LMFDB - Embedded newform 40.6.f.a.29.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [40,6,Mod(29,40)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(40, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("40.29");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 40 = 2^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	40.f (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.41535279252$
Analytic rank:	$0$
Dimension:	$28$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			29.19
Character	$\chi$	$=$	40.29
Dual form			40.6.f.a.29.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.25299 - 4.62796i) q^{2} -1.29818 q^{3} +(-10.8361 - 30.1095i) q^{4} +(-51.3939 + 21.9924i) q^{5} +(-4.22299 + 6.00795i) q^{6} -170.399i q^{7} +(-174.595 - 47.7971i) q^{8} -241.315 q^{9} +O(q^{10})$	\(q+(3.25299 - 4.62796i) q^{2} -1.29818 q^{3} +(-10.8361 - 30.1095i) q^{4} +(-51.3939 + 21.9924i) q^{5} +(-4.22299 + 6.00795i) q^{6} -170.399i q^{7} +(-174.595 - 47.7971i) q^{8} -241.315 q^{9} +(-65.4039 + 309.390i) q^{10} +39.8166i q^{11} +(14.0672 + 39.0876i) q^{12} +537.234 q^{13} +(-788.600 - 554.307i) q^{14} +(66.7187 - 28.5502i) q^{15} +(-789.160 + 652.536i) q^{16} -1355.83i q^{17} +(-784.995 + 1116.80i) q^{18} +1039.21i q^{19} +(1219.09 + 1309.13i) q^{20} +221.209i q^{21} +(184.270 + 129.523i) q^{22} -1610.62i q^{23} +(226.657 + 62.0494i) q^{24} +(2157.67 - 2260.55i) q^{25} +(1747.62 - 2486.30i) q^{26} +628.730 q^{27} +(-5130.62 + 1846.45i) q^{28} -5910.56i q^{29} +(84.9063 - 401.645i) q^{30} +9611.53 q^{31} +(452.776 + 5774.90i) q^{32} -51.6892i q^{33} +(-6274.71 - 4410.50i) q^{34} +(3747.49 + 8757.46i) q^{35} +(2614.90 + 7265.86i) q^{36} +5295.85 q^{37} +(4809.42 + 3380.54i) q^{38} -697.429 q^{39} +(10024.3 - 1383.29i) q^{40} -12105.1 q^{41} +(1023.75 + 719.592i) q^{42} -19338.2 q^{43} +(1198.86 - 431.455i) q^{44} +(12402.1 - 5307.10i) q^{45} +(-7453.87 - 5239.32i) q^{46} +7894.36i q^{47} +(1024.47 - 847.111i) q^{48} -12228.8 q^{49} +(-3442.89 - 17339.2i) q^{50} +1760.11i q^{51} +(-5821.50 - 16175.8i) q^{52} -18932.1 q^{53} +(2045.25 - 2909.74i) q^{54} +(-875.664 - 2046.33i) q^{55} +(-8144.57 + 29750.8i) q^{56} -1349.09i q^{57} +(-27353.9 - 19227.0i) q^{58} +32322.2i q^{59} +(-1582.60 - 1699.49i) q^{60} -48808.2i q^{61} +(31266.2 - 44481.8i) q^{62} +41119.8i q^{63} +(28198.9 + 16690.3i) q^{64} +(-27610.6 + 11815.1i) q^{65} +(-239.216 - 168.145i) q^{66} +882.245 q^{67} +(-40823.2 + 14691.8i) q^{68} +2090.88i q^{69} +(52719.8 + 11144.8i) q^{70} -8818.78 q^{71} +(42132.4 + 11534.1i) q^{72} +14380.4i q^{73} +(17227.4 - 24509.0i) q^{74} +(-2801.05 + 2934.62i) q^{75} +(31290.1 - 11260.9i) q^{76} +6784.70 q^{77} +(-2268.73 + 3227.68i) q^{78} +49813.9 q^{79} +(26207.2 - 50891.9i) q^{80} +57823.3 q^{81} +(-39377.9 + 56022.1i) q^{82} -13938.9 q^{83} +(6660.49 - 2397.03i) q^{84} +(29817.9 + 69681.2i) q^{85} +(-62906.9 + 89496.2i) q^{86} +7673.00i q^{87} +(1903.12 - 6951.78i) q^{88} +7581.49 q^{89} +(15782.9 - 74660.4i) q^{90} -91544.2i q^{91} +(-48494.8 + 17452.7i) q^{92} -12477.5 q^{93} +(36534.8 + 25680.3i) q^{94} +(-22854.8 - 53409.1i) q^{95} +(-587.787 - 7496.88i) q^{96} -66750.3i q^{97} +(-39780.2 + 56594.3i) q^{98} -9608.33i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 12 q^{4} - 156 q^{6} + 1940 q^{9}+O(q^{10}) $ 28 * q - 12 * q^4 - 156 * q^6 + 1940 * q^9	$ 28 q - 12 q^{4} - 156 q^{6} + 1940 q^{9} - 16 q^{10} - 692 q^{14} - 488 q^{15} + 1560 q^{16} + 2732 q^{20} - 2224 q^{24} + 1556 q^{25} - 9976 q^{26} - 15012 q^{30} + 4368 q^{31} + 13016 q^{34} - 34116 q^{36} + 23360 q^{39} - 22496 q^{40} - 2480 q^{41} + 10712 q^{44} + 58372 q^{46} - 38420 q^{49} + 45624 q^{50} - 3568 q^{54} - 48776 q^{55} + 110944 q^{56} + 111688 q^{60} - 46944 q^{64} + 37200 q^{65} - 136120 q^{66} - 112852 q^{70} - 69232 q^{71} + 34176 q^{74} - 13944 q^{76} - 35984 q^{79} - 47064 q^{80} + 122596 q^{81} - 165688 q^{84} - 73676 q^{86} - 178744 q^{89} + 51496 q^{90} + 314740 q^{94} + 89416 q^{95} - 236176 q^{96}+O(q^{100}) $ 28 * q - 12 * q^4 - 156 * q^6 + 1940 * q^9 - 16 * q^10 - 692 * q^14 - 488 * q^15 + 1560 * q^16 + 2732 * q^20 - 2224 * q^24 + 1556 * q^25 - 9976 * q^26 - 15012 * q^30 + 4368 * q^31 + 13016 * q^34 - 34116 * q^36 + 23360 * q^39 - 22496 * q^40 - 2480 * q^41 + 10712 * q^44 + 58372 * q^46 - 38420 * q^49 + 45624 * q^50 - 3568 * q^54 - 48776 * q^55 + 110944 * q^56 + 111688 * q^60 - 46944 * q^64 + 37200 * q^65 - 136120 * q^66 - 112852 * q^70 - 69232 * q^71 + 34176 * q^74 - 13944 * q^76 - 35984 * q^79 - 47064 * q^80 + 122596 * q^81 - 165688 * q^84 - 73676 * q^86 - 178744 * q^89 + 51496 * q^90 + 314740 * q^94 + 89416 * q^95 - 236176 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/40\mathbb{Z}\right)^\times$.

$n$	$17$	$21$	$31$
$\chi(n)$	$-1$	$-1$	$1$

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 $

$2$	3.25299	−	4.62796i	0.575054	−	0.818116i
$2$	3.25299	−	4.62796i	0.575054	−	0.818116i
$3$	−1.29818			−0.0832785			−0.0416393	−	0.999133i	$-0.513258\pi$
$3$	−1.29818			−0.0832785			−0.0416393	+	0.999133i	$0.513258\pi$
$4$	−10.8361	−	30.1095i	−0.338627	−	0.940921i
$5$	−51.3939	+	21.9924i	−0.919362	+	0.393413i
$5$	−51.3939	+	21.9924i	−0.919362	+	0.393413i
$6$	−4.22299	+	6.00795i	−0.0478896	+	0.0681315i
$7$		−	170.399i		−	1.31438i	−0.753724	−	0.657191i	$-0.771744\pi$
$7$		−	170.399i		−	1.31438i	0.753724	−	0.657191i	$-0.228256\pi$
$8$	−174.595	−	47.7971i	−0.964511	−	0.264044i
$9$	−241.315			−0.993065
$10$	−65.4039	+	309.390i	−0.206825	+	0.978378i
$11$			39.8166i			0.0992161i	0.998769	+	0.0496081i	$0.0157972\pi$
$11$			39.8166i			0.0992161i	−0.998769	+	0.0496081i	$0.984203\pi$
$12$	14.0672	+	39.0876i	0.0282003	+	0.0783585i
$13$	537.234			0.881669			0.440834	−	0.897588i	$-0.354683\pi$
$13$	537.234			0.881669			0.440834	+	0.897588i	$0.354683\pi$
$14$	−788.600	−	554.307i	−1.07532	−	0.755840i
$15$	66.7187	−	28.5502i	0.0765631	−	0.0327628i
$16$	−789.160	+	652.536i	−0.770664	+	0.637242i
$17$		−	1355.83i		−	1.13784i	−0.822392	−	0.568921i	$-0.807361\pi$
$17$		−	1355.83i		−	1.13784i	0.822392	−	0.568921i	$-0.192639\pi$
$18$	−784.995	+	1116.80i	−0.571065	+	0.812442i
$19$			1039.21i			0.660419i	0.943908	+	0.330209i	$0.107119\pi$
$19$			1039.21i			0.660419i	−0.943908	+	0.330209i	$0.892881\pi$
$20$	1219.09	+	1309.13i	0.681491	+	0.731827i
$21$			221.209i			0.109460i
$22$	184.270	+	129.523i	0.0811703	+	0.0570546i
$23$		−	1610.62i		−	0.634852i	−0.948283	−	0.317426i	$-0.897182\pi$
$23$		−	1610.62i		−	0.634852i	0.948283	−	0.317426i	$-0.102818\pi$
$24$	226.657	+	62.0494i	0.0803230	+	0.0219892i
$25$	2157.67	−	2260.55i	0.690453	−	0.723377i
$26$	1747.62	−	2486.30i	0.507007	−	0.721307i
$27$	628.730			0.165980
$28$	−5130.62	+	1846.45i	−1.23673	+	0.445085i
$29$		−	5910.56i		−	1.30507i	−0.757759	−	0.652535i	$-0.773706\pi$
$29$		−	5910.56i		−	1.30507i	0.757759	−	0.652535i	$-0.226294\pi$
$30$	84.9063	−	401.645i	0.0172241	−	0.0814779i
$31$	9611.53			1.79634			0.898169	−	0.439650i	$-0.144898\pi$
$31$	9611.53			1.79634			0.898169	+	0.439650i	$0.144898\pi$
$32$	452.776	+	5774.90i	0.0781643	+	0.996940i
$33$		−	51.6892i		−	0.00826257i
$34$	−6274.71	−	4410.50i	−0.930886	−	0.654320i
$35$	3747.49	+	8757.46i	0.517095	+	1.20839i
$36$	2614.90	+	7265.86i	0.336278	+	0.934395i
$37$	5295.85			0.635963			0.317981	−	0.948097i	$-0.396995\pi$
$37$	5295.85			0.635963			0.317981	+	0.948097i	$0.396995\pi$
$38$	4809.42	+	3380.54i	0.540299	+	0.379776i
$39$	−697.429			−0.0734241
$40$	10024.3	−	1383.29i	0.990613	−	0.136699i
$41$	−12105.1			−1.12463			−0.562315	−	0.826923i	$-0.690089\pi$
$41$	−12105.1			−1.12463			−0.562315	+	0.826923i	$0.690089\pi$
$42$	1023.75	+	719.592i	0.0895508	+	0.0629453i
$43$	−19338.2			−1.59494			−0.797469	−	0.603360i	$-0.793828\pi$
$43$	−19338.2			−1.59494			−0.797469	+	0.603360i	$0.793828\pi$
$44$	1198.86	−	431.455i	0.0933545	−	0.0335972i
$45$	12402.1	−	5307.10i	0.912986	−	0.390684i
$46$	−7453.87	−	5239.32i	−0.519382	−	0.365074i
$47$			7894.36i			0.521282i	0.965436	+	0.260641i	$0.0839338\pi$
$47$			7894.36i			0.521282i	−0.965436	+	0.260641i	$0.916066\pi$
$48$	1024.47	−	847.111i	0.0641798	−	0.0530686i
$49$	−12228.8			−0.727601
$50$	−3442.89	−	17339.2i	−0.194759	−	0.980851i
$51$			1760.11i			0.0947578i
$52$	−5821.50	−	16175.8i	−0.298557	−	0.829581i
$53$	−18932.1			−0.925783			−0.462891	−	0.886415i	$-0.653188\pi$
$53$	−18932.1			−0.925783			−0.462891	+	0.886415i	$0.653188\pi$
$54$	2045.25	−	2909.74i	0.0954471	−	0.135790i
$55$	−875.664	−	2046.33i	−0.0390329	−	0.0912155i
$56$	−8144.57	+	29750.8i	−0.347055	+	1.26774i
$57$		−	1349.09i		−	0.0549987i
$58$	−27353.9	−	19227.0i	−1.06770	−	0.750485i
$59$			32322.2i			1.20885i	0.796663	+	0.604424i	$0.206597\pi$
