LMFDB - Embedded newform 360.6.k.b.181.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [360,6,Mod(181,360)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(360, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("360.181");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 360 = 2^{3} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	360.k (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:	$57.7381751327$
Analytic rank:	$0$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 2 x^{19} - 17 x^{18} + 78 x^{17} + 253 x^{16} - 884 x^{15} + 2396 x^{14} + 19376 x^{13} + \cdots + 1099511627776 $ x^20 - 2x^19 - 17x^18 + 78x^17 + 253x^16 - 884x^15 + 2396x^14 + 19376x^13 - 109104x^12 - 96128x^11 + 3580672x^10 - 1538048x^9 - 27930624x^8 + 79364096x^7 + 157024256x^6 - 926941184x^5 + 4244635648x^4 + 20937965568x^3 - 73014444032x^2 - 137438953472*x + 1099511627776
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{42}\cdot 3^{8}\cdot 5^{12} $
Twist minimal:	no (minimal twist has level 40)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			181.3
Root			$3.72553 - 1.45618i$ of defining polynomial
Character	$\chi$	$=$	360.181
Dual form			360.6.k.b.181.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-5.18171 - 2.26935i) q^{2} +(21.7001 + 23.5182i) q^{4} -25.0000i q^{5} +163.706 q^{7} +(-59.0729 - 171.109i) q^{8} +(-56.7336 + 129.543i) q^{10} +321.520i q^{11} -128.246i q^{13} +(-848.277 - 371.506i) q^{14} +(-82.2074 + 1020.69i) q^{16} +2110.72 q^{17} +1454.37i q^{19} +(587.954 - 542.504i) q^{20} +(729.641 - 1666.02i) q^{22} +1231.18 q^{23} -625.000 q^{25} +(-291.033 + 664.531i) q^{26} +(3552.45 + 3850.07i) q^{28} +4073.19i q^{29} -3956.03 q^{31} +(2742.28 - 5102.38i) q^{32} +(-10937.1 - 4789.95i) q^{34} -4092.65i q^{35} -10656.6i q^{37} +(3300.46 - 7536.11i) q^{38} +(-4277.73 + 1476.82i) q^{40} +5907.19 q^{41} +16439.6i q^{43} +(-7561.57 + 6977.04i) q^{44} +(-6379.59 - 2793.96i) q^{46} -23238.8 q^{47} +9992.68 q^{49} +(3238.57 + 1418.34i) q^{50} +(3016.10 - 2782.95i) q^{52} +30634.0i q^{53} +8038.01 q^{55} +(-9670.60 - 28011.6i) q^{56} +(9243.47 - 21106.1i) q^{58} -25262.4i q^{59} +39115.5i q^{61} +(20499.0 + 8977.61i) q^{62} +(-25788.8 + 20215.9i) q^{64} -3206.14 q^{65} -20894.5i q^{67} +(45803.0 + 49640.3i) q^{68} +(-9287.64 + 21206.9i) q^{70} -13889.1 q^{71} -43451.2 q^{73} +(-24183.6 + 55219.6i) q^{74} +(-34204.1 + 31560.0i) q^{76} +52634.8i q^{77} -12546.4 q^{79} +(25517.4 + 2055.19i) q^{80} +(-30609.3 - 13405.4i) q^{82} -6680.84i q^{83} -52768.0i q^{85} +(37307.1 - 85185.1i) q^{86} +(55015.1 - 18993.2i) q^{88} +90400.9 q^{89} -20994.6i q^{91} +(26716.7 + 28955.0i) q^{92} +(120416. + 52736.8i) q^{94} +36359.2 q^{95} +149616. q^{97} +(-51779.1 - 22676.8i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 2 q^{2} - 32 q^{4} - 196 q^{7} - 248 q^{8} - 50 q^{10} - 2708 q^{14} + 3080 q^{16} + 1900 q^{20} + 13836 q^{22} + 4676 q^{23} - 12500 q^{25} + 8084 q^{26} + 2108 q^{28} + 7160 q^{31} - 6792 q^{32}+ \cdots - 216942 q^{98}+O(q^{100}) $ 20 * q - 2 * q^2 - 32 * q^4 - 196 * q^7 - 248 * q^8 - 50 * q^10 - 2708 * q^14 + 3080 * q^16 + 1900 * q^20 + 13836 * q^22 + 4676 * q^23 - 12500 * q^25 + 8084 * q^26 + 2108 * q^28 + 7160 * q^31 - 6792 * q^32 + 21132 * q^34 + 19580 * q^38 + 6200 * q^40 - 11608 * q^41 - 72296 * q^44 - 28516 * q^46 - 44180 * q^47 + 18756 * q^49 + 1250 * q^50 - 39680 * q^52 - 24200 * q^55 + 53624 * q^56 + 59496 * q^58 - 59824 * q^62 - 11264 * q^64 - 11576 * q^68 + 29800 * q^70 + 200312 * q^71 - 105136 * q^73 - 78876 * q^74 - 153872 * q^76 + 282080 * q^79 - 16000 * q^80 - 223032 * q^82 - 27452 * q^86 + 86896 * q^88 + 3160 * q^89 - 107916 * q^92 + 148820 * q^94 - 144400 * q^95 + 147376 * q^97 - 216942 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/360\mathbb{Z}\right)^\times$.

$n$	$181$	$217$	$271$	$281$
$\chi(n)$	$-1$	$1$	$1$	$1$

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 $

$2$	−5.18171	−	2.26935i	−0.916005	−	0.401167i
$2$	−5.18171	−	2.26935i	−0.916005	−	0.401167i
$3$		0			0
$3$		0			0
$4$	21.7001	+	23.5182i	0.678130	+	0.734942i
$5$		−	25.0000i		−	0.447214i
$5$		−	25.0000i		−	0.447214i
$6$		0			0
$7$	163.706			1.26276			0.631378	−	0.775475i	$-0.282490\pi$
$7$	163.706			1.26276			0.631378	+	0.775475i	$0.282490\pi$
$8$	−59.0729	−	171.109i	−0.326335	−	0.945254i
$9$		0			0
$10$	−56.7336	+	129.543i	−0.179407	+	0.409650i
$11$			321.520i			0.801174i	0.916259	+	0.400587i	$0.131194\pi$
$11$			321.520i			0.801174i	−0.916259	+	0.400587i	$0.868806\pi$
$12$		0			0
$13$		−	128.246i		−	0.210467i	−0.994448	−	0.105233i	$-0.966441\pi$
$13$		−	128.246i		−	0.210467i	0.994448	−	0.105233i	$-0.0335590\pi$
$14$	−848.277	−	371.506i	−1.15669	−	0.506577i
$15$		0			0
$16$	−82.2074	+	1020.69i	−0.0802807	+	0.996772i
$17$	2110.72			1.77137			0.885683	−	0.464290i	$-0.153690\pi$
$17$	2110.72			1.77137			0.885683	+	0.464290i	$0.153690\pi$
$18$		0			0
$19$			1454.37i			0.924252i	0.886814	+	0.462126i	$0.152913\pi$
$19$			1454.37i			0.924252i	−0.886814	+	0.462126i	$0.847087\pi$
$20$	587.954	−	542.504i	0.328676	−	0.303269i
$21$		0			0
$22$	729.641	−	1666.02i	0.321405	−	0.733879i
$23$	1231.18			0.485289			0.242645	−	0.970115i	$-0.421985\pi$
$23$	1231.18			0.485289			0.242645	+	0.970115i	$0.421985\pi$
$24$		0			0
$25$	−625.000			−0.200000
$26$	−291.033	+	664.531i	−0.0844325	+	0.192789i
$27$		0			0
$28$	3552.45	+	3850.07i	0.856313	+	0.928053i
$29$			4073.19i			0.899372i	0.893187	+	0.449686i	$0.148464\pi$
$29$			4073.19i			0.899372i	−0.893187	+	0.449686i	$0.851536\pi$
$30$		0			0
$31$	−3956.03			−0.739360			−0.369680	−	0.929159i	$-0.620533\pi$
$31$	−3956.03			−0.739360			−0.369680	+	0.929159i	$0.620533\pi$
$32$	2742.28	−	5102.38i	0.473410	−	0.880842i
$33$		0			0
$34$	−10937.1	−	4789.95i	−1.62258	−	0.710615i
$35$		−	4092.65i		−	0.564722i
$36$		0			0
$37$		−	10656.6i		−	1.27972i	−0.768490	−	0.639861i	$-0.778992\pi$
$37$		−	10656.6i		−	1.27972i	0.768490	−	0.639861i	$-0.221008\pi$
$38$	3300.46	−	7536.11i	0.370780	−	0.846620i
$39$		0			0
$40$	−4277.73	+	1476.82i	−0.422731	+	0.145941i
$41$	5907.19			0.548809			0.274404	−	0.961614i	$-0.411519\pi$
$41$	5907.19			0.548809			0.274404	+	0.961614i	$0.411519\pi$
$42$		0			0
$43$			16439.6i			1.35588i	0.735119	+	0.677938i	$0.237126\pi$
$43$			16439.6i			1.35588i	−0.735119	+	0.677938i	$0.762874\pi$
$44$	−7561.57	+	6977.04i	−0.588817	+	0.543300i
$45$		0			0
$46$	−6379.59	−	2793.96i	−0.444527	−	0.194682i
$47$	−23238.8			−1.53450			−0.767252	−	0.641345i	$-0.778377\pi$
$47$	−23238.8			−1.53450			−0.767252	+	0.641345i	$0.778377\pi$
$48$		0			0
$49$	9992.68			0.594555
$50$	3238.57	+	1418.34i	0.183201	+	0.0802335i
$51$		0			0
$52$	3016.10	−	2782.95i	0.154681	−	0.142724i
$53$			30634.0i			1.49801i	0.662567	+	0.749003i	$0.269467\pi$
$53$			30634.0i			1.49801i	−0.662567	+	0.749003i	$0.730533\pi$
$54$		0			0
$55$	8038.01			0.358296
$56$	−9670.60	−	28011.6i	−0.412082	−	1.19363i
$57$		0			0
$58$	9243.47	−	21106.1i	0.360799	−	0.823829i
