LMFDB - Embedded newform 74.8.f.b.33.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [74,8,Mod(7,74)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(74, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([16]))

N = Newforms(chi, 8, names="a")

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

chi := DirichletCharacter("74.7");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 74 = 2 \cdot 37 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	74.f (of order $9$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$23.1164918858$
Analytic rank:	$0$
Dimension:	$66$
Relative dimension:	$11$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			33.5
Character	$\chi$	$=$	74.33
Dual form			74.8.f.b.9.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.38919 + 7.87846i) q^{2} +(-2.39984 - 13.6102i) q^{3} +(-60.1403 - 21.8893i) q^{4} +(-34.7022 + 29.1186i) q^{5} +110.561 q^{6} +(-140.013 + 117.485i) q^{7} +(256.000 - 443.405i) q^{8} +(1875.63 - 682.674i) q^{9} +O(q^{10})$	\(q+(-1.38919 + 7.87846i) q^{2} +(-2.39984 - 13.6102i) q^{3} +(-60.1403 - 21.8893i) q^{4} +(-34.7022 + 29.1186i) q^{5} +110.561 q^{6} +(-140.013 + 117.485i) q^{7} +(256.000 - 443.405i) q^{8} +(1875.63 - 682.674i) q^{9} +(-181.202 - 313.852i) q^{10} +(-242.862 + 420.649i) q^{11} +(-153.590 + 871.051i) q^{12} +(381.274 + 138.772i) q^{13} +(-731.095 - 1266.29i) q^{14} +(479.590 + 402.424i) q^{15} +(3137.72 + 2632.86i) q^{16} +(-12523.2 + 4558.08i) q^{17} +(2772.82 + 15725.4i) q^{18} +(1371.19 + 7776.41i) q^{19} +(2724.39 - 991.597i) q^{20} +(1935.00 + 1623.66i) q^{21} +(-2976.68 - 2497.73i) q^{22} +(34537.2 + 59820.2i) q^{23} +(-6649.18 - 2420.10i) q^{24} +(-13209.9 + 74917.1i) q^{25} +(-1622.97 + 2811.07i) q^{26} +(-28904.8 - 50064.7i) q^{27} +(10992.1 - 4000.79i) q^{28} +(-67531.8 + 116969. i) q^{29} +(-3836.72 + 3219.39i) q^{30} -168321. q^{31} +(-25101.7 + 21062.9i) q^{32} +(6307.93 + 2295.90i) q^{33} +(-18513.6 - 104996. i) q^{34} +(1437.76 - 8153.97i) q^{35} -127744. q^{36} +(109883. + 287850. i) q^{37} -63171.0 q^{38} +(973.720 - 5522.24i) q^{39} +(4027.58 + 22841.5i) q^{40} +(-524509. - 190906. i) q^{41} +(-15480.0 + 12989.2i) q^{42} -632169. q^{43} +(23813.5 - 19981.9i) q^{44} +(-45210.0 + 78306.1i) q^{45} +(-519270. + 188999. i) q^{46} +(161379. + 279516. i) q^{47} +(28303.6 - 49023.3i) q^{48} +(-137206. + 778133. i) q^{49} +(-571881. - 208148. i) q^{50} +(92090.0 + 159505. i) q^{51} +(-19892.3 - 16691.6i) q^{52} +(-391642. - 328626. i) q^{53} +(434587. - 158177. i) q^{54} +(-3820.87 - 21669.2i) q^{55} +(16250.0 + 92158.5i) q^{56} +(102548. - 37324.3i) q^{57} +(-827718. - 694538. i) q^{58} +(1.70627e6 + 1.43173e6i) q^{59} +(-20033.9 - 34699.8i) q^{60} +(2.30063e6 + 837362. i) q^{61} +(233829. - 1.32611e6i) q^{62} +(-182409. + 315941. i) q^{63} +(-131072. - 227023. i) q^{64} +(-17271.9 + 6286.47i) q^{65} +(-26851.0 + 46507.4i) q^{66} +(-251802. + 211287. i) q^{67} +852924. q^{68} +(731280. - 613616. i) q^{69} +(62243.4 + 22654.8i) q^{70} +(56594.4 + 320963. i) q^{71} +(177460. - 1.00643e6i) q^{72} +3.75445e6 q^{73} +(-2.42046e6 + 465835. i) q^{74} +1.05134e6 q^{75} +(87756.2 - 497690. i) q^{76} +(-15416.0 - 87428.7i) q^{77} +(42154.1 + 15342.8i) q^{78} +(-1.50336e6 + 1.26147e6i) q^{79} -185551. q^{80} +(2.73196e6 - 2.29239e6i) q^{81} +(2.23268e6 - 3.86712e6i) q^{82} +(2.60792e6 - 949206. i) q^{83} +(-80830.7 - 140003. i) q^{84} +(301859. - 522835. i) q^{85} +(878200. - 4.98052e6i) q^{86} +(1.75403e6 + 638414. i) q^{87} +(124345. + 215372. i) q^{88} +(-770543. - 646562. i) q^{89} +(-554127. - 464967. i) q^{90} +(-69686.9 + 25364.0i) q^{91} +(-767657. - 4.35360e6i) q^{92} +(403944. + 2.29088e6i) q^{93} +(-2.42634e6 + 883116. i) q^{94} +(-274022. - 229932. i) q^{95} +(346910. + 291092. i) q^{96} +(160227. + 277521. i) q^{97} +(-5.93989e6 - 2.16194e6i) q^{98} +(-168353. + 954776. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 66 q - 39 q^{3} + 459 q^{5} - 918 q^{7} + 16896 q^{8} + 3237 q^{9}+O(q^{10}) $ 66 * q - 39 * q^3 + 459 * q^5 - 918 * q^7 + 16896 * q^8 + 3237 * q^9	\( 66 q - 39 q^{3} + 459 q^{5} - 918 q^{7} + 16896 q^{8} + 3237 q^{9} + 4704 q^{10} + 4539 q^{11} - 2496 q^{12} - 10542 q^{13} + 6744 q^{14} - 39894 q^{15} - 78822 q^{17} + 51792 q^{18} + 79461 q^{19} + 29376 q^{20} - 5835 q^{21} + 18168 q^{22} - 199479 q^{23} + 19968 q^{24} + 356301 q^{25} + 186744 q^{26} - 91689 q^{27} - 91584 q^{28} - 38526 q^{29} + 319152 q^{30} + 1917246 q^{31} - 902847 q^{33} - 205776 q^{34} - 1574793 q^{35} + 3079296 q^{36} - 396513 q^{37} - 692880 q^{38} + 2514306 q^{39} + 470016 q^{40} + 2989350 q^{41} + 46680 q^{42} + 6006348 q^{43} - 145344 q^{44} + 1083726 q^{45} - 588744 q^{46} - 894135 q^{47} + 7973742 q^{49} + 2012400 q^{50} - 524880 q^{51} - 2262720 q^{52} + 1457844 q^{53} + 1452312 q^{54} + 2415690 q^{55} - 1202688 q^{56} + 2734338 q^{57} - 3423360 q^{58} + 3099522 q^{59} - 3102912 q^{60} - 10968396 q^{61} - 3067320 q^{62} - 10727970 q^{63} - 8650752 q^{64} - 13497300 q^{65} - 4598712 q^{66} - 1978119 q^{67} + 5026176 q^{68} - 7251108 q^{69} + 435744 q^{70} - 19555002 q^{71} + 3314688 q^{72} - 31332840 q^{73} + 7607472 q^{74} + 44758074 q^{75} + 5085504 q^{76} + 1982007 q^{77} - 22512264 q^{78} + 10522902 q^{79} + 4816896 q^{80} - 7548876 q^{81} - 7150320 q^{82} + 19771926 q^{83} + 3556224 q^{84} - 6684072 q^{85} + 22982496 q^{86} - 67769667 q^{87} - 2323968 q^{88} - 42018963 q^{89} - 25158672 q^{90} + 4847565 q^{91} - 1096704 q^{92} - 14558475 q^{93} + 3175680 q^{94} + 4508415 q^{95} - 2555904 q^{96} - 39286662 q^{97} + 71630904 q^{98} + 66155463 q^{99}+O(q^{100}) \) 66 * q - 39 * q^3 + 459 * q^5 - 918 * q^7 + 16896 * q^8 + 3237 * q^9 + 4704 * q^10 + 4539 * q^11 - 2496 * q^12 - 10542 * q^13 + 6744 * q^14 - 39894 * q^15 - 78822 * q^17 + 51792 * q^18 + 79461 * q^19 + 29376 * q^20 - 5835 * q^21 + 18168 * q^22 - 199479 * q^23 + 19968 * q^24 + 356301 * q^25 + 186744 * q^26 - 91689 * q^27 - 91584 * q^28 - 38526 * q^29 + 319152 * q^30 + 1917246 * q^31 - 902847 * q^33 - 205776 * q^34 - 1574793 * q^35 + 3079296 * q^36 - 396513 * q^37 - 692880 * q^38 + 2514306 * q^39 + 470016 * q^40 + 2989350 * q^41 + 46680 * q^42 + 6006348 * q^43 - 145344 * q^44 + 1083726 * q^45 - 588744 * q^46 - 894135 * q^47 + 7973742 * q^49 + 2012400 * q^50 - 524880 * q^51 - 2262720 * q^52 + 1457844 * q^53 + 1452312 * q^54 + 2415690 * q^55 - 1202688 * q^56 + 2734338 * q^57 - 3423360 * q^58 + 3099522 * q^59 - 3102912 * q^60 - 10968396 * q^61 - 3067320 * q^62 - 10727970 * q^63 - 8650752 * q^64 - 13497300 * q^65 - 4598712 * q^66 - 1978119 * q^67 + 5026176 * q^68 - 7251108 * q^69 + 435744 * q^70 - 19555002 * q^71 + 3314688 * q^72 - 31332840 * q^73 + 7607472 * q^74 + 44758074 * q^75 + 5085504 * q^76 + 1982007 * q^77 - 22512264 * q^78 + 10522902 * q^79 + 4816896 * q^80 - 7548876 * q^81 - 7150320 * q^82 + 19771926 * q^83 + 3556224 * q^84 - 6684072 * q^85 + 22982496 * q^86 - 67769667 * q^87 - 2323968 * q^88 - 42018963 * q^89 - 25158672 * q^90 + 4847565 * q^91 - 1096704 * q^92 - 14558475 * q^93 + 3175680 * q^94 + 4508415 * q^95 - 2555904 * q^96 - 39286662 * q^97 + 71630904 * q^98 + 66155463 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/74\mathbb{Z}\right)^\times$.

