LMFDB - Embedded newform 43.7.d.a.37.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [43,7,Mod(7,43)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(43, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5]))

N = Newforms(chi, 7, names="a")

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

chi := DirichletCharacter("43.7");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 43 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	43.d (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$9.89232559565$
Analytic rank:	$0$
Dimension:	$42$
Relative dimension:	$21$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			37.9
Character	$\chi$	$=$	43.37
Dual form			43.7.d.a.7.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.61500i q^{2} +(-35.7187 - 20.6222i) q^{3} +57.1618 q^{4} +(121.716 + 70.2726i) q^{5} +(-53.9270 + 93.4043i) q^{6} +(140.639 - 81.1978i) q^{7} -316.838i q^{8} +(486.049 + 841.861i) q^{9} +O(q^{10})$	\(q-2.61500i q^{2} +(-35.7187 - 20.6222i) q^{3} +57.1618 q^{4} +(121.716 + 70.2726i) q^{5} +(-53.9270 + 93.4043i) q^{6} +(140.639 - 81.1978i) q^{7} -316.838i q^{8} +(486.049 + 841.861i) q^{9} +(183.763 - 318.286i) q^{10} +633.170 q^{11} +(-2041.74 - 1178.80i) q^{12} +(-2029.45 - 3515.10i) q^{13} +(-212.332 - 367.770i) q^{14} +(-2898.35 - 5020.09i) q^{15} +2829.82 q^{16} +(-1526.45 - 2643.88i) q^{17} +(2201.47 - 1271.02i) q^{18} +(1715.01 + 990.163i) q^{19} +(6957.49 + 4016.91i) q^{20} -6697.91 q^{21} -1655.74i q^{22} +(2766.29 - 4791.36i) q^{23} +(-6533.89 + 11317.0i) q^{24} +(2063.98 + 3574.91i) q^{25} +(-9191.99 + 5307.00i) q^{26} -10026.4i q^{27} +(8039.16 - 4641.41i) q^{28} +(19161.8 - 11063.0i) q^{29} +(-13127.5 + 7579.18i) q^{30} +(445.023 - 770.802i) q^{31} -27677.6i q^{32} +(-22616.0 - 13057.4i) q^{33} +(-6913.75 + 3991.66i) q^{34} +22823.9 q^{35} +(27783.4 + 48122.3i) q^{36} +(-32934.5 - 19014.7i) q^{37} +(2589.27 - 4484.75i) q^{38} +167406. i q^{39} +(22265.0 - 38564.2i) q^{40} -53188.1 q^{41} +17515.0i q^{42} +(79357.0 + 4881.64i) q^{43} +36193.2 q^{44} +136624. i q^{45} +(-12529.4 - 7233.86i) q^{46} +144957. q^{47} +(-101078. - 58357.1i) q^{48} +(-45638.3 + 79047.9i) q^{49} +(9348.39 - 5397.29i) q^{50} +125915. i q^{51} +(-116007. - 200930. i) q^{52} +(12646.2 - 21903.9i) q^{53} -26219.0 q^{54} +(77066.8 + 44494.5i) q^{55} +(-25726.6 - 44559.7i) q^{56} +(-40838.6 - 70734.6i) q^{57} +(-28929.9 - 50108.0i) q^{58} -168198. q^{59} +(-165675. - 286957. i) q^{60} +(278864. - 161002. i) q^{61} +(-2015.65 - 1163.73i) q^{62} +(136715. + 78932.2i) q^{63} +108732. q^{64} -570458. i q^{65} +(-34145.0 + 59140.8i) q^{66} +(-220086. + 381199. i) q^{67} +(-87254.4 - 151129. i) q^{68} +(-197617. + 114094. i) q^{69} -59684.5i q^{70} +(435989. - 251718. i) q^{71} +(266734. - 153999. i) q^{72} +(-579548. + 334602. i) q^{73} +(-49723.5 + 86123.7i) q^{74} -170255. i q^{75} +(98033.1 + 56599.5i) q^{76} +(89048.3 - 51412.1i) q^{77} +437768. q^{78} +(484554. + 839272. i) q^{79} +(344434. + 198859. i) q^{80} +(147563. - 255587. i) q^{81} +139087. i q^{82} +(-227845. + 394640. i) q^{83} -382864. q^{84} -429069. i q^{85} +(12765.5 - 207518. i) q^{86} -912577. q^{87} -200612. i q^{88} +(-833221. - 481060. i) q^{89} +357271. q^{90} +(-570837. - 329573. i) q^{91} +(158126. - 273883. i) q^{92} +(-31791.2 + 18354.7i) q^{93} -379063. i q^{94} +(139163. + 241037. i) q^{95} +(-570773. + 988607. i) q^{96} +554894. q^{97} +(206710. + 119344. i) q^{98} +(307752. + 533042. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 42 q - 3 q^{3} - 1194 q^{4} - 3 q^{5} + 111 q^{6} - 147 q^{7} + 3852 q^{9}+O(q^{10}) $ 42 * q - 3 * q^3 - 1194 * q^4 - 3 * q^5 + 111 * q^6 - 147 * q^7 + 3852 * q^9	\( 42 q - 3 q^{3} - 1194 q^{4} - 3 q^{5} + 111 q^{6} - 147 q^{7} + 3852 q^{9} - 981 q^{10} - 4104 q^{11} + 918 q^{12} + 4843 q^{13} + 2814 q^{14} - 163 q^{15} + 36678 q^{16} + 3641 q^{17} - 507 q^{18} - 5229 q^{19} - 1599 q^{20} - 29990 q^{21} + 6575 q^{23} - 4622 q^{24} + 68484 q^{25} + 189 q^{26} + 48948 q^{28} + 95361 q^{29} - 85041 q^{30} - 79373 q^{31} - 79638 q^{33} - 184743 q^{34} - 80582 q^{35} + 59972 q^{36} - 66063 q^{37} - 69820 q^{38} + 189951 q^{40} + 40632 q^{41} - 368728 q^{43} + 130330 q^{44} + 34056 q^{46} - 247820 q^{47} + 326907 q^{48} - 21876 q^{49} - 28638 q^{50} - 617150 q^{52} + 11639 q^{53} + 655904 q^{54} - 43638 q^{55} + 553875 q^{56} - 422859 q^{57} + 587796 q^{58} - 649352 q^{59} + 875455 q^{60} - 52251 q^{61} + 1335249 q^{62} + 93690 q^{63} - 792420 q^{64} + 160395 q^{66} - 173603 q^{67} + 22286 q^{68} + 870417 q^{69} + 1670505 q^{71} - 2068518 q^{72} - 2646201 q^{73} - 1625030 q^{74} - 80622 q^{76} - 486066 q^{77} + 2835040 q^{78} + 1897639 q^{79} - 817059 q^{80} + 2215367 q^{81} + 1584059 q^{83} - 824560 q^{84} - 2333682 q^{86} - 5547198 q^{87} + 2736939 q^{89} + 1092196 q^{90} - 3724131 q^{91} + 470257 q^{92} + 488433 q^{93} - 1289839 q^{95} + 1697650 q^{96} + 5260848 q^{97} + 4722621 q^{98} + 1375834 q^{99}+O(q^{100}) \) 42 * q - 3 * q^3 - 1194 * q^4 - 3 * q^5 + 111 * q^6 - 147 * q^7 + 3852 * q^9 - 981 * q^10 - 4104 * q^11 + 918 * q^12 + 4843 * q^13 + 2814 * q^14 - 163 * q^15 + 36678 * q^16 + 3641 * q^17 - 507 * q^18 - 5229 * q^19 - 1599 * q^20 - 29990 * q^21 + 6575 * q^23 - 4622 * q^24 + 68484 * q^25 + 189 * q^26 + 48948 * q^28 + 95361 * q^29 - 85041 * q^30 - 79373 * q^31 - 79638 * q^33 - 184743 * q^34 - 80582 * q^35 + 59972 * q^36 - 66063 * q^37 - 69820 * q^38 + 189951 * q^40 + 40632 * q^41 - 368728 * q^43 + 130330 * q^44 + 34056 * q^46 - 247820 * q^47 + 326907 * q^48 - 21876 * q^49 - 28638 * q^50 - 617150 * q^52 + 11639 * q^53 + 655904 * q^54 - 43638 * q^55 + 553875 * q^56 - 422859 * q^57 + 587796 * q^58 - 649352 * q^59 + 875455 * q^60 - 52251 * q^61 + 1335249 * q^62 + 93690 * q^63 - 792420 * q^64 + 160395 * q^66 - 173603 * q^67 + 22286 * q^68 + 870417 * q^69 + 1670505 * q^71 - 2068518 * q^72 - 2646201 * q^73 - 1625030 * q^74 - 80622 * q^76 - 486066 * q^77 + 2835040 * q^78 + 1897639 * q^79 - 817059 * q^80 + 2215367 * q^81 + 1584059 * q^83 - 824560 * q^84 - 2333682 * q^86 - 5547198 * q^87 + 2736939 * q^89 + 1092196 * q^90 - 3724131 * q^91 + 470257 * q^92 + 488433 * q^93 - 1289839 * q^95 + 1697650 * q^96 + 5260848 * q^97 + 4722621 * q^98 + 1375834 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/43\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{1}{6}\right)$

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 $

$2$		−	2.61500i		−	0.326875i	−0.986554	−	0.163437i	$-0.947742\pi$
$2$		−	2.61500i		−	0.326875i	0.986554	−	0.163437i	$-0.0522582\pi$
$3$	−35.7187	−	20.6222i	−1.32291	−	0.763785i	−0.338721	−	0.940887i	$-0.609994\pi$
$3$	−35.7187	−	20.6222i	−1.32291	−	0.763785i	−0.984192	+	0.177102i	$0.943328\pi$
$4$	57.1618			0.893153
$5$	121.716	+	70.2726i	0.973726	+	0.562181i	0.900370	−	0.435125i	$-0.143296\pi$
$5$	121.716	+	70.2726i	0.973726	+	0.562181i	0.0733556	+	0.997306i	$0.476629\pi$
$6$	−53.9270	+	93.4043i	−0.249662	+	0.432427i
$7$	140.639	−	81.1978i	0.410026	−	0.236728i	−0.280775	−	0.959774i	$-0.590592\pi$
$7$	140.639	−	81.1978i	0.410026	−	0.236728i	0.690801	+	0.723045i	$0.257258\pi$
$8$		−	316.838i		−	0.618824i
$9$	486.049	+	841.861i	0.666734	+	1.15482i
$10$	183.763	−	318.286i	0.183763	−	0.318286i
$11$	633.170			0.475710			0.237855	−	0.971301i	$-0.423556\pi$
$11$	633.170			0.475710			0.237855	+	0.971301i	$0.423556\pi$
$12$	−2041.74	−	1178.80i	−1.18156	−	0.682176i
$13$	−2029.45	−	3515.10i	−0.923735	−	1.59996i	−0.793583	−	0.608462i	$-0.791787\pi$
$13$	−2029.45	−	3515.10i	−0.923735	−	1.59996i	−0.130152	−	0.991494i	$-0.541546\pi$
$14$	−212.332	−	367.770i	−0.0773806	−	0.134027i
$15$	−2898.35	−	5020.09i	−0.858770	−	1.48743i
$16$	2829.82			0.690875
$17$	−1526.45	−	2643.88i	−0.310695	−	0.538140i	0.667818	−	0.744325i	$-0.267229\pi$
$17$	−1526.45	−	2643.88i	−0.310695	−	0.538140i	−0.978513	+	0.206185i	$0.933895\pi$
$18$	2201.47	−	1271.02i	0.377481	−	0.217938i
$19$	1715.01	+	990.163i	0.250038	+	0.144360i	0.619782	−	0.784774i	$-0.287221\pi$
$19$	1715.01	+	990.163i	0.250038	+	0.144360i	−0.369744	+	0.929134i	$0.620554\pi$
$20$	6957.49	+	4016.91i	0.869686	+	0.502113i
$21$	−6697.91			−0.723238
$22$		−	1655.74i		−	0.155498i
$23$	2766.29	−	4791.36i	0.227360	−	0.393800i	−0.729665	−	0.683805i	$-0.760324\pi$
$23$	2766.29	−	4791.36i	0.227360	−	0.393800i	0.957025	+	0.290005i	$0.0936571\pi$
$24$	−6533.89	+	11317.0i	−0.472648	+	0.818651i
$25$	2063.98	+	3574.91i	0.132094	+	0.228794i
$26$	−9191.99	+	5307.00i	−0.522985	+	0.301946i
$27$		−	10026.4i		−	0.509394i
$28$	8039.16	−	4641.41i	0.366215	−	0.211435i
$29$	19161.8	−	11063.0i	0.785672	−	0.453608i	−0.0527646	−	0.998607i	$-0.516803\pi$
$29$	19161.8	−	11063.0i	0.785672	−	0.453608i	0.838437	+	0.544999i	$0.183470\pi$
$30$	−13127.5	+	7579.18i	−0.486205	+	0.280710i
$31$	445.023	−	770.802i	0.0149382	−	0.0258737i	−0.858460	−	0.512881i	$-0.828578\pi$
$31$	445.023	−	770.802i	0.0149382	−	0.0258737i	0.873398	+	0.487007i	$0.161912\pi$
$32$		−	27677.6i		−	0.844654i
$33$	−22616.0	−	13057.4i	−0.629324	−	0.363340i
$34$	−6913.75	+	3991.66i	−0.175905	+	0.101559i
$35$	22823.9			0.532337
$36$	27783.4	+	48122.3i	0.595495	+	1.03143i
$37$	−32934.5	−	19014.7i	−0.650199	−	0.375392i	0.138334	−	0.990386i	$-0.455825\pi$
$37$	−32934.5	−	19014.7i	−0.650199	−	0.375392i	−0.788532	+	0.614993i	$0.789159\pi$
$38$	2589.27	−	4484.75i	0.0471875	−	0.0817312i
$39$			167406.i			2.82214i
$40$	22265.0	−	38564.2i	0.347891	−	0.602565i
$41$	−53188.1			−0.771725			−0.385863	−	0.922556i	$-0.626096\pi$
