651$		0			0
$652$	−1.40413e6	+	1.56097e7i	−0.129356	+	1.43805i
$653$	3.50930e6	−	2.02609e6i	0.322060	−	0.185942i	−0.330250	−	0.943893i	$-0.607133\pi$
$653$	3.50930e6	−	2.02609e6i	0.322060	−	0.185942i	0.652311	+	0.757952i	$0.273800\pi$
$654$		0			0
$655$	1.76854e7	+	1.02107e7i	1.61069	+	0.929934i
$656$	1.91515e6	−	686474.i	0.173758	−	0.0622823i
$657$		0			0
$658$	−1.87363e6	−	3.60997e6i	−0.168702	−	0.325042i
$659$	−3.07530e6	+	5.32657e6i	−0.275850	+	0.477787i	−0.970349	−	0.241707i	$-0.922293\pi$
$659$	−3.07530e6	+	5.32657e6i	−0.275850	+	0.477787i	0.694499	+	0.719494i	$0.255626\pi$
$660$		0			0
$661$	1.19391e6	+	2.06791e6i	0.106284	+	0.184089i	0.914262	−	0.405124i	$-0.132771\pi$
$661$	1.19391e6	+	2.06791e6i	0.106284	+	0.184089i	−0.807978	+	0.589212i	$0.799438\pi$
$662$	7.23798e6	−	1.13308e7i	0.641908	−	1.00488i
$663$		0			0
$664$	−1.14445e7	−	8.84853e6i	−1.00734	−	0.778844i
$665$		−	2.58744e7i		−	2.26890i
$666$		0			0
$667$			381493.i			0.0332026i
$668$	1.15790e6	+	2.49905e6i	0.100399	+	0.216688i
$669$		0			0
$670$	−1.24935e7	−	7.98071e6i	−1.07522	−	0.686838i
$671$	−2.15550e6	−	3.73344e6i	−0.184817	−	0.320113i
$672$		0			0
$673$	5.33582e6	−	9.24191e6i	0.454113	−	0.786546i	−0.544524	−	0.838745i	$-0.683290\pi$
$673$	5.33582e6	−	9.24191e6i	0.454113	−	0.786546i	0.998637	+	0.0521992i	$0.0166231\pi$
$674$	632469.	−	328261.i	0.0536278	−	0.0278336i
$675$		0			0
$676$	5.11670e6	−	7.26951e6i	0.430649	−	0.611841i
$677$	1.20806e7	+	6.97471e6i	1.01301	+	0.584864i	0.912073	−	0.410029i	$-0.134481\pi$
$677$	1.20806e7	+	6.97471e6i	1.01301	+	0.584864i	0.100941	+	0.994892i	$0.467815\pi$
$678$		0			0
$679$	1.46351e6	−	844957.i	0.121821	−	0.0703332i
$680$	−2.01964e7	+	8.27899e6i	−1.67495	+	0.686602i
$681$		0			0
$682$	1.70786e6	+	76658.3i	0.140602	+	0.00631100i
$683$	1.34097e7			1.09994			0.549968	−	0.835186i	$-0.314640\pi$
$683$	1.34097e7			1.09994			0.549968	+	0.835186i	$0.314640\pi$
$684$		0			0
$685$	−2.49311e7			−2.03009
$686$	−1.33726e7	−	600237.i	−1.08494	−	0.0486981i
$687$		0			0
$688$	3.12495e6	+	2.64829e6i	0.251694	+	0.213302i
$689$	−4.35030e6	+	2.51165e6i	−0.349118	+	0.201563i
$690$		0			0
$691$	−1.05848e6	−	611111.i	−0.0843307	−	0.0486883i	0.457242	−	0.889342i	$-0.348837\pi$
$691$	−1.05848e6	−	611111.i	−0.0843307	−	0.0486883i	−0.541572	+	0.840654i	$0.682171\pi$
$692$	−5.14055e6	−	3.61821e6i	−0.408079	−	0.287229i
$693$		0			0
$694$	5.79757e6	−	3.00902e6i	0.456927	−	0.237152i
$695$	−1.76686e6	+	3.06030e6i	−0.138753	+	0.240326i
$696$		0			0
$697$	1.23018e6	+	2.13074e6i	0.0959154	+	0.166130i
$698$	−1.73789e7	−	1.11015e7i	−1.35015	−	0.862465i
$699$		0			0
$700$	1.87452e7	−	8.68532e6i	1.44592	−	0.669948i
$701$			1.38380e7i			1.06360i	0.846870	+	0.531801i	$0.178484\pi$
$701$			1.38380e7i			1.06360i	−0.846870	+	0.531801i	$0.821516\pi$
$702$		0			0
