LMFDB - Embedded newform 336.7.bh.a.241.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [336,7,Mod(145,336)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(336, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 0, 5]))

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

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

chi := DirichletCharacter("336.145");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 336 = 2^{4} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	336.bh (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$77.2981720963$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2 x^{7} + 1061 x^{6} + 35442 x^{5} + 1155979 x^{4} + 17325616 x^{3} + 201523590 x^{2} + \cdots + 5192355364 $ x^8 - 2x^7 + 1061x^6 + 35442x^5 + 1155979x^4 + 17325616x^3 + 201523590x^2 + 1200774512*x + 5192355364
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{6}\cdot 3^{4}\cdot 7^{2} $
Twist minimal:	no (minimal twist has level 84)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			241.4
Root			$19.9925 + 34.6280i$ of defining polynomial
Character	$\chi$	$=$	336.241
Dual form			336.7.bh.a.145.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-13.5000 - 7.79423i) q^{3} +(113.293 - 65.4099i) q^{5} +(-298.353 - 169.217i) q^{7} +(121.500 + 210.444i) q^{9} +O(q^{10})$	\(q+(-13.5000 - 7.79423i) q^{3} +(113.293 - 65.4099i) q^{5} +(-298.353 - 169.217i) q^{7} +(121.500 + 210.444i) q^{9} +(148.754 - 257.650i) q^{11} -1921.40i q^{13} -2039.28 q^{15} +(-573.903 - 331.343i) q^{17} +(-5178.99 + 2990.09i) q^{19} +(2708.85 + 4609.86i) q^{21} +(-5470.63 - 9475.41i) q^{23} +(744.413 - 1289.36i) q^{25} -3788.00i q^{27} +24389.8 q^{29} +(-15835.6 - 9142.67i) q^{31} +(-4016.37 + 2318.85i) q^{33} +(-44869.9 + 344.109i) q^{35} +(6446.77 + 11166.1i) q^{37} +(-14975.8 + 25938.9i) q^{39} -67940.4i q^{41} -120053. q^{43} +(27530.3 + 15894.6i) q^{45} +(55208.2 - 31874.5i) q^{47} +(60380.2 + 100973. i) q^{49} +(5165.13 + 8946.26i) q^{51} +(-470.393 + 814.745i) q^{53} -38920.0i q^{55} +93221.7 q^{57} +(205238. + 118494. i) q^{59} +(-57621.2 + 33267.6i) q^{61} +(-639.188 - 83346.5i) q^{63} +(-125679. - 217682. i) q^{65} +(1025.29 - 1775.85i) q^{67} +170557. i q^{69} +635716. q^{71} +(-574591. - 331740. i) q^{73} +(-20099.2 + 11604.3i) q^{75} +(-87980.1 + 51699.0i) q^{77} +(-92909.0 - 160923. i) q^{79} +(-29524.5 + 51137.9i) q^{81} +298953. i q^{83} -86692.5 q^{85} +(-329262. - 190100. i) q^{87} +(-546677. + 315624. i) q^{89} +(-325134. + 573256. i) q^{91} +(142520. + 246852. i) q^{93} +(-391163. + 677514. i) q^{95} +1.31600e6i q^{97} +72294.6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 108 q^{3} - 294 q^{5} - 232 q^{7} + 972 q^{9}+O(q^{10}) $ 8 * q - 108 * q^3 - 294 * q^5 - 232 * q^7 + 972 * q^9	$ 8 q - 108 q^{3} - 294 q^{5} - 232 q^{7} + 972 q^{9} - 378 q^{11} + 5292 q^{15} + 852 q^{17} - 3690 q^{19} + 3942 q^{21} - 15600 q^{23} + 3386 q^{25} - 68604 q^{29} - 23028 q^{31} + 10206 q^{33} - 93828 q^{35} + 15914 q^{37} - 25326 q^{39} + 170044 q^{43} - 71442 q^{45} - 102180 q^{47} + 157340 q^{49} - 7668 q^{51} + 196410 q^{53} + 66420 q^{57} + 662550 q^{59} - 23928 q^{61} - 50058 q^{63} + 14892 q^{65} - 774838 q^{67} + 721896 q^{71} - 1219050 q^{73} - 91422 q^{75} + 1584738 q^{77} + 493868 q^{79} - 236196 q^{81} - 1329816 q^{85} + 926154 q^{87} + 604260 q^{89} - 3831690 q^{91} + 207252 q^{93} - 448944 q^{95} - 183708 q^{99}+O(q^{100}) $ 8 * q - 108 * q^3 - 294 * q^5 - 232 * q^7 + 972 * q^9 - 378 * q^11 + 5292 * q^15 + 852 * q^17 - 3690 * q^19 + 3942 * q^21 - 15600 * q^23 + 3386 * q^25 - 68604 * q^29 - 23028 * q^31 + 10206 * q^33 - 93828 * q^35 + 15914 * q^37 - 25326 * q^39 + 170044 * q^43 - 71442 * q^45 - 102180 * q^47 + 157340 * q^49 - 7668 * q^51 + 196410 * q^53 + 66420 * q^57 + 662550 * q^59 - 23928 * q^61 - 50058 * q^63 + 14892 * q^65 - 774838 * q^67 + 721896 * q^71 - 1219050 * q^73 - 91422 * q^75 + 1584738 * q^77 + 493868 * q^79 - 236196 * q^81 - 1329816 * q^85 + 926154 * q^87 + 604260 * q^89 - 3831690 * q^91 + 207252 * q^93 - 448944 * q^95 - 183708 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/336\mathbb{Z}\right)^\times$.

$n$	$85$	$113$	$127$	$241$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−13.5000	−	7.79423i	−0.500000	−	0.288675i
$3$	−13.5000	−	7.79423i	−0.500000	−	0.288675i
$4$		0			0
$5$	113.293	−	65.4099i	0.906346	−	0.523279i	0.0270925	−	0.999633i	$-0.491375\pi$
$5$	113.293	−	65.4099i	0.906346	−	0.523279i	0.879254	+	0.476354i	$0.158042\pi$
$6$		0			0
$7$	−298.353	−	169.217i	−0.869834	−	0.493344i
$7$	−298.353	−	169.217i	−0.869834	−	0.493344i
$8$		0			0
$9$	121.500	+	210.444i	0.166667	+	0.288675i
$10$		0			0
$11$	148.754	−	257.650i	0.111761	−	0.193576i	−0.804719	−	0.593656i	$-0.797684\pi$
$11$	148.754	−	257.650i	0.111761	−	0.193576i	0.916480	+	0.400079i	$0.131017\pi$
$12$		0			0
$13$		−	1921.40i		−	0.874557i	−0.899326	−	0.437278i	$-0.855942\pi$
$13$		−	1921.40i		−	0.874557i	0.899326	−	0.437278i	$-0.144058\pi$
$14$		0			0
$15$	−2039.28			−0.604231
$16$		0			0
$17$	−573.903	−	331.343i	−0.116813	−	0.0674421i	0.440455	−	0.897775i	$-0.354817\pi$
$17$	−573.903	−	331.343i	−0.116813	−	0.0674421i	−0.557268	+	0.830333i	$0.688150\pi$
$18$		0			0
$19$	−5178.99	+	2990.09i	−0.755064	+	0.435937i	−0.827521	−	0.561435i	$-0.810249\pi$
$19$	−5178.99	+	2990.09i	−0.755064	+	0.435937i	0.0724566	+	0.997372i	$0.476916\pi$
$20$		0			0
$21$	2708.85	+	4609.86i	0.292501	+	0.497772i
$22$		0			0
$23$	−5470.63	−	9475.41i	−0.449629	−	0.778780i	0.548733	−	0.835998i	$-0.315110\pi$
$23$	−5470.63	−	9475.41i	−0.449629	−	0.778780i	−0.998362	+	0.0572179i	$0.981777\pi$
$24$		0			0
$25$	744.413	−	1289.36i	0.0476425	−	0.0825192i
$26$		0			0
$27$		−	3788.00i		−	0.192450i
$28$		0			0
$29$	24389.8			1.00003			0.500017	−	0.866016i	$-0.333327\pi$
$29$	24389.8			1.00003			0.500017	+	0.866016i	$0.333327\pi$
$30$		0			0
$31$	−15835.6	−	9142.67i	−0.531555	−	0.306894i	0.210094	−	0.977681i	$-0.432623\pi$
$31$	−15835.6	−	9142.67i	−0.531555	−	0.306894i	−0.741650	+	0.670788i	$0.765956\pi$
$32$		0			0
$33$	−4016.37	+	2318.85i	−0.111761	+	0.0645254i
$34$		0			0
$35$	−44869.9	+	344.109i	−1.04653	+	0.00802586i
$36$		0			0
$37$	6446.77	+	11166.1i	0.127273	+	0.220444i	0.922619	−	0.385712i	$-0.126044\pi$
$37$	6446.77	+	11166.1i	0.127273	+	0.220444i	−0.795346	+	0.606156i	$0.792711\pi$
$38$		0			0
$39$	−14975.8	+	25938.9i	−0.252463	+	0.437278i
$40$		0			0
$41$		−	67940.4i		−	0.985772i	−0.870094	−	0.492886i	$-0.835942\pi$
$41$		−	67940.4i		−	0.985772i	0.870094	−	0.492886i	$-0.164058\pi$
$42$		0			0
$43$	−120053.			−1.50997			−0.754987	−	0.655740i	$-0.772357\pi$
$43$	−120053.			−1.50997			−0.754987	+	0.655740i	$0.772357\pi$
$44$		0			0
$45$	27530.3	+	15894.6i	0.302115	+	0.174426i
$46$		0			0
$47$	55208.2	−	31874.5i	0.531753	−	0.307008i	−0.209977	−	0.977706i	$-0.567339\pi$
$47$	55208.2	−	31874.5i	0.531753	−	0.307008i	0.741730	+	0.670699i	$0.234006\pi$
$48$		0			0
$49$	60380.2	+	100973.i	0.513224	+	0.858255i
$50$		0			0
$51$	5165.13	+	8946.26i	0.0389377	+	0.0674421i
$52$		0			0
