LMFDB - Embedded newform 224.3.n.a.145.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [224,3,Mod(17,224)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(224, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 1]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("224.17");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 224 = 2^{5} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	224.n (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.10355792167$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 56)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			145.3
Character	$\chi$	$=$	224.145
Dual form			224.3.n.a.17.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.93494 - 3.35141i) q^{3} +(2.33882 - 4.05096i) q^{5} +(-6.95505 - 0.792023i) q^{7} +(-2.98798 + 5.17534i) q^{9} +O(q^{10})$	\(q+(-1.93494 - 3.35141i) q^{3} +(2.33882 - 4.05096i) q^{5} +(-6.95505 - 0.792023i) q^{7} +(-2.98798 + 5.17534i) q^{9} +(12.6383 - 7.29671i) q^{11} -12.7102 q^{13} -18.1019 q^{15} +(-16.9068 + 9.76116i) q^{17} +(-8.86233 + 15.3500i) q^{19} +(10.8032 + 24.8418i) q^{21} +(4.43038 - 7.67364i) q^{23} +(1.55984 + 2.70172i) q^{25} -11.7027 q^{27} -35.4981i q^{29} +(-25.1331 + 14.5106i) q^{31} +(-48.9086 - 28.2374i) q^{33} +(-19.4751 + 26.3222i) q^{35} +(-10.5802 - 6.10847i) q^{37} +(24.5934 + 42.5970i) q^{39} -22.0903i q^{41} -79.8001i q^{43} +(13.9767 + 24.2084i) q^{45} +(36.5041 + 21.0756i) q^{47} +(47.7454 + 11.0171i) q^{49} +(65.4273 + 37.7745i) q^{51} +(31.3096 - 18.0766i) q^{53} -68.2627i q^{55} +68.5923 q^{57} +(1.20348 + 2.08449i) q^{59} +(14.6224 - 25.3268i) q^{61} +(24.8805 - 33.6282i) q^{63} +(-29.7268 + 51.4883i) q^{65} +(-35.2303 + 20.3402i) q^{67} -34.2900 q^{69} +22.6174 q^{71} +(66.1587 - 38.1967i) q^{73} +(6.03639 - 10.4553i) q^{75} +(-93.6789 + 40.7391i) q^{77} +(68.4014 - 118.475i) q^{79} +(49.5358 + 85.7985i) q^{81} -49.9942 q^{83} +91.3184i q^{85} +(-118.969 + 68.6866i) q^{87} +(0.970023 + 0.560043i) q^{89} +(88.3998 + 10.0667i) q^{91} +(97.2622 + 56.1544i) q^{93} +(41.4548 + 71.8018i) q^{95} -158.827i q^{97} +87.2097i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 4 q^{7} - 32 q^{9}+O(q^{10}) $ 28 * q + 4 * q^7 - 32 * q^9	$ 28 q + 4 q^{7} - 32 q^{9} - 28 q^{15} - 6 q^{17} - 30 q^{23} - 32 q^{25} + 6 q^{31} - 6 q^{33} + 20 q^{39} + 294 q^{47} - 20 q^{49} + 124 q^{57} - 432 q^{63} - 52 q^{65} + 136 q^{71} + 234 q^{73} + 162 q^{79} - 18 q^{81} - 48 q^{87} - 150 q^{89} - 290 q^{95}+O(q^{100}) $ 28 * q + 4 * q^7 - 32 * q^9 - 28 * q^15 - 6 * q^17 - 30 * q^23 - 32 * q^25 + 6 * q^31 - 6 * q^33 + 20 * q^39 + 294 * q^47 - 20 * q^49 + 124 * q^57 - 432 * q^63 - 52 * q^65 + 136 * q^71 + 234 * q^73 + 162 * q^79 - 18 * q^81 - 48 * q^87 - 150 * q^89 - 290 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/224\mathbb{Z}\right)^\times$.

$n$	$127$	$129$	$197$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$-1$

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
$3$	−1.93494	−	3.35141i	−0.644980	−	1.11714i	−0.984306	−	0.176469i	$-0.943532\pi$
$3$	−1.93494	−	3.35141i	−0.644980	−	1.11714i	0.339326	−	0.940669i	$-0.389801\pi$
$4$		0			0
$5$	2.33882	−	4.05096i	0.467764	−	0.810191i	−0.531557	−	0.847022i	$-0.678393\pi$
$5$	2.33882	−	4.05096i	0.467764	−	0.810191i	0.999322	+	0.0368311i	$0.0117264\pi$
$6$		0			0
$7$	−6.95505	−	0.792023i	−0.993578	−	0.113146i
$7$	−6.95505	−	0.792023i	−0.993578	−	0.113146i
$8$		0			0
$9$	−2.98798	+	5.17534i	−0.331998	+	0.575037i
$10$		0			0
$11$	12.6383	−	7.29671i	1.14893	−	0.663337i	0.200306	−	0.979733i	$-0.435806\pi$
$11$	12.6383	−	7.29671i	1.14893	−	0.663337i	0.948627	+	0.316396i	$0.102473\pi$
$12$		0			0
$13$	−12.7102			−0.977705			−0.488853	−	0.872366i	$-0.662584\pi$
$13$	−12.7102			−0.977705			−0.488853	+	0.872366i	$0.662584\pi$
$14$		0			0
$15$	−18.1019			−1.20679
$16$		0			0
$17$	−16.9068	+	9.76116i	−0.994519	+	0.574186i	−0.906622	−	0.421944i	$-0.861348\pi$
$17$	−16.9068	+	9.76116i	−0.994519	+	0.574186i	−0.0878969	+	0.996130i	$0.528015\pi$
$18$		0			0
$19$	−8.86233	+	15.3500i	−0.466439	+	0.807895i	−0.999265	−	0.0383291i	$-0.987796\pi$
$19$	−8.86233	+	15.3500i	−0.466439	+	0.807895i	0.532827	+	0.846224i	$0.321130\pi$
$20$		0			0
$21$	10.8032	+	24.8418i	0.514438	+	1.18294i
$22$		0			0
$23$	4.43038	−	7.67364i	0.192625	−	0.333636i	−0.753494	−	0.657454i	$-0.771633\pi$
$23$	4.43038	−	7.67364i	0.192625	−	0.333636i	0.946119	+	0.323818i	$0.104967\pi$
$24$		0			0
$25$	1.55984	+	2.70172i	0.0623936	+	0.108069i
$26$		0			0
$27$	−11.7027			−0.433432
$28$		0			0
$29$		−	35.4981i		−	1.22407i	−0.790830	−	0.612036i	$-0.790351\pi$
$29$		−	35.4981i		−	1.22407i	0.790830	−	0.612036i	$-0.209649\pi$
$30$		0			0
$31$	−25.1331	+	14.5106i	−0.810747	+	0.468085i	−0.847215	−	0.531250i	$-0.821722\pi$
$31$	−25.1331	+	14.5106i	−0.810747	+	0.468085i	0.0364685	+	0.999335i	$0.488389\pi$
$32$		0			0
$33$	−48.9086	−	28.2374i	−1.48208	−	0.855678i
$34$		0			0
$35$	−19.4751	+	26.3222i	−0.556430	+	0.752063i
$36$		0			0
$37$	−10.5802	−	6.10847i	−0.285951	−	0.165094i	0.350163	−	0.936689i	$-0.386126\pi$
$37$	−10.5802	−	6.10847i	−0.285951	−	0.165094i	−0.636114	+	0.771595i	$0.719459\pi$
$38$		0			0
$39$	24.5934	+	42.5970i	0.630600	+	1.09223i
$40$		0			0
$41$		−	22.0903i		−	0.538788i	−0.963030	−	0.269394i	$-0.913177\pi$
$41$		−	22.0903i		−	0.538788i	0.963030	−	0.269394i	$-0.0868233\pi$
$42$		0			0
$43$		−	79.8001i		−	1.85582i	−0.372809	−	0.927908i	$-0.621605\pi$
$43$		−	79.8001i		−	1.85582i	0.372809	−	0.927908i	$-0.378395\pi$
$44$		0			0
$45$	13.9767	+	24.2084i	0.310593	+	0.537964i
$46$		0			0
$47$	36.5041	+	21.0756i	0.776682	+	0.448418i	0.835253	−	0.549865i	$-0.185321\pi$
$47$	36.5041	+	21.0756i	0.776682	+	0.448418i	−0.0585708	+	0.998283i	$0.518654\pi$
$48$		0			0
$49$	47.7454	+	11.0171i	0.974396	+	0.224839i
$50$		0			0
$51$	65.4273	+	37.7745i	1.28289	+	0.740676i
$52$		0			0
$53$	31.3096	−	18.0766i	0.590748	−	0.341068i	−0.174645	−	0.984631i	$-0.555878\pi$
$53$	31.3096	−	18.0766i	0.590748	−	0.341068i	0.765393	+	0.643563i	$0.222545\pi$
$54$		0			0
$55$		−	68.2627i		−	1.24114i
$56$		0			0
$57$	68.5923			1.20337
$58$		0			0
$59$	1.20348	+	2.08449i	0.0203979	+	0.0353303i	0.876044	−	0.482231i	$-0.160173\pi$
$59$	1.20348	+	2.08449i	0.0203979	+	0.0353303i	−0.855646	+	0.517561i	$0.826840\pi$
$60$		0			0
$61$	14.6224	−	25.3268i	0.239712	−	0.415194i	−0.720919	−	0.693019i	$-0.756280\pi$
$61$	14.6224	−	25.3268i	0.239712	−	0.415194i	0.960632	+	0.277825i	$0.0896136\pi$
$62$		0			0
$63$	24.8805	−	33.6282i	0.394929	−	0.533780i
$64$		0			0
$65$	−29.7268	+	51.4883i	−0.457335	+	0.792128i
$66$		0			0
$67$	−35.2303	+	20.3402i	−0.525825	+	0.303585i	−0.739315	−	0.673360i	$-0.764850\pi$
