LMFDB - Embedded newform 756.2.ck.a.605.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(5,756)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(756, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 5, 15]))

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

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

chi := DirichletCharacter("756.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.ck (of order $18$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.03669039281$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$24$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			605.13
Character	$\chi$	$=$	756.605
Dual form			756.2.ck.a.5.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.212510 - 1.71896i) q^{3} +(0.455707 + 2.58444i) q^{5} +(2.64406 + 0.0947211i) q^{7} +(-2.90968 - 0.730593i) q^{9} +O(q^{10})$	\(q+(0.212510 - 1.71896i) q^{3} +(0.455707 + 2.58444i) q^{5} +(2.64406 + 0.0947211i) q^{7} +(-2.90968 - 0.730593i) q^{9} +(0.625382 + 0.110272i) q^{11} +(-2.83064 - 3.37342i) q^{13} +(4.53941 - 0.234125i) q^{15} +8.05877 q^{17} +3.96393i q^{19} +(0.724710 - 4.52491i) q^{21} +(3.59496 + 4.28431i) q^{23} +(-1.77321 + 0.645394i) q^{25} +(-1.87420 + 4.84638i) q^{27} +(4.88838 - 5.82574i) q^{29} +(1.20156 - 3.30125i) q^{31} +(0.322453 - 1.05158i) q^{33} +(0.960113 + 6.87657i) q^{35} +(-3.51540 + 6.08885i) q^{37} +(-6.40033 + 4.14888i) q^{39} +(4.16466 - 3.49456i) q^{41} +(-0.637408 + 0.231997i) q^{43} +(0.562216 - 7.85283i) q^{45} +(-2.65000 + 0.964522i) q^{47} +(6.98206 + 0.500896i) q^{49} +(1.71257 - 13.8527i) q^{51} +(-3.98038 - 2.29807i) q^{53} +1.66652i q^{55} +(6.81386 + 0.842375i) q^{57} +(-0.846158 + 0.710011i) q^{59} +(-0.698819 - 1.91999i) q^{61} +(-7.62415 - 2.20734i) q^{63} +(7.42847 - 8.85290i) q^{65} +(-2.32519 - 13.1868i) q^{67} +(8.12853 - 5.26915i) q^{69} +(6.01970 - 3.47547i) q^{71} +(4.04198 - 2.33364i) q^{73} +(0.732586 + 3.18523i) q^{75} +(1.64310 + 0.350801i) q^{77} +(-2.57678 + 14.6136i) q^{79} +(7.93247 + 4.25159i) q^{81} +(0.855255 + 0.717644i) q^{83} +(3.67243 + 20.8274i) q^{85} +(-8.97542 - 9.64098i) q^{87} -13.9067 q^{89} +(-7.16482 - 9.18763i) q^{91} +(-5.41939 - 2.76698i) q^{93} +(-10.2446 + 1.80639i) q^{95} +(-5.47800 - 15.0507i) q^{97} +(-1.73910 - 0.777756i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q + 6 q^{9}+O(q^{10}) $ 144 * q + 6 * q^9	$ 144 q + 6 q^{9} - 6 q^{11} + 12 q^{15} + 33 q^{21} + 21 q^{23} - 6 q^{29} + 27 q^{35} + 39 q^{39} - 54 q^{47} + 18 q^{49} - 9 q^{51} - 45 q^{53} + 3 q^{57} + 45 q^{59} + 39 q^{63} + 24 q^{65} - 36 q^{69} + 36 q^{71} + 45 q^{75} + 21 q^{77} - 18 q^{79} + 18 q^{81} + 36 q^{85} - 45 q^{87} + 9 q^{91} - 48 q^{93} - 66 q^{95}+O(q^{100}) $ 144 * q + 6 * q^9 - 6 * q^11 + 12 * q^15 + 33 * q^21 + 21 * q^23 - 6 * q^29 + 27 * q^35 + 39 * q^39 - 54 * q^47 + 18 * q^49 - 9 * q^51 - 45 * q^53 + 3 * q^57 + 45 * q^59 + 39 * q^63 + 24 * q^65 - 36 * q^69 + 36 * q^71 + 45 * q^75 + 21 * q^77 - 18 * q^79 + 18 * q^81 + 36 * q^85 - 45 * q^87 + 9 * q^91 - 48 * q^93 - 66 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/756\mathbb{Z}\right)^\times$.

$n$	$29$	$325$	$379$
$\chi(n)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{1}{6}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.212510	−	1.71896i	0.122693	−	0.992445i
$3$	0.212510	−	1.71896i	0.122693	−	0.992445i
$4$		0			0
$5$	0.455707	+	2.58444i	0.203798	+	1.15580i	0.899320	+	0.437292i	$0.144062\pi$
$5$	0.455707	+	2.58444i	0.203798	+	1.15580i	−0.695521	+	0.718505i	$0.744827\pi$
$6$		0			0
$7$	2.64406	+	0.0947211i	0.999359	+	0.0358012i
$7$	2.64406	+	0.0947211i	0.999359	+	0.0358012i
$8$		0			0
$9$	−2.90968	−	0.730593i	−0.969893	−	0.243531i
$10$		0			0
$11$	0.625382	+	0.110272i	0.188560	+	0.0332482i	0.267131	−	0.963660i	$-0.413925\pi$
$11$	0.625382	+	0.110272i	0.188560	+	0.0332482i	−0.0785707	+	0.996909i	$0.525036\pi$
$12$		0			0
$13$	−2.83064	−	3.37342i	−0.785077	−	0.935619i	0.214074	−	0.976817i	$-0.431327\pi$
$13$	−2.83064	−	3.37342i	−0.785077	−	0.935619i	−0.999151	+	0.0411989i	$0.986882\pi$
$14$		0			0
$15$	4.53941	−	0.234125i	1.17207	−	0.0604508i
$16$		0			0
$17$	8.05877			1.95454			0.977269	−	0.212003i	$-0.0679986\pi$
$17$	8.05877			1.95454			0.977269	+	0.212003i	$0.0679986\pi$
$18$		0			0
$19$			3.96393i			0.909389i	0.890647	+	0.454695i	$0.150252\pi$
$19$			3.96393i			0.909389i	−0.890647	+	0.454695i	$0.849748\pi$
$20$		0			0
$21$	0.724710	−	4.52491i	0.158145	−	0.987416i
$22$		0			0
$23$	3.59496	+	4.28431i	0.749601	+	0.893339i	0.997143	−	0.0755377i	$-0.0240673\pi$
$23$	3.59496	+	4.28431i	0.749601	+	0.893339i	−0.247542	+	0.968877i	$0.579623\pi$
$24$		0			0
$25$	−1.77321	+	0.645394i	−0.354641	+	0.129079i
$26$		0			0
$27$	−1.87420	+	4.84638i	−0.360690	+	0.932686i
$28$		0			0
$29$	4.88838	−	5.82574i	0.907749	−	1.08181i	−0.0885680	−	0.996070i	$-0.528229\pi$
$29$	4.88838	−	5.82574i	0.907749	−	1.08181i	0.996317	−	0.0857433i	$-0.0273265\pi$
$30$		0			0
$31$	1.20156	−	3.30125i	0.215806	−	0.592922i	−0.783800	−	0.621014i	$-0.786721\pi$
$31$	1.20156	−	3.30125i	0.215806	−	0.592922i	0.999605	+	0.0280923i	$0.00894324\pi$
$32$		0			0
$33$	0.322453	−	1.05158i	0.0561319	−	0.183056i
$34$		0			0
$35$	0.960113	+	6.87657i	0.162289	+	1.16235i
$36$		0			0
$37$	−3.51540	+	6.08885i	−0.577928	+	1.00100i	0.417789	+	0.908544i	$0.362805\pi$
$37$	−3.51540	+	6.08885i	−0.577928	+	1.00100i	−0.995717	+	0.0924566i	$0.970528\pi$
$38$		0			0
$39$	−6.40033	+	4.14888i	−1.02487	+	0.664352i
$40$		0			0
$41$	4.16466	−	3.49456i	0.650410	−	0.545759i	−0.256785	−	0.966468i	$-0.582663\pi$
$41$	4.16466	−	3.49456i	0.650410	−	0.545759i	0.907195	+	0.420710i	$0.138219\pi$
$42$		0			0
$43$	−0.637408	+	0.231997i	−0.0972038	+	0.0353793i	−0.390164	−	0.920745i	$-0.627582\pi$
$43$	−0.637408	+	0.231997i	−0.0972038	+	0.0353793i	0.292960	+	0.956125i	$0.405360\pi$
$44$		0			0
$45$	0.562216	−	7.85283i	0.0838102	−	1.17063i
$46$		0			0
$47$	−2.65000	+	0.964522i	−0.386542	+	0.140690i	−0.527979	−	0.849257i	$-0.677050\pi$
$47$	−2.65000	+	0.964522i	−0.386542	+	0.140690i	0.141437	+	0.989947i	$0.454828\pi$
$48$		0			0
$49$	6.98206	+	0.500896i	0.997437	+	0.0715565i
$50$		0			0
$51$	1.71257	−	13.8527i	0.239807	−	1.93977i
$52$		0			0
$53$	−3.98038	−	2.29807i	−0.546747	−	0.315665i	0.201062	−	0.979579i	$-0.435561\pi$
$53$	−3.98038	−	2.29807i	−0.546747	−	0.315665i	−0.747809	+	0.663914i	$0.768894\pi$
$54$		0			0
$55$			1.66652i			0.224713i
$56$		0			0
$57$	6.81386	+	0.842375i	0.902518	+	0.111575i
$58$		0			0
$59$	−0.846158	+	0.710011i	−0.110160	+	0.0924355i	−0.696204	−	0.717844i	$-0.745129\pi$
$59$	−0.846158	+	0.710011i	−0.110160	+	0.0924355i	0.586044	+	0.810279i	$0.300685\pi$
$60$		0			0
$61$	−0.698819	−	1.91999i	−0.0894745	−	0.245829i	0.886882	−	0.461996i	$-0.152867\pi$
$61$	−0.698819	−	1.91999i	−0.0894745	−	0.245829i	−0.976356	+	0.216167i	$0.930644\pi$
$62$		0			0
$63$	−7.62415	−	2.20734i	−0.960553	−	0.278098i
$64$		0			0
$65$	7.42847	−	8.85290i	0.921388	−	1.09807i