$59$			32322.2i			1.20885i	−0.796663	+	0.604424i	$0.793403\pi$
$60$	−1582.60	−	1699.49i	−0.0567536	−	0.0609455i
$61$		−	48808.2i		−	1.67945i	−0.543008	−	0.839727i	$-0.682715\pi$
$61$		−	48808.2i		−	1.67945i	0.543008	−	0.839727i	$-0.317285\pi$
$62$	31266.2	−	44481.8i	1.03299	−	1.46961i
$63$			41119.8i			1.30527i
$64$	28198.9	+	16690.3i	0.860561	+	0.509347i
$65$	−27610.6	+	11815.1i	−0.810573	+	0.346860i
$66$	−239.216	−	168.145i	−0.00675974	−	0.00475142i
$67$	882.245			0.0240106			0.0120053	−	0.999928i	$-0.496179\pi$
$67$	882.245			0.0240106			0.0120053	+	0.999928i	$0.496179\pi$
$68$	−40823.2	+	14691.8i	−1.07062	+	0.385304i
$69$			2090.88i			0.0528695i
$70$	52719.8	+	11144.8i	1.28596	+	0.271847i
$71$	−8818.78			−0.207617			−0.103808	−	0.994597i	$-0.533103\pi$
$71$	−8818.78			−0.207617			−0.103808	+	0.994597i	$0.533103\pi$
$72$	42132.4	+	11534.1i	0.957821	+	0.262213i
$73$			14380.4i			0.315837i	0.987452	+	0.157919i	$0.0504784\pi$
$73$			14380.4i			0.315837i	−0.987452	+	0.157919i	$0.949522\pi$
$74$	17227.4	−	24509.0i	0.365713	−	0.520291i
$75$	−2801.05	+	2934.62i	−0.0574999	+	0.0602418i
$76$	31290.1	−	11260.9i	0.621402	−	0.223635i
$77$	6784.70			0.130408
$78$	−2268.73	+	3227.68i	−0.0422228	+	0.0600694i
$79$	49813.9			0.898014			0.449007	−	0.893528i	$-0.351778\pi$
$79$	49813.9			0.898014			0.449007	+	0.893528i	$0.351778\pi$
$80$	26207.2	−	50891.9i	0.457820	−	0.889045i
$81$	57823.3			0.979242
$82$	−39377.9	+	56022.1i	−0.646723	+	0.920078i
$83$	−13938.9			−0.222092			−0.111046	−	0.993815i	$-0.535420\pi$
$83$	−13938.9			−0.222092			−0.111046	+	0.993815i	$0.535420\pi$
$84$	6660.49	−	2397.03i	0.102993	−	0.0370660i
$85$	29817.9	+	69681.2i	0.447641	+	1.04609i
$86$	−62906.9	+	89496.2i	−0.917175	+	1.30484i
$87$			7673.00i			0.108684i
$88$	1903.12	−	6951.78i	0.0261974	−	0.0956950i
$89$	7581.49			0.101456			0.0507282	−	0.998712i	$-0.483846\pi$
$89$	7581.49			0.101456			0.0507282	+	0.998712i	$0.483846\pi$
$90$	15782.9	−	74660.4i	0.205391	−	0.971593i
$91$		−	91544.2i		−	1.15885i
$92$	−48494.8	+	17452.7i	−0.597345	+	0.214978i
$93$	−12477.5			−0.149596
$94$	36534.8	+	25680.3i	0.426469	+	0.299765i
$95$	−22854.8	−	53409.1i	−0.259817	−	0.607164i
$96$	−587.787	−	7496.88i	−0.00650941	−	0.0830238i
$97$		−	66750.3i		−	0.720317i	−0.932891	−	0.360159i	$-0.882723\pi$
$97$		−	66750.3i		−	0.720317i	0.932891	−	0.360159i	$-0.117277\pi$
$98$	−39780.2	+	56594.3i	−0.418409	+	0.595262i
$99$		−	9608.33i		−	0.0985280i
$100$	−91444.7	−	40470.7i	−0.914447	−	0.404707i
$101$		−	66492.6i		−	0.648590i	−0.945956	−	0.324295i	$-0.894873\pi$
$101$		−	66492.6i		−	0.648590i	0.945956	−	0.324295i	$-0.105127\pi$
$102$	8145.73	+	5725.64i	0.0775228	+	0.0544908i
$103$		−	166310.i		−	1.54463i	−0.635237	−	0.772317i	$-0.719098\pi$
$103$		−	166310.i		−	1.54463i	0.635237	−	0.772317i	$-0.280902\pi$
$104$	−93798.5	−	25678.2i	−0.850379	−	0.232800i
$105$	−4864.93	−	11368.8i	−0.0430629	−	0.100633i
$106$	−61586.0	+	87617.0i	−0.532375	+	0.757398i
$107$	121647.			1.02717			0.513583	−	0.858040i	$-0.328318\pi$
$107$	121647.			1.02717			0.513583	+	0.858040i	$0.328318\pi$
$108$	−6812.95	−	18930.7i	−0.0562051	−	0.156174i
$109$			170773.i			1.37674i	0.725359	+	0.688370i	$0.241674\pi$
$109$			170773.i			1.37674i	−0.725359	+	0.688370i	$0.758326\pi$
$110$	−12318.9	−	2604.16i	−0.0970709	−	0.0205204i
$111$	−6874.99			−0.0529621
$112$	111191.	+	134472.i	0.837579	+	1.01295i
$113$		−	3705.12i		−	0.0272964i	−0.999907	−	0.0136482i	$-0.995656\pi$
$113$		−	3705.12i		−	0.0272964i	0.999907	−	0.0136482i	$-0.00434449\pi$
$114$	−6243.52	−	4388.57i	−0.0449953	−	0.0316272i
$115$	35421.4	+	82775.8i	0.249759	+	0.583658i
$116$	−177964.	+	64047.2i	−1.22797	+	0.441931i
$117$	−129643.			−0.875554
$118$	149586.	+	105144.i	0.988977	+	0.695152i
$119$	−231031.			−1.49556
$120$	−13013.4	+	1795.77i	−0.0824968	+	0.0113841i
$121$	159466.			0.990156
$122$	−225883.	−	158773.i	−1.37399	−	0.965777i
$123$	15714.7			0.0936576
$124$	−104151.	−	289398.i	−0.608288	−	1.69021i
$125$	−61175.7	+	163631.i	−0.350190	+	0.936679i
$126$	190301.	+	133762.i	1.06786	+	0.750598i
$127$			77574.6i			0.426786i	0.976966	+	0.213393i	$0.0684515\pi$
$127$			77574.6i			0.426786i	−0.976966	+	0.213393i	$0.931548\pi$
$128$	168973.	−	76209.9i	0.911574	−	0.411137i
$129$	25104.5			0.132824
$130$	−35137.2	+	166215.i	−0.182351	+	0.862605i
$131$		−	330023.i		−	1.68022i	−0.542418	−	0.840109i	$-0.682491\pi$
$131$		−	330023.i		−	1.68022i	0.542418	−	0.840109i	$-0.317509\pi$
$132$	−1556.34	+	560.107i	−0.00777443	+	0.00279793i
$133$	177080.			0.868043
$134$	2869.94	−	4083.00i	0.0138074	−	0.0196434i
$135$	−32312.9	+	13827.3i	−0.152595	+	0.0652985i
$136$	−64804.6	+	236721.i	−0.300440	+	1.09746i
$137$		−	135014.i		−	0.614578i	−0.951616	−	0.307289i	$-0.900578\pi$
$137$		−	135014.i		−	0.614578i	0.951616	−	0.307289i	$-0.0994219\pi$
$138$	9676.49	+	6801.61i	0.0432534	+	0.0304028i
$139$		−	130330.i		−	0.572146i	−0.958208	−	0.286073i	$-0.907650\pi$
$139$		−	130330.i		−	0.572146i	0.958208	−	0.286073i	$-0.0923500\pi$
$140$	223075.	−	207731.i	0.961900	−	0.895739i
$141$		−	10248.3i		−	0.0434116i
$142$	−28687.5	+	40813.0i	−0.119391	+	0.169855i
$143$			21390.8i			0.0874758i
$144$	190436.	−	157466.i	0.765319	−	0.632822i
$145$	129988.	+	303767.i	0.513431	+	1.19983i
$146$	66551.9	+	46779.3i	0.258392	+	0.181623i
$147$	15875.2			0.0605935
$148$	−57386.2	−	159455.i	−0.215354	−	0.598391i
$149$		−	56728.8i		−	0.209333i	−0.994507	−	0.104667i	$-0.966622\pi$
$149$		−	56728.8i		−	0.209333i	0.994507	−	0.104667i	$-0.0333775\pi$
$150$	4469.50	+	22509.4i	0.0162192	+	0.0816839i
$151$	272831.			0.973757			0.486879	−	0.873470i	$-0.338135\pi$
$151$	272831.			0.973757			0.486879	+	0.873470i	$0.338135\pi$
$152$	49671.2	−	181441.i	0.174380	−	0.636981i
$153$			327181.i			1.12995i
$154$	22070.6	−	31399.3i	0.0749915	−	0.106689i
$155$	−493974.	+	211381.i	−1.65148	+	0.706702i
$156$	7557.38	+	20999.2i	0.0248634	+	0.0690863i
$157$	−351466.			−1.13798			−0.568990	−	0.822345i	$-0.692666\pi$
$157$	−351466.			−1.13798			−0.568990	+	0.822345i	$0.692666\pi$
$158$	162044.	−	230537.i	0.516406	−	0.734679i
$159$	24577.4			0.0770979
$160$	−150274.	−	286837.i	−0.464070	−	0.885798i
$161$	−274447.			−0.834438
$162$	188099.	−	267604.i	0.563117	−	0.801133i
$163$	434277.			1.28026			0.640129	−	0.768268i	$-0.278881\pi$
$163$	434277.			1.28026			0.640129	+	0.768268i	$0.278881\pi$
$164$	131172.	+	364479.i	0.380830	+	1.05819i
$165$	1136.77	+	2656.51i	0.00325060	+	0.00759630i
$166$	−45343.1	+	64508.7i	−0.127715	+	0.181697i
$167$			580367.i			1.61032i	0.593059	+	0.805159i	$0.297920\pi$
$167$			580367.i			1.61032i	−0.593059	+	0.805159i	$0.702080\pi$
$168$	10573.2	−	38622.0i	0.0289022	−	0.105575i
$169$	−82672.1			−0.222660
$170$	419480.	+	88676.4i	1.11324	+	0.235334i
$171$		−	250777.i		−	0.655838i
$172$	209549.	+	582261.i	0.540089	+	1.50071i
$173$	243764.			0.619233			0.309617	−	0.950861i	$-0.399799\pi$
$173$	243764.			0.619233			0.309617	+	0.950861i	$0.399799\pi$
$174$	35510.3	+	24960.2i	0.0889163	+	0.0624993i
$175$	−385196.	−	367664.i	−0.950794	−	0.907519i
$176$	−25981.7	−	31421.6i	−0.0632246	−	0.0764623i
$177$		−	41960.2i		−	0.100671i
$178$	24662.5	−	35086.8i	0.0583429	−	0.0830031i
$179$			589838.i			1.37594i	0.725738	+	0.687971i	$0.241498\pi$
$179$			589838.i			1.37594i	−0.725738	+	0.687971i	$0.758502\pi$
$180$	−294184.	−	315913.i	−0.676764	−	0.726751i
$181$		−	306392.i		−	0.695154i	−0.937651	−	0.347577i	$-0.887005\pi$
$181$		−	306392.i		−	0.695154i	0.937651	−	0.347577i	$-0.112995\pi$
$182$	−423663.	−	297793.i	−0.948073	−	0.666401i
$183$			63362.0i			0.139863i
$184$	−76982.7	+	281205.i	−0.167629	+	0.612321i
$185$	−272175.	+	116469.i	−0.584680	+	0.250196i
$186$	−40589.3	+	57745.5i	−0.0860260	+	0.122387i
$187$	53984.4			0.112892
$188$	237695.	−	85543.7i	0.490485	−	0.176520i
$189$		−	107135.i		−	0.218161i
$190$	−321521.	−	67968.4i	−0.646139	−	0.136591i
$191$	−123083.			−0.244127			−0.122064	−	0.992522i	$-0.538951\pi$
$191$	−123083.			−0.244127			−0.122064	+	0.992522i	$0.538951\pi$
$192$	−36607.3	−	21667.0i	−0.0716663	−	0.0424177i
$193$		−	689437.i		−	1.33230i	−0.745819	−	0.666149i	$-0.767941\pi$
$193$		−	689437.i		−	1.33230i	0.745819	−	0.666149i	$-0.232059\pi$
$194$	−308918.	−	217138.i	−0.589303	−	0.414221i
$195$	35843.6	−	15338.2i	0.0675033	−	0.0288860i
$196$	132512.	+	368202.i	0.246385	+	0.684615i
$197$	−70782.9			−0.129946			−0.0649730	−	0.997887i	$-0.520696\pi$
$197$	−70782.9			−0.129946			−0.0649730	+	0.997887i	$0.520696\pi$
$198$	−44467.0	−	31255.8i	−0.0806073	−	0.0566589i
$199$	314584.			0.563123			0.281561	−	0.959543i	$-0.409148\pi$
$199$	314584.			0.563123			0.281561	+	0.959543i	$0.409148\pi$
