LMFDB - Embedded newform 675.2.l.g.76.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [675,2,Mod(76,675)] 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("675.76"); 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, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 675 = 3^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	675.l (of order $9$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [66,6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$5.38990213644$
Analytic rank:	$0$
Dimension:	$66$
Relative dimension:	$11$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			76.8
Character	$\chi$	$=$	675.76
Dual form			675.2.l.g.151.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.01600 - 0.852522i) q^{2} +(-0.196018 - 1.72092i) q^{3} +(-0.0418420 + 0.237298i) q^{4} +(-1.66628 - 1.58134i) q^{6} +(0.769922 + 4.36644i) q^{7} +(1.48608 + 2.57396i) q^{8} +(-2.92315 + 0.674663i) q^{9} +(3.91123 + 1.42357i) q^{11} +(0.416573 + 0.0254923i) q^{12} +(1.15946 + 0.972900i) q^{13} +(4.50473 + 3.77991i) q^{14} +(3.25136 + 1.18340i) q^{16} +(-0.568932 + 0.985419i) q^{17} +(-2.39475 + 3.17751i) q^{18} +(-3.37499 - 5.84565i) q^{19} +(7.36340 - 2.18088i) q^{21} +(5.18742 - 1.88807i) q^{22} +(-1.38642 + 7.86279i) q^{23} +(4.13830 - 3.06197i) q^{24} +2.00742 q^{26} +(1.73403 + 4.89828i) q^{27} -1.06836 q^{28} +(1.89402 - 1.58927i) q^{29} +(0.369663 - 2.09646i) q^{31} +(-1.27359 + 0.463549i) q^{32} +(1.68319 - 7.00997i) q^{33} +(0.262059 + 1.48621i) q^{34} +(-0.0377853 - 0.721887i) q^{36} +(4.99967 - 8.65969i) q^{37} +(-8.41252 - 3.06191i) q^{38} +(1.44701 - 2.18604i) q^{39} +(-0.384359 - 0.322515i) q^{41} +(5.62194 - 8.49322i) q^{42} +(0.102738 + 0.0373936i) q^{43} +(-0.501464 + 0.868561i) q^{44} +(5.29460 + 9.17051i) q^{46} +(-1.31484 - 7.45681i) q^{47} +(1.39921 - 5.82730i) q^{48} +(-11.8952 + 4.32950i) q^{49} +(1.80735 + 0.785929i) q^{51} +(-0.279381 + 0.234429i) q^{52} -3.96330 q^{53} +(5.93766 + 3.49833i) q^{54} +(-10.0949 + 8.47063i) q^{56} +(-9.39836 + 6.95395i) q^{57} +(0.569427 - 3.22938i) q^{58} +(7.67614 - 2.79389i) q^{59} +(-2.14296 - 12.1533i) q^{61} +(-1.41170 - 2.44514i) q^{62} +(-5.19648 - 12.2444i) q^{63} +(-4.35880 + 7.54966i) q^{64} +(-4.26604 - 8.55705i) q^{66} +(2.25173 + 1.88943i) q^{67} +(-0.210033 - 0.176238i) q^{68} +(13.8030 + 0.844680i) q^{69} +(-3.78880 + 6.56240i) q^{71} +(-6.08060 - 6.52149i) q^{72} +(5.12757 + 8.88121i) q^{73} +(-2.30293 - 13.0605i) q^{74} +(1.52838 - 0.556283i) q^{76} +(-3.20460 + 18.1742i) q^{77} +(-0.393490 - 3.45462i) q^{78} +(3.74388 - 3.14149i) q^{79} +(8.08966 - 3.94429i) q^{81} -0.665459 q^{82} +(2.78888 - 2.34014i) q^{83} +(0.209418 + 1.83857i) q^{84} +(0.136260 - 0.0495947i) q^{86} +(-3.10627 - 2.94793i) q^{87} +(2.14817 + 12.1829i) q^{88} +(5.74755 + 9.95505i) q^{89} +(-3.35542 + 5.81176i) q^{91} +(-1.80781 - 0.657989i) q^{92} +(-3.68031 - 0.225218i) q^{93} +(-7.69297 - 6.45516i) q^{94} +(1.04738 + 2.10089i) q^{96} +(7.36555 + 2.68084i) q^{97} +(-8.39449 + 14.5397i) q^{98} +(-12.3936 - 1.52256i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 66 q + 6 q^{2} - 6 q^{6} + 6 q^{7} + 12 q^{8} - 6 q^{9} + 15 q^{11} + 18 q^{12} + 15 q^{14} + 18 q^{16} + 30 q^{17} - 12 q^{18} + 12 q^{19} + 12 q^{21} - 45 q^{22} + 36 q^{23} - 39 q^{24} + 6 q^{26} + 51 q^{27}+ \cdots - 48 q^{99}+O(q^{100}) $ 66 * q + 6 * q^2 - 6 * q^6 + 6 * q^7 + 12 * q^8 - 6 * q^9 + 15 * q^11 + 18 * q^12 + 15 * q^14 + 18 * q^16 + 30 * q^17 - 12 * q^18 + 12 * q^19 + 12 * q^21 - 45 * q^22 + 36 * q^23 - 39 * q^24 + 6 * q^26 + 51 * q^27 - 36 * q^28 - 15 * q^29 + 3 * q^31 + 27 * q^32 - 3 * q^33 + 30 * q^36 + 6 * q^37 - 12 * q^38 - 15 * q^39 + 39 * q^41 + 48 * q^42 + 12 * q^43 + 51 * q^44 + 9 * q^46 + 30 * q^47 - 132 * q^48 - 6 * q^49 + 9 * q^52 - 24 * q^53 + 75 * q^54 + 144 * q^56 + 33 * q^57 + 27 * q^58 + 45 * q^59 - 54 * q^61 + 66 * q^62 - 120 * q^63 - 24 * q^64 + 48 * q^66 + 9 * q^67 - 69 * q^68 + 51 * q^69 - 15 * q^71 + 9 * q^72 - 15 * q^73 + 96 * q^74 - 48 * q^76 - 36 * q^77 - 18 * q^78 + 48 * q^79 - 54 * q^81 - 36 * q^82 + 30 * q^83 + 57 * q^84 - 111 * q^86 - 33 * q^87 + 36 * q^88 - 12 * q^89 + 9 * q^91 - 219 * q^92 + 63 * q^93 + 36 * q^94 - 249 * q^96 + 57 * q^97 + 75 * q^98 - 48 * 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 $

$2$	1.01600	−	0.852522i	0.718418	−	0.602824i	−0.208529	−	0.978016i	$-0.566868\pi$
$2$	1.01600	−	0.852522i	0.718418	−	0.602824i	0.926947	+	0.375192i	$0.122423\pi$
$3$	−0.196018	−	1.72092i	−0.113171	−	0.993576i
$3$	−0.196018	−	1.72092i	−0.113171	−	0.993576i
$4$	−0.0418420	+	0.237298i	−0.0209210	+	0.118649i
$5$		0			0
$5$		0			0
$6$	−1.66628	−	1.58134i	−0.680255	−	0.645580i
$7$	0.769922	+	4.36644i	0.291003	+	1.65036i	0.683018	+	0.730402i	$0.260667\pi$
$7$	0.769922	+	4.36644i	0.291003	+	1.65036i	−0.392015	+	0.919959i	$0.628222\pi$
$8$	1.48608	+	2.57396i	0.525408	+	0.910034i
$9$	−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	$0.395197\pi$
$12$	0.416573	+	0.0254923i	0.120254	+	0.00735900i
$13$	1.15946	+	0.972900i	0.321576	+	0.269834i	0.789257	−	0.614063i	$-0.210466\pi$
$13$	1.15946	+	0.972900i	0.321576	+	0.269834i	−0.467681	+	0.883897i	$0.654910\pi$
$14$	4.50473	+	3.77991i	1.20394	+	1.01022i
$15$		0			0
$16$	3.25136	+	1.18340i	0.812839	+	0.295849i
$17$	−0.568932	+	0.985419i	−0.137986	+	0.238999i	−0.926734	−	0.375717i	$-0.877396\pi$
$17$	−0.568932	+	0.985419i	−0.137986	+	0.238999i	0.788748	+	0.614717i	$0.210730\pi$
$18$	−2.39475	+	3.17751i	−0.564448	+	0.748946i
$19$	−3.37499	−	5.84565i	−0.774275	−	1.34108i	−0.935201	−	0.354118i	$-0.884781\pi$
$19$	−3.37499	−	5.84565i	−0.774275	−	1.34108i	0.160926	−	0.986967i	$-0.448552\pi$
$20$		0			0
$21$	7.36340	−	2.18088i	1.60683	−	0.475906i
$22$	5.18742	−	1.88807i	1.10596	−	0.402537i
$23$	−1.38642	+	7.86279i	−0.289089	+	1.63950i	0.401215	+	0.915984i	$0.368588\pi$
$23$	−1.38642	+	7.86279i	−0.289089	+	1.63950i	−0.690303	+	0.723520i	$0.742523\pi$
$24$	4.13830	−	3.06197i	0.844726	−	0.625022i
$25$		0			0
$26$	2.00742			0.393688
$27$	1.73403	+	4.89828i	0.333715	+	0.942674i
$28$	−1.06836			−0.201902
$29$	1.89402	−	1.58927i	0.351710	−	0.295120i	−0.449766	−	0.893146i	$-0.648493\pi$
$29$	1.89402	−	1.58927i	0.351710	−	0.295120i	0.801476	+	0.598026i	$0.204048\pi$
$30$		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	$-0.00567328\pi$
$32$	−1.27359	+	0.463549i	−0.225141	+	0.0819447i
$33$	1.68319	−	7.00997i	0.293005	−	1.22028i
$34$	0.262059	+	1.48621i	0.0449427	+	0.254883i
$35$		0			0
$36$	−0.0377853	−	0.721887i	−0.00629756	−	0.120315i
$37$	4.99967	−	8.65969i	0.821941	−	1.42364i	−0.0822930	−	0.996608i	$-0.526224\pi$
$37$	4.99967	−	8.65969i	0.821941	−	1.42364i	0.904235	−	0.427036i	$-0.140442\pi$
$38$	−8.41252	−	3.06191i	−1.36469	−	0.496707i
$39$	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	$0.734697\pi$
$42$	5.62194	−	8.49322i	0.867484	−	1.31053i
$43$	0.102738	+	0.0373936i	0.0156674	+	0.00570247i	0.349842	−	0.936809i	$-0.386235\pi$
$43$	0.102738	+	0.0373936i	0.0156674	+	0.00570247i	−0.334175	+	0.942511i	$0.608458\pi$
$44$	−0.501464	+	0.868561i	−0.0755985	+	0.130940i
$45$		0			0
$46$	5.29460	+	9.17051i	0.780646	+	1.35212i
$47$	−1.31484	−	7.45681i	−0.191789	−	1.08769i	−0.916918	−	0.399075i	$-0.869331\pi$
$47$	−1.31484	−	7.45681i	−0.191789	−	1.08769i	0.725129	−	0.688613i	$-0.241780\pi$
$48$	1.39921	−	5.82730i	0.201959	−	0.841099i
$49$	−11.8952	+	4.32950i	−1.69932	+	0.618500i
$50$		0			0
$51$	1.80735	+	0.785929i	0.253080	+	0.110052i
$52$	−0.279381	+	0.234429i	−0.0387432	+	0.0325094i
$53$	−3.96330			−0.544401			−0.272201	−	0.962241i	$-0.587751\pi$
$53$	−3.96330			−0.544401			−0.272201	+	0.962241i	$0.587751\pi$
$54$	5.93766	+	3.49833i	0.808013	+	0.476063i
$55$		0			0
$56$	−10.0949	+	8.47063i	−1.34899	+	1.13194i
$57$	−9.39836	+	6.95395i	−1.24484	+	0.921073i
$58$	0.569427	−	3.22938i	0.0747695	−	0.424039i
