LMFDB - Embedded newform 252.4.b.e.55.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [252,4,Mod(55,252)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(252, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0, 1]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("252.55");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 252 = 2^{2} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	252.b (of order $2$, degree $1$, 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:	$14.8684813214$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{11} - 2x^{10} - 6x^{9} + 56x^{7} - 448x^{6} + 448x^{5} - 3072x^{3} - 8192x^{2} - 32768x + 262144 $ x^12 - x^11 - 2x^10 - 6x^9 + 56x^7 - 448x^6 + 448x^5 - 3072x^3 - 8192x^2 - 32768x + 262144
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{13} $
Twist minimal:	no (minimal twist has level 84)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			55.6
Root			$0.965027 - 2.65871i$ of defining polynomial
Character	$\chi$	$=$	252.55
Dual form			252.4.b.e.55.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.965027 + 2.65871i) q^{2} +(-6.13744 - 5.13145i) q^{4} +19.4608i q^{5} +(-1.95109 + 18.4172i) q^{7} +(19.5658 - 11.3657i) q^{8} +O(q^{10})$	\(q+(-0.965027 + 2.65871i) q^{2} +(-6.13744 - 5.13145i) q^{4} +19.4608i q^{5} +(-1.95109 + 18.4172i) q^{7} +(19.5658 - 11.3657i) q^{8} +(-51.7405 - 18.7802i) q^{10} +24.6621i q^{11} -5.25549i q^{13} +(-47.0831 - 22.9605i) q^{14} +(11.3364 + 62.9880i) q^{16} +80.8832i q^{17} +86.5920 q^{19} +(99.8619 - 119.439i) q^{20} +(-65.5693 - 23.7996i) q^{22} -108.350i q^{23} -253.721 q^{25} +(13.9728 + 5.07169i) q^{26} +(106.482 - 103.023i) q^{28} -278.744 q^{29} +116.511 q^{31} +(-178.407 - 30.6449i) q^{32} +(-215.045 - 78.0545i) q^{34} +(-358.413 - 37.9698i) q^{35} +53.5203 q^{37} +(-83.5637 + 230.223i) q^{38} +(221.185 + 380.766i) q^{40} -303.555i q^{41} -176.565i q^{43} +(126.552 - 151.362i) q^{44} +(288.071 + 104.561i) q^{46} -102.276 q^{47} +(-335.386 - 71.8674i) q^{49} +(244.848 - 674.570i) q^{50} +(-26.9683 + 32.2552i) q^{52} -185.933 q^{53} -479.943 q^{55} +(171.149 + 382.523i) q^{56} +(268.996 - 741.099i) q^{58} +732.951 q^{59} +443.155i q^{61} +(-112.436 + 309.769i) q^{62} +(253.643 - 444.758i) q^{64} +102.276 q^{65} +166.969i q^{67} +(415.048 - 496.416i) q^{68} +(446.829 - 916.272i) q^{70} -378.024i q^{71} -664.824i q^{73} +(-51.6486 + 142.295i) q^{74} +(-531.454 - 444.343i) q^{76} +(-454.207 - 48.1181i) q^{77} +737.826i q^{79} +(-1225.79 + 220.616i) q^{80} +(807.065 + 292.939i) q^{82} +913.229 q^{83} -1574.05 q^{85} +(469.434 + 170.390i) q^{86} +(280.301 + 482.534i) q^{88} +1497.53i q^{89} +(96.7913 + 10.2540i) q^{91} +(-555.993 + 664.993i) q^{92} +(98.6989 - 271.921i) q^{94} +1685.15i q^{95} +1445.52i q^{97} +(514.732 - 822.340i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - q^{2} + 5 q^{4} - 10 q^{7} - 25 q^{8}+O(q^{10}) $ 12 * q - q^2 + 5 * q^4 - 10 * q^7 - 25 * q^8	$ 12 q - q^{2} + 5 q^{4} - 10 q^{7} - 25 q^{8} - 56 q^{10} - 101 q^{14} + 41 q^{16} + 84 q^{19} + 172 q^{20} - 182 q^{22} - 216 q^{25} + 300 q^{26} - 379 q^{28} - 200 q^{29} + 384 q^{31} + 159 q^{32} + 164 q^{34} + 84 q^{35} - 244 q^{37} + 268 q^{38} + 316 q^{40} - 190 q^{44} + 894 q^{46} + 280 q^{47} - 424 q^{49} + 1771 q^{50} + 796 q^{52} + 16 q^{53} - 212 q^{55} + 1759 q^{56} - 570 q^{58} + 1168 q^{59} - 384 q^{62} + 2705 q^{64} - 280 q^{65} + 1552 q^{68} + 2592 q^{70} - 1622 q^{74} + 788 q^{76} - 968 q^{77} - 3060 q^{80} + 2540 q^{82} - 968 q^{83} - 852 q^{85} + 258 q^{86} - 2186 q^{88} - 1648 q^{91} - 4298 q^{92} - 4256 q^{94} - 3137 q^{98}+O(q^{100}) $ 12 * q - q^2 + 5 * q^4 - 10 * q^7 - 25 * q^8 - 56 * q^10 - 101 * q^14 + 41 * q^16 + 84 * q^19 + 172 * q^20 - 182 * q^22 - 216 * q^25 + 300 * q^26 - 379 * q^28 - 200 * q^29 + 384 * q^31 + 159 * q^32 + 164 * q^34 + 84 * q^35 - 244 * q^37 + 268 * q^38 + 316 * q^40 - 190 * q^44 + 894 * q^46 + 280 * q^47 - 424 * q^49 + 1771 * q^50 + 796 * q^52 + 16 * q^53 - 212 * q^55 + 1759 * q^56 - 570 * q^58 + 1168 * q^59 - 384 * q^62 + 2705 * q^64 - 280 * q^65 + 1552 * q^68 + 2592 * q^70 - 1622 * q^74 + 788 * q^76 - 968 * q^77 - 3060 * q^80 + 2540 * q^82 - 968 * q^83 - 852 * q^85 + 258 * q^86 - 2186 * q^88 - 1648 * q^91 - 4298 * q^92 - 4256 * q^94 - 3137 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/252\mathbb{Z}\right)^\times$.

$n$	$29$	$73$	$127$
$\chi(n)$	$1$	$-1$	$-1$

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 $

$2$	−0.965027	+	2.65871i	−0.341189	+	0.939995i
$2$	−0.965027	+	2.65871i	−0.341189	+	0.939995i
$3$		0			0
$3$		0			0
$4$	−6.13744	−	5.13145i	−0.767180	−	0.641431i
$5$			19.4608i			1.74062i	0.492501	+	0.870312i	$0.336083\pi$
$5$			19.4608i			1.74062i	−0.492501	+	0.870312i	$0.663917\pi$
$6$		0			0
$7$	−1.95109	+	18.4172i	−0.105349	+	0.994435i
$7$	−1.95109	+	18.4172i	−0.105349	+	0.994435i
$8$	19.5658	−	11.3657i	0.864695	−	0.502297i
$9$		0			0
$10$	−51.7405	−	18.7802i	−1.63618	−	0.593881i
$11$			24.6621i			0.675991i	0.941148	+	0.337996i	$0.109749\pi$
$11$			24.6621i			0.675991i	−0.941148	+	0.337996i	$0.890251\pi$
$12$		0			0
$13$		−	5.25549i		−	0.112124i	−0.998427	−	0.0560619i	$-0.982146\pi$
$13$		−	5.25549i		−	0.112124i	0.998427	−	0.0560619i	$-0.0178544\pi$
$14$	−47.0831	−	22.9605i	−0.898820	−	0.438318i
$15$		0			0
$16$	11.3364	+	62.9880i	0.177132	+	0.984187i
$17$			80.8832i			1.15394i	0.816764	+	0.576972i	$0.195766\pi$
$17$			80.8832i			1.15394i	−0.816764	+	0.576972i	$0.804234\pi$
$18$		0			0
$19$	86.5920			1.04556			0.522778	−	0.852469i	$-0.324896\pi$
$19$	86.5920			1.04556			0.522778	+	0.852469i	$0.324896\pi$
$20$	99.8619	−	119.439i	1.11649	−	1.33537i
$21$		0			0
$22$	−65.5693	−	23.7996i	−0.635428	−	0.230641i
$23$		−	108.350i		−	0.982285i	−0.871079	−	0.491143i	$-0.836579\pi$
$23$		−	108.350i		−	0.982285i	0.871079	−	0.491143i	$-0.163421\pi$
$24$		0			0
$25$	−253.721			−2.02977
$26$	13.9728	+	5.07169i	0.105396	+	0.0382554i
$27$		0			0
$28$	106.482	−	103.023i	0.718684	−	0.695337i
$29$	−278.744			−1.78488			−0.892440	−	0.451167i	$-0.851008\pi$
$29$	−278.744			−1.78488			−0.892440	+	0.451167i	$0.851008\pi$
$30$		0			0
$31$	116.511			0.675032			0.337516	−	0.941320i	$-0.390413\pi$
$31$	116.511			0.675032			0.337516	+	0.941320i	$0.390413\pi$
$32$	−178.407	−	30.6449i	−0.985566	−	0.169291i
$33$		0			0
$34$	−215.045	−	78.0545i	−1.08470	−	0.393713i
$35$	−358.413	−	37.9698i	−1.73094	−	0.183373i
$36$		0			0
$37$	53.5203			0.237802			0.118901	−	0.992906i	$-0.462063\pi$
$37$	53.5203			0.237802			0.118901	+	0.992906i	$0.462063\pi$
$38$	−83.5637	+	230.223i	−0.356732	+	0.982817i
$39$		0			0
$40$	221.185	+	380.766i	0.874309	+	1.50511i
$41$		−	303.555i		−	1.15628i	−0.815938	−	0.578139i	$-0.803779\pi$
$41$		−	303.555i		−	1.15628i	0.815938	−	0.578139i	$-0.196221\pi$
$42$		0			0
$43$		−	176.565i		−	0.626183i	−0.949723	−	0.313092i	$-0.898635\pi$
$43$		−	176.565i		−	0.626183i	0.949723	−	0.313092i	$-0.101365\pi$
$44$	126.552	−	151.362i	0.433602	−	0.518607i
$45$		0			0
$46$	288.071	+	104.561i	0.923343	+	0.335145i
