LMFDB - Embedded newform 30.8.e.a.17.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [30,8,Mod(17,30)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(30, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1]))

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

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

chi := DirichletCharacter("30.17");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 30 = 2 \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	30.e (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$9.37155076452$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			17.12
Character	$\chi$	$=$	30.17
Dual form			30.8.e.a.23.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(5.65685 - 5.65685i) q^{2} +(0.750092 + 46.7594i) q^{3} -64.0000i q^{4} +(-268.955 + 76.0794i) q^{5} +(268.754 + 260.268i) q^{6} +(-661.697 - 661.697i) q^{7} +(-362.039 - 362.039i) q^{8} +(-2185.87 + 70.1477i) q^{9} +(-1091.07 + 1951.81i) q^{10} -6676.11i q^{11} +(2992.60 - 48.0059i) q^{12} +(-4252.25 + 4252.25i) q^{13} -7486.24 q^{14} +(-3759.17 - 12519.1i) q^{15} -4096.00 q^{16} +(-11523.1 + 11523.1i) q^{17} +(-11968.4 + 12762.0i) q^{18} +56529.5i q^{19} +(4869.08 + 17213.1i) q^{20} +(30444.2 - 31436.8i) q^{21} +(-37765.8 - 37765.8i) q^{22} +(-36833.1 - 36833.1i) q^{23} +(16657.1 - 17200.3i) q^{24} +(66548.8 - 40923.9i) q^{25} +48108.7i q^{26} +(-4919.67 - 102157. i) q^{27} +(-42348.6 + 42348.6i) q^{28} -34373.4 q^{29} +(-92083.8 - 49553.7i) q^{30} +154212. q^{31} +(-23170.5 + 23170.5i) q^{32} +(312171. - 5007.70i) q^{33} +130370. i q^{34} +(228308. + 127625. i) q^{35} +(4489.45 + 139896. i) q^{36} +(86338.1 + 86338.1i) q^{37} +(319779. + 319779. i) q^{38} +(-202022. - 195643. i) q^{39} +(124916. + 69828.5i) q^{40} -520858. i q^{41} +(-5615.37 - 350052. i) q^{42} +(-499651. + 499651. i) q^{43} -427271. q^{44} +(582566. - 185167. i) q^{45} -416719. q^{46} +(-47164.4 + 47164.4i) q^{47} +(-3072.38 - 191526. i) q^{48} +52142.1i q^{49} +(144956. - 607958. i) q^{50} +(-547458. - 530171. i) q^{51} +(272144. + 272144. i) q^{52} +(-315618. - 315618. i) q^{53} +(-605720. - 550060. i) q^{54} +(507915. + 1.79558e6i) q^{55} +479120. i q^{56} +(-2.64328e6 + 42402.3i) q^{57} +(-194445. + 194445. i) q^{58} -1.04851e6 q^{59} +(-801223. + 240587. i) q^{60} -1.20134e6 q^{61} +(872352. - 872352. i) q^{62} +(1.49280e6 + 1.39997e6i) q^{63} +262144. i q^{64} +(820155. - 1.46717e6i) q^{65} +(1.73758e6 - 1.79423e6i) q^{66} +(242323. + 242323. i) q^{67} +(737481. + 737481. i) q^{68} +(1.69466e6 - 1.74992e6i) q^{69} +(2.01346e6 - 569549. i) q^{70} +34141.9i q^{71} +(816767. + 765975. i) q^{72} +(-2.31111e6 + 2.31111e6i) q^{73} +976804. q^{74} +(1.96349e6 + 3.08108e6i) q^{75} +3.61789e6 q^{76} +(-4.41756e6 + 4.41756e6i) q^{77} +(-2.24953e6 + 36085.9i) q^{78} -7.82727e6i q^{79} +(1.10164e6 - 311621. i) q^{80} +(4.77313e6 - 306668. i) q^{81} +(-2.94642e6 - 2.94642e6i) q^{82} +(5.24218e6 + 5.24218e6i) q^{83} +(-2.01196e6 - 1.94843e6i) q^{84} +(2.22254e6 - 3.97588e6i) q^{85} +5.65291e6i q^{86} +(-25783.2 - 1.60728e6i) q^{87} +(-2.41701e6 + 2.41701e6i) q^{88} -5.17995e6 q^{89} +(2.24803e6 - 4.34295e6i) q^{90} +5.62739e6 q^{91} +(-2.35732e6 + 2.35732e6i) q^{92} +(115673. + 7.21083e6i) q^{93} +533605. i q^{94} +(-4.30073e6 - 1.52039e7i) q^{95} +(-1.10082e6 - 1.06606e6i) q^{96} +(114183. + 114183. i) q^{97} +(294960. + 294960. i) q^{98} +(468314. + 1.45931e7i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 52 q^{3} - 928 q^{6} - 1348 q^{7} - 416 q^{10} + 3328 q^{12} - 21840 q^{13} - 37672 q^{15} - 114688 q^{16} + 50624 q^{18} - 142744 q^{21} - 47008 q^{22} + 419744 q^{25} + 212972 q^{27} - 86272 q^{28}+ \cdots + 82948404 q^{97}+O(q^{100}) $ 28 * q - 52 * q^3 - 928 * q^6 - 1348 * q^7 - 416 * q^10 + 3328 * q^12 - 21840 * q^13 - 37672 * q^15 - 114688 * q^16 + 50624 * q^18 - 142744 * q^21 - 47008 * q^22 + 419744 * q^25 + 212972 * q^27 - 86272 * q^28 - 301152 * q^30 - 44936 * q^31 + 1398788 * q^33 + 50432 * q^36 + 608088 * q^37 + 339968 * q^40 - 624032 * q^42 - 1288968 * q^43 - 656648 * q^45 - 1486208 * q^46 + 212992 * q^48 + 4263064 * q^51 + 1397760 * q^52 - 3985428 * q^55 - 9921952 * q^57 - 416480 * q^58 - 365824 * q^60 - 14602248 * q^61 + 4050428 * q^63 + 10106816 * q^66 + 22755248 * q^67 + 551584 * q^70 - 3239936 * q^72 - 522380 * q^73 - 17815892 * q^75 - 4901888 * q^76 + 8835840 * q^78 + 33339556 * q^81 + 22502528 * q^82 + 27842408 * q^85 - 38505100 * q^87 - 3008512 * q^88 - 26143552 * q^90 - 77623680 * q^91 + 70200824 * q^93 + 3801088 * q^96 + 82948404 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/30\mathbb{Z}\right)^\times$.

$n$	$7$	$11$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$

Coefficient data

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

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

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

$2$	5.65685	−	5.65685i	0.500000	−	0.500000i
$2$	5.65685	−	5.65685i	0.500000	−	0.500000i
$3$	0.750092	+	46.7594i	0.0160395	+	0.999871i
$3$	0.750092	+	46.7594i	0.0160395	+	0.999871i
$4$		−	64.0000i		−	0.500000i
$5$	−268.955	+	76.0794i	−0.962244	+	0.272190i
$5$	−268.955	+	76.0794i	−0.962244	+	0.272190i
$6$	268.754	+	260.268i	0.507955	+	0.491916i
$7$	−661.697	−	661.697i	−0.729148	−	0.729148i	0.241302	−	0.970450i	$-0.422426\pi$
$7$	−661.697	−	661.697i	−0.729148	−	0.729148i	−0.970450	+	0.241302i	$0.922426\pi$
$8$	−362.039	−	362.039i	−0.250000	−	0.250000i
$9$	−2185.87	+	70.1477i	−0.999485	+	0.0320748i
$10$	−1091.07	+	1951.81i	−0.345027	+	0.617217i
$11$		−	6676.11i		−	1.51234i	−0.654376	−	0.756170i	$-0.727069\pi$
$11$		−	6676.11i		−	1.51234i	0.654376	−	0.756170i	$-0.272931\pi$
$12$	2992.60	−	48.0059i	0.499936	−	0.00801974i
$13$	−4252.25	+	4252.25i	−0.536805	+	0.536805i	−0.922589	−	0.385784i	$-0.873931\pi$
$13$	−4252.25	+	4252.25i	−0.536805	+	0.536805i	0.385784	+	0.922589i	$0.373931\pi$
$14$	−7486.24			−0.729148
$15$	−3759.17	−	12519.1i	−0.287589	−	0.957754i
$16$	−4096.00			−0.250000
$17$	−11523.1	+	11523.1i	−0.568853	+	0.568853i	−0.931807	−	0.362954i	$-0.881768\pi$
$17$	−11523.1	+	11523.1i	−0.568853	+	0.568853i	0.362954	+	0.931807i	$0.381768\pi$
$18$	−11968.4	+	12762.0i	−0.483705	+	0.515780i
$19$			56529.5i			1.89076i	0.325965	+	0.945382i	$0.394311\pi$
$19$			56529.5i			1.89076i	−0.325965	+	0.945382i	$0.605689\pi$
$20$	4869.08	+	17213.1i	0.136095	+	0.481122i
$21$	30444.2	−	31436.8i	0.717359	−	0.740750i
$22$	−37765.8	−	37765.8i	−0.756170	−	0.756170i
$23$	−36833.1	−	36833.1i	−0.631235	−	0.631235i	0.317143	−	0.948378i	$-0.397277\pi$
$23$	−36833.1	−	36833.1i	−0.631235	−	0.631235i	−0.948378	+	0.317143i	$0.897277\pi$
$24$	16657.1	−	17200.3i	0.245958	−	0.253978i
$25$	66548.8	−	40923.9i	0.851825	−	0.523826i
$26$			48108.7i			0.536805i
$27$	−4919.67	−	102157.i	−0.0481019	−	0.998842i
$28$	−42348.6	+	42348.6i	−0.364574	+	0.364574i
$29$	−34373.4			−0.261715			−0.130858	−	0.991401i	$-0.541773\pi$
$29$	−34373.4			−0.261715			−0.130858	+	0.991401i	$0.541773\pi$
$30$	−92083.8	−	49553.7i	−0.622671	−	0.335082i
$31$	154212.			0.929717			0.464859	−	0.885385i	$-0.346105\pi$
$31$	154212.			0.929717			0.464859	+	0.885385i	$0.346105\pi$
$32$	−23170.5	+	23170.5i	−0.125000	+	0.125000i
$33$	312171.	−	5007.70i	1.51214	−	0.0242571i
$34$			130370.i			0.568853i
$35$	228308.	+	127625.i	0.900085	+	0.503151i
$36$	4489.45	+	139896.i	0.0160374	+	0.499743i
$37$	86338.1	+	86338.1i	0.280218	+	0.280218i	0.833196	−	0.552978i	$-0.186509\pi$
$37$	86338.1	+	86338.1i	0.280218	+	0.280218i	−0.552978	+	0.833196i	$0.686509\pi$
$38$	319779.	+	319779.i	0.945382	+	0.945382i
$39$	−202022.	−	195643.i	−0.545346	−	0.528126i
$40$	124916.	+	69828.5i	0.308608	+	0.172513i
$41$		−	520858.i		−	1.18026i	−0.807310	−	0.590128i	$-0.799077\pi$
$41$		−	520858.i		−	1.18026i	0.807310	−	0.590128i	$-0.200923\pi$
$42$	−5615.37	−	350052.i	−0.0116952	−	0.729054i
$43$	−499651.	+	499651.i	−0.958357	+	0.958357i	−0.999167	−	0.0408103i	$-0.987006\pi$
$43$	−499651.	+	499651.i	−0.958357	+	0.958357i	0.0408103	+	0.999167i	$0.487006\pi$
$44$	−427271.			−0.756170
$45$	582566.	−	185167.i	0.953018	−	0.302914i
$46$	−416719.			−0.631235
$47$	−47164.4	+	47164.4i	−0.0662631	+	0.0662631i	−0.739462	−	0.673199i	$-0.764920\pi$
$47$	−47164.4	+	47164.4i	−0.0662631	+	0.0662631i	0.673199	+	0.739462i	$0.264920\pi$
$48$	−3072.38	−	191526.i	−0.00400987	−	0.249968i
$49$			52142.1i			0.0633144i
$50$	144956.	−	607958.i	0.163999	−	0.687826i
$51$	−547458.	−	530171.i	−0.577904	−	0.559655i
$52$	272144.	+	272144.i	0.268403	+	0.268403i
$53$	−315618.	−	315618.i	−0.291203	−	0.291203i	0.546352	−	0.837555i	$-0.316016\pi$
$53$	−315618.	−	315618.i	−0.291203	−	0.291203i	−0.837555	+	0.546352i	$0.816016\pi$
$54$	−605720.	−	550060.i	−0.523472	−	0.475370i
$55$	507915.	+	1.79558e6i	0.411644	+	1.45524i
$56$			479120.i			0.364574i
$57$	−2.64328e6	+	42402.3i	−1.89052	+	0.0303269i
$58$	−194445.	+	194445.i	−0.130858	+	0.130858i
$59$	−1.04851e6			−0.664648			−0.332324	−	0.943165i	$-0.607833\pi$
$59$	−1.04851e6			−0.664648			−0.332324	+	0.943165i	$0.607833\pi$
$60$	−801223.	+	240587.i	−0.478877	+	0.143794i
$61$	−1.20134e6			−0.677658			−0.338829	−	0.940848i	$-0.610031\pi$
$61$	−1.20134e6			−0.677658			−0.338829	+	0.940848i	$0.610031\pi$
$62$	872352.	−	872352.i	0.464859	−	0.464859i
$63$	1.49280e6	+	1.39997e6i	0.752160	+	0.705386i