$703$		−	1.16583e6i		−	0.0889704i
$704$	−3.41830e6	+	3.36853e6i	−0.259943	+	0.256158i
$705$		0			0
$706$	3.48249e6	−	5.45170e6i	0.262953	−	0.411643i
$707$	1.47660e6	+	2.55754e6i	0.111100	+	0.192430i
$708$		0			0
$709$	1.12116e7	−	1.94191e7i	0.837632	−	1.45082i	−0.0542381	−	0.998528i	$-0.517273\pi$
$709$	1.12116e7	−	1.94191e7i	0.837632	−	1.45082i	0.891870	−	0.452292i	$-0.149394\pi$
$710$	9.21314e6	+	1.77512e7i	0.685901	+	1.32155i
$711$		0			0
$712$	−1.73292e7	−	2.34610e6i	−1.28108	−	0.173439i
$713$	−302333.	−	174552.i	−0.0222722	−	0.0128588i
$714$		0			0
$715$	−9.95008e6	+	5.74468e6i	−0.727883	+	0.420243i
$716$	−1.11186e7	−	1.00014e6i	−0.810527	−	0.0729088i
$717$		0			0
$718$	28212.2	−	628536.i	0.00204233	−	0.0455008i
$719$	−1.71887e7			−1.24000			−0.619999	−	0.784603i	$-0.712867\pi$
$719$	−1.71887e7			−1.24000			−0.619999	+	0.784603i	$0.712867\pi$
$720$		0			0
$721$	1.55048e7			1.11078
$722$	1.10796e6	−	2.46841e7i	0.0791009	−	1.76228i
$723$		0			0
$724$	1.12706e6	+	101382.i	0.0799100	+	0.00718810i
$725$	−1.24122e7	+	7.16620e6i	−0.877010	+	0.506342i
$726$		0			0
$727$	−1.12449e7	−	6.49227e6i	−0.789081	−	0.455576i	0.0505582	−	0.998721i	$-0.483900\pi$
$727$	−1.12449e7	−	6.49227e6i	−0.789081	−	0.455576i	−0.839639	+	0.543145i	$0.817233\pi$
$728$	−1.46798e7	−	1.98742e6i	−1.02658	−	0.138983i
$729$		0			0
$730$	9.69361e6	+	1.86769e7i	0.673253	+	1.29718i
$731$	−2.47685e6	+	4.29002e6i	−0.171437	+	0.296938i
$732$		0			0
$733$	3.50187e6	+	6.06542e6i	0.240736	+	0.416967i	0.960924	−	0.276812i	$-0.0892780\pi$
$733$	3.50187e6	+	6.06542e6i	0.240736	+	0.416967i	−0.720188	+	0.693779i	$0.755945\pi$
$734$	1.32702e7	−	2.07740e7i	0.909154	−	1.42324i
$735$		0			0
$736$	936434.	−	288977.i	0.0637210	−	0.0196639i
$737$		−	3.94188e6i		−	0.267322i
$738$		0			0
$739$		−	2.74291e7i		−	1.84757i	−0.382917	−	0.923783i	$-0.625080\pi$
$739$		−	2.74291e7i		−	1.84757i	0.382917	−	0.923783i	$-0.374920\pi$
$740$	1.25986e6	−	583739.i	0.0845755	−	0.0391868i
$741$		0			0
$742$	3.01915e6	+	1.92860e6i	0.201315	+	0.128598i
$743$	3.05209e6	+	5.28638e6i	0.202827	+	0.351306i	0.949438	−	0.313954i	$-0.101654\pi$
$743$	3.05209e6	+	5.28638e6i	0.202827	+	0.351306i	−0.746611	+	0.665260i	$0.768320\pi$
$744$		0			0
$745$	−2.31176e7	+	4.00409e7i	−1.52599	+	2.64310i
$746$	1.35527e7	−	7.03404e6i	0.891617	−	0.462762i
$747$		0			0
$748$	−4.74605e6	−	3.34054e6i	−0.310155	−	0.218304i
$749$	1.40774e7	+	8.12760e6i	0.916893	+	0.529368i
$750$		0			0
$751$	1.95951e7	−	1.13132e7i	1.26779	−	0.731958i	0.293219	−	0.956045i	$-0.405274\pi$
$751$	1.95951e7	−	1.13132e7i	1.26779	−	0.731958i	0.974569	+	0.224088i	$0.0719402\pi$
$752$	4.68625e6	−	5.52972e6i	0.302190	−	0.356581i
$753$		0			0
$754$	1.02665e7	+	460820.i	0.657651	+	0.0295191i
$755$	−1.16901e7			−0.746366
$756$		0			0
$757$	2.79038e7			1.76980			0.884900	−	0.465781i	$-0.154226\pi$