$53$	−470.393	+	814.745i	−0.00315961	+	0.00547260i	−0.867601	−	0.497261i	$-0.834339\pi$
$53$	−470.393	+	814.745i	−0.00315961	+	0.00547260i	0.864441	+	0.502734i	$0.167672\pi$
$54$		0			0
$55$		−	38920.0i		−	0.233930i
$56$		0			0
$57$	93221.7			0.503376
$58$		0			0
$59$	205238.	+	118494.i	0.999315	+	0.576955i	0.908045	−	0.418872i	$-0.137574\pi$
$59$	205238.	+	118494.i	0.999315	+	0.576955i	0.0912693	+	0.995826i	$0.470908\pi$
$60$		0			0
$61$	−57621.2	+	33267.6i	−0.253859	+	0.146566i	−0.621530	−	0.783390i	$-0.713489\pi$
$61$	−57621.2	+	33267.6i	−0.253859	+	0.146566i	0.367671	+	0.929956i	$0.380155\pi$
$62$		0			0
$63$	−639.188	−	83346.5i	−0.00255627	−	0.333324i
$64$		0			0
$65$	−125679.	−	217682.i	−0.457637	−	0.792651i
$66$		0			0
$67$	1025.29	−	1775.85i	0.00340895	−	0.00590447i	−0.864316	−	0.502949i	$-0.832248\pi$
$67$	1025.29	−	1775.85i	0.00340895	−	0.00590447i	0.867725	+	0.497045i	$0.165582\pi$
$68$		0			0
$69$			170557.i			0.519187i
$70$		0			0
$71$	635716.			1.77618			0.888092	−	0.459665i	$-0.152031\pi$
$71$	635716.			1.77618			0.888092	+	0.459665i	$0.152031\pi$
$72$		0			0
$73$	−574591.	−	331740.i	−1.47703	−	0.852765i	−0.477369	−	0.878703i	$-0.658410\pi$
$73$	−574591.	−	331740.i	−1.47703	−	0.852765i	−0.999664	+	0.0259377i	$0.991743\pi$
$74$		0			0
$75$	−20099.2	+	11604.3i	−0.0476425	+	0.0275064i
$76$		0			0
$77$	−87980.1	+	51699.0i	−0.192714	+	0.113243i
$78$		0			0
$79$	−92909.0	−	160923.i	−0.188442	−	0.326390i	0.756289	−	0.654237i	$-0.227010\pi$
$79$	−92909.0	−	160923.i	−0.188442	−	0.326390i	−0.944731	+	0.327847i	$0.893677\pi$
$80$		0			0
$81$	−29524.5	+	51137.9i	−0.0555556	+	0.0962250i
$82$		0			0
$83$			298953.i			0.522840i	0.965225	+	0.261420i	$0.0841907\pi$
$83$			298953.i			0.522840i	−0.965225	+	0.261420i	$0.915809\pi$
$84$		0			0
$85$	−86692.5			−0.141164
$86$		0			0
$87$	−329262.	−	190100.i	−0.500017	−	0.288685i
$88$		0			0
$89$	−546677.	+	315624.i	−0.775463	+	0.447714i	−0.834820	−	0.550523i	$-0.814428\pi$
$89$	−546677.	+	315624.i	−0.775463	+	0.447714i	0.0593571	+	0.998237i	$0.481095\pi$
$90$		0			0
$91$	−325134.	+	573256.i	−0.431457	+	0.760720i
$92$		0			0
$93$	142520.	+	246852.i	0.177185	+	0.306894i
$94$		0			0
$95$	−391163.	+	677514.i	−0.456233	+	0.790219i
$96$		0			0
$97$			1.31600e6i			1.44192i	0.692978	+	0.720958i	$0.256298\pi$
$97$			1.31600e6i			1.44192i	−0.692978	+	0.720958i	$0.743702\pi$
$98$		0			0
$99$	72294.6			0.0745075
$100$		0			0
$101$	−782183.	−	451594.i	−0.759179	−	0.438312i	0.0698217	−	0.997559i	$-0.477757\pi$
$101$	−782183.	−	451594.i	−0.759179	−	0.438312i	−0.829001	+	0.559247i	$0.811090\pi$
$102$		0			0
$103$	−1.15204e6	+	665129.i	−1.05428	+	0.608687i	−0.923844	−	0.382770i	$-0.874970\pi$
$103$	−1.15204e6	+	665129.i	−1.05428	+	0.608687i	−0.130434	+	0.991457i	$0.541637\pi$
$104$		0			0
$105$	608425.	+	345081.i	0.525581	+	0.298094i
$106$		0			0
$107$	1.06334e6	+	1.84176e6i	0.868001	+	1.50342i	0.864037	+	0.503429i	$0.167929\pi$
$107$	1.06334e6	+	1.84176e6i	0.868001	+	1.50342i	0.00396416	+	0.999992i	$0.498738\pi$
$108$		0			0
$109$	−702480.	+	1.21673e6i	−0.542443	+	0.939539i	0.456320	+	0.889816i	$0.349167\pi$
$109$	−702480.	+	1.21673e6i	−0.542443	+	0.939539i	−0.998763	+	0.0497233i	$0.984166\pi$
$110$		0			0
$111$		−	200990.i		−	0.146962i
$112$		0			0
$113$	−2.06919e6			−1.43405			−0.717027	−	0.697045i	$-0.754498\pi$
$113$	−2.06919e6			−1.43405			−0.717027	+	0.697045i	$0.754498\pi$
$114$		0			0
$115$	−1.23957e6	−	715667.i	−0.815039	−	0.470563i
$116$		0			0
$117$	404348.	−	233450.i	0.252463	−	0.145759i
$118$		0			0
$119$	115157.	+	195971.i	0.0683360	+	0.116293i
$120$		0			0
$121$	841525.	+	1.45756e6i	0.475019	+	0.822757i
$122$		0			0
$123$	−529543.	+	917195.i	−0.284568	+	0.492886i
$124$		0			0
$125$			1.84929e6i			0.946837i
$126$		0			0
$127$	−1.91465e6			−0.934713			−0.467357	−	0.884069i	$-0.654794\pi$
$127$	−1.91465e6			−0.934713			−0.467357	+	0.884069i	$0.654794\pi$
$128$		0			0
$129$	1.62072e6	+	935724.i	0.754987	+	0.435892i
$130$		0			0
$131$	−3.47550e6	+	2.00658e6i	−1.54598	+	0.892571i	−0.547536	+	0.836782i	$0.684434\pi$
$131$	−3.47550e6	+	2.00658e6i	−1.54598	+	0.892571i	−0.998443	+	0.0557893i	$0.982232\pi$
$132$		0			0
$133$	2.05114e6	−	15730.3i	0.871847	−	0.00668623i
$134$		0			0
$135$	−247772.	−	429154.i	−0.100705	−	0.174426i
$136$		0			0
$137$	128637.	−	222807.i	0.0500272	−	0.0866496i	−0.839927	−	0.542699i	$-0.817403\pi$
$137$	128637.	−	222807.i	0.0500272	−	0.0866496i	0.889955	+	0.456049i	$0.150736\pi$
$138$		0			0
$139$			743691.i			0.276916i	0.990368	+	0.138458i	$0.0442146\pi$
$139$			743691.i			0.276916i	−0.990368	+	0.138458i	$0.955785\pi$
$140$		0			0
$141$	−993748.			−0.354502
$142$		0			0
$143$	−495049.	−	285817.i	−0.169293	−	0.0977416i
$144$		0			0
$145$	2.76320e6	−	1.59534e6i	0.906376	−	0.523297i
$146$		0			0
$147$	−28127.9	−	1.83375e6i	−0.00885492	−	0.577282i
$148$		0			0
$149$	−901534.	−	1.56150e6i	−0.272536	−	0.472045i	0.696975	−	0.717096i	$-0.254529\pi$
$149$	−901534.	−	1.56150e6i	−0.272536	−	0.472045i	−0.969510	+	0.245050i	$0.921196\pi$
$150$		0			0
$151$	2.11055e6	−	3.65558e6i	0.613006	−	1.06176i	−0.377725	−	0.925918i	$-0.623293\pi$
$151$	2.11055e6	−	3.65558e6i	0.613006	−	1.06176i	0.990731	−	0.135840i	$-0.0433733\pi$
$152$		0			0
$153$		−	161033.i		−	0.0449614i
$154$		0			0
$155$	−2.39208e6			−0.642364
$156$		0			0
$157$	−4.30997e6	−	2.48836e6i	−1.11372	−	0.643006i	−0.173929	−	0.984758i	$-0.555646\pi$
$157$	−4.30997e6	−	2.48836e6i	−1.11372	−	0.643006i	−0.939790	+	0.341752i	$0.888980\pi$
$158$		0			0
$159$	12700.6	−	7332.70i	0.00315961	−	0.00182420i
$160$		0			0
$161$	28779.9	+	3.75274e6i	0.00689624	+	0.899231i
$162$		0			0
$163$	3.10509e6	+	5.37818e6i	0.716988	+	1.24186i	0.962188	+	0.272386i	$0.0878129\pi$
$163$	3.10509e6	+	5.37818e6i	0.716988	+	1.24186i	−0.245200	+	0.969472i	$0.578854\pi$
$164$		0			0
$165$	−303352.	+	525420.i	−0.0675296	+	0.116965i
$166$		0			0
$167$			4.18195e6i			0.897903i	0.893556	+	0.448951i	$0.148202\pi$
$167$			4.18195e6i			0.897903i	−0.893556	+	0.448951i	$0.851798\pi$
$168$		0			0
$169$	1.13503e6			0.235150
$170$		0			0
$171$	−1.25849e6	−	726592.i	−0.251688	−	0.145312i
$172$		0			0
$173$	−2.18177e6	+	1.25964e6i	−0.421376	+	0.243282i	−0.695666	−	0.718366i	$-0.744891\pi$
$173$	−2.18177e6	+	1.25964e6i	−0.421376	+	0.243282i	0.274290	+	0.961647i	$0.411557\pi$
$174$		0			0
$175$	−440280.	+	258718.i	−0.0821514	+	0.0482739i
$176$		0			0
$177$	−1.84714e6	−	3.19935e6i	−0.333105	−	0.576955i
$178$		0			0
$179$	4.60658e6	−	7.97882e6i	0.803192	−	1.39117i	−0.114314	−	0.993445i	$-0.536467\pi$
$179$	4.60658e6	−	7.97882e6i	0.803192	−	1.39117i	0.917505	−	0.397724i	$-0.130200\pi$
$180$		0			0
$181$			1.24508e6i			0.209972i	0.994474	+	0.104986i	$0.0334797\pi$
$181$			1.24508e6i			0.209972i	−0.994474	+	0.104986i	$0.966520\pi$
$182$		0			0
$183$	1.03718e6			0.169240
$184$		0			0
$185$	1.46075e6	+	843365.i	0.230707	+	0.133199i
$186$		0			0
$187$	−170741.	+	98577.4i	−0.0261104	+	0.0150748i
$188$		0			0
$189$	−640993.	+	1.13016e6i	−0.0949441	+	0.167400i
$190$		0			0
$191$	3.74403e6	+	6.48485e6i	0.537327	+	0.930678i	0.999047	+	0.0436522i	$0.0138993\pi$