$67$	−35.2303	+	20.3402i	−0.525825	+	0.303585i	0.213490	+	0.976945i	$0.431517\pi$
$68$		0			0
$69$	−34.2900			−0.496957
$70$		0			0
$71$	22.6174			0.318554			0.159277	−	0.987234i	$-0.449084\pi$
$71$	22.6174			0.318554			0.159277	+	0.987234i	$0.449084\pi$
$72$		0			0
$73$	66.1587	−	38.1967i	0.906283	−	0.523243i	0.0270498	−	0.999634i	$-0.491389\pi$
$73$	66.1587	−	38.1967i	0.906283	−	0.523243i	0.879233	+	0.476391i	$0.158055\pi$
$74$		0			0
$75$	6.03639	−	10.4553i	0.0804852	−	0.139404i
$76$		0			0
$77$	−93.6789	+	40.7391i	−1.21661	+	0.529080i
$78$		0			0
$79$	68.4014	−	118.475i	0.865840	−	1.49968i	−0.000370612	−	1.00000i	$-0.500118\pi$
$79$	68.4014	−	118.475i	0.865840	−	1.49968i	0.866211	−	0.499679i	$-0.166549\pi$
$80$		0			0
$81$	49.5358	+	85.7985i	0.611553	+	1.05924i
$82$		0			0
$83$	−49.9942			−0.602340			−0.301170	−	0.953571i	$-0.597377\pi$
$83$	−49.9942			−0.602340			−0.301170	+	0.953571i	$0.597377\pi$
$84$		0			0
$85$			91.3184i			1.07433i
$86$		0			0
$87$	−118.969	+	68.6866i	−1.36746	+	0.789502i
$88$		0			0
$89$	0.970023	+	0.560043i	0.0108991	+	0.00629262i	0.505440	−	0.862862i	$-0.331330\pi$
$89$	0.970023	+	0.560043i	0.0108991	+	0.00629262i	−0.494541	+	0.869155i	$0.664664\pi$
$90$		0			0
$91$	88.3998	+	10.0667i	0.971427	+	0.110624i
$92$		0			0
$93$	97.2622	+	56.1544i	1.04583	+	0.603810i
$94$		0			0
$95$	41.4548	+	71.8018i	0.436366	+	0.755809i
$96$		0			0
$97$		−	158.827i		−	1.63740i	−0.574225	−	0.818698i	$-0.694696\pi$
$97$		−	158.827i		−	1.63740i	0.574225	−	0.818698i	$-0.305304\pi$
$98$		0			0
$99$			87.2097i			0.880906i
$100$		0			0
$101$	−34.8122	−	60.2965i	−0.344675	−	0.596995i	0.640620	−	0.767858i	$-0.278678\pi$
$101$	−34.8122	−	60.2965i	−0.344675	−	0.596995i	−0.985295	+	0.170864i	$0.945344\pi$
$102$		0			0
$103$	−16.9911	−	9.80983i	−0.164962	−	0.0952411i	0.415246	−	0.909709i	$-0.363696\pi$
$103$	−16.9911	−	9.80983i	−0.164962	−	0.0952411i	−0.580208	+	0.814468i	$0.697029\pi$
$104$		0			0
$105$	125.900	+	14.3371i	1.19904	+	0.136544i
$106$		0			0
$107$	−38.7540	−	22.3747i	−0.362187	−	0.209109i	0.307852	−	0.951434i	$-0.400390\pi$
$107$	−38.7540	−	22.3747i	−0.362187	−	0.209109i	−0.670040	+	0.742325i	$0.733723\pi$
$108$		0			0
$109$	−49.0210	+	28.3023i	−0.449734	+	0.259654i	−0.707718	−	0.706495i	$-0.750275\pi$
$109$	−49.0210	+	28.3023i	−0.449734	+	0.259654i	0.257984	+	0.966149i	$0.416942\pi$
$110$		0			0
$111$			47.2781i			0.425929i
$112$		0			0
$113$	−188.632			−1.66931			−0.834657	−	0.550770i	$-0.814334\pi$
$113$	−188.632			−1.66931			−0.834657	+	0.550770i	$0.814334\pi$
$114$		0			0
$115$	−20.7237	−	35.8945i	−0.180206	−	0.312126i
$116$		0			0
$117$	37.9777	−	65.7794i	0.324596	−	0.562217i
$118$		0			0
$119$	125.319	−	54.4987i	1.05310	−	0.457972i
$120$		0			0
$121$	45.9838	−	79.6463i	0.380032	−	0.658234i
$122$		0			0
$123$	−74.0337	+	42.7434i	−0.601900	+	0.347507i
$124$		0			0
$125$	131.534			1.05227
$126$		0			0
$127$	−45.8547			−0.361060			−0.180530	−	0.983569i	$-0.557781\pi$
$127$	−45.8547			−0.361060			−0.180530	+	0.983569i	$0.557781\pi$
$128$		0			0
$129$	−267.443	+	154.408i	−2.07320	+	1.19696i
$130$		0			0
$131$	60.4982	−	104.786i	0.461818	−	0.799893i	−0.537233	−	0.843434i	$-0.680531\pi$
$131$	60.4982	−	104.786i	0.461818	−	0.799893i	0.999052	+	0.0435409i	$0.0138639\pi$
$132$		0			0
$133$	73.7955	−	99.7409i	0.554854	−	0.749932i
$134$		0			0
$135$	−27.3704	+	47.4069i	−0.202744	+	0.351163i
$136$		0			0
$137$	72.6207	+	125.783i	0.530078	+	0.918122i	0.999384	+	0.0350869i	$0.0111708\pi$
$137$	72.6207	+	125.783i	0.530078	+	0.918122i	−0.469306	+	0.883036i	$0.655496\pi$
$138$		0			0
$139$	86.3503			0.621225			0.310613	−	0.950537i	$-0.399466\pi$
$139$	86.3503			0.621225			0.310613	+	0.950537i	$0.399466\pi$
$140$		0			0
$141$		−	163.120i		−	1.15688i
$142$		0			0
$143$	−160.634	+	92.7424i	−1.12332	+	0.648548i
$144$		0			0
$145$	−143.801	−	83.0236i	−0.991732	−	0.572577i
$146$		0			0
$147$	−55.4615	−	181.332i	−0.377289	−	1.23355i
$148$		0			0
$149$	−189.536	−	109.429i	−1.27205	−	0.734421i	−0.296680	−	0.954977i	$-0.595879\pi$
$149$	−189.536	−	109.429i	−1.27205	−	0.734421i	−0.975374	+	0.220556i	$0.929213\pi$
$150$		0			0
$151$	41.6552	+	72.1490i	0.275862	+	0.477808i	0.970352	−	0.241695i	$-0.0777033\pi$
$151$	41.6552	+	72.1490i	0.275862	+	0.477808i	−0.694490	+	0.719502i	$0.744370\pi$
$152$		0			0
$153$		−	116.665i		−	0.762514i
$154$		0			0
$155$			135.751i			0.875813i
$156$		0			0
$157$	17.7207	+	30.6932i	0.112871	+	0.195498i	0.916927	−	0.399056i	$-0.130662\pi$
$157$	17.7207	+	30.6932i	0.112871	+	0.195498i	−0.804056	+	0.594554i	$0.797329\pi$
$158$		0			0
$159$	−121.164	−	69.9543i	−0.762041	−	0.439964i
$160$		0			0
$161$	−36.8912	+	49.8616i	−0.229138	+	0.309699i
$162$		0			0
$163$	−9.05412	−	5.22740i	−0.0555468	−	0.0320699i	0.471969	−	0.881615i	$-0.343543\pi$
$163$	−9.05412	−	5.22740i	−0.0555468	−	0.0320699i	−0.527516	+	0.849545i	$0.676877\pi$
$164$		0			0
$165$	−228.777	+	132.084i	−1.38653	+	0.800511i
$166$		0			0
$167$		−	78.8843i		−	0.472361i	−0.971709	−	0.236181i	$-0.924104\pi$
$167$		−	78.8843i		−	0.472361i	0.971709	−	0.236181i	$-0.0758957\pi$
$168$		0			0
$169$	−7.45163			−0.0440925
$170$		0			0
$171$	−52.9610	−	91.7311i	−0.309713	−	0.536439i
$172$		0			0
$173$	−95.9208	+	166.140i	−0.554456	+	0.960345i	0.443490	+	0.896279i	$0.353740\pi$
$173$	−95.9208	+	166.140i	−0.554456	+	0.960345i	−0.997946	+	0.0640660i	$0.979593\pi$
$174$		0			0
$175$	−8.70893	−	20.0260i	−0.0497653	−	0.114434i
$176$		0			0
$177$	4.65732	−	8.06671i	0.0263125	−	0.0455746i
$178$		0			0
$179$	60.5426	−	34.9543i	0.338227	−	0.195275i	−0.321261	−	0.946991i	$-0.604107\pi$
$179$	60.5426	−	34.9543i	0.338227	−	0.195275i	0.659488	+	0.751715i	$0.270773\pi$
$180$		0			0
$181$	343.635			1.89853			0.949267	−	0.314472i	$-0.101827\pi$
$181$	343.635			1.89853			0.949267	+	0.314472i	$0.101827\pi$
$182$		0			0
$183$	−113.174			−0.618438
$184$		0			0
$185$	−49.4903	+	28.5732i	−0.267515	+	0.154450i
$186$		0			0
$187$	−142.449	+	246.728i	−0.761757	+	1.31940i
$188$		0			0
$189$	81.3925	+	9.26878i	0.430648	+	0.0490411i
$190$		0			0
$191$	−69.8895	+	121.052i	−0.365913	+	0.633781i	−0.988922	−	0.148434i	$-0.952577\pi$
$191$	−69.8895	+	121.052i	−0.365913	+	0.633781i	0.623009	+	0.782215i	$0.285910\pi$
$192$		0			0
$193$	−11.4616	−	19.8521i	−0.0593867	−	0.102861i	0.834804	−	0.550548i	$-0.185581\pi$
$193$	−11.4616	−	19.8521i	−0.0593867	−	0.102861i	−0.894190	+	0.447687i	$0.852248\pi$
$194$		0			0
$195$	230.078			1.17989
$196$		0			0
$197$			287.788i			1.46085i	0.682992	+	0.730426i	$0.260678\pi$
$197$			287.788i			1.46085i	−0.682992	+	0.730426i	$0.739322\pi$
$198$		0			0
$199$	56.7091	−	32.7410i	0.284970	−	0.164528i	−0.350701	−	0.936487i	$-0.614057\pi$
