LMFDB - Embedded newform 729.2.g.b.622.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [729,2,Mod(28,729)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(729, base_ring=CyclotomicField(54))

chi = DirichletCharacter(H, H._module([44]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("729.28");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 729 = 3^{6} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	729.g (of order $27$, degree $18$, not 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:	$5.82109430735$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$8$ over $\Q(\zeta_{27})$
Twist minimal:	no (minimal twist has level 81)
Sato-Tate group:	$\mathrm{SU}(2)[C_{27}]$

Embedding invariants

Embedding label			622.1
Character	$\chi$	$=$	729.622
Dual form			729.2.g.b.109.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.82254 + 1.93178i) q^{2} +(-0.293829 - 5.04485i) q^{4} +(-2.82892 - 0.330653i) q^{5} +(1.70942 - 0.858501i) q^{7} +(6.21207 + 5.21255i) q^{8} +O(q^{10})$	\(q+(-1.82254 + 1.93178i) q^{2} +(-0.293829 - 5.04485i) q^{4} +(-2.82892 - 0.330653i) q^{5} +(1.70942 - 0.858501i) q^{7} +(6.21207 + 5.21255i) q^{8} +(5.79455 - 4.86220i) q^{10} +(0.733735 - 1.70099i) q^{11} +(-0.131251 + 0.0311070i) q^{13} +(-1.45704 + 4.86686i) q^{14} +(-11.3528 + 1.32695i) q^{16} +(-0.193799 - 1.09909i) q^{17} +(-1.05411 + 5.97816i) q^{19} +(-0.836876 + 14.3686i) q^{20} +(1.94867 + 4.51753i) q^{22} +(-0.416930 - 0.209390i) q^{23} +(3.02821 + 0.717699i) q^{25} +(0.179118 - 0.310241i) q^{26} +(-4.83328 - 8.37149i) q^{28} +(0.125753 + 0.420043i) q^{29} +(-2.36480 + 1.55535i) q^{31} +(8.44238 - 11.3401i) q^{32} +(2.47640 + 1.62875i) q^{34} +(-5.11966 + 1.86340i) q^{35} +(-7.77306 - 2.82916i) q^{37} +(-9.62732 - 12.9317i) q^{38} +(-15.8499 - 16.7999i) q^{40} +(3.81865 + 4.04753i) q^{41} +(-4.47917 - 6.01657i) q^{43} +(-8.79682 - 3.20178i) q^{44} +(1.16437 - 0.423795i) q^{46} +(-7.12769 - 4.68795i) q^{47} +(-1.99503 + 2.67979i) q^{49} +(-6.90546 + 4.54179i) q^{50} +(0.195495 + 0.653000i) q^{52} +(2.94278 + 5.09704i) q^{53} +(-2.63811 + 4.56934i) q^{55} +(15.0940 + 3.57734i) q^{56} +(-1.04062 - 0.522618i) q^{58} +(-5.58328 - 12.9435i) q^{59} +(-0.446598 + 7.66779i) q^{61} +(1.30534 - 7.40295i) q^{62} +(2.55035 + 14.4637i) q^{64} +(0.381583 - 0.0446007i) q^{65} +(-3.24125 + 10.8265i) q^{67} +(-5.48779 + 1.30063i) q^{68} +(5.73109 - 13.2862i) q^{70} +(-0.604067 + 0.506872i) q^{71} +(-2.76505 - 2.32015i) q^{73} +(19.6320 - 9.85956i) q^{74} +(30.4687 + 3.56128i) q^{76} +(-0.206042 - 3.53761i) q^{77} +(8.76989 - 9.29554i) q^{79} +32.5547 q^{80} -14.7786 q^{82} +(-11.4722 + 12.1598i) q^{83} +(0.184824 + 3.17331i) q^{85} +(19.7861 + 2.31267i) q^{86} +(13.4245 - 6.74204i) q^{88} +(-8.34578 - 7.00294i) q^{89} +(-0.197657 + 0.165854i) q^{91} +(-0.933836 + 2.16488i) q^{92} +(22.0466 - 5.22513i) q^{94} +(4.95869 - 16.5632i) q^{95} +(-2.28615 + 0.267213i) q^{97} +(-1.54074 - 8.73797i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q - 9 q^{2} + 9 q^{4} - 9 q^{5} + 9 q^{7} + 18 q^{8}+O(q^{10}) $ 144 * q - 9 * q^2 + 9 * q^4 - 9 * q^5 + 9 * q^7 + 18 * q^8	$ 144 q - 9 q^{2} + 9 q^{4} - 9 q^{5} + 9 q^{7} + 18 q^{8} - 18 q^{10} - 9 q^{11} + 9 q^{13} - 9 q^{14} + 9 q^{16} + 18 q^{17} - 18 q^{19} + 63 q^{20} + 9 q^{22} - 36 q^{23} + 9 q^{25} - 45 q^{26} - 9 q^{28} + 45 q^{29} + 9 q^{31} - 63 q^{32} + 9 q^{34} - 9 q^{35} - 18 q^{37} + 9 q^{38} + 9 q^{40} + 27 q^{41} + 9 q^{43} - 54 q^{44} - 18 q^{46} - 63 q^{47} + 9 q^{49} + 225 q^{50} + 27 q^{52} - 45 q^{53} - 9 q^{55} - 99 q^{56} + 9 q^{58} + 117 q^{59} + 9 q^{61} - 81 q^{62} - 18 q^{64} - 81 q^{65} + 36 q^{67} + 18 q^{68} + 63 q^{70} + 90 q^{71} - 18 q^{73} - 81 q^{74} + 90 q^{76} - 81 q^{77} + 63 q^{79} + 288 q^{80} - 36 q^{82} - 45 q^{83} + 63 q^{85} - 81 q^{86} + 90 q^{88} + 81 q^{89} - 18 q^{91} + 63 q^{92} + 63 q^{94} - 153 q^{95} + 36 q^{97} - 81 q^{98}+O(q^{100}) $ 144 * q - 9 * q^2 + 9 * q^4 - 9 * q^5 + 9 * q^7 + 18 * q^8 - 18 * q^10 - 9 * q^11 + 9 * q^13 - 9 * q^14 + 9 * q^16 + 18 * q^17 - 18 * q^19 + 63 * q^20 + 9 * q^22 - 36 * q^23 + 9 * q^25 - 45 * q^26 - 9 * q^28 + 45 * q^29 + 9 * q^31 - 63 * q^32 + 9 * q^34 - 9 * q^35 - 18 * q^37 + 9 * q^38 + 9 * q^40 + 27 * q^41 + 9 * q^43 - 54 * q^44 - 18 * q^46 - 63 * q^47 + 9 * q^49 + 225 * q^50 + 27 * q^52 - 45 * q^53 - 9 * q^55 - 99 * q^56 + 9 * q^58 + 117 * q^59 + 9 * q^61 - 81 * q^62 - 18 * q^64 - 81 * q^65 + 36 * q^67 + 18 * q^68 + 63 * q^70 + 90 * q^71 - 18 * q^73 - 81 * q^74 + 90 * q^76 - 81 * q^77 + 63 * q^79 + 288 * q^80 - 36 * q^82 - 45 * q^83 + 63 * q^85 - 81 * q^86 + 90 * q^88 + 81 * q^89 - 18 * q^91 + 63 * q^92 + 63 * q^94 - 153 * q^95 + 36 * q^97 - 81 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/729\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{20}{27}\right)$

Coefficient data

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

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

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

$2$	−1.82254	+	1.93178i	−1.28873	+	1.36597i	−0.394159	+	0.919042i	$0.628964\pi$
$2$	−1.82254	+	1.93178i	−1.28873	+	1.36597i	−0.894569	+	0.446930i	$0.852517\pi$
$3$		0			0
$3$		0			0
$4$	−0.293829	−	5.04485i	−0.146914	−	2.52242i
$5$	−2.82892	−	0.330653i	−1.26513	−	0.147872i	−0.543061	−	0.839693i	$-0.682735\pi$
$5$	−2.82892	−	0.330653i	−1.26513	−	0.147872i	−0.722069	+	0.691821i	$0.756809\pi$
$6$		0			0
$7$	1.70942	−	0.858501i	0.646099	−	0.324483i	−0.0953983	−	0.995439i	$-0.530412\pi$
$7$	1.70942	−	0.858501i	0.646099	−	0.324483i	0.741497	+	0.670956i	$0.234116\pi$
$8$	6.21207	+	5.21255i	2.19630	+	1.84291i
$9$		0			0
$10$	5.79455	−	4.86220i	1.83240	−	1.53756i
$11$	0.733735	−	1.70099i	0.221229	−	0.512867i	−0.771067	−	0.636754i	$-0.780277\pi$
$11$	0.733735	−	1.70099i	0.221229	−	0.512867i	0.992296	+	0.123887i	$0.0395359\pi$
$12$		0			0
$13$	−0.131251	+	0.0311070i	−0.0364024	+	0.00862753i	−0.248777	−	0.968561i	$-0.580029\pi$
$13$	−0.131251	+	0.0311070i	−0.0364024	+	0.00862753i	0.212374	+	0.977188i	$0.431880\pi$
$14$	−1.45704	+	4.86686i	−0.389411	+	1.30072i
$15$		0			0
$16$	−11.3528	+	1.32695i	−2.83819	+	0.331737i
$17$	−0.193799	−	1.09909i	−0.0470031	−	0.266568i	0.952245	−	0.305334i	$-0.0987683\pi$
$17$	−0.193799	−	1.09909i	−0.0470031	−	0.266568i	−0.999248	+	0.0387665i	$0.987657\pi$
$18$		0			0
$19$	−1.05411	+	5.97816i	−0.241830	+	1.37148i	0.585912	+	0.810375i	$0.300737\pi$
$19$	−1.05411	+	5.97816i	−0.241830	+	1.37148i	−0.827741	+	0.561110i	$0.810375\pi$
$20$	−0.836876	+	14.3686i	−0.187131	+	3.21292i
$21$		0			0
$22$	1.94867	+	4.51753i	0.415458	+	0.963140i
$23$	−0.416930	−	0.209390i	−0.0869360	−	0.0436609i	0.404800	−	0.914405i	$-0.367341\pi$
