LMFDB - Embedded newform 336.4.q.h.289.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [336,4,Mod(193,336)]

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, 4]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("336.193");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 336 = 2^{4} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	336.q (of order $3$, 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:	$19.8246417619$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{-19})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 4x^{2} - 5x + 25 $ x^4 - x^3 - 4x^2 - 5x + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	no (minimal twist has level 84)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			289.1
Root			$-1.63746 + 1.52274i$ of defining polynomial
Character	$\chi$	$=$	336.289
Dual form			336.4.q.h.193.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.50000 - 2.59808i) q^{3} +(-4.91238 + 8.50848i) q^{5} +(16.3248 - 8.74657i) q^{7} +(-4.50000 + 7.79423i) q^{9} +O(q^{10})$	\(q+(-1.50000 - 2.59808i) q^{3} +(-4.91238 + 8.50848i) q^{5} +(16.3248 - 8.74657i) q^{7} +(-4.50000 + 7.79423i) q^{9} +(-7.08762 - 12.2761i) q^{11} -26.1238 q^{13} +29.4743 q^{15} +(39.2990 + 68.0679i) q^{17} +(36.5876 - 63.3716i) q^{19} +(-47.2114 - 29.2931i) q^{21} +(-48.0000 + 83.1384i) q^{23} +(14.2371 + 24.6594i) q^{25} +27.0000 q^{27} +173.021 q^{29} +(33.6238 + 58.2381i) q^{31} +(-21.2629 + 36.8284i) q^{33} +(-5.77326 + 181.865i) q^{35} +(150.835 - 261.254i) q^{37} +(39.1856 + 67.8715i) q^{39} +472.042 q^{41} +463.670 q^{43} +(-44.2114 - 76.5764i) q^{45} +(-45.5980 + 78.9781i) q^{47} +(189.995 - 285.571i) q^{49} +(117.897 - 204.204i) q^{51} +(81.6341 + 141.394i) q^{53} +139.268 q^{55} -219.526 q^{57} +(-300.263 - 520.071i) q^{59} +(-285.846 + 495.099i) q^{61} +(-5.28862 + 166.598i) q^{63} +(128.330 - 222.274i) q^{65} +(-269.711 - 467.154i) q^{67} +288.000 q^{69} +1064.39 q^{71} +(221.340 + 383.372i) q^{73} +(42.7114 - 73.9783i) q^{75} +(-223.078 - 138.412i) q^{77} +(-22.8505 + 39.5782i) q^{79} +(-40.5000 - 70.1481i) q^{81} +686.464 q^{83} -772.206 q^{85} +(-259.531 - 449.521i) q^{87} +(-330.072 + 571.702i) q^{89} +(-426.464 + 228.493i) q^{91} +(100.871 - 174.714i) q^{93} +(359.464 + 622.610i) q^{95} +658.320 q^{97} +127.577 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 6 q^{3} + 3 q^{5} + 20 q^{7} - 18 q^{9}+O(q^{10}) $ 4 * q - 6 * q^3 + 3 * q^5 + 20 * q^7 - 18 * q^9	$ 4 q - 6 q^{3} + 3 q^{5} + 20 q^{7} - 18 q^{9} - 51 q^{11} + 122 q^{13} - 18 q^{15} - 24 q^{17} + 169 q^{19} + 15 q^{21} - 192 q^{23} - 11 q^{25} + 108 q^{27} - 78 q^{29} - 92 q^{31} - 153 q^{33} + 294 q^{35} + 173 q^{37} - 183 q^{39} + 348 q^{41} + 994 q^{43} + 27 q^{45} + 180 q^{47} - 146 q^{49} - 72 q^{51} - 285 q^{53} - 666 q^{55} - 1014 q^{57} - 1269 q^{59} - 328 q^{61} - 225 q^{63} + 1374 q^{65} - 875 q^{67} + 1152 q^{69} + 2808 q^{71} + 1361 q^{73} - 33 q^{75} + 897 q^{77} - 182 q^{79} - 162 q^{81} + 798 q^{83} - 4176 q^{85} + 117 q^{87} - 822 q^{89} - 1955 q^{91} - 276 q^{93} - 510 q^{95} + 1682 q^{97} + 918 q^{99}+O(q^{100}) $ 4 * q - 6 * q^3 + 3 * q^5 + 20 * q^7 - 18 * q^9 - 51 * q^11 + 122 * q^13 - 18 * q^15 - 24 * q^17 + 169 * q^19 + 15 * q^21 - 192 * q^23 - 11 * q^25 + 108 * q^27 - 78 * q^29 - 92 * q^31 - 153 * q^33 + 294 * q^35 + 173 * q^37 - 183 * q^39 + 348 * q^41 + 994 * q^43 + 27 * q^45 + 180 * q^47 - 146 * q^49 - 72 * q^51 - 285 * q^53 - 666 * q^55 - 1014 * q^57 - 1269 * q^59 - 328 * q^61 - 225 * q^63 + 1374 * q^65 - 875 * q^67 + 1152 * q^69 + 2808 * q^71 + 1361 * q^73 - 33 * q^75 + 897 * q^77 - 182 * q^79 - 162 * q^81 + 798 * q^83 - 4176 * q^85 + 117 * q^87 - 822 * q^89 - 1955 * q^91 - 276 * q^93 - 510 * q^95 + 1682 * q^97 + 918 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$85$	$113$	$127$	$241$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{1}{3}\right)$

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	−	2.59808i	−0.288675	−	0.500000i
$3$	−1.50000	−	2.59808i	−0.288675	−	0.500000i
$4$		0			0
$5$	−4.91238	+	8.50848i	−0.439376	+	0.761022i	−0.997641	−	0.0686406i	$-0.978134\pi$
$5$	−4.91238	+	8.50848i	−0.439376	+	0.761022i	0.558265	+	0.829663i	$0.311467\pi$
$6$		0			0
$7$	16.3248	−	8.74657i	0.881454	−	0.472270i
$7$	16.3248	−	8.74657i	0.881454	−	0.472270i
$8$		0			0
$9$	−4.50000	+	7.79423i	−0.166667	+	0.288675i
$10$		0			0
$11$	−7.08762	−	12.2761i	−0.194273	−	0.336490i	0.752389	−	0.658719i	$-0.228901\pi$
$11$	−7.08762	−	12.2761i	−0.194273	−	0.336490i	−0.946662	+	0.322229i	$0.895568\pi$
$12$		0			0
$13$	−26.1238			−0.557341			−0.278670	−	0.960387i	$-0.589894\pi$
$13$	−26.1238			−0.557341			−0.278670	+	0.960387i	$0.589894\pi$
$14$		0			0
$15$	29.4743			0.507348
$16$		0			0
$17$	39.2990	+	68.0679i	0.560671	+	0.971111i	0.997438	+	0.0715361i	$0.0227901\pi$
$17$	39.2990	+	68.0679i	0.560671	+	0.971111i	−0.436767	+	0.899575i	$0.643877\pi$
$18$		0			0
$19$	36.5876	−	63.3716i	0.441778	−	0.765181i	−0.556044	−	0.831153i	$-0.687681\pi$
$19$	36.5876	−	63.3716i	0.441778	−	0.765181i	0.997822	+	0.0659715i	$0.0210147\pi$
$20$		0			0
$21$	−47.2114	−	29.2931i	−0.490589	−	0.304394i
$22$		0			0
$23$	−48.0000	+	83.1384i	−0.435161	+	0.753720i	−0.997309	−	0.0733164i	$-0.976642\pi$
$23$	−48.0000	+	83.1384i	−0.435161	+	0.753720i	0.562148	+	0.827037i	$0.309975\pi$
$24$		0			0
$25$	14.2371	+	24.6594i	0.113897	+	0.197275i
$26$		0			0
$27$	27.0000			0.192450
$28$		0			0
$29$	173.021			1.10790			0.553951	−	0.832549i	$-0.313120\pi$
$29$	173.021			1.10790			0.553951	+	0.832549i	$0.313120\pi$
$30$		0			0
$31$	33.6238	+	58.2381i	0.194807	+	0.337415i	0.946837	−	0.321713i	$-0.104259\pi$
$31$	33.6238	+	58.2381i	0.194807	+	0.337415i	−0.752030	+	0.659128i	$0.770925\pi$
$32$		0			0
$33$	−21.2629	+	36.8284i	−0.112163	+	0.194273i
$34$		0			0
$35$	−5.77326	+	181.865i	−0.0278817	+	0.878310i
$36$		0			0
$37$	150.835	−	261.254i	0.670193	−	1.16081i	−0.307656	−	0.951498i	$-0.599545\pi$
$37$	150.835	−	261.254i	0.670193	−	1.16081i	0.977849	−	0.209311i	$-0.0671221\pi$
$38$		0			0
$39$	39.1856	+	67.8715i	0.160890	+	0.278670i
$40$		0			0
$41$	472.042			1.79806			0.899031	−	0.437886i	$-0.144273\pi$
$41$	472.042			1.79806			0.899031	+	0.437886i	$0.144273\pi$
$42$		0			0
$43$	463.670			1.64440			0.822198	−	0.569201i	$-0.192747\pi$
$43$	463.670			1.64440			0.822198	+	0.569201i	$0.192747\pi$
$44$		0			0
$45$	−44.2114	−	76.5764i	−0.146459	−	0.253674i
$46$		0			0
$47$	−45.5980	+	78.9781i	−0.141514	+	0.245109i	−0.928067	−	0.372413i	$-0.878530\pi$
$47$	−45.5980	+	78.9781i	−0.141514	+	0.245109i	0.786553	+	0.617523i	$0.211864\pi$
$48$		0			0
$49$	189.995	−	285.571i	0.553921	−	0.832569i
$50$		0			0
$51$	117.897	−	204.204i	0.323704	−	0.560671i
$52$		0			0
$53$	81.6341	+	141.394i	0.211572	+	0.366453i	0.952207	−	0.305455i	$-0.0988084\pi$
