LMFDB - Embedded newform 180.3.c.c.91.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [180,3,Mod(91,180)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(180, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0, 0]))

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

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

chi := DirichletCharacter("180.91");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 180 = 2^{2} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	180.c (of order $2$, degree $1$, 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:	$4.90464475849$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.15012375625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 7x^{6} + 28x^{4} + 112x^{2} + 256 $ x^8 + 7x^6 + 28x^4 + 112*x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{10} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			91.6
Root			$-0.342371 + 1.97048i$ of defining polynomial
Character	$\chi$	$=$	180.91
Dual form			180.3.c.c.91.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.342371 + 1.97048i) q^{2} +(-3.76556 + 1.34927i) q^{4} -2.23607 q^{5} +11.5108i q^{7} +(-3.94792 - 6.95801i) q^{8} +O(q^{10})$	\(q+(0.342371 + 1.97048i) q^{2} +(-3.76556 + 1.34927i) q^{4} -2.23607 q^{5} +11.5108i q^{7} +(-3.94792 - 6.95801i) q^{8} +(-0.765564 - 4.40612i) q^{10} -9.97507i q^{11} -14.1245 q^{13} +(-22.6817 + 3.94096i) q^{14} +(12.3590 - 10.1615i) q^{16} -30.5776 q^{17} +12.2274i q^{19} +(8.42006 - 3.01706i) q^{20} +(19.6556 - 3.41517i) q^{22} +15.7638i q^{23} +5.00000 q^{25} +(-4.83582 - 27.8320i) q^{26} +(-15.5311 - 43.3446i) q^{28} +18.8943 q^{29} +35.2490i q^{31} +(24.2544 + 20.8740i) q^{32} +(-10.4689 - 60.2524i) q^{34} -25.7389i q^{35} +50.1245 q^{37} +(-24.0938 + 4.18631i) q^{38} +(8.82782 + 15.5586i) q^{40} +28.8444 q^{41} +24.4548i q^{43} +(13.4590 + 37.5618i) q^{44} +(-31.0623 + 5.39707i) q^{46} +55.6641i q^{47} -83.4981 q^{49} +(1.71185 + 9.85239i) q^{50} +(53.1868 - 19.0578i) q^{52} +2.46054 q^{53} +22.3049i q^{55} +(80.0921 - 45.4437i) q^{56} +(6.46887 + 37.2309i) q^{58} -64.6577i q^{59} -30.2490 q^{61} +(-69.4573 + 12.0682i) q^{62} +(-32.8278 + 54.9394i) q^{64} +31.5834 q^{65} +66.1981i q^{67} +(115.142 - 41.2574i) q^{68} +(50.7179 - 8.81224i) q^{70} +11.5775i q^{71} +2.24903 q^{73} +(17.1612 + 98.7692i) q^{74} +(-16.4981 - 46.0431i) q^{76} +114.821 q^{77} -78.4256i q^{79} +(-27.6355 + 22.7218i) q^{80} +(9.87548 + 56.8373i) q^{82} +146.061i q^{83} +68.3735 q^{85} +(-48.1877 + 8.37262i) q^{86} +(-69.4066 + 39.3808i) q^{88} -87.4311 q^{89} -162.584i q^{91} +(-21.2696 - 59.3597i) q^{92} +(-109.685 + 19.0578i) q^{94} -27.3413i q^{95} +126.747 q^{97} +(-28.5873 - 164.531i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 14 q^{4}+O(q^{10}) $ 8 * q - 14 * q^4	$ 8 q - 14 q^{4} + 10 q^{10} + 16 q^{13} - 14 q^{16} - 4 q^{22} + 40 q^{25} - 92 q^{28} - 116 q^{34} + 272 q^{37} - 10 q^{40} - 184 q^{46} - 152 q^{49} + 232 q^{52} + 84 q^{58} + 16 q^{61} - 182 q^{64} + 180 q^{70} - 240 q^{73} + 384 q^{76} + 208 q^{82} + 160 q^{85} - 652 q^{88} - 168 q^{94} + 240 q^{97}+O(q^{100}) $ 8 * q - 14 * q^4 + 10 * q^10 + 16 * q^13 - 14 * q^16 - 4 * q^22 + 40 * q^25 - 92 * q^28 - 116 * q^34 + 272 * q^37 - 10 * q^40 - 184 * q^46 - 152 * q^49 + 232 * q^52 + 84 * q^58 + 16 * q^61 - 182 * q^64 + 180 * q^70 - 240 * q^73 + 384 * q^76 + 208 * q^82 + 160 * q^85 - 652 * q^88 - 168 * q^94 + 240 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/180\mathbb{Z}\right)^\times$.

$n$	$37$	$91$	$101$
$\chi(n)$	$1$	$-1$	$1$

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 $

$2$	0.342371	+	1.97048i	0.171185	+	0.985239i
$2$	0.342371	+	1.97048i	0.171185	+	0.985239i
$3$		0			0
$3$		0			0
$4$	−3.76556	+	1.34927i	−0.941391	+	0.337317i
$5$	−2.23607			−0.447214
$5$	−2.23607			−0.447214
$6$		0			0
$7$			11.5108i			1.64440i	0.569201	+	0.822199i	$0.307253\pi$
$7$			11.5108i			1.64440i	−0.569201	+	0.822199i	$0.692747\pi$
$8$	−3.94792	−	6.95801i	−0.493490	−	0.869751i
$9$		0			0
$10$	−0.765564	−	4.40612i	−0.0765564	−	0.440612i
$11$		−	9.97507i		−	0.906824i	−0.891301	−	0.453412i	$-0.850207\pi$
$11$		−	9.97507i		−	0.906824i	0.891301	−	0.453412i	$-0.149793\pi$
$12$		0			0
$13$	−14.1245			−1.08650			−0.543251	−	0.839571i	$-0.682807\pi$
$13$	−14.1245			−1.08650			−0.543251	+	0.839571i	$0.682807\pi$
$14$	−22.6817	+	3.94096i	−1.62012	+	0.281497i
$15$		0			0
$16$	12.3590	−	10.1615i	0.772434	−	0.635095i
$17$	−30.5776			−1.79868			−0.899341	−	0.437249i	$-0.855953\pi$
$17$	−30.5776			−1.79868			−0.899341	+	0.437249i	$0.855953\pi$
$18$		0			0
$19$			12.2274i			0.643548i	0.946816	+	0.321774i	$0.104279\pi$
$19$			12.2274i			0.643548i	−0.946816	+	0.321774i	$0.895721\pi$
$20$	8.42006	−	3.01706i	0.421003	−	0.150853i
$21$		0			0
$22$	19.6556	−	3.41517i	0.893438	−	0.155235i
$23$			15.7638i			0.685384i	0.939448	+	0.342692i	$0.111339\pi$
$23$			15.7638i			0.685384i	−0.939448	+	0.342692i	$0.888661\pi$
$24$		0			0
$25$	5.00000			0.200000
$26$	−4.83582	−	27.8320i	−0.185993	−	1.07046i
$27$		0			0
$28$	−15.5311	−	43.3446i	−0.554683	−	1.54802i
$29$	18.8943			0.651529			0.325765	−	0.945451i	$-0.394378\pi$
$29$	18.8943			0.651529			0.325765	+	0.945451i	$0.394378\pi$
$30$		0			0
$31$			35.2490i			1.13706i	0.822661	+	0.568532i	$0.192488\pi$
$31$			35.2490i			1.13706i	−0.822661	+	0.568532i	$0.807512\pi$
$32$	24.2544	+	20.8740i	0.757949	+	0.652313i
$33$		0			0
$34$	−10.4689	−	60.2524i	−0.307908	−	1.77213i
$35$		−	25.7389i		−	0.735397i
$36$		0			0
$37$	50.1245			1.35472			0.677358	−	0.735653i	$-0.263125\pi$
$37$	50.1245			1.35472			0.677358	+	0.735653i	$0.263125\pi$
$38$	−24.0938	+	4.18631i	−0.634049	+	0.110166i
$39$		0			0
$40$	8.82782	+	15.5586i	0.220696	+	0.388965i
$41$	28.8444			0.703522			0.351761	−	0.936090i	$-0.385583\pi$
$41$	28.8444			0.703522			0.351761	+	0.936090i	$0.385583\pi$
$42$		0			0
$43$			24.4548i			0.568717i	0.958718	+	0.284359i	$0.0917806\pi$
$43$			24.4548i			0.568717i	−0.958718	+	0.284359i	$0.908219\pi$
$44$	13.4590	+	37.5618i	0.305887	+	0.853676i
$45$		0			0
$46$	−31.0623	+	5.39707i	−0.675266	+	0.117328i
$47$			55.6641i			1.18434i	0.805812	+	0.592171i	$0.201729\pi$
$47$			55.6641i			1.18434i	−0.805812	+	0.592171i	$0.798271\pi$
$48$		0			0
$49$	−83.4981			−1.70404
$50$	1.71185	+	9.85239i	0.0342371	+	0.197048i
$51$		0			0
$52$	53.1868	−	19.0578i	1.02282	−	0.366495i
$53$	2.46054			0.0464253			0.0232127	−	0.999731i	$-0.492611\pi$
$53$	2.46054			0.0464253			0.0232127	+	0.999731i	$0.492611\pi$
$54$		0			0
$55$			22.3049i			0.405544i
$56$	80.0921	−	45.4437i	1.43022	−	0.811494i
$57$		0			0
$58$	6.46887	+	37.2309i	0.111532	+	0.641912i
$59$		−	64.6577i		−	1.09589i	−0.836513	−	0.547947i	$-0.815410\pi$
$59$		−	64.6577i		−	1.09589i	0.836513	−	0.547947i	$-0.184590\pi$
