LMFDB - Embedded newform 729.2.g.c.136.1

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			136.1
Character	$\chi$	$=$	729.136
Dual form			729.2.g.c.595.1

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.42780 - 0.575399i) q^{2} +(3.77586 + 1.89631i) q^{4} +(-0.840538 + 1.12904i) q^{5} +(2.66534 + 1.75302i) q^{7} +(-4.25325 - 3.56890i) q^{8} +(2.69030 - 2.25743i) q^{10} +(4.70499 - 0.549934i) q^{11} +(-0.611668 + 2.04311i) q^{13} +(-5.46222 - 5.78962i) q^{14} +(3.22615 + 4.33347i) q^{16} +(0.520249 + 2.95048i) q^{17} +(1.23380 - 6.99724i) q^{19} +(-5.31475 + 2.66917i) q^{20} +(-11.7392 - 1.37211i) q^{22} +(2.52656 - 1.66174i) q^{23} +(0.865793 + 2.89195i) q^{25} +(2.66061 - 4.60832i) q^{26} +(6.73968 + 11.6735i) q^{28} +(-1.51122 + 1.60180i) q^{29} +(0.218978 + 3.75972i) q^{31} +(-0.940724 - 2.18084i) q^{32} +(0.434642 - 7.46252i) q^{34} +(-4.21955 + 1.53579i) q^{35} +(-6.31317 - 2.29781i) q^{37} +(-7.02162 + 16.2780i) q^{38} +(7.60443 - 1.80228i) q^{40} +(-4.12091 + 0.976673i) q^{41} +(0.314456 - 0.728991i) q^{43} +(18.8082 + 6.84563i) q^{44} +(-7.09015 + 2.58060i) q^{46} +(0.336396 - 5.77569i) q^{47} +(1.25839 + 2.91728i) q^{49} +(-0.437946 - 7.51925i) q^{50} +(-6.18394 + 6.55460i) q^{52} +(4.83254 + 8.37020i) q^{53} +(-3.33382 + 5.77435i) q^{55} +(-5.07999 - 16.9684i) q^{56} +(4.59063 - 3.01930i) q^{58} +(1.59501 + 0.186430i) q^{59} +(-1.03722 + 0.520912i) q^{61} +(1.63170 - 9.25383i) q^{62} +(-0.847235 - 4.80491i) q^{64} +(-1.79262 - 2.40791i) q^{65} +(4.10492 + 4.35096i) q^{67} +(-3.63063 + 12.1271i) q^{68} +(11.1279 - 1.30066i) q^{70} +(2.74773 - 2.30562i) q^{71} +(8.55952 + 7.18229i) q^{73} +(14.0050 + 9.21120i) q^{74} +(17.9276 - 24.0809i) q^{76} +(13.5044 + 6.78218i) q^{77} +(4.56192 + 1.08119i) q^{79} -7.60435 q^{80} +10.5667 q^{82} +(14.5564 + 3.44993i) q^{83} +(-3.76849 - 1.89261i) q^{85} +(-1.18290 + 1.58891i) q^{86} +(-21.9741 - 14.4526i) q^{88} +(3.17449 + 2.66371i) q^{89} +(-5.21193 + 4.37333i) q^{91} +(12.6911 - 1.48338i) q^{92} +(-4.14003 + 13.8286i) q^{94} +(6.86309 + 7.27445i) q^{95} +(7.51692 + 10.0970i) q^{97} +(-1.37652 - 7.80666i) q^{98} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$144 q + 9 q^{2} + 9 q^{4} + 9 q^{5} + 9 q^{7} - 18 q^{8} - 18 q^{10} + 9 q^{11} + 9 q^{13} + 9 q^{14} + 9 q^{16} - 18 q^{17} - 18 q^{19} - 63 q^{20} + 9 q^{22} + 36 q^{23} + 9 q^{25} + 45 q^{26} - 9 q^{28}+ \cdots + 81 q^{98}+O(q^{100})$ 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

Character values

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

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

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

)

