LMFDB - Embedded newform 630.3.bd.a.359.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [630,3,Mod(179,630)] 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("630.179"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(630, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 3, 4])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	630.bd (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,0,-8,0,0,0,0,0,-4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(10)] == traces)

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

Self dual:	no
Analytic conductor:	$17.1662566547$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{24})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			359.4
Root			$-0.965926 - 0.258819i$ of defining polynomial
Character	$\chi$	$=$	630.359
Dual form			630.3.bd.a.179.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.707107 - 1.22474i) q^{2} +(-1.00000 - 1.73205i) q^{4} +(4.64016 + 1.86250i) q^{5} +(6.06218 + 3.50000i) q^{7} -2.82843 q^{8} +(5.56218 - 4.36603i) q^{10} +(2.44949 - 1.41421i) q^{11} +5.00000i q^{13} +(8.57321 - 4.94975i) q^{14} +(-2.00000 + 3.46410i) q^{16} +(7.77817 + 13.4722i) q^{17} +(3.50000 - 6.06218i) q^{19} +(-1.41421 - 9.89949i) q^{20} -4.00000i q^{22} +(-10.6066 + 18.3712i) q^{23} +(18.0622 + 17.2846i) q^{25} +(6.12372 + 3.53553i) q^{26} -14.0000i q^{28} -12.7279i q^{29} +(10.5000 + 18.1865i) q^{31} +(2.82843 + 4.89898i) q^{32} +22.0000 q^{34} +(21.6107 + 27.5314i) q^{35} +(25.1147 + 14.5000i) q^{37} +(-4.94975 - 8.57321i) q^{38} +(-13.1244 - 5.26795i) q^{40} -76.3675i q^{41} +53.0000i q^{43} +(-4.89898 - 2.82843i) q^{44} +(15.0000 + 25.9808i) q^{46} +(0.707107 - 1.22474i) q^{47} +(24.5000 + 42.4352i) q^{49} +(33.9411 - 9.89949i) q^{50} +(8.66025 - 5.00000i) q^{52} +(-32.5269 - 56.3383i) q^{53} +(14.0000 - 2.00000i) q^{55} +(-17.1464 - 9.89949i) q^{56} +(-15.5885 - 9.00000i) q^{58} +(82.0579 - 47.3762i) q^{59} +(-8.00000 + 13.8564i) q^{61} +29.6985 q^{62} +8.00000 q^{64} +(-9.31251 + 23.2008i) q^{65} +(-18.1865 + 10.5000i) q^{67} +(15.5563 - 26.9444i) q^{68} +(49.0000 - 7.00000i) q^{70} -73.5391i q^{71} +(61.4878 - 35.5000i) q^{73} +(35.5176 - 20.5061i) q^{74} -14.0000 q^{76} +19.7990 q^{77} +(60.5000 - 104.789i) q^{79} +(-15.7322 + 12.3490i) q^{80} +(-93.5307 - 54.0000i) q^{82} -113.137 q^{83} +(11.0000 + 77.0000i) q^{85} +(64.9115 + 37.4767i) q^{86} +(-6.92820 + 4.00000i) q^{88} +(35.5176 + 20.5061i) q^{89} +(-17.5000 + 30.3109i) q^{91} +42.4264 q^{92} +(-1.00000 - 1.73205i) q^{94} +(27.5314 - 21.6107i) q^{95} +20.0000i q^{97} +69.2965 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{4} - 4 q^{10} - 16 q^{16} + 28 q^{19} + 96 q^{25} + 84 q^{31} + 176 q^{34} - 8 q^{40} + 120 q^{46} + 196 q^{49} + 112 q^{55} - 64 q^{61} + 64 q^{64} + 392 q^{70} - 112 q^{76} + 484 q^{79} + 88 q^{85}+ \cdots - 8 q^{94}+O(q^{100}) $ 8 * q - 8 * q^4 - 4 * q^10 - 16 * q^16 + 28 * q^19 + 96 * q^25 + 84 * q^31 + 176 * q^34 - 8 * q^40 + 120 * q^46 + 196 * q^49 + 112 * q^55 - 64 * q^61 + 64 * q^64 + 392 * q^70 - 112 * q^76 + 484 * q^79 + 88 * q^85 - 140 * q^91 - 8 * q^94

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/630\mathbb{Z}\right)^\times$.

$n$	$127$	$281$	$451$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	0.707107	−	1.22474i	0.353553	−	0.612372i
$2$	0.707107	−	1.22474i	0.353553	−	0.612372i
$3$		0			0
$3$		0			0
$4$	−1.00000	−	1.73205i	−0.250000	−	0.433013i
$5$	4.64016	+	1.86250i	0.928032	+	0.372500i
$5$	4.64016	+	1.86250i	0.928032	+	0.372500i
$6$		0			0
$7$	6.06218	+	3.50000i	0.866025	+	0.500000i
$7$	6.06218	+	3.50000i	0.866025	+	0.500000i
$8$	−2.82843			−0.353553
$9$		0			0
$10$	5.56218	−	4.36603i	0.556218	−	0.436603i
$11$	2.44949	−	1.41421i	0.222681	−	0.128565i	−0.384510	−	0.923121i	$-0.625630\pi$
$11$	2.44949	−	1.41421i	0.222681	−	0.128565i	0.607191	+	0.794556i	$0.292296\pi$
$12$		0			0
$13$			5.00000i			0.384615i	0.981335	+	0.192308i	$0.0615972\pi$
$13$			5.00000i			0.384615i	−0.981335	+	0.192308i	$0.938403\pi$
$14$	8.57321	−	4.94975i	0.612372	−	0.353553i
$15$		0			0
$16$	−2.00000	+	3.46410i	−0.125000	+	0.216506i
$17$	7.77817	+	13.4722i	0.457540	+	0.792482i	0.998830	−	0.0483536i	$-0.0153974\pi$
$17$	7.77817	+	13.4722i	0.457540	+	0.792482i	−0.541291	+	0.840836i	$0.682064\pi$
$18$		0			0
$19$	3.50000	−	6.06218i	0.184211	−	0.319062i	−0.759100	−	0.650974i	$-0.774361\pi$
$19$	3.50000	−	6.06218i	0.184211	−	0.319062i	0.943310	+	0.331912i	$0.107694\pi$
$20$	−1.41421	−	9.89949i	−0.0707107	−	0.494975i
$21$		0			0
$22$		−	4.00000i		−	0.181818i
$23$	−10.6066	+	18.3712i	−0.461157	+	0.798747i	−0.999019	−	0.0442861i	$-0.985899\pi$
$23$	−10.6066	+	18.3712i	−0.461157	+	0.798747i	0.537862	+	0.843033i	$0.319232\pi$
$24$		0			0
$25$	18.0622	+	17.2846i	0.722487	+	0.691384i
$26$	6.12372	+	3.53553i	0.235528	+	0.135982i
$27$		0			0
$28$		−	14.0000i		−	0.500000i
$29$		−	12.7279i		−	0.438894i	−0.975624	−	0.219447i	$-0.929575\pi$
$29$		−	12.7279i		−	0.438894i	0.975624	−	0.219447i	$-0.0704253\pi$
$30$		0			0
$31$	10.5000	+	18.1865i	0.338710	+	0.586662i	0.984190	−	0.177114i	$-0.0566762\pi$
$31$	10.5000	+	18.1865i	0.338710	+	0.586662i	−0.645481	+	0.763777i	$0.723343\pi$
$32$	2.82843	+	4.89898i	0.0883883	+	0.153093i
$33$		0			0
$34$	22.0000			0.647059
$35$	21.6107	+	27.5314i	0.617449	+	0.786611i
$36$		0			0
$37$	25.1147	+	14.5000i	0.678777	+	0.391892i	0.799394	−	0.600807i	$-0.205154\pi$
$37$	25.1147	+	14.5000i	0.678777	+	0.391892i	−0.120617	+	0.992699i	$0.538487\pi$
$38$	−4.94975	−	8.57321i	−0.130257	−	0.225611i
$39$		0			0
$40$	−13.1244	−	5.26795i	−0.328109	−	0.131699i
$41$		−	76.3675i		−	1.86262i	−0.364224	−	0.931311i	$-0.618666\pi$
$41$		−	76.3675i		−	1.86262i	0.364224	−	0.931311i	$-0.381334\pi$
$42$		0			0
$43$			53.0000i			1.23256i	0.787528	+	0.616279i	$0.211361\pi$
$43$			53.0000i			1.23256i	−0.787528	+	0.616279i	$0.788639\pi$
$44$	−4.89898	−	2.82843i	−0.111340	−	0.0642824i
$45$		0			0
$46$	15.0000	+	25.9808i	0.326087	+	0.564799i
$47$	0.707107	−	1.22474i	0.0150448	−	0.0260584i	−0.858405	−	0.512973i	$-0.828544\pi$
$47$	0.707107	−	1.22474i	0.0150448	−	0.0260584i	0.873450	+	0.486914i	$0.161878\pi$
$48$		0			0
$49$	24.5000	+	42.4352i	0.500000	+	0.866025i
$50$	33.9411	−	9.89949i	0.678823	−	0.197990i
$51$		0			0
$52$	8.66025	−	5.00000i	0.166543	−	0.0961538i
$53$	−32.5269	−	56.3383i	−0.613715	−	1.06299i	−0.990608	−	0.136729i	$-0.956341\pi$
$53$	−32.5269	−	56.3383i	−0.613715	−	1.06299i	0.376893	−	0.926257i	$-0.376992\pi$
$54$		0			0
$55$	14.0000	−	2.00000i	0.254545	−	0.0363636i
$56$	−17.1464	−	9.89949i	−0.306186	−	0.176777i
$57$		0			0
$58$	−15.5885	−	9.00000i	−0.268767	−	0.155172i
$59$	82.0579	−	47.3762i	1.39081	−	0.802986i	0.397407	−	0.917643i	$-0.369910\pi$
$59$	82.0579	−	47.3762i	1.39081	−	0.802986i	0.993405	+	0.114657i	$0.0365769\pi$
$60$		0			0
$61$	−8.00000	+	13.8564i	−0.131148	+	0.227154i	−0.924119	−	0.382104i	$-0.875199\pi$
$61$	−8.00000	+	13.8564i	−0.131148	+	0.227154i	0.792972	+	0.609259i	$0.208533\pi$
$62$	29.6985			0.479008
$63$		0			0
$64$	8.00000			0.125000
$65$	−9.31251	+	23.2008i	−0.143269	+	0.356935i
$66$		0			0
$67$	−18.1865	+	10.5000i	−0.271441	+	0.156716i	−0.629542	−	0.776966i	$-0.716758\pi$
$67$	−18.1865	+	10.5000i	−0.271441	+	0.156716i	0.358101	+	0.933683i	$0.383424\pi$