$757$	2.79038e7			1.76980			0.884900	+	0.465781i	$0.154226\pi$
$758$	1.16032e7	+	520819.i	0.733511	+	0.0329241i
$759$		0			0
$760$	4.26660e7	−	1.74898e7i	2.67946	−	1.09838i
$761$	−8.70509e6	+	5.02588e6i	−0.544893	+	0.314594i	−0.747060	−	0.664757i	$-0.768535\pi$
$761$	−8.70509e6	+	5.02588e6i	−0.544893	+	0.314594i	0.202166	+	0.979351i	$0.435202\pi$
$762$		0			0
$763$	−1.20315e7	−	6.94641e6i	−0.748186	−	0.431966i
$764$	1.60185e7	−	2.27582e7i	0.992864	−	1.41060i
$765$		0			0
$766$	−2.73407e7	+	1.41902e7i	−1.68360	+	0.873812i
$767$	1.34747e7	−	2.33388e7i	0.827046	−	1.43249i
$768$		0			0
$769$	1.07441e7	+	1.86093e7i	0.655169	+	1.13479i	0.981851	+	0.189652i	$0.0607361\pi$
$769$	1.07441e7	+	1.86093e7i	0.655169	+	1.13479i	−0.326682	+	0.945134i	$0.605931\pi$
$770$	6.90545e6	+	4.41113e6i	0.419725	+	0.268116i
$771$		0			0
$772$	−1.14774e7	−	2.47712e7i	−0.693105	−	1.49590i
$773$			3.11372e7i			1.87426i	0.348977	+	0.937131i	$0.386529\pi$
$773$			3.11372e7i			1.87426i	−0.348977	+	0.937131i	$0.613471\pi$
$774$		0			0
$775$		−	1.31156e7i		−	0.784392i
$776$	2.38257e6	+	1.84213e6i	0.142034	+	0.109816i
$777$		0			0
$778$	8.84612e6	−	1.38482e7i	0.523967	−	0.820249i
$779$	−2.59883e6	−	4.50131e6i	−0.153439	−	0.265763i
$780$		0			0
$781$	−2.65891e6	+	4.60537e6i	−0.155983	+	0.270170i
$782$	545964.	+	1.05192e6i	0.0319262	+	0.0615131i
$783$		0			0
$784$	−2.24229e6	−	6.25565e6i	−0.130287	−	0.363481i
$785$	1.87680e7	+	1.08357e7i	1.08703	+	0.627599i
$786$		0			0
$787$	−2.67812e7	+	1.54621e7i	−1.54132	+	0.889883i	−0.542567	+	0.840012i	$0.682548\pi$
$787$	−2.67812e7	+	1.54621e7i	−1.54132	+	0.889883i	−0.998756	+	0.0498707i	$0.984119\pi$
$788$	744939.	−	8.28148e6i	0.0427371	−	0.475108i
$789$		0			0
$790$	1.55583e6	−	3.46621e7i	0.0886939	−	1.97600i
$791$	3.41829e6			0.194253
$792$		0			0
$793$	2.37148e7			1.33917
$794$	405369.	−	9.03115e6i	0.0228191	−	0.508384i
$795$		0			0
$796$	−757950.	+	8.42612e6i	−0.0423992	+	0.471352i
$797$	3.04761e7	−	1.75954e7i	1.69947	−	0.981190i	0.753213	−	0.657777i	$-0.228503\pi$
$797$	3.04761e7	−	1.75954e7i	1.69947	−	0.981190i	0.946258	−	0.323413i	$-0.104830\pi$
$798$		0			0
$799$	7.59136e6	+	4.38287e6i	0.420681	+	0.242880i
$800$	2.69927e7	+	2.50394e7i	1.49115	+	1.38324i
$801$		0			0
$802$	4.47542e6	+	8.62291e6i	0.245696	+	0.473389i
$803$	−2.79757e6	+	4.84554e6i	−0.153106	+	0.265188i
$804$		0			0
$805$	−836638.	−	1.44910e6i	−0.0455038	−	0.0788150i
$806$	−5.06266e6	+	7.92539e6i	−0.274499	+	0.429717i
$807$		0			0
$808$	−3.21919e6	+	4.16363e6i	−0.173468	+	0.224359i
$809$			1.11312e7i			0.597960i	0.954259	+	0.298980i	$0.0966463\pi$
$809$			1.11312e7i			0.597960i	−0.954259	+	0.298980i	$0.903354\pi$
$810$		0			0
$811$			2.50552e7i			1.33766i	0.743416	+	0.668829i	$0.233204\pi$
$811$			2.50552e7i			1.33766i	−0.743416	+	0.668829i	$0.766796\pi$
