LMFDB - Embedded newform 40.6.f.a.29.8

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			29.8
Character	$\chi$	$=$	40.29
Dual form			40.6.f.a.29.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.53479 + 4.41648i) q^{2} -21.4357 q^{3} +(-7.01055 - 31.2226i) q^{4} +(-48.3867 + 27.9951i) q^{5} +(75.7708 - 94.6704i) q^{6} -39.9262i q^{7} +(162.675 + 79.4034i) q^{8} +216.491 q^{9} +O(q^{10})$	\(q+(-3.53479 + 4.41648i) q^{2} -21.4357 q^{3} +(-7.01055 - 31.2226i) q^{4} +(-48.3867 + 27.9951i) q^{5} +(75.7708 - 94.6704i) q^{6} -39.9262i q^{7} +(162.675 + 79.4034i) q^{8} +216.491 q^{9} +(47.3969 - 312.656i) q^{10} +141.626i q^{11} +(150.276 + 669.280i) q^{12} +700.139 q^{13} +(176.333 + 141.131i) q^{14} +(1037.20 - 600.096i) q^{15} +(-925.704 + 437.776i) q^{16} +960.152i q^{17} +(-765.249 + 956.126i) q^{18} -2202.13i q^{19} +(1213.30 + 1314.50i) q^{20} +855.847i q^{21} +(-625.488 - 500.618i) q^{22} -4492.21i q^{23} +(-3487.05 - 1702.07i) q^{24} +(1557.55 - 2709.18i) q^{25} +(-2474.84 + 3092.15i) q^{26} +568.247 q^{27} +(-1246.60 + 279.905i) q^{28} +4834.96i q^{29} +(-1015.99 + 6702.00i) q^{30} -1122.17 q^{31} +(1338.74 - 5635.80i) q^{32} -3035.86i q^{33} +(-4240.49 - 3393.93i) q^{34} +(1117.74 + 1931.90i) q^{35} +(-1517.72 - 6759.41i) q^{36} -8779.50 q^{37} +(9725.67 + 7784.07i) q^{38} -15008.0 q^{39} +(-10094.2 + 712.033i) q^{40} +11522.4 q^{41} +(-3779.83 - 3025.24i) q^{42} +17358.0 q^{43} +(4421.94 - 992.877i) q^{44} +(-10475.3 + 6060.68i) q^{45} +(19839.7 + 15879.0i) q^{46} +15167.7i q^{47} +(19843.2 - 9384.04i) q^{48} +15212.9 q^{49} +(6459.46 + 16455.3i) q^{50} -20581.6i q^{51} +(-4908.36 - 21860.2i) q^{52} +7119.05 q^{53} +(-2008.63 + 2509.65i) q^{54} +(-3964.84 - 6852.82i) q^{55} +(3170.28 - 6494.99i) q^{56} +47204.3i q^{57} +(-21353.5 - 17090.6i) q^{58} -41761.3i q^{59} +(-26007.9 - 28177.2i) q^{60} -20347.5i q^{61} +(3966.64 - 4956.04i) q^{62} -8643.65i q^{63} +(20158.2 + 25833.9i) q^{64} +(-33877.4 + 19600.5i) q^{65} +(13407.8 + 10731.1i) q^{66} -23764.7 q^{67} +(29978.4 - 6731.19i) q^{68} +96293.7i q^{69} +(-12483.2 - 1892.38i) q^{70} +881.677 q^{71} +(35217.6 + 17190.1i) q^{72} -7051.66i q^{73} +(31033.7 - 38774.5i) q^{74} +(-33387.1 + 58073.3i) q^{75} +(-68756.4 + 15438.2i) q^{76} +5654.59 q^{77} +(53050.1 - 66282.5i) q^{78} -47780.1 q^{79} +(32536.2 - 47097.7i) q^{80} -64788.0 q^{81} +(-40729.4 + 50888.6i) q^{82} +51692.3 q^{83} +(26721.8 - 5999.96i) q^{84} +(-26879.6 - 46458.6i) q^{85} +(-61356.8 + 76661.1i) q^{86} -103641. i q^{87} +(-11245.6 + 23039.0i) q^{88} +122761. q^{89} +(10261.0 - 67687.0i) q^{90} -27953.9i q^{91} +(-140258. + 31492.8i) q^{92} +24054.6 q^{93} +(-66987.8 - 53614.6i) q^{94} +(61649.0 + 106554. i) q^{95} +(-28696.9 + 120807. i) q^{96} -155549. i q^{97} +(-53774.4 + 67187.4i) q^{98} +30660.7i 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 $

$2$	−3.53479	+	4.41648i	−0.624868	+	0.780730i
$2$	−3.53479	+	4.41648i	−0.624868	+	0.780730i
$3$	−21.4357			−1.37510			−0.687551	−	0.726136i	$-0.741314\pi$
$3$	−21.4357			−1.37510			−0.687551	+	0.726136i	$0.741314\pi$
$4$	−7.01055	−	31.2226i	−0.219080	−	0.975707i
$5$	−48.3867	+	27.9951i	−0.865568	+	0.500792i
$5$	−48.3867	+	27.9951i	−0.865568	+	0.500792i
$6$	75.7708	−	94.6704i	0.859258	−	1.07358i
$7$		−	39.9262i		−	0.307973i	−0.988073	−	0.153987i	$-0.950789\pi$
$7$		−	39.9262i		−	0.307973i	0.988073	−	0.153987i	$-0.0492113\pi$
$8$	162.675	+	79.4034i	0.898660	+	0.438646i
$9$	216.491			0.890908
$10$	47.3969	−	312.656i	0.149882	−	0.988704i
$11$			141.626i			0.352908i	0.984309	+	0.176454i	$0.0564627\pi$
$11$			141.626i			0.352908i	−0.984309	+	0.176454i	$0.943537\pi$
$12$	150.276	+	669.280i	0.301257	+	1.34170i
$13$	700.139			1.14902			0.574508	−	0.818499i	$-0.305194\pi$
$13$	700.139			1.14902			0.574508	+	0.818499i	$0.305194\pi$
$14$	176.333	+	141.131i	0.240444	+	0.192443i
$15$	1037.20	−	600.096i	1.19024	−	0.688641i
$16$	−925.704	+	437.776i	−0.904008	+	0.427515i
$17$			960.152i			0.805782i	0.915248	+	0.402891i	$0.131995\pi$
$17$			960.152i			0.805782i	−0.915248	+	0.402891i	$0.868005\pi$
$18$	−765.249	+	956.126i	−0.556700	+	0.695559i
$19$		−	2202.13i		−	1.39946i	−0.714409	−	0.699728i	$-0.753304\pi$
$19$		−	2202.13i		−	1.39946i	0.714409	−	0.699728i	$-0.246696\pi$
$20$	1213.30	+	1314.50i	0.678255	+	0.734827i
$21$			855.847i			0.423495i
$22$	−625.488	−	500.618i	−0.275526	−	0.220521i
$23$		−	4492.21i		−	1.77068i	−0.464944	−	0.885340i	$-0.653926\pi$
$23$		−	4492.21i		−	1.77068i	0.464944	−	0.885340i	$-0.346074\pi$
$24$	−3487.05	−	1702.07i	−1.23575	−	0.603183i
$25$	1557.55	−	2709.18i	0.498415	−	0.866939i
$26$	−2474.84	+	3092.15i	−0.717983	+	0.897071i
$27$	568.247			0.150012
$28$	−1246.60	+	279.905i	−0.300492	+	0.0674707i
$29$			4834.96i			1.06757i	0.845619	+	0.533787i	$0.179232\pi$
$29$			4834.96i			1.06757i	−0.845619	+	0.533787i	$0.820768\pi$
$30$	−1015.99	+	6702.00i	−0.206103	+	1.35957i
$31$	−1122.17			−0.209727			−0.104864	−	0.994487i	$-0.533441\pi$
$31$	−1122.17			−0.209727			−0.104864	+	0.994487i	$0.533441\pi$
$32$	1338.74	−	5635.80i	0.231112	−	0.972927i
$33$		−	3035.86i		−	0.485285i
$34$	−4240.49	−	3393.93i	−0.629098	−	0.503507i
$35$	1117.74	+	1931.90i	0.154231	+	0.266572i
$36$	−1517.72	−	6759.41i	−0.195180	−	0.869265i
$37$	−8779.50			−1.05430			−0.527152	−	0.849771i	$-0.676740\pi$
$37$	−8779.50			−1.05430			−0.527152	+	0.849771i	$0.676740\pi$
$38$	9725.67	+	7784.07i	1.09260	+	0.874476i
$39$	−15008.0			−1.58001
$40$	−10094.2	+	712.033i	−0.997521	+	0.0703640i
$41$	11522.4			1.07050			0.535248	−	0.844695i	$-0.320218\pi$
$41$	11522.4			1.07050			0.535248	+	0.844695i	$0.320218\pi$
$42$	−3779.83	−	3025.24i	−0.330635	−	0.264628i
$43$	17358.0			1.43162			0.715811	−	0.698295i	$-0.246057\pi$
$43$	17358.0			1.43162			0.715811	+	0.698295i	$0.246057\pi$
$44$	4421.94	−	992.877i	0.344335	−	0.0773150i
$45$	−10475.3	+	6060.68i	−0.771141	+	0.446160i
$46$	19839.7	+	15879.0i	1.38242	+	1.10644i
$47$			15167.7i			1.00156i	0.865576	+	0.500778i	$0.166953\pi$
$47$			15167.7i			1.00156i	−0.865576	+	0.500778i	$0.833047\pi$
$48$	19843.2	−	9384.04i	1.24310	−	0.587877i
$49$	15212.9			0.905153
$50$	6459.46	+	16455.3i	0.365402	+	0.930850i
$51$		−	20581.6i		−	1.10803i
$52$	−4908.36	−	21860.2i	−0.251726	−	1.12110i
$53$	7119.05			0.348123			0.174061	−	0.984735i	$-0.444311\pi$
$53$	7119.05			0.348123			0.174061	+	0.984735i	$0.444311\pi$
$54$	−2008.63	+	2509.65i	−0.0937380	+	0.117119i
$55$	−3964.84	−	6852.82i	−0.176733	−	0.305466i
$56$	3170.28	−	6494.99i	0.135091	−	0.276763i
$57$			47204.3i			1.92440i
$58$	−21353.5	−	17090.6i	−0.833488	−	0.667093i
$59$		−	41761.3i		−	1.56187i	−0.624614	−	0.780934i	$-0.714744\pi$
$59$		−	41761.3i		−	1.56187i	0.624614	−	0.780934i	$-0.285256\pi$
$60$	−26007.9	−	28177.2i	−0.932670	−	1.01046i
$61$		−	20347.5i		−	0.700143i	−0.936723	−	0.350072i	$-0.886157\pi$
$61$		−	20347.5i		−	0.700143i	0.936723	−	0.350072i	$-0.113843\pi$
$62$	3966.64	−	4956.04i	0.131052	−	0.163740i
$63$		−	8643.65i		−	0.274376i
$64$	20158.2	+	25833.9i	0.615179	+	0.788387i
$65$	−33877.4	+	19600.5i	−0.994551	+	0.575418i
$66$	13407.8	+	10731.1i	0.378877	+	0.303239i
$67$	−23764.7			−0.646762			−0.323381	−	0.946269i	$-0.604820\pi$
$67$	−23764.7			−0.646762			−0.323381	+	0.946269i	$0.604820\pi$
$68$	29978.4	−	6731.19i	0.786207	−	0.176530i
$69$			96293.7i			2.43487i
$70$	−12483.2	−	1892.38i	−0.304494	−	0.0461596i
$71$	881.677			0.0207570			0.0103785	−	0.999946i	$-0.496696\pi$
$71$	881.677			0.0207570			0.0103785	+	0.999946i	$0.496696\pi$
$72$	35217.6	+	17190.1i	0.800623	+	0.390793i
$73$		−	7051.66i		−	0.154876i	−0.996997	−	0.0774381i	$-0.975326\pi$
$73$		−	7051.66i		−	0.154876i	0.996997	−	0.0774381i	$-0.0246740\pi$
$74$	31033.7	−	38774.5i	0.658800	−	0.823126i
$75$	−33387.1	+	58073.3i	−0.685371	+	1.19213i
$76$	−68756.4	+	15438.2i	−1.36546	+	0.306593i
$77$	5654.59			0.108686
$78$	53050.1	−	66282.5i	0.987301	−	1.23357i
$79$	−47780.1			−0.861350			−0.430675	−	0.902507i	$-0.641724\pi$
$79$	−47780.1			−0.861350			−0.430675	+	0.902507i	$0.641724\pi$
$80$	32536.2	−	47097.7i	0.568384	−	0.822763i
$81$	−64788.0			−1.09719
$82$	−40729.4	+	50888.6i	−0.668919	+	0.835768i
$83$	51692.3			0.823628			0.411814	−	0.911268i	$-0.364895\pi$