$64$			262144.i			0.125000i
$65$	820155.	−	1.46717e6i	0.370424	−	0.662650i
$66$	1.73758e6	−	1.79423e6i	0.743944	−	0.768201i
$67$	242323.	+	242323.i	0.0984314	+	0.0984314i	0.754608	−	0.656176i	$-0.227827\pi$
$67$	242323.	+	242323.i	0.0984314	+	0.0984314i	−0.656176	+	0.754608i	$0.727827\pi$
$68$	737481.	+	737481.i	0.284426	+	0.284426i
$69$	1.69466e6	−	1.74992e6i	0.621029	−	0.641279i
$70$	2.01346e6	−	569549.i	0.701618	−	0.198467i
$71$			34141.9i			0.0113210i	0.999984	+	0.00566048i	$0.00180180\pi$
$71$			34141.9i			0.0113210i	−0.999984	+	0.00566048i	$0.998198\pi$
$72$	816767.	+	765975.i	0.257890	+	0.241853i
$73$	−2.31111e6	+	2.31111e6i	−0.695330	+	0.695330i	−0.963399	−	0.268070i	$-0.913614\pi$
$73$	−2.31111e6	+	2.31111e6i	−0.695330	+	0.695330i	0.268070	+	0.963399i	$0.413614\pi$
$74$	976804.			0.280218
$75$	1.96349e6	+	3.08108e6i	0.537422	+	0.843314i
$76$	3.61789e6			0.945382
$77$	−4.41756e6	+	4.41756e6i	−1.10272	+	1.10272i
$78$	−2.24953e6	+	36085.9i	−0.536736	+	0.00861008i
$79$		−	7.82727e6i		−	1.78614i	−0.449917	−	0.893070i	$-0.648546\pi$
$79$		−	7.82727e6i		−	1.78614i	0.449917	−	0.893070i	$-0.351454\pi$
$80$	1.10164e6	−	311621.i	0.240561	−	0.0680475i
$81$	4.77313e6	−	306668.i	0.997942	−	0.0641167i
$82$	−2.94642e6	−	2.94642e6i	−0.590128	−	0.590128i
$83$	5.24218e6	+	5.24218e6i	1.00633	+	1.00633i	0.999980	+	0.00634664i	$0.00202021\pi$
$83$	5.24218e6	+	5.24218e6i	1.00633	+	1.00633i	0.00634664	+	0.999980i	$0.497980\pi$
$84$	−2.01196e6	−	1.94843e6i	−0.370375	−	0.358680i
$85$	2.22254e6	−	3.97588e6i	0.392539	−	0.702211i
$86$			5.65291e6i			0.958357i
$87$	−25783.2	−	1.60728e6i	−0.00419778	−	0.261682i
$88$	−2.41701e6	+	2.41701e6i	−0.378085	+	0.378085i
$89$	−5.17995e6			−0.778862			−0.389431	−	0.921056i	$-0.627328\pi$
$89$	−5.17995e6			−0.778862			−0.389431	+	0.921056i	$0.627328\pi$
$90$	2.24803e6	−	4.34295e6i	0.325052	−	0.627966i
$91$	5.62739e6			0.782821
$92$	−2.35732e6	+	2.35732e6i	−0.315618	+	0.315618i
$93$	115673.	+	7.21083e6i	0.0149122	+	0.929598i
$94$			533605.i			0.0662631i
$95$	−4.30073e6	−	1.52039e7i	−0.514647	−	1.81938i
$96$	−1.10082e6	−	1.06606e6i	−0.126989	−	0.122979i
$97$	114183.	+	114183.i	0.0127028	+	0.0127028i	0.713430	−	0.700727i	$-0.247141\pi$
$97$	114183.	+	114183.i	0.0127028	+	0.0127028i	−0.700727	+	0.713430i	$0.747141\pi$
$98$	294960.	+	294960.i	0.0316572	+	0.0316572i
$99$	468314.	+	1.45931e7i	0.0485080	+	1.51156i
$100$	−2.61913e6	−	4.25913e6i	−0.261913	−	0.425913i
$101$		−	1.20718e7i		−	1.16586i	−0.812522	−	0.582931i	$-0.801906\pi$
$101$		−	1.20718e7i		−	1.16586i	0.812522	−	0.582931i	$-0.198094\pi$
$102$	−6.09599e6	+	97789.2i	−0.568780	+	0.00912410i
$103$	−6.07066e6	+	6.07066e6i	−0.547401	+	0.547401i	−0.925688	−	0.378287i	$-0.876513\pi$
$103$	−6.07066e6	+	6.07066e6i	−0.547401	+	0.547401i	0.378287	+	0.925688i	$0.376513\pi$
$104$	3.07896e6			0.268403
$105$	−5.79642e6	+	1.07713e7i	−0.488650	+	0.908040i
$106$	−3.57081e6			−0.291203
$107$	2.24222e6	−	2.24222e6i	0.176943	−	0.176943i	−0.613079	−	0.790022i	$-0.710069\pi$
$107$	2.24222e6	−	2.24222e6i	0.176943	−	0.176943i	0.790022	+	0.613079i	$0.210069\pi$
$108$	−6.53808e6	+	314859.i	−0.499421	+	0.0240510i
$109$		−	2.08031e7i		−	1.53863i	−0.638869	−	0.769316i	$-0.720597\pi$
$109$		−	2.08031e7i		−	1.53863i	0.638869	−	0.769316i	$-0.279403\pi$
$110$	1.30305e7	+	7.28411e6i	0.933441	+	0.521797i
$111$	−3.97235e6	+	4.10187e6i	−0.275688	+	0.284677i
$112$	2.71031e6	+	2.71031e6i	0.182287	+	0.182287i
$113$	−1.18546e7	−	1.18546e7i	−0.772882	−	0.772882i	0.205727	−	0.978609i	$-0.434044\pi$
$113$	−1.18546e7	−	1.18546e7i	−0.772882	−	0.772882i	−0.978609	+	0.205727i	$0.934044\pi$
$114$	−1.47128e7	+	1.51925e7i	−0.930097	+	0.960424i
$115$	1.27087e7	+	7.10422e6i	0.779218	+	0.435586i
$116$			2.19990e6i			0.130858i
$117$	8.99659e6	−	9.59316e6i	0.519311	−	0.553747i
$118$	−5.93128e6	+	5.93128e6i	−0.332324	+	0.332324i
$119$	1.52497e7			0.829556
$120$	−3.17144e6	+	5.89336e6i	−0.167541	+	0.311336i
$121$	−2.50833e7			−1.28717
$122$	−6.79579e6	+	6.79579e6i	−0.338829	+	0.338829i
$123$	2.43550e7	−	390692.i	1.18010	−	0.0189307i
$124$		−	9.86954e6i		−	0.464859i
$125$	−1.47852e7	+	1.60697e7i	−0.677083	+	0.735907i
$126$	1.63640e7	−	525143.i	0.728773	−	0.0233873i
$127$	8.44428e6	+	8.44428e6i	0.365805	+	0.365805i	0.865945	−	0.500140i	$-0.166718\pi$
$127$	8.44428e6	+	8.44428e6i	0.365805	+	0.365805i	−0.500140	+	0.865945i	$0.666718\pi$
$128$	1.48291e6	+	1.48291e6i	0.0625000	+	0.0625000i
$129$	−2.37381e7	−	2.29886e7i	−0.973605	−	0.942862i
$130$	−3.66008e6	−	1.29391e7i	−0.146113	−	0.516537i
$131$		−	1.45441e7i		−	0.565244i	−0.959231	−	0.282622i	$-0.908796\pi$
$131$		−	1.45441e7i		−	0.565244i	0.959231	−	0.282622i	$-0.0912042\pi$
$132$	−320493.	−	1.99789e7i	−0.0121286	−	0.756072i
$133$	3.74054e7	−	3.74054e7i	1.37865	−	1.37865i
$134$	2.74158e6			0.0984314
$135$	9.09525e6	+	2.71015e7i	0.318161	+	0.948037i
$136$	8.34365e6			0.284426
$137$	−5.62961e6	+	5.62961e6i	−0.187049	+	0.187049i	−0.794419	−	0.607370i	$-0.792225\pi$
$137$	−5.62961e6	+	5.62961e6i	−0.187049	+	0.187049i	0.607370	+	0.794419i	$0.292225\pi$
$138$	−312578.	−	1.94855e7i	−0.0101247	−	0.631154i
$139$			4.74278e7i			1.49789i	0.662630	+	0.748947i	$0.269440\pi$
$139$			4.74278e7i			1.49789i	−0.662630	+	0.748947i	$0.730560\pi$
$140$	8.16802e6	−	1.46117e7i	0.251576	−	0.450043i
$141$	−2.24076e6	−	2.17000e6i	−0.0673174	−	0.0651918i
$142$	193136.	+	193136.i	0.00566048	+	0.00566048i
$143$	2.83885e7	+	2.83885e7i	0.811831	+	0.811831i
$144$	8.95334e6	−	287325.i	0.249871	−	0.00801871i
$145$	9.24490e6	−	2.61511e6i	0.251834	−	0.0712363i
$146$			2.61472e7i			0.695330i
$147$	−2.43813e6	+	39111.4i	−0.0633062	+	0.00101553i
$148$	5.52564e6	−	5.52564e6i	0.140109	−	0.140109i
$149$	4.33349e7			1.07321			0.536607	−	0.843832i	$-0.319706\pi$
$149$	4.33349e7			1.07321			0.536607	+	0.843832i	$0.319706\pi$
$150$	2.85364e7	+	6.32204e6i	0.690368	+	0.152946i
$151$	−6.29581e7			−1.48810			−0.744050	−	0.668124i	$-0.767098\pi$
$151$	−6.29581e7			−1.48810			−0.744050	+	0.668124i	$0.767098\pi$
$152$	2.04659e7	−	2.04659e7i	0.472691	−	0.472691i
$153$	2.43798e7	−	2.59965e7i	0.550314	−	0.586806i
$154$			4.99790e7i			1.10272i
$155$	−4.14760e7	+	1.17323e7i	−0.894615	+	0.253060i
$156$	−1.25211e7	+	1.29294e7i	−0.264063	+	0.272673i
$157$	2.02698e7	+	2.02698e7i	0.418024	+	0.418024i	0.884522	−	0.466498i	$-0.154485\pi$
$157$	2.02698e7	+	2.02698e7i	0.418024	+	0.418024i	−0.466498	+	0.884522i	$0.654485\pi$
$158$	−4.42777e7	−	4.42777e7i	−0.893070	−	0.893070i
$159$	1.45213e7	−	1.49948e7i	0.286495	−	0.295836i
$160$	4.46902e6	−	7.99462e6i	0.0862567	−	0.154304i
$161$			4.87447e7i			0.920528i
$162$	2.52661e7	−	2.87357e7i	0.466913	−	0.531030i
$163$	−3.74541e7	+	3.74541e7i	−0.677396	+	0.677396i	−0.959410	−	0.282014i	$-0.908997\pi$
$163$	−3.74541e7	+	3.74541e7i	−0.677396	+	0.677396i	0.282014	+	0.959410i	$0.408997\pi$
$164$	−3.33349e7			−0.590128
$165$	−8.35790e7	+	2.50966e7i	−1.44845	+	0.434932i
$166$	5.93085e7			1.00633
$167$	−2.57050e7	+	2.57050e7i	−0.427081	+	0.427081i	−0.887633	−	0.460552i	$-0.847652\pi$
$167$	−2.57050e7	+	2.57050e7i	−0.427081	+	0.427081i	0.460552	+	0.887633i	$0.347652\pi$
$168$	−2.24033e7	+	359384.i	−0.364527	+	0.00584758i
$169$			2.65853e7i			0.423680i
$170$	−9.91844e6	−	3.50636e7i	−0.154836	−	0.547375i
$171$	−3.96541e6	−	1.23566e8i	−0.0606459	−	1.88979i
$172$	3.19777e7	+	3.19777e7i	0.479178	+	0.479178i
$173$	−8.41199e7	−	8.41199e7i	−1.23520	−	1.23520i	−0.961940	−	0.273261i	$-0.911898\pi$
$173$	−8.41199e7	−	8.41199e7i	−1.23520	−	1.23520i	−0.273261	−	0.961940i	$-0.588102\pi$
$174$	−9.23798e6	−	8.94628e6i	−0.132940	−	0.128742i
$175$	−7.11144e7	−	1.69559e7i	−1.00305	−	0.239160i
$176$			2.73454e7i			0.378085i
$177$	−786481.	−	4.90278e7i	−0.0106606	−	0.664563i
$178$	−2.93022e7	+	2.93022e7i	−0.389431	+	0.389431i
$179$	8.83756e7			1.15172			0.575860	−	0.817548i	$-0.304667\pi$
$179$	8.83756e7			1.15172			0.575860	+	0.817548i	$0.304667\pi$
$180$	−1.18507e7	−	3.72842e7i	−0.151457	−	0.476509i
$181$	−2.85699e7			−0.358124			−0.179062	−	0.983838i	$-0.557306\pi$
$181$	−2.85699e7			−0.358124			−0.179062	+	0.983838i	$0.557306\pi$
$182$	3.18334e7	−	3.18334e7i	0.391411	−	0.391411i
$183$	−901114.	−	5.61738e7i	−0.0108693	−	0.677571i
$184$			2.66700e7i			0.315618i
$185$	−2.97896e7	−	1.66525e7i	−0.345911	−	0.193366i
$186$	4.14450e7	+	4.01363e7i	0.472255	+	0.457343i
$187$	7.69298e7	+	7.69298e7i	0.860298	+	0.860298i
$188$	3.01852e6	+	3.01852e6i	0.0331316	+	0.0331316i
$189$	−6.43419e7	+	7.08526e7i	−0.693231	+	0.763378i
$190$	−1.10335e8	−	6.16776e7i	−1.16701	−	0.652364i
$191$			8.58776e7i			0.891791i	0.895085	+	0.445896i	$0.147115\pi$
$191$			8.58776e7i			0.891791i	−0.895085	+	0.445896i	$0.852885\pi$
$192$	−1.22577e7	+	196632.i	−0.124984	+	0.00200494i
$193$	3.39490e7	−	3.39490e7i	0.339920	−	0.339920i	−0.516417	−	0.856337i	$-0.672735\pi$
$193$	3.39490e7	−	3.39490e7i	0.339920	−	0.339920i	0.856337	+	0.516417i	$0.172735\pi$
$194$	1.29183e6			0.0127028
$195$	6.92192e7	+	3.72494e7i	0.668506	+	0.359748i
$196$	3.33710e6			0.0316572
$197$	−2.12932e7	+	2.12932e7i	−0.198431	+	0.198431i	−0.799327	−	0.600896i	$-0.794810\pi$
$197$	−2.12932e7	+	2.12932e7i	−0.198431	+	0.198431i	0.600896	+	0.799327i	$0.294810\pi$
$198$	8.52005e7	+	7.99021e7i	0.780035	+	0.731526i
$199$		−	1.09790e8i		−	0.987594i	−0.869577	−	0.493797i	$-0.835609\pi$
$199$		−	1.09790e8i		−	0.987594i	0.869577	−	0.493797i	$-0.164391\pi$
