LMFDB - Embedded newform 80.6.l.a.61.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [80,6,Mod(21,80)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(80, base_ring=CyclotomicField(4))

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

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("80.21");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 80 = 2^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	80.l (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:	$12.8307055850$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$40$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			61.6
Character	$\chi$	$=$	80.61
Dual form			80.6.l.a.21.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-5.27573 + 2.04124i) q^{2} +(6.55397 + 6.55397i) q^{3} +(23.6666 - 21.5381i) q^{4} +(17.6777 - 17.6777i) q^{5} +(-47.9552 - 21.1987i) q^{6} +188.280i q^{7} +(-80.8943 + 161.939i) q^{8} -157.091i q^{9} +O(q^{10})$	\(q+(-5.27573 + 2.04124i) q^{2} +(6.55397 + 6.55397i) q^{3} +(23.6666 - 21.5381i) q^{4} +(17.6777 - 17.6777i) q^{5} +(-47.9552 - 21.1987i) q^{6} +188.280i q^{7} +(-80.8943 + 161.939i) q^{8} -157.091i q^{9} +(-57.1782 + 129.347i) q^{10} +(475.916 - 475.916i) q^{11} +(296.270 + 13.9504i) q^{12} +(118.177 + 118.177i) q^{13} +(-384.325 - 993.312i) q^{14} +231.718 q^{15} +(96.2203 - 1019.47i) q^{16} -738.511 q^{17} +(320.661 + 828.770i) q^{18} +(1844.77 + 1844.77i) q^{19} +(37.6277 - 799.115i) q^{20} +(-1233.98 + 1233.98i) q^{21} +(-1539.34 + 3482.26i) q^{22} +2770.70i q^{23} +(-1591.52 + 531.162i) q^{24} -625.000i q^{25} +(-864.698 - 382.242i) q^{26} +(2622.18 - 2622.18i) q^{27} +(4055.19 + 4455.95i) q^{28} +(5760.68 + 5760.68i) q^{29} +(-1222.48 + 472.992i) q^{30} -3006.33 q^{31} +(1573.35 + 5574.85i) q^{32} +6238.27 q^{33} +(3896.19 - 1507.48i) q^{34} +(3328.34 + 3328.34i) q^{35} +(-3383.44 - 3717.82i) q^{36} +(1145.11 - 1145.11i) q^{37} +(-13498.1 - 5966.87i) q^{38} +1549.06i q^{39} +(1432.67 + 4292.72i) q^{40} +9566.00i q^{41} +(3991.29 - 9028.99i) q^{42} +(-12971.5 + 12971.5i) q^{43} +(1013.01 - 21513.6i) q^{44} +(-2777.00 - 2777.00i) q^{45} +(-5655.67 - 14617.4i) q^{46} +20859.6 q^{47} +(7312.19 - 6050.94i) q^{48} -18642.2 q^{49} +(1275.78 + 3297.33i) q^{50} +(-4840.18 - 4840.18i) q^{51} +(5342.16 + 251.545i) q^{52} +(11956.5 - 11956.5i) q^{53} +(-8481.42 + 19186.4i) q^{54} -16826.2i q^{55} +(-30489.7 - 15230.7i) q^{56} +24181.1i q^{57} +(-42150.8 - 18632.8i) q^{58} +(28124.9 - 28124.9i) q^{59} +(5483.98 - 4990.76i) q^{60} +(-11808.5 - 11808.5i) q^{61} +(15860.6 - 6136.65i) q^{62} +29577.0 q^{63} +(-19680.2 - 26199.8i) q^{64} +4178.19 q^{65} +(-32911.4 + 12733.8i) q^{66} +(-8287.66 - 8287.66i) q^{67} +(-17478.1 + 15906.1i) q^{68} +(-18159.1 + 18159.1i) q^{69} +(-24353.4 - 10765.5i) q^{70} -20916.1i q^{71} +(25439.1 + 12707.8i) q^{72} +10484.3i q^{73} +(-3703.85 + 8378.75i) q^{74} +(4096.23 - 4096.23i) q^{75} +(83392.2 + 3926.67i) q^{76} +(89605.2 + 89605.2i) q^{77} +(-3162.00 - 8172.40i) q^{78} +24253.7 q^{79} +(-16320.9 - 19722.8i) q^{80} -3801.70 q^{81} +(-19526.5 - 50467.6i) q^{82} +(-80833.3 - 80833.3i) q^{83} +(-2626.58 + 55781.7i) q^{84} +(-13055.2 + 13055.2i) q^{85} +(41956.2 - 94912.3i) q^{86} +75510.6i q^{87} +(38570.2 + 115568. i) q^{88} +54884.0i q^{89} +(20319.3 + 8982.18i) q^{90} +(-22250.3 + 22250.3i) q^{91} +(59675.5 + 65573.1i) q^{92} +(-19703.4 - 19703.4i) q^{93} +(-110050. + 42579.5i) q^{94} +65222.3 q^{95} +(-26225.7 + 46849.1i) q^{96} -49424.6 q^{97} +(98351.2 - 38053.3i) q^{98} +(-74762.1 - 74762.1i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 44 q^{4} - 228 q^{6}+O(q^{10}) $ 80 * q + 44 * q^4 - 228 * q^6	\( 80 q + 44 q^{4} - 228 q^{6} - 100 q^{10} + 1208 q^{11} + 1572 q^{12} - 916 q^{14} - 1800 q^{15} + 2960 q^{16} + 6400 q^{18} + 2360 q^{19} - 3800 q^{20} - 3260 q^{22} - 13880 q^{24} - 880 q^{26} - 7464 q^{27} + 18764 q^{28} - 8144 q^{29} + 22400 q^{32} - 7440 q^{34} + 27948 q^{36} + 21296 q^{37} - 34820 q^{38} - 7260 q^{42} + 32072 q^{43} + 64392 q^{44} + 149268 q^{46} - 88360 q^{47} + 94040 q^{48} - 192080 q^{49} + 2500 q^{50} - 5920 q^{51} - 55016 q^{52} - 49456 q^{53} - 250784 q^{54} - 250352 q^{56} - 115988 q^{58} + 44984 q^{59} + 7700 q^{60} + 48080 q^{61} + 444328 q^{62} + 158760 q^{63} + 218096 q^{64} + 253440 q^{66} + 61160 q^{67} - 119792 q^{68} - 22320 q^{69} - 66200 q^{70} - 629480 q^{72} - 156664 q^{74} + 223232 q^{76} - 14896 q^{77} + 516176 q^{78} + 177680 q^{79} + 48400 q^{80} - 524880 q^{81} + 254476 q^{82} - 329240 q^{83} - 173248 q^{84} + 132400 q^{85} - 765740 q^{86} - 390400 q^{88} + 71100 q^{90} + 364832 q^{91} + 333532 q^{92} - 362352 q^{93} + 537844 q^{94} + 288800 q^{95} + 1151112 q^{96} + 52420 q^{98} + 659000 q^{99}+O(q^{100}) \) 80 * q + 44 * q^4 - 228 * q^6 - 100 * q^10 + 1208 * q^11 + 1572 * q^12 - 916 * q^14 - 1800 * q^15 + 2960 * q^16 + 6400 * q^18 + 2360 * q^19 - 3800 * q^20 - 3260 * q^22 - 13880 * q^24 - 880 * q^26 - 7464 * q^27 + 18764 * q^28 - 8144 * q^29 + 22400 * q^32 - 7440 * q^34 + 27948 * q^36 + 21296 * q^37 - 34820 * q^38 - 7260 * q^42 + 32072 * q^43 + 64392 * q^44 + 149268 * q^46 - 88360 * q^47 + 94040 * q^48 - 192080 * q^49 + 2500 * q^50 - 5920 * q^51 - 55016 * q^52 - 49456 * q^53 - 250784 * q^54 - 250352 * q^56 - 115988 * q^58 + 44984 * q^59 + 7700 * q^60 + 48080 * q^61 + 444328 * q^62 + 158760 * q^63 + 218096 * q^64 + 253440 * q^66 + 61160 * q^67 - 119792 * q^68 - 22320 * q^69 - 66200 * q^70 - 629480 * q^72 - 156664 * q^74 + 223232 * q^76 - 14896 * q^77 + 516176 * q^78 + 177680 * q^79 + 48400 * q^80 - 524880 * q^81 + 254476 * q^82 - 329240 * q^83 - 173248 * q^84 + 132400 * q^85 - 765740 * q^86 - 390400 * q^88 + 71100 * q^90 + 364832 * q^91 + 333532 * q^92 - 362352 * q^93 + 537844 * q^94 + 288800 * q^95 + 1151112 * q^96 + 52420 * q^98 + 659000 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/80\mathbb{Z}\right)^\times$.