$60$		0			0
$61$	−30.2490			−0.495886			−0.247943	−	0.968775i	$-0.579755\pi$
$61$	−30.2490			−0.495886			−0.247943	+	0.968775i	$0.579755\pi$
$62$	−69.4573	+	12.0682i	−1.12028	+	0.194649i
$63$		0			0
$64$	−32.8278	+	54.9394i	−0.512935	+	0.858428i
$65$	31.5834			0.485898
$66$		0			0
$67$			66.1981i			0.988032i	0.869453	+	0.494016i	$0.164472\pi$
$67$			66.1981i			0.988032i	−0.869453	+	0.494016i	$0.835528\pi$
$68$	115.142	−	41.2574i	1.69326	−	0.606726i
$69$		0			0
$70$	50.7179	−	8.81224i	0.724541	−	0.125889i
$71$			11.5775i			0.163064i	0.996671	+	0.0815318i	$0.0259812\pi$
$71$			11.5775i			0.163064i	−0.996671	+	0.0815318i	$0.974019\pi$
$72$		0			0
$73$	2.24903			0.0308086			0.0154043	−	0.999881i	$-0.495096\pi$
$73$	2.24903			0.0308086			0.0154043	+	0.999881i	$0.495096\pi$
$74$	17.1612	+	98.7692i	0.231908	+	1.33472i
$75$		0			0
$76$	−16.4981	−	46.0431i	−0.217080	−	0.605831i
$77$	114.821			1.49118
$78$		0			0
$79$		−	78.4256i		−	0.992729i	−0.868114	−	0.496364i	$-0.834668\pi$
$79$		−	78.4256i		−	0.992729i	0.868114	−	0.496364i	$-0.165332\pi$
$80$	−27.6355	+	22.7218i	−0.345443	+	0.284023i
$81$		0			0
$82$	9.87548	+	56.8373i	0.120433	+	0.693137i
$83$			146.061i			1.75977i	0.475189	+	0.879884i	$0.342380\pi$
$83$			146.061i			1.75977i	−0.475189	+	0.879884i	$0.657620\pi$
$84$		0			0
$85$	68.3735			0.804395
$86$	−48.1877	+	8.37262i	−0.560322	+	0.0973561i
$87$		0			0
$88$	−69.4066	+	39.3808i	−0.788712	+	0.447509i
$89$	−87.4311			−0.982372			−0.491186	−	0.871055i	$-0.663436\pi$
$89$	−87.4311			−0.982372			−0.491186	+	0.871055i	$0.663436\pi$
$90$		0			0
$91$		−	162.584i		−	1.78664i
$92$	−21.2696	−	59.3597i	−0.231192	−	0.645214i
$93$		0			0
$94$	−109.685	+	19.0578i	−1.16686	+	0.202742i
$95$		−	27.3413i		−	0.287803i
$96$		0			0
$97$	126.747			1.30667			0.653336	−	0.757068i	$-0.273369\pi$
$97$	126.747			1.30667			0.653336	+	0.757068i	$0.273369\pi$
$98$	−28.5873	−	164.531i	−0.291707	−	1.67889i
$99$		0			0
$100$	−18.8278	+	6.74634i	−0.188278	+	0.0674634i
$101$	−66.1841			−0.655289			−0.327644	−	0.944801i	$-0.606255\pi$
$101$	−66.1841			−0.655289			−0.327644	+	0.944801i	$0.606255\pi$
$102$		0			0
$103$		−	105.030i		−	1.01971i	−0.860260	−	0.509856i	$-0.829699\pi$
$103$		−	105.030i		−	1.01971i	0.860260	−	0.509856i	$-0.170301\pi$
$104$	55.7625	+	98.2785i	0.536178	+	0.944986i
$105$		0			0
$106$	0.842418	+	4.84844i	0.00794734	+	0.0457400i
$107$		−	68.2230i		−	0.637598i	−0.947822	−	0.318799i	$-0.896720\pi$
$107$		−	68.2230i		−	0.637598i	0.947822	−	0.318799i	$-0.103280\pi$
$108$		0			0
$109$	−33.5019			−0.307357			−0.153679	−	0.988121i	$-0.549112\pi$
$109$	−33.5019			−0.307357			−0.153679	+	0.988121i	$0.549112\pi$
$110$	−43.9514	+	7.63656i	−0.399558	+	0.0694232i
$111$		0			0
$112$	116.967	+	142.261i	1.04435	+	1.27019i
$113$	−143.944			−1.27384			−0.636919	−	0.770931i	$-0.719791\pi$
$113$	−143.944			−1.27384			−0.636919	+	0.770931i	$0.719791\pi$
$114$		0			0
$115$		−	35.2490i		−	0.306513i
$116$	−71.1479	+	25.4935i	−0.613344	+	0.219772i
$117$		0			0
$118$	127.407	−	22.1369i	1.07972	−	0.187601i
$119$		−	351.972i		−	2.95775i
$120$		0			0
$121$	21.4981			0.177670
$122$	−10.3564	−	59.6050i	−0.0848884	−	0.488566i
$123$		0			0
$124$	−47.5603	−	132.732i	−0.383551	−	1.07042i
$125$	−11.1803			−0.0894427
$126$		0			0
$127$		−	199.983i		−	1.57467i	−0.616525	−	0.787335i	$-0.711460\pi$
$127$		−	199.983i		−	1.57467i	0.616525	−	0.787335i	$-0.288540\pi$
$128$	−119.496	−	45.8769i	−0.933563	−	0.358413i
$129$		0			0
$130$	10.8132	+	62.2343i	0.0831787	+	0.478726i
$131$			247.414i			1.88866i	0.329007	+	0.944328i	$0.393286\pi$
$131$			247.414i			1.88866i	−0.329007	+	0.944328i	$0.606714\pi$
$132$		0			0
$133$	−140.747			−1.05825
$134$	−130.442	+	22.6643i	−0.973447	+	0.169137i
$135$		0			0
$136$	120.718	+	212.759i	0.887632	+	1.56441i
$137$	−141.375			−1.03194			−0.515968	−	0.856608i	$-0.672568\pi$
$137$	−141.375			−1.03194			−0.515968	+	0.856608i	$0.672568\pi$
$138$		0			0
$139$		−	58.2705i		−	0.419212i	−0.977786	−	0.209606i	$-0.932782\pi$
$139$		−	58.2705i		−	0.419212i	0.977786	−	0.209606i	$-0.0672182\pi$
$140$	34.7287	+	96.9214i	0.248062	+	0.692296i
$141$		0			0
$142$	−22.8132	+	3.96380i	−0.160657	+	0.0279141i
$143$			140.893i			0.985266i
$144$		0			0
$145$	−42.2490			−0.291373
$146$	0.770003	+	4.43167i	0.00527399	+	0.0303539i
$147$		0			0
$148$	−188.747	+	67.6314i	−1.27532	+	0.456969i
$149$	265.527			1.78206			0.891029	−	0.453947i	$-0.149984\pi$
$149$	265.527			1.78206			0.891029	+	0.453947i	$0.149984\pi$
$150$		0			0
$151$			217.988i			1.44363i	0.692086	+	0.721815i	$0.256692\pi$
$151$			217.988i			1.44363i	−0.692086	+	0.721815i	$0.743308\pi$
$152$	85.0785	−	48.2729i	0.559727	−	0.317585i
$153$		0			0
$154$	39.3113	+	226.252i	0.255268	+	1.46917i
$155$		−	78.8191i		−	0.508510i
$156$		0			0
$157$	66.3735			0.422761			0.211381	−	0.977404i	$-0.432204\pi$
$157$	66.3735			0.422761			0.211381	+	0.977404i	$0.432204\pi$
$158$	154.536	−	26.8506i	0.978075	−	0.169941i
$159$		0			0
$160$	−54.2344	−	46.6758i	−0.338965	−	0.291723i
$161$	−181.454			−1.12704
$162$		0			0
$163$		−	93.5195i		−	0.573739i	−0.957970	−	0.286870i	$-0.907385\pi$
$163$		−	93.5195i		−	0.573739i	0.957970	−	0.286870i	$-0.0926147\pi$
$164$	−108.615	+	38.9188i	−0.662290	+	0.237310i
$165$		0			0
$166$	−287.809	+	50.0069i	−1.73379	+	0.301247i
$167$		−	47.2915i		−	0.283182i	−0.989925	−	0.141591i	$-0.954778\pi$
$167$		−	47.2915i		−	0.283182i	0.989925	−	0.141591i	$-0.0452219\pi$
$168$		0			0
$169$	30.5019			0.180485
$170$	23.4091	+	134.729i	0.137701	+	0.792521i
$171$		0			0
$172$	−32.9961	−	92.0862i	−0.191838	−	0.535385i
$173$	229.534			1.32678			0.663392	−	0.748272i	$-0.269116\pi$
$173$	229.534			1.32678			0.663392	+	0.748272i	$0.269116\pi$
$174$		0			0
$175$			57.5539i			0.328879i
$176$	−101.362	−	123.281i	−0.575919	−	0.700462i
$177$		0			0
$178$	−29.9339	−	172.281i	−0.168168	−	0.967871i
$179$		−	150.868i		−	0.842838i	−0.906866	−	0.421419i	$-0.861532\pi$
$179$		−	150.868i		−	0.842838i	0.906866	−	0.421419i	$-0.138468\pi$
$180$		0			0
$181$	54.4981			0.301094			0.150547	−	0.988603i	$-0.451896\pi$
$181$	54.4981			0.301094			0.150547	+	0.988603i	$0.451896\pi$
$182$	320.369	−	55.6641i	1.76027	−	0.305847i
$183$		0			0
$184$	109.685	−	62.2343i	0.596113	−	0.338230i
$185$	−112.082			−0.605848
$186$		0			0
$187$			305.013i			1.63109i
$188$	−75.1058	−	209.607i	−0.399499	−	1.11493i
$189$		0			0
$190$	53.8755	−	9.36087i	0.283555	−	0.0492678i
$191$			225.861i			1.18252i	0.806481	+	0.591260i	$0.201369\pi$
$191$			225.861i			1.18252i	−0.806481	+	0.591260i	$0.798631\pi$
$192$		0			0
$193$	174.498			0.904135			0.452068	−	0.891984i	$-0.350687\pi$
$193$	174.498			0.904135			0.452068	+	0.891984i	$0.350687\pi$
$194$	43.3945	+	249.752i	0.223683	+	1.28738i
$195$		0			0
$196$	314.417	−	112.661i	1.60417	−	0.574802i
