LMFDB - Embedded newform 675.2.l.f.151.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [675,2,Mod(76,675)]

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

lf = mfeigenbasis(mf)

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")

//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);

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

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			151.4
Character	$\chi$	$=$	675.151
Dual form			675.2.l.f.76.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.01600 - 0.852522i) q^{2} +(0.196018 - 1.72092i) q^{3} +(-0.0418420 - 0.237298i) q^{4} +(-1.66628 + 1.58134i) q^{6} +(-0.769922 + 4.36644i) q^{7} +(-1.48608 + 2.57396i) q^{8} +(-2.92315 - 0.674663i) q^{9} +O(q^{10})$	\(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}+O(q^{10}) $ 66 * q - 6 * q^2 - 6 * q^6 - 6 * q^7 - 12 * q^8 - 6 * q^9	$ 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}+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

Display 100 coefficients 10 coefficients

Character values

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

$n$	$326$	$352$
$\chi(n)$	$e\left(\frac{2}{9}\right)$	$1$

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	$-0.433132\pi$
$2$	−1.01600	−	0.852522i	−0.718418	−	0.602824i	−0.926947	+	0.375192i	$0.877577\pi$
$3$	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	0.392015	+	0.919959i	$0.371778\pi$
$7$	−0.769922	+	4.36644i	−0.291003	+	1.65036i	−0.683018	+	0.730402i	$0.739333\pi$
$8$	−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	0.323332	−	0.946286i	$-0.395197\pi$
$11$	3.91123	−	1.42357i	1.17928	−	0.429223i	0.855947	+	0.517063i	$0.172975\pi$
$12$	−0.416573	+	0.0254923i	−0.120254	+	0.00735900i
$13$	−1.15946	+	0.972900i	−0.321576	+	0.269834i	−0.789257	−	0.614063i	$-0.789534\pi$
$13$	−1.15946	+	0.972900i	−0.321576	+	0.269834i	0.467681	+	0.883897i	$0.345090\pi$
$14$	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	$-0.122604\pi$
$17$	0.568932	+	0.985419i	0.137986	+	0.238999i	−0.788748	+	0.614717i	$0.789270\pi$
$18$	2.39475	+	3.17751i	0.564448	+	0.748946i
$19$	−3.37499	+	5.84565i	−0.774275	+	1.34108i	0.160926	+	0.986967i	$0.448552\pi$
$19$	−3.37499	+	5.84565i	−0.774275	+	1.34108i	−0.935201	+	0.354118i	$0.884781\pi$
$20$		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	0.690303	+	0.723520i	$0.257477\pi$
$23$	1.38642	+	7.86279i	0.289089	+	1.63950i	−0.401215	+	0.915984i	$0.631412\pi$
$24$	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	0.801476	−	0.598026i	$-0.204048\pi$
$29$	1.89402	+	1.58927i	0.351710	+	0.295120i	−0.449766	+	0.893146i	$0.648493\pi$
$30$		0			0
$31$	0.369663	+	2.09646i	0.0663933	+	0.376535i	0.999841	+	0.0178222i	$0.00567328\pi$
$31$	0.369663	+	2.09646i	0.0663933	+	0.376535i	−0.933448	+	0.358713i	$0.883216\pi$
$32$	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	−0.904235	−	0.427036i	$-0.859558\pi$
$37$	−4.99967	−	8.65969i	−0.821941	−	1.42364i	0.0822930	−	0.996608i	$-0.473776\pi$
$38$	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	−0.672307	−	0.740272i	$-0.734697\pi$
$41$	−0.384359	+	0.322515i	−0.0600268	+	0.0503685i	0.612281	+	0.790640i	$0.290252\pi$
