LMFDB - Embedded newform 180.3.c.c.91.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("180.91");

S:= CuspForms(chi, 3);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.90464475849$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.15012375625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 7x^{6} + 28x^{4} + 112x^{2} + 256 $ x^8 + 7x^6 + 28x^4 + 112*x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{10} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			91.2
Root			$1.46040 + 1.36646i$ of defining polynomial
Character	$\chi$	$=$	180.91
Dual form			180.3.c.c.91.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.46040 + 1.36646i) q^{2} +(0.265564 - 3.99117i) q^{4} -2.23607 q^{5} -1.87135i q^{7} +(5.06596 + 6.19161i) q^{8} +O(q^{10})$	\(q+(-1.46040 + 1.36646i) q^{2} +(0.265564 - 3.99117i) q^{4} -2.23607 q^{5} -1.87135i q^{7} +(5.06596 + 6.19161i) q^{8} +(3.26556 - 3.05550i) q^{10} +15.1162i q^{11} +18.1245 q^{13} +(2.55712 + 2.73292i) q^{14} +(-15.8590 - 2.11983i) q^{16} +12.6890 q^{17} +28.1867i q^{19} +(-0.593820 + 8.92454i) q^{20} +(-20.6556 - 22.0757i) q^{22} +10.9317i q^{23} +5.00000 q^{25} +(-26.4691 + 24.7665i) q^{26} +(-7.46887 - 0.496963i) q^{28} -9.95007 q^{29} +24.4440i q^{31} +(26.0572 - 18.5748i) q^{32} +(-18.5311 + 17.3391i) q^{34} +4.18446i q^{35} +17.8755 q^{37} +(-38.5161 - 41.1640i) q^{38} +(-11.3278 - 13.8449i) q^{40} -28.8444 q^{41} +56.3734i q^{43} +(60.3312 + 4.01431i) q^{44} +(-14.9377 - 15.9647i) q^{46} -49.5329i q^{47} +45.4981 q^{49} +(-7.30202 + 6.83231i) q^{50} +(4.81323 - 72.3381i) q^{52} +60.1494 q^{53} -33.8007i q^{55} +(11.5867 - 9.48016i) q^{56} +(14.5311 - 13.5964i) q^{58} -110.939i q^{59} +34.2490 q^{61} +(-33.4018 - 35.6982i) q^{62} +(-12.6722 + 62.7329i) q^{64} -40.5276 q^{65} -131.460i q^{67} +(3.36976 - 50.6442i) q^{68} +(-5.71790 - 6.11100i) q^{70} +52.0957i q^{71} -62.2490 q^{73} +(-26.1054 + 24.4262i) q^{74} +(112.498 + 7.48539i) q^{76} +28.2876 q^{77} +103.274i q^{79} +(35.4617 + 4.74008i) q^{80} +(42.1245 - 39.4148i) q^{82} +57.2212i q^{83} -28.3735 q^{85} +(-77.0321 - 82.3280i) q^{86} +(-93.5934 + 76.5778i) q^{88} -145.120 q^{89} -33.9173i q^{91} +(43.6303 + 2.90307i) q^{92} +(67.6848 + 72.3381i) q^{94} -63.0274i q^{95} -66.7471 q^{97} +(-66.4456 + 62.1714i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 14 q^{4}+O(q^{10}) $ 8 * q - 14 * q^4	$ 8 q - 14 q^{4} + 10 q^{10} + 16 q^{13} - 14 q^{16} - 4 q^{22} + 40 q^{25} - 92 q^{28} - 116 q^{34} + 272 q^{37} - 10 q^{40} - 184 q^{46} - 152 q^{49} + 232 q^{52} + 84 q^{58} + 16 q^{61} - 182 q^{64} + 180 q^{70} - 240 q^{73} + 384 q^{76} + 208 q^{82} + 160 q^{85} - 652 q^{88} - 168 q^{94} + 240 q^{97}+O(q^{100}) $ 8 * q - 14 * q^4 + 10 * q^10 + 16 * q^13 - 14 * q^16 - 4 * q^22 + 40 * q^25 - 92 * q^28 - 116 * q^34 + 272 * q^37 - 10 * q^40 - 184 * q^46 - 152 * q^49 + 232 * q^52 + 84 * q^58 + 16 * q^61 - 182 * q^64 + 180 * q^70 - 240 * q^73 + 384 * q^76 + 208 * q^82 + 160 * q^85 - 652 * q^88 - 168 * q^94 + 240 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−1.46040	+	1.36646i	−0.730202	+	0.683231i
$2$	−1.46040	+	1.36646i	−0.730202	+	0.683231i
$3$		0			0
$3$		0			0
$4$	0.265564	−	3.99117i	0.0663911	−	0.997794i
$5$	−2.23607			−0.447214
$5$	−2.23607			−0.447214
$6$		0			0
$7$		−	1.87135i		−	0.267335i	−0.991026	−	0.133668i	$-0.957325\pi$
$7$		−	1.87135i		−	0.267335i	0.991026	−	0.133668i	$-0.0426755\pi$
$8$	5.06596	+	6.19161i	0.633245	+	0.773952i
$9$		0			0
$10$	3.26556	−	3.05550i	0.326556	−	0.305550i
$11$			15.1162i			1.37420i	0.726565	+	0.687098i	$0.241116\pi$
$11$			15.1162i			1.37420i	−0.726565	+	0.687098i	$0.758884\pi$
$12$		0			0
$13$	18.1245			1.39419			0.697097	−	0.716977i	$-0.254475\pi$
$13$	18.1245			1.39419			0.697097	+	0.716977i	$0.254475\pi$
$14$	2.55712	+	2.73292i	0.182652	+	0.195209i
$15$		0			0
$16$	−15.8590	−	2.11983i	−0.991184	−	0.132489i
$17$	12.6890			0.746414			0.373207	−	0.927748i	$-0.378258\pi$
$17$	12.6890			0.746414			0.373207	+	0.927748i	$0.378258\pi$
$18$		0			0
$19$			28.1867i			1.48351i	0.670671	+	0.741755i	$0.266006\pi$
$19$			28.1867i			1.48351i	−0.670671	+	0.741755i	$0.733994\pi$
$20$	−0.593820	+	8.92454i	−0.0296910	+	0.446227i
$21$		0			0
$22$	−20.6556	−	22.0757i	−0.938893	−	1.00344i
$23$			10.9317i			0.475291i	0.971352	+	0.237646i	$0.0763757\pi$
$23$			10.9317i			0.475291i	−0.971352	+	0.237646i	$0.923624\pi$
$24$		0			0
$25$	5.00000			0.200000
$26$	−26.4691	+	24.7665i	−1.01804	+	0.952556i
$27$		0			0
$28$	−7.46887	−	0.496963i	−0.266745	−	0.0177487i
$29$	−9.95007			−0.343106			−0.171553	−	0.985175i	$-0.554878\pi$
$29$	−9.95007			−0.343106			−0.171553	+	0.985175i	$0.554878\pi$
$30$		0			0
$31$			24.4440i			0.788516i	0.919000	+	0.394258i	$0.128998\pi$
$31$			24.4440i			0.788516i	−0.919000	+	0.394258i	$0.871002\pi$
$32$	26.0572	−	18.5748i	0.814286	−	0.580464i
$33$		0			0
$34$	−18.5311	+	17.3391i	−0.545033	+	0.509973i
$35$			4.18446i			0.119556i
$36$		0			0
$37$	17.8755			0.483121			0.241561	−	0.970386i	$-0.422341\pi$
$37$	17.8755			0.483121			0.241561	+	0.970386i	$0.422341\pi$
$38$	−38.5161	−	41.1640i	−1.01358	−	1.08326i
$39$		0			0
$40$	−11.3278	−	13.8449i	−0.283196	−	0.346122i
$41$	−28.8444			−0.703522			−0.351761	−	0.936090i	$-0.614417\pi$
$41$	−28.8444			−0.703522			−0.351761	+	0.936090i	$0.614417\pi$
$42$		0			0
$43$			56.3734i			1.31101i	0.755191	+	0.655505i	$0.227544\pi$
$43$			56.3734i			1.31101i	−0.755191	+	0.655505i	$0.772456\pi$
$44$	60.3312	+	4.01431i	1.37116	+	0.0912344i
$45$		0			0
$46$	−14.9377	−	15.9647i	−0.324734	−	0.347059i
$47$		−	49.5329i		−	1.05389i	−0.849899	−	0.526946i	$-0.823337\pi$
$47$		−	49.5329i		−	1.05389i	0.849899	−	0.526946i	$-0.176663\pi$
$48$		0			0
$49$	45.4981			0.928532
$50$	−7.30202	+	6.83231i	−0.146040	+	0.136646i
$51$		0			0
$52$	4.81323	−	72.3381i	0.0925621	−	1.39112i
$53$	60.1494			1.13489			0.567447	−	0.823410i	$-0.307931\pi$
$53$	60.1494			1.13489			0.567447	+	0.823410i	$0.307931\pi$
$54$		0			0
$55$		−	33.8007i		−	0.614559i
$56$	11.5867	−	9.48016i	0.206905	−	0.169289i
$57$		0			0
$58$	14.5311	−	13.5964i	0.250537	−	0.234421i
$59$		−	110.939i		−	1.88032i	−0.340739	−	0.940158i	$-0.610677\pi$
$59$		−	110.939i		−	1.88032i	0.340739	−	0.940158i	$-0.389323\pi$
$60$		0			0
$61$	34.2490			0.561460			0.280730	−	0.959787i	$-0.409424\pi$
$61$	34.2490			0.561460			0.280730	+	0.959787i	$0.409424\pi$
$62$	−33.4018	−	35.6982i	−0.538739	−	0.575777i
$63$		0			0
$64$	−12.6722	+	62.7329i	−0.198003	+	0.980201i
$65$	−40.5276			−0.623502
$66$		0			0
$67$		−	131.460i		−	1.96209i	−0.193770	−	0.981047i	$-0.562072\pi$
$67$		−	131.460i		−	1.96209i	0.193770	−	0.981047i	$-0.437928\pi$
$68$	3.36976	−	50.6442i	0.0495552	−	0.744767i
$69$		0			0