$197$	−15.9849			−0.0811414			−0.0405707	−	0.999177i	$-0.512918\pi$
$197$	−15.9849			−0.0811414			−0.0405707	+	0.999177i	$0.512918\pi$
$198$		0			0
$199$			30.9492i			0.155523i	0.996972	+	0.0777617i	$0.0247773\pi$
$199$			30.9492i			0.155523i	−0.996972	+	0.0777617i	$0.975223\pi$
$200$	−19.7396	−	34.7901i	−0.0986981	−	0.173950i
$201$		0			0
$202$	−22.6595	−	130.414i	−0.112176	−	0.645616i
$203$			217.489i			1.07137i
$204$		0			0
$205$	−64.4981			−0.314625
$206$	206.960	−	35.9593i	1.00466	−	0.174560i
$207$		0			0
$208$	−174.564	+	143.526i	−0.839251	+	0.690031i
$209$	121.969			0.583585
$210$		0			0
$211$		−	190.667i		−	0.903634i	−0.892111	−	0.451817i	$-0.850776\pi$
$211$		−	190.667i		−	0.903634i	0.892111	−	0.451817i	$-0.149224\pi$
$212$	−9.26533	+	3.31993i	−0.0437044	+	0.0156600i
$213$		0			0
$214$	134.432	−	23.3576i	0.628187	−	0.109148i
$215$		−	54.6827i		−	0.254338i
$216$		0			0
$217$	−405.743			−1.86978
$218$	−11.4701	−	66.0148i	−0.0526151	−	0.302820i
$219$		0			0
$220$	−30.0953	−	83.9906i	−0.136797	−	0.381776i
$221$	431.893			1.95427
$222$		0			0
$223$			317.957i			1.42582i	0.701257	+	0.712909i	$0.252623\pi$
$223$			317.957i			1.42582i	−0.701257	+	0.712909i	$0.747377\pi$
$224$	−240.276	+	279.187i	−1.07266	+	1.24637i
$225$		0			0
$226$	−49.2821	−	283.638i	−0.218062	−	1.25503i
$227$			39.9003i			0.175772i	0.996131	+	0.0878860i	$0.0280111\pi$
$227$			39.9003i			0.175772i	−0.996131	+	0.0878860i	$0.971989\pi$
$228$		0			0
$229$	13.7510			0.0600479			0.0300239	−	0.999549i	$-0.490442\pi$
$229$	13.7510			0.0600479			0.0300239	+	0.999549i	$0.490442\pi$
$230$	69.4573	−	12.0682i	0.301988	−	0.0524705i
$231$		0			0
$232$	−74.5934	−	131.467i	−0.321523	−	0.566668i
$233$	−121.475			−0.521352			−0.260676	−	0.965426i	$-0.583945\pi$
$233$	−121.475			−0.521352			−0.260676	+	0.965426i	$0.583945\pi$
$234$		0			0
$235$		−	124.469i		−	0.529654i
$236$	87.2406	+	243.473i	0.369664	+	1.03166i
$237$		0			0
$238$	693.553	−	120.505i	2.91409	−	0.506323i
$239$		−	160.843i		−	0.672984i	−0.941686	−	0.336492i	$-0.890760\pi$
$239$		−	160.843i		−	0.672984i	0.941686	−	0.336492i	$-0.109240\pi$
$240$		0			0
$241$	−3.49419			−0.0144987			−0.00724935	−	0.999974i	$-0.502308\pi$
$241$	−3.49419			−0.0144987			−0.00724935	+	0.999974i	$0.502308\pi$
$242$	7.36031	+	42.3615i	0.0304145	+	0.175047i
$243$		0			0
$244$	113.905	−	40.8141i	0.466822	−	0.167271i
$245$	186.707			0.762071
$246$		0			0
$247$		−	172.706i		−	0.699216i
$248$	245.263	−	139.160i	0.988963	−	0.561130i
$249$		0			0
$250$	−3.82782	−	22.0306i	−0.0153113	−	0.0881224i
$251$		−	315.637i		−	1.25752i	−0.777601	−	0.628759i	$-0.783563\pi$
$251$		−	315.637i		−	1.25752i	0.777601	−	0.628759i	$-0.216437\pi$
$252$		0			0
$253$	157.245			0.621522
$254$	394.062	−	68.4684i	1.55143	−	0.269561i
$255$		0			0
$256$	49.4873	−	251.171i	0.193310	−	0.981138i
$257$	86.8117			0.337789			0.168894	−	0.985634i	$-0.445980\pi$
$257$	86.8117			0.337789			0.168894	+	0.985634i	$0.445980\pi$
$258$		0			0
$259$			576.972i			2.22769i
$260$	−118.929	+	42.6144i	−0.457420	+	0.163902i
$261$		0			0
$262$	−487.523	+	84.7073i	−1.86078	+	0.323310i
$263$			333.003i			1.26617i	0.774082	+	0.633086i	$0.218212\pi$
$263$			333.003i			1.26617i	−0.774082	+	0.633086i	$0.781788\pi$
$264$		0			0
$265$	−5.50194			−0.0207620
$266$	−48.1877	−	277.339i	−0.181157	−	1.04263i
$267$		0			0
$268$	−89.3190	−	249.273i	−0.333280	−	0.930124i
$269$	−191.063			−0.710271			−0.355136	−	0.934815i	$-0.615565\pi$
$269$	−191.063			−0.710271			−0.355136	+	0.934815i	$0.615565\pi$
$270$		0			0
$271$			261.165i			0.963708i	0.876252	+	0.481854i	$0.160036\pi$
$271$			261.165i			0.963708i	−0.876252	+	0.481854i	$0.839964\pi$
$272$	−377.907	+	310.714i	−1.38936	+	1.14233i
$273$		0			0
$274$	−48.4027	−	278.577i	−0.176652	−	1.01670i
$275$		−	49.8753i		−	0.181365i
$276$		0			0
$277$	−204.615			−0.738682			−0.369341	−	0.929294i	$-0.620417\pi$
$277$	−204.615			−0.738682			−0.369341	+	0.929294i	$0.620417\pi$
$278$	114.821	−	19.9501i	0.413024	−	0.0717631i
$279$		0			0
$280$	−179.091	+	101.615i	−0.639612	+	0.362911i
$281$	−458.726			−1.63248			−0.816239	−	0.577714i	$-0.803945\pi$
$281$	−458.726			−1.63248			−0.816239	+	0.577714i	$0.803945\pi$
$282$		0			0
$283$			336.724i			1.18984i	0.803786	+	0.594918i	$0.202816\pi$
$283$			336.724i			1.18984i	−0.803786	+	0.594918i	$0.797184\pi$
$284$	−15.6212	−	43.5959i	−0.0550041	−	0.153507i
$285$		0			0
$286$	−277.626	+	48.2376i	−0.970722	+	0.168663i
$287$			332.022i			1.15687i
$288$		0			0
$289$	645.988			2.23525
$290$	−14.4648	−	83.2508i	−0.0498787	−	0.287072i
$291$		0			0
$292$	−8.46887	+	3.03455i	−0.0290030	+	0.0103923i
$293$	−249.650			−0.852046			−0.426023	−	0.904712i	$-0.640086\pi$
$293$	−249.650			−0.852046			−0.426023	+	0.904712i	$0.640086\pi$
$294$		0			0
$295$			144.579i			0.490099i
$296$	−197.888	−	348.767i	−0.668539	−	1.17827i
$297$		0			0
$298$	90.9086	+	523.214i	0.305062	+	1.75575i
$299$		−	222.656i		−	0.744670i
$300$		0			0
$301$	−281.494			−0.935197
$302$	−429.541	+	74.6328i	−1.42232	+	0.247128i
$303$		0			0
$304$	124.249	+	151.118i	0.408714	+	0.497099i
$305$	67.6389			0.221767
$306$		0			0
$307$		−	156.851i		−	0.510916i	−0.966820	−	0.255458i	$-0.917774\pi$
$307$		−	156.851i		−	0.510916i	0.966820	−	0.255458i	$-0.0822262\pi$
$308$	−432.365	+	154.924i	−1.40378	+	0.503000i
$309$		0			0
$310$	155.311	−	26.9854i	0.501004	−	0.0870496i
$311$		−	164.769i		−	0.529803i	−0.964275	−	0.264902i	$-0.914661\pi$
$311$		−	164.769i		−	0.529803i	0.964275	−	0.264902i	$-0.0853395\pi$
$312$		0			0
$313$	−131.992			−0.421700			−0.210850	−	0.977518i	$-0.567623\pi$
$313$	−131.992			−0.421700			−0.210850	+	0.977518i	$0.567623\pi$
$314$	22.7244	+	130.788i	0.0723706	+	0.416521i
$315$		0			0
$316$	105.817	+	295.316i	0.334864	+	0.934546i
$317$	169.833			0.535752			0.267876	−	0.963453i	$-0.413678\pi$
$317$	169.833			0.535752			0.267876	+	0.963453i	$0.413678\pi$
$318$		0			0
$319$		−	188.472i		−	0.590822i
$320$	73.4052	−	122.848i	0.229391	−	0.383901i
$321$		0			0
$322$	−62.1245	−	357.551i	−0.192933	−	1.11041i
$323$		−	373.885i		−	1.15754i
$324$		0			0
$325$	−70.6226			−0.217300
$326$	184.278	−	32.0184i	0.565270	−	0.0982158i
$327$		0			0
$328$	−113.875	−	200.700i	−0.347181	−	0.611889i
$329$	−640.737			−1.94753
$330$		0			0
$331$			171.945i			0.519472i	0.965680	+	0.259736i	$0.0836355\pi$
$331$			171.945i			0.519472i	−0.965680	+	0.259736i	$0.916365\pi$
$332$	−197.075	−	550.001i	−0.593600	−	1.65663i
$333$		0			0
$334$	93.1868	−	16.1912i	0.279002	−	0.0484767i
$335$		−	148.024i		−	0.441861i
$336$		0			0
$337$	−470.249			−1.39540			−0.697699	−	0.716391i	$-0.745793\pi$
$337$	−470.249			−1.39540			−0.697699	+	0.716391i	$0.745793\pi$
$338$	10.4430	+	60.1034i	0.0308964	+	0.177821i
$339$		0			0
$340$	−257.465	+	92.2542i	−0.757250	+	0.271336i