$812$	−3.08128e6	−	6.65021e6i	−0.163999	−	0.353953i
$813$		0			0
$814$	311140.	+	198753.i	0.0164587	+	0.0105136i
$815$	2.38447e7	+	4.13002e7i	1.25747	+	2.17800i
$816$		0			0
$817$	5.23247e6	−	9.06291e6i	0.274253	−	0.475021i
$818$	−2.76146e7	+	1.43324e7i	−1.44297	+	0.748920i
$819$		0			0
$820$	3.56314e6	−	5.06231e6i	0.185054	−	0.262914i
$821$	5.80988e6	+	3.35434e6i	0.300822	+	0.173680i	0.642812	−	0.766024i	$-0.277768\pi$
$821$	5.80988e6	+	3.35434e6i	0.300822	+	0.173680i	−0.341990	+	0.939704i	$0.611101\pi$
$822$		0			0
$823$	−2.35383e7	+	1.35898e7i	−1.21136	+	0.699382i	−0.963057	−	0.269299i	$-0.913208\pi$
$823$	−2.35383e7	+	1.35898e7i	−1.21136	+	0.699382i	−0.248308	+	0.968681i	$0.579875\pi$
$824$	1.04805e7	+	2.55669e7i	0.537728	+	1.31177i
$825$		0			0
$826$	−1.92007e7	−	861833.i	−0.979188	−	0.0439514i
$827$	−8.21918e6			−0.417893			−0.208946	−	0.977927i	$-0.567003\pi$
$827$	−8.21918e6			−0.417893			−0.208946	+	0.977927i	$0.567003\pi$
$828$		0			0
$829$	−2.64615e7			−1.33730			−0.668649	−	0.743578i	$-0.733127\pi$
$829$	−2.64615e7			−1.33730			−0.668649	+	0.743578i	$0.733127\pi$
$830$	−4.39741e7	−	1.97381e6i	−2.21566	−	0.0994510i
$831$		0			0
$832$	−6.64564e6	−	2.55499e7i	−0.332834	−	1.27962i
$833$	6.95984e6	−	4.01827e6i	0.347526	−	0.200644i
$834$		0			0
$835$	7.25797e6	+	4.19039e6i	0.360246	+	0.207988i
$836$	1.00263e7	+	7.05707e6i	0.496163	+	0.349228i
$837$		0			0
$838$	3.23482e7	−	1.67892e7i	1.59126	−	0.825886i
$839$	−1.49153e6	+	2.58341e6i	−0.0731522	+	0.126703i	−0.900281	−	0.435309i	$-0.856639\pi$
$839$	−1.49153e6	+	2.58341e6i	−0.0731522	+	0.126703i	0.827129	+	0.562012i	$0.189973\pi$
$840$		0			0
$841$	−7.71324e6	−	1.33597e7i	−0.376051	−	0.651339i
$842$	−1.60859e7	−	1.02755e7i	−0.781925	−	0.499486i
$843$		0			0
$844$	2.98271e7	−	1.38199e7i	1.44130	−	0.667805i
$845$		−	2.70498e7i		−	1.30323i
$846$		0			0
$847$		−	1.41799e7i		−	0.679148i
$848$	−1.13940e6	+	6.28212e6i	−0.0544112	+	0.299997i
$849$		0			0
$850$	−2.39696e7	+	3.75234e7i	−1.13792	+	1.78137i
$851$	−37696.5	−	65292.3i	−0.00178434	−	0.00309057i
$852$		0			0
$853$	−1.05595e7	+	1.82895e7i	−0.496900	+	0.860656i	−0.999994	−	0.00357565i	$-0.998862\pi$
$853$	−1.05595e7	+	1.82895e7i	−0.496900	+	0.860656i	0.503093	+	0.864232i	$0.332195\pi$
$854$	−7.79129e6	−	1.50117e7i	−0.365565	−	0.704344i
$855$		0			0
$856$	−3.88650e6	+	2.87071e7i	−0.181290	+	1.33907i
$857$	449133.	+	259307.i	0.0208893	+	0.0120604i	0.510408	−	0.859932i	$-0.329494\pi$
$857$	449133.	+	259307.i	0.0208893	+	0.0120604i	−0.489519	+	0.871993i	$0.662828\pi$
$858$		0			0
$859$	2.14050e7	−	1.23582e7i	0.989767	−	0.571442i	0.0845625	−	0.996418i	$-0.473051\pi$
$859$	2.14050e7	−	1.23582e7i	0.989767	−	0.571442i	0.905205	+	0.424976i	$0.139717\pi$
$860$	1.24139e7	+	1.11666e6i	0.572350	+	0.0514843i
$861$		0			0
