LMFDB - Embedded newform 60.7.c.a.31.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [60,7,Mod(31,60)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(60, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("60.31");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 60 = 2^{2} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	60.c (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$13.8032450172$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			31.19
Character	$\chi$	$=$	60.31
Dual form			60.7.c.a.31.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(5.40467 - 5.89827i) q^{2} +15.5885i q^{3} +(-5.57916 - 63.7564i) q^{4} -55.9017 q^{5} +(91.9449 + 84.2504i) q^{6} -125.427i q^{7} +(-406.206 - 311.674i) q^{8} -243.000 q^{9} +O(q^{10})$	\(q+(5.40467 - 5.89827i) q^{2} +15.5885i q^{3} +(-5.57916 - 63.7564i) q^{4} -55.9017 q^{5} +(91.9449 + 84.2504i) q^{6} -125.427i q^{7} +(-406.206 - 311.674i) q^{8} -243.000 q^{9} +(-302.130 + 329.723i) q^{10} -685.839i q^{11} +(993.863 - 86.9705i) q^{12} -3316.77 q^{13} +(-739.803 - 677.892i) q^{14} -871.421i q^{15} +(-4033.75 + 711.414i) q^{16} -3071.82 q^{17} +(-1313.33 + 1433.28i) q^{18} -6082.98i q^{19} +(311.884 + 3564.09i) q^{20} +1955.22 q^{21} +(-4045.26 - 3706.73i) q^{22} -6974.95i q^{23} +(4858.52 - 6332.12i) q^{24} +3125.00 q^{25} +(-17926.0 + 19563.2i) q^{26} -3788.00i q^{27} +(-7996.78 + 699.778i) q^{28} -13736.6 q^{29} +(-5139.88 - 4709.74i) q^{30} +37542.0i q^{31} +(-17604.9 + 27637.1i) q^{32} +10691.2 q^{33} +(-16602.2 + 18118.4i) q^{34} +7011.59i q^{35} +(1355.74 + 15492.8i) q^{36} +64357.4 q^{37} +(-35879.0 - 32876.5i) q^{38} -51703.3i q^{39} +(22707.6 + 17423.1i) q^{40} +2744.47 q^{41} +(10567.3 - 11532.4i) q^{42} -100421. i q^{43} +(-43726.6 + 3826.40i) q^{44} +13584.1 q^{45} +(-41140.2 - 37697.3i) q^{46} -72930.9i q^{47} +(-11089.8 - 62879.9i) q^{48} +101917. q^{49} +(16889.6 - 18432.1i) q^{50} -47884.9i q^{51} +(18504.8 + 211465. i) q^{52} +99684.3 q^{53} +(-22342.6 - 20472.9i) q^{54} +38339.6i q^{55} +(-39092.5 + 50949.2i) q^{56} +94824.2 q^{57} +(-74241.8 + 81022.2i) q^{58} -237946. i q^{59} +(-55558.6 + 4861.80i) q^{60} +274238. q^{61} +(221433. + 202902. i) q^{62} +30478.8i q^{63} +(67862.0 + 253208. i) q^{64} +185413. q^{65} +(57782.2 - 63059.4i) q^{66} +444734. i q^{67} +(17138.2 + 195848. i) q^{68} +108729. q^{69} +(41356.3 + 37895.3i) q^{70} -324805. i q^{71} +(98708.0 + 75736.9i) q^{72} -689523. q^{73} +(347830. - 379597. i) q^{74} +48713.9i q^{75} +(-387829. + 33937.9i) q^{76} -86022.8 q^{77} +(-304960. - 279439. i) q^{78} +147732. i q^{79} +(225493. - 39769.2i) q^{80} +59049.0 q^{81} +(14832.9 - 16187.6i) q^{82} -355588. i q^{83} +(-10908.5 - 124657. i) q^{84} +171720. q^{85} +(-592309. - 542741. i) q^{86} -214133. i q^{87} +(-213758. + 278592. i) q^{88} +24831.9 q^{89} +(73417.6 - 80122.8i) q^{90} +416013. i q^{91} +(-444698. + 38914.4i) q^{92} -585221. q^{93} +(-430166. - 394167. i) q^{94} +340049. i q^{95} +(-430819. - 274434. i) q^{96} -938268. q^{97} +(550828. - 601134. i) q^{98} +166659. i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 20 q^{2} - 246 q^{4} + 162 q^{6} - 340 q^{8} - 5832 q^{9}+O(q^{10}) $ 24 * q + 20 * q^2 - 246 * q^4 + 162 * q^6 - 340 * q^8 - 5832 * q^9	\( 24 q + 20 q^{2} - 246 q^{4} + 162 q^{6} - 340 q^{8} - 5832 q^{9} - 750 q^{10} + 5040 q^{13} - 2596 q^{14} + 4194 q^{16} - 4860 q^{18} + 7000 q^{20} + 19440 q^{21} + 45780 q^{22} + 24786 q^{24} + 75000 q^{25} + 75852 q^{26} + 54300 q^{28} + 132800 q^{29} - 10700 q^{32} - 173484 q^{34} + 59778 q^{36} - 69840 q^{37} + 215800 q^{38} - 14250 q^{40} - 70448 q^{41} - 189540 q^{42} - 395668 q^{44} - 158760 q^{46} + 252720 q^{48} - 642984 q^{49} + 62500 q^{50} - 210240 q^{52} - 644320 q^{53} - 39366 q^{54} - 917708 q^{56} + 408240 q^{57} - 1345020 q^{58} + 222750 q^{60} - 222864 q^{61} + 1948520 q^{62} + 935922 q^{64} + 266000 q^{65} - 640548 q^{66} + 572680 q^{68} - 541728 q^{69} + 220500 q^{70} + 82620 q^{72} + 771120 q^{73} - 589164 q^{74} - 191544 q^{76} + 1383840 q^{77} - 693360 q^{78} - 946000 q^{80} + 1417176 q^{81} + 2672520 q^{82} + 1256796 q^{84} - 372000 q^{85} + 1781528 q^{86} + 956940 q^{88} - 1566224 q^{89} + 182250 q^{90} - 3040560 q^{92} + 1496880 q^{93} - 3788352 q^{94} - 413262 q^{96} - 1666800 q^{97} - 2709660 q^{98}+O(q^{100}) \) 24 * q + 20 * q^2 - 246 * q^4 + 162 * q^6 - 340 * q^8 - 5832 * q^9 - 750 * q^10 + 5040 * q^13 - 2596 * q^14 + 4194 * q^16 - 4860 * q^18 + 7000 * q^20 + 19440 * q^21 + 45780 * q^22 + 24786 * q^24 + 75000 * q^25 + 75852 * q^26 + 54300 * q^28 + 132800 * q^29 - 10700 * q^32 - 173484 * q^34 + 59778 * q^36 - 69840 * q^37 + 215800 * q^38 - 14250 * q^40 - 70448 * q^41 - 189540 * q^42 - 395668 * q^44 - 158760 * q^46 + 252720 * q^48 - 642984 * q^49 + 62500 * q^50 - 210240 * q^52 - 644320 * q^53 - 39366 * q^54 - 917708 * q^56 + 408240 * q^57 - 1345020 * q^58 + 222750 * q^60 - 222864 * q^61 + 1948520 * q^62 + 935922 * q^64 + 266000 * q^65 - 640548 * q^66 + 572680 * q^68 - 541728 * q^69 + 220500 * q^70 + 82620 * q^72 + 771120 * q^73 - 589164 * q^74 - 191544 * q^76 + 1383840 * q^77 - 693360 * q^78 - 946000 * q^80 + 1417176 * q^81 + 2672520 * q^82 + 1256796 * q^84 - 372000 * q^85 + 1781528 * q^86 + 956940 * q^88 - 1566224 * q^89 + 182250 * q^90 - 3040560 * q^92 + 1496880 * q^93 - 3788352 * q^94 - 413262 * q^96 - 1666800 * q^97 - 2709660 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/60\mathbb{Z}\right)^\times$.

$n$	$31$	$37$	$41$
$\chi(n)$	$-1$	$1$	$1$

Coefficient data

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

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

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

$2$	5.40467	−	5.89827i	0.675583	−	0.737284i
$2$	5.40467	−	5.89827i	0.675583	−	0.737284i
$3$			15.5885i			0.577350i
$3$			15.5885i			0.577350i
$4$	−5.57916	−	63.7564i	−0.0871743	−	0.996193i
$5$	−55.9017			−0.447214
$5$	−55.9017			−0.447214
$6$	91.9449	+	84.2504i	0.425671	+	0.390048i
$7$		−	125.427i		−	0.365677i	−0.983143	−	0.182838i	$-0.941471\pi$
$7$		−	125.427i		−	0.365677i	0.983143	−	0.182838i	$-0.0585285\pi$
$8$	−406.206	−	311.674i	−0.793370	−	0.608739i
$9$	−243.000			−0.333333
$10$	−302.130	+	329.723i	−0.302130	+	0.329723i
$11$		−	685.839i		−	0.515281i	−0.966241	−	0.257640i	$-0.917055\pi$
$11$		−	685.839i		−	0.515281i	0.966241	−	0.257640i	$-0.0829450\pi$
$12$	993.863	−	86.9705i	0.575152	−	0.0503301i
$13$	−3316.77			−1.50968			−0.754840	−	0.655909i	$-0.772286\pi$
$13$	−3316.77			−1.50968			−0.754840	+	0.655909i	$0.772286\pi$
$14$	−739.803	−	677.892i	−0.269608	−	0.247045i
$15$		−	871.421i		−	0.258199i
$16$	−4033.75	+	711.414i	−0.984801	+	0.173685i
$17$	−3071.82			−0.625243			−0.312621	−	0.949878i	$-0.601207\pi$
$17$	−3071.82			−0.625243			−0.312621	+	0.949878i	$0.601207\pi$
$18$	−1313.33	+	1433.28i	−0.225194	+	0.245761i
$19$		−	6082.98i		−	0.886861i	−0.896309	−	0.443430i	$-0.853761\pi$
$19$		−	6082.98i		−	0.886861i	0.896309	−	0.443430i	$-0.146239\pi$
$20$	311.884	+	3564.09i	0.0389856	+	0.445511i
$21$	1955.22			0.211124
$22$	−4045.26	−	3706.73i	−0.379908	−	0.348115i
$23$		−	6974.95i		−	0.573268i	−0.958040	−	0.286634i	$-0.907464\pi$
$23$		−	6974.95i		−	0.573268i	0.958040	−	0.286634i	$-0.0925364\pi$
$24$	4858.52	−	6332.12i	0.351456	−	0.458053i
$25$	3125.00			0.200000
$26$	−17926.0	+	19563.2i	−1.01991	+	1.11306i
$27$		−	3788.00i		−	0.192450i
$28$	−7996.78	+	699.778i	−0.364285	+	0.0318776i
$29$	−13736.6			−0.563230			−0.281615	−	0.959528i	$-0.590870\pi$
$29$	−13736.6			−0.563230			−0.281615	+	0.959528i	$0.590870\pi$
$30$	−5139.88	−	4709.74i	−0.190366	−	0.174435i
$31$			37542.0i			1.26018i	0.776523	+	0.630089i	$0.216982\pi$
$31$			37542.0i			1.26018i	−0.776523	+	0.630089i	$0.783018\pi$
$32$	−17604.9	+	27637.1i	−0.537260	+	0.843417i
$33$	10691.2			0.297498
$34$	−16602.2	+	18118.4i	−0.422404	+	0.460981i
$35$			7011.59i			0.163536i
$36$	1355.74	+	15492.8i	0.0290581	+	0.332064i
$37$	64357.4			1.27055			0.635277	−	0.772284i	$-0.280886\pi$
$37$	64357.4			1.27055			0.635277	+	0.772284i	$0.280886\pi$
$38$	−35879.0	−	32876.5i	−0.653868	−	0.599148i
$39$		−	51703.3i		−	0.871614i
$40$	22707.6	+	17423.1i	0.354806	+	0.272236i
$41$	2744.47			0.0398205			0.0199103	−	0.999802i	$-0.493662\pi$
$41$	2744.47			0.0398205			0.0199103	+	0.999802i	$0.493662\pi$
$42$	10567.3	−	11532.4i	0.142632	−	0.155658i
$43$		−	100421.i		−	1.26304i	−0.775358	−	0.631522i	$-0.782431\pi$
$43$		−	100421.i		−	1.26304i	0.775358	−	0.631522i	$-0.217569\pi$
$44$	−43726.6	+	3826.40i	−0.513319	+	0.0449193i
$45$	13584.1			0.149071
$46$	−41140.2	−	37697.3i	−0.422661	−	0.387290i