$341$	351.611			1.03112
$342$		0			0
$343$		−	397.100i		−	1.15772i
$344$	170.157	−	96.5458i	0.494642	−	0.280656i
$345$		0			0
$346$	78.5856	+	452.291i	0.227126	+	1.30720i
$347$			167.974i			0.484074i	0.970267	+	0.242037i	$0.0778155\pi$
$347$			167.974i			0.484074i	−0.970267	+	0.242037i	$0.922184\pi$
$348$		0			0
$349$	−158.747			−0.454863			−0.227431	−	0.973794i	$-0.573033\pi$
$349$	−158.747			−0.454863			−0.227431	+	0.973794i	$0.573033\pi$
$350$	−113.409	+	19.7048i	−0.324025	+	0.0562994i
$351$		0			0
$352$	208.220	−	241.939i	0.591534	−	0.687327i
$353$	−201.076			−0.569619			−0.284810	−	0.958584i	$-0.591930\pi$
$353$	−201.076			−0.569619			−0.284810	+	0.958584i	$0.591930\pi$
$354$		0			0
$355$		−	25.8881i		−	0.0729242i
$356$	329.228	−	117.968i	0.924796	−	0.331371i
$357$		0			0
$358$	297.282	−	51.6528i	0.830397	−	0.144282i
$359$			689.161i			1.91967i	0.280567	+	0.959835i	$0.409478\pi$
$359$			689.161i			1.91967i	−0.280567	+	0.959835i	$0.590522\pi$
$360$		0			0
$361$	211.490			0.585846
$362$	18.6585	+	107.387i	0.0515429	+	0.296650i
$363$		0			0
$364$	219.370	+	612.221i	0.602664	+	1.68193i
$365$	−5.02899			−0.0137780
$366$		0			0
$367$			11.5108i			0.0313645i	0.999877	+	0.0156823i	$0.00499202\pi$
$367$			11.5108i			0.0313645i	−0.999877	+	0.0156823i	$0.995008\pi$
$368$	160.184	+	194.824i	0.435283	+	0.529414i
$369$		0			0
$370$	−38.3735	−	220.855i	−0.103712	−	0.596905i
$371$			28.3228i			0.0763417i
$372$		0			0
$373$	356.864			0.956740			0.478370	−	0.878159i	$-0.341228\pi$
$373$	356.864			0.956740			0.478370	+	0.878159i	$0.341228\pi$
$374$	−601.022	+	104.428i	−1.60701	+	0.279218i
$375$		0			0
$376$	387.311	−	219.757i	1.03008	−	0.584461i
$377$	−266.873			−0.707887
$378$		0			0
$379$		−	554.623i		−	1.46338i	−0.681635	−	0.731692i	$-0.738731\pi$
$379$		−	554.623i		−	1.46338i	0.681635	−	0.731692i	$-0.261269\pi$
$380$	36.8908	+	102.956i	0.0970810	+	0.270936i
$381$		0			0
$382$	−445.055	+	77.3283i	−1.16506	+	0.202430i
$383$		−	442.368i		−	1.15501i	−0.816388	−	0.577504i	$-0.804027\pi$
$383$		−	442.368i		−	1.15501i	0.816388	−	0.577504i	$-0.195973\pi$
$384$		0			0
$385$	−256.747			−0.666876
$386$	59.7430	+	343.845i	0.154775	+	0.890789i
$387$		0			0
$388$	−477.274	+	171.016i	−1.23009	+	0.440762i
$389$	356.424			0.916257			0.458129	−	0.888886i	$-0.348520\pi$
$389$	356.424			0.916257			0.458129	+	0.888886i	$0.348520\pi$
$390$		0			0
$391$		−	482.020i		−	1.23279i
$392$	329.644	+	580.980i	0.840928	+	1.48209i
$393$		0			0
$394$	−5.47275	−	31.4978i	−0.0138902	−	0.0799436i
$395$			175.365i			0.443962i
$396$		0			0
$397$	512.864			1.29185			0.645924	−	0.763402i	$-0.276472\pi$
$397$	512.864			1.29185			0.645924	+	0.763402i	$0.276472\pi$
$398$	−60.9846	+	10.5961i	−0.153228	+	0.0266233i
$399$		0			0
$400$	61.7948	−	50.8076i	0.154487	−	0.127019i
$401$	10.3990			0.0259327			0.0129664	−	0.999916i	$-0.495873\pi$
$401$	10.3990			0.0259327			0.0129664	+	0.999916i	$0.495873\pi$
$402$		0			0
$403$		−	497.875i		−	1.23542i
$404$	249.221	−	89.3002i	0.616883	−	0.221040i
$405$		0			0
$406$	−428.556	+	74.4618i	−1.05556	+	0.183403i
$407$		−	499.995i		−	1.22849i
$408$		0			0
$409$	251.494			0.614900			0.307450	−	0.951564i	$-0.400524\pi$
$409$	251.494			0.614900			0.307450	+	0.951564i	$0.400524\pi$
$410$	−22.0823	−	127.092i	−0.0538592	−	0.309980i
$411$		0			0
$412$	141.714	+	395.498i	0.343966	+	0.959947i
$413$	744.261			1.80208
$414$		0			0
$415$		−	326.602i		−	0.786992i
$416$	−342.581	−	294.836i	−0.823513	−	0.708739i
$417$		0			0
$418$	41.7587	+	240.338i	0.0999012	+	0.574971i
$419$			205.551i			0.490574i	0.969450	+	0.245287i	$0.0788823\pi$
$419$			205.551i			0.490574i	−0.969450	+	0.245287i	$0.921118\pi$
$420$		0			0
$421$	811.230			1.92691			0.963456	−	0.267868i	$-0.0863191\pi$
$421$	811.230			1.92691			0.963456	+	0.267868i	$0.0863191\pi$
$422$	375.705	−	65.2788i	0.890296	−	0.154689i
$423$		0			0
$424$	−9.71403	−	17.1205i	−0.0229104	−	0.0403785i
$425$	−152.888			−0.359736
$426$		0			0
$427$		−	348.190i		−	0.815433i
$428$	92.0511	+	256.898i	0.215073	+	0.600229i
$429$		0			0
$430$	107.751	−	18.7217i	0.250584	−	0.0435390i
$431$		−	359.624i		−	0.834394i	−0.908816	−	0.417197i	$-0.863013\pi$
$431$		−	359.624i		−	0.834394i	0.908816	−	0.417197i	$-0.136987\pi$
$432$		0			0
$433$	−198.747			−0.459000			−0.229500	−	0.973309i	$-0.573709\pi$
$433$	−198.747			−0.459000			−0.229500	+	0.973309i	$0.573709\pi$
$434$	−138.915	−	799.508i	−0.320080	−	1.84218i
$435$		0			0
$436$	126.154	−	45.2031i	0.289343	−	0.103677i
$437$	−192.751			−0.441077
$438$		0			0
$439$			353.251i			0.804672i	0.915492	+	0.402336i	$0.131802\pi$
$439$			353.251i			0.804672i	−0.915492	+	0.402336i	$0.868198\pi$
$440$	155.198	−	88.0581i	0.352723	−	0.200132i
$441$		0			0
$442$	147.868	+	851.036i	0.334542	+	1.92542i
$443$			209.837i			0.473672i	0.971550	+	0.236836i	$0.0761104\pi$
$443$			209.837i			0.473672i	−0.971550	+	0.236836i	$0.923890\pi$
$444$		0			0
$445$	195.502			0.439330
$446$	−626.528	+	108.859i	−1.40477	+	0.244079i
$447$		0			0
$448$	−632.395	−	377.874i	−1.41160	−	0.843468i
$449$	617.155			1.37451			0.687255	−	0.726416i	$-0.258816\pi$
$449$	617.155			1.37451			0.687255	+	0.726416i	$0.258816\pi$
$450$		0			0
$451$		−	287.725i		−	0.637971i
$452$	542.029	−	194.219i	1.19918	−	0.429687i
$453$		0			0
$454$	−78.6226	+	13.6607i	−0.173177	+	0.0300896i
$455$			363.549i			0.799009i
$456$		0			0
$457$	−129.253			−0.282829			−0.141415	−	0.989950i	$-0.545165\pi$
$457$	−129.253			−0.282829			−0.141415	+	0.989950i	$0.545165\pi$
$458$	4.70793	+	27.0960i	0.0102793	+	0.0591615i
$459$		0			0
$460$	47.5603	+	132.732i	0.103392	+	0.288548i
$461$	18.6785			0.0405174			0.0202587	−	0.999795i	$-0.493551\pi$
$461$	18.6785			0.0405174			0.0202587	+	0.999795i	$0.493551\pi$
$462$		0			0
$463$			109.419i			0.236327i	0.992994	+	0.118163i	$0.0377007\pi$
$463$			109.419i			0.236327i	−0.992994	+	0.118163i	$0.962299\pi$
$464$	233.514	−	191.995i	0.503263	−	0.413782i
$465$		0			0
$466$	−41.5895	−	239.364i	−0.0892479	−	0.513656i
$467$			250.979i			0.537428i	0.963220	+	0.268714i	$0.0865987\pi$
$467$			250.979i			0.537428i	−0.963220	+	0.268714i	$0.913401\pi$
$468$		0			0
$469$	−761.992			−1.62472
$470$	245.263	−	42.6144i	0.521836	−	0.0906690i
$471$		0			0
$472$	−449.889	+	255.264i	−0.953155	+	0.540813i
$473$	243.939			0.515726
$474$		0			0
$475$			61.1371i			0.128710i
$476$	474.904	+	1325.37i	0.997698	+	2.78440i
$477$		0			0
$478$	316.938	−	55.0680i	0.663050	−	0.115205i
$479$			373.164i			0.779048i	0.921016	+	0.389524i	$0.127360\pi$
$479$			373.164i			0.779048i	−0.921016	+	0.389524i	$0.872640\pi$
$480$		0			0
$481$	−707.984			−1.47190
$482$	−1.19631	−	6.88522i	−0.00248197	−	0.0142847i
$483$		0			0
$484$	−80.9523	+	29.0066i	−0.167257	+	0.0599311i
$485$	−283.415			−0.584361