$59$	7.67614	−	2.79389i	0.999348	−	0.363733i	0.210015	−	0.977698i	$-0.432649\pi$
$59$	7.67614	−	2.79389i	0.999348	−	0.363733i	0.789333	+	0.613965i	$0.210426\pi$
$60$		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	$-0.345495\pi$
$62$	−1.41170	−	2.44514i	−0.179286	−	0.310533i
$63$	−5.19648	−	12.2444i	−0.654695	−	1.54264i
$64$	−4.35880	+	7.54966i	−0.544850	+	0.943708i
$65$		0			0
$66$	−4.26604	−	8.55705i	−0.525113	−	1.05330i
$67$	2.25173	+	1.88943i	0.275093	+	0.230830i	0.769887	−	0.638180i	$-0.220312\pi$
$67$	2.25173	+	1.88943i	0.275093	+	0.230830i	−0.494795	+	0.869010i	$0.664757\pi$
$68$	−0.210033	−	0.176238i	−0.0254702	−	0.0213720i
$69$	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	$0.315117\pi$
$72$	−6.08060	−	6.52149i	−0.716605	−	0.768565i
$73$	5.12757	+	8.88121i	0.600136	+	1.03947i	0.992800	+	0.119785i	$0.0382204\pi$
$73$	5.12757	+	8.88121i	0.600136	+	1.03947i	−0.392663	+	0.919682i	$0.628446\pi$
$74$	−2.30293	−	13.0605i	−0.267710	−	1.51826i
$75$		0			0
$76$	1.52838	−	0.556283i	0.175317	−	0.0638101i
$77$	−3.20460	+	18.1742i	−0.365198	+	2.07114i
$78$	−0.393490	−	3.45462i	−0.0445540	−	0.391159i
$79$	3.74388	−	3.14149i	0.421219	−	0.353445i	−0.407408	−	0.913246i	$-0.633567\pi$
$79$	3.74388	−	3.14149i	0.421219	−	0.353445i	0.828627	+	0.559802i	$0.189123\pi$
$80$		0			0
$81$	8.08966	−	3.94429i	0.898851	−	0.438254i
$82$	−0.665459			−0.0734876
$83$	2.78888	−	2.34014i	0.306119	−	0.256864i	−0.476767	−	0.879030i	$-0.658191\pi$
$83$	2.78888	−	2.34014i	0.306119	−	0.256864i	0.782886	+	0.622166i	$0.213747\pi$
$84$	0.209418	+	1.83857i	0.0228494	+	0.200604i
$85$		0			0
$86$	0.136260	−	0.0495947i	0.0146933	−	0.00534794i
$87$	−3.10627	−	2.94793i	−0.333027	−	0.316052i
$88$	2.14817	+	12.1829i	0.228996	+	1.29870i
$89$	5.74755	+	9.95505i	0.609239	+	1.05523i	0.991366	+	0.131123i	$0.0418583\pi$
$89$	5.74755	+	9.95505i	0.609239	+	1.05523i	−0.382127	+	0.924110i	$0.624808\pi$
$90$		0			0
$91$	−3.35542	+	5.81176i	−0.351744	+	0.609238i
$92$	−1.80781	−	0.657989i	−0.188477	−	0.0686001i
$93$	−3.68031	−	0.225218i	−0.381630	−	0.0233540i
$94$	−7.69297	−	6.45516i	−0.793469	−	0.665799i
$95$		0			0
$96$	1.04738	+	2.10089i	0.106898	+	0.214421i
$97$	7.36555	+	2.68084i	0.747858	+	0.272198i	0.687704	−	0.725991i	$-0.258619\pi$
$97$	7.36555	+	2.68084i	0.747858	+	0.272198i	0.0601538	+	0.998189i	$0.480841\pi$
$98$	−8.39449	+	14.5397i	−0.847971	+	1.46873i
$99$	−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	$-0.233325\pi$
$102$	2.50628	−	0.742306i	0.248159	−	0.0734993i
$103$	−7.83309	+	2.85101i	−0.771817	+	0.280918i	−0.697756	−	0.716335i	$-0.745818\pi$
$103$	−7.83309	+	2.85101i	−0.771817	+	0.280918i	−0.0740609	+	0.997254i	$0.523596\pi$
$104$	−0.781165	+	4.43021i	−0.0765996	+	0.434418i
$105$		0			0
$106$	−4.02670	+	3.37880i	−0.391107	+	0.328178i
$107$	12.1812			1.17760			0.588800	−	0.808279i	$-0.299601\pi$
$107$	12.1812			1.17760			0.588800	+	0.808279i	$0.299601\pi$
$108$	−1.23491	+	0.206528i	−0.118829	+	0.0198732i
$109$	−0.268688			−0.0257356			−0.0128678	−	0.999917i	$-0.504096\pi$
$109$	−0.268688			−0.0257356			−0.0128678	+	0.999917i	$0.504096\pi$
$110$		0			0
$111$	−15.8827	−	6.90660i	−1.50752	−	0.655546i
$112$	−2.66395	+	15.1080i	−0.251719	+	1.42757i
$113$	1.94653	−	0.708479i	0.183114	−	0.0666481i	−0.248836	−	0.968546i	$-0.580048\pi$
$113$	1.94653	−	0.708479i	0.183114	−	0.0666481i	0.431950	+	0.901898i	$0.357826\pi$
$114$	−3.62030	+	15.0775i	−0.339073	+	1.41214i
$115$		0			0
$116$	0.297881	+	0.515944i	0.0276575	+	0.0479042i
$117$	−4.04565	−	2.06170i	−0.374021	−	0.190604i
$118$	5.41708	−	9.38266i	0.498683	−	0.863743i
$119$	−4.74081	−	1.72551i	−0.434589	−	0.158178i
$120$		0			0
$121$	4.84466	+	4.06516i	0.440424	+	0.369560i
$122$	−12.5382	−	10.5208i	−1.13515	−	0.952508i
$123$	−0.479683	+	0.724671i	−0.0432516	+	0.0653414i
$124$	0.482018	+	0.175440i	0.0432865	+	0.0157550i
$125$		0			0
$126$	−15.7182	−	8.01010i	−1.40029	−	0.713597i
$127$	−7.59522	−	13.1553i	−0.673967	−	1.16735i	−0.976770	−	0.214292i	$-0.931256\pi$
$127$	−7.59522	−	13.1553i	−0.673967	−	1.16735i	0.302802	−	0.953053i	$-0.402078\pi$
$128$	1.53703	+	8.71693i	0.135855	+	0.770475i
$129$	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	$0.00824510\pi$
$132$	1.59302	+	0.692728i	0.138655	+	0.0602942i
$133$	22.9262	−	19.2374i	1.98796	−	1.66809i
$134$	3.89853			0.336782
$135$		0			0
$136$	−3.38191			−0.289997
$137$	−14.1918	+	11.9084i	−1.21249	+	1.01740i	−0.213306	+	0.976985i	$0.568423\pi$
$137$	−14.1918	+	11.9084i	−1.21249	+	1.01740i	−0.999183	+	0.0404136i	$0.987132\pi$
$138$	14.7439	−	10.9092i	1.25509	−	0.928651i
$139$	2.88601	−	16.3674i	0.244788	−	1.38826i	−0.576197	−	0.817311i	$-0.695464\pi$
$139$	2.88601	−	16.3674i	0.244788	−	1.38826i	0.820985	−	0.570950i	$-0.193425\pi$
$140$		0			0
$141$	−12.5749	+	3.72440i	−1.05900	+	0.313651i
$142$	1.74518	+	9.89741i	0.146452	+	0.830572i
$143$	3.14991	+	5.45581i	0.263409	+	0.456237i
$144$	−10.3026	−	1.26568i	−0.858551	−	0.105474i
$145$		0			0
$146$	12.7810	+	4.65191i	1.05776	+	0.384995i
$147$	9.78241	+	19.6221i	0.806840	+	1.61840i
$148$	1.84573	+	1.54875i	0.151718	+	0.127307i
$149$	−6.52625	−	5.47617i	−0.534651	−	0.448626i	0.335053	−	0.942199i	$-0.391246\pi$
$149$	−6.52625	−	5.47617i	−0.534651	−	0.448626i	−0.869704	+	0.493574i	$0.835690\pi$
$150$		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	$0.447649\pi$
$152$	10.0310	−	17.3742i	0.813621	−	1.40923i
$153$	0.998250	−	3.26437i	0.0807038	−	0.263909i
$154$	12.2380	+	21.1969i	0.986169	+	1.70810i
$155$		0			0
$156$	0.458197	+	0.434841i	0.0366851	+	0.0348152i
$157$	−12.2495	+	4.45846i	−0.977618	+	0.355824i	−0.780914	−	0.624639i	$-0.785246\pi$
$157$	−12.2495	+	4.45846i	−0.977618	+	0.355824i	−0.196704	+	0.980463i	$0.563024\pi$
$158$	1.12558	−	6.38347i	0.0895462	−	0.507842i
$159$	0.776877	+	6.82053i	0.0616103	+	0.540904i
$160$		0			0
$161$	−35.3999			−2.78990
$162$	4.85647	−	10.9040i	0.381561	−	0.856698i
$163$	15.2191			1.19205			0.596025	−	0.802966i	$-0.296746\pi$
$163$	15.2191			1.19205			0.596025	+	0.802966i	$0.296746\pi$
$164$	0.0926146	−	0.0777128i	0.00723198	−	0.00606835i
$165$		0			0
$166$	0.838462	−	4.75515i	0.0650773	−	0.369072i
$167$	−14.9634	+	5.44622i	−1.15790	+	0.421441i	−0.848347	−	0.529441i	$-0.822402\pi$
$167$	−14.9634	+	5.44622i	−1.15790	+	0.421441i	−0.309553	+	0.950882i	$0.600179\pi$
$168$	16.5561	+	15.7122i	1.27733	+	1.21222i
$169$	−1.85962	−	10.5464i	−0.143048	−	0.811264i
$170$		0			0
$171$	13.8095	+	14.8108i	1.05604	+	1.13261i
$172$	−0.0131722	+	0.0228149i	−0.00100437	+	0.00173962i
$173$	−12.0020	−	4.36838i	−0.912497	−	0.332122i	−0.157248	−	0.987559i	$-0.550262\pi$
$173$	−12.0020	−	4.36838i	−0.912497	−	0.332122i	−0.755249	+	0.655437i	$0.772484\pi$
$174$	−5.66914	−	0.346925i	−0.429776	−	0.0263003i
$175$		0			0
$176$	11.0322	+	9.25707i	0.831580	+	0.697778i
$177$	−6.31272	−	12.6624i	−0.474493	−	0.951764i
$178$	14.3264	+	5.21438i	1.07381	+	0.390834i
$179$	−1.85652	+	3.21558i	−0.138763	+	0.240344i	−0.927029	−	0.374991i	$-0.877646\pi$
$179$	−1.85652	+	3.21558i	−0.138763	+	0.240344i	0.788266	+	0.615335i	$0.210979\pi$
$180$		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	$0.869777\pi$
$182$	1.54556	+	8.76530i	0.114564	+	0.649727i
$183$	−20.4949	+	6.07013i	−1.51502	+	0.448717i
$184$	−22.2989	+	8.11612i	−1.64389	+	0.598328i
$185$		0			0
$186$	−3.93118	+	2.90872i	−0.288248	+	0.213278i
$187$	−3.62804	+	3.04428i	−0.265308	+	0.222620i
$188$	1.82450			0.133065
$189$	−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	$0.325874\pi$
$192$	13.8468	+	6.02129i	0.999306	+	0.434549i
$193$	−0.685014	+	3.88491i	−0.0493084	+	0.279642i	−0.999486	−	0.0320682i	$-0.989791\pi$
$193$	−0.685014	+	3.88491i	−0.0493084	+	0.279642i	0.950177	+	0.311710i	$0.100902\pi$
$194$	9.76884	−	3.55557i	0.701362	−	0.255275i
$195$		0			0