$47$		−	72930.9i		−	0.702455i	−0.936290	−	0.351227i	$-0.885764\pi$
$47$		−	72930.9i		−	0.702455i	0.936290	−	0.351227i	$-0.114236\pi$
$48$	−11089.8	−	62879.9i	−0.100277	−	0.568575i
$49$	101917.			0.866280
$50$	16889.6	−	18432.1i	0.135117	−	0.147457i
$51$		−	47884.9i		−	0.360984i
$52$	18504.8	+	211465.i	0.131605	+	1.50393i
$53$	99684.3			0.669575			0.334787	−	0.942294i	$-0.391335\pi$
$53$	99684.3			0.669575			0.334787	+	0.942294i	$0.391335\pi$
$54$	−22342.6	−	20472.9i	−0.141890	−	0.130016i
$55$			38339.6i			0.230441i
$56$	−39092.5	+	50949.2i	−0.222602	+	0.290117i
$57$	94824.2			0.512029
$58$	−74241.8	+	81022.2i	−0.380509	+	0.415260i
$59$		−	237946.i		−	1.15857i	−0.815126	−	0.579284i	$-0.803332\pi$
$59$		−	237946.i		−	1.15857i	0.815126	−	0.579284i	$-0.196668\pi$
$60$	−55558.6	+	4861.80i	−0.257216	+	0.0225083i
$61$	274238.			1.20820			0.604099	−	0.796909i	$-0.293533\pi$
$61$	274238.			1.20820			0.604099	+	0.796909i	$0.293533\pi$
$62$	221433.	+	202902.i	0.929108	+	0.851355i
$63$			30478.8i			0.121892i
$64$	67862.0	+	253208.i	0.258873	+	0.965911i
$65$	185413.			0.675150
$66$	57782.2	−	63059.4i	0.200984	−	0.219340i
$67$			444734.i			1.47869i	0.673329	+	0.739343i	$0.264864\pi$
$67$			444734.i			1.47869i	−0.673329	+	0.739343i	$0.735136\pi$
$68$	17138.2	+	195848.i	0.0545051	+	0.622863i
$69$	108729.			0.330977
$70$	41356.3	+	37895.3i	0.120572	+	0.110482i
$71$		−	324805.i		−	0.907502i	−0.891128	−	0.453751i	$-0.850086\pi$
$71$		−	324805.i		−	0.907502i	0.891128	−	0.453751i	$-0.149914\pi$
$72$	98708.0	+	75736.9i	0.264457	+	0.202913i
$73$	−689523.			−1.77247			−0.886237	−	0.463231i	$-0.846690\pi$
$73$	−689523.			−1.77247			−0.886237	+	0.463231i	$0.846690\pi$
$74$	347830.	−	379597.i	0.858365	−	0.936759i
$75$			48713.9i			0.115470i
$76$	−387829.	+	33937.9i	−0.883485	+	0.0773115i
$77$	−86022.8			−0.188426
$78$	−304960.	−	279439.i	−0.642627	−	0.588848i
$79$			147732.i			0.299636i	0.988714	+	0.149818i	$0.0478687\pi$
$79$			147732.i			0.299636i	−0.988714	+	0.149818i	$0.952131\pi$
$80$	225493.	−	39769.2i	0.440417	−	0.0776743i
$81$	59049.0			0.111111
$82$	14832.9	−	16187.6i	0.0269021	−	0.0293590i
$83$		−	355588.i		−	0.621889i	−0.950428	−	0.310944i	$-0.899355\pi$
$83$		−	355588.i		−	0.621889i	0.950428	−	0.310944i	$-0.100645\pi$
$84$	−10908.5	−	124657.i	−0.0184046	−	0.210320i
$85$	171720.			0.279617
$86$	−592309.	−	542741.i	−0.931221	−	0.853291i
$87$		−	214133.i		−	0.325181i
$88$	−213758.	+	278592.i	−0.313672	+	0.408809i
$89$	24831.9			0.0352241			0.0176121	−	0.999845i	$-0.494394\pi$
$89$	24831.9			0.0352241			0.0176121	+	0.999845i	$0.494394\pi$
$90$	73417.6	−	80122.8i	0.100710	−	0.109908i
$91$			416013.i			0.552055i
$92$	−444698.	+	38914.4i	−0.571086	+	0.0499743i
$93$	−585221.			−0.727564
$94$	−430166.	−	394167.i	−0.517908	−	0.474567i
$95$			340049.i			0.396616i
$96$	−430819.	−	274434.i	−0.486947	−	0.310187i
$97$	−938268.			−1.02804			−0.514022	−	0.857777i	$-0.671845\pi$
$97$	−938268.			−1.02804			−0.514022	+	0.857777i	$0.671845\pi$
$98$	550828.	−	601134.i	0.585245	−	0.638694i
$99$			166659.i			0.171760i
$100$	−17434.9	−	199239.i	−0.0174349	−	0.199239i
$101$	−1.57672e6			−1.53035			−0.765175	−	0.643822i	$-0.777348\pi$
$101$	−1.57672e6			−1.53035			−0.765175	+	0.643822i	$0.777348\pi$
$102$	−282438.	−	258802.i	−0.266148	−	0.243875i
$103$			1.87489e6i			1.71579i	0.513825	+	0.857895i	$0.328228\pi$
$103$			1.87489e6i			1.71579i	−0.513825	+	0.857895i	$0.671772\pi$
$104$	1.34729e6	+	1.03375e6i	1.19774	+	0.919002i
$105$	−109300.			−0.0944174
$106$	538760.	−	587965.i	0.452354	−	0.493667i
$107$		−	1.81947e6i		−	1.48523i	−0.669719	−	0.742615i	$-0.733585\pi$
$107$		−	1.81947e6i		−	1.48523i	0.669719	−	0.742615i	$-0.266415\pi$
$108$	−241509.	+	21133.8i	−0.191717	+	0.0167767i
$109$	1.10563e6			0.853747			0.426873	−	0.904311i	$-0.359615\pi$
$109$	1.10563e6			0.853747			0.426873	+	0.904311i	$0.359615\pi$
$110$	226137.	+	207213.i	0.169900	+	0.155682i
$111$			1.00323e6i			0.733555i
$112$	89230.6	+	505941.i	0.0635126	+	0.360119i
$113$	−2.60750e6			−1.80713			−0.903563	−	0.428454i	$-0.859058\pi$
$113$	−2.60750e6			−1.80713			−0.903563	+	0.428454i	$0.859058\pi$
$114$	512493.	−	559299.i	0.345918	−	0.377511i
$115$			389912.i			0.256373i
$116$	76638.7	+	875796.i	0.0490992	+	0.561086i
$117$	805975.			0.503227
$118$	−1.40347e6	−	1.28602e6i	−0.854193	−	0.782709i
$119$			385290.i			0.228637i
$120$	−271600.	+	353976.i	−0.157176	+	0.204847i
$121$	1.30119e6			0.734486
$122$	1.48216e6	−	1.61753e6i	0.816238	−	0.890784i
$123$			42782.0i			0.0229904i
$124$	2.39354e6	−	209452.i	1.25538	−	0.109855i
$125$	−174693.			−0.0894427
$126$	179772.	+	164728.i	0.0898692	+	0.0823484i
$127$			113916.i			0.0556127i	0.999613	+	0.0278064i	$0.00885218\pi$
$127$			113916.i			0.0556127i	−0.999613	+	0.0278064i	$0.991148\pi$
$128$	1.86026e6	+	968235.i	0.887041	+	0.461691i
$129$	1.56540e6			0.729218
$130$	1.00210e6	−	1.09362e6i	0.456120	−	0.497777i
$131$			305614.i			0.135944i	0.997687	+	0.0679720i	$0.0216528\pi$
$131$			305614.i			0.135944i	−0.997687	+	0.0679720i	$0.978347\pi$
$132$	−59647.7	−	681630.i	−0.0259342	−	0.296365i
$133$	−762971.			−0.324305
$134$	2.62316e6	+	2.40364e6i	1.09021	+	0.998976i
$135$			211755.i			0.0860663i
$136$	1.24779e6	+	957407.i	0.496049	+	0.380610i
$137$	−1.92315e6			−0.747913			−0.373957	−	0.927446i	$-0.621999\pi$
$137$	−1.92315e6			−0.747913			−0.373957	+	0.927446i	$0.621999\pi$
$138$	587643.	−	641311.i	0.223602	−	0.244024i
$139$			1.07520e6i			0.400353i	0.979760	+	0.200177i	$0.0641516\pi$
$139$			1.07520e6i			0.400353i	−0.979760	+	0.200177i	$0.935848\pi$
$140$	447034.	−	39118.8i	0.162913	−	0.0142561i
$141$	1.13688e6			0.405562
$142$	−1.91579e6	−	1.75546e6i	−0.669086	−	0.613093i
$143$			2.27477e6i			0.777909i
$144$	980200.	−	172873.i	0.328267	−	0.0578950i
$145$	767900.			0.251884
$146$	−3.72664e6	+	4.06699e6i	−1.19745	+	1.30682i
$147$			1.58873e6i			0.500147i
$148$	−359060.	−	4.10319e6i	−0.110760	−	1.26572i
$149$	3.38454e6			1.02315			0.511577	−	0.859238i	$-0.329062\pi$
$149$	3.38454e6			1.02315			0.511577	+	0.859238i	$0.329062\pi$
$150$	287328.	+	263283.i	0.0851342	+	0.0780096i
$151$		−	6.23793e6i		−	1.81180i	−0.423494	−	0.905899i	$-0.639197\pi$
$151$		−	6.23793e6i		−	1.81180i	0.423494	−	0.905899i	$-0.360803\pi$
$152$	−1.89591e6	+	2.47094e6i	−0.539867	+	0.703609i
$153$	746452.			0.208414
$154$	−464925.	+	507386.i	−0.127298	+	0.138924i
$155$		−	2.09866e6i		−	0.563569i
$156$	−3.29641e6	+	288461.i	−0.868296	+	0.0759824i
$157$	−249290.			−0.0644179			−0.0322090	−	0.999481i	$-0.510254\pi$
$157$	−249290.			−0.0644179			−0.0322090	+	0.999481i	$0.510254\pi$
$158$	871364.	+	798443.i	0.220916	+	0.202429i
$159$			1.55392e6i			0.386579i
$160$	984146.	−	1.54496e6i	0.240270	−	0.377187i
$161$	−874849.			−0.209631
$162$	319140.	−	348287.i	0.0750648	−	0.0819204i
$163$		−	1.98756e6i		−	0.458942i	−0.973316	−	0.229471i	$-0.926300\pi$
$163$		−	1.98756e6i		−	0.458942i	0.973316	−	0.229471i	$-0.0736996\pi$
$164$	−15311.8	−	174977.i	−0.00347133	−	0.0396689i
$165$	−597654.			−0.133045
$166$	−2.09735e6	−	1.92183e6i	−0.458509	−	0.420138i
$167$		−	4.42965e6i		−	0.951086i	−0.879693	−	0.475543i	$-0.842252\pi$
$167$		−	4.42965e6i		−	0.951086i	0.879693	−	0.475543i	$-0.157748\pi$
$168$	−794220.	−	609391.i	−0.167499	−	0.128519i
$169$	6.17414e6			1.27913
$170$	928089.	−	1.01285e6i	0.188905	−	0.206157i
$171$			1.47816e6i			0.295620i
$172$	−6.40246e6	+	560263.i	−1.25823	+	0.110105i
$173$	−7.51606e6			−1.45162			−0.725808	−	0.687897i	$-0.758534\pi$
$173$	−7.51606e6			−1.45162			−0.725808	+	0.687897i	$0.758534\pi$
$174$	−1.26301e6	−	1.15732e6i	−0.239751	−	0.219687i
$175$		−	391960.i		−	0.0731354i
$176$	487915.	+	2.76650e6i	0.0894965	+	0.507449i
$177$	3.70920e6			0.668899
$178$	134208.	−	146465.i	0.0237968	−	0.0259702i
$179$		−	2.01873e6i		−	0.351980i	−0.984392	−	0.175990i	$-0.943687\pi$
$179$		−	2.01873e6i		−	0.351980i	0.984392	−	0.175990i	$-0.0563127\pi$
$180$	−75787.9	−	866074.i	−0.0129952	−	0.148504i
$181$	6.78948e6			1.14499			0.572493	−	0.819909i	$-0.305976\pi$
$181$	6.78948e6			1.14499			0.572493	+	0.819909i	$0.305976\pi$
$182$	2.45376e6	+	2.24841e6i	0.407021	+	0.372959i
$183$			4.27495e6i			0.697553i
$184$	−2.17391e6	+	2.83327e6i	−0.348971	+	0.454814i
$185$	−3.59769e6			−0.568209
$186$	−3.16293e6	+	3.45179e6i	−0.491530	+	0.536421i
$187$			2.10677e6i			0.322176i
$188$	−4.64981e6	+	406893.i	−0.699780	+	0.0612360i
$189$	−475118.			−0.0703746
$190$	2.00570e6	+	1.83785e6i	0.292419	+	0.267947i
$191$		−	9.09426e6i		−	1.30517i	−0.757715	−	0.652585i	$-0.773684\pi$
$191$		−	9.09426e6i		−	1.30517i	0.757715	−	0.652585i	$-0.226316\pi$
$192$	−3.94712e6	+	1.05786e6i	−0.557669	+	0.149460i