$n$	$39$
$\chi(n)$	$e\left(\frac{5}{9}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.38919	+	7.87846i	−0.122788	+	0.696364i
$2$	−1.38919	+	7.87846i	−0.122788	+	0.696364i
$3$	−2.39984	−	13.6102i	−0.0513166	−	0.291031i	0.948339	−	0.317258i	$-0.102762\pi$
$3$	−2.39984	−	13.6102i	−0.0513166	−	0.291031i	−0.999656	+	0.0262265i	$0.991651\pi$
$4$	−60.1403	−	21.8893i	−0.469846	−	0.171010i
$5$	−34.7022	+	29.1186i	−0.124155	+	0.104178i	−0.702751	−	0.711436i	$-0.748045\pi$
$5$	−34.7022	+	29.1186i	−0.124155	+	0.104178i	0.578596	+	0.815614i	$0.303601\pi$
$6$	110.561			0.208965
$7$	−140.013	+	117.485i	−0.154285	+	0.129461i	−0.716663	−	0.697420i	$-0.754331\pi$
$7$	−140.013	+	117.485i	−0.154285	+	0.129461i	0.562377	+	0.826881i	$0.309887\pi$
$8$	256.000	−	443.405i	0.176777	−	0.306186i
$9$	1875.63	−	682.674i	0.857627	−	0.312151i
$10$	−181.202	−	313.852i	−0.0573012	−	0.0992486i
$11$	−242.862	+	420.649i	−0.0550154	+	0.0952895i	−0.892222	−	0.451598i	$-0.850854\pi$
$11$	−242.862	+	420.649i	−0.0550154	+	0.0952895i	0.837206	+	0.546887i	$0.184187\pi$
$12$	−153.590	+	871.051i	−0.0256583	+	0.145516i
$13$	381.274	+	138.772i	0.0481322	+	0.0175187i	0.365974	−	0.930625i	$-0.380736\pi$
$13$	381.274	+	138.772i	0.0481322	+	0.0175187i	−0.317842	+	0.948144i	$0.602958\pi$
$14$	−731.095	−	1266.29i	−0.0712075	−	0.123335i
$15$	479.590	+	402.424i	0.0366902	+	0.0307868i
$16$	3137.72	+	2632.86i	0.191511	+	0.160697i
$17$	−12523.2	+	4558.08i	−0.618223	+	0.225015i	−0.632097	−	0.774889i	$-0.717806\pi$
$17$	−12523.2	+	4558.08i	−0.618223	+	0.225015i	0.0138746	+	0.999904i	$0.495583\pi$
$18$	2772.82	+	15725.4i	0.112064	+	0.635549i
$19$	1371.19	+	7776.41i	0.0458628	+	0.260101i	0.999114	−	0.0420770i	$-0.0133975\pi$
$19$	1371.19	+	7776.41i	0.0458628	+	0.260101i	−0.953252	+	0.302178i	$0.902286\pi$
$20$	2724.39	−	991.597i	0.0761490	−	0.0277160i
$21$	1935.00	+	1623.66i	0.0455945	+	0.0382584i
$22$	−2976.68	−	2497.73i	−0.0596010	−	0.0500112i
$23$	34537.2	+	59820.2i	0.591888	+	1.02518i	0.993978	+	0.109580i	$0.0349506\pi$
$23$	34537.2	+	59820.2i	0.591888	+	1.02518i	−0.402090	+	0.915600i	$0.631716\pi$
$24$	−6649.18	−	2420.10i	−0.0981813	−	0.0357351i
$25$	−13209.9	+	74917.1i	−0.169087	+	0.958939i
$26$	−1622.97	+	2811.07i	−0.0181094	+	0.0313664i
$27$	−28904.8	−	50064.7i	−0.282616	−	0.489506i
$28$	10992.1	−	4000.79i	0.0946295	−	0.0344423i
$29$	−67531.8	+	116969.i	−0.514181	+	0.890587i	0.485684	+	0.874134i	$0.338571\pi$
$29$	−67531.8	+	116969.i	−0.514181	+	0.890587i	−0.999865	+	0.0164524i	$0.994763\pi$
$30$	−3836.72	+	3219.39i	−0.0259439	+	0.0217695i
$31$	−168321.			−1.01478			−0.507391	−	0.861716i	$-0.669390\pi$
$31$	−168321.			−1.01478			−0.507391	+	0.861716i	$0.669390\pi$
$32$	−25101.7	+	21062.9i	−0.135419	+	0.113630i
$33$	6307.93	+	2295.90i	0.0305554	+	0.0111213i
$34$	−18513.6	−	104996.i	−0.0807819	−	0.458137i
$35$	1437.76	−	8153.97i	0.00566826	−	0.0321463i
$36$	−127744.			−0.456334
$37$	109883.	+	287850.i	0.356637	+	0.934243i
$37$	109883.	+	287850.i	0.356637	+	0.934243i
$38$	−63171.0			−0.186756
$39$	973.720	−	5522.24i	0.00262850	−	0.0149070i
$40$	4027.58	+	22841.5i	0.00995025	+	0.0564307i
$41$	−524509.	−	190906.i	−1.18853	−	0.432589i	−0.329321	−	0.944218i	$-0.606820\pi$
$41$	−524509.	−	190906.i	−1.18853	−	0.432589i	−0.859206	+	0.511629i	$0.829042\pi$
$42$	−15480.0	+	12989.2i	−0.0322402	+	0.0270527i
$43$	−632169.			−1.21253			−0.606267	−	0.795261i	$-0.707334\pi$
$43$	−632169.			−1.21253			−0.606267	+	0.795261i	$0.707334\pi$
$44$	23813.5	−	19981.9i	0.0421442	−	0.0353632i
$45$	−45210.0	+	78306.1i	−0.0739590	+	0.128101i
$46$	−519270.	+	188999.i	−0.786576	+	0.286290i
$47$	161379.	+	279516.i	0.226727	+	0.392703i	0.956836	−	0.290628i	$-0.0938641\pi$
$47$	161379.	+	279516.i	0.226727	+	0.392703i	−0.730109	+	0.683331i	$0.760531\pi$
$48$	28303.6	−	49023.3i	0.0369401	−	0.0639821i
$49$	−137206.	+	778133.i	−0.166604	+	0.944860i
$50$	−571881.	−	208148.i	−0.647009	−	0.235492i
$51$	92090.0	+	159505.i	0.0972114	+	0.168375i
$52$	−19892.3	−	16691.6i	−0.0196189	−	0.0164622i
$53$	−391642.	−	328626.i	−0.361346	−	0.303205i	0.443981	−	0.896036i	$-0.353566\pi$
$53$	−391642.	−	328626.i	−0.361346	−	0.303205i	−0.805327	+	0.592831i	$0.798010\pi$
$54$	434587.	−	158177.i	0.375576	−	0.136699i
$55$	−3820.87	−	21669.2i	−0.00309666	−	0.0175620i
$56$	16250.0	+	92158.5i	0.0123651	+	0.0701257i
$57$	102548.	−	37324.3i	0.0733439	−	0.0266950i
$58$	−827718.	−	694538.i	−0.557038	−	0.467410i
$59$	1.70627e6	+	1.43173e6i	1.08160	+	0.907569i	0.996053	−	0.0887656i	$-0.0282922\pi$
$59$	1.70627e6	+	1.43173e6i	1.08160	+	0.907569i	0.0855457	+	0.996334i	$0.472737\pi$
$60$	−20033.9	−	34699.8i	−0.0119739	−	0.0207394i
$61$	2.30063e6	+	837362.i	1.29775	+	0.472344i	0.896265	−	0.443519i	$-0.146270\pi$
$61$	2.30063e6	+	837362.i	1.29775	+	0.472344i	0.401490	+	0.915863i	$0.368492\pi$
$62$	233829.	−	1.32611e6i	0.124603	−	0.706658i
$63$	−182409.	+	315941.i	−0.0919080	+	0.159189i
$64$	−131072.	−	227023.i	−0.0625000	−	0.108253i
$65$	−17271.9	+	6286.47i	−0.00780089	+	0.00283929i
$66$	−26851.0	+	46507.4i	−0.0114963	+	0.0199121i
$67$	−251802.	+	211287.i	−0.102281	+	0.0858243i	−0.692494	−	0.721423i	$-0.743488\pi$
$67$	−251802.	+	211287.i	−0.102281	+	0.0858243i	0.590213	+	0.807248i	$0.299044\pi$
$68$	852924.			0.328949
$69$	731280.	−	613616.i	0.267986	−	0.224867i
$70$	62243.4	+	22654.8i	0.0216895	+	0.00789435i
$71$	56594.4	+	320963.i	0.0187659	+	0.106427i	0.992752	−	0.120181i	$-0.0383475\pi$
$71$	56594.4	+	320963.i	0.0187659	+	0.106427i	−0.973986	+	0.226608i	$0.927236\pi$
$72$	177460.	−	1.00643e6i	0.0560322	−	0.317775i
$73$	3.75445e6			1.12958			0.564790	−	0.825235i	$-0.308957\pi$
$73$	3.75445e6			1.12958			0.564790	+	0.825235i	$0.308957\pi$
$74$	−2.42046e6	+	465835.i	−0.694364	+	0.133635i
$75$	1.05134e6			0.287758
$76$	87756.2	−	497690.i	0.0229314	−	0.130050i
$77$	−15416.0	−	87428.7i	−0.00384818	−	0.0218241i
$78$	42154.1	+	15342.8i	0.0100579	+	0.00366079i
$79$	−1.50336e6	+	1.26147e6i	−0.343059	+	0.287860i	−0.797996	−	0.602663i	$-0.794106\pi$
$79$	−1.50336e6	+	1.26147e6i	−0.343059	+	0.287860i	0.454937	+	0.890524i	$0.349662\pi$
$80$	−185551.			−0.0405181
$81$	2.73196e6	−	2.29239e6i	0.571185	−	0.479281i
$82$	2.23268e6	−	3.86712e6i	0.447176	−	0.774531i
$83$	2.60792e6	−	949206.i	0.500635	−	0.182216i	−0.0793446	−	0.996847i	$-0.525283\pi$
$83$	2.60792e6	−	949206.i	0.500635	−	0.182216i	0.579980	+	0.814631i	$0.303061\pi$
$84$	−80830.7	−	140003.i	−0.0148799	−	0.0257727i
$85$	301859.	−	522835.i	0.0533136	−	0.0923418i
$86$	878200.	−	4.98052e6i	0.148884	−	0.844365i
$87$	1.75403e6	+	638414.i	0.285574	+	0.103941i
$88$	124345.	+	215372.i	0.0194509	+	0.0336899i
$89$	−770543.	−	646562.i	−0.115859	−	0.0972177i	0.583017	−	0.812460i	$-0.301872\pi$
$89$	−770543.	−	646562.i	−0.115859	−	0.0972177i	−0.698877	+	0.715242i	$0.746316\pi$
$90$	−554127.	−	464967.i	−0.0801235	−	0.0672316i
$91$	−69686.9	+	25364.0i	−0.00969408	+	0.00352836i
$92$	−767657.	−	4.35360e6i	−0.102780	−	0.582896i
$93$	403944.	+	2.29088e6i	0.0520752	+	0.295333i
$94$	−2.42634e6	+	883116.i	−0.301304	+	0.109666i
$95$	−274022.	−	229932.i	−0.0327908	−	0.0275148i
$96$	346910.	+	291092.i	0.0400191	+	0.0335800i
$97$	160227.	+	277521.i	0.0178252	+	0.0308741i	0.874800	−	0.484484i	$-0.160992\pi$
$97$	160227.	+	277521.i	0.0178252	+	0.0308741i	−0.856975	+	0.515358i	$0.827659\pi$
$98$	−5.93989e6	−	2.16194e6i	−0.637510	−	0.232035i
$99$	−168353.	+	954776.i	−0.0174380	+	0.0988959i
$100$	2.43433e6	−	4.21639e6i	0.243433	−	0.421639i
$101$	−217811.	−	377259.i	−0.0210356	−	0.0364347i	0.855316	−	0.518107i	$-0.173363\pi$
$101$	−217811.	−	377259.i	−0.0210356	−	0.0364347i	−0.876352	+	0.481672i	$0.840030\pi$
$102$	−1.38458e6	+	503946.i	−0.129187	+	0.0470201i
$103$	3.79704e6	−	6.57666e6i	0.342385	−	0.593028i	−0.642490	−	0.766294i	$-0.722099\pi$
$103$	3.79704e6	−	6.57666e6i	0.342385	−	0.593028i	0.984875	+	0.173266i	$0.0554320\pi$
$104$	159139.	−	133533.i	0.0138726	−	0.0116405i
$105$	−114427.			−0.00964645
$106$	3.13313e6	−	2.62901e6i	0.255510	−	0.214399i
$107$	−8.91289e6	−	3.24403e6i	−0.703356	−	0.256001i	−0.0345131	−	0.999404i	$-0.510988\pi$
$107$	−8.91289e6	−	3.24403e6i	−0.703356	−	0.256001i	−0.668843	+	0.743404i	$0.733210\pi$
$108$	642467.	+	3.64361e6i	0.0490758	+	0.278323i
$109$	−1.53050e6	+	8.67987e6i	−0.113198	+	0.641978i	0.874428	+	0.485154i	$0.161237\pi$
$109$	−1.53050e6	+	8.67987e6i	−0.113198	+	0.641978i	−0.987627	+	0.156824i	$0.949874\pi$
$110$	176028.			0.0126098
$111$	3.65399e6	−	2.18633e6i	0.253592	−	0.151735i
$112$	−748642.			−0.0503513
$113$	−279562.	+	1.58547e6i	−0.0182265	+	0.103368i	−0.992564	−	0.121725i	$-0.961157\pi$