$53$	81.6341	+	141.394i	0.211572	+	0.366453i	−0.740635	+	0.671908i	$0.765475\pi$
$54$		0			0
$55$	139.268			0.341435
$56$		0			0
$57$	−219.526			−0.510121
$58$		0			0
$59$	−300.263	−	520.071i	−0.662558	−	1.14758i	−0.979941	−	0.199286i	$-0.936138\pi$
$59$	−300.263	−	520.071i	−0.662558	−	1.14758i	0.317384	−	0.948297i	$-0.397196\pi$
$60$		0			0
$61$	−285.846	+	495.099i	−0.599980	+	1.03920i	0.392844	+	0.919605i	$0.371491\pi$
$61$	−285.846	+	495.099i	−0.599980	+	1.03920i	−0.992823	+	0.119590i	$0.961842\pi$
$62$		0			0
$63$	−5.28862	+	166.598i	−0.0105762	+	0.333166i
$64$		0			0
$65$	128.330	−	222.274i	0.244882	−	0.424148i
$66$		0			0
$67$	−269.711	−	467.154i	−0.491798	−	0.851820i	0.508157	−	0.861264i	$-0.330327\pi$
$67$	−269.711	−	467.154i	−0.491798	−	0.851820i	−0.999955	+	0.00944469i	$0.996994\pi$
$68$		0			0
$69$	288.000			0.502480
$70$		0			0
$71$	1064.39			1.77916			0.889578	−	0.456783i	$-0.150998\pi$
$71$	1064.39			1.77916			0.889578	+	0.456783i	$0.150998\pi$
$72$		0			0
$73$	221.340	+	383.372i	0.354875	+	0.614662i	0.987097	−	0.160126i	$-0.0511900\pi$
$73$	221.340	+	383.372i	0.354875	+	0.614662i	−0.632221	+	0.774788i	$0.717857\pi$
$74$		0			0
$75$	42.7114	−	73.9783i	0.0657585	−	0.113897i
$76$		0			0
$77$	−223.078	−	138.412i	−0.330157	−	0.204851i
$78$		0			0
$79$	−22.8505	+	39.5782i	−0.0325428	+	0.0563658i	−0.881838	−	0.471552i	$-0.843694\pi$
$79$	−22.8505	+	39.5782i	−0.0325428	+	0.0563658i	0.849295	+	0.527918i	$0.177027\pi$
$80$		0			0
$81$	−40.5000	−	70.1481i	−0.0555556	−	0.0962250i
$82$		0			0
$83$	686.464			0.907822			0.453911	−	0.891047i	$-0.350028\pi$
$83$	686.464			0.907822			0.453911	+	0.891047i	$0.350028\pi$
$84$		0			0
$85$	−772.206			−0.985382
$86$		0			0
$87$	−259.531	−	449.521i	−0.319824	−	0.553951i
$88$		0			0
$89$	−330.072	+	571.702i	−0.393119	+	0.680902i	−0.992859	−	0.119293i	$-0.961937\pi$
$89$	−330.072	+	571.702i	−0.393119	+	0.680902i	0.599740	+	0.800195i	$0.295271\pi$
$90$		0			0
$91$	−426.464	+	228.493i	−0.491270	+	0.263215i
$92$		0			0
$93$	100.871	−	174.714i	0.112472	−	0.194807i
$94$		0			0
$95$	359.464	+	622.610i	0.388213	+	0.672405i
$96$		0			0
$97$	658.320			0.689095			0.344548	−	0.938769i	$-0.388032\pi$
$97$	658.320			0.689095			0.344548	+	0.938769i	$0.388032\pi$
$98$		0			0
$99$	127.577			0.129515
$100$		0			0
$101$	901.949	+	1562.22i	0.888586	+	1.53908i	0.841547	+	0.540184i	$0.181645\pi$
$101$	901.949	+	1562.22i	0.888586	+	1.53908i	0.0470394	+	0.998893i	$0.485021\pi$
$102$		0			0
$103$	−537.454	+	930.898i	−0.514145	+	0.890525i	0.485721	+	0.874114i	$0.338557\pi$
$103$	−537.454	+	930.898i	−0.514145	+	0.890525i	−0.999865	+	0.0164107i	$0.994776\pi$
$104$		0			0
$105$	481.160	−	257.799i	0.447204	−	0.239605i
$106$		0			0
$107$	−829.676	+	1437.04i	−0.749605	+	1.29835i	0.198407	+	0.980120i	$0.436423\pi$
$107$	−829.676	+	1437.04i	−0.749605	+	1.29835i	−0.948012	+	0.318235i	$0.896910\pi$
$108$		0			0
$109$	−299.464	−	518.687i	−0.263151	−	0.455791i	0.703927	−	0.710273i	$-0.251428\pi$
$109$	−299.464	−	518.687i	−0.263151	−	0.455791i	−0.967077	+	0.254482i	$0.918095\pi$
$110$		0			0
$111$	−905.011			−0.773872
$112$		0			0
$113$	−781.650			−0.650720			−0.325360	−	0.945590i	$-0.605486\pi$
$113$	−781.650			−0.650720			−0.325360	+	0.945590i	$0.605486\pi$
$114$		0			0
$115$	−471.588	−	816.815i	−0.382398	−	0.662333i
$116$		0			0
$117$	117.557	−	203.615i	0.0928901	−	0.160890i
$118$		0			0
$119$	1236.91	+	767.460i	0.952833	+	0.591201i
$120$		0			0
$121$	565.031	−	978.663i	0.424516	−	0.735284i
$122$		0			0
$123$	−708.062	−	1226.40i	−0.519056	−	0.899031i
$124$		0			0
$125$	−1507.85			−1.07893
$126$		0			0
$127$	−25.3722			−0.0177277			−0.00886385	−	0.999961i	$-0.502821\pi$
$127$	−25.3722			−0.0177277			−0.00886385	+	0.999961i	$0.502821\pi$
$128$		0			0
$129$	−695.505	−	1204.65i	−0.474696	−	0.822198i
$130$		0			0
$131$	−237.789	+	411.862i	−0.158593	+	0.274691i	−0.934362	−	0.356326i	$-0.884029\pi$
$131$	−237.789	+	411.862i	−0.158593	+	0.274691i	0.775768	+	0.631018i	$0.217362\pi$
$132$		0			0
$133$	42.9995	−	1354.54i	0.0280341	−	0.883111i
$134$		0			0
$135$	−132.634	+	229.729i	−0.0845580	+	0.146459i
$136$		0			0
$137$	−529.268	−	916.720i	−0.330062	−	0.571683i	0.652462	−	0.757821i	$-0.273736\pi$
$137$	−529.268	−	916.720i	−0.330062	−	0.571683i	−0.982524	+	0.186138i	$0.940403\pi$
$138$		0			0
$139$	−2580.99			−1.57494			−0.787470	−	0.616352i	$-0.788610\pi$
$139$	−2580.99			−1.57494			−0.787470	+	0.616352i	$0.788610\pi$
$140$		0			0
$141$	273.588			0.163406
$142$		0			0
$143$	185.155	+	320.699i	0.108276	+	0.187540i
$144$		0			0
$145$	−849.943	+	1472.14i	−0.486786	+	0.843138i
$146$		0			0
$147$	−1026.93	−	65.2648i	−0.576188	−	0.0366187i
$148$		0			0
$149$	50.9377	−	88.2266i	0.0280066	−	0.0485088i	−0.851682	−	0.524058i	$-0.824417\pi$
$149$	50.9377	−	88.2266i	0.0280066	−	0.0485088i	0.879689	+	0.475549i	$0.157751\pi$
$150$		0			0
$151$	−889.211	−	1540.16i	−0.479225	−	0.830042i	0.520491	−	0.853867i	$-0.325749\pi$
$151$	−889.211	−	1540.16i	−0.479225	−	0.830042i	−0.999716	+	0.0238249i	$0.992416\pi$
$152$		0			0
$153$	−707.382			−0.373781
$154$		0			0
$155$	−660.690			−0.342374
$156$		0			0
$157$	−699.629	−	1211.79i	−0.355646	−	0.615997i	0.631582	−	0.775309i	$-0.282406\pi$
$157$	−699.629	−	1211.79i	−0.355646	−	0.615997i	−0.987228	+	0.159312i	$0.949073\pi$
$158$		0			0
$159$	244.902	−	424.183i	0.122151	−	0.211572i
$160$		0			0
$161$	−56.4119	+	1777.05i	−0.0276142	+	0.869883i
$162$		0			0
$163$	1807.71	−	3131.05i	0.868656	−	1.50456i	0.00528615	−	0.999986i	$-0.498317\pi$
$163$	1807.71	−	3131.05i	0.868656	−	1.50456i	0.863370	−	0.504571i	$-0.168349\pi$
$164$		0			0
$165$	−208.902	−	361.830i	−0.0985638	−	0.170718i
$166$		0			0
$167$	1076.72			0.498917			0.249459	−	0.968385i	$-0.419747\pi$
$167$	1076.72			0.498917			0.249459	+	0.968385i	$0.419747\pi$
$168$		0			0
$169$	−1514.55			−0.689372
$170$		0			0
$171$	329.289	+	570.345i	0.147259	+	0.255060i
$172$		0			0
$173$	−936.815	+	1622.61i	−0.411704	+	0.713091i	−0.995076	−	0.0991132i	$-0.968399\pi$
$173$	−936.815	+	1622.61i	−0.411704	+	0.713091i	0.583373	+	0.812205i	$0.301733\pi$
$174$		0			0
$175$	448.103	+	278.033i	0.193562	+	0.120099i
$176$		0			0
$177$	−900.789	+	1560.21i	−0.382528	+	0.662558i
$178$		0			0
$179$	−1346.15	−	2331.59i	−0.562099	−	0.973583i	−0.997313	−	0.0732565i	$-0.976661\pi$
$179$	−1346.15	−	2331.59i	−0.562099	−	0.973583i	0.435215	−	0.900327i	$-0.356672\pi$
$180$		0			0
$181$	461.670			0.189589			0.0947947	−	0.995497i	$-0.469781\pi$
$181$	461.670			0.189589			0.0947947	+	0.995497i	$0.469781\pi$
$182$		0			0
$183$	1715.07			0.692797
$184$		0			0
$185$	1481.92	+	2566.76i	0.588934	+	1.02006i
$186$		0			0
$187$	557.073	−	964.879i	0.217846	−	0.377321i
$188$		0			0
$189$	440.768	−	236.157i	0.169636	−	0.0908885i
$190$		0			0
$191$	−1882.41	+	3260.43i	−0.713124	+	1.23517i	0.250555	+	0.968102i	$0.419387\pi$