$862$	429209.	−	9.56228e6i	0.0196743	−	0.438322i
$863$	−1.06376e7			−0.486202			−0.243101	−	0.970001i	$-0.578165\pi$
$863$	−1.06376e7			−0.486202			−0.243101	+	0.970001i	$0.578165\pi$
$864$		0			0
$865$	−1.91280e7			−0.869217
$866$	848061.	−	1.88938e7i	0.0384266	−	0.856102i
$867$		0			0
$868$	6.68014e6	+	600894.i	0.300944	+	0.0270707i
$869$	7.98974e6	−	4.61288e6i	0.358908	−	0.207216i
$870$		0			0
$871$	1.87791e7	+	1.08421e7i	0.838744	+	0.484249i
$872$	3.32167e6	−	2.45350e7i	0.147933	−	1.09269i
$873$		0			0
$874$	−1.15338e6	−	2.22225e6i	−0.0510732	−	0.0984042i
$875$	1.59781e7	−	2.76749e7i	0.705514	−	1.22199i
$876$		0			0
$877$	8.42674e6	+	1.45955e7i	0.369965	+	0.640798i	0.989560	−	0.144124i	$-0.0460364\pi$
$877$	8.42674e6	+	1.45955e7i	0.369965	+	0.640798i	−0.619595	+	0.784922i	$0.712703\pi$
$878$	−1.45058e7	+	2.27083e7i	−0.635047	+	0.994141i
$879$		0			0
$880$	−2.60606e6	+	1.43686e7i	−0.113443	+	0.625470i
$881$		−	1.43365e6i		−	0.0622305i	−0.999516	−	0.0311153i	$-0.990094\pi$
$881$		−	1.43365e6i		−	0.0622305i	0.999516	−	0.0311153i	$-0.00990589\pi$
$882$		0			0
$883$		−	9.05105e6i		−	0.390658i	−0.980738	−	0.195329i	$-0.937422\pi$
$883$		−	9.05105e6i		−	0.390658i	0.980738	−	0.195329i	$-0.0625775\pi$
$884$	2.89683e7	−	1.34220e7i	1.24679	−	0.577680i
$885$		0			0
$886$	2.08943e7	+	1.33471e7i	0.894218	+	0.571217i
$887$	−5.07142e6	−	8.78395e6i	−0.216431	−	0.374870i	0.737283	−	0.675584i	$-0.236108\pi$
$887$	−5.07142e6	−	8.78395e6i	−0.216431	−	0.374870i	−0.953714	+	0.300714i	$0.902775\pi$
$888$		0			0
$889$	−372891.	+	645867.i	−0.0158244	+	0.0274087i
$890$	−4.72285e7	+	2.45123e7i	−1.99862	+	1.03731i
$891$		0			0
$892$	−1.58615e7	−	1.11642e7i	−0.667470	−	0.469803i
$893$	−1.60372e7	−	9.25906e6i	−0.672975	−	0.388542i
$894$		0			0
$895$	−2.94177e7	+	1.69843e7i	−1.22758	+	0.708746i
$896$	−1.39900e7	+	1.26009e7i	−0.582165	+	0.524364i
$897$		0			0
$898$	−1.49312e7	−	670196.i	−0.617880	−	0.0277339i
$899$	−4.65299e6			−0.192014
$900$		0			0
$901$	−7.72119e6			−0.316863
$902$	1.64438e6	+	73809.1i	0.0672955	+	0.00302060i
$903$		0			0
$904$	2.31060e6	+	5.63665e6i	0.0940380	+	0.229403i
$905$	2.98199e6	−	1.72165e6i	0.121028	−	0.0698754i
$906$		0			0
$907$	2.75879e7	+	1.59279e7i	1.11353	+	0.642894i	0.939740	−	0.341890i	$-0.111067\pi$
$907$	2.75879e7	+	1.59279e7i	1.11353	+	0.642894i	0.173785	+	0.984784i	$0.444400\pi$
$908$	−3.15150e6	+	4.47748e6i	−0.126854	+	0.180227i
$909$		0			0
$910$	−4.00080e7	+	2.07647e7i	−1.60156	+	0.831233i
$911$	−1.33238e7	+	2.30775e7i	−0.531903	+	0.921283i	0.467404	+	0.884044i	$0.345189\pi$
$911$	−1.33238e7	+	2.30775e7i	−0.531903	+	0.921283i	−0.999306	+	0.0372385i	$0.988144\pi$
$912$		0			0
$913$	−5.85214e6	−	1.01362e7i	−0.232348	−	0.402438i
$914$	1.66063e7	+	1.06079e7i	0.657517	+	0.420016i
$915$		0			0
$916$	1.85391e7	+	4.00123e7i	0.730045	+	1.57563i
