LMFDB - Embedded newform 675.3.j.e.251.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [675,3,Mod(251,675)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("675.251"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(675, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([1, 0])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 675 = 3^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	675.j (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [20,0,0,18,0,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$18.3924178443$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 3 x^{18} - 19 x^{16} - 66 x^{14} + 109 x^{12} + 813 x^{10} + 981 x^{8} - 5346 x^{6} + \cdots + 59049 $ x^20 + 3x^18 - 19x^16 - 66x^14 + 109x^12 + 813x^10 + 981x^8 - 5346x^6 - 13851x^4 + 19683*x^2 + 59049
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{12} $
Twist minimal:	no (minimal twist has level 45)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			251.4
Root			$0.185238 + 1.72212i$ of defining polynomial
Character	$\chi$	$=$	675.251
Dual form			675.3.j.e.476.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.15863 - 0.668935i) q^{2} +(-1.10505 - 1.91401i) q^{4} +(4.10376 - 7.10792i) q^{7} +8.30831i q^{8} +(5.67242 + 3.27497i) q^{11} +(0.749233 + 1.29771i) q^{13} +(-9.50946 + 5.49029i) q^{14} +(1.13750 - 1.97021i) q^{16} -15.1237i q^{17} +25.9980 q^{19} +(-4.38149 - 7.58896i) q^{22} +(20.1010 - 11.6053i) q^{23} -2.00475i q^{26} -18.1395 q^{28} +(6.96344 + 4.02034i) q^{29} +(22.5107 + 38.9897i) q^{31} +(26.1449 - 15.0948i) q^{32} +(-10.1168 + 17.5228i) q^{34} -62.8487 q^{37} +(-30.1220 - 17.3909i) q^{38} +(-9.97361 + 5.75827i) q^{41} +(21.3253 - 36.9366i) q^{43} -14.4761i q^{44} -31.0528 q^{46} +(-14.2898 - 8.25020i) q^{47} +(-9.18167 - 15.9031i) q^{49} +(1.65588 - 2.86808i) q^{52} -66.0119i q^{53} +(59.0548 + 34.0953i) q^{56} +(-5.37870 - 9.31617i) q^{58} +(0.373843 - 0.215838i) q^{59} +(15.7923 - 27.3530i) q^{61} -60.2328i q^{62} -49.4897 q^{64} +(-47.9785 - 83.1011i) q^{67} +(-28.9469 + 16.7125i) q^{68} -84.2523i q^{71} -63.5769 q^{73} +(72.8183 + 42.0417i) q^{74} +(-28.7292 - 49.7604i) q^{76} +(46.5565 - 26.8794i) q^{77} +(-9.06687 + 15.7043i) q^{79} +15.4076 q^{82} +(87.4333 + 50.4796i) q^{83} +(-49.4163 + 28.5305i) q^{86} +(-27.2095 + 47.1282i) q^{88} -86.3067i q^{89} +12.2987 q^{91} +(-44.4254 - 25.6490i) q^{92} +(11.0377 + 19.1178i) q^{94} +(34.5230 - 59.7956i) q^{97} +24.5677i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 18 q^{4} + 24 q^{11} + 30 q^{14} - 26 q^{16} + 8 q^{19} - 114 q^{29} + 28 q^{31} + 4 q^{34} - 102 q^{41} + 116 q^{46} + 40 q^{49} + 618 q^{56} + 120 q^{59} - 50 q^{61} - 140 q^{64} + 504 q^{74} - 96 q^{76}+ \cdots - 218 q^{94}+O(q^{100}) $ 20 * q + 18 * q^4 + 24 * q^11 + 30 * q^14 - 26 * q^16 + 8 * q^19 - 114 * q^29 + 28 * q^31 + 4 * q^34 - 102 * q^41 + 116 * q^46 + 40 * q^49 + 618 * q^56 + 120 * q^59 - 50 * q^61 - 140 * q^64 + 504 * q^74 - 96 * q^76 + 128 * q^79 - 1488 * q^86 - 288 * q^91 - 218 * q^94

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/675\mathbb{Z}\right)^\times$.

$n$	$326$	$352$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$

Coefficient data

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

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

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

$2$	−1.15863	−	0.668935i	−0.579314	−	0.334467i	0.181547	−	0.983382i	$-0.441890\pi$
$2$	−1.15863	−	0.668935i	−0.579314	−	0.334467i	−0.760861	+	0.648915i	$0.775223\pi$
$3$		0			0
$3$		0			0
$4$	−1.10505	−	1.91401i	−0.276263	−	0.478502i
$5$		0			0
$5$		0			0
$6$		0			0
$7$	4.10376	−	7.10792i	0.586251	−	1.01542i	−0.408467	−	0.912773i	$-0.633936\pi$
$7$	4.10376	−	7.10792i	0.586251	−	1.01542i	0.994718	−	0.102644i	$-0.0327302\pi$
$8$			8.30831i			1.03854i
$9$		0			0
$10$		0			0
$11$	5.67242	+	3.27497i	0.515675	+	0.297725i	0.735163	−	0.677890i	$-0.237106\pi$
$11$	5.67242	+	3.27497i	0.515675	+	0.297725i	−0.219489	+	0.975615i	$0.570439\pi$
$12$		0			0
$13$	0.749233	+	1.29771i	0.0576333	+	0.0998238i	0.893403	−	0.449257i	$-0.148311\pi$
$13$	0.749233	+	1.29771i	0.0576333	+	0.0998238i	−0.835769	+	0.549081i	$0.814978\pi$
$14$	−9.50946	+	5.49029i	−0.679247	+	0.392164i
$15$		0			0
$16$	1.13750	−	1.97021i	0.0710939	−	0.123138i
$17$		−	15.1237i		−	0.889630i	−0.895622	−	0.444815i	$-0.853269\pi$
$17$		−	15.1237i		−	0.889630i	0.895622	−	0.444815i	$-0.146731\pi$
$18$		0			0
$19$	25.9980			1.36831			0.684157	−	0.729334i	$-0.260170\pi$
$19$	25.9980			1.36831			0.684157	+	0.729334i	$0.260170\pi$
$20$		0			0
$21$		0			0
$22$	−4.38149	−	7.58896i	−0.199158	−	0.344953i
$23$	20.1010	−	11.6053i	0.873958	−	0.504580i	0.00529637	−	0.999986i	$-0.498314\pi$
$23$	20.1010	−	11.6053i	0.873958	−	0.504580i	0.868661	+	0.495406i	$0.164981\pi$
$24$		0			0
$25$		0			0
$26$		−	2.00475i		−	0.0771058i
$27$		0			0
$28$	−18.1395			−0.647839
$29$	6.96344	+	4.02034i	0.240119	+	0.138633i	0.615231	−	0.788347i	$-0.289063\pi$
$29$	6.96344	+	4.02034i	0.240119	+	0.138633i	−0.375113	+	0.926979i	$0.622396\pi$
$30$		0			0
$31$	22.5107	+	38.9897i	0.726152	+	1.25773i	0.958498	+	0.285099i	$0.0920264\pi$
$31$	22.5107	+	38.9897i	0.726152	+	1.25773i	−0.232346	+	0.972633i	$0.574640\pi$
$32$	26.1449	−	15.0948i	0.817029	−	0.471712i
$33$		0			0
$34$	−10.1168	+	17.5228i	−0.297552	+	0.515375i
$35$		0			0
$36$		0			0
$37$	−62.8487			−1.69861			−0.849307	−	0.527900i	$-0.822980\pi$
$37$	−62.8487			−1.69861			−0.849307	+	0.527900i	$0.822980\pi$
$38$	−30.1220	−	17.3909i	−0.792684	−	0.457657i
$39$		0			0
$40$		0			0
$41$	−9.97361	+	5.75827i	−0.243259	+	0.140446i	−0.616674	−	0.787219i	$-0.711520\pi$
$41$	−9.97361	+	5.75827i	−0.243259	+	0.140446i	0.373415	+	0.927664i	$0.378187\pi$
$42$		0			0
$43$	21.3253	−	36.9366i	0.495938	−	0.858990i	−0.504051	−	0.863674i	$-0.668158\pi$
$43$	21.3253	−	36.9366i	0.495938	−	0.858990i	0.999989	+	0.00468401i	$0.00149097\pi$
$44$		−	14.4761i		−	0.329002i
$45$		0			0
$46$	−31.0528			−0.675062
$47$	−14.2898	−	8.25020i	−0.304037	−	0.175536i	0.340218	−	0.940347i	$-0.389499\pi$
$47$	−14.2898	−	8.25020i	−0.304037	−	0.175536i	−0.644255	+	0.764811i	$0.722833\pi$
$48$		0			0
$49$	−9.18167	−	15.9031i	−0.187381	−	0.324553i
$50$		0			0
$51$		0			0
$52$	1.65588	−	2.86808i	0.0318439	−	0.0551553i
$53$		−	66.0119i		−	1.24551i	−0.782418	−	0.622754i	$-0.786014\pi$
$53$		−	66.0119i		−	1.24551i	0.782418	−	0.622754i	$-0.213986\pi$
$54$		0			0
$55$		0			0
$56$	59.0548	+	34.0953i	1.05455	+	0.608845i
$57$		0			0
$58$	−5.37870	−	9.31617i	−0.0927361	−	0.160624i
$59$	0.373843	−	0.215838i	0.00633632	−	0.00365828i	−0.496828	−	0.867849i	$-0.665502\pi$
$59$	0.373843	−	0.215838i	0.00633632	−	0.00365828i	0.503165	+	0.864190i	$0.332169\pi$
$60$		0			0
