LMFDB - Embedded newform 90.6.c.c.19.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [90,6,Mod(19,90)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(90, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("90.19");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 90 = 2 \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	90.c (of order $2$, degree $1$, 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:	$14.4345437832$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(i, \sqrt{1249})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 625x^{2} + 97344 $ x^4 + 625*x^2 + 97344
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{3}\cdot 5 $
Twist minimal:	no (minimal twist has level 30)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			19.4
Root			$18.1706i$ of defining polynomial
Character	$\chi$	$=$	90.19
Dual form			90.6.c.c.19.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+4.00000i q^{2} -16.0000 q^{4} +(16.1706 - 53.5118i) q^{5} +119.706i q^{7} -64.0000i q^{8} +O(q^{10})$	\(q+4.00000i q^{2} -16.0000 q^{4} +(16.1706 - 53.5118i) q^{5} +119.706i q^{7} -64.0000i q^{8} +(214.047 + 64.6824i) q^{10} -263.706 q^{11} +851.118i q^{13} -478.824 q^{14} +256.000 q^{16} +1287.12i q^{17} -2060.47 q^{19} +(-258.730 + 856.189i) q^{20} -1054.82i q^{22} -55.5284i q^{23} +(-2602.02 - 1730.64i) q^{25} -3404.47 q^{26} -1915.30i q^{28} -5986.06 q^{29} +4781.76 q^{31} +1024.00i q^{32} -5148.47 q^{34} +(6405.68 + 1935.72i) q^{35} +12150.4i q^{37} -8241.89i q^{38} +(-3424.75 - 1034.92i) q^{40} -18500.0 q^{41} -2188.47i q^{43} +4219.30 q^{44} +222.113 q^{46} -5597.76i q^{47} +2477.48 q^{49} +(6922.54 - 10408.1i) q^{50} -13617.9i q^{52} +26463.4i q^{53} +(-4264.28 + 14111.4i) q^{55} +7661.18 q^{56} -23944.2i q^{58} +20825.6 q^{59} +45525.8 q^{61} +19127.1i q^{62} -4096.00 q^{64} +(45544.8 + 13763.1i) q^{65} +34354.7i q^{67} -20593.9i q^{68} +(-7742.87 + 25622.7i) q^{70} +57489.6 q^{71} -26956.8i q^{73} -48601.7 q^{74} +32967.5 q^{76} -31567.2i q^{77} -42097.8 q^{79} +(4139.67 - 13699.0i) q^{80} -74000.0i q^{82} -101733. i q^{83} +(68876.0 + 20813.5i) q^{85} +8753.86 q^{86} +16877.2i q^{88} -65551.2 q^{89} -101884. q^{91} +888.454i q^{92} +22391.1 q^{94} +(-33319.1 + 110260. i) q^{95} +82780.7i q^{97} +9909.92i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 64 q^{4} - 6 q^{5}+O(q^{10}) $ 4 * q - 64 * q^4 - 6 * q^5	$ 4 q - 64 q^{4} - 6 q^{5} + 8 q^{10} - 348 q^{11} + 912 q^{14} + 1024 q^{16} + 240 q^{19} + 96 q^{20} - 9984 q^{25} - 5136 q^{26} - 4860 q^{29} + 23368 q^{31} - 12112 q^{34} + 37356 q^{35} - 128 q^{40} - 49968 q^{41} + 5568 q^{44} + 34816 q^{46} - 70668 q^{49} + 29952 q^{50} - 11968 q^{55} - 14592 q^{56} - 47460 q^{59} + 114248 q^{61} - 16384 q^{64} + 113052 q^{65} - 51328 q^{70} + 22152 q^{71} - 140688 q^{74} - 3840 q^{76} - 28440 q^{79} - 1536 q^{80} + 113924 q^{85} + 193344 q^{86} - 120840 q^{89} - 301512 q^{91} + 106528 q^{94} - 150240 q^{95}+O(q^{100}) $ 4 * q - 64 * q^4 - 6 * q^5 + 8 * q^10 - 348 * q^11 + 912 * q^14 + 1024 * q^16 + 240 * q^19 + 96 * q^20 - 9984 * q^25 - 5136 * q^26 - 4860 * q^29 + 23368 * q^31 - 12112 * q^34 + 37356 * q^35 - 128 * q^40 - 49968 * q^41 + 5568 * q^44 + 34816 * q^46 - 70668 * q^49 + 29952 * q^50 - 11968 * q^55 - 14592 * q^56 - 47460 * q^59 + 114248 * q^61 - 16384 * q^64 + 113052 * q^65 - 51328 * q^70 + 22152 * q^71 - 140688 * q^74 - 3840 * q^76 - 28440 * q^79 - 1536 * q^80 + 113924 * q^85 + 193344 * q^86 - 120840 * q^89 - 301512 * q^91 + 106528 * q^94 - 150240 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/90\mathbb{Z}\right)^\times$.

$n$	$11$	$37$
$\chi(n)$	$1$	$-1$

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 $

$2$			4.00000i			0.707107i
$2$			4.00000i			0.707107i
$3$		0			0
$3$		0			0
$4$	−16.0000			−0.500000
$5$	16.1706	−	53.5118i	0.289268	−	0.957248i
$5$	16.1706	−	53.5118i	0.289268	−	0.957248i
$6$		0			0
$7$			119.706i			0.923359i	0.887047	+	0.461680i	$0.152753\pi$
$7$			119.706i			0.923359i	−0.887047	+	0.461680i	$0.847247\pi$
$8$		−	64.0000i		−	0.353553i
$9$		0			0
$10$	214.047	+	64.6824i	0.676877	+	0.204544i
$11$	−263.706			−0.657110			−0.328555	−	0.944485i	$-0.606562\pi$
$11$	−263.706			−0.657110			−0.328555	+	0.944485i	$0.606562\pi$
$12$		0			0
$13$			851.118i			1.39679i	0.715712	+	0.698395i	$0.246102\pi$
$13$			851.118i			1.39679i	−0.715712	+	0.698395i	$0.753898\pi$
$14$	−478.824			−0.652914
$15$		0			0
$16$	256.000			0.250000
$17$			1287.12i			1.08018i	0.841607	+	0.540090i	$0.181610\pi$
$17$			1287.12i			1.08018i	−0.841607	+	0.540090i	$0.818390\pi$
$18$		0			0
$19$	−2060.47			−1.30943			−0.654716	−	0.755875i	$-0.727212\pi$
$19$	−2060.47			−1.30943			−0.654716	+	0.755875i	$0.727212\pi$
$20$	−258.730	+	856.189i	−0.144634	+	0.478624i
$21$		0			0
$22$		−	1054.82i		−	0.464647i
$23$		−	55.5284i		−	0.0218875i	−0.999940	−	0.0109437i	$-0.996516\pi$
$23$		−	55.5284i		−	0.0218875i	0.999940	−	0.0109437i	$-0.00348357\pi$
$24$		0			0
$25$	−2602.02	−	1730.64i	−0.832648	−	0.553803i
$26$	−3404.47			−0.987680
$27$		0			0
$28$		−	1915.30i		−	0.461680i
$29$	−5986.06			−1.32174			−0.660870	−	0.750500i	$-0.729813\pi$
$29$	−5986.06			−1.32174			−0.660870	+	0.750500i	$0.729813\pi$
$30$		0			0
$31$	4781.76			0.893684			0.446842	−	0.894613i	$-0.352549\pi$
$31$	4781.76			0.893684			0.446842	+	0.894613i	$0.352549\pi$
$32$			1024.00i			0.176777i
$33$		0			0
$34$	−5148.47			−0.763802
$35$	6405.68	+	1935.72i	0.883884	+	0.267099i
$36$		0			0
$37$			12150.4i			1.45911i	0.683924	+	0.729553i	$0.260272\pi$
$37$			12150.4i			1.45911i	−0.683924	+	0.729553i	$0.739728\pi$
$38$		−	8241.89i		−	0.925908i
$39$		0			0
$40$	−3424.75	−	1034.92i	−0.338438	−	0.102272i
$41$	−18500.0			−1.71875			−0.859374	−	0.511348i	$-0.829146\pi$
$41$	−18500.0			−1.71875			−0.859374	+	0.511348i	$0.829146\pi$
$42$		0			0
$43$		−	2188.47i		−	0.180496i	−0.995919	−	0.0902482i	$-0.971234\pi$
$43$		−	2188.47i		−	0.180496i	0.995919	−	0.0902482i	$-0.0287660\pi$
$44$	4219.30			0.328555
$45$		0			0
$46$	222.113			0.0154768
$47$		−	5597.76i		−	0.369632i	−0.982773	−	0.184816i	$-0.940831\pi$
$47$		−	5597.76i		−	0.369632i	0.982773	−	0.184816i	$-0.0591690\pi$
$48$		0			0
$49$	2477.48			0.147408
$50$	6922.54	−	10408.1i	0.391598	−	0.588771i
$51$		0			0
$52$		−	13617.9i		−	0.698395i
$53$			26463.4i			1.29406i	0.762463	+	0.647031i	$0.223990\pi$
$53$			26463.4i			1.29406i	−0.762463	+	0.647031i	$0.776010\pi$