$917$			2.13030e7i			0.836601i
$918$		0			0
$919$			2.74009e7i			1.07023i	0.844780	+	0.535114i	$0.179731\pi$
$919$			2.74009e7i			1.07023i	−0.844780	+	0.535114i	$0.820269\pi$
$920$	1.82399e6	−	2.35911e6i	0.0710482	−	0.0918922i
$921$		0			0
$922$	1.03340e7	−	1.61774e7i	0.400350	−	0.626732i
$923$	−1.46266e7	−	2.53341e7i	−0.565119	−	0.978815i
$924$		0			0
$925$	1.41623e6	−	2.45298e6i	0.0544226	−	0.0942627i
$926$	−504540.	−	972111.i	−0.0193361	−	0.0372553i
$927$		0			0
$928$	8.88319e6	−	9.57614e6i	0.338609	−	0.365023i
$929$	−6.04164e6	−	3.48814e6i	−0.229676	−	0.132604i	0.380747	−	0.924679i	$-0.375667\pi$
$929$	−6.04164e6	−	3.48814e6i	−0.229676	−	0.132604i	−0.610423	+	0.792076i	$0.709000\pi$
$930$		0			0
$931$	−1.47030e7	+	8.48881e6i	−0.555947	+	0.320976i
$932$	−3.92462e6	+	4.36300e7i	−0.147999	+	1.64530i
$933$		0			0
$934$	822877.	−	1.83328e7i	0.0308651	−	0.687640i
$935$	−1.76600e7			−0.660636
$936$		0			0
$937$	4.72933e7			1.75975			0.879874	−	0.475207i	$-0.157627\pi$
$937$	4.72933e7			1.75975			0.879874	+	0.475207i	$0.157627\pi$
$938$	693457.	−	1.54494e7i	0.0257343	−	0.573331i
$939$		0			0
$940$	1.97597e6	−	2.19669e7i	0.0729392	−	0.810864i
$941$	−1.33836e7	+	7.72703e6i	−0.492719	+	0.284471i	−0.725702	−	0.688009i	$-0.758485\pi$
$941$	−1.33836e7	+	7.72703e6i	−0.492719	+	0.284471i	0.232983	+	0.972481i	$0.425151\pi$
$942$		0			0
$943$	−291096.	−	168065.i	−0.0106600	−	0.00615456i
$944$	−1.15576e7	−	3.22438e7i	−0.422121	−	1.17765i
$945$		0			0
$946$	1.52670e6	+	2.94153e6i	0.0554658	+	0.106867i
$947$	−1.20235e7	+	2.08253e7i	−0.435668	+	0.754600i	−0.997350	−	0.0727539i	$-0.976821\pi$
$947$	−1.20235e7	+	2.08253e7i	−0.435668	+	0.754600i	0.561682	+	0.827353i	$0.310155\pi$
$948$		0			0
$949$	−1.53894e7	−	2.66553e7i	−0.554698	−	0.960765i
$950$	5.06370e7	−	7.92702e7i	1.82037	−	2.84971i
$951$		0			0
$952$	−1.80135e7	−	1.39275e7i	−0.644179	−	0.498059i
$953$			5.61504e6i			0.200272i	0.994974	+	0.100136i	$0.0319278\pi$
$953$			5.61504e6i			0.200272i	−0.994974	+	0.100136i	$0.968072\pi$
$954$		0			0
$955$		−	8.46833e7i		−	3.00462i
$956$	4.18261e6	+	9.02719e6i	0.148014	+	0.319454i
$957$		0			0
$958$	−3.91579e7	−	2.50137e7i	−1.37850	−	0.880569i
$959$	−1.30037e7	−	2.25231e7i	−0.456584	−	0.790827i
$960$		0			0
$961$	−1.21856e7	+	2.11061e7i	−0.425636	+	0.737223i
$962$	−1.80265e6	+	935600.i	−0.0628019	+	0.0325951i
$963$		0			0
$964$	−7.22625e6	+	1.02666e7i	−0.250449	+	0.355824i
$965$	−7.19427e7	−	4.15361e7i	−2.48696	−	1.43585i
$966$		0			0
$967$	−183562.	+	105980.i	−0.00631272	+	0.00364465i	−0.503153	−	0.864197i	$-0.667827\pi$
$967$	−183562.	+	105980.i	−0.00631272	+	0.00364465i	0.496840	+	0.867842i	$0.334493\pi$
$968$	2.33822e7	−	9.58492e6i	0.802041	−	0.328776i
$969$		0			0
$970$	9.15474e6	+	410916.i	0.312404	+	0.0140225i
