LMFDB - Embedded newform 336.3.bh.g.145.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [336,3,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, 3, names="a")

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

chi := DirichletCharacter("336.145");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 336 = 2^{4} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
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:	$9.15533688251$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.35911766016.9
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} - 7x^{6} - 2x^{5} + 78x^{4} - 18x^{3} - 153x^{2} - 230x + 529 $ x^8 - 2x^7 - 7x^6 - 2x^5 + 78x^4 - 18x^3 - 153x^2 - 230*x + 529
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4}\cdot 7 $
Twist minimal:	no (minimal twist has level 168)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			145.1
Root			$1.83172 - 0.480194i$ of defining polynomial
Character	$\chi$	$=$	336.145
Dual form			336.3.bh.g.241.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.50000 + 0.866025i) q^{3} +(-6.80550 - 3.92916i) q^{5} +(-6.99187 - 0.337312i) q^{7} +(1.50000 - 2.59808i) q^{9} +O(q^{10})$	\(q+(-1.50000 + 0.866025i) q^{3} +(-6.80550 - 3.92916i) q^{5} +(-6.99187 - 0.337312i) q^{7} +(1.50000 - 2.59808i) q^{9} +(10.2197 + 17.7011i) q^{11} -4.69139i q^{13} +13.6110 q^{15} +(15.8805 - 9.16861i) q^{17} +(16.4286 + 9.48508i) q^{19} +(10.7799 - 5.54917i) q^{21} +(14.6631 - 25.3972i) q^{23} +(18.3766 + 31.8292i) q^{25} +5.19615i q^{27} +37.7152 q^{29} +(-29.4499 + 17.0029i) q^{31} +(-30.6591 - 17.7011i) q^{33} +(46.2578 + 29.7677i) q^{35} +(-21.4224 + 37.1047i) q^{37} +(4.06286 + 7.03708i) q^{39} -25.4518i q^{41} -10.5573 q^{43} +(-20.4165 + 11.7875i) q^{45} +(-8.64667 - 4.99215i) q^{47} +(48.7724 + 4.71688i) q^{49} +(-15.8805 + 27.5058i) q^{51} +(42.0439 + 72.8222i) q^{53} -160.620i q^{55} -32.8573 q^{57} +(12.3890 - 7.15277i) q^{59} +(41.7249 + 24.0899i) q^{61} +(-11.3642 + 17.6594i) q^{63} +(-18.4332 + 31.9272i) q^{65} +(-29.9519 - 51.8782i) q^{67} +50.7944i q^{69} +111.092 q^{71} +(34.5437 - 19.9438i) q^{73} +(-55.1297 - 31.8292i) q^{75} +(-65.4841 - 127.211i) q^{77} +(-42.2075 + 73.1056i) q^{79} +(-4.50000 - 7.79423i) q^{81} +41.7432i q^{83} -144.100 q^{85} +(-56.5727 + 32.6623i) q^{87} +(-4.10144 - 2.36797i) q^{89} +(-1.58246 + 32.8016i) q^{91} +(29.4499 - 51.0088i) q^{93} +(-74.5368 - 129.101i) q^{95} -138.026i q^{97} +61.3183 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 12 q^{3} - 6 q^{5} - 8 q^{7} + 12 q^{9}+O(q^{10}) $ 8 * q - 12 * q^3 - 6 * q^5 - 8 * q^7 + 12 * q^9	$ 8 q - 12 q^{3} - 6 q^{5} - 8 q^{7} + 12 q^{9} + 22 q^{11} + 12 q^{15} + 36 q^{17} - 42 q^{19} + 6 q^{21} - 48 q^{23} + 42 q^{25} + 68 q^{29} + 60 q^{31} - 66 q^{33} + 12 q^{35} - 118 q^{37} + 18 q^{39} + 92 q^{43} - 18 q^{45} + 12 q^{47} - 20 q^{49} - 36 q^{51} + 10 q^{53} + 84 q^{57} + 54 q^{59} + 24 q^{61} + 6 q^{63} - 148 q^{65} - 22 q^{67} + 392 q^{71} - 138 q^{73} - 126 q^{75} - 126 q^{77} - 164 q^{79} - 36 q^{81} + 200 q^{85} - 102 q^{87} - 60 q^{89} - 90 q^{91} - 60 q^{93} + 132 q^{99}+O(q^{100}) $ 8 * q - 12 * q^3 - 6 * q^5 - 8 * q^7 + 12 * q^9 + 22 * q^11 + 12 * q^15 + 36 * q^17 - 42 * q^19 + 6 * q^21 - 48 * q^23 + 42 * q^25 + 68 * q^29 + 60 * q^31 - 66 * q^33 + 12 * q^35 - 118 * q^37 + 18 * q^39 + 92 * q^43 - 18 * q^45 + 12 * q^47 - 20 * q^49 - 36 * q^51 + 10 * q^53 + 84 * q^57 + 54 * q^59 + 24 * q^61 + 6 * q^63 - 148 * q^65 - 22 * q^67 + 392 * q^71 - 138 * q^73 - 126 * q^75 - 126 * q^77 - 164 * q^79 - 36 * q^81 + 200 * q^85 - 102 * q^87 - 60 * q^89 - 90 * q^91 - 60 * q^93 + 132 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$85$	$113$	$127$	$241$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.50000	+	0.866025i	−0.500000	+	0.288675i
$3$	−1.50000	+	0.866025i	−0.500000	+	0.288675i
$4$		0			0
$5$	−6.80550	−	3.92916i	−1.36110	−	0.785832i	−0.371330	−	0.928501i	$-0.621098\pi$
$5$	−6.80550	−	3.92916i	−1.36110	−	0.785832i	−0.989770	+	0.142669i	$0.954431\pi$
$6$		0			0
$7$	−6.99187	−	0.337312i	−0.998838	−	0.0481874i
$7$	−6.99187	−	0.337312i	−0.998838	−	0.0481874i
$8$		0			0
$9$	1.50000	−	2.59808i	0.166667	−	0.288675i
$10$		0			0
$11$	10.2197	+	17.7011i	0.929065	+	1.60919i	0.784890	+	0.619636i	$0.212720\pi$
$11$	10.2197	+	17.7011i	0.929065	+	1.60919i	0.144175	+	0.989552i	$0.453947\pi$
$12$		0			0
$13$		−	4.69139i		−	0.360876i	−0.983586	−	0.180438i	$-0.942248\pi$
$13$		−	4.69139i		−	0.360876i	0.983586	−	0.180438i	$-0.0577515\pi$
$14$		0			0
$15$	13.6110			0.907400
$16$		0			0
$17$	15.8805	−	9.16861i	0.934147	−	0.539330i	0.0460264	−	0.998940i	$-0.485344\pi$
$17$	15.8805	−	9.16861i	0.934147	−	0.539330i	0.888121	+	0.459610i	$0.152011\pi$
$18$		0			0
$19$	16.4286	+	9.48508i	0.864666	+	0.499215i	0.865572	−	0.500785i	$-0.166955\pi$
$19$	16.4286	+	9.48508i	0.864666	+	0.499215i	−0.000906333		1.00000i	$0.500288\pi$
$20$		0			0
$21$	10.7799	−	5.54917i	0.513330	−	0.264246i
$22$		0			0
$23$	14.6631	−	25.3972i	0.637525	−	1.10423i	−0.348449	−	0.937328i	$-0.613292\pi$
$23$	14.6631	−	25.3972i	0.637525	−	1.10423i	0.985974	−	0.166898i	$-0.0533751\pi$
$24$		0			0
$25$	18.3766	+	31.8292i	0.735063	+	1.27317i
$26$		0			0
$27$			5.19615i			0.192450i
$28$		0			0
$29$	37.7152			1.30052			0.650261	−	0.759711i	$-0.274659\pi$
$29$	37.7152			1.30052			0.650261	+	0.759711i	$0.274659\pi$
$30$		0			0
$31$	−29.4499	+	17.0029i	−0.949998	+	0.548481i	−0.893080	−	0.449897i	$-0.851461\pi$
$31$	−29.4499	+	17.0029i	−0.949998	+	0.548481i	−0.0569175	+	0.998379i	$0.518127\pi$
$32$		0			0
$33$	−30.6591	−	17.7011i	−0.929065	−	0.536396i
$34$		0			0
$35$	46.2578	+	29.7677i	1.32165	+	0.850507i
$36$		0			0
$37$	−21.4224	+	37.1047i	−0.578984	+	1.00283i	0.416612	+	0.909084i	$0.363217\pi$
$37$	−21.4224	+	37.1047i	−0.578984	+	1.00283i	−0.995596	+	0.0937458i	$0.970116\pi$
$38$		0			0
$39$	4.06286	+	7.03708i	0.104176	+	0.180438i
$40$		0			0
$41$		−	25.4518i		−	0.620775i	−0.950610	−	0.310388i	$-0.899541\pi$
$41$		−	25.4518i		−	0.620775i	0.950610	−	0.310388i	$-0.100459\pi$
$42$		0			0
$43$	−10.5573			−0.245518			−0.122759	−	0.992436i	$-0.539174\pi$
$43$	−10.5573			−0.245518			−0.122759	+	0.992436i	$0.539174\pi$
$44$		0			0
$45$	−20.4165	+	11.7875i	−0.453700	+	0.261944i
$46$		0			0
$47$	−8.64667	−	4.99215i	−0.183972	−	0.106216i	0.405186	−	0.914234i	$-0.367207\pi$
$47$	−8.64667	−	4.99215i	−0.183972	−	0.106216i	−0.589157	+	0.808018i	$0.700540\pi$
$48$		0			0
$49$	48.7724	+	4.71688i	0.995356	+	0.0962629i
$50$		0			0
$51$	−15.8805	+	27.5058i	−0.311382	+	0.539330i
$52$		0			0
$53$	42.0439	+	72.8222i	0.793282	+	1.37400i	0.923925	+	0.382574i	$0.124962\pi$
$53$	42.0439	+	72.8222i	0.793282	+	1.37400i	−0.130643	+	0.991429i	$0.541704\pi$
$54$		0			0
$55$		−	160.620i		−	2.92035i
$56$		0			0