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

$2$	−2.42780	−	0.575399i	−1.71671	−	0.406868i	−0.749737	−	0.661736i	$-0.769820\pi$
$2$	−2.42780	−	0.575399i	−1.71671	−	0.406868i	−0.966976	+	0.254868i	$0.917968\pi$
$3$		0			0
$3$		0			0
$4$	3.77586	+	1.89631i	1.88793	+	0.948153i
$5$	−0.840538	+	1.12904i	−0.375900	+	0.504921i	−0.949307	−	0.314349i	$-0.898214\pi$
$5$	−0.840538	+	1.12904i	−0.375900	+	0.504921i	0.573408	+	0.819270i	$0.305621\pi$
$6$		0			0
$7$	2.66534	+	1.75302i	1.00740	+	0.662580i	0.942116	−	0.335287i	$-0.108833\pi$
$7$	2.66534	+	1.75302i	1.00740	+	0.662580i	0.0652876	+	0.997866i	$0.479204\pi$
$8$	−4.25325	−	3.56890i	−1.50375	−	1.26180i
$9$		0			0
$10$	2.69030	−	2.25743i	0.850749	−	0.713863i
$11$	4.70499	−	0.549934i	1.41861	−	0.165811i	0.628037	−	0.778183i	$-0.283859\pi$
$11$	4.70499	−	0.549934i	1.41861	−	0.165811i	0.790570	+	0.612372i	$0.209785\pi$
$12$		0			0
$13$	−0.611668	+	2.04311i	−0.169646	+	0.566658i	0.830310	+	0.557302i	$0.188163\pi$
$13$	−0.611668	+	2.04311i	−0.169646	+	0.566658i	−0.999956	+	0.00935611i	$0.997022\pi$
$14$	−5.46222	−	5.78962i	−1.45984	−	1.54734i
$15$		0			0
$16$	3.22615	+	4.33347i	0.806537	+	1.08337i
$17$	0.520249	+	2.95048i	0.126179	+	0.715596i	0.980601	+	0.196016i	$0.0628004\pi$
$17$	0.520249	+	2.95048i	0.126179	+	0.715596i	−0.854422	+	0.519580i	$0.826088\pi$
$18$		0			0
$19$	1.23380	−	6.99724i	0.283053	−	1.60528i	−0.429103	−	0.903255i	$-0.641170\pi$
$19$	1.23380	−	6.99724i	0.283053	−	1.60528i	0.712157	−	0.702020i	$-0.247718\pi$
$20$	−5.31475	+	2.66917i	−1.18841	+	0.596844i
$21$		0			0
$22$	−11.7392	−	1.37211i	−2.50280	−	0.292536i
$23$	2.52656	−	1.66174i	0.526824	−	0.346498i	−0.258071	−	0.966126i	$-0.583087\pi$
$23$	2.52656	−	1.66174i	0.526824	−	0.346498i	0.784896	+	0.619628i	$0.212717\pi$
$24$		0			0
$25$	0.865793	+	2.89195i	0.173159	+	0.578390i
$26$	2.66061	−	4.60832i	0.521789	−	0.903765i
$27$		0			0
$28$	6.73968	+	11.6735i	1.27368	+	2.20608i
$29$	−1.51122	+	1.60180i	−0.280627	+	0.297448i	−0.852320	−	0.523020i	$-0.824805\pi$
$29$	−1.51122	+	1.60180i	−0.280627	+	0.297448i	0.571693	+	0.820468i	$0.306287\pi$
$30$		0			0
$31$	0.218978	+	3.75972i	0.0393297	+	0.675265i	0.959145	+	0.282914i	$0.0913011\pi$
$31$	0.218978	+	3.75972i	0.0393297	+	0.675265i	−0.919816	+	0.392351i	$0.871662\pi$
$32$	−0.940724	−	2.18084i	−0.166298	−	0.385522i
$33$		0			0
$34$	0.434642	−	7.46252i	0.0745405	−	1.27981i
$35$	−4.21955	+	1.53579i	−0.713233	+	0.259596i
$36$		0			0
$37$	−6.31317	−	2.29781i	−1.03788	−	0.377757i	−0.233803	−	0.972284i	$-0.575117\pi$
$37$	−6.31317	−	2.29781i	−1.03788	−	0.377757i	−0.804076	+	0.594527i	$0.797339\pi$
$38$	−7.02162	+	16.2780i	−1.13906	+	2.64063i
$39$		0			0
$40$	7.60443	−	1.80228i	1.20237	−	0.284966i
$41$	−4.12091	+	0.976673i	−0.643578	+	0.152531i	−0.539429	−	0.842031i	$-0.681360\pi$
$41$	−4.12091	+	0.976673i	−0.643578	+	0.152531i	−0.104149	+	0.994562i	$0.533212\pi$
$42$		0			0
$43$	0.314456	−	0.728991i	0.0479541	−	0.111170i	−0.892555	−	0.450938i	$-0.851089\pi$
$43$	0.314456	−	0.728991i	0.0479541	−	0.111170i	0.940509	+	0.339768i	$0.110349\pi$
$44$	18.8082	+	6.84563i	2.83544	+	1.03202i
$45$		0			0
$46$	−7.09015	+	2.58060i	−1.04538	+	0.380489i
$47$	0.336396	−	5.77569i	0.0490683	−	0.842471i	−0.880551	−	0.473951i	$-0.842828\pi$
$47$	0.336396	−	5.77569i	0.0490683	−	0.842471i	0.929620	−	0.368520i	$-0.120135\pi$
$48$		0			0
$49$	1.25839	+	2.91728i	0.179770	+	0.416755i
$50$	−0.437946	−	7.51925i	−0.0619350	−	1.06338i
$51$		0			0
$52$	−6.18394	+	6.55460i	−0.857559	+	0.908959i
$53$	4.83254	+	8.37020i	0.663800	+	1.14973i	0.979609	+	0.200912i	$0.0643906\pi$
$53$	4.83254	+	8.37020i	0.663800	+	1.14973i	−0.315809	+	0.948823i	$0.602276\pi$
$54$		0			0
$55$	−3.33382	+	5.77435i	−0.449532	+	0.778613i
$56$	−5.07999	−	16.9684i	−0.678843	−	2.26749i
$57$		0			0
$58$	4.59063	−	3.01930i	0.602779	−	0.396454i
$59$	1.59501	+	0.186430i	0.207653	+	0.0242712i	0.219284	−	0.975661i	$-0.429628\pi$
$59$	1.59501	+	0.186430i	0.207653	+	0.0242712i	−0.0116303	+	0.999932i	$0.503702\pi$
$60$		0			0
$61$	−1.03722	+	0.520912i	−0.132803	+	0.0666959i	−0.513960	−	0.857814i	$-0.671822\pi$
$61$	−1.03722	+	0.520912i	−0.132803	+	0.0666959i	0.381157	+	0.924510i	$0.375526\pi$
$62$	1.63170	−	9.25383i	0.207226	−	1.17524i
$63$		0			0
$64$	−0.847235	−	4.80491i	−0.105904	−	0.600613i
$65$	−1.79262	−	2.40791i	−0.222348	−	0.298665i
$66$		0			0
$67$	4.10492	+	4.35096i	0.501496	+	0.531555i	0.927826	−	0.373013i	$-0.121675\pi$
$67$	4.10492	+	4.35096i	0.501496	+	0.531555i	−0.426330	+	0.904568i	$0.640194\pi$
$68$	−3.63063	+	12.1271i	−0.440278	+	1.47063i
$69$		0			0
$70$	11.1279	−	1.30066i	1.33004	−	0.155459i
$71$	2.74773	−	2.30562i	0.326095	−	0.273626i	−0.465011	−	0.885305i	$-0.653950\pi$
$71$	2.74773	−	2.30562i	0.326095	−	0.273626i	0.791107	+	0.611678i	$0.209505\pi$
$72$		0			0
$73$	8.55952	+	7.18229i	1.00182	+	0.840623i	0.987235	−	0.159270i	$-0.0509141\pi$
$73$	8.55952	+	7.18229i	1.00182	+	0.840623i	0.0145810	+	0.999894i	$0.495359\pi$
$74$	14.0050	+	9.21120i	1.62804	+	1.07078i
$75$		0			0
$76$	17.9276	−	24.0809i	2.05643	−	2.76227i
$77$	13.5044	+	6.78218i	1.53897	+	0.772901i
$78$		0			0
$79$	4.56192	+	1.08119i	0.513256	+	0.121644i	0.479079	−	0.877772i	$-0.340971\pi$
$79$	4.56192	+	1.08119i	0.513256	+	0.121644i	0.0341770	+	0.999416i	$0.489119\pi$
$80$	−7.60435			−0.850192
$81$		0			0
$82$	10.5667			1.16690
$83$	14.5564	+	3.44993i	1.59777	+	0.378679i	0.930545	−	0.366177i	$-0.119334\pi$
$83$	14.5564	+	3.44993i	1.59777	+	0.378679i	0.667226	+	0.744856i	$0.267482\pi$
$84$		0			0
$85$	−3.76849	−	1.89261i	−0.408750	−	0.205282i
$86$	−1.18290	+	1.58891i	−0.127555	+	0.171336i
$87$		0			0
$88$	−21.9741	−	14.4526i	−2.34245	−	1.54065i
$89$	3.17449	+	2.66371i	0.336495	+	0.282353i	0.795340	−	0.606164i	$-0.207292\pi$
$89$	3.17449	+	2.66371i	0.336495	+	0.282353i	−0.458845	+	0.888516i	$0.651737\pi$
$90$		0			0
$91$	−5.21193	+	4.37333i	−0.546358	+	0.458449i
$92$	12.6911	−	1.48338i	1.32314	−	0.154653i
$93$		0			0
$94$	−4.14003	+	13.8286i	−0.427011	+	1.42632i
$95$	6.86309	+	7.27445i	0.704138	+	0.746343i
$96$		0			0
$97$	7.51692	+	10.0970i	0.763227	+	1.02519i	0.998580	+	0.0532819i	$0.0169682\pi$
$97$	7.51692	+	10.0970i	0.763227	+	1.02519i	−0.235352	+	0.971910i	$0.575624\pi$
$98$	−1.37652	−	7.80666i	−0.139050	−	0.788591i
$99$		0			0
$100$	−2.21491	+	12.5614i	−0.221491	+	1.25614i
$101$	−4.02581	+	2.02184i	−0.400583	+	0.201180i	−0.637673	−	0.770307i	$-0.720103\pi$
$101$	−4.02581	+	2.02184i	−0.400583	+	0.201180i	0.237090	+	0.971488i	$0.423807\pi$
$102$		0			0
$103$	−13.8657	−	1.62067i	−1.36623	−	0.159690i	−0.598841	−	0.800868i	$-0.704372\pi$
$103$	−13.8657	−	1.62067i	−1.36623	−	0.159690i	−0.767392	+	0.641179i	$0.778446\pi$
$104$	9.89324	−	6.50689i	0.970112	−	0.638053i
$105$		0			0
$106$	−6.91622	−	23.1018i	−0.671763	−	2.24384i
$107$	−2.27719	+	3.94420i	−0.220144	+	0.381301i	−0.954852	−	0.297083i	$-0.903986\pi$
$107$	−2.27719	+	3.94420i	−0.220144	+	0.381301i	0.734708	+	0.678384i	$0.237319\pi$
$108$		0			0
$109$	−3.56879	−	6.18132i	−0.341828	−	0.592063i	0.642944	−	0.765913i	$-0.277713\pi$
$109$	−3.56879	−	6.18132i	−0.341828	−	0.592063i	−0.984772	+	0.173850i	$0.944379\pi$
$110$	11.4164	−	12.1007i	1.08851	−	1.15375i
$111$		0			0
$112$	1.00212	+	17.2057i	0.0946911	+	1.62578i
$113$	3.10118	+	7.18935i	0.291735	+	0.676317i	0.999547	−	0.0300831i	$-0.00957719\pi$
$113$	3.10118	+	7.18935i	0.291735	+	0.676317i	−0.707813	+	0.706400i	$0.750318\pi$
$114$		0			0
$115$	−0.247496	+	4.24934i	−0.0230791	+	0.396253i
$116$	−8.74368	+	3.18244i	−0.811830	+	0.295482i
$117$		0			0
$118$	−3.76510	−	1.37039i	−0.346606	−	0.126154i
$119$	−3.78561	+	8.77603i	−0.347026	+	0.804498i
$120$		0			0
$121$	11.1310	−	2.63809i	1.01191	−	0.239826i
$122$	2.81790	−	0.667854i	0.255120	−	0.0604646i
$123$		0			0
$124$	−6.30274	+	14.6114i	−0.566003	+	1.31214i
$125$	−10.6062	−	3.86035i	−0.948650	−	0.345280i
$126$		0			0
$127$	9.61531	−	3.49969i	0.853220	−	0.310547i	0.121868	−	0.992546i	$-0.461112\pi$
$127$	9.61531	−	3.49969i	0.853220	−	0.310547i	0.731353	+	0.681999i	$0.238889\pi$
$128$	−0.984021	+	16.8950i	−0.0869760	+	1.49332i
$129$		0			0
$130$	2.96662	+	6.87740i	0.260190	+	0.603188i
$131$	−0.500399	−	8.59153i	−0.0437201	−	0.750645i	−0.946929	−	0.321443i	$-0.895832\pi$
$131$	−0.500399	−	8.59153i	−0.0437201	−	0.750645i	0.903209	−	0.429202i	$-0.141205\pi$
$132$		0			0
$133$	15.5548	−	16.4871i	1.34877	−	1.42962i
$134$	−7.46238	−	12.9252i	−0.644652	−	1.11657i
$135$		0			0
$136$	8.31720	−	14.4058i	0.713194	−	1.23529i
$137$	−0.306497	−	1.02377i	−0.0261858	−	0.0874668i	0.943898	−	0.330238i	$-0.107129\pi$
$137$	−0.306497	−	1.02377i	−0.0261858	−	0.0874668i	−0.970084	+	0.242771i	$0.921944\pi$
$138$		0			0
$139$	6.22270	−	4.09274i	0.527803	−	0.347141i	−0.257475	−	0.966285i	$-0.582890\pi$
$139$	6.22270	−	4.09274i	0.527803	−	0.347141i	0.785278	+	0.619144i	$0.212520\pi$
$140$	−18.8447	−	2.20263i	−1.59267	−	0.186156i
$141$		0			0
$142$	−7.99758	+	4.01653i	−0.671142	+	0.337060i
$143$	−1.75431	+	9.94920i	−0.146703	+	0.831994i
$144$		0			0
$145$	−0.538257	−	3.05261i	−0.0446998	−	0.253505i
$146$	−16.6481	−	22.3623i	−1.37781	−	1.85072i
$147$		0			0
$148$	−19.4803	−	20.6479i	−1.60127	−	1.69725i
$149$	0.700209	−	2.33886i	0.0573634	−	0.191607i	−0.924505	−	0.381169i	$-0.875522\pi$