$41$	−53188.1			−0.771725			−0.385863	+	0.922556i	$0.626096\pi$
$42$			17515.0i			0.236408i
$43$	79357.0	+	4881.64i	0.998113	+	0.0613989i
$43$	79357.0	+	4881.64i	0.998113	+	0.0613989i
$44$	36193.2			0.424882
$45$			136624.i			1.49930i
$46$	−12529.4	−	7233.86i	−0.128723	−	0.0743184i
$47$	144957.			1.39619			0.698097	−	0.716003i	$-0.254030\pi$
$47$	144957.			1.39619			0.698097	+	0.716003i	$0.254030\pi$
$48$	−101078.	−	58357.1i	−0.913968	−	0.527679i
$49$	−45638.3	+	79047.9i	−0.387919	+	0.671896i
$50$	9348.39	−	5397.29i	0.0747871	−	0.0431783i
$51$			125915.i			0.949217i
$52$	−116007.	−	200930.i	−0.825036	−	1.42901i
$53$	12646.2	−	21903.9i	0.0849441	−	0.147128i	−0.820423	−	0.571757i	$-0.806262\pi$
$53$	12646.2	−	21903.9i	0.0849441	−	0.147128i	0.905367	+	0.424629i	$0.139595\pi$
$54$	−26219.0			−0.166508
$55$	77066.8	+	44494.5i	0.463211	+	0.267435i
$56$	−25726.6	−	44559.7i	−0.146493	−	0.253734i
$57$	−40838.6	−	70734.6i	−0.220519	−	0.381951i
$58$	−28929.9	−	50108.0i	−0.148273	−	0.256816i
$59$	−168198.			−0.818964			−0.409482	−	0.912318i	$-0.634291\pi$
$59$	−168198.			−0.818964			−0.409482	+	0.912318i	$0.634291\pi$
$60$	−165675.	−	286957.i	−0.767013	−	1.32851i
$61$	278864.	−	161002.i	1.22858	−	0.709320i	0.261846	−	0.965110i	$-0.415669\pi$
$61$	278864.	−	161002.i	1.22858	−	0.709320i	0.966732	+	0.255790i	$0.0823355\pi$
$62$	−2015.65	−	1163.73i	−0.00845745	−	0.00488291i
$63$	136715.	+	78932.2i	0.546756	+	0.315670i
$64$	108732.			0.414779
$65$		−	570458.i		−	2.07722i
$66$	−34145.0	+	59140.8i	−0.118767	+	0.205710i
$67$	−220086.	+	381199.i	−0.731757	+	1.26744i	0.224374	+	0.974503i	$0.427966\pi$
$67$	−220086.	+	381199.i	−0.731757	+	1.26744i	−0.956131	+	0.292938i	$0.905367\pi$
$68$	−87254.4	−	151129.i	−0.277498	−	0.480641i
$69$	−197617.	+	114094.i	−0.601556	+	0.347309i
$70$		−	59684.5i		−	0.174007i
$71$	435989.	−	251718.i	1.21815	−	0.703299i	0.253628	−	0.967302i	$-0.418376\pi$
$71$	435989.	−	251718.i	1.21815	−	0.703299i	0.964522	+	0.264003i	$0.0850429\pi$
$72$	266734.	−	153999.i	0.714628	−	0.412591i
$73$	−579548.	+	334602.i	−1.48978	+	0.860122i	−0.999932	−	0.0116885i	$-0.996279\pi$
$73$	−579548.	+	334602.i	−1.48978	+	0.860122i	−0.489843	+	0.871810i	$0.662946\pi$
$74$	−49723.5	+	86123.7i	−0.122706	+	0.212534i
$75$		−	170255.i		−	0.403567i
$76$	98033.1	+	56599.5i	0.223322	+	0.128935i
$77$	89048.3	−	51412.1i	0.195053	−	0.112614i
$78$	437768.			0.922486
$79$	484554.	+	839272.i	0.982790	+	1.70224i	0.651372	+	0.758759i	$0.274194\pi$
$79$	484554.	+	839272.i	0.982790	+	1.70224i	0.331419	+	0.943484i	$0.392473\pi$
$80$	344434.	+	198859.i	0.672722	+	0.388397i
$81$	147563.	−	255587.i	0.277666	−	0.480932i
$82$			139087.i			0.252258i
$83$	−227845.	+	394640.i	−0.398480	+	0.690187i	−0.993539	−	0.113495i	$-0.963795\pi$
$83$	−227845.	+	394640.i	−0.398480	+	0.690187i	0.595059	+	0.803682i	$0.297129\pi$
$84$	−382864.			−0.645962
$85$		−	429069.i		−	0.698668i
$86$	12765.5	−	207518.i	0.0200697	−	0.326258i
$87$	−912577.			−1.38584
$88$		−	200612.i		−	0.294381i
$89$	−833221.	−	481060.i	−1.18193	−	0.682385i	−0.225466	−	0.974251i	$-0.572391\pi$
$89$	−833221.	−	481060.i	−1.18193	−	0.682385i	−0.956459	+	0.291866i	$0.905724\pi$
$90$	357271.			0.490083
$91$	−570837.	−	329573.i	−0.757510	−	0.437349i
$92$	158126.	−	273883.i	0.203068	−	0.351723i
$93$	−31791.2	+	18354.7i	−0.0395238	+	0.0228191i
$94$		−	379063.i		−	0.456381i
$95$	139163.	+	241037.i	0.162312	+	0.281133i
$96$	−570773.	+	988607.i	−0.645133	+	1.11740i
$97$	554894.			0.607988			0.303994	−	0.952674i	$-0.401680\pi$
$97$	554894.			0.607988			0.303994	+	0.952674i	$0.401680\pi$
$98$	206710.	+	119344.i	0.219626	+	0.126801i
$99$	307752.	+	533042.i	0.317172	+	0.549358i
$100$	117981.	+	204348.i	0.117981	+	0.204348i
$101$	910340.	+	1.57675e6i	0.883567	+	1.53038i	0.847347	+	0.531039i	$0.178198\pi$
$101$	910340.	+	1.57675e6i	0.883567	+	1.53038i	0.0362195	+	0.999344i	$0.488468\pi$
$102$	329267.			0.310275
$103$	291389.	+	504701.i	0.266662	+	0.461873i	0.967998	−	0.250959i	$-0.0807458\pi$
$103$	291389.	+	504701.i	0.266662	+	0.461873i	−0.701335	+	0.712831i	$0.747412\pi$
$104$	−1.11372e6	+	643005.i	−0.990091	+	0.571629i
$105$	−815240.	−	470679.i	−0.704235	−	0.406590i
$106$	−57278.7	−	33069.9i	−0.0480923	−	0.0277661i
$107$	1.11880e6			0.913278			0.456639	−	0.889652i	$-0.349053\pi$
$107$	1.11880e6			0.913278			0.456639	+	0.889652i	$0.349053\pi$
$108$		−	573127.i		−	0.454967i
$109$	−671982.	+	1.16391e6i	−0.518893	+	0.898750i	0.480866	+	0.876794i	$0.340323\pi$
$109$	−671982.	+	1.16391e6i	−0.518893	+	0.898750i	−0.999759	+	0.0219554i	$0.993011\pi$
$110$	116353.	−	201530.i	0.0874178	−	0.151412i
$111$	784251.	+	1.35836e6i	0.573438	+	0.993223i
$112$	397983.	−	229775.i	0.283276	−	0.163550i
$113$			1.24946e6i			0.865938i	0.901409	+	0.432969i	$0.142534\pi$
$113$			1.24946e6i			0.865938i	−0.901409	+	0.432969i	$0.857466\pi$
$114$	−184971.	+	106793.i	−0.124850	+	0.0720822i
$115$	673403.	−	388789.i	0.442773	−	0.255635i
$116$	1.09532e6	−	632383.i	0.701725	−	0.405141i
$117$	1.97282e6	−	3.41702e6i	1.23177	−	2.13349i
$118$			439838.i			0.267699i
$119$	−429355.	−	247888.i	−0.254786	−	0.147101i
$120$	−1.59055e6	+	918307.i	−0.920459	+	0.531428i
$121$	−1.37066e6			−0.773700
$122$	−421020.	−	729229.i	−0.231859	−	0.401591i
$123$	1.89981e6	+	1.09685e6i	1.02093	+	0.589432i
$124$	25438.3	−	44060.4i	0.0133421	−	0.0231091i
$125$		−	1.61585e6i		−	0.827318i
$126$	206408.	−	357509.i	0.103184	−	0.178721i
$127$	−495247.			−0.241775			−0.120887	−	0.992666i	$-0.538574\pi$
$127$	−495247.			−0.241775			−0.120887	+	0.992666i	$0.538574\pi$
$128$		−	2.05570e6i		−	0.980234i
$129$	−2.73386e6	−	1.81088e6i	−1.27352	−	0.843569i
$130$	−1.49175e6			−0.678992
$131$		−	1.05164e6i		−	0.467793i	−0.972262	−	0.233896i	$-0.924852\pi$
$131$		−	1.05164e6i		−	0.467793i	0.972262	−	0.233896i	$-0.0751476\pi$
$132$	−1.29277e6	−	746382.i	−0.562082	−	0.324518i
$133$	321596.			0.136696
$134$	996836.	+	575524.i	0.414295	+	0.239193i
$135$	704582.	−	1.22037e6i	0.286372	−	0.496010i
$136$	−837682.	+	483636.i	−0.333014	+	0.192266i
$137$		−	391589.i		−	0.152289i	−0.997097	−	0.0761445i	$-0.975739\pi$
$137$		−	391589.i		−	0.152289i	0.997097	−	0.0761445i	$-0.0242610\pi$
$138$	298356.	+	516767.i	0.113527	+	0.196634i
$139$	−1.92910e6	+	3.34130e6i	−0.718308	+	1.24415i	0.243362	+	0.969935i	$0.421750\pi$
$139$	−1.92910e6	+	3.34130e6i	−0.718308	+	1.24415i	−0.961670	+	0.274210i	$0.911584\pi$
$140$	1.30466e6			0.475458
$141$	−5.17768e6	−	2.98933e6i	−1.84705	−	1.06639i
$142$	−658243.	−	1.14011e6i	−0.229891	−	0.398182i
$143$	−1.28499e6	−	2.22566e6i	−0.439430	−	0.761116i
$144$	1.37543e6	+	2.38232e6i	0.460629	+	0.797834i
$145$	3.10972e6			1.02004
$146$	874984.	+	1.51552e6i	0.281152	+	0.486970i
$147$	3.26028e6	−	1.88232e6i	1.02637	−	0.592574i
$148$	−1.88260e6	−	1.08692e6i	−0.580727	−	0.335283i
$149$	4.38285e6	+	2.53044e6i	1.32495	+	0.764958i	0.984513	−	0.175311i	$-0.0560931\pi$
$149$	4.38285e6	+	2.53044e6i	1.32495	+	0.764958i	0.340433	+	0.940269i	$0.389426\pi$
$150$	−445216.			−0.131916
$151$		−	1.79902e6i		−	0.522524i	−0.965268	−	0.261262i	$-0.915861\pi$
$151$		−	1.79902e6i		−	0.522524i	0.965268	−	0.261262i	$-0.0841387\pi$
$152$	313721.	−	543381.i	0.0893332	−	0.154730i
$153$	1.48386e6	−	2.57011e6i	0.414302	−	0.717592i
$154$	−134443.	−	232861.i	−0.0368107	−	0.0637581i
$155$	108333.	−	62545.8i	0.0290913	−	0.0167959i
$156$			9.56925e6i			2.52060i
$157$	−725892.	+	419094.i	−0.187574	+	0.108296i	−0.590846	−	0.806784i	$-0.701206\pi$
$157$	−725892.	+	419094.i	−0.187574	+	0.108296i	0.403272	+	0.915080i	$0.367873\pi$
$158$	2.19470e6	−	1.26711e6i	0.556420	−	0.321249i
$159$	−903413.	+	521586.i	−0.224748	+	0.129758i
$160$	1.94498e6	−	3.36880e6i	0.474848	−	0.822461i
$161$		−	898468.i		−	0.215291i
$162$	−668360.	−	385878.i	−0.157205	−	0.0907621i
$163$	−5.98386e6	+	3.45478e6i	−1.38172	+	0.797734i	−0.992363	−	0.123355i	$-0.960635\pi$
$163$	−5.98386e6	+	3.45478e6i	−1.38172	+	0.797734i	−0.389353	+	0.921089i	$0.627301\pi$
$164$	−3.04032e6			−0.689268
$165$	−1.83515e6	−	3.17857e6i	−0.408526	−	0.707587i
$166$	1.03198e6	+	595816.i	0.225605	+	0.130253i
$167$	2.89100e6	−	5.00735e6i	0.620723	−	1.07512i	−0.368628	−	0.929577i	$-0.620172\pi$
$167$	2.89100e6	−	5.00735e6i	0.620723	−	1.07512i	0.989351	−	0.145547i	$-0.0464944\pi$
$168$			2.12215e6i			0.447557i
$169$	−5.82389e6	+	1.00873e7i	−1.20657	+	2.08984i
$170$	−1.12202e6			−0.228377
$171$			1.92507e6i			0.384998i
$172$	4.53619e6	+	279043.i	0.891468	+	0.0548386i
$173$	8.14660e6			1.57340			0.786698	−	0.617338i	$-0.211789\pi$
$173$	8.14660e6			1.57340			0.786698	+	0.617338i	$0.211789\pi$
$174$			2.38639e6i			0.452995i
$175$	580550.	+	335181.i	0.108324	+	0.0625410i
$176$	1.79176e6			0.328656
$177$	6.00781e6	+	3.46861e6i	1.08342	+	0.625512i
$178$	−1.25797e6	+	2.17887e6i	−0.223055	+	0.386342i
$179$	7.57773e6	−	4.37500e6i	1.32123	−	0.762815i	0.337309	−	0.941394i	$-0.390483\pi$
$179$	7.57773e6	−	4.37500e6i	1.32123	−	0.762815i	0.983926	+	0.178579i	$0.0571499\pi$
$180$			7.80965e6i			1.33910i
$181$	−1.36423e6	−	2.36292e6i	−0.230066	−	0.398487i	0.727761	−	0.685831i	$-0.240561\pi$
$181$	−1.36423e6	−	2.36292e6i	−0.230066	−	0.398487i	−0.957827	+	0.287344i	$0.907228\pi$
$182$	−861833.	+	1.49274e6i	−0.142958	+	0.247611i
$183$	−1.32809e7			−2.16707
$184$	−1.51809e6	−	876467.i	−0.243693	−	0.140696i
$185$	−2.67243e6	−	4.62879e6i	−0.422077	−	0.731058i
$186$	47997.5	+	83134.0i	0.00745898	+	0.0129193i
$187$	−966501.	−	1.67403e6i	−0.147801	−	0.255999i
$188$	8.28601e6			1.24702
$189$	−814123.	−	1.41010e6i	−0.120588	−	0.208865i