$486$		0			0
$487$			182.784i			0.375326i	0.982233	+	0.187663i	$0.0600913\pi$
$487$			182.784i			0.375326i	−0.982233	+	0.187663i	$0.939909\pi$
$488$	119.421	+	210.473i	0.244715	+	0.431297i
$489$		0			0
$490$	63.9231	+	367.903i	0.130455	+	0.750822i
$491$			413.425i			0.842005i	0.907059	+	0.421003i	$0.138322\pi$
$491$			413.425i			0.842005i	−0.907059	+	0.421003i	$0.861678\pi$
$492$		0			0
$493$	−577.743			−1.17189
$494$	340.314	−	59.1296i	0.688895	−	0.119696i
$495$		0			0
$496$	358.183	+	435.640i	0.722143	+	0.878307i
$497$	−133.266			−0.268141
$498$		0			0
$499$		−	92.8475i		−	0.186067i	−0.995663	−	0.0930336i	$-0.970344\pi$
$499$		−	92.8475i		−	0.186067i	0.995663	−	0.0930336i	$-0.0296564\pi$
$500$	42.1003	−	15.0853i	0.0842006	−	0.0301706i
$501$		0			0
$502$	621.955	−	108.065i	1.23895	−	0.215269i
$503$		−	415.288i		−	0.825622i	−0.910817	−	0.412811i	$-0.864547\pi$
$503$		−	415.288i		−	0.825622i	0.910817	−	0.412811i	$-0.135453\pi$
$504$		0			0
$505$	147.992			0.293054
$506$	53.8362	+	309.848i	0.106396	+	0.612348i
$507$		0			0
$508$	269.831	+	753.049i	0.531163	+	1.48238i
$509$	396.009			0.778013			0.389006	−	0.921235i	$-0.372818\pi$
$509$	396.009			0.778013			0.389006	+	0.921235i	$0.372818\pi$
$510$		0			0
$511$			25.8881i			0.0506616i
$512$	511.870	+	11.5200i	0.999747	+	0.0225000i
$513$		0			0
$514$	29.7218	+	171.060i	0.0578245	+	0.332802i
$515$			234.855i			0.456029i
$516$		0			0
$517$	555.253			1.07399
$518$	−1136.91	+	197.538i	−2.19481	+	0.381348i
$519$		0			0
$520$	−124.689	−	219.757i	−0.239786	−	0.422611i
$521$	356.191			0.683668			0.341834	−	0.939760i	$-0.388952\pi$
$521$	356.191			0.683668			0.341834	+	0.939760i	$0.388952\pi$
$522$		0			0
$523$			261.837i			0.500644i	0.968163	+	0.250322i	$0.0805365\pi$
$523$			261.837i			0.500644i	−0.968163	+	0.250322i	$0.919464\pi$
$524$	−333.828	−	931.653i	−0.637075	−	1.77796i
$525$		0			0
$526$	−656.175	+	114.011i	−1.24748	+	0.216750i
$527$		−	1077.83i		−	2.04522i
$528$		0			0
$529$	280.502			0.530249
$530$	−1.88370	−	10.8414i	−0.00355416	−	0.0204556i
$531$		0			0
$532$	529.992	−	189.906i	0.996226	−	0.356965i
$533$	−407.413			−0.764378
$534$		0			0
$535$			152.551i			0.285143i
$536$	460.607	−	261.345i	0.859342	−	0.487584i
$537$		0			0
$538$	−65.4144	−	376.485i	−0.121588	−	0.699787i
$539$			832.899i			1.54527i
$540$		0			0
$541$	−581.984			−1.07576			−0.537878	−	0.843022i	$-0.680774\pi$
$541$	−581.984			−1.07576			−0.537878	+	0.843022i	$0.680774\pi$
$542$	−514.619	+	89.4152i	−0.949482	+	0.164973i
$543$		0			0
$544$	−741.640	−	638.277i	−1.36331	−	1.17330i
$545$	74.9126			0.137454
$546$		0			0
$547$		−	84.8307i		−	0.155083i	−0.996989	−	0.0775417i	$-0.975293\pi$
$547$		−	84.8307i		−	0.155083i	0.996989	−	0.0775417i	$-0.0247071\pi$
$548$	532.357	−	190.753i	0.971455	−	0.348089i
$549$		0			0
$550$	98.2782	−	17.0759i	0.178688	−	0.0310470i
$551$			231.029i			0.419290i
$552$		0			0
$553$	902.739			1.63244
$554$	−70.0541	−	403.189i	−0.126452	−	0.727778i
$555$		0			0
$556$	78.6226	+	219.421i	0.141408	+	0.394643i
$557$	708.933			1.27277			0.636385	−	0.771372i	$-0.280429\pi$
$557$	708.933			1.27277			0.636385	+	0.771372i	$0.280429\pi$
$558$		0			0
$559$		−	345.413i		−	0.617912i
$560$	−261.546	−	318.106i	−0.467046	−	0.568046i
$561$		0			0
$562$	−157.055	−	903.910i	−0.279456	−	1.60838i
$563$		−	1094.57i		−	1.94418i	−0.234607	−	0.972090i	$-0.575380\pi$
$563$		−	1094.57i		−	1.94418i	0.234607	−	0.972090i	$-0.424620\pi$
$564$		0			0
$565$	321.868			0.569677
$566$	−663.507	+	115.284i	−1.17227	+	0.203683i
$567$		0			0
$568$	80.5564	−	45.7071i	0.141825	−	0.0804703i
$569$	−769.082			−1.35164			−0.675819	−	0.737068i	$-0.736210\pi$
$569$	−769.082			−1.35164			−0.675819	+	0.737068i	$0.736210\pi$
$570$		0			0
$571$			871.192i			1.52573i	0.646558	+	0.762865i	$0.276208\pi$
$571$			871.192i			1.52573i	−0.646558	+	0.762865i	$0.723792\pi$
$572$	−190.102	−	530.542i	−0.332347	−	0.927520i
$573$		0			0
$574$	−654.241	+	113.675i	−1.13979	+	0.198039i
$575$			78.8191i			0.137077i
$576$		0			0
$577$	216.739			0.375631			0.187816	−	0.982204i	$-0.439859\pi$
$577$	216.739			0.375631			0.187816	+	0.982204i	$0.439859\pi$
$578$	221.168	+	1272.91i	0.382643	+	2.20226i
$579$		0			0
$580$	159.091	−	57.0053i	0.274296	−	0.0982849i
$581$	−1681.27			−2.89376
$582$		0			0
$583$		−	24.5441i		−	0.0420996i
$584$	−8.87900	−	15.6488i	−0.0152038	−	0.0267959i
$585$		0			0
$586$	−85.4727	−	491.929i	−0.145858	−	0.839469i
$587$		−	148.024i		−	0.252170i	−0.992019	−	0.126085i	$-0.959759\pi$
$587$		−	148.024i		−	0.252170i	0.992019	−	0.126085i	$-0.0402411\pi$
$588$		0			0
$589$	−431.004			−0.731755
$590$	−284.890	+	49.4997i	−0.482864	+	0.0838977i
$591$		0			0
$592$	619.486	−	509.341i	1.04643	−	0.860373i
$593$	102.473			0.172804			0.0864020	−	0.996260i	$-0.472463\pi$
$593$	102.473			0.172804			0.0864020	+	0.996260i	$0.472463\pi$
$594$		0			0
$595$			787.033i			1.32274i
$596$	−999.857	+	358.267i	−1.67761	+	0.601118i
$597$		0			0
$598$	438.739	−	76.2310i	0.733678	−	0.127477i
$599$			353.214i			0.589673i	0.955548	+	0.294836i	$0.0952651\pi$
$599$			353.214i			0.589673i	−0.955548	+	0.294836i	$0.904735\pi$
$600$		0			0
$601$	422.498			0.702992			0.351496	−	0.936189i	$-0.385673\pi$
$601$	422.498			0.702992			0.351496	+	0.936189i	$0.385673\pi$
$602$	−96.3754	−	554.678i	−0.160092	−	0.921392i
$603$		0			0
$604$	−294.125	−	820.849i	−0.486961	−	1.35902i
$605$	−48.0711			−0.0794564
$606$		0			0
$607$			958.261i			1.57868i	0.613954	+	0.789342i	$0.289578\pi$
$607$			958.261i			1.57868i	−0.613954	+	0.789342i	$0.710422\pi$
$608$	−255.235	+	296.568i	−0.419795	+	0.487777i
$609$		0			0
$610$	23.1576	+	133.281i	0.0379632	+	0.218493i
$611$		−	786.228i		−	1.28679i
$612$		0			0
$613$	−885.611			−1.44472			−0.722358	−	0.691519i	$-0.756942\pi$
$613$	−885.611			−1.44472			−0.722358	+	0.691519i	$0.756942\pi$
$614$	309.072	−	53.7012i	0.503374	−	0.0874613i
$615$		0			0
$616$	−453.304	−	798.924i	−0.735882	−	1.29695i
$617$	−37.8513			−0.0613473			−0.0306737	−	0.999529i	$-0.509765\pi$
$617$	−37.8513			−0.0613473			−0.0306737	+	0.999529i	$0.509765\pi$
$618$		0			0
$619$		−	544.679i		−	0.879934i	−0.898014	−	0.439967i	$-0.854990\pi$
$619$		−	544.679i		−	0.879934i	0.898014	−	0.439967i	$-0.145010\pi$
$620$	106.348	+	296.798i	0.171529	+	0.478707i
$621$		0			0
$622$	324.673	−	56.4120i	0.521983	−	0.0906946i
$623$		−	1006.40i		−	1.61541i
$624$		0			0
$625$	25.0000			0.0400000
$626$	−45.1903	−	260.088i	−0.0721890	−	0.415476i
$627$		0			0
$628$	−249.934	+	89.5557i	−0.397984	+	0.142605i
$629$	−1532.69			−2.43670
$630$		0			0
$631$		−	665.520i		−	1.05471i	−0.849646	−	0.527353i	$-0.823184\pi$
$631$		−	665.520i		−	1.05471i	0.849646	−	0.527353i	$-0.176816\pi$
$632$	−545.686	+	309.618i	−0.863427	+	0.489902i
$633$		0			0
$634$	58.1460	+	334.653i	0.0917129	+	0.527843i