$54$		0			0
$55$	−4264.28	+	14111.4i	−0.190081	+	0.629017i
$56$	7661.18			0.326457
$57$		0			0
$58$		−	23944.2i		−	0.934612i
$59$	20825.6			0.778875			0.389437	−	0.921053i	$-0.372669\pi$
$59$	20825.6			0.778875			0.389437	+	0.921053i	$0.372669\pi$
$60$		0			0
$61$	45525.8			1.56651			0.783254	−	0.621702i	$-0.213558\pi$
$61$	45525.8			1.56651			0.783254	+	0.621702i	$0.213558\pi$
$62$			19127.1i			0.631930i
$63$		0			0
$64$	−4096.00			−0.125000
$65$	45544.8	+	13763.1i	1.33708	+	0.404047i
$66$		0			0
$67$			34354.7i			0.934974i	0.884000	+	0.467487i	$0.154840\pi$
$67$			34354.7i			0.934974i	−0.884000	+	0.467487i	$0.845160\pi$
$68$		−	20593.9i		−	0.540090i
$69$		0			0
$70$	−7742.87	+	25622.7i	−0.188867	+	0.625000i
$71$	57489.6			1.35345			0.676726	−	0.736235i	$-0.263398\pi$
$71$	57489.6			1.35345			0.676726	+	0.736235i	$0.263398\pi$
$72$		0			0
$73$		−	26956.8i		−	0.592054i	−0.955180	−	0.296027i	$-0.904338\pi$
$73$		−	26956.8i		−	0.592054i	0.955180	−	0.296027i	$-0.0956619\pi$
$74$	−48601.7			−1.03174
$75$		0			0
$76$	32967.5			0.654716
$77$		−	31567.2i		−	0.606749i
$78$		0			0
$79$	−42097.8			−0.758912			−0.379456	−	0.925210i	$-0.623889\pi$
$79$	−42097.8			−0.758912			−0.379456	+	0.925210i	$0.623889\pi$
$80$	4139.67	−	13699.0i	0.0723171	−	0.239312i
$81$		0			0
$82$		−	74000.0i		−	1.21534i
$83$		−	101733.i		−	1.62094i	−0.585781	−	0.810469i	$-0.699212\pi$
$83$		−	101733.i		−	1.62094i	0.585781	−	0.810469i	$-0.300788\pi$
$84$		0			0
$85$	68876.0	+	20813.5i	1.03400	+	0.312462i
$86$	8753.86			0.127630
$87$		0			0
$88$			16877.2i			0.232324i
$89$	−65551.2			−0.877214			−0.438607	−	0.898679i	$-0.644528\pi$
$89$	−65551.2			−0.877214			−0.438607	+	0.898679i	$0.644528\pi$
$90$		0			0
$91$	−101884.			−1.28974
$92$			888.454i			0.0109437i
$93$		0			0
$94$	22391.1			0.261370
$95$	−33319.1	+	110260.i	−0.378777	+	1.25345i
$96$		0			0
$97$			82780.7i			0.893305i	0.894708	+	0.446653i	$0.147384\pi$
$97$			82780.7i			0.893305i	−0.894708	+	0.446653i	$0.852616\pi$
$98$			9909.92i			0.104233i
$99$		0			0
$100$	41632.4	+	27690.2i	0.416324	+	0.276902i
$101$	−14644.9			−0.142851			−0.0714255	−	0.997446i	$-0.522755\pi$
$101$	−14644.9			−0.142851			−0.0714255	+	0.997446i	$0.522755\pi$
$102$		0			0
$103$		−	199927.i		−	1.85686i	−0.371511	−	0.928429i	$-0.621160\pi$
$103$		−	199927.i		−	1.85686i	0.371511	−	0.928429i	$-0.378840\pi$
$104$	54471.5			0.493840
$105$		0			0
$106$	−105853.			−0.915041
$107$			34770.4i			0.293596i	0.989166	+	0.146798i	$0.0468967\pi$
$107$			34770.4i			0.293596i	−0.989166	+	0.146798i	$0.953103\pi$
$108$		0			0
$109$	19636.5			0.158306			0.0791529	−	0.996862i	$-0.474778\pi$
$109$	19636.5			0.158306			0.0791529	+	0.996862i	$0.474778\pi$
$110$	−56445.5	−	17057.1i	−0.444783	−	0.134408i
$111$		0			0
$112$			30644.7i			0.230840i
$113$			19716.6i			0.145256i	0.997359	+	0.0726282i	$0.0231386\pi$
$113$			19716.6i			0.145256i	−0.997359	+	0.0726282i	$0.976861\pi$
$114$		0			0
$115$	−2971.42	−	897.927i	−0.0209517	−	0.00633135i
$116$	95777.0			0.660870
$117$		0			0
$118$			83302.4i			0.550748i
$119$	−154076.			−0.997394
$120$		0			0
$121$	−91510.2			−0.568206
$122$			182103.i			1.10769i
$123$		0			0
$124$	−76508.2			−0.446842
$125$	−134686.	+	111254.i	−0.770986	+	0.636852i
$126$		0			0
$127$			55823.7i			0.307121i	0.988139	+	0.153560i	$0.0490739\pi$
$127$			55823.7i			0.307121i	−0.988139	+	0.153560i	$0.950926\pi$
$128$		−	16384.0i		−	0.0883883i
$129$		0			0
$130$	−55052.3	+	182179.i	−0.285705	+	0.945455i
$131$	−136377.			−0.694326			−0.347163	−	0.937805i	$-0.612855\pi$
$131$	−136377.			−0.694326			−0.347163	+	0.937805i	$0.612855\pi$
$132$		0			0
$133$		−	246651.i		−	1.20908i
$134$	−137419.			−0.661126
$135$		0			0
$136$	82375.5			0.381901
$137$		−	134387.i		−	0.611722i	−0.952076	−	0.305861i	$-0.901056\pi$
$137$		−	134387.i		−	0.611722i	0.952076	−	0.305861i	$-0.0989443\pi$
$138$		0			0
$139$	305523.			1.34124			0.670620	−	0.741801i	$-0.266028\pi$
$139$	305523.			1.34124			0.670620	+	0.741801i	$0.266028\pi$
$140$	−102491.	−	30971.5i	−0.441942	−	0.133549i
$141$		0			0
$142$			229958.i			0.957036i
$143$		−	224445.i		−	0.917846i
$144$		0			0
$145$	−96798.2	+	320325.i	−0.382338	+	1.26523i
$146$	107827.			0.418646
$147$		0			0
$148$		−	194407.i		−	0.729553i
$149$	349387.			1.28926			0.644630	−	0.764494i	$-0.277011\pi$
$149$	349387.			1.28926			0.644630	+	0.764494i	$0.277011\pi$
$150$		0			0
$151$	−314525.			−1.12257			−0.561284	−	0.827623i	$-0.689692\pi$
$151$	−314525.			−1.12257			−0.561284	+	0.827623i	$0.689692\pi$
$152$			131870.i			0.462954i
$153$		0			0
$154$	126269.			0.429036
$155$	77324.0	−	255881.i	0.258515	−	0.855477i
$156$		0			0
$157$			131302.i			0.425132i	0.977147	+	0.212566i	$0.0681820\pi$
$157$			131302.i			0.425132i	−0.977147	+	0.212566i	$0.931818\pi$
$158$		−	168391.i		−	0.536632i
$159$		0			0
$160$	54796.1	+	16558.7i	0.169219	+	0.0511359i
$161$	6647.08			0.0202100
$162$		0			0
$163$		−	633204.i		−	1.86670i	−0.358966	−	0.933351i	$-0.616871\pi$
$163$		−	633204.i		−	1.86670i	0.358966	−	0.933351i	$-0.383129\pi$
$164$	296000.			0.859374
$165$		0			0
$166$	406932.			1.14618
$167$			137690.i			0.382042i	0.981586	+	0.191021i	$0.0611799\pi$
$167$			137690.i			0.382042i	−0.981586	+	0.191021i	$0.938820\pi$
$168$		0			0
$169$	−353109.			−0.951024
$170$	−83253.9	+	275504.i	−0.220944	+	0.731148i
$171$		0			0
$172$			35015.5i			0.0902482i
$173$			90278.1i			0.229333i	0.993404	+	0.114667i	$0.0365800\pi$
$173$			90278.1i			0.229333i	−0.993404	+	0.114667i	$0.963420\pi$
$174$		0			0
$175$	207167.	−	311478.i	0.511359	−	0.768833i
$176$	−67508.7			−0.164278
$177$		0			0
$178$		−	262205.i		−	0.620284i
$179$	601579.			1.40333			0.701665	−	0.712507i	$-0.252440\pi$
$179$	601579.			1.40333			0.701665	+	0.712507i	$0.252440\pi$
$180$		0			0
$181$	447746.			1.01586			0.507931	−	0.861398i	$-0.330410\pi$
$181$	447746.			1.01586			0.507931	+	0.861398i	$0.330410\pi$
$182$		−	407536.i		−	0.911984i
$183$		0			0
$184$	−3553.81			−0.00773838
$185$	650190.	+	196479.i	1.39673	+	0.422073i
$186$		0			0
$187$		−	339421.i		−	0.709797i
$188$			89564.2i			0.184816i
$189$		0			0
$190$	−441038.	−	133276.i	−0.886323	−	0.267836i
$191$	−673846.			−1.33653			−0.668263	−	0.743925i	$-0.732962\pi$
$191$	−673846.			−1.33653			−0.668263	+	0.743925i	$0.732962\pi$
$192$		0			0
$193$			255962.i			0.494632i	0.968935	+	0.247316i	$0.0795485\pi$
$193$			255962.i			0.494632i	−0.968935	+	0.247316i	$0.920451\pi$
