LMFDB - Embedded newform 384.3.i.c.161.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [384,3,Mod(161,384)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(384, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3, 2]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("384.161");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 384 = 2^{7} \cdot 3 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	384.i (of order $4$, 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:	$10.4632421514$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 2 x^{18} + 6 x^{16} - 24 x^{14} - 24 x^{12} + 1216 x^{10} - 384 x^{8} - 6144 x^{6} + \cdots + 1048576 $ x^20 - 2x^18 + 6x^16 - 24x^14 - 24x^12 + 1216x^10 - 384x^8 - 6144x^6 + 24576x^4 - 131072*x^2 + 1048576
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{23} $
Twist minimal:	no (minimal twist has level 48)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			161.6
Root			$1.96139 - 0.391068i$ of defining polynomial
Character	$\chi$	$=$	384.161
Dual form			384.3.i.c.353.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.164573 - 2.99548i) q^{3} +(3.61305 + 3.61305i) q^{5} -12.2792i q^{7} +(-8.94583 + 0.985948i) q^{9} +O(q^{10})$	\(q+(-0.164573 - 2.99548i) q^{3} +(3.61305 + 3.61305i) q^{5} -12.2792i q^{7} +(-8.94583 + 0.985948i) q^{9} +(1.76932 + 1.76932i) q^{11} +(2.38826 + 2.38826i) q^{13} +(10.2282 - 11.4174i) q^{15} -20.0754i q^{17} +(-8.77090 - 8.77090i) q^{19} +(-36.7820 + 2.02081i) q^{21} +13.1821 q^{23} +1.10820i q^{25} +(4.42563 + 26.6348i) q^{27} +(6.51544 - 6.51544i) q^{29} -37.5922 q^{31} +(5.00877 - 5.59113i) q^{33} +(44.3652 - 44.3652i) q^{35} +(-10.0057 + 10.0057i) q^{37} +(6.76096 - 7.54704i) q^{39} -4.57407 q^{41} +(21.2835 - 21.2835i) q^{43} +(-35.8840 - 28.7594i) q^{45} -54.8366i q^{47} -101.778 q^{49} +(-60.1356 + 3.30386i) q^{51} +(-21.5215 - 21.5215i) q^{53} +12.7852i q^{55} +(-24.8296 + 27.7165i) q^{57} +(-53.6617 - 53.6617i) q^{59} +(19.2186 + 19.2186i) q^{61} +(12.1066 + 109.847i) q^{63} +17.2578i q^{65} +(31.5603 + 31.5603i) q^{67} +(-2.16941 - 39.4867i) q^{69} +65.1220 q^{71} +50.2451i q^{73} +(3.31960 - 0.182380i) q^{75} +(21.7257 - 21.7257i) q^{77} -20.9299 q^{79} +(79.0558 - 17.6403i) q^{81} +(-6.35791 + 6.35791i) q^{83} +(72.5334 - 72.5334i) q^{85} +(-20.5891 - 18.4446i) q^{87} +166.399 q^{89} +(29.3259 - 29.3259i) q^{91} +(6.18664 + 112.607i) q^{93} -63.3793i q^{95} +139.213 q^{97} +(-17.5725 - 14.0835i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 6 q^{3}+O(q^{10}) $ 20 * q - 6 * q^3	$ 20 q - 6 q^{3} - 92 q^{13} + 116 q^{15} - 52 q^{19} - 48 q^{21} + 18 q^{27} + 80 q^{31} + 60 q^{33} + 116 q^{37} + 172 q^{43} - 60 q^{45} - 364 q^{49} + 128 q^{51} + 244 q^{61} - 296 q^{63} + 356 q^{67} + 20 q^{69} - 146 q^{75} - 384 q^{79} - 188 q^{81} - 48 q^{85} + 136 q^{91} + 132 q^{93} + 472 q^{97} - 452 q^{99}+O(q^{100}) $ 20 * q - 6 * q^3 - 92 * q^13 + 116 * q^15 - 52 * q^19 - 48 * q^21 + 18 * q^27 + 80 * q^31 + 60 * q^33 + 116 * q^37 + 172 * q^43 - 60 * q^45 - 364 * q^49 + 128 * q^51 + 244 * q^61 - 296 * q^63 + 356 * q^67 + 20 * q^69 - 146 * q^75 - 384 * q^79 - 188 * q^81 - 48 * q^85 + 136 * q^91 + 132 * q^93 + 472 * q^97 - 452 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/384\mathbb{Z}\right)^\times$.

$n$	$127$	$133$	$257$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$-1$

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 $

$2$		0			0
$2$		0			0
$3$	−0.164573	−	2.99548i	−0.0548575	−	0.998494i
$3$	−0.164573	−	2.99548i	−0.0548575	−	0.998494i
$4$		0			0
$5$	3.61305	+	3.61305i	0.722609	+	0.722609i	0.969136	−	0.246527i	$-0.0792893\pi$
$5$	3.61305	+	3.61305i	0.722609	+	0.722609i	−0.246527	+	0.969136i	$0.579289\pi$
$6$		0			0
$7$		−	12.2792i		−	1.75417i	−0.480338	−	0.877083i	$-0.659486\pi$
$7$		−	12.2792i		−	1.75417i	0.480338	−	0.877083i	$-0.340514\pi$
$8$		0			0
$9$	−8.94583	+	0.985948i	−0.993981	+	0.109550i
$10$		0			0
$11$	1.76932	+	1.76932i	0.160847	+	0.160847i	0.782942	−	0.622095i	$-0.213718\pi$
$11$	1.76932	+	1.76932i	0.160847	+	0.160847i	−0.622095	+	0.782942i	$0.713718\pi$
$12$		0			0
$13$	2.38826	+	2.38826i	0.183713	+	0.183713i	0.792971	−	0.609259i	$-0.208533\pi$
$13$	2.38826	+	2.38826i	0.183713	+	0.183713i	−0.609259	+	0.792971i	$0.708533\pi$
$14$		0			0
$15$	10.2282	−	11.4174i	0.681881	−	0.761162i
$16$		0			0
$17$		−	20.0754i		−	1.18091i	−0.807072	−	0.590453i	$-0.798949\pi$
$17$		−	20.0754i		−	1.18091i	0.807072	−	0.590453i	$-0.201051\pi$
$18$		0			0
$19$	−8.77090	−	8.77090i	−0.461626	−	0.461626i	0.437562	−	0.899188i	$-0.355842\pi$
$19$	−8.77090	−	8.77090i	−0.461626	−	0.461626i	−0.899188	+	0.437562i	$0.855842\pi$
$20$		0			0
$21$	−36.7820	+	2.02081i	−1.75153	+	0.0962292i
$22$		0			0
$23$	13.1821			0.573134			0.286567	−	0.958060i	$-0.407486\pi$
$23$	13.1821			0.573134			0.286567	+	0.958060i	$0.407486\pi$
$24$		0			0
$25$			1.10820i			0.0443281i
$26$		0			0
$27$	4.42563	+	26.6348i	0.163912	+	0.986475i
$28$		0			0
$29$	6.51544	−	6.51544i	0.224670	−	0.224670i	−0.585792	−	0.810462i	$-0.699216\pi$
$29$	6.51544	−	6.51544i	0.224670	−	0.224670i	0.810462	+	0.585792i	$0.199216\pi$
$30$		0			0
$31$	−37.5922			−1.21265			−0.606326	−	0.795216i	$-0.707357\pi$
$31$	−37.5922			−1.21265			−0.606326	+	0.795216i	$0.707357\pi$
$32$		0			0
$33$	5.00877	−	5.59113i	0.151781	−	0.169428i
$34$		0			0
$35$	44.3652	−	44.3652i	1.26758	−	1.26758i
$36$		0			0
$37$	−10.0057	+	10.0057i	−0.270423	+	0.270423i	−0.829271	−	0.558847i	$-0.811244\pi$
$37$	−10.0057	+	10.0057i	−0.270423	+	0.270423i	0.558847	+	0.829271i	$0.311244\pi$
$38$		0			0
$39$	6.76096	−	7.54704i	0.173358	−	0.193514i
$40$		0			0
$41$	−4.57407			−0.111563			−0.0557814	−	0.998443i	$-0.517765\pi$
$41$	−4.57407			−0.111563			−0.0557814	+	0.998443i	$0.517765\pi$
$42$		0			0
$43$	21.2835	−	21.2835i	0.494966	−	0.494966i	−0.414901	−	0.909867i	$-0.636184\pi$
$43$	21.2835	−	21.2835i	0.494966	−	0.494966i	0.909867	+	0.414901i	$0.136184\pi$
$44$		0			0
$45$	−35.8840	−	28.7594i	−0.797422	−	0.639098i
$46$		0			0
$47$		−	54.8366i		−	1.16674i	−0.812208	−	0.583368i	$-0.801734\pi$
$47$		−	54.8366i		−	1.16674i	0.812208	−	0.583368i	$-0.198266\pi$
$48$		0			0
$49$	−101.778			−2.07710
$50$		0			0
$51$	−60.1356	+	3.30386i	−1.17913	+	0.0647816i
$52$		0			0
$53$	−21.5215	−	21.5215i	−0.406065	−	0.406065i	0.474299	−	0.880364i	$-0.342702\pi$
$53$	−21.5215	−	21.5215i	−0.406065	−	0.406065i	−0.880364	+	0.474299i	$0.842702\pi$
$54$		0			0
$55$			12.7852i			0.232459i
$56$		0			0
$57$	−24.8296	+	27.7165i	−0.435607	+	0.486255i
$58$		0			0
$59$	−53.6617	−	53.6617i	−0.909520	−	0.909520i	0.0867132	−	0.996233i	$-0.472364\pi$
