LMFDB - Embedded newform 230.5.f.b.47.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [230,5,Mod(47,230)]

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, 0]))

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("230.47");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 230 = 2 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	230.f (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:	$23.7750915093$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			47.11
Character	$\chi$	$=$	230.47
Dual form			230.5.f.b.93.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.00000 + 2.00000i) q^{2} +(-0.310392 + 0.310392i) q^{3} +8.00000i q^{4} +(6.21241 + 24.2158i) q^{5} -1.24157 q^{6} +(40.7961 + 40.7961i) q^{7} +(-16.0000 + 16.0000i) q^{8} +80.8073i q^{9} +O(q^{10})$	\(q+(2.00000 + 2.00000i) q^{2} +(-0.310392 + 0.310392i) q^{3} +8.00000i q^{4} +(6.21241 + 24.2158i) q^{5} -1.24157 q^{6} +(40.7961 + 40.7961i) q^{7} +(-16.0000 + 16.0000i) q^{8} +80.8073i q^{9} +(-36.0068 + 60.8565i) q^{10} +96.9505 q^{11} +(-2.48314 - 2.48314i) q^{12} +(160.204 - 160.204i) q^{13} +163.184i q^{14} +(-9.44469 - 5.58812i) q^{15} -64.0000 q^{16} +(-324.889 - 324.889i) q^{17} +(-161.615 + 161.615i) q^{18} +288.985i q^{19} +(-193.727 + 49.6993i) q^{20} -25.3256 q^{21} +(193.901 + 193.901i) q^{22} +(-77.9968 + 77.9968i) q^{23} -9.93256i q^{24} +(-547.812 + 300.877i) q^{25} +640.817 q^{26} +(-50.2238 - 50.2238i) q^{27} +(-326.369 + 326.369i) q^{28} +458.765i q^{29} +(-7.71314 - 30.0656i) q^{30} +417.319 q^{31} +(-128.000 - 128.000i) q^{32} +(-30.0927 + 30.0927i) q^{33} -1299.56i q^{34} +(-734.469 + 1241.35i) q^{35} -646.459 q^{36} +(994.982 + 994.982i) q^{37} +(-577.970 + 577.970i) q^{38} +99.4523i q^{39} +(-486.852 - 288.055i) q^{40} -1745.69 q^{41} +(-50.6512 - 50.6512i) q^{42} +(-1506.01 + 1506.01i) q^{43} +775.604i q^{44} +(-1956.82 + 502.008i) q^{45} -311.987 q^{46} +(659.512 + 659.512i) q^{47} +(19.8651 - 19.8651i) q^{48} +927.644i q^{49} +(-1697.38 - 493.869i) q^{50} +201.686 q^{51} +(1281.63 + 1281.63i) q^{52} +(2397.30 - 2397.30i) q^{53} -200.895i q^{54} +(602.296 + 2347.74i) q^{55} -1305.48 q^{56} +(-89.6988 - 89.6988i) q^{57} +(-917.531 + 917.531i) q^{58} -4449.90i q^{59} +(44.7050 - 75.5575i) q^{60} +4010.69 q^{61} +(834.638 + 834.638i) q^{62} +(-3296.62 + 3296.62i) q^{63} -512.000i q^{64} +(4874.73 + 2884.22i) q^{65} -120.371 q^{66} +(-4844.72 - 4844.72i) q^{67} +(2599.11 - 2599.11i) q^{68} -48.4192i q^{69} +(-3951.64 + 1013.77i) q^{70} -2190.15 q^{71} +(-1292.92 - 1292.92i) q^{72} +(-1486.86 + 1486.86i) q^{73} +3979.93i q^{74} +(76.6466 - 263.427i) q^{75} -2311.88 q^{76} +(3955.20 + 3955.20i) q^{77} +(-198.905 + 198.905i) q^{78} +2699.30i q^{79} +(-397.594 - 1549.81i) q^{80} -6514.21 q^{81} +(-3491.38 - 3491.38i) q^{82} +(864.355 - 864.355i) q^{83} -202.605i q^{84} +(5849.11 - 9885.80i) q^{85} -6024.04 q^{86} +(-142.397 - 142.397i) q^{87} +(-1551.21 + 1551.21i) q^{88} -6625.51i q^{89} +(-4917.65 - 2909.61i) q^{90} +13071.4 q^{91} +(-623.974 - 623.974i) q^{92} +(-129.533 + 129.533i) q^{93} +2638.05i q^{94} +(-6998.01 + 1795.29i) q^{95} +79.4604 q^{96} +(-2512.91 - 2512.91i) q^{97} +(-1855.29 + 1855.29i) q^{98} +7834.31i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + 88 q^{2} + 24 q^{5} - 80 q^{7} - 704 q^{8}+O(q^{10}) $ 44 * q + 88 * q^2 + 24 * q^5 - 80 * q^7 - 704 * q^8	$ 44 q + 88 q^{2} + 24 q^{5} - 80 q^{7} - 704 q^{8} - 136 q^{10} - 632 q^{11} + 500 q^{13} + 12 q^{15} - 2816 q^{16} + 120 q^{17} + 2648 q^{18} - 736 q^{20} - 856 q^{21} - 1264 q^{22} + 2052 q^{25} + 2000 q^{26} + 588 q^{27} + 640 q^{28} - 1704 q^{30} + 3220 q^{31} - 5632 q^{32} - 2884 q^{33} + 720 q^{35} + 10592 q^{36} + 1856 q^{37} - 1696 q^{38} - 1856 q^{40} - 5156 q^{41} - 1712 q^{42} + 960 q^{43} + 460 q^{45} - 1224 q^{47} + 4456 q^{50} + 3640 q^{51} + 4000 q^{52} + 13556 q^{53} + 12980 q^{55} + 2560 q^{56} - 3072 q^{57} - 3112 q^{58} - 6912 q^{60} - 4864 q^{61} + 6440 q^{62} - 13484 q^{63} - 4100 q^{65} - 11536 q^{66} - 1888 q^{67} - 960 q^{68} + 8824 q^{70} - 1060 q^{71} + 21184 q^{72} + 16616 q^{73} - 11044 q^{75} - 6784 q^{76} + 8892 q^{77} - 23152 q^{78} - 1536 q^{80} - 4044 q^{81} - 10312 q^{82} - 27024 q^{83} - 11068 q^{85} + 3840 q^{86} - 8392 q^{87} + 10112 q^{88} - 7184 q^{90} - 54024 q^{91} + 22528 q^{93} - 25968 q^{95} - 3252 q^{97} - 27984 q^{98}+O(q^{100}) $ 44 * q + 88 * q^2 + 24 * q^5 - 80 * q^7 - 704 * q^8 - 136 * q^10 - 632 * q^11 + 500 * q^13 + 12 * q^15 - 2816 * q^16 + 120 * q^17 + 2648 * q^18 - 736 * q^20 - 856 * q^21 - 1264 * q^22 + 2052 * q^25 + 2000 * q^26 + 588 * q^27 + 640 * q^28 - 1704 * q^30 + 3220 * q^31 - 5632 * q^32 - 2884 * q^33 + 720 * q^35 + 10592 * q^36 + 1856 * q^37 - 1696 * q^38 - 1856 * q^40 - 5156 * q^41 - 1712 * q^42 + 960 * q^43 + 460 * q^45 - 1224 * q^47 + 4456 * q^50 + 3640 * q^51 + 4000 * q^52 + 13556 * q^53 + 12980 * q^55 + 2560 * q^56 - 3072 * q^57 - 3112 * q^58 - 6912 * q^60 - 4864 * q^61 + 6440 * q^62 - 13484 * q^63 - 4100 * q^65 - 11536 * q^66 - 1888 * q^67 - 960 * q^68 + 8824 * q^70 - 1060 * q^71 + 21184 * q^72 + 16616 * q^73 - 11044 * q^75 - 6784 * q^76 + 8892 * q^77 - 23152 * q^78 - 1536 * q^80 - 4044 * q^81 - 10312 * q^82 - 27024 * q^83 - 11068 * q^85 + 3840 * q^86 - 8392 * q^87 + 10112 * q^88 - 7184 * q^90 - 54024 * q^91 + 22528 * q^93 - 25968 * q^95 - 3252 * q^97 - 27984 * 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 $

$2$	2.00000	+	2.00000i	0.500000	+	0.500000i
$2$	2.00000	+	2.00000i	0.500000	+	0.500000i
$3$	−0.310392	+	0.310392i	−0.0344880	+	0.0344880i	−0.724141	−	0.689652i	$-0.757763\pi$
$3$	−0.310392	+	0.310392i	−0.0344880	+	0.0344880i	0.689652	+	0.724141i	$0.257763\pi$
$4$			8.00000i			0.500000i
$5$	6.21241	+	24.2158i	0.248496	+	0.968633i
$5$	6.21241	+	24.2158i	0.248496	+	0.968633i
$6$	−1.24157			−0.0344880
$7$	40.7961	+	40.7961i	0.832574	+	0.832574i	0.987868	−	0.155295i	$-0.0496327\pi$
$7$	40.7961	+	40.7961i	0.832574	+	0.832574i	−0.155295	+	0.987868i	$0.549633\pi$
$8$	−16.0000	+	16.0000i	−0.250000	+	0.250000i
$9$			80.8073i			0.997621i
$10$	−36.0068	+	60.8565i	−0.360068	+	0.608565i
$11$	96.9505			0.801244			0.400622	−	0.916243i	$-0.368794\pi$
$11$	96.9505			0.801244			0.400622	+	0.916243i	$0.368794\pi$
$12$	−2.48314	−	2.48314i	−0.0172440	−	0.0172440i
$13$	160.204	−	160.204i	0.947954	−	0.947954i	−0.0507574	−	0.998711i	$-0.516164\pi$
$13$	160.204	−	160.204i	0.947954	−	0.947954i	0.998711	+	0.0507574i	$0.0161635\pi$
$14$			163.184i			0.832574i
$15$	−9.44469	−	5.58812i	−0.0419764	−	0.0248361i
$16$	−64.0000			−0.250000
$17$	−324.889	−	324.889i	−1.12418	−	1.12418i	−0.991106	−	0.133078i	$-0.957514\pi$
$17$	−324.889	−	324.889i	−1.12418	−	1.12418i	−0.133078	−	0.991106i	$-0.542486\pi$
$18$	−161.615	+	161.615i	−0.498811	+	0.498811i
$19$			288.985i			0.800513i	0.916403	+	0.400256i	$0.131079\pi$
$19$			288.985i			0.800513i	−0.916403	+	0.400256i	$0.868921\pi$
$20$	−193.727	+	49.6993i	−0.484316	+	0.124248i
$21$	−25.3256			−0.0574277
$22$	193.901	+	193.901i	0.400622	+	0.400622i
$23$	−77.9968	+	77.9968i	−0.147442	+	0.147442i
$23$	−77.9968	+	77.9968i	−0.147442	+	0.147442i
$24$		−	9.93256i		−	0.0172440i
$25$	−547.812	+	300.877i	−0.876499	+	0.481404i
$26$	640.817			0.947954
$27$	−50.2238	−	50.2238i	−0.0688940	−	0.0688940i
$28$	−326.369	+	326.369i	−0.416287	+	0.416287i
$29$			458.765i			0.545500i	0.962085	+	0.272750i	$0.0879332\pi$
$29$			458.765i			0.545500i	−0.962085	+	0.272750i	$0.912067\pi$
$30$	−7.71314	−	30.0656i	−0.00857016	−	0.0334062i
$31$	417.319			0.434255			0.217128	−	0.976143i	$-0.430331\pi$
$31$	417.319			0.434255			0.217128	+	0.976143i	$0.430331\pi$
$32$	−128.000	−	128.000i	−0.125000	−	0.125000i
$33$	−30.0927	+	30.0927i	−0.0276333	+	0.0276333i
$34$		−	1299.56i		−	1.12418i
$35$	−734.469	+	1241.35i	−0.599566	+	1.01335i
$36$	−646.459			−0.498811
$37$	994.982	+	994.982i	0.726795	+	0.726795i	0.969980	−	0.243185i	$-0.0781923\pi$
$37$	994.982	+	994.982i	0.726795	+	0.726795i	−0.243185	+	0.969980i	$0.578192\pi$
$38$	−577.970	+	577.970i	−0.400256	+	0.400256i
$39$			99.4523i			0.0653861i
$40$	−486.852	−	288.055i	−0.304282	−	0.180034i
$41$	−1745.69			−1.03848			−0.519241	−	0.854628i	$-0.673785\pi$
$41$	−1745.69			−1.03848			−0.519241	+	0.854628i	$0.673785\pi$
$42$	−50.6512	−	50.6512i	−0.0287138	−	0.0287138i
$43$	−1506.01	+	1506.01i	−0.814500	+	0.814500i	−0.985305	−	0.170805i	$-0.945363\pi$
$43$	−1506.01	+	1506.01i	−0.814500	+	0.814500i	0.170805	+	0.985305i	$0.445363\pi$
$44$			775.604i			0.400622i
$45$	−1956.82	+	502.008i	−0.966329	+	0.247905i
$46$	−311.987			−0.147442
$47$	659.512	+	659.512i	0.298557	+	0.298557i	0.840448	−	0.541892i	$-0.182292\pi$
$47$	659.512	+	659.512i	0.298557	+	0.298557i	−0.541892	+	0.840448i	$0.682292\pi$