$194$	−331123.			−0.631662
$195$		0			0
$196$	−39639.7			−0.0737038
$197$			196202.i			0.360195i	0.983649	+	0.180097i	$0.0576413\pi$
$197$			196202.i			0.360195i	−0.983649	+	0.180097i	$0.942359\pi$
$198$		0			0
$199$	−118265.			−0.211702			−0.105851	−	0.994382i	$-0.533757\pi$
$199$	−118265.			−0.211702			−0.105851	+	0.994382i	$0.533757\pi$
$200$	−110761.	+	166530.i	−0.195799	+	0.294385i
$201$		0			0
$202$		−	58579.7i		−	0.101011i
$203$		−	716567.i		−	1.22044i
$204$		0			0
$205$	−299156.	+	989968.i	−0.497179	+	1.64527i
$206$	799708.			1.31300
$207$		0			0
$208$			217886.i			0.349198i
$209$	543359.			0.860441
$210$		0			0
$211$	910278.			1.40756			0.703781	−	0.710417i	$-0.251493\pi$
$211$	910278.			1.40756			0.703781	+	0.710417i	$0.251493\pi$
$212$		−	423414.i		−	0.647031i
$213$		0			0
$214$	−139082.			−0.207604
$215$	−117109.	−	35388.8i	−0.172780	−	0.0522119i
$216$		0			0
$217$			572406.i			0.825191i
$218$			78545.9i			0.111939i
$219$		0			0
$220$	68228.5	−	225782.i	0.0950406	−	0.314509i
$221$	−1.09549e6			−1.50879
$222$		0			0
$223$			1.04513e6i			1.40737i	0.710514	+	0.703683i	$0.248462\pi$
$223$			1.04513e6i			1.40737i	−0.710514	+	0.703683i	$0.751538\pi$
$224$	−122579.			−0.163228
$225$		0			0
$226$	−78866.3			−0.102712
$227$			869120.i			1.11948i	0.828669	+	0.559739i	$0.189098\pi$
$227$			869120.i			1.11948i	−0.828669	+	0.559739i	$0.810902\pi$
$228$		0			0
$229$	1.39907e6			1.76299			0.881494	−	0.472195i	$-0.156538\pi$
$229$	1.39907e6			1.76299			0.881494	+	0.472195i	$0.156538\pi$
$230$	3591.71	−	11885.7i	0.00447694	−	0.0148151i
$231$		0			0
$232$			383108.i			0.467306i
$233$			403494.i			0.486908i	0.969912	+	0.243454i	$0.0782805\pi$
$233$			403494.i			0.486908i	−0.969912	+	0.243454i	$0.921720\pi$
$234$		0			0
$235$	−299546.	−	90519.2i	−0.353830	−	0.106923i
$236$	−333210.			−0.389437
$237$		0			0
$238$		−	616303.i		−	0.705264i
$239$	−611076.			−0.691991			−0.345995	−	0.938236i	$-0.612459\pi$
$239$	−611076.			−0.691991			−0.345995	+	0.938236i	$0.612459\pi$
$240$		0			0
$241$	−1.50639e6			−1.67068			−0.835342	−	0.549730i	$-0.814730\pi$
$241$	−1.50639e6			−1.67068			−0.835342	+	0.549730i	$0.814730\pi$
$242$		−	366041.i		−	0.401782i
$243$		0			0
$244$	−728412.			−0.783254
$245$	40062.3	−	132574.i	0.0426404	−	0.141106i
$246$		0			0
$247$		−	1.75370e6i		−	1.82900i
$248$		−	306033.i		−	0.315965i
$249$		0			0
$250$	−445014.	−	538743.i	−0.450323	−	0.545169i
$251$	−558727.			−0.559777			−0.279889	−	0.960032i	$-0.590298\pi$
$251$	−558727.			−0.559777			−0.279889	+	0.960032i	$0.590298\pi$
$252$		0			0
$253$			14643.2i			0.0143825i
$254$	−223295.			−0.217167
$255$		0			0
$256$	65536.0			0.0625000
$257$			680108.i			0.642310i	0.947027	+	0.321155i	$0.104071\pi$
$257$			680108.i			0.642310i	−0.947027	+	0.321155i	$0.895929\pi$
$258$		0			0
$259$	−1.45448e6			−1.34728
$260$	−728718.	−	220209.i	−0.668538	−	0.202024i
$261$		0			0
$262$		−	545508.i		−	0.490962i
$263$			428668.i			0.382148i	0.981576	+	0.191074i	$0.0611970\pi$
$263$			428668.i			0.382148i	−0.981576	+	0.191074i	$0.938803\pi$
$264$		0			0
$265$	1.41610e6	+	427928.i	1.23874	+	0.374332i
$266$	986603.			0.854945
$267$		0			0
$268$		−	549675.i		−	0.467487i
$269$	−1.51936e6			−1.28020			−0.640101	−	0.768291i	$-0.721108\pi$
$269$	−1.51936e6			−1.28020			−0.640101	+	0.768291i	$0.721108\pi$
$270$		0			0
$271$	−1.34595e6			−1.11329			−0.556643	−	0.830752i	$-0.687911\pi$
$271$	−1.34595e6			−1.11329			−0.556643	+	0.830752i	$0.687911\pi$
$272$			329502.i			0.270045i
$273$		0			0
$274$	537546.			0.432553
$275$	686169.	+	456379.i	0.547141	+	0.363910i
$276$		0			0
$277$			885541.i			0.693440i	0.937969	+	0.346720i	$0.112705\pi$
$277$			885541.i			0.693440i	−0.937969	+	0.346720i	$0.887295\pi$
$278$			1.22209e6i			0.948400i
$279$		0			0
$280$	123886.	−	409964.i	0.0944336	−	0.312500i
$281$	1.26803e6			0.957999			0.478999	−	0.877815i	$-0.341000\pi$
$281$	1.26803e6			0.957999			0.478999	+	0.877815i	$0.341000\pi$
$282$		0			0
$283$			685833.i			0.509040i	0.967067	+	0.254520i	$0.0819175\pi$
$283$			685833.i			0.509040i	−0.967067	+	0.254520i	$0.918082\pi$
$284$	−919833.			−0.676726
$285$		0			0
$286$	897779.			0.649015
$287$		−	2.21456e6i		−	1.58702i
$288$		0			0
$289$	−236816.			−0.166788
$290$	−1.28130e6	−	387193.i	−0.894655	−	0.270354i
$291$		0			0
$292$			431309.i			0.296027i
$293$			1.66857e6i			1.13547i	0.823211	+	0.567736i	$0.192181\pi$
$293$			1.66857e6i			1.13547i	−0.823211	+	0.567736i	$0.807819\pi$
$294$		0			0
$295$	336762.	−	1.11442e6i	0.225304	−	0.745576i
$296$	777626.			0.515872
$297$		0			0
$298$			1.39755e6i			0.911645i
$299$	47261.2			0.0305722
$300$		0			0
$301$	261972.			0.166663
$302$		−	1.25810e6i		−	0.793776i
$303$		0			0
$304$	−527481.			−0.327358
$305$	736179.	−	2.43617e6i	0.453141	−	1.49954i
$306$		0			0
$307$			560776.i			0.339581i	0.985480	+	0.169790i	$0.0543091\pi$
$307$			560776.i			0.339581i	−0.985480	+	0.169790i	$0.945691\pi$
$308$			505075.i			0.303374i
$309$		0			0
$310$	1.02352e6	+	309296.i	0.604914	+	0.182797i
$311$	1.33943e6			0.785268			0.392634	−	0.919695i	$-0.371564\pi$
$311$	1.33943e6			0.785268			0.392634	+	0.919695i	$0.371564\pi$
$312$		0			0
$313$			621225.i			0.358417i	0.983811	+	0.179208i	$0.0573536\pi$
$313$			621225.i			0.358417i	−0.983811	+	0.179208i	$0.942646\pi$
$314$	−525210.			−0.300614
$315$		0			0
$316$	673565.			0.379456
$317$			300282.i			0.167834i	0.996473	+	0.0839172i	$0.0267431\pi$
$317$			300282.i			0.167834i	−0.996473	+	0.0839172i	$0.973257\pi$
$318$		0			0
$319$	1.57856e6			0.868529
$320$	−66234.8	+	219184.i	−0.0361586	+	0.119656i
$321$		0			0
$322$			26588.3i			0.0142906i
$323$		−	2.65207e6i		−	1.41442i
$324$		0			0
$325$	1.47297e6	−	2.21463e6i	0.773547	−	1.16303i
$326$	2.53282e6			1.31996
$327$		0			0
$328$			1.18400e6i			0.607669i
$329$	670086.			0.341303
$330$		0			0
$331$	−1.94914e6			−0.977851			−0.488925	−	0.872326i	$-0.662611\pi$
$331$	−1.94914e6			−0.977851			−0.488925	+	0.872326i	$0.662611\pi$
$332$			1.62773e6i			0.810469i
$333$		0			0
$334$	−550760.			−0.270145
$335$	1.83838e6	+	555536.i	0.895002	+	0.270458i
$336$		0			0
$337$		−	253373.i		−	0.121530i	−0.998152	−	0.0607652i	$-0.980646\pi$
$337$		−	253373.i		−	0.121530i	0.998152	−	0.0607652i	$-0.0193541\pi$
$338$		−	1.41243e6i		−	0.672476i
$339$		0			0
$340$	−1.10202e6	−	333015.i	−0.517000	−	0.156231i
$341$	−1.26098e6			−0.587249
$342$		0			0