$61$	15.7923	−	27.3530i	0.258890	−	0.448410i	−0.707055	−	0.707158i	$-0.749977\pi$
$61$	15.7923	−	27.3530i	0.258890	−	0.448410i	0.965945	+	0.258748i	$0.0833101\pi$
$62$		−	60.2328i		−	0.971496i
$63$		0			0
$64$	−49.4897			−0.773277
$65$		0			0
$66$		0			0
$67$	−47.9785	−	83.1011i	−0.716096	−	1.24032i	−0.962535	−	0.271157i	$-0.912594\pi$
$67$	−47.9785	−	83.1011i	−0.716096	−	1.24032i	0.246439	−	0.969158i	$-0.420740\pi$
$68$	−28.9469	+	16.7125i	−0.425690	+	0.245772i
$69$		0			0
$70$		0			0
$71$		−	84.2523i		−	1.18665i	−0.804962	−	0.593326i	$-0.797814\pi$
$71$		−	84.2523i		−	1.18665i	0.804962	−	0.593326i	$-0.202186\pi$
$72$		0			0
$73$	−63.5769			−0.870916			−0.435458	−	0.900209i	$-0.643414\pi$
$73$	−63.5769			−0.870916			−0.435458	+	0.900209i	$0.643414\pi$
$74$	72.8183	+	42.0417i	0.984031	+	0.568131i
$75$		0			0
$76$	−28.7292	−	49.7604i	−0.378015	−	0.654741i
$77$	46.5565	−	26.8794i	0.604630	−	0.349083i
$78$		0			0
$79$	−9.06687	+	15.7043i	−0.114771	+	0.198788i	−0.917688	−	0.397302i	$-0.869947\pi$
$79$	−9.06687	+	15.7043i	−0.114771	+	0.198788i	0.802917	+	0.596090i	$0.203280\pi$
$80$		0			0
$81$		0			0
$82$	15.4076			0.187898
$83$	87.4333	+	50.4796i	1.05341	+	0.608188i	0.923603	−	0.383351i	$-0.125230\pi$
$83$	87.4333	+	50.4796i	1.05341	+	0.608188i	0.129810	+	0.991539i	$0.458563\pi$
$84$		0			0
$85$		0			0
$86$	−49.4163	+	28.5305i	−0.574608	+	0.331750i
$87$		0			0
$88$	−27.2095	+	47.1282i	−0.309199	+	0.535548i
$89$		−	86.3067i		−	0.969738i	−0.874587	−	0.484869i	$-0.838867\pi$
$89$		−	86.3067i		−	0.969738i	0.874587	−	0.484869i	$-0.161133\pi$
$90$		0			0
$91$	12.2987			0.135150
$92$	−44.4254	−	25.6490i	−0.482885	−	0.278794i
$93$		0			0
$94$	11.0377	+	19.1178i	0.117422	+	0.203381i
$95$		0			0
$96$		0			0
$97$	34.5230	−	59.7956i	0.355907	−	0.616450i	−0.631365	−	0.775485i	$-0.717505\pi$
$97$	34.5230	−	59.7956i	0.355907	−	0.616450i	0.987273	+	0.159036i	$0.0508385\pi$
$98$			24.5677i			0.250691i
$99$		0			0
$100$		0			0
$101$	−30.1891	−	17.4297i	−0.298902	−	0.172571i	0.343048	−	0.939318i	$-0.388541\pi$
$101$	−30.1891	−	17.4297i	−0.298902	−	0.172571i	−0.641949	+	0.766747i	$0.721874\pi$
$102$		0			0
$103$	11.0058	+	19.0625i	0.106852	+	0.185073i	0.914493	−	0.404601i	$-0.132590\pi$
$103$	11.0058	+	19.0625i	0.106852	+	0.185073i	−0.807641	+	0.589674i	$0.799256\pi$
$104$	−10.7818	+	6.22486i	−0.103671	+	0.0598544i
$105$		0			0
$106$	−44.1576	+	76.4833i	−0.416582	+	0.721540i
$107$		−	99.8598i		−	0.933269i	−0.884450	−	0.466635i	$-0.845466\pi$
$107$		−	99.8598i		−	0.933269i	0.884450	−	0.466635i	$-0.154534\pi$
$108$		0			0
$109$	11.7865			0.108133			0.0540664	−	0.998537i	$-0.482782\pi$
$109$	11.7865			0.108133			0.0540664	+	0.998537i	$0.482782\pi$
$110$		0			0
$111$		0			0
$112$	−9.33607	−	16.1706i	−0.0833578	−	0.144380i
$113$	11.7278	−	6.77103i	0.103786	−	0.0599206i	−0.447209	−	0.894430i	$-0.647582\pi$
$113$	11.7278	−	6.77103i	0.103786	−	0.0599206i	0.550994	+	0.834509i	$0.314249\pi$
$114$		0			0
$115$		0			0
$116$		−	17.7708i		−	0.153196i
$117$		0			0
$118$	−0.577527			−0.00489430
$119$	−107.498	−	62.0640i	−0.903345	−	0.521547i
$120$		0			0
$121$	−39.0491	−	67.6350i	−0.322720	−	0.558967i
$122$	−36.5947	+	21.1280i	−0.299957	+	0.173180i
$123$		0			0
$124$	49.7511	−	86.1714i	0.401218	−	0.694930i
$125$		0			0
$126$		0			0
$127$	−13.1983			−0.103924			−0.0519620	−	0.998649i	$-0.516547\pi$
$127$	−13.1983			−0.103924			−0.0519620	+	0.998649i	$0.516547\pi$
$128$	−47.2396	−	27.2738i	−0.369059	−	0.213076i
$129$		0			0
$130$		0			0
$131$	−184.044	+	106.258i	−1.40491	+	0.811127i	−0.994892	−	0.100949i	$-0.967812\pi$
$131$	−184.044	+	106.258i	−1.40491	+	0.811127i	−0.410022	+	0.912076i	$0.634479\pi$
$132$		0			0
$133$	106.689	−	184.792i	0.802176	−	1.38941i
$134$			128.378i			0.958043i
$135$		0			0
$136$	125.652			0.923915
$137$	129.866	+	74.9783i	0.947929	+	0.547287i	0.892437	−	0.451172i	$-0.148994\pi$
$137$	129.866	+	74.9783i	0.947929	+	0.547287i	0.0554918	+	0.998459i	$0.482327\pi$
$138$		0			0
$139$	2.80453	+	4.85759i	0.0201765	+	0.0349467i	0.875937	−	0.482425i	$-0.160244\pi$
$139$	2.80453	+	4.85759i	0.0201765	+	0.0349467i	−0.855761	+	0.517372i	$0.826911\pi$
$140$		0			0
$141$		0			0
$142$	−56.3593	+	97.6171i	−0.396896	+	0.687445i
$143$			9.81487i			0.0686355i
$144$		0			0
$145$		0			0
$146$	73.6620	+	42.5288i	0.504534	+	0.291293i
$147$		0			0
$148$	69.4512	+	120.293i	0.469265	+	0.812790i
$149$	−97.4936	+	56.2879i	−0.654319	+	0.377771i	−0.790109	−	0.612966i	$-0.789976\pi$
$149$	−97.4936	+	56.2879i	−0.654319	+	0.377771i	0.135790	+	0.990738i	$0.456643\pi$
$150$		0			0
$151$	30.3786	−	52.6172i	0.201183	−	0.348458i	−0.747727	−	0.664006i	$-0.768855\pi$
$151$	30.3786	−	52.6172i	0.201183	−	0.348458i	0.948910	+	0.315548i	$0.102188\pi$
$152$			215.999i			1.42105i
$153$		0			0
$154$	−71.9222			−0.467028
$155$		0			0
$156$		0			0
$157$	147.499	+	255.475i	0.939482	+	1.62723i	0.766439	+	0.642317i	$0.222027\pi$
$157$	147.499	+	255.475i	0.939482	+	1.62723i	0.173043	+	0.984914i	$0.444640\pi$
$158$	21.0103	−	12.1303i	0.132976	−	0.0767740i
$159$		0			0
$160$		0			0
$161$		−	190.502i		−	1.18324i
$162$		0			0
$163$	19.8284			0.121647			0.0608235	−	0.998149i	$-0.480627\pi$
$163$	19.8284			0.121647			0.0608235	+	0.998149i	$0.480627\pi$
$164$	22.0427	+	12.7264i	0.134407	+	0.0775999i
$165$		0			0
$166$	−67.5351	−	116.974i	−0.406838	−	0.704664i
$167$	−87.7198	+	50.6451i	−0.525268	+	0.303264i	−0.739087	−	0.673609i	$-0.764743\pi$
$167$	−87.7198	+	50.6451i	−0.525268	+	0.303264i	0.213819	+	0.976873i	$0.431410\pi$
$168$		0			0
$169$	83.3773	−	144.414i	0.493357	−	0.854519i
$170$		0			0
$171$		0			0
$172$	−94.2625			−0.548038
$173$	−95.8461	−	55.3368i	−0.554024	−	0.319866i	0.196720	−	0.980460i	$-0.436971\pi$
$173$	−95.8461	−	55.3368i	−0.554024	−	0.319866i	−0.750743	+	0.660594i	$0.770304\pi$
$174$		0			0
$175$		0			0
$176$	12.9048	−	7.45058i	0.0733226	−	0.0423328i
$177$		0			0
$178$	−57.7335	+	99.9974i	−0.324346	+	0.561783i
$179$		−	55.1312i		−	0.307995i	−0.988071	−	0.153998i	$-0.950785\pi$
$179$		−	55.1312i		−	0.307995i	0.988071	−	0.153998i	$-0.0492148\pi$
$180$		0			0
$181$	−27.6183			−0.152587			−0.0762935	−	0.997085i	$-0.524309\pi$
$181$	−27.6183			−0.152587			−0.0762935	+	0.997085i	$0.524309\pi$
$182$	−14.2496	−	8.22702i	−0.0782946	−	0.0452034i
$183$		0			0
$184$	96.4207	+	167.006i	0.524026	+	0.907639i
$185$		0			0
$186$		0			0
$187$	49.5297	−	85.7880i	0.264865	−	0.458760i
$188$			36.4676i			0.193977i
$189$		0			0
$190$		0			0
$191$	225.953	+	130.454i	1.18300	+	0.683004i	0.956706	−	0.291055i	$-0.0940064\pi$
$191$	225.953	+	130.454i	1.18300	+	0.683004i	0.226292	+	0.974060i	$0.427340\pi$
$192$		0			0
$193$	−57.8659	−	100.227i	−0.299823	−	0.519309i	0.676272	−	0.736652i	$-0.263594\pi$
