LMFDB - Embedded newform 162.7.d.b.53.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [162,7,Mod(53,162)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(162, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("162.53");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 162 = 2 \cdot 3^{4} $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	162.d (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:	$37.2687615464$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\sqrt{-2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{2} + 4 $ x^4 - 2*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{25}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 6)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			53.2
Root			$1.22474 + 0.707107i$ of defining polynomial
Character	$\chi$	$=$	162.53
Dual form			162.7.d.b.107.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(4.89898 - 2.82843i) q^{2} +(16.0000 - 27.7128i) q^{4} +(146.969 + 84.8528i) q^{5} +(-1.00000 - 1.73205i) q^{7} -181.019i q^{8} +O(q^{10})$	\(q+(4.89898 - 2.82843i) q^{2} +(16.0000 - 27.7128i) q^{4} +(146.969 + 84.8528i) q^{5} +(-1.00000 - 1.73205i) q^{7} -181.019i q^{8} +960.000 q^{10} +(-29.3939 + 16.9706i) q^{11} +(1475.00 - 2554.77i) q^{13} +(-9.79796 - 5.65685i) q^{14} +(-512.000 - 886.810i) q^{16} +4480.23i q^{17} +5258.00 q^{19} +(4703.02 - 2715.29i) q^{20} +(-96.0000 + 166.277i) q^{22} +(8876.95 + 5125.11i) q^{23} +(6587.50 + 11409.9i) q^{25} -16687.7i q^{26} -64.0000 q^{28} +(1910.60 - 1103.09i) q^{29} +(-11449.0 + 19830.2i) q^{31} +(-5016.55 - 2896.31i) q^{32} +(12672.0 + 21948.5i) q^{34} -339.411i q^{35} +34058.0 q^{37} +(25758.8 - 14871.9i) q^{38} +(15360.0 - 26604.3i) q^{40} +(14520.6 + 8383.46i) q^{41} +(3203.00 + 5547.76i) q^{43} +1086.12i q^{44} +57984.0 q^{46} +(155788. - 89944.0i) q^{47} +(58822.5 - 101884. i) q^{49} +(64544.1 + 37264.5i) q^{50} +(-47200.0 - 81752.8i) q^{52} -192548. i q^{53} -5760.00 q^{55} +(-313.535 + 181.019i) q^{56} +(6240.00 - 10808.0i) q^{58} +(283034. + 163410. i) q^{59} +(31283.0 + 54183.7i) q^{61} +129531. i q^{62} -32768.0 q^{64} +(433560. - 250316. i) q^{65} +(-219349. + 379924. i) q^{67} +(124160. + 71683.7i) q^{68} +(-960.000 - 1662.77i) q^{70} -68221.7i q^{71} -730510. q^{73} +(166849. - 96330.6i) q^{74} +(84128.0 - 145714. i) q^{76} +(58.7878 + 33.9411i) q^{77} +(-170281. - 294935. i) q^{79} -173779. i q^{80} +94848.0 q^{82} +(429768. - 248127. i) q^{83} +(-380160. + 658456. i) q^{85} +(31382.9 + 18118.9i) q^{86} +(3072.00 + 5320.86i) q^{88} -386725. i q^{89} -5900.00 q^{91} +(284062. - 164004. i) q^{92} +(508800. - 881267. i) q^{94} +(772765. + 446156. i) q^{95} +(140543. + 243428. i) q^{97} -665501. i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 64 q^{4} - 4 q^{7}+O(q^{10}) $ 4 * q + 64 * q^4 - 4 * q^7	$ 4 q + 64 q^{4} - 4 q^{7} + 3840 q^{10} + 5900 q^{13} - 2048 q^{16} + 21032 q^{19} - 384 q^{22} + 26350 q^{25} - 256 q^{28} - 45796 q^{31} + 50688 q^{34} + 136232 q^{37} + 61440 q^{40} + 12812 q^{43} + 231936 q^{46} + 235290 q^{49} - 188800 q^{52} - 23040 q^{55} + 24960 q^{58} + 125132 q^{61} - 131072 q^{64} - 877396 q^{67} - 3840 q^{70} - 2922040 q^{73} + 336512 q^{76} - 681124 q^{79} + 379392 q^{82} - 1520640 q^{85} + 12288 q^{88} - 23600 q^{91} + 2035200 q^{94} + 562172 q^{97}+O(q^{100}) $ 4 * q + 64 * q^4 - 4 * q^7 + 3840 * q^10 + 5900 * q^13 - 2048 * q^16 + 21032 * q^19 - 384 * q^22 + 26350 * q^25 - 256 * q^28 - 45796 * q^31 + 50688 * q^34 + 136232 * q^37 + 61440 * q^40 + 12812 * q^43 + 231936 * q^46 + 235290 * q^49 - 188800 * q^52 - 23040 * q^55 + 24960 * q^58 + 125132 * q^61 - 131072 * q^64 - 877396 * q^67 - 3840 * q^70 - 2922040 * q^73 + 336512 * q^76 - 681124 * q^79 + 379392 * q^82 - 1520640 * q^85 + 12288 * q^88 - 23600 * q^91 + 2035200 * q^94 + 562172 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/162\mathbb{Z}\right)^\times$.

$n$	$83$
$\chi(n)$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	4.89898	−	2.82843i	0.612372	−	0.353553i
$2$	4.89898	−	2.82843i	0.612372	−	0.353553i
$3$		0			0
$3$		0			0
$4$	16.0000	−	27.7128i	0.250000	−	0.433013i
$5$	146.969	+	84.8528i	1.17576	+	0.678823i	0.955029	−	0.296513i	$-0.0958239\pi$
$5$	146.969	+	84.8528i	1.17576	+	0.678823i	0.220726	+	0.975336i	$0.429157\pi$
$6$		0			0
$7$	−1.00000	−	1.73205i	−0.00291545	−	0.00504971i	0.864564	−	0.502523i	$-0.167595\pi$
$7$	−1.00000	−	1.73205i	−0.00291545	−	0.00504971i	−0.867479	+	0.497473i	$0.834261\pi$
$8$		−	181.019i		−	0.353553i
$9$		0			0
$10$	960.000			0.960000
$11$	−29.3939	+	16.9706i	−0.0220841	+	0.0127502i	−0.511001	−	0.859580i	$-0.670725\pi$
$11$	−29.3939	+	16.9706i	−0.0220841	+	0.0127502i	0.488917	+	0.872330i	$0.337392\pi$
$12$		0			0
$13$	1475.00	−	2554.77i	0.671370	−	1.16285i	−0.306146	−	0.951985i	$-0.599039\pi$
$13$	1475.00	−	2554.77i	0.671370	−	1.16285i	0.977516	−	0.210862i	$-0.0676272\pi$
$14$	−9.79796	−	5.65685i	−0.00357068	−	0.00206154i
$15$		0			0
$16$	−512.000	−	886.810i	−0.125000	−	0.216506i
$17$			4480.23i			0.911913i	0.890002	+	0.455956i	$0.150703\pi$
$17$			4480.23i			0.911913i	−0.890002	+	0.455956i	$0.849297\pi$
$18$		0			0
$19$	5258.00			0.766584			0.383292	−	0.923627i	$-0.374790\pi$
$19$	5258.00			0.766584			0.383292	+	0.923627i	$0.374790\pi$
$20$	4703.02	−	2715.29i	0.587878	−	0.339411i
$21$		0			0
$22$	−96.0000	+	166.277i	−0.00901578	+	0.0156158i
$23$	8876.95	+	5125.11i	0.729592	+	0.421230i	0.818273	−	0.574830i	$-0.194932\pi$
$23$	8876.95	+	5125.11i	0.729592	+	0.421230i	−0.0886806	+	0.996060i	$0.528265\pi$
$24$		0			0
$25$	6587.50	+	11409.9i	0.421600	+	0.730233i
$26$		−	16687.7i		−	0.949461i
$27$		0			0
$28$	−64.0000			−0.00291545
$29$	1910.60	−	1103.09i	0.0783387	−	0.0452289i	−0.460319	−	0.887754i	$-0.652265\pi$
$29$	1910.60	−	1103.09i	0.0783387	−	0.0452289i	0.538658	+	0.842525i	$0.318932\pi$
$30$		0			0
$31$	−11449.0	+	19830.2i	−0.384311	+	0.665646i	−0.991673	−	0.128779i	$-0.958894\pi$
$31$	−11449.0	+	19830.2i	−0.384311	+	0.665646i	0.607363	+	0.794425i	$0.292228\pi$
$32$	−5016.55	−	2896.31i	−0.153093	−	0.0883883i
$33$		0			0
$34$	12672.0	+	21948.5i	0.322410	+	0.558430i
$35$		−	339.411i		−	0.00791630i
$36$		0			0
$37$	34058.0			0.672379			0.336189	−	0.941794i	$-0.390862\pi$
$37$	34058.0			0.672379			0.336189	+	0.941794i	$0.390862\pi$
$38$	25758.8	−	14871.9i	0.469435	−	0.271028i
$39$		0			0
$40$	15360.0	−	26604.3i	0.240000	−	0.415692i
$41$	14520.6	+	8383.46i	0.210684	+	0.121639i	0.601629	−	0.798775i	$-0.294518\pi$
$41$	14520.6	+	8383.46i	0.210684	+	0.121639i	−0.390945	+	0.920414i	$0.627852\pi$
$42$		0			0
$43$	3203.00	+	5547.76i	0.0402858	+	0.0697770i	0.885465	−	0.464706i	$-0.153840\pi$
$43$	3203.00	+	5547.76i	0.0402858	+	0.0697770i	−0.845179	+	0.534483i	$0.820507\pi$
$44$			1086.12i			0.0127502i
$45$		0			0
$46$	57984.0			0.595710
$47$	155788.	−	89944.0i	1.50051	−	0.866320i	0.500511	−	0.865730i	$-0.333145\pi$
$47$	155788.	−	89944.0i	1.50051	−	0.866320i	1.00000		0.000590288i	$-0.000187895\pi$
$48$		0			0
$49$	58822.5	−	101884.i	0.499983	−	0.865996i
$50$	64544.1	+	37264.5i	0.516352	+	0.298116i
$51$		0			0
$52$	−47200.0	−	81752.8i	−0.335685	−	0.581424i
$53$		−	192548.i		−	1.29334i	−0.762772	−	0.646668i	$-0.776162\pi$
$53$		−	192548.i		−	1.29334i	0.762772	−	0.646668i	$-0.223838\pi$
$54$		0			0
$55$	−5760.00			−0.0346206
$56$	−313.535	+	181.019i	−0.00178534	+	0.00103077i
$57$		0			0
$58$	6240.00	−	10808.0i	0.0319816	−	0.0553938i
$59$	283034.	+	163410.i	1.37810	+	0.795649i	0.991931	−	0.126778i	$-0.0404635\pi$
$59$	283034.	+	163410.i	1.37810	+	0.795649i	0.386173	+	0.922426i	$0.373797\pi$
$60$		0			0
$61$	31283.0	+	54183.7i	0.137822	+	0.238715i	0.926672	−	0.375871i	$-0.122656\pi$
$61$	31283.0	+	54183.7i	0.137822	+	0.238715i	−0.788850	+	0.614586i	$0.789323\pi$
