LMFDB - Embedded newform 224.3.n.a.17.3

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			17.3
Character	$\chi$	$=$	224.17
Dual form			224.3.n.a.145.3

$q$-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 $\left(\mathbb{Z}/224\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.93494	+	3.35141i	−0.644980	+	1.11714i	0.339326	+	0.940669i	$0.389801\pi$
$3$	−1.93494	+	3.35141i	−0.644980	+	1.11714i	−0.984306	+	0.176469i	$0.943532\pi$
$4$		0			0
$5$	2.33882	+	4.05096i	0.467764	+	0.810191i	0.999322	−	0.0368311i	$-0.0117264\pi$
$5$	2.33882	+	4.05096i	0.467764	+	0.810191i	−0.531557	+	0.847022i	$0.678393\pi$
$6$		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	0.948627	−	0.316396i	$-0.102473\pi$
$11$	12.6383	+	7.29671i	1.14893	+	0.663337i	0.200306	+	0.979733i	$0.435806\pi$
$12$		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	−0.0878969	−	0.996130i	$-0.528015\pi$
$17$	−16.9068	−	9.76116i	−0.994519	−	0.574186i	−0.906622	+	0.421944i	$0.861348\pi$
$18$		0			0
$19$	−8.86233	−	15.3500i	−0.466439	−	0.807895i	0.532827	−	0.846224i	$-0.321130\pi$
$19$	−8.86233	−	15.3500i	−0.466439	−	0.807895i	−0.999265	+	0.0383291i	$0.987796\pi$
$20$		0			0
$21$	10.8032	−	24.8418i	0.514438	−	1.18294i
$22$		0			0
$23$	4.43038	+	7.67364i	0.192625	+	0.333636i	0.946119	−	0.323818i	$-0.104967\pi$
$23$	4.43038	+	7.67364i	0.192625	+	0.333636i	−0.753494	+	0.657454i	$0.771633\pi$
$24$		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	$0.209649\pi$
$29$			35.4981i			1.22407i	−0.790830	+	0.612036i	$0.790351\pi$
$30$		0			0
$31$	−25.1331	−	14.5106i	−0.810747	−	0.468085i	0.0364685	−	0.999335i	$-0.488389\pi$
$31$	−25.1331	−	14.5106i	−0.810747	−	0.468085i	−0.847215	+	0.531250i	$0.821722\pi$
$32$		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	−0.636114	−	0.771595i	$-0.719459\pi$
$37$	−10.5802	+	6.10847i	−0.285951	+	0.165094i	0.350163	+	0.936689i	$0.386126\pi$
$38$		0			0
$39$	24.5934	−	42.5970i	0.630600	−	1.09223i
$40$		0			0
$41$			22.0903i			0.538788i	0.963030	+	0.269394i	$0.0868233\pi$
$41$			22.0903i			0.538788i	−0.963030	+	0.269394i	$0.913177\pi$
$42$		0			0
$43$			79.8001i			1.85582i	0.372809	+	0.927908i	$0.378395\pi$
$43$			79.8001i			1.85582i	−0.372809	+	0.927908i	$0.621605\pi$
$44$		0			0
$45$	13.9767	−	24.2084i	0.310593	−	0.537964i
$46$		0			0
$47$	36.5041	−	21.0756i	0.776682	−	0.448418i	−0.0585708	−	0.998283i	$-0.518654\pi$
$47$	36.5041	−	21.0756i	0.776682	−	0.448418i	0.835253	+	0.549865i	$0.185321\pi$
$48$		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	0.765393	−	0.643563i	$-0.222545\pi$
$53$	31.3096	+	18.0766i	0.590748	+	0.341068i	−0.174645	+	0.984631i	$0.555878\pi$
$54$		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	−0.855646	−	0.517561i	$-0.826840\pi$
$59$	1.20348	−	2.08449i	0.0203979	−	0.0353303i	0.876044	+	0.482231i	$0.160173\pi$
$60$		0			0
$61$	14.6224	+	25.3268i	0.239712	+	0.415194i	0.960632	−	0.277825i	$-0.0896136\pi$
$61$	14.6224	+	25.3268i	0.239712	+	0.415194i	−0.720919	+	0.693019i	$0.756280\pi$
$62$		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	0.213490	−	0.976945i	$-0.431517\pi$
$67$	−35.2303	−	20.3402i	−0.525825	−	0.303585i	−0.739315	+	0.673360i	$0.764850\pi$
$68$		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	0.879233	−	0.476391i	$-0.158055\pi$
$73$	66.1587	+	38.1967i	0.906283	+	0.523243i	0.0270498	+	0.999634i	$0.491389\pi$