$70$	−5.71790	−	6.11100i	−0.0816843	−	0.0873000i
$71$			52.0957i			0.733742i	0.930272	+	0.366871i	$0.119571\pi$
$71$			52.0957i			0.733742i	−0.930272	+	0.366871i	$0.880429\pi$
$72$		0			0
$73$	−62.2490			−0.852726			−0.426363	−	0.904552i	$-0.640205\pi$
$73$	−62.2490			−0.852726			−0.426363	+	0.904552i	$0.640205\pi$
$74$	−26.1054	+	24.4262i	−0.352776	+	0.330083i
$75$		0			0
$76$	112.498	+	7.48539i	1.48024	+	0.0984919i
$77$	28.2876			0.367371
$78$		0			0
$79$			103.274i			1.30726i	0.756814	+	0.653630i	$0.226755\pi$
$79$			103.274i			1.30726i	−0.756814	+	0.653630i	$0.773245\pi$
$80$	35.4617	+	4.74008i	0.443271	+	0.0592510i
$81$		0			0
$82$	42.1245	−	39.4148i	0.513714	−	0.480668i
$83$			57.2212i			0.689413i	0.938711	+	0.344706i	$0.112021\pi$
$83$			57.2212i			0.689413i	−0.938711	+	0.344706i	$0.887979\pi$
$84$		0			0
$85$	−28.3735			−0.333806
$86$	−77.0321	−	82.3280i	−0.895722	−	0.957302i
$87$		0			0
$88$	−93.5934	+	76.5778i	−1.06356	+	0.870202i
$89$	−145.120			−1.63056			−0.815281	−	0.579066i	$-0.803417\pi$
$89$	−145.120			−1.63056			−0.815281	+	0.579066i	$0.803417\pi$
$90$		0			0
$91$		−	33.9173i		−	0.372717i
$92$	43.6303	+	2.90307i	0.474242	+	0.0315551i
$93$		0			0
$94$	67.6848	+	72.3381i	0.720051	+	0.769554i
$95$		−	63.0274i		−	0.663446i
$96$		0			0
$97$	−66.7471			−0.688114			−0.344057	−	0.938949i	$-0.611801\pi$
$97$	−66.7471			−0.688114			−0.344057	+	0.938949i	$0.611801\pi$
$98$	−66.4456	+	62.1714i	−0.678016	+	0.634402i
$99$		0			0
$100$	1.32782	−	19.9559i	0.0132782	−	0.199559i
$101$	164.571			1.62942			0.814709	−	0.579871i	$-0.196897\pi$
$101$	164.571			1.62942			0.814709	+	0.579871i	$0.196897\pi$
$102$		0			0
$103$		−	43.2740i		−	0.420136i	−0.977687	−	0.210068i	$-0.932631\pi$
$103$		−	43.2740i		−	0.420136i	0.977687	−	0.210068i	$-0.0673685\pi$
$104$	91.8180	+	112.220i	0.882865	+	1.07904i
$105$		0			0
$106$	−87.8424	+	82.1918i	−0.828702	+	0.775394i
$107$			173.025i			1.61706i	0.588458	+	0.808528i	$0.299735\pi$
$107$			173.025i			1.61706i	−0.588458	+	0.808528i	$0.700265\pi$
$108$		0			0
$109$	−162.498			−1.49081			−0.745404	−	0.666613i	$-0.767743\pi$
$109$	−162.498			−1.49081			−0.745404	+	0.666613i	$0.767743\pi$
$110$	46.1874	+	49.3628i	0.419886	+	0.448752i
$111$		0			0
$112$	−3.96693	+	29.6776i	−0.0354190	+	0.264979i
$113$	72.3895			0.640615			0.320307	−	0.947314i	$-0.396214\pi$
$113$	72.3895			0.640615			0.320307	+	0.947314i	$0.396214\pi$
$114$		0			0
$115$		−	24.4440i		−	0.212557i
$116$	−2.64238	+	39.7125i	−0.0227792	+	0.342349i
$117$		0			0
$118$	151.593	+	162.015i	1.28469	+	1.37301i
$119$		−	23.7456i		−	0.199543i
$120$		0			0
$121$	−107.498			−0.888414
$122$	−50.0174	+	46.8000i	−0.409979	+	0.383606i
$123$		0			0
$124$	97.5603	+	6.49146i	0.786777	+	0.0523505i
$125$	−11.1803			−0.0894427
$126$		0			0
$127$		−	148.535i		−	1.16957i	−0.811188	−	0.584785i	$-0.801179\pi$
$127$		−	148.535i		−	1.16957i	0.811188	−	0.584785i	$-0.198821\pi$
$128$	−67.2156	−	108.931i	−0.525122	−	0.851027i
$129$		0			0
$130$	59.1868	−	55.3795i	0.455283	−	0.425996i
$131$		−	26.7284i		−	0.204034i	−0.994783	−	0.102017i	$-0.967470\pi$
$131$		−	26.7284i		−	0.204034i	0.994783	−	0.102017i	$-0.0325296\pi$
$132$		0			0
$133$	52.7471			0.396595
$134$	179.635	+	191.985i	1.34056	+	1.43273i
$135$		0			0
$136$	64.2821	+	78.5656i	0.472662	+	0.577688i
$137$	−126.953			−0.926664			−0.463332	−	0.886185i	$-0.653346\pi$
$137$	−126.953			−0.926664			−0.463332	+	0.886185i	$0.653346\pi$
$138$		0			0
$139$		−	20.7013i		−	0.148930i	−0.997224	−	0.0744652i	$-0.976275\pi$
$139$		−	20.7013i		−	0.148930i	0.997224	−	0.0744652i	$-0.0237250\pi$
$140$	16.7009	+	1.11124i	0.119292	+	0.00793745i
$141$		0			0
$142$	−71.1868	−	76.0808i	−0.501315	−	0.535780i
$143$			273.973i			1.91589i
$144$		0			0
$145$	22.2490			0.153442
$146$	90.9088	−	85.0609i	0.622663	−	0.582609i
$147$		0			0
$148$	4.74709	−	71.3442i	0.0320750	−	0.482055i
$149$	−167.140			−1.12174			−0.560871	−	0.827903i	$-0.689534\pi$
$149$	−167.140			−1.12174			−0.560871	+	0.827903i	$0.689534\pi$
$150$		0			0
$151$		−	65.6136i		−	0.434527i	−0.976113	−	0.217264i	$-0.930287\pi$
$151$		−	65.6136i		−	0.434527i	0.976113	−	0.217264i	$-0.0697132\pi$
$152$	−174.521	+	142.793i	−1.14817	+	0.939425i
$153$		0			0
$154$	−41.3113	+	38.6539i	−0.268255	+	0.250999i
$155$		−	54.6585i		−	0.352635i
$156$		0			0
$157$	−30.3735			−0.193462			−0.0967310	−	0.995311i	$-0.530839\pi$
$157$	−30.3735			−0.193462			−0.0967310	+	0.995311i	$0.530839\pi$
$158$	−141.119	−	150.821i	−0.893161	−	0.954565i
$159$		0			0
$160$	−58.2656	+	41.5346i	−0.364160	+	0.259591i
$161$	20.4570			0.127062
$162$		0			0
$163$		−	45.1453i		−	0.276965i	−0.990365	−	0.138483i	$-0.955777\pi$
$163$		−	45.1453i		−	0.276965i	0.990365	−	0.138483i	$-0.0442225\pi$
$164$	−7.66005	+	115.123i	−0.0467076	+	0.701970i
$165$		0			0
$166$	−78.1906	−	83.5662i	−0.471028	−	0.503411i
$167$		−	32.7951i		−	0.196378i	−0.995168	−	0.0981889i	$-0.968695\pi$
$167$		−	32.7951i		−	0.196378i	0.995168	−	0.0981889i	$-0.0313049\pi$
$168$		0			0
$169$	159.498			0.943776
$170$	41.4369	−	38.7714i	0.243746	−	0.228067i
$171$		0			0
$172$	224.996	+	14.9708i	1.30812	+	0.0870394i
$173$	316.067			1.82698			0.913488	−	0.406865i	$-0.133378\pi$
$173$	316.067			1.82698			0.913488	+	0.406865i	$0.133378\pi$
$174$		0			0
$175$		−	9.35673i		−	0.0534670i
$176$	32.0436	−	239.726i	0.182066	−	1.36208i
$177$		0			0
$178$	211.934	−	198.301i	1.19064	−	1.11405i
$179$		−	258.857i		−	1.44613i	−0.690781	−	0.723064i	$-0.742733\pi$
$179$		−	258.857i		−	1.44613i	0.690781	−	0.723064i	$-0.257267\pi$
$180$		0			0
$181$	−74.4981			−0.411592			−0.205796	−	0.978595i	$-0.565978\pi$
$181$	−74.4981			−0.411592			−0.205796	+	0.978595i	$0.565978\pi$
$182$	46.3466	+	49.5329i	0.254652	+	0.272159i
$183$		0			0
$184$	−67.6848	+	55.3795i	−0.367852	+	0.300975i
$185$	−39.9708			−0.216058
$186$		0			0
$187$			191.809i			1.02572i
$188$	−197.695	−	13.1542i	−1.05157	−	0.0699690i
$189$		0			0
$190$	86.1245	+	92.0455i	0.453287	+	0.484450i
$191$		−	63.7080i		−	0.333550i	−0.985995	−	0.166775i	$-0.946665\pi$
$191$		−	63.7080i		−	0.333550i	0.985995	−	0.166775i	$-0.0533353\pi$
$192$		0			0
$193$	45.5019			0.235761			0.117881	−	0.993028i	$-0.462390\pi$
$193$	45.5019			0.235761			0.117881	+	0.993028i	$0.462390\pi$
$194$	97.4778	−	91.2074i	0.502463	−	0.470141i
$195$		0			0
$196$	12.0827	−	181.591i	0.0616463	−	0.926483i
$197$	185.926			0.943787			0.471893	−	0.881656i	$-0.343571\pi$
$197$	185.926			0.943787			0.471893	+	0.881656i	$0.343571\pi$
$198$		0			0
$199$		−	155.904i		−	0.783439i	−0.920085	−	0.391719i	$-0.871880\pi$
$199$		−	155.904i		−	0.783439i	0.920085	−	0.391719i	$-0.128120\pi$
$200$	25.3298	+	30.9581i	0.126649	+	0.154790i
$201$		0			0
$202$	−240.340	+	224.880i	−1.18980	+	1.11327i