$83$	51692.3			0.823628			0.411814	+	0.911268i	$0.364895\pi$
$84$	26721.8	−	5999.96i	0.413207	−	0.0927791i
$85$	−26879.6	−	46458.6i	−0.403529	−	0.697459i
$86$	−61356.8	+	76661.1i	−0.894574	+	1.11771i
$87$		−	103641.i		−	1.46802i
$88$	−11245.6	+	23039.0i	−0.154802	+	0.317144i
$89$	122761.			1.64281			0.821404	−	0.570347i	$-0.193191\pi$
$89$	122761.			1.64281			0.821404	+	0.570347i	$0.193191\pi$
$90$	10261.0	−	67687.0i	0.133531	−	0.880844i
$91$		−	27953.9i		−	0.353866i
$92$	−140258.	+	31492.8i	−1.72766	+	0.387920i
$93$	24054.6			0.288397
$94$	−66987.8	−	53614.6i	−0.781945	−	0.625840i
$95$	61649.0	+	106554.i	0.700837	+	1.21132i
$96$	−28696.9	+	120807.i	−0.317803	+	1.33788i
$97$		−	155549.i		−	1.67856i	−0.543696	−	0.839282i	$-0.682976\pi$
$97$		−	155549.i		−	1.67856i	0.543696	−	0.839282i	$-0.317024\pi$
$98$	−53774.4	+	67187.4i	−0.565601	+	0.706680i
$99$			30660.7i			0.314409i
$100$	−95507.1	−	29637.8i	−0.955071	−	0.296378i
$101$		−	195692.i		−	1.90884i	−0.298466	−	0.954420i	$-0.596475\pi$
$101$		−	195692.i		−	1.90884i	0.298466	−	0.954420i	$-0.403525\pi$
$102$	90898.0	+	72751.4i	0.865075	+	0.692374i
$103$			60625.8i			0.563073i	0.959551	+	0.281536i	$0.0908440\pi$
$103$			60625.8i			0.563073i	−0.959551	+	0.281536i	$0.909156\pi$
$104$	113895.	+	55593.4i	1.03257	+	0.504011i
$105$	−23959.6	−	41411.6i	−0.212083	−	0.366563i
$106$	−25164.3	+	31441.1i	−0.217531	+	0.271790i
$107$	10924.2			0.0922422			0.0461211	−	0.998936i	$-0.485314\pi$
$107$	10924.2			0.0922422			0.0461211	+	0.998936i	$0.485314\pi$
$108$	−3983.72	−	17742.1i	−0.0328647	−	0.146368i
$109$		−	11344.4i		−	0.0914569i	−0.998954	−	0.0457285i	$-0.985439\pi$
$109$		−	11344.4i		−	0.0914569i	0.998954	−	0.0457285i	$-0.0145609\pi$
$110$	44280.2	+	6712.63i	0.348921	+	0.0528946i
$111$	188195.			1.44978
$112$	17478.7	+	36959.9i	0.131663	+	0.278410i
$113$		−	66586.5i		−	0.490557i	−0.969453	−	0.245279i	$-0.921121\pi$
$113$		−	66586.5i		−	0.490557i	0.969453	−	0.245279i	$-0.0788795\pi$
$114$	−208477.	−	166857.i	−1.50244	−	1.20249i
$115$	125760.	+	217363.i	0.886743	+	1.53264i
$116$	150960.	−	33895.8i	1.04164	−	0.233884i
$117$	151574.			1.02367
$118$	184438.	+	147617.i	1.21940	+	0.975961i
$119$	38335.2			0.248159
$120$	216377.	−	15263.0i	1.37169	−	0.0967577i
$121$	140993.			0.875456
$122$	89864.4	+	71924.2i	0.546623	+	0.437497i
$123$	−246992.			−1.47204
$124$	7867.04	+	35037.1i	0.0459470	+	0.204632i
$125$	479.446	+	174692.i	0.00274451	+	0.999996i
$126$	38174.5	+	30553.5i	0.214214	+	0.171449i
$127$		−	88813.9i		−	0.488621i	−0.969697	−	0.244310i	$-0.921438\pi$
$127$		−	88813.9i		−	0.488621i	0.969697	−	0.244310i	$-0.0785616\pi$
$128$	−185350.	−	2289.02i	−0.999924	−	0.0123488i
$129$	−372081.			−1.96863
$130$	33184.4	−	218902.i	0.172217	−	1.13604i
$131$		−	83967.1i		−	0.427495i	−0.976889	−	0.213748i	$-0.931433\pi$
$131$		−	83967.1i		−	0.427495i	0.976889	−	0.213748i	$-0.0685670\pi$
$132$	−94787.5	+	21283.0i	−0.473496	+	0.106316i
$133$	−87922.8			−0.430995
$134$	84003.0	−	104956.i	0.404141	−	0.504947i
$135$	−27495.6	+	15908.1i	−0.129846	+	0.0751251i
$136$	−76239.3	+	156192.i	−0.353453	+	0.724124i
$137$			275285.i			1.25309i	0.779387	+	0.626543i	$0.215531\pi$
$137$			275285.i			1.25309i	−0.779387	+	0.626543i	$0.784469\pi$
$138$	−425279.	−	340378.i	−1.90097	−	1.52147i
$139$			153603.i			0.674317i	0.941448	+	0.337158i	$0.109466\pi$
$139$			153603.i			0.674317i	−0.941448	+	0.337158i	$0.890534\pi$
$140$	52482.9	−	48442.4i	0.226307	−	0.208884i
$141$		−	325131.i		−	1.37724i
$142$	−3116.54	+	3893.91i	−0.0129704	+	0.0162056i
$143$			99157.9i			0.405497i
$144$	−200406.	+	94774.3i	−0.805388	+	0.380877i
$145$	−135355.	−	233948.i	−0.534633	−	0.924058i
$146$	31143.5	+	24926.1i	0.120916	+	0.0967772i
$147$	−326100.			−1.24468
$148$	61549.1	+	274119.i	0.230976	+	1.02869i
$149$		−	30715.3i		−	0.113342i	−0.998393	−	0.0566708i	$-0.981951\pi$
$149$		−	30715.3i		−	0.113342i	0.998393	−	0.0566708i	$-0.0180486\pi$
$150$	−138463.	−	352730.i	−0.502465	−	1.28001i
$151$	−25896.6			−0.0924272			−0.0462136	−	0.998932i	$-0.514715\pi$
$151$	−25896.6			−0.0924272			−0.0462136	+	0.998932i	$0.514715\pi$
$152$	174857.	−	358232.i	0.613866	−	1.25764i
$153$			207864.i			0.717878i
$154$	−19987.8	+	24973.4i	−0.0679145	+	0.0848546i
$155$	54298.2	−	31415.3i	0.181533	−	0.105030i
$156$	105214.	+	468589.i	0.346149	+	1.54163i
$157$	334928.			1.08443			0.542216	−	0.840239i	$-0.317585\pi$
$157$	334928.			1.08443			0.542216	+	0.840239i	$0.317585\pi$
$158$	168893.	−	211020.i	0.538230	−	0.672482i
$159$	−152602.			−0.478704
$160$	92997.5	+	310176.i	0.287191	+	0.957873i
$161$	−179357.			−0.545322
$162$	229012.	−	286135.i	0.685600	−	0.856610i
$163$	203546.			0.600057			0.300029	−	0.953930i	$-0.403004\pi$
$163$	203546.			0.600057			0.300029	+	0.953930i	$0.403004\pi$
$164$	−80778.7	−	359761.i	−0.234524	−	1.04449i
$165$	84989.2	+	146895.i	0.243027	+	0.420047i
$166$	−182721.	+	228298.i	−0.514659	+	0.643031i
$167$			52221.5i			0.144897i	0.997372	+	0.0724483i	$0.0230812\pi$
$167$			52221.5i			0.144897i	−0.997372	+	0.0724483i	$0.976919\pi$
$168$	−67957.2	+	139225.i	−0.185764	+	0.380578i
$169$	118902.			0.320236
$170$	300197.	+	45508.2i	0.796680	+	0.120772i
$171$		−	476741.i		−	1.24679i
$172$	−121689.	−	541962.i	−0.313639	−	1.39684i
$173$	−503329.			−1.27861			−0.639303	−	0.768955i	$-0.720777\pi$
$173$	−503329.			−1.27861			−0.639303	+	0.768955i	$0.720777\pi$
$174$	457728.	+	366349.i	1.14613	+	0.917322i
$175$	−108167.	−	62186.9i	−0.266994	−	0.153498i
$176$	−62000.4	−	131104.i	−0.150873	−	0.319032i
$177$			895185.i			2.14773i
$178$	−433935.	+	542173.i	−1.02654	+	1.28259i
$179$			249706.i			0.582501i	0.956647	+	0.291251i	$0.0940713\pi$
$179$			249706.i			0.582501i	−0.956647	+	0.291251i	$0.905929\pi$
$180$	262668.	+	284577.i	0.604263	+	0.654663i
$181$			341157.i			0.774031i	0.922073	+	0.387015i	$0.126494\pi$
$181$			341157.i			0.774031i	−0.922073	+	0.387015i	$0.873506\pi$
$182$	123458.	+	98811.1i	0.276274	+	0.221120i
$183$			436164.i			0.962769i
$184$	356696.	−	730769.i	0.776702	−	1.59124i
$185$	424811.	−	245783.i	0.912571	−	0.527987i
$186$	−85027.8	+	106236.i	−0.180210	+	0.225160i
$187$	−135982.			−0.284367
$188$	473575.	−	106334.i	0.977225	−	0.219420i
$189$		−	22687.9i		−	0.0461998i
$190$	−688509.	−	104374.i	−1.38365	−	0.209753i
$191$	−592636.			−1.17545			−0.587726	−	0.809060i	$-0.699977\pi$
$191$	−592636.			−1.17545			−0.587726	+	0.809060i	$0.699977\pi$
$192$	−432106.	−	553768.i	−0.845935	−	1.08411i
$193$		−	771725.i		−	1.49131i	−0.666330	−	0.745657i	$-0.732136\pi$
$193$		−	771725.i		−	1.49131i	0.666330	−	0.745657i	$-0.267864\pi$
$194$	686979.	+	549833.i	1.31051	+	1.04888i
$195$	726187.	−	420151.i	1.36761	−	0.791259i
$196$	−106651.	−	474987.i	−0.198301	−	0.883164i
$197$	−190213.			−0.349200			−0.174600	−	0.984639i	$-0.555863\pi$
$197$	−190213.			−0.349200			−0.174600	+	0.984639i	$0.555863\pi$
$198$	−135412.	−	108379.i	−0.245468	−	0.196464i
$199$	949154.			1.69904			0.849521	−	0.527555i	$-0.176891\pi$
$199$	949154.			1.69904			0.849521	+	0.527555i	$0.176891\pi$
$200$	468492.	−	317042.i	0.828184	−	0.560456i
$201$	509413.			0.889364
$202$	864269.	+	691730.i	1.49029	+	1.19277i
$203$	193042.			0.328784
$204$	−642610.	+	144288.i	−1.08112	+	0.242748i
$205$	−557533.	+	322572.i	−0.926586	+	0.536096i
$206$	−267753.	−	214299.i	−0.439608	−	0.351846i
$207$		−	972521.i		−	1.57751i
$208$	−648122.	+	306504.i	−1.03872	+	0.491222i
$209$	311879.			0.493879
$210$	267585.	+	40564.5i	0.418711	+	0.0634743i
$211$		−	47751.4i		−	0.0738380i	−0.999318	−	0.0369190i	$-0.988246\pi$
$211$		−	47751.4i		−	0.0738380i	0.999318	−	0.0369190i	$-0.0117544\pi$
$212$	−49908.4	−	222275.i	−0.0762666	−	0.339666i
$213$	−18899.4			−0.0285430
$214$	−38614.7	+	48246.4i	−0.0576392	+	0.0720163i
$215$	−839896.	+	485939.i	−1.23916	+	0.716945i
$216$	92439.4	+	45120.7i	0.134810	+	0.0658024i
$217$			44804.0i			0.0645904i
$218$	50102.4	+	40100.2i	0.0714032	+	0.0571485i
$219$			151158.i			0.212971i
$220$	−186167.	+	171835.i	−0.259326	+	0.239361i
$221$			672239.i			0.925856i
$222$	−665229.	+	831159.i	−0.905918	+	1.13188i
$223$		−	648287.i		−	0.872982i	−0.899709	−	0.436491i	$-0.856221\pi$
$223$		−	648287.i		−	0.872982i	0.899709	−	0.436491i	$-0.143779\pi$
$224$	−225016.	−	53450.9i	−0.299635	−	0.0711762i