$47$	−102.276			−0.317414			−0.158707	−	0.987326i	$-0.550732\pi$
$47$	−102.276			−0.317414			−0.158707	+	0.987326i	$0.550732\pi$
$48$		0			0
$49$	−335.386	−	71.8674i	−0.977803	−	0.209526i
$50$	244.848	−	674.570i	0.692534	−	1.90797i
$51$		0			0
$52$	−26.9683	+	32.2552i	−0.0719197	+	0.0860192i
$53$	−185.933			−0.481885			−0.240942	−	0.970539i	$-0.577457\pi$
$53$	−185.933			−0.481885			−0.240942	+	0.970539i	$0.577457\pi$
$54$		0			0
$55$	−479.943			−1.17665
$56$	171.149	+	382.523i	0.408406	+	0.912800i
$57$		0			0
$58$	268.996	−	741.099i	0.608981	−	1.67778i
$59$	732.951			1.61732			0.808662	−	0.588274i	$-0.200192\pi$
$59$	732.951			1.61732			0.808662	+	0.588274i	$0.200192\pi$
$60$		0			0
$61$			443.155i			0.930167i	0.885267	+	0.465083i	$0.153976\pi$
$61$			443.155i			0.930167i	−0.885267	+	0.465083i	$0.846024\pi$
$62$	−112.436	+	309.769i	−0.230313	+	0.634527i
$63$		0			0
$64$	253.643	−	444.758i	0.495396	−	0.868667i
$65$	102.276			0.195165
$66$		0			0
$67$			166.969i			0.304455i	0.988345	+	0.152227i	$0.0486446\pi$
$67$			166.969i			0.304455i	−0.988345	+	0.152227i	$0.951355\pi$
$68$	415.048	−	496.416i	0.740176	−	0.885283i
$69$		0			0
$70$	446.829	−	916.272i	0.762946	−	1.56451i
$71$		−	378.024i		−	0.631877i	−0.948780	−	0.315938i	$-0.897681\pi$
$71$		−	378.024i		−	0.631877i	0.948780	−	0.315938i	$-0.102319\pi$
$72$		0			0
$73$		−	664.824i		−	1.06592i	−0.846142	−	0.532958i	$-0.821081\pi$
$73$		−	664.824i		−	1.06592i	0.846142	−	0.532958i	$-0.178919\pi$
$74$	−51.6486	+	142.295i	−0.0811354	+	0.223533i
$75$		0			0
$76$	−531.454	−	444.343i	−0.802130	−	0.670652i
$77$	−454.207	−	48.1181i	−0.672229	−	0.0712151i
$78$		0			0
$79$			737.826i			1.05078i	0.850860	+	0.525392i	$0.176081\pi$
$79$			737.826i			1.05078i	−0.850860	+	0.525392i	$0.823919\pi$
$80$	−1225.79	+	220.616i	−1.71310	+	0.308320i
$81$		0			0
$82$	807.065	+	292.939i	1.08689	+	0.394509i
$83$	913.229			1.20771			0.603855	−	0.797094i	$-0.293631\pi$
$83$	913.229			1.20771			0.603855	+	0.797094i	$0.293631\pi$
$84$		0			0
$85$	−1574.05			−2.00858
$86$	469.434	+	170.390i	0.588609	+	0.213647i
$87$		0			0
$88$	280.301	+	482.534i	0.339548	+	0.584526i
$89$			1497.53i			1.78358i	0.452453	+	0.891788i	$0.350549\pi$
$89$			1497.53i			1.78358i	−0.452453	+	0.891788i	$0.649451\pi$
$90$		0			0
$91$	96.7913	+	10.2540i	0.111500	+	0.0118122i
$92$	−555.993	+	664.993i	−0.630069	+	0.753590i
$93$		0			0
$94$	98.6989	−	271.921i	0.108298	−	0.298367i
$95$			1685.15i			1.81992i
$96$		0			0
$97$			1445.52i			1.51309i	0.653940	+	0.756547i	$0.273115\pi$
$97$			1445.52i			1.51309i	−0.653940	+	0.756547i	$0.726885\pi$
$98$	514.732	−	822.340i	0.530569	−	0.847642i
$99$		0			0
$100$	1557.20	+	1301.96i	1.55720	+	1.30196i
$101$		−	240.349i		−	0.236788i	−0.992967	−	0.118394i	$-0.962225\pi$
$101$		−	240.349i		−	0.236788i	0.992967	−	0.118394i	$-0.0377746\pi$
$102$		0			0
$103$	−1698.72			−1.62505			−0.812524	−	0.582927i	$-0.801907\pi$
$103$	−1698.72			−1.62505			−0.812524	+	0.582927i	$0.801907\pi$
$104$	−59.7321	−	102.828i	−0.0563194	−	0.0969529i
$105$		0			0
$106$	179.431	−	494.342i	0.164414	−	0.452969i
$107$			287.075i			0.259370i	0.991555	+	0.129685i	$0.0413966\pi$
$107$			287.075i			0.259370i	−0.991555	+	0.129685i	$0.958603\pi$
$108$		0			0
$109$	−14.9647			−0.0131500			−0.00657502	−	0.999978i	$-0.502093\pi$
$109$	−14.9647			−0.0131500			−0.00657502	+	0.999978i	$0.502093\pi$
$110$	463.158	−	1276.03i	0.401458	−	1.10604i
$111$		0			0
$112$	−1182.18	+	85.8899i	−0.997371	+	0.0724628i
$113$	737.215			0.613729			0.306864	−	0.951753i	$-0.400720\pi$
$113$	737.215			0.613729			0.306864	+	0.951753i	$0.400720\pi$
$114$		0			0
$115$	2108.58			1.70979
$116$	1710.78	+	1430.36i	1.36932	+	1.14488i
$117$		0			0
$118$	−707.318	+	1948.70i	−0.551813	+	1.52028i
$119$	−1489.64	−	157.811i	−1.14752	−	0.121567i
$120$		0			0
$121$	722.781			0.543036
$122$	−1178.22	−	427.657i	−0.874352	−	0.317362i
$123$		0			0
$124$	−715.080	−	597.871i	−0.517872	−	0.432987i
$125$		−	2505.01i		−	1.79244i
$126$		0			0
$127$			1572.28i			1.09856i	0.835637	+	0.549282i	$0.185099\pi$
$127$			1572.28i			1.09856i	−0.835637	+	0.549282i	$0.814901\pi$
$128$	937.708	+	1103.57i	0.647519	+	0.762049i
$129$		0			0
$130$	−98.6989	+	271.921i	−0.0665882	+	0.183454i
$131$	−941.864			−0.628176			−0.314088	−	0.949394i	$-0.601699\pi$
$131$	−941.864			−0.628176			−0.314088	+	0.949394i	$0.601699\pi$
$132$		0			0
$133$	−168.949	+	1594.78i	−0.110149	+	1.03974i
$134$	−443.921	−	161.129i	−0.286186	−	0.103877i
$135$		0			0
$136$	919.292	+	1582.55i	0.579622	+	0.997810i
$137$	−2087.46			−1.30178			−0.650889	−	0.759173i	$-0.725604\pi$
$137$	−2087.46			−1.30178			−0.650889	+	0.759173i	$0.725604\pi$
$138$		0			0
$139$	1894.46			1.15602			0.578008	−	0.816031i	$-0.303830\pi$
$139$	1894.46			1.15602			0.578008	+	0.816031i	$0.303830\pi$
$140$	2004.90	+	2072.21i	1.21032	+	1.25096i
$141$		0			0
$142$	1005.06	+	364.804i	0.593961	+	0.215589i
$143$	129.611			0.0757947
$144$		0			0
$145$		−	5424.57i		−	3.10680i
$146$	1767.57	+	641.574i	1.00195	+	0.363678i
$147$		0			0
$148$	−328.478	−	274.637i	−0.182437	−	0.152534i
$149$	2506.20			1.37796			0.688981	−	0.724780i	$-0.258058\pi$
$149$	2506.20			1.37796			0.688981	+	0.724780i	$0.258058\pi$
$150$		0			0
$151$			465.035i			0.250623i	0.992117	+	0.125311i	$0.0399930\pi$
$151$			465.035i			0.250623i	−0.992117	+	0.125311i	$0.960007\pi$
$152$	1694.24	−	984.176i	0.904088	−	0.525179i
$153$		0			0
$154$	566.254	−	1161.17i	0.296299	−	0.607594i
$155$			2267.39i			1.17498i
$156$		0			0
$157$		−	441.217i		−	0.224286i	−0.993692	−	0.112143i	$-0.964228\pi$
$157$		−	441.217i		−	0.224286i	0.993692	−	0.112143i	$-0.0357715\pi$
$158$	−1961.66	−	712.023i	−0.987732	−	0.358516i
$159$		0			0
$160$	596.372	−	3471.93i	0.294671	−	1.71550i
$161$	1995.51	+	211.401i	0.976819	+	0.103483i
$162$		0			0
$163$		−	374.876i		−	0.180139i	−0.995936	−	0.0900693i	$-0.971291\pi$
$163$		−	374.876i		−	0.180139i	0.995936	−	0.0900693i	$-0.0287089\pi$
$164$	−1557.68	+	1863.05i	−0.741673	+	0.887074i
$165$		0			0
$166$	−881.292	+	2428.01i	−0.412057	+	1.13524i
$167$	−986.292			−0.457015			−0.228508	−	0.973542i	$-0.573385\pi$
$167$	−986.292			−0.457015			−0.228508	+	0.973542i	$0.573385\pi$
$168$		0			0
$169$	2169.38			0.987428
$170$	1519.00	−	4184.93i	0.685306	−	1.88806i
$171$		0			0
$172$	−906.033	+	1083.66i	−0.401653	+	0.480395i
$173$			1618.78i			0.711407i	0.934599	+	0.355704i	$0.115759\pi$
$173$			1618.78i			0.711407i	−0.934599	+	0.355704i	$0.884241\pi$
$174$		0			0
$175$	495.034	−	4672.83i	0.213835	−	2.01847i
$176$	−1553.42	+	279.580i	−0.665302	+	0.119740i
$177$		0			0
$178$	−3981.50	−	1445.16i	−1.67655	−	0.608536i
$179$		−	3693.28i		−	1.54217i	−0.636730	−	0.771087i	$-0.719714\pi$
$179$		−	3693.28i		−	1.54217i	0.636730	−	0.771087i	$-0.280286\pi$
$180$		0			0
$181$			2447.09i			1.00492i	0.864600	+	0.502461i	$0.167572\pi$
$181$			2447.09i			1.00492i	−0.864600	+	0.502461i	$0.832428\pi$
$182$	−120.669	+	247.444i	−0.0491459	+	0.100779i
$183$		0			0
$184$	−1231.47	−	2119.96i	−0.493399	−	0.849378i