$203$			18.6200i			0.0917243i
$204$		0			0
$205$	64.4981			0.314625
$206$	59.1322	+	63.1975i	0.287050	+	0.306784i
$207$		0			0
$208$	−287.436	−	38.4209i	−1.38190	−	0.184716i
$209$	−426.075			−2.03863
$210$		0			0
$211$			242.219i			1.14796i	0.818870	+	0.573979i	$0.194601\pi$
$211$			242.219i			1.14796i	−0.818870	+	0.573979i	$0.805399\pi$
$212$	15.9735	−	240.067i	0.0753468	−	1.13239i
$213$		0			0
$214$	−236.432	−	252.686i	−1.10482	−	1.18078i
$215$		−	126.055i		−	0.586301i
$216$		0			0
$217$	45.7432			0.210798
$218$	237.313	−	222.047i	1.08859	−	1.01857i
$219$		0			0
$220$	−134.905	−	8.97628i	−0.613203	−	0.0408013i
$221$	229.983			1.04065
$222$		0			0
$223$			250.054i			1.12132i	0.828046	+	0.560660i	$0.189452\pi$
$223$			250.054i			1.12132i	−0.828046	+	0.560660i	$0.810548\pi$
$224$	−34.7600	−	48.7620i	−0.155178	−	0.217687i
$225$		0			0
$226$	−105.718	+	98.9174i	−0.467778	+	0.437688i
$227$		−	60.4646i		−	0.266364i	−0.991092	−	0.133182i	$-0.957481\pi$
$227$		−	60.4646i		−	0.266364i	0.991092	−	0.133182i	$-0.0425195\pi$
$228$		0			0
$229$	78.2490			0.341699			0.170849	−	0.985297i	$-0.445349\pi$
$229$	78.2490			0.341699			0.170849	+	0.985297i	$0.445349\pi$
$230$	33.4018	+	35.6982i	0.145225	+	0.155209i
$231$		0			0
$232$	−50.4066	−	61.6070i	−0.217270	−	0.265547i
$233$	−164.742			−0.707046			−0.353523	−	0.935426i	$-0.615016\pi$
$233$	−164.742			−0.707046			−0.353523	+	0.935426i	$0.615016\pi$
$234$		0			0
$235$			110.759i			0.471315i
$236$	−442.775	−	29.4614i	−1.87617	−	0.124836i
$237$		0			0
$238$	32.4474	+	34.6782i	0.136334	+	0.145707i
$239$		−	243.741i		−	1.01984i	−0.860223	−	0.509918i	$-0.829676\pi$
$239$		−	243.741i		−	1.01984i	0.860223	−	0.509918i	$-0.170324\pi$
$240$		0			0
$241$	383.494			1.59126			0.795631	−	0.605781i	$-0.207139\pi$
$241$	383.494			1.59126			0.795631	+	0.605781i	$0.207139\pi$
$242$	156.991	−	146.892i	0.648722	−	0.606992i
$243$		0			0
$244$	9.09532	−	136.694i	0.0372759	−	0.560221i
$245$	−101.737			−0.415252
$246$		0			0
$247$			510.870i			2.06830i
$248$	−151.348	+	123.832i	−0.610274	+	0.499324i
$249$		0			0
$250$	16.3278	−	15.2775i	0.0653113	−	0.0611100i
$251$			199.753i			0.795830i	0.917422	+	0.397915i	$0.130266\pi$
$251$			199.753i			0.795830i	−0.917422	+	0.397915i	$0.869734\pi$
$252$		0			0
$253$	−165.245			−0.653143
$254$	202.968	+	216.922i	0.799086	+	0.854023i
$255$		0			0
$256$	247.013	+	67.2365i	0.964893	+	0.262643i
$257$	−158.366			−0.616209			−0.308105	−	0.951352i	$-0.599695\pi$
$257$	−158.366			−0.616209			−0.308105	+	0.951352i	$0.599695\pi$
$258$		0			0
$259$		−	33.4512i		−	0.129155i
$260$	−10.7627	+	161.753i	−0.0413950	+	0.622127i
$261$		0			0
$262$	36.5234	+	39.0343i	0.139402	+	0.148986i
$263$		−	121.610i		−	0.462395i	−0.972907	−	0.231197i	$-0.925736\pi$
$263$		−	121.610i		−	0.462395i	0.972907	−	0.231197i	$-0.0742643\pi$
$264$		0			0
$265$	−134.498			−0.507540
$266$	−77.0321	+	72.0769i	−0.289594	+	0.270966i
$267$		0			0
$268$	−524.681	−	34.9112i	−1.95776	−	0.130266i
$269$	414.670			1.54152			0.770762	−	0.637124i	$-0.219876\pi$
$269$	414.670			1.54152			0.770762	+	0.637124i	$0.219876\pi$
$270$		0			0
$271$		−	193.331i		−	0.713399i	−0.934219	−	0.356700i	$-0.883902\pi$
$271$		−	193.331i		−	0.713399i	0.934219	−	0.356700i	$-0.116098\pi$
$272$	−201.235	−	26.8986i	−0.739834	−	0.0988918i
$273$		0			0
$274$	185.403	−	173.476i	0.676652	−	0.633126i
$275$			75.5808i			0.274839i
$276$		0			0
$277$	472.615			1.70619			0.853095	−	0.521755i	$-0.174722\pi$
$277$	472.615			1.70619			0.853095	+	0.521755i	$0.174722\pi$
$278$	28.2876	+	30.2323i	0.101754	+	0.108749i
$279$		0			0
$280$	−25.9086	+	21.1983i	−0.0925305	+	0.0757081i
$281$	−256.815			−0.913934			−0.456967	−	0.889484i	$-0.651064\pi$
$281$	−256.815			−0.913934			−0.456967	+	0.889484i	$0.651064\pi$
$282$		0			0
$283$		−	416.837i		−	1.47292i	−0.676480	−	0.736461i	$-0.736495\pi$
$283$		−	416.837i		−	1.47292i	0.676480	−	0.736461i	$-0.263505\pi$
$284$	207.923	+	13.8348i	0.732123	+	0.0487140i
$285$		0			0
$286$	−374.374	−	400.111i	−1.30900	−	1.39899i
$287$			53.9779i			0.188076i
$288$		0			0
$289$	−127.988			−0.442866
$290$	−32.4926	+	30.4025i	−0.112043	+	0.104836i
$291$		0			0
$292$	−16.5311	+	248.447i	−0.0566135	+	0.850845i
$293$	240.705			0.821520			0.410760	−	0.911744i	$-0.365263\pi$
$293$	240.705			0.821520			0.410760	+	0.911744i	$0.365263\pi$
$294$		0			0
$295$			248.066i			0.840903i
$296$	90.5564	+	110.678i	0.305934	+	0.373913i
$297$		0			0
$298$	244.091	−	228.390i	0.819099	−	0.766409i
$299$			198.132i			0.662648i
$300$		0			0
$301$	105.494			0.350479
$302$	89.6585	+	95.8225i	0.296883	+	0.317293i
$303$		0			0
$304$	59.7510	−	447.012i	0.196549	−	1.47043i
$305$	−76.5832			−0.251092
$306$		0			0
$307$			206.547i			0.672792i	0.941721	+	0.336396i	$0.109208\pi$
$307$			206.547i			0.672792i	−0.941721	+	0.336396i	$0.890792\pi$
$308$	7.51217	−	112.901i	0.0243902	−	0.366560i
$309$		0			0
$310$	74.6887	+	79.8235i	0.240931	+	0.257495i
$311$			458.610i			1.47463i	0.675549	+	0.737315i	$0.263907\pi$
$311$			458.610i			1.47463i	−0.675549	+	0.737315i	$0.736093\pi$
$312$		0			0
$313$	383.992			1.22681			0.613406	−	0.789768i	$-0.289799\pi$
$313$	383.992			1.22681			0.613406	+	0.789768i	$0.289799\pi$
$314$	44.3577	−	41.5043i	0.141266	−	0.132179i
$315$		0			0
$316$	412.183	+	27.4258i	1.30438	+	0.0867905i
$317$	429.433			1.35468			0.677339	−	0.735671i	$-0.263133\pi$
$317$	429.433			1.35468			0.677339	+	0.735671i	$0.263133\pi$
$318$		0			0
$319$		−	150.407i		−	0.471495i
$320$	28.3359	−	140.275i	0.0885495	−	0.438359i
$321$		0			0
$322$	−29.8755	+	27.9537i	−0.0927810	+	0.0868127i
$323$			357.662i			1.10731i
$324$		0			0
$325$	90.6226			0.278839
$326$	61.6894	+	65.9305i	0.189231	+	0.202241i
$327$		0			0
$328$	−146.125	−	178.593i	−0.445502	−	0.544492i
$329$	−92.6933			−0.281742
$330$		0			0
$331$		−	58.1282i		−	0.175614i	−0.996138	−	0.0878070i	$-0.972014\pi$
$331$		−	58.1282i		−	0.175614i	0.996138	−	0.0878070i	$-0.0279859\pi$
$332$	228.380	+	15.1959i	0.687892	+	0.0457709i
$333$		0			0
$334$	44.8132	+	47.8941i	0.134171	+	0.143395i
$335$			293.954i			0.877475i
$336$		0			0
$337$	−405.751			−1.20401			−0.602004	−	0.798493i	$-0.705631\pi$
$337$	−405.751			−1.20401			−0.602004	+	0.798493i	$0.705631\pi$
$338$	−232.932	+	217.948i	−0.689147	+	0.644817i
$339$		0			0
$340$	−7.53500	+	113.244i	−0.0221618	+	0.333070i
$341$	−369.499			−1.08358
$342$		0			0
$343$		−	176.839i		−	0.515565i
$344$	−349.042	+	285.585i	−1.01466	+	0.830190i
$345$		0			0
$346$	−461.586	+	431.893i	−1.33406	+	1.24825i
$347$		−	324.186i		−	0.934255i	−0.884190	−	0.467127i	$-0.845289\pi$
$347$		−	324.186i		−	0.934255i	0.884190	−	0.467127i	$-0.154711\pi$
$348$		0			0