$193$	−57.8659	−	100.227i	−0.299823	−	0.519309i	−0.976095	+	0.217343i	$0.930261\pi$
$194$	−79.9987	+	46.1873i	−0.412365	+	0.238079i
$195$		0			0
$196$	−20.2925	+	35.1476i	−0.103533	+	0.179324i
$197$			179.618i			0.911768i	0.890039	+	0.455884i	$0.150677\pi$
$197$			179.618i			0.911768i	−0.890039	+	0.455884i	$0.849323\pi$
$198$		0			0
$199$	132.649			0.666577			0.333289	−	0.942825i	$-0.391842\pi$
$199$	132.649			0.666577			0.333289	+	0.942825i	$0.391842\pi$
$200$		0			0
$201$		0			0
$202$	23.3186	+	40.3890i	0.115439	+	0.199946i
$203$	57.1526	−	32.9970i	0.281540	−	0.162547i
$204$		0			0
$205$		0			0
$206$		−	29.4485i		−	0.142954i
$207$		0			0
$208$	3.40902			0.0163895
$209$	147.471	+	85.1427i	0.705605	+	0.407381i
$210$		0			0
$211$	174.674	+	302.545i	0.827841	+	1.43386i	0.899729	+	0.436450i	$0.143764\pi$
$211$	174.674	+	302.545i	0.827841	+	1.43386i	−0.0718877	+	0.997413i	$0.522902\pi$
$212$	−126.347	+	72.9467i	−0.595978	+	0.344088i
$213$		0			0
$214$	−66.7997	+	115.700i	−0.312148	+	0.540656i
$215$		0			0
$216$		0			0
$217$	369.514			1.70283
$218$	−13.6562	−	7.88438i	−0.0626429	−	0.0361669i
$219$		0			0
$220$		0			0
$221$	19.6262	−	11.3312i	0.0888063	−	0.0512723i
$222$		0			0
$223$	−70.9086	+	122.817i	−0.317976	+	0.550750i	−0.980066	−	0.198674i	$-0.936336\pi$
$223$	−70.9086	+	122.817i	−0.317976	+	0.550750i	0.662090	+	0.749424i	$0.269670\pi$
$224$		−	247.781i		−	1.10617i
$225$		0			0
$226$	−18.1175			−0.0801660
$227$	−117.695	−	67.9512i	−0.518480	−	0.299344i	0.217833	−	0.975986i	$-0.430101\pi$
$227$	−117.695	−	67.9512i	−0.518480	−	0.299344i	−0.736312	+	0.676642i	$0.763435\pi$
$228$		0			0
$229$	−102.326	−	177.233i	−0.446837	−	0.773944i	0.551342	−	0.834280i	$-0.314116\pi$
$229$	−102.326	−	177.233i	−0.446837	−	0.773944i	−0.998178	+	0.0603360i	$0.980783\pi$
$230$		0			0
$231$		0			0
$232$	−33.4023	+	57.8544i	−0.143975	+	0.249373i
$233$			270.050i			1.15901i	0.814967	+	0.579507i	$0.196755\pi$
$233$			270.050i			1.15901i	−0.814967	+	0.579507i	$0.803245\pi$
$234$		0			0
$235$		0			0
$236$	−0.826233	−	0.477026i	−0.00350099	−	0.00202130i
$237$		0			0
$238$	83.0336	+	143.818i	0.348881	+	0.604279i
$239$	318.573	−	183.928i	1.33294	−	0.769575i	0.347193	−	0.937794i	$-0.387135\pi$
$239$	318.573	−	183.928i	1.33294	−	0.769575i	0.985750	+	0.168219i	$0.0538016\pi$
$240$		0			0
$241$	−19.7054	+	34.1307i	−0.0817650	+	0.141621i	−0.904008	−	0.427515i	$-0.859389\pi$
$241$	−19.7054	+	34.1307i	−0.0817650	+	0.141621i	0.822243	+	0.569136i	$0.192722\pi$
$242$			104.485i			0.431757i
$243$		0			0
$244$	−69.8052			−0.286087
$245$		0			0
$246$		0			0
$247$	19.4785	+	33.7378i	0.0788605	+	0.136590i
$248$	−323.938	+	187.026i	−1.30620	+	0.754137i
$249$		0			0
$250$		0			0
$251$			80.2388i			0.319677i	0.987143	+	0.159838i	$0.0510973\pi$
$251$			80.2388i			0.319677i	−0.987143	+	0.159838i	$0.948903\pi$
$252$		0			0
$253$	152.029			0.600904
$254$	15.2920	+	8.82883i	0.0602046	+	0.0347592i
$255$		0			0
$256$	135.468	+	234.638i	0.529173	+	0.916554i
$257$	112.839	−	65.1474i	0.439061	−	0.253492i	−0.264138	−	0.964485i	$-0.585088\pi$
$257$	112.839	−	65.1474i	0.439061	−	0.253492i	0.703199	+	0.710993i	$0.251754\pi$
$258$		0			0
$259$	−257.916	+	446.723i	−0.995814	+	1.72480i
$260$		0			0
$261$		0			0
$262$	284.318			1.08518
$263$	281.249	+	162.379i	1.06939	+	0.617411i	0.928014	−	0.372545i	$-0.121515\pi$
$263$	281.249	+	162.379i	1.06939	+	0.617411i	0.141374	+	0.989956i	$0.454848\pi$
$264$		0			0
$265$		0			0
$266$	−247.227	+	142.737i	−0.929424	+	0.536603i
$267$		0			0
$268$	−106.037	+	183.662i	−0.395662	+	0.685307i
$269$			353.608i			1.31453i	0.753660	+	0.657264i	$0.228286\pi$
$269$			353.608i			1.31453i	−0.753660	+	0.657264i	$0.771714\pi$
$270$		0			0
$271$	−332.793			−1.22802			−0.614010	−	0.789298i	$-0.710444\pi$
$271$	−332.793			−1.22802			−0.614010	+	0.789298i	$0.710444\pi$
$272$	−29.7969	−	17.2033i	−0.109547	−	0.0632473i
$273$		0			0
$274$	−100.311	−	173.744i	−0.366099	−	0.634102i
$275$		0			0
$276$		0			0
$277$	−42.0119	+	72.7668i	−0.151668	+	0.262696i	−0.931841	−	0.362868i	$-0.881798\pi$
$277$	−42.0119	+	72.7668i	−0.151668	+	0.262696i	0.780173	+	0.625564i	$0.215131\pi$
$278$		−	7.50419i		−	0.0269935i
$279$		0			0
$280$		0			0
$281$	322.954	+	186.458i	1.14930	+	0.663551i	0.948718	−	0.316125i	$-0.102382\pi$
$281$	322.954	+	186.458i	1.14930	+	0.663551i	0.200586	+	0.979676i	$0.435715\pi$
$282$		0			0
$283$	−80.2796	−	139.048i	−0.283674	−	0.491337i	0.688613	−	0.725129i	$-0.258220\pi$
$283$	−80.2796	−	139.048i	−0.283674	−	0.491337i	−0.972287	+	0.233792i	$0.924887\pi$
$284$	−161.260	+	93.1033i	−0.567816	+	0.327828i
$285$		0			0
$286$	6.56551	−	11.3718i	0.0229563	−	0.0397615i
$287$			94.5221i			0.329345i
$288$		0			0
$289$	60.2734			0.208559
$290$		0			0
$291$		0			0
$292$	70.2558	+	121.687i	0.240602	+	0.416735i
$293$	276.729	−	159.770i	0.944467	−	0.545288i	0.0531095	−	0.998589i	$-0.483087\pi$
$293$	276.729	−	159.770i	0.944467	−	0.545288i	0.891358	+	0.453300i	$0.149753\pi$
$294$		0			0
$295$		0			0
$296$		−	522.166i		−	1.76408i
$297$		0			0
$298$	150.612			0.505409
$299$	30.1207	+	17.3902i	0.100738	+	0.0581612i
$300$		0			0
$301$	−175.028	−	303.157i	−0.581489	−	1.00717i
$302$	−70.3949	+	40.6425i	−0.233096	+	0.134578i
$303$		0			0
$304$	29.5728	−	51.2215i	0.0972789	−	0.168492i
$305$		0			0
$306$		0			0
$307$	−336.649			−1.09658			−0.548288	−	0.836289i	$-0.684720\pi$
$307$	−336.649			−1.09658			−0.548288	+	0.836289i	$0.684720\pi$
$308$	−102.895	−	59.4063i	−0.334074	−	0.192878i
$309$		0			0
$310$		0			0
$311$	263.046	−	151.869i	0.845806	−	0.488326i	−0.0134276	−	0.999910i	$-0.504274\pi$
$311$	263.046	−	151.869i	0.845806	−	0.488326i	0.859234	+	0.511584i	$0.170941\pi$
$312$		0			0
$313$	114.618	−	198.525i	0.366193	−	0.634265i	−0.622774	−	0.782402i	$-0.713994\pi$
$313$	114.618	−	198.525i	0.366193	−	0.634265i	0.988967	+	0.148137i	$0.0473277\pi$
$314$		−	394.668i		−	1.25690i
$315$		0			0
$316$	40.0775			0.126828
$317$	372.001	+	214.775i	1.17351	+	0.677524i	0.954503	−	0.298201i	$-0.0963865\pi$
$317$	372.001	+	214.775i	1.17351	+	0.677524i	0.219002	+	0.975724i	$0.429720\pi$
$318$		0			0
$319$	26.3330	+	45.6102i	0.0825487	+	0.142979i
$320$		0			0
$321$		0			0
$322$	−127.433	+	220.721i	−0.395756	+	0.685469i
$323$		−	393.186i		−	1.21729i
$324$		0			0
$325$		0			0
$326$	−22.9738	−	13.2639i	−0.0704718	−	0.0406869i
$327$		0			0
$328$	−47.8415	−	82.8638i	−0.145858	−	0.252634i
$329$	−117.283	+	67.7136i	−0.356485	+	0.205816i
$330$		0			0
$331$	137.447	−	238.065i	0.415248	−	0.719230i	−0.580207	−	0.814469i	$-0.697028\pi$
$331$	137.447	−	238.065i	0.415248	−	0.719230i	0.995454	+	0.0952390i	$0.0303615\pi$
$332$		−	223.131i		−	0.672080i
$333$		0			0
$334$	135.513			0.405727
$335$		0			0
$336$		0			0
$337$	−128.494	−	222.557i	−0.381287	−	0.660408i	0.609960	−	0.792432i	$-0.291186\pi$