$62$			129531.i			0.543497i
$63$		0			0
$64$	−32768.0			−0.125000
$65$	433560.	−	250316.i	1.57873	−	0.911482i
$66$		0			0
$67$	−219349.	+	379924.i	−0.729308	+	1.26320i	0.227867	+	0.973692i	$0.426825\pi$
$67$	−219349.	+	379924.i	−0.729308	+	1.26320i	−0.957176	+	0.289507i	$0.906509\pi$
$68$	124160.	+	71683.7i	0.394870	+	0.227978i
$69$		0			0
$70$	−960.000	−	1662.77i	−0.00279883	−	0.00484772i
$71$		−	68221.7i		−	0.190611i	−0.995448	−	0.0953053i	$-0.969617\pi$
$71$		−	68221.7i		−	0.190611i	0.995448	−	0.0953053i	$-0.0303827\pi$
$72$		0			0
$73$	−730510.			−1.87784			−0.938918	−	0.344141i	$-0.888170\pi$
$73$	−730510.			−1.87784			−0.938918	+	0.344141i	$0.888170\pi$
$74$	166849.	−	96330.6i	0.411746	−	0.237722i
$75$		0			0
$76$	84128.0	−	145714.i	0.191646	−	0.331941i
$77$	58.7878	+	33.9411i	0.000128770	+	7.43454e-5i
$78$		0			0
$79$	−170281.	−	294935.i	−0.345370	−	0.598199i	0.640051	−	0.768333i	$-0.278913\pi$
$79$	−170281.	−	294935.i	−0.345370	−	0.598199i	−0.985421	+	0.170134i	$0.945580\pi$
$80$		−	173779.i		−	0.339411i
$81$		0			0
$82$	94848.0			0.172023
$83$	429768.	−	248127.i	0.751622	−	0.433949i	−0.0746575	−	0.997209i	$-0.523786\pi$
$83$	429768.	−	248127.i	0.751622	−	0.433949i	0.826280	+	0.563260i	$0.190453\pi$
$84$		0			0
$85$	−380160.	+	658456.i	−0.619027	+	1.07219i
$86$	31382.9	+	18118.9i	0.0493398	+	0.0284863i
$87$		0			0
$88$	3072.00	+	5320.86i	0.00450789	+	0.00780789i
$89$		−	386725.i		−	0.548570i	−0.961648	−	0.274285i	$-0.911559\pi$
$89$		−	386725.i		−	0.548570i	0.961648	−	0.274285i	$-0.0884412\pi$
$90$		0			0
$91$	−5900.00			−0.00782939
$92$	284062.	−	164004.i	0.364796	−	0.210615i
$93$		0			0
$94$	508800.	−	881267.i	0.612581	−	1.06102i
$95$	772765.	+	446156.i	0.901315	+	0.520375i
$96$		0			0
$97$	140543.	+	243428.i	0.153991	+	0.266719i	0.932691	−	0.360676i	$-0.117454\pi$
$97$	140543.	+	243428.i	0.153991	+	0.266719i	−0.778700	+	0.627396i	$0.784121\pi$
$98$		−	665501.i		−	0.707083i
$99$		0			0
$100$	421600.			0.421600
$101$	−818708.	+	472681.i	−0.794630	+	0.458780i	−0.841590	−	0.540117i	$-0.818380\pi$
$101$	−818708.	+	472681.i	−0.794630	+	0.458780i	0.0469603	+	0.998897i	$0.485047\pi$
$102$		0			0
$103$	432863.	−	749741.i	0.396131	−	0.686119i	−0.597114	−	0.802156i	$-0.703686\pi$
$103$	432863.	−	749741.i	0.396131	−	0.686119i	0.993245	+	0.116038i	$0.0370193\pi$
$104$	−462464.	−	267004.i	−0.411129	−	0.237365i
$105$		0			0
$106$	−544608.	−	943289.i	−0.457263	−	0.792003i
$107$			1.47410e6i			1.20330i	0.798759	+	0.601651i	$0.205490\pi$
$107$			1.47410e6i			1.20330i	−0.798759	+	0.601651i	$0.794510\pi$
$108$		0			0
$109$	650810.			0.502545			0.251272	−	0.967916i	$-0.419151\pi$
$109$	650810.			0.502545			0.251272	+	0.967916i	$0.419151\pi$
$110$	−28218.1	+	16291.7i	−0.0212007	+	0.0122402i
$111$		0			0
$112$	−1024.00	+	1773.62i	−0.000728863	+	0.00126243i
$113$	−1.51049e6	−	872083.i	−1.04685	−	0.604397i	−0.125082	−	0.992146i	$-0.539919\pi$
$113$	−1.51049e6	−	872083.i	−1.04685	−	0.604397i	−0.921765	+	0.387749i	$0.873253\pi$
$114$		0			0
$115$	869760.	+	1.50647e6i	0.571881	+	0.990527i
$116$		−	70597.5i		−	0.0452289i
$117$		0			0
$118$	1.84877e6			1.12522
$119$	7759.98	−	4480.23i	0.00460490	−	0.00265864i
$120$		0			0
$121$	−885204.	+	1.53322e6i	−0.499675	+	0.865462i
$122$	306510.	+	176963.i	0.168797	+	0.0974549i
$123$		0			0
$124$	366368.	+	634568.i	0.192155	+	0.332823i
$125$		−	415779.i		−	0.212879i
$126$		0			0
$127$	−2.28053e6			−1.11333			−0.556665	−	0.830737i	$-0.687919\pi$
$127$	−2.28053e6			−1.11333			−0.556665	+	0.830737i	$0.687919\pi$
$128$	−160530.	+	92681.9i	−0.0765466	+	0.0441942i
$129$		0			0
$130$	1.41600e6	−	2.45258e6i	0.644515	−	1.11633i
$131$	928347.	+	535981.i	0.412949	+	0.238416i	0.692056	−	0.721844i	$-0.256705\pi$
$131$	928347.	+	535981.i	0.412949	+	0.238416i	−0.279107	+	0.960260i	$0.590038\pi$
$132$		0			0
$133$	−5258.00	−	9107.12i	−0.00223494	−	0.00387103i
$134$			2.48165e6i			1.03140i
$135$		0			0
$136$	811008.			0.322410
$137$	−2.41047e6	+	1.39169e6i	−0.937434	+	0.541228i	−0.889155	−	0.457606i	$-0.848707\pi$
$137$	−2.41047e6	+	1.39169e6i	−0.937434	+	0.541228i	−0.0482791	+	0.998834i	$0.515374\pi$
$138$		0			0
$139$	−2.28697e6	+	3.96115e6i	−0.851563	+	1.47495i	0.0282348	+	0.999601i	$0.491011\pi$
$139$	−2.28697e6	+	3.96115e6i	−0.851563	+	1.47495i	−0.879798	+	0.475349i	$0.842322\pi$
$140$	−9406.04	−	5430.58i	−0.00342786	−	0.00197907i
$141$		0			0
$142$	−192960.	−	334217.i	−0.0673911	−	0.116725i
$143$			100126.i			0.0342405i
$144$		0			0
$145$	374400.			0.122809
$146$	−3.57875e6	+	2.06619e6i	−1.14993	+	0.663915i
$147$		0			0
$148$	544928.	−	943843.i	0.168095	−	0.291149i
$149$	−3.86256e6	−	2.23005e6i	−1.16766	−	0.674149i	−0.214533	−	0.976717i	$-0.568823\pi$
$149$	−3.86256e6	−	2.23005e6i	−1.16766	−	0.674149i	−0.953128	+	0.302568i	$0.902156\pi$
$150$		0			0
$151$	1.10405e6	+	1.91227e6i	0.320669	+	0.555415i	0.980626	−	0.195888i	$-0.0627590\pi$
$151$	1.10405e6	+	1.91227e6i	0.320669	+	0.555415i	−0.659957	+	0.751303i	$0.729426\pi$
$152$		−	951800.i		−	0.271028i
$153$		0			0
$154$	384.000			0.000105140
$155$	−3.36530e6	+	1.94296e6i	−0.903711	+	0.521758i
$156$		0			0
$157$	644435.	−	1.11619e6i	0.166525	−	0.288430i	−0.770671	−	0.637234i	$-0.780079\pi$
$157$	644435.	−	1.11619e6i	0.166525	−	0.288430i	0.937196	+	0.348803i	$0.113412\pi$
$158$	−1.66841e6	−	963255.i	−0.422990	−	0.244214i
$159$		0			0
$160$	−491520.	−	851338.i	−0.120000	−	0.207846i
$161$		−	20500.4i		−	0.00491231i
$162$		0			0
$163$	879914.			0.203178			0.101589	−	0.994826i	$-0.467607\pi$
$163$	879914.			0.203178			0.101589	+	0.994826i	$0.467607\pi$
$164$	464658.	−	268271.i	0.105342	−	0.0608193i
$165$		0			0
$166$	1.40362e6	−	2.43113e6i	0.306849	−	0.531477i
$167$	−5.16809e6	−	2.98380e6i	−1.10964	−	0.640649i	−0.170901	−	0.985288i	$-0.554668\pi$
$167$	−5.16809e6	−	2.98380e6i	−1.10964	−	0.640649i	−0.938735	+	0.344639i	$0.888001\pi$
$168$		0			0
$169$	−1.93785e6	−	3.35645e6i	−0.401475	−	0.695376i
$170$			4.30102e6i			0.875436i
$171$		0			0
$172$	204992.			0.0402858
$173$	362750.	−	209434.i	0.0700598	−	0.0404490i	−0.464561	−	0.885541i	$-0.653788\pi$
$173$	362750.	−	209434.i	0.0700598	−	0.0404490i	0.534621	+	0.845092i	$0.320454\pi$
$174$		0			0
$175$	13175.0	−	22819.8i	0.00245831	−	0.00425792i
$176$	30099.3	+	17377.9i	0.00552101	+	0.00318756i
$177$		0			0
$178$	−1.09382e6	−	1.89456e6i	−0.193949	−	0.335929i
$179$			302110.i			0.0526752i	0.999653	+	0.0263376i	$0.00838448\pi$
$179$			302110.i			0.0526752i	−0.999653	+	0.0263376i	$0.991616\pi$
$180$		0			0
$181$	−6.47618e6			−1.09215			−0.546076	−	0.837735i	$-0.683879\pi$
$181$	−6.47618e6			−1.09215			−0.546076	+	0.837735i	$0.683879\pi$
$182$	−28904.0	+	16687.7i	−0.00479450	+	0.00276811i
$183$		0			0
$184$	927744.	−	1.60690e6i	0.148927	−	0.257950i
$185$	5.00548e6	+	2.88992e6i	0.790553	+	0.456426i
$186$		0			0
$187$	−76032.0	−	131691.i	−0.0116271	−	0.0201387i
$188$		−	5.75641e6i		−	0.866320i
$189$		0			0
$190$	5.04768e6			0.735921
$191$	−4.34888e6	+	2.51083e6i	−0.624134	+	0.360344i	−0.778477	−	0.627674i	$-0.784007\pi$
$191$	−4.34888e6	+	2.51083e6i	−0.624134	+	0.360344i	0.154343	+	0.988017i	$0.450674\pi$
$192$		0			0
$193$	−1.75046e6	+	3.03189e6i	−0.243490	+	0.421737i	−0.961706	−	0.274083i	$-0.911626\pi$
$193$	−1.75046e6	+	3.03189e6i	−0.243490	+	0.421737i	0.718216	+	0.695820i	$0.244959\pi$
$194$	1.37703e6	+	795031.i	0.188599	+	0.108888i
$195$		0			0
$196$	−1.88232e6	−	3.26027e6i	−0.249992	−	0.432998i
$197$			4.85423e6i			0.634923i	0.948271	+	0.317462i	$0.102830\pi$
$197$			4.85423e6i			0.634923i	−0.948271	+	0.317462i	$0.897170\pi$
$198$		0			0
$199$	−9.50976e6			−1.20673			−0.603365	−	0.797465i	$-0.706174\pi$
$199$	−9.50976e6			−1.20673			−0.603365	+	0.797465i	$0.706174\pi$