$n$	$17$	$21$	$31$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$1$

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 $

$2$	−5.27573	+	2.04124i	−0.932626	+	0.360844i
$2$	−5.27573	+	2.04124i	−0.932626	+	0.360844i
$3$	6.55397	+	6.55397i	0.420437	+	0.420437i	0.885354	−	0.464917i	$-0.153916\pi$
$3$	6.55397	+	6.55397i	0.420437	+	0.420437i	−0.464917	+	0.885354i	$0.653916\pi$
$4$	23.6666	−	21.5381i	0.739583	−	0.673066i
$5$	17.6777	−	17.6777i	0.316228	−	0.316228i
$5$	17.6777	−	17.6777i	0.316228	−	0.316228i
$6$	−47.9552	−	21.1987i	−0.543823	−	0.240398i
$7$			188.280i			1.45231i	0.687533	+	0.726153i	$0.258694\pi$
$7$			188.280i			1.45231i	−0.687533	+	0.726153i	$0.741306\pi$
$8$	−80.8943	+	161.939i	−0.446882	+	0.894593i
$9$		−	157.091i		−	0.646465i
$10$	−57.1782	+	129.347i	−0.180813	+	0.409031i
$11$	475.916	−	475.916i	1.18590	−	1.18590i	0.207710	−	0.978190i	$-0.433399\pi$
$11$	475.916	−	475.916i	1.18590	−	1.18590i	0.978190	−	0.207710i	$-0.0666010\pi$
$12$	296.270	+	13.9504i	0.593930	+	0.0279662i
$13$	118.177	+	118.177i	0.193943	+	0.193943i	0.797398	−	0.603454i	$-0.206209\pi$
$13$	118.177	+	118.177i	0.193943	+	0.193943i	−0.603454	+	0.797398i	$0.706209\pi$
$14$	−384.325	−	993.312i	−0.524056	−	1.35446i
$15$	231.718			0.265908
$16$	96.2203	−	1019.47i	0.0939651	−	0.995575i
$17$	−738.511			−0.619776			−0.309888	−	0.950773i	$-0.600292\pi$
$17$	−738.511			−0.619776			−0.309888	+	0.950773i	$0.600292\pi$
$18$	320.661	+	828.770i	0.233273	+	0.602910i
$19$	1844.77	+	1844.77i	1.17235	+	1.17235i	0.981648	+	0.190702i	$0.0610765\pi$
$19$	1844.77	+	1844.77i	1.17235	+	1.17235i	0.190702	+	0.981648i	$0.438923\pi$
$20$	37.6277	−	799.115i	0.0210345	−	0.446719i
$21$	−1233.98	+	1233.98i	−0.610604	+	0.610604i
$22$	−1539.34	+	3482.26i	−0.678076	+	1.53393i
$23$			2770.70i			1.09212i	0.837747	+	0.546059i	$0.183872\pi$
$23$			2770.70i			1.09212i	−0.837747	+	0.546059i	$0.816128\pi$
$24$	−1591.52	+	531.162i	−0.564006	+	0.188234i
$25$		−	625.000i		−	0.200000i
$26$	−864.698	−	382.242i	−0.250860	−	0.110893i
$27$	2622.18	−	2622.18i	0.692235	−	0.692235i
$28$	4055.19	+	4455.95i	0.977497	+	1.07410i
$29$	5760.68	+	5760.68i	1.27198	+	1.27198i	0.945050	+	0.326926i	$0.106013\pi$
$29$	5760.68	+	5760.68i	1.27198	+	1.27198i	0.326926	+	0.945050i	$0.393987\pi$
$30$	−1222.48	+	472.992i	−0.247993	+	0.0959514i
$31$	−3006.33			−0.561865			−0.280932	−	0.959728i	$-0.590644\pi$
$31$	−3006.33			−0.561865			−0.280932	+	0.959728i	$0.590644\pi$
$32$	1573.35	+	5574.85i	0.271613	+	0.962406i
$33$	6238.27			0.997193
$34$	3896.19	−	1507.48i	0.578019	−	0.223643i
$35$	3328.34	+	3328.34i	0.459260	+	0.459260i
$36$	−3383.44	−	3717.82i	−0.435113	−	0.478114i
$37$	1145.11	−	1145.11i	0.137513	−	0.137513i	−0.635000	−	0.772513i	$-0.719000\pi$
$37$	1145.11	−	1145.11i	0.137513	−	0.137513i	0.772513	+	0.635000i	$0.219000\pi$
$38$	−13498.1	−	5966.87i	−1.51640	−	0.670328i
$39$			1549.06i			0.163082i
$40$	1432.67	+	4292.72i	0.141579	+	0.424212i
$41$			9566.00i			0.888732i	0.895845	+	0.444366i	$0.146571\pi$
$41$			9566.00i			0.888732i	−0.895845	+	0.444366i	$0.853429\pi$
$42$	3991.29	−	9028.99i	0.349132	−	0.789798i
$43$	−12971.5	+	12971.5i	−1.06984	+	1.06984i	−0.0724720	+	0.997370i	$0.523089\pi$