$57$	−32.8573			−0.576444
$58$		0			0
$59$	12.3890	−	7.15277i	0.209982	−	0.121233i	−0.391321	−	0.920254i	$-0.627982\pi$
$59$	12.3890	−	7.15277i	0.209982	−	0.121233i	0.601303	+	0.799021i	$0.294648\pi$
$60$		0			0
$61$	41.7249	+	24.0899i	0.684015	+	0.394916i	0.801366	−	0.598174i	$-0.204107\pi$
$61$	41.7249	+	24.0899i	0.684015	+	0.394916i	−0.117351	+	0.993090i	$0.537440\pi$
$62$		0			0
$63$	−11.3642	+	17.6594i	−0.180384	+	0.280309i
$64$		0			0
$65$	−18.4332	+	31.9272i	−0.283588	+	0.491188i
$66$		0			0
$67$	−29.9519	−	51.8782i	−0.447043	−	0.774302i	0.551149	−	0.834407i	$-0.314190\pi$
$67$	−29.9519	−	51.8782i	−0.447043	−	0.774302i	−0.998192	+	0.0601051i	$0.980856\pi$
$68$		0			0
$69$			50.7944i			0.736151i
$70$		0			0
$71$	111.092			1.56467			0.782337	−	0.622856i	$-0.214028\pi$
$71$	111.092			1.56467			0.782337	+	0.622856i	$0.214028\pi$
$72$		0			0
$73$	34.5437	−	19.9438i	0.473201	−	0.273203i	−0.244378	−	0.969680i	$-0.578584\pi$
$73$	34.5437	−	19.9438i	0.473201	−	0.273203i	0.717579	+	0.696477i	$0.245250\pi$
$74$		0			0
$75$	−55.1297	−	31.8292i	−0.735063	−	0.424389i
$76$		0			0
$77$	−65.4841	−	127.211i	−0.850443	−	1.65209i
$78$		0			0
$79$	−42.2075	+	73.1056i	−0.534273	+	0.925388i	0.464925	+	0.885350i	$0.346081\pi$
$79$	−42.2075	+	73.1056i	−0.534273	+	0.925388i	−0.999198	+	0.0400377i	$0.987252\pi$
$80$		0			0
$81$	−4.50000	−	7.79423i	−0.0555556	−	0.0962250i
$82$		0			0
$83$			41.7432i			0.502930i	0.967866	+	0.251465i	$0.0809123\pi$
$83$			41.7432i			0.502930i	−0.967866	+	0.251465i	$0.919088\pi$
$84$		0			0
$85$	−144.100			−1.69529
$86$		0			0
$87$	−56.5727	+	32.6623i	−0.650261	+	0.375429i
$88$		0			0
$89$	−4.10144	−	2.36797i	−0.0460836	−	0.0266064i	0.476781	−	0.879022i	$-0.341803\pi$
$89$	−4.10144	−	2.36797i	−0.0460836	−	0.0266064i	−0.522865	+	0.852416i	$0.675137\pi$
$90$		0			0
$91$	−1.58246	+	32.8016i	−0.0173897	+	0.360457i
$92$		0			0
$93$	29.4499	−	51.0088i	0.316666	−	0.548481i
$94$		0			0
$95$	−74.5368	−	129.101i	−0.784598	−	1.35896i
$96$		0			0
$97$		−	138.026i		−	1.42295i	−0.702712	−	0.711475i	$-0.748028\pi$
$97$		−	138.026i		−	1.42295i	0.702712	−	0.711475i	$-0.251972\pi$
$98$		0			0
$99$	61.3183			0.619377
$100$		0			0
$101$	34.2882	−	19.7963i	0.339487	−	0.196003i	−0.320558	−	0.947229i	$-0.603870\pi$
$101$	34.2882	−	19.7963i	0.339487	−	0.196003i	0.660045	+	0.751226i	$0.270537\pi$
$102$		0			0
$103$	65.5013	+	37.8172i	0.635935	+	0.367157i	0.783047	−	0.621962i	$-0.213664\pi$
$103$	65.5013	+	37.8172i	0.635935	+	0.367157i	−0.147112	+	0.989120i	$0.546998\pi$
$104$		0			0
$105$	−95.1663	−	4.59115i	−0.906346	−	0.0437253i
$106$		0			0
$107$	−23.4309	+	40.5835i	−0.218981	+	0.379285i	−0.954497	−	0.298222i	$-0.903606\pi$
$107$	−23.4309	+	40.5835i	−0.218981	+	0.379285i	0.735516	+	0.677507i	$0.236940\pi$
$108$		0			0
$109$	−33.1932	−	57.4923i	−0.304524	−	0.527452i	0.672631	−	0.739978i	$-0.265164\pi$
$109$	−33.1932	−	57.4923i	−0.304524	−	0.527452i	−0.977155	+	0.212526i	$0.931831\pi$
$110$		0			0
$111$		−	74.2094i		−	0.668554i
$112$		0			0
$113$	124.917			1.10546			0.552732	−	0.833359i	$-0.313585\pi$
$113$	124.917			1.10546			0.552732	+	0.833359i	$0.313585\pi$
$114$		0			0
$115$	−199.579	+	115.227i	−1.73547	+	1.00197i
$116$		0			0
$117$	−12.1886	−	7.03708i	−0.104176	−	0.0601460i
$118$		0			0
$119$	−114.127	+	58.7490i	−0.959051	+	0.493689i
$120$		0			0
$121$	−148.385	+	257.011i	−1.22632	+	2.12405i
$122$		0			0
$123$	22.0419	+	38.1777i	0.179202	+	0.310388i
$124$		0			0
$125$		−	92.3599i		−	0.738879i
$126$		0			0
$127$	56.5161			0.445008			0.222504	−	0.974932i	$-0.428577\pi$
$127$	56.5161			0.445008			0.222504	+	0.974932i	$0.428577\pi$
$128$		0			0
$129$	15.8359	−	9.14288i	0.122759	−	0.0708750i
$130$		0			0
$131$	−6.34153	−	3.66129i	−0.0484087	−	0.0279488i	0.475600	−	0.879661i	$-0.342231\pi$
$131$	−6.34153	−	3.66129i	−0.0484087	−	0.0279488i	−0.524009	+	0.851713i	$0.675564\pi$
$132$		0			0
$133$	−111.667	−	71.8600i	−0.839605	−	0.540301i
$134$		0			0
$135$	20.4165	−	35.3624i	0.151233	−	0.261944i
$136$		0			0
$137$	34.1750	+	59.1928i	0.249452	+	0.432064i	0.963374	−	0.268162i	$-0.0864161\pi$
$137$	34.1750	+	59.1928i	0.249452	+	0.432064i	−0.713922	+	0.700226i	$0.753083\pi$
$138$		0			0
$139$			222.603i			1.60146i	0.599025	+	0.800730i	$0.295555\pi$
$139$			222.603i			1.60146i	−0.599025	+	0.800730i	$0.704445\pi$
$140$		0			0
$141$	17.2933			0.122648
$142$		0			0
$143$	83.0426	−	47.9446i	0.580717	−	0.335277i
$144$		0			0
$145$	−256.671	−	148.189i	−1.77014	−	1.02199i
$146$		0			0
$147$	−77.2436	+	35.1629i	−0.525467	+	0.239203i
$148$		0			0
$149$	25.7499	−	44.6001i	0.172818	−	0.299329i	−0.766586	−	0.642142i	$-0.778046\pi$
$149$	25.7499	−	44.6001i	0.172818	−	0.299329i	0.939404	+	0.342812i	$0.111379\pi$
$150$		0			0
$151$	−25.3180	−	43.8521i	−0.167669	−	0.290411i	0.769931	−	0.638127i	$-0.220291\pi$
$151$	−25.3180	−	43.8521i	−0.167669	−	0.290411i	−0.937600	+	0.347716i	$0.886957\pi$
$152$		0			0
$153$		−	55.0117i		−	0.359553i
$154$		0			0
$155$	267.229			1.72406
$156$		0			0
$157$	176.316	−	101.796i	1.12303	−	0.648383i	0.180858	−	0.983509i	$-0.442112\pi$
$157$	176.316	−	101.796i	1.12303	−	0.648383i	0.942173	+	0.335127i	$0.108779\pi$
$158$		0			0
$159$	−126.132	−	72.8222i	−0.793282	−	0.458001i
$160$		0			0
$161$	−111.089	+	172.628i	−0.689994	+	1.07222i
$162$		0			0
$163$	33.6268	−	58.2434i	0.206300	−	0.357321i	−0.744246	−	0.667905i	$-0.767191\pi$
$163$	33.6268	−	58.2434i	0.206300	−	0.357321i	0.950546	+	0.310584i	$0.100524\pi$
$164$		0			0
$165$	139.101	+	240.929i	0.843034	+	1.46018i
$166$		0			0
$167$		−	203.126i		−	1.21632i	−0.793814	−	0.608161i	$-0.791908\pi$
$167$		−	203.126i		−	1.21632i	0.793814	−	0.608161i	$-0.208092\pi$
$168$		0			0
$169$	146.991			0.869769
$170$		0			0
$171$	49.2859	−	28.4552i	0.288222	−	0.166405i
$172$		0			0
$173$	146.230	+	84.4257i	0.845258	+	0.488010i	0.859048	−	0.511895i	$-0.171056\pi$
$173$	146.230	+	84.4257i	0.845258	+	0.488010i	−0.0137902	+	0.999905i	$0.504390\pi$
$174$		0			0
$175$	−117.750	−	228.744i	−0.672858	−	1.30711i
$176$		0			0
$177$	−12.3890	+	21.4583i	−0.0699942	+	0.121233i
$178$		0			0
$179$	11.8209	+	20.4745i	0.0660388	+	0.114383i	0.897154	−	0.441717i	$-0.145631\pi$
$179$	11.8209	+	20.4745i	0.0660388	+	0.114383i	−0.831116	+	0.556100i	$0.812297\pi$
$180$		0			0
$181$			36.1262i			0.199592i	0.995008	+	0.0997960i	$0.0318190\pi$
$181$			36.1262i			0.199592i	−0.995008	+	0.0997960i	$0.968181\pi$
$182$		0			0
$183$	−83.4498			−0.456010
$184$		0			0
$185$	291.581	−	168.344i	1.57611	−	0.909968i
$186$		0			0
$187$	324.588	+	187.401i	1.73577	+	1.00215i
$188$		0			0
$189$	1.75272	−	36.3308i	0.00927367	−	0.192227i
$190$		0			0
$191$	6.54251	−	11.3320i	0.0342540	−	0.0593297i	−0.848390	−	0.529371i	$-0.822428\pi$
$191$	6.54251	−	11.3320i	0.0342540	−	0.0593297i	0.882644	+	0.470042i	$0.155761\pi$