$68$	15.5563	−	26.9444i	0.228770	−	0.396241i
$69$		0			0
$70$	49.0000	−	7.00000i	0.700000	−	0.100000i
$71$		−	73.5391i		−	1.03576i	−0.855453	−	0.517881i	$-0.826721\pi$
$71$		−	73.5391i		−	1.03576i	0.855453	−	0.517881i	$-0.173279\pi$
$72$		0			0
$73$	61.4878	−	35.5000i	0.842299	−	0.486301i	−0.0157462	−	0.999876i	$-0.505012\pi$
$73$	61.4878	−	35.5000i	0.842299	−	0.486301i	0.858045	+	0.513575i	$0.171679\pi$
$74$	35.5176	−	20.5061i	0.479968	−	0.277109i
$75$		0			0
$76$	−14.0000			−0.184211
$77$	19.7990			0.257130
$78$		0			0
$79$	60.5000	−	104.789i	0.765823	−	1.32644i	−0.173988	−	0.984748i	$-0.555665\pi$
$79$	60.5000	−	104.789i	0.765823	−	1.32644i	0.939810	−	0.341696i	$-0.111001\pi$
$80$	−15.7322	+	12.3490i	−0.196653	+	0.154362i
$81$		0			0
$82$	−93.5307	−	54.0000i	−1.14062	−	0.658537i
$83$	−113.137			−1.36310			−0.681549	−	0.731773i	$-0.738693\pi$
$83$	−113.137			−1.36310			−0.681549	+	0.731773i	$0.738693\pi$
$84$		0			0
$85$	11.0000	+	77.0000i	0.129412	+	0.905882i
$86$	64.9115	+	37.4767i	0.754785	+	0.435775i
$87$		0			0
$88$	−6.92820	+	4.00000i	−0.0787296	+	0.0454545i
$89$	35.5176	+	20.5061i	0.399074	+	0.230406i	0.686084	−	0.727522i	$-0.259328\pi$
$89$	35.5176	+	20.5061i	0.399074	+	0.230406i	−0.287010	+	0.957928i	$0.592661\pi$
$90$		0			0
$91$	−17.5000	+	30.3109i	−0.192308	+	0.333087i
$92$	42.4264			0.461157
$93$		0			0
$94$	−1.00000	−	1.73205i	−0.0106383	−	0.0184261i
$95$	27.5314	−	21.6107i	0.289804	−	0.227481i
$96$		0			0
$97$			20.0000i			0.206186i	0.994672	+	0.103093i	$0.0328739\pi$
$97$			20.0000i			0.206186i	−0.994672	+	0.103093i	$0.967126\pi$
$98$	69.2965			0.707107
$99$		0			0
$100$	11.8756	−	48.5692i	0.118756	−	0.485692i
$101$	26.9444	−	15.5563i	0.266776	−	0.154023i	−0.360646	−	0.932703i	$-0.617444\pi$
$101$	26.9444	−	15.5563i	0.266776	−	0.154023i	0.627422	+	0.778680i	$0.284110\pi$
$102$		0			0
$103$	−64.9519	−	37.5000i	−0.630601	−	0.364078i	0.150384	−	0.988628i	$-0.451949\pi$
$103$	−64.9519	−	37.5000i	−0.630601	−	0.364078i	−0.780985	+	0.624550i	$0.785282\pi$
$104$		−	14.1421i		−	0.135982i
$105$		0			0
$106$	−92.0000			−0.867925
$107$	−23.3345	+	40.4166i	−0.218080	+	0.377725i	−0.954221	−	0.299103i	$-0.903313\pi$
$107$	−23.3345	+	40.4166i	−0.218080	+	0.377725i	0.736141	+	0.676828i	$0.236646\pi$
$108$		0			0
$109$	13.5000	+	23.3827i	0.123853	+	0.214520i	0.921284	−	0.388890i	$-0.127141\pi$
$109$	13.5000	+	23.3827i	0.123853	+	0.214520i	−0.797431	+	0.603410i	$0.793808\pi$
$110$	7.45001	−	18.5606i	0.0677273	−	0.168733i
$111$		0			0
$112$	−24.2487	+	14.0000i	−0.216506	+	0.125000i
$113$	−12.7279			−0.112636			−0.0563182	−	0.998413i	$-0.517936\pi$
$113$	−12.7279			−0.112636			−0.0563182	+	0.998413i	$0.517936\pi$
$114$		0			0
$115$	−83.4327	+	65.4904i	−0.725501	+	0.569482i
$116$	−22.0454	+	12.7279i	−0.190047	+	0.109723i
$117$		0			0
$118$		−	134.000i		−	1.13559i
$119$			108.894i			0.915079i
$120$		0			0
$121$	−56.5000	+	97.8609i	−0.466942	+	0.808768i
$122$	11.3137	+	19.5959i	0.0927353	+	0.160622i
$123$		0			0
$124$	21.0000	−	36.3731i	0.169355	−	0.293331i
$125$	51.6188	+	113.844i	0.412950	+	0.910754i
$126$		0			0
$127$			165.000i			1.29921i	0.760271	+	0.649606i	$0.225066\pi$
$127$			165.000i			1.29921i	−0.760271	+	0.649606i	$0.774934\pi$
$128$	5.65685	−	9.79796i	0.0441942	−	0.0765466i
$129$		0			0
$130$	21.8301	+	27.8109i	0.167924	+	0.213930i
$131$	−153.093	−	88.3883i	−1.16865	−	0.674720i	−0.215288	−	0.976551i	$-0.569069\pi$
$131$	−153.093	−	88.3883i	−1.16865	−	0.674720i	−0.953362	+	0.301830i	$0.902402\pi$
$132$		0			0
$133$	42.4352	−	24.5000i	0.319062	−	0.184211i
$134$			29.6985i			0.221630i
$135$		0			0
$136$	−22.0000	−	38.1051i	−0.161765	−	0.280185i
$137$	−75.6604	−	131.048i	−0.552266	−	0.956553i	−0.998111	−	0.0614423i	$-0.980430\pi$
$137$	−75.6604	−	131.048i	−0.552266	−	0.956553i	0.445845	−	0.895110i	$-0.352903\pi$
$138$		0			0
$139$	−151.000			−1.08633			−0.543165	−	0.839626i	$-0.682774\pi$
$139$	−151.000			−1.08633			−0.543165	+	0.839626i	$0.682774\pi$
$140$	26.0750	−	64.9622i	0.186250	−	0.464016i
$141$		0			0
$142$	−90.0666	−	52.0000i	−0.634272	−	0.366197i
$143$	7.07107	+	12.2474i	0.0494480	+	0.0856465i
$144$		0			0
$145$	23.7058	−	59.0596i	0.163488	−	0.407308i
$146$		−	100.409i		−	0.687734i
$147$		0			0
$148$		−	58.0000i		−	0.391892i
$149$	−29.3939	−	16.9706i	−0.197274	−	0.113896i	0.398109	−	0.917338i	$-0.369667\pi$
$149$	−29.3939	−	16.9706i	−0.197274	−	0.113896i	−0.595383	+	0.803442i	$0.703000\pi$
$150$		0			0
$151$	8.00000	+	13.8564i	0.0529801	+	0.0917643i	0.891299	−	0.453416i	$-0.149795\pi$
$151$	8.00000	+	13.8564i	0.0529801	+	0.0917643i	−0.838319	+	0.545180i	$0.816461\pi$
$152$	−9.89949	+	17.1464i	−0.0651283	+	0.112805i
$153$		0			0
$154$	14.0000	−	24.2487i	0.0909091	−	0.157459i
$155$	14.8492	+	103.945i	0.0958016	+	0.670611i
$156$		0			0
$157$	65.8179	−	38.0000i	0.419222	−	0.242038i	−0.275522	−	0.961295i	$-0.588851\pi$
$157$	65.8179	−	38.0000i	0.419222	−	0.242038i	0.694745	+	0.719257i	$0.255517\pi$
$158$	−85.5599	−	148.194i	−0.541518	−	0.937938i
$159$		0			0
$160$	4.00000	+	28.0000i	0.0250000	+	0.175000i
$161$	−128.598	+	74.2462i	−0.798747	+	0.461157i
$162$		0			0
$163$	72.7461	+	42.0000i	0.446295	+	0.257669i	0.706264	−	0.707948i	$-0.250379\pi$
$163$	72.7461	+	42.0000i	0.446295	+	0.257669i	−0.259969	+	0.965617i	$0.583712\pi$
$164$	−132.272	+	76.3675i	−0.806539	+	0.465656i
$165$		0			0
$166$	−80.0000	+	138.564i	−0.481928	+	0.834723i
$167$	−192.333			−1.15169			−0.575847	−	0.817557i	$-0.695328\pi$
$167$	−192.333			−1.15169			−0.575847	+	0.817557i	$0.695328\pi$
$168$		0			0
$169$	144.000			0.852071
$170$	102.084	+	40.9750i	0.600491	+	0.241030i
$171$		0			0
$172$	91.7987	−	53.0000i	0.533713	−	0.308140i
$173$	−60.8112	+	105.328i	−0.351510	+	0.608833i	−0.986514	−	0.163676i	$-0.947665\pi$
$173$	−60.8112	+	105.328i	−0.351510	+	0.608833i	0.635004	+	0.772508i	$0.280998\pi$
$174$		0			0
$175$	49.0000	+	168.000i	0.280000	+	0.960000i
$176$			11.3137i			0.0642824i
$177$		0			0
$178$	50.2295	−	29.0000i	0.282188	−	0.162921i
$179$	−182.487	+	105.359i	−1.01948	+	0.588597i	−0.913953	−	0.405819i	$-0.866986\pi$
$179$	−182.487	+	105.359i	−1.01948	+	0.588597i	−0.105527	+	0.994416i	$0.533653\pi$
$180$		0			0
$181$	−353.000			−1.95028			−0.975138	−	0.221598i	$-0.928873\pi$
$181$	−353.000			−1.95028			−0.975138	+	0.221598i	$0.928873\pi$
$182$	24.7487	+	42.8661i	0.135982	+	0.235528i
$183$		0			0
$184$	30.0000	−	51.9615i	0.163043	−	0.282400i
$185$	89.5301	+	114.059i	0.483947	+	0.616533i
$186$		0			0
$187$	38.1051	+	22.0000i	0.203771	+	0.117647i
$188$	−2.82843			−0.0150448
$189$		0			0
$190$	−7.00000	−	49.0000i	−0.0368421	−	0.257895i
$191$	−1.22474	−	0.707107i	−0.00641228	−	0.00370213i	0.496790	−	0.867871i	$-0.334512\pi$
$191$	−1.22474	−	0.707107i	−0.00641228	−	0.00370213i	−0.503203	+	0.864168i	$0.667845\pi$
$192$		0			0
$193$	241.621	−	139.500i	1.25192	−	0.722798i	0.280432	−	0.959874i	$-0.409522\pi$
$193$	241.621	−	139.500i	1.25192	−	0.722798i	0.971491	+	0.237076i	$0.0761891\pi$
$194$	24.4949	+	14.1421i	0.126262	+	0.0728976i
$195$		0			0
$196$	49.0000	−	84.8705i	0.250000	−	0.433013i
$197$	352.139			1.78751			0.893754	−	0.448557i	$-0.148062\pi$
$197$	352.139			1.78751			0.893754	+	0.448557i	$0.148062\pi$
$198$		0			0