$971$	4.76645e7			1.62236			0.811180	−	0.584797i	$-0.198826\pi$
$971$	4.76645e7			1.62236			0.811180	+	0.584797i	$0.198826\pi$
$972$		0			0
$973$	−3.68629e6			−0.124827
$974$	−9.26262e6	−	415758.i	−0.312850	−	0.0140425i
$975$		0			0
$976$	1.94873e7	−	2.29947e7i	0.654826	−	0.772688i
$977$	3.11073e6	−	1.79598e6i	0.104262	−	0.0601956i	−0.446962	−	0.894553i	$-0.647494\pi$
$977$	3.11073e6	−	1.79598e6i	0.104262	−	0.0601956i	0.551224	+	0.834357i	$0.314161\pi$
$978$		0			0
$979$	−1.22530e7	−	7.07424e6i	−0.408586	−	0.235897i
$980$	−1.65355e7	−	1.16386e7i	−0.549986	−	0.387111i
$981$		0			0
$982$	−2.04067e7	+	1.05914e7i	−0.675297	+	0.350489i
$983$	−1.09466e7	+	1.89600e7i	−0.361322	+	0.625827i	−0.988179	−	0.153307i	$-0.951008\pi$
$983$	−1.09466e7	+	1.89600e7i	−0.361322	+	0.625827i	0.626857	+	0.779134i	$0.284341\pi$
$984$		0			0
$985$	−1.26505e7	−	2.19112e7i	−0.415447	−	0.719575i
$986$	1.33121e7	+	8.50364e6i	0.436068	+	0.278556i
$987$		0			0
$988$	−6.11971e7	+	2.83547e7i	−1.99452	+	0.924131i
$989$		−	676760.i		−	0.0220011i
$990$		0			0
$991$			2.07362e7i			0.670725i	0.942089	+	0.335362i	$0.108859\pi$
$991$			2.07362e7i			0.670725i	−0.942089	+	0.335362i	$0.891141\pi$
$992$	3.52459e6	+	1.14215e7i	0.113718	+	0.368505i
$993$		0			0
$994$	−1.12313e7	+	1.75821e7i	−0.360547	+	0.564422i
$995$	1.28714e7	+	2.22939e7i	0.412162	+	0.713886i
$996$		0			0
$997$	9.72454e6	−	1.68434e7i	0.309836	−	0.536651i	−0.668491	−	0.743721i	$-0.733059\pi$
$997$	9.72454e6	−	1.68434e7i	0.309836	−	0.536651i	0.978326	+	0.207070i	$0.0663927\pi$
$998$	8.79241e6	+	1.69406e7i	0.279436	+	0.538397i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	108.6.h.a.35.13		56
3.2	odd	2		36.6.h.a.11.16	yes	56
4.3	odd	2	inner	108.6.h.a.35.23		56
9.4	even	3		36.6.h.a.23.6	yes	56
9.5	odd	6	inner	108.6.h.a.71.23		56
12.11	even	2		36.6.h.a.11.6	✓	56
36.23	even	6	inner	108.6.h.a.71.13		56
36.31	odd	6		36.6.h.a.23.16	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
36.6.h.a.11.6	✓	56	12.11	even	2
36.6.h.a.11.16	yes	56	3.2	odd	2
36.6.h.a.23.6	yes	56	9.4	even	3
36.6.h.a.23.16	yes	56	36.31	odd	6
108.6.h.a.35.13		56	1.1	even	1	trivial
108.6.h.a.35.23		56	4.3	odd	2	inner
108.6.h.a.71.13		56	36.23	even	6	inner
108.6.h.a.71.23		56	9.5	odd	6	inner

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.h (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.253656 + 5.65116i) q^{2} +(-31.8713 - 2.86690i) q^{4} +(-84.3255 + 48.6853i) q^{5} +(-87.9661 - 50.7872i) q^{7} +(24.2857 - 179.383i) q^{8} +O(q^{10})\)	\(q+(-0.253656 + 5.65116i) q^{2} +(-31.8713 - 2.86690i) q^{4} +(-84.3255 + 48.6853i) q^{5} +(-87.9661 - 50.7872i) q^{7} +(24.2857 - 179.383i) q^{8} +(-253.739 - 488.886i) q^{10} +(73.2291 - 126.837i) q^{11} +(402.832 + 697.726i) q^{13} +(309.320 - 484.228i) q^{14} +(1007.56 + 182.744i) q^{16} +1238.37i q^{17} -2616.12i