$42$	−5.62194	−	8.49322i	−0.867484	−	1.31053i
$43$	−0.102738	+	0.0373936i	−0.0156674	+	0.00570247i	−0.349842	−	0.936809i	$-0.613765\pi$
$43$	−0.102738	+	0.0373936i	−0.0156674	+	0.00570247i	0.334175	+	0.942511i	$0.391542\pi$
$44$	−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	−0.725129	−	0.688613i	$-0.758220\pi$
$47$	1.31484	−	7.45681i	0.191789	−	1.08769i	0.916918	−	0.399075i	$-0.130669\pi$
$48$	−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	$-0.412249\pi$
$53$	3.96330			0.544401			0.272201	+	0.962241i	$0.412249\pi$
$54$	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	0.789333	−	0.613965i	$-0.210426\pi$
$59$	7.67614	+	2.79389i	0.999348	+	0.363733i	0.210015	+	0.977698i	$0.432649\pi$
$60$		0			0
$61$	−2.14296	+	12.1533i	−0.274377	+	1.55607i	0.466555	+	0.884492i	$0.345495\pi$
$61$	−2.14296	+	12.1533i	−0.274377	+	1.55607i	−0.740932	+	0.671580i	$0.765616\pi$
$62$	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	$-0.779688\pi$
$67$	−2.25173	+	1.88943i	−0.275093	+	0.230830i	0.494795	+	0.869010i	$0.335243\pi$
$68$	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	0.548715	−	0.836010i	$-0.315117\pi$
$71$	−3.78880	−	6.56240i	−0.449648	−	0.778814i	−0.998363	+	0.0571960i	$0.981784\pi$
$72$	6.08060	−	6.52149i	0.716605	−	0.768565i
$73$	−5.12757	+	8.88121i	−0.600136	+	1.03947i	0.392663	+	0.919682i	$0.371554\pi$
$73$	−5.12757	+	8.88121i	−0.600136	+	1.03947i	−0.992800	+	0.119785i	$0.961780\pi$
$74$	−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	0.828627	−	0.559802i	$-0.189123\pi$
$79$	3.74388	+	3.14149i	0.421219	+	0.353445i	−0.407408	+	0.913246i	$0.633567\pi$
$80$		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	$-0.341809\pi$
$83$	−2.78888	−	2.34014i	−0.306119	−	0.256864i	−0.782886	+	0.622166i	$0.786253\pi$
$84$	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	−0.382127	−	0.924110i	$-0.624808\pi$
$89$	5.74755	−	9.95505i	0.609239	−	1.05523i	0.991366	−	0.131123i	$-0.0418583\pi$
$90$		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	$-0.741381\pi$
$97$	−7.36555	+	2.68084i	−0.747858	+	0.272198i	−0.0601538	+	0.998189i	$0.519159\pi$
$98$	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	0.743163	+	0.669110i	$0.233325\pi$
$101$	−1.84949	+	10.4890i	−0.184031	+	1.04369i	−0.927194	+	0.374581i	$0.877786\pi$
$102$	−2.50628	−	0.742306i	−0.248159	−	0.0734993i
$103$	7.83309	+	2.85101i	0.771817	+	0.280918i	0.697756	−	0.716335i	$-0.254182\pi$
$103$	7.83309	+	2.85101i	0.771817	+	0.280918i	0.0740609	+	0.997254i	$0.476404\pi$
$104$	−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	$-0.700399\pi$
$107$	−12.1812			−1.17760			−0.588800	+	0.808279i	$0.700399\pi$
$108$	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	$-0.419952\pi$
$113$	−1.94653	−	0.708479i	−0.183114	−	0.0666481i	−0.431950	+	0.901898i	$0.642174\pi$
$114$	−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	−0.302802	−	0.953053i	$-0.597922\pi$
$127$	7.59522	−	13.1553i	0.673967	−	1.16735i	0.976770	−	0.214292i	$-0.0687444\pi$
$128$	−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	0.999665	−	0.0258999i	$-0.00824510\pi$
$131$	0.588630	+	3.33829i	0.0514289	+	0.291668i	−0.948236	+	0.317568i	$0.897134\pi$