$343$			2.30847e6i			1.05947i
$344$	−140062.			−0.0638151
$345$		0			0
$346$	−361112.			−0.162163
$347$			1.60688e6i			0.716406i	0.933644	+	0.358203i	$0.116610\pi$
$347$			1.60688e6i			0.716406i	−0.933644	+	0.358203i	$0.883390\pi$
$348$		0			0
$349$	608374.			0.267367			0.133683	−	0.991024i	$-0.457320\pi$
$349$	608374.			0.267367			0.133683	+	0.991024i	$0.457320\pi$
$350$	1.24591e6	+	828669.i	0.543647	+	0.361586i
$351$		0			0
$352$		−	270035.i		−	0.116162i
$353$			3.83773e6i			1.63922i	0.572919	+	0.819612i	$0.305811\pi$
$353$			3.83773e6i			1.63922i	−0.572919	+	0.819612i	$0.694189\pi$
$354$		0			0
$355$	929640.	−	3.07637e6i	0.391511	−	1.29559i
$356$	1.04882e6			0.438607
$357$		0			0
$358$			2.40632e6i			0.992305i
$359$	2.13850e6			0.875738			0.437869	−	0.899039i	$-0.355733\pi$
$359$	2.13850e6			0.875738			0.437869	+	0.899039i	$0.355733\pi$
$360$		0			0
$361$	1.76944e6			0.714610
$362$			1.79098e6i			0.718323i
$363$		0			0
$364$	1.63014e6			0.644870
$365$	−1.44251e6	−	435908.i	−0.566743	−	0.171263i
$366$		0			0
$367$		−	4.50396e6i		−	1.74554i	−0.488133	−	0.872769i	$-0.662322\pi$
$367$		−	4.50396e6i		−	1.74554i	0.488133	−	0.872769i	$-0.337678\pi$
$368$		−	14215.3i		−	0.00547186i
$369$		0			0
$370$	−785918.	+	2.60076e6i	−0.298451	+	0.987634i
$371$	−3.16782e6			−1.19488
$372$		0			0
$373$		−	1.15223e6i		−	0.428811i	−0.976745	−	0.214406i	$-0.931219\pi$
$373$		−	1.15223e6i		−	0.428811i	0.976745	−	0.214406i	$-0.0687815\pi$
$374$	1.35768e6			0.501902
$375$		0			0
$376$	−358257.			−0.130685
$377$		−	5.09484e6i		−	1.84619i
$378$		0			0
$379$	−797740.			−0.285275			−0.142637	−	0.989775i	$-0.545558\pi$
$379$	−797740.			−0.285275			−0.142637	+	0.989775i	$0.545558\pi$
$380$	533105.	−	1.76415e6i	0.189389	−	0.626725i
$381$		0			0
$382$		−	2.69538e6i		−	0.945066i
$383$		−	1.02124e6i		−	0.355737i	−0.984054	−	0.177869i	$-0.943080\pi$
$383$		−	1.02124e6i		−	0.355737i	0.984054	−	0.177869i	$-0.0569202\pi$
$384$		0			0
$385$	−1.68922e6	−	510460.i	−0.580809	−	0.175513i
$386$	−1.02385e6			−0.349757
$387$		0			0
$388$		−	1.32449e6i		−	0.446653i
$389$	−1.06820e6			−0.357914			−0.178957	−	0.983857i	$-0.557272\pi$
$389$	−1.06820e6			−0.357914			−0.178957	+	0.983857i	$0.557272\pi$
$390$		0			0
$391$	71471.5			0.0236424
$392$		−	158559.i		−	0.0521165i
$393$		0			0
$394$	−784807.			−0.254696
$395$	−680746.	+	2.25273e6i	−0.219529	+	0.726467i
$396$		0			0
$397$		−	109330.i		−	0.0348148i	−0.999848	−	0.0174074i	$-0.994459\pi$
$397$		−	109330.i		−	0.0348148i	0.999848	−	0.0174074i	$-0.00554123\pi$
$398$		−	473061.i		−	0.149696i
$399$		0			0
$400$	−666118.	−	443043.i	−0.208162	−	0.138451i
$401$	−1.42131e6			−0.441395			−0.220697	−	0.975342i	$-0.570833\pi$
$401$	−1.42131e6			−0.441395			−0.220697	+	0.975342i	$0.570833\pi$
$402$		0			0
$403$			4.06985e6i			1.24829i
$404$	234319.			0.0714255
$405$		0			0
$406$	2.86627e6			0.862982
$407$		−	3.20414e6i		−	0.958793i
$408$		0			0
$409$	−3.07511e6			−0.908975			−0.454487	−	0.890753i	$-0.650177\pi$
$409$	−3.07511e6			−0.908975			−0.454487	+	0.890753i	$0.650177\pi$
$410$	−3.95987e6	−	1.19662e6i	−1.16338	−	0.351559i
$411$		0			0
$412$			3.19883e6i			0.928429i
$413$			2.49295e6i			0.719181i
$414$		0			0
$415$	−5.44391e6	−	1.64508e6i	−1.55164	−	0.468886i
$416$	−871545.			−0.246920
$417$		0			0
$418$			2.17343e6i			0.608423i
$419$	3.06462e6			0.852789			0.426395	−	0.904537i	$-0.359783\pi$
$419$	3.06462e6			0.852789			0.426395	+	0.904537i	$0.359783\pi$
$420$		0			0
$421$	837782.			0.230370			0.115185	−	0.993344i	$-0.463254\pi$
$421$	837782.			0.230370			0.115185	+	0.993344i	$0.463254\pi$
$422$			3.64111e6i			0.995297i
$423$		0			0
$424$	1.69366e6			0.457520
$425$	2.22753e6	−	3.34911e6i	0.598207	−	0.899409i
$426$		0			0
$427$			5.44971e6i			1.44645i
$428$		−	556326.i		−	0.146798i
$429$		0			0
$430$	141555.	−	468435.i	0.0369194	−	0.122174i
$431$	−5.90720e6			−1.53175			−0.765876	−	0.642988i	$-0.777694\pi$
$431$	−5.90720e6			−1.53175			−0.765876	+	0.642988i	$0.777694\pi$
$432$		0			0
$433$		−	1.84995e6i		−	0.474177i	−0.971488	−	0.237089i	$-0.923807\pi$
$433$		−	1.84995e6i		−	0.474177i	0.971488	−	0.237089i	$-0.0761932\pi$
$434$	−2.28962e6			−0.583498
$435$		0			0
$436$	−314183.			−0.0791529
$437$			114415.i			0.0286601i
$438$		0			0
$439$	2.81172e6			0.696323			0.348161	−	0.937435i	$-0.386806\pi$
$439$	2.81172e6			0.696323			0.348161	+	0.937435i	$0.386806\pi$
$440$	903128.	+	272914.i	0.222391	+	0.0672039i
$441$		0			0
$442$		−	4.38196e6i		−	1.06687i
$443$			2.41386e6i			0.584391i	0.956359	+	0.292196i	$0.0943858\pi$
$443$			2.41386e6i			0.584391i	−0.956359	+	0.292196i	$0.905614\pi$
$444$		0			0
$445$	−1.06000e6	+	3.50776e6i	−0.253750	+	0.839711i
$446$	−4.18051e6			−0.995158
$447$		0			0
$448$		−	490316.i		−	0.115420i
$449$	−507124.			−0.118713			−0.0593565	−	0.998237i	$-0.518905\pi$
$449$	−507124.			−0.118713			−0.0593565	+	0.998237i	$0.518905\pi$
$450$		0			0
$451$	4.87856e6			1.12941
$452$		−	315465.i		−	0.0726282i
$453$		0			0
$454$	−3.47648e6			−0.791590
$455$	−1.64752e6	+	5.45199e6i	−0.373081	+	1.23460i
$456$		0			0
$457$			1.09879e6i			0.246106i	0.992400	+	0.123053i	$0.0392686\pi$
$457$			1.09879e6i			0.246106i	−0.992400	+	0.123053i	$0.960731\pi$
$458$			5.59626e6i			1.24662i
$459$		0			0
$460$	47542.7	+	14366.8i	0.0104759	+	0.00316567i
$461$	−106066.			−0.0232446			−0.0116223	−	0.999932i	$-0.503700\pi$
$461$	−106066.			−0.0232446			−0.0116223	+	0.999932i	$0.503700\pi$
$462$		0			0
$463$		−	1.36176e6i		−	0.295222i	−0.989045	−	0.147611i	$-0.952842\pi$
$463$		−	1.36176e6i		−	0.295222i	0.989045	−	0.147611i	$-0.0471584\pi$
$464$	−1.53243e6			−0.330435
$465$		0			0
$466$	−1.61397e6			−0.344296
$467$			2.18710e6i			0.464062i	0.972708	+	0.232031i	$0.0745371\pi$
$467$			2.18710e6i			0.464062i	−0.972708	+	0.232031i	$0.925463\pi$
$468$		0			0
$469$	−4.11246e6			−0.863316
$470$	362077.	−	1.19819e6i	0.0756060	−	0.250195i
$471$		0			0
$472$		−	1.33284e6i		−	0.275374i
$473$			577111.i			0.118606i
$474$		0			0
$475$	5.36140e6	+	3.56592e6i	1.09029	+	0.725167i
$476$	2.46521e6			0.498697
$477$		0			0
$478$		−	2.44430e6i		−	0.489311i
$479$	1.01595e6			0.202318			0.101159	−	0.994870i	$-0.467745\pi$
$479$	1.01595e6			0.202318			0.101159	+	0.994870i	$0.467745\pi$
$480$		0			0
$481$	−1.03414e7			−2.03807
$482$		−	6.02555e6i		−	1.18135i
$483$		0			0
$484$	1.46416e6			0.284103
$485$	4.42974e6	+	1.33861e6i	0.855114	+	0.258405i
$486$		0			0