$193$	−7.91992e6			−1.10166			−0.550831	−	0.834616i	$-0.685689\pi$
$193$	−7.91992e6			−1.10166			−0.550831	+	0.834616i	$0.685689\pi$
$194$	−5.07103e6	+	5.53416e6i	−0.694530	+	0.757960i
$195$			2.89030e6i			0.389798i
$196$	−568611.	−	6.49786e6i	−0.0755174	−	0.862982i
$197$	1.10853e7			1.44994			0.724969	−	0.688781i	$-0.241854\pi$
$197$	1.10853e7			1.44994			0.724969	+	0.688781i	$0.241854\pi$
$198$	982999.	+	900735.i	0.126636	+	0.116038i
$199$		−	55779.8i		−	0.00707812i	−0.999994	−	0.00353906i	$-0.998873\pi$
$199$		−	55779.8i		−	0.00707812i	0.999994	−	0.00353906i	$-0.00112652\pi$
$200$	−1.26939e6	−	973983.i	−0.158674	−	0.121748i
$201$	−6.93272e6			−0.853720
$202$	−8.52165e6	+	9.29993e6i	−1.03388	+	1.12830i
$203$			1.72294e6i			0.205960i
$204$	−3.05297e6	+	267157.i	−0.359610	+	0.0314686i
$205$	−153421.			−0.0178083
$206$	1.10586e7	+	1.01332e7i	1.26502	+	1.15916i
$207$			1.69491e6i			0.191089i
$208$	1.33790e7	−	2.35959e6i	1.48674	−	0.262209i
$209$	−4.17194e6			−0.456982
$210$	−590730.	+	644680.i	−0.0637868	+	0.0696124i
$211$		−	1.32243e7i		−	1.40775i	−0.710322	−	0.703877i	$-0.751451\pi$
$211$		−	1.32243e7i		−	1.40775i	0.710322	−	0.703877i	$-0.248549\pi$
$212$	−556154.	−	6.35551e6i	−0.0583697	−	0.667026i
$213$	5.06321e6			0.523947
$214$	−1.07317e7	−	9.83363e6i	−1.09504	−	1.00340i
$215$			5.61369e6i			0.564850i
$216$	−1.18062e6	+	1.53870e6i	−0.117152	+	0.152684i
$217$	4.70878e6			0.460818
$218$	5.97554e6	−	6.52128e6i	0.576777	−	0.629453i
$219$		−	1.07486e7i		−	1.02334i
$220$	2.44439e6	−	213902.i	0.229563	−	0.0200885i
$221$	1.01885e7			0.943917
$222$	5.91733e6	+	5.42213e6i	0.540838	+	0.495577i
$223$			9.36634e6i			0.844609i	0.906454	+	0.422304i	$0.138779\pi$
$223$			9.36634e6i			0.844609i	−0.906454	+	0.422304i	$0.861221\pi$
$224$	3.46644e6	+	2.20814e6i	0.308418	+	0.196464i
$225$	−759375.			−0.0666667
$226$	−1.40927e7	+	1.53797e7i	−1.22086	+	1.33237i
$227$		−	1.58575e7i		−	1.35568i	−0.735211	−	0.677838i	$-0.762917\pi$
$227$		−	1.58575e7i		−	1.35568i	0.735211	−	0.677838i	$-0.237083\pi$
$228$	−529039.	−	6.04565e6i	−0.0446358	−	0.510080i
$229$	−1.61507e7			−1.34489			−0.672443	−	0.740149i	$-0.734755\pi$
$229$	−1.61507e7			−1.34489			−0.672443	+	0.740149i	$0.734755\pi$
$230$	2.29980e6	+	2.10734e6i	0.189020	+	0.173202i
$231$		−	1.34096e6i		−	0.108788i
$232$	5.57989e6	+	4.28135e6i	0.446850	+	0.342860i
$233$	−4.22772e6			−0.334224			−0.167112	−	0.985938i	$-0.553444\pi$
$233$	−4.22772e6			−0.334224			−0.167112	+	0.985938i	$0.553444\pi$
$234$	4.35602e6	−	4.75385e6i	0.339972	−	0.371021i
$235$			4.07696e6i			0.314147i
$236$	−1.51705e7	+	1.32754e6i	−1.15416	+	0.100997i
$237$	−2.30292e6			−0.172995
$238$	2.27254e6	+	2.08236e6i	0.168570	+	0.154463i
$239$			3.67362e6i			0.269092i	0.990907	+	0.134546i	$0.0429575\pi$
$239$			3.67362e6i			0.269092i	−0.990907	+	0.134546i	$0.957042\pi$
$240$	619941.	+	3.51509e6i	0.0448453	+	0.254275i
$241$	2.03391e7			1.45305			0.726526	−	0.687139i	$-0.241134\pi$
$241$	2.03391e7			1.45305			0.726526	+	0.687139i	$0.241134\pi$
$242$	7.03248e6	−	7.67475e6i	0.496206	−	0.541524i
$243$			920483.i			0.0641500i
$244$	−1.53002e6	−	1.74844e7i	−0.105324	−	1.20360i
$245$	−5.69733e6			−0.387412
$246$	252340.	+	231223.i	0.0169504	+	0.0155319i
$247$			2.01758e7i			1.33888i
$248$	1.17009e7	−	1.52498e7i	0.767120	−	0.999788i
$249$	5.54307e6			0.359048
$250$	−944156.	+	1.03039e6i	−0.0604260	+	0.0659447i
$251$		−	69668.3i		−	0.00440569i	−0.999998	−	0.00220285i	$-0.999299\pi$
$251$		−	69668.3i		−	0.00440569i	0.999998	−	0.00220285i	$-0.000701188\pi$
$252$	1.94322e6	−	170046.i	0.121428	−	0.0106259i
$253$	−4.78369e6			−0.295394
$254$	671908.	+	615679.i	0.0410023	+	0.0375710i
$255$			2.67685e6i			0.161437i
$256$	1.57650e7	−	5.73932e6i	0.939667	−	0.342090i
$257$	1.05098e7			0.619151			0.309575	−	0.950875i	$-0.399813\pi$
$257$	1.05098e7			0.619151			0.309575	+	0.950875i	$0.399813\pi$
$258$	8.46049e6	−	9.23318e6i	0.492648	−	0.537641i
$259$		−	8.07216e6i		−	0.464612i
$260$	−1.03445e6	−	1.18213e7i	−0.0588557	−	0.672579i
$261$	3.33800e6			0.187743
$262$	1.80260e6	+	1.65174e6i	0.100229	+	0.0918415i
$263$			3.25978e7i			1.79193i	0.444124	+	0.895965i	$0.353515\pi$
$263$			3.25978e7i			1.79193i	−0.444124	+	0.895965i	$0.646485\pi$
$264$	−4.34281e6	−	3.33216e6i	−0.236026	−	0.181098i
$265$	−5.57252e6			−0.299443
$266$	−4.12360e6	+	4.50021e6i	−0.219095	+	0.239104i
$267$			387091.i			0.0203367i
$268$	2.83546e7	−	2.48124e6i	1.47306	−	0.128903i
$269$	−1.89694e7			−0.974534			−0.487267	−	0.873253i	$-0.662006\pi$
$269$	−1.89694e7			−0.974534			−0.487267	+	0.873253i	$0.662006\pi$
$270$	1.24899e6	+	1.14447e6i	0.0634553	+	0.0581450i
$271$			1.42827e7i			0.717634i	0.933408	+	0.358817i	$0.116820\pi$
$271$			1.42827e7i			0.717634i	−0.933408	+	0.358817i	$0.883180\pi$
$272$	1.23909e7	−	2.18533e6i	0.615740	−	0.108595i
$273$	−6.48500e6			−0.318729
$274$	−1.03940e7	+	1.13432e7i	−0.505278	+	0.551424i
$275$		−	2.14325e6i		−	0.103056i
$276$	−606615.	−	6.93215e6i	−0.0288527	−	0.329716i
$277$	−120847.			−0.00568586			−0.00284293	−	0.999996i	$-0.500905\pi$
$277$	−120847.			−0.00568586			−0.00284293	+	0.999996i	$0.500905\pi$
$278$	6.34180e6	+	5.81108e6i	0.295174	+	0.270472i
$279$		−	9.12269e6i		−	0.420059i
$280$	2.18533e6	−	2.84815e6i	0.0995506	−	0.129744i
$281$	2.02777e7			0.913901			0.456951	−	0.889492i	$-0.348942\pi$
$281$	2.02777e7			0.913901			0.456951	+	0.889492i	$0.348942\pi$
$282$	6.14446e6	−	6.70563e6i	0.273991	−	0.299014i
$283$			2.06847e7i			0.912618i	0.889821	+	0.456309i	$0.150829\pi$
$283$			2.06847e7i			0.912618i	−0.889821	+	0.456309i	$0.849171\pi$
$284$	−2.07084e7	+	1.81214e6i	−0.904047	+	0.0791109i
$285$	−5.30084e6			−0.228986
$286$	1.34172e7	+	1.22944e7i	0.573540	+	0.525543i
$287$		−	344231.i		−	0.0145614i
$288$	4.27800e6	−	6.71581e6i	0.179087	−	0.281139i
$289$	−1.47015e7			−0.609071
$290$	4.15024e6	−	4.52928e6i	0.170169	−	0.185710i
$291$		−	1.46262e7i		−	0.593542i
$292$	3.84696e6	+	4.39615e7i	0.154514	+	1.76573i
$293$	−1.71395e6			−0.0681390			−0.0340695	−	0.999419i	$-0.510847\pi$
$293$	−1.71395e6			−0.0681390			−0.0340695	+	0.999419i	$0.510847\pi$
$294$	9.37075e6	+	8.58655e6i	0.368750	+	0.337891i
$295$			1.33016e7i			0.518127i
$296$	−2.61423e7	−	2.00585e7i	−1.00802	−	0.773436i
$297$	−2.59795e6			−0.0991658
$298$	1.82923e7	−	1.99629e7i	0.691225	−	0.754354i
$299$			2.31343e7i			0.865452i
$300$	3.10582e6	−	271783.i	0.115030	−	0.0100660i
$301$	−1.25955e7			−0.461866
$302$	−3.67930e7	−	3.37139e7i	−1.33581	−	1.22402i
$303$		−	2.45786e7i		−	0.883548i
$304$	4.32751e6	+	2.45372e7i	0.154034	+	0.873382i
$305$	−1.53304e7			−0.540322
$306$	4.03432e6	−	4.40277e6i	0.140801	−	0.153660i
$307$		−	2.97507e7i		−	1.02821i	−0.857727	−	0.514105i	$-0.828124\pi$
$307$		−	2.97507e7i		−	1.02821i	0.857727	−	0.514105i	$-0.171876\pi$
$308$	479935.	+	5.48450e6i	0.0164259	+	0.187709i
$309$	−2.92266e7			−0.990612
$310$	−1.23785e7	−	1.13426e7i	−0.415510	−	0.380738i
$311$			2.32545e7i			0.773084i	0.922272	+	0.386542i	$0.126331\pi$
$311$			2.32545e7i			0.773084i	−0.922272	+	0.386542i	$0.873669\pi$
$312$	−1.61146e7	+	2.10022e7i	−0.530586	+	0.691513i
$313$	−2.24367e7			−0.731688			−0.365844	−	0.930676i	$-0.619220\pi$
$313$	−2.24367e7			−0.731688			−0.365844	+	0.930676i	$0.619220\pi$
$314$	−1.34733e6	+	1.47038e6i	−0.0435197	+	0.0474943i
$315$		−	1.70382e6i		−	0.0545119i
$316$	9.41886e6	−	824221.i	0.298495	−	0.0261205i
$317$	−1.50965e7			−0.473914			−0.236957	−	0.971520i	$-0.576150\pi$
$317$	−1.50965e7			−0.473914			−0.236957	+	0.971520i	$0.576150\pi$
$318$	9.16546e6	+	8.39844e6i	0.285019	+	0.261166i
$319$			9.42110e6i			0.290222i
$320$	−3.79360e6	−	1.41547e7i	−0.115772	−	0.431969i
$321$	2.83627e7			0.857498
$322$	−4.72827e6	+	5.16009e6i	−0.141623	+	0.154557i
$323$			1.86858e7i			0.554503i
$324$	−329444.	−	3.76475e6i	−0.00968604	−	0.110688i
$325$	−1.03649e7			−0.301936
$326$	−1.17232e7	−	1.07421e7i	−0.338370	−	0.310053i
$327$			1.72350e7i			0.492911i
$328$	−1.11482e6	−	855381.i	−0.0315924	−	0.0242403i
$329$	−9.14752e6			−0.256871
$330$	−3.23012e6	+	3.52513e6i	−0.0898829	+	0.0980919i
$331$		−	5.09403e7i		−	1.40468i	−0.711842	−	0.702340i	$-0.752139\pi$
$331$		−	5.09403e7i		−	1.40468i	0.711842	−	0.702340i	$-0.247861\pi$
$332$	−2.26710e7	+	1.98388e6i	−0.619521	+	0.0542128i
$333$	−1.56388e7			−0.423518
$334$	−2.61272e7	−	2.39408e7i	−0.701220	−	0.642538i
$335$		−	2.48614e7i		−	0.661289i
$336$	−7.88685e6	+	1.39097e6i	−0.207915	+	0.0366690i
$337$	−3.39896e7			−0.888090			−0.444045	−	0.896005i	$-0.646457\pi$
$337$	−3.39896e7			−0.888090			−0.444045	+	0.896005i	$0.646457\pi$
$338$	3.33692e7	−	3.64167e7i	0.864162	−	0.943085i
$339$		−	4.06469e7i		−	1.04335i