$23$	−0.416930	−	0.209390i	−0.0869360	−	0.0436609i	−0.491736	+	0.870744i	$0.663637\pi$
$24$		0			0
$25$	3.02821	+	0.717699i	0.605642	+	0.143540i
$26$	0.179118	−	0.310241i	0.0351279	−	0.0608432i
$27$		0			0
$28$	−4.83328	−	8.37149i	−0.913405	−	1.58206i
$29$	0.125753	+	0.420043i	0.0233517	+	0.0780001i	0.968871	−	0.247565i	$-0.0796305\pi$
$29$	0.125753	+	0.420043i	0.0233517	+	0.0780001i	−0.945519	+	0.325566i	$0.894445\pi$
$30$		0			0
$31$	−2.36480	+	1.55535i	−0.424730	+	0.279350i	−0.743826	−	0.668373i	$-0.766991\pi$
$31$	−2.36480	+	1.55535i	−0.424730	+	0.279350i	0.319096	+	0.947722i	$0.396621\pi$
$32$	8.44238	−	11.3401i	1.49242	−	2.00466i
$33$		0			0
$34$	2.47640	+	1.62875i	0.424699	+	0.279329i
$35$	−5.11966	+	1.86340i	−0.865381	+	0.314973i
$36$		0			0
$37$	−7.77306	−	2.82916i	−1.27788	−	0.465112i	−0.388152	−	0.921595i	$-0.626886\pi$
$37$	−7.77306	−	2.82916i	−1.27788	−	0.465112i	−0.889732	+	0.456484i	$0.849109\pi$
$38$	−9.62732	−	12.9317i	−1.56176	−	2.09780i
$39$		0			0
$40$	−15.8499	−	16.7999i	−2.50609	−	2.65630i
$41$	3.81865	+	4.04753i	0.596373	+	0.632118i	0.953304	−	0.302012i	$-0.0976584\pi$
$41$	3.81865	+	4.04753i	0.596373	+	0.632118i	−0.356931	+	0.934131i	$0.616177\pi$
$42$		0			0
$43$	−4.47917	−	6.01657i	−0.683068	−	0.917519i	0.316449	−	0.948610i	$-0.397509\pi$
$43$	−4.47917	−	6.01657i	−0.683068	−	0.917519i	−0.999517	+	0.0310906i	$0.990102\pi$
$44$	−8.79682	−	3.20178i	−1.32617	−	0.482687i
$45$		0			0
$46$	1.16437	−	0.423795i	0.171676	−	0.0624851i
$47$	−7.12769	−	4.68795i	−1.03968	−	0.683808i	−0.0896522	−	0.995973i	$-0.528576\pi$
$47$	−7.12769	−	4.68795i	−1.03968	−	0.683808i	−0.950028	+	0.312165i	$0.898946\pi$
$48$		0			0
$49$	−1.99503	+	2.67979i	−0.285004	+	0.382827i
$50$	−6.90546	+	4.54179i	−0.976579	+	0.642306i
$51$		0			0
$52$	0.195495	+	0.653000i	0.0271103	+	0.0905549i
$53$	2.94278	+	5.09704i	0.404222	+	0.700133i	0.994231	−	0.107264i	$-0.0342090\pi$
$53$	2.94278	+	5.09704i	0.404222	+	0.700133i	−0.590009	+	0.807397i	$0.700876\pi$
$54$		0			0
$55$	−2.63811	+	4.56934i	−0.355723	+	0.616130i
$56$	15.0940	+	3.57734i	2.01702	+	0.478043i
$57$		0			0
$58$	−1.04062	−	0.522618i	−0.136640	−	0.0686231i
$59$	−5.58328	−	12.9435i	−0.726881	−	1.68510i	−0.728449	−	0.685100i	$-0.759759\pi$
$59$	−5.58328	−	12.9435i	−0.726881	−	1.68510i	0.00156855	−	0.999999i	$-0.499501\pi$
$60$		0			0
$61$	−0.446598	+	7.66779i	−0.0571810	+	0.981759i	0.840694	+	0.541510i	$0.182147\pi$
$61$	−0.446598	+	7.66779i	−0.0571810	+	0.981759i	−0.897875	+	0.440250i	$0.854890\pi$
$62$	1.30534	−	7.40295i	0.165778	−	0.940175i
$63$		0			0
$64$	2.55035	+	14.4637i	0.318793	+	1.80797i
$65$	0.381583	−	0.0446007i	0.0473296	−	0.00553203i
$66$		0			0
$67$	−3.24125	+	10.8265i	−0.395981	+	1.32267i	0.495104	+	0.868834i	$0.335130\pi$
$67$	−3.24125	+	10.8265i	−0.395981	+	1.32267i	−0.891085	+	0.453836i	$0.850055\pi$
$68$	−5.48779	+	1.30063i	−0.665492	+	0.157725i
$69$		0			0
$70$	5.73109	−	13.2862i	0.684996	−	1.58800i
$71$	−0.604067	+	0.506872i	−0.0716895	+	0.0601547i	−0.677928	−	0.735128i	$-0.737122\pi$
$71$	−0.604067	+	0.506872i	−0.0716895	+	0.0601547i	0.606239	+	0.795283i	$0.292678\pi$
$72$		0			0
$73$	−2.76505	−	2.32015i	−0.323625	−	0.271553i	0.466472	−	0.884536i	$-0.345525\pi$
$73$	−2.76505	−	2.32015i	−0.323625	−	0.271553i	−0.790096	+	0.612983i	$0.789969\pi$
$74$	19.6320	−	9.85956i	2.28217	−	1.14615i
$75$		0			0
$76$	30.4687	+	3.56128i	3.49499	+	0.408506i
$77$	−0.206042	−	3.53761i	−0.0234807	−	0.403148i
$78$		0			0
$79$	8.76989	−	9.29554i	0.986690	−	1.04583i	−0.0122562	−	0.999925i	$-0.503901\pi$
$79$	8.76989	−	9.29554i	0.986690	−	1.04583i	0.998946	−	0.0459050i	$-0.0146172\pi$
$80$	32.5547			3.63973
$81$		0			0
$82$	−14.7786			−1.63202
$83$	−11.4722	+	12.1598i	−1.25924	+	1.33472i	−0.340299	+	0.940317i	$0.610528\pi$
$83$	−11.4722	+	12.1598i	−1.25924	+	1.33472i	−0.918940	+	0.394398i	$0.870953\pi$
$84$		0			0
$85$	0.184824	+	3.17331i	0.0200470	+	0.344194i
$86$	19.7861	+	2.31267i	2.13359	+	0.249381i
$87$		0			0
$88$	13.4245	−	6.74204i	1.43106	−	0.718704i
$89$	−8.34578	−	7.00294i	−0.884651	−	0.742311i	0.0824788	−	0.996593i	$-0.473716\pi$
$89$	−8.34578	−	7.00294i	−0.884651	−	0.742311i	−0.967130	+	0.254282i	$0.918161\pi$
$90$		0			0
$91$	−0.197657	+	0.165854i	−0.0207201	+	0.0173862i
$92$	−0.933836	+	2.16488i	−0.0973592	+	0.225704i
$93$		0			0
$94$	22.0466	−	5.22513i	2.27393	−	0.538931i
$95$	4.95869	−	16.5632i	0.508751	−	1.69935i
$96$		0			0
$97$	−2.28615	+	0.267213i	−0.232124	+	0.0271313i	−0.231359	−	0.972868i	$-0.574317\pi$
$97$	−2.28615	+	0.267213i	−0.232124	+	0.0271313i	−0.000764163		1.00000i	$0.500243\pi$
$98$	−1.54074	−	8.73797i	−0.155638	−	0.882668i
$99$		0			0
$100$	2.73091	−	15.4877i	0.273091	−	1.54877i
$101$	−0.500707	+	8.59680i	−0.0498222	+	0.855414i	0.877134	+	0.480245i	$0.159452\pi$
$101$	−0.500707	+	8.59680i	−0.0498222	+	0.855414i	−0.926957	+	0.375169i	$0.877585\pi$
$102$		0			0
$103$	−3.18205	−	7.37683i	−0.313537	−	0.726861i	0.686463	−	0.727165i	$-0.259162\pi$
$103$	−3.18205	−	7.37683i	−0.313537	−	0.726861i	−1.00000		0.000304198i	$0.999903\pi$
$104$	−0.977487	−	0.490912i	−0.0958505	−	0.0481379i
$105$		0			0
$106$	−15.2097	−	3.60476i	−1.47729	−	0.350125i
$107$	−2.09736	+	3.63274i	−0.202760	+	0.351190i	−0.949417	−	0.314019i	$-0.898324\pi$
$107$	−2.09736	+	3.63274i	−0.202760	+	0.351190i	0.746657	+	0.665209i	$0.231658\pi$
$108$		0			0
$109$	−5.69325	−	9.86099i	−0.545314	−	0.944512i	−0.998587	−	0.0531401i	$-0.983077\pi$
$109$	−5.69325	−	9.86099i	−0.545314	−	0.944512i	0.453273	−	0.891372i	$-0.350256\pi$
$110$	−4.01889	−	13.4240i	−0.383186	−	1.27993i
$111$		0			0
$112$	−18.2674	+	12.0147i	−1.72611	+	1.13528i
$113$	−8.38939	+	11.2689i	−0.789207	+	1.06009i	0.207438	+	0.978248i	$0.433487\pi$
$113$	−8.38939	+	11.2689i	−0.789207	+	1.06009i	−0.996645	+	0.0818411i	$0.973920\pi$
$114$		0			0
$115$	1.11023	+	0.730207i	0.103529	+	0.0680921i
$116$	2.08211	−	0.757824i	0.193319	−	0.0703622i
$117$		0			0
$118$	35.1796	+	12.8043i	3.23855	+	1.17874i
$119$	−1.27485	−	1.71242i	−0.116865	−	0.156977i
$120$		0			0
$121$	5.19366	+	5.50496i	0.472151	+	0.500451i
$122$	−13.9985	−	14.8375i	−1.26736	−	1.34333i
$123$		0			0
$124$	8.54136	+	11.4730i	0.767037	+	1.03031i
$125$	5.05280	+	1.83907i	0.451936	+	0.164491i
$126$		0			0
$127$	6.95520	−	2.53149i	0.617174	−	0.224633i	−0.0144652	−	0.999895i	$-0.504605\pi$
$127$	6.95520	−	2.53149i	0.617174	−	0.224633i	0.631639	+	0.775262i	$0.282382\pi$
$128$	−8.96524	−	5.89653i	−0.792423	−	0.521185i
$129$		0			0
$130$	−0.609291	+	0.818420i	−0.0534383	+	0.0717801i
$131$	−6.01389	+	3.95540i	−0.525436	+	0.345584i	−0.784353	−	0.620315i	$-0.787005\pi$
$131$	−6.01389	+	3.95540i	−0.525436	+	0.345584i	0.258917	+	0.965900i	$0.416634\pi$
