LMFDB - Embedded newform 360.4.k.c.181.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [360,4,Mod(181,360)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("360.181"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(360, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1, 0, 0])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 360 = 2^{3} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	360.k (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [12] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$21.2406876021$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 4x^{11} + 7x^{10} - 12x^{9} + 21x^{8} - 68x^{6} + 336x^{4} - 768x^{3} + 1792x^{2} - 4096x + 4096 $ x^12 - 4x^11 + 7x^10 - 12x^9 + 21x^8 - 68x^6 + 336x^4 - 768x^3 + 1792x^2 - 4096*x + 4096
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{14}\cdot 5^{4} $
Twist minimal:	no (minimal twist has level 40)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			181.5
Root			$-0.428316 + 1.95360i$ of defining polynomial
Character	$\chi$	$=$	360.181
Dual form			360.4.k.c.181.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.52528 - 2.38191i) q^{2} +(-3.34703 + 7.26618i) q^{4} -5.00000i q^{5} +5.13620 q^{7} +(22.4126 - 3.11063i) q^{8} +(-11.9096 + 7.62641i) q^{10} +31.3403i q^{11} +4.75340i q^{13} +(-7.83414 - 12.2340i) q^{14} +(-41.5948 - 48.6403i) q^{16} -108.154 q^{17} -89.8913i q^{19} +(36.3309 + 16.7352i) q^{20} +(74.6499 - 47.8028i) q^{22} +68.5157 q^{23} -25.0000 q^{25} +(11.3222 - 7.25027i) q^{26} +(-17.1910 + 37.3205i) q^{28} -16.5719i q^{29} -300.523 q^{31} +(-52.4132 + 173.265i) q^{32} +(164.966 + 257.614i) q^{34} -25.6810i q^{35} +327.879i q^{37} +(-214.113 + 137.109i) q^{38} +(-15.5532 - 112.063i) q^{40} +73.4968 q^{41} -0.836008i q^{43} +(-227.724 - 104.897i) q^{44} +(-104.506 - 163.198i) q^{46} -228.335 q^{47} -316.619 q^{49} +(38.1320 + 59.5479i) q^{50} +(-34.5391 - 15.9098i) q^{52} +647.393i q^{53} +156.702 q^{55} +(115.115 - 15.9768i) q^{56} +(-39.4728 + 25.2768i) q^{58} +753.676i q^{59} -290.838i q^{61} +(458.383 + 715.821i) q^{62} +(492.648 - 139.435i) q^{64} +23.7670 q^{65} +801.801i q^{67} +(361.995 - 785.868i) q^{68} +(-61.1699 + 39.1707i) q^{70} -767.674 q^{71} -48.3194 q^{73} +(780.980 - 500.108i) q^{74} +(653.166 + 300.869i) q^{76} +160.970i q^{77} +451.701 q^{79} +(-243.201 + 207.974i) q^{80} +(-112.103 - 175.063i) q^{82} -976.099i q^{83} +540.771i q^{85} +(-1.99130 + 1.27515i) q^{86} +(97.4881 + 702.417i) q^{88} +1204.25 q^{89} +24.4144i q^{91} +(-229.324 + 497.847i) q^{92} +(348.275 + 543.873i) q^{94} -449.456 q^{95} -559.147 q^{97} +(482.934 + 754.161i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 2 q^{2} + 16 q^{4} + 28 q^{7} + 40 q^{8} + 30 q^{10} - 68 q^{14} - 56 q^{16} - 20 q^{20} - 164 q^{22} - 604 q^{23} - 300 q^{25} + 308 q^{26} - 436 q^{28} - 264 q^{31} - 72 q^{32} - 180 q^{34} - 820 q^{38}+ \cdots + 7266 q^{98}+O(q^{100}) $ 12 * q - 2 * q^2 + 16 * q^4 + 28 * q^7 + 40 * q^8 + 30 * q^10 - 68 * q^14 - 56 * q^16 - 20 * q^20 - 164 * q^22 - 604 * q^23 - 300 * q^25 + 308 * q^26 - 436 * q^28 - 264 * q^31 - 72 * q^32 - 180 * q^34 - 820 * q^38 + 120 * q^40 - 40 * q^41 + 472 * q^44 - 1268 * q^46 + 940 * q^47 + 1308 * q^49 + 50 * q^50 + 1024 * q^52 + 440 * q^55 + 728 * q^56 - 360 * q^58 - 592 * q^62 - 2048 * q^64 + 2344 * q^68 + 1160 * q^70 + 1592 * q^71 + 432 * q^73 + 420 * q^74 + 2256 * q^76 + 2016 * q^79 - 1600 * q^80 + 88 * q^82 + 244 * q^86 + 4080 * q^88 + 424 * q^89 + 900 * q^92 + 292 * q^94 + 1520 * q^95 - 1584 * q^97 + 7266 * q^98

Character values

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

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

Coefficient data

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

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

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

$2$	−1.52528	−	2.38191i	−0.539269	−	0.842134i
$2$	−1.52528	−	2.38191i	−0.539269	−	0.842134i
$3$		0			0
$3$		0			0
$4$	−3.34703	+	7.26618i	−0.418379	+	0.908273i
$5$		−	5.00000i		−	0.447214i
$5$		−	5.00000i		−	0.447214i
$6$		0			0
$7$	5.13620			0.277328			0.138664	−	0.990339i	$-0.455719\pi$
$7$	5.13620			0.277328			0.138664	+	0.990339i	$0.455719\pi$
$8$	22.4126	−	3.11063i	0.990506	−	0.137472i
$9$		0			0
$10$	−11.9096	+	7.62641i	−0.376614	+	0.241168i
$11$			31.3403i			0.859042i	0.903057	+	0.429521i	$0.141318\pi$
$11$			31.3403i			0.859042i	−0.903057	+	0.429521i	$0.858682\pi$
$12$		0			0
$13$			4.75340i			0.101412i	0.998714	+	0.0507060i	$0.0161471\pi$
$13$			4.75340i			0.101412i	−0.998714	+	0.0507060i	$0.983853\pi$
$14$	−7.83414	−	12.2340i	−0.149555	−	0.233548i
$15$		0			0
$16$	−41.5948	−	48.6403i	−0.649918	−	0.760004i
$17$	−108.154			−1.54301			−0.771507	−	0.636221i	$-0.780497\pi$
$17$	−108.154			−1.54301			−0.771507	+	0.636221i	$0.780497\pi$
$18$		0			0
$19$		−	89.8913i		−	1.08539i	−0.839929	−	0.542697i	$-0.817403\pi$
$19$		−	89.8913i		−	1.08539i	0.839929	−	0.542697i	$-0.182597\pi$
$20$	36.3309	+	16.7352i	0.406192	+	0.187105i
$21$		0			0
$22$	74.6499	−	47.8028i	0.723428	−	0.463254i
$23$	68.5157			0.621152			0.310576	−	0.950548i	$-0.399478\pi$
$23$	68.5157			0.621152			0.310576	+	0.950548i	$0.399478\pi$
$24$		0			0
$25$	−25.0000			−0.200000
$26$	11.3222	−	7.25027i	0.0854025	−	0.0546883i
$27$		0			0
$28$	−17.1910	+	37.3205i	−0.116028	+	0.251890i
$29$		−	16.5719i		−	0.106115i	−0.998591	−	0.0530573i	$-0.983103\pi$
$29$		−	16.5719i		−	0.106115i	0.998591	−	0.0530573i	$-0.0168966\pi$
$30$		0			0
$31$	−300.523			−1.74115			−0.870574	−	0.492037i	$-0.836252\pi$
$31$	−300.523			−1.74115			−0.870574	+	0.492037i	$0.836252\pi$
$32$	−52.4132	+	173.265i	−0.289545	+	0.957164i
$33$		0			0
$34$	164.966	+	257.614i	0.832099	+	1.29942i
$35$		−	25.6810i		−	0.124025i
$36$		0			0
$37$			327.879i			1.45684i	0.685132	+	0.728419i	$0.259744\pi$
$37$			327.879i			1.45684i	−0.685132	+	0.728419i	$0.740256\pi$
$38$	−214.113	+	137.109i	−0.914046	+	0.585318i
$39$		0			0
$40$	−15.5532	−	112.063i	−0.0614792	−	0.442968i
$41$	73.4968			0.279958			0.139979	−	0.990154i	$-0.455297\pi$
$41$	73.4968			0.279958			0.139979	+	0.990154i	$0.455297\pi$
$42$		0			0
$43$		−	0.836008i		−	0.00296489i	−0.999999	−	0.00148244i	$-0.999528\pi$
$43$		−	0.836008i		−	0.00296489i	0.999999	−	0.00148244i	$-0.000471876\pi$
$44$	−227.724	−	104.897i	−0.780244	−	0.359405i
$45$		0			0
$46$	−104.506	−	163.198i	−0.334968	−	0.523093i
$47$	−228.335			−0.708639			−0.354319	−	0.935124i	$-0.615287\pi$
$47$	−228.335			−0.708639			−0.354319	+	0.935124i	$0.615287\pi$
$48$		0			0
$49$	−316.619			−0.923089
$50$	38.1320	+	59.5479i	0.107854	+	0.168427i
$51$		0			0
$52$	−34.5391	−	15.9098i	−0.0921097	−	0.0424286i
$53$			647.393i			1.67785i	0.544244	+	0.838927i	$0.316817\pi$
$53$			647.393i			1.67785i	−0.544244	+	0.838927i	$0.683183\pi$
$54$		0			0
$55$	156.702			0.384175