$48$	19.8651	−	19.8651i	0.00862201	−	0.00862201i
$49$			927.644i			0.386357i
$50$	−1697.38	−	493.869i	−0.678951	−	0.197548i
$51$	201.686			0.0775418
$52$	1281.63	+	1281.63i	0.473977	+	0.473977i
$53$	2397.30	−	2397.30i	0.853437	−	0.853437i	−0.137118	−	0.990555i	$-0.543784\pi$
$53$	2397.30	−	2397.30i	0.853437	−	0.853437i	0.990555	+	0.137118i	$0.0437838\pi$
$54$		−	200.895i		−	0.0688940i
$55$	602.296	+	2347.74i	0.199106	+	0.776111i
$56$	−1305.48			−0.416287
$57$	−89.6988	−	89.6988i	−0.0276081	−	0.0276081i
$58$	−917.531	+	917.531i	−0.272750	+	0.272750i
$59$		−	4449.90i		−	1.27834i	−0.769066	−	0.639170i	$-0.779278\pi$
$59$		−	4449.90i		−	1.27834i	0.769066	−	0.639170i	$-0.220722\pi$
$60$	44.7050	−	75.5575i	0.0124180	−	0.0209882i
$61$	4010.69			1.07785			0.538926	−	0.842353i	$-0.318830\pi$
$61$	4010.69			1.07785			0.538926	+	0.842353i	$0.318830\pi$
$62$	834.638	+	834.638i	0.217128	+	0.217128i
$63$	−3296.62	+	3296.62i	−0.830593	+	0.830593i
$64$		−	512.000i		−	0.125000i
$65$	4874.73	+	2884.22i	1.15378	+	0.682656i
$66$	−120.371			−0.0276333
$67$	−4844.72	−	4844.72i	−1.07924	−	1.07924i	−0.996577	−	0.0826661i	$-0.973657\pi$
$67$	−4844.72	−	4844.72i	−1.07924	−	1.07924i	−0.0826661	−	0.996577i	$-0.526343\pi$
$68$	2599.11	−	2599.11i	0.562092	−	0.562092i
$69$		−	48.4192i		−	0.0101700i
$70$	−3951.64	+	1013.77i	−0.806458	+	0.206892i
$71$	−2190.15			−0.434467			−0.217234	−	0.976120i	$-0.569703\pi$
$71$	−2190.15			−0.434467			−0.217234	+	0.976120i	$0.569703\pi$
$72$	−1292.92	−	1292.92i	−0.249405	−	0.249405i
$73$	−1486.86	+	1486.86i	−0.279013	+	0.279013i	−0.832715	−	0.553702i	$-0.813215\pi$
$73$	−1486.86	+	1486.86i	−0.279013	+	0.279013i	0.553702	+	0.832715i	$0.313215\pi$
$74$			3979.93i			0.726795i
$75$	76.6466	−	263.427i	0.0136261	−	0.0468314i
$76$	−2311.88			−0.400256
$77$	3955.20	+	3955.20i	0.667094	+	0.667094i
$78$	−198.905	+	198.905i	−0.0326931	+	0.0326931i
$79$			2699.30i			0.432510i	0.976337	+	0.216255i	$0.0693843\pi$
$79$			2699.30i			0.432510i	−0.976337	+	0.216255i	$0.930616\pi$
$80$	−397.594	−	1549.81i	−0.0621241	−	0.242158i
$81$	−6514.21			−0.992869
$82$	−3491.38	−	3491.38i	−0.519241	−	0.519241i
$83$	864.355	−	864.355i	0.125469	−	0.125469i	−0.641584	−	0.767053i	$-0.721722\pi$
$83$	864.355	−	864.355i	0.125469	−	0.125469i	0.767053	+	0.641584i	$0.221722\pi$
$84$		−	202.605i		−	0.0287138i
$85$	5849.11	−	9885.80i	0.809565	−	1.36828i
$86$	−6024.04			−0.814500
$87$	−142.397	−	142.397i	−0.0188132	−	0.0188132i
$88$	−1551.21	+	1551.21i	−0.200311	+	0.200311i
$89$		−	6625.51i		−	0.836449i	−0.908344	−	0.418225i	$-0.862652\pi$
$89$		−	6625.51i		−	0.836449i	0.908344	−	0.418225i	$-0.137348\pi$
$90$	−4917.65	−	2909.61i	−0.607117	−	0.359212i
$91$	13071.4			1.57848
$92$	−623.974	−	623.974i	−0.0737210	−	0.0737210i
$93$	−129.533	+	129.533i	−0.0149766	+	0.0149766i
$94$			2638.05i			0.298557i
$95$	−6998.01	+	1795.29i	−0.775403	+	0.198925i
$96$	79.4604			0.00862201
$97$	−2512.91	−	2512.91i	−0.267075	−	0.267075i	0.560845	−	0.827921i	$-0.310476\pi$
$97$	−2512.91	−	2512.91i	−0.267075	−	0.267075i	−0.827921	+	0.560845i	$0.810476\pi$
$98$	−1855.29	+	1855.29i	−0.193179	+	0.193179i
$99$			7834.31i			0.799338i
$100$	−2407.02	−	4382.49i	−0.240702	−	0.438249i
$101$	10190.6			0.998980			0.499490	−	0.866320i	$-0.333521\pi$
$101$	10190.6			0.998980			0.499490	+	0.866320i	$0.333521\pi$
$102$	403.372	+	403.372i	0.0387709	+	0.0387709i
$103$	12838.4	−	12838.4i	1.21014	−	1.21014i	0.239165	−	0.970979i	$-0.423126\pi$
$103$	12838.4	−	12838.4i	1.21014	−	1.21014i	0.970979	−	0.239165i	$-0.0768737\pi$
$104$			5126.53i			0.473977i
$105$	−157.333	−	613.280i	−0.0142706	−	0.0556263i
$106$	9589.22			0.853437
$107$	7178.50	+	7178.50i	0.626998	+	0.626998i	0.947312	−	0.320313i	$-0.103788\pi$
$107$	7178.50	+	7178.50i	0.626998	+	0.626998i	−0.320313	+	0.947312i	$0.603788\pi$
$108$	401.790	−	401.790i	0.0344470	−	0.0344470i
$109$			15232.2i			1.28206i	0.767516	+	0.641030i	$0.221493\pi$
$109$			15232.2i			1.28206i	−0.767516	+	0.641030i	$0.778507\pi$
$110$	−3490.88	+	5900.06i	−0.288502	+	0.487609i
$111$	−617.670			−0.0501314
$112$	−2610.95	−	2610.95i	−0.208143	−	0.208143i
$113$	2542.46	−	2542.46i	0.199112	−	0.199112i	−0.600507	−	0.799619i	$-0.705035\pi$
$113$	2542.46	−	2542.46i	0.199112	−	0.199112i	0.799619	+	0.600507i	$0.205035\pi$
$114$		−	358.795i		−	0.0276081i
$115$	−2373.30	−	1404.21i	−0.179456	−	0.106178i
$116$	−3670.12			−0.272750
$117$	12945.7	+	12945.7i	0.945699	+	0.945699i
$118$	8899.80	−	8899.80i	0.639170	−	0.639170i
$119$		−	26508.4i		−	1.87193i
$120$	240.525	−	61.7051i	0.0167031	−	0.00428508i
$121$	−5241.60			−0.358008
$122$	8021.38	+	8021.38i	0.538926	+	0.538926i
$123$	541.848	−	541.848i	0.0358152	−	0.0358152i
$124$			3338.55i			0.217128i
$125$	−10689.2	−	11396.5i	−0.684110	−	0.729379i
$126$	−13186.5			−0.830593
$127$	1895.38	+	1895.38i	0.117514	+	0.117514i	0.763418	−	0.645904i	$-0.223520\pi$
$127$	1895.38	+	1895.38i	0.117514	+	0.117514i	−0.645904	+	0.763418i	$0.723520\pi$
$128$	1024.00	−	1024.00i	0.0625000	−	0.0625000i
$129$		−	934.909i		−	0.0561810i
$130$	3981.02	+	15517.9i	0.235563	+	0.918219i
$131$	17572.2			1.02396			0.511979	−	0.858998i	$-0.328912\pi$
$131$	17572.2			1.02396			0.511979	+	0.858998i	$0.328912\pi$
$132$	−240.742	−	240.742i	−0.0138167	−	0.0138167i
$133$	−11789.5	+	11789.5i	−0.666486	+	0.666486i
$134$		−	19378.9i		−	1.07924i
$135$	904.199	−	1528.22i	0.0496131	−	0.0838530i
$136$	10396.4			0.562092
$137$	16454.3	+	16454.3i	0.876676	+	0.876676i	0.993189	−	0.116513i	$-0.0371717\pi$
$137$	16454.3	+	16454.3i	0.876676	+	0.876676i	−0.116513	+	0.993189i	$0.537172\pi$
$138$	96.8384	−	96.8384i	0.00508498	−	0.00508498i
$139$		−	1278.90i		−	0.0661921i	−0.999452	−	0.0330960i	$-0.989463\pi$
$139$		−	1278.90i		−	0.0661921i	0.999452	−	0.0330960i	$-0.0105367\pi$
$140$	−9930.83	−	5875.75i	−0.506675	−	0.299783i
$141$	−409.415			−0.0205933
$142$	−4380.30	−	4380.30i	−0.217234	−	0.217234i
$143$	15531.9	−	15531.9i	0.759542	−	0.759542i
$144$		−	5171.67i		−	0.249405i
$145$	−11109.4	+	2850.04i	−0.528389	+	0.135555i
$146$	−5947.43			−0.279013
$147$	−287.934	−	287.934i	−0.0133247	−	0.0133247i
$148$	−7959.85	+	7959.85i	−0.363397	+	0.363397i
$149$			3752.60i			0.169029i	0.996422	+	0.0845143i	$0.0269339\pi$
$149$			3752.60i			0.169029i	−0.996422	+	0.0845143i	$0.973066\pi$
$150$	680.146	−	373.560i	0.0302287	−	0.0166027i
$151$	10018.7			0.439397			0.219699	−	0.975568i	$-0.429493\pi$
$151$	10018.7			0.439397			0.219699	+	0.975568i	$0.429493\pi$
$152$	−4623.76	−	4623.76i	−0.200128	−	0.200128i
$153$	26253.4	−	26253.4i	1.12151	−	1.12151i
$154$			15820.8i			0.667094i
$155$	2592.56	+	10105.7i	0.107911	+	0.420634i
$156$	−795.618			−0.0326931
$157$	31846.0	+	31846.0i	1.29198	+	1.29198i	0.933560	+	0.358421i	$0.116685\pi$
$157$	31846.0	+	31846.0i	1.29198	+	1.29198i	0.358421	+	0.933560i	$0.383315\pi$
$158$	−5398.59	+	5398.59i	−0.216255	+	0.216255i
$159$			1488.21i			0.0588668i
$160$	2304.44	−	3894.81i	0.0900170	−	0.152141i
$161$	−6363.93			−0.245513
$162$	−13028.4	−	13028.4i	−0.496435	−	0.496435i
$163$	12625.9	−	12625.9i	0.475212	−	0.475212i	−0.428385	−	0.903596i	$-0.640917\pi$
$163$	12625.9	−	12625.9i	0.475212	−	0.475212i	0.903596	+	0.428385i	$0.140917\pi$
$164$		−	13965.5i		−	0.519241i
$165$	−915.667	−	541.771i	−0.0336333	−	0.0198998i
$166$	3457.42			0.125469
$167$	−4610.15	−	4610.15i	−0.165303	−	0.165303i	0.619608	−	0.784911i	$-0.287292\pi$
$167$	−4610.15	−	4610.15i	−0.165303	−	0.165303i	−0.784911	+	0.619608i	$0.787292\pi$
$168$	405.210	−	405.210i	0.0143569	−	0.0143569i
$169$		−	22769.7i		−	0.797232i
$170$	31469.8	−	8073.38i	1.08892	−	0.279356i
$171$	−23352.1			−0.798608
$172$	−12048.1	−	12048.1i	−0.407250	−	0.407250i
$173$	33647.2	−	33647.2i	1.12423	−	1.12423i	0.133136	−	0.991098i	$-0.457495\pi$
$173$	33647.2	−	33647.2i	1.12423	−	1.12423i	0.991098	−	0.133136i	$-0.0425047\pi$
$174$		−	569.589i		−	0.0188132i
$175$	−34623.2	−	10074.0i	−1.13055	−	0.328946i
$176$	−6204.83			−0.200311
$177$	1381.22	+	1381.22i	0.0440874	+	0.0440874i
$178$	13251.0	−	13251.0i	0.418225	−	0.418225i
$179$		−	25675.7i		−	0.801339i	−0.916223	−	0.400669i	$-0.868778\pi$
$179$		−	25675.7i		−	0.801339i	0.916223	−	0.400669i	$-0.131222\pi$
$180$	−4016.07	−	15654.5i	−0.123953	−	0.483164i
$181$	−40019.0			−1.22154			−0.610772	−	0.791806i	$-0.709141\pi$
$181$	−40019.0			−1.22154			−0.610772	+	0.791806i	$0.709141\pi$
$182$	26142.8	+	26142.8i	0.789241	+	0.789241i
$183$	−1244.89	+	1244.89i	−0.0371730	+	0.0371730i
$184$		−	2495.90i		−	0.0737210i
$185$	−17913.1	+	30275.5i	−0.523391	+	0.884603i
$186$	−518.131			−0.0149766
$187$	−31498.1	−	31498.1i	−0.900745	−	0.900745i
$188$	−5276.10	+	5276.10i	−0.149278	+	0.149278i
