LMFDB - Embedded newform 230.4.e.a.137.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [230,4,Mod(137,230)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(230, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([1, 2]))

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

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

chi := DirichletCharacter("230.137");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 230 = 2 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	230.e (of order $4$, degree $2$, 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:	$13.5704393013$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$36$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			137.3
Character	$\chi$	$=$	230.137
Dual form			230.4.e.a.183.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.41421 - 1.41421i) q^{2} +(-4.47764 + 4.47764i) q^{3} +4.00000i q^{4} +(-11.1722 + 0.427507i) q^{5} +12.6647 q^{6} +(-6.97055 + 6.97055i) q^{7} +(5.65685 - 5.65685i) q^{8} -13.0984i q^{9} +O(q^{10})$	\(q+(-1.41421 - 1.41421i) q^{2} +(-4.47764 + 4.47764i) q^{3} +4.00000i q^{4} +(-11.1722 + 0.427507i) q^{5} +12.6647 q^{6} +(-6.97055 + 6.97055i) q^{7} +(5.65685 - 5.65685i) q^{8} -13.0984i q^{9} +(16.4044 + 15.1952i) q^{10} +51.7809i q^{11} +(-17.9105 - 17.9105i) q^{12} +(-44.4365 + 44.4365i) q^{13} +19.7157 q^{14} +(48.1107 - 51.9391i) q^{15} -16.0000 q^{16} +(-29.0282 + 29.0282i) q^{17} +(-18.5240 + 18.5240i) q^{18} -24.9171 q^{19} +(-1.71003 - 44.6887i) q^{20} -62.4232i q^{21} +(73.2293 - 73.2293i) q^{22} +(-0.405403 - 110.303i) q^{23} +50.6587i q^{24} +(124.634 - 9.55235i) q^{25} +125.685 q^{26} +(-62.2462 - 62.2462i) q^{27} +(-27.8822 - 27.8822i) q^{28} -154.623i q^{29} +(-141.492 + 5.41423i) q^{30} +219.615 q^{31} +(22.6274 + 22.6274i) q^{32} +(-231.856 - 231.856i) q^{33} +82.1042 q^{34} +(74.8962 - 80.8561i) q^{35} +52.3937 q^{36} +(-0.292240 + 0.292240i) q^{37} +(35.2381 + 35.2381i) q^{38} -397.941i q^{39} +(-60.7810 + 65.6176i) q^{40} +7.58700 q^{41} +(-88.2797 + 88.2797i) q^{42} +(-296.918 - 296.918i) q^{43} -207.124 q^{44} +(5.59967 + 146.338i) q^{45} +(-155.419 + 156.566i) q^{46} +(338.025 + 338.025i) q^{47} +(71.6422 - 71.6422i) q^{48} +245.823i q^{49} +(-189.769 - 162.751i) q^{50} -259.956i q^{51} +(-177.746 - 177.746i) q^{52} +(-185.770 - 185.770i) q^{53} +176.059i q^{54} +(-22.1367 - 578.505i) q^{55} +78.8628i q^{56} +(111.570 - 111.570i) q^{57} +(-218.669 + 218.669i) q^{58} -552.350i q^{59} +(207.756 + 192.443i) q^{60} +642.209i q^{61} +(-310.582 - 310.582i) q^{62} +(91.3033 + 91.3033i) q^{63} -64.0000i q^{64} +(477.455 - 515.449i) q^{65} +655.788i q^{66} +(-249.713 + 249.713i) q^{67} +(-116.113 - 116.113i) q^{68} +(495.714 + 492.083i) q^{69} +(-220.267 + 8.42860i) q^{70} +598.535 q^{71} +(-74.0959 - 74.0959i) q^{72} +(-595.081 + 595.081i) q^{73} +0.826580 q^{74} +(-515.296 + 600.840i) q^{75} -99.6685i q^{76} +(-360.942 - 360.942i) q^{77} +(-562.773 + 562.773i) q^{78} -1126.29 q^{79} +(178.755 - 6.84011i) q^{80} +911.089 q^{81} +(-10.7296 - 10.7296i) q^{82} +(-567.177 - 567.177i) q^{83} +249.693 q^{84} +(311.898 - 336.718i) q^{85} +839.811i q^{86} +(692.343 + 692.343i) q^{87} +(292.917 + 292.917i) q^{88} +1449.76 q^{89} +(199.034 - 214.872i) q^{90} -619.494i q^{91} +(441.214 - 1.62161i) q^{92} +(-983.354 + 983.354i) q^{93} -956.080i q^{94} +(278.378 - 10.6522i) q^{95} -202.635 q^{96} +(716.106 - 716.106i) q^{97} +(347.646 - 347.646i) q^{98} +678.249 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q - 16 q^{3} - 16 q^{6}+O(q^{10}) $ 72 * q - 16 * q^3 - 16 * q^6	$ 72 q - 16 q^{3} - 16 q^{6} - 64 q^{12} + 192 q^{13} - 1152 q^{16} + 32 q^{18} + 276 q^{23} + 880 q^{25} + 304 q^{26} + 728 q^{27} + 608 q^{31} + 688 q^{35} + 2816 q^{36} - 2208 q^{41} - 256 q^{46} + 144 q^{47} + 256 q^{48} + 272 q^{50} + 768 q^{52} - 2360 q^{55} - 1376 q^{62} - 1104 q^{70} + 4528 q^{71} + 128 q^{72} - 1296 q^{73} - 2568 q^{75} - 752 q^{77} + 6000 q^{78} - 11560 q^{81} + 80 q^{82} - 904 q^{85} + 6760 q^{87} + 1104 q^{92} - 5288 q^{93} + 9264 q^{95} + 256 q^{96} - 448 q^{98}+O(q^{100}) $ 72 * q - 16 * q^3 - 16 * q^6 - 64 * q^12 + 192 * q^13 - 1152 * q^16 + 32 * q^18 + 276 * q^23 + 880 * q^25 + 304 * q^26 + 728 * q^27 + 608 * q^31 + 688 * q^35 + 2816 * q^36 - 2208 * q^41 - 256 * q^46 + 144 * q^47 + 256 * q^48 + 272 * q^50 + 768 * q^52 - 2360 * q^55 - 1376 * q^62 - 1104 * q^70 + 4528 * q^71 + 128 * q^72 - 1296 * q^73 - 2568 * q^75 - 752 * q^77 + 6000 * q^78 - 11560 * q^81 + 80 * q^82 - 904 * q^85 + 6760 * q^87 + 1104 * q^92 - 5288 * q^93 + 9264 * q^95 + 256 * q^96 - 448 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/230\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$

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 $

$2$	−1.41421	−	1.41421i	−0.500000	−	0.500000i
$2$	−1.41421	−	1.41421i	−0.500000	−	0.500000i
$3$	−4.47764	+	4.47764i	−0.861721	+	0.861721i	−0.991538	−	0.129817i	$-0.958561\pi$
$3$	−4.47764	+	4.47764i	−0.861721	+	0.861721i	0.129817	+	0.991538i	$0.458561\pi$
$4$			4.00000i			0.500000i
$5$	−11.1722	+	0.427507i	−0.999269	+	0.0382374i
$5$	−11.1722	+	0.427507i	−0.999269	+	0.0382374i
$6$	12.6647			0.861721
$7$	−6.97055	+	6.97055i	−0.376374	+	0.376374i	−0.869792	−	0.493418i	$-0.835747\pi$
$7$	−6.97055	+	6.97055i	−0.376374	+	0.376374i	0.493418	+	0.869792i	$0.335747\pi$
$8$	5.65685	−	5.65685i	0.250000	−	0.250000i
$9$		−	13.0984i		−	0.485127i
$10$	16.4044	+	15.1952i	0.518753	+	0.480516i
$11$			51.7809i			1.41932i	0.704544	+	0.709660i	$0.251152\pi$
$11$			51.7809i			1.41932i	−0.704544	+	0.709660i	$0.748848\pi$
$12$	−17.9105	−	17.9105i	−0.430861	−	0.430861i
$13$	−44.4365	+	44.4365i	−0.948036	+	0.948036i	−0.998715	−	0.0506793i	$-0.983861\pi$
$13$	−44.4365	+	44.4365i	−0.948036	+	0.948036i	0.0506793	+	0.998715i	$0.483861\pi$
$14$	19.7157			0.376374
$15$	48.1107	−	51.9391i	0.828141	−	0.894041i
$16$	−16.0000			−0.250000
$17$	−29.0282	+	29.0282i	−0.414140	+	0.414140i	−0.883178	−	0.469038i	$-0.844601\pi$
$17$	−29.0282	+	29.0282i	−0.414140	+	0.414140i	0.469038	+	0.883178i	$0.344601\pi$
$18$	−18.5240	+	18.5240i	−0.242564	+	0.242564i
$19$	−24.9171			−0.300862			−0.150431	−	0.988620i	$-0.548066\pi$
$19$	−24.9171			−0.300862			−0.150431	+	0.988620i	$0.548066\pi$
$20$	−1.71003	−	44.6887i	−0.0191187	−	0.499634i
$21$		−	62.4232i		−	0.648660i
$22$	73.2293	−	73.2293i	0.709660	−	0.709660i
$23$	−0.405403	−	110.303i	−0.00367532	−	0.999993i
$23$	−0.405403	−	110.303i	−0.00367532	−	0.999993i
$24$			50.6587i			0.430861i
$25$	124.634	−	9.55235i	0.997076	−	0.0764188i
$26$	125.685			0.948036
$27$	−62.2462	−	62.2462i	−0.443677	−	0.443677i
$28$	−27.8822	−	27.8822i	−0.188187	−	0.188187i
$29$		−	154.623i		−	0.990092i	−0.868867	−	0.495046i	$-0.835151\pi$
$29$		−	154.623i		−	0.990092i	0.868867	−	0.495046i	$-0.164849\pi$
$30$	−141.492	+	5.41423i	−0.861091	+	0.0329500i
$31$	219.615			1.27239			0.636193	−	0.771530i	$-0.280508\pi$
$31$	219.615			1.27239			0.636193	+	0.771530i	$0.280508\pi$
$32$	22.6274	+	22.6274i	0.125000	+	0.125000i
$33$	−231.856	−	231.856i	−1.22306	−	1.22306i
$34$	82.1042			0.414140
$35$	74.8962	−	80.8561i	0.361708	−	0.390491i
$36$	52.3937			0.242564
$37$	−0.292240	+	0.292240i	−0.00129849	+	0.00129849i	−0.707756	−	0.706457i	$-0.750292\pi$
$37$	−0.292240	+	0.292240i	−0.00129849	+	0.00129849i	0.706457	+	0.707756i	$0.250292\pi$
$38$	35.2381	+	35.2381i	0.150431	+	0.150431i
$39$		−	397.941i		−	1.63389i
$40$	−60.7810	+	65.6176i	−0.240258	+	0.259377i
$41$	7.58700			0.0288997			0.0144499	−	0.999896i	$-0.495400\pi$
$41$	7.58700			0.0288997			0.0144499	+	0.999896i	$0.495400\pi$
$42$	−88.2797	+	88.2797i	−0.324330	+	0.324330i
$43$	−296.918	−	296.918i	−1.05301	−	1.05301i	−0.998514	−	0.0544999i	$-0.982644\pi$
$43$	−296.918	−	296.918i	−1.05301	−	1.05301i	−0.0544999	−	0.998514i	$-0.517356\pi$
$44$	−207.124			−0.709660
$45$	5.59967	+	146.338i	0.0185500	+	0.484772i
$46$	−155.419	+	156.566i	−0.498159	+	0.501834i
$47$	338.025	+	338.025i	1.04907	+	1.04907i	0.998732	+	0.0503329i	$0.0160282\pi$
$47$	338.025	+	338.025i	1.04907	+	1.04907i	0.0503329	+	0.998732i	$0.483972\pi$
$48$	71.6422	−	71.6422i	0.215430	−	0.215430i
$49$			245.823i			0.716684i
$50$	−189.769	−	162.751i	−0.536747	−	0.460329i
$51$		−	259.956i		−	0.713746i
$52$	−177.746	−	177.746i	−0.474018	−	0.474018i
$53$	−185.770	−	185.770i	−0.481462	−	0.481462i	0.424136	−	0.905598i	$-0.360578\pi$
$53$	−185.770	−	185.770i	−0.481462	−	0.481462i	−0.905598	+	0.424136i	$0.860578\pi$
$54$			176.059i			0.443677i
$55$	−22.1367	−	578.505i	−0.0542711	−	1.41828i