$191$	−1882.41	+	3260.43i	−0.713124	+	1.23517i	−0.963679	+	0.267064i	$0.913946\pi$
$192$		0			0
$193$	−1463.10	−	2534.16i	−0.545680	−	0.945145i	−0.998564	−	0.0535755i	$-0.982938\pi$
$193$	−1463.10	−	2534.16i	−0.545680	−	0.945145i	0.452884	−	0.891569i	$-0.350395\pi$
$194$		0			0
$195$	−769.978			−0.282766
$196$		0			0
$197$	5045.55			1.82477			0.912387	−	0.409330i	$-0.134237\pi$
$197$	5045.55			1.82477			0.912387	+	0.409330i	$0.134237\pi$
$198$		0			0
$199$	2146.12	+	3717.20i	0.764496	+	1.32415i	0.940513	+	0.339759i	$0.110346\pi$
$199$	2146.12	+	3717.20i	0.764496	+	1.32415i	−0.176016	+	0.984387i	$0.556321\pi$
$200$		0			0
$201$	−809.134	+	1401.46i	−0.283940	+	0.491798i
$202$		0			0
$203$	2824.52	−	1513.34i	0.976564	−	0.523229i
$204$		0			0
$205$	−2318.85	+	4016.36i	−0.790025	+	1.36836i
$206$		0			0
$207$	−432.000	−	748.246i	−0.145054	−	0.251240i
$208$		0			0
$209$	−1037.28			−0.343301
$210$		0			0
$211$	−3625.76			−1.18297			−0.591487	−	0.806315i	$-0.701459\pi$
$211$	−3625.76			−1.18297			−0.591487	+	0.806315i	$0.701459\pi$
$212$		0			0
$213$	−1596.59	−	2765.37i	−0.513598	−	0.889578i
$214$		0			0
$215$	−2277.72	+	3945.13i	−0.722509	+	1.25142i
$216$		0			0
$217$	1058.28	+	656.629i	0.331064	+	0.205414i
$218$		0			0
$219$	664.020	−	1150.12i	0.204887	−	0.354875i
$220$		0			0
$221$	−1026.64	−	1778.19i	−0.312485	−	0.541239i
$222$		0			0
$223$	3145.00			0.944417			0.472208	−	0.881487i	$-0.343457\pi$
$223$	3145.00			0.944417			0.472208	+	0.881487i	$0.343457\pi$
$224$		0			0
$225$	−256.268			−0.0759313
$226$		0			0
$227$	−772.873	−	1338.65i	−0.225980	−	0.391408i	0.730633	−	0.682770i	$-0.239225\pi$
$227$	−772.873	−	1338.65i	−0.225980	−	0.391408i	−0.956613	+	0.291362i	$0.905892\pi$
$228$		0			0
$229$	2036.07	−	3526.58i	0.587544	−	1.01766i	−0.407009	−	0.913424i	$-0.633428\pi$
$229$	2036.07	−	3526.58i	0.587544	−	1.01766i	0.994553	−	0.104232i	$-0.0332383\pi$
$230$		0			0
$231$	−24.9892	+	787.191i	−0.00711760	+	0.224214i
$232$		0			0
$233$	1507.86	−	2611.68i	0.423961	−	0.734322i	−0.572362	−	0.820001i	$-0.693973\pi$
$233$	1507.86	−	2611.68i	0.423961	−	0.734322i	0.996323	+	0.0856790i	$0.0273060\pi$
$234$		0			0
$235$	−447.989	−	775.940i	−0.124356	−	0.215390i
$236$		0			0
$237$	137.103			0.0375772
$238$		0			0
$239$	−4647.38			−1.25780			−0.628900	−	0.777486i	$-0.716495\pi$
$239$	−4647.38			−1.25780			−0.628900	+	0.777486i	$0.716495\pi$
$240$		0			0
$241$	−559.138	−	968.456i	−0.149449	−	0.258854i	0.781575	−	0.623812i	$-0.214417\pi$
$241$	−559.138	−	968.456i	−0.149449	−	0.258854i	−0.931024	+	0.364958i	$0.881083\pi$
$242$		0			0
$243$	−121.500	+	210.444i	−0.0320750	+	0.0555556i
$244$		0			0
$245$	1496.45	+	3019.40i	0.390223	+	0.787357i
$246$		0			0
$247$	−955.806	+	1655.50i	−0.246221	+	0.426467i
$248$		0			0
$249$	−1029.70	−	1783.49i	−0.262066	−	0.453911i
$250$		0			0
$251$	−883.518			−0.222180			−0.111090	−	0.993810i	$-0.535434\pi$
$251$	−883.518			−0.222180			−0.111090	+	0.993810i	$0.535434\pi$
$252$		0			0
$253$	1360.82			0.338159
$254$		0			0
$255$	1158.31	+	2006.25i	0.284455	+	0.492691i
$256$		0			0
$257$	2934.44	−	5082.61i	0.712240	−	1.23364i	−0.251775	−	0.967786i	$-0.581014\pi$
$257$	2934.44	−	5082.61i	0.712240	−	1.23364i	0.964015	−	0.265849i	$-0.0856523\pi$
$258$		0			0
$259$	177.269	−	5584.20i	0.0425287	−	1.33971i
$260$		0			0
$261$	−778.594	+	1348.56i	−0.184650	+	0.319824i
$262$		0			0
$263$	2437.81	+	4222.41i	0.571565	+	0.989980i	0.996406	+	0.0847114i	$0.0269968\pi$
$263$	2437.81	+	4222.41i	0.571565	+	0.989980i	−0.424841	+	0.905268i	$0.639670\pi$
$264$		0			0
$265$	−1604.07			−0.371839
$266$		0			0
$267$	1980.43			0.453935
$268$		0			0
$269$	2763.55	+	4786.61i	0.626382	+	1.08493i	0.988272	+	0.152704i	$0.0487983\pi$
$269$	2763.55	+	4786.61i	0.626382	+	1.08493i	−0.361890	+	0.932221i	$0.617868\pi$
$270$		0			0
$271$	−1612.37	+	2792.70i	−0.361418	+	0.625994i	−0.988194	−	0.153205i	$-0.951041\pi$
$271$	−1612.37	+	2792.70i	−0.361418	+	0.625994i	0.626777	+	0.779199i	$0.284374\pi$
$272$		0			0
$273$	1233.34	+	765.246i	0.273425	+	0.169651i
$274$		0			0
$275$	201.815	−	349.554i	0.0442542	−	0.0766504i
$276$		0			0
$277$	979.022	+	1695.72i	0.212360	+	0.367818i	0.952453	−	0.304687i	$-0.0985517\pi$
$277$	979.022	+	1695.72i	0.212360	+	0.367818i	−0.740093	+	0.672505i	$0.765218\pi$
$278$		0			0
$279$	−605.228			−0.129871
$280$		0			0
$281$	8531.16			1.81113			0.905563	−	0.424212i	$-0.139449\pi$
$281$	8531.16			1.81113			0.905563	+	0.424212i	$0.139449\pi$
$282$		0			0
$283$	3954.93	+	6850.14i	0.830728	+	1.43886i	0.897461	+	0.441093i	$0.145409\pi$
$283$	3954.93	+	6850.14i	0.830728	+	1.43886i	−0.0667331	+	0.997771i	$0.521258\pi$
$284$		0			0
$285$	1078.39	−	1867.83i	0.224135	−	0.388213i
$286$		0			0
$287$	7705.96	−	4128.74i	1.58491	−	0.849171i
$288$		0			0
$289$	−632.324	+	1095.22i	−0.128704	+	0.222922i
$290$		0			0
$291$	−987.480	−	1710.36i	−0.198925	−	0.344548i
$292$		0			0
$293$	−8321.41			−1.65919			−0.829594	−	0.558367i	$-0.811428\pi$
$293$	−8321.41			−1.65919			−0.829594	+	0.558367i	$0.811428\pi$
$294$		0			0
$295$	5900.02			1.16445
$296$		0			0
$297$	−191.366	−	331.455i	−0.0373878	−	0.0647575i
$298$		0			0
$299$	1253.94	−	2171.89i	0.242533	−	0.420079i
$300$		0			0
$301$	7569.30	−	4055.52i	1.44946	−	0.776600i
$302$		0			0
$303$	2705.85	−	4686.66i	0.513026	−	0.888586i
$304$		0			0
$305$	−2808.36	−	4864.22i	−0.527234	−	0.913196i
$306$		0			0
$307$	−2541.79			−0.472533			−0.236267	−	0.971688i	$-0.575924\pi$
$307$	−2541.79			−0.472533			−0.236267	+	0.971688i	$0.575924\pi$
$308$		0			0
$309$	3224.72			0.593683
$310$		0			0
$311$	−303.855	−	526.292i	−0.0554020	−	0.0959590i	0.836994	−	0.547212i	$-0.184311\pi$
$311$	−303.855	−	526.292i	−0.0554020	−	0.0959590i	−0.892396	+	0.451253i	$0.850977\pi$
$312$		0			0
$313$	−5513.64	+	9549.90i	−0.995684	+	1.72458i	−0.417471	+	0.908690i	$0.637084\pi$
$313$	−5513.64	+	9549.90i	−0.995684	+	1.72458i	−0.578213	+	0.815886i	$0.696250\pi$
$314$		0			0
$315$	−1391.52	−	863.392i	−0.248899	−	0.154434i
$316$		0			0
$317$	−3630.80	+	6288.73i	−0.643300	+	1.11423i	0.341391	+	0.939921i	$0.389102\pi$
$317$	−3630.80	+	6288.73i	−0.643300	+	1.11423i	−0.984691	+	0.174307i	$0.944231\pi$
$318$		0			0
$319$	−1226.31	−	2124.02i	−0.215235	−	0.372798i
$320$		0			0
$321$	4978.05			0.865570
$322$		0			0
$323$	5751.43			0.990768
$324$		0			0
$325$	−371.927	−	644.197i	−0.0634794	−	0.109950i
$326$		0			0
$327$	−898.392	+	1556.06i	−0.151930	+	0.263151i
$328$		0			0
$329$	−53.5890	+	1688.12i	−0.00898011	+	0.282885i
$330$		0			0
$331$	3316.36	−	5744.11i	0.550706	−	0.953851i	−0.447517	−	0.894275i	$-0.647692\pi$
$331$	3316.36	−	5744.11i	0.550706	−	0.953851i	0.998224	−	0.0595761i	$-0.0189749\pi$
$332$		0			0
$333$	1357.52	+	2351.29i	0.223398	+	0.386936i
$334$		0			0
$335$	5299.69			0.864338
