LMFDB - Embedded newform 360.4.k.c.181.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [360,4,Mod(181,360)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(360, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("360.181");

S:= CuspForms(chi, 4);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

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

Embedding invariants

Embedding label			181.10
Root			$-0.650488 - 1.89126i$ of defining polynomial
Character	$\chi$	$=$	360.181
Dual form			360.4.k.c.181.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.54175 + 1.24077i) q^{2} +(4.92097 + 6.30746i) q^{4} -5.00000i q^{5} +26.6173 q^{7} +(4.68175 + 22.1378i) q^{8} +O(q^{10})$	\(q+(2.54175 + 1.24077i) q^{2} +(4.92097 + 6.30746i) q^{4} -5.00000i q^{5} +26.6173 q^{7} +(4.68175 + 22.1378i) q^{8} +(6.20386 - 12.7087i) q^{10} -61.7277i q^{11} -45.0627i q^{13} +(67.6545 + 33.0260i) q^{14} +(-15.5681 + 62.0776i) q^{16} +71.8754 q^{17} +17.6319i q^{19} +(31.5373 - 24.6049i) q^{20} +(76.5900 - 156.896i) q^{22} -43.4131 q^{23} -25.0000 q^{25} +(55.9125 - 114.538i) q^{26} +(130.983 + 167.888i) q^{28} +267.633i q^{29} +50.2133 q^{31} +(-116.594 + 138.469i) q^{32} +(182.689 + 89.1810i) q^{34} -133.087i q^{35} -75.0720i q^{37} +(-21.8772 + 44.8160i) q^{38} +(110.689 - 23.4087i) q^{40} +221.685 q^{41} -188.998i q^{43} +(389.345 - 303.760i) q^{44} +(-110.345 - 53.8658i) q^{46} +384.142 q^{47} +365.481 q^{49} +(-63.5437 - 31.0193i) q^{50} +(284.231 - 221.752i) q^{52} -247.445i q^{53} -308.638 q^{55} +(124.616 + 589.248i) q^{56} +(-332.072 + 680.256i) q^{58} +518.596i q^{59} +62.0042i q^{61} +(127.630 + 62.3033i) q^{62} +(-468.162 + 207.287i) q^{64} -225.314 q^{65} +558.476i q^{67} +(353.697 + 453.351i) q^{68} +(165.130 - 338.273i) q^{70} -313.194 q^{71} -263.926 q^{73} +(93.1472 - 190.814i) q^{74} +(-111.213 + 86.7663i) q^{76} -1643.03i q^{77} -732.940 q^{79} +(310.388 + 77.8405i) q^{80} +(563.468 + 275.061i) q^{82} +717.705i q^{83} -359.377i q^{85} +(234.503 - 480.385i) q^{86} +(1366.51 - 288.994i) q^{88} -1634.69 q^{89} -1199.45i q^{91} +(-213.635 - 273.827i) q^{92} +(976.392 + 476.633i) q^{94} +88.1597 q^{95} -1367.12 q^{97} +(928.962 + 453.479i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 2 q^{2} + 16 q^{4} + 28 q^{7} + 40 q^{8}+O(q^{10}) $ 12 * q - 2 * q^2 + 16 * q^4 + 28 * q^7 + 40 * q^8	$ 12 q - 2 q^{2} + 16 q^{4} + 28 q^{7} + 40 q^{8} + 30 q^{10} - 68 q^{14} - 56 q^{16} - 20 q^{20} - 164 q^{22} - 604 q^{23} - 300 q^{25} + 308 q^{26} - 436 q^{28} - 264 q^{31} - 72 q^{32} - 180 q^{34} - 820 q^{38} + 120 q^{40} - 40 q^{41} + 472 q^{44} - 1268 q^{46} + 940 q^{47} + 1308 q^{49} + 50 q^{50} + 1024 q^{52} + 440 q^{55} + 728 q^{56} - 360 q^{58} - 592 q^{62} - 2048 q^{64} + 2344 q^{68} + 1160 q^{70} + 1592 q^{71} + 432 q^{73} + 420 q^{74} + 2256 q^{76} + 2016 q^{79} - 1600 q^{80} + 88 q^{82} + 244 q^{86} + 4080 q^{88} + 424 q^{89} + 900 q^{92} + 292 q^{94} + 1520 q^{95} - 1584 q^{97} + 7266 q^{98}+O(q^{100}) $ 12 * q - 2 * q^2 + 16 * q^4 + 28 * q^7 + 40 * q^8 + 30 * q^10 - 68 * q^14 - 56 * q^16 - 20 * q^20 - 164 * q^22 - 604 * q^23 - 300 * q^25 + 308 * q^26 - 436 * q^28 - 264 * q^31 - 72 * q^32 - 180 * q^34 - 820 * q^38 + 120 * q^40 - 40 * q^41 + 472 * q^44 - 1268 * q^46 + 940 * q^47 + 1308 * q^49 + 50 * q^50 + 1024 * q^52 + 440 * q^55 + 728 * q^56 - 360 * q^58 - 592 * q^62 - 2048 * q^64 + 2344 * q^68 + 1160 * q^70 + 1592 * q^71 + 432 * q^73 + 420 * q^74 + 2256 * q^76 + 2016 * q^79 - 1600 * q^80 + 88 * q^82 + 244 * q^86 + 4080 * q^88 + 424 * q^89 + 900 * q^92 + 292 * q^94 + 1520 * q^95 - 1584 * q^97 + 7266 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	2.54175	+	1.24077i	0.898644	+	0.438679i
$2$	2.54175	+	1.24077i	0.898644	+	0.438679i
$3$		0			0
$3$		0			0
$4$	4.92097	+	6.30746i	0.615121	+	0.788433i
$5$		−	5.00000i		−	0.447214i
$5$		−	5.00000i		−	0.447214i
$6$		0			0
$7$	26.6173			1.43720			0.718600	−	0.695424i	$-0.244783\pi$
$7$	26.6173			1.43720			0.718600	+	0.695424i	$0.244783\pi$
$8$	4.68175	+	22.1378i	0.206906	+	0.978361i
$9$		0			0
$10$	6.20386	−	12.7087i	0.196183	−	0.401886i
$11$		−	61.7277i		−	1.69196i	−0.533212	−	0.845982i	$-0.679015\pi$
$11$		−	61.7277i		−	1.69196i	0.533212	−	0.845982i	$-0.320985\pi$
$12$		0			0
$13$		−	45.0627i		−	0.961396i	−0.876886	−	0.480698i	$-0.840383\pi$
$13$		−	45.0627i		−	0.961396i	0.876886	−	0.480698i	$-0.159617\pi$
$14$	67.6545	+	33.0260i	1.29153	+	0.630470i
$15$		0			0
$16$	−15.5681	+	62.0776i	−0.243252	+	0.969963i
$17$	71.8754			1.02543			0.512716	−	0.858558i	$-0.328639\pi$
$17$	71.8754			1.02543			0.512716	+	0.858558i	$0.328639\pi$
$18$		0			0
$19$			17.6319i			0.212897i	0.994318	+	0.106449i	$0.0339480\pi$
$19$			17.6319i			0.212897i	−0.994318	+	0.106449i	$0.966052\pi$
$20$	31.5373	−	24.6049i	0.352598	−	0.275091i
$21$		0			0
$22$	76.5900	−	156.896i	0.742229	−	1.52047i
$23$	−43.4131			−0.393577			−0.196788	−	0.980446i	$-0.563051\pi$
$23$	−43.4131			−0.393577			−0.196788	+	0.980446i	$0.563051\pi$
$24$		0			0
$25$	−25.0000			−0.200000
$26$	55.9125	−	114.538i	0.421744	−	0.863952i
$27$		0			0
$28$	130.983	+	167.888i	0.884052	+	1.13314i
$29$			267.633i			1.71373i	0.515540	+	0.856866i	$0.327591\pi$
$29$			267.633i			1.71373i	−0.515540	+	0.856866i	$0.672409\pi$
$30$		0			0
$31$	50.2133			0.290922			0.145461	−	0.989364i	$-0.453533\pi$
$31$	50.2133			0.290922			0.145461	+	0.989364i	$0.453533\pi$
$32$	−116.594	+	138.469i	−0.644099	+	0.764942i
$33$		0			0
$34$	182.689	+	89.1810i	0.921498	+	0.449836i
$35$		−	133.087i		−	0.642735i
$36$		0			0
$37$		−	75.0720i		−	0.333561i	−0.985994	−	0.166781i	$-0.946663\pi$
$37$		−	75.0720i		−	0.333561i	0.985994	−	0.166781i	$-0.0533372\pi$
$38$	−21.8772	+	44.8160i	−0.0933935	+	0.191319i
$39$		0			0
$40$	110.689	−	23.4087i	0.437536	−	0.0925312i
$41$	221.685			0.844425			0.422213	−	0.906497i	$-0.361254\pi$
$41$	221.685			0.844425			0.422213	+	0.906497i	$0.361254\pi$
$42$		0			0
$43$		−	188.998i		−	0.670277i	−0.942169	−	0.335139i	$-0.891217\pi$
$43$		−	188.998i		−	0.670277i	0.942169	−	0.335139i	$-0.108783\pi$
$44$	389.345	−	303.760i	1.33400	−	1.04076i
$45$		0			0
$46$	−110.345	−	53.8658i	−0.353685	−	0.172654i
$47$	384.142			1.19219			0.596094	−	0.802914i	$-0.296718\pi$
$47$	384.142			1.19219			0.596094	+	0.802914i	$0.296718\pi$
$48$		0			0
$49$	365.481			1.06554
$50$	−63.5437	−	31.0193i	−0.179729	−	0.0877358i
$51$		0			0
$52$	284.231	−	221.752i	0.757996	−	0.591375i
$53$		−	247.445i		−	0.641306i	−0.947197	−	0.320653i	$-0.896098\pi$
$53$		−	247.445i		−	0.641306i	0.947197	−	0.320653i	$-0.103902\pi$
$54$		0			0
$55$	−308.638			−0.756669
$56$	124.616	+	589.248i	0.297365	+	1.40610i
$57$		0			0
$58$	−332.072	+	680.256i	−0.751778	+	1.54003i
$59$			518.596i			1.14433i	0.820139	+	0.572165i	$0.193896\pi$
$59$			518.596i			1.14433i	−0.820139	+	0.572165i	$0.806104\pi$
$60$		0			0
$61$			62.0042i			0.130145i	0.997881	+	0.0650723i	$0.0207278\pi$