$200$	2.06541e6	−	1.19246e6i	0.258176	−	0.149058i
$201$		0			0
$202$	−2.67389e6	+	4.63131e6i	−0.324406	+	0.561888i
$203$	−3821.20	−	2206.17i	−0.000456785	−	0.000263725i
$204$		0			0
$205$	1.42272e6	+	2.46422e6i	0.165142	+	0.286035i
$206$		−	4.89729e6i		−	0.560214i
$207$		0			0
$208$	−3.02080e6			−0.335685
$209$	−154553.	+	89231.2i	−0.0169293	+	0.00977413i
$210$		0			0
$211$	−3.53207e6	+	6.11772e6i	−0.375995	+	0.651242i	−0.990475	−	0.137690i	$-0.956032\pi$
$211$	−3.53207e6	+	6.11772e6i	−0.375995	+	0.651242i	0.614481	+	0.788932i	$0.289366\pi$
$212$	−5.33605e6	−	3.08077e6i	−0.560031	−	0.323334i
$213$		0			0
$214$	4.16938e6	+	7.22157e6i	0.425432	+	0.736869i
$215$			1.08713e6i			0.109388i
$216$		0			0
$217$	45796.0			0.00448176
$218$	3.18830e6	−	1.84077e6i	0.307745	−	0.177676i
$219$		0			0
$220$	−92160.0	+	159626.i	−0.00865515	+	0.0149912i
$221$	1.14460e7	+	6.60834e6i	1.06042	+	0.612231i
$222$		0			0
$223$	−2.33446e6	−	4.04340e6i	−0.210509	−	0.364613i	0.741365	−	0.671102i	$-0.234179\pi$
$223$	−2.33446e6	−	4.04340e6i	−0.210509	−	0.364613i	−0.951874	+	0.306490i	$0.900846\pi$
$224$			11585.2i			0.00103077i
$225$		0			0
$226$	−9.86650e6			−0.854747
$227$	1.70196e7	−	9.82624e6i	1.45503	−	0.840059i	0.456266	−	0.889844i	$-0.349187\pi$
$227$	1.70196e7	−	9.82624e6i	1.45503	−	0.840059i	0.998760	+	0.0497843i	$0.0158534\pi$
$228$		0			0
$229$	2.24089e6	−	3.88134e6i	0.186601	−	0.323203i	−0.757514	−	0.652819i	$-0.773586\pi$
$229$	2.24089e6	−	3.88134e6i	0.186601	−	0.323203i	0.944115	+	0.329617i	$0.106919\pi$
$230$	8.52187e6	+	4.92011e6i	0.700409	+	0.404381i
$231$		0			0
$232$	−199680.	−	345856.i	−0.0159908	−	0.0276969i
$233$			2.29286e6i			0.181263i	0.995884	+	0.0906316i	$0.0288886\pi$
$233$			2.29286e6i			0.181263i	−0.995884	+	0.0906316i	$0.971111\pi$
$234$		0			0
$235$	3.05280e7			2.35231
$236$	9.05708e6	−	5.22911e6i	0.689052	−	0.397824i
$237$		0			0
$238$	25344.0	−	43897.1i	0.00187994	−	0.00325615i
$239$	2.29119e6	+	1.32282e6i	0.167829	+	0.0968964i	0.581562	−	0.813502i	$-0.302442\pi$
$239$	2.29119e6	+	1.32282e6i	0.167829	+	0.0968964i	−0.413733	+	0.910398i	$0.635775\pi$
$240$		0			0
$241$	3.49790e6	+	6.05855e6i	0.249894	+	0.432830i	0.963496	−	0.267722i	$-0.0862707\pi$
$241$	3.49790e6	+	6.05855e6i	0.249894	+	0.432830i	−0.713602	+	0.700551i	$0.752937\pi$
$242$			1.00149e7i			0.706647i
$243$		0			0
$244$	2.00211e6			0.137822
$245$	1.72902e7	−	9.98251e6i	1.17572	−	0.678799i
$246$		0			0
$247$	7.75555e6	−	1.34330e7i	0.514662	−	0.891420i
$248$	3.58966e6	+	2.07249e6i	0.235341	+	0.135874i
$249$		0			0
$250$	−1.17600e6	−	2.03689e6i	−0.0752640	−	0.130361i
$251$		−	2.84990e7i		−	1.80223i	−0.433585	−	0.901113i	$-0.642752\pi$
$251$		−	2.84990e7i		−	1.80223i	0.433585	−	0.901113i	$-0.357248\pi$
$252$		0			0
$253$	−347904.			−0.0214831
$254$	−1.11723e7	+	6.45030e6i	−0.681773	+	0.393622i
$255$		0			0
$256$	−524288.	+	908093.i	−0.0312500	+	0.0541266i
$257$	161784.	+	93406.0i	0.00953094	+	0.00550269i	0.504758	−	0.863261i	$-0.331582\pi$
$257$	161784.	+	93406.0i	0.00953094	+	0.00550269i	−0.495227	+	0.868764i	$0.664915\pi$
$258$		0			0
$259$	−34058.0	−	58990.2i	−0.00196029	−	0.00339532i
$260$		−	1.60202e7i		−	0.911482i
$261$		0			0
$262$	6.06394e6			0.337171
$263$	−7.46117e6	+	4.30771e6i	−0.410147	+	0.236798i	−0.690853	−	0.722995i	$-0.742765\pi$
$263$	−7.46117e6	+	4.30771e6i	−0.410147	+	0.236798i	0.280706	+	0.959794i	$0.409431\pi$
$264$		0			0
$265$	1.63382e7	−	2.82987e7i	0.877946	−	1.52065i
$266$	−51517.7	−	29743.7i	−0.00273723	−	0.00158034i
$267$		0			0
$268$	7.01917e6	+	1.21576e7i	0.364654	+	0.631600i
$269$		−	7.55132e6i		−	0.387941i	−0.981007	−	0.193971i	$-0.937863\pi$
$269$		−	7.55132e6i		−	0.387941i	0.981007	−	0.193971i	$-0.0621367\pi$
$270$		0			0
$271$	1.39445e7			0.700642			0.350321	−	0.936630i	$-0.386073\pi$
$271$	1.39445e7			0.700642			0.350321	+	0.936630i	$0.386073\pi$
$272$	3.97311e6	−	2.29388e6i	0.197435	−	0.113989i
$273$		0			0
$274$	−7.87258e6	+	1.36357e7i	−0.382706	+	0.662866i
$275$	−387264.	−	223587.i	−0.0186213	−	0.0107510i
$276$		0			0
$277$	−1.40647e7	−	2.43607e7i	−0.661744	−	1.14617i	−0.980157	−	0.198222i	$-0.936483\pi$
$277$	−1.40647e7	−	2.43607e7i	−0.661744	−	1.14617i	0.318413	−	0.947952i	$-0.396850\pi$
$278$			2.58741e7i			1.20429i
$279$		0			0
$280$	−61440.0			−0.00279883
$281$	1.93496e7	−	1.11715e7i	0.872072	−	0.503491i	0.00403602	−	0.999992i	$-0.498715\pi$
$281$	1.93496e7	−	1.11715e7i	0.872072	−	0.503491i	0.868036	+	0.496501i	$0.165382\pi$
$282$		0			0
$283$	−5.07092e6	+	8.78310e6i	−0.223732	+	0.387515i	−0.955938	−	0.293568i	$-0.905157\pi$
$283$	−5.07092e6	+	8.78310e6i	−0.223732	+	0.387515i	0.732206	+	0.681083i	$0.238491\pi$
$284$	−1.89061e6	−	1.09155e6i	−0.0825368	−	0.0476527i
$285$		0			0
$286$	283200.	+	490517.i	0.0121058	+	0.0209679i
$287$		−	33533.8i		−	0.00141853i
$288$		0			0
$289$	4.06512e6			0.168415
$290$	1.83418e6	−	1.05896e6i	0.0752051	−	0.0434197i
$291$		0			0
$292$	−1.16882e7	+	2.02445e7i	−0.469459	+	0.813127i
$293$	2.41161e7	+	1.39234e7i	0.958746	+	0.553532i	0.895787	−	0.444484i	$-0.146613\pi$
$293$	2.41161e7	+	1.39234e7i	0.958746	+	0.553532i	0.0629590	+	0.998016i	$0.479946\pi$
$294$		0			0
$295$	2.77315e7	+	4.80324e7i	1.08021	+	1.87098i
$296$		−	6.16516e6i		−	0.237722i
$297$		0			0
$298$	−2.52301e7			−0.953391
$299$	2.61870e7	−	1.51191e7i	0.979653	−	0.565603i
$300$		0			0
$301$	6406.00	−	11095.5i	0.000234902	−	0.000406863i
$302$	1.08174e7	+	6.24543e6i	0.392737	+	0.226747i
$303$		0			0
$304$	−2.69210e6	−	4.66285e6i	−0.0958230	−	0.165970i
$305$			1.06178e7i			0.374227i
$306$		0			0
$307$	−3.63254e7			−1.25544			−0.627718	−	0.778440i	$-0.716011\pi$
$307$	−3.63254e7			−1.25544			−0.627718	+	0.778440i	$0.716011\pi$
$308$	1881.21	−	1086.12i	6.43850e−5	−	3.71727e-5i
$309$		0			0
$310$	−1.09910e7	+	1.90370e7i	−0.368938	+	0.639020i
$311$	−3.11700e7	−	1.79960e7i	−1.03623	−	0.598268i	−0.117467	−	0.993077i	$-0.537477\pi$
$311$	−3.11700e7	−	1.79960e7i	−1.03623	−	0.598268i	−0.918763	+	0.394809i	$0.870811\pi$
$312$		0			0
$313$	−2.00550e7	−	3.47362e7i	−0.654016	−	1.13279i	−0.982139	−	0.188155i	$-0.939749\pi$
$313$	−2.00550e7	−	3.47362e7i	−0.654016	−	1.13279i	0.328123	−	0.944635i	$-0.393584\pi$
$314$		−	7.29095e6i		−	0.235502i
$315$		0			0
$316$	−1.08980e7			−0.345370
$317$	−3.41540e7	+	1.97188e7i	−1.07217	+	0.619018i	−0.928774	−	0.370647i	$-0.879136\pi$
$317$	−3.41540e7	+	1.97188e7i	−1.07217	+	0.619018i	−0.143397	+	0.989665i	$0.545803\pi$
$318$		0			0
$319$	−37440.0	+	64848.0i	−0.00115336	+	0.00199767i
$320$	−4.81589e6	−	2.78046e6i	−0.146969	−	0.0848528i
$321$		0			0
$322$	−57984.0	−	100431.i	−0.00173676	−	0.00300816i
$323$			2.35570e7i			0.699058i
$324$		0			0
$325$	3.88662e7			1.13220
$326$	4.31068e6	−	2.48877e6i	0.124421	−	0.0718344i
$327$		0			0
$328$	1.51757e6	−	2.62850e6i	0.0430058	−	0.0744882i
$329$	−311575.	−	179888.i	−0.00874933	−	0.00505143i
$330$		0			0
$331$	−1.39181e7	−	2.41069e7i	−0.383793	−	0.664749i	0.607808	−	0.794084i	$-0.292049\pi$
$331$	−1.39181e7	−	2.41069e7i	−0.383793	−	0.664749i	−0.991601	+	0.129335i	$0.958716\pi$
$332$		−	1.58801e7i		−	0.433949i
$333$		0			0
$334$	−3.37578e7			−0.906014
$335$	−6.44752e7	+	3.72248e7i	−1.71498	+	0.990142i
$336$		0			0
$337$	1.18948e7	−	2.06025e7i	0.310791	−	0.538306i	−0.667743	−	0.744392i	$-0.732739\pi$
$337$	1.18948e7	−	2.06025e7i	0.310791	−	0.538306i	0.978534	+	0.206086i	$0.0660727\pi$
$338$	−1.89869e7	−	1.09621e7i	−0.491705	−	0.283886i
$339$		0			0
$340$	1.21651e7	+	2.10706e7i	0.309514	+	0.536093i
$341$		−	777184.i		−	0.0196002i
$342$		0			0
$343$	−470588.			−0.0116616
$344$	1.00425e6	−	579805.i	0.0246699	−	0.0142432i
$345$		0			0
$346$	1.18474e6	−	2.05202e6i	0.0286018	−	0.0495398i
$347$	4.62525e7	+	2.67039e7i	1.10700	+	0.639125i	0.938050	−	0.346500i	$-0.112630\pi$
