LMFDB - Embedded newform 63.7.m.c.19.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [63,7,Mod(10,63)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(63, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("63.10");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 63 = 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	63.m (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$14.4934072681$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + 212x^{6} - 787x^{5} + 38792x^{4} - 92833x^{3} + 1563109x^{2} + 3107772x + 38787984 $ x^8 - x^7 + 212x^6 - 787x^5 + 38792x^4 - 92833x^3 + 1563109x^2 + 3107772x + 38787984
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3\cdot 7^{2} $
Twist minimal:	no (minimal twist has level 21)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			19.1
Root			$-7.08935 + 12.2791i$ of defining polynomial
Character	$\chi$	$=$	63.19
Dual form			63.7.m.c.10.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-6.58935 + 11.4131i) q^{2} +(-54.8390 - 94.9839i) q^{4} +(68.9069 + 39.7834i) q^{5} +(284.244 + 191.975i) q^{7} +601.976 q^{8} +O(q^{10})$	\(q+(-6.58935 + 11.4131i) q^{2} +(-54.8390 - 94.9839i) q^{4} +(68.9069 + 39.7834i) q^{5} +(284.244 + 191.975i) q^{7} +601.976 q^{8} +(-908.103 + 524.293i) q^{10} +(411.119 + 712.080i) q^{11} +2429.15i q^{13} +(-4064.01 + 1979.11i) q^{14} +(-456.932 + 791.429i) q^{16} +(-6751.11 + 3897.76i) q^{17} +(5786.98 + 3341.12i) q^{19} -8726.73i q^{20} -10836.0 q^{22} +(9416.30 - 16309.5i) q^{23} +(-4647.06 - 8048.94i) q^{25} +(-27724.0 - 16006.5i) q^{26} +(2646.85 - 37526.3i) q^{28} -13888.2 q^{29} +(-24131.1 + 13932.1i) q^{31} +(13241.5 + 22934.9i) q^{32} -102735. i q^{34} +(11949.0 + 24536.6i) q^{35} +(-39837.6 + 69000.8i) q^{37} +(-76264.9 + 44031.5i) q^{38} +(41480.3 + 23948.6i) q^{40} -59196.1i q^{41} -91825.9 q^{43} +(45090.7 - 78099.4i) q^{44} +(124095. + 214938. i) q^{46} +(4347.44 + 2509.99i) q^{47} +(43940.4 + 109135. i) q^{49} +122484. q^{50} +(230730. - 133212. i) q^{52} +(93194.8 + 161418. i) q^{53} +65422.9i q^{55} +(171108. + 115564. i) q^{56} +(91514.3 - 158507. i) q^{58} +(-195032. + 112602. i) q^{59} +(-125018. - 72179.1i) q^{61} -367214. i q^{62} -407497. q^{64} +(-96639.7 + 167385. i) q^{65} +(117740. + 203932. i) q^{67} +(740448. + 427498. i) q^{68} +(-358774. - 25305.5i) q^{70} -96269.3 q^{71} +(238634. - 137775. i) q^{73} +(-525008. - 909340. i) q^{74} -732893. i q^{76} +(-19843.1 + 281329. i) q^{77} +(340667. - 590052. i) q^{79} +(-62971.5 + 36356.6i) q^{80} +(675610. + 390064. i) q^{82} +128019. i q^{83} -620264. q^{85} +(605073. - 1.04802e6i) q^{86} +(247484. + 428655. i) q^{88} +(322756. + 186343. i) q^{89} +(-466335. + 690470. i) q^{91} -2.06552e6 q^{92} +(-57293.5 + 33078.4i) q^{94} +(265842. + 460452. i) q^{95} +620049. i q^{97} +(-1.53511e6 - 217635. i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 5 q^{2} - 173 q^{4} + 42 q^{5} + 748 q^{7} + 454 q^{8}+O(q^{10}) $ 8 * q + 5 * q^2 - 173 * q^4 + 42 * q^5 + 748 * q^7 + 454 * q^8	$ 8 q + 5 q^{2} - 173 q^{4} + 42 q^{5} + 748 q^{7} + 454 q^{8} + 261 q^{10} + 1070 q^{11} - 6070 q^{14} + 3911 q^{16} - 7212 q^{17} - 24606 q^{19} - 78 q^{22} + 15224 q^{23} + 22274 q^{25} + 19044 q^{26} - 3415 q^{28} - 32524 q^{29} + 40200 q^{31} - 70203 q^{32} + 242436 q^{35} - 45670 q^{37} - 503310 q^{38} - 94941 q^{40} - 445660 q^{43} + 188829 q^{44} + 525804 q^{46} - 82884 q^{47} + 24116 q^{49} + 1218884 q^{50} + 722856 q^{52} + 13034 q^{53} - 127061 q^{56} - 159501 q^{58} - 1810362 q^{59} - 392856 q^{61} - 1410446 q^{64} + 389004 q^{65} + 384094 q^{67} + 1616346 q^{68} + 406005 q^{70} - 225688 q^{71} + 903078 q^{73} - 1185530 q^{74} + 327674 q^{77} - 559592 q^{79} - 847713 q^{80} + 347634 q^{82} + 1953576 q^{85} + 2302402 q^{86} + 304887 q^{88} + 1770036 q^{89} - 2960718 q^{91} + 113064 q^{92} - 1837620 q^{94} - 1160112 q^{95} - 5732467 q^{98}+O(q^{100}) $ 8 * q + 5 * q^2 - 173 * q^4 + 42 * q^5 + 748 * q^7 + 454 * q^8 + 261 * q^10 + 1070 * q^11 - 6070 * q^14 + 3911 * q^16 - 7212 * q^17 - 24606 * q^19 - 78 * q^22 + 15224 * q^23 + 22274 * q^25 + 19044 * q^26 - 3415 * q^28 - 32524 * q^29 + 40200 * q^31 - 70203 * q^32 + 242436 * q^35 - 45670 * q^37 - 503310 * q^38 - 94941 * q^40 - 445660 * q^43 + 188829 * q^44 + 525804 * q^46 - 82884 * q^47 + 24116 * q^49 + 1218884 * q^50 + 722856 * q^52 + 13034 * q^53 - 127061 * q^56 - 159501 * q^58 - 1810362 * q^59 - 392856 * q^61 - 1410446 * q^64 + 389004 * q^65 + 384094 * q^67 + 1616346 * q^68 + 406005 * q^70 - 225688 * q^71 + 903078 * q^73 - 1185530 * q^74 + 327674 * q^77 - 559592 * q^79 - 847713 * q^80 + 347634 * q^82 + 1953576 * q^85 + 2302402 * q^86 + 304887 * q^88 + 1770036 * q^89 - 2960718 * q^91 + 113064 * q^92 - 1837620 * q^94 - 1160112 * q^95 - 5732467 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/63\mathbb{Z}\right)^\times$.

$n$	$10$	$29$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$

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 $

$2$	−6.58935	+	11.4131i	−0.823668	+	1.42664i	0.0792645	+	0.996854i	$0.474743\pi$
$2$	−6.58935	+	11.4131i	−0.823668	+	1.42664i	−0.902933	+	0.429782i	$0.858591\pi$
$3$		0			0
$3$		0			0
$4$	−54.8390	−	94.9839i	−0.856859	−	1.48412i
$5$	68.9069	+	39.7834i	0.551255	+	0.318267i	0.749628	−	0.661859i	$-0.230232\pi$
$5$	68.9069	+	39.7834i	0.551255	+	0.318267i	−0.198373	+	0.980127i	$0.563566\pi$
$6$		0			0
$7$	284.244	+	191.975i	0.828700	+	0.559693i
$7$	284.244	+	191.975i	0.828700	+	0.559693i
$8$	601.976			1.17573
$9$		0			0
$10$	−908.103	+	524.293i	−0.908103	+	0.524293i
$11$	411.119	+	712.080i	0.308880	+	0.534996i	0.978118	−	0.208052i	$-0.0667125\pi$
$11$	411.119	+	712.080i	0.308880	+	0.534996i	−0.669238	+	0.743049i	$0.733379\pi$
$12$		0			0
$13$			2429.15i			1.10567i	0.833292	+	0.552833i	$0.186453\pi$
$13$			2429.15i			1.10567i	−0.833292	+	0.552833i	$0.813547\pi$
$14$	−4064.01	+	1979.11i	−1.48105	+	0.721251i
$15$		0			0
$16$	−456.932	+	791.429i	−0.111556	+	0.193220i
$17$	−6751.11	+	3897.76i	−1.37413	+	0.793355i	−0.991445	−	0.130523i	$-0.958334\pi$
$17$	−6751.11	+	3897.76i	−1.37413	+	0.793355i	−0.382687	+	0.923878i	$0.625001\pi$
$18$		0			0
$19$	5786.98	+	3341.12i	0.843706	+	0.487114i	0.858522	−	0.512776i	$-0.171383\pi$
$19$	5786.98	+	3341.12i	0.843706	+	0.487114i	−0.0148160	+	0.999890i	$0.504716\pi$
$20$		−	8726.73i		−	1.09084i
$21$		0			0
$22$	−10836.0			−1.01766
$23$	9416.30	−	16309.5i	0.773921	−	1.34047i	−0.161478	−	0.986876i	$-0.551626\pi$
$23$	9416.30	−	16309.5i	0.773921	−	1.34047i	0.935399	−	0.353594i	$-0.115041\pi$
$24$		0			0
$25$	−4647.06	−	8048.94i	−0.297412	−	0.515132i
$26$	−27724.0	−	16006.5i	−1.57738	−	0.910701i
$27$		0			0
$28$	2646.85	−	37526.3i	0.120575	−	1.70947i
$29$	−13888.2			−0.569446			−0.284723	−	0.958610i	$-0.591902\pi$
$29$	−13888.2			−0.569446			−0.284723	+	0.958610i	$0.591902\pi$
$30$		0			0
$31$	−24131.1	+	13932.1i	−0.810014	+	0.467662i	−0.846961	−	0.531655i	$-0.821570\pi$
$31$	−24131.1	+	13932.1i	−0.810014	+	0.467662i	0.0369467	+	0.999317i	$0.488237\pi$
$32$	13241.5	+	22934.9i	0.404097	+	0.699917i
$33$		0			0
$34$		−	102735.i		−	2.61385i
$35$	11949.0	+	24536.6i	0.278693	+	0.572282i
$36$		0			0
$37$	−39837.6	+	69000.8i	−0.786481	+	1.36223i	0.141629	+	0.989920i	$0.454766\pi$
$37$	−39837.6	+	69000.8i	−0.786481	+	1.36223i	−0.928110	+	0.372305i	$0.878567\pi$
$38$	−76264.9	+	44031.5i	−1.38987	+	0.802441i
$39$		0			0
$40$	41480.3	+	23948.6i	0.648129	+	0.374198i
$41$		−	59196.1i		−	0.858898i	−0.903091	−	0.429449i	$-0.858708\pi$
$41$		−	59196.1i		−	0.858898i	0.903091	−	0.429449i	$-0.141292\pi$
$42$		0			0
$43$	−91825.9			−1.15494			−0.577471	−	0.816411i	$-0.695960\pi$
$43$	−91825.9			−1.15494			−0.577471	+	0.816411i	$0.695960\pi$
$44$	45090.7	−	78099.4i	0.529333	−	0.916832i
$45$		0			0
$46$	124095.	+	214938.i	1.27491	+	2.20821i
$47$	4347.44	+	2509.99i	0.0418735	+	0.0241757i	0.520791	−	0.853684i	$-0.325637\pi$
$47$	4347.44	+	2509.99i	0.0418735	+	0.0241757i	−0.478917	+	0.877860i	$0.658971\pi$