$196$	−0.529662	−	3.00386i	−0.0378330	−	0.214562i
$197$	4.35710	+	7.54672i	0.310430	+	0.537681i	0.978456	−	0.206457i	$-0.0661935\pi$
$197$	4.35710	+	7.54672i	0.310430	+	0.537681i	−0.668025	+	0.744139i	$0.732860\pi$
$198$	−13.8898	+	9.01886i	−0.987106	+	0.640943i
$199$	6.70417	−	11.6120i	0.475246	−	0.823151i	−0.524352	−	0.851502i	$-0.675692\pi$
$199$	6.70417	−	11.6120i	0.475246	−	0.823151i	0.999598	+	0.0283510i	$0.00902560\pi$
$200$		0			0
$201$	2.81018	−	4.24542i	0.198215	−	0.299449i
$202$	−10.8211	−	9.08002i	−0.761373	−	0.638868i
$203$	8.39770	+	7.04651i	0.589403	+	0.494568i
$204$	−0.262122	+	0.395996i	−0.0183522	+	0.0277252i
$205$		0			0
$206$	−5.52784	+	9.57450i	−0.385143	+	0.667087i
$207$	−1.25200	−	23.9195i	−0.0870204	−	1.66252i
$208$	2.61848	+	4.53535i	0.181559	+	0.314470i
$209$	−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	$0.348442\pi$
$212$	0.165832	−	0.940482i	0.0113894	−	0.0645926i
$213$	12.0361	+	5.23390i	0.824697	+	0.358621i
$214$	12.3760	−	10.3847i	0.846009	−	0.709886i
$215$		0			0
$216$	−10.0311	+	11.7426i	−0.682529	+	0.798980i
$217$	9.43869			0.640740
$218$	−0.272986	+	0.229062i	−0.0184889	+	0.0155140i
$219$	14.2788	−	10.5650i	0.964871	−	0.713918i
$220$		0			0
$221$	−1.61837	+	0.589038i	−0.108863	+	0.0396230i
$222$	−22.0248	+	6.52326i	−1.47821	+	0.437812i
$223$	−1.82849	−	10.3699i	−0.122445	−	0.694417i	−0.982793	−	0.184711i	$-0.940865\pi$
$223$	−1.82849	−	10.3699i	−0.122445	−	0.694417i	0.860348	−	0.509707i	$-0.170246\pi$
$224$	−3.00463	−	5.20417i	−0.200755	−	0.347718i
$225$		0			0
$226$	1.37367	−	2.37927i	0.0913754	−	0.158267i
$227$	24.9055	+	9.06486i	1.65304	+	0.601656i	0.989246	−	0.146263i	$-0.0467245\pi$
$227$	24.9055	+	9.06486i	1.65304	+	0.601656i	0.663790	+	0.747919i	$0.268947\pi$
$228$	−1.25691	−	2.52118i	−0.0832409	−	0.166969i
$229$	−8.45322	−	7.09309i	−0.558605	−	0.468725i	0.319238	−	0.947675i	$-0.396573\pi$
$229$	−8.45322	−	7.09309i	−0.558605	−	0.468725i	−0.877842	+	0.478950i	$0.841018\pi$
$230$		0			0
$231$	31.9046	+	1.95241i	2.09917	+	0.128459i
$232$	6.90538	+	2.51335i	0.453361	+	0.165010i
$233$	6.70173	−	11.6077i	0.439045	−	0.760448i	−0.558571	−	0.829457i	$-0.688650\pi$
$233$	6.70173	−	11.6077i	0.439045	−	0.760448i	0.997616	+	0.0690083i	$0.0219835\pi$
$234$	−5.86801	+	1.35433i	−0.383604	+	0.0885356i
$235$		0			0
$236$	0.341798	+	1.93843i	0.0222492	+	0.126181i
$237$	−6.14012	−	5.82714i	−0.398844	−	0.378513i
$238$	−6.28768	+	2.28853i	−0.407570	+	0.148343i
$239$	−1.52780	+	8.66459i	−0.0988253	+	0.560466i	0.894683	+	0.446702i	$0.147402\pi$
$239$	−1.52780	+	8.66459i	−0.0988253	+	0.560466i	−0.993508	+	0.113763i	$0.963709\pi$
$240$		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	$0.434276\pi$
$242$	8.38779			0.539188
$243$	−8.37353	−	13.1485i	−0.537162	−	0.843479i
$244$	2.97362			0.190366
$245$		0			0
$246$	0.130442	+	1.14520i	0.00831666	+	0.0730155i
$247$	1.77408	−	10.0613i	0.112882	−	0.640186i
$248$	5.94556	−	2.16401i	0.377544	−	0.137415i
$249$	−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	$0.871834\pi$
$252$	3.12299	−	0.720784i	0.196730	−	0.0454052i
$253$	−16.6158	+	28.7795i	−1.04463	+	1.80935i
$254$	−18.9319	−	6.89065i	−1.18789	−	0.432358i
$255$		0			0
$256$	−4.36315	−	3.66112i	−0.272697	−	0.228820i
$257$	−6.25436	−	5.24803i	−0.390136	−	0.327363i	0.426530	−	0.904473i	$-0.359736\pi$
$257$	−6.25436	−	5.24803i	−0.390136	−	0.327363i	−0.816666	+	0.577110i	$0.804180\pi$
$258$	−0.112058	−	0.224772i	−0.00697644	−	0.0139937i
$259$	41.6614	+	15.1635i	2.58871	+	0.942215i
$260$		0			0
$261$	−4.46428	+	5.92350i	−0.276332	+	0.366656i
$262$	−2.24792	−	3.89351i	−0.138877	−	0.240542i
$263$	−4.83914	−	27.4441i	−0.298394	−	1.69228i	−0.653077	−	0.757291i	$-0.726522\pi$
$263$	−4.83914	−	27.4441i	−0.298394	−	1.69228i	0.354683	−	0.934987i	$-0.384589\pi$
$264$	20.5448	−	6.08491i	1.26444	−	0.374500i
$265$		0			0
$266$	6.89266	−	39.0902i	0.422616	−	2.39678i
$267$	16.0052	−	11.8425i	0.979505	−	0.724746i
$268$	−0.542574	+	0.455273i	−0.0331430	+	0.0278103i
$269$	−13.1520			−0.801893			−0.400947	−	0.916101i	$-0.631319\pi$
$269$	−13.1520			−0.801893			−0.400947	+	0.916101i	$0.631319\pi$
$270$		0			0
$271$	8.19664			0.497911			0.248955	−	0.968515i	$-0.419913\pi$
$271$	8.19664			0.497911			0.248955	+	0.968515i	$0.419913\pi$
$272$	−3.01594	+	2.53068i	−0.182868	+	0.153445i
$273$	10.6593	+	4.63522i	0.645132	+	0.280536i
$274$	−4.26670	+	24.1977i	−0.257761	+	1.46183i
$275$		0			0
$276$	−0.777987	+	3.24008i	−0.0468293	+	0.195030i
$277$	−5.06046	−	28.6993i	−0.304054	−	1.72437i	−0.627926	−	0.778273i	$-0.716096\pi$
$277$	−5.06046	−	28.6993i	−0.304054	−	1.72437i	0.323873	−	0.946101i	$-0.395015\pi$
$278$	−11.0214	−	19.0896i	−0.661017	−	1.14492i
$279$	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	$0.859720\pi$
$282$	−9.60089	+	14.5043i	−0.571724	+	0.863720i
$283$	−15.0763	−	12.6506i	−0.896195	−	0.751997i	0.0732477	−	0.997314i	$-0.476664\pi$
$283$	−15.0763	−	12.6506i	−0.896195	−	0.751997i	−0.969443	+	0.245317i	$0.921108\pi$
$284$	−1.39871	−	1.17366i	−0.0829983	−	0.0696438i
$285$		0			0
$286$	7.85149	+	2.85771i	0.464268	+	0.168980i
$287$	1.11232	−	1.92659i	0.0656581	−	0.113723i
$288$	3.41016	−	2.21427i	0.200946	−	0.130477i
$289$	7.85263	+	13.6012i	0.461920	+	0.800068i
$290$		0			0
$291$	3.16974	−	13.2010i	0.185814	−	0.773858i
$292$	−2.32204	+	0.845153i	−0.135887	+	0.0494588i
$293$	−1.07189	+	6.07899i	−0.0626205	+	0.355138i	0.937357	+	0.348371i	$0.113265\pi$
$293$	−1.07189	+	6.07899i	−0.0626205	+	0.355138i	−0.999977	+	0.00676709i	$0.997846\pi$
$294$	26.6671	+	11.5962i	1.55526	+	0.676306i
$295$		0			0
$296$	29.7196			1.72742
$297$	−0.190848	+	21.6268i	−0.0110742	+	1.25491i
$298$	−11.2992			−0.654545
$299$	−9.25720	+	7.76772i	−0.535358	+	0.449219i
$300$		0			0
$301$	−0.0841768	+	0.477390i	−0.00485187	+	0.0275163i
$302$	15.0470	−	5.47666i	0.865858	−	0.315147i
$303$	−17.6882	+	5.23885i	−1.01616	+	0.300964i
$304$	−4.05556	−	23.0002i	−0.232603	−	1.31915i
$305$		0			0
$306$	−1.76873	−	4.16762i	−0.101111	−	0.238247i
$307$	5.97167	−	10.3432i	0.340821	−	0.590320i	−0.643764	−	0.765224i	$-0.722628\pi$
$307$	5.97167	−	10.3432i	0.340821	−	0.590320i	0.984585	+	0.174904i	$0.0559616\pi$
$308$	−4.17861	−	1.52089i	−0.238098	−	0.0866607i
$309$	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	$0.471016\pi$
$312$	7.77717	+	0.475927i	0.440296	+	0.0269440i
$313$	−14.4140	−	5.24628i	−0.814729	−	0.296537i	−0.0991534	−	0.995072i	$-0.531613\pi$
$313$	−14.4140	−	5.24628i	−0.814729	−	0.296537i	−0.715576	+	0.698535i	$0.753836\pi$
$314$	−8.64453	+	14.9728i	−0.487839	+	0.844962i
$315$		0			0
$316$	0.588816	+	1.01986i	0.0331235	+	0.0573716i
$317$	−0.0427784	−	0.242608i	−0.00240267	−	0.0136262i	0.983583	−	0.180457i	$-0.0577577\pi$
$317$	−0.0427784	−	0.242608i	−0.00240267	−	0.0136262i	−0.985986	+	0.166831i	$0.946647\pi$
$318$	6.60396	+	6.26733i	0.370332	+	0.351455i
$319$	9.67037	−	3.51973i	0.541437	−	0.197067i
$320$		0			0
$321$	−2.38773	−	20.9629i	−0.133270	−	1.17003i
$322$	−35.9661	+	30.1791i	−2.00431	+	1.68182i
$323$	7.68055			0.427358
$324$	0.597483	+	2.08470i	0.0331935	+	0.115816i
$325$		0			0
$326$	15.4625	−	12.9746i	0.856390	−	0.718597i
$327$	0.0526675	+	0.462391i	0.00291252	+	0.0255703i
$328$	0.258955	−	1.46861i	0.0142984	−	0.0810904i
$329$	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	$-0.295995\pi$
$332$	0.438619	+	0.759710i	0.0240723	+	0.0416945i
$333$	−8.77245	+	28.6867i	−0.480727	+	1.57202i
$334$	−10.5597	+	18.2899i	−0.577801	+	1.00078i
$335$		0			0
$336$	26.5219	+	1.62301i	1.44689	+	0.0885427i
$337$	22.7032	+	19.0503i	1.23672	+	1.03773i	0.997773	+	0.0667018i	$0.0212476\pi$
$337$	22.7032	+	19.0503i	1.23672	+	1.03773i	0.238950	+	0.971032i	$0.423197\pi$
$338$	−10.8804	−	9.12976i	−0.591817	−	0.496594i
$339$	−1.60079	−	3.21096i	−0.0869431	−	0.174395i
$340$		0			0
$341$	4.43029	−	7.67349i	0.239914	−	0.415543i