$132$	−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	0.999183	+	0.0404136i	$0.0128676\pi$
$137$	14.1918	+	11.9084i	1.21249	+	1.01740i	0.213306	+	0.976985i	$0.431577\pi$
$138$	−14.7439	−	10.9092i	−1.25509	−	0.928651i
$139$	2.88601	+	16.3674i	0.244788	+	1.38826i	0.820985	+	0.570950i	$0.193425\pi$
$139$	2.88601	+	16.3674i	0.244788	+	1.38826i	−0.576197	+	0.817311i	$0.695464\pi$
$140$		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	−0.869704	−	0.493574i	$-0.835690\pi$
$149$	−6.52625	+	5.47617i	−0.534651	+	0.448626i	0.335053	+	0.942199i	$0.391246\pi$
$150$		0			0
$151$	11.3452	−	4.12932i	0.923259	−	0.336039i	0.163725	−	0.986506i	$-0.447649\pi$
$151$	11.3452	−	4.12932i	0.923259	−	0.336039i	0.759534	+	0.650467i	$0.225427\pi$
$152$	−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	$-0.214754\pi$
$157$	12.2495	+	4.45846i	0.977618	+	0.355824i	0.196704	+	0.980463i	$0.436976\pi$
$158$	−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	$-0.703254\pi$
$163$	−15.2191			−1.19205			−0.596025	+	0.802966i	$0.703254\pi$
$164$	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	$-0.177598\pi$
$167$	14.9634	+	5.44622i	1.15790	+	0.421441i	0.309553	+	0.950882i	$0.399821\pi$
$168$	−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	$-0.449738\pi$
$173$	12.0020	−	4.36838i	0.912497	−	0.332122i	0.755249	+	0.655437i	$0.227516\pi$
$174$	−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	0.788266	−	0.615335i	$-0.210979\pi$
$179$	−1.85652	−	3.21558i	−0.138763	−	0.240344i	−0.927029	+	0.374991i	$0.877646\pi$
$180$		0			0
$181$	−1.53697	+	2.66211i	−0.114242	+	0.197873i	−0.917477	−	0.397790i	$-0.869777\pi$
$181$	−1.53697	+	2.66211i	−0.114242	+	0.197873i	0.803234	+	0.595663i	$0.203111\pi$
$182$	−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	0.520156	−	0.854071i	$-0.325874\pi$
$191$	−3.18718	−	2.67436i	−0.230616	−	0.193510i	−0.750772	+	0.660561i	$0.770318\pi$
$192$	−13.8468	+	6.02129i	−0.999306	+	0.434549i
$193$	0.685014	+	3.88491i	0.0493084	+	0.279642i	0.999486	−	0.0320682i	$-0.0102094\pi$
$193$	0.685014	+	3.88491i	0.0493084	+	0.279642i	−0.950177	+	0.311710i	$0.899098\pi$
$194$	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	$-0.933807\pi$
$197$	−4.35710	+	7.54672i	−0.310430	+	0.537681i	0.668025	+	0.744139i	$0.267140\pi$
$198$	13.8898	+	9.01886i	0.987106	+	0.640943i
$199$	6.70417	+	11.6120i	0.475246	+	0.823151i	0.999598	−	0.0283510i	$-0.00902560\pi$
$199$	6.70417	+	11.6120i	0.475246	+	0.823151i	−0.524352	+	0.851502i	$0.675692\pi$
$200$		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	0.458347	−	0.888773i	$-0.348442\pi$
$211$	3.45959	+	1.25919i	0.238168	+	0.0866861i	−0.220179	+	0.975460i	$0.570664\pi$
$212$	−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	−0.860348	−	0.509707i	$-0.829754\pi$
$223$	1.82849	−	10.3699i	0.122445	−	0.694417i	0.982793	−	0.184711i	$-0.0591349\pi$
$224$	−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	$-0.953276\pi$
$227$	−24.9055	+	9.06486i	−1.65304	+	0.601656i	−0.663790	+	0.747919i	$0.731053\pi$
$228$	1.25691	−	2.52118i	0.0832409	−	0.166969i
$229$	−8.45322	+	7.09309i	−0.558605	+	0.468725i	−0.877842	−	0.478950i	$-0.841018\pi$