$225$	337194.	−	586513.i	0.444042	−	0.772363i
$226$	294078.	+	235369.i	0.382993	+	0.306534i
$227$	17476.8			0.0225111			0.0112556	−	0.999937i	$-0.496417\pi$
$227$	17476.8			0.0225111			0.0112556	+	0.999937i	$0.496417\pi$
$228$	1.47384e6	−	330928.i	1.87765	−	0.421596i
$229$		−	735371.i		−	0.926655i	−0.886187	−	0.463327i	$-0.846655\pi$
$229$		−	735371.i		−	0.926655i	0.886187	−	0.463327i	$-0.153345\pi$
$230$	−1.40451e6	−	212916.i	−1.75068	−	0.265393i
$231$	−121210.			−0.149455
$232$	−383913.	+	786527.i	−0.468287	+	0.959386i
$233$			70875.0i			0.0855270i	0.999085	+	0.0427635i	$0.0136162\pi$
$233$			70875.0i			0.0855270i	−0.999085	+	0.0427635i	$0.986384\pi$
$234$	−535780.	+	669421.i	−0.639657	+	0.799208i
$235$	−424622.	−	733915.i	−0.501571	−	0.866914i
$236$	−1.30390e6	+	292770.i	−1.52392	+	0.342173i
$237$	1.02420e6			1.18445
$238$	−135507.	+	169307.i	−0.155067	+	0.193745i
$239$	−516369.			−0.584743			−0.292372	−	0.956305i	$-0.594444\pi$
$239$	−516369.			−0.584743			−0.292372	+	0.956305i	$0.594444\pi$
$240$	−697437.	+	1.00957e6i	−0.781587	+	1.13138i
$241$	609937.			0.676460			0.338230	−	0.941064i	$-0.390172\pi$
$241$	609937.			0.676460			0.338230	+	0.941064i	$0.390172\pi$
$242$	−498381.	+	622693.i	−0.547045	+	0.683495i
$243$	1.25069e6			1.35874
$244$	−635303.	+	142647.i	−0.683135	+	0.153387i
$245$	−736102.	+	425887.i	−0.783471	+	0.453293i
$246$	873064.	−	1.09083e6i	0.919832	−	1.14927i
$247$		−	1.54180e6i		−	1.60800i
$248$	−182549.	−	89104.2i	−0.188474	−	0.0919960i
$249$	−1.10806e6			−1.13257
$250$	−773219.	−	615382.i	−0.782442	−	0.622723i
$251$		−	327106.i		−	0.327721i	−0.986484	−	0.163860i	$-0.947605\pi$
$251$		−	327106.i		−	0.327721i	0.986484	−	0.163860i	$-0.0523947\pi$
$252$	−269877.	+	60596.7i	−0.267710	+	0.0601102i
$253$	636213.			0.624887
$254$	392245.	+	313938.i	0.381481	+	0.305323i
$255$	576183.	+	995873.i	0.554894	+	0.959077i
$256$	665281.	−	810501.i	0.634462	−	0.772954i
$257$			882853.i			0.833788i	0.908955	+	0.416894i	$0.136881\pi$
$257$			882853.i			0.833788i	−0.908955	+	0.416894i	$0.863119\pi$
$258$	1.31523e6	−	1.64329e6i	1.23013	−	1.53697i
$259$			350532.i			0.324697i
$260$	849478.	+	920332.i	0.779325	+	0.844328i
$261$			1.04672e6i			0.951111i
$262$	370839.	+	296806.i	0.333758	+	0.267128i
$263$		−	454062.i		−	0.404786i	−0.979304	−	0.202393i	$-0.935128\pi$
$263$		−	454062.i		−	0.404786i	0.979304	−	0.202393i	$-0.0648719\pi$
$264$	241058.	−	493858.i	0.212868	−	0.436106i
$265$	−344467.	+	199299.i	−0.301324	+	0.174337i
$266$	310788.	−	388309.i	0.269315	−	0.336491i
$267$	−2.63148e6			−2.25903
$268$	166603.	+	741995.i	0.141692	+	0.631050i
$269$			384748.i			0.324187i	0.986775	+	0.162093i	$0.0518246\pi$
$269$			384748.i			0.324187i	−0.986775	+	0.162093i	$0.948175\pi$
$270$	26933.1	−	177665.i	0.0224842	−	0.148318i
$271$	1.36818e6			1.13167			0.565837	−	0.824517i	$-0.308553\pi$
$271$	1.36818e6			1.13167			0.565837	+	0.824517i	$0.308553\pi$
$272$	−420331.	−	888816.i	−0.344484	−	0.728433i
$273$			599212.i			0.486602i
$274$	−1.21579e6	−	973073.i	−0.978322	−	0.783013i
$275$	383691.	+	220589.i	0.305950	+	0.175894i
$276$	3.00654e6	−	675072.i	2.37572	−	0.533430i
$277$	567739.			0.444579			0.222290	−	0.974981i	$-0.428647\pi$
$277$	567739.			0.444579			0.222290	+	0.974981i	$0.428647\pi$
$278$	−678386.	−	542955.i	−0.526459	−	0.421359i
$279$	−242940.			−0.186848
$280$	28428.8	+	403023.i	0.0216702	+	0.307210i
$281$	−1.90809e6			−1.44156			−0.720779	−	0.693165i	$-0.756216\pi$
$281$	−1.90809e6			−1.44156			−0.720779	+	0.693165i	$0.756216\pi$
$282$	1.43593e6	+	1.14927e6i	1.07525	+	0.860594i
$283$	−873157.			−0.648077			−0.324038	−	0.946044i	$-0.605041\pi$
$283$	−873157.			−0.648077			−0.324038	+	0.946044i	$0.605041\pi$
$284$	−6181.04	−	27528.3i	−0.00454743	−	0.0202527i
$285$	−1.32149e6	−	2.28406e6i	−0.963723	−	1.66570i
$286$	−437929.	−	350502.i	−0.316584	−	0.253382i
$287$		−	460047.i		−	0.329684i
$288$	289825.	−	1.22010e6i	0.205899	−	0.866789i
$289$	497966.			0.350716
$290$	1.51168e6	+	229162.i	1.05552	+	0.160010i
$291$			3.33431e6i			2.30820i
$292$	−220171.	+	49436.0i	−0.151114	+	0.0339302i
$293$	422723.			0.287665			0.143832	−	0.989602i	$-0.454057\pi$
$293$	422723.			0.287665			0.143832	+	0.989602i	$0.454057\pi$
$294$	1.15269e6	−	1.44021e6i	0.777760	−	0.971758i
$295$	1.16911e6	+	2.02069e6i	0.782171	+	1.35190i
$296$	−1.42820e6	−	697122.i	−0.947460	−	0.462466i
$297$			80478.5i			0.0529406i
$298$	135654.	+	108572.i	0.0884893	+	0.0708236i
$299$		−	3.14517e6i		−	2.03454i
$300$	2.04726e6	+	635308.i	1.31332	+	0.407550i
$301$		−	693038.i		−	0.440901i
$302$	91538.9	−	114372.i	0.0577548	−	0.0721608i
$303$			4.19480e6i			2.62485i
$304$	964040.	+	2.03852e6i	0.598289	+	1.26512i
$305$	569632.	+	984550.i	0.350626	+	0.606021i
$306$	−918026.	−	734755.i	−0.560469	−	0.448579i
$307$	1.38323e6			0.837624			0.418812	−	0.908073i	$-0.362447\pi$
$307$	1.38323e6			0.837624			0.418812	+	0.908073i	$0.362447\pi$
$308$	−39641.8	−	176551.i	−0.0238109	−	0.106046i
$309$		−	1.29956e6i		−	0.774283i
$310$	−53187.4	+	350853.i	−0.0314344	+	0.207358i
$311$	−1.96775e6			−1.15363			−0.576817	−	0.816873i	$-0.695706\pi$
$311$	−1.96775e6			−1.15363			−0.576817	+	0.816873i	$0.695706\pi$
$312$	−2.44142e6	−	1.19169e6i	−1.41990	−	0.693067i
$313$		−	2.42724e6i		−	1.40040i	−0.713948	−	0.700199i	$-0.753095\pi$
$313$		−	2.42724e6i		−	1.40040i	0.713948	−	0.700199i	$-0.246905\pi$
$314$	−1.18390e6	+	1.47920e6i	−0.677627	+	0.846650i
$315$	241980.	+	418238.i	0.137405	+	0.237491i
$316$	334965.	+	1.49182e6i	0.188704	+	0.840425i
$317$	1.28631e6			0.718951			0.359475	−	0.933155i	$-0.382956\pi$
$317$	1.28631e6			0.718951			0.359475	+	0.933155i	$0.382956\pi$
$318$	539416.	−	673963.i	0.299127	−	0.373739i
$319$	−684757.			−0.376756
$320$	−1.69861e6	−	685684.i	−0.927297	−	0.374325i
$321$	−234168.			−0.126843
$322$	633988.	−	792125.i	0.340754	−	0.425749i
$323$	2.11438e6			1.12766
$324$	454200.	+	2.02285e6i	0.240372	+	1.07054i
$325$	1.09050e6	−	1.89680e6i	0.572686	−	0.996126i
$326$	−719491.	+	898955.i	−0.374957	+	0.468483i
$327$			243176.i			0.125763i
$328$	1.87441e6	+	914921.i	0.962012	+	0.469569i
$329$	605588.			0.308452
$330$	−949178.	−	143890.i	−0.479803	−	0.0727355i
$331$			3.07996e6i			1.54517i	0.634913	+	0.772584i	$0.281036\pi$
$331$			3.07996e6i			1.54517i	−0.634913	+	0.772584i	$0.718964\pi$
$332$	−362392.	−	1.61397e6i	−0.180440	−	0.803619i
$333$	−1.90068e6			−0.939287
$334$	−230635.	−	184592.i	−0.113125	−	0.0905413i
$335$	1.14989e6	−	665294.i	0.559816	−	0.323893i
$336$	−374669.	−	792262.i	−0.181050	−	0.382843i
$337$			1.51034e6i			0.724437i	0.932093	+	0.362218i	$0.117981\pi$
$337$			1.51034e6i			0.724437i	−0.932093	+	0.362218i	$0.882019\pi$
$338$	−420292.	+	525126.i	−0.200105	+	0.250018i
$339$			1.42733e6i			0.674567i
$340$	−1.26212e6	+	1.16495e6i	−0.592110	+	0.546525i
$341$		−	158929.i		−	0.0740144i
$342$	2.10552e6	+	1.68518e6i	0.973405	+	0.779078i
$343$		−	1.27843e6i		−	0.586736i
$344$	2.82371e6	+	1.37828e6i	1.28654	+	0.627975i
$345$	−2.69576e6	−	4.65934e6i	−1.21936	−	2.10754i
$346$	1.77916e6	−	2.22294e6i	0.798960	−	0.998246i
$347$	−4.01257e6			−1.78895			−0.894477	−	0.447113i	$-0.852452\pi$
$347$	−4.01257e6			−1.78895			−0.894477	+	0.447113i	$0.852452\pi$
$348$	−3.23594e6	+	726580.i	−1.43236	+	0.321614i
$349$			595449.i			0.261686i	0.991403	+	0.130843i	$0.0417684\pi$
$349$			595449.i			0.261686i	−0.991403	+	0.130843i	$0.958232\pi$
$350$	656996.	−	257902.i	0.286677	−	0.112534i
$351$	397852.			0.172367
$352$	798176.	+	189601.i	0.343354	+	0.0815612i
$353$		−	1.05328e6i		−	0.449890i	−0.974371	−	0.224945i	$-0.927780\pi$
$353$		−	1.05328e6i		−	0.449890i	0.974371	−	0.224945i	$-0.0722203\pi$
$354$	−3.95356e6	−	3.16429e6i	−1.67680	−	1.34205i
$355$	−42661.5	+	24682.7i	−0.0179666	+	0.0103949i
$356$	−860624.	−	3.83293e6i	−0.359906	−	1.60290i
$357$	−821743.			−0.341244
$358$	−1.10282e6	−	882659.i	−0.454776	−	0.363986i
$359$	549662.			0.225092			0.112546	−	0.993647i	$-0.464099\pi$
$359$	549662.			0.225092			0.112546	+	0.993647i	$0.464099\pi$
$360$	−2.18530e6	+	154149.i	−0.888700	+	0.0626878i
$361$	−2.37329e6			−0.958480
$362$	−1.50671e6	−	1.20592e6i	−0.604309	−	0.483667i
$363$	−3.02229e6			−1.20384
$364$	−872794.	+	195972.i	−0.345269	+	0.0775248i