$113$	−279562.	+	1.58547e6i	−0.0182265	+	0.103368i	0.974337	+	0.225093i	$0.0722685\pi$
$114$	151600.	+	859768.i	0.00958370	+	0.0543519i
$115$	−2.94040e6	−	1.07022e6i	−0.180287	−	0.0656191i
$116$	6.62175e6	−	5.55630e6i	0.393885	−	0.330509i
$117$	809865.			0.0467479
$118$	−1.36502e7	+	1.14539e7i	−0.764805	+	0.641748i
$119$	1.21791e6	−	2.10948e6i	0.0662521	−	0.114752i
$120$	301212.	−	109632.i	0.0159125	−	0.00579166i
$121$	9.62562e6	+	1.66721e7i	0.493947	+	0.855541i
$122$	−9.79312e6	+	1.69622e7i	−0.488272	+	0.845712i
$123$	−1.33952e6	+	7.59680e6i	−0.0649055	+	0.368097i
$124$	1.01229e7	+	3.68443e6i	0.476792	+	0.173538i
$125$	−3.49262e6	−	6.04940e6i	−0.159944	−	0.277030i
$126$	−2.23573e6	−	1.87600e6i	−0.0995686	−	0.0835480i
$127$	5.65418e6	+	4.74442e6i	0.244938	+	0.205528i	0.756989	−	0.653428i	$-0.226670\pi$
$127$	5.65418e6	+	4.74442e6i	0.244938	+	0.205528i	−0.512051	+	0.858955i	$0.671114\pi$
$128$	1.97068e6	−	717268.i	0.0830579	−	0.0302306i
$129$	1.51711e6	+	8.60394e6i	0.0622231	+	0.352885i
$130$	−25533.8	−	144809.i	−0.00101933	−	0.00578089i
$131$	−3.15569e7	+	1.14858e7i	−1.22644	+	0.446387i	−0.872376	−	0.488836i	$-0.837422\pi$
$131$	−3.15569e7	+	1.14858e7i	−1.22644	+	0.446387i	−0.354061	+	0.935222i	$0.615200\pi$
$132$	−329105.	−	276152.i	−0.0124545	−	0.0104506i
$133$	−1.10559e6	−	927704.i	−0.0407488	−	0.0341923i
$134$	−1.31481e6	−	2.27733e6i	−0.0472061	−	0.0817633i
$135$	2.46088e6	+	895686.i	0.0860839	+	0.0313320i
$136$	−1.18487e6	+	6.71973e6i	−0.0403910	+	0.229069i
$137$	−1.22199e7	+	2.11654e7i	−0.406017	+	0.703242i	−0.994439	−	0.105312i	$-0.966416\pi$
$137$	−1.22199e7	+	2.11654e7i	−0.406017	+	0.703242i	0.588422	+	0.808554i	$0.299749\pi$
$138$	3.81847e6	+	6.61379e6i	0.123684	+	0.214227i
$139$	−1.72113e7	+	6.26442e6i	−0.543579	+	0.197847i	−0.599192	−	0.800606i	$-0.704511\pi$
$139$	−1.72113e7	+	6.26442e6i	−0.543579	+	0.197847i	0.0556121	+	0.998452i	$0.482289\pi$
$140$	−264952.	+	458911.i	−0.00816055	+	0.0141345i
$141$	3.41698e6	−	2.86719e6i	0.102654	−	0.0861369i
$142$	−2.60732e6			−0.0764160
$143$	−150971.	+	126680.i	−0.00431736	+	0.00362269i
$144$	7.68258e6	+	2.79623e6i	0.214407	+	0.0780377i
$145$	−1.06246e6	−	6.02551e6i	−0.0289417	−	0.164137i
$146$	−5.21563e6	+	2.95793e7i	−0.138699	+	0.786598i
$147$	1.09198e7			0.283533
$148$	−307593.	−	1.97167e7i	−0.00779938	−	0.499939i
$149$	−2.05803e7			−0.509683			−0.254842	−	0.966983i	$-0.582023\pi$
$149$	−2.05803e7			−0.509683			−0.254842	+	0.966983i	$0.582023\pi$
$150$	−1.46050e6	+	8.28292e6i	−0.0353332	+	0.200385i
$151$	−1.10921e7	−	6.29066e7i	−0.262178	−	1.48688i	−0.776953	−	0.629559i	$-0.783236\pi$
$151$	−1.10921e7	−	6.29066e7i	−0.262178	−	1.48688i	0.514775	−	0.857325i	$-0.327875\pi$
$152$	3.79912e6	+	1.38277e6i	0.0877467	+	0.0319372i
$153$	−2.03773e7	+	1.70985e7i	−0.459966	+	0.385957i
$154$	710220.			0.0156700
$155$	5.84112e6	−	4.90129e6i	0.125990	−	0.105718i
$156$	−179438.	+	310795.i	−0.00378423	+	0.00655448i
$157$	4.73490e6	−	1.72336e6i	0.0976476	−	0.0355408i	−0.292734	−	0.956194i	$-0.594565\pi$
$157$	4.73490e6	−	1.72336e6i	0.0976476	−	0.0355408i	0.390382	+	0.920653i	$0.372343\pi$
$158$	−7.84999e6	−	1.35966e7i	−0.158332	−	0.274240i
$159$	−3.53279e6	+	6.11896e6i	−0.0696991	+	0.120722i
$160$	257765.	−	1.46186e6i	0.00497512	−	0.0282153i
$161$	−1.18636e7	−	4.31800e6i	−0.224040	−	0.0815440i
$162$	1.42653e7	+	2.47082e7i	0.263620	+	0.456603i
$163$	1.20341e7	+	1.00978e7i	0.217648	+	0.182629i	0.745093	−	0.666961i	$-0.232405\pi$
$163$	1.20341e7	+	1.00978e7i	0.217648	+	0.182629i	−0.527444	+	0.849590i	$0.676850\pi$
$164$	2.73653e7	+	2.29622e7i	0.484448	+	0.406500i
$165$	−285753.	+	104006.i	−0.00495218	+	0.00180245i
$166$	3.85539e6	+	2.18650e7i	0.0654170	+	0.370998i
$167$	−1.66383e7	−	9.43603e7i	−0.276440	−	1.56777i	−0.734351	−	0.678770i	$-0.762513\pi$
$167$	−1.66383e7	−	9.43603e7i	−0.276440	−	1.56777i	0.457911	−	0.888998i	$-0.348598\pi$
$168$	1.21530e6	−	442332.i	0.0197742	−	0.00719723i
$169$	−4.79420e7	−	4.02281e7i	−0.764035	−	0.641101i
$170$	3.69980e6	+	3.10450e6i	0.0577573	+	0.0484641i
$171$	7.88060e6	+	1.36496e7i	0.120524	+	0.208753i
$172$	3.80189e7	+	1.38377e7i	0.569704	+	0.207355i
$173$	6.19760e6	−	3.51483e7i	0.0910044	−	0.516111i	−0.904894	−	0.425636i	$-0.860050\pi$
$173$	6.19760e6	−	3.51483e7i	0.0910044	−	0.516111i	0.995899	−	0.0904751i	$-0.0288386\pi$
$174$	−7.46639e6	+	1.29322e7i	−0.107446	+	0.186101i
$175$	−6.95206e6	−	1.20413e7i	−0.0980575	−	0.169840i
$176$	−1.86954e6	+	680457.i	−0.0258488	+	0.00940819i
$177$	1.53913e7	−	2.66586e7i	0.208627	−	0.361352i
$178$	6.16434e6	−	5.17250e6i	0.0819250	−	0.0687433i
$179$	−2.74684e7			−0.357972			−0.178986	−	0.983852i	$-0.557282\pi$
$179$	−2.74684e7			−0.357972			−0.178986	+	0.983852i	$0.557282\pi$
$180$	4.43301e6	−	3.71974e6i	0.0566559	−	0.0475399i
$181$	9.33830e7	+	3.39886e7i	1.17056	+	0.426048i	0.852858	−	0.522143i	$-0.174867\pi$
$181$	9.33830e7	+	3.39886e7i	1.17056	+	0.426048i	0.317700	+	0.948191i	$0.397090\pi$
$182$	−103021.	−	584261.i	−0.00126671	−	0.00718385i
$183$	5.87549e6	−	3.33215e7i	0.0708704	−	0.401926i
$184$	3.53661e7			0.418528
$185$	−1.21950e7	−	6.78938e6i	−0.141606	−	0.0788368i
$186$	−1.86098e7			−0.212054
$187$	1.12406e6	−	6.37486e6i	0.0125702	−	0.0712894i
$188$	−3.58696e6	−	2.03427e7i	−0.0393708	−	0.223283i
$189$	9.92889e6	+	3.61382e6i	0.106975	+	0.0389359i
$190$	2.19218e6	−	1.83945e6i	0.0231866	−	0.0194559i
$191$	−2.87035e7			−0.298069			−0.149035	−	0.988832i	$-0.547617\pi$
$191$	−2.87035e7			−0.298069			−0.149035	+	0.988832i	$0.547617\pi$
$192$	−2.77528e6	+	2.32873e6i	−0.0282978	+	0.0237446i
$193$	5.07668e7	−	8.79306e7i	0.508310	−	0.880419i	−0.491643	−	0.870797i	$-0.663604\pi$
$193$	5.07668e7	−	8.79306e7i	0.508310	−	0.880419i	0.999954	−	0.00962258i	$-0.00306301\pi$
$194$	−2.40902e6	+	876811.i	−0.0236883	+	0.00862184i
$195$	127010.	+	219988.i	0.00122664	+	0.00212460i
$196$	2.52844e7	−	4.37938e7i	0.239859	−	0.415448i
$197$	−1.98035e7	+	1.12311e8i	−0.184549	+	1.04663i	0.741985	+	0.670416i	$0.233884\pi$
$197$	−1.98035e7	+	1.12311e8i	−0.184549	+	1.04663i	−0.926534	+	0.376211i	$0.877227\pi$
$198$	−7.28829e6	−	2.65272e6i	−0.0667264	−	0.0242864i
$199$	−1.04095e7	−	1.80298e7i	−0.0936362	−	0.162183i	0.815402	−	0.578895i	$-0.196516\pi$
$199$	−1.04095e7	−	1.80298e7i	−0.0936362	−	0.162183i	−0.909039	+	0.416712i	$0.863182\pi$
$200$	2.98369e7	+	2.50361e7i	0.263723	+	0.221290i
$201$	3.47993e6	+	2.92001e6i	0.0302263	+	0.0253629i
$202$	3.27480e6	−	1.19193e6i	0.0279547	−	0.0101747i
$203$	−4.28670e6	−	2.43111e7i	−0.0359656	−	0.203971i
$204$	−2.04688e6	−	1.16084e7i	−0.0168806	−	0.0957345i
$205$	2.37605e7	−	8.64813e6i	0.192627	−	0.0701106i
$206$	4.65392e7	+	3.90510e7i	0.370923	+	0.311241i
$207$	1.05617e8	+	8.86229e7i	0.827630	+	0.694464i
$208$	830962.	+	1.43927e6i	0.00640265	+	0.0110897i
$209$	−3.60414e6	−	1.31180e6i	−0.0273080	−	0.00993931i
$210$	158961.	−	901512.i	0.00118447	−	0.00671744i
$211$	1.33835e8	−	2.31810e8i	0.980804	−	1.69880i	0.321530	−	0.946899i	$-0.395803\pi$
$211$	1.33835e8	−	2.31810e8i	0.980804	−	1.69880i	0.659274	−	0.751903i	$-0.270864\pi$
$212$	1.63601e7	+	2.83365e7i	0.117926	+	0.204254i
$213$	4.23255e6	−	1.54052e6i	0.0300105	−	0.0109229i
$214$	3.79396e7	−	6.57133e7i	0.264633	−	0.458358i
$215$	2.19377e7	−	1.84079e7i	0.150542	−	0.126319i
$216$	−2.95986e7			−0.199840
$217$	2.35671e7	−	1.97752e7i	0.156566	−	0.131375i
$218$	−6.62579e7	−	2.41159e7i	−0.433151	−	0.157654i
$219$	−9.01009e6	−	5.10988e7i	−0.0579662	−	0.328743i
$220$	−244536.	+	1.38683e6i	−0.00154833	+	0.00878101i
$221$	−5.40732e6			−0.0336984
$222$	1.21488e7	+	3.18250e7i	0.0745245	+	0.195224i
$223$	9.62882e7			0.581441			0.290721	−	0.956808i	$-0.406105\pi$
$223$	9.62882e7			0.581441			0.290721	+	0.956808i	$0.406105\pi$
$224$	1.04000e6	−	5.89814e6i	0.00618253	−	0.0350629i
$225$	2.63670e7	+	1.49535e8i	0.154320	+	0.875193i
$226$	−1.21027e7	−	4.40503e6i	−0.0697435	−	0.0253846i
$227$	−3.35258e7	+	2.81315e7i	−0.190234	+	0.159625i	−0.732930	−	0.680304i	$-0.761848\pi$
$227$	−3.35258e7	+	2.81315e7i	−0.190234	+	0.159625i	0.542696	+	0.839929i	$0.317403\pi$
$228$	−6.98425e6			−0.0390255
$229$	−3.91250e7	+	3.28298e7i	−0.215293	+	0.180653i	−0.744056	−	0.668117i	$-0.767101\pi$
$229$	−3.91250e7	+	3.28298e7i	−0.215293	+	0.180653i	0.528763	+	0.848770i	$0.322656\pi$
$230$	1.25164e7	−	2.16791e7i	0.0678318	−	0.117488i
$231$	−1.15292e6	+	419630.i	−0.00615402	+	0.00223988i
$232$	3.45763e7	+	5.98879e7i	0.181790	+	0.314870i
$233$	−4.23574e7	+	7.33652e7i	−0.219373	+	0.379966i	−0.954617	−	0.297838i	$-0.903735\pi$
$233$	−4.23574e7	+	7.33652e7i	−0.219373	+	0.379966i	0.735243	+	0.677803i	$0.237068\pi$
$234$	−1.12505e6	+	6.38049e6i	−0.00574007	+	0.0325536i