$229$	−8.45322	+	7.09309i	−0.558605	+	0.468725i	0.319238	+	0.947675i	$0.396573\pi$
$230$		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	$-0.311350\pi$
$233$	−6.70173	−	11.6077i	−0.439045	−	0.760448i	−0.997616	+	0.0690083i	$0.978016\pi$
$234$	−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	−0.993508	−	0.113763i	$-0.963709\pi$
$239$	−1.52780	−	8.66459i	−0.0988253	−	0.560466i	0.894683	−	0.446702i	$-0.147402\pi$
$240$		0			0
$241$	−11.2282	−	9.42161i	−0.723274	−	0.606899i	0.205015	−	0.978759i	$-0.434276\pi$
$241$	−11.2282	−	9.42161i	−0.723274	−	0.606899i	−0.928289	+	0.371860i	$0.878720\pi$
$242$	−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	−0.920027	−	0.391854i	$-0.871834\pi$
$251$	−1.91159	+	3.31097i	−0.120658	+	0.208986i	0.799369	+	0.600840i	$0.205167\pi$
$252$	−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	$-0.640264\pi$
$257$	6.25436	−	5.24803i	0.390136	−	0.327363i	0.816666	+	0.577110i	$0.195820\pi$
$258$	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	−0.354683	−	0.934987i	$-0.615411\pi$
$263$	4.83914	−	27.4441i	0.298394	−	1.69228i	0.653077	−	0.757291i	$-0.273478\pi$
$264$	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	−0.323873	−	0.946101i	$-0.604985\pi$
$277$	5.06046	−	28.6993i	0.304054	−	1.72437i	0.627926	−	0.778273i	$-0.283904\pi$
$278$	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	−0.904453	−	0.426574i	$-0.859720\pi$
$281$	−22.1793	+	8.07261i	−1.32311	+	0.481572i	−0.418655	+	0.908145i	$0.637498\pi$
$282$	9.60089	+	14.5043i	0.571724	+	0.863720i
$283$	15.0763	−	12.6506i	0.896195	−	0.751997i	−0.0732477	−	0.997314i	$-0.523336\pi$
$283$	15.0763	−	12.6506i	0.896195	−	0.751997i	0.969443	+	0.245317i	$0.0788919\pi$
$284$	−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	0.999977	+	0.00676709i	$0.00215405\pi$
$293$	1.07189	+	6.07899i	0.0626205	+	0.355138i	−0.937357	+	0.348371i	$0.886735\pi$
$294$	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	$-0.277372\pi$
$307$	−5.97167	−	10.3432i	−0.340821	−	0.590320i	−0.984585	+	0.174904i	$0.944038\pi$
$308$	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	0.0909314	−	0.995857i	$-0.471016\pi$
$311$	19.1774	−	16.0917i	1.08745	−	0.912478i	0.996518	+	0.0833788i	$0.0265711\pi$
$312$	−7.77717	+	0.475927i	−0.440296	+	0.0269440i
$313$	14.4140	−	5.24628i	0.814729	−	0.296537i	0.0991534	−	0.995072i	$-0.468387\pi$
$313$	14.4140	−	5.24628i	0.814729	−	0.296537i	0.715576	+	0.698535i	$0.246164\pi$
$314$	−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	$-0.942242\pi$
$317$	0.0427784	−	0.242608i	0.00240267	−	0.0136262i	0.985986	+	0.166831i	$0.0533534\pi$
$318$	−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	0.597918	+	0.801558i	$0.295995\pi$
$331$	−4.33167	+	24.5661i	−0.238090	+	1.35028i	−0.836008	+	0.548718i	$0.815116\pi$
$332$	−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	−0.238950	+	0.971032i	$0.576803\pi$
$337$	−22.7032	+	19.0503i	−1.23672	+	1.03773i	−0.997773	+	0.0667018i	$0.978752\pi$
$338$	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	0.727274	+	0.686347i	$0.240787\pi$
$347$	5.18983	+	29.4330i	0.278604	+	1.58004i	−0.448670	+	0.893698i	$0.648102\pi$
$348$	−0.829511	−	0.613764i	−0.0444665	−	0.0329012i