$191$	3.74403e6	+	6.48485e6i	0.537327	+	0.930678i	−0.461720	+	0.887026i	$0.652767\pi$
$192$		0			0
$193$	−5.54357e6	+	9.60175e6i	−0.771113	+	1.33561i	0.165841	+	0.986152i	$0.446966\pi$
$193$	−5.54357e6	+	9.60175e6i	−0.771113	+	1.33561i	−0.936954	+	0.349454i	$0.886367\pi$
$194$		0			0
$195$			3.91827e6i			0.528434i
$196$		0			0
$197$	−1.13358e7			−1.48269			−0.741347	−	0.671122i	$-0.765813\pi$
$197$	−1.13358e7			−1.48269			−0.741347	+	0.671122i	$0.765813\pi$
$198$		0			0
$199$	5.27359e6	+	3.04471e6i	0.669187	+	0.386355i	0.795768	−	0.605601i	$-0.207067\pi$
$199$	5.27359e6	+	3.04471e6i	0.669187	+	0.386355i	−0.126582	+	0.991956i	$0.540401\pi$
$200$		0			0
$201$	−27682.7	+	15982.6i	−0.00340895	+	0.00196816i
$202$		0			0
$203$	−7.27678e6	−	4.12717e6i	−0.869863	−	0.493360i
$204$		0			0
$205$	−4.44397e6	−	7.69719e6i	−0.515834	−	0.893450i
$206$		0			0
$207$	1.32936e6	−	2.30253e6i	0.149876	−	0.259593i
$208$		0			0
$209$			1.77915e6i			0.194883i
$210$		0			0
$211$	5.97467e6			0.636014			0.318007	−	0.948088i	$-0.396987\pi$
$211$	5.97467e6			0.636014			0.318007	+	0.948088i	$0.396987\pi$
$212$		0			0
$213$	−8.58217e6	−	4.95492e6i	−0.888092	−	0.512740i
$214$		0			0
$215$	−1.36012e7	+	7.85268e6i	−1.36856	+	0.790138i
$216$		0			0
$217$	3.17750e6	+	5.40739e6i	0.310961	+	0.529186i
$218$		0			0
$219$	5.17132e6	+	8.95698e6i	0.492344	+	0.852765i
$220$		0			0
$221$	−636643.	+	1.10270e6i	−0.0589820	+	0.102160i
$222$		0			0
$223$			3.47512e6i			0.313368i	0.987649	+	0.156684i	$0.0500804\pi$
$223$			3.47512e6i			0.313368i	−0.987649	+	0.156684i	$0.949920\pi$
$224$		0			0
$225$	361785.			0.0317616
$226$		0			0
$227$	−1.41828e7	−	8.18846e6i	−1.21251	−	0.700043i	−0.249204	−	0.968451i	$-0.580169\pi$
$227$	−1.41828e7	−	8.18846e6i	−1.21251	−	0.700043i	−0.963305	+	0.268408i	$0.913502\pi$
$228$		0			0
$229$	1.33114e7	−	7.68535e6i	1.10845	−	0.639966i	0.170025	−	0.985440i	$-0.445615\pi$
$229$	1.33114e7	−	7.68535e6i	1.10845	−	0.639966i	0.938428	+	0.345474i	$0.112282\pi$
$230$		0			0
$231$	1.59068e6	−	12199.0i	0.129047	−	0.000989667i
$232$		0			0
$233$	3.41742e6	+	5.91914e6i	0.270166	+	0.467941i	0.968904	−	0.247437i	$-0.0795882\pi$
$233$	3.41742e6	+	5.91914e6i	0.270166	+	0.467941i	−0.698738	+	0.715377i	$0.746255\pi$
$234$		0			0
$235$	4.16981e6	−	7.22233e6i	0.321302	−	0.556511i
$236$		0			0
$237$			2.89662e6i			0.217594i
$238$		0			0
$239$	−6.59284e6			−0.482924			−0.241462	−	0.970410i	$-0.577627\pi$
$239$	−6.59284e6			−0.482924			−0.241462	+	0.970410i	$0.577627\pi$
$240$		0			0
$241$	−3.72815e6	−	2.15245e6i	−0.266344	−	0.153774i	0.360881	−	0.932612i	$-0.382476\pi$
$241$	−3.72815e6	−	2.15245e6i	−0.266344	−	0.153774i	−0.627225	+	0.778838i	$0.715809\pi$
$242$		0			0
$243$	797162.	−	460241.i	0.0555556	−	0.0320750i
$244$		0			0
$245$	1.34453e7	+	7.49008e6i	0.914265	+	0.509317i
$246$		0			0
$247$	5.74516e6	+	9.95091e6i	0.381251	+	0.660347i
$248$		0			0
$249$	2.33011e6	−	4.03587e6i	0.150931	−	0.261420i
$250$		0			0
$251$		−	2.89187e7i		−	1.82876i	−0.404855	−	0.914381i	$-0.632678\pi$
$251$		−	2.89187e7i		−	1.82876i	0.404855	−	0.914381i	$-0.367322\pi$
$252$		0			0
$253$	−3.25512e6			−0.201004
$254$		0			0
$255$	1.17035e6	+	675701.i	0.0705821	+	0.0407506i
$256$		0			0
$257$	2.54722e7	−	1.47064e7i	1.50061	−	0.866377i	0.500609	−	0.865674i	$-0.333110\pi$
$257$	2.54722e7	−	1.47064e7i	1.50061	−	0.866377i	1.00000		0.000703101i	$-0.000223804\pi$
$258$		0			0
$259$	−33915.2	−	4.42235e6i	−0.00195207	−	0.254539i
$260$		0			0
$261$	2.96336e6	+	5.13269e6i	0.166672	+	0.288685i
$262$		0			0
$263$	5.91325e6	−	1.02421e7i	0.325057	−	0.563015i	−0.656467	−	0.754355i	$-0.727950\pi$
$263$	5.91325e6	−	1.02421e7i	0.325057	−	0.563015i	0.981524	+	0.191340i	$0.0612833\pi$
$264$		0			0
$265$			123074.i			0.00661343i
$266$		0			0
$267$	9.84019e6			0.516975
$268$		0			0
$269$	−642579.	−	370993.i	−0.0330118	−	0.0190594i	0.483403	−	0.875398i	$-0.339400\pi$
$269$	−642579.	−	370993.i	−0.0330118	−	0.0190594i	−0.516415	+	0.856338i	$0.672734\pi$
$270$		0			0
$271$	−1.03985e7	+	6.00359e6i	−0.522473	+	0.301650i	−0.737946	−	0.674860i	$-0.764204\pi$
$271$	−1.03985e7	+	6.00359e6i	−0.522473	+	0.301650i	0.215473	+	0.976510i	$0.430871\pi$
$272$		0			0
$273$	8.85740e6	−	5.20479e6i	0.435329	−	0.255809i
$274$		0			0
$275$	−221469.	−	383596.i	−0.0106492	−	0.0184449i
$276$		0			0
$277$	1.25129e7	−	2.16730e7i	0.588735	−	1.01972i	−0.405663	−	0.914023i	$-0.632959\pi$
$277$	1.25129e7	−	2.16730e7i	0.588735	−	1.01972i	0.994398	−	0.105697i	$-0.0337073\pi$
$278$		0			0
$279$		−	4.44334e6i		−	0.204596i
$280$		0			0
$281$	−2.20158e6			−0.0992238			−0.0496119	−	0.998769i	$-0.515798\pi$
$281$	−2.20158e6			−0.0992238			−0.0496119	+	0.998769i	$0.515798\pi$
$282$		0			0
$283$	−1.40181e7	−	8.09333e6i	−0.618484	−	0.357082i	0.157794	−	0.987472i	$-0.449562\pi$
$283$	−1.40181e7	−	8.09333e6i	−0.618484	−	0.357082i	−0.776279	+	0.630390i	$0.782895\pi$
$284$		0			0
$285$	1.05614e7	−	6.09763e6i	0.456233	−	0.263406i
$286$		0			0
$287$	−1.14967e7	+	2.02702e7i	−0.486324	+	0.857458i
$288$		0			0
$289$	−1.18492e7	−	2.05234e7i	−0.490903	−	0.850269i
$290$		0			0
$291$	1.02572e7	−	1.77660e7i	0.416246	−	0.720958i
$292$		0			0
$293$			2.97558e7i			1.18296i	0.806321	+	0.591478i	$0.201455\pi$
$293$			2.97558e7i			1.18296i	−0.806321	+	0.591478i	$0.798545\pi$
$294$		0			0
$295$	3.10028e7			1.20763
$296$		0			0
$297$	−975977.	−	563481.i	−0.0372538	−	0.0215085i
$298$		0			0
$299$	−1.82061e7	+	1.05113e7i	−0.681087	+	0.393226i
$300$		0			0
$301$	3.58183e7	+	2.03151e7i	1.31343	+	0.744936i
$302$		0			0
$303$	7.03965e6	+	1.21930e7i	0.253060	+	0.438312i
$304$		0			0
$305$	−4.35207e6	+	7.53800e6i	−0.153390	+	0.265679i
$306$		0			0
$307$		−	3.47008e7i		−	1.19929i	−0.800266	−	0.599645i	$-0.795308\pi$
$307$		−	3.47008e7i		−	1.19929i	0.800266	−	0.599645i	$-0.204692\pi$
$308$		0			0
$309$	2.07367e7			0.702852
$310$		0			0
$311$	2.25688e7	+	1.30301e7i	0.750285	+	0.433177i	0.825797	−	0.563967i	$-0.190726\pi$
$311$	2.25688e7	+	1.30301e7i	0.750285	+	0.433177i	−0.0755116	+	0.997145i	$0.524059\pi$
$312$		0			0
$313$	9.28068e6	−	5.35820e6i	0.302654	−	0.174737i	−0.340980	−	0.940070i	$-0.610759\pi$
$313$	9.28068e6	−	5.35820e6i	0.302654	−	0.174737i	0.643635	+	0.765333i	$0.277426\pi$
$314$		0			0
$315$	−5.52411e6	−	9.40080e6i	−0.176738	−	0.300769i
$316$		0			0
$317$	−1.32884e7	−	2.30161e7i	−0.417151	−	0.722527i	0.578500	−	0.815682i	$-0.303638\pi$
$317$	−1.32884e7	−	2.30161e7i	−0.417151	−	0.722527i	−0.995652	+	0.0931549i	$0.970305\pi$
$318$		0			0
$319$	3.62809e6	−	6.28403e6i	0.111765	−	0.193583i
$320$		0			0
$321$		−	3.31516e7i		−	1.00228i
$322$		0			0
$323$	3.96298e6			0.117602
$324$		0			0
$325$	−2.47738e6	−	1.43032e6i	−0.0721677	−	0.0416660i
$326$		0			0
$327$	1.89669e7	−	1.09506e7i	0.542443	−	0.313180i
$328$		0			0
$329$	−2.18652e7	+	167685.i	−0.613998	+	0.00470877i
$330$		0			0
$331$	751949.	+	1.30241e6i	0.0207350	+	0.0359141i	0.876207	−	0.481935i	$-0.160066\pi$
$331$	751949.	+	1.30241e6i	0.0207350	+	0.0359141i	−0.855472	+	0.517850i	$0.826733\pi$
$332$		0			0
$333$	−1.56656e6	+	2.71337e6i	−0.0424244	+	0.0734812i