$342$	26.6568	+	3.27481i	1.44144	+	0.177082i
$343$	−12.5446	−	21.7279i	−0.677344	−	1.17319i
$344$	0.0564271	+	0.320014i	0.00304235	+	0.0172540i
$345$		0			0
$346$	−15.9181	+	5.79373i	−0.855765	+	0.311473i
$347$	−5.18983	+	29.4330i	−0.278604	+	1.58004i	0.448670	+	0.893698i	$0.351898\pi$
$347$	−5.18983	+	29.4330i	−0.278604	+	1.58004i	−0.727274	+	0.686347i	$0.759213\pi$
$348$	0.829511	−	0.613764i	0.0444665	−	0.0329012i
$349$	0.356538	−	0.299171i	0.0190850	−	0.0160142i	−0.633195	−	0.773992i	$-0.718257\pi$
$349$	0.356538	−	0.299171i	0.0190850	−	0.0160142i	0.652280	+	0.757978i	$0.273813\pi$
$350$		0			0
$351$	−2.75500	+	7.36639i	−0.147051	+	0.393189i
$352$	−5.64120			−0.300677
$353$	−1.25375	+	1.05202i	−0.0667304	+	0.0559934i	−0.675543	−	0.737321i	$-0.736091\pi$
$353$	−1.25375	+	1.05202i	−0.0667304	+	0.0559934i	0.608812	+	0.793314i	$0.291646\pi$
$354$	−17.2087	−	7.48321i	−0.914631	−	0.397728i
$355$		0			0
$356$	−2.60280	+	0.947342i	−0.137948	+	0.0502090i
$357$	−2.04019	+	8.49680i	−0.107979	+	0.449699i
$358$	0.855141	+	4.84974i	0.0451956	+	0.256317i
$359$	9.42812	+	16.3300i	0.497597	+	0.861863i	0.999996	−	0.00277241i	$-0.000882486\pi$
$359$	9.42812	+	16.3300i	0.497597	+	0.861863i	−0.502399	+	0.864636i	$0.667549\pi$
$360$		0			0
$361$	−13.2811	+	23.0035i	−0.699005	+	1.21071i
$362$	−3.83107	−	1.39439i	−0.201356	−	0.0732877i
$363$	6.04618	−	9.13414i	0.317342	−	0.479418i
$364$	−1.23872	−	1.03941i	−0.0649266	−	0.0544799i
$365$		0			0
$366$	−15.6478	+	23.6395i	−0.817922	+	1.23566i
$367$	9.61068	+	3.49800i	0.501673	+	0.182594i	0.580446	−	0.814298i	$-0.302878\pi$
$367$	9.61068	+	3.49800i	0.501673	+	0.182594i	−0.0787732	+	0.996893i	$0.525100\pi$
$368$	−13.8125	+	23.9240i	−0.720029	+	1.24713i
$369$	1.34113	+	0.683450i	0.0698164	+	0.0355790i
$370$		0			0
$371$	−3.05143	−	17.3055i	−0.158422	−	0.898458i
$372$	0.207435	−	0.863905i	0.0107550	−	0.0447914i
$373$	−6.52759	+	2.37585i	−0.337986	+	0.123017i	−0.505437	−	0.862864i	$-0.668669\pi$
$373$	−6.52759	+	2.37585i	−0.337986	+	0.123017i	0.167451	+	0.985880i	$0.446446\pi$
$374$	−1.09075	+	6.18596i	−0.0564014	+	0.319868i
$375$		0			0
$376$	17.2396	−	14.4658i	0.889065	−	0.746014i
$377$	3.74223			0.192735
$378$	−10.7037	+	28.6199i	−0.550541	+	1.47205i
$379$	8.93586			0.459004			0.229502	−	0.973308i	$-0.426290\pi$
$379$	8.93586			0.459004			0.229502	+	0.973308i	$0.426290\pi$
$380$		0			0
$381$	−21.1505	+	15.6495i	−1.08357	+	0.801747i
$382$	−0.958210	+	5.43428i	−0.0490263	+	0.278042i
$383$	19.4731	−	7.08761i	0.995026	−	0.362160i	0.207362	−	0.978264i	$-0.433512\pi$
$383$	19.4731	−	7.08761i	0.995026	−	0.362160i	0.787665	+	0.616104i	$0.211290\pi$
$384$	14.6999	−	4.35378i	0.750150	−	0.222178i
$385$		0			0
$386$	2.61600	+	4.53104i	0.133151	+	0.230624i
$387$	−0.325547	−	0.0399937i	−0.0165485	−	0.00203300i
$388$	−0.944347	+	1.63566i	−0.0479419	+	0.0830379i
$389$	−5.25158	−	1.91142i	−0.266266	−	0.0969127i	0.205437	−	0.978670i	$-0.434138\pi$
$389$	−5.25158	−	1.91142i	−0.266266	−	0.0969127i	−0.471703	+	0.881758i	$0.656361\pi$
$390$		0			0
$391$	−6.95936	−	5.83960i	−0.351950	−	0.295321i
$392$	−28.8212	−	24.1839i	−1.45569	−	1.22147i
$393$	−5.86032	−	0.358624i	−0.295614	−	0.0180902i
$394$	10.8605	+	3.95291i	0.547146	+	0.199145i
$395$		0			0
$396$	0.879871	−	2.87726i	0.0442152	−	0.144588i
$397$	−6.78805	−	11.7572i	−0.340682	−	0.590079i	0.643877	−	0.765129i	$-0.277325\pi$
$397$	−6.78805	−	11.7572i	−0.340682	−	0.590079i	−0.984560	+	0.175050i	$0.943991\pi$
$398$	−3.08804	−	17.5132i	−0.154790	−	0.877856i
$399$	−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	$0.895925\pi$
$402$	−0.764180	−	6.70907i	−0.0381138	−	0.334618i
$403$	2.46826	−	2.07111i	0.122953	−	0.103169i
$404$	2.56640			0.127683
$405$		0			0
$406$	14.5393			0.721575
$407$	31.8826	−	26.7526i	1.58036	−	1.32608i
$408$	0.662914	+	5.82001i	0.0328191	+	0.288133i
$409$	1.49345	−	8.46979i	0.0738464	−	0.418804i	−0.925364	−	0.379079i	$-0.876241\pi$
$409$	1.49345	−	8.46979i	0.0738464	−	0.418804i	0.999211	−	0.0397248i	$-0.0126481\pi$
$410$		0			0
$411$	23.2752	+	22.0888i	1.14808	+	1.08956i
$412$	−0.348787	−	1.97807i	−0.0171835	−	0.0974524i
$413$	18.1094	+	31.3664i	0.891104	+	1.54344i
$414$	−21.6639	−	23.2348i	−1.06472	−	1.14193i
$415$		0			0
$416$	−1.92766	−	0.701612i	−0.0945114	−	0.0343994i
$417$	−28.7327	−	1.75831i	−1.40705	−	0.0861046i
$418$	−28.5444	−	23.9516i	−1.39615	−	1.17151i
$419$	22.8459	+	19.1700i	1.11609	+	0.936515i	0.998401	−	0.0565354i	$-0.0180054\pi$
$419$	22.8459	+	19.1700i	1.11609	+	0.936515i	0.117694	+	0.993050i	$0.462450\pi$
$420$		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	$0.579184\pi$
$422$	2.44145	−	4.22871i	0.118848	−	0.205850i
$423$	8.87430	+	20.9103i	0.431483	+	1.01670i
$424$	−5.88978	−	10.2014i	−0.286033	−	0.495423i
$425$		0			0
$426$	16.6906	−	4.94339i	0.808662	−	0.239508i
$427$	51.4168	−	18.7142i	2.48823	−	0.905643i
$428$	−0.509685	+	2.89057i	−0.0246366	+	0.139721i
$429$	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	$0.122987\pi$
$432$	−0.158650	+	17.9781i	−0.00763305	+	0.864972i
$433$	13.0726			0.628230			0.314115	−	0.949385i	$-0.398292\pi$
$433$	13.0726			0.628230			0.314115	+	0.949385i	$0.398292\pi$
$434$	9.58967	−	8.04669i	0.460319	−	0.386253i
$435$		0			0
$436$	0.0112424	−	0.0637590i	0.000538415	−	0.00305350i
$437$	50.6423	−	18.4323i	2.42255	−	0.881735i
$438$	5.50027	−	22.9070i	0.262813	−	1.09454i
$439$	1.34135	+	7.60717i	0.0640191	+	0.363071i	0.999941	+	0.0108629i	$0.00345783\pi$
$439$	1.34135	+	7.60717i	0.0640191	+	0.363071i	−0.935922	+	0.352208i	$0.885431\pi$
$440$		0			0
$441$	31.8506	−	20.6811i	1.51669	−	0.984812i
$442$	−1.14209	+	1.97815i	−0.0543236	+	0.0940912i
$443$	20.4640	+	7.44827i	0.972272	+	0.353878i	0.778831	−	0.627234i	$-0.215813\pi$
$443$	20.4640	+	7.44827i	0.972272	+	0.353878i	0.193441	+	0.981112i	$0.438035\pi$
$444$	2.30349	−	3.47994i	0.109319	−	0.165151i
$445$		0			0
$446$	−10.6983	−	8.97692i	−0.506578	−	0.425069i
$447$	−8.14481	+	12.3046i	−0.385236	+	0.581988i
$448$	−36.3211	−	13.2198i	−1.71601	−	0.624577i
$449$	−15.4280	+	26.7221i	−0.728093	+	1.26109i	0.229595	+	0.973286i	$0.426260\pi$
$449$	−15.4280	+	26.7221i	−0.728093	+	1.26109i	−0.957688	+	0.287808i	$0.907073\pi$
$450$		0			0
$451$	−1.04419	−	1.80859i	−0.0491691	−	0.0851634i
$452$	0.0866738	+	0.491552i	0.00407679	+	0.0231206i
$453$	4.88238	−	20.3336i	0.229394	−	0.955358i
$454$	33.0319	−	12.0226i	1.55026	−	0.564250i
$455$		0			0
$456$	−31.8659	−	13.8569i	−1.49226	−	0.648910i
$457$	−24.8797	+	20.8765i	−1.16382	+	0.976564i	−0.999951	−	0.00991784i	$-0.996843\pi$
$457$	−24.8797	+	20.8765i	−1.16382	+	0.976564i	−0.163872	+	0.986482i	$0.552399\pi$
$458$	−14.6355			−0.683870
$459$	−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	$0.0750685\pi$
$462$	34.0794	−	25.2157i	1.58552	−	1.17314i
$463$	1.63666	−	9.28198i	0.0760622	−	0.431370i	−0.922868	−	0.385117i	$-0.874161\pi$
$463$	1.63666	−	9.28198i	0.0760622	−	0.431370i	0.998930	−	0.0462526i	$-0.0147279\pi$
$464$	8.03886	−	2.92591i	0.373195	−	0.135832i
$465$		0			0
$466$	−3.08692	−	17.5068i	−0.142999	−	0.810986i
$467$	−19.3386	−	33.4955i	−0.894885	−	1.54999i	−0.833947	−	0.551845i	$-0.813924\pi$
$467$	−19.3386	−	33.4955i	−0.894885	−	1.54999i	−0.0609381	−	0.998142i	$-0.519409\pi$
$468$	0.658514	−	0.873759i	0.0304398	−	0.0403895i
$469$	−6.51642	+	11.2868i	−0.300900	+	0.521175i
$470$		0			0
$471$	10.0738	+	20.2065i	0.464176	+	0.931068i
$472$	18.5987	+	15.6062i	0.856075	+	0.718332i
$473$	0.348600	+	0.292510i	0.0160286	+	0.0134496i
$474$	−11.2061	−	0.685761i	−0.514713	−	0.0314981i
$475$		0			0
$476$	0.607826	−	1.05279i	0.0278596	−	0.0482543i
$477$	11.5853	−	2.67389i	0.530456	−	0.122429i
$478$	5.83451	+	10.1057i	0.266864	+	0.462223i
$479$	6.46290	+	36.6529i	0.295297	+	1.67471i	0.665992	+	0.745959i	$0.268009\pi$
$479$	6.46290	+	36.6529i	0.295297	+	1.67471i	−0.370695	+	0.928755i	$0.620880\pi$