$199$	−76.0000	−	131.636i	−0.381910	−	0.661487i	0.609426	−	0.792843i	$-0.291400\pi$
$199$	−76.0000	−	131.636i	−0.381910	−	0.661487i	−0.991335	+	0.131356i	$0.958067\pi$
$200$	−51.0876	−	48.8883i	−0.255438	−	0.244441i
$201$		0			0
$202$		−	44.0000i		−	0.217822i
$203$	44.5477	−	77.1589i	0.219447	−	0.380093i
$204$		0			0
$205$	142.235	−	354.358i	0.693827	−	1.72857i
$206$	−91.8559	+	53.0330i	−0.445902	+	0.257442i
$207$		0			0
$208$	−17.3205	−	10.0000i	−0.0832717	−	0.0480769i
$209$		−	19.7990i		−	0.0947320i
$210$		0			0
$211$	−344.000			−1.63033			−0.815166	−	0.579228i	$-0.803354\pi$
$211$	−344.000			−1.63033			−0.815166	+	0.579228i	$0.803354\pi$
$212$	−65.0538	+	112.677i	−0.306858	+	0.531493i
$213$		0			0
$214$	33.0000	+	57.1577i	0.154206	+	0.267092i
$215$	−98.7126	+	245.929i	−0.459128	+	1.14385i
$216$		0			0
$217$			147.000i			0.677419i
$218$	38.1838			0.175155
$219$		0			0
$220$	−17.4641	−	22.2487i	−0.0793823	−	0.101131i
$221$	−67.3610	+	38.8909i	−0.304801	+	0.175977i
$222$		0			0
$223$		−	70.0000i		−	0.313901i	−0.987606	−	0.156951i	$-0.949834\pi$
$223$		−	70.0000i		−	0.313901i	0.987606	−	0.156951i	$-0.0501664\pi$
$224$			39.5980i			0.176777i
$225$		0			0
$226$	−9.00000	+	15.5885i	−0.0398230	+	0.0689755i
$227$	−18.3848	−	31.8434i	−0.0809902	−	0.140279i	0.822685	−	0.568497i	$-0.192475\pi$
$227$	−18.3848	−	31.8434i	−0.0809902	−	0.140279i	−0.903676	+	0.428218i	$0.859142\pi$
$228$		0			0
$229$	2.50000	−	4.33013i	0.0109170	−	0.0189089i	−0.860515	−	0.509425i	$-0.829858\pi$
$229$	2.50000	−	4.33013i	0.0109170	−	0.0189089i	0.871432	+	0.490516i	$0.163192\pi$
$230$	21.2132	+	148.492i	0.0922313	+	0.645619i
$231$		0			0
$232$			36.0000i			0.155172i
$233$	−108.187	+	187.386i	−0.464323	+	0.804232i	−0.999171	−	0.0407171i	$-0.987036\pi$
$233$	−108.187	+	187.386i	−0.464323	+	0.804232i	0.534847	+	0.844949i	$0.320369\pi$
$234$		0			0
$235$	5.56218	−	4.36603i	0.0236688	−	0.0185788i
$236$	−164.116	−	94.7523i	−0.695406	−	0.401493i
$237$		0			0
$238$	133.368	+	77.0000i	0.560369	+	0.323529i
$239$			354.968i			1.48522i	0.669724	+	0.742610i	$0.266412\pi$
$239$			354.968i			1.48522i	−0.669724	+	0.742610i	$0.733588\pi$
$240$		0			0
$241$	−178.000	−	308.305i	−0.738589	−	1.27927i	−0.953131	−	0.302559i	$-0.902159\pi$
$241$	−178.000	−	308.305i	−0.738589	−	1.27927i	0.214541	−	0.976715i	$-0.431174\pi$
$242$	79.9031	+	138.396i	0.330178	+	0.571885i
$243$		0			0
$244$	32.0000			0.131148
$245$	34.6482	+	242.538i	0.141421	+	0.989949i
$246$		0			0
$247$	30.3109	+	17.5000i	0.122716	+	0.0708502i
$248$	−29.6985	−	51.4393i	−0.119752	−	0.207416i
$249$		0			0
$250$	175.930	+	17.2801i	0.703720	+	0.0691206i
$251$		−	190.919i		−	0.760633i	−0.924856	−	0.380316i	$-0.875815\pi$
$251$		−	190.919i		−	0.760633i	0.924856	−	0.380316i	$-0.124185\pi$
$252$		0			0
$253$			60.0000i			0.237154i
$254$	202.083	+	116.673i	0.795602	+	0.459341i
$255$		0			0
$256$	−8.00000	−	13.8564i	−0.0312500	−	0.0541266i
$257$	−192.333	+	333.131i	−0.748378	+	1.29623i	0.200222	+	0.979750i	$0.435834\pi$
$257$	−192.333	+	333.131i	−0.748378	+	1.29623i	−0.948600	+	0.316478i	$0.897500\pi$
$258$		0			0
$259$	101.500	+	175.803i	0.391892	+	0.678777i
$260$	49.4975	−	7.07107i	0.190375	−	0.0271964i
$261$		0			0
$262$	−216.506	+	125.000i	−0.826360	+	0.477099i
$263$	−220.617	−	382.120i	−0.838849	−	1.45293i	−0.890858	−	0.454283i	$-0.849896\pi$
$263$	−220.617	−	382.120i	−0.838849	−	1.45293i	0.0520085	−	0.998647i	$-0.483438\pi$
$264$		0			0
$265$	−46.0000	−	322.000i	−0.173585	−	1.21509i
$266$		−	69.2965i		−	0.260513i
$267$		0			0
$268$	36.3731	+	21.0000i	0.135720	+	0.0783582i
$269$	35.5176	−	20.5061i	0.132036	−	0.0762308i	−0.432527	−	0.901621i	$-0.642378\pi$
$269$	35.5176	−	20.5061i	0.132036	−	0.0762308i	0.564563	+	0.825390i	$0.309045\pi$
$270$		0			0
$271$	−154.000	+	266.736i	−0.568266	+	0.984265i	0.428472	+	0.903555i	$0.359052\pi$
$271$	−154.000	+	266.736i	−0.568266	+	0.984265i	−0.996738	+	0.0807100i	$0.974281\pi$
$272$	−62.2254			−0.228770
$273$		0			0
$274$	−214.000			−0.781022
$275$	68.6872	+	16.7947i	0.249772	+	0.0610716i
$276$		0			0
$277$	435.611	−	251.500i	1.57260	−	0.907942i	0.576753	−	0.816918i	$-0.304319\pi$
$277$	435.611	−	251.500i	1.57260	−	0.907942i	0.995849	−	0.0910239i	$-0.0290140\pi$
$278$	−106.773	+	184.936i	−0.384076	+	0.665239i
$279$		0			0
$280$	−61.1244	−	77.8705i	−0.218301	−	0.278109i
$281$		−	48.0833i		−	0.171115i	−0.996333	−	0.0855574i	$-0.972733\pi$
$281$		−	48.0833i		−	0.171115i	0.996333	−	0.0855574i	$-0.0272671\pi$
$282$		0			0
$283$	−290.119	+	167.500i	−1.02515	+	0.591873i	−0.915593	−	0.402107i	$-0.868278\pi$
$283$	−290.119	+	167.500i	−1.02515	+	0.591873i	−0.109561	+	0.993980i	$0.534945\pi$
$284$	−127.373	+	73.5391i	−0.448498	+	0.258941i
$285$		0			0
$286$	20.0000			0.0699301
$287$	267.286	−	462.954i	0.931311	−	1.61308i
$288$		0			0
$289$	23.5000	−	40.7032i	0.0813149	−	0.140842i
$290$	−55.5704	−	70.7950i	−0.191622	−	0.244121i
$291$		0			0
$292$	−122.976	−	71.0000i	−0.421149	−	0.243151i
$293$	−22.6274			−0.0772267			−0.0386133	−	0.999254i	$-0.512294\pi$
$293$	−22.6274			−0.0772267			−0.0386133	+	0.999254i	$0.512294\pi$
$294$		0			0
$295$	469.000	−	67.0000i	1.58983	−	0.227119i
$296$	−71.0352	−	41.0122i	−0.239984	−	0.138555i
$297$		0			0
$298$	−41.5692	+	24.0000i	−0.139494	+	0.0805369i
$299$	−91.8559	−	53.0330i	−0.307210	−	0.177368i
$300$		0			0
$301$	−185.500	+	321.295i	−0.616279	+	1.06743i
$302$	22.6274			0.0749252
$303$		0			0
$304$	14.0000	+	24.2487i	0.0460526	+	0.0797655i
$305$	−62.9289	+	49.3959i	−0.206324	+	0.161954i
$306$		0			0
$307$		−	1.00000i		−	0.00325733i	−0.999999	−	0.00162866i	$-0.999482\pi$
$307$		−	1.00000i		−	0.00325733i	0.999999	−	0.00162866i	$-0.000518420\pi$
$308$	−19.7990	−	34.2929i	−0.0642824	−	0.111340i
$309$		0			0
$310$	137.806	+	55.3135i	0.444535	+	0.178431i
$311$	−41.6413	+	24.0416i	−0.133895	+	0.0773043i	−0.565451	−	0.824782i	$-0.691298\pi$
$311$	−41.6413	+	24.0416i	−0.133895	+	0.0773043i	0.431556	+	0.902086i	$0.357965\pi$
$312$		0			0
$313$	−349.008	−	201.500i	−1.11504	−	0.643770i	−0.174912	−	0.984584i	$-0.555964\pi$
$313$	−349.008	−	201.500i	−1.11504	−	0.643770i	−0.940131	+	0.340814i	$0.889297\pi$
$314$		−	107.480i		−	0.342294i
$315$		0			0
$316$	−242.000			−0.765823
$317$	221.324	−	383.345i	0.698184	−	1.20929i	−0.270911	−	0.962604i	$-0.587325\pi$
$317$	221.324	−	383.345i	0.698184	−	1.20929i	0.969095	−	0.246686i	$-0.0793417\pi$
$318$		0			0
$319$	−18.0000	−	31.1769i	−0.0564263	−	0.0977333i
$320$	37.1213	+	14.9000i	0.116004	+	0.0465625i
$321$		0			0
$322$			210.000i			0.652174i
$323$	108.894			0.337135
$324$		0			0
$325$	−86.4230	+	90.3109i	−0.265917	+	0.277880i
$326$	102.879	−	59.3970i	0.315578	−	0.182199i
$327$		0			0
$328$			216.000i			0.658537i
$329$	8.57321	−	4.94975i	0.0260584	−	0.0150448i
$330$		0			0
$331$	−88.5000	+	153.286i	−0.267372	+	0.463101i	−0.968182	−	0.250246i	$-0.919488\pi$
$331$	−88.5000	+	153.286i	−0.267372	+	0.463101i	0.700811	+	0.713347i	$0.252822\pi$
$332$	113.137	+	195.959i	0.340774	+	0.590238i
$333$		0			0
$334$	−136.000	+	235.559i	−0.407186	+	0.705266i
$335$	−103.945	+	14.8492i	−0.310283	+	0.0443261i
$336$		0			0
$337$		−	509.000i		−	1.51039i	−0.655503	−	0.755193i	$-0.727543\pi$
$337$		−	509.000i		−	1.51039i	0.655503	−	0.755193i	$-0.272457\pi$
$338$	101.823	−	176.363i	0.301253	−	0.521785i