$349$	34.7471			0.0995619			0.0497809	−	0.998760i	$-0.484148\pi$
$349$	34.7471			0.0995619			0.0497809	+	0.998760i	$0.484148\pi$
$350$	12.7856	+	13.6646i	0.0365303	+	0.0390418i
$351$		0			0
$352$	280.780	+	393.884i	0.797671	+	1.11899i
$353$	−13.5869			−0.0384899			−0.0192449	−	0.999815i	$-0.506126\pi$
$353$	−13.5869			−0.0384899			−0.0192449	+	0.999815i	$0.506126\pi$
$354$		0			0
$355$		−	116.490i		−	0.328139i
$356$	−38.5387	+	579.199i	−0.108255	+	1.62696i
$357$		0			0
$358$	353.718	+	378.036i	0.988039	+	1.05597i
$359$		−	139.028i		−	0.387265i	−0.981074	−	0.193633i	$-0.937973\pi$
$359$		−	139.028i		−	0.387265i	0.981074	−	0.193633i	$-0.0620270\pi$
$360$		0			0
$361$	−433.490			−1.20080
$362$	108.797	−	101.799i	0.300545	−	0.281212i
$363$		0			0
$364$	−135.370	−	9.00722i	−0.371895	−	0.0247451i
$365$	139.193			0.381351
$366$		0			0
$367$		−	1.87135i		−	0.00509904i	−0.999997	−	0.00254952i	$-0.999188\pi$
$367$		−	1.87135i		−	0.00509904i	0.999997	−	0.00254952i	$-0.000811538\pi$
$368$	23.1733	−	173.365i	0.0629710	−	0.471101i
$369$		0			0
$370$	58.3735	−	54.6186i	0.157766	−	0.147618i
$371$		−	112.560i		−	0.303397i
$372$		0			0
$373$	−384.864			−1.03181			−0.515903	−	0.856647i	$-0.672544\pi$
$373$	−384.864			−1.03181			−0.515903	+	0.856647i	$0.672544\pi$
$374$	−262.100	−	280.119i	−0.700803	−	0.748982i
$375$		0			0
$376$	306.689	−	250.932i	0.815661	−	0.667371i
$377$	−180.340			−0.478356
$378$		0			0
$379$		−	483.150i		−	1.27480i	−0.770533	−	0.637401i	$-0.780010\pi$
$379$		−	483.150i		−	1.27480i	0.770533	−	0.637401i	$-0.219990\pi$
$380$	−251.553	−	16.7378i	−0.661982	−	0.0440469i
$381$		0			0
$382$	87.0545	+	93.0394i	0.227891	+	0.243559i
$383$		−	130.500i		−	0.340730i	−0.985381	−	0.170365i	$-0.945505\pi$
$383$		−	130.500i		−	0.340730i	0.985381	−	0.170365i	$-0.0544947\pi$
$384$		0			0
$385$	−63.2529			−0.164293
$386$	−66.4512	+	62.1767i	−0.172153	+	0.161079i
$387$		0			0
$388$	−17.7257	+	266.399i	−0.0456847	+	0.686596i
$389$	10.2911			0.0264553			0.0132277	−	0.999913i	$-0.495789\pi$
$389$	10.2911			0.0264553			0.0132277	+	0.999913i	$0.495789\pi$
$390$		0			0
$391$			138.713i			0.354764i
$392$	230.491	+	281.706i	0.587988	+	0.718639i
$393$		0			0
$394$	−271.527	+	254.061i	−0.689155	+	0.644824i
$395$		−	230.927i		−	0.584625i
$396$		0			0
$397$	−228.864			−0.576483			−0.288242	−	0.957558i	$-0.593071\pi$
$397$	−228.864			−0.576483			−0.288242	+	0.957558i	$0.593071\pi$
$398$	213.037	+	227.683i	0.535269	+	0.572069i
$399$		0			0
$400$	−79.2948	−	10.5991i	−0.198237	−	0.0264979i
$401$	96.9322			0.241726			0.120863	−	0.992669i	$-0.461434\pi$
$401$	96.9322			0.241726			0.120863	+	0.992669i	$0.461434\pi$
$402$		0			0
$403$			443.036i			1.09934i
$404$	43.7042	−	656.832i	0.108179	−	1.62582i
$405$		0			0
$406$	−25.4436	−	27.1928i	−0.0626689	−	0.0669773i
$407$			270.209i			0.663903i
$408$		0			0
$409$	−135.494			−0.331282			−0.165641	−	0.986186i	$-0.552969\pi$
$409$	−135.494			−0.331282			−0.165641	+	0.986186i	$0.552969\pi$
$410$	−94.1933	+	88.1341i	−0.229740	+	0.214961i
$411$		0			0
$412$	−172.714	−	11.4920i	−0.419209	−	0.0278933i
$413$	−207.605			−0.502675
$414$		0			0
$415$		−	127.951i		−	0.308315i
$416$	472.273	−	336.660i	1.13527	−	0.809279i
$417$		0			0
$418$	622.241	−	582.215i	1.48862	−	1.39286i
$419$			384.912i			0.918643i	0.888270	+	0.459322i	$0.151907\pi$
$419$			384.912i			0.918643i	−0.888270	+	0.459322i	$0.848093\pi$
$420$		0			0
$421$	−543.230			−1.29033			−0.645166	−	0.764043i	$-0.723212\pi$
$421$	−543.230			−1.29033			−0.645166	+	0.764043i	$0.723212\pi$
$422$	−330.983	−	353.738i	−0.784321	−	0.838242i
$423$		0			0
$424$	304.714	+	372.422i	0.718665	+	0.878353i
$425$	63.4452			0.149283
$426$		0			0
$427$		−	64.0918i		−	0.150098i
$428$	690.573	+	45.9493i	1.61349	+	0.107358i
$429$		0			0
$430$	172.249	+	184.091i	0.400579	+	0.428119i
$431$		−	778.192i		−	1.80555i	−0.430113	−	0.902775i	$-0.641526\pi$
$431$		−	778.192i		−	1.80555i	0.430113	−	0.902775i	$-0.358474\pi$
$432$		0			0
$433$	−5.25291			−0.0121314			−0.00606571	−	0.999982i	$-0.501931\pi$
$433$	−5.25291			−0.0121314			−0.00606571	+	0.999982i	$0.501931\pi$
$434$	−66.8036	+	62.5064i	−0.153925	+	0.144024i
$435$		0			0
$436$	−43.1537	+	648.558i	−0.0989764	+	1.48752i
$437$	−308.128			−0.705099
$438$		0			0
$439$		−	208.302i		−	0.474492i	−0.971450	−	0.237246i	$-0.923755\pi$
$439$		−	208.302i		−	0.474492i	0.971450	−	0.237246i	$-0.0762447\pi$
$440$	209.281	−	171.233i	0.475639	−	0.389166i
$441$		0			0
$442$	−335.868	+	314.262i	−0.759882	+	0.711001i
$443$		−	735.826i		−	1.66101i	−0.557013	−	0.830504i	$-0.688053\pi$
$443$		−	735.826i		−	1.66101i	0.557013	−	0.830504i	$-0.311947\pi$
$444$		0			0
$445$	324.498			0.729209
$446$	−341.689	−	365.180i	−0.766120	−	0.818790i
$447$		0			0
$448$	117.395	+	23.7140i	0.262042	+	0.0529331i
$449$	617.155			1.37451			0.687255	−	0.726416i	$-0.258816\pi$
$449$	617.155			1.37451			0.687255	+	0.726416i	$0.258816\pi$
$450$		0			0
$451$		−	436.016i		−	0.966777i
$452$	19.2241	−	288.919i	0.0425311	−	0.639201i
$453$		0			0
$454$	82.6226	+	88.3028i	0.181988	+	0.194500i
$455$			75.8413i			0.166684i
$456$		0			0
$457$	−322.747			−0.706230			−0.353115	−	0.935580i	$-0.614878\pi$
$457$	−322.747			−0.706230			−0.353115	+	0.935580i	$0.614878\pi$
$458$	−114.275	+	106.924i	−0.249509	+	0.233459i
$459$		0			0
$460$	−97.5603	−	6.49146i	−0.212088	−	0.0141119i
$461$	509.034			1.10419			0.552097	−	0.833780i	$-0.313828\pi$
$461$	509.034			1.10419			0.552097	+	0.833780i	$0.313828\pi$
$462$		0			0
$463$		−	741.978i		−	1.60254i	−0.598300	−	0.801272i	$-0.704157\pi$
$463$		−	741.978i		−	1.60254i	0.598300	−	0.801272i	$-0.295843\pi$
$464$	157.798	+	21.0924i	0.340081	+	0.0454578i
$465$		0			0
$466$	240.590	−	225.113i	0.516287	−	0.483075i
$467$		−	310.692i		−	0.665293i	−0.943052	−	0.332647i	$-0.892058\pi$
$467$		−	310.692i		−	0.665293i	0.943052	−	0.332647i	$-0.107942\pi$
$468$		0			0
$469$	−246.008			−0.524537
$470$	−151.348	−	161.753i	−0.322017	−	0.344155i
$471$		0			0
$472$	686.889	−	562.010i	1.45527	−	1.19070i
$473$	−852.149			−1.80158
$474$		0			0
$475$			140.934i			0.296702i
$476$	−94.7728	−	6.30598i	−0.199102	−	0.0132479i
$477$		0			0
$478$	333.062	+	355.960i	0.696783	+	0.744686i
$479$			479.112i			1.00023i	0.865958	+	0.500117i	$0.166710\pi$
$479$			479.112i			1.00023i	−0.865958	+	0.500117i	$0.833290\pi$
$480$		0			0
$481$	323.984			0.673564
$482$	−560.057	+	524.030i	−1.16194	+	1.08720i
$483$		0			0
$484$	−28.5477	+	429.044i	−0.0589828	+	0.886454i
$485$	149.251			0.307734
$486$		0			0
$487$		−	572.858i		−	1.17630i	−0.808752	−	0.588150i	$-0.799857\pi$
$487$		−	572.858i		−	1.17630i	0.808752	−	0.588150i	$-0.200143\pi$
$488$	173.504	+	212.057i	0.355541	+	0.434543i
$489$		0			0
$490$	148.577	−	139.019i	0.303218	−	0.283713i