$43$	−12971.5	+	12971.5i	−1.06984	+	1.06984i	−0.997370	+	0.0724720i	$0.976911\pi$
$44$	1013.01	−	21513.6i	0.0788825	−	1.67526i
$45$	−2777.00	−	2777.00i	−0.204430	−	0.204430i
$46$	−5655.67	−	14617.4i	−0.394084	−	1.01854i
$47$	20859.6			1.37740			0.688702	−	0.725045i	$-0.258181\pi$
$47$	20859.6			1.37740			0.688702	+	0.725045i	$0.258181\pi$
$48$	7312.19	−	6050.94i	0.458083	−	0.379071i
$49$	−18642.2			−1.10919
$50$	1275.78	+	3297.33i	0.0721689	+	0.186525i
$51$	−4840.18	−	4840.18i	−0.260577	−	0.260577i
$52$	5342.16	+	251.545i	0.273973	+	0.0129005i
$53$	11956.5	−	11956.5i	0.584677	−	0.584677i	−0.351508	−	0.936185i	$-0.614331\pi$
$53$	11956.5	−	11956.5i	0.584677	−	0.584677i	0.936185	+	0.351508i	$0.114331\pi$
$54$	−8481.42	+	19186.4i	−0.395807	+	0.895386i
$55$		−	16826.2i		−	0.750029i
$56$	−30489.7	−	15230.7i	−1.29922	−	0.649010i
$57$			24181.1i			0.985799i
$58$	−42150.8	−	18632.8i	−1.64526	−	0.727292i
$59$	28124.9	−	28124.9i	1.05187	−	1.05187i	0.0532878	−	0.998579i	$-0.483030\pi$
$59$	28124.9	−	28124.9i	1.05187	−	1.05187i	0.998579	−	0.0532878i	$-0.0169701\pi$
$60$	5483.98	−	4990.76i	0.196661	−	0.178973i
$61$	−11808.5	−	11808.5i	−0.406323	−	0.406323i	0.474131	−	0.880454i	$-0.342762\pi$
$61$	−11808.5	−	11808.5i	−0.406323	−	0.406323i	−0.880454	+	0.474131i	$0.842762\pi$
$62$	15860.6	−	6136.65i	0.524010	−	0.202746i
$63$	29577.0			0.938865
$64$	−19680.2	−	26199.8i	−0.600593	−	0.799555i
$65$	4178.19			0.122660
$66$	−32911.4	+	12733.8i	−0.930009	+	0.359832i
$67$	−8287.66	−	8287.66i	−0.225551	−	0.225551i	0.585280	−	0.810831i	$-0.300985\pi$
$67$	−8287.66	−	8287.66i	−0.225551	−	0.225551i	−0.810831	+	0.585280i	$0.800985\pi$
$68$	−17478.1	+	15906.1i	−0.458376	+	0.417150i
$69$	−18159.1	+	18159.1i	−0.459167	+	0.459167i
$70$	−24353.4	−	10765.5i	−0.594039	−	0.262596i
$71$		−	20916.1i		−	0.492419i	−0.969217	−	0.246209i	$-0.920815\pi$
$71$		−	20916.1i		−	0.492419i	0.969217	−	0.246209i	$-0.0791851\pi$
$72$	25439.1	+	12707.8i	0.578323	+	0.288894i
$73$			10484.3i			0.230268i	0.993350	+	0.115134i	$0.0367298\pi$
$73$			10484.3i			0.230268i	−0.993350	+	0.115134i	$0.963270\pi$
$74$	−3703.85	+	8378.75i	−0.0786274	+	0.177869i
$75$	4096.23	−	4096.23i	0.0840875	−	0.0840875i
$76$	83392.2	+	3926.67i	1.65612	+	0.0779812i
$77$	89605.2	+	89605.2i	1.72229	+	1.72229i
$78$	−3162.00	−	8172.40i	−0.0588472	−	0.152094i
$79$	24253.7			0.437229			0.218615	−	0.975811i	$-0.429846\pi$
$79$	24253.7			0.437229			0.218615	+	0.975811i	$0.429846\pi$
$80$	−16320.9	−	19722.8i	−0.285114	−	0.344543i
$81$	−3801.70			−0.0643821
$82$	−19526.5	−	50467.6i	−0.320694	−	0.828855i
$83$	−80833.3	−	80833.3i	−1.28794	−	1.28794i	−0.936037	−	0.351901i	$-0.885535\pi$
$83$	−80833.3	−	80833.3i	−1.28794	−	1.28794i	−0.351901	−	0.936037i	$-0.614465\pi$
$84$	−2626.58	+	55781.7i	−0.0406155	+	0.862568i
$85$	−13055.2	+	13055.2i	−0.195990	+	0.195990i
$86$	41956.2	−	94912.3i	0.611716	−	1.38381i
$87$			75510.6i			1.06957i
$88$	38570.2	+	115568.i	0.530940	+	1.59086i
$89$			54884.0i			0.734465i	0.930129	+	0.367232i	$0.119695\pi$
$89$			54884.0i			0.734465i	−0.930129	+	0.367232i	$0.880305\pi$
$90$	20319.3	+	8982.18i	0.264424	+	0.116889i
$91$	−22250.3	+	22250.3i	−0.281665	+	0.281665i