$347$	4.62525e7	+	2.67039e7i	1.10700	+	0.639125i	0.168947	+	0.985625i	$0.445963\pi$
$348$		0			0
$349$	−2.35839e7	−	4.08484e7i	−0.554803	−	0.960946i	−0.997919	−	0.0644821i	$-0.979460\pi$
$349$	−2.35839e7	−	4.08484e7i	−0.554803	−	0.960946i	0.443116	−	0.896464i	$-0.353873\pi$
$350$		−	149058.i		−	0.00347657i
$351$		0			0
$352$	196608.			0.00450789
$353$	−1.51938e7	+	8.77215e6i	−0.345416	+	0.199426i	−0.662665	−	0.748916i	$-0.730574\pi$
$353$	−1.51938e7	+	8.77215e6i	−0.345416	+	0.199426i	0.317248	+	0.948342i	$0.397241\pi$
$354$		0			0
$355$	5.78880e6	−	1.00265e7i	0.129391	−	0.224111i
$356$	−1.07172e7	−	6.18760e6i	−0.237538	−	0.137143i
$357$		0			0
$358$	854496.	+	1.48003e6i	0.0186235	+	0.0322568i
$359$			6.18249e7i			1.33623i	0.744059	+	0.668113i	$0.232898\pi$
$359$			6.18249e7i			1.33623i	−0.744059	+	0.668113i	$0.767102\pi$
$360$		0			0
$361$	−1.93993e7			−0.412349
$362$	−3.17267e7	+	1.83174e7i	−0.668804	+	0.386134i
$363$		0			0
$364$	−94400.0	+	163506.i	−0.00195735	+	0.00339022i
$365$	−1.07363e8	−	6.19858e7i	−2.20787	−	1.27472i
$366$		0			0
$367$	1.70230e7	+	2.94848e7i	0.344381	+	0.596485i	0.985241	−	0.171173i	$-0.0547556\pi$
$367$	1.70230e7	+	2.94848e7i	0.344381	+	0.596485i	−0.640860	+	0.767657i	$0.721422\pi$
$368$		−	1.04962e7i		−	0.210615i
$369$		0			0
$370$	3.26957e7			0.645484
$371$	−333503.	+	192548.i	−0.00653097	+	0.00377066i
$372$		0			0
$373$	2.57891e7	−	4.46680e7i	0.496946	−	0.860736i	−0.503048	−	0.864259i	$-0.667788\pi$
$373$	2.57891e7	−	4.46680e7i	0.496946	−	0.860736i	0.999994	+	0.00352296i	$0.00112139\pi$
$374$	−744958.	−	430102.i	−0.0142402	−	0.00822160i
$375$		0			0
$376$	−1.62816e7	−	2.82006e7i	−0.306291	−	0.530511i
$377$		−	6.50821e6i		−	0.121461i
$378$		0			0
$379$	4.28828e7			0.787709			0.393855	−	0.919173i	$-0.371141\pi$
$379$	4.28828e7			0.787709			0.393855	+	0.919173i	$0.371141\pi$
$380$	2.47285e7	−	1.42770e7i	0.450658	−	0.260187i
$381$		0			0
$382$	−1.42034e7	+	2.46010e7i	−0.254802	+	0.441329i
$383$	−1.31036e7	−	7.56534e6i	−0.233235	−	0.134658i	0.378829	−	0.925467i	$-0.376327\pi$
$383$	−1.31036e7	−	7.56534e6i	−0.233235	−	0.134658i	−0.612063	+	0.790809i	$0.709660\pi$
$384$		0			0
$385$	5760.00	+	9976.61i	0.000100935	+	0.000174824i
$386$			1.98043e7i			0.344347i
$387$		0			0
$388$	8.99475e6			0.153991
$389$	−5.32882e7	+	3.07660e7i	−0.905278	+	0.522663i	−0.878909	−	0.476990i	$-0.841728\pi$
$389$	−5.32882e7	+	3.07660e7i	−0.905278	+	0.522663i	−0.0263694	+	0.999652i	$0.508395\pi$
$390$		0			0
$391$	−2.29617e7	+	3.97708e7i	−0.384125	+	0.665325i
$392$	−1.84429e7	−	1.06480e7i	−0.306176	−	0.176771i
$393$		0			0
$394$	1.37298e7	+	2.37808e7i	0.224479	+	0.388810i
$395$		−	5.77953e7i		−	0.937780i
$396$		0			0
$397$	−8.55816e7			−1.36776			−0.683878	−	0.729596i	$-0.739708\pi$
$397$	−8.55816e7			−1.36776			−0.683878	+	0.729596i	$0.739708\pi$
$398$	−4.65881e7	+	2.68977e7i	−0.738968	+	0.426644i
$399$		0			0
$400$	6.74560e6	−	1.16837e7i	0.105400	−	0.182558i
$401$	−3.54844e7	−	2.04869e7i	−0.550306	−	0.317719i	0.198939	−	0.980012i	$-0.436250\pi$
$401$	−3.54844e7	−	2.04869e7i	−0.550306	−	0.317719i	−0.749245	+	0.662292i	$0.769584\pi$
$402$		0			0
$403$	3.37746e7	+	5.84992e7i	0.516029	+	0.893789i
$404$			3.02516e7i			0.458780i
$405$		0			0
$406$	−24960.0			−0.000372964
$407$	−1.00110e6	+	577983.i	−0.0148488	+	0.00857299i
$408$		0			0
$409$	−3.05278e7	+	5.28757e7i	−0.446196	+	0.772834i	−0.998135	−	0.0610509i	$-0.980555\pi$
$409$	−3.05278e7	+	5.28757e7i	−0.446196	+	0.772834i	0.551939	+	0.833885i	$0.313888\pi$
$410$	1.39398e7	+	8.04812e6i	0.202257	+	0.116773i
$411$		0			0
$412$	−1.38516e7	−	2.39917e7i	−0.198065	−	0.343059i
$413$		−	653638.i		−	0.00927870i
$414$		0			0
$415$	8.42170e7			1.17830
$416$	−1.47988e7	+	8.54411e6i	−0.205564	+	0.118683i
$417$		0			0
$418$	−504768.	+	874284.i	−0.00691135	+	0.0119708i
$419$	2.93461e7	+	1.69430e7i	0.398941	+	0.230329i	0.686027	−	0.727576i	$-0.259353\pi$
$419$	2.93461e7	+	1.69430e7i	0.398941	+	0.230329i	−0.287086	+	0.957905i	$0.592687\pi$
$420$		0			0
$421$	9.80780e6	+	1.69876e7i	0.131439	+	0.227660i	0.924232	−	0.381832i	$-0.124707\pi$
$421$	9.80780e6	+	1.69876e7i	0.131439	+	0.227660i	−0.792792	+	0.609492i	$0.791373\pi$
$422$			3.99608e7i			0.531737i
$423$		0			0
$424$	−3.48549e7			−0.457263
$425$	−5.11189e7	+	2.95135e7i	−0.665909	+	0.384463i
$426$		0			0
$427$	62566.0	−	108367.i	0.000803627	−	0.00139192i
$428$	4.08514e7	+	2.35856e7i	0.521045	+	0.300826i
$429$		0			0
$430$	3.07488e6	+	5.32585e6i	0.0386743	+	0.0669859i
$431$			4.01587e7i			0.501589i	0.968040	+	0.250795i	$0.0806919\pi$
$431$			4.01587e7i			0.501589i	−0.968040	+	0.250795i	$0.919308\pi$
$432$		0			0
$433$	−845854.			−0.0104191			−0.00520957	−	0.999986i	$-0.501658\pi$
$433$	−845854.			−0.0104191			−0.00520957	+	0.999986i	$0.501658\pi$
$434$	224354.	−	129531.i	0.00274450	−	0.00158454i
$435$		0			0
$436$	1.04130e7	−	1.80358e7i	0.125636	−	0.217608i
$437$	4.66750e7	+	2.69478e7i	0.559294	+	0.322908i
$438$		0			0
$439$	3.74102e7	+	6.47964e7i	0.442177	+	0.765873i	0.997851	−	0.0655271i	$-0.0208729\pi$
$439$	3.74102e7	+	6.47964e7i	0.442177	+	0.765873i	−0.555674	+	0.831401i	$0.687540\pi$
$440$			1.04267e6i			0.0122402i
$441$		0			0
$442$	7.47648e7			0.865825
$443$	1.08466e8	−	6.26228e7i	1.24762	−	0.720313i	0.276985	−	0.960874i	$-0.410665\pi$
$443$	1.08466e8	−	6.26228e7i	1.24762	−	0.720313i	0.970634	+	0.240561i	$0.0773315\pi$
$444$		0			0
$445$	3.28147e7	−	5.68368e7i	0.372382	−	0.644985i
$446$	−2.28729e7	−	1.32057e7i	−0.257820	−	0.148853i
$447$		0			0
$448$	32768.0	+	56755.8i	0.000364431	+	0.000631214i
$449$		−	1.12812e8i		−	1.24628i	−0.782109	−	0.623142i	$-0.785856\pi$
$449$		−	1.12812e8i		−	1.24628i	0.782109	−	0.623142i	$-0.214144\pi$
$450$		0			0
$451$	−569088.			−0.00620369
$452$	−4.83358e7	+	2.79067e7i	−0.523424	+	0.302199i
$453$		0			0
$454$	5.55856e7	−	9.62771e7i	0.594012	−	1.02886i
$455$	−867119.	−	500632.i	−0.00920544	−	0.00531477i
$456$		0			0
$457$	−7.86792e7	−	1.36276e8i	−0.824350	−	1.42782i	−0.902415	−	0.430867i	$-0.858208\pi$
$457$	−7.86792e7	−	1.36276e8i	−0.824350	−	1.42782i	0.0780656	−	0.996948i	$-0.475126\pi$
$458$		−	2.53528e7i		−	0.263894i
$459$		0			0
$460$	5.56646e7			0.571881
$461$	1.58575e8	−	9.15536e7i	1.61858	−	0.934485i	0.631287	−	0.775549i	$-0.282527\pi$
$461$	1.58575e8	−	9.15536e7i	1.61858	−	0.934485i	0.987289	−	0.158936i	$-0.0508063\pi$
$462$		0			0
$463$	−8.89889e7	+	1.54133e8i	−0.896588	+	1.55294i	−0.0647610	+	0.997901i	$0.520628\pi$
$463$	−8.89889e7	+	1.54133e8i	−0.896588	+	1.55294i	−0.831827	+	0.555035i	$0.812705\pi$
$464$	−1.95646e6	−	1.12956e6i	−0.0195847	−	0.0113072i
$465$		0			0
$466$	6.48518e6	+	1.12327e7i	0.0640862	+	0.111001i
$467$			9.35797e7i			0.918821i	0.888224	+	0.459410i	$0.151939\pi$
$467$			9.35797e7i			0.918821i	−0.888224	+	0.459410i	$0.848061\pi$
$468$		0			0
$469$	877396.			0.00850505
$470$	1.49556e8	−	8.63462e7i	1.44049	−	0.831668i
$471$		0			0
$472$	2.95803e7	−	5.12346e7i	0.281304	−	0.487233i
$473$	−188297.	−	108713.i	−0.00177935	−	0.00102731i
$474$		0			0
$475$	3.46371e7	+	5.99932e7i	0.323192	+	0.559785i
$476$		−	286735.i		−	0.00265864i
$477$		0			0
$478$	1.49660e7			0.137032
$479$	−9.32381e7	+	5.38310e7i	−0.848373	+	0.489808i	−0.860102	−	0.510123i	$-0.829600\pi$
$479$	−9.32381e7	+	5.38310e7i	−0.848373	+	0.489808i	0.0117286	+	0.999931i	$0.496267\pi$
$480$		0			0
$481$	5.02356e7	−	8.70105e7i	0.451415	−	0.781874i
$482$	3.42723e7	+	1.97871e7i	0.306057	+	0.176702i
$483$		0			0
$484$	2.83265e7	+	4.90630e7i	0.249837	+	0.432731i
$485$			4.77019e7i			0.418129i
$486$		0			0
$487$	−4.14432e6			−0.0358811			−0.0179406	−	0.999839i	$-0.505711\pi$
$487$	−4.14432e6			−0.0358811			−0.0179406	+	0.999839i	$0.505711\pi$