$190$	630311.	−	363910.i	0.0918954	−	0.0530558i
$191$	−1.02803e7	−	5.93534e6i	−1.47539	−	0.851816i	−0.475773	−	0.879568i	$-0.657832\pi$
$191$	−1.02803e7	−	5.93534e6i	−1.47539	−	0.851816i	−0.999615	+	0.0277525i	$0.991165\pi$
$192$	−3.88375e6	−	2.24229e6i	−0.548716	−	0.316802i
$193$	5.91397e6			0.822634			0.411317	−	0.911492i	$-0.365069\pi$
$193$	5.91397e6			0.822634			0.411317	+	0.911492i	$0.365069\pi$
$194$		−	1.45105e6i		−	0.198736i
$195$	−1.17641e7	+	2.03760e7i	−1.58655	+	2.74799i
$196$	−2.60877e6	+	4.51852e6i	−0.346471	+	0.600106i
$197$	505414.	+	875402.i	0.0661071	+	0.114501i	0.897185	−	0.441656i	$-0.145609\pi$
$197$	505414.	+	875402.i	0.0661071	+	0.114501i	−0.831077	+	0.556157i	$0.812275\pi$
$198$	1.39390e6	−	804771.i	0.179571	−	0.103676i
$199$		−	2.76185e6i		−	0.350462i	−0.984527	−	0.175231i	$-0.943933\pi$
$199$		−	2.76185e6i		−	0.350462i	0.984527	−	0.175231i	$-0.0560672\pi$
$200$	1.13267e6	−	653946.i	0.141583	−	0.0817432i
$201$	1.57223e7	−	9.07729e6i	1.93610	−	1.11781i
$202$	4.12321e6	−	2.38054e6i	0.500244	−	0.288816i
$203$	1.79659e6	−	3.11179e6i	0.214764	−	0.371982i
$204$			7.19751e6i			0.847796i
$205$	−6.47382e6	−	3.73766e6i	−0.751448	−	0.433849i
$206$	1.31979e6	−	761982.i	0.150975	−	0.0871652i
$207$	5.37822e6			0.606355
$208$	−5.74297e6	−	9.94712e6i	−0.638185	−	1.10537i
$209$	1.08589e6	+	626942.i	0.118946	+	0.0686734i
$210$	−1.23083e6	+	2.13185e6i	−0.132904	+	0.230197i
$211$			733739.i			0.0781077i	0.999237	+	0.0390539i	$0.0124344\pi$
$211$			733739.i			0.0781077i	−0.999237	+	0.0390539i	$0.987566\pi$
$212$	722881.	−	1.25207e6i	0.0758681	−	0.131407i
$213$	−2.07639e7			−2.14868
$214$		−	2.92567e6i		−	0.298528i
$215$	9.31595e6	+	6.17079e6i	0.937371	+	0.620906i
$216$	−3.17675e6			−0.315225
$217$		−	144540.i		−	0.0141451i
$218$	3.04362e6	+	1.75723e6i	0.293779	+	0.169613i
$219$	2.76009e7			2.62779
$220$	4.40528e6	+	2.54339e6i	0.413719	+	0.238861i
$221$	−6.19568e6	+	1.07312e7i	−0.574000	+	0.994198i
$222$	3.55212e6	−	2.05082e6i	0.324660	−	0.187442i
$223$		−	699707.i		−	0.0630959i	−0.999502	−	0.0315480i	$-0.989956\pi$
$223$		−	699707.i		−	0.0630959i	0.999502	−	0.0315480i	$-0.0100437\pi$
$224$	−2.24736e6	−	3.89255e6i	−0.199953	−	0.346330i
$225$	−2.00639e6	+	3.47516e6i	−0.176144	+	0.305090i
$226$	3.26733e6			0.283053
$227$	−7.47188e6	−	4.31389e6i	−0.638782	−	0.368801i	0.145363	−	0.989378i	$-0.453565\pi$
$227$	−7.47188e6	−	4.31389e6i	−0.638782	−	0.368801i	−0.784145	+	0.620578i	$0.786898\pi$
$228$	−2.33441e6	−	4.04331e6i	−0.196957	−	0.341140i
$229$	−5.72252e6	−	9.91170e6i	−0.476520	−	0.825356i	0.523118	−	0.852260i	$-0.324769\pi$
$229$	−5.72252e6	−	9.91170e6i	−0.476520	−	0.825356i	−0.999638	+	0.0269037i	$0.991435\pi$
$230$	−1.01668e6	−	1.76095e6i	−0.0835608	−	0.144731i
$231$	−4.24092e6			−0.344052
$232$	−3.50519e6	−	6.07117e6i	−0.280704	−	0.486193i
$233$	3.09628e6	−	1.78764e6i	0.244778	−	0.141323i	−0.372593	−	0.927995i	$-0.621531\pi$
$233$	3.09628e6	−	1.78764e6i	0.244778	−	0.141323i	0.617371	+	0.786672i	$0.288198\pi$
$234$	−8.93551e6	−	5.15892e6i	−0.697384	−	0.402635i
$235$	1.76436e7	+	1.01865e7i	1.35951	+	0.784914i
$236$	−9.61450e6			−0.731460
$237$		−	3.99702e7i		−	3.00256i
$238$	−648228.	+	1.12276e6i	−0.0480836	+	0.0832832i
$239$	−1.27997e6	+	2.21698e6i	−0.0937576	+	0.162393i	−0.909089	−	0.416601i	$-0.863221\pi$
$239$	−1.27997e6	+	2.21698e6i	−0.0937576	+	0.162393i	0.815332	+	0.578994i	$0.196555\pi$
$240$	−8.20181e6	−	1.42060e7i	−0.593303	−	1.02763i
$241$	−4.42431e6	+	2.55438e6i	−0.316078	+	0.182488i	−0.649643	−	0.760239i	$-0.725082\pi$
$241$	−4.42431e6	+	2.55438e6i	−0.316078	+	0.182488i	0.333565	+	0.942727i	$0.391748\pi$
$242$			3.58426e6i			0.252903i
$243$	−1.68715e7	+	9.74078e6i	−1.17581	+	0.678851i
$244$	1.59404e7	−	9.20317e6i	1.09731	−	0.633531i
$245$	−1.11098e7	+	6.41425e6i	−0.755454	+	0.436162i
$246$	2.86827e6	−	4.96799e6i	0.192670	−	0.333715i
$247$		−	8.03792e6i		−	0.533400i
$248$	−244219.	−	141000.i	−0.0160112	−	0.00924409i
$249$	1.62767e7	−	9.39734e6i	1.05431	−	0.608705i
$250$	−4.22546e6			−0.270429
$251$	3.46205e6	+	5.99645e6i	0.218934	+	0.379204i	0.954482	−	0.298268i	$-0.0964088\pi$
$251$	3.46205e6	+	5.99645e6i	0.218934	+	0.379204i	−0.735549	+	0.677472i	$0.763076\pi$
$252$	7.81485e6	+	4.51191e6i	0.488336	+	0.281941i
$253$	1.75154e6	−	3.03375e6i	0.108158	−	0.187335i
$254$			1.29507e6i			0.0790300i
$255$	−8.84835e6	+	1.53258e7i	−0.533632	+	0.924277i
$256$	1.58318e6			0.0943647
$257$			1.46021e7i			0.860232i	0.902774	+	0.430116i	$0.141527\pi$
$257$			1.46021e7i			0.860232i	−0.902774	+	0.430116i	$0.858473\pi$
$258$	−4.73545e6	+	7.14903e6i	−0.275741	+	0.416282i
$259$	−6.17582e6			−0.355464
$260$		−	3.26084e7i		−	1.85528i
$261$	1.86271e7	+	1.07544e7i	1.04767	+	0.604871i
$262$	−2.75004e6			−0.152910
$263$	8.83321e6	+	5.09985e6i	0.485569	+	0.280344i	0.722734	−	0.691126i	$-0.242885\pi$
$263$	8.83321e6	+	5.09985e6i	0.485569	+	0.280344i	−0.237165	+	0.971469i	$0.576218\pi$
$264$	−4.13707e6	+	7.16561e6i	−0.224844	+	0.389441i
$265$	3.07849e6	−	1.77737e6i	0.165425	−	0.0955079i
$266$		−	840974.i		−	0.0446825i
$267$	1.98410e7	+	3.43657e7i	1.04239	+	1.80547i
$268$	−1.25805e7	+	2.17900e7i	−0.653571	+	1.13202i
$269$	−9.22613e6			−0.473983			−0.236991	−	0.971512i	$-0.576161\pi$
$269$	−9.22613e6			−0.473983			−0.236991	+	0.971512i	$0.576161\pi$
$270$	−3.19127e6	−	1.84248e6i	−0.162133	−	0.0936077i
$271$	1.39331e7	+	2.41328e7i	0.700066	+	1.21255i	0.968443	+	0.249237i	$0.0801796\pi$
$271$	1.39331e7	+	2.41328e7i	0.700066	+	1.21255i	−0.268376	+	0.963314i	$0.586487\pi$
$272$	−4.31957e6	−	7.48172e6i	−0.214652	−	0.371788i
$273$	1.35930e7	+	2.35438e7i	0.668080	+	1.15715i
$274$	−1.02400e6			−0.0497794
$275$	1.30685e6	+	2.26353e6i	0.0628387	+	0.108840i
$276$	−1.12961e7	+	6.52182e6i	−0.537282	+	0.310200i
$277$	1.61546e7	+	9.32684e6i	0.760074	+	0.438829i	0.829322	−	0.558771i	$-0.188727\pi$
$277$	1.61546e7	+	9.32684e6i	0.760074	+	0.438829i	−0.0692485	+	0.997599i	$0.522060\pi$
$278$	8.73750e6	+	5.04460e6i	0.406680	+	0.234797i
$279$	865211.			0.0398391
$280$		−	7.23149e6i		−	0.329423i
$281$	−1.52395e7	+	2.63956e7i	−0.686833	+	1.18963i	0.286023	+	0.958223i	$0.407666\pi$
$281$	−1.52395e7	+	2.63956e7i	−0.686833	+	1.18963i	−0.972857	+	0.231408i	$0.925667\pi$
$282$	−7.81710e6	+	1.35396e7i	−0.348577	+	0.603753i
$283$	880462.	+	1.52500e6i	0.0388464	+	0.0672840i	0.884795	−	0.465981i	$-0.154298\pi$
$283$	880462.	+	1.52500e6i	0.0388464	+	0.0672840i	−0.845949	+	0.533265i	$0.820965\pi$
$284$	2.49219e7	−	1.43887e7i	1.08799	−	0.628153i
$285$		−	1.14793e7i		−	0.495887i
$286$	−5.82010e6	+	3.36023e6i	−0.248790	+	0.143639i
$287$	−7.48030e6	+	4.31875e6i	−0.316427	+	0.182689i
$288$	2.33007e7	−	1.34527e7i	0.975420	−	0.563159i
$289$	7.40871e6	−	1.28323e7i	0.306937	−	0.531630i
$290$		−	8.13190e6i		−	0.333425i
$291$	−1.98201e7	−	1.14431e7i	−0.804316	−	0.464372i
$292$	−3.31280e7	+	1.91265e7i	−1.33060	+	0.768220i
$293$	−2.24591e7			−0.892872			−0.446436	−	0.894816i	$-0.647307\pi$
$293$	−2.24591e7			−0.892872			−0.446436	+	0.894816i	$0.647307\pi$
$294$	−4.92227e6	−	8.52563e6i	−0.193697	−	0.335494i
$295$	−2.04723e7	−	1.18197e7i	−0.797446	−	0.460406i
$296$	−6.02459e6	+	1.04349e7i	−0.232302	+	0.402359i
$297$		−	6.34843e6i		−	0.242324i
$298$	6.61710e6	−	1.14612e7i	0.250045	−	0.433091i
$299$	−2.24562e7			−0.840083
$300$		−	9.73206e6i		−	0.360447i
$301$	1.15570e7	−	5.75707e6i	0.423787	−	0.211107i
$302$	−4.70445e6			−0.170800
$303$		−	7.50928e7i		−	2.69942i
$304$	4.85318e6	+	2.80199e6i	0.172745	+	0.0997344i
$305$	4.52562e7			1.59506
$306$	−6.72084e6	−	3.88028e6i	−0.234563	−	0.135425i
$307$	−2.10068e7	+	3.63848e7i	−0.726013	+	1.25749i	0.232543	+	0.972586i	$0.425296\pi$
$307$	−2.10068e7	+	3.63848e7i	−0.726013	+	1.25749i	−0.958556	+	0.284905i	$0.908038\pi$
$308$	5.09016e6	−	2.93881e6i	0.174212	−	0.100582i
$309$		−	2.40363e7i		−	0.814690i
$310$	−163557.	−	283289.i	−0.00549015	−	0.00950923i
$311$	−1.29850e7	+	2.24907e7i	−0.431680	+	0.747691i	−0.997018	−	0.0771678i	$-0.975412\pi$
$311$	−1.29850e7	+	2.24907e7i	−0.431680	+	0.747691i	0.565338	+	0.824859i	$0.308746\pi$
$312$	5.30407e7			1.74641
$313$	−8.89847e6	−	5.13753e6i	−0.290190	−	0.167541i	0.347838	−	0.937555i	$-0.386916\pi$
$313$	−8.89847e6	−	5.13753e6i	−0.290190	−	0.167541i	−0.638027	+	0.770014i	$0.720249\pi$
$314$	1.09593e6	+	1.89821e6i	0.0353993	+	0.0613133i
$315$	1.10935e7	+	1.92146e7i	0.354927	+	0.614751i
$316$	2.76980e7	+	4.79743e7i	0.877782	+	1.52036i
$317$	−2.44920e7			−0.768859			−0.384429	−	0.923154i	$-0.625602\pi$
$317$	−2.44920e7			−0.768859			−0.384429	+	0.923154i	$0.625602\pi$
$318$	1.36395e6	+	2.36242e6i	0.0424146	+	0.0734643i
$319$	1.21327e7	−	7.00479e6i	0.373752	−	0.215786i
$320$	1.32344e7	+	7.64086e6i	0.403881	+	0.233181i
$321$	−3.99622e7	−	2.30722e7i	−1.20819	−	0.697548i
$322$	−2.34949e6			−0.0703731
$323$		−	6.04572e6i		−	0.179407i
$324$	8.43497e6	−	1.46098e7i	0.247998	−	0.429546i
$325$	8.37745e6	−	1.45102e7i	0.244040	−	0.422690i
$326$	9.03426e6	+	1.56478e7i	0.260759	+	0.451648i
$327$	4.80046e7	−	2.77155e7i	1.37290	−	0.792646i
$328$			1.68520e7i			0.477562i
$329$	2.03866e7	−	1.17702e7i	0.572476	−	0.330519i
$330$	−8.31196e6	+	4.79891e6i	−0.231293	+	0.133537i
$331$	−1.75029e7	+	1.01053e7i	−0.482642	+	0.278654i	−0.721517	−	0.692397i	$-0.756555\pi$
$331$	−1.75029e7	+	1.01053e7i	−0.482642	+	0.278654i	0.238875	+	0.971050i	$0.423221\pi$
$332$	−1.30240e7	+	2.25583e7i	−0.355903	+	0.616442i
$333$		−	3.69684e7i		−	1.00115i
$334$	−1.30942e7	−	7.55995e6i	−0.351431	−	0.202899i
$335$	−5.35757e7	+	3.09320e7i	−1.42506	+	0.822760i
$336$	−1.89539e7			−0.499667