$61$			62.0042i			0.130145i	−0.997881	+	0.0650723i	$0.979272\pi$
$62$	127.630	+	62.3033i	0.261435	+	0.127621i
$63$		0			0
$64$	−468.162	+	207.287i	−0.914380	+	0.404858i
$65$	−225.314			−0.429949
$66$		0			0
$67$			558.476i			1.01834i	0.860666	+	0.509169i	$0.170047\pi$
$67$			558.476i			1.01834i	−0.860666	+	0.509169i	$0.829953\pi$
$68$	353.697	+	453.351i	0.630765	+	0.808484i
$69$		0			0
$70$	165.130	−	338.273i	0.281955	−	0.577590i
$71$	−313.194			−0.523512			−0.261756	−	0.965134i	$-0.584301\pi$
$71$	−313.194			−0.523512			−0.261756	+	0.965134i	$0.584301\pi$
$72$		0			0
$73$	−263.926			−0.423153			−0.211576	−	0.977361i	$-0.567860\pi$
$73$	−263.926			−0.423153			−0.211576	+	0.977361i	$0.567860\pi$
$74$	93.1472	−	190.814i	0.146326	−	0.299753i
$75$		0			0
$76$	−111.213	+	86.7663i	−0.167855	+	0.130958i
$77$		−	1643.03i		−	2.43169i
$78$		0			0
$79$	−732.940			−1.04383			−0.521913	−	0.852999i	$-0.674781\pi$
$79$	−732.940			−1.04383			−0.521913	+	0.852999i	$0.674781\pi$
$80$	310.388	+	77.8405i	0.433781	+	0.108785i
$81$		0			0
$82$	563.468	+	275.061i	0.758837	+	0.370432i
$83$			717.705i			0.949137i	0.880218	+	0.474569i	$0.157396\pi$
$83$			717.705i			0.949137i	−0.880218	+	0.474569i	$0.842604\pi$
$84$		0			0
$85$		−	359.377i		−	0.458587i
$86$	234.503	−	480.385i	0.294037	−	0.602341i
$87$		0			0
$88$	1366.51	−	288.994i	1.65535	−	0.350077i
$89$	−1634.69			−1.94693			−0.973463	−	0.228845i	$-0.926505\pi$
$89$	−1634.69			−1.94693			−0.973463	+	0.228845i	$0.926505\pi$
$90$		0			0
$91$		−	1199.45i		−	1.38172i
$92$	−213.635	−	273.827i	−0.242097	−	0.310309i
$93$		0			0
$94$	976.392	+	476.633i	1.07135	+	0.522988i
$95$	88.1597			0.0952105
$96$		0			0
$97$	−1367.12			−1.43103			−0.715516	−	0.698596i	$-0.753809\pi$
$97$	−1367.12			−1.43103			−0.715516	+	0.698596i	$0.753809\pi$
$98$	928.962	+	453.479i	0.957544	+	0.467432i
$99$		0			0
$100$	−123.024	−	157.687i	−0.123024	−	0.157687i
$101$			58.3234i			0.0574594i	0.999587	+	0.0287297i	$0.00914620\pi$
$101$			58.3234i			0.0574594i	−0.999587	+	0.0287297i	$0.990854\pi$
$102$		0			0
$103$	−9.69032			−0.00927005			−0.00463503	−	0.999989i	$-0.501475\pi$
$103$	−9.69032			−0.00927005			−0.00463503	+	0.999989i	$0.501475\pi$
$104$	997.588	−	210.972i	0.940592	−	0.198919i
$105$		0			0
$106$	307.023	−	628.944i	0.281328	−	0.576306i
$107$			439.045i			0.396674i	0.980134	+	0.198337i	$0.0635540\pi$
$107$			439.045i			0.396674i	−0.980134	+	0.198337i	$0.936446\pi$
$108$		0			0
$109$		−	1616.51i		−	1.42049i	−0.703955	−	0.710245i	$-0.748584\pi$
$109$		−	1616.51i		−	1.42049i	0.703955	−	0.710245i	$-0.251416\pi$
$110$	−784.481	−	382.950i	−0.679976	−	0.331935i
$111$		0			0
$112$	−414.381	+	1652.34i	−0.349601	+	1.39403i
$113$	1281.25			1.06663			0.533316	−	0.845916i	$-0.320946\pi$
$113$	1281.25			1.06663			0.533316	+	0.845916i	$0.320946\pi$
$114$		0			0
$115$			217.066i			0.176013i
$116$	−1688.08	+	1317.01i	−1.35116	+	1.05415i
$117$		0			0
$118$	−643.459	+	1318.14i	−0.501993	+	1.02834i
$119$	1913.13			1.47375
$120$		0			0
$121$	−2479.31			−1.86274
$122$	−76.9330	+	157.599i	−0.0570917	+	0.116954i
$123$		0			0
$124$	247.098	+	316.718i	0.178952	+	0.229372i
$125$			125.000i			0.0894427i
$126$		0			0
$127$	235.326			0.164423			0.0822117	−	0.996615i	$-0.473802\pi$
$127$	235.326			0.164423			0.0822117	+	0.996615i	$0.473802\pi$
$128$	−1447.15	−	54.0113i	−0.999304	−	0.0372966i
$129$		0			0
$130$	−572.690	−	279.563i	−0.386371	−	0.188610i
$131$		−	993.121i		−	0.662362i	−0.943567	−	0.331181i	$-0.892553\pi$
$131$		−	993.121i		−	0.662362i	0.943567	−	0.331181i	$-0.107447\pi$
$132$		0			0
$133$			469.315i			0.305976i
$134$	−692.941	+	1419.51i	−0.446724	+	0.915124i
$135$		0			0
$136$	336.503	+	1591.16i	0.212168	+	1.00324i
$137$	−2070.09			−1.29095			−0.645474	−	0.763782i	$-0.723340\pi$
$137$	−2070.09			−1.29095			−0.645474	+	0.763782i	$0.723340\pi$
$138$		0			0
$139$			288.330i			0.175941i	0.996123	+	0.0879707i	$0.0280382\pi$
$139$			288.330i			0.175941i	−0.996123	+	0.0879707i	$0.971962\pi$
$140$	839.438	−	654.915i	0.506753	−	0.395360i
$141$		0			0
$142$	−796.061	−	388.603i	−0.470450	−	0.229654i
$143$	−2781.62			−1.62665
$144$		0			0
$145$	1338.17			0.766404
$146$	−670.832	−	327.471i	−0.380264	−	0.185628i
$147$		0			0
$148$	473.514	−	369.427i	0.262990	−	0.205181i
$149$		−	900.665i		−	0.495204i	−0.968862	−	0.247602i	$-0.920358\pi$
$149$		−	900.665i		−	0.495204i	0.968862	−	0.247602i	$-0.0796425\pi$
$150$		0			0
$151$	2005.71			1.08094			0.540472	−	0.841362i	$-0.318246\pi$
$151$	2005.71			1.08094			0.540472	+	0.841362i	$0.318246\pi$
$152$	−390.332	+	82.5483i	−0.208290	+	0.0440497i
$153$		0			0
$154$	2038.62	−	4176.16i	1.06673	−	2.18522i
$155$		−	251.067i		−	0.130104i
$156$		0			0
$157$		−	3098.13i		−	1.57489i	−0.616385	−	0.787445i	$-0.711403\pi$
$157$		−	3098.13i		−	1.57489i	0.616385	−	0.787445i	$-0.288597\pi$
$158$	−1862.95	−	909.412i	−0.938027	−	0.457905i
$159$		0			0
$160$	692.346	+	582.972i	0.342092	+	0.288050i
$161$	−1155.54			−0.565648
$162$		0			0
$163$			3566.57i			1.71383i	0.515454	+	0.856917i	$0.327623\pi$
$163$			3566.57i			1.71383i	−0.515454	+	0.856917i	$0.672377\pi$
$164$	1090.91	+	1398.27i	0.519424	+	0.665772i
$165$		0			0
$166$	−890.509	+	1824.23i	−0.416367	+	0.852936i
$167$	−1326.87			−0.614830			−0.307415	−	0.951576i	$-0.599464\pi$
$167$	−1326.87			−0.614830			−0.307415	+	0.951576i	$0.599464\pi$
$168$		0			0
$169$	166.353			0.0757180
$170$	445.905	−	913.446i	0.201173	−	0.412106i
$171$		0			0
$172$	1192.10	−	930.054i	0.528469	−	0.412302i
$173$		−	1035.22i		−	0.454952i	−0.973784	−	0.227476i	$-0.926953\pi$
$173$		−	1035.22i		−	0.454952i	0.973784	−	0.227476i	$-0.0730473\pi$
$174$		0			0
$175$	−665.433			−0.287440
$176$	3831.91	+	960.983i	1.64114	+	0.411573i
$177$		0			0
$178$	−4154.96	−	2028.27i	−1.74959	−	0.854076i
$179$		−	1811.28i		−	0.756319i	−0.925740	−	0.378160i	$-0.876557\pi$
$179$		−	1811.28i		−	0.756319i	0.925740	−	0.378160i	$-0.123443\pi$
$180$		0			0
$181$			2286.18i			0.938842i	0.882975	+	0.469421i	$0.155537\pi$
$181$			2286.18i			0.938842i	−0.882975	+	0.469421i	$0.844463\pi$
$182$	1488.24	−	3048.70i	0.606131	−	1.24167i
$183$		0			0
$184$	−203.249	−	961.070i	−0.0814334	−	0.385060i
$185$	−375.360			−0.149173
$186$		0			0
$187$		−	4436.70i		−	1.73499i
$188$	1890.35	+	2422.96i	0.733341	+	0.939960i
$189$		0			0
$190$	224.080	+	109.386i	0.0855603	+	0.0417669i
$191$	2392.90			0.906513			0.453256	−	0.891380i	$-0.350262\pi$
$191$	2392.90			0.906513			0.453256	+	0.891380i	$0.350262\pi$
$192$		0			0
$193$	−638.414			−0.238104			−0.119052	−	0.992888i	$-0.537985\pi$
$193$	−638.414			−0.238104			−0.119052	+	0.992888i	$0.537985\pi$
$194$	−3474.88	−	1696.29i	−1.28599	−	0.627764i
$195$		0			0
$196$	1798.52	+	2305.26i	0.655438	+	0.840109i
$197$		−	654.303i		−	0.236635i	−0.992976	−	0.118318i	$-0.962250\pi$
$197$		−	654.303i		−	0.236635i	0.992976	−	0.118318i	$-0.0377501\pi$