$149$	0.700209	−	2.33886i	0.0573634	−	0.191607i	0.981869	+	0.189562i	$0.0607068\pi$
$150$		0			0
$151$	−21.2332	+	2.48181i	−1.72794	+	0.201967i	−0.921239	−	0.388997i	$-0.872822\pi$
$151$	−21.2332	+	2.48181i	−1.72794	+	0.201967i	−0.806698	+	0.590964i	$0.798748\pi$
$152$	−30.2201	+	25.3577i	−2.45117	+	2.05678i
$153$		0			0
$154$	−28.8836	−	24.2362i	−2.32751	−	1.95301i
$155$	−4.42892	−	2.91295i	−0.355740	−	0.233974i
$156$		0			0
$157$	−3.85858	+	5.18298i	−0.307949	+	0.413647i	−0.928975	−	0.370143i	$-0.879309\pi$
$157$	−3.85858	+	5.18298i	−0.307949	+	0.413647i	0.621026	+	0.783790i	$0.286716\pi$
$158$	−10.4533	−	5.24984i	−0.831620	−	0.417655i
$159$		0			0
$160$	3.25297	+	0.770968i	0.257170	+	0.0609503i
$161$	9.64722			0.760307
$162$		0			0
$163$	−6.49040			−0.508367			−0.254184	−	0.967156i	$-0.581807\pi$
$163$	−6.49040			−0.508367			−0.254184	+	0.967156i	$0.581807\pi$
$164$	−17.4120	−	4.12673i	−1.35965	−	0.322243i
$165$		0			0
$166$	−33.3549	−	16.7515i	−2.58884	−	1.30016i
$167$	−2.33107	+	3.13117i	−0.180384	+	0.242298i	−0.883113	−	0.469159i	$-0.844557\pi$
$167$	−2.33107	+	3.13117i	−0.180384	+	0.242298i	0.702730	+	0.711457i	$0.251964\pi$
$168$		0			0
$169$	7.06116	+	4.64420i	0.543166	+	0.357246i
$170$	8.06013	+	6.76325i	0.618184	+	0.518718i
$171$		0			0
$172$	2.56973	−	2.15626i	0.195940	−	0.164413i
$173$	−16.2203	+	1.89588i	−1.23321	+	0.144141i	−0.707617	−	0.706596i	$-0.750230\pi$
$173$	−16.2203	+	1.89588i	−1.23321	+	0.144141i	−0.525591	+	0.850738i	$0.676156\pi$
$174$		0			0
$175$	−2.76202	+	9.22578i	−0.208789	+	0.697404i
$176$	17.5621	+	18.6148i	1.32379	+	1.40314i
$177$		0			0
$178$	−6.17432	−	8.29355i	−0.462785	−	0.621628i
$179$	−3.76729	−	21.3654i	−0.281581	−	1.59692i	−0.717250	−	0.696816i	$-0.754599\pi$
$179$	−3.76729	−	21.3654i	−0.281581	−	1.59692i	0.435670	−	0.900107i	$-0.356512\pi$
$180$		0			0
$181$	−1.10326	+	6.25687i	−0.0820043	+	0.465070i	0.915959	+	0.401273i	$0.131432\pi$
$181$	−1.10326	+	6.25687i	−0.0820043	+	0.465070i	−0.997963	+	0.0637968i	$0.979679\pi$
$182$	15.1699	−	7.61862i	1.12447	−	0.564730i
$183$		0			0
$184$	−16.6767	−	1.94922i	−1.22942	−	0.143699i
$185$	7.90077	−	5.19642i	0.580876	−	0.382048i
$186$		0			0
$187$	4.07033	+	13.5959i	0.297652	+	0.994227i
$188$	12.2227	−	21.1703i	0.891429	−	1.54400i
$189$		0			0
$190$	−12.4765	−	21.6099i	−0.905139	−	1.56775i
$191$	−9.47075	+	10.0384i	−0.685279	+	0.726354i	−0.972858	−	0.231403i	$-0.925668\pi$
$191$	−9.47075	+	10.0384i	−0.685279	+	0.726354i	0.287579	+	0.957757i	$0.407150\pi$
$192$		0			0
$193$	−0.219597	−	3.77034i	−0.0158069	−	0.271395i	−0.996946	−	0.0780922i	$-0.975117\pi$
$193$	−0.219597	−	3.77034i	−0.0158069	−	0.271395i	0.981139	−	0.193303i	$-0.0619199\pi$
$194$	−12.4398	−	28.8386i	−0.893124	−	2.07049i
$195$		0			0
$196$	−0.780551	+	13.4015i	−0.0557537	+	0.957253i
$197$	−5.18414	+	1.88687i	−0.369355	+	0.134434i	−0.520027	−	0.854150i	$-0.674078\pi$
$197$	−5.18414	+	1.88687i	−0.369355	+	0.134434i	0.150673	+	0.988584i	$0.451856\pi$
$198$		0			0
$199$	15.9504	+	5.80546i	1.13069	+	0.411538i	0.838543	−	0.544835i	$-0.183408\pi$
$199$	15.9504	+	5.80546i	1.13069	+	0.411538i	0.292148	+	0.956373i	$0.405630\pi$
$200$	6.63864	−	15.3901i	0.469423	−	1.08824i
$201$		0			0
$202$	10.9372	−	2.59217i	0.769540	−	0.182384i
$203$	−6.83592	+	1.62014i	−0.479788	+	0.113712i
$204$		0			0
$205$	2.36108	−	5.47359i	0.164905	−	0.382292i
$206$	32.7307	+	11.9130i	2.28046	+	0.830018i
$207$		0			0
$208$	−10.8271	+	3.94075i	−0.750725	+	0.273242i
$209$	1.95700	−	33.6004i	0.135369	−	2.32419i
$210$		0			0
$211$	7.64711	+	17.7280i	0.526449	+	1.22045i	0.949336	+	0.314263i	$0.101757\pi$
$211$	7.64711	+	17.7280i	0.526449	+	1.22045i	−0.422887	+	0.906182i	$0.638983\pi$
$212$	2.37450	+	40.7686i	0.163082	+	2.80000i
$213$		0			0
$214$	7.79804	−	8.26544i	0.533063	−	0.565014i
$215$	0.558746	+	0.967777i	0.0381062	+	0.0660018i
$216$		0			0
$217$	−6.00721	+	10.4048i	−0.407796	+	0.706323i
$218$	5.10757	+	17.0605i	0.345928	+	1.15548i
$219$		0			0
$220$	−23.5380	+	15.4812i	−1.58693	+	1.04374i
$221$	−6.34638	−	0.741786i	−0.426904	−	0.0498979i
$222$		0			0
$223$	−13.5260	+	6.79302i	−0.905769	+	0.454894i	−0.839780	−	0.542926i	$-0.817316\pi$
$223$	−13.5260	+	6.79302i	−0.905769	+	0.454894i	−0.0659882	+	0.997820i	$0.521020\pi$
$224$	1.31572	−	7.46180i	0.0879100	−	0.498562i
$225$		0			0
$226$	−3.39230	−	19.2387i	−0.225653	−	1.27974i
$227$	3.76307	+	5.05467i	0.249763	+	0.335491i	0.909269	−	0.416209i	$-0.136642\pi$
$227$	3.76307	+	5.05467i	0.249763	+	0.335491i	−0.659505	+	0.751700i	$0.729234\pi$
$228$		0			0
$229$	−6.39343	−	6.77664i	−0.422489	−	0.447813i	0.480809	−	0.876825i	$-0.340343\pi$
$229$	−6.39343	−	6.77664i	−0.422489	−	0.447813i	−0.903298	+	0.429013i	$0.858862\pi$
$230$	3.04594	−	10.1741i	0.200843	−	0.670863i
$231$		0			0
$232$	12.1443	−	1.41946i	0.797311	−	0.0931923i
$233$	−16.1221	+	13.5280i	−1.05619	+	0.886251i	−0.993731	−	0.111797i	$-0.964339\pi$
$233$	−16.1221	+	13.5280i	−1.05619	+	0.886251i	−0.0624612	+	0.998047i	$0.519895\pi$
$234$		0			0
$235$	6.23822	+	5.23449i	0.406937	+	0.341460i
$236$	5.66902	+	3.72857i	0.369022	+	0.242709i
$237$		0			0
$238$	14.2404	−	19.1282i	0.923069	−	1.23990i
$239$	−14.6556	−	7.36034i	−0.947995	−	0.476101i	−0.0935336	−	0.995616i	$-0.529816\pi$
$239$	−14.6556	−	7.36034i	−0.947995	−	0.476101i	−0.854461	+	0.519515i	$0.826113\pi$
$240$		0			0
$241$	1.60772	+	0.381038i	0.103563	+	0.0245448i	0.282070	−	0.959394i	$-0.408979\pi$
$241$	1.60772	+	0.381038i	0.103563	+	0.0245448i	−0.178508	+	0.983939i	$0.557127\pi$
$242$	−28.5417			−1.83473
$243$		0			0
$244$	−4.90421			−0.313960
$245$	−4.35145	−	1.03131i	−0.278004	−	0.0658882i
$246$		0			0
$247$	13.5415	+	6.80078i	0.861623	+	0.432724i
$248$	12.4867	−	16.7725i	0.792904	−	1.06506i
$249$		0			0
$250$	23.5285	+	15.4750i	1.48808	+	0.978723i
$251$	−16.6349	−	13.9583i	−1.04998	−	0.881040i	−0.0568910	−	0.998380i	$-0.518119\pi$
$251$	−16.6349	−	13.9583i	−1.04998	−	0.881040i	−0.993092	+	0.117340i	$0.962563\pi$
$252$		0			0
$253$	10.9736	−	9.20793i	0.689903	−	0.578898i
$254$	−25.3577	+	2.96390i	−1.59109	+	0.185971i
$255$		0			0
$256$	9.31172	−	31.1033i	0.581982	−	1.94396i
$257$	−4.22372	−	4.47688i	−0.263468	−	0.279260i	0.582112	−	0.813109i	$-0.302227\pi$
$257$	−4.22372	−	4.47688i	−0.263468	−	0.279260i	−0.845580	+	0.533849i	$0.820745\pi$
$258$		0			0
$259$	−12.7986	−	17.1916i	−0.795269	−	1.06823i
$260$	−2.20255	−	12.4913i	−0.136596	−	0.774677i
$261$		0			0
$262$	−3.72869	+	21.1464i	−0.230359	+	1.30643i
$263$	22.8145	−	11.4579i	1.40680	−	0.706522i	0.426584	−	0.904448i	$-0.359717\pi$
$263$	22.8145	−	11.4579i	1.40680	−	0.706522i	0.980217	+	0.197926i	$0.0634205\pi$
$264$		0			0
$265$	−13.5122	−	1.57935i	−0.830048	−	0.0970187i
$266$	−47.2506	+	31.0772i	−2.89712	+	1.90547i
$267$		0			0
$268$	7.24884	+	24.2128i	0.442793	+	1.47903i
$269$	8.19176	−	14.1885i	0.499460	−	0.865091i	−0.500539	−	0.865714i	$-0.666865\pi$
$269$	8.19176	−	14.1885i	0.499460	−	0.865091i	1.00000		0.000622889i	$0.000198272\pi$
$270$		0			0
$271$	13.6365	+	23.6192i	0.828361	+	1.43476i	0.899323	+	0.437284i	$0.144060\pi$
$271$	13.6365	+	23.6192i	0.828361	+	1.43476i	−0.0709627	+	0.997479i	$0.522607\pi$
$272$	−11.1074	+	11.7732i	−0.673485	+	0.713853i
$273$		0			0
$274$	0.155036	+	2.66187i	0.00936609	+	0.160809i
$275$	5.66393	+	13.1305i	0.341548	+	0.791796i
$276$		0			0
$277$	1.33171	−	22.8645i	0.0800145	−	1.37380i	−0.684417	−	0.729091i	$-0.739943\pi$
$277$	1.33171	−	22.8645i	0.0800145	−	1.37380i	0.764432	−	0.644705i	$-0.223020\pi$
$278$	−17.4624	+	6.35580i	−1.04733	+	0.381196i
$279$		0			0
$280$	23.4278	+	8.52704i	1.40008	+	0.509588i
$281$	11.8774	−	27.5349i	0.708545	−	1.64259i	−0.0563292	−	0.998412i	$-0.517940\pi$
$281$	11.8774	−	27.5349i	0.708545	−	1.64259i	0.764874	−	0.644180i	$-0.222801\pi$
$282$		0			0
$283$	15.0986	−	3.57842i	0.897516	−	0.212715i	0.244132	−	0.969742i	$-0.421497\pi$
$283$	15.0986	−	3.57842i	0.897516	−	0.212715i	0.653384	+	0.757027i	$0.273349\pi$
$284$	14.7472	−	3.49515i	0.875084	−	0.207399i
$285$		0			0
$286$	9.98388	−	23.1452i	0.590359	−	1.36861i
$287$	−12.6958	−	4.62088i	−0.749407	−	0.272762i
$288$		0			0
$289$	7.54012	−	2.74438i	0.443536	−	0.161434i
$290$	−0.449687	+	7.72083i	−0.0264065	+	0.453383i
$291$		0			0
$292$	18.6997	+	43.3508i	1.09432	+	2.53691i
$293$	0.447663	+	7.68608i	0.0261527	+	0.449025i	0.985811	+	0.167857i	$0.0536848\pi$
$293$	0.447663	+	7.68608i	0.0261527	+	0.449025i	−0.959659	+	0.281168i	$0.909278\pi$
$294$		0			0
$295$	−1.55116	+	1.64413i	−0.0903119	+	0.0957250i
$296$	18.6508	+	32.3042i	1.08406	+	1.87764i
$297$		0			0
$298$	−3.04574	+	5.27538i	−0.176435	+	0.305595i
$299$	1.84972	+	6.17849i	0.106972	+	0.357311i
$300$		0			0
$301$	2.11607	−	1.39176i	0.121968	−	0.0802197i
$302$	52.9781	+	6.19225i	3.04855	+	0.356324i
$303$		0			0
$304$	34.3027	−	17.2275i	1.96740	−	0.988064i
$305$	0.283694	−	1.60891i	0.0162443	−	0.0921258i
$306$		0			0
$307$	2.28454	+	12.9563i	0.130386	+	0.739454i	0.977962	+	0.208781i	$0.0669496\pi$
$307$	2.28454	+	12.9563i	0.130386	+	0.739454i	−0.847577	+	0.530673i	$0.821939\pi$
$308$	38.1297	+	51.2171i	2.17264	+	2.91837i
$309$		0			0
$310$	9.07642	+	9.62045i	0.515506	+	0.546405i
$311$	1.57181	−	5.25022i	0.0891293	−	0.297713i	−0.901789	−	0.432176i	$-0.857746\pi$