$337$	3.66489e6	+	6.34778e6i	0.0957572	+	0.165856i	0.909924	−	0.414774i	$-0.136139\pi$
$337$	3.66489e6	+	6.34778e6i	0.0957572	+	0.165856i	−0.814167	+	0.580631i	$0.802806\pi$
$338$	2.63782e7	+	1.52295e7i	0.683118	+	0.394398i
$339$	2.57666e7	−	4.46290e7i	0.661390	−	1.14556i
$340$		−	2.45264e7i		−	0.624017i
$341$	281775.	−	488049.i	0.00710624	−	0.0123084i
$342$	5.03405e6			0.125846
$343$			3.39286e7i			0.840783i
$344$	1.54669e6	−	2.51433e7i	0.0379951	−	0.617657i
$345$	−3.20707e7			−0.781001
$346$		−	2.13034e7i		−	0.514304i
$347$	4.89818e7	+	2.82796e7i	1.17232	+	0.676839i	0.954225	−	0.299089i	$-0.0966826\pi$
$347$	4.89818e7	+	2.82796e7i	1.17232	+	0.676839i	0.218094	+	0.975928i	$0.430016\pi$
$348$	−5.21645e7			−1.23776
$349$	1.24077e7	+	7.16361e6i	0.291888	+	0.168522i	0.638793	−	0.769379i	$-0.279434\pi$
$349$	1.24077e7	+	7.16361e6i	0.291888	+	0.168522i	−0.346905	+	0.937900i	$0.612767\pi$
$350$	876497.	−	1.51814e6i	0.0204431	−	0.0354085i
$351$	−3.52439e7	+	2.03481e7i	−0.815008	+	0.470545i
$352$		−	1.75246e7i		−	0.401811i
$353$	−2.45885e7	−	4.25885e7i	−0.558995	−	0.968207i	−0.997581	−	0.0695178i	$-0.977854\pi$
$353$	−2.45885e7	−	4.25885e7i	−0.558995	−	0.968207i	0.438586	−	0.898689i	$-0.355479\pi$
$354$	9.07041e6	−	1.57104e7i	0.204464	−	0.354142i
$355$	7.07556e7			1.58152
$356$	−4.76284e7	−	2.74983e7i	−1.05564	−	0.609474i
$357$	1.02240e7	+	1.77085e7i	0.224707	+	0.389203i
$358$	−1.14406e7	−	1.98158e7i	−0.249345	−	0.431878i
$359$	360559.	+	624506.i	0.00779278	+	0.0134975i	0.869895	−	0.493236i	$-0.164186\pi$
$359$	360559.	+	624506.i	0.00779278	+	0.0134975i	−0.862103	+	0.506734i	$0.830853\pi$
$360$	4.32876e7			0.927803
$361$	−2.15621e7	−	3.73466e7i	−0.458321	−	0.793835i
$362$	−6.17904e6	+	3.56747e6i	−0.130255	+	0.0752029i
$363$	4.89580e7	+	2.82659e7i	1.02354	+	0.590940i
$364$	−3.26301e7	−	1.88390e7i	−0.676572	−	0.390619i
$365$	−9.40534e7			−1.93418
$366$			3.47294e7i			0.708361i
$367$	9.56391e6	−	1.65652e7i	0.193481	−	0.335118i	−0.752921	−	0.658111i	$-0.771356\pi$
$367$	9.56391e6	−	1.65652e7i	0.193481	−	0.335118i	0.946401	+	0.322993i	$0.104689\pi$
$368$	7.82812e6	−	1.35587e7i	0.157078	−	0.272066i
$369$	−2.58520e7	−	4.47770e7i	−0.514535	−	0.891201i
$370$	−1.21043e7	+	6.98840e6i	−0.238965	+	0.137966i
$371$		−	4.10739e6i		−	0.0804347i
$372$	−1.81724e6	+	1.04919e6i	−0.0353008	+	0.0203809i
$373$	6.19137e7	−	3.57459e7i	1.19305	−	0.688810i	0.234056	−	0.972223i	$-0.424800\pi$
$373$	6.19137e7	−	3.57459e7i	1.19305	−	0.688810i	0.958998	+	0.283413i	$0.0914667\pi$
$374$	−4.37758e6	+	2.52740e6i	−0.0836796	+	0.0483124i
$375$	−3.33225e7	+	5.77162e7i	−0.631893	+	1.09447i
$376$		−	4.59279e7i		−	0.863999i
$377$	−7.77755e7	−	4.49037e7i	−1.45151	−	0.838027i
$378$	−3.68741e6	+	2.12893e6i	−0.0682726	+	0.0394172i
$379$	8.59176e7			1.57821			0.789105	−	0.614259i	$-0.210545\pi$
$379$	8.59176e7			1.57821			0.789105	+	0.614259i	$0.210545\pi$
$380$	7.95478e6	+	1.37781e7i	0.144970	+	0.251095i
$381$	1.76896e7	+	1.02131e7i	0.319847	+	0.184664i
$382$	−1.55209e7	+	2.68830e7i	−0.278437	+	0.482267i
$383$		−	5.66752e7i		−	1.00878i	−0.863476	−	0.504390i	$-0.831717\pi$
$383$		−	5.66752e7i		−	1.00878i	0.863476	−	0.504390i	$-0.168283\pi$
$384$	−4.23930e7	+	7.34269e7i	−0.748688	+	1.29677i
$385$	1.44514e7			0.253238
$386$		−	1.54650e7i		−	0.268899i
$387$	3.44617e7	+	6.91803e7i	0.594571	+	1.19357i
$388$	3.17187e7			0.543026
$389$			8.21732e7i			1.39599i	0.716104	+	0.697994i	$0.245924\pi$
$389$			8.21732e7i			1.39599i	−0.716104	+	0.697994i	$0.754076\pi$
$390$	5.32832e7	+	3.07631e7i	0.898248	+	0.518604i
$391$	−1.68904e7			−0.282559
$392$	2.50454e7	+	1.44600e7i	0.415785	+	0.240054i
$393$	−2.16871e7	+	3.75632e7i	−0.357293	+	0.618849i
$394$	2.28918e6	−	1.32166e6i	0.0374275	−	0.0216088i
$395$			1.36203e8i			2.21002i
$396$	1.75916e7	+	3.04696e7i	0.283283	+	0.490661i
$397$	1.91954e7	−	3.32474e7i	0.306779	−	0.531356i	−0.670877	−	0.741569i	$-0.734082\pi$
$397$	1.91954e7	−	3.32474e7i	0.306779	−	0.531356i	0.977656	+	0.210212i	$0.0674155\pi$
$398$	−7.22224e6			−0.114557
$399$	−1.14870e7	−	6.63202e6i	−0.180837	−	0.104406i
$400$	5.84069e6	+	1.01164e7i	0.0912607	+	0.158068i
$401$	−2.32963e7	−	4.03503e7i	−0.361288	−	0.625769i	0.626885	−	0.779111i	$-0.284329\pi$
$401$	−2.32963e7	−	4.03503e7i	−0.361288	−	0.625769i	−0.988173	+	0.153343i	$0.950996\pi$
$402$	−2.37371e7	−	4.11139e7i	−0.365384	−	0.632864i
$403$	−3.61260e6			−0.0551956
$404$	5.20366e7	+	9.01301e7i	0.789160	+	1.36687i
$405$	3.59215e7	−	2.07393e7i	0.540741	−	0.312197i
$406$	−8.13732e6	−	4.69808e6i	−0.121591	−	0.0702009i
$407$	−2.08532e7	−	1.20396e7i	−0.309306	−	0.178578i
$408$	3.98945e7			0.587399
$409$			2.09583e6i			0.0306328i	0.999883	+	0.0153164i	$0.00487555\pi$
$409$			2.09583e6i			0.0306328i	−0.999883	+	0.0153164i	$0.995124\pi$
$410$	−9.77398e6	+	1.69290e7i	−0.141814	+	0.245630i
$411$	−8.07541e6	+	1.39870e7i	−0.116316	+	0.201465i
$412$	1.66563e7	+	2.88496e7i	0.238170	+	0.412523i
$413$	−2.36552e7	+	1.36573e7i	−0.335796	+	0.193872i
$414$		−	1.40640e7i		−	0.198202i
$415$	−5.54647e7	+	3.20226e7i	−0.776019	+	0.448035i
$416$	−9.72897e7	+	5.61702e7i	−1.35141	+	0.780236i
$417$	1.37810e8	−	7.95645e7i	1.90052	−	1.09726i
$418$	1.63945e6	−	2.83961e6i	0.0224476	−	0.0388804i
$419$		−	2.52277e7i		−	0.342954i	−0.985188	−	0.171477i	$-0.945146\pi$
$419$		−	2.52277e7i		−	0.342954i	0.985188	−	0.171477i	$-0.0548539\pi$
$420$	−4.66006e7	−	2.69049e7i	−0.628990	−	0.363147i
$421$	8.66416e7	−	5.00225e7i	1.16113	−	0.670378i	0.209554	−	0.977797i	$-0.432799\pi$
$421$	8.66416e7	−	5.00225e7i	1.16113	−	0.670378i	0.951574	+	0.307420i	$0.0994655\pi$
$422$	1.91873e6			0.0255315
$423$	7.04562e7	+	1.22034e8i	0.930890	+	1.61235i
$424$	−6.93999e6	−	4.00680e6i	−0.0910461	−	0.0525655i
$425$	6.30110e6	−	1.09138e7i	0.0820823	−	0.142171i
$426$			5.42977e7i			0.702348i
$427$	2.61460e7	−	4.52863e7i	0.335832	−	0.581679i
$428$	6.39529e7			0.815697
$429$			1.05997e8i			1.34252i
$430$	1.61366e7	−	2.43612e7i	0.202958	−	0.306403i
$431$	4.84738e7			0.605446			0.302723	−	0.953079i	$-0.402104\pi$
$431$	4.84738e7			0.605446			0.302723	+	0.953079i	$0.402104\pi$
$432$		−	2.83730e7i		−	0.351928i
$433$	−8.35038e7	−	4.82109e7i	−1.02859	−	0.593857i	−0.112010	−	0.993707i	$-0.535729\pi$
$433$	−8.35038e7	−	4.82109e7i	−1.02859	−	0.593857i	−0.916581	+	0.399850i	$0.869062\pi$
$434$	−377971.			−0.00462369
$435$	−1.11075e8	−	6.41291e7i	−1.34942	−	0.779090i
$436$	−3.84117e7	+	6.65310e7i	−0.463451	+	0.802721i
$437$	9.48846e6	−	5.47816e6i	0.113698	−	0.0656433i
$438$		−	7.21763e7i		−	0.858959i
$439$	−6.52454e7	−	1.13008e8i	−0.771181	−	1.33572i	−0.936916	−	0.349554i	$-0.886333\pi$
$439$	−6.52454e7	−	1.13008e8i	−0.771181	−	1.33572i	0.165736	−	0.986170i	$-0.447000\pi$
$440$	1.40976e7	−	2.44177e7i	0.165495	−	0.286646i
$441$	−8.87298e7			−1.03456
$442$	2.80622e7	+	1.62017e7i	0.324978	+	0.187626i
$443$	5.13802e7	+	8.89932e7i	0.590996	+	1.02364i	0.994099	+	0.108481i	$0.0345986\pi$
$443$	5.13802e7	+	8.89932e7i	0.590996	+	1.02364i	−0.403102	+	0.915155i	$0.632068\pi$
$444$	4.48292e7	+	7.76464e7i	0.512167	+	0.887100i
$445$	−6.76107e7	−	1.17105e8i	−0.767247	−	1.32891i
$446$	−1.82973e6			−0.0206245
$447$	−1.04366e8	−	1.80768e8i	−1.16853	−	2.02395i
$448$	1.52919e7	−	8.82878e6i	0.170070	−	0.0981899i
$449$	−5.65678e7	−	3.26594e7i	−0.624928	−	0.360802i	0.153857	−	0.988093i	$-0.450830\pi$
$449$	−5.65678e7	−	3.26594e7i	−0.624928	−	0.360802i	−0.778785	+	0.627291i	$0.784164\pi$
$450$	9.08754e6	+	5.24670e6i	0.0997261	+	0.0575769i
$451$	−3.36771e7			−0.367118
$452$			7.14213e7i			0.773415i
$453$	−3.70998e7	+	6.42588e7i	−0.399096	+	0.691254i
$454$	−1.12808e7	+	1.95390e7i	−0.120552	+	0.208802i
$455$	−4.63199e7	−	8.02285e7i	−0.491738	−	0.851715i
$456$	−2.24114e7	+	1.29392e7i	−0.236360	+	0.136463i
$457$		−	1.25941e8i		−	1.31953i	−0.751473	−	0.659764i	$-0.770656\pi$
$457$		−	1.25941e8i		−	1.31953i	0.751473	−	0.659764i	$-0.229344\pi$
$458$	−2.59191e7	+	1.49644e7i	−0.269788	+	0.155762i
$459$	−2.65087e7	+	1.53048e7i	−0.274126	+	0.158266i
$460$	3.84929e7	−	2.22239e7i	0.395464	−	0.228321i
$461$	3.48608e6	−	6.03807e6i	0.0355823	−	0.0616304i	−0.847686	−	0.530499i	$-0.822005\pi$
$461$	3.48608e6	−	6.03807e6i	0.0355823	−	0.0616304i	0.883268	+	0.468868i	$0.155338\pi$
$462$			1.10900e7i			0.112462i
$463$	8.22185e7	+	4.74689e7i	0.828374	+	0.478262i	0.853296	−	0.521427i	$-0.174600\pi$
$463$	8.22185e7	+	4.74689e7i	0.828374	+	0.478262i	−0.0249214	+	0.999689i	$0.507934\pi$
$464$	5.42244e7	−	3.13065e7i	0.542801	−	0.313386i
$465$	−5.15932e6			−0.0513138
$466$	−4.67467e6	−	8.09677e6i	−0.0461948	−	0.0800118i
$467$	−1.95665e7	−	1.12967e7i	−0.192116	−	0.110918i	0.400857	−	0.916141i	$-0.368712\pi$
$467$	−1.95665e7	−	1.12967e7i	−0.192116	−	0.110918i	−0.592973	+	0.805223i	$0.702046\pi$
$468$	1.12770e8	−	1.95323e8i	1.10016	−	1.90553i
$469$			7.14819e7i			0.692911i
$470$	2.66377e7	−	4.61379e7i	0.256569	−	0.444390i
$471$	3.45705e7			0.330859
$472$			5.32915e7i			0.506795i
$473$	5.02465e7	+	3.09091e6i	0.474813	+	0.0292081i
$474$	−1.04522e8			−0.981461
$475$			8.17468e6i			0.0762764i
$476$	−2.45427e7	−	1.41697e7i	−0.227563	−	0.131384i
$477$	2.45867e7			0.226540
$478$	5.79739e6	+	3.34712e6i	0.0530822	+	0.0306470i
$479$	1.08190e8	−	1.87391e8i	0.984423	−	1.70507i	0.339951	−	0.940443i	$-0.389590\pi$
$479$	1.08190e8	−	1.87391e8i	0.984423	−	1.70507i	0.644472	−	0.764628i	$-0.277077\pi$
$480$	−1.38944e8	+	8.02194e7i	−1.25637	+	0.725363i
$481$			1.54358e8i			1.38705i
$482$	6.67969e6	+	1.15696e7i	0.0596507	+	0.103318i
$483$	−1.85284e7	+	3.20921e7i	−0.164436	+	0.284811i