$66$		0			0
$67$	−2.32519	−	13.1868i	−0.284067	−	1.61102i	−0.708601	−	0.705610i	$-0.750673\pi$
$67$	−2.32519	−	13.1868i	−0.284067	−	1.61102i	0.424534	−	0.905412i	$-0.360438\pi$
$68$		0			0
$69$	8.12853	−	5.26915i	0.978560	−	0.634331i
$70$		0			0
$71$	6.01970	−	3.47547i	0.714406	−	0.412463i	−0.0982840	−	0.995158i	$-0.531335\pi$
$71$	6.01970	−	3.47547i	0.714406	−	0.412463i	0.812690	+	0.582696i	$0.198002\pi$
$72$		0			0
$73$	4.04198	−	2.33364i	0.473078	−	0.273132i	−0.244449	−	0.969662i	$-0.578607\pi$
$73$	4.04198	−	2.33364i	0.473078	−	0.273132i	0.717527	+	0.696530i	$0.245274\pi$
$74$		0			0
$75$	0.732586	+	3.18523i	0.0845918	+	0.367799i
$76$		0			0
$77$	1.64310	+	0.350801i	0.187249	+	0.0399775i
$78$		0			0
$79$	−2.57678	+	14.6136i	−0.289910	+	1.64416i	0.397289	+	0.917693i	$0.369951\pi$
$79$	−2.57678	+	14.6136i	−0.289910	+	1.64416i	−0.687199	+	0.726469i	$0.741160\pi$
$80$		0			0
$81$	7.93247	+	4.25159i	0.881385	+	0.472398i
$82$		0			0
$83$	0.855255	+	0.717644i	0.0938764	+	0.0787717i	0.688518	−	0.725219i	$-0.258262\pi$
$83$	0.855255	+	0.717644i	0.0938764	+	0.0787717i	−0.594642	+	0.803991i	$0.702706\pi$
$84$		0			0
$85$	3.67243	+	20.8274i	0.398331	+	2.25905i
$86$		0			0
$87$	−8.97542	−	9.64098i	−0.962266	−	1.03362i
$88$		0			0
$89$	−13.9067			−1.47411			−0.737055	−	0.675833i	$-0.763784\pi$
$89$	−13.9067			−1.47411			−0.737055	+	0.675833i	$0.763784\pi$
$90$		0			0
$91$	−7.16482	−	9.18763i	−0.751078	−	0.963125i
$92$		0			0
$93$	−5.41939	−	2.76698i	−0.561964	−	0.286922i
$94$		0			0
$95$	−10.2446	+	1.80639i	−1.05107	+	0.185332i
$96$		0			0
$97$	−5.47800	−	15.0507i	−0.556207	−	1.52817i	−0.825095	−	0.564995i	$-0.808878\pi$
$97$	−5.47800	−	15.0507i	−0.556207	−	1.52817i	0.268887	−	0.963172i	$-0.413344\pi$
$98$		0			0
$99$	−1.73910	−	0.777756i	−0.174786	−	0.0781674i
$100$		0			0
$101$	2.40544	+	2.01841i	0.239350	+	0.200839i	0.754570	−	0.656219i	$-0.227845\pi$
$101$	2.40544	+	2.01841i	0.239350	+	0.200839i	−0.515220	+	0.857058i	$0.672290\pi$
$102$		0			0
$103$	−9.58707	+	1.69046i	−0.944642	+	0.166566i	−0.624694	−	0.780869i	$-0.714776\pi$
$103$	−9.58707	+	1.69046i	−0.944642	+	0.166566i	−0.319948	+	0.947435i	$0.603665\pi$
$104$		0			0
$105$	12.0246	−	0.189061i	1.17348	−	0.0184505i
$106$		0			0
$107$	−11.7794	+	6.80085i	−1.13876	+	0.657463i	−0.946123	−	0.323807i	$-0.895037\pi$
$107$	−11.7794	+	6.80085i	−1.13876	+	0.657463i	−0.192637	+	0.981270i	$0.561704\pi$
$108$		0			0
$109$	−7.11868	+	12.3299i	−0.681846	+	1.18099i	0.292571	+	0.956244i	$0.405489\pi$
$109$	−7.11868	+	12.3299i	−0.681846	+	1.18099i	−0.974417	+	0.224748i	$0.927844\pi$
$110$		0			0
$111$	9.71946	+	7.33679i	0.922531	+	0.696377i
$112$		0			0
$113$	−1.74448	+	4.79293i	−0.164107	+	0.450881i	−0.994303	−	0.106591i	$-0.966006\pi$
$113$	−1.74448	+	4.79293i	−0.164107	+	0.450881i	0.830196	+	0.557472i	$0.188229\pi$
$114$		0			0
$115$	−9.43429	+	11.2433i	−0.879752	+	1.04845i
$116$		0			0
$117$	5.77164	+	11.8836i	0.533589	+	1.09864i
$118$		0			0
$119$	21.3078	+	0.763335i	1.95329	+	0.0699748i
$120$		0			0
$121$	−9.95768	−	3.62430i	−0.905243	−	0.329482i
$122$		0			0
$123$	−5.12200	−	7.90153i	−0.461835	−	0.712457i
$124$		0			0
$125$	4.08473	+	7.07496i	0.365349	+	0.632804i
$126$		0			0
$127$	−4.26064	+	7.37965i	−0.378071	+	0.654838i	−0.990782	−	0.135469i	$-0.956746\pi$
$127$	−4.26064	+	7.37965i	−0.378071	+	0.654838i	0.612711	+	0.790307i	$0.290079\pi$
$128$		0			0
$129$	0.263340	+	1.14498i	0.0231858	+	0.100810i
$130$		0			0
$131$	13.8775	−	11.6446i	1.21248	−	1.01739i	0.213295	−	0.976988i	$-0.431580\pi$
$131$	13.8775	−	11.6446i	1.21248	−	1.01739i	0.999183	−	0.0404024i	$-0.0128640\pi$
$132$		0			0
$133$	−0.375468	+	10.4809i	−0.0325572	+	0.908806i
$134$		0			0
$135$	−13.3793	−	2.63523i	−1.15150	−	0.226805i
$136$		0			0
$137$	−0.318833	−	0.875986i	−0.0272397	−	0.0748406i	0.925327	−	0.379169i	$-0.123790\pi$
$137$	−0.318833	−	0.875986i	−0.0272397	−	0.0748406i	−0.952567	+	0.304329i	$0.901568\pi$
$138$		0			0
$139$	−5.49627	+	0.969140i	−0.466187	+	0.0822014i	−0.401808	−	0.915724i	$-0.631618\pi$
$139$	−5.49627	+	0.969140i	−0.466187	+	0.0822014i	−0.0643796	+	0.997925i	$0.520507\pi$
$140$		0			0
$141$	1.09483	+	4.76023i	0.0922011	+	0.400884i
$142$		0			0
$143$	−1.39824	−	2.42182i	−0.116926	−	0.202522i
$144$		0			0
$145$	17.2840	+	9.97890i	1.43535	+	0.828702i
$146$		0			0
$147$	2.34478	−	11.8955i	0.193394	−	0.981121i
$148$		0			0
$149$	−2.40615	+	6.61084i	−0.197119	+	0.541581i	−0.998390	−	0.0567208i	$-0.981936\pi$
$149$	−2.40615	+	6.61084i	−0.197119	+	0.541581i	0.801271	+	0.598302i	$0.204158\pi$
$150$		0			0
$151$	−2.67172	+	15.1521i	−0.217421	+	1.23306i	0.659234	+	0.751938i	$0.270881\pi$
$151$	−2.67172	+	15.1521i	−0.217421	+	1.23306i	−0.876655	+	0.481119i	$0.840231\pi$
$152$		0			0
$153$	−23.4484	−	5.88768i	−1.89569	−	0.475991i
$154$		0			0
$155$	9.07944	+	1.60095i	0.729278	+	0.128591i
$156$		0			0
$157$	−11.5994	−	13.8236i	−0.925731	−	1.10324i	−0.994408	−	0.105604i	$-0.966322\pi$
$157$	−11.5994	−	13.8236i	−0.925731	−	1.10324i	0.0686772	−	0.997639i	$-0.478122\pi$
$158$		0			0
$159$	−4.79618	+	6.35377i	−0.380362	+	0.503887i
$160$		0			0
$161$	9.09946	+	11.6685i	0.717138	+	0.919603i
$162$		0			0
$163$	2.76364	+	4.78676i	0.216465	+	0.374928i	0.953725	−	0.300681i	$-0.0972140\pi$
$163$	2.76364	+	4.78676i	0.216465	+	0.374928i	−0.737260	+	0.675609i	$0.763881\pi$
$164$		0			0
$165$	2.86468	+	0.354151i	0.223015	+	0.0275706i
$166$		0			0
$167$	0.905887	+	0.329716i	0.0700996	+	0.0255142i	0.376832	−	0.926282i	$-0.377013\pi$
$167$	0.905887	+	0.329716i	0.0700996	+	0.0255142i	−0.306732	+	0.951796i	$0.599236\pi$
$168$		0			0
$169$	−1.11004	+	6.29535i	−0.0853877	+	0.484258i
$170$		0			0
$171$	2.89602	−	11.5338i	0.221465	−	0.882010i
$172$		0			0
$173$	0.453368	+	0.380421i	0.0344690	+	0.0289229i	0.659859	−	0.751389i	$-0.270616\pi$
$173$	0.453368	+	0.380421i	0.0344690	+	0.0289229i	−0.625390	+	0.780312i	$0.715060\pi$
$174$		0			0
$175$	−4.74959	+	1.53850i	−0.359035	+	0.116300i
$176$		0			0
$177$	1.04067	+	1.60540i	0.0782213	+	0.120669i
$178$		0			0
$179$			15.4023i			1.15122i	0.817723	+	0.575612i	$0.195236\pi$
$179$			15.4023i			1.15122i	−0.817723	+	0.575612i	$0.804764\pi$
$180$		0			0
$181$	−0.932828	−	0.538569i	−0.0693366	−	0.0400315i	0.464931	−	0.885347i	$-0.346079\pi$
$181$	−0.932828	−	0.538569i	−0.0693366	−	0.0400315i	−0.534267	+	0.845315i	$0.679412\pi$
$182$		0			0
$183$	−3.44890	+	0.793228i	−0.254950	+	0.0586371i
$184$		0			0
$185$	−17.3383	−	6.31061i	−1.27474	−	0.463966i
$186$		0			0
$187$	5.03981	+	0.888654i	0.368547	+	0.0649848i
$188$		0			0
$189$	−5.41454	+	12.6366i	−0.393850	+	0.919175i
$190$		0			0
$191$	1.82347	+	0.321527i	0.131942	+	0.0232649i	0.239229	−	0.970963i	$-0.423105\pi$
$191$	1.82347	+	0.321527i	0.131942	+	0.0232649i	−0.107287	+	0.994228i	$0.534216\pi$
$192$		0			0
$193$	8.67241	+	3.15650i	0.624254	+	0.227210i	0.634728	−	0.772735i	$-0.281112\pi$
$193$	8.67241	+	3.15650i	0.624254	+	0.227210i	−0.0104744	+	0.999945i	$0.503334\pi$