$339$		0			0
$340$	122.368	−	96.0526i	0.359906	−	0.282508i
$341$	51.4393	+	29.6985i	0.150848	+	0.0870923i
$342$		0			0
$343$			343.000i			1.00000i
$344$		−	149.907i		−	0.435775i
$345$		0			0
$346$	86.0000	+	148.956i	0.248555	+	0.430510i
$347$	−281.428	−	487.448i	−0.811033	−	1.40475i	−0.912142	−	0.409875i	$-0.865572\pi$
$347$	−281.428	−	487.448i	−0.811033	−	1.40475i	0.101108	−	0.994875i	$-0.467761\pi$
$348$		0			0
$349$	564.000			1.61605			0.808023	−	0.589151i	$-0.200538\pi$
$349$	564.000			1.61605			0.808023	+	0.589151i	$0.200538\pi$
$350$	240.405	+	58.7814i	0.686872	+	0.167947i
$351$		0			0
$352$	13.8564	+	8.00000i	0.0393648	+	0.0227273i
$353$	237.588	+	411.514i	0.673053	+	1.16576i	0.977034	+	0.213085i	$0.0683510\pi$
$353$	237.588	+	411.514i	0.673053	+	1.16576i	−0.303980	+	0.952678i	$0.598316\pi$
$354$		0			0
$355$	136.967	−	341.233i	0.385822	−	0.961220i
$356$		−	82.0244i		−	0.230406i
$357$		0			0
$358$			298.000i			0.832402i
$359$	−13.4722	−	7.77817i	−0.0375270	−	0.0216662i	0.481119	−	0.876655i	$-0.340230\pi$
$359$	−13.4722	−	7.77817i	−0.0375270	−	0.0216662i	−0.518646	+	0.854989i	$0.673564\pi$
$360$		0			0
$361$	156.000	+	270.200i	0.432133	+	0.748476i
$362$	−249.609	+	432.335i	−0.689527	+	1.19430i
$363$		0			0
$364$	70.0000			0.192308
$365$	351.432	−	50.2046i	0.962828	−	0.137547i
$366$		0			0
$367$	−224.301	+	129.500i	−0.611173	+	0.352861i	−0.773424	−	0.633888i	$-0.781458\pi$
$367$	−224.301	+	129.500i	−0.611173	+	0.352861i	0.162251	+	0.986749i	$0.448124\pi$
$368$	−42.4264	−	73.4847i	−0.115289	−	0.199687i
$369$		0			0
$370$	203.000	−	29.0000i	0.548649	−	0.0783784i
$371$		−	455.377i		−	1.22743i
$372$		0			0
$373$	−407.898	−	235.500i	−1.09356	−	0.631367i	−0.159038	−	0.987272i	$-0.550839\pi$
$373$	−407.898	−	235.500i	−1.09356	−	0.631367i	−0.934522	+	0.355905i	$0.884173\pi$
$374$	53.8888	−	31.1127i	0.144088	−	0.0831890i
$375$		0			0
$376$	−2.00000	+	3.46410i	−0.00531915	+	0.00921304i
$377$	63.6396			0.168805
$378$		0			0
$379$	181.000			0.477573			0.238786	−	0.971072i	$-0.423250\pi$
$379$	181.000			0.477573			0.238786	+	0.971072i	$0.423250\pi$
$380$	−64.9622	−	26.0750i	−0.170953	−	0.0686185i
$381$		0			0
$382$	−1.73205	+	1.00000i	−0.00453416	+	0.00261780i
$383$	−63.6396	+	110.227i	−0.166161	+	0.287799i	−0.937067	−	0.349150i	$-0.886470\pi$
$383$	−63.6396	+	110.227i	−0.166161	+	0.287799i	0.770906	+	0.636949i	$0.219804\pi$
$384$		0			0
$385$	91.8705	+	36.8756i	0.238625	+	0.0957809i
$386$		−	394.566i		−	1.02219i
$387$		0			0
$388$	34.6410	−	20.0000i	0.0892810	−	0.0515464i
$389$	323.333	−	186.676i	0.831189	−	0.479887i	−0.0230704	−	0.999734i	$-0.507344\pi$
$389$	323.333	−	186.676i	0.831189	−	0.479887i	0.854260	+	0.519846i	$0.174011\pi$
$390$		0			0
$391$	−330.000			−0.843990
$392$	−69.2965	−	120.025i	−0.176777	−	0.306186i
$393$		0			0
$394$	249.000	−	431.281i	0.631980	−	1.09462i
$395$	475.899	−	373.557i	1.20481	−	0.945713i
$396$		0			0
$397$	−224.301	−	129.500i	−0.564989	−	0.326196i	0.190157	−	0.981754i	$-0.439100\pi$
$397$	−224.301	−	129.500i	−0.564989	−	0.326196i	−0.755145	+	0.655557i	$0.772434\pi$
$398$	−214.960			−0.540102
$399$		0			0
$400$	−96.0000	+	28.0000i	−0.240000	+	0.0700000i
$401$	−124.924	−	72.1249i	−0.311531	−	0.179863i	0.336080	−	0.941833i	$-0.390899\pi$
$401$	−124.924	−	72.1249i	−0.311531	−	0.179863i	−0.647611	+	0.761971i	$0.724232\pi$
$402$		0			0
$403$	−90.9327	+	52.5000i	−0.225639	+	0.130273i
$404$	−53.8888	−	31.1127i	−0.133388	−	0.0770116i
$405$		0			0
$406$	−63.0000	−	109.119i	−0.155172	−	0.268767i
$407$	82.0244			0.201534
$408$		0			0
$409$	−17.5000	−	30.3109i	−0.0427873	−	0.0741098i	0.843839	−	0.536597i	$-0.180290\pi$
$409$	−17.5000	−	30.3109i	−0.0427873	−	0.0741098i	−0.886626	+	0.462487i	$0.846957\pi$
$410$	−333.423	−	424.770i	−0.813226	−	1.03602i
$411$		0			0
$412$			150.000i			0.364078i
$413$	663.266			1.60597
$414$		0			0
$415$	−524.974	−	210.718i	−1.26500	−	0.507754i
$416$	−24.4949	+	14.1421i	−0.0588820	+	0.0339955i
$417$		0			0
$418$	−24.2487	−	14.0000i	−0.0580113	−	0.0334928i
$419$		−	165.463i		−	0.394900i	−0.980313	−	0.197450i	$-0.936734\pi$
$419$		−	165.463i		−	0.394900i	0.980313	−	0.197450i	$-0.0632660\pi$
$420$		0			0
$421$	349.000			0.828979			0.414489	−	0.910054i	$-0.363960\pi$
$421$	349.000			0.828979			0.414489	+	0.910054i	$0.363960\pi$
$422$	−243.245	+	421.312i	−0.576409	+	0.998370i
$423$		0			0
$424$	92.0000	+	159.349i	0.216981	+	0.375822i
$425$	−92.3708	+	377.780i	−0.217343	+	0.888894i
$426$		0			0
$427$	−96.9948	+	56.0000i	−0.227154	+	0.131148i
$428$	93.3381			0.218080
$429$		0			0
$430$	231.399	+	294.795i	0.538138	+	0.685571i
$431$	562.158	−	324.562i	1.30431	−	0.753044i	0.323170	−	0.946341i	$-0.395251\pi$
$431$	562.158	−	324.562i	1.30431	−	0.753044i	0.981140	+	0.193297i	$0.0619180\pi$
$432$		0			0
$433$		−	535.000i		−	1.23557i	−0.786349	−	0.617783i	$-0.788031\pi$
$433$		−	535.000i		−	1.23557i	0.786349	−	0.617783i	$-0.211969\pi$
$434$	180.037	+	103.945i	0.414833	+	0.239504i
$435$		0			0
$436$	27.0000	−	46.7654i	0.0619266	−	0.107260i
$437$	74.2462	+	128.598i	0.169900	+	0.294275i
$438$		0			0
$439$	315.000	−	545.596i	0.717540	−	1.24282i	−0.244432	−	0.969666i	$-0.578601\pi$
$439$	315.000	−	545.596i	0.717540	−	1.24282i	0.961972	−	0.273149i	$-0.0880652\pi$
$440$	−39.5980	+	5.65685i	−0.0899954	+	0.0128565i
$441$		0			0
$442$			110.000i			0.248869i
$443$	46.6690	−	80.8332i	0.105348	−	0.182468i	−0.808532	−	0.588452i	$-0.799738\pi$
$443$	46.6690	−	80.8332i	0.105348	−	0.182468i	0.913880	+	0.405984i	$0.133071\pi$
$444$		0			0
$445$	126.615	+	161.303i	0.284527	+	0.362479i
$446$	−85.7321	−	49.4975i	−0.192225	−	0.110981i
$447$		0			0
$448$	48.4974	+	28.0000i	0.108253	+	0.0625000i
$449$		−	199.404i		−	0.444107i	−0.975034	−	0.222054i	$-0.928724\pi$
$449$		−	199.404i		−	0.444107i	0.975034	−	0.222054i	$-0.0712760\pi$
$450$		0			0
$451$	−108.000	−	187.061i	−0.239468	−	0.414770i
$452$	12.7279	+	22.0454i	0.0281591	+	0.0487730i
$453$		0			0
$454$	−52.0000			−0.114537
$455$	−137.657	+	108.054i	−0.302543	+	0.237480i
$456$		0			0
$457$	300.511	+	173.500i	0.657573	+	0.379650i	0.791352	−	0.611361i	$-0.209378\pi$
$457$	300.511	+	173.500i	0.657573	+	0.379650i	−0.133779	+	0.991011i	$0.542711\pi$
$458$	−3.53553	−	6.12372i	−0.00771951	−	0.0133706i
$459$		0			0
$460$	196.865	+	79.0192i	0.427968	+	0.171781i
$461$		−	623.668i		−	1.35286i	−0.736507	−	0.676430i	$-0.763526\pi$
$461$		−	623.668i		−	1.35286i	0.736507	−	0.676430i	$-0.236474\pi$
$462$		0			0
$463$			759.000i			1.63931i	0.572858	+	0.819654i	$0.305835\pi$
$463$			759.000i			1.63931i	−0.572858	+	0.819654i	$0.694165\pi$
$464$	44.0908	+	25.4558i	0.0950233	+	0.0548617i
$465$		0			0
$466$	153.000	+	265.004i	0.328326	+	0.568678i
$467$	132.229	−	229.027i	0.283146	−	0.490422i	−0.689012	−	0.724750i	$-0.741955\pi$
$467$	132.229	−	229.027i	0.283146	−	0.490422i	0.972158	+	0.234327i	$0.0752887\pi$
$468$		0			0
$469$	−147.000			−0.313433
$470$	−1.41421	−	9.89949i	−0.00300897	−	0.0210628i
$471$		0			0
$472$	−232.095	+	134.000i	−0.491726	+	0.283898i
$473$	74.9533	+	129.823i	0.158464	+	0.274467i
$474$		0			0
$475$	168.000	−	49.0000i	0.353684	−	0.103158i
$476$	188.611	−	108.894i	0.396241	−	0.228770i
$477$		0			0
$478$	434.745	+	251.000i	0.909508	+	0.525105i