$132$		0			0
$133$	3.33034	+	11.1241i	0.288777	+	0.964584i
$134$	−15.0071	−	25.9931i	−1.29642	−	2.24546i
$135$		0			0
$136$	4.52516	−	7.83780i	0.388029	−	0.672086i
$137$	−13.7898	−	3.26824i	−1.17814	−	0.279225i	−0.405517	−	0.914087i	$-0.632909\pi$
$137$	−13.7898	−	3.26824i	−1.17814	−	0.279225i	−0.772625	+	0.634863i	$0.781057\pi$
$138$		0			0
$139$	12.2693	+	6.16188i	1.04067	+	0.522644i	0.885207	−	0.465198i	$-0.154017\pi$
$139$	12.2693	+	6.16188i	1.04067	+	0.522644i	0.155462	+	0.987842i	$0.450313\pi$
$140$	10.9049	+	25.2804i	0.921632	+	2.13658i
$141$		0			0
$142$	0.121770	−	2.09071i	0.0102187	−	0.175449i
$143$	−0.0433906	+	0.246080i	−0.00362851	+	0.0205783i
$144$		0			0
$145$	−0.216855	−	1.22985i	−0.0180089	−	0.102133i
$146$	9.52142	−	1.11289i	0.787998	−	0.0921038i
$147$		0			0
$148$	−11.9887	+	40.0452i	−0.985469	+	3.29170i
$149$	−1.99438	+	0.472677i	−0.163386	+	0.0387232i	−0.311495	−	0.950248i	$-0.600830\pi$
$149$	−1.99438	+	0.472677i	−0.163386	+	0.0387232i	0.148109	+	0.988971i	$0.452681\pi$
$150$		0			0
$151$	−4.85826	+	11.2627i	−0.395360	+	0.916547i	0.598000	+	0.801496i	$0.295962\pi$
$151$	−4.85826	+	11.2627i	−0.395360	+	0.916547i	−0.993360	+	0.115051i	$0.963297\pi$
$152$	−37.7097	+	31.6422i	−3.05866	+	2.56652i
$153$		0			0
$154$	7.20939	+	6.04940i	0.580949	+	0.487474i
$155$	7.20410	−	3.61803i	0.578647	−	0.290607i
$156$		0			0
$157$	−22.6120	−	2.64296i	−1.80463	−	0.210931i	−0.853792	−	0.520615i	$-0.825703\pi$
$157$	−22.6120	−	2.64296i	−1.80463	−	0.210931i	−0.950840	+	0.309683i	$0.899777\pi$
$158$	1.97346	+	33.8829i	0.157000	+	2.69558i
$159$		0			0
$160$	−27.6324	+	29.2887i	−2.18453	+	2.31547i
$161$	−0.892470			−0.0703365
$162$		0			0
$163$	−11.4061			−0.893393			−0.446697	−	0.894685i	$-0.647400\pi$
$163$	−11.4061			−0.893393			−0.446697	+	0.894685i	$0.647400\pi$
$164$	19.2972	−	20.4538i	1.50685	−	1.59717i
$165$		0			0
$166$	−2.58155	−	44.3235i	−0.200367	−	3.44017i
$167$	−5.33283	−	0.623319i	−0.412667	−	0.0482338i	−0.0927732	−	0.995687i	$-0.529573\pi$
$167$	−5.33283	−	0.623319i	−0.412667	−	0.0482338i	−0.319894	+	0.947453i	$0.603647\pi$
$168$		0			0
$169$	−11.6010	+	5.82622i	−0.892382	+	0.448171i
$170$	−6.46697	−	5.42643i	−0.495994	−	0.416188i
$171$		0			0
$172$	−29.0366	+	24.3646i	−2.21402	+	1.85778i
$173$	1.35044	−	3.13068i	0.102672	−	0.238021i	−0.859135	−	0.511749i	$-0.828998\pi$
$173$	1.35044	−	3.13068i	0.102672	−	0.238021i	0.961807	+	0.273728i	$0.0882569\pi$
$174$		0			0
$175$	5.79262	−	1.37288i	0.437881	−	0.103780i
$176$	−6.07279	+	20.2845i	−0.457754	+	1.52900i
$177$		0			0
$178$	28.7386	−	3.35906i	2.15405	−	0.251772i
$179$	1.16699	+	6.61830i	0.0872246	+	0.494675i	0.996854	+	0.0792553i	$0.0252542\pi$
$179$	1.16699	+	6.61830i	0.0872246	+	0.494675i	−0.909630	+	0.415420i	$0.863635\pi$
$180$		0			0
$181$	0.341126	−	1.93462i	0.0253557	−	0.143799i	−0.969502	−	0.245084i	$-0.921184\pi$
$181$	0.341126	−	1.93462i	0.0253557	−	0.143799i	0.994857	+	0.101285i	$0.0322954\pi$
$182$	0.0398445	−	0.684104i	0.00295347	−	0.0507091i
$183$		0			0
$184$	−1.49855	−	3.47402i	−0.110474	−	0.256108i
$185$	21.0539	+	10.5736i	1.54791	+	0.777390i
$186$		0			0
$187$	−2.01173	−	0.476790i	−0.147112	−	0.0348663i
$188$	−21.5557	+	37.3356i	−1.57211	+	2.72298i
$189$		0			0
$190$	22.9590	+	39.7661i	1.66562	+	2.88493i
$191$	1.34728	+	4.50022i	0.0974857	+	0.325625i	0.992796	−	0.119819i	$-0.0382313\pi$
$191$	1.34728	+	4.50022i	0.0974857	+	0.325625i	−0.895310	+	0.445443i	$0.853046\pi$
$192$		0			0
$193$	5.27148	−	3.46710i	0.379449	−	0.249568i	−0.345429	−	0.938445i	$-0.612267\pi$
$193$	5.27148	−	3.46710i	0.379449	−	0.249568i	0.724878	+	0.688877i	$0.241896\pi$
$194$	3.65040	−	4.90334i	0.262083	−	0.352039i
$195$		0			0
$196$	14.1053	+	9.27723i	1.00752	+	0.662659i
$197$	10.1410	−	3.69101i	0.722514	−	0.262973i	0.0455211	−	0.998963i	$-0.485505\pi$
$197$	10.1410	−	3.69101i	0.722514	−	0.262973i	0.676992	+	0.735990i	$0.263283\pi$
$198$		0			0
$199$	−2.20899	−	0.804005i	−0.156591	−	0.0569944i	0.262535	−	0.964922i	$-0.415441\pi$
$199$	−2.20899	−	0.804005i	−0.156591	−	0.0569944i	−0.419126	+	0.907928i	$0.637664\pi$
$200$	15.0704	+	20.2431i	1.06564	+	1.43140i
$201$		0			0
$202$	−15.6945	−	16.6352i	−1.10426	−	1.17045i
$203$	0.575571	+	0.610070i	0.0403972	+	0.0428185i
$204$		0			0
$205$	−9.46431	−	12.7128i	−0.661016	−	0.887899i
$206$	20.0498	+	7.29753i	1.39694	+	0.508443i
$207$		0			0
$208$	1.44878	−	0.527313i	0.100455	−	0.0365626i
$209$	9.39535	+	6.17942i	0.649890	+	0.427439i
$210$		0			0
$211$	−6.60517	+	8.87228i	−0.454718	+	0.610793i	−0.969070	−	0.246787i	$-0.920625\pi$
$211$	−6.60517	+	8.87228i	−0.454718	+	0.610793i	0.514351	+	0.857580i	$0.328033\pi$
$212$	24.8491	−	16.3435i	1.70665	−	1.12248i
$213$		0			0
$214$	−3.19512	−	10.6724i	−0.218414	−	0.729553i
$215$	10.6818	+	18.5014i	0.728493	+	1.26179i
$216$		0			0
$217$	−2.70715	+	4.68893i	−0.183774	+	0.318305i
$218$	29.4254	+	6.97394i	1.99294	+	0.472335i
$219$		0			0
$220$	23.8268	+	11.9663i	1.60640	+	0.806765i
$221$	0.0596256	+	0.138228i	0.00401085	+	0.00929820i
$222$		0			0
$223$	−0.235968	+	4.05141i	−0.0158016	+	0.271302i	0.981148	+	0.193257i	$0.0619050\pi$
$223$	−0.235968	+	4.05141i	−0.0158016	+	0.271302i	−0.996950	+	0.0780456i	$0.975132\pi$
$224$	4.69607	−	26.6327i	0.313769	−	1.77947i
$225$		0			0
$226$	−6.47903	−	36.7444i	−0.430979	−	2.44420i
$227$	−10.7086	+	1.25166i	−0.710756	+	0.0830755i	−0.463786	−	0.885947i	$-0.653509\pi$
$227$	−10.7086	+	1.25166i	−0.710756	+	0.0830755i	−0.246971	+	0.969023i	$0.579435\pi$
$228$		0			0
$229$	1.63605	−	5.46478i	0.108113	−	0.361123i	−0.886763	−	0.462224i	$-0.847051\pi$
$229$	1.63605	−	5.46478i	0.108113	−	0.361123i	0.994876	+	0.101101i	$0.0322366\pi$
$230$	−3.43402	+	0.813878i	−0.226433	+	0.0536656i
$231$		0			0
$232$	−1.40831	+	3.26483i	−0.0924602	+	0.214347i
$233$	20.2690	−	17.0077i	1.32787	−	1.11421i	0.343297	−	0.939227i	$-0.388456\pi$
$233$	20.2690	−	17.0077i	1.32787	−	1.11421i	0.984571	−	0.174987i	$-0.0559882\pi$
$234$		0			0
$235$	18.6135	+	15.6186i	1.21421	+	1.01885i
$236$	−63.6574	+	31.9700i	−4.14374	+	2.08107i
$237$		0			0
$238$	5.63148	+	0.658226i	0.365035	+	0.0426664i
$239$	−0.208731	−	3.58378i	−0.0135017	−	0.231816i	−0.998307	−	0.0581562i	$-0.981478\pi$
$239$	−0.208731	−	3.58378i	−0.0135017	−	0.231816i	0.984806	−	0.173659i	$-0.0555592\pi$
$240$		0			0
$241$	5.82337	−	6.17241i	0.375116	−	0.397600i	−0.512121	−	0.858913i	$-0.671140\pi$
$241$	5.82337	−	6.17241i	0.375116	−	0.397600i	0.887237	+	0.461313i	$0.152622\pi$
$242$	−20.1000			−1.29208
$243$		0			0
$244$	38.8140			2.48481
$245$	6.52985	−	6.92124i	0.417177	−	0.442182i
$246$		0			0
$247$	−0.0476098	−	0.817429i	−0.00302934	−	0.0520118i