$200$	−3.89093e7	−	9.27721e6i	−0.343913	−	0.0819997i
$201$	−1.11491e7	+	1.15127e7i	−0.0968399	+	0.0999975i
$202$	−6.82884e7	−	6.82884e7i	−0.582931	−	0.582931i
$203$	2.27447e7	+	2.27447e7i	0.190829	+	0.190829i
$204$	−3.39310e7	+	3.50373e7i	−0.279828	+	0.288952i
$205$	3.96266e7	+	1.40088e8i	0.321254	+	1.13569i
$206$			6.86816e7i			0.547401i
$207$	8.30963e7	+	7.79288e7i	0.651157	+	0.610663i
$208$	1.74172e7	−	1.74172e7i	0.134201	−	0.134201i
$209$	3.77397e8			2.85948
$210$	2.81420e7	+	9.37211e7i	0.209695	+	0.698345i
$211$	1.88528e8			1.38161			0.690807	−	0.723039i	$-0.257255\pi$
$211$	1.88528e8			1.38161			0.690807	+	0.723039i	$0.257255\pi$
$212$	−2.01995e7	+	2.01995e7i	−0.145601	+	0.145601i
$213$	−1.59645e6	+	25609.6i	−0.0113195	+	0.000181582i
$214$		−	2.53678e7i		−	0.176943i
$215$	9.63706e7	−	1.72397e8i	0.661317	−	1.18303i
$216$	−3.52038e7	+	3.87661e7i	−0.237685	+	0.261736i
$217$	−1.02041e8	−	1.02041e8i	−0.677902	−	0.677902i
$218$	−1.17680e8	−	1.17680e8i	−0.769316	−	0.769316i
$219$	−1.09800e8	−	1.06332e8i	−0.706393	−	0.684087i
$220$	1.14917e8	−	3.25065e7i	0.727619	−	0.205822i
$221$		−	9.79985e7i		−	0.610726i
$222$	732693.	+	4.56747e7i	0.00449456	+	0.280182i
$223$	1.69582e8	−	1.69582e8i	1.02403	−	1.02403i	0.0243277	−	0.999704i	$-0.492255\pi$
$223$	1.69582e8	−	1.69582e8i	1.02403	−	1.02403i	0.999704	−	0.0243277i	$-0.00774452\pi$
$224$	3.06637e7			0.182287
$225$	−1.42597e8	+	9.41228e7i	−0.834585	+	0.550879i
$226$	−1.34120e8			−0.772882
$227$	−1.85495e8	+	1.85495e8i	−1.05255	+	1.05255i	−0.0540048	+	0.998541i	$0.517199\pi$
$227$	−1.85495e8	+	1.85495e8i	−1.05255	+	1.05255i	−0.998541	+	0.0540048i	$0.982801\pi$
$228$	2.71375e6	+	1.69170e8i	0.0151634	+	0.945260i
$229$		−	1.00981e8i		−	0.555670i	−0.960629	−	0.277835i	$-0.910383\pi$
$229$		−	1.00981e8i		−	0.555670i	0.960629	−	0.277835i	$-0.0896169\pi$
$230$	1.12079e8	−	3.17038e7i	0.607402	−	0.171816i
$231$	−2.09876e8	−	2.03249e8i	−1.12026	−	1.08489i
$232$	1.24445e7	+	1.24445e7i	0.0654288	+	0.0654288i
$233$	7.25267e7	+	7.25267e7i	0.375623	+	0.375623i	0.869520	−	0.493897i	$-0.164428\pi$
$233$	7.25267e7	+	7.25267e7i	0.375623	+	0.375623i	−0.493897	+	0.869520i	$0.664428\pi$
$234$	−3.37471e6	−	1.05160e8i	−0.0172179	−	0.536529i
$235$	9.09688e6	−	1.62734e7i	0.0457251	−	0.0817975i
$236$			6.71048e7i			0.332324i
$237$	3.65998e8	−	5.87118e6i	1.78591	−	0.0286488i
$238$	8.62651e7	−	8.62651e7i	0.414778	−	0.414778i
$239$	−3.76628e8			−1.78452			−0.892258	−	0.451526i	$-0.850880\pi$
$239$	−3.76628e8			−1.78452			−0.892258	+	0.451526i	$0.850880\pi$
$240$	1.53975e7	+	5.12783e7i	0.0718972	+	0.239438i
$241$	−6.94841e7			−0.319761			−0.159881	−	0.987136i	$-0.551111\pi$
$241$	−6.94841e7			−0.319761			−0.159881	+	0.987136i	$0.551111\pi$
$242$	−1.41893e8	+	1.41893e8i	−0.643585	+	0.643585i
$243$	1.79199e7	+	2.22958e8i	0.0801149	+	0.996786i
$244$			7.68856e7i			0.338829i
$245$	−3.96694e6	−	1.40239e7i	−0.0172335	−	0.0609239i
$246$	1.35563e8	−	1.39983e8i	0.580587	−	0.599517i
$247$	−2.40377e8	−	2.40377e8i	−1.01497	−	1.01497i
$248$	−5.58305e7	−	5.58305e7i	−0.232429	−	0.232429i
$249$	−2.41189e8	+	2.49053e8i	−0.990056	+	1.02234i
$250$	7.26630e6	+	1.74542e8i	0.0294119	+	0.706495i
$251$			1.90916e8i			0.762052i	0.924564	+	0.381026i	$0.124429\pi$
$251$			1.90916e8i			0.762052i	−0.924564	+	0.381026i	$0.875571\pi$
$252$	8.95981e7	−	9.55394e7i	0.352693	−	0.376080i
$253$	−2.45902e8	+	2.45902e8i	−0.954641	+	0.954641i
$254$	9.55361e7			0.365805
$255$	1.87577e8	+	1.00942e8i	0.708417	+	0.381225i
$256$	1.67772e7			0.0625000
$257$	1.16268e8	−	1.16268e8i	0.427264	−	0.427264i	−0.460432	−	0.887695i	$-0.652305\pi$
$257$	1.16268e8	−	1.16268e8i	0.427264	−	0.427264i	0.887695	+	0.460432i	$0.152305\pi$
$258$	−2.64326e8	+	4.24020e6i	−0.958233	+	0.0153715i
$259$		−	1.14259e8i		−	0.408641i
$260$	−9.38990e7	−	5.24899e7i	−0.331325	−	0.185212i
$261$	7.51359e7	−	2.41121e6i	0.261581	−	0.00839448i
$262$	−8.22736e7	−	8.22736e7i	−0.282622	−	0.282622i
$263$	2.94044e7	+	2.94044e7i	0.0996705	+	0.0996705i	0.755184	−	0.655513i	$-0.227548\pi$
$263$	2.94044e7	+	2.94044e7i	0.0996705	+	0.0996705i	−0.655513	+	0.755184i	$0.727548\pi$
$264$	−1.14831e8	−	1.11205e8i	−0.384100	−	0.371972i
$265$	1.08899e8	+	6.08750e7i	0.359471	+	0.200946i
$266$		−	4.23193e8i		−	1.37865i
$267$	−3.88544e6	−	2.42211e8i	−0.0124925	−	0.778762i
$268$	1.55087e7	−	1.55087e7i	0.0492157	−	0.0492157i
$269$	9.05736e6			0.0283706			0.0141853	−	0.999899i	$-0.495485\pi$
$269$	9.05736e6			0.0283706			0.0141853	+	0.999899i	$0.495485\pi$
$270$	2.04760e8	+	1.01859e8i	0.633099	+	0.314938i
$271$	3.20432e7			0.0978010			0.0489005	−	0.998804i	$-0.484428\pi$
$271$	3.20432e7			0.0978010			0.0489005	+	0.998804i	$0.484428\pi$
$272$	4.71988e7	−	4.71988e7i	0.142213	−	0.142213i
$273$	4.22107e6	+	2.63133e8i	0.0125560	+	0.782720i
$274$			6.36917e7i			0.187049i
$275$	−2.73213e8	−	4.44287e8i	−0.792203	−	1.28825i
$276$	−1.11995e8	−	1.08459e8i	−0.320639	−	0.310515i
$277$	−4.31831e6	−	4.31831e6i	−0.0122077	−	0.0122077i	0.700977	−	0.713184i	$-0.252748\pi$
$277$	−4.31831e6	−	4.31831e6i	−0.0122077	−	0.0122077i	−0.713184	+	0.700977i	$0.752748\pi$
$278$	2.68292e8	+	2.68292e8i	0.748947	+	0.748947i
$279$	−3.37087e8	+	1.08176e7i	−0.929239	+	0.0298205i
$280$	−3.64511e7	−	1.28862e8i	−0.0992335	−	0.350809i
$281$			2.39886e8i			0.644960i	0.946576	+	0.322480i	$0.104516\pi$
$281$			2.39886e8i			0.644960i	−0.946576	+	0.322480i	$0.895484\pi$
$282$	−2.49510e7	+	400253.i	−0.0662546	+	0.00106283i
$283$	−3.38724e8	+	3.38724e8i	−0.888370	+	0.888370i	−0.994366	−	0.105997i	$-0.966197\pi$
$283$	−3.38724e8	+	3.38724e8i	−0.888370	+	0.888370i	0.105997	+	0.994366i	$0.466197\pi$
$284$	2.18508e6			0.00566048
$285$	7.07698e8	−	2.12504e8i	1.81089	−	0.543763i
$286$	3.21179e8			0.811831
$287$	−3.44650e8	+	3.44650e8i	−0.860581	+	0.860581i
$288$	4.90224e7	−	5.22731e7i	0.120926	−	0.128945i
$289$			1.44773e8i			0.352813i
$290$	3.75038e7	−	6.70903e7i	0.0902988	−	0.161535i
$291$	−5.25347e6	+	5.42476e6i	−0.0124974	+	0.0129049i
$292$	1.47911e8	+	1.47911e8i	0.347665	+	0.347665i
$293$	1.40487e8	+	1.40487e8i	0.326286	+	0.326286i	0.851172	−	0.524886i	$-0.175892\pi$
$293$	1.40487e8	+	1.40487e8i	0.326286	+	0.326286i	−0.524886	+	0.851172i	$0.675892\pi$
$294$	−1.35709e7	+	1.40134e7i	−0.0311454	+	0.0321609i
$295$	2.82003e8	−	7.97703e7i	0.639553	−	0.180911i
$296$		−	6.25155e7i		−	0.140109i
$297$	−6.82015e8	+	3.28442e7i	−1.51059	+	0.0727464i
$298$	2.45139e8	−	2.45139e8i	0.536607	−	0.536607i
$299$	3.13247e8			0.677700
$300$	1.97189e8	−	1.25664e8i	0.421657	−	0.268711i
$301$	6.61235e8			1.39757
$302$	−3.56145e8	+	3.56145e8i	−0.744050	+	0.744050i
$303$	5.64469e8	−	9.05496e6i	1.16571	−	0.0186998i
$304$		−	2.31545e8i		−	0.472691i
$305$	3.23106e8	−	9.13971e7i	0.652072	−	0.184452i
$306$	−9.14512e6	−	2.84971e8i	−0.0182459	−	0.568560i
$307$	−4.65228e8	−	4.65228e8i	−0.917660	−	0.917660i	0.0791992	−	0.996859i	$-0.474764\pi$
$307$	−4.65228e8	−	4.65228e8i	−0.917660	−	0.917660i	−0.996859	+	0.0791992i	$0.974764\pi$
$308$	2.82724e8	+	2.82724e8i	0.551360	+	0.551360i
$309$	−2.88414e8	−	2.79306e8i	−0.556110	−	0.538550i
$310$	−1.68256e8	+	3.00992e8i	−0.320777	+	0.573837i
$311$			3.33690e8i			0.629046i	0.949250	+	0.314523i	$0.101845\pi$
$311$			3.33690e8i			0.629046i	−0.949250	+	0.314523i	$0.898155\pi$
$312$	2.30950e6	+	1.43970e8i	0.00430504	+	0.268368i
$313$	−1.68738e8	+	1.68738e8i	−0.311034	+	0.311034i	−0.845310	−	0.534276i	$-0.820584\pi$
$313$	−1.68738e8	+	1.68738e8i	−0.311034	+	0.311034i	0.534276	+	0.845310i	$0.320584\pi$
$314$	2.29327e8			0.418024
$315$	−5.08006e8	−	2.62958e8i	−0.915760	−	0.474022i
$316$	−5.00946e8			−0.893070
$317$	5.32238e8	−	5.32238e8i	0.938423	−	0.938423i	−0.0597877	−	0.998211i	$-0.519042\pi$
$317$	5.32238e8	−	5.32238e8i	0.938423	−	0.938423i	0.998211	+	0.0597877i	$0.0190424\pi$
$318$	−2.67843e6	−	1.66969e8i	−0.00467074	−	0.291166i
$319$			2.29480e8i			0.395802i
$320$	−1.99438e7	−	7.05050e7i	−0.0340238	−	0.120280i
$321$	1.06527e8	+	1.03163e8i	0.179759	+	0.174083i
$322$	2.75742e8	+	2.75742e8i	0.460264	+	0.460264i
$323$	−6.51397e8	−	6.51397e8i	−1.07557	−	1.07557i
$324$	−1.96268e7	−	3.05480e8i	−0.0320583	−	0.498971i
$325$	−1.08963e8	+	4.57001e8i	−0.176071	+	0.738457i
$326$			4.23744e8i			0.677396i
$327$	9.72738e8	−	1.56042e7i	1.53843	−	0.0246788i
$328$	−1.88571e8	+	1.88571e8i	−0.295064	+	0.295064i
$329$	6.24171e7			0.0966313
$330$	−3.30826e8	+	6.14762e8i	−0.506758	+	0.941690i
$331$	8.98588e8			1.36195			0.680977	−	0.732305i	$-0.261555\pi$
$331$	8.98588e8			1.36195			0.680977	+	0.732305i	$0.261555\pi$
$332$	3.35500e8	−	3.35500e8i	0.503163	−	0.503163i
$333$	−1.94781e8	−	1.82668e8i	−0.289062	−	0.271086i
$334$			2.90819e8i			0.427081i
$335$	−8.36100e7	−	4.67383e7i	−0.121507	−	0.0679229i
$336$	−1.24699e8	+	1.28765e8i	−0.179340	+	0.185187i
$337$	4.32152e8	+	4.32152e8i	0.615081	+	0.615081i	0.944266	−	0.329185i	$-0.106774\pi$
$337$	4.32152e8	+	4.32152e8i	0.615081	+	0.615081i	−0.329185	+	0.944266i	$0.606774\pi$
$338$	1.50389e8	+	1.50389e8i	0.211840	+	0.211840i
$339$	5.45422e8	−	5.63207e8i	0.760386	−	0.785179i
$340$	−2.54457e8	−	1.42242e8i	−0.351105	−	0.196269i
$341$		−	1.02953e9i		−	1.40605i
$342$	−7.21428e8	−	6.76565e8i	−0.975218	−	0.914572i
$343$	−5.10433e8	+	5.10433e8i	−0.682983	+	0.682983i
$344$	3.61786e8			0.479178
$345$	−3.22656e8	+	5.99580e8i	−0.423032	+	0.786104i
$346$	−9.51708e8			−1.23520