$56$	115.115	−	15.9768i	0.274695	−	0.0381248i
$57$		0			0
$58$	−39.4728	+	25.2768i	−0.0893627	+	0.0572243i
$59$			753.676i			1.66305i	0.555484	+	0.831527i	$0.312533\pi$
$59$			753.676i			1.66305i	−0.555484	+	0.831527i	$0.687467\pi$
$60$		0			0
$61$		−	290.838i		−	0.610459i	−0.952279	−	0.305229i	$-0.901267\pi$
$61$		−	290.838i		−	0.610459i	0.952279	−	0.305229i	$-0.0987331\pi$
$62$	458.383	+	715.821i	0.938946	+	1.46628i
$63$		0			0
$64$	492.648	−	139.435i	0.962203	−	0.272333i
$65$	23.7670			0.0453528
$66$		0			0
$67$			801.801i			1.46202i	0.682364	+	0.731012i	$0.260952\pi$
$67$			801.801i			1.46202i	−0.682364	+	0.731012i	$0.739048\pi$
$68$	361.995	−	785.868i	0.645565	−	1.40148i
$69$		0			0
$70$	−61.1699	+	39.1707i	−0.104446	+	0.0668828i
$71$	−767.674			−1.28318			−0.641592	−	0.767046i	$-0.721726\pi$
$71$	−767.674			−1.28318			−0.641592	+	0.767046i	$0.721726\pi$
$72$		0			0
$73$	−48.3194			−0.0774707			−0.0387353	−	0.999250i	$-0.512333\pi$
$73$	−48.3194			−0.0774707			−0.0387353	+	0.999250i	$0.512333\pi$
$74$	780.980	−	500.108i	1.22685	−	0.785627i
$75$		0			0
$76$	653.166	+	300.869i	0.985833	+	0.454106i
$77$			160.970i			0.238237i
$78$		0			0
$79$	451.701			0.643296			0.321648	−	0.946859i	$-0.395763\pi$
$79$	451.701			0.643296			0.321648	+	0.946859i	$0.395763\pi$
$80$	−243.201	+	207.974i	−0.339884	+	0.290652i
$81$		0			0
$82$	−112.103	−	175.063i	−0.150973	−	0.235762i
$83$		−	976.099i		−	1.29085i	−0.763822	−	0.645427i	$-0.776680\pi$
$83$		−	976.099i		−	1.29085i	0.763822	−	0.645427i	$-0.223320\pi$
$84$		0			0
$85$			540.771i			0.690057i
$86$	−1.99130	+	1.27515i	−0.00249683	+	0.00159887i
$87$		0			0
$88$	97.4881	+	702.417i	0.118094	+	0.850886i
$89$	1204.25			1.43428			0.717139	−	0.696930i	$-0.245451\pi$
$89$	1204.25			1.43428			0.717139	+	0.696930i	$0.245451\pi$
$90$		0			0
$91$			24.4144i			0.0281244i
$92$	−229.324	+	497.847i	−0.259877	+	0.564176i
$93$		0			0
$94$	348.275	+	543.873i	0.382147	+	0.596769i
$95$	−449.456			−0.485403
$96$		0			0
$97$	−559.147			−0.585287			−0.292643	−	0.956222i	$-0.594535\pi$
$97$	−559.147			−0.585287			−0.292643	+	0.956222i	$0.594535\pi$
$98$	482.934	+	754.161i	0.497793	+	0.777364i
$99$		0			0
$100$	83.6758	−	181.655i	0.0836758	−	0.181655i
$101$			542.070i			0.534039i	0.963691	+	0.267020i	$0.0860389\pi$
$101$			542.070i			0.534039i	−0.963691	+	0.267020i	$0.913961\pi$
$102$		0			0
$103$	−1764.97			−1.68842			−0.844212	−	0.536009i	$-0.819931\pi$
$103$	−1764.97			−1.68842			−0.844212	+	0.536009i	$0.819931\pi$
$104$	14.7861	+	106.536i	0.0139413	+	0.100449i
$105$		0			0
$106$	1542.03	−	987.457i	1.41298	−	0.904814i
$107$			442.840i			0.400103i	0.979785	+	0.200051i	$0.0641109\pi$
$107$			442.840i			0.400103i	−0.979785	+	0.200051i	$0.935889\pi$
$108$		0			0
$109$			1547.20i			1.35959i	0.733403	+	0.679795i	$0.237931\pi$
$109$			1547.20i			1.35959i	−0.733403	+	0.679795i	$0.762069\pi$
$110$	−239.014	−	373.250i	−0.207174	−	0.323527i
$111$		0			0
$112$	−213.639	−	249.826i	−0.180241	−	0.210771i
$113$	−788.524			−0.656444			−0.328222	−	0.944601i	$-0.606449\pi$
$113$	−788.524			−0.656444			−0.328222	+	0.944601i	$0.606449\pi$
$114$		0			0
$115$		−	342.578i		−	0.277788i
$116$	120.414	+	55.4667i	0.0963810	+	0.0443961i
$117$		0			0
$118$	1795.19	−	1149.57i	1.40051	−	0.896833i
$119$	−555.501			−0.427922
$120$		0			0
$121$	348.785			0.262047
$122$	−692.751	+	443.610i	−0.514088	+	0.329201i
$123$		0			0
$124$	1005.86	−	2183.66i	0.728460	−	1.58144i
$125$			125.000i			0.0894427i
$126$		0			0
$127$	−1543.92			−1.07875			−0.539374	−	0.842066i	$-0.681339\pi$
$127$	−1543.92			−1.07875			−0.539374	+	0.842066i	$0.681339\pi$
$128$	−1083.55	−	960.768i	−0.748227	−	0.663443i
$129$		0			0
$130$	−36.2514	−	56.6110i	−0.0244574	−	0.0381932i
$131$		−	1933.26i		−	1.28938i	−0.764442	−	0.644692i	$-0.776986\pi$
$131$		−	1933.26i		−	1.28938i	0.764442	−	0.644692i	$-0.223014\pi$
$132$		0			0
$133$		−	461.699i		−	0.301010i
$134$	1909.82	−	1222.97i	1.23122	−	0.788424i
$135$		0			0
$136$	−2424.02	+	336.428i	−1.52836	+	0.212121i
$137$	−478.247			−0.298244			−0.149122	−	0.988819i	$-0.547645\pi$
$137$	−478.247			−0.298244			−0.149122	+	0.988819i	$0.547645\pi$
$138$		0			0
$139$		−	2057.45i		−	1.25547i	−0.778427	−	0.627735i	$-0.783982\pi$
$139$		−	2057.45i		−	1.25547i	0.778427	−	0.627735i	$-0.216018\pi$
$140$	186.603	+	85.9550i	0.112649	+	0.0518895i
$141$		0			0
$142$	1170.92	+	1828.53i	0.691981	+	1.08061i
$143$	−148.973			−0.0871172
$144$		0			0
$145$	−82.8595			−0.0474559
$146$	73.7007	+	115.093i	0.0417775	+	0.0652407i
$147$		0			0
$148$	−2382.43	−	1097.42i	−1.32321	−	0.609510i
$149$		−	2838.89i		−	1.56088i	−0.625231	−	0.780440i	$-0.714995\pi$
$149$		−	2838.89i		−	1.56088i	0.625231	−	0.780440i	$-0.285005\pi$
$150$		0			0
$151$	−2187.09			−1.17869			−0.589346	−	0.807881i	$-0.700615\pi$
$151$	−2187.09			−1.17869			−0.589346	+	0.807881i	$0.700615\pi$
$152$	−279.619	−	2014.70i	−0.149211	−	1.07509i
$153$		0			0
$154$	383.417	−	245.525i	0.200627	−	0.128474i
$155$			1502.62i			0.778665i
$156$		0			0
$157$		−	936.231i		−	0.475920i	−0.971275	−	0.237960i	$-0.923521\pi$
$157$		−	936.231i		−	0.475920i	0.971275	−	0.237960i	$-0.0764787\pi$
$158$	−688.972	−	1075.91i	−0.346909	−	0.541741i
$159$		0			0
$160$	866.326	+	262.066i	0.428057	+	0.129488i
$161$	351.910			0.172263
$162$		0			0
$163$			2329.68i			1.11948i	0.828670	+	0.559738i	$0.189098\pi$
$163$			2329.68i			1.11948i	−0.828670	+	0.559738i	$0.810902\pi$
$164$	−245.996	+	534.041i	−0.117128	+	0.254278i
$165$		0			0
$166$	−2324.98	+	1488.83i	−1.08707	+	0.696117i
$167$	−2020.42			−0.936195			−0.468097	−	0.883677i	$-0.655060\pi$
$167$	−2020.42			−0.936195			−0.468097	+	0.883677i	$0.655060\pi$
$168$		0			0
$169$	2174.41			0.989716
$170$	1288.07	−	824.828i	0.581120	−	0.372126i
$171$		0			0
$172$	6.07459	+	2.79815i	0.00269292	+	0.00124045i
$173$			912.153i			0.400866i	0.979707	+	0.200433i	$0.0642348\pi$
$173$			912.153i			0.400866i	−0.979707	+	0.200433i	$0.935765\pi$
$174$		0			0
$175$	−128.405			−0.0554657
$176$	1524.40	−	1303.59i	0.652875	−	0.558307i
$177$		0			0
$178$	−1836.83	−	2868.43i	−0.773461	−	1.20785i
$179$		−	3226.95i		−	1.34745i	−0.738982	−	0.673726i	$-0.764693\pi$
$179$		−	3226.95i		−	1.34745i	0.738982	−	0.673726i	$-0.235307\pi$
$180$		0			0
$181$		−	1003.43i		−	0.412068i	−0.978545	−	0.206034i	$-0.933944\pi$
$181$		−	1003.43i		−	0.412068i	0.978545	−	0.206034i	$-0.0660557\pi$
$182$	58.1530	−	37.2388i	0.0236845	−	0.0151666i
$183$		0			0
$184$	1535.61	−	213.127i	0.615255	−	0.0853909i
$185$	1639.40			0.651517
$186$		0			0
$187$		−	3389.59i		−	1.32551i
$188$	764.243	−	1659.12i	0.296480	−	0.643637i
$189$		0			0
$190$	685.547	+	1070.57i	0.261762	+	0.408774i
$191$	−1272.08			−0.481907			−0.240953	−	0.970537i	$-0.577460\pi$
$191$	−1272.08			−0.481907			−0.240953	+	0.970537i	$0.577460\pi$
$192$		0			0
$193$	−730.914			−0.272603			−0.136301	−	0.990667i	$-0.543522\pi$