$365$	197412.	+	341207.i	0.0775607	+	0.134056i
$366$	−1.92631e6	−	1.54175e6i	−0.751663	−	0.601604i
$367$			313163.i			0.121368i	0.998157	+	0.0606842i	$0.0193283\pi$
$367$			313163.i			0.121368i	−0.998157	+	0.0606842i	$0.980672\pi$
$368$	1.96658e6	+	4.15845e6i	0.756993	+	1.60071i
$369$	2.49450e6			0.953713
$370$	−416121.	+	2.74496e6i	−0.158021	+	1.04239i
$371$		−	284236.i		−	0.107212i
$372$	−168636.	−	751047.i	−0.0631818	−	0.281391i
$373$	251757.			0.0936935			0.0468468	−	0.998902i	$-0.485083\pi$
$373$	251757.			0.0936935			0.0468468	+	0.998902i	$0.485083\pi$
$374$	480669.	−	600564.i	0.177692	−	0.222014i
$375$	−10277.3	−	3.74465e6i	−0.00377399	−	1.37510i
$376$	−1.20437e6	+	2.46740e6i	−0.439328	+	0.900058i
$377$			3.38515e6i			1.22666i
$378$	100201.	+	80197.0i	0.0360696	+	0.0288688i
$379$		−	862618.i		−	0.308476i	−0.988034	−	0.154238i	$-0.950708\pi$
$379$		−	862618.i		−	0.308476i	0.988034	−	0.154238i	$-0.0492922\pi$
$380$	2.89470e6	−	2.67185e6i	1.02836	−	0.949188i
$381$			1.90379e6i			0.671904i
$382$	2.09484e6	−	2.61736e6i	0.734502	−	0.917711i
$383$		−	4.09103e6i		−	1.42507i	−0.701638	−	0.712534i	$-0.747547\pi$
$383$		−	4.09103e6i		−	1.42507i	0.701638	−	0.712534i	$-0.252453\pi$
$384$	3.97311e6	+	49066.9i	1.37500	+	0.0169809i
$385$	−273607.	+	158301.i	−0.0940752	+	0.0544292i
$386$	3.40831e6	+	2.72788e6i	1.16431	+	0.931875i
$387$	3.75784e6			1.27544
$388$	−4.85665e6	+	1.09048e6i	−1.63779	+	0.367739i
$389$			5.39187e6i			1.80661i	0.428995	+	0.903307i	$0.358868\pi$
$389$			5.39187e6i			1.80661i	−0.428995	+	0.903307i	$0.641132\pi$
$390$	−711332.	+	4.69233e6i	−0.236816	+	1.56217i
$391$	4.31320e6			1.42678
$392$	2.47476e6	+	1.20796e6i	0.813424	+	0.397042i
$393$			1.79990e6i			0.587850i
$394$	672363.	−	840072.i	0.218204	−	0.272631i
$395$	2.31192e6	−	1.33761e6i	0.745557	−	0.431357i
$396$	957308.	−	214949.i	0.306771	−	0.0688805i
$397$	5.41902e6			1.72562			0.862809	−	0.505529i	$-0.168703\pi$
$397$	5.41902e6			1.72562			0.862809	+	0.505529i	$0.168703\pi$
$398$	−3.35506e6	+	4.19192e6i	−1.06168	+	1.32649i
$399$	1.88469e6			0.592663
$400$	−255812.	+	3.18976e6i	−0.0799414	+	0.996800i
$401$	3.22720e6			1.00222			0.501112	−	0.865383i	$-0.332925\pi$
$401$	3.22720e6			1.00222			0.501112	+	0.865383i	$0.332925\pi$
$402$	−1.80067e6	+	2.24981e6i	−0.555735	+	0.694354i
$403$	−785676.			−0.240980
$404$	−6.11002e6	+	1.37191e6i	−1.86247	+	0.418188i
$405$	3.13488e6	−	1.81375e6i	0.949693	−	0.549464i
$406$	−682361.	+	852564.i	−0.205447	+	0.256692i
$407$		−	1.24341e6i		−	0.372072i
$408$	1.63425e6	−	3.34810e6i	0.486034	−	0.995745i
$409$	523436.			0.154723			0.0773616	−	0.997003i	$-0.475350\pi$
$409$	523436.			0.154723			0.0773616	+	0.997003i	$0.475350\pi$
$410$	546128.	−	3.60256e6i	0.160448	−	1.05840i
$411$		−	5.90093e6i		−	1.72312i
$412$	1.89290e6	−	425020.i	0.549394	−	0.123358i
$413$	−1.66737e6			−0.481013
$414$	4.29512e6	+	3.43765e6i	1.23161	+	0.985738i
$415$	−2.50122e6	+	1.44713e6i	−0.712906	+	0.412466i
$416$	937306.	−	3.94584e6i	0.265551	−	1.11791i
$417$		−	3.29260e6i		−	0.927255i
$418$	−1.10243e6	+	1.37741e6i	−0.308610	+	0.385587i
$419$		−	3.66116e6i		−	1.01879i	−0.860534	−	0.509393i	$-0.829870\pi$
$419$		−	3.66116e6i		−	1.01879i	0.860534	−	0.509393i	$-0.170130\pi$
$420$	−1.12501e6	+	1.03840e6i	−0.311195	+	0.287237i
$421$		−	3.15337e6i		−	0.867101i	−0.901129	−	0.433550i	$-0.857261\pi$
$421$		−	3.15337e6i		−	0.867101i	0.901129	−	0.433550i	$-0.142739\pi$
$422$	210893.	+	168791.i	0.0576476	+	0.0461390i
$423$			3.28366e6i			0.892294i
$424$	1.15809e6	+	565277.i	0.312844	+	0.152703i
$425$	2.60123e6	+	1.49548e6i	0.698564	+	0.401613i
$426$	66805.4	−	83468.8i	0.0178356	−	0.0222844i
$427$	−812399.			−0.215625
$428$	−76584.6	−	341082.i	−0.0202084	−	0.0900014i
$429$		−	2.12552e6i		−	0.557600i
$430$	822714.	−	5.42707e6i	0.214574	−	1.41545i
$431$	−1.92170e6			−0.498301			−0.249151	−	0.968465i	$-0.580151\pi$
$431$	−1.92170e6			−0.498301			−0.249151	+	0.968465i	$0.580151\pi$
$432$	−526028.	+	248764.i	−0.135613	+	0.0641326i
$433$			3.16413e6i			0.811025i	0.914089	+	0.405513i	$0.132907\pi$
$433$			3.16413e6i			0.811025i	−0.914089	+	0.405513i	$0.867093\pi$
$434$	−197876.	−	158373.i	−0.0504277	−	0.0403605i
$435$	2.90144e6	+	5.01485e6i	0.735175	+	1.27067i
$436$	−354203.	+	79530.7i	−0.0892352	+	0.0200364i
$437$	−9.89244e6			−2.47799
$438$	−667584.	−	534310.i	−0.166273	−	0.133079i
$439$	−7.05163e6			−1.74634			−0.873169	−	0.487417i	$-0.837939\pi$
$439$	−7.05163e6			−1.74634			−0.873169	+	0.487417i	$0.837939\pi$
$440$	−100842.	−	1.42960e6i	−0.0248320	−	0.352033i
$441$	3.29345e6			0.806408
$442$	−2.96893e6	−	2.37622e6i	−0.722844	−	0.578538i
$443$	−722258.			−0.174857			−0.0874285	−	0.996171i	$-0.527865\pi$
$443$	−722258.			−0.174857			−0.0874285	+	0.996171i	$0.527865\pi$
$444$	−1.31935e6	−	5.87594e6i	−0.317616	−	1.41456i
$445$	−5.94002e6	+	3.43672e6i	−1.42196	+	0.822705i
$446$	2.86314e6	+	2.29156e6i	0.681563	+	0.545498i
$447$			658406.i			0.155856i
$448$	1.03145e6	−	804840.i	0.242802	−	0.189459i
$449$	1.24334e6			0.291055			0.145528	−	0.989354i	$-0.453512\pi$
$449$	1.24334e6			0.291055			0.145528	+	0.989354i	$0.453512\pi$
$450$	1.39841e6	+	3.56241e6i	0.325540	+	0.829302i
$451$			1.63188e6i			0.377786i
$452$	−2.07900e6	+	466808.i	−0.478640	+	0.107471i
$453$	555112.			0.127097
$454$	−61776.8	+	77185.9i	−0.0140665	+	0.0175751i
$455$	782573.	+	1.35260e6i	0.177213	+	0.306295i
$456$	−3.74819e6	+	7.67896e6i	−0.844129	+	1.72938i
$457$		−	4.26434e6i		−	0.955127i	−0.878597	−	0.477564i	$-0.841520\pi$
$457$		−	4.26434e6i		−	0.955127i	0.878597	−	0.477564i	$-0.158480\pi$
$458$	3.24775e6	+	2.59938e6i	0.723467	+	0.579037i
$459$			545603.i			0.120877i
$460$	5.90500e6	−	5.45039e6i	1.30114	−	1.20097i
$461$			3.17128e6i			0.694997i	0.937681	+	0.347498i	$0.112969\pi$
$461$			3.17128e6i			0.694997i	−0.937681	+	0.347498i	$0.887031\pi$
$462$	428453.	−	535323.i	0.0933895	−	0.116684i
$463$			605017.i			0.131164i	0.997847	+	0.0655821i	$0.0208904\pi$
$463$			605017.i			0.131164i	−0.997847	+	0.0655821i	$0.979110\pi$
$464$	−2.11663e6	−	4.47575e6i	−0.456404	−	0.965096i
$465$	−1.16392e6	+	673411.i	−0.249627	+	0.144427i
$466$	−313018.	−	250528.i	−0.0667735	−	0.0534431i
$467$	7.35248e6			1.56006			0.780031	−	0.625741i	$-0.215203\pi$
$467$	7.35248e6			1.56006			0.780031	+	0.625741i	$0.215203\pi$
$468$	−1.06261e6	−	4.73252e6i	−0.224265	−	0.998799i
$469$			948832.i			0.199185i
$470$	4.74227e6	+	718901.i	0.990242	+	0.150115i
$471$	−7.17943e6			−1.49121
$472$	3.31599e6	−	6.79352e6i	0.685107	−	1.40359i
$473$			2.45834e6i			0.505230i
$474$	−3.62034e6	+	4.52337e6i	−0.740122	+	0.924732i
$475$	−5.96598e6	−	3.42992e6i	−1.21324	−	0.697510i
$476$	−268751.	−	1.19693e6i	−0.0543666	−	0.242131i
$477$	1.54121e6			0.310145
$478$	1.82525e6	−	2.28053e6i	0.365388	−	0.456527i
$479$	−3.01150e6			−0.599714			−0.299857	−	0.953984i	$-0.596939\pi$
$479$	−3.01150e6			−0.599714			−0.299857	+	0.953984i	$0.596939\pi$
$480$	−1.99347e6	−	6.64885e6i	−0.394918	−	1.31717i
$481$	−6.14687e6			−1.21141
$482$	−2.15600e6	+	2.69377e6i	−0.422698	+	0.528133i
$483$	3.84464e6			0.749874
$484$	−988439.	−	4.40217e6i	−0.191795	−	0.854189i
$485$	4.35461e6	+	7.52650e6i	0.840612	+	1.45291i
$486$	−4.42094e6	+	5.52367e6i	−0.849032	+	1.06081i
$487$			3.76217e6i			0.718813i	0.933181	+	0.359407i	$0.117021\pi$
$487$			3.76217e6i			0.718813i	−0.933181	+	0.359407i	$0.882979\pi$
$488$	1.61566e6	−	3.31003e6i	0.307115	−	0.629191i
$489$	−4.36315e6			−0.825141
$490$	721044.	−	4.75640e6i	0.135666	−	0.894928i
$491$		−	5.68936e6i		−	1.06502i	−0.846422	−	0.532512i	$-0.821248\pi$
$491$		−	5.68936e6i		−	1.06502i	0.846422	−	0.532512i	$-0.178752\pi$
$492$	1.73155e6	+	7.71174e6i	0.322494	+	1.43628i
$493$	−4.64230e6			−0.860232
$494$	6.80932e6	+	5.44993e6i	1.25541	+	1.00479i
$495$	−858351.	−	1.48357e6i	−0.157453	−	0.272142i
$496$	1.03880e6	−	491259.i	0.189595	−	0.0896616i
$497$		−	35202.0i		−	0.00639259i
$498$	3.91677e6	−	4.89374e6i	0.707709	−	0.884234i
$499$			8.16772e6i			1.46842i	0.678924	+	0.734208i	$0.262447\pi$
$499$			8.16772e6i			1.46842i	−0.678924	+	0.734208i	$0.737553\pi$
$500$	5.45099e6	−	1.23966e6i	0.975102	−	0.221757i
$501$		−	1.11941e6i		−	0.199248i
$502$	1.44466e6	+	1.15625e6i	0.255862	+	0.204782i