$480$		0			0
$481$	14.2219	−	5.17636i	0.648464	−	0.236022i
$482$	−3.37571	+	19.1446i	−0.153760	+	0.872014i
$483$	6.93900	+	60.9204i	0.315735	+	2.77198i
$484$	−1.16736	+	0.979534i	−0.0530620	+	0.0445243i
$485$		0			0
$486$	−19.7169	−	6.22024i	−0.894376	−	0.282156i
$487$	−38.1901			−1.73056			−0.865279	−	0.501290i	$-0.832859\pi$
$487$	−38.1901			−1.73056			−0.865279	+	0.501290i	$0.832859\pi$
$488$	28.0976	−	23.5767i	1.27192	−	1.06727i
$489$	−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	$0.390612\pi$
$492$	−0.151892	−	0.144149i	−0.00684782	−	0.00649876i
$493$	0.488529	+	2.77059i	0.0220023	+	0.124781i
$494$	−6.77503	−	11.7347i	−0.304823	−	0.527969i
$495$		0			0
$496$	3.68285	−	6.37888i	0.165365	−	0.286420i
$497$	−31.5714	−	11.4911i	−1.41617	−	0.515445i
$498$	−8.34761	−	0.510835i	−0.374065	−	0.0228911i
$499$	−15.4596	−	12.9721i	−0.692067	−	0.580713i	0.227438	−	0.973793i	$-0.426965\pi$
$499$	−15.4596	−	12.9721i	−0.692067	−	0.580713i	−0.919504	+	0.393080i	$0.871410\pi$
$500$		0			0
$501$	12.3056	+	24.6832i	0.549774	+	1.10277i
$502$	−4.76484	−	1.73426i	−0.212665	−	0.0774037i
$503$	10.8170	−	18.7357i	0.482308	−	0.835382i	−0.517486	−	0.855692i	$-0.673132\pi$
$503$	10.8170	−	18.7357i	0.482308	−	0.835382i	0.999794	+	0.0203102i	$0.00646537\pi$
$504$	23.7941	−	31.5716i	1.05988	−	1.40631i
$505$		0			0
$506$	7.65351	+	43.4052i	0.340240	+	1.92960i
$507$	−17.7851	+	5.26755i	−0.789863	+	0.233940i
$508$	3.43953	−	1.25189i	0.152604	−	0.0555434i
$509$	−3.61621	+	20.5086i	−0.160286	+	0.909026i	0.793507	+	0.608561i	$0.208253\pi$
$509$	−3.61621	+	20.5086i	−0.160286	+	0.909026i	−0.953793	+	0.300465i	$0.902858\pi$
$510$		0			0
$511$	−34.8315	+	29.2271i	−1.54085	+	1.29293i
$512$	−25.2569			−1.11621
$513$	22.7813	−	26.6682i	1.00582	−	1.17743i
$514$	−10.8285			−0.477623
$515$		0			0
$516$	0.0418447	+	0.0181962i	0.00184211	+	0.000801043i
$517$	5.47267	−	31.0371i	0.240688	−	1.36501i
$518$	55.2551	−	20.1112i	2.42777	−	0.883635i
$519$	−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	$0.776755\pi$
$522$	0.514220	+	9.82416i	0.0225068	+	0.429992i
$523$	−10.2876	+	17.8186i	−0.449845	+	0.779154i	−0.998376	−	0.0569761i	$-0.981854\pi$
$523$	−10.2876	+	17.8186i	−0.449845	+	0.779154i	0.548531	+	0.836131i	$0.315187\pi$
$524$	0.767539	+	0.279361i	0.0335301	+	0.0122040i
$525$		0			0
$526$	−28.3133	−	23.7577i	−1.23452	−	1.03588i
$527$	1.85558	+	1.55702i	0.0808303	+	0.0678247i
$528$	13.7682	−	20.8000i	0.599185	−	0.905205i
$529$	−38.2883	−	13.9358i	−1.66471	−	0.605904i
$530$		0			0
$531$	−20.5536	+	13.3458i	−0.891951	+	0.579157i
$532$	3.60571	+	6.24528i	0.156327	+	0.270767i
$533$	−0.131872	−	0.747886i	−0.00571203	−	0.0323945i
$534$	6.16532	−	25.6767i	0.266799	−	1.11114i
$535$		0			0
$536$	−1.51707	+	8.60371i	−0.0655273	+	0.371624i
$537$	5.89768	+	2.56461i	0.254504	+	0.110671i
$538$	−13.3624	+	11.2124i	−0.576094	+	0.483400i
$539$	−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	$0.785264\pi$
$542$	8.32776	−	6.98782i	0.357708	−	0.300152i
$543$	−4.28002	+	3.16683i	−0.183673	+	0.135902i
$544$	0.267797	−	1.51875i	0.0114817	−	0.0651159i
$545$		0			0
$546$	14.7815	−	4.37794i	0.632588	−	0.187359i
$547$	−2.24700	−	12.7434i	−0.0960749	−	0.544868i	−0.994413	−	0.105563i	$-0.966336\pi$
$547$	−2.24700	−	12.7434i	−0.0960749	−	0.544868i	0.898338	−	0.439306i	$-0.144775\pi$
$548$	−2.23201	−	3.86596i	−0.0953468	−	0.165145i
$549$	14.4636	+	34.0802i	0.617290	+	1.45451i
$550$		0			0
$551$	−15.6826	−	5.70800i	−0.668101	−	0.243169i
$552$	18.3382	+	36.7837i	0.780525	+	1.56562i
$553$	16.5996	+	13.9287i	0.705887	+	0.592310i
$554$	−29.6082	−	24.8442i	−1.25793	−	1.05553i
$555$		0			0
$556$	3.76318	+	1.36969i	0.159594	+	0.0580876i
$557$	−8.28524	+	14.3505i	−0.351057	+	0.608049i	−0.986435	−	0.164153i	$-0.947511\pi$
$557$	−8.28524	+	14.3505i	−0.351057	+	0.608049i	0.635378	+	0.772201i	$0.280844\pi$
$558$	5.77627	+	6.19510i	0.244529	+	0.262260i
$559$	0.0827402	+	0.143310i	0.00349954	+	0.00606138i
$560$		0			0
$561$	5.95014	+	5.64684i	0.251215	+	0.238410i
$562$	−29.4162	+	10.7066i	−1.24085	+	0.451631i
$563$	−1.76244	+	9.99530i	−0.0742781	+	0.421252i	0.924881	+	0.380256i	$0.124164\pi$
$563$	−1.76244	+	9.99530i	−0.0742781	+	0.421252i	−0.999159	+	0.0409958i	$0.986947\pi$
$564$	−0.357634	−	3.13983i	−0.0150591	−	0.132211i
$565$		0			0
$566$	−26.1024			−1.09716
$567$	23.4509	+	32.2863i	0.984846	+	1.35590i
$568$	−22.5218			−0.944996
$569$	21.4282	−	17.9804i	0.898317	−	0.753777i	−0.0715441	−	0.997437i	$-0.522793\pi$
$569$	21.4282	−	17.9804i	0.898317	−	0.753777i	0.969861	+	0.243660i	$0.0783482\pi$
$570$		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	$0.919577\pi$
$572$	−1.42645	+	0.519185i	−0.0596428	+	0.0217082i
$573$	5.22711	+	4.96067i	0.218366	+	0.207235i
$574$	−0.512351	−	2.90569i	−0.0213851	−	0.121281i
$575$		0			0
$576$	7.64797	−	25.0095i	0.318665	−	1.04206i
$577$	1.56447	−	2.70975i	0.0651299	−	0.112808i	−0.831622	−	0.555343i	$-0.812587\pi$
$577$	1.56447	−	2.70975i	0.0651299	−	0.112808i	0.896752	+	0.442534i	$0.145920\pi$
$578$	19.5735	+	7.12418i	0.814151	+	0.296327i
$579$	6.81990	+	0.417346i	0.283426	+	0.0173443i
$580$		0			0
$581$	12.3653	+	10.3757i	0.513000	+	0.430458i
$582$	−8.03372	−	16.1145i	−0.333009	−	0.667966i
$583$	−15.5014	−	5.64204i	−0.642001	−	0.233669i
$584$	−15.2399	+	26.3964i	−0.630633	+	1.09229i
$585$		0			0
$586$	4.09344	+	7.09004i	0.169098	+	0.292887i
$587$	7.65127	+	43.3925i	0.315802	+	1.79100i	0.567688	+	0.823244i	$0.307838\pi$
$587$	7.65127	+	43.3925i	0.315802	+	1.79100i	−0.251887	+	0.967757i	$0.581051\pi$
$588$	−5.06559	+	1.50032i	−0.208902	+	0.0618720i
$589$	−13.5028	+	4.91461i	−0.556372	+	0.202503i
$590$		0			0
$591$	12.1333	−	8.97752i	0.499095	−	0.369286i
$592$	26.5036	−	22.2391i	1.08929	−	0.914023i
$593$	10.1063			0.415015			0.207507	−	0.978233i	$-0.433465\pi$
$593$	10.1063			0.415015			0.207507	+	0.978233i	$0.433465\pi$
$594$	18.2434	+	22.1354i	0.748537	+	0.908228i
$595$		0			0
$596$	1.57256	−	1.31953i	0.0644144	−	0.0540501i
$597$	−21.2974	−	9.26122i	−0.871647	−	0.379036i
$598$	−2.78313	+	15.7839i	−0.113811	+	0.645453i
$599$	1.62169	−	0.590247i	0.0662605	−	0.0241169i	−0.308677	−	0.951167i	$-0.599886\pi$
$599$	1.62169	−	0.590247i	0.0662605	−	0.0241169i	0.374938	+	0.927050i	$0.377664\pi$
$600$		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	$0.805259\pi$
$602$	0.321462	+	0.556789i	0.0131018	+	0.0226930i
$603$	−7.85688	−	4.00393i	−0.319957	−	0.163053i
$604$	−1.45458	+	2.51941i	−0.0591862	+	0.102513i
$605$		0			0
$606$	−13.5049	+	20.4022i	−0.548598	+	0.828783i
$607$	−1.55129	−	1.30168i	−0.0629648	−	0.0528337i	0.610762	−	0.791814i	$-0.290863\pi$
$607$	−1.55129	−	1.30168i	−0.0629648	−	0.0528337i	−0.673727	+	0.738980i	$0.735308\pi$
$608$	7.00810	+	5.88050i	0.284216	+	0.238486i
$609$	10.4804	−	15.8330i	0.424687	−	0.641587i
$610$		0			0
$611$	5.73024	−	9.92506i	0.231821	−	0.401525i
$612$	0.732859	+	0.373470i	0.0296241	+	0.0150966i
$613$	15.5244	+	26.8891i	0.627027	+	1.08604i	0.988145	+	0.153522i	$0.0490616\pi$
$613$	15.5244	+	26.8891i	0.627027	+	1.08604i	−0.361119	+	0.932520i	$0.617605\pi$
$614$	−2.75064	−	15.5997i	−0.111007	−	0.629551i
$615$		0			0
$616$	−51.5420	+	18.7598i	−2.07669	+	0.755852i
$617$	1.47195	−	8.34783i	0.0592584	−	0.336071i	−0.940737	−	0.339137i	$-0.889865\pi$
$617$	1.47195	−	8.34783i	0.0592584	−	0.336071i	0.999995	+	0.00306626i	$0.000976023\pi$
$618$	17.5605	+	7.63621i	0.706388	+	0.307174i
$619$	−32.3309	+	27.1288i	−1.29949	+	1.09040i	−0.309255	+	0.950979i	$0.600080\pi$
$619$	−32.3309	+	27.1288i	−1.29949	+	1.09040i	−0.990233	+	0.139421i	$0.955476\pi$
$620$		0			0
$621$	−40.9182	+	6.84325i	−1.64199	+	0.274610i
$622$	33.2027			1.33131
$623$	−39.0430	+	32.7610i	−1.56422	+	1.31254i
$624$	7.29171	−	5.39522i	0.291902	−	0.215982i
$625$		0			0