$311$	1.57181	−	5.25022i	0.0891293	−	0.297713i	0.990919	+	0.134463i	$0.0429311\pi$
$312$		0			0
$313$	−24.0168	+	2.80716i	−1.35751	+	0.158670i	−0.763510	−	0.645796i	$-0.776526\pi$
$313$	−24.0168	+	2.80716i	−1.35751	+	0.158670i	−0.593999	+	0.804466i	$0.702452\pi$
$314$	12.3501	−	10.3630i	0.696959	−	0.584818i
$315$		0			0
$316$	15.1749	+	12.7332i	0.853653	+	0.716300i
$317$	−8.64348	−	5.68491i	−0.485466	−	0.319296i	0.283073	−	0.959098i	$-0.408646\pi$
$317$	−8.64348	−	5.68491i	−0.485466	−	0.319296i	−0.768540	+	0.639802i	$0.779016\pi$
$318$		0			0
$319$	−6.22940	+	8.36754i	−0.348780	+	0.468492i
$320$	6.13706	+	3.08215i	0.343072	+	0.172297i
$321$		0			0
$322$	−23.4215	−	5.55100i	−1.30523	−	0.309345i
$323$	21.2871			1.18444
$324$		0			0
$325$	−6.43816			−0.357125
$326$	15.7574	+	3.73457i	0.872721	+	0.206839i
$327$		0			0
$328$	21.0129	+	10.5531i	1.16024	+	0.582696i
$329$	11.0215	−	14.8045i	0.607636	−	0.816197i
$330$		0			0
$331$	25.7030	+	16.9051i	1.41276	+	0.929188i	0.999830	+	0.0184267i	$0.00586572\pi$
$331$	25.7030	+	16.9051i	1.41276	+	0.929188i	0.412932	+	0.910762i	$0.364505\pi$
$332$	48.4207	+	40.6298i	2.65743	+	2.22985i
$333$		0			0
$334$	7.46105	−	6.26056i	0.408250	−	0.342563i
$335$	−8.36274	+	0.977464i	−0.456905	+	0.0534046i
$336$		0			0
$337$	9.44732	−	31.5562i	0.514628	−	1.71898i	−0.165797	−	0.986160i	$-0.553020\pi$
$337$	9.44732	−	31.5562i	0.514628	−	1.71898i	0.680425	−	0.732818i	$-0.261795\pi$
$338$	−14.4708	−	15.3382i	−0.787109	−	0.834286i
$339$		0			0
$340$	−10.6403	−	14.2924i	−0.577052	−	0.775116i
$341$	3.09789	+	17.5690i	0.167760	+	0.951414i
$342$		0			0
$343$	2.11774	−	12.0103i	0.114347	−	0.648496i
$344$	−3.93915	+	1.97832i	−0.212385	+	0.106664i
$345$		0			0
$346$	40.4705	+	4.73033i	2.17571	+	0.254304i
$347$	21.6672	−	14.2507i	1.16316	−	0.765019i	0.187057	−	0.982349i	$-0.440105\pi$
$347$	21.6672	−	14.2507i	1.16316	−	0.765019i	0.976098	+	0.217330i	$0.0697347\pi$
$348$		0			0
$349$	−4.23854	−	14.1577i	−0.226884	−	0.757845i	−0.993307	−	0.115508i	$-0.963150\pi$
$349$	−4.23854	−	14.1577i	−0.226884	−	0.757845i	0.766423	−	0.642337i	$-0.222035\pi$
$350$	12.0141	−	20.8091i	0.642182	−	1.11229i
$351$		0			0
$352$	−5.62541	−	9.74350i	−0.299836	−	0.519330i
$353$	−4.75868	+	5.04391i	−0.253279	+	0.268460i	−0.841520	−	0.540225i	$-0.818339\pi$
$353$	−4.75868	+	5.04391i	−0.253279	+	0.268460i	0.588241	+	0.808685i	$0.299820\pi$
$354$		0			0
$355$	0.293561	+	5.04025i	0.0155806	+	0.267508i
$356$	6.93519	+	16.0776i	0.367565	+	0.852110i
$357$		0			0
$358$	−3.14738	+	54.0385i	−0.166344	+	2.85602i
$359$	28.2850	−	10.2949i	1.49283	−	0.543344i	0.538634	−	0.842540i	$-0.318940\pi$
$359$	28.2850	−	10.2949i	1.49283	−	0.543344i	0.954192	+	0.299195i	$0.0967182\pi$
$360$		0			0
$361$	−29.5849	−	10.7680i	−1.55710	−	0.566738i
$362$	6.27868	−	14.5556i	0.330000	−	0.765026i
$363$		0			0
$364$	−27.9727	+	6.62964i	−1.46617	+	0.347488i
$365$	−15.3037	+	3.62704i	−0.801031	+	0.189848i
$366$		0			0
$367$	−9.11370	+	21.1279i	−0.475731	+	1.10287i	0.496328	+	0.868135i	$0.334681\pi$
$367$	−9.11370	+	21.1279i	−0.475731	+	1.10287i	−0.972060	+	0.234734i	$0.924578\pi$
$368$	15.3522	+	5.58774i	0.800288	+	0.291281i
$369$		0			0
$370$	−22.1715	+	8.06976i	−1.15264	+	0.419527i
$371$	−1.79279	+	30.7810i	−0.0930768	+	1.59807i
$372$		0			0
$373$	−12.4804	−	28.9329i	−0.646212	−	1.49809i	−0.854194	−	0.519955i	$-0.825949\pi$
$373$	−12.4804	−	28.9329i	−0.646212	−	1.49809i	0.207982	−	0.978133i	$-0.433310\pi$
$374$	−2.05891	−	35.3501i	−0.106464	−	1.82791i
$375$		0			0
$376$	−22.0436	+	23.3649i	−1.13681	+	1.20495i
$377$	−2.34830	−	4.06738i	−0.120944	−	0.209481i
$378$		0			0
$379$	9.45804	−	16.3818i	0.485827	−	0.841477i	−0.514040	−	0.857766i	$-0.671852\pi$
$379$	9.45804	−	16.3818i	0.485827	−	0.841477i	0.999867	+	0.0162889i	$0.00518516\pi$
$380$	12.1195	+	40.4818i	0.621715	+	2.07667i
$381$		0			0
$382$	28.7692	−	18.9218i	1.47196	−	0.968122i
$383$	−29.6105	−	3.46097i	−1.51302	−	0.176847i	−0.681287	−	0.732017i	$-0.738579\pi$
$383$	−29.6105	−	3.46097i	−1.51302	−	0.176847i	−0.831737	+	0.555169i	$0.812653\pi$
$384$		0			0
$385$	−19.0083	+	9.54634i	−0.968754	+	0.486527i
$386$	−1.63631	+	9.27997i	−0.0832859	+	0.472338i
$387$		0			0
$388$	9.23585	+	52.3791i	0.468879	+	2.65915i
$389$	3.48266	+	4.67803i	0.176578	+	0.237186i	0.881597	−	0.472003i	$-0.156469\pi$
$389$	3.48266	+	4.67803i	0.176578	+	0.237186i	−0.705019	+	0.709189i	$0.749061\pi$
$390$		0			0
$391$	6.21738	+	6.59004i	0.314426	+	0.333273i
$392$	5.05923	−	16.8990i	0.255530	−	0.853528i
$393$		0			0
$394$	13.6717	−	1.59800i	0.688773	−	0.0805060i
$395$	−5.05517	+	4.24179i	−0.254353	+	0.213428i
$396$		0			0
$397$	4.50462	+	3.77983i	0.226081	+	0.189704i	0.748791	−	0.662806i	$-0.230635\pi$
$397$	4.50462	+	3.77983i	0.226081	+	0.189704i	−0.522710	+	0.852510i	$0.675079\pi$
$398$	−35.3838	−	23.2723i	−1.77363	−	1.16654i
$399$		0			0
$400$	−9.73900	+	13.0817i	−0.486950	+	0.654087i
$401$	9.58879	+	4.81567i	0.478841	+	0.240483i	0.671812	−	0.740721i	$-0.265516\pi$
$401$	9.58879	+	4.81567i	0.478841	+	0.240483i	−0.192971	+	0.981204i	$0.561812\pi$
$402$		0			0
$403$	−7.81547	−	1.85230i	−0.389316	−	0.0922697i
$404$	−19.0349			−0.947023
$405$		0			0
$406$	17.5285			0.869924
$407$	−30.9670	−	7.33932i	−1.53498	−	0.363797i
$408$		0			0
$409$	2.97505	+	1.49413i	0.147107	+	0.0738798i	0.520830	−	0.853661i	$-0.325623\pi$
$409$	2.97505	+	1.49413i	0.147107	+	0.0738798i	−0.373723	+	0.927540i	$0.621919\pi$
$410$	−8.88172	+	11.9302i	−0.438637	+	0.589192i
$411$		0			0
$412$	−49.2818	−	32.4131i	−2.42794	−	1.59688i
$413$	3.92444	+	3.29300i	0.193109	+	0.162038i
$414$		0			0
$415$	−16.1303	+	13.5349i	−0.791805	+	0.664403i
$416$	5.03112	−	0.588054i	0.246671	−	0.0288317i
$417$		0			0
$418$	−24.0848	+	80.4490i	−1.17803	+	3.93489i
$419$	−1.96238	−	2.08000i	−0.0958684	−	0.101615i	0.677663	−	0.735373i	$-0.262993\pi$
$419$	−1.96238	−	2.08000i	−0.0958684	−	0.101615i	−0.773531	+	0.633758i	$0.781511\pi$
$420$		0			0
$421$	−3.75394	−	5.04242i	−0.182956	−	0.245752i	0.701178	−	0.712986i	$-0.252658\pi$
$421$	−3.75394	−	5.04242i	−0.182956	−	0.245752i	−0.884134	+	0.467234i	$0.845251\pi$
$422$	−8.36498	−	47.4401i	−0.407201	−	2.30935i
$423$		0			0
$424$	9.31841	−	52.8473i	0.452542	−	2.56649i
$425$	−8.08220	+	4.05904i	−0.392045	+	0.196892i
$426$		0			0
$427$	−3.67772	−	0.429863i	−0.177977	−	0.0208025i
$428$	−16.0778	+	10.5745i	−0.777148	+	0.511138i
$429$		0			0
$430$	−0.799666	−	2.67107i	−0.0385633	−	0.128810i
$431$	−8.66111	+	15.0015i	−0.417191	+	0.722596i	−0.995656	−	0.0931115i	$-0.970319\pi$
$431$	−8.66111	+	15.0015i	−0.417191	+	0.722596i	0.578465	+	0.815707i	$0.303652\pi$
$432$		0			0
$433$	−6.83316	−	11.8354i	−0.328381	−	0.568772i	0.653810	−	0.756659i	$-0.273170\pi$
$433$	−6.83316	−	11.8354i	−0.328381	−	0.568772i	−0.982191	+	0.187887i	$0.939836\pi$
$434$	20.5712	−	21.8042i	0.987449	−	1.04664i
$435$		0			0
$436$	−1.75355	−	30.1073i	−0.0839798	−	1.44188i
$437$	−8.51035	−	19.7292i	−0.407105	−	0.943776i
$438$		0			0
$439$	2.16809	−	37.2247i	0.103477	−	1.77664i	−0.403791	−	0.914851i	$-0.632308\pi$
$439$	2.16809	−	37.2247i	0.103477	−	1.77664i	0.507269	−	0.861788i	$-0.330655\pi$
$440$	34.7876	−	12.6617i	1.65843	−	0.603621i
$441$		0			0
$442$	14.9809	+	5.45261i	0.712570	+	0.259354i
$443$	−1.76851	+	4.09987i	−0.0840246	+	0.194791i	−0.955048	−	0.296450i	$-0.904197\pi$
$443$	−1.76851	+	4.09987i	−0.0840246	+	0.194791i	0.871024	+	0.491241i	$0.163456\pi$
$444$		0			0
$445$	−5.67570	+	1.34517i	−0.269054	+	0.0637670i
$446$	36.7471	−	8.70923i	1.74003	−	0.412394i
$447$		0			0
$448$	6.16494	−	14.2919i	0.291266	−	0.675230i
$449$	−3.44438	−	1.25365i	−0.162550	−	0.0591635i	0.259463	−	0.965753i	$-0.416454\pi$
$449$	−3.44438	−	1.25365i	−0.162550	−	0.0591635i	−0.422014	+	0.906589i	$0.638677\pi$
$450$		0			0
$451$	−18.8517	+	6.86146i	−0.887693	+	0.323094i
$452$	−1.92359	+	33.0268i	−0.0904780	+	1.55345i
$453$		0			0
$454$	−6.22751	−	14.4370i	−0.292272	−	0.677562i
$455$	−0.556830	−	9.56041i	−0.0261046	−	0.448199i
$456$		0			0
$457$	12.6070	−	13.3626i	0.589729	−	0.625076i	−0.361940	−	0.932201i	$-0.617886\pi$
$457$	12.6070	−	13.3626i	0.589729	−	0.625076i	0.951669	+	0.307125i	$0.0993670\pi$
$458$	11.6227	+	20.1311i	0.543092	+	0.940664i
$459$		0			0
$460$	−8.99256	+	15.5756i	−0.419280	+	0.726215i
$461$	3.45976	+	11.5564i	0.161137	+	0.538235i	0.999981	−	0.00613654i	$-0.00195333\pi$
$461$	3.45976	+	11.5564i	0.161137	+	0.538235i	−0.838844	+	0.544372i	$0.816768\pi$
$462$		0			0
$463$	−2.30037	+	1.51298i	−0.106907	+	0.0703141i	−0.601837	−	0.798619i	$-0.705564\pi$
$463$	−2.30037	+	1.51298i	−0.106907	+	0.0703141i	0.494929	+	0.868933i	$0.335194\pi$
$464$	−11.8168	−	1.38119i	−0.548581	−	0.0641200i
$465$		0			0
$466$	46.9252	−	23.5667i	2.17377	−	1.09171i
$467$	5.46587	−	30.9985i	0.252930	−	1.43444i	−0.548399	−	0.836216i	$-0.684763\pi$
$467$	5.46587	−	30.9985i	0.252930	−	1.43444i	0.801330	−	0.598223i	$-0.204126\pi$
$468$		0			0
$469$	3.31368	+	18.7928i	0.153011	+	0.867771i
$470$	−12.1332	−	16.2977i	−0.559664	−	0.751759i
$471$		0			0
$472$	−6.11864	−	6.48538i	−0.281633	−	0.298514i
$473$	1.07861	−	3.60282i	0.0495947	−	0.165658i
$474$		0			0
$475$	21.3039	−	2.49007i	0.977489	−	0.114252i
$476$	−30.9360	+	25.9584i	−1.41795	+	1.18980i
$477$		0			0