$479$	281.691	−	162.635i	0.588082	−	0.339529i	−0.176257	−	0.984344i	$-0.556399\pi$
$479$	281.691	−	162.635i	0.588082	−	0.339529i	0.764339	+	0.644815i	$0.223066\pi$
$480$		0			0
$481$	−72.5000	+	125.574i	−0.150728	+	0.261068i
$482$	−503.460			−1.04452
$483$		0			0
$484$	226.000			0.466942
$485$	−37.2500	+	92.8032i	−0.0768042	+	0.191347i
$486$		0			0
$487$	579.371	−	334.500i	1.18967	−	0.686858i	0.231441	−	0.972849i	$-0.425656\pi$
$487$	579.371	−	334.500i	1.18967	−	0.686858i	0.958232	+	0.285991i	$0.0923226\pi$
$488$	22.6274	−	39.1918i	0.0463677	−	0.0803111i
$489$		0			0
$490$	321.547	+	129.065i	0.656218	+	0.263397i
$491$			390.323i			0.794955i	0.917612	+	0.397478i	$0.130114\pi$
$491$			390.323i			0.794955i	−0.917612	+	0.397478i	$0.869886\pi$
$492$		0			0
$493$	171.473	−	99.0000i	0.347815	−	0.200811i
$494$	42.8661	−	24.7487i	0.0867734	−	0.0500987i
$495$		0			0
$496$	−84.0000			−0.169355
$497$	257.387	−	445.807i	0.517881	−	0.896996i
$498$		0			0
$499$	−270.500	+	468.520i	−0.542084	+	0.938917i	0.456700	+	0.889621i	$0.349031\pi$
$499$	−270.500	+	468.520i	−0.542084	+	0.938917i	−0.998784	+	0.0492966i	$0.984302\pi$
$500$	145.565	−	203.251i	0.291130	−	0.406501i
$501$		0			0
$502$	−233.827	−	135.000i	−0.465791	−	0.268924i
$503$	420.021			0.835033			0.417516	−	0.908669i	$-0.362901\pi$
$503$	420.021			0.835033			0.417516	+	0.908669i	$0.362901\pi$
$504$		0			0
$505$	154.000	−	22.0000i	0.304950	−	0.0435644i
$506$	73.4847	+	42.4264i	0.145227	+	0.0838467i
$507$		0			0
$508$	285.788	−	165.000i	0.562576	−	0.324803i
$509$	383.345	+	221.324i	0.753134	+	0.434822i	0.826825	−	0.562459i	$-0.190145\pi$
$509$	383.345	+	221.324i	0.753134	+	0.434822i	−0.0736913	+	0.997281i	$0.523478\pi$
$510$		0			0
$511$	497.000			0.972603
$512$	−22.6274			−0.0441942
$513$		0			0
$514$	272.000	+	471.118i	0.529183	+	0.916572i
$515$	−231.543	−	294.979i	−0.449599	−	0.572775i
$516$		0			0
$517$		−	4.00000i		−	0.00773694i
$518$	287.085			0.554219
$519$		0			0
$520$	26.3397	−	65.6218i	0.0506534	−	0.126196i
$521$	−426.211	+	246.073i	−0.818064	+	0.472309i	−0.849748	−	0.527189i	$-0.823246\pi$
$521$	−426.211	+	246.073i	−0.818064	+	0.472309i	0.0316846	+	0.999498i	$0.489913\pi$
$522$		0			0
$523$	−480.644	−	277.500i	−0.919014	−	0.530593i	−0.0356933	−	0.999363i	$-0.511364\pi$
$523$	−480.644	−	277.500i	−0.919014	−	0.530593i	−0.883320	+	0.468770i	$0.844697\pi$
$524$			353.553i			0.674720i
$525$		0			0
$526$	−624.000			−1.18631
$527$	−163.342	+	282.916i	−0.309946	+	0.536843i
$528$		0			0
$529$	39.5000	+	68.4160i	0.0746692	+	0.129331i
$530$	−426.895	−	171.350i	−0.805462	−	0.323302i
$531$		0			0
$532$	−84.8705	−	49.0000i	−0.159531	−	0.0921053i
$533$	381.838			0.716393
$534$		0			0
$535$	−183.552	+	144.079i	−0.343088	+	0.269306i
$536$	51.4393	−	29.6985i	0.0959688	−	0.0554076i
$537$		0			0
$538$		−	58.0000i		−	0.107807i
$539$	120.025	+	69.2965i	0.222681	+	0.128565i
$540$		0			0
$541$	−435.500	+	754.308i	−0.804991	+	1.39428i	0.111307	+	0.993786i	$0.464496\pi$
$541$	−435.500	+	754.308i	−0.804991	+	1.39428i	−0.916297	+	0.400499i	$0.868837\pi$
$542$	217.789	+	377.221i	0.401825	+	0.695980i
$543$		0			0
$544$	−44.0000	+	76.2102i	−0.0808824	+	0.140092i
$545$	19.0919	+	133.643i	0.0350310	+	0.245217i
$546$		0			0
$547$			526.000i			0.961609i	0.876828	+	0.480804i	$0.159655\pi$
$547$			526.000i			0.961609i	−0.876828	+	0.480804i	$0.840345\pi$
$548$	−151.321	+	262.095i	−0.276133	+	0.478276i
$549$		0			0
$550$	69.1384	−	72.2487i	0.125706	−	0.131361i
$551$	−77.1589	−	44.5477i	−0.140034	−	0.0808489i
$552$		0			0
$553$	733.524	−	423.500i	1.32644	−	0.765823i
$554$		−	711.349i		−	1.28402i
$555$		0			0
$556$	151.000	+	261.540i	0.271583	+	0.470395i
$557$	−214.253	−	371.098i	−0.384656	−	0.666244i	0.607065	−	0.794652i	$-0.292347\pi$
$557$	−214.253	−	371.098i	−0.384656	−	0.666244i	−0.991721	+	0.128408i	$0.959013\pi$
$558$		0			0
$559$	−265.000			−0.474061
$560$	−138.593	+	19.7990i	−0.247487	+	0.0353553i
$561$		0			0
$562$	−58.8897	−	34.0000i	−0.104786	−	0.0604982i
$563$	477.297	+	826.703i	0.847775	+	1.46839i	0.883190	+	0.469016i	$0.155391\pi$
$563$	477.297	+	826.703i	0.847775	+	1.46839i	−0.0354151	+	0.999373i	$0.511275\pi$
$564$		0			0
$565$	−59.0596	−	23.7058i	−0.104530	−	0.0419571i
$566$			473.762i			0.837035i
$567$		0			0
$568$			208.000i			0.366197i
$569$	−154.318	−	89.0955i	−0.271209	−	0.156583i	0.358228	−	0.933634i	$-0.383381\pi$
$569$	−154.318	−	89.0955i	−0.271209	−	0.156583i	−0.629437	+	0.777052i	$0.716714\pi$
$570$		0			0
$571$	−156.500	−	271.066i	−0.274081	−	0.474721i	0.695822	−	0.718214i	$-0.255040\pi$
$571$	−156.500	−	271.066i	−0.274081	−	0.474721i	−0.969903	+	0.243493i	$0.921707\pi$
$572$	14.1421	−	24.4949i	0.0247240	−	0.0428232i
$573$		0			0
$574$	−378.000	−	654.715i	−0.658537	−	1.14062i
$575$	−509.117	+	148.492i	−0.885421	+	0.258248i
$576$		0			0
$577$	870.356	−	502.500i	1.50842	−	0.870884i	0.508463	−	0.861084i	$-0.330214\pi$
$577$	870.356	−	502.500i	1.50842	−	0.870884i	0.999952	−	0.00980013i	$-0.00311953\pi$
$578$	−33.2340	−	57.5630i	−0.0574983	−	0.0995900i
$579$		0			0
$580$	−126.000	+	18.0000i	−0.217241	+	0.0310345i
$581$	−685.857	−	395.980i	−1.18048	−	0.681549i
$582$		0			0
$583$	−159.349	−	92.0000i	−0.273325	−	0.157804i
$584$	−173.914	+	100.409i	−0.297798	+	0.171933i
$585$		0			0
$586$	−16.0000	+	27.7128i	−0.0273038	+	0.0472915i
$587$	−875.398			−1.49131			−0.745654	−	0.666333i	$-0.767863\pi$
$587$	−875.398			−1.49131			−0.745654	+	0.666333i	$0.767863\pi$
$588$		0			0
$589$	147.000			0.249576
$590$	249.575	−	621.781i	0.423009	−	1.05387i
$591$		0			0
$592$	−100.459	+	58.0000i	−0.169694	+	0.0979730i
$593$	−354.968	+	614.822i	−0.598596	+	1.03680i	0.394432	+	0.918925i	$0.370941\pi$
$593$	−354.968	+	614.822i	−0.598596	+	1.03680i	−0.993029	+	0.117874i	$0.962392\pi$
$594$		0			0
$595$	−202.816	+	505.288i	−0.340867	+	0.849223i
$596$			67.8823i			0.113896i
$597$		0			0
$598$	−129.904	+	75.0000i	−0.217230	+	0.125418i
$599$	97.9796	−	56.5685i	0.163572	−	0.0944383i	−0.415979	−	0.909374i	$-0.636561\pi$
$599$	97.9796	−	56.5685i	0.163572	−	0.0944383i	0.579551	+	0.814936i	$0.303228\pi$
$600$		0			0
$601$	927.000			1.54243			0.771215	−	0.636575i	$-0.219650\pi$
$601$	927.000			1.54243			0.771215	+	0.636575i	$0.219650\pi$
$602$	262.337	+	454.380i	0.435775	+	0.754785i
$603$		0			0
$604$	16.0000	−	27.7128i	0.0264901	−	0.0458821i
$605$	−444.435	+	348.859i	−0.734603	+	0.576626i
$606$		0			0
$607$	−452.931	−	261.500i	−0.746180	−	0.430807i	0.0781320	−	0.996943i	$-0.475104\pi$
$607$	−452.931	−	261.500i	−0.746180	−	0.430807i	−0.824312	+	0.566136i	$0.808438\pi$
$608$	39.5980			0.0651283
$609$		0			0
$610$	16.0000	+	112.000i	0.0262295	+	0.183607i
$611$	6.12372	+	3.53553i	0.0100225	+	0.00578647i
$612$		0			0
$613$	−356.802	+	206.000i	−0.582059	+	0.336052i	−0.761951	−	0.647634i	$-0.775759\pi$
$613$	−356.802	+	206.000i	−0.582059	+	0.336052i	0.179892	+	0.983686i	$0.442425\pi$
$614$	−1.22474	−	0.707107i	−0.00199470	−	0.00115164i
$615$		0			0
$616$	−56.0000			−0.0909091
$617$	394.566			0.639490			0.319745	−	0.947504i	$-0.396403\pi$
$617$	394.566			0.639490			0.319745	+	0.947504i	$0.396403\pi$
$618$		0			0
$619$	19.5000	+	33.7750i	0.0315024	+	0.0545638i	0.881347	−	0.472470i	$-0.156637\pi$
$619$	19.5000	+	33.7750i	0.0315024	+	0.0545638i	−0.849844	+	0.527034i	$0.823304\pi$