$336$		0			0
$337$	8104.59			1.31005			0.655023	−	0.755609i	$-0.272659\pi$
$337$	8104.59			1.31005			0.655023	+	0.755609i	$0.272659\pi$
$338$		0			0
$339$	1172.47	+	2030.78i	0.187847	+	0.325360i
$340$		0			0
$341$	476.625	−	825.539i	0.0756912	−	0.131101i
$342$		0			0
$343$	603.854	−	6323.68i	0.0950584	−	0.995472i
$344$		0			0
$345$	−1414.76	+	2450.44i	−0.220778	+	0.382398i
$346$		0			0
$347$	−2968.64	−	5141.83i	−0.459265	−	0.795470i	0.539657	−	0.841885i	$-0.318554\pi$
$347$	−2968.64	−	5141.83i	−0.459265	−	0.795470i	−0.998922	+	0.0464146i	$0.985220\pi$
$348$		0			0
$349$	268.472			0.0411775			0.0205888	−	0.999788i	$-0.493446\pi$
$349$	268.472			0.0411775			0.0205888	+	0.999788i	$0.493446\pi$
$350$		0			0
$351$	−705.341			−0.107260
$352$		0			0
$353$	−1331.40	−	2306.06i	−0.200747	−	0.347703i	0.748023	−	0.663673i	$-0.231003\pi$
$353$	−1331.40	−	2306.06i	−0.200747	−	0.347703i	−0.948769	+	0.315970i	$0.897670\pi$
$354$		0			0
$355$	−5228.69	+	9056.36i	−0.781719	+	1.35398i
$356$		0			0
$357$	138.558	−	4364.77i	0.0205414	−	0.647081i
$358$		0			0
$359$	−781.637	+	1353.83i	−0.114911	+	0.199032i	−0.917744	−	0.397172i	$-0.869992\pi$
$359$	−781.637	+	1353.83i	−0.114911	+	0.199032i	0.802833	+	0.596204i	$0.203325\pi$
$360$		0			0
$361$	752.192	+	1302.83i	0.109665	+	0.189945i
$362$		0			0
$363$	−3390.19			−0.490189
$364$		0			0
$365$	−4349.22			−0.623695
$366$		0			0
$367$	605.408	+	1048.60i	0.0861091	+	0.149145i	0.905863	−	0.423570i	$-0.139223\pi$
$367$	605.408	+	1048.60i	0.0861091	+	0.149145i	−0.819754	+	0.572716i	$0.805890\pi$
$368$		0			0
$369$	−2124.19	+	3679.20i	−0.299677	+	0.519056i
$370$		0			0
$371$	2569.37	+	1594.21i	0.359556	+	0.223093i
$372$		0			0
$373$	2385.93	−	4132.55i	0.331203	−	0.573661i	−0.651545	−	0.758610i	$-0.725879\pi$
$373$	2385.93	−	4132.55i	0.331203	−	0.573661i	0.982748	+	0.184949i	$0.0592121\pi$
$374$		0			0
$375$	2261.77	+	3917.50i	0.311459	+	0.539464i
$376$		0			0
$377$	−4519.95			−0.617479
$378$		0			0
$379$	4118.66			0.558209			0.279104	−	0.960261i	$-0.409962\pi$
$379$	4118.66			0.558209			0.279104	+	0.960261i	$0.409962\pi$
$380$		0			0
$381$	38.0583	+	65.9189i	0.00511754	+	0.00886385i
$382$		0			0
$383$	1767.99	−	3062.25i	0.235875	−	0.408547i	−0.723652	−	0.690165i	$-0.757538\pi$
$383$	1767.99	−	3062.25i	0.235875	−	0.408547i	0.959527	+	0.281618i	$0.0908712\pi$
$384$		0			0
$385$	2273.52	−	1218.12i	0.300959	−	0.161250i
$386$		0			0
$387$	−2086.52	+	3613.95i	−0.274066	+	0.474696i
$388$		0			0
$389$	−4803.23	−	8319.44i	−0.626050	−	1.08435i	−0.988337	−	0.152284i	$-0.951337\pi$
$389$	−4803.23	−	8319.44i	−0.626050	−	1.08435i	0.362287	−	0.932067i	$-0.381996\pi$
$390$		0			0
$391$	−7545.41			−0.975928
$392$		0			0
$393$	1426.73			0.183127
$394$		0			0
$395$	−224.500	−	388.846i	−0.0285971	−	0.0495316i
$396$		0			0
$397$	−2683.54	+	4648.02i	−0.339252	+	0.587601i	−0.984292	−	0.176547i	$-0.943507\pi$
$397$	−2683.54	+	4648.02i	−0.339252	+	0.587601i	0.645041	+	0.764148i	$0.276840\pi$
$398$		0			0
$399$	−3583.70	+	1920.10i	−0.449648	+	0.240915i
$400$		0			0
$401$	7032.91	−	12181.4i	0.875828	−	1.51698i	0.0199492	−	0.999801i	$-0.493650\pi$
$401$	7032.91	−	12181.4i	0.875828	−	1.51698i	0.855878	−	0.517177i	$-0.173017\pi$
$402$		0			0
$403$	−878.379	−	1521.40i	−0.108574	−	0.188055i
$404$		0			0
$405$	795.805			0.0976392
$406$		0			0
$407$	−4276.25			−0.520801
$408$		0			0
$409$	−1636.22	−	2834.02i	−0.197814	−	0.342624i	0.750005	−	0.661432i	$-0.230051\pi$
$409$	−1636.22	−	2834.02i	−0.197814	−	0.342624i	−0.947819	+	0.318808i	$0.896718\pi$
$410$		0			0
$411$	−1587.80	+	2750.16i	−0.190561	+	0.330062i
$412$		0			0
$413$	−9450.55	−	5863.75i	−1.12598	−	0.698635i
$414$		0			0
$415$	−3372.17	+	5840.77i	−0.398876	+	0.690873i
$416$		0			0
$417$	3871.49	+	6705.61i	0.454646	+	0.787470i
$418$		0			0
$419$	−8077.07			−0.941744			−0.470872	−	0.882202i	$-0.656061\pi$
$419$	−8077.07			−0.941744			−0.470872	+	0.882202i	$0.656061\pi$
$420$		0			0
$421$	8051.68			0.932101			0.466051	−	0.884758i	$-0.345676\pi$
$421$	8051.68			0.932101			0.466051	+	0.884758i	$0.345676\pi$
$422$		0			0
$423$	−410.382	−	710.803i	−0.0471713	−	0.0817031i
$424$		0			0
$425$	−1119.01	+	1938.18i	−0.127718	+	0.221213i
$426$		0			0
$427$	−335.939	+	10582.5i	−0.0380732	+	1.19936i
$428$		0			0
$429$	555.466	−	962.096i	0.0625132	−	0.108276i
$430$		0			0
$431$	−4950.11	−	8573.84i	−0.553221	−	0.958207i	−0.998040	−	0.0625863i	$-0.980065\pi$
$431$	−4950.11	−	8573.84i	−0.553221	−	0.958207i	0.444818	−	0.895621i	$-0.353268\pi$
$432$		0			0
$433$	−511.795			−0.0568021			−0.0284010	−	0.999597i	$-0.509042\pi$
$433$	−511.795			−0.0568021			−0.0284010	+	0.999597i	$0.509042\pi$
$434$		0			0
$435$	5099.66			0.562092
$436$		0			0
$437$	3512.41	+	6083.68i	0.384488	+	0.665954i
$438$		0			0
$439$	−651.130	+	1127.79i	−0.0707898	+	0.122612i	−0.899248	−	0.437440i	$-0.855885\pi$
$439$	−651.130	+	1127.79i	−0.0707898	+	0.122612i	0.828458	+	0.560051i	$0.189219\pi$
$440$		0			0
$441$	1370.83	+	2765.93i	0.148022	+	0.298665i
$442$		0			0
$443$	−4100.16	+	7101.69i	−0.439739	+	0.761651i	−0.997669	−	0.0682372i	$-0.978263\pi$
$443$	−4100.16	+	7101.69i	−0.439739	+	0.761651i	0.557930	+	0.829888i	$0.311596\pi$
$444$		0			0
$445$	−3242.88	−	5616.83i	−0.345454	−	0.598344i
$446$		0			0
$447$	−305.626			−0.0323392
$448$		0			0
$449$	−5788.12			−0.608370			−0.304185	−	0.952613i	$-0.598384\pi$
$449$	−5788.12			−0.608370			−0.304185	+	0.952613i	$0.598384\pi$
$450$		0			0
$451$	−3345.65	−	5794.84i	−0.349314	−	0.605030i
$452$		0			0
$453$	−2667.63	+	4620.48i	−0.276681	+	0.479225i
$454$		0			0
$455$	150.819	−	4751.01i	0.0155396	−	0.489518i
$456$		0			0
$457$	−3629.59	+	6286.63i	−0.371521	+	0.643493i	−0.989800	−	0.142466i	$-0.954497\pi$
$457$	−3629.59	+	6286.63i	−0.371521	+	0.643493i	0.618279	+	0.785959i	$0.287830\pi$
$458$		0			0
$459$	1061.07	+	1837.83i	0.107901	+	0.186890i
$460$		0			0
$461$	−5966.92			−0.602835			−0.301418	−	0.953492i	$-0.597460\pi$
$461$	−5966.92			−0.602835			−0.301418	+	0.953492i	$0.597460\pi$
$462$		0			0
$463$	8884.02			0.891740			0.445870	−	0.895098i	$-0.352894\pi$
$463$	8884.02			0.891740			0.445870	+	0.895098i	$0.352894\pi$
$464$		0			0
$465$	991.035	+	1716.52i	0.0988347	+	0.171187i
$466$		0			0
$467$	−2014.68	+	3489.53i	−0.199632	+	0.345774i	−0.948409	−	0.317049i	$-0.897308\pi$
$467$	−2014.68	+	3489.53i	−0.199632	+	0.345774i	0.748777	+	0.662822i	$0.230641\pi$
$468$		0			0
$469$	−8488.96	−	5267.12i	−0.835787	−	0.518578i
$470$		0			0
$471$	−2098.89	+	3635.38i	−0.205332	+	0.355646i
$472$		0			0
$473$	−3286.32	−	5692.07i	−0.319461	−	0.553323i
$474$		0			0
$475$	2083.61			0.201269
$476$		0			0
$477$	−1469.41			−0.141048
$478$		0			0
$479$	−8720.33	−	15104.0i	−0.831820	−	1.44075i	−0.896593	−	0.442855i	$-0.853966\pi$
$479$	−8720.33	−	15104.0i	−0.831820	−	1.44075i	0.0647733	−	0.997900i	$-0.479368\pi$