$340$	−958052.	−	1.09482e7i	−0.0243754	−	0.278553i
$341$	2.57477e7			0.649345
$342$	8.71861e6	+	7.98898e6i	0.217956	+	0.199716i
$343$		−	2.75396e7i		−	0.682456i
$344$	−3.12986e7	+	4.07915e7i	−0.768864	+	1.00206i
$345$	−6.07812e6			−0.148017
$346$	−4.06218e7	+	4.43317e7i	−0.980687	+	1.07025i
$347$		−	7.60373e7i		−	1.81986i	−0.414761	−	0.909931i	$-0.636135\pi$
$347$		−	7.60373e7i		−	1.81986i	0.414761	−	0.909931i	$-0.363865\pi$
$348$	−1.36523e7	+	1.19468e6i	−0.323943	+	0.0283474i
$349$	3.85106e7			0.905949			0.452975	−	0.891523i	$-0.350363\pi$
$349$	3.85106e7			0.905949			0.452975	+	0.891523i	$0.350363\pi$
$350$	−2.31189e6	−	2.11841e6i	−0.0539215	−	0.0494091i
$351$			1.25639e7i			0.290538i
$352$	1.89546e7	+	1.20742e7i	0.434596	+	0.276840i
$353$	7.10717e7			1.61574			0.807872	−	0.589358i	$-0.200619\pi$
$353$	7.10717e7			1.61574			0.807872	+	0.589358i	$0.200619\pi$
$354$	2.00470e7	−	2.18779e7i	0.451897	−	0.493169i
$355$			1.81572e7i			0.405847i
$356$	−138541.	−	1.58319e6i	−0.00307064	−	0.0350900i
$357$	−6.00607e6			−0.132004
$358$	−1.19070e7	−	1.09105e7i	−0.259509	−	0.237792i
$359$			7.94912e7i			1.71805i	0.511934	+	0.859025i	$0.328929\pi$
$359$			7.94912e7i			1.71805i	−0.511934	+	0.859025i	$0.671071\pi$
$360$	−5.51794e6	−	4.23382e6i	−0.118269	−	0.0907455i
$361$	1.00433e7			0.213478
$362$	3.66949e7	−	4.00462e7i	0.773534	−	0.844180i
$363$			2.02835e7i			0.424055i
$364$	2.65235e7	−	2.32100e6i	0.549954	−	0.0481251i
$365$	3.85455e7			0.792675
$366$	2.52148e7	+	2.31047e7i	0.514295	+	0.471255i
$367$			4.00489e6i			0.0810200i	0.999179	+	0.0405100i	$0.0128983\pi$
$367$			4.00489e6i			0.0810200i	−0.999179	+	0.0405100i	$0.987102\pi$
$368$	4.96208e6	+	2.81352e7i	0.0995680	+	0.564555i
$369$	−666906.			−0.0132735
$370$	−1.94443e7	+	2.12201e7i	−0.383873	+	0.418931i
$371$		−	1.25031e7i		−	0.244848i
$372$	3.26504e6	+	3.73116e7i	0.0634249	+	0.724794i
$373$	3.28411e6			0.0632836			0.0316418	−	0.999499i	$-0.489926\pi$
$373$	3.28411e6			0.0632836			0.0316418	+	0.999499i	$0.489926\pi$
$374$	1.24263e7	+	1.13864e7i	0.237535	+	0.217656i
$375$		−	2.72319e6i		−	0.0516398i
$376$	−2.27307e7	+	2.96250e7i	−0.427612	+	0.557307i
$377$	4.55612e7			0.850297
$378$	−2.56785e6	+	2.80237e6i	−0.0475439	+	0.0518860i
$379$		−	3.03692e7i		−	0.557848i	−0.960313	−	0.278924i	$-0.910022\pi$
$379$		−	3.03692e7i		−	0.557848i	0.960313	−	0.278924i	$-0.0899778\pi$
$380$	2.16803e7	−	1.89719e6i	0.395106	−	0.0345748i
$381$	−1.77578e6			−0.0321080
$382$	−5.36404e7	−	4.91514e7i	−0.962281	−	0.881752i
$383$			8.62249e7i			1.53475i	0.641201	+	0.767373i	$0.278437\pi$
$383$			8.62249e7i			1.53475i	−0.641201	+	0.767373i	$0.721563\pi$
$384$	−1.50933e7	+	2.89986e7i	−0.266557	+	0.512133i
$385$	4.80882e6			0.0842668
$386$	−4.28045e7	+	4.67138e7i	−0.744265	+	0.812238i
$387$			2.44022e7i			0.421014i
$388$	5.23475e6	+	5.98206e7i	0.0896191	+	1.02413i
$389$	9.20364e7			1.56355			0.781773	−	0.623563i	$-0.214315\pi$
$389$	9.20364e7			1.56355			0.781773	+	0.623563i	$0.214315\pi$
$390$	1.70478e7	+	1.56211e7i	0.287392	+	0.263341i
$391$			2.14258e7i			0.358432i
$392$	−4.13993e7	−	3.17649e7i	−0.687281	−	0.527339i
$393$	−4.76406e6			−0.0784873
$394$	5.99125e7	−	6.53842e7i	0.979554	−	1.06902i
$395$		−	8.25847e6i		−	0.134001i
$396$	1.06256e7	−	929816.i	0.171106	−	0.0149731i
$397$	8.16043e7			1.30419			0.652096	−	0.758136i	$-0.273890\pi$
$397$	8.16043e7			1.30419			0.652096	+	0.758136i	$0.273890\pi$
$398$	−329004.	−	301471.i	−0.00521858	−	0.00478186i
$399$		−	1.18935e7i		−	0.187237i
$400$	−1.26055e7	+	2.22317e6i	−0.196960	+	0.0347370i
$401$	4.00404e7			0.620962			0.310481	−	0.950580i	$-0.399510\pi$
$401$	4.00404e7			0.620962			0.310481	+	0.950580i	$0.399510\pi$
$402$	−3.74690e7	+	4.08910e7i	−0.576759	+	0.629434i
$403$		−	1.24518e8i		−	1.90247i
$404$	8.79678e6	+	1.00526e8i	0.133407	+	1.52452i
$405$	−3.30094e6			−0.0496904
$406$	1.01624e7	+	9.31194e6i	0.151851	+	0.139143i
$407$		−	4.41388e7i		−	0.654692i
$408$	−1.49245e7	+	1.94511e7i	−0.219745	+	0.286394i
$409$	1.10874e8			1.62054			0.810272	−	0.586054i	$-0.199319\pi$
$409$	1.10874e8			1.62054			0.810272	+	0.586054i	$0.199319\pi$
$410$	−829187.	+	904915.i	−0.0120310	+	0.0131297i
$411$		−	2.99789e7i		−	0.431808i
$412$	1.19536e8	−	1.04603e7i	1.70926	−	0.149573i
$413$	−2.98448e7			−0.423662
$414$	9.99706e6	+	9.16044e6i	0.140887	+	0.129097i
$415$			1.98780e7i			0.278117i
$416$	5.83915e7	−	9.16658e7i	0.811091	−	1.27329i
$417$	−1.67606e7			−0.231144
$418$	−2.25480e7	+	2.46072e7i	−0.308730	+	0.336926i
$419$		−	6.94644e7i		−	0.944322i	−0.881512	−	0.472161i	$-0.843474\pi$
$419$		−	6.94644e7i		−	0.944322i	0.881512	−	0.472161i	$-0.156526\pi$
$420$	609802.	+	6.96856e6i	0.00823077	+	0.0940579i
$421$	−7.39798e7			−0.991441			−0.495721	−	0.868482i	$-0.665096\pi$
$421$	−7.39798e7			−0.991441			−0.495721	+	0.868482i	$0.665096\pi$
$422$	−7.80008e7	−	7.14732e7i	−1.03791	−	0.951055i
$423$			1.77222e7i			0.234152i
$424$	−4.04923e7	−	3.10691e7i	−0.531221	−	0.407596i
$425$	−9.59943e6			−0.125049
$426$	2.73650e7	−	2.98642e7i	0.353970	−	0.386297i
$427$		−	3.43969e7i		−	0.441810i
$428$	−1.16003e8	+	1.01511e7i	−1.47958	+	0.129474i
$429$	−3.54601e7			−0.449126
$430$	3.31111e7	+	3.03401e7i	0.416455	+	0.381603i
$431$			2.84179e7i			0.354945i	0.984126	+	0.177472i	$0.0567920\pi$
$431$			2.84179e7i			0.354945i	−0.984126	+	0.177472i	$0.943208\pi$
$432$	2.69483e6	+	1.52798e7i	0.0334257	+	0.189525i
$433$	−1.07801e8			−1.32788			−0.663938	−	0.747787i	$-0.731116\pi$
$433$	−1.07801e8			−1.32788			−0.663938	+	0.747787i	$0.731116\pi$
$434$	2.54494e7	−	2.77737e7i	0.311321	−	0.339754i
$435$			1.19704e7i			0.145425i
$436$	−6.16847e6	−	7.04907e7i	−0.0744248	−	0.850497i
$437$	−4.24285e7			−0.508409
$438$	−6.33981e7	−	5.80926e7i	−0.754491	−	0.691351i
$439$		−	2.74240e7i		−	0.324144i	−0.986779	−	0.162072i	$-0.948182\pi$
$439$		−	2.74240e7i		−	0.324144i	0.986779	−	0.162072i	$-0.0518177\pi$
$440$	1.19495e7	−	1.55737e7i	0.140278	−	0.182825i
$441$	−2.47658e7			−0.288760
$442$	5.50655e7	−	6.00946e7i	0.637694	−	0.695934i
$443$			1.05313e6i			0.0121135i	0.999982	+	0.00605677i	$0.00192794\pi$
$443$			1.05313e6i			0.0121135i	−0.999982	+	0.00605677i	$0.998072\pi$
$444$	6.39624e7	−	5.59719e6i	0.730762	−	0.0639471i
$445$	−1.38815e6			−0.0157527
$446$	5.52452e7	+	5.06220e7i	0.622716	+	0.570604i
$447$			5.27597e7i			0.590718i
$448$	3.17592e7	−	8.51175e6i	0.353212	−	0.0946639i
$449$	−1.37073e8			−1.51431			−0.757153	−	0.653237i	$-0.773411\pi$
$449$	−1.37073e8			−1.51431			−0.757153	+	0.653237i	$0.773411\pi$
$450$	−4.10417e6	+	4.47900e6i	−0.0450389	+	0.0491522i
$451$		−	1.88226e6i		−	0.0205187i
$452$	1.45476e7	+	1.66245e8i	0.157535	+	1.80025i
$453$	9.72397e7			1.04604
$454$	−9.35315e7	−	8.57042e7i	−0.999518	−	0.915872i
$455$		−	2.32558e7i		−	0.246887i
$456$	−3.85181e7	−	2.95543e7i	−0.406229	−	0.311692i
$457$	−1.02848e7			−0.107757			−0.0538786	−	0.998547i	$-0.517158\pi$
$457$	−1.02848e7			−0.107757			−0.0538786	+	0.998547i	$0.517158\pi$
$458$	−8.72893e7	+	9.52613e7i	−0.908583	+	0.991563i
$459$			1.16360e7i			0.120328i
$460$	2.48594e7	−	2.17538e6i	0.255397	−	0.0223492i
$461$	−1.70299e8			−1.73824			−0.869119	−	0.494603i	$-0.835314\pi$
$461$	−1.70299e8			−1.73824			−0.869119	+	0.494603i	$0.835314\pi$
$462$	−7.90936e6	−	7.24746e6i	−0.0802076	−	0.0734954i
$463$		−	8.24512e7i		−	0.830719i	−0.909657	−	0.415360i	$-0.863656\pi$
$463$		−	8.24512e7i		−	0.830719i	0.909657	−	0.415360i	$-0.136344\pi$
$464$	5.54100e7	−	9.77241e6i	0.554670	−	0.0978246i
$465$	3.27149e7			0.325376
$466$	−2.28494e7	+	2.49362e7i	−0.225796	+	0.246418i
$467$			1.65279e8i			1.62281i	0.584487	+	0.811403i	$0.301296\pi$
$467$			1.65279e8i			1.62281i	−0.584487	+	0.811403i	$0.698704\pi$
$468$	−4.49666e6	−	5.13860e7i	−0.0438685	−	0.501311i
$469$	5.57817e7			0.540721
$470$	2.40470e7	+	2.20346e7i	0.231616	+	0.212233i
$471$		−	3.88605e6i		−	0.0371917i
$472$	−7.41615e7	+	9.66548e7i	−0.705266	+	0.919173i
$473$	−6.88725e7			−0.650822
$474$	−1.24465e7	+	1.35832e7i	−0.116872	+	0.127546i
$475$		−	1.90093e7i		−	0.177372i
$476$	2.45647e7	−	2.14959e6i	0.227766	−	0.0199313i
$477$	−2.42233e7			−0.223192
$478$	2.16680e7	+	1.98547e7i	0.198397	+	0.181794i
$479$			1.47850e8i			1.34529i	0.739965	+	0.672645i	$0.234842\pi$
$479$			1.47850e8i			1.34529i	−0.739965	+	0.672645i	$0.765158\pi$
$480$	2.40835e7	+	1.53413e7i	0.217769	+	0.138720i
$481$	−2.13458e8			−1.91813
$482$	1.09926e8	−	1.19966e8i	0.981657	−	1.07131i
$483$		−	1.36375e7i		−	0.121030i
$484$	−7.25952e6	−	8.29589e7i	−0.0640283	−	0.731690i
$485$	5.24508e7			0.459755
$486$	5.42926e6	+	4.97490e6i	0.0472968	+	0.0433387i
$487$			2.20767e8i			1.91138i	0.294379	+	0.955689i	$0.404887\pi$
