LMFDB - Embedded newform 675.2.u.e.49.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [675,2,Mod(49,675)] 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("675.49"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(675, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([14, 9])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 675 = 3^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	675.u (of order $18$, degree $6$, not minimal)

Newform invariants

comment:select newform

sage:traces = [132] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$5.38990213644$
Analytic rank:	$0$
Dimension:	$132$
Relative dimension:	$22$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			49.7
Character	$\chi$	$=$	675.49
Dual form			675.2.u.e.124.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.852522 - 1.01600i) q^{2} +(1.72092 - 0.196018i) q^{3} +(0.0418420 - 0.237298i) q^{4} +(-1.66628 - 1.58134i) q^{6} +(4.36644 - 0.769922i) q^{7} +(-2.57396 + 1.48608i) q^{8} +(2.92315 - 0.674663i) q^{9} +(3.91123 + 1.42357i) q^{11} +(0.0254923 - 0.416573i) q^{12} +(-0.972900 + 1.15946i) q^{13} +(-4.50473 - 3.77991i) q^{14} +(3.25136 + 1.18340i) q^{16} +(0.985419 + 0.568932i) q^{17} +(-3.17751 - 2.39475i) q^{18} +(3.37499 + 5.84565i) q^{19} +(7.36340 - 2.18088i) q^{21} +(-1.88807 - 5.18742i) q^{22} +(-7.86279 - 1.38642i) q^{23} +(-4.13830 + 3.06197i) q^{24} +2.00742 q^{26} +(4.89828 - 1.73403i) q^{27} -1.06836i q^{28} +(-1.89402 + 1.58927i) q^{29} +(0.369663 - 2.09646i) q^{31} +(0.463549 + 1.27359i) q^{32} +(7.00997 + 1.68319i) q^{33} +(-0.262059 - 1.48621i) q^{34} +(-0.0377853 - 0.721887i) q^{36} +(-8.65969 - 4.99967i) q^{37} +(3.06191 - 8.41252i) q^{38} +(-1.44701 + 2.18604i) q^{39} +(-0.384359 - 0.322515i) q^{41} +(-8.49322 - 5.62194i) q^{42} +(-0.0373936 + 0.102738i) q^{43} +(0.501464 - 0.868561i) q^{44} +(5.29460 + 9.17051i) q^{46} +(-7.45681 + 1.31484i) q^{47} +(5.82730 + 1.39921i) q^{48} +(11.8952 - 4.32950i) q^{49} +(1.80735 + 0.785929i) q^{51} +(0.234429 + 0.279381i) q^{52} -3.96330i q^{53} +(-5.93766 - 3.49833i) q^{54} +(-10.0949 + 8.47063i) q^{56} +(6.95395 + 9.39836i) q^{57} +(3.22938 + 0.569427i) q^{58} +(-7.67614 + 2.79389i) q^{59} +(-2.14296 - 12.1533i) q^{61} +(-2.44514 + 1.41170i) q^{62} +(12.2444 - 5.19648i) q^{63} +(4.35880 - 7.54966i) q^{64} +(-4.26604 - 8.55705i) q^{66} +(1.88943 - 2.25173i) q^{67} +(0.176238 - 0.210033i) q^{68} +(-13.8030 - 0.844680i) q^{69} +(-3.78880 + 6.56240i) q^{71} +(-6.52149 + 6.08060i) q^{72} +(-8.88121 + 5.12757i) q^{73} +(2.30293 + 13.0605i) q^{74} +(1.52838 - 0.556283i) q^{76} +(18.1742 + 3.20460i) q^{77} +(3.45462 - 0.393490i) q^{78} +(-3.74388 + 3.14149i) q^{79} +(8.08966 - 3.94429i) q^{81} +0.665459i q^{82} +(2.34014 + 2.78888i) q^{83} +(-0.209418 - 1.83857i) q^{84} +(0.136260 - 0.0495947i) q^{86} +(-2.94793 + 3.10627i) q^{87} +(-12.1829 + 2.14817i) q^{88} +(-5.74755 - 9.95505i) q^{89} +(-3.35542 + 5.81176i) q^{91} +(-0.657989 + 1.80781i) q^{92} +(0.225218 - 3.68031i) q^{93} +(7.69297 + 6.45516i) q^{94} +(1.04738 + 2.10089i) q^{96} +(2.68084 - 7.36555i) q^{97} +(-14.5397 - 8.39449i) q^{98} +(12.3936 + 1.52256i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 132 q - 12 q^{6} + 12 q^{9} + 30 q^{11} - 30 q^{14} + 36 q^{16} - 24 q^{19} + 24 q^{21} + 78 q^{24} + 12 q^{26} + 30 q^{29} + 6 q^{31} + 60 q^{36} + 30 q^{39} + 78 q^{41} - 102 q^{44} + 18 q^{46} + 12 q^{49}+ \cdots + 96 q^{99}+O(q^{100}) $ 132 * q - 12 * q^6 + 12 * q^9 + 30 * q^11 - 30 * q^14 + 36 * q^16 - 24 * q^19 + 24 * q^21 + 78 * q^24 + 12 * q^26 + 30 * q^29 + 6 * q^31 + 60 * q^36 + 30 * q^39 + 78 * q^41 - 102 * q^44 + 18 * q^46 + 12 * q^49 - 150 * q^54 + 288 * q^56 - 90 * q^59 - 108 * q^61 + 48 * q^64 + 96 * q^66 - 102 * q^69 - 30 * q^71 - 192 * q^74 - 96 * q^76 - 96 * q^79 - 108 * q^81 - 114 * q^84 - 222 * q^86 + 24 * q^89 + 18 * q^91 - 72 * q^94 - 498 * q^96 + 96 * q^99

Character values

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

$n$	$326$	$352$
$\chi(n)$	$e\left(\frac{7}{9}\right)$	$-1$

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 $

$2$	−0.852522	−	1.01600i	−0.602824	−	0.718418i	0.375192	−	0.926947i	$-0.377577\pi$
$2$	−0.852522	−	1.01600i	−0.602824	−	0.718418i	−0.978016	+	0.208529i	$0.933132\pi$
$3$	1.72092	−	0.196018i	0.993576	−	0.113171i
$3$	1.72092	−	0.196018i	0.993576	−	0.113171i
$4$	0.0418420	−	0.237298i	0.0209210	−	0.118649i
$5$		0			0
$5$		0			0
$6$	−1.66628	−	1.58134i	−0.680255	−	0.645580i
$7$	4.36644	−	0.769922i	1.65036	−	0.291003i	0.730402	−	0.683018i	$-0.239333\pi$
$7$	4.36644	−	0.769922i	1.65036	−	0.291003i	0.919959	+	0.392015i	$0.128222\pi$
$8$	−2.57396	+	1.48608i	−0.910034	+	0.525408i
$9$	2.92315	−	0.674663i	0.974385	−	0.224888i
$10$		0			0
$11$	3.91123	+	1.42357i	1.17928	+	0.429223i	0.855947	−	0.517063i	$-0.172975\pi$
$11$	3.91123	+	1.42357i	1.17928	+	0.429223i	0.323332	+	0.946286i	$0.395197\pi$
$12$	0.0254923	−	0.416573i	0.00735900	−	0.120254i
$13$	−0.972900	+	1.15946i	−0.269834	+	0.321576i	−0.883897	−	0.467681i	$-0.845090\pi$
$13$	−0.972900	+	1.15946i	−0.269834	+	0.321576i	0.614063	+	0.789257i	$0.289534\pi$
$14$	−4.50473	−	3.77991i	−1.20394	−	1.01022i
$15$		0			0
$16$	3.25136	+	1.18340i	0.812839	+	0.295849i
$17$	0.985419	+	0.568932i	0.238999	+	0.137986i	0.614717	−	0.788748i	$-0.289270\pi$
$17$	0.985419	+	0.568932i	0.238999	+	0.137986i	−0.375717	+	0.926734i	$0.622604\pi$
$18$	−3.17751	−	2.39475i	−0.748946	−	0.564448i
$19$	3.37499	+	5.84565i	0.774275	+	1.34108i	0.935201	+	0.354118i	$0.115219\pi$
$19$	3.37499	+	5.84565i	0.774275	+	1.34108i	−0.160926	+	0.986967i	$0.551448\pi$
$20$		0			0
$21$	7.36340	−	2.18088i	1.60683	−	0.475906i
$22$	−1.88807	−	5.18742i	−0.402537	−	1.10596i
$23$	−7.86279	−	1.38642i	−1.63950	−	0.289089i	−0.723520	−	0.690303i	$-0.757477\pi$
$23$	−7.86279	−	1.38642i	−1.63950	−	0.289089i	−0.915984	+	0.401215i	$0.868588\pi$
$24$	−4.13830	+	3.06197i	−0.844726	+	0.625022i
$25$		0			0
$26$	2.00742			0.393688
$27$	4.89828	−	1.73403i	0.942674	−	0.333715i
$28$		−	1.06836i		−	0.201902i
$29$	−1.89402	+	1.58927i	−0.351710	+	0.295120i	−0.801476	−	0.598026i	$-0.795952\pi$
$29$	−1.89402	+	1.58927i	−0.351710	+	0.295120i	0.449766	+	0.893146i	$0.351507\pi$
$30$		0			0
$31$	0.369663	−	2.09646i	0.0663933	−	0.376535i	−0.933448	−	0.358713i	$-0.883216\pi$
$31$	0.369663	−	2.09646i	0.0663933	−	0.376535i	0.999841	−	0.0178222i	$-0.00567328\pi$
$32$	0.463549	+	1.27359i	0.0819447	+	0.225141i
$33$	7.00997	+	1.68319i	1.22028	+	0.293005i
$34$	−0.262059	−	1.48621i	−0.0449427	−	0.254883i
$35$		0			0
$36$	−0.0377853	−	0.721887i	−0.00629756	−	0.120315i
$37$	−8.65969	−	4.99967i	−1.42364	−	0.821941i	−0.427036	−	0.904235i	$-0.640442\pi$
$37$	−8.65969	−	4.99967i	−1.42364	−	0.821941i	−0.996608	+	0.0822930i	$0.973776\pi$
$38$	3.06191	−	8.41252i	0.496707	−	1.36469i
$39$	−1.44701	+	2.18604i	−0.231708	+	0.350047i
$40$		0			0
$41$	−0.384359	−	0.322515i	−0.0600268	−	0.0503685i	0.612281	−	0.790640i	$-0.290252\pi$
$41$	−0.384359	−	0.322515i	−0.0600268	−	0.0503685i	−0.672307	+	0.740272i	$0.734697\pi$
$42$	−8.49322	−	5.62194i	−1.31053	−	0.867484i
$43$	−0.0373936	+	0.102738i	−0.00570247	+	0.0156674i	−0.942511	−	0.334175i	$-0.891542\pi$
$43$	−0.0373936	+	0.102738i	−0.00570247	+	0.0156674i	0.936809	+	0.349842i	$0.113765\pi$
$44$	0.501464	−	0.868561i	0.0755985	−	0.130940i
$45$		0			0
$46$	5.29460	+	9.17051i	0.780646	+	1.35212i
$47$	−7.45681	+	1.31484i	−1.08769	+	0.191789i	−0.688613	−	0.725129i	$-0.741780\pi$
$47$	−7.45681	+	1.31484i	−1.08769	+	0.191789i	−0.399075	+	0.916918i	$0.630669\pi$
$48$	5.82730	+	1.39921i	0.841099	+	0.201959i
$49$	11.8952	−	4.32950i	1.69932	−	0.618500i
$50$		0			0
$51$	1.80735	+	0.785929i	0.253080	+	0.110052i
$52$	0.234429	+	0.279381i	0.0325094	+	0.0387432i
$53$		−	3.96330i		−	0.544401i	−0.962241	−	0.272201i	$-0.912249\pi$
$53$		−	3.96330i		−	0.544401i	0.962241	−	0.272201i	$-0.0877514\pi$
$54$	−5.93766	−	3.49833i	−0.808013	−	0.476063i
$55$		0			0
$56$	−10.0949	+	8.47063i	−1.34899	+	1.13194i
$57$	6.95395	+	9.39836i	0.921073	+	1.24484i
$58$	3.22938	+	0.569427i	0.424039	+	0.0747695i
$59$	−7.67614	+	2.79389i	−0.999348	+	0.363733i	−0.789333	−	0.613965i	$-0.789574\pi$
$59$	−7.67614	+	2.79389i	−0.999348	+	0.363733i	−0.210015	+	0.977698i	$0.567351\pi$
$60$		0			0
$61$	−2.14296	−	12.1533i	−0.274377	−	1.55607i	−0.740932	−	0.671580i	$-0.765616\pi$
$61$	−2.14296	−	12.1533i	−0.274377	−	1.55607i	0.466555	−	0.884492i	$-0.345495\pi$
$62$	−2.44514	+	1.41170i	−0.310533	+	0.179286i
