LMFDB - Embedded newform 360.3.p.g.19.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [360,3,Mod(19,360)]

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([1, 1, 0, 1]))

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

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

chi := DirichletCharacter("360.19");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 360 = 2^{3} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	360.p (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:	$9.80928951697$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.53824000000.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 6x^{6} + 36x^{4} + 96x^{2} + 256 $ x^8 + 6x^6 + 36x^4 + 96*x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{5} $
Twist minimal:	no (minimal twist has level 40)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			19.1
Root			$-1.34500 - 1.48020i$ of defining polynomial
Character	$\chi$	$=$	360.19
Dual form			360.3.p.g.19.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.34500 - 1.48020i) q^{2} +(-0.381966 + 3.98172i) q^{4} +(-4.35250 - 2.46084i) q^{5} -7.67752 q^{7} +(6.40747 - 4.79002i) q^{8} +(2.21158 + 9.75238i) q^{10} +0.472136 q^{11} -4.10995 q^{13} +(10.3262 + 11.3642i) q^{14} +(-15.7082 - 3.04176i) q^{16} +2.26154i q^{17} +26.3607 q^{19} +(11.4609 - 16.3905i) q^{20} +(-0.635021 - 0.698854i) q^{22} +9.73249 q^{23} +(12.8885 + 21.4216i) q^{25} +(5.52786 + 6.08353i) q^{26} +(2.93255 - 30.5697i) q^{28} +41.6971i q^{29} +22.0104i q^{31} +(16.6251 + 27.3424i) q^{32} +(3.34752 - 3.04176i) q^{34} +(33.4164 + 18.8931i) q^{35} +51.7449 q^{37} +(-35.4550 - 39.0190i) q^{38} +(-39.6760 + 5.08080i) q^{40} -15.0557 q^{41} -9.31310i q^{43} +(-0.180340 + 1.87991i) q^{44} +(-13.0902 - 14.4060i) q^{46} +8.76226 q^{47} +9.94427 q^{49} +(14.3732 - 47.8896i) q^{50} +(1.56986 - 16.3647i) q^{52} +39.9002 q^{53} +(-2.05497 - 1.16185i) q^{55} +(-49.1935 + 36.7754i) q^{56} +(61.7200 - 56.0825i) q^{58} +77.1935 q^{59} -14.7650i q^{61} +(32.5797 - 29.6039i) q^{62} +(18.1115 - 61.3838i) q^{64} +(17.8885 + 10.1139i) q^{65} +75.8395i q^{67} +(-9.00482 - 0.863831i) q^{68} +(-16.9794 - 74.8741i) q^{70} -81.0705i q^{71} +83.4249i q^{73} +(-69.5967 - 76.5927i) q^{74} +(-10.0689 + 104.961i) q^{76} -3.62483 q^{77} -100.757i q^{79} +(60.8847 + 51.8946i) q^{80} +(20.2499 + 22.2854i) q^{82} -0.266939i q^{83} +(5.56528 - 9.84336i) q^{85} +(-13.7852 + 12.5261i) q^{86} +(3.02520 - 2.26154i) q^{88} -85.5542 q^{89} +31.5542 q^{91} +(-3.71748 + 38.7521i) q^{92} +(-11.7852 - 12.9699i) q^{94} +(-114.735 - 64.8694i) q^{95} +99.1297i q^{97} +(-13.3750 - 14.7195i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 12 q^{4} + 20 q^{10} - 32 q^{11} + 20 q^{14} - 72 q^{16} + 32 q^{19} - 20 q^{20} - 40 q^{25} + 80 q^{26} + 152 q^{34} + 160 q^{35} - 80 q^{40} - 192 q^{41} + 88 q^{44} - 60 q^{46} + 8 q^{49} + 200 q^{50}+ \cdots - 300 q^{94}+O(q^{100}) $ 8 * q - 12 * q^4 + 20 * q^10 - 32 * q^11 + 20 * q^14 - 72 * q^16 + 32 * q^19 - 20 * q^20 - 40 * q^25 + 80 * q^26 + 152 * q^34 + 160 * q^35 - 80 * q^40 - 192 * q^41 + 88 * q^44 - 60 * q^46 + 8 * q^49 + 200 * q^50 + 224 * q^59 + 288 * q^64 + 340 * q^70 - 360 * q^74 + 152 * q^76 + 280 * q^80 - 316 * q^86 - 112 * q^89 - 320 * q^91 - 300 * q^94

Character values

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

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

Coefficient data

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

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

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

$2$	−1.34500	−	1.48020i	−0.672499	−	0.740098i
$2$	−1.34500	−	1.48020i	−0.672499	−	0.740098i
$3$		0			0
$3$		0			0
$4$	−0.381966	+	3.98172i	−0.0954915	+	0.995430i
$5$	−4.35250	−	2.46084i	−0.870500	−	0.492168i
$5$	−4.35250	−	2.46084i	−0.870500	−	0.492168i
$6$		0			0
$7$	−7.67752			−1.09679			−0.548394	−	0.836220i	$-0.684761\pi$
$7$	−7.67752			−1.09679			−0.548394	+	0.836220i	$0.684761\pi$
$8$	6.40747	−	4.79002i	0.800934	−	0.598752i
$9$		0			0
$10$	2.21158	+	9.75238i	0.221158	+	0.975238i
$11$	0.472136			0.0429215			0.0214607	−	0.999770i	$-0.493168\pi$
$11$	0.472136			0.0429215			0.0214607	+	0.999770i	$0.493168\pi$
$12$		0			0
$13$	−4.10995			−0.316150			−0.158075	−	0.987427i	$-0.550529\pi$
$13$	−4.10995			−0.316150			−0.158075	+	0.987427i	$0.550529\pi$
$14$	10.3262	+	11.3642i	0.737588	+	0.811731i
$15$		0			0
$16$	−15.7082	−	3.04176i	−0.981763	−	0.190110i
$17$			2.26154i			0.133032i	0.997785	+	0.0665159i	$0.0211883\pi$
$17$			2.26154i			0.133032i	−0.997785	+	0.0665159i	$0.978812\pi$
$18$		0			0
$19$	26.3607			1.38740			0.693702	−	0.720262i	$-0.255978\pi$
$19$	26.3607			1.38740			0.693702	+	0.720262i	$0.255978\pi$
$20$	11.4609	−	16.3905i	0.573044	−	0.819525i
$21$		0			0
$22$	−0.635021	−	0.698854i	−0.0288646	−	0.0317661i
$23$	9.73249			0.423152			0.211576	−	0.977362i	$-0.432140\pi$
$23$	9.73249			0.423152			0.211576	+	0.977362i	$0.432140\pi$
$24$		0			0
$25$	12.8885	+	21.4216i	0.515542	+	0.856864i
$26$	5.52786	+	6.08353i	0.212610	+	0.233982i
$27$		0			0
$28$	2.93255	−	30.5697i	0.104734	−	1.09178i
$29$			41.6971i			1.43783i	0.695097	+	0.718916i	$0.255361\pi$
$29$			41.6971i			1.43783i	−0.695097	+	0.718916i	$0.744639\pi$
$30$		0			0
$31$			22.0104i			0.710013i	0.934864	+	0.355007i	$0.115521\pi$
$31$			22.0104i			0.710013i	−0.934864	+	0.355007i	$0.884479\pi$
$32$	16.6251	+	27.3424i	0.519534	+	0.854450i
$33$		0			0
$34$	3.34752	−	3.04176i	0.0984566	−	0.0894637i
$35$	33.4164	+	18.8931i	0.954755	+	0.539804i
$36$		0			0
$37$	51.7449			1.39851			0.699256	−	0.714872i	$-0.253515\pi$
$37$	51.7449			1.39851			0.699256	+	0.714872i	$0.253515\pi$
$38$	−35.4550	−	39.0190i	−0.933027	−	1.02682i
$39$		0			0
$40$	−39.6760	+	5.08080i	−0.991900	+	0.127020i
$41$	−15.0557			−0.367213			−0.183606	−	0.983000i	$-0.558777\pi$
$41$	−15.0557			−0.367213			−0.183606	+	0.983000i	$0.558777\pi$
$42$		0			0
$43$		−	9.31310i		−	0.216584i	−0.994119	−	0.108292i	$-0.965462\pi$
$43$		−	9.31310i		−	0.216584i	0.994119	−	0.108292i	$-0.0345381\pi$
$44$	−0.180340	+	1.87991i	−0.00409863	+	0.0427253i
$45$		0			0
$46$	−13.0902	−	14.4060i	−0.284569	−	0.313174i
$47$	8.76226			0.186431			0.0932156	−	0.995646i	$-0.470285\pi$
$47$	8.76226			0.186431			0.0932156	+	0.995646i	$0.470285\pi$
$48$		0			0
$49$	9.94427			0.202944
$50$	14.3732	−	47.8896i	0.287463	−	0.957792i
$51$		0			0
$52$	1.56986	−	16.3647i	0.0301896	−	0.314705i
$53$	39.9002			0.752834			0.376417	−	0.926450i	$-0.377156\pi$
$53$	39.9002			0.752834			0.376417	+	0.926450i	$0.377156\pi$
$54$		0			0
$55$	−2.05497	−	1.16185i	−0.0373631	−	0.0211246i
$56$	−49.1935	+	36.7754i	−0.878455	+	0.656704i
$57$		0			0
$58$	61.7200	−	56.0825i	1.06414	−	0.966940i
$59$	77.1935			1.30836			0.654182	−	0.756337i	$-0.273013\pi$
$59$	77.1935			1.30836			0.654182	+	0.756337i	$0.273013\pi$
$60$		0			0
$61$		−	14.7650i		−	0.242050i	−0.992649	−	0.121025i	$-0.961382\pi$
$61$		−	14.7650i		−	0.242050i	0.992649	−	0.121025i	$-0.0386181\pi$
$62$	32.5797	−	29.6039i	0.525480	−	0.477483i