$92$	59675.5	+	65573.1i	0.735067	+	0.807711i
$93$	−19703.4	−	19703.4i	−0.236229	−	0.236229i
$94$	−110050.	+	42579.5i	−1.28460	+	0.497028i
$95$	65222.3			0.741459
$96$	−26225.7	+	46849.1i	−0.290435	+	0.518828i
$97$	−49424.6			−0.533351			−0.266676	−	0.963786i	$-0.585925\pi$
$97$	−49424.6			−0.533351			−0.266676	+	0.963786i	$0.585925\pi$
$98$	98351.2	−	38053.3i	1.03446	−	0.400246i
$99$	−74762.1	−	74762.1i	−0.766643	−	0.766643i
$100$	−13461.3	−	14791.7i	−0.134613	−	0.147917i
$101$	−136068.	+	136068.i	−1.32725	+	1.32725i	−0.419486	+	0.907762i	$0.637790\pi$
$101$	−136068.	+	136068.i	−1.32725	+	1.32725i	−0.907762	+	0.419486i	$0.862210\pi$
$102$	35415.5	+	15655.5i	0.337049	+	0.148993i
$103$		−	154767.i		−	1.43742i	−0.695309	−	0.718711i	$-0.744733\pi$
$103$		−	154767.i		−	1.43742i	0.695309	−	0.718711i	$-0.255267\pi$
$104$	−28697.3	+	9577.57i	−0.260170	+	0.0868304i
$105$			43627.7i			0.386180i
$106$	−38673.2	+	87485.7i	−0.334307	+	0.756262i
$107$	96953.4	−	96953.4i	0.818660	−	0.818660i	−0.167254	−	0.985914i	$-0.553490\pi$
$107$	96953.4	−	96953.4i	0.818660	−	0.818660i	0.985914	+	0.167254i	$0.0534899\pi$
$108$	5581.43	−	118535.i	0.0460454	−	0.977885i
$109$	−9912.42	−	9912.42i	−0.0799123	−	0.0799123i	0.666021	−	0.745933i	$-0.267996\pi$
$109$	−9912.42	−	9912.42i	−0.0799123	−	0.0799123i	−0.745933	+	0.666021i	$0.767996\pi$
$110$	34346.3	+	88770.3i	0.270644	+	0.699497i
$111$	15010.1			0.115631
$112$	191945.	+	18116.3i	1.44588	+	0.136466i
$113$	48808.0			0.359579			0.179790	−	0.983705i	$-0.442458\pi$
$113$	48808.0			0.359579			0.179790	+	0.983705i	$0.442458\pi$
$114$	−49359.5	−	127573.i	−0.355720	−	0.919382i
$115$	48979.4	+	48979.4i	0.345358	+	0.345358i
$116$	260410.	+	12261.9i	1.79685	+	0.0846080i
$117$	18564.5	−	18564.5i	0.125377	−	0.125377i
$118$	−90969.6	+	205789.i	−0.601438	+	1.36056i
$119$		−	139047.i		−	0.900105i
$120$	−18744.6	+	37524.1i	−0.118829	+	0.237879i
$121$		−	291940.i		−	1.81272i
$122$	86402.7	+	38194.5i	0.525566	+	0.232328i
$123$	−62695.3	+	62695.3i	−0.373656	+	0.373656i
$124$	−71149.7	+	64750.6i	−0.415546	+	0.378172i
$125$	−11048.5	−	11048.5i	−0.0632456	−	0.0632456i
$126$	−156040.	+	60373.9i	−0.875610	+	0.338784i
$127$	−61464.2			−0.338153			−0.169076	−	0.985603i	$-0.554078\pi$
$127$	−61464.2			−0.338153			−0.169076	+	0.985603i	$0.554078\pi$
$128$	157308.	+	98051.0i	0.848643	+	0.528965i
$129$	−170030.			−0.899603
$130$	−22043.0	+	8528.70i	−0.114396	+	0.0442613i
$131$	35243.6	+	35243.6i	0.179433	+	0.179433i	0.791109	−	0.611676i	$-0.209504\pi$
$131$	35243.6	+	35243.6i	0.179433	+	0.179433i	−0.611676	+	0.791109i	$0.709504\pi$
$132$	147639.	−	134361.i	0.737507	−	0.671177i
$133$	−347332.	+	347332.i	−1.70261	+	1.70261i
$134$	60640.6	+	26806.3i	0.291744	+	0.128966i
$135$		−	92708.2i		−	0.437808i
$136$	59741.4	−	119593.i	0.276967	−	0.554447i
$137$		−	299820.i		−	1.36477i	−0.730993	−	0.682385i	$-0.760943\pi$
$137$		−	299820.i		−	1.36477i	0.730993	−	0.682385i	$-0.239057\pi$
$138$	58735.2	−	132869.i	0.262543	−	0.593919i
$139$	−131820.	+	131820.i	−0.578688	+	0.578688i	−0.934542	−	0.355854i	$-0.884190\pi$
$139$	−131820.	+	131820.i	−0.578688	+	0.578688i	0.355854	+	0.934542i	$0.384190\pi$
$140$	150457.	+	7084.53i	0.648772	+	0.0305486i