$63$	12.2444	−	5.19648i	1.54264	−	0.654695i
$64$	4.35880	−	7.54966i	0.544850	−	0.943708i
$65$		0			0
$66$	−4.26604	−	8.55705i	−0.525113	−	1.05330i
$67$	1.88943	−	2.25173i	0.230830	−	0.275093i	−0.638180	−	0.769887i	$-0.720312\pi$
$67$	1.88943	−	2.25173i	0.230830	−	0.275093i	0.869010	+	0.494795i	$0.164757\pi$
$68$	0.176238	−	0.210033i	0.0213720	−	0.0254702i
$69$	−13.8030	−	0.844680i	−1.66169	−	0.101688i
$70$		0			0
$71$	−3.78880	+	6.56240i	−0.449648	+	0.778814i	−0.998363	−	0.0571960i	$-0.981784\pi$
$71$	−3.78880	+	6.56240i	−0.449648	+	0.778814i	0.548715	+	0.836010i	$0.315117\pi$
$72$	−6.52149	+	6.08060i	−0.768565	+	0.716605i
$73$	−8.88121	+	5.12757i	−1.03947	+	0.600136i	−0.919682	−	0.392663i	$-0.871554\pi$
$73$	−8.88121	+	5.12757i	−1.03947	+	0.600136i	−0.119785	+	0.992800i	$0.538220\pi$
$74$	2.30293	+	13.0605i	0.267710	+	1.51826i
$75$		0			0
$76$	1.52838	−	0.556283i	0.175317	−	0.0638101i
$77$	18.1742	+	3.20460i	2.07114	+	0.365198i
$78$	3.45462	−	0.393490i	0.391159	−	0.0445540i
$79$	−3.74388	+	3.14149i	−0.421219	+	0.353445i	−0.828627	−	0.559802i	$-0.810877\pi$
$79$	−3.74388	+	3.14149i	−0.421219	+	0.353445i	0.407408	+	0.913246i	$0.366433\pi$
$80$		0			0
$81$	8.08966	−	3.94429i	0.898851	−	0.438254i
$82$			0.665459i			0.0734876i
$83$	2.34014	+	2.78888i	0.256864	+	0.306119i	0.879030	−	0.476767i	$-0.158191\pi$
$83$	2.34014	+	2.78888i	0.256864	+	0.306119i	−0.622166	+	0.782886i	$0.713747\pi$
$84$	−0.209418	−	1.83857i	−0.0228494	−	0.200604i
$85$		0			0
$86$	0.136260	−	0.0495947i	0.0146933	−	0.00534794i
$87$	−2.94793	+	3.10627i	−0.316052	+	0.333027i
$88$	−12.1829	+	2.14817i	−1.29870	+	0.228996i
$89$	−5.74755	−	9.95505i	−0.609239	−	1.05523i	−0.991366	−	0.131123i	$-0.958142\pi$
$89$	−5.74755	−	9.95505i	−0.609239	−	1.05523i	0.382127	−	0.924110i	$-0.375192\pi$
$90$		0			0
$91$	−3.35542	+	5.81176i	−0.351744	+	0.609238i
$92$	−0.657989	+	1.80781i	−0.0686001	+	0.188477i
$93$	0.225218	−	3.68031i	0.0233540	−	0.381630i
$94$	7.69297	+	6.45516i	0.793469	+	0.665799i
$95$		0			0
$96$	1.04738	+	2.10089i	0.106898	+	0.214421i
$97$	2.68084	−	7.36555i	0.272198	−	0.747858i	−0.725991	−	0.687704i	$-0.758619\pi$
$97$	2.68084	−	7.36555i	0.272198	−	0.747858i	0.998189	−	0.0601538i	$-0.0191591\pi$
$98$	−14.5397	−	8.39449i	−1.46873	−	0.847971i
$99$	12.3936	+	1.52256i	1.24560	+	0.153023i
$100$		0			0
$101$	−1.84949	−	10.4890i	−0.184031	−	1.04369i	−0.927194	−	0.374581i	$-0.877786\pi$
$101$	−1.84949	−	10.4890i	−0.184031	−	1.04369i	0.743163	−	0.669110i	$-0.233325\pi$
$102$	−0.742306	−	2.50628i	−0.0734993	−	0.248159i
$103$	−2.85101	−	7.83309i	−0.280918	−	0.771817i	−0.997254	−	0.0740609i	$-0.976404\pi$
$103$	−2.85101	−	7.83309i	−0.280918	−	0.771817i	0.716335	−	0.697756i	$-0.245818\pi$
$104$	0.781165	−	4.43021i	0.0765996	−	0.434418i
$105$		0			0
$106$	−4.02670	+	3.37880i	−0.391107	+	0.328178i
$107$		−	12.1812i		−	1.17760i	−0.808279	−	0.588800i	$-0.799601\pi$
$107$		−	12.1812i		−	1.17760i	0.808279	−	0.588800i	$-0.200399\pi$
$108$	−0.206528	−	1.23491i	−0.0198732	−	0.118829i
$109$	0.268688			0.0257356			0.0128678	−	0.999917i	$-0.495904\pi$
$109$	0.268688			0.0257356			0.0128678	+	0.999917i	$0.495904\pi$
$110$		0			0
$111$	−15.8827	−	6.90660i	−1.50752	−	0.655546i
$112$	15.1080	+	2.66395i	1.42757	+	0.251719i
$113$	0.708479	+	1.94653i	0.0666481	+	0.183114i	0.968546	−	0.248836i	$-0.0800479\pi$
$113$	0.708479	+	1.94653i	0.0666481	+	0.183114i	−0.901898	+	0.431950i	$0.857826\pi$
$114$	3.62030	−	15.0775i	0.339073	−	1.41214i
$115$		0			0
$116$	0.297881	+	0.515944i	0.0276575	+	0.0479042i
$117$	−2.06170	+	4.04565i	−0.190604	+	0.374021i
$118$	9.38266	+	5.41708i	0.863743	+	0.498683i
$119$	4.74081	+	1.72551i	0.434589	+	0.158178i
$120$		0			0
$121$	4.84466	+	4.06516i	0.440424	+	0.369560i
$122$	−10.5208	+	12.5382i	−0.952508	+	1.13515i
$123$	−0.724671	−	0.479683i	−0.0653414	−	0.0432516i
$124$	−0.482018	−	0.175440i	−0.0432865	−	0.0157550i
$125$		0			0
$126$	−15.7182	−	8.01010i	−1.40029	−	0.713597i
$127$	−13.1553	+	7.59522i	−1.16735	+	0.673967i	−0.953053	−	0.302802i	$-0.902078\pi$
$127$	−13.1553	+	7.59522i	−1.16735	+	0.673967i	−0.214292	+	0.976770i	$0.568744\pi$
$128$	−8.71693	+	1.53703i	−0.770475	+	0.135855i
$129$	−0.0442131	+	0.184134i	−0.00389274	+	0.0162121i
$130$		0			0
$131$	0.588630	−	3.33829i	0.0514289	−	0.291668i	−0.948236	−	0.317568i	$-0.897134\pi$
$131$	0.588630	−	3.33829i	0.0514289	−	0.291668i	0.999665	+	0.0258999i	$0.00824510\pi$
$132$	0.692728	−	1.59302i	0.0602942	−	0.138655i
$133$	19.2374	+	22.9262i	1.66809	+	1.98796i
$134$	−3.89853			−0.336782
$135$		0			0
$136$	−3.38191			−0.289997
$137$	11.9084	+	14.1918i	1.01740	+	1.21249i	0.976985	+	0.213306i	$0.0684231\pi$
$137$	11.9084	+	14.1918i	1.01740	+	1.21249i	0.0404136	+	0.999183i	$0.487132\pi$
$138$	10.9092	+	14.7439i	0.928651	+	1.25509i
$139$	−2.88601	+	16.3674i	−0.244788	+	1.38826i	0.576197	+	0.817311i	$0.304536\pi$
$139$	−2.88601	+	16.3674i	−0.244788	+	1.38826i	−0.820985	+	0.570950i	$0.806575\pi$
$140$		0			0
$141$	−12.5749	+	3.72440i	−1.05900	+	0.313651i
$142$	9.89741	−	1.74518i	0.830572	−	0.146452i
$143$	−5.45581	+	3.14991i	−0.456237	+	0.263409i
$144$	10.3026	+	1.26568i	0.858551	+	0.105474i
$145$		0			0
$146$	12.7810	+	4.65191i	1.05776	+	0.384995i
$147$	19.6221	−	9.78241i	1.61840	−	0.806840i
$148$	−1.54875	+	1.84573i	−0.127307	+	0.151718i
$149$	6.52625	+	5.47617i	0.534651	+	0.448626i	0.869704	−	0.493574i	$-0.164310\pi$
$149$	6.52625	+	5.47617i	0.534651	+	0.448626i	−0.335053	+	0.942199i	$0.608754\pi$
$150$		0			0
$151$	11.3452	+	4.12932i	0.923259	+	0.336039i	0.759534	−	0.650467i	$-0.225427\pi$
$151$	11.3452	+	4.12932i	0.923259	+	0.336039i	0.163725	+	0.986506i	$0.447649\pi$
$152$	−17.3742	−	10.0310i	−1.40923	−	0.813621i
$153$	3.26437	+	0.998250i	0.263909	+	0.0807038i
$154$	−12.2380	−	21.1969i	−0.986169	−	1.70810i
$155$		0			0
$156$	0.458197	+	0.434841i	0.0366851	+	0.0348152i
$157$	4.45846	+	12.2495i	0.355824	+	0.977618i	0.980463	+	0.196704i	$0.0630239\pi$
$157$	4.45846	+	12.2495i	0.355824	+	0.977618i	−0.624639	+	0.780914i	$0.714754\pi$
$158$	6.38347	+	1.12558i	0.507842	+	0.0895462i
$159$	−0.776877	−	6.82053i	−0.0616103	−	0.540904i
$160$		0			0
$161$	−35.3999			−2.78990
$162$	−10.9040	−	4.85647i	−0.856698	−	0.381561i
$163$			15.2191i			1.19205i	0.802966	+	0.596025i	$0.203254\pi$
$163$			15.2191i			1.19205i	−0.802966	+	0.596025i	$0.796746\pi$
$164$	−0.0926146	+	0.0777128i	−0.00723198	+	0.00606835i
$165$		0			0
$166$	0.838462	−	4.75515i	0.0650773	−	0.369072i
$167$	5.44622	+	14.9634i	0.421441	+	1.15790i	0.950882	+	0.309553i	$0.100179\pi$
$167$	5.44622	+	14.9634i	0.421441	+	1.15790i	−0.529441	+	0.848347i	$0.677598\pi$
$168$	−15.7122	+	16.5561i	−1.21222	+	1.27733i
$169$	1.85962	+	10.5464i	0.143048	+	0.811264i
$170$		0			0
$171$	13.8095	+	14.8108i	1.05604	+	1.13261i
$172$	0.0228149	+	0.0131722i	0.00173962	+	0.00100437i
$173$	4.36838	−	12.0020i	0.332122	−	0.912497i	−0.655437	−	0.755249i	$-0.727516\pi$
$173$	4.36838	−	12.0020i	0.332122	−	0.912497i	0.987559	−	0.157248i	$-0.0502621\pi$
$174$	5.66914	+	0.346925i	0.429776	+	0.0263003i
$175$		0			0
$176$	11.0322	+	9.25707i	0.831580	+	0.697778i
$177$	−12.6624	+	6.31272i	−0.951764	+	0.474493i
$178$	−5.21438	+	14.3264i	−0.390834	+	1.07381i
$179$	1.85652	−	3.21558i	0.138763	−	0.240344i	−0.788266	−	0.615335i	$-0.789021\pi$
$179$	1.85652	−	3.21558i	0.138763	−	0.240344i	0.927029	+	0.374991i	$0.122354\pi$
$180$		0			0
$181$	−1.53697	−	2.66211i	−0.114242	−	0.197873i	0.803234	−	0.595663i	$-0.203111\pi$
$181$	−1.53697	−	2.66211i	−0.114242	−	0.197873i	−0.917477	+	0.397790i	$0.869777\pi$
$182$	8.76530	−	1.54556i	0.649727	−	0.114564i
$183$	−6.07013	−	20.4949i	−0.448717	−	1.51502i
$184$	22.2989	−	8.11612i	1.64389	−	0.598328i
$185$		0			0
$186$	−3.93118	+	2.90872i	−0.288248	+	0.213278i
$187$	3.04428	+	3.62804i	0.222620	+	0.265308i
$188$			1.82450i			0.133065i
$189$	20.0530	−	11.3428i	1.45864	−	0.825071i
$190$		0			0
$191$	−3.18718	+	2.67436i	−0.230616	+	0.193510i	−0.750772	−	0.660561i	$-0.770318\pi$
$191$	−3.18718	+	2.67436i	−0.230616	+	0.193510i	0.520156	+	0.854071i	$0.325874\pi$
$192$	6.02129	−	13.8468i	0.434549	−	0.999306i
$193$	−3.88491	−	0.685014i	−0.279642	−	0.0493084i	0.0320682	−	0.999486i	$-0.489791\pi$
$193$	−3.88491	−	0.685014i	−0.279642	−	0.0493084i	−0.311710	+	0.950177i	$0.600902\pi$
$194$	−9.76884	+	3.55557i	−0.701362	+	0.255275i
$195$		0			0
$196$	−0.529662	−	3.00386i	−0.0378330	−	0.214562i
$197$	7.54672	−	4.35710i	0.537681	−	0.310430i	−0.206457	−	0.978456i	$-0.566193\pi$