$337$	−128.494	−	222.557i	−0.381287	−	0.660408i	−0.991246	+	0.132024i	$0.957852\pi$
$338$	−193.207	+	111.548i	−0.571617	+	0.330023i
$339$		0			0
$340$		0			0
$341$			294.888i			0.864774i
$342$		0			0
$343$	251.451			0.733093
$344$	306.880	+	177.177i	0.892094	+	0.515051i
$345$		0			0
$346$	74.0333	+	128.229i	0.213969	+	0.370605i
$347$	−221.381	+	127.814i	−0.637986	+	0.368341i	−0.783838	−	0.620965i	$-0.786741\pi$
$347$	−221.381	+	127.814i	−0.637986	+	0.368341i	0.145853	+	0.989306i	$0.453407\pi$
$348$		0			0
$349$	146.497	−	253.740i	0.419761	−	0.727048i	−0.576154	−	0.817341i	$-0.695447\pi$
$349$	146.497	−	253.740i	0.419761	−	0.727048i	0.995915	+	0.0902933i	$0.0287804\pi$
$350$		0			0
$351$		0			0
$352$	197.740			0.561762
$353$	33.2985	+	19.2249i	0.0943301	+	0.0544615i	0.546423	−	0.837509i	$-0.315989\pi$
$353$	33.2985	+	19.2249i	0.0943301	+	0.0544615i	−0.452093	+	0.891971i	$0.649322\pi$
$354$		0			0
$355$		0			0
$356$	−165.192	+	95.3734i	−0.464022	+	0.267903i
$357$		0			0
$358$	−36.8792	+	63.8766i	−0.103014	+	0.178426i
$359$		−	168.269i		−	0.468716i	−0.972150	−	0.234358i	$-0.924701\pi$
$359$		−	168.269i		−	0.468716i	0.972150	−	0.234358i	$-0.0752988\pi$
$360$		0			0
$361$	314.895			0.872286
$362$	31.9993	+	18.4748i	0.0883959	+	0.0510354i
$363$		0			0
$364$	−13.5907	−	23.5398i	−0.0373371	−	0.0646698i
$365$		0			0
$366$		0			0
$367$	23.5376	−	40.7684i	0.0641353	−	0.111086i	−0.832175	−	0.554513i	$-0.812904\pi$
$367$	23.5376	−	40.7684i	0.0641353	−	0.111086i	0.896310	+	0.443428i	$0.146238\pi$
$368$		−	52.8044i		−	0.143490i
$369$		0			0
$370$		0			0
$371$	−469.207	−	270.897i	−1.26471	−	0.730180i
$372$		0			0
$373$	−128.563	−	222.678i	−0.344674	−	0.596993i	0.640621	−	0.767858i	$-0.278677\pi$
$373$	−128.563	−	222.678i	−0.344674	−	0.596993i	−0.985294	+	0.170865i	$0.945344\pi$
$374$	−114.773	+	66.2643i	−0.306880	+	0.177177i
$375$		0			0
$376$	68.5452	−	118.724i	0.182301	−	0.315755i
$377$			12.0487i			0.0319594i
$378$		0			0
$379$	−194.506			−0.513210			−0.256605	−	0.966516i	$-0.582604\pi$
$379$	−194.506			−0.513210			−0.256605	+	0.966516i	$0.582604\pi$
$380$		0			0
$381$		0			0
$382$	−174.530	−	302.295i	−0.456885	−	0.791348i
$383$	178.271	−	102.925i	0.465460	−	0.268733i	−0.248877	−	0.968535i	$-0.580062\pi$
$383$	178.271	−	102.925i	0.465460	−	0.268733i	0.714337	+	0.699802i	$0.246728\pi$
$384$		0			0
$385$		0			0
$386$			154.834i			0.401124i
$387$		0			0
$388$	−152.599			−0.393297
$389$	−296.754	−	171.331i	−0.762863	−	0.440439i	0.0674597	−	0.997722i	$-0.478511\pi$
$389$	−296.754	−	171.331i	−0.762863	−	0.440439i	−0.830323	+	0.557283i	$0.811844\pi$
$390$		0			0
$391$	−175.516	−	304.002i	−0.448889	−	0.777499i
$392$	132.128	−	76.2842i	0.337061	−	0.194602i
$393$		0			0
$394$	120.153	−	208.111i	0.304957	−	0.528201i
$395$		0			0
$396$		0			0
$397$	−332.225			−0.836838			−0.418419	−	0.908254i	$-0.637416\pi$
$397$	−332.225			−0.836838			−0.418419	+	0.908254i	$0.637416\pi$
$398$	−153.691	−	88.7334i	−0.386158	−	0.222948i
$399$		0			0
$400$		0			0
$401$	−414.101	+	239.081i	−1.03267	+	0.596213i	−0.917749	−	0.397161i	$-0.869995\pi$
$401$	−414.101	+	239.081i	−1.03267	+	0.596213i	−0.114923	+	0.993374i	$0.536662\pi$
$402$		0			0
$403$	−33.7315	+	58.4247i	−0.0837011	+	0.144975i
$404$			77.0429i			0.190700i
$405$		0			0
$406$	−88.2915			−0.217467
$407$	−356.504	−	205.828i	−0.875932	−	0.505719i
$408$		0			0
$409$	91.4354	+	158.371i	0.223559	+	0.387215i	0.955886	−	0.293738i	$-0.0948993\pi$
$409$	91.4354	+	158.371i	0.223559	+	0.387215i	−0.732327	+	0.680953i	$0.761566\pi$
$410$		0			0
$411$		0			0
$412$	24.3239	−	42.1302i	0.0590386	−	0.102258i
$413$		−	3.54299i		−	0.00857868i
$414$		0			0
$415$		0			0
$416$	39.1773	+	22.6190i	0.0941762	+	0.0543727i
$417$		0			0
$418$	−113.910	−	197.298i	−0.272511	−	0.472004i
$419$	−352.311	+	203.407i	−0.840839	+	0.485459i	−0.857549	−	0.514402i	$-0.828014\pi$
$419$	−352.311	+	203.407i	−0.840839	+	0.485459i	0.0167104	+	0.999860i	$0.494681\pi$
$420$		0			0
$421$	−224.098	+	388.148i	−0.532298	+	0.921968i	0.466991	+	0.884262i	$0.345338\pi$
$421$	−224.098	+	388.148i	−0.532298	+	0.921968i	−0.999289	+	0.0377055i	$0.987995\pi$
$422$		−	467.383i		−	1.10754i
$423$		0			0
$424$	548.447			1.29351
$425$		0			0
$426$		0			0
$427$	−129.615	−	224.500i	−0.303549	−	0.525762i
$428$	−191.132	+	110.350i	−0.446571	+	0.257828i
$429$		0			0
$430$		0			0
$431$		−	254.466i		−	0.590409i	−0.955434	−	0.295204i	$-0.904612\pi$
$431$		−	254.466i		−	0.590409i	0.955434	−	0.295204i	$-0.0953877\pi$
$432$		0			0
$433$	−82.9913			−0.191666			−0.0958329	−	0.995397i	$-0.530551\pi$
$433$	−82.9913			−0.191666			−0.0958329	+	0.995397i	$0.530551\pi$
$434$	−428.130	−	247.181i	−0.986474	−	0.569541i
$435$		0			0
$436$	−13.0247	−	22.5594i	−0.0298731	−	0.0517418i
$437$	522.586	−	301.715i	1.19585	−	0.690424i
$438$		0			0
$439$	129.457	−	224.226i	0.294891	−	0.510765i	−0.680069	−	0.733148i	$-0.738050\pi$
$439$	129.457	−	224.226i	0.294891	−	0.510765i	0.974959	+	0.222383i	$0.0713835\pi$
$440$		0			0
$441$		0			0
$442$	−30.3193			−0.0685957
$443$	−142.835	−	82.4657i	−0.322426	−	0.186153i	0.330047	−	0.943964i	$-0.392935\pi$
$443$	−142.835	−	82.4657i	−0.322426	−	0.186153i	−0.652473	+	0.757812i	$0.726269\pi$
$444$		0			0
$445$		0			0
$446$	164.313	−	94.8664i	0.368416	−	0.212705i
$447$		0			0
$448$	−203.094	+	351.769i	−0.453335	+	0.785198i
$449$			628.421i			1.39960i	0.714338	+	0.699800i	$0.246728\pi$
$449$			628.421i			1.39960i	−0.714338	+	0.699800i	$0.753272\pi$
$450$		0			0
$451$	−75.4327			−0.167256
$452$	−25.9196	−	14.9647i	−0.0573443	−	0.0331077i
$453$		0			0
$454$	90.9097	+	157.460i	0.200242	+	0.346829i
$455$		0			0
$456$		0			0
$457$	374.823	−	649.213i	0.820183	−	1.42060i	−0.0853634	−	0.996350i	$-0.527205\pi$
$457$	374.823	−	649.213i	0.820183	−	1.42060i	0.905546	−	0.424248i	$-0.139462\pi$
$458$			273.796i			0.597809i
$459$		0			0
$460$		0			0
$461$	−325.037	−	187.660i	−0.705069	−	0.407072i	0.104163	−	0.994560i	$-0.466784\pi$
$461$	−325.037	−	187.660i	−0.705069	−	0.407072i	−0.809233	+	0.587488i	$0.800117\pi$
$462$		0			0
$463$	82.4936	+	142.883i	0.178172	+	0.308603i	0.941254	−	0.337698i	$-0.109648\pi$
$463$	82.4936	+	142.883i	0.178172	+	0.308603i	−0.763082	+	0.646301i	$0.776315\pi$
$464$	15.8419	−	9.14630i	0.0341420	−	0.0197119i
$465$		0			0
$466$	180.646	−	312.888i	0.387652	−	0.671434i
$467$		−	751.743i		−	1.60973i	−0.593460	−	0.804864i	$-0.702238\pi$
$467$		−	751.743i		−	1.60973i	0.593460	−	0.804864i	$-0.297762\pi$
$468$		0			0
$469$	−787.568			−1.67925
$470$		0			0
$471$		0			0
$472$	1.79325	+	3.10600i	0.00379926	+	0.00658052i
$473$	241.933	−	139.680i	0.511485	−	0.295306i
$474$		0			0
$475$		0			0
$476$			274.336i			0.576337i
$477$		0			0
$478$	−492.144			−1.02959