$141$	136713.	+	136713.i	0.579112	+	0.579112i
$142$	42694.9	+	110348.i	0.177687	+	0.459243i
$143$	112485.			0.459994
$144$	−160149.	−	15115.3i	−0.643605	−	0.0607452i
$145$	203671.			0.804468
$146$	−21401.1	−	55312.6i	−0.0830910	−	0.214754i
$147$	−122180.	−	122180.i	−0.466346	−	0.466346i
$148$	2437.42	−	51764.5i	0.00914695	−	0.194257i
$149$	157459.	−	157459.i	0.581033	−	0.581033i	−0.354154	−	0.935187i	$-0.615231\pi$
$149$	157459.	−	157459.i	0.581033	−	0.581033i	0.935187	+	0.354154i	$0.115231\pi$
$150$	−13249.2	+	29972.0i	−0.0480797	+	0.108765i
$151$			209247.i			0.746823i	0.927666	+	0.373412i	$0.121812\pi$
$151$			209247.i			0.746823i	−0.927666	+	0.373412i	$0.878188\pi$
$152$	−447970.	+	149508.i	−1.57268	+	0.524874i
$153$			116013.i			0.400664i
$154$	−655639.	−	289827.i	−2.22773	−	0.984774i
$155$	−53144.8	+	53144.8i	−0.177677	+	0.177677i
$156$	33363.7	+	36661.0i	0.109765	+	0.120613i
$157$	223193.	+	223193.i	0.722657	+	0.722657i	0.969146	−	0.246489i	$-0.0792769\pi$
$157$	223193.	+	223193.i	0.722657	+	0.722657i	−0.246489	+	0.969146i	$0.579277\pi$
$158$	−127956.	+	49507.6i	−0.407772	+	0.157772i
$159$	156726.			0.491640
$160$	126364.	+	70737.2i	0.390231	+	0.218448i
$161$	−521665.			−1.58609
$162$	20056.7	−	7760.19i	0.0600444	−	0.0232319i
$163$	−176691.	−	176691.i	−0.520889	−	0.520889i	0.396951	−	0.917840i	$-0.370068\pi$
$163$	−176691.	−	176691.i	−0.520889	−	0.520889i	−0.917840	+	0.396951i	$0.870068\pi$
$164$	206034.	+	226395.i	0.598175	+	0.657291i
$165$	110278.	−	110278.i	0.315340	−	0.315340i
$166$	591455.	+	261454.i	1.66591	+	0.736420i
$167$		−	230417.i		−	0.639327i	−0.947531	−	0.319664i	$-0.896430\pi$
$167$		−	230417.i		−	0.639327i	0.947531	−	0.319664i	$-0.103570\pi$
$168$	−100007.	−	299651.i	−0.273374	−	0.819109i
$169$		−	343361.i		−	0.924772i
$170$	42226.7	−	95524.2i	0.112064	−	0.253508i
$171$	289796.	−	289796.i	0.757883	−	0.757883i
$172$	−27610.5	+	586374.i	−0.0711627	+	1.51131i
$173$	−376017.	−	376017.i	−0.955196	−	0.955196i	0.0438422	−	0.999038i	$-0.486040\pi$
$173$	−376017.	−	376017.i	−0.955196	−	0.955196i	−0.999038	+	0.0438422i	$0.986040\pi$
$174$	−154136.	−	398374.i	−0.385949	−	0.997511i
$175$	117675.			0.290461
$176$	−439389.	−	530974.i	−1.06922	−	1.29209i
$177$	368659.			0.884488
$178$	−112032.	−	289553.i	−0.265027	−	0.684981i
$179$	16495.3	+	16495.3i	0.0384793	+	0.0384793i	0.726085	−	0.687605i	$-0.241338\pi$
$179$	16495.3	+	16495.3i	0.0384793	+	0.0384793i	−0.687605	+	0.726085i	$0.741338\pi$
$180$	−125534.	−	5910.97i	−0.288788	−	0.0135981i
$181$	−64756.9	+	64756.9i	−0.146923	+	0.146923i	−0.776742	−	0.629819i	$-0.783129\pi$
$181$	−64756.9	+	64756.9i	−0.146923	+	0.146923i	0.629819	+	0.776742i	$0.283129\pi$
$182$	71968.3	−	162805.i	0.161051	−	0.364325i
$183$		−	154785.i		−	0.341666i
$184$	−448683.	−	224134.i	−0.977000	−	0.488048i
$185$		−	40485.8i		−	0.0869708i
$186$	144169.	+	63730.3i	0.305555	+	0.135071i
$187$	−351469.	+	351469.i	−0.734993	+	0.734993i
$188$	493677.	−	449276.i	1.01870	−	0.927083i
$189$	493704.	+	493704.i	1.00534	+	1.00534i
$190$	−344095.	+	133135.i	−0.691504	+	0.267551i
$191$	496507.			0.984787			0.492393	−	0.870373i	$-0.336122\pi$
$191$	496507.			0.984787			0.492393	+	0.870373i	$0.336122\pi$