$197$	7.54672	−	4.35710i	0.537681	−	0.310430i	0.744139	+	0.668025i	$0.232860\pi$
$198$	−9.01886	−	13.8898i	−0.640943	−	0.987106i
$199$	−6.70417	+	11.6120i	−0.475246	+	0.823151i	−0.999598	−	0.0283510i	$-0.990974\pi$
$199$	−6.70417	+	11.6120i	−0.475246	+	0.823151i	0.524352	+	0.851502i	$0.324308\pi$
$200$		0			0
$201$	2.81018	−	4.24542i	0.198215	−	0.299449i
$202$	−9.08002	+	10.8211i	−0.638868	+	0.761373i
$203$	−7.04651	+	8.39770i	−0.494568	+	0.589403i
$204$	0.262122	−	0.395996i	0.0183522	−	0.0277252i
$205$		0			0
$206$	−5.52784	+	9.57450i	−0.385143	+	0.667087i
$207$	−23.9195	+	1.25200i	−1.66252	+	0.0870204i
$208$	−4.53535	+	2.61848i	−0.314470	+	0.181559i
$209$	4.87865	+	27.6682i	0.337463	+	1.91385i
$210$		0			0
$211$	3.45959	−	1.25919i	0.238168	−	0.0866861i	−0.220179	−	0.975460i	$-0.570664\pi$
$211$	3.45959	−	1.25919i	0.238168	−	0.0866861i	0.458347	+	0.888773i	$0.348442\pi$
$212$	−0.940482	−	0.165832i	−0.0645926	−	0.0113894i
$213$	−5.23390	+	12.0361i	−0.358621	+	0.824697i
$214$	−12.3760	+	10.3847i	−0.846009	+	0.709886i
$215$		0			0
$216$	−10.0311	+	11.7426i	−0.682529	+	0.798980i
$217$		−	9.43869i		−	0.640740i
$218$	−0.229062	−	0.272986i	−0.0155140	−	0.0184889i
$219$	−14.2788	+	10.5650i	−0.964871	+	0.713918i
$220$		0			0
$221$	−1.61837	+	0.589038i	−0.108863	+	0.0396230i
$222$	6.52326	+	22.0248i	0.437812	+	1.47821i
$223$	10.3699	−	1.82849i	0.694417	−	0.122445i	0.184711	−	0.982793i	$-0.440865\pi$
$223$	10.3699	−	1.82849i	0.694417	−	0.122445i	0.509707	+	0.860348i	$0.329754\pi$
$224$	3.00463	+	5.20417i	0.200755	+	0.347718i
$225$		0			0
$226$	1.37367	−	2.37927i	0.0913754	−	0.158267i
$227$	9.06486	−	24.9055i	0.601656	−	1.65304i	−0.146263	−	0.989246i	$-0.546724\pi$
$227$	9.06486	−	24.9055i	0.601656	−	1.65304i	0.747919	−	0.663790i	$-0.231053\pi$
$228$	2.52118	−	1.25691i	0.166969	−	0.0832409i
$229$	8.45322	+	7.09309i	0.558605	+	0.468725i	0.877842	−	0.478950i	$-0.158982\pi$
$229$	8.45322	+	7.09309i	0.558605	+	0.468725i	−0.319238	+	0.947675i	$0.603427\pi$
$230$		0			0
$231$	31.9046	+	1.95241i	2.09917	+	0.128459i
$232$	2.51335	−	6.90538i	0.165010	−	0.453361i
$233$	11.6077	+	6.70173i	0.760448	+	0.439045i	0.829457	−	0.558571i	$-0.188650\pi$
$233$	11.6077	+	6.70173i	0.760448	+	0.439045i	−0.0690083	+	0.997616i	$0.521984\pi$
$234$	5.86801	−	1.35433i	0.383604	−	0.0885356i
$235$		0			0
$236$	0.341798	+	1.93843i	0.0222492	+	0.126181i
$237$	−5.82714	+	6.14012i	−0.378513	+	0.398844i
$238$	−2.28853	−	6.28768i	−0.148343	−	0.407570i
$239$	1.52780	−	8.66459i	0.0988253	−	0.560466i	−0.894683	−	0.446702i	$-0.852598\pi$
$239$	1.52780	−	8.66459i	0.0988253	−	0.560466i	0.993508	−	0.113763i	$-0.0362906\pi$
$240$		0			0
$241$	−11.2282	+	9.42161i	−0.723274	+	0.606899i	−0.928289	−	0.371860i	$-0.878720\pi$
$241$	−11.2282	+	9.42161i	−0.723274	+	0.606899i	0.205015	+	0.978759i	$0.434276\pi$
$242$		−	8.38779i		−	0.539188i
$243$	13.1485	−	8.37353i	0.843479	−	0.537162i
$244$	−2.97362			−0.190366
$245$		0			0
$246$	0.130442	+	1.14520i	0.00831666	+	0.0730155i
$247$	−10.0613	−	1.77408i	−0.640186	−	0.112882i
$248$	2.16401	+	5.94556i	0.137415	+	0.377544i
$249$	4.57388	+	4.34073i	0.289858	+	0.275083i
$250$		0			0
$251$	−1.91159	−	3.31097i	−0.120658	−	0.208986i	0.799369	−	0.600840i	$-0.205167\pi$
$251$	−1.91159	−	3.31097i	−0.120658	−	0.208986i	−0.920027	+	0.391854i	$0.871834\pi$
$252$	−0.720784	−	3.12299i	−0.0454052	−	0.196730i
$253$	−28.7795	−	16.6158i	−1.80935	−	1.04463i
$254$	18.9319	+	6.89065i	1.18789	+	0.432358i
$255$		0			0
$256$	−4.36315	−	3.66112i	−0.272697	−	0.228820i
$257$	−5.24803	+	6.25436i	−0.327363	+	0.390136i	−0.904473	−	0.426530i	$-0.859736\pi$
$257$	−5.24803	+	6.25436i	−0.327363	+	0.390136i	0.577110	+	0.816666i	$0.304180\pi$
$258$	0.224772	−	0.112058i	0.0139937	−	0.00697644i
$259$	−41.6614	−	15.1635i	−2.58871	−	0.942215i
$260$		0			0
$261$	−4.46428	+	5.92350i	−0.276332	+	0.366656i
$262$	−3.89351	+	2.24792i	−0.240542	+	0.138877i
$263$	27.4441	−	4.83914i	1.69228	−	0.298394i	0.757291	−	0.653077i	$-0.226522\pi$
$263$	27.4441	−	4.83914i	1.69228	−	0.298394i	0.934987	+	0.354683i	$0.115411\pi$
$264$	−20.5448	+	6.08491i	−1.26444	+	0.374500i
$265$		0			0
$266$	6.89266	−	39.0902i	0.422616	−	2.39678i
$267$	−11.8425	−	16.0052i	−0.724746	−	0.979505i
$268$	−0.455273	−	0.542574i	−0.0278103	−	0.0331430i
$269$	13.1520			0.801893			0.400947	−	0.916101i	$-0.368681\pi$
$269$	13.1520			0.801893			0.400947	+	0.916101i	$0.368681\pi$
$270$		0			0
$271$	8.19664			0.497911			0.248955	−	0.968515i	$-0.419913\pi$
$271$	8.19664			0.497911			0.248955	+	0.968515i	$0.419913\pi$
$272$	2.53068	+	3.01594i	0.153445	+	0.182868i
$273$	−4.63522	+	10.6593i	−0.280536	+	0.645132i
$274$	4.26670	−	24.1977i	0.257761	−	1.46183i
$275$		0			0
$276$	−0.777987	+	3.24008i	−0.0468293	+	0.195030i
$277$	−28.6993	+	5.06046i	−1.72437	+	0.304054i	−0.946101	−	0.323873i	$-0.895015\pi$
$277$	−28.6993	+	5.06046i	−1.72437	+	0.304054i	−0.778273	+	0.627926i	$0.783904\pi$
$278$	19.0896	−	11.0214i	1.14492	−	0.661017i
$279$	−0.333823	−	6.37767i	−0.0199855	−	0.381821i
$280$		0			0
$281$	−22.1793	−	8.07261i	−1.32311	−	0.481572i	−0.418655	−	0.908145i	$-0.637498\pi$
$281$	−22.1793	−	8.07261i	−1.32311	−	0.481572i	−0.904453	+	0.426574i	$0.859720\pi$
$282$	14.5043	+	9.60089i	0.863720	+	0.571724i
$283$	12.6506	−	15.0763i	0.751997	−	0.896195i	−0.245317	−	0.969443i	$-0.578892\pi$
$283$	12.6506	−	15.0763i	0.751997	−	0.896195i	0.997314	+	0.0732477i	$0.0233364\pi$
$284$	1.39871	+	1.17366i	0.0829983	+	0.0696438i
$285$		0			0
$286$	7.85149	+	2.85771i	0.464268	+	0.168980i
$287$	−1.92659	−	1.11232i	−0.113723	−	0.0656581i
$288$	2.21427	+	3.41016i	0.130477	+	0.200946i
$289$	−7.85263	−	13.6012i	−0.461920	−	0.800068i
$290$		0			0
$291$	3.16974	−	13.2010i	0.185814	−	0.773858i
$292$	0.845153	+	2.32204i	0.0494588	+	0.135887i
$293$	−6.07899	−	1.07189i	−0.355138	−	0.0626205i	−0.00676709	−	0.999977i	$-0.502154\pi$
$293$	−6.07899	−	1.07189i	−0.355138	−	0.0626205i	−0.348371	+	0.937357i	$0.613265\pi$
$294$	−26.6671	−	11.5962i	−1.55526	−	0.676306i
$295$		0			0
$296$	29.7196			1.72742
$297$	21.6268	+	0.190848i	1.25491	+	0.0110742i
$298$		−	11.2992i		−	0.654545i
$299$	9.25720	−	7.76772i	0.535358	−	0.449219i
$300$		0			0
$301$	−0.0841768	+	0.477390i	−0.00485187	+	0.0275163i
$302$	−5.47666	−	15.0470i	−0.315147	−	0.865858i
$303$	−5.23885	−	17.6882i	−0.300964	−	1.01616i
$304$	4.05556	+	23.0002i	0.232603	+	1.31915i
$305$		0			0
$306$	−1.76873	−	4.16762i	−0.101111	−	0.238247i
$307$	−10.3432	−	5.97167i	−0.590320	−	0.340821i	0.174904	−	0.984585i	$-0.444038\pi$
$307$	−10.3432	−	5.97167i	−0.590320	−	0.340821i	−0.765224	+	0.643764i	$0.777372\pi$
$308$	1.52089	−	4.17861i	0.0866607	−	0.238098i
$309$	−6.44179	−	12.9213i	−0.366461	−	0.735067i
$310$		0			0
$311$	19.1774	+	16.0917i	1.08745	+	0.912478i	0.996518	−	0.0833788i	$-0.0265711\pi$
$311$	19.1774	+	16.0917i	1.08745	+	0.912478i	0.0909314	+	0.995857i	$0.471016\pi$
$312$	0.475927	−	7.77717i	0.0269440	−	0.440296i
$313$	5.24628	−	14.4140i	0.296537	−	0.814729i	−0.698535	−	0.715576i	$-0.746164\pi$
$313$	5.24628	−	14.4140i	0.296537	−	0.814729i	0.995072	−	0.0991534i	$-0.0316135\pi$
$314$	8.64453	−	14.9728i	0.487839	−	0.844962i
$315$		0			0
$316$	0.588816	+	1.01986i	0.0331235	+	0.0573716i
$317$	−0.242608	+	0.0427784i	−0.0136262	+	0.00240267i	−0.180457	−	0.983583i	$-0.557758\pi$
$317$	−0.242608	+	0.0427784i	−0.0136262	+	0.00240267i	0.166831	+	0.985986i	$0.446647\pi$
$318$	−6.26733	+	6.60396i	−0.351455	+	0.370332i
$319$	−9.67037	+	3.51973i	−0.541437	+	0.197067i
$320$		0			0
$321$	−2.38773	−	20.9629i	−0.133270	−	1.17003i
$322$	30.1791	+	35.9661i	1.68182	+	2.00431i
$323$			7.68055i			0.427358i
$324$	−0.597483	−	2.08470i	−0.0331935	−	0.115816i
$325$		0			0
$326$	15.4625	−	12.9746i	0.856390	−	0.718597i
$327$	0.462391	−	0.0526675i	0.0255703	−	0.00291252i
$328$	1.46861	+	0.258955i	0.0810904	+	0.0142984i
$329$	−31.5474	+	11.4823i	−1.73927	+	0.633041i
$330$		0			0
$331$	−4.33167	−	24.5661i	−0.238090	−	1.35028i	−0.836008	−	0.548718i	$-0.815116\pi$
$331$	−4.33167	−	24.5661i	−0.238090	−	1.35028i	0.597918	−	0.801558i	$-0.295995\pi$
$332$	0.759710	−	0.438619i	0.0416945	−	0.0240723i
$333$	−28.6867	−	8.77245i	−1.57202	−	0.480727i
$334$	10.5597	−	18.2899i	0.577801	−	1.00078i
$335$		0			0
$336$	26.5219	+	1.62301i	1.44689	+	0.0885427i
$337$	19.0503	−	22.7032i	1.03773	−	1.23672i	0.0667018	−	0.997773i	$-0.478752\pi$
$337$	19.0503	−	22.7032i	1.03773	−	1.23672i	0.971032	−	0.238950i	$-0.0768032\pi$