$192$		0			0
$193$	−38.9899	−	67.5324i	−0.202020	−	0.349909i	0.747159	−	0.664645i	$-0.231417\pi$
$193$	−38.9899	−	67.5324i	−0.202020	−	0.349909i	−0.949179	+	0.314736i	$0.898084\pi$
$194$		0			0
$195$		−	63.8545i		−	0.327459i
$196$		0			0
$197$	−198.036			−1.00526			−0.502630	−	0.864502i	$-0.667634\pi$
$197$	−198.036			−1.00526			−0.502630	+	0.864502i	$0.667634\pi$
$198$		0			0
$199$	−41.3721	+	23.8862i	−0.207900	+	0.120031i	−0.600335	−	0.799749i	$-0.704966\pi$
$199$	−41.3721	+	23.8862i	−0.207900	+	0.120031i	0.392435	+	0.919780i	$0.371633\pi$
$200$		0			0
$201$	89.8557	+	51.8782i	0.447043	+	0.258101i
$202$		0			0
$203$	−263.699	−	12.7218i	−1.29901	−	0.0626688i
$204$		0			0
$205$	−100.004	+	173.212i	−0.487825	+	0.844937i
$206$		0			0
$207$	−43.9892	−	76.1916i	−0.212508	−	0.368075i
$208$		0			0
$209$			387.739i			1.85521i
$210$		0			0
$211$	210.519			0.997719			0.498859	−	0.866683i	$-0.333752\pi$
$211$	210.519			0.997719			0.498859	+	0.866683i	$0.333752\pi$
$212$		0			0
$213$	−166.638	+	96.2083i	−0.782337	+	0.451682i
$214$		0			0
$215$	71.8476	+	41.4812i	0.334175	+	0.192936i
$216$		0			0
$217$	211.645	−	108.948i	0.975324	−	0.502066i
$218$		0			0
$219$	−34.5437	+	59.8314i	−0.157734	+	0.273203i
$220$		0			0
$221$	−43.0135	−	74.5016i	−0.194631	−	0.337111i
$222$		0			0
$223$		−	20.9020i		−	0.0937307i	−0.998901	−	0.0468654i	$-0.985077\pi$
$223$		−	20.9020i		−	0.0937307i	0.998901	−	0.0468654i	$-0.0149232\pi$
$224$		0			0
$225$	110.259			0.490042
$226$		0			0
$227$	−78.5392	+	45.3446i	−0.345988	+	0.199756i	−0.662917	−	0.748693i	$-0.730682\pi$
$227$	−78.5392	+	45.3446i	−0.345988	+	0.199756i	0.316929	+	0.948449i	$0.397348\pi$
$228$		0			0
$229$	228.431	+	131.885i	0.997515	+	0.575915i	0.907512	−	0.420026i	$-0.137979\pi$
$229$	228.431	+	131.885i	0.997515	+	0.575915i	0.0900028	+	0.995942i	$0.471312\pi$
$230$		0			0
$231$	208.394	+	134.105i	0.902138	+	0.580542i
$232$		0			0
$233$	−24.4685	+	42.3807i	−0.105015	+	0.181891i	−0.913744	−	0.406290i	$-0.866822\pi$
$233$	−24.4685	+	42.3807i	−0.105015	+	0.181891i	0.808729	+	0.588181i	$0.200156\pi$
$234$		0			0
$235$	39.2299	+	67.9482i	0.166936	+	0.289141i
$236$		0			0
$237$		−	146.211i		−	0.616925i
$238$		0			0
$239$	−133.256			−0.557557			−0.278779	−	0.960355i	$-0.589930\pi$
$239$	−133.256			−0.557557			−0.278779	+	0.960355i	$0.589930\pi$
$240$		0			0
$241$	−386.069	+	222.897i	−1.60195	+	0.924884i	−0.610849	+	0.791747i	$0.709172\pi$
$241$	−386.069	+	222.897i	−1.60195	+	0.924884i	−0.991098	+	0.133138i	$0.957495\pi$
$242$		0			0
$243$	13.5000	+	7.79423i	0.0555556	+	0.0320750i
$244$		0			0
$245$	−313.388	−	223.735i	−1.27913	−	0.913206i
$246$		0			0
$247$	44.4982	−	77.0731i	0.180155	−	0.312037i
$248$		0			0
$249$	−36.1507	−	62.6148i	−0.145183	−	0.251465i
$250$		0			0
$251$		−	400.268i		−	1.59469i	−0.603521	−	0.797347i	$-0.706236\pi$
$251$		−	400.268i		−	1.59469i	0.603521	−	0.797347i	$-0.293764\pi$
$252$		0			0
$253$	599.410			2.36921
$254$		0			0
$255$	216.150	−	124.794i	0.847645	−	0.489388i
$256$		0			0
$257$	328.560	+	189.694i	1.27844	+	0.738109i	0.976562	−	0.215236i	$-0.0690522\pi$
$257$	328.560	+	189.694i	1.27844	+	0.738109i	0.301881	+	0.953346i	$0.402386\pi$
$258$		0			0
$259$	162.299	−	252.205i	0.626636	−	0.973766i
$260$		0			0
$261$	56.5727	−	97.9868i	0.216754	−	0.375429i
$262$		0			0
$263$	138.740	+	240.305i	0.527529	+	0.913707i	0.999485	+	0.0320852i	$0.0102148\pi$
$263$	138.740	+	240.305i	0.527529	+	0.913707i	−0.471956	+	0.881622i	$0.656452\pi$
$264$		0			0
$265$		−	660.789i		−	2.49354i
$266$		0			0
$267$	8.20288			0.0307224
$268$		0			0
$269$	−436.117	+	251.792i	−1.62125	+	0.936031i	−0.634669	+	0.772784i	$0.718864\pi$
$269$	−436.117	+	251.792i	−1.62125	+	0.936031i	−0.986585	+	0.163247i	$0.947803\pi$
$270$		0			0
$271$	206.930	+	119.471i	0.763579	+	0.440853i	0.830579	−	0.556900i	$-0.188009\pi$
$271$	206.930	+	119.471i	0.763579	+	0.440853i	−0.0670000	+	0.997753i	$0.521343\pi$
$272$		0			0
$273$	−26.0333	−	50.5728i	−0.0953601	−	0.185248i
$274$		0			0
$275$	−375.607	+	650.570i	−1.36584	+	2.36571i
$276$		0			0
$277$	214.988	+	372.369i	0.776128	+	1.34429i	0.934158	+	0.356859i	$0.116152\pi$
$277$	214.988	+	372.369i	0.776128	+	1.34429i	−0.158030	+	0.987434i	$0.550514\pi$
$278$		0			0
$279$			102.018i			0.365654i
$280$		0			0
$281$	212.529			0.756330			0.378165	−	0.925738i	$-0.376555\pi$
$281$	212.529			0.756330			0.378165	+	0.925738i	$0.376555\pi$
$282$		0			0
$283$	−100.109	+	57.7979i	−0.353742	+	0.204233i	−0.666332	−	0.745655i	$-0.732137\pi$
$283$	−100.109	+	57.7979i	−0.353742	+	0.204233i	0.312590	+	0.949888i	$0.398803\pi$
$284$		0			0
$285$	223.610	+	129.101i	0.784598	+	0.452988i
$286$		0			0
$287$	−8.58519	+	177.955i	−0.0299136	+	0.620054i
$288$		0			0
$289$	23.6269	−	40.9230i	0.0817540	−	0.141602i
$290$		0			0
$291$	119.534	+	207.039i	0.410770	+	0.711475i
$292$		0			0
$293$		−	62.5116i		−	0.213350i	−0.994294	−	0.106675i	$-0.965980\pi$
$293$		−	62.5116i		−	0.213350i	0.994294	−	0.106675i	$-0.0340204\pi$
$294$		0			0
$295$	−112.418			−0.381076
$296$		0			0
$297$	−91.9774	+	53.1032i	−0.309688	+	0.178799i
$298$		0			0
$299$	−119.148	−	68.7902i	−0.398489	−	0.230068i
$300$		0			0
$301$	73.8152	+	3.56110i	0.245233	+	0.0118309i
$302$		0			0
$303$	−34.2882	+	59.3890i	−0.113162	+	0.196003i
$304$		0			0
$305$	−189.306	−	327.887i	−0.620675	−	1.07504i
$306$		0			0
$307$		−	256.529i		−	0.835601i	−0.908539	−	0.417800i	$-0.862801\pi$
$307$		−	256.529i		−	0.835601i	0.908539	−	0.417800i	$-0.137199\pi$
$308$		0			0
$309$	−131.003			−0.423957
$310$		0			0
$311$	149.417	−	86.2662i	0.480442	−	0.277383i	−0.240159	−	0.970734i	$-0.577199\pi$
$311$	149.417	−	86.2662i	0.480442	−	0.277383i	0.720601	+	0.693350i	$0.243866\pi$
$312$		0			0
$313$	−246.705	−	142.435i	−0.788194	−	0.455064i	0.0511326	−	0.998692i	$-0.483717\pi$
$313$	−246.705	−	142.435i	−0.788194	−	0.455064i	−0.839326	+	0.543628i	$0.817050\pi$
$314$		0			0
$315$	146.726	−	75.5297i	0.465795	−	0.239777i
$316$		0			0
$317$	225.083	−	389.856i	0.710042	−	1.22983i	−0.254799	−	0.966994i	$-0.582009\pi$
$317$	225.083	−	389.856i	0.710042	−	1.22983i	0.964841	−	0.262834i	$-0.0846572\pi$
$318$		0			0
$319$	385.438	+	667.598i	1.20827	+	2.09279i
$320$		0			0
$321$		−	81.1671i		−	0.252857i
$322$		0			0
$323$	347.860			1.07697
$324$		0			0
$325$	149.323	−	86.2116i	0.459455	−	0.265267i
$326$		0			0
$327$	99.5795	+	57.4923i	0.304524	+	0.175817i
$328$		0			0
$329$	58.7724	+	37.8211i	0.178640	+	0.114958i
$330$		0			0
$331$	206.954	−	358.455i	0.625238	−	1.08294i	−0.363256	−	0.931689i	$-0.618335\pi$
$331$	206.954	−	358.455i	0.625238	−	1.08294i	0.988495	−	0.151255i	$-0.0483316\pi$
$332$		0			0
$333$	64.2673	+	111.314i	0.192995	+	0.334277i
$334$		0			0
$335$			470.743i			1.40520i
$336$		0			0