$198$		0			0
$199$	−1637.06			−0.583155			−0.291578	−	0.956547i	$-0.594180\pi$
$199$	−1637.06			−0.583155			−0.291578	+	0.956547i	$0.594180\pi$
$200$	−117.044	−	553.444i	−0.0413812	−	0.195672i
$201$		0			0
$202$	−72.3661	+	148.243i	−0.0252062	+	0.0516355i
$203$			7123.67i			2.46297i
$204$		0			0
$205$		−	1108.43i		−	0.377638i
$206$	−24.6304	−	12.0235i	−0.00833048	−	0.00406658i
$207$		0			0
$208$	2797.39	+	701.541i	0.932519	+	0.233861i
$209$	1088.38			0.360214
$210$		0			0
$211$			2769.26i			0.903524i	0.892139	+	0.451762i	$0.149204\pi$
$211$			2769.26i			0.903524i	−0.892139	+	0.451762i	$0.850796\pi$
$212$	1560.75	−	1217.67i	0.505627	−	0.394481i
$213$		0			0
$214$	−544.755	+	1115.94i	−0.174012	+	0.356468i
$215$	−944.990			−0.299757
$216$		0			0
$217$	1336.54			0.418113
$218$	2005.72	−	4108.76i	0.623139	−	1.27651i
$219$		0			0
$220$	−1518.80	−	1946.72i	−0.465443	−	0.596582i
$221$		−	3238.90i		−	0.985846i
$222$		0			0
$223$	−4312.57			−1.29503			−0.647514	−	0.762054i	$-0.724191\pi$
$223$	−4312.57			−1.29503			−0.647514	+	0.762054i	$0.724191\pi$
$224$	−3103.43	+	3685.68i	−0.925699	+	1.09937i
$225$		0			0
$226$	3256.60	+	1589.73i	0.958523	+	0.467909i
$227$			575.097i			0.168152i	0.996459	+	0.0840761i	$0.0267939\pi$
$227$			575.097i			0.168152i	−0.996459	+	0.0840761i	$0.973206\pi$
$228$		0			0
$229$		−	2396.42i		−	0.691529i	−0.938321	−	0.345765i	$-0.887620\pi$
$229$		−	2396.42i		−	0.691529i	0.938321	−	0.345765i	$-0.112380\pi$
$230$	−269.329	+	551.726i	−0.0772132	+	0.158173i
$231$		0			0
$232$	−5924.80	+	1252.99i	−1.67665	+	0.354581i
$233$	−3307.22			−0.929885			−0.464943	−	0.885341i	$-0.653925\pi$
$233$	−3307.22			−0.929885			−0.464943	+	0.885341i	$0.653925\pi$
$234$		0			0
$235$		−	1920.71i		−	0.533163i
$236$	−3271.02	+	2551.99i	−0.902227	+	0.703901i
$237$		0			0
$238$	4862.69	+	2373.76i	1.32438	+	0.646504i
$239$	1534.33			0.415262			0.207631	−	0.978207i	$-0.433425\pi$
$239$	1534.33			0.415262			0.207631	+	0.978207i	$0.433425\pi$
$240$		0			0
$241$	−461.143			−0.123257			−0.0616283	−	0.998099i	$-0.519629\pi$
$241$	−461.143			−0.123257			−0.0616283	+	0.998099i	$0.519629\pi$
$242$	−6301.77	−	3076.25i	−1.67394	−	0.817145i
$243$		0			0
$244$	−391.089	+	305.121i	−0.102610	+	0.0800547i
$245$		−	1827.41i		−	0.476526i
$246$		0			0
$247$	794.543			0.204678
$248$	235.086	+	1111.61i	0.0601935	+	0.284627i
$249$		0			0
$250$	−155.096	+	317.719i	−0.0392367	+	0.0803771i
$251$			6200.39i			1.55922i	0.626263	+	0.779612i	$0.284584\pi$
$251$			6200.39i			1.55922i	−0.626263	+	0.779612i	$0.715416\pi$
$252$		0			0
$253$			2679.79i			0.665917i
$254$	598.139	+	291.986i	0.147758	+	0.0721291i
$255$		0			0
$256$	−3611.27	−	1932.86i	−0.881657	−	0.471890i
$257$	2381.71			0.578082			0.289041	−	0.957317i	$-0.406664\pi$
$257$	2381.71			0.578082			0.289041	+	0.957317i	$0.406664\pi$
$258$		0			0
$259$		−	1998.22i		−	0.479394i
$260$	−1108.76	−	1421.16i	−0.264471	−	0.338986i
$261$		0			0
$262$	1232.24	−	2524.26i	0.290564	−	0.595227i
$263$	420.996			0.0987061			0.0493531	−	0.998781i	$-0.484284\pi$
$263$	420.996			0.0987061			0.0493531	+	0.998781i	$0.484284\pi$
$264$		0			0
$265$	−1237.23			−0.286801
$266$	−582.313	+	1192.88i	−0.134225	+	0.274963i
$267$		0			0
$268$	−3522.56	+	2748.24i	−0.802891	+	0.626402i
$269$		−	6748.92i		−	1.52970i	−0.644209	−	0.764849i	$-0.722813\pi$
$269$		−	6748.92i		−	1.52970i	0.644209	−	0.764849i	$-0.277187\pi$
$270$		0			0
$271$	5718.47			1.28182			0.640908	−	0.767618i	$-0.278558\pi$
$271$	5718.47			1.28182			0.640908	+	0.767618i	$0.278558\pi$
$272$	−1118.96	+	4461.86i	−0.249438	+	0.994631i
$273$		0			0
$274$	−5261.65	−	2568.51i	−1.16010	−	0.566312i
$275$			1543.19i			0.338393i
$276$		0			0
$277$			6245.97i			1.35481i	0.735608	+	0.677407i	$0.236897\pi$
$277$			6245.97i			1.35481i	−0.735608	+	0.677407i	$0.763103\pi$
$278$	−357.752	+	732.863i	−0.0771818	+	0.158109i
$279$		0			0
$280$	2946.24	−	623.078i	0.628827	−	0.132986i
$281$	−2883.17			−0.612084			−0.306042	−	0.952018i	$-0.599005\pi$
$281$	−2883.17			−0.612084			−0.306042	+	0.952018i	$0.599005\pi$
$282$		0			0
$283$			7520.83i			1.57974i	0.613273	+	0.789871i	$0.289852\pi$
$283$			7520.83i			1.57974i	−0.613273	+	0.789871i	$0.710148\pi$
$284$	−1541.22	−	1975.46i	−0.322023	−	0.412754i
$285$		0			0
$286$	−7070.17	−	3451.35i	−1.46178	−	0.713576i
$287$	5900.67			1.21361
$288$		0			0
$289$	253.072			0.0515107
$290$	3401.28	+	1660.36i	0.688724	+	0.336205i
$291$		0			0
$292$	−1298.77	−	1664.70i	−0.260290	−	0.333627i
$293$			6762.89i			1.34844i	0.738531	+	0.674219i	$0.235520\pi$
$293$			6762.89i			1.34844i	−0.738531	+	0.674219i	$0.764480\pi$
$294$		0			0
$295$	2592.98			0.511760
$296$	1661.93	−	351.468i	0.326343	−	0.0690158i
$297$		0			0
$298$	1117.52	−	2289.26i	0.217236	−	0.445012i
$299$			1956.31i			0.378383i
$300$		0			0
$301$		−	5030.62i		−	0.963323i
$302$	5098.01	+	2488.63i	0.971383	+	0.474187i
$303$		0			0
$304$	−1094.55	−	274.496i	−0.206502	−	0.0517876i
$305$	310.021			0.0582024
$306$		0			0
$307$			10085.5i			1.87495i	0.348058	+	0.937473i	$0.386841\pi$
$307$			10085.5i			1.87495i	−0.348058	+	0.937473i	$0.613159\pi$
$308$	10363.3	−	8085.28i	1.91722	−	1.49578i
$309$		0			0
$310$	311.516	−	638.148i	0.0570740	−	0.116917i
$311$	7683.50			1.40094			0.700469	−	0.713683i	$-0.252974\pi$
$311$	7683.50			1.40094			0.700469	+	0.713683i	$0.252974\pi$
$312$		0			0
$313$	1253.17			0.226304			0.113152	−	0.993578i	$-0.463905\pi$
$313$	1253.17			0.226304			0.113152	+	0.993578i	$0.463905\pi$
$314$	3844.07	−	7874.67i	0.690872	−	1.41527i
$315$		0			0
$316$	−3606.78	−	4622.99i	−0.642079	−	0.822986i
$317$			958.616i			0.169846i	0.996388	+	0.0849231i	$0.0270645\pi$
$317$			958.616i			0.169846i	−0.996388	+	0.0849231i	$0.972936\pi$
$318$		0			0
$319$	16520.4			2.89957
$320$	1036.44	+	2340.81i	0.181058	+	0.408923i
$321$		0			0
$322$	−2937.09	−	1433.76i	−0.508316	−	0.248138i
$323$			1267.30i			0.218312i
$324$		0			0
$325$			1126.57i			0.192279i
$326$	−4425.29	+	9065.31i	−0.751823	+	1.54013i
$327$		0			0
$328$	1037.87	+	4907.62i	0.174717	+	0.826152i
$329$	10224.8			1.71341
$330$		0			0
$331$			4252.70i			0.706192i	0.935587	+	0.353096i	$0.114871\pi$
$331$			4252.70i			0.706192i	−0.935587	+	0.353096i	$0.885129\pi$
$332$	−4526.90	+	3531.81i	−0.748331	+	0.583835i
$333$		0			0
$334$	−3372.58	−	1646.35i	−0.552513	−	0.269713i
$335$	2792.38			0.455415
$336$		0			0
$337$	7662.86			1.23864			0.619321	−	0.785138i	$-0.287408\pi$
$337$	7662.86			1.23864			0.619321	+	0.785138i	$0.287408\pi$
$338$	422.826	+	206.406i	0.0680435	+	0.0332159i
$339$		0			0
$340$	2266.76	−	1768.48i	0.361565	−	0.282087i
$341$		−	3099.55i		−	0.492229i
$342$		0			0
$343$	598.394			0.0941990
$344$	4184.00	−	884.841i	0.655773	−	0.138684i
$345$		0			0
$346$	1284.48	−	2631.28i	0.199578	−	0.408840i
$347$		−	3626.75i		−	0.561078i	−0.959843	−	0.280539i	$-0.909487\pi$