$478$	31.3458	+	26.3023i	1.43372	+	1.20304i
$479$	−2.32908	−	1.53186i	−0.106418	−	0.0699925i	0.495184	−	0.868788i	$-0.335101\pi$
$479$	−2.32908	−	1.53186i	−0.106418	−	0.0699925i	−0.601603	+	0.798795i	$0.705471\pi$
$480$		0			0
$481$	8.55625	−	11.4930i	0.390131	−	0.524037i
$482$	−3.68398	−	1.85017i	−0.167801	−	0.0842727i
$483$		0			0
$484$	47.0316	+	11.1467i	2.13780	+	0.506668i
$485$	−17.7181			−0.804538
$486$		0			0
$487$	−31.6987			−1.43640			−0.718202	−	0.695835i	$-0.755035\pi$
$487$	−31.6987			−1.43640			−0.718202	+	0.695835i	$0.755035\pi$
$488$	6.27064	+	1.48617i	0.283858	+	0.0672757i
$489$		0			0
$490$	9.97103	+	5.00764i	0.450445	+	0.226222i
$491$	−21.0164	+	28.2299i	−0.948455	+	1.27400i	0.0132501	+	0.999912i	$0.495782\pi$
$491$	−21.0164	+	28.2299i	−0.948455	+	1.27400i	−0.961706	+	0.274085i	$0.911625\pi$
$492$		0			0
$493$	−5.51230	−	3.62550i	−0.248262	−	0.163284i
$494$	−28.9628	−	24.3027i	−1.30310	−	1.09343i
$495$		0			0
$496$	−15.5862	+	13.0783i	−0.699839	+	0.587235i
$497$	11.3654	−	1.32843i	0.509809	−	0.0595881i
$498$		0			0
$499$	2.29147	−	7.65404i	0.102580	−	0.342642i	−0.891256	−	0.453501i	$-0.850175\pi$
$499$	2.29147	−	7.65404i	0.102580	−	0.342642i	0.993836	+	0.110859i	$0.0353601\pi$
$500$	−32.7272	−	34.6888i	−1.46360	−	1.55133i
$501$		0			0
$502$	32.3545	+	43.4596i	1.44405	+	1.93970i
$503$	−2.70376	−	15.3338i	−0.120555	−	0.683700i	−0.983849	−	0.178999i	$-0.942714\pi$
$503$	−2.70376	−	15.3338i	−0.120555	−	0.683700i	0.863294	−	0.504701i	$-0.168397\pi$
$504$		0			0
$505$	1.10111	−	6.24473i	0.0489989	−	0.277887i
$506$	−31.9399	+	16.0408i	−1.41990	+	0.713101i
$507$		0			0
$508$	42.9425	+	5.01926i	1.90527	+	0.222694i
$509$	14.4368	−	9.49526i	0.639901	−	0.420870i	−0.187669	−	0.982232i	$-0.560093\pi$
$509$	14.4368	−	9.49526i	0.639901	−	0.420870i	0.827570	+	0.561363i	$0.189723\pi$
$510$		0			0
$511$	10.2233	+	34.1483i	0.452253	+	1.51063i
$512$	−23.5802	+	40.8420i	−1.04211	+	1.80498i
$513$		0			0
$514$	7.67834	+	13.2993i	0.338677	+	0.586606i
$515$	13.4845	−	14.2927i	0.594197	−	0.629812i
$516$		0			0
$517$	−1.59351	−	27.3595i	−0.0700826	−	1.20327i
$518$	21.1805	+	49.1020i	0.930619	+	2.15742i
$519$		0			0
$520$	−0.969119	+	16.6391i	−0.0424987	+	0.729674i
$521$	−33.0219	+	12.0190i	−1.44672	+	0.526562i	−0.941672	−	0.336531i	$-0.890746\pi$
$521$	−33.0219	+	12.0190i	−1.44672	+	0.526562i	−0.505045	+	0.863093i	$0.668524\pi$
$522$		0			0
$523$	2.55225	+	0.928943i	0.111602	+	0.0406198i	0.397218	−	0.917724i	$-0.369976\pi$
$523$	2.55225	+	0.928943i	0.111602	+	0.0406198i	−0.285616	+	0.958344i	$0.592198\pi$
$524$	14.4027	−	33.3893i	0.629186	−	1.45862i
$525$		0			0
$526$	−61.9818	+	14.6900i	−2.70254	+	0.640513i
$527$	−10.9790	+	2.60208i	−0.478254	+	0.113348i
$528$		0			0
$529$	−5.48772	+	12.7220i	−0.238597	+	0.553129i
$530$	31.8961	+	11.6092i	1.38548	+	0.504273i
$531$		0			0
$532$	89.9974	−	32.7564i	3.90188	−	1.42017i
$533$	0.525174	−	9.01689i	0.0227478	−	0.390565i
$534$		0			0
$535$	−2.53909	−	5.88628i	−0.109775	−	0.254486i
$536$	−1.93110	−	33.1558i	−0.0834109	−	1.43211i
$537$		0			0
$538$	−28.0520	+	29.7334i	−1.20941	+	1.28190i
$539$	7.52504	+	13.0337i	0.324126	+	0.561403i
$540$		0			0
$541$	19.9581	−	34.5684i	0.858065	−	1.48621i	−0.0157071	−	0.999877i	$-0.505000\pi$
$541$	19.9581	−	34.5684i	0.858065	−	1.48621i	0.873772	−	0.486336i	$-0.161667\pi$
$542$	−19.5163	−	65.1891i	−0.838298	−	2.80011i
$543$		0			0
$544$	5.94512	−	3.91017i	0.254895	−	0.167647i
$545$	9.97864	+	1.16634i	0.427438	+	0.0499604i
$546$		0			0
$547$	−8.30462	+	4.17074i	−0.355080	+	0.178328i	−0.617393	−	0.786655i	$-0.711811\pi$
$547$	−8.30462	+	4.17074i	−0.355080	+	0.178328i	0.262313	+	0.964983i	$0.415515\pi$
$548$	0.784096	−	4.44683i	0.0334949	−	0.189959i
$549$		0			0
$550$	−6.19562	−	35.1371i	−0.264182	−	1.49825i
$551$	9.34365	+	12.5507i	0.398053	+	0.534678i
$552$		0			0
$553$	10.2637	+	10.8789i	0.436457	+	0.462617i
$554$	−16.3893	+	54.7442i	−0.696316	+	2.32586i
$555$		0			0
$556$	31.2571	−	3.65343i	1.32560	−	0.154940i
$557$	28.8895	−	24.2411i	1.22409	−	1.02713i	0.225485	−	0.974247i	$-0.427603\pi$
$557$	28.8895	−	24.2411i	1.22409	−	1.02713i	0.998601	−	0.0528835i	$-0.0168412\pi$
$558$		0			0
$559$	1.29707	+	1.08837i	0.0548602	+	0.0460332i
$560$	−20.2682	−	13.3306i	−0.856487	−	0.563320i
$561$		0			0
$562$	−44.6794	+	60.0149i	−1.88469	+	2.53157i
$563$	−35.6493	−	17.9037i	−1.50244	−	0.754553i	−0.508149	−	0.861269i	$-0.669670\pi$
$563$	−35.6493	−	17.9037i	−1.50244	−	0.754553i	−0.994290	+	0.106716i	$0.965966\pi$
$564$		0			0
$565$	−10.7237	−	2.54157i	−0.451150	−	0.106924i
$566$	−38.7153			−1.62732
$567$		0			0
$568$	−19.9153			−0.835626
$569$	30.3673	+	7.19719i	1.27306	+	0.301722i	0.810959	−	0.585103i	$-0.198946\pi$
$569$	30.3673	+	7.19719i	1.27306	+	0.301722i	0.462106	+	0.886825i	$0.347094\pi$
$570$		0			0
$571$	−19.2217	−	9.65350i	−0.804403	−	0.403986i	−0.00142790	−	0.999999i	$-0.500455\pi$
$571$	−19.2217	−	9.65350i	−0.804403	−	0.403986i	−0.802975	+	0.596013i	$0.796751\pi$
$572$	−25.4908	+	34.2401i	−1.06582	+	1.43165i
$573$		0			0
$574$	28.1639	+	18.5237i	1.17554	+	0.773163i
$575$	6.99316	+	5.86796i	0.291635	+	0.244711i
$576$		0			0
$577$	1.05985	−	0.889324i	0.0441223	−	0.0370230i	−0.620460	−	0.784238i	$-0.713054\pi$
$577$	1.05985	−	0.889324i	0.0441223	−	0.0370230i	0.664582	+	0.747215i	$0.268610\pi$
$578$	−19.8850	+	2.32422i	−0.827107	+	0.0966749i
$579$		0			0
$580$	3.75630	−	12.5469i	0.155972	−	0.520982i
$581$	32.7499	+	34.7129i	1.35870	+	1.44013i
$582$		0			0
$583$	27.3401	+	36.7241i	1.13231	+	1.52096i
$584$	−10.7729	−	61.0961i	−0.445785	−	2.52817i
$585$		0			0
$586$	3.33572	−	18.9178i	0.137797	−	0.781488i
$587$	−7.16312	+	3.59745i	−0.295654	+	0.148483i	−0.590443	−	0.807079i	$-0.701047\pi$
$587$	−7.16312	+	3.59745i	−0.295654	+	0.148483i	0.294789	+	0.955562i	$0.404751\pi$
$588$		0			0
$589$	26.5778	+	3.10650i	1.09512	+	0.128001i
$590$	4.71193	−	3.09908i	0.193987	−	0.127587i
$591$		0			0
$592$	−10.4098	−	34.7710i	−0.427838	−	1.42908i
$593$	−10.7066	+	18.5444i	−0.439668	+	0.761527i	−0.997664	−	0.0683166i	$-0.978237\pi$
$593$	−10.7066	+	18.5444i	−0.439668	+	0.761527i	0.557996	+	0.829844i	$0.311571\pi$
$594$		0			0
$595$	−6.72652	−	11.6507i	−0.275761	−	0.477631i
$596$	7.07909	−	7.50339i	0.289971	−	0.307351i
$597$		0			0
$598$	−0.935648	−	16.0645i	−0.0382615	−	0.656924i
$599$	−9.21537	−	21.3636i	−0.376530	−	0.872894i	−0.996123	−	0.0879711i	$-0.971962\pi$
$599$	−9.21537	−	21.3636i	−0.376530	−	0.872894i	0.619593	−	0.784923i	$-0.287298\pi$
$600$		0			0
$601$	1.83568	−	31.5174i	0.0748790	−	1.28562i	−0.726375	−	0.687298i	$-0.758797\pi$
$601$	1.83568	−	31.5174i	0.0748790	−	1.28562i	0.801254	−	0.598324i	$-0.204166\pi$
$602$	−5.93821	+	2.16133i	−0.242023	+	0.0880893i
$603$		0			0
$604$	−84.8800	−	30.8938i	−3.45372	−	1.25705i
$605$	−6.37750	+	14.7847i	−0.259282	+	0.601084i
$606$		0			0
$607$	−4.58040	+	1.08557i	−0.185913	+	0.0440621i	−0.322517	−	0.946564i	$-0.604529\pi$
$607$	−4.58040	+	1.08557i	−0.185913	+	0.0440621i	0.136605	+	0.990626i	$0.456381\pi$
$608$	−16.4205	+	3.89174i	−0.665941	+	0.157831i
$609$		0			0
$610$	−1.61452	+	3.74287i	−0.0653698	+	0.151544i
$611$	11.5946	+	4.22010i	0.469069	+	0.170727i
$612$		0			0
$613$	41.2145	−	15.0009i	1.66464	−	0.605879i	0.673558	−	0.739134i	$-0.264765\pi$
$613$	41.2145	−	15.0009i	1.66464	−	0.605879i	0.991082	+	0.133255i	$0.0425429\pi$
$614$	1.90862	−	32.7698i	0.0770257	−	1.32248i
$615$		0			0
$616$	−33.2328	−	77.0422i	−1.33899	−	3.10412i
$617$	1.03567	+	17.7818i	0.0416947	+	0.715870i	0.952782	+	0.303656i	$0.0982074\pi$
$617$	1.03567	+	17.7818i	0.0416947	+	0.715870i	−0.911087	+	0.412214i	$0.864756\pi$
$618$		0			0
$619$	−3.84631	+	4.07685i	−0.154596	+	0.163862i	−0.800043	−	0.599943i	$-0.795190\pi$
$619$	−3.84631	+	4.07685i	−0.154596	+	0.163862i	0.645446	+	0.763806i	$0.276671\pi$
$620$	−11.1991	−	19.3975i	−0.449768	−	0.779021i
$621$		0			0
$622$	−6.83702	+	11.8421i	−0.274139	+	0.474823i
$623$	3.79154	+	12.6646i	0.151905	+	0.507398i
$624$		0			0
$625$	0.662691	−	0.435859i	0.0265076	−	0.0174344i
$626$	59.9232	+	7.00401i	2.39501	+	0.279937i
$627$		0			0
$628$	−24.3980	+	12.2531i	−0.973585	+	0.488953i
$629$	3.49521	−	19.8223i	0.139363	−	0.790367i
$630$		0			0
$631$	−2.84022	−	16.1077i	−0.113067	−	0.641237i	−0.987689	−	0.156431i	$-0.950001\pi$
$631$	−2.84022	−	16.1077i	−0.113067	−	0.641237i	0.874622	−	0.484806i	$-0.161110\pi$
$632$	−15.5443	−	20.8796i	−0.618318	−	0.830546i
$633$		0			0
$634$	17.7135	+	18.7753i	0.703495	+	0.745661i
$635$	−4.13075	+	13.7977i	−0.163924	+	0.547544i
$636$		0			0
$637$	−6.73006	+	0.786632i	−0.266655	+	0.0311675i
$638$	19.9384	−	16.7303i	0.789369	−	0.662360i
$639$		0			0
$640$	−18.2480	−	15.3119i	−0.721314	−	0.605255i
$641$	−19.4911	−	12.8195i	−0.769852	−	0.506340i	0.102788	−	0.994703i	$-0.467224\pi$
$641$	−19.4911	−	12.8195i	−0.769852	−	0.506340i	−0.872640	+	0.488364i	$0.837594\pi$
$642$		0			0
$643$	−8.71491	+	11.7062i	−0.343683	+	0.461646i	−0.940036	−	0.341076i	$-0.889208\pi$
$643$	−8.71491	+	11.7062i	−0.343683	+	0.461646i	0.596353	+	0.802722i	$0.296616\pi$
$644$	36.4265	+	18.2941i	1.43541	+	0.720888i
$645$		0			0
$646$	−51.6807	−	12.2486i	−2.03335	−	0.481913i
$647$	1.33592			0.0525205			0.0262602	−	0.999655i	$-0.491640\pi$