$74$		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	0.866211	+	0.499679i	$0.166549\pi$
$79$	68.4014	+	118.475i	0.865840	+	1.49968i	−0.000370612		1.00000i	$0.500118\pi$
$80$		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	−0.494541	−	0.869155i	$-0.664664\pi$
$89$	0.970023	−	0.560043i	0.0108991	−	0.00629262i	0.505440	+	0.862862i	$0.331330\pi$
$90$		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	$0.305304\pi$
$97$			158.827i			1.63740i	−0.574225	+	0.818698i	$0.694696\pi$
$98$		0			0
$99$		−	87.2097i		−	0.880906i
$100$		0			0
$101$	−34.8122	+	60.2965i	−0.344675	+	0.596995i	−0.985295	−	0.170864i	$-0.945344\pi$
$101$	−34.8122	+	60.2965i	−0.344675	+	0.596995i	0.640620	+	0.767858i	$0.278678\pi$
$102$		0			0
$103$	−16.9911	+	9.80983i	−0.164962	+	0.0952411i	−0.580208	−	0.814468i	$-0.697029\pi$
$103$	−16.9911	+	9.80983i	−0.164962	+	0.0952411i	0.415246	+	0.909709i	$0.363696\pi$
$104$		0			0
$105$	125.900	−	14.3371i	1.19904	−	0.136544i
$106$		0			0
$107$	−38.7540	+	22.3747i	−0.362187	+	0.209109i	−0.670040	−	0.742325i	$-0.733723\pi$
$107$	−38.7540	+	22.3747i	−0.362187	+	0.209109i	0.307852	+	0.951434i	$0.400390\pi$
$108$		0			0
$109$	−49.0210	−	28.3023i	−0.449734	−	0.259654i	0.257984	−	0.966149i	$-0.416942\pi$
$109$	−49.0210	−	28.3023i	−0.449734	−	0.259654i	−0.707718	+	0.706495i	$0.750275\pi$
$110$		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	0.999052	−	0.0435409i	$-0.0138639\pi$
$131$	60.4982	+	104.786i	0.461818	+	0.799893i	−0.537233	+	0.843434i	$0.680531\pi$
$132$		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	−0.469306	−	0.883036i	$-0.655496\pi$
$137$	72.6207	−	125.783i	0.530078	−	0.918122i	0.999384	−	0.0350869i	$-0.0111708\pi$
$138$		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	−0.975374	−	0.220556i	$-0.929213\pi$
$149$	−189.536	+	109.429i	−1.27205	+	0.734421i	−0.296680	+	0.954977i	$0.595879\pi$
$150$		0			0
$151$	41.6552	−	72.1490i	0.275862	−	0.477808i	−0.694490	−	0.719502i	$-0.744370\pi$
$151$	41.6552	−	72.1490i	0.275862	−	0.477808i	0.970352	+	0.241695i	$0.0777033\pi$
$152$		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	−0.804056	−	0.594554i	$-0.797329\pi$
$157$	17.7207	−	30.6932i	0.112871	−	0.195498i	0.916927	+	0.399056i	$0.130662\pi$
$158$		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	−0.527516	−	0.849545i	$-0.676877\pi$
$163$	−9.05412	+	5.22740i	−0.0555468	+	0.0320699i	0.471969	+	0.881615i	$0.343543\pi$
$164$		0			0
$165$	−228.777	−	132.084i	−1.38653	−	0.800511i
$166$		0			0
$167$			78.8843i			0.472361i	0.971709	+	0.236181i	$0.0758957\pi$
$167$			78.8843i			0.472361i	−0.971709	+	0.236181i	$0.924104\pi$
$168$		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	−0.997946	−	0.0640660i	$-0.979593\pi$
$173$	−95.9208	−	166.140i	−0.554456	−	0.960345i	0.443490	−	0.896279i	$-0.353740\pi$
$174$		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	0.659488	−	0.751715i	$-0.270773\pi$
$179$	60.5426	+	34.9543i	0.338227	+	0.195275i	−0.321261	+	0.946991i	$0.604107\pi$
$180$		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	0.623009	−	0.782215i	$-0.285910\pi$
$191$	−69.8895	−	121.052i	−0.365913	−	0.633781i	−0.988922	+	0.148434i	$0.952577\pi$
$192$		0			0
$193$	−11.4616	+	19.8521i	−0.0593867	+	0.102861i	−0.894190	−	0.447687i	$-0.852248\pi$
$193$	−11.4616	+	19.8521i	−0.0593867	+	0.102861i	0.834804	+	0.550548i	$0.185581\pi$