$189$		−	4097.87i		−	0.114719i
$190$	−17586.6	−	10405.4i	−0.487164	−	0.288239i
$191$	54883.3			1.50443			0.752217	−	0.658915i	$-0.228984\pi$
$191$	54883.3			1.50443			0.752217	+	0.658915i	$0.228984\pi$
$192$	158.921	+	158.921i	0.00431101	+	0.00431101i
$193$	−12486.2	+	12486.2i	−0.335208	+	0.335208i	−0.854560	−	0.519352i	$-0.826173\pi$
$193$	−12486.2	+	12486.2i	−0.335208	+	0.335208i	0.519352	+	0.854560i	$0.326173\pi$
$194$		−	10051.6i		−	0.267075i
$195$	−2408.32	+	617.839i	−0.0633351	+	0.0162482i
$196$	−7421.15			−0.193179
$197$	46286.0	+	46286.0i	1.19266	+	1.19266i	0.976317	+	0.216345i	$0.0694137\pi$
$197$	46286.0	+	46286.0i	1.19266	+	1.19266i	0.216345	+	0.976317i	$0.430586\pi$
$198$	−15668.6	+	15668.6i	−0.399669	+	0.399669i
$199$			12048.6i			0.304249i	0.988361	+	0.152125i	$0.0486115\pi$
$199$			12048.6i			0.304249i	−0.988361	+	0.152125i	$0.951388\pi$
$200$	3950.95	−	13579.0i	0.0987738	−	0.339476i
$201$	3007.53			0.0744420
$202$	20381.2	+	20381.2i	0.499490	+	0.499490i
$203$	−18715.8	+	18715.8i	−0.454169	+	0.454169i
$204$			1613.49i			0.0387709i
$205$	−10844.9	−	42273.3i	−0.258059	−	1.00591i
$206$	51353.7			1.21014
$207$	−6302.71	−	6302.71i	−0.147091	−	0.147091i
$208$	−10253.1	+	10253.1i	−0.236988	+	0.236988i
$209$			28017.2i			0.641406i
$210$	911.894	−	1541.23i	0.0206779	−	0.0349484i
$211$	15769.5			0.354203			0.177101	−	0.984193i	$-0.443328\pi$
$211$	15769.5			0.354203			0.177101	+	0.984193i	$0.443328\pi$
$212$	19178.4	+	19178.4i	0.426719	+	0.426719i
$213$	679.806	−	679.806i	0.0149839	−	0.0149839i
$214$			28714.0i			0.626998i
$215$	−45825.3	−	27113.3i	−0.991352	−	0.586551i
$216$	1607.16			0.0344470
$217$	17025.0	+	17025.0i	0.361549	+	0.361549i
$218$	−30464.3	+	30464.3i	−0.641030	+	0.641030i
$219$		−	923.019i		−	0.0192452i
$220$	−18781.9	+	4818.37i	−0.388055	+	0.0995531i
$221$	−104097.			−2.13135
$222$	−1235.34	−	1235.34i	−0.0250657	−	0.0250657i
$223$	−2751.97	+	2751.97i	−0.0553393	+	0.0553393i	−0.734235	−	0.678896i	$-0.762459\pi$
$223$	−2751.97	+	2751.97i	−0.0553393	+	0.0553393i	0.678896	+	0.734235i	$0.262459\pi$
$224$		−	10443.8i		−	0.208143i
$225$	−24313.1	−	44267.2i	−0.480258	−	0.874414i
$226$	10169.9			0.199112
$227$	7249.84	+	7249.84i	0.140694	+	0.140694i	0.773946	−	0.633252i	$-0.218280\pi$
$227$	7249.84	+	7249.84i	0.140694	+	0.140694i	−0.633252	+	0.773946i	$0.718280\pi$
$228$	717.590	−	717.590i	0.0138041	−	0.0138041i
$229$			30724.4i			0.585884i	0.956130	+	0.292942i	$0.0946343\pi$
$229$			30724.4i			0.585884i	−0.956130	+	0.292942i	$0.905366\pi$
$230$	−1938.19	−	7555.03i	−0.0366388	−	0.142817i
$231$	−2455.33			−0.0460136
$232$	−7340.25	−	7340.25i	−0.136375	−	0.136375i
$233$	−12504.0	+	12504.0i	−0.230323	+	0.230323i	−0.812828	−	0.582504i	$-0.802073\pi$
$233$	−12504.0	+	12504.0i	−0.230323	+	0.230323i	0.582504	+	0.812828i	$0.302073\pi$
$234$			51782.7i			0.945699i
$235$	−11873.5	+	20067.8i	−0.215002	+	0.363382i
$236$	35599.2			0.639170
$237$	−837.841	−	837.841i	−0.0149164	−	0.0149164i
$238$	53016.8	−	53016.8i	0.935965	−	0.935965i
$239$		−	8587.76i		−	0.150343i	−0.997171	−	0.0751717i	$-0.976050\pi$
$239$		−	8587.76i		−	0.150343i	0.997171	−	0.0751717i	$-0.0239505\pi$
$240$	604.460	+	357.640i	0.0104941	+	0.00620902i
$241$	−36487.1			−0.628210			−0.314105	−	0.949388i	$-0.601704\pi$
$241$	−36487.1			−0.628210			−0.314105	+	0.949388i	$0.601704\pi$
$242$	−10483.2	−	10483.2i	−0.179004	−	0.179004i
$243$	6090.09	−	6090.09i	0.103136	−	0.103136i
$244$			32085.5i			0.538926i
$245$	−22463.7	+	5762.91i	−0.374238	+	0.0960085i
$246$	2167.39			0.0358152
$247$	46296.6	+	46296.6i	0.758849	+	0.758849i
$248$	−6677.11	+	6677.11i	−0.108564	+	0.108564i
$249$			536.578i			0.00865435i
$250$	1414.63	−	44171.5i	0.0226341	−	0.706744i
$251$	−96801.7			−1.53651			−0.768255	−	0.640144i	$-0.778875\pi$
$251$	−96801.7			−1.53651			−0.768255	+	0.640144i	$0.778875\pi$
$252$	−26373.0	−	26373.0i	−0.415296	−	0.415296i
$253$	−7561.83	+	7561.83i	−0.118137	+	0.118137i
$254$			7581.53i			0.117514i
$255$	1252.96	+	4883.99i	0.0192689	+	0.0751095i
$256$	4096.00			0.0625000
$257$	−15012.3	−	15012.3i	−0.227290	−	0.227290i	0.584269	−	0.811560i	$-0.301381\pi$
$257$	−15012.3	−	15012.3i	−0.227290	−	0.227290i	−0.811560	+	0.584269i	$0.801381\pi$
$258$	1869.82	−	1869.82i	0.0280905	−	0.0280905i
$259$			81182.8i			1.21022i
$260$	−23073.8	+	38997.8i	−0.341328	+	0.576891i
$261$	−37071.6			−0.544202
$262$	35144.3	+	35144.3i	0.511979	+	0.511979i
$263$	73987.5	−	73987.5i	1.06966	−	1.06966i	0.0722781	−	0.997385i	$-0.476973\pi$
$263$	73987.5	−	73987.5i	1.06966	−	1.06966i	0.997385	−	0.0722781i	$-0.0230269\pi$
$264$		−	962.966i		−	0.0138167i
$265$	72945.8	+	43159.7i	1.03874	+	0.614591i
$266$	−47157.9			−0.666486
$267$	2056.51	+	2056.51i	0.0288475	+	0.0288475i
$268$	38757.8	−	38757.8i	0.539622	−	0.539622i
$269$			119306.i			1.64876i	0.566038	+	0.824379i	$0.308475\pi$
$269$			119306.i			1.64876i	−0.566038	+	0.824379i	$0.691525\pi$
$270$	4864.84	−	1248.04i	0.0667330	−	0.0171199i
$271$	−25716.8			−0.350170			−0.175085	−	0.984553i	$-0.556020\pi$
$271$	−25716.8			−0.350170			−0.175085	+	0.984553i	$0.556020\pi$
$272$	20792.9	+	20792.9i	0.281046	+	0.281046i
$273$	−4057.27	+	4057.27i	−0.0544388	+	0.0544388i
$274$			65817.3i			0.876676i
$275$	−53110.6	+	29170.2i	−0.702289	+	0.385722i
$276$	387.354			0.00508498
$277$	−92174.1	−	92174.1i	−1.20129	−	1.20129i	−0.973773	−	0.227522i	$-0.926938\pi$
$277$	−92174.1	−	92174.1i	−1.20129	−	1.20129i	−0.227522	−	0.973773i	$-0.573062\pi$
$278$	2557.79	−	2557.79i	0.0330960	−	0.0330960i
$279$			33722.4i			0.433222i
$280$	−8110.15	−	31613.2i	−0.103446	−	0.403229i
$281$	−92509.0			−1.17158			−0.585789	−	0.810463i	$-0.699215\pi$
$281$	−92509.0			−1.17158			−0.585789	+	0.810463i	$0.699215\pi$
$282$	−818.830	−	818.830i	−0.0102966	−	0.0102966i
$283$	−24235.6	+	24235.6i	−0.302608	+	0.302608i	−0.842033	−	0.539425i	$-0.818642\pi$
$283$	−24235.6	+	24235.6i	−0.302608	+	0.302608i	0.539425	+	0.842033i	$0.318642\pi$
$284$		−	17521.2i		−	0.217234i
$285$	1614.88	−	2729.37i	0.0198816	−	0.0336026i
$286$	62127.5			0.759542
$287$	−71217.3	−	71217.3i	−0.864612	−	0.864612i
$288$	10343.3	−	10343.3i	0.124703	−	0.124703i
$289$			127585.i			1.52758i
$290$	−27918.8	−	16518.7i	−0.331972	−	0.196417i
$291$	1559.98			0.0184218
$292$	−11894.9	−	11894.9i	−0.139506	−	0.139506i
$293$	106590.	−	106590.i	1.24160	−	1.24160i	0.282263	−	0.959337i	$-0.408915\pi$
$293$	106590.	−	106590.i	1.24160	−	1.24160i	0.959337	−	0.282263i	$-0.0910849\pi$
$294$		−	1151.73i		−	0.0133247i
$295$	107758.	−	27644.6i	1.23824	−	0.317663i
$296$	−31839.4			−0.363397
$297$	−4869.22	−	4869.22i	−0.0552009	−	0.0552009i
$298$	−7505.20	+	7505.20i	−0.0845143	+	0.0845143i
$299$			24990.8i			0.279536i
$300$	2107.41	+	613.173i	0.0234157	+	0.00681303i
$301$	−122879.			−1.35626
$302$	20037.4	+	20037.4i	0.219699	+	0.219699i
$303$	−3163.08	+	3163.08i	−0.0344529	+	0.0344529i
$304$		−	18495.0i		−	0.200128i
$305$	24916.1	+	97122.1i	0.267843	+	1.04404i
$306$	105014.			1.12151
$307$	121665.	+	121665.i	1.29089	+	1.29089i	0.934236	+	0.356654i	$0.116083\pi$
$307$	121665.	+	121665.i	1.29089	+	1.29089i	0.356654	+	0.934236i	$0.383917\pi$
$308$	−31641.6	+	31641.6i	−0.333547	+	0.333547i
$309$			7969.89i			0.0834710i
$310$	−15026.3	+	25396.6i	−0.156361	+	0.264272i
$311$	−118185.			−1.22192			−0.610960	−	0.791661i	$-0.709216\pi$
$311$	−118185.			−1.22192			−0.610960	+	0.791661i	$0.709216\pi$
$312$	−1591.24	−	1591.24i	−0.0163465	−	0.0163465i
$313$	26746.4	−	26746.4i	0.273009	−	0.273009i	−0.557301	−	0.830310i	$-0.688163\pi$
$313$	26746.4	−	26746.4i	0.273009	−	0.273009i	0.830310	+	0.557301i	$0.188163\pi$
$314$			127384.i			1.29198i
$315$	−100310.	−	59350.5i	−1.01094	−	0.598140i
$316$	−21594.4			−0.216255
$317$	35364.5	+	35364.5i	0.351924	+	0.351924i	0.860825	−	0.508901i	$-0.169948\pi$
$317$	35364.5	+	35364.5i	0.351924	+	0.351924i	−0.508901	+	0.860825i	$0.669948\pi$
$318$	−2976.42	+	2976.42i	−0.0294334	+	0.0294334i
$319$			44477.5i			0.437078i
$320$	12398.5	−	3180.75i	0.121079	−	0.0310621i
$321$	−4456.30			−0.0432479
$322$	−12727.9	−	12727.9i	−0.122756	−	0.122756i
$323$	93888.1	−	93888.1i	0.899923	−	0.899923i
$324$		−	52113.7i		−	0.496435i
$325$	−39559.9	+	135964.i	−0.374532	+	1.28723i
$326$	50503.6			0.475212
$327$	−4727.94	−	4727.94i	−0.0442157	−	0.0442157i
$328$	27931.0	−	27931.0i	0.259620	−	0.259620i
$329$			53811.1i			0.497141i
$330$	−747.793	−	2914.88i	−0.00686678	−	0.0267665i
$331$	3356.77			0.0306384			0.0153192	−	0.999883i	$-0.495124\pi$
$331$	3356.77			0.0306384			0.0153192	+	0.999883i	$0.495124\pi$
$332$	6914.84	+	6914.84i	0.0627344	+	0.0627344i
$333$	−80401.8	+	80401.8i	−0.725066	+	0.725066i
$334$		−	18440.6i		−	0.165303i
$335$	87221.5	−	147416.i	0.777202	−	1.31358i