$347$	−7.18768e8	+	7.18768e8i	−0.923497	+	0.923497i	−0.997275	−	0.0737780i	$-0.976494\pi$
$347$	−7.18768e8	+	7.18768e8i	−0.923497	+	0.923497i	0.0737780	+	0.997275i	$0.476494\pi$
$348$	−1.02866e8	+	1.65012e6i	−0.130841	+	0.00209889i
$349$			3.24847e8i			0.409063i	0.978860	+	0.204531i	$0.0655670\pi$
$349$			3.24847e8i			0.409063i	−0.978860	+	0.204531i	$0.934433\pi$
$350$	−4.98201e8	+	3.06366e8i	−0.621107	+	0.381947i
$351$	4.55318e8	+	4.13479e8i	0.562005	+	0.510362i
$352$	1.54689e8	+	1.54689e8i	0.189042	+	0.189042i
$353$	−8.23396e8	−	8.23396e8i	−0.996316	−	0.996316i	0.00367700	−	0.999993i	$-0.498830\pi$
$353$	−8.23396e8	−	8.23396e8i	−0.996316	−	0.996316i	−0.999993	+	0.00367700i	$0.998830\pi$
$354$	−2.81792e8	−	2.72894e8i	−0.337612	−	0.326951i
$355$	−2.59750e6	−	9.18264e6i	−0.00308145	−	0.0108935i
$356$			3.31517e8i			0.389431i
$357$	1.14386e7	+	7.13064e8i	0.0133056	+	0.829449i
$358$	4.99928e8	−	4.99928e8i	0.575860	−	0.575860i
$359$	−2.51163e8			−0.286500			−0.143250	−	0.989687i	$-0.545755\pi$
$359$	−2.51163e8			−0.286500			−0.143250	+	0.989687i	$0.545755\pi$
$360$	−2.77949e8	−	1.43874e8i	−0.313983	−	0.162526i
$361$	−2.30171e9			−2.57499
$362$	−1.61616e8	+	1.61616e8i	−0.179062	+	0.179062i
$363$	−1.88148e7	−	1.17288e9i	−0.0206455	−	1.28700i
$364$		−	3.60153e8i		−	0.391411i
$365$	4.45757e8	−	7.97413e8i	0.479815	−	0.858338i
$366$	−3.22864e8	−	3.12669e8i	−0.344220	−	0.333351i
$367$	5.77098e8	+	5.77098e8i	0.609423	+	0.609423i	0.942795	−	0.333373i	$-0.108187\pi$
$367$	5.77098e8	+	5.77098e8i	0.609423	+	0.609423i	−0.333373	+	0.942795i	$0.608187\pi$
$368$	1.50868e8	+	1.50868e8i	0.157809	+	0.157809i
$369$	3.65370e7	+	1.13853e9i	0.0378565	+	1.17965i
$370$	−2.62717e8	+	7.43147e7i	−0.269638	+	0.0762726i
$371$			4.17686e8i			0.424660i
$372$	4.61493e8	−	7.40307e6i	0.464799	−	0.00745609i
$373$	1.14505e9	−	1.14505e9i	1.14247	−	1.14247i	0.154470	−	0.987997i	$-0.450633\pi$
$373$	1.14505e9	−	1.14505e9i	1.14247	−	1.14247i	0.987997	−	0.154470i	$-0.0493671\pi$
$374$	8.70361e8			0.860298
$375$	−7.62499e8	−	6.79292e8i	−0.746672	−	0.665192i
$376$	3.41507e7			0.0331316
$377$	1.46164e8	−	1.46164e8i	0.140490	−	0.140490i
$378$	3.68298e7	+	7.64776e8i	0.0350734	+	0.728304i
$379$		−	6.24053e8i		−	0.588822i	−0.955679	−	0.294411i	$-0.904876\pi$
$379$		−	6.24053e8i		−	0.588822i	0.955679	−	0.294411i	$-0.0951235\pi$
$380$	−9.73049e8	+	2.75247e8i	−0.909688	+	0.257324i
$381$	−3.88515e8	+	4.01183e8i	−0.359891	+	0.371625i
$382$	4.85797e8	+	4.85797e8i	0.445896	+	0.445896i
$383$	−1.12571e8	−	1.12571e8i	−0.102383	−	0.102383i	0.654060	−	0.756443i	$-0.273065\pi$
$383$	−1.12571e8	−	1.12571e8i	−0.102383	−	0.102383i	−0.756443	+	0.654060i	$0.773065\pi$
$384$	−6.82276e7	+	7.04523e7i	−0.0614895	+	0.0634944i
$385$	8.52041e8	−	1.52421e9i	0.760935	−	1.36123i
$386$		−	3.84090e8i		−	0.339920i
$387$	1.05713e9	−	1.12722e9i	0.927124	−	0.988603i
$388$	7.30770e6	−	7.30770e6i	0.00635141	−	0.00635141i
$389$	−5.19958e8			−0.447862			−0.223931	−	0.974605i	$-0.571889\pi$
$389$	−5.19958e8			−0.447862			−0.223931	+	0.974605i	$0.571889\pi$
$390$	6.02278e8	−	1.80849e8i	0.514127	−	0.154379i
$391$	8.48867e8			0.718160
$392$	1.88775e7	−	1.88775e7i	0.0158286	−	0.0158286i
$393$	6.80071e8	−	1.09094e7i	0.565171	−	0.00906622i
$394$			2.40905e8i			0.198431i
$395$	5.95495e8	+	2.10519e9i	0.486170	+	1.71870i
$396$	9.33961e8	−	2.99721e7i	0.755781	−	0.0242540i
$397$	−8.77781e8	−	8.77781e8i	−0.704076	−	0.704076i	0.261207	−	0.965283i	$-0.415879\pi$
$397$	−8.77781e8	−	8.77781e8i	−0.704076	−	0.704076i	−0.965283	+	0.261207i	$0.915879\pi$
$398$	−6.21068e8	−	6.21068e8i	−0.493797	−	0.493797i
$399$	1.77711e9	+	1.72099e9i	1.40058	+	1.35636i
$400$	−2.72584e8	+	1.67624e8i	−0.212956	+	0.130957i
$401$			1.79053e9i			1.38668i	0.720612	+	0.693338i	$0.243861\pi$
$401$			1.79053e9i			1.38668i	−0.720612	+	0.693338i	$0.756139\pi$
$402$	2.05644e6	+	1.28194e8i	0.00157879	+	0.0984187i
$403$	−6.55745e8	+	6.55745e8i	−0.499077	+	0.499077i
$404$	−7.72594e8			−0.582931
$405$	−1.26043e9	+	4.45617e8i	−0.942812	+	0.333326i
$406$	2.57327e8			0.190829
$407$	5.76403e8	−	5.76403e8i	0.423785	−	0.423785i
$408$	6.25851e6	+	3.90144e8i	0.00456205	+	0.284390i
$409$		−	4.81089e8i		−	0.347692i	−0.984773	−	0.173846i	$-0.944381\pi$
$409$		−	4.81089e8i		−	0.347692i	0.984773	−	0.173846i	$-0.0556194\pi$
$410$	1.01662e9	+	5.68293e8i	0.728474	+	0.407220i
$411$	−2.67459e8	−	2.59014e8i	−0.190025	−	0.184025i
$412$	3.88522e8	+	3.88522e8i	0.273700	+	0.273700i
$413$	6.93798e8	+	6.93798e8i	0.484627	+	0.484627i
$414$	9.10896e8	−	2.92319e7i	0.630910	−	0.0202468i
$415$	−1.80874e9	−	1.01109e9i	−1.24224	−	0.694419i
$416$		−	1.97053e8i		−	0.134201i
$417$	−2.21769e9	+	3.55752e7i	−1.49770	+	0.0240255i
$418$	2.13488e9	−	2.13488e9i	1.42974	−	1.42974i
$419$	1.06990e9			0.710549			0.355275	−	0.934762i	$-0.384387\pi$
$419$	1.06990e9			0.710549			0.355275	+	0.934762i	$0.384387\pi$
$420$	6.89362e8	+	3.70971e8i	0.454020	+	0.244325i
$421$	2.63062e9			1.71819			0.859095	−	0.511817i	$-0.171027\pi$
$421$	2.63062e9			1.71819			0.859095	+	0.511817i	$0.171027\pi$
$422$	1.06647e9	−	1.06647e9i	0.690807	−	0.690807i
$423$	9.97871e7	−	1.06404e8i	0.0641037	−	0.0683544i
$424$			2.28532e8i			0.145601i
$425$	−2.95280e8	+	1.23842e9i	−0.186583	+	0.782543i
$426$	−8.88604e6	+	9.17577e6i	−0.00556896	+	0.00575055i
$427$	7.94921e8	+	7.94921e8i	0.494113	+	0.494113i
$428$	−1.43502e8	−	1.43502e8i	−0.0884717	−	0.0884717i
$429$	−1.30613e9	+	1.34872e9i	−0.798706	+	0.824748i
$430$	−4.30070e8	−	1.52038e9i	−0.260855	−	0.922172i
$431$			3.33688e8i			0.200757i	0.994949	+	0.100378i	$0.0320053\pi$
$431$			3.33688e8i			0.200757i	−0.994949	+	0.100378i	$0.967995\pi$
$432$	2.01510e7	+	4.18437e8i	0.0120255	+	0.249711i
$433$	−1.12847e9	+	1.12847e9i	−0.668008	+	0.668008i	−0.957255	−	0.289247i	$-0.906595\pi$
$433$	−1.12847e9	+	1.12847e9i	−0.668008	+	0.668008i	0.289247	+	0.957255i	$0.406595\pi$
$434$	−1.15447e9			−0.677902
$435$	1.29215e8	+	4.30324e8i	0.0752664	+	0.250659i
$436$	−1.33140e9			−0.769316
$437$	2.08216e9	−	2.08216e9i	1.19352	−	1.19352i
$438$	−1.22263e9	+	1.96128e7i	−0.695240	+	0.0111527i
$439$		−	4.51964e8i		−	0.254963i	−0.991841	−	0.127482i	$-0.959311\pi$
$439$		−	4.51964e8i		−	0.254963i	0.991841	−	0.127482i	$-0.0406894\pi$
$440$	4.66183e8	−	8.33952e8i	0.260899	−	0.466721i
$441$	−3.65765e6	−	1.13976e8i	−0.00203080	−	0.0632818i
$442$	−5.54363e8	−	5.54363e8i	−0.305363	−	0.305363i
$443$	−6.00898e8	−	6.00898e8i	−0.328388	−	0.328388i	0.523585	−	0.851973i	$-0.324594\pi$
$443$	−6.00898e8	−	6.00898e8i	−0.328388	−	0.328388i	−0.851973	+	0.523585i	$0.824594\pi$
$444$	2.62520e8	+	2.54231e8i	0.142338	+	0.137844i
$445$	1.39317e9	−	3.94088e8i	0.749455	−	0.211998i
$446$		−	1.91860e9i		−	1.02403i
$447$	3.25052e7	+	2.02631e9i	0.0172138	+	1.07308i
$448$	1.73460e8	−	1.73460e8i	0.0911435	−	0.0911435i
$449$	−3.08560e9			−1.60871			−0.804354	−	0.594150i	$-0.797488\pi$
$449$	−3.08560e9			−1.60871			−0.804354	+	0.594150i	$0.797488\pi$
$450$	−2.74210e8	+	1.33909e9i	−0.141853	+	0.692732i
$451$	−3.47731e9			−1.78495
$452$	−7.58696e8	+	7.58696e8i	−0.386441	+	0.386441i
$453$	−4.72244e7	−	2.94388e9i	−0.0238683	−	1.48791i
$454$			2.09863e9i			1.05255i
$455$	−1.51352e9	+	4.28129e8i	−0.753264	+	0.213076i
$456$	9.72321e8	+	9.41619e8i	0.480212	+	0.465048i
$457$	−2.13005e9	−	2.13005e9i	−1.04396	−	1.04396i	−0.998988	−	0.0449691i	$-0.985681\pi$
$457$	−2.13005e9	−	2.13005e9i	−1.04396	−	1.04396i	−0.0449691	−	0.998988i	$-0.514319\pi$
$458$	−5.71237e8	−	5.71237e8i	−0.277835	−	0.277835i
$459$	1.23387e9	+	1.12049e9i	0.595557	+	0.540831i
$460$	4.54670e8	−	8.13357e8i	0.217793	−	0.389609i
$461$		−	3.55188e9i		−	1.68852i	−0.535936	−	0.844259i	$-0.680041\pi$
$461$		−	3.55188e9i		−	1.68852i	0.535936	−	0.844259i	$-0.319959\pi$
$462$	−2.33699e9	+	3.74889e7i	−1.10258	+	0.0176870i
$463$	−5.49134e8	+	5.49134e8i	−0.257126	+	0.257126i	−0.823884	−	0.566758i	$-0.808197\pi$
$463$	−5.49134e8	+	5.49134e8i	−0.257126	+	0.257126i	0.566758	+	0.823884i	$0.308197\pi$
$464$	1.40793e8			0.0654288
$465$	−5.79707e8	−	1.93059e9i	−0.267376	−	0.890440i
$466$	8.20546e8			0.375623
$467$	2.58849e8	−	2.58849e8i	0.117608	−	0.117608i	−0.645853	−	0.763462i	$-0.723498\pi$
$467$	2.58849e8	−	2.58849e8i	0.117608	−	0.117608i	0.763462	+	0.645853i	$0.223498\pi$
$468$	−6.13962e8	−	5.75782e8i	−0.276873	−	0.259655i
$469$		−	3.20689e8i		−	0.143542i
$470$	−4.05963e7	−	1.43516e8i	−0.0180362	−	0.0637613i
$471$	−9.32599e8	+	9.63007e8i	−0.411265	+	0.424675i
$472$	3.79602e8	+	3.79602e8i	0.166162	+	0.166162i
$473$	3.33573e9	+	3.33573e9i	1.44936	+	1.44936i
$474$	2.03719e9	−	2.10361e9i	0.878631	−	0.907280i
$475$	2.31341e9	+	3.76197e9i	0.990432	+	1.61060i
$476$		−	9.75978e8i		−	0.414778i
$477$	7.12041e8	+	6.67761e8i	0.300393	+	0.281713i
$478$	−2.13053e9	+	2.13053e9i	−0.892258	+	0.892258i
$479$	1.55118e9			0.644892			0.322446	−	0.946588i	$-0.395495\pi$
$479$	1.55118e9			0.644892			0.322446	+	0.946588i	$0.395495\pi$
$480$	3.77175e8	+	2.02972e8i	0.155668	+	0.0837706i
$481$	−7.34262e8			−0.300845
$482$	−3.93062e8	+	3.93062e8i	−0.159881	+	0.159881i
$483$	−2.27927e9	+	3.65630e7i	−0.920409	+	0.0147648i
$484$			1.60533e9i			0.643585i
$485$	−3.93970e7	−	2.20231e7i	−0.0156808	−	0.00876562i
$486$	1.36261e9	+	1.15987e9i	0.538450	+	0.458335i
$487$	1.50250e9	+	1.50250e9i	0.589470	+	0.589470i	0.937488	−	0.348018i	$-0.113145\pi$