$194$		0			0
$195$	230.078			1.17989
$196$		0			0
$197$		−	287.788i		−	1.46085i	−0.682992	−	0.730426i	$-0.739322\pi$
$197$		−	287.788i		−	1.46085i	0.682992	−	0.730426i	$-0.260678\pi$
$198$		0			0
$199$	56.7091	+	32.7410i	0.284970	+	0.164528i	0.635671	−	0.771960i	$-0.280723\pi$
$199$	56.7091	+	32.7410i	0.284970	+	0.164528i	−0.350701	+	0.936487i	$0.614057\pi$
$200$		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	$0.0135047\pi$
$211$			17.8985i			0.0848270i	−0.999100	+	0.0424135i	$0.986495\pi$
$212$		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	$0.197205\pi$
$223$			258.973i			1.16132i	−0.814148	+	0.580658i	$0.802795\pi$
$224$		0			0
$225$	−18.6431			−0.0828581
$226$		0			0
$227$	−58.6721	+	101.623i	−0.258468	+	0.447679i	−0.965832	−	0.259171i	$-0.916551\pi$
$227$	−58.6721	+	101.623i	−0.258468	+	0.447679i	0.707364	+	0.706849i	$0.249884\pi$
$228$		0			0
$229$	−43.5475	−	75.4264i	−0.190164	−	0.329373i	0.755141	−	0.655563i	$-0.227569\pi$
$229$	−43.5475	−	75.4264i	−0.190164	−	0.329373i	−0.945304	+	0.326190i	$0.894235\pi$
$230$		0			0
$231$	317.797	−	235.129i	1.37574	−	1.01787i
$232$		0			0
$233$	155.825	+	269.897i	0.668778	+	1.15836i	0.978246	+	0.207448i	$0.0665159\pi$
$233$	155.825	+	269.897i	0.668778	+	1.15836i	−0.309468	+	0.950910i	$0.600151\pi$
$234$		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	0.411106	−	0.911588i	$-0.365143\pi$
$241$	−41.6447	−	24.0436i	−0.172799	−	0.0997658i	−0.583905	+	0.811822i	$0.698476\pi$
$242$		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	−0.234066	−	0.972221i	$-0.575203\pi$
$257$	126.153	−	72.8347i	0.490869	−	0.283403i	0.724935	+	0.688817i	$0.241870\pi$
$258$		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	−0.305529	−	0.952183i	$-0.598833\pi$
$263$	176.696	−	306.047i	0.671850	−	1.16368i	0.977379	−	0.211495i	$-0.0678333\pi$
$264$		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	−0.962906	−	0.269838i	$-0.913030\pi$
$269$	−66.6490	+	115.439i	−0.247766	+	0.429143i	0.715140	+	0.698981i	$0.246363\pi$
$270$		0			0
$271$	326.342	−	188.414i	1.20421	−	0.695253i	0.242725	−	0.970095i	$-0.421959\pi$
$271$	326.342	−	188.414i	1.20421	−	0.695253i	0.961489	+	0.274842i	$0.0886255\pi$
$272$		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	0.616833	−	0.787094i	$-0.288415\pi$
$277$	67.4788	+	38.9589i	0.243606	+	0.140646i	−0.373227	+	0.927740i	$0.621749\pi$
$278$		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	−0.470304	−	0.882505i	$-0.655856\pi$
$283$	149.741	−	259.359i	0.529119	−	0.916462i	0.999423	−	0.0339572i	$-0.0108110\pi$
$284$		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	0.213534	−	0.976936i	$-0.431503\pi$
$311$	−163.508	−	94.4017i	−0.525751	−	0.303542i	−0.739284	+	0.673393i	$0.764836\pi$
$312$		0			0
$313$	−22.2463	+	12.8439i	−0.0710745	+	0.0410349i	−0.535116	−	0.844779i	$-0.679732\pi$
$313$	−22.2463	+	12.8439i	−0.0710745	+	0.0410349i	0.464042	+	0.885813i	$0.346399\pi$
$314$		0			0
$315$	−78.0351	+	179.440i	−0.247730	+	0.569651i
$316$		0			0
$317$	432.257	−	249.564i	1.36359	−	0.787268i	0.373489	−	0.927635i	$-0.378162\pi$
$317$	432.257	−	249.564i	1.36359	−	0.787268i	0.990100	+	0.140367i	$0.0448282\pi$
$318$		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	−0.136154	−	0.990688i	$-0.543474\pi$