$48$		0			0
$49$	43940.4	+	109135.i	0.373487	+	0.927635i
$50$	122484.			0.979875
$51$		0			0
$52$	230730.	−	133212.i	1.64094	−	0.947399i
$53$	93194.8	+	161418.i	0.625985	+	1.08424i	0.988350	+	0.152201i	$0.0486362\pi$
$53$	93194.8	+	161418.i	0.625985	+	1.08424i	−0.362365	+	0.932036i	$0.618030\pi$
$54$		0			0
$55$			65422.9i			0.393226i
$56$	171108.	+	115564.i	0.974330	+	0.658050i
$57$		0			0
$58$	91514.3	−	158507.i	0.469035	−	0.812392i
$59$	−195032.	+	112602.i	−0.949618	+	0.548262i	−0.892962	−	0.450132i	$-0.851377\pi$
$59$	−195032.	+	112602.i	−0.949618	+	0.548262i	−0.0566558	+	0.998394i	$0.518044\pi$
$60$		0			0
$61$	−125018.	−	72179.1i	−0.550786	−	0.317996i	0.198653	−	0.980070i	$-0.436343\pi$
$61$	−125018.	−	72179.1i	−0.550786	−	0.317996i	−0.749439	+	0.662074i	$0.769677\pi$
$62$		−	367214.i		−	1.54079i
$63$		0			0
$64$	−407497.			−1.55448
$65$	−96639.7	+	167385.i	−0.351897	+	0.609504i
$66$		0			0
$67$	117740.	+	203932.i	0.391471	+	0.678048i	0.992644	−	0.121071i	$-0.0386329\pi$
$67$	117740.	+	203932.i	0.391471	+	0.678048i	−0.601173	+	0.799119i	$0.705300\pi$
$68$	740448.	+	427498.i	2.35487	+	1.35959i
$69$		0			0
$70$	−358774.	−	25305.5i	−1.04599	−	0.0737770i
$71$	−96269.3			−0.268975			−0.134488	−	0.990915i	$-0.542939\pi$
$71$	−96269.3			−0.268975			−0.134488	+	0.990915i	$0.542939\pi$
$72$		0			0
$73$	238634.	−	137775.i	0.613428	−	0.354163i	−0.160878	−	0.986974i	$-0.551433\pi$
$73$	238634.	−	137775.i	0.613428	−	0.354163i	0.774306	+	0.632812i	$0.218099\pi$
$74$	−525008.	−	909340.i	−1.29560	−	2.24404i
$75$		0			0
$76$		−	732893.i		−	1.66955i
$77$	−19843.1	+	281329.i	−0.0434647	+	0.616229i
$78$		0			0
$79$	340667.	−	590052.i	0.690953	−	1.19677i	−0.280573	−	0.959833i	$-0.590524\pi$
$79$	340667.	−	590052.i	0.690953	−	1.19677i	0.971526	−	0.236933i	$-0.0761423\pi$
$80$	−62971.5	+	36356.6i	−0.122991	+	0.0710090i
$81$		0			0
$82$	675610.	+	390064.i	1.22533	+	0.707447i
$83$			128019.i			0.223893i	0.993714	+	0.111946i	$0.0357085\pi$
$83$			128019.i			0.223893i	−0.993714	+	0.111946i	$0.964291\pi$
$84$		0			0
$85$	−620264.			−1.01000
$86$	605073.	−	1.04802e6i	0.951288	−	1.64768i
$87$		0			0
$88$	247484.	+	428655.i	0.363161	+	0.629013i
$89$	322756.	+	186343.i	0.457829	+	0.264328i	0.711131	−	0.703059i	$-0.248183\pi$
$89$	322756.	+	186343.i	0.457829	+	0.264328i	−0.253302	+	0.967387i	$0.581517\pi$
$90$		0			0
$91$	−466335.	+	690470.i	−0.618833	+	0.916265i
$92$	−2.06552e6			−2.65257
$93$		0			0
$94$	−57293.5	+	33078.4i	−0.0689798	+	0.0398255i
$95$	265842.	+	460452.i	0.310065	+	0.537048i
$96$		0			0
$97$			620049.i			0.679377i	0.940538	+	0.339688i	$0.110322\pi$
$97$			620049.i			0.679377i	−0.940538	+	0.339688i	$0.889678\pi$
$98$	−1.53511e6	−	217635.i	−1.63103	−	0.231234i
$99$		0			0
$100$	−509680.	+	882792.i	−0.509680	+	0.882792i
$101$	578698.	−	334111.i	0.561678	−	0.324285i	−0.192141	−	0.981367i	$-0.561543\pi$
$101$	578698.	−	334111.i	0.561678	−	0.324285i	0.753819	+	0.657082i	$0.228210\pi$
$102$		0			0
$103$	1.34180e6	+	774691.i	1.22794	+	0.708952i	0.966599	−	0.256294i	$-0.0825016\pi$
$103$	1.34180e6	+	774691.i	1.22794	+	0.708952i	0.261342	+	0.965246i	$0.415835\pi$
$104$			1.46229e6i			1.29997i
$105$		0			0
$106$	−2.45637e6			−2.06242
$107$	−477948.	+	827829.i	−0.390148	+	0.675755i	−0.992469	−	0.122498i	$-0.960909\pi$
$107$	−477948.	+	827829.i	−0.390148	+	0.675755i	0.602321	+	0.798254i	$0.294243\pi$
$108$		0			0
$109$	−785863.	−	1.36115e6i	−0.606830	−	1.05106i	−0.991759	−	0.128115i	$-0.959107\pi$
$109$	−785863.	−	1.36115e6i	−0.606830	−	1.05106i	0.384929	−	0.922946i	$-0.374226\pi$
$110$	−746677.	−	431094.i	−0.560990	−	0.323888i
$111$		0			0
$112$	−281814.	+	137240.i	−0.200590	+	0.0976845i
$113$	2.47576e6			1.71582			0.857912	−	0.513797i	$-0.171762\pi$
$113$	2.47576e6			1.71582			0.857912	+	0.513797i	$0.171762\pi$
$114$		0			0
$115$	1.29770e6	−	749225.i	0.853256	−	0.492628i
$116$	761615.	+	1.31916e6i	0.487935	+	0.845128i
$117$		0			0
$118$		−	2.96788e6i		−	1.80634i
$119$	−2.66723e6	−	188129.i	−1.58278	−	0.111639i
$120$		0			0
$121$	547742.	−	948717.i	0.309186	−	0.535526i
$122$	1.64757e6	−	951226.i	0.907329	−	0.523847i
$123$		0			0
$124$	2.64665e6	+	1.52805e6i	1.38814	+	0.801441i
$125$		−	1.98274e6i		−	1.01516i
$126$		0			0
$127$	292592.			0.142840			0.0714202	−	0.997446i	$-0.477247\pi$
$127$	292592.			0.142840			0.0714202	+	0.997446i	$0.477247\pi$
$128$	1.83769e6	−	3.18297e6i	0.876278	−	1.51776i
$129$		0			0
$130$	−1.27359e6	−	2.20591e6i	−0.579693	−	1.00406i
$131$	2.36324e6	+	1.36442e6i	1.05122	+	0.606924i	0.922991	−	0.384820i	$-0.125737\pi$
$131$	2.36324e6	+	1.36442e6i	1.05122	+	0.606924i	0.128231	+	0.991744i	$0.459070\pi$
$132$		0			0
$133$	1.00351e6	+	2.06065e6i	0.426545	+	0.875888i
$134$	−3.10332e6			−1.28977
$135$		0			0
$136$	−4.06400e6	+	2.34635e6i	−1.61561	+	0.932775i
$137$	−453922.	−	786216.i	−0.176530	−	0.305760i	0.764159	−	0.645027i	$-0.223154\pi$
$137$	−453922.	−	786216.i	−0.176530	−	0.305760i	−0.940690	+	0.339268i	$0.889821\pi$
$138$		0			0
$139$		−	4640.07i		−	0.00172775i	−1.00000		0.000863874i	$-0.999725\pi$
$139$		−	4640.07i		−	0.00172775i	1.00000		0.000863874i	$-0.000274980\pi$
$140$	1.67531e6	−	2.48052e6i	0.610536	−	0.903980i
$141$		0			0
$142$	634352.	−	1.09873e6i	0.221547	−	0.383730i
$143$	−1.72975e6	+	998669.i	−0.591526	+	0.341518i
$144$		0			0
$145$	−956994.	−	552521.i	−0.313910	−	0.181236i
$146$			3.63140e6i			1.16685i
$147$		0			0
$148$	8.73862e6			2.69561
$149$	−823601.	+	1.42652e6i	−0.248976	+	0.431240i	−0.963242	−	0.268635i	$-0.913427\pi$
$149$	−823601.	+	1.42652e6i	−0.248976	+	0.431240i	0.714266	+	0.699875i	$0.246761\pi$
$150$		0			0
$151$	1.22295e6	+	2.11820e6i	0.355203	+	0.615229i	0.987153	−	0.159780i	$-0.0510785\pi$
$151$	1.22295e6	+	2.11820e6i	0.355203	+	0.615229i	−0.631950	+	0.775009i	$0.717745\pi$
$152$	3.48362e6	+	2.01127e6i	0.991974	+	0.572716i
$153$		0			0
$154$	−3.08008e6	−	2.08024e6i	−0.843334	−	0.569577i
$155$	−2.21707e6			−0.595366
$156$		0			0
$157$	−2.43822e6	+	1.40771e6i	−0.630049	+	0.363759i	−0.780771	−	0.624817i	$-0.785174\pi$
$157$	−2.43822e6	+	1.40771e6i	−0.630049	+	0.363759i	0.150722	+	0.988576i	$0.451840\pi$
$158$	4.48954e6	+	7.77612e6i	1.13823	+	1.97148i
$159$		0			0
$160$			2.10716e6i			0.514444i
$161$	5.80754e6	−	2.82819e6i	1.39160	−	0.677690i
$162$		0			0
$163$	781407.	−	1.35344e6i	0.180432	−	0.312518i	−0.761596	−	0.648053i	$-0.775584\pi$
$163$	781407.	−	1.35344e6i	0.180432	−	0.312518i	0.942028	+	0.335535i	$0.108917\pi$
$164$	−5.62268e6	+	3.24625e6i	−1.27471	+	0.735955i
$165$		0			0
$166$	−1.46109e6	−	843562.i	−0.319414	−	0.184414i
$167$		−	1.15538e6i		−	0.248070i	−0.992278	−	0.124035i	$-0.960416\pi$
$167$		−	1.15538e6i		−	0.248070i	0.992278	−	0.124035i	$-0.0395835\pi$
$168$		0			0
$169$	−1.07394e6			−0.222495
$170$	4.08713e6	−	7.07913e6i	0.831902	−	1.44090i
$171$		0			0
$172$	5.03564e6	+	8.72198e6i	0.989622	+	1.71408i
$173$	4.98920e6	+	2.88052e6i	0.963591	+	0.556330i	0.897277	−	0.441469i	$-0.145542\pi$
$173$	4.98920e6	+	2.88052e6i	0.963591	+	0.556330i	0.0663149	+	0.997799i	$0.478876\pi$
$174$		0			0
$175$	224295.	−	3.17998e6i	0.0418509	−	0.593350i
$176$	−751414.			−0.137829
$177$		0			0
$178$	−4.25350e6	+	2.45576e6i	−0.754199	+	0.435437i
$179$	−597801.	−	1.03542e6i	−0.104231	−	0.180534i	0.809193	−	0.587543i	$-0.199905\pi$
$179$	−597801.	−	1.03542e6i	−0.104231	−	0.180534i	−0.913424	+	0.407010i	$0.866571\pi$
$180$		0			0
$181$			1.00030e7i			1.68692i	0.537191	+	0.843461i	$0.319486\pi$
$181$			1.00030e7i			1.68692i	−0.537191	+	0.843461i	$0.680514\pi$
$182$	−4.80756e6	−	9.87207e6i	−0.797462	−	1.63755i
$183$		0			0
$184$	5.66838e6	−	9.81793e6i	0.909925	−	1.57604i
$185$	−5.49017e6	+	3.16975e6i	−0.867104	+	0.500622i
$186$		0			0
$187$	−5.55102e6	−	3.20489e6i	−0.848884	−	0.490103i
$188$		−	550582.i		−	0.0828606i
$189$		0			0
$190$	−7.00690e6			−1.02156
$191$	−3.79135e6	+	6.56682e6i	−0.544120	+	0.942443i	0.454542	+	0.890725i	$0.349803\pi$