$488$	9.80831e6	−	5.66283e6i	0.0843985	−	0.0487275i
$489$		0			0
$490$	5.64696e7	−	9.78082e7i	0.479984	−	0.831356i
$491$	1.03357e8	+	5.96733e7i	0.873164	+	0.504122i	0.868398	−	0.495867i	$-0.165150\pi$
$491$	1.03357e8	+	5.96733e7i	0.873164	+	0.504122i	0.00476582	+	0.999989i	$0.498483\pi$
$492$		0			0
$493$	4.94208e6	+	8.55993e6i	0.0412448	+	0.0714381i
$494$		−	8.77440e7i		−	0.727841i
$495$		0			0
$496$	2.34476e7			0.192155
$497$	−118163.	+	68221.7i	−0.000962529	+	0.000555716i
$498$		0			0
$499$	−5.87178e7	+	1.01702e8i	−0.472572	+	0.818519i	−0.999507	−	0.0313868i	$-0.990008\pi$
$499$	−5.87178e7	+	1.01702e8i	−0.472572	+	0.818519i	0.526935	+	0.849905i	$0.323341\pi$
$500$	−1.15224e7	−	6.65246e6i	−0.0921792	−	0.0532197i
$501$		0			0
$502$	−8.06075e7	−	1.39616e8i	−0.637183	−	1.10363i
$503$		−	1.99753e8i		−	1.56960i	−0.619747	−	0.784802i	$-0.712765\pi$
$503$		−	1.99753e8i		−	1.56960i	0.619747	−	0.784802i	$-0.287235\pi$
$504$		0			0
$505$	−1.60433e8			−1.24572
$506$	−1.70437e6	+	984021.i	−0.0131557	+	0.00759544i
$507$		0			0
$508$	−3.64884e7	+	6.31998e7i	−0.278332	+	0.482086i
$509$	9.76227e7	+	5.63625e7i	0.740282	+	0.427402i	0.822172	−	0.569239i	$-0.192762\pi$
$509$	9.76227e7	+	5.63625e7i	0.740282	+	0.427402i	−0.0818896	+	0.996641i	$0.526096\pi$
$510$		0			0
$511$	730510.	+	1.26528e6i	0.00547474	+	0.00948253i
$512$			5.93164e6i			0.0441942i
$513$		0			0
$514$	1.05677e6			0.00778198
$515$	1.27235e8	−	7.34593e7i	0.931506	−	0.537805i
$516$		0			0
$517$	−3.05280e6	+	5.28760e6i	−0.0220916	+	0.0382637i
$518$	−333699.	−	192661.i	−0.00240085	−	0.00138613i
$519$		0			0
$520$	−4.53120e7	−	7.84827e7i	−0.322258	−	0.558167i
$521$			1.14581e8i			0.810215i	0.914269	+	0.405108i	$0.132766\pi$
$521$			1.14581e8i			0.810215i	−0.914269	+	0.405108i	$0.867234\pi$
$522$		0			0
$523$	−1.49806e8			−1.04719			−0.523594	−	0.851968i	$-0.675409\pi$
$523$	−1.49806e8			−1.04719			−0.523594	+	0.851968i	$0.675409\pi$
$524$	2.97071e7	−	1.71514e7i	0.206474	−	0.119208i
$525$		0			0
$526$	−2.43681e7	+	4.22067e7i	−0.167442	+	0.290018i
$527$	−8.88441e7	−	5.12941e7i	−0.607011	−	0.350458i
$528$		0			0
$529$	−2.14844e7	−	3.72121e7i	−0.145130	−	0.251372i
$530$		−	1.84846e8i		−	1.24160i
$531$		0			0
$532$	−336512.			−0.00223494
$533$	4.28357e7	−	2.47312e7i	0.282894	−	0.163329i
$534$		0			0
$535$	−1.25081e8	+	2.16647e8i	−0.816829	+	1.41479i
$536$	6.87735e7	+	3.97064e7i	0.446608	+	0.257849i
$537$		0			0
$538$	−2.13584e7	−	3.69938e7i	−0.137158	−	0.237565i
$539$			3.99300e6i			0.0254996i
$540$		0			0
$541$	−1.57017e8			−0.991644			−0.495822	−	0.868424i	$-0.665133\pi$
$541$	−1.57017e8			−0.991644			−0.495822	+	0.868424i	$0.665133\pi$
$542$	6.83140e7	−	3.94411e7i	0.429054	−	0.247714i
$543$		0			0
$544$	1.29761e7	−	2.24753e7i	0.0806025	−	0.139608i
$545$	9.56491e7	+	5.52231e7i	0.590870	+	0.341139i
$546$		0			0
$547$	1.39734e8	+	2.42027e8i	0.853770	+	1.47877i	0.877781	+	0.479061i	$0.159023\pi$
$547$	1.39734e8	+	2.42027e8i	0.853770	+	1.47877i	−0.0240114	+	0.999712i	$0.507644\pi$
$548$			8.90680e7i			0.541228i
$549$		0			0
$550$	−2.52960e6			−0.0152042
$551$	1.00459e7	−	5.80003e6i	0.0600532	−	0.0346717i
$552$		0			0
$553$	−340562.	+	589871.i	−0.00201382	+	0.00348804i
$554$	−1.37805e8	−	7.95617e7i	−0.810467	−	0.467924i
$555$		0			0
$556$	7.31831e7	+	1.26757e8i	0.425781	+	0.737475i
$557$		−	1.50294e8i		−	0.869712i	−0.900500	−	0.434856i	$-0.856799\pi$
$557$		−	1.50294e8i		−	0.869712i	0.900500	−	0.434856i	$-0.143201\pi$
$558$		0			0
$559$	1.88977e7			0.108187
$560$	−300993.	+	173779.i	−0.00171393	+	0.000989537i
$561$		0			0
$562$	6.31955e7	−	1.09458e8i	0.356022	−	0.616648i
$563$	7.16927e7	+	4.13918e7i	0.401744	+	0.231947i	0.687236	−	0.726434i	$-0.258824\pi$
$563$	7.16927e7	+	4.13918e7i	0.401744	+	0.231947i	−0.285492	+	0.958381i	$0.592157\pi$
$564$		0			0
$565$	−1.47997e8	−	2.56339e8i	−0.820557	−	1.42125i
$566$			5.73710e7i			0.316405i
$567$		0			0
$568$	−1.23494e7			−0.0673911
$569$	2.22768e8	−	1.28615e8i	1.20925	−	0.698160i	0.246653	−	0.969104i	$-0.420669\pi$
$569$	2.22768e8	−	1.28615e8i	1.20925	−	0.698160i	0.962595	+	0.270944i	$0.0873359\pi$
$570$		0			0
$571$	−1.42020e7	+	2.45985e7i	−0.0762852	+	0.132130i	−0.901644	−	0.432478i	$-0.857639\pi$
$571$	−1.42020e7	+	2.45985e7i	−0.0762852	+	0.132130i	0.825359	+	0.564608i	$0.190973\pi$
$572$	2.77478e6	+	1.60202e6i	0.0148266	+	0.00856013i
$573$		0			0
$574$	−94848.0	−	164282.i	−0.000501525	−	0.000868667i
$575$			1.35047e8i			0.710363i
$576$		0			0
$577$	6.52476e7			0.339654			0.169827	−	0.985474i	$-0.445679\pi$
$577$	6.52476e7			0.339654			0.169827	+	0.985474i	$0.445679\pi$
$578$	1.99149e7	−	1.14979e7i	0.103133	−	0.0595436i
$579$		0			0
$580$	5.99040e6	−	1.03757e7i	0.0307024	−	0.0531781i
$581$	−859536.	−	496253.i	−0.00438264	−	0.00253032i
$582$		0			0
$583$	3.26765e6	+	5.65973e6i	0.0164903	+	0.0285621i
$584$			1.32236e8i			0.663915i
$585$		0			0
$586$	1.57525e8			0.782813
$587$	−5.77414e7	+	3.33370e7i	−0.285478	+	0.164821i	−0.635901	−	0.771771i	$-0.719371\pi$
$587$	−5.77414e7	+	3.33370e7i	−0.285478	+	0.164821i	0.350423	+	0.936592i	$0.386038\pi$
$588$		0			0
$589$	−6.01988e7	+	1.04267e8i	−0.294606	+	0.510273i
$590$	2.71712e8	+	1.56873e8i	1.32298	+	0.763823i
$591$		0			0
$592$	−1.74377e7	−	3.02030e7i	−0.0840473	−	0.145574i
$593$			1.53324e8i			0.735271i	0.929970	+	0.367635i	$0.119833\pi$
$593$			1.53324e8i			0.735271i	−0.929970	+	0.367635i	$0.880167\pi$
$594$		0			0
$595$	1.52064e6			0.00721897
$596$	−1.23602e8	+	7.13616e7i	−0.583830	+	0.337075i
$597$		0			0
$598$	8.55264e7	−	1.48136e8i	0.399942	−	0.692719i
$599$	−1.89048e8	−	1.09147e8i	−0.879614	−	0.507846i	−0.00908314	−	0.999959i	$-0.502891\pi$
$599$	−1.89048e8	−	1.09147e8i	−0.879614	−	0.507846i	−0.870531	+	0.492113i	$0.836225\pi$
$600$		0			0
$601$	−5.42388e7	−	9.39444e7i	−0.249854	−	0.432760i	0.713631	−	0.700522i	$-0.247049\pi$
$601$	−5.42388e7	−	9.39444e7i	−0.249854	−	0.432760i	−0.963485	+	0.267762i	$0.913716\pi$
$602$		−	72475.6i		−	0.000332202i
$603$		0			0
$604$	7.06590e7			0.320669
$605$	−2.60196e8	+	1.50224e8i	−1.17499	+	0.678381i
$606$		0			0
$607$	1.71661e8	−	2.97325e8i	0.767547	−	1.32943i	−0.171343	−	0.985212i	$-0.554811\pi$
$607$	1.71661e8	−	2.97325e8i	0.767547	−	1.32943i	0.938889	−	0.344219i	$-0.111856\pi$
$608$	−2.63770e7	−	1.52288e7i	−0.117359	−	0.0677571i
$609$		0			0
$610$	3.00317e7	+	5.20164e7i	0.132309	+	0.229166i
$611$		−	5.30669e8i		−	2.32649i
$612$		0			0
$613$	2.96325e8			1.28643			0.643216	−	0.765685i	$-0.277600\pi$
$613$	2.96325e8			1.28643			0.643216	+	0.765685i	$0.277600\pi$
$614$	−1.77957e8	+	1.02744e8i	−0.768795	+	0.443864i
$615$		0			0
$616$	6144.00	−	10641.7i	2.62851e−5	−	4.55271e-5i
$617$	1.14900e8	+	6.63378e7i	0.489177	+	0.282426i	0.724233	−	0.689555i	$-0.242194\pi$
$617$	1.14900e8	+	6.63378e7i	0.489177	+	0.282426i	−0.235056	+	0.971982i	$0.575527\pi$
$618$		0			0
$619$	2.07387e8	+	3.59204e8i	0.874397	+	1.51450i	0.857404	+	0.514644i	$0.172076\pi$
$619$	2.07387e8	+	3.59204e8i	0.874397	+	1.51450i	0.0169931	+	0.999856i	$0.494591\pi$
$620$			1.24349e8i			0.521758i
$621$		0			0
$622$	−2.03602e8			−0.846078
$623$	−669828.	+	386725.i	−0.00277012	+	0.00159933i
$624$		0			0
$625$	1.38210e8	−	2.39386e8i	0.566107	−	0.980526i
$626$	−1.96498e8	−	1.13448e8i	−0.801003	−	0.462459i
$627$		0			0
$628$	−2.06219e7	−	3.57182e7i	−0.0832626	−	0.144215i
$629$			1.52588e8i			0.613151i
$630$		0			0
$631$	3.03858e8			1.20944			0.604718	−	0.796440i	$-0.293286\pi$
$631$	3.03858e8			1.20944			0.604718	+	0.796440i	$0.293286\pi$
$632$	−5.33890e7	+	3.08242e7i	−0.211495	+	0.122107i
$633$		0			0
$634$	−1.11547e8	+	1.93204e8i	−0.437712	+	0.758139i
$635$	−3.35168e8	−	1.93509e8i	−1.30900	−	0.755753i
$636$		0			0
$637$	−1.73526e8	−	3.00556e8i	−0.671347	−	1.16281i
$638$			423585.i			0.00163109i