$626$	−19.1172	+	6.95808i	−0.764076	+	0.278101i
$627$	−46.6586	+	13.8192i	−1.86336	+	0.551887i
$628$	−0.545438	−	3.09333i	−0.0217654	−	0.123437i
$629$	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	$-0.0270573\pi$
$632$	13.6498	+	4.96811i	0.542959	+	0.197621i
$633$	−2.84511	−	5.70687i	−0.113083	−	0.226828i
$634$	−0.250291	−	0.210019i	−0.00994034	−	0.00834094i
$635$		0			0
$636$	−1.65100	−	0.101034i	−0.0654666	−	0.00400625i
$637$	−18.0042	−	6.55298i	−0.713351	−	0.259638i
$638$	6.82442	−	11.8202i	0.270181	−	0.467968i
$639$	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	$-0.172218\pi$
$642$	−20.2972	−	19.2626i	−0.801069	−	0.760235i
$643$	14.9832	−	5.45343i	0.590879	−	0.215062i	−0.0292372	−	0.999573i	$-0.509308\pi$
$643$	14.9832	−	5.45343i	0.590879	−	0.215062i	0.620116	+	0.784510i	$0.287086\pi$
$644$	1.48120	−	8.40031i	0.0583675	−	0.331018i
$645$		0			0
$646$	7.80341	−	6.54784i	0.307021	−	0.257621i
$647$	−13.7644			−0.541133			−0.270567	−	0.962701i	$-0.587211\pi$
$647$	−13.7644			−0.541133			−0.270567	+	0.962701i	$0.587211\pi$
$648$	22.1743	+	14.9610i	0.871090	+	0.587723i
$649$	34.0004			1.33463
$650$		0			0
$651$	−1.85015	−	16.2433i	−0.0725131	−	0.636624i
$652$	−0.636797	+	3.61146i	−0.0249389	+	0.141436i
$653$	−15.9602	+	5.80905i	−0.624573	+	0.227326i	−0.634867	−	0.772621i	$-0.718945\pi$
$653$	−15.9602	+	5.80905i	−0.624573	+	0.227326i	0.0102948	+	0.999947i	$0.496723\pi$
$654$	0.447708	+	0.424887i	0.0175068	+	0.0166144i
$655$		0			0
$656$	−0.868024	−	1.50346i	−0.0338907	−	0.0587003i
$657$	−20.9805	−	22.5018i	−0.818527	−	0.877877i
$658$	22.2631	−	38.5609i	0.867907	−	1.50326i
$659$	10.6118	+	3.86239i	0.413378	+	0.150457i	0.540333	−	0.841451i	$-0.318298\pi$
$659$	10.6118	+	3.86239i	0.413378	+	0.150457i	−0.126955	+	0.991908i	$0.540520\pi$
$660$		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	$0.743491\pi$
$662$	−25.3441	−	21.2662i	−0.985027	−	0.826535i
$663$	1.33092	+	2.66962i	0.0516885	+	0.103680i
$664$	10.1679	+	3.70083i	0.394592	+	0.143620i
$665$		0			0
$666$	15.5433	+	36.6243i	0.602289	+	1.41916i
$667$	9.87018	+	17.0957i	0.382175	+	0.661946i
$668$	−0.666279	−	3.77865i	−0.0257791	−	0.146201i
$669$	−17.4873	+	5.17936i	−0.676099	+	0.200246i
$670$		0			0
$671$	8.91950	−	50.5850i	0.344334	−	1.95281i
$672$	−8.36702	+	6.19084i	−0.322765	+	0.238817i
$673$	20.0688	−	16.8397i	0.773595	−	0.649123i	−0.168032	−	0.985782i	$-0.553741\pi$
$673$	20.0688	−	16.8397i	0.773595	−	0.649123i	0.941627	+	0.336658i	$0.109297\pi$
$674$	39.3071			1.51405
$675$		0			0
$676$	2.58045			0.0992482
$677$	−14.4837	+	12.1532i	−0.556653	+	0.467087i	−0.877186	−	0.480150i	$-0.840582\pi$
$677$	−14.4837	+	12.1532i	−0.556653	+	0.467087i	0.320534	+	0.947237i	$0.396138\pi$
$678$	−4.36381	−	1.89761i	−0.167591	−	0.0728772i
$679$	−6.03484	+	34.2253i	−0.231596	+	1.31345i
$680$		0			0
$681$	10.7180	−	44.6373i	0.410715	−	1.71051i
$682$	−2.04066	−	11.5732i	−0.0781409	−	0.443159i
$683$	−12.2251	−	21.1745i	−0.467782	−	0.810222i	0.531541	−	0.847033i	$-0.321613\pi$
$683$	−12.2251	−	21.1745i	−0.467782	−	0.810222i	−0.999322	+	0.0368112i	$0.988280\pi$
$684$	−4.09238	+	2.65724i	−0.156476	+	0.101602i
$685$		0			0
$686$	−31.2687	−	11.3809i	−1.19385	−	0.434524i
$687$	−10.5497	+	15.9377i	−0.402496	+	0.608062i
$688$	0.289787	+	0.243160i	0.0110480	+	0.00927039i
$689$	−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	$0.494199\pi$
$692$	1.53880	−	2.66527i	0.0584962	−	0.101318i
$693$	−2.89391	−	55.2880i	−0.109931	−	2.10022i
$694$	19.8194	+	34.3282i	0.752334	+	1.30308i
$695$		0			0
$696$	2.97171	−	12.3763i	0.112642	−	0.469122i
$697$	0.536487	−	0.195265i	0.0203209	−	0.00739620i
$698$	0.107191	−	0.607913i	0.00405725	−	0.0230098i
$699$	−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	$0.635542\pi$
$702$	3.48094	+	9.83292i	0.131380	+	0.371120i
$703$	−67.4954			−2.54564
$704$	−27.7957	+	23.3234i	−1.04759	+	0.879034i
$705$		0			0
$706$	−0.376934	+	2.13770i	−0.0141861	+	0.0804533i
$707$	44.3755	−	16.1514i	1.66891	−	0.607435i
$708$	3.26890	−	0.968175i	0.122853	−	0.0363863i
$709$	−5.59910	−	31.7541i	−0.210279	−	1.19255i	−0.888914	−	0.458074i	$-0.848539\pi$
$709$	−5.59910	−	31.7541i	−0.210279	−	1.19255i	0.678636	−	0.734475i	$-0.262572\pi$
$710$		0			0
$711$	−8.82449	+	11.7089i	−0.330944	+	0.439118i
$712$	−17.0826	+	29.5880i	−0.640198	+	1.10886i
$713$	15.9715	+	5.81315i	0.598138	+	0.217704i
$714$	5.17088	+	10.3720i	0.193515	+	0.388163i
$715$		0			0
$716$	−0.685371	−	0.575094i	−0.0256135	−	0.0214923i
$717$	15.2106	+	0.930816i	0.568049	+	0.0347620i
$718$	23.5006	+	8.55352i	0.877035	+	0.319214i
$719$	21.9733	−	38.0589i	0.819467	−	1.41936i	−0.0866093	−	0.996242i	$-0.527603\pi$
$719$	21.9733	−	38.0589i	0.819467	−	1.41936i	0.906076	−	0.423115i	$-0.139063\pi$
$720$		0			0
$721$	−18.4796	−	32.0077i	−0.688218	−	1.19203i
$722$	6.11747	+	34.6939i	0.227669	+	1.29117i
$723$	18.4148	+	17.4761i	0.684854	+	0.649944i
$724$	0.696024	−	0.253332i	0.0258675	−	0.00941501i
$725$		0			0
$726$	−1.64416	−	14.4347i	−0.0610203	−	0.535724i
$727$	−6.81176	+	5.71575i	−0.252634	+	0.211985i	−0.760306	−	0.649565i	$-0.774951\pi$
$727$	−6.81176	+	5.71575i	−0.252634	+	0.211985i	0.507671	+	0.861551i	$0.330506\pi$
$728$	−19.9457			−0.739237
$729$	−20.9863	+	16.9875i	−0.777269	+	0.629168i
$730$		0			0
$731$	−0.0952994	+	0.0799657i	−0.00352478	+	0.00295764i
$732$	−0.582882	−	5.11737i	−0.0215439	−	0.189143i
$733$	0.294938	−	1.67268i	0.0108938	−	0.0617818i	−0.978876	−	0.204454i	$-0.934458\pi$
$733$	0.294938	−	1.67268i	0.0108938	−	0.0617818i	0.989770	+	0.142672i	$0.0455694\pi$
$734$	12.7465	−	4.63936i	0.470483	−	0.171242i
$735$		0			0
$736$	−1.87906	−	10.6567i	−0.0692629	−	0.392809i
$737$	6.11730	+	10.5955i	0.225334	+	0.390289i
$738$	1.94524	−	0.448960i	0.0716052	−	0.0165265i
$739$	−20.4924	+	35.4939i	−0.753826	+	1.30566i	0.192130	+	0.981369i	$0.438460\pi$
$739$	−20.4924	+	35.4939i	−0.753826	+	1.30566i	−0.945956	+	0.324295i	$0.894873\pi$
$740$		0			0
$741$	−17.6625	−	1.08086i	−0.648848	−	0.0397065i
$742$	−17.8536	−	14.9809i	−0.655426	−	0.549967i
$743$	−40.7602	−	34.2019i	−1.49535	−	1.25475i	−0.887600	−	0.460614i	$-0.847629\pi$
$743$	−40.7602	−	34.2019i	−1.49535	−	1.25475i	−0.607747	−	0.794131i	$-0.707926\pi$
$744$	−4.88953	−	9.80767i	−0.179259	−	0.359567i
$745$		0			0
$746$	−4.60655	+	7.97877i	−0.168658	+	0.292124i
$747$	−6.57351	+	8.72215i	−0.240512	+	0.319127i
$748$	−0.570598	−	0.988304i	−0.0208631	−	0.0361360i
$749$	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	$0.291594\pi$
$752$	4.54937	−	25.8007i	0.165898	−	0.940856i
$753$	−5.32321	+	3.93870i	−0.193989	+	0.143534i
$754$	3.80210	−	3.19034i	0.138464	−	0.116185i
$755$		0			0
$756$	−1.85258	−	5.23314i	−0.0673775	−	0.190327i
$757$	−5.75782			−0.209271			−0.104636	−	0.994511i	$-0.533368\pi$
$757$	−5.75782			−0.209271			−0.104636	+	0.994511i	$0.533368\pi$
$758$	9.07880	−	7.61802i	0.329757	−	0.276699i
$759$	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	$0.626249\pi$
$762$	−8.14730	+	33.9311i	−0.295145	+	1.22919i
$763$	−0.206869	−	1.17321i	−0.00748914	−	0.0424730i
$764$	−0.501262	−	0.868212i	−0.0181350	−	0.0314108i
$765$		0			0
$766$	13.7422	−	23.8022i	0.496526	−	0.860008i
$767$	11.6183	+	4.22873i	0.419514	+	0.152690i
$768$	−5.44525	+	8.22630i	−0.196489	+	0.296841i
$769$	13.8998	+	11.6633i	0.501239	+	0.420589i	0.858034	−	0.513593i	$-0.171686\pi$
$769$	13.8998	+	11.6633i	0.501239	+	0.420589i	−0.356795	+	0.934183i	$0.616130\pi$
$770$		0			0
$771$	−7.80549	+	11.7920i	−0.281108	+	0.424678i
$772$	−0.893218	−	0.325105i	−0.0321476	−	0.0117008i
$773$	−11.0792	+	19.1897i	−0.398490	+	0.690206i	−0.993540	−	0.113483i	$-0.963799\pi$
$773$	−11.0792	+	19.1897i	−0.398490	+	0.690206i	0.595049	+	0.803689i	$0.297132\pi$
$774$	−0.364850	+	0.236903i	−0.0131143	+	0.00851530i
$775$		0			0
$776$	4.04540	+	22.9426i	0.145221	+	0.823591i