$338$	9.12976	−	10.8804i	0.496594	−	0.591817i
$339$	1.60079	+	3.21096i	0.0869431	+	0.174395i
$340$		0			0
$341$	4.43029	−	7.67349i	0.239914	−	0.415543i
$342$	3.27481	−	26.6568i	0.177082	−	1.44144i
$343$	21.7279	−	12.5446i	1.17319	−	0.677344i
$344$	−0.0564271	−	0.320014i	−0.00304235	−	0.0172540i
$345$		0			0
$346$	−15.9181	+	5.79373i	−0.855765	+	0.311473i
$347$	29.4330	+	5.18983i	1.58004	+	0.278604i	0.893698	−	0.448670i	$-0.148102\pi$
$347$	29.4330	+	5.18983i	1.58004	+	0.278604i	0.686347	+	0.727274i	$0.259213\pi$
$348$	0.613764	+	0.829511i	0.0329012	+	0.0444665i
$349$	−0.356538	+	0.299171i	−0.0190850	+	0.0160142i	−0.652280	−	0.757978i	$-0.726187\pi$
$349$	−0.356538	+	0.299171i	−0.0190850	+	0.0160142i	0.633195	+	0.773992i	$0.281743\pi$
$350$		0			0
$351$	−2.75500	+	7.36639i	−0.147051	+	0.393189i
$352$			5.64120i			0.300677i
$353$	−1.05202	−	1.25375i	−0.0559934	−	0.0667304i	0.737321	−	0.675543i	$-0.236091\pi$
$353$	−1.05202	−	1.25375i	−0.0559934	−	0.0667304i	−0.793314	+	0.608812i	$0.791646\pi$
$354$	17.2087	+	7.48321i	0.914631	+	0.397728i
$355$		0			0
$356$	−2.60280	+	0.947342i	−0.137948	+	0.0502090i
$357$	8.49680	+	2.04019i	0.449699	+	0.107979i
$358$	−4.84974	+	0.855141i	−0.256317	+	0.0451956i
$359$	−9.42812	−	16.3300i	−0.497597	−	0.861863i	0.502399	−	0.864636i	$-0.332451\pi$
$359$	−9.42812	−	16.3300i	−0.497597	−	0.861863i	−0.999996	+	0.00277241i	$0.999118\pi$
$360$		0			0
$361$	−13.2811	+	23.0035i	−0.699005	+	1.21071i
$362$	−1.39439	+	3.83107i	−0.0732877	+	0.201356i
$363$	9.13414	+	6.04618i	0.479418	+	0.317342i
$364$	1.23872	+	1.03941i	0.0649266	+	0.0544799i
$365$		0			0
$366$	−15.6478	+	23.6395i	−0.817922	+	1.23566i
$367$	3.49800	−	9.61068i	0.182594	−	0.501673i	−0.814298	−	0.580446i	$-0.802878\pi$
$367$	3.49800	−	9.61068i	0.182594	−	0.501673i	0.996893	+	0.0787732i	$0.0251003\pi$
$368$	−23.9240	−	13.8125i	−1.24713	−	0.720029i
$369$	−1.34113	−	0.683450i	−0.0698164	−	0.0355790i
$370$		0			0
$371$	−3.05143	−	17.3055i	−0.158422	−	0.898458i
$372$	−0.863905	−	0.207435i	−0.0447914	−	0.0107550i
$373$	−2.37585	−	6.52759i	−0.123017	−	0.337986i	0.862864	−	0.505437i	$-0.168669\pi$
$373$	−2.37585	−	6.52759i	−0.123017	−	0.337986i	−0.985880	+	0.167451i	$0.946446\pi$
$374$	1.09075	−	6.18596i	0.0564014	−	0.319868i
$375$		0			0
$376$	17.2396	−	14.4658i	0.889065	−	0.746014i
$377$		−	3.74223i		−	0.192735i
$378$	−28.6199	−	10.7037i	−1.47205	−	0.550541i
$379$	−8.93586			−0.459004			−0.229502	−	0.973308i	$-0.573710\pi$
$379$	−8.93586			−0.459004			−0.229502	+	0.973308i	$0.573710\pi$
$380$		0			0
$381$	−21.1505	+	15.6495i	−1.08357	+	0.801747i
$382$	5.43428	+	0.958210i	0.278042	+	0.0490263i
$383$	7.08761	+	19.4731i	0.362160	+	0.995026i	0.978264	+	0.207362i	$0.0664878\pi$
$383$	7.08761	+	19.4731i	0.362160	+	0.995026i	−0.616104	+	0.787665i	$0.711290\pi$
$384$	−14.6999	+	4.35378i	−0.750150	+	0.222178i
$385$		0			0
$386$	2.61600	+	4.53104i	0.133151	+	0.230624i
$387$	−0.0399937	+	0.325547i	−0.00203300	+	0.0165485i
$388$	−1.63566	−	0.944347i	−0.0830379	−	0.0479419i
$389$	5.25158	+	1.91142i	0.266266	+	0.0969127i	0.471703	−	0.881758i	$-0.343639\pi$
$389$	5.25158	+	1.91142i	0.266266	+	0.0969127i	−0.205437	+	0.978670i	$0.565862\pi$
$390$		0			0
$391$	−6.95936	−	5.83960i	−0.351950	−	0.295321i
$392$	−24.1839	+	28.8212i	−1.22147	+	1.45569i
$393$	0.358624	−	5.86032i	0.0180902	−	0.295614i
$394$	−10.8605	−	3.95291i	−0.547146	−	0.199145i
$395$		0			0
$396$	0.879871	−	2.87726i	0.0442152	−	0.144588i
$397$	−11.7572	+	6.78805i	−0.590079	+	0.340682i	−0.765129	−	0.643877i	$-0.777325\pi$
$397$	−11.7572	+	6.78805i	−0.590079	+	0.340682i	0.175050	+	0.984560i	$0.443991\pi$
$398$	17.5132	−	3.08804i	0.877856	−	0.154790i
$399$	37.6000	+	35.6834i	1.88236	+	1.78641i
$400$		0			0
$401$	−3.34334	+	18.9610i	−0.166958	+	0.946868i	0.780064	+	0.625700i	$0.215187\pi$
$401$	−3.34334	+	18.9610i	−0.166958	+	0.946868i	−0.947022	+	0.321168i	$0.895925\pi$
$402$	−6.70907	+	0.764180i	−0.334618	+	0.0381138i
$403$	2.07111	+	2.46826i	0.103169	+	0.122953i
$404$	−2.56640			−0.127683
$405$		0			0
$406$	14.5393			0.721575
$407$	−26.7526	−	31.8826i	−1.32608	−	1.58036i
$408$	−5.82001	+	0.662914i	−0.288133	+	0.0328191i
$409$	−1.49345	+	8.46979i	−0.0738464	+	0.418804i	0.925364	+	0.379079i	$0.123759\pi$
$409$	−1.49345	+	8.46979i	−0.0738464	+	0.418804i	−0.999211	+	0.0397248i	$0.987352\pi$
$410$		0			0
$411$	23.2752	+	22.0888i	1.14808	+	1.08956i
$412$	−1.97807	+	0.348787i	−0.0974524	+	0.0171835i
$413$	−31.3664	+	18.1094i	−1.54344	+	0.891104i
$414$	21.6639	+	23.2348i	1.06472	+	1.14193i
$415$		0			0
$416$	−1.92766	−	0.701612i	−0.0945114	−	0.0343994i
$417$	−1.75831	+	28.7327i	−0.0861046	+	1.40705i
$418$	23.9516	−	28.5444i	1.17151	−	1.39615i
$419$	−22.8459	−	19.1700i	−1.11609	−	0.936515i	−0.117694	−	0.993050i	$-0.537550\pi$
$419$	−22.8459	−	19.1700i	−1.11609	−	0.936515i	−0.998401	+	0.0565354i	$0.981995\pi$
$420$		0			0
$421$	3.86135	+	1.40541i	0.188190	+	0.0684957i	0.434396	−	0.900722i	$-0.356962\pi$
$421$	3.86135	+	1.40541i	0.188190	+	0.0684957i	−0.246206	+	0.969218i	$0.579184\pi$
$422$	−4.22871	−	2.44145i	−0.205850	−	0.118848i
$423$	−20.9103	+	8.87430i	−1.01670	+	0.431483i
$424$	5.88978	+	10.2014i	0.286033	+	0.495423i
$425$		0			0
$426$	16.6906	−	4.94339i	0.808662	−	0.239508i
$427$	−18.7142	−	51.4168i	−0.905643	−	2.48823i
$428$	−2.89057	−	0.509685i	−0.139721	−	0.0246366i
$429$	−8.77159	+	6.49019i	−0.423496	+	0.313349i
$430$		0			0
$431$	38.4602			1.85256			0.926281	−	0.376833i	$-0.122987\pi$
$431$	38.4602			1.85256			0.926281	+	0.376833i	$0.122987\pi$
$432$	17.9781	+	0.158650i	0.864972	+	0.00763305i
$433$			13.0726i			0.628230i	0.949385	+	0.314115i	$0.101708\pi$
$433$			13.0726i			0.628230i	−0.949385	+	0.314115i	$0.898292\pi$
$434$	−9.58967	+	8.04669i	−0.460319	+	0.386253i
$435$		0			0
$436$	0.0112424	−	0.0637590i	0.000538415	−	0.00305350i
$437$	−18.4323	−	50.6423i	−0.881735	−	2.42255i
$438$	22.9070	+	5.50027i	1.09454	+	0.262813i
$439$	−1.34135	−	7.60717i	−0.0640191	−	0.363071i	−0.999941	−	0.0108629i	$-0.996542\pi$
$439$	−1.34135	−	7.60717i	−0.0640191	−	0.363071i	0.935922	−	0.352208i	$-0.114569\pi$
$440$		0			0
$441$	31.8506	−	20.6811i	1.51669	−	0.984812i
$442$	1.97815	+	1.14209i	0.0940912	+	0.0543236i
$443$	−7.44827	+	20.4640i	−0.353878	+	0.972272i	0.627234	+	0.778831i	$0.284187\pi$
$443$	−7.44827	+	20.4640i	−0.353878	+	0.972272i	−0.981112	+	0.193441i	$0.938035\pi$
$444$	−2.30349	+	3.47994i	−0.109319	+	0.165151i
$445$		0			0
$446$	−10.6983	−	8.97692i	−0.506578	−	0.425069i
$447$	12.3046	+	8.14481i	0.581988	+	0.385236i
$448$	13.2198	−	36.3211i	0.624577	−	1.71601i
$449$	15.4280	−	26.7221i	0.728093	−	1.26109i	−0.229595	−	0.973286i	$-0.573740\pi$
$449$	15.4280	−	26.7221i	0.728093	−	1.26109i	0.957688	−	0.287808i	$-0.0929267\pi$
$450$		0			0
$451$	−1.04419	−	1.80859i	−0.0491691	−	0.0851634i
$452$	0.491552	−	0.0866738i	0.0231206	−	0.00407679i
$453$	20.3336	+	4.88238i	0.955358	+	0.229394i
$454$	−33.0319	+	12.0226i	−1.55026	+	0.564250i
$455$		0			0
$456$	−31.8659	−	13.8569i	−1.49226	−	0.648910i
$457$	20.8765	+	24.8797i	0.976564	+	1.16382i	0.986482	+	0.163872i	$0.0523986\pi$
$457$	20.8765	+	24.8797i	0.976564	+	1.16382i	−0.00991784	+	0.999951i	$0.503157\pi$
$458$		−	14.6355i		−	0.683870i
$459$	5.81340	+	1.07804i	0.271346	+	0.0503185i
$460$		0			0
$461$	19.5612	−	16.4138i	0.911056	−	0.764467i	−0.0612635	−	0.998122i	$-0.519513\pi$
$461$	19.5612	−	16.4138i	0.911056	−	0.764467i	0.972320	+	0.233655i	$0.0750685\pi$
$462$	−25.2157	−	34.0794i	−1.17314	−	1.58552i
$463$	9.28198	+	1.63666i	0.431370	+	0.0760622i	0.385117	−	0.922868i	$-0.374161\pi$
$463$	9.28198	+	1.63666i	0.431370	+	0.0760622i	0.0462526	+	0.998930i	$0.485272\pi$
$464$	−8.03886	+	2.92591i	−0.373195	+	0.135832i
$465$		0			0
$466$	−3.08692	−	17.5068i	−0.142999	−	0.810986i
$467$	−33.4955	+	19.3386i	−1.54999	+	0.894885i	−0.551845	+	0.833947i	$0.686076\pi$
$467$	−33.4955	+	19.3386i	−1.54999	+	0.894885i	−0.998142	+	0.0609381i	$0.980591\pi$
$468$	0.873759	+	0.658514i	0.0403895	+	0.0304398i
$469$	6.51642	−	11.2868i	0.300900	−	0.521175i
$470$		0			0
$471$	10.0738	+	20.2065i	0.464176	+	0.931068i
$472$	15.6062	−	18.5987i	0.718332	−	0.856075i
$473$	−0.292510	+	0.348600i	−0.0134496	+	0.0160286i
$474$	11.2061	+	0.685761i	0.514713	+	0.0314981i
$475$		0			0
$476$	0.607826	−	1.05279i	0.0278596	−	0.0482543i
$477$	−2.67389	−	11.5853i	−0.122429	−	0.530456i
$478$	−10.1057	+	5.83451i	−0.462223	+	0.266864i
$479$	−6.46290	−	36.6529i	−0.295297	−	1.67471i	−0.665992	−	0.745959i	$-0.731991\pi$