$56$			78.8628i			0.188187i
$57$	111.570	−	111.570i	0.259259	−	0.259259i
$58$	−218.669	+	218.669i	−0.495046	+	0.495046i
$59$		−	552.350i		−	1.21881i	−0.792859	−	0.609406i	$-0.791408\pi$
$59$		−	552.350i		−	1.21881i	0.792859	−	0.609406i	$-0.208592\pi$
$60$	207.756	+	192.443i	0.447021	+	0.414071i
$61$			642.209i			1.34797i	0.738743	+	0.673987i	$0.235420\pi$
$61$			642.209i			1.34797i	−0.738743	+	0.673987i	$0.764580\pi$
$62$	−310.582	−	310.582i	−0.636193	−	0.636193i
$63$	91.3033	+	91.3033i	0.182589	+	0.182589i
$64$		−	64.0000i		−	0.125000i
$65$	477.455	−	515.449i	0.911092	−	0.983593i
$66$			655.788i			1.22306i
$67$	−249.713	+	249.713i	−0.455333	+	0.455333i	−0.897120	−	0.441787i	$-0.854345\pi$
$67$	−249.713	+	249.713i	−0.455333	+	0.455333i	0.441787	+	0.897120i	$0.354345\pi$
$68$	−116.113	−	116.113i	−0.207070	−	0.207070i
$69$	495.714	+	492.083i	0.864883	+	0.858548i
$70$	−220.267	+	8.42860i	−0.376099	+	0.0143916i
$71$	598.535			1.00047			0.500233	−	0.865891i	$-0.333248\pi$
$71$	598.535			1.00047			0.500233	+	0.865891i	$0.333248\pi$
$72$	−74.0959	−	74.0959i	−0.121282	−	0.121282i
$73$	−595.081	+	595.081i	−0.954095	+	0.954095i	−0.998992	−	0.0448970i	$-0.985704\pi$
$73$	−595.081	+	595.081i	−0.954095	+	0.954095i	0.0448970	+	0.998992i	$0.485704\pi$
$74$	0.826580			0.00129849
$75$	−515.296	+	600.840i	−0.793350	+	0.925053i
$76$		−	99.6685i		−	0.150431i
$77$	−360.942	−	360.942i	−0.534196	−	0.534196i
$78$	−562.773	+	562.773i	−0.816943	+	0.816943i
$79$	−1126.29			−1.60403			−0.802013	−	0.597306i	$-0.796238\pi$
$79$	−1126.29			−1.60403			−0.802013	+	0.597306i	$0.796238\pi$
$80$	178.755	−	6.84011i	0.249817	−	0.00955934i
$81$	911.089			1.24978
$82$	−10.7296	−	10.7296i	−0.0144499	−	0.0144499i
$83$	−567.177	−	567.177i	−0.750069	−	0.750069i	0.224423	−	0.974492i	$-0.427950\pi$
$83$	−567.177	−	567.177i	−0.750069	−	0.750069i	−0.974492	+	0.224423i	$0.927950\pi$
$84$	249.693			0.324330
$85$	311.898	−	336.718i	0.398002	−	0.429673i
$86$			839.811i			1.05301i
$87$	692.343	+	692.343i	0.853184	+	0.853184i
$88$	292.917	+	292.917i	0.354830	+	0.354830i
$89$	1449.76			1.72668			0.863339	−	0.504624i	$-0.168369\pi$
$89$	1449.76			1.72668			0.863339	+	0.504624i	$0.168369\pi$
$90$	199.034	−	214.872i	0.233111	−	0.251661i
$91$		−	619.494i		−	0.713633i
$92$	441.214	−	1.62161i	0.499997	−	0.00183766i
$93$	−983.354	+	983.354i	−1.09644	+	1.09644i
$94$		−	956.080i		−	1.04907i
$95$	278.378	−	10.6522i	0.300642	−	0.0115042i
$96$	−202.635			−0.215430
$97$	716.106	−	716.106i	0.749583	−	0.749583i	−0.224817	−	0.974401i	$-0.572179\pi$
$97$	716.106	−	716.106i	0.749583	−	0.749583i	0.974401	+	0.224817i	$0.0721786\pi$
$98$	347.646	−	347.646i	0.358342	−	0.358342i
$99$	678.249			0.688551
$100$	38.2094	+	498.538i	0.0382094	+	0.498538i
$101$	691.878			0.681628			0.340814	−	0.940131i	$-0.389297\pi$
$101$	691.878			0.681628			0.340814	+	0.940131i	$0.389297\pi$
$102$	−367.633	+	367.633i	−0.356873	+	0.356873i
$103$	1426.36	+	1426.36i	1.36450	+	1.36450i	0.868082	+	0.496421i	$0.165353\pi$
$103$	1426.36	+	1426.36i	1.36450	+	1.36450i	0.496421	+	0.868082i	$0.334647\pi$
$104$			502.741i			0.474018i
$105$	26.6863	+	697.402i	0.0248030	+	0.648185i
$106$			525.438i			0.481462i
$107$	−176.317	+	176.317i	−0.159301	+	0.159301i	−0.782257	−	0.622956i	$-0.785932\pi$
$107$	−176.317	+	176.317i	−0.159301	+	0.159301i	0.622956	+	0.782257i	$0.285932\pi$
$108$	248.985	−	248.985i	0.221838	−	0.221838i
$109$	191.805			0.168547			0.0842735	−	0.996443i	$-0.473143\pi$
$109$	191.805			0.168547			0.0842735	+	0.996443i	$0.473143\pi$
$110$	−786.823	+	849.435i	−0.682006	+	0.736277i
$111$		−	2.61709i		−	0.00223787i
$112$	111.529	−	111.529i	0.0940936	−	0.0940936i
$113$	−298.860	−	298.860i	−0.248800	−	0.248800i	0.571678	−	0.820478i	$-0.306293\pi$
$113$	−298.860	−	298.860i	−0.248800	−	0.248800i	−0.820478	+	0.571678i	$0.806293\pi$
$114$	−315.567			−0.259259
$115$	51.6847	+	1232.15i	0.0419097	+	0.999121i
$116$	618.490			0.495046
$117$	582.048	+	582.048i	0.459918	+	0.459918i
$118$	−781.141	+	781.141i	−0.609406	+	0.609406i
$119$		−	404.686i		−	0.311743i
$120$	−21.6569	−	565.967i	−0.0164750	−	0.430546i
$121$	−1350.26			−1.01447
$122$	908.220	−	908.220i	0.673987	−	0.673987i
$123$	−33.9718	+	33.9718i	−0.0249035	+	0.0249035i
$124$			878.458i			0.636193i
$125$	−1388.35	+	160.003i	−0.993425	+	0.114488i
$126$		−	258.245i		−	0.182589i
$127$	−735.493	−	735.493i	−0.513893	−	0.513893i	0.401824	−	0.915717i	$-0.368376\pi$
$127$	−735.493	−	735.493i	−0.513893	−	0.513893i	−0.915717	+	0.401824i	$0.868376\pi$
$128$	−90.5097	+	90.5097i	−0.0625000	+	0.0625000i
$129$	2658.98			1.81481
$130$	−1404.18	+	53.7313i	−0.947342	+	0.0362504i
$131$	−160.365			−0.106955			−0.0534777	−	0.998569i	$-0.517031\pi$
$131$	−160.365			−0.106955			−0.0534777	+	0.998569i	$0.517031\pi$
$132$	927.424	−	927.424i	0.611530	−	0.611530i
$133$	173.686	−	173.686i	0.113237	−	0.113237i
$134$	706.296			0.455333
$135$	722.035	+	668.814i	0.460318	+	0.426387i
$136$			328.417i			0.207070i
$137$	−713.945	+	713.945i	−0.445229	+	0.445229i	−0.893765	−	0.448536i	$-0.851946\pi$
$137$	−713.945	+	713.945i	−0.445229	+	0.445229i	0.448536	+	0.893765i	$0.351946\pi$
$138$	−5.13430	−	1396.96i	−0.00316710	−	0.861715i
$139$		−	2601.65i		−	1.58755i	−0.608214	−	0.793773i	$-0.708114\pi$
$139$		−	2601.65i		−	1.58755i	0.608214	−	0.793773i	$-0.291886\pi$
$140$	323.424	+	299.585i	0.195245	+	0.180854i
$141$	−3027.11			−1.80800
$142$	−846.457	−	846.457i	−0.500233	−	0.500233i
$143$	−2300.96	−	2300.96i	−1.34557	−	1.34557i
$144$			209.575i			0.121282i
$145$	66.1022	+	1727.47i	0.0378585	+	0.989368i
$146$	1683.14			0.954095
$147$	−1100.70	−	1100.70i	−0.617582	−	0.617582i
$148$	−1.16896	−	1.16896i	−0.000649243	−	0.000649243i
$149$	50.2335			0.0276194			0.0138097	−	0.999905i	$-0.495604\pi$
$149$	50.2335			0.0276194			0.0138097	+	0.999905i	$0.495604\pi$
$150$	1578.45	−	120.977i	0.859201	−	0.0658517i
$151$	−2186.91			−1.17860			−0.589298	−	0.807916i	$-0.700596\pi$
$151$	−2186.91			−1.17860			−0.589298	+	0.807916i	$0.700596\pi$
$152$	−140.953	+	140.953i	−0.0752156	+	0.0752156i
$153$	380.224	+	380.224i	0.200911	+	0.200911i
$154$			1020.90i			0.534196i
$155$	−2453.57	+	93.8867i	−1.27145	+	0.0486527i
$156$	1591.76			0.816943
$157$	−654.732	+	654.732i	−0.332824	+	0.332824i	−0.853658	−	0.520834i	$-0.825621\pi$
$157$	−654.732	+	654.732i	−0.332824	+	0.332824i	0.520834	+	0.853658i	$0.325621\pi$
$158$	1592.82	+	1592.82i	0.802013	+	0.802013i
$159$	1663.62			0.829773
$160$	−262.471	−	243.124i	−0.129688	−	0.120129i
$161$	771.701	+	766.050i	0.377755	+	0.374989i
$162$	−1288.47	−	1288.47i	−0.624889	−	0.624889i
$163$	−552.679	+	552.679i	−0.265578	+	0.265578i	−0.827315	−	0.561738i	$-0.810133\pi$
$163$	−552.679	+	552.679i	−0.265578	+	0.265578i	0.561738	+	0.827315i	$0.310133\pi$
$164$			30.3480i			0.0144499i
$165$	2689.45	+	2491.21i	1.26893	+	1.17540i
$166$			1604.22i			0.750069i
$167$	−540.282	−	540.282i	−0.250349	−	0.250349i	0.570765	−	0.821114i	$-0.306647\pi$
$167$	−540.282	−	540.282i	−0.250349	−	0.250349i	−0.821114	+	0.570765i	$0.806647\pi$
$168$	−353.119	−	353.119i	−0.162165	−	0.162165i
$169$		−	1752.20i		−	0.797543i
$170$	−917.282	+	35.1001i	−0.413837	+	0.0158356i
$171$			326.375i			0.145956i
$172$	1187.67	−	1187.67i	0.526507	−	0.526507i
$173$	260.654	−	260.654i	0.114550	−	0.114550i	−0.647508	−	0.762058i	$-0.724189\pi$
$173$	260.654	−	260.654i	0.114550	−	0.114550i	0.762058	+	0.647508i	$0.224189\pi$
$174$		−	1958.24i		−	0.853184i
$175$	−802.186	+	935.356i	−0.346512	+	0.404036i
$176$		−	828.495i		−	0.354830i
$177$	2473.22	+	2473.22i	1.05028	+	1.05028i
$178$	−2050.27	−	2050.27i	−0.863339	−	0.863339i
$179$		−	1542.00i		−	0.643881i	−0.946760	−	0.321940i	$-0.895665\pi$
$179$		−	1542.00i		−	0.643881i	0.946760	−	0.321940i	$-0.104335\pi$
$180$	−585.351	+	22.3987i	−0.242386	+	0.00927499i
$181$			2050.93i			0.842234i	0.907006	+	0.421117i	$0.138362\pi$
$181$			2050.93i			0.842234i	−0.907006	+	0.421117i	$0.861638\pi$
$182$	−876.097	+	876.097i	−0.356816	+	0.356816i
$183$	−2875.58	−	2875.58i	−1.16158	−	1.16158i
$184$	−626.263	−	621.677i	−0.250917	−	0.249079i
$185$	3.14002	−	3.38989i	0.00124789	−	0.00134719i
$186$	2781.34			1.09644
$187$	−1503.11	−	1503.11i	−0.587798	−	0.587798i
$188$	−1352.10	+	1352.10i	−0.524533	+	0.524533i
$189$	867.780			0.333977
$190$	−408.751	−	378.622i	−0.156073	−	0.144569i
$191$		−	3145.02i		−	1.19144i	−0.803191	−	0.595722i	$-0.796866\pi$
$191$		−	3145.02i		−	1.19144i	0.803191	−	0.595722i	$-0.203134\pi$
$192$	286.569	+	286.569i	0.107715	+	0.107715i