$334$		0			0
$335$		−	268255.i		−	0.00713533i
$336$		0			0
$337$	−2.47283e7			−0.646108			−0.323054	−	0.946380i	$-0.604710\pi$
$337$	−2.47283e7			−0.646108			−0.323054	+	0.946380i	$0.604710\pi$
$338$		0			0
$339$	2.79341e7	+	1.61278e7i	0.717027	+	0.413976i
$340$		0			0
$341$	−4.71122e6	+	2.72002e6i	−0.118815	+	0.0685977i
$342$		0			0
$343$	−928320.	−	4.03429e7i	−0.0230046	−	0.999735i
$344$		0			0
$345$	1.11561e7	+	1.93230e7i	0.271680	+	0.470563i
$346$		0			0
$347$	−4.53873e6	+	7.86131e6i	−0.108629	+	0.188151i	−0.915215	−	0.402966i	$-0.867979\pi$
$347$	−4.53873e6	+	7.86131e6i	−0.108629	+	0.188151i	0.806586	+	0.591117i	$0.201313\pi$
$348$		0			0
$349$		−	6.17244e7i		−	1.45205i	−0.687670	−	0.726024i	$-0.741366\pi$
$349$		−	6.17244e7i		−	1.45205i	0.687670	−	0.726024i	$-0.258634\pi$
$350$		0			0
$351$	−7.27826e6			−0.168309
$352$		0			0
$353$	−5.78507e7	−	3.34001e7i	−1.31518	−	0.759319i	−0.332230	−	0.943198i	$-0.607801\pi$
$353$	−5.78507e7	−	3.34001e7i	−1.31518	−	0.759319i	−0.982949	+	0.183880i	$0.941134\pi$
$354$		0			0
$355$	7.20224e7	−	4.15821e7i	1.60984	−	0.929441i
$356$		0			0
$357$	−27172.7	−	3.54317e6i	−0.000597212	−	0.0778732i
$358$		0			0
$359$	2.06463e7	+	3.57605e7i	0.446231	+	0.772894i	0.998137	−	0.0610119i	$-0.0194327\pi$
$359$	2.06463e7	+	3.57605e7i	0.446231	+	0.772894i	−0.551906	+	0.833906i	$0.686099\pi$
$360$		0			0
$361$	−5.64168e6	+	9.77168e6i	−0.119919	+	0.207705i
$362$		0			0
$363$		−	2.62361e7i		−	0.548504i
$364$		0			0
$365$	−8.67964e7			−1.78494
$366$		0			0
$367$	8.13669e6	+	4.69772e6i	0.164607	+	0.0950362i	0.580041	−	0.814588i	$-0.303037\pi$
$367$	8.13669e6	+	4.69772e6i	0.164607	+	0.0950362i	−0.415433	+	0.909624i	$0.636370\pi$
$368$		0			0
$369$	1.42977e7	−	8.25475e6i	0.284568	−	0.164295i
$370$		0			0
$371$	278212.	−	163483.i	0.00544821	−	0.00320148i
$372$		0			0
$373$	1.69899e6	+	2.94273e6i	0.0327389	+	0.0567054i	0.881931	−	0.471379i	$-0.156244\pi$
$373$	1.69899e6	+	2.94273e6i	0.0327389	+	0.0567054i	−0.849192	+	0.528085i	$0.822910\pi$
$374$		0			0
$375$	1.44138e7	−	2.49654e7i	0.273328	−	0.473419i
$376$		0			0
$377$		−	4.68626e7i		−	0.874586i
$378$		0			0
$379$	−6.20243e7			−1.13932			−0.569658	−	0.821882i	$-0.692924\pi$
$379$	−6.20243e7			−1.13932			−0.569658	+	0.821882i	$0.692924\pi$
$380$		0			0
$381$	2.58478e7	+	1.49232e7i	0.467357	+	0.269828i
$382$		0			0
$383$	1.45871e7	−	8.42187e6i	0.259641	−	0.149904i	−0.364530	−	0.931192i	$-0.618770\pi$
$383$	1.45871e7	−	8.42187e6i	0.259641	−	0.149904i	0.624171	+	0.781288i	$0.285437\pi$
$384$		0			0
$385$	−6.58593e6	+	1.16119e7i	−0.115408	+	0.203480i
$386$		0			0
$387$	−1.45865e7	−	2.52645e7i	−0.251662	−	0.435892i
$388$		0			0
$389$	−2.03119e7	+	3.51813e7i	−0.345066	+	0.597673i	−0.985366	−	0.170453i	$-0.945477\pi$
$389$	−2.03119e7	+	3.51813e7i	−0.345066	+	0.597673i	0.640299	+	0.768125i	$0.278810\pi$
$390$		0			0
$391$			7.25063e6i			0.121296i
$392$		0			0
$393$	6.25590e7			1.03065
$394$		0			0
$395$	−2.10519e7	−	1.21543e7i	−0.341587	−	0.197215i
$396$		0			0
$397$	5.29902e7	−	3.05939e7i	0.846884	−	0.488949i	−0.0127145	−	0.999919i	$-0.504047\pi$
$397$	5.29902e7	−	3.05939e7i	0.846884	−	0.488949i	0.859598	+	0.510971i	$0.170714\pi$
$398$		0			0
$399$	−2.78130e7	−	1.57747e7i	−0.437854	−	0.248338i
$400$		0			0
$401$	8.33332e6	+	1.44337e7i	0.129236	+	0.223844i	0.923381	−	0.383885i	$-0.125414\pi$
$401$	8.33332e6	+	1.44337e7i	0.129236	+	0.223844i	−0.794145	+	0.607729i	$0.792081\pi$
$402$		0			0
$403$	−1.75667e7	+	3.04265e7i	−0.268396	+	0.464875i
$404$		0			0
$405$			7.72478e6i			0.116284i
$406$		0			0
$407$	3.83594e6			0.0568969
$408$		0			0
$409$	6.98374e7	+	4.03206e7i	1.02075	+	0.589328i	0.914320	−	0.404992i	$-0.132726\pi$
$409$	6.98374e7	+	4.03206e7i	1.02075	+	0.589328i	0.106427	+	0.994321i	$0.466059\pi$
$410$		0			0
$411$	−3.47321e6	+	2.00526e6i	−0.0500272	+	0.0288832i
$412$		0			0
$413$	−4.11822e7	−	7.00830e7i	−0.584601	−	0.994861i
$414$		0			0
$415$	1.95545e7	+	3.38694e7i	0.273591	+	0.473874i
$416$		0			0
$417$	5.79650e6	−	1.00398e7i	0.0799388	−	0.138458i
$418$		0			0
$419$		−	2.85787e7i		−	0.388509i	−0.980951	−	0.194254i	$-0.937771\pi$
$419$		−	2.85787e7i		−	0.388509i	0.980951	−	0.194254i	$-0.0622287\pi$
$420$		0			0
$421$	1.19672e8			1.60378			0.801892	−	0.597469i	$-0.203827\pi$
$421$	1.19672e8			1.60378			0.801892	+	0.597469i	$0.203827\pi$
$422$		0			0
$423$	1.34156e7	+	7.74550e6i	0.177251	+	0.102336i
$424$		0			0
$425$	−854442.	+	493312.i	−0.0111305	+	0.00642622i
$426$		0			0
$427$	2.28209e7	−	175015.i	0.293123	−	0.00224797i
$428$		0			0
$429$	4.45544e6	+	7.71705e6i	0.0564312	+	0.0977416i
$430$		0			0
$431$	−6.16496e7	+	1.06780e8i	−0.770014	+	1.33370i	0.167541	+	0.985865i	$0.446417\pi$
$431$	−6.16496e7	+	1.06780e8i	−0.770014	+	1.33370i	−0.937555	+	0.347838i	$0.886916\pi$
$432$		0			0
$433$		−	1.28584e7i		−	0.158389i	−0.996859	−	0.0791945i	$-0.974765\pi$
$433$		−	1.28584e7i		−	0.158389i	0.996859	−	0.0791945i	$-0.0252348\pi$
$434$		0			0
$435$	−4.97376e7			−0.604251
$436$		0			0
$437$	5.66647e7	+	3.27154e7i	0.678997	+	0.392019i
$438$		0			0
$439$	6.02389e7	−	3.47789e7i	0.712006	−	0.411077i	−0.0997976	−	0.995008i	$-0.531820\pi$
$439$	6.02389e7	−	3.47789e7i	0.712006	−	0.411077i	0.811803	+	0.583931i	$0.198486\pi$
$440$		0			0
$441$	−1.39129e7	+	2.49749e7i	−0.162220	+	0.291197i
$442$		0			0
$443$	−1.68461e7	−	2.91783e7i	−0.193770	−	0.335620i	0.752726	−	0.658334i	$-0.228738\pi$
$443$	−1.68461e7	−	2.91783e7i	−0.193770	−	0.335620i	−0.946497	+	0.322713i	$0.895405\pi$
$444$		0			0
$445$	−4.12899e7	+	7.15162e7i	−0.468559	+	0.811567i
$446$		0			0
$447$			2.81070e7i			0.314697i
$448$		0			0
$449$	−8.08742e7			−0.893451			−0.446725	−	0.894671i	$-0.647410\pi$
$449$	−8.08742e7			−0.893451			−0.446725	+	0.894671i	$0.647410\pi$
$450$		0			0
$451$	−1.75048e7	−	1.01064e7i	−0.190822	−	0.110171i
$452$		0			0
$453$	−5.69849e7	+	3.29002e7i	−0.613006	+	0.353919i
$454$		0			0
$455$	661171.	+	8.62131e7i	0.00701907	+	0.915248i
$456$		0			0
$457$	6.53821e7	+	1.13245e8i	0.685031	+	1.18651i	0.973427	+	0.228997i	$0.0735445\pi$
$457$	6.53821e7	+	1.13245e8i	0.685031	+	1.18651i	−0.288397	+	0.957511i	$0.593122\pi$
$458$		0			0
$459$	−1.25513e6	+	2.17394e6i	−0.0129792	+	0.0224807i
$460$		0			0
$461$			3.77601e7i			0.385417i	0.981256	+	0.192708i	$0.0617271\pi$
$461$			3.77601e7i			0.385417i	−0.981256	+	0.192708i	$0.938273\pi$
$462$		0			0
$463$	−5.13671e7			−0.517538			−0.258769	−	0.965939i	$-0.583317\pi$
$463$	−5.13671e7			−0.517538			−0.258769	+	0.965939i	$0.583317\pi$
$464$		0			0
$465$	3.22931e7	+	1.86445e7i	0.321182	+	0.185435i
$466$		0			0
$467$	−1.36450e8	+	7.87797e7i	−1.33975	+	0.773506i	−0.986770	−	0.162125i	$-0.948165\pi$
$467$	−1.36450e8	+	7.87797e7i	−1.33975	+	0.773506i	−0.352981	+	0.935630i	$0.614832\pi$
$468$		0			0
$469$	−606400.	+	356334.i	−0.00587815	+	0.00345413i
$470$		0			0
$471$	3.87898e7	+	6.71858e7i	0.371240	+	0.643006i
$472$		0			0
$473$	−1.78585e7	+	3.09318e7i	−0.168757	+	0.292295i
$474$		0			0
$475$			8.90345e6i			0.0830763i
$476$		0			0
$477$	−228611.			−0.00210641
$478$		0			0