$200$	−484766.	+	291552.i	−0.856953	+	0.515395i
$201$	−1145.32			−0.00199956
$202$	−307725.	−	216300.i	−0.530622	−	0.372974i
$203$	−1.00715e6			−1.71536
$204$	52996.0	−	19072.7i	0.0891596	−	0.0320875i
$205$	622130.	−	266221.i	1.03394	−	0.442444i
$206$	−769677.	−	541006.i	−1.26369	−	0.888248i
$207$			388665.i			0.630449i
$208$	−423964.	+	350565.i	−0.679470	+	0.561836i
$209$	−41377.8			−0.0655242
$210$	−68439.9	−	14467.9i	−0.107093	−	0.0226391i
$211$			1.09357e6i			1.69098i	0.533989	+	0.845491i	$0.320692\pi$
$211$			1.09357e6i			1.69098i	−0.533989	+	0.845491i	$0.679308\pi$
$212$	205149.	+	570035.i	0.313495	+	0.871088i
$213$	11448.4			0.0172900
$214$	395716.	−	562976.i	0.590675	−	0.840341i
$215$	993863.	−	425293.i	1.46633	−	0.627469i
$216$	−109773.	−	30051.5i	−0.160089	−	0.0438259i
$217$		−	1.63779e6i		−	2.36107i
$218$	790330.	+	555523.i	1.12633	+	0.791700i
$219$		−	18668.4i		−	0.0263025i
$220$	−52125.1	+	48539.9i	−0.0726090	+	0.0676149i
$221$		−	728397.i		−	1.00320i
$222$	−22364.3	+	31817.2i	−0.0304560	+	0.0433291i
$223$		−	917927.i		−	1.23608i	−0.786147	−	0.618039i	$-0.787927\pi$
$223$		−	917927.i		−	1.23608i	0.786147	−	0.618039i	$-0.212073\pi$
$224$	984036.	−	77152.6i	1.31036	−	0.102738i
$225$	−520676.	+	545505.i	−0.685664	+	0.718361i
$226$	−17147.1	−	12052.7i	−0.0223316	−	0.0156969i
$227$	1.20791e6			1.55585			0.777926	−	0.628356i	$-0.216272\pi$
$227$	1.20791e6			1.55585			0.777926	+	0.628356i	$0.216272\pi$
$228$	−40620.3	+	14618.8i	−0.0517494	+	0.0186240i
$229$			323648.i			0.407834i	0.978988	+	0.203917i	$0.0653673\pi$
$229$			323648.i			0.407834i	−0.978988	+	0.203917i	$0.934633\pi$
$230$	498309.	+	105341.i	0.621125	+	0.131303i
$231$	−8807.79			−0.0108602
$232$	−282508.	+	1.03195e6i	−0.344596	+	1.25875i
$233$			1.34719e6i			1.62570i	0.582476	+	0.812848i	$0.302084\pi$
$233$			1.34719e6i			1.62570i	−0.582476	+	0.812848i	$0.697916\pi$
$234$	−421727.	+	599981.i	−0.503491	+	0.716305i
$235$	−173616.	−	405722.i	−0.205079	−	0.479247i
$236$	973206.	−	350246.i	1.13743	−	0.409348i
$237$	−64667.7			−0.0747853
$238$	−751544.	+	1.06920e6i	−0.860027	+	1.22354i
$239$	997494.			1.12958			0.564788	−	0.825236i	$-0.308958\pi$
$239$	997494.			1.12958			0.564788	+	0.825236i	$0.308958\pi$
$240$	−34021.7	+	66067.0i	−0.0381266	+	0.0740384i
$241$	610095.			0.676636			0.338318	−	0.941032i	$-0.390142\pi$
$241$	610095.			0.676636			0.338318	+	0.941032i	$0.390142\pi$
$242$	518741.	−	738001.i	0.569393	−	0.810062i
$243$	−227847.			−0.247529
$244$	−1.46959e6	+	528888.i	−1.58023	+	0.568708i
$245$	628485.	−	268941.i	0.668928	−	0.286247i
$246$	51119.8	−	72727.0i	0.0538581	−	0.0766227i
$247$			558300.i			0.582271i
$248$	−1.67812e6	−	459403.i	−1.73259	−	0.474313i
$249$	18095.2			0.0184955
$250$	558274.	+	815410.i	0.564933	+	0.825137i
$251$			691093.i			0.692392i	0.938162	+	0.346196i	$0.112527\pi$
$251$			691093.i			0.692392i	−0.938162	+	0.346196i	$0.887473\pi$
$252$	1.23809e6	−	445576.i	1.22815	−	0.441998i
$253$	64129.2			0.0629875
$254$	359012.	+	252350.i	0.349161	+	0.245425i
$255$	−38709.2	−	90459.0i	−0.0372789	−	0.0871167i
$256$	196971.	−	1.02991e6i	0.187846	−	0.982198i
$257$		−	755800.i		−	0.713796i	−0.934143	−	0.356898i	$-0.883834\pi$
$257$		−	755800.i		−	0.713796i	0.934143	−	0.356898i	$-0.116166\pi$
$258$	81664.7	−	116183.i	0.0763810	−	0.108665i
$259$		−	902408.i		−	0.835898i
$260$	654936.	+	703311.i	0.600849	+	0.645229i
$261$			1.42631e6i			1.29602i
$262$	−1.52733e6	−	1.07356e6i	−1.37461	−	0.966215i
$263$			316724.i			0.282353i	0.989984	+	0.141176i	$0.0450885\pi$
$263$			316724.i			0.282353i	−0.989984	+	0.141176i	$0.954912\pi$
$264$	−2470.60	+	9024.69i	−0.00218168	+	0.00796934i
$265$	972994.	−	416363.i	0.851130	−	0.364215i
$266$	576041.	−	819521.i	0.499171	−	0.710159i
$267$	−9842.17			−0.00844914
$268$	−9560.05	−	26563.9i	−0.00813061	−	0.0225920i
$269$		−	1.50082e6i		−	1.26458i	−0.774731	−	0.632291i	$-0.782115\pi$
$269$		−	1.50082e6i		−	1.26458i	0.774731	−	0.632291i	$-0.217885\pi$
$270$	−41121.4	+	194523.i	−0.0343288	+	0.162391i
$271$	−660806.			−0.546576			−0.273288	−	0.961932i	$-0.588111\pi$
$271$	−660806.			−0.546576			−0.273288	+	0.961932i	$0.588111\pi$
$272$	884725.	+	1.06996e6i	0.725080	+	0.876894i
$273$			118841.i			0.0965073i
$274$	−624839.	−	439200.i	−0.502796	−	0.353415i
$275$	90007.5	+	85910.8i	0.0717707	+	0.0685040i
$276$	62955.1	−	22656.8i	0.0497460	−	0.0179030i
$277$	−1.57567e6			−1.23386			−0.616931	−	0.787017i	$-0.711624\pi$
$277$	−1.57567e6			−1.23386			−0.616931	+	0.787017i	$0.711624\pi$
$278$	−603161.	−	423962.i	−0.468082	−	0.329015i
$279$	−2.31940e6			−1.78388
$280$	−235712.	−	1.70813e6i	−0.179674	−	1.30204i
$281$	−1.45729e6			−1.10098			−0.550491	−	0.834841i	$-0.685560\pi$
$281$	−1.45729e6			−1.10098			−0.550491	+	0.834841i	$0.685560\pi$
$282$	−47428.9	−	33337.8i	−0.0355157	−	0.0249640i
$283$	−1.38341e6			−1.02680			−0.513400	−	0.858149i	$-0.671614\pi$
$283$	−1.38341e6			−1.02680			−0.513400	+	0.858149i	$0.671614\pi$
$284$	95560.8	+	265529.i	0.0703046	+	0.195351i
$285$	29669.7	+	69334.8i	0.0216372	+	0.0505637i
$286$	98996.0	+	69584.3i	0.0715653	+	0.0503033i
$287$			2.06270e6i			1.47819i
$288$	−109262.	−	1.39357e6i	−0.0776222	−	0.990026i
$289$	−418409.			−0.294684
$290$	1.82867e6	+	386574.i	1.27685	+	0.269921i
$291$			86654.2i			0.0599870i
$292$	432986.	−	155827.i	0.297178	−	0.106951i
$293$	−544523.			−0.370551			−0.185275	−	0.982687i	$-0.559318\pi$
$293$	−544523.			−0.370551			−0.185275	+	0.982687i	$0.559318\pi$
$294$	51642.0	−	73469.9i	0.0348445	−	0.0495725i
$295$	−710845.	−	1.66117e6i	−0.475576	−	1.11137i
$296$	−924630.	−	253126.i	−0.613393	−	0.167922i
$297$			25033.9i			0.0164678i
$298$	−262539.	−	184538.i	−0.171259	−	0.120378i
$299$		−	865278.i		−	0.559729i
$300$	118712.	+	52538.4i	0.0761538	+	0.0337034i
$301$			3.29520e6i			2.09636i
$302$	887516.	−	1.26265e6i	0.559963	−	0.796646i
$303$			86319.7i			0.0540136i
$304$	−678121.	−	820103.i	−0.420846	−	0.508961i
$305$	1.07341e6	+	2.50844e6i	0.660719	+	1.54403i
$306$	1.51418e6	+	1.06432e6i	0.924430	+	0.649782i
$307$	2.70567e6			1.63843			0.819216	−	0.573485i	$-0.194409\pi$
$307$	2.70567e6			1.63843			0.819216	+	0.573485i	$0.194409\pi$
$308$	−73519.4	−	204284.i	−0.0441596	−	0.122704i
$309$			215901.i			0.128635i
$310$	−628631.	+	2.97371e6i	−0.371528	+	1.75750i
$311$	−309689.			−0.181562			−0.0907810	−	0.995871i	$-0.528936\pi$
$311$	−309689.			−0.181562			−0.0907810	+	0.995871i	$0.528936\pi$
$312$	121768.	+	33335.1i	0.0708183	+	0.0193872i
$313$			1.89714e6i			1.09456i	0.836950	+	0.547279i	$0.184336\pi$
$313$			1.89714e6i			1.09456i	−0.836950	+	0.547279i	$0.815664\pi$
$314$	−1.14332e6	+	1.62657e6i	−0.654399	+	0.930999i
$315$	−904324.	−	2.11330e6i	−0.513508	−	1.20001i
$316$	−539786.	−	1.49987e6i	−0.304091	−	0.844960i
$317$	−546064.			−0.305207			−0.152604	−	0.988287i	$-0.548766\pi$
$317$	−546064.			−0.305207			−0.152604	+	0.988287i	$0.548766\pi$
$318$	79950.0	−	113743.i	0.0443354	−	0.0630750i
$319$	235338.			0.129484
$320$	−1.81631e6	−	237616.i	−0.991551	−	0.129718i
$321$	−157920.			−0.0855409
$322$	−892775.	+	1.27013e6i	−0.479846	+	0.682667i
$323$	1.40899e6			0.751452
$324$	−626576.	−	1.74103e6i	−0.331597	−	0.921389i
$325$	1.15917e6	−	1.21445e6i	0.608751	−	0.637779i
$326$	1.41270e6	−	2.00981e6i	0.736217	−	1.04740i
$327$		−	221694.i		−	0.114653i
$328$	2.11350e6	+	578590.i	1.08472	+	0.296952i
$329$	1.34519e6			0.685163
$330$	15992.1	+	3380.68i	0.00808392	+	0.00170891i
$331$		−	1.57476e6i		−	0.790029i	−0.918675	−	0.395015i	$-0.870740\pi$
$331$		−	1.57476e6i		−	0.790029i	0.918675	−	0.395015i	$-0.129260\pi$
$332$	151043.	+	419693.i	0.0752063	+	0.208971i
$333$	−1.27797e6			−0.631552
$334$	2.68592e6	+	1.88793e6i	1.31743	+	0.926020i
$335$	−45342.0	+	19402.7i	−0.0220744	+	0.00944606i
$336$	−144347.	−	174569.i	−0.0697524	−	0.0843568i
$337$			77460.4i			0.0371540i	0.999827	+	0.0185770i	$0.00591358\pi$
$337$			77460.4i			0.0371540i	−0.999827	+	0.0185770i	$0.994086\pi$
$338$	−268932.	+	382603.i	−0.128041	+	0.182162i
$339$			4809.92i			0.00227321i
$340$	1.77496e6	−	1.65287e6i	0.832703	−	0.775429i
$341$			382698.i			0.178226i
$342$	−1.16058e6	−	815775.i	−0.536552	−	0.377142i
$343$		−	780123.i		−	0.358037i
$344$	3.37635e6	+	924308.i	1.53833	+	0.421134i
$345$	−45983.4	−	107458.i	−0.0207995	−	0.0486062i
$346$	792963.	−	1.12813e6i	0.356092	−	0.506605i
$347$	−2.74014e6			−1.22165			−0.610827	−	0.791764i	$-0.709163\pi$
$347$	−2.74014e6			−1.22165			−0.610827	+	0.791764i	$0.709163\pi$
$348$	231030.	−	83145.0i	0.102263	−	0.0368034i
$349$			2.65302e6i			1.16594i	0.812493	+	0.582972i	$0.198110\pi$
$349$			2.65302e6i			1.16594i	−0.812493	+	0.582972i	$0.801890\pi$
$350$	−2.95457e6	+	586664.i	−1.28921	+	0.255988i