$487$			2.02339e6i			0.386596i	0.981140	+	0.193298i	$0.0619185\pi$
$487$			2.02339e6i			0.386596i	−0.981140	+	0.193298i	$0.938082\pi$
$488$		−	2.91365e6i		−	0.553844i
$489$		0			0
$490$	530298.	+	160249.i	0.0997768	+	0.0301513i
$491$	4.22487e6			0.790878			0.395439	−	0.918492i	$-0.370592\pi$
$491$	4.22487e6			0.790878			0.395439	+	0.918492i	$0.370592\pi$
$492$		0			0
$493$		−	7.70477e6i		−	1.42772i
$494$	7.01482e6			1.29330
$495$		0			0
$496$	1.22413e6			0.223421
$497$			6.88184e6i			1.24972i
$498$		0			0
$499$	6.71381e6			1.20703			0.603515	−	0.797352i	$-0.293767\pi$
$499$	6.71381e6			1.20703			0.603515	+	0.797352i	$0.293767\pi$
$500$	2.15497e6	−	1.78006e6i	0.385493	−	0.318426i
$501$		0			0
$502$		−	2.23491e6i		−	0.395822i
$503$		−	5.36486e6i		−	0.945450i	−0.881210	−	0.472725i	$-0.843270\pi$
$503$		−	5.36486e6i		−	0.945450i	0.881210	−	0.472725i	$-0.156730\pi$
$504$		0			0
$505$	−236817.	+	783676.i	−0.0413223	+	0.136744i
$506$	−58572.6			−0.0101699
$507$		0			0
$508$		−	893179.i		−	0.153560i
$509$	1.10627e6			0.189264			0.0946318	−	0.995512i	$-0.469833\pi$
$509$	1.10627e6			0.189264			0.0946318	+	0.995512i	$0.469833\pi$
$510$		0			0
$511$	3.22689e6			0.546679
$512$			262144.i			0.0441942i
$513$		0			0
$514$	−2.72043e6			−0.454182
$515$	−1.06985e7	−	3.23294e6i	−1.77747	−	0.537130i
$516$		0			0
$517$			1.47616e6i			0.242889i
$518$		−	5.81791e6i		−	0.952670i
$519$		0			0
$520$	880837.	−	2.91487e6i	0.142852	−	0.472727i
$521$	3.11641e6			0.502991			0.251495	−	0.967859i	$-0.419078\pi$
$521$	3.11641e6			0.502991			0.251495	+	0.967859i	$0.419078\pi$
$522$		0			0
$523$			9.29324e6i			1.48564i	0.669492	+	0.742819i	$0.266512\pi$
$523$			9.29324e6i			1.48564i	−0.669492	+	0.742819i	$0.733488\pi$
$524$	2.18203e6			0.347163
$525$		0			0
$526$	−1.71467e6			−0.270219
$527$			6.15469e6i			0.965339i
$528$		0			0
$529$	6.43326e6			0.999521
$530$	−1.71171e6	+	5.66441e6i	−0.264692	+	0.875921i
$531$		0			0
$532$			3.94641e6i			0.604538i
$533$		−	1.57457e7i		−	2.40073i
$534$		0			0
$535$	1.86063e6	+	562258.i	0.281044	+	0.0849281i
$536$	2.19870e6			0.330563
$537$		0			0
$538$		−	6.07742e6i		−	0.905240i
$539$	−653326.			−0.0968631
$540$		0			0
$541$	1.00152e7			1.47118			0.735592	−	0.677425i	$-0.236904\pi$
$541$	1.00152e7			1.47118			0.735592	+	0.677425i	$0.236904\pi$
$542$		−	5.38382e6i		−	0.787213i
$543$		0			0
$544$	−1.31801e6			−0.190951
$545$	317533.	−	1.05078e6i	0.0457929	−	0.151538i
$546$		0			0
$547$			605416.i			0.0865138i	0.999064	+	0.0432569i	$0.0137734\pi$
$547$			605416.i			0.0865138i	−0.999064	+	0.0432569i	$0.986227\pi$
$548$			2.15018e6i			0.305861i
$549$		0			0
$550$	−1.82552e6	+	2.74468e6i	−0.257323	+	0.386887i
$551$	1.23341e7			1.73073
$552$		0			0
$553$		−	5.03936e6i		−	0.700749i
$554$	−3.54216e6			−0.490336
$555$		0			0
$556$	−4.88836e6			−0.670620
$557$		−	9.21693e6i		−	1.25878i	−0.777091	−	0.629388i	$-0.783306\pi$
$557$		−	9.21693e6i		−	1.25878i	0.777091	−	0.629388i	$-0.216694\pi$
$558$		0			0
$559$	1.86264e6			0.252116
$560$	1.63985e6	+	495544.i	0.220971	+	0.0667747i
$561$		0			0
$562$			5.07213e6i			0.677407i
$563$			9.44213e6i			1.25545i	0.778436	+	0.627724i	$0.216014\pi$
$563$			9.44213e6i			1.25545i	−0.778436	+	0.627724i	$0.783986\pi$
$564$		0			0
$565$	1.05507e6	+	318829.i	0.139046	+	0.0420181i
$566$	−2.74333e6			−0.359946
$567$		0			0
$568$		−	3.67933e6i		−	0.478518i
$569$	−1.24216e6			−0.160841			−0.0804206	−	0.996761i	$-0.525626\pi$
$569$	−1.24216e6			−0.160841			−0.0804206	+	0.996761i	$0.525626\pi$
$570$		0			0
$571$	−1.35633e7			−1.74090			−0.870450	−	0.492256i	$-0.836172\pi$
$571$	−1.35633e7			−1.74090			−0.870450	+	0.492256i	$0.836172\pi$
$572$			3.59112e6i			0.458923i
$573$		0			0
$574$	8.85824e6			1.12219
$575$	−96099.3	+	144486.i	−0.0121213	+	0.0182245i
$576$		0			0
$577$		−	6.75669e6i		−	0.844879i	−0.906391	−	0.422440i	$-0.861174\pi$
$577$		−	6.75669e6i		−	0.844879i	0.906391	−	0.422440i	$-0.138826\pi$
$578$		−	947262.i		−	0.117937i
$579$		0			0
$580$	1.54877e6	−	5.12520e6i	0.191169	−	0.632617i
$581$	1.21780e7			1.49671
$582$		0			0
$583$		−	6.97855e6i		−	0.850342i
$584$	−1.72524e6			−0.209323
$585$		0			0
$586$	−6.67430e6			−0.802900
$587$			1.08655e7i			1.30153i	0.759280	+	0.650764i	$0.225551\pi$
$587$			1.08655e7i			1.30153i	−0.759280	+	0.650764i	$0.774449\pi$
$588$		0			0
$589$	−9.85269e6			−1.17022
$590$	4.45766e6	+	1.34705e6i	0.527202	+	0.159314i
$591$		0			0
$592$			3.11051e6i			0.364776i
$593$			1.20061e6i			0.140205i	0.997540	+	0.0701027i	$0.0223327\pi$
$593$			1.20061e6i			0.140205i	−0.997540	+	0.0701027i	$0.977667\pi$
$594$		0			0
$595$	−2.49150e6	+	8.24487e6i	−0.288515	+	0.954753i
$596$	−5.59019e6			−0.644630
$597$		0			0
$598$			189045.i			0.0216178i
$599$	−6.77826e6			−0.771882			−0.385941	−	0.922523i	$-0.626123\pi$
$599$	−6.77826e6			−0.771882			−0.385941	+	0.922523i	$0.626123\pi$
$600$		0			0
$601$	6.32426e6			0.714207			0.357103	−	0.934065i	$-0.383764\pi$
$601$	6.32426e6			0.714207			0.357103	+	0.934065i	$0.383764\pi$
$602$			1.04789e6i			0.117849i
$603$		0			0
$604$	5.03240e6			0.561284
$605$	−1.47977e6	+	4.89687e6i	−0.164364	+	0.543914i
$606$		0			0
$607$			2.63732e6i			0.290530i	0.989393	+	0.145265i	$0.0464035\pi$
$607$			2.63732e6i			0.290530i	−0.989393	+	0.145265i	$0.953596\pi$
$608$		−	2.10992e6i		−	0.231477i
$609$		0			0
$610$	9.74466e6	+	2.94472e6i	1.06033	+	0.320419i
$611$	4.76436e6			0.516299
$612$		0			0
$613$		−	1.43305e7i		−	1.54031i	−0.637854	−	0.770157i	$-0.720178\pi$
$613$		−	1.43305e7i		−	1.54031i	0.637854	−	0.770157i	$-0.279822\pi$
$614$	−2.24310e6			−0.240120
$615$		0			0
$616$	−2.02030e6			−0.214518
$617$		−	29265.6i		−	0.00309489i	−0.999999	−	0.00154744i	$-0.999507\pi$
$617$		−	29265.6i		−	0.00309489i	0.999999	−	0.00154744i	$-0.000492567\pi$
$618$		0			0
$619$	−7.84138e6			−0.822557			−0.411279	−	0.911510i	$-0.634918\pi$
$619$	−7.84138e6			−0.822557			−0.411279	+	0.911510i	$0.634918\pi$
$620$	−1.23718e6	+	4.09409e6i	−0.129257	+	0.427739i
$621$		0			0
$622$			5.35771e6i			0.555269i
$623$		−	7.84687e6i		−	0.809984i
$624$		0			0
$625$	3.77543e6	+	9.00631e6i	0.386604	+	0.922246i
$626$	−2.48490e6			−0.253439
$627$		0			0
$628$		−	2.10084e6i		−	0.212566i
$629$	−1.56390e7			−1.57610
$630$		0			0
$631$	−668942.			−0.0668829			−0.0334414	−	0.999441i	$-0.510647\pi$
$631$	−668942.			−0.0668829			−0.0334414	+	0.999441i	$0.510647\pi$
$632$			2.69426e6i			0.268316i
$633$		0			0
$634$	−1.20113e6			−0.118677