$248$	−22.7977	−	2.66466i	−1.44765	−	0.169206i
$249$		0			0
$250$	−12.7616	+	6.40911i	−0.807114	+	0.405348i
$251$	3.14926	+	2.64255i	0.198780	+	0.166796i	0.736744	−	0.676171i	$-0.236362\pi$
$251$	3.14926	+	2.64255i	0.198780	+	0.166796i	−0.537965	+	0.842967i	$0.680807\pi$
$252$		0			0
$253$	−0.662087	+	0.555557i	−0.0416251	+	0.0349276i
$254$	−7.78584	+	18.0496i	−0.488527	+	1.13253i
$255$		0			0
$256$	−0.851704	+	0.201858i	−0.0532315	+	0.0126161i
$257$	−1.65693	+	5.53454i	−0.103357	+	0.345235i	−0.993988	−	0.109492i	$-0.965078\pi$
$257$	−1.65693	+	5.53454i	−0.103357	+	0.345235i	0.890631	+	0.454726i	$0.150263\pi$
$258$		0			0
$259$	−15.7162	+	1.83696i	−0.976559	+	0.114143i
$260$	−0.337124	−	1.91192i	−0.0209075	−	0.118573i
$261$		0			0
$262$	3.31959	−	18.8263i	0.205085	−	1.16309i
$263$	0.836130	−	14.3558i	0.0515580	−	0.885216i	−0.869049	−	0.494726i	$-0.835268\pi$
$263$	0.836130	−	14.3558i	0.0515580	−	0.885216i	0.920607	−	0.390490i	$-0.127695\pi$
$264$		0			0
$265$	−6.63952	−	15.3921i	−0.407863	−	0.945532i
$266$	−27.5590	−	13.8406i	−1.68975	−	0.848624i
$267$		0			0
$268$	55.5705	+	13.1705i	3.39451	+	0.804514i
$269$	−4.14565	+	7.18047i	−0.252765	+	0.437801i	−0.964286	−	0.264863i	$-0.914673\pi$
$269$	−4.14565	+	7.18047i	−0.252765	+	0.437801i	0.711521	+	0.702664i	$0.248006\pi$
$270$		0			0
$271$	4.28409	+	7.42026i	0.260240	+	0.450748i	0.966306	−	0.257398i	$-0.0828651\pi$
$271$	4.28409	+	7.42026i	0.260240	+	0.450748i	−0.706066	+	0.708146i	$0.749532\pi$
$272$	3.65858	+	12.2205i	0.221834	+	0.740977i
$273$		0			0
$274$	31.4459	−	20.6823i	1.89972	−	1.24946i
$275$	3.44270	−	4.62435i	0.207603	−	0.278859i
$276$		0			0
$277$	−25.6364	−	16.8613i	−1.54034	−	1.01310i	−0.983169	−	0.182700i	$-0.941516\pi$
$277$	−25.6364	−	16.8613i	−1.54034	−	1.01310i	−0.557171	−	0.830398i	$-0.688113\pi$
$278$	−34.2646	+	12.4713i	−2.05506	+	0.747979i
$279$		0			0
$280$	−41.5168	−	15.1109i	−2.48110	−	0.903048i
$281$	−2.22640	−	2.99057i	−0.132816	−	0.178403i	0.730740	−	0.682656i	$-0.239175\pi$
$281$	−2.22640	−	2.99057i	−0.132816	−	0.178403i	−0.863556	+	0.504253i	$0.831768\pi$
$282$		0			0
$283$	−4.88380	−	5.17653i	−0.290312	−	0.307713i	0.565759	−	0.824570i	$-0.308583\pi$
$283$	−4.88380	−	5.17653i	−0.290312	−	0.307713i	−0.856071	+	0.516858i	$0.827102\pi$
$284$	2.73459	+	2.89849i	0.162268	+	0.171994i
$285$		0			0
$286$	−0.396291	−	0.532312i	−0.0234332	−	0.0314762i
$287$	10.0025	+	3.64060i	0.590427	+	0.214898i
$288$		0			0
$289$	14.8043	−	5.38834i	0.870843	−	0.316961i
$290$	2.77102	+	1.82253i	0.162720	+	0.107022i
$291$		0			0
$292$	−10.8924	+	14.6310i	−0.637427	+	0.856214i
$293$	7.14612	−	4.70008i	0.417481	−	0.274581i	−0.323342	−	0.946282i	$-0.604806\pi$
$293$	7.14612	−	4.70008i	0.417481	−	0.274581i	0.740823	+	0.671701i	$0.234436\pi$
$294$		0			0
$295$	11.5148	+	38.4622i	0.670419	+	2.23935i
$296$	−33.5397	−	58.0924i	−1.94945	−	3.37655i
$297$		0			0
$298$	2.72173	−	4.71417i	0.157665	−	0.273085i
$299$	0.0612360	+	0.0145132i	0.00354137	+	0.000839320i
$300$		0			0
$301$	−12.8220	−	6.43945i	−0.739048	−	0.371164i
$302$	−12.9027	−	29.9118i	−0.742466	−	1.72123i
$303$		0			0
$304$	4.03436	−	69.2674i	0.231387	−	3.97276i
$305$	3.79876	−	21.5439i	0.217516	−	1.23360i
$306$		0			0
$307$	2.00083	+	11.3473i	0.114194	+	0.647624i	0.987146	+	0.159819i	$0.0510911\pi$
$307$	2.00083	+	11.3473i	0.114194	+	0.647624i	−0.872953	+	0.487805i	$0.837798\pi$
$308$	−17.7862	+	2.07890i	−1.01346	+	0.118457i
$309$		0			0
$310$	−6.14050	+	20.5107i	−0.348757	+	1.16493i
$311$	24.9086	−	5.90345i	1.41244	−	0.334754i	0.547572	−	0.836759i	$-0.315552\pi$
$311$	24.9086	−	5.90345i	1.41244	−	0.334754i	0.864865	+	0.502005i	$0.167404\pi$
$312$		0			0
$313$	0.597467	−	1.38508i	0.0337708	−	0.0782896i	−0.900496	−	0.434864i	$-0.856796\pi$
$313$	0.597467	−	1.38508i	0.0337708	−	0.0782896i	0.934267	+	0.356575i	$0.116056\pi$
$314$	46.3167	−	38.8644i	2.61381	−	2.19324i
$315$		0			0
$316$	−49.4714	−	41.5115i	−2.78299	−	2.33520i
$317$	−6.75232	+	3.39114i	−0.379248	+	0.190466i	−0.628203	−	0.778050i	$-0.716209\pi$
$317$	−6.75232	+	3.39114i	−0.379248	+	0.190466i	0.248955	+	0.968515i	$0.419913\pi$
$318$		0			0
$319$	0.806758	+	0.0942965i	0.0451698	+	0.00527959i
$320$	−2.43224	−	41.7600i	−0.135966	−	2.33445i
$321$		0			0
$322$	1.62656	−	1.72405i	0.0906446	−	0.0960776i
$323$	6.77481			0.376961
$324$		0			0
$325$	−0.419780			−0.0232852
$326$	20.7880	−	22.0340i	1.15134	−	1.22035i
$327$		0			0
$328$	2.62377	+	45.0485i	0.144874	+	2.48739i
$329$	−16.2088	−	1.89454i	−0.893620	−	0.104449i
$330$		0			0
$331$	27.0102	−	13.5650i	1.48461	−	0.745601i	0.492427	−	0.870354i	$-0.336110\pi$
$331$	27.0102	−	13.5650i	1.48461	−	0.745601i	0.992188	+	0.124753i	$0.0398137\pi$
$332$	64.7154	+	54.3027i	3.55172	+	2.98025i
$333$		0			0
$334$	10.9234	−	9.16582i	0.597701	−	0.501531i
$335$	12.7490	−	29.5556i	0.696554	−	1.61479i
$336$		0			0
$337$	21.9824	−	5.20993i	1.19746	−	0.283803i	0.416940	−	0.908934i	$-0.363103\pi$
$337$	21.9824	−	5.20993i	1.19746	−	0.283803i	0.780520	+	0.625131i	$0.214955\pi$
$338$	9.88823	−	33.0290i	0.537849	−	1.79654i
$339$		0			0
$340$	15.9545	−	1.86482i	0.865257	−	0.101134i
$341$	0.910502	+	5.16371i	0.0493064	+	0.279631i
$342$		0			0
$343$	−3.43492	+	19.4804i	−0.185468	+	1.05184i
$344$	3.53673	−	60.7233i	0.190688	−	3.27398i
$345$		0			0
$346$	3.58653	+	8.31452i	0.192813	+	0.446991i
$347$	16.0215	+	8.04632i	0.860082	+	0.431949i	0.823456	−	0.567380i	$-0.192043\pi$
$347$	16.0215	+	8.04632i	0.860082	+	0.431949i	0.0366256	+	0.999329i	$0.488339\pi$
$348$		0			0
$349$	−26.1088	−	6.18789i	−1.39757	−	0.331230i	−0.538300	−	0.842753i	$-0.680933\pi$
$349$	−26.1088	−	6.18789i	−1.39757	−	0.331230i	−0.859269	+	0.511523i	$0.829081\pi$
$350$	−7.90517	+	13.6921i	−0.422549	+	0.731876i
$351$		0			0
$352$	−13.0949	−	22.6810i	−0.697960	−	1.20890i
$353$	5.99125	+	20.0122i	0.318882	+	1.06514i	0.955753	+	0.294170i	$0.0950431\pi$
$353$	5.99125	+	20.0122i	0.318882	+	1.06514i	−0.636871	+	0.770970i	$0.719772\pi$
$354$		0			0
$355$	1.87645	−	1.23416i	0.0995918	−	0.0655025i
$356$	−32.8766	+	44.1609i	−1.74245	+	2.34052i
$357$		0			0
$358$	−14.9119	−	9.80774i	−0.788121	−	0.518355i
$359$	12.6815	−	4.61568i	0.669303	−	0.243606i	0.0150553	−	0.999887i	$-0.495208\pi$
$359$	12.6815	−	4.61568i	0.669303	−	0.243606i	0.654248	+	0.756280i	$0.272985\pi$
$360$		0			0
$361$	−16.7731	−	6.10492i	−0.882796	−	0.321311i
$362$	3.11554	+	4.18490i	0.163749	+	0.219953i
$363$		0			0
$364$	0.894785	+	0.948416i	0.0468995	+	0.0497105i
$365$	7.05493	+	7.47779i	0.369272	+	0.391405i
$366$		0			0
$367$	−5.89270	−	7.91527i	−0.307596	−	0.413173i	0.621265	−	0.783600i	$-0.286619\pi$
$367$	−5.89270	−	7.91527i	−0.307596	−	0.413173i	−0.928862	+	0.370427i	$0.879211\pi$