$487$	1.50250e9	+	1.50250e9i	0.589470	+	0.589470i	−0.348018	+	0.937488i	$0.613145\pi$
$488$	4.34931e8	+	4.34931e8i	0.169415	+	0.169415i
$489$	−1.77942e9	−	1.72323e9i	−0.688174	−	0.666444i
$490$	−1.01772e8	−	5.68907e7i	−0.0390787	−	0.0218452i
$491$			2.41834e9i			0.922004i	0.887399	+	0.461002i	$0.152510\pi$
$491$			2.41834e9i			0.922004i	−0.887399	+	0.461002i	$0.847490\pi$
$492$	−2.50043e7	−	1.55872e9i	−0.00946534	−	0.590052i
$493$	3.96089e8	−	3.96089e8i	0.148877	−	0.148877i
$494$	−2.71956e9			−1.01497
$495$	−1.23619e9	−	3.88927e9i	−0.458108	−	1.44129i
$496$	−6.31650e8			−0.232429
$497$	2.25916e7	−	2.25916e7i	0.00825466	−	0.00825466i
$498$	4.44869e7	+	2.77323e9i	0.0161410	+	1.00620i
$499$		−	3.02016e9i		−	1.08812i	−0.839046	−	0.544061i	$-0.816886\pi$
$499$		−	3.02016e9i		−	1.08812i	0.839046	−	0.544061i	$-0.183114\pi$
$500$	1.02846e9	+	9.46252e8i	0.367953	+	0.338541i
$501$	−1.22123e9	−	1.18267e9i	−0.433876	−	0.420176i
$502$	1.07998e9	+	1.07998e9i	0.381026	+	0.381026i
$503$	1.26473e9	+	1.26473e9i	0.443107	+	0.443107i	0.893055	−	0.449948i	$-0.148558\pi$
$503$	1.26473e9	+	1.26473e9i	0.443107	+	0.443107i	−0.449948	+	0.893055i	$0.648558\pi$
$504$	−3.36091e7	−	1.04730e9i	−0.0116937	−	0.364387i
$505$	9.18415e8	+	3.24677e9i	0.317336	+	1.12184i
$506$			2.78206e9i			0.954641i
$507$	−1.24311e9	+	1.99414e7i	−0.423626	+	0.00679562i
$508$	5.40434e8	−	5.40434e8i	0.182903	−	0.182903i
$509$	−2.77528e9			−0.932812			−0.466406	−	0.884571i	$-0.654451\pi$
$509$	−2.77528e9			−0.932812			−0.466406	+	0.884571i	$0.654451\pi$
$510$	1.63211e9	−	4.90081e8i	0.544821	−	0.163596i
$511$	3.05851e9			1.01400
$512$	9.49063e7	−	9.49063e7i	0.0312500	−	0.0312500i
$513$	5.77491e9	−	2.78106e8i	1.88857	−	0.0909494i
$514$		−	1.31543e9i		−	0.427264i
$515$	1.17088e9	−	2.09459e9i	0.377736	−	0.675730i
$516$	−1.47127e9	+	1.51924e9i	−0.471431	+	0.486802i
$517$	3.14875e8	+	3.14875e8i	0.100212	+	0.100212i
$518$	−6.46348e8	−	6.46348e8i	−0.204321	−	0.204321i
$519$	3.87030e9	−	3.99649e9i	1.21523	−	1.25485i
$520$	−8.28101e8	+	2.34245e8i	−0.258269	+	0.0730565i
$521$		−	5.35817e9i		−	1.65991i	−0.557831	−	0.829955i	$-0.688366\pi$
$521$		−	5.35817e9i		−	1.65991i	0.557831	−	0.829955i	$-0.311634\pi$
$522$	4.11393e8	−	4.38673e8i	0.126593	−	0.134988i
$523$	7.09968e7	−	7.09968e7i	0.0217012	−	0.0217012i	−0.696173	−	0.717874i	$-0.745115\pi$
$523$	7.09968e7	−	7.09968e7i	0.0217012	−	0.0217012i	0.717874	+	0.696173i	$0.245115\pi$
$524$	−9.30820e8			−0.282622
$525$	7.39506e8	−	3.33798e9i	0.223041	−	1.00676i
$526$	3.32672e8			0.0996705
$527$	−1.77700e9	+	1.77700e9i	−0.528872	+	0.528872i
$528$	−1.27865e9	+	2.05115e7i	−0.378036	+	0.00606428i
$529$		−	6.91468e8i		−	0.203085i
$530$	9.60387e8	−	2.71665e8i	0.280208	−	0.0792626i
$531$	2.29192e9	−	7.35507e7i	0.664306	−	0.0213185i
$532$	−2.39394e9	−	2.39394e9i	−0.689324	−	0.689324i
$533$	2.21482e9	+	2.21482e9i	0.633567	+	0.633567i
$534$	−1.39213e9	−	1.34817e9i	−0.395627	−	0.383135i
$535$	−4.32470e8	+	7.73643e8i	−0.122100	+	0.218425i
$536$		−	1.75461e8i		−	0.0492157i
$537$	6.62899e7	+	4.13239e9i	0.0184730	+	1.15157i
$538$	5.12362e7	−	5.12362e7i	0.0141853	−	0.0141853i
$539$	3.48107e8			0.0957528
$540$	1.73450e9	−	5.82096e8i	0.474018	−	0.159080i
$541$	2.08295e8			0.0565573			0.0282787	−	0.999600i	$-0.490997\pi$
$541$	2.08295e8			0.0565573			0.0282787	+	0.999600i	$0.490997\pi$
$542$	1.81264e8	−	1.81264e8i	0.0489005	−	0.0489005i
$543$	−2.14300e7	−	1.33591e9i	−0.00574412	−	0.358078i
$544$		−	5.33994e8i		−	0.142213i
$545$	1.58269e9	+	5.59509e9i	0.418800	+	1.48054i
$546$	1.51238e9	+	1.46463e9i	0.397638	+	0.385082i
$547$	1.59142e9	+	1.59142e9i	0.415747	+	0.415747i	0.883735	−	0.467988i	$-0.155021\pi$
$547$	1.59142e9	+	1.59142e9i	0.415747	+	0.415747i	−0.467988	+	0.883735i	$0.655021\pi$
$548$	3.60295e8	+	3.60295e8i	0.0935246	+	0.0935246i
$549$	2.62597e9	−	8.42710e7i	0.677309	−	0.0217358i
$550$	−4.05879e9	−	9.67745e8i	−1.04023	−	0.248023i
$551$		−	1.94311e9i		−	0.494842i
$552$	−1.24707e9	+	2.00050e7i	−0.315577	+	0.00506234i
$553$	−5.17928e9	+	5.17928e9i	−1.30236	+	1.30236i
$554$	−4.88561e7			−0.0122077
$555$	7.56316e8	−	1.40543e9i	0.187792	−	0.348968i
$556$	3.03538e9			0.748947
$557$	−1.70195e9	+	1.70195e9i	−0.417305	+	0.417305i	−0.884274	−	0.466969i	$-0.845346\pi$
$557$	−1.70195e9	+	1.70195e9i	−0.417305	+	0.417305i	0.466969	+	0.884274i	$0.345346\pi$
$558$	−1.84566e9	+	1.96805e9i	−0.449709	+	0.479530i
$559$		−	4.24928e9i		−	1.02890i
$560$	−9.35151e8	−	5.22753e8i	−0.225021	−	0.125788i
$561$	−3.53948e9	+	3.65489e9i	−0.846389	+	0.873986i
$562$	1.35700e9	+	1.35700e9i	0.322480	+	0.322480i
$563$	−1.21787e9	−	1.21787e9i	−0.287622	−	0.287622i	0.548517	−	0.836139i	$-0.315192\pi$
$563$	−1.21787e9	−	1.21787e9i	−0.287622	−	0.287622i	−0.836139	+	0.548517i	$0.815192\pi$
$564$	−1.38880e8	+	1.43408e8i	−0.0325959	+	0.0336587i
$565$	4.09026e9	+	2.28647e9i	0.954071	+	0.533330i
$566$			3.83223e9i			0.888370i
$567$	−3.36128e9	−	2.95544e9i	−0.774399	−	0.680897i
$568$	1.23607e7	−	1.23607e7i	0.00283024	−	0.00283024i
$569$	1.05145e9			0.239274			0.119637	−	0.992818i	$-0.461827\pi$
$569$	1.05145e9			0.239274			0.119637	+	0.992818i	$0.461827\pi$
$570$	2.80124e9	−	5.20545e9i	0.633562	−	1.17732i
$571$	4.36857e9			0.982004			0.491002	−	0.871159i	$-0.336631\pi$
$571$	4.36857e9			0.982004			0.491002	+	0.871159i	$0.336631\pi$
$572$	1.81686e9	−	1.81686e9i	0.405916	−	0.405916i
$573$	−4.01558e9	+	6.44162e7i	−0.891677	+	0.0143039i
$574$			3.89927e9i			0.860581i
$575$	−3.95856e9	−	9.43846e8i	−0.868359	−	0.207044i
$576$	−1.83888e7	−	5.73014e8i	−0.00400935	−	0.124936i
$577$	−5.02534e9	−	5.02534e9i	−1.08906	−	1.08906i	−0.995626	−	0.0934291i	$-0.970217\pi$
$577$	−5.02534e9	−	5.02534e9i	−1.08906	−	1.08906i	−0.0934291	−	0.995626i	$-0.529783\pi$
$578$	8.18959e8	+	8.18959e8i	0.176407	+	0.176407i
$579$	1.61290e9	+	1.56197e9i	0.345329	+	0.334424i
$580$	−1.67367e8	−	5.91673e8i	−0.0356182	−	0.125917i
$581$		−	6.93747e9i		−	1.46752i
$582$	968993.	+	6.04052e7i	0.000203747	+	0.0127012i
$583$	−2.10710e9	+	2.10710e9i	−0.440398	+	0.440398i
$584$	1.67342e9			0.347665
$585$	−1.68984e9	+	3.26459e9i	−0.348979	+	0.674191i
$586$	1.58942e9			0.326286
$587$	−2.79539e9	+	2.79539e9i	−0.570438	+	0.570438i	−0.932251	−	0.361813i	$-0.882158\pi$
$587$	−2.79539e9	+	2.79539e9i	−0.570438	+	0.570438i	0.361813	+	0.932251i	$0.382158\pi$
$588$	2.50313e6	+	1.56040e8i	0.000507765	+	0.0316531i
$589$			8.71750e9i			1.75788i
$590$	1.14400e9	−	2.04650e9i	0.229321	−	0.410232i
$591$	−1.01163e9	−	9.79684e8i	−0.201588	−	0.195222i
$592$	−3.53641e8	−	3.53641e8i	−0.0700546	−	0.0700546i
$593$	−1.16539e8	−	1.16539e8i	−0.0229499	−	0.0229499i	0.695539	−	0.718489i	$-0.255166\pi$
$593$	−1.16539e8	−	1.16539e8i	−0.0229499	−	0.0229499i	−0.718489	+	0.695539i	$0.755166\pi$
$594$	−3.67226e9	+	4.04385e9i	−0.718921	+	0.791667i
$595$	−4.10147e9	+	1.16019e9i	−0.798235	+	0.225797i
$596$		−	2.77344e9i		−	0.536607i
$597$	5.13373e9	−	8.23529e7i	0.987467	−	0.0158405i
$598$	1.77199e9	−	1.77199e9i	0.338850	−	0.338850i
$599$	−6.39357e9			−1.21548			−0.607742	−	0.794134i	$-0.707925\pi$
$599$	−6.39357e9			−1.21548			−0.607742	+	0.794134i	$0.707925\pi$
$600$	4.04611e8	−	1.82633e9i	0.0764730	−	0.345184i
$601$	−4.56178e9			−0.857183			−0.428592	−	0.903498i	$-0.640990\pi$
$601$	−4.56178e9			−0.857183			−0.428592	+	0.903498i	$0.640990\pi$
$602$	3.74051e9	−	3.74051e9i	0.698784	−	0.698784i
$603$	−5.46687e8	−	5.12690e8i	−0.101538	−	0.0952236i
$604$			4.02932e9i			0.744050i
$605$	6.74628e9	−	1.90832e9i	1.23857	−	0.350355i
$606$	3.14190e9	−	3.24434e9i	0.573506	−	0.592205i
$607$	−6.56778e9	−	6.56778e9i	−1.19195	−	1.19195i	−0.976519	−	0.215433i	$-0.930884\pi$
$607$	−6.56778e9	−	6.56778e9i	−1.19195	−	1.19195i	−0.215433	−	0.976519i	$-0.569116\pi$
$608$	−1.30981e9	−	1.30981e9i	−0.236345	−	0.236345i
$609$	−1.04647e9	+	1.08059e9i	−0.187744	+	0.193866i
$610$	1.31074e9	−	2.34478e9i	0.233810	−	0.418262i
$611$		−	4.01109e8i		−	0.0711408i
$612$	−1.66377e9	−	1.56031e9i	−0.293403	−	0.275157i
$613$	4.99817e9	−	4.99817e9i	0.876394	−	0.876394i	−0.116766	−	0.993159i	$-0.537253\pi$
$613$	4.99817e9	−	4.99817e9i	0.876394	−	0.876394i	0.993159	+	0.116766i	$0.0372526\pi$
$614$	−5.26346e9			−0.917660
$615$	−6.52068e9	+	1.95799e9i	−1.13039	+	0.339428i
$616$	3.19866e9			0.551360
$617$	2.34903e9	−	2.34903e9i	0.402615	−	0.402615i	−0.476539	−	0.879154i	$-0.658109\pi$
$617$	2.34903e9	−	2.34903e9i	0.402615	−	0.402615i	0.879154	+	0.476539i	$0.158109\pi$
$618$	−3.21151e9	+	5.15176e7i	−0.547330	+	0.00878002i
$619$		−	8.82741e9i		−	1.49595i	−0.663729	−	0.747973i	$-0.731027\pi$
$619$		−	8.82741e9i		−	1.49595i	0.663729	−	0.747973i	$-0.268973\pi$
$620$	7.50869e8	+	2.65446e9i	0.126530	+	0.447307i
$621$	−3.58157e9	+	3.94399e9i	−0.600141	+	0.660868i
$622$	1.88764e9	+	1.88764e9i	0.314523	+	0.314523i
$623$	3.42756e9	+	3.42756e9i	0.567906	+	0.567906i
$624$	8.27482e8	+	8.01353e8i	0.136337	+	0.132032i
$625$	2.75398e9	−	5.44688e9i	0.451212	−	0.892417i
$626$			1.90905e9i			0.311034i
$627$	2.83083e8	+	1.76468e10i	0.0458645	+	2.85911i
$628$	1.29727e9	−	1.29727e9i	0.209012	−	0.209012i
$629$	−1.98977e9			−0.318806
$630$	−4.36123e9	+	1.38620e9i	−0.694891	+	0.220869i
$631$	−2.05327e9			−0.325345			−0.162672	−	0.986680i	$-0.552011\pi$
$631$	−2.05327e9			−0.325345			−0.162672	+	0.986680i	$0.552011\pi$
$632$	−2.83378e9	+	2.83378e9i	−0.446535	+	0.446535i
$633$	1.41413e8	+	8.81544e9i	0.0221604	+	1.38144i