$199$	56.7091	−	32.7410i	0.284970	−	0.164528i	0.635671	+	0.771960i	$0.280723\pi$
$200$		0			0
$201$	136.337	+	78.7141i	0.678293	+	0.391613i
$202$		0			0
$203$	−28.1153	+	246.891i	−0.138499	+	1.21621i
$204$		0			0
$205$	−89.4868	−	51.6652i	−0.436521	−	0.252026i
$206$		0			0
$207$	26.4758	+	45.8574i	0.127902	+	0.221533i
$208$		0			0
$209$			258.663i			1.23762i
$210$		0			0
$211$		−	17.8985i		−	0.0848270i	−0.999100	−	0.0424135i	$-0.986495\pi$
$211$		−	17.8985i		−	0.0848270i	0.999100	−	0.0424135i	$-0.0135047\pi$
$212$		0			0
$213$	−43.7632	−	75.8001i	−0.205461	−	0.355869i
$214$		0			0
$215$	−323.267	−	186.638i	−1.50357	−	0.868084i
$216$		0			0
$217$	186.295	−	81.0161i	0.858502	−	0.373346i
$218$		0			0
$219$	−256.026	−	147.817i	−1.16907	−	0.674962i
$220$		0			0
$221$	214.889	−	124.066i	0.972346	−	0.561384i
$222$		0			0
$223$		−	258.973i		−	1.16132i	−0.814148	−	0.580658i	$-0.802795\pi$
$223$		−	258.973i		−	1.16132i	0.814148	−	0.580658i	$-0.197205\pi$
$224$		0			0
$225$	−18.6431			−0.0828581
$226$		0			0
$227$	−58.6721	−	101.623i	−0.258468	−	0.447679i	0.707364	−	0.706849i	$-0.249884\pi$
$227$	−58.6721	−	101.623i	−0.258468	−	0.447679i	−0.965832	+	0.259171i	$0.916551\pi$
$228$		0			0
$229$	−43.5475	+	75.4264i	−0.190164	+	0.329373i	−0.945304	−	0.326190i	$-0.894235\pi$
$229$	−43.5475	+	75.4264i	−0.190164	+	0.329373i	0.755141	+	0.655563i	$0.227569\pi$
$230$		0			0
$231$	317.797	+	235.129i	1.37574	+	1.01787i
$232$		0			0
$233$	155.825	−	269.897i	0.668778	−	1.15836i	−0.309468	−	0.950910i	$-0.600151\pi$
$233$	155.825	−	269.897i	0.668778	−	1.15836i	0.978246	−	0.207448i	$-0.0665159\pi$
$234$		0			0
$235$	170.753	−	98.5843i	0.726608	−	0.419507i
$236$		0			0
$237$	−529.410			−2.23380
$238$		0			0
$239$	140.823			0.589218			0.294609	−	0.955618i	$-0.404811\pi$
$239$	140.823			0.589218			0.294609	+	0.955618i	$0.404811\pi$
$240$		0			0
$241$	−41.6447	+	24.0436i	−0.172799	+	0.0997658i	−0.583905	−	0.811822i	$-0.698476\pi$
$241$	−41.6447	+	24.0436i	−0.172799	+	0.0997658i	0.411106	+	0.911588i	$0.365143\pi$
$242$		0			0
$243$	139.035	−	240.816i	0.572162	−	0.991014i
$244$		0			0
$245$	156.298	−	167.647i	0.637950	−	0.684275i
$246$		0			0
$247$	112.642	−	195.101i	0.456039	−	0.789883i
$248$		0			0
$249$	96.7357	+	167.551i	0.388497	+	0.672896i
$250$		0			0
$251$	152.080			0.605895			0.302947	−	0.953007i	$-0.402029\pi$
$251$	152.080			0.605895			0.302947	+	0.953007i	$0.402029\pi$
$252$		0			0
$253$		−	129.309i		−	0.511101i
$254$		0			0
$255$	306.046	−	176.696i	1.20018	−	0.692924i
$256$		0			0
$257$	126.153	+	72.8347i	0.490869	+	0.283403i	0.724935	−	0.688817i	$-0.241870\pi$
$257$	126.153	+	72.8347i	0.490869	+	0.283403i	−0.234066	+	0.972221i	$0.575203\pi$
$258$		0			0
$259$	68.7477	+	50.8645i	0.265435	+	0.196388i
$260$		0			0
$261$	183.714	+	106.068i	0.703887	+	0.406389i
$262$		0			0
$263$	176.696	+	306.047i	0.671850	+	1.16368i	0.977379	+	0.211495i	$0.0678333\pi$
$263$	176.696	+	306.047i	0.671850	+	1.16368i	−0.305529	+	0.952183i	$0.598833\pi$
$264$		0			0
$265$		−	169.112i		−	0.638158i
$266$		0			0
$267$		−	4.33460i		−	0.0162345i
$268$		0			0
$269$	−66.6490	−	115.439i	−0.247766	−	0.429143i	0.715140	−	0.698981i	$-0.246363\pi$
$269$	−66.6490	−	115.439i	−0.247766	−	0.429143i	−0.962906	+	0.269838i	$0.913030\pi$
$270$		0			0
$271$	326.342	+	188.414i	1.20421	+	0.695253i	0.961489	−	0.274842i	$-0.0886255\pi$
$271$	326.342	+	188.414i	1.20421	+	0.695253i	0.242725	+	0.970095i	$0.421959\pi$
$272$		0			0
$273$	−137.310	−	315.743i	−0.502969	−	1.15657i
$274$		0			0
$275$	39.4273	+	22.7634i	0.143372	+	0.0827759i
$276$		0			0
$277$	67.4788	−	38.9589i	0.243606	−	0.140646i	−0.373227	−	0.927740i	$-0.621749\pi$
$277$	67.4788	−	38.9589i	0.243606	−	0.140646i	0.616833	+	0.787094i	$0.288415\pi$
$278$		0			0
$279$		−	173.430i		−	0.621613i
$280$		0			0
$281$	324.564			1.15503			0.577516	−	0.816380i	$-0.304022\pi$
$281$	324.564			1.15503			0.577516	+	0.816380i	$0.304022\pi$
$282$		0			0
$283$	149.741	+	259.359i	0.529119	+	0.916462i	0.999423	+	0.0339572i	$0.0108110\pi$
$283$	149.741	+	259.359i	0.529119	+	0.916462i	−0.470304	+	0.882505i	$0.655856\pi$
$284$		0			0
$285$	160.425	−	277.864i	0.562895	−	0.974963i
$286$		0			0
$287$	−17.4960	+	153.639i	−0.0609618	+	0.535328i
$288$		0			0
$289$	46.0604	−	79.7789i	0.159378	−	0.276052i
$290$		0			0
$291$	−532.296	+	307.321i	−1.82920	+	1.05609i
$292$		0			0
$293$	81.7250			0.278925			0.139463	−	0.990227i	$-0.455463\pi$
$293$	81.7250			0.278925			0.139463	+	0.990227i	$0.455463\pi$
$294$		0			0
$295$	11.2589			0.0381657
$296$		0			0
$297$	−147.901	+	85.3908i	−0.497984	+	0.287511i
$298$		0			0
$299$	−56.3108	+	97.5332i	−0.188331	+	0.326198i
$300$		0			0
$301$	−63.2035	+	555.013i	−0.209979	+	1.84390i
$302$		0			0
$303$	−134.719	+	233.340i	−0.444617	+	0.770099i
$304$		0			0
$305$	−68.3986	−	118.470i	−0.224258	−	0.388425i
$306$		0			0
$307$	−361.930			−1.17892			−0.589462	−	0.807796i	$-0.700660\pi$
$307$	−361.930			−1.17892			−0.589462	+	0.807796i	$0.700660\pi$
$308$		0			0
$309$			75.9257i			0.245714i
$310$		0			0
$311$	−163.508	+	94.4017i	−0.525751	+	0.303542i	−0.739284	−	0.673393i	$-0.764836\pi$
$311$	−163.508	+	94.4017i	−0.525751	+	0.303542i	0.213534	+	0.976936i	$0.431503\pi$
$312$		0			0
$313$	−22.2463	−	12.8439i	−0.0710745	−	0.0410349i	0.464042	−	0.885813i	$-0.346399\pi$
$313$	−22.2463	−	12.8439i	−0.0710745	−	0.0410349i	−0.535116	+	0.844779i	$0.679732\pi$
$314$		0			0
$315$	−78.0351	−	179.440i	−0.247730	−	0.569651i
$316$		0			0
$317$	432.257	+	249.564i	1.36359	+	0.787268i	0.990100	−	0.140367i	$-0.0448282\pi$
$317$	432.257	+	249.564i	1.36359	+	0.787268i	0.373489	+	0.927635i	$0.378162\pi$
$318$		0			0
$319$	−259.019	−	448.634i	−0.811972	−	1.40638i
$320$		0			0
$321$			173.174i			0.539484i
$322$		0			0
$323$		−	346.027i		−	1.07129i
$324$		0			0
$325$	−19.8258	−	34.3393i	−0.0610025	−	0.105659i
$326$		0			0
$327$	189.705	+	109.526i	0.580138	+	0.334943i
$328$		0			0
$329$	−237.195	−	175.494i	−0.720958	−	0.533417i
$330$		0			0
$331$	216.384	+	124.930i	0.653729	+	0.377431i	0.789883	−	0.613257i	$-0.210141\pi$
$331$	216.384	+	124.930i	0.653729	+	0.377431i	−0.136154	+	0.990688i	$0.543474\pi$
$332$		0			0
$333$	63.2268	−	36.5040i	0.189870	−	0.109622i
$334$		0			0
$335$			190.288i			0.568025i
$336$		0			0
$337$	−84.4039			−0.250457			−0.125228	−	0.992128i	$-0.539966\pi$
$337$	−84.4039			−0.250457			−0.125228	+	0.992128i	$0.539966\pi$
$338$		0			0
$339$	364.992	+	632.185i	1.07667	+	1.86485i
$340$		0			0
$341$	−211.760	+	366.778i	−0.620996	+	1.07560i
$342$		0			0
$343$	−323.346	−	114.440i	−0.942699	−	0.333645i
$344$		0			0
$345$	−80.1982	+	138.907i	−0.232459	+	0.402630i