$484$	−7.83491e7			−0.691032
$485$	6.75394e7	+	3.89939e7i	0.592014	+	0.341799i
$486$	2.54721e7	+	4.41190e7i	0.221899	+	0.384341i
$487$	−2.86728e7	−	4.96628e7i	−0.248247	−	0.429976i	0.714793	−	0.699336i	$-0.246521\pi$
$487$	−2.86728e7	−	4.96628e7i	−0.248247	−	0.429976i	−0.963039	+	0.269361i	$0.913188\pi$
$488$	−5.10116e7	−	8.83547e7i	−0.438944	−	0.760274i
$489$	2.84981e8			2.43719
$490$	1.67732e7	+	2.90521e7i	0.142570	+	0.246939i
$491$	1.42149e6	−	820697.i	0.0120088	−	0.00693328i	−0.493984	−	0.869471i	$-0.664460\pi$
$491$	1.42149e6	−	820697.i	0.0120088	−	0.00693328i	0.505992	+	0.862538i	$0.331126\pi$
$492$	1.08596e8	+	6.26981e7i	0.911843	+	0.526453i
$493$	−5.84988e7	−	3.37743e7i	−0.488209	−	0.281868i
$494$	−2.10192e7			−0.174355
$495$			8.65061e7i			0.713232i
$496$	1.25934e6	−	2.18123e6i	0.0103204	−	0.0178755i
$497$	4.08780e7	−	7.08027e7i	0.332982	−	0.576741i
$498$	−2.45740e7	−	4.25635e7i	−0.198970	−	0.344627i
$499$	−5.07497e6	+	2.93004e6i	−0.0408443	+	0.0235815i	−0.520283	−	0.853994i	$-0.674174\pi$
$499$	−5.07497e6	+	2.93004e6i	−0.0408443	+	0.0235815i	0.479439	+	0.877575i	$0.340840\pi$
$500$		−	9.23651e7i		−	0.738921i
$501$	−2.06525e8	+	1.19237e8i	−1.64233	+	0.948198i
$502$	1.56807e7	−	9.05326e6i	0.123952	−	0.0715639i
$503$	−1.00325e8	+	5.79226e7i	−0.788324	+	0.455139i	−0.839372	−	0.543557i	$-0.817077\pi$
$503$	−1.00325e8	+	5.79226e7i	−0.788324	+	0.455139i	0.0510483	+	0.998696i	$0.483744\pi$
$504$	2.50087e7	−	4.33164e7i	0.195344	−	0.338346i
$505$			2.55888e8i			1.98690i
$506$	−7.93325e6	−	4.58026e6i	−0.0612350	−	0.0353540i
$507$	4.16044e8	−	2.40203e8i	3.19238	−	1.84312i
$508$	−2.83092e7			−0.215942
$509$	5.39647e7	+	9.34695e7i	0.409219	+	0.708789i	0.994802	−	0.101824i	$-0.0324678\pi$
$509$	5.39647e7	+	9.34695e7i	0.409219	+	0.708789i	−0.585583	+	0.810612i	$0.699134\pi$
$510$	4.00769e7	+	2.31384e7i	0.302123	+	0.174431i
$511$	−5.43379e7	+	9.41160e7i	−0.407231	+	0.705344i
$512$		−	1.35705e8i		−	1.01108i
$513$	9.92777e6	−	1.71954e7i	0.0735360	−	0.127368i
$514$	3.81845e7			0.281188
$515$			8.19067e7i			0.599650i
$516$	−1.56272e8	−	1.03513e8i	−1.13745	−	0.753436i
$517$	9.17826e7			0.664184
$518$			1.61498e7i			0.116192i
$519$	−2.90986e8	−	1.68001e8i	−2.08147	−	1.20174i
$520$	−1.80743e8			−1.28544
$521$	−2.22388e7	−	1.28396e7i	−0.157253	−	0.0907899i	0.419309	−	0.907844i	$-0.362273\pi$
$521$	−2.22388e7	−	1.28396e7i	−0.157253	−	0.0907899i	−0.576561	+	0.817054i	$0.695606\pi$
$522$	2.81226e7	−	4.87098e7i	0.197717	−	0.342456i
$523$	−4.51965e7	+	2.60942e7i	−0.315937	+	0.182406i	−0.649580	−	0.760293i	$-0.725055\pi$
$523$	−4.51965e7	+	2.60942e7i	−0.315937	+	0.182406i	0.333643	+	0.942699i	$0.391722\pi$
$524$		−	6.01136e7i		−	0.417810i
$525$	−1.38243e7	−	2.39444e7i	−0.0955357	−	0.165473i
$526$	1.33361e7	−	2.30988e7i	0.0916372	−	0.158720i
$527$	−2.71721e6			−0.0185649
$528$	−6.39993e7	−	3.69500e7i	−0.434784	−	0.251023i
$529$	5.87132e7	+	1.01694e8i	0.396614	+	0.686956i
$530$	−4.64781e6	−	8.05025e6i	−0.0312191	−	0.0540731i
$531$	−8.17524e7	−	1.41599e8i	−0.546031	−	0.945753i
$532$	1.83830e7			0.122090
$533$	1.07942e8	+	1.86962e8i	0.712869	+	1.23473i
$534$	8.98662e7	−	5.18843e7i	0.590164	−	0.340731i
$535$	1.36176e8	+	7.86213e7i	0.889282	+	0.513427i
$536$	1.20778e8	+	6.97315e7i	0.784323	+	0.452829i
$537$	−3.60889e8			−2.33051
$538$			2.41263e7i			0.154933i
$539$	−2.88968e7	+	5.00508e7i	−0.184537	+	0.319628i
$540$	4.02751e7	−	6.97586e7i	0.255774	−	0.443013i
$541$	1.79639e7	+	3.11144e7i	0.113451	+	0.196503i	0.917160	−	0.398520i	$-0.130476\pi$
$541$	1.79639e7	+	3.11144e7i	0.113451	+	0.196503i	−0.803708	+	0.595023i	$0.797143\pi$
$542$	6.31073e7	−	3.64350e7i	0.396352	−	0.228834i
$543$			1.12534e8i			0.702885i
$544$	−7.31764e7	+	4.22484e7i	−0.454542	+	0.262430i
$545$	−1.63582e8	+	9.44438e7i	−1.01052	+	0.583424i
$546$	6.15671e7	−	3.55458e7i	0.378243	−	0.218379i
$547$	−7.35241e7	+	1.27348e8i	−0.449229	+	0.778088i	−0.998336	−	0.0576644i	$-0.981635\pi$
$547$	−7.35241e7	+	1.27348e8i	−0.449229	+	0.778088i	0.549107	+	0.835752i	$0.314968\pi$
$548$		−	2.23839e7i		−	0.136017i
$549$	2.71083e8	+	1.56510e8i	1.63827	+	0.945855i
$550$	5.91912e6	−	3.41741e6i	0.0355770	−	0.0205404i
$551$	4.38169e7			0.261931
$552$	3.61493e7	+	6.26125e7i	0.214923	+	0.372258i
$553$	1.36294e8	+	7.86895e7i	0.805938	+	0.465309i
$554$	2.43897e7	−	4.22441e7i	0.143442	−	0.248449i
$555$			2.20445e8i			1.28950i
$556$	−1.10271e8	+	1.90995e8i	−0.641559	+	1.11121i
$557$	2.58624e8			1.49659			0.748297	−	0.663364i	$-0.230872\pi$
$557$	2.58624e8			1.49659			0.748297	+	0.663364i	$0.230872\pi$
$558$		−	2.26253e6i		−	0.0130224i
$559$	−1.43891e8	−	2.88855e8i	−0.823757	−	1.65365i
$560$	6.45877e7			0.367778
$561$			7.97254e7i			0.451553i
$562$	6.90244e7	+	3.98512e7i	0.388860	+	0.224509i
$563$	−1.13189e8			−0.634276			−0.317138	−	0.948379i	$-0.602722\pi$
$563$	−1.13189e8			−0.634276			−0.317138	+	0.948379i	$0.602722\pi$
$564$	−2.95965e8	−	1.70876e8i	−1.64969	−	0.952451i
$565$	−8.78027e7	+	1.52079e8i	−0.486813	+	0.843186i
$566$	3.98788e6	−	2.30241e6i	0.0219934	−	0.0126979i
$567$		−	4.79272e7i		−	0.262926i
$568$	−7.97539e7	−	1.38138e8i	−0.435218	−	0.753820i
$569$	−8.65739e7	+	1.49950e8i	−0.469949	+	0.813975i	−0.999410	−	0.0343594i	$-0.989061\pi$
$569$	−8.65739e7	+	1.49950e8i	−0.469949	+	0.813975i	0.529461	+	0.848334i	$0.322394\pi$
$570$	−3.00185e7			−0.162093
$571$	−7.67800e7	−	4.43289e7i	−0.412420	−	0.238111i	0.279409	−	0.960172i	$-0.409861\pi$
$571$	−7.67800e7	−	4.43289e7i	−0.412420	−	0.238111i	−0.691829	+	0.722061i	$0.743195\pi$
$572$	−7.34520e7	−	1.27223e8i	−0.392478	−	0.679793i
$573$	2.44799e8	+	4.24005e8i	1.30121	+	2.25376i
$574$	1.12935e7	+	1.95610e7i	0.0597165	+	0.103432i
$575$	2.28383e7			0.120132
$576$	5.28489e7	+	9.15371e7i	0.276547	+	0.478993i
$577$	5.72908e7	−	3.30768e7i	0.298234	−	0.172185i	−0.343415	−	0.939184i	$-0.611584\pi$
$577$	5.72908e7	−	3.30768e7i	0.298234	−	0.172185i	0.641649	+	0.766998i	$0.278250\pi$
$578$	−3.35563e7	−	1.93738e7i	−0.173776	−	0.100330i
$579$	−2.11239e8	−	1.21959e8i	−1.08827	−	0.628315i
$580$	1.77757e8			0.911051
$581$			7.40022e7i			0.377326i
$582$	−2.99238e7	+	5.18295e7i	−0.151791	+	0.262911i
$583$	8.00722e6	−	1.38689e7i	0.0404088	−	0.0699901i
$584$	1.06015e8	+	1.83623e8i	0.532264	+	0.921909i
$585$	4.80246e8	−	2.77270e8i	2.39881	−	1.38496i
$586$			5.87305e7i			0.291857i
$587$	3.01658e8	−	1.74162e8i	1.49142	−	0.861072i	0.491469	−	0.870895i	$-0.336460\pi$
$587$	3.01658e8	−	1.74162e8i	1.49142	−	0.861072i	0.999952	+	0.00982261i	$0.00312668\pi$
$588$	1.86363e8	−	1.07597e8i	0.916703	−	0.529259i
$589$	1.52644e6	−	881290.i	0.00747022	−	0.00431293i
$590$	−3.09085e7	+	5.35351e7i	−0.150495	+	0.260665i
$591$		−	4.16909e7i		−	0.201966i
$592$	−9.31988e7	−	5.38084e7i	−0.449206	−	0.259349i
$593$	−1.10172e8	+	6.36078e7i	−0.528332	+	0.305032i	−0.740337	−	0.672236i	$-0.765334\pi$
$593$	−1.10172e8	+	6.36078e7i	−0.528332	+	0.305032i	0.212005	+	0.977269i	$0.432001\pi$
$594$	−1.66011e7			−0.0792097
$595$	−3.48395e7	−	6.03438e7i	−0.165395	−	0.286472i
$596$	2.50532e8	+	1.44645e8i	1.18338	+	0.683224i
$597$	−5.69554e7	+	9.86496e7i	−0.267678	+	0.463631i
$598$			5.87229e7i			0.274602i
$599$	1.88530e8	−	3.26543e8i	0.877202	−	1.51936i	0.0228026	−	0.999740i	$-0.492741\pi$
$599$	1.88530e8	−	3.26543e8i	0.877202	−	1.51936i	0.854399	−	0.519618i	$-0.173926\pi$
$600$	−5.39431e7			−0.249737
$601$		−	2.12943e8i		−	0.980934i	−0.871460	−	0.490467i	$-0.836826\pi$
$601$		−	2.12943e8i		−	0.980934i	0.871460	−	0.490467i	$-0.163174\pi$
$602$	−1.50547e7	−	3.02217e7i	−0.0690055	−	0.138525i
$603$	−4.27889e8			−1.95155
$604$		−	1.02835e8i		−	0.466694i
$605$	−1.66830e8	−	9.63196e7i	−0.753371	−	0.434959i
$606$	−1.96368e8			−0.882372
$607$	−2.97713e8	−	1.71885e8i	−1.33117	−	0.768549i	−0.345687	−	0.938350i	$-0.612354\pi$
$607$	−2.97713e8	−	1.71885e8i	−1.33117	−	0.768549i	−0.985478	+	0.169801i	$0.945688\pi$
$608$	2.74053e7	−	4.74674e7i	0.121934	−	0.211196i
$609$	−1.28344e8	+	7.40992e7i	−0.568228	+	0.328066i
$610$		−	1.18345e8i		−	0.521386i
$611$	−2.94183e8	−	5.09539e8i	−1.28971	−	2.23385i
$612$	8.48198e7	−	1.46912e8i	0.370035	−	0.640920i
$613$	−1.96524e8			−0.853168			−0.426584	−	0.904448i	$-0.640283\pi$
$613$	−1.96524e8			−0.853168			−0.426584	+	0.904448i	$0.640283\pi$
$614$	9.51463e7	+	5.49327e7i	0.411042	+	0.237315i
$615$	1.54158e8	+	2.67009e8i	0.662734	+	1.14789i
$616$	−1.62893e7	−	2.82139e7i	−0.0696883	−	0.120704i
$617$	−1.61965e8	−	2.80532e8i	−0.689552	−	1.19434i	−0.971983	−	0.235051i	$-0.924474\pi$
$617$	−1.61965e8	−	2.80532e8i	−0.689552	−	1.19434i	0.282431	−	0.959287i	$-0.408859\pi$
$618$	−6.28549e7			−0.266302
$619$	1.96166e8	+	3.39770e8i	0.827089	+	1.43256i	0.900312	+	0.435244i	$0.143338\pi$
$619$	1.96166e8	+	3.39770e8i	0.827089	+	1.43256i	−0.0732237	+	0.997316i	$0.523329\pi$
$620$	6.19248e6	−	3.57523e6i	0.0259830	−	0.0150013i
$621$	−4.80402e7	−	2.77360e7i	−0.200599	−	0.115816i
$622$	5.88132e7	+	3.39558e7i	0.244401	+	0.141105i
$623$	−1.56244e8			−0.646160
$624$			4.73730e8i			1.94974i
$625$	1.45800e8	−	2.52533e8i	0.597197	−	1.03437i
$626$	−1.34346e7	+	2.32695e7i	−0.0547650	+	0.0948558i
$627$	−2.58578e7	−	4.47870e7i	−0.104903	−	0.181698i
$628$	−4.14933e7	+	2.39562e7i	−0.167532	+	0.0967249i
$629$			1.16100e8i			0.466531i
$630$	5.02461e7	−	2.90096e7i	0.200947	−	0.116017i
$631$	1.57874e8	−	9.11487e7i	0.628381	−	0.362796i	−0.151744	−	0.988420i	$-0.548489\pi$
$631$	1.57874e8	−	9.11487e7i	0.628381	−	0.362796i	0.780125	+	0.625624i	$0.215156\pi$
$632$	2.65913e8	−	1.53525e8i	1.05339	−	0.608174i
$633$	1.51313e7	−	2.62082e7i	0.0596575	−	0.103330i
