LMFDB - Embedded newform 230.4.e.a.137.7

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			137.7
Character	$\chi$	$=$	230.137
Dual form			230.4.e.a.183.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.41421 - 1.41421i) q^{2} +(-2.02411 + 2.02411i) q^{3} +4.00000i q^{4} +(-2.14096 + 10.9734i) q^{5} +5.72506 q^{6} +(-1.46247 + 1.46247i) q^{7} +(5.65685 - 5.65685i) q^{8} +18.8059i q^{9} +O(q^{10})$	\(q+(-1.41421 - 1.41421i) q^{2} +(-2.02411 + 2.02411i) q^{3} +4.00000i q^{4} +(-2.14096 + 10.9734i) q^{5} +5.72506 q^{6} +(-1.46247 + 1.46247i) q^{7} +(5.65685 - 5.65685i) q^{8} +18.8059i q^{9} +(18.5466 - 12.4910i) q^{10} +21.4009i q^{11} +(-8.09645 - 8.09645i) q^{12} +(14.5475 - 14.5475i) q^{13} +4.13650 q^{14} +(-17.8779 - 26.5450i) q^{15} -16.0000 q^{16} +(34.9835 - 34.9835i) q^{17} +(26.5956 - 26.5956i) q^{18} -102.683 q^{19} +(-43.8937 - 8.56385i) q^{20} -5.92042i q^{21} +(30.2655 - 30.2655i) q^{22} +(41.1151 + 102.355i) q^{23} +22.9002i q^{24} +(-115.833 - 46.9874i) q^{25} -41.1464 q^{26} +(-92.7164 - 92.7164i) q^{27} +(-5.84989 - 5.84989i) q^{28} -275.499i q^{29} +(-12.2571 + 62.8235i) q^{30} -44.8903 q^{31} +(22.6274 + 22.6274i) q^{32} +(-43.3179 - 43.3179i) q^{33} -98.9483 q^{34} +(-12.9172 - 19.1794i) q^{35} -75.2237 q^{36} +(-244.472 + 244.472i) q^{37} +(145.216 + 145.216i) q^{38} +58.8914i q^{39} +(49.9640 + 74.1862i) q^{40} -399.252 q^{41} +(-8.37274 + 8.37274i) q^{42} +(311.304 + 311.304i) q^{43} -85.6038 q^{44} +(-206.366 - 40.2628i) q^{45} +(86.6062 - 202.897i) q^{46} +(-403.349 - 403.349i) q^{47} +(32.3858 - 32.3858i) q^{48} +338.722i q^{49} +(97.3617 + 230.262i) q^{50} +141.621i q^{51} +(58.1898 + 58.1898i) q^{52} +(40.1517 + 40.1517i) q^{53} +262.242i q^{54} +(-234.842 - 45.8186i) q^{55} +16.5460i q^{56} +(207.843 - 207.843i) q^{57} +(-389.615 + 389.615i) q^{58} -99.7810i q^{59} +(106.180 - 71.5117i) q^{60} -534.925i q^{61} +(63.4845 + 63.4845i) q^{62} +(-27.5032 - 27.5032i) q^{63} -64.0000i q^{64} +(128.490 + 190.781i) q^{65} +122.522i q^{66} +(-83.3100 + 83.3100i) q^{67} +(139.934 + 139.934i) q^{68} +(-290.400 - 123.956i) q^{69} +(-8.85608 + 45.3916i) q^{70} -236.189 q^{71} +(106.382 + 106.382i) q^{72} +(782.038 - 782.038i) q^{73} +691.472 q^{74} +(329.566 - 139.350i) q^{75} -410.733i q^{76} +(-31.2983 - 31.2983i) q^{77} +(83.2850 - 83.2850i) q^{78} -648.939 q^{79} +(34.2554 - 175.575i) q^{80} -132.423 q^{81} +(564.627 + 564.627i) q^{82} +(113.220 + 113.220i) q^{83} +23.6817 q^{84} +(308.991 + 458.787i) q^{85} -880.500i q^{86} +(557.641 + 557.641i) q^{87} +(121.062 + 121.062i) q^{88} -1256.85 q^{89} +(234.905 + 348.785i) q^{90} +42.5505i q^{91} +(-409.420 + 164.461i) q^{92} +(90.8631 - 90.8631i) q^{93} +1140.84i q^{94} +(219.841 - 1126.79i) q^{95} -91.6009 q^{96} +(1036.42 - 1036.42i) q^{97} +(479.026 - 479.026i) q^{98} -402.465 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
$3$	−2.02411	+	2.02411i	−0.389541	+	0.389541i	−0.874524	−	0.484983i	$-0.838826\pi$
$3$	−2.02411	+	2.02411i	−0.389541	+	0.389541i	0.484983	+	0.874524i	$0.338826\pi$
$4$			4.00000i			0.500000i
$5$	−2.14096	+	10.9734i	−0.191493	+	0.981494i
$5$	−2.14096	+	10.9734i	−0.191493	+	0.981494i
$6$	5.72506			0.389541
$7$	−1.46247	+	1.46247i	−0.0789661	+	0.0789661i	−0.745487	−	0.666521i	$-0.767783\pi$
$7$	−1.46247	+	1.46247i	−0.0789661	+	0.0789661i	0.666521	+	0.745487i	$0.267783\pi$
$8$	5.65685	−	5.65685i	0.250000	−	0.250000i
$9$			18.8059i			0.696516i
$10$	18.5466	−	12.4910i	0.586494	−	0.395000i
$11$			21.4009i			0.586603i	0.956020	+	0.293301i	$0.0947539\pi$
$11$			21.4009i			0.586603i	−0.956020	+	0.293301i	$0.905246\pi$
$12$	−8.09645	−	8.09645i	−0.194770	−	0.194770i
$13$	14.5475	−	14.5475i	0.310364	−	0.310364i	−0.534686	−	0.845051i	$-0.679570\pi$
$13$	14.5475	−	14.5475i	0.310364	−	0.310364i	0.845051	+	0.534686i	$0.179570\pi$
$14$	4.13650			0.0789661
$15$	−17.8779	−	26.5450i	−0.307737	−	0.456926i
$16$	−16.0000			−0.250000
$17$	34.9835	−	34.9835i	0.499103	−	0.499103i	−0.412056	−	0.911159i	$-0.635189\pi$
$17$	34.9835	−	34.9835i	0.499103	−	0.499103i	0.911159	+	0.412056i	$0.135189\pi$
$18$	26.5956	−	26.5956i	0.348258	−	0.348258i
$19$	−102.683			−1.23985			−0.619925	−	0.784661i	$-0.712837\pi$
$19$	−102.683			−1.23985			−0.619925	+	0.784661i	$0.712837\pi$
$20$	−43.8937	−	8.56385i	−0.490747	−	0.0957467i
$21$		−	5.92042i		−	0.0615210i
$22$	30.2655	−	30.2655i	0.293301	−	0.293301i
$23$	41.1151	+	102.355i	0.372743	+	0.927934i
$23$	41.1151	+	102.355i	0.372743	+	0.927934i
$24$			22.9002i			0.194770i
$25$	−115.833	−	46.9874i	−0.926660	−	0.375899i
$26$	−41.1464			−0.310364
$27$	−92.7164	−	92.7164i	−0.660862	−	0.660862i
$28$	−5.84989	−	5.84989i	−0.0394830	−	0.0394830i
$29$		−	275.499i		−	1.76410i	−0.471156	−	0.882050i	$-0.656163\pi$
$29$		−	275.499i		−	1.76410i	0.471156	−	0.882050i	$-0.343837\pi$
$30$	−12.2571	+	62.8235i	−0.0745945	+	0.382332i
$31$	−44.8903			−0.260082			−0.130041	−	0.991509i	$-0.541511\pi$
$31$	−44.8903			−0.260082			−0.130041	+	0.991509i	$0.541511\pi$
$32$	22.6274	+	22.6274i	0.125000	+	0.125000i
$33$	−43.3179	−	43.3179i	−0.228506	−	0.228506i
$34$	−98.9483			−0.499103
$35$	−12.9172	−	19.1794i	−0.0623832	−	0.0926262i
$36$	−75.2237			−0.348258
$37$	−244.472	+	244.472i	−1.08624	+	1.08624i	−0.0903307	+	0.995912i	$0.528792\pi$
$37$	−244.472	+	244.472i	−1.08624	+	1.08624i	−0.995912	+	0.0903307i	$0.971208\pi$
$38$	145.216	+	145.216i	0.619925	+	0.619925i
$39$			58.8914i			0.241799i
$40$	49.9640	+	74.1862i	0.197500	+	0.293247i
$41$	−399.252			−1.52080			−0.760398	−	0.649458i	$-0.774996\pi$
$41$	−399.252			−1.52080			−0.760398	+	0.649458i	$0.774996\pi$
$42$	−8.37274	+	8.37274i	−0.0307605	+	0.0307605i
$43$	311.304	+	311.304i	1.10403	+	1.10403i	0.993919	+	0.110112i	$0.0351211\pi$
$43$	311.304	+	311.304i	1.10403	+	1.10403i	0.110112	+	0.993919i	$0.464879\pi$
$44$	−85.6038			−0.293301
$45$	−206.366	−	40.2628i	−0.683626	−	0.133378i
$46$	86.6062	−	202.897i	0.277596	−	0.650339i
$47$	−403.349	−	403.349i	−1.25180	−	1.25180i	−0.954914	−	0.296884i	$-0.904053\pi$
$47$	−403.349	−	403.349i	−1.25180	−	1.25180i	−0.296884	−	0.954914i	$-0.595947\pi$
$48$	32.3858	−	32.3858i	0.0973852	−	0.0973852i
$49$			338.722i			0.987529i
$50$	97.3617	+	230.262i	0.275381	+	0.651280i
$51$			141.621i			0.388841i
$52$	58.1898	+	58.1898i	0.155182	+	0.155182i
$53$	40.1517	+	40.1517i	0.104062	+	0.104062i	0.757221	−	0.653159i	$-0.226557\pi$
$53$	40.1517	+	40.1517i	0.104062	+	0.104062i	−0.653159	+	0.757221i	$0.726557\pi$
$54$			262.242i			0.660862i
$55$	−234.842	−	45.8186i	−0.575747	−	0.112331i
$56$			16.5460i			0.0394830i
$57$	207.843	−	207.843i	0.482972	−	0.482972i
$58$	−389.615	+	389.615i	−0.882050	+	0.882050i
$59$		−	99.7810i		−	0.220176i	−0.993922	−	0.110088i	$-0.964887\pi$
$59$		−	99.7810i		−	0.220176i	0.993922	−	0.110088i	$-0.0351132\pi$
$60$	106.180	−	71.5117i	0.228463	−	0.153869i
$61$		−	534.925i		−	1.12279i	−0.827549	−	0.561394i	$-0.810265\pi$
$61$		−	534.925i		−	1.12279i	0.827549	−	0.561394i	$-0.189735\pi$
$62$	63.4845	+	63.4845i	0.130041	+	0.130041i
$63$	−27.5032	−	27.5032i	−0.0550012	−	0.0550012i
$64$		−	64.0000i		−	0.125000i
$65$	128.490	+	190.781i	0.245188	+	0.364054i
$66$			122.522i			0.228506i
$67$	−83.3100	+	83.3100i	−0.151910	+	0.151910i	−0.778970	−	0.627061i	$-0.784258\pi$
$67$	−83.3100	+	83.3100i	−0.151910	+	0.151910i	0.627061	+	0.778970i	$0.284258\pi$
$68$	139.934	+	139.934i	0.249551	+	0.249551i
$69$	−290.400	−	123.956i	−0.506667	−	0.216270i
$70$	−8.85608	+	45.3916i	−0.0151215	+	0.0775047i
$71$	−236.189			−0.394796			−0.197398	−	0.980323i	$-0.563249\pi$
$71$	−236.189			−0.394796			−0.197398	+	0.980323i	$0.563249\pi$
$72$	106.382	+	106.382i	0.174129	+	0.174129i
$73$	782.038	−	782.038i	1.25384	−	1.25384i	0.299862	−	0.953983i	$-0.403059\pi$
$73$	782.038	−	782.038i	1.25384	−	1.25384i	0.953983	−	0.299862i	$-0.0969406\pi$
$74$	691.472			1.08624
$75$	329.566	−	139.350i	0.507400	−	0.214544i
$76$		−	410.733i		−	0.619925i
$77$	−31.2983	−	31.2983i	−0.0463217	−	0.0463217i
$78$	83.2850	−	83.2850i	0.120900	−	0.120900i
$79$	−648.939			−0.924194			−0.462097	−	0.886829i	$-0.652903\pi$
$79$	−648.939			−0.924194			−0.462097	+	0.886829i	$0.652903\pi$