$639$		0			0
$640$	−3.14573e7			−0.120000
$641$	−1.57295e8	+	9.08145e7i	−0.597230	+	0.344811i	−0.767951	−	0.640508i	$-0.778724\pi$
$641$	−1.57295e8	+	9.08145e7i	−0.597230	+	0.344811i	0.170721	+	0.985319i	$0.445390\pi$
$642$		0			0
$643$	−8.69053e7	+	1.50524e8i	−0.326899	+	0.566206i	−0.981895	−	0.189427i	$-0.939337\pi$
$643$	−8.69053e7	+	1.50524e8i	−0.326899	+	0.566206i	0.654996	+	0.755632i	$0.272670\pi$
$644$	−568125.	−	328007.i	−0.00212709	−	0.00122808i
$645$		0			0
$646$	6.66294e7	+	1.15405e8i	0.247154	+	0.428084i
$647$			2.43137e8i			0.897713i	0.893604	+	0.448856i	$0.148168\pi$
$647$			2.43137e8i			0.897713i	−0.893604	+	0.448856i	$0.851832\pi$
$648$		0			0
$649$	−1.10926e7			−0.0405788
$650$	1.90405e8	−	1.09930e8i	0.693327	−	0.400293i
$651$		0			0
$652$	1.40786e7	−	2.43849e7i	0.0507946	−	0.0879788i
$653$	3.87600e7	+	2.23781e7i	0.139202	+	0.0803681i	0.567983	−	0.823040i	$-0.307724\pi$
$653$	3.87600e7	+	2.23781e7i	0.139202	+	0.0803681i	−0.428782	+	0.903408i	$0.641057\pi$
$654$		0			0
$655$	9.09590e7	+	1.57546e8i	0.323685	+	0.560638i
$656$		−	1.71693e7i		−	0.0608193i
$657$		0			0
$658$	−2.03520e6			−0.00714380
$659$	−9.83576e7	+	5.67868e7i	−0.343678	+	0.198423i	−0.661897	−	0.749595i	$-0.730249\pi$
$659$	−9.83576e7	+	5.67868e7i	−0.343678	+	0.198423i	0.318219	+	0.948017i	$0.396915\pi$
$660$		0			0
$661$	4.96732e7	−	8.60365e7i	0.171996	−	0.297905i	−0.767122	−	0.641502i	$-0.778312\pi$
$661$	4.96732e7	−	8.60365e7i	0.171996	−	0.297905i	0.939118	+	0.343596i	$0.111645\pi$
$662$	−1.36369e8	−	7.87329e7i	−0.470049	−	0.271383i
$663$		0			0
$664$	−4.49157e7	−	7.77963e7i	−0.153424	−	0.265739i
$665$		−	1.78462e6i		−	0.00606851i
$666$		0			0
$667$	2.26138e7			0.0762071
$668$	−1.65379e8	+	9.54815e7i	−0.554818	+	0.320324i
$669$		0			0
$670$	−2.10575e8	+	3.64727e8i	−0.700136	+	1.21267i
$671$	−1.83906e6	−	1.06178e6i	−0.00608734	−	0.00351453i
$672$		0			0
$673$	1.39706e8	+	2.41978e8i	0.458321	+	0.793835i	0.998872	−	0.0474759i	$-0.0151177\pi$
$673$	1.39706e8	+	2.41978e8i	0.458321	+	0.793835i	−0.540552	+	0.841311i	$0.681784\pi$
$674$		−	1.34575e8i		−	0.439525i
$675$		0			0
$676$	−1.24022e8			−0.401475
$677$	3.54458e7	−	2.04646e7i	0.114235	−	0.0659536i	−0.441794	−	0.897117i	$-0.645658\pi$
$677$	3.54458e7	−	2.04646e7i	0.114235	−	0.0659536i	0.556029	+	0.831163i	$0.312324\pi$
$678$		0			0
$679$	281086.	−	486855.i	0.000897904	−	0.00155522i
$680$	1.19193e8	+	6.88163e7i	0.379075	+	0.218859i
$681$		0			0
$682$	−2.19821e6	−	3.80741e6i	−0.00692972	−	0.0120026i
$683$			3.74260e8i			1.17466i	0.809348	+	0.587329i	$0.199820\pi$
$683$			3.74260e8i			1.17466i	−0.809348	+	0.587329i	$0.800180\pi$
$684$		0			0
$685$	−4.72355e8			−1.46959
$686$	−2.30540e6	+	1.33102e6i	−0.00714125	+	0.00412300i
$687$		0			0
$688$	3.27987e6	−	5.68090e6i	0.0100714	−	0.0174442i
$689$	−4.91917e8	−	2.84008e8i	−1.50395	−	0.868307i
$690$		0			0
$691$	−5.75822e7	−	9.97353e7i	−0.174524	−	0.302284i	0.765473	−	0.643468i	$-0.222505\pi$
$691$	−5.75822e7	−	9.97353e7i	−0.174524	−	0.302284i	−0.939996	+	0.341185i	$0.889172\pi$
$692$		−	1.34038e7i		−	0.0404490i
$693$		0			0
$694$	3.02120e8			0.903859
$695$	−6.72230e8	+	3.88112e8i	−2.00246	+	1.15612i
$696$		0			0
$697$	−3.75598e7	+	6.50555e7i	−0.110924	+	0.192126i
$698$	−2.31074e8	−	1.33410e8i	−0.679492	−	0.392305i
$699$		0			0
$700$	−421600.	−	730233.i	−0.00122915	−	0.00212896i
$701$			5.65717e7i			0.164227i	0.996623	+	0.0821137i	$0.0261671\pi$
$701$			5.65717e7i			0.164227i	−0.996623	+	0.0821137i	$0.973833\pi$
$702$		0			0
$703$	1.79077e8			0.515435
$704$	963179.	−	556091.i	0.00276051	−	0.00159378i
$705$		0			0
$706$	−4.96228e7	+	8.59492e7i	−0.141016	+	0.244246i
$707$	1.63742e6	+	945362.i	0.00463341	+	0.00267510i
$708$		0			0
$709$	6.43259e7	+	1.11416e8i	0.180488	+	0.312614i	0.942047	−	0.335482i	$-0.108899\pi$
$709$	6.43259e7	+	1.11416e8i	0.180488	+	0.312614i	−0.761559	+	0.648095i	$0.775566\pi$
$710$		−	6.54928e7i		−	0.182986i
$711$		0			0
$712$	−7.00047e7			−0.193949
$713$	−2.03264e8	+	1.17355e8i	−0.560780	+	0.323767i
$714$		0			0
$715$	−8.49600e6	+	1.47155e7i	−0.0232432	+	0.0402584i
$716$	8.37232e6	+	4.83376e6i	0.0228090	+	0.0131688i
$717$		0			0
$718$	1.74867e8	+	3.02879e8i	0.472428	+	0.818268i
$719$		−	2.01053e8i		−	0.540908i	−0.962733	−	0.270454i	$-0.912826\pi$
$719$		−	2.01053e8i		−	0.540908i	0.962733	−	0.270454i	$-0.0871738\pi$
$720$		0			0
$721$	−1.73145e6			−0.00461960
$722$	−9.50369e7	+	5.48696e7i	−0.252511	+	0.145787i
$723$		0			0
$724$	−1.03619e8	+	1.79473e8i	−0.273038	+	0.472916i
$725$	2.51722e7	+	1.45332e7i	0.0660552	+	0.0381370i
$726$		0			0
$727$	−2.61604e8	−	4.53111e8i	−0.680833	−	1.17924i	−0.974727	−	0.223400i	$-0.928284\pi$
$727$	−2.61604e8	−	4.53111e8i	−0.680833	−	1.17924i	0.293894	−	0.955838i	$-0.405049\pi$
$728$			1.06801e6i			0.00276811i
$729$		0			0
$730$	−7.01290e8			−1.80272
$731$	−2.48552e7	+	1.43502e7i	−0.0636305	+	0.0367371i
$732$		0			0
$733$	3.28686e8	−	5.69301e8i	0.834583	−	1.44554i	−0.0597863	−	0.998211i	$-0.519042\pi$
$733$	3.28686e8	−	5.69301e8i	0.834583	−	1.44554i	0.894369	−	0.447329i	$-0.147625\pi$
$734$	1.66791e8	+	9.62968e7i	0.421778	+	0.243514i
$735$		0			0
$736$	−2.96878e7	−	5.14208e7i	−0.0744637	−	0.128975i
$737$		−	1.48899e7i		−	0.0371954i
$738$		0			0
$739$	3.50495e8			0.868458			0.434229	−	0.900803i	$-0.357021\pi$
$739$	3.50495e8			0.868458			0.434229	+	0.900803i	$0.357021\pi$
$740$	1.60175e8	−	9.24773e7i	0.395276	−	0.228213i
$741$		0			0
$742$	−1.08922e6	+	1.88658e6i	−0.00266626	+	0.00461810i
$743$	4.04146e8	+	2.33334e8i	0.985307	+	0.568867i	0.903868	−	0.427811i	$-0.140715\pi$
$743$	4.04146e8	+	2.33334e8i	0.985307	+	0.568867i	0.0814387	+	0.996678i	$0.474049\pi$
$744$		0			0
$745$	−3.78452e8	−	6.55498e8i	−0.915255	−	1.58527i
$746$		−	2.91770e8i		−	0.702788i
$747$		0			0
$748$	−4.86605e6			−0.0116271
$749$	2.55321e6	−	1.47410e6i	0.00607633	−	0.00350817i
$750$		0			0
$751$	1.68497e7	−	2.91845e7i	0.0397806	−	0.0689020i	−0.845450	−	0.534055i	$-0.820667\pi$
$751$	1.68497e7	−	2.91845e7i	0.0397806	−	0.0689020i	0.885230	+	0.465153i	$0.154001\pi$
$752$	−1.59526e8	−	9.21026e7i	−0.375128	−	0.216580i
$753$		0			0
$754$	−1.84080e7	−	3.18836e7i	−0.0429430	−	0.0743795i
$755$			3.74726e8i			0.870709i
$756$		0			0
$757$	2.98552e8			0.688227			0.344113	−	0.938928i	$-0.388180\pi$
$757$	2.98552e8			0.688227			0.344113	+	0.938928i	$0.388180\pi$
$758$	2.10082e8	−	1.21291e8i	0.482371	−	0.278497i
$759$		0			0
$760$	8.07629e7	−	1.39885e8i	0.183980	−	0.318663i
$761$	3.45286e8	+	1.99351e8i	0.783475	+	0.452340i	0.837660	−	0.546191i	$-0.183923\pi$
$761$	3.45286e8	+	1.99351e8i	0.783475	+	0.452340i	−0.0541853	+	0.998531i	$0.517256\pi$
$762$		0			0
$763$	−650810.	−	1.12724e6i	−0.00146514	−	0.00253771i
$764$			1.60693e8i			0.360344i
$765$		0			0
$766$	−8.55921e7			−0.190435
$767$	8.34949e8	−	4.82058e8i	1.85044	−	1.06835i
$768$		0			0
$769$	2.58686e8	−	4.48058e8i	0.568845	−	0.985269i	−0.427835	−	0.903857i	$-0.640724\pi$
$769$	2.58686e8	−	4.48058e8i	0.568845	−	0.985269i	0.996681	−	0.0814123i	$-0.0259431\pi$
$770$	56436.2	+	32583.5i	0.000123619	+	7.13716e-5i
$771$		0			0
$772$	5.60149e7	+	9.70206e7i	0.121745	+	0.210869i
$773$			1.83241e8i			0.396719i	0.980129	+	0.198360i	$0.0635614\pi$
$773$			1.83241e8i			0.396719i	−0.980129	+	0.198360i	$0.936439\pi$
$774$		0			0
$775$	−3.01681e8			−0.648102
$776$	4.40651e7	−	2.54410e7i	0.0942996	−	0.0544439i
$777$		0			0
$778$	−1.74038e8	+	3.01444e8i	−0.369578	+	0.640128i
$779$	7.63492e7	+	4.40802e7i	0.161507	+	0.0932463i
$780$		0			0
$781$	1.15776e6	+	2.00530e6i	0.00243033	+	0.00420946i
$782$			2.59782e8i			0.543235i
$783$		0			0
$784$	−1.20468e8			−0.249992
$785$	1.89424e8	−	1.09364e8i	0.391586	−	0.226082i
$786$		0			0