q^{19} +(2827.14 - 1309.91i) q^{20} +(698.199 + 446.002i) q^{22} +(-84.5912 - 146.516i) q^{23} +(3178.02 - 5504.50i) q^{25} +(-4045.15 + 2099.49i) q^{26} +(2657.99 + 1870.85i) q^{28} +(-1952.82 - 1127.46i) q^{29} +(1787.03 - 1031.74i) q^{31} +(-1288.29 + 5647.54i) q^{32} +(-6998.21 - 314.119i) q^{34} +9890.37 q^{35} +445.632 q^{37} +(14784.1 + 663.594i) q^{38} +(6685.41 + 16308.9i) q^{40} +(1720.61 - 993.393i) q^{41} +(3464.26 + 2000.09i) q^{43} +(-2697.54 + 3832.51i) q^{44} +(849.444 - 440.874i) q^{46} +(3539.24 - 6130.14i) q^{47} +(-3244.81 - 5620.18i) q^{49} +(30300.7 + 19355.8i) q^{50} +(-10838.5 - 23392.3i) q^{52} +6234.98i q^{53} +14260.7i q^{55} +(-11246.7 + 14546.2i) q^{56} +(6866.81 - 10749.7i) q^{58} +(-16724.9 - 28968.4i) q^{59} +(14717.5 - 25491.5i) q^{61} +(5377.25 + 10360.5i) q^{62} +(-31588.4 - 8712.87i) q^{64} +(-67938.0 - 39224.1i) q^{65} +(23308.8 - 13457.4i) q^{67} +(3550.28 - 39468.4i) q^{68} +(-2508.75 + 55892.1i) q^{70} -36309.5 q^{71} -38203.0 q^{73} +(-113.037 + 2518.34i) q^{74} +(-7500.15 + 83379.1i) q^{76} +(-12883.4 + 7438.21i) q^{77} +(54553.0 + 31496.2i) q^{79} +(-93860.1 + 33643.5i) q^{80} +(5177.38 + 9975.41i) q^{82} +(39957.8 - 69208.9i) q^{83} +(-60290.3 - 104426. i) q^{85} +(-12181.6 + 19069.8i) q^{86} +(-20973.9 - 16216.4i) q^{88} -96604.3i q^{89} -81835.0i q^{91} +(2275.98 + 4912.18i) q^{92} +(33744.7 + 21555.8i) q^{94} +(127367. + 220605. i) q^{95} +(-8318.60 + 14408.2i) q^{97} +(32583.6 - 16911.4i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 3 q^{2} - q^{4} + 6 q^{5}+O(q^{10}) \) 56 * q + 3 * q^2 - q^4 + 6 * q^5	\( 56 q + 3 q^{2} - q^{4} + 6 q^{5} - 68 q^{10} - 2 q^{13} + 1518 q^{14} - q^{16} + 1242 q^{20} + 63 q^{22} + 12498 q^{25} - 2052 q^{28} + 11946 q^{29} + 7233 q^{32} + 6361 q^{34} - 8 q^{37} + 14877 q^{38} - 1526 q^{40} + 43536 q^{41} - 26880 q^{46} + 38414 q^{49} - 38631 q^{50} + 24988 q^{52} - 21186 q^{56} - 3314 q^{58} - 2 q^{61} - 106342 q^{64} - 35970 q^{65} - 31413 q^{68} + 10524 q^{70} + 53620 q^{73} + 20406 q^{74} + 26193 q^{76} - 26178 q^{77} - 151286 q^{82} + 6248 q^{85} - 279237 q^{86} - 122541 q^{88} - 435804 q^{92} + 63480 q^{94} - 58148 q^{97}+O(q^{100}) \) 56 * q + 3 * q^2 - q^4 + 6 * q^5 - 68 * q^10 - 2 * q^13 + 1518 * q^14 - q^16 + 1242 * q^20 + 63 * q^22 + 12498 * q^25 - 2052 * q^28 + 11946 * q^29 + 7233 * q^32 + 6361 * q^34 - 8 * q^37 + 14877 * q^38 - 1526 * q^40 + 43536 * q^41 - 26880 * q^46 + 38414 * q^49 - 38631 * q^50 + 24988 * q^52 - 21186 * q^56 - 3314 * q^58 - 2 * q^61 - 106342 * q^64 - 35970 * q^65 - 31413 * q^68 + 10524 * q^70 + 53620 * q^73 + 20406 * q^74 + 26193 * q^76 - 26178 * q^77 - 151286 * q^82 + 6248 * q^85 - 279237 * q^86 - 122541 * q^88 - 435804 * q^92 + 63480 * q^94 - 58148 * q^97

Introduction

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