$620$	165.188	−	129.664i	0.266433	−	0.209136i
$621$		0			0
$622$			68.0000i			0.109325i
$623$	143.543	+	248.623i	0.230406	+	0.399074i
$624$		0			0
$625$	27.4845	+	624.395i	0.0439753	+	0.999033i
$626$	−493.572	+	284.964i	−0.788454	+	0.455214i
$627$		0			0
$628$	−131.636	−	76.0000i	−0.209611	−	0.121019i
$629$			451.134i			0.717224i
$630$		0			0
$631$	168.000			0.266244			0.133122	−	0.991100i	$-0.457500\pi$
$631$	168.000			0.266244			0.133122	+	0.991100i	$0.457500\pi$
$632$	−171.120	+	296.388i	−0.270759	+	0.468969i
$633$		0			0
$634$	−313.000	−	542.132i	−0.493691	−	0.855098i
$635$	−307.313	+	765.626i	−0.483957	+	1.20571i
$636$		0			0
$637$	−212.176	+	122.500i	−0.333087	+	0.192308i
$638$	−50.9117			−0.0797989
$639$		0			0
$640$	44.4974	−	34.9282i	0.0695272	−	0.0545753i
$641$	393.143	−	226.981i	0.613328	−	0.354105i	−0.160939	−	0.986964i	$-0.551452\pi$
$641$	393.143	−	226.981i	0.613328	−	0.354105i	0.774267	+	0.632859i	$0.218119\pi$
$642$		0			0
$643$			487.000i			0.757387i	0.925522	+	0.378694i	$0.123627\pi$
$643$			487.000i			0.757387i	−0.925522	+	0.378694i	$0.876373\pi$
$644$	257.196	+	148.492i	0.399373	+	0.230578i
$645$		0			0
$646$	77.0000	−	133.368i	0.119195	−	0.206452i
$647$	−519.016	−	898.963i	−0.802189	−	1.38943i	−0.918172	−	0.396181i	$-0.870335\pi$
$647$	−519.016	−	898.963i	−0.802189	−	1.38943i	0.115983	−	0.993251i	$-0.462998\pi$
$648$		0			0
$649$	134.000	−	232.095i	0.206471	−	0.357619i
$650$	49.4975	+	169.706i	0.0761500	+	0.261086i
$651$		0			0
$652$		−	168.000i		−	0.257669i
$653$	−185.262	+	320.883i	−0.283709	+	0.491398i	−0.972295	−	0.233756i	$-0.924898\pi$
$653$	−185.262	+	320.883i	−0.283709	+	0.491398i	0.688586	+	0.725154i	$0.258232\pi$
$654$		0			0
$655$	−545.753	−	695.272i	−0.833211	−	1.06148i
$656$	264.545	+	152.735i	0.403270	+	0.232828i
$657$		0			0
$658$		−	14.0000i		−	0.0212766i
$659$			1026.72i			1.55800i	0.627027	+	0.778998i	$0.284272\pi$
$659$			1026.72i			1.55800i	−0.627027	+	0.778998i	$0.715728\pi$
$660$		0			0
$661$	−582.500	−	1008.92i	−0.881241	−	1.52635i	−0.849963	−	0.526843i	$-0.823376\pi$
$661$	−582.500	−	1008.92i	−0.881241	−	1.52635i	−0.0312777	−	0.999511i	$-0.509958\pi$
$662$	125.158	+	216.780i	0.189060	+	0.327462i
$663$		0			0
$664$	320.000			0.481928
$665$	242.538	−	34.6482i	0.364718	−	0.0521026i
$666$		0			0
$667$	233.827	+	135.000i	0.350565	+	0.202399i
$668$	192.333	+	333.131i	0.287924	+	0.498699i
$669$		0			0
$670$	−55.3135	+	137.806i	−0.0825574	+	0.205680i
$671$			45.2548i			0.0674439i
$672$		0			0
$673$			507.000i			0.753343i	0.926347	+	0.376672i	$0.122931\pi$
$673$			507.000i			0.753343i	−0.926347	+	0.376672i	$0.877069\pi$
$674$	−623.395	−	359.917i	−0.924919	−	0.534002i
$675$		0			0
$676$	−144.000	−	249.415i	−0.213018	−	0.368958i
$677$	540.937	−	936.930i	0.799020	−	1.38394i	−0.121235	−	0.992624i	$-0.538685\pi$
$677$	540.937	−	936.930i	0.799020	−	1.38394i	0.920255	−	0.391320i	$-0.127981\pi$
$678$		0			0
$679$	−70.0000	+	121.244i	−0.103093	+	0.178562i
$680$	−31.1127	−	217.789i	−0.0457540	−	0.320278i
$681$		0			0
$682$	72.7461	−	42.0000i	0.106666	−	0.0615836i
$683$	−408.001	−	706.678i	−0.597365	−	1.03467i	−0.993208	−	0.116349i	$-0.962881\pi$
$683$	−408.001	−	706.678i	−0.597365	−	1.03467i	0.395843	−	0.918318i	$-0.370452\pi$
$684$		0			0
$685$	−107.000	−	749.000i	−0.156204	−	1.09343i
$686$	420.087	+	242.538i	0.612372	+	0.353553i
$687$		0			0
$688$	−183.597	−	106.000i	−0.266857	−	0.154070i
$689$	281.691	−	162.635i	0.408841	−	0.236044i
$690$		0			0
$691$	416.500	−	721.399i	0.602750	−	1.04399i	−0.389653	−	0.920962i	$-0.627405\pi$
$691$	416.500	−	721.399i	0.602750	−	1.04399i	0.992403	−	0.123031i	$-0.0392616\pi$
$692$	243.245			0.351510
$693$		0			0
$694$	−796.000			−1.14697
$695$	−700.664	−	281.238i	−1.00815	−	0.404659i
$696$		0			0
$697$	1028.84	−	594.000i	1.47609	−	0.852224i
$698$	398.808	−	690.756i	0.571358	−	0.989622i
$699$		0			0
$700$	241.985	−	252.870i	0.345692	−	0.361244i
$701$			1022.48i			1.45860i	0.684196	+	0.729298i	$0.260153\pi$
$701$			1022.48i			1.45860i	−0.684196	+	0.729298i	$0.739847\pi$
$702$		0			0
$703$	175.803	−	101.500i	0.250076	−	0.144381i
$704$	19.5959	−	11.3137i	0.0278351	−	0.0160706i
$705$		0			0
$706$	672.000			0.951841
$707$	217.789			0.308047
$708$		0			0
$709$	20.0000	−	34.6410i	0.0282087	−	0.0488590i	−0.851576	−	0.524231i	$-0.824353\pi$
$709$	20.0000	−	34.6410i	0.0282087	−	0.0488590i	0.879785	+	0.475372i	$0.157686\pi$
$710$	−321.074	−	409.038i	−0.452216	−	0.576109i
$711$		0			0
$712$	−100.459	−	58.0000i	−0.141094	−	0.0814607i
$713$	−445.477			−0.624793
$714$		0			0
$715$	10.0000	+	70.0000i	0.0139860	+	0.0979021i
$716$	364.974	+	210.718i	0.509740	+	0.294299i
$717$		0			0
$718$	−19.0526	+	11.0000i	−0.0265356	+	0.0153203i
$719$	−905.086	−	522.552i	−1.25881	−	0.726776i	−0.285969	−	0.958239i	$-0.592315\pi$
$719$	−905.086	−	522.552i	−1.25881	−	0.726776i	−0.972844	+	0.231463i	$0.925649\pi$
$720$		0			0
$721$	−262.500	−	454.663i	−0.364078	−	0.630601i
$722$	441.235			0.611128
$723$		0			0
$724$	353.000	+	611.414i	0.487569	+	0.844494i
$725$	219.997	−	229.894i	0.303444	−	0.317095i
$726$		0			0
$727$			845.000i			1.16231i	0.813793	+	0.581155i	$0.197399\pi$
$727$			845.000i			1.16231i	−0.813793	+	0.581155i	$0.802601\pi$
$728$	49.4975	−	85.7321i	0.0679910	−	0.117764i
$729$		0			0
$730$	187.012	−	465.915i	0.256181	−	0.638239i
$731$	−714.026	+	412.243i	−0.976780	+	0.563944i
$732$		0			0
$733$	−85.7365	−	49.5000i	−0.116967	−	0.0675307i	0.440375	−	0.897814i	$-0.354845\pi$
$733$	−85.7365	−	49.5000i	−0.116967	−	0.0675307i	−0.557342	+	0.830283i	$0.688179\pi$
$734$			366.281i			0.499021i
$735$		0			0
$736$	−120.000			−0.163043
$737$	−29.6985	+	51.4393i	−0.0402965	+	0.0697955i
$738$		0			0
$739$	−480.500	−	832.250i	−0.650203	−	1.12618i	−0.983073	−	0.183212i	$-0.941351\pi$
$739$	−480.500	−	832.250i	−0.650203	−	1.12618i	0.332870	−	0.942973i	$-0.391983\pi$
$740$	108.025	−	269.129i	0.145980	−	0.363688i
$741$		0			0
$742$	−557.720	−	322.000i	−0.751645	−	0.433962i
$743$	−87.6812			−0.118010			−0.0590049	−	0.998258i	$-0.518793\pi$
$743$	−87.6812			−0.118010			−0.0590049	+	0.998258i	$0.518793\pi$
$744$		0			0
$745$	−104.785	−	133.492i	−0.140650	−	0.179184i
$746$	−576.855	+	333.047i	−0.773264	+	0.446444i
$747$		0			0
$748$		−	88.0000i		−	0.117647i
$749$	−282.916	+	163.342i	−0.377725	+	0.218080i
$750$		0			0
$751$	−441.500	+	764.700i	−0.587883	+	1.01824i	0.406626	+	0.913595i	$0.366705\pi$
$751$	−441.500	+	764.700i	−0.587883	+	1.01824i	−0.994509	+	0.104648i	$0.966628\pi$
$752$	2.82843	+	4.89898i	0.00376121	+	0.00651460i
$753$		0			0
$754$	45.0000	−	77.9423i	0.0596817	−	0.103372i
$755$	11.3137	+	79.1960i	0.0149850	+	0.104895i
$756$		0			0
$757$			412.000i			0.544254i	0.962261	+	0.272127i	$0.0877270\pi$
$757$			412.000i			0.544254i	−0.962261	+	0.272127i	$0.912273\pi$
$758$	127.986	−	221.679i	0.168847	−	0.292452i
$759$		0			0
$760$	−77.8705	+	61.1244i	−0.102461	+	0.0804268i
$761$	1150.04	+	663.973i	1.51122	+	0.872501i	0.999914	+	0.0130998i	$0.00416992\pi$
$761$	1150.04	+	663.973i	1.51122	+	0.872501i	0.511302	+	0.859401i	$0.329163\pi$
$762$		0			0
$763$			189.000i			0.247706i
$764$			2.82843i			0.00370213i
$765$		0			0
$766$	90.0000	+	155.885i	0.117493	+	0.203505i
$767$	236.881	+	410.290i	0.308841	+	0.534928i
$768$		0			0