$185$			1041.55i			0.413924i
$186$		0			0
$187$	−1994.75			−0.780056
$188$	627.712	+	524.823i	0.243514	+	0.203599i
$189$		0			0
$190$	−4480.31	−	1626.21i	−1.71071	−	0.620936i
$191$		−	9.19972i		−	0.00348518i	−0.999998	−	0.00174259i	$-0.999445\pi$
$191$		−	9.19972i		−	0.00348518i	0.999998	−	0.00174259i	$-0.000554683\pi$
$192$		0			0
$193$	−1468.72			−0.547776			−0.273888	−	0.961762i	$-0.588310\pi$
$193$	−1468.72			−0.547776			−0.273888	+	0.961762i	$0.588310\pi$
$194$	−3843.21	−	1394.96i	−1.42230	−	0.516250i
$195$		0			0
$196$	1689.63	+	2162.10i	0.615755	+	0.787938i
$197$	−3914.64			−1.41577			−0.707884	−	0.706328i	$-0.750350\pi$
$197$	−3914.64			−1.41577			−0.707884	+	0.706328i	$0.750350\pi$
$198$		0			0
$199$	−2960.22			−1.05449			−0.527247	−	0.849712i	$-0.676776\pi$
$199$	−2960.22			−1.05449			−0.527247	+	0.849712i	$0.676776\pi$
$200$	−4964.26	+	2883.71i	−1.75513	+	1.01955i
$201$		0			0
$202$	639.016	+	231.943i	0.222579	+	0.0807893i
$203$	543.856	−	5133.69i	0.188036	−	1.77495i
$204$		0			0
$205$	5907.42			2.01264
$206$	1639.31	−	4516.40i	0.554448	−	1.52754i
$207$		0			0
$208$	331.032	−	59.5785i	0.110351	−	0.0198607i
$209$			2135.54i			0.706787i
$210$		0			0
$211$		−	1329.13i		−	0.433654i	−0.976210	−	0.216827i	$-0.930429\pi$
$211$		−	1329.13i		−	0.433654i	0.976210	−	0.216827i	$-0.0695708\pi$
$212$	1141.16	+	954.108i	0.369693	+	0.309096i
$213$		0			0
$214$	−763.248	−	277.035i	−0.243806	−	0.0884941i
$215$	3436.08			1.08995
$216$		0			0
$217$	−227.324	+	2145.81i	−0.0711141	+	0.671276i
$218$	14.4413	−	39.7866i	0.00448665	−	0.0123610i
$219$		0			0
$220$	2945.62	+	2462.80i	0.902700	+	0.754737i
$221$	425.080			0.129385
$222$		0			0
$223$	850.725			0.255465			0.127733	−	0.991809i	$-0.459230\pi$
$223$	850.725			0.255465			0.127733	+	0.991809i	$0.459230\pi$
$224$	912.481	−	3225.96i	0.272177	−	0.962247i
$225$		0			0
$226$	−711.433	+	1960.04i	−0.209397	+	0.576902i
$227$	2626.60			0.767988			0.383994	−	0.923336i	$-0.374548\pi$
$227$	2626.60			0.767988			0.383994	+	0.923336i	$0.374548\pi$
$228$		0			0
$229$			1681.55i			0.485239i	0.970122	+	0.242620i	$0.0780067\pi$
$229$			1681.55i			0.485239i	−0.970122	+	0.242620i	$0.921993\pi$
$230$	−2034.83	+	5606.08i	−0.583361	+	1.60719i
$231$		0			0
$232$	−5453.86	+	3168.12i	−1.54338	+	0.896539i
$233$	1824.86			0.513093			0.256547	−	0.966532i	$-0.417415\pi$
$233$	1824.86			0.513093			0.256547	+	0.966532i	$0.417415\pi$
$234$		0			0
$235$		−	1990.36i		−	0.552498i
$236$	−4498.45	−	3761.10i	−1.24078	−	1.03740i
$237$		0			0
$238$	1857.12	−	3808.23i	0.505794	−	1.03719i
$239$			776.076i			0.210043i	0.994470	+	0.105021i	$0.0334911\pi$
$239$			776.076i			0.210043i	−0.994470	+	0.105021i	$0.966509\pi$
$240$		0			0
$241$		−	40.5909i		−	0.0108493i	−0.999985	−	0.00542466i	$-0.998273\pi$
$241$		−	40.5909i		−	0.0108493i	0.999985	−	0.00542466i	$-0.00172673\pi$
$242$	−697.504	+	1921.66i	−0.185278	+	0.510451i
$243$		0			0
$244$	2274.03	−	2719.84i	0.596638	−	0.713606i
$245$	1398.59	−	6526.88i	0.364706	−	1.70199i
$246$		0			0
$247$		−	455.083i		−	0.117232i
$248$	2279.64	−	1324.23i	0.583697	−	0.339066i
$249$		0			0
$250$	6660.09	+	2417.41i	1.68488	+	0.611561i
$251$	−4231.68			−1.06415			−0.532074	−	0.846698i	$-0.678587\pi$
$251$	−4231.68			−1.06415			−0.532074	+	0.846698i	$0.678587\pi$
$252$		0			0
$253$	2672.14			0.664016
$254$	−4180.24	−	1517.30i	−1.03264	−	0.374817i
$255$		0			0
$256$	−3838.97	+	1428.12i	−0.937249	+	0.348662i
$257$			1872.50i			0.454489i	0.973838	+	0.227244i	$0.0729716\pi$
$257$			1872.50i			0.454489i	−0.973838	+	0.227244i	$0.927028\pi$
$258$		0			0
$259$	−104.423	+	985.694i	−0.0250523	+	0.236479i
$260$	−627.712	−	524.823i	−0.149727	−	0.125185i
$261$		0			0
$262$	908.925	−	2504.14i	0.214327	−	0.590482i
$263$			5126.25i			1.20190i	0.799288	+	0.600948i	$0.205210\pi$
$263$			5126.25i			1.20190i	−0.799288	+	0.600948i	$0.794790\pi$
$264$		0			0
$265$		−	3618.40i		−	0.838780i
$266$	−4077.02	−	1988.19i	−0.939767	−	0.458286i
$267$		0			0
$268$	856.792	−	1024.76i	0.195287	−	0.233572i
$269$		−	2399.98i		−	0.543975i	−0.962301	−	0.271988i	$-0.912319\pi$
$269$		−	2399.98i		−	0.543975i	0.962301	−	0.271988i	$-0.0876810\pi$
$270$		0			0
$271$	5666.29			1.27012			0.635060	−	0.772462i	$-0.280975\pi$
$271$	5666.29			1.27012			0.635060	+	0.772462i	$0.280975\pi$
$272$	−5094.67	+	916.927i	−1.13570	+	0.204400i
$273$		0			0
$274$	2014.45	−	5549.94i	0.444152	−	1.22366i
$275$		−	6257.30i		−	1.37211i
$276$		0			0
$277$	−1089.92			−0.236414			−0.118207	−	0.992989i	$-0.537715\pi$
$277$	−1089.92			−0.236414			−0.118207	+	0.992989i	$0.537715\pi$
$278$	−1828.21	+	5036.82i	−0.394420	+	1.08665i
$279$		0			0
$280$	−7444.19	+	3330.69i	−1.58884	+	0.710882i
$281$	3251.98			0.690381			0.345191	−	0.938533i	$-0.387814\pi$
$281$	3251.98			0.690381			0.345191	+	0.938533i	$0.387814\pi$
$282$		0			0
$283$	−8087.11			−1.69869			−0.849344	−	0.527840i	$-0.823002\pi$
$283$	−8087.11			−1.69869			−0.849344	+	0.527840i	$0.823002\pi$
$284$	−1939.81	+	2320.10i	−0.405305	+	0.484763i
$285$		0			0
$286$	−125.078	+	344.598i	−0.0258603	+	0.0712466i
$287$	5590.64	+	592.265i	1.14984	+	0.121813i
$288$		0			0
$289$	−1629.09			−0.331587
$290$	14422.4	+	5234.86i	2.92038	+	1.06001i
$291$		0			0
$292$	−3411.51	+	4080.32i	−0.683711	+	0.817749i
$293$		−	1615.35i		−	0.322080i	−0.986948	−	0.161040i	$-0.948515\pi$
$293$		−	1615.35i		−	0.322080i	0.986948	−	0.161040i	$-0.0514849\pi$
$294$		0			0
$295$			14263.8i			2.81515i
$296$	1047.17	−	608.294i	0.205627	−	0.119447i
$297$		0			0
$298$	−2418.56	+	6663.26i	−0.470145	+	1.29528i
$299$	−569.433			−0.110138
$300$		0			0
$301$	3251.83	+	344.495i	0.622699	+	0.0659679i
$302$	−1236.39	−	448.772i	−0.235584	−	0.0855096i
$303$		0			0
$304$	981.645	+	5454.25i	0.185201	+	1.02902i
$305$	−8624.13			−1.61907
$306$		0			0
$307$	−2726.45			−0.506863			−0.253431	−	0.967353i	$-0.581559\pi$
$307$	−2726.45			−0.506863			−0.253431	+	0.967353i	$0.581559\pi$
$308$	2540.75	+	2626.06i	0.470042	+	0.485824i
$309$		0			0
$310$	−6028.34	−	2188.10i	−1.10447	−	0.400889i
$311$	−6495.92			−1.18441			−0.592203	−	0.805789i	$-0.701742\pi$
$311$	−6495.92			−1.18441			−0.592203	+	0.805789i	$0.701742\pi$
$312$		0			0
$313$		−	2315.02i		−	0.418059i	−0.977909	−	0.209030i	$-0.932970\pi$
$313$		−	2315.02i		−	0.418059i	0.977909	−	0.209030i	$-0.0670305\pi$
$314$	1173.07	+	425.786i	0.210828	+	0.0765239i
$315$		0			0
$316$	3786.12	−	4528.37i	0.674006	−	0.806141i
$317$	3545.18			0.628130			0.314065	−	0.949402i	$-0.398309\pi$
$317$	3545.18			0.628130			0.314065	+	0.949402i	$0.398309\pi$
$318$		0			0
$319$		−	6874.42i		−	1.20656i
$320$	8655.32	+	4936.08i	1.51202	+	0.862298i
$321$		0			0
$322$	−2487.77	+	5101.46i	−0.430553	+	0.882898i
$323$			7003.83i			1.20651i
$324$		0			0
$325$			1333.43i			0.227585i
$326$	996.687	+	361.766i	0.169329	+	0.0614613i
$327$		0			0
$328$	−3450.11	−	5939.31i	−0.580794	−	0.999828i
$329$	199.550	−	1883.63i	0.0334393	−	0.315648i
$330$		0			0
$331$		−	5480.40i		−	0.910060i	−0.890476	−	0.455030i	$-0.849629\pi$
$331$		−	5480.40i		−	0.910060i	0.890476	−	0.455030i	$-0.150371\pi$