$491$			0.260515i			0.000530580i	1.00000		0.000265290i	$8.44445e-5\pi$
$491$			0.260515i			0.000530580i	−1.00000		0.000265290i	$0.999916\pi$
$492$		0			0
$493$	−126.257			−0.256099
$494$	−698.085	−	746.078i	−1.41313	−	1.51028i
$495$		0			0
$496$	51.8171	−	387.656i	0.104470	−	0.781565i
$497$	97.4891			0.196155
$498$		0			0
$499$			467.713i			0.937300i	0.883384	+	0.468650i	$0.155260\pi$
$499$			467.713i			0.937300i	−0.883384	+	0.468650i	$0.844740\pi$
$500$	−2.96910	+	44.6227i	−0.00593820	+	0.0892454i
$501$		0			0
$502$	−272.955	−	291.721i	−0.543736	−	0.581117i
$503$		−	728.659i		−	1.44863i	−0.689471	−	0.724313i	$-0.742157\pi$
$503$		−	728.659i		−	1.44863i	0.689471	−	0.724313i	$-0.257843\pi$
$504$		0			0
$505$	−367.992			−0.728698
$506$	241.325	−	225.801i	0.476927	−	0.446247i
$507$		0			0
$508$	−592.831	−	39.4457i	−1.16699	−	0.0776491i
$509$	453.697			0.891350			0.445675	−	0.895195i	$-0.352964\pi$
$509$	453.697			0.891350			0.445675	+	0.895195i	$0.352964\pi$
$510$		0			0
$511$			116.490i			0.227964i
$512$	−452.615	+	239.341i	−0.884013	+	0.467463i
$513$		0			0
$514$	231.278	−	216.401i	0.449958	−	0.421013i
$515$			96.7636i			0.187890i
$516$		0			0
$517$	748.747			1.44825
$518$	45.7098	+	48.8523i	0.0882429	+	0.0943095i
$519$		0			0
$520$	−205.311	−	250.932i	−0.394829	−	0.482561i
$521$	−624.519			−1.19869			−0.599346	−	0.800490i	$-0.704573\pi$
$521$	−624.519			−1.19869			−0.599346	+	0.800490i	$0.704573\pi$
$522$		0			0
$523$			319.527i			0.610950i	0.952200	+	0.305475i	$0.0988153\pi$
$523$			319.527i			0.610950i	−0.952200	+	0.305475i	$0.901185\pi$
$524$	−106.678	−	7.09812i	−0.203584	−	0.0135460i
$525$		0			0
$526$	166.175	+	177.600i	0.315922	+	0.337642i
$527$			310.171i			0.588560i
$528$		0			0
$529$	409.498			0.774098
$530$	196.422	−	183.786i	0.370607	−	0.346767i
$531$		0			0
$532$	14.0078	−	210.523i	0.0263304	−	0.395720i
$533$	−522.791			−0.980846
$534$		0			0
$535$		−	386.895i		−	0.723169i
$536$	813.951	−	665.972i	1.51857	−	1.24249i
$537$		0			0
$538$	−605.586	+	566.630i	−1.12562	+	1.05322i
$539$			687.756i			1.27598i
$540$		0			0
$541$	449.984			0.831764			0.415882	−	0.909419i	$-0.363473\pi$
$541$	449.984			0.831764			0.415882	+	0.909419i	$0.363473\pi$
$542$	264.180	+	282.342i	0.487416	+	0.520926i
$543$		0			0
$544$	330.640	−	235.697i	0.607794	−	0.433266i
$545$	363.357			0.666710
$546$		0			0
$547$		−	650.049i		−	1.18839i	−0.804321	−	0.594195i	$-0.797471\pi$
$547$		−	650.049i		−	1.18839i	0.804321	−	0.594195i	$-0.202529\pi$
$548$	−33.7142	+	506.692i	−0.0615223	+	0.924620i
$549$		0			0
$550$	−103.278	−	110.379i	−0.187779	−	0.200688i
$551$		−	280.460i		−	0.509001i
$552$		0			0
$553$	193.261			0.349477
$554$	−690.209	+	645.810i	−1.24586	+	1.16572i
$555$		0			0
$556$	−82.6226	−	5.49753i	−0.148602	−	0.00988765i
$557$	−127.555			−0.229004			−0.114502	−	0.993423i	$-0.536527\pi$
$557$	−127.555			−0.229004			−0.114502	+	0.993423i	$0.536527\pi$
$558$		0			0
$559$			1021.74i			1.82780i
$560$	8.87033	−	66.3611i	0.0158399	−	0.118502i
$561$		0			0
$562$	375.055	−	350.928i	0.667357	−	0.624428i
$563$			474.827i			0.843387i	0.906738	+	0.421694i	$0.138564\pi$
$563$			474.827i			0.843387i	−0.906738	+	0.421694i	$0.861436\pi$
$564$		0			0
$565$	−161.868			−0.286492
$566$	569.592	+	608.751i	1.00635	+	1.07553i
$567$		0			0
$568$	−322.556	+	263.914i	−0.567881	+	0.464638i
$569$	125.095			0.219850			0.109925	−	0.993940i	$-0.464939\pi$
$569$	125.095			0.219850			0.109925	+	0.993940i	$0.464939\pi$
$570$		0			0
$571$			190.288i			0.333253i	0.986020	+	0.166627i	$0.0532874\pi$
$571$			190.288i			0.333253i	−0.986020	+	0.166627i	$0.946713\pi$
$572$	1093.47	+	72.7575i	1.91167	+	0.127198i
$573$		0			0
$574$	−73.7587	−	78.8296i	−0.128500	−	0.137334i
$575$			54.6585i			0.0950582i
$576$		0			0
$577$	−492.739			−0.853968			−0.426984	−	0.904259i	$-0.640424\pi$
$577$	−492.739			−0.853968			−0.426984	+	0.904259i	$0.640424\pi$
$578$	186.915	−	174.891i	0.323382	−	0.302580i
$579$		0			0
$580$	5.90855	−	88.7998i	0.0101872	−	0.153103i
$581$	107.081			0.184304
$582$		0			0
$583$			909.227i			1.55957i
$584$	−315.351	−	385.422i	−0.539984	−	0.659969i
$585$		0			0
$586$	−351.527	+	328.915i	−0.599876	+	0.561288i
$587$			293.954i			0.500774i	0.968146	+	0.250387i	$0.0805578\pi$
$587$			293.954i			0.500774i	−0.968146	+	0.250387i	$0.919442\pi$
$588$		0			0
$589$	−688.996			−1.16977
$590$	−338.973	−	362.277i	−0.574531	−	0.614029i
$591$		0			0
$592$	−283.486	−	37.8930i	−0.478862	−	0.0640084i
$593$	434.184			0.732181			0.366091	−	0.930579i	$-0.380696\pi$
$593$	434.184			0.732181			0.366091	+	0.930579i	$0.380696\pi$
$594$		0			0
$595$			53.0967i			0.0892382i
$596$	−44.3863	+	667.083i	−0.0744737	+	1.11927i
$597$		0			0
$598$	−270.739	−	289.352i	−0.452741	−	0.483867i
$599$			509.345i			0.850325i	0.905117	+	0.425162i	$0.139783\pi$
$599$			509.345i			0.850325i	−0.905117	+	0.425162i	$0.860217\pi$
$600$		0			0
$601$	293.502			0.488356			0.244178	−	0.969730i	$-0.421482\pi$
$601$	293.502			0.488356			0.244178	+	0.969730i	$0.421482\pi$
$602$	−154.064	+	144.154i	−0.255921	+	0.239458i
$603$		0			0
$604$	−261.875	−	17.4246i	−0.433569	−	0.0288488i
$605$	240.373			0.397311
$606$		0			0
$607$		−	35.0896i		−	0.0578082i	−0.999582	−	0.0289041i	$-0.990798\pi$
$607$		−	35.0896i		−	0.0578082i	0.999582	−	0.0289041i	$-0.00920174\pi$
$608$	523.564	+	734.465i	0.861124	+	1.20800i
$609$		0			0
$610$	111.842	−	104.648i	0.183348	−	0.171554i
$611$		−	897.760i		−	1.46933i
$612$		0			0
$613$	49.6109			0.0809314			0.0404657	−	0.999181i	$-0.487116\pi$
$613$	49.6109			0.0809314			0.0404657	+	0.999181i	$0.487116\pi$
$614$	−282.239	−	301.642i	−0.459672	−	0.491274i
$615$		0			0
$616$	143.304	+	175.146i	0.232636	+	0.284327i
$617$	−427.251			−0.692465			−0.346232	−	0.938149i	$-0.612539\pi$
$617$	−427.251			−0.692465			−0.346232	+	0.938149i	$0.612539\pi$
$618$		0			0
$619$			903.263i			1.45923i	0.683858	+	0.729615i	$0.260301\pi$
$619$			903.263i			1.45923i	−0.683858	+	0.729615i	$0.739699\pi$
$620$	−218.152	−	14.5153i	−0.351857	−	0.0234118i
$621$		0			0
$622$	−626.673	−	669.756i	−1.00751	−	1.07678i
$623$			271.570i			0.435906i
$624$		0			0
$625$	25.0000			0.0400000
$626$	−560.784	+	524.711i	−0.895821	+	0.838196i
$627$		0			0
$628$	−8.06613	+	121.226i	−0.0128442	+	0.193035i
$629$	226.823			0.360608
$630$		0			0
$631$			681.512i			1.08005i	0.841649	+	0.540026i	$0.181585\pi$
$631$			681.512i			1.08005i	−0.841649	+	0.540026i	$0.818415\pi$
$632$	−639.430	+	523.179i	−1.01176	+	0.827816i
$633$		0			0
$634$	−627.146	+	586.804i	−0.989189	+	0.925558i
$635$			332.135i			0.523048i
$636$		0			0
$637$	824.630			1.29455
$638$	205.525	+	219.655i	0.322140	+	0.344286i
$639$		0			0
$640$	150.299	+	243.578i	0.234842	+	0.380591i