$368$	5.01116	+	1.82391i	0.261225	+	0.0950780i
$369$		0			0
$370$	−58.7974	+	21.4005i	−3.05673	+	1.11256i
$371$	9.40625	+	6.18659i	0.488348	+	0.321192i
$372$		0			0
$373$	6.44396	−	8.65574i	0.333655	−	0.448177i	−0.603358	−	0.797471i	$-0.706171\pi$
$373$	6.44396	−	8.65574i	0.333655	−	0.448177i	0.937013	+	0.349293i	$0.113578\pi$
$374$	4.58751	−	3.01725i	0.237214	−	0.156018i
$375$		0			0
$376$	−19.8415	−	66.2753i	−1.02325	−	3.41789i
$377$	−0.0295714	−	0.0512192i	−0.00152301	−	0.00263792i
$378$		0			0
$379$	−6.41085	+	11.1039i	−0.329303	+	0.570370i	−0.982374	−	0.186927i	$-0.940147\pi$
$379$	−6.41085	+	11.1039i	−0.329303	+	0.570370i	0.653071	+	0.757297i	$0.273480\pi$
$380$	−85.0157	−	20.1491i	−4.36121	−	1.03363i
$381$		0			0
$382$	−11.1489	−	5.59918i	−0.570427	−	0.286479i
$383$	5.50565	+	12.7635i	0.281326	+	0.652186i	0.999024	−	0.0441680i	$-0.0140637\pi$
$383$	5.50565	+	12.7635i	0.281326	+	0.652186i	−0.717699	+	0.696354i	$0.754804\pi$
$384$		0			0
$385$	−0.586844	+	10.0757i	−0.0299084	+	0.513507i
$386$	−2.90979	+	16.5022i	−0.148104	+	0.839942i
$387$		0			0
$388$	2.01979	+	11.4548i	0.102539	+	0.581528i
$389$	34.5433	−	4.03753i	1.75141	−	0.204711i	0.820926	−	0.571034i	$-0.193458\pi$
$389$	34.5433	−	4.03753i	1.75141	−	0.204711i	0.930488	+	0.366324i	$0.119384\pi$
$390$		0			0
$391$	−0.149338	+	0.498823i	−0.00755234	+	0.0252266i
$392$	−26.3618	+	6.24787i	−1.33147	+	0.315565i
$393$		0			0
$394$	−11.3521	+	26.3171i	−0.571909	+	1.32583i
$395$	−27.8829	+	23.3965i	−1.40294	+	1.17721i
$396$		0			0
$397$	11.3325	+	9.50911i	0.568763	+	0.477249i	0.881235	−	0.472678i	$-0.156713\pi$
$397$	11.3325	+	9.50911i	0.568763	+	0.477249i	−0.312472	+	0.949927i	$0.601157\pi$
$398$	5.57911	−	2.80194i	0.279656	−	0.140448i
$399$		0			0
$400$	−35.3309	−	4.12958i	−1.76654	−	0.206479i
$401$	−1.50994	−	25.9247i	−0.0754029	−	1.29462i	−0.797708	−	0.603044i	$-0.793954\pi$
$401$	−1.50994	−	25.9247i	−0.0754029	−	1.29462i	0.722305	−	0.691574i	$-0.243083\pi$
$402$		0			0
$403$	0.261999	−	0.277703i	0.0130511	−	0.0138334i
$404$	43.5167			2.16504
$405$		0			0
$406$	−2.22752			−0.110550
$407$	−10.5157	+	11.1460i	−0.521246	+	0.552488i
$408$		0			0
$409$	−1.20574	−	20.7018i	−0.0596200	−	1.02364i	−0.886934	−	0.461896i	$-0.847169\pi$
$409$	−1.20574	−	20.7018i	−0.0596200	−	1.02364i	0.827314	−	0.561740i	$-0.189868\pi$
$410$	41.8073	+	4.88657i	2.06471	+	0.241331i
$411$		0			0
$412$	−36.2800	+	18.2205i	−1.78739	+	0.897660i
$413$	−20.6561	−	17.3326i	−1.01642	−	0.852880i
$414$		0			0
$415$	36.4746	−	30.6058i	1.79047	−	1.50238i
$416$	−0.755313	+	1.75101i	−0.0370323	+	0.0858505i
$417$		0			0
$418$	−29.0606	+	6.88749i	−1.42140	+	0.336878i
$419$	−2.60357	+	8.69653i	−0.127193	+	0.424853i	−0.997737	−	0.0672367i	$-0.978582\pi$
$419$	−2.60357	+	8.69653i	−0.127193	+	0.424853i	0.870544	+	0.492090i	$0.163767\pi$
$420$		0			0
$421$	25.6584	−	2.99904i	1.25051	−	0.146164i	0.535054	−	0.844818i	$-0.320291\pi$
$421$	25.6584	−	2.99904i	1.25051	−	0.146164i	0.715460	+	0.698654i	$0.246217\pi$
$422$	−5.10110	−	28.9298i	−0.248318	−	1.40828i
$423$		0			0
$424$	−8.28783	+	47.0026i	−0.402492	+	2.28265i
$425$	0.201951	−	3.46736i	0.00979604	−	0.168192i
$426$		0			0
$427$	5.81938	+	13.4908i	0.281620	+	0.652868i
$428$	18.9429	+	9.51347i	0.915639	+	0.459851i
$429$		0			0
$430$	−55.2086	−	13.0847i	−2.66240	−	0.630999i
$431$	10.5319	−	18.2418i	0.507305	−	0.878678i	−0.492659	−	0.870222i	$-0.663975\pi$
$431$	10.5319	−	18.2418i	0.507305	−	0.878678i	0.999964	−	0.00845587i	$-0.00269162\pi$
$432$		0			0
$433$	−14.6179	−	25.3190i	−0.702493	−	1.21675i	−0.967589	−	0.252532i	$-0.918737\pi$
$433$	−14.6179	−	25.3190i	−0.702493	−	1.21675i	0.265095	−	0.964222i	$-0.414597\pi$
$434$	−4.12407	−	13.7754i	−0.197962	−	0.661238i
$435$		0			0
$436$	−48.0744	+	31.6190i	−2.30235	+	1.51428i
$437$	1.69126	−	2.27176i	0.0809040	−	0.108673i
$438$		0			0
$439$	20.4577	+	13.4553i	0.976394	+	0.642185i	0.934134	−	0.356922i	$-0.116174\pi$
$439$	20.4577	+	13.4553i	0.976394	+	0.642185i	0.0422600	+	0.999107i	$0.486544\pi$
$440$	−40.2061	+	14.6338i	−1.91675	+	0.697640i
$441$		0			0
$442$	−0.375695	−	0.136742i	−0.0178700	−	0.00650414i
$443$	12.1100	+	16.2665i	0.575363	+	0.772846i	0.990589	−	0.136872i	$-0.0437049\pi$
$443$	12.1100	+	16.2665i	0.575363	+	0.772846i	−0.415226	+	0.909718i	$0.636297\pi$
$444$		0			0
$445$	21.2940	+	22.5703i	1.00943	+	1.06993i
$446$	−7.39635	−	7.83967i	−0.350227	−	0.371219i
$447$		0			0
$448$	16.7767	+	22.5351i	0.792627	+	1.06468i
$449$	−29.1855	−	10.6227i	−1.37735	−	0.501314i	−0.455976	−	0.889992i	$-0.650710\pi$
$449$	−29.1855	−	10.6227i	−1.37735	−	0.501314i	−0.921374	+	0.388678i	$0.872932\pi$
$450$		0			0
$451$	9.68668	−	3.52566i	0.456128	−	0.166017i
$452$	59.3150	+	39.0121i	2.78994	+	1.83497i
$453$		0			0
$454$	17.0989	−	22.9679i	0.802493	−	1.07793i
$455$	0.613995	−	0.403831i	0.0287845	−	0.0189319i
$456$		0			0
$457$	1.55375	+	5.18989i	0.0726815	+	0.242773i	0.986609	−	0.163105i	$-0.0521509\pi$
$457$	1.55375	+	5.18989i	0.0726815	+	0.242773i	−0.913927	+	0.405878i	$0.866966\pi$
$458$	7.57498	+	13.1202i	0.353956	+	0.613069i
$459$		0			0
$460$	3.35757	−	5.81548i	0.156547	−	0.271148i
$461$	16.3680	+	3.87929i	0.762335	+	0.180677i	0.593353	−	0.804942i	$-0.297804\pi$
$461$	16.3680	+	3.87929i	0.762335	+	0.180677i	0.168982	+	0.985619i	$0.445952\pi$
$462$		0			0
$463$	5.82307	+	2.92446i	0.270621	+	0.135911i	0.578935	−	0.815374i	$-0.303468\pi$
$463$	5.82307	+	2.92446i	0.270621	+	0.135911i	−0.308314	+	0.951285i	$0.599765\pi$
$464$	−1.98501	−	4.60178i	−0.0921520	−	0.213632i
$465$		0			0
$466$	−4.08591	+	70.1524i	−0.189276	+	3.24975i
$467$	1.70237	−	9.65460i	0.0787761	−	0.446761i	−0.919751	−	0.392503i	$-0.871609\pi$
$467$	1.70237	−	9.65460i	0.0787761	−	0.446761i	0.998527	−	0.0542586i	$-0.0172795\pi$
$468$		0			0
$469$	3.75394	+	21.2896i	0.173341	+	0.983064i
$470$	−64.0955	+	7.49169i	−2.95651	+	0.345566i
$471$		0			0
$472$	32.7848	−	109.509i	1.50904	−	5.04056i
$473$	−13.5207	+	3.20445i	−0.621680	+	0.147341i
$474$		0			0
$475$	−7.48259	+	17.3466i	−0.343325	+	0.795916i
$476$	−8.26432	+	6.93459i	−0.378795	+	0.317846i
$477$		0			0
$478$	7.30348	+	6.12835i	0.334054	+	0.280304i
$479$	−3.29029	+	1.65245i	−0.150337	+	0.0755022i	−0.522377	−	0.852715i	$-0.674955\pi$
$479$	−3.29029	+	1.65245i	−0.150337	+	0.0755022i	0.372040	+	0.928217i	$0.378658\pi$
$480$		0			0
$481$	1.10823	+	0.129533i	0.0505308	+	0.00590621i
$482$	1.31041	+	22.4989i	0.0596876	+	1.02480i
$483$		0			0
$484$	26.2456	−	27.8188i	1.19298	−	1.26449i
$485$	6.55569			0.297678
$486$		0			0
$487$	21.6887			0.982808			0.491404	−	0.870932i	$-0.336484\pi$
$487$	21.6887			0.982808			0.491404	+	0.870932i	$0.336484\pi$