$479$	−23.9669	−	13.8373i	−0.0500352	−	0.0288879i	0.474774	−	0.880108i	$-0.342530\pi$
$479$	−23.9669	−	13.8373i	−0.0500352	−	0.0288879i	−0.524809	+	0.851220i	$0.675863\pi$
$480$		0			0
$481$	−47.0883	−	81.5594i	−0.0978967	−	0.169562i
$482$	45.6624	−	26.3632i	0.0947353	−	0.0546955i
$483$		0			0
$484$	−86.3027	+	149.481i	−0.178311	+	0.308844i
$485$		0			0
$486$		0			0
$487$	−690.293			−1.41744			−0.708720	−	0.705490i	$-0.750727\pi$
$487$	−690.293			−1.41744			−0.708720	+	0.705490i	$0.750727\pi$
$488$	227.257	+	131.207i	0.465691	+	0.268867i
$489$		0			0
$490$		0			0
$491$	308.987	−	178.394i	0.629302	−	0.363328i	−0.151180	−	0.988506i	$-0.548307\pi$
$491$	308.987	−	178.394i	0.629302	−	0.363328i	0.780482	+	0.625179i	$0.214974\pi$
$492$		0			0
$493$	60.8025	−	105.313i	0.123332	−	0.213617i
$494$		−	52.1195i		−	0.105505i
$495$		0			0
$496$	102.424			0.206500
$497$	−598.859	−	345.751i	−1.20495	−	0.695676i
$498$		0			0
$499$	18.4485	+	31.9538i	0.0369710	+	0.0640356i	0.883919	−	0.467640i	$-0.154896\pi$
$499$	18.4485	+	31.9538i	0.0369710	+	0.0640356i	−0.846948	+	0.531676i	$0.821562\pi$
$500$		0			0
$501$		0			0
$502$	53.6745	−	92.9670i	0.106921	−	0.185193i
$503$		−	283.649i		−	0.563914i	−0.959427	−	0.281957i	$-0.909016\pi$
$503$		−	283.649i		−	0.563914i	0.959427	−	0.281957i	$-0.0909836\pi$
$504$		0			0
$505$		0			0
$506$	−176.145	−	101.697i	−0.348112	−	0.200983i
$507$		0			0
$508$	14.5849	+	25.2617i	0.0287104	+	0.0497278i
$509$	833.302	−	481.107i	1.63714	−	0.945201i	0.655324	−	0.755348i	$-0.272532\pi$
$509$	833.302	−	481.107i	1.63714	−	0.945201i	0.981813	−	0.189853i	$-0.0608012\pi$
$510$		0			0
$511$	−260.904	+	451.899i	−0.510576	+	0.884343i
$512$		−	144.287i		−	0.281811i
$513$		0			0
$514$	−174.318			−0.339139
$515$		0			0
$516$		0			0
$517$	−54.0383	−	93.5971i	−0.104523	−	0.181039i
$518$	597.658	−	345.058i	1.15378	−	0.666135i
$519$		0			0
$520$		0			0
$521$			643.651i			1.23541i	0.786408	+	0.617707i	$0.211938\pi$
$521$			643.651i			1.23541i	−0.786408	+	0.617707i	$0.788062\pi$
$522$		0			0
$523$	−539.982			−1.03247			−0.516235	−	0.856447i	$-0.672667\pi$
$523$	−539.982			−1.03247			−0.516235	+	0.856447i	$0.672667\pi$
$524$	406.756	+	234.841i	0.776252	+	0.448169i
$525$		0			0
$526$	−217.242	−	376.274i	−0.413008	−	0.715350i
$527$	589.669	−	340.445i	1.11892	−	0.646006i
$528$		0			0
$529$	4.86759	−	8.43092i	0.00920150	−	0.0159375i
$530$		0			0
$531$		0			0
$532$	−471.590			−0.886447
$533$	−14.9451	−	8.62857i	−0.0280396	−	0.0161887i
$534$		0			0
$535$		0			0
$536$	690.430	−	398.620i	1.28812	−	0.743694i
$537$		0			0
$538$	236.541	−	409.700i	0.439667	−	0.761525i
$539$		−	120.279i		−	0.223152i
$540$		0			0
$541$	726.214			1.34235			0.671177	−	0.741297i	$-0.265789\pi$
$541$	726.214			1.34235			0.671177	+	0.741297i	$0.265789\pi$
$542$	385.584	+	222.617i	0.711409	+	0.410732i
$543$		0			0
$544$	−228.289	−	395.408i	−0.419649	−	0.726854i
$545$		0			0
$546$		0			0
$547$	−314.233	+	544.268i	−0.574467	+	0.995006i	0.421632	+	0.906767i	$0.361457\pi$
$547$	−314.233	+	544.268i	−0.574467	+	0.995006i	−0.996099	+	0.0882392i	$0.971876\pi$
$548$		−	331.420i		−	0.604781i
$549$		0			0
$550$		0			0
$551$	181.035	+	104.521i	0.328558	+	0.189693i
$552$		0			0
$553$	74.4165	+	128.893i	0.134569	+	0.233080i
$554$	97.3525	−	56.2065i	0.175726	−	0.101456i
$555$		0			0
$556$	6.19831	−	10.7358i	0.0111480	−	0.0193090i
$557$			821.989i			1.47574i	0.674941	+	0.737872i	$0.264169\pi$
$557$			821.989i			1.47574i	−0.674941	+	0.737872i	$0.735831\pi$
$558$		0			0
$559$	63.9106			0.114330
$560$		0			0
$561$		0			0
$562$	−249.456	−	432.071i	−0.443872	−	0.768809i
$563$	−763.584	+	440.856i	−1.35628	+	0.783047i	−0.989120	−	0.147111i	$-0.953002\pi$
$563$	−763.584	+	440.856i	−1.35628	+	0.783047i	−0.367158	+	0.930159i	$0.619669\pi$
$564$		0			0
$565$		0			0
$566$			214.807i			0.379518i
$567$		0			0
$568$	699.994			1.23238
$569$	−238.573	−	137.740i	−0.419284	−	0.242074i	0.275487	−	0.961305i	$-0.411161\pi$
$569$	−238.573	−	137.740i	−0.419284	−	0.242074i	−0.694771	+	0.719231i	$0.744494\pi$
$570$		0			0
$571$	216.022	+	374.161i	0.378322	+	0.655273i	0.990818	−	0.135200i	$-0.0431678\pi$
$571$	216.022	+	374.161i	0.378322	+	0.655273i	−0.612496	+	0.790474i	$0.709834\pi$
$572$	18.7857	−	10.8460i	0.0328422	−	0.0189615i
$573$		0			0
$574$	63.2291	−	109.516i	0.110155	−	0.190794i
$575$		0			0
$576$		0			0
$577$	1060.42			1.83782			0.918911	−	0.394466i	$-0.129070\pi$
$577$	1060.42			1.83782			0.918911	+	0.394466i	$0.129070\pi$
$578$	−69.8345	−	40.3190i	−0.120821	−	0.0697560i
$579$		0			0
$580$		0			0
$581$	717.610	−	414.312i	1.23513	−	0.713102i
$582$		0			0
$583$	216.187	−	374.447i	0.370819	−	0.642277i
$584$		−	528.216i		−	0.904480i
$585$		0			0
$586$	−427.501			−0.729525
$587$	149.127	+	86.0987i	0.254050	+	0.146676i	0.621617	−	0.783321i	$-0.286476\pi$
$587$	149.127	+	86.0987i	0.254050	+	0.146676i	−0.367567	+	0.929997i	$0.619809\pi$
$588$		0			0
$589$	585.233	+	1013.65i	0.993604	+	1.72097i
$590$		0			0
$591$		0			0
$592$	−71.4906	+	123.825i	−0.120761	+	0.209164i
$593$			534.948i			0.902104i	0.892498	+	0.451052i	$0.148951\pi$
$593$			534.948i			0.902104i	−0.892498	+	0.451052i	$0.851049\pi$
$594$		0			0
$595$		0			0
$596$	215.471	+	124.402i	0.361529	+	0.208729i
$597$		0			0
$598$	−23.2658	−	40.2976i	−0.0389060	−	0.0673872i
$599$	646.293	−	373.137i	1.07895	−	0.622934i	0.148339	−	0.988937i	$-0.452607\pi$
$599$	646.293	−	373.137i	1.07895	−	0.622934i	0.930614	+	0.366003i	$0.119274\pi$
$600$		0			0
$601$	−134.353	+	232.706i	−0.223549	+	0.387199i	−0.955883	−	0.293747i	$-0.905098\pi$
$601$	−134.353	+	232.706i	−0.223549	+	0.387199i	0.732334	+	0.680946i	$0.238431\pi$
$602$			468.329i			0.777956i
$603$		0			0
$604$	−134.280			−0.222317
$605$		0			0
$606$		0			0
$607$	255.867	+	443.175i	0.421527	+	0.730107i	0.996089	−	0.0883543i	$-0.0281608\pi$
$607$	255.867	+	443.175i	0.421527	+	0.730107i	−0.574562	+	0.818461i	$0.694827\pi$
$608$	679.716	−	392.434i	1.11795	−	0.645451i
$609$		0			0
$610$		0			0
$611$		−	24.7253i		−	0.0404669i
$612$		0			0
$613$	606.924			0.990088			0.495044	−	0.868868i	$-0.335152\pi$
$613$	606.924			0.990088			0.495044	+	0.868868i	$0.335152\pi$
$614$	390.051	+	225.196i	0.635263	+	0.366769i
$615$		0			0
$616$	223.322	+	386.806i	0.362536	+	0.627931i
$617$	−710.901	+	410.439i	−1.15219	+	0.665217i	−0.949420	−	0.314010i	$-0.898327\pi$
$617$	−710.901	+	410.439i	−1.15219	+	0.665217i	−0.202769	+	0.979227i	$0.564994\pi$
$618$		0			0
$619$	−292.071	+	505.881i	−0.471843	+	0.817256i	−0.999481	−	0.0322136i	$-0.989744\pi$
$619$	−292.071	+	505.881i	−0.471843	+	0.817256i	0.527638	+	0.849469i	$0.323078\pi$
$620$		0			0
$621$		0			0
$622$	−406.363			−0.653317
$623$	−613.461	−	354.182i	−0.984688	−	0.568510i
$624$		0			0
$625$		0			0
$626$	−265.600	+	153.344i	−0.424282	+	0.244959i