$787$	−1.57359e8	+	2.72554e8i	−0.322825	+	0.559149i	−0.981070	−	0.193655i	$-0.937966\pi$
$787$	−1.57359e8	+	2.72554e8i	−0.322825	+	0.559149i	0.658245	+	0.752804i	$0.271299\pi$
$788$	1.34524e8	+	7.76676e7i	0.274930	+	0.158731i
$789$		0			0
$790$	−1.63470e8	−	2.83138e8i	−0.331555	−	0.574271i
$791$			3.48833e6i			0.00704837i
$792$		0			0
$793$	1.84570e8			0.370119
$794$	−4.19262e8	+	2.42061e8i	−0.837576	+	0.483575i
$795$		0			0
$796$	−1.52156e8	+	2.63542e8i	−0.301683	+	0.522530i
$797$	−6.82574e8	−	3.94084e8i	−1.34826	−	0.778420i	−0.360260	−	0.932852i	$-0.617312\pi$
$797$	−6.82574e8	−	3.94084e8i	−1.34826	−	0.778420i	−0.988003	+	0.154432i	$0.950645\pi$
$798$		0			0
$799$	4.02970e8	+	6.97964e8i	0.790009	+	1.36834i
$800$		−	7.63178e7i		−	0.149058i
$801$		0			0
$802$	−2.31783e8			−0.449323
$803$	2.14725e7	−	1.23972e7i	0.0414702	−	0.0239428i
$804$		0			0
$805$	1.73952e6	−	3.01294e6i	0.00333458	−	0.00577567i
$806$	3.30922e8	+	1.91058e8i	0.632004	+	0.364888i
$807$		0			0
$808$	8.55644e7	+	1.48202e8i	0.162203	+	0.280944i
$809$		−	1.04745e9i		−	1.97828i	−0.146993	−	0.989138i	$-0.546959\pi$
$809$		−	1.04745e9i		−	1.97828i	0.146993	−	0.989138i	$-0.453041\pi$
$810$		0			0
$811$	−1.17930e8			−0.221086			−0.110543	−	0.993871i	$-0.535259\pi$
$811$	−1.17930e8			−0.221086			−0.110543	+	0.993871i	$0.535259\pi$
$812$	−122279.	+	70597.5i	−0.000228393	+	0.000131863i
$813$		0			0
$814$	−3.26957e6	+	5.66306e6i	−0.00606202	+	0.0104997i
$815$	1.29320e8	+	7.46632e7i	0.238888	+	0.137922i
$816$		0			0
$817$	1.68414e7	+	2.91701e7i	0.0308824	+	0.0534899i
$818$			3.45382e8i			0.631016i
$819$		0			0
$820$	9.10541e7			0.165142
$821$	−5.21295e7	+	3.00970e7i	−0.0942007	+	0.0543868i	−0.546360	−	0.837550i	$-0.683987\pi$
$821$	−5.21295e7	+	3.00970e7i	−0.0942007	+	0.0543868i	0.452160	+	0.891937i	$0.350654\pi$
$822$		0			0
$823$	−8.03102e6	+	1.39101e7i	−0.0144069	+	0.0249535i	−0.873139	−	0.487471i	$-0.837919\pi$
$823$	−8.03102e6	+	1.39101e7i	−0.0144069	+	0.0249535i	0.858732	+	0.512425i	$0.171253\pi$
$824$	−1.35718e8	−	7.83566e7i	−0.242580	−	0.140053i
$825$		0			0
$826$	−1.84877e6	−	3.20216e6i	−0.00328052	−	0.00568202i
$827$		−	3.66665e8i		−	0.648266i	−0.946012	−	0.324133i	$-0.894928\pi$
$827$		−	3.66665e8i		−	0.648266i	0.946012	−	0.324133i	$-0.105072\pi$
$828$		0			0
$829$	−3.63153e8			−0.637421			−0.318711	−	0.947852i	$-0.603250\pi$
$829$	−3.63153e8			−0.637421			−0.318711	+	0.947852i	$0.603250\pi$
$830$	4.12577e8	−	2.38202e8i	0.721557	−	0.416591i
$831$		0			0
$832$	−4.83328e7	+	8.37149e7i	−0.0839213	+	0.145356i
$833$	4.56462e8	+	2.63538e8i	0.789713	+	0.455941i
$834$		0			0
$835$	−5.06367e8	−	8.77054e8i	−0.869774	−	1.50649i
$836$			5.71080e6i			0.00977413i
$837$		0			0
$838$	1.91688e8			0.325734
$839$	7.62709e8	−	4.40350e8i	1.29144	−	0.745611i	0.312527	−	0.949909i	$-0.398824\pi$
$839$	7.62709e8	−	4.40350e8i	1.29144	−	0.745611i	0.978909	+	0.204298i	$0.0654912\pi$
$840$		0			0
$841$	−2.94978e8	+	5.10917e8i	−0.495909	+	0.858939i
$842$	9.60965e7	+	5.54813e7i	0.160980	+	0.0929417i
$843$		0			0
$844$	1.13026e8	+	1.95767e8i	0.187997	+	0.325621i
$845$		−	6.57727e8i		−	1.09012i
$846$		0			0
$847$	3.54082e6			0.00582711
$848$	−1.70753e8	+	9.85846e7i	−0.280015	+	0.161667i
$849$		0			0
$850$	−1.66954e8	+	2.89172e8i	−0.271856	+	0.470869i
$851$	3.02331e8	+	1.74551e8i	0.490562	+	0.283226i
$852$		0			0
$853$	1.92362e8	+	3.33181e8i	0.309936	+	0.536826i	0.978348	−	0.206966i	$-0.0663589\pi$
$853$	1.92362e8	+	3.33181e8i	0.309936	+	0.536826i	−0.668412	+	0.743791i	$0.733026\pi$
$854$		−	707853.i		−	0.00113650i
$855$		0			0
$856$	2.66840e8			0.425432
$857$	2.96741e8	−	1.71323e8i	0.471449	−	0.272191i	−0.245397	−	0.969423i	$-0.578918\pi$
$857$	2.96741e8	−	1.71323e8i	0.471449	−	0.272191i	0.716846	+	0.697231i	$0.245585\pi$
$858$		0			0
$859$	1.93721e8	−	3.35535e8i	0.305631	−	0.529369i	−0.671770	−	0.740760i	$-0.734466\pi$
$859$	1.93721e8	−	3.35535e8i	0.305631	−	0.529369i	0.977402	+	0.211390i	$0.0677991\pi$
$860$	3.01275e7	+	1.73941e7i	0.0473662	+	0.0273469i
$861$		0			0
$862$	1.13586e8	+	1.96737e8i	0.177339	+	0.307159i
$863$		−	6.46530e7i		−	0.100590i	−0.998734	−	0.0502951i	$-0.983984\pi$
$863$		−	6.46530e7i		−	0.100590i	0.998734	−	0.0502951i	$-0.0160162\pi$
$864$		0			0
$865$	7.10842e7			0.109831
$866$	−4.14382e6	+	2.39244e6i	−0.00638039	+	0.00368372i
$867$		0			0
$868$	732736.	−	1.26914e6i	0.00112044	−	0.00194066i
$869$	1.00104e7	+	5.77953e6i	0.0152544	+	0.00880710i
$870$		0			0
$871$	6.47080e8	+	1.12077e9i	0.979272	+	1.69615i
$872$		−	1.17809e8i		−	0.177676i
$873$		0			0
$874$	3.04880e8			0.456662
$875$	−720150.	+	415779.i	−0.00107498	+	0.000620638i
$876$		0			0
$877$	2.49641e8	−	4.32390e8i	0.370098	−	0.641028i	−0.619482	−	0.785011i	$-0.712657\pi$
$877$	2.49641e8	−	4.32390e8i	0.370098	−	0.641028i	0.989580	+	0.143982i	$0.0459908\pi$
$878$	3.66544e8	+	2.11624e8i	0.541554	+	0.312667i
$879$		0			0
$880$	2.94912e6	+	5.10803e6i	0.00432757	+	0.00749558i
$881$			9.14796e8i			1.33782i	0.743345	+	0.668908i	$0.233238\pi$
$881$			9.14796e8i			1.33782i	−0.743345	+	0.668908i	$0.766762\pi$
$882$		0			0
$883$	7.85211e6			0.0114052			0.00570261	−	0.999984i	$-0.498185\pi$
$883$	7.85211e6			0.0114052			0.00570261	+	0.999984i	$0.498185\pi$
$884$	3.66271e8	−	2.11467e8i	0.530208	−	0.306116i
$885$		0			0
$886$	3.54248e8	−	6.13575e8i	0.509338	−	0.882200i
$887$	9.59008e8	+	5.53684e8i	1.37420	+	0.793397i	0.991454	−	0.130454i	$-0.0416436\pi$
$887$	9.59008e8	+	5.53684e8i	1.37420	+	0.793397i	0.382750	+	0.923852i	$0.374977\pi$
$888$		0			0
$889$	2.28053e6	+	3.94999e6i	0.00324586	+	0.00562199i
$890$		−	3.71256e8i		−	0.526628i
$891$		0			0
$892$	−1.49405e8			−0.210509
$893$	8.19131e8	−	4.72925e8i	1.15027	−	0.664107i
$894$		0			0
$895$	−2.56349e7	+	4.44009e7i	−0.0357571	+	0.0619331i
$896$	321060.	+	185364.i	0.000446336	+	0.000257692i
$897$		0			0
$898$	−3.19081e8	−	5.52664e8i	−0.440628	−	0.763190i
$899$			5.05170e7i			0.0695277i
$900$		0			0
$901$	8.62659e8			1.17941
$902$	−2.78795e6	+	1.60962e6i	−0.00379897	+	0.00219333i
$903$		0			0
$904$	−1.57864e8	+	2.73428e8i	−0.213687	+	0.370116i
$905$	−9.51800e8	−	5.49522e8i	−1.28410	−	0.741378i
$906$		0			0
$907$	−5.80964e8	−	1.00626e9i	−0.778623	−	1.34861i	−0.932735	−	0.360562i	$-0.882585\pi$
$907$	−5.80964e8	−	1.00626e9i	−0.778623	−	1.34861i	0.154112	−	0.988053i	$-0.450748\pi$
$908$		−	6.28880e8i		−	0.840059i
$909$		0			0
$910$	−5.66400e6			−0.00751621
$911$	3.13015e8	−	1.80719e8i	0.414009	−	0.239028i	−0.278502	−	0.960436i	$-0.589838\pi$
$911$	3.13015e8	−	1.80719e8i	0.414009	−	0.239028i	0.692511	+	0.721407i	$0.256504\pi$
$912$		0			0
$913$	−8.42170e6	+	1.45868e7i	−0.0110659	+	0.0191667i
$914$	−7.70896e8	−	4.45077e8i	−1.00962	−	0.582903i
$915$		0			0
$916$	−7.17085e7	−	1.24203e8i	−0.0933006	−	0.161601i
$917$		−	2.14393e6i		−	0.00278036i
$918$		0			0
$919$	1.20431e9			1.55164			0.775820	−	0.630954i	$-0.217336\pi$
$919$	1.20431e9			1.55164			0.775820	+	0.630954i	$0.217336\pi$
$920$	2.72700e8	−	1.57443e8i	0.350204	−	0.202191i
$921$		0			0
$922$	5.17905e8	−	8.97038e8i	0.660781	−	1.14451i
$923$	−1.74291e8	−	1.00627e8i	−0.221651	−	0.127970i
$924$		0			0
$925$	2.24357e8	+	3.88598e8i	0.283475	+	0.490993i
$926$			1.00679e9i			1.26797i
$927$		0			0
$928$	−1.27795e7			−0.0159908
$929$	−5.48995e8	+	3.16962e8i	−0.684732	+	0.395330i	−0.801636	−	0.597813i	$-0.796037\pi$
$929$	−5.48995e8	+	3.16962e8i	−0.684732	+	0.395330i	0.116903	+	0.993143i	$0.462703\pi$
$930$		0			0
$931$	3.09289e8	−	5.35704e8i	0.383279	−	0.663859i
$932$	6.35416e7	+	3.66857e7i	0.0784893	+	0.0453158i
$933$		0			0
$934$	2.64683e8	+	4.58445e8i	0.324852	+	0.562660i
$935$		−	2.58061e7i		−	0.0315710i
$936$		0			0
$937$	−2.47138e8			−0.300414			−0.150207	−	0.988655i	$-0.547994\pi$
$937$	−2.47138e8			−0.300414			−0.150207	+	0.988655i	$0.547994\pi$