$488$	−42.7430	+	45.3049i	−1.93489	+	2.05086i
$489$		0			0
$490$	1.46939	+	25.2284i	0.0663802	+	1.13970i
$491$	−13.4650	−	1.57383i	−0.607666	−	0.0710259i	−0.193305	−	0.981139i	$-0.561921\pi$
$491$	−13.4650	−	1.57383i	−0.607666	−	0.0710259i	−0.414361	+	0.910113i	$0.635995\pi$
$492$		0			0
$493$	0.437294	−	0.219617i	0.0196947	−	0.00989106i
$494$	1.66586	+	1.39782i	0.0749506	+	0.0628910i
$495$		0			0
$496$	24.7831	−	20.7955i	1.11279	−	0.933745i
$497$	−0.597451	+	1.38505i	−0.0267993	+	0.0621279i
$498$		0			0
$499$	5.14154	−	1.21857i	0.230167	−	0.0545506i	−0.113914	−	0.993491i	$-0.536339\pi$
$499$	5.14154	−	1.21857i	0.230167	−	0.0545506i	0.344081	+	0.938940i	$0.388191\pi$
$500$	7.79317	−	26.0310i	0.348521	−	1.16414i
$501$		0			0
$502$	−10.8445	+	1.26754i	−0.484012	+	0.0565729i
$503$	3.77163	+	21.3900i	0.168169	+	0.953731i	0.945737	+	0.324933i	$0.105342\pi$
$503$	3.77163	+	21.3900i	0.168169	+	0.953731i	−0.777568	+	0.628798i	$0.783547\pi$
$504$		0			0
$505$	4.25901	−	24.1541i	0.189524	−	1.07484i
$506$	0.133466	−	2.29153i	0.00593330	−	0.101871i
$507$		0			0
$508$	−14.8146	−	34.3441i	−0.657292	−	1.52377i
$509$	−18.1154	−	9.09792i	−0.802953	−	0.403258i	−0.000519625	−	1.00000i	$-0.500165\pi$
$509$	−18.1154	−	9.09792i	−0.802953	−	0.403258i	−0.802433	+	0.596742i	$0.796462\pi$
$510$		0			0
$511$	−6.71847	−	1.59231i	−0.297208	−	0.0704395i
$512$	11.8929	−	20.5990i	0.525595	−	0.910358i
$513$		0			0
$514$	−7.67167	−	13.2877i	−0.338383	−	0.586096i
$515$	6.56259	+	21.9206i	0.289182	+	0.965936i
$516$		0			0
$517$	−13.2040	+	8.68440i	−0.580711	+	0.381940i
$518$	25.0948	−	33.7082i	1.10260	−	1.48105i
$519$		0			0
$520$	2.60291	+	1.71196i	0.114145	+	0.0750743i
$521$	−14.6420	+	5.32927i	−0.641479	+	0.233479i	−0.642220	−	0.766520i	$-0.721986\pi$
$521$	−14.6420	+	5.32927i	−0.641479	+	0.233479i	0.000740713		1.00000i	$0.499764\pi$
$522$		0			0
$523$	−12.3756	−	4.50436i	−0.541148	−	0.196962i	0.0569613	−	0.998376i	$-0.481859\pi$
$523$	−12.3756	−	4.50436i	−0.541148	−	0.196962i	−0.598109	+	0.801415i	$0.704081\pi$
$524$	21.7214	+	29.1769i	0.948905	+	1.27460i
$525$		0			0
$526$	26.2083	+	27.7792i	1.14274	+	1.21123i
$527$	2.16776	+	2.29770i	0.0944293	+	0.100089i
$528$		0			0
$529$	−13.6047	−	18.2742i	−0.591507	−	0.794532i
$530$	41.8350	+	15.2267i	1.81719	+	0.661405i
$531$		0			0
$532$	55.1410	−	20.0697i	2.39066	−	0.870131i
$533$	−0.627108	−	0.412455i	−0.0271630	−	0.0178654i
$534$		0			0
$535$	7.13444	−	9.58321i	0.308449	−	0.414318i
$536$	−76.5686	+	50.3600i	−3.30726	+	2.17522i
$537$		0			0
$538$	−6.31547	−	21.0951i	−0.272279	−	0.909476i
$539$	3.09447	+	5.35978i	0.133288	+	0.230862i
$540$		0			0
$541$	12.1790	−	21.0947i	0.523618	−	0.906933i	−0.476004	−	0.879443i	$-0.657915\pi$
$541$	12.1790	−	21.0947i	0.523618	−	0.906933i	0.999622	−	0.0274896i	$-0.00875133\pi$
$542$	−22.1422	−	5.24779i	−0.951088	−	0.225412i
$543$		0			0
$544$	−14.0999	−	7.08123i	−0.604527	−	0.303605i
$545$	12.8452	+	29.7784i	0.550226	+	1.27557i
$546$		0			0
$547$	0.838665	−	14.3993i	0.0358587	−	0.615671i	−0.931732	−	0.363147i	$-0.881702\pi$
$547$	0.838665	−	14.3993i	0.0358587	−	0.615671i	0.967591	−	0.252524i	$-0.0812606\pi$
$548$	−12.4359	+	70.5278i	−0.531237	+	3.01280i
$549$		0			0
$550$	2.65876	+	15.0786i	0.113370	+	0.642952i
$551$	−2.64364	+	0.308998i	−0.112623	+	0.0131637i
$552$		0			0
$553$	7.01116	−	23.4189i	0.298145	−	0.995873i
$554$	79.2955	−	18.7934i	3.36894	−	0.798454i
$555$		0			0
$556$	27.4807	−	63.7073i	1.16544	−	2.70179i
$557$	−17.7225	+	14.8710i	−0.750928	+	0.630103i	−0.935748	−	0.352669i	$-0.885274\pi$
$557$	−17.7225	+	14.8710i	−0.750928	+	0.630103i	0.184821	+	0.982772i	$0.440830\pi$
$558$		0			0
$559$	0.775053	+	0.650347i	0.0327812	+	0.0275067i
$560$	55.6496	−	27.9483i	2.35162	−	1.18103i
$561$		0			0
$562$	9.83481	+	1.14952i	0.414857	+	0.0484898i
$563$	0.0302164	+	0.518796i	0.00127347	+	0.0218647i	0.998885	−	0.0472090i	$-0.0150327\pi$
$563$	0.0302164	+	0.518796i	0.00127347	+	0.0218647i	−0.997612	+	0.0690737i	$0.977996\pi$
$564$		0			0
$565$	27.4590	−	29.1048i	1.15521	−	1.22445i
$566$	18.9008			0.794460
$567$		0			0
$568$	−6.39460			−0.268312
$569$	−2.27935	+	2.41597i	−0.0955553	+	0.101283i	−0.773386	−	0.633935i	$-0.781439\pi$
$569$	−2.27935	+	2.41597i	−0.0955553	+	0.101283i	0.677831	+	0.735218i	$0.262920\pi$
$570$		0			0
$571$	1.38043	+	23.7011i	0.0577693	+	0.991861i	0.895298	+	0.445468i	$0.146963\pi$
$571$	1.38043	+	23.7011i	0.0577693	+	0.991861i	−0.837529	+	0.546394i	$0.816000\pi$
$572$	1.25419	+	0.146594i	0.0524402	+	0.00612939i
$573$		0			0
$574$	−25.2627	+	12.6874i	−1.05444	+	0.529562i
$575$	−1.11227	−	0.933308i	−0.0463850	−	0.0389216i
$576$		0			0
$577$	−30.1749	+	25.3198i	−1.25620	+	1.05408i	−0.260123	+	0.965576i	$0.583763\pi$
$577$	−30.1749	+	25.3198i	−1.25620	+	1.05408i	−0.996076	+	0.0885007i	$0.971792\pi$
$578$	−16.5724	+	38.4191i	−0.689320	+	1.59802i
$579$		0			0
$580$	−6.14068	+	1.45537i	−0.254978	+	0.0604308i
$581$	−9.17155	+	30.6351i	−0.380500	+	1.27096i
$582$		0			0
$583$	10.8292	−	1.26576i	0.448501	−	0.0524223i
$584$	−5.08279	−	28.8259i	−0.210327	−	1.19282i
$585$		0			0
$586$	−3.94457	+	22.3708i	−0.162949	+	0.924128i
$587$	0.576562	−	9.89918i	0.0237972	−	0.408583i	−0.965283	−	0.261206i	$-0.915880\pi$
$587$	0.576562	−	9.89918i	0.0237972	−	0.408583i	0.989080	−	0.147377i	$-0.0470831\pi$
$588$		0			0
$589$	−6.80539	−	15.7767i	−0.280411	−	0.650066i
$590$	−95.2865	−	47.8547i	−3.92288	−	1.97015i
$591$		0			0
$592$	91.9998	+	21.8044i	3.78117	+	0.896153i
$593$	−5.22061	+	9.04237i	−0.214385	+	0.371326i	−0.953082	−	0.302712i	$-0.902108\pi$
$593$	−5.22061	+	9.04237i	−0.214385	+	0.371326i	0.738697	+	0.674037i	$0.235441\pi$
$594$		0			0
$595$	3.04023	+	5.26583i	0.124637	+	0.215878i
$596$	2.97059	+	9.92247i	0.121680	+	0.406440i
$597$		0			0
$598$	−0.139641	+	0.0918434i	−0.00571035	+	0.00375575i
$599$	27.1659	−	36.4901i	1.10997	−	1.49095i	0.258890	−	0.965907i	$-0.416643\pi$
$599$	27.1659	−	36.4901i	1.10997	−	1.49095i	0.851078	−	0.525039i	$-0.175949\pi$
$600$		0			0
$601$	7.83707	+	5.15452i	0.319681	+	0.210257i	0.699199	−	0.714927i	$-0.253540\pi$
$601$	7.83707	+	5.15452i	0.319681	+	0.210257i	−0.379518	+	0.925184i	$0.623910\pi$
$602$	35.8082	−	13.0331i	1.45943	−	0.531190i
$603$		0			0
$604$	58.2462	+	21.1999i	2.37000	+	0.862611i
$605$	−12.8722	−	17.2904i	−0.523329	−	0.702953i
$606$		0			0
$607$	−21.8779	−	23.1892i	−0.887997	−	0.941221i	0.110617	−	0.993863i	$-0.464717\pi$
$607$	−21.8779	−	23.1892i	−0.887997	−	0.941221i	−0.998613	+	0.0526417i	$0.983236\pi$
$608$	58.8937	+	62.4237i	2.38845	+	2.53161i
$609$		0			0
$610$	34.6945	+	46.6028i	1.40474	+	1.88689i
$611$	1.08134	+	0.393577i	0.0437465	+	0.0159224i
$612$		0			0