$331$	216.384	−	124.930i	0.653729	−	0.377431i	0.789883	+	0.613257i	$0.210141\pi$
$332$		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	0.890436	−	0.455109i	$-0.150400\pi$
$347$	326.707	+	188.624i	0.941518	+	0.543586i	0.0510824	+	0.998694i	$0.483733\pi$
$348$		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	0.816973	−	0.576676i	$-0.195650\pi$
$353$	256.293	+	147.971i	0.726043	+	0.419181i	−0.0909296	+	0.995857i	$0.528984\pi$
$354$		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	0.687035	−	0.726624i	$-0.258912\pi$
$359$	−102.587	−	177.686i	−0.285757	−	0.494946i	−0.972793	+	0.231678i	$0.925578\pi$
$360$		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	0.855349	−	0.518052i	$-0.173343\pi$
$367$	306.216	+	176.794i	0.834377	+	0.481728i	−0.0209719	+	0.999780i	$0.506676\pi$
$368$		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	−0.854285	−	0.519804i	$-0.826005\pi$
$373$	−310.062	+	179.014i	−0.831264	+	0.479931i	0.0230210	+	0.999735i	$0.492672\pi$
$374$		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	$0.237585\pi$
$379$			514.679i			1.35799i	−0.734142	+	0.678996i	$0.762415\pi$
$380$		0			0
$381$	88.7260	−	153.678i	0.232877	−	0.403354i
$382$		0			0
$383$	−450.193	+	259.919i	−1.17544	+	0.678639i	−0.954955	−	0.296752i	$-0.904097\pi$
$383$	−450.193	+	259.919i	−1.17544	+	0.678639i	−0.220483	+	0.975391i	$0.570763\pi$
$384$		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	0.377997	−	0.925807i	$-0.376613\pi$
$389$	−91.3278	−	52.7281i	−0.234776	−	0.135548i	−0.612773	+	0.790259i	$0.709946\pi$
$390$		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	0.999328	−	0.0366619i	$-0.0116725\pi$
$397$	185.762	+	321.749i	0.467914	+	0.810450i	−0.531414	+	0.847112i	$0.678339\pi$
$398$		0			0
$399$	−477.063	+	54.3267i	−1.19565	+	0.136157i
$400$		0			0
$401$	−149.636	−	259.177i	−0.373157	−	0.646327i	0.616893	−	0.787047i	$-0.288391\pi$
$401$	−149.636	−	259.177i	−0.373157	−	0.646327i	−0.990049	+	0.140721i	$0.955058\pi$
$402$		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	0.478279	−	0.878208i	$-0.341261\pi$
$409$	−17.6410	−	10.1850i	−0.0431320	−	0.0249023i	−0.521411	+	0.853306i	$0.674594\pi$
$410$		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	$0.113141\pi$
$421$			293.022i			0.696014i	−0.937492	+	0.348007i	$0.886859\pi$
$422$		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	−0.906354	−	0.422520i	$-0.861146\pi$
$431$	−37.6108	+	65.1439i	−0.0872641	+	0.151146i	0.819090	+	0.573666i	$0.194479\pi$
$432$		0			0
$433$			506.209i			1.16907i	0.811367	+	0.584536i	$0.198724\pi$
$433$			506.209i			1.16907i	−0.811367	+	0.584536i	$0.801276\pi$
$434$		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	−0.330284	−	0.943882i	$-0.607144\pi$
$439$	141.358	−	81.6130i	0.322000	−	0.185907i	0.652284	+	0.757975i	$0.273811\pi$
$440$		0			0
$441$	−199.680	−	214.180i	−0.452788	−	0.485668i
$442$		0			0
$443$	−98.4732	+	56.8535i	−0.222287	+	0.128338i	−0.607009	−	0.794695i	$-0.707631\pi$
$443$	−98.4732	+	56.8535i	−0.222287	+	0.128338i	0.384722	+	0.923033i	$0.374297\pi$
$444$		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	−0.987997	−	0.154471i	$-0.950633\pi$
$457$	−286.893	−	496.913i	−0.627774	−	1.08734i	0.360223	−	0.932866i	$-0.382701\pi$
$458$		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	−0.972546	−	0.232709i	$-0.925241\pi$
$467$	−321.205	−	556.343i	−0.687805	−	1.19131i	0.284741	−	0.958604i	$-0.408092\pi$