$634$			6.40466e7i			0.251321i
$635$	−6.02793e7	−	3.48023e7i	−0.235422	−	0.135921i
$636$	−5.16407e7	+	2.98148e7i	−0.200734	+	0.115894i
$637$	3.70482e8			1.43334
$638$	−1.83175e7	−	3.17269e7i	−0.0705350	−	0.122170i
$639$	4.23824e8	+	2.44695e8i	1.62436	+	0.937826i
$640$	1.44459e8	−	2.50211e8i	0.551069	−	0.954479i
$641$			8.80558e7i			0.334337i	0.985928	+	0.167168i	$0.0534623\pi$
$641$			8.80558e7i			0.334337i	−0.985928	+	0.167168i	$0.946538\pi$
$642$	−6.03338e7	+	1.04501e8i	−0.228011	+	0.394926i
$643$	5.93241e7			0.223151			0.111575	−	0.993756i	$-0.464410\pi$
$643$	5.93241e7			0.223151			0.111575	+	0.993756i	$0.464410\pi$
$644$		−	5.13581e7i		−	0.192287i
$645$	−2.05498e8	−	4.12528e8i	−0.765823	−	1.53735i
$646$	−1.58096e7			−0.0586438
$647$		−	2.41880e8i		−	0.893075i	−0.894765	−	0.446537i	$-0.852657\pi$
$647$		−	2.41880e8i		−	0.893075i	0.894765	−	0.446537i	$-0.147343\pi$
$648$	−8.09796e7	−	4.67536e7i	−0.297612	−	0.171826i
$649$	−1.06498e8			−0.389590
$650$	−3.79441e7	−	2.19070e7i	−0.138167	−	0.0797707i
$651$	−2.98072e6	+	5.16276e6i	−0.0108038	+	0.0187128i
$652$	−3.42048e8	+	1.97482e8i	−1.23408	+	0.712498i
$653$			4.63037e8i			1.66294i	0.555571	+	0.831469i	$0.312500\pi$
$653$			4.63037e8i			1.66294i	−0.555571	+	0.831469i	$0.687500\pi$
$654$	−7.24759e7	−	1.25532e8i	−0.259096	−	0.448767i
$655$	7.39015e7	−	1.28001e8i	0.262984	−	0.455502i
$656$	−1.50513e8			−0.533165
$657$	−5.63377e8	−	3.25266e8i	−1.98657	−	1.14694i
$658$	−3.07791e7	−	5.33109e7i	−0.108038	−	0.187128i
$659$	1.57206e8	+	2.72289e8i	0.549305	+	0.951424i	0.998322	+	0.0579008i	$0.0184407\pi$
$659$	1.57206e8	+	2.72289e8i	0.549305	+	0.951424i	−0.449018	+	0.893523i	$0.648226\pi$
$660$	−1.04900e8	−	1.81693e8i	−0.364876	−	0.631984i
$661$	−9.08469e7			−0.314561			−0.157281	−	0.987554i	$-0.550273\pi$
$661$	−9.08469e7			−0.314561			−0.157281	+	0.987554i	$0.550273\pi$
$662$	2.64253e7	+	4.57700e7i	0.0910849	+	0.157764i
$663$	4.42603e8	−	2.55537e8i	1.51871	−	0.876825i
$664$	1.25037e8	+	7.21901e7i	0.427104	+	0.246589i
$665$	3.91433e7	+	2.25994e7i	0.133104	+	0.0768479i
$666$	−9.66723e7			−0.327250
$667$		−	1.22415e8i		−	0.412530i
$668$	1.65255e8	−	2.86229e8i	0.554401	−	0.960251i
$669$	−1.44295e7	+	2.49926e7i	−0.0481917	+	0.0834705i
$670$	8.08871e7	+	1.40101e8i	0.268940	+	0.465817i
$671$	1.76568e8	−	1.01942e8i	0.584447	−	0.337431i
$672$			1.85382e8i			0.610886i
$673$	−1.08523e7	+	6.26555e6i	−0.0356020	+	0.0205548i	−0.517695	−	0.855565i	$-0.673210\pi$
$673$	−1.08523e7	+	6.26555e6i	−0.0356020	+	0.0205548i	0.482093	+	0.876120i	$0.339877\pi$
$674$	1.65994e7	−	9.58369e6i	0.0542143	−	0.0313006i
$675$	3.58435e7	−	2.06943e7i	0.116546	−	0.0672881i
$676$	−3.32904e8	+	5.76607e8i	−1.07765	+	1.86655i
$677$			5.24044e7i			0.168889i	0.996428	+	0.0844447i	$0.0269116\pi$
$677$			5.24044e7i			0.168889i	−0.996428	+	0.0844447i	$0.973088\pi$
$678$	−1.16705e8	−	6.73795e7i	−0.374455	−	0.216192i
$679$	7.80396e7	−	4.50562e7i	0.249291	−	0.143928i
$680$	−1.35945e8			−0.432353
$681$	1.77924e8	+	3.08173e8i	0.563369	+	0.975783i
$682$	−1.27625e6	−	736842.i	−0.00402329	−	0.00232285i
$683$	−6.25647e7	+	1.08365e8i	−0.196367	+	0.340117i	−0.947348	−	0.320207i	$-0.896248\pi$
$683$	−6.25647e7	+	1.08365e8i	−0.196367	+	0.340117i	0.750981	+	0.660324i	$0.229581\pi$
$684$			1.10040e8i			0.343862i
$685$	2.75180e7	−	4.76625e7i	0.0856139	−	0.148288i
$686$	8.87233e7			0.274831
$687$			4.72043e8i			1.45583i
$688$	2.24566e8	+	1.38142e7i	0.689571	+	0.0424189i
$689$	−1.02659e8			−0.313863
$690$			8.38650e7i			0.255290i
$691$	1.87876e8	+	1.08470e8i	0.569425	+	0.328758i	0.756920	−	0.653508i	$-0.226703\pi$
$691$	1.87876e8	+	1.08470e8i	0.569425	+	0.328758i	−0.187495	+	0.982266i	$0.560037\pi$
$692$	4.65674e8			1.40528
$693$	8.65637e7	+	4.99776e7i	0.260097	+	0.150167i
$694$	7.39512e7	−	1.28087e8i	0.221242	−	0.383202i
$695$	−4.69604e8	+	2.71126e8i	−1.39887	+	0.807638i
$696$			2.89139e8i			0.857588i
$697$	8.11887e7	+	1.40623e8i	0.239771	+	0.415296i
$698$	1.87328e7	−	3.24462e7i	0.0550854	−	0.0954108i
$699$	−1.47460e8			−0.431760
$700$	3.31853e7	+	1.91595e7i	0.0967500	+	0.0558587i
$701$	−7.29910e7	−	1.26424e8i	−0.211892	−	0.367009i	0.740414	−	0.672151i	$-0.234629\pi$
$701$	−7.29910e7	−	1.26424e8i	−0.211892	−	0.367009i	−0.952307	+	0.305142i	$0.901296\pi$
$702$	5.32101e7	+	9.21626e7i	0.153809	+	0.266406i
$703$	−3.76554e7	−	6.52210e7i	−0.108383	−	0.187725i
$704$	6.88457e7			0.197315
$705$	−4.20136e8	−	7.27697e8i	−1.19901	−	2.07675i
$706$	−1.11369e8	+	6.42989e7i	−0.316483	+	0.182721i
$707$	2.56058e8	+	1.47835e8i	0.724570	+	0.418331i
$708$	3.43417e8	+	1.98272e8i	0.967658	+	0.558678i
$709$	−4.32547e8			−1.21365			−0.606827	−	0.794834i	$-0.707558\pi$
$709$	−4.32547e8			−1.21365			−0.606827	+	0.794834i	$0.707558\pi$
$710$		−	1.85026e8i		−	0.516961i
$711$	−4.71034e8	+	8.15854e8i	−1.31052	+	2.26988i
$712$	−1.52418e8	+	2.63996e8i	−0.422276	+	0.731404i
$713$	−2.46213e6	−	4.26453e6i	−0.00679269	−	0.0117653i
$714$	4.63077e7	−	2.67357e7i	0.127221	−	0.0734510i
$715$		−	3.61197e8i		−	0.988157i
$716$	4.33157e8	−	2.50083e8i	1.18006	−	0.681311i
$717$	9.14377e7	−	5.27916e7i	0.248066	−	0.143221i
$718$	1.63308e6	−	942860.i	0.00441199	−	0.00254726i
$719$	2.09587e8	−	3.63015e8i	0.563868	−	0.976647i	−0.433286	−	0.901256i	$-0.642646\pi$
$719$	2.09587e8	−	3.63015e8i	0.563868	−	0.976647i	0.997154	−	0.0753911i	$-0.0240205\pi$
$720$			3.86621e8i			1.03583i
$721$	8.19612e7	+	4.73203e7i	0.218677	+	0.126253i
$722$	−9.76614e7	+	5.63849e7i	−0.259485	+	0.149813i
$723$	2.10707e8			0.557526
$724$	−7.79820e7	−	1.35069e8i	−0.205484	−	0.355909i
$725$	7.90988e7	+	4.56677e7i	0.207566	+	0.119838i
$726$	7.39154e7	−	1.28025e8i	0.193163	−	0.334569i
$727$		−	746594.i		−	0.00194304i	−1.00000		0.000971519i	$-0.999691\pi$
$727$		−	746594.i		−	0.00194304i	1.00000		0.000971519i	$-0.000309244\pi$
$728$	−1.04421e8	+	1.80863e8i	−0.270642	+	0.468765i
$729$	5.88357e8			1.51865
$730$			2.45950e8i			0.632234i
$731$	−1.08228e8	−	2.17262e8i	−0.277068	−	0.556201i
$732$	−7.59158e8			−1.93552
$733$		−	2.65891e8i		−	0.675137i	−0.941301	−	0.337569i	$-0.890396\pi$
$733$		−	2.65891e8i		−	0.675137i	0.941301	−	0.337569i	$-0.109604\pi$
$734$	−4.33179e7	−	2.50096e7i	−0.109542	−	0.0632439i
$735$	5.29103e8			1.33253
$736$	−1.32613e8	−	7.65644e7i	−0.332624	−	0.192041i
$737$	−1.39352e8	+	2.41364e8i	−0.348105	+	0.602935i
$738$	−1.17092e8	+	6.76029e7i	−0.291311	+	0.168189i
$739$		−	5.26534e8i		−	1.30465i	−0.757941	−	0.652323i	$-0.773795\pi$
$739$		−	5.26534e8i		−	1.30465i	0.757941	−	0.652323i	$-0.226205\pi$
$740$	−1.52761e8	−	2.64590e8i	−0.376979	−	0.652947i
$741$	−1.65760e8	+	2.87104e8i	−0.407403	+	0.705642i
$742$	−1.07408e7			−0.0262921
$743$	−2.90256e8	−	1.67580e8i	−0.707644	−	0.408559i	0.102544	−	0.994728i	$-0.467302\pi$
$743$	−2.90256e8	−	1.67580e8i	−0.707644	−	0.408559i	−0.810188	+	0.586170i	$0.800635\pi$
$744$	5.81546e6	+	1.00727e7i	0.0141210	+	0.0244583i
$745$	3.55641e8	+	6.15989e8i	0.860089	+	1.48972i
$746$	−9.34755e7	−	1.61904e8i	−0.225155	−	0.389979i
$747$	−4.42976e8			−1.06272
$748$	−5.52469e7	−	9.56905e7i	−0.132009	−	0.228646i
$749$	1.57347e8	−	9.08445e7i	0.374467	−	0.216199i
$750$	1.50928e8	+	8.71382e7i	0.357755	+	0.206550i
$751$	1.20622e8	+	6.96411e7i	0.284778	+	0.164417i	0.635584	−	0.772031i	$-0.280759\pi$
$751$	1.20622e8	+	6.96411e7i	0.284778	+	0.164417i	−0.350807	+	0.936448i	$0.614093\pi$
$752$	4.10203e8			0.964596
$753$		−	2.85580e8i		−	0.668873i
$754$	−1.17423e8	+	2.03383e8i	−0.273930	+	0.474461i
$755$	1.26422e8	−	2.18970e8i	0.293753	−	0.508795i
$756$	−4.65367e7	−	8.06039e7i	−0.107704	−	0.186548i
$757$	−2.41720e8	+	1.39557e8i	−0.557218	+	0.321710i	−0.752028	−	0.659131i	$-0.770924\pi$
$757$	−2.41720e8	+	1.39557e8i	−0.557218	+	0.321710i	0.194810	+	0.980841i	$0.437591\pi$
$758$		−	2.24674e8i		−	0.515877i
$759$	−1.25125e8	+	7.22410e7i	−0.286167	+	0.165218i
$760$	7.63696e7	−	4.40920e7i	0.173972	−	0.100443i
$761$	5.78400e8	−	3.33939e8i	1.31242	−	0.757728i	0.329927	−	0.944007i	$-0.392976\pi$
$761$	5.78400e8	−	3.33939e8i	1.31242	−	0.757728i	0.982497	+	0.186278i	$0.0596426\pi$
$762$	2.67072e7	−	4.62582e7i	0.0603619	−	0.104550i
$763$			2.18254e8i			0.491347i
$764$	−5.87641e8	−	3.39275e8i	−1.31775	−	0.760801i
$765$	3.61217e8	−	2.08549e8i	0.806833	−	0.465825i
$766$	−1.48206e8			−0.329745
$767$	3.41349e8	+	5.91233e8i	0.756505	+	1.31031i
$768$	−5.65490e7	−	3.26486e7i	−0.124836	−	0.0720743i
$769$	−1.53671e8	+	2.66166e8i	−0.337920	+	0.585294i	−0.984041	−	0.177940i	$-0.943057\pi$
$769$	−1.53671e8	+	2.66166e8i	−0.337920	+	0.585294i	0.646122	+	0.763235i	$0.276390\pi$
$770$		−	3.77905e7i		−	0.0827771i
$771$	3.01127e8	−	5.21567e8i	0.657032	−	1.13801i
$772$	3.38053e8			0.734738
$773$			8.90049e8i			1.92697i	0.267758	+	0.963486i	$0.413717\pi$
$773$			8.90049e8i			1.92697i	−0.267758	+	0.963486i	$0.586283\pi$
$774$	1.80906e8	−	9.01173e7i	0.390149	−	0.194350i
$775$	3.67406e6			0.00789299
$776$		−	1.75812e8i		−	0.376238i
$777$	2.20592e8	+	1.27359e8i	0.470248	+	0.271498i
$778$	2.14883e8			0.456313
$779$	−9.12182e7	−	5.26648e7i	−0.192961	−	0.111406i
$780$	−6.72456e8	+	1.16473e9i	−1.41703	+	2.45437i
$781$	2.76055e8	−	1.59381e8i	0.579486	−	0.334567i
$782$			4.41684e7i			0.0923616i
$783$	−1.10923e8	−	1.92124e8i	−0.231065	−	0.400217i
$784$	−1.29148e8	+	2.23692e8i	−0.268004	+	0.464196i
$785$	−1.17803e8			−0.243528
$786$	9.82277e7	+	5.67118e7i	0.202286	+	0.116790i
$787$	1.02362e8	+	1.77296e8i	0.209998	+	0.363726i	0.951713	−	0.306988i	$-0.0993211\pi$
$787$	1.02362e8	+	1.77296e8i	0.209998	+	0.363726i	−0.741716	+	0.670714i	$0.765988\pi$