$479$	−9.75743e7	−	5.63345e7i	−0.887828	−	0.512588i	−0.0145967	−	0.999893i	$-0.504646\pi$
$479$	−9.75743e7	−	5.63345e7i	−0.887828	−	0.512588i	−0.873231	+	0.487306i	$0.837980\pi$
$480$		0			0
$481$	2.14546e7	−	1.23868e7i	0.192790	−	0.111308i
$482$		0			0
$483$	2.88612e7	−	5.08864e7i	0.256138	−	0.451606i
$484$		0			0
$485$	8.60793e7	+	1.49094e8i	0.754525	+	1.30688i
$486$		0			0
$487$	−5.23866e7	+	9.07362e7i	−0.453558	+	0.785586i	−0.998604	−	0.0528201i	$-0.983179\pi$
$487$	−5.23866e7	+	9.07362e7i	−0.453558	+	0.785586i	0.545046	+	0.838406i	$0.316512\pi$
$488$		0			0
$489$		−	9.68072e7i		−	0.827906i
$490$		0			0
$491$	1.89632e7			0.160202			0.0801010	−	0.996787i	$-0.474476\pi$
$491$	1.89632e7			0.160202			0.0801010	+	0.996787i	$0.474476\pi$
$492$		0			0
$493$	−1.39974e7	−	8.08140e6i	−0.116817	−	0.0674444i
$494$		0			0
$495$	8.19049e6	−	4.72878e6i	0.0675296	−	0.0389883i
$496$		0			0
$497$	−1.89668e8	−	1.07574e8i	−1.54499	−	0.876270i
$498$		0			0
$499$	−9.68819e7	−	1.67804e8i	−0.779725	−	1.35052i	−0.932100	−	0.362200i	$-0.882026\pi$
$499$	−9.68819e7	−	1.67804e8i	−0.779725	−	1.35052i	0.152376	−	0.988323i	$-0.451308\pi$
$500$		0			0
$501$	3.25951e7	−	5.64563e7i	0.259202	−	0.448951i
$502$		0			0
$503$		−	5.71078e7i		−	0.448736i	−0.974504	−	0.224368i	$-0.927968\pi$
$503$		−	5.71078e7i		−	0.448736i	0.974504	−	0.224368i	$-0.0720318\pi$
$504$		0			0
$505$	−1.18155e8			−0.917439
$506$		0			0
$507$	−1.53228e7	−	8.84665e6i	−0.117575	−	0.0678821i
$508$		0			0
$509$	−1.57539e8	+	9.09555e7i	−1.19464	+	0.689724i	−0.959355	−	0.282203i	$-0.908935\pi$
$509$	−1.57539e8	+	9.09555e7i	−1.19464	+	0.689724i	−0.235282	+	0.971927i	$0.575602\pi$
$510$		0			0
$511$	1.15295e8	+	1.96206e8i	0.864067	+	1.47045i
$512$		0			0
$513$	1.13264e7	+	1.96180e7i	0.0838960	+	0.145312i
$514$		0			0
$515$	−8.70121e7	+	1.50709e8i	−0.637027	+	1.10336i
$516$		0			0
$517$		−	1.89659e7i		−	0.137246i
$518$		0			0
$519$	3.92718e7			0.280917
$520$		0			0
$521$	5.42953e7	+	3.13474e7i	0.383928	+	0.221661i	0.679526	−	0.733652i	$-0.262186\pi$
$521$	5.42953e7	+	3.13474e7i	0.383928	+	0.221661i	−0.295598	+	0.955312i	$0.595519\pi$
$522$		0			0
$523$	1.38919e8	−	8.02050e7i	0.971085	−	0.560656i	0.0715182	−	0.997439i	$-0.477216\pi$
$523$	1.38919e8	−	8.02050e7i	0.971085	−	0.560656i	0.899567	+	0.436783i	$0.143882\pi$
$524$		0			0
$525$	7.96029e6	−	61047.7i	0.0550111	−	0.000421883i
$526$		0			0
$527$	6.05872e6	+	1.04940e7i	0.0413951	+	0.0716984i
$528$		0			0
$529$	1.41623e7	−	2.45298e7i	0.0956680	−	0.165702i
$530$		0			0
$531$			5.75883e7i			0.384636i
$532$		0			0
$533$	−1.30541e8			−0.862113
$534$		0			0
$535$	2.40938e8	+	1.39106e8i	1.57342	+	0.908414i
$536$		0			0
$537$	−1.24378e8	+	7.18094e7i	−0.803192	+	0.463723i
$538$		0			0
$539$	3.49975e7	−	536826.i	0.223496	−	0.00342821i
$540$		0			0
$541$	−7.84474e7	−	1.35875e8i	−0.495435	−	0.858118i	0.504551	−	0.863382i	$-0.331658\pi$
$541$	−7.84474e7	−	1.35875e8i	−0.495435	−	0.858118i	−0.999986	+	0.00526328i	$0.998325\pi$
$542$		0			0
$543$	9.70443e6	−	1.68086e7i	0.0606136	−	0.104986i
$544$		0			0
$545$			1.83797e8i			1.13540i
$546$		0			0
$547$	−2.12416e8			−1.29785			−0.648927	−	0.760851i	$-0.724782\pi$
$547$	−2.12416e8			−1.29785			−0.648927	+	0.760851i	$0.724782\pi$
$548$		0			0
$549$	−1.40020e7	−	8.08404e6i	−0.0846198	−	0.0488553i
$550$		0			0
$551$	−1.26314e8	+	7.29277e7i	−0.755089	+	0.435951i
$552$		0			0
$553$	488776.	+	6.37337e7i	0.00289025	+	0.376872i
$554$		0			0
$555$	−1.31468e7	−	2.27708e7i	−0.0769024	−	0.133199i
$556$		0			0
$557$	1.19400e7	−	2.06806e7i	0.0690935	−	0.119673i	−0.829409	−	0.558642i	$-0.811323\pi$
$557$	1.19400e7	−	2.06806e7i	0.0690935	−	0.119673i	0.898502	+	0.438968i	$0.144656\pi$
$558$		0			0
$559$			2.30671e8i			1.32056i
$560$		0			0
$561$	3.07334e6			0.0174069
$562$		0			0
$563$	−1.49256e8	−	8.61730e7i	−0.836386	−	0.482887i	0.0196484	−	0.999807i	$-0.493745\pi$
$563$	−1.49256e8	−	8.61730e7i	−0.836386	−	0.482887i	−0.856034	+	0.516920i	$0.827079\pi$
$564$		0			0
$565$	−2.34426e8	+	1.35346e8i	−1.29975	+	0.750411i
$566$		0			0
$567$	1.74621e7	−	1.02611e7i	0.0957962	−	0.0562919i
$568$		0			0
$569$	1.11919e8	+	1.93849e8i	0.607529	+	1.05227i	0.991646	+	0.128986i	$0.0411724\pi$
$569$	1.11919e8	+	1.93849e8i	0.607529	+	1.05227i	−0.384118	+	0.923284i	$0.625494\pi$
$570$		0			0
$571$	5.91537e7	−	1.02457e8i	0.317741	−	0.550344i	−0.662275	−	0.749261i	$-0.730409\pi$
$571$	5.91537e7	−	1.02457e8i	0.317741	−	0.550344i	0.980016	+	0.198917i	$0.0637424\pi$
$572$		0			0
$573$		−	1.16727e8i		−	0.620452i
$574$		0			0
$575$	−1.62896e7			−0.0856857
$576$		0			0
$577$	−1.98569e8	−	1.14644e8i	−1.03367	−	0.596792i	−0.115639	−	0.993291i	$-0.536891\pi$
$577$	−1.98569e8	−	1.14644e8i	−1.03367	−	0.596792i	−0.918035	+	0.396500i	$0.870225\pi$
$578$		0			0
$579$	1.49676e8	−	8.64157e7i	0.771113	−	0.445202i
$580$		0			0
$581$	5.05879e7	−	8.91936e7i	0.257940	−	0.454784i
$582$		0			0
$583$	139946.	+	242394.i	0.000706244	+	0.00122325i
$584$		0			0
$585$	3.05399e7	−	5.28967e7i	0.152546	−	0.264217i
$586$		0			0
$587$		−	3.93045e8i		−	1.94324i	−0.236538	−	0.971622i	$-0.576013\pi$
$587$		−	3.93045e8i		−	1.94324i	0.236538	−	0.971622i	$-0.423987\pi$
$588$		0			0
$589$	1.09350e8			0.535145
$590$		0			0
$591$	1.53033e8	+	8.83535e7i	0.741347	+	0.428017i
$592$		0			0
$593$	−1.85937e8	+	1.07351e8i	−0.891667	+	0.514804i	−0.874487	−	0.485048i	$-0.838802\pi$
$593$	−1.85937e8	+	1.07351e8i	−0.891667	+	0.514804i	−0.0171794	+	0.999852i	$0.505469\pi$
$594$		0			0
$595$	2.58650e7	+	1.46698e7i	0.122790	+	0.0696425i
$596$		0			0
$597$	−4.74623e7	−	8.22072e7i	−0.223062	−	0.386355i
$598$		0			0
$599$	−1.82414e8	+	3.15950e8i	−0.848746	+	1.47007i	0.0335819	+	0.999436i	$0.489309\pi$
$599$	−1.82414e8	+	3.15950e8i	−0.848746	+	1.47007i	−0.882328	+	0.470635i	$0.844025\pi$
$600$		0			0
$601$		−	3.77469e8i		−	1.73883i	−0.494078	−	0.869417i	$-0.664494\pi$
$601$		−	3.77469e8i		−	1.73883i	0.494078	−	0.869417i	$-0.335506\pi$
$602$		0			0
$603$	498289.			0.00227263
$604$		0			0
$605$	1.90678e8	+	1.10088e8i	0.861063	+	0.497135i
$606$		0			0
$607$	2.37723e8	−	1.37250e8i	1.06293	−	0.613684i	0.136690	−	0.990614i	$-0.456353\pi$
$607$	2.37723e8	−	1.37250e8i	1.06293	−	0.613684i	0.926242	+	0.376930i	$0.123020\pi$
$608$		0			0
$609$	6.60684e7	+	1.12434e8i	0.292511	+	0.497788i
$610$		0			0
$611$	−6.12437e7	−	1.06077e8i	−0.268496	−	0.465048i
$612$		0			0
$613$	−1.07584e8	+	1.86341e8i	−0.467053	+	0.808960i	−0.999292	−	0.0376344i	$-0.988018\pi$
$613$	−1.07584e8	+	1.86341e8i	−0.467053	+	0.808960i	0.532238	+	0.846595i	$0.321351\pi$
$614$		0			0
$615$			1.38549e8i			0.595634i
$616$		0			0
$617$	1.39293e7			0.0593025			0.0296512	−	0.999560i	$-0.490560\pi$
$617$	1.39293e7			0.0593025			0.0296512	+	0.999560i	$0.490560\pi$
$618$		0			0
$619$	6.69963e7	+	3.86803e7i	0.282474	+	0.163087i	0.634543	−	0.772888i	$-0.281188\pi$
$619$	6.69963e7	+	3.86803e7i	0.282474	+	0.163087i	−0.352069	+	0.935974i	$0.614522\pi$
$620$		0			0
$621$	−3.58928e7	+	2.07227e7i	−0.149876	+	0.0865311i
$622$		0			0
$623$	2.16512e8	−	1.66044e6i	0.895401	−	0.00686686i
$624$		0			0
$625$	1.32593e8	+	2.29659e8i	0.543103	+	0.940682i