$613$	−23.7444	+	8.64224i	−0.959025	+	0.349057i	−0.773652	−	0.633611i	$-0.781572\pi$
$613$	−23.7444	+	8.64224i	−0.959025	+	0.349057i	−0.185374	+	0.982668i	$0.559350\pi$
$614$	−25.5670	−	16.8157i	−1.03180	−	0.678626i
$615$		0			0
$616$	17.1600	−	23.0499i	0.691397	−	0.928707i
$617$	−6.63890	+	4.36647i	−0.267272	+	0.175788i	−0.676070	−	0.736837i	$-0.736318\pi$
$617$	−6.63890	+	4.36647i	−0.267272	+	0.175788i	0.408798	+	0.912625i	$0.365948\pi$
$618$		0			0
$619$	10.2509	+	34.2405i	0.412019	+	1.37624i	0.872519	+	0.488580i	$0.162485\pi$
$619$	10.2509	+	34.2405i	0.412019	+	1.37624i	−0.460500	+	0.887660i	$0.652330\pi$
$620$	−20.3692	−	35.2805i	−0.818047	−	1.41690i
$621$		0			0
$622$	−33.9927	+	58.8771i	−1.36298	+	2.36076i
$623$	−20.2785	−	4.80608i	−0.812439	−	0.192552i
$624$		0			0
$625$	−27.5912	−	13.8568i	−1.10365	−	0.554273i
$626$	1.58677	+	3.67854i	0.0634200	+	0.147024i
$627$		0			0
$628$	−6.68928	+	114.851i	−0.266931	+	4.58304i
$629$	−1.60309	+	9.09157i	−0.0639193	+	0.362504i
$630$		0			0
$631$	−3.64311	−	20.6611i	−0.145030	−	0.822506i	−0.967343	−	0.253471i	$-0.918428\pi$
$631$	−3.64311	−	20.6611i	−0.145030	−	0.822506i	0.822313	−	0.569035i	$-0.192683\pi$
$632$	102.933	−	12.0311i	4.09444	−	0.478572i
$633$		0			0
$634$	5.75542	−	19.2245i	0.228577	−	0.763501i
$635$	−20.5127	+	4.86160i	−0.814022	+	0.192927i
$636$		0			0
$637$	0.178489	−	0.413784i	0.00707199	−	0.0163947i
$638$	−1.65251	+	1.38662i	−0.0654233	+	0.0548967i
$639$		0			0
$640$	23.4122	+	19.6452i	0.925449	+	0.776544i
$641$	4.26195	−	2.14043i	0.168337	−	0.0845420i	−0.362636	−	0.931931i	$-0.618123\pi$
$641$	4.26195	−	2.14043i	0.168337	−	0.0845420i	0.530973	+	0.847389i	$0.321827\pi$
$642$		0			0
$643$	8.05217	+	0.941164i	0.317547	+	0.0371159i	0.273373	−	0.961908i	$-0.411861\pi$
$643$	8.05217	+	0.941164i	0.317547	+	0.0371159i	0.0441733	+	0.999024i	$0.485935\pi$
$644$	0.262233	+	4.50237i	0.0103334	+	0.177418i
$645$		0			0
$646$	−12.3473	+	13.0874i	−0.485800	+	0.514918i
$647$	−10.4984			−0.412736			−0.206368	−	0.978474i	$-0.566164\pi$
$647$	−10.4984			−0.412736			−0.206368	+	0.978474i	$0.566164\pi$
$648$		0			0
$649$	−26.1134			−1.02504
$650$	0.765065	−	0.810922i	0.0300083	−	0.0318070i
$651$		0			0
$652$	3.35144	+	57.5420i	0.131252	+	2.25352i
$653$	−46.4167	−	5.42533i	−1.81642	−	0.212310i	−0.861215	−	0.508240i	$-0.830296\pi$
$653$	−46.4167	−	5.42533i	−1.81642	−	0.212310i	−0.955209	+	0.295931i	$0.904370\pi$
$654$		0			0
$655$	18.3206	−	9.20097i	0.715847	−	0.359512i
$656$	−48.7230	−	40.8835i	−1.90231	−	1.59623i
$657$		0			0
$658$	33.2010	−	27.8589i	1.29431	−	1.08605i
$659$	−6.00323	+	13.9170i	−0.233852	+	0.542131i	−0.994220	−	0.107362i	$-0.965760\pi$
$659$	−6.00323	+	13.9170i	−0.233852	+	0.542131i	0.760368	+	0.649493i	$0.225019\pi$
$660$		0			0
$661$	−46.7631	+	11.0831i	−1.81888	+	0.431081i	−0.991449	−	0.130494i	$-0.958344\pi$
$661$	−46.7631	+	11.0831i	−1.81888	+	0.431081i	−0.827426	+	0.561575i	$0.810196\pi$
$662$	−23.0225	+	76.9004i	−0.894794	+	2.98882i
$663$		0			0
$664$	−134.650	+	15.7383i	−5.22543	+	0.610765i
$665$	−5.74304	−	32.5704i	−0.222706	−	1.26303i
$666$		0			0
$667$	0.0355229	−	0.201460i	0.00137545	−	0.00780057i
$668$	−1.57761	+	27.0865i	−0.0610395	+	1.04801i
$669$		0			0
$670$	33.8592	+	78.4944i	1.30809	+	3.03250i
$671$	12.7151	+	6.38578i	0.490862	+	0.246520i
$672$		0			0
$673$	−25.8107	−	6.11725i	−0.994930	−	0.235803i	−0.299266	−	0.954170i	$-0.596742\pi$
$673$	−25.8107	−	6.11725i	−0.994930	−	0.235803i	−0.695664	+	0.718367i	$0.744890\pi$
$674$	−29.9994	+	51.9604i	−1.15553	+	2.00144i
$675$		0			0
$676$	32.8011	+	56.8132i	1.26158	+	2.18512i
$677$	−13.5662	−	45.3143i	−0.521392	−	1.74157i	−0.660041	−	0.751230i	$-0.729461\pi$
$677$	−13.5662	−	45.3143i	−0.521392	−	1.74157i	0.138649	−	0.990342i	$-0.455724\pi$
$678$		0			0
$679$	−3.67858	+	2.41944i	−0.141171	+	0.0928496i
$680$	−15.3929	+	20.6762i	−0.590290	+	0.792897i
$681$		0			0
$682$	−11.6346	−	7.65217i	−0.445510	−	0.293017i
$683$	−14.6776	+	5.34220i	−0.561622	+	0.204414i	−0.607203	−	0.794547i	$-0.707708\pi$
$683$	−14.6776	+	5.34220i	−0.561622	+	0.204414i	0.0455809	+	0.998961i	$0.485486\pi$
$684$		0			0
$685$	37.9295	+	13.8052i	1.44921	+	0.527470i
$686$	−31.3715	−	42.1392i	−1.19777	−	1.60888i
$687$		0			0
$688$	58.8346	+	62.3611i	2.24305	+	2.37749i
$689$	−0.544796	−	0.577450i	−0.0207551	−	0.0219991i
$690$		0			0
$691$	3.91734	+	5.26190i	0.149023	+	0.200172i	0.870366	−	0.492406i	$-0.163882\pi$
$691$	3.91734	+	5.26190i	0.149023	+	0.200172i	−0.721343	+	0.692578i	$0.756475\pi$
$692$	−16.1906	−	5.89289i	−0.615474	−	0.224014i
$693$		0			0
$694$	−44.7436	+	16.2853i	−1.69844	+	0.618182i
$695$	−32.6714	−	21.4883i	−1.23930	−	0.815098i
$696$		0			0
$697$	3.70854	−	4.98144i	0.140471	−	0.188685i
$698$	59.5378	−	39.1586i	2.25354	−	1.48218i
$699$		0			0
$700$	−8.62799	−	28.8195i	−0.326107	−	1.08927i
$701$	−11.9474	−	20.6936i	−0.451249	−	0.781586i	0.547215	−	0.836992i	$-0.315688\pi$
$701$	−11.9474	−	20.6936i	−0.451249	−	0.781586i	−0.998464	+	0.0554061i	$0.982355\pi$
$702$		0			0
$703$	25.1069	−	43.4864i	0.946924	−	1.64012i
$704$	26.4739	+	6.27444i	0.997774	+	0.236477i
$705$		0			0
$706$	−49.5783	−	24.8992i	−1.86590	−	0.937092i
$707$	6.52445	+	15.1254i	0.245377	+	0.568848i
$708$		0			0
$709$	2.69978	−	46.3535i	0.101393	−	1.74084i	−0.438165	−	0.898894i	$-0.644372\pi$
$709$	2.69978	−	46.3535i	0.101393	−	1.74084i	0.539558	−	0.841948i	$-0.318591\pi$
$710$	−1.03578	+	5.87419i	−0.0388721	+	0.220455i
$711$		0			0
$712$	−15.3414	−	87.0056i	−0.574945	−	3.26067i
$713$	1.31163	−	0.153308i	0.0491210	−	0.00574142i
$714$		0			0
$715$	0.204116	−	0.681794i	0.00763349	−	0.0254976i
$716$	33.0454	−	7.83191i	1.23497	−	0.292692i
$717$		0			0
$718$	−14.1960	+	32.9100i	−0.529790	+	1.22819i
$719$	−3.57771	+	3.00206i	−0.133426	+	0.111958i	−0.707059	−	0.707155i	$-0.749978\pi$
$719$	−3.57771	+	3.00206i	−0.133426	+	0.111958i	0.573632	+	0.819113i	$0.305534\pi$
$720$		0			0
$721$	−11.7725	−	9.87828i	−0.438430	−	0.367886i
$722$	42.3630	−	21.2755i	1.57659	−	0.791791i
$723$		0			0
$724$	−9.86011	−	1.15248i	−0.366448	−	0.0428316i
$725$	0.0793410	+	1.36223i	0.00294665	+	0.0505920i
$726$		0			0
$727$	23.7620	−	25.1863i	0.881285	−	0.934107i	−0.116972	−	0.993135i	$-0.537319\pi$
$727$	23.7620	−	25.1863i	0.881285	−	0.934107i	0.998256	+	0.0590282i	$0.0188002\pi$
$728$	−2.09238			−0.0775488
$729$		0			0
$730$	−27.3033			−1.01054
$731$	−5.74469	+	6.08901i	−0.212475	+	0.225210i
$732$		0			0
$733$	2.61871	+	44.9615i	0.0967242	+	1.66069i	0.602570	+	0.798066i	$0.294143\pi$
$733$	2.61871	+	44.9615i	0.0967242	+	1.66069i	−0.505846	+	0.862624i	$0.668820\pi$
$734$	26.0302	+	3.04249i	0.960791	+	0.112300i
$735$		0			0
$736$	−5.89439	+	2.96027i	−0.217270	+	0.109117i