$80$	34.2554	−	175.575i	0.0478734	−	0.245373i
$81$	−132.423			−0.181651
$82$	564.627	+	564.627i	0.760398	+	0.760398i
$83$	113.220	+	113.220i	0.149729	+	0.149729i	0.777997	−	0.628268i	$-0.216236\pi$
$83$	113.220	+	113.220i	0.149729	+	0.149729i	−0.628268	+	0.777997i	$0.716236\pi$
$84$	23.6817			0.0307605
$85$	308.991	+	458.787i	0.394291	+	0.585441i
$86$		−	880.500i		−	1.10403i
$87$	557.641	+	557.641i	0.687189	+	0.687189i
$88$	121.062	+	121.062i	0.146651	+	0.146651i
$89$	−1256.85			−1.49692			−0.748461	−	0.663178i	$-0.769207\pi$
$89$	−1256.85			−1.49692			−0.748461	+	0.663178i	$0.769207\pi$
$90$	234.905	+	348.785i	0.275124	+	0.408502i
$91$			42.5505i			0.0490165i
$92$	−409.420	+	164.461i	−0.463967	+	0.186372i
$93$	90.8631	−	90.8631i	0.101313	−	0.101313i
$94$			1140.84i			1.25180i
$95$	219.841	−	1126.79i	0.237423	−	1.21691i
$96$	−91.6009			−0.0973852
$97$	1036.42	−	1036.42i	1.08487	−	1.08487i	0.0888263	−	0.996047i	$-0.471688\pi$
$97$	1036.42	−	1036.42i	1.08487	−	1.08487i	0.996047	−	0.0888263i	$-0.0283116\pi$
$98$	479.026	−	479.026i	0.493764	−	0.493764i
$99$	−402.465			−0.408578
$100$	187.950	−	463.330i	0.187950	−	0.463330i
$101$	1606.48			1.58268			0.791340	−	0.611376i	$-0.209384\pi$
$101$	1606.48			1.58268			0.791340	+	0.611376i	$0.209384\pi$
$102$	200.282	−	200.282i	0.194421	−	0.194421i
$103$	1047.71	+	1047.71i	1.00227	+	1.00227i	0.999997	+	0.00227448i	$0.000723989\pi$
$103$	1047.71	+	1047.71i	1.00227	+	1.00227i	0.00227448	+	0.999997i	$0.499276\pi$
$104$		−	164.586i		−	0.155182i
$105$	64.9673	+	12.6754i	0.0603825	+	0.0117809i
$106$		−	113.566i		−	0.104062i
$107$	−612.872	+	612.872i	−0.553725	+	0.553725i	−0.927514	−	0.373789i	$-0.878058\pi$
$107$	−612.872	+	612.872i	−0.553725	+	0.553725i	0.373789	+	0.927514i	$0.378058\pi$
$108$	370.866	−	370.866i	0.330431	−	0.330431i
$109$	666.261			0.585470			0.292735	−	0.956194i	$-0.405435\pi$
$109$	666.261			0.585470			0.292735	+	0.956194i	$0.405435\pi$
$110$	267.319	+	396.914i	0.231708	+	0.344039i
$111$		−	989.678i		−	0.846271i
$112$	23.3996	−	23.3996i	0.0197415	−	0.0197415i
$113$	−123.588	−	123.588i	−0.102887	−	0.102887i	0.653790	−	0.756676i	$-0.273178\pi$
$113$	−123.588	−	123.588i	−0.102887	−	0.102887i	−0.756676	+	0.653790i	$0.773178\pi$
$114$	−587.868			−0.482972
$115$	−1211.21	+	232.036i	−0.982140	+	0.188152i
$116$	1102.00			0.882050
$117$	273.578	+	273.578i	0.216174	+	0.216174i
$118$	−141.112	+	141.112i	−0.110088	+	0.110088i
$119$			102.325i			0.0788244i
$120$	−251.294	−	49.0285i	−0.191166	−	0.0372972i
$121$	872.999			0.655897
$122$	−756.498	+	756.498i	−0.561394	+	0.561394i
$123$	808.130	−	808.130i	0.592412	−	0.592412i
$124$		−	179.561i		−	0.130041i
$125$	763.607	−	1170.48i	0.546392	−	0.837529i
$126$			77.7907i			0.0550012i
$127$	181.275	+	181.275i	0.126658	+	0.126658i	0.767594	−	0.640936i	$-0.221454\pi$
$127$	181.275	+	181.275i	0.126658	+	0.126658i	−0.640936	+	0.767594i	$0.721454\pi$
$128$	−90.5097	+	90.5097i	−0.0625000	+	0.0625000i
$129$	−1260.23			−0.860130
$130$	88.0929	−	451.517i	0.0594328	−	0.304621i
$131$	−2301.62			−1.53507			−0.767533	−	0.641010i	$-0.778516\pi$
$131$	−2301.62			−1.53507			−0.767533	+	0.641010i	$0.778516\pi$
$132$	173.272	−	173.272i	0.114253	−	0.114253i
$133$	150.172	−	150.172i	0.0979062	−	0.0979062i
$134$	235.636			0.151910
$135$	1215.92	−	818.915i	0.775183	−	0.522081i
$136$		−	395.793i		−	0.249551i
$137$	600.407	−	600.407i	0.374425	−	0.374425i	−0.494661	−	0.869086i	$-0.664708\pi$
$137$	600.407	−	600.407i	0.374425	−	0.374425i	0.869086	+	0.494661i	$0.164708\pi$
$138$	235.386	+	585.988i	0.145199	+	0.361468i
$139$			2409.43i			1.47026i	0.677929	+	0.735128i	$0.262878\pi$
$139$			2409.43i			1.47026i	−0.677929	+	0.735128i	$0.737122\pi$
$140$	76.7178	−	51.6690i	0.0463131	−	0.0311916i
$141$	1632.85			0.975252
$142$	334.022	+	334.022i	0.197398	+	0.197398i
$143$	311.329	+	311.329i	0.182061	+	0.182061i
$144$		−	300.895i		−	0.174129i
$145$	3023.17	+	589.833i	1.73145	+	0.337814i
$146$	−2211.94			−1.25384
$147$	−685.612	−	685.612i	−0.384683	−	0.384683i
$148$	−977.889	−	977.889i	−0.543121	−	0.543121i
$149$	−2195.79			−1.20729			−0.603645	−	0.797253i	$-0.706286\pi$
$149$	−2195.79			−1.20729			−0.603645	+	0.797253i	$0.706286\pi$
$150$	−663.148	−	269.006i	−0.360972	−	0.146428i
$151$	−973.922			−0.524878			−0.262439	−	0.964949i	$-0.584527\pi$
$151$	−973.922			−0.524878			−0.262439	+	0.964949i	$0.584527\pi$
$152$	−580.865	+	580.865i	−0.309963	+	0.309963i
$153$	657.897	+	657.897i	0.347633	+	0.347633i
$154$			88.5250i			0.0463217i
$155$	96.1085	−	492.601i	0.0498040	−	0.255269i
$156$	−235.565			−0.120900
$157$	−2065.40	+	2065.40i	−1.04992	+	1.04992i	−0.0512306	+	0.998687i	$0.516314\pi$
$157$	−2065.40	+	2065.40i	−1.04992	+	1.04992i	−0.998687	+	0.0512306i	$0.983686\pi$
$158$	917.738	+	917.738i	0.462097	+	0.462097i
$159$	−162.543			−0.0810724
$160$	−296.745	+	199.856i	−0.146623	+	0.0987501i
$161$	−209.821	−	89.5616i	−0.102709	−	0.0438413i
$162$	187.275	+	187.275i	0.0908254	+	0.0908254i
$163$	−2205.79	+	2205.79i	−1.05994	+	1.05994i	−0.0618598	+	0.998085i	$0.519703\pi$
$163$	−2205.79	+	2205.79i	−1.05994	+	1.05994i	−0.998085	+	0.0618598i	$0.980297\pi$
$164$		−	1597.01i		−	0.760398i
$165$	568.089	−	382.605i	0.268034	−	0.180520i
$166$		−	320.234i		−	0.149729i
$167$	120.590	+	120.590i	0.0558773	+	0.0558773i	0.734493	−	0.678616i	$-0.237420\pi$
$167$	120.590	+	120.590i	0.0558773	+	0.0558773i	−0.678616	+	0.734493i	$0.737420\pi$
$168$	−33.4909	−	33.4909i	−0.0153803	−	0.0153803i
$169$			1773.74i			0.807348i
$170$	211.844	−	1085.80i	0.0955749	−	0.489866i
$171$		−	1931.06i		−	0.863576i
$172$	−1245.21	+	1245.21i	−0.552016	+	0.552016i
$173$	−251.885	+	251.885i	−0.110696	+	0.110696i	−0.760285	−	0.649589i	$-0.774941\pi$
$173$	−251.885	+	251.885i	−0.110696	+	0.110696i	0.649589	+	0.760285i	$0.274941\pi$
$174$		−	1577.25i		−	0.687189i
$175$	238.120	−	100.684i	0.102858	−	0.0434915i
$176$		−	342.415i		−	0.146651i
$177$	201.968	+	201.968i	0.0857674	+	0.0857674i
$178$	1777.46	+	1777.46i	0.748461	+	0.748461i
$179$			236.800i			0.0988786i	0.998777	+	0.0494393i	$0.0157434\pi$
$179$			236.800i			0.0988786i	−0.998777	+	0.0494393i	$0.984257\pi$
$180$	161.051	−	825.463i	0.0666891	−	0.341813i
$181$			4508.39i			1.85142i	0.378239	+	0.925708i	$0.376530\pi$
$181$			4508.39i			1.85142i	−0.378239	+	0.925708i	$0.623470\pi$
$182$	60.1755	−	60.1755i	0.0245083	−	0.0245083i
$183$	1082.75	+	1082.75i	0.437372	+	0.437372i
$184$	811.590	+	346.425i	0.325169	+	0.138798i
$185$	−2159.29	−	3206.10i	−0.858132	−	1.27415i
$186$	−257.000			−0.101313
$187$	748.680	+	748.680i	0.292775	+	0.292775i
$188$	1613.40	−	1613.40i	0.625899	−	0.625899i
$189$	271.190			0.104371
$190$	−1904.42	+	1282.62i	−0.727165	+	0.489741i
$191$			2180.02i			0.825869i	0.910761	+	0.412934i	$0.135496\pi$
$191$			2180.02i			0.825869i	−0.910761	+	0.412934i	$0.864504\pi$
$192$	129.543	+	129.543i	0.0486926	+	0.0486926i
$193$	−129.993	+	129.993i	−0.0484823	+	0.0484823i	−0.730932	−	0.682450i	$-0.760914\pi$
$193$	−129.993	+	129.993i	−0.0484823	+	0.0484823i	0.682450	+	0.730932i	$0.260914\pi$
$194$	−2931.44			−1.08487
$195$	−646.241	−	126.084i	−0.237324	−	0.0463030i
$196$	−1354.89			−0.493764
$197$	365.502	+	365.502i	0.132187	+	0.132187i	0.770105	−	0.637917i	$-0.220204\pi$
$197$	365.502	+	365.502i	0.132187	+	0.132187i	−0.637917	+	0.770105i	$0.720204\pi$
$198$	569.171	+	569.171i	0.204289	+	0.204289i
$199$	−2293.61			−0.817032			−0.408516	−	0.912751i	$-0.633954\pi$
$199$	−2293.61			−0.817032			−0.408516	+	0.912751i	$0.633954\pi$
$200$	−921.049	+	389.447i	−0.325640	+	0.137690i
$201$		−	337.258i		−	0.118350i
$202$	−2271.91	−	2271.91i	−0.791340	−	0.791340i
$203$	402.910	+	402.910i	0.139304	+	0.139304i
$204$	−566.484			−0.194421
$205$	854.782	−	4381.16i	0.291222	−	1.49265i
$206$		−	2963.37i		−	1.00227i
$207$	−1924.88	+	773.209i	−0.646321	+	0.259622i
$208$	−232.759	+	232.759i	−0.0775911	+	0.0775911i
$209$		−	2197.52i		−	0.727300i
$210$	−73.9520	−	109.803i	−0.0243008	−	0.0360817i
$211$	−1789.11			−0.583732			−0.291866	−	0.956459i	$-0.594276\pi$
$211$	−1789.11			−0.583732			−0.291866	+	0.956459i	$0.594276\pi$