$349$	0.356538	+	0.299171i	0.0190850	+	0.0160142i	0.652280	−	0.757978i	$-0.273813\pi$
$349$	0.356538	+	0.299171i	0.0190850	+	0.0160142i	−0.633195	+	0.773992i	$0.718257\pi$
$350$		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	$-0.263909\pi$
$353$	1.25375	+	1.05202i	0.0667304	+	0.0559934i	−0.608812	+	0.793314i	$0.708354\pi$
$354$	−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	−0.502399	−	0.864636i	$-0.667549\pi$
$359$	9.42812	−	16.3300i	0.497597	−	0.861863i	0.999996	+	0.00277241i	$0.000882486\pi$
$360$		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	$-0.697122\pi$
$367$	−9.61068	+	3.49800i	−0.501673	+	0.182594i	0.0787732	+	0.996893i	$0.474900\pi$
$368$	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	$-0.331331\pi$
$373$	6.52759	+	2.37585i	0.337986	+	0.123017i	−0.167451	+	0.985880i	$0.553554\pi$
$374$	−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	$-0.566488\pi$
$383$	−19.4731	−	7.08761i	−0.995026	−	0.362160i	−0.787665	+	0.616104i	$0.788710\pi$
$384$	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	−0.471703	−	0.881758i	$-0.656361\pi$
$389$	−5.25158	+	1.91142i	−0.266266	+	0.0969127i	0.205437	+	0.978670i	$0.434138\pi$
$390$		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	$-0.722675\pi$
$397$	6.78805	−	11.7572i	0.340682	−	0.590079i	0.984560	+	0.175050i	$0.0560086\pi$
$398$	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	−0.947022	−	0.321168i	$-0.895925\pi$
$401$	−3.34334	−	18.9610i	−0.166958	−	0.946868i	0.780064	−	0.625700i	$-0.215187\pi$
$402$	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	0.999211	+	0.0397248i	$0.0126481\pi$
$409$	1.49345	+	8.46979i	0.0738464	+	0.418804i	−0.925364	+	0.379079i	$0.876241\pi$
$410$		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	0.117694	−	0.993050i	$-0.462450\pi$
$419$	22.8459	−	19.1700i	1.11609	−	0.936515i	0.998401	+	0.0565354i	$0.0180054\pi$
$420$		0			0
$421$	3.86135	−	1.40541i	0.188190	−	0.0684957i	−0.246206	−	0.969218i	$-0.579184\pi$
$421$	3.86135	−	1.40541i	0.188190	−	0.0684957i	0.434396	+	0.900722i	$0.356962\pi$
$422$	−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	$-0.601708\pi$
$433$	−13.0726			−0.628230			−0.314115	+	0.949385i	$0.601708\pi$
$434$	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	−0.935922	−	0.352208i	$-0.885431\pi$
$439$	1.34135	−	7.60717i	0.0640191	−	0.363071i	0.999941	−	0.0108629i	$-0.00345783\pi$
$440$		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	$-0.784187\pi$
$443$	−20.4640	+	7.44827i	−0.972272	+	0.353878i	−0.193441	+	0.981112i	$0.561965\pi$
$444$	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	−0.957688	−	0.287808i	$-0.907073\pi$
$449$	−15.4280	−	26.7221i	−0.728093	−	1.26109i	0.229595	−	0.973286i	$-0.426260\pi$
$450$		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	$-0.00315700\pi$
$457$	24.8797	+	20.8765i	1.16382	+	0.976564i	0.163872	+	0.986482i	$0.447601\pi$
$458$	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	0.972320	−	0.233655i	$-0.0750685\pi$
$461$	19.5612	+	16.4138i	0.911056	+	0.764467i	−0.0612635	+	0.998122i	$0.519513\pi$
$462$	−34.0794	−	25.2157i	−1.58552	−	1.17314i
$463$	−1.63666	−	9.28198i	−0.0760622	−	0.431370i	−0.998930	−	0.0462526i	$-0.985272\pi$