$337$	188.175			0.558383			0.279191	−	0.960236i	$-0.409934\pi$
$337$	188.175			0.558383			0.279191	+	0.960236i	$0.409934\pi$
$338$		0			0
$339$	−187.376	+	108.182i	−0.552732	+	0.319120i
$340$		0			0
$341$	−601.940	−	347.530i	−1.76522	−	1.01915i
$342$		0			0
$343$	−339.419	−	49.4313i	−0.989561	−	0.144115i
$344$		0			0
$345$	199.579	−	345.681i	0.578491	−	1.00197i
$346$		0			0
$347$	−123.208	−	213.403i	−0.355066	−	0.614993i	0.632063	−	0.774917i	$-0.282208\pi$
$347$	−123.208	−	213.403i	−0.355066	−	0.614993i	−0.987129	+	0.159924i	$0.948875\pi$
$348$		0			0
$349$			204.676i			0.586463i	0.956041	+	0.293231i	$0.0947306\pi$
$349$			204.676i			0.586463i	−0.956041	+	0.293231i	$0.905269\pi$
$350$		0			0
$351$	24.3772			0.0694506
$352$		0			0
$353$	−586.912	+	338.854i	−1.66264	+	0.959926i	−0.691193	+	0.722670i	$0.742914\pi$
$353$	−586.912	+	338.854i	−1.66264	+	0.959926i	−0.971447	+	0.237255i	$0.923752\pi$
$354$		0			0
$355$	−756.035	−	436.497i	−2.12968	−	1.22957i
$356$		0			0
$357$	120.312	−	186.961i	0.337010	−	0.523699i
$358$		0			0
$359$	−51.8837	+	89.8651i	−0.144523	+	0.250321i	−0.929195	−	0.369590i	$-0.879498\pi$
$359$	−51.8837	+	89.8651i	−0.144523	+	0.250321i	0.784672	+	0.619911i	$0.212831\pi$
$360$		0			0
$361$	−0.566407	−	0.981045i	−0.00156899	−	0.00271758i
$362$		0			0
$363$		−	514.021i		−	1.41604i
$364$		0			0
$365$	−313.449			−0.858765
$366$		0			0
$367$	−449.493	+	259.515i	−1.22478	+	0.707126i	−0.965933	−	0.258793i	$-0.916675\pi$
$367$	−449.493	+	259.515i	−1.22478	+	0.707126i	−0.258845	+	0.965919i	$0.583342\pi$
$368$		0			0
$369$	−66.1257	−	38.1777i	−0.179202	−	0.103463i
$370$		0			0
$371$	−269.402	−	523.345i	−0.726150	−	1.41063i
$372$		0			0
$373$	−195.214	+	338.121i	−0.523363	+	0.906491i	0.476267	+	0.879301i	$0.341990\pi$
$373$	−195.214	+	338.121i	−0.523363	+	0.906491i	−0.999630	+	0.0271908i	$0.991344\pi$
$374$		0			0
$375$	79.9860	+	138.540i	0.213296	+	0.369440i
$376$		0			0
$377$		−	176.936i		−	0.469327i
$378$		0			0
$379$	−749.262			−1.97695			−0.988473	−	0.151399i	$-0.951622\pi$
$379$	−749.262			−1.97695			−0.988473	+	0.151399i	$0.951622\pi$
$380$		0			0
$381$	−84.7741	+	48.9444i	−0.222504	+	0.128463i
$382$		0			0
$383$	−186.970	−	107.947i	−0.488172	−	0.281846i	0.235644	−	0.971839i	$-0.424280\pi$
$383$	−186.970	−	107.947i	−0.488172	−	0.281846i	−0.723816	+	0.689993i	$0.757613\pi$
$384$		0			0
$385$	−54.1789	+	1123.03i	−0.140724	+	2.91696i
$386$		0			0
$387$	−15.8359	+	27.4286i	−0.0409197	+	0.0708750i
$388$		0			0
$389$	−146.832	−	254.321i	−0.377461	−	0.653782i	0.613231	−	0.789904i	$-0.289870\pi$
$389$	−146.832	−	254.321i	−0.377461	−	0.653782i	−0.990692	+	0.136122i	$0.956536\pi$
$390$		0			0
$391$		−	537.760i		−	1.37535i
$392$		0			0
$393$	12.6831			0.0322724
$394$		0			0
$395$	574.487	−	331.680i	1.45440	−	0.839697i
$396$		0			0
$397$	−493.173	−	284.734i	−1.24225	−	0.717213i	−0.272698	−	0.962100i	$-0.587916\pi$
$397$	−493.173	−	284.734i	−1.24225	−	0.717213i	−0.969552	+	0.244886i	$0.921249\pi$
$398$		0			0
$399$	229.734	+	11.0832i	0.575774	+	0.0277773i
$400$		0			0
$401$	−220.987	+	382.761i	−0.551091	+	0.954517i	0.447106	+	0.894481i	$0.352455\pi$
$401$	−220.987	+	382.761i	−0.551091	+	0.954517i	−0.998196	+	0.0600358i	$0.980879\pi$
$402$		0			0
$403$	79.7673	+	138.161i	0.197934	+	0.342831i
$404$		0			0
$405$			70.7248i			0.174629i
$406$		0			0
$407$	−875.724			−2.15166
$408$		0			0
$409$	−20.1035	+	11.6067i	−0.0491527	+	0.0283783i	−0.524375	−	0.851487i	$-0.675701\pi$
$409$	−20.1035	+	11.6067i	−0.0491527	+	0.0283783i	0.475222	+	0.879866i	$0.342368\pi$
$410$		0			0
$411$	−102.525	−	59.1928i	−0.249452	−	0.144021i
$412$		0			0
$413$	−89.0347	+	45.8323i	−0.215580	+	0.110974i
$414$		0			0
$415$	164.016	−	284.083i	0.395218	−	0.684538i
$416$		0			0
$417$	−192.780	−	333.904i	−0.462302	−	0.800730i
$418$		0			0
$419$			613.930i			1.46523i	0.680646	+	0.732613i	$0.261699\pi$
$419$			613.930i			1.46523i	−0.680646	+	0.732613i	$0.738301\pi$
$420$		0			0
$421$	−114.168			−0.271182			−0.135591	−	0.990765i	$-0.543293\pi$
$421$	−114.168			−0.271182			−0.135591	+	0.990765i	$0.543293\pi$
$422$		0			0
$423$	−25.9400	+	14.9765i	−0.0613239	+	0.0354054i
$424$		0			0
$425$	583.658	+	336.975i	1.37331	+	0.792883i
$426$		0			0
$427$	−283.609	−	182.508i	−0.664190	−	0.427418i
$428$		0			0
$429$	−83.0426	+	143.834i	−0.193572	+	0.335277i
$430$		0			0
$431$	−248.633	−	430.645i	−0.576875	−	0.999176i	−0.995835	−	0.0911717i	$-0.970939\pi$
$431$	−248.633	−	430.645i	−0.576875	−	0.999176i	0.418961	−	0.908004i	$-0.362395\pi$
$432$		0			0
$433$		−	277.450i		−	0.640762i	−0.947289	−	0.320381i	$-0.896189\pi$
$433$		−	277.450i		−	0.640762i	0.947289	−	0.320381i	$-0.103811\pi$
$434$		0			0
$435$	513.341			1.18009
$436$		0			0
$437$	481.789	−	278.161i	1.10249	−	0.636524i
$438$		0			0
$439$	406.226	+	234.535i	0.925345	+	0.534248i	0.885336	−	0.464951i	$-0.153928\pi$
$439$	406.226	+	234.535i	0.925345	+	0.534248i	0.0400087	+	0.999199i	$0.487261\pi$
$440$		0			0
$441$	85.4135	−	119.639i	0.193681	−	0.271291i
$442$		0			0
$443$	33.8980	−	58.7130i	0.0765191	−	0.132535i	−0.825227	−	0.564802i	$-0.808953\pi$
$443$	33.8980	−	58.7130i	0.0765191	−	0.132535i	0.901746	+	0.432267i	$0.142286\pi$
$444$		0			0
$445$	18.6082	+	32.2304i	0.0418163	+	0.0724279i
$446$		0			0
$447$			89.2001i			0.199553i
$448$		0			0
$449$	560.411			1.24813			0.624065	−	0.781372i	$-0.285480\pi$
$449$	560.411			1.24813			0.624065	+	0.781372i	$0.285480\pi$
$450$		0			0
$451$	450.524	−	260.110i	0.998944	−	0.576740i
$452$		0			0
$453$	75.9540	+	43.8521i	0.167669	+	0.0968037i
$454$		0			0
$455$	139.652	−	217.013i	0.306927	−	0.476952i
$456$		0			0
$457$	406.421	−	703.942i	0.889324	−	1.54035i	0.0486474	−	0.998816i	$-0.484509\pi$
$457$	406.421	−	703.942i	0.889324	−	1.54035i	0.840676	−	0.541538i	$-0.182158\pi$
$458$		0			0
$459$	47.6415	+	82.5175i	0.103794	+	0.179777i
$460$		0			0
$461$		−	100.938i		−	0.218955i	−0.993989	−	0.109477i	$-0.965082\pi$
$461$		−	100.938i		−	0.218955i	0.993989	−	0.109477i	$-0.0349177\pi$
$462$		0			0
$463$	659.901			1.42527			0.712636	−	0.701534i	$-0.247501\pi$
$463$	659.901			1.42527			0.712636	+	0.701534i	$0.247501\pi$
$464$		0			0
$465$	−400.843	+	231.427i	−0.862028	+	0.497692i
$466$		0			0
$467$	−60.1687	−	34.7384i	−0.128841	−	0.0743863i	0.434194	−	0.900819i	$-0.357033\pi$
$467$	−60.1687	−	34.7384i	−0.128841	−	0.0743863i	−0.563035	+	0.826433i	$0.690366\pi$
$468$		0			0
$469$	191.921	+	372.829i	0.409213	+	0.794944i
$470$		0			0
$471$	−176.316	+	305.388i	−0.374344	+	0.648383i
$472$		0			0
$473$	−107.892	−	186.875i	−0.228102	−	0.395085i
$474$		0			0
$475$			697.213i			1.46782i
$476$		0			0
$477$	252.264			0.528854
$478$		0			0
$479$	0.917534	−	0.529739i	0.00191552	−	0.00110593i	−0.499042	−	0.866578i	$-0.666315\pi$
$479$	0.917534	−	0.529739i	0.00191552	−	0.00110593i	0.500957	+	0.865472i	$0.332981\pi$