$332$	−5604.89	−	4686.19i	−0.926532	−	0.774663i
$333$		0			0
$334$	951.799	−	2622.26i	0.155928	−	0.429592i
$335$	−3249.34			−0.529941
$336$		0			0
$337$	−142.057			−0.0229624			−0.0114812	−	0.999934i	$-0.503655\pi$
$337$	−142.057			−0.0229624			−0.0114812	+	0.999934i	$0.503655\pi$
$338$	−2093.51	+	5767.75i	−0.336899	+	0.928177i
$339$		0			0
$340$	9660.63	+	8077.15i	1.54094	+	1.28837i
$341$			2873.41i			0.456316i
$342$		0			0
$343$	1977.97	−	6036.66i	0.311371	−	0.950288i
$344$	−2006.78	−	3454.64i	−0.314530	−	0.541458i
$345$		0			0
$346$	−4303.86	−	1562.17i	−0.668719	−	0.242724i
$347$			1106.02i			0.171108i	0.996334	+	0.0855540i	$0.0272660\pi$
$347$			1106.02i			0.171108i	−0.996334	+	0.0855540i	$0.972734\pi$
$348$		0			0
$349$		−	5314.57i		−	0.815136i	−0.913175	−	0.407568i	$-0.866377\pi$
$349$		−	5314.57i		−	0.815136i	0.913175	−	0.407568i	$-0.133623\pi$
$350$	11946.0	+	5825.56i	1.82440	+	0.889684i
$351$		0			0
$352$	755.767	−	4399.88i	0.114439	−	0.666234i
$353$			10581.0i			1.59538i	0.603068	+	0.797690i	$0.293945\pi$
$353$			10581.0i			1.59538i	−0.603068	+	0.797690i	$0.706055\pi$
$354$		0			0
$355$	7356.64			1.09986
$356$	7684.52	−	9191.03i	1.14404	−	1.36832i
$357$		0			0
$358$	9819.36	+	3564.12i	1.44963	+	0.526172i
$359$			2661.07i			0.391214i	0.980682	+	0.195607i	$0.0626677\pi$
$359$			2661.07i			0.391214i	−0.980682	+	0.195607i	$0.937332\pi$
$360$		0			0
$361$	639.174			0.0931876
$362$	−6506.10	−	2361.51i	−0.944621	−	0.342868i
$363$		0			0
$364$	−541.434	−	559.613i	−0.0779638	−	0.0805816i
$365$	12938.0			1.85536
$366$		0			0
$367$	5895.68			0.838562			0.419281	−	0.907857i	$-0.362282\pi$
$367$	5895.68			0.838562			0.419281	+	0.907857i	$0.362282\pi$
$368$	6824.75	−	1228.30i	0.966753	−	0.173994i
$369$		0			0
$370$	−2769.16	−	1005.12i	−0.389087	−	0.141226i
$371$	362.774	−	3424.37i	0.0507662	−	0.479203i
$372$		0			0
$373$	−6208.52			−0.861837			−0.430918	−	0.902391i	$-0.641810\pi$
$373$	−6208.52			−0.861837			−0.430918	+	0.902391i	$0.641810\pi$
$374$	1924.99	−	5303.45i	0.266146	−	0.733248i
$375$		0			0
$376$	−2001.11	+	1162.43i	−0.274466	+	0.159436i
$377$			1464.94i			0.200127i
$378$		0			0
$379$			3532.73i			0.478797i	0.970921	+	0.239399i	$0.0769503\pi$
$379$			3532.73i			0.478797i	−0.970921	+	0.239399i	$0.923050\pi$
$380$	8647.24	−	10342.5i	1.16735	−	1.39621i
$381$		0			0
$382$	24.4594	+	8.87799i	0.00327605	+	0.00118910i
$383$	9380.75			1.25153			0.625763	−	0.780014i	$-0.284788\pi$
$383$	9380.75			1.25153			0.625763	+	0.780014i	$0.284788\pi$
$384$		0			0
$385$	936.414	−	8839.21i	0.123959	−	1.17010i
$386$	1417.35	−	3904.89i	0.186895	−	0.514907i
$387$		0			0
$388$	7417.60	−	8871.78i	0.970545	−	1.16082i
$389$	−5267.14			−0.686516			−0.343258	−	0.939241i	$-0.611531\pi$
$389$	−5267.14			−0.686516			−0.343258	+	0.939241i	$0.611531\pi$
$390$		0			0
$391$	8763.70			1.13350
$392$	−7378.93	+	2405.75i	−0.950746	+	0.309971i
$393$		0			0
$394$	3777.73	−	10407.9i	0.483044	−	1.33082i
$395$	−14358.7			−1.82902
$396$		0			0
$397$			8515.34i			1.07651i	0.842783	+	0.538253i	$0.180915\pi$
$397$			8515.34i			1.07651i	−0.842783	+	0.538253i	$0.819085\pi$
$398$	2856.69	−	7870.35i	0.359781	−	0.991218i
$399$		0			0
$400$	−2876.29	−	15981.4i	−0.359537	−	1.99767i
$401$	2804.56			0.349259			0.174629	−	0.984634i	$-0.444127\pi$
$401$	2804.56			0.349259			0.174629	+	0.984634i	$0.444127\pi$
$402$		0			0
$403$		−	612.322i		−	0.0756872i
$404$	−1233.34	+	1475.13i	−0.151883	+	0.181659i
$405$		0			0
$406$	13124.1	+	6400.10i	1.60429	+	0.782344i
$407$			1319.92i			0.160752i
$408$		0			0
$409$			13823.4i			1.67121i	0.549334	+	0.835603i	$0.314882\pi$
$409$			13823.4i			1.67121i	−0.549334	+	0.835603i	$0.685118\pi$
$410$	−5700.82	+	15706.1i	−0.686691	+	1.89187i
$411$		0			0
$412$	10425.8	+	8716.91i	1.24671	+	1.04236i
$413$	−1430.06	+	13498.9i	−0.170384	+	1.60832i
$414$		0			0
$415$			17772.1i			2.10217i
$416$	−161.054	+	937.613i	−0.0189815	+	0.110505i
$417$		0			0
$418$	−5677.77	−	2060.85i	−0.664376	−	0.241148i
$419$	5047.91			0.588560			0.294280	−	0.955719i	$-0.404920\pi$
$419$	5047.91			0.588560			0.294280	+	0.955719i	$0.404920\pi$
$420$		0			0
$421$	6467.30			0.748686			0.374343	−	0.927290i	$-0.377868\pi$
$421$	6467.30			0.748686			0.374343	+	0.927290i	$0.377868\pi$
$422$	3533.76	+	1282.65i	0.407633	+	0.147958i
$423$		0			0
$424$	−3637.94	+	2113.26i	−0.416684	+	0.242049i
$425$		−	20521.8i		−	2.34224i
$426$		0			0
$427$	−8161.67	−	864.637i	−0.924990	−	0.0979923i
$428$	1473.11	−	1761.91i	0.166368	−	0.198984i
$429$		0			0
$430$	−3315.92	+	9135.54i	−0.371878	+	1.02455i
$431$			12799.9i			1.43051i	0.698861	+	0.715257i	$0.253691\pi$
$431$			12799.9i			1.43051i	−0.698861	+	0.715257i	$0.746309\pi$
$432$		0			0
$433$			7154.28i			0.794025i	0.917813	+	0.397013i	$0.129953\pi$
$433$			7154.28i			0.794025i	−0.917813	+	0.397013i	$0.870047\pi$
$434$	−5485.70	−	2675.15i	−0.606733	−	0.295879i
$435$		0			0
$436$	91.8447	+	76.7904i	0.0100885	+	0.00843485i
$437$		−	9382.25i		−	1.02703i
$438$		0			0
$439$	−10688.8			−1.16207			−0.581034	−	0.813879i	$-0.697352\pi$
$439$	−10688.8			−1.16207			−0.581034	+	0.813879i	$0.697352\pi$
$440$	−9390.48	+	5454.88i	−1.01744	+	0.591025i
$441$		0			0
$442$	−410.214	+	1130.16i	−0.0441446	+	0.121621i
$443$		−	4652.95i		−	0.499025i	−0.968372	−	0.249513i	$-0.919730\pi$
$443$		−	4652.95i		−	0.499025i	0.968372	−	0.249513i	$-0.0802704\pi$
$444$		0			0
$445$	−29143.2			−3.10453
$446$	−820.973	+	2261.83i	−0.0871619	+	0.240136i
$447$		0			0
$448$	7696.31	+	5539.16i	0.811644	+	0.584153i
$449$	−16721.0			−1.75749			−0.878743	−	0.477296i	$-0.841617\pi$
$449$	−16721.0			−1.75749			−0.878743	+	0.477296i	$0.841617\pi$
$450$		0			0
$451$	7486.31			0.781633
$452$	−4524.62	−	3782.98i	−0.470841	−	0.393665i
$453$		0			0
$454$	−2534.74	+	6983.35i	−0.262029	+	0.721905i
$455$	−199.550	+	1883.63i	−0.0205605	+	0.194079i
$456$		0			0
$457$	−7571.11			−0.774971			−0.387485	−	0.921876i	$-0.626656\pi$
$457$	−7571.11			−0.774971			−0.387485	+	0.921876i	$0.626656\pi$
$458$	−4470.74	−	1622.74i	−0.456122	−	0.165558i
$459$		0			0
$460$	−12941.3	−	10820.1i	−1.31172	−	1.09671i
$461$			8410.07i			0.849666i	0.905272	+	0.424833i	$0.139667\pi$
$461$			8410.07i			0.849666i	−0.905272	+	0.424833i	$0.860333\pi$
$462$		0			0
$463$			10100.0i			1.01379i	0.862007	+	0.506897i	$0.169208\pi$
$463$			10100.0i			1.01379i	−0.862007	+	0.506897i	$0.830792\pi$
$464$	−3159.97	−	17557.5i	−0.316159	−	1.75666i
$465$		0			0
$466$	−1761.04	+	4851.78i	−0.175062	+	0.482305i
$467$	−2012.75			−0.199441			−0.0997207	−	0.995015i	$-0.531795\pi$
$467$	−2012.75			−0.199441			−0.0997207	+	0.995015i	$0.531795\pi$
$468$		0			0
$469$	−3075.10	−	325.772i	−0.302761	−	0.0320741i
$470$	5291.79	+	1920.76i	0.519345	+	0.188506i
$471$		0			0
$472$	14340.8	−	8330.48i	1.39849	−	0.812376i
$473$	4354.46			0.423294
$474$		0			0
$475$	−21970.2			−2.12224
$476$	8332.79	+	8612.58i	0.802380	+	0.829321i
$477$		0			0
$478$	−2063.36	−	748.934i	−0.197439	−	0.0716641i
$479$	13299.9			1.26866			0.634330	−	0.773062i	$-0.281276\pi$