$479$	−6.46290	−	36.6529i	−0.295297	−	1.67471i	0.370695	−	0.928755i	$-0.379120\pi$
$480$		0			0
$481$	14.2219	−	5.17636i	0.648464	−	0.236022i
$482$	19.1446	+	3.37571i	0.872014	+	0.153760i
$483$	−60.9204	+	6.93900i	−2.77198	+	0.315735i
$484$	1.16736	−	0.979534i	0.0530620	−	0.0445243i
$485$		0			0
$486$	−19.7169	−	6.22024i	−0.894376	−	0.282156i
$487$			38.1901i			1.73056i	0.501290	+	0.865279i	$0.332859\pi$
$487$			38.1901i			1.73056i	−0.501290	+	0.865279i	$0.667141\pi$
$488$	23.5767	+	28.0976i	1.06727	+	1.27192i
$489$	2.98321	+	26.1909i	0.134905	+	1.18439i
$490$		0			0
$491$	−0.225443	+	0.0820546i	−0.0101741	+	0.00370307i	−0.347102	−	0.937827i	$-0.612834\pi$
$491$	−0.225443	+	0.0820546i	−0.0101741	+	0.00370307i	0.336928	+	0.941530i	$0.390612\pi$
$492$	−0.144149	+	0.151892i	−0.00649876	+	0.00684782i
$493$	−2.77059	+	0.488529i	−0.124781	+	0.0220023i
$494$	6.77503	+	11.7347i	0.304823	+	0.527969i
$495$		0			0
$496$	3.68285	−	6.37888i	0.165365	−	0.286420i
$497$	−11.4911	+	31.5714i	−0.515445	+	1.41617i
$498$	0.510835	−	8.34761i	0.0228911	−	0.374065i
$499$	15.4596	+	12.9721i	0.692067	+	0.580713i	0.919504	−	0.393080i	$-0.128590\pi$
$499$	15.4596	+	12.9721i	0.692067	+	0.580713i	−0.227438	+	0.973793i	$0.573035\pi$
$500$		0			0
$501$	12.3056	+	24.6832i	0.549774	+	1.10277i
$502$	−1.73426	+	4.76484i	−0.0774037	+	0.212665i
$503$	18.7357	+	10.8170i	0.835382	+	0.482308i	0.855692	−	0.517486i	$-0.173132\pi$
$503$	18.7357	+	10.8170i	0.835382	+	0.482308i	−0.0203102	+	0.999794i	$0.506465\pi$
$504$	−23.7941	+	31.5716i	−1.05988	+	1.40631i
$505$		0			0
$506$	7.65351	+	43.4052i	0.340240	+	1.92960i
$507$	5.26755	+	17.7851i	0.233940	+	0.789863i
$508$	1.25189	+	3.43953i	0.0555434	+	0.152604i
$509$	3.61621	−	20.5086i	0.160286	−	0.909026i	−0.793507	−	0.608561i	$-0.791747\pi$
$509$	3.61621	−	20.5086i	0.160286	−	0.909026i	0.953793	−	0.300465i	$-0.0971418\pi$
$510$		0			0
$511$	−34.8315	+	29.2271i	−1.54085	+	1.29293i
$512$			25.2569i			1.11621i
$513$	26.6682	+	22.7813i	1.17743	+	1.00582i
$514$	10.8285			0.477623
$515$		0			0
$516$	0.0418447	+	0.0181962i	0.00184211	+	0.000801043i
$517$	−31.0371	−	5.47267i	−1.36501	−	0.240688i
$518$	20.1112	+	55.2551i	0.883635	+	2.42777i
$519$	5.16504	−	21.5108i	0.226720	−	0.944221i
$520$		0			0
$521$	4.03581	+	6.99023i	0.176812	+	0.306247i	0.940787	−	0.338999i	$-0.110088\pi$
$521$	4.03581	+	6.99023i	0.176812	+	0.306247i	−0.763975	+	0.645246i	$0.776755\pi$
$522$	9.82416	−	0.514220i	0.429992	−	0.0225068i
$523$	−17.8186	−	10.2876i	−0.779154	−	0.449845i	0.0569761	−	0.998376i	$-0.481854\pi$
$523$	−17.8186	−	10.2876i	−0.779154	−	0.449845i	−0.836131	+	0.548531i	$0.815187\pi$
$524$	−0.767539	−	0.279361i	−0.0335301	−	0.0122040i
$525$		0			0
$526$	−28.3133	−	23.7577i	−1.23452	−	1.03588i
$527$	1.55702	−	1.85558i	0.0678247	−	0.0808303i
$528$	20.8000	+	13.7682i	0.905205	+	0.599185i
$529$	38.2883	+	13.9358i	1.66471	+	0.605904i
$530$		0			0
$531$	−20.5536	+	13.3458i	−0.891951	+	0.579157i
$532$	6.24528	−	3.60571i	0.270767	−	0.156327i
$533$	0.747886	−	0.131872i	0.0323945	−	0.00571203i
$534$	−6.16532	+	25.6767i	−0.266799	+	1.11114i
$535$		0			0
$536$	−1.51707	+	8.60371i	−0.0655273	+	0.371624i
$537$	2.56461	−	5.89768i	0.110671	−	0.254504i
$538$	−11.2124	−	13.3624i	−0.483400	−	0.576094i
$539$	52.6882			2.26944
$540$		0			0
$541$	−36.3288			−1.56190			−0.780949	−	0.624595i	$-0.785264\pi$
$541$	−36.3288			−1.56190			−0.780949	+	0.624595i	$0.785264\pi$
$542$	−6.98782	−	8.32776i	−0.300152	−	0.357708i
$543$	−3.16683	−	4.28002i	−0.135902	−	0.183673i
$544$	−0.267797	+	1.51875i	−0.0114817	+	0.0651159i
$545$		0			0
$546$	14.7815	−	4.37794i	0.632588	−	0.187359i
$547$	−12.7434	+	2.24700i	−0.544868	+	0.0960749i	−0.439306	−	0.898338i	$-0.644775\pi$
$547$	−12.7434	+	2.24700i	−0.544868	+	0.0960749i	−0.105563	+	0.994413i	$0.533664\pi$
$548$	3.86596	−	2.23201i	0.165145	−	0.0953468i
$549$	−14.4636	−	34.0802i	−0.617290	−	1.45451i
$550$		0			0
$551$	−15.6826	−	5.70800i	−0.668101	−	0.243169i
$552$	36.7837	−	18.3382i	1.56562	−	0.780525i
$553$	−13.9287	+	16.5996i	−0.592310	+	0.705887i
$554$	29.6082	+	24.8442i	1.25793	+	1.05553i
$555$		0			0
$556$	3.76318	+	1.36969i	0.159594	+	0.0580876i
$557$	14.3505	+	8.28524i	0.608049	+	0.351057i	0.772201	−	0.635378i	$-0.219156\pi$
$557$	14.3505	+	8.28524i	0.608049	+	0.351057i	−0.164153	+	0.986435i	$0.552489\pi$
$558$	−6.19510	+	5.77627i	−0.262260	+	0.244529i
$559$	−0.0827402	−	0.143310i	−0.00349954	−	0.00606138i
$560$		0			0
$561$	5.95014	+	5.64684i	0.251215	+	0.238410i
$562$	10.7066	+	29.4162i	0.451631	+	1.24085i
$563$	−9.99530	−	1.76244i	−0.421252	−	0.0742781i	−0.0409958	−	0.999159i	$-0.513053\pi$
$563$	−9.99530	−	1.76244i	−0.421252	−	0.0742781i	−0.380256	+	0.924881i	$0.624164\pi$
$564$	0.357634	+	3.13983i	0.0150591	+	0.132211i
$565$		0			0
$566$	−26.1024			−1.09716
$567$	32.2863	−	23.4509i	1.35590	−	0.984846i
$568$		−	22.5218i		−	0.944996i
$569$	−21.4282	+	17.9804i	−0.898317	+	0.753777i	−0.969861	−	0.243660i	$-0.921652\pi$
$569$	−21.4282	+	17.9804i	−0.898317	+	0.753777i	0.0715441	+	0.997437i	$0.477207\pi$
$570$		0			0
$571$	−3.43834	+	19.4998i	−0.143890	+	0.816041i	0.824362	+	0.566064i	$0.191534\pi$
$571$	−3.43834	+	19.4998i	−0.143890	+	0.816041i	−0.968252	+	0.249978i	$0.919577\pi$
$572$	0.519185	+	1.42645i	0.0217082	+	0.0596428i
$573$	−4.96067	+	5.22711i	−0.207235	+	0.218366i
$574$	0.512351	+	2.90569i	0.0213851	+	0.121281i
$575$		0			0
$576$	7.64797	−	25.0095i	0.318665	−	1.04206i
$577$	−2.70975	−	1.56447i	−0.112808	−	0.0651299i	0.442534	−	0.896752i	$-0.354080\pi$
$577$	−2.70975	−	1.56447i	−0.112808	−	0.0651299i	−0.555343	+	0.831622i	$0.687413\pi$
$578$	−7.12418	+	19.5735i	−0.296327	+	0.814151i
$579$	−6.81990	−	0.417346i	−0.283426	−	0.0173443i
$580$		0			0
$581$	12.3653	+	10.3757i	0.513000	+	0.430458i
$582$	−16.1145	+	8.03372i	−0.667966	+	0.333009i
$583$	5.64204	−	15.5014i	0.233669	−	0.642001i
$584$	15.2399	−	26.3964i	0.630633	−	1.09229i
$585$		0			0
$586$	4.09344	+	7.09004i	0.169098	+	0.292887i
$587$	43.3925	−	7.65127i	1.79100	−	0.315802i	0.823244	−	0.567688i	$-0.192162\pi$
$587$	43.3925	−	7.65127i	1.79100	−	0.315802i	0.967757	+	0.251887i	$0.0810510\pi$
$588$	−1.50032	−	5.06559i	−0.0618720	−	0.208902i
$589$	13.5028	−	4.91461i	0.556372	−	0.202503i
$590$		0			0
$591$	12.1333	−	8.97752i	0.499095	−	0.369286i
$592$	−22.2391	−	26.5036i	−0.914023	−	1.08929i
$593$			10.1063i			0.415015i	0.978233	+	0.207507i	$0.0665351\pi$
$593$			10.1063i			0.415015i	−0.978233	+	0.207507i	$0.933465\pi$
$594$	−18.2434	−	22.1354i	−0.748537	−	0.908228i
$595$		0			0
$596$	1.57256	−	1.31953i	0.0644144	−	0.0540501i
$597$	−9.26122	+	21.2974i	−0.379036	+	0.871647i
$598$	−15.7839	−	2.78313i	−0.645453	−	0.113811i
$599$	−1.62169	+	0.590247i	−0.0662605	+	0.0241169i	−0.374938	−	0.927050i	$-0.622336\pi$
$599$	−1.62169	+	0.590247i	−0.0662605	+	0.0241169i	0.308677	+	0.951167i	$0.400114\pi$
$600$		0			0
$601$	3.60539	+	20.4472i	0.147067	+	0.834058i	0.965684	+	0.259719i	$0.0836299\pi$
$601$	3.60539	+	20.4472i	0.147067	+	0.834058i	−0.818617	+	0.574339i	$0.805259\pi$
$602$	0.556789	−	0.321462i	0.0226930	−	0.0131018i
$603$	4.00393	−	7.85688i	0.163053	−	0.319957i
$604$	1.45458	−	2.51941i	0.0591862	−	0.102513i
$605$		0			0
$606$	−13.5049	+	20.4022i	−0.548598	+	0.828783i
$607$	−1.30168	+	1.55129i	−0.0528337	+	0.0629648i	−0.791814	−	0.610762i	$-0.790863\pi$
$607$	−1.30168	+	1.55129i	−0.0528337	+	0.0629648i	0.738980	+	0.673727i	$0.235308\pi$
$608$	−5.88050	+	7.00810i	−0.238486	+	0.284216i
$609$	−10.4804	+	15.8330i	−0.424687	+	0.641587i
$610$		0			0
$611$	5.73024	−	9.92506i	0.231821	−	0.401525i
$612$	0.373470	−	0.732859i	0.0150966	−	0.0296241i
$613$	−26.8891	+	15.5244i	−1.08604	+	0.627027i	−0.932520	−	0.361119i	$-0.882395\pi$
$613$	−26.8891	+	15.5244i	−1.08604	+	0.627027i	−0.153522	+	0.988145i	$0.549062\pi$
$614$	2.75064	+	15.5997i	0.111007	+	0.629551i
$615$		0			0
$616$	−51.5420	+	18.7598i	−2.07669	+	0.755852i
$617$	−8.34783	−	1.47195i	−0.336071	−	0.0592584i	0.00306626	−	0.999995i	$-0.499024\pi$
$617$	−8.34783	−	1.47195i	−0.336071	−	0.0592584i	−0.339137	+	0.940737i	$0.610135\pi$
$618$	−7.63621	+	17.5605i	−0.307174	+	0.706388i
$619$	32.3309	−	27.1288i	1.29949	−	1.09040i	0.309255	−	0.950979i	$-0.399920\pi$
$619$	32.3309	−	27.1288i	1.29949	−	1.09040i	0.990233	−	0.139421i	$-0.0445241\pi$
$620$		0			0
$621$	−40.9182	+	6.84325i	−1.64199	+	0.274610i
$622$		−	33.2027i		−	1.33131i
$623$	−32.7610	−	39.0430i	−1.31254	−	1.56422i
$624$	−7.29171	+	5.39522i	−0.291902	+	0.215982i