$480$		0			0
$481$	−3940.38	+	6824.94i	−0.373526	+	0.646966i
$482$		0			0
$483$	4701.53	−	2519.01i	0.442913	−	0.237306i
$484$		0			0
$485$	−3233.91	+	5601.30i	−0.302772	+	0.524417i
$486$		0			0
$487$	−2136.14	−	3699.90i	−0.198763	−	0.344268i	0.749364	−	0.662158i	$-0.230359\pi$
$487$	−2136.14	−	3699.90i	−0.198763	−	0.344268i	−0.948128	+	0.317890i	$0.897026\pi$
$488$		0			0
$489$	−10846.3			−1.00304
$490$		0			0
$491$	−2013.29			−0.185048			−0.0925240	−	0.995710i	$-0.529493\pi$
$491$	−2013.29			−0.185048			−0.0925240	+	0.995710i	$0.529493\pi$
$492$		0			0
$493$	6799.54	+	11777.2i	0.621169	+	1.07590i
$494$		0			0
$495$	−626.707	+	1085.49i	−0.0569059	+	0.0985638i
$496$		0			0
$497$	17375.9	−	9309.78i	1.56824	−	0.840243i
$498$		0			0
$499$	−2440.23	+	4226.60i	−0.218917	+	0.379176i	−0.954477	−	0.298284i	$-0.903586\pi$
$499$	−2440.23	+	4226.60i	−0.218917	+	0.379176i	0.735560	+	0.677460i	$0.236919\pi$
$500$		0			0
$501$	−1615.08	−	2797.40i	−0.144025	−	0.249459i
$502$		0			0
$503$	−12961.9			−1.14899			−0.574496	−	0.818508i	$-0.694802\pi$
$503$	−12961.9			−1.14899			−0.574496	+	0.818508i	$0.694802\pi$
$504$		0			0
$505$	−17722.8			−1.56170
$506$		0			0
$507$	2271.82	+	3934.91i	0.199004	+	0.344686i
$508$		0			0
$509$	−4077.69	+	7062.77i	−0.355089	+	0.615033i	−0.987133	−	0.159900i	$-0.948883\pi$
$509$	−4077.69	+	7062.77i	−0.355089	+	0.615033i	0.632044	+	0.774932i	$0.282216\pi$
$510$		0			0
$511$	6966.51	+	4322.49i	0.603093	+	0.374199i
$512$		0			0
$513$	987.866	−	1711.03i	0.0850202	−	0.147259i
$514$		0			0
$515$	−5280.35	−	9145.84i	−0.451806	−	0.782551i
$516$		0			0
$517$	1292.73			0.109969
$518$		0			0
$519$	5620.89			0.475394
$520$		0			0
$521$	166.009	+	287.536i	0.0139597	+	0.0241789i	0.872921	−	0.487862i	$-0.162223\pi$
$521$	166.009	+	287.536i	0.0139597	+	0.0241789i	−0.858961	+	0.512041i	$0.828890\pi$
$522$		0			0
$523$	3627.42	−	6282.87i	0.303281	−	0.525298i	−0.673596	−	0.739099i	$-0.735251\pi$
$523$	3627.42	−	6282.87i	0.303281	−	0.525298i	0.976877	+	0.213802i	$0.0685847\pi$
$524$		0			0
$525$	50.1965	−	1581.26i	0.00417286	−	0.131451i
$526$		0			0
$527$	−2642.76	+	4577.40i	−0.218445	+	0.378358i
$528$		0			0
$529$	1475.50	+	2555.64i	0.121271	+	0.210047i
$530$		0			0
$531$	5404.73			0.441705
$532$		0			0
$533$	−12331.5			−1.00213
$534$		0			0
$535$	−8151.36	−	14118.6i	−0.658718	−	1.14093i
$536$		0			0
$537$	−4038.44	+	6994.78i	−0.324528	+	0.562099i
$538$		0			0
$539$	−4852.32	−	308.382i	−0.387763	−	0.0246437i
$540$		0			0
$541$	−2705.10	+	4685.36i	−0.214974	+	0.372347i	−0.953265	−	0.302137i	$-0.902300\pi$
$541$	−2705.10	+	4685.36i	−0.214974	+	0.372347i	0.738290	+	0.674483i	$0.235633\pi$
$542$		0			0
$543$	−692.505	−	1199.45i	−0.0547297	−	0.0947947i
$544$		0			0
$545$	5884.32			0.462489
$546$		0			0
$547$	18673.9			1.45967			0.729834	−	0.683625i	$-0.239597\pi$
$547$	18673.9			1.45967			0.729834	+	0.683625i	$0.239597\pi$
$548$		0			0
$549$	−2572.61	−	4455.89i	−0.199993	−	0.346399i
$550$		0			0
$551$	6330.42	−	10964.6i	0.489446	−	0.847746i
$552$		0			0
$553$	−26.8550	+	845.968i	−0.00206508	+	0.0650528i
$554$		0			0
$555$	4445.75	−	7700.27i	0.340021	−	0.588934i
$556$		0			0
$557$	4104.74	+	7109.62i	0.312250	+	0.540833i	0.978849	−	0.204583i	$-0.0655839\pi$
$557$	4104.74	+	7109.62i	0.312250	+	0.540833i	−0.666599	+	0.745417i	$0.732251\pi$
$558$		0			0
$559$	−12112.8			−0.916489
$560$		0			0
$561$	−3342.44			−0.251547
$562$		0			0
$563$	8761.10	+	15174.7i	0.655837	+	1.13594i	0.981683	+	0.190521i	$0.0610176\pi$
$563$	8761.10	+	15174.7i	0.655837	+	1.13594i	−0.325846	+	0.945423i	$0.605649\pi$
$564$		0			0
$565$	3839.76	−	6650.65i	0.285911	−	0.495212i
$566$		0			0
$567$	−1274.71	−	790.914i	−0.0944139	−	0.0585807i
$568$		0			0
$569$	4528.41	−	7843.44i	0.333640	−	0.577881i	−0.649583	−	0.760291i	$-0.725056\pi$
$569$	4528.41	−	7843.44i	0.333640	−	0.577881i	0.983223	+	0.182410i	$0.0583898\pi$
$570$		0			0
$571$	5358.27	+	9280.80i	0.392709	+	0.680191i	0.992806	−	0.119736i	$-0.0382047\pi$
$571$	5358.27	+	9280.80i	0.392709	+	0.680191i	−0.600097	+	0.799927i	$0.704871\pi$
$572$		0			0
$573$	11294.5			0.823444
$574$		0			0
$575$	−2733.53			−0.198254
$576$		0			0
$577$	−1608.62	−	2786.21i	−0.116062	−	0.201025i	0.802142	−	0.597133i	$-0.203694\pi$
$577$	−1608.62	−	2786.21i	−0.116062	−	0.201025i	−0.918204	+	0.396109i	$0.870360\pi$
$578$		0			0
$579$	−4389.30	+	7602.49i	−0.315048	+	0.545680i
$580$		0			0
$581$	11206.4	−	6004.21i	0.800203	−	0.428738i
$582$		0			0
$583$	1157.18	−	2004.30i	0.0822053	−	0.142384i
$584$		0			0
$585$	1154.97	+	2000.46i	0.0816274	+	0.141383i
$586$		0			0
$587$	−3248.45			−0.228412			−0.114206	−	0.993457i	$-0.536432\pi$
$587$	−3248.45			−0.228412			−0.114206	+	0.993457i	$0.536432\pi$
$588$		0			0
$589$	4920.85			0.344245
$590$		0			0
$591$	−7568.32	−	13108.7i	−0.526767	−	0.912387i
$592$		0			0
$593$	10555.2	−	18282.1i	0.730945	−	1.26603i	−0.225535	−	0.974235i	$-0.572413\pi$
$593$	10555.2	−	18282.1i	0.730945	−	1.26603i	0.956480	−	0.291799i	$-0.0942537\pi$
$594$		0			0
$595$	−12606.1	+	6754.15i	−0.868569	+	0.465367i
$596$		0			0
$597$	6438.37	−	11151.6i	0.441382	−	0.764496i
$598$		0			0
$599$	−7868.98	−	13629.5i	−0.536758	−	0.929692i	−0.999076	−	0.0429777i	$-0.986316\pi$
$599$	−7868.98	−	13629.5i	−0.536758	−	0.929692i	0.462318	−	0.886714i	$-0.347018\pi$
$600$		0			0
$601$	−4856.96			−0.329650			−0.164825	−	0.986323i	$-0.552706\pi$
$601$	−4856.96			−0.329650			−0.164825	+	0.986323i	$0.552706\pi$
$602$		0			0
$603$	4854.80			0.327866
$604$		0			0
$605$	5551.29	+	9615.12i	0.373045	+	0.646132i
$606$		0			0
$607$	−8629.29	+	14946.4i	−0.577022	+	0.999431i	0.418797	+	0.908080i	$0.362452\pi$
$607$	−8629.29	+	14946.4i	−0.577022	+	0.999431i	−0.995819	+	0.0913513i	$0.970881\pi$
$608$		0			0
$609$	−8168.55	−	5068.31i	−0.543524	−	0.337239i
$610$		0			0
$611$	1191.19	−	2063.20i	0.0788714	−	0.136609i
$612$		0			0
$613$	−8058.53	−	13957.8i	−0.530964	−	0.919657i	−0.999347	−	0.0361315i	$-0.988496\pi$
$613$	−8058.53	−	13957.8i	−0.530964	−	0.919657i	0.468383	−	0.883526i	$-0.344837\pi$
$614$		0			0
$615$	13913.1			0.912243
$616$		0			0
$617$	−17507.3			−1.14233			−0.571164	−	0.820836i	$-0.693508\pi$
$617$	−17507.3			−1.14233			−0.571164	+	0.820836i	$0.693508\pi$
$618$		0			0
$619$	4859.24	+	8416.46i	0.315524	+	0.546504i	0.979549	−	0.201207i	$-0.0644863\pi$
$619$	4859.24	+	8416.46i	0.315524	+	0.546504i	−0.664025	+	0.747711i	$0.731153\pi$
$620$		0			0
$621$	−1296.00	+	2244.74i	−0.0837467	+	0.145054i
$622$		0			0
$623$	−387.917	+	12219.9i	−0.0249463	+	0.785842i
$624$		0			0
$625$	5627.47	−	9747.06i	0.360158	−	0.623812i
$626$		0			0
$627$	1555.92	+	2694.93i	0.0991025	+	0.171651i
$628$		0			0
$629$	23710.7			1.50303
$630$		0			0
$631$	−5144.78			−0.324580			−0.162290	−	0.986743i	$-0.551888\pi$