$212$	−160.607	+	160.607i	−0.0520308	+	0.0520308i
$213$	478.073	−	478.073i	0.153789	−	0.153789i
$214$	1733.46			0.553725
$215$	−4082.56	+	2749.58i	−1.29501	+	0.872185i
$216$	−1048.97			−0.330431
$217$	65.6509	−	65.6509i	0.0205377	−	0.0205377i
$218$	−942.235	−	942.235i	−0.292735	−	0.292735i
$219$			3165.87i			0.976847i
$220$	183.274	−	939.368i	0.0561653	−	0.287873i
$221$		−	1017.84i		−	0.309807i
$222$	−1399.62	+	1399.62i	−0.423136	+	0.423136i
$223$	−832.236	+	832.236i	−0.249913	+	0.249913i	−0.820935	−	0.571022i	$-0.806547\pi$
$223$	−832.236	+	832.236i	−0.249913	+	0.249913i	0.571022	+	0.820935i	$0.306547\pi$
$224$	−66.1839			−0.0197415
$225$	883.642	−	2178.34i	0.261820	−	0.645434i
$226$			349.560i			0.102887i
$227$	−1211.67	+	1211.67i	−0.354278	+	0.354278i	−0.861699	−	0.507420i	$-0.830599\pi$
$227$	−1211.67	+	1211.67i	−0.354278	+	0.354278i	0.507420	+	0.861699i	$0.330599\pi$
$228$	831.370	+	831.370i	0.241486	+	0.241486i
$229$	1234.69			0.356290			0.178145	−	0.984004i	$-0.442990\pi$
$229$	1234.69			0.356290			0.178145	+	0.984004i	$0.442990\pi$
$230$	2041.06	+	1384.76i	0.585146	+	0.396994i
$231$	126.703			0.0360884
$232$	−1558.46	−	1558.46i	−0.441025	−	0.441025i
$233$	1995.30	−	1995.30i	0.561016	−	0.561016i	−0.368580	−	0.929596i	$-0.620156\pi$
$233$	1995.30	−	1995.30i	0.561016	−	0.561016i	0.929596	+	0.368580i	$0.120156\pi$
$234$		−	773.797i		−	0.216174i
$235$	5289.68	−	3562.57i	1.46834	−	0.988921i
$236$	399.124			0.110088
$237$	1313.53	−	1313.53i	0.360011	−	0.360011i
$238$	144.709	−	144.709i	0.0394122	−	0.0394122i
$239$		−	602.969i		−	0.163192i	−0.996665	−	0.0815959i	$-0.973998\pi$
$239$		−	602.969i		−	0.163192i	0.996665	−	0.0815959i	$-0.0260017\pi$
$240$	286.047	+	424.720i	0.0769343	+	0.114232i
$241$		−	504.639i		−	0.134882i	−0.997723	−	0.0674412i	$-0.978516\pi$
$241$		−	504.639i		−	0.134882i	0.997723	−	0.0674412i	$-0.0214835\pi$
$242$	−1234.61	−	1234.61i	−0.327949	−	0.327949i
$243$	2771.38	−	2771.38i	0.731622	−	0.731622i
$244$	2139.70			0.561394
$245$	−3716.95	−	725.192i	−0.969253	−	0.189105i
$246$	−2285.74			−0.592412
$247$	−1493.78	+	1493.78i	−0.384806	+	0.384806i
$248$	−253.938	+	253.938i	−0.0650205	+	0.0650205i
$249$	−458.339			−0.116651
$250$	−2735.22	+	575.410i	−0.691961	+	0.145568i
$251$			6317.84i			1.58876i	0.607421	+	0.794380i	$0.292204\pi$
$251$			6317.84i			1.58876i	−0.607421	+	0.794380i	$0.707796\pi$
$252$	110.013	−	110.013i	0.0275006	−	0.0275006i
$253$	−2190.49	+	879.903i	−0.544329	+	0.218652i
$254$		−	512.722i		−	0.126658i
$255$	−1554.07	−	303.205i	−0.381646	−	0.0744606i
$256$	256.000			0.0625000
$257$	254.814	+	254.814i	0.0618477	+	0.0618477i	0.737354	−	0.675506i	$-0.236075\pi$
$257$	254.814	+	254.814i	0.0618477	+	0.0618477i	−0.675506	+	0.737354i	$0.736075\pi$
$258$	1782.23	+	1782.23i	0.430065	+	0.430065i
$259$		−	715.068i		−	0.171553i
$260$	−763.124	+	513.960i	−0.182027	+	0.122594i
$261$	5181.02			1.22872
$262$	3254.98	+	3254.98i	0.767533	+	0.767533i
$263$	−4467.23	−	4467.23i	−1.04738	−	1.04738i	−0.998820	−	0.0485614i	$-0.984536\pi$
$263$	−4467.23	−	4467.23i	−1.04738	−	1.04738i	−0.0485614	−	0.998820i	$-0.515464\pi$
$264$	−490.086			−0.114253
$265$	−526.565	+	354.639i	−0.122063	+	0.0822086i
$266$	−424.749			−0.0979062
$267$	2544.01	−	2544.01i	0.583112	−	0.583112i
$268$	−333.240	−	333.240i	−0.0759548	−	0.0759548i
$269$		−	1414.11i		−	0.320519i	−0.987075	−	0.160260i	$-0.948767\pi$
$269$		−	1414.11i		−	0.320519i	0.987075	−	0.160260i	$-0.0512331\pi$
$270$	−2877.69	−	561.449i	−0.648632	−	0.126551i
$271$	4790.75			1.07387			0.536933	−	0.843625i	$-0.319583\pi$
$271$	4790.75			1.07387			0.536933	+	0.843625i	$0.319583\pi$
$272$	−559.736	+	559.736i	−0.124776	+	0.124776i
$273$	−86.1270	−	86.1270i	−0.0190939	−	0.0190939i
$274$	−1698.21			−0.374425
$275$	1005.58	−	2478.93i	0.220504	−	0.543582i
$276$	495.826	−	1161.60i	0.108135	−	0.253333i
$277$	2172.86	+	2172.86i	0.471315	+	0.471315i	0.902340	−	0.431025i	$-0.141848\pi$
$277$	2172.86	+	2172.86i	0.471315	+	0.471315i	−0.431025	+	0.902340i	$0.641848\pi$
$278$	3407.45	−	3407.45i	0.735128	−	0.735128i
$279$		−	844.205i		−	0.181151i
$280$	−181.566	−	35.4243i	−0.0387524	−	0.00756075i
$281$		−	2239.44i		−	0.475423i	−0.971336	−	0.237712i	$-0.923603\pi$
$281$		−	2239.44i		−	0.475423i	0.971336	−	0.237712i	$-0.0763973\pi$
$282$	−2309.19	−	2309.19i	−0.487626	−	0.487626i
$283$	5162.16	+	5162.16i	1.08431	+	1.08431i	0.996102	+	0.0882037i	$0.0281126\pi$
$283$	5162.16	+	5162.16i	1.08431	+	1.08431i	0.0882037	+	0.996102i	$0.471887\pi$
$284$		−	944.756i		−	0.197398i
$285$	1835.76	+	2725.73i	0.381548	+	0.566520i
$286$		−	880.572i		−	0.182061i
$287$	583.894	−	583.894i	0.120091	−	0.120091i
$288$	−425.530	+	425.530i	−0.0870645	+	0.0870645i
$289$			2465.31i			0.501793i
$290$	−3441.26	−	5109.56i	−0.696820	−	1.03463i
$291$			4195.67i			0.845205i
$292$	3128.15	+	3128.15i	0.626922	+	0.626922i
$293$	2475.68	+	2475.68i	0.493620	+	0.493620i	0.909445	−	0.415825i	$-0.136507\pi$
$293$	2475.68	+	2475.68i	0.493620	+	0.493620i	−0.415825	+	0.909445i	$0.636507\pi$
$294$			1939.20i			0.384683i
$295$	1094.94	+	213.627i	0.216101	+	0.0421622i
$296$			2765.89i			0.543121i
$297$	1984.22	−	1984.22i	0.387663	−	0.387663i
$298$	3105.32	+	3105.32i	0.603645	+	0.603645i
$299$	2087.12	+	890.884i	0.403684	+	0.172312i
$300$	557.401	+	1318.26i	0.107272	+	0.253700i
$301$	−910.546			−0.174362
$302$	1377.33	+	1377.33i	0.262439	+	0.262439i
$303$	−3251.70	+	3251.70i	−0.616519	+	0.616519i
$304$	1642.93			0.309963
$305$	5869.96	+	1145.25i	1.10201	+	0.215007i
$306$		−	1860.81i		−	0.347633i
$307$	1057.43	+	1057.43i	0.196582	+	0.196582i	0.798533	−	0.601951i	$-0.205610\pi$
$307$	1057.43	+	1057.43i	0.196582	+	0.196582i	−0.601951	+	0.798533i	$0.705610\pi$
$308$	125.193	−	125.193i	0.0231609	−	0.0231609i
$309$	−4241.37			−0.780851
$310$	−832.561	+	560.725i	−0.152536	+	0.102732i
$311$	4357.67			0.794537			0.397268	−	0.917702i	$-0.369958\pi$
$311$	4357.67			0.794537			0.397268	+	0.917702i	$0.369958\pi$
$312$	333.140	+	333.140i	0.0604498	+	0.0604498i
$313$	−4240.85	−	4240.85i	−0.765837	−	0.765837i	0.211533	−	0.977371i	$-0.432154\pi$
$313$	−4240.85	−	4240.85i	−0.765837	−	0.765837i	−0.977371	+	0.211533i	$0.932154\pi$
$314$	5841.84			1.04992
$315$	360.687	−	242.921i	0.0645157	−	0.0434509i
$316$		−	2595.76i		−	0.462097i
$317$	−583.945	−	583.945i	−0.103463	−	0.103463i	0.653481	−	0.756943i	$-0.273308\pi$
$317$	−583.945	−	583.945i	−0.103463	−	0.103463i	−0.756943	+	0.653481i	$0.773308\pi$
$318$	229.871	+	229.871i	0.0405362	+	0.0405362i
$319$	5895.94			1.03483
$320$	702.300	+	137.022i	0.122687	+	0.0239367i
$321$		−	2481.04i		−	0.431397i
$322$	170.073	+	423.391i	0.0294341	+	0.0732754i
$323$	−3592.22	+	3592.22i	−0.618813	+	0.618813i
$324$		−	529.694i		−	0.0908254i
$325$	−2368.62	+	1001.52i	−0.404268	+	0.170937i
$326$	6238.92			1.05994
$327$	−1348.59	+	1348.59i	−0.228064	+	0.228064i
$328$	−2258.51	+	2258.51i	−0.380199	+	0.380199i
$329$	1179.77			0.197699
$330$	−1344.48	−	262.314i	−0.224277	−	0.0437573i
$331$	−8718.06			−1.44770			−0.723849	−	0.689959i	$-0.757629\pi$
$331$	−8718.06			−1.44770			−0.723849	+	0.689959i	$0.757629\pi$
$332$	−452.879	+	452.879i	−0.0748644	+	0.0748644i
$333$	−4597.53	−	4597.53i	−0.756585	−	0.756585i
$334$		−	341.079i		−	0.0558773i
$335$	−735.834	−	1092.56i	−0.120009	−	0.178188i
$336$			94.7267i			0.0153803i
$337$	−2282.42	+	2282.42i	−0.368936	+	0.368936i	−0.867089	−	0.498153i	$-0.834012\pi$
$337$	−2282.42	+	2282.42i	−0.368936	+	0.368936i	0.498153	+	0.867089i	$0.334012\pi$
$338$	2508.45	−	2508.45i	0.403674	−	0.403674i
$339$	500.312			0.0801570
$340$	−1835.15	+	1235.96i	−0.292720	+	0.197146i
$341$		−	960.696i		−	0.152565i
$342$	−2730.93	+	2730.93i	−0.431788	+	0.431788i
$343$	−997.000	−	997.000i	−0.156947	−	0.156947i
$344$	3522.00			0.552016
$345$	1981.96	−	2921.30i	0.309291	−	0.455876i
$346$	712.438			0.110696
$347$	3519.43	+	3519.43i	0.544475	+	0.544475i	0.924838	−	0.380362i	$-0.124201\pi$
$347$	3519.43	+	3519.43i	0.544475	+	0.544475i	−0.380362	+	0.924838i	$0.624201\pi$
$348$	−2230.57	+	2230.57i	−0.343594	+	0.343594i
$349$			4270.61i			0.655016i	0.944848	+	0.327508i	$0.106209\pi$