$346$		0			0
$347$	326.707	−	188.624i	0.941518	−	0.543586i	0.0510824	−	0.998694i	$-0.483733\pi$
$347$	326.707	−	188.624i	0.941518	−	0.543586i	0.890436	+	0.455109i	$0.150400\pi$
$348$		0			0
$349$	−400.193			−1.14668			−0.573342	−	0.819316i	$-0.694353\pi$
$349$	−400.193			−1.14668			−0.573342	+	0.819316i	$0.694353\pi$
$350$		0			0
$351$	148.743			0.423768
$352$		0			0
$353$	256.293	−	147.971i	0.726043	−	0.419181i	−0.0909296	−	0.995857i	$-0.528984\pi$
$353$	256.293	−	147.971i	0.726043	−	0.419181i	0.816973	+	0.576676i	$0.195650\pi$
$354$		0			0
$355$	52.8980	−	91.6220i	0.149008	−	0.258090i
$356$		0			0
$357$	−425.132	−	314.543i	−1.19085	−	0.881074i
$358$		0			0
$359$	−102.587	+	177.686i	−0.285757	+	0.494946i	−0.972793	−	0.231678i	$-0.925578\pi$
$359$	−102.587	+	177.686i	−0.285757	+	0.494946i	0.687035	+	0.726624i	$0.258912\pi$
$360$		0			0
$361$	23.4181	+	40.5613i	0.0648701	+	0.112358i
$362$		0			0
$363$	−355.904			−0.980451
$364$		0			0
$365$		−	357.341i		−	0.979017i
$366$		0			0
$367$	306.216	−	176.794i	0.834377	−	0.481728i	−0.0209719	−	0.999780i	$-0.506676\pi$
$367$	306.216	−	176.794i	0.834377	−	0.481728i	0.855349	+	0.518052i	$0.173343\pi$
$368$		0			0
$369$	114.325	+	66.0054i	0.309823	+	0.178876i
$370$		0			0
$371$	−232.077	+	100.926i	−0.625545	+	0.272037i
$372$		0			0
$373$	−310.062	−	179.014i	−0.831264	−	0.479931i	0.0230210	−	0.999735i	$-0.492672\pi$
$373$	−310.062	−	179.014i	−0.831264	−	0.479931i	−0.854285	+	0.519804i	$0.826005\pi$
$374$		0			0
$375$	−254.510	−	440.824i	−0.678693	−	1.17553i
$376$		0			0
$377$			451.187i			1.19678i
$378$		0			0
$379$		−	514.679i		−	1.35799i	−0.734142	−	0.678996i	$-0.762415\pi$
$379$		−	514.679i		−	1.35799i	0.734142	−	0.678996i	$-0.237585\pi$
$380$		0			0
$381$	88.7260	+	153.678i	0.232877	+	0.403354i
$382$		0			0
$383$	−450.193	−	259.919i	−1.17544	−	0.678639i	−0.220483	−	0.975391i	$-0.570763\pi$
$383$	−450.193	−	259.919i	−1.17544	−	0.678639i	−0.954955	+	0.296752i	$0.904097\pi$
$384$		0			0
$385$	−54.0657	+	474.771i	−0.140430	+	1.23317i
$386$		0			0
$387$	412.992	+	238.441i	1.06716	+	0.616127i
$388$		0			0
$389$	−91.3278	+	52.7281i	−0.234776	+	0.135548i	−0.612773	−	0.790259i	$-0.709946\pi$
$389$	−91.3278	+	52.7281i	−0.234776	+	0.135548i	0.377997	+	0.925807i	$0.376613\pi$
$390$		0			0
$391$			172.982i			0.442410i
$392$		0			0
$393$	−468.241			−1.19145
$394$		0			0
$395$	−319.957	−	554.182i	−0.810018	−	1.40299i
$396$		0			0
$397$	185.762	−	321.749i	0.467914	−	0.810450i	−0.531414	−	0.847112i	$-0.678339\pi$
$397$	185.762	−	321.749i	0.467914	−	0.810450i	0.999328	+	0.0366619i	$0.0116725\pi$
$398$		0			0
$399$	−477.063	−	54.3267i	−1.19565	−	0.136157i
$400$		0			0
$401$	−149.636	+	259.177i	−0.373157	+	0.646327i	−0.990049	−	0.140721i	$-0.955058\pi$
$401$	−149.636	+	259.177i	−0.373157	+	0.646327i	0.616893	+	0.787047i	$0.288391\pi$
$402$		0			0
$403$	319.446	−	184.433i	0.792671	−	0.457649i
$404$		0			0
$405$	463.421			1.14425
$406$		0			0
$407$	−178.287			−0.438052
$408$		0			0
$409$	−17.6410	+	10.1850i	−0.0431320	+	0.0249023i	−0.521411	−	0.853306i	$-0.674594\pi$
$409$	−17.6410	+	10.1850i	−0.0431320	+	0.0249023i	0.478279	+	0.878208i	$0.341261\pi$
$410$		0			0
$411$	281.033	−	486.764i	0.683780	−	1.18434i
$412$		0			0
$413$	−6.71929	−	15.4509i	−0.0162695	−	0.0374113i
$414$		0			0
$415$	−116.927	+	202.524i	−0.281753	+	0.488010i
$416$		0			0
$417$	−167.083	−	289.396i	−0.400678	−	0.693994i
$418$		0			0
$419$	−183.085			−0.436956			−0.218478	−	0.975842i	$-0.570109\pi$
$419$	−183.085			−0.436956			−0.218478	+	0.975842i	$0.570109\pi$
$420$		0			0
$421$		−	293.022i		−	0.696014i	−0.937492	−	0.348007i	$-0.886859\pi$
$421$		−	293.022i		−	0.696014i	0.937492	−	0.348007i	$-0.113141\pi$
$422$		0			0
$423$	−218.147	+	125.947i	−0.515714	+	0.297748i
$424$		0			0
$425$	−52.7438	−	30.4517i	−0.124103	−	0.0716510i
$426$		0			0
$427$	−121.759	+	164.568i	−0.285150	+	0.385405i
$428$		0			0
$429$	621.636	+	358.902i	1.44903	+	0.836601i
$430$		0			0
$431$	−37.6108	−	65.1439i	−0.0872641	−	0.151146i	0.819090	−	0.573666i	$-0.194479\pi$
$431$	−37.6108	−	65.1439i	−0.0872641	−	0.151146i	−0.906354	+	0.422520i	$0.861146\pi$
$432$		0			0
$433$		−	506.209i		−	1.16907i	−0.811367	−	0.584536i	$-0.801276\pi$
$433$		−	506.209i		−	1.16907i	0.811367	−	0.584536i	$-0.198724\pi$
$434$		0			0
$435$			642.583i			1.47720i
$436$		0			0
$437$	78.5269	+	136.013i	0.179696	+	0.311242i
$438$		0			0
$439$	141.358	+	81.6130i	0.322000	+	0.185907i	0.652284	−	0.757975i	$-0.273811\pi$
$439$	141.358	+	81.6130i	0.322000	+	0.185907i	−0.330284	+	0.943882i	$0.607144\pi$
$440$		0			0
$441$	−199.680	+	214.180i	−0.452788	+	0.485668i
$442$		0			0
$443$	−98.4732	−	56.8535i	−0.222287	−	0.128338i	0.384722	−	0.923033i	$-0.374297\pi$
$443$	−98.4732	−	56.8535i	−0.222287	−	0.128338i	−0.607009	+	0.794695i	$0.707631\pi$
$444$		0			0
$445$	4.53742	−	2.61968i	0.0101964	−	0.00588692i
$446$		0			0
$447$			846.952i			1.89475i
$448$		0			0
$449$	391.120			0.871091			0.435546	−	0.900167i	$-0.356555\pi$
$449$	391.120			0.871091			0.435546	+	0.900167i	$0.356555\pi$
$450$		0			0
$451$	−161.186	−	279.183i	−0.357398	−	0.619031i
$452$		0			0
$453$	161.201	−	279.208i	0.355851	−	0.616353i
$454$		0			0
$455$	247.531	−	334.559i	0.544025	−	0.735296i
$456$		0			0
$457$	−286.893	+	496.913i	−0.627774	+	1.08734i	0.360223	+	0.932866i	$0.382701\pi$
$457$	−286.893	+	496.913i	−0.627774	+	1.08734i	−0.987997	+	0.154471i	$0.950633\pi$
$458$		0			0
$459$	197.855	−	114.231i	0.431056	−	0.248870i
$460$		0			0
$461$	−847.131			−1.83759			−0.918797	−	0.394729i	$-0.870838\pi$
$461$	−847.131			−1.83759			−0.918797	+	0.394729i	$0.870838\pi$
$462$		0			0
$463$	−109.055			−0.235539			−0.117770	−	0.993041i	$-0.537574\pi$
$463$	−109.055			−0.235539			−0.117770	+	0.993041i	$0.537574\pi$
$464$		0			0
$465$	454.958	−	262.670i	0.978404	−	0.564882i
$466$		0			0
$467$	−321.205	+	556.343i	−0.687805	+	1.19131i	0.284741	+	0.958604i	$0.408092\pi$
$467$	−321.205	+	556.343i	−0.687805	+	1.19131i	−0.972546	+	0.232709i	$0.925241\pi$
$468$		0			0
$469$	261.138	−	113.564i	0.556798	−	0.242141i
$470$		0			0
$471$	68.5771	−	118.779i	0.145599	−	0.252185i
$472$		0			0
$473$	−582.278	−	1008.53i	−1.23103	−	2.13221i
$474$		0			0
$475$	−55.2952			−0.116411
$476$		0			0
$477$			216.050i			0.452936i
$478$		0			0
$479$	367.909	−	212.412i	0.768077	−	0.443449i	−0.0641112	−	0.997943i	$-0.520421\pi$
$479$	367.909	−	212.412i	0.768077	−	0.443449i	0.832188	+	0.554493i	$0.187088\pi$
$480$		0			0
$481$	134.476	+	77.6397i	0.279576	+	0.161413i
$482$		0			0
$483$	238.489	+	27.1585i	0.493766	+	0.0562288i
$484$		0			0
$485$	−643.403	−	371.469i	−1.32660	−	0.765915i
$486$		0			0