$634$		−	6.02159e9i		−	0.938423i
$635$	−2.91357e9	−	1.62870e9i	−0.451562	−	0.252425i
$636$	−9.59669e8	−	9.29366e8i	−0.147918	−	0.143247i
$637$	−2.21721e8	−	2.21721e8i	−0.0339875	−	0.0339875i
$638$	1.29814e9	+	1.29814e9i	0.197901	+	0.197901i
$639$	−2.39498e6	−	7.46299e7i	−0.000363118	−	0.0113151i
$640$	−5.11656e8	−	2.86018e8i	−0.0771521	−	0.0431283i
$641$			4.55381e9i			0.682923i	0.939896	+	0.341461i	$0.110922\pi$
$641$			4.55381e9i			0.682923i	−0.939896	+	0.341461i	$0.889078\pi$
$642$	1.18618e9	−	1.90282e7i	0.176921	−	0.00283808i
$643$	6.29461e9	−	6.29461e9i	0.933750	−	0.933750i	−0.0641883	−	0.997938i	$-0.520446\pi$
$643$	6.29461e9	−	6.29461e9i	0.933750	−	0.933750i	0.997938	+	0.0641883i	$0.0204458\pi$
$644$	3.11966e9			0.460264
$645$	8.13346e9	+	4.37691e9i	1.19348	+	0.642257i
$646$	−7.36972e9			−1.07557
$647$	7.40915e9	−	7.40915e9i	1.07548	−	1.07548i	0.0785738	−	0.996908i	$-0.474963\pi$
$647$	7.40915e9	−	7.40915e9i	1.07548	−	1.07548i	0.996908	−	0.0785738i	$-0.0250366\pi$
$648$	−1.83908e9	−	1.61703e9i	−0.265515	−	0.233456i
$649$			6.99999e9i			1.00517i
$650$	1.96880e9	+	3.20158e9i	0.281193	+	0.457264i
$651$	4.69484e9	−	4.84792e9i	0.666941	−	0.688688i
$652$	2.39706e9	+	2.39706e9i	0.338698	+	0.338698i
$653$	−7.12337e9	−	7.12337e9i	−1.00113	−	1.00113i	−0.999999	−	0.00112784i	$-0.999641\pi$
$653$	−7.12337e9	−	7.12337e9i	−1.00113	−	1.00113i	−0.00112784	−	0.999999i	$-0.500359\pi$
$654$	5.41436e9	−	5.59091e9i	0.756877	−	0.781556i
$655$	1.10650e9	+	3.91170e9i	0.153854	+	0.543902i
$656$			2.13344e9i			0.295064i
$657$	4.88968e9	−	5.21392e9i	0.672669	−	0.717274i
$658$	3.53084e8	−	3.53084e8i	0.0483157	−	0.0483157i
$659$	4.96125e9			0.675294			0.337647	−	0.941273i	$-0.390369\pi$
$659$	4.96125e9			0.675294			0.337647	+	0.941273i	$0.390369\pi$
$660$	1.60618e9	+	5.34905e9i	0.217466	+	0.724224i
$661$	−2.47575e7			−0.00333428			−0.00166714	−	0.999999i	$-0.500531\pi$
$661$	−2.47575e7			−0.00333428			−0.00166714	+	0.999999i	$0.500531\pi$
$662$	5.08318e9	−	5.08318e9i	0.680977	−	0.680977i
$663$	4.58235e9	−	7.35079e7i	0.610648	−	0.00979573i
$664$		−	3.79575e9i		−	0.503163i
$665$	−7.21459e9	+	1.29061e10i	−0.951340	+	1.70185i
$666$	−2.13517e9	+	6.85205e7i	−0.280074	+	0.00898795i
$667$	1.26608e9	+	1.26608e9i	0.165204	+	0.165204i
$668$	1.64512e9	+	1.64512e9i	0.213540	+	0.213540i
$669$	8.05676e9	+	7.80236e9i	1.04032	+	1.00748i
$670$	−7.37361e8	+	2.08578e8i	−0.0947150	+	0.0267920i
$671$			8.02026e9i			1.02485i
$672$	2.30006e7	+	1.43381e9i	0.00292379	+	0.182264i
$673$	7.83270e9	−	7.83270e9i	0.990510	−	0.990510i	−0.00944549	−	0.999955i	$-0.503007\pi$
$673$	7.83270e9	−	7.83270e9i	0.990510	−	0.990510i	0.999955	+	0.00944549i	$0.00300664\pi$
$674$	4.88925e9			0.615081
$675$	−4.50808e9	−	6.59713e9i	−0.564194	−	0.825642i
$676$	1.70146e9			0.211840
$677$	5.20965e9	−	5.20965e9i	0.645280	−	0.645280i	−0.306568	−	0.951849i	$-0.599181\pi$
$677$	5.20965e9	−	5.20965e9i	0.645280	−	0.645280i	0.951849	+	0.306568i	$0.0991808\pi$
$678$	−1.00602e8	−	6.27135e9i	−0.0123966	−	0.772783i
$679$		−	1.51109e8i		−	0.0185245i
$680$	−2.24407e9	+	6.34780e8i	−0.273687	+	0.0774180i
$681$	−8.81275e9	−	8.53447e9i	−1.06929	−	1.03553i
$682$	−5.82392e9	−	5.82392e9i	−0.703024	−	0.703024i
$683$	−3.27856e9	−	3.27856e9i	−0.393741	−	0.393741i	0.482277	−	0.876019i	$-0.339810\pi$
$683$	−3.27856e9	−	3.27856e9i	−0.393741	−	0.393741i	−0.876019	+	0.482277i	$0.839810\pi$
$684$	−7.90824e9	+	2.53786e8i	−0.944895	+	0.0303230i
$685$	1.08581e9	−	1.94241e9i	0.129074	−	0.230900i
$686$			5.77490e9i			0.682983i
$687$	4.72183e9	−	7.57454e7i	0.555599	−	0.00891266i
$688$	2.04657e9	−	2.04657e9i	0.239589	−	0.239589i
$689$	2.68417e9			0.312639
$690$	1.56652e9	+	5.21695e9i	0.181536	+	0.604568i
$691$	−4.22632e9			−0.487292			−0.243646	−	0.969864i	$-0.578343\pi$
$691$	−4.22632e9			−0.487292			−0.243646	+	0.969864i	$0.578343\pi$
$692$	−5.38367e9	+	5.38367e9i	−0.617600	+	0.617600i
$693$	9.34635e9	−	9.96612e9i	1.06678	−	1.13752i
$694$			8.13193e9i			0.923497i
$695$	−3.60828e9	−	1.27560e10i	−0.407712	−	1.44134i
$696$	−5.72562e8	+	5.91231e8i	−0.0643710	+	0.0664699i
$697$	6.00193e9	+	6.00193e9i	0.671392	+	0.671392i
$698$	1.83761e9	+	1.83761e9i	0.204531	+	0.204531i
$699$	−3.33690e9	+	3.44570e9i	−0.369550	+	0.381600i
$700$	−1.08518e9	+	4.55132e9i	−0.119580	+	0.501527i
$701$			8.01143e9i			0.878410i	0.898387	+	0.439205i	$0.144740\pi$
$701$			8.01143e9i			0.878410i	−0.898387	+	0.439205i	$0.855260\pi$
$702$	4.91466e9	−	2.36679e8i	0.536184	−	0.0258214i
$703$	−4.88065e9	+	4.88065e9i	−0.529826	+	0.529826i
$704$	1.75010e9			0.189042
$705$	7.67755e8	+	4.13158e8i	0.0825203	+	0.0444072i
$706$	−9.31566e9			−0.996316
$707$	−7.98786e9	+	7.98786e9i	−0.850086	+	0.850086i
$708$	−3.13778e9	+	5.03348e7i	−0.332281	+	0.00533031i
$709$		−	6.28682e9i		−	0.662474i	−0.943548	−	0.331237i	$-0.892534\pi$
$709$		−	6.28682e9i		−	0.662474i	0.943548	−	0.331237i	$-0.107466\pi$
$710$	−6.66385e7	−	3.72512e7i	−0.00698749	−	0.00390604i
$711$	5.49065e8	+	1.71094e10i	0.0572902	+	1.78522i
$712$	1.87534e9	+	1.87534e9i	0.194715	+	0.194715i
$713$	−5.68009e9	−	5.68009e9i	−0.586870	−	0.586870i
$714$	4.09841e9	+	3.96899e9i	0.421377	+	0.408072i
$715$	−9.79501e9	−	5.47545e9i	−1.00215	−	0.560207i
$716$		−	5.65604e9i		−	0.575860i
$717$	−2.82506e8	−	1.76109e10i	−0.0286227	−	1.78429i
$718$	−1.42079e9	+	1.42079e9i	−0.143250	+	0.143250i
$719$	2.58283e9			0.259146			0.129573	−	0.991570i	$-0.458639\pi$
$719$	2.58283e9			0.259146			0.129573	+	0.991570i	$0.458639\pi$
$720$	−2.38619e9	+	7.58443e8i	−0.238254	+	0.0757285i
$721$	8.03387e9			0.798273
$722$	−1.30204e10	+	1.30204e10i	−1.28749	+	1.28749i
$723$	−5.21195e7	−	3.24903e9i	−0.00512881	−	0.319720i
$724$			1.82847e9i			0.179062i
$725$	−2.28751e9	+	1.40669e9i	−0.222936	+	0.137093i
$726$	−6.74124e9	−	6.52837e9i	−0.653825	−	0.633179i
$727$	1.10330e10	+	1.10330e10i	1.06494	+	1.06494i	0.997740	+	0.0671994i	$0.0214064\pi$
$727$	1.10330e10	+	1.10330e10i	1.06494	+	1.06494i	0.0671994	+	0.997740i	$0.478594\pi$
$728$	−2.03733e9	−	2.03733e9i	−0.195705	−	0.195705i
$729$	−1.04119e10	+	1.00516e9i	−0.995372	+	0.0960925i
$730$	−1.98927e9	−	7.03244e9i	−0.189262	−	0.669076i
$731$		−	1.15151e10i		−	1.09033i
$732$	−3.59512e9	+	5.76713e7i	−0.338785	+	0.00543464i
$733$	−8.27693e9	+	8.27693e9i	−0.776257	+	0.776257i	−0.979192	−	0.202935i	$-0.934952\pi$
$733$	−8.27693e9	+	8.27693e9i	−0.776257	+	0.776257i	0.202935	+	0.979192i	$0.434952\pi$
$734$	6.52912e9			0.609423
$735$	6.52773e8	−	1.96011e8i	0.0606396	−	0.0182085i
$736$	1.70688e9			0.157809
$737$	1.61778e9	−	1.61778e9i	0.148862	−	0.148862i
$738$	6.64719e9	+	6.23382e9i	0.608752	+	0.570896i
$739$			2.90689e9i			0.264955i	0.991186	+	0.132478i	$0.0422933\pi$
$739$			2.90689e9i			0.264955i	−0.991186	+	0.132478i	$0.957707\pi$
$740$	−1.06576e9	+	1.90654e9i	−0.0966828	+	0.172955i
$741$	1.10596e10	−	1.14202e10i	0.998561	−	1.03112i
$742$	2.36279e9	+	2.36279e9i	0.212330	+	0.212330i
$743$	−1.41461e10	−	1.41461e10i	−1.26524	−	1.26524i	−0.948516	−	0.316728i	$-0.897416\pi$
$743$	−1.41461e10	−	1.41461e10i	−1.26524	−	1.26524i	−0.316728	−	0.948516i	$-0.602584\pi$
$744$	2.56872e9	−	2.65248e9i	0.228671	−	0.236127i
$745$	−1.16552e10	+	3.29690e9i	−1.03269	+	0.292118i
$746$		−	1.29548e10i		−	1.14247i
$747$	−1.18265e10	−	1.10910e10i	−1.03809	−	0.973531i
$748$	4.92351e9	−	4.92351e9i	0.430149	−	0.430149i
$749$	−2.96734e9			−0.258036
$750$	−8.15600e9	+	4.70690e8i	−0.705932	+	0.0407399i
$751$	6.52059e9			0.561756			0.280878	−	0.959744i	$-0.409374\pi$
$751$	6.52059e9			0.561756			0.280878	+	0.959744i	$0.409374\pi$
$752$	1.93185e8	−	1.93185e8i	0.0165658	−	0.0165658i
$753$	−8.92711e9	+	1.43205e8i	−0.761954	+	0.0122229i
$754$		−	1.65366e9i		−	0.140490i
$755$	1.69329e10	−	4.78981e9i	1.43191	−	0.405046i
$756$	4.53457e9	+	4.11788e9i	0.381689	+	0.346615i
$757$	3.49234e9	+	3.49234e9i	0.292604	+	0.292604i	0.838108	−	0.545504i	$-0.183662\pi$
$757$	3.49234e9	+	3.49234e9i	0.292604	+	0.292604i	−0.545504	+	0.838108i	$0.683662\pi$
$758$	−3.53018e9	−	3.53018e9i	−0.294411	−	0.294411i
$759$	−1.16827e10	−	1.13138e10i	−0.969831	−	0.939207i
$760$	−3.94737e9	+	7.06143e9i	−0.326182	+	0.583506i
$761$			1.40877e10i			1.15876i	0.815058	+	0.579379i	$0.196705\pi$
$761$			1.40877e10i			1.15876i	−0.815058	+	0.579379i	$0.803295\pi$
$762$	7.16609e7	+	4.46721e9i	0.00586732	+	0.365758i
$763$	−1.37653e10	+	1.37653e10i	−1.12189	+	1.12189i
$764$	5.49617e9			0.445896
$765$	−4.57929e9	+	8.84669e9i	−0.369813	+	0.714440i
$766$	−1.27359e9			−0.102383
$767$	4.45854e9	−	4.45854e9i	0.356787	−	0.356787i
$768$	1.25845e7	+	7.84492e8i	0.00100247	+	0.0624920i
$769$			1.74258e10i			1.38182i	0.722941	+	0.690910i	$0.242790\pi$
$769$			1.74258e10i			1.38182i	−0.722941	+	0.690910i	$0.757210\pi$
$770$	−3.80237e9	−	1.34421e10i	−0.300149	−	1.06108i
$771$	5.52385e9	+	5.34943e9i	0.434062	+	0.420356i
$772$	−2.17274e9	−	2.17274e9i	−0.169960	−	0.169960i
$773$	9.20009e9	+	9.20009e9i	0.716414	+	0.716414i	0.967869	−	0.251455i	$-0.0809091\pi$
$773$	9.20009e9	+	9.20009e9i	0.716414	+	0.716414i	−0.251455	+	0.967869i	$0.580909\pi$
$774$	−3.96538e8	−	1.23565e10i	−0.0307391	−	0.957864i
$775$	1.02626e10	−	6.31094e9i	0.791957	−	0.487010i
$776$		−	8.26772e7i		−	0.00635141i
$777$	5.34269e9	−	8.57050e7i	0.408589	−	0.00655439i
$778$	−2.94133e9	+	2.94133e9i	−0.223931	+	0.223931i
$779$	2.94438e10			2.23158
$780$	2.38396e9	−	4.43003e9i	0.179874	−	0.334253i