$635$			447.176i			0.704214i
$636$		0			0
$637$	1179.37			1.85144
$638$	371.380	−	64.5274i	0.582101	−	0.101140i
$639$		0			0
$640$	267.201	+	102.584i	0.417502	+	0.160287i
$641$	1089.06			1.69901			0.849504	−	0.527582i	$-0.176901\pi$
$641$	1089.06			1.69901			0.849504	+	0.527582i	$0.176901\pi$
$642$		0			0
$643$			277.692i			0.431869i	0.976408	+	0.215935i	$0.0692798\pi$
$643$			277.692i			0.431869i	−0.976408	+	0.215935i	$0.930720\pi$
$644$	683.276	−	244.830i	1.06099	−	0.380171i
$645$		0			0
$646$	736.732	−	128.007i	1.14045	−	0.198154i
$647$			1049.77i			1.62251i	0.584690	+	0.811257i	$0.301216\pi$
$647$			1049.77i			1.62251i	−0.584690	+	0.811257i	$0.698784\pi$
$648$		0			0
$649$	−644.965			−0.993783
$650$	−24.1791	−	139.160i	−0.0371986	−	0.214093i
$651$		0			0
$652$	126.183	+	352.154i	0.193532	+	0.540113i
$653$	110.008			0.168465			0.0842325	−	0.996446i	$-0.473156\pi$
$653$	110.008			0.168465			0.0842325	+	0.996446i	$0.473156\pi$
$654$		0			0
$655$		−	553.234i		−	0.844632i
$656$	356.487	−	293.103i	0.543425	−	0.446803i
$657$		0			0
$658$	−219.370	−	1262.56i	−0.333389	−	1.91878i
$659$			363.189i			0.551121i	0.961284	+	0.275561i	$0.0888635\pi$
$659$			363.189i			0.551121i	−0.961284	+	0.275561i	$0.911137\pi$
$660$		0			0
$661$	−801.735			−1.21291			−0.606456	−	0.795117i	$-0.707410\pi$
$661$	−801.735			−1.21291			−0.606456	+	0.795117i	$0.707410\pi$
$662$	−338.814	+	58.8690i	−0.511803	+	0.0889259i
$663$		0			0
$664$	1016.29	−	576.636i	1.53056	−	0.868428i
$665$	314.720			0.473263
$666$		0			0
$667$			297.847i			0.446547i
$668$	63.8089	+	178.079i	0.0955223	+	0.266585i
$669$		0			0
$670$	291.677	−	50.6789i	0.435339	−	0.0756402i
$671$			301.736i			0.449681i
$672$		0			0
$673$	−447.743			−0.665295			−0.332647	−	0.943051i	$-0.607942\pi$
$673$	−447.743			−0.665295			−0.332647	+	0.943051i	$0.607942\pi$
$674$	−161.000	−	926.615i	−0.238872	−	1.37480i
$675$		0			0
$676$	−114.857	+	41.1553i	−0.169907	+	0.0608806i
$677$	299.167			0.441901			0.220950	−	0.975285i	$-0.429084\pi$
$677$	299.167			0.441901			0.220950	+	0.975285i	$0.429084\pi$
$678$		0			0
$679$			1458.96i			2.14869i
$680$	−269.933	−	475.744i	−0.396961	−	0.699623i
$681$		0			0
$682$	120.381	+	692.841i	0.176512	+	1.01590i
$683$		−	339.673i		−	0.497326i	−0.968590	−	0.248663i	$-0.920009\pi$
$683$		−	339.673i		−	0.497326i	0.968590	−	0.248663i	$-0.0799911\pi$
$684$		0			0
$685$	316.125			0.461496
$686$	782.476	−	135.955i	1.14064	−	0.198186i
$687$		0			0
$688$	248.498	+	302.236i	0.361189	+	0.439297i
$689$	−34.7540			−0.0504412
$690$		0			0
$691$			764.773i			1.10676i	0.832928	+	0.553381i	$0.186663\pi$
$691$			764.773i			1.10676i	−0.832928	+	0.553381i	$0.813337\pi$
$692$	−864.324	+	309.702i	−1.24902	+	0.447547i
$693$		0			0
$694$	−330.988	+	57.5093i	−0.476928	+	0.0828664i
$695$			130.297i			0.187478i
$696$		0			0
$697$	−881.992			−1.26541
$698$	−54.3504	−	312.808i	−0.0778659	−	0.448148i
$699$		0			0
$700$	−77.6556	−	216.723i	−0.110937	−	0.309604i
$701$	308.111			0.439531			0.219765	−	0.975553i	$-0.429471\pi$
$701$	308.111			0.439531			0.219765	+	0.975553i	$0.429471\pi$
$702$		0			0
$703$			612.893i			0.871825i
$704$	548.024	+	327.460i	0.778443	+	0.465142i
$705$		0			0
$706$	−68.8424	−	396.215i	−0.0975105	−	0.561211i
$707$		−	761.831i		−	1.07755i
$708$		0			0
$709$	−882.249			−1.24436			−0.622178	−	0.782875i	$-0.713752\pi$
$709$	−882.249			−1.24436			−0.622178	+	0.782875i	$0.713752\pi$
$710$	51.0119	−	8.86333i	0.0718478	−	0.0124836i
$711$		0			0
$712$	345.171	+	608.347i	0.484791	+	0.854420i
$713$	−555.659			−0.779325
$714$		0			0
$715$		−	315.046i		−	0.440624i
$716$	203.561	+	568.103i	0.284304	+	0.793440i
$717$		0			0
$718$	−1357.98	+	235.949i	−1.89133	+	0.328619i
$719$			766.999i			1.06676i	0.845876	+	0.533379i	$0.179078\pi$
$719$			766.999i			1.06676i	−0.845876	+	0.533379i	$0.820922\pi$
$720$		0			0
$721$	1208.98			1.67681
$722$	72.4081	+	416.737i	0.100288	+	0.577198i
$723$		0			0
$724$	−205.216	+	73.5325i	−0.283447	+	0.101564i
$725$	94.4717			0.130306
$726$		0			0
$727$			735.301i			1.01142i	0.862704	+	0.505709i	$0.168769\pi$
$727$			735.301i			1.01142i	−0.862704	+	0.505709i	$0.831231\pi$
$728$	−1131.26	+	641.870i	−1.55393	+	0.881689i
$729$		0			0
$730$	−1.72178	−	9.90950i	−0.00235860	−	0.0135747i
$731$		−	747.770i		−	1.02294i
$732$		0			0
$733$	269.377			0.367500			0.183750	−	0.982973i	$-0.441176\pi$
$733$	269.377			0.367500			0.183750	+	0.982973i	$0.441176\pi$
$734$	−22.6817	+	3.94096i	−0.0309015	+	0.00536915i
$735$		0			0
$736$	−329.055	+	382.342i	−0.447085	+	0.519486i
$737$	660.331			0.895971
$738$		0			0
$739$			807.949i			1.09330i	0.837361	+	0.546650i	$0.184097\pi$
$739$			807.949i			1.09330i	−0.837361	+	0.546650i	$0.815903\pi$
$740$	422.051	−	151.228i	0.570340	−	0.204363i
$741$		0			0
$742$	−55.8094	+	9.69688i	−0.0752148	+	0.0130686i
$743$			1017.72i			1.36974i	0.728665	+	0.684870i	$0.240141\pi$
$743$			1017.72i			1.36974i	−0.728665	+	0.684870i	$0.759859\pi$
$744$		0			0
$745$	−593.735			−0.796960
$746$	122.180	+	703.192i	0.163780	+	0.942617i
$747$		0			0
$748$	−411.545	−	1148.55i	−0.550194	−	1.53549i
$749$	785.300			1.04846
$750$		0			0
$751$		−	551.845i		−	0.734814i	−0.930060	−	0.367407i	$-0.880246\pi$
$751$		−	551.845i		−	0.734814i	0.930060	−	0.367407i	$-0.119754\pi$
$752$	565.631	+	687.950i	0.752169	+	0.914827i
$753$		0			0
$754$	−91.3697	−	525.868i	−0.121180	−	0.697438i
$755$		−	487.436i		−	0.645611i
$756$		0			0
$757$	1168.86			1.54407			0.772037	−	0.635578i	$-0.219238\pi$
$757$	1168.86			1.54407			0.772037	+	0.635578i	$0.219238\pi$
$758$	1092.87	−	189.887i	1.44178	−	0.250510i
$759$		0			0
$760$	−190.241	+	107.941i	−0.250317	+	0.142028i
$761$	−221.811			−0.291473			−0.145737	−	0.989323i	$-0.546555\pi$
$761$	−221.811			−0.291473			−0.145737	+	0.989323i	$0.546555\pi$
$762$		0			0
$763$		−	385.633i		−	0.505417i
$764$	−304.747	−	850.495i	−0.398884	−	1.11321i
$765$		0			0
$766$	871.677	−	151.454i	1.13796	−	0.197721i
$767$			913.259i			1.19069i
$768$		0			0
$769$	34.5136			0.0448811			0.0224406	−	0.999748i	$-0.492856\pi$
$769$	34.5136			0.0448811			0.0224406	+	0.999748i	$0.492856\pi$
$770$	−87.9027	−	505.914i	−0.114159	−	0.657032i
$771$		0			0
$772$	−657.084	+	235.445i	−0.851145	+	0.304980i
$773$	−401.055			−0.518829			−0.259415	−	0.965766i	$-0.583530\pi$
$773$	−401.055			−0.518829			−0.259415	+	0.965766i	$0.583530\pi$
$774$		0			0
$775$			176.245i			0.227413i
$776$	−500.388	−	881.908i	−0.644829	−	1.13648i
$777$		0			0
$778$	122.029	+	702.326i	0.156850	+	0.902732i
$779$			352.693i			0.452750i
$780$		0			0
$781$	115.486			0.147870
$782$	949.809	−	165.029i	1.21459	−	0.211035i
$783$		0			0
$784$	−1031.95	+	848.467i	−1.31626	+	1.08223i
$785$	−148.416			−0.189065
$786$		0			0
$787$		−	1030.24i		−	1.30907i	−0.756032	−	0.654534i	$-0.772865\pi$