$191$	−3.79135e6	+	6.56682e6i	−0.544120	+	0.942443i	−0.998662	+	0.0517175i	$0.983530\pi$
$192$		0			0
$193$	−3.54806e6	−	6.14542e6i	−0.493537	−	0.854830i	0.506436	−	0.862278i	$-0.330963\pi$
$193$	−3.54806e6	−	6.14542e6i	−0.493537	−	0.854830i	−0.999972	+	0.00744730i	$0.997629\pi$
$194$	−7.07667e6	−	4.08572e6i	−0.969223	−	0.559581i
$195$		0			0
$196$	7.95645e6	−	1.01585e7i	1.05670	−	1.34915i
$197$	−2.00096e6			−0.261722			−0.130861	−	0.991401i	$-0.541774\pi$
$197$	−2.00096e6			−0.261722			−0.130861	+	0.991401i	$0.541774\pi$
$198$		0			0
$199$	−3.76381e6	+	2.17304e6i	−0.477605	+	0.275745i	−0.719418	−	0.694578i	$-0.755591\pi$
$199$	−3.76381e6	+	2.17304e6i	−0.477605	+	0.275745i	0.241813	+	0.970323i	$0.422258\pi$
$200$	−2.79742e6	−	4.84527e6i	−0.349677	−	0.605658i
$201$		0			0
$202$			8.80630e6i			1.06841i
$203$	−3.94764e6	−	2.66619e6i	−0.471900	−	0.318715i
$204$		0			0
$205$	2.35502e6	−	4.07902e6i	0.273359	−	0.473472i
$206$	−1.76832e7	+	1.02094e7i	−2.02283	+	1.16788i
$207$		0			0
$208$	−1.92250e6	−	1.10995e6i	−0.213637	−	0.123343i
$209$			5.49439e6i			0.601839i
$210$		0			0
$211$	1.03642e7			1.10328			0.551641	−	0.834082i	$-0.314002\pi$
$211$	1.03642e7			1.10328			0.551641	+	0.834082i	$0.314002\pi$
$212$	1.02214e7	−	1.77040e7i	1.07276	−	1.85808i
$213$		0			0
$214$	−6.29872e6	−	1.09097e7i	−0.642704	−	1.11320i
$215$	−6.32744e6	−	3.65315e6i	−0.636667	−	0.367580i
$216$		0			0
$217$	−9.53375e6	−	672446.i	−0.933006	−	0.0658079i
$218$	2.07133e7			1.99931
$219$		0			0
$220$	6.21413e6	−	3.58773e6i	0.583596	−	0.336939i
$221$	−9.46822e6	−	1.63994e7i	−0.877185	−	1.51933i
$222$		0			0
$223$		−	4.84791e6i		−	0.437159i	−0.975819	−	0.218580i	$-0.929858\pi$
$223$		−	4.84791e6i		−	0.437159i	0.975819	−	0.218580i	$-0.0701424\pi$
$224$	−639111.	+	9.06113e6i	−0.0568633	+	0.806192i
$225$		0			0
$226$	−1.63136e7	+	2.82560e7i	−1.41327	+	2.44785i
$227$	1.30838e7	−	7.55396e6i	1.11856	−	0.645798i	0.177524	−	0.984117i	$-0.443191\pi$
$227$	1.30838e7	−	7.55396e6i	1.11856	−	0.645798i	0.941032	+	0.338318i	$0.109858\pi$
$228$		0			0
$229$	−3.68382e6	−	2.12685e6i	−0.306755	−	0.177105i	0.338718	−	0.940888i	$-0.390007\pi$
$229$	−3.68382e6	−	2.12685e6i	−0.306755	−	0.177105i	−0.645474	+	0.763783i	$0.723340\pi$
$230$			1.97476e7i			1.62305i
$231$		0			0
$232$	−8.36037e6			−0.669517
$233$	6.29087e6	−	1.08961e7i	0.497328	−	0.861397i	−0.502667	−	0.864480i	$-0.667648\pi$
$233$	6.29087e6	−	1.08961e7i	0.497328	−	0.861397i	0.999995	+	0.00308269i	$0.000981254\pi$
$234$		0			0
$235$	199712.	+	345912.i	0.0153887	+	0.0266540i
$236$	2.13907e7	+	1.23499e7i	1.62738	+	0.939567i
$237$		0			0
$238$	1.97225e7	−	2.92017e7i	1.46295	−	2.16609i
$239$	−7.54342e6			−0.552554			−0.276277	−	0.961078i	$-0.589101\pi$
$239$	−7.54342e6			−0.552554			−0.276277	+	0.961078i	$0.589101\pi$
$240$		0			0
$241$	1.69553e7	−	9.78914e6i	1.21131	−	0.699348i	0.248262	−	0.968693i	$-0.420140\pi$
$241$	1.69553e7	−	9.78914e6i	1.21131	−	0.699348i	0.963044	+	0.269345i	$0.0868071\pi$
$242$	7.21853e6	+	1.25029e7i	0.509334	+	0.882192i
$243$		0			0
$244$			1.58329e7i			1.08991i
$245$	−1.31398e6	+	9.26828e6i	−0.0893492	+	0.630233i
$246$		0			0
$247$	−8.11606e6	+	1.40574e7i	−0.538585	+	0.932857i
$248$	−1.45264e7	+	8.38679e6i	−0.952361	+	0.549846i
$249$		0			0
$250$	2.26291e7	+	1.30649e7i	1.44826	+	0.836156i
$251$			1.39590e7i			0.882743i	0.897324	+	0.441372i	$0.145508\pi$
$251$			1.39590e7i			0.882743i	−0.897324	+	0.441372i	$0.854492\pi$
$252$		0			0
$253$	1.54849e7			0.956195
$254$	−1.92799e6	+	3.33938e6i	−0.117653	+	0.203781i
$255$		0			0
$256$	1.11784e7	+	1.93616e7i	0.666285	+	1.15404i
$257$	567649.	+	327732.i	0.0334411	+	0.0193072i	0.516627	−	0.856210i	$-0.327187\pi$
$257$	567649.	+	327732.i	0.0334411	+	0.0193072i	−0.483186	+	0.875518i	$0.660521\pi$
$258$		0			0
$259$	−2.45700e7	+	1.19652e7i	−1.41418	+	0.688688i
$260$	2.11985e7			1.20610
$261$		0			0
$262$	−3.11445e7	+	1.79813e7i	−1.73172	+	0.999808i
$263$	−7.46998e6	−	1.29384e7i	−0.410632	−	0.711235i	0.584327	−	0.811518i	$-0.301358\pi$
$263$	−7.46998e6	−	1.29384e7i	−0.410632	−	0.711235i	−0.994959	+	0.100283i	$0.968025\pi$
$264$		0			0
$265$			1.48304e7i			0.796922i
$266$	−3.01308e7	−	2.12522e6i	−1.60090	−	0.112917i
$267$		0			0
$268$	1.29135e7	−	2.23668e7i	0.670871	−	1.16198i
$269$	2.72017e7	−	1.57049e7i	1.39746	−	0.806825i	0.403335	−	0.915052i	$-0.367851\pi$
$269$	2.72017e7	−	1.57049e7i	1.39746	−	0.806825i	0.994126	+	0.108227i	$0.0345174\pi$
$270$		0			0
$271$	−1.29500e6	−	747670.i	−0.0650673	−	0.0375666i	0.467113	−	0.884197i	$-0.345294\pi$
$271$	−1.29500e6	−	747670.i	−0.0650673	−	0.0375666i	−0.532181	+	0.846631i	$0.678627\pi$
$272$		−	7.12403e6i		−	0.354013i
$273$		0			0
$274$	1.19642e7			0.581610
$275$	3.82099e6	−	6.61815e6i	0.183729	−	0.318228i
$276$		0			0
$277$	991747.	+	1.71776e6i	0.0466618	+	0.0808207i	0.888413	−	0.459045i	$-0.151808\pi$
$277$	991747.	+	1.71776e6i	0.0466618	+	0.0808207i	−0.841751	+	0.539866i	$0.818475\pi$
$278$	52957.5	+	30575.1i	0.00246487	+	0.00142309i
$279$		0			0
$280$	7.19299e6	+	1.47704e7i	0.327669	+	0.672851i
$281$	3.50353e6			0.157902			0.0789508	−	0.996879i	$-0.474843\pi$
$281$	3.50353e6			0.157902			0.0789508	+	0.996879i	$0.474843\pi$
$282$		0			0
$283$	2.82715e7	−	1.63226e7i	1.24736	−	0.720161i	0.276774	−	0.960935i	$-0.410735\pi$
$283$	2.82715e7	−	1.63226e7i	1.24736	−	0.720161i	0.970581	+	0.240774i	$0.0774012\pi$
$284$	5.27931e6	+	9.14403e6i	0.230474	+	0.399193i
$285$		0			0
$286$		−	2.63223e7i		−	1.12519i
$287$	1.13642e7	−	1.68261e7i	0.480719	−	0.711769i
$288$		0			0
$289$	1.83162e7	−	3.17246e7i	0.758826	−	1.31432i
$290$	1.26119e7	−	7.28150e6i	0.517115	−	0.298557i
$291$		0			0
$292$	−2.61729e7	−	1.51109e7i	−1.05124	−	0.606935i
$293$		−	2.57653e7i		−	1.02431i	−0.858892	−	0.512156i	$-0.828847\pi$
$293$		−	2.57653e7i		−	1.02431i	0.858892	−	0.512156i	$-0.171153\pi$
$294$		0			0
$295$	−1.79187e7			−0.697976
$296$	−2.39813e7	+	4.15368e7i	−0.924692	+	1.60161i
$297$		0			0
$298$	−1.08540e7	−	1.87996e7i	−0.410148	−	0.710397i
$299$	3.96182e7	+	2.28736e7i	1.48211	+	0.855698i
$300$		0			0
$301$	−2.61010e7	−	1.76283e7i	−0.957100	−	0.646413i
$302$	−3.22336e7			−1.17028
$303$		0			0
$304$	−5.28851e6	+	3.05332e6i	−0.188240	+	0.108681i
$305$	−5.74306e6	−	9.94727e6i	−0.202416	−	0.350594i
$306$		0			0
$307$		−	1.89894e7i		−	0.656289i	−0.944628	−	0.328145i	$-0.893577\pi$
$307$		−	1.89894e7i		−	0.656289i	0.944628	−	0.328145i	$-0.106423\pi$
$308$	2.78099e7	−	1.35430e7i	0.951803	−	0.463515i
$309$		0			0
$310$	1.46090e7	−	2.53036e7i	0.490384	−	0.849370i
$311$	−2.80365e7	+	1.61869e7i	−0.932057	+	0.538124i	−0.887462	−	0.460881i	$-0.847533\pi$
$311$	−2.80365e7	+	1.61869e7i	−0.932057	+	0.538124i	−0.0445958	+	0.999005i	$0.514200\pi$
$312$		0			0
$313$	2.81397e7	+	1.62465e7i	0.917671	+	0.529818i	0.882891	−	0.469577i	$-0.155594\pi$
$313$	2.81397e7	+	1.62465e7i	0.917671	+	0.529818i	0.0347798	+	0.999395i	$0.488927\pi$
$314$		−	3.71035e7i		−	1.19847i
$315$		0			0
$316$	−7.47273e7			−2.36820
$317$	−8.17142e6	+	1.41533e7i	−0.256519	+	0.444304i	−0.965307	−	0.261118i	$-0.915909\pi$
$317$	−8.17142e6	+	1.41533e7i	−0.256519	+	0.444304i	0.708788	+	0.705422i	$0.249242\pi$
$318$		0			0
$319$	−5.70972e6	−	9.88952e6i	−0.175891	−	0.304651i
$320$	−2.80794e7	−	1.62116e7i	−0.856915	−	0.494740i
$321$		0			0
$322$	−5.98953e6	+	8.49179e7i	−0.179401	+	2.54350i
$323$	−5.20914e7			−1.54582
$324$		0			0
$325$	1.95521e7	−	1.12884e7i	0.569564	−	0.328838i
$326$	1.02979e7	+	1.78365e7i	0.297233	+	0.514822i
$327$		0			0
$328$		−	3.56346e7i		−	1.00984i
$329$	753878.	+	1.54805e6i	0.0211696	+	0.0434707i
$330$		0			0
$331$	−2.58785e7	+	4.48229e7i	−0.713601	+	1.23599i	0.249896	+	0.968273i	$0.419604\pi$
$331$	−2.58785e7	+	4.48229e7i	−0.713601	+	1.23599i	−0.963497	+	0.267720i	$0.913730\pi$
$332$	1.21598e7	−	7.02044e6i	0.332285	−	0.191845i
$333$		0			0
$334$	1.31864e7	+	7.61318e6i	0.353905	+	0.204327i
$335$			1.87364e7i			0.498370i
$336$		0			0