$769$	−1125.00			−1.46294			−0.731469	−	0.681874i	$-0.761165\pi$
$769$	−1125.00			−1.46294			−0.731469	+	0.681874i	$0.761165\pi$
$770$	110.126	−	86.4429i	0.143020	−	0.112263i
$771$		0			0
$772$	−483.242	−	279.000i	−0.625961	−	0.361399i
$773$	−584.070	−	1011.64i	−0.755589	−	1.30872i	−0.945081	−	0.326836i	$-0.894017\pi$
$773$	−584.070	−	1011.64i	−0.755589	−	1.30872i	0.189492	−	0.981882i	$-0.439316\pi$
$774$		0			0
$775$	−124.694	+	509.977i	−0.160896	+	0.658035i
$776$		−	56.5685i		−	0.0728976i
$777$		0			0
$778$		−	528.000i		−	0.678663i
$779$	−462.954	−	267.286i	−0.594292	−	0.343115i
$780$		0			0
$781$	−104.000	−	180.133i	−0.133163	−	0.230644i
$782$	−233.345	+	404.166i	−0.298395	+	0.516836i
$783$		0			0
$784$	−196.000			−0.250000
$785$	376.181	−	53.7401i	0.479211	−	0.0684587i
$786$		0			0
$787$	−325.626	+	188.000i	−0.413755	+	0.238882i	−0.692402	−	0.721512i	$-0.743448\pi$
$787$	−325.626	+	188.000i	−0.413755	+	0.238882i	0.278647	+	0.960394i	$0.410114\pi$
$788$	−352.139	−	609.923i	−0.446877	−	0.774014i
$789$		0			0
$790$	−121.000	−	847.000i	−0.153165	−	1.07215i
$791$	−77.1589	−	44.5477i	−0.0975461	−	0.0563182i
$792$		0			0
$793$	−69.2820	−	40.0000i	−0.0873670	−	0.0504414i
$794$	−317.209	+	183.141i	−0.399507	+	0.230656i
$795$		0			0
$796$	−152.000	+	263.272i	−0.190955	+	0.330743i
$797$	−598.212			−0.750580			−0.375290	−	0.926907i	$-0.622457\pi$
$797$	−598.212			−0.750580			−0.375290	+	0.926907i	$0.622457\pi$
$798$		0			0
$799$	22.0000			0.0275344
$800$	−33.5894	+	137.374i	−0.0419867	+	0.171718i
$801$		0			0
$802$	−176.669	+	102.000i	−0.220286	+	0.127182i
$803$	100.409	−	173.914i	0.125043	−	0.216580i
$804$		0			0
$805$	−735.000	+	105.000i	−0.913043	+	0.130435i
$806$			148.492i			0.184234i
$807$		0			0
$808$	−76.2102	+	44.0000i	−0.0943196	+	0.0544554i
$809$	−929.581	+	536.694i	−1.14905	+	0.663404i	−0.948656	−	0.316311i	$-0.897556\pi$
$809$	−929.581	+	536.694i	−1.14905	+	0.663404i	−0.200394	+	0.979715i	$0.564222\pi$
$810$		0			0
$811$	824.000			1.01603			0.508015	−	0.861348i	$-0.330380\pi$
$811$	824.000			1.01603			0.508015	+	0.861348i	$0.330380\pi$
$812$	−178.191			−0.219447
$813$		0			0
$814$	58.0000	−	100.459i	0.0712531	−	0.123414i
$815$	259.329	+	330.377i	0.318195	+	0.405370i
$816$		0			0
$817$	321.295	+	185.500i	0.393262	+	0.227050i
$818$	−49.4975			−0.0605104
$819$		0			0
$820$	−756.000	+	108.000i	−0.921951	+	0.131707i
$821$	411.514	+	237.588i	0.501235	+	0.289388i	0.729224	−	0.684275i	$-0.239881\pi$
$821$	411.514	+	237.588i	0.501235	+	0.289388i	−0.227988	+	0.973664i	$0.573215\pi$
$822$		0			0
$823$	−1001.13	+	578.000i	−1.21643	+	0.702309i	−0.964153	−	0.265345i	$-0.914514\pi$
$823$	−1001.13	+	578.000i	−1.21643	+	0.702309i	−0.252281	+	0.967654i	$0.581181\pi$
$824$	183.712	+	106.066i	0.222951	+	0.128721i
$825$		0			0
$826$	469.000	−	812.332i	0.567797	−	0.983453i
$827$	−284.257			−0.343721			−0.171860	−	0.985121i	$-0.554978\pi$
$827$	−284.257			−0.343721			−0.171860	+	0.985121i	$0.554978\pi$
$828$		0			0
$829$	−147.500	−	255.477i	−0.177925	−	0.308176i	0.763245	−	0.646110i	$-0.223605\pi$
$829$	−147.500	−	255.477i	−0.177925	−	0.308176i	−0.941170	+	0.337934i	$0.890272\pi$
$830$	−629.289	+	493.959i	−0.758179	+	0.595132i
$831$		0			0
$832$			40.0000i			0.0480769i
$833$	−381.131	+	660.137i	−0.457540	+	0.792482i
$834$		0			0
$835$	−892.456	−	358.221i	−1.06881	−	0.429007i
$836$	−34.2929	+	19.7990i	−0.0410202	+	0.0236830i
$837$		0			0
$838$	−202.650	−	117.000i	−0.241826	−	0.139618i
$839$			295.571i			0.352289i	0.984364	+	0.176145i	$0.0563626\pi$
$839$			295.571i			0.352289i	−0.984364	+	0.176145i	$0.943637\pi$
$840$		0			0
$841$	679.000			0.807372
$842$	246.780	−	427.436i	0.293088	−	0.507644i
$843$		0			0
$844$	344.000	+	595.825i	0.407583	+	0.705954i
$845$	668.183	+	268.200i	0.790749	+	0.317397i
$846$		0			0
$847$	−685.026	+	395.500i	−0.808768	+	0.466942i
$848$	260.215			0.306858
$849$		0			0
$850$	397.368	+	380.261i	0.467492	+	0.447366i
$851$	−532.764	+	307.591i	−0.626045	+	0.361447i
$852$		0			0
$853$		−	317.000i		−	0.371630i	−0.982585	−	0.185815i	$-0.940508\pi$
$853$		−	317.000i		−	0.371630i	0.982585	−	0.185815i	$-0.0594924\pi$
$854$			158.392i			0.185471i
$855$		0			0
$856$	66.0000	−	114.315i	0.0771028	−	0.133546i
$857$	440.528	+	763.016i	0.514034	+	0.890334i	0.999867	+	0.0162821i	$0.00518299\pi$
$857$	440.528	+	763.016i	0.514034	+	0.890334i	−0.485833	+	0.874052i	$0.661484\pi$
$858$		0			0
$859$	−174.000	+	301.377i	−0.202561	+	0.350846i	−0.949353	−	0.314212i	$-0.898260\pi$
$859$	−174.000	+	301.377i	−0.202561	+	0.350846i	0.746792	+	0.665058i	$0.231593\pi$
$860$	524.673	−	74.9533i	0.610085	−	0.0871550i
$861$		0			0
$862$		−	918.000i		−	1.06497i
$863$	10.6066	−	18.3712i	0.0122904	−	0.0212876i	−0.859815	−	0.510606i	$-0.829421\pi$
$863$	10.6066	−	18.3712i	0.0122904	−	0.0212876i	0.872105	+	0.489318i	$0.162754\pi$
$864$		0			0
$865$	−478.347	+	375.478i	−0.553003	+	0.434079i
$866$	−655.239	−	378.302i	−0.756626	−	0.436838i
$867$		0			0
$868$	254.611	−	147.000i	0.293331	−	0.169355i
$869$		−	342.240i		−	0.393832i
$870$		0			0
$871$	−52.5000	−	90.9327i	−0.0602755	−	0.104400i
$872$	−38.1838	−	66.1362i	−0.0437887	−	0.0758443i
$873$		0			0
$874$	210.000			0.240275
$875$	−85.5324	+	870.810i	−0.0977513	+	0.995211i
$876$		0			0
$877$	25.9808	+	15.0000i	0.0296246	+	0.0171038i	0.514739	−	0.857347i	$-0.327889\pi$
$877$	25.9808	+	15.0000i	0.0296246	+	0.0171038i	−0.485115	+	0.874451i	$0.661222\pi$
$878$	−445.477	−	771.589i	−0.507377	−	0.878803i
$879$		0			0
$880$	−21.0718	+	52.4974i	−0.0239452	+	0.0596562i
$881$		−	93.3381i		−	0.105946i	−0.998596	−	0.0529728i	$-0.983130\pi$
$881$		−	93.3381i		−	0.105946i	0.998596	−	0.0529728i	$-0.0168697\pi$
$882$		0			0
$883$			331.000i			0.374858i	0.982278	+	0.187429i	$0.0600155\pi$
$883$			331.000i			0.374858i	−0.982278	+	0.187429i	$0.939984\pi$
$884$	134.722	+	77.7817i	0.152400	+	0.0879884i
$885$		0			0
$886$	−66.0000	−	114.315i	−0.0744921	−	0.129024i
$887$	106.066	−	183.712i	0.119578	−	0.207116i	−0.800022	−	0.599970i	$-0.795179\pi$
$887$	106.066	−	183.712i	0.119578	−	0.207116i	0.919601	+	0.392854i	$0.128512\pi$
$888$		0			0
$889$	−577.500	+	1000.26i	−0.649606	+	1.12515i
$890$	287.085	−	41.0122i	0.322568	−	0.0460811i
$891$		0			0
$892$	−121.244	+	70.0000i	−0.135923	+	0.0784753i
$893$	−4.94975	−	8.57321i	−0.00554283	−	0.00960046i
$894$		0			0
$895$	−1043.00	+	149.000i	−1.16536	+	0.166480i
$896$	68.5857	−	39.5980i	0.0765466	−	0.0441942i
$897$		0			0
$898$	−244.219	−	141.000i	−0.271959	−	0.157016i
$899$	231.477	−	133.643i	0.257483	−	0.148658i
$900$		0			0
$901$	506.000	−	876.418i	0.561598	−	0.972717i
$902$	−305.470			−0.338659
$903$		0			0
$904$	36.0000			0.0398230
$905$	−1637.98	−	657.463i	−1.80992	−	0.726478i
$906$		0			0
$907$	1142.29	−	659.500i	1.25941	−	0.727122i	0.286453	−	0.958094i	$-0.407524\pi$
$907$	1142.29	−	659.500i	1.25941	−	0.727122i	0.972960	+	0.230972i	$0.0741906\pi$
$908$	−36.7696	+	63.6867i	−0.0404951	+	0.0701396i
$909$		0			0
$910$	35.0000	+	245.000i	0.0384615	+	0.269231i
$911$			1404.31i			1.54151i	0.637133	+	0.770754i	$0.280120\pi$
$911$			1404.31i			1.54151i	−0.637133	+	0.770754i	$0.719880\pi$
$912$		0			0
$913$	−277.128	+	160.000i	−0.303536	+	0.175246i
$914$	424.986	−	245.366i	0.464974	−	0.268453i
$915$		0			0
$916$	−10.0000			−0.0109170