$647$	1.33592			0.0525205			0.0262602	+	0.999655i	$0.491640\pi$
$648$		0			0
$649$	7.60705			0.298603
$650$	15.6306	+	3.70451i	0.613081	+	0.145303i
$651$		0			0
$652$	−24.5068	−	12.3078i	−0.959761	−	0.482010i
$653$	9.84060	−	13.2182i	0.385092	−	0.517269i	−0.566736	−	0.823899i	$-0.691794\pi$
$653$	9.84060	−	13.2182i	0.385092	−	0.517269i	0.951829	+	0.306630i	$0.0992016\pi$
$654$		0			0
$655$	10.1208	+	6.65653i	0.395451	+	0.260092i
$656$	−17.5271	−	14.7069i	−0.684316	−	0.574210i
$657$		0			0
$658$	−35.2765	+	29.6005i	−1.37522	+	1.15395i
$659$	44.7076	−	5.22557i	1.74156	−	0.203559i	0.814937	−	0.579550i	$-0.196771\pi$
$659$	44.7076	−	5.22557i	1.74156	−	0.203559i	0.926624	+	0.375990i	$0.122697\pi$
$660$		0			0
$661$	−7.13320	+	23.8265i	−0.277449	+	0.926745i	0.699744	+	0.714394i	$0.253297\pi$
$661$	−7.13320	+	23.8265i	−0.277449	+	0.926745i	−0.977193	+	0.212352i	$0.931888\pi$
$662$	−52.6744	−	55.8316i	−2.04725	−	2.16996i
$663$		0			0
$664$	−49.5995	−	66.6236i	−1.92483	−	2.58550i
$665$	5.54020	+	31.4200i	0.214840	+	1.21842i
$666$		0			0
$667$	−1.15641	+	6.55832i	−0.0447764	+	0.253939i
$668$	−14.7395	+	7.40244i	−0.570287	+	0.286409i
$669$		0			0
$670$	20.8655	+	2.43883i	0.806104	+	0.0942200i
$671$	−4.59364	+	3.02129i	−0.177336	+	0.116636i
$672$		0			0
$673$	−0.567997	−	1.89724i	−0.0218947	−	0.0731334i	0.946344	−	0.323161i	$-0.104746\pi$
$673$	−0.567997	−	1.89724i	−0.0218947	−	0.0731334i	−0.968239	+	0.250028i	$0.919560\pi$
$674$	−41.0936	+	71.1762i	−1.58287	+	2.74161i
$675$		0			0
$676$	17.8551	+	30.9260i	0.686735	+	1.18946i
$677$	−19.5523	+	20.7242i	−0.751455	+	0.796496i	−0.984391	−	0.175996i	$-0.943685\pi$
$677$	−19.5523	+	20.7242i	−0.751455	+	0.796496i	0.232936	+	0.972492i	$0.425167\pi$
$678$		0			0
$679$	2.33493	+	40.0892i	0.0896063	+	1.53848i
$680$	9.27379	+	21.4991i	0.355634	+	0.824452i
$681$		0			0
$682$	2.58813	−	44.4365i	0.0991047	−	1.70156i
$683$	27.6811	−	10.0751i	1.05919	−	0.385512i	0.247064	−	0.968999i	$-0.420534\pi$
$683$	27.6811	−	10.0751i	1.05919	−	0.385512i	0.812123	+	0.583487i	$0.198312\pi$
$684$		0			0
$685$	1.41350	+	0.514472i	0.0540071	+	0.0196570i
$686$	−12.0522	+	27.9401i	−0.460154	+	1.06676i
$687$		0			0
$688$	4.17354	−	0.989148i	0.159115	−	0.0377109i
$689$	−20.0572	+	4.75364i	−0.764118	+	0.181099i
$690$		0			0
$691$	19.2512	−	44.6294i	0.732352	−	1.69778i	0.0161701	−	0.999869i	$-0.494853\pi$
$691$	19.2512	−	44.6294i	0.732352	−	1.69778i	0.716182	−	0.697914i	$-0.245888\pi$
$692$	−64.8408	−	23.6001i	−2.46488	−	0.897141i
$693$		0			0
$694$	−60.8034	+	22.1306i	−2.30807	+	0.840067i
$695$	−0.609562	+	10.4658i	−0.0231220	+	0.396989i
$696$		0			0
$697$	−5.02555	−	11.6505i	−0.190356	−	0.441296i
$698$	2.14399	+	36.8109i	0.0811513	+	1.39331i
$699$		0			0
$700$	−27.9239	+	29.5976i	−1.05542	+	1.11868i
$701$	3.03784	+	5.26170i	0.114738	+	0.198732i	0.917675	−	0.397332i	$-0.130064\pi$
$701$	3.03784	+	5.26170i	0.114738	+	0.198732i	−0.802937	+	0.596064i	$0.796731\pi$
$702$		0			0
$703$	−23.8675	+	41.3397i	−0.900179	+	1.55916i
$704$	−6.62861	−	22.1411i	−0.249825	−	0.834474i
$705$		0			0
$706$	14.4554	−	9.50745i	0.544035	−	0.357818i
$707$	−14.2745	−	1.66845i	−0.536847	−	0.0627484i
$708$		0			0
$709$	−19.3944	+	9.74021i	−0.728370	+	0.365801i	−0.774024	−	0.633156i	$-0.781759\pi$
$709$	−19.3944	+	9.74021i	−0.728370	+	0.365801i	0.0456540	+	0.998957i	$0.485463\pi$
$710$	2.18745	−	12.4056i	0.0820934	−	0.465575i
$711$		0			0
$712$	−3.99536	−	22.6588i	−0.149733	−	0.849175i
$713$	6.80095	+	9.13526i	0.254698	+	0.342118i
$714$		0			0
$715$	−9.75846	−	10.3434i	−0.364946	−	0.386820i
$716$	26.2905	−	87.8165i	0.982524	−	3.28186i
$717$		0			0
$718$	−74.5940	+	8.71879i	−2.78382	+	0.325382i
$719$	−11.8323	+	9.92847i	−0.441270	+	0.370269i	−0.836184	−	0.548449i	$-0.815219\pi$
$719$	−11.8323	+	9.92847i	−0.441270	+	0.370269i	0.394915	+	0.918718i	$0.370774\pi$
$720$		0			0
$721$	−34.1158	−	28.6266i	−1.27054	−	1.06611i
$722$	65.6302	+	43.1657i	2.44250	+	1.60646i
$723$		0			0
$724$	−16.0307	+	21.5329i	−0.595776	+	0.800266i
$725$	−5.94075	−	2.98355i	−0.220634	−	0.110806i
$726$		0			0
$727$	−25.0624	−	5.93991i	−0.929514	−	0.220299i	−0.262147	−	0.965028i	$-0.584431\pi$
$727$	−25.0624	−	5.93991i	−0.929514	−	0.220299i	−0.667367	+	0.744729i	$0.732579\pi$
$728$	37.7756			1.40006
$729$		0			0
$730$	39.2412			1.45238
$731$	2.31447	+	0.548539i	0.0856036	+	0.0202884i
$732$		0			0
$733$	26.0836	+	13.0997i	0.963421	+	0.483848i	0.859723	−	0.510761i	$-0.170636\pi$
$733$	26.0836	+	13.0997i	0.963421	+	0.483848i	0.103698	+	0.994609i	$0.466932\pi$
$734$	34.2832	−	46.0503i	1.26542	−	1.69975i
$735$		0			0
$736$	−6.00080	−	3.94679i	−0.221192	−	0.145481i
$737$	21.7063	+	18.2138i	0.799563	+	0.670913i
$738$		0			0
$739$	15.6599	−	13.1402i	0.576058	−	0.483370i	−0.307592	−	0.951518i	$-0.599523\pi$
$739$	15.6599	−	13.1402i	0.576058	−	0.483370i	0.883650	+	0.468148i	$0.155079\pi$
$740$	39.6862	−	4.63865i	1.45889	−	0.170520i
$741$		0			0
$742$	22.0639	−	73.6984i	0.809989	−	2.70555i
$743$	16.1251	+	17.0916i	0.591573	+	0.627031i	0.952125	−	0.305708i	$-0.0988933\pi$
$743$	16.1251	+	17.0916i	0.591573	+	0.627031i	−0.360552	+	0.932739i	$0.617412\pi$
$744$		0			0
$745$	2.05211	+	2.75646i	0.0751835	+	0.100989i
$746$	13.6520	+	77.4244i	0.499836	+	2.83471i
$747$		0			0
$748$	−10.4129	+	59.0546i	−0.380734	+	2.15925i
$749$	−12.9838	+	6.52069i	−0.474416	+	0.238261i
$750$		0			0
$751$	−34.8595	−	4.07449i	−1.27204	−	0.148680i	−0.546851	−	0.837230i	$-0.684174\pi$
$751$	−34.8595	−	4.07449i	−1.27204	−	0.148680i	−0.725189	+	0.688550i	$0.758248\pi$
$752$	26.1140	−	17.1755i	0.952281	−	0.626325i
$753$		0			0
$754$	3.36084	+	11.2260i	0.122395	+	0.408826i
$755$	15.0453	−	26.0592i	0.547554	−	0.948391i
$756$		0			0
$757$	−23.1445	−	40.0875i	−0.841202	−	1.45701i	−0.888879	−	0.458142i	$-0.848515\pi$
$757$	−23.1445	−	40.0875i	−0.841202	−	1.45701i	0.0476764	−	0.998863i	$-0.484818\pi$
$758$	−32.3883	+	34.3296i	−1.17640	+	1.24691i
$759$		0			0
$760$	−3.22864	−	55.4337i	−0.117115	−	2.01079i
$761$	2.80588	+	6.50477i	0.101713	+	0.235798i	0.961472	−	0.274902i	$-0.0886455\pi$
$761$	2.80588	+	6.50477i	0.101713	+	0.235798i	−0.859759	+	0.510700i	$0.829386\pi$
$762$		0			0
$763$	1.32396	−	22.7315i	0.0479305	−	0.822935i
$764$	−54.7961	+	19.9441i	−1.98245	+	0.721554i
$765$		0			0
$766$	69.8968	+	25.4404i	2.52547	+	0.919198i
$767$	−1.35652	+	3.14476i	−0.0489811	+	0.113551i
$768$		0			0
$769$	−42.1559	+	9.99112i	−1.52018	+	0.360289i	−0.904075	−	0.427375i	$-0.859438\pi$
$769$	−42.1559	+	9.99112i	−1.52018	+	0.360289i	−0.616105	+	0.787664i	$0.711290\pi$
$770$	51.6413	−	12.2392i	1.86102	−	0.441071i
$771$		0			0
$772$	6.32055	−	14.6527i	0.227481	−	0.527361i
$773$	33.8164	+	12.3082i	1.21629	+	0.442694i	0.868881	−	0.495020i	$-0.164839\pi$
$773$	33.8164	+	12.3082i	1.21629	+	0.442694i	0.347409	+	0.937714i	$0.387062\pi$
$774$		0			0
$775$	−10.6833	+	3.88841i	−0.383756	+	0.139676i
$776$	4.06376	−	69.7720i	0.145880	−	2.50467i
$777$		0			0
$778$	−5.76348	−	13.3612i	−0.206631	−	0.479024i
$779$	1.74963	+	30.0400i	0.0626870	+	1.07629i
$780$		0			0
$781$	11.6601	−	12.3590i	0.417231	−	0.442239i
$782$	−11.3026	−	19.5768i	−0.404182	−	0.700063i
$783$		0			0
$784$	−8.58220	+	14.8648i	−0.306507	+	0.530886i
$785$	−2.60849	−	8.71297i	−0.0931011	−	0.310979i
$786$		0			0
$787$	−17.5455	+	11.5399i	−0.625431	+	0.411352i	−0.822281	−	0.569081i	$-0.807299\pi$
$787$	−17.5455	+	11.5399i	−0.625431	+	0.411352i	0.196850	+	0.980434i	$0.436929\pi$
$788$	−23.1527	−	2.70616i	−0.824779	−	0.0964029i
$789$		0			0
$790$	14.7137	−	7.38948i	0.523489	−	0.262906i
$791$	−4.33738	+	24.5985i	−0.154219	+	0.874622i
$792$		0			0
$793$	−0.429848	−	2.43779i	−0.0152643	−	0.0865683i
$794$	−8.76141	−	11.7686i	−0.310931	−	0.417653i
$795$		0			0
$796$	49.2174	+	52.1674i	1.74446	+	1.84902i
$797$	12.1044	−	40.4315i	0.428760	−	1.43216i	−0.421996	−	0.906598i	$-0.638670\pi$
$797$	12.1044	−	40.4315i	0.428760	−	1.43216i	0.850756	−	0.525561i	$-0.176144\pi$
$798$		0			0
$799$	17.2160	−	2.01227i	0.609060	−	0.0711889i
$800$	5.49242	−	4.60868i	0.194186	−	0.162942i
$801$		0			0
$802$	−20.5087	−	17.2089i	−0.724188	−	0.607666i
$803$	44.2222	+	29.0854i	1.56057	+	1.02640i
$804$		0			0
$805$	−8.10885	+	10.8921i	−0.285799	+	0.383895i
$806$	17.9086	+	8.99403i	0.630803	+	0.316801i
$807$		0			0
$808$	24.3385	+	5.76833i	0.856225	+	0.202929i
$809$	15.1427			0.532390			0.266195	−	0.963919i	$-0.414233\pi$
$809$	15.1427			0.532390			0.266195	+	0.963919i	$0.414233\pi$
$810$		0			0
$811$	30.4862			1.07051			0.535257	−	0.844689i	$-0.320215\pi$
$811$	30.4862			1.07051			0.535257	+	0.844689i	$0.320215\pi$
$812$	−28.8838	−	6.84558i	−1.01362	−	0.240233i
$813$		0			0
$814$	70.9587	+	35.6368i	2.48710	+	1.24907i
$815$	5.45542	−	7.32791i	0.191095	−	0.256685i
$816$		0			0
$817$	−4.71294	−	3.09975i	−0.164885	−	0.108447i
$818$	−6.36311	−	5.33928i	−0.222481	−	0.186684i
$819$		0			0
$820$	19.2947	−	16.1902i	0.673800	−	0.565386i
$821$	44.1428	−	5.15955i	1.54059	−	0.180070i	0.697008	−	0.717064i	$-0.254514\pi$
$821$	44.1428	−	5.15955i	1.54059	−	0.180070i	0.843586	+	0.536994i	$0.180440\pi$
$822$		0			0
$823$	6.79746	−	22.7051i	0.236944	−	0.791450i	−0.753964	−	0.656915i	$-0.771861\pi$
$823$	6.79746	−	22.7051i	0.236944	−	0.791450i	0.990909	−	0.134534i	$-0.0429539\pi$
$824$	53.1904	+	56.3785i	1.85298	+	1.96404i