$193$	−730.914			−0.272603			−0.136301	+	0.990667i	$0.543522\pi$
$194$	852.857	+	1331.84i	0.315627	+	0.492890i
$195$		0			0
$196$	1059.74	−	2300.61i	0.386201	−	0.838416i
$197$			3582.02i			1.29547i	0.761864	+	0.647737i	$0.224284\pi$
$197$			3582.02i			1.29547i	−0.761864	+	0.647737i	$0.775716\pi$
$198$		0			0
$199$	2007.64			0.715166			0.357583	−	0.933881i	$-0.383601\pi$
$199$	2007.64			0.715166			0.357583	+	0.933881i	$0.383601\pi$
$200$	−560.315	+	77.7658i	−0.198101	+	0.0274944i
$201$		0			0
$202$	1291.16	−	826.809i	0.449733	−	0.287991i
$203$		−	85.1165i		−	0.0294286i
$204$		0			0
$205$		−	367.484i		−	0.125201i
$206$	2692.08	+	4204.01i	0.910514	+	1.42188i
$207$		0			0
$208$	231.207	−	197.717i	0.0770736	−	0.0659095i
$209$	2817.22			0.932398
$210$		0			0
$211$			1414.79i			0.461603i	0.973001	+	0.230802i	$0.0741349\pi$
$211$			1414.79i			0.461603i	−0.973001	+	0.230802i	$0.925865\pi$
$212$	−4704.07	−	2166.84i	−1.52395	−	0.701979i
$213$		0			0
$214$	1054.81	−	675.456i	0.336940	−	0.215763i
$215$	−4.18004			−0.00132594
$216$		0			0
$217$	−1543.55			−0.482870
$218$	3685.31	−	2359.92i	1.14496	−	0.733184i
$219$		0			0
$220$	−524.485	+	1138.62i	−0.160731	+	0.348936i
$221$		−	514.100i		−	0.156480i
$222$		0			0
$223$	1.69909			0.000510221			0.000255111	−	1.00000i	$-0.499919\pi$
$223$	1.69909			0.000510221			0.000255111		1.00000i	$0.499919\pi$
$224$	−269.205	+	889.924i	−0.0802990	+	0.265449i
$225$		0			0
$226$	1202.72	+	1878.20i	0.353999	+	0.552813i
$227$		−	3374.87i		−	0.986775i	−0.869810	−	0.493387i	$-0.835759\pi$
$227$		−	3374.87i		−	0.986775i	0.869810	−	0.493387i	$-0.164241\pi$
$228$		0			0
$229$			1330.69i			0.383994i	0.981396	+	0.191997i	$0.0614964\pi$
$229$			1330.69i			0.383994i	−0.981396	+	0.191997i	$0.938504\pi$
$230$	−815.992	+	522.528i	−0.233935	+	0.149802i
$231$		0			0
$232$	−51.5491	−	371.419i	−0.0145878	−	0.105107i
$233$	4373.02			1.22955			0.614776	−	0.788701i	$-0.289246\pi$
$233$	4373.02			1.22955			0.614776	+	0.788701i	$0.289246\pi$
$234$		0			0
$235$			1141.67i			0.316913i
$236$	−5476.34	−	2522.58i	−1.51051	−	0.695787i
$237$		0			0
$238$	847.296	+	1323.16i	0.230765	+	0.360367i
$239$	−794.613			−0.215060			−0.107530	−	0.994202i	$-0.534294\pi$
$239$	−794.613			−0.215060			−0.107530	+	0.994202i	$0.534294\pi$
$240$		0			0
$241$	617.471			0.165041			0.0825204	−	0.996589i	$-0.473703\pi$
$241$	617.471			0.165041			0.0825204	+	0.996589i	$0.473703\pi$
$242$	−531.995	−	830.776i	−0.141314	−	0.220679i
$243$		0			0
$244$	2113.28	+	973.444i	0.554463	+	0.255403i
$245$			1583.10i			0.412818i
$246$		0			0
$247$	427.289			0.110072
$248$	−6735.51	+	934.817i	−1.72462	+	0.239359i
$249$		0			0
$250$	297.739	−	190.660i	0.0753227	−	0.0482336i
$251$		−	907.026i		−	0.228092i	−0.993475	−	0.114046i	$-0.963619\pi$
$251$		−	907.026i		−	0.228092i	0.993475	−	0.114046i	$-0.0363811\pi$
$252$		0			0
$253$			2147.30i			0.533596i
$254$	2354.92	+	3677.49i	0.581735	+	0.908450i
$255$		0			0
$256$	−635.751	+	4046.36i	−0.155213	+	0.987881i
$257$	4350.70			1.05599			0.527994	−	0.849248i	$-0.322944\pi$
$257$	4350.70			1.05599			0.527994	+	0.849248i	$0.322944\pi$
$258$		0			0
$259$			1684.05i			0.404022i
$260$	−79.5489	+	172.695i	−0.0189747	+	0.0411927i
$261$		0			0
$262$	−4604.85	+	2948.76i	−1.08583	+	0.695324i
$263$	−3606.18			−0.845499			−0.422750	−	0.906246i	$-0.638935\pi$
$263$	−3606.18			−0.845499			−0.422750	+	0.906246i	$0.638935\pi$
$264$		0			0
$265$	3236.96			0.750359
$266$	−1099.73	+	704.221i	−0.253491	+	0.162325i
$267$		0			0
$268$	−5826.03	−	2683.65i	−1.32792	−	0.611680i
$269$			6501.85i			1.47370i	0.676057	+	0.736849i	$0.263687\pi$
$269$			6501.85i			1.47370i	−0.676057	+	0.736849i	$0.736313\pi$
$270$		0			0
$271$	1011.82			0.226803			0.113401	−	0.993549i	$-0.463825\pi$
$271$	1011.82			0.226803			0.113401	+	0.993549i	$0.463825\pi$
$272$	4498.65	+	5260.65i	1.00283	+	1.17270i
$273$		0			0
$274$	729.461	+	1139.14i	0.160833	+	0.251161i
$275$		−	783.508i		−	0.171808i
$276$		0			0
$277$			2618.50i			0.567979i	0.958827	+	0.283990i	$0.0916582\pi$
$277$			2618.50i			0.567979i	−0.958827	+	0.283990i	$0.908342\pi$
$278$	−4900.66	+	3138.19i	−1.05727	+	0.677036i
$279$		0			0
$280$	−79.8840	−	575.577i	−0.0170499	−	0.122848i
$281$	−2302.29			−0.488766			−0.244383	−	0.969679i	$-0.578585\pi$
$281$	−2302.29			−0.488766			−0.244383	+	0.969679i	$0.578585\pi$
$282$		0			0
$283$		−	6591.42i		−	1.38452i	−0.721648	−	0.692260i	$-0.756615\pi$
$283$		−	6591.42i		−	1.38452i	0.721648	−	0.692260i	$-0.243385\pi$
$284$	2569.43	−	5578.06i	0.536857	−	1.16548i
$285$		0			0
$286$	227.226	+	354.841i	0.0469795	+	0.0733643i
$287$	377.494			0.0776403
$288$		0			0
$289$	6784.33			1.38089
$290$	126.384	+	197.364i	0.0255915	+	0.0399642i
$291$		0			0
$292$	161.727	−	351.098i	0.0324121	−	0.0703645i
$293$			4765.54i			0.950190i	0.879934	+	0.475095i	$0.157586\pi$
$293$			4765.54i			0.950190i	−0.879934	+	0.475095i	$0.842414\pi$
$294$		0			0
$295$	3768.38			0.743741
$296$	1019.91	+	7348.62i	0.200274	+	1.44301i
$297$		0			0
$298$	−6762.00	+	4330.11i	−1.31447	+	0.841733i
$299$			325.682i			0.0629923i
$300$		0			0
$301$		−	4.29390i		−	0.000822247i
$302$	3335.92	+	5209.45i	0.635632	+	0.992617i
$303$		0			0
$304$	−4372.34	+	3739.01i	−0.824903	+	0.705417i
$305$	−1454.19			−0.273005
$306$		0			0
$307$		−	117.958i		−	0.0219290i	−0.999940	−	0.0109645i	$-0.996510\pi$
$307$		−	117.958i		−	0.0219290i	0.999940	−	0.0109645i	$-0.00349018\pi$
$308$	−1169.64	−	538.771i	−0.216384	−	0.0996732i
$309$		0			0
$310$	3579.11	−	2291.91i	0.655740	−	0.419910i
$311$	−4085.06			−0.744832			−0.372416	−	0.928066i	$-0.621470\pi$
$311$	−4085.06			−0.744832			−0.372416	+	0.928066i	$0.621470\pi$
$312$		0			0
$313$	904.680			0.163372			0.0816861	−	0.996658i	$-0.473969\pi$
$313$	904.680			0.163372			0.0816861	+	0.996658i	$0.473969\pi$
$314$	−2230.02	+	1428.02i	−0.400788	+	0.256648i
$315$		0			0
$316$	−1511.86	+	3282.14i	−0.269141	+	0.584288i
$317$		−	5437.26i		−	0.963366i	−0.876346	−	0.481683i	$-0.840026\pi$
$317$		−	5437.26i		−	0.963366i	0.876346	−	0.481683i	$-0.159974\pi$
$318$		0			0
$319$	519.369			0.0911569
$320$	−697.173	−	2463.24i	−0.121791	−	0.430310i
$321$		0			0
$322$	−536.762	−	838.219i	−0.0928961	−	0.145069i
$323$			9722.12i			1.67478i
$324$		0			0
$325$		−	118.835i		−	0.0202824i
$326$	5549.10	−	3553.42i	0.942749	−	0.603698i
$327$		0			0
$328$	1647.25	−	228.621i	0.277300	−	0.0384863i
$329$	−1172.77			−0.196526
$330$		0			0
$331$		−	5944.03i		−	0.987049i	−0.869732	−	0.493525i	$-0.835708\pi$
$331$		−	5944.03i		−	0.987049i	0.869732	−	0.493525i	$-0.164292\pi$
$332$	7092.51	+	3267.03i	1.17245	+	0.540066i
$333$		0			0
$334$	3081.71	+	4812.46i	0.504860	+	0.788401i
$335$	4009.01			0.653837
$336$		0			0
$337$	5636.91			0.911164			0.455582	−	0.890194i	$-0.349431\pi$
$337$	5636.91			0.911164			0.455582	+	0.890194i	$0.349431\pi$
$338$	−3316.58	−	5179.25i	−0.533722	−	0.833473i