$626$		0			0
$627$	1.38671e7	−	2.40186e7i	0.0562580	−	0.0974417i
$628$		0			0
$629$		−	8.54437e6i		−	0.0343343i
$630$		0			0
$631$	−4.23656e8			−1.68626			−0.843131	−	0.537709i	$-0.819290\pi$
$631$	−4.23656e8			−1.68626			−0.843131	+	0.537709i	$0.819290\pi$
$632$		0			0
$633$	−8.06580e7	−	4.65679e7i	−0.318007	−	0.183601i
$634$		0			0
$635$	−2.16917e8	+	1.25237e8i	−0.847174	+	0.489116i
$636$		0			0
$637$	1.94009e8	−	1.16015e8i	0.750593	−	0.448843i
$638$		0			0
$639$	7.72395e7	+	1.33783e8i	0.296031	+	0.512740i
$640$		0			0
$641$	2.20616e8	−	3.82119e8i	0.837652	−	1.45086i	−0.0542004	−	0.998530i	$-0.517261\pi$
$641$	2.20616e8	−	3.82119e8i	0.837652	−	1.45086i	0.891853	−	0.452326i	$-0.149406\pi$
$642$		0			0
$643$		−	3.25129e8i		−	1.22299i	−0.791248	−	0.611495i	$-0.790568\pi$
$643$		−	3.25129e8i		−	1.22299i	0.791248	−	0.611495i	$-0.209432\pi$
$644$		0			0
$645$	2.44822e8			0.912372
$646$		0			0
$647$	−6.17898e7	−	3.56744e7i	−0.228141	−	0.131717i	0.381573	−	0.924339i	$-0.375382\pi$
$647$	−6.17898e7	−	3.56744e7i	−0.228141	−	0.131717i	−0.609714	+	0.792621i	$0.708716\pi$
$648$		0			0
$649$	6.10602e7	−	3.52531e7i	0.223369	−	0.128962i
$650$		0			0
$651$	−749771.	−	9.77659e7i	−0.00271760	−	0.354360i
$652$		0			0
$653$	1.84029e8	+	3.18748e8i	0.660918	+	1.14474i	0.980375	+	0.197142i	$0.0631661\pi$
$653$	1.84029e8	+	3.18748e8i	0.660918	+	1.14474i	−0.319457	+	0.947601i	$0.603501\pi$
$654$		0			0
$655$	−2.62501e8	+	4.54664e8i	−0.934128	+	1.61796i
$656$		0			0
$657$		−	1.61226e8i		−	0.568510i
$658$		0			0
$659$	−3.66035e7			−0.127899			−0.0639493	−	0.997953i	$-0.520370\pi$
$659$	−3.66035e7			−0.127899			−0.0639493	+	0.997953i	$0.520370\pi$
$660$		0			0
$661$	2.13393e8	+	1.23202e8i	0.738883	+	0.426594i	0.821663	−	0.569973i	$-0.193047\pi$
$661$	2.13393e8	+	1.23202e8i	0.738883	+	0.426594i	−0.0827799	+	0.996568i	$0.526380\pi$
$662$		0			0
$663$	1.71894e7	−	9.92428e6i	0.0589820	−	0.0340533i
$664$		0			0
$665$	2.31352e8	−	1.35947e8i	0.786697	−	0.462280i
$666$		0			0
$667$	−1.33428e8	−	2.31104e8i	−0.449644	−	0.778806i
$668$		0			0
$669$	2.70859e7	−	4.69141e7i	0.0904616	−	0.156684i
$670$		0			0
$671$			1.97948e7i			0.0655215i
$672$		0			0
$673$	1.20112e7			0.0394042			0.0197021	−	0.999806i	$-0.493728\pi$
$673$	1.20112e7			0.0394042			0.0197021	+	0.999806i	$0.493728\pi$
$674$		0			0
$675$	−4.88410e6	−	2.81983e6i	−0.0158808	−	0.00916879i
$676$		0			0
$677$	1.80637e8	−	1.04291e8i	0.582156	−	0.336108i	−0.179833	−	0.983697i	$-0.557556\pi$
$677$	1.80637e8	−	1.04291e8i	0.582156	−	0.336108i	0.761990	+	0.647589i	$0.224223\pi$
$678$		0			0
$679$	2.22689e8	−	3.92632e8i	0.711361	−	1.25423i
$680$		0			0
$681$	1.27645e8	+	2.21088e8i	0.404170	+	0.700043i
$682$		0			0
$683$	2.47639e8	−	4.28924e8i	0.777244	−	1.34623i	−0.156281	−	0.987713i	$-0.549950\pi$
$683$	2.47639e8	−	4.28924e8i	0.777244	−	1.34623i	0.933525	−	0.358513i	$-0.116716\pi$
$684$		0			0
$685$		−	3.36567e7i		−	0.104713i
$686$		0			0
$687$	−2.39605e8			−0.738969
$688$		0			0
$689$	1.56545e6	+	903814.i	0.00478610	+	0.00276326i
$690$		0			0
$691$	−8.01560e7	+	4.62781e7i	−0.242942	+	0.140262i	−0.616528	−	0.787333i	$-0.711461\pi$
$691$	−8.01560e7	+	4.62781e7i	−0.242942	+	0.140262i	0.373586	+	0.927595i	$0.378128\pi$
$692$		0			0
$693$	−2.15693e7	−	1.22335e7i	−0.0648092	−	0.0367578i
$694$		0			0
$695$	4.86448e7	+	8.42552e7i	0.144904	+	0.250982i
$696$		0			0
$697$	−2.25116e7	+	3.89912e7i	−0.0664825	+	0.115151i
$698$		0			0
$699$		−	1.06545e8i		−	0.311961i
$700$		0			0
$701$	−5.76637e8			−1.67397			−0.836987	−	0.547223i	$-0.815685\pi$
$701$	−5.76637e8			−1.67397			−0.836987	+	0.547223i	$0.815685\pi$
$702$		0			0
$703$	−6.67754e7	−	3.85528e7i	−0.192199	−	0.110966i
$704$		0			0
$705$	−1.12585e8	+	6.50009e7i	−0.321302	+	0.185504i
$706$		0			0
$707$	1.56950e8	+	2.67093e8i	0.444121	+	0.755796i
$708$		0			0
$709$	−2.80327e8	−	4.85540e8i	−0.786549	−	1.36234i	−0.928069	−	0.372408i	$-0.878532\pi$
$709$	−2.80327e8	−	4.85540e8i	−0.786549	−	1.36234i	0.141520	−	0.989935i	$-0.454801\pi$
$710$		0			0
$711$	2.25769e7	−	3.91043e7i	0.0628138	−	0.108797i
$712$		0			0
$713$			2.00065e8i			0.551953i
$714$		0			0
$715$	−7.47810e7			−0.204585
$716$		0			0
$717$	8.90033e7	+	5.13861e7i	0.241462	+	0.139408i
$718$		0			0
$719$	−6.84495e7	+	3.95194e7i	−0.184155	+	0.106322i	−0.589243	−	0.807956i	$-0.700574\pi$
$719$	−6.84495e7	+	3.95194e7i	−0.184155	+	0.106322i	0.405088	+	0.914278i	$0.367241\pi$
$720$		0			0
$721$	4.56265e8	−	3.49912e6i	1.21734	−	0.00933582i
$722$		0			0
$723$	3.35534e7	+	5.81161e7i	0.0887812	+	0.153774i
$724$		0			0
$725$	1.81561e7	−	3.14473e7i	0.0476440	−	0.0825219i
$726$		0			0
$727$			4.27900e8i			1.11362i	0.830639	+	0.556812i	$0.187976\pi$
$727$			4.27900e8i			1.11362i	−0.830639	+	0.556812i	$0.812024\pi$
$728$		0			0
$729$	−1.43489e7			−0.0370370
$730$		0			0
$731$	6.88990e7	+	3.97789e7i	0.176385	+	0.101836i
$732$		0			0
$733$	−4.00265e8	+	2.31093e8i	−1.01633	+	0.586780i	−0.913039	−	0.407871i	$-0.866271\pi$
$733$	−4.00265e8	+	2.31093e8i	−1.01633	+	0.586780i	−0.103293	+	0.994651i	$0.532938\pi$
$734$		0			0
$735$	−1.23132e8	−	2.05912e8i	−0.310106	−	0.518584i
$736$		0			0
$737$	−305031.	−	528330.i	−0.000761977	−	0.00131978i
$738$		0			0
$739$	1.04040e7	−	1.80203e7i	0.0257791	−	0.0446506i	−0.852848	−	0.522159i	$-0.825127\pi$
$739$	1.04040e7	−	1.80203e7i	0.0257791	−	0.0446506i	0.878627	+	0.477509i	$0.158460\pi$
$740$		0			0
$741$		−	1.79116e8i		−	0.440231i
$742$		0			0
$743$	6.81198e8			1.66076			0.830380	−	0.557197i	$-0.188123\pi$
$743$	6.81198e8			1.66076			0.830380	+	0.557197i	$0.188123\pi$
$744$		0			0
$745$	−2.04275e8	−	1.17938e8i	−0.494023	−	0.285224i
$746$		0			0
$747$	−6.29129e7	+	3.63228e7i	−0.150931	+	0.0871400i
$748$		0			0
$749$	−5.59402e6	−	7.29429e8i	−0.0133131	−	1.73595i
$750$		0			0
$751$	1.25252e8	+	2.16942e8i	0.295708	+	0.512182i	0.975149	−	0.221548i	$-0.0711111\pi$
$751$	1.25252e8	+	2.16942e8i	0.295708	+	0.512182i	−0.679441	+	0.733730i	$0.737778\pi$
$752$		0			0
$753$	−2.25399e8	+	3.90402e8i	−0.527918	+	0.914381i
$754$		0			0
$755$		−	5.52204e8i		−	1.28309i
$756$		0			0
$757$	−3.79092e8			−0.873890			−0.436945	−	0.899488i	$-0.643940\pi$
$757$	−3.79092e8			−0.873890			−0.436945	+	0.899488i	$0.643940\pi$
$758$		0			0
$759$	4.39441e7	+	2.53712e7i	0.100502	+	0.0580250i
$760$		0			0
$761$	6.69089e8	−	3.86299e8i	1.51820	−	0.876535i	0.518433	−	0.855118i	$-0.326516\pi$
$761$	6.69089e8	−	3.86299e8i	1.51820	−	0.876535i	0.999771	−	0.0214166i	$-0.00681762\pi$
$762$		0			0
$763$	4.15478e8	−	2.44144e8i	0.935352	−	0.549632i
$764$		0			0
$765$	−1.05331e7	−	1.82439e7i	−0.0235274	−	0.0407506i
$766$		0			0
$767$	2.27675e8	−	3.94345e8i	0.504580	−	0.873958i
$768$		0			0
$769$			3.95070e8i			0.868751i	0.900732	+	0.434376i	$0.143031\pi$
$769$			3.95070e8i			0.868751i	−0.900732	+	0.434376i	$0.856969\pi$
$770$		0			0
$771$	−4.58500e8			−1.00041
$772$		0			0
$773$	9.73736e7	+	5.62187e7i	0.210816	+	0.121714i	0.601690	−	0.798729i	$-0.294494\pi$
$773$	9.73736e7	+	5.62187e7i	0.210816	+	0.121714i	−0.390875	+	0.920444i	$0.627827\pi$
$774$		0			0
$775$	−2.35764e7	+	1.36118e7i	−0.0506492	+	0.0292423i