$631$	−5144.78			−0.324580			−0.162290	+	0.986743i	$0.551888\pi$
$632$		0			0
$633$	5438.63	+	9419.99i	0.341495	+	0.591487i
$634$		0			0
$635$	124.638	−	215.879i	0.00778913	−	0.0134912i
$636$		0			0
$637$	−4963.38	+	7460.19i	−0.308723	+	0.464024i
$638$		0			0
$639$	−4789.76	+	8296.12i	−0.296526	+	0.513598i
$640$		0			0
$641$	−10843.0	−	18780.7i	−0.668135	−	1.15724i	−0.978425	−	0.206602i	$-0.933760\pi$
$641$	−10843.0	−	18780.7i	−0.668135	−	1.15724i	0.310290	−	0.950642i	$-0.399574\pi$
$642$		0			0
$643$	14171.1			0.869132			0.434566	−	0.900640i	$-0.356902\pi$
$643$	14171.1			0.869132			0.434566	+	0.900640i	$0.356902\pi$
$644$		0			0
$645$	13666.3			0.834281
$646$		0			0
$647$	10026.6	+	17366.6i	0.609254	+	1.05526i	0.991364	+	0.131142i	$0.0418645\pi$
$647$	10026.6	+	17366.6i	0.609254	+	1.05526i	−0.382109	+	0.924117i	$0.624802\pi$
$648$		0			0
$649$	−4256.30	+	7372.13i	−0.257434	+	0.445888i
$650$		0			0
$651$	118.549	−	3734.44i	0.00713716	−	0.224830i
$652$		0			0
$653$	−11820.6	+	20473.8i	−0.708385	+	1.22696i	0.257072	+	0.966392i	$0.417242\pi$
$653$	−11820.6	+	20473.8i	−0.708385	+	1.22696i	−0.965456	+	0.260566i	$0.916091\pi$
$654$		0			0
$655$	−2336.21	−	4046.44i	−0.139364	−	0.241386i
$656$		0			0
$657$	−3984.12			−0.236584
$658$		0			0
$659$	−2367.34			−0.139937			−0.0699685	−	0.997549i	$-0.522290\pi$
$659$	−2367.34			−0.139937			−0.0699685	+	0.997549i	$0.522290\pi$
$660$		0			0
$661$	194.991	+	337.733i	0.0114739	+	0.0198734i	0.871705	−	0.490030i	$-0.163014\pi$
$661$	194.991	+	337.733i	0.0114739	+	0.0198734i	−0.860231	+	0.509904i	$0.829681\pi$
$662$		0			0
$663$	−3079.91	+	5334.57i	−0.180413	+	0.312485i
$664$		0			0
$665$	11313.9	+	7019.88i	0.659749	+	0.409352i
$666$		0			0
$667$	−8305.00	+	14384.7i	−0.482115	+	0.835048i
$668$		0			0
$669$	−4717.50	−	8170.96i	−0.272630	−	0.472208i
$670$		0			0
$671$	8103.86			0.466239
$672$		0			0
$673$	28764.5			1.64753			0.823766	−	0.566930i	$-0.191869\pi$
$673$	28764.5			1.64753			0.823766	+	0.566930i	$0.191869\pi$
$674$		0			0
$675$	384.402	+	665.805i	0.0219195	+	0.0379657i
$676$		0			0
$677$	881.061	−	1526.04i	0.0500176	−	0.0866331i	−0.839933	−	0.542691i	$-0.817406\pi$
$677$	881.061	−	1526.04i	0.0500176	−	0.0866331i	0.889950	+	0.456058i	$0.150739\pi$
$678$		0			0
$679$	10746.9	−	5758.04i	0.607406	−	0.325439i
$680$		0			0
$681$	−2318.62	+	4015.96i	−0.130469	+	0.225980i
$682$		0			0
$683$	−1114.44	−	1930.26i	−0.0624344	−	0.108140i	0.833119	−	0.553094i	$-0.186553\pi$
$683$	−1114.44	−	1930.26i	−0.0624344	−	0.108140i	−0.895553	+	0.444955i	$0.853220\pi$
$684$		0			0
$685$	10399.9			0.580085
$686$		0			0
$687$	−12216.4			−0.678437
$688$		0			0
$689$	−2132.59	−	3693.76i	−0.117918	−	0.204239i
$690$		0			0
$691$	8672.14	−	15020.6i	0.477429	−	0.826932i	−0.522236	−	0.852801i	$-0.674902\pi$
$691$	8672.14	−	15020.6i	0.477429	−	0.826932i	0.999665	+	0.0258690i	$0.00823527\pi$
$692$		0			0
$693$	2082.67	−	1115.86i	0.114162	−	0.0611661i
$694$		0			0
$695$	12678.8	−	21960.3i	0.691992	−	1.19856i
$696$		0			0
$697$	18550.8	+	32130.9i	1.00812	+	1.74612i
$698$		0			0
$699$	−9047.14			−0.489548
$700$		0			0
$701$	−23697.7			−1.27682			−0.638409	−	0.769697i	$-0.720407\pi$
$701$	−23697.7			−1.27682			−0.638409	+	0.769697i	$0.720407\pi$
$702$		0			0
$703$	−11037.4	−	19117.3i	−0.592153	−	1.02564i
$704$		0			0
$705$	−1343.97	+	2327.82i	−0.0717968	+	0.124356i
$706$		0			0
$707$	28388.2	+	17613.9i	1.51011	+	0.936972i
$708$		0			0
$709$	11395.5	−	19737.6i	0.603620	−	1.04550i	−0.388648	−	0.921386i	$-0.627058\pi$
$709$	11395.5	−	19737.6i	0.603620	−	1.04550i	0.992268	−	0.124114i	$-0.0396088\pi$
$710$		0			0
$711$	−205.654	−	356.204i	−0.0108476	−	0.0187886i
$712$		0			0
$713$	−6455.76			−0.339089
$714$		0			0
$715$	−3638.21			−0.190296
$716$		0			0
$717$	6971.08	+	12074.3i	0.363096	+	0.628900i
$718$		0			0
$719$	15922.4	−	27578.4i	0.825876	−	1.43046i	−0.0753721	−	0.997155i	$-0.524014\pi$
$719$	15922.4	−	27578.4i	0.825876	−	1.43046i	0.901248	−	0.433304i	$-0.142652\pi$
$720$		0			0
$721$	−631.642	+	19897.5i	−0.0326263	+	1.02777i
$722$		0			0
$723$	−1677.41	+	2905.37i	−0.0862845	+	0.149449i
$724$		0			0
$725$	2463.32	+	4266.59i	0.126187	+	0.218562i
$726$		0			0
$727$	22500.0			1.14784			0.573920	−	0.818912i	$-0.305422\pi$
$727$	22500.0			1.14784			0.573920	+	0.818912i	$0.305422\pi$
$728$		0			0
$729$	729.000			0.0370370
$730$		0			0
$731$	18221.8	+	31561.1i	0.921966	+	1.59689i
$732$		0			0
$733$	1611.38	−	2790.99i	0.0811972	−	0.140638i	−0.822567	−	0.568668i	$-0.807459\pi$
$733$	1611.38	−	2790.99i	0.0811972	−	0.140638i	0.903764	+	0.428030i	$0.140792\pi$
$734$		0			0
$735$	5599.96	−	8417.00i	0.281031	−	0.422402i
$736$		0			0
$737$	−3823.23	+	6622.02i	−0.191086	+	0.330971i
$738$		0			0
$739$	9179.77	+	15899.8i	0.456946	+	0.791454i	0.998798	−	0.0490199i	$-0.0156098\pi$
$739$	9179.77	+	15899.8i	0.456946	+	0.791454i	−0.541851	+	0.840474i	$0.682276\pi$
$740$		0			0
$741$	5734.84			0.284311
$742$		0			0
$743$	−12890.4			−0.636478			−0.318239	−	0.948010i	$-0.603091\pi$
$743$	−12890.4			−0.636478			−0.318239	+	0.948010i	$0.603091\pi$
$744$		0			0
$745$	500.450	+	866.805i	0.0246108	+	0.0426272i
$746$		0			0
$747$	−3089.09	+	5350.46i	−0.151304	+	0.262066i
$748$		0			0
$749$	−975.075	+	30716.1i	−0.0475680	+	1.49846i
$750$		0			0
$751$	7695.10	−	13328.3i	0.373899	−	0.647612i	−0.616263	−	0.787541i	$-0.711354\pi$
$751$	7695.10	−	13328.3i	0.373899	−	0.647612i	0.990162	+	0.139929i	$0.0446873\pi$
$752$		0			0
$753$	1325.28	+	2295.45i	0.0641378	+	0.111090i
$754$		0			0
$755$	17472.6			0.842241
$756$		0			0
$757$	13974.6			0.670957			0.335479	−	0.942048i	$-0.391102\pi$
$757$	13974.6			0.670957			0.335479	+	0.942048i	$0.391102\pi$
$758$		0			0
$759$	−2041.24	−	3535.52i	−0.0976181	−	0.169080i
$760$		0			0
$761$	1687.57	−	2922.96i	0.0803868	−	0.139234i	−0.823029	−	0.567999i	$-0.807718\pi$
$761$	1687.57	−	2922.96i	0.0803868	−	0.139234i	0.903416	+	0.428765i	$0.141051\pi$
$762$		0			0
$763$	−9425.40	−	5848.15i	−0.447212	−	0.277480i
$764$		0			0
$765$	3474.93	−	6018.75i	0.164230	−	0.284455i
$766$		0			0
$767$	7843.99	+	13586.2i	0.369270	+	0.639595i
$768$		0			0
$769$	−31253.9			−1.46560			−0.732798	−	0.680446i	$-0.761786\pi$
$769$	−31253.9			−1.46560			−0.732798	+	0.680446i	$0.761786\pi$
$770$		0			0
$771$	−17606.7			−0.822423
$772$		0			0
$773$	−11581.8	−	20060.2i	−0.538897	−	0.933396i	−0.998964	−	0.0455122i	$-0.985508\pi$
$773$	−11581.8	−	20060.2i	−0.538897	−	0.933396i	0.460067	−	0.887884i	$-0.347825\pi$
$774$		0			0
$775$	−957.411	+	1658.29i	−0.0443758	+	0.0768611i
$776$		0			0
$777$	−14774.1	+	7915.74i	−0.682133	+	0.365477i
$778$		0			0
$779$	17270.9	−	29914.0i	0.794343	−	1.37584i
$780$		0			0
$781$	−7544.01	−	13066.6i	−0.345641	−	0.598668i
$782$		0			0
$783$	4671.56			0.213216
$784$		0			0
$785$	13747.4			0.625050
$786$		0			0