$59$	−53.6617	−	53.6617i	−0.909520	−	0.909520i	−0.996233	+	0.0867132i	$0.972364\pi$
$60$		0			0
$61$	19.2186	+	19.2186i	0.315059	+	0.315059i	0.846866	−	0.531807i	$-0.178487\pi$
$61$	19.2186	+	19.2186i	0.315059	+	0.315059i	−0.531807	+	0.846866i	$0.678487\pi$
$62$		0			0
$63$	12.1066	+	109.847i	0.192169	+	1.74361i
$64$		0			0
$65$			17.2578i			0.265505i
$66$		0			0
$67$	31.5603	+	31.5603i	0.471049	+	0.471049i	0.902254	−	0.431205i	$-0.141911\pi$
$67$	31.5603	+	31.5603i	0.471049	+	0.471049i	−0.431205	+	0.902254i	$0.641911\pi$
$68$		0			0
$69$	−2.16941	−	39.4867i	−0.0314407	−	0.572271i
$70$		0			0
$71$	65.1220			0.917211			0.458606	−	0.888640i	$-0.348349\pi$
$71$	65.1220			0.917211			0.458606	+	0.888640i	$0.348349\pi$
$72$		0			0
$73$			50.2451i			0.688290i	0.938917	+	0.344145i	$0.111831\pi$
$73$			50.2451i			0.688290i	−0.938917	+	0.344145i	$0.888169\pi$
$74$		0			0
$75$	3.31960	−	0.182380i	0.0442614	−	0.00243173i
$76$		0			0
$77$	21.7257	−	21.7257i	0.282152	−	0.282152i
$78$		0			0
$79$	−20.9299			−0.264935			−0.132468	−	0.991187i	$-0.542290\pi$
$79$	−20.9299			−0.264935			−0.132468	+	0.991187i	$0.542290\pi$
$80$		0			0
$81$	79.0558	−	17.6403i	0.975998	−	0.217781i
$82$		0			0
$83$	−6.35791	+	6.35791i	−0.0766013	+	0.0766013i	−0.744369	−	0.667768i	$-0.767250\pi$
$83$	−6.35791	+	6.35791i	−0.0766013	+	0.0766013i	0.667768	+	0.744369i	$0.267250\pi$
$84$		0			0
$85$	72.5334	−	72.5334i	0.853334	−	0.853334i
$86$		0			0
$87$	−20.5891	−	18.4446i	−0.236657	−	0.212007i
$88$		0			0
$89$	166.399			1.86966			0.934828	−	0.355102i	$-0.115554\pi$
$89$	166.399			1.86966			0.934828	+	0.355102i	$0.115554\pi$
$90$		0			0
$91$	29.3259	−	29.3259i	0.322262	−	0.322262i
$92$		0			0
$93$	6.18664	+	112.607i	0.0665231	+	1.21083i
$94$		0			0
$95$		−	63.3793i		−	0.667151i
$96$		0			0
$97$	139.213			1.43519			0.717593	−	0.696463i	$-0.245244\pi$
$97$	139.213			1.43519			0.717593	+	0.696463i	$0.245244\pi$
$98$		0			0
$99$	−17.5725	−	14.0835i	−0.177500	−	0.142258i
$100$		0			0
$101$	125.879	+	125.879i	1.24632	+	1.24632i	0.957331	+	0.288994i	$0.0933207\pi$
$101$	125.879	+	125.879i	1.24632	+	1.24632i	0.288994	+	0.957331i	$0.406679\pi$
$102$		0			0
$103$			26.3937i			0.256250i	0.991758	+	0.128125i	$0.0408958\pi$
$103$			26.3937i			0.256250i	−0.991758	+	0.128125i	$0.959104\pi$
$104$		0			0
$105$	−140.196	−	125.594i	−1.33520	−	1.19613i
$106$		0			0
$107$	83.9534	+	83.9534i	0.784611	+	0.784611i	0.980605	−	0.195994i	$-0.0627933\pi$
$107$	83.9534	+	83.9534i	0.784611	+	0.784611i	−0.195994	+	0.980605i	$0.562793\pi$
$108$		0			0
$109$	−2.29518	−	2.29518i	−0.0210567	−	0.0210567i	0.696500	−	0.717557i	$-0.254740\pi$
$109$	−2.29518	−	2.29518i	−0.0210567	−	0.0210567i	−0.717557	+	0.696500i	$0.754740\pi$
$110$		0			0
$111$	31.6184	+	28.3251i	0.284851	+	0.255181i
$112$		0			0
$113$			177.630i			1.57195i	0.618260	+	0.785974i	$0.287838\pi$
$113$			177.630i			1.57195i	−0.618260	+	0.785974i	$0.712162\pi$
$114$		0			0
$115$	47.6275	+	47.6275i	0.414152	+	0.414152i
$116$		0			0
$117$	−23.7197	−	19.0103i	−0.202733	−	0.162481i
$118$		0			0
$119$	−246.509			−2.07151
$120$		0			0
$121$		−	114.739i		−	0.948257i
$122$		0			0
$123$	0.752766	+	13.7016i	0.00612005	+	0.111395i
$124$		0			0
$125$	86.3222	−	86.3222i	0.690577	−	0.690577i
$126$		0			0
$127$	152.167			1.19816			0.599082	−	0.800687i	$-0.295532\pi$
$127$	152.167			1.19816			0.599082	+	0.800687i	$0.295532\pi$
$128$		0			0
$129$	−67.2571	−	60.2517i	−0.521373	−	0.467068i
$130$		0			0
$131$	−65.6955	+	65.6955i	−0.501492	+	0.501492i	−0.911901	−	0.410409i	$-0.865386\pi$
$131$	−65.6955	+	65.6955i	−0.501492	+	0.501492i	0.410409	+	0.911901i	$0.365386\pi$
$132$		0			0
$133$	−107.699	+	107.699i	−0.809769	+	0.809769i
$134$		0			0
$135$	−80.2428	+	112.223i	−0.594391	+	0.831280i
$136$		0			0
$137$	53.1509			0.387963			0.193982	−	0.981005i	$-0.437860\pi$
$137$	53.1509			0.387963			0.193982	+	0.981005i	$0.437860\pi$
$138$		0			0
$139$	−161.324	+	161.324i	−1.16060	+	1.16060i	−0.176261	+	0.984343i	$0.556400\pi$
$139$	−161.324	+	161.324i	−1.16060	+	1.16060i	−0.984343	+	0.176261i	$0.943600\pi$
$140$		0			0
$141$	−164.262	+	9.02460i	−1.16498	+	0.0640043i
$142$		0			0
$143$			8.45118i			0.0590992i
$144$		0			0
$145$	47.0811			0.324698
$146$		0			0
$147$	16.7498	+	304.874i	0.113945	+	2.07397i
$148$		0			0
$149$	116.911	+	116.911i	0.784638	+	0.784638i	0.980610	−	0.195971i	$-0.0627859\pi$
$149$	116.911	+	116.911i	0.784638	+	0.784638i	−0.195971	+	0.980610i	$0.562786\pi$
$150$		0			0
$151$			10.9723i			0.0726643i	0.999340	+	0.0363321i	$0.0115674\pi$
$151$			10.9723i			0.0726643i	−0.999340	+	0.0363321i	$0.988433\pi$
$152$		0			0
$153$	19.7933	+	179.591i	0.129368	+	1.17380i
$154$		0			0
$155$	−135.822	−	135.822i	−0.876273	−	0.876273i
$156$		0			0
$157$	−49.8246	−	49.8246i	−0.317354	−	0.317354i	0.530396	−	0.847750i	$-0.322043\pi$
$157$	−49.8246	−	49.8246i	−0.317354	−	0.317354i	−0.847750	+	0.530396i	$0.822043\pi$
$158$		0			0
$159$	−60.9253	+	68.0090i	−0.383178	+	0.427730i
$160$		0			0
$161$		−	161.865i		−	1.00537i
$162$		0			0
$163$	−66.4240	−	66.4240i	−0.407509	−	0.407509i	0.473360	−	0.880869i	$-0.343041\pi$
$163$	−66.4240	−	66.4240i	−0.407509	−	0.407509i	−0.880869	+	0.473360i	$0.843041\pi$
$164$		0			0
$165$	38.2980	−	2.10410i	0.232109	−	0.0127521i
$166$		0			0
$167$	182.851			1.09492			0.547459	−	0.836832i	$-0.315595\pi$
$167$	182.851			1.09492			0.547459	+	0.836832i	$0.315595\pi$
$168$		0			0
$169$		−	157.592i		−	0.932499i
$170$		0			0
$171$	87.1106	+	69.8153i	0.509419	+	0.408277i
$172$		0			0
$173$	−123.809	+	123.809i	−0.715661	+	0.715661i	−0.967714	−	0.252052i	$-0.918894\pi$
$173$	−123.809	+	123.809i	−0.715661	+	0.715661i	0.252052	+	0.967714i	$0.418894\pi$
$174$		0			0
$175$	13.6078			0.0777589
$176$		0			0
$177$	−151.911	+	169.574i	−0.858257	+	0.958045i
$178$		0			0
$179$	168.642	−	168.642i	0.942134	−	0.942134i	−0.0562807	−	0.998415i	$-0.517924\pi$
$179$	168.642	−	168.642i	0.942134	−	0.942134i	0.998415	+	0.0562807i	$0.0179242\pi$
$180$		0			0
$181$	162.162	−	162.162i	0.895920	−	0.895920i	−0.0991520	−	0.995072i	$-0.531613\pi$
$181$	162.162	−	162.162i	0.895920	−	0.895920i	0.995072	+	0.0991520i	$0.0316130\pi$
$182$		0			0
$183$	54.4061	−	60.7318i	0.297301	−	0.331868i
$184$		0			0
$185$	−72.3018			−0.390821
$186$		0			0
$187$	35.5198	−	35.5198i	0.189945	−	0.189945i
$188$		0			0
$189$	327.053	−	54.3430i	1.73044	−	0.287529i
$190$		0			0
$191$		−	60.8777i		−	0.318731i	−0.987220	−	0.159366i	$-0.949055\pi$
$191$		−	60.8777i		−	0.318731i	0.987220	−	0.159366i	$-0.0509449\pi$
$192$		0			0
$193$	177.871			0.921611			0.460806	−	0.887501i	$-0.347561\pi$