$193$	417.949	−	417.949i	0.155879	−	0.155879i	−0.624859	−	0.780738i	$-0.714843\pi$
$193$	417.949	−	417.949i	0.155879	−	0.155879i	0.780738	+	0.624859i	$0.214843\pi$
$194$	−2025.46			−0.749583
$195$	170.122	+	4445.86i	0.0624755	+	1.63269i
$196$	−983.291			−0.358342
$197$	979.186	+	979.186i	0.354133	+	0.354133i	0.861645	−	0.507512i	$-0.169435\pi$
$197$	979.186	+	979.186i	0.354133	+	0.354133i	−0.507512	+	0.861645i	$0.669435\pi$
$198$	−959.188	−	959.188i	−0.344276	−	0.344276i
$199$	−987.266			−0.351686			−0.175843	−	0.984418i	$-0.556265\pi$
$199$	−987.266			−0.351686			−0.175843	+	0.984418i	$0.556265\pi$
$200$	651.003	−	759.075i	0.230164	−	0.268374i
$201$		−	2236.25i		−	0.784741i
$202$	−978.463	−	978.463i	−0.340814	−	0.340814i
$203$	1077.80	+	1077.80i	0.372646	+	0.372646i
$204$	1039.82			0.356873
$205$	−84.7632	+	3.24349i	−0.0288786	+	0.00110505i
$206$		−	4034.37i		−	1.36450i
$207$	−1444.80	+	5.31015i	−0.485124	+	0.00178300i
$208$	710.984	−	710.984i	0.237009	−	0.237009i
$209$		−	1290.23i		−	0.427020i
$210$	948.535	−	1024.02i	0.311691	−	0.336494i
$211$	63.7201			0.0207899			0.0103950	−	0.999946i	$-0.496691\pi$
$211$	63.7201			0.0207899			0.0103950	+	0.999946i	$0.496691\pi$
$212$	743.081	−	743.081i	0.240731	−	0.240731i
$213$	−2680.02	+	2680.02i	−0.862123	+	0.862123i
$214$	498.699			0.159301
$215$	3444.15	+	3190.28i	1.09251	+	1.01198i
$216$	−704.235			−0.221838
$217$	−1530.84	+	1530.84i	−0.478893	+	0.478893i
$218$	−271.254	−	271.254i	−0.0842735	−	0.0842735i
$219$		−	5329.11i		−	1.64433i
$220$	2314.02	−	88.5467i	0.709142	−	0.0271355i
$221$		−	2579.83i		−	0.785239i
$222$	−3.70112	+	3.70112i	−0.00111893	+	0.00111893i
$223$	1548.18	−	1548.18i	0.464906	−	0.464906i	−0.435354	−	0.900260i	$-0.643377\pi$
$223$	1548.18	−	1548.18i	0.464906	−	0.464906i	0.900260	+	0.435354i	$0.143377\pi$
$224$	−315.451			−0.0940936
$225$	−125.121	−	1632.52i	−0.0370728	−	0.483708i
$226$			845.303i			0.248800i
$227$	2885.42	−	2885.42i	0.843665	−	0.843665i	−0.145668	−	0.989333i	$-0.546533\pi$
$227$	2885.42	−	2885.42i	0.843665	−	0.843665i	0.989333	+	0.145668i	$0.0465333\pi$
$228$	446.279	+	446.279i	0.129630	+	0.129630i
$229$	−3736.32			−1.07818			−0.539090	−	0.842248i	$-0.681232\pi$
$229$	−3736.32			−1.07818			−0.539090	+	0.842248i	$0.681232\pi$
$230$	1669.44	−	1815.62i	0.478606	−	0.520516i
$231$	3232.33			0.920657
$232$	−874.677	−	874.677i	−0.247523	−	0.247523i
$233$	1170.33	−	1170.33i	0.329059	−	0.329059i	−0.523170	−	0.852228i	$-0.675251\pi$
$233$	1170.33	−	1170.33i	0.329059	−	0.329059i	0.852228	+	0.523170i	$0.175251\pi$
$234$		−	1646.28i		−	0.459918i
$235$	−3920.98	−	3631.97i	−1.08841	−	1.00818i
$236$	2209.40			0.609406
$237$	5043.14	−	5043.14i	1.38222	−	1.38222i
$238$	−572.312	+	572.312i	−0.155872	+	0.155872i
$239$			3649.64i			0.987764i	0.869529	+	0.493882i	$0.164422\pi$
$239$			3649.64i			0.987764i	−0.869529	+	0.493882i	$0.835578\pi$
$240$	−769.770	+	831.025i	−0.207035	+	0.223510i
$241$			1029.02i			0.275043i	0.990499	+	0.137521i	$0.0439136\pi$
$241$			1029.02i			0.275043i	−0.990499	+	0.137521i	$0.956086\pi$
$242$	1909.56	+	1909.56i	0.507236	+	0.507236i
$243$	−2398.88	+	2398.88i	−0.633284	+	0.633284i
$244$	−2568.83			−0.673987
$245$	−105.091	−	2746.37i	−0.0274041	−	0.716160i
$246$	96.0868			0.0249035
$247$	1107.23	−	1107.23i	0.285228	−	0.285228i
$248$	1242.33	−	1242.33i	0.318096	−	0.318096i
$249$	5079.22			1.29270
$250$	2189.71	+	1737.15i	0.553957	+	0.439468i
$251$			1005.19i			0.252776i	0.991981	+	0.126388i	$0.0403385\pi$
$251$			1005.19i			0.252776i	−0.991981	+	0.126388i	$0.959662\pi$
$252$	−365.213	+	365.213i	−0.0912947	+	0.0912947i
$253$	5711.61	−	20.9921i	1.41931	−	0.00521646i
$254$			2080.29i			0.513893i
$255$	111.133	+	2904.27i	0.0272918	+	0.713225i
$256$	256.000			0.0625000
$257$	−3959.48	−	3959.48i	−0.961033	−	0.961033i	0.0382354	−	0.999269i	$-0.487826\pi$
$257$	−3959.48	−	3959.48i	−0.961033	−	0.961033i	−0.999269	+	0.0382354i	$0.987826\pi$
$258$	−3760.37	−	3760.37i	−0.907404	−	0.907404i
$259$		−	4.07415i		−	0.000977434i
$260$	2061.79	+	1909.82i	0.491796	+	0.455546i
$261$	−2025.31			−0.480321
$262$	226.790	+	226.790i	0.0534777	+	0.0534777i
$263$	−2447.47	−	2447.47i	−0.573832	−	0.573832i	0.359365	−	0.933197i	$-0.382993\pi$
$263$	−2447.47	−	2447.47i	−0.573832	−	0.573832i	−0.933197	+	0.359365i	$0.882993\pi$
$264$	−2623.15			−0.611530
$265$	2154.87	+	1996.04i	0.499520	+	0.462701i
$266$	−491.259			−0.113237
$267$	−6491.50	+	6491.50i	−1.48792	+	1.48792i
$268$	−998.853	−	998.853i	−0.227667	−	0.227667i
$269$			5246.57i			1.18918i	0.804029	+	0.594589i	$0.202685\pi$
$269$			5246.57i			1.18918i	−0.804029	+	0.594589i	$0.797315\pi$
$270$	−75.2663	−	1966.96i	−0.0169650	−	0.443352i
$271$	−8393.89			−1.88152			−0.940761	−	0.339071i	$-0.889887\pi$
$271$	−8393.89			−1.88152			−0.940761	+	0.339071i	$0.889887\pi$
$272$	464.452	−	464.452i	0.103535	−	0.103535i
$273$	2773.87	+	2773.87i	0.614953	+	0.614953i
$274$	2019.34			0.445229
$275$	494.629	+	6453.69i	0.108463	+	1.41517i
$276$	−1968.33	+	1982.85i	−0.429274	+	0.432441i
$277$	2385.61	+	2385.61i	0.517464	+	0.517464i	0.916803	−	0.399339i	$-0.130760\pi$
$277$	2385.61	+	2385.61i	0.517464	+	0.517464i	−0.399339	+	0.916803i	$0.630760\pi$
$278$	−3679.29	+	3679.29i	−0.793773	+	0.793773i
$279$		−	2876.61i		−	0.617269i
$280$	−33.7144	−	881.068i	−0.00719578	−	0.188050i
$281$		−	8064.71i		−	1.71210i	−0.516893	−	0.856050i	$-0.672911\pi$
$281$		−	8064.71i		−	1.71210i	0.516893	−	0.856050i	$-0.327089\pi$
$282$	4280.98	+	4280.98i	0.904002	+	0.904002i
$283$	4608.48	+	4608.48i	0.968006	+	0.968006i	0.999504	−	0.0314983i	$-0.0100279\pi$
$283$	4608.48	+	4608.48i	0.968006	+	0.968006i	−0.0314983	+	0.999504i	$0.510028\pi$
$284$			2394.14i			0.500233i
$285$	−1198.78	+	1294.17i	−0.249156	+	0.268983i
$286$			6508.10i			1.34557i
$287$	−52.8856	+	52.8856i	−0.0108771	+	0.0108771i
$288$	296.384	−	296.384i	0.0606409	−	0.0606409i
$289$			3227.72i			0.656976i
$290$	2349.53	−	2536.49i	0.475755	−	0.513613i
$291$			6412.93i			1.29186i
$292$	−2380.32	−	2380.32i	−0.477047	−	0.477047i
$293$	5716.13	+	5716.13i	1.13973	+	1.13973i	0.988499	+	0.151227i	$0.0483224\pi$
$293$	5716.13	+	5716.13i	1.13973	+	1.13973i	0.151227	+	0.988499i	$0.451678\pi$
$294$			3113.26i			0.617582i
$295$	236.133	+	6170.95i	0.0466041	+	1.21792i
$296$			3.30632i			0.000649243i
$297$	3223.16	−	3223.16i	0.629720	−	0.629720i
$298$	−71.0408	−	71.0408i	−0.0138097	−	0.0138097i
$299$	4919.51	+	4883.48i	0.951514	+	0.944545i
$300$	−2403.36	−	2061.18i	−0.462527	−	0.396675i
$301$	4139.37			0.792655
$302$	3092.75	+	3092.75i	0.589298	+	0.589298i
$303$	−3097.98	+	3097.98i	−0.587373	+	0.587373i
$304$	398.674			0.0752156
$305$	−274.549	−	7174.86i	−0.0515430	−	1.34699i
$306$		−	1075.44i		−	0.200911i
$307$	−4891.06	−	4891.06i	−0.909275	−	0.909275i	0.0869391	−	0.996214i	$-0.472291\pi$
$307$	−4891.06	−	4891.06i	−0.909275	−	0.909275i	−0.996214	+	0.0869391i	$0.972291\pi$
$308$	1443.77	−	1443.77i	0.267098	−	0.267098i
$309$	−12773.5			−2.35164
$310$	3602.65	+	3337.10i	0.660054	+	0.611401i
$311$	−1593.35			−0.290516			−0.145258	−	0.989394i	$-0.546401\pi$
$311$	−1593.35			−0.290516			−0.145258	+	0.989394i	$0.546401\pi$
$312$	−2251.09	−	2251.09i	−0.408471	−	0.408471i
$313$	−3496.11	−	3496.11i	−0.631348	−	0.631348i	0.317058	−	0.948406i	$-0.397305\pi$
$313$	−3496.11	−	3496.11i	−0.631348	−	0.631348i	−0.948406	+	0.317058i	$0.897305\pi$
$314$	1851.86			0.332824
$315$	−1059.09	−	981.023i	−0.189438	−	0.175474i
$316$		−	4505.18i		−	0.802013i
$317$	327.929	+	327.929i	0.0581020	+	0.0581020i	0.735561	−	0.677459i	$-0.236919\pi$
$317$	327.929	+	327.929i	0.0581020	+	0.0581020i	−0.677459	+	0.735561i	$0.736919\pi$
$318$	−2352.72	−	2352.72i	−0.414886	−	0.414886i
$319$	8006.49			1.40526
$320$	27.3604	+	715.018i	0.00477967	+	0.124909i
$321$		−	1578.96i		−	0.274546i
$322$	−7.99281	−	2174.71i	−0.00138330	−	0.376372i
$323$	723.300	−	723.300i	0.124599	−	0.124599i
$324$			3644.35i			0.624889i
$325$	−5113.85	+	5962.79i	−0.872816	+	1.01771i
$326$	1563.21			0.265578
$327$	−858.835	+	858.835i	−0.145241	+	0.145241i
$328$	42.9185	−	42.9185i	0.00722494	−	0.00722494i
$329$	−4712.45			−0.789683
$330$	−280.354	−	7326.57i	−0.0467666	−	1.22216i
$331$	−467.778			−0.0776780			−0.0388390	−	0.999245i	$-0.512366\pi$
$331$	−467.778			−0.0776780			−0.0388390	+	0.999245i	$0.512366\pi$
$332$	2268.71	−	2268.71i	0.375035	−	0.375035i
$333$	3.82789	+	3.82789i	0.000629931	+	0.000629931i
$334$			1528.15i			0.250349i
$335$	2683.08	−	2896.59i	0.437590	−	0.472411i
$336$			998.771i			0.162165i
$337$	−2796.59	+	2796.59i	−0.452048	+	0.452048i	−0.896034	−	0.443986i	$-0.853564\pi$