$347$		−	3626.75i		−	0.561078i	0.959843	−	0.280539i	$-0.0905132\pi$
$348$		0			0
$349$		−	8867.03i		−	1.36000i	−0.733210	−	0.680002i	$-0.761979\pi$
$349$		−	8867.03i		−	1.36000i	0.733210	−	0.680002i	$-0.238021\pi$
$350$	−1691.36	−	825.650i	−0.258306	−	0.126094i
$351$		0			0
$352$	8547.39	+	7197.10i	1.29425	+	1.08979i
$353$	−8775.59			−1.32317			−0.661583	−	0.749872i	$-0.730115\pi$
$353$	−8775.59			−1.32317			−0.661583	+	0.749872i	$0.730115\pi$
$354$		0			0
$355$			1565.97i			0.234121i
$356$	−8044.24	−	10310.7i	−1.19760	−	1.53502i
$357$		0			0
$358$	2247.38	−	4603.81i	0.331782	−	0.679662i
$359$	−7668.51			−1.12738			−0.563688	−	0.825988i	$-0.690618\pi$
$359$	−7668.51			−1.12738			−0.563688	+	0.825988i	$0.690618\pi$
$360$		0			0
$361$	6548.11			0.954675
$362$	−2836.63	+	5810.89i	−0.411850	+	0.843684i
$363$		0			0
$364$	7565.47	−	5902.45i	1.08939	−	0.849924i
$365$			1319.63i			0.189240i
$366$		0			0
$367$	−8276.28			−1.17716			−0.588581	−	0.808438i	$-0.700313\pi$
$367$	−8276.28			−1.17716			−0.588581	+	0.808438i	$0.700313\pi$
$368$	675.860	−	2694.99i	0.0957382	−	0.381755i
$369$		0			0
$370$	−954.071	−	465.736i	−0.134053	−	0.0654391i
$371$		−	6586.33i		−	0.921685i
$372$		0			0
$373$		−	270.669i		−	0.0375730i	−0.999824	−	0.0187865i	$-0.994020\pi$
$373$		−	270.669i		−	0.0375730i	0.999824	−	0.0187865i	$-0.00598028\pi$
$374$	5504.93	−	11277.0i	0.761105	−	1.55914i
$375$		0			0
$376$	1798.46	+	8504.05i	0.246671	+	1.16639i
$377$	12060.3			1.64757
$378$		0			0
$379$		−	8455.66i		−	1.14601i	−0.819551	−	0.573006i	$-0.805777\pi$
$379$		−	8455.66i		−	1.14601i	0.819551	−	0.573006i	$-0.194223\pi$
$380$	433.831	+	556.064i	0.0585660	+	0.0750671i
$381$		0			0
$382$	6082.14	+	2969.04i	0.814632	+	0.397668i
$383$	6527.25			0.870827			0.435414	−	0.900231i	$-0.356602\pi$
$383$	6527.25			0.870827			0.435414	+	0.900231i	$0.356602\pi$
$384$		0			0
$385$	−8215.13			−1.08748
$386$	−1622.69	−	792.126i	−0.213971	−	0.104451i
$387$		0			0
$388$	−6727.57	−	8623.07i	−0.880259	−	1.12827i
$389$		−	683.173i		−	0.0890443i	−0.999008	−	0.0445222i	$-0.985823\pi$
$389$		−	683.173i		−	0.0890443i	0.999008	−	0.0445222i	$-0.0141765\pi$
$390$		0			0
$391$	−3120.34			−0.403586
$392$	1711.09	+	8090.95i	0.220467	+	1.04249i
$393$		0			0
$394$	811.840	−	1663.07i	0.103807	−	0.212651i
$395$			3664.70i			0.466813i
$396$		0			0
$397$			2579.34i			0.326079i	0.986620	+	0.163040i	$0.0521298\pi$
$397$			2579.34i			0.326079i	−0.986620	+	0.163040i	$0.947870\pi$
$398$	−4160.99	−	2031.21i	−0.524049	−	0.255818i
$399$		0			0
$400$	389.203	−	1551.94i	0.0486503	−	0.193993i
$401$	8344.02			1.03910			0.519552	−	0.854439i	$-0.326099\pi$
$401$	8344.02			1.03910			0.519552	+	0.854439i	$0.326099\pi$
$402$		0			0
$403$		−	2262.75i		−	0.279691i
$404$	−367.873	+	287.008i	−0.0453028	+	0.0353445i
$405$		0			0
$406$	−8838.85	+	18106.6i	−1.08046	+	2.21334i
$407$	−4634.02			−0.564373
$408$		0			0
$409$	1939.68			0.234501			0.117251	−	0.993102i	$-0.462592\pi$
$409$	1939.68			0.234501			0.117251	+	0.993102i	$0.462592\pi$
$410$	1375.30	−	2817.34i	0.165662	−	0.339362i
$411$		0			0
$412$	−47.6858	−	61.1213i	−0.00570221	−	0.00730881i
$413$			13803.6i			1.64463i
$414$		0			0
$415$	3588.53			0.424467
$416$	6239.80	+	5254.06i	0.735412	+	0.619234i
$417$		0			0
$418$	2766.39	+	1350.43i	0.323704	+	0.158018i
$419$			4046.49i			0.471799i	0.971777	+	0.235900i	$0.0758037\pi$
$419$			4046.49i			0.471799i	−0.971777	+	0.235900i	$0.924196\pi$
$420$		0			0
$421$			3305.28i			0.382636i	0.981528	+	0.191318i	$0.0612761\pi$
$421$			3305.28i			0.382636i	−0.981528	+	0.191318i	$0.938724\pi$
$422$	−3436.02	+	7038.76i	−0.396357	+	0.811946i
$423$		0			0
$424$	5477.89	−	1158.48i	0.627429	−	0.132690i
$425$	−1796.88			−0.205086
$426$		0			0
$427$			1650.38i			0.187044i
$428$	−2769.26	+	2160.53i	−0.312750	+	0.244002i
$429$		0			0
$430$	−2401.93	−	1172.52i	−0.269375	−	0.131497i
$431$	2953.12			0.330038			0.165019	−	0.986290i	$-0.447231\pi$
$431$	2953.12			0.330038			0.165019	+	0.986290i	$0.447231\pi$
$432$		0			0
$433$	1380.70			0.153239			0.0766193	−	0.997060i	$-0.475587\pi$
$433$	1380.70			0.153239			0.0766193	+	0.997060i	$0.475587\pi$
$434$	3397.16	+	1658.35i	0.375735	+	0.183417i
$435$		0			0
$436$	10196.1	−	7954.79i	1.11996	−	0.873774i
$437$		−	765.458i		−	0.0837914i
$438$		0			0
$439$	−14233.4			−1.54743			−0.773717	−	0.633532i	$-0.781605\pi$
$439$	−14233.4			−1.54743			−0.773717	+	0.633532i	$0.781605\pi$
$440$	−1444.97	−	6832.57i	−0.156559	−	0.740295i
$441$		0			0
$442$	4018.74	−	8232.47i	0.432470	−	0.885924i
$443$		−	8541.25i		−	0.916042i	−0.888941	−	0.458021i	$-0.848558\pi$
$443$		−	8541.25i		−	0.916042i	0.888941	−	0.458021i	$-0.151442\pi$
$444$		0			0
$445$			8173.43i			0.870692i
$446$	−10961.5	−	5350.92i	−1.16377	−	0.568101i
$447$		0			0
$448$	−12461.2	+	5517.42i	−1.31415	+	0.581861i
$449$	−9994.76			−1.05052			−0.525258	−	0.850943i	$-0.676031\pi$
$449$	−9994.76			−1.05052			−0.525258	+	0.850943i	$0.676031\pi$
$450$		0			0
$451$		−	13684.1i		−	1.42874i
$452$	6304.97	+	8081.41i	0.656108	+	0.840968i
$453$		0			0
$454$	−713.564	+	1461.75i	−0.0737648	+	0.151109i
$455$	−5997.24			−0.617923
$456$		0			0
$457$	6435.58			0.658739			0.329370	−	0.944201i	$-0.393164\pi$
$457$	6435.58			0.658739			0.329370	+	0.944201i	$0.393164\pi$
$458$	2973.42	−	6091.11i	0.303359	−	0.621438i
$459$		0			0
$460$	−1369.13	+	1068.17i	−0.138774	+	0.108269i
$461$		−	7851.78i		−	0.793262i	−0.917978	−	0.396631i	$-0.870179\pi$
$461$		−	7851.78i		−	0.793262i	0.917978	−	0.396631i	$-0.129821\pi$
$462$		0			0
$463$	7073.58			0.710016			0.355008	−	0.934863i	$-0.384478\pi$
$463$	7073.58			0.710016			0.355008	+	0.934863i	$0.384478\pi$
$464$	−16614.0	−	4166.54i	−1.66226	−	0.416868i
$465$		0			0
$466$	−8406.12	−	4103.51i	−0.835635	−	0.407921i
$467$			15753.8i			1.56102i	0.625142	+	0.780511i	$0.285041\pi$
$467$			15753.8i			1.56102i	−0.625142	+	0.780511i	$0.714959\pi$
$468$		0			0
$469$			14865.1i			1.46356i
$470$	2383.16	−	4881.96i	0.233887	−	0.479124i
$471$		0			0
$472$	−11480.6	+	2427.94i	−1.11957	+	0.236769i
$473$	−11666.4			−1.13408
$474$		0			0
$475$		−	440.799i		−	0.0425794i
$476$	9414.46	+	12067.0i	0.906535	+	1.16195i
$477$		0			0
$478$	3899.88	+	1903.75i	0.373172	+	0.182167i
$479$	−14747.9			−1.40678			−0.703391	−	0.710803i	$-0.748332\pi$
$479$	−14747.9			−1.40678			−0.703391	+	0.710803i	$0.748332\pi$
$480$		0			0
$481$	−3382.95			−0.320684
$482$	−1172.11	−	572.173i	−0.110764	−	0.0540701i
$483$		0			0
$484$	−12200.6	−	15638.1i	−1.14581	−	1.46864i
$485$			6835.61i			0.639977i
$486$		0			0
$487$	5631.77			0.524024			0.262012	−	0.965065i	$-0.415614\pi$
$487$	5631.77			0.524024			0.262012	+	0.965065i	$0.415614\pi$
$488$	−1372.63	+	290.288i	−0.127328	+	0.0269277i
$489$		0			0
$490$	2267.40	−	4644.81i	0.209042	−	0.428227i
$491$		−	18259.0i		−	1.67824i	−0.543945	−	0.839121i	$-0.683070\pi$
$491$		−	18259.0i		−	1.67824i	0.543945	−	0.839121i	$-0.316930\pi$