$193$	177.871			0.921611			0.460806	+	0.887501i	$0.347561\pi$
$194$		0			0
$195$	51.6955	−	2.84016i	0.265105	−	0.0145649i
$196$		0			0
$197$	−66.9411	−	66.9411i	−0.339803	−	0.339803i	0.516490	−	0.856293i	$-0.327238\pi$
$197$	−66.9411	−	66.9411i	−0.339803	−	0.339803i	−0.856293	+	0.516490i	$0.827238\pi$
$198$		0			0
$199$			0.826328i			0.00415240i	0.999998	+	0.00207620i	$0.000660875\pi$
$199$			0.826328i			0.00415240i	−0.999998	+	0.00207620i	$0.999339\pi$
$200$		0			0
$201$	89.3443	−	99.7322i	0.444499	−	0.496180i
$202$		0			0
$203$	−80.0041	−	80.0041i	−0.394109	−	0.394109i
$204$		0			0
$205$	−16.5263	−	16.5263i	−0.0806162	−	0.0806162i
$206$		0			0
$207$	−117.925	+	12.9969i	−0.569685	+	0.0627868i
$208$		0			0
$209$		−	31.0370i		−	0.148502i
$210$		0			0
$211$	−181.344	−	181.344i	−0.859448	−	0.859448i	0.131825	−	0.991273i	$-0.457916\pi$
$211$	−181.344	−	181.344i	−0.859448	−	0.859448i	−0.991273	+	0.131825i	$0.957916\pi$
$212$		0			0
$213$	−10.7173	−	195.072i	−0.0503159	−	0.915830i
$214$		0			0
$215$	153.797			0.715333
$216$		0			0
$217$			461.601i			2.12719i
$218$		0			0
$219$	150.508	−	8.26897i	0.687253	−	0.0377579i
$220$		0			0
$221$	47.9454	−	47.9454i	0.216947	−	0.216947i
$222$		0			0
$223$	17.7339			0.0795241			0.0397621	−	0.999209i	$-0.487340\pi$
$223$	17.7339			0.0795241			0.0397621	+	0.999209i	$0.487340\pi$
$224$		0			0
$225$	−1.09263	−	9.91380i	−0.00485614	−	0.0440613i
$226$		0			0
$227$	7.53766	−	7.53766i	0.0332055	−	0.0332055i	−0.690309	−	0.723515i	$-0.742525\pi$
$227$	7.53766	−	7.53766i	0.0332055	−	0.0332055i	0.723515	+	0.690309i	$0.242525\pi$
$228$		0			0
$229$	−223.748	+	223.748i	−0.977063	+	0.977063i	−0.999743	−	0.0226794i	$-0.992780\pi$
$229$	−223.748	+	223.748i	−0.977063	+	0.977063i	0.0226794	+	0.999743i	$0.492780\pi$
$230$		0			0
$231$	−68.6545	−	61.5036i	−0.297205	−	0.266249i
$232$		0			0
$233$	−123.585			−0.530406			−0.265203	−	0.964193i	$-0.585439\pi$
$233$	−123.585			−0.530406			−0.265203	+	0.964193i	$0.585439\pi$
$234$		0			0
$235$	198.127	−	198.127i	0.843095	−	0.843095i
$236$		0			0
$237$	3.44448	+	62.6951i	0.0145337	+	0.264536i
$238$		0			0
$239$			118.501i			0.495820i	0.968783	+	0.247910i	$0.0797437\pi$
$239$			118.501i			0.495820i	−0.968783	+	0.247910i	$0.920256\pi$
$240$		0			0
$241$	−264.162			−1.09611			−0.548053	−	0.836443i	$-0.684631\pi$
$241$	−264.162			−1.09611			−0.548053	+	0.836443i	$0.684631\pi$
$242$		0			0
$243$	−65.8515	−	233.907i	−0.270994	−	0.962581i
$244$		0			0
$245$	−367.728	−	367.728i	−1.50093	−	1.50093i
$246$		0			0
$247$		−	41.8944i		−	0.169613i
$248$		0			0
$249$	20.0913	+	17.9987i	0.0806881	+	0.0722838i
$250$		0			0
$251$	152.477	+	152.477i	0.607478	+	0.607478i	0.942286	−	0.334808i	$-0.108672\pi$
$251$	152.477	+	152.477i	0.607478	+	0.607478i	−0.334808	+	0.942286i	$0.608672\pi$
$252$		0			0
$253$	23.3233	+	23.3233i	0.0921869	+	0.0921869i
$254$		0			0
$255$	−229.210	−	205.336i	−0.898861	−	0.805238i
$256$		0			0
$257$		−	113.118i		−	0.440147i	−0.975483	−	0.220074i	$-0.929370\pi$
$257$		−	113.118i		−	0.440147i	0.975483	−	0.220074i	$-0.0706298\pi$
$258$		0			0
$259$	122.861	+	122.861i	0.474367	+	0.474367i
$260$		0			0
$261$	−51.8621	+	64.7099i	−0.198705	+	0.247931i
$262$		0			0
$263$	−129.324			−0.491727			−0.245864	−	0.969304i	$-0.579072\pi$
$263$	−129.324			−0.491727			−0.245864	+	0.969304i	$0.579072\pi$
$264$		0			0
$265$		−	155.516i		−	0.586853i
$266$		0			0
$267$	−27.3848	−	498.446i	−0.102565	−	1.86684i
$268$		0			0
$269$	−129.457	+	129.457i	−0.481253	+	0.481253i	−0.905532	−	0.424278i	$-0.860528\pi$
$269$	−129.457	+	129.457i	−0.481253	+	0.481253i	0.424278	+	0.905532i	$0.360528\pi$
$270$		0			0
$271$	−170.727			−0.629990			−0.314995	−	0.949093i	$-0.602003\pi$
$271$	−170.727			−0.629990			−0.314995	+	0.949093i	$0.602003\pi$
$272$		0			0
$273$	−92.6714	−	83.0189i	−0.339456	−	0.304099i
$274$		0			0
$275$	−1.96076	+	1.96076i	−0.00713004	+	0.00713004i
$276$		0			0
$277$	−114.051	+	114.051i	−0.411737	+	0.411737i	−0.882343	−	0.470606i	$-0.844035\pi$
$277$	−114.051	+	114.051i	−0.411737	+	0.411737i	0.470606	+	0.882343i	$0.344035\pi$
$278$		0			0
$279$	336.294	−	37.0640i	1.20535	−	0.132846i
$280$		0			0
$281$	136.468			0.485650			0.242825	−	0.970070i	$-0.421926\pi$
$281$	136.468			0.485650			0.242825	+	0.970070i	$0.421926\pi$
$282$		0			0
$283$	−132.657	+	132.657i	−0.468752	+	0.468752i	−0.901510	−	0.432758i	$-0.857540\pi$
$283$	−132.657	+	132.657i	−0.468752	+	0.468752i	0.432758	+	0.901510i	$0.357540\pi$
$284$		0			0
$285$	−189.852	+	10.4305i	−0.666146	+	0.0365982i
$286$		0			0
$287$			56.1658i			0.195700i
$288$		0			0
$289$	−114.022			−0.394541
$290$		0			0
$291$	−22.9106	−	417.010i	−0.0787307	−	1.43303i
$292$		0			0
$293$	143.968	+	143.968i	0.491360	+	0.491360i	0.908735	−	0.417375i	$-0.137050\pi$
$293$	143.968	+	143.968i	0.491360	+	0.491360i	−0.417375	+	0.908735i	$0.637050\pi$
$294$		0			0
$295$		−	387.764i		−	1.31446i
$296$		0			0
$297$	−39.2951	+	54.9557i	−0.132307	+	0.185036i
$298$		0			0
$299$	31.4823	+	31.4823i	0.105292	+	0.105292i
$300$		0			0
$301$	−261.344	−	261.344i	−0.868252	−	0.868252i
$302$		0			0
$303$	356.352	−	397.784i	1.17608	−	1.31282i
$304$		0			0
$305$			138.875i			0.455328i
$306$		0			0
$307$	−89.3258	−	89.3258i	−0.290964	−	0.290964i	0.546497	−	0.837461i	$-0.315961\pi$
$307$	−89.3258	−	89.3258i	−0.290964	−	0.290964i	−0.837461	+	0.546497i	$0.815961\pi$
$308$		0			0
$309$	79.0619	−	4.34368i	0.255864	−	0.0140572i
$310$		0			0
$311$	314.507			1.01128			0.505638	−	0.862746i	$-0.331257\pi$
$311$	314.507			1.01128			0.505638	+	0.862746i	$0.331257\pi$
$312$		0			0
$313$			103.874i			0.331867i	0.986137	+	0.165934i	$0.0530638\pi$
$313$			103.874i			0.331867i	−0.986137	+	0.165934i	$0.946936\pi$
$314$		0			0
$315$	−353.142	+	440.625i	−1.12108	+	1.39881i
$316$		0			0
$317$	321.109	−	321.109i	1.01296	−	1.01296i	0.0130482	−	0.999915i	$-0.495847\pi$
$317$	321.109	−	321.109i	1.01296	−	1.01296i	0.999915	−	0.0130482i	$-0.00415349\pi$
$318$		0			0
$319$	23.0557			0.0722750
$320$		0			0
$321$	237.665	−	265.297i	0.740388	−	0.826472i
$322$		0			0
$323$	−176.079	+	176.079i	−0.545138	+	0.545138i
$324$		0			0
$325$	−2.64668	+	2.64668i	−0.00814363	+	0.00814363i
$326$		0			0
$327$	−6.49746	+	7.25291i	−0.0198699	+	0.0221801i
$328$		0			0
$329$	−673.348			−2.04665
$330$		0			0
$331$	−313.858	+	313.858i	−0.948213	+	0.948213i	−0.998724	−	0.0505107i	$-0.983915\pi$
$331$	−313.858	+	313.858i	−0.948213	+	0.948213i	0.0505107	+	0.998724i	$0.483915\pi$
$332$		0			0
$333$	79.6439	−	99.3740i	0.239171	−	0.298420i
$334$		0			0
$335$			228.057i			0.680768i
$336$		0			0