$336$	1620.84			0.0143569
$337$	35559.3	+	35559.3i	0.313107	+	0.313107i	0.846112	−	0.533005i	$-0.178937\pi$
$337$	35559.3	+	35559.3i	0.313107	+	0.313107i	−0.533005	+	0.846112i	$0.678937\pi$
$338$	45539.5	−	45539.5i	0.398616	−	0.398616i
$339$			1578.32i			0.0137340i
$340$	79086.4	+	46792.9i	0.684138	+	0.404783i
$341$	40459.3			0.347944
$342$	−46704.2	−	46704.2i	−0.399304	−	0.399304i
$343$	60107.2	−	60107.2i	0.510903	−	0.510903i
$344$		−	48192.4i		−	0.407250i
$345$	1172.51	−	300.800i	0.00985096	−	0.00252720i
$346$	134589.			1.12423
$347$	−154689.	−	154689.i	−1.28470	−	1.28470i	−0.937964	−	0.346734i	$-0.887291\pi$
$347$	−154689.	−	154689.i	−1.28470	−	1.28470i	−0.346734	−	0.937964i	$-0.612709\pi$
$348$	1139.18	−	1139.18i	0.00940661	−	0.00940661i
$349$		−	106958.i		−	0.878139i	−0.898453	−	0.439069i	$-0.855308\pi$
$349$		−	106958.i		−	0.878139i	0.898453	−	0.439069i	$-0.144692\pi$
$350$	−49098.5	−	89394.4i	−0.400804	−	0.729750i
$351$	−16092.1			−0.130617
$352$	−12409.7	−	12409.7i	−0.100155	−	0.100155i
$353$	−45564.8	+	45564.8i	−0.365663	+	0.365663i	−0.865893	−	0.500230i	$-0.833249\pi$
$353$	−45564.8	+	45564.8i	−0.365663	+	0.365663i	0.500230	+	0.865893i	$0.333249\pi$
$354$			5524.86i			0.0440874i
$355$	−13606.1	−	53036.3i	−0.107964	−	0.420839i
$356$	53004.1			0.418225
$357$	8228.01	+	8228.01i	0.0645592	+	0.0645592i
$358$	51351.4	−	51351.4i	0.400669	−	0.400669i
$359$		−	82039.2i		−	0.636550i	−0.947998	−	0.318275i	$-0.896896\pi$
$359$		−	82039.2i		−	0.636550i	0.947998	−	0.318275i	$-0.103104\pi$
$360$	23276.9	−	39341.2i	0.179606	−	0.303558i
$361$	46808.6			0.359179
$362$	−80038.0	−	80038.0i	−0.610772	−	0.610772i
$363$	1626.95	−	1626.95i	0.0123470	−	0.0123470i
$364$			104571.i			0.789241i
$365$	−45242.5	−	26768.5i	−0.339594	−	0.200927i
$366$	−4979.55			−0.0371730
$367$	−130831.	−	130831.i	−0.971354	−	0.971354i	0.0282471	−	0.999601i	$-0.491007\pi$
$367$	−130831.	−	130831.i	−0.971354	−	0.971354i	−0.999601	+	0.0282471i	$0.991007\pi$
$368$	4991.79	−	4991.79i	0.0368605	−	0.0368605i
$369$		−	141064.i		−	1.03601i
$370$	−96377.2	+	24724.9i	−0.703997	+	0.180606i
$371$	195601.			1.42110
$372$	−1036.26	−	1036.26i	−0.00748830	−	0.00748830i
$373$	36089.7	−	36089.7i	0.259397	−	0.259397i	−0.565412	−	0.824809i	$-0.691283\pi$
$373$	36089.7	−	36089.7i	0.259397	−	0.259397i	0.824809	+	0.565412i	$0.191283\pi$
$374$		−	125993.i		−	0.900745i
$375$	6855.25	+	219.546i	0.0487485	+	0.00156121i
$376$	−21104.4			−0.149278
$377$	73496.1	+	73496.1i	0.517109	+	0.517109i
$378$	8195.73	−	8195.73i	0.0573594	−	0.0573594i
$379$		−	77724.9i		−	0.541106i	−0.962705	−	0.270553i	$-0.912794\pi$
$379$		−	77724.9i		−	0.541106i	0.962705	−	0.270553i	$-0.0872065\pi$
$380$	−14362.4	−	55984.1i	−0.0994623	−	0.387701i
$381$	−1176.63			−0.00810566
$382$	109767.	+	109767.i	0.752217	+	0.752217i
$383$	179630.	−	179630.i	1.22456	−	1.22456i	0.258573	−	0.965992i	$-0.416748\pi$
$383$	179630.	−	179630.i	1.22456	−	1.22456i	0.965992	−	0.258573i	$-0.0832522\pi$
$384$			635.684i			0.00431101i
$385$	−71207.1	+	120350.i	−0.480399	+	0.811940i
$386$	−49944.7			−0.335208
$387$	−121697.	−	121697.i	−0.812563	−	0.812563i
$388$	20103.3	−	20103.3i	0.133538	−	0.133538i
$389$		−	157773.i		−	1.04264i	−0.853361	−	0.521320i	$-0.825440\pi$
$389$		−	157773.i		−	1.04264i	0.853361	−	0.521320i	$-0.174560\pi$
$390$	−6052.32	−	3580.96i	−0.0397917	−	0.0235435i
$391$	50680.6			0.331504
$392$	−14842.3	−	14842.3i	−0.0965893	−	0.0965893i
$393$	−5454.26	+	5454.26i	−0.0353143	+	0.0353143i
$394$			185144.i			1.19266i
$395$	−65365.6	+	16769.1i	−0.418943	+	0.107477i
$396$	−62674.5			−0.399669
$397$	176357.	+	176357.i	1.11895	+	1.11895i	0.991896	+	0.127055i	$0.0405526\pi$
$397$	176357.	+	176357.i	1.11895	+	1.11895i	0.127055	+	0.991896i	$0.459447\pi$
$398$	−24097.2	+	24097.2i	−0.152125	+	0.152125i
$399$		−	7318.72i		−	0.0459716i
$400$	35060.0	−	19256.1i	0.219125	−	0.120351i
$401$	208539.			1.29687			0.648437	−	0.761268i	$-0.275423\pi$
$401$	208539.			1.29687			0.648437	+	0.761268i	$0.275423\pi$
$402$	6015.06	+	6015.06i	0.0372210	+	0.0372210i
$403$	66856.3	−	66856.3i	0.411654	−	0.411654i
$404$			81524.8i			0.499490i
$405$	−40469.0	−	157747.i	−0.246724	−	0.961726i
$406$	−74863.4			−0.454169
$407$	96464.0	+	96464.0i	0.582340	+	0.582340i
$408$	−3226.98	+	3226.98i	−0.0193854	+	0.0193854i
$409$		−	22284.1i		−	0.133214i	−0.997779	−	0.0666069i	$-0.978783\pi$
$409$		−	22284.1i		−	0.133214i	0.997779	−	0.0666069i	$-0.0212173\pi$
$410$	62856.7	−	106236.i	0.373924	−	0.631983i
$411$	−10214.6			−0.0604697
$412$	102707.	+	102707.i	0.605072	+	0.605072i
$413$	181539.	−	181539.i	1.06431	−	1.06431i
$414$		−	25210.8i		−	0.147091i
$415$	26300.8	+	15561.3i	0.152712	+	0.0903546i
$416$	−41012.3			−0.236988
$417$	396.960	+	396.960i	0.00228283	+	0.00228283i
$418$	−56034.5	+	56034.5i	−0.320703	+	0.320703i
$419$		−	305424.i		−	1.73970i	−0.493313	−	0.869852i	$-0.664214\pi$
$419$		−	305424.i		−	1.73970i	0.493313	−	0.869852i	$-0.335786\pi$
$420$	4906.24	−	1258.66i	0.0278132	−	0.00713529i
$421$	88617.9			0.499985			0.249993	−	0.968248i	$-0.419572\pi$
$421$	88617.9			0.499985			0.249993	+	0.968248i	$0.419572\pi$
$422$	31538.9	+	31538.9i	0.177101	+	0.177101i
$423$	−53293.4	+	53293.4i	−0.297847	+	0.297847i
$424$			76713.8i			0.426719i
$425$	275730.	+	80226.3i	1.52653	+	0.444160i
$426$	2719.22			0.0149839
$427$	163620.	+	163620.i	0.897392	+	0.897392i
$428$	−57428.0	+	57428.0i	−0.313499	+	0.313499i
$429$			9641.95i			0.0523902i
$430$	−37423.8	−	145877.i	−0.202400	−	0.788952i
$431$	−202106.			−1.08799			−0.543996	−	0.839088i	$-0.683089\pi$
$431$	−202106.			−1.08799			−0.543996	+	0.839088i	$0.683089\pi$
$432$	3214.32	+	3214.32i	0.0172235	+	0.0172235i
$433$	−214641.	+	214641.i	−1.14482	+	1.14482i	−0.157264	+	0.987557i	$0.550267\pi$
$433$	−214641.	+	214641.i	−1.14482	+	1.14482i	−0.987557	+	0.157264i	$0.949733\pi$
$434$			68100.0i			0.361549i
$435$	2563.64	−	4332.90i	0.0135481	−	0.0228981i
$436$	−121857.			−0.641030
$437$	−22539.9	−	22539.9i	−0.118029	−	0.118029i
$438$	1846.04	−	1846.04i	0.00962260	−	0.00962260i
$439$			296557.i			1.53879i	0.638775	+	0.769394i	$0.279441\pi$
$439$			296557.i			1.53879i	−0.638775	+	0.769394i	$0.720559\pi$
$440$	−47200.5	−	27927.0i	−0.243804	−	0.144251i
$441$	−74960.4			−0.385438
$442$	−208194.	−	208194.i	−1.06567	−	1.06567i
$443$	37390.0	−	37390.0i	0.190523	−	0.190523i	−0.605399	−	0.795922i	$-0.706986\pi$
$443$	37390.0	−	37390.0i	0.190523	−	0.190523i	0.795922	+	0.605399i	$0.206986\pi$
$444$		−	4941.36i		−	0.0250657i
$445$	160442.	−	41160.4i	0.810212	−	0.207855i
$446$	−11007.9			−0.0553393
$447$	−1164.78	−	1164.78i	−0.00582946	−	0.00582946i
$448$	20887.6	−	20887.6i	0.104072	−	0.104072i
$449$			330924.i			1.64148i	0.571302	+	0.820740i	$0.306439\pi$
$449$			330924.i			1.64148i	−0.571302	+	0.820740i	$0.693561\pi$
$450$	39908.2	−	137161.i	0.197078	−	0.677336i
$451$	−169245.			−0.832077
$452$	20339.7	+	20339.7i	0.0995561	+	0.0995561i
$453$	−3109.73	+	3109.73i	−0.0151539	+	0.0151539i
$454$			28999.4i			0.140694i
$455$	81205.0	+	316535.i	0.392247	+	1.52897i
$456$	2870.36			0.0138041
$457$	210937.	+	210937.i	1.01000	+	1.01000i	0.999950	+	0.0100474i	$0.00319824\pi$
$457$	210937.	+	210937.i	1.01000	+	1.01000i	0.0100474	+	0.999950i	$0.496802\pi$
$458$	−61448.7	+	61448.7i	−0.292942	+	0.292942i
$459$			32634.3i			0.154899i
$460$	11233.7	−	18986.4i	0.0530892	−	0.0897280i
$461$	−221790.			−1.04361			−0.521807	−	0.853064i	$-0.674742\pi$
$461$	−221790.			−1.04361			−0.521807	+	0.853064i	$0.674742\pi$
$462$	−4910.66	−	4910.66i	−0.0230068	−	0.0230068i
$463$	236973.	−	236973.i	1.10544	−	1.10544i	0.111702	−	0.993742i	$-0.464370\pi$
$463$	236973.	−	236973.i	1.10544	−	1.10544i	0.993742	−	0.111702i	$-0.0356301\pi$
$464$		−	29361.0i		−	0.136375i
$465$	−3941.45	−	2332.03i	−0.0182285	−	0.0107852i
$466$	−50016.1			−0.230323
$467$	−225155.	−	225155.i	−1.03240	−	1.03240i	−0.999457	−	0.0329429i	$-0.989512\pi$
$467$	−225155.	−	225155.i	−1.03240	−	1.03240i	−0.0329429	−	0.999457i	$-0.510488\pi$
$468$	−103565.	+	103565.i	−0.472849	+	0.472849i
$469$		−	395292.i		−	1.79710i
$470$	−63882.5	+	16388.6i	−0.289192	+	0.0741903i
$471$	−19769.5			−0.0891158
$472$	71198.4	+	71198.4i	0.319585	+	0.319585i
$473$	−146009.	+	146009.i	−0.652613	+	0.652613i
$474$		−	3351.36i		−	0.0149164i
$475$	−86949.1	−	158309.i	−0.385370	−	0.701649i
$476$	212067.			0.935965
$477$	193720.	+	193720.i	0.851407	+	0.851407i
$478$	17175.5	−	17175.5i	0.0751717	−	0.0751717i
$479$		−	404367.i		−	1.76240i	−0.472742	−	0.881201i	$-0.656736\pi$
$479$		−	404367.i		−	1.76240i	0.472742	−	0.881201i	$-0.343264\pi$
$480$	493.641	+	1924.20i	0.00214254	+	0.00835156i
$481$	318800.			1.37794
$482$	−72974.2	−	72974.2i	−0.314105	−	0.314105i