$635$	2.98722e6	+	902702.i	0.293991	+	0.0888403i
$636$		0			0
$637$			2.10863e6i			0.205898i
$638$			6.31424e6i			0.614143i
$639$		0			0
$640$	−876737.	−	264939.i	−0.0846096	−	0.0255680i
$641$	−1.26732e7			−1.21826			−0.609130	−	0.793070i	$-0.708481\pi$
$641$	−1.26732e7			−1.21826			−0.609130	+	0.793070i	$0.708481\pi$
$642$		0			0
$643$			6.26256e6i			0.597344i	0.954356	+	0.298672i	$0.0965436\pi$
$643$			6.26256e6i			0.597344i	−0.954356	+	0.298672i	$0.903456\pi$
$644$	−106353.			−0.0101050
$645$		0			0
$646$	1.06083e7			1.00015
$647$		−	8.69452e6i		−	0.816554i	−0.912858	−	0.408277i	$-0.866130\pi$
$647$		−	8.69452e6i		−	0.816554i	0.912858	−	0.408277i	$-0.133870\pi$
$648$		0			0
$649$	−5.49184e6			−0.511807
$650$	8.85852e6	+	5.89190e6i	0.822390	+	0.546981i
$651$		0			0
$652$			1.01313e7i			0.933351i
$653$			4.56532e6i			0.418976i	0.977811	+	0.209488i	$0.0671796\pi$
$653$			4.56532e6i			0.418976i	−0.977811	+	0.209488i	$0.932820\pi$
$654$		0			0
$655$	−2.20530e6	+	7.29778e6i	−0.200847	+	0.664642i
$656$	−4.73600e6			−0.429687
$657$		0			0
$658$			2.68034e6i			0.241338i
$659$	1.00273e7			0.899437			0.449718	−	0.893170i	$-0.351524\pi$
$659$	1.00273e7			0.899437			0.449718	+	0.893170i	$0.351524\pi$
$660$		0			0
$661$	−8.14715e6			−0.725274			−0.362637	−	0.931930i	$-0.618123\pi$
$661$	−8.14715e6			−0.725274			−0.362637	+	0.931930i	$0.618123\pi$
$662$		−	7.79655e6i		−	0.691445i
$663$		0			0
$664$	−6.51091e6			−0.573088
$665$	−1.31987e7	−	3.98849e6i	−1.15738	−	0.349747i
$666$		0			0
$667$			332396.i			0.0289295i
$668$		−	2.20304e6i		−	0.191021i
$669$		0			0
$670$	−2.22214e6	+	7.35353e6i	−0.191243	+	0.632862i
$671$	−1.20054e7			−1.02937
$672$		0			0
$673$		−	1.16421e6i		−	0.0990818i	−0.998772	−	0.0495409i	$-0.984224\pi$
$673$		−	1.16421e6i		−	0.0990818i	0.998772	−	0.0495409i	$-0.0157758\pi$
$674$	1.01349e6			0.0859350
$675$		0			0
$676$	5.64974e6			0.475512
$677$			1.20869e7i			1.01355i	0.862079	+	0.506775i	$0.169162\pi$
$677$			1.20869e7i			1.01355i	−0.862079	+	0.506775i	$0.830838\pi$
$678$		0			0
$679$	−9.90934e6			−0.824841
$680$	1.33206e6	−	4.40806e6i	0.110472	−	0.365574i
$681$		0			0
$682$		−	5.04392e6i		−	0.415248i
$683$		−	7.57524e6i		−	0.621362i	−0.950514	−	0.310681i	$-0.899443\pi$
$683$		−	7.57524e6i		−	0.621362i	0.950514	−	0.310681i	$-0.100557\pi$
$684$		0			0
$685$	−7.19126e6	−	2.17311e6i	−0.585570	−	0.176952i
$686$	−9.23387e6			−0.749158
$687$		0			0
$688$		−	560247.i		−	0.0451241i
$689$	−2.25234e7			−1.80753
$690$		0			0
$691$	2.32589e7			1.85308			0.926539	−	0.376198i	$-0.122769\pi$
$691$	2.32589e7			1.85308			0.926539	+	0.376198i	$0.122769\pi$
$692$		−	1.44445e6i		−	0.114667i
$693$		0			0
$694$	−6.42751e6			−0.506575
$695$	4.94049e6	−	1.63491e7i	0.387978	−	1.28390i
$696$		0			0
$697$		−	2.38117e7i		−	1.85656i
$698$			2.43350e6i			0.189057i
$699$		0			0
$700$	−3.31468e6	+	4.98364e6i	−0.255680	+	0.384416i
$701$	1.11461e7			0.856700			0.428350	−	0.903613i	$-0.359095\pi$
$701$	1.11461e7			0.856700			0.428350	+	0.903613i	$0.359095\pi$
$702$		0			0
$703$		−	2.50356e7i		−	1.91060i
$704$	1.08014e6			0.0821388
$705$		0			0
$706$	−1.53509e7			−1.15911
$707$		−	1.75308e6i		−	0.131903i
$708$		0			0
$709$	−264391.			−0.0197529			−0.00987646	−	0.999951i	$-0.503144\pi$
$709$	−264391.			−0.0197529			−0.00987646	+	0.999951i	$0.503144\pi$
$710$	1.23055e7	+	3.71856e6i	0.916120	+	0.276840i
$711$		0			0
$712$			4.19528e6i			0.310142i
$713$		−	265523.i		−	0.0195605i
$714$		0			0
$715$	−1.20104e7	−	3.62941e6i	−0.878606	−	0.265504i
$716$	−9.62526e6			−0.701665
$717$		0			0
$718$			8.55402e6i			0.619240i
$719$	7.09616e6			0.511919			0.255959	−	0.966688i	$-0.417609\pi$
$719$	7.09616e6			0.511919			0.255959	+	0.966688i	$0.417609\pi$
$720$		0			0
$721$	2.39325e7			1.71455
$722$			7.07778e6i			0.505305i
$723$		0			0
$724$	−7.16393e6			−0.507931
$725$	1.55759e7	+	1.03597e7i	1.10054	+	0.731984i
$726$		0			0
$727$		−	3.83492e6i		−	0.269104i	−0.990907	−	0.134552i	$-0.957040\pi$
$727$		−	3.83492e6i		−	0.269104i	0.990907	−	0.134552i	$-0.0429596\pi$
$728$			6.52057e6i			0.455992i
$729$		0			0
$730$	1.74363e6	−	5.77003e6i	0.121101	−	0.400748i
$731$	2.81681e6			0.194969
$732$		0			0
$733$			1.25850e7i			0.865151i	0.901598	+	0.432575i	$0.142395\pi$
$733$			1.25850e7i			0.865151i	−0.901598	+	0.432575i	$0.857605\pi$
$734$	1.80158e7			1.23428
$735$		0			0
$736$	56861.0			0.00386919
$737$		−	9.05954e6i		−	0.614381i
$738$		0			0
$739$	1.48983e7			1.00352			0.501761	−	0.865006i	$-0.332686\pi$
$739$	1.48983e7			1.00352			0.501761	+	0.865006i	$0.332686\pi$
$740$	−1.04030e7	−	3.14367e6i	−0.698363	−	0.211037i
$741$		0			0
$742$		−	1.26713e7i		−	0.844911i
$743$			921340.i			0.0612277i	0.999531	+	0.0306139i	$0.00974621\pi$
$743$			921340.i			0.0612277i	−0.999531	+	0.0306139i	$0.990254\pi$
$744$		0			0
$745$	5.64979e6	−	1.86963e7i	0.372942	−	1.23414i
$746$	4.60891e6			0.303215
$747$		0			0
$748$			5.43073e6i			0.354899i
$749$	−4.16222e6			−0.271095
$750$		0			0
$751$	−1.19124e7			−0.770726			−0.385363	−	0.922765i	$-0.625924\pi$
$751$	−1.19124e7			−0.770726			−0.385363	+	0.922765i	$0.625924\pi$
$752$		−	1.43303e6i		−	0.0924081i
$753$		0			0
$754$	2.03794e7			1.30546
$755$	−5.08606e6	+	1.68308e7i	−0.324724	+	1.07458i
$756$		0			0
$757$			1.43092e7i			0.907558i	0.891114	+	0.453779i	$0.149924\pi$
$757$			1.43092e7i			0.907558i	−0.891114	+	0.453779i	$0.850076\pi$
$758$		−	3.19096e6i		−	0.201720i
$759$		0			0
$760$	7.05661e6	+	2.13242e6i	0.443162	+	0.133918i
$761$	1.78549e6			0.111762			0.0558812	−	0.998437i	$-0.482203\pi$
$761$	1.78549e6			0.111762			0.0558812	+	0.998437i	$0.482203\pi$
$762$		0			0
$763$			2.35060e6i			0.146173i
$764$	1.07815e7			0.668263
$765$		0			0
$766$	4.08494e6			0.251544
$767$			1.77250e7i			1.08792i
$768$		0			0
$769$	1.03207e7			0.629350			0.314675	−	0.949200i	$-0.398105\pi$
$769$	1.03207e7			0.629350			0.314675	+	0.949200i	$0.398105\pi$
$770$	2.04184e6	−	6.75687e6i	0.124107	−	0.410694i
$771$		0			0
$772$		−	4.09539e6i		−	0.247316i
$773$		−	6.93308e6i		−	0.417328i	−0.977987	−	0.208664i	$-0.933089\pi$
$773$		−	6.93308e6i		−	0.417328i	0.977987	−	0.208664i	$-0.0669115\pi$
$774$		0			0
$775$	−1.24423e7	−	8.27549e6i	−0.744124	−	0.494925i
$776$	5.29797e6			0.315831
$777$		0			0
$778$		−	4.27281e6i		−	0.253084i
$779$	3.81187e7			2.25058
$780$		0			0
$781$	−1.51603e7			−0.889368
$782$			285886.i			0.0167177i
$783$		0			0
$784$	634235.			0.0368519