$235$	−1.37393e7	−	5.00071e6i	−0.0690602	−	0.0251359i
$236$	−7.12761e7	−	1.23454e8i	−0.352982	−	0.611382i
$237$	2.07767e7	+	1.74337e7i	0.101381	+	0.0850687i
$238$	1.49275e7	+	1.25257e7i	0.0717743	+	0.0602258i
$239$	−8.08403e7	+	2.94235e7i	−0.383032	+	0.139412i	−0.526358	−	0.850263i	$-0.676443\pi$
$239$	−8.08403e7	+	2.94235e7i	−0.383032	+	0.139412i	0.143325	+	0.989676i	$0.454220\pi$
$240$	445293.	+	2.52538e6i	0.00207925	+	0.0117920i
$241$	6.34093e7	+	3.59612e8i	0.291805	+	1.65491i	0.679911	+	0.733295i	$0.262018\pi$
$241$	6.34093e7	+	3.59612e8i	0.291805	+	1.65491i	−0.388106	+	0.921615i	$0.626871\pi$
$242$	−1.44722e8	+	5.26745e7i	−0.656419	+	0.238917i
$243$	−1.34607e8	−	1.12949e8i	−0.601791	−	0.504962i
$244$	−1.20032e8	−	1.00718e8i	−0.528970	−	0.443858i
$245$	−1.78968e7	−	3.09982e7i	−0.0777490	−	0.134665i
$246$	−5.79903e7	−	2.11067e7i	−0.248360	−	0.0903957i
$247$	−556352.	+	3.15523e6i	−0.00234915	+	0.0133227i
$248$	−4.30902e7	+	7.46345e7i	−0.179390	+	0.310712i
$249$	−1.91775e7	−	3.32163e7i	−0.0787215	−	0.136350i
$250$	5.25119e7	−	1.91128e7i	0.212553	−	0.0773631i
$251$	−8.21534e7	+	1.42294e8i	−0.327920	+	0.567973i	−0.982099	−	0.188366i	$-0.939681\pi$
$251$	−8.21534e7	+	1.42294e8i	−0.327920	+	0.567973i	0.654179	+	0.756339i	$0.273014\pi$
$252$	1.78858e7	−	1.50080e7i	0.0704056	−	0.0590773i
$253$	−3.35510e7			−0.130252
$254$	−4.52334e7	+	3.79554e7i	−0.173198	+	0.145330i
$255$	−7.84029e6	−	2.85363e6i	−0.0296102	−	0.0107772i
$256$	2.91333e6	+	1.65223e7i	0.0108530	+	0.0615505i
$257$	−6.95974e7	+	3.94706e8i	−0.255757	+	1.45047i	0.538366	+	0.842711i	$0.319042\pi$
$257$	−6.95974e7	+	3.94706e8i	−0.255757	+	1.45047i	−0.794123	+	0.607757i	$0.792069\pi$
$258$	−6.98933e7			−0.253377
$259$	−4.92031e7	−	2.73931e7i	−0.175972	−	0.0979696i
$260$	1.17635e6			0.00415077
$261$	−4.68134e7	+	2.65492e8i	−0.162978	+	0.924293i
$262$	−4.66519e7	−	2.64576e8i	−0.160256	−	0.908858i
$263$	−1.54464e8	−	5.62203e7i	−0.523578	−	0.190567i	0.0666903	−	0.997774i	$-0.478756\pi$
$263$	−1.54464e8	−	5.62203e7i	−0.523578	−	0.190567i	−0.590269	+	0.807207i	$0.700978\pi$
$264$	2.63284e6	−	2.20922e6i	0.00880666	−	0.00738967i
$265$	2.31600e7			0.0764501
$266$	8.84475e6	−	7.42163e6i	0.0288138	−	0.0241776i
$267$	−6.95064e6	+	1.20389e7i	−0.0223478	+	0.0387076i
$268$	1.97683e7	−	7.19509e6i	0.0627334	−	0.0228331i
$269$	−1.05940e7	−	1.83493e7i	−0.0331838	−	0.0574761i	0.848957	−	0.528463i	$-0.177231\pi$
$269$	−1.05940e7	−	1.83493e7i	−0.0331838	−	0.0574761i	−0.882140	+	0.470987i	$0.843898\pi$
$270$	−1.04752e7	+	1.81437e7i	−0.0323885	+	0.0560986i
$271$	5.48428e7	−	3.11029e8i	0.167389	−	0.949310i	−0.779178	−	0.626803i	$-0.784363\pi$
$271$	5.48428e7	−	3.11029e8i	0.167389	−	0.949310i	0.946567	−	0.322507i	$-0.104526\pi$
$272$	−5.12951e7	−	1.86699e7i	−0.154556	−	0.0562537i
$273$	512446.	+	887582.i	0.00152433	+	0.00264021i
$274$	−1.49775e8	−	1.25676e8i	−0.439859	−	0.369085i
$275$	−2.83056e7	−	2.37512e7i	−0.0820745	−	0.0688686i
$276$	−5.74110e7	+	2.08959e7i	−0.164367	+	0.0598245i
$277$	2.44231e7	+	1.38510e8i	0.0690433	+	0.391564i	0.999672	+	0.0255999i	$0.00814959\pi$
$277$	2.44231e7	+	1.38510e8i	0.0690433	+	0.391564i	−0.930629	+	0.365964i	$0.880739\pi$
$278$	−2.54442e7	−	1.44301e8i	−0.0710285	−	0.402822i
$279$	−3.15708e8	+	1.14908e8i	−0.870305	+	0.316765i
$280$	−3.24744e6	−	2.72493e6i	−0.00884074	−	0.00741826i
$281$	−5.45865e7	−	4.58035e7i	−0.146762	−	0.123148i	0.566451	−	0.824096i	$-0.308316\pi$
$281$	−5.45865e7	−	4.58035e7i	−0.146762	−	0.123148i	−0.713213	+	0.700948i	$0.752761\pi$
$282$	1.78422e7	+	3.09036e7i	0.0473780	+	0.0820611i
$283$	2.56694e8	+	9.34291e7i	0.673231	+	0.245036i	0.655938	−	0.754815i	$-0.272273\pi$
$283$	2.56694e8	+	9.34291e7i	0.673231	+	0.245036i	0.0172923	+	0.999850i	$0.494495\pi$
$284$	3.62204e6	−	2.05416e7i	0.00938295	−	0.0532134i
$285$	−2.47180e6	+	4.28129e6i	−0.00632494	+	0.0109551i
$286$	−788316.	−	1.36540e6i	−0.00199260	−	0.00345128i
$287$	9.58665e7	−	3.48925e7i	0.239376	−	0.0871256i
$288$	−3.27025e7	+	5.66424e7i	−0.0806692	+	0.139723i
$289$	−1.78283e8	+	1.49597e8i	−0.434477	+	0.364569i
$290$	4.89477e7			0.117853
$291$	3.39259e6	−	2.84672e6i	0.00807059	−	0.00677203i
$292$	−2.25794e8	−	8.21823e7i	−0.530729	−	0.193169i
$293$	4.42363e7	+	2.50877e8i	0.102741	+	0.582671i	0.992099	+	0.125460i	$0.0400406\pi$
$293$	4.42363e7	+	2.50877e8i	0.102741	+	0.582671i	−0.889358	+	0.457211i	$0.848848\pi$
$294$	−1.51696e7	+	8.60312e7i	−0.0348144	+	0.197442i
$295$	−1.00902e8			−0.228834
$296$	1.55764e8	+	2.49667e7i	0.349097	+	0.0559552i
$297$	2.80795e7			0.0621930
$298$	2.85899e7	−	1.62141e8i	0.0625829	−	0.354925i
$299$	4.86675e6	+	2.76007e7i	0.0105291	+	0.0597133i
$300$	−6.32278e7	−	2.30130e7i	−0.135202	−	0.0492095i
$301$	8.85118e7	−	7.42702e7i	0.187076	−	0.156976i
$302$	5.11017e8			1.06761
$303$	−4.61185e6	+	3.86980e6i	−0.00952415	+	0.00799171i
$304$	−1.61718e7	+	2.80103e7i	−0.0330141	+	0.0571822i
$305$	−1.04220e8	+	3.79329e7i	−0.210330	+	0.0765539i
$306$	−1.06402e8	−	1.84294e8i	−0.212289	−	0.367695i
$307$	1.90959e8	−	3.30751e8i	0.376666	−	0.652405i	−0.613909	−	0.789377i	$-0.710404\pi$
$307$	1.90959e8	−	3.30751e8i	0.376666	−	0.652405i	0.990575	+	0.136972i	$0.0437371\pi$
$308$	−986627.	+	5.59544e6i	−0.00192409	+	0.0109121i
$309$	−9.86218e7	−	3.58954e7i	−0.190160	−	0.0692124i
$310$	3.05002e7	+	5.28279e7i	0.0581482	+	0.100716i
$311$	2.97564e8	+	2.49686e8i	0.560943	+	0.470687i	0.878626	−	0.477510i	$-0.158461\pi$
$311$	2.97564e8	+	2.49686e8i	0.560943	+	0.470687i	−0.317684	+	0.948197i	$0.602905\pi$
$312$	−2.19932e6	−	1.84545e6i	−0.00409965	−	0.00344001i
$313$	6.04405e8	−	2.19985e8i	1.11410	−	0.405498i	0.281602	−	0.959531i	$-0.409134\pi$
$313$	6.04405e8	−	2.19985e8i	1.11410	−	0.405498i	0.832495	+	0.554033i	$0.186912\pi$
$314$	6.99979e6	+	3.96978e7i	0.0127594	+	0.0723623i
$315$	−2.86978e6	−	1.62754e7i	−0.00517324	−	0.0293389i
$316$	1.18025e8	−	4.29577e7i	0.210412	−	0.0765837i
$317$	6.74598e8	+	5.66055e8i	1.18943	+	0.998047i	0.999869	+	0.0161776i	$0.00514970\pi$
$317$	6.74598e8	+	5.66055e8i	1.18943	+	0.998047i	0.189557	+	0.981870i	$0.439295\pi$
$318$	−4.33003e7	−	3.63333e7i	−0.0755086	−	0.0633592i
$319$	−3.28018e7	−	5.68143e7i	−0.0565757	−	0.0979920i
$320$	1.11591e7	+	4.06158e6i	0.0190373	+	0.00692900i
$321$	−2.27623e7	+	1.29091e8i	−0.0384103	+	0.217836i
$322$	5.05000e7	−	8.74685e7i	0.0842938	−	0.146001i
$323$	−5.26172e7	−	9.11357e7i	−0.0868799	−	0.150480i
$324$	−2.14480e8	+	7.80643e7i	−0.350331	+	0.127510i
$325$	−1.54330e7	+	2.67308e7i	−0.0249379	+	0.0431937i
$326$	−9.62725e7	+	8.07822e7i	−0.153901	+	0.129138i
$327$	1.21808e8			0.192645
$328$	−2.18923e8	+	1.83698e8i	−0.342557	+	0.287439i
$329$	−5.54340e7	−	2.01763e7i	−0.0858204	−	0.0312361i
$330$	−422440.	−	2.39578e6i	−0.000647092	−	0.00366984i
$331$	1.61341e8	−	9.15009e8i	0.244538	−	1.38684i	−0.577025	−	0.816726i	$-0.695787\pi$
$331$	1.61341e8	−	9.15009e8i	0.244538	−	1.38684i	0.821563	−	0.570117i	$-0.193102\pi$
$332$	−1.77619e8			−0.266382
$333$	4.02608e8	+	4.64885e8i	0.597486	+	0.689908i
$334$	7.66528e8			1.12568
$335$	2.58570e6	−	1.46642e7i	0.00375769	−	0.0213109i
$336$	1.79662e6	+	1.01891e7i	0.00258386	+	0.0146538i
$337$	−2.84824e8	−	1.03667e8i	−0.405389	−	0.147549i	0.131274	−	0.991346i	$-0.458093\pi$
$337$	−2.84824e8	−	1.03667e8i	−0.405389	−	0.147549i	−0.536663	+	0.843797i	$0.680315\pi$
$338$	3.83536e8	−	3.21825e8i	0.540254	−	0.453327i
$339$	2.22495e7			0.0310185
$340$	−2.95984e7	+	2.48360e7i	−0.0408406	+	0.0342693i
$341$	4.08788e7	−	7.08041e7i	0.0558287	−	0.0966981i
$342$	−1.18485e8	+	4.31252e7i	−0.160167	+	0.0582961i
$343$	−1.47469e8	−	2.55424e8i	−0.197320	−	0.341769i
$344$	−1.61835e8	+	2.80307e8i	−0.214348	+	0.371261i
$345$	−7.50937e6	+	4.25877e7i	−0.00984547	+	0.0558364i
$346$	2.68305e8	+	9.76551e7i	0.348227	+	0.126744i
$347$	−5.00948e8	−	8.67667e8i	−0.643635	−	1.11481i	−0.984615	−	0.174738i	$-0.944092\pi$
$347$	−5.00948e8	−	8.67667e8i	−0.643635	−	1.11481i	0.340980	−	0.940070i	$-0.389241\pi$
$348$	−9.15134e7	−	7.67889e7i	−0.116401	−	0.0976722i
$349$	1.63182e8	+	1.36926e8i	0.205486	+	0.172424i	0.739723	−	0.672911i	$-0.234956\pi$
$349$	1.63182e8	+	1.36926e8i	0.205486	+	0.172424i	−0.534237	+	0.845335i	$0.679401\pi$
$350$	1.04525e8	−	3.80439e7i	0.130311	−	0.0474294i
$351$	−4.07307e6	−	2.30995e7i	−0.00502745	−	0.0285121i
$352$	−2.76381e6	−	1.56744e7i	−0.00337761	−	0.0191554i
$353$	4.47076e8	−	1.62722e8i	0.540966	−	0.196896i	−0.0570620	−	0.998371i	$-0.518173\pi$
$353$	4.47076e8	−	1.62722e8i	0.540966	−	0.196896i	0.598028	+	0.801475i	$0.295951\pi$
$354$	1.88647e8	+	1.58294e8i	0.226016	+	0.189650i
$355$	−1.13100e7	−	9.49019e6i	−0.0134172	−	0.0112584i