$468$		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	0.832188	−	0.554493i	$-0.187088\pi$
$479$	367.909	+	212.412i	0.768077	+	0.443449i	−0.0641112	+	0.997943i	$0.520421\pi$
$480$		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	−0.122949	−	0.992413i	$-0.539235\pi$
$487$	388.616	−	673.103i	0.797980	−	1.38214i	0.920929	−	0.389729i	$-0.127431\pi$
$488$		0			0
$489$		−	40.4588i		−	0.0827379i
$490$		0			0
$491$		−	476.370i		−	0.970203i	−0.874458	−	0.485102i	$-0.838783\pi$
$491$		−	476.370i		−	0.970203i	0.874458	−	0.485102i	$-0.161217\pi$
$492$		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	−0.827728	−	0.561129i	$-0.810367\pi$
$499$	−377.065	+	217.698i	−0.755641	+	0.436269i	0.0720876	+	0.997398i	$0.477034\pi$
$500$		0			0
$501$	−264.374	−	152.636i	−0.527693	−	0.304663i
$502$		0			0
$503$			375.404i			0.746329i	0.927765	+	0.373165i	$0.121727\pi$
$503$			375.404i			0.746329i	−0.927765	+	0.373165i	$0.878273\pi$
$504$		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	0.784242	−	0.620456i	$-0.213052\pi$
$509$	−73.9117	−	128.019i	−0.145210	−	0.251510i	−0.929451	+	0.368945i	$0.879719\pi$
$510$		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	0.998464	−	0.0554019i	$-0.0176440\pi$
$521$	755.302	+	436.074i	1.44972	+	0.836994i	0.451253	+	0.892396i	$0.350977\pi$
$522$		0			0
$523$	−178.600	−	309.344i	−0.341491	−	0.591480i	0.643219	−	0.765683i	$-0.277599\pi$
$523$	−178.600	−	309.344i	−0.341491	−	0.591480i	−0.984710	+	0.174202i	$0.944265\pi$
$524$		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	−0.999958	−	0.00911085i	$-0.997100\pi$
$541$	−807.198	+	466.036i	−1.49205	+	0.861434i	−0.492089	+	0.870545i	$0.663767\pi$
$542$		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	$-0.955808\pi$
$547$		−	151.397i		−	0.276778i	0.990378	−	0.138389i	$-0.0441924\pi$
$548$		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	0.993586	−	0.113082i	$-0.0360722\pi$
$557$	775.593	+	447.789i	1.39245	+	0.803929i	0.398861	+	0.917011i	$0.369406\pi$
$558$		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	−0.963136	−	0.269017i	$-0.913301\pi$
$563$	−139.958	+	242.414i	−0.248592	+	0.430575i	0.714543	+	0.699591i	$0.246635\pi$
$564$		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	0.689207	−	0.724564i	$-0.257959\pi$
$569$	−160.963	−	278.796i	−0.282887	−	0.489975i	−0.972095	+	0.234589i	$0.924626\pi$
$570$		0			0
$571$	−712.583	−	411.410i	−1.24796	−	0.720508i	−0.277255	−	0.960796i	$-0.589425\pi$
$571$	−712.583	−	411.410i	−1.24796	−	0.720508i	−0.970702	+	0.240288i	$0.922758\pi$
$572$		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	0.998111	−	0.0614420i	$-0.0195699\pi$
$577$	833.162	+	481.027i	1.44396	+	0.833668i	0.445845	+	0.895110i	$0.352903\pi$
$578$		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	−0.234330	−	0.972157i	$-0.575290\pi$
$593$	290.818	−	167.904i	0.490418	−	0.283143i	0.724748	+	0.689014i	$0.241956\pi$
$594$		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	−0.890097	−	0.455771i	$-0.849364\pi$
$599$	−30.1532	+	52.2269i	−0.0503393	+	0.0871902i	0.839758	+	0.542961i	$0.182697\pi$
$600$		0			0
$601$		−	509.153i		−	0.847176i	−0.905855	−	0.423588i	$-0.860770\pi$
$601$		−	509.153i		−	0.847176i	0.905855	−	0.423588i	$-0.139230\pi$
$602$		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	0.483480	−	0.875355i	$-0.339373\pi$