$825$		0			0
$826$	−7.63296	−	10.2528i	−0.265585	−	0.356742i
$827$	0.904516	+	5.12977i	0.0314531	+	0.178379i	0.996487	−	0.0837448i	$-0.0266881\pi$
$827$	0.904516	+	5.12977i	0.0314531	+	0.178379i	−0.965034	+	0.262124i	$0.915577\pi$
$828$		0			0
$829$	1.35636	−	7.69231i	0.0471084	−	0.267165i	−0.952152	−	0.305626i	$-0.901134\pi$
$829$	1.35636	−	7.69231i	0.0471084	−	0.267165i	0.999260	+	0.0384608i	$0.0122455\pi$
$830$	46.9491	−	23.5787i	1.62963	−	0.818429i
$831$		0			0
$832$	10.3352	+	1.20801i	0.358309	+	0.0418803i
$833$	−7.95270	+	5.23057i	−0.275545	+	0.181229i
$834$		0			0
$835$	−1.57586	−	5.26374i	−0.0545349	−	0.182159i
$836$	71.1060	−	123.159i	2.45925	−	4.25955i
$837$		0			0
$838$	3.56743	+	6.17897i	0.123235	+	0.213449i
$839$	20.6517	−	21.8896i	0.712977	−	0.755712i	−0.265040	−	0.964238i	$-0.585385\pi$
$839$	20.6517	−	21.8896i	0.712977	−	0.755712i	0.978017	+	0.208526i	$0.0668665\pi$
$840$		0			0
$841$	1.40422	+	24.1096i	0.0484215	+	0.831364i
$842$	6.21241	+	14.4020i	0.214094	+	0.496325i
$843$		0			0
$844$	−4.74332	+	81.4396i	−0.163272	+	2.80327i
$845$	−11.1787	+	4.06870i	−0.384557	+	0.139967i
$846$		0			0
$847$	34.2925	+	12.4814i	1.17830	+	0.428867i
$848$	−20.6815	+	47.9451i	−0.710206	+	1.64644i
$849$		0			0
$850$	21.9575	−	5.20403i	0.753137	−	0.178497i
$851$	−19.7690	+	4.68533i	−0.677672	+	0.160611i
$852$		0			0
$853$	2.20744	−	5.11743i	0.0755814	−	0.175217i	−0.876236	−	0.481882i	$-0.839954\pi$
$853$	2.20744	−	5.11743i	0.0755814	−	0.175217i	0.951818	+	0.306664i	$0.0992128\pi$
$854$	8.68141	+	3.15978i	0.297072	+	0.108125i
$855$		0			0
$856$	23.7619	−	8.64862i	0.812165	−	0.295604i
$857$	−1.01822	+	17.4822i	−0.0347818	+	0.597180i	0.935218	+	0.354073i	$0.115204\pi$
$857$	−1.01822	+	17.4822i	−0.0347818	+	0.597180i	−0.970000	+	0.243107i	$0.921833\pi$
$858$		0			0
$859$	−13.2998	−	30.8323i	−0.453782	−	1.05198i	−0.979522	−	0.201339i	$-0.935471\pi$
$859$	−13.2998	−	30.8323i	−0.453782	−	1.05198i	0.525740	−	0.850645i	$-0.323788\pi$
$860$	0.274544	+	4.71374i	0.00936188	+	0.160737i
$861$		0			0
$862$	29.6593	−	31.4370i	1.01020	−	1.07075i
$863$	−5.63576	−	9.76143i	−0.191844	−	0.332283i	0.754018	−	0.656854i	$-0.228113\pi$
$863$	−5.63576	−	9.76143i	−0.191844	−	0.332283i	−0.945861	+	0.324571i	$0.894780\pi$
$864$		0			0
$865$	11.4933	−	19.9069i	0.390782	−	0.676855i
$866$	9.77948	+	32.6657i	0.332320	+	1.11003i
$867$		0			0
$868$	−42.4131	+	27.8955i	−1.43959	+	0.946835i
$869$	22.0583	+	2.57825i	0.748278	+	0.0874612i
$870$		0			0
$871$	−11.4004	+	5.72548i	−0.386287	+	0.194000i
$872$	−6.88157	+	39.0273i	−0.233039	+	1.32163i
$873$		0			0
$874$	9.30925	+	52.7954i	0.314890	+	1.78583i
$875$	−21.5019	−	28.8821i	−0.726898	−	0.976393i
$876$		0			0
$877$	−25.2546	−	26.7683i	−0.852786	−	0.903901i	0.143531	−	0.989646i	$-0.454154\pi$
$877$	−25.2546	−	26.7683i	−0.852786	−	0.903901i	−0.996317	+	0.0857451i	$0.972673\pi$
$878$	−26.6828	+	89.1266i	−0.900499	+	3.00788i
$879$		0			0
$880$	−35.7784	+	4.18189i	−1.20609	+	0.140972i
$881$	−10.8033	+	9.06508i	−0.363974	+	0.305410i	−0.806372	−	0.591408i	$-0.798572\pi$
$881$	−10.8033	+	9.06508i	−0.363974	+	0.305410i	0.442398	+	0.896819i	$0.354128\pi$
$882$		0			0
$883$	−26.7963	−	22.4847i	−0.901767	−	0.756672i	0.0687683	−	0.997633i	$-0.478093\pi$
$883$	−26.7963	−	22.4847i	−0.901767	−	0.756672i	−0.970535	+	0.240961i	$0.922538\pi$
$884$	−22.5564	−	14.8356i	−0.758653	−	0.498974i
$885$		0			0
$886$	6.65266	−	8.93607i	0.223500	−	0.300213i
$887$	39.1164	+	19.6450i	1.31340	+	0.659614i	0.961081	−	0.276266i	$-0.0890970\pi$
$887$	39.1164	+	19.6450i	1.31340	+	0.659614i	0.352319	+	0.935880i	$0.385393\pi$
$888$		0			0
$889$	31.7631	+	7.52799i	1.06530	+	0.252481i
$890$	14.5535			0.487833
$891$		0			0
$892$	−63.9539			−2.14134
$893$	−39.9988	−	9.47989i	−1.33851	−	0.317232i
$894$		0			0
$895$	27.2889	+	13.7050i	0.912166	+	0.458107i
$896$	−32.2400	+	43.3059i	−1.07706	+	1.44675i
$897$		0			0
$898$	7.64091	+	5.02550i	0.254980	+	0.167703i
$899$	−6.35325	−	5.33101i	−0.211893	−	0.177799i
$900$		0			0
$901$	−22.1820	+	18.6129i	−0.738988	+	0.620085i
$902$	49.7163	−	5.81100i	1.65537	−	0.193485i
$903$		0			0
$904$	12.4680	−	41.6459i	0.414678	−	1.38512i
$905$	−6.13692	−	6.50475i	−0.203998	−	0.216225i
$906$		0			0
$907$	−9.98553	−	13.4129i	−0.331564	−	0.445368i	0.604811	−	0.796369i	$-0.293249\pi$
$907$	−9.98553	−	13.4129i	−0.331564	−	0.445368i	−0.936375	+	0.351001i	$0.885841\pi$
$908$	4.62359	+	26.2217i	0.153439	+	0.870196i
$909$		0			0
$910$	−4.14918	+	23.5311i	−0.137544	+	0.780050i
$911$	−17.0600	+	8.56784i	−0.565222	+	0.283865i	−0.708376	−	0.705835i	$-0.750572\pi$
$911$	−17.0600	+	8.56784i	−0.565222	+	0.283865i	0.143154	+	0.989700i	$0.454276\pi$
$912$		0			0
$913$	70.3848	+	8.22681i	2.32940	+	0.272268i
$914$	−38.2960	+	25.1877i	−1.26672	+	0.833134i
$915$		0			0
$916$	−11.2901	−	37.7115i	−0.373035	−	1.24602i
$917$	13.7274	−	23.7765i	0.453319	−	0.785171i
$918$		0			0
$919$	−2.23912	−	3.87828i	−0.0738619	−	0.127933i	0.826729	−	0.562600i	$-0.190199\pi$
$919$	−2.23912	−	3.87828i	−0.0738619	−	0.127933i	−0.900591	+	0.434668i	$0.856866\pi$
$920$	16.2181	−	17.1902i	0.534696	−	0.566744i
$921$		0			0
$922$	−1.75006	−	30.0473i	−0.0576351	−	0.989557i
$923$	3.02994	+	7.02419i	0.0997317	+	0.231204i
$924$		0			0
$925$	1.17924	−	20.2468i	0.0387732	−	0.665711i
$926$	6.45541	−	2.34958i	0.212138	−	0.0772119i
$927$		0			0
$928$	4.91493	+	1.78889i	0.161340	+	0.0587231i
$929$	−16.1432	+	37.4242i	−0.529642	+	1.22785i	0.417981	+	0.908456i	$0.362738\pi$
$929$	−16.1432	+	37.4242i	−0.529642	+	1.22785i	−0.947623	+	0.319392i	$0.896521\pi$
$930$		0			0
$931$	21.9655	−	5.20593i	0.719891	−	0.170617i
$932$	−86.5280	+	20.5075i	−2.83432	+	0.671746i
$933$		0			0
$934$	−31.1065	+	72.1131i	−1.01784	+	2.35961i
$935$	−18.7715	−	6.83227i	−0.613894	−	0.223439i
$936$		0			0
$937$	−25.7954	+	9.38877i	−0.842700	+	0.306718i	−0.727060	−	0.686574i	$-0.759114\pi$
$937$	−25.7954	+	9.38877i	−0.842700	+	0.306718i	−0.115640	+	0.993291i	$0.536892\pi$
$938$	2.76841	−	47.5318i	0.0903919	−	1.55197i
$939$		0			0
$940$	13.6284	+	31.5943i	0.444510	+	1.03049i
$941$	0.146957	+	2.52316i	0.00479067	+	0.0822526i	0.999856	−	0.0169692i	$-0.00540172\pi$
$941$	0.146957	+	2.52316i	0.00479067	+	0.0822526i	−0.995065	+	0.0992217i	$0.968365\pi$
$942$		0			0
$943$	−8.78874	+	9.31552i	−0.286201	+	0.303355i
$944$	4.33786	+	7.51340i	0.141185	+	0.244540i
$945$		0			0
$946$	−4.69172	+	8.12630i	−0.152541	+	0.264209i
$947$	3.66188	+	12.2315i	0.118995	+	0.397472i	0.996646	−	0.0818282i	$-0.0260759\pi$
$947$	3.66188	+	12.2315i	0.118995	+	0.397472i	−0.877651	+	0.479300i	$0.840891\pi$
$948$		0			0
$949$	−19.9098	+	13.0949i	−0.646300	+	0.425078i
$950$	−53.1543	−	6.21285i	−1.72455	−	0.201571i
$951$		0			0
$952$	47.4219	−	23.8162i	1.53695	−	0.771886i
$953$	1.62376	−	9.20879i	0.0525987	−	0.298302i	−0.947148	−	0.320796i	$-0.896050\pi$
$953$	1.62376	−	9.20879i	0.0525987	−	0.298302i	0.999747	+	0.0224940i	$0.00716067\pi$
$954$		0			0
$955$	−3.37322	−	19.1305i	−0.109155	−	0.619048i
$956$	−41.3802	−	55.5832i	−1.33833	−	1.79769i
$957$		0			0
$958$	4.77311	+	5.05920i	0.154212	+	0.163455i
$959$	0.977775	−	3.26600i	0.0315740	−	0.105465i
$960$		0			0
$961$	16.7029	−	1.95229i	0.538803	−	0.0629770i
$962$	−27.3859	+	22.9795i	−0.882958	+	0.740890i
$963$		0			0
$964$	5.34797	+	4.48748i	0.172247	+	0.144532i
$965$	4.44143	+	2.92117i	0.142975	+	0.0940359i
$966$		0			0
$967$	−1.28161	+	1.72150i	−0.0412139	+	0.0553599i	−0.822252	−	0.569123i	$-0.807283\pi$
$967$	−1.28161	+	1.72150i	−0.0412139	+	0.0553599i	0.781039	+	0.624483i	$0.214690\pi$
$968$	−56.7579	−	28.5049i	−1.82427	−	0.916181i
$969$		0			0
$970$	43.0160	+	10.1950i	1.38116	+	0.327341i
$971$	−18.8603			−0.605255			−0.302627	−	0.953109i	$-0.597864\pi$
$971$	−18.8603			−0.605255			−0.302627	+	0.953109i	$0.597864\pi$
$972$		0			0
$973$	23.7603			0.761719
$974$	76.9580	+	18.2394i	2.46589	+	0.584427i
$975$		0			0
$976$	−5.60359	−	2.81423i	−0.179366	−	0.0900812i
$977$	35.8982	−	48.2196i	1.14848	−	1.54268i	0.354165	−	0.935183i	$-0.384765\pi$
$977$	35.8982	−	48.2196i	1.14848	−	1.54268i	0.794320	−	0.607500i	$-0.207827\pi$
$978$		0			0
$979$	16.4008	+	10.7870i	0.524171	+	0.344753i
$980$	−14.4748	−	12.1458i	−0.462380	−	0.387983i
$981$		0			0
$982$	67.2670	−	56.4437i	2.14657	−	1.80119i
$983$	−31.9073	+	3.72943i	−1.01769	+	0.118950i	−0.608544	−	0.793520i	$-0.708246\pi$
$983$	−31.9073	+	3.72943i	−1.01769	+	0.118950i	−0.409142	+	0.912471i	$0.634172\pi$
$984$		0			0
$985$	2.22711	−	7.43907i	0.0709617	−	0.237029i
$986$	11.2966	+	11.9737i	0.359759	+	0.381322i
$987$		0			0
$988$	38.2343	+	51.3576i	1.21640	+	1.63390i
$989$	−0.416905	−	2.36439i	−0.0132568	−	0.0751831i
$990$		0			0
$991$	−2.05455	+	11.6519i	−0.0652648	+	0.370135i	0.934630	+	0.355622i	$0.115731\pi$
$991$	−2.05455	+	11.6519i	−0.0652648	+	0.370135i	−0.999895	+	0.0145131i	$0.995380\pi$
$992$	7.99335	−	4.01441i	0.253789	−	0.127458i
$993$		0			0
$994$	−28.3573	−	3.31450i	−0.899440	−	0.105129i
$995$	−19.9615	+	13.1289i	−0.632821	+	0.416213i
$996$		0			0
$997$	12.1837	+	40.6963i	0.385861	+	1.28886i	0.901768	+	0.432220i	$0.142270\pi$
$997$	12.1837	+	40.6963i	0.385861	+	1.28886i	−0.515908	+	0.856644i	$0.672545\pi$
$998$	−9.96735	+	17.2640i	−0.315511	+	0.546481i
$999$		0			0