$641$	252.576			0.394035			0.197018	−	0.980400i	$-0.436874\pi$
$641$	252.576			0.394035			0.197018	+	0.980400i	$0.436874\pi$
$642$		0			0
$643$			15.2038i			0.0236451i	0.999930	+	0.0118225i	$0.00376332\pi$
$643$			15.2038i			0.0236451i	−0.999930	+	0.0118225i	$0.996237\pi$
$644$	5.43265	−	81.6474i	0.00843579	−	0.126782i
$645$		0			0
$646$	−488.732	−	522.331i	−0.756550	−	0.808563i
$647$			463.576i			0.716501i	0.933626	+	0.358250i	$0.116627\pi$
$647$			463.576i			0.716501i	−0.933626	+	0.358250i	$0.883373\pi$
$648$		0			0
$649$	1676.97			2.58392
$650$	−132.346	+	123.832i	−0.203609	+	0.190511i
$651$		0			0
$652$	−180.183	−	11.9890i	−0.276354	−	0.0183880i
$653$	−351.503			−0.538289			−0.269145	−	0.963100i	$-0.586741\pi$
$653$	−351.503			−0.538289			−0.269145	+	0.963100i	$0.586741\pi$
$654$		0			0
$655$			59.7666i			0.0912467i
$656$	457.442	+	61.1452i	0.697320	+	0.0932091i
$657$		0			0
$658$	135.370	−	126.662i	0.205729	−	0.192495i
$659$			494.229i			0.749967i	0.927031	+	0.374984i	$0.122352\pi$
$659$			494.229i			0.749967i	−0.927031	+	0.374984i	$0.877648\pi$
$660$		0			0
$661$	165.735			0.250734			0.125367	−	0.992110i	$-0.459989\pi$
$661$	165.735			0.250734			0.125367	+	0.992110i	$0.459989\pi$
$662$	79.4300	+	84.8908i	0.119985	+	0.128234i
$663$		0			0
$664$	−354.292	+	289.880i	−0.533572	+	0.436567i
$665$	−117.946			−0.177363
$666$		0			0
$667$		−	108.771i		−	0.163075i
$668$	−130.891	−	8.70921i	−0.195944	−	0.0130377i
$669$		0			0
$670$	−401.677	−	429.292i	−0.599518	−	0.640734i
$671$			517.714i			0.771555i
$672$		0			0
$673$	3.74322			0.00556199			0.00278099	−	0.999996i	$-0.499115\pi$
$673$	3.74322			0.00556199			0.00278099	+	0.999996i	$0.499115\pi$
$674$	592.561	−	554.443i	0.879170	−	0.822616i
$675$		0			0
$676$	42.3570	−	636.585i	0.0626583	−	0.941693i
$677$	−969.987			−1.43277			−0.716386	−	0.697704i	$-0.754205\pi$
$677$	−969.987			−1.43277			−0.716386	+	0.697704i	$0.754205\pi$
$678$		0			0
$679$			124.907i			0.183957i
$680$	−143.739	−	175.678i	−0.211381	−	0.258350i
$681$		0			0
$682$	539.619	−	504.907i	0.791230	−	0.740333i
$683$		−	808.424i		−	1.18364i	−0.806071	−	0.591819i	$-0.798410\pi$
$683$		−	808.424i		−	1.18364i	0.806071	−	0.591819i	$-0.201590\pi$
$684$		0			0
$685$	283.875			0.414417
$686$	241.643	+	258.256i	0.352250	+	0.376466i
$687$		0			0
$688$	119.502	−	894.023i	0.173695	−	1.29945i
$689$	1090.18			1.58226
$690$		0			0
$691$		−	395.903i		−	0.572942i	−0.958089	−	0.286471i	$-0.907518\pi$
$691$		−	395.903i		−	0.572942i	0.958089	−	0.286471i	$-0.0924821\pi$
$692$	83.9361	−	1261.48i	0.121295	−	1.82295i
$693$		0			0
$694$	442.988	+	473.443i	0.638312	+	0.682195i
$695$			46.2896i			0.0666037i
$696$		0			0
$697$	−366.008			−0.525119
$698$	−50.7448	+	47.4806i	−0.0727003	+	0.0680237i
$699$		0			0
$700$	−37.3444	−	2.48482i	−0.0533491	−	0.00354974i
$701$	−961.043			−1.37096			−0.685480	−	0.728091i	$-0.740408\pi$
$701$	−961.043			−1.37096			−0.685480	+	0.728091i	$0.740408\pi$
$702$		0			0
$703$			503.851i			0.716716i
$704$	−948.280	−	191.555i	−1.34699	−	0.272095i
$705$		0			0
$706$	19.8424	−	18.5660i	0.0281054	−	0.0262975i
$707$		−	307.970i		−	0.435601i
$708$		0			0
$709$	−817.751			−1.15339			−0.576693	−	0.816961i	$-0.695657\pi$
$709$	−817.751			−1.15339			−0.576693	+	0.816961i	$0.695657\pi$
$710$	159.178	+	170.122i	0.224195	+	0.239608i
$711$		0			0
$712$	−735.171	−	898.527i	−1.03254	−	1.26198i
$713$	−267.214			−0.374775
$714$		0			0
$715$		−	612.622i		−	0.856814i
$716$	−1033.14	−	68.7432i	−1.44294	−	0.0960100i
$717$		0			0
$718$	189.977	+	203.037i	0.264592	+	0.282782i
$719$			91.2179i			0.126868i	0.997986	+	0.0634339i	$0.0202052\pi$
$719$			91.2179i			0.126868i	−0.997986	+	0.0634339i	$0.979795\pi$
$720$		0			0
$721$	−80.9806			−0.112317
$722$	633.071	−	592.348i	0.876830	−	0.820427i
$723$		0			0
$724$	−19.7840	+	297.335i	−0.0273260	+	0.410683i
$725$	−49.7503			−0.0686212
$726$		0			0
$727$		−	662.682i		−	0.911530i	−0.890100	−	0.455765i	$-0.849366\pi$
$727$		−	662.682i		−	0.911530i	0.890100	−	0.455765i	$-0.150634\pi$
$728$	210.003	−	171.823i	0.288465	−	0.236021i
$729$		0			0
$730$	−203.278	+	190.202i	−0.278463	+	0.260551i
$731$			715.324i			0.978556i
$732$		0			0
$733$	430.623			0.587480			0.293740	−	0.955885i	$-0.405100\pi$
$733$	430.623			0.587480			0.293740	+	0.955885i	$0.405100\pi$
$734$	2.55712	+	2.73292i	0.00348382	+	0.00372333i
$735$		0			0
$736$	203.055	+	284.849i	0.275889	+	0.387023i
$737$	1987.17			2.69630
$738$		0			0
$739$		−	523.620i		−	0.708552i	−0.935141	−	0.354276i	$-0.884727\pi$
$739$		−	523.620i		−	0.708552i	0.935141	−	0.354276i	$-0.115273\pi$
$740$	−10.6148	+	159.530i	−0.0143444	+	0.215582i
$741$		0			0
$742$	153.809	+	164.384i	0.207290	+	0.221541i
$743$		−	880.661i		−	1.18528i	−0.805469	−	0.592638i	$-0.798086\pi$
$743$		−	880.661i		−	1.18528i	0.805469	−	0.592638i	$-0.201914\pi$
$744$		0			0
$745$	373.735			0.501658
$746$	562.057	−	525.902i	0.753428	−	0.704962i
$747$		0			0
$748$	765.545	+	50.9378i	1.02346	+	0.0680986i
$749$	323.790			0.432296
$750$		0			0
$751$			602.683i			0.802507i	0.915967	+	0.401254i	$0.131425\pi$
$751$			602.683i			0.802507i	−0.915967	+	0.401254i	$0.868575\pi$
$752$	−105.001	+	785.540i	−0.139629	+	1.04460i
$753$		0			0
$754$	263.370	−	246.428i	0.349297	−	0.326828i
$755$			146.717i			0.194327i
$756$		0			0
$757$	427.136			0.564249			0.282124	−	0.959378i	$-0.408961\pi$
$757$	427.136			0.564249			0.282124	+	0.959378i	$0.408961\pi$
$758$	660.206	+	705.594i	0.870984	+	0.930863i
$759$		0			0
$760$	390.241	−	319.294i	0.513475	−	0.420124i
$761$	239.700			0.314980			0.157490	−	0.987521i	$-0.449660\pi$
$761$	239.700			0.314980			0.157490	+	0.987521i	$0.449660\pi$
$762$		0			0
$763$			304.090i			0.398545i
$764$	−254.270	−	16.9186i	−0.332814	−	0.0221447i
$765$		0			0
$766$	178.323	+	190.582i	0.232798	+	0.248802i
$767$		−	2010.71i		−	2.62152i
$768$		0			0
$769$	937.486			1.21910			0.609549	−	0.792748i	$-0.291351\pi$
$769$	937.486			1.21910			0.609549	+	0.792748i	$0.291351\pi$
$770$	92.3748	−	86.4327i	0.119967	−	0.112250i
$771$		0			0
$772$	12.0837	−	181.606i	0.0156525	−	0.235241i
$773$	−1468.30			−1.89948			−0.949740	−	0.313040i	$-0.898653\pi$
$773$	−1468.30			−1.89948			−0.949740	+	0.313040i	$0.898653\pi$
$774$		0			0
$775$			122.220i			0.157703i
$776$	−338.138	−	413.272i	−0.435745	−	0.532567i
$777$		0			0
$778$	−15.0292	+	14.0624i	−0.0193177	+	0.0180751i
$779$		−	813.029i		−	1.04368i
$780$		0			0
$781$	−787.486			−1.00831
$782$	−189.546	−	202.577i	−0.242386	−	0.259049i
$783$		0			0
$784$	−721.552	−	96.4481i	−0.920346	−	0.123020i
$785$	67.9173			0.0865189
$786$		0			0
$787$			408.886i			0.519550i	0.965669	+	0.259775i	$0.0836483\pi$
$787$			408.886i			0.519550i	−0.965669	+	0.259775i	$0.916352\pi$