$480$		0			0
$481$	174.073	+	100.501i	0.361897	+	0.208942i
$482$		0			0
$483$	17.1336	−	355.148i	0.0354732	−	0.735296i
$484$		0			0
$485$	−542.326	+	939.337i	−1.11820	+	1.93678i
$486$		0			0
$487$	73.5153	+	127.332i	0.150955	+	0.261463i	0.931579	−	0.363539i	$-0.118432\pi$
$487$	73.5153	+	127.332i	0.150955	+	0.261463i	−0.780623	+	0.625002i	$0.785098\pi$
$488$		0			0
$489$			116.487i			0.238214i
$490$		0			0
$491$	−444.341			−0.904972			−0.452486	−	0.891772i	$-0.649463\pi$
$491$	−444.341			−0.904972			−0.452486	+	0.891772i	$0.649463\pi$
$492$		0			0
$493$	598.936	−	345.796i	1.21488	−	0.701411i
$494$		0			0
$495$	−417.302	−	240.929i	−0.843034	−	0.486726i
$496$		0			0
$497$	−776.739	−	37.4726i	−1.56286	−	0.0753976i
$498$		0			0
$499$	437.119	−	757.112i	0.875989	−	1.51726i	0.0202838	−	0.999794i	$-0.493543\pi$
$499$	437.119	−	757.112i	0.875989	−	1.51726i	0.855705	−	0.517463i	$-0.173124\pi$
$500$		0			0
$501$	175.912	+	304.689i	0.351122	+	0.608161i
$502$		0			0
$503$			423.655i			0.842256i	0.907001	+	0.421128i	$0.138366\pi$
$503$			423.655i			0.842256i	−0.907001	+	0.421128i	$0.861634\pi$
$504$		0			0
$505$	−311.132			−0.616102
$506$		0			0
$507$	−220.486	+	127.298i	−0.434884	+	0.251081i
$508$		0			0
$509$	498.283	+	287.684i	0.978945	+	0.565194i	0.901951	−	0.431838i	$-0.142135\pi$
$509$	498.283	+	287.684i	0.978945	+	0.565194i	0.0769934	+	0.997032i	$0.475468\pi$
$510$		0			0
$511$	−248.252	+	127.792i	−0.485816	+	0.250083i
$512$		0			0
$513$	−49.2859	+	85.3657i	−0.0960739	+	0.166405i
$514$		0			0
$515$	−297.180	−	514.730i	−0.577048	−	0.999476i
$516$		0			0
$517$		−	204.074i		−	0.394727i
$518$		0			0
$519$	−292.459			−0.563505
$520$		0			0
$521$	−280.294	+	161.828i	−0.537993	+	0.310610i	−0.744265	−	0.667884i	$-0.767200\pi$
$521$	−280.294	+	161.828i	−0.537993	+	0.310610i	0.206272	+	0.978495i	$0.433867\pi$
$522$		0			0
$523$	300.282	+	173.368i	0.574153	+	0.331488i	0.758806	−	0.651316i	$-0.225783\pi$
$523$	300.282	+	173.368i	0.574153	+	0.331488i	−0.184653	+	0.982804i	$0.559116\pi$
$524$		0			0
$525$	374.723	+	241.141i	0.713759	+	0.459316i
$526$		0			0
$527$	−311.786	+	540.030i	−0.591625	+	1.02472i
$528$		0			0
$529$	−165.512	−	286.675i	−0.312877	−	0.541918i
$530$		0			0
$531$		−	42.9166i		−	0.0808223i
$532$		0			0
$533$	−119.404			−0.224023
$534$		0			0
$535$	318.918	−	184.128i	0.596109	−	0.344164i
$536$		0			0
$537$	−35.4628	−	20.4745i	−0.0660388	−	0.0381275i
$538$		0			0
$539$	414.947	+	911.529i	0.769845	+	1.69115i
$540$		0			0
$541$	206.062	−	356.911i	0.380892	−	0.659724i	−0.610298	−	0.792172i	$-0.708950\pi$
$541$	206.062	−	356.911i	0.380892	−	0.659724i	0.991190	+	0.132448i	$0.0422837\pi$
$542$		0			0
$543$	−31.2862	−	54.1892i	−0.0576173	−	0.0997960i
$544$		0			0
$545$			521.685i			0.957220i
$546$		0			0
$547$	−499.987			−0.914053			−0.457027	−	0.889453i	$-0.651086\pi$
$547$	−499.987			−0.914053			−0.457027	+	0.889453i	$0.651086\pi$
$548$		0			0
$549$	125.175	−	72.2696i	0.228005	−	0.131639i
$550$		0			0
$551$	619.609	+	357.731i	1.12452	+	0.649240i
$552$		0			0
$553$	319.769	−	496.908i	0.578244	−	0.898567i
$554$		0			0
$555$	−291.581	+	505.032i	−0.525371	+	0.909968i
$556$		0			0
$557$	−450.635	−	780.522i	−0.809039	−	1.40130i	−0.913530	−	0.406771i	$-0.866655\pi$
$557$	−450.635	−	780.522i	−0.809039	−	1.40130i	0.104491	−	0.994526i	$-0.466679\pi$
$558$		0			0
$559$			49.5283i			0.0886017i
$560$		0			0
$561$	−649.177			−1.15718
$562$		0			0
$563$	659.377	−	380.691i	1.17118	−	0.676184i	0.217226	−	0.976121i	$-0.430299\pi$
$563$	659.377	−	380.691i	1.17118	−	0.676184i	0.953959	+	0.299938i	$0.0969659\pi$
$564$		0			0
$565$	−850.125	−	490.820i	−1.50465	−	0.868708i
$566$		0			0
$567$	28.8343	+	56.0141i	0.0508542	+	0.0987903i
$568$		0			0
$569$	367.391	−	636.341i	0.645679	−	1.11835i	−0.338465	−	0.940979i	$-0.609908\pi$
$569$	367.391	−	636.341i	0.645679	−	1.11835i	0.984144	−	0.177370i	$-0.0567590\pi$
$570$		0			0
$571$	235.155	+	407.300i	0.411830	+	0.713311i	0.995090	−	0.0989750i	$-0.0315564\pi$
$571$	235.155	+	407.300i	0.411830	+	0.713311i	−0.583260	+	0.812286i	$0.698223\pi$
$572$		0			0
$573$			22.6639i			0.0395531i
$574$		0			0
$575$	1077.83			1.87448
$576$		0			0
$577$	−253.625	+	146.431i	−0.439559	+	0.253779i	−0.703410	−	0.710784i	$-0.748340\pi$
$577$	−253.625	+	146.431i	−0.439559	+	0.253779i	0.263852	+	0.964563i	$0.415007\pi$
$578$		0			0
$579$	116.970	+	67.5324i	0.202020	+	0.116636i
$580$		0			0
$581$	14.0805	−	291.863i	0.0242349	−	0.502346i
$582$		0			0
$583$	−859.354	+	1488.44i	−1.47402	+	2.55308i
$584$		0			0
$585$	55.2996	+	95.7817i	0.0945293	+	0.163729i
$586$		0			0
$587$		−	592.898i		−	1.01005i	−0.863105	−	0.505024i	$-0.831484\pi$
$587$		−	592.898i		−	1.01005i	0.863105	−	0.505024i	$-0.168516\pi$
$588$		0			0
$589$	−645.097			−1.09524
$590$		0			0
$591$	297.054	−	171.504i	0.502630	−	0.290194i
$592$		0			0
$593$	669.878	+	386.754i	1.12964	+	0.652199i	0.943845	−	0.330389i	$-0.107180\pi$
$593$	669.878	+	386.754i	1.12964	+	0.652199i	0.185797	+	0.982588i	$0.440513\pi$
$594$		0			0
$595$	1007.53	+	48.6066i	1.69332	+	0.0816917i
$596$		0			0
$597$	41.3721	−	71.6585i	0.0692999	−	0.120031i
$598$		0			0
$599$	−54.6663	−	94.6849i	−0.0912627	−	0.158072i	0.816780	−	0.576949i	$-0.195757\pi$
$599$	−54.6663	−	94.6849i	−0.0912627	−	0.158072i	−0.908043	+	0.418878i	$0.862424\pi$
$600$		0			0
$601$			921.173i			1.53273i	0.642403	+	0.766367i	$0.277938\pi$
$601$			921.173i			1.53273i	−0.642403	+	0.766367i	$0.722062\pi$
$602$		0			0
$603$	−179.711			−0.298029
$604$		0			0
$605$	2019.67	−	1166.06i	3.33830	−	1.92737i
$606$		0			0
$607$	−498.175	−	287.622i	−0.820717	−	0.473841i	0.0299464	−	0.999552i	$-0.490466\pi$
$607$	−498.175	−	287.622i	−0.820717	−	0.473841i	−0.850664	+	0.525710i	$0.823800\pi$
$608$		0			0
$609$	406.566	−	209.288i	0.667597	−	0.343658i
$610$		0			0
$611$	−23.4201	+	40.5649i	−0.0383308	+	0.0663909i
$612$		0			0
$613$	131.001	+	226.901i	0.213705	+	0.370149i	0.952871	−	0.303375i	$-0.0981134\pi$
$613$	131.001	+	226.901i	0.213705	+	0.370149i	−0.739166	+	0.673523i	$0.764780\pi$
$614$		0			0
$615$		−	346.424i		−	0.563291i
$616$		0			0
$617$	900.571			1.45960			0.729798	−	0.683663i	$-0.239614\pi$
$617$	900.571			1.45960			0.729798	+	0.683663i	$0.239614\pi$
$618$		0			0
$619$	−242.523	+	140.021i	−0.391798	+	0.226205i	−0.682939	−	0.730476i	$-0.739298\pi$
$619$	−242.523	+	140.021i	−0.391798	+	0.226205i	0.291141	+	0.956680i	$0.405965\pi$
$620$		0			0
$621$	131.968	+	76.1916i	0.212508	+	0.122692i
$622$		0			0
$623$	27.8780	+	17.9400i	0.0447480	+	0.0287961i
$624$		0			0
$625$	96.5176	−	167.173i	0.154428	−	0.267477i
$626$		0			0
$627$	−335.792	−	581.609i	−0.535554	−	0.927606i
$628$		0			0
$629$			785.655i			1.24905i
$630$		0			0
$631$	672.961			1.06650			0.533250	−	0.845958i	$-0.320971\pi$