$492$		0			0
$493$			19236.2i			1.75731i
$494$	2019.53	+	985.847i	0.183933	+	0.0897882i
$495$		0			0
$496$	−781.726	+	3117.12i	−0.0707672	+	0.282183i
$497$	−8336.39			−0.752391
$498$		0			0
$499$			729.599i			0.0654536i	0.999464	+	0.0327268i	$0.0104191\pi$
$499$			729.599i			0.0654536i	−0.999464	+	0.0327268i	$0.989581\pi$
$500$	−788.433	+	615.121i	−0.0705195	+	0.0550181i
$501$		0			0
$502$	−7693.27	+	15759.8i	−0.683999	+	1.40119i
$503$	−1551.81			−0.137558			−0.0687790	−	0.997632i	$-0.521910\pi$
$503$	−1551.81			−0.137558			−0.0687790	+	0.997632i	$0.521910\pi$
$504$		0			0
$505$	291.617			0.0256966
$506$	−3325.01	+	6811.36i	−0.292124	+	0.598423i
$507$		0			0
$508$	1158.03	+	1484.31i	0.101140	+	0.129637i
$509$			6145.59i			0.535164i	0.963535	+	0.267582i	$0.0862247\pi$
$509$			6145.59i			0.535164i	−0.963535	+	0.267582i	$0.913775\pi$
$510$		0			0
$511$	−7024.99			−0.608155
$512$	−6780.69	−	9393.61i	−0.585287	−	0.810826i
$513$		0			0
$514$	6053.71	+	2955.16i	0.519490	+	0.253593i
$515$			48.4516i			0.00414569i
$516$		0			0
$517$		−	23712.2i		−	2.01714i
$518$	2479.33	−	5078.96i	0.210300	−	0.430804i
$519$		0			0
$520$	−1054.86	−	4987.94i	−0.0889591	−	0.420646i
$521$	−588.432			−0.0494812			−0.0247406	−	0.999694i	$-0.507876\pi$
$521$	−588.432			−0.0494812			−0.0247406	+	0.999694i	$0.507876\pi$
$522$		0			0
$523$		−	866.147i		−	0.0724168i	−0.999344	−	0.0362084i	$-0.988472\pi$
$523$		−	866.147i		−	0.0724168i	0.999344	−	0.0362084i	$-0.0115280\pi$
$524$	6264.07	−	4887.12i	0.522228	−	0.407433i
$525$		0			0
$526$	1070.07	+	522.360i	0.0887016	+	0.0433003i
$527$	3609.10			0.298321
$528$		0			0
$529$	−10282.3			−0.845097
$530$	−3144.72	−	1535.12i	−0.257732	−	0.125814i
$531$		0			0
$532$	−2960.19	+	2309.49i	−0.241241	+	0.188212i
$533$		−	9989.74i		−	0.811827i
$534$		0			0
$535$	2195.22			0.177398
$536$	−12363.4	+	2614.64i	−0.996303	+	0.210700i
$537$		0			0
$538$	8373.87	−	17154.1i	0.671047	−	1.37465i
$539$		−	22560.3i		−	1.80286i
$540$		0			0
$541$		−	10380.3i		−	0.824926i	−0.910974	−	0.412463i	$-0.864669\pi$
$541$		−	10380.3i		−	0.824926i	0.910974	−	0.412463i	$-0.135331\pi$
$542$	14534.9	+	7095.31i	1.15190	+	0.562306i
$543$		0			0
$544$	−8380.27	+	9952.53i	−0.660480	+	0.784396i
$545$	−8082.54			−0.635262
$546$		0			0
$547$		−	1208.43i		−	0.0944584i	−0.998884	−	0.0472292i	$-0.984961\pi$
$547$		−	1208.43i		−	0.0944584i	0.998884	−	0.0472292i	$-0.0150391\pi$
$548$	−10186.9	−	13057.0i	−0.794090	−	1.01783i
$549$		0			0
$550$	−1914.75	+	3922.41i	−0.148446	+	0.304094i
$551$	−4718.89			−0.364849
$552$		0			0
$553$	−19508.9			−1.50019
$554$	−7749.82	+	15875.7i	−0.594329	+	1.21750i
$555$		0			0
$556$	−1818.63	+	1418.86i	−0.138718	+	0.108225i
$557$		−	10284.9i		−	0.782379i	−0.920310	−	0.391190i	$-0.872064\pi$
$557$		−	10284.9i		−	0.782379i	0.920310	−	0.391190i	$-0.127936\pi$
$558$		0			0
$559$	−8516.76			−0.644402
$560$	8261.70	+	2071.91i	0.623430	+	0.156346i
$561$		0			0
$562$	−7328.29	−	3577.36i	−0.550045	−	0.268508i
$563$			18420.7i			1.37894i	0.724316	+	0.689469i	$0.242156\pi$
$563$			18420.7i			1.37894i	−0.724316	+	0.689469i	$0.757844\pi$
$564$		0			0
$565$		−	6406.23i		−	0.477013i
$566$	−9331.63	+	19116.1i	−0.693000	+	1.41963i
$567$		0			0
$568$	−1466.30	−	6933.43i	−0.108318	−	0.512183i
$569$	13111.3			0.966002			0.483001	−	0.875620i	$-0.339547\pi$
$569$	13111.3			0.966002			0.483001	+	0.875620i	$0.339547\pi$
$570$		0			0
$571$		−	12226.6i		−	0.896088i	−0.894012	−	0.448044i	$-0.852121\pi$
$571$		−	12226.6i		−	0.896088i	0.894012	−	0.448044i	$-0.147879\pi$
$572$	−13688.3	−	17544.9i	−1.00058	−	1.28250i
$573$		0			0
$574$	14998.0	+	7321.38i	1.09060	+	0.532384i
$575$	1085.33			0.0787153
$576$		0			0
$577$	3294.12			0.237671			0.118836	−	0.992914i	$-0.462084\pi$
$577$	3294.12			0.237671			0.118836	+	0.992914i	$0.462084\pi$
$578$	643.246	+	314.005i	0.0462898	+	0.0225967i
$579$		0			0
$580$	6585.07	+	8440.42i	0.471431	+	0.604258i
$581$			19103.4i			1.36410i
$582$		0			0
$583$	−15274.2			−1.08507
$584$	−1235.63	−	5842.73i	−0.0875529	−	0.413996i
$585$		0			0
$586$	−8391.21	+	17189.6i	−0.591532	+	1.21177i
$587$		−	16607.6i		−	1.16775i	−0.811844	−	0.583874i	$-0.801536\pi$
$587$		−	16607.6i		−	1.16775i	0.811844	−	0.583874i	$-0.198464\pi$
$588$		0			0
$589$			885.358i			0.0619364i
$590$	6590.70	+	3217.30i	0.459890	+	0.224498i
$591$		0			0
$592$	4660.29	+	1168.73i	0.323542	+	0.0811393i
$593$	15288.4			1.05872			0.529359	−	0.848398i	$-0.322433\pi$
$593$	15288.4			1.05872			0.529359	+	0.848398i	$0.322433\pi$
$594$		0			0
$595$		−	9565.65i		−	0.659081i
$596$	5680.91	−	4432.15i	0.390435	−	0.304610i
$597$		0			0
$598$	−2427.34	+	4972.46i	−0.165989	+	0.340032i
$599$	23543.0			1.60591			0.802955	−	0.596040i	$-0.203260\pi$
$599$	23543.0			1.60591			0.802955	+	0.596040i	$0.203260\pi$
$600$		0			0
$601$	−15689.7			−1.06488			−0.532442	−	0.846467i	$-0.678725\pi$
$601$	−15689.7			−1.06488			−0.532442	+	0.846467i	$0.678725\pi$
$602$	6241.85	−	12786.6i	0.422590	−	0.865684i
$603$		0			0
$604$	9870.05	+	12650.9i	0.664911	+	0.852251i
$605$			12396.5i			0.833043i
$606$		0			0
$607$	−26462.9			−1.76952			−0.884759	−	0.466048i	$-0.845677\pi$
$607$	−26462.9			−1.76952			−0.884759	+	0.466048i	$0.845677\pi$
$608$	−2441.48	−	2055.79i	−0.162854	−	0.137127i
$609$		0			0
$610$	787.995	+	384.665i	0.0523032	+	0.0255322i
$611$		−	17310.5i		−	1.14617i
$612$		0			0
$613$		−	18256.6i		−	1.20290i	−0.798912	−	0.601448i	$-0.794591\pi$
$613$		−	18256.6i		−	1.20290i	0.798912	−	0.601448i	$-0.205409\pi$
$614$	−12513.8	+	25634.7i	−0.822500	+	1.68491i
$615$		0			0
$616$	36372.9	−	7692.23i	2.37907	−	0.503131i
$617$	−393.579			−0.0256805			−0.0128403	−	0.999918i	$-0.504087\pi$
$617$	−393.579			−0.0256805			−0.0128403	+	0.999918i	$0.504087\pi$
$618$		0			0
$619$			23039.6i			1.49602i	0.663685	+	0.748012i	$0.268991\pi$
$619$			23039.6i			1.49602i	−0.663685	+	0.748012i	$0.731009\pi$
$620$	1583.59	−	1235.49i	0.102578	−	0.0800299i
$621$		0			0
$622$	19529.5	+	9533.47i	1.25894	+	0.614562i
$623$	−43511.0			−2.79812
$624$		0			0
$625$	625.000			0.0400000
$626$	3185.24	+	1554.90i	0.203367	+	0.0992750i
$627$		0			0
$628$	19541.3	−	15245.8i	1.24169	−	0.968749i
$629$		−	5395.83i		−	0.342044i
$630$		0			0
$631$	28960.4			1.82709			0.913547	−	0.406734i	$-0.133332\pi$
$631$	28960.4			1.82709			0.913547	+	0.406734i	$0.133332\pi$
$632$	−3431.44	−	16225.7i	−0.215974	−	1.02124i
$633$		0			0
$634$	−1189.42	+	2436.56i	−0.0745080	+	0.152631i
$635$		−	1176.63i		−	0.0735324i
$636$		0			0
$637$		−	16469.6i		−	1.02441i
$638$	41990.6	+	20498.0i	2.60568	+	1.27198i
$639$		0			0
$640$	−270.057	+	7235.74i	−0.0166796	+	0.446902i
$641$	7160.30			0.441209			0.220604	−	0.975363i	$-0.429197\pi$
$641$	7160.30			0.441209			0.220604	+	0.975363i	$0.429197\pi$
$642$		0			0
$643$			1843.33i			0.113054i	0.998401	+	0.0565270i	$0.0180027\pi$
$643$			1843.33i			0.113054i	−0.998401	+	0.0565270i	$0.981997\pi$