$487$	388.616	+	673.103i	0.797980	+	1.38214i	0.920929	+	0.389729i	$0.127431\pi$
$487$	388.616	+	673.103i	0.797980	+	1.38214i	−0.122949	+	0.992413i	$0.539235\pi$
$488$		0			0
$489$			40.4588i			0.0827379i
$490$		0			0
$491$			476.370i			0.970203i	0.874458	+	0.485102i	$0.161217\pi$
$491$			476.370i			0.970203i	−0.874458	+	0.485102i	$0.838783\pi$
$492$		0			0
$493$	346.502	+	600.160i	0.702845	+	1.21736i
$494$		0			0
$495$	353.283	+	203.968i	0.713702	+	0.412056i
$496$		0			0
$497$	−157.305	−	17.9135i	−0.316509	−	0.0360432i
$498$		0			0
$499$	−377.065	−	217.698i	−0.755641	−	0.436269i	0.0720876	−	0.997398i	$-0.477034\pi$
$499$	−377.065	−	217.698i	−0.755641	−	0.436269i	−0.827728	+	0.561129i	$0.810367\pi$
$500$		0			0
$501$	−264.374	+	152.636i	−0.527693	+	0.304663i
$502$		0			0
$503$		−	375.404i		−	0.746329i	−0.927765	−	0.373165i	$-0.878273\pi$
$503$		−	375.404i		−	0.746329i	0.927765	−	0.373165i	$-0.121727\pi$
$504$		0			0
$505$	−325.678			−0.644907
$506$		0			0
$507$	14.4185	+	24.9735i	0.0284388	+	0.0492574i
$508$		0			0
$509$	−73.9117	+	128.019i	−0.145210	+	0.251510i	−0.929451	−	0.368945i	$-0.879719\pi$
$509$	−73.9117	+	128.019i	−0.145210	+	0.251510i	0.784242	+	0.620456i	$0.213052\pi$
$510$		0			0
$511$	−490.389	+	213.261i	−0.959666	+	0.417340i
$512$		0			0
$513$	103.713	−	179.636i	0.202169	−	0.350167i
$514$		0			0
$515$	−79.4784	+	45.8869i	−0.154327	+	0.0891007i
$516$		0			0
$517$	615.131			1.18981
$518$		0			0
$519$	742.404			1.43045
$520$		0			0
$521$	755.302	−	436.074i	1.44972	−	0.836994i	0.451253	−	0.892396i	$-0.350977\pi$
$521$	755.302	−	436.074i	1.44972	−	0.836994i	0.998464	+	0.0554019i	$0.0176440\pi$
$522$		0			0
$523$	−178.600	+	309.344i	−0.341491	+	0.591480i	−0.984710	−	0.174202i	$-0.944265\pi$
$523$	−178.600	+	309.344i	−0.341491	+	0.591480i	0.643219	+	0.765683i	$0.277599\pi$
$524$		0			0
$525$	−50.2642	+	67.9364i	−0.0957414	+	0.129403i
$526$		0			0
$527$	283.281	−	490.657i	0.537535	−	0.931038i
$528$		0			0
$529$	225.244	+	390.133i	0.425791	+	0.737492i
$530$		0			0
$531$	−14.3839			−0.0270883
$532$		0			0
$533$			280.771i			0.526776i
$534$		0			0
$535$	−181.278	+	104.661i	−0.338836	+	0.195627i
$536$		0			0
$537$	−234.293	−	135.269i	−0.436299	−	0.251897i
$538$		0			0
$539$	683.808	−	209.147i	1.26866	−	0.388028i
$540$		0			0
$541$	−807.198	−	466.036i	−1.49205	−	0.861434i	−0.492089	−	0.870545i	$-0.663767\pi$
$541$	−807.198	−	466.036i	−1.49205	−	0.861434i	−0.999958	+	0.00911085i	$0.997100\pi$
$542$		0			0
$543$	−664.912	−	1151.66i	−1.22452	−	2.12092i
$544$		0			0
$545$			264.776i			0.485827i
$546$		0			0
$547$			151.397i			0.276778i	0.990378	+	0.138389i	$0.0441924\pi$
$547$			151.397i			0.276778i	−0.990378	+	0.138389i	$0.955808\pi$
$548$		0			0
$549$	87.3832	+	151.352i	0.159168	+	0.275687i
$550$		0			0
$551$	544.896	+	314.596i	0.988922	+	0.570954i
$552$		0			0
$553$	−569.569	+	769.821i	−1.02996	+	1.39208i
$554$		0			0
$555$	191.522	+	110.575i	0.345084	+	0.199234i
$556$		0			0
$557$	775.593	−	447.789i	1.39245	−	0.803929i	0.398861	−	0.917011i	$-0.369406\pi$
$557$	775.593	−	447.789i	1.39245	−	0.803929i	0.993586	+	0.113082i	$0.0360722\pi$
$558$		0			0
$559$			1014.27i			1.81444i
$560$		0			0
$561$	1102.52			1.96527
$562$		0			0
$563$	−139.958	−	242.414i	−0.248592	−	0.430575i	0.714543	−	0.699591i	$-0.246635\pi$
$563$	−139.958	−	242.414i	−0.248592	−	0.430575i	−0.963136	+	0.269017i	$0.913301\pi$
$564$		0			0
$565$	−441.177	+	764.142i	−0.780845	+	1.35246i
$566$		0			0
$567$	−276.569	−	635.966i	−0.487776	−	1.12163i
$568$		0			0
$569$	−160.963	+	278.796i	−0.282887	+	0.489975i	−0.972095	−	0.234589i	$-0.924626\pi$
$569$	−160.963	+	278.796i	−0.282887	+	0.489975i	0.689207	+	0.724564i	$0.257959\pi$
$570$		0			0
$571$	−712.583	+	411.410i	−1.24796	+	0.720508i	−0.970702	−	0.240288i	$-0.922758\pi$
$571$	−712.583	+	411.410i	−1.24796	+	0.720508i	−0.277255	+	0.960796i	$0.589425\pi$
$572$		0			0
$573$	540.928			0.944027
$574$		0			0
$575$	27.6427			0.0480742
$576$		0			0
$577$	833.162	−	481.027i	1.44396	−	0.833668i	0.445845	−	0.895110i	$-0.352903\pi$
$577$	833.162	−	481.027i	1.44396	−	0.833668i	0.998111	+	0.0614420i	$0.0195699\pi$
$578$		0			0
$579$	−44.3551	+	76.8253i	−0.0766064	+	0.132686i
$580$		0			0
$581$	347.712	+	39.5966i	0.598472	+	0.0681524i
$582$		0			0
$583$	263.800	−	456.914i	0.452486	−	0.783729i
$584$		0			0
$585$	−177.646	−	307.692i	−0.303669	−	0.525970i
$586$		0			0
$587$	885.638			1.50875			0.754377	−	0.656442i	$-0.227939\pi$
$587$	885.638			1.50875			0.754377	+	0.656442i	$0.227939\pi$
$588$		0			0
$589$		−	514.392i		−	0.873331i
$590$		0			0
$591$	964.496	−	556.852i	1.63197	−	0.942220i
$592$		0			0
$593$	290.818	+	167.904i	0.490418	+	0.283143i	0.724748	−	0.689014i	$-0.241956\pi$
$593$	290.818	+	167.904i	0.490418	+	0.283143i	−0.234330	+	0.972157i	$0.575290\pi$
$594$		0			0
$595$	72.3263	−	635.124i	0.121557	−	1.06743i
$596$		0			0
$597$	−219.457	−	126.704i	−0.367600	−	0.212234i
$598$		0			0
$599$	−30.1532	−	52.2269i	−0.0503393	−	0.0871902i	0.839758	−	0.542961i	$-0.182697\pi$
$599$	−30.1532	−	52.2269i	−0.0503393	−	0.0871902i	−0.890097	+	0.455771i	$0.849364\pi$
$600$		0			0
$601$			509.153i			0.847176i	0.905855	+	0.423588i	$0.139230\pi$
$601$			509.153i			0.847176i	−0.905855	+	0.423588i	$0.860770\pi$
$602$		0			0
$603$		−	243.105i		−	0.403159i
$604$		0			0
$605$	−215.096	−	372.557i	−0.355530	−	0.615797i
$606$		0			0
$607$	900.363	+	519.825i	1.48330	+	0.856384i	0.999820	−	0.0189717i	$-0.00603923\pi$
$607$	900.363	+	519.825i	1.48330	+	0.856384i	0.483480	+	0.875355i	$0.339373\pi$
$608$		0			0
$609$	881.835	−	383.493i	1.44800	−	0.629709i
$610$		0			0
$611$	−463.973	−	267.875i	−0.759366	−	0.438420i
$612$		0			0
$613$	172.277	−	99.4641i	0.281039	−	0.162258i	−0.352855	−	0.935678i	$-0.614789\pi$
$613$	172.277	−	99.4641i	0.281039	−	0.162258i	0.633894	+	0.773420i	$0.281456\pi$
$614$		0			0
$615$			399.876i			0.650206i
$616$		0			0
$617$	136.689			0.221538			0.110769	−	0.993846i	$-0.464669\pi$
$617$	136.689			0.221538			0.110769	+	0.993846i	$0.464669\pi$
$618$		0			0
$619$	230.938	+	399.997i	0.373083	+	0.646199i	0.990038	−	0.140799i	$-0.0449673\pi$
$619$	230.938	+	399.997i	0.373083	+	0.646199i	−0.616955	+	0.786998i	$0.711634\pi$
$620$		0			0
$621$	−51.8472	+	89.8019i	−0.0834898	+	0.144609i
$622$		0			0
$623$	−6.30299	−	4.66341i	−0.0101172	−	0.00748541i
$624$		0			0
$625$	268.638	−	465.294i	0.429821	−	0.744471i
$626$		0			0
$627$	866.888	−	500.498i	1.38260	−	0.798242i
$628$		0			0
$629$	238.503			0.379178
$630$		0			0
$631$	−1042.33			−1.65187			−0.825933	−	0.563768i	$-0.809351\pi$
$631$	−1042.33			−1.65187			−0.825933	+	0.563768i	$0.809351\pi$
$632$		0			0
$633$	−59.9853	+	34.6325i	−0.0947635	+	0.0547117i