$59$		−	25262.4i		−	0.944810i	−0.881382	−	0.472405i	$-0.843386\pi$
$59$		−	25262.4i		−	0.944810i	0.881382	−	0.472405i	$-0.156614\pi$
$60$		0			0
$61$			39115.5i			1.34594i	0.739672	+	0.672968i	$0.234981\pi$
$61$			39115.5i			1.34594i	−0.739672	+	0.672968i	$0.765019\pi$
$62$	20499.0	+	8977.61i	0.677257	+	0.296607i
$63$		0			0
$64$	−25788.8	+	20215.9i	−0.787011	+	0.616939i
$65$	−3206.14			−0.0941237
$66$		0			0
$67$		−	20894.5i		−	0.568651i	−0.958728	−	0.284325i	$-0.908230\pi$
$67$		−	20894.5i		−	0.568651i	0.958728	−	0.284325i	$-0.0917696\pi$
$68$	45803.0	+	49640.3i	1.20122	+	1.30185i
$69$		0			0
$70$	−9287.64	+	21206.9i	−0.226548	+	0.517288i
$71$	−13889.1			−0.326984			−0.163492	−	0.986545i	$-0.552276\pi$
$71$	−13889.1			−0.326984			−0.163492	+	0.986545i	$0.552276\pi$
$72$		0			0
$73$	−43451.2			−0.954321			−0.477161	−	0.878816i	$-0.658334\pi$
$73$	−43451.2			−0.954321			−0.477161	+	0.878816i	$0.658334\pi$
$74$	−24183.6	+	55219.6i	−0.513383	+	1.17223i
$75$		0			0
$76$	−34204.1	+	31560.0i	−0.679272	+	0.626763i
$77$			52634.8i			1.01169i
$78$		0			0
$79$	−12546.4			−0.226179			−0.113089	−	0.993585i	$-0.536075\pi$
$79$	−12546.4			−0.226179			−0.113089	+	0.993585i	$0.536075\pi$
$80$	25517.4	+	2055.19i	0.445770	+	0.0359026i
$81$		0			0
$82$	−30609.3	−	13405.4i	−0.502711	−	0.220164i
$83$		−	6680.84i		−	0.106448i	−0.998583	−	0.0532238i	$-0.983050\pi$
$83$		−	6680.84i		−	0.106448i	0.998583	−	0.0532238i	$-0.0169497\pi$
$84$		0			0
$85$		−	52768.0i		−	0.792179i
$86$	37307.1	−	85185.1i	0.543933	−	1.24199i
$87$		0			0
$88$	55015.1	−	18993.2i	0.757313	−	0.261451i
$89$	90400.9			1.20976			0.604878	−	0.796318i	$-0.293222\pi$
$89$	90400.9			1.20976			0.604878	+	0.796318i	$0.293222\pi$
$90$		0			0
$91$		−	20994.6i		−	0.265769i
$92$	26716.7	+	28955.0i	0.329089	+	0.356660i
$93$		0			0
$94$	120416.	+	52736.8i	1.40561	+	0.615593i
$95$	36359.2			0.413338
$96$		0			0
$97$	149616.			1.61454			0.807269	−	0.590184i	$-0.200945\pi$
$97$	149616.			1.61454			0.807269	+	0.590184i	$0.200945\pi$
$98$	−51779.1	−	22676.8i	−0.544615	−	0.238516i
$99$		0			0
$100$	−13562.6	−	14698.8i	−0.135626	−	0.146988i
$101$		−	114822.i		−	1.12001i	−0.828491	−	0.560003i	$-0.810800\pi$
$101$		−	114822.i		−	1.12001i	0.828491	−	0.560003i	$-0.189200\pi$
$102$		0			0
$103$	38586.9			0.358382			0.179191	−	0.983814i	$-0.442652\pi$
$103$	38586.9			0.358382			0.179191	+	0.983814i	$0.442652\pi$
$104$	−21944.0	+	7575.84i	−0.198945	+	0.0686827i
$105$		0			0
$106$	69519.0	−	158736.i	0.600951	−	1.37218i
$107$			189459.i			1.59976i	0.600158	+	0.799881i	$0.295104\pi$
$107$			189459.i			1.59976i	−0.600158	+	0.799881i	$0.704896\pi$
$108$		0			0
$109$			24392.6i			0.196649i	0.995154	+	0.0983245i	$0.0313483\pi$
$109$			24392.6i			0.196649i	−0.995154	+	0.0983245i	$0.968652\pi$
$110$	−41650.6	−	18241.0i	−0.328201	−	0.143737i
$111$		0			0
$112$	−13457.9	+	167094.i	−0.101375	+	1.25868i
$113$	52918.6			0.389863			0.194932	−	0.980817i	$-0.437552\pi$
$113$	52918.6			0.389863			0.194932	+	0.980817i	$0.437552\pi$
$114$		0			0
$115$		−	30779.4i		−	0.217028i
$116$	−95793.8	+	88388.7i	−0.660987	+	0.609891i
$117$		0			0
$118$	−57329.1	+	130902.i	−0.379027	+	0.865450i
$119$	345538.			2.23681
$120$		0			0
$121$	57675.7			0.358120
$122$	88766.6	−	202685.i	0.539945	−	1.23288i
$123$		0			0
$124$	−85846.5	−	93038.6i	−0.501382	−	0.543387i
$125$			15625.0i			0.0894427i
$126$		0			0
$127$	293650.			1.61555			0.807777	−	0.589489i	$-0.200671\pi$
$127$	293650.			1.61555			0.807777	+	0.589489i	$0.200671\pi$
$128$	179507.	−	46229.0i	0.968402	−	0.249396i
$129$		0			0
$130$	16613.3	+	7275.83i	0.0862177	+	0.0377593i
$131$			317738.i			1.61767i	0.588032	+	0.808837i	$0.299903\pi$
$131$			317738.i			1.61767i	−0.588032	+	0.808837i	$0.700097\pi$
$132$		0			0
$133$			238089.i			1.16711i
$134$	−47416.9	+	108269.i	−0.228124	+	0.520887i
$135$		0			0
$136$	−124687.	−	361164.i	−0.578059	−	1.67439i
$137$	162285.			0.738717			0.369358	−	0.929287i	$-0.379577\pi$
$137$	162285.			0.738717			0.369358	+	0.929287i	$0.379577\pi$
$138$		0			0
$139$			306759.i			1.34667i	0.739338	+	0.673334i	$0.235139\pi$
$139$			306759.i			1.34667i	−0.739338	+	0.673334i	$0.764861\pi$
$140$	96251.6	−	88811.1i	0.415038	−	0.382955i
$141$		0			0
$142$	71969.0	+	31519.1i	0.299519	+	0.131175i
$143$	41233.5			0.168621
$144$		0			0
$145$	101830.			0.402211
$146$	225151.	+	98605.8i	0.874163	+	0.382842i
$147$		0			0
$148$	250625.	−	231251.i	0.940523	−	0.867818i
$149$		−	368107.i		−	1.35834i	−0.733981	−	0.679170i	$-0.762340\pi$
$149$		−	368107.i		−	1.35834i	0.733981	−	0.679170i	$-0.237660\pi$
$150$		0			0
$151$	336822.			1.20215			0.601075	−	0.799193i	$-0.294739\pi$
$151$	336822.			1.20215			0.601075	+	0.799193i	$0.294739\pi$
$152$	248856.	−	85913.8i	0.873653	−	0.301616i
$153$		0			0
$154$	119447.	−	272738.i	0.405856	−	0.926711i
$155$			98900.9i			0.330652i
$156$		0			0
$157$			271253.i			0.878264i	0.898423	+	0.439132i	$0.144714\pi$
$157$			271253.i			0.878264i	−0.898423	+	0.439132i	$0.855286\pi$
$158$	65011.8	+	28472.1i	0.207181	+	0.0907356i
$159$		0			0
$160$	−127560.	−	68557.1i	−0.393925	−	0.211715i
$161$	201551.			0.612802
$162$		0			0
$163$		−	121354.i		−	0.357756i	−0.983871	−	0.178878i	$-0.942753\pi$
$163$		−	121354.i		−	0.357756i	0.983871	−	0.178878i	$-0.0572467\pi$
$164$	128187.	+	138926.i	0.372163	+	0.403343i
$165$		0			0
$166$	−15161.1	+	34618.1i	−0.0427033	+	0.0975065i
$167$	−56095.4			−0.155645			−0.0778227	−	0.996967i	$-0.524797\pi$
$167$	−56095.4			−0.155645			−0.0778227	+	0.996967i	$0.524797\pi$
$168$		0			0
$169$	354846.			0.955704
$170$	−119749.	+	273428.i	−0.317797	+	0.725640i
$171$		0			0
$172$	−386629.	+	356741.i	−0.996490	+	0.919459i
$173$		−	167666.i		−	0.425921i	−0.977061	−	0.212960i	$-0.931689\pi$
$173$		−	167666.i		−	0.425921i	0.977061	−	0.212960i	$-0.0683105\pi$
$174$		0			0
$175$	−102316.			−0.252551
$176$	−328174.	−	26431.4i	−0.798588	−	0.0643188i
$177$		0			0
$178$	−468431.	−	205151.i	−1.10814	−	0.485314i
$179$		−	535921.i		−	1.25017i	−0.780558	−	0.625083i	$-0.785065\pi$
$179$		−	535921.i		−	1.25017i	0.780558	−	0.625083i	$-0.214935\pi$
$180$		0			0
$181$		−	113446.i		−	0.257391i	−0.991684	−	0.128696i	$-0.958921\pi$
$181$		−	113446.i		−	0.257391i	0.991684	−	0.128696i	$-0.0410790\pi$
$182$	−47643.9	+	108788.i	−0.106618	+	0.243445i
$183$		0			0
$184$	−72729.2	−	210666.i	−0.158367	−	0.458722i
$185$	−266416.			−0.572309
$186$		0			0
$187$			678640.i			1.41917i
$188$	−504284.	−	546533.i	−1.04059	−	1.12777i
$189$		0			0
$190$	−188403.	−	82511.6i	−0.378620	−	0.165818i
$191$	−391808.			−0.777124			−0.388562	−	0.921423i	$-0.627028\pi$
$191$	−391808.			−0.777124			−0.388562	+	0.921423i	$0.627028\pi$
$192$		0			0
$193$	−261513.			−0.505359			−0.252680	−	0.967550i	$-0.581312\pi$
$193$	−261513.			−0.505359			−0.252680	+	0.967550i	$0.581312\pi$
$194$	−775265.	−	339530.i	−1.47892	−	0.647700i
$195$		0			0
$196$	216843.	+	235009.i	0.403185	+	0.436963i
$197$			898947.i			1.65032i	0.564898	+	0.825161i	$0.308916\pi$
$197$			898947.i			1.65032i	−0.564898	+	0.825161i	$0.691084\pi$