$627$		0			0
$628$	325.988	−	564.628i	0.519089	−	0.899088i
$629$			950.505i			1.51114i
$630$		0			0
$631$	−273.744			−0.433825			−0.216913	−	0.976191i	$-0.569599\pi$
$631$	−273.744			−0.433825			−0.216913	+	0.976191i	$0.569599\pi$
$632$	−130.476	−	75.3304i	−0.206449	−	0.119194i
$633$		0			0
$634$	−287.341	−	497.689i	−0.453219	−	0.784998i
$635$		0			0
$636$		0			0
$637$	13.7584	−	23.8303i	0.0215988	−	0.0374102i
$638$		−	70.4603i		−	0.110439i
$639$		0			0
$640$		0			0
$641$	−641.498	−	370.369i	−1.00078	−	0.577799i	−0.0922990	−	0.995731i	$-0.529422\pi$
$641$	−641.498	−	370.369i	−1.00078	−	0.577799i	−0.908478	+	0.417932i	$0.862755\pi$
$642$		0			0
$643$	−35.2027	−	60.9729i	−0.0547476	−	0.0948256i	0.837353	−	0.546663i	$-0.184102\pi$
$643$	−35.2027	−	60.9729i	−0.0547476	−	0.0948256i	−0.892100	+	0.451837i	$0.850769\pi$
$644$	−364.622	+	210.515i	−0.566184	+	0.326886i
$645$		0			0
$646$	−263.016	+	455.556i	−0.407145	+	0.705196i
$647$		−	470.408i		−	0.727060i	−0.931582	−	0.363530i	$-0.881571\pi$
$647$		−	470.408i		−	0.727060i	0.931582	−	0.363530i	$-0.118429\pi$
$648$		0			0
$649$	2.82746			0.00435664
$650$		0			0
$651$		0			0
$652$	−21.9115	−	37.9518i	−0.0336066	−	0.0582083i
$653$	−208.519	+	120.389i	−0.319325	+	0.184362i	−0.651092	−	0.758999i	$-0.725689\pi$
$653$	−208.519	+	120.389i	−0.319325	+	0.184362i	0.331767	+	0.943362i	$0.392355\pi$
$654$		0			0
$655$		0			0
$656$			26.2002i			0.0399393i
$657$		0			0
$658$	181.184			0.275355
$659$	−616.489	−	355.930i	−0.935491	−	0.540106i	−0.0469470	−	0.998897i	$-0.514949\pi$
$659$	−616.489	−	355.930i	−0.935491	−	0.540106i	−0.888544	+	0.458791i	$0.848283\pi$
$660$		0			0
$661$	216.848	+	375.592i	0.328060	+	0.568217i	0.982127	−	0.188220i	$-0.0602717\pi$
$661$	216.848	+	375.592i	0.328060	+	0.568217i	−0.654067	+	0.756437i	$0.726938\pi$
$662$	−318.500	+	183.886i	−0.481118	+	0.277774i
$663$		0			0
$664$	−419.400	+	726.422i	−0.631627	+	1.09401i
$665$		0			0
$666$		0			0
$667$	186.630			0.279805
$668$	193.870	+	111.931i	0.290225	+	0.167561i
$669$		0			0
$670$		0			0
$671$	179.161	−	103.438i	0.267006	−	0.154156i
$672$		0			0
$673$	−543.562	+	941.477i	−0.807671	+	1.39893i	0.106803	+	0.994280i	$0.465939\pi$
$673$	−543.562	+	941.477i	−0.807671	+	1.39893i	−0.914473	+	0.404646i	$0.867395\pi$
$674$			343.815i			0.510112i
$675$		0			0
$676$	−368.545			−0.545185
$677$	740.549	+	427.556i	1.09387	+	0.631545i	0.934604	−	0.355691i	$-0.115754\pi$
$677$	740.549	+	427.556i	1.09387	+	0.631545i	0.159265	+	0.987236i	$0.449088\pi$
$678$		0			0
$679$	−283.348	−	490.774i	−0.417302	−	0.722789i
$680$		0			0
$681$		0			0
$682$	197.261	−	341.666i	0.289239	−	0.500976i
$683$		−	96.8904i		−	0.141860i	−0.997481	−	0.0709300i	$-0.977403\pi$
$683$		−	96.8904i		−	0.141860i	0.997481	−	0.0709300i	$-0.0225967\pi$
$684$		0			0
$685$		0			0
$686$	−291.338	−	168.204i	−0.424691	−	0.245196i
$687$		0			0
$688$	−48.5152	−	84.0309i	−0.0705163	−	0.122138i
$689$	85.6643	−	49.4583i	0.124331	−	0.0717827i
$690$		0			0
$691$	410.189	−	710.468i	0.593616	−	1.02817i	−0.400125	−	0.916461i	$-0.631033\pi$
$691$	410.189	−	710.468i	0.593616	−	1.02817i	0.993741	−	0.111712i	$-0.0356335\pi$
$692$			244.600i			0.353469i
$693$		0			0
$694$	341.998			0.492792
$695$		0			0
$696$		0			0
$697$	87.0863	+	150.838i	0.124945	+	0.216410i
$698$	−339.471	+	195.993i	−0.486347	+	0.280793i
$699$		0			0
$700$		0			0
$701$			1180.09i			1.68343i	0.539919	+	0.841717i	$0.318455\pi$
$701$			1180.09i			1.68343i	−0.539919	+	0.841717i	$0.681545\pi$
$702$		0			0
$703$	−1633.94			−2.32424
$704$	−280.727	−	162.078i	−0.398759	−	0.230224i
$705$		0			0
$706$	−25.7204	−	44.5491i	−0.0364312	−	0.0631007i
$707$	−247.777	+	143.054i	−0.350463	+	0.202340i
$708$		0			0
$709$	450.319	−	779.975i	0.635146	−	1.10011i	−0.351338	−	0.936249i	$-0.614273\pi$
$709$	450.319	−	779.975i	0.635146	−	1.10011i	0.986484	−	0.163857i	$-0.0523936\pi$
$710$		0			0
$711$		0			0
$712$	717.062			1.00711
$713$	904.977	+	522.489i	1.26925	+	0.732803i
$714$		0			0
$715$		0			0
$716$	−105.522	+	60.9229i	−0.147376	+	0.0850878i
$717$		0			0
$718$	−112.561	+	194.961i	−0.156770	+	0.271534i
$719$			710.264i			0.987850i	0.869505	+	0.493925i	$0.164438\pi$
$719$			710.264i			0.987850i	−0.869505	+	0.493925i	$0.835562\pi$
$720$		0			0
$721$	180.660			0.250569
$722$	−364.846	−	210.644i	−0.505327	−	0.291751i
$723$		0			0
$724$	30.5196	+	52.8616i	0.0421542	+	0.0730132i
$725$		0			0
$726$		0			0
$727$	−177.728	+	307.833i	−0.244467	+	0.423429i	−0.961982	−	0.273114i	$-0.911946\pi$
$727$	−177.728	+	307.833i	−0.244467	+	0.423429i	0.717515	+	0.696543i	$0.245280\pi$
$728$			102.181i			0.140359i
$729$		0			0
$730$		0			0
$731$	−558.618	−	322.518i	−0.764183	−	0.441201i
$732$		0			0
$733$	661.951	+	1146.53i	0.903071	+	1.56416i	0.823486	+	0.567337i	$0.192026\pi$
$733$	661.951	+	1146.53i	0.903071	+	1.56416i	0.0795852	+	0.996828i	$0.474640\pi$
$734$	−54.5428	+	31.4903i	−0.0743089	+	0.0429023i
$735$		0			0
$736$	350.360	−	606.842i	0.476033	−	0.824513i
$737$		−	628.513i		−	0.852799i
$738$		0			0
$739$	1145.75			1.55040			0.775202	−	0.631713i	$-0.217648\pi$
$739$	1145.75			1.55040			0.775202	+	0.631713i	$0.217648\pi$
$740$		0			0
$741$		0			0
$742$	362.425	+	627.738i	0.488443	+	0.846008i
$743$	−686.107	+	396.124i	−0.923428	+	0.533141i	−0.884727	−	0.466110i	$-0.845655\pi$
$743$	−686.107	+	396.124i	−0.923428	+	0.533141i	−0.0387008	+	0.999251i	$0.512322\pi$
$744$		0			0
$745$		0			0
$746$			344.002i			0.461129i
$747$		0			0
$748$	−218.932			−0.292690
$749$	−709.795	−	409.801i	−0.947657	−	0.547130i
$750$		0			0
$751$	159.251	+	275.830i	0.212051	+	0.367284i	0.952356	−	0.304987i	$-0.0986523\pi$
$751$	159.251	+	275.830i	0.212051	+	0.367284i	−0.740305	+	0.672271i	$0.765319\pi$
$752$	−32.5093	+	18.7692i	−0.0432304	+	0.0249591i
$753$		0			0
$754$	8.05979	−	13.9600i	0.0106894	−	0.0185146i
$755$		0			0
$756$		0			0
$757$	−174.964			−0.231128			−0.115564	−	0.993300i	$-0.536868\pi$
$757$	−174.964			−0.231128			−0.115564	+	0.993300i	$0.536868\pi$
$758$	225.361	+	130.112i	0.297310	+	0.171652i
$759$		0			0
$760$		0			0
$761$	1032.43	−	596.072i	1.35667	−	0.783275i	0.367498	−	0.930024i	$-0.380214\pi$
$761$	1032.43	−	596.072i	1.35667	−	0.783275i	0.989174	+	0.146749i	$0.0468810\pi$
$762$		0			0
$763$	48.3689	−	83.7773i	0.0633930	−	0.109800i
$764$		−	576.634i		−	0.754756i
$765$		0			0
$766$	−275.400			−0.359530
$767$	0.560191	+	0.323427i	0.000730367	+	0.000421677i
$768$		0			0
$769$	−424.901	−	735.950i	−0.552537	−	0.957022i	−0.998091	−	0.0617670i	$-0.980326\pi$
$769$	−424.901	−	735.950i	−0.552537	−	0.957022i	0.445553	−	0.895255i	$-0.353007\pi$
$770$		0			0
$771$		0			0
$772$	−127.890	+	221.511i	−0.165660	+	0.286932i
$773$			344.791i			0.446042i	0.974814	+	0.223021i	$0.0715919\pi$