$776$		0			0
$777$	−3.40110e7	+	5.99661e7i	−0.0725030	+	0.127833i
$778$		0			0
$779$	2.03148e8	+	3.51862e8i	0.429734	+	0.744321i
$780$		0			0
$781$	9.45655e7	−	1.63792e8i	0.198509	−	0.343827i
$782$		0			0
$783$		−	9.23885e7i		−	0.192456i
$784$		0			0
$785$	−6.51055e8			−1.34589
$786$		0			0
$787$	−4.37268e8	−	2.52457e8i	−0.897064	−	0.517920i	−0.0208176	−	0.999783i	$-0.506627\pi$
$787$	−4.37268e8	−	2.52457e8i	−0.897064	−	0.517920i	−0.876247	+	0.481863i	$0.839960\pi$
$788$		0			0
$789$	−1.59658e8	+	9.21785e7i	−0.325057	+	0.187672i
$790$		0			0
$791$	6.17350e8	+	3.50143e8i	1.24739	+	0.707482i
$792$		0			0
$793$	6.39205e7	+	1.10714e8i	0.128180	+	0.222014i
$794$		0			0
$795$	959263.	−	1.66149e6i	0.00190913	−	0.00330672i
$796$		0			0
$797$			5.70316e7i			0.112652i	0.998412	+	0.0563262i	$0.0179387\pi$
$797$			5.70316e7i			0.112652i	−0.998412	+	0.0563262i	$0.982061\pi$
$798$		0			0
$799$	−4.22455e7			−0.0828210
$800$		0			0
$801$	−1.32843e8	−	7.66967e7i	−0.258488	−	0.149238i
$802$		0			0
$803$	−1.70946e8	+	9.86956e7i	−0.330150	+	0.190612i
$804$		0			0
$805$	2.48727e8	+	4.23278e8i	0.476799	+	0.811406i
$806$		0			0
$807$	5.78321e6	+	1.00168e7i	0.0110039	+	0.0190594i
$808$		0			0
$809$	1.56604e8	−	2.71245e8i	0.295771	−	0.512291i	−0.679393	−	0.733775i	$-0.737757\pi$
$809$	1.56604e8	−	2.71245e8i	0.295771	−	0.512291i	0.975164	+	0.221484i	$0.0710900\pi$
$810$		0			0
$811$			2.87234e8i			0.538485i	0.963072	+	0.269242i	$0.0867733\pi$
$811$			2.87234e8i			0.538485i	−0.963072	+	0.269242i	$0.913227\pi$
$812$		0			0
$813$	1.87173e8			0.348315
$814$		0			0
$815$	7.03572e8	+	4.06208e8i	1.29968	+	0.750370i
$816$		0			0
$817$	6.21755e8	−	3.58970e8i	1.14013	−	0.658252i
$818$		0			0
$819$	−1.60142e8	+	1.22814e6i	−0.291510	+	0.00223560i
$820$		0			0
$821$	−4.68369e8	−	8.11239e8i	−0.846367	−	1.46595i	−0.884429	−	0.466675i	$-0.845452\pi$
$821$	−4.68369e8	−	8.11239e8i	−0.846367	−	1.46595i	0.0380619	−	0.999275i	$-0.487882\pi$
$822$		0			0
$823$	5.45064e8	−	9.44078e8i	0.977795	−	1.69359i	0.307409	−	0.951577i	$-0.400538\pi$
$823$	5.45064e8	−	9.44078e8i	0.977795	−	1.69359i	0.670386	−	0.742013i	$-0.266129\pi$
$824$		0			0
$825$			6.90473e6i			0.0122966i
$826$		0			0
$827$	7.51770e8			1.32913			0.664566	−	0.747229i	$-0.268616\pi$
$827$	7.51770e8			1.32913			0.664566	+	0.747229i	$0.268616\pi$
$828$		0			0
$829$	4.00742e8	+	2.31369e8i	0.703399	+	0.406107i	0.808612	−	0.588342i	$-0.200219\pi$
$829$	4.00742e8	+	2.31369e8i	0.703399	+	0.406107i	−0.105213	+	0.994450i	$0.533553\pi$
$830$		0			0
$831$	−3.37849e8	+	1.95057e8i	−0.588735	+	0.339906i
$832$		0			0
$833$	−1.19575e6	−	7.79552e7i	−0.00206874	−	0.134868i
$834$		0			0
$835$	2.73541e8	+	4.73787e8i	0.469854	+	0.813811i
$836$		0			0
$837$	−3.46324e7	+	5.99850e7i	−0.0590617	+	0.102298i
$838$		0			0
$839$		−	6.92632e8i		−	1.17278i	−0.810029	−	0.586390i	$-0.800548\pi$
$839$		−	6.92632e8i		−	1.17278i	0.810029	−	0.586390i	$-0.199452\pi$
$840$		0			0
$841$	39354.8			6.61622e−5
$842$		0			0
$843$	2.97214e7	+	1.71596e7i	0.0496119	+	0.0286435i
$844$		0			0
$845$	1.28591e8	−	7.42419e7i	0.213128	−	0.123049i
$846$		0			0
$847$	−4.42710e6	−	5.77269e8i	−0.00728566	−	0.950010i
$848$		0			0
$849$	1.26163e8	+	2.18520e8i	0.206161	+	0.357082i
$850$		0			0
$851$	7.05358e7	−	1.22172e8i	0.114451	−	0.198235i
$852$		0			0
$853$		−	8.55770e8i		−	1.37883i	−0.724368	−	0.689414i	$-0.757868\pi$
$853$		−	8.55770e8i		−	1.37883i	0.724368	−	0.689414i	$-0.242132\pi$
$854$		0			0
$855$	−1.90105e8			−0.304155
$856$		0			0
$857$	−7.27810e7	−	4.20201e7i	−0.115631	−	0.0667598i	0.441069	−	0.897473i	$-0.354599\pi$
$857$	−7.27810e7	−	4.20201e7i	−0.115631	−	0.0667598i	−0.556700	+	0.830713i	$0.687933\pi$
$858$		0			0
$859$	−1.17533e8	+	6.78578e7i	−0.185430	+	0.107058i	−0.589842	−	0.807519i	$-0.700810\pi$
$859$	−1.17533e8	+	6.78578e7i	−0.185430	+	0.107058i	0.404411	+	0.914577i	$0.367476\pi$
$860$		0			0
$861$	3.13196e8	−	1.84040e8i	0.490689	−	0.288339i
$862$		0			0
$863$	5.33387e7	+	9.23853e7i	0.0829869	+	0.143738i	0.904532	−	0.426407i	$-0.140221\pi$
$863$	5.33387e7	+	9.23853e7i	0.0829869	+	0.143738i	−0.821545	+	0.570144i	$0.806887\pi$
$864$		0			0
$865$	−1.64786e8	+	2.85418e8i	−0.254608	+	0.440995i
$866$		0			0
$867$			3.69422e8i			0.566846i
$868$		0			0
$869$	−5.52825e7			−0.0842419
$870$		0			0
$871$	−3.41211e6	−	1.96998e6i	−0.00516380	−	0.00298132i
$872$		0			0
$873$	−2.76944e8	+	1.59894e8i	−0.416246	+	0.240319i
$874$		0			0
$875$	3.12932e8	−	5.51742e8i	0.467116	−	0.823592i
$876$		0			0
$877$	1.47121e8	+	2.54822e8i	0.218111	+	0.377779i	0.954230	−	0.299073i	$-0.0966773\pi$
$877$	1.47121e8	+	2.54822e8i	0.218111	+	0.377779i	−0.736120	+	0.676851i	$0.763344\pi$
$878$		0			0
$879$	2.31923e8	−	4.01703e8i	0.341490	−	0.591478i
$880$		0			0
$881$		−	8.33292e8i		−	1.21862i	−0.792931	−	0.609312i	$-0.791446\pi$
$881$		−	8.33292e8i		−	1.21862i	0.792931	−	0.609312i	$-0.208554\pi$
$882$		0			0
$883$	−1.56980e8			−0.228015			−0.114007	−	0.993480i	$-0.536369\pi$
$883$	−1.56980e8			−0.228015			−0.114007	+	0.993480i	$0.536369\pi$
$884$		0			0
$885$	−4.18538e8	−	2.41643e8i	−0.603817	−	0.348614i
$886$		0			0
$887$	−4.08718e8	+	2.35974e8i	−0.585670	+	0.338137i	−0.763384	−	0.645945i	$-0.776463\pi$
$887$	−4.08718e8	+	2.35974e8i	−0.585670	+	0.338137i	0.177713	+	0.984082i	$0.443130\pi$
$888$		0			0
$889$	5.71242e8	+	3.23991e8i	0.813046	+	0.461135i
$890$		0			0
$891$	8.78379e6	+	1.52140e7i	0.0124179	+	0.0215085i
$892$		0			0
$893$	−1.90615e8	+	3.30155e8i	−0.267672	+	0.463621i
$894$		0			0
$895$		−	1.20526e9i		−	1.68117i
$896$		0			0
$897$	3.27709e8			0.454058
$898$		0			0
$899$	−3.86226e8	−	2.22988e8i	−0.531573	−	0.306904i
$900$		0			0
$901$	539920.	−	311723.i	0.000738168	−	0.000426182i
$902$		0			0
$903$	−3.25207e8	−	5.53430e8i	−0.441669	−	0.751622i
$904$		0			0
$905$	8.14405e7	+	1.41059e8i	0.109874	+	0.190307i
$906$		0			0
$907$	−4.82395e8	+	8.35532e8i	−0.646518	+	1.11980i	0.337431	+	0.941350i	$0.390442\pi$
$907$	−4.82395e8	+	8.35532e8i	−0.646518	+	1.11980i	−0.983949	+	0.178452i	$0.942891\pi$
$908$		0			0
$909$		−	2.19475e8i		−	0.292208i
$910$		0			0
$911$	−1.18097e9			−1.56201			−0.781005	−	0.624525i	$-0.785293\pi$
$911$	−1.18097e9			−1.56201			−0.781005	+	0.624525i	$0.785293\pi$
$912$		0			0
$913$	7.70252e7	+	4.44705e7i	0.101209	+	0.0584333i
$914$		0			0
$915$	1.17506e8	−	6.78420e7i	0.153390	−	0.0885596i
$916$		0			0
$917$	1.37647e9	−	1.05562e7i	1.78509	−	0.0136899i
$918$		0			0
$919$	4.97774e8	+	8.62170e8i	0.641336	+	1.11083i	0.985135	+	0.171784i	$0.0549530\pi$
$919$	4.97774e8	+	8.62170e8i	0.641336	+	1.11083i	−0.343798	+	0.939044i	$0.611714\pi$
$920$		0			0
$921$	−2.70466e8	+	4.68461e8i	−0.346205	+	0.599645i
$922$		0			0
$923$		−	1.22147e9i		−	1.55337i
$924$		0			0
$925$	1.91962e7			0.0242544
$926$		0			0
$927$	−2.79945e8	−	1.61626e8i	−0.351426	−	0.202896i
$928$		0			0
$929$	1.20436e9	−	6.95339e8i	1.50214	−	0.867260i	0.502141	−	0.864786i	$-0.332546\pi$
$929$	1.20436e9	−	6.95339e8i	1.50214	−	0.867260i	0.999997	−	0.00247377i	$-0.000787425\pi$
$930$		0			0
$931$	−6.14626e8	−	3.42395e8i	−0.761661	−	0.424305i