$479$	13299.9			1.26866			0.634330	+	0.773062i	$0.281276\pi$
$480$		0			0
$481$		−	281.275i		−	0.0266633i
$482$	107.919	+	39.1713i	0.0101983	+	0.00370167i
$483$		0			0
$484$	−4436.03	−	3708.92i	−0.416607	−	0.348320i
$485$	−28130.9			−2.63372
$486$		0			0
$487$		−	2587.62i		−	0.240773i	−0.992727	−	0.120386i	$-0.961587\pi$
$487$		−	2587.62i		−	0.240773i	0.992727	−	0.120386i	$-0.0384134\pi$
$488$	5036.75	+	8670.69i	0.467219	+	0.804311i
$489$		0			0
$490$	16003.4	+	10017.1i	1.47543	+	0.923520i
$491$			588.505i			0.0540913i	0.999634	+	0.0270457i	$0.00860996\pi$
$491$			588.505i			0.0540913i	−0.999634	+	0.0270457i	$0.991390\pi$
$492$		0			0
$493$		−	22545.7i		−	2.05965i
$494$	1209.93	+	439.168i	0.110197	+	0.0399981i
$495$		0			0
$496$	1320.82	+	7338.80i	0.119570	+	0.664358i
$497$	6962.15	+	737.561i	0.628360	+	0.0665677i
$498$		0			0
$499$		−	16006.0i		−	1.43592i	−0.696083	−	0.717961i	$-0.745075\pi$
$499$		−	16006.0i		−	1.43592i	0.696083	−	0.717961i	$-0.254925\pi$
$500$	−12854.3	+	15374.4i	−1.14973	+	1.37513i
$501$		0			0
$502$	4083.69	−	11250.8i	0.363075	−	1.00029i
$503$	10633.0			0.942551			0.471276	−	0.881986i	$-0.343794\pi$
$503$	10633.0			0.942551			0.471276	+	0.881986i	$0.343794\pi$
$504$		0			0
$505$	4677.36			0.412158
$506$	−2578.69	+	7104.44i	−0.226555	+	0.624172i
$507$		0			0
$508$	8068.09	−	9649.80i	0.704653	−	0.842796i
$509$		−	2697.13i		−	0.234869i	−0.993081	−	0.117434i	$-0.962533\pi$
$509$		−	2697.13i		−	0.234869i	0.993081	−	0.117434i	$-0.0374670\pi$
$510$		0			0
$511$	12244.2	+	1297.14i	1.05998	+	0.112293i
$512$	−92.2362	−	11584.9i	−0.00796152	−	0.999968i
$513$		0			0
$514$	−4978.44	−	1807.02i	−0.427217	−	0.155066i
$515$		−	33058.4i		−	2.82860i
$516$		0			0
$517$		−	2522.33i		−	0.214569i
$518$	−2519.90	−	1228.85i	−0.213741	−	0.104233i
$519$		0			0
$520$	2001.11	−	1162.43i	0.168759	−	0.0980309i
$521$		−	11342.2i		−	0.953766i	−0.878967	−	0.476883i	$-0.841767\pi$
$521$		−	11342.2i		−	0.953766i	0.878967	−	0.476883i	$-0.158233\pi$
$522$		0			0
$523$	−4722.12			−0.394807			−0.197403	−	0.980322i	$-0.563251\pi$
$523$	−4722.12			−0.394807			−0.197403	+	0.980322i	$0.563251\pi$
$524$	5780.64	+	4833.13i	0.481924	+	0.402932i
$525$		0			0
$526$	−13629.2	−	4946.98i	−1.12978	−	0.410073i
$527$			9423.78i			0.778950i
$528$		0			0
$529$	427.252			0.0351156
$530$	9620.27	+	3491.86i	0.788449	+	0.286182i
$531$		0			0
$532$	9220.46	−	8920.93i	0.751424	−	0.727014i
$533$	−1595.33			−0.129646
$534$		0			0
$535$	−5586.70			−0.451465
$536$	1897.71	+	3266.88i	0.152927	+	0.263261i
$537$		0			0
$538$	6380.84	+	2316.05i	0.511334	+	0.185598i
$539$	1772.40	−	8271.33i	0.141638	−	0.660986i
$540$		0			0
$541$	−6125.28			−0.486777			−0.243389	−	0.969929i	$-0.578259\pi$
$541$	−6125.28			−0.486777			−0.243389	+	0.969929i	$0.578259\pi$
$542$	−5468.13	+	15065.0i	−0.433351	+	1.19391i
$543$		0			0
$544$	2478.65	−	14430.1i	0.195352	−	1.13729i
$545$		−	291.224i		−	0.0228893i
$546$		0			0
$547$			25304.7i			1.97797i	0.148015	+	0.988985i	$0.452712\pi$
$547$			25304.7i			1.97797i	−0.148015	+	0.988985i	$0.547288\pi$
$548$	12811.7	+	10711.7i	0.998699	+	0.835001i
$549$		0			0
$550$	16636.3	+	6038.46i	1.28977	+	0.468147i
$551$	−24137.0			−1.86619
$552$		0			0
$553$	−13588.7	−	1439.57i	−1.04494	−	0.110699i
$554$	1051.80	−	2897.77i	0.0806620	−	0.222228i
$555$		0			0
$556$	−11627.2	−	9721.34i	−0.886873	−	0.741505i
$557$	−9686.90			−0.736889			−0.368444	−	0.929650i	$-0.620109\pi$
$557$	−9686.90			−0.736889			−0.368444	+	0.929650i	$0.620109\pi$
$558$		0			0
$559$	−927.934			−0.0702100
$560$	−1671.48	−	23006.1i	−0.126130	−	1.73605i
$561$		0			0
$562$	−3138.25	+	8646.07i	−0.235550	+	0.648955i
$563$	6110.70			0.457434			0.228717	−	0.973493i	$-0.426547\pi$
$563$	6110.70			0.457434			0.228717	+	0.973493i	$0.426547\pi$
$564$		0			0
$565$			14346.8i			1.06827i
$566$	7804.28	−	21501.2i	0.579573	−	1.59676i
$567$		0			0
$568$	−4296.50	−	7396.36i	−0.317389	−	0.546381i
$569$	16843.7			1.24099			0.620497	−	0.784209i	$-0.286931\pi$
$569$	16843.7			1.24099			0.620497	+	0.784209i	$0.286931\pi$
$570$		0			0
$571$		−	15796.9i		−	1.15775i	−0.815415	−	0.578877i	$-0.803491\pi$
$571$		−	15796.9i		−	1.15775i	0.815415	−	0.578877i	$-0.196509\pi$
$572$	−795.482	−	665.094i	−0.0581482	−	0.0486171i
$573$		0			0
$574$	−6969.78	+	14292.3i	−0.506817	+	1.03929i
$575$			27490.7i			1.99381i
$576$		0			0
$577$			6756.48i			0.487480i	0.969841	+	0.243740i	$0.0783743\pi$
$577$			6756.48i			0.487480i	−0.969841	+	0.243740i	$0.921626\pi$
$578$	1572.11	−	4331.26i	0.113134	−	0.311690i
$579$		0			0
$580$	−27835.9	+	33293.0i	−1.99280	+	2.38348i
$581$	−1781.80	+	16819.1i	−0.127231	+	1.20099i
$582$		0			0
$583$		−	4585.50i		−	0.325750i
$584$	−7556.18	−	13007.8i	−0.535405	−	0.921692i
$585$		0			0
$586$	4294.73	+	1558.85i	0.302754	+	0.109890i
$587$	20504.0			1.44172			0.720861	−	0.693080i	$-0.243747\pi$
$587$	20504.0			1.44172			0.720861	+	0.693080i	$0.243747\pi$
$588$		0			0
$589$	10088.9			0.705784
$590$	−37923.2	−	13764.9i	−2.64623	−	0.960498i
$591$		0			0
$592$	606.729	+	3371.14i	0.0421223	+	0.234042i
$593$		−	1432.90i		−	0.0992281i	−0.998768	−	0.0496140i	$-0.984201\pi$
$593$		−	1432.90i		−	0.0992281i	0.998768	−	0.0496140i	$-0.0157991\pi$
$594$		0			0
$595$	3071.12	−	28989.6i	0.211603	−	1.99740i
$596$	−15381.7	−	12860.5i	−1.05715	−	0.883868i
$597$		0			0
$598$	549.518	−	1513.95i	0.0375777	−	0.103529i
$599$		−	21643.1i		−	1.47632i	−0.674628	−	0.738158i	$-0.735696\pi$
$599$		−	21643.1i		−	1.47632i	0.674628	−	0.738158i	$-0.264304\pi$
$600$		0			0
$601$			9462.88i			0.642261i	0.947035	+	0.321131i	$0.104063\pi$
$601$			9462.88i			0.642261i	−0.947035	+	0.321131i	$0.895937\pi$
$602$	−4054.01	+	8313.21i	−0.274467	+	0.562826i
$603$		0			0
$604$	2386.30	−	2854.13i	0.160757	−	0.192273i
$605$			14065.9i			0.945221i
$606$		0			0
$607$	−523.640			−0.0350146			−0.0175073	−	0.999847i	$-0.505573\pi$
$607$	−523.640			−0.0350146			−0.0175073	+	0.999847i	$0.505573\pi$
$608$	−15448.6	−	2653.60i	−1.03046	−	0.177003i
$609$		0			0
$610$	8322.52	−	22929.0i	0.552408	−	1.52192i
$611$			537.509i			0.0355897i
$612$		0			0
$613$	25130.7			1.65582			0.827912	−	0.560858i	$-0.189529\pi$
$613$	25130.7			1.65582			0.827912	+	0.560858i	$0.189529\pi$
$614$	2631.10	−	7248.84i	0.172936	−	0.476448i
$615$		0			0
$616$	−9433.82	+	4220.90i	−0.617045	+	0.276079i
$617$	22315.2			1.45604			0.728021	−	0.685555i	$-0.240440\pi$
$617$	22315.2			1.45604			0.728021	+	0.685555i	$0.240440\pi$
$618$		0			0
$619$	20000.9			1.29871			0.649357	−	0.760484i	$-0.275038\pi$
$619$	20000.9			1.29871			0.649357	+	0.760484i	$0.275038\pi$
$620$	11635.0	−	13916.0i	0.753667	−	0.901420i
$621$		0			0
$622$	6268.75	−	17270.8i	0.404106	−	1.11333i
$623$	−27580.4	−	2921.83i	−1.77365	−	0.187898i
$624$		0			0
$625$	17034.3			1.09019
$626$	6154.95	+	2234.06i	0.392973	+	0.142637i
$627$		0			0
$628$	−2264.08	+	2707.94i	−0.143864	+	0.172068i
$629$			4328.89i			0.274411i
$630$		0			0
$631$			6793.62i			0.428605i	0.976767	+	0.214302i	$0.0687478\pi$