$773$			344.791i			0.446042i	−0.974814	+	0.223021i	$0.928408\pi$
$774$		0			0
$775$		0			0
$776$	496.801	+	286.828i	0.640207	+	0.369624i
$777$		0			0
$778$	229.218	+	397.018i	0.294625	+	0.510305i
$779$	−259.294	+	149.703i	−0.332855	+	0.192174i
$780$		0			0
$781$	275.924	−	477.915i	0.353296	−	0.611926i
$782$			469.634i			0.600555i
$783$		0			0
$784$	−41.7767			−0.0532866
$785$		0			0
$786$		0			0
$787$	625.961	+	1084.20i	0.795376	+	1.37763i	0.922600	+	0.385758i	$0.126060\pi$
$787$	625.961	+	1084.20i	0.795376	+	1.37763i	−0.127224	+	0.991874i	$0.540607\pi$
$788$	343.791	−	198.488i	0.436283	−	0.251888i
$789$		0			0
$790$		0			0
$791$		−	111.147i		−	0.140514i
$792$		0			0
$793$	47.3284			0.0596827
$794$	384.925	+	222.237i	0.484792	+	0.279895i
$795$		0			0
$796$	−146.584	−	253.891i	−0.184151	−	0.318959i
$797$	−375.640	+	216.876i	−0.471318	+	0.272115i	−0.716791	−	0.697288i	$-0.754390\pi$
$797$	−375.640	+	216.876i	−0.471318	+	0.272115i	0.245473	+	0.969403i	$0.421057\pi$
$798$		0			0
$799$	−124.774	+	216.114i	−0.156162	+	0.270481i
$800$		0			0
$801$		0			0
$802$	639.719			0.797655
$803$	−360.635	−	208.213i	−0.449109	−	0.259293i
$804$		0			0
$805$		0			0
$806$	78.1647	−	45.1284i	0.0969785	−	0.0559905i
$807$		0			0
$808$	144.811	−	250.820i	0.179222	−	0.310421i
$809$		−	900.166i		−	1.11269i	−0.830951	−	0.556345i	$-0.812203\pi$
$809$		−	900.166i		−	1.11269i	0.830951	−	0.556345i	$-0.187797\pi$
$810$		0			0
$811$	−112.379			−0.138569			−0.0692844	−	0.997597i	$-0.522072\pi$
$811$	−112.379			−0.138569			−0.0692844	+	0.997597i	$0.522072\pi$
$812$	−126.313	−	72.9270i	−0.155558	−	0.0898116i
$813$		0			0
$814$	275.371	+	476.956i	0.338293	+	0.585941i
$815$		0			0
$816$		0			0
$817$	554.416	−	960.276i	0.678599	−	1.17537i
$818$		−	244.657i		−	0.299092i
$819$		0			0
$820$		0			0
$821$	−1244.40	−	718.457i	−1.51572	−	0.875100i	−0.999830	−	0.0184448i	$-0.994128\pi$
$821$	−1244.40	−	718.457i	−1.51572	−	0.875100i	−0.515889	−	0.856656i	$-0.672538\pi$
$822$		0			0
$823$	35.2627	+	61.0768i	0.0428465	+	0.0742123i	0.886653	−	0.462435i	$-0.153024\pi$
$823$	35.2627	+	61.0768i	0.0428465	+	0.0742123i	−0.843807	+	0.536647i	$0.819691\pi$
$824$	−158.377	+	91.4393i	−0.192206	+	0.110970i
$825$		0			0
$826$	−2.37003	+	4.10501i	−0.00286929	+	0.00496975i
$827$			1406.58i			1.70082i	0.526122	+	0.850409i	$0.323646\pi$
$827$			1406.58i			1.70082i	−0.526122	+	0.850409i	$0.676354\pi$
$828$		0			0
$829$	771.482			0.930618			0.465309	−	0.885148i	$-0.345943\pi$
$829$	771.482			0.930618			0.465309	+	0.885148i	$0.345943\pi$
$830$		0			0
$831$		0			0
$832$	−37.0793	−	64.2233i	−0.0445665	−	0.0771915i
$833$	−240.514	+	138.861i	−0.288732	+	0.166700i
$834$		0			0
$835$		0			0
$836$		−	376.349i		−	0.450178i
$837$		0			0
$838$	544.264			0.649480
$839$	552.639	+	319.066i	0.658687	+	0.380293i	0.791777	−	0.610811i	$-0.209156\pi$
$839$	552.639	+	319.066i	0.658687	+	0.380293i	−0.133089	+	0.991104i	$0.542490\pi$
$840$		0			0
$841$	−388.174	−	672.336i	−0.461562	−	0.799449i
$842$	519.292	−	299.813i	0.616736	−	0.356073i
$843$		0			0
$844$	386.049	−	668.657i	0.457404	−	0.792247i
$845$		0			0
$846$		0			0
$847$	−640.992			−0.756780
$848$	−130.057	−	75.0887i	−0.153370	−	0.0885480i
$849$		0			0
$850$		0			0
$851$	−1263.32	+	729.380i	−1.48452	+	0.857086i
$852$		0			0
$853$	185.429	−	321.173i	0.217385	−	0.376521i	−0.736623	−	0.676304i	$-0.763581\pi$
$853$	185.429	−	321.173i	0.217385	−	0.376521i	0.954008	+	0.299782i	$0.0969141\pi$
$854$			346.817i			0.406108i
$855$		0			0
$856$	829.666			0.969236
$857$	562.649	+	324.846i	0.656533	+	0.379050i	0.790955	−	0.611875i	$-0.209584\pi$
$857$	562.649	+	324.846i	0.656533	+	0.379050i	−0.134421	+	0.990924i	$0.542918\pi$
$858$		0			0
$859$	25.4224	+	44.0328i	0.0295953	+	0.0512606i	0.880444	−	0.474151i	$-0.157245\pi$
$859$	25.4224	+	44.0328i	0.0295953	+	0.0512606i	−0.850848	+	0.525411i	$0.823911\pi$
$860$		0			0
$861$		0			0
$862$	−170.221	+	294.832i	−0.197472	+	0.342032i
$863$			254.583i			0.294997i	0.989062	+	0.147499i	$0.0471222\pi$
$863$			254.583i			0.294997i	−0.989062	+	0.147499i	$0.952878\pi$
$864$		0			0
$865$		0			0
$866$	96.1561	+	55.5157i	0.111035	+	0.0641059i
$867$		0			0
$868$	−408.333	−	707.253i	−0.470429	−	0.814808i
$869$	−102.862	+	59.3875i	−0.118369	+	0.0683401i
$870$		0			0
$871$	71.8941	−	124.524i	0.0825420	−	0.142967i
$872$			97.9257i			0.112300i
$873$		0			0
$874$	−807.311			−0.923697
$875$		0			0
$876$		0			0
$877$	285.665	+	494.786i	0.325729	+	0.564180i	0.981660	−	0.190642i	$-0.0610568\pi$
$877$	285.665	+	494.786i	0.325729	+	0.564180i	−0.655930	+	0.754821i	$0.727723\pi$
$878$	−299.985	+	173.196i	−0.341669	+	0.197263i
$879$		0			0
$880$		0			0
$881$		−	671.733i		−	0.762466i	−0.924479	−	0.381233i	$-0.875499\pi$
$881$		−	671.733i		−	0.762466i	0.924479	−	0.381233i	$-0.124501\pi$
$882$		0			0
$883$	858.151			0.971858			0.485929	−	0.873998i	$-0.338481\pi$
$883$	858.151			0.971858			0.485929	+	0.873998i	$0.338481\pi$
$884$	−43.3760	−	25.0431i	−0.0490678	−	0.0283293i
$885$		0			0
$886$	110.328	+	191.094i	0.124524	+	0.215682i
$887$	−1364.45	+	787.767i	−1.53828	+	0.888125i	−0.539337	+	0.842090i	$0.681325\pi$
$887$	−1364.45	+	787.767i	−1.53828	+	0.888125i	−0.998940	+	0.0460349i	$0.985341\pi$
$888$		0			0
$889$	−54.1628	+	93.8127i	−0.0609255	+	0.105526i
$890$		0			0
$891$		0			0
$892$	313.431			0.351380
$893$	−371.505	−	214.488i	−0.416019	−	0.240189i
$894$		0			0
$895$		0			0
$896$	−387.719	+	223.850i	−0.432723	+	0.249833i
$897$		0			0
$898$	420.372	−	728.106i	0.468121	−	0.810809i
$899$			362.003i			0.402673i
$900$		0			0
$901$	−998.345			−1.10804
$902$	87.3984	+	50.4595i	0.0968941	+	0.0559418i
$903$		0			0
$904$	56.2558	+	97.4379i	0.0622299	+	0.107785i
$905$		0			0
$906$		0			0
$907$	−547.384	+	948.097i	−0.603511	+	1.04531i	0.388774	+	0.921333i	$0.372899\pi$
$907$	−547.384	+	948.097i	−0.603511	+	1.04531i	−0.992285	+	0.123978i	$0.960435\pi$
$908$			300.359i			0.330791i
$909$		0			0
$910$		0			0
$911$	695.184	+	401.365i	0.763100	+	0.440576i	0.830408	−	0.557156i	$-0.188108\pi$
$911$	695.184	+	401.365i	0.763100	+	0.440576i	−0.0673079	+	0.997732i	$0.521441\pi$
$912$		0			0
$913$	330.639	+	572.683i	0.362145	+	0.627254i
$914$	−868.562	+	501.465i	−0.950287	+	0.548648i
$915$		0			0
$916$	−226.150	+	391.704i	−0.246889	+	0.427624i
$917$			1744.22i			1.90210i
$918$		0			0
$919$	−1294.88			−1.40901			−0.704506	−	0.709698i	$-0.748831\pi$
$919$	−1294.88			−1.40901			−0.704506	+	0.709698i	$0.748831\pi$
$920$		0			0
$921$		0			0
$922$	251.065	+	434.857i	0.272305	+	0.471645i
$923$	109.335	−	63.1246i	0.118456	−	0.0683907i
$924$		0			0
$925$		0			0
$926$		−	220.731i		−	0.238371i
$927$		0			0
$928$	242.745			0.261579
$929$	−450.703	−	260.214i	−0.485149	−	0.280101i	0.237411	−	0.971409i	$-0.423701\pi$