$787$	−4951.47	−	8576.20i	−0.224271	−	0.388448i	0.731830	−	0.681488i	$-0.238667\pi$
$787$	−4951.47	−	8576.20i	−0.224271	−	0.388448i	−0.956100	+	0.293039i	$0.905333\pi$
$788$		0			0
$789$	7313.42	−	12667.2i	0.329993	−	0.571565i
$790$		0			0
$791$	−12760.2	+	6836.75i	−0.573580	+	0.307316i
$792$		0			0
$793$	7467.36	−	12933.8i	0.334393	−	0.579186i
$794$		0			0
$795$	2406.11	+	4167.50i	0.107341	+	0.185919i
$796$		0			0
$797$	16844.5			0.748638			0.374319	−	0.927300i	$-0.377877\pi$
$797$	16844.5			0.748638			0.374319	+	0.927300i	$0.377877\pi$
$798$		0			0
$799$	−7167.83			−0.317371
$800$		0			0
$801$	−2970.65	−	5145.32i	−0.131040	−	0.226967i
$802$		0			0
$803$	3137.55	−	5434.40i	0.137885	−	0.238824i
$804$		0			0
$805$	−14842.9	−	9209.52i	−0.649867	−	0.403221i
$806$		0			0
$807$	8290.66	−	14359.8i	0.361642	−	0.626382i
$808$		0			0
$809$	17215.3	+	29817.8i	0.748157	+	1.29585i	0.948705	+	0.316162i	$0.102394\pi$
$809$	17215.3	+	29817.8i	0.748157	+	1.29585i	−0.200549	+	0.979684i	$0.564272\pi$
$810$		0			0
$811$	62.4498			0.00270396			0.00135198	−	0.999999i	$-0.499570\pi$
$811$	62.4498			0.00270396			0.00135198	+	0.999999i	$0.499570\pi$
$812$		0			0
$813$	9674.20			0.417329
$814$		0			0
$815$	17760.3	+	30761.8i	0.763334	+	1.32213i
$816$		0			0
$817$	16964.6	−	29383.5i	0.726458	−	1.25826i
$818$		0			0
$819$	138.159	−	4352.18i	0.00589457	−	0.185687i
$820$		0			0
$821$	−19475.8	+	33733.1i	−0.827906	+	1.43398i	0.0717711	+	0.997421i	$0.477135\pi$
$821$	−19475.8	+	33733.1i	−0.827906	+	1.43398i	−0.899678	+	0.436555i	$0.856198\pi$
$822$		0			0
$823$	−17741.2	−	30728.6i	−0.751420	−	1.30150i	−0.947135	−	0.320836i	$-0.896036\pi$
$823$	−17741.2	−	30728.6i	−0.751420	−	1.30150i	0.195715	−	0.980661i	$-0.437297\pi$
$824$		0			0
$825$	−1210.89			−0.0511003
$826$		0			0
$827$	−7945.87			−0.334105			−0.167053	−	0.985948i	$-0.553425\pi$
$827$	−7945.87			−0.334105			−0.167053	+	0.985948i	$0.553425\pi$
$828$		0			0
$829$	−20318.2	−	35192.2i	−0.851243	−	1.47440i	−0.880087	−	0.474812i	$-0.842516\pi$
$829$	−20318.2	−	35192.2i	−0.851243	−	1.47440i	0.0288439	−	0.999584i	$-0.490817\pi$
$830$		0			0
$831$	2937.07	−	5087.15i	0.122606	−	0.212360i
$832$		0			0
$833$	26904.8	+	1709.90i	1.11908	+	0.0711217i
$834$		0			0
$835$	−5289.26	+	9161.26i	−0.219212	+	0.379687i
$836$		0			0
$837$	907.841	+	1572.43i	0.0374906	+	0.0649355i
$838$		0			0
$839$	−27723.5			−1.14079			−0.570394	−	0.821371i	$-0.693209\pi$
$839$	−27723.5			−1.14079			−0.570394	+	0.821371i	$0.693209\pi$
$840$		0			0
$841$	5547.19			0.227446
$842$		0			0
$843$	−12796.7	−	22164.6i	−0.522827	−	0.905563i
$844$		0			0
$845$	7440.04	−	12886.5i	0.302893	−	0.524627i
$846$		0			0
$847$	664.052	−	20918.5i	0.0269387	−	0.848605i
$848$		0			0
$849$	11864.8	−	20550.4i	0.479621	−	0.830728i
$850$		0			0
$851$	14480.2	+	25080.4i	0.583283	+	1.01028i
$852$		0			0
$853$	37599.1			1.50922			0.754612	−	0.656171i	$-0.227825\pi$
$853$	37599.1			1.50922			0.754612	+	0.656171i	$0.227825\pi$
$854$		0			0
$855$	−6470.36			−0.258809
$856$		0			0
$857$	−12805.0	−	22178.9i	−0.510397	−	0.884034i	−0.999927	−	0.0120476i	$-0.996165\pi$
$857$	−12805.0	−	22178.9i	−0.510397	−	0.884034i	0.489530	−	0.871986i	$-0.337168\pi$
$858$		0			0
$859$	−1989.70	+	3446.26i	−0.0790309	+	0.136886i	−0.902832	−	0.429993i	$-0.858516\pi$
$859$	−1989.70	+	3446.26i	−0.0790309	+	0.136886i	0.823801	+	0.566879i	$0.191849\pi$
$860$		0			0
$861$	−22285.7	−	13827.6i	−0.882109	−	0.547319i
$862$		0			0
$863$	−12410.2	+	21495.0i	−0.489510	+	0.847856i	−0.999927	−	0.0120708i	$-0.996158\pi$
$863$	−12410.2	+	21495.0i	−0.489510	+	0.847856i	0.510417	+	0.859927i	$0.329491\pi$
$864$		0			0
$865$	−9203.97	−	15941.7i	−0.361786	−	0.626631i
$866$		0			0
$867$	3793.94			0.148615
$868$		0			0
$869$	647.823			0.0252887
$870$		0			0
$871$	7045.87	+	12203.8i	0.274099	+	0.474754i
$872$		0			0
$873$	−2962.44	+	5131.09i	−0.114849	+	0.198925i
$874$		0			0
$875$	−24615.2	+	13188.5i	−0.951024	+	0.509545i
$876$		0			0
$877$	−25009.7	+	43318.1i	−0.962963	+	1.66790i	−0.247971	+	0.968767i	$0.579764\pi$
$877$	−25009.7	+	43318.1i	−0.962963	+	1.66790i	−0.714992	+	0.699133i	$0.753570\pi$
$878$		0			0
$879$	12482.1	+	21619.7i	0.478966	+	0.829594i
$880$		0			0
$881$	−10386.4			−0.397193			−0.198596	−	0.980081i	$-0.563638\pi$
$881$	−10386.4			−0.397193			−0.198596	+	0.980081i	$0.563638\pi$
$882$		0			0
$883$	−36366.4			−1.38599			−0.692994	−	0.720944i	$-0.743709\pi$
$883$	−36366.4			−1.38599			−0.692994	+	0.720944i	$0.743709\pi$
$884$		0			0
$885$	−8850.02	−	15328.7i	−0.336147	−	0.582224i
$886$		0			0
$887$	−3803.65	+	6588.12i	−0.143984	+	0.249388i	−0.928994	−	0.370096i	$-0.879325\pi$
$887$	−3803.65	+	6588.12i	−0.143984	+	0.249388i	0.785009	+	0.619484i	$0.212658\pi$
$888$		0			0
$889$	−414.195	+	221.920i	−0.0156261	+	0.00837227i
$890$		0			0
$891$	−574.098	+	994.366i	−0.0215858	+	0.0373878i
$892$		0			0
$893$	3336.65	+	5779.24i	0.125035	+	0.216568i
$894$		0			0
$895$	26451.1			0.987891
$896$		0			0
$897$	−7523.64			−0.280053
$898$		0			0
$899$	5817.61	+	10076.4i	0.215827	+	0.373823i
$900$		0			0
$901$	−6416.28	+	11113.3i	−0.237245	+	0.410920i
$902$		0			0
$903$	−21890.5	−	13582.3i	−0.806723	−	0.500545i
$904$		0			0
$905$	−2267.90	+	3928.11i	−0.0833011	+	0.144282i
$906$		0			0
$907$	12901.5	+	22346.1i	0.472314	+	0.818072i	0.999498	−	0.0316794i	$-0.0100856\pi$
$907$	12901.5	+	22346.1i	0.472314	+	0.818072i	−0.527184	+	0.849751i	$0.676752\pi$
$908$		0			0
$909$	−16235.1			−0.592391
$910$		0			0
$911$	−8165.21			−0.296954			−0.148477	−	0.988916i	$-0.547437\pi$
$911$	−8165.21			−0.296954			−0.148477	+	0.988916i	$0.547437\pi$
$912$		0			0
$913$	−4865.40	−	8427.12i	−0.176365	−	0.305473i
$914$		0			0
$915$	−8425.08	+	14592.7i	−0.304399	+	0.527234i
$916$		0			0
$917$	−279.461	+	8803.38i	−0.0100639	+	0.317026i
$918$		0			0
$919$	296.804	−	514.079i	0.0106536	−	0.0184526i	−0.860649	−	0.509198i	$-0.829942\pi$
$919$	296.804	−	514.079i	0.0106536	−	0.0184526i	0.871303	+	0.490745i	$0.163275\pi$
$920$		0			0
$921$	3812.69	+	6603.77i	0.136409	+	0.236267i
$922$		0			0
$923$	−27805.9			−0.991596
$924$		0			0
$925$	8589.84			0.305332
$926$		0			0
$927$	−4837.09	−	8378.08i	−0.171382	−	0.296842i
$928$		0			0
$929$	16573.7	−	28706.5i	0.585323	−	1.01381i	−0.409512	−	0.912305i	$-0.634301\pi$
$929$	16573.7	−	28706.5i	0.585323	−	1.01381i	0.994835	−	0.101504i	$-0.0323655\pi$
$930$		0			0
$931$	−11145.6	−	22488.7i	−0.392356	−	0.791661i
$932$		0			0
$933$	−911.564	+	1578.87i	−0.0319863	+	0.0554020i
$934$		0			0
$935$	5473.11	+	9479.70i	0.191433	+	0.331571i
$936$		0			0
$937$	−24883.8			−0.867575			−0.433788	−	0.901015i	$-0.642823\pi$
$937$	−24883.8			−0.867575			−0.433788	+	0.901015i	$0.642823\pi$
$938$		0			0
$939$	33081.8			1.14972
$940$		0			0
$941$	13065.1	+	22629.5i	0.452616	+	0.783954i	0.998548	−	0.0538758i	$-0.0171575\pi$