$337$	−2796.59	+	2796.59i	−0.452048	+	0.452048i	0.443986	+	0.896034i	$0.353564\pi$
$338$	−2477.99	+	2477.99i	−0.398772	+	0.398772i
$339$	2676.37			0.428792
$340$	1346.87	+	1247.59i	0.214836	+	0.199001i
$341$			11371.8i			1.80592i
$342$	461.564	−	461.564i	0.0729782	−	0.0729782i
$343$	−4104.42	−	4104.42i	−0.646116	−	0.646116i
$344$	−3359.25			−0.526507
$345$	−5748.56	−	5285.71i	−0.897079	−	0.824850i
$346$	−737.240			−0.114550
$347$	−5730.92	−	5730.92i	−0.886605	−	0.886605i	0.107591	−	0.994195i	$-0.465686\pi$
$347$	−5730.92	−	5730.92i	−0.886605	−	0.886605i	−0.994195	+	0.107591i	$0.965686\pi$
$348$	−2769.37	+	2769.37i	−0.426592	+	0.426592i
$349$		−	58.4140i		−	0.00895939i	−0.999990	−	0.00447970i	$-0.998574\pi$
$349$		−	58.4140i		−	0.00895939i	0.999990	−	0.00447970i	$-0.00142594\pi$
$350$	2457.26	−	188.331i	0.375274	−	0.0287621i
$351$	5532.00			0.841243
$352$	−1171.67	+	1171.67i	−0.177415	+	0.177415i
$353$	443.174	−	443.174i	0.0668208	−	0.0668208i	−0.672907	−	0.739727i	$-0.734954\pi$
$353$	443.174	−	443.174i	0.0668208	−	0.0668208i	0.739727	+	0.672907i	$0.234954\pi$
$354$		−	6995.33i		−	1.05028i
$355$	−6686.94	+	255.878i	−0.999734	+	0.0382552i
$356$			5799.05i			0.863339i
$357$	1812.03	+	1812.03i	0.268636	+	0.268636i
$358$	−2180.72	+	2180.72i	−0.321940	+	0.321940i
$359$	−1993.12			−0.293017			−0.146508	−	0.989209i	$-0.546804\pi$
$359$	−1993.12			−0.293017			−0.146508	+	0.989209i	$0.546804\pi$
$360$	859.488	+	796.135i	0.125831	+	0.116556i
$361$	−6238.14			−0.909482
$362$	2900.45	−	2900.45i	0.421117	−	0.421117i
$363$	6045.98	−	6045.98i	0.874192	−	0.874192i
$364$	2477.98			0.356816
$365$	6393.94	−	6902.74i	0.916915	−	0.989879i
$366$			8133.36i			1.16158i
$367$	9307.21	−	9307.21i	1.32379	−	1.32379i	0.413116	−	0.910679i	$-0.364441\pi$
$367$	9307.21	−	9307.21i	1.32379	−	1.32379i	0.910679	−	0.413116i	$-0.135559\pi$
$368$	6.48645	+	1764.85i	0.000918831	+	0.249998i
$369$		−	99.3777i		−	0.0140200i
$370$	−9.23469	+	0.353369i	−0.00129754	+	4.96507e-5i
$371$	2589.84			0.362420
$372$	−3933.42	−	3933.42i	−0.548221	−	0.548221i
$373$	−3090.58	−	3090.58i	−0.429020	−	0.429020i	0.459275	−	0.888294i	$-0.348109\pi$
$373$	−3090.58	−	3090.58i	−0.429020	−	0.429020i	−0.888294	+	0.459275i	$0.848109\pi$
$374$			4251.43i			0.587798i
$375$	5500.11	−	6932.97i	0.757398	−	0.954712i
$376$	3824.32			0.524533
$377$	6870.88	+	6870.88i	0.938643	+	0.938643i
$378$	−1227.23	−	1227.23i	−0.166989	−	0.166989i
$379$	−10617.2			−1.43896			−0.719482	−	0.694511i	$-0.755621\pi$
$379$	−10617.2			−1.43896			−0.719482	+	0.694511i	$0.755621\pi$
$380$	42.6090	+	1113.51i	0.00575209	+	0.150321i
$381$	6586.54			0.885665
$382$	−4447.73	+	4447.73i	−0.595722	+	0.595722i
$383$	1578.27	+	1578.27i	0.210563	+	0.210563i	0.804507	−	0.593944i	$-0.202430\pi$
$383$	1578.27	+	1578.27i	0.210563	+	0.210563i	−0.593944	+	0.804507i	$0.702430\pi$
$384$		−	810.539i		−	0.107715i
$385$	4186.80	+	3878.19i	0.554232	+	0.513379i
$386$	−1182.14			−0.155879
$387$	−3889.16	+	3889.16i	−0.510845	+	0.510845i
$388$	2864.43	+	2864.43i	0.374792	+	0.374792i
$389$	8402.59			1.09519			0.547594	−	0.836744i	$-0.315544\pi$
$389$	8402.59			1.09519			0.547594	+	0.836744i	$0.315544\pi$
$390$	6046.80	−	6527.98i	0.785107	−	0.847583i
$391$	3213.68	+	3190.14i	0.415659	+	0.412615i
$392$	1390.58	+	1390.58i	0.179171	+	0.179171i
$393$	718.056	−	718.056i	0.0921657	−	0.0921657i
$394$		−	2769.56i		−	0.354133i
$395$	12583.2	−	481.499i	1.60285	−	0.0613337i
$396$			2712.99i			0.344276i
$397$	−2906.30	−	2906.30i	−0.367413	−	0.367413i	0.499120	−	0.866533i	$-0.333657\pi$
$397$	−2906.30	−	2906.30i	−0.367413	−	0.367413i	−0.866533	+	0.499120i	$0.833657\pi$
$398$	1396.20	+	1396.20i	0.175843	+	0.175843i
$399$			1555.41i			0.195157i
$400$	−1994.15	+	152.838i	−0.249269	+	0.0191047i
$401$		−	8744.17i		−	1.08894i	−0.838782	−	0.544468i	$-0.816732\pi$
$401$		−	8744.17i		−	1.08894i	0.838782	−	0.544468i	$-0.183268\pi$
$402$	−3162.54	+	3162.54i	−0.392370	+	0.392370i
$403$	−9758.90	+	9758.90i	−1.20627	+	1.20627i
$404$			2767.51i			0.340814i
$405$	−10178.8	+	389.497i	−1.24886	+	0.0477882i
$406$		−	3048.49i		−	0.372646i
$407$	−15.1325	−	15.1325i	−0.00184297	−	0.00184297i
$408$	−1470.53	−	1470.53i	−0.178437	−	0.178437i
$409$			9858.67i			1.19188i	0.803028	+	0.595941i	$0.203221\pi$
$409$			9858.67i			1.19188i	−0.803028	+	0.595941i	$0.796779\pi$
$410$	124.460	+	115.286i	0.0149918	+	0.0138868i
$411$		−	6393.57i		−	0.767327i
$412$	−5705.45	+	5705.45i	−0.682251	+	0.682251i
$413$	3850.19	+	3850.19i	0.458730	+	0.458730i
$414$	2050.77	+	2035.75i	0.243453	+	0.241670i
$415$	6579.06	+	6094.12i	0.778201	+	0.720840i
$416$	−2010.97			−0.237009
$417$	11649.2	+	11649.2i	1.36802	+	1.36802i
$418$	−1824.66	+	1824.66i	−0.213510	+	0.213510i
$419$	−15886.0			−1.85223			−0.926113	−	0.377247i	$-0.876871\pi$
$419$	−15886.0			−1.85223			−0.926113	+	0.377247i	$0.876871\pi$
$420$	−2789.61	+	106.745i	−0.324093	+	0.0124015i
$421$		−	13457.0i		−	1.55785i	−0.627118	−	0.778924i	$-0.715766\pi$
$421$		−	13457.0i		−	1.55785i	0.627118	−	0.778924i	$-0.284234\pi$
$422$	−90.1139	−	90.1139i	−0.0103950	−	0.0103950i
$423$	4427.60	−	4427.60i	0.508930	−	0.508930i
$424$	−2101.75			−0.240731
$425$	−3340.63	+	3895.21i	−0.381281	+	0.444577i
$426$	7580.25			0.862123
$427$	−4476.55	−	4476.55i	−0.507343	−	0.507343i
$428$	−705.267	−	705.267i	−0.0796503	−	0.0796503i
$429$	20605.7			2.31901
$430$	−359.025	−	9382.51i	−0.0402645	−	1.05224i
$431$			6029.27i			0.673828i	0.941536	+	0.336914i	$0.109383\pi$
$431$			6029.27i			0.673828i	−0.941536	+	0.336914i	$0.890617\pi$
$432$	995.938	+	995.938i	0.110919	+	0.110919i
$433$	7098.52	+	7098.52i	0.787837	+	0.787837i	0.981139	−	0.193303i	$-0.0619199\pi$
$433$	7098.52	+	7098.52i	0.787837	+	0.787837i	−0.193303	+	0.981139i	$0.561920\pi$
$434$	4329.86			0.478893
$435$	−8030.95	−	7438.99i	−0.885183	−	0.819936i
$436$			767.222i			0.0842735i
$437$	10.1015	+	2748.44i	0.00110577	+	0.300860i
$438$	−7536.50	+	7536.50i	−0.822164	+	0.822164i
$439$		−	17376.9i		−	1.88919i	−0.328240	−	0.944594i	$-0.606455\pi$
$439$		−	17376.9i		−	1.88919i	0.328240	−	0.944594i	$-0.393545\pi$
$440$	−3397.74	−	3147.29i	−0.368139	−	0.341003i
$441$	3219.89			0.347683
$442$	−3648.42	+	3648.42i	−0.392620	+	0.392620i
$443$	3670.37	−	3670.37i	0.393645	−	0.393645i	−0.482339	−	0.875984i	$-0.660213\pi$
$443$	3670.37	−	3670.37i	0.393645	−	0.393645i	0.875984	+	0.482339i	$0.160213\pi$
$444$	10.4684			0.00111893
$445$	−16197.0	+	619.783i	−1.72542	+	0.0660236i
$446$	−4378.92			−0.464906
$447$	−224.927	+	224.927i	−0.0238002	+	0.0238002i
$448$	446.115	+	446.115i	0.0470468	+	0.0470468i
$449$		−	2126.19i		−	0.223477i	−0.993738	−	0.111739i	$-0.964358\pi$
$449$		−	2126.19i		−	0.223477i	0.993738	−	0.111739i	$-0.0356420\pi$
$450$	−2131.78	+	2485.67i	−0.223318	+	0.260391i
$451$			392.862i			0.0410180i
$452$	1195.44	−	1195.44i	0.124400	−	0.124400i
$453$	9792.17	−	9792.17i	1.01562	−	1.01562i
$454$	−8161.20			−0.843665
$455$	264.838	+	6921.09i	0.0272874	+	0.713111i
$456$		−	1262.27i		−	0.129630i
$457$	5750.32	−	5750.32i	0.588597	−	0.588597i	−0.348655	−	0.937251i	$-0.613361\pi$
$457$	5750.32	−	5750.32i	0.588597	−	0.588597i	0.937251	+	0.348655i	$0.113361\pi$
$458$	5283.96	+	5283.96i	0.539090	+	0.539090i
$459$	3613.79			0.367489
$460$	−4928.62	+	206.739i	−0.499561	+	0.0209549i
$461$	−15988.4			−1.61530			−0.807652	−	0.589660i	$-0.799262\pi$
$461$	−15988.4			−1.61530			−0.807652	+	0.589660i	$0.799262\pi$
$462$	−4571.20	−	4571.20i	−0.460328	−	0.460328i
$463$	12475.9	−	12475.9i	1.25227	−	1.25227i	0.297574	−	0.954699i	$-0.403822\pi$
$463$	12475.9	−	12475.9i	1.25227	−	1.25227i	0.954699	−	0.297574i	$-0.0961776\pi$
$464$			2473.96i			0.247523i
$465$	10565.8	−	11406.6i	1.05371	−	1.13756i
$466$	−3310.18			−0.329059
$467$	8588.98	−	8588.98i	0.851072	−	0.851072i	−0.139193	−	0.990265i	$-0.544451\pi$
$467$	8588.98	−	8588.98i	0.851072	−	0.851072i	0.990265	+	0.139193i	$0.0444509\pi$
$468$	−2328.19	+	2328.19i	−0.229959	+	0.229959i
$469$		−	3481.28i		−	0.342752i
$470$	408.731	+	10681.5i	0.0401135	+	1.04830i
$471$		−	5863.30i		−	0.573603i
$472$	−3124.56	−	3124.56i	−0.304703	−	0.304703i
$473$	15374.7	−	15374.7i	1.49456	−	1.49456i
$474$	−14264.1			−1.38222
$475$	−3105.53	+	238.017i	−0.299982	+	0.0229915i
$476$	1618.74			0.155872
$477$	−2433.30	+	2433.30i	−0.233570	+	0.233570i
$478$	5161.37	−	5161.37i	0.493882	−	0.493882i
$479$	−6811.32			−0.649723			−0.324861	−	0.945762i	$-0.605318\pi$
$479$	−6811.32			−0.649723			−0.324861	+	0.945762i	$0.605318\pi$