$349$			4270.61i			0.655016i	−0.944848	+	0.327508i	$0.893791\pi$
$350$	−479.141	−	194.363i	−0.0731748	−	0.0296833i
$351$	−2697.57			−0.410216
$352$	−484.248	+	484.248i	−0.0733253	+	0.0733253i
$353$	4251.54	−	4251.54i	0.641039	−	0.641039i	−0.309772	−	0.950811i	$-0.600253\pi$
$353$	4251.54	−	4251.54i	0.641039	−	0.641039i	0.950811	+	0.309772i	$0.100253\pi$
$354$		−	571.252i		−	0.0857674i
$355$	505.672	−	2591.81i	0.0756008	−	0.387489i
$356$		−	5027.41i		−	0.748461i
$357$	−207.117	−	207.117i	−0.0307053	−	0.0307053i
$358$	334.886	−	334.886i	0.0494393	−	0.0494393i
$359$	−2105.98			−0.309608			−0.154804	−	0.987945i	$-0.549475\pi$
$359$	−2105.98			−0.309608			−0.154804	+	0.987945i	$0.549475\pi$
$360$	−1395.14	+	939.620i	−0.204251	+	0.137562i
$361$	3684.86			0.537230
$362$	6375.83	−	6375.83i	0.925708	−	0.925708i
$363$	−1767.05	+	1767.05i	−0.255499	+	0.255499i
$364$	−170.202			−0.0245083
$365$	6907.33	+	10256.0i	0.990538	+	1.47074i
$366$		−	3062.47i		−	0.437372i
$367$	1314.21	−	1314.21i	0.186925	−	0.186925i	−0.607440	−	0.794365i	$-0.707804\pi$
$367$	1314.21	−	1314.21i	0.186925	−	0.186925i	0.794365	+	0.607440i	$0.207804\pi$
$368$	−657.842	−	1637.68i	−0.0931858	−	0.231984i
$369$		−	7508.30i		−	1.05926i
$370$	−1480.41	+	7587.82i	−0.208008	+	1.06614i
$371$	−117.442			−0.0164347
$372$	363.452	+	363.452i	0.0506563	+	0.0506563i
$373$	−2647.37	−	2647.37i	−0.367494	−	0.367494i	0.499068	−	0.866563i	$-0.333676\pi$
$373$	−2647.37	−	2647.37i	−0.367494	−	0.367494i	−0.866563	+	0.499068i	$0.833676\pi$
$374$		−	2117.59i		−	0.292775i
$375$	823.564	+	3914.82i	0.113410	+	0.539094i
$376$	−4563.37			−0.625899
$377$	−4007.81	−	4007.81i	−0.547514	−	0.547514i
$378$	−383.521	−	383.521i	−0.0521857	−	0.0521857i
$379$	−9496.14			−1.28703			−0.643515	−	0.765434i	$-0.722524\pi$
$379$	−9496.14			−1.28703			−0.643515	+	0.765434i	$0.722524\pi$
$380$	4507.15	+	879.364i	0.608453	+	0.118712i
$381$	−733.841			−0.0986766
$382$	3083.02	−	3083.02i	0.412934	−	0.412934i
$383$	−2514.70	−	2514.70i	−0.335496	−	0.335496i	0.519173	−	0.854669i	$-0.326240\pi$
$383$	−2514.70	−	2514.70i	−0.335496	−	0.335496i	−0.854669	+	0.519173i	$0.826240\pi$
$384$		−	366.404i		−	0.0486926i
$385$	410.458	−	276.441i	0.0543348	−	0.0365942i
$386$	367.675			0.0484823
$387$	−5854.36	+	5854.36i	−0.768976	+	0.768976i
$388$	4145.69	+	4145.69i	0.542437	+	0.542437i
$389$	1372.78			0.178927			0.0894637	−	0.995990i	$-0.471485\pi$
$389$	1372.78			0.178927			0.0894637	+	0.995990i	$0.471485\pi$
$390$	735.612	+	1092.23i	0.0955107	+	0.141814i
$391$	5019.09	+	2142.38i	0.649172	+	0.277097i
$392$	1916.10	+	1916.10i	0.246882	+	0.246882i
$393$	4658.74	−	4658.74i	0.597970	−	0.597970i
$394$		−	1033.79i		−	0.132187i
$395$	1389.35	−	7121.09i	0.176977	−	0.907091i
$396$		−	1609.86i		−	0.204289i
$397$	6275.00	+	6275.00i	0.793283	+	0.793283i	0.982026	−	0.188744i	$-0.0604416\pi$
$397$	6275.00	+	6275.00i	0.793283	+	0.793283i	−0.188744	+	0.982026i	$0.560442\pi$
$398$	3243.65	+	3243.65i	0.408516	+	0.408516i
$399$			607.928i			0.0762769i
$400$	1853.32	+	751.799i	0.231665	+	0.0939748i
$401$		−	7026.82i		−	0.875069i	−0.899202	−	0.437534i	$-0.855852\pi$
$401$		−	7026.82i		−	0.875069i	0.899202	−	0.437534i	$-0.144148\pi$
$402$	−476.955	+	476.955i	−0.0591750	+	0.0591750i
$403$	−653.040	+	653.040i	−0.0807202	+	0.0807202i
$404$			6425.92i			0.791340i
$405$	283.514	−	1453.14i	0.0347849	−	0.178289i
$406$		−	1139.60i		−	0.139304i
$407$	−5231.94	−	5231.94i	−0.637193	−	0.637193i
$408$	801.130	+	801.130i	0.0972104	+	0.0972104i
$409$			5300.72i			0.640840i	0.947276	+	0.320420i	$0.103824\pi$
$409$			5300.72i			0.640840i	−0.947276	+	0.320420i	$0.896176\pi$
$410$	−7404.74	+	4987.05i	−0.891937	+	0.600715i
$411$			2430.58i			0.291707i
$412$	−4190.84	+	4190.84i	−0.501136	+	0.501136i
$413$	145.927	+	145.927i	0.0173864	+	0.0173864i
$414$	3815.68	+	1628.71i	0.452972	+	0.193350i
$415$	−1484.81	+	1000.01i	−0.175630	+	0.118286i
$416$	658.343			0.0775911
$417$	−4876.97	−	4876.97i	−0.572724	−	0.572724i
$418$	−3107.76	+	3107.76i	−0.363650	+	0.363650i
$419$	13062.7			1.52304			0.761520	−	0.648141i	$-0.224453\pi$
$419$	13062.7			1.52304			0.761520	+	0.648141i	$0.224453\pi$
$420$	−50.7016	+	259.869i	−0.00589044	+	0.0301912i
$421$			11742.6i			1.35938i	0.733501	+	0.679688i	$0.237885\pi$
$421$			11742.6i			1.35938i	−0.733501	+	0.679688i	$0.762115\pi$
$422$	2530.18	+	2530.18i	0.291866	+	0.291866i
$423$	7585.35	−	7585.35i	0.871897	−	0.871897i
$424$	454.265			0.0520308
$425$	−5696.01	+	2408.44i	−0.650111	+	0.274886i
$426$	−1352.20			−0.153789
$427$	782.313	+	782.313i	0.0886622	+	0.0886622i
$428$	−2451.49	−	2451.49i	−0.276862	−	0.276862i
$429$	−1260.33			−0.141840
$430$	9662.10	+	1885.12i	1.08360	+	0.211415i
$431$			3706.66i			0.414254i	0.978314	+	0.207127i	$0.0664113\pi$
$431$			3706.66i			0.414254i	−0.978314	+	0.207127i	$0.933589\pi$
$432$	1483.46	+	1483.46i	0.165216	+	0.165216i
$433$	−9775.05	−	9775.05i	−1.08489	−	1.08489i	−0.996045	−	0.0888486i	$-0.971681\pi$
$433$	−9775.05	−	9775.05i	−1.08489	−	1.08489i	−0.0888486	−	0.996045i	$-0.528319\pi$
$434$	−185.689			−0.0205377
$435$	−7313.13	+	4925.35i	−0.806064	+	0.542879i
$436$			2665.04i			0.292735i
$437$	−4221.84	−	10510.2i	−0.462146	−	1.15050i
$438$	4477.21	−	4477.21i	0.488423	−	0.488423i
$439$		−	9100.38i		−	0.989379i	−0.869070	−	0.494689i	$-0.835282\pi$
$439$		−	9100.38i		−	0.989379i	0.869070	−	0.494689i	$-0.164718\pi$
$440$	−1587.66	+	1069.28i	−0.172019	+	0.115854i
$441$	−6369.99			−0.687830
$442$	−1439.45	+	1439.45i	−0.154904	+	0.154904i
$443$	−6345.58	+	6345.58i	−0.680559	+	0.680559i	−0.960126	−	0.279567i	$-0.909809\pi$
$443$	−6345.58	+	6345.58i	−0.680559	+	0.680559i	0.279567	+	0.960126i	$0.409809\pi$
$444$	3958.71			0.423136
$445$	2690.87	−	13792.0i	0.286651	−	1.46922i
$446$	2353.92			0.249913
$447$	4444.53	−	4444.53i	0.470288	−	0.470288i
$448$	93.5982	+	93.5982i	0.00987076	+	0.00987076i
$449$		−	14161.7i		−	1.48849i	−0.667904	−	0.744247i	$-0.732808\pi$
$449$		−	14161.7i		−	1.48849i	0.667904	−	0.744247i	$-0.267192\pi$
$450$	−4330.30	+	1830.98i	−0.453627	+	0.191807i
$451$		−	8544.36i		−	0.892103i
$452$	494.352	−	494.352i	0.0514433	−	0.0514433i
$453$	1971.33	−	1971.33i	0.204461	−	0.204461i
$454$	3427.11			0.354278
$455$	−466.925	−	91.0990i	−0.0481094	−	0.00938635i
$456$		−	2351.47i		−	0.241486i
$457$	4949.33	−	4949.33i	0.506608	−	0.506608i	−0.406875	−	0.913484i	$-0.633382\pi$
$457$	4949.33	−	4949.33i	0.506608	−	0.506608i	0.913484	+	0.406875i	$0.133382\pi$
$458$	−1746.11	−	1746.11i	−0.178145	−	0.178145i
$459$	−6487.09			−0.659676
$460$	−928.144	−	4844.85i	−0.0940760	−	0.491070i
$461$	−2095.77			−0.211735			−0.105868	−	0.994380i	$-0.533762\pi$
$461$	−2095.77			−0.211735			−0.105868	+	0.994380i	$0.533762\pi$
$462$	−179.185	−	179.185i	−0.0180442	−	0.0180442i
$463$	−11824.8	+	11824.8i	−1.18692	+	1.18692i	−0.209010	+	0.977914i	$0.567024\pi$
$463$	−11824.8	+	11824.8i	−1.18692	+	1.18692i	−0.977914	+	0.209010i	$0.932976\pi$
$464$			4407.99i			0.441025i
$465$	802.546	+	1191.61i	0.0800369	+	0.118838i
$466$	−5643.57			−0.561016
$467$	2527.06	−	2527.06i	0.250403	−	0.250403i	−0.570733	−	0.821136i	$-0.693341\pi$
$467$	2527.06	−	2527.06i	0.250403	−	0.250403i	0.821136	+	0.570733i	$0.193341\pi$
$468$	−1094.31	+	1094.31i	−0.108087	+	0.108087i
$469$		−	243.677i		−	0.0239914i
$470$	−12519.0	−	2442.50i	−1.22863	−	0.239711i
$471$		−	8361.21i		−	0.817971i
$472$	−564.446	−	564.446i	−0.0550440	−	0.0550440i
$473$	−6662.19	+	6662.19i	−0.647628	+	0.647628i
$474$	−3715.21			−0.360011
$475$	11894.1	+	4824.82i	1.14892	+	0.466059i
$476$	−409.299			−0.0394122
$477$	−755.090	+	755.090i	−0.0724805	+	0.0724805i
$478$	−852.727	+	852.727i	−0.0815959	+	0.0815959i
$479$	−7581.73			−0.723211			−0.361605	−	0.932331i	$-0.617771\pi$
$479$	−7581.73			−0.723211			−0.361605	+	0.932331i	$0.617771\pi$
$480$	196.114	−	1005.18i	0.0186486	−	0.0955830i
$481$			7112.89i			0.674262i
$482$	−713.667	+	713.667i	−0.0674412	+	0.0674412i
$483$	605.984	−	243.419i	0.0570875	−	0.0229316i
$484$			3492.00i			0.327949i
$485$	9154.17	+	13592.1i	0.857050	+	1.27254i
$486$	−7838.65			−0.731622
$487$	−9569.75	−	9569.75i	−0.890445	−	0.890445i	0.104120	−	0.994565i	$-0.466797\pi$