$625$		0			0
$626$	−19.1172	+	6.95808i	−0.764076	+	0.278101i
$627$	13.8192	+	46.6586i	0.551887	+	1.86336i
$628$	3.09333	−	0.545438i	0.123437	−	0.0217654i
$629$	−5.68895	−	9.85355i	−0.226833	−	0.392887i
$630$		0			0
$631$	14.3615	−	24.8748i	0.571721	−	0.990250i	−0.424668	−	0.905349i	$-0.639609\pi$
$631$	14.3615	−	24.8748i	0.571721	−	0.990250i	0.996389	−	0.0849008i	$-0.0270573\pi$
$632$	4.96811	−	13.6498i	0.197621	−	0.542959i
$633$	5.70687	−	2.84511i	0.226828	−	0.113083i
$634$	0.250291	+	0.210019i	0.00994034	+	0.00834094i
$635$		0			0
$636$	−1.65100	−	0.101034i	−0.0654666	−	0.00400625i
$637$	−6.55298	+	18.0042i	−0.259638	+	0.713351i
$638$	11.8202	+	6.82442i	0.467968	+	0.270181i
$639$	−6.64785	+	21.7391i	−0.262985	+	0.859985i
$640$		0			0
$641$	−3.15096	−	17.8700i	−0.124456	−	0.705822i	−0.981630	−	0.190796i	$-0.938893\pi$
$641$	−3.15096	−	17.8700i	−0.124456	−	0.705822i	0.857174	−	0.515026i	$-0.172218\pi$
$642$	−19.2626	+	20.2972i	−0.760235	+	0.801069i
$643$	5.45343	+	14.9832i	0.215062	+	0.590879i	0.999573	−	0.0292372i	$-0.00930781\pi$
$643$	5.45343	+	14.9832i	0.215062	+	0.590879i	−0.784510	+	0.620116i	$0.787086\pi$
$644$	−1.48120	+	8.40031i	−0.0583675	+	0.331018i
$645$		0			0
$646$	7.80341	−	6.54784i	0.307021	−	0.257621i
$647$			13.7644i			0.541133i	0.962701	+	0.270567i	$0.0872110\pi$
$647$			13.7644i			0.541133i	−0.962701	+	0.270567i	$0.912789\pi$
$648$	−14.9610	+	22.1743i	−0.587723	+	0.871090i
$649$	−34.0004			−1.33463
$650$		0			0
$651$	−1.85015	−	16.2433i	−0.0725131	−	0.636624i
$652$	3.61146	+	0.636797i	0.141436	+	0.0249389i
$653$	−5.80905	−	15.9602i	−0.227326	−	0.624573i	0.772621	−	0.634867i	$-0.218945\pi$
$653$	−5.80905	−	15.9602i	−0.227326	−	0.624573i	−0.999947	+	0.0102948i	$0.996723\pi$
$654$	−0.447708	−	0.424887i	−0.0175068	−	0.0166144i
$655$		0			0
$656$	−0.868024	−	1.50346i	−0.0338907	−	0.0587003i
$657$	−22.5018	+	20.9805i	−0.877877	+	0.818527i
$658$	38.5609	+	22.2631i	1.50326	+	0.867907i
$659$	−10.6118	−	3.86239i	−0.413378	−	0.150457i	0.126955	−	0.991908i	$-0.459480\pi$
$659$	−10.6118	−	3.86239i	−0.413378	−	0.150457i	−0.540333	+	0.841451i	$0.681702\pi$
$660$		0			0
$661$	−2.63000	−	2.20683i	−0.102295	−	0.0858358i	0.590206	−	0.807253i	$-0.299047\pi$
$661$	−2.63000	−	2.20683i	−0.102295	−	0.0858358i	−0.692501	+	0.721417i	$0.743491\pi$
$662$	−21.2662	+	25.3441i	−0.826535	+	0.985027i
$663$	−2.66962	+	1.33092i	−0.103680	+	0.0516885i
$664$	−10.1679	−	3.70083i	−0.394592	−	0.143620i
$665$		0			0
$666$	15.5433	+	36.6243i	0.602289	+	1.41916i
$667$	17.0957	−	9.87018i	0.661946	−	0.382175i
$668$	3.77865	−	0.666279i	0.146201	−	0.0257791i
$669$	17.4873	−	5.17936i	0.676099	−	0.200246i
$670$		0			0
$671$	8.91950	−	50.5850i	0.344334	−	1.95281i
$672$	6.19084	+	8.36702i	0.238817	+	0.322765i
$673$	16.8397	+	20.0688i	0.649123	+	0.773595i	0.985782	−	0.168032i	$-0.0537412\pi$
$673$	16.8397	+	20.0688i	0.649123	+	0.773595i	−0.336658	+	0.941627i	$0.609297\pi$
$674$	−39.3071			−1.51405
$675$		0			0
$676$	2.58045			0.0992482
$677$	12.1532	+	14.4837i	0.467087	+	0.556653i	0.947237	−	0.320534i	$-0.103862\pi$
$677$	12.1532	+	14.4837i	0.467087	+	0.556653i	−0.480150	+	0.877186i	$0.659418\pi$
$678$	1.89761	−	4.36381i	0.0728772	−	0.167591i
$679$	6.03484	−	34.2253i	0.231596	−	1.31345i
$680$		0			0
$681$	10.7180	−	44.6373i	0.410715	−	1.71051i
$682$	−11.5732	+	2.04066i	−0.443159	+	0.0781409i
$683$	21.1745	−	12.2251i	0.810222	−	0.467782i	−0.0368112	−	0.999322i	$-0.511720\pi$
$683$	21.1745	−	12.2251i	0.810222	−	0.467782i	0.847033	+	0.531541i	$0.178387\pi$
$684$	4.09238	−	2.65724i	0.156476	−	0.101602i
$685$		0			0
$686$	−31.2687	−	11.3809i	−1.19385	−	0.434524i
$687$	15.9377	+	10.5497i	0.608062	+	0.402496i
$688$	−0.243160	+	0.289787i	−0.00927039	+	0.0110480i
$689$	4.59528	+	3.85590i	0.175066	+	0.146898i
$690$		0			0
$691$	17.7400	+	6.45685i	0.674863	+	0.245630i	0.656640	−	0.754204i	$-0.271977\pi$
$691$	17.7400	+	6.45685i	0.674863	+	0.245630i	0.0182226	+	0.999834i	$0.494199\pi$
$692$	−2.66527	−	1.53880i	−0.101318	−	0.0584962i
$693$	55.2880	−	2.89391i	2.10022	−	0.109931i
$694$	−19.8194	−	34.3282i	−0.752334	−	1.30308i
$695$		0			0
$696$	2.97171	−	12.3763i	0.112642	−	0.469122i
$697$	−0.195265	−	0.536487i	−0.00739620	−	0.0203209i
$698$	0.607913	+	0.107191i	0.0230098	+	0.00405725i
$699$	21.2897	+	9.25785i	0.805250	+	0.350164i
$700$		0			0
$701$	−21.8730			−0.826131			−0.413066	−	0.910701i	$-0.635542\pi$
$701$	−21.8730			−0.826131			−0.413066	+	0.910701i	$0.635542\pi$
$702$	9.83292	−	3.48094i	0.371120	−	0.131380i
$703$		−	67.4954i		−	2.54564i
$704$	27.7957	−	23.3234i	1.04759	−	0.879034i
$705$		0			0
$706$	−0.376934	+	2.13770i	−0.0141861	+	0.0804533i
$707$	−16.1514	−	44.3755i	−0.607435	−	1.66891i
$708$	0.968175	+	3.26890i	0.0363863	+	0.122853i
$709$	5.59910	+	31.7541i	0.210279	+	1.19255i	0.888914	+	0.458074i	$0.151461\pi$
$709$	5.59910	+	31.7541i	0.210279	+	1.19255i	−0.678636	+	0.734475i	$0.737428\pi$
$710$		0			0
$711$	−8.82449	+	11.7089i	−0.330944	+	0.439118i
$712$	29.5880	+	17.0826i	1.10886	+	0.640198i
$713$	−5.81315	+	15.9715i	−0.217704	+	0.598138i
$714$	−5.17088	−	10.3720i	−0.193515	−	0.388163i
$715$		0			0
$716$	−0.685371	−	0.575094i	−0.0256135	−	0.0214923i
$717$	0.930816	−	15.2106i	0.0347620	−	0.568049i
$718$	−8.55352	+	23.5006i	−0.319214	+	0.877035i
$719$	−21.9733	+	38.0589i	−0.819467	+	1.41936i	0.0866093	+	0.996242i	$0.472397\pi$
$719$	−21.9733	+	38.0589i	−0.819467	+	1.41936i	−0.906076	+	0.423115i	$0.860937\pi$
$720$		0			0
$721$	−18.4796	−	32.0077i	−0.688218	−	1.19203i
$722$	34.6939	−	6.11747i	1.29117	−	0.227669i
$723$	−17.4761	+	18.4148i	−0.649944	+	0.684854i
$724$	−0.696024	+	0.253332i	−0.0258675	+	0.00941501i
$725$		0			0
$726$	−1.64416	−	14.4347i	−0.0610203	−	0.535724i
$727$	5.71575	+	6.81176i	0.211985	+	0.252634i	0.861551	−	0.507671i	$-0.169494\pi$
$727$	5.71575	+	6.81176i	0.211985	+	0.252634i	−0.649565	+	0.760306i	$0.725049\pi$
$728$		−	19.9457i		−	0.739237i
$729$	20.9863	−	16.9875i	0.777269	−	0.629168i
$730$		0			0
$731$	−0.0952994	+	0.0799657i	−0.00352478	+	0.00295764i
$732$	−5.11737	+	0.582882i	−0.189143	+	0.0215439i
$733$	1.67268	+	0.294938i	0.0617818	+	0.0108938i	0.204454	−	0.978876i	$-0.434458\pi$
$733$	1.67268	+	0.294938i	0.0617818	+	0.0108938i	−0.142672	+	0.989770i	$0.545569\pi$
$734$	−12.7465	+	4.63936i	−0.470483	+	0.171242i
$735$		0			0
$736$	−1.87906	−	10.6567i	−0.0692629	−	0.392809i
$737$	10.5955	−	6.11730i	0.390289	−	0.225334i
$738$	0.448960	+	1.94524i	0.0165265	+	0.0716052i
$739$	20.4924	−	35.4939i	0.753826	−	1.30566i	−0.192130	−	0.981369i	$-0.561540\pi$
$739$	20.4924	−	35.4939i	0.753826	−	1.30566i	0.945956	−	0.324295i	$-0.105127\pi$
$740$		0			0
$741$	−17.6625	−	1.08086i	−0.648848	−	0.0397065i
$742$	−14.9809	+	17.8536i	−0.549967	+	0.655426i
$743$	34.2019	−	40.7602i	1.25475	−	1.49535i	0.460614	−	0.887600i	$-0.347629\pi$
$743$	34.2019	−	40.7602i	1.25475	−	1.49535i	0.794131	−	0.607747i	$-0.207926\pi$
$744$	4.88953	+	9.80767i	0.179259	+	0.359567i
$745$		0			0
$746$	−4.60655	+	7.97877i	−0.168658	+	0.292124i
$747$	8.72215	+	6.57351i	0.319127	+	0.240512i
$748$	0.988304	−	0.570598i	0.0361360	−	0.0208631i
$749$	−9.37857	−	53.1885i	−0.342685	−	1.94347i
$750$		0			0
$751$	15.4986	−	5.64104i	0.565554	−	0.205845i	−0.0433900	−	0.999058i	$-0.513816\pi$
$751$	15.4986	−	5.64104i	0.565554	−	0.205845i	0.608944	+	0.793214i	$0.291594\pi$
$752$	−25.8007	−	4.54937i	−0.940856	−	0.165898i
$753$	−3.93870	−	5.32321i	−0.143534	−	0.193989i
$754$	−3.80210	+	3.19034i	−0.138464	+	0.116185i
$755$		0			0
$756$	−1.85258	−	5.23314i	−0.0673775	−	0.190327i
$757$			5.75782i			0.209271i	0.994511	+	0.104636i	$0.0333677\pi$
$757$			5.75782i			0.209271i	−0.994511	+	0.104636i	$0.966632\pi$
$758$	7.61802	+	9.07880i	0.276699	+	0.329757i
$759$	−52.7843	−	22.9533i	−1.91595	−	0.833152i
$760$		0			0
$761$	−35.1758	+	12.8029i	−1.27512	+	0.464106i	−0.888816	−	0.458265i	$-0.848471\pi$
$761$	−35.1758	+	12.8029i	−1.27512	+	0.464106i	−0.386305	+	0.922371i	$0.626249\pi$
$762$	33.9311	+	8.14730i	1.22919	+	0.295145i
$763$	1.17321	−	0.206869i	0.0424730	−	0.00748914i
$764$	0.501262	+	0.868212i	0.0181350	+	0.0314108i
$765$		0			0
$766$	13.7422	−	23.8022i	0.496526	−	0.860008i
$767$	4.22873	−	11.6183i	0.152690	−	0.419514i
$768$	−8.22630	−	5.44525i	−0.296841	−	0.196489i
$769$	−13.8998	−	11.6633i	−0.501239	−	0.420589i	0.356795	−	0.934183i	$-0.383870\pi$
$769$	−13.8998	−	11.6633i	−0.501239	−	0.420589i	−0.858034	+	0.513593i	$0.828314\pi$
$770$		0			0