$480$	2263.87	−	86.6277i	0.215273	−	0.00823749i
$481$		−	25.9723i		−	0.00246202i
$482$	1455.26	−	1455.26i	0.137521	−	0.137521i
$483$	−6885.49	+	25.3066i	−0.648655	+	0.00238403i
$484$		−	5401.05i		−	0.507236i
$485$	−7694.32	+	8306.60i	−0.720373	+	0.777697i
$486$	6785.05			0.633284
$487$	8576.21	+	8576.21i	0.797998	+	0.797998i	0.982780	−	0.184782i	$-0.0591577\pi$
$487$	8576.21	+	8576.21i	0.797998	+	0.797998i	−0.184782	+	0.982780i	$0.559158\pi$
$488$	3632.88	+	3632.88i	0.336993	+	0.336993i
$489$		−	4949.39i		−	0.457708i
$490$	−3735.34	+	4032.58i	−0.344378	+	0.371782i
$491$	551.214			0.0506639			0.0253319	−	0.999679i	$-0.491936\pi$
$491$	551.214			0.0506639			0.0253319	+	0.999679i	$0.491936\pi$
$492$	−135.887	−	135.887i	−0.0124518	−	0.0124518i
$493$	4488.42	+	4488.42i	0.410037	+	0.410037i
$494$	−3131.72			−0.285228
$495$	−7577.50	+	289.956i	−0.688048	+	0.0263284i
$496$	−3513.83			−0.318096
$497$	−4172.12	+	4172.12i	−0.376550	+	0.376550i
$498$	−7183.10	−	7183.10i	−0.646351	−	0.646351i
$499$			9172.70i			0.822898i	0.911433	+	0.411449i	$0.134977\pi$
$499$			9172.70i			0.822898i	−0.911433	+	0.411449i	$0.865023\pi$
$500$	−640.010	−	5553.41i	−0.0572442	−	0.496712i
$501$	4838.37			0.431462
$502$	1421.55	−	1421.55i	0.126388	−	0.126388i
$503$	−2911.03	−	2911.03i	−0.258045	−	0.258045i	0.566214	−	0.824258i	$-0.308408\pi$
$503$	−2911.03	−	2911.03i	−0.258045	−	0.258045i	−0.824258	+	0.566214i	$0.808408\pi$
$504$	1032.98			0.0912947
$505$	−7729.77	+	295.782i	−0.681129	+	0.0260636i
$506$	−8107.12	−	8047.75i	−0.712264	−	0.707047i
$507$	7845.72	+	7845.72i	0.687260	+	0.687260i
$508$	2941.97	−	2941.97i	0.256947	−	0.256947i
$509$		−	9384.37i		−	0.817200i	−0.912714	−	0.408600i	$-0.866017\pi$
$509$		−	9384.37i		−	0.817200i	0.912714	−	0.408600i	$-0.133983\pi$
$510$	3950.09	−	4264.42i	0.342966	−	0.370258i
$511$		−	8296.08i		−	0.718194i
$512$	−362.039	−	362.039i	−0.0312500	−	0.0312500i
$513$	1551.00	+	1551.00i	0.133486	+	0.133486i
$514$			11199.1i			0.961033i
$515$	−16545.3	−	15325.8i	−1.41568	−	1.31133i
$516$			10635.9i			0.907404i
$517$	−17503.3	+	17503.3i	−1.48896	+	1.48896i
$518$	−5.76172	+	5.76172i	−0.000488717	+	0.000488717i
$519$			2334.22i			0.197420i
$520$	−214.925	−	5616.71i	−0.0181252	−	0.473671i
$521$		−	1948.18i		−	0.163822i	−0.996640	−	0.0819112i	$-0.973898\pi$
$521$		−	1948.18i		−	0.163822i	0.996640	−	0.0819112i	$-0.0261024\pi$
$522$	2864.22	+	2864.22i	0.240160	+	0.240160i
$523$	4799.07	+	4799.07i	0.401240	+	0.401240i	0.878670	−	0.477430i	$-0.158431\pi$
$523$	4799.07	+	4799.07i	0.401240	+	0.401240i	−0.477430	+	0.878670i	$0.658431\pi$
$524$		−	641.460i		−	0.0534777i
$525$	−596.288	−	7780.08i	−0.0495698	−	0.646763i
$526$			6922.50i			0.573832i
$527$	−6375.02	+	6375.02i	−0.526946	+	0.526946i
$528$	3709.70	+	3709.70i	0.305765	+	0.305765i
$529$	−12166.7	+	89.4347i	−0.999973	+	0.00735060i
$530$	−224.628	−	5870.28i	−0.0184099	−	0.481110i
$531$	−7234.92			−0.591278
$532$	694.745	+	694.745i	0.0566184	+	0.0566184i
$533$	−337.139	+	337.139i	−0.0273980	+	0.0273980i
$534$	18360.7			1.48792
$535$	1894.46	−	2045.22i	0.153093	−	0.165275i
$536$			2825.18i			0.227667i
$537$	6904.52	+	6904.52i	0.554846	+	0.554846i
$538$	7419.77	−	7419.77i	0.594589	−	0.594589i
$539$	−12728.9			−1.01721
$540$	−2675.25	+	2888.14i	−0.213194	+	0.230159i
$541$	−7969.32			−0.633323			−0.316662	−	0.948539i	$-0.602562\pi$
$541$	−7969.32			−0.633323			−0.316662	+	0.948539i	$0.602562\pi$
$542$	11870.8	+	11870.8i	0.940761	+	0.940761i
$543$	−9183.31	−	9183.31i	−0.725771	−	0.725771i
$544$	−1313.67			−0.103535
$545$	−2142.88	+	81.9981i	−0.168424	+	0.00644480i
$546$		−	7845.68i		−	0.614953i
$547$	−8656.35	−	8656.35i	−0.676634	−	0.676634i	0.282603	−	0.959237i	$-0.408802\pi$
$547$	−8656.35	−	8656.35i	−0.676634	−	0.676634i	−0.959237	+	0.282603i	$0.908802\pi$
$548$	−2855.78	−	2855.78i	−0.222615	−	0.222615i
$549$	8411.93			0.653939
$550$	8427.38	−	9826.40i	0.653354	−	0.761817i
$551$			3852.75i			0.297881i
$552$	5587.82	−	20.5372i	0.430858	−	0.00158355i
$553$	7850.90	−	7850.90i	0.603715	−	0.603715i
$554$		−	6747.53i		−	0.517464i
$555$	1.11882	+	29.2386i	8.55701e−5	+	0.00223623i
$556$	10406.6			0.793773
$557$	−16408.0	+	16408.0i	−1.24817	+	1.24817i	−0.291638	+	0.956529i	$0.594200\pi$
$557$	−16408.0	+	16408.0i	−1.24817	+	1.24817i	−0.956529	+	0.291638i	$0.905800\pi$
$558$	−4068.14	+	4068.14i	−0.308634	+	0.308634i
$559$	26388.0			1.99659
$560$	−1198.34	+	1293.70i	−0.0904269	+	0.0976227i
$561$	13460.7			1.01304
$562$	−11405.2	+	11405.2i	−0.856050	+	0.856050i
$563$	−3089.98	−	3089.98i	−0.231309	−	0.231309i	0.581930	−	0.813239i	$-0.302298\pi$
$563$	−3089.98	−	3089.98i	−0.231309	−	0.231309i	−0.813239	+	0.581930i	$0.802298\pi$
$564$		−	12108.4i		−	0.904002i
$565$	3466.67	+	3211.14i	0.258131	+	0.239104i
$566$		−	13034.7i		−	0.968006i
$567$	−6350.79	+	6350.79i	−0.470385	+	0.470385i
$568$	3385.83	−	3385.83i	0.250117	−	0.250117i
$569$	−11259.7			−0.829578			−0.414789	−	0.909918i	$-0.636145\pi$
$569$	−11259.7			−0.829578			−0.414789	+	0.909918i	$0.636145\pi$
$570$	3525.57	−	134.907i	0.259070	−	0.00991340i
$571$		−	13634.8i		−	0.999300i	−0.866227	−	0.499650i	$-0.833462\pi$
$571$		−	13634.8i		−	0.999300i	0.866227	−	0.499650i	$-0.166538\pi$
$572$	9203.85	−	9203.85i	0.672783	−	0.672783i
$573$	14082.3	+	14082.3i	1.02669	+	1.02669i
$574$	149.583			0.0108771
$575$	−1104.18	−	13743.7i	−0.0800829	−	0.996788i
$576$	−838.300			−0.0606409
$577$	9168.22	+	9168.22i	0.661487	+	0.661487i	0.955731	−	0.294243i	$-0.0950676\pi$
$577$	9168.22	+	9168.22i	0.661487	+	0.661487i	−0.294243	+	0.955731i	$0.595068\pi$
$578$	4564.69	−	4564.69i	0.328488	−	0.328488i
$579$			3742.85i			0.268649i
$580$	−6909.87	+	264.409i	−0.494684	+	0.0189293i
$581$	7907.07			0.564614
$582$	9069.25	−	9069.25i	0.645932	−	0.645932i
$583$	9619.35	−	9619.35i	0.683350	−	0.683350i
$584$			6732.57i			0.477047i
$585$	−6751.57	−	6253.91i	−0.477167	−	0.441995i
$586$		−	16167.7i		−	1.13973i
$587$	−4637.50	−	4637.50i	−0.326082	−	0.326082i	0.525012	−	0.851095i	$-0.324061\pi$
$587$	−4637.50	−	4637.50i	−0.326082	−	0.326082i	−0.851095	+	0.525012i	$0.824061\pi$
$588$	4402.82	−	4402.82i	0.308791	−	0.308791i
$589$	−5472.17			−0.382813
$590$	8393.09	−	9060.98i	0.585658	−	0.632262i
$591$	−8768.87			−0.610327
$592$	4.67584	−	4.67584i	0.000324622	−	0.000324622i
$593$	−8180.46	+	8180.46i	−0.566494	+	0.566494i	−0.931145	−	0.364650i	$-0.881189\pi$
$593$	−8180.46	+	8180.46i	−0.566494	+	0.566494i	0.364650	+	0.931145i	$0.381189\pi$
$594$	−9116.48			−0.629720
$595$	173.006	+	4521.21i	0.0119202	+	0.311515i
$596$			200.934i			0.0138097i
$597$	4420.62	−	4420.62i	0.303055	−	0.303055i
$598$	−50.9533	−	13863.5i	−0.00348434	−	0.948029i
$599$		−	7954.90i		−	0.542618i	−0.962492	−	0.271309i	$-0.912543\pi$
$599$		−	7954.90i		−	0.542618i	0.962492	−	0.271309i	$-0.0874566\pi$
$600$	483.909	+	6313.82i	0.0329259	+	0.429601i
$601$	−22674.9			−1.53898			−0.769492	−	0.638656i	$-0.779491\pi$
$601$	−22674.9			−1.53898			−0.769492	+	0.638656i	$0.779491\pi$
$602$	−5853.95	−	5853.95i	−0.396327	−	0.396327i
$603$	3270.85	+	3270.85i	0.220895	+	0.220895i
$604$		−	8747.63i		−	0.589298i
$605$	15085.4	−	577.246i	1.01373	−	0.0387907i
$606$	8762.40			0.587373
$607$	13049.1	+	13049.1i	0.872564	+	0.872564i	0.992751	−	0.120187i	$-0.0383495\pi$
$607$	13049.1	+	13049.1i	0.872564	+	0.872564i	−0.120187	+	0.992751i	$0.538350\pi$
$608$	−563.810	−	563.810i	−0.0376078	−	0.0376078i
$609$	−9652.03			−0.642233
$610$	−9758.52	+	10535.1i	−0.647723	+	0.699265i
$611$	−30041.3			−1.98910
$612$	−1520.90	+	1520.90i	−0.100455	+	0.100455i
$613$	15666.9	+	15666.9i	1.03226	+	1.03226i	0.999462	+	0.0328027i	$0.0104433\pi$
$613$	15666.9	+	15666.9i	1.03226	+	1.03226i	0.0328027	+	0.999462i	$0.489557\pi$
$614$			13834.0i			0.909275i
$615$	365.015	−	394.062i	0.0239331	−	0.0258376i
$616$	−4083.59			−0.267098
$617$	−13210.8	+	13210.8i	−0.861988	+	0.861988i	−0.991569	−	0.129581i	$-0.958637\pi$
$617$	−13210.8	+	13210.8i	−0.861988	+	0.861988i	0.129581	+	0.991569i	$0.458637\pi$
$618$	18064.4	+	18064.4i	1.17582	+	1.17582i
$619$	6580.71			0.427304			0.213652	−	0.976910i	$-0.431464\pi$
$619$	6580.71			0.427304			0.213652	+	0.976910i	$0.431464\pi$
$620$	−375.547	−	9814.28i	−0.0243263	−	0.635727i
$621$	−6840.73	+	6891.20i	−0.442043	+	0.445305i
$622$	2253.34	+	2253.34i	0.145258	+	0.145258i
$623$	−10105.6	+	10105.6i	−0.649878	+	0.649878i
$624$			6367.05i			0.408471i
$625$	15442.5	−	2381.10i	0.988320	−	0.152391i
$626$			9888.50i			0.631348i
$627$	5777.19	+	5777.19i	0.367972	+	0.367972i
$628$	−2618.93	−	2618.93i	−0.166412	−	0.166412i