$487$	−9569.75	−	9569.75i	−0.890445	−	0.890445i	−0.994565	+	0.104120i	$0.966797\pi$
$488$	−3025.99	−	3025.99i	−0.280697	−	0.280697i
$489$		−	8929.54i		−	0.825783i
$490$	4230.98	+	6282.13i	0.390074	+	0.579179i
$491$	−504.301			−0.0463519			−0.0231759	−	0.999731i	$-0.507378\pi$
$491$	−504.301			−0.0463519			−0.0231759	+	0.999731i	$0.507378\pi$
$492$	3232.52	+	3232.52i	0.296206	+	0.296206i
$493$	−9637.92	−	9637.92i	−0.880467	−	0.880467i
$494$	4225.05			0.384806
$495$	861.662	−	4416.42i	0.0782401	−	0.401017i
$496$	718.245			0.0650205
$497$	345.420	−	345.420i	0.0311755	−	0.0311755i
$498$	648.190	+	648.190i	0.0583255	+	0.0583255i
$499$			3192.61i			0.286414i	0.989693	+	0.143207i	$0.0457415\pi$
$499$			3192.61i			0.286414i	−0.989693	+	0.143207i	$0.954258\pi$
$500$	4681.93	+	3054.43i	0.418765	+	0.273196i
$501$	−488.174			−0.0435330
$502$	8934.78	−	8934.78i	0.794380	−	0.794380i
$503$	9492.00	+	9492.00i	0.841406	+	0.841406i	0.989042	−	0.147636i	$-0.0471663\pi$
$503$	9492.00	+	9492.00i	0.841406	+	0.841406i	−0.147636	+	0.989042i	$0.547166\pi$
$504$	−311.163			−0.0275006
$505$	−3439.41	+	17628.6i	−0.303073	+	1.55339i
$506$	4342.20	+	1853.46i	0.381491	+	0.162838i
$507$	−3590.26	−	3590.26i	−0.314495	−	0.314495i
$508$	−725.099	+	725.099i	−0.0633288	+	0.0633288i
$509$			10590.2i			0.922207i	0.887346	+	0.461103i	$0.152546\pi$
$509$			10590.2i			0.922207i	−0.887346	+	0.461103i	$0.847454\pi$
$510$	1768.99	+	2626.58i	0.153592	+	0.228053i
$511$			2287.42i			0.198022i
$512$	−362.039	−	362.039i	−0.0312500	−	0.0312500i
$513$	9520.42	+	9520.42i	0.819370	+	0.819370i
$514$		−	720.723i		−	0.0618477i
$515$	−13740.1	+	9253.88i	−1.17565	+	0.791795i
$516$		−	5040.91i		−	0.430065i
$517$	8632.05	−	8632.05i	0.734308	−	0.734308i
$518$	−1011.26	+	1011.26i	−0.0857763	+	0.0857763i
$519$		−	1019.69i		−	0.0862414i
$520$	1806.07	+	352.372i	0.152310	+	0.0297164i
$521$			16235.9i			1.36527i	0.730759	+	0.682635i	$0.239166\pi$
$521$			16235.9i			1.36527i	−0.730759	+	0.682635i	$0.760834\pi$
$522$	−7327.07	−	7327.07i	−0.614362	−	0.614362i
$523$	−10268.7	−	10268.7i	−0.858543	−	0.858543i	0.132623	−	0.991167i	$-0.457660\pi$
$523$	−10268.7	−	10268.7i	−0.858543	−	0.858543i	−0.991167	+	0.132623i	$0.957660\pi$
$524$		−	9206.48i		−	0.767533i
$525$	−278.185	+	685.777i	−0.0231257	+	0.0570091i
$526$			12635.2i			1.04738i
$527$	−1570.42	+	1570.42i	−0.129808	+	0.129808i
$528$	693.087	+	693.087i	0.0571264	+	0.0571264i
$529$	−8786.09	+	8416.68i	−0.722125	+	0.691763i
$530$	1246.21	+	243.141i	0.102136	+	0.0199271i
$531$	1876.47			0.153356
$532$	600.686	+	600.686i	0.0489531	+	0.0489531i
$533$	−5808.09	+	5808.09i	−0.472001	+	0.472001i
$534$	−7195.55			−0.583112
$535$	−5413.17	−	8037.45i	−0.437443	−	0.649512i
$536$			942.545i			0.0759548i
$537$	−479.310	−	479.310i	−0.0385172	−	0.0385172i
$538$	−1999.85	+	1999.85i	−0.160260	+	0.160260i
$539$	−7248.98			−0.579287
$540$	3275.66	+	4863.68i	0.261041	+	0.387591i
$541$	13972.7			1.11041			0.555206	−	0.831713i	$-0.312640\pi$
$541$	13972.7			1.11041			0.555206	+	0.831713i	$0.312640\pi$
$542$	−6775.15	−	6775.15i	−0.536933	−	0.536933i
$543$	−9125.50	−	9125.50i	−0.721202	−	0.721202i
$544$	1583.17			0.124776
$545$	−1426.44	+	7311.17i	−0.112114	+	0.574635i
$546$			243.604i			0.0190939i
$547$	−9478.72	−	9478.72i	−0.740915	−	0.740915i	0.231839	−	0.972754i	$-0.425526\pi$
$547$	−9478.72	−	9478.72i	−0.740915	−	0.740915i	−0.972754	+	0.231839i	$0.925526\pi$
$548$	2401.63	+	2401.63i	0.187212	+	0.187212i
$549$	10059.8			0.782040
$550$	−4927.83	+	2083.63i	−0.382043	+	0.161539i
$551$			28289.2i			2.18722i
$552$	−2343.95	+	941.546i	−0.180734	+	0.0725994i
$553$	949.056	−	949.056i	0.0729800	−	0.0729800i
$554$		−	6145.77i		−	0.471315i
$555$	10860.2	+	2118.86i	0.830610	+	0.162055i
$556$	−9637.74			−0.735128
$557$	14372.3	−	14372.3i	1.09331	−	1.09331i	0.0981405	−	0.995173i	$-0.468711\pi$
$557$	14372.3	−	14372.3i	1.09331	−	1.09331i	0.995173	−	0.0981405i	$-0.0312895\pi$
$558$	−1193.89	+	1193.89i	−0.0905756	+	0.0905756i
$559$	9057.35			0.685304
$560$	206.676	+	306.871i	0.0155958	+	0.0231566i
$561$	−3030.83			−0.228095
$562$	−3167.05	+	3167.05i	−0.237712	+	0.237712i
$563$	−16032.9	−	16032.9i	−1.20019	−	1.20019i	−0.974110	−	0.226075i	$-0.927410\pi$
$563$	−16032.9	−	16032.9i	−1.20019	−	1.20019i	−0.226075	−	0.974110i	$-0.572590\pi$
$564$			6531.39i			0.487626i
$565$	1620.78	−	1091.59i	0.120685	−	0.0812804i
$566$		−	14600.8i		−	1.08431i
$567$	193.666	−	193.666i	0.0143443	−	0.0143443i
$568$	−1336.09	+	1336.09i	−0.0986989	+	0.0986989i
$569$	−4526.88			−0.333526			−0.166763	−	0.985997i	$-0.553332\pi$
$569$	−4526.88			−0.333526			−0.166763	+	0.985997i	$0.553332\pi$
$570$	1258.60	−	6450.93i	0.0924861	−	0.474034i
$571$			25254.0i			1.85087i	0.378907	+	0.925435i	$0.376300\pi$
$571$			25254.0i			1.85087i	−0.378907	+	0.925435i	$0.623700\pi$
$572$	−1245.32	+	1245.32i	−0.0910303	+	0.0910303i
$573$	−4412.61	−	4412.61i	−0.321710	−	0.321710i
$574$	−1651.50			−0.120091
$575$	46.9259	−	13787.9i	0.00340338	−	0.999994i
$576$	1203.58			0.0870645
$577$	−10123.6	−	10123.6i	−0.730417	−	0.730417i	0.240286	−	0.970702i	$-0.422759\pi$
$577$	−10123.6	−	10123.6i	−0.730417	−	0.730417i	−0.970702	+	0.240286i	$0.922759\pi$
$578$	3486.48	−	3486.48i	0.250897	−	0.250897i
$579$		−	526.240i		−	0.0377716i
$580$	−2359.33	+	12092.7i	−0.168907	+	0.865727i
$581$	−331.162			−0.0236470
$582$	5933.57	−	5933.57i	0.422602	−	0.422602i
$583$	−859.284	+	859.284i	−0.0610428	+	0.0610428i
$584$		−	8847.75i		−	0.626922i
$585$	−3587.82	+	2416.37i	−0.253569	+	0.170777i
$586$		−	7002.28i		−	0.493620i
$587$	4266.97	+	4266.97i	0.300028	+	0.300028i	0.841025	−	0.540997i	$-0.181953\pi$
$587$	4266.97	+	4266.97i	0.300028	+	0.300028i	−0.540997	+	0.841025i	$0.681953\pi$
$588$	2742.45	−	2742.45i	0.192341	−	0.192341i
$589$	4609.49			0.322463
$590$	−1246.36	−	1850.59i	−0.0869695	−	0.129132i
$591$	−1479.63			−0.102985
$592$	3911.55	−	3911.55i	0.271561	−	0.271561i
$593$	−7285.42	+	7285.42i	−0.504513	+	0.504513i	−0.912837	−	0.408324i	$-0.866113\pi$
$593$	−7285.42	+	7285.42i	−0.504513	+	0.504513i	0.408324	+	0.912837i	$0.366113\pi$
$594$	−5612.22			−0.387663
$595$	−1122.85	−	219.073i	−0.0773656	−	0.0150943i
$596$		−	8783.16i		−	0.603645i
$597$	4642.52	−	4642.52i	0.318267	−	0.318267i
$598$	−1691.74	−	4211.54i	−0.115686	−	0.287998i
$599$			10165.0i			0.693372i	0.937981	+	0.346686i	$0.112693\pi$
$599$			10165.0i			0.693372i	−0.937981	+	0.346686i	$0.887307\pi$
$600$	1076.02	−	2652.59i	0.0732140	−	0.180486i
$601$	4382.70			0.297461			0.148730	−	0.988878i	$-0.452481\pi$
$601$	4382.70			0.297461			0.148730	+	0.988878i	$0.452481\pi$
$602$	1287.71	+	1287.71i	0.0871810	+	0.0871810i
$603$	−1566.72	−	1566.72i	−0.105807	−	0.105807i
$604$		−	3895.69i		−	0.262439i
$605$	−1869.06	+	9579.80i	−0.125600	+	0.643759i
$606$	9197.19			0.616519
$607$	15757.8	+	15757.8i	1.05369	+	1.05369i	0.998475	+	0.0552130i	$0.0175838\pi$
$607$	15757.8	+	15757.8i	1.05369	+	1.05369i	0.0552130	+	0.998475i	$0.482416\pi$
$608$	−2323.46	−	2323.46i	−0.154981	−	0.154981i
$609$	−1631.07			−0.108529
$610$	−6681.75	−	9921.01i	−0.443502	−	0.658508i
$611$	−11735.4			−0.777027
$612$	−2631.59	+	2631.59i	−0.173816	+	0.173816i
$613$	17915.7	+	17915.7i	1.18044	+	1.18044i	0.979630	+	0.200809i	$0.0643572\pi$
$613$	17915.7	+	17915.7i	1.18044	+	1.18044i	0.200809	+	0.979630i	$0.435643\pi$
$614$		−	2990.86i		−	0.196582i
$615$	7137.79	+	10598.1i	0.468005	+	0.694891i
$616$	−354.100			−0.0231609
$617$	−207.234	+	207.234i	−0.0135218	+	0.0135218i	−0.713835	−	0.700314i	$-0.753044\pi$
$617$	−207.234	+	207.234i	−0.0135218	+	0.0135218i	0.700314	+	0.713835i	$0.253044\pi$
$618$	5998.20	+	5998.20i	0.390426	+	0.390426i
$619$	16082.3			1.04427			0.522135	−	0.852863i	$-0.325136\pi$
$619$	16082.3			1.04427			0.522135	+	0.852863i	$0.325136\pi$
$620$	1970.40	+	384.434i	0.127634	+	0.0249020i
$621$	5677.94	−	13302.0i	0.366905	−	0.859569i
$622$	−6162.68	−	6162.68i	−0.397268	−	0.397268i
$623$	1838.11	−	1838.11i	0.118206	−	0.118206i
$624$		−	942.262i		−	0.0604498i
$625$	11209.4	+	10885.3i	0.717399	+	0.696662i
$626$			11994.9i			0.765837i
$627$	4448.03	+	4448.03i	0.283313	+	0.283313i