$356$	3.21879e7	+	5.57511e7i	0.0378110	+	0.0654905i
$357$	−3.16332e7	−	1.15135e7i	−0.0367963	−	0.0133927i
$358$	3.81588e7	−	2.16409e8i	0.0439545	−	0.249279i
$359$	4.48559e8	−	7.76926e8i	0.511668	−	0.886236i	−0.488240	−	0.872709i	$-0.662361\pi$
$359$	4.48559e8	−	7.76926e8i	0.511668	−	0.886236i	0.999909	−	0.0135262i	$-0.00430566\pi$
$360$	2.31475e7	+	4.00927e7i	0.0261485	+	0.0452905i
$361$	7.81372e8	−	2.84396e8i	0.874144	−	0.318162i
$362$	−3.97504e8	+	6.88498e8i	−0.440415	+	0.762821i
$363$	2.03810e8	−	1.71017e8i	0.223641	−	0.187657i
$364$	4.74619e6			0.00515811
$365$	−1.30288e8	+	1.09325e8i	−0.140242	+	0.117677i
$366$	2.54360e8	+	9.25796e7i	0.271185	+	0.0987033i
$367$	−2.34881e8	−	1.33208e9i	−0.248038	−	1.40669i	−0.813331	−	0.581801i	$-0.802348\pi$
$367$	−2.34881e8	−	1.33208e9i	−0.248038	−	1.40669i	0.565293	−	0.824890i	$-0.308763\pi$
$368$	−4.91301e7	+	2.78630e8i	−0.0513902	+	0.291448i
$369$	−1.11411e9			−1.15435
$370$	7.04310e7	−	8.66461e7i	0.0722866	−	0.0889289i
$371$	9.34435e7			0.0950037
$372$	2.58524e7	−	1.46616e8i	0.0260376	−	0.147667i
$373$	−1.74483e8	−	9.89540e8i	−0.174089	−	0.987308i	−0.939190	−	0.343398i	$-0.888422\pi$
$373$	−1.74483e8	−	9.89540e8i	−0.174089	−	0.987308i	0.765101	−	0.643910i	$-0.222689\pi$
$374$	4.86625e7	+	1.77117e7i	0.0480999	+	0.0175069i
$375$	−7.39517e7	+	6.20529e7i	−0.0724167	+	0.0607648i
$376$	1.65252e8			0.160320
$377$	−4.19802e7	+	3.52255e7i	−0.0403505	+	0.0338581i
$378$	−4.22644e7	+	7.32041e7i	−0.0402488	+	0.0697130i
$379$	2.99306e8	−	1.08938e8i	0.282409	−	0.102788i	−0.196932	−	0.980417i	$-0.563098\pi$
$379$	2.99306e8	−	1.08938e8i	0.282409	−	0.102788i	0.479341	+	0.877629i	$0.340876\pi$
$380$	1.14467e7	+	1.98263e7i	0.0107014	+	0.0185353i
$381$	5.10033e7	−	8.83403e7i	0.0472455	−	0.0818316i
$382$	3.98744e7	−	2.26139e8i	0.0365993	−	0.207565i
$383$	−9.80168e8	−	3.56752e8i	−0.891466	−	0.324467i	−0.144638	−	0.989485i	$-0.546202\pi$
$383$	−9.80168e8	−	3.56752e8i	−0.891466	−	0.324467i	−0.746828	+	0.665017i	$0.768424\pi$
$384$	−1.44915e7	−	2.51000e7i	−0.0130603	−	0.0226211i
$385$	3.08078e6	+	2.58508e6i	0.00275136	+	0.00230867i
$386$	6.22234e8	+	5.22116e8i	0.550678	+	0.462074i
$387$	−1.18572e9	+	4.31565e8i	−1.03990	+	0.378493i
$388$	−3.56135e6	−	2.01974e7i	−0.00309531	−	0.0175544i
$389$	3.11851e8	+	1.76860e9i	0.268611	+	1.52337i	0.758552	+	0.651613i	$0.225907\pi$
$389$	3.11851e8	+	1.76860e9i	0.268611	+	1.52337i	−0.489941	+	0.871756i	$0.662982\pi$
$390$	−1.90960e6	+	695039.i	−0.00163011	+	0.000593312i
$391$	−7.05182e8	−	5.91718e8i	−0.596599	−	0.500606i
$392$	3.09903e8	+	2.60040e8i	0.259851	+	0.218041i
$393$	2.32055e8	+	4.01932e8i	0.192849	+	0.334024i
$394$	−8.57330e8	−	3.12043e8i	−0.706173	−	0.257026i
$395$	1.54377e7	−	8.75517e7i	0.0126036	−	0.0714784i
$396$	3.10242e7	−	5.37354e7i	0.0251054	−	0.0434838i
$397$	−2.91620e8	−	5.05101e8i	−0.233911	−	0.405146i	0.725045	−	0.688702i	$-0.241819\pi$
$397$	−2.91620e8	−	5.05101e8i	−0.233911	−	0.405146i	−0.958956	+	0.283556i	$0.908486\pi$
$398$	1.56508e8	−	5.69641e7i	0.124436	−	0.0452909i
$399$	−9.97296e6	+	1.72737e7i	−0.00785994	+	0.0136138i
$400$	−2.38695e8	+	2.00289e8i	−0.186481	+	0.156476i
$401$	−1.26568e9			−0.980212			−0.490106	−	0.871663i	$-0.663042\pi$
$401$	−1.26568e9			−0.980212			−0.490106	+	0.871663i	$0.663042\pi$
$402$	−2.78395e7	+	2.33601e7i	−0.0213732	+	0.0179342i
$403$	−6.41765e7	−	2.33583e7i	−0.0488437	−	0.0177776i
$404$	4.84127e6	+	2.74562e7i	0.00365279	+	0.0207160i
$405$	−2.80540e7	+	1.59102e8i	−0.0209847	+	0.119010i
$406$	1.97489e8			0.146454
$407$	−1.47770e8	−	2.36854e7i	−0.108644	−	0.0174141i
$408$	9.43002e7			0.0687388
$409$	−2.14290e8	+	1.21530e9i	−0.154871	+	0.878319i	0.804032	+	0.594586i	$0.202684\pi$
$409$	−2.14290e8	+	1.21530e9i	−0.154871	+	0.878319i	−0.958903	+	0.283733i	$0.908427\pi$
$410$	3.51262e7	+	1.99210e8i	0.0251702	+	0.142747i
$411$	3.17391e8	+	1.15521e8i	0.225501	+	0.0820756i
$412$	−3.72313e8	+	3.12408e8i	−0.262282	+	0.220081i
$413$	−4.07107e8			−0.284369
$414$	−8.44933e8	+	7.08983e8i	−0.585223	+	0.491060i
$415$	−6.28611e7	+	1.08879e8i	−0.0431732	+	0.0747781i
$416$	−1.24936e7	+	4.54729e6i	−0.00850865	+	0.00309689i
$417$	1.26564e8	+	2.19216e8i	0.0854742	+	0.148046i
$418$	1.53418e7	−	2.65728e7i	0.0102745	−	0.0177959i
$419$	−2.90365e8	+	1.64674e9i	−0.192839	+	1.09364i	0.722623	+	0.691242i	$0.242936\pi$
$419$	−2.90365e8	+	1.64674e9i	−0.192839	+	1.09364i	−0.915463	+	0.402403i	$0.868175\pi$
$420$	6.88170e6	+	2.50473e6i	0.00453235	+	0.00164964i
$421$	1.19815e8	+	2.07526e8i	0.0782573	+	0.135546i	0.902498	−	0.430694i	$-0.141731\pi$
$421$	1.19815e8	+	2.07526e8i	0.0782573	+	0.135546i	−0.824241	+	0.566239i	$0.808398\pi$
$422$	1.64038e9	+	1.37644e9i	1.06255	+	0.891589i
$423$	4.93505e8	+	4.14100e8i	0.317030	+	0.266020i
$424$	−2.45975e8	+	8.95275e7i	−0.156715	+	0.0570396i
$425$	−1.76048e8	−	9.98416e8i	−0.111242	−	0.630885i
$426$	6.25714e6	+	3.54860e7i	0.00392141	+	0.0222394i
$427$	−4.20495e8	+	1.53048e8i	−0.261375	+	0.0951326i
$428$	4.65015e8	+	3.90194e8i	0.286691	+	0.240562i
$429$	2.08644e6	+	1.75073e6i	0.00127587	+	0.00107058i
$430$	1.14550e8	+	1.98407e8i	0.0694796	+	0.120342i
$431$	5.60264e8	+	2.03920e8i	0.337072	+	0.122684i	0.505010	−	0.863113i	$-0.331489\pi$
$431$	5.60264e8	+	2.03920e8i	0.337072	+	0.122684i	−0.167938	+	0.985797i	$0.553711\pi$
$432$	4.11179e7	−	2.33191e8i	0.0245379	−	0.139161i
$433$	9.85561e8	−	1.70704e9i	0.583413	−	1.01050i	−0.411658	−	0.911338i	$-0.635050\pi$
$433$	9.85561e8	−	1.70704e9i	0.583413	−	1.01050i	0.995071	−	0.0991624i	$-0.0316163\pi$
$434$	1.23059e8	+	2.13144e8i	0.0722602	+	0.125158i
$435$	−7.94585e7	+	2.89205e7i	−0.0462837	+	0.0168459i
$436$	2.82041e8	−	4.88509e8i	0.162970	−	0.282273i
$437$	−4.17829e8	+	3.50600e8i	−0.239505	+	0.200968i
$438$	4.15096e8			0.236042
$439$	2.85035e7	−	2.39173e7i	0.0160795	−	0.0134923i	−0.634712	−	0.772748i	$-0.718881\pi$
$439$	2.85035e7	−	2.39173e7i	0.0160795	−	0.0134923i	0.650792	+	0.759256i	$0.274437\pi$
$440$	−1.05864e7	−	3.85313e6i	−0.00592466	−	0.00215640i
$441$	2.73863e8	+	1.55316e9i	0.152054	+	0.862343i
$442$	7.51176e6	−	4.26013e7i	0.00413775	−	0.0234663i
$443$	−1.73770e9			−0.949648			−0.474824	−	0.880081i	$-0.657488\pi$
$443$	−1.73770e9			−0.949648			−0.474824	+	0.880081i	$0.657488\pi$
$444$	−2.67609e8	+	5.15032e7i	−0.145098	+	0.0279251i
$445$	4.55666e7			0.0245124
$446$	−1.33762e8	+	7.58603e8i	−0.0713939	+	0.404895i
$447$	4.93895e7	+	2.80102e8i	0.0261552	+	0.148334i
$448$	4.50236e7	+	1.63872e7i	0.0236574	+	0.00861058i
$449$	−1.87670e9	+	1.57474e9i	−0.978435	+	0.821004i	−0.983853	−	0.178981i	$-0.942720\pi$
$449$	−1.87670e9	+	1.57474e9i	−0.978435	+	0.821004i	0.00541783	+	0.999985i	$0.498275\pi$
$450$	−1.21473e9			−0.628402
$451$	2.07687e8	−	1.74270e8i	0.106608	−	0.0894551i
$452$	5.15178e7	−	8.92315e7i	0.0262406	−	0.0454500i
$453$	−8.29551e8	+	3.01932e8i	−0.419276	+	0.152604i
$454$	−1.75059e8	−	3.03211e8i	−0.0877990	−	0.152072i
$455$	1.67973e6	−	2.90938e6i	0.000835986	−	0.00144797i
$456$	9.70242e6	−	5.50252e7i	0.00479185	−	0.0271759i
$457$	1.84784e9	+	6.72558e8i	0.905643	+	0.329627i	0.752512	−	0.658579i	$-0.228842\pi$
$457$	1.84784e9	+	6.72558e8i	0.905643	+	0.329627i	0.153131	+	0.988206i	$0.451064\pi$
$458$	−2.04296e8	−	3.53852e8i	−0.0993646	−	0.172105i
$459$	5.90181e8	+	4.95220e8i	0.284866	+	0.239031i
$460$	1.53410e8	+	1.28727e8i	0.0734856	+	0.0616617i
$461$	1.52383e9	−	5.54627e8i	0.724406	−	0.263662i	0.0466109	−	0.998913i	$-0.485158\pi$
$461$	1.52383e9	−	5.54627e8i	0.724406	−	0.263662i	0.677795	+	0.735251i	$0.262936\pi$
$462$	−1.70442e6	−	9.66622e6i	−0.000804134	−	0.00456047i
$463$	−1.81875e8	−	1.03147e9i	−0.0851610	−	0.482972i	−0.997322	−	0.0731393i	$-0.976698\pi$
$463$	−1.81875e8	−	1.03147e9i	−0.0851610	−	0.482972i	0.912161	−	0.409833i	$-0.134413\pi$
$464$	−5.19858e8	+	1.89213e8i	−0.241586	+	0.0879300i
$465$	−8.07251e7	−	6.77364e7i	−0.0372326	−	0.0312419i
$466$	−5.19162e8	−	4.35629e8i	−0.237658	−	0.199419i
$467$	−4.74078e8	−	8.21128e8i	−0.215398	−	0.373080i	0.737998	−	0.674803i	$-0.235771\pi$
$467$	−4.74078e8	−	8.21128e8i	−0.215398	−	0.373080i	−0.953396	+	0.301723i	$0.902438\pi$
$468$	−4.87056e7	−	1.77274e7i	−0.0219643	−	0.00799436i
$469$	1.04325e7	−	5.91657e7i	0.00466964	−	0.0264829i
$470$	5.84844e7	−	1.01298e8i	0.0259835	−	0.0450047i
$471$	−3.48183e7	−	6.03070e7i	−0.0153544	−	0.0265947i
$472$	1.07164e9	−	3.90046e8i	0.469086	−	0.170733i
$473$	1.53530e8	−	2.65921e8i	0.0667080	−	0.115542i
$474$	−1.66213e8	+	1.39469e8i	−0.0716872	+	0.0601527i
$475$	−6.00700e8			−0.257176
$476$	−1.19420e8	+	1.00206e8i	−0.0507521	+	0.0425861i
$477$	−9.58919e8	−	3.49018e8i	−0.404546	−	0.147243i