$788$	49.3753	−	742.063i	0.0626591	−	0.941705i
$789$		0			0
$790$	315.553	+	337.247i	0.399434	+	0.426894i
$791$		−	135.466i		−	0.171259i
$792$		0			0
$793$	620.747			0.782783
$794$	334.234	−	312.734i	0.420949	−	0.393871i
$795$		0			0
$796$	−622.241	−	41.4026i	−0.781710	−	0.0520134i
$797$	400.122			0.502035			0.251018	−	0.967982i	$-0.419235\pi$
$797$	400.122			0.502035			0.251018	+	0.967982i	$0.419235\pi$
$798$		0			0
$799$		−	628.525i		−	0.786639i
$800$	130.286	−	92.8742i	0.162857	−	0.116093i
$801$		0			0
$802$	−141.560	+	132.454i	−0.176509	+	0.165155i
$803$		−	940.966i		−	1.17181i
$804$		0			0
$805$	−45.7432			−0.0568239
$806$	−605.392	−	647.012i	−0.751106	−	0.802744i
$807$		0			0
$808$	833.710	+	1018.96i	1.03182	+	1.26109i
$809$	255.486			0.315805			0.157902	−	0.987455i	$-0.449527\pi$
$809$	255.486			0.315805			0.157902	+	0.987455i	$0.449527\pi$
$810$		0			0
$811$			295.549i			0.364425i	0.983259	+	0.182213i	$0.0583259\pi$
$811$			295.549i			0.364425i	−0.983259	+	0.182213i	$0.941674\pi$
$812$	74.3158	+	4.94482i	0.0915219	+	0.00608968i
$813$		0			0
$814$	−369.230	−	394.614i	−0.453599	−	0.484784i
$815$			100.948i			0.123863i
$816$		0			0
$817$	−1588.98			−1.94490
$818$	197.876	−	185.148i	0.241903	−	0.226342i
$819$		0			0
$820$	17.1284	−	257.423i	0.0208883	−	0.313931i
$821$	−1227.23			−1.49480			−0.747402	−	0.664372i	$-0.768699\pi$
$821$	−1227.23			−1.49480			−0.747402	+	0.664372i	$0.768699\pi$
$822$		0			0
$823$		−	881.623i		−	1.07123i	−0.844462	−	0.535615i	$-0.820080\pi$
$823$		−	881.623i		−	1.07123i	0.844462	−	0.535615i	$-0.179920\pi$
$824$	267.936	−	219.224i	0.325165	−	0.266049i
$825$		0			0
$826$	303.187	−	283.684i	0.367054	−	0.343443i
$827$			850.269i			1.02814i	0.857749	+	0.514068i	$0.171862\pi$
$827$			850.269i			1.02814i	−0.857749	+	0.514068i	$0.828138\pi$
$828$		0			0
$829$	−1328.47			−1.60250			−0.801251	−	0.598328i	$-0.795832\pi$
$829$	−1328.47			−1.60250			−0.801251	+	0.598328i	$0.795832\pi$
$830$	174.840	+	186.860i	0.210650	+	0.225132i
$831$		0			0
$832$	−229.677	+	1137.00i	−0.276054	+	1.36659i
$833$	577.327			0.693069
$834$		0			0
$835$			73.3320i			0.0878228i
$836$	−113.150	+	1700.54i	−0.135347	+	2.03414i
$837$		0			0
$838$	−525.967	−	562.127i	−0.627646	−	0.670796i
$839$			55.3391i			0.0659583i	0.999456	+	0.0329792i	$0.0104995\pi$
$839$			55.3391i			0.0659583i	−0.999456	+	0.0329792i	$0.989500\pi$
$840$		0			0
$841$	−741.996			−0.882278
$842$	793.335	−	742.303i	0.942203	−	0.881594i
$843$		0			0
$844$	966.739	+	64.3248i	1.14543	+	0.0762142i
$845$	−356.649			−0.422069
$846$		0			0
$847$			201.166i			0.237504i
$848$	−953.906	−	127.506i	−1.12489	−	0.150361i
$849$		0			0
$850$	−92.6556	+	86.6954i	−0.109007	+	0.101995i
$851$			195.409i			0.229623i
$852$		0			0
$853$	−742.887			−0.870911			−0.435456	−	0.900210i	$-0.643413\pi$
$853$	−742.887			−0.870911			−0.435456	+	0.900210i	$0.643413\pi$
$854$	87.5790	+	93.6000i	0.102552	+	0.109602i
$855$		0			0
$856$	−1071.30	+	876.537i	−1.25152	+	1.02399i
$857$	−679.145			−0.792468			−0.396234	−	0.918150i	$-0.629683\pi$
$857$	−679.145			−0.792468			−0.396234	+	0.918150i	$0.629683\pi$
$858$		0			0
$859$			756.133i			0.880248i	0.897937	+	0.440124i	$0.145066\pi$
$859$			756.133i			0.880248i	−0.897937	+	0.440124i	$0.854934\pi$
$860$	−503.107	−	33.4757i	−0.585008	−	0.0389252i
$861$		0			0
$862$	1063.37	+	1136.48i	1.23361	+	1.31842i
$863$			1130.05i			1.30944i	0.755871	+	0.654721i	$0.227214\pi$
$863$			1130.05i			1.30944i	−0.755871	+	0.654721i	$0.772786\pi$
$864$		0			0
$865$	−706.747			−0.817049
$866$	7.67137	−	7.17790i	0.00885840	−	0.00828856i
$867$		0			0
$868$	12.1478	−	182.569i	0.0139951	−	0.210333i
$869$	−1561.10			−1.79643
$870$		0			0
$871$		−	2382.65i		−	2.73554i
$872$	−823.208	−	1006.13i	−0.944046	−	1.15381i
$873$		0			0
$874$	449.992	−	421.046i	0.514865	−	0.481746i
$875$			20.9223i			0.0239112i
$876$		0			0
$877$	910.607			1.03832			0.519160	−	0.854677i	$-0.326245\pi$
$877$	910.607			1.03832			0.519160	+	0.854677i	$0.326245\pi$
$878$	284.637	+	304.205i	0.324188	+	0.346475i
$879$		0			0
$880$	−71.6518	+	536.044i	−0.0814225	+	0.609141i
$881$	405.402			0.460161			0.230080	−	0.973172i	$-0.426101\pi$
$881$	405.402			0.460161			0.230080	+	0.973172i	$0.426101\pi$
$882$		0			0
$883$		−	819.868i		−	0.928503i	−0.885703	−	0.464252i	$-0.846323\pi$
$883$		−	819.868i		−	0.928503i	0.885703	−	0.464252i	$-0.153677\pi$
$884$	61.0752	−	917.901i	0.0690896	−	1.03835i
$885$		0			0
$886$	1005.48	+	1074.60i	1.13485	+	1.21287i
$887$		−	1003.99i		−	1.13190i	−0.824440	−	0.565949i	$-0.808510\pi$
$887$		−	1003.99i		−	1.13190i	0.824440	−	0.565949i	$-0.191490\pi$
$888$		0			0
$889$	−277.961			−0.312667
$890$	−473.899	+	443.414i	−0.532470	+	0.498218i
$891$		0			0
$892$	998.010	+	66.4055i	1.11885	+	0.0744456i
$893$	1396.17			1.56346
$894$		0			0
$895$			578.821i			0.646728i
$896$	−203.849	+	125.784i	−0.227510	+	0.140384i
$897$		0			0
$898$	−901.296	+	843.318i	−1.00367	+	0.939107i
$899$		−	243.220i		−	0.270545i
$900$		0			0
$901$	763.237			0.847100
$902$	595.800	+	636.761i	0.660532	+	0.705943i
$903$		0			0
$904$	366.722	+	448.208i	0.405666	+	0.495805i
$905$	166.583			0.184069
$906$		0			0
$907$		−	361.629i		−	0.398709i	−0.979927	−	0.199354i	$-0.936116\pi$
$907$		−	361.629i		−	0.398709i	0.979927	−	0.199354i	$-0.0638845\pi$
$908$	−241.325	−	16.0572i	−0.265776	−	0.0176842i
$909$		0			0
$910$	−103.634	−	110.759i	−0.113884	−	0.121713i
$911$			294.475i			0.323244i	0.986853	+	0.161622i	$0.0516725\pi$
$911$			294.475i			0.323244i	−0.986853	+	0.161622i	$0.948327\pi$
$912$		0			0
$913$	−864.965			−0.947388
$914$	471.341	−	441.022i	0.515691	−	0.482518i
$915$		0			0
$916$	20.7802	−	312.306i	0.0226858	−	0.340945i
$917$	−50.0182			−0.0545454
$918$		0			0
$919$			17.4246i			0.0189604i	0.999955	+	0.00948022i	$0.00301769\pi$
$919$			17.4246i			0.0189604i	−0.999955	+	0.00948022i	$0.996982\pi$
$920$	151.348	−	123.832i	0.164509	−	0.134600i
$921$		0			0
$922$	−743.395	+	695.575i	−0.806285	+	0.754420i
$923$			944.209i			1.02298i
$924$		0			0
$925$	89.3774			0.0966242
$926$	1013.88	+	1083.59i	1.09491	+	1.17018i
$927$		0			0
$928$	−259.270	+	184.821i	−0.279386	+	0.199161i
$929$	743.488			0.800310			0.400155	−	0.916447i	$-0.368956\pi$
$929$	743.488			0.800310			0.400155	+	0.916447i	$0.368956\pi$
$930$		0			0
$931$			1282.44i			1.37749i
$932$	−43.7495	+	657.513i	−0.0469416	+	0.705486i
$933$		0			0
$934$	424.549	+	453.736i	0.454549	+	0.485799i
$935$		−	428.899i		−	0.458715i
$936$		0			0
$937$	−802.514			−0.856471			−0.428236	−	0.903667i	$-0.640865\pi$
$937$	−802.514			−0.856471			−0.428236	+	0.903667i	$0.640865\pi$
$938$	359.271	−	336.160i	0.383018	−	0.358380i
$939$		0			0
$940$	442.058	+	29.4136i	0.470275	+	0.0312911i