$644$	−5686.38	−	7288.53i	−0.347942	−	0.445976i
$645$		0			0
$646$	−1572.43	+	3221.17i	−0.0957687	+	0.196184i
$647$	−28494.4			−1.73142			−0.865712	−	0.500542i	$-0.833134\pi$
$647$	−28494.4			−1.73142			−0.865712	+	0.500542i	$0.833134\pi$
$648$		0			0
$649$	32011.7			1.93616
$650$	−1397.81	+	2863.45i	−0.0843489	+	0.172790i
$651$		0			0
$652$	−22496.0	+	17551.0i	−1.35124	+	1.05422i
$653$			15898.2i			0.952746i	0.879243	+	0.476373i	$0.158049\pi$
$653$			15898.2i			0.952746i	−0.879243	+	0.476373i	$0.841951\pi$
$654$		0			0
$655$	−4965.61			−0.296217
$656$	−3451.22	+	13761.7i	−0.205408	+	0.819061i
$657$		0			0
$658$	25988.9	+	12686.7i	1.53975	+	0.751639i
$659$			6729.26i			0.397776i	0.980022	+	0.198888i	$0.0637331\pi$
$659$			6729.26i			0.397776i	−0.980022	+	0.198888i	$0.936267\pi$
$660$		0			0
$661$			24516.3i			1.44262i	0.692611	+	0.721311i	$0.256460\pi$
$661$			24516.3i			1.44262i	−0.692611	+	0.721311i	$0.743540\pi$
$662$	−5276.63	+	10809.3i	−0.309792	+	0.634615i
$663$		0			0
$664$	−15888.4	+	3360.12i	−0.928599	+	0.196382i
$665$	2346.58			0.136837
$666$		0			0
$667$		−	11618.8i		−	0.674485i
$668$	−6529.51	−	8369.20i	−0.378195	−	0.484752i
$669$		0			0
$670$	7097.53	+	3464.71i	0.409256	+	0.199781i
$671$	3827.37			0.220200
$672$		0			0
$673$	−8192.84			−0.469258			−0.234629	−	0.972085i	$-0.575388\pi$
$673$	−8192.84			−0.469258			−0.234629	+	0.972085i	$0.575388\pi$
$674$	19477.1	+	9507.86i	1.11310	+	0.543367i
$675$		0			0
$676$	818.616	+	1049.26i	0.0465758	+	0.0596986i
$677$		−	5219.11i		−	0.296287i	−0.988966	−	0.148144i	$-0.952670\pi$
$677$		−	5219.11i		−	0.296287i	0.988966	−	0.148144i	$-0.0473298\pi$
$678$		0			0
$679$	−36389.1			−2.05668
$680$	7955.81	−	1682.51i	0.448664	−	0.0948844i
$681$		0			0
$682$	3845.84	−	7878.28i	0.215931	−	0.442339i
$683$		−	7903.11i		−	0.442759i	−0.975188	−	0.221379i	$-0.928944\pi$
$683$		−	7903.11i		−	0.442759i	0.975188	−	0.221379i	$-0.0710559\pi$
$684$		0			0
$685$			10350.5i			0.577330i
$686$	1520.97	+	742.471i	0.0846513	+	0.0413231i
$687$		0			0
$688$	11732.6	+	2942.34i	0.650144	+	0.163046i
$689$	−11150.6			−0.616549
$690$		0			0
$691$		−	13969.2i		−	0.769051i	−0.923114	−	0.384526i	$-0.874365\pi$
$691$		−	13969.2i		−	0.769051i	0.923114	−	0.384526i	$-0.125635\pi$
$692$	6529.64	−	5094.31i	0.358699	−	0.279851i
$693$		0			0
$694$	4499.97	−	9218.28i	0.246133	−	0.504209i
$695$	1441.65			0.0786834
$696$		0			0
$697$	15933.7			0.865900
$698$	11002.0	−	22537.8i	0.596605	−	1.22216i
$699$		0			0
$700$	−3274.58	−	4197.19i	−0.176810	−	0.226627i
$701$			1929.28i			0.103948i	0.998648	+	0.0519742i	$0.0165514\pi$
$701$			1929.28i			0.103948i	−0.998648	+	0.0519742i	$0.983449\pi$
$702$		0			0
$703$	1323.67			0.0710142
$704$	12795.3	+	28898.6i	0.685004	+	1.54710i
$705$		0			0
$706$	−22305.3	−	10888.5i	−1.18905	−	0.580445i
$707$			1552.41i			0.0825806i
$708$		0			0
$709$		−	33077.6i		−	1.75213i	−0.482197	−	0.876063i	$-0.660161\pi$
$709$		−	33077.6i		−	1.75213i	0.482197	−	0.876063i	$-0.339839\pi$
$710$	−1943.01	+	3980.31i	−0.102704	+	0.210392i
$711$		0			0
$712$	−7653.19	−	36188.3i	−0.402831	−	1.90480i
$713$	−2179.92			−0.114500
$714$		0			0
$715$			13908.1i			0.727458i
$716$	11424.6	−	8913.24i	0.596307	−	0.465228i
$717$		0			0
$718$	−19491.4	−	9514.87i	−1.01311	−	0.494557i
$719$	5643.22			0.292707			0.146354	−	0.989232i	$-0.453246\pi$
$719$	5643.22			0.292707			0.146354	+	0.989232i	$0.453246\pi$
$720$		0			0
$721$	−257.930			−0.0133229
$722$	16643.7	+	8124.72i	0.857913	+	0.418796i
$723$		0			0
$724$	−14420.0	+	11250.2i	−0.740213	+	0.577502i
$725$		−	6690.83i		−	0.342746i
$726$		0			0
$727$	17112.0			0.872969			0.436484	−	0.899712i	$-0.356223\pi$
$727$	17112.0			0.872969			0.436484	+	0.899712i	$0.356223\pi$
$728$	26553.1	−	5615.52i	1.35182	−	0.285886i
$729$		0			0
$730$	−1637.36	+	3354.16i	−0.0830155	+	0.170059i
$731$		−	13584.3i		−	0.687324i
$732$		0			0
$733$			20314.2i			1.02363i	0.859095	+	0.511817i	$0.171027\pi$
$733$			20314.2i			1.02363i	−0.859095	+	0.511817i	$0.828973\pi$
$734$	−21036.2	−	10269.0i	−1.05785	−	0.516396i
$735$		0			0
$736$	5061.73	−	6011.39i	0.253502	−	0.301063i
$737$	34473.4			1.72299
$738$		0			0
$739$			5845.97i			0.290998i	0.989358	+	0.145499i	$0.0464788\pi$
$739$			5845.97i			0.290998i	−0.989358	+	0.145499i	$0.953521\pi$
$740$	−1847.14	−	2367.57i	−0.0917595	−	0.117613i
$741$		0			0
$742$	8172.13	−	16740.8i	0.404324	−	0.828267i
$743$	−4964.00			−0.245103			−0.122551	−	0.992462i	$-0.539108\pi$
$743$	−4964.00			−0.245103			−0.122551	+	0.992462i	$0.539108\pi$
$744$		0			0
$745$	−4503.32			−0.221462
$746$	335.839	−	687.973i	0.0164825	−	0.0337647i
$747$		0			0
$748$	27984.3	−	21832.9i	1.36793	−	1.06723i
$749$			11686.2i			0.570099i
$750$		0			0
$751$	30765.7			1.49488			0.747441	−	0.664329i	$-0.231282\pi$
$751$	30765.7			1.49488			0.747441	+	0.664329i	$0.231282\pi$
$752$	−5980.36	+	23846.6i	−0.290002	+	1.15638i
$753$		0			0
$754$	30654.2	+	14964.0i	1.48058	+	0.722756i
$755$		−	10028.6i		−	0.483413i
$756$		0			0
$757$			34346.8i			1.64908i	0.565801	+	0.824542i	$0.308567\pi$
$757$			34346.8i			1.64908i	−0.565801	+	0.824542i	$0.691433\pi$
$758$	10491.5	−	21492.2i	0.502731	−	1.02986i
$759$		0			0
$760$	412.742	+	1951.66i	0.0196996	+	0.0931502i
$761$	12083.9			0.575610			0.287805	−	0.957689i	$-0.407074\pi$
$761$	12083.9			0.575610			0.287805	+	0.957689i	$0.407074\pi$
$762$		0			0
$763$		−	43027.1i		−	2.04153i
$764$	11775.4	+	15093.1i	0.557615	+	0.714724i
$765$		0			0
$766$	16590.6	+	8098.82i	0.782563	+	0.382014i
$767$	23369.3			1.10015
$768$		0			0
$769$	9054.84			0.424611			0.212305	−	0.977203i	$-0.431903\pi$
$769$	9054.84			0.424611			0.212305	+	0.977203i	$0.431903\pi$
$770$	−20880.8	−	10193.1i	−0.977261	−	0.477057i
$771$		0			0
$772$	−3141.62	−	4026.77i	−0.146463	−	0.187729i
$773$			13846.2i			0.644260i	0.946695	+	0.322130i	$0.104399\pi$
$773$			13846.2i			0.644260i	−0.946695	+	0.322130i	$0.895601\pi$
$774$		0			0
$775$	−1255.33			−0.0581844
$776$	−6400.52	−	30265.0i	−0.296089	−	1.40007i
$777$		0			0
$778$	847.662	−	1736.45i	0.0390619	−	0.0800191i
$779$			3908.74i			0.179776i
$780$		0			0
$781$			19332.8i			0.885762i
$782$	−7931.11	−	3871.63i	−0.362680	−	0.177045i
$783$		0			0
$784$	−5689.85	+	22688.2i	−0.259195	+	1.03354i
$785$	−15490.7			−0.704312
$786$		0			0
$787$		−	9393.21i		−	0.425454i	−0.977112	−	0.212727i	$-0.931766\pi$
$787$		−	9393.21i		−	0.425454i	0.977112	−	0.212727i	$-0.0682344\pi$
$788$	4126.99	−	3219.80i	0.186571	−	0.145559i
$789$		0			0
$790$	−4547.06	+	9314.75i	−0.204781	+	0.419499i
$791$	34103.3			1.53296
$792$		0			0
$793$	2794.08			0.125120
$794$	−3200.37	+	6556.04i	−0.143044	+	0.293029i
$795$		0			0
$796$	−8055.91	−	10325.7i	−0.358711	−	0.459779i
$797$			7921.92i			0.352081i	0.984383	+	0.176041i	$0.0563290\pi$
$797$			7921.92i			0.352081i	−0.984383	+	0.176041i	$0.943671\pi$
$798$		0			0
$799$	27610.4			1.22251