$192$	42729.3	−	300696.i	0.0836512	−	0.588674i
$193$	−258207.			−0.498969			−0.249485	−	0.968379i	$-0.580261\pi$
$193$	−258207.			−0.498969			−0.249485	+	0.968379i	$0.580261\pi$
$194$	260751.	−	100888.i	0.497417	−	0.192457i
$195$	27383.7	+	27383.7i	0.0515710	+	0.0515710i
$196$	−441199.	+	401518.i	−0.820340	+	0.746560i
$197$	−486630.	+	486630.i	−0.893374	+	0.893374i	−0.994839	−	0.101465i	$-0.967647\pi$
$197$	−486630.	+	486630.i	−0.893374	+	0.893374i	0.101465	+	0.994839i	$0.467647\pi$
$198$	547032.	+	241817.i	0.991630	+	0.438352i
$199$			191663.i			0.343089i	0.985176	+	0.171544i	$0.0548757\pi$
$199$			191663.i			0.343089i	−0.985176	+	0.171544i	$0.945124\pi$
$200$	101212.	+	50558.9i	0.178919	+	0.0893764i
$201$		−	108634.i		−	0.189660i
$202$	440110.	−	995605.i	0.758896	−	1.71676i
$203$	−1.08462e6	+	1.08462e6i	−1.84730	+	1.84730i
$204$	−218799.	−	10302.5i	−0.368104	−	0.0173328i
$205$	169105.	+	169105.i	0.281042	+	0.281042i
$206$	315916.	+	816506.i	0.518685	+	1.34058i
$207$	435251.			0.706016
$208$	131849.	−	109107.i	0.211309	−	0.174861i
$209$	1.75591e6			2.78058
$210$	−89054.8	−	230168.i	−0.139351	−	0.360161i
$211$	−133840.	−	133840.i	−0.206958	−	0.206958i	0.596015	−	0.802973i	$-0.296750\pi$
$211$	−133840.	−	133840.i	−0.206958	−	0.206958i	−0.802973	+	0.596015i	$0.796750\pi$
$212$	25450.0	−	540492.i	0.0388909	−	0.825942i
$213$	137083.	−	137083.i	0.207031	−	0.207031i
$214$	−313594.	+	709405.i	−0.468095	+	1.05891i
$215$			458613.i			0.676628i
$216$	212513.	+	636753.i	0.309921	+	0.928616i
$217$		−	566030.i		−	0.816000i
$218$	72528.9	+	32061.6i	0.103364	+	0.0456924i
$219$	−68714.0	+	68714.0i	−0.0968133	+	0.0968133i
$220$	−362403.	−	398219.i	−0.504819	−	0.554709i
$221$	−87275.0	−	87275.0i	−0.120201	−	0.120201i
$222$	−79189.0	+	30639.2i	−0.107841	+	0.0417249i
$223$	84519.7			0.113814			0.0569070	−	0.998379i	$-0.481876\pi$
$223$	84519.7			0.113814			0.0569070	+	0.998379i	$0.481876\pi$
$224$	−1.04963e6	+	296230.i	−1.39771	+	0.394466i
$225$	−98181.9			−0.129293
$226$	−257498.	+	99629.0i	−0.335353	+	0.129752i
$227$	615963.	+	615963.i	0.793395	+	0.793395i	0.982045	−	0.188649i	$-0.0604109\pi$
$227$	615963.	+	615963.i	0.793395	+	0.793395i	−0.188649	+	0.982045i	$0.560411\pi$
$228$	520815.	+	572285.i	0.663508	+	0.729080i
$229$	53816.6	−	53816.6i	0.0678153	−	0.0678153i	−0.672386	−	0.740201i	$-0.734730\pi$
$229$	53816.6	−	53816.6i	0.0678153	−	0.0678153i	0.740201	+	0.672386i	$0.234730\pi$
$230$	−358381.	−	158423.i	−0.446710	−	0.197469i
$231$			1.17454e6i			1.44823i
$232$	−1.39888e6	+	466870.i	−1.70632	+	0.569477i
$233$			105869.i			0.127755i	0.997958	+	0.0638775i	$0.0203467\pi$
$233$			105869.i			0.127755i	−0.997958	+	0.0638775i	$0.979653\pi$
$234$	−60046.7	+	135836.i	−0.0716885	+	0.162172i
$235$	368749.	−	368749.i	0.435573	−	0.435573i
$236$	59865.1	−	1.27138e6i	0.0699670	−	1.48592i
$237$	158958.	+	158958.i	0.183828	+	0.183828i
$238$	283828.	+	733572.i	0.324798	+	0.839461i
$239$	1.34879e6			1.52738			0.763692	−	0.645581i	$-0.223385\pi$
$239$	1.34879e6			1.52738			0.763692	+	0.645581i	$0.223385\pi$
$240$	22296.0	−	236229.i	0.0249861	−	0.264731i
$241$	−586117.			−0.650042			−0.325021	−	0.945707i	$-0.605371\pi$
$241$	−586117.			−0.650042			−0.325021	+	0.945707i	$0.605371\pi$