$351$	337775.			0.146339
$352$	−229937.	+	18028.0i	−0.0989126	+	0.00775516i
$353$		−	2.88565e6i		−	1.23256i	−0.787528	−	0.616279i	$-0.788640\pi$
$353$		−	2.88565e6i		−	1.23256i	0.787528	−	0.616279i	$-0.211360\pi$
$354$	−194190.	−	136496.i	−0.0823606	−	0.0578913i
$355$	453232.	−	193947.i	0.190875	−	0.0816792i
$356$	−82153.4	−	228275.i	−0.0343559	−	0.0954625i
$357$	299921.			0.124548
$358$	2.72975e6	+	1.91874e6i	1.12568	+	0.791241i
$359$	1.66246e6			0.680794			0.340397	−	0.940282i	$-0.389439\pi$
$359$	1.66246e6			0.680794			0.340397	+	0.940282i	$0.389439\pi$
$360$	−2.41901e6	+	333809.i	−0.983742	+	0.135751i
$361$	1.39614e6			0.563847
$362$	−1.41797e6	−	996692.i	−0.568716	−	0.399751i
$363$	−207016.			−0.0824588
$364$	−2.75635e6	+	991977.i	−1.09039	+	0.392417i
$365$	−316260.	−	739064.i	−0.124254	−	0.290369i
$366$	293237.	+	206116.i	0.114424	+	0.0804285i
$367$		−	183532.i		−	0.0711291i	−0.999367	−	0.0355645i	$-0.988677\pi$
$367$		−	183532.i		−	0.0711291i	0.999367	−	0.0355645i	$-0.0113229\pi$
$368$	1.05098e6	+	1.27103e6i	0.404554	+	0.489257i
$369$	2.92115e6			1.11683
$370$	−346370.	+	1.63849e6i	−0.131533	+	0.622212i
$371$			3.22601e6i			1.21683i
$372$	135207.	+	375692.i	0.0506573	+	0.140758i
$373$	2.57701e6			0.959056			0.479528	−	0.877527i	$-0.340808\pi$
$373$	2.57701e6			0.959056			0.479528	+	0.877527i	$0.340808\pi$
$374$	175611.	−	249838.i	0.0649191	−	0.0923589i
$375$	79417.3	−	212423.i	0.0291633	−	0.0780052i
$376$	377328.	−	1.37832e6i	0.137641	−	0.502782i
$377$		−	3.17536e6i		−	1.15064i
$378$	−495816.	−	348509.i	−0.178481	−	0.125454i
$379$		−	1.87753e6i		−	0.671412i	−0.941967	−	0.335706i	$-0.891025\pi$
$379$		−	1.87753e6i		−	0.671412i	0.941967	−	0.335706i	$-0.108975\pi$
$380$	−1.36046e6	+	1.26689e6i	−0.483312	+	0.450069i
$381$		−	100706.i		−	0.0355421i
$382$	−400390.	+	569625.i	−0.140386	+	0.199724i
$383$		−	1.41226e6i		−	0.491945i	−0.969277	−	0.245973i	$-0.920893\pi$
$383$		−	1.41226e6i		−	0.491945i	0.969277	−	0.245973i	$-0.0791073\pi$
$384$	−219358.	+	98934.5i	−0.0759145	+	0.0342389i
$385$	−348692.	+	149212.i	−0.119892	+	0.0513041i
$386$	−3.19069e6	−	2.24273e6i	−1.08997	−	0.766143i
$387$	4.66658e6			1.58388
$388$	−2.00982e6	+	723310.i	−0.677762	+	0.243919i
$389$		−	2.90646e6i		−	0.973846i	−0.873445	−	0.486923i	$-0.838119\pi$
$389$		−	2.90646e6i		−	0.973846i	0.873445	−	0.486923i	$-0.161881\pi$
$390$	45614.6	−	215778.i	0.0151860	−	0.0718365i
$391$	−2.18372e6			−0.722361
$392$	2.13509e6	+	584500.i	0.701779	+	0.192119i
$393$			428430.i			0.139926i
$394$	−230256.	+	327581.i	−0.0747259	+	0.106311i
$395$	−2.56013e6	+	1.09553e6i	−0.825600	+	0.353290i
$396$	−289302.	+	104116.i	−0.0927071	+	0.0333642i
$397$	−2.30169e6			−0.732943			−0.366472	−	0.930429i	$-0.619434\pi$
$397$	−2.30169e6			−0.732943			−0.366472	+	0.930429i	$0.619434\pi$
$398$	1.02334e6	−	1.45588e6i	0.323826	−	0.460700i
$399$	−229883.			−0.0722893
$400$	−227651.	+	3.19189e6i	−0.0711409	+	0.997466i
$401$	−2.58744e6			−0.803544			−0.401772	−	0.915740i	$-0.631606\pi$
$401$	−2.58744e6			−0.803544			−0.401772	+	0.915740i	$0.631606\pi$
$402$	−3725.71	+	5300.48i	−0.00114986	+	0.00163587i
$403$	5.16364e6			1.58378
$404$	−2.00206e6	+	720518.i	−0.610272	+	0.219630i
$405$	−2.97176e6	+	1.27167e6i	−0.900278	+	0.385246i
$406$	−3.27626e6	+	4.66107e6i	−0.986424	+	1.40336i
$407$			210863.i			0.0630978i
$408$	84128.3	−	307307.i	0.0250202	−	0.0913949i
$409$	−3.17301e6			−0.937916			−0.468958	−	0.883221i	$-0.655370\pi$
$409$	−3.17301e6			−0.937916			−0.468958	+	0.883221i	$0.655370\pi$
$410$	791723.	−	3.74521e6i	0.232602	−	1.10031i
$411$			175273.i			0.0511812i
$412$	−5.00751e6	+	1.80215e6i	−1.45338	+	0.523054i
$413$	5.50768e6			1.58889
$414$	1.79873e6	+	1.26433e6i	0.515780	+	0.362542i
$415$	716374.	−	306550.i	0.204183	−	0.0873738i
$416$	243247.	+	3.10247e6i	0.0689151	+	0.878971i
$417$			169192.i			0.0476475i
$418$	−134602.	+	191495.i	−0.0376799	+	0.0536064i
$419$			6.16028e6i			1.71422i	0.515137	+	0.857108i	$0.327741\pi$
$419$			6.16028e6i			1.71422i	−0.515137	+	0.857108i	$0.672259\pi$
$420$	−289592.	+	269673.i	−0.0801056	+	0.0745959i
$421$		−	2.93941e6i		−	0.808268i	−0.914700	−	0.404134i	$-0.867573\pi$
$421$		−	2.93941e6i		−	0.808268i	0.914700	−	0.404134i	$-0.132427\pi$
$422$	5.06098e6	+	3.55737e6i	1.38342	+	0.972406i
$423$		−	1.90503e6i		−	0.517666i
$424$	3.30545e6	+	904900.i	0.892927	+	0.244448i
$425$	−3.06492e6	−	2.92542e6i	−0.823089	−	0.785626i
$426$	37241.6	−	52982.8i	0.00994270	−	0.0141453i
$427$	−8.31687e6			−2.20745
$428$	−1.31817e6	−	3.66271e6i	−0.347826	−	0.966482i
$429$		−	27769.2i		−	0.00728485i
$430$	1.26479e6	−	5.98304e6i	0.329874	−	1.56045i
$431$	2.60556e6			0.675629			0.337815	−	0.941213i	$-0.390312\pi$
$431$	2.60556e6			0.675629			0.337815	+	0.941213i	$0.390312\pi$
$432$	−496168.	+	410268.i	−0.127914	+	0.105769i
$433$			525118.i			0.134597i	0.997733	+	0.0672987i	$0.0214381\pi$
$433$			525118.i			0.134597i	−0.997733	+	0.0672987i	$0.978562\pi$
$434$	−7.57964e6	−	5.32773e6i	−1.93163	−	1.35774i
$435$	−168748.	−	394345.i	−0.0427578	−	0.0999202i
$436$	5.14188e6	−	1.85050e6i	1.29540	−	0.466201i
$437$	1.67377e6			0.419268
$438$	−86396.6	−	60728.2i	−0.0215185	−	0.0151253i
$439$	3.48971e6			0.864228			0.432114	−	0.901819i	$-0.357768\pi$
$439$	3.48971e6			0.864228			0.432114	+	0.901819i	$0.357768\pi$
$440$	55078.0	+	399133.i	0.0135627	+	0.0982847i
$441$	2.95099e6			0.722555
$442$	−3.37099e6	−	2.36947e6i	−0.820733	−	0.576894i
$443$	−5.36353e6			−1.29850			−0.649250	−	0.760575i	$-0.724917\pi$
$443$	−5.36353e6			−1.29850			−0.649250	+	0.760575i	$0.724917\pi$
$444$	74497.8	+	207002.i	0.0179344	+	0.0498331i
$445$	−389642.	+	166735.i	−0.0932752	+	0.0399143i
$446$	−4.24813e6	−	2.98601e6i	−1.01126	−	0.710811i
$447$			73644.4i			0.0174330i
$448$	2.84400e6	−	4.80506e6i	0.669476	−	1.13111i
$449$	−5.64299e6			−1.32097			−0.660486	−	0.750838i	$-0.729650\pi$
$449$	−5.64299e6			−1.32097			−0.660486	+	0.750838i	$0.729650\pi$
$450$	830819.	+	4.18419e6i	0.193408	+	0.974049i
$451$		−	481985.i		−	0.111581i
$452$	−111559.	+	40148.8i	−0.0256838	+	0.00924329i
$453$	−354184.			−0.0810931
$454$	3.92931e6	−	5.59014e6i	0.894698	−	1.27287i
$455$	2.01328e6	+	4.70481e6i	0.455906	+	1.06540i
$456$	−64482.4	+	235544.i	−0.0145221	+	0.0530468i
$457$			6.54027e6i			1.46489i	0.680825	+	0.732446i	$0.261621\pi$
$457$			6.54027e6i			1.46489i	−0.680825	+	0.732446i	$0.738379\pi$
$458$	1.49783e6	+	1.05282e6i	0.333656	+	0.234527i
$459$		−	852448.i		−	0.188858i
$460$	2.10851e6	−	1.96348e6i	0.464601	−	0.432645i
$461$		−	7.92791e6i		−	1.73743i	−0.495315	−	0.868713i	$-0.664947\pi$
$461$		−	7.92791e6i		−	1.73743i	0.495315	−	0.868713i	$-0.335053\pi$
$462$	−28651.7	+	40762.1i	−0.00624519	+	0.00888488i
$463$			5.43590e6i			1.17847i	0.807961	+	0.589235i	$0.200571\pi$
$463$			5.43590e6i			1.17847i	−0.807961	+	0.589235i	$0.799429\pi$
$464$	3.85685e6	+	4.66438e6i	0.831645	+	1.00577i
$465$	641269.	−	274411.i	0.137533	−	0.0588531i
$466$	6.23475e6	+	4.38240e6i	1.33001	+	0.934862i
$467$	1.47407e6			0.312771			0.156386	−	0.987696i	$-0.450016\pi$
$467$	1.47407e6			0.312771			0.156386	+	0.987696i	$0.450016\pi$
$468$	1.40481e6	+	3.90347e6i	0.296486	+	0.823827i
$469$		−	150334.i		−	0.0315590i
$470$	−2.44244e6	−	516322.i	−0.510011	−	0.107814i
$471$	456268.			0.0947692
$472$	1.54491e6	−	5.64330e6i	0.319189	−	1.16595i
$473$		−	769979.i		−	0.158244i
$474$	−210364.	+	299279.i	−0.0430056	+	0.0611830i
$475$	2.34919e6	+	2.24227e6i	0.477732	+	0.455988i
$476$	2.50347e6	+	6.95623e6i	0.506436	+	1.40720i
$477$	4.56859e6			0.919362
$478$	3.24484e6	−	4.61636e6i	0.649567	−	0.924124i
$479$	−4.13083e6			−0.822618			−0.411309	−	0.911496i	$-0.634928\pi$
$479$	−4.13083e6			−0.822618			−0.411309	+	0.911496i	$0.634928\pi$
$480$	195083.	+	372367.i	0.0386471	+	0.0737680i
$481$	2.84512e6			0.560709
$482$	1.98464e6	−	2.82350e6i	0.389102	−	0.553566i
$483$	356283.			0.0694908
$484$	−1.72798e6	−	4.80143e6i	−0.335293	−	0.931659i
$485$	1.46800e6	+	3.43056e6i	0.283382	+	0.662232i
$486$	−741184.	+	1.05446e6i	−0.142343	+	0.202508i
$487$			2.24605e6i			0.429138i	0.976709	+	0.214569i	$0.0688347\pi$
$487$			2.24605e6i			0.429138i	−0.976709	+	0.214569i	$0.931165\pi$
$488$	−2.33289e6	+	8.52167e6i	−0.443450	+	1.61985i
$489$	−563771.			−0.106618
$490$	799810.	−	3.78347e6i	0.150486	−	0.711868i
$491$		−	578316.i		−	0.108258i	−0.998534	−	0.0541292i	$-0.982762\pi$
$491$		−	578316.i		−	0.108258i	0.998534	−	0.0541292i	$-0.0172383\pi$
$492$	−170285.	−	473161.i	−0.0317150	−	0.0881244i
$493$	−8.01370e6			−1.48496
$494$	2.58379e6	+	1.81615e6i	0.476365	+	0.334837i
$495$	211311.	+	493809.i	0.0387622	+	0.0905829i
$496$	−7.58503e6	+	6.27186e6i	−1.38437	+	1.14470i