$198$		0			0
$199$	−83719.3			−0.149862			−0.0749312	−	0.997189i	$-0.523874\pi$
$199$	−83719.3			−0.149862			−0.0749312	+	0.997189i	$0.523874\pi$
$200$	36920.6	+	106943.i	0.0652670	+	0.189051i
$201$		0			0
$202$	−260570.	+	594972.i	−0.449310	+	1.02593i
$203$			666805.i			1.13569i
$204$		0			0
$205$		−	147680.i		−	0.245435i
$206$	−199946.	−	87566.9i	−0.328280	−	0.143771i
$207$		0			0
$208$	130900.	+	10542.7i	0.209788	+	0.0168964i
$209$	−467609.			−0.740487
$210$		0			0
$211$			553641.i			0.856095i	0.903756	+	0.428047i	$0.140798\pi$
$211$			553641.i			0.856095i	−0.903756	+	0.428047i	$0.859202\pi$
$212$	−720454.	+	664761.i	−1.10095	+	1.01584i
$213$		0			0
$214$	429948.	−	981720.i	0.641772	−	1.46539i
$215$	410990.			0.606366
$216$		0			0
$217$	−647627.			−0.933632
$218$	55355.2	−	126395.i	0.0788892	−	0.180131i
$219$		0			0
$220$	174426.	+	189039.i	0.242971	+	0.263327i
$221$		−	270691.i		−	0.372814i
$222$		0			0
$223$	279400.			0.376239			0.188120	−	0.982146i	$-0.439761\pi$
$223$	279400.			0.376239			0.188120	+	0.982146i	$0.439761\pi$
$224$	448929.	−	835291.i	0.597802	−	1.11229i
$225$		0			0
$226$	−274209.	−	120091.i	−0.357116	−	0.156400i
$227$			593068.i			0.763905i	0.924182	+	0.381953i	$0.124748\pi$
$227$			593068.i			0.763905i	−0.924182	+	0.381953i	$0.875252\pi$
$228$		0			0
$229$		−	927873.i		−	1.16923i	−0.811311	−	0.584615i	$-0.801246\pi$
$229$		−	927873.i		−	1.16923i	0.811311	−	0.584615i	$-0.198754\pi$
$230$	−69849.1	+	159490.i	−0.0870645	+	0.198799i
$231$		0			0
$232$	696960.	−	240615.i	0.850135	−	0.293496i
$233$	1.09279e6			1.31871			0.659353	−	0.751833i	$-0.270830\pi$
$233$	1.09279e6			1.31871			0.659353	+	0.751833i	$0.270830\pi$
$234$		0			0
$235$			580969.i			0.686251i
$236$	594125.	−	548197.i	0.694381	−	0.640703i
$237$		0			0
$238$	−1.79048e6	−	784145.i	−2.04892	−	0.897333i
$239$	797967.			0.903630			0.451815	−	0.892112i	$-0.350777\pi$
$239$	797967.			0.903630			0.451815	+	0.892112i	$0.350777\pi$
$240$		0			0
$241$	−1.61861e6			−1.79515			−0.897573	−	0.440865i	$-0.854672\pi$
$241$	−1.61861e6			−1.79515			−0.897573	+	0.440865i	$0.854672\pi$
$242$	−298858.	−	130886.i	−0.328040	−	0.143666i
$243$		0			0
$244$	−919924.	+	848812.i	−0.989185	+	0.912719i
$245$		−	249817.i		−	0.265893i
$246$		0			0
$247$	186516.			0.194525
$248$	233695.	+	676914.i	0.241279	+	0.698883i
$249$		0			0
$250$	35458.5	−	80964.1i	0.0358815	−	0.0819300i
$251$		−	449688.i		−	0.450533i	−0.974297	−	0.225266i	$-0.927675\pi$
$251$		−	449688.i		−	0.450533i	0.974297	−	0.225266i	$-0.0723253\pi$
$252$		0			0
$253$			395848.i			0.388801i
$254$	−1.52161e6	−	666394.i	−1.47985	−	0.648107i
$255$		0			0
$256$	−1.03506e6	−	167817.i	−0.987110	−	0.160043i
$257$	−396434.			−0.374402			−0.187201	−	0.982322i	$-0.559942\pi$
$257$	−396434.			−0.374402			−0.187201	+	0.982322i	$0.559942\pi$
$258$		0			0
$259$		−	1.74456e6i		−	1.61598i
$260$	−69573.7	−	75402.5i	−0.0638280	−	0.0691755i
$261$		0			0
$262$	721058.	−	1.64643e6i	0.648958	−	1.48180i
$263$	−1.93423e6			−1.72432			−0.862160	−	0.506635i	$-0.830889\pi$
$263$	−1.93423e6			−1.72432			−0.862160	+	0.506635i	$0.830889\pi$
$264$		0			0
$265$	765849.			0.669928
$266$	540306.	−	1.23371e6i	0.468205	−	1.06907i
$267$		0			0
$268$	491401.	−	453414.i	0.417926	−	0.385619i
$269$			670016.i			0.564553i	0.959333	+	0.282276i	$0.0910895\pi$
$269$			670016.i			0.564553i	−0.959333	+	0.282276i	$0.908910\pi$
$270$		0			0
$271$	2.08940e6			1.72822			0.864109	−	0.503305i	$-0.167883\pi$
$271$	2.08940e6			1.72822			0.864109	+	0.503305i	$0.167883\pi$
$272$	−173517.	+	2.15440e6i	−0.142207	+	1.76565i
$273$		0			0
$274$	−840915.	−	368281.i	−0.676668	−	0.296349i
$275$		−	200950.i		−	0.160235i
$276$		0			0
$277$			828834.i			0.649035i	0.945880	+	0.324517i	$0.105202\pi$
$277$			828834.i			0.649035i	−0.945880	+	0.324517i	$0.894798\pi$
$278$	696143.	−	1.58954e6i	0.540240	−	1.23356i
$279$		0			0
$280$	−700291.	+	241765.i	−0.533806	+	0.184289i
$281$	−2.39932e6			−1.81268			−0.906342	−	0.422545i	$-0.861137\pi$
$281$	−2.39932e6			−1.81268			−0.906342	+	0.422545i	$0.861137\pi$
$282$		0			0
$283$			2.00868e6i			1.49089i	0.666568	+	0.745444i	$0.267763\pi$
$283$			2.00868e6i			1.49089i	−0.666568	+	0.745444i	$0.732237\pi$
$284$	−301395.	−	326645.i	−0.221738	−	0.240315i
$285$		0			0
$286$	−213660.	−	93573.2i	−0.154457	−	0.0676451i
$287$	967042.			0.693012
$288$		0			0
$289$	3.03529e6			2.13774
$290$	−527651.	−	231087.i	−0.368427	−	0.161354i
$291$		0			0
$292$	−942897.	−	1.02189e6i	−0.647153	−	0.701371i
$293$		−	1.74203e6i		−	1.18546i	−0.805402	−	0.592729i	$-0.798050\pi$
$293$		−	1.74203e6i		−	1.18546i	0.805402	−	0.592729i	$-0.201950\pi$
$294$		0			0
$295$	−631560.			−0.422532
$296$	−1.82345e6	+	629519.i	−1.20966	+	0.417618i
$297$		0			0
$298$	−835362.	+	1.90742e6i	−0.544922	+	1.24425i
$299$		−	157893.i		−	0.102137i
$300$		0			0
$301$			2.69126e6i			1.71214i
$302$	−1.74531e6	−	764366.i	−1.10118	−	0.482263i
$303$		0			0
$304$	−1.48447e6	−	119560.i	−0.921269	−	0.0741996i
$305$	977887.			0.601921
$306$		0			0
$307$		−	978690.i		−	0.592651i	−0.955087	−	0.296326i	$-0.904239\pi$
$307$		−	978690.i		−	0.592651i	0.955087	−	0.296326i	$-0.0957614\pi$
$308$	−1.23787e6	+	1.14218e6i	−0.743532	+	0.686055i
$309$		0			0
$310$	224440.	−	512475.i	0.132647	−	0.302879i
$311$	1.57652e6			0.924268			0.462134	−	0.886810i	$-0.347084\pi$
$311$	1.57652e6			0.924268			0.462134	+	0.886810i	$0.347084\pi$
$312$		0			0
$313$	1.60962e6			0.928670			0.464335	−	0.885660i	$-0.346293\pi$
$313$	1.60962e6			0.928670			0.464335	+	0.885660i	$0.346293\pi$
$314$	615566.	−	1.40555e6i	0.352331	−	0.804494i
$315$		0			0
$316$	−272259.	−	295069.i	−0.153379	−	0.166228i
$317$		−	1.50670e6i		−	0.842130i	−0.907030	−	0.421065i	$-0.861656\pi$
$317$		−	1.50670e6i		−	0.842130i	0.907030	−	0.421065i	$-0.138344\pi$
$318$		0			0
$319$	−1.30961e6			−0.720553
$320$	505396.	+	644719.i	0.275904	+	0.351962i
$321$		0			0
$322$	−1.04438e6	−	457389.i	−0.561330	−	0.245836i
$323$			3.06977e6i			1.63719i
$324$		0			0
$325$			80153.5i			0.0420934i
$326$	−275395.	+	628823.i	−0.143520	+	0.327706i
$327$		0			0
$328$	−348955.	−	1.01077e6i	−0.179095	−	0.518764i
$329$	−3.80433e6			−1.93771
$330$		0			0
$331$			394453.i			0.197891i	0.995093	+	0.0989454i	$0.0315469\pi$
$331$			394453.i			0.197891i	−0.995093	+	0.0989454i	$0.968453\pi$
$332$	157121.	−	144975.i	0.0782328	−	0.0721852i
$333$		0			0
$334$	290670.	+	127300.i	0.142572	+	0.0624398i
$335$	−522363.			−0.254308
$336$		0			0
$337$	−1.36879e6			−0.656543			−0.328272	−	0.944583i	$-0.606466\pi$
$337$	−1.36879e6			−0.656543			−0.328272	+	0.944583i	$0.606466\pi$
$338$	−1.83871e6	−	805268.i	−0.875429	−	0.383397i
$339$		0			0
$340$	1.24101e6	−	1.14507e6i	0.582206	−	0.537200i
$341$		−	1.27195e6i		−	0.592356i
$342$		0			0
$343$	−1.11555e6			−0.511979
$344$	2.81297e6	−	971135.i	1.28165	−	0.442470i
$345$		0			0
$346$	−380491.	+	868794.i	−0.170865	+	0.390145i
$347$			569376.i			0.253849i	0.991912	+	0.126925i	$0.0405106\pi$
$347$			569376.i			0.253849i	−0.991912	+	0.126925i	$0.959489\pi$