$737$	16.0376	+	13.4571i	0.590752	+	0.495699i
$738$		0			0
$739$	−38.9851	+	32.7123i	−1.43409	+	1.20334i	−0.490842	+	0.871249i	$0.663311\pi$
$739$	−38.9851	+	32.7123i	−1.43409	+	1.20334i	−0.943246	+	0.332094i	$0.892245\pi$
$740$	47.1562	−	109.320i	1.73350	−	4.01870i
$741$		0			0
$742$	−29.0943	+	6.89549i	−1.06809	+	0.253141i
$743$	5.23961	−	17.5015i	0.192222	−	0.642068i	−0.806486	−	0.591254i	$-0.798633\pi$
$743$	5.23961	−	17.5015i	0.192222	−	0.642068i	0.998708	−	0.0508142i	$-0.0161816\pi$
$744$		0			0
$745$	5.79823	−	0.677716i	0.212431	−	0.0248296i
$746$	4.97660	+	28.2237i	0.182206	+	1.03334i
$747$		0			0
$748$	−1.81423	+	10.2890i	−0.0663347	+	0.376203i
$749$	−0.466556	+	8.01045i	−0.0170476	+	0.292696i
$750$		0			0
$751$	8.78368	+	20.3629i	0.320521	+	0.743051i	0.999957	+	0.00931599i	$0.00296541\pi$
$751$	8.78368	+	20.3629i	0.320521	+	0.743051i	−0.679436	+	0.733735i	$0.737775\pi$
$752$	87.1395	+	43.7631i	3.17765	+	1.59588i
$753$		0			0
$754$	0.152839	+	0.0362235i	0.00556607	+	0.00131918i
$755$	17.4677	−	30.2549i	0.635713	−	1.10109i
$756$		0			0
$757$	−1.95553	−	3.38708i	−0.0710750	−	0.123106i	0.828298	−	0.560288i	$-0.189310\pi$
$757$	−1.95553	−	3.38708i	−0.0710750	−	0.123106i	−0.899373	+	0.437183i	$0.855976\pi$
$758$	−9.76627	−	32.6216i	−0.354727	−	1.18487i
$759$		0			0
$760$	117.140	−	77.0443i	4.24912	−	2.79469i
$761$	−1.87452	+	2.51792i	−0.0679514	+	0.0912745i	−0.834800	−	0.550554i	$-0.814417\pi$
$761$	−1.87452	+	2.51792i	−0.0679514	+	0.0912745i	0.766848	+	0.641829i	$0.221824\pi$
$762$		0			0
$763$	−18.1978	−	11.9689i	−0.658805	−	0.433303i
$764$	22.3071	−	8.11911i	0.807042	−	0.293739i
$765$		0			0
$766$	−34.6905	−	12.6263i	−1.25342	−	0.456207i
$767$	1.13544	+	1.52516i	0.0409985	+	0.0550705i
$768$		0			0
$769$	14.2206	+	15.0729i	0.512808	+	0.543544i	0.931098	−	0.364769i	$-0.118852\pi$
$769$	14.2206	+	15.0729i	0.512808	+	0.543544i	−0.418290	+	0.908313i	$0.637371\pi$
$770$	−18.3945	−	19.4970i	−0.662892	−	0.702624i
$771$		0			0
$772$	−19.0399	−	25.5751i	−0.685262	−	0.920467i
$773$	−18.6463	−	6.78668i	−0.670659	−	0.244100i	−0.0158274	−	0.999875i	$-0.505038\pi$
$773$	−18.6463	−	6.78668i	−0.670659	−	0.244100i	−0.654832	+	0.755775i	$0.727260\pi$
$774$		0			0
$775$	−8.27738	+	3.01272i	−0.297332	+	0.108220i
$776$	−15.5946	−	10.2567i	−0.559814	−	0.368195i
$777$		0			0
$778$	−55.1568	+	74.0884i	−1.97747	+	2.65620i
$779$	−28.2221	+	18.5620i	−1.01116	+	0.665051i
$780$		0			0
$781$	0.418959	+	1.39942i	0.0149915	+	0.0500752i
$782$	−0.691441	−	1.19761i	−0.0247259	−	0.0428264i
$783$		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:	\( N \)	\(=\)	\( 729 = 3^{6} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	729.g (of order \(27\), degree \(18\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.82254 + 1.93178i) q^{2} +(-0.293829 - 5.04485i) q^{4} +(-2.82892 - 0.330653i) q^{5} +(1.70942 - 0.858501i) q^{7} +(6.21207 + 5.21255i) q^{8} +O(q^{10})\)	\(q+(-1.82254 + 1.93178i) q^{2} +(-0.293829 - 5.04485i) q^{4} +(-2.82892 - 0.330653i) q^{5} +(1.70942 - 0.858501i) q^{7} +(6.21207 + 5.21255i) q^{8} +(5.79455 - 4.86220i) q^{10} +(0.733735 - 1.70099i) q^{11} +(-0.131251 + 0.0311070i) q^{13} +(-1.45704 + 4.86686i) q^{14} +(-11.3528 + 1.32695i) q^{16} +(-0.193799 - 1.09909i) q^{17} +(-1.05411 + 5.97816i) q^{19} +(-0.836876 + 14.3686i) q^{20} +(1.94867 + 4.51753i) q^{22} +(-0.416930 - 0.209390i) q^{23} +(3.02821 + 0.717699i) q^{25} +(0.179118 - 0.310241i) q^{26} +(-4.83328 - 8.37149i) q^{28} +(0.125753 + 0.420043i) q^{29} +(-2.36480 + 1.55535i) q^{31} +(8.44238 - 11.3401i) q^{32} +(2.47640 + 1.62875i) q^{34} +(-5.11966 + 1.86340i) q^{35} +(-7.77306 - 2.82916i) q^{37} +(-9.62732 - 12.9317i) q^{38} +(-15.8499 - 16.7999i) q^{40} +(3.81865 + 4.04753i) q^{41} +(-4.47917 - 6.01657i) q^{43} +(-8.79682 - 3.20178i) q^{44} +(1.16437 - 0.423795i) q^{46} +(-7.12769 - 4.68795i) q^{47} +(-1.99503 + 2.67979i) q^{49} +(-6.90546 + 4.54179i) q^{50} +(0.195495 + 0.653000i) q^{52} +(2.94278 + 5.09704i) q^{53} +(-2.63811 + 4.56934i) q^{55} +(15.0940 + 3.57734i) q^{56} +(-1.04062 - 0.522618i) q^{58} +(-5.58328 - 12.9435i) q^{59} +(-0.446598 + 7.66779i) q^{61} +(1.30534 - 7.40295i) q^{62} +(2.55035 + 14.4637i) q^{64} +(0.381583 - 0.0446007i) q^{65} +(-3.24125 + 10.8265i) q^{67} +(-5.48779 + 1.30063i) q^{68} +(5.73109 - 13.2862i) q^{70} +(-0.604067 + 0.506872i) q^{71} +(-2.76505 - 2.32015i) q^{73} +(19.6320 - 9.85956i) q^{74} +(30.4687 + 3.56128i) q^{76} +(-0.206042 - 3.53761i) q^{77} +(8.76989 - 9.29554i) q^{79} +32.5547 q^{80} -14.7786 q^{82} +(-11.4722 + 12.1598i) q^{83} +(0.184824 + 3.17331i) q^{85} +(19.7861 + 2.31267i) q^{86} +(13.4245 - 6.74204i) q^{88} +(-8.34578 - 7.00294i) q^{89} +(-0.197657 + 0.165854i) q^{91} +(-0.933836 + 2.16488i) q^{92} +(22.0466 - 5.22513i) q^{94} +(4.95869 - 16.5632i) q^{95} +(-2.28615 + 0.267213i) q^{97} +(-1.54074 - 8.73797i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q - 9 q^{2} + 9 q^{4} - 9 q^{5} + 9 q^{7} + 18 q^{8}+O(q^{10}) \) 144 * q - 9 * q^2 + 9 * q^4 - 9 * q^5 + 9 * q^7 + 18 * q^8	\( 144 q - 9 q^{2} + 9 q^{4} - 9 q^{5} + 9 q^{7} + 18 q^{8} - 18 q^{10} - 9 q^{11} + 9 q^{13} - 9 q^{14} + 9 q^{16} + 18 q^{17} - 18 q^{19} + 63 q^{20} + 9 q^{22} - 36 q^{23} + 9 q^{25} - 45 q^{26} - 9 q^{28} + 45 q^{29} + 9 q^{31} - 63 q^{32} + 9 q^{34} - 9 q^{35} - 18 q^{37} + 9 q^{38} + 9 q^{40} + 27 q^{41} + 9 q^{43} - 54 q^{44} - 18 q^{46} - 63 q^{47} + 9 q^{49} + 225 q^{50} + 27 q^{52} - 45 q^{53} - 9 q^{55} - 99 q^{56} + 9 q^{58} + 117 q^{59} + 9 q^{61} - 81 q^{62} - 18 q^{64} - 81 q^{65} + 36 q^{67} + 18 q^{68} + 63 q^{70} + 90 q^{71} - 18 q^{73} - 81 q^{74} + 90 q^{76} - 81 q^{77} + 63 q^{79} + 288 q^{80} - 36 q^{82} - 45 q^{83} + 63 q^{85} - 81 q^{86} + 90 q^{88} + 81 q^{89} - 18 q^{91} + 63 q^{92} + 63 q^{94} - 153 q^{95} + 36 q^{97} - 81 q^{98}+O(q^{100}) \) 144 * q - 9 * q^2 + 9 * q^4 - 9 * q^5 + 9 * q^7 + 18 * q^8 - 18 * q^10 - 9 * q^11 + 9 * q^13 - 9 * q^14 + 9 * q^16 + 18 * q^17 - 18 * q^19 + 63 * q^20 + 9 * q^22 - 36 * q^23 + 9 * q^25 - 45 * q^26 - 9 * q^28 + 45 * q^29 + 9 * q^31 - 63 * q^32 + 9 * q^34 - 9 * q^35 - 18 * q^37 + 9 * q^38 + 9 * q^40 + 27 * q^41 + 9 * q^43 - 54 * q^44 - 18 * q^46 - 63 * q^47 + 9 * q^49 + 225 * q^50 + 27 * q^52 - 45 * q^53 - 9 * q^55 - 99 * q^56 + 9 * q^58 + 117 * q^59 + 9 * q^61 - 81 * q^62 - 18 * q^64 - 81 * q^65 + 36 * q^67 + 18 * q^68 + 63 * q^70 + 90 * q^71 - 18 * q^73 - 81 * q^74 + 90 * q^76 - 81 * q^77 + 63 * q^79 + 288 * q^80 - 36 * q^82 - 45 * q^83 + 63 * q^85 - 81 * q^86 + 90 * q^88 + 81 * q^89 - 18 * q^91 + 63 * q^92 + 63 * q^94 - 153 * q^95 + 36 * q^97 - 81 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more