$339$		0			0
$340$	−3929.34	−	1809.98i	−0.626760	−	0.288705i
$341$		−	9418.50i		−	1.49572i
$342$		0			0
$343$	−3387.93			−0.533327
$344$	−2.60051	−	18.7371i	−0.000407588	−	0.00293674i
$345$		0			0
$346$	2172.67	−	1391.29i	0.337582	−	0.216174i
$347$		−	7761.12i		−	1.20069i	−0.799742	−	0.600344i	$-0.795030\pi$
$347$		−	7761.12i		−	1.20069i	0.799742	−	0.600344i	$-0.204970\pi$
$348$		0			0
$349$		−	8709.62i		−	1.33586i	−0.744224	−	0.667930i	$-0.767181\pi$
$349$		−	8709.62i		−	1.33586i	0.744224	−	0.667930i	$-0.232819\pi$
$350$	195.854	+	305.849i	0.0299109	+	0.0467095i
$351$		0			0
$352$	−5430.19	−	1642.65i	−0.822244	−	0.248731i
$353$	986.323			0.148716			0.0743579	−	0.997232i	$-0.476309\pi$
$353$	986.323			0.148716			0.0743579	+	0.997232i	$0.476309\pi$
$354$		0			0
$355$			3838.37i			0.573858i
$356$	−4030.68	+	8750.33i	−0.600072	+	1.30272i
$357$		0			0
$358$	−7686.32	+	4922.01i	−1.13473	+	0.726638i
$359$	11470.1			1.68626			0.843131	−	0.537708i	$-0.180710\pi$
$359$	11470.1			1.68626			0.843131	+	0.537708i	$0.180710\pi$
$360$		0			0
$361$	−1221.44			−0.178078
$362$	−2390.08	+	1530.51i	−0.347016	+	0.222215i
$363$		0			0
$364$	−177.399	−	81.7157i	−0.0255447	−	0.0117667i
$365$			241.597i			0.0346459i
$366$		0			0
$367$	3330.42			0.473697			0.236848	−	0.971547i	$-0.423886\pi$
$367$	3330.42			0.473697			0.236848	+	0.971547i	$0.423886\pi$
$368$	−2849.89	−	3332.62i	−0.403698	−	0.472078i
$369$		0			0
$370$	−2500.54	−	3904.90i	−0.351343	−	0.548665i
$371$			3325.14i			0.465317i
$372$		0			0
$373$			9398.88i			1.30471i	0.757915	+	0.652354i	$0.226218\pi$
$373$			9398.88i			1.30471i	−0.757915	+	0.652354i	$0.773782\pi$
$374$	−8073.70	+	5170.07i	−1.11626	+	0.714808i
$375$		0			0
$376$	−5117.57	+	710.265i	−0.701911	+	0.0974178i
$377$	78.7729			0.0107613
$378$		0			0
$379$			3840.58i			0.520521i	0.965538	+	0.260260i	$0.0838084\pi$
$379$			3840.58i			0.520521i	−0.965538	+	0.260260i	$0.916192\pi$
$380$	1504.34	−	3265.83i	0.203082	−	0.440878i
$381$		0			0
$382$	1940.27	+	3029.98i	0.259877	+	0.405830i
$383$	2969.97			0.396236			0.198118	−	0.980178i	$-0.436517\pi$
$383$	2969.97			0.396236			0.198118	+	0.980178i	$0.436517\pi$
$384$		0			0
$385$	804.850			0.106543
$386$	1114.85	+	1740.98i	0.147006	+	0.229568i
$387$		0			0
$388$	1871.48	−	4062.86i	0.244872	−	0.531600i
$389$			8349.10i			1.08822i	0.839015	+	0.544108i	$0.183132\pi$
$389$			8349.10i			1.08822i	−0.839015	+	0.544108i	$0.816868\pi$
$390$		0			0
$391$	−7410.26			−0.958447
$392$	−7096.26	+	984.886i	−0.914325	+	0.126899i
$393$		0			0
$394$	8532.06	−	5463.59i	1.09096	−	0.698608i
$395$		−	2258.51i		−	0.287691i
$396$		0			0
$397$			4506.27i			0.569680i	0.958575	+	0.284840i	$0.0919405\pi$
$397$			4506.27i			0.569680i	−0.958575	+	0.284840i	$0.908060\pi$
$398$	−3062.22	−	4782.03i	−0.385666	−	0.602265i
$399$		0			0
$400$	1039.87	+	1216.01i	0.129984	+	0.152001i
$401$	7654.44			0.953228			0.476614	−	0.879113i	$-0.341864\pi$
$401$	7654.44			0.953228			0.476614	+	0.879113i	$0.341864\pi$
$402$		0			0
$403$		−	1428.51i		−	0.176573i
$404$	−3938.78	−	1814.32i	−0.485053	−	0.223431i
$405$		0			0
$406$	−202.740	+	129.827i	−0.0247828	+	0.0158699i
$407$	−10275.8			−1.25148
$408$		0			0
$409$	2603.53			0.314758			0.157379	−	0.987538i	$-0.449696\pi$
$409$	2603.53			0.314758			0.157379	+	0.987538i	$0.449696\pi$
$410$	−875.316	+	560.517i	−0.105436	+	0.0675170i
$411$		0			0
$412$	5907.41	−	12824.6i	0.706401	−	1.53355i
$413$			3871.03i			0.461212i
$414$		0			0
$415$	−4880.50			−0.577287
$416$	−823.599	−	249.141i	−0.0970680	−	0.0293633i
$417$		0			0
$418$	−4297.05	−	6710.38i	−0.502813	−	0.785204i
$419$		−	525.993i		−	0.0613280i	−0.999530	−	0.0306640i	$-0.990238\pi$
$419$		−	525.993i		−	0.0613280i	0.999530	−	0.0306640i	$-0.00976219\pi$
$420$		0			0
$421$		−	15126.1i		−	1.75107i	−0.483157	−	0.875534i	$-0.660510\pi$
$421$		−	15126.1i		−	1.75107i	0.483157	−	0.875534i	$-0.339490\pi$
$422$	3369.91	−	2157.96i	0.388732	−	0.248928i
$423$		0			0
$424$	2013.80	+	14509.7i	0.230658	+	1.66192i
$425$	2703.86			0.308603
$426$		0			0
$427$		−	1493.80i		−	0.169298i
$428$	−3217.76	−	1482.20i	−0.363402	−	0.167394i
$429$		0			0
$430$	6.37574	+	9.95650i	0.000715036	+	0.00111662i
$431$	−4887.92			−0.546271			−0.273135	−	0.961976i	$-0.588061\pi$
$431$	−4887.92			−0.546271			−0.273135	+	0.961976i	$0.588061\pi$
$432$		0			0
$433$	−6944.15			−0.770704			−0.385352	−	0.922770i	$-0.625920\pi$
$433$	−6944.15			−0.770704			−0.385352	+	0.922770i	$0.625920\pi$
$434$	2354.34	+	3676.60i	0.260397	+	0.406641i
$435$		0			0
$436$	−11242.3	−	5178.54i	−1.23488	−	0.568823i
$437$		−	6158.96i		−	0.674195i
$438$		0			0
$439$	577.528			0.0627879			0.0313940	−	0.999507i	$-0.490005\pi$
$439$	577.528			0.0627879			0.0313940	+	0.999507i	$0.490005\pi$
$440$	3512.09	−	487.441i	0.380528	−	0.0528132i
$441$		0			0
$442$	−1224.54	+	784.148i	−0.131777	+	0.0843848i
$443$			7039.42i			0.754973i	0.926015	+	0.377486i	$0.123211\pi$
$443$			7039.42i			0.754973i	−0.926015	+	0.377486i	$0.876789\pi$
$444$		0			0
$445$		−	6021.27i		−	0.641429i
$446$	−2.59159	−	4.04708i	−0.000275146	−	0.000429674i
$447$		0			0
$448$	2530.34	−	716.163i	0.266846	−	0.0755257i
$449$	−6396.99			−0.672366			−0.336183	−	0.941797i	$-0.609136\pi$
$449$	−6396.99			−0.672366			−0.336183	+	0.941797i	$0.609136\pi$
$450$		0			0
$451$			2303.41i			0.240496i
$452$	2639.22	−	5729.56i	0.274642	−	0.596230i
$453$		0			0
$454$	−8038.65	+	5147.62i	−0.830996	+	0.532136i
$455$	122.072			0.0125776
$456$		0			0
$457$	−7015.85			−0.718135			−0.359068	−	0.933312i	$-0.616905\pi$
$457$	−7015.85			−0.718135			−0.359068	+	0.933312i	$0.616905\pi$
$458$	3169.60	−	2029.68i	0.323374	−	0.207076i
$459$		0			0
$460$	2489.24	+	1146.62i	0.252307	+	0.116221i
$461$		−	13374.1i		−	1.35118i	−0.737279	−	0.675588i	$-0.763890\pi$
$461$		−	13374.1i		−	1.35118i	0.737279	−	0.675588i	$-0.236110\pi$
$462$		0			0
$463$	15414.3			1.54722			0.773611	−	0.633661i	$-0.218449\pi$
$463$	15414.3			1.54722			0.773611	+	0.633661i	$0.218449\pi$
$464$	−806.062	+	689.304i	−0.0806476	+	0.0689658i
$465$		0			0
$466$	−6670.08	−	10416.1i	−0.663059	−	1.03545i
$467$		−	1796.43i		−	0.178006i	−0.996031	−	0.0890032i	$-0.971632\pi$
$467$		−	1796.43i		−	0.178006i	0.996031	−	0.0890032i	$-0.0283681\pi$
$468$		0			0
$469$			4118.21i			0.405461i
$470$	2719.37	−	1741.37i	0.266883	−	0.170901i
$471$		0			0
$472$	2344.41	+	16891.8i	0.228623	+	1.64727i
$473$	26.2008			0.00254696
$474$		0			0
$475$			2247.28i			0.217079i
$476$	1859.28	−	4036.37i	0.179033	−	0.388670i
$477$		0			0
$478$	1212.01	+	1892.70i	0.115975	+	0.181109i
$479$	−11789.0			−1.12454			−0.562270	−	0.826954i	$-0.690072\pi$
$479$	−11789.0			−1.12454			−0.562270	+	0.826954i	$0.690072\pi$
$480$		0			0
$481$	−1558.54			−0.147741
$482$	−941.818	−	1470.76i	−0.0890013	−	0.138986i
$483$		0			0
$484$	−1167.39	+	2534.33i	−0.109635	+	0.238010i
$485$			2795.74i			0.261748i