$348$		0			0
$349$		−	2.20053e6i		−	0.967081i	−0.875322	−	0.483541i	$-0.839351\pi$
$349$		−	2.20053e6i		−	0.967081i	0.875322	−	0.483541i	$-0.160649\pi$
$350$	530173.	+	232191.i	0.231338	+	0.101315i
$351$		0			0
$352$	1.64052e6	+	881700.i	0.705708	+	0.379284i
$353$	2.51557e6			1.07448			0.537242	−	0.843428i	$-0.319466\pi$
$353$	2.51557e6			1.07448			0.537242	+	0.843428i	$0.319466\pi$
$354$		0			0
$355$			347226.i			0.146232i
$356$	1.96171e6	+	2.12606e6i	0.820371	+	0.889100i
$357$		0			0
$358$	−1.21619e6	+	2.77698e6i	−0.501526	+	1.14516i
$359$	794808.			0.325481			0.162741	−	0.986669i	$-0.447967\pi$
$359$	794808.			0.325481			0.162741	+	0.986669i	$0.447967\pi$
$360$		0			0
$361$	360911.			0.145758
$362$	−257449.	+	587845.i	−0.103257	+	0.235772i
$363$		0			0
$364$	493754.	−	455585.i	0.195325	−	0.180225i
$365$			1.08628e6i			0.426785i
$366$		0			0
$367$	−874302.			−0.338841			−0.169421	−	0.985544i	$-0.554190\pi$
$367$	−874302.			−0.338841			−0.169421	+	0.985544i	$0.554190\pi$
$368$	−101212.	+	1.25666e6i	−0.0389594	+	0.483723i
$369$		0			0
$370$	1.38049e6	+	604590.i	0.524238	+	0.229592i
$371$			5.01497e6i			1.89162i
$372$		0			0
$373$		−	4.86205e6i		−	1.80945i	−0.425994	−	0.904726i	$-0.640076\pi$
$373$		−	4.86205e6i		−	1.80945i	0.425994	−	0.904726i	$-0.359924\pi$
$374$	1.54007e6	−	3.51651e6i	0.569326	−	1.29997i
$375$		0			0
$376$	1.37278e6	+	3.97637e6i	0.500763	+	1.45050i
$377$	522368.			0.189288
$378$		0			0
$379$			1.24150e6i			0.443964i	0.975051	+	0.221982i	$0.0712527\pi$
$379$			1.24150e6i			0.443964i	−0.975051	+	0.221982i	$0.928747\pi$
$380$	789000.	+	855102.i	0.280297	+	0.303780i
$381$		0			0
$382$	2.03024e6	+	889149.i	0.711849	+	0.311757i
$383$	30969.9			0.0107880			0.00539402	−	0.999985i	$-0.498283\pi$
$383$	30969.9			0.0107880			0.00539402	+	0.999985i	$0.498283\pi$
$384$		0			0
$385$	1.31587e6			0.452440
$386$	1.35508e6	+	593463.i	0.462911	+	0.202734i
$387$		0			0
$388$	3.24669e6	+	3.51869e6i	1.09487	+	1.18659i
$389$		−	4.27860e6i		−	1.43360i	−0.697279	−	0.716800i	$-0.745606\pi$
$389$		−	4.27860e6i		−	1.43360i	0.697279	−	0.716800i	$-0.254394\pi$
$390$		0			0
$391$	2.59867e6			0.859626
$392$	−590297.	−	1.70984e6i	−0.194024	−	0.562005i
$393$		0			0
$394$	2.04002e6	−	4.65808e6i	0.662055	−	1.51170i
$395$			313660.i			0.101150i
$396$		0			0
$397$		−	2.31119e6i		−	0.735968i	−0.929832	−	0.367984i	$-0.880048\pi$
$397$		−	2.31119e6i		−	0.735968i	0.929832	−	0.367984i	$-0.119952\pi$
$398$	433809.	+	189988.i	0.137275	+	0.0601199i
$399$		0			0
$400$	51379.7	−	637934.i	0.0160561	−	0.199354i
$401$	−996347.			−0.309421			−0.154710	−	0.987960i	$-0.549444\pi$
$401$	−996347.			−0.309421			−0.154710	+	0.987960i	$0.549444\pi$
$402$		0			0
$403$			507344.i			0.155611i
$404$	2.70039e6	−	2.49165e6i	0.823140	−	0.759509i
$405$		0			0
$406$	1.51321e6	−	3.45519e6i	0.455601	−	1.04030i
$407$	3.42633e6			1.02528
$408$		0			0
$409$	−5.17948e6			−1.53101			−0.765505	−	0.643430i	$-0.777511\pi$
$409$	−5.17948e6			−1.53101			−0.765505	+	0.643430i	$0.777511\pi$
$410$	−335136.	+	765232.i	−0.0984604	+	0.224819i
$411$		0			0
$412$	837341.	+	907492.i	0.243030	+	0.263390i
$413$		−	4.13561e6i		−	1.19306i
$414$		0			0
$415$	−167021.			−0.0476048
$416$	−654358.	−	351686.i	−0.185388	−	0.0996371i
$417$		0			0
$418$	2.42301e6	+	1.06117e6i	0.678289	+	0.297059i
$419$			3.57698e6i			0.995363i	0.867360	+	0.497682i	$0.165815\pi$
$419$			3.57698e6i			0.995363i	−0.867360	+	0.497682i	$0.834185\pi$
$420$		0			0
$421$		−	2.15848e6i		−	0.593531i	−0.954950	−	0.296765i	$-0.904092\pi$
$421$		−	2.15848e6i		−	0.593531i	0.954950	−	0.296765i	$-0.0959080\pi$
$422$	1.25640e6	−	2.86880e6i	0.343437	−	0.784187i
$423$		0			0
$424$	5.24175e6	−	1.80964e6i	1.41600	−	0.488852i
$425$	−1.31920e6			−0.354273
$426$		0			0
$427$			6.40344e6i			1.69959i
$428$	−4.45572e6	+	4.11128e6i	−1.17573	+	1.08485i
$429$		0			0
$430$	−2.12963e6	−	932678.i	−0.555434	−	0.243254i
$431$	1.80890e6			0.469052			0.234526	−	0.972110i	$-0.424646\pi$
$431$	1.80890e6			0.469052			0.234526	+	0.972110i	$0.424646\pi$
$432$		0			0
$433$	1.28911e6			0.330423			0.165211	−	0.986258i	$-0.447169\pi$
$433$	1.28911e6			0.330423			0.165211	+	0.986258i	$0.447169\pi$
$434$	3.35581e6	+	1.46969e6i	0.855211	+	0.374542i
$435$		0			0
$436$	−573669.	+	529323.i	−0.144526	+	0.133354i
$437$			1.79058e6i			0.448530i
$438$		0			0
$439$	1.89694e6			0.469777			0.234889	−	0.972022i	$-0.424527\pi$
$439$	1.89694e6			0.469777			0.234889	+	0.972022i	$0.424527\pi$
$440$	−474829.	−	1.37538e6i	−0.116924	−	0.338681i
$441$		0			0
$442$	−614290.	+	1.40264e6i	−0.149561	+	0.341500i
$443$		−	6.01979e6i		−	1.45738i	−0.684845	−	0.728689i	$-0.740130\pi$
$443$		−	6.01979e6i		−	1.45738i	0.684845	−	0.728689i	$-0.259870\pi$
$444$		0			0
$445$		−	2.26002e6i		−	0.541019i
$446$	−1.44777e6	−	634055.i	−0.344637	−	0.150935i
$447$		0			0
$448$	−4.22178e6	+	3.30946e6i	−0.993803	+	0.779044i
$449$	2.40081e6			0.562007			0.281003	−	0.959707i	$-0.409333\pi$
$449$	2.40081e6			0.562007			0.281003	+	0.959707i	$0.409333\pi$
$450$		0			0
$451$			1.89928e6i			0.439691i
$452$	1.14834e6	+	1.24455e6i	0.264378	+	0.286527i
$453$		0			0
$454$	1.34588e6	−	3.07310e6i	0.306454	−	0.699741i
$455$	−524864.			−0.118855
$456$		0			0
$457$	−858952.			−0.192388			−0.0961941	−	0.995363i	$-0.530667\pi$
$457$	−858952.			−0.192388			−0.0961941	+	0.995363i	$0.530667\pi$
$458$	−2.10567e6	+	4.80797e6i	−0.469057	+	1.07102i
$459$		0			0
$460$	723875.	−	667918.i	0.159503	−	0.147173i
$461$			2.33481e6i			0.511680i	0.966719	+	0.255840i	$0.0823521\pi$
$461$			2.33481e6i			0.511680i	−0.966719	+	0.255840i	$0.917648\pi$
$462$		0			0
$463$	−1.35195e6			−0.293096			−0.146548	−	0.989204i	$-0.546816\pi$
$463$	−1.35195e6			−0.293096			−0.146548	+	0.989204i	$0.546816\pi$
$464$	−4.15748e6	−	334846.i	−0.896469	−	0.0722022i
$465$		0			0
$466$	−5.66253e6	−	2.47993e6i	−1.20794	−	0.529022i
$467$			6.44013e6i			1.36648i	0.730195	+	0.683239i	$0.239429\pi$
$467$			6.44013e6i			1.36648i	−0.730195	+	0.683239i	$0.760571\pi$
$468$		0			0
$469$		−	3.42056e6i		−	0.718068i
$470$	1.31842e6	−	3.01041e6i	0.275302	−	0.628610i
$471$		0			0
$472$	−4.32263e6	+	1.49232e6i	−0.893085	+	0.308324i
$473$	−5.28566e6			−1.08629
$474$		0			0
$475$		−	908980.i		−	0.184850i
$476$	7.49822e6	+	8.12641e6i	1.51684	+	1.64392i
$477$		0			0
$478$	−4.13483e6	−	1.81086e6i	−0.827729	−	0.362507i
$479$	1.85358e6			0.369124			0.184562	−	0.982821i	$-0.440913\pi$
$479$	1.85358e6			0.369124			0.184562	+	0.982821i	$0.440913\pi$
$480$		0			0
$481$	−1.36667e6			−0.269339
$482$	8.38717e6	+	3.67319e6i	1.64436	+	0.720154i
$483$		0			0
$484$	1.25157e6	+	1.35643e6i	0.242852	+	0.263198i
$485$		−	3.74040e6i		−	0.722043i
$486$		0			0
$487$	2.51668e6			0.480846			0.240423	−	0.970668i	$-0.422714\pi$
$487$	2.51668e6			0.480846			0.240423	+	0.970668i	$0.422714\pi$
$488$	6.69302e6	−	2.31067e6i	1.27225	−	0.439226i
$489$		0			0
$490$	−566921.	+	1.29448e6i	−0.106668	+	0.243559i
$491$		−	5.39115e6i		−	1.00920i	−0.863353	−	0.504601i	$-0.831640\pi$