$628$	−8261.61	−	8261.61i	−0.524959	−	0.524959i
$629$			17105.0i			1.08429i
$630$	−853.631	−	166.547i	−0.0539833	−	0.0105324i
$631$		−	28225.8i		−	1.78075i	−0.455232	−	0.890373i	$-0.650444\pi$
$631$		−	28225.8i		−	1.78075i	0.455232	−	0.890373i	$-0.349556\pi$
$632$	−3670.95	+	3670.95i	−0.231049	+	0.231049i
$633$	3621.36	−	3621.36i	0.227387	−	0.227387i
$634$			1651.65i			0.103463i
$635$	−2377.31	+	1601.10i	−0.148568	+	0.100060i
$636$		−	650.173i		−	0.0405362i
$637$	4927.55	+	4927.55i	0.306494	+	0.306494i
$638$	−8338.12	−	8338.12i	−0.517413	−	0.517413i
$639$		−	4441.76i		−	0.274981i
$640$	−799.424	−	1186.98i	−0.0493750	−	0.0733117i
$641$		−	5990.99i		−	0.369157i	−0.982818	−	0.184579i	$-0.940908\pi$
$641$		−	5990.99i		−	0.369157i	0.982818	−	0.184579i	$-0.0590920\pi$
$642$	−3508.73	+	3508.73i	−0.215698	+	0.215698i
$643$	−9267.78	−	9267.78i	−0.568407	−	0.568407i	0.363275	−	0.931682i	$-0.381658\pi$
$643$	−9267.78	−	9267.78i	−0.568407	−	0.568407i	−0.931682	+	0.363275i	$0.881658\pi$
$644$	358.246	−	839.284i	0.0219206	−	0.0513547i
$645$	2698.10	−	13829.0i	0.164709	−	0.844213i
$646$	10160.3			0.618813
$647$	6718.31	+	6718.31i	0.408229	+	0.408229i	0.881121	−	0.472892i	$-0.156790\pi$
$647$	6718.31	+	6718.31i	0.408229	+	0.408229i	−0.472892	+	0.881121i	$0.656790\pi$
$648$	−749.100	+	749.100i	−0.0454127	+	0.0454127i
$649$	2135.41			0.129156
$650$	4766.09	+	1933.36i	0.287602	+	0.116666i
$651$			265.770i			0.0160005i
$652$	−8823.17	−	8823.17i	−0.529972	−	0.529972i
$653$	−7687.55	+	7687.55i	−0.460700	+	0.460700i	−0.898885	−	0.438185i	$-0.855622\pi$
$653$	−7687.55	+	7687.55i	−0.460700	+	0.460700i	0.438185	+	0.898885i	$0.355622\pi$
$654$	3814.38			0.228064
$655$	4927.68	−	25256.7i	0.293955	−	1.50666i
$656$	6388.02			0.380199
$657$	14707.0	+	14707.0i	0.873323	+	0.873323i
$658$	−1668.45	−	1668.45i	−0.0988496	−	0.0988496i
$659$	6970.36			0.412029			0.206014	−	0.978549i	$-0.433951\pi$
$659$	6970.36			0.412029			0.206014	+	0.978549i	$0.433951\pi$
$660$	1530.42	+	2272.35i	0.0902598	+	0.134017i
$661$		−	1749.59i		−	0.102952i	−0.998674	−	0.0514760i	$-0.983607\pi$
$661$		−	1749.59i		−	0.102952i	0.998674	−	0.0514760i	$-0.0163926\pi$
$662$	12329.2	+	12329.2i	0.723849	+	0.723849i
$663$	2060.23	+	2060.23i	0.120683	+	0.120683i
$664$	1280.94			0.0748644
$665$	1326.39	+	1969.41i	0.0773459	+	0.114843i
$666$			13003.8i			0.756585i
$667$	28198.7	−	11327.2i	1.63697	−	0.657557i
$668$	−482.359	+	482.359i	−0.0279386	+	0.0279386i
$669$		−	3369.08i		−	0.194703i
$670$	−504.489	+	2585.74i	−0.0290897	+	0.149098i
$671$	11447.9			0.658631
$672$	133.964	−	133.964i	0.00769013	−	0.00769013i
$673$	−6865.94	+	6865.94i	−0.393258	+	0.393258i	−0.875847	−	0.482589i	$-0.839696\pi$
$673$	−6865.94	+	6865.94i	−0.393258	+	0.393258i	0.482589	+	0.875847i	$0.339696\pi$
$674$	6455.66			0.368936
$675$	6383.07	+	15096.1i	0.363977	+	0.860812i
$676$	−7094.97			−0.403674
$677$	19242.4	−	19242.4i	1.09238	−	1.09238i	0.0971102	−	0.995274i	$-0.469040\pi$
$677$	19242.4	−	19242.4i	1.09238	−	1.09238i	0.995274	−	0.0971102i	$-0.0309599\pi$
$678$	−707.548	−	707.548i	−0.0400785	−	0.0400785i
$679$			3031.48i			0.171336i
$680$	4343.21	+	847.378i	0.244933	+	0.0477874i
$681$		−	4905.10i		−	0.276012i
$682$	−1358.63	+	1358.63i	−0.0762824	+	0.0762824i
$683$	19906.2	−	19906.2i	1.11521	−	1.11521i	0.122775	−	0.992434i	$-0.460821\pi$
$683$	19906.2	−	19906.2i	1.11521	−	1.11521i	0.992434	−	0.122775i	$-0.0391795\pi$
$684$	7724.22			0.431788
$685$	5303.08	+	7873.97i	0.295796	+	0.439196i
$686$			2819.94i			0.156947i
$687$	−2499.15	+	2499.15i	−0.138789	+	0.138789i
$688$	−4980.86	−	4980.86i	−0.276008	−	0.276008i
$689$	1168.21			0.0645940
$690$	−6934.26	+	1328.42i	−0.382583	+	0.0732928i
$691$	30343.4			1.67050			0.835252	−	0.549867i	$-0.185322\pi$
$691$	30343.4			1.67050			0.835252	+	0.549867i	$0.185322\pi$
$692$	−1007.54	−	1007.54i	−0.0553481	−	0.0553481i
$693$	588.594	−	588.594i	0.0322638	−	0.0322638i
$694$		−	9954.45i		−	0.544475i
$695$	−26439.8	−	5158.51i	−1.44305	−	0.281544i
$696$	6308.99			0.343594
$697$	−13967.2	+	13967.2i	−0.759033	+	0.759033i
$698$	6039.55	−	6039.55i	0.327508	−	0.327508i
$699$			8077.44i			0.437077i
$700$	402.737	+	952.479i	0.0217457	+	0.0514290i
$701$		−	3724.38i		−	0.200668i	−0.994954	−	0.100334i	$-0.968009\pi$
$701$		−	3724.38i		−	0.200668i	0.994954	−	0.100334i	$-0.0319911\pi$
$702$	3814.95	+	3814.95i	0.205108	+	0.205108i
$703$	25103.2	−	25103.2i	1.34678	−	1.34678i
$704$	1369.66			0.0733253
$705$	−3495.86	+	17917.9i	−0.186754	+	0.957204i
$706$	−12025.2			−0.641039
$707$	−2349.43	+	2349.43i	−0.124978	+	0.124978i
$708$	−807.872	+	807.872i	−0.0428837	+	0.0428837i
$709$	2383.74			0.126267			0.0631334	−	0.998005i	$-0.479891\pi$
$709$	2383.74			0.126267			0.0631334	+	0.998005i	$0.479891\pi$
$710$	−4380.49	+	2950.24i	−0.231545	+	0.155944i
$711$		−	12203.9i		−	0.643716i
$712$	−7109.83	+	7109.83i	−0.374231	+	0.374231i
$713$	−1845.67	−	4594.75i	−0.0969438	−	0.241339i
$714$			585.815i			0.0307053i
$715$	−4082.90	+	2749.81i	−0.213555	+	0.143828i
$716$	−947.200			−0.0494393
$717$	1220.48	+	1220.48i	0.0635698	+	0.0635698i
$718$	2978.30	+	2978.30i	0.154804	+	0.154804i
$719$			10295.5i			0.534014i	0.963695	+	0.267007i	$0.0860347\pi$
$719$			10295.5i			0.534014i	−0.963695	+	0.267007i	$0.913965\pi$
$720$	3301.85	+	644.205i	0.170907	+	0.0333446i
$721$	−3064.50			−0.158291
$722$	−5211.18	−	5211.18i	−0.268615	−	0.268615i
$723$	1021.45	+	1021.45i	0.0525422	+	0.0525422i
$724$	−18033.6			−0.925708
$725$	−12945.0	+	31911.8i	−0.663124	+	1.63472i
$726$	4997.97			0.255499
$727$	−1174.92	+	1174.92i	−0.0599384	+	0.0599384i	−0.736441	−	0.676502i	$-0.763495\pi$
$727$	−1174.92	+	1174.92i	−0.0599384	+	0.0599384i	0.676502	+	0.736441i	$0.263495\pi$
$728$	240.702	+	240.702i	0.0122541	+	0.0122541i
$729$			7643.75i			0.388343i
$730$	4735.68	−	24272.6i	0.240103	−	1.23064i
$731$	21781.0			1.10205
$732$	−4330.99	+	4330.99i	−0.218686	+	0.218686i
$733$	13922.8	+	13922.8i	0.701567	+	0.701567i	0.964747	−	0.263180i	$-0.0847713\pi$
$733$	13922.8	+	13922.8i	0.701567	+	0.701567i	−0.263180	+	0.964747i	$0.584771\pi$
$734$	−3717.16			−0.186925
$735$	8991.39	−	6055.65i	0.451228	−	0.303899i
$736$	−1385.70	+	3246.36i	−0.0693989	+	0.162585i
$737$	−1782.91	−	1782.91i	−0.0891105	−	0.0891105i
$738$	−10618.3	+	10618.3i	−0.529629	+	0.529629i
$739$		−	36558.7i		−	1.81980i	−0.414825	−	0.909901i	$-0.636157\pi$
$739$		−	36558.7i		−	1.81980i	0.414825	−	0.909901i	$-0.363843\pi$
$740$	12824.4	−	8637.17i	0.637074	−	0.429066i
$741$		−	6047.16i		−	0.299795i
$742$	166.087	+	166.087i	0.00821733	+	0.00821733i
$743$	26288.7	+	26288.7i	1.29803	+	1.29803i	0.929691	+	0.368340i	$0.120074\pi$
$743$	26288.7	+	26288.7i	1.29803	+	1.29803i	0.368340	+	0.929691i	$0.379926\pi$
$744$		−	1028.00i		−	0.0506563i
$745$	4701.10	−	24095.4i	0.231188	−	1.18495i
$746$			7487.88i			0.367494i
$747$	−2129.20	+	2129.20i	−0.104289	+	0.104289i
$748$	−2994.72	+	2994.72i	−0.146387	+	0.146387i
$749$		−	1792.62i		−	0.0874510i
$750$	4371.69	−	6701.08i	0.212842	−	0.326252i
$751$			26736.8i			1.29912i	0.760311	+	0.649559i	$0.225047\pi$
$751$			26736.8i			1.29912i	−0.760311	+	0.649559i	$0.774953\pi$
$752$	6453.58	+	6453.58i	0.312949	+	0.312949i
$753$	−12788.0	−	12788.0i	−0.618887	−	0.618887i
$754$			11335.8i			0.547514i
$755$	2085.13	−	10687.3i	0.100511	−	0.515165i
$756$			1084.76i			0.0521857i
$757$	−5491.59	+	5491.59i	−0.263666	+	0.263666i	−0.826542	−	0.562876i	$-0.809695\pi$
$757$	−5491.59	+	5491.59i	−0.263666	+	0.263666i	0.562876	+	0.826542i	$0.309695\pi$
$758$	13429.6	+	13429.6i	0.643515	+	0.643515i
$759$	2652.78	−	6214.83i	0.126864	−	0.297212i
$760$	−5130.47	−	7617.69i	−0.244871	−	0.363582i
$761$	−5875.86			−0.279895			−0.139947	−	0.990159i	$-0.544693\pi$
$761$	−5875.86			−0.279895			−0.139947	+	0.990159i	$0.544693\pi$
$762$	1037.81	+	1037.81i	0.0493383	+	0.0493383i
$763$	−974.388	+	974.388i	−0.0462323	+	0.0462323i
$764$	−8720.09			−0.412934
$765$	−8627.93	+	5810.86i	−0.407769	+	0.274630i
$766$			7112.64i			0.335496i
$767$	−1451.56	−	1451.56i	−0.0683347	−	0.0683347i
$768$	−518.173	+	518.173i	−0.0243463	+	0.0243463i