$486$		0			0
$487$	18083.0			1.68258			0.841291	−	0.540582i	$-0.181796\pi$
$487$	18083.0			1.68258			0.841291	+	0.540582i	$0.181796\pi$
$488$	−904.690	−	6518.43i	−0.0839208	−	0.604663i
$489$		0			0
$490$	3770.80	−	2414.67i	0.347648	−	0.222620i
$491$		−	11259.2i		−	1.03487i	−0.855722	−	0.517435i	$-0.826887\pi$
$491$		−	11259.2i		−	1.03487i	0.855722	−	0.517435i	$-0.173113\pi$
$492$		0			0
$493$			1792.32i			0.163736i
$494$	−651.736	−	1017.77i	−0.0593583	−	0.0926953i
$495$		0			0
$496$	12500.2	+	14617.5i	1.13160	+	1.32328i
$497$	−3942.92			−0.355864
$498$		0			0
$499$		−	4589.82i		−	0.411761i	−0.978577	−	0.205880i	$-0.933994\pi$
$499$		−	4589.82i		−	0.411761i	0.978577	−	0.205880i	$-0.0660058\pi$
$500$	−908.273	−	418.379i	−0.0812384	−	0.0374209i
$501$		0			0
$502$	−2160.46	+	1383.47i	−0.192084	+	0.123003i
$503$	5257.43			0.466038			0.233019	−	0.972472i	$-0.425140\pi$
$503$	5257.43			0.466038			0.233019	+	0.972472i	$0.425140\pi$
$504$		0			0
$505$	2710.35			0.238830
$506$	5114.69	−	3275.24i	0.449359	−	0.287751i
$507$		0			0
$508$	5167.56	−	11218.4i	0.451325	−	0.979797i
$509$		−	2451.99i		−	0.213522i	−0.994285	−	0.106761i	$-0.965952\pi$
$509$		−	2451.99i		−	0.213522i	0.994285	−	0.106761i	$-0.0340479\pi$
$510$		0			0
$511$	−248.178			−0.0214848
$512$	10607.8	−	4657.54i	0.915629	−	0.402023i
$513$		0			0
$514$	−6636.04	−	10363.0i	−0.569461	−	0.889283i
$515$			8824.85i			0.755086i
$516$		0			0
$517$		−	7156.08i		−	0.608750i
$518$	4011.26	−	2568.65i	0.340241	−	0.217877i
$519$		0			0
$520$	532.680	−	73.9304i	0.0449222	−	0.00623473i
$521$	−10677.6			−0.897878			−0.448939	−	0.893562i	$-0.648198\pi$
$521$	−10677.6			−0.897878			−0.448939	+	0.893562i	$0.648198\pi$
$522$		0			0
$523$			19565.8i			1.63585i	0.575323	+	0.817927i	$0.304876\pi$
$523$			19565.8i			1.63585i	−0.575323	+	0.817927i	$0.695124\pi$
$524$	14047.4	+	6470.67i	1.17111	+	0.539451i
$525$		0			0
$526$	5500.43	+	8589.60i	0.455951	+	0.712024i
$527$	32502.9			2.68662
$528$		0			0
$529$	−7472.60			−0.614170
$530$	−4937.28	−	7710.17i	−0.404645	−	0.631903i
$531$		0			0
$532$	3354.79	+	1545.32i	0.273400	+	0.125936i
$533$			349.360i			0.0283911i
$534$		0			0
$535$	2214.20			0.178931
$536$	2494.11	+	17970.4i	0.200987	+	1.44814i
$537$		0			0
$538$	15486.9	−	9917.16i	1.24105	−	0.794719i
$539$		−	9922.95i		−	0.792972i
$540$		0			0
$541$		−	3313.01i		−	0.263286i	−0.991297	−	0.131643i	$-0.957975\pi$
$541$		−	3313.01i		−	0.263286i	0.991297	−	0.131643i	$-0.0420252\pi$
$542$	−1543.31	−	2410.07i	−0.122308	−	0.190998i
$543$		0			0
$544$	5668.71	−	18739.4i	0.446772	−	1.47692i
$545$	7736.02			0.608027
$546$		0			0
$547$		−	25040.9i		−	1.95735i	−0.205414	−	0.978675i	$-0.565854\pi$
$547$		−	25040.9i		−	1.95735i	0.205414	−	0.978675i	$-0.434146\pi$
$548$	1600.71	−	3475.03i	0.124779	−	0.270887i
$549$		0			0
$550$	−1866.25	+	1195.07i	−0.144686	+	0.0926508i
$551$	−1489.67			−0.115176
$552$		0			0
$553$	2320.03			0.178404
$554$	6237.04	−	3993.95i	0.478315	−	0.306293i
$555$		0			0
$556$	14949.8	+	6886.34i	1.14031	+	0.525263i
$557$			2708.11i			0.206008i	0.994681	+	0.103004i	$0.0328454\pi$
$557$			2708.11i			0.206008i	−0.994681	+	0.103004i	$0.967155\pi$
$558$		0			0
$559$	3.97388			0.000300675
$560$	−1249.13	+	1068.19i	−0.0942596	+	0.0806061i
$561$		0			0
$562$	3511.64	+	5483.86i	0.263576	+	0.411606i
$563$			9374.67i			0.701768i	0.936419	+	0.350884i	$0.114119\pi$
$563$			9374.67i			0.701768i	−0.936419	+	0.350884i	$0.885881\pi$
$564$		0			0
$565$			3942.62i			0.293571i
$566$	−15700.2	+	10053.8i	−1.16595	+	0.746628i
$567$		0			0
$568$	−17205.6	+	2387.95i	−1.27100	+	0.176402i
$569$	−12092.5			−0.890938			−0.445469	−	0.895297i	$-0.646963\pi$
$569$	−12092.5			−0.890938			−0.445469	+	0.895297i	$0.646963\pi$
$570$		0			0
$571$			10847.4i			0.795008i	0.917601	+	0.397504i	$0.130123\pi$
$571$			10847.4i			0.795008i	−0.917601	+	0.397504i	$0.869877\pi$
$572$	498.617	−	1082.47i	0.0364480	−	0.0791261i
$573$		0			0
$574$	−575.785	−	899.158i	−0.0418690	−	0.0653835i
$575$	−1712.89			−0.124230
$576$		0			0
$577$	−22325.8			−1.61080			−0.805402	−	0.592729i	$-0.798051\pi$
$577$	−22325.8			−1.61080			−0.805402	+	0.592729i	$0.798051\pi$
$578$	−10348.0	−	16159.7i	−0.744673	−	1.16290i
$579$		0			0
$580$	277.333	−	602.072i	0.0198546	−	0.0431029i
$581$		−	5013.44i		−	0.357990i
$582$		0			0
$583$	−20289.5			−1.44135
$584$	−1082.96	+	150.304i	−0.0767351	+	0.0106500i
$585$		0			0
$586$	11351.1	−	7268.79i	0.800187	−	0.512408i
$587$			281.244i			0.0197754i	0.999951	+	0.00988770i	$0.00314741\pi$
$587$			281.244i			0.0197754i	−0.999951	+	0.00988770i	$0.996853\pi$
$588$		0			0
$589$			27014.4i			1.88983i
$590$	−5747.84	−	8975.95i	−0.401076	−	0.626329i
$591$		0			0
$592$	15948.1	−	13638.1i	1.10720	−	0.946825i
$593$	934.658			0.0647248			0.0323624	−	0.999476i	$-0.489697\pi$
$593$	934.658			0.0647248			0.0323624	+	0.999476i	$0.489697\pi$
$594$		0			0
$595$			2777.51i			0.191372i
$596$	20627.9	+	9501.86i	1.41770	+	0.653039i
$597$		0			0
$598$	775.748	−	496.757i	0.0530480	−	0.0339698i
$599$	15278.2			1.04215			0.521077	−	0.853510i	$-0.325530\pi$
$599$	15278.2			1.04215			0.521077	+	0.853510i	$0.325530\pi$
$600$		0			0
$601$	10958.6			0.743780			0.371890	−	0.928277i	$-0.378710\pi$
$601$	10958.6			0.743780			0.371890	+	0.928277i	$0.378710\pi$
$602$	−10.2277	+	6.54941i	−0.000692442	+	0.000443412i
$603$		0			0
$604$	7320.24	−	15891.8i	0.493140	−	1.07057i
$605$		−	1743.92i		−	0.117191i
$606$		0			0
$607$	−24850.2			−1.66167			−0.830837	−	0.556515i	$-0.812138\pi$
$607$	−24850.2			−1.66167			−0.830837	+	0.556515i	$0.812138\pi$
$608$	15575.0	+	4711.49i	1.03890	+	0.314270i
$609$		0			0
$610$	2218.05	+	3463.76i	0.147223	+	0.229907i
$611$		−	1085.37i		−	0.0718645i
$612$		0			0
$613$		−	3961.58i		−	0.261022i	−0.991447	−	0.130511i	$-0.958338\pi$
$613$		−	3961.58i		−	0.261022i	0.991447	−	0.130511i	$-0.0416618\pi$
$614$	−280.965	+	179.919i	−0.0184671	+	0.0118256i
$615$		0			0
$616$	500.718	+	3607.75i	0.0327508	+	0.235975i
$617$	−20732.3			−1.35275			−0.676377	−	0.736555i	$-0.736451\pi$
$617$	−20732.3			−1.35275			−0.676377	+	0.736555i	$0.736451\pi$
$618$		0			0
$619$		−	7801.96i		−	0.506603i	−0.967387	−	0.253301i	$-0.918484\pi$
$619$		−	7801.96i		−	0.506603i	0.967387	−	0.253301i	$-0.0815164\pi$
$620$	−10918.3	−	5029.31i	−0.707240	−	0.325777i
$621$		0			0
$622$	6230.87	+	9730.27i	0.401664	+	0.627248i
$623$	6185.29			0.397766
$624$		0			0
$625$	625.000			0.0400000
$626$	−1379.89	−	2154.87i	−0.0881015	−	0.137581i
$627$		0			0
$628$	6802.82	+	3133.59i	0.432265	+	0.199115i
$629$		−	35461.5i		−	2.24792i
$630$		0			0
$631$	−9359.85			−0.590507			−0.295253	−	0.955419i	$-0.595404\pi$
$631$	−9359.85			−0.590507			−0.295253	+	0.955419i	$0.595404\pi$
$632$	10123.8	−	1405.08i	0.637188	−	0.0884350i
$633$		0			0
$634$	−12951.1	+	8293.36i	−0.811283	+	0.519513i
$635$			7719.61i			0.482431i
$636$		0			0