$785$	7.02623e6	+	2.12324e6i	0.406957	+	0.122977i
$786$		0			0
$787$			3.05516e7i			1.75831i	0.476532	+	0.879157i	$0.341894\pi$
$787$			3.05516e7i			1.75831i	−0.476532	+	0.879157i	$0.658106\pi$
$788$		−	3.13923e6i		−	0.180097i
$789$		0			0
$790$	−9.01091e6	−	2.72299e6i	−0.513690	−	0.155231i
$791$	−2.36019e6			−0.134124
$792$		0			0
$793$			3.87478e7i			2.18808i
$794$	437321.			0.0246178
$795$		0			0
$796$	1.89225e6			0.105851
$797$		−	2.76107e7i		−	1.53968i	−0.638236	−	0.769841i	$-0.720336\pi$
$797$		−	2.76107e7i		−	1.53968i	0.638236	−	0.769841i	$-0.279664\pi$
$798$		0			0
$799$	7.20498e6			0.399269
$800$	1.77217e6	−	2.66447e6i	0.0978995	−	0.147193i
$801$		0			0
$802$		−	5.68523e6i		−	0.312113i
$803$			7.10867e6i			0.389045i
$804$		0			0
$805$	107487.	−	355697.i	0.00584611	−	0.0193460i
$806$	−1.62794e7			−0.882674
$807$		0			0
$808$			937275.i			0.0505055i
$809$	9.60377e6			0.515906			0.257953	−	0.966157i	$-0.416952\pi$
$809$	9.60377e6			0.515906			0.257953	+	0.966157i	$0.416952\pi$
$810$		0			0
$811$	1.77352e7			0.946856			0.473428	−	0.880832i	$-0.343016\pi$
$811$	1.77352e7			0.946856			0.473428	+	0.880832i	$0.343016\pi$
$812$			1.14651e7i			0.610221i
$813$		0			0
$814$	1.28165e7			0.677969
$815$	−3.38839e7	−	1.02393e7i	−1.78690	−	0.539978i
$816$		0			0
$817$			4.50927e6i			0.236348i
$818$		−	1.23004e7i		−	0.642742i
$819$		0			0
$820$	4.78650e6	−	1.58395e7i	0.248590	−	0.822634i
$821$	2.66186e7			1.37825			0.689125	−	0.724643i	$-0.257995\pi$
$821$	2.66186e7			1.37825			0.689125	+	0.724643i	$0.257995\pi$
$822$		0			0
$823$		−	1.38059e7i		−	0.710504i	−0.934771	−	0.355252i	$-0.884395\pi$
$823$		−	1.38059e7i		−	0.710504i	0.934771	−	0.355252i	$-0.115605\pi$
$824$	−1.27953e7			−0.656498
$825$		0			0
$826$	−9.97180e6			−0.508538
$827$		−	3.25738e7i		−	1.65617i	−0.560604	−	0.828084i	$-0.689431\pi$
$827$		−	3.25738e7i		−	1.65617i	0.560604	−	0.828084i	$-0.310569\pi$
$828$		0			0
$829$	−1.67628e7			−0.847150			−0.423575	−	0.905861i	$-0.639225\pi$
$829$	−1.67628e7			−0.847150			−0.423575	+	0.905861i	$0.639225\pi$
$830$	6.58033e6	−	2.17757e7i	0.331553	−	1.09718i
$831$		0			0
$832$		−	3.48618e6i		−	0.174599i
$833$			3.18881e6i			0.159227i
$834$		0			0
$835$	7.36804e6	+	2.22653e6i	0.365709	+	0.110513i
$836$	−8.69374e6			−0.430220
$837$		0			0
$838$			1.22585e7i			0.603013i
$839$	−1.54475e6			−0.0757625			−0.0378812	−	0.999282i	$-0.512061\pi$
$839$	−1.54475e6			−0.0757625			−0.0378812	+	0.999282i	$0.512061\pi$
$840$		0			0
$841$	1.53218e7			0.746998
$842$			3.35113e6i			0.162896i
$843$		0			0
$844$	−1.45644e7			−0.703781
$845$	−5.70998e6	+	1.88955e7i	−0.275101	+	0.910366i
$846$		0			0
$847$		−	1.09543e7i		−	0.524658i
$848$			6.77462e6i			0.323516i
$849$		0			0
$850$	1.33964e7	+	8.91013e6i	0.635978	+	0.422996i
$851$	674692.			0.0319361
$852$		0			0
$853$			2.39801e7i			1.12844i	0.825625	+	0.564220i	$0.190823\pi$
$853$			2.39801e7i			1.12844i	−0.825625	+	0.564220i	$0.809177\pi$
$854$	−2.17988e7			−1.02279
$855$		0			0
$856$	2.22531e6			0.103802
$857$			3.48306e7i			1.61998i	0.586445	+	0.809989i	$0.300527\pi$
$857$			3.48306e7i			1.61998i	−0.586445	+	0.809989i	$0.699473\pi$
$858$		0			0
$859$	1.01532e7			0.469482			0.234741	−	0.972058i	$-0.424576\pi$
$859$	1.01532e7			0.469482			0.234741	+	0.972058i	$0.424576\pi$
$860$	1.87374e6	+	566221.i	0.0863899	+	0.0261060i
$861$		0			0
$862$		−	2.36288e7i		−	1.08311i
$863$			2.71085e7i			1.23902i	0.784989	+	0.619510i	$0.212669\pi$
$863$			2.71085e7i			1.23902i	−0.784989	+	0.619510i	$0.787331\pi$
$864$		0			0
$865$	4.83094e6	+	1.45985e6i	0.219529	+	0.0663389i
$866$	7.39981e6			0.335294
$867$		0			0
$868$		−	9.15849e6i		−	0.412596i
$869$	1.11014e7			0.498689
$870$		0			0
$871$	−2.92399e7			−1.30596
$872$		−	1.25673e6i		−	0.0559696i
$873$		0			0
$874$	−457658.			−0.0202658
$875$	−1.33177e7	−	1.61227e7i	−0.588044	−	0.711897i
$876$		0			0
$877$			5.76852e6i			0.253259i	0.991950	+	0.126630i	$0.0404160\pi$
$877$			5.76852e6i			0.253259i	−0.991950	+	0.126630i	$0.959584\pi$
$878$			1.12469e7i			0.492374i
$879$		0			0
$880$	−1.09166e6	+	3.61251e6i	−0.0475203	+	0.157254i
$881$	3.56949e7			1.54941			0.774705	−	0.632322i	$-0.217898\pi$
$881$	3.56949e7			1.54941			0.774705	+	0.632322i	$0.217898\pi$
$882$		0			0
$883$		−	4.55843e6i		−	0.196749i	−0.995149	−	0.0983747i	$-0.968636\pi$
$883$		−	4.55843e6i		−	0.196749i	0.995149	−	0.0983747i	$-0.0313644\pi$
$884$	1.75278e7			0.754393
$885$		0			0
$886$	−9.65546e6			−0.413227
$887$		−	3.23885e6i		−	0.138223i	−0.997609	−	0.0691117i	$-0.977984\pi$
$887$		−	3.23885e6i		−	0.138223i	0.997609	−	0.0691117i	$-0.0220165\pi$
$888$		0			0
$889$	−6.68243e6			−0.283583
$890$	−1.40310e7	−	4.24001e6i	−0.593766	−	0.179429i
$891$		0			0
$892$		−	1.67220e7i		−	0.703683i
$893$			1.15340e7i			0.484008i
$894$		0			0
$895$	9.72789e6	−	3.21916e7i	0.405939	−	1.34334i
$896$	1.96126e6			0.0816142
$897$		0			0
$898$		−	2.02850e6i		−	0.0839428i
$899$	−2.86239e7			−1.18122
$900$		0			0
$901$	−3.40615e7			−1.39782
$902$			1.95142e7i			0.798611i
$903$		0			0
$904$	1.26186e6			0.0513559
$905$	7.24032e6	−	2.39597e7i	0.293857	−	0.972433i
$906$		0			0
$907$		−	168518.i		−	0.00680186i	−0.999994	−	0.00340093i	$-0.998917\pi$
$907$		−	168518.i		−	0.00680186i	0.999994	−	0.00340093i	$-0.00108255\pi$
$908$		−	1.39059e7i		−	0.559739i
$909$		0			0
$910$	−2.18080e7	−	6.59009e6i	−0.872995	−	0.263808i
$911$	−3.36451e7			−1.34315			−0.671577	−	0.740935i	$-0.734383\pi$
$911$	−3.36451e7			−1.34315			−0.671577	+	0.740935i	$0.734383\pi$
$912$		0			0
$913$			2.68276e7i			1.06514i
$914$	−4.39514e6			−0.174023
$915$		0			0
$916$	−2.23851e7			−0.881494
$917$		−	1.63252e7i		−	0.641112i
$918$		0			0
$919$	−6.60944e6			−0.258152			−0.129076	−	0.991635i	$-0.541201\pi$
$919$	−6.60944e6			−0.258152			−0.129076	+	0.991635i	$0.541201\pi$
$920$	−57467.3	+	190171.i	−0.00223847	+	0.00740755i
$921$		0			0
$922$		−	424262.i		−	0.0164364i
$923$			4.89304e7i			1.89049i
$924$		0			0
$925$	2.10279e7	−	3.16157e7i	0.808057	−	1.21492i
$926$	5.44706e6			0.208754
$927$		0			0
$928$		−	6.12973e6i		−	0.233653i
$929$	−4.55946e7			−1.73330			−0.866651	−	0.498915i	$-0.833732\pi$
$929$	−4.55946e7			−1.73330			−0.866651	+	0.498915i	$0.833732\pi$
$930$		0			0
$931$	−5.10478e6			−0.193020
$932$		−	6.45590e6i		−	0.243454i
$933$		0			0
$934$	−8.74839e6			−0.328141
$935$	−1.81630e7	−	5.48864e6i	−0.679452	−	0.205322i
$936$		0			0