$63$		0			0
$64$	18.1115	−	61.3838i	0.282992	−	0.959122i
$65$	17.8885	+	10.1139i	0.275208	+	0.155599i
$66$		0			0
$67$			75.8395i			1.13193i	0.824428	+	0.565966i	$0.191497\pi$
$67$			75.8395i			1.13193i	−0.824428	+	0.565966i	$0.808503\pi$
$68$	−9.00482	−	0.863831i	−0.132424	−	0.0127034i
$69$		0			0
$70$	−16.9794	−	74.8741i	−0.242563	−	1.06963i
$71$		−	81.0705i		−	1.14184i	−0.821006	−	0.570919i	$-0.806587\pi$
$71$		−	81.0705i		−	1.14184i	0.821006	−	0.570919i	$-0.193413\pi$
$72$		0			0
$73$			83.4249i			1.14281i	0.820669	+	0.571403i	$0.193601\pi$
$73$			83.4249i			1.14281i	−0.820669	+	0.571403i	$0.806399\pi$
$74$	−69.5967	−	76.5927i	−0.940497	−	1.03504i
$75$		0			0
$76$	−10.0689	+	104.961i	−0.132485	+	1.38106i
$77$	−3.62483			−0.0470757
$78$		0			0
$79$		−	100.757i		−	1.27541i	−0.770281	−	0.637704i	$-0.779884\pi$
$79$		−	100.757i		−	1.27541i	0.770281	−	0.637704i	$-0.220116\pi$
$80$	60.8847	+	51.8946i	0.761059	+	0.648683i
$81$		0			0
$82$	20.2499	+	22.2854i	0.246950	+	0.271774i
$83$		−	0.266939i		−	0.00321613i	−0.999999	−	0.00160806i	$-0.999488\pi$
$83$		−	0.266939i		−	0.00321613i	0.999999	−	0.00160806i	$-0.000511863\pi$
$84$		0			0
$85$	5.56528	−	9.84336i	0.0654739	−	0.115804i
$86$	−13.7852	+	12.5261i	−0.160293	+	0.145652i
$87$		0			0
$88$	3.02520	−	2.26154i	0.0343773	−	0.0256993i
$89$	−85.5542			−0.961283			−0.480641	−	0.876917i	$-0.659596\pi$
$89$	−85.5542			−0.961283			−0.480641	+	0.876917i	$0.659596\pi$
$90$		0			0
$91$	31.5542			0.346749
$92$	−3.71748	+	38.7521i	−0.0404074	+	0.421218i
$93$		0			0
$94$	−11.7852	−	12.9699i	−0.125375	−	0.137977i
$95$	−114.735	−	64.8694i	−1.20774	−	0.682836i
$96$		0			0
$97$			99.1297i			1.02196i	0.859594	+	0.510978i	$0.170716\pi$
$97$			99.1297i			1.02196i	−0.859594	+	0.510978i	$0.829284\pi$
$98$	−13.3750	−	14.7195i	−0.136480	−	0.150199i
$99$		0			0
$100$	−90.2179	+	43.1363i	−0.902179	+	0.431363i
$101$			105.405i			1.04361i	0.853065	+	0.521805i	$0.174741\pi$
$101$			105.405i			1.04361i	−0.853065	+	0.521805i	$0.825259\pi$
$102$		0			0
$103$	−101.863			−0.988958			−0.494479	−	0.869190i	$-0.664641\pi$
$103$	−101.863			−0.988958			−0.494479	+	0.869190i	$0.664641\pi$
$104$	−26.3344	+	19.6867i	−0.253215	+	0.189295i
$105$		0			0
$106$	−53.6656	−	59.0601i	−0.506280	−	0.557171i
$107$		−	32.9962i		−	0.308376i	−0.988042	−	0.154188i	$-0.950724\pi$
$107$		−	32.9962i		−	0.308376i	0.988042	−	0.154188i	$-0.0492762\pi$
$108$		0			0
$109$			181.554i			1.66563i	0.553552	+	0.832814i	$0.313272\pi$
$109$			181.554i			1.66563i	−0.553552	+	0.832814i	$0.686728\pi$
$110$	1.04416	+	4.60445i	0.00949240	+	0.0418586i
$111$		0			0
$112$	120.600	+	23.3532i	1.07679	+	0.208511i
$113$			76.6403i			0.678233i	0.940744	+	0.339116i	$0.110128\pi$
$113$			76.6403i			0.678233i	−0.940744	+	0.339116i	$0.889872\pi$
$114$		0			0
$115$	−42.3607	−	23.9501i	−0.368354	−	0.208262i
$116$	−166.026	−	15.9269i	−1.43126	−	0.137301i
$117$		0			0
$118$	−103.825	−	114.262i	−0.879873	−	0.968318i
$119$		−	17.3630i		−	0.145908i
$120$		0			0
$121$	−120.777			−0.998158
$122$	−21.8552	+	19.8589i	−0.179141	+	0.162778i
$123$		0			0
$124$	−87.6393	−	8.40723i	−0.706769	−	0.0678002i
$125$	−3.38228	−	124.954i	−0.0270582	−	0.999634i
$126$		0			0
$127$	142.962			1.12569			0.562843	−	0.826564i	$-0.309708\pi$
$127$	142.962			1.12569			0.562843	+	0.826564i	$0.309708\pi$
$128$	−115.220	+	55.7526i	−0.900156	+	0.435567i
$129$		0			0
$130$	−9.08946	−	40.0818i	−0.0699189	−	0.308321i
$131$	−110.138			−0.840746			−0.420373	−	0.907351i	$-0.638101\pi$
$131$	−110.138			−0.840746			−0.420373	+	0.907351i	$0.638101\pi$
$132$		0			0
$133$	−202.385			−1.52169
$134$	112.257	−	102.004i	0.837741	−	0.761223i
$135$		0			0
$136$	10.8328	+	14.4908i	0.0796531	+	0.106550i
$137$			225.398i			1.64524i	0.568592	+	0.822620i	$0.307488\pi$
$137$			225.398i			1.64524i	−0.568592	+	0.822620i	$0.692512\pi$
$138$		0			0
$139$	97.4164			0.700837			0.350419	−	0.936593i	$-0.386039\pi$
$139$	97.4164			0.700837			0.350419	+	0.936593i	$0.386039\pi$
$140$	−87.9911	+	125.838i	−0.628508	+	0.898845i
$141$		0			0
$142$	−120.000	+	109.040i	−0.845073	+	0.767885i
$143$	−1.94045			−0.0135696
$144$		0			0
$145$	102.610	−	181.487i	0.707655	−	1.25163i
$146$	123.485	−	112.206i	0.845790	−	0.768536i
$147$		0			0
$148$	−19.7648	+	206.034i	−0.133546	+	1.39212i
$149$			191.397i			1.28454i	0.766477	+	0.642271i	$0.222008\pi$
$149$			191.397i			1.28454i	−0.766477	+	0.642271i	$0.777992\pi$
$150$		0			0
$151$		−	68.3549i		−	0.452682i	−0.974048	−	0.226341i	$-0.927324\pi$
$151$		−	68.3549i		−	0.452682i	0.974048	−	0.226341i	$-0.0726763\pi$
$152$	168.905	−	126.268i	1.11122	−	0.830711i
$153$		0			0
$154$	4.87539	+	5.36547i	0.0316584	+	0.0348407i
$155$	54.1641	−	95.8004i	0.349446	−	0.618067i
$156$		0			0
$157$	155.235			0.988756			0.494378	−	0.869247i	$-0.335396\pi$
$157$	155.235			0.988756			0.494378	+	0.869247i	$0.335396\pi$
$158$	−149.141	+	135.518i	−0.943928	+	0.857710i
$159$		0			0
$160$	−5.07544	−	159.919i	−0.0317215	−	0.999497i
$161$	−74.7214			−0.464108
$162$		0			0
$163$		−	90.4765i		−	0.555070i	−0.960715	−	0.277535i	$-0.910482\pi$
$163$		−	90.4765i		−	0.555070i	0.960715	−	0.277535i	$-0.0895175\pi$
$164$	5.75078	−	59.9477i	0.0350657	−	0.365535i
$165$		0			0
$166$	−0.395122	+	0.359032i	−0.00238025	+	0.00216284i
$167$	−100.778			−0.603461			−0.301730	−	0.953393i	$-0.597564\pi$
$167$	−100.778			−0.603461			−0.301730	+	0.953393i	$0.597564\pi$
$168$		0			0
$169$	−152.108			−0.900049
$170$	−22.0554	+	5.00157i	−0.129738	+	0.0294210i
$171$		0			0
$172$	37.0822	+	3.55729i	0.215594	+	0.0206819i
$173$	54.6556			0.315928			0.157964	−	0.987445i	$-0.449507\pi$
$173$	54.6556			0.315928			0.157964	+	0.987445i	$0.449507\pi$
$174$		0			0
$175$	−98.9520	−	164.465i	−0.565440	−	0.939799i
$176$	−7.41641	−	1.43613i	−0.0421387	−	0.00815981i
$177$		0			0
$178$	115.070	+	126.637i	0.646461	+	0.711444i
$179$	106.807			0.596684			0.298342	−	0.954459i	$-0.403566\pi$
$179$	106.807			0.596684			0.298342	+	0.954459i	$0.403566\pi$
$180$		0			0
$181$		−	144.778i		−	0.799879i	−0.916542	−	0.399939i	$-0.869031\pi$
$181$		−	144.778i		−	0.799879i	0.916542	−	0.399939i	$-0.130969\pi$
$182$	−42.4403	−	46.7064i	−0.233188	−	0.256629i
$183$		0			0
$184$	62.3607	−	46.6188i	0.338917	−	0.253363i
$185$	−225.220	−	127.336i	−1.21740	−	0.688302i
$186$		0			0
$187$			1.06775i			0.00570992i
$188$	−3.34689	+	34.8889i	−0.0178026	+	0.185579i
$189$		0			0
$190$	58.2986	+	257.079i	0.306835	+	1.35305i
$191$		−	210.809i		−	1.10371i	−0.833939	−	0.551857i	$-0.813919\pi$
$191$		−	210.809i		−	1.10371i	0.833939	−	0.551857i	$-0.186081\pi$
$192$		0			0
$193$		−	108.176i		−	0.560496i	−0.959928	−	0.280248i	$-0.909583\pi$
$193$		−	108.176i		−	0.560496i	0.959928	−	0.280248i	$-0.0904168\pi$
$194$	146.731	−	133.329i	0.756347	−	0.687263i
$195$		0			0
$196$	−3.79837	+	39.5953i	−0.0193795	+	0.202017i
$197$	308.300			1.56497			0.782487	−	0.622667i	$-0.213951\pi$
$197$	308.300			1.56497			0.782487	+	0.622667i	$0.213951\pi$
$198$		0			0
$199$			247.859i			1.24552i	0.782412	+	0.622761i	$0.213989\pi$