$497$			1.50271e6i			0.272888i
$498$	58863.7	−	83744.1i	0.0106359	−	0.0151315i
$499$		−	307235.i		−	0.0552357i	−0.999619	−	0.0276178i	$-0.991208\pi$
$499$		−	307235.i		−	0.0552357i	0.999619	−	0.0276178i	$-0.00879215\pi$
$500$	5.58975e6	+	68853.6i	0.999924	+	0.0123169i
$501$		−	753424.i		−	0.134105i
$502$	3.19835e6	+	2.24812e6i	0.566457	+	0.398162i
$503$			3.87678e6i			0.683206i	0.939844	+	0.341603i	$0.110970\pi$
$503$			3.87678e6i			0.683206i	−0.939844	+	0.341603i	$0.889030\pi$
$504$	1.96541e6	−	7.17931e6i	0.344648	−	1.25894i
$505$	1.46234e6	+	3.41732e6i	0.255164	+	0.596289i
$506$	208612.	−	296787.i	0.0362212	−	0.0515311i
$507$	107324.			0.0185428
$508$	2.33573e6	−	840603.i	0.401572	−	0.144521i
$509$		−	4.90268e6i		−	0.838762i	−0.907810	−	0.419381i	$-0.862247\pi$
$509$		−	4.90268e6i		−	0.838762i	0.907810	−	0.419381i	$-0.137753\pi$
$510$	−544562.	−	115118.i	−0.0927089	−	0.0195983i
$511$	2.45040e6			0.415131
$512$	−4.12564e6	−	4.26186e6i	−0.695531	−	0.718497i
$513$			653382.i			0.109616i
$514$	−3.49781e6	−	2.45861e6i	−0.583967	−	0.410471i
$515$	3.65757e6	+	8.54733e6i	0.607679	+	1.42008i
$516$	−272033.	−	755882.i	−0.0449778	−	0.124977i
$517$	−314327.			−0.0517195
$518$	−4.17631e6	−	2.93553e6i	−0.683862	−	0.480686i
$519$	−316451.			−0.0515689
$520$	5.38540e6	−	743152.i	0.873392	−	0.120523i
$521$	−5.57462e6			−0.899749			−0.449874	−	0.893092i	$-0.648531\pi$
$521$	−5.57462e6			−0.899749			−0.449874	+	0.893092i	$0.648531\pi$
$522$	6.60089e6	+	4.63976e6i	1.06029	+	0.745280i
$523$	−1.23492e6			−0.197417			−0.0987087	−	0.995116i	$-0.531471\pi$
$523$	−1.23492e6			−0.197417			−0.0987087	+	0.995116i	$0.531471\pi$
$524$	−9.93681e6	+	3.57614e6i	−1.58095	+	0.568967i
$525$	500055.	+	477295.i	0.0791808	+	0.0755769i
$526$	1.46579e6	+	1.03030e6i	0.230997	+	0.162368i
$527$		−	1.30316e7i		−	2.04395i
$528$	33729.1	+	40791.1i	0.00526526	+	0.00636767i
$529$	3.84226e6			0.596963
$530$	1.23823e6	−	5.85741e6i	0.191475	−	0.905766i
$531$		−	7.79983e6i		−	1.20046i
$532$	−1.91885e6	−	5.33179e6i	−0.293942	−	0.816759i
$533$	−6.50329e6			−0.991552
$534$	−32016.5	+	45549.2i	−0.00485871	+	0.00691238i
$535$	−6.25189e6	+	2.67531e6i	−0.944337	+	0.404100i
$536$	−154036.	−	42168.7i	−0.0231584	−	0.00633985i
$537$		−	765718.i		−	0.114586i
$538$	−6.94572e6	−	4.88215e6i	−1.03457	−	0.727203i
$539$		−	486908.i		−	0.0721897i
$540$	766476.	+	823090.i	0.113113	+	0.121468i
$541$			2.07857e6i			0.305332i	0.988278	+	0.152666i	$0.0487858\pi$
$541$			2.07857e6i			0.305332i	−0.988278	+	0.152666i	$0.951214\pi$
$542$	−2.14960e6	+	3.05818e6i	−0.314310	+	0.447162i
$543$			397753.i			0.0578914i
$544$	7.82976e6	−	613886.i	1.13436	−	0.0889386i
$545$	−3.75571e6	−	8.77668e6i	−0.541627	−	1.26572i
$546$	549992.	+	386590.i	0.0789542	+	0.0554969i
$547$	−6.52487e6			−0.932403			−0.466201	−	0.884679i	$-0.654378\pi$
$547$	−6.52487e6			−0.932403			−0.466201	+	0.884679i	$0.654378\pi$
$548$	−4.06520e6	+	1.46302e6i	−0.578269	+	0.208113i
$549$			1.17781e7i			1.66781i
$550$	690386.	−	137084.i	0.0973162	−	0.0193232i
$551$	6.14232e6			0.861893
$552$	99937.8	−	365056.i	0.0139599	−	0.0509932i
$553$		−	8.48824e6i		−	1.18033i
$554$	−5.12566e6	+	7.29216e6i	−0.709537	+	1.00944i
$555$	353333.	−	151198.i	0.0486913	−	0.0208359i
$556$	−3.92416e6	+	1.41226e6i	−0.538344	+	0.193744i
$557$	1.09214e7			1.49156			0.745778	−	0.666194i	$-0.232078\pi$
$557$	1.09214e7			1.49156			0.745778	+	0.666194i	$0.232078\pi$
$558$	−7.54500e6	+	1.07341e7i	−1.02583	+	1.45942i
$559$	−1.03891e7			−1.40621
$560$	−8.67192e6	−	4.46567e6i	−1.16854	−	0.601751i
$561$	−70081.7			−0.00940150
$562$	−4.74056e6	+	6.74428e6i	−0.633124	+	0.900731i
$563$	3.64784e6			0.485025			0.242513	−	0.970148i	$-0.422028\pi$
$563$	3.64784e6			0.485025			0.242513	+	0.970148i	$0.422028\pi$
$564$	−308572.	+	111052.i	−0.0408469	+	0.0147003i
$565$	81484.5	+	190420.i	0.0107388	+	0.0250953i
$566$	−4.50024e6	+	6.40239e6i	−0.590466	+	0.840042i
$567$		−	9.85302e6i		−	1.28710i
$568$	1.53972e6	+	421512.i	0.200249	+	0.0548200i
$569$	7.78255e6			1.00772			0.503861	−	0.863784i	$-0.331912\pi$
$569$	7.78255e6			1.00772			0.503861	+	0.863784i	$0.331912\pi$
$570$	417394.	+	88235.5i	0.0538095	+	0.0113751i
$571$		−	1.52835e7i		−	1.96170i	−0.194753	−	0.980852i	$-0.562391\pi$
$571$		−	1.52835e7i		−	1.96170i	0.194753	−	0.980852i	$-0.437609\pi$
$572$	644067.	−	231792.i	0.0823078	−	0.0296216i
$573$	159785.			0.0203306
$574$	9.54610e6	+	6.70995e6i	1.20933	+	0.850041i
$575$	−3.64088e6	−	3.47517e6i	−0.459237	−	0.438335i
$576$	−6.80480e6	−	4.02761e6i	−0.854593	−	0.505814i
$577$			1.01412e7i			1.26809i	0.773296	+	0.634046i	$0.218607\pi$
$577$			1.01412e7i			1.26809i	−0.773296	+	0.634046i	$0.781393\pi$
$578$	−1.36108e6	+	1.93638e6i	−0.169459	+	0.241085i
$579$			895016.i			0.110952i
$580$	7.73770e6	−	7.20549e6i	0.955085	−	0.889393i
$581$			2.37517e6i			0.291914i
$582$	401032.	+	281886.i	0.0490763	+	0.0344957i
$583$		−	753811.i		−	0.0918526i
$584$	687341.	−	2.51075e6i	0.0833950	−	0.304629i
$585$	6.66284e6	−	2.85116e6i	0.804951	−	0.344454i
$586$	−1.77133e6	+	2.52003e6i	−0.213086	+	0.303153i
$587$	3.15239e6			0.377612			0.188806	−	0.982014i	$-0.439538\pi$
$587$	3.15239e6			0.377612			0.188806	+	0.982014i	$0.439538\pi$
$588$	−172025.	−	477994.i	−0.0205186	−	0.0570137i
$589$			9.98839e6i			1.18634i
$590$	−1.00002e7	−	2.11400e6i	−1.18271	−	0.250020i
$591$	91889.3			0.0108217
$592$	−4.17928e6	+	3.45573e6i	−0.490114	+	0.405262i
$593$			2.82025e6i			0.329345i	0.986348	+	0.164673i	$0.0526568\pi$
$593$			2.82025e6i			0.329345i	−0.986348	+	0.164673i	$0.947343\pi$
$594$	115856.	+	81435.0i	0.0134726	+	0.00946989i
$595$	1.18736e7	−	5.08094e6i	1.37496	−	0.588372i
$596$	−1.70807e6	+	614716.i	−0.196966	+	0.0708858i
$597$	−408387.			−0.0468961
$598$	−4.00447e6	−	2.81475e6i	−0.457923	−	0.321874i
$599$	1.25796e7			1.43252			0.716261	−	0.697833i	$-0.245852\pi$
$599$	1.25796e7			1.43252			0.716261	+	0.697833i	$0.245852\pi$
$600$	629315.	−	378488.i	0.0713658	−	0.0429214i
$601$	3.63021e6			0.409964			0.204982	−	0.978766i	$-0.434286\pi$
$601$	3.63021e6			0.409964			0.204982	+	0.978766i	$0.434286\pi$
$602$	1.52501e7	+	1.07193e7i	1.71506	+	1.20552i
$603$	−212899.			−0.0238440
$604$	−2.95641e6	−	8.21478e6i	−0.329740	−	0.916228i
$605$	−8.19556e6	+	3.50704e6i	−0.910312	+	0.389540i
$606$	399484.	+	280797.i	0.0441894	+	0.0310607i
$607$		−	322555.i		−	0.0355331i	−0.999842	−	0.0177665i	$-0.994344\pi$
$607$		−	322555.i		−	0.0355331i	0.999842	−	0.0177665i	$-0.00565556\pi$
$608$	−6.00133e6	+	470530.i	−0.658398	+	0.0516212i
$609$	1.30747e6			0.142853
$610$	1.51008e7	+	3.19225e6i	1.64314	+	0.347354i
$611$			4.24112e6i			0.459598i
$612$	9.85124e6	−	3.54535e6i	1.06319	−	0.382631i
$613$	1.51954e6			0.163329			0.0816643	−	0.996660i	$-0.473976\pi$
$613$	1.51954e6			0.163329			0.0816643	+	0.996660i	$0.473976\pi$
$614$	8.80152e6	−	1.25217e7i	0.942187	−	1.34043i
$615$	−807639.	+	345604.i	−0.0861052	+	0.0368461i
$616$	−1.18458e6	−	324289.i	−0.125780	−	0.0344334i
$617$			8.51821e6i			0.900815i	0.892823	+	0.450408i	$0.148721\pi$
$617$			8.51821e6i			0.900815i	−0.892823	+	0.450408i	$0.851279\pi$
$618$	999182.	+	702325.i	0.105238	+	0.0739720i
$619$			6.08130e6i			0.637926i	0.947767	+	0.318963i	$0.103335\pi$
$619$			6.08130e6i			0.637926i	−0.947767	+	0.318963i	$0.896665\pi$
$620$	1.17173e7	+	1.25828e7i	1.22419	+	1.31461i
$621$		−	1.01264e6i		−	0.105372i
$622$	−1.00742e6	+	1.43323e6i	−0.104408	+	0.148539i
$623$		−	1.29188e6i		−	0.133353i
$624$	550383.	−	455097.i	0.0565853	−	0.0467889i
$625$	−454587.	−	9.75504e6i	−0.0465497	−	0.998916i
$626$	8.77989e6	+	6.17139e6i	0.895475	+	0.629429i
$627$	53716.0			0.00545676
$628$	3.80850e6	+	1.05825e7i	0.385350	+	1.07075i
$629$		−	7.18026e6i		−	0.723625i
$630$	−1.27221e7	−	2.68939e6i	−1.27704	−	0.269962i
$631$	−1.52443e7			−1.52417			−0.762086	−	0.647476i	$-0.775825\pi$
$631$	−1.52443e7			−1.52417			−0.762086	+	0.647476i	$0.775825\pi$
$632$	−8.69727e6	−	2.38096e6i	−0.866144	−	0.237115i
$633$		−	1.41965e6i		−	0.140823i
$634$	−1.77634e6	+	2.52716e6i	−0.175511	+	0.249695i
$635$	−1.70606e6	−	3.98686e6i	−0.167903	−	0.392371i
$636$	−266321.	−	740011.i	−0.0261074	−	0.0725430i
$637$	−6.56972e6			−0.641503
$638$	765554.	−	1.08914e6i	0.0744602	−	0.105933i
$639$	2.12810e6			0.206177
$640$	−7.00812e6	+	7.63285e6i	−0.676319	+	0.736608i
$641$	1.58871e7			1.52722			0.763609	−	0.645679i	$-0.223426\pi$
$641$	1.58871e7			1.52722			0.763609	+	0.645679i	$0.223426\pi$
$642$	−513712.	+	730846.i	−0.0491906	+	0.0699823i
$643$	3.42866e6			0.327037			0.163519	−	0.986540i	$-0.447716\pi$
$643$	3.42866e6			0.327037			0.163519	+	0.986540i	$0.447716\pi$
$644$	2.97392e6	+	8.26346e6i	0.282563	+	0.785140i
$645$	−1.29022e6	+	552109.i	−0.122113	+	0.0522547i