$194$		0			0
$195$	−13.6392	−	14.6506i	−0.976724	−	1.04915i
$196$		0			0
$197$	10.0512	+	5.80304i	0.716116	+	0.413450i	0.813321	−	0.581815i	$-0.197657\pi$
$197$	10.0512	+	5.80304i	0.716116	+	0.413450i	−0.0972057	+	0.995264i	$0.530990\pi$
$198$		0			0
$199$		−	11.0159i		−	0.780899i	−0.920624	−	0.390449i	$-0.872320\pi$
$199$		−	11.0159i		−	0.780899i	0.920624	−	0.390449i	$-0.127680\pi$
$200$		0			0
$201$	−23.1617	+	1.19459i	−1.63370	+	0.0842600i
$202$		0			0
$203$	13.4770	−	14.9406i	0.945898	−	1.04862i
$204$		0			0
$205$	10.9294	+	9.17082i	0.763339	+	0.640518i
$206$		0			0
$207$	−7.33009	−	15.0924i	−0.509477	−	1.04899i
$208$		0			0
$209$	−0.437110	+	2.47897i	−0.0302355	+	0.171474i
$210$		0			0
$211$	−19.8285	−	7.21697i	−1.36505	−	0.496837i	−0.447437	−	0.894316i	$-0.647663\pi$
$211$	−19.8285	−	7.21697i	−1.36505	−	0.496837i	−0.917611	+	0.397479i	$0.869885\pi$
$212$		0			0
$213$	−4.69497	−	11.0862i	−0.321694	−	0.759615i
$214$		0			0
$215$	−0.890055	−	1.54162i	−0.0607012	−	0.105138i
$216$		0			0
$217$	3.48968	−	8.61487i	0.236895	−	0.584815i
$218$		0			0
$219$	−3.15248	−	7.44395i	−0.213025	−	0.503015i
$220$		0			0
$221$	−22.8114	−	27.1856i	−1.53446	−	1.82870i
$222$		0			0
$223$	−23.8990	−	4.21405i	−1.60040	−	0.282193i	−0.698979	−	0.715142i	$-0.746362\pi$
$223$	−23.8990	−	4.21405i	−1.60040	−	0.282193i	−0.901419	+	0.432948i	$0.857473\pi$
$224$		0			0
$225$	5.63098	−	0.582397i	0.375399	−	0.0388265i
$226$		0			0
$227$	−0.446322	+	2.53122i	−0.0296234	+	0.168003i	−0.996030	−	0.0890139i	$-0.971628\pi$
$227$	−0.446322	+	2.53122i	−0.0296234	+	0.168003i	0.966407	+	0.257017i	$0.0827396\pi$
$228$		0			0
$229$	4.64890	−	12.7728i	0.307208	−	0.844047i	−0.685990	−	0.727611i	$-0.740631\pi$
$229$	4.64890	−	12.7728i	0.307208	−	0.844047i	0.993198	−	0.116436i	$-0.0371471\pi$
$230$		0			0
$231$	0.952190	−	2.74988i	0.0626495	−	0.180929i
$232$		0			0
$233$	13.0968	+	7.56146i	0.858002	+	0.495368i	0.863343	−	0.504618i	$-0.168367\pi$
$233$	13.0968	+	7.56146i	0.858002	+	0.495368i	−0.00534083	+	0.999986i	$0.501700\pi$
$234$		0			0
$235$	−3.70037	−	6.40923i	−0.241386	−	0.418092i
$236$		0			0
$237$	24.5727	+	7.53493i	1.59617	+	0.489446i
$238$		0			0
$239$	−19.9067	+	3.51009i	−1.28766	+	0.227049i	−0.775228	−	0.631681i	$-0.782365\pi$
$239$	−19.9067	+	3.51009i	−1.28766	+	0.227049i	−0.512428	+	0.858730i	$0.671254\pi$
$240$		0			0
$241$	−4.89339	−	13.4445i	−0.315211	−	0.866034i	−0.991583	−	0.129474i	$-0.958671\pi$
$241$	−4.89339	−	13.4445i	−0.315211	−	0.866034i	0.676372	−	0.736560i	$-0.263551\pi$
$242$		0			0
$243$	8.99405	−	12.7321i	0.576969	−	0.816766i
$244$		0			0
$245$	1.88723	+	18.2730i	0.120571	+	1.16742i
$246$		0			0
$247$	13.3720	−	11.2205i	0.850841	−	0.713941i
$248$		0			0
$249$	1.41535	−	1.31765i	0.0896945	−	0.0835025i
$250$		0			0
$251$	−11.6736	+	20.2193i	−0.736831	+	1.27623i	0.217085	+	0.976153i	$0.430345\pi$
$251$	−11.6736	+	20.2193i	−0.736831	+	1.27623i	−0.953916	+	0.300075i	$0.902988\pi$
$252$		0			0
$253$	1.77579	+	3.07575i	0.111643	+	0.193371i
$254$		0			0
$255$	36.5820	−	1.88676i	2.29085	−	0.118153i
$256$		0			0
$257$	−11.2872	−	4.10819i	−0.704074	−	0.256262i	−0.0349244	−	0.999390i	$-0.511119\pi$
$257$	−11.2872	−	4.10819i	−0.704074	−	0.256262i	−0.669149	+	0.743128i	$0.733341\pi$
$258$		0			0
$259$	−9.87165	+	15.7663i	−0.613395	+	0.979669i
$260$		0			0
$261$	−18.4799	+	13.3796i	−1.14387	+	0.828178i
$262$		0			0
$263$	−19.4451	+	23.1738i	−1.19904	+	1.42896i	−0.323213	+	0.946326i	$0.604763\pi$
$263$	−19.4451	+	23.1738i	−1.19904	+	1.42896i	−0.875824	+	0.482630i	$0.839681\pi$
$264$		0			0
$265$	4.12535	−	11.3343i	0.253418	−	0.696261i
$266$		0			0
$267$	−2.95531	+	23.9052i	−0.180862	+	1.46297i
$268$		0			0
$269$	12.1233	−	20.9981i	0.739170	−	1.28028i	−0.213700	−	0.976899i	$-0.568551\pi$
$269$	12.1233	−	20.9981i	0.739170	−	1.28028i	0.952870	−	0.303380i	$-0.0981152\pi$
$270$		0			0
$271$	20.5884	−	11.8867i	1.25066	−	0.722067i	0.279417	−	0.960170i	$-0.409859\pi$
$271$	20.5884	−	11.8867i	1.25066	−	0.722067i	0.971240	+	0.238103i	$0.0765255\pi$
$272$		0			0
$273$	−17.3158	+	10.3636i	−1.04800	+	0.627235i
$274$		0			0
$275$	−1.18010	+	0.208084i	−0.0711627	+	0.0125479i
$276$		0			0
$277$	−14.7173	−	12.3493i	−0.884278	−	0.741997i	0.0827763	−	0.996568i	$-0.473621\pi$
$277$	−14.7173	−	12.3493i	−0.884278	−	0.741997i	−0.967054	+	0.254571i	$0.918066\pi$
$278$		0			0
$279$	−5.90801	+	8.72772i	−0.353703	+	0.522515i
$280$		0			0
$281$	−4.71932	−	12.9662i	−0.281531	−	0.773500i	−0.997180	−	0.0750405i	$-0.976091\pi$
$281$	−4.71932	−	12.9662i	−0.281531	−	0.773500i	0.715649	−	0.698460i	$-0.246131\pi$
$282$		0			0
$283$	−24.4150	+	4.30502i	−1.45132	+	0.255907i	−0.843055	−	0.537828i	$-0.819245\pi$
$283$	−24.4150	+	4.30502i	−1.45132	+	0.255907i	−0.608264	+	0.793735i	$0.708134\pi$
$284$		0			0
$285$	0.928056	+	17.9939i	0.0549733	+	1.06587i
$286$		0			0
$287$	11.3426	−	8.84533i	0.669532	−	0.522124i
$288$		0			0
$289$	47.9437			2.82022
$290$		0			0
$291$	−27.0357	+	6.21808i	−1.58486	+	0.364510i
$292$		0			0
$293$	−1.54464	−	8.76011i	−0.0902391	−	0.511771i	−0.996103	−	0.0882016i	$-0.971888\pi$
$293$	−1.54464	−	8.76011i	−0.0902391	−	0.511771i	0.905864	−	0.423570i	$-0.139223\pi$
$294$		0			0
$295$	−2.22058	−	1.86329i	−0.129287	−	0.108485i
$296$		0			0
$297$	−1.70651	+	2.82417i	−0.0990217	+	0.163875i
$298$		0			0
$299$	4.27674	−	24.2546i	0.247330	−	1.40268i
$300$		0			0
$301$	−1.70732	+	0.553038i	−0.0984081	+	0.0318766i
$302$		0			0
$303$	3.98075	−	3.70594i	0.228688	−	0.212901i
$304$		0			0
$305$	4.64364	−	2.68101i	0.265894	−	0.153514i
$306$		0			0
$307$	19.1446	−	11.0532i	1.09264	−	0.630837i	0.158364	−	0.987381i	$-0.449378\pi$
$307$	19.1446	−	11.0532i	1.09264	−	0.630837i	0.934279	+	0.356543i	$0.116045\pi$
$308$		0			0
$309$	0.868494	+	16.8391i	0.0494069	+	0.957942i
$310$		0			0
$311$	4.68231	+	26.5547i	0.265509	+	1.50578i	0.767581	+	0.640952i	$0.221460\pi$
$311$	4.68231	+	26.5547i	0.265509	+	1.50578i	−0.502071	+	0.864826i	$0.667429\pi$
$312$		0			0
$313$	14.7236	−	17.5469i	0.832226	−	0.991808i	−0.167756	−	0.985829i	$-0.553652\pi$
$313$	14.7236	−	17.5469i	0.832226	−	0.991808i	0.999982	−	0.00597981i	$-0.00190344\pi$
$314$		0			0
$315$	2.23036	−	20.7101i	0.125666	−	1.16688i
$316$		0			0
$317$	−1.47509	−	4.05276i	−0.0828490	−	0.227626i	0.891350	−	0.453315i	$-0.149759\pi$
$317$	−1.47509	−	4.05276i	−0.0828490	−	0.227626i	−0.974199	+	0.225689i	$0.927537\pi$
$318$		0			0
$319$	3.69952	−	3.10427i	0.207133	−	0.173806i
$320$		0			0
$321$	9.18719	+	21.6937i	0.512779	+	1.21082i
$322$		0			0
$323$			31.9444i			1.77744i
$324$		0			0
$325$	7.19649	+	4.15489i	0.399189	+	0.230472i
$326$		0			0
$327$	19.6819	+	14.8570i	1.08841	+	0.821593i
$328$		0			0
$329$	−7.09811	+	2.29924i	−0.391331	+	0.126761i
$330$		0			0
$331$	−24.2303	+	8.81912i	−1.33182	+	0.484743i	−0.907227	−	0.420642i	$-0.861805\pi$
$331$	−24.2303	+	8.81912i	−1.33182	+	0.484743i	−0.424592	+	0.905385i	$0.639583\pi$
$332$		0			0
$333$	14.6772	−	15.1483i	0.804303	−	0.830120i