$463$	−1.63666	−	9.28198i	−0.0760622	−	0.431370i	0.922868	−	0.385117i	$-0.125839\pi$
$464$	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	0.0609381	−	0.998142i	$-0.480591\pi$
$467$	19.3386	−	33.4955i	0.894885	−	1.54999i	0.833947	−	0.551845i	$-0.186076\pi$
$468$	−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	−0.370695	−	0.928755i	$-0.620880\pi$
$479$	6.46290	−	36.6529i	0.295297	−	1.67471i	0.665992	−	0.745959i	$-0.268009\pi$
$480$		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	$-0.167141\pi$
$487$	38.1901			1.73056			0.865279	+	0.501290i	$0.167141\pi$
$488$	−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	0.336928	−	0.941530i	$-0.390612\pi$
$491$	−0.225443	−	0.0820546i	−0.0101741	−	0.00370307i	−0.347102	+	0.937827i	$0.612834\pi$
$492$	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	−0.919504	−	0.393080i	$-0.871410\pi$
$499$	−15.4596	+	12.9721i	−0.692067	+	0.580713i	0.227438	+	0.973793i	$0.426965\pi$
$500$		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	$-0.326868\pi$
$503$	−10.8170	−	18.7357i	−0.482308	−	0.835382i	−0.999794	+	0.0203102i	$0.993535\pi$
$504$	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	−0.953793	−	0.300465i	$-0.902858\pi$
$509$	−3.61621	−	20.5086i	−0.160286	−	0.909026i	0.793507	−	0.608561i	$-0.208253\pi$
$510$		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	−0.763975	−	0.645246i	$-0.776755\pi$
$521$	4.03581	−	6.99023i	0.176812	−	0.306247i	0.940787	+	0.338999i	$0.110088\pi$
$522$	−0.514220	+	9.82416i	−0.0225068	+	0.429992i
$523$	10.2876	+	17.8186i	0.449845	+	0.779154i	0.998376	−	0.0569761i	$-0.0181459\pi$
$523$	10.2876	+	17.8186i	0.449845	+	0.779154i	−0.548531	+	0.836131i	$0.684813\pi$
$524$	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	−0.898338	−	0.439306i	$-0.855225\pi$
$547$	2.24700	−	12.7434i	0.0960749	−	0.544868i	0.994413	−	0.105563i	$-0.0336643\pi$
$548$	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	$-0.0524890\pi$
$557$	8.28524	+	14.3505i	0.351057	+	0.608049i	−0.635378	+	0.772201i	$0.719156\pi$
$558$	−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	0.999159	+	0.0409958i	$0.0130530\pi$
$563$	1.76244	+	9.99530i	0.0742781	+	0.421252i	−0.924881	+	0.380256i	$0.875836\pi$
$564$	−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	0.969861	−	0.243660i	$-0.0783482\pi$
$569$	21.4282	+	17.9804i	0.898317	+	0.753777i	−0.0715441	+	0.997437i	$0.522793\pi$
$570$		0			0
$571$	−3.43834	−	19.4998i	−0.143890	−	0.816041i	−0.968252	−	0.249978i	$-0.919577\pi$
$571$	−3.43834	−	19.4998i	−0.143890	−	0.816041i	0.824362	−	0.566064i	$-0.191534\pi$
$572$	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	$-0.187413\pi$
$577$	−1.56447	−	2.70975i	−0.0651299	−	0.112808i	−0.896752	+	0.442534i	$0.854080\pi$
$578$	−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	0.251887	+	0.967757i	$0.418949\pi$
$587$	−7.65127	+	43.3925i	−0.315802	+	1.79100i	−0.567688	+	0.823244i	$0.692162\pi$
$588$	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	$-0.566535\pi$
$593$	−10.1063			−0.415015			−0.207507	+	0.978233i	$0.566535\pi$
$594$	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	0.374938	−	0.927050i	$-0.377664\pi$