$337$	−236.028			−0.700380			−0.350190	−	0.936679i	$-0.613883\pi$
$337$	−236.028			−0.700380			−0.350190	+	0.936679i	$0.613883\pi$
$338$		0			0
$339$	532.088	−	29.2330i	1.56958	−	0.0862331i
$340$		0			0
$341$	−66.5125	−	66.5125i	−0.195051	−	0.195051i
$342$		0			0
$343$			648.069i			1.88941i
$344$		0			0
$345$	134.829	−	150.506i	0.390809	−	0.436248i
$346$		0			0
$347$	441.946	+	441.946i	1.27362	+	1.27362i	0.944175	+	0.329445i	$0.106862\pi$
$347$	441.946	+	441.946i	1.27362	+	1.27362i	0.329445	+	0.944175i	$0.393138\pi$
$348$		0			0
$349$	476.643	+	476.643i	1.36574	+	1.36574i	0.866417	+	0.499321i	$0.166417\pi$
$349$	476.643	+	476.643i	1.36574	+	1.36574i	0.499321	+	0.866417i	$0.333583\pi$
$350$		0			0
$351$	−53.0414	+	74.1805i	−0.151115	+	0.211341i
$352$		0			0
$353$		−	452.246i		−	1.28115i	−0.767895	−	0.640575i	$-0.778696\pi$
$353$		−	452.246i		−	1.28115i	0.767895	−	0.640575i	$-0.221304\pi$
$354$		0			0
$355$	235.289	+	235.289i	0.662785	+	0.662785i
$356$		0			0
$357$	40.5687	+	738.415i	0.113638	+	2.06839i
$358$		0			0
$359$	−617.295			−1.71948			−0.859742	−	0.510728i	$-0.829376\pi$
$359$	−617.295			−1.71948			−0.859742	+	0.510728i	$0.829376\pi$
$360$		0			0
$361$		−	207.143i		−	0.573803i
$362$		0			0
$363$	−343.699	+	18.8829i	−0.946829	+	0.0520190i
$364$		0			0
$365$	−181.538	+	181.538i	−0.497364	+	0.497364i
$366$		0			0
$367$	11.3588			0.0309505			0.0154753	−	0.999880i	$-0.495074\pi$
$367$	11.3588			0.0309505			0.0154753	+	0.999880i	$0.495074\pi$
$368$		0			0
$369$	40.9189	−	4.50980i	0.110891	−	0.0122217i
$370$		0			0
$371$	−264.266	+	264.266i	−0.712306	+	0.712306i
$372$		0			0
$373$	59.4092	−	59.4092i	0.159274	−	0.159274i	−0.622971	−	0.782245i	$-0.714075\pi$
$373$	59.4092	−	59.4092i	0.159274	−	0.159274i	0.782245	+	0.622971i	$0.214075\pi$
$374$		0			0
$375$	−272.783	−	244.370i	−0.727421	−	0.651654i
$376$		0			0
$377$	31.1212			0.0825495
$378$		0			0
$379$	435.432	−	435.432i	1.14890	−	1.14890i	0.162129	−	0.986770i	$-0.448164\pi$
$379$	435.432	−	435.432i	1.14890	−	1.14890i	0.986770	−	0.162129i	$-0.0518359\pi$
$380$		0			0
$381$	−25.0425	−	455.813i	−0.0657283	−	1.19636i
$382$		0			0
$383$		−	272.117i		−	0.710488i	−0.934774	−	0.355244i	$-0.884398\pi$
$383$		−	272.117i		−	0.710488i	0.934774	−	0.355244i	$-0.115602\pi$
$384$		0			0
$385$	156.992			0.407772
$386$		0			0
$387$	−169.414	+	211.383i	−0.437763	+	0.546210i
$388$		0			0
$389$	−260.985	−	260.985i	−0.670913	−	0.670913i	0.287013	−	0.957927i	$-0.407338\pi$
$389$	−260.985	−	260.985i	−0.670913	−	0.670913i	−0.957927	+	0.287013i	$0.907338\pi$
$390$		0			0
$391$		−	264.636i		−	0.676818i
$392$		0			0
$393$	207.601	+	185.978i	0.528248	+	0.473226i
$394$		0			0
$395$	−75.6206	−	75.6206i	−0.191445	−	0.191445i
$396$		0			0
$397$	−258.248	−	258.248i	−0.650500	−	0.650500i	0.302614	−	0.953113i	$-0.402141\pi$
$397$	−258.248	−	258.248i	−0.650500	−	0.650500i	−0.953113	+	0.302614i	$0.902141\pi$
$398$		0			0
$399$	340.336	+	304.887i	0.852972	+	0.764128i
$400$		0			0
$401$			430.073i			1.07250i	0.844059	+	0.536250i	$0.180160\pi$
$401$			430.073i			1.07250i	−0.844059	+	0.536250i	$0.819840\pi$
$402$		0			0
$403$	−89.7801	−	89.7801i	−0.222779	−	0.222779i
$404$		0			0
$405$	349.367	+	221.897i	0.862635	+	0.547894i
$406$		0			0
$407$	−35.4063			−0.0869935
$408$		0			0
$409$		−	207.501i		−	0.507337i	−0.967291	−	0.253668i	$-0.918363\pi$
$409$		−	207.501i		−	0.507337i	0.967291	−	0.253668i	$-0.0816372\pi$
$410$		0			0
$411$	−8.74718	−	159.213i	−0.0212827	−	0.387379i
$412$		0			0
$413$	−658.921	+	658.921i	−1.59545	+	1.59545i
$414$		0			0
$415$	−45.9428			−0.110706
$416$		0			0
$417$	509.793	+	456.694i	1.22253	+	1.09519i
$418$		0			0
$419$	−108.717	+	108.717i	−0.259467	+	0.259467i	−0.824837	−	0.565370i	$-0.808733\pi$
$419$	−108.717	+	108.717i	−0.259467	+	0.259467i	0.565370	+	0.824837i	$0.308733\pi$
$420$		0			0
$421$	484.985	−	484.985i	1.15198	−	1.15198i	0.165829	−	0.986155i	$-0.446970\pi$
$421$	484.985	−	484.985i	1.15198	−	1.15198i	0.986155	−	0.165829i	$-0.0530300\pi$
$422$		0			0
$423$	54.0661	+	490.559i	0.127816	+	1.15971i
$424$		0			0
$425$	22.2476			0.0523474
$426$		0			0
$427$	235.988	−	235.988i	0.552665	−	0.552665i
$428$		0			0
$429$	25.3154	−	1.39083i	0.0590102	−	0.00324203i
$430$		0			0
$431$			213.570i			0.495522i	0.968821	+	0.247761i	$0.0796947\pi$
$431$			213.570i			0.495522i	−0.968821	+	0.247761i	$0.920305\pi$
$432$		0			0
$433$	440.669			1.01771			0.508856	−	0.860852i	$-0.330069\pi$
$433$	440.669			1.01771			0.508856	+	0.860852i	$0.330069\pi$
$434$		0			0
$435$	−7.74826	−	141.031i	−0.0178121	−	0.324209i
$436$		0			0
$437$	−115.619	−	115.619i	−0.264574	−	0.264574i
$438$		0			0
$439$		−	400.367i		−	0.911998i	−0.889980	−	0.455999i	$-0.849282\pi$
$439$		−	400.367i		−	0.911998i	0.889980	−	0.455999i	$-0.150718\pi$
$440$		0			0
$441$	910.488	−	100.348i	2.06460	−	0.227546i
$442$		0			0
$443$	−324.076	−	324.076i	−0.731549	−	0.731549i	0.239378	−	0.970926i	$-0.423057\pi$
$443$	−324.076	−	324.076i	−0.731549	−	0.731549i	−0.970926	+	0.239378i	$0.923057\pi$
$444$		0			0
$445$	601.208	+	601.208i	1.35103	+	1.35103i
$446$		0			0
$447$	330.965	−	369.446i	0.740414	−	0.826500i
$448$		0			0
$449$			691.918i			1.54102i	0.637427	+	0.770510i	$0.279999\pi$
$449$			691.918i			1.54102i	−0.637427	+	0.770510i	$0.720001\pi$
$450$		0			0
$451$	−8.09298	−	8.09298i	−0.0179445	−	0.0179445i
$452$		0			0
$453$	32.8674	−	1.80574i	0.0725549	−	0.00398618i
$454$		0			0
$455$	211.912			0.465740
$456$		0			0
$457$		−	385.436i		−	0.843404i	−0.906734	−	0.421702i	$-0.861433\pi$
$457$		−	385.436i		−	0.843404i	0.906734	−	0.421702i	$-0.138567\pi$
$458$		0			0
$459$	534.705	−	88.8463i	1.16494	−	0.193565i
$460$		0			0
$461$	312.070	−	312.070i	0.676942	−	0.676942i	−0.282365	−	0.959307i	$-0.591119\pi$
$461$	312.070	−	312.070i	0.676942	−	0.676942i	0.959307	+	0.282365i	$0.0911190\pi$
$462$		0			0
$463$	−718.961			−1.55283			−0.776416	−	0.630220i	$-0.782965\pi$
$463$	−718.961			−1.55283			−0.776416	+	0.630220i	$0.782965\pi$
$464$		0			0
$465$	−384.501	+	429.206i	−0.826884	+	0.923024i
$466$		0			0
$467$	−82.7894	+	82.7894i	−0.177279	+	0.177279i	−0.790169	−	0.612889i	$-0.790007\pi$
$467$	−82.7894	+	82.7894i	−0.177279	+	0.177279i	0.612889	+	0.790169i	$0.290007\pi$
$468$		0			0
$469$	387.534	−	387.534i	0.826298	−	0.826298i
$470$		0			0
$471$	−141.049	+	157.448i	−0.299467	+	0.334285i
$472$		0			0
$473$	75.3145			0.159227
$474$		0			0
$475$	9.71993	−	9.71993i	0.0204630	−	0.0204630i
$476$		0			0
$477$	213.746	+	171.308i	0.448106	+	0.359137i
$478$		0			0
$479$			749.099i			1.56388i	0.623353	+	0.781941i	$0.285770\pi$
$479$			749.099i			1.56388i	−0.623353	+	0.781941i	$0.714230\pi$