$769$	−23418.9			−1.09819			−0.549094	−	0.835761i	$-0.685027\pi$
$769$	−23418.9			−1.09819			−0.549094	+	0.835761i	$0.685027\pi$
$770$	−971.423	−	189.529i	−0.0454645	−	0.00887031i
$771$	−1031.55			−0.0481844
$772$	−519.971	−	519.971i	−0.0242411	−	0.0242411i
$773$	−17153.4	−	17153.4i	−0.798142	−	0.798142i	0.184660	−	0.982802i	$-0.440882\pi$
$773$	−17153.4	−	17153.4i	−0.798142	−	0.798142i	−0.982802	+	0.184660i	$0.940882\pi$
$774$	16558.6			0.768976
$775$	5199.76	+	2109.28i	0.241008	+	0.0977646i
$776$		−	11725.8i		−	0.542437i
$777$	1447.38	+	1447.38i	0.0668267	+	0.0668267i
$778$	−1941.40	−	1941.40i	−0.0894637	−	0.0894637i
$779$	40996.5			1.88556
$780$	504.337	−	2584.96i	0.0231515	−	0.118662i
$781$		−	5054.67i		−	0.231588i
$782$	−4068.27	−	10127.8i	−0.186037	−	0.463134i
$783$	−25543.3	+	25543.3i	−1.16583	+	1.16583i
$784$		−	5419.56i		−	0.246882i
$785$	−18242.6	−	27086.5i	−0.829435	−	1.23154i
$786$	−13176.9			−0.597970
$787$	−23248.2	+	23248.2i	−1.05300	+	1.05300i	−0.0544806	+	0.998515i	$0.517350\pi$
$787$	−23248.2	+	23248.2i	−1.05300	+	1.05300i	−0.998515	+	0.0544806i	$0.982650\pi$
$788$	−1462.01	+	1462.01i	−0.0660937	+	0.0660937i
$789$	18084.4			0.815996
$790$	−12035.6	+	8105.90i	−0.542034	+	0.365057i
$791$	361.488			0.0162491
$792$	−2276.69	+	2276.69i	−0.102145	+	0.102145i
$793$	−7781.79	−	7781.79i	−0.348473	−	0.348473i
$794$		−	17748.4i		−	0.793283i
$795$	347.999	−	1783.66i	0.0155248	−	0.0795720i
$796$		−	9174.43i		−	0.408516i
$797$	−13023.3	+	13023.3i	−0.578807	+	0.578807i	−0.934574	−	0.355768i	$-0.884219\pi$
$797$	−13023.3	+	13023.3i	−0.578807	+	0.578807i	0.355768	+	0.934574i	$0.384219\pi$
$798$	859.740	−	859.740i	0.0381384	−	0.0381384i
$799$	−28221.1			−1.24955
$800$	−1557.79	−	3684.20i	−0.0688451	−	0.162820i
$801$		−	23636.3i		−	1.04263i
$802$	−9937.42	+	9937.42i	−0.437534	+	0.437534i
$803$	16736.4	+	16736.4i	0.735508	+	0.735508i
$804$	1349.03			0.0591750
$805$	1432.02	−	2110.71i	0.0626981	−	0.0924134i
$806$	1847.08			0.0807202
$807$	2862.31	+	2862.31i	0.124855	+	0.124855i
$808$	9087.62	−	9087.62i	0.395670	−	0.395670i
$809$			1584.83i			0.0688746i	0.999407	+	0.0344373i	$0.0109639\pi$
$809$			1584.83i			0.0688746i	−0.999407	+	0.0344373i	$0.989036\pi$
$810$	−2456.00	+	1654.10i	−0.106537	+	0.0717521i
$811$	18794.2			0.813753			0.406876	−	0.913483i	$-0.366618\pi$
$811$	18794.2			0.813753			0.406876	+	0.913483i	$0.366618\pi$
$812$	−1611.64	+	1611.64i	−0.0696521	+	0.0696521i
$813$	−9697.02	+	9697.02i	−0.418314	+	0.418314i
$814$			14798.2i			0.637193i
$815$	−19482.6	−	28927.6i	−0.837357	−	1.24330i
$816$		−	2265.94i		−	0.0972104i
$817$	−31965.7	−	31965.7i	−1.36883	−	1.36883i
$818$	7496.35	−	7496.35i	0.320420	−	0.320420i
$819$	−800.202			−0.0341408
$820$	17524.6	+	3419.13i	0.746326	+	0.145611i
$821$	−34985.7			−1.48722			−0.743610	−	0.668613i	$-0.766888\pi$
$821$	−34985.7			−1.48722			−0.743610	+	0.668613i	$0.766888\pi$
$822$	3437.36	−	3437.36i	0.145854	−	0.145854i
$823$	13746.8	−	13746.8i	0.582239	−	0.582239i	−0.353279	−	0.935518i	$-0.614933\pi$
$823$	13746.8	−	13746.8i	0.582239	−	0.582239i	0.935518	+	0.353279i	$0.114933\pi$
$824$	11853.5			0.501136
$825$	2982.23	+	7053.03i	0.125852	+	0.297642i
$826$		−	412.744i		−	0.0173864i
$827$	−17539.6	+	17539.6i	−0.737500	+	0.737500i	−0.972094	−	0.234594i	$-0.924624\pi$
$827$	−17539.6	+	17539.6i	−0.737500	+	0.737500i	0.234594	+	0.972094i	$0.424624\pi$
$828$	−3092.83	−	7699.53i	−0.129811	−	0.323161i
$829$			11663.0i			0.488627i	0.969696	+	0.244313i	$0.0785626\pi$
$829$			11663.0i			0.488627i	−0.969696	+	0.244313i	$0.921437\pi$
$830$	3514.07	+	685.609i	0.146958	+	0.0286721i
$831$	−8796.21			−0.367193
$832$	−931.037	−	931.037i	−0.0387956	−	0.0387956i
$833$	11849.7	+	11849.7i	0.492878	+	0.492878i
$834$			13794.1i			0.572724i
$835$	−1581.46	+	1065.10i	−0.0655434	+	0.0441431i
$836$	8790.08			0.363650
$837$	4162.07	+	4162.07i	0.171878	+	0.171878i
$838$	−18473.4	−	18473.4i	−0.761520	−	0.761520i
$839$	16585.9			0.682488			0.341244	−	0.939975i	$-0.389152\pi$
$839$	16585.9			0.682488			0.341244	+	0.939975i	$0.389152\pi$
$840$	439.214	−	295.808i	0.0180408	−	0.0121504i
$841$	−51510.8			−2.11205
$842$	16606.5	−	16606.5i	0.679688	−	0.679688i
$843$	4532.88	+	4532.88i	0.185197	+	0.185197i
$844$		−	7156.44i		−	0.291866i
$845$	−19464.1	−	3797.52i	−0.792407	−	0.154602i
$846$	−21454.6			−0.871897
$847$	−1276.74	+	1276.74i	−0.0517936	+	0.0517936i
$848$	−642.427	−	642.427i	−0.0260154	−	0.0260154i
$849$	−20897.6			−0.844763
$850$	11461.4	+	4649.32i	0.462499	+	0.187612i
$851$	−35074.5	−	14971.4i	−1.41285	−	0.603072i
$852$	1912.29	+	1912.29i	0.0768945	+	0.0768945i
$853$	−14342.3	+	14342.3i	−0.575700	+	0.575700i	−0.933716	−	0.358016i	$-0.883453\pi$
$853$	−14342.3	+	14342.3i	−0.575700	+	0.575700i	0.358016	+	0.933716i	$0.383453\pi$
$854$		−	2212.71i		−	0.0886622i
$855$	21190.3	+	4134.32i	0.847595	+	0.165369i
$856$			6933.85i			0.276862i
$857$	−26019.6	−	26019.6i	−1.03712	−	1.03712i	−0.999284	−	0.0378354i	$-0.987954\pi$
$857$	−26019.6	−	26019.6i	−1.03712	−	1.03712i	−0.0378354	−	0.999284i	$-0.512046\pi$
$858$	1782.38	+	1782.38i	0.0709200	+	0.0709200i
$859$		−	32177.3i		−	1.27809i	−0.769171	−	0.639043i	$-0.779331\pi$
$859$		−	32177.3i		−	1.27809i	0.769171	−	0.639043i	$-0.220669\pi$
$860$	−10998.3	−	16330.2i	−0.436093	−	0.647507i
$861$			2363.74i			0.0935609i
$862$	5242.00	−	5242.00i	0.207127	−	0.207127i
$863$	−4223.98	+	4223.98i	−0.166612	+	0.166612i	−0.785488	−	0.618876i	$-0.787588\pi$
$863$	−4223.98	+	4223.98i	−0.166612	+	0.166612i	0.618876	+	0.785488i	$0.287588\pi$
$864$		−	4195.86i		−	0.165216i
$865$	−2224.77	−	3303.32i	−0.0874501	−	0.129845i
$866$			27648.0i			1.08489i
$867$	−4990.07	−	4990.07i	−0.195469	−	0.195469i
$868$	262.603	+	262.603i	0.0102688	+	0.0102688i
$869$		−	13887.9i		−	0.542135i
$870$	17307.8	+	3376.83i	0.674472	+	0.131592i
$871$			2423.90i			0.0942946i
$872$	3768.94	−	3768.94i	0.146368	−	0.146368i
$873$	19490.9	+	19490.9i	0.755632	+	0.755632i
$874$	−8893.02	+	20834.2i	−0.344177	+	0.806323i
$875$	595.045	+	2828.55i	0.0229900	+	0.109283i
$876$	−12663.5			−0.488423
$877$	31720.6	+	31720.6i	1.22136	+	1.22136i	0.967150	+	0.254206i	$0.0818141\pi$
$877$	31720.6	+	31720.6i	1.22136	+	1.22136i	0.254206	+	0.967150i	$0.418186\pi$
$878$	−12869.9	+	12869.9i	−0.494689	+	0.494689i
$879$	−10022.1			−0.384570
$880$	3757.47	+	733.098i	0.143937	+	0.0280826i
$881$			46126.6i			1.76395i	0.471292	+	0.881977i	$0.343788\pi$
$881$			46126.6i			1.76395i	−0.471292	+	0.881977i	$0.656212\pi$
$882$	9008.53	+	9008.53i	0.343915	+	0.343915i
$883$	23431.9	−	23431.9i	0.893033	−	0.893033i	−0.101775	−	0.994807i	$-0.532452\pi$
$883$	23431.9	−	23431.9i	0.893033	−	0.893033i	0.994807	+	0.101775i	$0.0324521\pi$
$884$	4071.37			0.154904
$885$	−2648.69	+	1783.88i	−0.100604	+	0.0677563i
$886$	17948.0			0.680559
$887$	6042.83	+	6042.83i	0.228747	+	0.228747i	0.812169	−	0.583422i	$-0.198287\pi$
$887$	6042.83	+	6042.83i	0.228747	+	0.228747i	−0.583422	+	0.812169i	$0.698287\pi$
$888$	−5598.47	−	5598.47i	−0.211568	−	0.211568i
$889$	−530.218			−0.0200033
$890$	−23310.3	+	15699.4i	−0.877936	+	0.591285i
$891$		−	2833.99i		−	0.106557i
$892$	−3328.94	−	3328.94i	−0.124957	−	0.124957i
$893$	41417.2	+	41417.2i	1.55204	+	1.55204i
$894$	−12571.0			−0.470288
$895$	−2598.51	−	506.980i	−0.0970487	−	0.0189346i
$896$		−	264.736i		−	0.00987076i
$897$	−6027.83	+	2421.33i	−0.224374	+	0.0901290i
$898$	−20027.7	+	20027.7i	−0.744247	+	0.744247i
$899$			12367.2i			0.458811i
$900$	8713.36	+	3534.57i	0.322717	+	0.130910i
$901$	2809.29			0.103875
$902$	−12083.6	+	12083.6i	−0.446051	+	0.446051i
$903$	1843.05	−	1843.05i	0.0679211	−	0.0679211i
$904$	−1398.24			−0.0514433
$905$	−49472.6	−	9652.30i	−1.81715	−	0.354534i
$906$	−5575.76			−0.204461
$907$	−27446.8	+	27446.8i	−1.00480	+	1.00480i	−0.00481366	+	0.999988i	$0.501532\pi$
$907$	−27446.8	+	27446.8i	−1.00480	+	1.00480i	−0.999988	+	0.00481366i	$0.998468\pi$
$908$	−4846.67	−	4846.67i	−0.177139	−	0.177139i
$909$			30211.4i			1.10236i
$910$	531.498	+	789.165i	0.0193615	+	0.0287479i
$911$		−	17603.9i		−	0.640224i	−0.947380	−	0.320112i	$-0.896280\pi$
$911$		−	17603.9i		−	0.640224i	0.947380	−	0.320112i	$-0.103720\pi$