$199$			247.859i			1.24552i	−0.782412	+	0.622761i	$0.786011\pi$
$200$	185.193	+	75.5221i	0.925965	+	0.377610i
$201$		0			0
$202$	156.020	−	141.769i	0.772375	−	0.701826i
$203$		−	320.130i		−	1.57700i
$204$		0			0
$205$	65.5301	+	37.0497i	0.319659	+	0.180730i
$206$	137.005	+	150.777i	0.665073	+	0.731926i
$207$		0			0
$208$	64.5599	+	12.5015i	0.310384	+	0.0601033i
$209$	12.4458			0.0595494
$210$		0			0
$211$	230.584			1.09281			0.546407	−	0.837520i	$-0.315995\pi$
$211$	230.584			1.09281			0.546407	+	0.837520i	$0.315995\pi$
$212$	−15.2405	+	158.871i	−0.0718892	+	0.749393i
$213$		0			0
$214$	−48.8409	+	44.3799i	−0.228229	+	0.207383i
$215$	−22.9180	+	40.5353i	−0.106595	+	0.188536i
$216$		0			0
$217$		−	168.985i		−	0.778734i
$218$	268.735	−	244.189i	1.23273	−	1.12013i
$219$		0			0
$220$	5.41109	−	7.73854i	0.0245959	−	0.0351752i
$221$		−	9.29480i		−	0.0420579i
$222$		0			0
$223$	177.782			0.797229			0.398615	−	0.917118i	$-0.369491\pi$
$223$	177.782			0.797229			0.398615	+	0.917118i	$0.369491\pi$
$224$	−127.639	−	209.922i	−0.569818	−	0.937151i
$225$		0			0
$226$	113.443	−	103.081i	0.501959	−	0.456110i
$227$			203.301i			0.895601i	0.894134	+	0.447800i	$0.147792\pi$
$227$			203.301i			0.895601i	−0.894134	+	0.447800i	$0.852208\pi$
$228$		0			0
$229$			81.0705i			0.354020i	0.984209	+	0.177010i	$0.0566425\pi$
$229$			81.0705i			0.354020i	−0.984209	+	0.177010i	$0.943358\pi$
$230$	21.5241	+	94.9149i	0.0935832	+	0.412674i
$231$		0			0
$232$	199.730	+	267.173i	0.860905	+	1.15161i
$233$		−	56.2864i		−	0.241573i	−0.992679	−	0.120786i	$-0.961458\pi$
$233$		−	56.2864i		−	0.241573i	0.992679	−	0.120786i	$-0.0385416\pi$
$234$		0			0
$235$	−38.1378	−	21.5625i	−0.162288	−	0.0917554i
$236$	−29.4853	+	307.363i	−0.124938	+	1.30239i
$237$		0			0
$238$	−25.7007	+	23.3532i	−0.107986	+	0.0981227i
$239$			360.235i			1.50726i	0.657300	+	0.753629i	$0.271699\pi$
$239$			360.235i			1.50726i	−0.657300	+	0.753629i	$0.728301\pi$
$240$		0			0
$241$	−197.495			−0.819483			−0.409741	−	0.912202i	$-0.634381\pi$
$241$	−197.495			−0.819483			−0.409741	+	0.912202i	$0.634381\pi$
$242$	162.445	+	178.774i	0.671260	+	0.738735i
$243$		0			0
$244$	58.7902	+	5.63974i	0.240944	+	0.0231137i
$245$	−43.2825	−	24.4713i	−0.176663	−	0.0998827i
$246$		0			0
$247$	−108.341			−0.438627
$248$	105.430	+	141.031i	0.425122	+	0.568674i
$249$		0			0
$250$	−180.408	+	173.070i	−0.721631	+	0.692278i
$251$	178.361			0.710600			0.355300	−	0.934752i	$-0.384379\pi$
$251$	178.361			0.710600			0.355300	+	0.934752i	$0.384379\pi$
$252$		0			0
$253$	4.59506			0.0181623
$254$	−192.284	−	211.612i	−0.757022	−	0.833119i
$255$		0			0
$256$	237.495	+	95.5613i	0.927716	+	0.373286i
$257$		−	453.183i		−	1.76336i	−0.471849	−	0.881679i	$-0.656413\pi$
$257$		−	453.183i		−	1.76336i	0.471849	−	0.881679i	$-0.343587\pi$
$258$		0			0
$259$	−397.272			−1.53387
$260$	−47.1036	+	67.3640i	−0.181168	+	0.259092i
$261$		0			0
$262$	148.135	+	163.026i	0.565401	+	0.622235i
$263$	−21.0921			−0.0801981			−0.0400990	−	0.999196i	$-0.512767\pi$
$263$	−21.0921			−0.0801981			−0.0400990	+	0.999196i	$0.512767\pi$
$264$		0			0
$265$	−173.666	−	98.1879i	−0.655342	−	0.370520i
$266$	272.207	+	299.569i	1.02333	+	1.12620i
$267$		0			0
$268$	−301.972	−	28.9681i	−1.12676	−	0.108090i
$269$			92.4148i			0.343549i	0.985136	+	0.171775i	$0.0549501\pi$
$269$			92.4148i			0.343549i	−0.985136	+	0.171775i	$0.945050\pi$
$270$		0			0
$271$			188.799i			0.696675i	0.937369	+	0.348337i	$0.113254\pi$
$271$			188.799i			0.696675i	−0.937369	+	0.348337i	$0.886746\pi$
$272$	6.87907	−	35.5247i	0.0252907	−	0.130606i
$273$		0			0
$274$	333.633	−	303.159i	1.21764	−	1.10642i
$275$	6.08514	+	10.1139i	0.0221278	+	0.0367779i
$276$		0			0
$277$	70.1251			0.253159			0.126580	−	0.991956i	$-0.459600\pi$
$277$	70.1251			0.253159			0.126580	+	0.991956i	$0.459600\pi$
$278$	−131.025	−	144.195i	−0.471312	−	0.518689i
$279$		0			0
$280$	304.613	−	39.0079i	1.08790	−	0.139314i
$281$	506.269			1.80167			0.900835	−	0.434161i	$-0.142955\pi$
$281$	506.269			1.80167			0.900835	+	0.434161i	$0.142955\pi$
$282$		0			0
$283$		−	501.350i		−	1.77156i	−0.464110	−	0.885778i	$-0.653626\pi$
$283$		−	501.350i		−	1.77156i	0.464110	−	0.885778i	$-0.346374\pi$
$284$	322.800	+	30.9662i	1.13662	+	0.109036i
$285$		0			0
$286$	2.60990	+	2.87225i	0.00912554	+	0.0100428i
$287$	115.591			0.402755
$288$		0			0
$289$	283.885			0.982303
$290$	−406.646	+	92.2163i	−1.40223	+	0.317987i
$291$		0			0
$292$	−332.175	−	31.8655i	−1.13758	−	0.109128i
$293$	−324.026			−1.10589			−0.552945	−	0.833218i	$-0.686496\pi$
$293$	−324.026			−1.10589			−0.552945	+	0.833218i	$0.686496\pi$
$294$		0			0
$295$	−335.985	−	189.961i	−1.13893	−	0.643935i
$296$	331.554	−	247.859i	1.12012	−	0.837362i
$297$		0			0
$298$	283.305	−	257.428i	0.950688	−	0.863853i
$299$	−40.0000			−0.133779
$300$		0			0
$301$			71.5015i			0.237546i
$302$	−101.179	+	91.9372i	−0.335029	+	0.304428i
$303$		0			0
$304$	−414.079	−	80.1830i	−1.36210	−	0.263760i
$305$	−36.3344	+	64.2648i	−0.119129	+	0.210704i
$306$		0			0
$307$		−	9.84697i		−	0.0320748i	−0.999871	−	0.0160374i	$-0.994895\pi$
$307$		−	9.84697i		−	0.0320748i	0.999871	−	0.0160374i	$-0.00510509\pi$
$308$	1.38456	−	14.4331i	0.00449533	−	0.0468606i
$309$		0			0
$310$	−214.654	+	48.6777i	−0.692432	+	0.157025i
$311$		−	200.417i		−	0.644429i	−0.946667	−	0.322214i	$-0.895573\pi$
$311$		−	200.417i		−	0.644429i	0.946667	−	0.322214i	$-0.104427\pi$
$312$		0			0
$313$			261.582i			0.835727i	0.908510	+	0.417863i	$0.137221\pi$
$313$			261.582i			0.835727i	−0.908510	+	0.417863i	$0.862779\pi$
$314$	−208.790	−	229.778i	−0.664937	−	0.731777i
$315$		0			0
$316$	401.187	+	38.4858i	1.26958	+	0.121791i
$317$	−322.341			−1.01685			−0.508425	−	0.861107i	$-0.669772\pi$
$317$	−322.341			−1.01685			−0.508425	+	0.861107i	$0.669772\pi$
$318$		0			0
$319$			19.6867i			0.0617138i
$320$	−229.886	+	222.604i	−0.718393	+	0.695637i
$321$		0			0
$322$	100.500	+	110.602i	0.312112	+	0.343485i
$323$			59.6157i			0.184569i
$324$		0			0
$325$	−52.9712	−	88.0416i	−0.162988	−	0.270897i
$326$	−133.923	+	121.691i	−0.410807	+	0.373284i
$327$		0			0
$328$	−96.4692	+	72.1172i	−0.294113	+	0.219870i
$329$	−67.2724			−0.204475
$330$		0			0
$331$	−61.0883			−0.184557			−0.0922783	−	0.995733i	$-0.529415\pi$
$331$	−61.0883			−0.184557			−0.0922783	+	0.995733i	$0.529415\pi$
$332$	1.06287	+	0.101961i	0.00320143	+	0.000307113i
$333$		0			0
$334$	135.546	+	149.171i	0.405826	+	0.446620i
$335$	186.629	−	330.091i	0.557101	−	0.985348i
$336$		0			0
$337$			114.960i			0.341129i	0.985347	+	0.170564i	$0.0545591\pi$
$337$			114.960i			0.341129i	−0.985347	+	0.170564i	$0.945441\pi$
$338$	204.585	+	225.150i	0.605282	+	0.666125i
$339$		0			0
$340$	37.0677	+	25.9192i	0.109023	+	0.0762331i
$341$			10.3919i			0.0304748i
$342$		0			0
$343$	299.851			0.874201
$344$	−44.6099	−	59.6734i	−0.129680	−	0.173469i
$345$		0			0
$346$	−73.5116	−	80.9010i	−0.212461	−	0.233818i
$347$		−	143.967i		−	0.414892i	−0.978246	−	0.207446i	$-0.933485\pi$
$347$		−	143.967i		−	0.414892i	0.978246	−	0.207446i	$-0.0665151\pi$