$483$	1975.32	−	1975.32i	0.00846725	−	0.00846725i
$484$		−	41932.8i		−	0.179004i
$485$	45241.0	−	76463.4i	0.192331	−	0.325065i
$486$	24360.3			0.103136
$487$	94355.6	+	94355.6i	0.397841	+	0.397841i	0.877471	−	0.479630i	$-0.159229\pi$
$487$	94355.6	+	94355.6i	0.397841	+	0.397841i	−0.479630	+	0.877471i	$0.659229\pi$
$488$	−64171.0	+	64171.0i	−0.269463	+	0.269463i
$489$			7837.97i			0.0327782i
$490$	−56453.1	−	33401.5i	−0.235123	−	0.139115i
$491$	−334116.			−1.38591			−0.692955	−	0.720981i	$-0.743691\pi$
$491$	−334116.			−1.38591			−0.692955	+	0.720981i	$0.743691\pi$
$492$	4334.78	+	4334.78i	0.0179076	+	0.0179076i
$493$	149048.	−	149048.i	0.613242	−	0.613242i
$494$			185186.i			0.758849i
$495$	−189714.	+	48670.0i	−0.774265	+	0.198633i
$496$	−26708.4			−0.108564
$497$	−89349.6	−	89349.6i	−0.361726	−	0.361726i
$498$	−1073.16	+	1073.16i	−0.00432717	+	0.00432717i
$499$		−	196922.i		−	0.790847i	−0.918499	−	0.395424i	$-0.870598\pi$
$499$		−	196922.i		−	0.790847i	0.918499	−	0.395424i	$-0.129402\pi$
$500$	91172.3	−	85513.8i	0.364689	−	0.342055i
$501$	2861.91			0.0114020
$502$	−193603.	−	193603.i	−0.768255	−	0.768255i
$503$	−61935.5	+	61935.5i	−0.244796	+	0.244796i	−0.818831	−	0.574035i	$-0.805377\pi$
$503$	−61935.5	+	61935.5i	−0.244796	+	0.244796i	0.574035	+	0.818831i	$0.305377\pi$
$504$		−	105492.i		−	0.415296i
$505$	63308.2	+	246774.i	0.248243	+	0.967645i
$506$	−30247.3			−0.118137
$507$	7067.56	+	7067.56i	0.0274950	+	0.0274950i
$508$	−15163.1	+	15163.1i	−0.0587570	+	0.0587570i
$509$			342517.i			1.32205i	0.750365	+	0.661024i	$0.229878\pi$
$509$			342517.i			1.32205i	−0.750365	+	0.661024i	$0.770122\pi$
$510$	−7262.08	+	12273.9i	−0.0279203	+	0.0471892i
$511$	−121316.			−0.464597
$512$	8192.00	+	8192.00i	0.0312500	+	0.0312500i
$513$	14513.9	−	14513.9i	0.0551506	−	0.0551506i
$514$		−	60049.2i		−	0.227290i
$515$	390650.	+	231135.i	1.47290	+	0.871469i
$516$	7479.27			0.0280905
$517$	63940.0	+	63940.0i	0.239217	+	0.239217i
$518$	−162366.	+	162366.i	−0.605110	+	0.605110i
$519$			20887.7i			0.0775452i
$520$	−124143.	+	31848.1i	−0.459109	+	0.117782i
$521$	37498.2			0.138145			0.0690726	−	0.997612i	$-0.477996\pi$
$521$	37498.2			0.138145			0.0690726	+	0.997612i	$0.477996\pi$
$522$	−74143.2	−	74143.2i	−0.272101	−	0.272101i
$523$	−149502.	+	149502.i	−0.546566	+	0.546566i	−0.925446	−	0.378880i	$-0.876309\pi$
$523$	−149502.	+	149502.i	−0.546566	+	0.546566i	0.378880	+	0.925446i	$0.376309\pi$
$524$			140577.i			0.511979i
$525$	13873.7	−	7619.90i	0.0503353	−	0.0276459i
$526$	295950.			1.06966
$527$	−135582.	−	135582.i	−0.488182	−	0.488182i
$528$	1925.93	−	1925.93i	0.00690833	−	0.00690833i
$529$		−	12167.0i		−	0.0434783i
$530$	59572.2	+	232211.i	0.212076	+	0.826667i
$531$	359585.			1.27530
$532$	−94315.7	−	94315.7i	−0.333243	−	0.333243i
$533$	−279666.	+	279666.i	−0.984432	+	0.984432i
$534$			8226.04i			0.0288475i
$535$	−129237.	+	218429.i	−0.451524	+	0.763138i
$536$	155031.			0.539622
$537$	7969.54	+	7969.54i	0.0276366	+	0.0276366i
$538$	−238612.	+	238612.i	−0.824379	+	0.824379i
$539$			89935.6i			0.309566i
$540$	12225.8	+	7233.59i	0.0419265	+	0.0248066i
$541$	−143380.			−0.489884			−0.244942	−	0.969538i	$-0.578769\pi$
$541$	−143380.			−0.489884			−0.244942	+	0.969538i	$0.578769\pi$
$542$	−51433.7	−	51433.7i	−0.175085	−	0.175085i
$543$	12421.6	−	12421.6i	0.0421287	−	0.0421287i
$544$			83171.6i			0.281046i
$545$	−368859.	+	94628.4i	−1.24185	+	0.318587i
$546$	−16229.1			−0.0544388
$547$	335815.	+	335815.i	1.12234	+	1.12234i	0.991388	+	0.130956i	$0.0418045\pi$
$547$	335815.	+	335815.i	1.12234	+	1.12234i	0.130956	+	0.991388i	$0.458195\pi$
$548$	−131635.	+	131635.i	−0.438338	+	0.438338i
$549$			324093.i			1.07529i
$550$	−164562.	−	47880.9i	−0.544006	−	0.158284i
$551$	−132576.			−0.436680
$552$	774.708	+	774.708i	0.00254249	+	0.00254249i
$553$	−110121.	+	110121.i	−0.360096	+	0.360096i
$554$		−	368697.i		−	1.20129i
$555$	−3837.22	−	14957.4i	−0.0124575	−	0.0485590i
$556$	10231.2			0.0330960
$557$	−12051.6	−	12051.6i	−0.0388450	−	0.0388450i	0.687417	−	0.726262i	$-0.258744\pi$
$557$	−12051.6	−	12051.6i	−0.0388450	−	0.0388450i	−0.726262	+	0.687417i	$0.758744\pi$
$558$	−67444.9	+	67444.9i	−0.216611	+	0.216611i
$559$			482539.i			1.54422i
$560$	47006.0	−	79446.6i	0.149892	−	0.253337i
$561$	19553.6			0.0621299
$562$	−185018.	−	185018.i	−0.585789	−	0.585789i
$563$	74730.4	−	74730.4i	0.235766	−	0.235766i	−0.579328	−	0.815094i	$-0.696685\pi$
$563$	74730.4	−	74730.4i	0.235766	−	0.235766i	0.815094	+	0.579328i	$0.196685\pi$
$564$		−	3275.32i		−	0.0102966i
$565$	77362.7	+	45773.0i	0.242345	+	0.143388i
$566$	−96942.3			−0.302608
$567$	−265755.	−	265755.i	−0.826637	−	0.826637i
$568$	35042.4	−	35042.4i	0.108617	−	0.108617i
$569$		−	88629.7i		−	0.273750i	−0.990588	−	0.136875i	$-0.956294\pi$
$569$		−	88629.7i		−	0.273750i	0.990588	−	0.136875i	$-0.0437059\pi$
$570$	8688.52	−	2228.98i	0.0267421	−	0.00686052i
$571$	−326124.			−1.00026			−0.500128	−	0.865952i	$-0.666714\pi$
$571$	−326124.			−1.00026			−0.500128	+	0.865952i	$0.666714\pi$
$572$	124255.	+	124255.i	0.379771	+	0.379771i
$573$	−17035.4	+	17035.4i	−0.0518850	+	0.0518850i
$574$		−	284869.i		−	0.864612i
$575$	19260.1	−	66195.0i	0.0582536	−	0.200212i
$576$	41373.3			0.124703
$577$	122803.	+	122803.i	0.368857	+	0.368857i	0.867060	−	0.498204i	$-0.166007\pi$
$577$	122803.	+	122803.i	0.368857	+	0.368857i	−0.498204	+	0.867060i	$0.666007\pi$
$578$	−255169.	+	255169.i	−0.763788	+	0.763788i
$579$		−	7751.23i		−	0.0231214i
$580$	−22800.3	−	88875.0i	−0.0677774	−	0.264195i
$581$	70524.6			0.208924
$582$	3119.95	+	3119.95i	0.00921090	+	0.00921090i
$583$	232420.	−	232420.i	0.683811	−	0.683811i
$584$		−	47579.5i		−	0.139506i
$585$	−233066.	+	393914.i	−0.681032	+	1.15104i
$586$	426360.			1.24160
$587$	−301482.	−	301482.i	−0.874954	−	0.874954i	0.118053	−	0.993007i	$-0.462335\pi$
$587$	−301482.	−	301482.i	−0.874954	−	0.874954i	−0.993007	+	0.118053i	$0.962335\pi$
$588$	2303.47	−	2303.47i	0.00666235	−	0.00666235i
$589$			120599.i			0.347627i
$590$	270805.	+	160227.i	0.777952	+	0.460289i
$591$	−28733.7			−0.0822652
$592$	−63678.8	−	63678.8i	−0.181699	−	0.181699i
$593$	−243152.	+	243152.i	−0.691463	+	0.691463i	−0.962554	−	0.271091i	$-0.912616\pi$
$593$	−243152.	+	243152.i	−0.691463	+	0.691463i	0.271091	+	0.962554i	$0.412616\pi$
$594$		−	19476.9i		−	0.0552009i
$595$	641923.	−	164681.i	1.81321	−	0.465168i
$596$	−30020.8			−0.0845143
$597$	−3739.79	−	3739.79i	−0.0104930	−	0.0104930i
$598$	−49981.6	+	49981.6i	−0.139768	+	0.139768i
$599$		−	454488.i		−	1.26669i	−0.773871	−	0.633343i	$-0.781682\pi$
$599$		−	454488.i		−	1.26669i	0.773871	−	0.633343i	$-0.218318\pi$
$600$	2988.48	+	5441.17i	0.00830133	+	0.0151144i
$601$	452586.			1.25300			0.626501	−	0.779420i	$-0.284486\pi$
$601$	452586.			1.25300			0.626501	+	0.779420i	$0.284486\pi$
$602$	−245758.	−	245758.i	−0.678131	−	0.678131i
$603$	391489.	−	391489.i	1.07668	−	1.07668i
$604$			80149.6i			0.219699i
$605$	−32563.0	−	126930.i	−0.0889638	−	0.346779i
$606$	−12652.3			−0.0344529
$607$	387613.	+	387613.i	1.05201	+	1.05201i	0.998571	+	0.0534422i	$0.0170193\pi$
$607$	387613.	+	387613.i	1.05201	+	1.05201i	0.0534422	+	0.998571i	$0.482981\pi$
$608$	36990.1	−	36990.1i	0.100064	−	0.100064i
$609$		−	11618.5i		−	0.0313268i
$610$	−144412.	+	244076.i	−0.388100	+	0.655943i
$611$	211313.			0.566036
$612$	210027.	+	210027.i	0.560755	+	0.560755i
$613$	−200158.	+	200158.i	−0.532662	+	0.532662i	−0.921364	−	0.388701i	$-0.872924\pi$
$613$	−200158.	+	200158.i	−0.532662	+	0.532662i	0.388701	+	0.921364i	$0.372924\pi$
$614$			486661.i			1.29089i
$615$	16487.5	+	9755.11i	0.0435917	+	0.0257918i
$616$	−126566.			−0.333547
$617$	−445259.	−	445259.i	−1.16961	−	1.16961i	−0.982300	−	0.187312i	$-0.940022\pi$
$617$	−445259.	−	445259.i	−1.16961	−	1.16961i	−0.187312	−	0.982300i	$-0.559978\pi$
$618$	−15939.8	+	15939.8i	−0.0417355	+	0.0417355i
$619$		−	224055.i		−	0.584754i	−0.956303	−	0.292377i	$-0.905554\pi$
$619$		−	224055.i		−	0.584754i	0.956303	−	0.292377i	$-0.0944463\pi$
$620$	−80845.8	+	20740.5i	−0.210317	+	0.0539554i
$621$	7834.58			0.0203157
$622$	−236371.	−	236371.i	−0.610960	−	0.610960i
$623$	270295.	−	270295.i	0.696406	−	0.696406i
$624$		−	6364.95i		−	0.0163465i
$625$	209571.	−	329648.i	0.536501	−	0.843900i
$626$	106986.			0.273009
$627$	−8696.34	−	8696.34i	−0.0221208	−	0.0221208i
$628$	−254768.	+	254768.i	−0.645991	+	0.645991i
$629$		−	646517.i		−	1.63410i
$630$	−81919.9	−	319322.i	−0.206399	−	0.804540i
$631$	−393964.			−0.989460			−0.494730	−	0.869047i	$-0.664733\pi$
$631$	−393964.			−0.989460			−0.494730	+	0.869047i	$0.664733\pi$
$632$	−43188.7	−	43188.7i	−0.108128	−	0.108128i
$633$	−4894.72	+	4894.72i	−0.0122158	+	0.0122158i