$337$	6.13986e7			1.60424			0.802119	−	0.597164i	$-0.203706\pi$
$337$	6.13986e7			1.60424			0.802119	+	0.597164i	$0.203706\pi$
$338$	7.07658e6	−	1.22570e7i	0.183262	−	0.317420i
$339$		0			0
$340$	3.40146e7	+	5.89151e7i	0.865424	+	1.49896i
$341$	−1.98416e7	−	1.14555e7i	−0.500395	−	0.288903i
$342$		0			0
$343$	−8.46143e6	+	3.94565e7i	−0.209682	+	0.977770i
$344$	−5.52770e7			−1.35790
$345$		0			0
$346$	−6.57512e7	+	3.79615e7i	−1.58736	+	0.916462i
$347$	1.77833e7	+	3.08017e7i	0.425623	+	0.737200i	0.996478	−	0.0838501i	$-0.0267217\pi$
$347$	1.77833e7	+	3.08017e7i	0.425623	+	0.737200i	−0.570855	+	0.821051i	$0.693388\pi$
$348$		0			0
$349$		−	5.17156e7i		−	1.21659i	−0.793710	−	0.608297i	$-0.791853\pi$
$349$		−	5.17156e7i		−	1.21659i	0.793710	−	0.608297i	$-0.208147\pi$
$350$	3.48154e7	+	2.35139e7i	0.812022	+	0.548429i
$351$		0			0
$352$	−1.08876e7	+	1.88579e7i	−0.249635	+	0.432381i
$353$	669058.	−	386281.i	0.0152104	−	0.00878171i	−0.492376	−	0.870383i	$-0.663871\pi$
$353$	669058.	−	386281.i	0.0152104	−	0.00878171i	0.507586	+	0.861601i	$0.330538\pi$
$354$		0			0
$355$	−6.63362e6	−	3.82992e6i	−0.148274	−	0.0856061i
$356$		−	4.08754e7i		−	0.905967i
$357$		0			0
$358$	1.57565e7			0.343407
$359$	−2.08340e7	+	3.60856e7i	−0.450287	+	0.779920i	−0.998404	−	0.0564819i	$-0.982012\pi$
$359$	−2.08340e7	+	3.60856e7i	−0.450287	+	0.779920i	0.548117	+	0.836402i	$0.315345\pi$
$360$		0			0
$361$	−1.19684e6	−	2.07298e6i	−0.0254398	−	0.0440630i
$362$	−1.14165e8	−	6.59133e7i	−2.40662	−	1.38946i
$363$		0			0
$364$	9.11569e7	+	6.42959e6i	1.89010	+	0.133315i
$365$	2.19247e7			0.450874
$366$		0			0
$367$	5.71734e6	−	3.30091e6i	0.115663	−	0.0667783i	−0.441052	−	0.897481i	$-0.645395\pi$
$367$	5.71734e6	−	3.30091e6i	0.115663	−	0.0667783i	0.556716	+	0.830703i	$0.312061\pi$
$368$	8.60521e6	+	1.49047e7i	0.172670	+	0.299074i
$369$		0			0
$370$		−	8.35464e7i		−	1.64939i
$371$	−4.49813e6	+	6.37732e7i	−0.0880867	+	1.24887i
$372$		0			0
$373$	2.47581e6	−	4.28823e6i	0.0477080	−	0.0826326i	−0.841185	−	0.540747i	$-0.818142\pi$
$373$	2.47581e6	−	4.28823e6i	0.0477080	−	0.0826326i	0.888893	+	0.458114i	$0.151475\pi$
$374$	7.31553e7	−	4.22362e7i	1.39840	−	0.807365i
$375$		0			0
$376$	2.61705e6	+	1.51095e6i	0.0492321	+	0.0284242i
$377$		−	3.37365e7i		−	0.629616i
$378$		0			0
$379$	−1.05876e8			−1.94482			−0.972409	−	0.233282i	$-0.925053\pi$
$379$	−1.05876e8			−1.94482			−0.972409	+	0.233282i	$0.925053\pi$
$380$	2.91570e7	−	5.05014e7i	0.531364	−	0.920349i
$381$		0			0
$382$	−4.99651e7	−	8.65421e7i	−0.896348	−	1.55252i
$383$	4.26092e7	+	2.46004e7i	0.758414	+	0.437871i	0.828726	−	0.559654i	$-0.189066\pi$
$383$	4.26092e7	+	2.46004e7i	0.758414	+	0.437871i	−0.0703117	+	0.997525i	$0.522399\pi$
$384$		0			0
$385$	−1.25596e7	+	1.85961e7i	−0.220086	+	0.325866i
$386$	9.35177e7			1.62604
$387$		0			0
$388$	5.88947e7	−	3.40028e7i	1.00828	−	0.582130i
$389$	3.33099e7	+	5.76945e7i	0.565880	+	0.980134i	0.996967	+	0.0778231i	$0.0247969\pi$
$389$	3.33099e7	+	5.76945e7i	0.565880	+	0.980134i	−0.431087	+	0.902310i	$0.641870\pi$
$390$		0			0
$391$			1.46810e8i			2.45598i
$392$	2.64511e7	+	6.56968e7i	0.439122	+	1.09065i
$393$		0			0
$394$	1.31850e7	−	2.28372e7i	0.215572	−	0.373382i
$395$	4.69486e7	−	2.71058e7i	0.761783	−	0.439816i
$396$		0			0
$397$	4.16040e7	+	2.40201e7i	0.664911	+	0.383887i	0.794146	−	0.607727i	$-0.207919\pi$
$397$	4.16040e7	+	2.40201e7i	0.664911	+	0.383887i	−0.129234	+	0.991614i	$0.541252\pi$
$398$		−	5.72756e7i		−	0.908491i
$399$		0			0
$400$	8.49355e6			0.132712
$401$	6.97156e6	−	1.20751e7i	0.108118	−	0.187265i	−0.806890	−	0.590702i	$-0.798851\pi$
$401$	6.97156e6	−	1.20751e7i	0.108118	−	0.187265i	0.915008	+	0.403436i	$0.132184\pi$
$402$		0			0
$403$	−3.38431e7	−	5.86180e7i	−0.517077	−	0.895604i
$404$	−6.34704e7	−	3.66446e7i	−0.962558	−	0.555733i
$405$		0			0
$406$	5.64418e7	−	2.74864e7i	0.843379	−	0.410714i
$407$	−6.55121e7			−0.971713
$408$		0			0
$409$	1.93849e7	−	1.11919e7i	0.283331	−	0.163581i	−0.351599	−	0.936151i	$-0.614362\pi$
$409$	1.93849e7	−	1.11919e7i	0.283331	−	0.163581i	0.634931	+	0.772569i	$0.281029\pi$
$410$	3.10361e7	+	5.37562e7i	0.450315	+	0.779968i
$411$		0			0
$412$		−	1.69933e8i		−	2.42989i
$413$	−7.70532e7	−	5.43482e6i	−1.09381	−	0.0771498i
$414$		0			0
$415$	−5.09304e6	+	8.82140e6i	−0.0712578	+	0.123422i
$416$	−5.57122e7	+	3.21654e7i	−0.773874	+	0.446796i
$417$		0			0
$418$	−6.27079e7	−	3.62044e7i	−0.858605	−	0.495716i
$419$			5.41233e7i			0.735770i	0.929871	+	0.367885i	$0.119918\pi$
$419$			5.41233e7i			0.735770i	−0.929871	+	0.367885i	$0.880082\pi$
$420$		0			0
$421$	−1.30034e8			−1.74265			−0.871323	−	0.490709i	$-0.836738\pi$
$421$	−1.30034e8			−1.74265			−0.871323	+	0.490709i	$0.836738\pi$
$422$	−6.82930e7	+	1.18287e8i	−0.908738	+	1.57398i
$423$		0			0
$424$	5.61010e7	+	9.71697e7i	0.735992	+	1.27477i
$425$	6.27456e7	+	3.62262e7i	0.817366	+	0.471907i
$426$		0			0
$427$	−2.16790e7	−	4.45167e7i	−0.278456	−	0.571794i
$428$	1.04841e8			1.33721
$429$		0			0
$430$	8.33874e7	−	4.81437e7i	1.04881	−	0.605528i
$431$	−5.99710e7	−	1.03873e8i	−0.749047	−	1.29739i	−0.948280	−	0.317436i	$-0.897178\pi$
$431$	−5.99710e7	−	1.03873e8i	−0.749047	−	1.29739i	0.199233	−	0.979952i	$-0.436155\pi$
$432$		0			0
$433$			1.11549e8i			1.37404i	0.726636	+	0.687022i	$0.241083\pi$
$433$			1.11549e8i			1.37404i	−0.726636	+	0.687022i	$0.758917\pi$
$434$	7.04958e7	−	1.04378e8i	0.862371	−	1.27686i
$435$		0			0
$436$	−8.61918e7	+	1.49289e8i	−1.03994	+	1.80122i
$437$	1.08984e8	−	6.29219e7i	1.30592	−	0.753976i
$438$		0			0
$439$	1.06743e8	+	6.16284e7i	1.26168	+	0.728429i	0.973399	−	0.229118i	$-0.0735842\pi$
$439$	1.06743e8	+	6.16284e7i	1.26168	+	0.728429i	0.288277	+	0.957547i	$0.406918\pi$
$440$			3.93830e7i			0.462329i
$441$		0			0
$442$	2.49557e8			2.89004
$443$	−3.55708e7	+	6.16104e7i	−0.409150	+	0.708669i	−0.994795	−	0.101899i	$-0.967508\pi$
$443$	−3.55708e7	+	6.16104e7i	−0.409150	+	0.708669i	0.585645	+	0.810568i	$0.300841\pi$
$444$		0			0
$445$	1.48267e7	+	2.56806e7i	0.168254	+	0.291424i
$446$	5.53296e7	+	3.19445e7i	0.623667	+	0.360074i
$447$		0			0
$448$	−1.15829e8	−	7.82292e7i	−1.28820	−	0.870031i
$449$	1.07566e8			1.18833			0.594165	−	0.804343i	$-0.297483\pi$
$449$	1.07566e8			1.18833			0.594165	+	0.804343i	$0.297483\pi$
$450$		0			0
$451$	4.21524e7	−	2.43367e7i	0.459507	−	0.265297i
$452$	−1.35768e8	−	2.35157e8i	−1.47022	−	2.54649i
$453$		0			0
$454$			1.99103e8i			2.12769i
$455$	−5.96030e7	+	2.90258e7i	−0.632752	+	0.308141i
$456$		0			0
$457$	−6.43381e6	+	1.11437e7i	−0.0674093	+	0.116756i	−0.897760	−	0.440485i	$-0.854807\pi$
$457$	−6.43381e6	+	1.11437e7i	−0.0674093	+	0.116756i	0.830351	+	0.557241i	$0.188140\pi$
$458$	4.85479e7	−	2.80292e7i	0.505329	−	0.291752i
$459$		0			0
$460$	−1.42329e8	−	8.21735e7i	−1.46224	−	0.844225i
$461$			7.08717e6i			0.0723386i	0.999346	+	0.0361693i	$0.0115156\pi$
$461$			7.08717e6i			0.0723386i	−0.999346	+	0.0361693i	$0.988484\pi$
$462$		0			0
$463$	1.44698e8			1.45788			0.728938	−	0.684580i	$-0.240014\pi$
$463$	1.44698e8			1.45788			0.728938	+	0.684580i	$0.240014\pi$
$464$	6.34596e6	−	1.09915e7i	0.0635249	−	0.110028i
$465$		0			0
$466$	8.29054e7	+	1.43596e8i	0.819267	+	1.41901i
$467$	−7.34759e7	−	4.24214e7i	−0.721431	−	0.416518i	0.0938485	−	0.995586i	$-0.470083\pi$
$467$	−7.34759e7	−	4.24214e7i	−0.721431	−	0.416518i	−0.815279	+	0.579068i	$0.803416\pi$
$468$		0			0
$469$	−5.68283e6	+	8.05695e7i	−0.0550866	+	0.781002i
$470$	−5.26389e6			−0.0507006
$471$		0			0
$472$	−1.17404e8	+	6.77834e7i	−1.11650	+	0.644610i
$473$	−3.77514e7	−	6.53874e7i	−0.356738	−	0.617889i
$474$		0			0
$475$		−	6.21054e7i		−	0.579494i
$476$	1.28399e8	+	2.63661e8i	1.19053	+	2.44470i
$477$		0			0
$478$	4.97062e7	−	8.60937e7i	0.455121	−	0.788293i
$479$	−1.38250e8	+	7.98185e7i	−1.25793	+	0.726268i	−0.972672	−	0.232182i	$-0.925414\pi$
$479$	−1.38250e8	+	7.98185e7i	−1.25793	+	0.726268i	−0.285261	+	0.958450i	$0.592080\pi$
$480$		0			0
$481$	−1.67613e8	−	9.67714e7i	−1.50616	−	0.869585i
$482$			2.58016e8i			2.30412i