$787$		−	1030.24i		−	1.30907i	0.756032	−	0.654534i	$-0.227135\pi$
$788$	60.1920	−	21.5679i	0.0763858	−	0.0273704i
$789$		0			0
$790$	−345.553	+	60.0398i	−0.437408	+	0.0759998i
$791$		−	1656.90i		−	2.09469i
$792$		0			0
$793$	427.253			0.538780
$794$	175.590	+	1010.59i	0.221146	+	1.27278i
$795$		0			0
$796$	−41.7587	−	116.541i	−0.0524607	−	0.146408i
$797$	−1070.94			−1.34372			−0.671859	−	0.740679i	$-0.734504\pi$
$797$	−1070.94			−1.34372			−0.671859	+	0.740679i	$0.734504\pi$
$798$		0			0
$799$		−	1702.07i		−	2.13025i
$800$	121.272	+	104.370i	0.151590	+	0.130463i
$801$		0			0
$802$	3.56032	+	20.4910i	0.00443930	+	0.0255499i
$803$		−	22.4342i		−	0.0279380i
$804$		0			0
$805$	405.743			0.504029
$806$	981.051	−	170.458i	1.21718	−	0.211486i
$807$		0			0
$808$	261.290	+	460.510i	0.323379	+	0.569938i
$809$	1265.04			1.56371			0.781854	−	0.623461i	$-0.214274\pi$
$809$	1265.04			1.56371			0.781854	+	0.623461i	$0.214274\pi$
$810$		0			0
$811$			966.144i			1.19130i	0.803244	+	0.595650i	$0.203105\pi$
$811$			966.144i			1.19130i	−0.803244	+	0.595650i	$0.796895\pi$
$812$	−293.450	−	818.967i	−0.361392	−	1.00858i
$813$		0			0
$814$	985.230	−	171.184i	1.21036	−	0.210300i
$815$			209.116i			0.256584i
$816$		0			0
$817$	−299.019			−0.365997
$818$	86.1043	+	495.564i	0.105262	+	0.605824i
$819$		0			0
$820$	242.872	−	87.0252i	0.296185	−	0.106128i
$821$	878.408			1.06992			0.534962	−	0.844876i	$-0.320326\pi$
$821$	878.408			1.06992			0.534962	+	0.844876i	$0.320326\pi$
$822$		0			0
$823$		−	887.674i		−	1.07858i	−0.842119	−	0.539292i	$-0.818692\pi$
$823$		−	887.674i		−	1.07858i	0.842119	−	0.539292i	$-0.181308\pi$
$824$	−730.802	+	414.651i	−0.886895	+	0.503218i
$825$		0			0
$826$	254.813	+	1466.55i	0.308491	+	1.77548i
$827$			82.2846i			0.0994977i	0.998762	+	0.0497489i	$0.0158421\pi$
$827$			82.2846i			0.0994977i	−0.998762	+	0.0497489i	$0.984158\pi$
$828$		0			0
$829$	348.475			0.420356			0.210178	−	0.977663i	$-0.432596\pi$
$829$	348.475			0.420356			0.210178	+	0.977663i	$0.432596\pi$
$830$	643.561	−	111.819i	0.775375	−	0.134722i
$831$		0			0
$832$	463.677	−	775.992i	0.557304	−	0.932683i
$833$	2553.17			3.06503
$834$		0			0
$835$			105.747i			0.126643i
$836$	−459.283	+	164.569i	−0.549382	+	0.196853i
$837$		0			0
$838$	−405.033	+	70.3746i	−0.483333	+	0.0839792i
$839$		−	174.383i		−	0.207847i	−0.994585	−	0.103923i	$-0.966860\pi$
$839$		−	174.383i		−	0.207847i	0.994585	−	0.103923i	$-0.0331397\pi$
$840$		0			0
$841$	−484.004			−0.575510
$842$	277.741	+	1598.51i	0.329859	+	1.89847i
$843$		0			0
$844$	257.261	+	717.968i	0.304811	+	0.850673i
$845$	−68.2044			−0.0807153
$846$		0			0
$847$			247.459i			0.292160i
$848$	30.4097	−	25.0028i	0.0358605	−	0.0294845i
$849$		0			0
$850$	−52.3444	−	301.262i	−0.0615816	−	0.354426i
$851$			790.154i			0.928500i
$852$		0			0
$853$	−1549.11			−1.81608			−0.908038	−	0.418888i	$-0.862420\pi$
$853$	−1549.11			−1.81608			−0.908038	+	0.418888i	$0.862420\pi$
$854$	686.101	−	119.210i	0.803396	−	0.139590i
$855$		0			0
$856$	−474.696	+	269.339i	−0.554552	+	0.314649i
$857$	−376.279			−0.439065			−0.219533	−	0.975605i	$-0.570453\pi$
$857$	−376.279			−0.439065			−0.219533	+	0.975605i	$0.570453\pi$
$858$		0			0
$859$		−	1495.73i		−	1.74124i	−0.491952	−	0.870622i	$-0.663716\pi$
$859$		−	1495.73i		−	1.74124i	0.491952	−	0.870622i	$-0.336284\pi$
$860$	73.7816	+	205.911i	0.0857925	+	0.239432i
$861$		0			0
$862$	708.630	−	123.125i	0.822077	−	0.142836i
$863$			104.458i			0.121041i	0.998167	+	0.0605204i	$0.0192760\pi$
$863$			104.458i			0.121041i	−0.998167	+	0.0605204i	$0.980724\pi$
$864$		0			0
$865$	−513.253			−0.593356
$866$	−68.0452	−	391.627i	−0.0785741	−	0.452225i
$867$		0			0
$868$	1527.85	−	547.456i	1.76020	−	0.630710i
$869$	−782.300			−0.900230
$870$		0			0
$871$		−	935.017i		−	1.07350i
$872$	132.263	+	233.107i	0.151678	+	0.267324i
$873$		0			0
$874$	−65.9922	−	379.811i	−0.0755060	−	0.434567i
$875$		−	128.694i		−	0.147079i
$876$		0			0
$877$	−282.607			−0.322243			−0.161121	−	0.986935i	$-0.551511\pi$
$877$	−282.607			−0.322243			−0.161121	+	0.986935i	$0.551511\pi$
$878$	−696.073	+	120.943i	−0.792794	+	0.137748i
$879$		0			0
$880$	226.652	+	275.665i	0.257559	+	0.313256i
$881$	578.468			0.656604			0.328302	−	0.944573i	$-0.393524\pi$
$881$	578.468			0.656604			0.328302	+	0.944573i	$0.393524\pi$
$882$		0			0
$883$		−	1267.53i		−	1.43548i	−0.696311	−	0.717741i	$-0.745176\pi$
$883$		−	1267.53i		−	1.43548i	0.696311	−	0.717741i	$-0.254824\pi$
$884$	−1626.32	+	582.740i	−1.83973	+	0.659208i
$885$		0			0
$886$	−413.479	+	71.8420i	−0.466680	+	0.0810858i
$887$		−	49.7756i		−	0.0561168i	−0.999606	−	0.0280584i	$-0.991068\pi$
$887$		−	49.7756i		−	0.0561168i	0.999606	−	0.0280584i	$-0.00893243\pi$
$888$		0			0
$889$	2301.96			2.58938
$890$	66.9342	+	385.232i	0.0752069	+	0.432845i
$891$		0			0
$892$	−429.010	−	1197.29i	−0.480953	−	1.34225i
$893$	−680.628			−0.762181
$894$		0			0
$895$			337.351i			0.376929i
$896$	528.078	−	1375.49i	0.589373	−	1.53515i
$897$		0			0
$898$	211.296	+	1216.09i	0.235296	+	1.35422i
$899$			666.006i			0.740830i
$900$		0			0
$901$	−75.2374			−0.0835043
$902$	566.955	−	98.5086i	0.628554	−	0.109211i
$903$		0			0
$904$	568.278	+	1001.56i	0.628626	+	1.10792i
$905$	−121.861			−0.134653
$906$		0			0
$907$		−	1487.71i		−	1.64026i	−0.572180	−	0.820128i	$-0.693902\pi$
$907$		−	1487.71i		−	1.64026i	0.572180	−	0.820128i	$-0.306098\pi$
$908$	−53.8362	−	150.247i	−0.0592909	−	0.165470i
$909$		0			0
$910$	−716.366	+	124.469i	−0.787215	+	0.136779i
$911$			678.826i			0.745144i	0.928003	+	0.372572i	$0.121524\pi$
$911$			678.826i			0.745144i	−0.928003	+	0.372572i	$0.878476\pi$
$912$		0			0
$913$	1456.97			1.59580
$914$	−44.2524	−	254.690i	−0.0484162	−	0.278654i
$915$		0			0
$916$	−51.7802	+	18.5537i	−0.0565286	+	0.0202552i
$917$	−2847.93			−3.10570
$918$		0			0
$919$			820.849i			0.893198i	0.894734	+	0.446599i	$0.147365\pi$
$919$			820.849i			0.893198i	−0.894734	+	0.446599i	$0.852635\pi$
$920$	−245.263	+	139.160i	−0.266590	+	0.151261i
$921$		0			0
$922$	6.39499	+	36.8056i	0.00693599	+	0.0399193i
$923$		−	163.527i		−	0.177169i
$924$		0			0
$925$	250.623			0.270943
$926$	−215.608	+	37.4620i	−0.232838	+	0.0404557i
$927$		0			0
$928$	458.270	+	394.401i	0.493826	+	0.425001i
$929$	455.044			0.489821			0.244911	−	0.969546i	$-0.421241\pi$
$929$	455.044			0.489821			0.244911	+	0.969546i	$0.421241\pi$
$930$		0			0
$931$		−	1020.97i		−	1.09663i
$932$	457.422	−	163.902i	0.490796	−	0.175861i
$933$		0			0
$934$	−494.549	+	85.9279i	−0.529495	+	0.0919999i
$935$		−	682.031i		−	0.729445i
$936$		0			0
$937$	−1705.49			−1.82016			−0.910078	−	0.414437i	$-0.863979\pi$
$937$	−1705.49			−1.82016			−0.910078	+	0.414437i	$0.863979\pi$
$938$	−260.884	−	1501.49i	−0.278128	−	1.60073i
$939$		0			0