$487$			2.20767e8i			1.91138i	−0.294379	+	0.955689i	$0.595113\pi$
$488$	−1.11397e8	−	8.54730e7i	−0.958548	−	0.735477i
$489$	3.09830e7			0.264970
$490$	−3.07922e7	+	3.36044e7i	−0.261729	+	0.285633i
$491$		−	3.00650e7i		−	0.253990i	−0.991903	−	0.126995i	$-0.959467\pi$
$491$		−	3.00650e7i		−	0.253990i	0.991903	−	0.126995i	$-0.0405333\pi$
$492$	2.72763e6	−	238688.i	0.0229029	−	0.00200417i
$493$	4.21964e7			0.352155
$494$	1.19002e8	+	1.09044e8i	0.987132	+	0.904522i
$495$		−	9.31651e6i		−	0.0768135i
$496$	−2.67079e7	−	1.51435e8i	−0.218874	−	1.24102i
$497$	−4.07394e7			−0.331853
$498$	2.99584e7	−	3.26945e7i	0.242567	−	0.264720i
$499$			7.22660e7i			0.581611i	0.956782	+	0.290805i	$0.0939233\pi$
$499$			7.22660e7i			0.581611i	−0.956782	+	0.290805i	$0.906077\pi$
$500$	974639.	+	1.11378e7i	0.00779711	+	0.0891022i
$501$	6.90514e7			0.549110
$502$	−410922.	−	376534.i	−0.00324824	−	0.00297641i
$503$		−	5.97200e7i		−	0.469262i	−0.972084	−	0.234631i	$-0.924612\pi$
$503$		−	5.97200e7i		−	0.469262i	0.972084	−	0.234631i	$-0.0753882\pi$
$504$	9.49947e6	−	1.23807e7i	0.0742006	−	0.0967058i
$505$	8.81414e7			0.684393
$506$	−2.58543e7	+	2.82155e7i	−0.199563	+	0.217789i
$507$			9.62453e7i			0.738509i
$508$	7.26288e6	−	635556.i	0.0554010	−	0.00484800i
$509$	−4.00798e7			−0.303929			−0.151964	−	0.988386i	$-0.548560\pi$
$509$	−4.00798e7			−0.303929			−0.151964	+	0.988386i	$0.548560\pi$
$510$	1.57888e7	+	1.44675e7i	0.119025	+	0.109064i
$511$			8.64849e7i			0.648153i
$512$	5.13525e7	−	1.24005e8i	0.382606	−	0.923912i
$513$	−2.30423e7			−0.170676
$514$	5.68021e7	−	6.19898e7i	0.418288	−	0.456490i
$515$		−	1.04810e8i		−	0.767325i
$516$	−8.73364e6	−	9.98045e7i	−0.0635691	−	0.726442i
$517$	−5.00189e7			−0.361961
$518$	−4.76118e7	−	4.36274e7i	−0.342551	−	0.313884i
$519$		−	1.17164e8i		−	0.838091i
$520$	−7.53158e7	−	5.77885e7i	−0.535644	−	0.410990i
$521$	1.91011e7			0.135066			0.0675328	−	0.997717i	$-0.478487\pi$
$521$	1.91011e7			0.135066			0.0675328	+	0.997717i	$0.478487\pi$
$522$	1.80408e7	−	1.96884e7i	0.126836	−	0.138420i
$523$		−	3.75454e7i		−	0.262453i	−0.991352	−	0.131226i	$-0.958108\pi$
$523$		−	3.75454e7i		−	0.262453i	0.991352	−	0.131226i	$-0.0418915\pi$
$524$	1.94849e7	−	1.70507e6i	0.135426	−	0.0118508i
$525$	6.11005e6			0.0422247
$526$	1.92271e8	+	1.76180e8i	1.32116	+	1.21060i
$527$		−	1.15322e8i		−	0.787917i
$528$	−4.31255e7	+	7.60584e6i	−0.292976	+	0.0516708i
$529$	9.93859e7			0.671364
$530$	−3.01176e7	+	3.28682e7i	−0.202299	+	0.220774i
$531$			5.78208e7i			0.386189i
$532$	4.25674e6	+	4.86442e7i	0.0282710	+	0.323070i
$533$	−9.10277e6			−0.0601162
$534$	2.28317e6	+	2.09210e6i	0.0149939	+	0.0137391i
$535$			1.01711e8i			0.664215i
$536$	1.38612e8	−	1.80653e8i	0.900134	−	1.17315i
$537$	3.14688e7			0.203216
$538$	−1.02523e8	+	1.11887e8i	−0.658379	+	0.718508i
$539$		−	6.98986e7i		−	0.446378i
$540$	1.35008e7	−	1.18142e6i	0.0857386	−	0.00750277i
$541$	−8.06882e7			−0.509587			−0.254793	−	0.966996i	$-0.582007\pi$
$541$	−8.06882e7			−0.509587			−0.254793	+	0.966996i	$0.582007\pi$
$542$	8.42433e7	+	7.71933e7i	0.529100	+	0.484822i
$543$			1.05837e8i			0.661059i
$544$	5.40792e7	−	8.48961e7i	0.335918	−	0.527340i
$545$	−6.18064e7			−0.381807
$546$	−3.50493e7	+	3.82503e7i	−0.215328	+	0.234994i
$547$			1.82861e7i			0.111727i	0.998438	+	0.0558635i	$0.0177912\pi$
$547$			1.82861e7i			0.111727i	−0.998438	+	0.0558635i	$0.982209\pi$
$548$	1.07296e7	+	1.22613e8i	0.0651988	+	0.745066i
$549$	−6.66398e7			−0.402733
$550$	−1.26414e7	−	1.15835e7i	−0.0759816	−	0.0696230i
$551$			8.35595e7i			0.499506i
$552$	−4.41662e7	−	3.38880e7i	−0.262587	−	0.201478i
$553$	1.85296e7			0.109570
$554$	−653137.	+	712787.i	−0.00384127	+	0.00419209i
$555$		−	5.60824e7i		−	0.328056i
$556$	6.85506e7	−	5.99869e6i	0.398829	−	0.0349005i
$557$	−4.93908e7			−0.285812			−0.142906	−	0.989736i	$-0.545645\pi$
$557$	−4.93908e7			−0.285812			−0.142906	+	0.989736i	$0.545645\pi$
$558$	−5.38081e7	−	4.93051e7i	−0.309703	−	0.283785i
$559$			3.33072e8i			1.90679i
$560$	−4.98814e6	−	2.82830e7i	−0.0284037	−	0.161050i
$561$	−3.28413e7			−0.186008
$562$	1.09594e8	−	1.19603e8i	0.617417	−	0.673805i
$563$		−	3.24854e8i		−	1.82038i	−0.414186	−	0.910192i	$-0.635934\pi$
$563$		−	3.24854e8i		−	1.82038i	0.414186	−	0.910192i	$-0.364066\pi$
$564$	−6.34284e6	−	7.24834e7i	−0.0353546	−	0.404018i
$565$	1.45764e8			0.808172
$566$	1.22004e8	+	1.11794e8i	0.672858	+	0.616550i
$567$		−	7.40635e6i		−	0.0406308i
$568$	−1.01233e8	+	1.31938e8i	−0.552432	+	0.719985i
$569$	1.91757e7			0.104091			0.0520457	−	0.998645i	$-0.483426\pi$
$569$	1.91757e7			0.104091			0.0520457	+	0.998645i	$0.483426\pi$
$570$	−2.86493e7	+	3.12658e7i	−0.154699	+	0.168828i
$571$			1.60446e8i			0.861825i	0.902394	+	0.430913i	$0.141808\pi$
$571$			1.60446e8i			0.861825i	−0.902394	+	0.430913i	$0.858192\pi$
$572$	1.45031e8	−	1.26913e7i	0.774948	−	0.0678137i
$573$	1.41766e8			0.753541
$574$	−2.03037e6	−	1.86045e6i	−0.0107359	−	0.00983747i
$575$		−	2.17967e7i		−	0.114654i
$576$	−1.64905e7	−	6.15295e7i	−0.0862911	−	0.321970i
$577$	−2.87271e6			−0.0149543			−0.00747713	−	0.999972i	$-0.502380\pi$
$577$	−2.87271e6			−0.0149543			−0.00747713	+	0.999972i	$0.502380\pi$
$578$	−7.94567e7	+	8.67134e7i	−0.411478	+	0.449058i
$579$		−	1.23459e8i		−	0.636045i
$580$	−4.28424e6	−	4.89585e7i	−0.0219578	−	0.250925i
$581$	−4.46004e7			−0.227410
$582$	−8.62690e7	−	7.90495e7i	−0.437609	−	0.400987i
$583$		−	6.83674e7i		−	0.345019i
$584$	2.80088e8	+	2.14907e8i	1.40623	+	1.07897i
$585$	−4.50553e7			−0.225050
$586$	−9.26333e6	+	1.01093e7i	−0.0460335	+	0.0502377i
$587$		−	3.45048e8i		−	1.70595i	−0.521954	−	0.852974i	$-0.674797\pi$
$587$		−	3.45048e8i		−	1.70595i	0.521954	−	0.852974i	$-0.325203\pi$
$588$	1.01292e8	−	8.86377e6i	0.498243	−	0.0436000i
$589$	2.28367e8			1.11760
$590$	7.84562e7	+	7.18905e7i	0.382007	+	0.350038i
$591$			1.72803e8i			0.837122i
$592$	−2.59601e8	+	4.57847e7i	−1.25124	+	0.220676i
$593$	2.63257e8			1.26246			0.631228	−	0.775598i	$-0.282551\pi$
$593$	2.63257e8			1.26246			0.631228	+	0.775598i	$0.282551\pi$
$594$	−1.40411e7	+	1.53234e7i	−0.0669948	+	0.0731134i
$595$		−	2.15383e7i		−	0.102250i
$596$	−1.88829e7	−	2.15786e8i	−0.0891927	−	1.01926i
$597$	869521.			0.00408655
$598$	1.36452e8	+	1.25033e8i	0.638083	+	0.584685i
$599$		−	3.84709e8i		−	1.78999i	−0.446072	−	0.894997i	$-0.647178\pi$
$599$		−	3.84709e8i		−	1.78999i	0.446072	−	0.894997i	$-0.352822\pi$
$600$	1.51829e7	−	1.97879e7i	0.0702911	−	0.0916105i
$601$	−3.33173e7			−0.153478			−0.0767390	−	0.997051i	$-0.524451\pi$
$601$	−3.33173e7			−0.153478			−0.0767390	+	0.997051i	$0.524451\pi$
$602$	−6.80745e7	+	7.42916e7i	−0.312029	+	0.340526i
$603$		−	1.08070e8i		−	0.492895i
$604$	−3.97708e8	+	3.48024e7i	−1.80490	+	0.157942i
$605$	−7.27385e7			−0.328472
$606$	−1.44971e8	−	1.32839e8i	−0.651425	−	0.596910i
$607$		−	2.17537e8i		−	0.972672i	−0.873772	−	0.486336i	$-0.838333\pi$
$607$		−	2.17537e8i		−	0.972672i	0.873772	−	0.486336i	$-0.161667\pi$
$608$	1.68116e8	+	1.07090e8i	0.747993	+	0.476475i
$609$	−2.68581e7			−0.118911
$610$	−8.28555e7	+	9.04226e7i	−0.365033	+	0.398371i
$611$			2.41895e8i			1.06048i
$612$	−4.16457e6	−	4.75910e7i	−0.0181684	−	0.207621i
$613$	2.89945e8			1.25874			0.629368	−	0.777108i	$-0.283314\pi$
$613$	2.89945e8			1.25874			0.629368	+	0.777108i	$0.283314\pi$
$614$	−1.75477e8	−	1.60792e8i	−0.758082	−	0.694641i
$615$		−	2.39159e6i		−	0.0102816i
$616$	3.49430e7	+	2.68111e7i	0.149492	+	0.114702i
$617$	3.03530e6			0.0129225			0.00646124	−	0.999979i	$-0.497943\pi$
$617$	3.03530e6			0.0129225			0.00646124	+	0.999979i	$0.497943\pi$
$618$	−1.57960e8	+	1.72387e8i	−0.669241	+	0.730362i
$619$			3.35021e8i			1.41254i	0.707944	+	0.706268i	$0.249623\pi$
$619$			3.35021e8i			1.41254i	−0.707944	+	0.706268i	$0.750377\pi$
$620$	−1.33803e8	+	1.17087e7i	−0.561423	+	0.0491287i
$621$	−2.64211e7			−0.110326
$622$	1.37161e8	+	1.25683e8i	0.569982	+	0.522282i
$623$		−	3.11460e6i		−	0.0128806i
$624$	3.67824e7	+	2.08558e8i	0.151386	+	0.858367i
$625$	9.76562e6			0.0400000
$626$	−1.21263e8	+	1.32338e8i	−0.494316	+	0.539461i
$627$		−	6.50341e7i		−	0.263839i
$628$	1.39083e6	+	1.58939e7i	0.00561559	+	0.0641727i
$629$	−1.97694e8			−0.794405
$630$	−1.00496e7	−	9.20856e6i	−0.0401907	−	0.0368273i
$631$		−	2.24962e8i		−	0.895408i	−0.894182	−	0.447704i	$-0.852242\pi$
$631$		−	2.24962e8i		−	0.895408i	0.894182	−	0.447704i	$-0.147758\pi$
$632$	4.60443e7	−	6.00096e7i	0.182400	−	0.237722i
$633$	2.06147e8			0.812767
$634$	−8.15918e7	+	8.90435e7i	−0.320169	+	0.349409i
$635$		−	6.36811e6i		−	0.0248708i
$636$	9.90726e7	−	8.66959e6i	0.385108	−	0.0336998i
$637$	−3.38035e8			−1.30781