$631$	672.961			1.06650			0.533250	+	0.845958i	$0.320971\pi$
$632$		0			0
$633$	−315.778	+	182.314i	−0.498859	+	0.288017i
$634$		0			0
$635$	−384.620	−	222.061i	−0.605701	−	0.349702i
$636$		0			0
$637$	22.1287	−	228.810i	0.0347390	−	0.359200i
$638$		0			0
$639$	166.638	−	288.625i	0.260779	−	0.451682i
$640$		0			0
$641$	−154.676	−	267.907i	−0.241304	−	0.417951i	0.719782	−	0.694200i	$-0.244242\pi$
$641$	−154.676	−	267.907i	−0.241304	−	0.417951i	−0.961086	+	0.276249i	$0.910908\pi$
$642$		0			0
$643$			1096.87i			1.70586i	0.522022	+	0.852932i	$0.325178\pi$
$643$			1096.87i			1.70586i	−0.522022	+	0.852932i	$0.674822\pi$
$644$		0			0
$645$	−143.695			−0.222783
$646$		0			0
$647$	868.056	−	501.173i	1.34166	−	0.774610i	0.354612	−	0.935013i	$-0.384613\pi$
$647$	868.056	−	501.173i	1.34166	−	0.774610i	0.987052	+	0.160403i	$0.0512795\pi$
$648$		0			0
$649$	253.223	+	146.199i	0.390175	+	0.225268i
$650$		0			0
$651$	−223.116	+	346.713i	−0.342728	+	0.532585i
$652$		0			0
$653$	−6.71739	+	11.6349i	−0.0102870	+	0.0178175i	−0.871123	−	0.491065i	$-0.836608\pi$
$653$	−6.71739	+	11.6349i	−0.0102870	+	0.0178175i	0.860836	+	0.508882i	$0.169941\pi$
$654$		0			0
$655$	28.7715	+	49.8338i	0.0439260	+	0.0760821i
$656$		0			0
$657$		−	119.663i		−	0.182135i
$658$		0			0
$659$	291.381			0.442157			0.221078	−	0.975256i	$-0.429042\pi$
$659$	291.381			0.442157			0.221078	+	0.975256i	$0.429042\pi$
$660$		0			0
$661$	−591.615	+	341.569i	−0.895030	+	0.516746i	−0.875584	−	0.483065i	$-0.839523\pi$
$661$	−591.615	+	341.569i	−0.895030	+	0.516746i	−0.0194454	+	0.999811i	$0.506190\pi$
$662$		0			0
$663$	129.041	+	74.5016i	0.194631	+	0.112370i
$664$		0			0
$665$	477.604	+	927.803i	0.718201	+	1.39519i
$666$		0			0
$667$	553.020	−	957.859i	0.829116	−	1.43607i
$668$		0			0
$669$	18.1016	+	31.3529i	0.0270577	+	0.0468654i
$670$		0			0
$671$			984.767i			1.46761i
$672$		0			0
$673$	301.224			0.447583			0.223792	−	0.974637i	$-0.428156\pi$
$673$	301.224			0.447583			0.223792	+	0.974637i	$0.428156\pi$
$674$		0			0
$675$	−165.389	+	95.4875i	−0.245021	+	0.141463i
$676$		0			0
$677$	−150.495	−	86.8881i	−0.222296	−	0.128343i	0.384717	−	0.923035i	$-0.374299\pi$
$677$	−150.495	−	86.8881i	−0.222296	−	0.128343i	−0.607013	+	0.794692i	$0.707632\pi$
$678$		0			0
$679$	−46.5579	+	965.060i	−0.0685683	+	1.42130i
$680$		0			0
$681$	78.5392	−	136.034i	0.115329	−	0.199756i
$682$		0			0
$683$	−476.041	−	824.527i	−0.696985	−	1.20721i	−0.969507	−	0.245064i	$-0.921191\pi$
$683$	−476.041	−	824.527i	−0.696985	−	1.20721i	0.272522	−	0.962150i	$-0.412142\pi$
$684$		0			0
$685$		−	537.115i		−	0.784110i
$686$		0			0
$687$	−456.862			−0.665010
$688$		0			0
$689$	341.637	−	197.244i	0.495845	−	0.286276i
$690$		0			0
$691$	229.103	+	132.273i	0.331553	+	0.191422i	0.656530	−	0.754300i	$-0.272023\pi$
$691$	229.103	+	132.273i	0.331553	+	0.191422i	−0.324977	+	0.945722i	$0.605357\pi$
$692$		0			0
$693$	−428.729	−	20.6834i	−0.618657	−	0.0298462i
$694$		0			0
$695$	874.642	−	1514.92i	1.25848	−	2.17975i
$696$		0			0
$697$	−233.358	−	404.187i	−0.334803	−	0.579895i
$698$		0			0
$699$		−	84.7613i		−	0.121261i
$700$		0			0
$701$	−191.891			−0.273739			−0.136870	−	0.990589i	$-0.543704\pi$
$701$	−191.891			−0.273739			−0.136870	+	0.990589i	$0.543704\pi$
$702$		0			0
$703$	−703.883	+	406.387i	−1.00126	+	0.578075i
$704$		0			0
$705$	−117.690	−	67.9482i	−0.166936	−	0.0963805i
$706$		0			0
$707$	−246.416	+	126.847i	−0.348538	+	0.179416i
$708$		0			0
$709$	−549.045	+	950.974i	−0.774394	+	1.34129i	0.160741	+	0.986997i	$0.448612\pi$
$709$	−549.045	+	950.974i	−0.774394	+	1.34129i	−0.935135	+	0.354293i	$0.884722\pi$
$710$		0			0
$711$	126.623	+	219.317i	0.178091	+	0.308463i
$712$		0			0
$713$			997.261i			1.39868i
$714$		0			0
$715$	−753.528			−1.05389
$716$		0			0
$717$	199.884	−	115.403i	0.278779	−	0.160953i
$718$		0			0
$719$	404.587	+	233.589i	0.562708	+	0.324880i	0.754232	−	0.656608i	$-0.228009\pi$
$719$	404.587	+	233.589i	0.562708	+	0.324880i	−0.191523	+	0.981488i	$0.561343\pi$
$720$		0			0
$721$	−445.220	−	286.507i	−0.617504	−	0.397375i
$722$		0			0
$723$	386.069	−	668.691i	0.533982	−	0.924884i
$724$		0			0
$725$	693.075	+	1200.44i	0.955966	+	1.65578i
$726$		0			0
$727$		−	897.725i		−	1.23484i	−0.786635	−	0.617418i	$-0.788179\pi$
$727$		−	897.725i		−	1.23484i	0.786635	−	0.617418i	$-0.211821\pi$
$728$		0			0
$729$	−27.0000			−0.0370370
$730$		0			0
$731$	−167.655	+	96.7957i	−0.229350	+	0.132415i
$732$		0			0
$733$	−639.104	−	368.987i	−0.871902	−	0.503393i	−0.00392218	−	0.999992i	$-0.501248\pi$
$733$	−639.104	−	368.987i	−0.871902	−	0.503393i	−0.867980	+	0.496599i	$0.834582\pi$
$734$		0			0
$735$	663.842	+	64.2015i	0.903186	+	0.0873490i
$736$		0			0
$737$	612.200	−	1060.36i	0.830665	−	1.43875i
$738$		0			0
$739$	−597.710	−	1035.26i	−0.808809	−	1.40090i	−0.913689	−	0.406413i	$-0.866779\pi$
$739$	−597.710	−	1035.26i	−0.808809	−	1.40090i	0.104880	−	0.994485i	$-0.466554\pi$
$740$		0			0
$741$			154.146i			0.208025i
$742$		0			0
$743$	−816.965			−1.09955			−0.549774	−	0.835313i	$-0.685286\pi$
$743$	−816.965			−1.09955			−0.549774	+	0.835313i	$0.685286\pi$
$744$		0			0
$745$	−350.481	+	202.351i	−0.470445	+	0.271611i
$746$		0			0
$747$	108.452	+	62.6148i	0.145183	+	0.0838216i
$748$		0			0
$749$	177.515	−	275.851i	0.237003	−	0.368293i
$750$		0			0
$751$	608.954	−	1054.74i	0.810857	−	1.40445i	−0.101407	−	0.994845i	$-0.532335\pi$
$751$	608.954	−	1054.74i	0.810857	−	1.40445i	0.912265	−	0.409601i	$-0.134332\pi$
$752$		0			0
$753$	346.643	+	600.403i	0.460349	+	0.797347i
$754$		0			0
$755$			397.914i			0.527038i
$756$		0			0
$757$	−790.017			−1.04362			−0.521808	−	0.853063i	$-0.674742\pi$
$757$	−790.017			−1.04362			−0.521808	+	0.853063i	$0.674742\pi$
$758$		0			0
$759$	−899.115	+	519.104i	−1.18460	+	0.683932i
$760$		0			0
$761$	−798.463	−	460.993i	−1.04923	−	0.605772i	−0.126795	−	0.991929i	$-0.540469\pi$
$761$	−798.463	−	460.993i	−1.04923	−	0.605772i	−0.922433	+	0.386157i	$0.873802\pi$
$762$		0			0
$763$	212.689	+	413.175i	0.278754	+	0.541513i
$764$		0			0
$765$	−216.150	+	374.382i	−0.282548	+	0.489388i
$766$		0			0
$767$	−33.5564	−	58.1214i	−0.0437502	−	0.0757776i
$768$		0			0
$769$			1046.94i			1.36143i	0.732548	+	0.680715i	$0.238331\pi$
$769$			1046.94i			1.36143i	−0.732548	+	0.680715i	$0.761669\pi$
$770$		0			0
$771$	−657.120			−0.852295
$772$		0			0
$773$	103.396	−	59.6959i	0.133760	−	0.0772262i	−0.431627	−	0.902052i	$-0.642060\pi$
$773$	103.396	−	59.6959i	0.133760	−	0.0772262i	0.565387	+	0.824826i	$0.308727\pi$
$774$		0			0
$775$	−1082.38	−	624.911i	−1.39662	−	0.806337i
$776$		0			0
$777$	−25.0317	+	518.863i	−0.0322159	+	0.667777i
$778$		0			0
$779$	241.412	−	418.138i	0.309900	−	0.536763i
$780$		0			0
$781$	1135.33	+	1966.44i	1.45368	+	2.51785i