$491$		−	5.39115e6i		−	1.00920i	0.863353	−	0.504601i	$-0.168360\pi$
$492$		0			0
$493$			8.59736e6i			1.59312i
$494$	−966472.	−	423270.i	−0.178185	−	0.0780369i
$495$		0			0
$496$	325215.	−	4.03790e6i	0.0593563	−	0.736973i
$497$	−2.27372e6			−0.412902
$498$		0			0
$499$		−	3.18358e6i		−	0.572353i	−0.958177	−	0.286177i	$-0.907616\pi$
$499$		−	3.18358e6i		−	0.572353i	0.958177	−	0.286177i	$-0.0923844\pi$
$500$	−367471.	+	339065.i	−0.0657352	+	0.0606537i
$501$		0			0
$502$	−1.02050e6	+	2.33015e6i	−0.180739	+	0.412690i
$503$	8.99291e6			1.58482			0.792410	−	0.609989i	$-0.208826\pi$
$503$	8.99291e6			1.58482			0.792410	+	0.609989i	$0.208826\pi$
$504$		0			0
$505$	−2.87054e6			−0.500882
$506$	898317.	−	2.05117e6i	0.155974	−	0.356144i
$507$		0			0
$508$	6.37226e6	+	6.90612e6i	1.09555	+	1.18734i
$509$		−	5.35388e6i		−	0.915956i	−0.888964	−	0.457978i	$-0.848574\pi$
$509$		−	5.35388e6i		−	0.915956i	0.888964	−	0.457978i	$-0.151426\pi$
$510$		0			0
$511$	−7.11322e6			−1.20508
$512$	4.98254e6	+	3.21849e6i	0.839993	+	0.542597i
$513$		0			0
$514$	2.05420e6	+	899646.i	0.342954	+	0.150198i
$515$		−	964672.i		−	0.160273i
$516$		0			0
$517$		−	7.47173e6i		−	1.22941i
$518$	−3.95900e6	+	9.03978e6i	−0.648278	+	1.48024i
$519$		0			0
$520$	189396.	+	548600.i	0.0307158	+	0.0889708i
$521$	2.62401e6			0.423518			0.211759	−	0.977322i	$-0.432081\pi$
$521$	2.62401e6			0.423518			0.211759	+	0.977322i	$0.432081\pi$
$522$		0			0
$523$			1.31228e6i			0.209784i	0.994484	+	0.104892i	$0.0334497\pi$
$523$			1.31228e6i			0.209784i	−0.994484	+	0.104892i	$0.966550\pi$
$524$	−7.47262e6	+	6.89497e6i	−1.18890	+	1.09699i
$525$		0			0
$526$	1.00226e7	+	4.38943e6i	1.57949	+	0.691741i
$527$	−8.35008e6			−1.30968
$528$		0			0
$529$	−4.92055e6			−0.764494
$530$	−3.96840e6	−	1.73798e6i	−0.613658	−	0.268753i
$531$		0			0
$532$	−5.59941e6	+	5.16657e6i	−0.857756	+	0.791449i
$533$		−	757570.i		−	0.115506i
$534$		0			0
$535$	4.73647e6			0.715435
$536$	−3.57525e6	+	1.23430e6i	−0.537520	+	0.185571i
$537$		0			0
$538$	1.52050e6	−	3.47183e6i	0.226480	−	0.517133i
$539$			3.21285e6i			0.476342i
$540$		0			0
$541$			6.84935e6i			1.00613i	0.864247	+	0.503067i	$0.167795\pi$
$541$			6.84935e6i			1.00613i	−0.864247	+	0.503067i	$0.832205\pi$
$542$	−1.08267e7	−	4.74157e6i	−1.58306	−	0.693304i
$543$		0			0
$544$	5.78820e6	−	1.07697e7i	0.838583	−	1.56029i
$545$	609815.			0.0879441
$546$		0			0
$547$		−	6.39084e6i		−	0.913251i	−0.889659	−	0.456625i	$-0.849058\pi$
$547$		−	6.39084e6i		−	0.913251i	0.889659	−	0.456625i	$-0.150942\pi$
$548$	3.52162e6	+	3.81665e6i	0.500946	+	0.542914i
$549$		0			0
$550$	−456025.	+	1.04126e6i	−0.0642810	+	0.146776i
$551$	−5.92391e6			−0.831246
$552$		0			0
$553$	−2.05392e6			−0.285609
$554$	1.88091e6	−	4.29477e6i	0.260372	−	0.594519i
$555$		0			0
$556$	−7.21441e6	+	6.65672e6i	−0.989724	+	0.913216i
$557$		−	463389.i		−	0.0632861i	−0.999499	−	0.0316430i	$-0.989926\pi$
$557$		−	463389.i		−	0.0632861i	0.999499	−	0.0316430i	$-0.0100740\pi$
$558$		0			0
$559$	2.10830e6			0.285367
$560$	4.17735e6	+	336446.i	0.562899	+	0.0453363i
$561$		0			0
$562$	1.24326e7	+	5.44488e6i	1.66043	+	0.727189i
$563$			1.07609e7i			1.43080i	0.698715	+	0.715400i	$0.253756\pi$
$563$			1.07609e7i			1.43080i	−0.698715	+	0.715400i	$0.746244\pi$
$564$		0			0
$565$		−	1.32296e6i		−	0.174352i
$566$	4.55839e6	−	1.04084e7i	0.598096	−	1.36566i
$567$		0			0
$568$	820467.	+	2.37655e6i	0.106706	+	0.309083i
$569$	1.04253e7			1.34992			0.674961	−	0.737853i	$-0.264160\pi$
$569$	1.04253e7			1.34992			0.674961	+	0.737853i	$0.264160\pi$
$570$		0			0
$571$			1.58675e6i			0.203666i	0.994802	+	0.101833i	$0.0324707\pi$
$571$			1.58675e6i			0.203666i	−0.994802	+	0.101833i	$0.967529\pi$
$572$	894774.	+	969737.i	0.114347	+	0.123926i
$573$		0			0
$574$	−5.01093e6	−	2.19455e6i	−0.634802	−	0.278014i
$575$	−769485.			−0.0970579
$576$		0			0
$577$	−2.79056e6			−0.348941			−0.174471	−	0.984662i	$-0.555821\pi$
$577$	−2.79056e6			−0.348941			−0.174471	+	0.984662i	$0.555821\pi$
$578$	−1.57280e7	−	6.88811e6i	−1.95818	−	0.857592i
$579$		0			0
$580$	2.20972e6	+	2.39485e6i	0.272751	+	0.295602i
$581$		−	1.09369e6i		−	0.134417i
$582$		0			0
$583$	−9.84944e6			−1.20016
$584$	2.56679e6	+	7.43490e6i	0.311428	+	0.902076i
$585$		0			0
$586$	−3.95327e6	+	9.02668e6i	−0.475567	+	1.08589i
$587$			1.94272e6i			0.232710i	0.993208	+	0.116355i	$0.0371210\pi$
$587$			1.94272e6i			0.232710i	−0.993208	+	0.116355i	$0.962879\pi$
$588$		0			0
$589$		−	5.75353e6i		−	0.683355i
$590$	3.27256e6	+	1.43323e6i	0.387041	+	0.169506i
$591$		0			0
$592$	1.08772e7	+	876055.i	1.27559	+	0.102737i
$593$	−8.14862e6			−0.951584			−0.475792	−	0.879558i	$-0.657839\pi$
$593$	−8.14862e6			−0.951584			−0.475792	+	0.879558i	$0.657839\pi$
$594$		0			0
$595$		−	8.63845e6i		−	1.00033i
$596$	8.65720e6	−	7.98798e6i	0.998302	−	0.921131i
$597$		0			0
$598$	−358313.	+	818154.i	−0.0409742	+	0.0935583i
$599$	−1.49677e6			−0.170447			−0.0852234	−	0.996362i	$-0.527160\pi$
$599$	−1.49677e6			−0.170447			−0.0852234	+	0.996362i	$0.527160\pi$
$600$		0			0
$601$	−9.04082e6			−1.02099			−0.510495	−	0.859881i	$-0.670538\pi$
$601$	−9.04082e6			−1.02099			−0.510495	+	0.859881i	$0.670538\pi$
$602$	6.10740e6	−	1.39453e7i	0.686855	−	1.56833i
$603$		0			0
$604$	7.30910e6	+	7.92144e6i	0.815213	+	0.883511i
$605$		−	1.44189e6i		−	0.160156i
$606$		0			0
$607$	−3.63200e6			−0.400105			−0.200052	−	0.979785i	$-0.564111\pi$
$607$	−3.63200e6			−0.400105			−0.200052	+	0.979785i	$0.564111\pi$
$608$	7.42075e6	+	3.98829e6i	0.814120	+	0.437550i
$609$		0			0
$610$	−5.06712e6	−	2.21916e6i	−0.551362	−	0.241471i
$611$			2.98027e6i			0.322962i
$612$		0			0
$613$		−	1.89937e6i		−	0.204154i	−0.994776	−	0.102077i	$-0.967451\pi$
$613$		−	1.89937e6i		−	0.204154i	0.994776	−	0.102077i	$-0.0325488\pi$
$614$	−2.22099e6	+	5.07128e6i	−0.237752	+	0.542871i
$615$		0			0
$616$	9.00631e6	−	3.10929e6i	0.956302	−	0.330149i
$617$	−5.96746e6			−0.631069			−0.315534	−	0.948914i	$-0.602184\pi$
$617$	−5.96746e6			−0.631069			−0.315534	+	0.948914i	$0.602184\pi$
$618$		0			0
$619$		−	1.46307e7i		−	1.53475i	−0.641196	−	0.767377i	$-0.721561\pi$
$619$		−	1.46307e7i		−	1.53475i	0.641196	−	0.767377i	$-0.278439\pi$
$620$	−2.32597e6	+	2.14616e6i	−0.243010	+	0.224225i
$621$		0			0
$622$	−8.16905e6	−	3.57766e6i	−0.846634	−	0.370786i
$623$	1.47992e7			1.52763
$624$		0			0
$625$	390625.			0.0400000
$626$	−8.34055e6	−	3.65277e6i	−0.850666	−	0.372552i
$627$		0			0
$628$	−6.37936e6	+	5.88622e6i	−0.645473	+	0.595577i
$629$		−	2.24932e7i		−	2.26686i
$630$		0			0
$631$	−1.47747e7			−1.47722			−0.738609	−	0.674134i	$-0.764517\pi$
$631$	−1.47747e7			−1.47722			−0.738609	+	0.674134i	$0.764517\pi$
$632$	741154.	+	2.14681e6i	0.0738101	+	0.213796i
$633$		0			0
$634$	−3.41923e6	+	7.80729e6i	−0.337835	+	0.771395i
$635$		−	7.34126e6i		−	0.722497i
$636$		0			0
$637$		−	1.28152e6i		−	0.125134i
$638$	6.78603e6	+	2.97196e6i	0.660030	+	0.289062i
$639$		0			0
$640$	−1.15572e6	−	4.48766e6i	−0.111533	−	0.433082i