$607$	900.363	−	519.825i	1.48330	−	0.856384i	0.999820	+	0.0189717i	$0.00603923\pi$
$608$		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	0.633894	−	0.773420i	$-0.281456\pi$
$613$	172.277	+	99.4641i	0.281039	+	0.162258i	−0.352855	+	0.935678i	$0.614789\pi$
$614$		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	−0.616955	−	0.786998i	$-0.711634\pi$
$619$	230.938	−	399.997i	0.373083	−	0.646199i	0.990038	+	0.140799i	$0.0449673\pi$
$620$		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	−0.909894	−	0.414841i	$-0.863837\pi$
$641$	−61.3334	+	106.233i	−0.0956840	+	0.165730i	0.814210	+	0.580571i	$0.197170\pi$
$642$		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	0.0502683	−	0.998736i	$-0.483992\pi$
$647$	−510.825	−	294.925i	−0.789528	−	0.455834i	−0.839796	+	0.542901i	$0.817326\pi$
$648$		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	−0.326008	−	0.945367i	$-0.605704\pi$
$653$	215.294	−	124.300i	0.329700	−	0.190352i	0.655708	+	0.755015i	$0.272370\pi$
$654$		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	$0.161647\pi$
$659$			640.918i			0.972562i	−0.873802	+	0.486281i	$0.838353\pi$
$660$		0			0
$661$	−483.321	+	837.137i	−0.731197	+	1.26647i	0.225175	+	0.974318i	$0.427705\pi$
$661$	−483.321	+	837.137i	−0.731197	+	1.26647i	−0.956372	+	0.292152i	$0.905629\pi$
$662$		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	0.997256	+	0.0740362i	$0.0235880\pi$
$677$	380.978	+	659.874i	0.562745	+	0.974703i	−0.434511	+	0.900667i	$0.643079\pi$
$678$		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	−0.0657781	−	0.997834i	$-0.520953\pi$
$683$	−657.604	−	379.668i	−0.962817	−	0.555883i	−0.897039	+	0.441952i	$0.854286\pi$
$684$		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	0.632393	−	0.774648i	$-0.282073\pi$
$691$	−245.076	−	424.484i	−0.354669	−	0.614304i	−0.987061	+	0.160344i	$0.948740\pi$
$692$		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	$-0.864853\pi$
$701$		−	577.533i		−	0.823870i	0.911213	−	0.411935i	$-0.135147\pi$
$702$		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	0.00169497	−	0.999999i	$-0.499460\pi$
$709$	615.814	−	355.540i	0.868567	−	0.501467i	0.866872	+	0.498531i	$0.166127\pi$
$710$		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	−0.391721	−	0.920084i	$-0.628120\pi$
$719$	150.440	−	86.8564i	0.209235	−	0.120802i	0.600956	+	0.799282i	$0.294787\pi$
$720$		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	$0.258930\pi$
$727$			1056.57i			1.45333i	−0.686993	+	0.726664i	$0.741070\pi$
$728$		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	0.776596	−	0.629999i	$-0.216945\pi$
$733$	−115.299	−	199.703i	−0.157297	−	0.272446i	−0.933893	+	0.357553i	$0.883611\pi$
$734$		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	0.551517	−	0.834164i	$-0.314049\pi$
$739$	77.4971	+	44.7430i	0.104868	+	0.0605453i	−0.446649	+	0.894709i	$0.647383\pi$
$740$		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	−0.732877	−	0.680361i	$-0.761823\pi$
$751$	−717.692	−	1243.08i	−0.955649	−	1.65523i	−0.222772	−	0.974871i	$-0.571510\pi$
$752$		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	$-0.848747\pi$
$757$		−	692.645i		−	0.914987i	0.889213	−	0.457494i	$-0.151253\pi$
$758$		0			0
$759$	−433.367	−	250.204i	−0.570971	−	0.329650i
$760$		0			0