$800$	2914.86	−	3461.73i	0.128820	−	0.152988i
$801$		0			0
$802$	21208.4	+	10353.0i	0.933784	+	0.455833i
$803$			16291.5i			0.715959i
$804$		0			0
$805$			5777.71i			0.252966i
$806$	2807.55	−	5751.34i	0.122695	−	0.251343i
$807$		0			0
$808$	−1291.15	+	273.056i	−0.0562160	+	0.0118887i
$809$	−8042.02			−0.349496			−0.174748	−	0.984613i	$-0.555911\pi$
$809$	−8042.02			−0.349496			−0.174748	+	0.984613i	$0.555911\pi$
$810$		0			0
$811$		−	28973.7i		−	1.25451i	−0.778816	−	0.627253i	$-0.784179\pi$
$811$		−	28973.7i		−	1.25451i	0.778816	−	0.627253i	$-0.215821\pi$
$812$	−44932.3	+	35055.4i	−1.94189	+	1.51503i
$813$		0			0
$814$	−11778.5	−	5749.76i	−0.507170	−	0.247579i
$815$	17832.8			0.766450
$816$		0			0
$817$	3332.40			0.142700
$818$	4930.18	+	2406.70i	0.210733	+	0.102871i
$819$		0			0
$820$	6991.36	−	5454.53i	0.297742	−	0.232293i
$821$		−	11126.0i		−	0.472960i	−0.971636	−	0.236480i	$-0.924006\pi$
$821$		−	11126.0i		−	0.472960i	0.971636	−	0.236480i	$-0.0759937\pi$
$822$		0			0
$823$	3077.71			0.130355			0.0651775	−	0.997874i	$-0.479239\pi$
$823$	3077.71			0.130355			0.0651775	+	0.997874i	$0.479239\pi$
$824$	−45.3676	−	214.522i	−0.00191803	−	0.00906946i
$825$		0			0
$826$	−17127.2	+	35085.4i	−0.721465	+	1.47794i
$827$		−	37902.1i		−	1.59369i	−0.604181	−	0.796847i	$-0.706499\pi$
$827$		−	37902.1i		−	1.59369i	0.604181	−	0.796847i	$-0.293501\pi$
$828$		0			0
$829$			38596.7i			1.61703i	0.588474	+	0.808516i	$0.299729\pi$
$829$			38596.7i			1.61703i	−0.588474	+	0.808516i	$0.700271\pi$
$830$	9121.13	+	4452.54i	0.381445	+	0.186205i
$831$		0			0
$832$	9340.92	+	21096.7i	0.389228	+	0.879081i
$833$	26269.1			1.09264
$834$		0			0
$835$			6634.37i			0.274960i
$836$	5355.88	+	6864.91i	0.221575	+	0.284005i
$837$		0			0
$838$	−5020.77	+	10285.2i	−0.206968	+	0.423979i
$839$	7585.24			0.312123			0.156062	−	0.987747i	$-0.450120\pi$
$839$	7585.24			0.312123			0.156062	+	0.987747i	$0.450120\pi$
$840$		0			0
$841$	−47238.4			−1.93687
$842$	−4101.10	+	8401.20i	−0.167854	+	0.343853i
$843$		0			0
$844$	−17467.0	+	13627.4i	−0.712368	+	0.555777i
$845$		−	831.763i		−	0.0338621i
$846$		0			0
$847$	−65992.5			−2.67713
$848$	15360.8	+	3852.26i	0.622044	+	0.155999i
$849$		0			0
$850$	−4567.23	−	2229.52i	−0.184300	−	0.0899671i
$851$			3259.11i			0.131282i
$852$		0			0
$853$		−	37228.6i		−	1.49435i	−0.664625	−	0.747177i	$-0.731409\pi$
$853$		−	37228.6i		−	1.49435i	0.664625	−	0.747177i	$-0.268591\pi$
$854$	−2047.75	+	4194.86i	−0.0820522	+	0.168086i
$855$		0			0
$856$	−9719.48	+	2055.50i	−0.388090	+	0.0820741i
$857$	−7510.28			−0.299354			−0.149677	−	0.988735i	$-0.547823\pi$
$857$	−7510.28			−0.299354			−0.149677	+	0.988735i	$0.547823\pi$
$858$		0			0
$859$		−	19383.6i		−	0.769918i	−0.922934	−	0.384959i	$-0.874216\pi$
$859$		−	19383.6i		−	0.769918i	0.922934	−	0.384959i	$-0.125784\pi$
$860$	−4650.27	−	5960.49i	−0.184387	−	0.236338i
$861$		0			0
$862$	7506.08	+	3664.14i	0.296587	+	0.144781i
$863$	−7835.20			−0.309054			−0.154527	−	0.987989i	$-0.549385\pi$
$863$	−7835.20			−0.309054			−0.154527	+	0.987989i	$0.549385\pi$
$864$		0			0
$865$	−5176.12			−0.203461
$866$	3509.40	+	1713.14i	0.137707	+	0.0672226i
$867$		0			0
$868$	6577.09	+	8430.20i	0.257190	+	0.329654i
$869$			45242.7i			1.76611i
$870$		0			0
$871$	25166.4			0.979026
$872$	35785.9	−	7568.09i	1.38975	−	0.293908i
$873$		0			0
$874$	949.759	−	1945.60i	0.0367575	−	0.0752986i
$875$			3327.16i			0.128547i
$876$		0			0
$877$		−	8353.53i		−	0.321640i	−0.986984	−	0.160820i	$-0.948586\pi$
$877$		−	8353.53i		−	0.321640i	0.986984	−	0.160820i	$-0.0514139\pi$
$878$	−36177.7	−	17660.4i	−1.39059	−	0.678827i
$879$		0			0
$880$	4804.92	−	19159.5i	0.184061	−	0.733941i
$881$	−17964.9			−0.687008			−0.343504	−	0.939151i	$-0.611614\pi$
$881$	−17964.9			−0.687008			−0.343504	+	0.939151i	$0.611614\pi$
$882$		0			0
$883$			34012.6i			1.29628i	0.761521	+	0.648140i	$0.224453\pi$
$883$			34012.6i			1.29628i	−0.761521	+	0.648140i	$0.775547\pi$
$884$	20429.2	−	15938.5i	0.777273	−	0.606415i
$885$		0			0
$886$	10597.7	−	21709.7i	0.401849	−	0.823196i
$887$	−32352.3			−1.22467			−0.612335	−	0.790598i	$-0.709770\pi$
$887$	−32352.3			−1.22467			−0.612335	+	0.790598i	$0.709770\pi$
$888$		0			0
$889$	6263.74			0.236309
$890$	−10141.4	+	20774.8i	−0.381954	+	0.782442i
$891$		0			0
$892$	−21222.0	−	27201.4i	−0.796599	−	1.02104i
$893$			6773.17i			0.253814i
$894$		0			0
$895$	−9056.38			−0.338236
$896$	−38519.2	−	1437.64i	−1.43620	−	0.0536027i
$897$		0			0
$898$	−25404.2	−	12401.2i	−0.944040	−	0.460840i
$899$			13438.7i			0.498562i
$900$		0			0
$901$		−	17785.2i		−	0.657616i
$902$	16978.9	−	34781.6i	0.626757	−	1.28392i
$903$		0			0
$904$	5998.47	+	28363.9i	0.220693	+	1.04355i
$905$	11430.9			0.419863
$906$		0			0
$907$			15523.0i			0.568284i	0.958782	+	0.284142i	$0.0917088\pi$
$907$			15523.0i			0.568284i	−0.958782	+	0.284142i	$0.908291\pi$
$908$	−3627.40	+	2830.04i	−0.132577	+	0.103434i
$909$		0			0
$910$	−15243.5	−	7441.21i	−0.555293	−	0.271070i
$911$	−8000.66			−0.290970			−0.145485	−	0.989360i	$-0.546474\pi$
$911$	−8000.66			−0.290970			−0.145485	+	0.989360i	$0.546474\pi$
$912$		0			0
$913$	44302.3			1.60591
$914$	16357.6	+	7985.09i	0.591972	+	0.288975i
$915$		0			0
$916$	15115.4	−	11792.7i	0.545224	−	0.425374i
$917$		−	26434.2i		−	0.951946i
$918$		0			0
$919$	−23631.8			−0.848251			−0.424125	−	0.905603i	$-0.639418\pi$
$919$	−23631.8			−0.848251			−0.424125	+	0.905603i	$0.639418\pi$
$920$	−4805.35	+	1016.25i	−0.172204	+	0.0364181i
$921$		0			0
$922$	9742.27	−	19957.2i	0.347987	−	0.712860i
$923$			14113.4i			0.503302i
$924$		0			0
$925$			1876.80i			0.0667122i
$926$	17979.3	+	8776.70i	0.638051	+	0.311469i
$927$		0			0
$928$	−37059.0	−	31204.5i	−1.31091	−	1.10381i
$929$	7564.75			0.267160			0.133580	−	0.991038i	$-0.457353\pi$
$929$	7564.75			0.267160			0.133580	+	0.991038i	$0.457353\pi$
$930$		0			0
$931$			6444.15i			0.226851i
$932$	−16274.7	−	20860.2i	−0.571992	−	0.733152i
$933$		0			0
$934$	−19546.8	+	40042.1i	−0.684788	+	1.40280i
$935$	−22183.5			−0.775913
$936$		0			0
$937$	6226.13			0.217074			0.108537	−	0.994092i	$-0.465383\pi$
$937$	6226.13			0.217074			0.108537	+	0.994092i	$0.465383\pi$
$938$	−18444.2	+	37783.4i	−0.642031	+	1.31522i
$939$		0			0
$940$	12114.8	−	9451.76i	0.420363	−	0.327960i
$941$		−	14012.2i		−	0.485426i	−0.970098	−	0.242713i	$-0.921963\pi$
$941$		−	14012.2i		−	0.485426i	0.970098	−	0.242713i	$-0.0780373\pi$
$942$		0			0
$943$	−9624.05			−0.332346
$944$	−32193.2	−	8073.56i	−1.10996	−	0.278360i
$945$		0			0
$946$	−29653.1	−	14475.4i	−1.01914	−	0.497499i
$947$		−	39575.5i		−	1.35801i	−0.734135	−	0.679003i	$-0.762412\pi$
$947$		−	39575.5i		−	1.35801i	0.734135	−	0.679003i	$-0.237588\pi$
$948$		0			0
$949$			11893.2i			0.406817i
$950$	546.931	−	1120.40i	0.0186787	−	0.0382637i
$951$		0			0
$952$	8956.79	+	42352.4i	0.304928	+	1.44186i
$953$	−36806.3			−1.25107			−0.625537	−	0.780194i	$-0.715120\pi$