$637$		−	1505.02i		−	0.0936123i
$638$	−792.183	−	1237.09i	−0.0491581	−	0.0767663i
$639$		0			0
$640$	−4803.84	+	5417.74i	−0.296701	+	0.334617i
$641$	−19129.1			−1.17871			−0.589356	−	0.807873i	$-0.700619\pi$
$641$	−19129.1			−1.17871			−0.589356	+	0.807873i	$0.700619\pi$
$642$		0			0
$643$			11243.5i			0.689582i	0.938680	+	0.344791i	$0.112050\pi$
$643$			11243.5i			0.689582i	−0.938680	+	0.344791i	$0.887950\pi$
$644$	−1177.85	+	2557.04i	−0.0720713	+	0.156462i
$645$		0			0
$646$	23157.3	−	14829.0i	1.41039	−	0.903155i
$647$	−11887.6			−0.722331			−0.361166	−	0.932502i	$-0.617621\pi$
$647$	−11887.6			−0.722331			−0.361166	+	0.932502i	$0.617621\pi$
$648$		0			0
$649$	−23620.4			−1.42863
$650$	−283.055	+	181.257i	−0.0170805	+	0.0109377i
$651$		0			0
$652$	−16927.9	−	7797.51i	−1.01679	−	0.468365i
$653$			5327.46i			0.319264i	0.987177	+	0.159632i	$0.0510308\pi$
$653$			5327.46i			0.319264i	−0.987177	+	0.159632i	$0.948969\pi$
$654$		0			0
$655$	−9666.28			−0.576630
$656$	−3057.08	−	3574.91i	−0.181950	−	0.212769i
$657$		0			0
$658$	1788.81	+	2793.44i	0.105980	+	0.165501i
$659$			26016.2i			1.53786i	0.639334	+	0.768929i	$0.279210\pi$
$659$			26016.2i			1.53786i	−0.639334	+	0.768929i	$0.720790\pi$
$660$		0			0
$661$		−	5961.64i		−	0.350803i	−0.984497	−	0.175401i	$-0.943878\pi$
$661$		−	5961.64i		−	0.350803i	0.984497	−	0.175401i	$-0.0561224\pi$
$662$	−14158.2	+	9066.32i	−0.831228	+	0.532285i
$663$		0			0
$664$	−3036.28	−	21876.9i	−0.177456	−	1.27860i
$665$	−2308.50			−0.134616
$666$		0			0
$667$		−	1135.43i		−	0.0659134i
$668$	6762.40	−	14680.7i	0.391684	−	0.850320i
$669$		0			0
$670$	−6114.87	−	9549.11i	−0.352594	−	0.550618i
$671$	9114.95			0.524410
$672$		0			0
$673$	17544.1			1.00487			0.502435	−	0.864615i	$-0.332438\pi$
$673$	17544.1			1.00487			0.502435	+	0.864615i	$0.332438\pi$
$674$	−8597.88	−	13426.6i	−0.491362	−	0.767322i
$675$		0			0
$676$	−7277.80	+	15799.6i	−0.414076	+	0.898932i
$677$			17000.0i			0.965088i	0.875872	+	0.482544i	$0.160287\pi$
$677$			17000.0i			0.965088i	−0.875872	+	0.482544i	$0.839713\pi$
$678$		0			0
$679$	−2871.89			−0.162317
$680$	1682.14	+	12120.1i	0.0948634	+	0.683505i
$681$		0			0
$682$	−22434.1	+	14365.9i	−1.25960	+	0.806594i
$683$			5386.68i			0.301780i	0.988551	+	0.150890i	$0.0482139\pi$
$683$			5386.68i			0.301780i	−0.988551	+	0.150890i	$0.951786\pi$
$684$		0			0
$685$			2391.23i			0.133379i
$686$	5167.55	+	8069.77i	0.287607	+	0.449133i
$687$		0			0
$688$	−40.6637	+	34.7736i	−0.00225333	+	0.00192693i
$689$	−3077.32			−0.170155
$690$		0			0
$691$			18049.0i			0.993658i	0.867849	+	0.496829i	$0.165502\pi$
$691$			18049.0i			0.993658i	−0.867849	+	0.496829i	$0.834498\pi$
$692$	−6627.87	−	3053.01i	−0.364095	−	0.167714i
$693$		0			0
$694$	−18486.3	+	11837.9i	−1.01114	+	0.647493i
$695$	−10287.2			−0.561464
$696$		0			0
$697$	−7948.99			−0.431979
$698$	−20745.6	+	13284.6i	−1.12497	+	0.720387i
$699$		0			0
$700$	429.775	−	933.013i	0.0232057	−	0.0503780i
$701$			7991.13i			0.430558i	0.976553	+	0.215279i	$0.0690660\pi$
$701$			7991.13i			0.430558i	−0.976553	+	0.215279i	$0.930934\pi$
$702$		0			0
$703$	29473.5			1.58124
$704$	4369.92	+	15439.7i	0.233946	+	0.826573i
$705$		0			0
$706$	−1504.42	−	2349.34i	−0.0801977	−	0.125239i
$707$			2784.18i			0.148104i
$708$		0			0
$709$		−	11306.8i		−	0.598920i	−0.954109	−	0.299460i	$-0.903194\pi$
$709$		−	11306.8i		−	0.598920i	0.954109	−	0.299460i	$-0.0968065\pi$
$710$	9142.67	−	5854.59i	0.483265	−	0.309463i
$711$		0			0
$712$	26990.5	−	3745.99i	1.42066	−	0.197173i
$713$	−20590.6			−1.08152
$714$		0			0
$715$			744.865i			0.0389600i
$716$	23447.6	+	10800.7i	1.22385	+	0.563745i
$717$		0			0
$718$	−17495.1	−	27320.8i	−0.909348	−	1.42006i
$719$	−30968.9			−1.60632			−0.803160	−	0.595763i	$-0.796850\pi$
$719$	−30968.9			−1.60632			−0.803160	+	0.595763i	$0.796850\pi$
$720$		0			0
$721$	−9065.23			−0.468248
$722$	1863.04	+	2909.36i	0.0960320	+	0.149966i
$723$		0			0
$724$	7291.09	+	3358.51i	0.374270	+	0.172400i
$725$			414.298i			0.0212229i
$726$		0			0
$727$	26520.2			1.35293			0.676466	−	0.736474i	$-0.263511\pi$
$727$	26520.2			1.35293			0.676466	+	0.736474i	$0.263511\pi$
$728$	75.9442	+	547.190i	0.00386632	+	0.0278574i
$729$		0			0
$730$	575.463	−	368.504i	0.0291765	−	0.0186835i
$731$			90.4178i			0.00457486i
$732$		0			0
$733$		−	15980.8i		−	0.805270i	−0.915361	−	0.402635i	$-0.868094\pi$
$733$		−	15980.8i		−	0.805270i	0.915361	−	0.402635i	$-0.131906\pi$
$734$	−5079.83	−	7932.78i	−0.255450	−	0.398916i
$735$		0			0
$736$	−3591.13	+	11871.4i	−0.179851	+	0.594545i
$737$	−25128.7			−1.25594
$738$		0			0
$739$		−	10163.8i		−	0.505927i	−0.967476	−	0.252964i	$-0.918595\pi$
$739$		−	10163.8i		−	0.505927i	0.967476	−	0.252964i	$-0.0814053\pi$
$740$	−5487.11	+	11912.1i	−0.272581	+	0.591755i
$741$		0			0
$742$	7920.19	−	5071.77i	0.391859	−	0.250931i
$743$	37765.7			1.86472			0.932360	−	0.361530i	$-0.117746\pi$
$743$	37765.7			1.86472			0.932360	+	0.361530i	$0.117746\pi$
$744$		0			0
$745$	−14194.5			−0.698047
$746$	22387.3	−	14335.9i	1.09874	−	0.703588i
$747$		0			0
$748$	24629.3	+	11345.1i	1.20393	+	0.554567i
$749$			2274.51i			0.110960i
$750$		0			0
$751$	−20234.4			−0.983175			−0.491587	−	0.870828i	$-0.663583\pi$
$751$	−20234.4			−0.983175			−0.491587	+	0.870828i	$0.663583\pi$
$752$	9497.52	+	11106.3i	0.460557	+	0.538568i
$753$		0			0
$754$	−120.151	−	187.630i	−0.00580323	−	0.00906245i
$755$			10935.4i			0.527127i
$756$		0			0
$757$			27066.9i			1.29956i	0.760124	+	0.649778i	$0.225138\pi$
$757$			27066.9i			1.29956i	−0.760124	+	0.649778i	$0.774862\pi$
$758$	9147.94	−	5857.97i	0.438348	−	0.280701i
$759$		0			0
$760$	−10073.5	+	1398.09i	−0.480794	+	0.0667291i
$761$	30797.4			1.46702			0.733512	−	0.679677i	$-0.237880\pi$
$761$	30797.4			1.46702			0.733512	+	0.679677i	$0.237880\pi$
$762$		0			0
$763$			7946.74i			0.377053i
$764$	4257.68	−	9243.13i	0.201620	−	0.437703i
$765$		0			0
$766$	−4530.05	−	7074.22i	−0.213678	−	0.333684i
$767$	−3582.52			−0.168654
$768$		0			0
$769$	−35490.2			−1.66425			−0.832125	−	0.554588i	$-0.812876\pi$
$769$	−35490.2			−1.66425			−0.832125	+	0.554588i	$0.812876\pi$
$770$	−1227.62	−	1917.08i	−0.0574551	−	0.0897232i
$771$		0			0
$772$	2446.39	−	5310.96i	0.114051	−	0.247598i
$773$			37364.0i			1.73854i	0.494339	+	0.869269i	$0.335410\pi$
$773$			37364.0i			1.73854i	−0.494339	+	0.869269i	$0.664590\pi$
$774$		0			0
$775$	7513.09			0.348230
$776$	−12531.9	+	1739.30i	−0.579730	+	0.0804604i
$777$		0			0
$778$	19886.8	−	12734.7i	0.916424	−	0.586841i
$779$		−	6606.72i		−	0.303864i
$780$		0			0
$781$		−	24059.1i		−	1.10231i
$782$	11302.7	+	17650.6i	0.516860	+	0.807141i
$783$		0			0
$784$	13169.7	+	15400.5i	0.599932	+	0.701551i
$785$	−4681.16			−0.212838
$786$		0			0
$787$			28529.7i			1.29222i	0.763246	+	0.646108i	$0.223605\pi$
$787$			28529.7i			1.29222i	−0.763246	+	0.646108i	$0.776395\pi$
$788$	−26027.6	−	11989.1i	−1.17664	−	0.541999i