$634$		0			0
$635$	−107.246	+	185.755i	−0.168891	+	0.292528i
$636$		0			0
$637$	−606.852	−	140.029i	−0.952672	−	0.219826i
$638$		0			0
$639$	−67.5803	+	117.052i	−0.105759	+	0.183181i
$640$		0			0
$641$	−61.3334	−	106.233i	−0.0956840	−	0.165730i	0.814210	−	0.580571i	$-0.197170\pi$
$641$	−61.3334	−	106.233i	−0.0956840	−	0.165730i	−0.909894	+	0.414841i	$0.863837\pi$
$642$		0			0
$643$	720.813			1.12102			0.560508	−	0.828149i	$-0.310606\pi$
$643$	720.813			1.12102			0.560508	+	0.828149i	$0.310606\pi$
$644$		0			0
$645$			1444.53i			2.23959i
$646$		0			0
$647$	−510.825	+	294.925i	−0.789528	+	0.455834i	−0.839796	−	0.542901i	$-0.817326\pi$
$647$	−510.825	+	294.925i	−0.789528	+	0.455834i	0.0502683	+	0.998736i	$0.483992\pi$
$648$		0			0
$649$	30.4198	+	17.5629i	0.0468717	+	0.0270614i
$650$		0			0
$651$	−631.988	−	467.590i	−0.970796	−	0.718265i
$652$		0			0
$653$	215.294	+	124.300i	0.329700	+	0.190352i	0.655708	−	0.755015i	$-0.272370\pi$
$653$	215.294	+	124.300i	0.329700	+	0.190352i	−0.326008	+	0.945367i	$0.605704\pi$
$654$		0			0
$655$	−282.989	−	490.151i	−0.432044	−	0.748322i
$656$		0			0
$657$			456.524i			0.694862i
$658$		0			0
$659$		−	640.918i		−	0.972562i	−0.873802	−	0.486281i	$-0.838353\pi$
$659$		−	640.918i		−	0.972562i	0.873802	−	0.486281i	$-0.161647\pi$
$660$		0			0
$661$	−483.321	−	837.137i	−0.731197	−	1.26647i	−0.956372	−	0.292152i	$-0.905629\pi$
$661$	−483.321	−	837.137i	−0.731197	−	1.26647i	0.225175	−	0.974318i	$-0.427705\pi$
$662$		0			0
$663$	−831.593	−	480.120i	−1.25429	−	0.724163i
$664$		0			0
$665$	−231.451	−	532.218i	−0.348047	−	0.800328i
$666$		0			0
$667$	−272.399	−	157.270i	−0.408395	−	0.235787i
$668$		0			0
$669$	−867.927	+	501.098i	−1.29735	+	0.749025i
$670$		0			0
$671$		−	426.783i		−	0.636040i
$672$		0			0
$673$	−754.537			−1.12115			−0.560577	−	0.828102i	$-0.689421\pi$
$673$	−754.537			−1.12115			−0.560577	+	0.828102i	$0.689421\pi$
$674$		0			0
$675$	−18.2543	−	31.6173i	−0.0270433	−	0.0468404i
$676$		0			0
$677$	380.978	−	659.874i	0.562745	−	0.974703i	−0.434511	−	0.900667i	$-0.643079\pi$
$677$	380.978	−	659.874i	0.562745	−	0.974703i	0.997256	−	0.0740362i	$-0.0235880\pi$
$678$		0			0
$679$	−125.795	+	1104.65i	−0.185265	+	1.62688i
$680$		0			0
$681$	−227.054	+	393.269i	−0.333413	+	0.577488i
$682$		0			0
$683$	−657.604	+	379.668i	−0.962817	+	0.555883i	−0.897039	−	0.441952i	$-0.854286\pi$
$683$	−657.604	+	379.668i	−0.962817	+	0.555883i	−0.0657781	+	0.997834i	$0.520953\pi$
$684$		0			0
$685$	679.387			0.991806
$686$		0			0
$687$	337.047			0.490607
$688$		0			0
$689$	−397.951	+	229.757i	−0.577577	+	0.333464i
$690$		0			0
$691$	−245.076	+	424.484i	−0.354669	+	0.614304i	−0.987061	−	0.160344i	$-0.948740\pi$
$691$	−245.076	+	424.484i	−0.354669	+	0.614304i	0.632393	+	0.774648i	$0.282073\pi$
$692$		0			0
$693$	69.0721	−	606.548i	0.0996711	−	0.875249i
$694$		0			0
$695$	201.958	−	349.801i	0.290587	−	0.503311i
$696$		0			0
$697$	215.627	+	373.477i	0.309364	+	0.535835i
$698$		0			0
$699$	−1206.05			−1.72539
$700$		0			0
$701$			577.533i			0.823870i	0.911213	+	0.411935i	$0.135147\pi$
$701$			577.533i			0.823870i	−0.911213	+	0.411935i	$0.864853\pi$
$702$		0			0
$703$	187.530	−	108.271i	0.266757	−	0.154012i
$704$		0			0
$705$	−660.793	−	381.509i	−0.937295	−	0.541148i
$706$		0			0
$707$	194.364	+	446.937i	0.274914	+	0.632160i
$708$		0			0
$709$	615.814	+	355.540i	0.868567	+	0.501467i	0.866872	−	0.498531i	$-0.166127\pi$
$709$	615.814	+	355.540i	0.868567	+	0.501467i	0.00169497	+	0.999999i	$0.499460\pi$
$710$		0			0
$711$	408.764	+	708.000i	0.574914	+	0.995781i
$712$		0			0
$713$			257.150i			0.360659i
$714$		0			0
$715$			867.631i			1.21347i
$716$		0			0
$717$	−272.484	−	471.957i	−0.380034	−	0.658238i
$718$		0			0
$719$	150.440	+	86.8564i	0.209235	+	0.120802i	0.600956	−	0.799282i	$-0.294787\pi$
$719$	150.440	+	86.8564i	0.209235	+	0.120802i	−0.391721	+	0.920084i	$0.628120\pi$
$720$		0			0
$721$	110.404	+	81.6852i	0.153127	+	0.113294i
$722$		0			0
$723$	161.160	+	93.0457i	0.222904	+	0.128694i
$724$		0			0
$725$	95.9059	−	55.3713i	0.132284	−	0.0763742i
$726$		0			0
$727$		−	1056.57i		−	1.45333i	−0.686993	−	0.726664i	$-0.741070\pi$
$727$		−	1056.57i		−	1.45333i	0.686993	−	0.726664i	$-0.258930\pi$
$728$		0			0
$729$	−184.457			−0.253028
$730$		0			0
$731$	778.941	+	1349.17i	1.06558	+	1.84564i
$732$		0			0
$733$	−115.299	+	199.703i	−0.157297	+	0.272446i	−0.933893	−	0.357553i	$-0.883611\pi$
$733$	−115.299	+	199.703i	−0.157297	+	0.272446i	0.776596	+	0.629999i	$0.216945\pi$
$734$		0			0
$735$	−864.283	−	199.431i	−1.17589	−	0.271334i
$736$		0			0
$737$	−296.833	+	514.130i	−0.402758	+	0.697598i
$738$		0			0
$739$	77.4971	−	44.7430i	0.104868	−	0.0605453i	−0.446649	−	0.894709i	$-0.647383\pi$
$739$	77.4971	−	44.7430i	0.104868	−	0.0605453i	0.551517	+	0.834164i	$0.314049\pi$
$740$		0			0
$741$	−871.820			−1.17654
$742$		0			0
$743$	236.120			0.317793			0.158897	−	0.987295i	$-0.449206\pi$
$743$	236.120			0.317793			0.158897	+	0.987295i	$0.449206\pi$
$744$		0			0
$745$	−886.581	+	511.868i	−1.19004	+	0.687071i
$746$		0			0
$747$	149.382	−	258.737i	0.199976	−	0.346368i
$748$		0			0
$749$	251.815	+	186.311i	0.336202	+	0.248746i
$750$		0			0
$751$	−717.692	+	1243.08i	−0.955649	+	1.65523i	−0.222772	+	0.974871i	$0.571510\pi$
$751$	−717.692	+	1243.08i	−0.955649	+	1.65523i	−0.732877	+	0.680361i	$0.761823\pi$
$752$		0			0
$753$	−294.265	−	509.682i	−0.390790	−	0.676868i
$754$		0			0
$755$	389.696			0.516154
$756$		0			0
$757$			692.645i			0.914987i	0.889213	+	0.457494i	$0.151253\pi$
$757$			692.645i			0.914987i	−0.889213	+	0.457494i	$0.848747\pi$
$758$		0			0
$759$	−433.367	+	250.204i	−0.570971	+	0.329650i
$760$		0			0
$761$	−999.810	−	577.241i	−1.31381	−	0.758529i	−0.331086	−	0.943601i	$-0.607415\pi$
$761$	−999.810	−	577.241i	−1.31381	−	0.758529i	−0.982725	+	0.185071i	$0.940748\pi$
$762$		0			0
$763$	363.359	−	158.018i	0.476224	−	0.207101i
$764$		0			0
$765$	−472.603	−	272.858i	−0.617782	−	0.356677i
$766$		0			0
$767$	−15.2964	−	26.4942i	−0.0199432	−	0.0345426i
$768$		0			0
$769$		−	894.095i		−	1.16267i	−0.813663	−	0.581336i	$-0.802530\pi$
$769$		−	894.095i		−	1.16267i	0.813663	−	0.581336i	$-0.197470\pi$
$770$		0			0
$771$		−	563.723i		−	0.731158i
$772$		0			0
$773$	464.538	+	804.603i	0.600954	+	1.04088i	0.992677	+	0.120800i	$0.0385460\pi$
$773$	464.538	+	804.603i	0.600954	+	1.04088i	−0.391722	+	0.920083i	$0.628121\pi$
$774$		0			0
$775$	−78.4073	−	45.2685i	−0.101171	−	0.0584109i
$776$		0			0
$777$	37.4454	−	328.822i	0.0481922	−	0.423194i
$778$		0			0
$779$	339.086	+	195.772i	0.435284	+	0.251311i
$780$		0			0
$781$	285.844	−	165.032i	0.365998	−	0.211309i
$782$		0			0