$334$		0			0
$335$	33.0209	−	12.0186i	1.80412	−	0.656647i
$336$		0			0
$337$	21.8311	−	18.3185i	1.18922	−	0.997871i	0.189344	−	0.981911i	$-0.439364\pi$
$337$	21.8311	−	18.3185i	1.18922	−	0.997871i	0.999873	−	0.0159600i	$-0.00508043\pi$
$338$		0			0
$339$	7.86816	+	4.01725i	0.427340	+	0.218187i
$340$		0			0
$341$	1.11547	−	1.93204i	0.0604059	−	0.104626i
$342$		0			0
$343$	18.4135	+	1.98574i	0.994235	+	0.107220i
$344$		0			0
$345$	17.3220	+	18.6065i	0.932587	+	1.00174i
$346$		0			0
$347$	7.03408	−	19.3260i	0.377609	−	1.03747i	−0.594735	−	0.803922i	$-0.702743\pi$
$347$	7.03408	−	19.3260i	0.377609	−	1.03747i	0.972344	−	0.233551i	$-0.0750347\pi$
$348$		0			0
$349$	−6.15541	+	7.33574i	−0.329492	+	0.392673i	−0.905203	−	0.424980i	$-0.860281\pi$
$349$	−6.15541	+	7.33574i	−0.329492	+	0.392673i	0.575711	+	0.817653i	$0.304725\pi$
$350$		0			0
$351$	21.6540	−	7.39587i	1.15581	−	0.394762i
$352$		0			0
$353$	8.12157	−	2.95601i	0.432268	−	0.157333i	−0.116717	−	0.993165i	$-0.537237\pi$
$353$	8.12157	−	2.95601i	0.432268	−	0.157333i	0.548984	+	0.835833i	$0.315015\pi$
$354$		0			0
$355$	11.7254	+	13.9738i	0.622318	+	0.741650i
$356$		0			0
$357$	5.84027	−	36.4652i	0.309100	−	1.92994i
$358$		0			0
$359$		−	9.01772i		−	0.475937i	−0.971273	−	0.237969i	$-0.923518\pi$
$359$		−	9.01772i		−	0.475937i	0.971273	−	0.237969i	$-0.0764815\pi$
$360$		0			0
$361$	3.28722			0.173012
$362$		0			0
$363$	−8.34614	+	16.3467i	−0.438059	+	0.857979i
$364$		0			0
$365$	7.87312	+	9.38281i	0.412098	+	0.491119i
$366$		0			0
$367$	21.3238	+	3.75995i	1.11309	+	0.196268i	0.699806	−	0.714333i	$-0.253270\pi$
$367$	21.3238	+	3.75995i	1.11309	+	0.196268i	0.413286	+	0.910601i	$0.364381\pi$
$368$		0			0
$369$	−14.6709	+	7.12538i	−0.763738	+	0.370933i
$370$		0			0
$371$	−10.3067	−	6.45326i	−0.535096	−	0.335037i
$372$		0			0
$373$	5.14431	+	29.1748i	0.266362	+	1.51062i	0.765128	+	0.643878i	$0.222676\pi$
$373$	5.14431	+	29.1748i	0.266362	+	1.51062i	−0.498766	+	0.866737i	$0.666213\pi$
$374$		0			0
$375$	13.0297	−	5.51801i	0.672848	−	0.284949i
$376$		0			0
$377$	−33.4899			−1.72482
$378$		0			0
$379$	−21.5189			−1.10535			−0.552675	−	0.833397i	$-0.686393\pi$
$379$	−21.5189			−1.10535			−0.552675	+	0.833397i	$0.686393\pi$
$380$		0			0
$381$	11.7799	+	8.89214i	0.603504	+	0.455558i
$382$		0			0
$383$	−2.27975	−	12.9291i	−0.116490	−	0.660645i	−0.986002	−	0.166734i	$-0.946678\pi$
$383$	−2.27975	−	12.9291i	−0.116490	−	0.660645i	0.869512	−	0.493911i	$-0.164433\pi$
$384$		0			0
$385$	−0.157854	+	4.40636i	−0.00804499	+	0.224569i
$386$		0			0
$387$	2.02415	−	0.209352i	0.102893	−	0.0106420i
$388$		0			0
$389$	17.4811	+	3.08238i	0.886325	+	0.156283i	0.598235	−	0.801321i	$-0.295869\pi$
$389$	17.4811	+	3.08238i	0.886325	+	0.156283i	0.288089	+	0.957604i	$0.406980\pi$
$390$		0			0
$391$	28.9709	+	34.5262i	1.46512	+	1.74607i
$392$		0			0
$393$	−17.0675	−	26.3294i	−0.860942	−	1.32814i
$394$		0			0
$395$	−38.9423			−1.95940
$396$		0			0
$397$			9.43024i			0.473290i	0.971596	+	0.236645i	$0.0760478\pi$
$397$			9.43024i			0.473290i	−0.971596	+	0.236645i	$0.923952\pi$
$398$		0			0
$399$	17.9364	+	2.87270i	0.897945	+	0.143815i
$400$		0			0
$401$	−17.3157	−	20.6360i	−0.864703	−	1.03051i	−0.999216	−	0.0396008i	$-0.987391\pi$
$401$	−17.3157	−	20.6360i	−0.864703	−	1.03051i	0.134513	−	0.990912i	$-0.457053\pi$
$402$		0			0
$403$	−14.5377	+	5.29128i	−0.724173	+	0.263577i
$404$		0			0
$405$	−7.37310	+	22.4385i	−0.366372	+	1.11498i
$406$		0			0
$407$	−2.86990	+	3.42021i	−0.142255	+	0.169533i
$408$		0			0
$409$	10.5588	−	29.0100i	0.522097	−	1.43445i	−0.346084	−	0.938204i	$-0.612489\pi$
$409$	10.5588	−	29.0100i	0.522097	−	1.43445i	0.868181	−	0.496247i	$-0.165289\pi$
$410$		0			0
$411$	−1.57354	+	0.361907i	−0.0776172	+	0.0178516i
$412$		0			0
$413$	−2.30454	+	1.79716i	−0.113399	+	0.0884324i
$414$		0			0
$415$	−1.46496	+	2.53739i	−0.0719122	+	0.124556i
$416$		0			0
$417$	0.497907	+	9.65384i	0.0243826	+	0.472751i
$418$		0			0
$419$	−1.30333	+	1.09362i	−0.0636717	+	0.0534269i	−0.674068	−	0.738669i	$-0.735455\pi$
$419$	−1.30333	+	1.09362i	−0.0636717	+	0.0534269i	0.610396	+	0.792096i	$0.291010\pi$
$420$		0			0
$421$	−4.04181	+	1.47110i	−0.196986	+	0.0716969i	−0.438629	−	0.898668i	$-0.644536\pi$
$421$	−4.04181	+	1.47110i	−0.196986	+	0.0716969i	0.241643	+	0.970365i	$0.422314\pi$
$422$		0			0
$423$	8.41533	−	0.870375i	0.409167	−	0.0423191i
$424$		0			0
$425$	−14.2899	+	5.20108i	−0.693160	+	0.252290i
$426$		0			0
$427$	−1.66585	−	5.14275i	−0.0806162	−	0.248875i
$428$		0			0
$429$	−4.46016	+	1.88886i	−0.215338	+	0.0911950i
$430$		0			0
$431$	−3.63284	−	2.09742i	−0.174988	−	0.101029i	0.409948	−	0.912109i	$-0.365547\pi$
$431$	−3.63284	−	2.09742i	−0.174988	−	0.101029i	−0.584936	+	0.811080i	$0.698880\pi$
$432$		0			0
$433$			8.83087i			0.424385i	0.977228	+	0.212192i	$0.0680603\pi$
$433$			8.83087i			0.424385i	−0.977228	+	0.212192i	$0.931940\pi$
$434$		0			0
$435$	20.8264	−	27.5899i	0.998549	−	1.32283i
$436$		0			0
$437$	−16.9827	+	14.2502i	−0.812393	+	0.681679i
$438$		0			0
$439$	1.68330	+	4.62482i	0.0803393	+	0.220730i	0.973359	−	0.229288i	$-0.0736397\pi$
$439$	1.68330	+	4.62482i	0.0803393	+	0.220730i	−0.893019	+	0.450018i	$0.851417\pi$
$440$		0			0
$441$	−19.9496	−	6.55849i	−0.949981	−	0.312309i
$442$		0			0
$443$	11.1745	−	13.3173i	0.530917	−	0.632722i	−0.432209	−	0.901773i	$-0.642266\pi$
$443$	11.1745	−	13.3173i	0.530917	−	0.632722i	0.963126	+	0.269052i	$0.0867102\pi$
$444$		0			0
$445$	−6.33739	−	35.9411i	−0.300421	−	1.70377i
$446$		0			0
$447$	10.8525	+	5.54096i	0.513304	+	0.262078i
$448$		0			0
$449$	1.41048	−	0.814341i	0.0665647	−	0.0384311i	−0.466348	−	0.884601i	$-0.654431\pi$
$449$	1.41048	−	0.814341i	0.0665647	−	0.0384311i	0.532913	+	0.846170i	$0.321097\pi$
$450$		0			0
$451$	2.98985	−	1.72619i	0.140787	−	0.0812832i
$452$		0			0
$453$	25.4781	+	7.81254i	1.19706	+	0.367065i
$454$		0			0
$455$	20.4798	−	22.7039i	0.960110	−	1.06438i
$456$		0			0
$457$	−5.43057	+	30.7983i	−0.254031	+	1.44068i	0.544515	+	0.838751i	$0.316714\pi$
$457$	−5.43057	+	30.7983i	−0.254031	+	1.44068i	−0.798547	+	0.601933i	$0.794398\pi$
$458$		0			0
$459$	−15.1037	+	39.0558i	−0.704982	+	1.82297i
$460$		0			0
$461$	−20.4541	−	17.1630i	−0.952641	−	0.799361i	0.0270990	−	0.999633i	$-0.491373\pi$
$461$	−20.4541	−	17.1630i	−0.952641	−	0.799361i	−0.979740	+	0.200272i	$0.935817\pi$
$462$		0			0
$463$	−1.82238	−	10.3352i	−0.0846931	−	0.480318i	−0.997422	−	0.0717534i	$-0.977141\pi$
$463$	−1.82238	−	10.3352i	−0.0846931	−	0.480318i	0.912729	−	0.408565i	$-0.133971\pi$
$464$		0			0
$465$	4.68145	−	15.2670i	0.217097	−	0.707991i
$466$		0			0
$467$	3.69568			0.171016			0.0855078	−	0.996338i	$-0.472749\pi$
$467$	3.69568			0.171016			0.0855078	+	0.996338i	$0.472749\pi$
$468$		0			0
$469$	−4.89885	−	35.0868i	−0.226208	−	1.62016i
$470$		0			0
$471$	−26.2273	+	17.0013i	−1.20849	+	0.783377i
$472$		0			0
$473$	−0.424206	+	0.0747990i	−0.0195050	+	0.00343926i
$474$		0			0