$348$		0			0
$349$			35.9526i			0.103016i	0.998673	+	0.0515080i	$0.0164028\pi$
$349$			35.9526i			0.103016i	−0.998673	+	0.0515080i	$0.983597\pi$
$350$	−110.350	+	367.673i	−0.315286	+	1.05049i
$351$		0			0
$352$	7.84930	+	12.9093i	0.0222991	+	0.0366742i
$353$			252.536i			0.715400i	0.933837	+	0.357700i	$0.116439\pi$
$353$			252.536i			0.715400i	−0.933837	+	0.357700i	$0.883561\pi$
$354$		0			0
$355$	−199.502	+	352.860i	−0.561976	+	0.993971i
$356$	32.6788	−	340.653i	0.0917943	−	0.956890i
$357$		0			0
$358$	−143.654	−	158.095i	−0.401269	−	0.441605i
$359$			594.152i			1.65502i	0.561452	+	0.827509i	$0.310243\pi$
$359$			594.152i			1.65502i	−0.561452	+	0.827509i	$0.689757\pi$
$360$		0			0
$361$	333.885			0.924890
$362$	−214.300	+	194.726i	−0.591989	+	0.537917i
$363$		0			0
$364$	−12.0526	+	125.640i	−0.0331116	+	0.345165i
$365$	205.295	−	363.107i	0.562453	−	0.994814i
$366$		0			0
$367$	−88.9062			−0.242251			−0.121126	−	0.992637i	$-0.538650\pi$
$367$	−88.9062			−0.242251			−0.121126	+	0.992637i	$0.538650\pi$
$368$	−152.880	−	29.6039i	−0.415435	−	0.0804455i
$369$		0			0
$370$	114.438	+	504.636i	0.309291	+	1.36388i
$371$	−306.334			−0.825699
$372$		0			0
$373$	−83.6542			−0.224274			−0.112137	−	0.993693i	$-0.535770\pi$
$373$	−83.6542			−0.224274			−0.112137	+	0.993693i	$0.535770\pi$
$374$	1.58049	−	1.43613i	0.00422590	−	0.00383991i
$375$		0			0
$376$	56.1440	−	41.9714i	0.149319	−	0.111626i
$377$		−	171.373i		−	0.454570i
$378$		0			0
$379$	−135.135			−0.356556			−0.178278	−	0.983980i	$-0.557053\pi$
$379$	−135.135			−0.356556			−0.178278	+	0.983980i	$0.557053\pi$
$380$	302.117	−	432.064i	0.795044	−	1.13701i
$381$		0			0
$382$	−312.039	+	283.538i	−0.816857	+	0.742246i
$383$	498.526			1.30164			0.650818	−	0.759234i	$-0.274426\pi$
$383$	498.526			1.30164			0.650818	+	0.759234i	$0.274426\pi$
$384$		0			0
$385$	15.7771	+	8.92013i	0.0409794	+	0.0231692i
$386$	−160.122	+	145.496i	−0.414823	+	0.376933i
$387$		0			0
$388$	−394.707	−	37.8642i	−1.01729	−	0.0975880i
$389$			308.420i			0.792854i	0.918066	+	0.396427i	$0.129750\pi$
$389$			308.420i			0.792854i	−0.918066	+	0.396427i	$0.870250\pi$
$390$		0			0
$391$			22.0104i			0.0562926i
$392$	63.7177	−	47.6332i	0.162545	−	0.121513i
$393$		0			0
$394$	−414.663	−	456.345i	−1.05244	−	1.15824i
$395$	−247.947	+	438.546i	−0.627715	+	1.11024i
$396$		0			0
$397$	−297.682			−0.749828			−0.374914	−	0.927060i	$-0.622328\pi$
$397$	−297.682			−0.749828			−0.374914	+	0.927060i	$0.622328\pi$
$398$	366.880	−	333.370i	0.921810	−	0.837612i
$399$		0			0
$400$	−137.296	−	375.699i	−0.343241	−	0.939247i
$401$	−148.663			−0.370729			−0.185365	−	0.982670i	$-0.559347\pi$
$401$	−148.663			−0.370729			−0.185365	+	0.982670i	$0.559347\pi$
$402$		0			0
$403$		−	90.4616i		−	0.224470i
$404$	−419.692	−	40.2610i	−1.03884	−	0.0996559i
$405$		0			0
$406$	−473.856	+	430.574i	−1.16713	+	1.06053i
$407$	24.4306			0.0600261
$408$		0			0
$409$	442.387			1.08163			0.540815	−	0.841141i	$-0.318116\pi$
$409$	442.387			1.08163			0.540815	+	0.841141i	$0.318116\pi$
$410$	−33.2969	−	146.829i	−0.0812119	−	0.358120i
$411$		0			0
$412$	38.9081	−	405.589i	0.0944371	−	0.984439i
$413$	−592.654			−1.43500
$414$		0			0
$415$	−0.656893	+	1.16185i	−0.00158287	+	0.00279964i
$416$	−68.3282	−	112.376i	−0.164250	−	0.270134i
$417$		0			0
$418$	−16.7396	−	18.4223i	−0.0400469	−	0.0440724i
$419$	−536.184			−1.27968			−0.639838	−	0.768510i	$-0.720999\pi$
$419$	−536.184			−1.27968			−0.639838	+	0.768510i	$0.720999\pi$
$420$		0			0
$421$		−	514.582i		−	1.22228i	−0.791521	−	0.611142i	$-0.790710\pi$
$421$		−	514.582i		−	1.22228i	0.791521	−	0.611142i	$-0.209290\pi$
$422$	−310.134	−	341.309i	−0.734915	−	0.808789i
$423$		0			0
$424$	255.659	−	191.123i	0.602970	−	0.450761i
$425$	−48.4458	+	29.1480i	−0.113990	+	0.0685834i
$426$		0			0
$427$			113.359i			0.265477i
$428$	131.382	+	12.6034i	0.306967	+	0.0294473i
$429$		0			0
$430$	90.8249	−	20.5966i	0.211221	−	0.0478991i
$431$		−	86.8151i		−	0.201427i	−0.994915	−	0.100714i	$-0.967887\pi$
$431$		−	86.8151i		−	0.201427i	0.994915	−	0.100714i	$-0.0321126\pi$
$432$		0			0
$433$			494.017i			1.14092i	0.821327	+	0.570458i	$0.193234\pi$
$433$			494.017i			1.14092i	−0.821327	+	0.570458i	$0.806766\pi$
$434$	−250.132	+	227.285i	−0.576340	+	0.523698i
$435$		0			0
$436$	−722.895	−	69.3473i	−1.65802	−	0.159053i
$437$	256.555			0.587082
$438$		0			0
$439$			524.700i			1.19522i	0.801789	+	0.597608i	$0.203882\pi$
$439$			524.700i			1.19522i	−0.801789	+	0.597608i	$0.796118\pi$
$440$	−18.7325	+	2.39883i	−0.0425738	+	0.00545188i
$441$		0			0
$442$	−13.7581	+	12.5015i	−0.0311270	+	0.0282839i
$443$			496.575i			1.12094i	0.828176	+	0.560469i	$0.189379\pi$
$443$			496.575i			1.12094i	−0.828176	+	0.560469i	$0.810621\pi$
$444$		0			0
$445$	372.375	+	210.535i	0.836797	+	0.473112i
$446$	−239.116	−	263.153i	−0.536136	−	0.590028i
$447$		0			0
$448$	−139.051	+	471.275i	−0.310382	+	1.05195i
$449$	332.158			0.739773			0.369886	−	0.929077i	$-0.379397\pi$
$449$	332.158			0.739773			0.369886	+	0.929077i	$0.379397\pi$
$450$		0			0
$451$	−7.10835			−0.0157613
$452$	−305.160	−	29.2740i	−0.675133	−	0.0647655i
$453$		0			0
$454$	300.926	−	273.440i	0.662833	−	0.602290i
$455$	−137.340	−	77.6497i	−0.301845	−	0.170659i
$456$		0			0
$457$		−	252.788i		−	0.553147i	−0.960993	−	0.276574i	$-0.910801\pi$
$457$		−	252.788i		−	0.553147i	0.960993	−	0.276574i	$-0.0891990\pi$
$458$	120.000	−	109.040i	0.262010	−	0.238078i
$459$		0			0
$460$	111.543	−	159.520i	0.242485	−	0.346783i
$461$		−	832.716i		−	1.80633i	−0.429299	−	0.903163i	$-0.641239\pi$
$461$		−	832.716i		−	1.80633i	0.429299	−	0.903163i	$-0.358761\pi$
$462$		0			0
$463$	854.205			1.84494			0.922468	−	0.386074i	$-0.126169\pi$
$463$	854.205			1.84494			0.922468	+	0.386074i	$0.126169\pi$
$464$	126.833	−	654.987i	0.273347	−	1.41161i
$465$		0			0
$466$	−83.3150	+	75.7051i	−0.178788	+	0.162457i
$467$			102.726i			0.219970i	0.993933	+	0.109985i	$0.0350802\pi$
$467$			102.726i			0.219970i	−0.993933	+	0.109985i	$0.964920\pi$
$468$		0			0
$469$		−	582.259i		−	1.24149i
$470$	19.3784	+	85.4529i	0.0412307	+	0.181815i
$471$		0			0
$472$	494.615	−	369.758i	1.04791	−	0.783386i
$473$		−	4.39705i		−	0.00929608i
$474$		0			0
$475$	339.751	+	564.688i	0.715265	+	1.18882i
$476$	69.1347	+	6.63208i	0.145241	+	0.0139329i
$477$		0			0
$478$	533.218	−	484.515i	1.11552	−	1.01363i
$479$			268.772i			0.561111i	0.959838	+	0.280556i	$0.0905187\pi$
$479$			268.772i			0.561111i	−0.959838	+	0.280556i	$0.909481\pi$
$480$		0			0
$481$	−212.669			−0.442139
$482$	265.631	+	292.332i	0.551101	+	0.606498i
$483$		0			0
$484$	46.1327	−	480.901i	0.0953156	−	0.993596i
$485$	243.942	−	431.462i	0.502973	−	0.889612i
$486$		0			0
$487$	−504.065			−1.03504			−0.517520	−	0.855671i	$-0.673145\pi$
$487$	−504.065			−1.03504			−0.517520	+	0.855671i	$0.673145\pi$
$488$	−70.7248	−	94.6066i	−0.144928	−	0.193866i
$489$		0			0
$490$	21.9925	+	96.9803i	0.0448827	+	0.197919i
$491$	−130.020			−0.264807			−0.132403	−	0.991196i	$-0.542269\pi$
$491$	−130.020			−0.264807			−0.132403	+	0.991196i	$0.542269\pi$