$631$			6793.62i			0.428605i	−0.976767	+	0.214302i	$0.931252\pi$
$632$	8385.89	+	14436.2i	0.527805	+	0.908608i
$633$		0			0
$634$	−3421.20	+	9425.59i	−0.214311	+	0.590439i
$635$	−30597.8			−1.91218
$636$		0			0
$637$	−377.698	+	1762.62i	−0.0234928	+	0.109635i
$638$	18277.1	+	6634.00i	1.13416	+	0.411665i
$639$		0			0
$640$	−21476.2	+	18248.5i	−1.32644	+	1.12709i
$641$	1369.18			0.0843675			0.0421837	−	0.999110i	$-0.486569\pi$
$641$	1369.18			0.0843675			0.0421837	+	0.999110i	$0.486569\pi$
$642$		0			0
$643$	24036.2			1.47417			0.737087	−	0.675797i	$-0.236201\pi$
$643$	24036.2			1.47417			0.737087	+	0.675797i	$0.236201\pi$
$644$	−11162.5	−	11537.3i	−0.683019	−	0.705952i
$645$		0			0
$646$	−18621.1	−	6758.89i	−1.13412	−	0.411649i
$647$	13781.3			0.837403			0.418702	−	0.908124i	$-0.362485\pi$
$647$	13781.3			0.837403			0.418702	+	0.908124i	$0.362485\pi$
$648$		0			0
$649$			18076.1i			1.09330i
$650$	−3545.19	−	1286.79i	−0.213929	−	0.0776496i
$651$		0			0
$652$	−1923.66	+	2300.78i	−0.115547	+	0.138199i
$653$	10312.2			0.617991			0.308995	−	0.951064i	$-0.400007\pi$
$653$	10312.2			0.617991			0.308995	+	0.951064i	$0.400007\pi$
$654$		0			0
$655$		−	18329.4i		−	1.09342i
$656$	19120.3	−	3441.24i	1.13799	−	0.204814i
$657$		0			0
$658$	4815.46	+	2348.30i	0.285298	+	0.139128i
$659$		−	18371.4i		−	1.08596i	−0.839745	−	0.542980i	$-0.817296\pi$
$659$		−	18371.4i		−	1.08596i	0.839745	−	0.542980i	$-0.182704\pi$
$660$		0			0
$661$		−	19068.1i		−	1.12203i	−0.827806	−	0.561015i	$-0.810411\pi$
$661$		−	19068.1i		−	1.12203i	0.827806	−	0.561015i	$-0.189589\pi$
$662$	14570.8	+	5288.73i	0.855452	+	0.310502i
$663$		0			0
$664$	17868.1	−	10379.5i	1.04430	−	0.606629i
$665$	−31035.7	−	3287.88i	−1.80979	−	0.191727i
$666$		0			0
$667$			30202.0i			1.75326i
$668$	6053.31	+	5061.11i	0.350613	+	0.293144i
$669$		0			0
$670$	3135.70	−	8639.04i	0.180810	−	0.498142i
$671$	−10929.1			−0.628784
$672$		0			0
$673$	−5215.69			−0.298737			−0.149368	−	0.988782i	$-0.547724\pi$
$673$	−5215.69			−0.298737			−0.149368	+	0.988782i	$0.547724\pi$
$674$	137.089	−	377.688i	0.00783453	−	0.0215846i
$675$		0			0
$676$	−13314.4	−	11132.1i	−0.757536	−	0.633367i
$677$		−	5346.63i		−	0.303527i	−0.988417	−	0.151764i	$-0.951505\pi$
$677$		−	5346.63i		−	0.303527i	0.988417	−	0.151764i	$-0.0484952\pi$
$678$		0			0
$679$	−26622.4	−	2820.34i	−1.50467	−	0.159403i
$680$	−30797.5	+	17890.1i	−1.73681	+	1.00890i
$681$		0			0
$682$	−7639.55	−	2772.92i	−0.428935	−	0.155690i
$683$			7087.40i			0.397060i	0.980095	+	0.198530i	$0.0636167\pi$
$683$			7087.40i			0.397060i	−0.980095	+	0.198530i	$0.936383\pi$
$684$		0			0
$685$		−	40623.5i		−	2.26591i
$686$	14140.9	+	11084.4i	0.787030	+	0.616915i
$687$		0			0
$688$	11121.5	−	2001.62i	0.616281	−	0.110917i
$689$			977.170i			0.0540308i
$690$		0			0
$691$	29981.3			1.65057			0.825284	−	0.564718i	$-0.191015\pi$
$691$	29981.3			1.65057			0.825284	+	0.564718i	$0.191015\pi$
$692$	8306.68	−	9935.16i	0.456319	−	0.545778i
$693$		0			0
$694$	−2940.59	−	1067.34i	−0.160841	−	0.0583801i
$695$			36867.7i			2.01219i
$696$		0			0
$697$	24552.5			1.33428
$698$	14129.9	+	5128.71i	0.766224	+	0.278115i
$699$		0			0
$700$	−27016.7	+	26139.0i	−1.45876	+	1.41137i
$701$	4928.54			0.265547			0.132773	−	0.991146i	$-0.457612\pi$
$701$	4928.54			0.265547			0.132773	+	0.991146i	$0.457612\pi$
$702$		0			0
$703$	4634.43			0.248636
$704$	10968.7	+	6255.37i	0.587211	+	0.334883i
$705$		0			0
$706$	−28131.7	−	10210.9i	−1.49965	−	0.544326i
$707$	4426.55	+	468.943i	0.235470	+	0.0249454i
$708$		0			0
$709$	22659.0			1.20025			0.600125	−	0.799906i	$-0.295117\pi$
$709$	22659.0			1.20025			0.600125	+	0.799906i	$0.295117\pi$
$710$	−7099.36	+	19559.2i	−0.375260	+	1.03386i
$711$		0			0
$712$	17020.5	+	29300.5i	0.895884	+	1.54225i
$713$		−	12624.0i		−	0.663074i
$714$		0			0
$715$			2522.33i			0.131930i
$716$	−18951.9	+	22667.3i	−0.989198	+	1.18313i
$717$		0			0
$718$	−7075.00	−	2568.01i	−0.367739	−	0.133478i
$719$	23078.3			1.19705			0.598523	−	0.801106i	$-0.295754\pi$
$719$	23078.3			1.19705			0.598523	+	0.801106i	$0.295754\pi$
$720$		0			0
$721$	3314.37	−	31285.7i	0.171198	−	1.61601i
$722$	−616.820	+	1699.38i	−0.0317946	+	0.0875959i
$723$		0			0
$724$	12557.1	−	15018.9i	0.644588	−	0.770956i
$725$	70723.3			3.62289
$726$		0			0
$727$	−24974.6			−1.27408			−0.637039	−	0.770831i	$-0.719841\pi$
$727$	−24974.6			−1.27408			−0.637039	+	0.770831i	$0.719841\pi$
$728$	2010.35	−	899.472i	0.102347	−	0.0457921i
$729$		0			0
$730$	−12485.5	+	34398.3i	−0.633027	+	1.74403i
$731$	14281.1			0.722580
$732$		0			0
$733$		−	642.353i		−	0.0323682i	−0.999869	−	0.0161841i	$-0.994848\pi$
$733$		−	642.353i		−	0.0323682i	0.999869	−	0.0161841i	$-0.00515178\pi$
$734$	−5689.50	+	15674.9i	−0.286108	+	0.788244i
$735$		0			0
$736$	−3320.37	+	19330.4i	−0.166292	+	0.968107i
$737$	−4117.80			−0.205809
$738$		0			0
$739$		−	32931.9i		−	1.63927i	−0.572888	−	0.819633i	$-0.694177\pi$
$739$		−	32931.9i		−	1.63927i	0.572888	−	0.819633i	$-0.305823\pi$
$740$	5344.64	−	6392.43i	0.265504	−	0.317555i
$741$		0			0
$742$	8754.31	+	4269.12i	0.433128	+	0.211219i
$743$			24636.6i			1.21646i	0.793762	+	0.608229i	$0.208120\pi$
$743$			24636.6i			1.21646i	−0.793762	+	0.608229i	$0.791880\pi$
$744$		0			0
$745$			48772.6i			2.39851i
$746$	5991.40	−	16506.6i	0.294049	−	0.810122i
$747$		0			0
$748$	12242.7	+	10236.0i	0.598444	+	0.500352i
$749$	−5287.12	−	560.110i	−0.257927	−	0.0273244i
$750$		0			0
$751$			32225.0i			1.56579i	0.622156	+	0.782893i	$0.286257\pi$
$751$			32225.0i			1.56579i	−0.622156	+	0.782893i	$0.713743\pi$
$752$	−1159.44	−	6442.14i	−0.0562241	−	0.312395i
$753$		0			0
$754$	−3894.84	−	1413.70i	−0.188119	−	0.0682812i
$755$	−9049.93			−0.436240
$756$		0			0
$757$	−16949.5			−0.813792			−0.406896	−	0.913474i	$-0.633389\pi$
$757$	−16949.5			−0.813792			−0.406896	+	0.913474i	$0.633389\pi$
$758$	−9392.50	−	3409.18i	−0.450067	−	0.163360i
$759$		0			0
$760$	19152.8	+	32971.3i	0.914139	+	1.57368i
$761$		−	3896.80i		−	0.185623i	−0.995684	−	0.0928114i	$-0.970415\pi$
$761$		−	3896.80i		−	0.185623i	0.995684	−	0.0928114i	$-0.0295854\pi$
$762$		0			0
$763$	29.1975	−	275.607i	0.00138535	−	0.0130769i
$764$	−47.2079	+	56.4628i	−0.00223550	+	0.00267376i
$765$		0			0
$766$	−9052.69	+	24940.7i	−0.427006	+	1.17643i
$767$		−	3852.01i		−	0.181340i
$768$		0			0
$769$		−	18651.6i		−	0.874634i	−0.899307	−	0.437317i	$-0.855929\pi$
$769$		−	18651.6i		−	0.874634i	0.899307	−	0.437317i	$-0.144071\pi$
$770$	22597.2	+	11019.7i	1.05759	+	0.515745i
$771$		0			0
$772$	9014.18	+	7536.66i	0.420243	+	0.351361i
$773$		−	30262.1i		−	1.40809i	−0.710156	−	0.704045i	$-0.751376\pi$
$773$		−	30262.1i		−	1.40809i	0.710156	−	0.704045i	$-0.248624\pi$
$774$		0			0
$775$	−29561.3			−1.37016
$776$	16429.3	+	28282.7i	0.760021	+	1.30836i
$777$		0			0
$778$	5082.94	−	14003.8i	0.234232	−	0.645321i
$779$		−	26285.5i		−	1.20895i
$780$		0			0
$781$	9322.87			0.427143
$782$	−8457.21	+	23300.1i	−0.386738	+	1.06549i
$783$		0			0
$784$	724.695	−	21940.0i	0.0330127	−	0.999455i
$785$	8586.42			0.390398
$786$		0			0