$475$	−2.55830	−	7.02887i	−0.117383	−	0.322507i
$476$		0			0
$477$	9.90268	+	9.59470i	0.453412	+	0.439311i
$478$		0			0
$479$	16.3218	+	13.6956i	0.745762	+	0.625768i	0.934378	−	0.356283i	$-0.115956\pi$
$479$	16.3218	+	13.6956i	0.745762	+	0.625768i	−0.188617	+	0.982051i	$0.560400\pi$
$480$		0			0
$481$	30.4911	−	5.37640i	1.39027	−	0.245143i
$482$		0			0
$483$	21.9914	−	13.1620i	1.00064	−	0.598891i
$484$		0			0
$485$	36.4013	−	21.0163i	1.65290	−	0.954300i
$486$		0			0
$487$	−4.17289	+	7.22766i	−0.189092	+	0.327516i	−0.944948	−	0.327222i	$-0.893888\pi$
$487$	−4.17289	+	7.22766i	−0.189092	+	0.327516i	0.755856	+	0.654738i	$0.227221\pi$
$488$		0			0
$489$	8.81557	−	3.73336i	0.398654	−	0.168828i
$490$		0			0
$491$	−2.78557	+	7.65329i	−0.125711	+	0.345388i	−0.986543	−	0.163501i	$-0.947721\pi$
$491$	−2.78557	+	7.65329i	−0.125711	+	0.345388i	0.860832	+	0.508889i	$0.169944\pi$
$492$		0			0
$493$	39.3943	−	46.9483i	1.77423	−	2.11445i
$494$		0			0
$495$	1.21755	−	4.84902i	0.0547246	−	0.217947i
$496$		0			0
$497$	16.2456	−	8.61915i	0.728715	−	0.386622i
$498$		0			0
$499$	−25.8300	−	9.40134i	−1.15631	−	0.420862i	−0.308531	−	0.951214i	$-0.599837\pi$
$499$	−25.8300	−	9.40134i	−1.15631	−	0.420862i	−0.847777	+	0.530353i	$0.822059\pi$
$500$		0			0
$501$	0.759280	−	1.48712i	0.0339221	−	0.0664396i
$502$		0			0
$503$	0.341404	+	0.591329i	0.0152225	+	0.0263661i	0.873536	−	0.486759i	$-0.161821\pi$
$503$	0.341404	+	0.591329i	0.0152225	+	0.0263661i	−0.858314	+	0.513125i	$0.828488\pi$
$504$		0			0
$505$	−4.12028	+	7.13653i	−0.183350	+	0.317571i
$506$		0			0
$507$	10.5856	+	3.24594i	0.470123	+	0.144157i
$508$		0			0
$509$	−33.1189	+	27.7901i	−1.46797	+	1.23177i	−0.549975	+	0.835181i	$0.685363\pi$
$509$	−33.1189	+	27.7901i	−1.46797	+	1.23177i	−0.917995	+	0.396592i	$0.870193\pi$
$510$		0			0
$511$	10.9083	−	5.78741i	0.482554	−	0.256020i
$512$		0			0
$513$	−19.2107	−	7.42921i	−0.848174	−	0.328007i
$514$		0			0
$515$	−8.73779	−	24.0069i	−0.385033	−	1.05787i
$516$		0			0
$517$	−1.76362	+	0.310974i	−0.0775640	+	0.0136766i
$518$		0			0
$519$	0.750276	−	0.698481i	0.0329335	−	0.0306599i
$520$		0			0
$521$	16.7897	+	29.0805i	0.735568	+	1.27404i	0.954474	+	0.298296i	$0.0964181\pi$
$521$	16.7897	+	29.0805i	0.735568	+	1.27404i	−0.218905	+	0.975746i	$0.570249\pi$
$522$		0			0
$523$	−13.7285	−	7.92615i	−0.600305	−	0.346586i	0.168857	−	0.985641i	$-0.445993\pi$
$523$	−13.7285	−	7.92615i	−0.600305	−	0.346586i	−0.769162	+	0.639054i	$0.779326\pi$
$524$		0			0
$525$	1.63529	+	8.49132i	0.0713699	+	0.370592i
$526$		0			0
$527$	9.68306	−	26.6040i	0.421801	−	1.15889i
$528$		0			0
$529$	−1.43763	+	8.15323i	−0.0625058	+	0.354488i
$530$		0			0
$531$	2.98078	−	1.44771i	0.129355	−	0.0628251i
$532$		0			0
$533$	−23.5773	−	4.15731i	−1.02124	−	0.180073i
$534$		0			0
$535$	−22.9444	−	27.3440i	−0.991972	−	1.18219i
$536$		0			0
$537$	26.4761	+	3.27314i	1.14253	+	0.141247i
$538$		0			0
$539$	4.31122	+	1.08317i	0.185697	+	0.0466556i
$540$		0			0
$541$	−8.71319	−	15.0917i	−0.374609	−	0.648842i	0.615659	−	0.788012i	$-0.288890\pi$
$541$	−8.71319	−	15.0917i	−0.374609	−	0.648842i	−0.990268	+	0.139170i	$0.955556\pi$
$542$		0			0
$543$	−1.12402	+	1.48905i	−0.0482361	+	0.0639011i
$544$		0			0
$545$	−35.1100	−	12.7790i	−1.50395	−	0.547392i
$546$		0			0
$547$	5.05757	−	28.6829i	0.216246	−	1.22639i	−0.662485	−	0.749075i	$-0.730498\pi$
$547$	5.05757	−	28.6829i	0.216246	−	1.22639i	0.878731	−	0.477317i	$-0.158391\pi$
$548$		0			0
$549$	0.630607	+	6.09710i	0.0269136	+	0.260218i
$550$		0			0
$551$	23.0929	+	19.3772i	0.983789	+	0.825497i
$552$		0			0
$553$	−8.19736	+	38.3952i	−0.348587	+	1.63273i
$554$		0			0
$555$	−14.5323	+	28.4628i	−0.616861	+	1.20818i
$556$		0			0
$557$		−	4.54341i		−	0.192510i	−0.995357	−	0.0962552i	$-0.969314\pi$
$557$		−	4.54341i		−	0.192510i	0.995357	−	0.0962552i	$-0.0306865\pi$
$558$		0			0
$559$	2.58689	+	1.49354i	0.109414	+	0.0631702i
$560$		0			0
$561$	2.59857	−	8.47441i	0.109712	−	0.357790i
$562$		0			0
$563$	−4.51721	−	1.64413i	−0.190378	−	0.0692918i	0.245072	−	0.969505i	$-0.421188\pi$
$563$	−4.51721	−	1.64413i	−0.190378	−	0.0692918i	−0.435450	+	0.900213i	$0.643411\pi$
$564$		0			0
$565$	−13.1820	−	2.32435i	−0.554572	−	0.0977860i
$566$		0			0
$567$	20.5712	+	11.9928i	0.863908	+	0.503650i
$568$		0			0
$569$	−35.5964	−	6.27661i	−1.49228	−	0.263129i	−0.632806	−	0.774310i	$-0.718097\pi$
$569$	−35.5964	−	6.27661i	−1.49228	−	0.263129i	−0.859473	+	0.511181i	$0.829208\pi$
$570$		0			0
$571$	12.1039	+	4.40545i	0.506532	+	0.184363i	0.582630	−	0.812738i	$-0.302024\pi$
$571$	12.1039	+	4.40545i	0.506532	+	0.184363i	−0.0760977	+	0.997100i	$0.524246\pi$
$572$		0			0
$573$	0.940198	−	3.06615i	0.0392773	−	0.128090i
$574$		0			0
$575$	−9.13967	−	5.27679i	−0.381151	−	0.220057i
$576$		0			0
$577$			6.71260i			0.279449i	0.990190	+	0.139725i	$0.0446217\pi$
$577$			6.71260i			0.279449i	−0.990190	+	0.139725i	$0.955378\pi$
$578$		0			0
$579$	7.26889	−	14.2368i	0.302085	−	0.591661i
$580$		0			0
$581$	2.19336	+	1.97850i	0.0909961	+	0.0820821i
$582$		0			0
$583$	−2.23585	−	1.87610i	−0.0925993	−	0.0777001i
$584$		0			0
$585$	−28.0823	+	20.3319i	−1.16106	+	0.840621i
$586$		0			0
$587$	−2.54009	+	14.4056i	−0.104841	+	0.594581i	0.886443	+	0.462837i	$0.153169\pi$
$587$	−2.54009	+	14.4056i	−0.104841	+	0.594581i	−0.991284	+	0.131743i	$0.957943\pi$
$588$		0			0
$589$	13.0859	+	4.76289i	0.539196	+	0.196251i
$590$		0			0
$591$	12.1112	−	16.0444i	0.498188	−	0.659978i
$592$		0			0
$593$	−20.4263	−	35.3794i	−0.838809	−	1.45286i	−0.890891	−	0.454217i	$-0.849919\pi$
$593$	−20.4263	−	35.3794i	−0.838809	−	1.45286i	0.0520821	−	0.998643i	$-0.483414\pi$
$594$		0			0
$595$	7.73732	+	55.4167i	0.317199	+	2.27186i
$596$		0			0
$597$	−18.9360	−	2.34099i	−0.774999	−	0.0958104i
$598$		0			0
$599$	21.5274	+	25.6553i	0.879585	+	1.04825i	0.998468	+	0.0553401i	$0.0176243\pi$
$599$	21.5274	+	25.6553i	0.879585	+	1.04825i	−0.118883	+	0.992908i	$0.537931\pi$
$600$		0			0
$601$	39.7569	+	7.01021i	1.62172	+	0.285953i	0.909406	−	0.415911i	$-0.136537\pi$
$601$	39.7569	+	7.01021i	1.62172	+	0.285953i	0.712312	+	0.701863i	$0.247648\pi$
$602$		0			0
$603$	−2.86863	+	40.0681i	−0.116820	+	1.63170i
$604$		0			0
$605$	4.82900	−	27.3866i	0.196327	−	1.11343i
$606$		0			0
$607$	6.69163	−	18.3851i	0.271605	−	0.746228i	−0.726641	−	0.687018i	$-0.758920\pi$
$607$	6.69163	−	18.3851i	0.271605	−	0.746228i	0.998246	−	0.0592102i	$-0.0188582\pi$
$608$		0			0
$609$	−22.8183	−	26.3414i	−0.924644	−	1.06741i
$610$		0			0
$611$	10.7549	+	6.20936i	0.435098	+	0.251204i
$612$		0			0
$613$	−10.5161	−	18.2144i	−0.424742	−	0.735675i	0.571654	−	0.820495i	$-0.306302\pi$
$613$	−10.5161	−	18.2144i	−0.424742	−	0.735675i	−0.996396	+	0.0848199i	$0.972968\pi$
$614$		0			0
$615$	18.0869	−	16.8383i	0.729334	−	0.678985i
$616$		0			0
$617$	−16.9370	+	2.98646i	−0.681859	+	0.120230i	−0.503840	−	0.863797i	$-0.668080\pi$
$617$	−16.9370	+	2.98646i	−0.681859	+	0.120230i	−0.178019	+	0.984027i	$0.556969\pi$
$618$		0			0