$912$	−3325.48	+	3325.48i	−0.120743	+	0.120743i
$913$	−2423.01	+	2423.01i	−0.0878313	+	0.0878313i
$914$	−13998.8			−0.506608
$915$	−14199.6	+	9563.34i	−0.513031	+	0.345524i
$916$			4938.75i			0.178145i
$917$	3366.06	−	3366.06i	0.121218	−	0.121218i
$918$	9174.12	+	9174.12i	0.329838	+	0.329838i
$919$	40754.7			1.46286			0.731432	−	0.681914i	$-0.238852\pi$
$919$	40754.7			1.46286			0.731432	+	0.681914i	$0.238852\pi$
$920$	−5539.05	+	8164.24i	−0.198497	+	0.292573i
$921$	−4280.71			−0.153153
$922$	2963.87	+	2963.87i	0.105868	+	0.105868i
$923$	−3435.95	+	3435.95i	−0.122531	+	0.122531i
$924$			506.810i			0.0180442i
$925$	39805.0	−	16830.7i	1.41490	−	0.598260i
$926$	33445.6			1.18692
$927$	−19703.2	+	19703.2i	−0.698099	+	0.698099i
$928$	6233.83	−	6233.83i	0.220513	−	0.220513i
$929$		−	22141.5i		−	0.781959i	−0.920399	−	0.390979i	$-0.872136\pi$
$929$		−	22141.5i		−	0.781959i	0.920399	−	0.390979i	$-0.127864\pi$
$930$	550.227	−	2820.17i	0.0194007	−	0.0994376i
$931$		−	34781.1i		−	1.22439i
$932$	7981.22	+	7981.22i	0.280508	+	0.280508i
$933$	−8820.42	+	8820.42i	−0.309504	+	0.309504i
$934$	−7147.60			−0.250403
$935$	−9818.49	+	6612.70i	−0.343421	+	0.231292i
$936$	3095.19			0.108087
$937$	−9917.29	+	9917.29i	−0.345767	+	0.345767i	−0.858530	−	0.512763i	$-0.828622\pi$
$937$	−9917.29	+	9917.29i	−0.345767	+	0.345767i	0.512763	+	0.858530i	$0.328622\pi$
$938$	−344.612	+	344.612i	−0.0119957	+	0.0119957i
$939$	17167.9			0.596650
$940$	14250.3	+	21158.7i	0.494460	+	0.734171i
$941$		−	17344.3i		−	0.600860i	−0.953804	−	0.300430i	$-0.902870\pi$
$941$		−	17344.3i		−	0.600860i	0.953804	−	0.300430i	$-0.0971302\pi$
$942$	−11824.5	+	11824.5i	−0.408986	+	0.408986i
$943$	−16415.3	−	40865.4i	−0.566866	−	1.41120i
$944$			1596.50i			0.0550440i
$945$	−580.608	+	2975.89i	−0.0199864	+	0.102440i
$946$	18843.5			0.647628
$947$	6278.50	+	6278.50i	0.215442	+	0.215442i	0.806575	−	0.591132i	$-0.201319\pi$
$947$	6278.50	+	6278.50i	0.215442	+	0.215442i	−0.591132	+	0.806575i	$0.701319\pi$
$948$	5254.10	+	5254.10i	0.180006	+	0.180006i
$949$		−	22753.3i		−	0.778297i
$950$	−9997.43	−	23644.1i	−0.341431	−	0.807490i
$951$	2363.94			0.0806058
$952$	578.836	+	578.836i	0.0197061	+	0.0197061i
$953$	6697.55	+	6697.55i	0.227655	+	0.227655i	0.811712	−	0.584057i	$-0.198536\pi$
$953$	6697.55	+	6697.55i	0.227655	+	0.227655i	−0.584057	+	0.811712i	$0.698536\pi$
$954$	2135.72			0.0724805
$955$	−23922.3	−	4667.35i	−0.810585	−	0.158149i
$956$	2411.88			0.0815959
$957$	−11934.1	+	11934.1i	−0.403107	+	0.403107i
$958$	10722.2	+	10722.2i	0.361605	+	0.361605i
$959$			1756.16i			0.0591337i
$960$	−1698.88	+	1144.19i	−0.0571158	+	0.0384672i
$961$	−27775.9			−0.932357
$962$	10059.2	−	10059.2i	0.337131	−	0.337131i
$963$	−11525.6	−	11525.6i	−0.385678	−	0.385678i
$964$	2018.56			0.0674412
$965$	−1148.16	−	1704.78i	−0.0383010	−	0.0568691i
$966$	−1201.24	−	512.745i	−0.0400095	−	0.0170780i
$967$	−14463.5	−	14463.5i	−0.480989	−	0.480989i	0.424459	−	0.905447i	$-0.360464\pi$
$967$	−14463.5	−	14463.5i	−0.480989	−	0.480989i	−0.905447	+	0.424459i	$0.860464\pi$
$968$	4938.43	−	4938.43i	0.163974	−	0.163974i
$969$		−	14542.1i		−	0.482105i
$970$	6276.11	−	32168.0i	0.207746	−	1.06480i
$971$		−	36508.4i		−	1.20660i	−0.797514	−	0.603301i	$-0.793852\pi$
$971$		−	36508.4i		−	1.20660i	0.797514	−	0.603301i	$-0.206148\pi$
$972$	11085.5	+	11085.5i	0.365811	+	0.365811i
$973$	−3523.73	−	3523.73i	−0.116100	−	0.116100i
$974$			27067.3i			0.890445i
$975$	2767.15	−	6821.54i	0.0908921	−	0.224066i
$976$			8558.79i			0.280697i
$977$	10905.2	−	10905.2i	0.357101	−	0.357101i	−0.505642	−	0.862743i	$-0.668744\pi$
$977$	10905.2	−	10905.2i	0.357101	−	0.357101i	0.862743	+	0.505642i	$0.168744\pi$
$978$	−12628.3	+	12628.3i	−0.412892	+	0.412892i
$979$		−	26897.8i		−	0.878099i
$980$	2900.77	−	14867.8i	0.0945527	−	0.484627i
$981$			12529.7i			0.407789i
$982$	713.189	+	713.189i	0.0231759	+	0.0231759i
$983$	15211.6	+	15211.6i	0.493566	+	0.493566i	0.909428	−	0.415862i	$-0.136520\pi$
$983$	15211.6	+	15211.6i	0.493566	+	0.493566i	−0.415862	+	0.909428i	$0.636520\pi$
$984$		−	9142.95i		−	0.296206i
$985$	−4793.33	+	3228.28i	−0.155054	+	0.104428i
$986$			27260.2i			0.880467i
$987$	−2387.99	+	2387.99i	−0.0770119	+	0.0770119i
$988$	−5975.12	−	5975.12i	−0.192403	−	0.192403i
$989$	−19064.2	+	44662.8i	−0.612948	+	1.43599i
$990$	−7464.34	+	5027.19i	−0.239629	+	0.161388i
$991$	3972.59			0.127339			0.0636697	−	0.997971i	$-0.479720\pi$
$991$	3972.59			0.127339			0.0636697	+	0.997971i	$0.479720\pi$
$992$	−1015.75	−	1015.75i	−0.0325102	−	0.0325102i
$993$	17646.3	−	17646.3i	0.563937	−	0.563937i
$994$	−976.995			−0.0311755
$995$	4910.52	−	25168.7i	0.156456	−	0.801912i
$996$		−	1833.36i		−	0.0583255i
$997$	10795.0	+	10795.0i	0.342909	+	0.342909i	0.857460	−	0.514551i	$-0.172041\pi$
$997$	10795.0	+	10795.0i	0.342909	+	0.342909i	−0.514551	+	0.857460i	$0.672041\pi$
$998$	4515.03	−	4515.03i	0.143207	−	0.143207i
$999$	45333.1			1.43571

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.4.e.a.137.7	✓	72
5.3	odd	4	inner	230.4.e.a.183.8	yes	72
23.22	odd	2	inner	230.4.e.a.137.8	yes	72
115.68	even	4	inner	230.4.e.a.183.7	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.4.e.a.137.7	✓	72	1.1	even	1	trivial
230.4.e.a.137.8	yes	72	23.22	odd	2	inner
230.4.e.a.183.7	yes	72	115.68	even	4	inner
230.4.e.a.183.8	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)

\(f(q)\)	\(=\)	\(q+(-1.41421 - 1.41421i) q^{2} +(-2.02411 + 2.02411i) q^{3} +4.00000i q^{4} +(-2.14096 + 10.9734i) q^{5} +5.72506 q^{6} +(-1.46247 + 1.46247i) q^{7} +(5.65685 - 5.65685i) q^{8} +18.8059i q^{9} +O(q^{10})\)	\(q+(-1.41421 - 1.41421i) q^{2} +(-2.02411 + 2.02411i) q^{3} +4.00000i q^{4} +(-2.14096 + 10.9734i) q^{5} +5.72506 q^{6} +(-1.46247 + 1.46247i) q^{7} +(5.65685 - 5.65685i) q^{8} +18.8059i q^{9} +(18.5466 - 12.4910i) q^{10} +21.4009i q^{11} +(-8.09645 - 8.09645i) q^{12} +(14.5475 - 14.5475i) q^{13} +4.13650 q^{14} +(-17.8779 - 26.5450i) q^{15} -16.0000 q^{16} +(34.9835 - 34.9835i) q^{17} +(26.5956 - 26.5956i) q^{18} -102.683 q^{19} +(-43.8937 - 8.56385i) q^{20} -5.92042i q^{21} +(30.2655 - 30.2655i) q^{22} +(41.1151 + 102.355i) q^{23} +22.9002i q^{24} +(-115.833 - 46.9874i) q^{25} -41.1464 q^{26} +(-92.7164 - 92.7164i) q^{27} +(-5.84989 - 5.84989i) q^{28} -275.499i q^{29} +(-12.2571 + 62.8235i) q^{30} -44.8903 q^{31} +(22.6274 + 22.6274i) q^{32} +(-43.3179 - 43.3179i) q^{33} -98.9483 q^{34} +(-12.9172 - 19.1794i) q^{35} -75.2237 q^{36} +(-244.472 + 244.472i) q^{37} +(145.216 + 145.216i) q^{38} +58.8914i q^{39} +(49.9640 + 74.1862i) q^{40} -399.252 q^{41} +(-8.37274 + 8.37274i) q^{42} +(311.304 + 311.304i) q^{43} -85.6038 q^{44} +(-206.366 - 40.2628i) q^{45} +(86.6062 - 202.897i) q^{46} +(-403.349 - 403.349i) q^{47} +(32.3858 - 32.3858i) q^{48} +338.722i q^{49} +(97.3617 + 230.262i) q^{50} +141.621i q^{51} +(58.1898 + 58.1898i) q^{52} +(40.1517 + 40.1517i) q^{53} +262.242i q^{54} +(-234.842 - 45.8186i) q^{55} +16.5460i q^{56} +(207.843 - 207.843i) q^{57} +(-389.615 + 389.615i) q^{58} -99.7810i q^{59} +(106.180 - 71.5117i) q^{60} -534.925i q^{61} +(63.4845 + 63.4845i) q^{62} +(-27.5032 - 27.5032i) q^{63} -64.0000i q^{64} +(128.490 + 190.781i) q^{65} +122.522i q^{66} +(-83.3100 + 83.3100i) q^{67} +(139.934 + 139.934i) q^{68} +(-290.400 - 123.956i) q^{69} +(-8.85608 + 45.3916i) q^{70} -236.189 q^{71} +(106.382 + 106.382i) q^{72} +(782.038 - 782.038i) q^{73} +691.472 q^{74} +(329.566 - 139.350i) q^{75} -410.733i q^{76} +(-31.2983 - 31.2983i) q^{77} +(83.2850 - 83.2850i) q^{78} -648.939 q^{79} +(34.2554 - 175.575i) q^{80} -132.423 q^{81} +(564.627 + 564.627i) q^{82} +(113.220 + 113.220i) q^{83} +23.6817 q^{84} +(308.991 + 458.787i) q^{85} -880.500i q^{86} +(557.641 + 557.641i) q^{87} +(121.062 + 121.062i) q^{88} -1256.85 q^{89} +(234.905 + 348.785i) q^{90} +42.5505i q^{91} +(-409.420 + 164.461i) q^{92} +(90.8631 - 90.8631i) q^{93} +1140.84i q^{94} +(219.841 - 1126.79i) q^{95} -91.6009 q^{96} +(1036.42 - 1036.42i) q^{97} +(479.026 - 479.026i) q^{98} -402.465 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

Related objects

Downloads

Learn more