$761$	−999.810	+	577.241i	−1.31381	+	0.758529i	−0.982725	−	0.185071i	$-0.940748\pi$
$761$	−999.810	+	577.241i	−1.31381	+	0.758529i	−0.331086	+	0.943601i	$0.607415\pi$
$762$		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	$0.197470\pi$
$769$			894.095i			1.16267i	−0.813663	+	0.581336i	$0.802530\pi$
$770$		0			0
$771$			563.723i			0.731158i
$772$		0			0
$773$	464.538	−	804.603i	0.600954	−	1.04088i	−0.391722	−	0.920083i	$-0.628121\pi$
$773$	464.538	−	804.603i	0.600954	−	1.04088i	0.992677	−	0.120800i	$-0.0385460\pi$
$774$		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	−0.0298746	+	0.999554i	$0.509511\pi$
$787$	−693.013	+	1200.33i	−0.880576	+	1.52520i	−0.850702	+	0.525649i	$0.823823\pi$
$788$		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	−0.979510	−	0.201395i	$-0.935453\pi$
$809$	−255.112	+	441.867i	−0.315342	+	0.546189i	0.664168	+	0.747583i	$0.268786\pi$
$810$		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	−0.598271	−	0.801294i	$-0.704145\pi$
$821$	−167.045	+	96.4438i	−0.203466	+	0.117471i	0.394805	+	0.918765i	$0.370812\pi$
$822$		0			0
$823$	71.3241	−	123.537i	0.0866636	−	0.150106i	−0.819435	−	0.573172i	$-0.805713\pi$
$823$	71.3241	−	123.537i	0.0866636	−	0.150106i	0.906099	+	0.423066i	$0.139046\pi$
$824$		0			0
$825$			176.183i			0.213555i
$826$		0			0
$827$			91.3639i			0.110476i	0.998473	+	0.0552382i	$0.0175918\pi$
$827$			91.3639i			0.110476i	−0.998473	+	0.0552382i	$0.982408\pi$
$828$		0			0
$829$	232.999	−	403.567i	0.281061	−	0.486812i	−0.690586	−	0.723251i	$-0.742647\pi$
$829$	232.999	−	403.567i	0.281061	−	0.486812i	0.971646	+	0.236439i	$0.0759804\pi$
$830$		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	$0.00473168\pi$
$839$			24.9426i			0.0297289i	−0.999890	+	0.0148645i	$0.995268\pi$
$840$		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	0.421688	−	0.906741i	$-0.361438\pi$
$857$	−130.888	−	75.5681i	−0.152728	−	0.0881775i	−0.574416	+	0.818563i	$0.694771\pi$
$858$		0			0
$859$	450.007	+	779.435i	0.523873	+	0.907374i	0.999614	+	0.0277890i	$0.00884664\pi$
$859$	450.007	+	779.435i	0.523873	+	0.907374i	−0.475741	+	0.879585i	$0.657820\pi$
$860$		0			0
$861$	548.762	+	238.646i	0.637354	+	0.277173i
$862$		0			0
$863$	207.932	+	360.149i	0.240941	+	0.417322i	0.960983	−	0.276609i	$-0.0892107\pi$
$863$	207.932	+	360.149i	0.240941	+	0.417322i	−0.720042	+	0.693931i	$0.755877\pi$
$864$		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	0.749052	−	0.662511i	$-0.230509\pi$
$877$	1488.56	−	859.419i	1.69733	−	0.979954i	0.948278	−	0.317442i	$-0.102824\pi$
$878$		0			0
$879$	−158.133	+	273.894i	−0.179901	+	0.311598i
$880$		0			0
$881$		−	1094.47i		−	1.24231i	−0.783689	−	0.621153i	$-0.786664\pi$
$881$		−	1094.47i		−	1.24231i	0.783689	−	0.621153i	$-0.213336\pi$
$882$		0			0
$883$		−	527.301i		−	0.597170i	−0.954383	−	0.298585i	$-0.903485\pi$
$883$		−	527.301i		−	0.597170i	0.954383	−	0.298585i	$-0.0965146\pi$
$884$		0			0
$885$	−21.7853	+	37.7332i	−0.0246161	+	0.0426363i
$886$		0			0
$887$	−1459.99	+	842.925i	−1.64599	+	0.950310i	−0.667341	+	0.744752i	$0.732568\pi$
$887$	−1459.99	+	842.925i	−1.64599	+	0.950310i	−0.978645	+	0.205558i	$0.934099\pi$
$888$		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	0.993804	+	0.111149i	$0.0354530\pi$
$907$	1439.38	+	831.024i	1.58696	+	0.916234i	0.593160	+	0.805085i	$0.297880\pi$