$940$	167.942	+	468.695i	0.178661	+	0.498612i
$941$	−77.3558			−0.0822060			−0.0411030	−	0.999155i	$-0.513087\pi$
$941$	−77.3558			−0.0822060			−0.0411030	+	0.999155i	$0.513087\pi$
$942$		0			0
$943$			454.698i			0.482183i
$944$	−657.020	−	799.102i	−0.695996	−	0.846506i
$945$		0			0
$946$	83.5174	+	480.675i	0.0882848	+	0.508114i
$947$			382.779i			0.404201i	0.979365	+	0.202101i	$0.0647768\pi$
$947$			382.779i			0.404201i	−0.979365	+	0.202101i	$0.935223\pi$
$948$		0			0
$949$	−31.7665			−0.0334736
$950$	−120.469	+	20.9316i	−0.126810	+	0.0220332i
$951$		0			0
$952$	−2449.02	+	1389.56i	−2.57250	+	1.45962i
$953$	−1101.29			−1.15560			−0.577800	−	0.816178i	$-0.696089\pi$
$953$	−1101.29			−1.15560			−0.577800	+	0.816178i	$0.696089\pi$
$954$		0			0
$955$		−	505.041i		−	0.528839i
$956$	217.020	+	605.665i	0.227009	+	0.633541i
$957$		0			0
$958$	−735.311	+	127.760i	−0.767548	+	0.133362i
$959$		−	1627.34i		−	1.69691i
$960$		0			0
$961$	−281.490			−0.292914
$962$	−242.393	−	1395.07i	−0.251968	−	1.45017i
$963$		0			0
$964$	13.1576	−	4.71459i	0.0136489	−	0.00489066i
$965$	−390.190			−0.404341
$966$		0			0
$967$		−	1339.59i		−	1.38531i	−0.721269	−	0.692655i	$-0.756441\pi$
$967$		−	1339.59i		−	1.38531i	0.721269	−	0.692655i	$-0.243559\pi$
$968$	−84.8727	−	149.584i	−0.0876784	−	0.154529i
$969$		0			0
$970$	−97.0331	−	558.463i	−0.100034	−	0.575735i
$971$		−	288.556i		−	0.297174i	−0.988899	−	0.148587i	$-0.952527\pi$
$971$		−	288.556i		−	0.297174i	0.988899	−	0.148587i	$-0.0474725\pi$
$972$		0			0
$973$	670.739			0.689352
$974$	−360.171	+	62.5799i	−0.369786	+	0.0642504i
$975$		0			0
$976$	−373.846	+	307.376i	−0.383039	+	0.314934i
$977$	1781.05			1.82298			0.911490	−	0.411322i	$-0.134933\pi$
$977$	1781.05			1.82298			0.911490	+	0.411322i	$0.134933\pi$
$978$		0			0
$979$			872.131i			0.890839i
$980$	−703.059	+	251.918i	−0.717407	+	0.257059i
$981$		0			0
$982$	−814.644	+	141.545i	−0.829576	+	0.144139i
$983$		−	1179.28i		−	1.19968i	−0.800122	−	0.599838i	$-0.795232\pi$
$983$		−	1179.28i		−	1.19968i	0.800122	−	0.599838i	$-0.204768\pi$
$984$		0			0
$985$	35.7432			0.0362875
$986$	−197.802	−	1138.43i	−0.200611	−	1.15459i
$987$		0			0
$988$	233.027	+	650.337i	0.235857	+	0.658236i
$989$	−385.502			−0.389789
$990$		0			0
$991$			363.373i			0.366673i	0.983050	+	0.183337i	$0.0586898\pi$
$991$			363.373i			0.366673i	−0.983050	+	0.183337i	$0.941310\pi$
$992$	−735.788	+	854.942i	−0.741722	+	0.861837i
$993$		0			0
$994$	−45.6265	−	262.598i	−0.0459019	−	0.264183i
$995$		−	69.2044i		−	0.0695522i
$996$		0			0
$997$	412.630			0.413872			0.206936	−	0.978354i	$-0.433651\pi$
$997$	412.630			0.413872			0.206936	+	0.978354i	$0.433651\pi$
$998$	182.954	−	31.7883i	0.183321	−	0.0318520i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	180.3.c.c.91.6	yes	8
3.2	odd	2	inner	180.3.c.c.91.3	✓	8
4.3	odd	2	inner	180.3.c.c.91.5	yes	8
5.2	odd	4		900.3.f.i.199.3		16
5.3	odd	4		900.3.f.i.199.14		16
5.4	even	2		900.3.c.o.451.3		8
8.3	odd	2		2880.3.e.i.2431.5		8
8.5	even	2		2880.3.e.i.2431.8		8
12.11	even	2	inner	180.3.c.c.91.4	yes	8
15.2	even	4		900.3.f.i.199.13		16
15.8	even	4		900.3.f.i.199.4		16
15.14	odd	2		900.3.c.o.451.6		8
20.3	even	4		900.3.f.i.199.1		16
20.7	even	4		900.3.f.i.199.16		16
20.19	odd	2		900.3.c.o.451.4		8
24.5	odd	2		2880.3.e.i.2431.4		8
24.11	even	2		2880.3.e.i.2431.1		8
60.23	odd	4		900.3.f.i.199.15		16
60.47	odd	4		900.3.f.i.199.2		16
60.59	even	2		900.3.c.o.451.5		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
180.3.c.c.91.3	✓	8	3.2	odd	2	inner
180.3.c.c.91.4	yes	8	12.11	even	2	inner
180.3.c.c.91.5	yes	8	4.3	odd	2	inner
180.3.c.c.91.6	yes	8	1.1	even	1	trivial
900.3.c.o.451.3		8	5.4	even	2
900.3.c.o.451.4		8	20.19	odd	2
900.3.c.o.451.5		8	60.59	even	2
900.3.c.o.451.6		8	15.14	odd	2
900.3.f.i.199.1		16	20.3	even	4
900.3.f.i.199.2		16	60.47	odd	4
900.3.f.i.199.3		16	5.2	odd	4
900.3.f.i.199.4		16	15.8	even	4
900.3.f.i.199.13		16	15.2	even	4
900.3.f.i.199.14		16	5.3	odd	4
900.3.f.i.199.15		16	60.23	odd	4
900.3.f.i.199.16		16	20.7	even	4
2880.3.e.i.2431.1		8	24.11	even	2
2880.3.e.i.2431.4		8	24.5	odd	2
2880.3.e.i.2431.5		8	8.3	odd	2
2880.3.e.i.2431.8		8	8.5	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 180 = 2^{2} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	180.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.342371 + 1.97048i) q^{2} +(-3.76556 + 1.34927i) q^{4} -2.23607 q^{5} +11.5108i q^{7} +(-3.94792 - 6.95801i) q^{8} +O(q^{10})\)	\(q+(0.342371 + 1.97048i) q^{2} +(-3.76556 + 1.34927i) q^{4} -2.23607 q^{5} +11.5108i q^{7} +(-3.94792 - 6.95801i) q^{8} +(-0.765564 - 4.40612i) q^{10} -9.97507i q^{11} -14.1245 q^{13} +(-22.6817 + 3.94096i) q^{14} +(12.3590 - 10.1615i) q^{16} -30.5776 q^{17} +12.2274i q^{19} +(8.42006 - 3.01706i) q^{20} +(19.6556 - 3.41517i) q^{22} +15.7638i q^{23} +5.00000 q^{25} +(-4.83582 - 27.8320i) q^{26} +(-15.5311 - 43.3446i) q^{28} +18.8943 q^{29} +35.2490i q^{31} +(24.2544 + 20.8740i) q^{32} +(-10.4689 - 60.2524i) q^{34} -25.7389i q^{35} +50.1245 q^{37} +(-24.0938 + 4.18631i) q^{38} +(8.82782 + 15.5586i) q^{40} +28.8444 q^{41} +24.4548i q^{43} +(13.4590 + 37.5618i) q^{44} +(-31.0623 + 5.39707i) q^{46} +55.6641i q^{47} -83.4981 q^{49} +(1.71185 + 9.85239i) q^{50} +(53.1868 - 19.0578i) q^{52} +2.46054 q^{53} +22.3049i q^{55} +(80.0921 - 45.4437i) q^{56} +(6.46887 + 37.2309i) q^{58} -64.6577i q^{59} -30.2490 q^{61} +(-69.4573 + 12.0682i) q^{62} +(-32.8278 + 54.9394i) q^{64} +31.5834 q^{65} +66.1981i q^{67} +(115.142 - 41.2574i) q^{68} +(50.7179 - 8.81224i) q^{70} +11.5775i q^{71} +2.24903 q^{73} +(17.1612 + 98.7692i) q^{74} +(-16.4981 - 46.0431i) q^{76} +114.821 q^{77} -78.4256i q^{79} +(-27.6355 + 22.7218i) q^{80} +(9.87548 + 56.8373i) q^{82} +146.061i q^{83} +68.3735 q^{85} +(-48.1877 + 8.37262i) q^{86} +(-69.4066 + 39.3808i) q^{88} -87.4311 q^{89} -162.584i q^{91} +(-21.2696 - 59.3597i) q^{92} +(-109.685 + 19.0578i) q^{94} -27.3413i q^{95} +126.747 q^{97} +(-28.5873 - 164.531i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 14 q^{4}+O(q^{10}) \) 8 * q - 14 * q^4	\( 8 q - 14 q^{4} + 10 q^{10} + 16 q^{13} - 14 q^{16} - 4 q^{22} + 40 q^{25} - 92 q^{28} - 116 q^{34} + 272 q^{37} - 10 q^{40} - 184 q^{46} - 152 q^{49} + 232 q^{52} + 84 q^{58} + 16 q^{61} - 182 q^{64} + 180 q^{70} - 240 q^{73} + 384 q^{76} + 208 q^{82} + 160 q^{85} - 652 q^{88} - 168 q^{94} + 240 q^{97}+O(q^{100}) \) 8 * q - 14 * q^4 + 10 * q^10 + 16 * q^13 - 14 * q^16 - 4 * q^22 + 40 * q^25 - 92 * q^28 - 116 * q^34 + 272 * q^37 - 10 * q^40 - 184 * q^46 - 152 * q^49 + 232 * q^52 + 84 * q^58 + 16 * q^61 - 182 * q^64 + 180 * q^70 - 240 * q^73 + 384 * q^76 + 208 * q^82 + 160 * q^85 - 652 * q^88 - 168 * q^94 + 240 * q^97

Introduction

L-functions

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