$771$	−7.80549	+	11.7920i	−0.281108	+	0.424678i
$772$	−0.325105	+	0.893218i	−0.0117008	+	0.0321476i
$773$	−19.1897	−	11.0792i	−0.690206	−	0.398490i	0.113483	−	0.993540i	$-0.463799\pi$
$773$	−19.1897	−	11.0792i	−0.690206	−	0.398490i	−0.803689	+	0.595049i	$0.797132\pi$
$774$	0.364850	−	0.236903i	0.0131143	−	0.00851530i
$775$		0			0
$776$	4.04540	+	22.9426i	0.145221	+	0.823591i
$777$	−74.6684	−	17.9289i	−2.67871	−	0.643195i
$778$	−2.53509	−	6.96511i	−0.0908874	−	0.249711i
$779$	0.588106	−	3.33531i	0.0210711	−	0.119500i
$780$		0			0
$781$	−24.1609	+	20.2734i	−0.864546	+	0.725440i
$782$			12.0491i			0.430874i
$783$	−6.52158	+	11.0690i	−0.233062	+	0.395573i
$784$	43.7991			1.56425
$785$		0			0
$786$	−6.25980	+	4.63169i	−0.223280	+	0.165207i
$787$	11.4591	+	2.02055i	0.408473	+	0.0720248i	0.374109	−	0.927385i	$-0.377949\pi$
$787$	11.4591	+	2.02055i	0.408473	+	0.0720248i	0.0343635	+	0.999409i	$0.489060\pi$
$788$	−0.718160	−	1.97313i	−0.0255834	−	0.0702898i
$789$	46.2807	−	13.7073i	1.64764	−	0.487994i
$790$		0			0
$791$	4.59221	+	7.95394i	0.163280	+	0.282810i
$792$	−34.1632	+	14.4988i	−1.21394	+	0.515192i
$793$	16.1761	+	9.33929i	0.574431	+	0.331648i
$794$	16.9199	+	6.15835i	0.600466	+	0.218552i
$795$		0			0
$796$	2.47498	+	2.07675i	0.0877233	+	0.0736086i
$797$	−34.9669	+	41.6719i	−1.23859	+	1.47610i	−0.414090	+	0.910236i	$0.635900\pi$
$797$	−34.9669	+	41.6719i	−1.23859	+	1.47610i	−0.824501	+	0.565860i	$0.808544\pi$
$798$	4.19937	−	68.6224i	0.148656	−	2.42921i
$799$	−8.09614	−	2.94675i	−0.286421	−	0.104249i
$800$		0			0
$801$	−23.5173	−	25.2225i	−0.830942	−	0.891192i
$802$	22.1146	−	12.7679i	0.780893	−	0.450849i
$803$	−42.0359	+	7.41206i	−1.48341	+	0.261566i
$804$	−0.889845	−	0.844486i	−0.0313824	−	0.0297827i
$805$		0			0
$806$	0.742069	−	4.20848i	0.0261383	−	0.148238i
$807$	22.6336	−	2.57803i	0.796741	−	0.0907509i
$808$	20.3480	+	24.2497i	0.715838	+	0.853103i
$809$	9.51410			0.334498			0.167249	−	0.985915i	$-0.446512\pi$
$809$	9.51410			0.334498			0.167249	+	0.985915i	$0.446512\pi$
$810$		0			0
$811$	−16.3207			−0.573098			−0.286549	−	0.958066i	$-0.592508\pi$
$811$	−16.3207			−0.573098			−0.286549	+	0.958066i	$0.592508\pi$
$812$	1.69792	+	2.02350i	0.0595852	+	0.0710109i
$813$	14.1058	−	1.60669i	0.494712	−	0.0563490i
$814$	−9.58534	+	54.3611i	−0.335966	+	1.90536i
$815$		0			0
$816$	4.94628	+	4.69415i	0.173154	+	0.164328i
$817$	−0.726774	+	0.128150i	−0.0254266	+	0.00448340i
$818$	9.87847	−	5.70334i	0.345393	−	0.199413i
$819$	−5.88744	+	19.2525i	−0.205724	+	0.672735i
$820$		0			0
$821$	15.3844	+	5.59945i	0.536918	+	0.195422i	0.596224	−	0.802818i	$-0.296667\pi$
$821$	15.3844	+	5.59945i	0.536918	+	0.195422i	−0.0593069	+	0.998240i	$0.518889\pi$
$822$	2.59950	−	42.4787i	0.0906679	−	1.48161i
$823$	−1.36101	+	1.62199i	−0.0474419	+	0.0565391i	−0.789244	−	0.614080i	$-0.789527\pi$
$823$	−1.36101	+	1.62199i	−0.0474419	+	0.0565391i	0.741802	+	0.670619i	$0.233972\pi$
$824$	18.9790	+	15.9253i	0.661164	+	0.554783i
$825$		0			0
$826$	45.1396	+	16.4295i	1.57061	+	0.571654i
$827$	16.4944	+	9.52304i	0.573566	+	0.331148i	0.758572	−	0.651589i	$-0.225897\pi$
$827$	16.4944	+	9.52304i	0.573566	+	0.331148i	−0.185006	+	0.982737i	$0.559231\pi$
$828$	−0.703742	+	5.72843i	−0.0244567	+	0.199077i
$829$	14.7459	+	25.5407i	0.512148	+	0.887066i	0.999901	+	0.0140841i	$0.00448326\pi$
$829$	14.7459	+	25.5407i	0.512148	+	0.887066i	−0.487753	+	0.872982i	$0.662183\pi$
$830$		0			0
$831$	−48.3973	+	14.3342i	−1.67889	+	0.497249i
$832$	4.51284	+	12.3989i	0.156454	+	0.429855i
$833$	14.1850	+	2.50119i	0.491480	+	0.0866611i
$834$	30.6913	−	22.7088i	1.06275	−	0.786342i
$835$		0			0
$836$	6.76974			0.234136
$837$	−1.82462	−	10.9101i	−0.0630681	−	0.377107i
$838$			39.5542i			1.36638i
$839$	−20.6987	+	17.3682i	−0.714597	+	0.599618i	−0.925885	−	0.377806i	$-0.876679\pi$
$839$	−20.6987	+	17.3682i	−0.714597	+	0.599618i	0.211288	+	0.977424i	$0.432234\pi$
$840$		0			0
$841$	−3.97427	+	22.5392i	−0.137044	+	0.777214i
$842$	−1.86399	−	5.12126i	−0.0642372	−	0.176490i
$843$	−39.7513	−	9.54481i	−1.36911	−	0.328741i
$844$	−0.154046	−	0.873641i	−0.00530250	−	0.0300719i
$845$		0			0
$846$	26.8428	+	13.6793i	0.922874	+	0.470303i
$847$	24.2838	+	14.0203i	0.834401	+	0.481742i
$848$	4.69016	−	12.8861i	0.161061	−	0.442511i
$849$	18.8154	−	28.4250i	0.645743	−	0.975542i
$850$		0			0
$851$	61.1576	+	51.3174i	2.09646	+	1.75914i
$852$	2.63713	+	1.74560i	0.0903467	+	0.0598034i
$853$	−2.29637	+	6.30921i	−0.0786260	+	0.216023i	−0.972777	−	0.231742i	$-0.925558\pi$
$853$	−2.29637	+	6.30921i	−0.0786260	+	0.216023i	0.894151	+	0.447765i	$0.147780\pi$
$854$	−36.2850	+	62.8475i	−1.24165	+	2.15060i
$855$		0			0
$856$	18.1022	+	31.3539i	0.618721	+	1.07166i
$857$	−6.45695	+	1.13853i	−0.220565	+	0.0388916i	−0.282839	−	0.959168i	$-0.591276\pi$
$857$	−6.45695	+	1.13853i	−0.220565	+	0.0388916i	0.0622733	+	0.998059i	$0.480165\pi$
$858$	14.0720	+	3.37887i	0.480409	+	0.115353i
$859$	−46.0053	+	16.7446i	−1.56968	+	0.571317i	−0.972928	−	0.231109i	$-0.925765\pi$
$859$	−46.0053	+	16.7446i	−1.56968	+	0.571317i	−0.596752	+	0.802426i	$0.703542\pi$
$860$		0			0
$861$	−3.53355	−	1.53657i	−0.120423	−	0.0523662i
$862$	−32.7882	−	39.0754i	−1.11677	−	1.33091i
$863$			24.9816i			0.850383i	0.905103	+	0.425192i	$0.139793\pi$
$863$			24.9816i			0.850383i	−0.905103	+	0.425192i	$0.860207\pi$
$864$	4.47904	+	5.43460i	0.152380	+	0.184889i
$865$		0			0
$866$	13.2817	−	11.1447i	0.451332	−	0.378712i
$867$	−16.1798	−	21.8673i	−0.549496	−	0.742652i
$868$	−2.23978	−	0.394934i	−0.0760231	−	0.0134049i
$869$	−19.1153	+	6.95739i	−0.648442	+	0.236013i
$870$		0			0
$871$	0.772563	+	4.38142i	0.0261773	+	0.148459i
$872$	−0.691592	+	0.399291i	−0.0234203	+	0.0135217i
$873$	2.86725	−	23.3393i	0.0970417	−	0.789915i
$874$	−35.7384	+	61.9007i	−1.20887	+	2.09382i
$875$		0			0
$876$	1.90960	+	3.83039i	0.0645195	+	0.129417i
$877$	−2.52652	+	3.01099i	−0.0853144	+	0.101674i	−0.807013	−	0.590534i	$-0.798917\pi$
$877$	−2.52652	+	3.01099i	−0.0853144	+	0.101674i	0.721699	+	0.692208i	$0.243362\pi$
$878$	−6.58533	+	7.84809i	−0.222244	+	0.264860i
$879$	−10.6716	−	0.653051i	−0.359944	−	0.0220269i
$880$		0			0
$881$	6.07726	−	10.5261i	0.204748	−	0.354634i	−0.745304	−	0.666724i	$-0.767696\pi$
$881$	6.07726	−	10.5261i	0.204748	−	0.354634i	0.950052	+	0.312090i	$0.101029\pi$
$882$	−48.1652	−	14.7290i	−1.62181	−	0.495951i
$883$	15.1061	−	8.72154i	0.508362	−	0.293503i	−0.223798	−	0.974636i	$-0.571846\pi$
$883$	15.1061	−	8.72154i	0.508362	−	0.293503i	0.732160	+	0.681132i	$0.238512\pi$
$884$	0.0720616	+	0.408682i	0.00242369	+	0.0137454i
$885$		0			0
$886$	27.1411	−	9.87856i	0.911823	−	0.331877i
$887$	38.5770	+	6.80216i	1.29529	+	0.228394i	0.778460	−	0.627695i	$-0.216001\pi$
$887$	38.5770	+	6.80216i	1.29529	+	0.228394i	0.516828	+	0.856089i	$0.327113\pi$
$888$	51.1452	−	5.82557i	1.71632	−	0.195493i
$889$	−51.5942	+	43.2927i	−1.73041	+	1.45199i
$890$		0			0
$891$	37.2555	−	3.91080i	1.24811	−	0.131017i
$892$		−	2.53725i		−	0.0849535i
$893$	−32.8527	−	39.1524i	−1.09937	−	1.31018i
$894$	−2.21484	−	19.4451i	−0.0740754	−	0.650340i
$895$		0			0
$896$	−36.8786	+	13.4227i	−1.23203	+	0.448421i
$897$	14.4083	−	15.1822i	0.481080	−	0.506920i
$898$	−40.3023	+	7.10638i	−1.34491	+	0.237143i
$899$	2.63169	+	4.55823i	0.0877719	+	0.152025i
$900$		0			0
$901$	2.25485	−	3.90551i	0.0751199	−	0.130111i
$902$	−0.947327	+	2.60276i	−0.0315426	+	0.0866625i
$903$	−0.0512849	+	0.838052i	−0.00170665	+	0.0278886i
$904$	−4.71630	−	3.95744i	−0.156862	−	0.131623i
$905$		0			0
$906$	−12.3744	−	24.8212i	−0.411112	−	0.824630i
$907$	−10.1184	+	27.8001i	−0.335977	+	0.923088i	0.650546	+	0.759466i	$0.274540\pi$
$907$	−10.1184	+	27.8001i	−0.335977	+	0.923088i	−0.986523	+	0.163622i	$0.947682\pi$
$908$	−5.53073	−	3.19317i	−0.183544	−	0.105969i
$909$	−12.4829	−	29.4131i	−0.414030	−	0.975571i
$910$		0			0
$911$	−8.01745	−	45.4692i	−0.265630	−	1.50646i	−0.767235	−	0.641366i	$-0.778368\pi$
$911$	−8.01745	−	45.4692i	−0.265630	−	1.50646i	0.501605	−	0.865097i	$-0.332743\pi$
$912$	11.4878	+	38.7867i	0.380398	+	1.28436i
$913$	5.18268	+	14.2393i	0.171522	+	0.471252i
$914$	7.47996	−	42.4210i	0.247415	−	1.40316i
$915$		0			0
$916$	2.03688	−	1.70914i	0.0673003	−	0.0564716i
$917$		−	15.0297i		−	0.496323i
$918$	−3.86077	−	6.82545i	−0.127424	−	0.225273i
$919$	−3.32517			−0.109687			−0.0548435	−	0.998495i	$-0.517466\pi$
$919$	−3.32517			−0.109687			−0.0548435	+	0.998495i	$0.517466\pi$
$920$		0			0
$921$	−18.9705	−	8.24933i	−0.625098	−	0.271825i