$781$	2.27935e8			0.0171211
$782$	4.80192e9	−	4.80192e9i	0.359080	−	0.359080i
$783$	1.69106e8	+	3.51150e9i	0.0125890	+	0.261412i
$784$		−	2.13574e8i		−	0.0158286i
$785$	−6.99379e9	−	3.90955e9i	−0.516022	−	0.288459i
$786$	3.78535e9	−	3.90877e9i	0.278053	−	0.287119i
$787$	1.64623e9	+	1.64623e9i	0.120387	+	0.120387i	0.764733	−	0.644347i	$-0.222871\pi$
$787$	1.64623e9	+	1.64623e9i	0.120387	+	0.120387i	−0.644347	+	0.764733i	$0.722871\pi$
$788$	1.36276e9	+	1.36276e9i	0.0992153	+	0.0992153i
$789$	−1.35287e9	+	1.39699e9i	−0.0980590	+	0.101256i
$790$	1.52774e10	+	8.54011e9i	1.10244	+	0.616266i
$791$			1.56883e10i			1.12709i
$792$	5.11373e9	−	5.45283e9i	0.365763	−	0.390017i
$793$	5.10838e9	−	5.10838e9i	0.363770	−	0.363770i
$794$	−9.93096e9			−0.704076
$795$	−2.76479e9	+	5.13771e9i	−0.195154	+	0.362648i
$796$	−7.02659e9			−0.493797
$797$	−1.45349e10	+	1.45349e10i	−1.01697	+	1.01697i	−0.0171143	+	0.999854i	$0.505448\pi$
$797$	−1.45349e10	+	1.45349e10i	−1.01697	+	1.01697i	−0.999854	+	0.0171143i	$0.994552\pi$
$798$	1.97882e10	−	3.17434e8i	1.37847	−	0.0221128i
$799$		−	1.08697e9i		−	0.0753879i
$800$	−5.93741e8	+	2.49019e9i	−0.0409999	+	0.171956i
$801$	1.13227e10	−	3.63361e8i	0.778461	−	0.0249819i
$802$	1.01287e10	+	1.01287e10i	0.693338	+	0.693338i
$803$	1.54292e10	+	1.54292e10i	1.05157	+	1.05157i
$804$	7.36810e8	+	7.13544e8i	0.0499988	+	0.0484200i
$805$	−3.70847e9	−	1.31101e10i	−0.250559	−	0.885772i
$806$			7.41891e9i			0.499077i
$807$	6.79386e6	+	4.23516e8i	0.000455050	+	0.0283670i
$808$	−4.37045e9	+	4.37045e9i	−0.291465	+	0.291465i
$809$	−1.44299e9			−0.0958174			−0.0479087	−	0.998852i	$-0.515256\pi$
$809$	−1.44299e9			−0.0958174			−0.0479087	+	0.998852i	$0.515256\pi$
$810$	−4.60926e9	+	9.65084e9i	−0.304743	+	0.638069i
$811$	4.73097e9			0.311442			0.155721	−	0.987801i	$-0.450230\pi$
$811$	4.73097e9			0.311442			0.155721	+	0.987801i	$0.450230\pi$
$812$	1.45566e9	−	1.45566e9i	0.0954146	−	0.0954146i
$813$	2.40354e7	+	1.49832e9i	0.00156868	+	0.0977884i
$814$		−	6.52125e9i		−	0.423785i
$815$	7.22398e9	−	1.29230e10i	0.467439	−	0.836200i
$816$	2.24239e9	+	2.17158e9i	0.144476	+	0.139914i
$817$	−2.82450e10	−	2.82450e10i	−1.81203	−	1.81203i
$818$	−2.72145e9	−	2.72145e9i	−0.173846	−	0.173846i
$819$	−1.23008e10	+	3.94749e8i	−0.782418	+	0.0251089i
$820$	8.96560e9	−	2.53610e9i	0.567847	−	0.160627i
$821$			5.46533e9i			0.344679i	0.985038	+	0.172340i	$0.0551327\pi$
$821$			5.46533e9i			0.344679i	−0.985038	+	0.172340i	$0.944867\pi$
$822$	−2.97818e9	+	4.77747e7i	−0.187025	+	0.00300017i
$823$	3.47565e9	−	3.47565e9i	0.217338	−	0.217338i	−0.590038	−	0.807376i	$-0.700887\pi$
$823$	3.47565e9	−	3.47565e9i	0.217338	−	0.217338i	0.807376	+	0.590038i	$0.200887\pi$
$824$	4.39563e9			0.273700
$825$	2.05697e10	−	1.31085e10i	1.27538	−	0.812764i
$826$	7.84942e9			0.484627
$827$	−2.27169e10	+	2.27169e10i	−1.39662	+	1.39662i	−0.587132	+	0.809491i	$0.699743\pi$
$827$	−2.27169e10	+	2.27169e10i	−1.39662	+	1.39662i	−0.809491	+	0.587132i	$0.800257\pi$
$828$	4.98745e9	−	5.31817e9i	0.305332	−	0.325578i
$829$		−	6.24125e9i		−	0.380479i	−0.981738	−	0.190240i	$-0.939074\pi$
$829$		−	6.24125e9i		−	0.380479i	0.981738	−	0.190240i	$-0.0609265\pi$
$830$	−1.59513e10	+	4.51216e9i	−0.968331	+	0.273912i
$831$	1.98682e8	−	2.05161e8i	0.0120103	−	0.0124020i
$832$	−1.11470e9	−	1.11470e9i	−0.0671006	−	0.0671006i
$833$	−6.00841e8	−	6.00841e8i	−0.0360166	−	0.0360166i
$834$	−1.23439e10	+	1.27464e10i	−0.736838	+	0.760864i
$835$	4.95788e9	−	8.86912e9i	0.294709	−	0.527203i
$836$		−	2.41534e10i		−	1.42974i
$837$	−7.58670e8	−	1.57539e10i	−0.0447212	−	0.928641i
$838$	6.05227e9	−	6.05227e9i	0.355275	−	0.355275i
$839$	1.93981e10			1.13395			0.566973	−	0.823736i	$-0.308114\pi$
$839$	1.93981e10			1.13395			0.566973	+	0.823736i	$0.308114\pi$
$840$	5.99815e9	−	1.80109e9i	0.349172	−	0.104847i
$841$	−1.60683e10			−0.931505
$842$	1.48810e10	−	1.48810e10i	0.859095	−	0.859095i
$843$	−1.12169e10	+	1.79937e8i	−0.644877	+	0.0103448i
$844$		−	1.20658e10i		−	0.690807i
$845$	−2.02260e9	−	7.15026e9i	−0.115322	−	0.407684i
$846$	−3.74311e7	−	1.16639e9i	−0.00212538	−	0.0662291i
$847$	1.65975e10	+	1.65975e10i	0.938538	+	0.938538i
$848$	1.29277e9	+	1.29277e9i	0.0728007	+	0.0728007i
$849$	−1.60926e10	−	1.55845e10i	−0.902504	−	0.874006i
$850$	5.33523e9	+	8.67594e9i	0.297980	+	0.484563i
$851$		−	6.36020e9i		−	0.353767i
$852$	1.63901e6	+	1.02173e8i	9.07912e−5	+	0.00565976i
$853$	−1.82356e10	+	1.82356e10i	−1.00600	+	1.00600i	−0.00601662	+	0.999982i	$0.501915\pi$
$853$	−1.82356e10	+	1.82356e10i	−1.00600	+	1.00600i	−0.999982	+	0.00601662i	$0.998085\pi$
$854$	8.99351e9			0.494113
$855$	1.04674e10	+	3.29321e10i	0.572738	+	1.80193i
$856$	−1.62354e9			−0.0884717
$857$	7.54295e9	−	7.54295e9i	0.409363	−	0.409363i	−0.472154	−	0.881516i	$-0.656523\pi$
$857$	7.54295e9	−	7.54295e9i	0.409363	−	0.409363i	0.881516	+	0.472154i	$0.156523\pi$
$858$	2.40914e8	+	1.50181e10i	0.0130214	+	0.811727i
$859$			2.51811e9i			0.135550i	0.997701	+	0.0677748i	$0.0215899\pi$
$859$			2.51811e9i			0.135550i	−0.997701	+	0.0677748i	$0.978410\pi$
$860$	−1.10334e10	−	6.16772e9i	−0.591514	−	0.330659i
$861$	−1.63741e10	−	1.58571e10i	−0.874274	−	0.846667i
$862$	1.88762e9	+	1.88762e9i	0.100378	+	0.100378i
$863$	5.60021e9	+	5.60021e9i	0.296597	+	0.296597i	0.839679	−	0.543082i	$-0.182743\pi$
$863$	5.60021e9	+	5.60021e9i	0.296597	+	0.296597i	−0.543082	+	0.839679i	$0.682743\pi$
$864$	2.48103e9	+	2.25305e9i	0.130868	+	0.118843i
$865$	2.90243e10	+	1.62247e10i	1.52477	+	0.852354i
$866$			1.27672e10i			0.668008i
$867$	−6.76949e9	+	1.08593e8i	−0.352768	+	0.00565894i
$868$	−6.53064e9	+	6.53064e9i	−0.338951	+	0.338951i
$869$	−5.22558e10			−2.70125
$870$	3.16523e9	+	1.70333e9i	0.162963	+	0.0876962i
$871$	−2.06084e9			−0.105677
$872$	−7.53151e9	+	7.53151e9i	−0.384658	+	0.384658i
$873$	−2.57599e8	−	2.41580e8i	−0.0131037	−	0.0122888i
$874$		−	2.35569e10i		−	1.19352i
$875$	2.04166e10	−	8.49958e8i	1.03028	−	0.0428913i
$876$	−6.80528e9	+	7.02717e9i	−0.342044	+	0.353196i
$877$	1.05803e8	+	1.05803e8i	0.00529661	+	0.00529661i	0.709750	−	0.704454i	$-0.248808\pi$
$877$	1.05803e8	+	1.05803e8i	0.00529661	+	0.00529661i	−0.704454	+	0.709750i	$0.748808\pi$
$878$	−2.55669e9	−	2.55669e9i	−0.127482	−	0.127482i
$879$	−6.46369e9	+	6.67444e9i	−0.321011	+	0.331477i
$880$	−2.08042e9	−	7.35468e9i	−0.102911	−	0.363810i
$881$		−	9.68685e8i		−	0.0477273i	−0.999715	−	0.0238637i	$-0.992403\pi$
$881$		−	9.68685e8i		−	0.0477273i	0.999715	−	0.0238637i	$-0.00759676\pi$
$882$	−6.65437e8	−	6.24056e8i	−0.0326563	−	0.0306255i
$883$	5.01947e9	−	5.01947e9i	0.245355	−	0.245355i	−0.573706	−	0.819061i	$-0.694495\pi$
$883$	5.01947e9	−	5.01947e9i	0.245355	−	0.245355i	0.819061	+	0.573706i	$0.194495\pi$
$884$	−6.27190e9			−0.305363
$885$	3.94153e9	+	1.31264e10i	0.191145	+	0.636569i
$886$	−6.79839e9			−0.328388
$887$	5.70163e9	−	5.70163e9i	0.274326	−	0.274326i	−0.556513	−	0.830839i	$-0.687861\pi$
$887$	5.70163e9	−	5.70163e9i	0.274326	−	0.274326i	0.830839	+	0.556513i	$0.187861\pi$
$888$	2.92318e9	−	4.68924e7i	0.140091	−	0.00224728i
$889$		−	1.11751e10i		−	0.533452i
$890$	5.65169e9	−	1.01103e10i	0.268728	−	0.480727i
$891$	−2.04735e9	−	3.18659e10i	−0.0969661	−	1.50923i
$892$	−1.08533e10	−	1.08533e10i	−0.512016	−	0.512016i
$893$	−2.66618e9	−	2.66618e9i	−0.125288	−	0.125288i
$894$	1.16464e10	+	1.12787e10i	0.545145	+	0.527931i
$895$	−2.37691e10	+	6.72357e9i	−1.10823	+	0.313487i
$896$		−	1.96247e9i		−	0.0911435i
$897$	2.34964e8	+	1.46472e10i	0.0108700	+	0.677613i
$898$	−1.74548e10	+	1.74548e10i	−0.804354	+	0.804354i
$899$	−5.30077e9			−0.243321
$900$	6.02386e9	+	9.12619e9i	0.275439	+	0.417293i
$901$	7.27382e9			0.331303
$902$	−1.96706e10	+	1.96706e10i	−0.892473	+	0.892473i
$903$	4.95987e8	+	3.09189e10i	0.0224163	+	1.39739i
$904$			8.58366e9i			0.386441i
$905$	7.68402e9	−	2.17358e9i	0.344602	−	0.0974778i
$906$	−1.69202e10	−	1.63860e10i	−0.755888	−	0.732020i
$907$	−7.14355e9	−	7.14355e9i	−0.317898	−	0.317898i	0.530061	−	0.847959i	$-0.322169\pi$
$907$	−7.14355e9	−	7.14355e9i	−0.317898	−	0.317898i	−0.847959	+	0.530061i	$0.822169\pi$
$908$	1.18717e10	+	1.18717e10i	0.526273	+	0.526273i
$909$	8.46808e8	+	2.63874e10i	0.0373948	+	1.16526i
$910$	−6.13988e9	+	1.09836e10i	−0.270094	+	0.483170i
$911$		−	7.12663e9i		−	0.312298i	−0.987733	−	0.156149i	$-0.950092\pi$
$911$		−	7.12663e9i		−	0.312298i	0.987733	−	0.156149i	$-0.0499081\pi$
$912$	1.08269e10	−	1.73680e8i	0.472630	−	0.00758172i
$913$	3.49974e10	−	3.49974e10i	1.52191	−	1.52191i
$914$	−2.40987e10			−1.04396
$915$	4.51603e9	+	1.50397e10i	0.194887	+	0.649030i
$916$	−6.46281e9			−0.277835
$917$	−9.62375e9	+	9.62375e9i	−0.412147	+	0.412147i
$918$	1.33182e10	−	6.41375e8i	0.568194	−	0.0273629i
$919$		−	7.47046e9i		−	0.317500i	−0.987319	−	0.158750i	$-0.949254\pi$
$919$		−	7.47046e9i		−	0.317500i	0.987319	−	0.158750i	$-0.0507463\pi$
$920$	−2.02904e9	−	7.17304e9i	−0.0859080	−	0.303701i
$921$	2.14048e10	−	2.21027e10i	0.902823	−	0.932260i
$922$	−2.00925e10	−	2.00925e10i	−0.844259	−	0.844259i
$923$	−1.45180e8	−	1.45180e8i	−0.00607715	−	0.00607715i
$924$	−1.30079e10	+	1.34321e10i	−0.542445	+	0.560132i
$925$	9.27899e9	+	2.21241e9i	0.385483	+	0.0919113i
$926$			6.21275e9i			0.257126i
$927$	1.28439e10	−	1.36955e10i	0.529561	−	0.564677i
$928$	7.96447e8	−	7.96447e8i	0.0327144	−	0.0327144i
$929$	2.65804e10			1.08769			0.543847	−	0.839184i	$-0.316967\pi$