$938$	4.29835e6	−	2.48165e6i	0.00520826	−	0.00300699i
$939$		0			0
$940$	4.88448e8	−	8.46017e8i	0.588078	−	1.01858i
$941$	8.11774e8	+	4.68678e8i	0.974240	+	0.562478i	0.900526	−	0.434802i	$-0.143181\pi$
$941$	8.11774e8	+	4.68678e8i	0.974240	+	0.562478i	0.0737139	+	0.997279i	$0.476515\pi$
$942$		0			0
$943$	8.59323e7	+	1.48839e8i	0.102476	+	0.177493i
$944$		−	3.34663e8i		−	0.397824i
$945$		0			0
$946$	−1.22995e6			−0.00145283
$947$	−1.29692e9	+	7.48778e8i	−1.52709	+	0.881664i	−0.527605	+	0.849490i	$0.676910\pi$
$947$	−1.29692e9	+	7.48778e8i	−1.52709	+	0.881664i	−0.999482	+	0.0321742i	$0.989757\pi$
$948$		0			0
$949$	−1.07750e9	+	1.86629e9i	−1.26072	+	2.18364i
$950$	3.39373e8	+	1.95937e8i	0.395828	+	0.228531i
$951$		0			0
$952$	−811008.	−	1.40471e6i	−0.000939971	−	0.00162808i
$953$			4.28296e7i			0.0494840i	0.999694	+	0.0247420i	$0.00787643\pi$
$953$			4.28296e7i			0.0494840i	−0.999694	+	0.0247420i	$0.992124\pi$
$954$		0			0
$955$	−8.52204e8			−0.978438
$956$	7.33182e7	−	4.23303e7i	0.0839147	−	0.0484482i
$957$		0			0
$958$	−3.04514e8	+	5.27434e8i	−0.346347	+	0.599890i
$959$	4.82095e6	+	2.78338e6i	0.00546609	+	0.00315585i
$960$		0			0
$961$	1.81593e8	+	3.14528e8i	0.204611	+	0.354396i
$962$		−	5.68350e8i		−	0.638397i
$963$		0			0
$964$	2.23866e8			0.249894
$965$	−5.14530e8	+	2.97064e8i	−0.572570	+	0.330573i
$966$		0			0
$967$	5.81610e8	−	1.00738e9i	0.643210	−	1.11407i	−0.341502	−	0.939881i	$-0.610936\pi$
$967$	5.81610e8	−	1.00738e9i	0.643210	−	1.11407i	0.984712	−	0.174191i	$-0.0557310\pi$
$968$	2.77542e8	+	1.60239e8i	0.305987	+	0.176662i
$969$		0			0
$970$	1.34921e8	+	2.33691e8i	0.147831	+	0.256051i
$971$			1.39293e9i			1.52150i	0.649045	+	0.760750i	$0.275169\pi$
$971$			1.39293e9i			1.52150i	−0.649045	+	0.760750i	$0.724831\pi$
$972$		0			0
$973$	9.14789e6			0.00993076
$974$	−2.03029e7	+	1.17219e7i	−0.0219726	+	0.0126859i
$975$		0			0
$976$	3.20338e7	−	5.54842e7i	0.0344555	−	0.0596787i
$977$	6.77194e8	+	3.90978e8i	0.726155	+	0.419246i	0.817014	−	0.576618i	$-0.195628\pi$
$977$	6.77194e8	+	3.90978e8i	0.726155	+	0.419246i	−0.0908589	+	0.995864i	$0.528961\pi$
$978$		0			0
$979$	6.56294e6	+	1.13674e7i	0.00699440	+	0.0121147i
$980$		−	6.38881e8i		−	0.678799i
$981$		0			0
$982$	6.75126e8			0.712936
$983$	7.62293e8	−	4.40110e8i	0.802530	−	0.463341i	−0.0418250	−	0.999125i	$-0.513317\pi$
$983$	7.62293e8	−	4.40110e8i	0.802530	−	0.463341i	0.844355	+	0.535784i	$0.179984\pi$
$984$		0			0
$985$	−4.11895e8	+	7.13423e8i	−0.431000	+	0.746514i
$986$	4.84223e7	+	2.79566e7i	0.0505143	+	0.0291645i
$987$		0			0
$988$	−2.48178e8	−	4.29856e8i	−0.257331	−	0.445710i
$989$			6.56629e7i			0.0678783i
$990$		0			0
$991$	−1.83915e9			−1.88971			−0.944857	−	0.327483i	$-0.893800\pi$
$991$	−1.83915e9			−1.88971			−0.944857	+	0.327483i	$0.893800\pi$
$992$	1.14869e8	−	6.63197e7i	0.117671	−	0.0679372i
$993$		0			0
$994$	−385920.	+	668433.i	−0.000392951	+	0.000680611i
$995$	−1.39764e9	−	8.06930e8i	−1.41882	−	0.819156i
$996$		0			0
$997$	−2.84964e8	−	4.93572e8i	−0.287544	−	0.498040i	0.685679	−	0.727904i	$-0.259505\pi$
$997$	−2.84964e8	−	4.93572e8i	−0.287544	−	0.498040i	−0.973223	+	0.229864i	$0.926172\pi$
$998$			6.64316e8i			0.668318i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	162.7.d.b.53.2		4
3.2	odd	2	inner	162.7.d.b.53.1		4
9.2	odd	6	inner	162.7.d.b.107.2		4
9.4	even	3		6.7.b.a.5.2	yes	2
9.5	odd	6		6.7.b.a.5.1	✓	2
9.7	even	3	inner	162.7.d.b.107.1		4
36.23	even	6		48.7.e.b.17.2		2
36.31	odd	6		48.7.e.b.17.1		2
45.4	even	6		150.7.d.a.101.1		2
45.13	odd	12		150.7.b.a.149.4		4
45.14	odd	6		150.7.d.a.101.2		2
45.22	odd	12		150.7.b.a.149.1		4
45.23	even	12		150.7.b.a.149.2		4
45.32	even	12		150.7.b.a.149.3		4
63.13	odd	6		294.7.b.a.197.2		2
63.41	even	6		294.7.b.a.197.1		2
72.5	odd	6		192.7.e.c.65.2		2
72.13	even	6		192.7.e.c.65.1		2
72.59	even	6		192.7.e.f.65.1		2
72.67	odd	6		192.7.e.f.65.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6.7.b.a.5.1	✓	2	9.5	odd	6
6.7.b.a.5.2	yes	2	9.4	even	3
48.7.e.b.17.1		2	36.31	odd	6
48.7.e.b.17.2		2	36.23	even	6
150.7.b.a.149.1		4	45.22	odd	12
150.7.b.a.149.2		4	45.23	even	12
150.7.b.a.149.3		4	45.32	even	12
150.7.b.a.149.4		4	45.13	odd	12
150.7.d.a.101.1		2	45.4	even	6
150.7.d.a.101.2		2	45.14	odd	6
162.7.d.b.53.1		4	3.2	odd	2	inner
162.7.d.b.53.2		4	1.1	even	1	trivial
162.7.d.b.107.1		4	9.7	even	3	inner
162.7.d.b.107.2		4	9.2	odd	6	inner
192.7.e.c.65.1		2	72.13	even	6
192.7.e.c.65.2		2	72.5	odd	6
192.7.e.f.65.1		2	72.59	even	6
192.7.e.f.65.2		2	72.67	odd	6
294.7.b.a.197.1		2	63.41	even	6
294.7.b.a.197.2		2	63.13	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 162 = 2 \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	162.d (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(4.89898 - 2.82843i) q^{2} +(16.0000 - 27.7128i) q^{4} +(146.969 + 84.8528i) q^{5} +(-1.00000 - 1.73205i) q^{7} -181.019i q^{8} +O(q^{10})\)	\(q+(4.89898 - 2.82843i) q^{2} +(16.0000 - 27.7128i) q^{4} +(146.969 + 84.8528i) q^{5} +(-1.00000 - 1.73205i) q^{7} -181.019i q^{8} +960.000 q^{10} +(-29.3939 + 16.9706i) q^{11} +(1475.00 - 2554.77i) q^{13} +(-9.79796 - 5.65685i) q^{14} +(-512.000 - 886.810i) q^{16} +4480.23i q^{17} +5258.00 q^{19} +(4703.02 - 2715.29i) q^{20} +(-96.0000 + 166.277i) q^{22} +(8876.95 + 5125.11i) q^{23} +(6587.50 + 11409.9i) q^{25} -16687.7i q^{26} -64.0000 q^{28} +(1910.60 - 1103.09i) q^{29} +(-11449.0 + 19830.2i) q^{31} +(-5016.55 - 2896.31i) q^{32} +(12672.0 + 21948.5i) q^{34} -339.411i q^{35} +34058.0 q^{37} +(25758.8 - 14871.9i) q^{38} +(15360.0 - 26604.3i) q^{40} +(14520.6 + 8383.46i) q^{41} +(3203.00 + 5547.76i) q^{43} +1086.12i q^{44} +57984.0 q^{46} +(155788. - 89944.0i) q^{47} +(58822.5 - 101884. i) q^{49} +(64544.1 + 37264.5i) q^{50} +(-47200.0 - 81752.8i) q^{52} -192548. i q^{53} -5760.00 q^{55} +(-313.535 + 181.019i) q^{56} +(6240.00 - 10808.0i) q^{58} +(283034. + 163410. i) q^{59} +(31283.0 + 54183.7i) q^{61} +129531. i q^{62} -32768.0 q^{64} +(433560. - 250316. i) q^{65} +(-219349. + 379924. i) q^{67} +(124160. + 71683.7i) q^{68} +(-960.000 - 1662.77i) q^{70} -68221.7i q^{71} -730510. q^{73} +(166849. - 96330.6i) q^{74} +(84128.0 - 145714. i) q^{76} +(58.7878 + 33.9411i) q^{77} +(-170281. - 294935. i) q^{79} -173779. i q^{80} +94848.0 q^{82} +(429768. - 248127. i) q^{83} +(-380160. + 658456. i) q^{85} +(31382.9 + 18118.9i) q^{86} +(3072.00 + 5320.86i) q^{88} -386725. i q^{89} -5900.00 q^{91} +(284062. - 164004. i) q^{92} +(508800. - 881267. i) q^{94} +(772765. + 446156. i) q^{95} +(140543. + 243428. i) q^{97} -665501. i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 64 q^{4} - 4 q^{7}+O(q^{10}) \) 4 * q + 64 * q^4 - 4 * q^7	\( 4 q + 64 q^{4} - 4 q^{7} + 3840 q^{10} + 5900 q^{13} - 2048 q^{16} + 21032 q^{19} - 384 q^{22} + 26350 q^{25} - 256 q^{28} - 45796 q^{31} + 50688 q^{34} + 136232 q^{37} + 61440 q^{40} + 12812 q^{43} + 231936 q^{46} + 235290 q^{49} - 188800 q^{52} - 23040 q^{55} + 24960 q^{58} + 125132 q^{61} - 131072 q^{64} - 877396 q^{67} - 3840 q^{70} - 2922040 q^{73} + 336512 q^{76} - 681124 q^{79} + 379392 q^{82} - 1520640 q^{85} + 12288 q^{88} - 23600 q^{91} + 2035200 q^{94} + 562172 q^{97}+O(q^{100}) \) 4 * q + 64 * q^4 - 4 * q^7 + 3840 * q^10 + 5900 * q^13 - 2048 * q^16 + 21032 * q^19 - 384 * q^22 + 26350 * q^25 - 256 * q^28 - 45796 * q^31 + 50688 * q^34 + 136232 * q^37 + 61440 * q^40 + 12812 * q^43 + 231936 * q^46 + 235290 * q^49 - 188800 * q^52 - 23040 * q^55 + 24960 * q^58 + 125132 * q^61 - 131072 * q^64 - 877396 * q^67 - 3840 * q^70 - 2922040 * q^73 + 336512 * q^76 - 681124 * q^79 + 379392 * q^82 - 1520640 * q^85 + 12288 * q^88 - 23600 * q^91 + 2035200 * q^94 + 562172 * q^97

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