$638$	5.55682e7	+	5.09179e7i	0.213976	+	0.196069i
$639$			7.89276e7i			0.302501i
$640$	−1.03992e8	−	5.41260e7i	−0.396697	−	0.206474i
$641$	1.37727e8			0.522931			0.261466	−	0.965213i	$-0.415794\pi$
$641$	1.37727e8			0.522931			0.261466	+	0.965213i	$0.415794\pi$
$642$	1.53291e8	−	1.67291e8i	0.579311	−	0.632219i
$643$		−	2.19532e8i		−	0.825781i	−0.910781	−	0.412890i	$-0.864519\pi$
$643$		−	2.19532e8i		−	0.825781i	0.910781	−	0.412890i	$-0.135481\pi$
$644$	4.88092e6	+	5.57772e7i	0.0182744	+	0.208833i
$645$	−8.75088e7			−0.326116
$646$	1.10214e8	+	1.00991e8i	0.408826	+	0.374613i
$647$			2.78194e8i			1.02715i	0.858043	+	0.513577i	$0.171680\pi$
$647$			2.78194e8i			1.02715i	−0.858043	+	0.513577i	$0.828320\pi$
$648$	−2.39860e7	−	1.84041e7i	−0.0881523	−	0.0676377i
$649$	−1.63192e8			−0.596988
$650$	−5.60188e7	+	6.11350e7i	−0.203983	+	0.222613i
$651$			7.34026e7i			0.266053i
$652$	−1.26720e8	+	1.10889e7i	−0.457195	+	0.0400080i
$653$	3.99925e8			1.43628			0.718140	−	0.695898i	$-0.244994\pi$
$653$	3.99925e8			1.43628			0.718140	+	0.695898i	$0.244994\pi$
$654$	1.01657e8	+	9.31495e7i	0.363415	+	0.333002i
$655$		−	1.70844e7i		−	0.0607960i
$656$	−1.10705e7	+	1.95245e6i	−0.0392153	+	0.00691622i
$657$	1.67554e8			0.590825
$658$	−4.94393e7	+	5.39546e7i	−0.173538	+	0.189387i
$659$		−	2.98899e8i		−	1.04440i	−0.852822	−	0.522202i	$-0.825111\pi$
$659$		−	2.98899e8i		−	1.04440i	0.852822	−	0.522202i	$-0.174889\pi$
$660$	3.33441e6	+	3.81043e7i	0.0115981	+	0.132538i
$661$	3.58267e8			1.24052			0.620258	−	0.784397i	$-0.287028\pi$
$661$	3.58267e8			1.24052			0.620258	+	0.784397i	$0.287028\pi$
$662$	−3.00459e8	−	2.75315e8i	−1.03565	−	0.948978i
$663$			1.58823e8i			0.544971i
$664$	−1.10828e8	+	1.44442e8i	−0.378568	+	0.493388i
$665$	4.26514e7			0.145033
$666$	−8.45227e7	+	9.22421e7i	−0.286122	+	0.312253i
$667$			9.58122e7i			0.322882i
$668$	−2.82418e8	+	2.47137e7i	−0.947465	+	0.0829103i
$669$	−1.46007e8			−0.487635
$670$	−1.46639e8	−	1.34368e8i	−0.487557	−	0.446755i
$671$		−	1.88083e8i		−	0.622561i
$672$	−3.44215e7	+	5.40365e7i	−0.113428	+	0.178065i
$673$	−4.43991e8			−1.45656			−0.728281	−	0.685279i	$-0.759680\pi$
$673$	−4.43991e8			−1.45656			−0.728281	+	0.685279i	$0.759680\pi$
$674$	−1.83703e8	+	2.00480e8i	−0.599979	+	0.654774i
$675$		−	1.18375e7i		−	0.0384900i
$676$	−3.44465e7	−	3.93641e8i	−0.111508	−	1.27427i
$677$	−2.82838e8			−0.911533			−0.455767	−	0.890099i	$-0.650635\pi$
$677$	−2.82838e8			−0.911533			−0.455767	+	0.890099i	$0.650635\pi$
$678$	−2.39746e8	−	2.19683e8i	−0.769241	−	0.704867i
$679$			1.17684e8i			0.375932i
$680$	−6.97536e7	−	5.35207e7i	−0.221840	−	0.170214i
$681$	2.47193e8			0.782700
$682$	1.39158e8	−	1.51867e8i	0.438687	−	0.478752i
$683$			5.76518e8i			1.80947i	0.425978	+	0.904733i	$0.359930\pi$
$683$			5.76518e8i			1.80947i	−0.425978	+	0.904733i	$0.640070\pi$
$684$	9.42423e7	−	8.24691e6i	0.294495	−	0.0257705i
$685$	1.07507e8			0.334477
$686$	−1.62436e8	−	1.48842e8i	−0.503163	−	0.461056i
$687$		−	2.51765e8i		−	0.776470i
$688$	7.14407e7	+	4.05072e8i	0.219372	+	1.24385i
$689$	−3.30630e8			−1.01084
$690$	−3.28502e7	+	3.58504e7i	−0.0999979	+	0.109131i
$691$		−	2.97209e8i		−	0.900799i	−0.892827	−	0.450399i	$-0.851282\pi$
$691$		−	2.97209e8i		−	0.900799i	0.892827	−	0.450399i	$-0.148718\pi$
$692$	4.19333e7	+	4.79196e8i	0.126544	+	1.44609i
$693$	2.09035e7			0.0628088
$694$	−4.48488e8	−	4.10956e8i	−1.34175	−	1.22947i
$695$		−	6.01053e7i		−	0.179043i
$696$	−6.67397e7	+	8.69819e7i	−0.197950	+	0.257989i
$697$	−8.43051e6			−0.0248975
$698$	2.08137e8	−	2.27146e8i	0.612044	−	0.667942i
$699$		−	6.59036e7i		−	0.192964i
$700$	−2.49899e7	+	2.18681e6i	−0.0728570	+	0.00637553i
$701$	−4.28723e8			−1.24458			−0.622289	−	0.782787i	$-0.713797\pi$
$701$	−4.28723e8			−1.24458			−0.622289	+	0.782787i	$0.713797\pi$
$702$	7.41053e7	+	6.79037e7i	0.214209	+	0.196283i
$703$		−	3.91484e8i		−	1.12680i
$704$	1.73660e8	−	4.65424e7i	0.497716	−	0.133392i
$705$	−6.35536e7			−0.181373
$706$	3.84119e8	−	4.19200e8i	1.09157	−	1.19126i
$707$			1.97764e8i			0.559614i
$708$	−2.06942e7	−	2.36485e8i	−0.0583109	−	0.666353i
$709$	−1.53889e8			−0.431785			−0.215893	−	0.976417i	$-0.569266\pi$
$709$	−1.53889e8			−0.431785			−0.215893	+	0.976417i	$0.569266\pi$
$710$	1.07096e8	+	9.81333e7i	0.299225	+	0.274184i
$711$		−	3.58989e7i		−	0.0998786i
$712$	−1.00869e7	−	7.73947e6i	−0.0279458	−	0.0214423i
$713$	2.61853e8			0.722420
$714$	−3.24608e7	+	3.54254e7i	−0.0891794	+	0.0973241i
$715$		−	1.27163e8i		−	0.347892i
$716$	−1.28707e8	+	1.12628e7i	−0.350640	+	0.0306837i
$717$	−5.72660e7			−0.155360
$718$	4.68860e8	+	4.29623e8i	1.26669	+	1.16069i
$719$			1.95775e7i			0.0526709i	0.999653	+	0.0263354i	$0.00838380\pi$
$719$			1.95775e7i			0.0526709i	−0.999653	+	0.0263354i	$0.991616\pi$
$720$	−5.47949e7	+	9.66392e6i	−0.146806	+	0.0258914i
$721$	2.35162e8			0.627425
$722$	5.42805e7	−	5.92379e7i	0.144222	−	0.157394i
$723$			3.17055e8i			0.838920i
$724$	−3.78796e7	−	4.32872e8i	−0.0998135	−	1.14063i
$725$	−4.29269e7			−0.112646
$726$	1.19637e8	+	1.09625e8i	0.312649	+	0.286485i
$727$		−	2.39913e8i		−	0.624383i	−0.950019	−	0.312192i	$-0.898937\pi$
$727$		−	2.39913e8i		−	0.624383i	0.950019	−	0.312192i	$-0.101063\pi$
$728$	1.29661e8	−	1.68987e8i	0.336058	−	0.437984i
$729$	−1.43489e7			−0.0370370
$730$	2.08326e8	−	2.27352e8i	0.535518	−	0.584426i
$731$			3.08474e8i			0.789709i
$732$	2.72555e8	−	2.38506e7i	0.694898	−	0.0608088i
$733$	1.15594e8			0.293510			0.146755	−	0.989173i	$-0.453117\pi$
$733$	1.15594e8			0.293510			0.146755	+	0.989173i	$0.453117\pi$
$734$	2.36219e7	+	2.16451e7i	0.0597348	+	0.0547358i
$735$		−	8.88127e7i		−	0.223673i
$736$	1.92767e8	+	1.22794e8i	0.483504	+	0.307994i
$737$	3.05016e8			0.761939
$738$	−3.60441e6	+	3.93359e6i	−0.00896736	+	0.00978634i
$739$			1.13904e8i			0.282232i	0.989993	+	0.141116i	$0.0450690\pi$
$739$			1.13904e8i			0.282232i	−0.989993	+	0.141116i	$0.954931\pi$
$740$	2.00721e7	+	2.29375e8i	0.0495332	+	0.566046i
$741$	−3.14510e8			−0.773001
$742$	−7.37468e7	−	6.75752e7i	−0.180522	−	0.165415i
$743$		−	2.71020e8i		−	0.660747i	−0.943850	−	0.330373i	$-0.892825\pi$
$743$		−	2.71020e8i		−	0.660747i	0.943850	−	0.330373i	$-0.107175\pi$
$744$	2.37720e8	+	1.82398e8i	0.577228	+	0.442897i
$745$	−1.89201e8			−0.457568
$746$	1.77495e7	−	1.93706e7i	0.0427533	−	0.0466579i
$747$			8.64079e7i			0.207296i
$748$	1.34320e8	−	1.17540e7i	0.320949	−	0.0280855i
$749$	−2.28211e8			−0.543114
$750$	−1.60621e7	−	1.47179e7i	−0.0380732	−	0.0348870i
$751$		−	8.80268e7i		−	0.207824i	−0.994587	−	0.103912i	$-0.966864\pi$
$751$		−	8.80268e7i		−	0.207824i	0.994587	−	0.103912i	$-0.0331360\pi$
$752$	5.18841e7	+	2.94185e8i	0.122006	+	0.691778i
$753$	1.08602e6			0.00254363
$754$	2.46243e8	−	2.68732e8i	0.574447	−	0.626910i
$755$			3.48711e8i			0.810261i
$756$	2.65076e6	+	3.02918e7i	0.00613486	+	0.0701067i
$757$	4.60925e8			1.06253			0.531266	−	0.847205i	$-0.321716\pi$
$757$	4.60925e8			1.06253			0.531266	+	0.847205i	$0.321716\pi$
$758$	−1.79126e8	−	1.64136e8i	−0.411293	−	0.376873i
$759$		−	7.45704e7i		−	0.170546i
$760$	1.05985e8	−	1.38130e8i	0.241436	−	0.314664i
$761$	1.29119e8			0.292980			0.146490	−	0.989212i	$-0.453202\pi$
$761$	1.29119e8			0.292980			0.146490	+	0.989212i	$0.453202\pi$
$762$	−9.59748e6	+	1.04740e7i	−0.0216916	+	0.0236727i
$763$		−	1.38676e8i		−	0.312195i
$764$	−5.79817e8	+	5.07383e7i	−1.30020	+	0.113777i
$765$	−4.17279e7			−0.0932057
$766$	5.08578e8	+	4.66017e8i	1.13154	+	1.03685i
$767$			7.89210e8i			1.74907i
$768$	8.94672e7	+	2.45752e8i	0.197506	+	0.542517i
$769$	3.63552e8			0.799443			0.399722	−	0.916637i	$-0.369107\pi$
$769$	3.63552e8			0.799443			0.399722	+	0.916637i	$0.369107\pi$
$770$	2.59901e7	−	2.83637e7i	0.0569293	−	0.0621285i
$771$			1.63832e8i			0.357467i
$772$	4.41865e7	+	5.04945e8i	0.0960367	+	1.09747i
$773$	2.47148e8			0.535080			0.267540	−	0.963547i	$-0.413789\pi$
$773$	2.47148e8			0.535080			0.267540	+	0.963547i	$0.413789\pi$
$774$	1.43931e8	+	1.31886e8i	0.310407	+	0.284430i
$775$			1.17319e8i			0.252036i
$776$	3.81130e8	+	2.92434e8i	0.815620	+	0.625811i
$777$	1.25833e8			0.268244
$778$	4.97426e8	−	5.42855e8i	1.05631	−	1.15278i
$779$		−	1.66945e7i		−	0.0353152i
$780$	1.84275e8	−	1.61255e7i	0.388314	−	0.0339804i
$781$	−2.22764e8			−0.467618
$782$	1.26375e8	+	1.15799e8i	0.264266	+	0.242151i
$783$			5.20342e7i			0.108394i
$784$	−4.11107e8	+	7.25052e7i	−0.853114	+	0.150460i
$785$	1.39358e7			0.0288086
$786$	−2.57481e7	+	2.80997e7i	−0.0530247	+	0.0578674i
$787$			1.61696e8i			0.331722i	0.986149	+	0.165861i	$0.0530403\pi$
$787$			1.61696e8i			0.331722i	−0.986149	+	0.165861i	$0.946960\pi$
$788$	−6.18468e7	−	7.06760e8i	−0.126397	−	1.44442i
$789$	−5.08150e8			−1.03457