$641$	−1.81017e7			−1.74010			−0.870050	−	0.492964i	$-0.835913\pi$
$641$	−1.81017e7			−1.74010			−0.870050	+	0.492964i	$0.835913\pi$
$642$		0			0
$643$			7.21849e6i			0.688524i	0.938874	+	0.344262i	$0.111871\pi$
$643$			7.21849e6i			0.688524i	−0.938874	+	0.344262i	$0.888129\pi$
$644$	4.37369e6	+	4.74011e6i	0.415559	+	0.450374i
$645$		0			0
$646$	6.96636e6	−	1.59066e7i	0.656787	−	1.49967i
$647$	−2.44672e6			−0.229786			−0.114893	−	0.993378i	$-0.536653\pi$
$647$	−2.44672e6			−0.229786			−0.114893	+	0.993378i	$0.536653\pi$
$648$		0			0
$649$	8.12237e6			0.756957
$650$	181896.	−	415332.i	0.0168865	−	0.0385577i
$651$		0			0
$652$	2.85403e6	−	2.63341e6i	0.262930	−	0.242605i
$653$			5.92231e6i			0.543511i	0.962366	+	0.271755i	$0.0876041\pi$
$653$			5.92231e6i			0.543511i	−0.962366	+	0.271755i	$0.912396\pi$
$654$		0			0
$655$	7.94346e6			0.723446
$656$	−485615.	+	6.02943e6i	−0.0440587	+	0.547037i
$657$		0			0
$658$	1.97129e7	+	8.63333e6i	1.77495	+	0.777345i
$659$			2.68146e6i			0.240523i	0.992742	+	0.120262i	$0.0383734\pi$
$659$			2.68146e6i			0.240523i	−0.992742	+	0.120262i	$0.961627\pi$
$660$		0			0
$661$		−	1.14098e7i		−	1.01572i	−0.861440	−	0.507859i	$-0.830437\pi$
$661$		−	1.14098e7i		−	1.01572i	0.861440	−	0.507859i	$-0.169563\pi$
$662$	895150.	−	2.04394e6i	0.0793873	−	0.181269i
$663$		0			0
$664$	−1.14315e6	+	394657.i	−0.100620	+	0.0347376i
$665$	5.95223e6			0.521946
$666$		0			0
$667$			5.01481e6i			0.436456i
$668$	−1.21728e6	−	1.31926e6i	−0.105548	−	0.114390i
$669$		0			0
$670$	2.70673e6	+	1.18542e6i	0.232948	+	0.102020i
$671$	−1.25764e7			−1.07833
$672$		0			0
$673$	−5.13646e6			−0.437146			−0.218573	−	0.975821i	$-0.570140\pi$
$673$	−5.13646e6			−0.437146			−0.218573	+	0.975821i	$0.570140\pi$
$674$	7.09269e6	+	3.10627e6i	0.601397	+	0.263384i
$675$		0			0
$676$	7.70021e6	+	8.34533e6i	0.648091	+	0.702387i
$677$		−	4.91407e6i		−	0.412068i	−0.978545	−	0.206034i	$-0.933944\pi$
$677$		−	4.91407e6i		−	0.412068i	0.978545	−	0.206034i	$-0.0660558\pi$
$678$		0			0
$679$	2.44930e7			2.03877
$680$	−9.02910e6	+	3.11716e6i	−0.748811	+	0.258516i
$681$		0			0
$682$	−2.88648e6	+	6.59085e6i	−0.237634	+	0.542601i
$683$		−	4.30841e6i		−	0.353399i	−0.984265	−	0.176700i	$-0.943458\pi$
$683$		−	4.30841e6i		−	0.353399i	0.984265	−	0.176700i	$-0.0565421\pi$
$684$		0			0
$685$		−	4.05713e6i		−	0.330364i
$686$	5.78043e6	+	2.53156e6i	0.468975	+	0.205389i
$687$		0			0
$688$	−1.67798e7	−	1.35146e6i	−1.35150	−	0.108851i
$689$	3.92867e6			0.315281
$690$		0			0
$691$			2.17672e6i			0.173423i	0.996233	+	0.0867116i	$0.0276359\pi$
$691$			2.17672e6i			0.173423i	−0.996233	+	0.0867116i	$0.972364\pi$
$692$	3.94319e6	−	3.63837e6i	0.313027	−	0.288829i
$693$		0			0
$694$	1.29211e6	−	2.95034e6i	0.101836	−	0.232527i
$695$	7.66898e6			0.602249
$696$		0			0
$697$	1.24684e7			0.972142
$698$	−4.99375e6	+	1.14025e7i	−0.387961	+	0.885851i
$699$		0			0
$700$	−2.22028e6	−	2.40629e6i	−0.171263	−	0.185611i
$701$			1.31991e6i			0.101450i	0.998713	+	0.0507248i	$0.0161531\pi$
$701$			1.31991e6i			0.101450i	−0.998713	+	0.0507248i	$0.983847\pi$
$702$		0			0
$703$	1.54987e7			1.18279
$704$	−6.49981e6	−	8.29162e6i	−0.494275	−	0.630533i
$705$		0			0
$706$	−1.30349e7	−	5.70870e6i	−0.984232	−	0.431048i
$707$		−	1.87970e7i		−	1.41429i
$708$		0			0
$709$			1.33410e7i			0.996721i	0.866970	+	0.498360i	$0.166064\pi$
$709$			1.33410e7i			0.996721i	−0.866970	+	0.498360i	$0.833936\pi$
$710$	787977.	−	1.79923e6i	0.0586634	−	0.133949i
$711$		0			0
$712$	−5.34024e6	−	1.54684e7i	−0.394785	−	1.14353i
$713$	−4.87058e6			−0.358803
$714$		0			0
$715$		−	1.03084e6i		−	0.0754094i
$716$	1.26039e7	−	1.16296e7i	0.918800	−	0.847775i
$717$		0			0
$718$	−4.11846e6	−	1.80369e6i	−0.298143	−	0.130573i
$719$	−2.25289e7			−1.62524			−0.812620	−	0.582794i	$-0.801960\pi$
$719$	−2.25289e7			−1.62524			−0.812620	+	0.582794i	$0.801960\pi$
$720$		0			0
$721$	6.31691e6			0.452550
$722$	−1.87013e6	−	819031.i	−0.133515	−	0.0584732i
$723$		0			0
$724$	2.66805e6	−	2.46180e6i	0.189168	−	0.174545i
$725$		−	2.54574e6i		−	0.179874i
$726$		0			0
$727$	−1.49088e7			−1.04618			−0.523091	−	0.852277i	$-0.675221\pi$
$727$	−1.49088e7			−1.04618			−0.523091	+	0.852277i	$0.675221\pi$
$728$	−3.59237e6	+	1.24021e6i	−0.251219	+	0.0867296i
$729$		0			0
$730$	2.46514e6	−	5.62878e6i	0.171212	−	0.390937i
$731$			3.46994e7i			2.40175i
$732$		0			0
$733$			7.98329e6i			0.548810i	0.961614	+	0.274405i	$0.0884809\pi$
$733$			7.98329e6i			0.548810i	−0.961614	+	0.274405i	$0.911519\pi$
$734$	4.53037e6	+	1.98409e6i	0.310380	+	0.135932i
$735$		0			0
$736$	3.37624e6	−	6.28193e6i	0.229741	−	0.427463i
$737$	6.71802e6			0.455588
$738$		0			0
$739$		−	3.81018e6i		−	0.256646i	−0.991732	−	0.128323i	$-0.959041\pi$
$739$		−	3.81018e6i		−	0.256646i	0.991732	−	0.128323i	$-0.0409594\pi$
$740$	−5.78127e6	−	6.26561e6i	−0.388100	−	0.420615i
$741$		0			0
$742$	1.13807e7	−	2.59861e7i	0.758855	−	1.73273i
$743$	−8.99457e6			−0.597734			−0.298867	−	0.954295i	$-0.596609\pi$
$743$	−8.99457e6			−0.597734			−0.298867	+	0.954295i	$0.596609\pi$
$744$		0			0
$745$	−9.20268e6			−0.607468
$746$	−1.10337e7	+	2.51937e7i	−0.725893	+	1.65747i
$747$		0			0
$748$	−1.59604e7	+	1.47266e7i	−1.04301	+	0.962383i
$749$			3.10156e7i			2.02011i
$750$		0			0
$751$	1.18325e7			0.765559			0.382779	−	0.923840i	$-0.374967\pi$
$751$	1.18325e7			0.765559			0.382779	+	0.923840i	$0.374967\pi$
$752$	1.91040e6	−	2.37197e7i	0.123191	−	1.52955i
$753$		0			0
$754$	−2.70676e6	−	1.18543e6i	−0.173389	−	0.0759362i
$755$		−	8.42056e6i		−	0.537618i
$756$		0			0
$757$		−	5.14086e6i		−	0.326059i	−0.986621	−	0.163030i	$-0.947873\pi$
$757$		−	5.14086e6i		−	0.326059i	0.986621	−	0.163030i	$-0.0521266\pi$
$758$	2.81739e6	−	6.43308e6i	0.178104	−	0.406673i
$759$		0			0
$760$	−2.14785e6	−	6.22140e6i	−0.134887	−	0.390710i
$761$	−8.21979e6			−0.514516			−0.257258	−	0.966343i	$-0.582819\pi$
$761$	−8.21979e6			−0.514516			−0.257258	+	0.966343i	$0.582819\pi$
$762$		0			0
$763$			3.99322e6i			0.248320i
$764$	−8.50230e6	−	9.21461e6i	−0.526991	−	0.571142i
$765$		0			0
$766$	−160477.	−	70281.3i	−0.00988189	−	0.00432781i
$767$	−3.23979e6			−0.198851
$768$		0			0
$769$	−1.11390e7			−0.679251			−0.339626	−	0.940561i	$-0.610300\pi$
$769$	−1.11390e7			−0.679251			−0.339626	+	0.940561i	$0.610300\pi$
$770$	−6.81846e6	−	2.98617e6i	−0.414438	−	0.181504i
$771$		0			0
$772$	−5.67487e6	−	6.15030e6i	−0.342699	−	0.371410i
$773$			5.63671e6i			0.339294i	0.985505	+	0.169647i	$0.0542628\pi$
$773$			5.63671e6i			0.339294i	−0.985505	+	0.169647i	$0.945737\pi$
$774$		0			0
$775$	2.47252e6			0.147872
$776$	−8.83825e6	−	2.56007e7i	−0.526880	−	1.52615i
$777$		0			0
$778$	−9.70963e6	+	2.21705e7i	−0.575113	+	1.31318i
$779$			8.59123e6i			0.507238i
$780$		0			0
$781$		−	4.46561e6i		−	0.261971i
$782$	−1.34655e7	−	5.89728e6i	−0.787421	−	0.344854i
$783$		0			0
$784$	−821473.	+	1.01995e7i	−0.0477313	+	0.592636i
$785$	6.78132e6			0.392771
$786$		0			0
$787$			3.07197e7i			1.76799i	0.467495	+	0.883996i	$0.345157\pi$
$787$			3.07197e7i			1.76799i	−0.467495	+	0.883996i	$0.654843\pi$