$787$	−25673.9			−1.16286			−0.581432	−	0.813595i	$-0.697507\pi$
$787$	−25673.9			−1.16286			−0.581432	+	0.813595i	$0.697507\pi$
$788$	24025.9	+	20087.8i	1.08615	+	0.908118i
$789$		0			0
$790$	13856.5	−	38175.5i	0.624041	−	1.71927i
$791$	−1438.38	+	13577.4i	−0.0646558	+	0.610314i
$792$		0			0
$793$	2328.99			0.104294
$794$	−22639.8	−	8217.54i	−1.01191	−	0.367292i
$795$		0			0
$796$	18168.2	+	15190.2i	0.808987	+	0.676385i
$797$			9725.85i			0.432255i	0.976365	+	0.216127i	$0.0693427\pi$
$797$			9725.85i			0.432255i	−0.976365	+	0.216127i	$0.930657\pi$
$798$		0			0
$799$		−	8272.39i		−	0.366278i
$800$	45265.5	+	7775.25i	2.00047	+	0.343621i
$801$		0			0
$802$	−2706.47	+	7456.49i	−0.119163	+	0.328301i
$803$	16396.0			0.720549
$804$		0			0
$805$	−4114.03	+	38834.1i	−0.180125	+	1.70027i
$806$	1627.99	+	590.908i	0.0711456	+	0.0258236i
$807$		0			0
$808$	−2731.72	−	4702.62i	−0.118938	−	0.204749i
$809$	−22322.4			−0.970106			−0.485053	−	0.874485i	$-0.661200\pi$
$809$	−22322.4			−0.970106			−0.485053	+	0.874485i	$0.661200\pi$
$810$		0			0
$811$	−8693.62			−0.376417			−0.188209	−	0.982129i	$-0.560268\pi$
$811$	−8693.62			−0.376417			−0.188209	+	0.982129i	$0.560268\pi$
$812$	−29681.1	+	28716.9i	−1.28276	+	1.24109i
$813$		0			0
$814$	−3509.29	−	1273.76i	−0.151106	−	0.0548468i
$815$	7295.38			0.313553
$816$		0			0
$817$		−	15289.1i		−	0.654710i
$818$	−36752.4	−	13340.0i	−1.57093	−	0.570197i
$819$		0			0
$820$	−36256.4	−	30313.6i	−1.54406	−	1.29097i
$821$	15530.6			0.660196			0.330098	−	0.943947i	$-0.392918\pi$
$821$	15530.6			0.660196			0.330098	+	0.943947i	$0.392918\pi$
$822$		0			0
$823$			37619.9i			1.59337i	0.604392	+	0.796687i	$0.293416\pi$
$823$			37619.9i			1.59337i	−0.604392	+	0.796687i	$0.706584\pi$
$824$	−33236.9	+	19307.1i	−1.40517	+	0.816256i
$825$		0			0
$826$	−34509.6	−	16828.9i	−1.45368	−	0.708902i
$827$		−	22298.2i		−	0.937587i	−0.883308	−	0.468794i	$-0.844689\pi$
$827$		−	22298.2i		−	0.937587i	0.883308	−	0.468794i	$-0.155311\pi$
$828$		0			0
$829$		−	26664.3i		−	1.11712i	−0.829465	−	0.558559i	$-0.811354\pi$
$829$		−	26664.3i		−	1.11712i	0.829465	−	0.558559i	$-0.188646\pi$
$830$	−47250.9	−	17150.6i	−1.97603	−	0.717236i
$831$		0			0
$832$	−2337.42	−	1333.02i	−0.0973983	−	0.0555457i
$833$	5812.86	−	27127.1i	0.241781	−	1.12833i
$834$		0			0
$835$		−	19194.0i		−	0.795491i
$836$	10958.4	−	13106.8i	0.453355	−	0.542233i
$837$		0			0
$838$	−4871.38	+	13420.9i	−0.200810	+	0.553244i
$839$	−33449.9			−1.37642			−0.688212	−	0.725510i	$-0.741604\pi$
$839$	−33449.9			−1.37642			−0.688212	+	0.725510i	$0.741604\pi$
$840$		0			0
$841$	53309.3			2.18579
$842$	−6241.12	+	17194.6i	−0.255443	+	0.703761i
$843$		0			0
$844$	−6820.36	+	8157.46i	−0.278159	+	0.332691i
$845$			42217.8i			1.71874i
$846$		0			0
$847$	−1410.21	+	13311.6i	−0.0572084	+	0.540014i
$848$	−2107.82	−	11711.6i	−0.0853572	−	0.474265i
$849$		0			0
$850$	54561.4	+	19804.1i	2.20169	+	0.799146i
$851$		−	5798.93i		−	0.233590i
$852$		0			0
$853$			47864.2i			1.92127i	0.277822	+	0.960633i	$0.410387\pi$
$853$			47864.2i			1.92127i	−0.277822	+	0.960633i	$0.589613\pi$
$854$	10175.1	−	20865.1i	0.407709	−	0.836052i
$855$		0			0
$856$	3262.80	+	5616.86i	0.130281	+	0.224276i
$857$			2792.59i			0.111310i	0.998450	+	0.0556552i	$0.0177248\pi$
$857$			2792.59i			0.111310i	−0.998450	+	0.0556552i	$0.982275\pi$
$858$		0			0
$859$	24841.7			0.986715			0.493357	−	0.869827i	$-0.335769\pi$
$859$	24841.7			0.986715			0.493357	+	0.869827i	$0.335769\pi$
$860$	−21088.8	−	17632.1i	−0.836188	−	0.699127i
$861$		0			0
$862$	−34031.3	−	12352.3i	−1.34468	−	0.488076i
$863$			12119.8i			0.478058i	0.971012	+	0.239029i	$0.0768291\pi$
$863$			12119.8i			0.478058i	−0.971012	+	0.239029i	$0.923171\pi$
$864$		0			0
$865$	−31502.7			−1.23829
$866$	−19021.1	−	6904.08i	−0.746380	−	0.270912i
$867$		0			0
$868$	12406.3	−	12003.3i	0.485135	−	0.469375i
$869$	−18196.3			−0.710321
$870$		0			0
$871$	877.502			0.0341366
$872$	−292.796	+	170.083i	−0.0113708	+	0.00660522i
$873$		0			0
$874$	24944.7	+	9054.13i	0.965407	+	0.350413i
$875$	46135.3	+	4887.52i	1.78247	+	0.188832i
$876$		0			0
$877$	14849.8			0.571770			0.285885	−	0.958264i	$-0.407712\pi$
$877$	14849.8			0.571770			0.285885	+	0.958264i	$0.407712\pi$
$878$	10315.0	−	28418.3i	0.396484	−	1.09234i
$879$		0			0
$880$	−5440.84	−	30230.6i	−0.208421	−	1.15804i
$881$			20213.3i			0.772990i	0.922291	+	0.386495i	$0.126314\pi$
$881$			20213.3i			0.772990i	−0.922291	+	0.386495i	$0.873686\pi$
$882$		0			0
$883$			9218.17i			0.351321i	0.984451	+	0.175660i	$0.0562061\pi$
$883$			9218.17i			0.351321i	−0.984451	+	0.175660i	$0.943794\pi$
$884$	−2608.91	−	2181.28i	−0.0992613	−	0.0829913i
$885$		0			0
$886$	12370.8	+	4490.22i	0.469081	+	0.170262i
$887$	42349.9			1.60312			0.801561	−	0.597913i	$-0.204003\pi$
$887$	42349.9			1.60312			0.801561	+	0.597913i	$0.204003\pi$
$888$		0			0
$889$	−28957.0	−	3067.67i	−1.09245	−	0.115733i
$890$	28123.9	−	77483.1i	1.05923	−	2.91825i
$891$		0			0
$892$	−5221.28	−	4365.45i	−0.195988	−	0.163863i
$893$	−8856.26			−0.331874
$894$		0			0
$895$	71874.1			2.68434
$896$	−22154.1	+	15116.8i	−0.826024	+	0.563634i
$897$		0			0
$898$	16136.2	−	44456.1i	0.599634	−	1.65203i
$899$	−32476.8			−1.20485
$900$		0			0
$901$		−	15038.9i		−	0.556068i
$902$	−7224.50	+	19903.9i	−0.266684	+	0.734731i
$903$		0			0
$904$	14424.2	−	8378.94i	0.530688	−	0.308274i
$905$	−47622.2			−1.74919
$906$		0			0
$907$		−	40185.9i		−	1.47117i	−0.677432	−	0.735586i	$-0.736907\pi$
$907$		−	40185.9i		−	1.47117i	0.677432	−	0.735586i	$-0.263093\pi$
$908$	−16120.6	−	13478.3i	−0.589186	−	0.492612i
$909$		0			0
$910$	−4815.46	−	2348.30i	−0.175418	−	0.0855444i
$911$			11410.6i			0.414984i	0.978237	+	0.207492i	$0.0665301\pi$
$911$			11410.6i			0.414984i	−0.978237	+	0.207492i	$0.933470\pi$
$912$		0			0
$913$			22522.2i			0.816401i
$914$	7306.33	−	20129.4i	0.264411	−	0.728469i
$915$		0			0
$916$	8628.77	−	10320.4i	0.311247	−	0.372266i
$917$	1837.67	−	17346.5i	0.0661779	−	0.624680i
$918$		0			0
$919$		−	27571.5i		−	0.989662i	−0.868989	−	0.494831i	$-0.835230\pi$
$919$		−	27571.5i		−	0.989662i	0.868989	−	0.494831i	$-0.164770\pi$
$920$	41256.0	−	23965.4i	1.47845	−	0.858821i
$921$		0			0
$922$	−22359.9	−	8115.95i	−0.798682	−	0.289896i
$923$	−1986.70			−0.0708484
$924$		0			0
$925$	−13579.2			−0.482684
$926$	−26852.9	−	9746.77i	−0.952961	−	0.345895i
$927$		0			0
$928$	49729.8	+	8542.08i	1.75912	+	0.302163i
$929$			25071.2i			0.885424i	0.896664	+	0.442712i	$0.145984\pi$
$929$			25071.2i			0.885424i	−0.896664	+	0.442712i	$0.854016\pi$
$930$		0			0
$931$	−29041.8	−	6223.14i	−1.02235	−	0.219071i
$932$	−11200.0	−	9364.19i	−0.393635	−	0.329114i
$933$		0			0
$934$	1942.36	−	5351.32i	0.0680471	−	0.187474i
$935$		−	38819.3i		−	1.35778i
$936$		0			0
$937$			19811.3i			0.690721i	0.938470	+	0.345360i	$0.112243\pi$
$937$			19811.3i			0.690721i	−0.938470	+	0.345360i	$0.887757\pi$
$938$	3833.68	−	7861.40i	0.133448	−	0.273650i
$939$		0			0
$940$	−10213.5	+	12215.7i	−0.354389	+	0.423866i
$941$		−	3182.72i		−	0.110259i	−0.998479	−	0.0551295i	$-0.982443\pi$