$629$		−	16.9664i		−	0.00107551i
$630$	110.401	+	2885.15i	0.00698174	+	0.182456i
$631$			882.483i			0.0556753i	0.999612	+	0.0278376i	$0.00886214\pi$
$631$			882.483i			0.0556753i	−0.999612	+	0.0278376i	$0.991138\pi$
$632$	−6371.29	+	6371.29i	−0.401007	+	0.401007i
$633$	−285.315	+	285.315i	−0.0179151	+	0.0179151i
$634$		−	927.524i		−	0.0581020i
$635$	8531.47	+	7902.62i	0.533167	+	0.493867i
$636$			6654.49i			0.414886i
$637$	−10923.5	−	10923.5i	−0.679442	−	0.679442i
$638$	−11322.9	−	11322.9i	−0.702630	−	0.702630i
$639$		−	7839.88i		−	0.485353i
$640$	972.495	−	1049.88i	0.0600645	−	0.0648441i
$641$		−	28392.9i		−	1.74953i	−0.484544	−	0.874767i	$-0.661015\pi$
$641$		−	28392.9i		−	1.74953i	0.484544	−	0.874767i	$-0.338985\pi$
$642$	−2232.99	+	2232.99i	−0.137273	+	0.137273i
$643$	19354.8	+	19354.8i	1.18706	+	1.18706i	0.977877	+	0.209180i	$0.0670793\pi$
$643$	19354.8	+	19354.8i	1.18706	+	1.18706i	0.209180	+	0.977877i	$0.432921\pi$
$644$	−3064.20	+	3086.81i	−0.187494	+	0.188878i
$645$	−29706.6	+	1136.73i	−1.81348	+	0.0693935i
$646$	−2045.80			−0.124599
$647$	8501.59	+	8501.59i	0.516587	+	0.516587i	0.916537	−	0.399950i	$-0.130972\pi$
$647$	8501.59	+	8501.59i	0.516587	+	0.516587i	−0.399950	+	0.916537i	$0.630972\pi$
$648$	5153.90	−	5153.90i	0.312445	−	0.312445i
$649$	28601.2			1.72988
$650$	15664.7	−	1200.59i	0.945263	−	0.0724478i
$651$		−	13709.0i		−	0.825345i
$652$	−2210.72	−	2210.72i	−0.132789	−	0.132789i
$653$	−16146.4	+	16146.4i	−0.967620	+	0.967620i	−0.999492	−	0.0318717i	$-0.989853\pi$
$653$	−16146.4	+	16146.4i	−0.967620	+	0.967620i	0.0318717	+	0.999492i	$0.489853\pi$
$654$	2429.15			0.145241
$655$	1791.62	−	68.5571i	0.106877	−	0.00408969i
$656$	−121.392			−0.00722494
$657$	7794.62	+	7794.62i	0.462857	+	0.462857i
$658$	6664.41	+	6664.41i	0.394841	+	0.394841i
$659$	14512.5			0.857855			0.428927	−	0.903339i	$-0.358892\pi$
$659$	14512.5			0.857855			0.428927	+	0.903339i	$0.358892\pi$
$660$	−9964.85	+	10757.8i	−0.587699	+	0.634466i
$661$			6343.82i			0.373292i	0.982427	+	0.186646i	$0.0597618\pi$
$661$			6343.82i			0.373292i	−0.982427	+	0.186646i	$0.940238\pi$
$662$	661.539	+	661.539i	0.0388390	+	0.0388390i
$663$	11551.5	+	11551.5i	0.676657	+	0.676657i
$664$	−6416.87			−0.375035
$665$	−1866.20	+	2014.70i	−0.108824	+	0.117484i
$666$		−	10.8269i		−	0.000629931i
$667$	−17055.4	+	62.6845i	−0.990086	+	0.00363891i
$668$	2161.13	−	2161.13i	0.125175	−	0.125175i
$669$			13864.4i			0.801239i
$670$	−7890.85	+	301.946i	−0.455000	+	0.0174107i
$671$	−33254.2			−1.91321
$672$	1412.48	−	1412.48i	0.0810825	−	0.0810825i
$673$	−22089.6	+	22089.6i	−1.26522	+	1.26522i	−0.316690	+	0.948529i	$0.602571\pi$
$673$	−22089.6	+	22089.6i	−1.26522	+	1.26522i	−0.948529	+	0.316690i	$0.897429\pi$
$674$	7909.95			0.452048
$675$	−8352.61	−	7163.42i	−0.476285	−	0.408474i
$676$	7008.81			0.398772
$677$	−16091.2	+	16091.2i	−0.913491	+	0.913491i	−0.996545	−	0.0830540i	$-0.973533\pi$
$677$	−16091.2	+	16091.2i	−0.913491	+	0.913491i	0.0830540	+	0.996545i	$0.473533\pi$
$678$	−3784.96	−	3784.96i	−0.214396	−	0.214396i
$679$			9983.32i			0.564248i
$680$	−140.400	−	3669.13i	−0.00791781	−	0.206919i
$681$			25839.7i			1.45401i
$682$	16082.2	−	16082.2i	0.902962	−	0.902962i
$683$	−11073.8	+	11073.8i	−0.620392	+	0.620392i	−0.945632	−	0.325239i	$-0.894555\pi$
$683$	−11073.8	+	11073.8i	−0.620392	+	0.620392i	0.325239	+	0.945632i	$0.394555\pi$
$684$	−1305.50			−0.0729782
$685$	7671.09	−	8281.52i	0.427879	−	0.461928i
$686$			11609.1i			0.646116i
$687$	16729.9	−	16729.9i	0.929090	−	0.929090i
$688$	4750.69	+	4750.69i	0.263253	+	0.263253i
$689$	16510.0			0.912887
$690$	654.569	+	15604.8i	0.0361145	+	0.860964i
$691$	23261.7			1.28063			0.640315	−	0.768112i	$-0.278804\pi$
$691$	23261.7			1.28063			0.640315	+	0.768112i	$0.278804\pi$
$692$	1042.61	+	1042.61i	0.0572749	+	0.0572749i
$693$	−4727.77	+	4727.77i	−0.259153	+	0.259153i
$694$			16209.5i			0.886605i
$695$	1112.22	+	29066.0i	0.0607036	+	1.58639i
$696$	7832.97			0.426592
$697$	−220.237	+	220.237i	−0.0119685	+	0.0119685i
$698$	−82.6098	+	82.6098i	−0.00447970	+	0.00447970i
$699$			10480.6i			0.567114i
$700$	−3741.43	−	3208.74i	−0.202018	−	0.173256i
$701$			9330.35i			0.502714i	0.967894	+	0.251357i	$0.0808768\pi$
$701$			9330.35i			0.502714i	−0.967894	+	0.251357i	$0.919123\pi$
$702$	−7823.43	−	7823.43i	−0.420622	−	0.420622i
$703$	7.28179	−	7.28179i	0.000390665	−	0.000390665i
$704$	3313.98			0.177415
$705$	33819.4	−	1294.11i	1.80668	−	0.0691333i
$706$	−1253.48			−0.0668208
$707$	−4822.77	+	4822.77i	−0.256547	+	0.256547i
$708$	−9892.89	+	9892.89i	−0.525138	+	0.525138i
$709$	−7652.27			−0.405342			−0.202671	−	0.979247i	$-0.564962\pi$
$709$	−7652.27			−0.405342			−0.202671	+	0.979247i	$0.564962\pi$
$710$	9818.62	+	9094.89i	0.518995	+	0.480740i
$711$			14752.7i			0.778157i
$712$	8201.09	−	8201.09i	0.431670	−	0.431670i
$713$	−89.0325	−	24224.2i	−0.00467643	−	1.27238i
$714$		−	5125.21i		−	0.268636i
$715$	26690.4	+	24723.0i	1.39603	+	1.29313i
$716$	6168.01			0.321940
$717$	−16341.8	−	16341.8i	−0.851177	−	0.851177i
$718$	2818.70	+	2818.70i	0.146508	+	0.146508i
$719$			24096.1i			1.24984i	0.780689	+	0.624919i	$0.214868\pi$
$719$			24096.1i			1.24984i	−0.780689	+	0.624919i	$0.785132\pi$
$720$	−89.5947	−	2341.41i	−0.00463750	−	0.121193i
$721$	−19885.1			−1.02713
$722$	8822.06	+	8822.06i	0.454741	+	0.454741i
$723$	−4607.60	−	4607.60i	−0.237010	−	0.237010i
$724$	−8203.71			−0.421117
$725$	−1477.01	−	19271.3i	−0.0756617	−	0.987197i
$726$	−17100.6			−0.874192
$727$	13958.4	−	13958.4i	0.712087	−	0.712087i	−0.254885	−	0.966971i	$-0.582038\pi$
$727$	13958.4	−	13958.4i	0.712087	−	0.712087i	0.966971	+	0.254885i	$0.0820376\pi$
$728$	−3504.39	−	3504.39i	−0.178408	−	0.178408i
$729$			3116.81i			0.158350i
$730$	−18804.3	+	719.555i	−0.953397	+	0.0364821i
$731$	17238.0			0.872190
$732$	11502.3	−	11502.3i	0.580789	−	0.580789i
$733$	−23185.6	−	23185.6i	−1.16832	−	1.16832i	−0.982603	−	0.185720i	$-0.940538\pi$
$733$	−23185.6	−	23185.6i	−1.16832	−	1.16832i	−0.185720	−	0.982603i	$-0.559462\pi$
$734$	−26324.8			−1.32379
$735$	12767.8	+	11826.7i	0.640745	+	0.593516i
$736$	2486.71	−	2505.05i	0.124540	−	0.125459i
$737$	−12930.4	−	12930.4i	−0.646264	−	0.646264i
$738$	−140.541	+	140.541i	−0.00701002	+	0.00701002i
$739$		−	11951.9i		−	0.594935i	−0.954732	−	0.297467i	$-0.903858\pi$
$739$		−	11951.9i		−	0.594935i	0.954732	−	0.297467i	$-0.0961420\pi$
$740$	13.5596	+	12.5601i	0.000673594	+	0.000623943i
$741$			9915.54i			0.491574i
$742$	−3662.59	−	3662.59i	−0.181210	−	0.181210i
$743$	16378.4	+	16378.4i	0.808703	+	0.808703i	0.984438	−	0.175734i	$-0.0562299\pi$
$743$	16378.4	+	16378.4i	0.808703	+	0.808703i	−0.175734	+	0.984438i	$0.556230\pi$
$744$			11125.4i			0.548221i
$745$	−561.216	+	21.4751i	−0.0275992	+	0.00105609i
$746$			8741.49i			0.429020i
$747$	−7429.13	+	7429.13i	−0.363879	+	0.363879i
$748$	6012.43	−	6012.43i	0.293899	−	0.293899i
$749$		−	2458.05i		−	0.119913i
$750$	−17583.0	+	2026.38i	−0.856055	+	0.0986572i
$751$		−	7864.80i		−	0.382144i	−0.981576	−	0.191072i	$-0.938804\pi$
$751$		−	7864.80i		−	0.382144i	0.981576	−	0.191072i	$-0.0611965\pi$
$752$	−5408.41	−	5408.41i	−0.262266	−	0.262266i
$753$	−4500.86	−	4500.86i	−0.217823	−	0.217823i
$754$		−	19433.8i		−	0.938643i
$755$	24432.5	−	934.917i	1.17773	−	0.0450664i
$756$			3471.12i			0.166989i
$757$	18320.9	−	18320.9i	0.879636	−	0.879636i	−0.113861	−	0.993497i	$-0.536322\pi$
$757$	18320.9	−	18320.9i	0.879636	−	0.879636i	0.993497	+	0.113861i	$0.0363217\pi$
$758$	15014.9	+	15014.9i	0.719482	+	0.719482i
$759$	−25480.5	+	25668.5i	−1.21856	+	1.22755i
$760$	1514.49	−	1635.00i	0.0722845	−	0.0780366i
$761$	34657.3			1.65089			0.825445	−	0.564483i	$-0.190924\pi$
$761$	34657.3			1.65089			0.825445	+	0.564483i	$0.190924\pi$
$762$	−9314.77	−	9314.77i	−0.442833	−	0.442833i
$763$	−1336.99	+	1336.99i	−0.0634368	+	0.0634368i
$764$	12580.1			0.595722
$765$	−4410.48	−	4085.38i	−0.208446	−	0.193081i
$766$		−	4464.01i		−	0.210563i
$767$	24544.5	+	24544.5i	1.15548	+	1.15548i
$768$	−1146.27	+	1146.27i	−0.0538576	+	0.0538576i
$769$	−32741.2			−1.53534			−0.767671	−	0.640844i	$-0.778584\pi$
$769$	−32741.2			−1.53534			−0.767671	+	0.640844i	$0.778584\pi$
$770$	−436.440	−	11405.6i	−0.0204263	−	0.533806i
$771$	35458.2			1.65629
$772$	1671.80	+	1671.80i	0.0779395	+	0.0779395i
$773$	−14189.8	−	14189.8i	−0.660248	−	0.660248i	0.295191	−	0.955438i	$-0.404617\pi$
$773$	−14189.8	−	14189.8i	−0.660248	−	0.660248i	−0.955438	+	0.295191i	$0.904617\pi$
$774$	11000.2			0.510845
$775$	27371.5	−	2097.84i	1.26866	−	0.0972342i