$788$	2.88903e7	+	5.00395e7i	0.0590438	+	0.102267i
$789$	−2.10340e8	−	3.64320e8i	−0.428244	−	0.741740i
$790$	3.56172e8			0.722401
$791$	1.01453e8	+	1.75722e8i	0.204992	+	0.355057i
$792$	1.68888e8	−	9.75074e7i	0.339956	−	0.196274i
$793$	−1.13188e9	−	6.53490e8i	−2.26976	−	1.31045i
$794$	−8.69419e7	−	5.01959e7i	−0.173687	−	0.100278i
$795$	−1.46613e8			−0.291790
$796$		−	1.57872e8i		−	0.313016i
$797$	−4.07974e8	+	7.06632e8i	−0.805857	+	1.39579i	0.109854	+	0.993948i	$0.464962\pi$
$797$	−4.07974e8	+	7.06632e8i	−0.805857	+	1.39579i	−0.915711	+	0.401837i	$0.868372\pi$
$798$	−1.73427e7	+	3.00385e7i	−0.0341278	+	0.0591111i
$799$	−2.21269e8	−	3.83250e8i	−0.433791	−	0.751349i
$800$	9.89450e7	−	5.71259e7i	0.193252	−	0.111574i
$801$		−	9.35275e8i		−	1.81988i
$802$	−1.05516e8	+	6.09197e7i	−0.204548	+	0.118096i
$803$	−3.66953e8	+	2.11860e8i	−0.708701	+	0.409169i
$804$	8.98716e8	−	5.18874e8i	1.72924	−	0.998375i
$805$	6.31377e7	−	1.09358e8i	0.121032	−	0.209634i
$806$			9.44694e6i			0.0180421i
$807$	3.29545e8	+	1.90263e8i	0.627038	+	0.362021i
$808$	4.99576e8	−	2.88430e8i	0.947038	−	0.546772i
$809$	8.21425e7			0.155139			0.0775697	−	0.996987i	$-0.475284\pi$
$809$	8.21425e7			0.155139			0.0775697	+	0.996987i	$0.475284\pi$
$810$	−5.42332e7	−	9.39347e7i	−0.102049	−	0.176755i
$811$	5.69171e7	+	3.28611e7i	0.106704	+	0.0616055i	0.552402	−	0.833578i	$-0.313711\pi$
$811$	5.69171e7	+	3.28611e7i	0.106704	+	0.0616055i	−0.445698	+	0.895183i	$0.647045\pi$
$812$	1.02696e8	−	1.77875e8i	0.191817	−	0.332237i
$813$		−	1.14932e9i		−	2.13880i
$814$	−3.14835e7	+	5.45310e7i	−0.0583727	+	0.101104i
$815$	−9.71106e8			−1.79388
$816$			3.56316e8i			0.655790i
$817$	1.31265e8	+	8.69484e7i	0.240703	+	0.159439i
$818$	5.48060e6			0.0100131
$819$		−	6.40755e8i		−	1.16638i
$820$	−3.70055e8	−	2.13651e8i	−0.671158	−	0.387493i
$821$	1.11810e8			0.202047			0.101024	−	0.994884i	$-0.467788\pi$
$821$	1.11810e8			0.202047			0.101024	+	0.994884i	$0.467788\pi$
$822$	3.65761e7	+	2.11172e7i	0.0658539	+	0.0380208i
$823$	−3.45162e8	+	5.97837e8i	−0.619188	+	1.07247i	0.370446	+	0.928854i	$0.379205\pi$
$823$	−3.45162e8	+	5.97837e8i	−0.619188	+	1.07247i	−0.989634	+	0.143612i	$0.954128\pi$
$824$	1.59908e8	−	9.23231e7i	0.285818	−	0.165017i
$825$		−	1.07800e8i		−	0.191981i
$826$	3.57138e7	+	6.18582e7i	0.0633719	+	0.109763i
$827$	−2.11173e8	+	3.65763e8i	−0.373355	+	0.646670i	−0.990079	−	0.140509i	$-0.955126\pi$
$827$	−2.11173e8	+	3.65763e8i	−0.373355	+	0.646670i	0.616724	+	0.787179i	$0.288459\pi$
$828$	3.07428e8			0.541568
$829$	−4.74804e8	−	2.74128e8i	−0.833394	−	0.481160i	0.0216192	−	0.999766i	$-0.493118\pi$
$829$	−4.74804e8	−	2.74128e8i	−0.833394	−	0.481160i	−0.855013	+	0.518606i	$0.826451\pi$
$830$	8.37390e7	+	1.45040e8i	0.146451	+	0.253661i
$831$	−3.84679e8	−	6.66284e8i	−0.670341	−	1.16107i
$832$	−2.20665e8	−	3.82203e8i	−0.383146	−	0.663628i
$833$	2.78658e8			0.482099
$834$	−2.08061e8	−	3.60373e8i	−0.358668	−	0.621232i
$835$	7.03759e8	−	4.06316e8i	1.20883	−	0.697918i
$836$	6.20717e7	+	3.58371e7i	0.106237	+	0.0613358i
$837$	−7.72837e6	−	4.46198e6i	−0.0131799	−	0.00760941i
$838$	−6.59704e7			−0.112103
$839$			1.16270e8i			0.196870i	0.995143	+	0.0984352i	$0.0313837\pi$
$839$			1.16270e8i			0.196870i	−0.995143	+	0.0984352i	$0.968616\pi$
$840$	−1.49129e8	+	2.58299e8i	−0.251608	+	0.435798i
$841$	−5.26297e7	+	9.11573e7i	−0.0884796	+	0.153251i
$842$	−1.30809e8	−	2.26568e8i	−0.219130	−	0.379544i
$843$	1.08867e9	−	6.28543e8i	1.81724	−	1.04919i
$844$			4.19418e7i			0.0697622i
$845$	−1.41772e9	+	8.18520e8i	−2.34974	+	1.35662i
$846$	3.19118e8	−	1.84243e8i	0.527036	−	0.304285i
$847$	−1.92767e8	+	1.11294e8i	−0.317237	+	0.183157i
$848$	3.57866e7	−	6.19842e7i	0.0586858	−	0.101647i
$849$		−	7.26282e7i		−	0.118681i
$850$	−2.85396e7	−	1.64774e7i	−0.0464720	−	0.0268306i
$851$	−1.82213e8	+	1.05201e8i	−0.295659	+	0.170699i
$852$	−1.18690e9			−1.91910
$853$	−3.15890e8	−	5.47137e8i	−0.508965	−	0.881554i	−0.999946	−	0.0103833i	$-0.996695\pi$
$853$	−3.15890e8	−	5.47137e8i	−0.508965	−	0.881554i	0.490981	−	0.871170i	$-0.336638\pi$
$854$	−1.18424e8	−	6.83719e7i	−0.190136	−	0.109775i
$855$	−1.35280e8	+	2.34311e8i	−0.216438	+	0.374882i
$856$		−	3.54480e8i		−	0.565158i
$857$	−3.09518e8	+	5.36101e8i	−0.491749	+	0.851734i	−0.999955	−	0.00950128i	$-0.996976\pi$
$857$	−3.09518e8	+	5.36101e8i	−0.491749	+	0.851734i	0.508206	+	0.861236i	$0.330309\pi$
$858$	2.77181e8			0.438836
$859$		−	3.19498e8i		−	0.504068i	−0.967718	−	0.252034i	$-0.918901\pi$
$859$		−	3.19498e8i		−	0.504068i	0.967718	−	0.252034i	$-0.0810994\pi$
$860$	5.32516e8	+	3.52734e8i	0.837216	+	0.554564i
$861$	3.56249e8			0.558141
$862$		−	1.26759e8i		−	0.197905i
$863$	7.64871e8	+	4.41598e8i	1.19002	+	0.687061i	0.958312	−	0.285724i	$-0.0922340\pi$
$863$	7.64871e8	+	4.41598e8i	1.19002	+	0.687061i	0.231712	+	0.972784i	$0.425567\pi$
$864$	−2.77507e8			−0.430262
$865$	9.91569e8	+	5.72483e8i	1.53206	+	0.884533i
$866$	−1.26072e8	+	2.18362e8i	−0.194117	+	0.336220i
$867$	−5.29258e8	+	3.05567e8i	−0.812102	+	0.468867i
$868$		−	8.26214e6i		−	0.0126338i
$869$	3.06805e8	+	5.31402e8i	0.467524	+	0.809774i
$870$	−1.67698e8	+	2.90461e8i	−0.254665	+	0.441093i
$871$	1.78661e9			2.70380
$872$	3.68770e8	+	2.12909e8i	0.556168	+	0.321104i
$873$	2.69706e8	+	4.67144e8i	0.405366	+	0.702115i
$874$	−1.43254e7	−	2.48123e7i	−0.0214572	−	0.0371649i
$875$	−1.31204e8	−	2.27252e8i	−0.195850	−	0.339221i
$876$	1.57772e9			2.34702
$877$	−3.98005e8	−	6.89365e8i	−0.590052	−	1.02200i	−0.994225	−	0.107317i	$-0.965774\pi$
$877$	−3.98005e8	−	6.89365e8i	−0.590052	−	1.02200i	0.404173	−	0.914682i	$-0.367559\pi$
$878$	−2.95517e8	+	1.70617e8i	−0.436615	+	0.252080i
$879$	8.02208e8	+	4.63155e8i	1.18119	+	0.681962i
$880$	2.18085e8	+	1.25912e8i	0.320021	+	0.184764i
$881$	−8.36778e8			−1.22372			−0.611861	−	0.790965i	$-0.709579\pi$
$881$	−8.36778e8			−1.22372			−0.611861	+	0.790965i	$0.709579\pi$
$882$			2.32028e8i			0.338170i
$883$	−6.47103e8	+	1.12081e9i	−0.939920	+	1.62799i	−0.174305	+	0.984692i	$0.555768\pi$
$883$	−6.47103e8	+	1.12081e9i	−0.939920	+	1.62799i	−0.765616	+	0.643298i	$0.777566\pi$
$884$	−3.54156e8	+	6.13416e8i	−0.512670	+	0.887971i
$885$	4.87496e8	+	8.44368e8i	0.703301	+	1.21815i
$886$	2.32717e8	−	1.34359e8i	0.334601	−	0.193182i
$887$			6.83076e8i			0.978809i	0.872057	+	0.489405i	$0.162786\pi$
$887$			6.83076e8i			0.978809i	−0.872057	+	0.489405i	$0.837214\pi$
$888$	4.30381e8	−	2.48481e8i	0.614630	−	0.354857i
$889$	−6.96509e7	+	4.02130e7i	−0.0991337	+	0.0572349i
$890$	−3.06230e8	+	1.76802e8i	−0.434388	+	0.250794i
$891$	9.34326e7	−	1.61830e8i	0.132089	−	0.228784i
$892$		−	3.99965e7i		−	0.0563543i
$893$	2.48603e8	+	1.43531e8i	0.349102	+	0.201554i
$894$	−4.72708e8	+	2.72918e8i	−0.661577	+	0.381962i
$895$	1.22977e9			1.71536
$896$	−1.66918e8	−	2.89111e8i	−0.232049	−	0.401921i
$897$	8.02105e8	+	4.63095e8i	1.11136	+	0.641642i
$898$	−8.54043e7	+	1.47925e8i	−0.117937	+	0.204273i
$899$		−	1.96932e7i		−	0.0271043i
$900$	−1.14689e8	+	1.98646e8i	−0.157323	+	0.272492i
$901$	−7.72152e7			−0.105567
$902$			8.80656e7i			0.120002i
$903$	−5.31526e8	−	3.26968e7i	−0.721873	−	0.0444060i
$904$	3.95876e8			0.535863
$905$		−	3.83473e8i		−	0.517356i
$906$	1.68037e8	+	9.70160e7i	0.225954	+	0.130454i
$907$	1.00718e8			0.134984			0.0674921	−	0.997720i	$-0.478500\pi$
$907$	1.00718e8			0.134984			0.0674921	+	0.997720i	$0.478500\pi$
$908$	−4.27106e8	−	2.46590e8i	−0.570530	−	0.329395i
$909$	−8.84939e8	+	1.53276e9i	−1.17821	+	2.04072i
$910$	−2.09797e8	+	1.21127e8i	−0.278404	+	0.160737i
$911$			1.24630e8i			0.164842i	0.996598	+	0.0824212i	$0.0262653\pi$
$911$			1.24630e8i			0.164842i	−0.996598	+	0.0824212i	$0.973735\pi$
$912$	−1.15566e8	−	2.00166e8i	−0.152351	−	0.263880i
$913$	−1.44265e8	+	2.49874e8i	−0.189561	+	0.328329i
$914$	−3.29336e8			−0.431320
$915$	−1.61649e9	−	9.33281e8i	−2.11013	−	1.21829i
$916$	−3.27109e8	−	5.66570e8i	−0.425605	−	0.737169i
$917$	−8.53909e7	−	1.47901e8i	−0.110740	−	0.191807i
$918$	4.00220e7	+	6.93201e7i	0.0517333	+	0.0896048i
$919$	−5.35434e8			−0.689858			−0.344929	−	0.938629i	$-0.612097\pi$
$919$	−5.35434e8			−0.689858			−0.344929	+	0.938629i	$0.612097\pi$
$920$	−1.23183e8	−	2.13360e8i	−0.158193	−	0.273999i
$921$	1.50067e9	−	8.66412e8i	1.92091	−	1.10904i
$922$	−1.57895e7	−	9.11610e6i	−0.0201454	−	0.0116310i
$923$	−1.76963e9	−	1.02170e9i	−2.25049	−	1.29932i
$924$	−2.42418e8			−0.307291
$925$		−	1.56984e8i		−	0.198349i
$926$	1.24131e8	−	2.15001e8i	0.156332	−	0.270775i
$927$	−2.83259e8	+	4.90618e8i	−0.355585	+	0.615892i
$928$	−3.06199e8	−	5.30352e8i	−0.383142	−	0.663621i
$929$	−7.42398e6	+	4.28624e6i	−0.00925954	+	0.00534600i	−0.504623	−	0.863340i	$-0.668368\pi$
$929$	−7.42398e6	+	4.28624e6i	−0.00925954	+	0.00534600i	0.495363	+	0.868686i	$0.335035\pi$
$930$			1.34916e7i			0.0167732i
$931$	−1.56541e8	+	9.03787e7i	−0.193989	+	0.112000i
$932$	1.76989e8	−	1.02185e8i	0.218624	−	0.126223i
$933$	9.27616e8	−	5.35559e8i	1.14215	−	0.659421i
$934$	−2.95409e7	+	5.11664e7i	−0.0362563	+	0.0627978i
$935$		−	2.71674e8i		−	0.332364i
$936$	−1.08264e9	−	6.25064e8i	−1.32025	−	0.762249i
$937$	−5.04973e8	+	2.91546e8i	−0.613832	+	0.354396i	−0.774464	−	0.632618i	$-0.781980\pi$
$937$	−5.04973e8	+	2.91546e8i	−0.613832	+	0.354396i	0.160632	+	0.987014i	$0.448647\pi$
$938$	1.86925e8			0.226495
$939$	2.11894e8	+	3.67012e8i	0.255931	+	0.443285i
$940$	1.00854e9	+	5.82279e8i	1.21425	+	0.701048i
$941$	−2.10234e8	+	3.64136e8i	−0.252310	+	0.437013i	−0.964161	−	0.265317i	$-0.914524\pi$
$941$	−2.10234e8	+	3.64136e8i	−0.252310	+	0.437013i	0.711852	+	0.702330i	$0.247857\pi$