$634$			141458.i			0.351924i
$635$	−34123.4	+	57673.2i	−0.0846261	+	0.143030i
$636$	−11905.7			−0.0294334
$637$	148612.	+	148612.i	0.366249	+	0.366249i
$638$	−88955.1	+	88955.1i	−0.218539	+	0.218539i
$639$		−	176980.i		−	0.433434i
$640$	31158.5	+	18435.5i	0.0760706	+	0.0450085i
$641$	−537461.			−1.30807			−0.654035	−	0.756464i	$-0.726925\pi$
$641$	−537461.			−1.30807			−0.654035	+	0.756464i	$0.726925\pi$
$642$	−8912.61	−	8912.61i	−0.0216239	−	0.0216239i
$643$	−511989.	+	511989.i	−1.23834	+	1.23834i	−0.277655	+	0.960681i	$0.589557\pi$
$643$	−511989.	+	511989.i	−1.23834	+	1.23834i	−0.960681	+	0.277655i	$0.910443\pi$
$644$		−	50911.4i		−	0.122756i
$645$	22639.6	−	5808.04i	0.0544188	−	0.0139608i
$646$	375552.			0.899923
$647$	61087.7	+	61087.7i	0.145930	+	0.145930i	0.776297	−	0.630367i	$-0.217096\pi$
$647$	61087.7	+	61087.7i	0.145930	+	0.145930i	−0.630367	+	0.776297i	$0.717096\pi$
$648$	104227.	−	104227.i	0.248217	−	0.248217i
$649$		−	431420.i		−	1.02426i
$650$	−351047.	+	192807.i	−0.830880	+	0.456348i
$651$	−10568.9			−0.0249382
$652$	101007.	+	101007.i	0.237606	+	0.237606i
$653$	−286182.	+	286182.i	−0.671144	+	0.671144i	−0.957980	−	0.286836i	$-0.907396\pi$
$653$	−286182.	+	286182.i	−0.671144	+	0.671144i	0.286836	+	0.957980i	$0.407396\pi$
$654$		−	18911.8i		−	0.0442157i
$655$	109165.	+	425524.i	0.254450	+	0.991840i
$656$	111724.			0.259620
$657$	−120149.	−	120149.i	−0.278349	−	0.278349i
$658$	−107622.	+	107622.i	−0.248571	+	0.248571i
$659$		−	734470.i		−	1.69123i	−0.533792	−	0.845616i	$-0.679234\pi$
$659$		−	734470.i		−	1.69123i	0.533792	−	0.845616i	$-0.320766\pi$
$660$	4334.17	−	7325.34i	0.00994988	−	0.0168167i
$661$	−289771.			−0.663211			−0.331606	−	0.943418i	$-0.607590\pi$
$661$	−289771.			−0.663211			−0.331606	+	0.943418i	$0.607590\pi$
$662$	6713.55	+	6713.55i	0.0153192	+	0.0153192i
$663$	32311.0	−	32311.0i	0.0735060	−	0.0735060i
$664$			27659.3i			0.0627344i
$665$	−358733.	−	212251.i	−0.811199	−	0.479961i
$666$	−321607.			−0.725066
$667$	−35782.2	−	35782.2i	−0.0804296	−	0.0804296i
$668$	36881.2	−	36881.2i	0.0826517	−	0.0826517i
$669$		−	1708.38i		−	0.00381709i
$670$	469276.	−	120390.i	1.04539	−	0.268188i
$671$	388838.			0.863623
$672$	3241.68	+	3241.68i	0.00717846	+	0.00717846i
$673$	462937.	−	462937.i	1.02210	−	1.02210i	0.0223454	−	0.999750i	$-0.492887\pi$
$673$	462937.	−	462937.i	1.02210	−	1.02210i	0.999750	−	0.0223454i	$-0.00711334\pi$
$674$			142237.i			0.313107i
$675$	42624.4	+	12402.0i	0.0935514	+	0.0272197i
$676$	182158.			0.398616
$677$	−471283.	−	471283.i	−1.02826	−	1.02826i	−0.999589	−	0.0286740i	$-0.990872\pi$
$677$	−471283.	−	471283.i	−1.02826	−	1.02826i	−0.0286740	−	0.999589i	$-0.509128\pi$
$678$	−3156.65	+	3156.65i	−0.00686699	+	0.00686699i
$679$		−	205034.i		−	0.444720i
$680$	64587.0	+	251758.i	0.139678	+	0.544460i
$681$	−4500.59			−0.00970455
$682$	80918.6	+	80918.6i	0.173972	+	0.173972i
$683$	−250886.	+	250886.i	−0.537817	+	0.537817i	−0.922887	−	0.385070i	$-0.874177\pi$
$683$	−250886.	+	250886.i	−0.537817	+	0.537817i	0.385070	+	0.922887i	$0.374177\pi$
$684$		−	186817.i		−	0.399304i
$685$	−296234.	+	500676.i	−0.631326	+	1.06703i
$686$	240429.			0.510903
$687$	−9536.61	−	9536.61i	−0.0202060	−	0.0202060i
$688$	96384.7	−	96384.7i	0.203625	−	0.203625i
$689$		−	768116.i		−	1.61804i
$690$	2946.62	+	1743.42i	0.00618908	+	0.00366188i
$691$	663126.			1.38880			0.694400	−	0.719589i	$-0.255670\pi$
$691$	663126.			1.38880			0.694400	+	0.719589i	$0.255670\pi$
$692$	269178.	+	269178.i	0.562117	+	0.562117i
$693$	−319609.	+	319609.i	−0.665507	+	0.665507i
$694$		−	618757.i		−	1.28470i
$695$	30969.5	−	7945.03i	0.0641158	−	0.0164485i
$696$	4556.71			0.00940661
$697$	567155.	+	567155.i	1.16744	+	1.16744i
$698$	213916.	−	213916.i	0.439069	−	0.439069i
$699$		−	7762.31i		−	0.0158868i
$700$	80591.7	−	276986.i	0.164473	−	0.565277i
$701$	−845911.			−1.72143			−0.860714	−	0.509089i	$-0.829982\pi$
$701$	−845911.			−1.72143			−0.860714	+	0.509089i	$0.829982\pi$
$702$	−32184.2	−	32184.2i	−0.0653084	−	0.0653084i
$703$	−287535.	+	287535.i	−0.581808	+	0.581808i
$704$		−	49638.7i		−	0.100155i
$705$	−2543.46	−	9914.32i	−0.00511736	−	0.0199473i
$706$	−182259.			−0.365663
$707$	415737.	+	415737.i	0.831725	+	0.831725i
$708$	−11049.7	+	11049.7i	−0.0220437	+	0.0220437i
$709$			447433.i			0.890093i	0.895508	+	0.445046i	$0.146813\pi$
$709$			447433.i			0.890093i	−0.895508	+	0.445046i	$0.853187\pi$
$710$	78860.3	−	133285.i	0.156438	−	0.264401i
$711$	−218123.			−0.431481
$712$	106008.	+	106008.i	0.209112	+	0.209112i
$713$	−32549.6	+	32549.6i	−0.0640274	+	0.0640274i
$714$			32912.0i			0.0645592i
$715$	472607.	+	279627.i	0.924461	+	0.546974i
$716$	205406.			0.400669
$717$	2665.58	+	2665.58i	0.00518505	+	0.00518505i
$718$	164078.	−	164078.i	0.318275	−	0.318275i
$719$			588314.i			1.13802i	0.822329	+	0.569012i	$0.192674\pi$
$719$			588314.i			1.13802i	−0.822329	+	0.569012i	$0.807326\pi$
$720$	125236.	−	32128.5i	0.241582	−	0.0619763i
$721$	1.04751e6			2.01507
$722$	93617.2	+	93617.2i	0.179590	+	0.179590i
$723$	11325.3	−	11325.3i	0.0216657	−	0.0216657i
$724$		−	320152.i		−	0.610772i
$725$	−138032.	−	251317.i	−0.262606	−	0.478130i
$726$	6507.81			0.0123470
$727$	426308.	+	426308.i	0.806594	+	0.806594i	0.984117	−	0.177523i	$-0.0568085\pi$
$727$	426308.	+	426308.i	0.806594	+	0.806594i	−0.177523	+	0.984117i	$0.556808\pi$
$728$	−209143.	+	209143.i	−0.394621	+	0.394621i
$729$		−	523871.i		−	0.985755i
$730$	−36947.9	−	144022.i	−0.0693337	−	0.270261i
$731$	978573.			1.83130
$732$	−9959.10	−	9959.10i	−0.0185865	−	0.0185865i
$733$	123022.	−	123022.i	0.228967	−	0.228967i	−0.583294	−	0.812261i	$-0.698236\pi$
$733$	123022.	−	123022.i	0.228967	−	0.228967i	0.812261	+	0.583294i	$0.198236\pi$
$734$		−	523323.i		−	0.971354i
$735$	5183.79	−	8761.31i	0.00959561	−	0.0162179i
$736$	19967.2			0.0368605
$737$	−469698.	−	469698.i	−0.864737	−	0.864737i
$738$	282129.	−	282129.i	0.518006	−	0.518006i
$739$			212461.i			0.389036i	0.980899	+	0.194518i	$0.0623143\pi$
$739$			212461.i			0.389036i	−0.980899	+	0.194518i	$0.937686\pi$
$740$	−242204.	−	143305.i	−0.442302	−	0.261696i
$741$	−28740.2			−0.0523424
$742$	391203.	+	391203.i	0.710549	+	0.710549i
$743$	−318930.	+	318930.i	−0.577720	+	0.577720i	−0.934275	−	0.356555i	$-0.883951\pi$
$743$	−318930.	+	318930.i	−0.577720	+	0.577720i	0.356555	+	0.934275i	$0.383951\pi$
$744$		−	4145.04i		−	0.00748830i
$745$	−90872.3	+	23312.7i	−0.163727	+	0.0420030i
$746$	144359.			0.259397
$747$	69846.2	+	69846.2i	0.125170	+	0.125170i
$748$	251985.	−	251985.i	0.450372	−	0.450372i
$749$			585710.i			1.04404i
$750$	13271.4	+	14149.6i	0.0235936	+	0.0251548i
$751$	−659348.			−1.16905			−0.584527	−	0.811374i	$-0.698720\pi$
$751$	−659348.			−1.16905			−0.584527	+	0.811374i	$0.698720\pi$
$752$	−42208.8	−	42208.8i	−0.0746392	−	0.0746392i
$753$	30046.5	−	30046.5i	0.0529912	−	0.0529912i
$754$			293984.i			0.517109i
$755$	62240.3	+	242611.i	0.109189	+	0.425614i
$756$	32782.9			0.0573594
$757$	−424075.	−	424075.i	−0.740032	−	0.740032i	0.232552	−	0.972584i	$-0.425292\pi$
$757$	−424075.	−	424075.i	−0.740032	−	0.740032i	−0.972584	+	0.232552i	$0.925292\pi$
$758$	155450.	−	155450.i	0.270553	−	0.270553i
$759$		−	4694.27i		−	0.00814862i
$760$	83243.5	−	140693.i	0.144120	−	0.243582i
$761$	795906.			1.37433			0.687167	−	0.726499i	$-0.258854\pi$
$761$	795906.			1.37433			0.687167	+	0.726499i	$0.258854\pi$
$762$	−2353.25	−	2353.25i	−0.00405283	−	0.00405283i
$763$	−621413.	+	621413.i	−1.06741	+	1.06741i
$764$			439066.i			0.752217i
$765$	798845.	+	472651.i	1.36502	+	0.807639i
$766$	718521.			1.22456
$767$	−712893.	−	712893.i	−1.21181	−	1.21181i
$768$	−1271.37	+	1271.37i	−0.00215550	+	0.00215550i
$769$		−	885160.i		−	1.49682i	−0.663237	−	0.748409i	$-0.730818\pi$
$769$		−	885160.i		−	1.49682i	0.663237	−	0.748409i	$-0.269182\pi$
$770$	−383114.	+	98285.4i	−0.646169	+	0.165771i
$771$	9319.41			0.0156776
$772$	−99889.4	−	99889.4i	−0.167604	−	0.167604i
$773$	83173.8	−	83173.8i	0.139196	−	0.139196i	−0.634075	−	0.773271i	$-0.718619\pi$
$773$	83173.8	−	83173.8i	0.139196	−	0.139196i	0.773271	+	0.634075i	$0.218619\pi$
$774$		−	486787.i		−	0.812563i
$775$	−228612.	+	125562.i	−0.380624	+	0.209052i
$776$	80413.2			0.133538
$777$	−25198.5	−	25198.5i	−0.0417381	−	0.0417381i
$778$	315547.	−	315547.i	0.521320	−	0.521320i
$779$		−	504478.i		−	0.831318i
$780$	−4942.71	−	19266.6i	−0.00812411	−	0.0316676i
$781$	−212336.			−0.348114
$782$	101361.	+	101361.i	0.165752	+	0.165752i
$783$	23040.9	−	23040.9i	0.0375817	−	0.0375817i
$784$		−	59369.2i		−	0.0965893i
$785$	−573337.	+	969019.i	−0.930403	+	1.57251i
$786$	−21817.1			−0.0353143
$787$	−694388.	−	694388.i	−1.12112	−	1.12112i	−0.991573	−	0.129548i	$-0.958647\pi$