$776$		−	8101.82i		−	0.374792i
$777$	18.2426	+	18.2426i	0.000842276	+	0.000842276i
$778$	−11883.1	−	11883.1i	−0.547594	−	0.547594i
$779$	−189.046			−0.00869484
$780$	−17783.4	+	680.489i	−0.816345	+	0.0312377i
$781$			30992.7i			1.41998i
$782$	−33.2853	−	9056.37i	−0.00152210	−	0.414137i
$783$	−9624.66	+	9624.66i	−0.439281	+	0.439281i
$784$		−	3933.16i		−	0.179171i
$785$	7034.87	−	7594.68i	0.319854	−	0.345307i
$786$	−2030.97			−0.0921657
$787$	27138.1	−	27138.1i	1.22919	−	1.22919i	0.264914	−	0.964272i	$-0.414656\pi$
$787$	27138.1	−	27138.1i	1.22919	−	1.22919i	0.964272	−	0.264914i	$-0.0853436\pi$
$788$	−3916.74	+	3916.74i	−0.177066	+	0.177066i
$789$	21917.8			0.988966
$790$	−18476.2	−	17114.3i	−0.832093	−	0.770760i
$791$	4166.43			0.187284
$792$	3836.75	−	3836.75i	0.172138	−	0.172138i
$793$	−28537.5	−	28537.5i	−1.27793	−	1.27793i
$794$			8220.26i			0.367413i
$795$	−18586.3	+	711.210i	−0.829166	+	0.0317283i
$796$		−	3949.06i		−	0.175843i
$797$	23348.3	−	23348.3i	1.03769	−	1.03769i	0.0384301	−	0.999261i	$-0.487764\pi$
$797$	23348.3	−	23348.3i	1.03769	−	1.03769i	0.999261	−	0.0384301i	$-0.0122357\pi$
$798$	2199.68	−	2199.68i	0.0975786	−	0.0975786i
$799$	−19624.6			−0.868920
$800$	3036.30	+	2604.01i	0.134187	+	0.115082i
$801$		−	18989.6i		−	0.837659i
$802$	−12366.1	+	12366.1i	−0.544468	+	0.544468i
$803$	−30813.8	−	30813.8i	−1.35417	−	1.35417i
$804$	8945.00			0.392370
$805$	−8949.07	−	8228.52i	−0.391818	−	0.360270i
$806$	27602.3			1.20627
$807$	−23492.2	−	23492.2i	−1.02474	−	1.02474i
$808$	3913.85	−	3913.85i	0.170407	−	0.170407i
$809$		−	20236.4i		−	0.879450i	−0.898132	−	0.439725i	$-0.855076\pi$
$809$		−	20236.4i		−	0.879450i	0.898132	−	0.439725i	$-0.144924\pi$
$810$	14945.9	+	13844.2i	0.648327	+	0.600538i
$811$	27503.3			1.19084			0.595421	−	0.803414i	$-0.296985\pi$
$811$	27503.3			1.19084			0.595421	+	0.803414i	$0.296985\pi$
$812$	−4311.22	+	4311.22i	−0.186323	+	0.186323i
$813$	37584.8	−	37584.8i	1.62135	−	1.62135i
$814$			42.8011i			0.00184297i
$815$	5938.34	−	6410.89i	0.255228	−	0.275538i
$816$			4159.29i			0.178437i
$817$	7398.35	+	7398.35i	0.316812	+	0.316812i
$818$	13942.3	−	13942.3i	0.595941	−	0.595941i
$819$	−8114.40			−0.346203
$820$	−12.9740	−	339.053i	−0.000552525	−	0.0144393i
$821$	−6622.81			−0.281532			−0.140766	−	0.990043i	$-0.544957\pi$
$821$	−6622.81			−0.281532			−0.140766	+	0.990043i	$0.544957\pi$
$822$	−9041.87	+	9041.87i	−0.383664	+	0.383664i
$823$	−24755.5	+	24755.5i	−1.04851	+	1.04851i	−0.0497452	+	0.998762i	$0.515841\pi$
$823$	−24755.5	+	24755.5i	−1.04851	+	1.04851i	−0.998762	+	0.0497452i	$0.984159\pi$
$824$	16137.5			0.682251
$825$	−31112.0	−	26682.5i	−1.31295	−	1.12602i
$826$		−	10890.0i		−	0.458730i
$827$	8024.96	−	8024.96i	0.337431	−	0.337431i	−0.517969	−	0.855400i	$-0.673312\pi$
$827$	8024.96	−	8024.96i	0.337431	−	0.337431i	0.855400	+	0.517969i	$0.173312\pi$
$828$	−21.2406	−	5779.21i	−0.000891499	−	0.242562i
$829$			15147.2i			0.634601i	0.948325	+	0.317301i	$0.102776\pi$
$829$			15147.2i			0.634601i	−0.948325	+	0.317301i	$0.897224\pi$
$830$	−685.814	−	17922.6i	−0.0286807	−	0.749521i
$831$	−21363.8			−0.891820
$832$	2843.94	+	2843.94i	0.118504	+	0.118504i
$833$	−7135.80	−	7135.80i	−0.296808	−	0.296808i
$834$		−	32949.0i		−	1.36802i
$835$	6267.09	+	5805.15i	0.259739	+	0.240593i
$836$	5160.93			0.213510
$837$	−13670.2	−	13670.2i	−0.564528	−	0.564528i
$838$	22466.2	+	22466.2i	0.926113	+	0.926113i
$839$	−16895.4			−0.695225			−0.347612	−	0.937638i	$-0.613007\pi$
$839$	−16895.4			−0.695225			−0.347612	+	0.937638i	$0.613007\pi$
$840$	4096.06	+	3794.14i	0.168247	+	0.155846i
$841$	480.874			0.0197168
$842$	−19031.1	+	19031.1i	−0.778924	+	0.778924i
$843$	36110.8	+	36110.8i	1.47535	+	1.47535i
$844$			254.880i			0.0103950i
$845$	749.079	+	19575.9i	0.0304960	+	0.796960i
$846$	−12523.2			−0.508930
$847$	9412.08	−	9412.08i	0.381821	−	0.381821i
$848$	2972.32	+	2972.32i	0.120366	+	0.120366i
$849$	−41270.2			−1.66830
$850$	10233.0	−	784.288i	0.412929	−	0.0316481i
$851$	32.3536	+	32.1166i	0.00130325	+	0.00129371i
$852$	−10720.1	−	10720.1i	−0.431061	−	0.431061i
$853$	−19774.0	+	19774.0i	−0.793725	+	0.793725i	−0.982098	−	0.188373i	$-0.939679\pi$
$853$	−19774.0	+	19774.0i	−0.793725	+	0.793725i	0.188373	+	0.982098i	$0.439679\pi$
$854$			12661.6i			0.507343i
$855$	−139.528	−	3646.32i	−0.00558099	−	0.145850i
$856$			1994.80i			0.0796503i
$857$	−13832.5	−	13832.5i	−0.551353	−	0.551353i	0.375478	−	0.926831i	$-0.377478\pi$
$857$	−13832.5	−	13832.5i	−0.551353	−	0.551353i	−0.926831	+	0.375478i	$0.877478\pi$
$858$	−29140.9	−	29140.9i	−1.15950	−	1.15950i
$859$			39139.7i			1.55463i	0.629111	+	0.777316i	$0.283419\pi$
$859$			39139.7i			1.55463i	−0.629111	+	0.777316i	$0.716581\pi$
$860$	−12761.1	+	13776.6i	−0.505990	+	0.546254i
$861$		−	473.604i		−	0.0187461i
$862$	8526.67	−	8526.67i	0.336914	−	0.336914i
$863$	20049.6	−	20049.6i	0.790843	−	0.790843i	−0.190788	−	0.981631i	$-0.561104\pi$
$863$	20049.6	−	20049.6i	0.790843	−	0.790843i	0.981631	+	0.190788i	$0.0611045\pi$
$864$		−	2816.94i		−	0.110919i
$865$	−2800.63	+	3023.50i	−0.110086	+	0.118846i
$866$		−	20077.7i		−	0.787837i
$867$	−14452.6	−	14452.6i	−0.566130	−	0.566130i
$868$	−6123.34	−	6123.34i	−0.239447	−	0.239447i
$869$		−	58320.6i		−	2.27663i
$870$	837.162	+	21877.8i	0.0326235	+	0.852560i
$871$		−	22192.8i		−	0.863345i
$872$	1085.02	−	1085.02i	0.0421368	−	0.0421368i
$873$	−9379.87	−	9379.87i	−0.363643	−	0.363643i
$874$	3872.60	−	3901.17i	0.149877	−	0.150983i
$875$	8562.28	−	10792.9i	0.330809	−	0.416990i
$876$	21316.4			0.822164
$877$	20713.0	+	20713.0i	0.797522	+	0.797522i	0.982704	−	0.185182i	$-0.0592875\pi$
$877$	20713.0	+	20713.0i	0.797522	+	0.797522i	−0.185182	+	0.982704i	$0.559287\pi$
$878$	−24574.6	+	24574.6i	−0.944594	+	0.944594i
$879$	−51189.5			−1.96425
$880$	354.187	+	9256.08i	0.0135678	+	0.354571i
$881$			35113.5i			1.34280i	0.741097	+	0.671398i	$0.234306\pi$
$881$			35113.5i			1.34280i	−0.741097	+	0.671398i	$0.765694\pi$
$882$	−4553.62	−	4553.62i	−0.173842	−	0.173842i
$883$	16219.3	−	16219.3i	0.618146	−	0.618146i	−0.326910	−	0.945056i	$-0.606007\pi$
$883$	16219.3	−	16219.3i	0.618146	−	0.618146i	0.945056	+	0.326910i	$0.106007\pi$
$884$	10319.3			0.392620
$885$	−28688.6	−	26573.9i	−1.08967	−	1.00935i
$886$	−10381.4			−0.393645
$887$	−10173.1	−	10173.1i	−0.385095	−	0.385095i	0.487838	−	0.872934i	$-0.337786\pi$
$887$	−10173.1	−	10173.1i	−0.385095	−	0.385095i	−0.872934	+	0.487838i	$0.837786\pi$
$888$	−14.8045	−	14.8045i	−0.000559467	−	0.000559467i
$889$	10253.6			0.386833
$890$	23782.5	+	22029.5i	0.895720	+	0.829696i
$891$			47177.0i			1.77384i
$892$	6192.73	+	6192.73i	0.232453	+	0.232453i
$893$	−8422.62	−	8422.62i	−0.315624	−	0.315624i
$894$	636.190			0.0238002
$895$	659.216	+	17227.5i	0.0246203	+	0.643410i
$896$		−	1261.80i		−	0.0470468i
$897$	−43894.2	+	161.326i	−1.63387	+	0.00600505i
$898$	−3006.89	+	3006.89i	−0.111739	+	0.111739i
$899$		−	33957.4i		−	1.25978i
$900$	6530.06	−	500.483i	0.241854	−	0.0185364i
$901$	10785.2			0.398786
$902$	555.590	−	555.590i	0.0205090	−	0.0205090i
$903$	−18534.6	+	18534.6i	−0.683048	+	0.683048i
$904$	−3381.21			−0.124400
$905$	−876.786	−	22913.3i	−0.0322048	−	0.841618i
$906$	−27696.4			−1.01562
$907$	−8637.68	+	8637.68i	−0.316218	+	0.316218i	−0.847313	−	0.531095i	$-0.821781\pi$
$907$	−8637.68	+	8637.68i	−0.316218	+	0.316218i	0.531095	+	0.847313i	$0.321781\pi$
$908$	11541.7	+	11541.7i	0.421833	+	0.421833i
$909$		−	9062.51i		−	0.330676i
$910$	9413.36	−	10162.4i	0.342912	−	0.370199i
$911$			5750.23i			0.209126i	0.994518	+	0.104563i	$0.0333444\pi$
$911$			5750.23i			0.209126i	−0.994518	+	0.104563i	$0.966656\pi$
$912$	−1785.12	+	1785.12i	−0.0648148	+	0.0648148i
$913$	29368.9	−	29368.9i	1.06459	−	1.06459i
$914$	−16264.4			−0.588597
$915$	33355.7	+	30897.1i	1.20514	+	1.11631i
$916$		−	14945.3i		−	0.539090i
$917$	1117.83	−	1117.83i	0.0402553	−	0.0402553i
$918$	−5110.67	−	5110.67i	−0.183744	−	0.183744i
$919$	39006.4			1.40011			0.700056	−	0.714088i	$-0.253158\pi$
$919$	39006.4			1.40011			0.700056	+	0.714088i	$0.253158\pi$
$920$	7262.49	+	6677.74i	0.260258	+	0.239303i
$921$	43800.7			1.56708
$922$	22611.0	+	22611.0i	0.807652	+	0.807652i
$923$	−26596.8	+	26596.8i	−0.948478	+	0.948478i
$924$			12929.3i			0.460328i
$925$	−33.6316	+	39.2148i	−0.00119546	+	0.00139392i
$926$	−35287.1			−1.25227
$927$	18683.1	−	18683.1i	0.661957	−	0.661957i
$928$	3498.71	−	3498.71i	0.123762	−	0.123762i
$929$		−	3246.41i		−	0.114652i	−0.998356	−	0.0573258i	$-0.981743\pi$
$929$		−	3246.41i		−	0.114652i	0.998356	−	0.0573258i	$-0.0182574\pi$