$492$		0			0
$493$	−94.2997			−0.191277
$494$	145.718	+	160.366i	0.294976	+	0.324627i
$495$		0			0
$496$	66.9505	−	345.744i	0.134981	−	0.697065i
$497$			622.421i			1.25236i
$498$		0			0
$499$	664.184			1.33103			0.665515	−	0.746384i	$-0.268212\pi$
$499$	664.184			1.33103			0.665515	+	0.746384i	$0.268212\pi$
$500$	498.825	+	34.2610i	0.997650	+	0.0685220i
$501$		0			0
$502$	−239.895	−	264.009i	−0.477878	−	0.525914i
$503$	−550.015			−1.09347			−0.546735	−	0.837306i	$-0.684129\pi$
$503$	−550.015			−1.09347			−0.546735	+	0.837306i	$0.684129\pi$
$504$		0			0
$505$	259.384	−	458.774i	0.513631	−	0.908463i
$506$	−6.18034	−	6.80159i	−0.0122141	−	0.0134419i
$507$		0			0
$508$	−54.6067	+	569.235i	−0.107493	+	1.12054i
$509$		−	349.843i		−	0.687314i	−0.939095	−	0.343657i	$-0.888334\pi$
$509$		−	349.843i		−	0.687314i	0.939095	−	0.343657i	$-0.111666\pi$
$510$		0			0
$511$		−	640.496i		−	1.25342i
$512$	−177.981	−	480.070i	−0.347619	−	0.937636i
$513$		0			0
$514$	−670.800	+	609.530i	−1.30506	+	1.18586i
$515$	443.358	+	250.668i	0.860888	+	0.486733i
$516$		0			0
$517$	4.13698			0.00800189
$518$	534.330	+	588.041i	1.03153	+	1.13522i
$519$		0			0
$520$	163.066	−	20.8818i	0.313589	−	0.0401573i
$521$	−29.7771			−0.0571537			−0.0285769	−	0.999592i	$-0.509098\pi$
$521$	−29.7771			−0.0571537			−0.0285769	+	0.999592i	$0.509098\pi$
$522$		0			0
$523$			603.023i			1.15301i	0.817094	+	0.576504i	$0.195584\pi$
$523$			603.023i			1.15301i	−0.817094	+	0.576504i	$0.804416\pi$
$524$	42.0689	−	438.538i	0.0802841	−	0.836904i
$525$		0			0
$526$	28.3688	+	31.2205i	0.0539331	+	0.0593545i
$527$	−49.7774			−0.0944543
$528$		0			0
$529$	−434.279			−0.820943
$530$	88.2423	+	389.122i	0.166495	+	0.734192i
$531$		0			0
$532$	77.3040	−	805.839i	0.145308	−	1.51473i
$533$	61.8782			0.116094
$534$		0			0
$535$	−81.1985	+	143.616i	−0.151773	+	0.268442i
$536$	363.272	+	485.939i	0.677747	+	0.906603i
$537$		0			0
$538$	136.792	−	124.298i	0.254260	−	0.231036i
$539$	4.69505			0.00871066
$540$		0			0
$541$			163.368i			0.301974i	0.988536	+	0.150987i	$0.0482451\pi$
$541$			163.368i			0.301974i	−0.988536	+	0.150987i	$0.951755\pi$
$542$	279.460	−	253.934i	0.515608	−	0.468513i
$543$		0			0
$544$	−61.8359	+	37.5983i	−0.113669	+	0.0691145i
$545$	446.774	−	790.212i	0.819769	−	1.44993i
$546$		0			0
$547$			524.218i			0.958350i	0.877719	+	0.479175i	$0.159064\pi$
$547$			524.218i			0.958350i	−0.877719	+	0.479175i	$0.840936\pi$
$548$	−897.471	−	86.0943i	−1.63772	−	0.157106i
$549$		0			0
$550$	6.78608	−	22.6104i	0.0123383	−	0.0411098i
$551$			1099.16i			1.99485i
$552$		0			0
$553$			773.566i			1.39885i
$554$	−94.3181	−	103.799i	−0.170249	−	0.187363i
$555$		0			0
$556$	−37.2098	+	387.885i	−0.0669240	+	0.697635i
$557$	−589.515			−1.05837			−0.529187	−	0.848505i	$-0.677503\pi$
$557$	−589.515			−1.05837			−0.529187	+	0.848505i	$0.677503\pi$
$558$		0			0
$559$			38.2763i			0.0684728i
$560$	−467.443	−	398.422i	−0.834720	−	0.711468i
$561$		0			0
$562$	−680.931	−	749.378i	−1.21162	−	1.33341i
$563$		−	557.763i		−	0.990698i	−0.868694	−	0.495349i	$-0.835040\pi$
$563$		−	557.763i		−	0.990698i	0.868694	−	0.495349i	$-0.164960\pi$
$564$		0			0
$565$	188.599	−	333.577i	0.333804	−	0.590402i
$566$	−742.097	+	674.315i	−1.31113	+	1.19137i
$567$		0			0
$568$	−388.329	−	519.457i	−0.683678	−	0.914538i
$569$	542.715			0.953805			0.476903	−	0.878956i	$-0.341759\pi$
$569$	542.715			0.953805			0.476903	+	0.878956i	$0.341759\pi$
$570$		0			0
$571$	−476.695			−0.834842			−0.417421	−	0.908713i	$-0.637066\pi$
$571$	−476.695			−0.834842			−0.417421	+	0.908713i	$0.637066\pi$
$572$	0.741187	−	7.72634i	0.00129578	−	0.0135076i
$573$		0			0
$574$	−155.469	−	171.097i	−0.270852	−	0.298078i
$575$	125.438	+	208.486i	0.218152	+	0.362584i
$576$		0			0
$577$		−	865.659i		−	1.50027i	−0.661282	−	0.750137i	$-0.729987\pi$
$577$		−	865.659i		−	1.50027i	0.661282	−	0.750137i	$-0.270013\pi$
$578$	−381.825	−	420.206i	−0.660597	−	0.727001i
$579$		0			0
$580$	683.436	+	477.886i	1.17834	+	0.823941i
$581$			2.04943i			0.00352741i
$582$		0			0
$583$	18.8383			0.0323127
$584$	399.607	+	534.543i	0.684258	+	0.915313i
$585$		0			0
$586$	435.813	+	479.622i	0.743709	+	0.818467i
$587$			567.091i			0.966083i	0.875597	+	0.483041i	$0.160468\pi$
$587$			567.091i			0.966083i	−0.875597	+	0.483041i	$0.839532\pi$
$588$		0			0
$589$			580.209i			0.985075i
$590$	170.719	+	752.820i	0.289355	+	1.27597i
$591$		0			0
$592$	−812.820	−	157.396i	−1.37301	−	0.265871i
$593$			421.774i			0.711254i	0.934628	+	0.355627i	$0.115733\pi$
$593$			421.774i			0.711254i	−0.934628	+	0.355627i	$0.884267\pi$
$594$		0			0
$595$	−42.7276	+	75.5725i	−0.0718110	+	0.127013i
$596$	−762.089	−	73.1071i	−1.27867	−	0.122663i
$597$		0			0
$598$	53.7999	+	59.2079i	0.0899664	+	0.0990098i
$599$			120.444i			0.201075i	0.994933	+	0.100538i	$0.0320563\pi$
$599$			120.444i			0.201075i	−0.994933	+	0.100538i	$0.967944\pi$
$600$		0			0
$601$	340.158			0.565986			0.282993	−	0.959122i	$-0.408673\pi$
$601$	340.158			0.565986			0.282993	+	0.959122i	$0.408673\pi$
$602$	105.836	−	96.1693i	0.175808	−	0.159750i
$603$		0			0
$604$	272.170	+	26.1093i	0.450613	+	0.0432273i
$605$	525.682	+	297.213i	0.868897	+	0.491261i
$606$		0			0
$607$	−115.621			−0.190479			−0.0952396	−	0.995454i	$-0.530362\pi$
$607$	−115.621			−0.190479			−0.0952396	+	0.995454i	$0.530362\pi$
$608$	438.248	+	720.764i	0.720803	+	1.18547i
$609$		0			0
$610$	143.994	−	32.6540i	0.236056	−	0.0535311i
$611$	−36.0124			−0.0589401
$612$		0			0
$613$	−1095.63			−1.78733			−0.893663	−	0.448738i	$-0.851874\pi$
$613$	−1095.63			−1.78733			−0.893663	+	0.448738i	$0.851874\pi$
$614$	−14.5755	+	13.2442i	−0.0237385	+	0.0215703i
$615$		0			0
$616$	−23.2260	+	17.3630i	−0.0377046	+	0.0281867i
$617$		−	716.775i		−	1.16171i	−0.814007	−	0.580855i	$-0.802718\pi$
$617$		−	716.775i		−	1.16171i	0.814007	−	0.580855i	$-0.197282\pi$
$618$		0			0
$619$	118.584			0.191573			0.0957864	−	0.995402i	$-0.469463\pi$
$619$	118.584			0.191573			0.0957864	+	0.995402i	$0.469463\pi$
$620$	360.761	+	252.259i	0.581873	+	0.406869i
$621$		0			0
$622$	−296.657	+	269.561i	−0.476941	+	0.433378i
$623$	656.844			1.05432
$624$		0			0
$625$	−292.771	+	552.187i	−0.468433	+	0.883499i
$626$	387.193	−	351.828i	0.618520	−	0.562025i
$627$		0			0
$628$	−59.2944	+	618.101i	−0.0944178	+	0.984238i
$629$			117.023i			0.186046i
$630$		0			0
$631$			1168.62i			1.85201i	0.377515	+	0.926004i	$0.376779\pi$
$631$			1168.62i			1.85201i	−0.377515	+	0.926004i	$0.623221\pi$
$632$	−482.629	−	645.600i	−0.763654	−	1.02152i
$633$		0			0
$634$	433.548	+	477.128i	0.683830	+	0.752569i
$635$	−622.243	−	351.807i	−0.979910	−	0.554026i
$636$		0			0
$637$	−40.8704			−0.0641608
$638$	29.1402	−	26.4786i	0.0456743	−	0.0415025i
$639$		0			0
$640$	638.693	+	40.8748i	0.997958	+	0.0638669i
$641$	244.158			0.380902			0.190451	−	0.981697i	$-0.439005\pi$
$641$	244.158			0.380902			0.190451	+	0.981697i	$0.439005\pi$
$642$		0			0
$643$		−	868.847i		−	1.35124i	−0.737250	−	0.675620i	$-0.763876\pi$
$643$		−	868.847i		−	1.35124i	0.737250	−	0.675620i	$-0.236124\pi$