$619$	3.37863	+	9.28271i	0.135799	+	0.373104i	0.988888	−	0.148661i	$-0.0474962\pi$
$619$	3.37863	+	9.28271i	0.135799	+	0.373104i	−0.853090	+	0.521764i	$0.825274\pi$
$620$		0			0
$621$	−27.5010	+	9.39289i	−1.10358	+	0.376924i
$622$		0			0
$623$	−36.7701	−	1.31726i	−1.47316	−	0.0527749i
$624$		0			0
$625$	−23.6510	+	19.8456i	−0.946042	+	0.793823i
$626$		0			0
$627$	4.16838	+	1.27818i	0.166469	+	0.0510457i
$628$		0			0
$629$	−28.3298	+	49.0686i	−1.12958	+	1.95649i
$630$		0			0
$631$	13.3688	+	23.1555i	0.532204	+	0.921804i	0.999293	+	0.0375939i	$0.0119693\pi$
$631$	13.3688	+	23.1555i	0.532204	+	0.921804i	−0.467089	+	0.884210i	$0.654697\pi$
$632$		0			0
$633$	−16.6195	+	32.5508i	−0.660564	+	1.29378i
$634$		0			0
$635$	−21.0139	−	7.64842i	−0.833910	−	0.303518i
$636$		0			0
$637$	−18.0739	−	24.9713i	−0.716115	−	0.989398i
$638$		0			0
$639$	−20.0545	+	5.71456i	−0.793345	+	0.226065i
$640$		0			0
$641$	−12.5657	+	14.9752i	−0.496315	+	0.591485i	−0.954812	−	0.297211i	$-0.903944\pi$
$641$	−12.5657	+	14.9752i	−0.496315	+	0.591485i	0.458497	+	0.888696i	$0.348388\pi$
$642$		0			0
$643$	8.14572	−	22.3802i	0.321236	−	0.882588i	−0.669010	−	0.743254i	$-0.733281\pi$
$643$	8.14572	−	22.3802i	0.321236	−	0.882588i	0.990245	−	0.139334i	$-0.0444963\pi$
$644$		0			0
$645$	−2.83914	+	1.20236i	−0.111791	+	0.0473430i
$646$		0			0
$647$	−5.30690	+	9.19182i	−0.208636	+	0.361368i	−0.951285	−	0.308313i	$-0.900236\pi$
$647$	−5.30690	+	9.19182i	−0.208636	+	0.361368i	0.742649	+	0.669680i	$0.233569\pi$
$648$		0			0
$649$	−0.607466	+	0.350721i	−0.0238451	+	0.0137670i
$650$		0			0
$651$	−14.0671	−	7.82938i	−0.551332	−	0.306857i
$652$		0			0
$653$	27.6321	−	4.87229i	1.08133	−	0.190667i	0.395526	−	0.918455i	$-0.370562\pi$
$653$	27.6321	−	4.87229i	1.08133	−	0.190667i	0.685803	+	0.727787i	$0.259451\pi$
$654$		0			0
$655$	36.4187	+	30.5590i	1.42300	+	1.19404i
$656$		0			0
$657$	−13.4658	+	3.83710i	−0.525352	+	0.149699i
$658$		0			0
$659$	14.7119	+	40.4206i	0.573094	+	1.57456i	0.799587	+	0.600551i	$0.205052\pi$
$659$	14.7119	+	40.4206i	0.573094	+	1.57456i	−0.226492	+	0.974013i	$0.572726\pi$
$660$		0			0
$661$	−27.1091	+	4.78007i	−1.05442	+	0.185923i	−0.673880	−	0.738840i	$-0.735374\pi$
$661$	−27.1091	+	4.78007i	−1.05442	+	0.185923i	−0.380542	+	0.924764i	$0.624263\pi$
$662$		0			0
$663$	−51.5788	+	33.4348i	−2.00315	+	1.29850i
$664$		0			0
$665$	−27.2583	+	3.80582i	−1.05703	+	0.147584i
$666$		0			0
$667$	42.5328			1.64688
$668$		0			0
$669$	−12.3226	+	40.1861i	−0.476418	+	1.55368i
$670$		0			0
$671$	−0.225308	−	1.27779i	−0.00869793	−	0.0493284i
$672$		0			0
$673$	−11.0731	−	9.29143i	−0.426836	−	0.358158i	0.403920	−	0.914794i	$-0.367647\pi$
$673$	−11.0731	−	9.29143i	−0.426836	−	0.358158i	−0.830757	+	0.556636i	$0.812092\pi$
$674$		0			0
$675$	0.195518	−	9.80322i	0.00752549	−	0.377326i
$676$		0			0
$677$	2.52350	−	14.3115i	0.0969858	−	0.550034i	−0.897135	−	0.441757i	$-0.854355\pi$
$677$	2.52350	−	14.3115i	0.0969858	−	0.550034i	0.994121	−	0.108277i	$-0.0345334\pi$
$678$		0			0
$679$	−13.0585	−	40.3137i	−0.501140	−	1.54710i
$680$		0			0
$681$	4.25623	+	1.30512i	0.163099	+	0.0500123i
$682$		0			0
$683$	37.7172	−	21.7760i	1.44321	−	0.833236i	0.445146	−	0.895458i	$-0.353152\pi$
$683$	37.7172	−	21.7760i	1.44321	−	0.833236i	0.998062	+	0.0622218i	$0.0198186\pi$
$684$		0			0
$685$	2.11864	−	1.22320i	0.0809491	−	0.0467360i
$686$		0			0
$687$	−20.9680	−	10.7056i	−0.799978	−	0.408445i
$688$		0			0
$689$	3.51464	+	19.9325i	0.133897	+	0.759368i
$690$		0			0
$691$	2.75307	−	3.28098i	0.104732	−	0.124814i	−0.711132	−	0.703058i	$-0.751817\pi$
$691$	2.75307	−	3.28098i	0.104732	−	0.124814i	0.815864	+	0.578244i	$0.196262\pi$
$692$		0			0
$693$	−4.52460	−	2.22116i	−0.171875	−	0.0843748i
$694$		0			0
$695$	−5.00937	−	13.7631i	−0.190016	−	0.522065i
$696$		0			0
$697$	33.5620	−	28.1619i	1.27125	−	1.06671i
$698$		0			0
$699$	15.7811	−	20.9061i	0.596895	−	0.790741i
$700$		0			0
$701$			18.9199i			0.714595i	0.933991	+	0.357297i	$0.116302\pi$
$701$			18.9199i			0.714595i	−0.933991	+	0.357297i	$0.883698\pi$
$702$		0			0
$703$	−24.1358	−	13.9348i	−0.910299	−	0.525562i
$704$		0			0
$705$	−11.8036	+	4.99879i	−0.444550	+	0.188265i
$706$		0			0
$707$	6.16894	+	5.56462i	0.232007	+	0.209279i
$708$		0			0
$709$	−2.84439	+	1.03527i	−0.106823	+	0.0388805i	−0.394879	−	0.918733i	$-0.629213\pi$
$709$	−2.84439	+	1.03527i	−0.106823	+	0.0388805i	0.288056	+	0.957614i	$0.406991\pi$
$710$		0			0
$711$	18.1742	−	40.6384i	0.681587	−	1.52406i
$712$		0			0
$713$	18.4631	−	6.72002i	0.691449	−	0.251667i
$714$		0			0
$715$	5.62186	−	4.71730i	0.210246	−	0.176417i
$716$		0			0
$717$	1.80335	+	34.9648i	0.0673473	+	1.30579i
$718$		0			0
$719$	0.271522	−	0.470290i	0.0101261	−	0.0175388i	−0.860918	−	0.508744i	$-0.830110\pi$
$719$	0.271522	−	0.470290i	0.0101261	−	0.0175388i	0.871044	+	0.491205i	$0.163443\pi$
$720$		0			0
$721$	−25.5089	+	3.56157i	−0.950000	+	0.132640i
$722$		0			0
$723$	−24.1505	+	5.55448i	−0.898165	+	0.206573i
$724$		0			0
$725$	−4.90820	+	13.4852i	−0.182286	+	0.500827i
$726$		0			0
$727$	24.2349	−	28.8820i	0.898821	−	1.07117i	−0.0982857	−	0.995158i	$-0.531336\pi$
$727$	24.2349	−	28.8820i	0.898821	−	1.07117i	0.997107	−	0.0760149i	$-0.0242197\pi$
$728$		0			0
$729$	−19.9748	−	18.1662i	−0.739806	−	0.672821i
$730$		0			0
$731$	−5.13672	+	1.86961i	−0.189988	+	0.0691501i
$732$		0			0
$733$	−5.80284	−	6.91556i	−0.214333	−	0.255432i	0.648157	−	0.761507i	$-0.275540\pi$
$733$	−5.80284	−	6.91556i	−0.214333	−	0.255432i	−0.862489	+	0.506075i	$0.831096\pi$
$734$		0			0
$735$	31.8117	+	0.639096i	1.17339	+	0.0235734i
$736$		0			0
$737$		−	8.50318i		−	0.313219i
$738$		0			0
$739$	19.6599			0.723200			0.361600	−	0.932333i	$-0.382231\pi$
$739$	19.6599			0.723200			0.361600	+	0.932333i	$0.382231\pi$
$740$		0			0
$741$	−16.4459	−	25.3705i	−0.604155	−	0.932008i
$742$		0			0
$743$	−7.89524	−	9.40918i	−0.289648	−	0.345189i	0.601524	−	0.798855i	$-0.294561\pi$
$743$	−7.89524	−	9.40918i	−0.289648	−	0.345189i	−0.891172	+	0.453665i	$0.850116\pi$
$744$		0			0
$745$	−18.1818	−	3.20595i	−0.666131	−	0.117457i
$746$		0			0
$747$	−1.96421	−	2.71296i	−0.0718667	−	0.0992619i
$748$		0			0
$749$	−31.7896	+	16.8661i	−1.16157	+	0.616273i
$750$		0			0
$751$	−2.66917	−	15.1376i	−0.0973993	−	0.552379i	−0.993986	−	0.109510i	$-0.965072\pi$
$751$	−2.66917	−	15.1376i	−0.0973993	−	0.552379i	0.896586	−	0.442869i	$-0.146039\pi$
$752$		0			0
$753$	32.2754	+	24.3633i	1.17618	+	0.887847i
$754$		0			0
$755$	−40.3771			−1.46947
$756$		0			0
$757$	19.2152			0.698390			0.349195	−	0.937050i	$-0.386455\pi$
$757$	19.2152			0.698390			0.349195	+	0.937050i	$0.386455\pi$
$758$		0			0
$759$	5.66448	−	2.39889i	0.205608	−	0.0870740i
$760$		0			0
$761$	5.78604	+	32.8143i	0.209744	+	1.18952i	0.889798	+	0.456354i	$0.150845\pi$
$761$	5.78604	+	32.8143i	0.209744	+	1.18952i	−0.680054	+	0.733162i	$0.738044\pi$
$762$		0			0
$763$	−19.9901	+	31.9267i	−0.723690	+	1.15582i
$764$		0			0
$765$	4.53076	−	63.2841i	0.163810	−	2.28804i