$782$		0			0
$783$			195.974i			0.250286i
$784$		0			0
$785$	−1599.89			−2.03808
$786$		0			0
$787$	−764.754	+	441.531i	−0.971733	+	0.561030i	−0.899764	−	0.436377i	$-0.856262\pi$
$787$	−764.754	+	441.531i	−0.971733	+	0.561030i	−0.0719688	+	0.997407i	$0.522928\pi$
$788$		0			0
$789$	−416.220	−	240.305i	−0.527529	−	0.304569i
$790$		0			0
$791$	−873.406	−	42.1361i	−1.10418	−	0.0532694i
$792$		0			0
$793$	113.015	−	195.748i	0.142516	−	0.246844i
$794$		0			0
$795$	572.260	+	991.183i	0.719824	+	1.24677i
$796$		0			0
$797$			669.317i			0.839795i	0.907572	+	0.419897i	$0.137934\pi$
$797$			669.317i			0.839795i	−0.907572	+	0.419897i	$0.862066\pi$
$798$		0			0
$799$	−183.085			−0.229142
$800$		0			0
$801$	−12.3043	+	7.10391i	−0.0153612	+	0.00886880i
$802$		0			0
$803$	706.053	+	407.640i	0.879269	+	0.507646i
$804$		0			0
$805$	1434.30	−	738.332i	1.78174	−	0.917183i
$806$		0			0
$807$	436.117	−	755.377i	0.540418	−	0.936031i
$808$		0			0
$809$	−332.944	−	576.677i	−0.411551	−	0.712827i	0.583509	−	0.812107i	$-0.301679\pi$
$809$	−332.944	−	576.677i	−0.411551	−	0.712827i	−0.995060	+	0.0992802i	$0.968346\pi$
$810$		0			0
$811$		−	292.174i		−	0.360264i	−0.983642	−	0.180132i	$-0.942347\pi$
$811$		−	292.174i		−	0.360264i	0.983642	−	0.180132i	$-0.0576526\pi$
$812$		0			0
$813$	−413.860			−0.509053
$814$		0			0
$815$	−457.695	+	264.250i	−0.561589	+	0.324234i
$816$		0			0
$817$	−173.442	−	100.137i	−0.212291	−	0.122566i
$818$		0			0
$819$	82.8473	+	53.3137i	0.101157	+	0.0650961i
$820$		0			0
$821$	−19.4011	+	33.6038i	−0.0236311	+	0.0409303i	−0.877599	−	0.479395i	$-0.840856\pi$
$821$	−19.4011	+	33.6038i	−0.0236311	+	0.0409303i	0.853968	+	0.520326i	$0.174189\pi$
$822$		0			0
$823$	−258.531	−	447.789i	−0.314132	−	0.544093i	0.665120	−	0.746736i	$-0.268380\pi$
$823$	−258.531	−	447.789i	−0.314132	−	0.544093i	−0.979253	+	0.202643i	$0.935047\pi$
$824$		0			0
$825$		−	1301.14i		−	1.57714i
$826$		0			0
$827$	963.993			1.16565			0.582825	−	0.812597i	$-0.301947\pi$
$827$	963.993			1.16565			0.582825	+	0.812597i	$0.301947\pi$
$828$		0			0
$829$	1030.59	−	595.013i	1.24318	−	0.717748i	0.273436	−	0.961890i	$-0.411840\pi$
$829$	1030.59	−	595.013i	1.24318	−	0.717748i	0.969739	+	0.244142i	$0.0785065\pi$
$830$		0			0
$831$	−644.963	−	372.369i	−0.776128	−	0.448098i
$832$		0			0
$833$	817.778	−	372.269i	0.981726	−	0.446902i
$834$		0			0
$835$	−798.113	+	1382.37i	−0.955824	+	1.65554i
$836$		0			0
$837$	−88.3498	−	153.026i	−0.105555	−	0.182827i
$838$		0			0
$839$		−	327.407i		−	0.390235i	−0.980780	−	0.195117i	$-0.937491\pi$
$839$		−	327.407i		−	0.390235i	0.980780	−	0.195117i	$-0.0625087\pi$
$840$		0			0
$841$	581.433			0.691359
$842$		0			0
$843$	−318.793	+	184.055i	−0.378165	+	0.218334i
$844$		0			0
$845$	−1000.35	−	577.550i	−1.18384	−	0.683492i
$846$		0			0
$847$	1124.18	−	1746.93i	1.32725	−	2.06249i
$848$		0			0
$849$	100.109	−	173.394i	0.117914	−	0.204233i
$850$		0			0
$851$	628.237	+	1088.14i	0.738234	+	1.27866i
$852$		0			0
$853$		−	101.105i		−	0.118528i	−0.998242	−	0.0592641i	$-0.981125\pi$
$853$		−	101.105i		−	0.118528i	0.998242	−	0.0592641i	$-0.0188754\pi$
$854$		0			0
$855$	−447.221			−0.523065
$856$		0			0
$857$	−311.955	+	180.107i	−0.364008	+	0.210160i	−0.670837	−	0.741604i	$-0.734065\pi$
$857$	−311.955	+	180.107i	−0.364008	+	0.210160i	0.306829	+	0.951765i	$0.400732\pi$
$858$		0			0
$859$	37.9073	+	21.8858i	0.0441295	+	0.0254782i	0.521902	−	0.853005i	$-0.325222\pi$
$859$	37.9073	+	21.8858i	0.0441295	+	0.0254782i	−0.477773	+	0.878483i	$0.658556\pi$
$860$		0			0
$861$	−141.236	−	274.368i	−0.164037	−	0.318662i
$862$		0			0
$863$	207.891	−	360.077i	0.240893	−	0.417239i	−0.720076	−	0.693895i	$-0.755893\pi$
$863$	207.891	−	360.077i	0.240893	−	0.417239i	0.960969	+	0.276656i	$0.0892264\pi$
$864$		0			0
$865$	−663.444	−	1149.12i	−0.766987	−	1.32846i
$866$		0			0
$867$			81.8460i			0.0944014i
$868$		0			0
$869$	−1725.40			−1.98550
$870$		0			0
$871$	−243.381	+	140.516i	−0.279427	+	0.161327i
$872$		0			0
$873$	−358.602	−	207.039i	−0.410770	−	0.237158i
$874$		0			0
$875$	−31.1541	+	645.768i	−0.0356047	+	0.738021i
$876$		0			0
$877$	−65.5323	+	113.505i	−0.0747233	+	0.129424i	−0.900966	−	0.433890i	$-0.857141\pi$
$877$	−65.5323	+	113.505i	−0.0747233	+	0.129424i	0.826243	+	0.563314i	$0.190474\pi$
$878$		0			0
$879$	54.1366	+	93.7673i	0.0615888	+	0.106675i
$880$		0			0
$881$		−	1307.44i		−	1.48405i	−0.670375	−	0.742023i	$-0.733867\pi$
$881$		−	1307.44i		−	1.48405i	0.670375	−	0.742023i	$-0.266133\pi$
$882$		0			0
$883$	144.356			0.163483			0.0817417	−	0.996654i	$-0.473952\pi$
$883$	144.356			0.163483			0.0817417	+	0.996654i	$0.473952\pi$
$884$		0			0
$885$	168.626	−	97.3564i	0.190538	−	0.110007i
$886$		0			0
$887$	1041.38	+	601.240i	1.17404	+	0.677835i	0.954629	−	0.297796i	$-0.0962516\pi$
$887$	1041.38	+	601.240i	1.17404	+	0.677835i	0.219416	+	0.975631i	$0.429585\pi$
$888$		0			0
$889$	−395.153	−	19.0635i	−0.444492	−	0.0214438i
$890$		0			0
$891$	91.9774	−	159.310i	0.103229	−	0.178799i
$892$		0			0
$893$	−94.7020	−	164.029i	−0.106049	−	0.183683i
$894$		0			0
$895$		−	185.786i		−	0.207582i
$896$		0			0
$897$	238.296			0.265659
$898$		0			0
$899$	−1110.71	+	641.268i	−1.23549	+	0.713312i
$900$		0			0
$901$	1335.36	+	770.969i	1.48208	+	0.855681i
$902$		0			0
$903$	−113.807	+	58.5841i	−0.126032	+	0.0648772i
$904$		0			0
$905$	141.945	−	245.857i	0.156846	−	0.271665i
$906$		0			0
$907$	−56.5391	−	97.9285i	−0.0623364	−	0.107970i	0.833173	−	0.553012i	$-0.186522\pi$
$907$	−56.5391	−	97.9285i	−0.0623364	−	0.107970i	−0.895509	+	0.445043i	$0.853188\pi$
$908$		0			0
$909$		−	118.778i		−	0.130669i
$910$		0			0
$911$	−375.770			−0.412481			−0.206241	−	0.978501i	$-0.566123\pi$
$911$	−375.770			−0.412481			−0.206241	+	0.978501i	$0.566123\pi$
$912$		0			0
$913$	−738.899	+	426.603i	−0.809309	+	0.467255i
$914$		0			0
$915$	567.918	+	327.887i	0.620675	+	0.358347i
$916$		0			0
$917$	43.1042	+	27.7383i	0.0470056	+	0.0302490i
$918$		0			0
$919$	−141.087	+	244.369i	−0.153522	+	0.265908i	−0.932520	−	0.361119i	$-0.882395\pi$
$919$	−141.087	+	244.369i	−0.153522	+	0.265908i	0.778998	+	0.627026i	$0.215728\pi$
$920$		0			0
$921$	222.161	+	384.794i	0.241217	+	0.417800i
$922$		0			0
$923$		−	521.175i		−	0.564653i
$924$		0			0
$925$	−1574.68			−1.70236
$926$		0			0
$927$	196.504	−	113.452i	0.211978	−	0.122386i
$928$		0			0
$929$	482.185	+	278.390i	0.519037	+	0.299666i	0.736540	−	0.676394i	$-0.236458\pi$
$929$	482.185	+	278.390i	0.519037	+	0.299666i	−0.217504	+	0.976059i	$0.569791\pi$
$930$		0			0
$931$	756.525	+	540.103i	0.812594	+	0.580132i
$932$		0			0
$933$	−149.417	+	258.799i	−0.160147	+	0.277383i
$934$		0			0
$935$	−1472.66	−	2550.72i	−1.57504	−	2.72804i
$936$		0			0
$937$		−	700.632i		−	0.747739i	−0.927481	−	0.373870i	$-0.878031\pi$