$787$	−694388.	−	694388.i	−1.12112	−	1.12112i	−0.129548	−	0.991573i	$-0.541353\pi$
$788$	−370288.	+	370288.i	−0.596331	+	0.596331i
$789$			45930.3i			0.0737811i
$790$	−164270.	−	97193.0i	−0.263210	−	0.155733i
$791$	207445.			0.331551
$792$	−125349.	−	125349.i	−0.199834	−	0.199834i
$793$	642529.	−	642529.i	1.02175	−	1.02175i
$794$			705427.i			1.11895i
$795$	−36038.2	+	9245.38i	−0.0570203	+	0.0146282i
$796$	−96388.6			−0.152125
$797$	720171.	+	720171.i	1.13375	+	1.13375i	0.989547	+	0.144208i	$0.0460633\pi$
$797$	720171.	+	720171.i	1.13375	+	1.13375i	0.144208	+	0.989547i	$0.453937\pi$
$798$	14637.4	−	14637.4i	0.0229858	−	0.0229858i
$799$		−	428536.i		−	0.671265i
$800$	108632.	+	31607.6i	0.169738	+	0.0493869i
$801$	535390.			0.834459
$802$	417077.	+	417077.i	0.648437	+	0.648437i
$803$	−144152.	+	144152.i	−0.223557	+	0.223557i
$804$			24060.2i			0.0372210i
$805$	−39535.4	−	154108.i	−0.0610090	−	0.237812i
$806$	267425.			0.411654
$807$	−37031.6	−	37031.6i	−0.0568624	−	0.0568624i
$808$	−163050.	+	163050.i	−0.249745	+	0.249745i
$809$			367251.i			0.561133i	0.959835	+	0.280567i	$0.0905223\pi$
$809$			367251.i			0.561133i	−0.959835	+	0.280567i	$0.909478\pi$
$810$	234556.	−	396432.i	0.357501	−	0.604225i
$811$	−372668.			−0.566605			−0.283303	−	0.959031i	$-0.591430\pi$
$811$	−372668.			−0.566605			−0.283303	+	0.959031i	$0.591430\pi$
$812$	−149727.	−	149727.i	−0.227084	−	0.227084i
$813$	7982.31	−	7982.31i	0.0120767	−	0.0120767i
$814$			385856.i			0.582340i
$815$	384184.	+	227309.i	0.578394	+	0.342217i
$816$	−12907.9			−0.0193854
$817$	−435215.	−	435215.i	−0.652018	−	0.652018i
$818$	44568.3	−	44568.3i	0.0666069	−	0.0666069i
$819$			1.05627e6i			1.57473i
$820$	338186.	−	86759.4i	0.502954	−	0.129030i
$821$	407778.			0.604975			0.302487	−	0.953153i	$-0.402183\pi$
$821$	407778.			0.604975			0.302487	+	0.953153i	$0.402183\pi$
$822$	−20429.2	−	20429.2i	−0.0302348	−	0.0302348i
$823$	−553699.	+	553699.i	−0.817474	+	0.817474i	−0.985741	−	0.168267i	$-0.946183\pi$
$823$	−553699.	+	553699.i	−0.817474	+	0.817474i	0.168267	+	0.985741i	$0.446183\pi$
$824$			410829.i			0.605072i
$825$	7430.93	−	25539.3i	0.0109178	−	0.0375234i
$826$	726154.			1.06431
$827$	−493991.	−	493991.i	−0.722285	−	0.722285i	0.246785	−	0.969070i	$-0.420626\pi$
$827$	−493991.	−	493991.i	−0.722285	−	0.722285i	−0.969070	+	0.246785i	$0.920626\pi$
$828$	50421.7	−	50421.7i	0.0735456	−	0.0735456i
$829$		−	522112.i		−	0.759722i	−0.925044	−	0.379861i	$-0.875972\pi$
$829$		−	522112.i		−	0.759722i	0.925044	−	0.379861i	$-0.124028\pi$
$830$	21478.9	+	83724.2i	0.0311786	+	0.121533i
$831$	57220.3			0.0828606
$832$	−82024.5	−	82024.5i	−0.118494	−	0.118494i
$833$	301381.	−	301381.i	0.434337	−	0.434337i
$834$			1587.84i			0.00228283i
$835$	82998.4	−	140279.i	0.119041	−	0.201196i
$836$	−224138.			−0.320703
$837$	−20959.3	−	20959.3i	−0.0299176	−	0.0299176i
$838$	610848.	−	610848.i	0.869852	−	0.869852i
$839$		−	953794.i		−	1.35497i	−0.735535	−	0.677486i	$-0.763069\pi$
$839$		−	953794.i		−	1.35497i	0.735535	−	0.677486i	$-0.236931\pi$
$840$	12329.8	+	7295.15i	0.0174742	+	0.0103389i
$841$	496815.			0.702430
$842$	177236.	+	177236.i	0.249993	+	0.249993i
$843$	28714.1	−	28714.1i	0.0404054	−	0.0404054i
$844$			126156.i			0.177101i
$845$	551388.	−	141455.i	0.772225	−	0.198109i
$846$	−213174.			−0.297847
$847$	−213837.	−	213837.i	−0.298068	−	0.298068i
$848$	−153428.	+	153428.i	−0.213359	+	0.213359i
$849$		−	15045.1i		−	0.0208727i
$850$	391007.	+	711912.i	0.541186	+	0.985346i
$851$	−155211.			−0.214320
$852$	5438.45	+	5438.45i	0.00749196	+	0.00749196i
$853$	−420757.	+	420757.i	−0.578274	+	0.578274i	−0.934427	−	0.356153i	$-0.884088\pi$
$853$	−420757.	+	420757.i	−0.578274	+	0.578274i	0.356153	+	0.934427i	$0.384088\pi$
$854$			654482.i			0.897392i
$855$	−145073.	−	565490.i	−0.198451	−	0.773558i
$856$	−229712.			−0.313499
$857$	−313462.	−	313462.i	−0.426800	−	0.426800i	0.460737	−	0.887537i	$-0.347585\pi$
$857$	−313462.	−	313462.i	−0.426800	−	0.426800i	−0.887537	+	0.460737i	$0.847585\pi$
$858$	−19283.9	+	19283.9i	−0.0261951	+	0.0261951i
$859$		−	681023.i		−	0.922945i	−0.887155	−	0.461472i	$-0.847321\pi$
$859$		−	681023.i		−	0.922945i	0.887155	−	0.461472i	$-0.152679\pi$
$860$	216907.	−	366602.i	0.293276	−	0.495676i
$861$	44210.6			0.0596376
$862$	−404213.	−	404213.i	−0.543996	−	0.543996i
$863$	−103464.	+	103464.i	−0.138921	+	0.138921i	−0.773147	−	0.634227i	$-0.781319\pi$
$863$	−103464.	+	103464.i	−0.138921	+	0.138921i	0.634227	+	0.773147i	$0.281319\pi$
$864$			12857.3i			0.0172235i
$865$	1.02382e6	+	605764.i	1.36834	+	0.809602i
$866$	−858565.			−1.14482
$867$	−39601.3	−	39601.3i	−0.0526831	−	0.0526831i
$868$	−136200.	+	136200.i	−0.180775	+	0.180775i
$869$			261698.i			0.346546i
$870$	13793.1	−	3538.52i	0.0182231	−	0.00467502i
$871$	−1.55229e6			−2.04615
$872$	−243714.	−	243714.i	−0.320515	−	0.320515i
$873$	203062.	−	203062.i	0.266440	−	0.266440i
$874$		−	90159.6i		−	0.118029i
$875$	28855.7	−	901013.i	0.0376891	−	1.17683i
$876$	7384.15			0.00962260
$877$	−457863.	−	457863.i	−0.595301	−	0.595301i	0.343758	−	0.939058i	$-0.388300\pi$
$877$	−457863.	−	457863.i	−0.595301	−	0.595301i	−0.939058	+	0.343758i	$0.888300\pi$
$878$	−593113.	+	593113.i	−0.769394	+	0.769394i
$879$			66169.5i			0.0856407i
$880$	−38547.0	−	150255.i	−0.0497766	−	0.194028i
$881$	−4747.09			−0.00611612			−0.00305806	−	0.999995i	$-0.500973\pi$
$881$	−4747.09			−0.00611612			−0.00305806	+	0.999995i	$0.500973\pi$
$882$	−149921.	−	149921.i	−0.192719	−	0.192719i
$883$	762640.	−	762640.i	0.978133	−	0.978133i	−0.0216328	−	0.999766i	$-0.506886\pi$
$883$	762640.	−	762640.i	0.978133	−	0.978133i	0.999766	+	0.0216328i	$0.00688648\pi$
$884$		−	832777.i		−	1.06567i
$885$	−24866.6	+	42027.9i	−0.0317490	+	0.0536601i
$886$	149560.			0.190523
$887$	−133855.	−	133855.i	−0.170133	−	0.170133i	0.616905	−	0.787038i	$-0.288386\pi$
$887$	−133855.	−	133855.i	−0.170133	−	0.170133i	−0.787038	+	0.616905i	$0.788386\pi$
$888$	9882.71	−	9882.71i	0.0125329	−	0.0125329i
$889$			154649.i			0.195678i
$890$	403205.	+	238564.i	0.509033	+	0.301179i
$891$	−631556.			−0.795530
$892$	−22015.7	−	22015.7i	−0.0276696	−	0.0276696i
$893$	−190589.	+	190589.i	−0.238999	+	0.238999i
$894$		−	4659.12i		−	0.00582946i
$895$	621758.	−	159508.i	0.776203	−	0.199130i
$896$	83550.4			0.104072
$897$	−7756.96	−	7756.96i	−0.00964066	−	0.00964066i
$898$	−661848.	+	661848.i	−0.820740	+	0.820740i
$899$			191452.i			0.236886i
$900$	354138.	−	194505.i	0.437207	−	0.240129i
$901$	−1.55772e6			−1.91884
$902$	−338491.	−	338491.i	−0.416038	−	0.416038i
$903$	38140.6	−	38140.6i	0.0467748	−	0.0467748i
$904$			81358.8i			0.0995561i
$905$	−248615.	−	969093.i	−0.303549	−	1.18323i
$906$	−12438.9			−0.0151539
$907$	−630401.	−	630401.i	−0.766306	−	0.766306i	0.211148	−	0.977454i	$-0.432280\pi$
$907$	−630401.	−	630401.i	−0.766306	−	0.766306i	−0.977454	+	0.211148i	$0.932280\pi$
$908$	−57998.7	+	57998.7i	−0.0703472	+	0.0703472i
$909$			823475.i			0.996604i
$910$	−470660.	+	795480.i	−0.568361	+	0.960608i
$911$	−147233.			−0.177406			−0.0887032	−	0.996058i	$-0.528272\pi$
$911$	−147233.			−0.177406			−0.0887032	+	0.996058i	$0.528272\pi$
$912$	5740.72	+	5740.72i	0.00690203	+	0.00690203i
$913$	83799.6	−	83799.6i	0.100531	−	0.100531i
$914$			843747.i			1.01000i
$915$	−37879.7	−	22412.2i	−0.0452444	−	0.0267696i
$916$	−245795.			−0.292942
$917$	716875.	+	716875.i	0.852521	+	0.852521i
$918$	−65268.6	+	65268.6i	−0.0774495	+	0.0774495i
$919$			314934.i			0.372897i	0.982465	+	0.186448i	$0.0596977\pi$
$919$			314934.i			0.372897i	−0.982465	+	0.186448i	$0.940302\pi$
$920$	60440.2	−	15505.5i	0.0714086	−	0.0183194i
$921$	−75527.9			−0.0890406
$922$	−443580.	−	443580.i	−0.521807	−	0.521807i
$923$	−350871.	+	350871.i	−0.411855	+	0.411855i
$924$		−	19642.6i		−	0.0230068i
$925$	−844430.	−	245695.i	−0.986916	−	0.287153i
$926$	947891.			1.10544
$927$	1.03744e6	+	1.03744e6i	1.20727	+	1.20727i
$928$	58722.0	−	58722.0i	0.0681875	−	0.0681875i
$929$			41324.8i			0.0478827i	0.999713	+	0.0239414i	$0.00762150\pi$
$929$			41324.8i			0.0478827i	−0.999713	+	0.0239414i	$0.992378\pi$
$930$	−3218.84	−	12547.0i	−0.00372163	−	0.0145068i
$931$	−268075.			−0.309284
$932$	−100032.	−	100032.i	−0.115162	−	0.115162i
$933$	36683.8	−	36683.8i	0.0421416	−	0.0421416i
$934$		−	900620.i		−	1.03240i
$935$	567074.	−	958433.i	0.648659	−	1.09632i
$936$	−414261.			−0.472849
$937$	405441.	+	405441.i	0.461794	+	0.461794i	0.899243	−	0.437449i	$-0.144118\pi$
$937$	405441.	+	405441.i	0.461794	+	0.461794i	−0.437449	+	0.899243i	$0.644118\pi$
$938$	790583.	−	790583.i	0.898549	−	0.898549i
$939$			16603.8i			0.0188311i
$940$	−160542.	−	94987.7i	−0.181691	−	0.107501i