$483$		0			0
$484$	−1.20150e8			−1.05972
$485$	−2.46677e7	+	4.27256e7i	−0.216223	+	0.374510i
$486$		0			0
$487$	−6.90017e7	−	1.19515e8i	−0.597411	−	1.03475i	−0.993202	−	0.116405i	$-0.962863\pi$
$487$	−6.90017e7	−	1.19515e8i	−0.597411	−	1.03475i	0.395791	−	0.918341i	$-0.370471\pi$
$488$	−7.52577e7	−	4.34501e7i	−0.647577	−	0.373879i
$489$		0			0
$490$	−9.71214e7	−	7.60685e7i	−0.825518	−	0.646571i
$491$	3.91824e7			0.331014			0.165507	−	0.986209i	$-0.447074\pi$
$491$	3.91824e7			0.331014			0.165507	+	0.986209i	$0.447074\pi$
$492$		0			0
$493$	9.37609e7	−	5.41329e7i	0.782494	−	0.451773i
$494$	−1.06959e8	−	1.85258e8i	−0.887231	−	1.53673i
$495$		0			0
$496$		−	2.54641e7i		−	0.208681i
$497$	−2.73640e7	−	1.84813e7i	−0.222900	−	0.150544i
$498$		0			0
$499$	−1.14482e7	+	1.98288e7i	−0.0921370	+	0.159586i	−0.908410	−	0.418080i	$-0.862703\pi$
$499$	−1.14482e7	+	1.98288e7i	−0.0921370	+	0.159586i	0.816273	+	0.577666i	$0.196036\pi$
$500$	−1.88328e8	+	1.08731e8i	−1.50662	+	0.869849i
$501$		0			0
$502$	−1.59316e8	−	9.19810e7i	−1.25935	−	0.727088i
$503$		−	1.38751e8i		−	1.09027i	−0.838349	−	0.545133i	$-0.816479\pi$
$503$		−	1.38751e8i		−	1.09027i	0.838349	−	0.545133i	$-0.183521\pi$
$504$		0			0
$505$	5.31683e7			0.412837
$506$	−1.02035e8	+	1.76730e8i	−0.787588	+	1.36414i
$507$		0			0
$508$	−1.60454e7	−	2.77915e7i	−0.122394	−	0.211993i
$509$	5.07588e7	+	2.93056e7i	0.384909	+	0.222227i	0.679952	−	0.733257i	$-0.262001\pi$
$509$	5.07588e7	+	2.93056e7i	0.384909	+	0.222227i	−0.295043	+	0.955484i	$0.595334\pi$
$510$		0			0
$511$	9.42796e7	+	6.64985e6i	0.706570	+	0.0498367i
$512$	−5.94097e7			−0.442636
$513$		0			0
$514$	−7.48087e6	+	4.31908e6i	−0.0550888	+	0.0318055i
$515$	6.16397e7	+	1.06763e8i	0.451272	+	0.781627i
$516$		0			0
$517$			4.12763e6i			0.0298696i
$518$	2.53400e7	−	3.59263e8i	0.182313	−	2.58478i
$519$		0			0
$520$	−5.81748e7	+	1.00762e8i	−0.413737	+	0.716614i
$521$	1.88084e8	−	1.08590e8i	1.32996	−	0.767853i	0.344668	−	0.938725i	$-0.387992\pi$
$521$	1.88084e8	−	1.08590e8i	1.32996	−	0.767853i	0.985293	+	0.170872i	$0.0546583\pi$
$522$		0			0
$523$	1.64929e7	+	9.52217e6i	0.115290	+	0.0665627i	0.556536	−	0.830823i	$-0.312130\pi$
$523$	1.64929e7	+	9.52217e6i	0.115290	+	0.0665627i	−0.441246	+	0.897386i	$0.645463\pi$
$524$		−	2.99294e8i		−	2.08019i
$525$		0			0
$526$	1.96889e8			1.35290
$527$	1.08608e8	−	1.88114e8i	0.742044	−	1.28526i
$528$		0			0
$529$	−1.03315e8	−	1.78948e8i	−0.697908	−	1.20881i
$530$	−1.69261e8	−	9.77228e7i	−1.13692	−	0.656400i
$531$		0			0
$532$	1.40697e8	−	2.08321e8i	0.934437	−	1.38356i
$533$	1.43796e8			0.949654
$534$		0			0
$535$	−6.58678e7	+	3.80288e7i	−0.430142	+	0.248342i
$536$	7.08766e7	+	1.22762e8i	0.460266	+	0.797204i
$537$		0			0
$538$			4.13941e8i			2.65822i
$539$	−5.96483e7	+	7.61567e7i	−0.380918	+	0.486342i
$540$		0			0
$541$	5.05360e7	−	8.75310e7i	0.319161	−	0.552803i	−0.661152	−	0.750252i	$-0.729932\pi$
$541$	5.05360e7	−	8.75310e7i	0.319161	−	0.552803i	0.980313	+	0.197449i	$0.0632657\pi$
$542$	1.70664e7	−	9.85332e6i	0.107188	−	0.0618849i
$543$		0			0
$544$	−1.78789e8	−	1.03224e8i	−1.11057	−	0.641185i
$545$		−	1.25057e8i		−	0.772537i
$546$		0			0
$547$	−2.29198e7			−0.140039			−0.0700196	−	0.997546i	$-0.522306\pi$
$547$	−2.29198e7			−0.140039			−0.0700196	+	0.997546i	$0.522306\pi$
$548$	−4.97852e7	+	8.62305e7i	−0.302523	+	0.523986i
$549$		0			0
$550$	5.03557e7	+	8.72186e7i	0.302664	+	0.524229i
$551$	−8.03708e7	−	4.64021e7i	−0.480445	−	0.277385i
$552$		0			0
$553$	2.10108e8	−	1.02319e8i	1.24241	−	0.605038i
$554$	−2.61399e7			−0.153735
$555$		0			0
$556$	−440732.	+	254457.i	−0.00256419	+	0.00148044i
$557$	6.91655e7	+	1.19798e8i	0.400243	+	0.693242i	0.993755	−	0.111584i	$-0.0355923\pi$
$557$	6.91655e7	+	1.19798e8i	0.400243	+	0.693242i	−0.593512	+	0.804825i	$0.702259\pi$
$558$		0			0
$559$		−	2.23059e8i		−	1.27698i
$560$	−2.48788e7	−	1.75478e6i	−0.141666	−	0.00999217i
$561$		0			0
$562$	−2.30859e7	+	3.99860e7i	−0.130059	+	0.225268i
$563$	−1.95097e8	+	1.12639e8i	−1.09326	+	0.631195i	−0.934443	−	0.356112i	$-0.884102\pi$
$563$	−1.95097e8	+	1.12639e8i	−1.09326	+	0.631195i	−0.158819	+	0.987308i	$0.550769\pi$
$564$		0			0
$565$	1.70597e8	+	9.84941e7i	0.945857	+	0.546091i
$566$			4.30221e8i			2.37270i
$567$		0			0
$568$	−5.79518e7			−0.316244
$569$	1.10276e8	−	1.91003e8i	0.598609	−	1.03682i	−0.394417	−	0.918931i	$-0.629054\pi$
$569$	1.10276e8	−	1.91003e8i	0.598609	−	1.03682i	0.993027	−	0.117890i	$-0.0376131\pi$
$570$		0			0
$571$	3.36594e7	+	5.82999e7i	0.180800	+	0.313155i	0.942153	−	0.335182i	$-0.108798\pi$
$571$	3.36594e7	+	5.82999e7i	0.180800	+	0.313155i	−0.761353	+	0.648337i	$0.775465\pi$
$572$	1.89715e8	+	1.09532e8i	1.01371	+	0.585265i
$573$		0			0
$574$	1.17156e8	+	2.40573e8i	0.619481	+	1.27207i
$575$	−1.75032e8			−0.920693
$576$		0			0
$577$	−9.29650e6	+	5.36734e6i	−0.0483941	+	0.0279403i	−0.524002	−	0.851717i	$-0.675562\pi$
$577$	−9.29650e6	+	5.36734e6i	−0.0483941	+	0.0279403i	0.475608	+	0.879657i	$0.342228\pi$
$578$	2.41384e8	+	4.18089e8i	1.25004	+	2.16513i
$579$		0			0
$580$			1.21199e8i			0.621175i
$581$	−2.45764e7	+	3.63887e7i	−0.125311	+	0.185540i
$582$		0			0
$583$	−7.66284e7	+	1.32724e8i	−0.386709	+	0.669799i
$584$	1.43652e8	−	8.29374e7i	0.721228	−	0.416401i
$585$		0			0
$586$	2.94062e8	+	1.69777e8i	1.46132	+	0.843694i
$587$			2.34143e8i			1.15762i	0.815461	+	0.578812i	$0.196484\pi$
$587$			2.34143e8i			1.15762i	−0.815461	+	0.578812i	$0.803516\pi$
$588$		0			0
$589$	−1.86195e8			−0.911219
$590$	1.18073e8	−	2.04508e8i	0.574901	−	0.995757i
$591$		0			0
$592$	−3.64061e7	−	6.30573e7i	−0.175473	−	0.303928i
$593$	−1.45328e8	−	8.39054e7i	−0.696926	−	0.402370i	0.109275	−	0.994012i	$-0.465147\pi$
$593$	−1.45328e8	−	8.39054e7i	−0.696926	−	0.402370i	−0.806202	+	0.591641i	$0.798480\pi$
$594$		0			0
$595$	−1.76306e8	−	1.19075e8i	−0.836984	−	0.565288i
$596$	1.80662e8			0.853350
$597$		0			0
$598$	−5.22116e8	+	3.01444e8i	−2.44154	+	1.40962i
$599$	2.72137e7	+	4.71356e7i	0.126622	+	0.219315i	0.922366	−	0.386318i	$-0.126253\pi$
$599$	2.72137e7	+	4.71356e7i	0.126622	+	0.219315i	−0.795744	+	0.605633i	$0.792920\pi$
$600$		0			0
$601$		−	1.02729e7i		−	0.0473226i	−0.999720	−	0.0236613i	$-0.992468\pi$
$601$		−	1.02729e7i		−	0.0473226i	0.999720	−	0.0236613i	$-0.00753233\pi$
$602$	3.73181e8	−	1.81734e8i	1.71053	−	0.833003i
$603$		0			0
$604$	1.34130e8	−	2.32320e8i	0.608717	−	1.05433i
$605$	7.54864e7	−	4.35821e7i	0.340881	−	0.196808i
$606$		0			0
$607$	3.20092e8	+	1.84805e8i	1.43123	+	0.826319i	0.997214	−	0.0745880i	$-0.0237642\pi$
$607$	3.20092e8	+	1.84805e8i	1.43123	+	0.826319i	0.434012	+	0.900907i	$0.357098\pi$
$608$			1.76965e8i			0.787366i
$609$		0			0
$610$	1.51372e8			0.666893
$611$	−6.09714e6	+	1.05606e7i	−0.0267302	+	0.0462981i
$612$		0			0
$613$	−2.33412e7	−	4.04282e7i	−0.101331	−	0.175510i	0.810902	−	0.585182i	$-0.198977\pi$
$613$	−2.33412e7	−	4.04282e7i	−0.101331	−	0.175510i	−0.912233	+	0.409671i	$0.865643\pi$
$614$	2.16727e8	+	1.25127e8i	0.936285	+	0.540565i
$615$		0			0
$616$	−1.19450e7	+	1.69353e8i	−0.0511029	+	0.724521i
$617$	−4.39158e8			−1.86967			−0.934836	−	0.355080i	$-0.884454\pi$
$617$	−4.39158e8			−1.86967			−0.934836	+	0.355080i	$0.884454\pi$
$618$		0			0
$619$	−1.84752e8	+	1.06666e8i	−0.778962	+	0.449734i	−0.836062	−	0.548635i	$-0.815148\pi$
$619$	−1.84752e8	+	1.06666e8i	−0.778962	+	0.449734i	0.0571005	+	0.998368i	$0.481814\pi$
$620$	1.21582e8	+	2.10586e8i	0.510145	+	0.883596i
$621$		0			0
$622$		−	4.26644e8i		−	1.77294i
$623$	5.59682e7	+	1.14928e8i	0.231461	+	0.475292i
$624$		0			0
$625$	6.26968e6	−	1.08594e7i	0.0256806	−	0.0444801i
$626$	−3.70845e8	+	2.14107e8i	−1.51171	+	0.872788i
$627$		0			0
$628$	2.67419e8	+	1.54395e8i	1.07973	+	0.623381i
$629$		−	6.21109e8i		−	2.49584i
$630$		0			0
$631$	2.58817e8			1.03016			0.515080	−	0.857142i	$-0.327762\pi$
$631$	2.58817e8			1.03016			0.515080	+	0.857142i	$0.327762\pi$
$632$	2.05073e8	−	3.55197e8i	0.812377	−	1.40708i
$633$		0			0