$789$		0			0
$790$	−5379.57	+	3444.86i	−0.242274	+	0.155142i
$791$	−4050.01			−0.182051
$792$		0			0
$793$	1382.47			0.0619078
$794$	10733.5	−	6873.33i	0.479747	−	0.307211i
$795$		0			0
$796$	−6719.64	+	14587.9i	−0.299210	+	0.649565i
$797$		−	7130.44i		−	0.316905i	−0.987367	−	0.158452i	$-0.949350\pi$
$797$		−	7130.44i		−	0.316905i	0.987367	−	0.158452i	$-0.0506504\pi$
$798$		0			0
$799$	24695.3			1.09344
$800$	1310.33	−	4331.63i	0.0579090	−	0.191433i
$801$		0			0
$802$	−11675.2	−	18232.2i	−0.514046	−	0.802745i
$803$		−	1514.35i		−	0.0665505i
$804$		0			0
$805$		−	1759.55i		−	0.0770385i
$806$	−3402.58	+	2178.88i	−0.148698	+	0.0952204i
$807$		0			0
$808$	1686.18	+	12149.2i	0.0734153	+	0.528969i
$809$	11060.3			0.480665			0.240333	−	0.970691i	$-0.422743\pi$
$809$	11060.3			0.480665			0.240333	+	0.970691i	$0.422743\pi$
$810$		0			0
$811$			27381.5i			1.18557i	0.805361	+	0.592784i	$0.201971\pi$
$811$			27381.5i			1.18557i	−0.805361	+	0.592784i	$0.798029\pi$
$812$	618.472	+	284.888i	0.0267292	+	0.0123123i
$813$		0			0
$814$	15673.5	+	24476.1i	0.674886	+	1.05392i
$815$	11648.4			0.500645
$816$		0			0
$817$	−75.1498			−0.00321807
$818$	−3971.11	−	6201.38i	−0.169739	−	0.265069i
$819$		0			0
$820$	2670.21	+	1229.98i	0.113717	+	0.0523815i
$821$		−	30033.9i		−	1.27672i	−0.769736	−	0.638362i	$-0.779612\pi$
$821$		−	30033.9i		−	1.27672i	0.769736	−	0.638362i	$-0.220388\pi$
$822$		0			0
$823$	3186.93			0.134981			0.0674906	−	0.997720i	$-0.478501\pi$
$823$	3186.93			0.134981			0.0674906	+	0.997720i	$0.478501\pi$
$824$	−39557.5	+	5490.17i	−1.67239	+	0.232111i
$825$		0			0
$826$	9220.45	−	5904.40i	0.388403	−	0.248717i
$827$		−	18326.0i		−	0.770563i	−0.922799	−	0.385282i	$-0.874104\pi$
$827$		−	18326.0i		−	0.770563i	0.922799	−	0.385282i	$-0.125896\pi$
$828$		0			0
$829$		−	4370.27i		−	0.183095i	−0.995801	−	0.0915475i	$-0.970819\pi$
$829$		−	4370.27i		−	0.183095i	0.995801	−	0.0915475i	$-0.0291813\pi$
$830$	7444.13	+	11624.9i	0.311313	+	0.486153i
$831$		0			0
$832$	662.788	+	2341.75i	0.0276179	+	0.0975789i
$833$	34243.7			1.42434
$834$		0			0
$835$			10102.1i			0.418679i
$836$	−9429.32	+	20470.4i	−0.390096	+	0.846872i
$837$		0			0
$838$	−1252.87	+	802.288i	−0.0516464	+	0.0330723i
$839$	29789.0			1.22578			0.612890	−	0.790168i	$-0.290007\pi$
$839$	29789.0			1.22578			0.612890	+	0.790168i	$0.290007\pi$
$840$		0			0
$841$	24114.4			0.988740
$842$	−36029.0	+	23071.5i	−1.47463	+	0.944296i
$843$		0			0
$844$	−10280.1	−	4735.35i	−0.419262	−	0.193125i
$845$		−	10872.0i		−	0.442614i
$846$		0			0
$847$	1791.43			0.0726732
$848$	31489.4	−	26928.2i	1.27518	−	1.09047i
$849$		0			0
$850$	−4124.14	−	6440.35i	−0.166420	−	0.259885i
$851$			22464.9i			0.904918i
$852$		0			0
$853$			39023.7i			1.56641i	0.621764	+	0.783205i	$0.286416\pi$
$853$			39023.7i			1.56641i	−0.621764	+	0.783205i	$0.713584\pi$
$854$	−3558.10	+	2278.47i	−0.142571	+	0.0912969i
$855$		0			0
$856$	1377.51	+	9925.19i	0.0550028	+	0.396304i
$857$	2749.52			0.109594			0.0547969	−	0.998498i	$-0.482549\pi$
$857$	2749.52			0.109594			0.0547969	+	0.998498i	$0.482549\pi$
$858$		0			0
$859$		−	48225.6i		−	1.91553i	−0.287559	−	0.957763i	$-0.592844\pi$
$859$		−	48225.6i		−	1.91553i	0.287559	−	0.957763i	$-0.407156\pi$
$860$	13.9907	−	30.3729i	0.000554744	−	0.00120431i
$861$		0			0
$862$	7455.45	+	11642.6i	0.294587	+	0.460033i
$863$	12421.1			0.489942			0.244971	−	0.969530i	$-0.421222\pi$
$863$	12421.1			0.489942			0.244971	+	0.969530i	$0.421222\pi$
$864$		0			0
$865$	4560.77			0.179273
$866$	10591.8	+	16540.4i	0.415616	+	0.649036i
$867$		0			0
$868$	5166.30	−	11215.7i	0.202023	−	0.438578i
$869$			14156.5i			0.552618i
$870$		0			0
$871$	−3811.28			−0.148267
$872$	4812.78	+	34676.8i	0.186905	+	1.34668i
$873$		0			0
$874$	−14670.1	+	9394.15i	−0.567762	+	0.363572i
$875$			642.024i			0.0248050i
$876$		0			0
$877$			38301.8i			1.47475i	0.675482	+	0.737377i	$0.263936\pi$
$877$			38301.8i			1.47475i	−0.675482	+	0.737377i	$0.736064\pi$
$878$	−880.892	−	1375.62i	−0.0338595	−	0.0528758i
$879$		0			0
$880$	−6517.96	−	7622.01i	−0.249682	−	0.291975i
$881$	−14792.0			−0.565671			−0.282836	−	0.959168i	$-0.591275\pi$
$881$	−14792.0			−0.565671			−0.282836	+	0.959168i	$0.591275\pi$
$882$		0			0
$883$			2064.99i			0.0787002i	0.999225	+	0.0393501i	$0.0125288\pi$
$883$			2064.99i			0.0787002i	−0.999225	+	0.0393501i	$0.987471\pi$
$884$	3735.55	+	1720.71i	0.142127	+	0.0654680i
$885$		0			0
$886$	16767.3	−	10737.1i	0.635788	−	0.407133i
$887$	−19268.8			−0.729406			−0.364703	−	0.931124i	$-0.618829\pi$
$887$	−19268.8			−0.729406			−0.364703	+	0.931124i	$0.618829\pi$
$888$		0			0
$889$	−7929.89			−0.299167
$890$	−14342.2	+	9184.14i	−0.540169	+	0.345902i
$891$		0			0
$892$	−5.68690	+	12.3459i	−0.000213466	+	0.000463420i
$893$			20525.3i			0.769152i
$894$		0			0
$895$	−16134.8			−0.602598
$896$	−5565.31	−	4934.69i	−0.207505	−	0.183992i
$897$		0			0
$898$	9757.21	+	15237.1i	0.362586	+	0.566223i
$899$			4980.24i			0.184761i
$900$		0			0
$901$		−	70018.3i		−	2.58895i
$902$	5486.53	−	3513.35i	0.202529	−	0.129692i
$903$		0			0
$904$	−17672.9	+	2452.81i	−0.650211	+	0.0902425i
$905$	−5017.14			−0.184282
$906$		0			0
$907$		−	46355.6i		−	1.69704i	−0.529165	−	0.848519i	$-0.677495\pi$
$907$		−	46355.6i		−	1.69704i	0.529165	−	0.848519i	$-0.322505\pi$
$908$	24522.4	+	11295.8i	0.896260	+	0.412846i
$909$		0			0
$910$	−186.194	−	290.765i	−0.00678272	−	0.0105920i
$911$	−23365.5			−0.849761			−0.424881	−	0.905249i	$-0.639684\pi$
$911$	−23365.5			−0.849761			−0.424881	+	0.905249i	$0.639684\pi$
$912$		0			0
$913$	30591.3			1.10890
$914$	10701.2	+	16711.2i	0.387268	+	0.604766i
$915$		0			0
$916$	−9669.05	−	4453.87i	−0.348771	−	0.160655i
$917$		−	9929.58i		−	0.357583i
$918$		0			0
$919$	−36178.5			−1.29860			−0.649302	−	0.760530i	$-0.724939\pi$
$919$	−36178.5			−1.29860			−0.649302	+	0.760530i	$0.724939\pi$
$920$	−1065.63	−	7678.07i	−0.0381880	−	0.275150i
$921$		0			0
$922$	−31855.9	+	20399.2i	−1.13787	+	0.728647i
$923$		−	3649.06i		−	0.130130i
$924$		0			0
$925$		−	8196.98i		−	0.291367i
$926$	−23511.2	−	36715.5i	−0.834368	−	1.30297i
$927$		0			0
$928$	2871.33	+	868.587i	0.101569	+	0.0307249i
$929$	−17014.6			−0.600895			−0.300447	−	0.953798i	$-0.597136\pi$
$929$	−17014.6			−0.600895			−0.300447	+	0.953798i	$0.597136\pi$
$930$		0			0
$931$			28461.3i			1.00191i
$932$	−14636.6	+	31775.1i	−0.514419	+	1.11677i
$933$		0			0
$934$	−4278.95	+	2740.07i	−0.149905	+	0.0959933i
$935$	−16947.9			−0.592788
$936$		0			0
$937$	16898.8			0.589179			0.294589	−	0.955624i	$-0.404817\pi$
$937$	16898.8			0.589179			0.294589	+	0.955624i	$0.404817\pi$
$938$	9809.22	−	6281.43i	0.341452	−	0.218652i
$939$		0			0
$940$	−8295.60	−	3821.22i	−0.287843	−	0.132590i
$941$		−	43995.9i		−	1.52415i	−0.647489	−	0.762074i	$-0.724181\pi$
$941$		−	43995.9i		−	1.52415i	0.647489	−	0.762074i	$-0.275819\pi$
$942$		0			0