$783$			415.422i			0.530552i
$784$		0			0
$785$	165.782			0.211188
$786$		0			0
$787$	−693.013	−	1200.33i	−0.880576	−	1.52520i	−0.850702	−	0.525649i	$-0.823823\pi$
$787$	−693.013	−	1200.33i	−0.880576	−	1.52520i	−0.0298746	−	0.999554i	$-0.509511\pi$
$788$		0			0
$789$	683.794	−	1184.37i	0.866659	−	1.50110i
$790$		0			0
$791$	1311.95	+	149.401i	1.65859	+	0.188876i
$792$		0			0
$793$	−185.854	+	321.908i	−0.234368	+	0.405937i
$794$		0			0
$795$	−566.764	+	327.221i	−0.712910	+	0.411599i
$796$		0			0
$797$	−388.524			−0.487484			−0.243742	−	0.969840i	$-0.578375\pi$
$797$	−388.524			−0.487484			−0.243742	+	0.969840i	$0.578375\pi$
$798$		0			0
$799$	−822.890			−1.02990
$800$		0			0
$801$	−5.79682	+	3.34680i	−0.00723698	+	0.00417827i
$802$		0			0
$803$	557.421	−	965.481i	0.694173	−	1.20234i
$804$		0			0
$805$	115.705	+	266.062i	0.143733	+	0.330512i
$806$		0			0
$807$	−257.924	+	446.737i	−0.319608	+	0.553577i
$808$		0			0
$809$	−255.112	−	441.867i	−0.315342	−	0.546189i	0.664168	−	0.747583i	$-0.268786\pi$
$809$	−255.112	−	441.867i	−0.315342	−	0.546189i	−0.979510	+	0.201395i	$0.935453\pi$
$810$		0			0
$811$	54.8689			0.0676558			0.0338279	−	0.999428i	$-0.489230\pi$
$811$	54.8689			0.0676558			0.0338279	+	0.999428i	$0.489230\pi$
$812$		0			0
$813$		−	1458.28i		−	1.79370i
$814$		0			0
$815$	−42.3519	+	24.4519i	−0.0519656	+	0.0300023i
$816$		0			0
$817$	1224.93	+	707.215i	1.49931	+	0.865624i
$818$		0			0
$819$	−316.236	+	427.420i	−0.386124	+	0.521880i
$820$		0			0
$821$	−167.045	−	96.4438i	−0.203466	−	0.117471i	0.394805	−	0.918765i	$-0.370812\pi$
$821$	−167.045	−	96.4438i	−0.203466	−	0.117471i	−0.598271	+	0.801294i	$0.704145\pi$
$822$		0			0
$823$	71.3241	+	123.537i	0.0866636	+	0.150106i	0.906099	−	0.423066i	$-0.139046\pi$
$823$	71.3241	+	123.537i	0.0866636	+	0.150106i	−0.819435	+	0.573172i	$0.805713\pi$
$824$		0			0
$825$		−	176.183i		−	0.213555i
$826$		0			0
$827$		−	91.3639i		−	0.110476i	−0.998473	−	0.0552382i	$-0.982408\pi$
$827$		−	91.3639i		−	0.110476i	0.998473	−	0.0552382i	$-0.0175918\pi$
$828$		0			0
$829$	232.999	+	403.567i	0.281061	+	0.486812i	0.971646	−	0.236439i	$-0.0759804\pi$
$829$	232.999	+	403.567i	0.281061	+	0.486812i	−0.690586	+	0.723251i	$0.742647\pi$
$830$		0			0
$831$	−261.135	−	150.766i	−0.314242	−	0.181428i
$832$		0			0
$833$	−914.763	+	279.786i	−1.09815	+	0.335877i
$834$		0			0
$835$	−319.557	−	184.496i	−0.382703	−	0.220954i
$836$		0			0
$837$	294.125	−	169.813i	0.351403	−	0.202883i
$838$		0			0
$839$		−	24.9426i		−	0.0297289i	−0.999890	−	0.0148645i	$-0.995268\pi$
$839$		−	24.9426i		−	0.0297289i	0.999890	−	0.0148645i	$-0.00473168\pi$
$840$		0			0
$841$	−419.114			−0.498352
$842$		0			0
$843$	−628.011	−	1087.75i	−0.744972	−	1.29033i
$844$		0			0
$845$	−17.4280	+	30.1862i	−0.0206249	+	0.0357234i
$846$		0			0
$847$	−382.901	+	517.524i	−0.452068	+	0.611008i
$848$		0			0
$849$	579.479	−	1003.69i	0.682543	−	1.18220i
$850$		0			0
$851$	−93.7484	+	54.1257i	−0.110163	+	0.0636025i
$852$		0			0
$853$	−1642.90			−1.92603			−0.963016	−	0.269445i	$-0.913160\pi$
$853$	−1642.90			−1.92603			−0.963016	+	0.269445i	$0.913160\pi$
$854$		0			0
$855$	−495.465			−0.579491
$856$		0			0
$857$	−130.888	+	75.5681i	−0.152728	+	0.0881775i	−0.574416	−	0.818563i	$-0.694771\pi$
$857$	−130.888	+	75.5681i	−0.152728	+	0.0881775i	0.421688	+	0.906741i	$0.361438\pi$
$858$		0			0
$859$	450.007	−	779.435i	0.523873	−	0.907374i	−0.475741	−	0.879585i	$-0.657820\pi$
$859$	450.007	−	779.435i	0.523873	−	0.907374i	0.999614	−	0.0277890i	$-0.00884664\pi$
$860$		0			0
$861$	548.762	−	238.646i	0.637354	−	0.277173i
$862$		0			0
$863$	207.932	−	360.149i	0.240941	−	0.417322i	−0.720042	−	0.693931i	$-0.755877\pi$
$863$	207.932	−	360.149i	0.240941	−	0.417322i	0.960983	+	0.276609i	$0.0892107\pi$
$864$		0			0
$865$	448.683	+	777.142i	0.518709	+	0.898430i
$866$		0			0
$867$	−356.496			−0.411184
$868$		0			0
$869$		−	1996.42i		−	2.29737i
$870$		0			0
$871$	447.783	−	258.527i	0.514102	−	0.296817i
$872$		0			0
$873$	821.985	+	474.573i	0.941564	+	0.543612i
$874$		0			0
$875$	−914.824	−	104.178i	−1.04551	−	0.119060i
$876$		0			0
$877$	1488.56	+	859.419i	1.69733	+	0.979954i	0.948278	+	0.317442i	$0.102824\pi$
$877$	1488.56	+	859.419i	1.69733	+	0.979954i	0.749052	+	0.662511i	$0.230509\pi$
$878$		0			0
$879$	−158.133	−	273.894i	−0.179901	−	0.311598i
$880$		0			0
$881$			1094.47i			1.24231i	0.783689	+	0.621153i	$0.213336\pi$
$881$			1094.47i			1.24231i	−0.783689	+	0.621153i	$0.786664\pi$
$882$		0			0
$883$			527.301i			0.597170i	0.954383	+	0.298585i	$0.0965146\pi$
$883$			527.301i			0.597170i	−0.954383	+	0.298585i	$0.903485\pi$
$884$		0			0
$885$	−21.7853	−	37.7332i	−0.0246161	−	0.0426363i
$886$		0			0
$887$	−1459.99	−	842.925i	−1.64599	−	0.950310i	−0.978645	−	0.205558i	$-0.934099\pi$
$887$	−1459.99	−	842.925i	−1.64599	−	0.950310i	−0.667341	−	0.744752i	$-0.732568\pi$
$888$		0			0
$889$	318.921	+	36.3180i	0.358742	+	0.0408526i
$890$		0			0
$891$	1252.09	+	722.896i	1.40527	+	0.811331i
$892$		0			0
$893$	−647.023	+	373.559i	−0.724549	+	0.418319i
$894$		0			0
$895$		−	327.007i		−	0.365371i
$896$		0			0
$897$	435.832			0.485878
$898$		0			0
$899$	515.099	+	892.178i	0.572969	+	0.992412i
$900$		0			0
$901$	−352.897	+	611.236i	−0.391673	+	0.678398i
$902$		0			0
$903$	1982.37	−	862.096i	2.19532	−	0.954702i
$904$		0			0
$905$	803.700	−	1392.05i	0.888066	−	1.53818i
$906$		0			0
$907$	1439.38	−	831.024i	1.58696	−	0.916234i	0.593160	−	0.805085i	$-0.297880\pi$
$907$	1439.38	−	831.024i	1.58696	−	0.916234i	0.993804	−	0.111149i	$-0.0354530\pi$
$908$		0			0
$909$	416.073			0.457726
$910$		0			0
$911$	1220.19			1.33940			0.669698	−	0.742633i	$-0.266423\pi$
$911$	1220.19			1.33940			0.669698	+	0.742633i	$0.266423\pi$
$912$		0			0
$913$	−631.840	+	364.793i	−0.692048	+	0.399554i
$914$		0			0
$915$	−264.694	+	458.464i	−0.289283	+	0.501053i
$916$		0			0
$917$	−503.761	+	680.875i	−0.549357	+	0.742503i
$918$		0			0
$919$	−38.1217	+	66.0288i	−0.0414817	+	0.0718485i	−0.886021	−	0.463645i	$-0.846541\pi$
$919$	−38.1217	+	66.0288i	−0.0414817	+	0.0718485i	0.844539	+	0.535494i	$0.179875\pi$
$920$		0			0
$921$	700.312	+	1212.98i	0.760382	+	1.31702i
$922$		0			0
$923$	−287.471			−0.311452
$924$		0			0
$925$		−	38.1129i		−	0.0412032i
$926$		0			0
$927$	101.538	−	58.6232i	0.109534	−	0.0632397i
$928$		0			0
$929$	200.762	+	115.910i	0.216106	+	0.124769i	0.604146	−	0.796874i	$-0.293514\pi$
$929$	200.762	+	115.910i	0.216106	+	0.124769i	−0.388040	+	0.921643i	$0.626848\pi$
$930$		0			0
$931$	−592.249	+	635.255i	−0.636142	+	0.682336i
$932$		0			0
$933$	632.758	+	365.323i	0.678197	+	0.391557i
$934$		0			0
$935$	666.323	+	1154.11i	0.712645	+	1.23434i
$936$		0			0