$929$	2.65804e10			1.08769			0.543847	+	0.839184i	$0.316967\pi$
$930$	−1.42004e10	−	7.64175e9i	−0.578908	−	0.311532i
$931$	−2.94757e9			−0.119713
$932$	4.64171e9	−	4.64171e9i	0.187812	−	0.187812i
$933$	−1.56031e10	+	2.50299e8i	−0.628965	+	0.0100896i
$934$		−	2.92854e9i		−	0.117608i
$935$	−2.65435e10	−	1.48379e10i	−1.06198	−	0.593652i
$936$	−6.73021e9	+	2.15982e8i	−0.268264	+	0.00860897i
$937$	4.69611e9	+	4.69611e9i	0.186488	+	0.186488i	0.794176	−	0.607688i	$-0.207903\pi$
$937$	4.69611e9	+	4.69611e9i	0.186488	+	0.186488i	−0.607688	+	0.794176i	$0.707903\pi$
$938$	−1.81409e9	−	1.81409e9i	−0.0717711	−	0.0717711i
$939$	−8.01664e9	−	7.76350e9i	−0.315982	−	0.306005i
$940$	−1.04150e9	−	5.82200e8i	−0.0408987	−	0.0228626i
$941$			1.48675e10i			0.581668i	0.956774	+	0.290834i	$0.0939327\pi$
$941$			1.48675e10i			0.581668i	−0.956774	+	0.290834i	$0.906067\pi$
$942$	1.72016e8	+	1.07232e10i	0.00670488	+	0.417970i
$943$	−1.91848e10	+	1.91848e10i	−0.745019	+	0.745019i
$944$	4.29471e9			0.166162
$945$	1.19147e10	−	2.39513e10i	0.459273	−	0.923246i
$946$	3.77394e10			1.44936
$947$	2.02863e10	−	2.02863e10i	0.776209	−	0.776209i	−0.202975	−	0.979184i	$-0.565061\pi$
$947$	2.02863e10	−	2.02863e10i	0.776209	−	0.776209i	0.979184	+	0.202975i	$0.0650609\pi$
$948$	−3.75755e8	−	2.34239e10i	−0.0143244	−	0.892956i
$949$		−	1.96548e10i		−	0.746513i
$950$	3.43675e10	+	8.19431e9i	1.30052	+	0.310084i
$951$	2.52864e10	+	2.44879e10i	0.953355	+	0.923251i
$952$	−5.52097e9	−	5.52097e9i	−0.207389	−	0.207389i
$953$	−9.35730e9	−	9.35730e9i	−0.350208	−	0.350208i	0.509979	−	0.860187i	$-0.329653\pi$
$953$	−9.35730e9	−	9.35730e9i	−0.350208	−	0.350208i	−0.860187	+	0.509979i	$0.829653\pi$
$954$	7.80534e9	−	2.50484e8i	0.291053	−	0.00934029i
$955$	−6.53352e9	−	2.30972e10i	−0.242737	−	0.858120i
$956$			2.41042e10i			0.892258i
$957$	−1.07304e10	+	1.72132e8i	−0.395751	+	0.00634846i
$958$	8.77478e9	−	8.77478e9i	0.322446	−	0.322446i
$959$	7.45018e9			0.272773
$960$	3.28181e9	−	9.85443e8i	0.119719	−	0.0359486i
$961$	−3.73141e9			−0.135626
$962$	−4.15361e9	+	4.15361e9i	−0.150423	+	0.150423i
$963$	−4.74392e9	+	5.05849e9i	−0.171177	+	0.182528i
$964$			4.44698e9i			0.159881i
$965$	−6.54795e9	+	1.17136e10i	−0.234563	+	0.419609i
$966$	−1.26867e10	+	1.31003e10i	−0.452822	+	0.467587i
$967$	−1.14031e10	−	1.14031e10i	−0.405537	−	0.405537i	0.474642	−	0.880179i	$-0.342577\pi$
$967$	−1.14031e10	−	1.14031e10i	−0.405537	−	0.405537i	−0.880179	+	0.474642i	$0.842577\pi$
$968$	9.08112e9	+	9.08112e9i	0.321792	+	0.321792i
$969$	2.99703e10	−	3.09475e10i	1.05818	−	1.09268i
$970$	−3.47445e8	+	9.82818e7i	−0.0122232	+	0.00345758i
$971$		−	3.89442e9i		−	0.136513i	−0.997668	−	0.0682567i	$-0.978256\pi$
$971$		−	3.89442e9i		−	0.136513i	0.997668	−	0.0682567i	$-0.0217437\pi$
$972$	1.42693e10	−	1.14687e9i	0.498393	−	0.0400574i
$973$	3.13828e10	−	3.13828e10i	1.09219	−	1.09219i
$974$	1.69988e10			0.589470
$975$	−2.14508e10	−	4.75227e9i	−0.741186	−	0.164204i
$976$	4.92068e9			0.169415
$977$	−2.04105e10	+	2.04105e10i	−0.700202	+	0.700202i	−0.964454	−	0.264252i	$-0.914875\pi$
$977$	−2.04105e10	+	2.04105e10i	−0.700202	+	0.700202i	0.264252	+	0.964454i	$0.414875\pi$
$978$	−1.98140e10	+	3.17847e8i	−0.677309	+	0.0108651i
$979$			3.45819e10i			1.17790i
$980$	−8.97529e8	+	2.53884e8i	−0.0304619	+	0.00861677i
$981$	1.45929e9	+	4.54729e10i	0.0493513	+	1.53784i
$982$	1.36802e10	+	1.36802e10i	0.461002	+	0.461002i
$983$	−2.15633e10	−	2.15633e10i	−0.724066	−	0.724066i	0.245365	−	0.969431i	$-0.421092\pi$
$983$	−2.15633e10	−	2.15633e10i	−0.724066	−	0.724066i	−0.969431	+	0.245365i	$0.921092\pi$
$984$	−8.95890e9	−	8.67600e9i	−0.299759	−	0.290293i
$985$	4.10694e9	−	7.34689e9i	0.136928	−	0.244949i
$986$		−	4.48124e9i		−	0.148877i
$987$	4.68186e7	+	2.91858e9i	0.00154992	+	0.0966189i
$988$	−1.53841e10	+	1.53841e10i	−0.507486	+	0.507486i
$989$	3.68074e10			1.20990
$990$	−2.89940e10	−	1.50081e10i	−0.949697	−	0.491589i
$991$	1.91180e10			0.623999			0.312000	−	0.950082i	$-0.399001\pi$
$991$	1.91180e10			0.623999			0.312000	+	0.950082i	$0.399001\pi$
$992$	−3.57315e9	+	3.57315e9i	−0.116215	+	0.116215i
$993$	6.74024e8	+	4.20174e10i	0.0218450	+	1.36178i
$994$		−	2.55595e8i		−	0.00825466i
$995$	8.35279e9	+	2.95287e10i	0.268813	+	0.950306i
$996$	1.59394e10	+	1.54361e10i	0.511169	+	0.495028i
$997$	−3.08953e9	−	3.08953e9i	−0.0987322	−	0.0987322i	0.656015	−	0.754748i	$-0.272241\pi$
$997$	−3.08953e9	−	3.08953e9i	−0.0987322	−	0.0987322i	−0.754748	+	0.656015i	$0.772241\pi$
$998$	−1.70846e10	−	1.70846e10i	−0.544061	−	0.544061i
$999$	8.39533e9	−	9.24484e9i	0.266415	−	0.293373i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	30.8.e.a.17.12	yes	28
3.2	odd	2	inner	30.8.e.a.17.1	✓	28
5.2	odd	4		150.8.e.b.143.14		28
5.3	odd	4	inner	30.8.e.a.23.1	yes	28
5.4	even	2		150.8.e.b.107.7		28
15.2	even	4		150.8.e.b.143.7		28
15.8	even	4	inner	30.8.e.a.23.12	yes	28
15.14	odd	2		150.8.e.b.107.14		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
30.8.e.a.17.1	✓	28	3.2	odd	2	inner
30.8.e.a.17.12	yes	28	1.1	even	1	trivial
30.8.e.a.23.1	yes	28	5.3	odd	4	inner
30.8.e.a.23.12	yes	28	15.8	even	4	inner
150.8.e.b.107.7		28	5.4	even	2
150.8.e.b.107.14		28	15.14	odd	2
150.8.e.b.143.7		28	15.2	even	4
150.8.e.b.143.14		28	5.2	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 30 = 2 \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	30.e (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(5.65685 - 5.65685i) q^{2} +(0.750092 + 46.7594i) q^{3} -64.0000i q^{4} +(-268.955 + 76.0794i) q^{5} +(268.754 + 260.268i) q^{6} +(-661.697 - 661.697i) q^{7} +(-362.039 - 362.039i) q^{8} +(-2185.87 + 70.1477i) q^{9} +(-1091.07 + 1951.81i) q^{10} -6676.11i q^{11} +(2992.60 - 48.0059i) q^{12} +(-4252.25 + 4252.25i) q^{13} -7486.24 q^{14} +(-3759.17 - 12519.1i) q^{15} -4096.00 q^{16} +(-11523.1 + 11523.1i) q^{17} +(-11968.4 + 12762.0i) q^{18} +56529.5i q^{19} +(4869.08 + 17213.1i) q^{20} +(30444.2 - 31436.8i) q^{21} +(-37765.8 - 37765.8i) q^{22} +(-36833.1 - 36833.1i) q^{23} +(16657.1 - 17200.3i) q^{24} +(66548.8 - 40923.9i) q^{25} +48108.7i q^{26} +(-4919.67 - 102157. i) q^{27} +(-42348.6 + 42348.6i) q^{28} -34373.4 q^{29} +(-92083.8 - 49553.7i) q^{30} +154212. q^{31} +(-23170.5 + 23170.5i) q^{32} +(312171. - 5007.70i) q^{33} +130370. i q^{34} +(228308. + 127625. i) q^{35} +(4489.45 + 139896. i) q^{36} +(86338.1 + 86338.1i) q^{37} +(319779. + 319779. i) q^{38} +(-202022. - 195643. i) q^{39} +(124916. + 69828.5i) q^{40} -520858. i q^{41} +(-5615.37 - 350052. i) q^{42} +(-499651. + 499651. i) q^{43} -427271. q^{44} +(582566. - 185167. i) q^{45} -416719. q^{46} +(-47164.4 + 47164.4i) q^{47} +(-3072.38 - 191526. i) q^{48} +52142.1i q^{49} +(144956. - 607958. i) q^{50} +(-547458. - 530171. i) q^{51} +(272144. + 272144. i) q^{52} +(-315618. - 315618. i) q^{53} +(-605720. - 550060. i) q^{54} +(507915. + 1.79558e6i) q^{55} +479120. i q^{56} +(-2.64328e6 + 42402.3i) q^{57} +(-194445. + 194445. i) q^{58} -1.04851e6 q^{59} +(-801223. + 240587. i) q^{60} -1.20134e6 q^{61} +(872352. - 872352. i) q^{62} +(1.49280e6 + 1.39997e6i) q^{63} +262144. i q^{64} +(820155. - 1.46717e6i) q^{65} +(1.73758e6 - 1.79423e6i) q^{66} +(242323. + 242323. i) q^{67} +(737481. + 737481. i) q^{68} +(1.69466e6 - 1.74992e6i) q^{69} +(2.01346e6 - 569549. i) q^{70} +34141.9i q^{71} +(816767. + 765975. i) q^{72} +(-2.31111e6 + 2.31111e6i) q^{73} +976804. q^{74} +(1.96349e6 + 3.08108e6i) q^{75} +3.61789e6 q^{76} +(-4.41756e6 + 4.41756e6i) q^{77} +(-2.24953e6 + 36085.9i) q^{78} -7.82727e6i q^{79} +(1.10164e6 - 311621. i) q^{80} +(4.77313e6 - 306668. i) q^{81} +(-2.94642e6 - 2.94642e6i) q^{82} +(5.24218e6 + 5.24218e6i) q^{83} +(-2.01196e6 - 1.94843e6i) q^{84} +(2.22254e6 - 3.97588e6i) q^{85} +5.65291e6i q^{86} +(-25783.2 - 1.60728e6i) q^{87} +(-2.41701e6 + 2.41701e6i) q^{88} -5.17995e6 q^{89} +(2.24803e6 - 4.34295e6i) q^{90} +5.62739e6 q^{91} +(-2.35732e6 + 2.35732e6i) q^{92} +(115673. + 7.21083e6i) q^{93} +533605. i q^{94} +(-4.30073e6 - 1.52039e7i) q^{95} +(-1.10082e6 - 1.06606e6i) q^{96} +(114183. + 114183. i) q^{97} +(294960. + 294960. i) q^{98} +(468314. + 1.45931e7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 52 q^{3} - 928 q^{6} - 1348 q^{7} - 416 q^{10} + 3328 q^{12} - 21840 q^{13} - 37672 q^{15} - 114688 q^{16} + 50624 q^{18} - 142744 q^{21} - 47008 q^{22} + 419744 q^{25} + 212972 q^{27} - 86272 q^{28}+ \cdots + 82948404 q^{97}+O(q^{100}) \) 28 * q - 52 * q^3 - 928 * q^6 - 1348 * q^7 - 416 * q^10 + 3328 * q^12 - 21840 * q^13 - 37672 * q^15 - 114688 * q^16 + 50624 * q^18 - 142744 * q^21 - 47008 * q^22 + 419744 * q^25 + 212972 * q^27 - 86272 * q^28 - 301152 * q^30 - 44936 * q^31 + 1398788 * q^33 + 50432 * q^36 + 608088 * q^37 + 339968 * q^40 - 624032 * q^42 - 1288968 * q^43 - 656648 * q^45 - 1486208 * q^46 + 212992 * q^48 + 4263064 * q^51 + 1397760 * q^52 - 3985428 * q^55 - 9921952 * q^57 - 416480 * q^58 - 365824 * q^60 - 14602248 * q^61 + 4050428 * q^63 + 10106816 * q^66 + 22755248 * q^67 + 551584 * q^70 - 3239936 * q^72 - 522380 * q^73 - 17815892 * q^75 - 4901888 * q^76 + 8835840 * q^78 + 33339556 * q^81 + 22502528 * q^82 + 27842408 * q^85 - 38505100 * q^87 - 3008512 * q^88 - 26143552 * q^90 - 77623680 * q^91 + 70200824 * q^93 + 3801088 * q^96 + 82948404 * q^97

Introduction

L-functions

Modular forms

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