$943$	5035.68			0.173897
$944$	36659.0	−	31349.0i	1.26393	−	1.08085i
$945$		0			0
$946$	−39.9635	−	62.4080i	−0.00137350	−	0.00214488i
$947$			2588.13i			0.0888099i	0.999014	+	0.0444050i	$0.0141392\pi$
$947$			2588.13i			0.0888099i	−0.999014	+	0.0444050i	$0.985861\pi$
$948$		0			0
$949$		−	229.681i		−	0.00785646i
$950$	5352.83	−	3427.74i	0.182809	−	0.117064i
$951$		0			0
$952$	−12450.2	+	1727.96i	−0.423859	+	0.0588272i
$953$	−7309.24			−0.248447			−0.124223	−	0.992254i	$-0.539644\pi$
$953$	−7309.24			−0.248447			−0.124223	+	0.992254i	$0.539644\pi$
$954$		0			0
$955$			6360.38i			0.215515i
$956$	2659.60	−	5773.80i	0.0899764	−	0.195333i
$957$		0			0
$958$	17981.6	+	28080.5i	0.606429	+	0.947013i
$959$	−2456.37			−0.0827115
$960$		0			0
$961$	60523.3			2.03160
$962$	2377.21	+	3712.31i	0.0796720	+	0.124418i
$963$		0			0
$964$	−2066.70	+	4486.66i	−0.0690496	+	0.149902i
$965$			3654.57i			0.121912i
$966$		0			0
$967$	27600.6			0.917866			0.458933	−	0.888471i	$-0.348232\pi$
$967$	27600.6			0.917866			0.458933	+	0.888471i	$0.348232\pi$
$968$	7817.17	−	1084.94i	0.259559	−	0.0360241i
$969$		0			0
$970$	6659.20	−	4264.29i	0.220427	−	0.141153i
$971$			22638.5i			0.748201i	0.927388	+	0.374100i	$0.122048\pi$
$971$			22638.5i			0.748201i	−0.927388	+	0.374100i	$0.877952\pi$
$972$		0			0
$973$		−	10567.5i		−	0.348178i
$974$	−27581.6	−	43072.1i	−0.907364	−	1.41696i
$975$		0			0
$976$	−14146.4	+	12097.3i	−0.463951	+	0.396748i
$977$	18390.3			0.602208			0.301104	−	0.953591i	$-0.402645\pi$
$977$	18390.3			0.602208			0.301104	+	0.953591i	$0.402645\pi$
$978$		0			0
$979$			37741.7i			1.23210i
$980$	−11503.1	−	5298.68i	−0.374951	−	0.172714i
$981$		0			0
$982$	−26818.5	+	17173.5i	−0.871499	+	0.558073i
$983$	−11139.1			−0.361425			−0.180712	−	0.983536i	$-0.557840\pi$
$983$	−11139.1			−0.361425			−0.180712	+	0.983536i	$0.557840\pi$
$984$		0			0
$985$	17910.1			0.579353
$986$	4269.15	−	2733.79i	0.137888	−	0.0882979i
$987$		0			0
$988$	−1430.15	+	3104.76i	−0.0460518	+	0.0999753i
$989$		−	57.2797i		−	0.00184165i
$990$		0			0
$991$	30232.3			0.969083			0.484542	−	0.874768i	$-0.338986\pi$
$991$	30232.3			0.969083			0.484542	+	0.874768i	$0.338986\pi$
$992$	15751.4	−	52070.3i	0.504141	−	1.66657i
$993$		0			0
$994$	6014.07	+	9391.70i	0.191906	+	0.299685i
$995$		−	10038.2i		−	0.319832i
$996$		0			0
$997$			9623.78i			0.305705i	0.988249	+	0.152853i	$0.0488460\pi$
$997$			9623.78i			0.305705i	−0.988249	+	0.152853i	$0.951154\pi$
$998$	−10932.6	+	7000.77i	−0.346758	+	0.222050i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	360.4.k.c.181.5		12
3.2	odd	2		40.4.d.a.21.8	yes	12
4.3	odd	2		1440.4.k.c.721.4		12
8.3	odd	2		1440.4.k.c.721.10		12
8.5	even	2	inner	360.4.k.c.181.6		12
12.11	even	2		160.4.d.a.81.5		12
15.2	even	4		200.4.f.c.149.2		12
15.8	even	4		200.4.f.b.149.11		12
15.14	odd	2		200.4.d.b.101.5		12
24.5	odd	2		40.4.d.a.21.7	✓	12
24.11	even	2		160.4.d.a.81.8		12
48.5	odd	4		1280.4.a.bc.1.4		6
48.11	even	4		1280.4.a.ba.1.3		6
48.29	odd	4		1280.4.a.bb.1.3		6
48.35	even	4		1280.4.a.bd.1.4		6
60.23	odd	4		800.4.f.c.49.8		12
60.47	odd	4		800.4.f.b.49.5		12
60.59	even	2		800.4.d.d.401.8		12
120.29	odd	2		200.4.d.b.101.6		12
120.53	even	4		200.4.f.c.149.1		12
120.59	even	2		800.4.d.d.401.5		12
120.77	even	4		200.4.f.b.149.12		12
120.83	odd	4		800.4.f.b.49.6		12
120.107	odd	4		800.4.f.c.49.7		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
40.4.d.a.21.7	✓	12	24.5	odd	2
40.4.d.a.21.8	yes	12	3.2	odd	2
160.4.d.a.81.5		12	12.11	even	2
160.4.d.a.81.8		12	24.11	even	2
200.4.d.b.101.5		12	15.14	odd	2
200.4.d.b.101.6		12	120.29	odd	2
200.4.f.b.149.11		12	15.8	even	4
200.4.f.b.149.12		12	120.77	even	4
200.4.f.c.149.1		12	120.53	even	4
200.4.f.c.149.2		12	15.2	even	4
360.4.k.c.181.5		12	1.1	even	1	trivial
360.4.k.c.181.6		12	8.5	even	2	inner
800.4.d.d.401.5		12	120.59	even	2
800.4.d.d.401.8		12	60.59	even	2
800.4.f.b.49.5		12	60.47	odd	4
800.4.f.b.49.6		12	120.83	odd	4
800.4.f.c.49.7		12	120.107	odd	4
800.4.f.c.49.8		12	60.23	odd	4
1280.4.a.ba.1.3		6	48.11	even	4
1280.4.a.bb.1.3		6	48.29	odd	4
1280.4.a.bc.1.4		6	48.5	odd	4
1280.4.a.bd.1.4		6	48.35	even	4
1440.4.k.c.721.4		12	4.3	odd	2
1440.4.k.c.721.10		12	8.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 360 = 2^{3} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	360.k (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.52528 - 2.38191i) q^{2} +(-3.34703 + 7.26618i) q^{4} -5.00000i q^{5} +5.13620 q^{7} +(22.4126 - 3.11063i) q^{8} +(-11.9096 + 7.62641i) q^{10} +31.3403i q^{11} +4.75340i q^{13} +(-7.83414 - 12.2340i) q^{14} +(-41.5948 - 48.6403i) q^{16} -108.154 q^{17} -89.8913i q^{19} +(36.3309 + 16.7352i) q^{20} +(74.6499 - 47.8028i) q^{22} +68.5157 q^{23} -25.0000 q^{25} +(11.3222 - 7.25027i) q^{26} +(-17.1910 + 37.3205i) q^{28} -16.5719i q^{29} -300.523 q^{31} +(-52.4132 + 173.265i) q^{32} +(164.966 + 257.614i) q^{34} -25.6810i q^{35} +327.879i q^{37} +(-214.113 + 137.109i) q^{38} +(-15.5532 - 112.063i) q^{40} +73.4968 q^{41} -0.836008i q^{43} +(-227.724 - 104.897i) q^{44} +(-104.506 - 163.198i) q^{46} -228.335 q^{47} -316.619 q^{49} +(38.1320 + 59.5479i) q^{50} +(-34.5391 - 15.9098i) q^{52} +647.393i q^{53} +156.702 q^{55} +(115.115 - 15.9768i) q^{56} +(-39.4728 + 25.2768i) q^{58} +753.676i q^{59} -290.838i q^{61} +(458.383 + 715.821i) q^{62} +(492.648 - 139.435i) q^{64} +23.7670 q^{65} +801.801i q^{67} +(361.995 - 785.868i) q^{68} +(-61.1699 + 39.1707i) q^{70} -767.674 q^{71} -48.3194 q^{73} +(780.980 - 500.108i) q^{74} +(653.166 + 300.869i) q^{76} +160.970i q^{77} +451.701 q^{79} +(-243.201 + 207.974i) q^{80} +(-112.103 - 175.063i) q^{82} -976.099i q^{83} +540.771i q^{85} +(-1.99130 + 1.27515i) q^{86} +(97.4881 + 702.417i) q^{88} +1204.25 q^{89} +24.4144i q^{91} +(-229.324 + 497.847i) q^{92} +(348.275 + 543.873i) q^{94} -449.456 q^{95} -559.147 q^{97} +(482.934 + 754.161i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 2 q^{2} + 16 q^{4} + 28 q^{7} + 40 q^{8} + 30 q^{10} - 68 q^{14} - 56 q^{16} - 20 q^{20} - 164 q^{22} - 604 q^{23} - 300 q^{25} + 308 q^{26} - 436 q^{28} - 264 q^{31} - 72 q^{32} - 180 q^{34} - 820 q^{38}+ \cdots + 7266 q^{98}+O(q^{100}) \) 12 * q - 2 * q^2 + 16 * q^4 + 28 * q^7 + 40 * q^8 + 30 * q^10 - 68 * q^14 - 56 * q^16 - 20 * q^20 - 164 * q^22 - 604 * q^23 - 300 * q^25 + 308 * q^26 - 436 * q^28 - 264 * q^31 - 72 * q^32 - 180 * q^34 - 820 * q^38 + 120 * q^40 - 40 * q^41 + 472 * q^44 - 1268 * q^46 + 940 * q^47 + 1308 * q^49 + 50 * q^50 + 1024 * q^52 + 440 * q^55 + 728 * q^56 - 360 * q^58 - 592 * q^62 - 2048 * q^64 + 2344 * q^68 + 1160 * q^70 + 1592 * q^71 + 432 * q^73 + 420 * q^74 + 2256 * q^76 + 2016 * q^79 - 1600 * q^80 + 88 * q^82 + 244 * q^86 + 4080 * q^88 + 424 * q^89 + 900 * q^92 + 292 * q^94 + 1520 * q^95 - 1584 * q^97 + 7266 * q^98

Introduction

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