$480$		0			0
$481$	−47.7923			−0.0993603
$482$		0			0
$483$	−484.864	+	26.6385i	−1.00386	+	0.0551523i
$484$		0			0
$485$	502.983	+	502.983i	1.03708	+	1.03708i
$486$		0			0
$487$			533.210i			1.09489i	0.836843	+	0.547443i	$0.184399\pi$
$487$			533.210i			1.09489i	−0.836843	+	0.547443i	$0.815601\pi$
$488$		0			0
$489$	−188.040	+	209.904i	−0.384541	+	0.429251i
$490$		0			0
$491$	−6.75013	−	6.75013i	−0.0137477	−	0.0137477i	0.700200	−	0.713947i	$-0.253094\pi$
$491$	−6.75013	−	6.75013i	−0.0137477	−	0.0137477i	−0.713947	+	0.700200i	$0.753094\pi$
$492$		0			0
$493$	−130.800	−	130.800i	−0.265315	−	0.265315i
$494$		0			0
$495$	−12.6056	−	114.375i	−0.0254658	−	0.231060i
$496$		0			0
$497$		−	799.644i		−	1.60894i
$498$		0			0
$499$	556.347	+	556.347i	1.11492	+	1.11492i	0.992475	+	0.122448i	$0.0390746\pi$
$499$	556.347	+	556.347i	1.11492	+	1.11492i	0.122448	+	0.992475i	$0.460925\pi$
$500$		0			0
$501$	−30.0923	−	547.728i	−0.0600645	−	1.09327i
$502$		0			0
$503$	−304.892			−0.606147			−0.303074	−	0.952967i	$-0.598013\pi$
$503$	−304.892			−0.606147			−0.303074	+	0.952967i	$0.598013\pi$
$504$		0			0
$505$			909.612i			1.80121i
$506$		0			0
$507$	−472.065	+	25.9354i	−0.931095	+	0.0511546i
$508$		0			0
$509$	118.591	−	118.591i	0.232988	−	0.232988i	−0.580951	−	0.813939i	$-0.697319\pi$
$509$	118.591	−	118.591i	0.232988	−	0.232988i	0.813939	+	0.580951i	$0.197319\pi$
$510$		0			0
$511$	616.968			1.20737
$512$		0			0
$513$	194.795	−	272.428i	0.379716	−	0.531049i
$514$		0			0
$515$	−95.3617	+	95.3617i	−0.185168	+	0.185168i
$516$		0			0
$517$	97.0233	−	97.0233i	0.187666	−	0.187666i
$518$		0			0
$519$	391.244	+	350.493i	0.753843	+	0.675324i
$520$		0			0
$521$	−105.077			−0.201683			−0.100842	−	0.994902i	$-0.532154\pi$
$521$	−105.077			−0.201683			−0.100842	+	0.994902i	$0.532154\pi$
$522$		0			0
$523$	−479.455	+	479.455i	−0.916740	+	0.916740i	−0.996791	−	0.0800507i	$-0.974492\pi$
$523$	−479.455	+	479.455i	−0.916740	+	0.916740i	0.0800507	+	0.996791i	$0.474492\pi$
$524$		0			0
$525$	−2.23947	−	40.7619i	−0.00426566	−	0.0776418i
$526$		0			0
$527$			754.679i			1.43203i
$528$		0			0
$529$	−355.232			−0.671517
$530$		0			0
$531$	532.956	+	427.141i	1.00368	+	0.804408i
$532$		0			0
$533$	−10.9241	−	10.9241i	−0.0204955	−	0.0204955i
$534$		0			0
$535$			606.655i			1.13393i
$536$		0			0
$537$	−532.918	−	477.410i	−0.992399	−	0.889032i
$538$		0			0
$539$	−180.077	−	180.077i	−0.334095	−	0.334095i
$540$		0			0
$541$	−726.230	−	726.230i	−1.34238	−	1.34238i	−0.893680	−	0.448704i	$-0.851886\pi$
$541$	−726.230	−	726.230i	−1.34238	−	1.34238i	−0.448704	−	0.893680i	$-0.648114\pi$
$542$		0			0
$543$	−512.439	−	459.065i	−0.943719	−	0.845423i
$544$		0			0
$545$		−	16.5852i		−	0.0304316i
$546$		0			0
$547$	314.507	+	314.507i	0.574966	+	0.574966i	0.933512	−	0.358546i	$-0.116727\pi$
$547$	314.507	+	314.507i	0.574966	+	0.574966i	−0.358546	+	0.933512i	$0.616727\pi$
$548$		0			0
$549$	−190.875	−	152.978i	−0.347677	−	0.278648i
$550$		0			0
$551$	−114.292			−0.207427
$552$		0			0
$553$			257.002i			0.464741i
$554$		0			0
$555$	11.8989	+	216.579i	0.0214394	+	0.390232i
$556$		0			0
$557$	−134.274	+	134.274i	−0.241066	+	0.241066i	−0.817291	−	0.576225i	$-0.804525\pi$
$557$	−134.274	+	134.274i	−0.241066	+	0.241066i	0.576225	+	0.817291i	$0.304525\pi$
$558$		0			0
$559$	101.661			0.181863
$560$		0			0
$561$	−112.244	−	100.553i	−0.200079	−	0.179239i
$562$		0			0
$563$	102.810	−	102.810i	0.182612	−	0.182612i	−0.609881	−	0.792493i	$-0.708783\pi$
$563$	102.810	−	102.810i	0.182612	−	0.182612i	0.792493	+	0.609881i	$0.208783\pi$
$564$		0			0
$565$	−641.785	+	641.785i	−1.13590	+	1.13590i
$566$		0			0
$567$	−216.608	−	970.739i	−0.382024	−	1.71206i
$568$		0			0
$569$	78.4572			0.137886			0.0689430	−	0.997621i	$-0.478037\pi$
$569$	78.4572			0.137886			0.0689430	+	0.997621i	$0.478037\pi$
$570$		0			0
$571$	363.164	−	363.164i	0.636013	−	0.636013i	−0.313556	−	0.949570i	$-0.601520\pi$
$571$	363.164	−	363.164i	0.636013	−	0.636013i	0.949570	+	0.313556i	$0.101520\pi$
$572$		0			0
$573$	−182.358	+	10.0188i	−0.318251	+	0.0174848i
$574$		0			0
$575$			14.6084i			0.0254060i
$576$		0			0
$577$	−566.880			−0.982460			−0.491230	−	0.871030i	$-0.663453\pi$
$577$	−566.880			−0.982460			−0.491230	+	0.871030i	$0.663453\pi$
$578$		0			0
$579$	−29.2727	−	532.809i	−0.0505573	−	0.920223i
$580$		0			0
$581$	78.0698	+	78.0698i	0.134371	+	0.134371i
$582$		0			0
$583$		−	76.1565i		−	0.130629i
$584$		0			0
$585$	−17.0153	−	154.385i	−0.0290860	−	0.263907i
$586$		0			0
$587$	73.3693	+	73.3693i	0.124990	+	0.124990i	0.766835	−	0.641845i	$-0.221831\pi$
$587$	73.3693	+	73.3693i	0.124990	+	0.124990i	−0.641845	+	0.766835i	$0.721831\pi$
$588$		0			0
$589$	329.717	+	329.717i	0.559792	+	0.559792i
$590$		0			0
$591$	−189.504	+	211.538i	−0.320650	+	0.357932i
$592$		0			0
$593$			458.708i			0.773538i	0.922177	+	0.386769i	$0.126409\pi$
$593$			458.708i			0.773538i	−0.922177	+	0.386769i	$0.873591\pi$
$594$		0			0
$595$	−890.650	−	890.650i	−1.49689	−	1.49689i
$596$		0			0
$597$	2.47525	−	0.135991i	0.00414615	−	0.000227790i
$598$		0			0
$599$	423.611			0.707197			0.353599	−	0.935397i	$-0.384958\pi$
$599$	423.611			0.707197			0.353599	+	0.935397i	$0.384958\pi$
$600$		0			0
$601$		−	795.376i		−	1.32342i	−0.749759	−	0.661711i	$-0.769831\pi$
$601$		−	795.376i		−	1.32342i	0.749759	−	0.661711i	$-0.230169\pi$
$602$		0			0
$603$	−313.450	−	251.216i	−0.519817	−	0.416610i
$604$		0			0
$605$	414.557	−	414.557i	0.685219	−	0.685219i
$606$		0			0
$607$	631.699			1.04069			0.520345	−	0.853956i	$-0.325803\pi$
$607$	631.699			1.04069			0.520345	+	0.853956i	$0.325803\pi$
$608$		0			0
$609$	−226.484	+	252.817i	−0.371896	+	0.415135i
$610$		0			0
$611$	130.964	−	130.964i	0.214344	−	0.214344i
$612$		0			0
$613$	−385.264	+	385.264i	−0.628490	+	0.628490i	−0.947688	−	0.319198i	$-0.896586\pi$
$613$	−385.264	+	385.264i	−0.628490	+	0.628490i	0.319198	+	0.947688i	$0.396586\pi$
$614$		0			0
$615$	−46.7846	+	52.2241i	−0.0760724	+	0.0849173i
$616$		0			0
$617$	953.333			1.54511			0.772555	−	0.634947i	$-0.218978\pi$
$617$	953.333			1.54511			0.772555	+	0.634947i	$0.218978\pi$
$618$		0			0
$619$	−574.046	+	574.046i	−0.927377	+	0.927377i	−0.997536	−	0.0701591i	$-0.977649\pi$
$619$	−574.046	+	574.046i	−0.927377	+	0.927377i	0.0701591	+	0.997536i	$0.477649\pi$
$620$		0			0
$621$	58.3390	+	351.103i	0.0939437	+	0.565383i
$622$		0			0
$623$		−	2043.24i		−	3.27969i
$624$		0			0
$625$	651.477			1.04236
$626$		0			0
$627$	−92.9707	+	5.10783i	−0.148279	+	0.00814646i
$628$		0			0
$629$	200.868	+	200.868i	0.319345	+	0.319345i
$630$		0			0