$599$	1.62169	+	0.590247i	0.0662605	+	0.0241169i	−0.308677	+	0.951167i	$0.599886\pi$
$600$		0			0
$601$	3.60539	−	20.4472i	0.147067	−	0.834058i	−0.818617	−	0.574339i	$-0.805259\pi$
$601$	3.60539	−	20.4472i	0.147067	−	0.834058i	0.965684	−	0.259719i	$-0.0836299\pi$
$602$	−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	$-0.709137\pi$
$607$	1.55129	−	1.30168i	0.0629648	−	0.0528337i	0.673727	+	0.738980i	$0.264692\pi$
$608$	−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	0.361119	+	0.932520i	$0.382395\pi$
$613$	−15.5244	+	26.8891i	−0.627027	+	1.08604i	−0.988145	+	0.153522i	$0.950938\pi$
$614$	−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	$-0.110135\pi$
$617$	−1.47195	−	8.34783i	−0.0592584	−	0.336071i	−0.999995	+	0.00306626i	$0.999024\pi$
$618$	−17.5605	+	7.63621i	−0.706388	+	0.307174i
$619$	−32.3309	−	27.1288i	−1.29949	−	1.09040i	−0.990233	−	0.139421i	$-0.955476\pi$
$619$	−32.3309	−	27.1288i	−1.29949	−	1.09040i	−0.309255	−	0.950979i	$-0.600080\pi$
$620$		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	0.996389	+	0.0849008i	$0.0270573\pi$
$631$	14.3615	+	24.8748i	0.571721	+	0.990250i	−0.424668	+	0.905349i	$0.639609\pi$
$632$	−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	0.857174	+	0.515026i	$0.172218\pi$
$641$	−3.15096	+	17.8700i	−0.124456	+	0.705822i	−0.981630	+	0.190796i	$0.938893\pi$
$642$	20.2972	−	19.2626i	0.801069	−	0.760235i
$643$	−14.9832	−	5.45343i	−0.590879	−	0.215062i	0.0292372	−	0.999573i	$-0.490692\pi$
$643$	−14.9832	−	5.45343i	−0.590879	−	0.215062i	−0.620116	+	0.784510i	$0.712914\pi$
$644$	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	$-0.412789\pi$
$647$	13.7644			0.541133			0.270567	+	0.962701i	$0.412789\pi$
$648$	−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	$-0.281055\pi$
$653$	15.9602	+	5.80905i	0.624573	+	0.227326i	−0.0102948	+	0.999947i	$0.503277\pi$
$654$	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	−0.126955	−	0.991908i	$-0.540520\pi$
$659$	10.6118	−	3.86239i	0.413378	−	0.150457i	0.540333	+	0.841451i	$0.318298\pi$
$660$		0			0
$661$	−2.63000	+	2.20683i	−0.102295	+	0.0858358i	−0.692501	−	0.721417i	$-0.743491\pi$
$661$	−2.63000	+	2.20683i	−0.102295	+	0.0858358i	0.590206	+	0.807253i	$0.299047\pi$
$662$	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	$-0.446259\pi$
$673$	−20.0688	−	16.8397i	−0.773595	−	0.649123i	−0.941627	+	0.336658i	$0.890703\pi$
$674$	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	$-0.159418\pi$
$677$	14.4837	+	12.1532i	0.556653	+	0.467087i	−0.320534	+	0.947237i	$0.603862\pi$
$678$	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	$-0.678387\pi$
$683$	12.2251	−	21.1745i	0.467782	−	0.810222i	0.999322	+	0.0368112i	$0.0117200\pi$
$684$	−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	0.0182226	−	0.999834i	$-0.494199\pi$
$691$	17.7400	−	6.45685i	0.674863	−	0.245630i	0.656640	+	0.754204i	$0.271977\pi$
$692$	−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	0.678636	+	0.734475i	$0.262572\pi$
$709$	−5.59910	+	31.7541i	−0.210279	+	1.19255i	−0.888914	+	0.458074i	$0.848539\pi$
$710$		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	0.906076	+	0.423115i	$0.139063\pi$