$917$	−618.718	−	1071.65i	−0.674720	−	1.16865i
$918$		0			0
$919$	−519.500	+	899.800i	−0.565288	+	0.979108i	0.431734	+	0.902001i	$0.357902\pi$
$919$	−519.500	+	899.800i	−0.565288	+	0.979108i	−0.997023	+	0.0771074i	$0.975432\pi$
$920$	235.983	−	185.235i	0.256503	−	0.201342i
$921$		0			0
$922$	−763.834	−	441.000i	−0.828454	−	0.478308i
$923$	367.696			0.398370
$924$		0			0
$925$	203.000	+	696.000i	0.219459	+	0.752432i
$926$	929.581	+	536.694i	1.00387	+	0.579583i
$927$		0			0
$928$	62.3538	−	36.0000i	0.0671916	−	0.0387931i
$929$	58.7878	+	33.9411i	0.0632807	+	0.0365351i	0.531307	−	0.847180i	$-0.321701\pi$
$929$	58.7878	+	33.9411i	0.0632807	+	0.0365351i	−0.468026	+	0.883715i	$0.655035\pi$
$930$		0			0
$931$	343.000			0.368421
$932$	432.749			0.464323
$933$		0			0
$934$	−187.000	−	323.894i	−0.200214	−	0.346781i
$935$	135.839	+	173.054i	0.145282	+	0.185085i
$936$		0			0
$937$			1679.00i			1.79189i	0.444166	+	0.895945i	$0.353500\pi$
$937$			1679.00i			1.79189i	−0.444166	+	0.895945i	$0.646500\pi$
$938$	−103.945	+	180.037i	−0.110815	+	0.191938i
$939$		0			0
$940$	−13.1244	−	5.26795i	−0.0139621	−	0.00560420i
$941$	−11.0227	+	6.36396i	−0.0117138	+	0.00676298i	−0.505845	−	0.862624i	$-0.668819\pi$
$941$	−11.0227	+	6.36396i	−0.0117138	+	0.00676298i	0.494132	+	0.869387i	$0.335486\pi$
$942$		0			0
$943$	1402.96	+	810.000i	1.48776	+	0.858961i
$944$			379.009i			0.401493i
$945$		0			0
$946$	212.000			0.224101
$947$	156.978	−	271.893i	0.165763	−	0.287110i	−0.771163	−	0.636638i	$-0.780325\pi$
$947$	156.978	−	271.893i	0.165763	−	0.287110i	0.936926	+	0.349528i	$0.113658\pi$
$948$		0			0
$949$	177.500	+	307.439i	0.187039	+	0.323961i
$950$	58.7814	−	240.405i	0.0618752	−	0.253058i
$951$		0			0
$952$		−	308.000i		−	0.323529i
$953$	−1349.16			−1.41570			−0.707849	−	0.706364i	$-0.750334\pi$
$953$	−1349.16			−1.41570			−0.707849	+	0.706364i	$0.750334\pi$
$954$		0			0
$955$	−4.36603	−	5.56218i	−0.00457175	−	0.00582427i
$956$	614.822	−	354.968i	0.643119	−	0.371305i
$957$		0			0
$958$		−	460.000i		−	0.480167i
$959$		−	1059.25i		−	1.10453i
$960$		0			0
$961$	260.000	−	450.333i	0.270552	−	0.468609i
$962$	102.530	+	177.588i	0.106581	+	0.184603i
$963$		0			0
$964$	−356.000	+	616.610i	−0.369295	+	0.639637i
$965$	1380.98	−	197.283i	1.43107	−	0.204438i
$966$		0			0
$967$		−	1557.00i		−	1.61013i	−0.593184	−	0.805067i	$-0.702129\pi$
$967$		−	1557.00i		−	1.61013i	0.593184	−	0.805067i	$-0.297871\pi$
$968$	159.806	−	276.792i	0.165089	−	0.285943i
$969$		0			0
$970$	87.3205	+	111.244i	0.0900211	+	0.114684i
$971$	742.195	+	428.507i	0.764362	+	0.441305i	0.830860	−	0.556482i	$-0.187849\pi$
$971$	742.195	+	428.507i	0.764362	+	0.441305i	−0.0664978	+	0.997787i	$0.521183\pi$
$972$		0			0
$973$	−915.389	−	528.500i	−0.940790	−	0.543165i
$974$		−	946.109i		−	0.971364i
$975$		0			0
$976$	−32.0000	−	55.4256i	−0.0327869	−	0.0567886i
$977$	852.771	+	1477.04i	0.872846	+	1.51181i	0.859039	+	0.511909i	$0.171062\pi$
$977$	852.771	+	1477.04i	0.872846	+	1.51181i	0.0138068	+	0.999905i	$0.495605\pi$
$978$		0			0
$979$	116.000			0.118488
$980$	385.439	−	302.550i	0.393305	−	0.308725i
$981$		0			0
$982$	478.046	+	276.000i	0.486809	+	0.281059i
$983$	−328.805	−	569.506i	−0.334491	−	0.579355i	0.648896	−	0.760877i	$-0.275231\pi$
$983$	−328.805	−	569.506i	−0.334491	−	0.579355i	−0.983387	+	0.181522i	$0.941898\pi$
$984$		0			0
$985$	1633.98	+	655.860i	1.65887	+	0.665847i
$986$		−	280.014i		−	0.283990i
$987$		0			0
$988$		−	70.0000i		−	0.0708502i
$989$	−973.672	−	562.150i	−0.984502	−	0.568402i
$990$		0			0
$991$	−37.5000	−	64.9519i	−0.0378406	−	0.0655418i	0.846485	−	0.532413i	$-0.178715\pi$
$991$	−37.5000	−	64.9519i	−0.0378406	−	0.0655418i	−0.884325	+	0.466871i	$0.845381\pi$
$992$	−59.3970	+	102.879i	−0.0598760	+	0.103708i
$993$		0			0
$994$	−364.000	−	630.466i	−0.366197	−	0.634272i
$995$	−107.480	−	752.362i	−0.108020	−	0.756142i
$996$		0			0
$997$	−104.789	+	60.5000i	−0.105104	+	0.0606820i	−0.551631	−	0.834088i	$-0.685994\pi$
$997$	−104.789	+	60.5000i	−0.105104	+	0.0606820i	0.446526	+	0.894770i	$0.352661\pi$
$998$	382.545	+	662.587i	0.383311	+	0.663915i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.3.bd.a.359.4	yes	8
3.2	odd	2	inner	630.3.bd.a.359.1	yes	8
5.4	even	2	inner	630.3.bd.a.359.2	yes	8
7.4	even	3	inner	630.3.bd.a.179.3	yes	8
15.14	odd	2	inner	630.3.bd.a.359.3	yes	8
21.11	odd	6	inner	630.3.bd.a.179.2	yes	8
35.4	even	6	inner	630.3.bd.a.179.1	✓	8
105.74	odd	6	inner	630.3.bd.a.179.4	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.3.bd.a.179.1	✓	8	35.4	even	6	inner
630.3.bd.a.179.2	yes	8	21.11	odd	6	inner
630.3.bd.a.179.3	yes	8	7.4	even	3	inner
630.3.bd.a.179.4	yes	8	105.74	odd	6	inner
630.3.bd.a.359.1	yes	8	3.2	odd	2	inner
630.3.bd.a.359.2	yes	8	5.4	even	2	inner
630.3.bd.a.359.3	yes	8	15.14	odd	2	inner
630.3.bd.a.359.4	yes	8	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	630.bd (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 - 1.22474i) q^{2} +(-1.00000 - 1.73205i) q^{4} +(4.64016 + 1.86250i) q^{5} +(6.06218 + 3.50000i) q^{7} -2.82843 q^{8} +(5.56218 - 4.36603i) q^{10} +(2.44949 - 1.41421i) q^{11} +5.00000i q^{13} +(8.57321 - 4.94975i) q^{14} +(-2.00000 + 3.46410i) q^{16} +(7.77817 + 13.4722i) q^{17} +(3.50000 - 6.06218i) q^{19} +(-1.41421 - 9.89949i) q^{20} -4.00000i q^{22} +(-10.6066 + 18.3712i) q^{23} +(18.0622 + 17.2846i) q^{25} +(6.12372 + 3.53553i) q^{26} -14.0000i q^{28} -12.7279i q^{29} +(10.5000 + 18.1865i) q^{31} +(2.82843 + 4.89898i) q^{32} +22.0000 q^{34} +(21.6107 + 27.5314i) q^{35} +(25.1147 + 14.5000i) q^{37} +(-4.94975 - 8.57321i) q^{38} +(-13.1244 - 5.26795i) q^{40} -76.3675i q^{41} +53.0000i q^{43} +(-4.89898 - 2.82843i) q^{44} +(15.0000 + 25.9808i) q^{46} +(0.707107 - 1.22474i) q^{47} +(24.5000 + 42.4352i) q^{49} +(33.9411 - 9.89949i) q^{50} +(8.66025 - 5.00000i) q^{52} +(-32.5269 - 56.3383i) q^{53} +(14.0000 - 2.00000i) q^{55} +(-17.1464 - 9.89949i) q^{56} +(-15.5885 - 9.00000i) q^{58} +(82.0579 - 47.3762i) q^{59} +(-8.00000 + 13.8564i) q^{61} +29.6985 q^{62} +8.00000 q^{64} +(-9.31251 + 23.2008i) q^{65} +(-18.1865 + 10.5000i) q^{67} +(15.5563 - 26.9444i) q^{68} +(49.0000 - 7.00000i) q^{70} -73.5391i q^{71} +(61.4878 - 35.5000i) q^{73} +(35.5176 - 20.5061i) q^{74} -14.0000 q^{76} +19.7990 q^{77} +(60.5000 - 104.789i) q^{79} +(-15.7322 + 12.3490i) q^{80} +(-93.5307 - 54.0000i) q^{82} -113.137 q^{83} +(11.0000 + 77.0000i) q^{85} +(64.9115 + 37.4767i) q^{86} +(-6.92820 + 4.00000i) q^{88} +(35.5176 + 20.5061i) q^{89} +(-17.5000 + 30.3109i) q^{91} +42.4264 q^{92} +(-1.00000 - 1.73205i) q^{94} +(27.5314 - 21.6107i) q^{95} +20.0000i q^{97} +69.2965 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{4} - 4 q^{10} - 16 q^{16} + 28 q^{19} + 96 q^{25} + 84 q^{31} + 176 q^{34} - 8 q^{40} + 120 q^{46} + 196 q^{49} + 112 q^{55} - 64 q^{61} + 64 q^{64} + 392 q^{70} - 112 q^{76} + 484 q^{79} + 88 q^{85}+ \cdots - 8 q^{94}+O(q^{100}) \) 8 * q - 8 * q^4 - 4 * q^10 - 16 * q^16 + 28 * q^19 + 96 * q^25 + 84 * q^31 + 176 * q^34 - 8 * q^40 + 120 * q^46 + 196 * q^49 + 112 * q^55 - 64 * q^61 + 64 * q^64 + 392 * q^70 - 112 * q^76 + 484 * q^79 + 88 * q^85 - 140 * q^91 - 8 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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