$631$		−	138.048i		−	0.218777i	−0.993999	−	0.109389i	$-0.965111\pi$
$631$		−	138.048i		−	0.218777i	0.993999	−	0.109389i	$-0.0348893\pi$
$632$		0			0
$633$	−513.367	+	573.056i	−0.811007	+	0.905301i
$634$		0			0
$635$	549.786	+	549.786i	0.865805	+	0.865805i
$636$		0			0
$637$	−243.072	−	243.072i	−0.381589	−	0.381589i
$638$		0			0
$639$	−582.570	+	64.2069i	−0.911691	+	0.100480i
$640$		0			0
$641$		−	784.889i		−	1.22448i	−0.790673	−	0.612238i	$-0.790269\pi$
$641$		−	784.889i		−	1.22448i	0.790673	−	0.612238i	$-0.209731\pi$
$642$		0			0
$643$	−238.456	−	238.456i	−0.370850	−	0.370850i	0.496937	−	0.867787i	$-0.334458\pi$
$643$	−238.456	−	238.456i	−0.370850	−	0.370850i	−0.867787	+	0.496937i	$0.834458\pi$
$644$		0			0
$645$	−25.3107	−	460.695i	−0.0392414	−	0.714256i
$646$		0			0
$647$	681.751			1.05371			0.526855	−	0.849955i	$-0.323371\pi$
$647$	681.751			1.05371			0.526855	+	0.849955i	$0.323371\pi$
$648$		0			0
$649$		−	189.889i		−	0.292587i
$650$		0			0
$651$	1382.72	−	75.9668i	2.12399	−	0.116693i
$652$		0			0
$653$	−636.071	+	636.071i	−0.974075	+	0.974075i	−0.999672	−	0.0255977i	$-0.991851\pi$
$653$	−636.071	+	636.071i	−0.974075	+	0.974075i	0.0255977	+	0.999672i	$0.491851\pi$
$654$		0			0
$655$	−474.721			−0.724766
$656$		0			0
$657$	−49.5391	−	449.485i	−0.0754020	−	0.684147i
$658$		0			0
$659$	−91.6052	+	91.6052i	−0.139006	+	0.139006i	−0.773186	−	0.634179i	$-0.781338\pi$
$659$	−91.6052	+	91.6052i	−0.139006	+	0.139006i	0.634179	+	0.773186i	$0.281338\pi$
$660$		0			0
$661$	−721.715	+	721.715i	−1.09185	+	1.09185i	−0.0965216	+	0.995331i	$0.530772\pi$
$661$	−721.715	+	721.715i	−1.09185	+	1.09185i	−0.995331	+	0.0965216i	$0.969228\pi$
$662$		0			0
$663$	−151.510	−	135.729i	−0.228522	−	0.204720i
$664$		0			0
$665$	−778.245			−1.17029
$666$		0			0
$667$	85.8871	−	85.8871i	0.128766	−	0.128766i
$668$		0			0
$669$	−2.91851	−	53.1215i	−0.00436250	−	0.0794044i
$670$		0			0
$671$			68.0074i			0.101352i
$672$		0			0
$673$	417.305			0.620067			0.310033	−	0.950726i	$-0.399660\pi$
$673$	417.305			0.620067			0.310033	+	0.950726i	$0.399660\pi$
$674$		0			0
$675$	−29.5168	+	4.90449i	−0.0437286	+	0.00726592i
$676$		0			0
$677$	−585.326	−	585.326i	−0.864587	−	0.864587i	0.127280	−	0.991867i	$-0.459375\pi$
$677$	−585.326	−	585.326i	−0.864587	−	0.864587i	−0.991867	+	0.127280i	$0.959375\pi$
$678$		0			0
$679$		−	1709.42i		−	2.51756i
$680$		0			0
$681$	−23.8194	−	21.3384i	−0.0349771	−	0.0313340i
$682$		0			0
$683$	−104.261	−	104.261i	−0.152651	−	0.152651i	0.626650	−	0.779301i	$-0.284426\pi$
$683$	−104.261	−	104.261i	−0.152651	−	0.152651i	−0.779301	+	0.626650i	$0.784426\pi$
$684$		0			0
$685$	192.037	+	192.037i	0.280346	+	0.280346i
$686$		0			0
$687$	707.054	+	633.409i	1.02919	+	0.921993i
$688$		0			0
$689$		−	102.798i		−	0.149199i
$690$		0			0
$691$	−335.701	−	335.701i	−0.485818	−	0.485818i	0.421165	−	0.906984i	$-0.361621\pi$
$691$	−335.701	−	335.701i	−0.485818	−	0.485818i	−0.906984	+	0.421165i	$0.861621\pi$
$692$		0			0
$693$	−172.934	+	215.775i	−0.249544	+	0.311364i
$694$		0			0
$695$	−1165.74			−1.67733
$696$		0			0
$697$			91.8264i			0.131745i
$698$		0			0
$699$	20.3386	+	370.196i	0.0290968	+	0.529608i
$700$		0			0
$701$	490.458	−	490.458i	0.699655	−	0.699655i	−0.264681	−	0.964336i	$-0.585267\pi$
$701$	490.458	−	490.458i	0.699655	−	0.699655i	0.964336	+	0.264681i	$0.0852666\pi$
$702$		0			0
$703$	175.517			0.249669
$704$		0			0
$705$	−626.093	−	560.881i	−0.888075	−	0.795575i
$706$		0			0
$707$	1545.69	−	1545.69i	2.18626	−	2.18626i
$708$		0			0
$709$	−435.817	+	435.817i	−0.614692	+	0.614692i	−0.944165	−	0.329473i	$-0.893129\pi$
$709$	−435.817	+	435.817i	−0.614692	+	0.614692i	0.329473	+	0.944165i	$0.393129\pi$
$710$		0			0
$711$	187.235	−	20.6358i	0.263341	−	0.0290236i
$712$		0			0
$713$	−495.544			−0.695012
$714$		0			0
$715$	−30.5345	+	30.5345i	−0.0427056	+	0.0427056i
$716$		0			0
$717$	354.968	−	19.5020i	0.495073	−	0.0271994i
$718$		0			0
$719$		−	1083.05i		−	1.50633i	−0.657831	−	0.753166i	$-0.728526\pi$
$719$		−	1083.05i		−	1.50633i	0.657831	−	0.753166i	$-0.271474\pi$
$720$		0			0
$721$	324.093			0.449505
$722$		0			0
$723$	43.4738	+	791.292i	0.0601297	+	1.09446i
$724$		0			0
$725$	7.22042	+	7.22042i	0.00995921	+	0.00995921i
$726$		0			0
$727$			513.215i			0.705935i	0.935636	+	0.352968i	$0.114827\pi$
$727$			513.215i			0.705935i	−0.935636	+	0.352968i	$0.885173\pi$
$728$		0			0
$729$	−689.828	+	235.752i	−0.946266	+	0.323390i
$730$		0			0
$731$	−427.276	−	427.276i	−0.584508	−	0.584508i
$732$		0			0
$733$	−73.6001	−	73.6001i	−0.100409	−	0.100409i	0.655118	−	0.755527i	$-0.272619\pi$
$733$	−73.6001	−	73.6001i	−0.100409	−	0.100409i	−0.755527	+	0.655118i	$0.772619\pi$
$734$		0			0
$735$	−1041.01	+	1162.04i	−1.41633	+	1.58101i
$736$		0			0
$737$			111.680i			0.151533i
$738$		0			0
$739$	152.386	+	152.386i	0.206206	+	0.206206i	0.802653	−	0.596447i	$-0.203421\pi$
$739$	152.386	+	152.386i	0.206206	+	0.206206i	−0.596447	+	0.802653i	$0.703421\pi$
$740$		0			0
$741$	−125.494	+	6.89467i	−0.169358	+	0.00930455i
$742$		0			0
$743$	574.044			0.772603			0.386302	−	0.922373i	$-0.373752\pi$
$743$	574.044			0.772603			0.386302	+	0.922373i	$0.373752\pi$
$744$		0			0
$745$			844.811i			1.13397i
$746$		0			0
$747$	50.6082	−	63.1454i	0.0677486	−	0.0845319i
$748$		0			0
$749$	1030.88	−	1030.88i	1.37634	−	1.37634i
$750$		0			0
$751$	1014.28			1.35058			0.675289	−	0.737553i	$-0.264019\pi$
$751$	1014.28			1.35058			0.675289	+	0.737553i	$0.264019\pi$
$752$		0			0
$753$	431.649	−	481.836i	0.573239	−	0.639888i
$754$		0			0
$755$	−39.6435	+	39.6435i	−0.0525079	+	0.0525079i
$756$		0			0
$757$	1003.73	−	1003.73i	1.32594	−	1.32594i	0.417057	−	0.908880i	$-0.363062\pi$
$757$	1003.73	−	1003.73i	1.32594	−	1.32594i	0.908880	−	0.417057i	$-0.136938\pi$
$758$		0			0
$759$	66.0261	−	73.7028i	0.0869909	−	0.0971052i
$760$		0			0
$761$	54.1069			0.0710997			0.0355499	−	0.999368i	$-0.488682\pi$
$761$	54.1069			0.0710997			0.0355499	+	0.999368i	$0.488682\pi$
$762$		0			0
$763$	−28.1829	+	28.1829i	−0.0369370	+	0.0369370i
$764$		0			0
$765$	−577.358	+	720.386i	−0.754716	+	0.941681i
$766$		0			0
$767$		−	256.316i		−	0.334181i
$768$		0			0
$769$	143.904			0.187132			0.0935659	−	0.995613i	$-0.470173\pi$
$769$	143.904			0.187132			0.0935659	+	0.995613i	$0.470173\pi$
$770$		0			0
$771$	−338.843	+	18.6161i	−0.439485	+	0.0241454i
$772$		0			0
$773$	−339.143	−	339.143i	−0.438736	−	0.438736i	0.452850	−	0.891586i	$-0.350407\pi$
$773$	−339.143	−	339.143i	−0.438736	−	0.438736i	−0.891586	+	0.452850i	$0.850407\pi$
$774$		0			0
$775$		−	41.6598i		−	0.0537546i
$776$		0			0
$777$	347.809	−	388.248i	0.447630	−	0.499676i
$778$		0			0