$932$		0			0
$933$	−2.03119e8	−	3.51812e8i	−0.250095	−	0.433177i
$934$		0			0
$935$	−1.28959e7	+	2.23363e7i	−0.0157767	+	0.0273261i
$936$		0			0
$937$		−	1.40807e9i		−	1.71161i	−0.517300	−	0.855804i	$-0.673063\pi$
$937$		−	1.40807e9i		−	1.71161i	0.517300	−	0.855804i	$-0.326937\pi$
$938$		0			0
$939$	−1.67052e8			−0.201769
$940$		0			0
$941$	1.14033e9	+	6.58373e8i	1.36856	+	0.790138i	0.990744	−	0.135743i	$-0.0433423\pi$
$941$	1.14033e9	+	6.58373e8i	1.36856	+	0.790138i	0.377815	+	0.925881i	$0.376676\pi$
$942$		0			0
$943$	−6.43763e8	+	3.71677e8i	−0.767699	+	0.443231i
$944$		0			0
$945$	1.30348e6	+	1.69967e8i	0.00154458	+	0.201404i
$946$		0			0
$947$	5.17638e8	+	8.96575e8i	0.609504	+	1.05569i	0.991322	+	0.131454i	$0.0419645\pi$
$947$	5.17638e8	+	8.96575e8i	0.609504	+	1.05569i	−0.381819	+	0.924237i	$0.624702\pi$
$948$		0			0
$949$	−6.37406e8	+	1.10402e9i	−0.745792	+	1.29175i
$950$		0			0
$951$			4.14290e8i			0.481685i
$952$		0			0
$953$	−8.21998e8			−0.949713			−0.474856	−	0.880063i	$-0.657500\pi$
$953$	−8.21998e8			−0.949713			−0.474856	+	0.880063i	$0.657500\pi$
$954$		0			0
$955$	8.48346e8	+	4.89793e8i	0.974009	+	0.562344i
$956$		0			0
$957$	−9.79584e7	+	5.65563e7i	−0.111765	+	0.0645276i
$958$		0			0
$959$	−7.60821e7	+	4.47074e7i	−0.0862634	+	0.0506902i
$960$		0			0
$961$	−2.76575e8	−	4.79042e8i	−0.311633	−	0.539763i
$962$		0			0
$963$	−2.58391e8	+	4.47547e8i	−0.289334	+	0.501140i
$964$		0			0
$965$			1.45042e9i			1.61403i
$966$		0			0
$967$	−1.02503e9			−1.13360			−0.566798	−	0.823857i	$-0.691818\pi$
$967$	−1.02503e9			−1.13360			−0.566798	+	0.823857i	$0.691818\pi$
$968$		0			0
$969$	−5.35002e7	−	3.08884e7i	−0.0588010	−	0.0339488i
$970$		0			0
$971$	−1.02732e9	+	5.93122e8i	−1.12214	+	0.647868i	−0.941946	−	0.335763i	$-0.891006\pi$
$971$	−1.02732e9	+	5.93122e8i	−1.12214	+	0.647868i	−0.180194	+	0.983631i	$0.557672\pi$
$972$		0			0
$973$	1.25845e8	−	2.21883e8i	0.136615	−	0.240871i
$974$		0			0
$975$	2.22964e7	+	3.86186e7i	0.0240559	+	0.0416660i
$976$		0			0
$977$	−3.15841e8	+	5.47053e8i	−0.338677	+	0.586605i	−0.984184	−	0.177149i	$-0.943313\pi$
$977$	−3.15841e8	+	5.47053e8i	−0.338677	+	0.586605i	0.645507	+	0.763754i	$0.276646\pi$
$978$		0			0
$979$			1.87802e8i			0.200148i
$980$		0			0
$981$	−3.41405e8			−0.361629
$982$		0			0
$983$	3.71426e8	+	2.14443e8i	0.391031	+	0.225762i	0.682607	−	0.730786i	$-0.260846\pi$
$983$	3.71426e8	+	2.14443e8i	0.391031	+	0.225762i	−0.291576	+	0.956548i	$0.594180\pi$
$984$		0			0
$985$	−1.28426e9	+	7.41471e8i	−1.34383	+	0.775863i
$986$		0			0
$987$	2.96488e8	+	1.68159e8i	0.308358	+	0.174891i
$988$		0			0
$989$	6.56768e8	+	1.13756e9i	0.678927	+	1.17594i
$990$		0			0
$991$	−4.63340e8	+	8.02528e8i	−0.476079	+	0.824592i	−0.999624	−	0.0274052i	$-0.991276\pi$
$991$	−4.63340e8	+	8.02528e8i	−0.476079	+	0.824592i	0.523546	+	0.851998i	$0.324609\pi$
$992$		0			0
$993$		−	2.34434e7i		−	0.0239427i
$994$		0			0
$995$	7.96617e8			0.808687
$996$		0			0
$997$	−7.83801e8	−	4.52528e8i	−0.790897	−	0.456625i	0.0493809	−	0.998780i	$-0.484275\pi$
$997$	−7.83801e8	−	4.52528e8i	−0.790897	−	0.456625i	−0.840278	+	0.542155i	$0.817609\pi$
$998$		0			0
$999$	4.22972e7	−	2.44203e7i	0.0424244	−	0.0244937i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.7.bh.a.241.4		8
4.3	odd	2		84.7.m.b.73.4	yes	8
7.5	odd	6	inner	336.7.bh.a.145.4		8
12.11	even	2		252.7.z.e.73.1		8
28.3	even	6		588.7.d.a.97.5		8
28.11	odd	6		588.7.d.a.97.4		8
28.19	even	6		84.7.m.b.61.4	✓	8
28.23	odd	6		588.7.m.b.313.1		8
28.27	even	2		588.7.m.b.325.1		8
84.47	odd	6		252.7.z.e.145.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
84.7.m.b.61.4	✓	8	28.19	even	6
84.7.m.b.73.4	yes	8	4.3	odd	2
252.7.z.e.73.1		8	12.11	even	2
252.7.z.e.145.1		8	84.47	odd	6
336.7.bh.a.145.4		8	7.5	odd	6	inner
336.7.bh.a.241.4		8	1.1	even	1	trivial
588.7.d.a.97.4		8	28.11	odd	6
588.7.d.a.97.5		8	28.3	even	6
588.7.m.b.313.1		8	28.23	odd	6
588.7.m.b.325.1		8	28.27	even	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:	\( N \)	\(=\)	\( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	336.bh (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-13.5000 - 7.79423i) q^{3} +(113.293 - 65.4099i) q^{5} +(-298.353 - 169.217i) q^{7} +(121.500 + 210.444i) q^{9} +O(q^{10})\)	\(q+(-13.5000 - 7.79423i) q^{3} +(113.293 - 65.4099i) q^{5} +(-298.353 - 169.217i) q^{7} +(121.500 + 210.444i) q^{9} +(148.754 - 257.650i) q^{11} -1921.40i q^{13} -2039.28 q^{15} +(-573.903 - 331.343i) q^{17} +(-5178.99 + 2990.09i) q^{19} +(2708.85 + 4609.86i) q^{21} +(-5470.63 - 9475.41i) q^{23} +(744.413 - 1289.36i) q^{25} -3788.00i q^{27} +24389.8 q^{29} +(-15835.6 - 9142.67i) q^{31} +(-4016.37 + 2318.85i) q^{33} +(-44869.9 + 344.109i) q^{35} +(6446.77 + 11166.1i) q^{37} +(-14975.8 + 25938.9i) q^{39} -67940.4i q^{41} -120053. q^{43} +(27530.3 + 15894.6i) q^{45} +(55208.2 - 31874.5i) q^{47} +(60380.2 + 100973. i) q^{49} +(5165.13 + 8946.26i) q^{51} +(-470.393 + 814.745i) q^{53} -38920.0i q^{55} +93221.7 q^{57} +(205238. + 118494. i) q^{59} +(-57621.2 + 33267.6i) q^{61} +(-639.188 - 83346.5i) q^{63} +(-125679. - 217682. i) q^{65} +(1025.29 - 1775.85i) q^{67} +170557. i q^{69} +635716. q^{71} +(-574591. - 331740. i) q^{73} +(-20099.2 + 11604.3i) q^{75} +(-87980.1 + 51699.0i) q^{77} +(-92909.0 - 160923. i) q^{79} +(-29524.5 + 51137.9i) q^{81} +298953. i q^{83} -86692.5 q^{85} +(-329262. - 190100. i) q^{87} +(-546677. + 315624. i) q^{89} +(-325134. + 573256. i) q^{91} +(142520. + 246852. i) q^{93} +(-391163. + 677514. i) q^{95} +1.31600e6i q^{97} +72294.6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 108 q^{3} - 294 q^{5} - 232 q^{7} + 972 q^{9}+O(q^{10}) \) 8 * q - 108 * q^3 - 294 * q^5 - 232 * q^7 + 972 * q^9	\( 8 q - 108 q^{3} - 294 q^{5} - 232 q^{7} + 972 q^{9} - 378 q^{11} + 5292 q^{15} + 852 q^{17} - 3690 q^{19} + 3942 q^{21} - 15600 q^{23} + 3386 q^{25} - 68604 q^{29} - 23028 q^{31} + 10206 q^{33} - 93828 q^{35} + 15914 q^{37} - 25326 q^{39} + 170044 q^{43} - 71442 q^{45} - 102180 q^{47} + 157340 q^{49} - 7668 q^{51} + 196410 q^{53} + 66420 q^{57} + 662550 q^{59} - 23928 q^{61} - 50058 q^{63} + 14892 q^{65} - 774838 q^{67} + 721896 q^{71} - 1219050 q^{73} - 91422 q^{75} + 1584738 q^{77} + 493868 q^{79} - 236196 q^{81} - 1329816 q^{85} + 926154 q^{87} + 604260 q^{89} - 3831690 q^{91} + 207252 q^{93} - 448944 q^{95} - 183708 q^{99}+O(q^{100}) \) 8 * q - 108 * q^3 - 294 * q^5 - 232 * q^7 + 972 * q^9 - 378 * q^11 + 5292 * q^15 + 852 * q^17 - 3690 * q^19 + 3942 * q^21 - 15600 * q^23 + 3386 * q^25 - 68604 * q^29 - 23028 * q^31 + 10206 * q^33 - 93828 * q^35 + 15914 * q^37 - 25326 * q^39 + 170044 * q^43 - 71442 * q^45 - 102180 * q^47 + 157340 * q^49 - 7668 * q^51 + 196410 * q^53 + 66420 * q^57 + 662550 * q^59 - 23928 * q^61 - 50058 * q^63 + 14892 * q^65 - 774838 * q^67 + 721896 * q^71 - 1219050 * q^73 - 91422 * q^75 + 1584738 * q^77 + 493868 * q^79 - 236196 * q^81 - 1329816 * q^85 + 926154 * q^87 + 604260 * q^89 - 3831690 * q^91 + 207252 * q^93 - 448944 * q^95 - 183708 * q^99

Introduction

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