$503$			207353.i			0.0365419i	0.999833	+	0.0182709i	$0.00581615\pi$
$503$			207353.i			0.0365419i	−0.999833	+	0.0182709i	$0.994184\pi$
$504$	686335.	−	1.40610e6i	0.120354	−	0.246571i
$505$	5.47842e6	+	9.46889e6i	0.955932	+	1.65223i
$506$	−2.24888e6	+	2.80982e6i	−0.390472	+	0.487868i
$507$	−2.54874e6			−0.440358
$508$	−2.77300e6	+	622635.i	−0.476751	+	0.107047i
$509$		−	4.43777e6i		−	0.759224i	−0.925146	−	0.379612i	$-0.876057\pi$
$509$		−	4.43777e6i		−	0.759224i	0.925146	−	0.379612i	$-0.123943\pi$
$510$	−6.43494e6	−	975501.i	−1.09552	−	0.166074i
$511$	−281546.			−0.0476977
$512$	1.22793e6	+	5.80315e6i	0.207014	+	0.978338i
$513$		−	1.25135e6i		−	0.209936i
$514$	−3.89910e6	−	3.12070e6i	−0.650963	−	0.521007i
$515$	−1.69723e6	−	2.93348e6i	−0.281982	−	0.487377i
$516$	2.60849e6	+	1.16173e7i	0.431286	+	1.92080i
$517$	−2.14814e6			−0.353457
$518$	−1.54812e6	−	1.23906e6i	−0.253501	−	0.202893i
$519$	1.07892e7			1.75821
$520$	−7.06735e6	+	498522.i	−1.14617	+	0.0808493i
$521$	8.59405e6			1.38709			0.693543	−	0.720415i	$-0.256049\pi$
$521$	8.59405e6			1.38709			0.693543	+	0.720415i	$0.256049\pi$
$522$	−4.62284e6	−	3.69995e6i	−0.742561	−	0.594319i
$523$	−4.23189e6			−0.676519			−0.338259	−	0.941053i	$-0.609838\pi$
$523$	−4.23189e6			−0.676519			−0.338259	+	0.941053i	$0.609838\pi$
$524$	−2.62167e6	+	588656.i	−0.417110	+	0.0936555i
$525$	2.31865e6	+	1.33302e6i	0.367144	+	0.211076i
$526$	2.00535e6	+	1.60501e6i	0.316029	+	0.252938i
$527$		−	1.07745e6i		−	0.168994i
$528$	1.32902e6	+	2.81031e6i	0.207467	+	0.438701i
$529$	−1.37436e7			−2.13531
$530$	337420.	−	2.22581e6i	0.0521773	−	0.344190i
$531$		−	9.04094e6i		−	1.39148i
$532$	616387.	+	2.74518e6i	0.0944223	+	0.420525i
$533$	8.06731e6			1.23002
$534$	9.30172e6	−	1.16219e7i	1.41160	−	1.76369i
$535$	−528585.	+	305824.i	−0.0798419	+	0.0461942i
$536$	−3.86591e6	−	1.88699e6i	−0.581219	−	0.283700i
$537$		−	5.35264e6i		−	0.800999i
$538$	−1.69923e6	−	1.36000e6i	−0.253103	−	0.202574i
$539$			2.15454e6i			0.319436i
$540$	689453.	+	746959.i	0.101747	+	0.110233i
$541$		−	1.04071e7i		−	1.52875i	−0.644770	−	0.764377i	$-0.723047\pi$
$541$		−	1.04071e7i		−	1.52875i	0.644770	−	0.764377i	$-0.276953\pi$
$542$	−4.83624e6	+	6.04255e6i	−0.707147	+	0.883532i
$543$		−	7.31296e6i		−	1.06437i
$544$	5.41122e6	+	1.28540e6i	0.783967	+	0.186226i
$545$	317589.	+	548920.i	0.0458009	+	0.0791622i
$546$	−2.64641e6	−	2.11809e6i	−0.379905	−	0.304062i
$547$	2.44104e6			0.348825			0.174412	−	0.984673i	$-0.444197\pi$
$547$	2.44104e6			0.348825			0.174412	+	0.984673i	$0.444197\pi$
$548$	8.59511e6	−	1.92990e6i	1.22264	−	0.274526i
$549$		−	4.40505e6i		−	0.623763i
$550$	−2.33049e6	+	914827.i	−0.328504	+	0.128953i
$551$	1.06472e7			1.49402
$552$	−7.64605e6	+	1.56646e7i	−1.06804	+	2.18812i
$553$			1.90768e6i			0.265273i
$554$	−2.00684e6	+	2.50740e6i	−0.277803	+	0.347096i
$555$	−9.10614e6	+	5.26854e6i	−1.25488	+	0.726036i
$556$	4.79590e6	−	1.07684e6i	0.657935	−	0.147729i
$557$	2.55398e6			0.348803			0.174402	−	0.984675i	$-0.444201\pi$
$557$	2.55398e6			0.348803			0.174402	+	0.984675i	$0.444201\pi$
$558$	858740.	−	1.07294e6i	0.116755	−	0.145878i
$559$	1.21530e7			1.64495
$560$	−1.88043e6	−	1.29905e6i	−0.253389	−	0.175047i
$561$	2.91488e6			0.391034
$562$	6.74468e6	−	8.42702e6i	0.900784	−	1.12547i
$563$	6.75752e6			0.898496			0.449248	−	0.893407i	$-0.351692\pi$
$563$	6.75752e6			0.898496			0.449248	+	0.893407i	$0.351692\pi$
$564$	−1.01514e7	+	2.27934e6i	−1.34378	+	0.301726i
$565$	1.86410e6	+	3.22190e6i	0.245667	+	0.424611i
$566$	3.08643e6	−	3.85628e6i	0.404963	−	0.505973i
$567$			2.58674e6i			0.337905i
$568$	143427.	+	70008.2i	0.0186535	+	0.00910496i
$569$	9.34676e6			1.21027			0.605133	−	0.796125i	$-0.293120\pi$
$569$	9.34676e6			1.21027			0.605133	+	0.796125i	$0.293120\pi$
$570$	1.47587e7	+	2.23734e6i	1.90266	+	0.288433i
$571$		−	1.78748e6i		−	0.229431i	−0.993398	−	0.114715i	$-0.963404\pi$
$571$		−	1.78748e6i		−	0.229431i	0.993398	−	0.114715i	$-0.0365956\pi$
$572$	3.09597e6	−	695152.i	0.395646	−	0.0888361i
$573$	1.27036e7			1.61637
$574$	2.03179e6	+	1.62617e6i	0.257394	+	0.206009i
$575$	−1.21702e7	−	6.99682e6i	−1.53507	−	0.882533i
$576$	4.36406e6	+	5.59279e6i	0.548068	+	0.702381i
$577$		−	8.09579e6i		−	1.01232i	−0.862438	−	0.506162i	$-0.831064\pi$
$577$		−	8.09579e6i		−	1.01232i	0.862438	−	0.506162i	$-0.168936\pi$
$578$	−1.76020e6	+	2.19926e6i	−0.219151	+	0.273814i
$579$			1.65425e7i			2.05071i
$580$	−6.35555e6	+	5.86626e6i	−0.784483	+	0.724087i
$581$		−	2.06388e6i		−	0.253655i
$582$	−1.47259e7	−	1.17861e7i	−1.80208	−	1.44232i
$583$			1.00824e6i			0.122855i
$584$	559926.	−	1.14713e6i	0.0679358	−	0.139181i
$585$	−7.33414e6	+	4.24332e6i	−0.886053	+	0.512644i
$586$	−1.49424e6	+	1.86695e6i	−0.179753	+	0.224589i
$587$	3.38443e6			0.405407			0.202703	−	0.979240i	$-0.435027\pi$
$587$	3.38443e6			0.405407			0.202703	+	0.979240i	$0.435027\pi$
$588$	2.28614e6	+	1.01817e7i	0.272684	+	1.21444i
$589$			2.47117e6i			0.293504i
$590$	−1.30569e7	−	1.97936e6i	−1.54422	−	0.234096i
$591$	4.07736e6			0.480186
$592$	8.12722e6	−	3.84345e6i	0.953099	−	0.450731i
$593$		−	1.19814e7i		−	1.39917i	−0.714549	−	0.699585i	$-0.753368\pi$
$593$		−	1.19814e7i		−	1.39917i	0.714549	−	0.699585i	$-0.246632\pi$
$594$	−355432.	−	284475.i	−0.0413323	−	0.0330809i
$595$	−1.85491e6	+	1.07320e6i	−0.214799	+	0.124276i
$596$	−959013.	+	215331.i	−0.110588	+	0.0248309i
$597$	−2.03458e7			−2.33636
$598$	1.38906e7	+	1.11175e7i	1.58843	+	1.27132i
$599$	−5.66907e6			−0.645572			−0.322786	−	0.946472i	$-0.604619\pi$
$599$	−5.66907e6			−0.645572			−0.322786	+	0.946472i	$0.604619\pi$
$600$	−1.00425e7	+	6.79602e6i	−1.13884	+	0.770684i
$601$	−2.59514e6			−0.293072			−0.146536	−	0.989205i	$-0.546812\pi$
$601$	−2.59514e6			−0.293072			−0.146536	+	0.989205i	$0.546812\pi$
$602$	3.06079e6	+	2.44974e6i	0.344225	+	0.275505i
$603$	−5.14483e6			−0.576206
$604$	181549.	+	808559.i	0.0202489	+	0.0901819i
$605$	−6.82219e6	+	3.94712e6i	−0.757766	+	0.438421i
$606$	−1.85262e7	−	1.48277e7i	−2.04930	−	1.64019i
$607$			1.37152e7i			1.51089i	0.655214	+	0.755443i	$0.272578\pi$
$607$			1.37152e7i			1.51089i	−0.655214	+	0.755443i	$0.727422\pi$
$608$	−1.24108e7	−	2.94809e6i	−1.36157	−	0.323431i
$609$	−4.13799e6			−0.452112
$610$	−6.36177e6	−	964409.i	−0.692234	−	0.104939i
$611$			1.06195e7i			1.15080i
$612$	6.49006e6	−	1.45724e6i	0.700438	−	0.157272i
$613$	8.09513e6			0.870107			0.435054	−	0.900405i	$-0.356729\pi$
$613$	8.09513e6			0.870107			0.435054	+	0.900405i	$0.356729\pi$
$614$	−4.88943e6	+	6.10902e6i	−0.523405	+	0.653959i
$615$	1.19511e7	−	6.91457e6i	1.27415	−	0.737187i
$616$	919859.	+	448994.i	0.0976719	+	0.0476748i
$617$		−	5.98284e6i		−	0.632695i	−0.948643	−	0.316347i	$-0.897543\pi$
$617$		−	5.98284e6i		−	0.632695i	0.948643	−	0.316347i	$-0.102457\pi$
$618$	5.73947e6	+	4.59366e6i	0.604506	+	0.483825i
$619$			719050.i			0.0754280i	0.999289	+	0.0377140i	$0.0120076\pi$
$619$			719050.i			0.0754280i	−0.999289	+	0.0377140i	$0.987992\pi$
$620$	−1.36153e6	−	1.47509e6i	−0.142248	−	0.154113i
$621$		−	2.55268e6i		−	0.265624i
$622$	6.95557e6	−	8.69051e6i	0.720870	−	0.900678i
$623$		−	4.90139e6i		−	0.505940i
$624$	1.38930e7	−	6.57013e6i	1.42835	−	0.675480i
$625$	−4.91373e6	−	8.43935e6i	−0.503166	−	0.864190i
$626$	1.07198e7	+	8.57977e6i	1.09333	+	0.875064i
$627$	−6.68536e6			−0.679135
$628$	−2.34803e6	−	1.04573e7i	−0.237577	−	1.05809i
$629$		−	8.42965e6i		−	0.849538i
$630$	−2.70249e6	−	409682.i	−0.271276	−	0.0411240i
$631$	−8.84500e6			−0.884350			−0.442175	−	0.896929i	$-0.645793\pi$
$631$	−8.84500e6			−0.884350			−0.442175	+	0.896929i	$0.645793\pi$
$632$	−7.77263e6	−	3.79391e6i	−0.774061	−	0.377828i
$633$			1.02359e6i			0.101535i
$634$	−4.54685e6	+	5.68098e6i	−0.449249	+	0.561307i
$635$	2.48636e6	+	4.29741e6i	0.244697	+	0.422934i
$636$	1.06982e6	+	4.76463e6i	0.104874	+	0.467075i
$637$	1.06511e7			1.04003
$638$	2.42047e6	−	3.02421e6i	0.235423	−	0.294144i
$639$	190875.			0.0184925
$640$	9.03254e6	−	5.07813e6i	0.871686	−	0.490065i
$641$	−1.09511e7			−1.05272			−0.526360	−	0.850262i	$-0.676443\pi$
$641$	−1.09511e7			−1.05272			−0.526360	+	0.850262i	$0.676443\pi$
$642$	827734.	−	1.03420e6i	0.0792599	−	0.0990298i
$643$	−3.55893e6			−0.339462			−0.169731	−	0.985490i	$-0.554290\pi$