$929$	−450.703	−	260.214i	−0.485149	−	0.280101i	−0.722560	+	0.691309i	$0.757035\pi$
$930$		0			0
$931$	−238.705	−	413.449i	−0.256396	−	0.444091i
$932$	516.879	−	298.420i	0.554591	−	0.320193i
$933$		0			0
$934$	−502.867	+	870.990i	−0.538401	+	0.932538i
$935$		0			0
$936$		0			0
$937$	255.010			0.272155			0.136078	−	0.990698i	$-0.456550\pi$
$937$	255.010			0.272155			0.136078	+	0.990698i	$0.456550\pi$
$938$	912.499	+	526.831i	0.972813	+	0.561654i
$939$		0			0
$940$		0			0
$941$	528.359	−	305.048i	0.561487	−	0.324175i	−0.192255	−	0.981345i	$-0.561580\pi$
$941$	528.359	−	305.048i	0.561487	−	0.324175i	0.753742	+	0.657170i	$0.228247\pi$
$942$		0			0
$943$	−133.653	+	231.494i	−0.141732	+	0.245487i
$944$		−	0.982067i		−	0.00104033i
$945$		0			0
$946$	−373.747			−0.395081
$947$	−915.897	−	528.793i	−0.967156	−	0.558388i	−0.0687878	−	0.997631i	$-0.521913\pi$
$947$	−915.897	−	528.793i	−0.967156	−	0.558388i	−0.898368	+	0.439244i	$0.855246\pi$
$948$		0			0
$949$	−47.6339	−	82.5043i	−0.0501938	−	0.0869382i
$950$		0			0
$951$		0			0
$952$	515.647	−	893.127i	0.541646	−	0.938159i
$953$		−	605.977i		−	0.635862i	−0.948114	−	0.317931i	$-0.897012\pi$
$953$		−	605.977i		−	0.635862i	0.948114	−	0.317931i	$-0.102988\pi$
$954$		0			0
$955$		0			0
$956$	−704.081	−	406.501i	−0.736486	−	0.425211i
$957$		0			0
$958$	18.5125	+	32.0645i	0.0193241	+	0.0334703i
$959$	1065.88	−	615.386i	1.11145	−	0.641695i
$960$		0			0
$961$	−532.964	+	923.121i	−0.554593	+	0.960584i
$962$			125.996i			0.130973i
$963$		0			0
$964$	87.1019			0.0903547
$965$		0			0
$966$		0			0
$967$	−447.513	−	775.116i	−0.462785	−	0.801567i	0.536313	−	0.844019i	$-0.319816\pi$
$967$	−447.513	−	775.116i	−0.462785	−	0.801567i	−0.999099	+	0.0424516i	$0.986483\pi$
$968$	561.933	−	324.432i	0.580509	−	0.335157i
$969$		0			0
$970$		0			0
$971$			1442.25i			1.48532i	0.669666	+	0.742662i	$0.266437\pi$
$971$			1442.25i			1.48532i	−0.669666	+	0.742662i	$0.733563\pi$
$972$		0			0
$973$	46.0364			0.0473139
$974$	799.794	+	461.761i	0.821143	+	0.474087i
$975$		0			0
$976$	−35.9275	−	62.2282i	−0.0368109	−	0.0637584i
$977$	316.520	−	182.743i	0.323972	−	0.187045i	−0.329190	−	0.944264i	$-0.606776\pi$
$977$	316.520	−	182.743i	0.323972	−	0.187045i	0.653161	+	0.757219i	$0.273442\pi$
$978$		0			0
$979$	282.652	−	489.568i	0.288715	−	0.500069i
$980$		0			0
$981$		0			0
$982$	−477.335			−0.486085
$983$	−617.048	−	356.253i	−0.627719	−	0.362414i	0.152149	−	0.988358i	$-0.451381\pi$
$983$	−617.048	−	356.253i	−0.627719	−	0.362414i	−0.779868	+	0.625944i	$0.784714\pi$
$984$		0			0
$985$		0			0
$986$	−140.895	+	81.3458i	−0.142896	+	0.0825008i
$987$		0			0
$988$	43.0497	−	74.5642i	0.0435725	−	0.0754698i
$989$		−	989.951i		−	1.00096i
$990$		0			0
$991$	831.784			0.839338			0.419669	−	0.907677i	$-0.362146\pi$
$991$	831.784			0.839338			0.419669	+	0.907677i	$0.362146\pi$
$992$	1177.08	+	679.589i	1.18657	+	0.685069i
$993$		0			0
$994$	462.570	+	801.194i	0.465362	+	0.806031i
$995$		0			0
$996$		0			0
$997$	−439.170	+	760.664i	−0.440491	+	0.762953i	−0.997726	−	0.0674021i	$-0.978529\pi$
$997$	−439.170	+	760.664i	−0.440491	+	0.762953i	0.557235	+	0.830355i	$0.311862\pi$
$998$		−	49.3634i		−	0.0494623i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	675.3.j.e.251.4		20
3.2	odd	2		225.3.j.e.101.7		20
5.2	odd	4		135.3.h.a.89.7		20
5.3	odd	4		135.3.h.a.89.4		20
5.4	even	2	inner	675.3.j.e.251.7		20
9.4	even	3		225.3.j.e.176.7		20
9.5	odd	6	inner	675.3.j.e.476.4		20
15.2	even	4		45.3.h.a.29.4	yes	20
15.8	even	4		45.3.h.a.29.7	yes	20
15.14	odd	2		225.3.j.e.101.4		20
45.2	even	12		405.3.d.a.404.14		20
45.4	even	6		225.3.j.e.176.4		20
45.7	odd	12		405.3.d.a.404.7		20
45.13	odd	12		45.3.h.a.14.4	✓	20
45.14	odd	6	inner	675.3.j.e.476.7		20
45.22	odd	12		45.3.h.a.14.7	yes	20
45.23	even	12		135.3.h.a.44.7		20
45.32	even	12		135.3.h.a.44.4		20
45.38	even	12		405.3.d.a.404.8		20
45.43	odd	12		405.3.d.a.404.13		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.3.h.a.14.4	✓	20	45.13	odd	12
45.3.h.a.14.7	yes	20	45.22	odd	12
45.3.h.a.29.4	yes	20	15.2	even	4
45.3.h.a.29.7	yes	20	15.8	even	4
135.3.h.a.44.4		20	45.32	even	12
135.3.h.a.44.7		20	45.23	even	12
135.3.h.a.89.4		20	5.3	odd	4
135.3.h.a.89.7		20	5.2	odd	4
225.3.j.e.101.4		20	15.14	odd	2
225.3.j.e.101.7		20	3.2	odd	2
225.3.j.e.176.4		20	45.4	even	6
225.3.j.e.176.7		20	9.4	even	3
405.3.d.a.404.7		20	45.7	odd	12
405.3.d.a.404.8		20	45.38	even	12
405.3.d.a.404.13		20	45.43	odd	12
405.3.d.a.404.14		20	45.2	even	12
675.3.j.e.251.4		20	1.1	even	1	trivial
675.3.j.e.251.7		20	5.4	even	2	inner
675.3.j.e.476.4		20	9.5	odd	6	inner
675.3.j.e.476.7		20	45.14	odd	6	inner

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 675 = 3^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	675.j (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.15863 - 0.668935i) q^{2} +(-1.10505 - 1.91401i) q^{4} +(4.10376 - 7.10792i) q^{7} +8.30831i q^{8} +(5.67242 + 3.27497i) q^{11} +(0.749233 + 1.29771i) q^{13} +(-9.50946 + 5.49029i) q^{14} +(1.13750 - 1.97021i) q^{16} -15.1237i q^{17} +25.9980 q^{19} +(-4.38149 - 7.58896i) q^{22} +(20.1010 - 11.6053i) q^{23} -2.00475i q^{26} -18.1395 q^{28} +(6.96344 + 4.02034i) q^{29} +(22.5107 + 38.9897i) q^{31} +(26.1449 - 15.0948i) q^{32} +(-10.1168 + 17.5228i) q^{34} -62.8487 q^{37} +(-30.1220 - 17.3909i) q^{38} +(-9.97361 + 5.75827i) q^{41} +(21.3253 - 36.9366i) q^{43} -14.4761i q^{44} -31.0528 q^{46} +(-14.2898 - 8.25020i) q^{47} +(-9.18167 - 15.9031i) q^{49} +(1.65588 - 2.86808i) q^{52} -66.0119i q^{53} +(59.0548 + 34.0953i) q^{56} +(-5.37870 - 9.31617i) q^{58} +(0.373843 - 0.215838i) q^{59} +(15.7923 - 27.3530i) q^{61} -60.2328i q^{62} -49.4897 q^{64} +(-47.9785 - 83.1011i) q^{67} +(-28.9469 + 16.7125i) q^{68} -84.2523i q^{71} -63.5769 q^{73} +(72.8183 + 42.0417i) q^{74} +(-28.7292 - 49.7604i) q^{76} +(46.5565 - 26.8794i) q^{77} +(-9.06687 + 15.7043i) q^{79} +15.4076 q^{82} +(87.4333 + 50.4796i) q^{83} +(-49.4163 + 28.5305i) q^{86} +(-27.2095 + 47.1282i) q^{88} -86.3067i q^{89} +12.2987 q^{91} +(-44.4254 - 25.6490i) q^{92} +(11.0377 + 19.1178i) q^{94} +(34.5230 - 59.7956i) q^{97} +24.5677i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 18 q^{4} + 24 q^{11} + 30 q^{14} - 26 q^{16} + 8 q^{19} - 114 q^{29} + 28 q^{31} + 4 q^{34} - 102 q^{41} + 116 q^{46} + 40 q^{49} + 618 q^{56} + 120 q^{59} - 50 q^{61} - 140 q^{64} + 504 q^{74} - 96 q^{76}+ \cdots - 218 q^{94}+O(q^{100}) \) 20 * q + 18 * q^4 + 24 * q^11 + 30 * q^14 - 26 * q^16 + 8 * q^19 - 114 * q^29 + 28 * q^31 + 4 * q^34 - 102 * q^41 + 116 * q^46 + 40 * q^49 + 618 * q^56 + 120 * q^59 - 50 * q^61 - 140 * q^64 + 504 * q^74 - 96 * q^76 + 128 * q^79 - 1488 * q^86 - 288 * q^91 - 218 * q^94

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