$779$	40.1187	+	40.1187i	0.0515003	+	0.0515003i
$780$		0			0
$781$	115.221	+	115.221i	0.147531	+	0.147531i
$782$		0			0
$783$	202.372	+	144.703i	0.258458	+	0.184805i
$784$		0			0
$785$		−	360.037i		−	0.458646i
$786$		0			0
$787$	−924.878	−	924.878i	−1.17519	−	1.17519i	−0.980954	−	0.194241i	$-0.937776\pi$
$787$	−924.878	−	924.878i	−1.17519	−	1.17519i	−0.194241	−	0.980954i	$-0.562224\pi$
$788$		0			0
$789$	21.2832	+	387.389i	0.0269749	+	0.490987i
$790$		0			0
$791$	2181.15			2.75746
$792$		0			0
$793$			91.7980i			0.115760i
$794$		0			0
$795$	−465.846	+	25.5937i	−0.585970	+	0.0321933i
$796$		0			0
$797$	−707.837	+	707.837i	−0.888127	+	0.888127i	−0.994343	−	0.106216i	$-0.966127\pi$
$797$	−707.837	+	707.837i	−0.888127	+	0.888127i	0.106216	+	0.994343i	$0.466127\pi$
$798$		0			0
$799$	−1100.87			−1.37781
$800$		0			0
$801$	−1488.58	+	164.061i	−1.85840	+	0.204820i
$802$		0			0
$803$	−88.8995	+	88.8995i	−0.110709	+	0.110709i
$804$		0			0
$805$	584.826	−	584.826i	0.726492	−	0.726492i
$806$		0			0
$807$	409.092	+	366.482i	0.506929	+	0.454128i
$808$		0			0
$809$	1107.83			1.36938			0.684689	−	0.728836i	$-0.259938\pi$
$809$	1107.83			1.36938			0.684689	+	0.728836i	$0.259938\pi$
$810$		0			0
$811$	217.697	−	217.697i	0.268431	−	0.268431i	−0.560037	−	0.828468i	$-0.689213\pi$
$811$	217.697	−	217.697i	0.268431	−	0.268431i	0.828468	+	0.560037i	$0.189213\pi$
$812$		0			0
$813$	28.0970	+	511.411i	0.0345597	+	0.629042i
$814$		0			0
$815$		−	479.986i		−	0.588940i
$816$		0			0
$817$	−373.351			−0.456978
$818$		0			0
$819$	−233.431	+	291.258i	−0.285019	+	0.355627i
$820$		0			0
$821$	761.374	+	761.374i	0.927374	+	0.927374i	0.997536	−	0.0701619i	$-0.0223516\pi$
$821$	761.374	+	761.374i	0.927374	+	0.927374i	−0.0701619	+	0.997536i	$0.522352\pi$
$822$		0			0
$823$		−	46.9015i		−	0.0569884i	−0.999594	−	0.0284942i	$-0.990929\pi$
$823$		−	46.9015i		−	0.0569884i	0.999594	−	0.0284942i	$-0.00907122\pi$
$824$		0			0
$825$	6.19611	+	5.55074i	0.00751044	+	0.00672817i
$826$		0			0
$827$	−116.383	−	116.383i	−0.140729	−	0.140729i	0.633232	−	0.773962i	$-0.281728\pi$
$827$	−116.383	−	116.383i	−0.140729	−	0.140729i	−0.773962	+	0.633232i	$0.781728\pi$
$828$		0			0
$829$	−821.995	−	821.995i	−0.991550	−	0.991550i	0.00841482	−	0.999965i	$-0.497321\pi$
$829$	−821.995	−	821.995i	−0.991550	−	0.991550i	−0.999965	+	0.00841482i	$0.997321\pi$
$830$		0			0
$831$	360.408	+	322.868i	0.433704	+	0.388530i
$832$		0			0
$833$			2043.23i			2.45286i
$834$		0			0
$835$	660.650	+	660.650i	0.791198	+	0.791198i
$836$		0			0
$837$	−166.369	−	1001.26i	−0.198768	−	1.19625i
$838$		0			0
$839$	−1328.92			−1.58393			−0.791966	−	0.610565i	$-0.790942\pi$
$839$	−1328.92			−1.58393			−0.791966	+	0.610565i	$0.790942\pi$
$840$		0			0
$841$			756.098i			0.899047i
$842$		0			0
$843$	−22.4588	−	408.786i	−0.0266415	−	0.484919i
$844$		0			0
$845$	569.389	−	569.389i	0.673833	−	0.673833i
$846$		0			0
$847$	−1408.90			−1.66340
$848$		0			0
$849$	419.203	+	375.540i	0.493761	+	0.442332i
$850$		0			0
$851$	−131.896	+	131.896i	−0.154989	+	0.154989i
$852$		0			0
$853$	74.3835	−	74.3835i	0.0872022	−	0.0872022i	−0.662160	−	0.749362i	$-0.730360\pi$
$853$	74.3835	−	74.3835i	0.0872022	−	0.0872022i	0.749362	+	0.662160i	$0.230360\pi$
$854$		0			0
$855$	62.4887	+	566.981i	0.0730862	+	0.663135i
$856$		0			0
$857$	1113.91			1.29977			0.649887	−	0.760030i	$-0.274816\pi$
$857$	1113.91			1.29977			0.649887	+	0.760030i	$0.274816\pi$
$858$		0			0
$859$	−78.5892	+	78.5892i	−0.0914891	+	0.0914891i	−0.751370	−	0.659881i	$-0.770607\pi$
$859$	−78.5892	+	78.5892i	−0.0914891	+	0.0914891i	0.659881	+	0.751370i	$0.270607\pi$
$860$		0			0
$861$	168.244	−	9.24334i	0.195405	−	0.0107356i
$862$		0			0
$863$			814.226i			0.943483i	0.881737	+	0.471741i	$0.156374\pi$
$863$			814.226i			0.943483i	−0.881737	+	0.471741i	$0.843626\pi$
$864$		0			0
$865$	−894.658			−1.03429
$866$		0			0
$867$	18.7650	+	341.552i	0.0216436	+	0.393947i
$868$		0			0
$869$	−37.0316	−	37.0316i	−0.0426140	−	0.0426140i
$870$		0			0
$871$			150.748i			0.173075i
$872$		0			0
$873$	−1245.38	+	137.257i	−1.42655	+	0.157224i
$874$		0			0
$875$	−1059.96	−	1059.96i	−1.21139	−	1.21139i
$876$		0			0
$877$	36.8840	+	36.8840i	0.0420571	+	0.0420571i	0.727823	−	0.685765i	$-0.240532\pi$
$877$	36.8840	+	36.8840i	0.0420571	+	0.0420571i	−0.685765	+	0.727823i	$0.740532\pi$
$878$		0			0
$879$	407.562	−	454.948i	0.463665	−	0.517575i
$880$		0			0
$881$		−	69.7752i		−	0.0792000i	−0.999216	−	0.0396000i	$-0.987392\pi$
$881$		−	69.7752i		−	0.0792000i	0.999216	−	0.0396000i	$-0.0126084\pi$
$882$		0			0
$883$	410.405	+	410.405i	0.464785	+	0.464785i	0.900220	−	0.435435i	$-0.143406\pi$
$883$	410.405	+	410.405i	0.464785	+	0.464785i	−0.435435	+	0.900220i	$0.643406\pi$
$884$		0			0
$885$	−1161.54	+	63.8153i	−1.31248	+	0.0721077i
$886$		0			0
$887$	−1290.54			−1.45495			−0.727475	−	0.686135i	$-0.759306\pi$
$887$	−1290.54			−1.45495			−0.727475	+	0.686135i	$0.759306\pi$
$888$		0			0
$889$		−	1868.48i		−	2.10178i
$890$		0			0
$891$	171.086	+	108.664i	0.192016	+	0.121957i
$892$		0			0
$893$	−480.966	+	480.966i	−0.538596	+	0.538596i
$894$		0			0
$895$	1218.62			1.36159
$896$		0			0
$897$	89.1236	−	99.4858i	0.0993574	−	0.110909i
$898$		0			0
$899$	−244.930	+	244.930i	−0.272447	+	0.272447i
$900$		0			0
$901$	−432.052	+	432.052i	−0.479525	+	0.479525i
$902$		0			0
$903$	−739.841	+	825.861i	−0.819315	+	0.914575i
$904$		0			0
$905$	1171.79			1.29480
$906$		0			0
$907$	395.420	−	395.420i	0.435964	−	0.435964i	−0.454687	−	0.890651i	$-0.650249\pi$
$907$	395.420	−	395.420i	0.435964	−	0.435964i	0.890651	+	0.454687i	$0.150249\pi$
$908$		0			0
$909$	−1250.20	−	1001.98i	−1.37536	−	1.10229i
$910$		0			0
$911$			1451.84i			1.59367i	0.604195	+	0.796837i	$0.293495\pi$
$911$			1451.84i			1.59367i	−0.604195	+	0.796837i	$0.706505\pi$
$912$		0			0
$913$	−22.4983			−0.0246422
$914$		0			0
$915$	415.998	−	22.8550i	0.454643	−	0.0249782i
$916$		0			0
$917$	806.686	+	806.686i	0.879701	+	0.879701i
$918$		0			0
$919$			1626.08i			1.76940i	0.466161	+	0.884700i	$0.345637\pi$
$919$			1626.08i			1.76940i	−0.466161	+	0.884700i	$0.654363\pi$
$920$		0			0
$921$	−252.873	+	282.275i	−0.274564	+	0.306487i
$922$		0			0
$923$	155.528	+	155.528i	0.168503	+	0.168503i
$924$		0			0
$925$	−11.0883	−	11.0883i	−0.0119874	−	0.0119874i
$926$		0			0
$927$	−26.0228	−	236.114i	−0.0280721	−	0.254707i
$928$		0			0
$929$		−	864.883i		−	0.930983i	−0.885052	−	0.465491i	$-0.845878\pi$
$929$		−	864.883i		−	0.930983i	0.885052	−	0.465491i	$-0.154122\pi$
$930$		0			0
$931$	892.684	+	892.684i	0.958844	+	0.958844i
$932$		0			0
$933$	−51.7592	−	942.100i	−0.0554761	−	1.00975i