$643$	−3.55893e6			−0.339462			−0.169731	+	0.985490i	$0.554290\pi$
$644$	1.25739e6	+	5.59999e6i	0.119469	+	0.532074i
$645$	1.80038e7	−	1.04165e7i	1.70398	−	0.985873i
$646$	−7.47389e6	+	9.33812e6i	−0.704637	+	0.880396i
$647$			2.00678e7i			1.88469i	0.334649	+	0.942343i	$0.391382\pi$
$647$			2.00678e7i			1.88469i	−0.334649	+	0.942343i	$0.608618\pi$
$648$	−1.05394e7	−	5.14439e6i	−0.986001	−	0.481278i
$649$	5.91449e6			0.551195
$650$	4.52252e6	+	1.15210e7i	0.419853	+	1.06956i
$651$		−	960407.i		−	0.0888184i
$652$	−1.42697e6	−	6.35523e6i	−0.131460	−	0.585480i
$653$	−1.67704e7			−1.53907			−0.769537	−	0.638602i	$-0.779513\pi$
$653$	−1.67704e7			−1.53907			−0.769537	+	0.638602i	$0.779513\pi$
$654$	−1.07398e6	−	859576.i	−0.0981867	−	0.0785851i
$655$	2.35067e6	+	4.06289e6i	0.214086	+	0.370026i
$656$	−1.06664e7	+	5.04424e6i	−0.967737	+	0.457653i
$657$		−	1.52662e6i		−	0.137980i
$658$	−2.14063e6	+	2.67457e6i	−0.192742	+	0.240818i
$659$		−	1.99619e7i		−	1.79055i	−0.445510	−	0.895277i	$-0.646978\pi$
$659$		−	1.99619e7i		−	1.79055i	0.445510	−	0.895277i	$-0.353022\pi$
$660$	3.99063e6	−	3.68340e6i	0.356600	−	0.329147i
$661$		−	4.41003e6i		−	0.392589i	−0.980545	−	0.196295i	$-0.937109\pi$
$661$		−	4.41003e6i		−	0.392589i	0.980545	−	0.196295i	$-0.0628909\pi$
$662$	−1.36026e7	−	1.08870e7i	−1.20636	−	0.965526i
$663$		−	1.44099e7i		−	1.27315i
$664$	8.40904e6	+	4.10455e6i	0.740161	+	0.361281i
$665$	4.25429e6	−	2.46141e6i	0.373055	−	0.215839i
$666$	6.71850e6	−	8.39431e6i	0.586931	−	0.733330i
$667$	2.17197e7			1.89033
$668$	1.63049e6	−	366102.i	0.141377	−	0.0317439i
$669$			1.38965e7i			1.20044i
$670$	−1.12637e6	+	7.43015e6i	−0.0969380	+	0.639456i
$671$	2.88174e6			0.247086
$672$	4.82338e6	+	1.14576e6i	0.412030	+	0.0978747i
$673$			1.91274e7i			1.62787i	0.580959	+	0.813933i	$0.302678\pi$
$673$			1.91274e7i			1.62787i	−0.580959	+	0.813933i	$0.697322\pi$
$674$	−6.67039e6	−	5.33874e6i	−0.565590	−	0.452677i
$675$	885070.	−	1.53948e6i	0.0747684	−	0.130052i
$676$	−833565.	−	3.71242e6i	−0.0701573	−	0.312457i
$677$	−1.47330e7			−1.23544			−0.617718	−	0.786399i	$-0.711943\pi$
$677$	−1.47330e7			−1.23544			−0.617718	+	0.786399i	$0.711943\pi$
$678$	−6.30377e6	−	5.04531e6i	−0.526655	−	0.421515i
$679$	−6.21048e6			−0.516953
$680$	−683660.	−	9.69197e6i	−0.0566980	−	0.803785i
$681$	−374628.			−0.0309551
$682$	701905.	+	561779.i	0.0577853	+	0.0462493i
$683$	−2.53230e6			−0.207713			−0.103856	−	0.994592i	$-0.533118\pi$
$683$	−2.53230e6			−0.207713			−0.103856	+	0.994592i	$0.533118\pi$
$684$	−1.48851e7	+	3.34222e6i	−1.21650	+	0.273146i
$685$	−7.70663e6	−	1.33201e7i	−0.627535	−	1.08463i
$686$	5.64617e6	+	4.51899e6i	0.458082	+	0.366633i
$687$			1.57632e7i			1.27425i
$688$	−1.60684e7	+	7.59890e6i	−1.29420	+	0.612040i
$689$	4.98432e6			0.399998
$690$	3.01068e7	+	4.56402e6i	2.40736	+	0.364943i
$691$			2.97284e6i			0.236852i	0.992963	+	0.118426i	$0.0377848\pi$
$691$			2.97284e6i			0.236852i	−0.992963	+	0.118426i	$0.962215\pi$
$692$	3.52861e6	+	1.57152e7i	0.280116	+	1.24754i
$693$	1.22417e6			0.0968294
$694$	1.41836e7	−	1.77214e7i	1.11786	−	1.39669i
$695$	−4.30015e6	−	7.43236e6i	−0.337692	−	0.583667i
$696$	8.22945e6	−	1.68598e7i	0.643943	−	1.31926i
$697$			1.10633e7i			0.862586i
$698$	−2.62979e6	−	2.10479e6i	−0.204306	−	0.163519i
$699$		−	1.51926e6i		−	0.117608i
$700$	−1.18332e6	+	3.81323e6i	−0.0912764	+	0.294136i
$701$			9.09229e6i			0.698841i	0.936966	+	0.349420i	$0.113621\pi$
$701$			9.09229e6i			0.698841i	−0.936966	+	0.349420i	$0.886379\pi$
$702$	−1.40632e6	+	1.75710e6i	−0.107706	+	0.134572i
$703$			1.93336e7i			1.47545i
$704$	−3.65875e6	+	2.85493e6i	−0.278228	+	0.217102i
$705$	9.10207e6	+	1.57320e7i	0.689712	+	1.19210i
$706$	4.65178e6	+	3.72312e6i	0.351243	+	0.281122i
$707$	−7.81324e6			−0.587872
$708$	2.79500e7	−	6.27574e6i	2.09555	−	0.470524i
$709$			3.91601e6i			0.292569i	0.989243	+	0.146284i	$0.0467315\pi$
$709$			3.91601e6i			0.292569i	−0.989243	+	0.146284i	$0.953269\pi$
$710$	41788.7	−	275661.i	0.00311110	−	0.0205225i
$711$	−1.03440e7			−0.767384
$712$	1.99702e7	+	9.74767e6i	1.47632	+	0.720611i
$713$			5.04103e6i			0.371360i
$714$	2.90469e6	−	3.62921e6i	0.213233	−	0.266420i
$715$	−2.77594e6	−	4.79792e6i	−0.203070	−	0.350985i
$716$	7.79648e6	−	1.75058e6i	0.568350	−	0.127614i
$717$	1.10687e7			0.804082
$718$	−1.94294e6	+	2.42757e6i	−0.140653	+	0.175736i
$719$	−1.30009e7			−0.937890			−0.468945	−	0.883227i	$-0.655366\pi$
$719$	−1.30009e7			−0.937890			−0.468945	+	0.883227i	$0.655366\pi$
$720$	7.04378e6	−	1.01962e7i	0.506378	−	0.733007i
$721$	2.42056e6			0.173411
$722$	8.38908e6	−	1.04816e7i	0.598924	−	0.748314i
$723$	−1.30744e7			−0.930202
$724$	1.06518e7	−	2.39170e6i	0.755227	−	0.169574i
$725$	1.30988e7	+	7.53068e6i	0.925522	+	0.532095i
$726$	1.06832e7	−	1.33479e7i	0.752243	−	0.939876i
$727$		−	2.08574e7i		−	1.46361i	−0.681515	−	0.731804i	$-0.738679\pi$
$727$		−	2.08574e7i		−	1.46361i	0.681515	−	0.731804i	$-0.261321\pi$
$728$	2.21963e6	−	4.54739e6i	0.155222	−	0.318005i
$729$	−1.10661e7			−0.771214
$730$	−2.20474e6	−	334227.i	−0.153127	−	0.0232132i
$731$			1.66663e7i			1.15357i
$732$	1.36182e7	−	3.05775e6i	0.939381	−	0.210923i
$733$	−2.35771e6			−0.162081			−0.0810403	−	0.996711i	$-0.525824\pi$
$733$	−2.35771e6			−0.162081			−0.0810403	+	0.996711i	$0.525824\pi$
$734$	−1.38308e6	−	1.10697e6i	−0.0947560	−	0.0758393i
$735$	1.57789e7	−	9.12920e6i	1.07735	−	0.623325i
$736$	−2.53172e7	−	6.01391e6i	−1.72274	−	0.409225i
$737$		−	3.36569e6i		−	0.228247i
$738$	−8.81753e6	+	1.10169e7i	−0.595945	+	0.744593i
$739$		−	1.75976e7i		−	1.18534i	−0.805445	−	0.592670i	$-0.798074\pi$
$739$		−	1.75976e7i		−	1.18534i	0.805445	−	0.592670i	$-0.201926\pi$
$740$	−1.06522e7	−	1.15406e7i	−0.715086	−	0.774730i
$741$			3.30496e7i			2.21116i
$742$	1.25532e6	+	1.00472e6i	0.0837040	+	0.0669936i
$743$			2.71312e6i			0.180301i	0.995928	+	0.0901504i	$0.0287348\pi$
$743$			2.71312e6i			0.180301i	−0.995928	+	0.0901504i	$0.971265\pi$
$744$	3.91307e6	+	1.91001e6i	0.259170	+	0.126504i
$745$	859880.	+	1.48621e6i	0.0567606	+	0.0981049i
$746$	−889908.	+	1.11188e6i	−0.0585461	+	0.0731494i
$747$	1.11909e7			0.733777
$748$	953312.	+	4.24573e6i	0.0622990	+	0.277459i
$749$		−	436161.i		−	0.0284081i
$750$	1.65745e7	+	1.31912e7i	1.07594	+	0.856308i
$751$	1.51201e7			0.978262			0.489131	−	0.872210i	$-0.337314\pi$
$751$	1.51201e7			0.978262			0.489131	+	0.872210i	$0.337314\pi$
$752$	−6.64005e6	−	1.40408e7i	−0.428180	−	0.905414i
$753$			7.01176e6i			0.450650i
$754$	−1.49504e7	−	1.19658e7i	−0.957690	−	0.766500i
$755$	1.25305e6	−	724978.i	0.0800020	−	0.0462868i
$756$	−708377.	+	159055.i	−0.0450775	+	0.0101214i
$757$	−1.87944e7			−1.19204			−0.596018	−	0.802971i	$-0.703251\pi$
$757$	−1.87944e7			−1.19204			−0.596018	+	0.802971i	$0.703251\pi$
$758$	3.80974e6	+	3.04917e6i	0.240836	+	0.192757i
$759$	−1.36377e7			−0.859284
$760$	1.56799e6	+	2.22288e7i	0.0984714	+	1.39599i
$761$	−1.06723e7			−0.668031			−0.334016	−	0.942567i	$-0.608404\pi$
$761$	−1.06723e7			−0.668031			−0.334016	+	0.942567i	$0.608404\pi$
$762$	−8.40805e6	−	6.72950e6i	−0.524576	−	0.419851i
$763$	−452940.			−0.0281663
$764$	4.15471e6	+	1.85037e7i	0.257518	+	1.14690i
$765$	−5.81918e6	−	1.00578e7i	−0.359507	−	0.621372i
$766$	1.80679e7	+	1.44609e7i	1.11259	+	0.890480i
$767$		−	2.92387e7i		−	1.79461i
$768$	−1.42608e7	+	1.73737e7i	−0.872450	+	1.06289i
$769$	2.98430e7			1.81981			0.909905	−	0.414816i	$-0.136154\pi$
$769$	2.98430e7			1.81981			0.909905	+	0.414816i	$0.136154\pi$
$770$	268010.	−	1.76794e6i	0.0162901	−	0.107458i
$771$		−	1.89246e7i		−	1.14654i
$772$	−2.40953e7	+	5.41022e6i	−1.45509	+	0.326717i
$773$	−1.33577e6			−0.0804049			−0.0402024	−	0.999192i	$-0.512800\pi$
$773$	−1.33577e6			−0.0804049			−0.0402024	+	0.999192i	$0.512800\pi$
$774$	−1.32832e7	+	1.65964e7i	−0.796984	+	0.995777i
$775$	−1.74783e6	+	3.04017e6i	−0.104531	+	0.181821i
$776$	1.23511e7	−	2.53039e7i	0.736295	−	1.50846i
$777$		−	7.51391e6i		−	0.446492i
$778$	−2.38131e7	−	1.90591e7i	−1.41048	−	1.12890i
$779$		−	2.53740e7i		−	1.49811i
$780$	−1.82092e7	−	1.97280e7i	−1.07165	−	1.16104i
$781$			124868.i			0.00732530i
$782$	−1.52462e7	+	1.90491e7i	−0.891550	+	1.11393i
$783$			2.74745e6i			0.160150i
$784$	−1.40826e7	+	6.65983e6i	−0.818265	+	0.386966i