$634$	−1.07689e8	−	1.86522e8i	−0.422573	−	0.731918i
$635$	2.01616e7	+	1.16403e7i	0.0787415	+	0.0454614i
$636$		0			0
$637$	−2.65106e8	+	1.06738e8i	−1.02565	+	0.412952i
$638$	1.50493e8			0.579502
$639$		0			0
$640$	2.53259e8	−	1.46219e8i	0.966106	−	0.557781i
$641$	6.64356e7	+	1.15070e8i	0.252247	+	0.436905i	0.964144	−	0.265379i	$-0.0854970\pi$
$641$	6.64356e7	+	1.15070e8i	0.252247	+	0.436905i	−0.711897	+	0.702284i	$0.752164\pi$
$642$		0			0
$643$		−	1.84168e8i		−	0.692757i	−0.938095	−	0.346378i	$-0.887411\pi$
$643$		−	1.84168e8i		−	0.692757i	0.938095	−	0.346378i	$-0.112589\pi$
$644$	−5.87112e8	−	3.96528e8i	−2.19818	−	1.48462i
$645$		0			0
$646$	3.43248e8	−	5.94523e8i	1.27324	−	2.20532i
$647$	2.88189e8	−	1.66386e8i	1.06405	−	0.614332i	0.137504	−	0.990501i	$-0.456092\pi$
$647$	2.88189e8	−	1.66386e8i	1.06405	−	0.614332i	0.926551	+	0.376169i	$0.122759\pi$
$648$		0			0
$649$	−1.60363e8	−	9.25854e7i	−0.586636	−	0.338695i
$650$			2.97532e8i			1.08341i
$651$		0			0
$652$	−1.71406e8			−0.618420
$653$	1.28291e8	−	2.22206e8i	0.460741	−	0.798026i	−0.538257	−	0.842780i	$-0.680917\pi$
$653$	1.28291e8	−	2.22206e8i	0.460741	−	0.798026i	0.998998	+	0.0447544i	$0.0142505\pi$
$654$		0			0
$655$	1.08563e8	+	1.88036e8i	0.386328	+	0.669140i
$656$	4.68495e7	+	2.70486e7i	0.165956	+	0.0958149i
$657$		0			0
$658$	−2.26356e7	−	1.59656e6i	−0.0794536	−	0.00560412i
$659$	−1.84717e8			−0.645431			−0.322715	−	0.946496i	$-0.604596\pi$
$659$	−1.84717e8			−0.645431			−0.322715	+	0.946496i	$0.604596\pi$
$660$		0			0
$661$	1.74480e8	−	1.00736e8i	0.604144	−	0.348803i	−0.166526	−	0.986037i	$-0.553255\pi$
$661$	1.74480e8	−	1.00736e8i	0.604144	−	0.348803i	0.770670	+	0.637234i	$0.219922\pi$
$662$	−3.41045e8	−	5.90707e8i	−1.17554	−	2.03610i
$663$		0			0
$664$			7.70644e7i			0.263239i
$665$	−1.28311e7	+	1.81916e8i	−0.0436314	+	0.618593i
$666$		0			0
$667$	−1.30776e8	+	2.26510e8i	−0.440706	+	0.763326i
$668$	−1.09742e8	+	6.33597e7i	−0.368166	+	0.212561i
$669$		0			0
$670$	−2.13840e8	−	1.23461e8i	−0.710992	−	0.410492i
$671$		−	1.18697e8i		−	0.392891i
$672$		0			0
$673$	−4.93893e8			−1.62027			−0.810135	−	0.586243i	$-0.800606\pi$
$673$	−4.93893e8			−1.62027			−0.810135	+	0.586243i	$0.800606\pi$
$674$	−4.04577e8	+	7.00747e8i	−1.32136	+	2.28866i
$675$		0			0
$676$	5.88939e7	+	1.02007e8i	0.190647	+	0.330211i
$677$	2.71512e8	+	1.56758e8i	0.875030	+	0.505199i	0.869017	−	0.494783i	$-0.164752\pi$
$677$	2.71512e8	+	1.56758e8i	0.875030	+	0.505199i	0.00601364	+	0.999982i	$0.498086\pi$
$678$		0			0
$679$	−1.19034e8	+	1.76245e8i	−0.380243	+	0.563000i
$680$	−3.73384e8			−1.18749
$681$		0			0
$682$	2.61486e8	−	1.50969e8i	0.824318	−	0.475920i
$683$	−7.42502e7	−	1.28605e8i	−0.233043	−	0.403642i	0.725659	−	0.688054i	$-0.241535\pi$
$683$	−7.42502e7	−	1.28605e8i	−0.233043	−	0.403642i	−0.958702	+	0.284412i	$0.908202\pi$
$684$		0			0
$685$		−	7.22343e7i		−	0.224735i
$686$	−3.94565e8	−	3.56564e8i	−1.22221	−	1.10450i
$687$		0			0
$688$	4.19582e7	−	7.26737e7i	0.128840	−	0.223158i
$689$	−3.92108e8	+	2.26384e8i	−1.19880	+	0.692130i
$690$		0			0
$691$	−3.35862e8	−	1.93910e8i	−1.01795	−	0.587714i	−0.104441	−	0.994531i	$-0.533305\pi$
$691$	−3.35862e8	−	1.93910e8i	−1.01795	−	0.587714i	−0.913510	+	0.406817i	$0.866639\pi$
$692$		−	6.31859e8i		−	1.90678i
$693$		0			0
$694$	−4.68722e8			−1.40229
$695$	184598.	−	319733.i	0.000549886	−	0.000952430i
$696$		0			0
$697$	2.30732e8	+	3.99640e8i	0.681412	+	1.18024i
$698$	5.90235e8	+	3.40772e8i	1.73564	+	1.00207i
$699$		0			0
$700$	−3.14347e8	+	1.53083e8i	−0.916464	+	0.446305i
$701$	−4.86782e7			−0.141312			−0.0706562	−	0.997501i	$-0.522509\pi$
$701$	−4.86782e7			−0.141312			−0.0706562	+	0.997501i	$0.522509\pi$
$702$		0			0
$703$	−4.61079e8	+	2.66204e8i	−1.32712	+	0.766212i
$704$	−1.67530e8	−	2.90171e8i	−0.480148	−	0.831640i
$705$		0			0
$706$			1.01814e7i			0.0289329i
$707$	2.28632e8	+	1.61262e7i	0.646963	+	0.0456324i
$708$		0			0
$709$	1.58977e8	−	2.75357e8i	0.446064	−	0.772605i	−0.552062	−	0.833803i	$-0.686159\pi$
$709$	1.58977e8	−	2.75357e8i	0.446064	−	0.772605i	0.998126	+	0.0611981i	$0.0194921\pi$
$710$	8.74224e7	−	5.04734e7i	0.244257	−	0.141022i
$711$		0			0
$712$	1.94291e8	+	1.12174e8i	0.538285	+	0.310779i
$713$			5.24756e8i			1.44773i
$714$		0			0
$715$	−1.58922e8			−0.434776
$716$	−6.55655e7	+	1.13563e8i	−0.178623	+	0.309384i
$717$		0			0
$718$	−2.74565e8	−	4.75561e8i	−0.741774	−	1.28479i
$719$	1.50536e8	+	8.69119e7i	0.404998	+	0.233826i	0.688638	−	0.725105i	$-0.258209\pi$
$719$	1.50536e8	+	8.69119e7i	0.404998	+	0.233826i	−0.283640	+	0.958931i	$0.591542\pi$
$720$		0			0
$721$	2.32679e8	+	4.77794e8i	0.620799	+	1.27478i
$722$	3.15455e7			0.0838157
$723$		0			0
$724$	9.50125e8	−	5.48555e8i	2.50360	−	1.44545i
$725$	6.45394e7	+	1.11785e8i	0.169360	+	0.293340i
$726$		0			0
$727$		−	4.58803e8i		−	1.19405i	−0.802222	−	0.597026i	$-0.796349\pi$
$727$		−	4.58803e8i		−	1.19405i	0.802222	−	0.597026i	$-0.203651\pi$
$728$	−2.80722e8	+	4.15646e8i	−0.727583	+	1.07728i
$729$		0			0
$730$	−1.44469e8	+	2.50228e8i	−0.371370	+	0.643232i
$731$	6.19927e8	−	3.57915e8i	1.58704	−	0.916279i
$732$		0			0
$733$	5.55746e8	+	3.20860e8i	1.41112	+	0.814711i	0.995494	−	0.0948235i	$-0.0302287\pi$
$733$	5.55746e8	+	3.20860e8i	1.41112	+	0.814711i	0.415627	+	0.909535i	$0.363562\pi$
$734$			8.70033e7i			0.220013i
$735$		0			0
$736$	4.98742e8			1.25096
$737$	−9.68105e7	+	1.67681e8i	−0.241835	+	0.418871i
$738$		0			0
$739$	1.70001e8	+	2.94450e8i	0.421229	+	0.729590i	0.996060	−	0.0886823i	$-0.0282656\pi$
$739$	1.70001e8	+	2.94450e8i	0.421229	+	0.729590i	−0.574831	+	0.818272i	$0.694932\pi$
$740$	6.02151e8	+	3.47652e8i	1.48597	+	0.857926i
$741$		0			0
$742$	−6.98209e8	−	4.71561e8i	−1.70912	−	1.15432i
$743$	−6.08554e8			−1.48365			−0.741827	−	0.670591i	$-0.766040\pi$
$743$	−6.08554e8			−1.48365			−0.741827	+	0.670591i	$0.766040\pi$
$744$		0			0
$745$	−1.13504e8	+	6.55313e7i	−0.274499	+	0.158482i
$746$	3.26280e7	+	5.65133e7i	0.0785911	+	0.136124i
$747$		0			0
$748$			7.03011e8i			1.67980i
$749$	−2.94776e8	+	1.43552e8i	−0.701531	+	0.341636i
$750$		0			0
$751$	−8.06132e7	+	1.39626e8i	−0.190321	+	0.329645i	−0.945357	−	0.326038i	$-0.894286\pi$
$751$	−8.06132e7	+	1.39626e8i	−0.190321	+	0.329645i	0.755036	+	0.655684i	$0.227619\pi$
$752$	−3.97296e6	+	2.29379e6i	−0.00934245	+	0.00539387i
$753$		0			0
$754$	3.85038e8	+	2.22302e8i	0.898233	+	0.518595i
$755$			1.94612e8i			0.452198i
$756$		0			0
$757$	1.60953e8			0.371031			0.185516	−	0.982641i	$-0.440604\pi$
$757$	1.60953e8			0.371031			0.185516	+	0.982641i	$0.440604\pi$
$758$	6.97652e8	−	1.20837e9i	1.60189	−	2.77455i
$759$		0			0
$760$	1.60030e8	+	2.77181e8i	0.364554	+	0.631426i
$761$	3.75605e8	+	2.16856e8i	0.852271	+	0.492059i	0.861416	−	0.507899i	$-0.169578\pi$
$761$	3.75605e8	+	2.16856e8i	0.852271	+	0.492059i	−0.00914540	+	0.999958i	$0.502911\pi$
$762$		0			0
$763$	3.79304e7	−	5.37766e8i	0.0853913	−	1.21065i
$764$	8.31656e8			1.86493
$765$		0			0
$766$	−5.61533e8	+	3.24201e8i	−1.24936	+	0.721321i
$767$	−2.73526e8	−	4.73760e8i	−0.606194	−	1.04996i
$768$		0			0
$769$		−	3.73405e8i		−	0.821110i	−0.911836	−	0.410555i	$-0.865335\pi$
$769$		−	3.73405e8i		−	0.821110i	0.911836	−	0.410555i	$-0.134665\pi$
$770$	−1.29479e8	−	2.65879e8i	−0.283615	−	0.582388i
$771$		0			0
$772$	−3.89144e8	+	6.74018e8i	−0.845782	+	1.46494i
$773$	−5.92885e8	+	3.42302e8i	−1.28361	+	0.741090i	−0.977506	−	0.210909i	$-0.932358\pi$
$773$	−5.92885e8	+	3.42302e8i	−1.28361	+	0.741090i	−0.306100	+	0.951999i	$0.599024\pi$
$774$		0			0
$775$	2.24278e8	+	1.29487e8i	0.481816	+	0.278176i
$776$			3.73254e8i			0.798766i
$777$		0			0
$778$	−8.77962e8			−1.86439
$779$	1.97781e8	−	3.42567e8i	0.418381	−	0.724658i
$780$		0			0
$781$	−3.95782e7	−	6.85514e7i	−0.0830812	−	0.143901i
$782$	−1.67555e9	−	9.67380e8i	−3.50379	−	2.02291i
$783$		0			0
$784$	−1.06451e8	−	1.50917e7i	−0.220902	−	0.0313177i
$785$	−2.24014e8			−0.463091
$786$		0			0
$787$	6.27494e8	−	3.62284e8i	1.28732	−	0.743233i	0.309142	−	0.951016i	$-0.399958\pi$