$644$	28.5410	−	297.520i	0.0443184	−	0.461987i
$645$		0			0
$646$	88.2430	−	80.1830i	0.136599	−	0.124122i
$647$	−35.1333			−0.0543019			−0.0271510	−	0.999631i	$-0.508643\pi$
$647$	−35.1333			−0.0543019			−0.0271510	+	0.999631i	$0.508643\pi$
$648$		0			0
$649$	36.4458			0.0561569
$650$	−59.0729	+	196.824i	−0.0908813	+	0.302806i
$651$		0			0
$652$	360.252	+	34.5589i	0.552534	+	0.0530045i
$653$	580.068			0.888313			0.444157	−	0.895949i	$-0.353503\pi$
$653$	580.068			0.888313			0.444157	+	0.895949i	$0.353503\pi$
$654$		0			0
$655$	479.375	+	271.031i	0.731870	+	0.413788i
$656$	236.498	+	45.7960i	0.360516	+	0.0698109i
$657$		0			0
$658$	90.4812	+	99.5764i	0.137509	+	0.151332i
$659$	992.788			1.50651			0.753253	−	0.657731i	$-0.228483\pi$
$659$	992.788			1.50651			0.753253	+	0.657731i	$0.228483\pi$
$660$		0			0
$661$			719.647i			1.08872i	0.838850	+	0.544362i	$0.183228\pi$
$661$			719.647i			1.08872i	−0.838850	+	0.544362i	$0.816772\pi$
$662$	82.1635	+	90.4226i	0.124114	+	0.136590i
$663$		0			0
$664$	−1.27864	−	1.71040i	−0.00192566	−	0.00257591i
$665$	880.879	+	498.036i	1.32463	+	0.748926i
$666$		0			0
$667$			405.817i			0.608421i
$668$	38.4938	−	401.270i	0.0576254	−	0.600703i
$669$		0			0
$670$	−739.615	+	167.725i	−1.10390	+	0.250335i
$671$		−	6.97110i		−	0.0103891i
$672$		0			0
$673$			189.591i			0.281711i	0.990030	+	0.140855i	$0.0449852\pi$
$673$			189.591i			0.281711i	−0.990030	+	0.140855i	$0.955015\pi$
$674$	170.164	−	154.621i	0.252469	−	0.229409i
$675$		0			0
$676$	58.1002	−	605.653i	0.0859471	−	0.895936i
$677$	327.192			0.483297			0.241649	−	0.970364i	$-0.422312\pi$
$677$	327.192			0.483297			0.241649	+	0.970364i	$0.422312\pi$
$678$		0			0
$679$		−	761.070i		−	1.12087i
$680$	−11.4904	−	89.7289i	−0.0168977	−	0.131954i
$681$		0			0
$682$	15.3821	−	13.9771i	0.0225544	−	0.0204943i
$683$		−	673.539i		−	0.986148i	−0.869987	−	0.493074i	$-0.835873\pi$
$683$		−	673.539i		−	0.986148i	0.869987	−	0.493074i	$-0.164127\pi$
$684$		0			0
$685$	554.668	−	981.044i	0.809734	−	1.43218i
$686$	−403.299	−	443.839i	−0.587899	−	0.646995i
$687$		0			0
$688$	−28.3282	+	146.292i	−0.0411748	+	0.212634i
$689$	−163.988			−0.238008
$690$		0			0
$691$	237.036			0.343033			0.171516	−	0.985181i	$-0.445133\pi$
$691$	237.036			0.343033			0.171516	+	0.985181i	$0.445133\pi$
$692$	−20.8766	+	217.623i	−0.0301685	+	0.314485i
$693$		0			0
$694$	−213.100	+	193.636i	−0.307061	+	0.279014i
$695$	−424.005	−	239.726i	−0.610079	−	0.344930i
$696$		0			0
$697$		−	34.0491i		−	0.0488510i
$698$	53.2170	−	48.3562i	0.0762421	−	0.0692782i
$699$		0			0
$700$	692.649	−	331.179i	0.989499	−	0.473113i
$701$			476.306i			0.679466i	0.940522	+	0.339733i	$0.110337\pi$
$701$			476.306i			0.679466i	−0.940522	+	0.339733i	$0.889663\pi$
$702$		0			0
$703$	1364.03			1.94030
$704$	8.55107	−	28.9815i	0.0121464	−	0.0411669i
$705$		0			0
$706$	373.803	−	339.661i	0.529467	−	0.481106i
$707$		−	809.246i		−	1.14462i
$708$		0			0
$709$			964.778i			1.36076i	0.732860	+	0.680380i	$0.238185\pi$
$709$			964.778i			1.36076i	−0.732860	+	0.680380i	$0.761815\pi$
$710$	790.631	−	179.294i	1.11356	−	0.252526i
$711$		0			0
$712$	−548.186	+	409.806i	−0.769924	+	0.575570i
$713$			214.216i			0.300443i
$714$		0			0
$715$	8.44582	+	4.77514i	0.0118123	+	0.00667852i
$716$	−40.7965	+	425.274i	−0.0569783	+	0.593958i
$717$		0			0
$718$	879.461	−	799.132i	1.22488	−	1.11300i
$719$		−	899.974i		−	1.25170i	−0.779943	−	0.625851i	$-0.784752\pi$
$719$		−	899.974i		−	1.25170i	0.779943	−	0.625851i	$-0.215248\pi$
$720$		0			0
$721$	782.053			1.08468
$722$	−449.075	−	494.216i	−0.621987	−	0.684510i
$723$		0			0
$724$	576.466	+	55.3003i	0.796224	+	0.0763816i
$725$	−893.220	+	537.415i	−1.23203	+	0.741262i
$726$		0			0
$727$	−908.888			−1.25019			−0.625095	−	0.780549i	$-0.714940\pi$
$727$	−908.888			−1.25019			−0.625095	+	0.780549i	$0.714940\pi$
$728$	202.183	−	151.145i	0.277723	−	0.207617i
$729$		0			0
$730$	−813.591	+	184.500i	−1.11451	+	0.252740i
$731$	21.0619			0.0288125
$732$		0			0
$733$	−433.283			−0.591109			−0.295554	−	0.955326i	$-0.595504\pi$
$733$	−433.283			−0.591109			−0.295554	+	0.955326i	$0.595504\pi$
$734$	119.579	+	131.599i	0.162914	+	0.179290i
$735$		0			0
$736$	161.803	+	266.110i	0.219842	+	0.361562i
$737$			35.8065i			0.0485842i
$738$		0			0
$739$	−886.138			−1.19910			−0.599552	−	0.800336i	$-0.704655\pi$
$739$	−886.138			−1.19910			−0.599552	+	0.800336i	$0.704655\pi$
$740$	593.042	−	848.124i	0.801408	−	1.14611i
$741$		0			0
$742$	412.019	+	453.435i	0.555281	+	0.611099i
$743$	895.305			1.20499			0.602493	−	0.798124i	$-0.294174\pi$
$743$	895.305			1.20499			0.602493	+	0.798124i	$0.294174\pi$
$744$		0			0
$745$	470.997	−	833.055i	0.632211	−	1.11820i
$746$	112.515	+	123.825i	0.150824	+	0.165985i
$747$		0			0
$748$	−4.25150	−	0.407846i	−0.00568382	−	0.000545248i
$749$			253.329i			0.338223i
$750$		0			0
$751$		−	1297.13i		−	1.72720i	−0.504176	−	0.863601i	$-0.668204\pi$
$751$		−	1297.13i		−	1.72720i	0.504176	−	0.863601i	$-0.331796\pi$
$752$	−137.639	−	26.6527i	−0.183031	−	0.0354425i
$753$		0			0
$754$	−253.666	+	230.496i	−0.336427	+	0.305698i
$755$	−168.210	+	297.515i	−0.222795	+	0.394060i
$756$		0			0
$757$	421.694			0.557060			0.278530	−	0.960428i	$-0.410153\pi$
$757$	421.694			0.557060			0.278530	+	0.960428i	$0.410153\pi$
$758$	181.756	+	200.026i	0.239783	+	0.263886i
$759$		0			0
$760$	−1045.89	+	133.933i	−1.37617	+	0.176228i
$761$	−1415.76			−1.86039			−0.930196	−	0.367063i	$-0.880363\pi$
$761$	−1415.76			−1.86039			−0.930196	+	0.367063i	$0.880363\pi$
$762$		0			0
$763$		−	1393.88i		−	1.82684i
$764$	839.384	+	80.5220i	1.09867	+	0.105395i
$765$		0			0
$766$	−670.517	−	737.917i	−0.875348	−	0.963339i
$767$	−317.261			−0.413639
$768$		0			0
$769$	−414.210			−0.538635			−0.269318	−	0.963051i	$-0.586798\pi$
$769$	−414.210			−0.538635			−0.269318	+	0.963051i	$0.586798\pi$
$770$	−8.01659	−	35.3507i	−0.0104112	−	0.0459101i
$771$		0			0
$772$	430.726	+	41.3195i	0.557935	+	0.0535226i
$773$	−727.056			−0.940564			−0.470282	−	0.882516i	$-0.655848\pi$
$773$	−727.056			−0.940564			−0.470282	+	0.882516i	$0.655848\pi$
$774$		0			0
$775$	−471.498	+	283.682i	−0.608385	+	0.366042i
$776$	474.833	+	635.171i	0.611898	+	0.818519i
$777$		0			0
$778$	456.522	−	414.824i	0.586790	−	0.533193i
$779$	−396.879			−0.509473
$780$		0			0
$781$		−	38.2763i		−	0.0490094i
$782$	32.5797	−	29.6039i	0.0416621	−	0.0378567i
$783$		0			0
$784$	−156.207	−	30.2481i	−0.199243	−	0.0385818i
$785$	−675.659	−	382.008i	−0.860713	−	0.486634i
$786$		0			0
$787$		−	1030.11i		−	1.30890i	−0.756104	−	0.654451i	$-0.772900\pi$
$787$		−	1030.11i		−	1.30890i	0.756104	−	0.654451i	$-0.227100\pi$
$788$	−117.760	+	1227.56i	−0.149442	+	1.55782i
$789$		0			0
$790$	982.623	−	222.832i	1.24383	−	0.282066i
$791$		−	588.407i		−	0.743878i
$792$		0			0
$793$			60.6835i			0.0765239i
$794$	400.381	+	440.627i	0.504258	+	0.554946i
$795$		0			0
$796$	−986.906	−	94.6737i	−1.23983	−	0.118937i
$797$	−371.202			−0.465750			−0.232875	−	0.972507i	$-0.574813\pi$
$797$	−371.202			−0.465750			−0.232875	+	0.972507i	$0.574813\pi$