$941$	13065.1	+	22629.5i	0.452616	+	0.783954i	−0.545932	+	0.837830i	$0.683824\pi$
$942$		0			0
$943$	−22658.0	+	39244.8i	−0.782445	+	1.35523i
$944$		0			0
$945$	−155.878	+	4910.36i	−0.00536583	+	0.169031i
$946$		0			0
$947$	3984.35	−	6901.09i	0.136720	−	0.236806i	−0.789533	−	0.613708i	$-0.789677\pi$
$947$	3984.35	−	6901.09i	0.136720	−	0.236806i	0.926253	+	0.376902i	$0.123011\pi$
$948$		0			0
$949$	−5782.24	−	10015.1i	−0.197786	−	0.342576i
$950$		0			0
$951$	21784.8			0.742819
$952$		0			0
$953$	−6742.36			−0.229178			−0.114589	−	0.993413i	$-0.536555\pi$
$953$	−6742.36			−0.229178			−0.114589	+	0.993413i	$0.536555\pi$
$954$		0			0
$955$	−18494.2	−	32033.0i	−0.626659	−	1.08541i
$956$		0			0
$957$	−3678.92	+	6372.07i	−0.124266	+	0.215235i
$958$		0			0
$959$	−16658.3	−	10335.9i	−0.560923	−	0.348034i
$960$		0			0
$961$	12634.4	−	21883.4i	0.424101	−	0.734564i
$962$		0			0
$963$	−7467.08	−	12933.4i	−0.249868	−	0.432785i
$964$		0			0
$965$	28749.2			0.959035
$966$		0			0
$967$	7202.50			0.239521			0.119760	−	0.992803i	$-0.461787\pi$
$967$	7202.50			0.239521			0.119760	+	0.992803i	$0.461787\pi$
$968$		0			0
$969$	−8627.14	−	14942.7i	−0.286010	−	0.495384i
$970$		0			0
$971$	6852.86	−	11869.5i	0.226487	−	0.392286i	−0.730278	−	0.683150i	$-0.760609\pi$
$971$	6852.86	−	11869.5i	0.226487	−	0.392286i	0.956764	+	0.290864i	$0.0939427\pi$
$972$		0			0
$973$	−42134.0	+	22574.8i	−1.38824	+	0.743798i
$974$		0			0
$975$	−1115.78	+	1932.59i	−0.0366499	+	0.0634794i
$976$		0			0
$977$	28274.0	+	48972.0i	0.925860	+	1.60364i	0.790173	+	0.612884i	$0.209991\pi$
$977$	28274.0	+	48972.0i	0.925860	+	1.60364i	0.135687	+	0.990752i	$0.456676\pi$
$978$		0			0
$979$	9357.71			0.305489
$980$		0			0
$981$	5390.35			0.175434
$982$		0			0
$983$	8681.87	+	15037.4i	0.281698	+	0.487914i	0.971803	−	0.235794i	$-0.0757692\pi$
$983$	8681.87	+	15037.4i	0.281698	+	0.487914i	−0.690105	+	0.723709i	$0.742436\pi$
$984$		0			0
$985$	−24785.6	+	42930.0i	−0.801762	+	1.38869i
$986$		0			0
$987$	4466.26	−	2392.96i	0.144035	−	0.0771719i
$988$		0			0
$989$	−22256.2	+	38548.8i	−0.715576	+	1.23941i
$990$		0			0
$991$	24519.7	+	42469.4i	0.785968	+	1.36134i	0.928419	+	0.371535i	$0.121168\pi$
$991$	24519.7	+	42469.4i	0.785968	+	1.36134i	−0.142451	+	0.989802i	$0.545498\pi$
$992$		0			0
$993$	−19898.2			−0.635901
$994$		0			0
$995$	−42170.3			−1.34361
$996$		0			0
$997$	4558.30	+	7895.21i	0.144797	+	0.250796i	0.929297	−	0.369333i	$-0.120414\pi$
$997$	4558.30	+	7895.21i	0.144797	+	0.250796i	−0.784500	+	0.620129i	$0.787080\pi$
$998$		0			0
$999$	4072.55	−	7053.86i	0.128979	−	0.223398i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.4.q.h.289.1		4
4.3	odd	2		84.4.i.b.37.1	yes	4
7.2	even	3		2352.4.a.cb.1.2		2
7.4	even	3	inner	336.4.q.h.193.1		4
7.5	odd	6		2352.4.a.bp.1.1		2
12.11	even	2		252.4.k.d.37.2		4
28.3	even	6		588.4.i.i.361.2		4
28.11	odd	6		84.4.i.b.25.1	✓	4
28.19	even	6		588.4.a.h.1.1		2
28.23	odd	6		588.4.a.g.1.2		2
28.27	even	2		588.4.i.i.373.2		4
84.11	even	6		252.4.k.d.109.2		4
84.23	even	6		1764.4.a.x.1.1		2
84.47	odd	6		1764.4.a.p.1.2		2
84.59	odd	6		1764.4.k.z.361.1		4
84.83	odd	2		1764.4.k.z.1549.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
84.4.i.b.25.1	✓	4	28.11	odd	6
84.4.i.b.37.1	yes	4	4.3	odd	2
252.4.k.d.37.2		4	12.11	even	2
252.4.k.d.109.2		4	84.11	even	6
336.4.q.h.193.1		4	7.4	even	3	inner
336.4.q.h.289.1		4	1.1	even	1	trivial
588.4.a.g.1.2		2	28.23	odd	6
588.4.a.h.1.1		2	28.19	even	6
588.4.i.i.361.2		4	28.3	even	6
588.4.i.i.373.2		4	28.27	even	2
1764.4.a.p.1.2		2	84.47	odd	6
1764.4.a.x.1.1		2	84.23	even	6
1764.4.k.z.361.1		4	84.59	odd	6
1764.4.k.z.1549.1		4	84.83	odd	2
2352.4.a.bp.1.1		2	7.5	odd	6
2352.4.a.cb.1.2		2	7.2	even	3

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:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	336.q (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.50000 - 2.59808i) q^{3} +(-4.91238 + 8.50848i) q^{5} +(16.3248 - 8.74657i) q^{7} +(-4.50000 + 7.79423i) q^{9} +O(q^{10})\)	\(q+(-1.50000 - 2.59808i) q^{3} +(-4.91238 + 8.50848i) q^{5} +(16.3248 - 8.74657i) q^{7} +(-4.50000 + 7.79423i) q^{9} +(-7.08762 - 12.2761i) q^{11} -26.1238 q^{13} +29.4743 q^{15} +(39.2990 + 68.0679i) q^{17} +(36.5876 - 63.3716i) q^{19} +(-47.2114 - 29.2931i) q^{21} +(-48.0000 + 83.1384i) q^{23} +(14.2371 + 24.6594i) q^{25} +27.0000 q^{27} +173.021 q^{29} +(33.6238 + 58.2381i) q^{31} +(-21.2629 + 36.8284i) q^{33} +(-5.77326 + 181.865i) q^{35} +(150.835 - 261.254i) q^{37} +(39.1856 + 67.8715i) q^{39} +472.042 q^{41} +463.670 q^{43} +(-44.2114 - 76.5764i) q^{45} +(-45.5980 + 78.9781i) q^{47} +(189.995 - 285.571i) q^{49} +(117.897 - 204.204i) q^{51} +(81.6341 + 141.394i) q^{53} +139.268 q^{55} -219.526 q^{57} +(-300.263 - 520.071i) q^{59} +(-285.846 + 495.099i) q^{61} +(-5.28862 + 166.598i) q^{63} +(128.330 - 222.274i) q^{65} +(-269.711 - 467.154i) q^{67} +288.000 q^{69} +1064.39 q^{71} +(221.340 + 383.372i) q^{73} +(42.7114 - 73.9783i) q^{75} +(-223.078 - 138.412i) q^{77} +(-22.8505 + 39.5782i) q^{79} +(-40.5000 - 70.1481i) q^{81} +686.464 q^{83} -772.206 q^{85} +(-259.531 - 449.521i) q^{87} +(-330.072 + 571.702i) q^{89} +(-426.464 + 228.493i) q^{91} +(100.871 - 174.714i) q^{93} +(359.464 + 622.610i) q^{95} +658.320 q^{97} +127.577 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 6 q^{3} + 3 q^{5} + 20 q^{7} - 18 q^{9}+O(q^{10}) \) 4 * q - 6 * q^3 + 3 * q^5 + 20 * q^7 - 18 * q^9	\( 4 q - 6 q^{3} + 3 q^{5} + 20 q^{7} - 18 q^{9} - 51 q^{11} + 122 q^{13} - 18 q^{15} - 24 q^{17} + 169 q^{19} + 15 q^{21} - 192 q^{23} - 11 q^{25} + 108 q^{27} - 78 q^{29} - 92 q^{31} - 153 q^{33} + 294 q^{35} + 173 q^{37} - 183 q^{39} + 348 q^{41} + 994 q^{43} + 27 q^{45} + 180 q^{47} - 146 q^{49} - 72 q^{51} - 285 q^{53} - 666 q^{55} - 1014 q^{57} - 1269 q^{59} - 328 q^{61} - 225 q^{63} + 1374 q^{65} - 875 q^{67} + 1152 q^{69} + 2808 q^{71} + 1361 q^{73} - 33 q^{75} + 897 q^{77} - 182 q^{79} - 162 q^{81} + 798 q^{83} - 4176 q^{85} + 117 q^{87} - 822 q^{89} - 1955 q^{91} - 276 q^{93} - 510 q^{95} + 1682 q^{97} + 918 q^{99}+O(q^{100}) \) 4 * q - 6 * q^3 + 3 * q^5 + 20 * q^7 - 18 * q^9 - 51 * q^11 + 122 * q^13 - 18 * q^15 - 24 * q^17 + 169 * q^19 + 15 * q^21 - 192 * q^23 - 11 * q^25 + 108 * q^27 - 78 * q^29 - 92 * q^31 - 153 * q^33 + 294 * q^35 + 173 * q^37 - 183 * q^39 + 348 * q^41 + 994 * q^43 + 27 * q^45 + 180 * q^47 - 146 * q^49 - 72 * q^51 - 285 * q^53 - 666 * q^55 - 1014 * q^57 - 1269 * q^59 - 328 * q^61 - 225 * q^63 + 1374 * q^65 - 875 * q^67 + 1152 * q^69 + 2808 * q^71 + 1361 * q^73 - 33 * q^75 + 897 * q^77 - 182 * q^79 - 162 * q^81 + 798 * q^83 - 4176 * q^85 + 117 * q^87 - 822 * q^89 - 1955 * q^91 - 276 * q^93 - 510 * q^95 + 1682 * q^97 + 918 * q^99

Introduction

L-functions

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