$930$	−31073.6	+	1189.04i	−1.09564	+	0.0419250i
$931$		−	6125.20i		−	0.215623i
$932$	4681.31	+	4681.31i	0.164529	+	0.164529i
$933$	7134.44	−	7134.44i	0.250344	−	0.250344i
$934$	−24293.3			−0.851072
$935$	17435.6	+	16150.4i	0.609844	+	0.564892i
$936$	6585.12			0.229959
$937$	5320.73	−	5320.73i	0.185508	−	0.185508i	−0.608243	−	0.793751i	$-0.708125\pi$
$937$	5320.73	−	5320.73i	0.185508	−	0.185508i	0.793751	+	0.608243i	$0.208125\pi$
$938$	−4923.27	+	4923.27i	−0.171376	+	0.171376i
$939$	31308.6			1.08809
$940$	14527.9	−	15683.9i	0.504092	−	0.544206i
$941$		−	6849.99i		−	0.237304i	−0.992936	−	0.118652i	$-0.962143\pi$
$941$		−	6849.99i		−	0.237304i	0.992936	−	0.118652i	$-0.0378573\pi$
$942$	−8291.96	+	8291.96i	−0.286801	+	0.286801i
$943$	−3.07579	−	836.871i	−0.000106216	−	0.0288996i
$944$			8837.60i			0.304703i
$945$	−9694.98	+	370.982i	−0.333733	+	0.0127704i
$946$	−43486.2			−1.49456
$947$	−7809.32	−	7809.32i	−0.267971	−	0.267971i	0.560311	−	0.828282i	$-0.310682\pi$
$947$	−7809.32	−	7809.32i	−0.267971	−	0.267971i	−0.828282	+	0.560311i	$0.810682\pi$
$948$	20172.5	+	20172.5i	0.691112	+	0.691112i
$949$		−	52886.6i		−	1.80903i
$950$	4728.50	+	4055.28i	0.161487	+	0.138495i
$951$	−2936.69			−0.100135
$952$	−2289.25	−	2289.25i	−0.0779359	−	0.0779359i
$953$	−26304.7	−	26304.7i	−0.894117	−	0.894117i	0.100791	−	0.994908i	$-0.467863\pi$
$953$	−26304.7	−	26304.7i	−0.894117	−	0.894117i	−0.994908	+	0.100791i	$0.967863\pi$
$954$	6882.41			0.233570
$955$	1344.52	+	35136.7i	0.0455577	+	1.19057i
$956$	−14598.6			−0.493882
$957$	−35850.2	+	35850.2i	−1.21094	+	1.21094i
$958$	9632.66	+	9632.66i	0.324861	+	0.324861i
$959$		−	9953.18i		−	0.335146i
$960$	−3324.10	−	3079.08i	−0.111755	−	0.103518i
$961$	18439.6			0.618964
$962$	−36.7303	+	36.7303i	−0.00123101	+	0.00123101i
$963$	2309.47	+	2309.47i	0.0772811	+	0.0772811i
$964$	−4116.10			−0.137521
$965$	−4490.72	+	4848.07i	−0.149805	+	0.161725i
$966$	9773.34	+	9701.76i	0.325520	+	0.323136i
$967$	−26217.4	−	26217.4i	−0.871868	−	0.871868i	0.120808	−	0.992676i	$-0.461451\pi$
$967$	−26217.4	−	26217.4i	−0.871868	−	0.871868i	−0.992676	+	0.120808i	$0.961451\pi$
$968$	−7638.24	+	7638.24i	−0.253618	+	0.253618i
$969$			6477.35i			0.214739i
$970$	22628.7	−	865.896i	0.749035	−	0.0286621i
$971$		−	26622.6i		−	0.879877i	−0.898028	−	0.439939i	$-0.855000\pi$
$971$		−	26622.6i		−	0.879877i	0.898028	−	0.439939i	$-0.145000\pi$
$972$	−9595.51	−	9595.51i	−0.316642	−	0.316642i
$973$	18134.9	+	18134.9i	0.597512	+	0.597512i
$974$		−	24257.2i		−	0.797998i
$975$	−3801.27	−	49597.1i	−0.124860	−	1.62911i
$976$		−	10275.3i		−	0.336993i
$977$	1330.25	−	1330.25i	0.0435603	−	0.0435603i	−0.684991	−	0.728551i	$-0.740194\pi$
$977$	1330.25	−	1330.25i	0.0435603	−	0.0435603i	0.728551	+	0.684991i	$0.240194\pi$
$978$	−6999.49	+	6999.49i	−0.228854	+	0.228854i
$979$			75070.0i			2.45071i
$980$	10985.5	−	420.364i	0.358080	−	0.0137021i
$981$		−	2512.35i		−	0.0817668i
$982$	−779.535	−	779.535i	−0.0253319	−	0.0253319i
$983$	−18969.5	−	18969.5i	−0.615498	−	0.615498i	0.328875	−	0.944373i	$-0.393330\pi$
$983$	−18969.5	−	18969.5i	−0.615498	−	0.615498i	−0.944373	+	0.328875i	$0.893330\pi$
$984$			384.347i			0.0124518i
$985$	−11358.2	−	10521.0i	−0.367415	−	0.340332i
$986$		−	12695.2i		−	0.410037i
$987$	21100.6	−	21100.6i	0.680487	−	0.680487i
$988$	4428.92	+	4428.92i	0.142614	+	0.142614i
$989$	−32630.7	+	32871.4i	−1.04914	+	1.05688i
$990$	11126.3	+	10306.2i	0.357188	+	0.330860i
$991$	−3399.32			−0.108964			−0.0544818	−	0.998515i	$-0.517351\pi$
$991$	−3399.32			−0.108964			−0.0544818	+	0.998515i	$0.517351\pi$
$992$	4969.31	+	4969.31i	0.159048	+	0.159048i
$993$	2094.54	−	2094.54i	0.0669368	−	0.0669368i
$994$	11800.5			0.376550
$995$	11029.9	−	422.063i	0.351428	−	0.0134475i
$996$			20316.9i			0.646351i
$997$	26201.0	+	26201.0i	0.832290	+	0.832290i	0.987830	−	0.155540i	$-0.0497116\pi$
$997$	26201.0	+	26201.0i	0.832290	+	0.832290i	−0.155540	+	0.987830i	$0.549712\pi$
$998$	12972.1	−	12972.1i	0.411449	−	0.411449i
$999$	36.3817			0.00115222

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.4.e.a.137.3	✓	72
5.3	odd	4	inner	230.4.e.a.183.4	yes	72
23.22	odd	2	inner	230.4.e.a.137.4	yes	72
115.68	even	4	inner	230.4.e.a.183.3	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.4.e.a.137.3	✓	72	1.1	even	1	trivial
230.4.e.a.137.4	yes	72	23.22	odd	2	inner
230.4.e.a.183.3	yes	72	115.68	even	4	inner
230.4.e.a.183.4	yes	72	5.3	odd	4	inner

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:	\( N \)	\(=\)	\( 230 = 2 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	230.e (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.41421 - 1.41421i) q^{2} +(-4.47764 + 4.47764i) q^{3} +4.00000i q^{4} +(-11.1722 + 0.427507i) q^{5} +12.6647 q^{6} +(-6.97055 + 6.97055i) q^{7} +(5.65685 - 5.65685i) q^{8} -13.0984i q^{9} +O(q^{10})\)	\(q+(-1.41421 - 1.41421i) q^{2} +(-4.47764 + 4.47764i) q^{3} +4.00000i q^{4} +(-11.1722 + 0.427507i) q^{5} +12.6647 q^{6} +(-6.97055 + 6.97055i) q^{7} +(5.65685 - 5.65685i) q^{8} -13.0984i q^{9} +(16.4044 + 15.1952i) q^{10} +51.7809i q^{11} +(-17.9105 - 17.9105i) q^{12} +(-44.4365 + 44.4365i) q^{13} +19.7157 q^{14} +(48.1107 - 51.9391i) q^{15} -16.0000 q^{16} +(-29.0282 + 29.0282i) q^{17} +(-18.5240 + 18.5240i) q^{18} -24.9171 q^{19} +(-1.71003 - 44.6887i) q^{20} -62.4232i q^{21} +(73.2293 - 73.2293i) q^{22} +(-0.405403 - 110.303i) q^{23} +50.6587i q^{24} +(124.634 - 9.55235i) q^{25} +125.685 q^{26} +(-62.2462 - 62.2462i) q^{27} +(-27.8822 - 27.8822i) q^{28} -154.623i q^{29} +(-141.492 + 5.41423i) q^{30} +219.615 q^{31} +(22.6274 + 22.6274i) q^{32} +(-231.856 - 231.856i) q^{33} +82.1042 q^{34} +(74.8962 - 80.8561i) q^{35} +52.3937 q^{36} +(-0.292240 + 0.292240i) q^{37} +(35.2381 + 35.2381i) q^{38} -397.941i q^{39} +(-60.7810 + 65.6176i) q^{40} +7.58700 q^{41} +(-88.2797 + 88.2797i) q^{42} +(-296.918 - 296.918i) q^{43} -207.124 q^{44} +(5.59967 + 146.338i) q^{45} +(-155.419 + 156.566i) q^{46} +(338.025 + 338.025i) q^{47} +(71.6422 - 71.6422i) q^{48} +245.823i q^{49} +(-189.769 - 162.751i) q^{50} -259.956i q^{51} +(-177.746 - 177.746i) q^{52} +(-185.770 - 185.770i) q^{53} +176.059i q^{54} +(-22.1367 - 578.505i) q^{55} +78.8628i q^{56} +(111.570 - 111.570i) q^{57} +(-218.669 + 218.669i) q^{58} -552.350i q^{59} +(207.756 + 192.443i) q^{60} +642.209i q^{61} +(-310.582 - 310.582i) q^{62} +(91.3033 + 91.3033i) q^{63} -64.0000i q^{64} +(477.455 - 515.449i) q^{65} +655.788i q^{66} +(-249.713 + 249.713i) q^{67} +(-116.113 - 116.113i) q^{68} +(495.714 + 492.083i) q^{69} +(-220.267 + 8.42860i) q^{70} +598.535 q^{71} +(-74.0959 - 74.0959i) q^{72} +(-595.081 + 595.081i) q^{73} +0.826580 q^{74} +(-515.296 + 600.840i) q^{75} -99.6685i q^{76} +(-360.942 - 360.942i) q^{77} +(-562.773 + 562.773i) q^{78} -1126.29 q^{79} +(178.755 - 6.84011i) q^{80} +911.089 q^{81} +(-10.7296 - 10.7296i) q^{82} +(-567.177 - 567.177i) q^{83} +249.693 q^{84} +(311.898 - 336.718i) q^{85} +839.811i q^{86} +(692.343 + 692.343i) q^{87} +(292.917 + 292.917i) q^{88} +1449.76 q^{89} +(199.034 - 214.872i) q^{90} -619.494i q^{91} +(441.214 - 1.62161i) q^{92} +(-983.354 + 983.354i) q^{93} -956.080i q^{94} +(278.378 - 10.6522i) q^{95} -202.635 q^{96} +(716.106 - 716.106i) q^{97} +(347.646 - 347.646i) q^{98} +678.249 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - 16 q^{3} - 16 q^{6}+O(q^{10}) \) 72 * q - 16 * q^3 - 16 * q^6	\( 72 q - 16 q^{3} - 16 q^{6} - 64 q^{12} + 192 q^{13} - 1152 q^{16} + 32 q^{18} + 276 q^{23} + 880 q^{25} + 304 q^{26} + 728 q^{27} + 608 q^{31} + 688 q^{35} + 2816 q^{36} - 2208 q^{41} - 256 q^{46} + 144 q^{47} + 256 q^{48} + 272 q^{50} + 768 q^{52} - 2360 q^{55} - 1376 q^{62} - 1104 q^{70} + 4528 q^{71} + 128 q^{72} - 1296 q^{73} - 2568 q^{75} - 752 q^{77} + 6000 q^{78} - 11560 q^{81} + 80 q^{82} - 904 q^{85} + 6760 q^{87} + 1104 q^{92} - 5288 q^{93} + 9264 q^{95} + 256 q^{96} - 448 q^{98}+O(q^{100}) \) 72 * q - 16 * q^3 - 16 * q^6 - 64 * q^12 + 192 * q^13 - 1152 * q^16 + 32 * q^18 + 276 * q^23 + 880 * q^25 + 304 * q^26 + 728 * q^27 + 608 * q^31 + 688 * q^35 + 2816 * q^36 - 2208 * q^41 - 256 * q^46 + 144 * q^47 + 256 * q^48 + 272 * q^50 + 768 * q^52 - 2360 * q^55 - 1376 * q^62 - 1104 * q^70 + 4528 * q^71 + 128 * q^72 - 1296 * q^73 - 2568 * q^75 - 752 * q^77 + 6000 * q^78 - 11560 * q^81 + 80 * q^82 - 904 * q^85 + 6760 * q^87 + 1104 * q^92 - 5288 * q^93 + 9264 * q^95 + 256 * q^96 - 448 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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