$937$		−	3.05380e6i		−	0.113630i	−0.998385	−	0.0568148i	$-0.981906\pi$
$937$		−	3.05380e6i		−	0.113630i	0.998385	−	0.0568148i	$-0.0180945\pi$
$938$		−	1.64499e7i		−	0.610457i
$939$		0			0
$940$	4.79274e6	+	1.44831e6i	0.176915	+	0.0534615i
$941$	−3.36840e7			−1.24008			−0.620040	−	0.784570i	$-0.712884\pi$
$941$	−3.36840e7			−1.24008			−0.620040	+	0.784570i	$0.712884\pi$
$942$		0			0
$943$			1.02727e6i			0.0376190i
$944$	5.33135e6			0.194719
$945$		0			0
$946$	−2.30845e6			−0.0838671
$947$		−	5.69161e6i		−	0.206234i	−0.994669	−	0.103117i	$-0.967118\pi$
$947$		−	5.69161e6i		−	0.206234i	0.994669	−	0.103117i	$-0.0328816\pi$
$948$		0			0
$949$	2.29434e7			0.826976
$950$	−1.42637e7	+	2.14456e7i	−0.512771	+	0.770955i
$951$		0			0
$952$			9.86084e6i			0.352632i
$953$			1.73627e7i			0.619278i	0.950854	+	0.309639i	$0.100208\pi$
$953$			1.73627e7i			0.619278i	−0.950854	+	0.309639i	$0.899792\pi$
$954$		0			0
$955$	−1.08965e7	+	3.60587e7i	−0.386615	+	1.27939i
$956$	9.77721e6			0.345995
$957$		0			0
$958$			4.06380e6i			0.143060i
$959$	1.60869e7			0.564839
$960$		0			0
$961$	−5.76388e6			−0.201329
$962$		−	4.13657e7i		−	1.44113i
$963$		0			0
$964$	2.41022e7			0.835342
$965$	1.36970e7	+	4.13905e6i	0.473485	+	0.143081i
$966$		0			0
$967$		−	4.93082e7i		−	1.69572i	−0.530224	−	0.847858i	$-0.677892\pi$
$967$		−	4.93082e7i		−	1.69572i	0.530224	−	0.847858i	$-0.322108\pi$
$968$			5.85665e6i			0.200891i
$969$		0			0
$970$	−5.35445e6	+	1.77190e7i	−0.182720	+	0.604657i
$971$	−3.23520e7			−1.10117			−0.550584	−	0.834780i	$-0.685595\pi$
$971$	−3.23520e7			−1.10117			−0.550584	+	0.834780i	$0.685595\pi$
$972$		0			0
$973$			3.65729e7i			1.23845i
$974$	−8.09357e6			−0.273365
$975$		0			0
$976$	1.16546e7			0.391627
$977$			2.61290e7i			0.875763i	0.899033	+	0.437882i	$0.144271\pi$
$977$			2.61290e7i			0.875763i	−0.899033	+	0.437882i	$0.855729\pi$
$978$		0			0
$979$	1.72862e7			0.576426
$980$	−640997.	+	2.12119e6i	−0.0213202	+	0.0705528i
$981$		0			0
$982$			1.68995e7i			0.559235i
$983$		−	3.19496e7i		−	1.05458i	−0.849684	−	0.527292i	$-0.823207\pi$
$983$		−	3.19496e7i		−	1.05458i	0.849684	−	0.527292i	$-0.176793\pi$
$984$		0			0
$985$	1.04991e7	+	3.17270e6i	0.344796	+	0.104193i
$986$	3.08191e7			1.00955
$987$		0			0
$988$			2.80593e7i			0.914501i
$989$	−121522.			−0.00395061
$990$		0			0
$991$	1.14783e7			0.371272			0.185636	−	0.982619i	$-0.440565\pi$
$991$	1.14783e7			0.371272			0.185636	+	0.982619i	$0.440565\pi$
$992$			4.89653e6i			0.157982i
$993$		0			0
$994$	−2.75274e7			−0.883688
$995$	−1.91242e6	+	6.32859e6i	−0.0612387	+	0.202651i
$996$		0			0
$997$			5.48929e7i			1.74895i	0.485068	+	0.874476i	$0.338795\pi$
$997$			5.48929e7i			1.74895i	−0.485068	+	0.874476i	$0.661205\pi$
$998$			2.68552e7i			0.853499i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	90.6.c.c.19.4		4
3.2	odd	2		30.6.c.b.19.1	✓	4
4.3	odd	2		720.6.f.i.289.3		4
5.2	odd	4		450.6.a.bb.1.1		2
5.3	odd	4		450.6.a.bc.1.2		2
5.4	even	2	inner	90.6.c.c.19.2		4
12.11	even	2		240.6.f.b.49.1		4
15.2	even	4		150.6.a.o.1.1		2
15.8	even	4		150.6.a.n.1.2		2
15.14	odd	2		30.6.c.b.19.3	yes	4
20.19	odd	2		720.6.f.i.289.4		4
60.59	even	2		240.6.f.b.49.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
30.6.c.b.19.1	✓	4	3.2	odd	2
30.6.c.b.19.3	yes	4	15.14	odd	2
90.6.c.c.19.2		4	5.4	even	2	inner
90.6.c.c.19.4		4	1.1	even	1	trivial
150.6.a.n.1.2		2	15.8	even	4
150.6.a.o.1.1		2	15.2	even	4
240.6.f.b.49.1		4	12.11	even	2
240.6.f.b.49.3		4	60.59	even	2
450.6.a.bb.1.1		2	5.2	odd	4
450.6.a.bc.1.2		2	5.3	odd	4
720.6.f.i.289.3		4	4.3	odd	2
720.6.f.i.289.4		4	20.19	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 90 = 2 \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	90.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+4.00000i q^{2} -16.0000 q^{4} +(16.1706 - 53.5118i) q^{5} +119.706i q^{7} -64.0000i q^{8} +O(q^{10})\)	\(q+4.00000i q^{2} -16.0000 q^{4} +(16.1706 - 53.5118i) q^{5} +119.706i q^{7} -64.0000i q^{8} +(214.047 + 64.6824i) q^{10} -263.706 q^{11} +851.118i q^{13} -478.824 q^{14} +256.000 q^{16} +1287.12i q^{17} -2060.47 q^{19} +(-258.730 + 856.189i) q^{20} -1054.82i q^{22} -55.5284i q^{23} +(-2602.02 - 1730.64i) q^{25} -3404.47 q^{26} -1915.30i q^{28} -5986.06 q^{29} +4781.76 q^{31} +1024.00i q^{32} -5148.47 q^{34} +(6405.68 + 1935.72i) q^{35} +12150.4i q^{37} -8241.89i q^{38} +(-3424.75 - 1034.92i) q^{40} -18500.0 q^{41} -2188.47i q^{43} +4219.30 q^{44} +222.113 q^{46} -5597.76i q^{47} +2477.48 q^{49} +(6922.54 - 10408.1i) q^{50} -13617.9i q^{52} +26463.4i q^{53} +(-4264.28 + 14111.4i) q^{55} +7661.18 q^{56} -23944.2i q^{58} +20825.6 q^{59} +45525.8 q^{61} +19127.1i q^{62} -4096.00 q^{64} +(45544.8 + 13763.1i) q^{65} +34354.7i q^{67} -20593.9i q^{68} +(-7742.87 + 25622.7i) q^{70} +57489.6 q^{71} -26956.8i q^{73} -48601.7 q^{74} +32967.5 q^{76} -31567.2i q^{77} -42097.8 q^{79} +(4139.67 - 13699.0i) q^{80} -74000.0i q^{82} -101733. i q^{83} +(68876.0 + 20813.5i) q^{85} +8753.86 q^{86} +16877.2i q^{88} -65551.2 q^{89} -101884. q^{91} +888.454i q^{92} +22391.1 q^{94} +(-33319.1 + 110260. i) q^{95} +82780.7i q^{97} +9909.92i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 64 q^{4} - 6 q^{5}+O(q^{10}) \) 4 * q - 64 * q^4 - 6 * q^5	\( 4 q - 64 q^{4} - 6 q^{5} + 8 q^{10} - 348 q^{11} + 912 q^{14} + 1024 q^{16} + 240 q^{19} + 96 q^{20} - 9984 q^{25} - 5136 q^{26} - 4860 q^{29} + 23368 q^{31} - 12112 q^{34} + 37356 q^{35} - 128 q^{40} - 49968 q^{41} + 5568 q^{44} + 34816 q^{46} - 70668 q^{49} + 29952 q^{50} - 11968 q^{55} - 14592 q^{56} - 47460 q^{59} + 114248 q^{61} - 16384 q^{64} + 113052 q^{65} - 51328 q^{70} + 22152 q^{71} - 140688 q^{74} - 3840 q^{76} - 28440 q^{79} - 1536 q^{80} + 113924 q^{85} + 193344 q^{86} - 120840 q^{89} - 301512 q^{91} + 106528 q^{94} - 150240 q^{95}+O(q^{100}) \) 4 * q - 64 * q^4 - 6 * q^5 + 8 * q^10 - 348 * q^11 + 912 * q^14 + 1024 * q^16 + 240 * q^19 + 96 * q^20 - 9984 * q^25 - 5136 * q^26 - 4860 * q^29 + 23368 * q^31 - 12112 * q^34 + 37356 * q^35 - 128 * q^40 - 49968 * q^41 + 5568 * q^44 + 34816 * q^46 - 70668 * q^49 + 29952 * q^50 - 11968 * q^55 - 14592 * q^56 - 47460 * q^59 + 114248 * q^61 - 16384 * q^64 + 113052 * q^65 - 51328 * q^70 + 22152 * q^71 - 140688 * q^74 - 3840 * q^76 - 28440 * q^79 - 1536 * q^80 + 113924 * q^85 + 193344 * q^86 - 120840 * q^89 - 301512 * q^91 + 106528 * q^94 - 150240 * q^95

Introduction

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