$942$		−	9.04019e7i		−	0.108150i
$943$	−1.47134e8	+	2.54843e8i	−0.175460	+	0.303905i
$944$	−4.75970e8			−0.565801
$945$		−	2.28842e8i		−	0.271169i
$946$	8.08273e6	−	1.31395e8i	0.00954739	−	0.155204i
$947$	−7.52360e8			−0.885882			−0.442941	−	0.896551i	$-0.646065\pi$
$947$	−7.52360e8			−0.885882			−0.442941	+	0.896551i	$0.646065\pi$
$948$		−	2.28477e9i		−	2.68175i
$949$	2.35232e9	+	1.35811e9i	2.75231	+	1.58905i
$950$	2.13768e7			0.0249328
$951$	8.74822e8	+	5.05079e8i	1.01713	+	0.587243i
$952$	−7.85404e7	+	1.36036e8i	−0.0910295	+	0.157668i
$953$	1.27147e9	−	7.34086e8i	1.46902	−	0.848141i	0.469627	−	0.882865i	$-0.344389\pi$
$953$	1.27147e9	−	7.34086e8i	1.46902	−	0.848141i	0.999397	+	0.0347239i	$0.0110552\pi$
$954$		−	6.42943e7i		−	0.0740504i
$955$	−8.34184e8	−	1.44485e9i	−0.957749	−	1.65887i
$956$	−7.31654e7	+	1.26726e8i	−0.0837399	+	0.145042i
$957$	−5.77817e8			−0.659256
$958$	−4.90028e8	−	2.82918e8i	−0.557345	−	0.321783i
$959$	−3.17961e7	−	5.50725e7i	−0.0360511	−	0.0624424i
$960$	−3.15143e8	−	5.45843e8i	−0.356200	−	0.616956i
$961$	4.43356e8	+	7.67915e8i	0.499554	+	0.865252i
$962$	4.03645e8			0.453392
$963$	5.43794e8	+	9.41878e8i	0.608913	+	1.05467i
$964$	−2.52902e8	+	1.46013e8i	−0.282306	+	0.162990i
$965$	7.19823e8	+	4.15590e8i	0.801020	+	0.462469i
$966$	8.39208e7	+	4.84517e7i	0.0930975	+	0.0537499i
$967$	6.58479e7			0.0728220			0.0364110	−	0.999337i	$-0.488407\pi$
$967$	6.58479e7			0.0728220			0.0364110	+	0.999337i	$0.488407\pi$
$968$			4.34276e8i			0.478784i
$969$	−1.24676e8	+	2.15945e8i	−0.137029	+	0.237341i
$970$	1.01969e8	−	1.76615e8i	0.111726	−	0.193514i
$971$	7.33393e8	+	1.27027e9i	0.801086	+	1.38752i	0.918902	+	0.394487i	$0.129078\pi$
$971$	7.33393e8	+	1.27027e9i	0.801086	+	1.38752i	−0.117815	+	0.993036i	$0.537589\pi$
$972$	−9.64406e8	+	5.56800e8i	−1.05017	+	0.606318i
$973$			6.26555e8i			0.680175i
$974$	−1.29868e8	+	7.49794e7i	−0.140548	+	0.0811456i
$975$	−5.98463e8	+	3.45523e8i	−0.645689	+	0.372789i
$976$	7.89135e8	−	4.55608e8i	0.848794	−	0.490051i
$977$	8.04131e8	−	1.39280e9i	0.862270	−	1.49350i	−0.00746261	−	0.999972i	$-0.502375\pi$
$977$	8.04131e8	−	1.39280e9i	0.862270	−	1.49350i	0.869733	−	0.493523i	$-0.164291\pi$
$978$		−	7.45224e8i		−	0.796655i
$979$	−5.27571e8	−	3.04593e8i	−0.562254	−	0.324618i
$980$	−6.35056e8	+	3.66650e8i	−0.674736	+	0.389559i
$981$	−1.30646e9			−1.38385
$982$	−2.14612e6	−	3.71719e6i	−0.00226631	−	0.00392537i
$983$	−5.69005e8	−	3.28515e8i	−0.599039	−	0.345856i	0.169624	−	0.985509i	$-0.445745\pi$
$983$	−5.69005e8	−	3.28515e8i	−0.599039	−	0.345856i	−0.768664	+	0.639653i	$0.779078\pi$
$984$	3.47525e8	−	6.01931e8i	0.364754	−	0.631773i
$985$			1.42067e8i			0.148657i
$986$	−8.83197e7	+	1.52974e8i	−0.0921355	+	0.159583i
$987$	−9.70909e8			−1.00978
$988$		−	4.59462e8i		−	0.476408i
$989$	2.42915e8	−	3.66724e8i	0.251110	−	0.379097i
$990$	2.26213e8			0.233138
$991$		−	3.10136e8i		−	0.318663i	−0.987225	−	0.159332i	$-0.949066\pi$
$991$		−	3.10136e8i		−	0.318663i	0.987225	−	0.159332i	$-0.0509339\pi$
$992$	−2.13340e7	−	1.23172e7i	−0.0218543	−	0.0126176i
$993$	8.33572e8			0.851325
$994$	−1.85149e8	−	1.06896e8i	−0.188522	−	0.108843i
$995$	1.94082e8	−	3.36161e8i	0.197023	−	0.341254i
$996$	9.30403e8	−	5.37169e8i	0.941658	−	0.543667i
$997$			1.44959e9i			1.46271i	0.681996	+	0.731356i	$0.261112\pi$
$997$			1.44959e9i			1.46271i	−0.681996	+	0.731356i	$0.738888\pi$
$998$	7.66204e6	+	1.32710e7i	0.00770820	+	0.0133510i
$999$	−1.90650e8	+	3.30215e8i	−0.191223	+	0.331207i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.7.d.a.37.9	yes	42
43.7	odd	6	inner	43.7.d.a.7.13	✓	42

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.7.d.a.7.13	✓	42	43.7	odd	6	inner
43.7.d.a.37.9	yes	42	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 43 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	43.d (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-2.61500i q^{2} +(-35.7187 - 20.6222i) q^{3} +57.1618 q^{4} +(121.716 + 70.2726i) q^{5} +(-53.9270 + 93.4043i) q^{6} +(140.639 - 81.1978i) q^{7} -316.838i q^{8} +(486.049 + 841.861i) q^{9} +O(q^{10})\)	\(q-2.61500i q^{2} +(-35.7187 - 20.6222i) q^{3} +57.1618 q^{4} +(121.716 + 70.2726i) q^{5} +(-53.9270 + 93.4043i) q^{6} +(140.639 - 81.1978i) q^{7} -316.838i q^{8} +(486.049 + 841.861i) q^{9} +(183.763 - 318.286i) q^{10} +633.170 q^{11} +(-2041.74 - 1178.80i) q^{12} +(-2029.45 - 3515.10i) q^{13} +(-212.332 - 367.770i) q^{14} +(-2898.35 - 5020.09i) q^{15} +2829.82 q^{16} +(-1526.45 - 2643.88i) q^{17} +(2201.47 - 1271.02i) q^{18} +(1715.01 + 990.163i) q^{19} +(6957.49 + 4016.91i) q^{20} -6697.91 q^{21} -1655.74i q^{22} +(2766.29 - 4791.36i) q^{23} +(-6533.89 + 11317.0i) q^{24} +(2063.98 + 3574.91i) q^{25} +(-9191.99 + 5307.00i) q^{26} -10026.4i q^{27} +(8039.16 - 4641.41i) q^{28} +(19161.8 - 11063.0i) q^{29} +(-13127.5 + 7579.18i) q^{30} +(445.023 - 770.802i) q^{31} -27677.6i q^{32} +(-22616.0 - 13057.4i) q^{33} +(-6913.75 + 3991.66i) q^{34} +22823.9 q^{35} +(27783.4 + 48122.3i) q^{36} +(-32934.5 - 19014.7i) q^{37} +(2589.27 - 4484.75i) q^{38} +167406. i q^{39} +(22265.0 - 38564.2i) q^{40} -53188.1 q^{41} +17515.0i q^{42} +(79357.0 + 4881.64i) q^{43} +36193.2 q^{44} +136624. i q^{45} +(-12529.4 - 7233.86i) q^{46} +144957. q^{47} +(-101078. - 58357.1i) q^{48} +(-45638.3 + 79047.9i) q^{49} +(9348.39 - 5397.29i) q^{50} +125915. i q^{51} +(-116007. - 200930. i) q^{52} +(12646.2 - 21903.9i) q^{53} -26219.0 q^{54} +(77066.8 + 44494.5i) q^{55} +(-25726.6 - 44559.7i) q^{56} +(-40838.6 - 70734.6i) q^{57} +(-28929.9 - 50108.0i) q^{58} -168198. q^{59} +(-165675. - 286957. i) q^{60} +(278864. - 161002. i) q^{61} +(-2015.65 - 1163.73i) q^{62} +(136715. + 78932.2i) q^{63} +108732. q^{64} -570458. i q^{65} +(-34145.0 + 59140.8i) q^{66} +(-220086. + 381199. i) q^{67} +(-87254.4 - 151129. i) q^{68} +(-197617. + 114094. i) q^{69} -59684.5i q^{70} +(435989. - 251718. i) q^{71} +(266734. - 153999. i) q^{72} +(-579548. + 334602. i) q^{73} +(-49723.5 + 86123.7i) q^{74} -170255. i q^{75} +(98033.1 + 56599.5i) q^{76} +(89048.3 - 51412.1i) q^{77} +437768. q^{78} +(484554. + 839272. i) q^{79} +(344434. + 198859. i) q^{80} +(147563. - 255587. i) q^{81} +139087. i q^{82} +(-227845. + 394640. i) q^{83} -382864. q^{84} -429069. i q^{85} +(12765.5 - 207518. i) q^{86} -912577. q^{87} -200612. i q^{88} +(-833221. - 481060. i) q^{89} +357271. q^{90} +(-570837. - 329573. i) q^{91} +(158126. - 273883. i) q^{92} +(-31791.2 + 18354.7i) q^{93} -379063. i q^{94} +(139163. + 241037. i) q^{95} +(-570773. + 988607. i) q^{96} +554894. q^{97} +(206710. + 119344. i) q^{98} +(307752. + 533042. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 42 q - 3 q^{3} - 1194 q^{4} - 3 q^{5} + 111 q^{6} - 147 q^{7} + 3852 q^{9}+O(q^{10}) \) 42 * q - 3 * q^3 - 1194 * q^4 - 3 * q^5 + 111 * q^6 - 147 * q^7 + 3852 * q^9	\( 42 q - 3 q^{3} - 1194 q^{4} - 3 q^{5} + 111 q^{6} - 147 q^{7} + 3852 q^{9} - 981 q^{10} - 4104 q^{11} + 918 q^{12} + 4843 q^{13} + 2814 q^{14} - 163 q^{15} + 36678 q^{16} + 3641 q^{17} - 507 q^{18} - 5229 q^{19} - 1599 q^{20} - 29990 q^{21} + 6575 q^{23} - 4622 q^{24} + 68484 q^{25} + 189 q^{26} + 48948 q^{28} + 95361 q^{29} - 85041 q^{30} - 79373 q^{31} - 79638 q^{33} - 184743 q^{34} - 80582 q^{35} + 59972 q^{36} - 66063 q^{37} - 69820 q^{38} + 189951 q^{40} + 40632 q^{41} - 368728 q^{43} + 130330 q^{44} + 34056 q^{46} - 247820 q^{47} + 326907 q^{48} - 21876 q^{49} - 28638 q^{50} - 617150 q^{52} + 11639 q^{53} + 655904 q^{54} - 43638 q^{55} + 553875 q^{56} - 422859 q^{57} + 587796 q^{58} - 649352 q^{59} + 875455 q^{60} - 52251 q^{61} + 1335249 q^{62} + 93690 q^{63} - 792420 q^{64} + 160395 q^{66} - 173603 q^{67} + 22286 q^{68} + 870417 q^{69} + 1670505 q^{71} - 2068518 q^{72} - 2646201 q^{73} - 1625030 q^{74} - 80622 q^{76} - 486066 q^{77} + 2835040 q^{78} + 1897639 q^{79} - 817059 q^{80} + 2215367 q^{81} + 1584059 q^{83} - 824560 q^{84} - 2333682 q^{86} - 5547198 q^{87} + 2736939 q^{89} + 1092196 q^{90} - 3724131 q^{91} + 470257 q^{92} + 488433 q^{93} - 1289839 q^{95} + 1697650 q^{96} + 5260848 q^{97} + 4722621 q^{98} + 1375834 q^{99}+O(q^{100}) \) 42 * q - 3 * q^3 - 1194 * q^4 - 3 * q^5 + 111 * q^6 - 147 * q^7 + 3852 * q^9 - 981 * q^10 - 4104 * q^11 + 918 * q^12 + 4843 * q^13 + 2814 * q^14 - 163 * q^15 + 36678 * q^16 + 3641 * q^17 - 507 * q^18 - 5229 * q^19 - 1599 * q^20 - 29990 * q^21 + 6575 * q^23 - 4622 * q^24 + 68484 * q^25 + 189 * q^26 + 48948 * q^28 + 95361 * q^29 - 85041 * q^30 - 79373 * q^31 - 79638 * q^33 - 184743 * q^34 - 80582 * q^35 + 59972 * q^36 - 66063 * q^37 - 69820 * q^38 + 189951 * q^40 + 40632 * q^41 - 368728 * q^43 + 130330 * q^44 + 34056 * q^46 - 247820 * q^47 + 326907 * q^48 - 21876 * q^49 - 28638 * q^50 - 617150 * q^52 + 11639 * q^53 + 655904 * q^54 - 43638 * q^55 + 553875 * q^56 - 422859 * q^57 + 587796 * q^58 - 649352 * q^59 + 875455 * q^60 - 52251 * q^61 + 1335249 * q^62 + 93690 * q^63 - 792420 * q^64 + 160395 * q^66 - 173603 * q^67 + 22286 * q^68 + 870417 * q^69 + 1670505 * q^71 - 2068518 * q^72 - 2646201 * q^73 - 1625030 * q^74 - 80622 * q^76 - 486066 * q^77 + 2835040 * q^78 + 1897639 * q^79 - 817059 * q^80 + 2215367 * q^81 + 1584059 * q^83 - 824560 * q^84 - 2333682 * q^86 - 5547198 * q^87 + 2736939 * q^89 + 1092196 * q^90 - 3724131 * q^91 + 470257 * q^92 + 488433 * q^93 - 1289839 * q^95 + 1697650 * q^96 + 5260848 * q^97 + 4722621 * q^98 + 1375834 * q^99

Introduction

L-functions

Modular forms

Varieties

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