$785$	−1.62061e7	+	9.37636e6i	−0.938650	+	0.543075i
$786$	−7.94921e6	−	6.36226e6i	−0.458952	−	0.367329i
$787$	1.08897e7			0.626729			0.313364	−	0.949633i	$-0.398544\pi$
$787$	1.08897e7			0.626729			0.313364	+	0.949633i	$0.398544\pi$
$788$	1.33350e6	+	5.93895e6i	0.0765027	+	0.340717i
$789$			9.73315e6i			0.556623i
$790$	−2.26463e6	+	1.49387e7i	−0.129101	+	0.851620i
$791$	−2.65854e6			−0.151078
$792$	−2.43457e6	+	4.98773e6i	−0.137914	+	0.282546i
$793$		−	1.42461e7i		−	0.804476i
$794$	−1.91551e7	+	2.39330e7i	−1.07828	+	1.34724i
$795$	7.38391e6	−	4.27211e6i	0.414351	−	0.239731i
$796$	−6.65409e6	−	2.96351e7i	−0.372226	−	1.65777i
$797$	1.87183e7			1.04381			0.521904	−	0.853004i	$-0.325222\pi$
$797$	1.87183e7			1.04381			0.521904	+	0.853004i	$0.325222\pi$
$798$	−6.66198e6	+	8.32369e6i	−0.370336	+	0.462710i
$799$	−1.45633e7			−0.807035
$800$	−1.31833e7	−	1.24049e7i	−0.728279	−	0.685281i
$801$	2.65767e7			1.46359
$802$	−1.14075e7	+	1.42528e7i	−0.626258	+	0.782466i
$803$	998699.			0.0546570
$804$	−3.57126e6	−	1.59052e7i	−0.194842	−	0.867759i
$805$	8.67848e6	−	5.02111e6i	0.472013	−	0.273093i
$806$	2.77720e6	−	3.46992e6i	0.150581	−	0.188140i
$807$		−	8.24735e6i		−	0.445790i
$808$	1.55386e7	−	3.18342e7i	0.837305	−	1.71540i
$809$	−1.03428e6			−0.0555608			−0.0277804	−	0.999614i	$-0.508844\pi$
$809$	−1.03428e6			−0.0555608			−0.0277804	+	0.999614i	$0.508844\pi$
$810$	−3.07075e6	+	2.02563e7i	−0.164449	+	1.08480i
$811$			2.15728e7i			1.15174i	0.817542	+	0.575870i	$0.195336\pi$
$811$			2.15728e7i			1.15174i	−0.817542	+	0.575870i	$0.804664\pi$
$812$	−1.35333e6	−	6.02727e6i	−0.0720300	−	0.320797i
$813$	−2.93280e7			−1.55617
$814$	5.49147e6	+	4.39518e6i	0.290488	+	0.232496i
$815$	−9.84890e6	+	5.69829e6i	−0.519390	+	0.300504i
$816$	9.01010e6	+	1.90524e7i	0.473701	+	1.00167i
$817$		−	3.82246e7i		−	2.00349i
$818$	−1.85024e6	+	2.31174e6i	−0.0966816	+	0.120797i
$819$		−	6.05176e6i		−	0.315262i
$820$	1.39802e7	+	1.51462e7i	0.726069	+	0.786629i
$821$		−	1.19912e7i		−	0.620874i	−0.950594	−	0.310437i	$-0.899525\pi$
$821$		−	1.19912e7i		−	0.620874i	0.950594	−	0.310437i	$-0.100475\pi$
$822$	2.60613e7	+	2.08585e7i	1.34529	+	1.07672i
$823$		−	1.47880e7i		−	0.761045i	−0.924772	−	0.380523i	$-0.875744\pi$
$823$		−	1.47880e7i		−	0.761045i	0.924772	−	0.380523i	$-0.124256\pi$
$824$	−4.81390e6	+	9.86229e6i	−0.246990	+	0.506011i
$825$	−8.22470e6	−	4.72849e6i	−0.420712	−	0.241873i
$826$	5.89380e6	−	7.36391e6i	0.300570	−	0.375542i
$827$	−3.13464e6			−0.159376			−0.0796882	−	0.996820i	$-0.525392\pi$
$827$	−3.13464e6			−0.159376			−0.0796882	+	0.996820i	$0.525392\pi$
$828$	−3.03647e7	+	6.81791e6i	−1.53919	+	0.345601i
$829$			1.80218e7i			0.910777i	0.890293	+	0.455389i	$0.150500\pi$
$829$			1.80218e7i			0.910777i	−0.890293	+	0.455389i	$0.849500\pi$
$830$	2.45006e6	−	1.61619e7i	0.123447	−	0.814324i
$831$	−1.21699e7			−0.611342
$832$	1.41135e7	+	1.80873e7i	0.706851	+	0.905869i
$833$			1.46067e7i			0.729355i
$834$	1.45417e7	+	1.16386e7i	0.723936	+	0.579412i
$835$	−1.46195e6	−	2.52683e6i	−0.0725631	−	0.125418i
$836$	−2.18645e6	−	9.73769e6i	−0.108199	−	0.481882i
$837$	−637670.			−0.0314617
$838$	1.61694e7	+	1.29414e7i	0.795398	+	0.636607i
$839$	3.26760e7			1.60260			0.801298	−	0.598265i	$-0.204143\pi$
$839$	3.26760e7			1.60260			0.801298	+	0.598265i	$0.204143\pi$
$840$	−609392.	−	8.63910e6i	−0.0297988	−	0.422445i
$841$	−2.86572e6			−0.139715
$842$	1.39268e7	+	1.11465e7i	0.676972	+	0.541824i
$843$	4.09012e7			1.98229
$844$	−1.49092e6	+	334764.i	−0.0720443	+	0.0161764i
$845$	−5.75325e6	+	3.32866e6i	−0.277186	+	0.160372i
$846$	−1.45022e7	−	1.16071e7i	−0.696641	−	0.557566i
$847$		−	5.62932e6i		−	0.269617i
$848$	−6.59013e6	+	3.11654e6i	−0.314706	+	0.148828i
$849$	1.87168e7			0.891172
$850$	−1.57995e7	+	6.20206e6i	−0.750062	+	0.294434i
$851$			3.94393e7i			1.86683i
$852$	132495.	+	590089.i	0.00625318	+	0.0278496i
$853$	−3.87723e6			−0.182452			−0.0912261	−	0.995830i	$-0.529079\pi$
$853$	−3.87723e6			−0.182452			−0.0912261	+	0.995830i	$0.529079\pi$
$854$	2.87166e6	−	3.58794e6i	0.134737	−	0.168345i
$855$	1.33464e7	+	2.30679e7i	0.624381	+	1.07918i
$856$	1.77709e6	+	867418.i	0.0828944	+	0.0404617i
$857$		−	3.53502e6i		−	0.164414i	−0.996615	−	0.0822071i	$-0.973803\pi$
$857$		−	3.53502e6i		−	0.164414i	0.996615	−	0.0822071i	$-0.0261969\pi$
$858$	9.38732e6	+	7.51327e6i	0.435335	+	0.348426i
$859$			2.22265e7i			1.02775i	0.857864	+	0.513877i	$0.171791\pi$
$859$			2.22265e7i			1.02775i	−0.857864	+	0.513877i	$0.828209\pi$
$860$	2.10604e7	+	2.28170e7i	0.971004	+	1.05199i
$861$			9.86145e6i			0.453349i
$862$	6.79279e6	−	8.48714e6i	0.311373	−	0.389039i
$863$			1.10828e7i			0.506549i	0.967394	+	0.253274i	$0.0815075\pi$
$863$			1.10828e7i			0.506549i	−0.967394	+	0.253274i	$0.918492\pi$
$864$	760736.	−	3.20252e6i	0.0346697	−	0.145951i
$865$	2.43544e7	−	1.40908e7i	1.10672	−	0.640315i
$866$	−1.39743e7	−	1.11845e7i	−0.633192	−	0.506784i
$867$	−1.06743e7			−0.482270
$868$	1.39890e6	−	314101.i	0.0630213	−	0.0141504i
$869$		−	6.76691e6i		−	0.303977i
$870$	−3.24039e7	−	4.91226e6i	−1.45144	−	0.220031i
$871$	−1.66386e7			−0.743139
$872$	900787.	−	1.84545e6i	0.0401172	−	0.0821887i
$873$		−	3.36749e7i		−	1.49545i
$874$	3.49677e7	−	4.36897e7i	1.54842	−	1.93464i
$875$	6.97479e6	−	19142.5i	0.307972	−	0.000845236i
$876$	4.71954e6	−	1.05970e6i	0.207797	−	0.0466575i
$877$	1.24789e7			0.547869			0.273934	−	0.961748i	$-0.411675\pi$
$877$	1.24789e7			0.547869			0.273934	+	0.961748i	$0.411675\pi$
$878$	2.49260e7	−	3.11434e7i	1.09123	−	1.36342i
$879$	−9.06137e6			−0.395569
$880$	6.67026e6	+	4.60797e6i	0.290360	+	0.200587i
$881$	−5.51270e6			−0.239290			−0.119645	−	0.992817i	$-0.538176\pi$
$881$	−5.51270e6			−0.239290			−0.119645	+	0.992817i	$0.538176\pi$
$882$	−1.16417e7	+	1.45455e7i	−0.503899	+	0.629587i
$883$	−3.28692e7			−1.41869			−0.709346	−	0.704861i	$-0.751009\pi$
$883$	−3.28692e7			−1.41869			−0.709346	+	0.704861i	$0.751009\pi$
$884$	2.09891e7	−	4.71277e6i	0.903364	−	0.202836i
$885$	−2.50608e7	−	4.33150e7i	−1.07557	−	1.85900i
$886$	2.55303e6	−	3.18984e6i	0.109263	−	0.136516i
$887$			2.60618e7i			1.11223i	0.831105	+	0.556115i	$0.187709\pi$
$887$			2.60618e7i			1.11223i	−0.831105	+	0.556115i	$0.812291\pi$
$888$	3.06146e7	+	1.49433e7i	1.30285	+	0.635938i
$889$	−3.54600e6			−0.150482
$890$	5.81850e6	−	3.83820e7i	0.246227	−	1.62425i
$891$		−	9.17567e6i		−	0.387207i
$892$	−2.02412e7	+	4.54485e6i	−0.851774	+	0.191253i
$893$	3.34013e7			1.40163
$894$	−2.90783e6	−	2.32732e6i	−0.121682	−	0.0973897i
$895$	−6.99056e6	−	1.20825e7i	−0.291712	−	0.504194i
$896$	−91392.0	+	7.40031e6i	−0.00380311	+	0.307950i
$897$			6.74190e7i			2.79770i
$898$	−4.39496e6	+	5.49120e6i	−0.181871	+	0.227236i
$899$		−	5.42566e6i		−	0.223900i
$900$	−2.06764e7	−	6.41631e6i	−0.850880	−	0.264046i
$901$			6.83536e6i			0.280511i
$902$	−7.20715e6	−	5.76834e6i	−0.294949	−	0.236067i
$903$			1.48558e7i			0.606284i
$904$	5.28719e6	−	1.08319e7i	0.215181	−	0.440844i
$905$	−9.55074e6	−	1.65075e7i	−0.387628	−	0.669976i
$906$	−1.96220e6	+	2.45164e6i	−0.0794189	+	0.0992285i
$907$	−1.70037e7			−0.686319			−0.343160	−	0.939277i	$-0.611497\pi$
$907$	−1.70037e7			−0.686319			−0.343160	+	0.939277i	$0.611497\pi$
$908$	−122522.	−	545672.i	−0.00493173	−	0.0219643i
$909$		−	4.23655e7i		−	1.70060i
$910$	−8.73994e6	−	1.32493e6i	−0.349869	−	0.0530381i
$911$	2.80920e7			1.12147			0.560734	−	0.827996i	$-0.310519\pi$
$911$	2.80920e7			1.12147			0.560734	+	0.827996i	$0.310519\pi$
$912$	−2.06649e7	−	4.36973e7i	−0.822709	−	1.73967i
$913$			7.32098e6i			0.290665i
$914$	1.88334e7	+	1.50735e7i	0.745697	+	0.596829i
$915$	−1.22105e7	−	2.11045e7i	−0.482147	−	0.833342i
$916$	−2.29602e7	+	5.15536e6i	−0.904143	+	0.203011i
$917$	−3.35249e6			−0.131657
$918$	−2.40964e6	−	1.92859e6i	−0.0943726	−	0.0755324i
$919$	4.45468e7			1.73992			0.869958	−	0.493126i	$-0.164146\pi$
$919$	4.45468e7			1.73992			0.869958	+	0.493126i	$0.164146\pi$
$920$	3.19860e6	+	4.53453e7i	0.124592	+	1.76629i
$921$	−2.96506e7			−1.15182
$922$	−1.40059e7	−	1.12098e7i	−0.542605	−	0.434281i
$923$	617297.			0.0238501
$924$	849751.	+	3.78450e6i	0.0327425	+	0.145824i
$925$	−1.36745e7	+	2.37853e7i	−0.525480	+	0.914016i
$926$	−2.67204e6	−	2.13861e6i	−0.102404	−	0.0819603i