$941$	1.29924e6			1.46727			0.733634	−	0.679545i	$-0.237823\pi$
$941$	1.29924e6			1.46727			0.733634	+	0.679545i	$0.237823\pi$
$942$	−39539.1	−	39539.1i	−0.0445579	−	0.0445579i
$943$	136158.	−	136158.i	0.153116	−	0.153116i
$944$			284794.i			0.319585i
$945$	99233.2	−	25457.6i	0.111120	−	0.0285072i
$946$	−584034.			−0.652613
$947$	202034.	+	202034.i	0.225281	+	0.225281i	0.810718	−	0.585437i	$-0.199077\pi$
$947$	202034.	+	202034.i	0.225281	+	0.225281i	−0.585437	+	0.810718i	$0.699077\pi$
$948$	6702.73	−	6702.73i	0.00745821	−	0.00745821i
$949$			476402.i			0.528982i
$950$	142721.	−	490517.i	0.158139	−	0.543509i
$951$	−21953.8			−0.0242744
$952$	424135.	+	424135.i	0.467983	+	0.467983i
$953$	789666.	−	789666.i	0.869476	−	0.869476i	−0.122938	−	0.992414i	$-0.539232\pi$
$953$	789666.	−	789666.i	0.869476	−	0.869476i	0.992414	+	0.122938i	$0.0392317\pi$
$954$			774879.i			0.851407i
$955$	340958.	+	1.32904e6i	0.373847	+	1.45724i
$956$	68702.1			0.0751717
$957$	−13805.5	−	13805.5i	−0.0150740	−	0.0150740i
$958$	808734.	−	808734.i	0.881201	−	0.881201i
$959$			1.34255e6i			1.45979i
$960$	−2861.12	+	4835.68i	−0.00310451	+	0.00524705i
$961$	−749366.			−0.811423
$962$	637601.	+	637601.i	0.688968	+	0.688968i
$963$	−580075.	+	580075.i	−0.625507	+	0.625507i
$964$		−	291897.i		−	0.314105i
$965$	−379932.	−	224794.i	−0.407992	−	0.241396i
$966$	7901.26			0.00846725
$967$	1.06564e6	+	1.06564e6i	1.13961	+	1.13961i	0.988520	+	0.151089i	$0.0482780\pi$
$967$	1.06564e6	+	1.06564e6i	1.13961	+	1.13961i	0.151089	+	0.988520i	$0.451722\pi$
$968$	83865.6	−	83865.6i	0.0895021	−	0.0895021i
$969$			58284.3i			0.0620732i
$970$	243409.	−	62445.0i	0.258698	−	0.0663673i
$971$	245234.			0.260101			0.130050	−	0.991507i	$-0.458486\pi$
$971$	245234.			0.260101			0.130050	+	0.991507i	$0.458486\pi$
$972$	48720.7	+	48720.7i	0.0515681	+	0.0515681i
$973$	52174.0	−	52174.0i	0.0551098	−	0.0551098i
$974$			377422.i			0.397841i
$975$	−29922.9	−	54481.1i	−0.0314771	−	0.0573109i
$976$	−256684.			−0.269463
$977$	784300.	+	784300.i	0.821662	+	0.821662i	0.986346	−	0.164684i	$-0.0526605\pi$
$977$	784300.	+	784300.i	0.821662	+	0.821662i	−0.164684	+	0.986346i	$0.552661\pi$
$978$	−15675.9	+	15675.9i	−0.0163891	+	0.0163891i
$979$		−	642347.i		−	0.670200i
$980$	−46103.3	−	179709.i	−0.0480042	−	0.187119i
$981$	−1.23087e6			−1.27901
$982$	−668233.	−	668233.i	−0.692955	−	0.692955i
$983$	−850786.	+	850786.i	−0.880468	+	0.880468i	−0.993582	−	0.113114i	$-0.963917\pi$
$983$	−850786.	+	850786.i	−0.880468	+	0.880468i	0.113114	+	0.993582i	$0.463917\pi$
$984$			17339.1i			0.0179076i
$985$	−833306.	+	1.40840e6i	−0.858879	+	1.45162i
$986$	596191.			0.613242
$987$	−16702.5	−	16702.5i	−0.0171454	−	0.0171454i
$988$	−370373.	+	370373.i	−0.379424	+	0.379424i
$989$		−	234928.i		−	0.240183i
$990$	−476768.	−	282089.i	−0.486449	−	0.287816i
$991$	−1.74305e6			−1.77485			−0.887427	−	0.460948i	$-0.847509\pi$
$991$	−1.74305e6			−1.77485			−0.887427	+	0.460948i	$0.847509\pi$
$992$	−53416.8	−	53416.8i	−0.0542819	−	0.0542819i
$993$	−1041.92	+	1041.92i	−0.00105666	+	0.00105666i
$994$		−	357398.i		−	0.361726i
$995$	−291766.	+	74850.7i	−0.294706	+	0.0756049i
$996$	−4292.62			−0.00432717
$997$	−1.16258e6	−	1.16258e6i	−1.16959	−	1.16959i	−0.982306	−	0.187284i	$-0.940032\pi$
$997$	−1.16258e6	−	1.16258e6i	−1.16959	−	1.16959i	−0.187284	−	0.982306i	$-0.559968\pi$
$998$	393843.	−	393843.i	0.395424	−	0.395424i
$999$		−	99943.5i		−	0.100144i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.5.f.b.47.11	✓	44
5.3	odd	4	inner	230.5.f.b.93.11	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.5.f.b.47.11	✓	44	1.1	even	1	trivial
230.5.f.b.93.11	yes	44	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:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	230.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.00000 + 2.00000i) q^{2} +(-0.310392 + 0.310392i) q^{3} +8.00000i q^{4} +(6.21241 + 24.2158i) q^{5} -1.24157 q^{6} +(40.7961 + 40.7961i) q^{7} +(-16.0000 + 16.0000i) q^{8} +80.8073i q^{9} +O(q^{10})\)	\(q+(2.00000 + 2.00000i) q^{2} +(-0.310392 + 0.310392i) q^{3} +8.00000i q^{4} +(6.21241 + 24.2158i) q^{5} -1.24157 q^{6} +(40.7961 + 40.7961i) q^{7} +(-16.0000 + 16.0000i) q^{8} +80.8073i q^{9} +(-36.0068 + 60.8565i) q^{10} +96.9505 q^{11} +(-2.48314 - 2.48314i) q^{12} +(160.204 - 160.204i) q^{13} +163.184i q^{14} +(-9.44469 - 5.58812i) q^{15} -64.0000 q^{16} +(-324.889 - 324.889i) q^{17} +(-161.615 + 161.615i) q^{18} +288.985i q^{19} +(-193.727 + 49.6993i) q^{20} -25.3256 q^{21} +(193.901 + 193.901i) q^{22} +(-77.9968 + 77.9968i) q^{23} -9.93256i q^{24} +(-547.812 + 300.877i) q^{25} +640.817 q^{26} +(-50.2238 - 50.2238i) q^{27} +(-326.369 + 326.369i) q^{28} +458.765i q^{29} +(-7.71314 - 30.0656i) q^{30} +417.319 q^{31} +(-128.000 - 128.000i) q^{32} +(-30.0927 + 30.0927i) q^{33} -1299.56i q^{34} +(-734.469 + 1241.35i) q^{35} -646.459 q^{36} +(994.982 + 994.982i) q^{37} +(-577.970 + 577.970i) q^{38} +99.4523i q^{39} +(-486.852 - 288.055i) q^{40} -1745.69 q^{41} +(-50.6512 - 50.6512i) q^{42} +(-1506.01 + 1506.01i) q^{43} +775.604i q^{44} +(-1956.82 + 502.008i) q^{45} -311.987 q^{46} +(659.512 + 659.512i) q^{47} +(19.8651 - 19.8651i) q^{48} +927.644i q^{49} +(-1697.38 - 493.869i) q^{50} +201.686 q^{51} +(1281.63 + 1281.63i) q^{52} +(2397.30 - 2397.30i) q^{53} -200.895i q^{54} +(602.296 + 2347.74i) q^{55} -1305.48 q^{56} +(-89.6988 - 89.6988i) q^{57} +(-917.531 + 917.531i) q^{58} -4449.90i q^{59} +(44.7050 - 75.5575i) q^{60} +4010.69 q^{61} +(834.638 + 834.638i) q^{62} +(-3296.62 + 3296.62i) q^{63} -512.000i q^{64} +(4874.73 + 2884.22i) q^{65} -120.371 q^{66} +(-4844.72 - 4844.72i) q^{67} +(2599.11 - 2599.11i) q^{68} -48.4192i q^{69} +(-3951.64 + 1013.77i) q^{70} -2190.15 q^{71} +(-1292.92 - 1292.92i) q^{72} +(-1486.86 + 1486.86i) q^{73} +3979.93i q^{74} +(76.6466 - 263.427i) q^{75} -2311.88 q^{76} +(3955.20 + 3955.20i) q^{77} +(-198.905 + 198.905i) q^{78} +2699.30i q^{79} +(-397.594 - 1549.81i) q^{80} -6514.21 q^{81} +(-3491.38 - 3491.38i) q^{82} +(864.355 - 864.355i) q^{83} -202.605i q^{84} +(5849.11 - 9885.80i) q^{85} -6024.04 q^{86} +(-142.397 - 142.397i) q^{87} +(-1551.21 + 1551.21i) q^{88} -6625.51i q^{89} +(-4917.65 - 2909.61i) q^{90} +13071.4 q^{91} +(-623.974 - 623.974i) q^{92} +(-129.533 + 129.533i) q^{93} +2638.05i q^{94} +(-6998.01 + 1795.29i) q^{95} +79.4604 q^{96} +(-2512.91 - 2512.91i) q^{97} +(-1855.29 + 1855.29i) q^{98} +7834.31i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 88 q^{2} + 24 q^{5} - 80 q^{7} - 704 q^{8}+O(q^{10}) \) 44 * q + 88 * q^2 + 24 * q^5 - 80 * q^7 - 704 * q^8	\( 44 q + 88 q^{2} + 24 q^{5} - 80 q^{7} - 704 q^{8} - 136 q^{10} - 632 q^{11} + 500 q^{13} + 12 q^{15} - 2816 q^{16} + 120 q^{17} + 2648 q^{18} - 736 q^{20} - 856 q^{21} - 1264 q^{22} + 2052 q^{25} + 2000 q^{26} + 588 q^{27} + 640 q^{28} - 1704 q^{30} + 3220 q^{31} - 5632 q^{32} - 2884 q^{33} + 720 q^{35} + 10592 q^{36} + 1856 q^{37} - 1696 q^{38} - 1856 q^{40} - 5156 q^{41} - 1712 q^{42} + 960 q^{43} + 460 q^{45} - 1224 q^{47} + 4456 q^{50} + 3640 q^{51} + 4000 q^{52} + 13556 q^{53} + 12980 q^{55} + 2560 q^{56} - 3072 q^{57} - 3112 q^{58} - 6912 q^{60} - 4864 q^{61} + 6440 q^{62} - 13484 q^{63} - 4100 q^{65} - 11536 q^{66} - 1888 q^{67} - 960 q^{68} + 8824 q^{70} - 1060 q^{71} + 21184 q^{72} + 16616 q^{73} - 11044 q^{75} - 6784 q^{76} + 8892 q^{77} - 23152 q^{78} - 1536 q^{80} - 4044 q^{81} - 10312 q^{82} - 27024 q^{83} - 11068 q^{85} + 3840 q^{86} - 8392 q^{87} + 10112 q^{88} - 7184 q^{90} - 54024 q^{91} + 22528 q^{93} - 25968 q^{95} - 3252 q^{97} - 27984 q^{98}+O(q^{100}) \) 44 * q + 88 * q^2 + 24 * q^5 - 80 * q^7 - 704 * q^8 - 136 * q^10 - 632 * q^11 + 500 * q^13 + 12 * q^15 - 2816 * q^16 + 120 * q^17 + 2648 * q^18 - 736 * q^20 - 856 * q^21 - 1264 * q^22 + 2052 * q^25 + 2000 * q^26 + 588 * q^27 + 640 * q^28 - 1704 * q^30 + 3220 * q^31 - 5632 * q^32 - 2884 * q^33 + 720 * q^35 + 10592 * q^36 + 1856 * q^37 - 1696 * q^38 - 1856 * q^40 - 5156 * q^41 - 1712 * q^42 + 960 * q^43 + 460 * q^45 - 1224 * q^47 + 4456 * q^50 + 3640 * q^51 + 4000 * q^52 + 13556 * q^53 + 12980 * q^55 + 2560 * q^56 - 3072 * q^57 - 3112 * q^58 - 6912 * q^60 - 4864 * q^61 + 6440 * q^62 - 13484 * q^63 - 4100 * q^65 - 11536 * q^66 - 1888 * q^67 - 960 * q^68 + 8824 * q^70 - 1060 * q^71 + 21184 * q^72 + 16616 * q^73 - 11044 * q^75 - 6784 * q^76 + 8892 * q^77 - 23152 * q^78 - 1536 * q^80 - 4044 * q^81 - 10312 * q^82 - 27024 * q^83 - 11068 * q^85 + 3840 * q^86 - 8392 * q^87 + 10112 * q^88 - 7184 * q^90 - 54024 * q^91 + 22528 * q^93 - 25968 * q^95 - 3252 * q^97 - 27984 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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