$934$		0			0
$935$	256.669			0.274512
$936$		0			0
$937$		−	177.635i		−	0.189579i	−0.995497	−	0.0947893i	$-0.969782\pi$
$937$		−	177.635i		−	0.189579i	0.995497	−	0.0947893i	$-0.0302177\pi$
$938$		0			0
$939$	311.154	−	17.0949i	0.331368	−	0.0182054i
$940$		0			0
$941$	−49.5787	+	49.5787i	−0.0526872	+	0.0526872i	−0.732959	−	0.680272i	$-0.761862\pi$
$941$	−49.5787	+	49.5787i	−0.0526872	+	0.0526872i	0.680272	+	0.732959i	$0.261862\pi$
$942$		0			0
$943$	−60.2958			−0.0639404
$944$		0			0
$945$	1378.00	+	985.315i	1.45820	+	1.04266i
$946$		0			0
$947$	−801.785	+	801.785i	−0.846658	+	0.846658i	−0.989714	−	0.143057i	$-0.954307\pi$
$947$	−801.785	+	801.785i	−0.846658	+	0.846658i	0.143057	+	0.989714i	$0.454307\pi$
$948$		0			0
$949$	−119.999	+	119.999i	−0.126447	+	0.126447i
$950$		0			0
$951$	−1014.72	−	909.032i	−1.06701	−	0.955869i
$952$		0			0
$953$	−633.331			−0.664565			−0.332283	−	0.943180i	$-0.607819\pi$
$953$	−633.331			−0.664565			−0.332283	+	0.943180i	$0.607819\pi$
$954$		0			0
$955$	219.954	−	219.954i	0.230318	−	0.230318i
$956$		0			0
$957$	−3.79434	−	69.0630i	−0.00396483	−	0.0721662i
$958$		0			0
$959$		−	652.649i		−	0.680552i
$960$		0			0
$961$	452.174			0.470525
$962$		0			0
$963$	−833.807	−	668.259i	−0.865843	−	0.693935i
$964$		0			0
$965$	642.656	+	642.656i	0.665965	+	0.665965i
$966$		0			0
$967$			734.798i			0.759873i	0.925013	+	0.379937i	$0.124054\pi$
$967$			734.798i			0.759873i	−0.925013	+	0.379937i	$0.875946\pi$
$968$		0			0
$969$	556.421	+	498.465i	0.574222	+	0.514412i
$970$		0			0
$971$	1255.23	+	1255.23i	1.29272	+	1.29272i	0.933097	+	0.359625i	$0.117095\pi$
$971$	1255.23	+	1255.23i	1.29272	+	1.29272i	0.359625	+	0.933097i	$0.382905\pi$
$972$		0			0
$973$	1980.93	+	1980.93i	2.03589	+	2.03589i
$974$		0			0
$975$	8.36365	+	7.49251i	0.00857811	+	0.00768463i
$976$		0			0
$977$		−	75.9504i		−	0.0777384i	−0.999244	−	0.0388692i	$-0.987624\pi$
$977$		−	75.9504i		−	0.0777384i	0.999244	−	0.0388692i	$-0.0123756\pi$
$978$		0			0
$979$	294.413	+	294.413i	0.300728	+	0.300728i
$980$		0			0
$981$	22.7953	+	18.2694i	0.0232368	+	0.0186232i
$982$		0			0
$983$	−211.646			−0.215306			−0.107653	−	0.994189i	$-0.534334\pi$
$983$	−211.646			−0.215306			−0.107653	+	0.994189i	$0.534334\pi$
$984$		0			0
$985$		−	483.723i		−	0.491089i
$986$		0			0
$987$	110.815	+	2017.00i	0.112274	+	2.04357i
$988$		0			0
$989$	280.561	−	280.561i	0.283682	−	0.283682i
$990$		0			0
$991$	728.452			0.735067			0.367534	−	0.930010i	$-0.380202\pi$
$991$	728.452			0.735067			0.367534	+	0.930010i	$0.380202\pi$
$992$		0			0
$993$	991.810	+	888.505i	0.998802	+	0.894768i
$994$		0			0
$995$	−2.98556	+	2.98556i	−0.00300056	+	0.00300056i
$996$		0			0
$997$	955.300	−	955.300i	0.958175	−	0.958175i	−0.0409850	−	0.999160i	$-0.513050\pi$
$997$	955.300	−	955.300i	0.958175	−	0.958175i	0.999160	+	0.0409850i	$0.0130496\pi$
$998$		0			0
$999$	−310.780	−	222.218i	−0.311091	−	0.222440i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	384.3.i.c.161.6		20
3.2	odd	2	inner	384.3.i.c.161.1		20
4.3	odd	2		384.3.i.d.161.5		20
8.3	odd	2		48.3.i.b.29.10	yes	20
8.5	even	2		192.3.i.b.17.5		20
12.11	even	2		384.3.i.d.161.10		20
16.3	odd	4		48.3.i.b.5.1	✓	20
16.5	even	4	inner	384.3.i.c.353.1		20
16.11	odd	4		384.3.i.d.353.10		20
16.13	even	4		192.3.i.b.113.10		20
24.5	odd	2		192.3.i.b.17.10		20
24.11	even	2		48.3.i.b.29.1	yes	20
48.5	odd	4	inner	384.3.i.c.353.6		20
48.11	even	4		384.3.i.d.353.5		20
48.29	odd	4		192.3.i.b.113.5		20
48.35	even	4		48.3.i.b.5.10	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
48.3.i.b.5.1	✓	20	16.3	odd	4
48.3.i.b.5.10	yes	20	48.35	even	4
48.3.i.b.29.1	yes	20	24.11	even	2
48.3.i.b.29.10	yes	20	8.3	odd	2
192.3.i.b.17.5		20	8.5	even	2
192.3.i.b.17.10		20	24.5	odd	2
192.3.i.b.113.5		20	48.29	odd	4
192.3.i.b.113.10		20	16.13	even	4
384.3.i.c.161.1		20	3.2	odd	2	inner
384.3.i.c.161.6		20	1.1	even	1	trivial
384.3.i.c.353.1		20	16.5	even	4	inner
384.3.i.c.353.6		20	48.5	odd	4	inner
384.3.i.d.161.5		20	4.3	odd	2
384.3.i.d.161.10		20	12.11	even	2
384.3.i.d.353.5		20	48.11	even	4
384.3.i.d.353.10		20	16.11	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 384 = 2^{7} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	384.i (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.164573 - 2.99548i) q^{3} +(3.61305 + 3.61305i) q^{5} -12.2792i q^{7} +(-8.94583 + 0.985948i) q^{9} +O(q^{10})\)	\(q+(-0.164573 - 2.99548i) q^{3} +(3.61305 + 3.61305i) q^{5} -12.2792i q^{7} +(-8.94583 + 0.985948i) q^{9} +(1.76932 + 1.76932i) q^{11} +(2.38826 + 2.38826i) q^{13} +(10.2282 - 11.4174i) q^{15} -20.0754i q^{17} +(-8.77090 - 8.77090i) q^{19} +(-36.7820 + 2.02081i) q^{21} +13.1821 q^{23} +1.10820i q^{25} +(4.42563 + 26.6348i) q^{27} +(6.51544 - 6.51544i) q^{29} -37.5922 q^{31} +(5.00877 - 5.59113i) q^{33} +(44.3652 - 44.3652i) q^{35} +(-10.0057 + 10.0057i) q^{37} +(6.76096 - 7.54704i) q^{39} -4.57407 q^{41} +(21.2835 - 21.2835i) q^{43} +(-35.8840 - 28.7594i) q^{45} -54.8366i q^{47} -101.778 q^{49} +(-60.1356 + 3.30386i) q^{51} +(-21.5215 - 21.5215i) q^{53} +12.7852i q^{55} +(-24.8296 + 27.7165i) q^{57} +(-53.6617 - 53.6617i) q^{59} +(19.2186 + 19.2186i) q^{61} +(12.1066 + 109.847i) q^{63} +17.2578i q^{65} +(31.5603 + 31.5603i) q^{67} +(-2.16941 - 39.4867i) q^{69} +65.1220 q^{71} +50.2451i q^{73} +(3.31960 - 0.182380i) q^{75} +(21.7257 - 21.7257i) q^{77} -20.9299 q^{79} +(79.0558 - 17.6403i) q^{81} +(-6.35791 + 6.35791i) q^{83} +(72.5334 - 72.5334i) q^{85} +(-20.5891 - 18.4446i) q^{87} +166.399 q^{89} +(29.3259 - 29.3259i) q^{91} +(6.18664 + 112.607i) q^{93} -63.3793i q^{95} +139.213 q^{97} +(-17.5725 - 14.0835i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 6 q^{3}+O(q^{10}) \) 20 * q - 6 * q^3	\( 20 q - 6 q^{3} - 92 q^{13} + 116 q^{15} - 52 q^{19} - 48 q^{21} + 18 q^{27} + 80 q^{31} + 60 q^{33} + 116 q^{37} + 172 q^{43} - 60 q^{45} - 364 q^{49} + 128 q^{51} + 244 q^{61} - 296 q^{63} + 356 q^{67} + 20 q^{69} - 146 q^{75} - 384 q^{79} - 188 q^{81} - 48 q^{85} + 136 q^{91} + 132 q^{93} + 472 q^{97} - 452 q^{99}+O(q^{100}) \) 20 * q - 6 * q^3 - 92 * q^13 + 116 * q^15 - 52 * q^19 - 48 * q^21 + 18 * q^27 + 80 * q^31 + 60 * q^33 + 116 * q^37 + 172 * q^43 - 60 * q^45 - 364 * q^49 + 128 * q^51 + 244 * q^61 - 296 * q^63 + 356 * q^67 + 20 * q^69 - 146 * q^75 - 384 * q^79 - 188 * q^81 - 48 * q^85 + 136 * q^91 + 132 * q^93 + 472 * q^97 - 452 * q^99

Introduction

L-functions

Modular forms

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Representations

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Database

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