$927$			1.31249e7i			0.501646i
$928$	2.72489e7	+	6.47277e6i	1.03867	+	0.246729i
$929$	−2.74746e7			−1.04446			−0.522229	−	0.852805i	$-0.674900\pi$
$929$	−2.74746e7			−1.04446			−0.522229	+	0.852805i	$0.674900\pi$
$930$	1.14011e6	−	7.52080e6i	0.0432255	−	0.285139i
$931$		−	3.35008e7i		−	1.26672i
$932$	2.21290e6	−	496873.i	0.0834493	−	0.0187372i
$933$	4.21801e7			1.58637
$934$	−2.59895e7	+	3.24721e7i	−0.974833	+	1.21799i
$935$	6.57974e6	−	3.80685e6i	0.246139	−	0.142409i
$936$	2.46572e7	+	1.20355e7i	0.919929	+	0.449028i
$937$			2.68158e7i			0.997795i	0.866661	+	0.498898i	$0.166262\pi$
$937$			2.68158e7i			0.997795i	−0.866661	+	0.498898i	$0.833738\pi$
$938$	−4.19050e6	−	3.35392e6i	−0.155510	−	0.124465i
$939$			5.20296e7i			1.92569i
$940$	−1.99379e7	+	1.84029e7i	−0.735970	+	0.679309i
$941$		−	431928.i		−	0.0159015i	−0.999968	−	0.00795074i	$-0.997469\pi$
$941$		−	431928.i		−	0.0159015i	0.999968	−	0.00795074i	$-0.00253083\pi$
$942$	2.53778e7	−	3.17078e7i	0.931807	−	1.16423i
$943$		−	5.17612e7i		−	1.89551i
$944$	1.82821e7	+	3.86586e7i	0.667722	+	1.41194i
$945$	635151.	+	1.09779e6i	0.0231365	+	0.0399891i
$946$	−1.08572e7	−	8.68972e6i	−0.394449	−	0.315702i
$947$	−4.14162e7			−1.50070			−0.750352	−	0.661039i	$-0.770116\pi$
$947$	−4.14162e7			−1.50070			−0.750352	+	0.661039i	$0.770116\pi$
$948$	−7.18022e6	−	3.19783e7i	−0.259488	−	1.15567i
$949$		−	4.93714e6i		−	0.177955i
$950$	3.62367e7	−	1.42246e7i	1.30268	−	0.511364i
$951$	−2.75731e7			−0.988631
$952$	6.23617e6	+	3.04395e6i	0.223011	+	0.108854i
$953$			2.33270e7i			0.832006i	0.909363	+	0.416003i	$0.136569\pi$
$953$			2.33270e7i			0.832006i	−0.909363	+	0.416003i	$0.863431\pi$
$954$	−5.44784e6	+	6.80671e6i	−0.193800	+	0.242140i
$955$	2.86757e7	−	1.65909e7i	1.01743	−	0.588657i
$956$	3.62003e6	+	1.61224e7i	0.128105	+	0.570538i
$957$	1.46783e7			0.518078
$958$	1.06450e7	−	1.33002e7i	0.374742	−	0.468215i
$959$	1.09911e7			0.385917
$960$	3.64110e7	+	1.46982e7i	1.27513	+	0.514736i
$961$	−2.73699e7			−0.956014
$962$	2.17279e7	−	2.71475e7i	0.756972	−	0.945785i
$963$	2.36498e6			0.0821793
$964$	−4.27599e6	−	1.90438e7i	−0.148199	−	0.660027i
$965$	2.16045e7	+	3.73412e7i	0.746838	+	1.29083i
$966$	−1.35900e7	+	1.69798e7i	−0.468572	+	0.585449i
$967$		−	2.07177e7i		−	0.712485i	−0.934393	−	0.356243i	$-0.884058\pi$
$967$		−	2.07177e7i		−	0.712485i	0.934393	−	0.356243i	$-0.115942\pi$
$968$	2.29360e7	+	1.11953e7i	0.786737	+	0.384015i
$969$	−4.53233e7			−1.55064
$970$	−4.86333e7	−	7.37254e6i	−1.65960	−	0.251587i
$971$			1.95292e7i			0.664716i	0.943153	+	0.332358i	$0.107844\pi$
$971$			1.95292e7i			0.664716i	−0.943153	+	0.332358i	$0.892156\pi$
$972$	−8.76806e6	−	3.90500e7i	−0.297672	−	1.32573i
$973$	6.13280e6			0.207671
$974$	−1.66155e7	−	1.32985e7i	−0.561199	−	0.449164i
$975$	−2.33756e7	+	4.06594e7i	−0.787502	+	1.36978i
$976$	8.90765e6	+	1.88358e7i	0.299322	+	0.632935i
$977$			3.94484e7i			1.32219i	0.750304	+	0.661093i	$0.229907\pi$
$977$			3.94484e7i			1.32219i	−0.750304	+	0.661093i	$0.770093\pi$
$978$	1.54228e7	−	1.92698e7i	0.515604	−	0.644212i
$979$			1.73862e7i			0.579760i
$980$	1.84578e7	+	1.99973e7i	0.613924	+	0.665131i
$981$		−	2.45596e6i		−	0.0814797i
$982$	2.51269e7	+	2.01107e7i	0.831497	+	0.665500i
$983$			5.47261e7i			1.80639i	0.429233	+	0.903194i	$0.358784\pi$
$983$			5.47261e7i			1.80639i	−0.429233	+	0.903194i	$0.641216\pi$
$984$	−4.01794e7	−	1.96120e7i	−1.32287	−	0.645705i
$985$	9.20378e6	−	5.32504e6i	0.302257	−	0.174877i
$986$	1.64095e7	−	2.05026e7i	0.537532	−	0.671609i
$987$	−1.29812e7			−0.424153
$988$	−4.81390e7	+	1.08089e7i	−1.56893	+	0.352280i
$989$		−	7.79756e7i		−	2.53494i
$990$	9.58625e6	+	1.45322e6i	0.310857	+	0.0471242i
$991$	3.95278e7			1.27855			0.639276	−	0.768977i	$-0.279234\pi$
$991$	3.95278e7			1.27855			0.639276	+	0.768977i	$0.279234\pi$
$992$	−1.50230e6	+	6.32433e6i	−0.0484705	+	0.204049i
$993$		−	6.60213e7i		−	2.12476i
$994$	155469.	+	124432.i	0.00499089	+	0.00399452i
$995$	−4.59264e7	+	2.65717e7i	−1.47064	+	0.850867i
$996$	7.76813e6	+	3.45966e7i	0.248124	+	1.10506i
$997$	1.20027e7			0.382421			0.191210	−	0.981549i	$-0.438759\pi$
$997$	1.20027e7			0.382421			0.191210	+	0.981549i	$0.438759\pi$
$998$	−3.60725e7	−	2.88711e7i	−1.14644	−	0.917567i
$999$	−4.98892e6			−0.158159

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	40.6.f.a.29.8	yes	28
4.3	odd	2		160.6.f.a.49.24		28
5.2	odd	4		200.6.d.e.101.7		28
5.3	odd	4		200.6.d.e.101.22		28
5.4	even	2	inner	40.6.f.a.29.21	yes	28
8.3	odd	2		160.6.f.a.49.6		28
8.5	even	2	inner	40.6.f.a.29.22	yes	28
20.3	even	4		800.6.d.e.401.18		28
20.7	even	4		800.6.d.e.401.11		28
20.19	odd	2		160.6.f.a.49.5		28
40.3	even	4		800.6.d.e.401.17		28
40.13	odd	4		200.6.d.e.101.21		28
40.19	odd	2		160.6.f.a.49.23		28
40.27	even	4		800.6.d.e.401.12		28
40.29	even	2	inner	40.6.f.a.29.7	✓	28
40.37	odd	4		200.6.d.e.101.8		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
40.6.f.a.29.7	✓	28	40.29	even	2	inner
40.6.f.a.29.8	yes	28	1.1	even	1	trivial
40.6.f.a.29.21	yes	28	5.4	even	2	inner
40.6.f.a.29.22	yes	28	8.5	even	2	inner
160.6.f.a.49.5		28	20.19	odd	2
160.6.f.a.49.6		28	8.3	odd	2
160.6.f.a.49.23		28	40.19	odd	2
160.6.f.a.49.24		28	4.3	odd	2
200.6.d.e.101.7		28	5.2	odd	4
200.6.d.e.101.8		28	40.37	odd	4
200.6.d.e.101.21		28	40.13	odd	4
200.6.d.e.101.22		28	5.3	odd	4
800.6.d.e.401.11		28	20.7	even	4
800.6.d.e.401.12		28	40.27	even	4
800.6.d.e.401.17		28	40.3	even	4
800.6.d.e.401.18		28	20.3	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)

\(f(q)\)	\(=\)	\(q+(-3.53479 + 4.41648i) q^{2} -21.4357 q^{3} +(-7.01055 - 31.2226i) q^{4} +(-48.3867 + 27.9951i) q^{5} +(75.7708 - 94.6704i) q^{6} -39.9262i q^{7} +(162.675 + 79.4034i) q^{8} +216.491 q^{9} +O(q^{10})\)	\(q+(-3.53479 + 4.41648i) q^{2} -21.4357 q^{3} +(-7.01055 - 31.2226i) q^{4} +(-48.3867 + 27.9951i) q^{5} +(75.7708 - 94.6704i) q^{6} -39.9262i q^{7} +(162.675 + 79.4034i) q^{8} +216.491 q^{9} +(47.3969 - 312.656i) q^{10} +141.626i q^{11} +(150.276 + 669.280i) q^{12} +700.139 q^{13} +(176.333 + 141.131i) q^{14} +(1037.20 - 600.096i) q^{15} +(-925.704 + 437.776i) q^{16} +960.152i q^{17} +(-765.249 + 956.126i) q^{18} -2202.13i q^{19} +(1213.30 + 1314.50i) q^{20} +855.847i q^{21} +(-625.488 - 500.618i) q^{22} -4492.21i q^{23} +(-3487.05 - 1702.07i) q^{24} +(1557.55 - 2709.18i) q^{25} +(-2474.84 + 3092.15i) q^{26} +568.247 q^{27} +(-1246.60 + 279.905i) q^{28} +4834.96i q^{29} +(-1015.99 + 6702.00i) q^{30} -1122.17 q^{31} +(1338.74 - 5635.80i) q^{32} -3035.86i q^{33} +(-4240.49 - 3393.93i) q^{34} +(1117.74 + 1931.90i) q^{35} +(-1517.72 - 6759.41i) q^{36} -8779.50 q^{37} +(9725.67 + 7784.07i) q^{38} -15008.0 q^{39} +(-10094.2 + 712.033i) q^{40} +11522.4 q^{41} +(-3779.83 - 3025.24i) q^{42} +17358.0 q^{43} +(4421.94 - 992.877i) q^{44} +(-10475.3 + 6060.68i) q^{45} +(19839.7 + 15879.0i) q^{46} +15167.7i q^{47} +(19843.2 - 9384.04i) q^{48} +15212.9 q^{49} +(6459.46 + 16455.3i) q^{50} -20581.6i q^{51} +(-4908.36 - 21860.2i) q^{52} +7119.05 q^{53} +(-2008.63 + 2509.65i) q^{54} +(-3964.84 - 6852.82i) q^{55} +(3170.28 - 6494.99i) q^{56} +47204.3i q^{57} +(-21353.5 - 17090.6i) q^{58} -41761.3i q^{59} +(-26007.9 - 28177.2i) q^{60} -20347.5i q^{61} +(3966.64 - 4956.04i) q^{62} -8643.65i q^{63} +(20158.2 + 25833.9i) q^{64} +(-33877.4 + 19600.5i) q^{65} +(13407.8 + 10731.1i) q^{66} -23764.7 q^{67} +(29978.4 - 6731.19i) q^{68} +96293.7i q^{69} +(-12483.2 - 1892.38i) q^{70} +881.677 q^{71} +(35217.6 + 17190.1i) q^{72} -7051.66i q^{73} +(31033.7 - 38774.5i) q^{74} +(-33387.1 + 58073.3i) q^{75} +(-68756.4 + 15438.2i) q^{76} +5654.59 q^{77} +(53050.1 - 66282.5i) q^{78} -47780.1 q^{79} +(32536.2 - 47097.7i) q^{80} -64788.0 q^{81} +(-40729.4 + 50888.6i) q^{82} +51692.3 q^{83} +(26721.8 - 5999.96i) q^{84} +(-26879.6 - 46458.6i) q^{85} +(-61356.8 + 76661.1i) q^{86} -103641. i q^{87} +(-11245.6 + 23039.0i) q^{88} +122761. q^{89} +(10261.0 - 67687.0i) q^{90} -27953.9i q^{91} +(-140258. + 31492.8i) q^{92} +24054.6 q^{93} +(-66987.8 - 53614.6i) q^{94} +(61649.0 + 106554. i) q^{95} +(-28696.9 + 120807. i) q^{96} -155549. i q^{97} +(-53774.4 + 67187.4i) q^{98} +30660.7i 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

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