$478$	−1.19509e8	−	6.77772e8i	−0.0500501	−	0.283848i
$479$	1.60637e8	−	9.11015e8i	0.0667837	−	0.378749i	−0.933036	−	0.359782i	$-0.882851\pi$
$479$	1.60637e8	−	9.11015e8i	0.0667837	−	0.378749i	0.999820	−	0.0189671i	$-0.00603777\pi$
$480$	−2.05147e7			−0.00846684
$481$	1.95006e6	+	1.24998e8i	0.000798987	+	0.0512150i
$482$	−2.92127e9			−1.18825
$483$	−3.02980e7	+	1.71828e8i	−0.0122349	+	0.0693873i
$484$	−2.13948e8	−	1.21336e9i	−0.0857729	−	0.486442i
$485$	−1.36412e7	−	4.96501e6i	−0.00542948	−	0.00197617i
$486$	1.07686e9	−	9.03589e8i	0.425530	−	0.357062i
$487$	2.68749e9			1.05438			0.527188	−	0.849749i	$-0.323246\pi$
$487$	2.68749e9			1.05438			0.527188	+	0.849749i	$0.323246\pi$
$488$	9.60252e8	−	8.05747e8i	0.374038	−	0.313855i
$489$	1.08553e8	−	1.88019e8i	0.0419817	−	0.0727144i
$490$	2.69080e8	−	9.79372e7i	0.103323	−	0.0376064i
$491$	8.49150e8	+	1.47077e9i	0.323742	+	0.560738i	0.981257	−	0.192704i	$-0.0617256\pi$
$491$	8.49150e8	+	1.47077e9i	0.323742	+	0.560738i	−0.657515	+	0.753442i	$0.728392\pi$
$492$	2.46848e8	−	4.27553e8i	0.0934440	−	0.161850i
$493$	3.12564e8	−	1.77264e9i	0.117483	−	0.666279i
$494$	−2.40855e7	−	8.76639e6i	−0.00898898	−	0.00327172i
$495$	−2.19596e7	−	3.80351e7i	−0.00813777	−	0.0140950i
$496$	−5.28145e8	−	4.43166e8i	−0.194342	−	0.163072i
$497$	−4.56322e7	−	3.82900e7i	−0.0166734	−	0.0139906i
$498$	2.88335e8	−	1.04945e8i	0.104615	−	0.0380768i
$499$	1.50579e8	+	8.53977e8i	0.0542516	+	0.307676i	0.999844	−	0.0176782i	$-0.00562745\pi$
$499$	1.50579e8	+	8.53977e8i	0.0542516	+	0.307676i	−0.945592	+	0.325355i	$0.894516\pi$
$500$	7.76305e7	+	4.40264e8i	0.0277739	+	0.157514i
$501$	−1.24433e9	+	4.52900e8i	−0.442083	+	0.160905i
$502$	−1.00693e9	−	8.44915e8i	−0.355252	−	0.298092i
$503$	1.25129e9	+	1.04996e9i	0.438401	+	0.367862i	0.835111	−	0.550082i	$-0.185404\pi$
$503$	1.25129e9	+	1.04996e9i	0.438401	+	0.367862i	−0.396710	+	0.917944i	$0.629848\pi$
$504$	9.33932e7	+	1.61762e8i	0.0324944	+	0.0562819i
$505$	1.85438e7	+	6.74939e6i	0.00640735	+	0.00233209i
$506$	4.66086e7	−	2.64331e8i	0.0159933	−	0.0907028i
$507$	−4.32459e8	+	7.49041e8i	−0.147373	+	0.255257i
$508$	−2.36192e8	−	4.09097e8i	−0.0799361	−	0.138453i
$509$	1.05418e9	−	3.83691e8i	0.354327	−	0.128964i	−0.158723	−	0.987323i	$-0.550738\pi$
$509$	1.05418e9	−	3.83691e8i	0.354327	−	0.128964i	0.513050	+	0.858359i	$0.328516\pi$
$510$	3.33738e7	−	5.78052e7i	0.0111407	−	0.0192962i
$511$	−5.25672e8	+	4.41091e8i	−0.174278	+	0.146236i
$512$	−1.34218e8			−0.0441942
$513$	3.49689e8	−	2.93424e8i	0.114359	−	0.0959588i
$514$	−3.01300e9	−	1.09664e9i	−0.978650	−	0.356200i
$515$	5.97377e7	+	3.38789e8i	0.0192718	+	0.109296i
$516$	9.70948e7	−	5.50652e8i	0.0311116	−	0.176442i
$517$	−1.56771e8			−0.0498940
$518$	2.84167e8	−	3.49590e8i	0.0898297	−	0.110511i
$519$	−4.93248e8			−0.154875
$520$	−1.63416e6	+	9.26780e6i	−0.000509663	+	0.00289045i
$521$	−9.99177e8	−	5.66661e9i	−0.309535	−	1.75546i	−0.601348	−	0.798987i	$-0.705370\pi$
$521$	−9.99177e8	−	5.66661e9i	−0.309535	−	1.75546i	0.291813	−	0.956475i	$-0.405742\pi$
$522$	−2.02664e9	−	7.37635e8i	−0.623633	−	0.226984i
$523$	2.64276e9	−	2.21754e9i	0.807797	−	0.677822i	−0.142284	−	0.989826i	$-0.545445\pi$
$523$	2.64276e9	−	2.21754e9i	0.807797	−	0.677822i	0.950081	+	0.312003i	$0.101000\pi$
$524$	2.14926e9			0.652574
$525$	−1.47201e8	+	1.23516e8i	−0.0443969	+	0.0372534i
$526$	6.57508e8	−	1.13884e9i	0.196993	−	0.341202i
$527$	2.10792e9	−	7.67222e8i	0.627361	−	0.228341i
$528$	1.37477e7	+	2.38118e7i	0.00406455	+	0.00704001i
$529$	−6.83224e8	+	1.18338e9i	−0.200663	+	0.347559i
$530$	−3.21735e7	+	1.82465e8i	−0.00938714	+	0.0532371i
$531$	4.17774e9	+	1.52057e9i	1.21091	+	0.440734i
$532$	4.61840e7	+	7.99931e7i	0.0132984	+	0.0230336i
$533$	−1.73489e8	−	1.45575e8i	−0.0496280	−	0.0416429i
$534$	−8.51920e7	−	7.14846e7i	−0.0242105	−	0.0203151i
$535$	4.03759e8	−	1.46956e8i	0.113995	−	0.0414906i
$536$	2.92243e7	+	1.65739e8i	0.00819725	+	0.0464889i
$537$	6.59199e7	+	3.73850e8i	0.0183699	+	0.104181i
$538$	1.59282e8	−	5.79737e7i	0.0440989	−	0.0160507i
$539$	−2.93998e8	−	2.46694e8i	−0.0808694	−	0.0678575i
$540$	−1.28392e8	−	1.07734e8i	−0.0350881	−	0.0294424i
$541$	2.50436e9	+	4.33768e9i	0.679996	+	1.17779i	0.974981	+	0.222286i	$0.0713519\pi$
$541$	2.50436e9	+	4.33768e9i	0.679996	+	1.17779i	−0.294985	+	0.955502i	$0.595315\pi$
$542$	2.37424e9	+	8.64154e8i	0.640512	+	0.233127i
$543$	2.38487e8	−	1.35253e9i	0.0639242	−	0.362532i
$544$	2.18348e8	−	3.78191e8i	0.0581506	−	0.100720i
$545$	−1.99634e8	−	3.45777e8i	−0.0528260	−	0.0914973i
$546$	−7.70466e6	+	2.80427e6i	−0.00202572	+	0.000737302i
$547$	−1.12673e9	+	1.95156e9i	−0.294350	+	0.509830i	−0.974834	−	0.222934i	$-0.928437\pi$
$547$	−1.12673e9	+	1.95156e9i	−0.294350	+	0.509830i	0.680483	+	0.732764i	$0.261770\pi$
$548$	1.19820e9	−	1.00541e9i	0.311027	−	0.260983i
$549$	4.88678e9			1.26043
$550$	2.26445e8	−	1.90010e8i	0.0580354	−	0.0486975i
$551$	−1.00219e9	−	3.64769e8i	−0.255224	−	0.0928939i
$552$	−8.48730e7	−	4.81339e8i	−0.0214775	−	0.121805i
$553$	6.22865e7	−	3.53244e8i	0.0156623	−	0.0888253i
$554$	−1.12518e9			−0.281149
$555$	−6.31386e7	+	1.82270e8i	−0.0156772	+	0.0452573i
$556$	1.17222e9			0.289233
$557$	2.48070e8	−	1.40688e9i	0.0608249	−	0.344955i	−0.939174	−	0.343442i	$-0.888407\pi$
$557$	2.48070e8	−	1.40688e9i	0.0608249	−	0.344955i	0.999999	−	0.00151344i	$-0.000481742\pi$
$558$	−4.66724e8	−	2.64693e9i	−0.113721	−	0.644944i
$559$	−2.41030e8	−	8.77276e7i	−0.0583619	−	0.0212420i
$560$	2.59795e7	−	2.17994e7i	0.00625135	−	0.00524550i
$561$	−8.94605e7			−0.0213925
$562$	4.36692e8	−	3.66428e8i	0.103776	−	0.0870787i
$563$	2.22455e9	−	3.85303e9i	0.525366	−	0.909961i	−0.474197	−	0.880419i	$-0.657262\pi$
$563$	2.22455e9	−	3.85303e9i	0.525366	−	0.909961i	0.999564	−	0.0295423i	$-0.00940499\pi$
$564$	−2.68259e8	+	9.76383e7i	−0.0629618	+	0.0229162i
$565$	−3.64654e7	−	6.31600e7i	−0.00850573	−	0.0147324i
$566$	−1.09267e9	+	1.89257e9i	−0.253299	+	0.438726i
$567$	−1.13189e8	+	6.41928e8i	−0.0260774	+	0.147892i
$568$	1.56805e8	+	5.70723e7i	0.0359038	+	0.0130679i
$569$	9.04629e6	+	1.56686e7i	0.00205863	+	0.00356565i	0.867053	−	0.498216i	$-0.166011\pi$
$569$	9.04629e6	+	1.56686e7i	0.00205863	+	0.00356565i	−0.864994	+	0.501782i	$0.832678\pi$
$570$	−3.02962e7	−	2.54215e7i	−0.00685213	−	0.00574962i
$571$	5.44287e9	+	4.56711e9i	1.22349	+	1.02663i	0.998634	+	0.0522425i	$0.0166369\pi$
$571$	5.44287e9	+	4.56711e9i	1.22349	+	1.02663i	0.224860	+	0.974391i	$0.427808\pi$
$572$	1.18524e7	−	4.31392e6i	0.00264801	−	0.000963797i
$573$	6.88837e7	+	3.90659e8i	0.0152959	+	0.0867475i
$574$	1.41723e8	+	8.03752e8i	0.0312788	+	0.177391i
$575$	−4.93779e9	+	1.79721e9i	−1.08317	+	0.394240i
$576$	−4.00825e8	−	3.36332e8i	−0.0873930	−	0.0733314i
$577$	3.97074e9	+	3.33184e9i	0.860509	+	0.722053i	0.962078	−	0.272775i	$-0.0879416\pi$
$577$	3.97074e9	+	3.33184e9i	0.860509	+	0.722053i	−0.101568	+	0.994829i	$0.532386\pi$
$578$	−9.30926e8	−	1.61241e9i	−0.200525	−	0.347319i
$579$	−1.31858e9	−	4.79925e8i	−0.282314	−	0.102754i
$580$	−6.79974e7	+	3.85633e8i	−0.0144709	+	0.0820683i
$581$	−2.53625e8	+	4.39292e8i	−0.0536508	+	0.0929259i
$582$	1.77148e7	+	3.06830e7i	0.00372483	+	0.00645159i
$583$	2.33351e8	−	8.49328e7i	0.0487719	−	0.0177515i
$584$	9.61140e8	−	1.66474e9i	0.199683	−	0.345862i
$585$	−2.81041e7	+	2.35822e7i	−0.00580397	+	0.00487011i
$586$	−2.03797e9			−0.418367
$587$	−6.47657e9	+	5.43449e9i	−1.32164	+	1.10898i	−0.335681	+	0.941976i	$0.608966\pi$
$587$	−6.47657e9	+	5.43449e9i	−1.32164	+	1.10898i	−0.985955	+	0.167009i	$0.946589\pi$
$588$	−6.56720e8	−	2.39027e8i	−0.133217	−	0.0484870i
$589$	−2.30801e8	−	1.30893e9i	−0.0465407	−	0.263946i
$590$	1.40171e8	−	7.94949e8i	0.0280980	−	0.159352i
$591$	1.57610e9			0.314072
$592$	−4.13085e8	+	1.19250e9i	−0.0818301	+	0.236228i
$593$	−4.40529e9			−0.867528			−0.433764	−	0.901026i	$-0.642815\pi$
$593$	−4.40529e9			−0.867528			−0.433764	+	0.901026i	$0.642815\pi$
$594$	−3.90076e7	+	2.21223e8i	−0.00763655	+	0.0433090i
$595$	1.91610e7	+	1.08667e8i	0.00372914	+	0.0211490i
$596$	1.23771e9	+	4.50489e8i	0.239473	+	0.0871610i
$597$	−2.20407e8	+	1.84944e8i	−0.0423951	+	0.0355737i
$598$	−2.24212e8			−0.0428750
$599$	−2.02663e9	+	1.70054e9i	−0.385283	+	0.323291i	−0.814772	−	0.579781i	$-0.803138\pi$
$599$	−2.02663e9	+	1.70054e9i	−0.385283	+	0.323291i	0.429489	+	0.903072i	$0.358694\pi$
$600$	2.69142e8	−	4.66168e8i	0.0508689	−	0.0881076i
$601$	−5.88708e9	+	2.14272e9i	−1.10621	+	0.402629i	−0.829603	−	0.558353i	$-0.811433\pi$
$601$	−5.88708e9	+	2.14272e9i	−1.10621	+	0.402629i	−0.276611	+	0.960982i	$0.589211\pi$
$602$	4.62176e8	+	8.00512e8i	0.0863415	+	0.149548i
$603$	−3.28047e8	+	5.68194e8i	−0.0609292	+	0.105532i