$798$		0			0
$799$			19.8162i			0.0248013i
$800$	−371.445	+	708.540i	−0.464307	+	0.885675i
$801$		0			0
$802$	199.951	+	220.050i	0.249315	+	0.274376i
$803$			39.3879i			0.0490509i
$804$		0			0
$805$	325.225	+	183.877i	0.404006	+	0.228419i
$806$	−133.901	+	121.671i	−0.166130	+	0.150956i
$807$		0			0
$808$	504.890	+	675.378i	0.624864	+	0.835863i
$809$	−77.7771			−0.0961398			−0.0480699	−	0.998844i	$-0.515307\pi$
$809$	−77.7771			−0.0961398			−0.0480699	+	0.998844i	$0.515307\pi$
$810$		0			0
$811$	−1407.90			−1.73600			−0.868000	−	0.496564i	$-0.834595\pi$
$811$	−1407.90			−1.73600			−0.868000	+	0.496564i	$0.834595\pi$
$812$	1274.67	+	122.279i	1.56979	+	0.150590i
$813$		0			0
$814$	−32.8591	−	36.1621i	−0.0403675	−	0.0444252i
$815$	−222.648	+	393.799i	−0.273188	+	0.483189i
$816$		0			0
$817$		−	245.500i		−	0.300489i
$818$	−595.009	−	654.820i	−0.727395	−	0.800513i
$819$		0			0
$820$	−172.552	+	246.771i	−0.210429	+	0.300940i
$821$		−	820.275i		−	0.999116i	−0.866280	−	0.499558i	$-0.833496\pi$
$821$		−	820.275i		−	0.999116i	0.866280	−	0.499558i	$-0.166504\pi$
$822$		0			0
$823$	−1385.41			−1.68336			−0.841681	−	0.539976i	$-0.818433\pi$
$823$	−1385.41			−1.68336			−0.841681	+	0.539976i	$0.818433\pi$
$824$	−652.683	+	487.924i	−0.792091	+	0.592141i
$825$		0			0
$826$	797.118	+	877.245i	0.965034	+	1.06204i
$827$			258.898i			0.313057i	0.987673	+	0.156529i	$0.0500303\pi$
$827$			258.898i			0.313057i	−0.987673	+	0.156529i	$0.949970\pi$
$828$		0			0
$829$		−	1299.31i		−	1.56732i	−0.621190	−	0.783660i	$-0.713351\pi$
$829$		−	1299.31i		−	1.56732i	0.621190	−	0.783660i	$-0.286649\pi$
$830$	2.60329	−	0.590355i	0.00313649	−	0.000711271i
$831$		0			0
$832$	−74.4371	+	252.284i	−0.0894677	+	0.303226i
$833$			22.4894i			0.0269980i
$834$		0			0
$835$	438.636	+	247.998i	0.525313	+	0.297004i
$836$	−4.75388	+	49.5558i	−0.00568646	+	0.0592773i
$837$		0			0
$838$	721.166	+	793.658i	0.860580	+	0.947086i
$839$		−	804.961i		−	0.959429i	−0.877425	−	0.479715i	$-0.840740\pi$
$839$		−	804.961i		−	0.959429i	0.877425	−	0.479715i	$-0.159260\pi$
$840$		0			0
$841$	−897.650			−1.06736
$842$	−761.683	+	692.111i	−0.904611	+	0.821985i
$843$		0			0
$844$	−88.0751	+	918.120i	−0.104354	+	1.08782i
$845$	662.052	+	374.314i	0.783493	+	0.442975i
$846$		0			0
$847$	927.268			1.09477
$848$	−626.760	−	121.367i	−0.739104	−	0.143121i
$849$		0			0
$850$	108.304	+	32.5055i	0.127417	+	0.0382417i
$851$	503.607			0.591782
$852$		0			0
$853$	470.811			0.551948			0.275974	−	0.961165i	$-0.411000\pi$
$853$	470.811			0.551948			0.275974	+	0.961165i	$0.411000\pi$
$854$	167.793	−	152.467i	0.196479	−	0.178533i
$855$		0			0
$856$	−158.053	−	211.423i	−0.184641	−	0.246989i
$857$		−	266.105i		−	0.310508i	−0.987875	−	0.155254i	$-0.950380\pi$
$857$		−	266.105i		−	0.310508i	0.987875	−	0.155254i	$-0.0496196\pi$
$858$		0			0
$859$	1442.02			1.67872			0.839360	−	0.543576i	$-0.182930\pi$
$859$	1442.02			1.67872			0.839360	+	0.543576i	$0.182930\pi$
$860$	−152.646	−	106.736i	−0.177496	−	0.124112i
$861$		0			0
$862$	−128.503	+	116.766i	−0.149076	+	0.135459i
$863$	364.495			0.422358			0.211179	−	0.977447i	$-0.432270\pi$
$863$	364.495			0.422358			0.211179	+	0.977447i	$0.432270\pi$
$864$		0			0
$865$	−237.889	−	134.499i	−0.275016	−	0.155490i
$866$	731.242	−	664.451i	0.844391	−	0.767265i
$867$		0			0
$868$	672.852	+	64.5466i	0.775176	+	0.0743625i
$869$		−	47.5711i		−	0.0547424i
$870$		0			0
$871$		−	311.696i		−	0.357860i
$872$	869.645	+	1163.30i	0.997299	+	1.33406i
$873$		0			0
$874$	−345.066	−	379.752i	−0.394812	−	0.434499i
$875$	25.9675	+	959.338i	0.0296771	+	1.09639i
$876$		0			0
$877$	77.4289			0.0882883			0.0441442	−	0.999025i	$-0.485944\pi$
$877$	77.4289			0.0882883			0.0441442	+	0.999025i	$0.485944\pi$
$878$	776.659	−	705.719i	0.884577	−	0.803781i
$879$		0			0
$880$	28.7459	+	24.5013i	0.0326657	+	0.0278424i
$881$	−724.932			−0.822851			−0.411426	−	0.911443i	$-0.634969\pi$
$881$	−724.932			−0.822851			−0.411426	+	0.911443i	$0.634969\pi$
$882$		0			0
$883$		−	493.342i		−	0.558711i	−0.960188	−	0.279356i	$-0.909879\pi$
$883$		−	493.342i		−	0.558711i	0.960188	−	0.279356i	$-0.0901208\pi$
$884$	37.0093	+	3.55030i	0.0418657	+	0.00401618i
$885$		0			0
$886$	735.029	−	667.892i	0.829604	−	0.753828i
$887$	−1514.47			−1.70741			−0.853705	−	0.520758i	$-0.825649\pi$
$887$	−1514.47			−1.70741			−0.853705	+	0.520758i	$0.825649\pi$
$888$		0			0
$889$	−1097.59			−1.23464
$890$	−189.210	−	834.357i	−0.212595	−	0.937480i
$891$		0			0
$892$	−67.9067	+	707.879i	−0.0761286	+	0.793586i
$893$	230.979			0.258655
$894$		0			0
$895$	−464.876	−	262.834i	−0.519414	−	0.293669i
$896$	884.604	−	428.041i	0.987281	−	0.477725i
$897$		0			0
$898$	−446.751	−	491.659i	−0.497496	−	0.547505i
$899$	−917.771			−1.02088
$900$		0			0
$901$			90.2359i			0.100151i
$902$	9.56071	+	10.5218i	0.0105995	+	0.0116649i
$903$		0			0
$904$	367.108	+	491.071i	0.406093	+	0.543220i
$905$	−356.276	+	630.147i	−0.393675	+	0.696295i
$906$		0			0
$907$		−	851.570i		−	0.938887i	−0.882963	−	0.469443i	$-0.844455\pi$
$907$		−	851.570i		−	0.938887i	0.882963	−	0.469443i	$-0.155545\pi$
$908$	−809.489	−	77.6542i	−0.891508	−	0.0855223i
$909$		0			0
$910$	69.7844	+	307.728i	0.0766862	+	0.338163i
$911$			517.728i			0.568308i	0.958779	+	0.284154i	$0.0917127\pi$
$911$			517.728i			0.568308i	−0.958779	+	0.284154i	$0.908287\pi$
$912$		0			0
$913$		−	0.126031i		−	0.000138041i
$914$	−374.177	+	340.000i	−0.409383	+	0.371991i
$915$		0			0
$916$	−322.800	−	30.9662i	−0.352402	−	0.0338059i
$917$	845.585			0.922121
$918$		0			0
$919$			657.730i			0.715701i	0.933779	+	0.357851i	$0.116490\pi$
$919$			657.730i			0.715701i	−0.933779	+	0.357851i	$0.883510\pi$
$920$	−386.146	+	49.4488i	−0.419724	+	0.0537487i
$921$		0			0
$922$	−1232.58	+	1120.00i	−1.33686	+	1.21475i
$923$			333.195i			0.360992i
$924$		0			0
$925$	666.917	+	1108.46i	0.720991	+	1.19833i
$926$	−1148.90	−	1264.39i	−1.24072	−	1.36543i
$927$		0			0
$928$	−1140.10	+	693.218i	−1.22856	+	0.747002i
$929$	−1206.28			−1.29847			−0.649237	−	0.760586i	$-0.724912\pi$
$929$	−1206.28			−1.29847			−0.649237	+	0.760586i	$0.724912\pi$
$930$		0			0
$931$	262.138			0.281566
$932$	224.117	+	21.4995i	0.240469	+	0.0230681i
$933$		0			0
$934$	152.055	−	138.166i	0.162799	−	0.147929i
$935$	2.62757	−	4.64740i	0.00281024	−	0.00497048i
$936$		0			0
$937$			216.730i			0.231302i	0.993290	+	0.115651i	$0.0368954\pi$
$937$			216.730i			0.231302i	−0.993290	+	0.115651i	$0.963105\pi$
$938$	−861.858	+	783.136i	−0.918825	+	0.834900i
$939$		0			0
$940$	100.423	−	143.618i	0.106833	−	0.152785i
$941$			749.322i			0.796304i	0.917320	+	0.398152i	$0.130348\pi$
$941$			749.322i			0.796304i	−0.917320	+	0.398152i	$0.869652\pi$
$942$		0			0
$943$	−146.530			−0.155387
$944$	−1212.57	−	234.804i	−1.28450	−	0.248733i
$945$		0			0
$946$	−6.50850	+	5.91402i	−0.00688002	+	0.00625160i
$947$		−	114.160i		−	0.120549i	−0.998182	−	0.0602743i	$-0.980802\pi$
$947$		−	114.160i		−	0.120549i	0.998182	−	0.0602743i	$-0.0191976\pi$
$948$		0			0
$949$		−	342.872i		−	0.361298i