$787$	6.27494e8	−	3.62284e8i	1.28732	−	0.743233i	0.978175	+	0.207783i	$0.0666247\pi$
$788$	1.09731e8	+	1.90059e8i	0.224259	+	0.388428i
$789$		0			0
$790$			7.14438e8i			1.44905i
$791$	7.03719e8	+	4.75283e8i	1.42190	+	0.960335i
$792$		0			0
$793$	1.75334e8	−	3.03687e8i	0.351597	−	0.608984i
$794$	−5.48287e8	+	3.16553e8i	−1.09533	+	0.632391i
$795$		0			0
$796$	4.12807e8	+	2.38334e8i	0.818480	+	0.472550i
$797$		−	5.85510e7i		−	0.115654i	−0.998327	−	0.0578268i	$-0.981583\pi$
$797$		−	5.85510e7i		−	0.115654i	0.998327	−	0.0578268i	$-0.0184171\pi$
$798$		0			0
$799$	−3.91334e7			−0.0767197
$800$	1.23068e8	−	2.13159e8i	0.240367	−	0.416327i
$801$		0			0
$802$	9.18761e7	+	1.59134e8i	0.178106	+	0.308489i
$803$	1.96214e8	+	1.13284e8i	0.378951	+	0.218788i
$804$		0			0
$805$	5.12695e8	+	3.61620e7i	0.982814	+	0.0693211i
$806$	8.92017e8			1.70360
$807$		0			0
$808$	3.48362e8	−	2.01127e8i	0.660384	−	0.381273i
$809$	2.55763e8	+	4.42994e8i	0.483049	+	0.836666i	0.999811	−	0.0194637i	$-0.00619588\pi$
$809$	2.55763e8	+	4.42994e8i	0.483049	+	0.836666i	−0.516761	+	0.856129i	$0.672863\pi$
$810$		0			0
$811$		−	7.81509e8i		−	1.46511i	−0.680706	−	0.732557i	$-0.738327\pi$
$811$		−	7.81509e8i		−	1.46511i	0.680706	−	0.732557i	$-0.261673\pi$
$812$	−3.67601e7	+	5.21173e8i	−0.0686607	+	0.973451i
$813$		0			0
$814$	4.31682e8	−	7.47695e8i	0.800370	−	1.38628i
$815$	1.07689e8	−	6.21741e7i	0.198929	−	0.114851i
$816$		0			0
$817$	−5.31395e8	−	3.06801e8i	−0.974431	−	0.562588i
$818$			2.94989e8i			0.538947i
$819$		0			0
$820$	−5.16588e8			−0.936921
$821$	−2.75815e8	+	4.77726e8i	−0.498412	+	0.863275i	−0.999998	−	0.00183255i	$-0.999417\pi$
$821$	−2.75815e8	+	4.77726e8i	−0.498412	+	0.863275i	0.501586	+	0.865108i	$0.332750\pi$
$822$		0			0
$823$	1.78646e8	+	3.09423e8i	0.320474	+	0.555077i	0.980586	−	0.196090i	$-0.0628245\pi$
$823$	1.78646e8	+	3.09423e8i	0.320474	+	0.555077i	−0.660112	+	0.751167i	$0.729491\pi$
$824$	8.07733e8	+	4.66345e8i	1.44373	+	0.833539i
$825$		0			0
$826$	5.69758e8	−	8.43603e8i	1.01100	−	1.49692i
$827$	4.42420e8			0.782201			0.391101	−	0.920348i	$-0.372094\pi$
$827$	4.42420e8			0.782201			0.391101	+	0.920348i	$0.372094\pi$
$828$		0			0
$829$	−1.02602e8	+	5.92376e7i	−0.180092	+	0.103976i	−0.587336	−	0.809343i	$-0.699823\pi$
$829$	−1.02602e8	+	5.92376e7i	−0.180092	+	0.103976i	0.407244	+	0.913319i	$0.366490\pi$
$830$	−6.71196e7	−	1.16255e8i	−0.117386	−	0.203318i
$831$		0			0
$832$		−	9.89871e8i		−	1.71873i
$833$	−7.22029e8	−	5.65516e8i	−1.24917	−	0.978385i
$834$		0			0
$835$	4.59648e7	−	7.96134e7i	0.0789526	−	0.136750i
$836$	5.21878e8	−	3.01307e8i	0.893204	−	0.515691i
$837$		0			0
$838$	−6.17714e8	−	3.56637e8i	−1.04968	−	0.606031i
$839$		−	1.02452e9i		−	1.73474i	−0.497660	−	0.867372i	$-0.665807\pi$
$839$		−	1.02452e9i		−	1.73474i	0.497660	−	0.867372i	$-0.334193\pi$
$840$		0			0
$841$	−4.01941e8			−0.675731
$842$	8.56837e8	−	1.48408e9i	1.43536	−	2.48612i
$843$		0			0
$844$	−5.68359e8	−	9.84427e8i	−0.945357	−	1.63741i
$845$	−7.40021e7	−	4.27251e7i	−0.122652	−	0.0708130i
$846$		0			0
$847$	3.37822e8	−	1.64515e8i	0.555953	−	0.270741i
$848$	−1.70335e8			−0.279328
$849$		0			0
$850$	−8.26905e8	+	4.77414e8i	−1.34648	+	0.777389i
$851$	7.50246e8	+	1.29946e9i	1.21735	+	2.10851i
$852$		0			0
$853$			1.03709e9i			1.67097i	0.549517	+	0.835483i	$0.314812\pi$
$853$			1.03709e9i			1.67097i	−0.549517	+	0.835483i	$0.685188\pi$
$854$	6.50924e8	+	4.59118e7i	1.04510	+	0.0737141i
$855$		0			0
$856$	−2.87713e8	+	4.98333e8i	−0.458710	+	0.794508i
$857$	−4.76107e8	+	2.74881e8i	−0.756419	+	0.436719i	−0.828009	−	0.560715i	$-0.810526\pi$
$857$	−4.76107e8	+	2.74881e8i	−0.756419	+	0.436719i	0.0715895	+	0.997434i	$0.477193\pi$
$858$		0			0
$859$	1.23390e8	+	7.12392e7i	0.194671	+	0.112393i	0.594167	−	0.804342i	$-0.297482\pi$
$859$	1.23390e8	+	7.12392e7i	0.194671	+	0.112393i	−0.399497	+	0.916735i	$0.630815\pi$
$860$			8.01340e8i			1.25986i
$861$		0			0
$862$	1.58068e9			2.46787
$863$	−2.00417e8	+	3.47132e8i	−0.311818	+	0.540085i	−0.978756	−	0.205028i	$-0.934271\pi$
$863$	−2.00417e8	+	3.47132e8i	−0.311818	+	0.540085i	0.666938	+	0.745113i	$0.267605\pi$
$864$		0			0
$865$	2.29194e8	+	3.96975e8i	0.354123	+	0.613359i
$866$	−1.27311e9	−	7.35033e8i	−1.96026	−	1.13176i
$867$		0			0
$868$	4.58949e8	+	9.42428e8i	0.701787	+	1.44108i
$869$	5.60219e8			0.853687
$870$		0			0
$871$	−4.95380e8	+	2.86008e8i	−0.749694	+	0.432836i
$872$	−4.73070e8	−	8.19382e8i	−0.713471	−	1.23577i
$873$		0			0
$874$			1.65846e9i			2.48410i
$875$	3.80635e8	−	5.63581e8i	0.568178	−	0.841263i
$876$		0			0
$877$	1.80269e8	−	3.12235e8i	0.267252	−	0.462895i	−0.700899	−	0.713261i	$-0.747218\pi$
$877$	1.80269e8	−	3.12235e8i	0.267252	−	0.462895i	0.968151	+	0.250366i	$0.0805509\pi$
$878$	−1.40674e9	+	8.12181e8i	−2.07840	+	1.19997i
$879$		0			0
$880$	−5.17776e7	−	2.98938e7i	−0.0759791	−	0.0438665i
$881$		−	1.27541e9i		−	1.86519i	−0.360924	−	0.932595i	$-0.617539\pi$
$881$		−	1.27541e9i		−	1.86519i	0.360924	−	0.932595i	$-0.382461\pi$
$882$		0			0
$883$	−2.92638e8			−0.425058			−0.212529	−	0.977155i	$-0.568170\pi$
$883$	−2.92638e8			−0.425058			−0.212529	+	0.977155i	$0.568170\pi$
$884$	−1.03845e9	+	1.79866e9i	−1.50325	+	2.60370i
$885$		0			0
$886$	−4.68777e8	−	8.11945e8i	−0.674008	−	1.16742i
$887$	7.14682e8	+	4.12622e8i	1.02410	+	0.591264i	0.915289	−	0.402798i	$-0.131962\pi$
$887$	7.14682e8	+	4.12622e8i	1.02410	+	0.591264i	0.108811	+	0.994062i	$0.465296\pi$
$888$		0			0
$889$	8.31675e7	+	5.61703e7i	0.118372	+	0.0799468i
$890$	−3.90794e8			−0.554342
$891$		0			0
$892$	−4.60473e8	+	2.65854e8i	−0.648798	+	0.374584i
$893$	1.67724e7	+	2.90506e7i	0.0235526	+	0.0407944i
$894$		0			0
$895$		−	9.51302e7i		−	0.132693i
$896$	1.13340e9	−	5.51951e8i	1.57565	−	0.767319i
$897$		0			0
$898$	−7.08792e8	+	1.22766e9i	−0.978790	+	1.69531i
$899$	3.35138e8	−	1.93492e8i	0.461259	−	0.266308i
$900$		0			0
$901$	−1.25834e9	−	7.26501e8i	−1.72037	−	0.993257i
$902$			6.41451e8i			0.874065i
$903$		0			0
$904$	1.49035e9			2.01735
$905$	−3.97954e8	+	6.89276e8i	−0.536892	+	0.929924i
$906$		0			0
$907$	4.80348e8	+	8.31987e8i	0.643775	+	1.11505i	0.984583	+	0.174918i	$0.0559662\pi$
$907$	4.80348e8	+	8.31987e8i	0.643775	+	1.11505i	−0.340808	+	0.940133i	$0.610700\pi$
$908$	−1.43501e9	−	8.28502e8i	−1.91689	−	1.10672i
$909$		0			0
$910$	6.14708e7	−	8.71514e8i	0.0815726	−	1.15651i
$911$	−1.01677e9			−1.34483			−0.672413	−	0.740176i	$-0.734742\pi$
$911$	−1.01677e9			−1.34483			−0.672413	+	0.740176i	$0.734742\pi$
$912$		0			0
$913$	−9.11598e7	+	5.26311e7i	−0.119782	+	0.0691561i
$914$	−8.47892e7	−	1.46859e8i	−0.111046	−	0.192337i
$915$		0			0
$916$			4.66538e8i			0.607017i
$917$	4.09804e8	+	8.41512e8i	0.531457	+	1.09132i
$918$		0			0
$919$	2.43093e8	−	4.21050e8i	0.313203	−	0.542484i	−0.665851	−	0.746085i	$-0.731931\pi$
$919$	2.43093e8	−	4.21050e8i	0.313203	−	0.542484i	0.979054	+	0.203601i	$0.0652646\pi$
$920$	7.81181e8	−	4.51015e8i	1.00320	−	0.579199i
$921$		0			0
$922$	−8.08865e7	−	4.66998e7i	−0.103201	−	0.0595830i
$923$		−	2.33852e8i		−	0.297397i
$924$		0			0
$925$	7.40511e8			0.935635
$926$	−9.53467e8	+	1.65145e9i	−1.20081	+	2.07986i
$927$		0			0
$928$	−1.83900e8	−	3.18525e8i	−0.230112	−	0.398565i
$929$	−7.80354e8	−	4.50538e8i	−0.973295	−	0.561932i	−0.0730561	−	0.997328i	$-0.523275\pi$
$929$	−7.80354e8	−	4.50538e8i	−0.973295	−	0.561932i	−0.900239	+	0.435395i	$0.856609\pi$
$930$		0			0
$931$	−1.10352e8	+	7.78374e8i	−0.136751	+	0.964583i
$932$	−1.37994e9			−1.70456
$933$		0			0
$934$	9.68317e8	−	5.59058e8i	1.18844	−	0.686146i
$935$	−2.55003e8	−	4.41677e8i	−0.311968	−	0.540344i
$936$		0			0
$937$			6.19442e8i			0.752977i	0.926421	+	0.376489i	$0.122869\pi$
$937$			6.19442e8i			0.752977i	−0.926421	+	0.376489i	$0.877131\pi$
$938$	−8.82100e8	−	5.95759e8i	−1.06883	−	0.721875i
$939$		0			0
$940$	2.19040e7	−	3.79389e7i	0.0263718	−	0.0456774i
$941$	4.29312e8	−	2.47863e8i	0.515234	−	0.297470i	−0.219749	−	0.975557i	$-0.570524\pi$