$937$		−	985.061i		−	1.05129i	−0.850703	−	0.525646i	$-0.823824\pi$
$937$		−	985.061i		−	1.05129i	0.850703	−	0.525646i	$-0.176176\pi$
$938$		0			0
$939$			99.4088i			0.105867i
$940$		0			0
$941$	704.239	+	1219.78i	0.748394	+	1.29626i	0.948592	+	0.316501i	$0.102508\pi$
$941$	704.239	+	1219.78i	0.748394	+	1.29626i	−0.200198	+	0.979756i	$0.564158\pi$
$942$		0			0
$943$	−169.513	−	97.8683i	−0.179759	−	0.103784i
$944$		0			0
$945$	227.910	−	308.040i	0.241175	−	0.325968i
$946$		0			0
$947$	144.121	+	83.2085i	0.152187	+	0.0878654i	0.574160	−	0.818743i	$-0.305329\pi$
$947$	144.121	+	83.2085i	0.152187	+	0.0878654i	−0.421972	+	0.906609i	$0.638662\pi$
$948$		0			0
$949$	−840.888	+	485.487i	−0.886078	+	0.511577i
$950$		0			0
$951$		−	1931.56i		−	2.03109i
$952$		0			0
$953$	815.618			0.855843			0.427921	−	0.903816i	$-0.359246\pi$
$953$	815.618			0.855843			0.427921	+	0.903816i	$0.359246\pi$
$954$		0			0
$955$	326.918	+	566.238i	0.342322	+	0.592920i
$956$		0			0
$957$	−1002.37	+	1736.16i	−1.04741	+	1.81417i
$958$		0			0
$959$	−405.458	−	932.343i	−0.422792	−	0.972203i
$960$		0			0
$961$	−59.3833	+	102.855i	−0.0617933	+	0.107029i
$962$		0			0
$963$	231.593	−	133.710i	0.240491	−	0.138848i
$964$		0			0
$965$	−107.227			−0.111116
$966$		0			0
$967$	86.3395			0.0892860			0.0446430	−	0.999003i	$-0.485785\pi$
$967$	86.3395			0.0892860			0.0446430	+	0.999003i	$0.485785\pi$
$968$		0			0
$969$	−1159.68	+	669.540i	−1.19678	+	0.690960i
$970$		0			0
$971$	339.651	−	588.292i	0.349795	−	0.605862i	−0.636418	−	0.771344i	$-0.719585\pi$
$971$	339.651	−	588.292i	0.349795	−	0.605862i	0.986213	+	0.165482i	$0.0529180\pi$
$972$		0			0
$973$	−600.571	−	68.3915i	−0.617236	−	0.0702893i
$974$		0			0
$975$	−76.7235	+	132.889i	−0.0786908	+	0.136296i
$976$		0			0
$977$	107.029	+	185.379i	0.109548	+	0.189743i	0.915587	−	0.402119i	$-0.131726\pi$
$977$	107.029	+	185.379i	0.109548	+	0.189743i	−0.806039	+	0.591862i	$0.798393\pi$
$978$		0			0
$979$	16.3459			0.0166965
$980$		0			0
$981$		−	338.267i		−	0.344818i
$982$		0			0
$983$	−1559.10	+	900.146i	−1.58606	+	0.915713i	−0.592114	+	0.805854i	$0.701707\pi$
$983$	−1559.10	+	900.146i	−1.58606	+	0.915713i	−0.993947	+	0.109859i	$0.964960\pi$
$984$		0			0
$985$	1165.82	+	673.084i	1.18357	+	0.683334i
$986$		0			0
$987$	−129.195	+	1134.51i	−0.130897	+	1.14945i
$988$		0			0
$989$	−612.357	−	353.544i	−0.619168	−	0.357477i
$990$		0			0
$991$	205.714	+	356.306i	0.207582	+	0.359542i	0.950952	−	0.309338i	$-0.100107\pi$
$991$	205.714	+	356.306i	0.207582	+	0.359542i	−0.743370	+	0.668880i	$0.766774\pi$
$992$		0			0
$993$		−	966.925i		−	0.973741i
$994$		0			0
$995$		−	306.302i		−	0.307841i
$996$		0			0
$997$	−806.000	−	1396.03i	−0.808425	−	1.40023i	−0.913954	−	0.405817i	$-0.866987\pi$
$997$	−806.000	−	1396.03i	−0.808425	−	1.40023i	0.105529	−	0.994416i	$-0.466346\pi$
$998$		0			0
$999$	123.816	+	71.4854i	0.123940	+	0.0715569i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	224.3.n.a.145.3		28
4.3	odd	2		56.3.j.a.5.9	✓	28
7.2	even	3		1568.3.h.a.881.23		28
7.3	odd	6	inner	224.3.n.a.17.12		28
7.5	odd	6		1568.3.h.a.881.5		28
8.3	odd	2		56.3.j.a.5.11	yes	28
8.5	even	2	inner	224.3.n.a.145.12		28
28.3	even	6		56.3.j.a.45.11	yes	28
28.11	odd	6		392.3.j.e.325.11		28
28.19	even	6		392.3.h.a.293.4		28
28.23	odd	6		392.3.h.a.293.3		28
28.27	even	2		392.3.j.e.117.9		28
56.3	even	6		56.3.j.a.45.9	yes	28
56.5	odd	6		1568.3.h.a.881.24		28
56.11	odd	6		392.3.j.e.325.9		28
56.19	even	6		392.3.h.a.293.1		28
56.27	even	2		392.3.j.e.117.11		28
56.37	even	6		1568.3.h.a.881.6		28
56.45	odd	6	inner	224.3.n.a.17.3		28
56.51	odd	6		392.3.h.a.293.2		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
56.3.j.a.5.9	✓	28	4.3	odd	2
56.3.j.a.5.11	yes	28	8.3	odd	2
56.3.j.a.45.9	yes	28	56.3	even	6
56.3.j.a.45.11	yes	28	28.3	even	6
224.3.n.a.17.3		28	56.45	odd	6	inner
224.3.n.a.17.12		28	7.3	odd	6	inner
224.3.n.a.145.3		28	1.1	even	1	trivial
224.3.n.a.145.12		28	8.5	even	2	inner
392.3.h.a.293.1		28	56.19	even	6
392.3.h.a.293.2		28	56.51	odd	6
392.3.h.a.293.3		28	28.23	odd	6
392.3.h.a.293.4		28	28.19	even	6
392.3.j.e.117.9		28	28.27	even	2
392.3.j.e.117.11		28	56.27	even	2
392.3.j.e.325.9		28	56.11	odd	6
392.3.j.e.325.11		28	28.11	odd	6
1568.3.h.a.881.5		28	7.5	odd	6
1568.3.h.a.881.6		28	56.37	even	6
1568.3.h.a.881.23		28	7.2	even	3
1568.3.h.a.881.24		28	56.5	odd	6

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:	\( N \)	\(=\)	\( 224 = 2^{5} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	224.n (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.93494 - 3.35141i) q^{3} +(2.33882 - 4.05096i) q^{5} +(-6.95505 - 0.792023i) q^{7} +(-2.98798 + 5.17534i) q^{9} +O(q^{10})\)	\(q+(-1.93494 - 3.35141i) q^{3} +(2.33882 - 4.05096i) q^{5} +(-6.95505 - 0.792023i) q^{7} +(-2.98798 + 5.17534i) q^{9} +(12.6383 - 7.29671i) q^{11} -12.7102 q^{13} -18.1019 q^{15} +(-16.9068 + 9.76116i) q^{17} +(-8.86233 + 15.3500i) q^{19} +(10.8032 + 24.8418i) q^{21} +(4.43038 - 7.67364i) q^{23} +(1.55984 + 2.70172i) q^{25} -11.7027 q^{27} -35.4981i q^{29} +(-25.1331 + 14.5106i) q^{31} +(-48.9086 - 28.2374i) q^{33} +(-19.4751 + 26.3222i) q^{35} +(-10.5802 - 6.10847i) q^{37} +(24.5934 + 42.5970i) q^{39} -22.0903i q^{41} -79.8001i q^{43} +(13.9767 + 24.2084i) q^{45} +(36.5041 + 21.0756i) q^{47} +(47.7454 + 11.0171i) q^{49} +(65.4273 + 37.7745i) q^{51} +(31.3096 - 18.0766i) q^{53} -68.2627i q^{55} +68.5923 q^{57} +(1.20348 + 2.08449i) q^{59} +(14.6224 - 25.3268i) q^{61} +(24.8805 - 33.6282i) q^{63} +(-29.7268 + 51.4883i) q^{65} +(-35.2303 + 20.3402i) q^{67} -34.2900 q^{69} +22.6174 q^{71} +(66.1587 - 38.1967i) q^{73} +(6.03639 - 10.4553i) q^{75} +(-93.6789 + 40.7391i) q^{77} +(68.4014 - 118.475i) q^{79} +(49.5358 + 85.7985i) q^{81} -49.9942 q^{83} +91.3184i q^{85} +(-118.969 + 68.6866i) q^{87} +(0.970023 + 0.560043i) q^{89} +(88.3998 + 10.0667i) q^{91} +(97.2622 + 56.1544i) q^{93} +(41.4548 + 71.8018i) q^{95} -158.827i q^{97} +87.2097i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 4 q^{7} - 32 q^{9}+O(q^{10}) \) 28 * q + 4 * q^7 - 32 * q^9	\( 28 q + 4 q^{7} - 32 q^{9} - 28 q^{15} - 6 q^{17} - 30 q^{23} - 32 q^{25} + 6 q^{31} - 6 q^{33} + 20 q^{39} + 294 q^{47} - 20 q^{49} + 124 q^{57} - 432 q^{63} - 52 q^{65} + 136 q^{71} + 234 q^{73} + 162 q^{79} - 18 q^{81} - 48 q^{87} - 150 q^{89} - 290 q^{95}+O(q^{100}) \) 28 * q + 4 * q^7 - 32 * q^9 - 28 * q^15 - 6 * q^17 - 30 * q^23 - 32 * q^25 + 6 * q^31 - 6 * q^33 + 20 * q^39 + 294 * q^47 - 20 * q^49 + 124 * q^57 - 432 * q^63 - 52 * q^65 + 136 * q^71 + 234 * q^73 + 162 * q^79 - 18 * q^81 - 48 * q^87 - 150 * q^89 - 290 * q^95

Introduction

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