$777$	17.9289	−	74.6684i	0.643195	−	2.67871i
$778$	−6.96511	+	2.53509i	−0.249711	+	0.0908874i
$779$	−0.588106	+	3.33531i	−0.0210711	+	0.119500i
$780$		0			0
$781$	−24.1609	+	20.2734i	−0.864546	+	0.725440i
$782$	−12.0491			−0.430874
$783$	11.0690	+	6.52158i	0.395573	+	0.233062i
$784$	−43.7991			−1.56425
$785$		0			0
$786$	−6.25980	+	4.63169i	−0.223280	+	0.165207i
$787$	−2.02055	+	11.4591i	−0.0720248	+	0.408473i	0.927385	+	0.374109i	$0.122051\pi$
$787$	−2.02055	+	11.4591i	−0.0720248	+	0.408473i	−0.999409	+	0.0343635i	$0.989060\pi$
$788$	−1.97313	+	0.718160i	−0.0702898	+	0.0255834i
$789$	−46.2807	+	13.7073i	−1.64764	+	0.487994i
$790$		0			0
$791$	4.59221	+	7.95394i	0.163280	+	0.282810i
$792$	−14.4988	−	34.1632i	−0.515192	−	1.21394i
$793$	9.33929	−	16.1761i	0.331648	−	0.574431i
$794$	−16.9199	−	6.15835i	−0.600466	−	0.218552i
$795$		0			0
$796$	2.47498	+	2.07675i	0.0877233	+	0.0736086i
$797$	−41.6719	−	34.9669i	−1.47610	−	1.23859i	−0.910236	−	0.414090i	$-0.864100\pi$
$797$	−41.6719	−	34.9669i	−1.47610	−	1.23859i	−0.565860	−	0.824501i	$-0.691456\pi$
$798$	−68.6224	−	4.19937i	−2.42921	−	0.148656i
$799$	8.09614	+	2.94675i	0.286421	+	0.104249i
$800$		0			0
$801$	−23.5173	−	25.2225i	−0.830942	−	0.891192i
$802$	12.7679	+	22.1146i	0.450849	+	0.780893i
$803$	7.41206	+	42.0359i	0.261566	+	1.48341i
$804$	0.889845	+	0.844486i	0.0313824	+	0.0297827i
$805$		0			0
$806$	0.742069	−	4.20848i	0.0261383	−	0.148238i
$807$	2.57803	+	22.6336i	0.0907509	+	0.796741i
$808$	24.2497	−	20.3480i	0.853103	−	0.715838i
$809$	−9.51410			−0.334498			−0.167249	−	0.985915i	$-0.553488\pi$
$809$	−9.51410			−0.334498			−0.167249	+	0.985915i	$0.553488\pi$
$810$		0			0
$811$	−16.3207			−0.573098			−0.286549	−	0.958066i	$-0.592508\pi$
$811$	−16.3207			−0.573098			−0.286549	+	0.958066i	$0.592508\pi$
$812$	−2.02350	+	1.69792i	−0.0710109	+	0.0595852i
$813$	−1.60669	−	14.1058i	−0.0563490	−	0.494712i
$814$	9.58534	−	54.3611i	0.335966	−	1.90536i
$815$		0			0
$816$	4.94628	+	4.69415i	0.173154	+	0.164328i
$817$	−0.128150	−	0.726774i	−0.00448340	−	0.0254266i
$818$	−5.70334	−	9.87847i	−0.199413	−	0.345393i
$819$	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	$0.518889\pi$
$822$	42.4787	+	2.59950i	1.48161	+	0.0906679i
$823$	1.62199	+	1.36101i	0.0565391	+	0.0474419i	0.670619	−	0.741802i	$-0.266028\pi$
$823$	1.62199	+	1.36101i	0.0565391	+	0.0474419i	−0.614080	+	0.789244i	$0.710473\pi$
$824$	−18.9790	−	15.9253i	−0.661164	−	0.554783i
$825$		0			0
$826$	45.1396	+	16.4295i	1.57061	+	0.571654i
$827$	−9.52304	+	16.4944i	−0.331148	+	0.573566i	−0.982737	−	0.185006i	$-0.940769\pi$
$827$	−9.52304	+	16.4944i	−0.331148	+	0.573566i	0.651589	+	0.758572i	$0.274103\pi$
$828$	5.72843	+	0.703742i	0.199077	+	0.0244567i
$829$	−14.7459	−	25.5407i	−0.512148	−	0.887066i	−0.999901	−	0.0140841i	$-0.995517\pi$
$829$	−14.7459	−	25.5407i	−0.512148	−	0.887066i	0.487753	−	0.872982i	$-0.337817\pi$
$830$		0			0
$831$	−48.3973	+	14.3342i	−1.67889	+	0.497249i
$832$	−12.3989	+	4.51284i	−0.429855	+	0.156454i
$833$	2.50119	−	14.1850i	0.0866611	−	0.491480i
$834$	−30.6913	+	22.7088i	−1.06275	+	0.786342i
$835$		0			0
$836$	6.76974			0.234136
$837$	10.9101	−	1.82462i	0.377107	−	0.0630681i
$838$	39.5542			1.36638
$839$	20.6987	−	17.3682i	0.714597	−	0.599618i	−0.211288	−	0.977424i	$-0.567766\pi$
$839$	20.6987	−	17.3682i	0.714597	−	0.599618i	0.925885	+	0.377806i	$0.123321\pi$
$840$		0			0
$841$	−3.97427	+	22.5392i	−0.137044	+	0.777214i
$842$	5.12126	−	1.86399i	0.176490	−	0.0642372i
$843$	−9.54481	+	39.7513i	−0.328741	+	1.36911i
$844$	0.154046	+	0.873641i	0.00530250	+	0.0300719i
$845$		0			0
$846$	26.8428	+	13.6793i	0.922874	+	0.470303i
$847$	−14.0203	+	24.2838i	−0.481742	+	0.834401i
$848$	−12.8861	−	4.69016i	−0.442511	−	0.161061i
$849$	−18.8154	+	28.4250i	−0.645743	+	0.975542i
$850$		0			0
$851$	61.1576	+	51.3174i	2.09646	+	1.75914i
$852$	−1.74560	+	2.63713i	−0.0598034	+	0.0903467i
$853$	6.30921	+	2.29637i	0.216023	+	0.0786260i	0.447765	−	0.894151i	$-0.352220\pi$
$853$	6.30921	+	2.29637i	0.216023	+	0.0786260i	−0.231742	+	0.972777i	$0.574442\pi$
$854$	36.2850	−	62.8475i	1.24165	−	2.15060i
$855$		0			0
$856$	18.1022	+	31.3539i	0.618721	+	1.07166i
$857$	−1.13853	−	6.45695i	−0.0388916	−	0.220565i	0.959168	−	0.282839i	$-0.0912761\pi$
$857$	−1.13853	−	6.45695i	−0.0388916	−	0.220565i	−0.998059	+	0.0622733i	$0.980165\pi$
$858$	3.37887	−	14.0720i	0.115353	−	0.480409i
$859$	46.0053	−	16.7446i	1.56968	−	0.571317i	0.596752	−	0.802426i	$-0.296458\pi$
$859$	46.0053	−	16.7446i	1.56968	−	0.571317i	0.972928	+	0.231109i	$0.0742354\pi$
$860$		0			0
$861$	−3.53355	−	1.53657i	−0.120423	−	0.0523662i
$862$	39.0754	−	32.7882i	1.33091	−	1.11677i
$863$	24.9816			0.850383			0.425192	−	0.905103i	$-0.360207\pi$
$863$	24.9816			0.850383			0.425192	+	0.905103i	$0.360207\pi$
$864$	−4.47904	−	5.43460i	−0.152380	−	0.184889i
$865$		0			0
$866$	13.2817	−	11.1447i	0.451332	−	0.378712i
$867$	21.8673	−	16.1798i	0.742652	−	0.549496i
$868$	−0.394934	+	2.23978i	−0.0134049	+	0.0760231i
$869$	19.1153	−	6.95739i	0.648442	−	0.236013i
$870$		0			0
$871$	0.772563	+	4.38142i	0.0261773	+	0.148459i
$872$	−0.399291	−	0.691592i	−0.0135217	−	0.0234203i
$873$	−23.3393	−	2.86725i	−0.789915	−	0.0970417i
$874$	35.7384	−	61.9007i	1.20887	−	2.09382i
$875$		0			0
$876$	1.90960	+	3.83039i	0.0645195	+	0.129417i
$877$	−3.01099	−	2.52652i	−0.101674	−	0.0853144i	0.590534	−	0.807013i	$-0.298917\pi$
$877$	−3.01099	−	2.52652i	−0.101674	−	0.0853144i	−0.692208	+	0.721699i	$0.743362\pi$
$878$	7.84809	+	6.58533i	0.264860	+	0.222244i
$879$	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	$0.101029\pi$
$882$	14.7290	−	48.1652i	0.495951	−	1.62181i
$883$	−8.72154	−	15.1061i	−0.293503	−	0.508362i	0.681132	−	0.732160i	$-0.261488\pi$
$883$	−8.72154	−	15.1061i	−0.293503	−	0.508362i	−0.974636	+	0.223798i	$0.928154\pi$
$884$	−0.0720616	−	0.408682i	−0.00242369	−	0.0137454i
$885$		0			0
$886$	27.1411	−	9.87856i	0.911823	−	0.331877i
$887$	−6.80216	+	38.5770i	−0.228394	+	1.29529i	0.627695	+	0.778460i	$0.283999\pi$
$887$	−6.80216	+	38.5770i	−0.228394	+	1.29529i	−0.856089	+	0.516828i	$0.827113\pi$
$888$	−5.82557	−	51.1452i	−0.195493	−	1.71632i
$889$	51.5942	−	43.2927i	1.73041	−	1.45199i
$890$		0			0
$891$	37.2555	−	3.91080i	1.24811	−	0.131017i
$892$	2.53725			0.0849535
$893$	−39.1524	+	32.8527i	−1.31018	+	1.09937i
$894$	2.21484	+	19.4451i	0.0740754	+	0.650340i
$895$		0			0
$896$	−36.8786	+	13.4227i	−1.23203	+	0.448421i
$897$	15.1822	+	14.4083i	0.506920	+	0.481080i
$898$	7.10638	+	40.3023i	0.237143	+	1.34491i
$899$	−2.63169	−	4.55823i	−0.0877719	−	0.152025i
$900$		0			0
$901$	2.25485	−	3.90551i	0.0751199	−	0.130111i
$902$	−2.60276	−	0.947327i	−0.0866625	−	0.0315426i
$903$	0.838052	+	0.0512849i	0.0278886	+	0.00170665i
$904$	4.71630	+	3.95744i	0.156862	+	0.131623i
$905$		0			0
$906$	−12.3744	−	24.8212i	−0.411112	−	0.824630i
$907$	−27.8001	−	10.1184i	−0.923088	−	0.335977i	−0.163622	−	0.986523i	$-0.552318\pi$
$907$	−27.8001	−	10.1184i	−0.923088	−	0.335977i	−0.759466	+	0.650546i	$0.774540\pi$
$908$	−3.19317	+	5.53073i	−0.105969	+	0.183544i
$909$	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	$-0.332743\pi$
$912$	−38.7867	+	11.4878i	−1.28436	+	0.380398i
$913$	14.2393	−	5.18268i	0.471252	−	0.171522i
$914$	−7.47996	+	42.4210i	−0.247415	+	1.40316i
$915$		0			0
$916$	2.03688	−	1.70914i	0.0673003	−	0.0564716i
$917$	15.0297			0.496323
$918$	−6.82545	+	3.86077i	−0.225273	+	0.127424i
$919$	3.32517			0.109687			0.0548435	−	0.998495i	$-0.482534\pi$
$919$	3.32517			0.109687			0.0548435	+	0.998495i	$0.482534\pi$
$920$		0			0
$921$	−18.9705	−	8.24933i	−0.625098	−	0.271825i
$922$	5.88098	−	33.3527i	0.193680	−	1.09841i
$923$	−10.7775	+	3.92270i	−0.354746	+	0.129117i
$924$	−1.79825	+	7.48919i	−0.0591582	+	0.246376i
$925$		0			0
$926$	−6.25025	−	10.8257i	−0.205396	−	0.355756i