$788$	−2.11416e7	+	1.95073e7i	−1.21289	+	1.11913i
$789$		0			0
$790$	711804.	−	1.62530e6i	0.0405782	−	0.0926541i
$791$	8.66309e6			0.492302
$792$		0			0
$793$	5.01639e6			0.283275
$794$	−5.24489e6	+	1.19759e7i	−0.295246	+	0.674151i
$795$		0			0
$796$	−1.81672e6	−	1.96892e6i	−0.101626	−	0.110140i
$797$		−	2.22339e7i		−	1.23985i	−0.784660	−	0.619926i	$-0.787163\pi$
$797$		−	2.22339e7i		−	1.23985i	0.784660	−	0.619926i	$-0.212837\pi$
$798$		0			0
$799$	−4.90505e7			−2.71817
$800$	−1.71393e6	+	3.18899e6i	−0.0946820	+	0.176168i
$801$		0			0
$802$	5.16278e6	+	2.26106e6i	0.283431	+	0.124130i
$803$		−	1.39704e7i		−	0.764577i
$804$		0			0
$805$		−	5.03878e6i		−	0.274054i
$806$	1.15134e6	−	2.62891e6i	0.0624260	−	0.142540i
$807$		0			0
$808$	−1.96470e7	+	6.78285e6i	−1.05869	+	0.365497i
$809$	−1.51247e7			−0.812484			−0.406242	−	0.913765i	$-0.633161\pi$
$809$	−1.51247e7			−0.812484			−0.406242	+	0.913765i	$0.633161\pi$
$810$		0			0
$811$			1.35982e7i			0.725990i	0.931791	+	0.362995i	$0.118246\pi$
$811$			1.35982e7i			0.725990i	−0.931791	+	0.362995i	$0.881754\pi$
$812$	−1.56820e7	+	1.44698e7i	−0.834665	+	0.770143i
$813$		0			0
$814$	−1.77542e7	−	7.77552e6i	−0.939162	−	0.411309i
$815$	−3.03386e6			−0.159993
$816$		0			0
$817$	−2.39092e7			−1.25317
$818$	2.68385e7	+	1.17540e7i	1.40241	+	0.614191i
$819$		0			0
$820$	3.47315e6	−	3.20467e6i	0.180380	−	0.166437i
$821$			2.56951e7i			1.33043i	0.746651	+	0.665216i	$0.231660\pi$
$821$			2.56951e7i			1.33043i	−0.746651	+	0.665216i	$0.768340\pi$
$822$		0			0
$823$	8.73184e6			0.449372			0.224686	−	0.974431i	$-0.427864\pi$
$823$	8.73184e6			0.449372			0.224686	+	0.974431i	$0.427864\pi$
$824$	−2.27944e6	−	6.60257e6i	−0.116953	−	0.338762i
$825$		0			0
$826$	−9.38512e6	+	2.14295e7i	−0.478619	+	1.09285i
$827$		−	1.46565e6i		−	0.0745191i	−0.999306	−	0.0372596i	$-0.988137\pi$
$827$		−	1.46565e6i		−	0.0745191i	0.999306	−	0.0372596i	$-0.0118628\pi$
$828$		0			0
$829$		−	4.49887e6i		−	0.227362i	−0.993517	−	0.113681i	$-0.963736\pi$
$829$		−	4.49887e6i		−	0.227362i	0.993517	−	0.113681i	$-0.0362641\pi$
$830$	865453.	+	379028.i	0.0436062	+	0.0190975i
$831$		0			0
$832$	2.59259e6	+	3.30729e6i	0.129845	+	0.165640i
$833$	2.10918e7			1.05317
$834$		0			0
$835$			1.40239e6i			0.0696067i
$836$	−1.01472e7	−	1.09973e7i	−0.502146	−	0.544215i
$837$		0			0
$838$	8.11741e6	−	1.85349e7i	0.399307	−	0.911758i
$839$	1.43801e7			0.705273			0.352636	−	0.935760i	$-0.385285\pi$
$839$	1.43801e7			0.705273			0.352636	+	0.935760i	$0.385285\pi$
$840$		0			0
$841$	3.92030e6			0.191130
$842$	−4.89834e6	+	1.11846e7i	−0.238105	+	0.543677i
$843$		0			0
$844$	−1.30206e7	+	1.20141e7i	−0.629180	+	0.580543i
$845$		−	8.87115e6i		−	0.427404i
$846$		0			0
$847$	9.44185e6			0.452219
$848$	−3.12679e7	−	2.51834e6i	−1.49317	−	0.120261i
$849$		0			0
$850$	6.83571e6	+	2.99372e6i	0.324516	+	0.142123i
$851$		−	1.31202e7i		−	0.621036i
$852$		0			0
$853$		−	2.62365e7i		−	1.23462i	−0.786720	−	0.617310i	$-0.788222\pi$
$853$		−	2.62365e7i		−	1.23462i	0.786720	−	0.617310i	$-0.211778\pi$
$854$	1.45316e7	−	3.31808e7i	0.681820	−	1.55683i
$855$		0			0
$856$	3.24182e7	−	1.11919e7i	1.51218	−	0.522058i
$857$	6.34066e6			0.294905			0.147453	−	0.989069i	$-0.452893\pi$
$857$	6.34066e6			0.294905			0.147453	+	0.989069i	$0.452893\pi$
$858$		0			0
$859$		−	1.09488e7i		−	0.506273i	−0.967431	−	0.253137i	$-0.918538\pi$
$859$		−	1.09488e7i		−	0.506273i	0.967431	−	0.253137i	$-0.0814622\pi$
$860$	8.91854e6	+	9.66572e6i	0.411195	+	0.445644i
$861$		0			0
$862$	−9.37318e6	−	4.10501e6i	−0.429654	−	0.188168i
$863$	3.28604e6			0.150192			0.0750958	−	0.997176i	$-0.476074\pi$
$863$	3.28604e6			0.150192			0.0750958	+	0.997176i	$0.476074\pi$
$864$		0			0
$865$	−4.19164e6			−0.190478
$866$	−6.67978e6	−	2.92543e6i	−0.302669	−	0.132555i
$867$		0			0
$868$	−1.40536e7	−	1.52310e7i	−0.633123	−	0.686165i
$869$		−	4.03393e6i		−	0.181209i
$870$		0			0
$871$	−2.67963e6			−0.119682
$872$	4.17380e6	−	1.44094e6i	0.185883	−	0.0641735i
$873$		0			0
$874$	4.06345e6	−	9.27828e6i	0.179936	−	0.410855i
$875$			2.55791e6i			0.112944i
$876$		0			0
$877$			7.75326e6i			0.340397i	0.985410	+	0.170198i	$0.0544409\pi$
$877$			7.75326e6i			0.340397i	−0.985410	+	0.170198i	$0.945559\pi$
$878$	−9.82937e6	−	4.30481e6i	−0.430318	−	0.188459i
$879$		0			0
$880$	−660784.	+	8.20435e6i	−0.0287642	+	0.357139i
$881$	449453.			0.0195094			0.00975471	−	0.999952i	$-0.496895\pi$
$881$	449453.			0.0195094			0.00975471	+	0.999952i	$0.496895\pi$
$882$		0			0
$883$		−	2.42001e7i		−	1.04452i	−0.852787	−	0.522259i	$-0.825089\pi$
$883$		−	2.42001e7i		−	1.04452i	0.852787	−	0.522259i	$-0.174911\pi$
$884$	6.36614e6	−	5.87402e6i	0.273997	−	0.252816i
$885$		0			0
$886$	−1.36610e7	+	3.11928e7i	−0.584652	+	1.33496i
$887$	−8.80204e6			−0.375642			−0.187821	−	0.982203i	$-0.560143\pi$
$887$	−8.80204e6			−0.375642			−0.187821	+	0.982203i	$0.560143\pi$
$888$		0			0
$889$	4.80724e7			2.04005
$890$	−5.12877e6	+	1.17108e7i	−0.217039	+	0.495576i
$891$		0			0
$892$	6.06302e6	+	6.57097e6i	0.255139	+	0.276514i
$893$		−	3.37977e7i		−	1.41827i
$894$		0			0
$895$	−1.33980e7			−0.559091
$896$	2.93863e7	−	7.56797e6i	1.22286	−	0.314926i
$897$		0			0
$898$	−1.24403e7	−	5.44826e6i	−0.514801	−	0.225459i
$899$		−	1.61137e7i		−	0.664959i
$900$		0			0
$901$			6.46597e7i			2.65352i
$902$	4.31012e6	−	9.84151e6i	0.176390	−	0.402759i
$903$		0			0
$904$	−3.12606e6	−	9.05486e6i	−0.127226	−	0.368520i
$905$	−2.83616e6			−0.115109
$906$		0			0
$907$		−	1.35035e7i		−	0.545040i	−0.962150	−	0.272520i	$-0.912143\pi$
$907$		−	1.35035e7i		−	0.545040i	0.962150	−	0.272520i	$-0.0878571\pi$
$908$	−1.39479e7	+	1.28697e7i	−0.561426	+	0.518027i
$909$		0			0
$910$	2.71969e6	+	1.19110e6i	0.108872	+	0.0476809i
$911$	1.74802e7			0.697831			0.348915	−	0.937154i	$-0.386550\pi$
$911$	1.74802e7			0.697831			0.348915	+	0.937154i	$0.386550\pi$
$912$		0			0
$913$	2.14803e6			0.0852830
$914$	4.45083e6	+	1.94926e6i	0.176228	+	0.0771798i
$915$		0			0
$916$	2.18219e7	−	2.01350e7i	0.859317	−	0.792890i
$917$			5.20157e7i			2.04273i
$918$		0			0
$919$	3.84416e7			1.50146			0.750728	−	0.660612i	$-0.229703\pi$
$919$	3.84416e7			1.50146			0.750728	+	0.660612i	$0.229703\pi$
$920$	−5.26664e6	+	1.81823e6i	−0.205147	+	0.0708238i
$921$		0			0
$922$	5.29849e6	−	1.20983e7i	0.205270	−	0.468702i
$923$			1.78121e6i			0.0688194i
$924$		0			0
$925$			6.66040e6i			0.255945i
$926$	7.00542e6	+	3.06805e6i	0.268477	+	0.117580i
$927$		0			0
$928$	2.07830e7	+	1.11698e7i	0.792205	+	0.425772i
$929$	694053.			0.0263848			0.0131924	−	0.999913i	$-0.495801\pi$
$929$	694053.			0.0263848			0.0131924	+	0.999913i	$0.495801\pi$
$930$		0			0
$931$			1.45330e7i			0.549518i
$932$	2.37138e7	+	2.57005e7i	0.894254	+	0.969174i
$933$		0			0
$934$	1.46149e7	−	3.33709e7i	0.548186	−	1.25170i
$935$	1.69660e7			0.634673
$936$		0			0
$937$	4.08849e7			1.52130			0.760648	−	0.649165i	$-0.224881\pi$
$937$	4.08849e7			1.52130			0.760648	+	0.649165i	$0.224881\pi$
$938$	−7.76244e6	+	1.77243e7i	−0.288065	+	0.657753i