$646$	4.58343e6	−	6.52075e6i	0.432125	−	0.614775i
$647$		−	3.99640e6i		−	0.375326i	−0.982234	−	0.187663i	$-0.939909\pi$
$647$		−	3.99640e6i		−	0.375326i	0.982234	−	0.187663i	$-0.0600912\pi$
$648$	−1.00957e7	−	2.76378e6i	−0.944489	−	0.258563i
$649$	−1.28696e6			−0.119937
$650$	−1.84964e6	−	9.31520e6i	−0.171713	−	0.864786i
$651$			2.12616e6i			0.196627i
$652$	−4.70584e6	−	1.30758e7i	−0.433529	−	1.20462i
$653$	−6.78426e6			−0.622615			−0.311308	−	0.950309i	$-0.600767\pi$
$653$	−6.78426e6			−0.622615			−0.311308	+	0.950309i	$0.600767\pi$
$654$	−1.02599e6	−	721171.i	−0.0937994	−	0.0659316i
$655$	7.25801e6	+	1.69612e7i	0.661019	+	1.54473i
$656$	9.55288e6	−	7.89903e6i	0.866712	−	0.716661i
$657$		−	3.47020e6i		−	0.313647i
$658$	4.37590e6	−	6.22549e6i	0.394006	−	0.560543i
$659$		−	1.38518e7i		−	1.24249i	−0.783617	−	0.621244i	$-0.786628\pi$
$659$		−	1.38518e7i		−	1.24249i	0.783617	−	0.621244i	$-0.213372\pi$
$660$	67668.0	−	63013.7i	0.00604677	−	0.00563087i
$661$		−	7.99240e6i		−	0.711498i	−0.934582	−	0.355749i	$-0.884226\pi$
$661$		−	7.99240e6i		−	0.711498i	0.934582	−	0.355749i	$-0.115774\pi$
$662$	−7.28791e6	−	5.12267e6i	−0.646335	−	0.454309i
$663$			945593.i			0.0835450i
$664$	2.43366e6	+	666239.i	0.214210	+	0.0586421i
$665$	−9.10084e6	+	3.89443e6i	−0.798045	+	0.341499i
$666$	−4.15722e6	+	5.91439e6i	−0.363176	+	0.516683i
$667$	−9.51964e6			−0.828526
$668$	1.74746e7	−	6.28889e6i	1.51518	−	0.545297i
$669$			1.19164e6i			0.102939i
$670$	−57702.3	+	272958.i	−0.00496599	+	0.0234914i
$671$	1.94338e6			0.166629
$672$	−1.27746e6	+	100158.i	−0.109125	+	0.00855586i
$673$			1.10858e7i			0.943471i	0.881740	+	0.471735i	$0.156372\pi$
$673$			1.10858e7i			0.943471i	−0.881740	+	0.471735i	$0.843628\pi$
$674$	358484.	+	251978.i	0.0303962	+	0.0213655i
$675$	1.35659e6	−	1.42128e6i	0.114601	−	0.120066i
$676$	895839.	+	2.48921e6i	0.0753986	+	0.209505i
$677$	1.70523e7			1.42992			0.714958	−	0.699167i	$-0.246446\pi$
$677$	1.70523e7			1.42992			0.714958	+	0.699167i	$0.246446\pi$
$678$	22260.1	+	15646.6i	0.00185975	+	0.00130722i
$679$	−1.13742e7			−0.946772
$680$	−1.87550e6	−	1.35912e7i	−0.155541	−	1.12716i
$681$	−1.56808e6			−0.129569
$682$	1.77111e6	+	1.24491e6i	0.145809	+	0.102489i
$683$	−4.24549e6			−0.348238			−0.174119	−	0.984725i	$-0.555708\pi$
$683$	−4.24549e6			−0.348238			−0.174119	+	0.984725i	$0.555708\pi$
$684$	−7.55075e6	+	2.71743e6i	−0.617092	+	0.222084i
$685$	2.96929e6	+	6.93889e6i	0.241783	+	0.565020i
$686$	−3.61038e6	−	2.53774e6i	−0.292916	−	0.205890i
$687$		−	420154.i		−	0.0339639i
$688$	1.52609e7	−	1.26188e7i	1.22916	−	1.01636i
$689$	−1.01710e7			−0.816234
$690$	−646896.	−	136751.i	−0.0517264	−	0.0109348i
$691$			8.87637e6i			0.707196i	0.935397	+	0.353598i	$0.115042\pi$
$691$			8.87637e6i			0.707196i	−0.935397	+	0.353598i	$0.884958\pi$
$692$	−2.64144e6	−	7.33961e6i	−0.209689	−	0.582650i
$693$	−1.63725e6			−0.129503
$694$	−8.91365e6	+	1.26812e7i	−0.702517	+	0.999455i
$695$	2.86627e6	+	6.69816e6i	0.225090	+	0.526009i
$696$	366747.	−	1.33967e6i	0.0286975	−	0.104827i
$697$			1.64125e7i			1.27965i
$698$	1.22781e7	+	8.63027e6i	0.953876	+	0.670480i
$699$		−	1.74890e6i		−	0.135386i
$700$	−6.89616e6	+	1.55821e7i	−0.531939	+	1.20193i
$701$			1.25460e7i			0.964298i	0.876089	+	0.482149i	$0.160144\pi$
$701$			1.25460e7i			0.964298i	−0.876089	+	0.482149i	$0.839856\pi$
$702$	1.09878e6	−	1.56321e6i	0.0841528	−	0.119722i
$703$			5.50351e6i			0.420002i
$704$	−664550.	+	1.12278e6i	−0.0505354	+	0.0853816i
$705$	225386.	+	526702.i	0.0170787	+	0.0399110i
$706$	−1.33547e7	−	9.38701e6i	−1.00837	−	0.708786i
$707$	−1.13303e7			−0.852495
$708$	−1.26340e6	+	454683.i	−0.0947235	+	0.0340899i
$709$		−	6.92792e6i		−	0.517592i	−0.965932	−	0.258796i	$-0.916674\pi$
$709$		−	6.92792e6i		−	0.517592i	0.965932	−	0.258796i	$-0.0833257\pi$
$710$	576783.	−	2.72845e6i	0.0429404	−	0.203128i
$711$	−1.20208e7			−0.891786
$712$	−1.32369e6	−	362373.i	−0.0978558	−	0.0267890i
$713$		−	1.54805e7i		−	1.14041i
$714$	975642.	−	1.38802e6i	0.0716218	−	0.101895i
$715$	−470437.	−	1.09936e6i	−0.0344141	−	0.0804219i
$716$	1.77597e7	−	6.39152e6i	1.29465	−	0.465931i
$717$	−1.29493e6			−0.0940694
$718$	5.40798e6	−	7.69381e6i	0.391493	−	0.556968i
$719$	5.47581e6			0.395026			0.197513	−	0.980300i	$-0.436713\pi$
$719$	5.47581e6			0.395026			0.197513	+	0.980300i	$0.436713\pi$
$720$	−6.32417e6	+	1.22810e7i	−0.454645	+	0.882879i
$721$	−2.83391e7			−2.03024
$722$	4.54164e6	−	6.46129e6i	0.324242	−	0.461292i
$723$	−792016.			−0.0563492
$724$	−9.22530e6	+	3.32008e6i	−0.654085	+	0.235398i
$725$	−1.33611e7	−	1.27530e7i	−0.944058	−	0.901089i
$726$	−673421.	+	958061.i	−0.0474182	+	0.0674608i
$727$		−	1.16133e7i		−	0.814926i	−0.913222	−	0.407463i	$-0.866414\pi$
$727$		−	1.16133e7i		−	0.814926i	0.913222	−	0.407463i	$-0.133586\pi$
$728$	−4.37555e6	+	1.59832e7i	−0.305988	+	1.11772i
$729$	−1.37553e7			−0.958628
$730$	−4.44915e6	−	940534.i	−0.309008	−	0.0653232i
$731$			2.62192e7i			1.81479i
$732$	1.90780e6	−	686594.i	0.131600	−	0.0473612i
$733$	1.43863e7			0.988984			0.494492	−	0.869182i	$-0.335354\pi$
$733$	1.43863e7			0.988984			0.494492	+	0.869182i	$0.335354\pi$
$734$	−849380.	−	597029.i	−0.0581918	−	0.0409030i
$735$	−815889.	+	349135.i	−0.0557074	+	0.0238383i
$736$	9.30114e6	−	729248.i	0.632909	−	0.0496228i
$737$			35128.0i			0.00238223i
$738$	9.50247e6	−	1.35190e7i	0.642238	−	0.913697i
$739$			8.91435e6i			0.600452i	0.953868	+	0.300226i	$0.0970621\pi$
$739$			8.91435e6i			0.600452i	−0.953868	+	0.300226i	$0.902938\pi$
$740$	6.45611e6	+	6.93297e6i	0.433403	+	0.465415i
$741$		−	724775.i		−	0.0484906i
$742$	1.49298e7	+	1.04942e7i	0.995510	+	0.699744i
$743$			9.84971e6i			0.654563i	0.944927	+	0.327281i	$0.106133\pi$
$743$			9.84971e6i			0.654563i	−0.944927	+	0.327281i	$0.893867\pi$
$744$	2.17851e6	+	596390.i	0.144287	+	0.0395001i
$745$	1.24760e6	+	2.91551e6i	0.0823543	+	0.192453i
$746$	8.38300e6	−	1.19263e7i	0.551509	−	0.784619i
$747$	3.36366e6			0.220552
$748$	−584978.	−	1.62544e6i	−0.0382283	−	0.106223i
$749$		−	2.07284e7i		−	1.35009i
$750$	−724742.	−	1.05855e6i	−0.0470468	−	0.0687162i
$751$	2.31729e7			1.49928			0.749638	−	0.661849i	$-0.230228\pi$
$751$	2.31729e7			1.49928			0.749638	+	0.661849i	$0.230228\pi$
$752$	−5.15135e6	−	6.22992e6i	−0.332182	−	0.401733i
$753$		−	897165.i		−	0.0576614i
$754$	−1.46954e7	−	1.03294e7i	−0.941356	−	0.661679i
$755$	−1.40218e7	+	6.00021e6i	−0.895235	+	0.383089i
$756$	−3.22577e6	+	1.16092e6i	−0.205272	+	0.0738750i
$757$	−1.04310e7			−0.661586			−0.330793	−	0.943703i	$-0.607316\pi$
$757$	−1.04310e7			−0.661586			−0.330793	+	0.943703i	$0.607316\pi$
$758$	−8.68914e6	−	6.10760e6i	−0.549292	−	0.386098i
$759$	−83251.5			−0.00524551
$760$	1.43753e6	+	1.04173e7i	0.0902783	+	0.654219i
$761$	7.98132e6			0.499589			0.249795	−	0.968299i	$-0.419637\pi$
$761$	7.98132e6			0.499589			0.249795	+	0.968299i	$0.419637\pi$
$762$	−466064.	−	327597.i	−0.0290776	−	0.0204386i
$763$	2.90995e7			1.80956
$764$	1.33374e6	+	3.70598e6i	0.0826680	+	0.229704i
$765$	−7.19551e6	−	1.68151e7i	−0.444537	−	1.03883i
$766$	−6.53587e6	−	4.59406e6i	−0.402468	−	0.282895i
$767$			1.73646e7i			1.06580i
$768$	−255704.	+	1.33701e6i	−0.0156435	+	0.0817961i
$769$	1.28302e7			0.782378			0.391189	−	0.920310i	$-0.372064\pi$
$769$	1.28302e7			0.782378			0.391189	+	0.920310i	$0.372064\pi$
$770$	−443746.	+	2.09912e6i	−0.0269717	+	0.127588i
$771$			981167.i			0.0594439i
$772$	−2.07586e7	+	7.47078e6i	−1.25359	+	0.451152i
$773$	1.70361e7			1.02547			0.512733	−	0.858548i	$-0.328633\pi$
$773$	1.70361e7			1.02547			0.512733	+	0.858548i	$0.328633\pi$
$774$	1.51804e7	−	2.15968e7i	0.910814	−	1.29579i
$775$	2.07385e7	−	2.17274e7i	1.24029	−	1.29943i
$776$	−3.19047e6	+	1.16543e7i	−0.190196	+	0.694754i
$777$			1.17149e6i			0.0696124i
$778$	−1.34510e7	−	9.45470e6i	−0.796719	−	0.560014i
$779$		−	1.25798e7i		−	0.742727i
$780$	−850227.	−	913027.i	−0.0500378	−	0.0537337i
$781$		−	351134.i		−	0.0205989i
$782$	−7.10361e6	+	1.01061e7i	−0.415396	+	0.590975i
$783$		−	3.71615e6i		−	0.216615i
$784$	9.65047e6	−	7.97972e6i	0.560736	−	0.463658i
$785$	1.80632e7	−	7.72960e6i	1.04621	−	0.447695i
$786$	1.98276e6	+	1.39368e6i	0.114476	+	0.0804650i
$787$	−2.17976e7			−1.25450			−0.627252	−	0.778817i	$-0.715820\pi$
$787$	−2.17976e7			−1.25450			−0.627252	+	0.778817i	$0.715820\pi$
$788$	767007.	+	2.13124e6i	0.0440032	+	0.122269i
$789$		−	411167.i		−	0.0235139i
$790$	−3.25803e6	+	1.54119e7i	−0.185732	+	0.878597i
$791$	−631348.			−0.0358779
$792$	−459250.	+	1.67757e6i	−0.0260157	+	0.0950313i
$793$		−	2.62215e7i		−	1.48072i
$794$	−7.48738e6	+	1.06521e7i	−0.421482	+	0.599632i
$795$	−1.26313e6	+	540516.i	−0.0708808	+	0.0303313i