$766$		0			0
$767$	4.79033	+	0.844664i	0.172969	+	0.0304991i
$768$		0			0
$769$	1.96014	+	2.33600i	0.0706843	+	0.0842383i	0.800228	−	0.599696i	$-0.204712\pi$
$769$	1.96014	+	2.33600i	0.0706843	+	0.0842383i	−0.729543	+	0.683934i	$0.760267\pi$
$770$		0			0
$771$	−9.46046	+	18.5292i	−0.340710	+	0.667313i
$772$		0			0
$773$	−23.9908			−0.862890			−0.431445	−	0.902139i	$-0.641996\pi$
$773$	−23.9908			−0.862890			−0.431445	+	0.902139i	$0.641996\pi$
$774$		0			0
$775$			6.62927i			0.238130i
$776$		0			0
$777$	25.0038	+	20.3195i	0.897008	+	0.728958i
$778$		0			0
$779$	13.8522	+	16.5084i	0.496307	+	0.591476i
$780$		0			0
$781$	4.14786	−	1.50970i	0.148422	−	0.0540212i
$782$		0			0
$783$	19.0720	+	34.6095i	0.681576	+	1.23684i
$784$		0			0
$785$	30.4404	−	36.2774i	1.08646	−	1.29480i
$786$		0			0
$787$	−4.98408	+	13.6936i	−0.177663	+	0.488125i	−0.996276	−	0.0862201i	$-0.972521\pi$
$787$	−4.98408	+	13.6936i	−0.177663	+	0.488125i	0.818613	+	0.574346i	$0.194743\pi$
$788$		0			0
$789$	35.7026	+	38.3501i	1.27105	+	1.36530i
$790$		0			0
$791$	−5.06650	+	12.5075i	−0.180144	+	0.444717i
$792$		0			0
$793$	−4.49883	+	7.79220i	−0.159758	+	0.276709i
$794$		0			0
$795$	−18.6066	−	9.49999i	−0.659908	−	0.336930i
$796$		0			0
$797$	32.9880	−	27.6802i	1.16850	−	0.980484i	0.168509	−	0.985700i	$-0.446105\pi$
$797$	32.9880	−	27.6802i	1.16850	−	0.980484i	0.999986	+	0.00521632i	$0.00166041\pi$
$798$		0			0
$799$	−21.3557	+	7.77285i	−0.755512	+	0.274984i
$800$		0			0
$801$	40.4641	+	10.1602i	1.42973	+	0.358992i
$802$		0			0
$803$	2.78512	−	1.01370i	0.0982847	−	0.0357727i
$804$		0			0
$805$	−26.0098	+	28.8344i	−0.916724	+	1.01628i
$806$		0			0
$807$	−33.5188	−	25.3018i	−1.17992	−	0.890666i
$808$		0			0
$809$	−11.1160	−	6.41785i	−0.390819	−	0.225640i	0.291696	−	0.956511i	$-0.405781\pi$
$809$	−11.1160	−	6.41785i	−0.390819	−	0.225640i	−0.682515	+	0.730871i	$0.739114\pi$
$810$		0			0
$811$		−	17.1111i		−	0.600851i	−0.953805	−	0.300425i	$-0.902871\pi$
$811$		−	17.1111i		−	0.600851i	0.953805	−	0.300425i	$-0.0971286\pi$
$812$		0			0
$813$	−16.0576	−	37.9168i	−0.563165	−	1.32980i
$814$		0			0
$815$	−11.1117	+	9.32381i	−0.389226	+	0.326599i
$816$		0			0
$817$	−0.919623	−	2.52664i	−0.0321735	−	0.0883960i
$818$		0			0
$819$	14.1349	+	31.9676i	0.493914	+	1.11704i
$820$		0			0
$821$	22.9713	−	27.3762i	0.801705	−	0.955435i	−0.197988	−	0.980204i	$-0.563441\pi$
$821$	22.9713	−	27.3762i	0.801705	−	0.955435i	0.999693	+	0.0247692i	$0.00788509\pi$
$822$		0			0
$823$	2.51073	+	14.2391i	0.0875185	+	0.496342i	0.996785	+	0.0801270i	$0.0255326\pi$
$823$	2.51073	+	14.2391i	0.0875185	+	0.496342i	−0.909266	+	0.416215i	$0.863356\pi$
$824$		0			0
$825$	0.106905	+	2.07277i	0.00372197	+	0.0721646i
$826$		0			0
$827$	−11.6145	+	6.70561i	−0.403874	+	0.233177i	−0.688154	−	0.725564i	$-0.741579\pi$
$827$	−11.6145	+	6.70561i	−0.403874	+	0.233177i	0.284280	+	0.958741i	$0.408245\pi$
$828$		0			0
$829$	−42.2130	+	24.3717i	−1.46612	+	0.846464i	−0.999282	−	0.0378803i	$-0.987939\pi$
$829$	−42.2130	+	24.3717i	−1.46612	+	0.846464i	−0.466836	+	0.884344i	$0.654606\pi$
$830$		0			0
$831$	−24.3556	+	22.6742i	−0.844885	+	0.786559i
$832$		0			0
$833$	56.2668	+	4.03660i	1.94953	+	0.139860i
$834$		0			0
$835$	−0.439313	+	2.49147i	−0.0152030	+	0.0862207i
$836$		0			0
$837$	13.7471	+	12.0104i	0.475171	+	0.415140i
$838$		0			0
$839$	12.0259	+	10.0909i	0.415179	+	0.348377i	0.826326	−	0.563192i	$-0.190427\pi$
$839$	12.0259	+	10.0909i	0.415179	+	0.348377i	−0.411146	+	0.911569i	$0.634871\pi$
$840$		0			0
$841$	−5.00724	−	28.3975i	−0.172663	−	0.979223i
$842$		0			0
$843$	−23.2914	+	5.35690i	−0.802198	+	0.184501i
$844$		0			0
$845$	−16.7758			−0.577106
$846$		0			0
$847$	−25.9853	−	10.5260i	−0.892867	−	0.361679i
$848$		0			0
$849$	2.21175	+	42.8833i	0.0759072	+	1.47175i
$850$		0			0
$851$	−38.7242	+	6.82812i	−1.32745	+	0.234065i
$852$		0			0
$853$	7.29133	+	20.0328i	0.249650	+	0.685909i	0.999699	+	0.0245263i	$0.00780774\pi$
$853$	7.29133	+	20.0328i	0.249650	+	0.685909i	−0.750049	+	0.661382i	$0.769970\pi$
$854$		0			0
$855$	31.1281	+	2.22859i	1.06456	+	0.0762160i
$856$		0			0
$857$	−3.30256	−	2.77117i	−0.112813	−	0.0946615i	0.584636	−	0.811296i	$-0.301237\pi$
$857$	−3.30256	−	2.77117i	−0.112813	−	0.0946615i	−0.697449	+	0.716634i	$0.745682\pi$
$858$		0			0
$859$	30.9228	−	5.45252i	1.05507	−	0.186038i	0.380903	−	0.924615i	$-0.375613\pi$
$859$	30.9228	−	5.45252i	1.05507	−	0.186038i	0.674169	+	0.738577i	$0.264502\pi$
$860$		0			0
$861$	−12.7944	−	21.3772i	−0.436032	−	0.728534i
$862$		0			0
$863$	22.4488	−	12.9608i	0.764165	−	0.441191i	−0.0666239	−	0.997778i	$-0.521223\pi$
$863$	22.4488	−	12.9608i	0.764165	−	0.441191i	0.830789	+	0.556587i	$0.187889\pi$
$864$		0			0
$865$	−0.776573	+	1.34506i	−0.0264043	+	0.0457336i
$866$		0			0
$867$	10.1885	−	82.4136i	0.346020	−	2.79891i
$868$		0			0
$869$	−3.22294	+	8.85496i	−0.109331	+	0.300384i
$870$		0			0
$871$	−37.9028	+	45.1708i	−1.28429	+	1.53055i
$872$		0			0
$873$	4.94330	+	47.7949i	0.167305	+	1.61761i
$874$		0			0
$875$	10.1301	+	19.0935i	0.342460	+	0.645478i
$876$		0			0
$877$	47.4039	+	17.2536i	1.60072	+	0.582613i	0.979574	−	0.201084i	$-0.0644465\pi$
$877$	47.4039	+	17.2536i	1.60072	+	0.582613i	0.621143	+	0.783697i	$0.286669\pi$
$878$		0			0
$879$	−15.3866	+	0.793580i	−0.518976	+	0.0267668i
$880$		0			0
$881$	−13.2598	−	22.9666i	−0.446734	−	0.773766i	0.551437	−	0.834216i	$-0.314080\pi$
$881$	−13.2598	−	22.9666i	−0.446734	−	0.773766i	−0.998171	+	0.0604506i	$0.980746\pi$
$882$		0			0
$883$	17.7664	−	30.7722i	0.597885	−	1.03557i	−0.395247	−	0.918575i	$-0.629341\pi$
$883$	17.7664	−	30.7722i	0.597885	−	1.03557i	0.993133	−	0.116993i	$-0.0373255\pi$
$884$		0			0
$885$	−3.67482	+	3.42113i	−0.123528	+	0.115000i
$886$		0			0
$887$	−7.50194	+	6.29487i	−0.251890	+	0.211361i	−0.759986	−	0.649940i	$-0.774794\pi$
$887$	−7.50194	+	6.29487i	−0.251890	+	0.211361i	0.508095	+	0.861301i	$0.330350\pi$
$888$		0			0
$889$	−11.9644	+	19.1086i	−0.401272	+	0.640883i
$890$		0			0
$891$	4.49199	+	3.53359i	0.150487	+	0.118380i
$892$		0			0
$893$	−3.82330	−	10.5044i	−0.127942	−	0.351517i
$894$		0			0
$895$	−39.8064	+	7.01895i	−1.33058	+	0.234617i
$896$		0			0
$897$	−40.7840	−	12.5059i	−1.36174	−	0.417560i
$898$		0			0
$899$	−13.3586	−	23.1377i	−0.445533	−	0.771686i
$900$		0			0
$901$	−32.0770	−	18.5196i	−1.06864	−	0.616979i
$902$		0			0
$903$	0.587831	+	3.05234i	0.0195618	+	0.101576i
$904$		0			0
$905$	0.966803	−	2.65627i	0.0321376	−	0.0882974i
$906$		0			0
$907$	2.04130	−	11.5768i	0.0677804	−	0.384402i	−0.931980	−	0.362510i	$-0.881920\pi$
$907$	2.04130	−	11.5768i	0.0677804	−	0.384402i	0.999760	−	0.0218919i	$-0.00696895\pi$
$908$		0			0
$909$	−5.52443	−	7.63031i	−0.183234	−	0.253082i
$910$		0			0
$911$	56.5365	+	9.96892i	1.87314	+	0.330285i	0.990250	−	0.139298i	$-0.0444846\pi$
$911$	56.5365	+	9.96892i	1.87314	+	0.330285i	0.882888	+	0.469583i	$0.155596\pi$
$912$		0			0
$913$	0.455725	+	0.543112i	0.0150823	+	0.0179744i