$604$	−7.09897e8	+	4.02602e9i	−0.131089	+	0.743442i
$605$	−8.19499e8	−	2.98273e8i	−0.150454	−	0.0547609i
$606$	−2.40814e7	−	4.17102e7i	−0.00439569	−	0.00761356i
$607$	2.63733e9	+	2.21298e9i	0.478634	+	0.401621i	0.849932	−	0.526892i	$-0.176643\pi$
$607$	2.63733e9	+	2.21298e9i	0.478634	+	0.401621i	−0.371298	+	0.928514i	$0.621087\pi$
$608$	−1.98213e8	−	1.66320e8i	−0.0357659	−	0.0300111i
$609$	−3.20591e8	+	1.16685e8i	−0.0575162	+	0.0209342i
$610$	−1.54072e8	−	8.73789e8i	−0.0274834	−	0.155866i
$611$	2.27404e7	+	1.28967e8i	0.00403324	+	0.0228736i
$612$	1.59977e9	−	5.82268e8i	0.282116	−	0.102682i
$613$	−3.35733e9	−	2.81714e9i	−0.588685	−	0.493965i	0.299101	−	0.954221i	$-0.403313\pi$
$613$	−3.35733e9	−	2.81714e9i	−0.588685	−	0.493965i	−0.887786	+	0.460256i	$0.847758\pi$
$614$	2.34053e9	+	1.96394e9i	0.408061	+	0.342404i
$615$	−1.74724e8	−	3.02631e8i	−0.0302893	−	0.0524627i
$616$	−4.27129e7	−	1.55462e7i	−0.00736251	−	0.00267974i
$617$	1.36147e9	−	7.72127e9i	0.233351	−	1.32340i	−0.612708	−	0.790309i	$-0.709920\pi$
$617$	1.36147e9	−	7.72127e9i	0.233351	−	1.32340i	0.846059	−	0.533089i	$-0.178969\pi$
$618$	4.19805e8	−	7.27123e8i	0.0715464	−	0.123922i
$619$	3.05348e9	+	5.28878e9i	0.517461	+	0.896269i	0.999794	+	0.0202812i	$0.00645615\pi$
$619$	3.05348e9	+	5.28878e9i	0.517461	+	0.896269i	−0.482333	+	0.875988i	$0.660211\pi$
$620$	−4.58573e8	+	1.66907e8i	−0.0772747	+	0.0281257i
$621$	1.99658e9	−	3.45819e9i	0.334555	−	0.579466i
$622$	−2.38051e9	+	1.99748e9i	−0.396646	+	0.332826i
$623$	1.83847e8			0.0304613
$624$	1.75945e7	−	1.47636e7i	0.00289889	−	0.00243246i
$625$	−5.28742e9	−	1.92446e9i	−0.866291	−	0.315304i
$626$	8.93516e8	+	5.06738e9i	0.145577	+	0.825607i
$627$	−9.20448e6	+	5.22012e7i	−0.00149129	+	0.00845754i
$628$	−3.22481e8			−0.0519572
$629$	−2.68814e9	−	3.10395e9i	−0.430699	−	0.497322i
$630$	1.32211e8			0.0210658
$631$	−1.17719e9	+	6.67619e9i	−0.186528	+	1.05785i	0.737448	+	0.675404i	$0.236031\pi$
$631$	−1.17719e9	+	6.67619e9i	−0.186528	+	1.05785i	−0.923976	+	0.382450i	$0.875080\pi$
$632$	1.74482e8	+	9.89534e8i	0.0274941	+	0.155927i
$633$	−3.47615e9	−	1.26522e9i	−0.544736	−	0.198268i
$634$	−5.39678e9	+	4.52844e9i	−0.841051	+	0.705726i
$635$	−3.34364e8			−0.0518217
$636$	3.46403e8	−	2.90666e8i	0.0533926	−	0.0448017i
$637$	−1.60296e8	+	2.77641e8i	−0.0245717	+	0.0425595i
$638$	4.93177e8	−	1.79502e8i	0.0751849	−	0.0273651i
$639$	3.25263e8	+	5.63372e8i	0.0493153	+	0.0854167i
$640$	−4.75011e7	+	8.22743e7i	−0.00716265	+	0.0124061i
$641$	5.42874e7	−	3.07879e8i	0.00814135	−	0.0461719i	−0.980466	−	0.196686i	$-0.936982\pi$
$641$	5.42874e7	−	3.07879e8i	0.00814135	−	0.0461719i	0.988608	+	0.150515i	$0.0480930\pi$
$642$	−9.85419e8	−	3.58663e8i	−0.146977	−	0.0534951i
$643$	−1.26024e9	−	2.18280e9i	−0.186945	−	0.323798i	0.757285	−	0.653084i	$-0.226525\pi$
$643$	−1.26024e9	−	2.18280e9i	−0.186945	−	0.323798i	−0.944230	+	0.329286i	$0.893192\pi$
$644$	6.18964e8	+	5.19372e8i	0.0913197	+	0.0766263i
$645$	−3.03182e8	−	2.54400e8i	−0.0444881	−	0.0373300i
$646$	7.91104e8	−	2.87938e8i	0.115457	−	0.0420229i
$647$	−1.40600e9	−	7.97381e9i	−0.204089	−	1.15745i	−0.898867	−	0.438222i	$-0.855608\pi$
$647$	−1.40600e9	−	7.97381e9i	−0.204089	−	1.15745i	0.694778	−	0.719224i	$-0.255503\pi$
$648$	−3.17074e8	−	1.79822e9i	−0.0457771	−	0.259615i
$649$	−1.01664e9	+	3.70028e8i	−0.145986	+	0.0531347i
$650$	−1.89158e8	−	1.58723e8i	−0.0270165	−	0.0226695i
$651$	−3.25701e8	−	2.73296e8i	−0.0462685	−	0.0388239i
$652$	−5.02699e8	−	8.70701e8i	−0.0710300	−	0.123028i
$653$	−3.85234e9	−	1.40214e9i	−0.541412	−	0.197058i	0.0568145	−	0.998385i	$-0.481906\pi$
$653$	−3.85234e9	−	1.40214e9i	−0.541412	−	0.197058i	−0.598227	+	0.801327i	$0.704128\pi$
$654$	−1.69213e8	+	9.59656e8i	−0.0236544	+	0.134151i
$655$	7.60646e8	−	1.31748e9i	0.105764	−	0.183189i
$656$	−1.14313e9	−	1.97996e9i	−0.158101	−	0.273838i
$657$	7.04196e9	−	2.56307e9i	0.968757	−	0.352599i
$658$	2.35966e8	−	4.08706e8i	0.0322894	−	0.0559268i
$659$	−1.00727e10	+	8.45198e9i	−1.37103	+	1.15043i	−0.398626	+	0.917114i	$0.630513\pi$
$659$	−1.00727e10	+	8.45198e9i	−1.37103	+	1.15043i	−0.972401	+	0.233315i	$0.925043\pi$
$660$	1.94619e7			0.00263500
$661$	−4.79260e9	+	4.02147e9i	−0.645455	+	0.541601i	−0.905688	−	0.423945i	$-0.860645\pi$
$661$	−4.79260e9	+	4.02147e9i	−0.645455	+	0.541601i	0.260233	+	0.965546i	$0.416201\pi$
$662$	6.98473e9	+	2.54223e9i	0.935722	+	0.340575i
$663$	1.29767e7	+	7.35945e7i	0.00172929	+	0.00980727i
$664$	2.46745e8	−	1.39936e9i	0.0327085	−	0.185499i
$665$	6.53801e7			0.00862124
$666$	−4.22188e9	+	2.52612e9i	−0.553791	+	0.331355i
$667$	−9.32944e9			−1.21735
$668$	−1.06485e9	+	6.03906e9i	−0.138220	+	0.783884i
$669$	−2.31076e8	−	1.31050e9i	−0.0298376	−	0.169218i
$670$	1.11940e8	+	4.07427e7i	0.0143788	+	0.00523345i
$671$	−9.10970e8	+	7.64395e8i	−0.116406	+	0.0976762i
$672$	−8.27706e7			−0.0105217
$673$	2.26172e9	−	1.89781e9i	0.286013	−	0.239994i	−0.488481	−	0.872574i	$-0.662449\pi$
$673$	2.26172e9	−	1.89781e9i	0.286013	−	0.239994i	0.774494	+	0.632581i	$0.218004\pi$
$674$	1.21241e9	−	2.09996e9i	0.152525	−	0.264181i
$675$	4.13253e9	−	1.50412e9i	0.517193	−	0.188243i
$676$	2.00268e9	+	3.46875e9i	0.249344	+	0.431877i
$677$	3.51719e9	−	6.09194e9i	0.435647	−	0.754563i	−0.561701	−	0.827340i	$-0.689853\pi$
$677$	3.51719e9	−	6.09194e9i	0.435647	−	0.754563i	0.997348	+	0.0727772i	$0.0231862\pi$
$678$	−3.09087e7	+	1.75292e8i	−0.00380870	+	0.0216002i
$679$	−5.50382e7	−	2.00323e7i	−0.00674715	−	0.00245576i
$680$	−1.54552e8	−	2.67691e8i	−0.0188492	−	0.0326478i
$681$	4.63331e8	+	3.88781e8i	0.0562181	+	0.0471726i
$682$	5.01039e8	+	4.20422e8i	0.0604820	+	0.0507504i
$683$	4.11839e9	−	1.49897e9i	0.494601	−	0.180020i	−0.0826632	−	0.996578i	$-0.526343\pi$
$683$	4.11839e9	−	1.49897e9i	0.494601	−	0.180020i	0.577264	+	0.816558i	$0.304120\pi$
$684$	−1.75162e8	−	9.93392e8i	−0.0209287	−	0.118693i
$685$	−1.92252e8	−	1.09031e9i	−0.0228535	−	0.129609i
$686$	2.21721e9	−	8.06999e8i	0.262224	−	0.0954418i
$687$	5.40713e8	+	4.53712e8i	0.0636237	+	0.0533866i
$688$	−1.98357e9	−	1.66441e9i	−0.232214	−	0.194850i
$689$	−1.03719e8	−	1.79646e8i	−0.0120806	−	0.0209242i
$690$	−3.25094e8	−	1.18325e8i	−0.0376736	−	0.0137121i
$691$	−1.86816e9	+	1.05948e10i	−0.215397	+	1.22158i	0.664819	+	0.747005i	$0.268509\pi$
$691$	−1.86816e9	+	1.05948e10i	−0.215397	+	1.22158i	−0.880216	+	0.474574i	$0.842602\pi$
$692$	−1.14210e9	+	1.97817e9i	−0.131018	+	0.226930i
$693$	−8.86001e7	−	1.53460e8i	−0.0101127	−	0.0175157i
$694$	7.53179e9	−	2.74135e9i	0.855343	−	0.311319i
$695$	4.14861e8	−	7.18560e8i	0.0468766	−	0.0811926i
$696$	7.32108e8	−	6.14311e8i	0.0823081	−	0.0690647i
$697$	7.43870e9			0.832113
$698$	−1.30546e9	+	1.09541e9i	−0.145301	+	0.121922i
$699$	1.10016e9	+	4.00427e8i	0.121839	+	0.0443459i
$700$	1.54523e8	+	8.76345e8i	0.0170275	+	0.0965677i
$701$	2.27870e9	−	1.29231e10i	0.249847	−	1.41695i	−0.559115	−	0.829090i	$-0.688859\pi$
$701$	2.27870e9	−	1.29231e10i	0.249847	−	1.41695i	0.808962	−	0.587861i	$-0.200030\pi$
$702$	1.87647e8			0.0204721
$703$	−2.08777e9	+	1.24920e9i	−0.226641	+	0.135608i
$704$	1.27329e8			0.0137539
$705$	−3.50883e7	+	1.98996e8i	−0.00377138	+	0.0213886i
$706$	6.60931e8	+	3.74833e9i	0.0706870	+	0.400886i
$707$	7.48185e7	+	2.72317e7i	0.00796234	+	0.00289806i
$708$	−1.50918e9	+	1.26635e9i	−0.159817	+	0.134103i
$709$	7.05155e9			0.743058			0.371529	−	0.928421i	$-0.378834\pi$
$709$	7.05155e9			0.743058			0.371529	+	0.928421i	$0.378834\pi$
$710$	9.04797e7	−	7.59215e7i	0.00948739	−	0.00796087i
$711$	−1.95858e9	+	3.39236e9i	−0.204361	+	0.353963i
$712$	−4.83948e8	+	1.76143e8i	−0.0502480	+	0.0182888i
$713$	−5.81334e9	−	1.00690e10i	−0.600638	−	1.04034i
$714$	1.34653e8	−	2.33226e8i	0.0138444	−	0.0239791i
$715$	1.55029e6	−	8.79215e6i	0.000158614	−	0.000899547i
$716$	1.65196e9	+	6.01265e8i	0.168192	+	0.0612167i
$717$	5.94462e8	+	1.02964e9i	0.0602292	+	0.104320i
$718$	5.49785e9	+	4.61325e9i	0.554316	+	0.465126i
$719$	5.78409e9	+	4.85343e9i	0.580342	+	0.486965i	0.885059	−	0.465478i	$-0.154118\pi$
$719$	5.78409e9	+	4.85343e9i	0.580342	+	0.486965i	−0.304717	+	0.952443i	$0.598562\pi$
$720$	−3.48025e8	+	1.26671e8i	−0.0347494	+	0.0126477i
$721$	2.41023e8	+	1.36691e9i	0.0239489	+	0.135821i
$722$	1.15513e9	+	6.55109e9i	0.114223	+	0.647789i
$723$	4.74221e9	−	1.72602e9i	0.466656	−	0.169849i
$724$	−4.87210e9	−	4.08817e9i	−0.477123	−	0.400354i
$725$	−7.87086e9	−	6.60444e9i	−0.767078	−	0.643654i
$726$	1.06422e9	+	1.84328e9i	0.103217	+	0.178778i
$727$	8.89177e9	+	3.23634e9i	0.858258	+	0.312380i	0.733402	−	0.679795i	$-0.237931\pi$
$727$	8.89177e9	+	3.23634e9i	0.858258	+	0.312380i	0.124855	+	0.992175i	$0.460153\pi$