$950$	378.886	−	1262.40i	0.398827	−	1.32884i
$951$		0			0
$952$	−83.1691	−	111.253i	−0.0873625	−	0.116862i
$953$		−	820.680i		−	0.861154i	−0.902554	−	0.430577i	$-0.858310\pi$
$953$		−	820.680i		−	0.861154i	0.902554	−	0.430577i	$-0.141690\pi$
$954$		0			0
$955$	−518.768	+	917.548i	−0.543212	+	0.960783i
$956$	−1434.35	−	137.597i	−1.50037	−	0.143930i
$957$		0			0
$958$	397.836	−	361.498i	0.415278	−	0.377347i
$959$		−	1730.50i		−	1.80448i
$960$		0			0
$961$	476.542			0.495881
$962$	286.039	+	314.792i	0.297338	+	0.327226i
$963$		0			0
$964$	75.4365	−	786.371i	0.0782536	−	0.815738i
$965$	−266.203	+	470.835i	−0.275858	+	0.487912i
$966$		0			0
$967$	−1108.56			−1.14639			−0.573194	−	0.819420i	$-0.694296\pi$
$967$	−1108.56			−1.14639			−0.573194	+	0.819420i	$0.694296\pi$
$968$	−773.876	+	578.524i	−0.799459	+	0.597649i
$969$		0			0
$970$	−966.750	+	219.233i	−0.996650	+	0.226013i
$971$	1372.41			1.41340			0.706698	−	0.707516i	$-0.250184\pi$
$971$	1372.41			1.41340			0.706698	+	0.707516i	$0.250184\pi$
$972$		0			0
$973$	−747.916			−0.768670
$974$	677.966	+	746.115i	0.696063	+	0.766032i
$975$		0			0
$976$	−44.9117	+	231.932i	−0.0460161	+	0.237635i
$977$		−	927.224i		−	0.949052i	−0.880241	−	0.474526i	$-0.842619\pi$
$977$		−	927.224i		−	0.949052i	0.880241	−	0.474526i	$-0.157381\pi$
$978$		0			0
$979$	−40.3932			−0.0412597
$980$	113.970	−	162.991i	0.116296	−	0.166318i
$981$		0			0
$982$	174.877	+	192.455i	0.178082	+	0.195983i
$983$	−354.106			−0.360230			−0.180115	−	0.983646i	$-0.557647\pi$
$983$	−354.106			−0.360230			−0.180115	+	0.983646i	$0.557647\pi$
$984$		0			0
$985$	−1341.88	−	758.677i	−1.36231	−	0.770230i
$986$	126.833	+	139.582i	0.128634	+	0.141564i
$987$		0			0
$988$	41.3826	−	431.383i	0.0418852	−	0.436623i
$989$		−	90.6396i		−	0.0916478i
$990$		0			0
$991$			537.545i			0.542427i	0.962519	+	0.271213i	$0.0874249\pi$
$991$			537.545i			0.542427i	−0.962519	+	0.271213i	$0.912575\pi$
$992$	−601.817	+	365.925i	−0.606671	+	0.368876i
$993$		0			0
$994$	921.305	−	837.154i	0.926866	−	0.842207i
$995$	609.941	−	1078.81i	0.613006	−	1.08423i
$996$		0			0
$997$	441.759			0.443088			0.221544	−	0.975150i	$-0.428890\pi$
$997$	441.759			0.443088			0.221544	+	0.975150i	$0.428890\pi$
$998$	−893.326	−	983.123i	−0.895116	−	0.985094i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	360.3.p.g.19.1		8
3.2	odd	2		40.3.e.c.19.8	yes	8
4.3	odd	2		1440.3.p.g.559.1		8
5.4	even	2	inner	360.3.p.g.19.8		8
8.3	odd	2	inner	360.3.p.g.19.7		8
8.5	even	2		1440.3.p.g.559.8		8
12.11	even	2		160.3.e.c.79.8		8
15.2	even	4		200.3.g.h.51.4		8
15.8	even	4		200.3.g.h.51.5		8
15.14	odd	2		40.3.e.c.19.1	✓	8
20.19	odd	2		1440.3.p.g.559.7		8
24.5	odd	2		160.3.e.c.79.7		8
24.11	even	2		40.3.e.c.19.2	yes	8
40.19	odd	2	inner	360.3.p.g.19.2		8
40.29	even	2		1440.3.p.g.559.2		8
48.5	odd	4		1280.3.h.m.1279.2		16
48.11	even	4		1280.3.h.m.1279.14		16
48.29	odd	4		1280.3.h.m.1279.15		16
48.35	even	4		1280.3.h.m.1279.3		16
60.23	odd	4		800.3.g.h.751.1		8
60.47	odd	4		800.3.g.h.751.8		8
60.59	even	2		160.3.e.c.79.1		8
120.29	odd	2		160.3.e.c.79.2		8
120.53	even	4		800.3.g.h.751.2		8
120.59	even	2		40.3.e.c.19.7	yes	8
120.77	even	4		800.3.g.h.751.7		8
120.83	odd	4		200.3.g.h.51.6		8
120.107	odd	4		200.3.g.h.51.3		8
240.29	odd	4		1280.3.h.m.1279.4		16
240.59	even	4		1280.3.h.m.1279.1		16
240.149	odd	4		1280.3.h.m.1279.13		16
240.179	even	4		1280.3.h.m.1279.16		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
40.3.e.c.19.1	✓	8	15.14	odd	2
40.3.e.c.19.2	yes	8	24.11	even	2
40.3.e.c.19.7	yes	8	120.59	even	2
40.3.e.c.19.8	yes	8	3.2	odd	2
160.3.e.c.79.1		8	60.59	even	2
160.3.e.c.79.2		8	120.29	odd	2
160.3.e.c.79.7		8	24.5	odd	2
160.3.e.c.79.8		8	12.11	even	2
200.3.g.h.51.3		8	120.107	odd	4
200.3.g.h.51.4		8	15.2	even	4
200.3.g.h.51.5		8	15.8	even	4
200.3.g.h.51.6		8	120.83	odd	4
360.3.p.g.19.1		8	1.1	even	1	trivial
360.3.p.g.19.2		8	40.19	odd	2	inner
360.3.p.g.19.7		8	8.3	odd	2	inner
360.3.p.g.19.8		8	5.4	even	2	inner
800.3.g.h.751.1		8	60.23	odd	4
800.3.g.h.751.2		8	120.53	even	4
800.3.g.h.751.7		8	120.77	even	4
800.3.g.h.751.8		8	60.47	odd	4
1280.3.h.m.1279.1		16	240.59	even	4
1280.3.h.m.1279.2		16	48.5	odd	4
1280.3.h.m.1279.3		16	48.35	even	4
1280.3.h.m.1279.4		16	240.29	odd	4
1280.3.h.m.1279.13		16	240.149	odd	4
1280.3.h.m.1279.14		16	48.11	even	4
1280.3.h.m.1279.15		16	48.29	odd	4
1280.3.h.m.1279.16		16	240.179	even	4
1440.3.p.g.559.1		8	4.3	odd	2
1440.3.p.g.559.2		8	40.29	even	2
1440.3.p.g.559.7		8	20.19	odd	2
1440.3.p.g.559.8		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:	\( N \)	\(=\)	\( 360 = 2^{3} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	360.p (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.34500 - 1.48020i) q^{2} +(-0.381966 + 3.98172i) q^{4} +(-4.35250 - 2.46084i) q^{5} -7.67752 q^{7} +(6.40747 - 4.79002i) q^{8} +(2.21158 + 9.75238i) q^{10} +0.472136 q^{11} -4.10995 q^{13} +(10.3262 + 11.3642i) q^{14} +(-15.7082 - 3.04176i) q^{16} +2.26154i q^{17} +26.3607 q^{19} +(11.4609 - 16.3905i) q^{20} +(-0.635021 - 0.698854i) q^{22} +9.73249 q^{23} +(12.8885 + 21.4216i) q^{25} +(5.52786 + 6.08353i) q^{26} +(2.93255 - 30.5697i) q^{28} +41.6971i q^{29} +22.0104i q^{31} +(16.6251 + 27.3424i) q^{32} +(3.34752 - 3.04176i) q^{34} +(33.4164 + 18.8931i) q^{35} +51.7449 q^{37} +(-35.4550 - 39.0190i) q^{38} +(-39.6760 + 5.08080i) q^{40} -15.0557 q^{41} -9.31310i q^{43} +(-0.180340 + 1.87991i) q^{44} +(-13.0902 - 14.4060i) q^{46} +8.76226 q^{47} +9.94427 q^{49} +(14.3732 - 47.8896i) q^{50} +(1.56986 - 16.3647i) q^{52} +39.9002 q^{53} +(-2.05497 - 1.16185i) q^{55} +(-49.1935 + 36.7754i) q^{56} +(61.7200 - 56.0825i) q^{58} +77.1935 q^{59} -14.7650i q^{61} +(32.5797 - 29.6039i) q^{62} +(18.1115 - 61.3838i) q^{64} +(17.8885 + 10.1139i) q^{65} +75.8395i q^{67} +(-9.00482 - 0.863831i) q^{68} +(-16.9794 - 74.8741i) q^{70} -81.0705i q^{71} +83.4249i q^{73} +(-69.5967 - 76.5927i) q^{74} +(-10.0689 + 104.961i) q^{76} -3.62483 q^{77} -100.757i q^{79} +(60.8847 + 51.8946i) q^{80} +(20.2499 + 22.2854i) q^{82} -0.266939i q^{83} +(5.56528 - 9.84336i) q^{85} +(-13.7852 + 12.5261i) q^{86} +(3.02520 - 2.26154i) q^{88} -85.5542 q^{89} +31.5542 q^{91} +(-3.71748 + 38.7521i) q^{92} +(-11.7852 - 12.9699i) q^{94} +(-114.735 - 64.8694i) q^{95} +99.1297i q^{97} +(-13.3750 - 14.7195i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 12 q^{4} + 20 q^{10} - 32 q^{11} + 20 q^{14} - 72 q^{16} + 32 q^{19} - 20 q^{20} - 40 q^{25} + 80 q^{26} + 152 q^{34} + 160 q^{35} - 80 q^{40} - 192 q^{41} + 88 q^{44} - 60 q^{46} + 8 q^{49} + 200 q^{50}+ \cdots - 300 q^{94}+O(q^{100}) \) 8 * q - 12 * q^4 + 20 * q^10 - 32 * q^11 + 20 * q^14 - 72 * q^16 + 32 * q^19 - 20 * q^20 - 40 * q^25 + 80 * q^26 + 152 * q^34 + 160 * q^35 - 80 * q^40 - 192 * q^41 + 88 * q^44 - 60 * q^46 + 8 * q^49 + 200 * q^50 + 224 * q^59 + 288 * q^64 + 340 * q^70 - 360 * q^74 + 152 * q^76 + 280 * q^80 - 316 * q^86 - 112 * q^89 - 320 * q^91 - 300 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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