$790$	−4.87107e7	−	4.46343e7i	−0.0987969	−	0.0905289i
$791$			3.27051e8i			0.660825i
$792$	5.19433e7	−	6.76978e7i	0.104557	−	0.136270i
$793$	−9.09584e8			−1.82399
$794$	4.41044e8	−	4.81324e8i	0.881091	−	0.961560i
$795$		−	8.68670e7i		−	0.172883i
$796$	−3.55632e6	+	311204.i	−0.00705117	+	0.000617030i
$797$	4.99320e8			0.986289			0.493145	−	0.869947i	$-0.335847\pi$
$797$	4.99320e8			0.986289			0.493145	+	0.869947i	$0.335847\pi$
$798$	−7.01513e7	−	6.42806e7i	−0.138047	−	0.126494i
$799$			2.24031e8i			0.439205i
$800$	−5.50154e7	+	8.63659e7i	−0.107452	+	0.168683i
$801$	−6.03415e6			−0.0117414
$802$	2.16405e8	−	2.36169e8i	0.419512	−	0.457825i
$803$			4.72901e8i			0.913322i
$804$	3.86787e7	+	4.42005e8i	0.0744225	+	0.850470i
$805$	4.89055e7			0.0937498
$806$	−7.34440e8	−	6.72978e8i	−1.40266	−	1.28527i
$807$		−	2.95704e8i		−	0.562648i
$808$	6.40473e8	+	4.91424e8i	1.21413	+	0.931584i
$809$	2.05478e8			0.388080			0.194040	−	0.980994i	$-0.437841\pi$
$809$	2.05478e8			0.388080			0.194040	+	0.980994i	$0.437841\pi$
$810$	−1.78405e7	+	1.94698e7i	−0.0335700	+	0.0366359i
$811$			9.59217e7i			0.179827i	0.995950	+	0.0899134i	$0.0286590\pi$
$811$			9.59217e7i			0.179827i	−0.995950	+	0.0899134i	$0.971341\pi$
$812$	1.09849e8	−	9.61258e6i	0.205176	−	0.0179544i
$813$	−2.22646e8			−0.414326
$814$	−2.60342e8	−	2.38555e8i	−0.482694	−	0.442299i
$815$			1.11108e8i			0.205245i
$816$	3.40660e7	+	1.93156e8i	0.0626975	+	0.355498i
$817$	−6.10857e8			−1.12014
$818$	5.99238e8	−	6.53966e8i	1.09481	−	1.19480i
$819$		−	1.01091e8i		−	0.184018i
$820$	855957.	+	9.78153e6i	0.00155242	+	0.0177405i
$821$	3.51793e8			0.635707			0.317854	−	0.948140i	$-0.397038\pi$
$821$	3.51793e8			0.635707			0.317854	+	0.948140i	$0.397038\pi$
$822$	−1.76824e8	−	1.62026e8i	−0.318365	−	0.291722i
$823$		−	5.22244e8i		−	0.936858i	−0.883501	−	0.468429i	$-0.844820\pi$
$823$		−	5.22244e8i		−	0.936858i	0.883501	−	0.468429i	$-0.155180\pi$
$824$	5.84355e8	−	7.61591e8i	1.04447	−	1.36126i
$825$	3.34099e7			0.0594995
$826$	−1.61301e8	+	1.76033e8i	−0.286219	+	0.312359i
$827$			6.50393e8i			1.14990i	0.818189	+	0.574949i	$0.194978\pi$
$827$			6.50393e8i			1.14990i	−0.818189	+	0.574949i	$0.805022\pi$
$828$	1.08062e8	−	9.45619e6i	0.190362	−	0.0166581i
$829$	4.18752e8			0.735010			0.367505	−	0.930021i	$-0.380212\pi$
$829$	4.18752e8			0.735010			0.367505	+	0.930021i	$0.380212\pi$
$830$	1.17246e8	+	1.07434e8i	0.205051	+	0.187891i
$831$		−	1.88382e6i		−	0.00328273i
$832$	−2.25083e8	−	8.39832e8i	−0.390816	−	1.45822i
$833$	−3.13071e8			−0.541636
$834$	−9.05857e7	+	9.88588e7i	−0.156157	+	0.170419i
$835$			2.47625e8i			0.425338i
$836$	2.32759e7	+	2.65988e8i	0.0398371	+	0.455243i
$837$	1.42209e8			0.242521
$838$	−4.09720e8	−	3.75432e8i	−0.696233	−	0.637968i
$839$		−	7.73205e8i		−	1.30921i	−0.755972	−	0.654604i	$-0.772835\pi$
$839$		−	7.73205e8i		−	1.30921i	0.755972	−	0.654604i	$-0.227165\pi$
$840$	4.43982e7	+	3.40660e7i	0.0749080	+	0.0574756i
$841$	−4.06129e8			−0.682772
$842$	−3.99836e8	+	4.36353e8i	−0.669801	+	0.730973i
$843$			3.16098e8i			0.527641i
$844$	−8.43136e8	+	7.37807e7i	−1.40239	+	0.122720i
$845$	−3.45145e8			−0.572046
$846$	1.04530e8	+	9.57827e7i	0.172636	+	0.158189i
$847$		−	1.63204e8i		−	0.268584i
$848$	−4.02101e8	+	7.09168e7i	−0.659398	+	0.116295i
$849$	−3.22442e8			−0.526900
$850$	−5.18817e7	+	5.66200e7i	−0.0844807	+	0.0921963i
$851$		−	4.48890e8i		−	0.728368i
$852$	−2.82484e7	−	3.22812e8i	−0.0456747	−	0.521952i
$853$	−9.22089e8			−1.48568			−0.742841	−	0.669468i	$-0.766522\pi$
$853$	−9.22089e8			−1.48568			−0.742841	+	0.669468i	$0.766522\pi$
$854$	−2.02882e8	−	1.85904e8i	−0.325739	−	0.298480i
$855$		−	8.26319e7i		−	0.132205i
$856$	−5.67082e8	+	7.39079e8i	−0.904117	+	1.17834i
$857$	3.54555e8			0.563302			0.281651	−	0.959517i	$-0.409118\pi$
$857$	3.54555e8			0.563302			0.281651	+	0.959517i	$0.409118\pi$
$858$	−1.91650e8	+	2.09153e8i	−0.303422	+	0.331133i
$859$			6.72411e8i			1.06085i	0.847731	+	0.530427i	$0.177968\pi$
$859$			6.72411e8i			1.06085i	−0.847731	+	0.530427i	$0.822032\pi$
$860$	3.57909e8	−	3.13197e7i	0.562700	−	0.0492404i
$861$	5.36603e6			0.00840705
$862$	1.67617e8	+	1.53589e8i	0.261695	+	0.239795i
$863$			1.60578e7i			0.0249835i	0.999922	+	0.0124918i	$0.00397635\pi$
$863$			1.60578e7i			0.0249835i	−0.999922	+	0.0124918i	$0.996024\pi$
$864$	1.04689e8	+	6.66874e7i	0.162316	+	0.103396i
$865$	4.20160e8			0.649182
$866$	−5.82626e8	+	6.35837e8i	−0.897091	+	0.979021i
$867$		−	2.29174e8i		−	0.351648i
$868$	−2.62710e7	−	3.00215e8i	−0.0401715	−	0.459064i
$869$	1.01320e8			0.154397
$870$	7.06045e7	+	6.46959e7i	0.107220	+	0.0982469i
$871$		−	1.47508e9i		−	2.23234i
$872$	−4.49112e8	−	3.44596e8i	−0.677337	−	0.519709i
$873$	2.27999e8			0.342681
$874$	−2.29312e8	+	2.50255e8i	−0.343473	+	0.374842i
$875$			2.19112e7i			0.0327071i
$876$	−6.85291e8	+	5.99681e7i	−1.01944	+	0.0892089i
$877$	−3.21125e8			−0.476075			−0.238038	−	0.971256i	$-0.576504\pi$
$877$	−3.21125e8			−0.476075			−0.238038	+	0.971256i	$0.576504\pi$
$878$	−1.61754e8	−	1.48218e8i	−0.238986	−	0.218986i
$879$		−	2.67179e7i		−	0.0393400i
$880$	−2.72753e7	−	1.54652e8i	−0.0400241	−	0.226938i
$881$	6.86314e8			1.00368			0.501840	−	0.864961i	$-0.332657\pi$
$881$	6.86314e8			1.00368			0.501840	+	0.864961i	$0.332657\pi$
$882$	−1.33851e8	+	1.46076e8i	−0.195082	+	0.212898i
$883$			1.05998e9i			1.53963i	0.638268	+	0.769814i	$0.279651\pi$
$883$			1.05998e9i			1.53963i	−0.638268	+	0.769814i	$0.720349\pi$
$884$	−5.68433e7	−	6.49582e8i	−0.0822853	−	0.940323i
$885$	−2.07351e8			−0.299141
$886$	6.21165e6	+	5.69182e6i	0.00893111	+	0.00818370i
$887$		−	2.80760e8i		−	0.402313i	−0.979559	−	0.201156i	$-0.935530\pi$
$887$		−	2.80760e8i		−	0.402313i	0.979559	−	0.201156i	$-0.0644699\pi$
$888$	3.12682e8	−	4.07519e8i	0.446543	−	0.581981i
$889$	1.42882e7			0.0203363
$890$	−7.50247e6	+	8.18766e6i	−0.0106423	+	0.0116142i
$891$		−	4.04981e7i		−	0.0572534i
$892$	5.97164e8	−	5.22563e7i	0.841393	−	0.0736282i
$893$	−4.43637e8			−0.622979
$894$	3.11191e8	+	2.85149e8i	0.435527	+	0.399079i
$895$			1.12850e8i			0.157410i
$896$	1.21443e8	−	2.33327e8i	0.168830	−	0.324370i
$897$	−3.60628e8			−0.499669
$898$	−7.40836e8	+	8.08495e8i	−1.02304	+	1.11647i
$899$		−	5.15699e8i		−	0.709770i
$900$	4.23667e6	+	4.84150e7i	0.00581162	+	0.0664129i
$901$	−3.06212e8			−0.418647
$902$	−1.11021e7	−	1.01730e7i	−0.0151281	−	0.0138621i
$903$		−	1.96344e8i		−	0.266658i
$904$	1.05918e9	+	8.12691e8i	1.43372	+	1.10007i
$905$	−3.79543e8			−0.512054
$906$	5.25548e8	−	5.73546e8i	0.706688	−	0.771230i
$907$		−	7.59957e8i		−	1.01851i	−0.860614	−	0.509257i	$-0.829920\pi$
$907$		−	7.59957e8i		−	1.01851i	0.860614	−	0.509257i	$-0.170080\pi$
$908$	−1.01101e9	+	8.84712e7i	−1.35051	+	0.118180i
$909$	3.83143e8			0.510117
$910$	−1.37169e8	−	1.25690e8i	−0.182025	−	0.166792i
$911$		−	6.11240e8i		−	0.808457i	−0.914658	−	0.404228i	$-0.867540\pi$
$911$		−	6.11240e8i		−	0.808457i	0.914658	−	0.404228i	$-0.132460\pi$
$912$	−3.82497e8	+	6.74593e7i	−0.504247	+	0.0889318i
$913$	−2.43876e8			−0.320447
$914$	−5.55858e7	+	6.06624e7i	−0.0727990	+	0.0794477i
$915$		−	2.38977e8i		−	0.311955i
$916$	9.01074e7	+	1.02971e9i	0.117240	+	1.33977i
$917$	3.83324e7			0.0497116
$918$	6.86324e7	+	6.28889e7i	0.0887159	+	0.0812916i
$919$			8.12935e8i			1.04739i	0.851905	+	0.523696i	$0.175447\pi$
$919$			8.12935e8i			1.04739i	−0.851905	+	0.523696i	$0.824553\pi$
$920$	1.21526e8	−	1.58384e8i	0.156064	−	0.203399i
$921$	4.63767e8			0.593637
$922$	−9.20409e8	+	1.00447e9i	−1.17432	+	1.28157i
$923$			1.07730e9i			1.37004i
$924$	−8.54949e7	+	7.48145e6i	−0.108374	+	0.00948352i
$925$	2.01117e8			0.254111
$926$	−4.86320e8	−	4.45622e8i	−0.612476	−	0.561220i
$927$		−	4.55598e8i		−	0.571930i
$928$	2.41832e8	−	3.79640e8i	0.302601	−	0.475037i
$929$	1.24366e9			1.55116			0.775579	−	0.631251i	$-0.217458\pi$
$929$	1.24366e9			1.55116			0.775579	+	0.631251i	$0.217458\pi$
$930$	1.76813e8	−	1.92961e8i	0.219819	−	0.239895i
$931$		−	6.19959e8i		−	0.768270i
$932$	2.35871e7	+	2.69544e8i	0.0291358	+	0.332952i
$933$	−3.62502e8			−0.446340
$934$	9.74859e8	+	8.93277e8i	1.19647	+	1.09634i
$935$		−	1.17772e8i		−	0.144081i
$936$	−3.27391e8	−	2.51202e8i	−0.399245	−	0.306334i
$937$	8.86708e8			1.07786			0.538929	−	0.842351i	$-0.318829\pi$
$937$	8.86708e8			1.07786			0.538929	+	0.842351i	$0.318829\pi$
$938$	3.01482e8	−	3.29016e8i	0.365302	−	0.398665i
$939$		−	3.49753e8i		−	0.422440i
$940$	2.59932e8	−	2.27460e7i	0.312951	−	0.0273856i
$941$	9.67276e8			1.16086			0.580432	−	0.814309i	$-0.302884\pi$
$941$	9.67276e8			1.16086			0.580432	+	0.814309i	$0.302884\pi$
$942$	−2.29210e7	−	2.10028e7i	−0.0274208	−	0.0251261i