$922$	−33.3527	−	5.88098i	−1.09841	−	0.193680i
$923$	−3.92270	−	10.7775i	−0.129117	−	0.354746i
$924$	1.79825	−	7.48919i	0.0591582	−	0.246376i
$925$		0			0
$926$	−6.25025	−	10.8257i	−0.205396	−	0.355756i
$927$	−13.6186	−	20.9739i	−0.447295	−	0.688872i
$928$	−2.90205	−	1.67550i	−0.0952645	−	0.0550010i
$929$	−5.41753	−	1.97182i	−0.177743	−	0.0646933i	0.251615	−	0.967827i	$-0.419038\pi$
$929$	−5.41753	−	1.97182i	−0.177743	−	0.0646933i	−0.429359	+	0.903134i	$0.641260\pi$
$930$		0			0
$931$	65.4549	+	54.9232i	2.14520	+	1.80004i
$932$	2.07600	−	2.47408i	0.0680016	−	0.0810411i
$933$	36.1571	+	23.9335i	1.18373	+	0.783549i
$934$	48.2036	+	17.5447i	1.57727	+	0.574079i
$935$		0			0
$936$	−0.705430	−	13.4772i	−0.0230577	−	0.440516i
$937$	23.1923	−	13.3901i	0.757661	−	0.437436i	−0.0707946	−	0.997491i	$-0.522553\pi$
$937$	23.1923	−	13.3901i	0.757661	−	0.437436i	0.828455	+	0.560055i	$0.189220\pi$
$938$	−17.0227	+	3.00156i	−0.555811	+	0.0980045i
$939$	6.20304	−	25.8338i	0.202429	−	0.843055i
$940$		0			0
$941$	−7.05048	+	39.9852i	−0.229839	+	1.30348i	0.623376	+	0.781922i	$0.285761\pi$
$941$	−7.05048	+	39.9852i	−0.229839	+	1.30348i	−0.853215	+	0.521559i	$0.825351\pi$
$942$	11.9416	−	27.4614i	0.389080	−	0.894742i
$943$	2.57499	+	3.06875i	0.0838532	+	0.0999324i
$944$	−28.2642			−0.919920
$945$		0			0
$946$	0.603547			0.0196230
$947$	−4.53195	−	5.40097i	−0.147269	−	0.175508i	0.687367	−	0.726310i	$-0.258766\pi$
$947$	−4.53195	−	5.40097i	−0.147269	−	0.175508i	−0.834636	+	0.550802i	$0.814322\pi$
$948$	1.21322	+	1.63968i	0.0394035	+	0.0532544i
$949$	2.69533	−	15.2860i	0.0874942	−	0.496204i
$950$		0			0
$951$	−0.409125	+	0.121174i	−0.0132668	+	0.00392933i
$952$	−14.7669	+	2.60381i	−0.478599	+	0.0843899i
$953$	−18.5197	+	10.6923i	−0.599911	+	0.346359i	−0.769007	−	0.639241i	$-0.779249\pi$
$953$	−18.5197	+	10.6923i	−0.599911	+	0.346359i	0.169095	+	0.985600i	$0.445915\pi$
$954$	−9.49110	+	12.5934i	−0.307286	+	0.407727i
$955$		0			0
$956$	−1.99216	−	0.725088i	−0.0644311	−	0.0234510i
$957$	−15.9520	+	7.95275i	−0.515656	+	0.257076i
$958$	−31.7294	+	37.8137i	−1.02513	+	1.22170i
$959$	62.9237	+	52.7993i	2.03191	+	1.70498i
$960$		0			0
$961$	24.8720	+	9.05266i	0.802322	+	0.292021i
$962$	−17.3837	−	10.0365i	−0.560472	−	0.323589i
$963$	−8.21819	−	35.6075i	−0.264828	−	1.14744i
$964$	1.76591	+	3.05865i	0.0568763	+	0.0985126i
$965$		0			0
$966$	58.9860	+	55.9793i	1.89784	+	1.80110i
$967$	−11.2223	−	30.8331i	−0.360886	−	0.991527i	−0.978717	−	0.205216i	$-0.934210\pi$
$967$	−11.2223	−	30.8331i	−0.360886	−	0.991527i	0.617831	−	0.786311i	$-0.288012\pi$
$968$	−18.5111	−	3.26401i	−0.594970	−	0.104909i
$969$	1.50552	+	13.2176i	0.0483644	+	0.424612i
$970$		0			0
$971$	2.11522			0.0678807			0.0339404	−	0.999424i	$-0.489194\pi$
$971$	2.11522			0.0678807			0.0339404	+	0.999424i	$0.489194\pi$
$972$	−1.43686	−	3.47048i	−0.0460873	−	0.111316i
$973$			73.6892i			2.36237i
$974$	38.8010	−	32.5579i	1.24326	−	1.04322i
$975$		0			0
$976$	7.41468	−	42.0507i	0.237338	−	1.34601i
$977$	−6.16678	−	16.9431i	−0.197293	−	0.542058i	0.801112	−	0.598514i	$-0.204242\pi$
$977$	−6.16678	−	16.9431i	−0.197293	−	0.542058i	−0.998405	+	0.0564564i	$0.982020\pi$
$978$	24.0666	−	25.3592i	0.769564	−	0.810899i
$979$	−8.30826	−	47.1185i	−0.265533	−	1.50591i
$980$		0			0
$981$	0.785415	−	0.181274i	0.0250764	−	0.00578762i
$982$	0.275562	+	0.159096i	0.00879355	+	0.00507696i
$983$	6.30480	−	17.3223i	0.201092	−	0.552496i	−0.797624	−	0.603155i	$-0.793910\pi$
$983$	6.30480	−	17.3223i	0.201092	−	0.552496i	0.998716	+	0.0506592i	$0.0161322\pi$
$984$	2.57812	+	0.157769i	0.0821876	+	0.00502950i
$985$		0			0
$986$	2.85833	+	2.39842i	0.0910278	+	0.0763814i
$987$	−52.0400	+	25.9441i	−1.65645	+	0.825808i
$988$	−0.841971	+	2.31330i	−0.0267867	+	0.0735958i
$989$	0.436456	−	0.755965i	0.0138785	−	0.0240383i
$990$		0			0
$991$	−17.5641	−	30.4220i	−0.557943	−	0.966386i	−0.997668	−	0.0682536i	$-0.978257\pi$
$991$	−17.5641	−	30.4220i	−0.557943	−	0.966386i	0.439725	−	0.898133i	$-0.355076\pi$
$992$	2.84139	−	0.501014i	0.0902143	−	0.0159072i
$993$	−12.2699	−	41.4273i	−0.389372	−	1.31466i
$994$	41.8728	−	15.2405i	1.32813	−	0.483398i
$995$		0			0
$996$	1.22143	−	0.903746i	0.0387024	−	0.0286363i
$997$	−11.3032	−	13.4706i	−0.357976	−	0.426620i	0.556758	−	0.830674i	$-0.312045\pi$
$997$	−11.3032	−	13.4706i	−0.357976	−	0.426620i	−0.914735	+	0.404055i	$0.867600\pi$
$998$		−	26.7659i		−	0.847261i
$999$	−51.0872	−	9.47361i	−1.61633	−	0.299732i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	675.2.u.e.49.7		132
5.2	odd	4		675.2.l.g.76.8	yes	66
5.3	odd	4		675.2.l.f.76.4	✓	66
5.4	even	2	inner	675.2.u.e.49.16		132
27.16	even	9	inner	675.2.u.e.124.16		132
135.43	odd	36		675.2.l.f.151.4	yes	66
135.97	odd	36		675.2.l.g.151.8	yes	66
135.124	even	18	inner	675.2.u.e.124.7		132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
675.2.l.f.76.4	✓	66	5.3	odd	4
675.2.l.f.151.4	yes	66	135.43	odd	36
675.2.l.g.76.8	yes	66	5.2	odd	4
675.2.l.g.151.8	yes	66	135.97	odd	36
675.2.u.e.49.7		132	1.1	even	1	trivial
675.2.u.e.49.16		132	5.4	even	2	inner
675.2.u.e.124.7		132	135.124	even	18	inner
675.2.u.e.124.16		132	27.16	even	9	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:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	675.u (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.852522 - 1.01600i) q^{2} +(1.72092 - 0.196018i) q^{3} +(0.0418420 - 0.237298i) q^{4} +(-1.66628 - 1.58134i) q^{6} +(4.36644 - 0.769922i) q^{7} +(-2.57396 + 1.48608i) q^{8} +(2.92315 - 0.674663i) q^{9} +(3.91123 + 1.42357i) q^{11} +(0.0254923 - 0.416573i) q^{12} +(-0.972900 + 1.15946i) q^{13} +(-4.50473 - 3.77991i) q^{14} +(3.25136 + 1.18340i) q^{16} +(0.985419 + 0.568932i) q^{17} +(-3.17751 - 2.39475i) q^{18} +(3.37499 + 5.84565i) q^{19} +(7.36340 - 2.18088i) q^{21} +(-1.88807 - 5.18742i) q^{22} +(-7.86279 - 1.38642i) q^{23} +(-4.13830 + 3.06197i) q^{24} +2.00742 q^{26} +(4.89828 - 1.73403i) q^{27} -1.06836i q^{28} +(-1.89402 + 1.58927i) q^{29} +(0.369663 - 2.09646i) q^{31} +(0.463549 + 1.27359i) q^{32} +(7.00997 + 1.68319i) q^{33} +(-0.262059 - 1.48621i) q^{34} +(-0.0377853 - 0.721887i) q^{36} +(-8.65969 - 4.99967i) q^{37} +(3.06191 - 8.41252i) q^{38} +(-1.44701 + 2.18604i) q^{39} +(-0.384359 - 0.322515i) q^{41} +(-8.49322 - 5.62194i) q^{42} +(-0.0373936 + 0.102738i) q^{43} +(0.501464 - 0.868561i) q^{44} +(5.29460 + 9.17051i) q^{46} +(-7.45681 + 1.31484i) q^{47} +(5.82730 + 1.39921i) q^{48} +(11.8952 - 4.32950i) q^{49} +(1.80735 + 0.785929i) q^{51} +(0.234429 + 0.279381i) q^{52} -3.96330i q^{53} +(-5.93766 - 3.49833i) q^{54} +(-10.0949 + 8.47063i) q^{56} +(6.95395 + 9.39836i) q^{57} +(3.22938 + 0.569427i) q^{58} +(-7.67614 + 2.79389i) q^{59} +(-2.14296 - 12.1533i) q^{61} +(-2.44514 + 1.41170i) q^{62} +(12.2444 - 5.19648i) q^{63} +(4.35880 - 7.54966i) q^{64} +(-4.26604 - 8.55705i) q^{66} +(1.88943 - 2.25173i) q^{67} +(0.176238 - 0.210033i) q^{68} +(-13.8030 - 0.844680i) q^{69} +(-3.78880 + 6.56240i) q^{71} +(-6.52149 + 6.08060i) q^{72} +(-8.88121 + 5.12757i) q^{73} +(2.30293 + 13.0605i) q^{74} +(1.52838 - 0.556283i) q^{76} +(18.1742 + 3.20460i) q^{77} +(3.45462 - 0.393490i) q^{78} +(-3.74388 + 3.14149i) q^{79} +(8.08966 - 3.94429i) q^{81} +0.665459i q^{82} +(2.34014 + 2.78888i) q^{83} +(-0.209418 - 1.83857i) q^{84} +(0.136260 - 0.0495947i) q^{86} +(-2.94793 + 3.10627i) q^{87} +(-12.1829 + 2.14817i) q^{88} +(-5.74755 - 9.95505i) q^{89} +(-3.35542 + 5.81176i) q^{91} +(-0.657989 + 1.80781i) q^{92} +(0.225218 - 3.68031i) q^{93} +(7.69297 + 6.45516i) q^{94} +(1.04738 + 2.10089i) q^{96} +(2.68084 - 7.36555i) q^{97} +(-14.5397 - 8.39449i) q^{98} +(12.3936 + 1.52256i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q - 12 q^{6} + 12 q^{9} + 30 q^{11} - 30 q^{14} + 36 q^{16} - 24 q^{19} + 24 q^{21} + 78 q^{24} + 12 q^{26} + 30 q^{29} + 6 q^{31} + 60 q^{36} + 30 q^{39} + 78 q^{41} - 102 q^{44} + 18 q^{46} + 12 q^{49}+ \cdots + 96 q^{99}+O(q^{100}) \) 132 * q - 12 * q^6 + 12 * q^9 + 30 * q^11 - 30 * q^14 + 36 * q^16 - 24 * q^19 + 24 * q^21 + 78 * q^24 + 12 * q^26 + 30 * q^29 + 6 * q^31 + 60 * q^36 + 30 * q^39 + 78 * q^41 - 102 * q^44 + 18 * q^46 + 12 * q^49 - 150 * q^54 + 288 * q^56 - 90 * q^59 - 108 * q^61 + 48 * q^64 + 96 * q^66 - 102 * q^69 - 30 * q^71 - 192 * q^74 - 96 * q^76 - 96 * q^79 - 108 * q^81 - 114 * q^84 - 222 * q^86 + 24 * q^89 + 18 * q^91 - 72 * q^94 - 498 * q^96 + 96 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more