$719$	21.9733	+	38.0589i	0.819467	+	1.41936i	−0.0866093	+	0.996242i	$0.527603\pi$
$720$		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	$-0.225049\pi$
$727$	6.81176	+	5.71575i	0.252634	+	0.211985i	−0.507671	+	0.861551i	$0.669494\pi$
$728$	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	$-0.0655418\pi$
$733$	−0.294938	−	1.67268i	−0.0108938	−	0.0617818i	−0.989770	+	0.142672i	$0.954431\pi$
$734$	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	−0.945956	−	0.324295i	$-0.894873\pi$
$739$	−20.4924	−	35.4939i	−0.753826	−	1.30566i	0.192130	−	0.981369i	$-0.438460\pi$
$740$		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	0.607747	−	0.794131i	$-0.292074\pi$
$743$	40.7602	−	34.2019i	1.49535	−	1.25475i	0.887600	−	0.460614i	$-0.152371\pi$
$744$	−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	0.608944	−	0.793214i	$-0.291594\pi$
$751$	15.4986	+	5.64104i	0.565554	+	0.205845i	−0.0433900	+	0.999058i	$0.513816\pi$
$752$	−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	$-0.466632\pi$
$757$	5.75782			0.209271			0.104636	+	0.994511i	$0.466632\pi$
$758$	−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	−0.386305	−	0.922371i	$-0.626249\pi$
$761$	−35.1758	−	12.8029i	−1.27512	−	0.464106i	−0.888816	+	0.458265i	$0.848471\pi$
$762$	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	−0.356795	−	0.934183i	$-0.616130\pi$
$769$	13.8998	−	11.6633i	0.501239	−	0.420589i	0.858034	+	0.513593i	$0.171686\pi$
$770$		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	$-0.0362009\pi$
$773$	11.0792	+	19.1897i	0.398490	+	0.690206i	−0.595049	+	0.803689i	$0.702868\pi$
$774$	−0.364850	−	0.236903i	−0.0131143	−	0.00851530i
$775$		0			0

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-1.01600 - 0.852522i) q^{2} +(0.196018 - 1.72092i) q^{3} +(-0.0418420 - 0.237298i) q^{4} +(-1.66628 + 1.58134i) q^{6} +(-0.769922 + 4.36644i) q^{7} +(-1.48608 + 2.57396i) q^{8} +(-2.92315 - 0.674663i) q^{9} +O(q^{10})\)	\(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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 66 q - 6 q^{2} - 6 q^{6} - 6 q^{7} - 12 q^{8} - 6 q^{9}+O(q^{10}) \) 66 * q - 6 * q^2 - 6 * q^6 - 6 * q^7 - 12 * q^8 - 6 * q^9	\( 66 q - 6 q^{2} - 6 q^{6} - 6 q^{7} - 12 q^{8} - 6 q^{9} + 15 q^{11} - 18 q^{12} + 15 q^{14} + 18 q^{16} - 30 q^{17} + 12 q^{18} + 12 q^{19} + 12 q^{21} + 45 q^{22} - 36 q^{23} - 39 q^{24} + 6 q^{26} - 51 q^{27} + 36 q^{28} - 15 q^{29} + 3 q^{31} - 27 q^{32} + 3 q^{33} + 30 q^{36} - 6 q^{37} + 12 q^{38} - 15 q^{39} + 39 q^{41} - 48 q^{42} - 12 q^{43} + 51 q^{44} + 9 q^{46} - 30 q^{47} + 132 q^{48} - 6 q^{49} - 9 q^{52} + 24 q^{53} + 75 q^{54} + 144 q^{56} - 33 q^{57} - 27 q^{58} + 45 q^{59} - 54 q^{61} - 66 q^{62} + 120 q^{63} - 24 q^{64} + 48 q^{66} - 9 q^{67} + 69 q^{68} + 51 q^{69} - 15 q^{71} - 9 q^{72} + 15 q^{73} + 96 q^{74} - 48 q^{76} + 36 q^{77} + 18 q^{78} + 48 q^{79} - 54 q^{81} + 36 q^{82} - 30 q^{83} + 57 q^{84} - 111 q^{86} + 33 q^{87} - 36 q^{88} - 12 q^{89} + 9 q^{91} + 219 q^{92} - 63 q^{93} + 36 q^{94} - 249 q^{96} - 57 q^{97} - 75 q^{98} - 48 q^{99}+O(q^{100}) \) 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

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