$796$	−3.40884e6	−	9.47194e6i	−0.190688	−	0.529854i
$797$	7.68922e6			0.428782			0.214391	−	0.976748i	$-0.431223\pi$
$797$	7.68922e6			0.428782			0.214391	+	0.976748i	$0.431223\pi$
$798$	−747807.	+	1.06389e6i	−0.0415702	+	0.0591410i
$799$	1.07034e7			0.593136
$800$	1.40314e7	+	1.14368e7i	0.775133	+	0.631798i
$801$	−1.82953e6			−0.100753
$802$	−8.41694e6	+	1.19746e7i	−0.462081	+	0.657392i
$803$	−572578.			−0.0313362
$804$	12410.7	+	34484.9i	0.000677106	+	0.00188143i
$805$	1.41049e7	−	6.03576e6i	0.767150	−	0.328278i
$806$	1.67973e7	−	2.38971e7i	0.910756	−	1.29571i
$807$			1.94834e6i			0.105313i
$808$	−3.17816e6	+	1.16093e7i	−0.171256	+	0.625572i
$809$	4.70149e6			0.252560			0.126280	−	0.991995i	$-0.459696\pi$
$809$	4.70149e6			0.252560			0.126280	+	0.991995i	$0.459696\pi$
$810$	−3.78187e6	+	1.78900e7i	−0.202532	+	0.958069i
$811$			1.31175e7i			0.700322i	0.936689	+	0.350161i	$0.113873\pi$
$811$			1.31175e7i			0.700322i	−0.936689	+	0.350161i	$0.886127\pi$
$812$	1.09136e7	+	3.03248e7i	0.580867	+	1.61402i
$813$	857847.			0.0455180
$814$	975865.	+	685936.i	0.0516213	+	0.0362846i
$815$	−2.23192e7	+	9.55080e6i	−1.17702	+	0.503670i
$816$	−1.14854e6	−	1.38901e6i	−0.0603836	−	0.0730264i
$817$		−	2.00964e7i		−	1.05333i
$818$	−1.03218e7	+	1.46846e7i	−0.539352	+	0.767324i
$819$			2.20910e7i			1.15081i
$820$	−1.47572e7	−	1.58472e7i	−0.766425	−	0.823035i
$821$			2.69837e7i			1.39715i	0.715537	+	0.698575i	$0.246182\pi$
$821$			2.69837e7i			1.39715i	−0.715537	+	0.698575i	$0.753818\pi$
$822$	811156.	+	570162.i	0.0418721	+	0.0294319i
$823$		−	279830.i		−	0.0144011i	−0.999974	−	0.00720053i	$-0.997708\pi$
$823$		−	279830.i		−	0.0144011i	0.999974	−	0.00720053i	$-0.00229202\pi$
$824$	−7.94914e6	+	2.90369e7i	−0.407852	+	1.48982i
$825$	−116846.	−	111528.i	−0.00597696	−	0.00570492i
$826$	1.79164e7	−	2.54893e7i	0.913696	−	1.29989i
$827$	2.31889e7			1.17901			0.589504	−	0.807765i	$-0.299323\pi$
$827$	2.31889e7			1.17901			0.589504	+	0.807765i	$0.299323\pi$
$828$	1.17025e7	−	4.21160e6i	0.593202	−	0.213487i
$829$		−	5.30543e6i		−	0.268123i	−0.990973	−	0.134062i	$-0.957198\pi$
$829$		−	5.30543e6i		−	0.268123i	0.990973	−	0.134062i	$-0.0428020\pi$
$830$	911658.	−	4.31256e6i	0.0459343	−	0.217290i
$831$	2.04551e6			0.102754
$832$	1.51494e7	+	8.96659e6i	0.758730	+	0.449075i
$833$			1.65801e7i			0.827894i
$834$	783015.	+	550381.i	0.0389812	+	0.0273999i
$835$	−1.27637e7	−	2.98273e7i	−0.633520	−	1.48047i
$836$	448372.	+	1.24586e6i	0.0221882	+	0.0616531i
$837$	6.04305e6			0.298155
$838$	2.85095e7	+	2.00394e7i	1.40243	+	0.985766i
$839$	1.39887e7			0.686077			0.343039	−	0.939321i	$-0.388544\pi$
$839$	1.39887e7			0.686077			0.343039	+	0.939321i	$0.388544\pi$
$840$	305997.	+	2.21747e6i	0.0149630	+	0.108432i
$841$	−1.44236e7			−0.703207
$842$	−1.36035e7	−	9.56190e6i	−0.661257	−	0.464798i
$843$	1.89183e6			0.0916882
$844$	3.29267e7	−	1.18499e7i	1.59108	−	0.572612i
$845$	4.24884e6	−	1.81816e6i	0.204705	−	0.0875973i
$846$	−8.81639e6	−	6.19704e6i	−0.423511	−	0.297686i
$847$		−	2.71728e7i		−	1.30144i
$848$	1.49405e7	−	1.23539e7i	0.713468	−	0.589947i
$849$	1.79593e6			0.0855105
$850$	−2.35089e7	+	4.66796e6i	−1.11605	+	0.221605i
$851$		−	8.52958e6i		−	0.403742i
$852$	−124056.	−	344705.i	−0.00585487	−	0.0162686i
$853$	−1.48401e7			−0.698335			−0.349168	−	0.937060i	$-0.613536\pi$
$853$	−1.48401e7			−0.698335			−0.349168	+	0.937060i	$0.613536\pi$
$854$	−2.70547e7	+	3.84901e7i	−1.26940	+	1.80595i
$855$	5.51519e6	+	1.28884e7i	0.258015	+	0.602953i
$856$	−2.12389e7	−	5.81435e6i	−0.990712	−	0.271217i
$857$		−	8.97091e6i		−	0.417239i	−0.977997	−	0.208619i	$-0.933103\pi$
$857$		−	8.97091e6i		−	0.417239i	0.977997	−	0.208619i	$-0.0668970\pi$
$858$	−128515.	−	90333.2i	−0.00595985	−	0.00418918i
$859$			2.21880e7i			1.02597i	0.858398	+	0.512985i	$0.171460\pi$
$859$			2.21880e7i			1.02597i	−0.858398	+	0.512985i	$0.828540\pi$
$860$	−2.35749e7	−	2.53162e7i	−1.08694	−	1.16722i
$861$		−	2.67777e6i		−	0.123102i
$862$	8.47588e6	−	1.20584e7i	0.388523	−	0.552743i
$863$		−	2.60169e7i		−	1.18913i	−0.804047	−	0.594565i	$-0.797324\pi$
$863$		−	2.60169e7i		−	1.18913i	0.804047	−	0.594565i	$-0.202676\pi$
$864$	284674.	+	3.63085e6i	0.0129737	+	0.165472i
$865$	−1.25280e7	+	5.36097e6i	−0.569300	+	0.243614i
$866$	2.43022e6	+	1.70820e6i	0.110116	+	0.0774008i
$867$	543172.			0.0245408
$868$	−4.93131e7	+	1.77472e7i	−2.22158	+	0.799523i
$869$			1.98342e6i			0.0890975i
$870$	−2.37395e6	−	501844.i	−0.106334	−	0.0224787i
$871$	473972.			0.0211694
$872$	8.16244e6	−	2.98161e7i	0.363520	−	1.32788i
$873$			1.61078e7i			0.715322i
$874$	5.44476e6	−	7.74613e6i	0.241102	−	0.343010i
$875$	2.78825e7	+	1.04243e7i	1.23115	+	0.460284i
$876$	−562095.	+	202292.i	−0.0247485	+	0.00890672i
$877$	5.75323e6			0.252588			0.126294	−	0.991993i	$-0.459692\pi$
$877$	5.75323e6			0.252588			0.126294	+	0.991993i	$0.459692\pi$
$878$	1.13520e7	−	1.61503e7i	0.496977	−	0.707039i
$879$	706892.			0.0308589
$880$	2.02634e6	+	1.04348e6i	0.0882076	+	0.0454231i
$881$	−1.39231e7			−0.604362			−0.302181	−	0.953251i	$-0.597715\pi$
$881$	−1.39231e7			−0.604362			−0.302181	+	0.953251i	$0.597715\pi$
$882$	9.59954e6	−	1.36570e7i	0.415508	−	0.591133i
$883$	−4.47703e7			−1.93236			−0.966180	−	0.257867i	$-0.916980\pi$
$883$	−4.47703e7			−1.93236			−0.966180	+	0.257867i	$0.916980\pi$
$884$	−2.19316e7	+	7.89295e6i	−0.943931	+	0.339710i
$885$	922808.	+	2.15650e6i	0.0396053	+	0.0925531i
$886$	−1.74475e7	+	2.48222e7i	−0.746707	+	1.06232i
$887$			1.25115e7i			0.533949i	0.963704	+	0.266974i	$0.0860239\pi$
$887$			1.25115e7i			0.533949i	−0.963704	+	0.266974i	$0.913976\pi$
$888$	1.20034e6	+	328605.i	0.0510825	+	0.0139843i
$889$	1.32186e7			0.560960
$890$	−495859.	+	2.34564e6i	−0.0209838	+	0.0992627i
$891$			2.30232e6i			0.0971566i
$892$	−2.76383e7	+	9.94670e6i	−1.16305	+	0.418569i
$893$	−8.20390e6			−0.344264
$894$	340824.	+	239565.i	0.0142622	+	0.0100249i
$895$	−1.29720e7	−	3.03141e7i	−0.541313	−	1.26499i
$896$	−1.29861e7	−	2.87928e7i	−0.540391	−	1.19816i
$897$			1.12329e6i			0.0466134i
$898$	−1.83566e7	+	2.61156e7i	−0.759630	+	1.08071i
$899$		−	5.68095e7i		−	2.34435i
$900$	2.20669e7	+	9.76617e6i	0.908105	+	0.401900i
$901$			2.56686e7i			1.05339i
$902$	−2.23061e6	−	1.56789e6i	−0.0912865	−	0.0641653i
$903$		−	4.27778e6i		−	0.174582i
$904$	−177094.	+	646895.i	−0.00720746	+	0.0263277i
$905$	6.73831e6	+	1.57467e7i	0.273482	+	0.639098i
$906$	−1.15216e6	+	1.63915e6i	−0.0466329	+	0.0663435i
$907$	3.38418e7			1.36595			0.682975	−	0.730442i	$-0.260686\pi$
$907$	3.38418e7			1.36595			0.682975	+	0.730442i	$0.260686\pi$
$908$	−1.30889e7	−	3.63694e7i	−0.526853	−	1.46393i
$909$			1.60457e7i			0.644092i
$910$	2.83229e7	+	5.98735e6i	1.13379	+	0.239679i
$911$	−3.39018e7			−1.35340			−0.676701	−	0.736258i	$-0.736591\pi$
$911$	−3.39018e7			−1.35340			−0.676701	+	0.736258i	$0.736591\pi$
$912$	880326.	+	1.06464e6i	0.0350475	+	0.0423855i
$913$		−	554999.i		−	0.0220351i
$914$	3.02681e7	+	2.12755e7i	1.19845	+	0.842391i
$915$	−1.39349e6	−	3.25642e6i	−0.0550237	−	0.128584i
$916$	9.74486e6	−	3.50706e6i	0.383740	−	0.138104i
$917$	−5.62355e7			−2.20845
$918$	−3.94510e6	−	2.77301e6i	−0.154508	−	0.108604i
$919$	−2.44903e7			−0.956544			−0.478272	−	0.878212i	$-0.658737\pi$
$919$	−2.44903e7			−0.956544			−0.478272	+	0.878212i	$0.658737\pi$
$920$	−2.22795e6	−	1.61453e7i	−0.0867833	−	0.628892i
$921$	−3.51245e6			−0.136446
$922$	−3.66901e7	−	2.57895e7i	−1.42142	−	0.999113i
$923$	−4.73776e6			−0.183049
$924$	95441.7	+	265198.i	0.00367755	+	0.0102186i
$925$	1.14267e7	−	1.19716e7i	0.439102	−	0.460041i
$926$	2.51571e7	+	1.76829e7i	0.964125	+	0.677684i
$927$			4.01331e7i			1.53392i
$928$	3.41329e7	−	2.67616e6i	1.30108	−	0.102010i
$929$	4.91159e6			0.186717			0.0933583	−	0.995633i	$-0.470240\pi$
$929$	4.91159e6			0.186717			0.0933583	+	0.995633i	$0.470240\pi$
$930$	816079.	−	3.86043e6i	0.0309403	−	0.146362i
$931$		−	1.27083e7i		−	0.480521i
$932$	4.05632e7	−	1.45982e7i	1.52965	−	0.550504i
$933$	402034.			0.0151202
$934$	4.79515e6	−	6.82196e6i	0.179860	−	0.255883i
$935$	−2.77447e6	+	1.18725e6i	−0.103789	+	0.0444132i
$936$	2.26350e7	+	6.19654e6i	0.844481	+	0.231185i
$937$		−	2.63398e7i		−	0.980083i	−0.871699	−	0.490042i	$-0.836982\pi$
$937$		−	2.63398e7i		−	0.980083i	0.871699	−	0.490042i	$-0.163018\pi$
$938$	−695738.	−	489034.i	−0.0258190	−	0.0181481i
$939$		−	2.46284e6i		−	0.0911532i
$940$	−1.03348e7	+	9.62392e6i	−0.381488	+	0.355249i
$941$			3.47907e6i			0.128082i	0.997947	+	0.0640411i	$0.0203989\pi$
$941$			3.47907e6i			0.128082i	−0.997947	+	0.0640411i	$0.979601\pi$
$942$	1.48424e6	−	2.11159e6i	0.0544974	−	0.0775322i
$943$			1.94967e7i			0.713973i
$944$	−2.10914e7	−	2.55074e7i	−0.770328	−	0.931615i