$914$		0			0
$915$	−3.62174	−	8.55199i	−0.119731	−	0.282720i
$916$		0			0
$917$	37.7957	−	29.4744i	1.24813	−	0.973330i
$918$		0			0
$919$	6.33126	+	10.9661i	0.208849	+	0.361737i	0.951352	−	0.308105i	$-0.0996949\pi$
$919$	6.33126	+	10.9661i	0.208849	+	0.361737i	−0.742503	+	0.669843i	$0.766362\pi$
$920$		0			0
$921$	−14.9316	−	35.2579i	−0.492012	−	1.16179i
$922$		0			0
$923$	−28.7638	−	10.4692i	−0.946772	−	0.344597i
$924$		0			0
$925$	2.30382	−	13.0656i	0.0757491	−	0.429595i
$926$		0			0
$927$	29.1303	+	2.08556i	0.956766	+	0.0684987i
$928$		0			0
$929$	−32.1186	−	26.9507i	−1.05378	−	0.884224i	−0.0602910	−	0.998181i	$-0.519203\pi$
$929$	−32.1186	−	26.9507i	−1.05378	−	0.884224i	−0.993486	+	0.113957i	$0.963647\pi$
$930$		0			0
$931$	−1.98552	+	27.6764i	−0.0650727	+	0.907058i
$932$		0			0
$933$	46.6416	−	2.40559i	1.52698	−	0.0787556i
$934$		0			0
$935$			13.4301i			0.439210i
$936$		0			0
$937$	−32.3294	−	18.6654i	−1.05616	−	0.609772i	−0.131790	−	0.991278i	$-0.542072\pi$
$937$	−32.3294	−	18.6654i	−1.05616	−	0.609772i	−0.924367	+	0.381505i	$0.875406\pi$
$938$		0			0
$939$	−27.0336	−	29.0382i	−0.882207	−	0.947626i
$940$		0			0
$941$	23.4877	+	8.54884i	0.765678	+	0.278684i	0.695188	−	0.718828i	$-0.255321\pi$
$941$	23.4877	+	8.54884i	0.765678	+	0.278684i	0.0704906	+	0.997512i	$0.477544\pi$
$942$		0			0
$943$	29.9435	+	5.27985i	0.975096	+	0.171936i
$944$		0			0
$945$	−35.1259	−	8.23500i	−1.14265	−	0.267885i
$946$		0			0
$947$	−24.0513	−	4.24089i	−0.781562	−	0.137810i	−0.231389	−	0.972861i	$-0.574327\pi$
$947$	−24.0513	−	4.24089i	−0.781562	−	0.137810i	−0.550173	+	0.835051i	$0.685438\pi$
$948$		0			0
$949$	−19.3137	−	7.02962i	−0.626950	−	0.228191i
$950$		0			0
$951$	−7.28003	+	1.67437i	−0.236071	+	0.0542951i
$952$		0			0
$953$	21.6346	+	12.4907i	0.700812	+	0.404614i	0.807650	−	0.589662i	$-0.200739\pi$
$953$	21.6346	+	12.4907i	0.700812	+	0.404614i	−0.106838	+	0.994276i	$0.534073\pi$
$954$		0			0
$955$			4.85917i			0.157239i
$956$		0			0
$957$	−4.54994	−	7.01903i	−0.147079	−	0.226893i
$958$		0			0
$959$	−0.760038	−	2.34636i	−0.0245429	−	0.0757678i
$960$		0			0
$961$	14.2929	+	11.9931i	0.461061	+	0.386876i
$962$		0			0
$963$	39.2430	−	11.1823i	1.26459	−	0.360346i
$964$		0			0
$965$	−4.20571	+	23.8518i	−0.135387	+	0.767816i
$966$		0			0
$967$	−2.06564	−	0.751830i	−0.0664263	−	0.0241772i	0.308593	−	0.951194i	$-0.400142\pi$
$967$	−2.06564	−	0.751830i	−0.0664263	−	0.0241772i	−0.375020	+	0.927017i	$0.622364\pi$
$968$		0			0
$969$	54.9113	+	6.78850i	1.76401	+	0.218078i
$970$		0			0
$971$	13.9368	+	24.1393i	0.447253	+	0.774666i	0.998206	−	0.0598708i	$-0.0190689\pi$
$971$	13.9368	+	24.1393i	0.447253	+	0.774666i	−0.550953	+	0.834536i	$0.685736\pi$
$972$		0			0
$973$	−14.6242	+	2.04185i	−0.468831	+	0.0654586i
$974$		0			0
$975$	8.67144	−	11.4876i	0.277708	−	0.367896i
$976$		0			0
$977$	4.93989	+	5.88713i	0.158041	+	0.188346i	0.839254	−	0.543739i	$-0.182992\pi$
$977$	4.93989	+	5.88713i	0.158041	+	0.188346i	−0.681213	+	0.732085i	$0.738547\pi$
$978$		0			0
$979$	−8.69702	−	1.53352i	−0.277958	−	0.0490115i
$980$		0			0
$981$	29.7212	−	30.6752i	0.948926	−	0.979385i
$982$		0			0
$983$	−10.8330	+	61.4367i	−0.345518	+	1.95953i	−0.0732125	+	0.997316i	$0.523325\pi$
$983$	−10.8330	+	61.4367i	−0.345518	+	1.95953i	−0.272305	+	0.962211i	$0.587786\pi$
$984$		0			0
$985$	−10.4172	+	28.6211i	−0.331921	+	0.911945i
$986$		0			0
$987$	2.44389	+	12.6900i	0.0777899	+	0.403927i
$988$		0			0
$989$	−3.28540	−	1.89683i	−0.104470	−	0.0603156i
$990$		0			0
$991$	8.84323	+	15.3169i	0.280914	+	0.486558i	0.971610	−	0.236587i	$-0.0760290\pi$
$991$	8.84323	+	15.3169i	0.280914	+	0.486558i	−0.690696	+	0.723145i	$0.742696\pi$
$992$		0			0
$993$	10.0106	+	43.5252i	0.317676	+	1.38123i
$994$		0			0
$995$	28.4700	−	5.02003i	0.902561	−	0.159146i
$996$		0			0
$997$	6.37062	+	17.5031i	0.201759	+	0.554330i	0.998767	−	0.0496395i	$-0.0158073\pi$
$997$	6.37062	+	17.5031i	0.201759	+	0.554330i	−0.797008	+	0.603969i	$0.793585\pi$
$998$		0			0
$999$	−22.9203	−	28.4487i	−0.725167	−	0.900076i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.ck.a.605.13	yes	144
7.5	odd	6		756.2.ca.a.173.3	✓	144
27.5	odd	18		756.2.ca.a.437.3	yes	144
189.5	even	18	inner	756.2.ck.a.5.13	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.ca.a.173.3	✓	144	7.5	odd	6
756.2.ca.a.437.3	yes	144	27.5	odd	18
756.2.ck.a.5.13	yes	144	189.5	even	18	inner
756.2.ck.a.605.13	yes	144	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	756.ck (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.212510 - 1.71896i) q^{3} +(0.455707 + 2.58444i) q^{5} +(2.64406 + 0.0947211i) q^{7} +(-2.90968 - 0.730593i) q^{9} +O(q^{10})\)	\(q+(0.212510 - 1.71896i) q^{3} +(0.455707 + 2.58444i) q^{5} +(2.64406 + 0.0947211i) q^{7} +(-2.90968 - 0.730593i) q^{9} +(0.625382 + 0.110272i) q^{11} +(-2.83064 - 3.37342i) q^{13} +(4.53941 - 0.234125i) q^{15} +8.05877 q^{17} +3.96393i q^{19} +(0.724710 - 4.52491i) q^{21} +(3.59496 + 4.28431i) q^{23} +(-1.77321 + 0.645394i) q^{25} +(-1.87420 + 4.84638i) q^{27} +(4.88838 - 5.82574i) q^{29} +(1.20156 - 3.30125i) q^{31} +(0.322453 - 1.05158i) q^{33} +(0.960113 + 6.87657i) q^{35} +(-3.51540 + 6.08885i) q^{37} +(-6.40033 + 4.14888i) q^{39} +(4.16466 - 3.49456i) q^{41} +(-0.637408 + 0.231997i) q^{43} +(0.562216 - 7.85283i) q^{45} +(-2.65000 + 0.964522i) q^{47} +(6.98206 + 0.500896i) q^{49} +(1.71257 - 13.8527i) q^{51} +(-3.98038 - 2.29807i) q^{53} +1.66652i q^{55} +(6.81386 + 0.842375i) q^{57} +(-0.846158 + 0.710011i) q^{59} +(-0.698819 - 1.91999i) q^{61} +(-7.62415 - 2.20734i) q^{63} +(7.42847 - 8.85290i) q^{65} +(-2.32519 - 13.1868i) q^{67} +(8.12853 - 5.26915i) q^{69} +(6.01970 - 3.47547i) q^{71} +(4.04198 - 2.33364i) q^{73} +(0.732586 + 3.18523i) q^{75} +(1.64310 + 0.350801i) q^{77} +(-2.57678 + 14.6136i) q^{79} +(7.93247 + 4.25159i) q^{81} +(0.855255 + 0.717644i) q^{83} +(3.67243 + 20.8274i) q^{85} +(-8.97542 - 9.64098i) q^{87} -13.9067 q^{89} +(-7.16482 - 9.18763i) q^{91} +(-5.41939 - 2.76698i) q^{93} +(-10.2446 + 1.80639i) q^{95} +(-5.47800 - 15.0507i) q^{97} +(-1.73910 - 0.777756i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 6 q^{9}+O(q^{10}) \) 144 * q + 6 * q^9	\( 144 q + 6 q^{9} - 6 q^{11} + 12 q^{15} + 33 q^{21} + 21 q^{23} - 6 q^{29} + 27 q^{35} + 39 q^{39} - 54 q^{47} + 18 q^{49} - 9 q^{51} - 45 q^{53} + 3 q^{57} + 45 q^{59} + 39 q^{63} + 24 q^{65} - 36 q^{69} + 36 q^{71} + 45 q^{75} + 21 q^{77} - 18 q^{79} + 18 q^{81} + 36 q^{85} - 45 q^{87} + 9 q^{91} - 48 q^{93} - 66 q^{95}+O(q^{100}) \) 144 * q + 6 * q^9 - 6 * q^11 + 12 * q^15 + 33 * q^21 + 21 * q^23 - 6 * q^29 + 27 * q^35 + 39 * q^39 - 54 * q^47 + 18 * q^49 - 9 * q^51 - 45 * q^53 + 3 * q^57 + 45 * q^59 + 39 * q^63 + 24 * q^65 - 36 * q^69 + 36 * q^71 + 45 * q^75 + 21 * q^77 - 18 * q^79 + 18 * q^81 + 36 * q^85 - 45 * q^87 + 9 * q^91 - 48 * q^93 - 66 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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