$941$	4.29312e8	−	2.47863e8i	0.515234	−	0.297470i	0.734982	+	0.678086i	$0.237190\pi$
$942$		0			0
$943$	−9.65460e8	−	5.57408e8i	−1.15133	−	0.664720i
$944$		−	2.05805e8i		−	0.244647i
$945$		0			0
$946$	9.95029e8			1.17534
$947$	5.84700e8	−	1.01273e9i	0.688467	−	1.19246i	−0.283866	−	0.958864i	$-0.591617\pi$
$947$	5.84700e8	−	1.01273e9i	0.688467	−	1.19246i	0.972334	−	0.233597i	$-0.0750495\pi$
$948$		0			0
$949$	3.34676e8	+	5.79677e8i	0.391585	+	0.678246i
$950$	7.08815e8	+	4.09234e8i	0.826726	+	0.477311i
$951$		0			0
$952$	−1.60561e9	−	1.13249e8i	−1.86093	−	0.131257i
$953$	2.23017e8			0.257667			0.128834	−	0.991666i	$-0.458877\pi$
$953$	2.23017e8			0.257667			0.128834	+	0.991666i	$0.458877\pi$
$954$		0			0
$955$	−5.22501e8	+	3.01666e8i	−0.599897	+	0.346351i
$956$	4.13673e8	+	7.16503e8i	0.473461	+	0.820058i
$957$		0			0
$958$		−	2.10381e9i		−	2.39282i
$959$	2.19089e7	−	3.10619e8i	0.0248408	−	0.352186i
$960$		0			0
$961$	−5.55442e7	+	9.62054e7i	−0.0625847	+	0.108400i
$962$	2.20892e9	−	1.27532e9i	2.48116	−	1.43250i
$963$		0			0
$964$	−1.85962e9	−	1.07365e9i	−2.07584	−	1.19849i
$965$		−	5.64616e8i		−	0.628306i
$966$		0			0
$967$	4.77842e8			0.528451			0.264226	−	0.964461i	$-0.414884\pi$
$967$	4.77842e8			0.528451			0.264226	+	0.964461i	$0.414884\pi$
$968$	3.29727e8	−	5.71105e8i	0.363521	−	0.629636i
$969$		0			0
$970$	−3.25088e8	−	5.63068e8i	−0.356193	−	0.616944i
$971$	−8.66630e8	−	5.00349e8i	−0.946621	−	0.546532i	−0.0545914	−	0.998509i	$-0.517386\pi$
$971$	−8.66630e8	−	5.00349e8i	−0.946621	−	0.546532i	−0.892030	+	0.451977i	$0.850719\pi$
$972$		0			0
$973$	890777.	−	1.31891e6i	0.000967009	−	0.00143178i
$974$	1.81871e9			1.96827
$975$		0			0
$976$	1.14249e8	−	6.59618e7i	0.122886	−	0.0709485i
$977$	−2.65667e8	−	4.60149e8i	−0.284875	−	0.493417i	0.687704	−	0.725991i	$-0.258619\pi$
$977$	−2.65667e8	−	4.60149e8i	−0.284875	−	0.493417i	−0.972579	+	0.232574i	$0.925285\pi$
$978$		0			0
$979$			3.06437e8i			0.326583i
$980$	9.52395e8	−	3.83456e8i	1.01190	−	0.407415i
$981$		0			0
$982$	−2.58186e8	+	4.47192e8i	−0.272646	+	0.472236i
$983$	−6.03725e8	+	3.48561e8i	−0.635592	+	0.366959i	−0.782915	−	0.622129i	$-0.786268\pi$
$983$	−6.03725e8	+	3.48561e8i	−0.635592	+	0.366959i	0.147322	+	0.989089i	$0.452935\pi$
$984$		0			0
$985$	−1.37880e8	−	7.96052e7i	−0.144276	−	0.0832976i
$986$			1.42680e9i			1.48844i
$987$		0			0
$988$	1.78031e9			1.84597
$989$	−8.64660e8	+	1.49764e9i	−0.893833	+	1.54816i
$990$		0			0
$991$	−3.67589e8	−	6.36684e8i	−0.377696	−	0.654188i	0.613031	−	0.790059i	$-0.289950\pi$
$991$	−3.67589e8	−	6.36684e8i	−0.377696	−	0.654188i	−0.990727	+	0.135871i	$0.956617\pi$
$992$	−6.39063e8	−	3.68963e8i	−0.654649	−	0.377962i
$993$		0			0
$994$	3.91239e8	−	1.90528e8i	0.398367	−	0.193999i
$995$	−3.45803e8			−0.351043
$996$		0			0
$997$	−4.85470e8	+	2.80286e8i	−0.489866	+	0.282824i	−0.724519	−	0.689255i	$-0.757938\pi$
$997$	−4.85470e8	+	2.80286e8i	−0.489866	+	0.282824i	0.234653	+	0.972079i	$0.424605\pi$
$998$	−1.50872e8	−	2.61318e8i	−0.151781	−	0.262892i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	63.7.m.c.19.1		8
3.2	odd	2		21.7.f.b.19.4	yes	8
7.2	even	3		441.7.d.d.244.7		8
7.3	odd	6	inner	63.7.m.c.10.1		8
7.5	odd	6		441.7.d.d.244.8		8
12.11	even	2		336.7.bh.b.145.2		8
21.2	odd	6		147.7.d.a.97.2		8
21.5	even	6		147.7.d.a.97.1		8
21.11	odd	6		147.7.f.a.31.4		8
21.17	even	6		21.7.f.b.10.4	✓	8
21.20	even	2		147.7.f.a.19.4		8
84.59	odd	6		336.7.bh.b.241.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.7.f.b.10.4	✓	8	21.17	even	6
21.7.f.b.19.4	yes	8	3.2	odd	2
63.7.m.c.10.1		8	7.3	odd	6	inner
63.7.m.c.19.1		8	1.1	even	1	trivial
147.7.d.a.97.1		8	21.5	even	6
147.7.d.a.97.2		8	21.2	odd	6
147.7.f.a.19.4		8	21.20	even	2
147.7.f.a.31.4		8	21.11	odd	6
336.7.bh.b.145.2		8	12.11	even	2
336.7.bh.b.241.2		8	84.59	odd	6
441.7.d.d.244.7		8	7.2	even	3
441.7.d.d.244.8		8	7.5	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 63 = 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	63.m (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-6.58935 + 11.4131i) q^{2} +(-54.8390 - 94.9839i) q^{4} +(68.9069 + 39.7834i) q^{5} +(284.244 + 191.975i) q^{7} +601.976 q^{8} +O(q^{10})\)	\(q+(-6.58935 + 11.4131i) q^{2} +(-54.8390 - 94.9839i) q^{4} +(68.9069 + 39.7834i) q^{5} +(284.244 + 191.975i) q^{7} +601.976 q^{8} +(-908.103 + 524.293i) q^{10} +(411.119 + 712.080i) q^{11} +2429.15i q^{13} +(-4064.01 + 1979.11i) q^{14} +(-456.932 + 791.429i) q^{16} +(-6751.11 + 3897.76i) q^{17} +(5786.98 + 3341.12i) q^{19} -8726.73i q^{20} -10836.0 q^{22} +(9416.30 - 16309.5i) q^{23} +(-4647.06 - 8048.94i) q^{25} +(-27724.0 - 16006.5i) q^{26} +(2646.85 - 37526.3i) q^{28} -13888.2 q^{29} +(-24131.1 + 13932.1i) q^{31} +(13241.5 + 22934.9i) q^{32} -102735. i q^{34} +(11949.0 + 24536.6i) q^{35} +(-39837.6 + 69000.8i) q^{37} +(-76264.9 + 44031.5i) q^{38} +(41480.3 + 23948.6i) q^{40} -59196.1i q^{41} -91825.9 q^{43} +(45090.7 - 78099.4i) q^{44} +(124095. + 214938. i) q^{46} +(4347.44 + 2509.99i) q^{47} +(43940.4 + 109135. i) q^{49} +122484. q^{50} +(230730. - 133212. i) q^{52} +(93194.8 + 161418. i) q^{53} +65422.9i q^{55} +(171108. + 115564. i) q^{56} +(91514.3 - 158507. i) q^{58} +(-195032. + 112602. i) q^{59} +(-125018. - 72179.1i) q^{61} -367214. i q^{62} -407497. q^{64} +(-96639.7 + 167385. i) q^{65} +(117740. + 203932. i) q^{67} +(740448. + 427498. i) q^{68} +(-358774. - 25305.5i) q^{70} -96269.3 q^{71} +(238634. - 137775. i) q^{73} +(-525008. - 909340. i) q^{74} -732893. i q^{76} +(-19843.1 + 281329. i) q^{77} +(340667. - 590052. i) q^{79} +(-62971.5 + 36356.6i) q^{80} +(675610. + 390064. i) q^{82} +128019. i q^{83} -620264. q^{85} +(605073. - 1.04802e6i) q^{86} +(247484. + 428655. i) q^{88} +(322756. + 186343. i) q^{89} +(-466335. + 690470. i) q^{91} -2.06552e6 q^{92} +(-57293.5 + 33078.4i) q^{94} +(265842. + 460452. i) q^{95} +620049. i q^{97} +(-1.53511e6 - 217635. i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 5 q^{2} - 173 q^{4} + 42 q^{5} + 748 q^{7} + 454 q^{8}+O(q^{10}) \) 8 * q + 5 * q^2 - 173 * q^4 + 42 * q^5 + 748 * q^7 + 454 * q^8	\( 8 q + 5 q^{2} - 173 q^{4} + 42 q^{5} + 748 q^{7} + 454 q^{8} + 261 q^{10} + 1070 q^{11} - 6070 q^{14} + 3911 q^{16} - 7212 q^{17} - 24606 q^{19} - 78 q^{22} + 15224 q^{23} + 22274 q^{25} + 19044 q^{26} - 3415 q^{28} - 32524 q^{29} + 40200 q^{31} - 70203 q^{32} + 242436 q^{35} - 45670 q^{37} - 503310 q^{38} - 94941 q^{40} - 445660 q^{43} + 188829 q^{44} + 525804 q^{46} - 82884 q^{47} + 24116 q^{49} + 1218884 q^{50} + 722856 q^{52} + 13034 q^{53} - 127061 q^{56} - 159501 q^{58} - 1810362 q^{59} - 392856 q^{61} - 1410446 q^{64} + 389004 q^{65} + 384094 q^{67} + 1616346 q^{68} + 406005 q^{70} - 225688 q^{71} + 903078 q^{73} - 1185530 q^{74} + 327674 q^{77} - 559592 q^{79} - 847713 q^{80} + 347634 q^{82} + 1953576 q^{85} + 2302402 q^{86} + 304887 q^{88} + 1770036 q^{89} - 2960718 q^{91} + 113064 q^{92} - 1837620 q^{94} - 1160112 q^{95} - 5732467 q^{98}+O(q^{100}) \) 8 * q + 5 * q^2 - 173 * q^4 + 42 * q^5 + 748 * q^7 + 454 * q^8 + 261 * q^10 + 1070 * q^11 - 6070 * q^14 + 3911 * q^16 - 7212 * q^17 - 24606 * q^19 - 78 * q^22 + 15224 * q^23 + 22274 * q^25 + 19044 * q^26 - 3415 * q^28 - 32524 * q^29 + 40200 * q^31 - 70203 * q^32 + 242436 * q^35 - 45670 * q^37 - 503310 * q^38 - 94941 * q^40 - 445660 * q^43 + 188829 * q^44 + 525804 * q^46 - 82884 * q^47 + 24116 * q^49 + 1218884 * q^50 + 722856 * q^52 + 13034 * q^53 - 127061 * q^56 - 159501 * q^58 - 1810362 * q^59 - 392856 * q^61 - 1410446 * q^64 + 389004 * q^65 + 384094 * q^67 + 1616346 * q^68 + 406005 * q^70 - 225688 * q^71 + 903078 * q^73 - 1185530 * q^74 + 327674 * q^77 - 559592 * q^79 - 847713 * q^80 + 347634 * q^82 + 1953576 * q^85 + 2302402 * q^86 + 304887 * q^88 + 1770036 * q^89 - 2960718 * q^91 + 113064 * q^92 - 1837620 * q^94 - 1160112 * q^95 - 5732467 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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