$943$		−	1.91425e7i		−	0.0228278i
$944$	1.69278e8	+	9.59812e8i	0.201226	+	1.14096i
$945$	2.65599e7			0.0314725
$946$	−3.72233e8	+	4.06228e8i	−0.439684	+	0.479840i
$947$			3.74099e8i			0.440490i	0.975445	+	0.220245i	$0.0706858\pi$
$947$			3.74099e8i			0.440490i	−0.975445	+	0.220245i	$0.929314\pi$
$948$	1.28483e7	+	1.46825e8i	0.0150807	+	0.172336i
$949$	2.28699e9			2.67587
$950$	−1.12122e8	−	1.02739e8i	−0.130774	−	0.119830i
$951$		−	2.35332e8i		−	0.273614i
$952$	1.20085e8	−	1.56507e8i	0.139180	−	0.181394i
$953$	−9.95055e8			−1.14966			−0.574828	−	0.818274i	$-0.694931\pi$
$953$	−9.95055e8			−1.14966			−0.574828	+	0.818274i	$0.694931\pi$
$954$	−1.30919e8	+	1.42875e8i	−0.150785	+	0.164556i
$955$			5.08385e8i			0.583690i
$956$	2.34216e8	−	2.04957e7i	0.268067	−	0.0234579i
$957$	−1.46860e8			−0.167559
$958$	8.72062e8	+	7.99082e8i	0.991861	+	0.908856i
$959$			2.41215e8i			0.273495i
$960$	2.20651e8	−	5.91364e7i	0.249397	−	0.0668408i
$961$	−5.21895e8			−0.588048
$962$	−1.15367e9	+	1.25904e9i	−1.29586	+	1.41421i
$963$			4.42131e8i			0.495077i
$964$	−1.13475e8	−	1.29675e9i	−0.126669	−	1.44752i
$965$	4.42737e8			0.492679
$966$	−8.04379e7	−	7.37064e7i	−0.0892338	−	0.0817662i
$967$		−	1.05489e9i		−	1.16661i	−0.812253	−	0.583306i	$-0.801759\pi$
$967$		−	1.05489e9i		−	1.16661i	0.812253	−	0.583306i	$-0.198241\pi$
$968$	−5.28549e8	−	4.05547e8i	−0.582719	−	0.447110i
$969$	−2.91283e8			−0.320143
$970$	2.83479e8	−	3.09369e8i	0.310603	−	0.338970i
$971$			2.83455e8i			0.309618i	0.987944	+	0.154809i	$0.0494762\pi$
$971$			2.83455e8i			0.309618i	−0.987944	+	0.154809i	$0.950524\pi$
$972$	5.86866e7	−	5.13552e6i	0.0639058	−	0.00559224i
$973$	1.34859e8			0.146400
$974$	1.30214e9	+	1.19317e9i	1.40923	+	1.29129i
$975$		−	1.61573e8i		−	0.174323i
$976$	−1.10621e9	+	1.95097e8i	−1.18983	+	0.209846i
$977$	5.25300e7			0.0563279			0.0281640	−	0.999603i	$-0.491034\pi$
$977$	5.25300e7			0.0563279			0.0281640	+	0.999603i	$0.491034\pi$
$978$	1.67453e8	−	1.82746e8i	0.179009	−	0.195358i
$979$		−	1.70307e7i		−	0.0181503i
$980$	3.17863e7	+	3.63241e8i	0.0337724	+	0.385938i
$981$	−2.68667e8			−0.284582
$982$	−1.77332e8	−	1.62492e8i	−0.187263	−	0.171592i
$983$		−	7.39378e8i		−	0.778406i	−0.921152	−	0.389203i	$-0.872751\pi$
$983$		−	7.39378e8i		−	0.778406i	0.921152	−	0.389203i	$-0.127249\pi$
$984$	1.33341e7	−	1.73783e7i	0.0139951	−	0.0182399i
$985$	−6.19688e8			−0.648432
$986$	2.28057e8	−	2.48886e8i	0.237910	−	0.259638i
$987$		−	1.42596e8i		−	0.148305i
$988$	1.28634e9	−	1.12564e8i	1.33378	−	0.116716i
$989$	−7.00430e8			−0.724062
$990$	−5.49513e7	−	5.03526e7i	−0.0566334	−	0.0518939i
$991$			1.15167e9i			1.18333i	0.806184	+	0.591665i	$0.201529\pi$
$991$			1.15167e9i			1.18333i	−0.806184	+	0.591665i	$0.798471\pi$
$992$	−1.03755e9	−	6.60924e8i	−1.06285	−	0.677043i
$993$	7.94080e8			0.810992
$994$	−2.20183e8	+	2.40292e8i	−0.224194	+	0.244670i
$995$			3.11819e6i			0.00316543i
$996$	−3.09257e7	−	3.53406e8i	−0.0312997	−	0.357681i
$997$	6.18361e8			0.623960			0.311980	−	0.950089i	$-0.399008\pi$
$997$	6.18361e8			0.623960			0.311980	+	0.950089i	$0.399008\pi$
$998$	4.26245e8	+	3.90574e8i	0.428812	+	0.392927i
$999$		−	2.43785e8i		−	0.244518i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	60.7.c.a.31.19	✓	24
3.2	odd	2		180.7.c.b.91.6		24
4.3	odd	2	inner	60.7.c.a.31.20	yes	24
12.11	even	2		180.7.c.b.91.5		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
60.7.c.a.31.19	✓	24	1.1	even	1	trivial
60.7.c.a.31.20	yes	24	4.3	odd	2	inner
180.7.c.b.91.5		24	12.11	even	2
180.7.c.b.91.6		24	3.2	odd	2

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:	\( N \)	\(=\)	\( 60 = 2^{2} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	60.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(5.40467 - 5.89827i) q^{2} +15.5885i q^{3} +(-5.57916 - 63.7564i) q^{4} -55.9017 q^{5} +(91.9449 + 84.2504i) q^{6} -125.427i q^{7} +(-406.206 - 311.674i) q^{8} -243.000 q^{9} +O(q^{10})\)	\(q+(5.40467 - 5.89827i) q^{2} +15.5885i q^{3} +(-5.57916 - 63.7564i) q^{4} -55.9017 q^{5} +(91.9449 + 84.2504i) q^{6} -125.427i q^{7} +(-406.206 - 311.674i) q^{8} -243.000 q^{9} +(-302.130 + 329.723i) q^{10} -685.839i q^{11} +(993.863 - 86.9705i) q^{12} -3316.77 q^{13} +(-739.803 - 677.892i) q^{14} -871.421i q^{15} +(-4033.75 + 711.414i) q^{16} -3071.82 q^{17} +(-1313.33 + 1433.28i) q^{18} -6082.98i q^{19} +(311.884 + 3564.09i) q^{20} +1955.22 q^{21} +(-4045.26 - 3706.73i) q^{22} -6974.95i q^{23} +(4858.52 - 6332.12i) q^{24} +3125.00 q^{25} +(-17926.0 + 19563.2i) q^{26} -3788.00i q^{27} +(-7996.78 + 699.778i) q^{28} -13736.6 q^{29} +(-5139.88 - 4709.74i) q^{30} +37542.0i q^{31} +(-17604.9 + 27637.1i) q^{32} +10691.2 q^{33} +(-16602.2 + 18118.4i) q^{34} +7011.59i q^{35} +(1355.74 + 15492.8i) q^{36} +64357.4 q^{37} +(-35879.0 - 32876.5i) q^{38} -51703.3i q^{39} +(22707.6 + 17423.1i) q^{40} +2744.47 q^{41} +(10567.3 - 11532.4i) q^{42} -100421. i q^{43} +(-43726.6 + 3826.40i) q^{44} +13584.1 q^{45} +(-41140.2 - 37697.3i) q^{46} -72930.9i q^{47} +(-11089.8 - 62879.9i) q^{48} +101917. q^{49} +(16889.6 - 18432.1i) q^{50} -47884.9i q^{51} +(18504.8 + 211465. i) q^{52} +99684.3 q^{53} +(-22342.6 - 20472.9i) q^{54} +38339.6i q^{55} +(-39092.5 + 50949.2i) q^{56} +94824.2 q^{57} +(-74241.8 + 81022.2i) q^{58} -237946. i q^{59} +(-55558.6 + 4861.80i) q^{60} +274238. q^{61} +(221433. + 202902. i) q^{62} +30478.8i q^{63} +(67862.0 + 253208. i) q^{64} +185413. q^{65} +(57782.2 - 63059.4i) q^{66} +444734. i q^{67} +(17138.2 + 195848. i) q^{68} +108729. q^{69} +(41356.3 + 37895.3i) q^{70} -324805. i q^{71} +(98708.0 + 75736.9i) q^{72} -689523. q^{73} +(347830. - 379597. i) q^{74} +48713.9i q^{75} +(-387829. + 33937.9i) q^{76} -86022.8 q^{77} +(-304960. - 279439. i) q^{78} +147732. i q^{79} +(225493. - 39769.2i) q^{80} +59049.0 q^{81} +(14832.9 - 16187.6i) q^{82} -355588. i q^{83} +(-10908.5 - 124657. i) q^{84} +171720. q^{85} +(-592309. - 542741. i) q^{86} -214133. i q^{87} +(-213758. + 278592. i) q^{88} +24831.9 q^{89} +(73417.6 - 80122.8i) q^{90} +416013. i q^{91} +(-444698. + 38914.4i) q^{92} -585221. q^{93} +(-430166. - 394167. i) q^{94} +340049. i q^{95} +(-430819. - 274434. i) q^{96} -938268. q^{97} +(550828. - 601134. i) q^{98} +166659. i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 20 q^{2} - 246 q^{4} + 162 q^{6} - 340 q^{8} - 5832 q^{9}+O(q^{10}) \) 24 * q + 20 * q^2 - 246 * q^4 + 162 * q^6 - 340 * q^8 - 5832 * q^9	\( 24 q + 20 q^{2} - 246 q^{4} + 162 q^{6} - 340 q^{8} - 5832 q^{9} - 750 q^{10} + 5040 q^{13} - 2596 q^{14} + 4194 q^{16} - 4860 q^{18} + 7000 q^{20} + 19440 q^{21} + 45780 q^{22} + 24786 q^{24} + 75000 q^{25} + 75852 q^{26} + 54300 q^{28} + 132800 q^{29} - 10700 q^{32} - 173484 q^{34} + 59778 q^{36} - 69840 q^{37} + 215800 q^{38} - 14250 q^{40} - 70448 q^{41} - 189540 q^{42} - 395668 q^{44} - 158760 q^{46} + 252720 q^{48} - 642984 q^{49} + 62500 q^{50} - 210240 q^{52} - 644320 q^{53} - 39366 q^{54} - 917708 q^{56} + 408240 q^{57} - 1345020 q^{58} + 222750 q^{60} - 222864 q^{61} + 1948520 q^{62} + 935922 q^{64} + 266000 q^{65} - 640548 q^{66} + 572680 q^{68} - 541728 q^{69} + 220500 q^{70} + 82620 q^{72} + 771120 q^{73} - 589164 q^{74} - 191544 q^{76} + 1383840 q^{77} - 693360 q^{78} - 946000 q^{80} + 1417176 q^{81} + 2672520 q^{82} + 1256796 q^{84} - 372000 q^{85} + 1781528 q^{86} + 956940 q^{88} - 1566224 q^{89} + 182250 q^{90} - 3040560 q^{92} + 1496880 q^{93} - 3788352 q^{94} - 413262 q^{96} - 1666800 q^{97} - 2709660 q^{98}+O(q^{100}) \) 24 * q + 20 * q^2 - 246 * q^4 + 162 * q^6 - 340 * q^8 - 5832 * q^9 - 750 * q^10 + 5040 * q^13 - 2596 * q^14 + 4194 * q^16 - 4860 * q^18 + 7000 * q^20 + 19440 * q^21 + 45780 * q^22 + 24786 * q^24 + 75000 * q^25 + 75852 * q^26 + 54300 * q^28 + 132800 * q^29 - 10700 * q^32 - 173484 * q^34 + 59778 * q^36 - 69840 * q^37 + 215800 * q^38 - 14250 * q^40 - 70448 * q^41 - 189540 * q^42 - 395668 * q^44 - 158760 * q^46 + 252720 * q^48 - 642984 * q^49 + 62500 * q^50 - 210240 * q^52 - 644320 * q^53 - 39366 * q^54 - 917708 * q^56 + 408240 * q^57 - 1345020 * q^58 + 222750 * q^60 - 222864 * q^61 + 1948520 * q^62 + 935922 * q^64 + 266000 * q^65 - 640548 * q^66 + 572680 * q^68 - 541728 * q^69 + 220500 * q^70 + 82620 * q^72 + 771120 * q^73 - 589164 * q^74 - 191544 * q^76 + 1383840 * q^77 - 693360 * q^78 - 946000 * q^80 + 1417176 * q^81 + 2672520 * q^82 + 1256796 * q^84 - 372000 * q^85 + 1781528 * q^86 + 956940 * q^88 - 1566224 * q^89 + 182250 * q^90 - 3040560 * q^92 + 1496880 * q^93 - 3788352 * q^94 - 413262 * q^96 - 1666800 * q^97 - 2709660 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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