$937$		−	700.632i		−	0.747739i	0.927481	−	0.373870i	$-0.121969\pi$
$938$		0			0
$939$	493.409			0.525462
$940$		0			0
$941$	1181.61	−	682.202i	1.25569	−	0.724975i	0.283460	−	0.958984i	$-0.408518\pi$
$941$	1181.61	−	682.202i	1.25569	−	0.724975i	0.972235	+	0.234009i	$0.0751844\pi$
$942$		0			0
$943$	−646.404	−	373.201i	−0.685476	−	0.395760i
$944$		0			0
$945$	−154.678	+	240.363i	−0.163680	+	0.254352i
$946$		0			0
$947$	−827.678	+	1433.58i	−0.874000	+	1.51381i	−0.0161755	+	0.999869i	$0.505149\pi$
$947$	−827.678	+	1433.58i	−0.874000	+	1.51381i	−0.857824	+	0.513943i	$0.828184\pi$
$948$		0			0
$949$	−93.5641	−	162.058i	−0.0985923	−	0.170767i
$950$		0			0
$951$			779.711i			0.819885i
$952$		0			0
$953$	−350.369			−0.367648			−0.183824	−	0.982959i	$-0.558848\pi$
$953$	−350.369			−0.367648			−0.183824	+	0.982959i	$0.558848\pi$
$954$		0			0
$955$	−89.0502	+	51.4131i	−0.0932463	+	0.0538358i
$956$		0			0
$957$	−1156.31	−	667.598i	−1.20827	−	0.697595i
$958$		0			0
$959$	−218.980	−	425.396i	−0.228342	−	0.443583i
$960$		0			0
$961$	97.6989	−	169.219i	0.101664	−	0.176087i
$962$		0			0
$963$	70.2927	+	121.751i	0.0729935	+	0.126428i
$964$		0			0
$965$			612.789i			0.635015i
$966$		0			0
$967$	−870.330			−0.900031			−0.450015	−	0.893021i	$-0.648581\pi$
$967$	−870.330			−0.900031			−0.450015	+	0.893021i	$0.648581\pi$
$968$		0			0
$969$	−521.790	+	301.256i	−0.538483	+	0.310893i
$970$		0			0
$971$	−67.8214	−	39.1567i	−0.0698470	−	0.0403262i	0.464670	−	0.885484i	$-0.346173\pi$
$971$	−67.8214	−	39.1567i	−0.0698470	−	0.0403262i	−0.534517	+	0.845158i	$0.679506\pi$
$972$		0			0
$973$	75.0866	−	1556.41i	0.0771702	−	1.59960i
$974$		0			0
$975$	−149.323	+	258.635i	−0.153152	+	0.265267i
$976$		0			0
$977$	−43.3616	−	75.1045i	−0.0443824	−	0.0768726i	0.842981	−	0.537944i	$-0.180799\pi$
$977$	−43.3616	−	75.1045i	−0.0443824	−	0.0768726i	−0.887363	+	0.461071i	$0.847465\pi$
$978$		0			0
$979$		−	96.7999i		−	0.0988763i
$980$		0			0
$981$	−199.159			−0.203016
$982$		0			0
$983$	−468.572	+	270.530i	−0.476676	+	0.275209i	−0.719030	−	0.694979i	$-0.755414\pi$
$983$	−468.572	+	270.530i	−0.476676	+	0.275209i	0.242354	+	0.970188i	$0.422080\pi$
$984$		0			0
$985$	1347.74	+	778.116i	1.36826	+	0.789965i
$986$		0			0
$987$	−120.913	−	5.83325i	−0.122505	−	0.00591008i
$988$		0			0
$989$	−154.802	+	268.125i	−0.156524	+	0.271108i
$990$		0			0
$991$	−740.526	−	1282.63i	−0.747251	−	1.29428i	−0.949136	−	0.314867i	$-0.898040\pi$
$991$	−740.526	−	1282.63i	−0.747251	−	1.29428i	0.201885	−	0.979409i	$-0.435293\pi$
$992$		0			0
$993$			716.909i			0.721963i
$994$		0			0
$995$	375.410			0.377297
$996$		0			0
$997$	−1412.11	+	815.282i	−1.41636	+	0.817736i	−0.995977	−	0.0896112i	$-0.971438\pi$
$997$	−1412.11	+	815.282i	−1.41636	+	0.817736i	−0.420383	+	0.907347i	$0.638104\pi$
$998$		0			0
$999$	−192.802	−	111.314i	−0.192995	−	0.111426i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.3.bh.g.145.1		8
3.2	odd	2		1008.3.cg.p.145.4		8
4.3	odd	2		168.3.z.b.145.1	yes	8
7.2	even	3		2352.3.f.g.97.4		8
7.3	odd	6	inner	336.3.bh.g.241.1		8
7.5	odd	6		2352.3.f.g.97.5		8
12.11	even	2		504.3.by.c.145.4		8
21.17	even	6		1008.3.cg.p.577.4		8
28.3	even	6		168.3.z.b.73.1	✓	8
28.11	odd	6		1176.3.z.c.913.4		8
28.19	even	6		1176.3.f.c.97.1		8
28.23	odd	6		1176.3.f.c.97.8		8
28.27	even	2		1176.3.z.c.313.4		8
84.23	even	6		3528.3.f.b.2449.1		8
84.47	odd	6		3528.3.f.b.2449.8		8
84.59	odd	6		504.3.by.c.73.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.3.z.b.73.1	✓	8	28.3	even	6
168.3.z.b.145.1	yes	8	4.3	odd	2
336.3.bh.g.145.1		8	1.1	even	1	trivial
336.3.bh.g.241.1		8	7.3	odd	6	inner
504.3.by.c.73.4		8	84.59	odd	6
504.3.by.c.145.4		8	12.11	even	2
1008.3.cg.p.145.4		8	3.2	odd	2
1008.3.cg.p.577.4		8	21.17	even	6
1176.3.f.c.97.1		8	28.19	even	6
1176.3.f.c.97.8		8	28.23	odd	6
1176.3.z.c.313.4		8	28.27	even	2
1176.3.z.c.913.4		8	28.11	odd	6
2352.3.f.g.97.4		8	7.2	even	3
2352.3.f.g.97.5		8	7.5	odd	6
3528.3.f.b.2449.1		8	84.23	even	6
3528.3.f.b.2449.8		8	84.47	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-1.50000 + 0.866025i) q^{3} +(-6.80550 - 3.92916i) q^{5} +(-6.99187 - 0.337312i) q^{7} +(1.50000 - 2.59808i) q^{9} +O(q^{10})\)	\(q+(-1.50000 + 0.866025i) q^{3} +(-6.80550 - 3.92916i) q^{5} +(-6.99187 - 0.337312i) q^{7} +(1.50000 - 2.59808i) q^{9} +(10.2197 + 17.7011i) q^{11} -4.69139i q^{13} +13.6110 q^{15} +(15.8805 - 9.16861i) q^{17} +(16.4286 + 9.48508i) q^{19} +(10.7799 - 5.54917i) q^{21} +(14.6631 - 25.3972i) q^{23} +(18.3766 + 31.8292i) q^{25} +5.19615i q^{27} +37.7152 q^{29} +(-29.4499 + 17.0029i) q^{31} +(-30.6591 - 17.7011i) q^{33} +(46.2578 + 29.7677i) q^{35} +(-21.4224 + 37.1047i) q^{37} +(4.06286 + 7.03708i) q^{39} -25.4518i q^{41} -10.5573 q^{43} +(-20.4165 + 11.7875i) q^{45} +(-8.64667 - 4.99215i) q^{47} +(48.7724 + 4.71688i) q^{49} +(-15.8805 + 27.5058i) q^{51} +(42.0439 + 72.8222i) q^{53} -160.620i q^{55} -32.8573 q^{57} +(12.3890 - 7.15277i) q^{59} +(41.7249 + 24.0899i) q^{61} +(-11.3642 + 17.6594i) q^{63} +(-18.4332 + 31.9272i) q^{65} +(-29.9519 - 51.8782i) q^{67} +50.7944i q^{69} +111.092 q^{71} +(34.5437 - 19.9438i) q^{73} +(-55.1297 - 31.8292i) q^{75} +(-65.4841 - 127.211i) q^{77} +(-42.2075 + 73.1056i) q^{79} +(-4.50000 - 7.79423i) q^{81} +41.7432i q^{83} -144.100 q^{85} +(-56.5727 + 32.6623i) q^{87} +(-4.10144 - 2.36797i) q^{89} +(-1.58246 + 32.8016i) q^{91} +(29.4499 - 51.0088i) q^{93} +(-74.5368 - 129.101i) q^{95} -138.026i q^{97} +61.3183 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 12 q^{3} - 6 q^{5} - 8 q^{7} + 12 q^{9}+O(q^{10}) \) 8 * q - 12 * q^3 - 6 * q^5 - 8 * q^7 + 12 * q^9	\( 8 q - 12 q^{3} - 6 q^{5} - 8 q^{7} + 12 q^{9} + 22 q^{11} + 12 q^{15} + 36 q^{17} - 42 q^{19} + 6 q^{21} - 48 q^{23} + 42 q^{25} + 68 q^{29} + 60 q^{31} - 66 q^{33} + 12 q^{35} - 118 q^{37} + 18 q^{39} + 92 q^{43} - 18 q^{45} + 12 q^{47} - 20 q^{49} - 36 q^{51} + 10 q^{53} + 84 q^{57} + 54 q^{59} + 24 q^{61} + 6 q^{63} - 148 q^{65} - 22 q^{67} + 392 q^{71} - 138 q^{73} - 126 q^{75} - 126 q^{77} - 164 q^{79} - 36 q^{81} + 200 q^{85} - 102 q^{87} - 60 q^{89} - 90 q^{91} - 60 q^{93} + 132 q^{99}+O(q^{100}) \) 8 * q - 12 * q^3 - 6 * q^5 - 8 * q^7 + 12 * q^9 + 22 * q^11 + 12 * q^15 + 36 * q^17 - 42 * q^19 + 6 * q^21 - 48 * q^23 + 42 * q^25 + 68 * q^29 + 60 * q^31 - 66 * q^33 + 12 * q^35 - 118 * q^37 + 18 * q^39 + 92 * q^43 - 18 * q^45 + 12 * q^47 - 20 * q^49 - 36 * q^51 + 10 * q^53 + 84 * q^57 + 54 * q^59 + 24 * q^61 + 6 * q^63 - 148 * q^65 - 22 * q^67 + 392 * q^71 - 138 * q^73 - 126 * q^75 - 126 * q^77 - 164 * q^79 - 36 * q^81 + 200 * q^85 - 102 * q^87 - 60 * q^89 - 90 * q^91 - 60 * q^93 + 132 * q^99

Introduction

L-functions

Modular forms

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Database

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