$941$	730.288			0.776076			0.388038	−	0.921643i	$-0.373153\pi$
$941$	730.288			0.776076			0.388038	+	0.921643i	$0.373153\pi$
$942$		0			0
$943$		−	315.318i		−	0.334378i
$944$	−235.171	+	1759.37i	−0.249122	+	1.86374i
$945$		0			0
$946$	1244.48	−	1164.43i	1.31552	−	1.23090i
$947$			882.383i			0.931767i	0.884846	+	0.465884i	$0.154263\pi$
$947$			882.383i			0.931767i	−0.884846	+	0.465884i	$0.845737\pi$
$948$		0			0
$949$	−1128.23			−1.18887
$950$	−192.580	−	205.820i	−0.202716	−	0.216653i
$951$		0			0
$952$	147.023	−	120.294i	0.154436	−	0.126359i
$953$	1047.62			1.09929			0.549644	−	0.835399i	$-0.314763\pi$
$953$	1047.62			1.09929			0.549644	+	0.835399i	$0.314763\pi$
$954$		0			0
$955$			142.455i			0.149168i
$956$	−972.811	−	64.7288i	−1.01759	−	0.0677080i
$957$		0			0
$958$	−654.689	−	699.698i	−0.683391	−	0.730374i
$959$			237.573i			0.247730i
$960$		0			0
$961$	363.490			0.378242
$962$	−473.149	+	442.712i	−0.491838	+	0.460200i
$963$		0			0
$964$	101.842	−	1530.59i	0.105646	−	1.58775i
$965$	−101.745			−0.105436
$966$		0			0
$967$			519.528i			0.537258i	0.963244	+	0.268629i	$0.0865705\pi$
$967$			519.528i			0.537258i	−0.963244	+	0.268629i	$0.913430\pi$
$968$	−544.580	−	665.587i	−0.562583	−	0.687589i
$969$		0			0
$970$	−217.967	+	203.946i	−0.224708	+	0.210253i
$971$		−	398.406i		−	0.410305i	−0.978730	−	0.205152i	$-0.934231\pi$
$971$		−	398.406i		−	0.410305i	0.978730	−	0.205152i	$-0.0657690\pi$
$972$		0			0
$973$	−38.7393			−0.0398143
$974$	782.788	+	836.604i	0.803684	+	0.858937i
$975$		0			0
$976$	−543.154	−	72.6021i	−0.556510	−	0.0743874i
$977$	−367.857			−0.376517			−0.188258	−	0.982120i	$-0.560284\pi$
$977$	−367.857			−0.376517			−0.188258	+	0.982120i	$0.560284\pi$
$978$		0			0
$979$		−	2193.66i		−	2.24071i
$980$	−27.0177	+	406.049i	−0.0275690	+	0.414336i
$981$		0			0
$982$	−0.355984	−	0.380457i	−0.000362509	−	0.000387431i
$983$			1473.69i			1.49918i	0.661902	+	0.749590i	$0.269749\pi$
$983$			1473.69i			1.49918i	−0.661902	+	0.749590i	$0.730251\pi$
$984$		0			0
$985$	−415.743			−0.422074
$986$	184.386	−	172.525i	0.187004	−	0.174975i
$987$		0			0
$988$	2038.97	+	135.669i	2.06374	+	0.137317i
$989$	−616.257			−0.623111
$990$		0			0
$991$		−	753.090i		−	0.759929i	−0.925001	−	0.379964i	$-0.875936\pi$
$991$		−	753.090i		−	0.759929i	0.925001	−	0.379964i	$-0.124064\pi$
$992$	454.044	+	636.941i	0.457705	+	0.642078i
$993$		0			0
$994$	−142.374	+	133.215i	−0.143233	+	0.134019i
$995$			348.613i			0.350364i
$996$		0			0
$997$	767.370			0.769679			0.384839	−	0.922984i	$-0.374257\pi$
$997$	767.370			0.769679			0.384839	+	0.922984i	$0.374257\pi$
$998$	−639.112	−	683.050i	−0.640393	−	0.684419i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	180.3.c.c.91.2	yes	8
3.2	odd	2	inner	180.3.c.c.91.7	yes	8
4.3	odd	2	inner	180.3.c.c.91.1	✓	8
5.2	odd	4		900.3.f.i.199.6		16
5.3	odd	4		900.3.f.i.199.11		16
5.4	even	2		900.3.c.o.451.7		8
8.3	odd	2		2880.3.e.i.2431.7		8
8.5	even	2		2880.3.e.i.2431.6		8
12.11	even	2	inner	180.3.c.c.91.8	yes	8
15.2	even	4		900.3.f.i.199.12		16
15.8	even	4		900.3.f.i.199.5		16
15.14	odd	2		900.3.c.o.451.2		8
20.3	even	4		900.3.f.i.199.8		16
20.7	even	4		900.3.f.i.199.9		16
20.19	odd	2		900.3.c.o.451.8		8
24.5	odd	2		2880.3.e.i.2431.2		8
24.11	even	2		2880.3.e.i.2431.3		8
60.23	odd	4		900.3.f.i.199.10		16
60.47	odd	4		900.3.f.i.199.7		16
60.59	even	2		900.3.c.o.451.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
180.3.c.c.91.1	✓	8	4.3	odd	2	inner
180.3.c.c.91.2	yes	8	1.1	even	1	trivial
180.3.c.c.91.7	yes	8	3.2	odd	2	inner
180.3.c.c.91.8	yes	8	12.11	even	2	inner
900.3.c.o.451.1		8	60.59	even	2
900.3.c.o.451.2		8	15.14	odd	2
900.3.c.o.451.7		8	5.4	even	2
900.3.c.o.451.8		8	20.19	odd	2
900.3.f.i.199.5		16	15.8	even	4
900.3.f.i.199.6		16	5.2	odd	4
900.3.f.i.199.7		16	60.47	odd	4
900.3.f.i.199.8		16	20.3	even	4
900.3.f.i.199.9		16	20.7	even	4
900.3.f.i.199.10		16	60.23	odd	4
900.3.f.i.199.11		16	5.3	odd	4
900.3.f.i.199.12		16	15.2	even	4
2880.3.e.i.2431.2		8	24.5	odd	2
2880.3.e.i.2431.3		8	24.11	even	2
2880.3.e.i.2431.6		8	8.5	even	2
2880.3.e.i.2431.7		8	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:	\( N \)	\(=\)	\( 180 = 2^{2} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	180.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.46040 + 1.36646i) q^{2} +(0.265564 - 3.99117i) q^{4} -2.23607 q^{5} -1.87135i q^{7} +(5.06596 + 6.19161i) q^{8} +O(q^{10})\)	\(q+(-1.46040 + 1.36646i) q^{2} +(0.265564 - 3.99117i) q^{4} -2.23607 q^{5} -1.87135i q^{7} +(5.06596 + 6.19161i) q^{8} +(3.26556 - 3.05550i) q^{10} +15.1162i q^{11} +18.1245 q^{13} +(2.55712 + 2.73292i) q^{14} +(-15.8590 - 2.11983i) q^{16} +12.6890 q^{17} +28.1867i q^{19} +(-0.593820 + 8.92454i) q^{20} +(-20.6556 - 22.0757i) q^{22} +10.9317i q^{23} +5.00000 q^{25} +(-26.4691 + 24.7665i) q^{26} +(-7.46887 - 0.496963i) q^{28} -9.95007 q^{29} +24.4440i q^{31} +(26.0572 - 18.5748i) q^{32} +(-18.5311 + 17.3391i) q^{34} +4.18446i q^{35} +17.8755 q^{37} +(-38.5161 - 41.1640i) q^{38} +(-11.3278 - 13.8449i) q^{40} -28.8444 q^{41} +56.3734i q^{43} +(60.3312 + 4.01431i) q^{44} +(-14.9377 - 15.9647i) q^{46} -49.5329i q^{47} +45.4981 q^{49} +(-7.30202 + 6.83231i) q^{50} +(4.81323 - 72.3381i) q^{52} +60.1494 q^{53} -33.8007i q^{55} +(11.5867 - 9.48016i) q^{56} +(14.5311 - 13.5964i) q^{58} -110.939i q^{59} +34.2490 q^{61} +(-33.4018 - 35.6982i) q^{62} +(-12.6722 + 62.7329i) q^{64} -40.5276 q^{65} -131.460i q^{67} +(3.36976 - 50.6442i) q^{68} +(-5.71790 - 6.11100i) q^{70} +52.0957i q^{71} -62.2490 q^{73} +(-26.1054 + 24.4262i) q^{74} +(112.498 + 7.48539i) q^{76} +28.2876 q^{77} +103.274i q^{79} +(35.4617 + 4.74008i) q^{80} +(42.1245 - 39.4148i) q^{82} +57.2212i q^{83} -28.3735 q^{85} +(-77.0321 - 82.3280i) q^{86} +(-93.5934 + 76.5778i) q^{88} -145.120 q^{89} -33.9173i q^{91} +(43.6303 + 2.90307i) q^{92} +(67.6848 + 72.3381i) q^{94} -63.0274i q^{95} -66.7471 q^{97} +(-66.4456 + 62.1714i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 14 q^{4}+O(q^{10}) \) 8 * q - 14 * q^4	\( 8 q - 14 q^{4} + 10 q^{10} + 16 q^{13} - 14 q^{16} - 4 q^{22} + 40 q^{25} - 92 q^{28} - 116 q^{34} + 272 q^{37} - 10 q^{40} - 184 q^{46} - 152 q^{49} + 232 q^{52} + 84 q^{58} + 16 q^{61} - 182 q^{64} + 180 q^{70} - 240 q^{73} + 384 q^{76} + 208 q^{82} + 160 q^{85} - 652 q^{88} - 168 q^{94} + 240 q^{97}+O(q^{100}) \) 8 * q - 14 * q^4 + 10 * q^10 + 16 * q^13 - 14 * q^16 - 4 * q^22 + 40 * q^25 - 92 * q^28 - 116 * q^34 + 272 * q^37 - 10 * q^40 - 184 * q^46 - 152 * q^49 + 232 * q^52 + 84 * q^58 + 16 * q^61 - 182 * q^64 + 180 * q^70 - 240 * q^73 + 384 * q^76 + 208 * q^82 + 160 * q^85 - 652 * q^88 - 168 * q^94 + 240 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more