$927$	20.9739	−	13.6186i	0.688872	−	0.447295i
$928$	−1.67550	+	2.90205i	−0.0550010	+	0.0952645i
$929$	5.41753	+	1.97182i	0.177743	+	0.0646933i	0.429359	−	0.903134i	$-0.358740\pi$
$929$	5.41753	+	1.97182i	0.177743	+	0.0646933i	−0.251615	+	0.967827i	$0.580962\pi$
$930$		0			0
$931$	65.4549	+	54.9232i	2.14520	+	1.80004i
$932$	2.47408	+	2.07600i	0.0810411	+	0.0680016i
$933$	23.9335	−	36.1571i	0.783549	−	1.18373i
$934$	−48.2036	−	17.5447i	−1.57727	−	0.574079i
$935$		0			0
$936$	−0.705430	−	13.4772i	−0.0230577	−	0.440516i
$937$	13.3901	+	23.1923i	0.437436	+	0.757661i	0.997491	−	0.0707946i	$-0.0225535\pi$
$937$	13.3901	+	23.1923i	0.437436	+	0.757661i	−0.560055	+	0.828455i	$0.689220\pi$
$938$	3.00156	+	17.0227i	0.0980045	+	0.555811i
$939$	−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	$0.825351\pi$
$942$	27.4614	+	11.9416i	0.894742	+	0.389080i
$943$	3.06875	−	2.57499i	0.0999324	−	0.0838532i
$944$	28.2642			0.919920
$945$		0			0
$946$	0.603547			0.0196230
$947$	5.40097	−	4.53195i	0.175508	−	0.147269i	−0.550802	−	0.834636i	$-0.685678\pi$
$947$	5.40097	−	4.53195i	0.175508	−	0.147269i	0.726310	+	0.687367i	$0.241234\pi$
$948$	1.63968	−	1.21322i	0.0532544	−	0.0394035i
$949$	−2.69533	+	15.2860i	−0.0874942	+	0.496204i
$950$		0			0
$951$	−0.409125	+	0.121174i	−0.0132668	+	0.00392933i
$952$	−2.60381	−	14.7669i	−0.0843899	−	0.478599i
$953$	10.6923	+	18.5197i	0.346359	+	0.599911i	0.985600	−	0.169095i	$-0.0540846\pi$
$953$	10.6923	+	18.5197i	0.346359	+	0.599911i	−0.639241	+	0.769007i	$0.720751\pi$
$954$	9.49110	−	12.5934i	0.307286	−	0.407727i
$955$		0			0
$956$	−1.99216	−	0.725088i	−0.0644311	−	0.0234510i
$957$	−7.95275	−	15.9520i	−0.257076	−	0.515656i
$958$	37.8137	+	31.7294i	1.22170	+	1.02513i
$959$	−62.9237	−	52.7993i	−2.03191	−	1.70498i
$960$		0			0
$961$	24.8720	+	9.05266i	0.802322	+	0.292021i
$962$	10.0365	−	17.3837i	0.323589	−	0.560472i
$963$	−35.6075	+	8.21819i	−1.14744	+	0.264828i
$964$	−1.76591	−	3.05865i	−0.0568763	−	0.0985126i
$965$		0			0
$966$	58.9860	+	55.9793i	1.89784	+	1.80110i
$967$	30.8331	−	11.2223i	0.991527	−	0.360886i	0.205216	−	0.978717i	$-0.434210\pi$
$967$	30.8331	−	11.2223i	0.991527	−	0.360886i	0.786311	+	0.617831i	$0.211988\pi$
$968$	−3.26401	+	18.5111i	−0.104909	+	0.594970i
$969$	−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	$0.489194\pi$
$972$	3.47048	−	1.43686i	0.111316	−	0.0460873i
$973$	73.6892			2.36237
$974$	−38.8010	+	32.5579i	−1.24326	+	1.04322i
$975$		0			0
$976$	7.41468	−	42.0507i	0.237338	−	1.34601i
$977$	16.9431	−	6.16678i	0.542058	−	0.197293i	−0.0564564	−	0.998405i	$-0.517980\pi$
$977$	16.9431	−	6.16678i	0.542058	−	0.197293i	0.598514	+	0.801112i	$0.295758\pi$
$978$	−25.3592	−	24.0666i	−0.810899	−	0.769564i
$979$	8.30826	+	47.1185i	0.265533	+	1.50591i
$980$		0			0
$981$	0.785415	−	0.181274i	0.0250764	−	0.00578762i
$982$	−0.159096	+	0.275562i	−0.00507696	+	0.00879355i
$983$	−17.3223	−	6.30480i	−0.552496	−	0.201092i	0.0506592	−	0.998716i	$-0.483868\pi$
$983$	−17.3223	−	6.30480i	−0.552496	−	0.201092i	−0.603155	+	0.797624i	$0.706090\pi$
$984$	−2.57812	−	0.157769i	−0.0821876	−	0.00502950i
$985$		0			0
$986$	2.85833	+	2.39842i	0.0910278	+	0.0763814i
$987$	−25.9441	−	52.0400i	−0.825808	−	1.65645i
$988$	2.31330	+	0.841971i	0.0735958	+	0.0267867i
$989$	−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	$-0.355076\pi$
$992$	0.501014	+	2.84139i	0.0159072	+	0.0902143i
$993$	−41.4273	+	12.2699i	−1.31466	+	0.389372i
$994$	−41.8728	+	15.2405i	−1.32813	+	0.483398i
$995$		0			0
$996$	1.22143	−	0.903746i	0.0387024	−	0.0286363i
$997$	13.4706	−	11.3032i	0.426620	−	0.357976i	−0.404055	−	0.914735i	$-0.632400\pi$
$997$	13.4706	−	11.3032i	0.426620	−	0.357976i	0.830674	+	0.556758i	$0.187955\pi$
$998$	−26.7659			−0.847261
$999$	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.l.g.76.8	yes	66
5.2	odd	4		675.2.u.e.49.16		132
5.3	odd	4		675.2.u.e.49.7		132
5.4	even	2		675.2.l.f.76.4	✓	66
27.16	even	9	inner	675.2.l.g.151.8	yes	66
135.43	odd	36		675.2.u.e.124.16		132
135.97	odd	36		675.2.u.e.124.7		132
135.124	even	18		675.2.l.f.151.4	yes	66

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

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.l (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(1.01600 - 0.852522i) q^{2} +(-0.196018 - 1.72092i) q^{3} +(-0.0418420 + 0.237298i) q^{4} +(-1.66628 - 1.58134i) q^{6} +(0.769922 + 4.36644i) q^{7} +(1.48608 + 2.57396i) q^{8} +(-2.92315 + 0.674663i) q^{9} +(3.91123 + 1.42357i) q^{11} +(0.416573 + 0.0254923i) q^{12} +(1.15946 + 0.972900i) q^{13} +(4.50473 + 3.77991i) q^{14} +(3.25136 + 1.18340i) q^{16} +(-0.568932 + 0.985419i) q^{17} +(-2.39475 + 3.17751i) q^{18} +(-3.37499 - 5.84565i) q^{19} +(7.36340 - 2.18088i) q^{21} +(5.18742 - 1.88807i) q^{22} +(-1.38642 + 7.86279i) q^{23} +(4.13830 - 3.06197i) q^{24} +2.00742 q^{26} +(1.73403 + 4.89828i) q^{27} -1.06836 q^{28} +(1.89402 - 1.58927i) q^{29} +(0.369663 - 2.09646i) q^{31} +(-1.27359 + 0.463549i) q^{32} +(1.68319 - 7.00997i) q^{33} +(0.262059 + 1.48621i) q^{34} +(-0.0377853 - 0.721887i) q^{36} +(4.99967 - 8.65969i) q^{37} +(-8.41252 - 3.06191i) q^{38} +(1.44701 - 2.18604i) q^{39} +(-0.384359 - 0.322515i) q^{41} +(5.62194 - 8.49322i) q^{42} +(0.102738 + 0.0373936i) q^{43} +(-0.501464 + 0.868561i) q^{44} +(5.29460 + 9.17051i) q^{46} +(-1.31484 - 7.45681i) q^{47} +(1.39921 - 5.82730i) q^{48} +(-11.8952 + 4.32950i) q^{49} +(1.80735 + 0.785929i) q^{51} +(-0.279381 + 0.234429i) q^{52} -3.96330 q^{53} +(5.93766 + 3.49833i) q^{54} +(-10.0949 + 8.47063i) q^{56} +(-9.39836 + 6.95395i) q^{57} +(0.569427 - 3.22938i) q^{58} +(7.67614 - 2.79389i) q^{59} +(-2.14296 - 12.1533i) q^{61} +(-1.41170 - 2.44514i) q^{62} +(-5.19648 - 12.2444i) q^{63} +(-4.35880 + 7.54966i) q^{64} +(-4.26604 - 8.55705i) q^{66} +(2.25173 + 1.88943i) q^{67} +(-0.210033 - 0.176238i) q^{68} +(13.8030 + 0.844680i) q^{69} +(-3.78880 + 6.56240i) q^{71} +(-6.08060 - 6.52149i) q^{72} +(5.12757 + 8.88121i) q^{73} +(-2.30293 - 13.0605i) q^{74} +(1.52838 - 0.556283i) q^{76} +(-3.20460 + 18.1742i) q^{77} +(-0.393490 - 3.45462i) q^{78} +(3.74388 - 3.14149i) q^{79} +(8.08966 - 3.94429i) q^{81} -0.665459 q^{82} +(2.78888 - 2.34014i) q^{83} +(0.209418 + 1.83857i) q^{84} +(0.136260 - 0.0495947i) q^{86} +(-3.10627 - 2.94793i) q^{87} +(2.14817 + 12.1829i) q^{88} +(5.74755 + 9.95505i) q^{89} +(-3.35542 + 5.81176i) q^{91} +(-1.80781 - 0.657989i) q^{92} +(-3.68031 - 0.225218i) q^{93} +(-7.69297 - 6.45516i) q^{94} +(1.04738 + 2.10089i) q^{96} +(7.36555 + 2.68084i) q^{97} +(-8.39449 + 14.5397i) q^{98} +(-12.3936 - 1.52256i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 66 q + 6 q^{2} - 6 q^{6} + 6 q^{7} + 12 q^{8} - 6 q^{9} + 15 q^{11} + 18 q^{12} + 15 q^{14} + 18 q^{16} + 30 q^{17} - 12 q^{18} + 12 q^{19} + 12 q^{21} - 45 q^{22} + 36 q^{23} - 39 q^{24} + 6 q^{26} + 51 q^{27}+ \cdots - 48 q^{99}+O(q^{100}) \) 66 * q + 6 * q^2 - 6 * q^6 + 6 * q^7 + 12 * q^8 - 6 * q^9 + 15 * q^11 + 18 * q^12 + 15 * q^14 + 18 * q^16 + 30 * q^17 - 12 * q^18 + 12 * q^19 + 12 * q^21 - 45 * q^22 + 36 * q^23 - 39 * q^24 + 6 * q^26 + 51 * q^27 - 36 * q^28 - 15 * q^29 + 3 * q^31 + 27 * q^32 - 3 * q^33 + 30 * q^36 + 6 * q^37 - 12 * q^38 - 15 * q^39 + 39 * q^41 + 48 * q^42 + 12 * q^43 + 51 * q^44 + 9 * q^46 + 30 * q^47 - 132 * q^48 - 6 * q^49 + 9 * q^52 - 24 * q^53 + 75 * q^54 + 144 * q^56 + 33 * q^57 + 27 * q^58 + 45 * q^59 - 54 * q^61 + 66 * q^62 - 120 * q^63 - 24 * q^64 + 48 * q^66 + 9 * q^67 - 69 * q^68 + 51 * q^69 - 15 * q^71 + 9 * q^72 - 15 * q^73 + 96 * q^74 - 48 * q^76 - 36 * q^77 - 18 * q^78 + 48 * q^79 - 54 * q^81 - 36 * q^82 + 30 * q^83 + 57 * q^84 - 111 * q^86 - 33 * q^87 + 36 * q^88 - 12 * q^89 + 9 * q^91 - 219 * q^92 + 63 * q^93 + 36 * q^94 - 249 * q^96 + 57 * q^97 + 75 * q^98 - 48 * q^99

Introduction

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