$939$		0			0
$940$	−1.36633e7	+	1.26071e7i	−0.504355	+	0.465367i
$941$			1.21324e7i			0.446655i	0.974743	+	0.223328i	$0.0716920\pi$
$941$			1.21324e7i			0.446655i	−0.974743	+	0.223328i	$0.928308\pi$
$942$		0			0
$943$	7.27279e6			0.266331
$944$	2.57852e7	+	2.07676e6i	0.941760	+	0.0758500i
$945$		0			0
$946$	2.73887e7	+	1.19950e7i	0.995049	+	0.435785i
$947$		−	3.38948e7i		−	1.22817i	−0.789241	−	0.614084i	$-0.789526\pi$
$947$		−	3.38948e7i		−	1.22817i	0.789241	−	0.614084i	$-0.210474\pi$
$948$		0			0
$949$			5.57242e6i			0.200853i
$950$	−2.06279e6	+	4.71007e6i	−0.0741560	+	0.169324i
$951$		0			0
$952$	−2.04119e7	−	5.91247e7i	−0.729948	−	2.11435i
$953$	5.18152e7			1.84810			0.924049	−	0.382274i	$-0.124859\pi$
$953$	5.18152e7			1.84810			0.924049	+	0.382274i	$0.124859\pi$
$954$		0			0
$955$			9.79521e6i			0.347541i
$956$	1.73160e7	+	1.87667e7i	0.612778	+	0.664116i
$957$		0			0
$958$	−9.60470e6	−	4.20641e6i	−0.338119	−	0.148080i
$959$	2.65671e7			0.932819
$960$		0			0
$961$	−1.29789e7			−0.453347
$962$	7.08166e6	+	3.10144e6i	0.246716	+	0.108050i
$963$		0			0
$964$	−3.51241e7	−	3.80667e7i	−1.21734	−	1.31933i
$965$			6.53783e6i			0.226003i
$966$		0			0
$967$	−4.41440e7			−1.51812			−0.759058	−	0.651023i	$-0.774340\pi$
$967$	−4.41440e7			−1.51812			−0.759058	+	0.651023i	$0.774340\pi$
$968$	−3.40707e6	−	9.86884e6i	−0.116867	−	0.338515i
$969$		0			0
$970$	−8.48825e6	+	1.93816e7i	−0.289660	+	0.661395i
$971$			2.25369e7i			0.767091i	0.923522	+	0.383546i	$0.125297\pi$
$971$			2.25369e7i			0.767091i	−0.923522	+	0.383546i	$0.874703\pi$
$972$		0			0
$973$			5.02184e7i			1.70052i
$974$	−1.30407e7	−	5.71122e6i	−0.440457	−	0.192900i
$975$		0			0
$976$	−3.99250e7	−	3.21558e6i	−1.34159	−	0.108053i
$977$	508955.			0.0170586			0.00852929	−	0.999964i	$-0.497285\pi$
$977$	508955.			0.0170586			0.00852929	+	0.999964i	$0.497285\pi$
$978$		0			0
$979$			2.90657e7i			0.969224i
$980$	5.87523e6	−	5.42106e6i	0.195416	−	0.180310i
$981$		0			0
$982$	−1.22344e7	+	2.79354e7i	−0.404859	+	0.924433i
$983$	1.38312e7			0.456536			0.228268	−	0.973598i	$-0.426694\pi$
$983$	1.38312e7			0.456536			0.228268	+	0.973598i	$0.426694\pi$
$984$		0			0
$985$	2.24737e7			0.738046
$986$	1.95104e7	−	4.45490e7i	0.639107	−	1.45930i
$987$		0			0
$988$	4.04743e6	+	4.38652e6i	0.131913	+	0.142964i
$989$			2.02400e7i			0.657992i
$990$		0			0
$991$	1.13368e7			0.366696			0.183348	−	0.983048i	$-0.441307\pi$
$991$	1.13368e7			0.366696			0.183348	+	0.983048i	$0.441307\pi$
$992$	−1.08486e7	+	2.01852e7i	−0.350020	+	0.651259i
$993$		0			0
$994$	1.17818e7	+	5.15986e6i	0.378220	+	0.165643i
$995$			2.09298e6i			0.0670205i
$996$		0			0
$997$			3.66390e7i			1.16736i	0.811983	+	0.583681i	$0.198388\pi$
$997$			3.66390e7i			1.16736i	−0.811983	+	0.583681i	$0.801612\pi$
$998$	−7.22464e6	+	1.64964e7i	−0.229609	+	0.524278i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	360.6.k.b.181.3		20
3.2	odd	2		40.6.d.a.21.18	yes	20
8.5	even	2	inner	360.6.k.b.181.4		20
12.11	even	2		160.6.d.a.81.14		20
15.2	even	4		200.6.f.b.149.8		20
15.8	even	4		200.6.f.c.149.13		20
15.14	odd	2		200.6.d.b.101.3		20
24.5	odd	2		40.6.d.a.21.17	✓	20
24.11	even	2		160.6.d.a.81.7		20
60.23	odd	4		800.6.f.b.49.8		20
60.47	odd	4		800.6.f.c.49.13		20
60.59	even	2		800.6.d.c.401.7		20
120.29	odd	2		200.6.d.b.101.4		20
120.53	even	4		200.6.f.b.149.7		20
120.59	even	2		800.6.d.c.401.14		20
120.77	even	4		200.6.f.c.149.14		20
120.83	odd	4		800.6.f.c.49.14		20
120.107	odd	4		800.6.f.b.49.7		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
40.6.d.a.21.17	✓	20	24.5	odd	2
40.6.d.a.21.18	yes	20	3.2	odd	2
160.6.d.a.81.7		20	24.11	even	2
160.6.d.a.81.14		20	12.11	even	2
200.6.d.b.101.3		20	15.14	odd	2
200.6.d.b.101.4		20	120.29	odd	2
200.6.f.b.149.7		20	120.53	even	4
200.6.f.b.149.8		20	15.2	even	4
200.6.f.c.149.13		20	15.8	even	4
200.6.f.c.149.14		20	120.77	even	4
360.6.k.b.181.3		20	1.1	even	1	trivial
360.6.k.b.181.4		20	8.5	even	2	inner
800.6.d.c.401.7		20	60.59	even	2
800.6.d.c.401.14		20	120.59	even	2
800.6.f.b.49.7		20	120.107	odd	4
800.6.f.b.49.8		20	60.23	odd	4
800.6.f.c.49.13		20	60.47	odd	4
800.6.f.c.49.14		20	120.83	odd	4

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:	\( N \)	\(=\)	\( 360 = 2^{3} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	360.k (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-5.18171 - 2.26935i) q^{2} +(21.7001 + 23.5182i) q^{4} -25.0000i q^{5} +163.706 q^{7} +(-59.0729 - 171.109i) q^{8} +(-56.7336 + 129.543i) q^{10} +321.520i q^{11} -128.246i q^{13} +(-848.277 - 371.506i) q^{14} +(-82.2074 + 1020.69i) q^{16} +2110.72 q^{17} +1454.37i q^{19} +(587.954 - 542.504i) q^{20} +(729.641 - 1666.02i) q^{22} +1231.18 q^{23} -625.000 q^{25} +(-291.033 + 664.531i) q^{26} +(3552.45 + 3850.07i) q^{28} +4073.19i q^{29} -3956.03 q^{31} +(2742.28 - 5102.38i) q^{32} +(-10937.1 - 4789.95i) q^{34} -4092.65i q^{35} -10656.6i q^{37} +(3300.46 - 7536.11i) q^{38} +(-4277.73 + 1476.82i) q^{40} +5907.19 q^{41} +16439.6i q^{43} +(-7561.57 + 6977.04i) q^{44} +(-6379.59 - 2793.96i) q^{46} -23238.8 q^{47} +9992.68 q^{49} +(3238.57 + 1418.34i) q^{50} +(3016.10 - 2782.95i) q^{52} +30634.0i q^{53} +8038.01 q^{55} +(-9670.60 - 28011.6i) q^{56} +(9243.47 - 21106.1i) q^{58} -25262.4i q^{59} +39115.5i q^{61} +(20499.0 + 8977.61i) q^{62} +(-25788.8 + 20215.9i) q^{64} -3206.14 q^{65} -20894.5i q^{67} +(45803.0 + 49640.3i) q^{68} +(-9287.64 + 21206.9i) q^{70} -13889.1 q^{71} -43451.2 q^{73} +(-24183.6 + 55219.6i) q^{74} +(-34204.1 + 31560.0i) q^{76} +52634.8i q^{77} -12546.4 q^{79} +(25517.4 + 2055.19i) q^{80} +(-30609.3 - 13405.4i) q^{82} -6680.84i q^{83} -52768.0i q^{85} +(37307.1 - 85185.1i) q^{86} +(55015.1 - 18993.2i) q^{88} +90400.9 q^{89} -20994.6i q^{91} +(26716.7 + 28955.0i) q^{92} +(120416. + 52736.8i) q^{94} +36359.2 q^{95} +149616. q^{97} +(-51779.1 - 22676.8i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 2 q^{2} - 32 q^{4} - 196 q^{7} - 248 q^{8} - 50 q^{10} - 2708 q^{14} + 3080 q^{16} + 1900 q^{20} + 13836 q^{22} + 4676 q^{23} - 12500 q^{25} + 8084 q^{26} + 2108 q^{28} + 7160 q^{31} - 6792 q^{32}+ \cdots - 216942 q^{98}+O(q^{100}) \) 20 * q - 2 * q^2 - 32 * q^4 - 196 * q^7 - 248 * q^8 - 50 * q^10 - 2708 * q^14 + 3080 * q^16 + 1900 * q^20 + 13836 * q^22 + 4676 * q^23 - 12500 * q^25 + 8084 * q^26 + 2108 * q^28 + 7160 * q^31 - 6792 * q^32 + 21132 * q^34 + 19580 * q^38 + 6200 * q^40 - 11608 * q^41 - 72296 * q^44 - 28516 * q^46 - 44180 * q^47 + 18756 * q^49 + 1250 * q^50 - 39680 * q^52 - 24200 * q^55 + 53624 * q^56 + 59496 * q^58 - 59824 * q^62 - 11264 * q^64 - 11576 * q^68 + 29800 * q^70 + 200312 * q^71 - 105136 * q^73 - 78876 * q^74 - 153872 * q^76 + 282080 * q^79 - 16000 * q^80 - 223032 * q^82 - 27452 * q^86 + 86896 * q^88 + 3160 * q^89 - 107916 * q^92 + 148820 * q^94 - 144400 * q^95 + 147376 * q^97 - 216942 * q^98

Introduction

L-functions

Modular forms

Varieties

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Database

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