$953$	−36806.3			−1.25107			−0.625537	+	0.780194i	$0.715120\pi$
$954$		0			0
$955$		−	11964.5i		−	0.405405i
$956$	7550.39	+	9677.73i	0.255436	+	0.327406i
$957$		0			0
$958$	−37485.4	−	18298.8i	−1.26420	−	0.617126i
$959$	−55100.3			−1.85535
$960$		0			0
$961$	−27269.6			−0.915364
$962$	−8598.60	−	4197.47i	−0.288181	−	0.140678i
$963$		0			0
$964$	−2269.27	−	2908.64i	−0.0758177	−	0.0971795i
$965$			3192.07i			0.106483i
$966$		0			0
$967$	33422.7			1.11148			0.555740	−	0.831356i	$-0.312435\pi$
$967$	33422.7			1.11148			0.555740	+	0.831356i	$0.312435\pi$
$968$	−11607.5	−	54886.3i	−0.385412	−	1.82243i
$969$		0			0
$970$	−8481.43	+	17374.4i	−0.280745	+	0.575112i
$971$			35405.1i			1.17014i	0.810983	+	0.585069i	$0.198933\pi$
$971$			35405.1i			1.17014i	−0.810983	+	0.585069i	$0.801067\pi$
$972$		0			0
$973$			7674.58i			0.252863i
$974$	14314.5	+	6987.74i	0.470911	+	0.229878i
$975$		0			0
$976$	−3849.07	−	965.287i	−0.126235	−	0.0316579i
$977$	45772.5			1.49887			0.749433	−	0.662080i	$-0.230326\pi$
$977$	45772.5			1.49887			0.749433	+	0.662080i	$0.230326\pi$
$978$		0			0
$979$			100905.i			3.29413i
$980$	11526.3	−	8992.62i	0.375708	−	0.293121i
$981$		0			0
$982$	22655.2	−	46409.8i	0.736210	−	1.50814i
$983$	18452.9			0.598736			0.299368	−	0.954138i	$-0.403224\pi$
$983$	18452.9			0.598736			0.299368	+	0.954138i	$0.403224\pi$
$984$		0			0
$985$	−3271.51			−0.105826
$986$	−23867.8	+	48893.7i	−0.770897	+	1.57920i
$987$		0			0
$988$	3909.92	+	5011.55i	0.125902	+	0.161375i
$989$			8205.00i			0.263806i
$990$		0			0
$991$	34921.1			1.11938			0.559689	−	0.828703i	$-0.310920\pi$
$991$	34921.1			1.11938			0.559689	+	0.828703i	$0.310920\pi$
$992$	−5854.59	+	6953.00i	−0.187383	+	0.222538i
$993$		0			0
$994$	−21189.0	−	10343.6i	−0.676131	−	0.330058i
$995$			8185.29i			0.260795i
$996$		0			0
$997$		−	18316.5i		−	0.581835i	−0.956748	−	0.290917i	$-0.906039\pi$
$997$		−	18316.5i		−	0.581835i	0.956748	−	0.290917i	$-0.0939605\pi$
$998$	−905.266	+	1854.46i	−0.0287131	+	0.0588195i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	360.4.k.c.181.10		12
3.2	odd	2		40.4.d.a.21.3	✓	12
4.3	odd	2		1440.4.k.c.721.1		12
8.3	odd	2		1440.4.k.c.721.7		12
8.5	even	2	inner	360.4.k.c.181.9		12
12.11	even	2		160.4.d.a.81.6		12
15.2	even	4		200.4.f.c.149.7		12
15.8	even	4		200.4.f.b.149.6		12
15.14	odd	2		200.4.d.b.101.10		12
24.5	odd	2		40.4.d.a.21.4	yes	12
24.11	even	2		160.4.d.a.81.7		12
48.5	odd	4		1280.4.a.bc.1.3		6
48.11	even	4		1280.4.a.ba.1.4		6
48.29	odd	4		1280.4.a.bb.1.4		6
48.35	even	4		1280.4.a.bd.1.3		6
60.23	odd	4		800.4.f.c.49.6		12
60.47	odd	4		800.4.f.b.49.7		12
60.59	even	2		800.4.d.d.401.7		12
120.29	odd	2		200.4.d.b.101.9		12
120.53	even	4		200.4.f.c.149.8		12
120.59	even	2		800.4.d.d.401.6		12
120.77	even	4		200.4.f.b.149.5		12
120.83	odd	4		800.4.f.b.49.8		12
120.107	odd	4		800.4.f.c.49.5		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
40.4.d.a.21.3	✓	12	3.2	odd	2
40.4.d.a.21.4	yes	12	24.5	odd	2
160.4.d.a.81.6		12	12.11	even	2
160.4.d.a.81.7		12	24.11	even	2
200.4.d.b.101.9		12	120.29	odd	2
200.4.d.b.101.10		12	15.14	odd	2
200.4.f.b.149.5		12	120.77	even	4
200.4.f.b.149.6		12	15.8	even	4
200.4.f.c.149.7		12	15.2	even	4
200.4.f.c.149.8		12	120.53	even	4
360.4.k.c.181.9		12	8.5	even	2	inner
360.4.k.c.181.10		12	1.1	even	1	trivial
800.4.d.d.401.6		12	120.59	even	2
800.4.d.d.401.7		12	60.59	even	2
800.4.f.b.49.7		12	60.47	odd	4
800.4.f.b.49.8		12	120.83	odd	4
800.4.f.c.49.5		12	120.107	odd	4
800.4.f.c.49.6		12	60.23	odd	4
1280.4.a.ba.1.4		6	48.11	even	4
1280.4.a.bb.1.4		6	48.29	odd	4
1280.4.a.bc.1.3		6	48.5	odd	4
1280.4.a.bd.1.3		6	48.35	even	4
1440.4.k.c.721.1		12	4.3	odd	2
1440.4.k.c.721.7		12	8.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(2.54175 + 1.24077i) q^{2} +(4.92097 + 6.30746i) q^{4} -5.00000i q^{5} +26.6173 q^{7} +(4.68175 + 22.1378i) q^{8} +O(q^{10})\)	\(q+(2.54175 + 1.24077i) q^{2} +(4.92097 + 6.30746i) q^{4} -5.00000i q^{5} +26.6173 q^{7} +(4.68175 + 22.1378i) q^{8} +(6.20386 - 12.7087i) q^{10} -61.7277i q^{11} -45.0627i q^{13} +(67.6545 + 33.0260i) q^{14} +(-15.5681 + 62.0776i) q^{16} +71.8754 q^{17} +17.6319i q^{19} +(31.5373 - 24.6049i) q^{20} +(76.5900 - 156.896i) q^{22} -43.4131 q^{23} -25.0000 q^{25} +(55.9125 - 114.538i) q^{26} +(130.983 + 167.888i) q^{28} +267.633i q^{29} +50.2133 q^{31} +(-116.594 + 138.469i) q^{32} +(182.689 + 89.1810i) q^{34} -133.087i q^{35} -75.0720i q^{37} +(-21.8772 + 44.8160i) q^{38} +(110.689 - 23.4087i) q^{40} +221.685 q^{41} -188.998i q^{43} +(389.345 - 303.760i) q^{44} +(-110.345 - 53.8658i) q^{46} +384.142 q^{47} +365.481 q^{49} +(-63.5437 - 31.0193i) q^{50} +(284.231 - 221.752i) q^{52} -247.445i q^{53} -308.638 q^{55} +(124.616 + 589.248i) q^{56} +(-332.072 + 680.256i) q^{58} +518.596i q^{59} +62.0042i q^{61} +(127.630 + 62.3033i) q^{62} +(-468.162 + 207.287i) q^{64} -225.314 q^{65} +558.476i q^{67} +(353.697 + 453.351i) q^{68} +(165.130 - 338.273i) q^{70} -313.194 q^{71} -263.926 q^{73} +(93.1472 - 190.814i) q^{74} +(-111.213 + 86.7663i) q^{76} -1643.03i q^{77} -732.940 q^{79} +(310.388 + 77.8405i) q^{80} +(563.468 + 275.061i) q^{82} +717.705i q^{83} -359.377i q^{85} +(234.503 - 480.385i) q^{86} +(1366.51 - 288.994i) q^{88} -1634.69 q^{89} -1199.45i q^{91} +(-213.635 - 273.827i) q^{92} +(976.392 + 476.633i) q^{94} +88.1597 q^{95} -1367.12 q^{97} +(928.962 + 453.479i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 2 q^{2} + 16 q^{4} + 28 q^{7} + 40 q^{8}+O(q^{10}) \) 12 * q - 2 * q^2 + 16 * q^4 + 28 * q^7 + 40 * q^8	\( 12 q - 2 q^{2} + 16 q^{4} + 28 q^{7} + 40 q^{8} + 30 q^{10} - 68 q^{14} - 56 q^{16} - 20 q^{20} - 164 q^{22} - 604 q^{23} - 300 q^{25} + 308 q^{26} - 436 q^{28} - 264 q^{31} - 72 q^{32} - 180 q^{34} - 820 q^{38} + 120 q^{40} - 40 q^{41} + 472 q^{44} - 1268 q^{46} + 940 q^{47} + 1308 q^{49} + 50 q^{50} + 1024 q^{52} + 440 q^{55} + 728 q^{56} - 360 q^{58} - 592 q^{62} - 2048 q^{64} + 2344 q^{68} + 1160 q^{70} + 1592 q^{71} + 432 q^{73} + 420 q^{74} + 2256 q^{76} + 2016 q^{79} - 1600 q^{80} + 88 q^{82} + 244 q^{86} + 4080 q^{88} + 424 q^{89} + 900 q^{92} + 292 q^{94} + 1520 q^{95} - 1584 q^{97} + 7266 q^{98}+O(q^{100}) \) 12 * q - 2 * q^2 + 16 * q^4 + 28 * q^7 + 40 * q^8 + 30 * q^10 - 68 * q^14 - 56 * q^16 - 20 * q^20 - 164 * q^22 - 604 * q^23 - 300 * q^25 + 308 * q^26 - 436 * q^28 - 264 * q^31 - 72 * q^32 - 180 * q^34 - 820 * q^38 + 120 * q^40 - 40 * q^41 + 472 * q^44 - 1268 * q^46 + 940 * q^47 + 1308 * q^49 + 50 * q^50 + 1024 * q^52 + 440 * q^55 + 728 * q^56 - 360 * q^58 - 592 * q^62 - 2048 * q^64 + 2344 * q^68 + 1160 * q^70 + 1592 * q^71 + 432 * q^73 + 420 * q^74 + 2256 * q^76 + 2016 * q^79 - 1600 * q^80 + 88 * q^82 + 244 * q^86 + 4080 * q^88 + 424 * q^89 + 900 * q^92 + 292 * q^94 + 1520 * q^95 - 1584 * q^97 + 7266 * q^98

Introduction

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