$728$	−6.59334e6	+	3.73927e7i	−0.000633353	+	0.00359192i
$729$	2.68556e9	−	4.65152e9i	0.256737	−	0.444681i
$730$	−6.80315e8	−	1.17834e9i	−0.0647262	−	0.112109i
$731$	7.91680e9	−	2.88148e9i	0.749616	−	0.272838i
$732$	−1.08274e9	+	1.87536e9i	−0.102032	+	0.176724i
$733$	1.32544e8	−	1.11218e8i	0.0124307	−	0.0104306i	−0.636551	−	0.771235i	$-0.719640\pi$
$733$	1.32544e8	−	1.11218e8i	0.0124307	−	0.0104306i	0.648982	+	0.760804i	$0.275195\pi$
$734$	1.08210e10			1.01003
$735$	−3.78942e8	+	3.17970e8i	−0.0352019	+	0.0295379i
$736$	−2.12693e9	−	7.74139e8i	−0.196644	−	0.0715725i
$737$	−2.77245e7	−	1.57233e8i	−0.00255110	−	0.0144680i
$738$	1.54771e9	−	8.77748e9i	0.141740	−	0.803845i
$739$	−1.09005e10			−0.993551			−0.496775	−	0.867879i	$-0.665483\pi$
$739$	−1.09005e10			−0.993551			−0.496775	+	0.867879i	$0.665483\pi$
$740$	5.84796e8	+	6.75255e8i	0.0530510	+	0.0612572i
$741$	4.42784e7			0.00399786
$742$	−1.29810e8	+	7.36191e8i	−0.0116653	+	0.0661571i
$743$	−2.70469e9	−	1.53391e10i	−0.241912	−	1.37195i	−0.827557	−	0.561382i	$-0.810270\pi$
$743$	−2.70469e9	−	1.53391e10i	−0.241912	−	1.37195i	0.585645	−	0.810567i	$-0.300841\pi$
$744$	1.11920e9	+	4.07355e8i	0.0996327	+	0.0362633i
$745$	7.14184e8	−	5.99271e8i	0.0632795	−	0.0530978i
$746$	8.03844e9			0.708902
$747$	4.24350e9	−	3.56072e9i	0.372479	−	0.312547i
$748$	−2.07142e8	+	3.58781e8i	−0.0180973	+	0.0313454i
$749$	1.62904e9	−	5.92923e8i	0.141660	−	0.0515599i
$750$	−3.86148e8	−	6.68829e8i	−0.0334226	−	0.0578896i
$751$	2.06152e8	−	3.57065e8i	0.0177602	−	0.0307615i	−0.857009	−	0.515302i	$-0.827680\pi$
$751$	2.06152e8	−	3.57065e8i	0.0177602	−	0.0307615i	0.874769	+	0.484540i	$0.161013\pi$
$752$	−2.29565e8	+	1.30193e9i	−0.0196854	+	0.111641i
$753$	2.13380e9	+	7.76639e8i	0.182126	+	0.0662883i
$754$	−2.19205e8	−	3.79674e8i	−0.0186230	−	0.0322560i
$755$	2.21668e9	+	1.86001e9i	0.187451	+	0.157290i
$756$	−5.18022e8	−	4.34672e8i	−0.0436036	−	0.0365878i
$757$	−3.81024e9	+	1.38681e9i	−0.319239

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:	\( N \)	\(=\)	\( 74 = 2 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	74.f (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.38919 + 7.87846i) q^{2} +(-2.39984 - 13.6102i) q^{3} +(-60.1403 - 21.8893i) q^{4} +(-34.7022 + 29.1186i) q^{5} +110.561 q^{6} +(-140.013 + 117.485i) q^{7} +(256.000 - 443.405i) q^{8} +(1875.63 - 682.674i) q^{9} +O(q^{10})\)	\(q+(-1.38919 + 7.87846i) q^{2} +(-2.39984 - 13.6102i) q^{3} +(-60.1403 - 21.8893i) q^{4} +(-34.7022 + 29.1186i) q^{5} +110.561 q^{6} +(-140.013 + 117.485i) q^{7} +(256.000 - 443.405i) q^{8} +(1875.63 - 682.674i) q^{9} +(-181.202 - 313.852i) q^{10} +(-242.862 + 420.649i) q^{11} +(-153.590 + 871.051i) q^{12} +(381.274 + 138.772i) q^{13} +(-731.095 - 1266.29i) q^{14} +(479.590 + 402.424i) q^{15} +(3137.72 + 2632.86i) q^{16} +(-12523.2 + 4558.08i) q^{17} +(2772.82 + 15725.4i) q^{18} +(1371.19 + 7776.41i) q^{19} +(2724.39 - 991.597i) q^{20} +(1935.00 + 1623.66i) q^{21} +(-2976.68 - 2497.73i) q^{22} +(34537.2 + 59820.2i) q^{23} +(-6649.18 - 2420.10i) q^{24} +(-13209.9 + 74917.1i) q^{25} +(-1622.97 + 2811.07i) q^{26} +(-28904.8 - 50064.7i) q^{27} +(10992.1 - 4000.79i) q^{28} +(-67531.8 + 116969. i) q^{29} +(-3836.72 + 3219.39i) q^{30} -168321. q^{31} +(-25101.7 + 21062.9i) q^{32} +(6307.93 + 2295.90i) q^{33} +(-18513.6 - 104996. i) q^{34} +(1437.76 - 8153.97i) q^{35} -127744. q^{36} +(109883. + 287850. i) q^{37} -63171.0 q^{38} +(973.720 - 5522.24i) q^{39} +(4027.58 + 22841.5i) q^{40} +(-524509. - 190906. i) q^{41} +(-15480.0 + 12989.2i) q^{42} -632169. q^{43} +(23813.5 - 19981.9i) q^{44} +(-45210.0 + 78306.1i) q^{45} +(-519270. + 188999. i) q^{46} +(161379. + 279516. i) q^{47} +(28303.6 - 49023.3i) q^{48} +(-137206. + 778133. i) q^{49} +(-571881. - 208148. i) q^{50} +(92090.0 + 159505. i) q^{51} +(-19892.3 - 16691.6i) q^{52} +(-391642. - 328626. i) q^{53} +(434587. - 158177. i) q^{54} +(-3820.87 - 21669.2i) q^{55} +(16250.0 + 92158.5i) q^{56} +(102548. - 37324.3i) q^{57} +(-827718. - 694538. i) q^{58} +(1.70627e6 + 1.43173e6i) q^{59} +(-20033.9 - 34699.8i) q^{60} +(2.30063e6 + 837362. i) q^{61} +(233829. - 1.32611e6i) q^{62} +(-182409. + 315941. i) q^{63} +(-131072. - 227023. i) q^{64} +(-17271.9 + 6286.47i) q^{65} +(-26851.0 + 46507.4i) q^{66} +(-251802. + 211287. i) q^{67} +852924. q^{68} +(731280. - 613616. i) q^{69} +(62243.4 + 22654.8i) q^{70} +(56594.4 + 320963. i) q^{71} +(177460. - 1.00643e6i) q^{72} +3.75445e6 q^{73} +(-2.42046e6 + 465835. i) q^{74} +1.05134e6 q^{75} +(87756.2 - 497690. i) q^{76} +(-15416.0 - 87428.7i) q^{77} +(42154.1 + 15342.8i) q^{78} +(-1.50336e6 + 1.26147e6i) q^{79} -185551. q^{80} +(2.73196e6 - 2.29239e6i) q^{81} +(2.23268e6 - 3.86712e6i) q^{82} +(2.60792e6 - 949206. i) q^{83} +(-80830.7 - 140003. i) q^{84} +(301859. - 522835. i) q^{85} +(878200. - 4.98052e6i) q^{86} +(1.75403e6 + 638414. i) q^{87} +(124345. + 215372. i) q^{88} +(-770543. - 646562. i) q^{89} +(-554127. - 464967. i) q^{90} +(-69686.9 + 25364.0i) q^{91} +(-767657. - 4.35360e6i) q^{92} +(403944. + 2.29088e6i) q^{93} +(-2.42634e6 + 883116. i) q^{94} +(-274022. - 229932. i) q^{95} +(346910. + 291092. i) q^{96} +(160227. + 277521. i) q^{97} +(-5.93989e6 - 2.16194e6i) q^{98} +(-168353. + 954776. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 66 q - 39 q^{3} + 459 q^{5} - 918 q^{7} + 16896 q^{8} + 3237 q^{9}+O(q^{10}) \) 66 * q - 39 * q^3 + 459 * q^5 - 918 * q^7 + 16896 * q^8 + 3237 * q^9	\( 66 q - 39 q^{3} + 459 q^{5} - 918 q^{7} + 16896 q^{8} + 3237 q^{9} + 4704 q^{10} + 4539 q^{11} - 2496 q^{12} - 10542 q^{13} + 6744 q^{14} - 39894 q^{15} - 78822 q^{17} + 51792 q^{18} + 79461 q^{19} + 29376 q^{20} - 5835 q^{21} + 18168 q^{22} - 199479 q^{23} + 19968 q^{24} + 356301 q^{25} + 186744 q^{26} - 91689 q^{27} - 91584 q^{28} - 38526 q^{29} + 319152 q^{30} + 1917246 q^{31} - 902847 q^{33} - 205776 q^{34} - 1574793 q^{35} + 3079296 q^{36} - 396513 q^{37} - 692880 q^{38} + 2514306 q^{39} + 470016 q^{40} + 2989350 q^{41} + 46680 q^{42} + 6006348 q^{43} - 145344 q^{44} + 1083726 q^{45} - 588744 q^{46} - 894135 q^{47} + 7973742 q^{49} + 2012400 q^{50} - 524880 q^{51} - 2262720 q^{52} + 1457844 q^{53} + 1452312 q^{54} + 2415690 q^{55} - 1202688 q^{56} + 2734338 q^{57} - 3423360 q^{58} + 3099522 q^{59} - 3102912 q^{60} - 10968396 q^{61} - 3067320 q^{62} - 10727970 q^{63} - 8650752 q^{64} - 13497300 q^{65} - 4598712 q^{66} - 1978119 q^{67} + 5026176 q^{68} - 7251108 q^{69} + 435744 q^{70} - 19555002 q^{71} + 3314688 q^{72} - 31332840 q^{73} + 7607472 q^{74} + 44758074 q^{75} + 5085504 q^{76} + 1982007 q^{77} - 22512264 q^{78} + 10522902 q^{79} + 4816896 q^{80} - 7548876 q^{81} - 7150320 q^{82} + 19771926 q^{83} + 3556224 q^{84} - 6684072 q^{85} + 22982496 q^{86} - 67769667 q^{87} - 2323968 q^{88} - 42018963 q^{89} - 25158672 q^{90} + 4847565 q^{91} - 1096704 q^{92} - 14558475 q^{93} + 3175680 q^{94} + 4508415 q^{95} - 2555904 q^{96} - 39286662 q^{97} + 71630904 q^{98} + 66155463 q^{99}+O(q^{100}) \) 66 * q - 39 * q^3 + 459 * q^5 - 918 * q^7 + 16896 * q^8 + 3237 * q^9 + 4704 * q^10 + 4539 * q^11 - 2496 * q^12 - 10542 * q^13 + 6744 * q^14 - 39894 * q^15 - 78822 * q^17 + 51792 * q^18 + 79461 * q^19 + 29376 * q^20 - 5835 * q^21 + 18168 * q^22 - 199479 * q^23 + 19968 * q^24 + 356301 * q^25 + 186744 * q^26 - 91689 * q^27 - 91584 * q^28 - 38526 * q^29 + 319152 * q^30 + 1917246 * q^31 - 902847 * q^33 - 205776 * q^34 - 1574793 * q^35 + 3079296 * q^36 - 396513 * q^37 - 692880 * q^38 + 2514306 * q^39 + 470016 * q^40 + 2989350 * q^41 + 46680 * q^42 + 6006348 * q^43 - 145344 * q^44 + 1083726 * q^45 - 588744 * q^46 - 894135 * q^47 + 7973742 * q^49 + 2012400 * q^50 - 524880 * q^51 - 2262720 * q^52 + 1457844 * q^53 + 1452312 * q^54 + 2415690 * q^55 - 1202688 * q^56 + 2734338 * q^57 - 3423360 * q^58 + 3099522 * q^59 - 3102912 * q^60 - 10968396 * q^61 - 3067320 * q^62 - 10727970 * q^63 - 8650752 * q^64 - 13497300 * q^65 - 4598712 * q^66 - 1978119 * q^67 + 5026176 * q^68 - 7251108 * q^69 + 435744 * q^70 - 19555002 * q^71 + 3314688 * q^72 - 31332840 * q^73 + 7607472 * q^74 + 44758074 * q^75 + 5085504 * q^76 + 1982007 * q^77 - 22512264 * q^78 + 10522902 * q^79 + 4816896 * q^80 - 7548876 * q^81 - 7150320 * q^82 + 19771926 * q^83 + 3556224 * q^84 - 6684072 * q^85 + 22982496 * q^86 - 67769667 * q^87 - 2323968 * q^88 - 42018963 * q^89 - 25158672 * q^90 + 4847565 * q^91 - 1096704 * q^92 - 14558475 * q^93 + 3175680 * q^94 + 4508415 * q^95 - 2555904 * q^96 - 39286662 * q^97 + 71630904 * q^98 + 66155463 * q^99

Introduction

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