$941$		−	3182.72i		−	0.110259i	0.998479	−	0.0551295i	$-0.0175572\pi$
$942$		0			0
$943$	−32890.3			−1.13579
$944$	8309.05	+	46167.1i	0.286479	+	1.59175i
$945$		0			0
$946$	−4202.17	+	11577.2i	−0.144423	+	0.397894i
$947$			25087.2i			0.860848i	0.902627	+	0.430424i	$0.141636\pi$
$947$			25087.2i			0.860848i	−0.902627	+	0.430424i	$0.858364\pi$
$948$		0			0
$949$	−3493.97			−0.119514
$950$	21201.9	−	58412.4i	0.724084	−	1.99489i
$951$		0			0
$952$	−30939.7	+	13843.1i	−1.05332	+	0.471278i
$953$	−247.587			−0.00841568			−0.00420784	−	0.999991i	$-0.501339\pi$
$953$	−247.587			−0.00841568			−0.00420784	+	0.999991i	$0.501339\pi$
$954$		0			0
$955$	179.034			0.00606638
$956$	3982.39	−	4763.12i	0.134728	−	0.161141i
$957$		0			0
$958$	−12834.8	+	35360.6i	−0.432853	+	1.19253i
$959$	4072.83	−	38445.1i	0.137141	−	1.29453i
$960$		0			0
$961$	−16216.2			−0.544331
$962$	747.828	+	271.438i	0.0250634	+	0.00909722i
$963$		0			0
$964$	−208.290	+	249.124i	−0.00695909	+	0.00832339i
$965$		−	28582.4i		−	0.953471i
$966$		0			0
$967$		−	31623.0i		−	1.05163i	−0.850598	−	0.525816i	$-0.823760\pi$
$967$		−	31623.0i		−	1.05163i	0.850598	−	0.525816i	$-0.176240\pi$
$968$	14141.8	−	8214.89i	0.469561	−	0.272765i
$969$		0			0
$970$	27147.1	−	74791.7i	0.898597	−	2.47569i
$971$	−33729.9			−1.11477			−0.557386	−	0.830253i	$-0.688196\pi$
$971$	−33729.9			−1.11477			−0.557386	+	0.830253i	$0.688196\pi$
$972$		0			0
$973$	−3696.28	+	34890.7i	−0.121785	+	1.14958i
$974$	6879.73	+	2497.13i	0.226325	+	0.0821490i
$975$		0			0
$976$	−27913.4	+	5023.80i	−0.915458	+	0.164762i
$977$	45295.7			1.48325			0.741626	−	0.670813i	$-0.234055\pi$
$977$	45295.7			1.48325			0.741626	+	0.670813i	$0.234055\pi$
$978$		0			0
$979$	−36932.3			−1.20568
$980$	−42076.1	+	32881.5i	−1.37150	+	1.07180i
$981$		0			0
$982$	−1564.66	−	567.923i	−0.0508456	−	0.0184554i
$983$	−43789.8			−1.42083			−0.710416	−	0.703782i	$-0.751493\pi$
$983$	−43789.8			−1.42083			−0.710416	+	0.703782i	$0.751493\pi$
$984$		0			0
$985$		−	76181.8i		−	2.46432i
$986$	59942.4	+	21757.2i	1.93606	+	0.702730i
$987$		0			0
$988$	−2335.24	+	2793.05i	−0.0751961	+	0.0899379i
$989$	−19130.8			−0.615090
$990$		0			0
$991$			398.825i			0.0127842i	0.999980	+	0.00639208i	$0.00203468\pi$
$991$			398.825i			0.0127842i	−0.999980	+	0.00639208i	$0.997965\pi$
$992$	−20786.3	−	3570.47i	−0.665289	−	0.114277i
$993$		0			0
$994$	−8679.63	+	17798.5i	−0.276963	+	0.567943i
$995$		−	57608.1i		−	1.83548i
$996$		0			0
$997$		−	40219.6i		−	1.27760i	−0.769373	−	0.638800i	$-0.779431\pi$
$997$		−	40219.6i		−	1.27760i	0.769373	−	0.638800i	$-0.220569\pi$
$998$	42555.2	+	15446.2i	1.34976	+	0.489921i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.4.b.e.55.6		12
3.2	odd	2		84.4.b.b.55.7	yes	12
4.3	odd	2		252.4.b.f.55.5		12
7.6	odd	2		252.4.b.f.55.6		12
12.11	even	2		84.4.b.a.55.8	yes	12
21.20	even	2		84.4.b.a.55.7	✓	12
24.5	odd	2		1344.4.b.g.895.12		12
24.11	even	2		1344.4.b.h.895.12		12
28.27	even	2	inner	252.4.b.e.55.5		12
84.83	odd	2		84.4.b.b.55.8	yes	12
168.83	odd	2		1344.4.b.g.895.1		12
168.125	even	2		1344.4.b.h.895.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
84.4.b.a.55.7	✓	12	21.20	even	2
84.4.b.a.55.8	yes	12	12.11	even	2
84.4.b.b.55.7	yes	12	3.2	odd	2
84.4.b.b.55.8	yes	12	84.83	odd	2
252.4.b.e.55.5		12	28.27	even	2	inner
252.4.b.e.55.6		12	1.1	even	1	trivial
252.4.b.f.55.5		12	4.3	odd	2
252.4.b.f.55.6		12	7.6	odd	2
1344.4.b.g.895.1		12	168.83	odd	2
1344.4.b.g.895.12		12	24.5	odd	2
1344.4.b.h.895.1		12	168.125	even	2
1344.4.b.h.895.12		12	24.11	even	2

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:	\( N \)	\(=\)	\( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	252.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.965027 + 2.65871i) q^{2} +(-6.13744 - 5.13145i) q^{4} +19.4608i q^{5} +(-1.95109 + 18.4172i) q^{7} +(19.5658 - 11.3657i) q^{8} +O(q^{10})\)	\(q+(-0.965027 + 2.65871i) q^{2} +(-6.13744 - 5.13145i) q^{4} +19.4608i q^{5} +(-1.95109 + 18.4172i) q^{7} +(19.5658 - 11.3657i) q^{8} +(-51.7405 - 18.7802i) q^{10} +24.6621i q^{11} -5.25549i q^{13} +(-47.0831 - 22.9605i) q^{14} +(11.3364 + 62.9880i) q^{16} +80.8832i q^{17} +86.5920 q^{19} +(99.8619 - 119.439i) q^{20} +(-65.5693 - 23.7996i) q^{22} -108.350i q^{23} -253.721 q^{25} +(13.9728 + 5.07169i) q^{26} +(106.482 - 103.023i) q^{28} -278.744 q^{29} +116.511 q^{31} +(-178.407 - 30.6449i) q^{32} +(-215.045 - 78.0545i) q^{34} +(-358.413 - 37.9698i) q^{35} +53.5203 q^{37} +(-83.5637 + 230.223i) q^{38} +(221.185 + 380.766i) q^{40} -303.555i q^{41} -176.565i q^{43} +(126.552 - 151.362i) q^{44} +(288.071 + 104.561i) q^{46} -102.276 q^{47} +(-335.386 - 71.8674i) q^{49} +(244.848 - 674.570i) q^{50} +(-26.9683 + 32.2552i) q^{52} -185.933 q^{53} -479.943 q^{55} +(171.149 + 382.523i) q^{56} +(268.996 - 741.099i) q^{58} +732.951 q^{59} +443.155i q^{61} +(-112.436 + 309.769i) q^{62} +(253.643 - 444.758i) q^{64} +102.276 q^{65} +166.969i q^{67} +(415.048 - 496.416i) q^{68} +(446.829 - 916.272i) q^{70} -378.024i q^{71} -664.824i q^{73} +(-51.6486 + 142.295i) q^{74} +(-531.454 - 444.343i) q^{76} +(-454.207 - 48.1181i) q^{77} +737.826i q^{79} +(-1225.79 + 220.616i) q^{80} +(807.065 + 292.939i) q^{82} +913.229 q^{83} -1574.05 q^{85} +(469.434 + 170.390i) q^{86} +(280.301 + 482.534i) q^{88} +1497.53i q^{89} +(96.7913 + 10.2540i) q^{91} +(-555.993 + 664.993i) q^{92} +(98.6989 - 271.921i) q^{94} +1685.15i q^{95} +1445.52i q^{97} +(514.732 - 822.340i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - q^{2} + 5 q^{4} - 10 q^{7} - 25 q^{8}+O(q^{10}) \) 12 * q - q^2 + 5 * q^4 - 10 * q^7 - 25 * q^8	\( 12 q - q^{2} + 5 q^{4} - 10 q^{7} - 25 q^{8} - 56 q^{10} - 101 q^{14} + 41 q^{16} + 84 q^{19} + 172 q^{20} - 182 q^{22} - 216 q^{25} + 300 q^{26} - 379 q^{28} - 200 q^{29} + 384 q^{31} + 159 q^{32} + 164 q^{34} + 84 q^{35} - 244 q^{37} + 268 q^{38} + 316 q^{40} - 190 q^{44} + 894 q^{46} + 280 q^{47} - 424 q^{49} + 1771 q^{50} + 796 q^{52} + 16 q^{53} - 212 q^{55} + 1759 q^{56} - 570 q^{58} + 1168 q^{59} - 384 q^{62} + 2705 q^{64} - 280 q^{65} + 1552 q^{68} + 2592 q^{70} - 1622 q^{74} + 788 q^{76} - 968 q^{77} - 3060 q^{80} + 2540 q^{82} - 968 q^{83} - 852 q^{85} + 258 q^{86} - 2186 q^{88} - 1648 q^{91} - 4298 q^{92} - 4256 q^{94} - 3137 q^{98}+O(q^{100}) \) 12 * q - q^2 + 5 * q^4 - 10 * q^7 - 25 * q^8 - 56 * q^10 - 101 * q^14 + 41 * q^16 + 84 * q^19 + 172 * q^20 - 182 * q^22 - 216 * q^25 + 300 * q^26 - 379 * q^28 - 200 * q^29 + 384 * q^31 + 159 * q^32 + 164 * q^34 + 84 * q^35 - 244 * q^37 + 268 * q^38 + 316 * q^40 - 190 * q^44 + 894 * q^46 + 280 * q^47 - 424 * q^49 + 1771 * q^50 + 796 * q^52 + 16 * q^53 - 212 * q^55 + 1759 * q^56 - 570 * q^58 + 1168 * q^59 - 384 * q^62 + 2705 * q^64 - 280 * q^65 + 1552 * q^68 + 2592 * q^70 - 1622 * q^74 + 788 * q^76 - 968 * q^77 - 3060 * q^80 + 2540 * q^82 - 968 * q^83 - 852 * q^85 + 258 * q^86 - 2186 * q^88 - 1648 * q^91 - 4298 * q^92 - 4256 * q^94 - 3137 * q^98

Introduction

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