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	729.2.g.c.136.1		144
3.2	odd	2		729.2.g.b.136.8		144
9.2	odd	6		729.2.g.a.379.1		144
9.4	even	3		81.2.g.a.70.8	yes	144
9.5	odd	6		243.2.g.a.127.1		144
9.7	even	3		729.2.g.d.379.8		144
81.5	odd	54		729.2.g.b.595.8		144
81.20	odd	54		6561.2.a.d.1.67		72
81.22	even	27		729.2.g.d.352.8		144
81.32	odd	54		243.2.g.a.199.1		144
81.49	even	27		81.2.g.a.22.8	✓	144
81.59	odd	54		729.2.g.a.352.1		144
81.61	even	27		6561.2.a.c.1.6		72
81.76	even	27	inner	729.2.g.c.595.1		144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
81.2.g.a.22.8	✓	144	81.49	even	27
81.2.g.a.70.8	yes	144	9.4	even	3
243.2.g.a.127.1		144	9.5	odd	6
243.2.g.a.199.1		144	81.32	odd	54
729.2.g.a.352.1		144	81.59	odd	54
729.2.g.a.379.1		144	9.2	odd	6
729.2.g.b.136.8		144	3.2	odd	2
729.2.g.b.595.8		144	81.5	odd	54
729.2.g.c.136.1		144	1.1	even	1	trivial
729.2.g.c.595.1		144	81.76	even	27	inner
729.2.g.d.352.8		144	81.22	even	27
729.2.g.d.379.8		144	9.7	even	3
6561.2.a.c.1.6		72	81.61	even	27
6561.2.a.d.1.67		72	81.20	odd	54

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

Newform invariants

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$q$ -expansion

Character values

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Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	729.2.g.c.136.1

Level	$729$
Weight	$2$
Character	729.136
Analytic conductor	$5.821$
Analytic rank	$0$
Dimension	$144$
Inner twists	$2$