$908$		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	0.844539	−	0.535494i	$-0.179875\pi$
$919$	−38.1217	−	66.0288i	−0.0414817	−	0.0718485i	−0.886021	+	0.463645i	$0.846541\pi$
$920$		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	−0.388040	−	0.921643i	$-0.626848\pi$
$929$	200.762	−	115.910i	0.216106	−	0.124769i	0.604146	+	0.796874i	$0.293514\pi$
$930$		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	$0.176176\pi$
$937$			985.061i			1.05129i	−0.850703	+	0.525646i	$0.823824\pi$
$938$		0			0
$939$		−	99.4088i		−	0.105867i
$940$		0			0
$941$	704.239	−	1219.78i	0.748394	−	1.29626i	−0.200198	−	0.979756i	$-0.564158\pi$
$941$	704.239	−	1219.78i	0.748394	−	1.29626i	0.948592	−	0.316501i	$-0.102508\pi$
$942$		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	−0.421972	−	0.906609i	$-0.638662\pi$
$947$	144.121	−	83.2085i	0.152187	−	0.0878654i	0.574160	+	0.818743i	$0.305329\pi$
$948$		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	0.986213	−	0.165482i	$-0.0529180\pi$
$971$	339.651	+	588.292i	0.349795	+	0.605862i	−0.636418	+	0.771344i	$0.719585\pi$
$972$		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	−0.806039	−	0.591862i	$-0.798393\pi$
$977$	107.029	−	185.379i	0.109548	−	0.189743i	0.915587	+	0.402119i	$0.131726\pi$
$978$		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	−0.993947	−	0.109859i	$-0.964960\pi$
$983$	−1559.10	−	900.146i	−1.58606	−	0.915713i	−0.592114	−	0.805854i	$-0.701707\pi$
$984$		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	−0.743370	−	0.668880i	$-0.766774\pi$
$991$	205.714	−	356.306i	0.207582	−	0.359542i	0.950952	+	0.309338i	$0.100107\pi$
$992$		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	0.105529	+	0.994416i	$0.466346\pi$
$997$	−806.000	+	1396.03i	−0.808425	+	1.40023i	−0.913954	+	0.405817i	$0.866987\pi$
$998$		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.17.3		28
4.3	odd	2		56.3.j.a.45.9	yes	28
7.3	odd	6		1568.3.h.a.881.6		28
7.4	even	3		1568.3.h.a.881.24		28
7.5	odd	6	inner	224.3.n.a.145.12		28
8.3	odd	2		56.3.j.a.45.11	yes	28
8.5	even	2	inner	224.3.n.a.17.12		28
28.3	even	6		392.3.h.a.293.2		28
28.11	odd	6		392.3.h.a.293.1		28
28.19	even	6		56.3.j.a.5.11	yes	28
28.23	odd	6		392.3.j.e.117.11		28
28.27	even	2		392.3.j.e.325.9		28
56.3	even	6		392.3.h.a.293.3		28
56.5	odd	6	inner	224.3.n.a.145.3		28
56.11	odd	6		392.3.h.a.293.4		28
56.19	even	6		56.3.j.a.5.9	✓	28
56.27	even	2		392.3.j.e.325.11		28
56.45	odd	6		1568.3.h.a.881.23		28
56.51	odd	6		392.3.j.e.117.9		28
56.53	even	6		1568.3.h.a.881.5		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
56.3.j.a.5.9	✓	28	56.19	even	6
56.3.j.a.5.11	yes	28	28.19	even	6
56.3.j.a.45.9	yes	28	4.3	odd	2
56.3.j.a.45.11	yes	28	8.3	odd	2
224.3.n.a.17.3		28	1.1	even	1	trivial
224.3.n.a.17.12		28	8.5	even	2	inner
224.3.n.a.145.3		28	56.5	odd	6	inner
224.3.n.a.145.12		28	7.5	odd	6	inner
392.3.h.a.293.1		28	28.11	odd	6
392.3.h.a.293.2		28	28.3	even	6
392.3.h.a.293.3		28	56.3	even	6
392.3.h.a.293.4		28	56.11	odd	6
392.3.j.e.117.9		28	56.51	odd	6
392.3.j.e.117.11		28	28.23	odd	6
392.3.j.e.325.9		28	28.27	even	2
392.3.j.e.325.11		28	56.27	even	2
1568.3.h.a.881.5		28	56.53	even	6
1568.3.h.a.881.6		28	7.3	odd	6
1568.3.h.a.881.23		28	56.45	odd	6
1568.3.h.a.881.24		28	7.4	even	3

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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