$945$	2.35616e6	+	5.50608e6i	0.0858271	+	0.200568i
$946$	−3.56343e6	−	2.50474e6i	−0.129462	−	0.0909985i
$947$	1.24338e7			0.450537			0.225268	−	0.974297i	$-0.427674\pi$
$947$	1.24338e7			0.450537			0.225268	+	0.974297i	$0.427674\pi$
$948$	700742.	+	1.94711e6i	0.0253243	+	0.0703670i
$949$			7.72564e6i			0.278464i
$950$	1.80190e7	−	3.57788e6i	0.647772	−	0.128622i
$951$	708891.			0.0254172
$952$	4.03369e7	+	1.10426e7i	1.44248	+	0.394894i
$953$			4.64549e7i			1.65691i	0.560056	+	0.828455i	$0.310780\pi$
$953$			4.64549e7i			1.65691i	−0.560056	+	0.828455i	$0.689220\pi$
$954$	1.48616e7	−	2.11433e7i	0.528683	−	0.752145i
$955$	6.32574e6	−	2.70691e6i	0.224441	−	0.0960428i
$956$	−1.08089e7	−	3.00340e7i	−0.382504	−	1.06284i
$957$	−305512.			−0.0107832
$958$	−1.34376e7	+	1.91173e7i	−0.473050	+	0.672997i
$959$	−2.30062e7			−0.807791
$960$	2.35790e6	+	308470.i	0.0825749	+	0.0108027i
$961$	6.37523e7			2.22683
$962$	9.25515e6	−	1.31671e7i	0.322438	−	0.458725i
$963$	−2.93551e7			−1.02004
$964$	−6.61102e6	−	1.83696e7i	−0.229127	−	0.636661i
$965$	1.51624e7	+	3.54329e7i	0.524143	+	1.22486i
$966$	1.15899e6	−	1.64886e6i	0.0399609	−	0.0568515i
$967$			4.66797e7i			1.60532i	0.596435	+	0.802661i	$0.296583\pi$
$967$			4.66797e7i			1.60532i	−0.596435	+	0.802661i	$0.703417\pi$
$968$	−2.78419e7	−	7.62199e6i	−0.955016	−	0.261445i
$969$	−1.82913e6			−0.0625798
$970$	2.06519e7	+	4.36573e6i	0.704743	+	0.148980i
$971$		−	1.61987e7i		−	0.551357i	−0.961250	−	0.275678i	$-0.911098\pi$
$971$		−	1.61987e7i		−	0.551357i	0.961250	−	0.275678i	$-0.0889025\pi$
$972$	2.46896e6	+	6.86034e6i	0.0838200	+	0.232906i
$973$	−2.22081e7			−0.752019
$974$	1.03946e7	+	7.30639e6i	0.351085	+	0.246777i
$975$	−1.50482e6	+	1.57658e6i	−0.0506959	+	0.0531133i
$976$	3.18491e7	+	3.85175e7i	1.07022	+	1.29430i
$977$			1.46888e7i			0.492322i	0.969229	+	0.246161i	$0.0791693\pi$
$977$			1.46888e7i			0.492322i	−0.969229	+	0.246161i	$0.920831\pi$
$978$	−1.83394e6	+	2.60911e6i	−0.0613111	+	0.0872258i
$979$			301869.i			0.0100661i
$980$	−1.49080e7	−	1.60091e7i	−0.495853	−	0.532478i
$981$		−	4.12100e7i		−	1.36719i
$982$	−2.67642e6	−	1.88126e6i	−0.0885679	−	0.0622544i
$983$		−	4.22739e6i		−	0.139537i	−0.997563	−	0.0697684i	$-0.977774\pi$
$983$		−	4.22739e6i		−	0.139537i	0.997563	−	0.0697684i	$-0.0222260\pi$
$984$	−2.74371e6	−	751116.i	−0.0903337	−	0.0247297i
$985$	3.63781e6	−	1.55669e6i	0.119467	−	0.0511224i
$986$	−2.60685e7	+	3.70871e7i	−0.853933	+	1.21487i
$987$	−1.74631e6			−0.0570594
$988$	1.68101e7	−	6.04976e6i	0.547871	−	0.197172i
$989$			3.11463e7i			1.01255i
$990$	2.97272e6	+	628422.i	0.0963976	+	0.0203781i
$991$	1.49618e7			0.483948			0.241974	−	0.970283i	$-0.422205\pi$
$991$	1.49618e7			0.483948			0.241974	+	0.970283i	$0.422205\pi$
$992$	4.35187e6	+	5.55056e7i	0.140410	+	1.79084i
$993$			2.04432e6i			0.0657925i
$994$	6.95449e6	+	4.88831e6i	0.223254	+	0.156925i
$995$	−1.61677e7	+	6.91846e6i	−0.517714	+	0.221540i
$996$	−196081.	−	544838.i	−0.00626307	−	0.0174028i
$997$	3.45075e7			1.09945			0.549724	−	0.835346i	$-0.314733\pi$
$997$	3.45075e7			1.09945			0.549724	+	0.835346i	$0.314733\pi$
$998$	−1.42187e6	−	999435.i	−0.0451892	−	0.0317635i
$999$	3.32966e6			0.105557

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	40.6.f.a.29.19	yes	28
4.3	odd	2		160.6.f.a.49.15		28
5.2	odd	4		200.6.d.e.101.24		28
5.3	odd	4		200.6.d.e.101.5		28
5.4	even	2	inner	40.6.f.a.29.10	yes	28
8.3	odd	2		160.6.f.a.49.13		28
8.5	even	2	inner	40.6.f.a.29.9	✓	28
20.3	even	4		800.6.d.e.401.4		28
20.7	even	4		800.6.d.e.401.25		28
20.19	odd	2		160.6.f.a.49.14		28
40.3	even	4		800.6.d.e.401.3		28
40.13	odd	4		200.6.d.e.101.6		28
40.19	odd	2		160.6.f.a.49.16		28
40.27	even	4		800.6.d.e.401.26		28
40.29	even	2	inner	40.6.f.a.29.20	yes	28
40.37	odd	4		200.6.d.e.101.23		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
40.6.f.a.29.9	✓	28	8.5	even	2	inner
40.6.f.a.29.10	yes	28	5.4	even	2	inner
40.6.f.a.29.19	yes	28	1.1	even	1	trivial
40.6.f.a.29.20	yes	28	40.29	even	2	inner
160.6.f.a.49.13		28	8.3	odd	2
160.6.f.a.49.14		28	20.19	odd	2
160.6.f.a.49.15		28	4.3	odd	2
160.6.f.a.49.16		28	40.19	odd	2
200.6.d.e.101.5		28	5.3	odd	4
200.6.d.e.101.6		28	40.13	odd	4
200.6.d.e.101.23		28	40.37	odd	4
200.6.d.e.101.24		28	5.2	odd	4
800.6.d.e.401.3		28	40.3	even	4
800.6.d.e.401.4		28	20.3	even	4
800.6.d.e.401.25		28	20.7	even	4
800.6.d.e.401.26		28	40.27	even	4

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:	\( N \)	\(=\)	\( 40 = 2^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	40.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(3.25299 - 4.62796i) q^{2} -1.29818 q^{3} +(-10.8361 - 30.1095i) q^{4} +(-51.3939 + 21.9924i) q^{5} +(-4.22299 + 6.00795i) q^{6} -170.399i q^{7} +(-174.595 - 47.7971i) q^{8} -241.315 q^{9} +O(q^{10})\)	\(q+(3.25299 - 4.62796i) q^{2} -1.29818 q^{3} +(-10.8361 - 30.1095i) q^{4} +(-51.3939 + 21.9924i) q^{5} +(-4.22299 + 6.00795i) q^{6} -170.399i q^{7} +(-174.595 - 47.7971i) q^{8} -241.315 q^{9} +(-65.4039 + 309.390i) q^{10} +39.8166i q^{11} +(14.0672 + 39.0876i) q^{12} +537.234 q^{13} +(-788.600 - 554.307i) q^{14} +(66.7187 - 28.5502i) q^{15} +(-789.160 + 652.536i) q^{16} -1355.83i q^{17} +(-784.995 + 1116.80i) q^{18} +1039.21i q^{19} +(1219.09 + 1309.13i) q^{20} +221.209i q^{21} +(184.270 + 129.523i) q^{22} -1610.62i q^{23} +(226.657 + 62.0494i) q^{24} +(2157.67 - 2260.55i) q^{25} +(1747.62 - 2486.30i) q^{26} +628.730 q^{27} +(-5130.62 + 1846.45i) q^{28} -5910.56i q^{29} +(84.9063 - 401.645i) q^{30} +9611.53 q^{31} +(452.776 + 5774.90i) q^{32} -51.6892i q^{33} +(-6274.71 - 4410.50i) q^{34} +(3747.49 + 8757.46i) q^{35} +(2614.90 + 7265.86i) q^{36} +5295.85 q^{37} +(4809.42 + 3380.54i) q^{38} -697.429 q^{39} +(10024.3 - 1383.29i) q^{40} -12105.1 q^{41} +(1023.75 + 719.592i) q^{42} -19338.2 q^{43} +(1198.86 - 431.455i) q^{44} +(12402.1 - 5307.10i) q^{45} +(-7453.87 - 5239.32i) q^{46} +7894.36i q^{47} +(1024.47 - 847.111i) q^{48} -12228.8 q^{49} +(-3442.89 - 17339.2i) q^{50} +1760.11i q^{51} +(-5821.50 - 16175.8i) q^{52} -18932.1 q^{53} +(2045.25 - 2909.74i) q^{54} +(-875.664 - 2046.33i) q^{55} +(-8144.57 + 29750.8i) q^{56} -1349.09i q^{57} +(-27353.9 - 19227.0i) q^{58} +32322.2i q^{59} +(-1582.60 - 1699.49i) q^{60} -48808.2i q^{61} +(31266.2 - 44481.8i) q^{62} +41119.8i q^{63} +(28198.9 + 16690.3i) q^{64} +(-27610.6 + 11815.1i) q^{65} +(-239.216 - 168.145i) q^{66} +882.245 q^{67} +(-40823.2 + 14691.8i) q^{68} +2090.88i q^{69} +(52719.8 + 11144.8i) q^{70} -8818.78 q^{71} +(42132.4 + 11534.1i) q^{72} +14380.4i q^{73} +(17227.4 - 24509.0i) q^{74} +(-2801.05 + 2934.62i) q^{75} +(31290.1 - 11260.9i) q^{76} +6784.70 q^{77} +(-2268.73 + 3227.68i) q^{78} +49813.9 q^{79} +(26207.2 - 50891.9i) q^{80} +57823.3 q^{81} +(-39377.9 + 56022.1i) q^{82} -13938.9 q^{83} +(6660.49 - 2397.03i) q^{84} +(29817.9 + 69681.2i) q^{85} +(-62906.9 + 89496.2i) q^{86} +7673.00i q^{87} +(1903.12 - 6951.78i) q^{88} +7581.49 q^{89} +(15782.9 - 74660.4i) q^{90} -91544.2i q^{91} +(-48494.8 + 17452.7i) q^{92} -12477.5 q^{93} +(36534.8 + 25680.3i) q^{94} +(-22854.8 - 53409.1i) q^{95} +(-587.787 - 7496.88i) q^{96} -66750.3i q^{97} +(-39780.2 + 56594.3i) q^{98} -9608.33i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 12 q^{4} - 156 q^{6} + 1940 q^{9}+O(q^{10}) \) 28 * q - 12 * q^4 - 156 * q^6 + 1940 * q^9	\( 28 q - 12 q^{4} - 156 q^{6} + 1940 q^{9} - 16 q^{10} - 692 q^{14} - 488 q^{15} + 1560 q^{16} + 2732 q^{20} - 2224 q^{24} + 1556 q^{25} - 9976 q^{26} - 15012 q^{30} + 4368 q^{31} + 13016 q^{34} - 34116 q^{36} + 23360 q^{39} - 22496 q^{40} - 2480 q^{41} + 10712 q^{44} + 58372 q^{46} - 38420 q^{49} + 45624 q^{50} - 3568 q^{54} - 48776 q^{55} + 110944 q^{56} + 111688 q^{60} - 46944 q^{64} + 37200 q^{65} - 136120 q^{66} - 112852 q^{70} - 69232 q^{71} + 34176 q^{74} - 13944 q^{76} - 35984 q^{79} - 47064 q^{80} + 122596 q^{81} - 165688 q^{84} - 73676 q^{86} - 178744 q^{89} + 51496 q^{90} + 314740 q^{94} + 89416 q^{95} - 236176 q^{96}+O(q^{100}) \) 28 * q - 12 * q^4 - 156 * q^6 + 1940 * q^9 - 16 * q^10 - 692 * q^14 - 488 * q^15 + 1560 * q^16 + 2732 * q^20 - 2224 * q^24 + 1556 * q^25 - 9976 * q^26 - 15012 * q^30 + 4368 * q^31 + 13016 * q^34 - 34116 * q^36 + 23360 * q^39 - 22496 * q^40 - 2480 * q^41 + 10712 * q^44 + 58372 * q^46 - 38420 * q^49 + 45624 * q^50 - 3568 * q^54 - 48776 * q^55 + 110944 * q^56 + 111688 * q^60 - 46944 * q^64 + 37200 * q^65 - 136120 * q^66 - 112852 * q^70 - 69232 * q^71 + 34176 * q^74 - 13944 * q^76 - 35984 * q^79 - 47064 * q^80 + 122596 * q^81 - 165688 * q^84 - 73676 * q^86 - 178744 * q^89 + 51496 * q^90 + 314740 * q^94 + 89416 * q^95 - 236176 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more