$242$	595921.	+	1.54020e6i	0.654110	+	1.69059i
$243$	−662107.	−	662107.i	−0.719304	−	0.719304i
$244$	−533802.	−	25135.0i	−0.573991	−	0.0270274i
$245$	−329551.	+	329551.i	−0.350758	+	0.350758i
$246$	202787.	−	458740.i	0.213650	−	0.483313i
$247$			436018.i			0.454739i
$248$	243195.	−	486840.i	0.251087	−	0.502640i
$249$		−	1.05956e6i		−	1.08299i
$250$	80841.9	+	35736.4i	0.0818063	+	0.0361626i
$251$	−709430.	+	709430.i	−0.710764	+	0.710764i	−0.966695	−	0.255931i	$-0.917618\pi$
$251$	−709430.	+	709430.i	−0.710764	+	0.710764i	0.255931	+	0.966695i	$0.417618\pi$
$252$	699989.	−	637033.i	0.694368	−	0.631918i
$253$	1.31862e6	+	1.31862e6i	1.29514	+	1.29514i
$254$	324268.	−	125463.i	0.315370	−	0.122020i
$255$	−171126.			−0.164803
$256$	−1.03006e6	−	196187.i	−0.982341	−	0.187099i
$257$	−63656.1			−0.0601184			−0.0300592	−	0.999548i	$-0.509570\pi$
$257$	−63656.1			−0.0601184			−0.0300592	+	0.999548i	$0.509570\pi$
$258$	897032.	−	347073.i	0.838993	−	0.324617i
$259$	215601.	+	215601.i	0.199711	+	0.199711i
$260$	98883.7	−	89990.2i	0.0907175	−	0.0825585i
$261$	904951.	−	904951.i	0.822288	−	0.822288i
$262$	−257877.	−	113995.i	−0.232091	−	0.102597i
$263$		−	124272.i		−	0.110786i	−0.998465	−	0.0553930i	$-0.982359\pi$
$263$		−	124272.i		−	0.110786i	0.998465	−	0.0553930i	$-0.0176412\pi$
$264$	−504641.	+	1.01022e6i	−0.445628	+	0.892082i
$265$		−	422727.i		−	0.369782i
$266$	1.12344e6	−	2.54142e6i	0.973522	−	2.20228i
$267$	−359708.	+	359708.i	−0.308796	+	0.308796i
$268$	−374642.	−	17640.7i	−0.318624	−	0.0150030i
$269$	−20337.2	−	20337.2i	−0.0171361	−	0.0171361i	0.698487	−	0.715623i	$-0.253857\pi$
$269$	−20337.2	−	20337.2i	−0.0171361	−	0.0171361i	−0.715623	+	0.698487i	$0.753857\pi$
$270$	189240.	+	489103.i	0.157981	+	0.408311i
$271$	−561937.			−0.464798			−0.232399	−	0.972621i	$-0.574658\pi$
$271$	−561937.			−0.464798			−0.232399	+	0.972621i	$0.574658\pi$
$272$	−71059.8	+	752889.i	−0.0582373	+	0.617034i
$273$	−291656.			−0.236845
$274$	612006.	+	1.58177e6i	0.492470	+	1.27282i
$275$	−297447.	−	297447.i	−0.237180	−	0.237180i
$276$	−38652.3	+	820875.i	−0.0305424	+	0.648641i
$277$	−66494.3	+	66494.3i	−0.0520697	+	0.0520697i	−0.732662	−	0.680593i	$-0.761722\pi$
$277$	−66494.3	+	66494.3i	−0.0520697	+	0.0520697i	0.680593	+	0.732662i	$0.261722\pi$
$278$	426370.	−	964524.i	0.330883	−	0.748516i
$279$			472267.i			0.363226i
$280$	−808232.	+	269743.i	−0.616085	+	0.205615i
$281$		−	2.09033e6i		−	1.57925i	−0.613592	−	0.789623i	$-0.710276\pi$
$281$		−	2.09033e6i		−	1.57925i	0.613592	−	0.789623i	$-0.289724\pi$
$282$	−1.00033e6	−	442197.i	−0.749064	−	0.331125i
$283$	682110.	−	682110.i	0.506277	−	0.506277i	−0.407105	−	0.913382i	$-0.633462\pi$
$283$	682110.	−	682110.i	0.506277	−	0.506277i	0.913382	+	0.407105i	$0.133462\pi$
$284$	−450493.	−	495014.i	−0.331430	−	0.364185i
$285$	427465.	+	427465.i	0.311737	+	0.311737i
$286$	−593438.	+	229608.i	−0.429003	+	0.165986i
$287$	−1.80108e6			−1.29071
$288$	875759.	−	247160.i	0.622162	−	0.175589i
$289$	−874458.			−0.615878
$290$	−1.07451e6	+	415742.i	−0.750268	+	0.290288i
$291$	−323927.	−	323927.i	−0.224241	−	0.224241i
$292$	225813.	+	248129.i	0.154986	+	0.170302i
$293$	−341569.	+	341569.i	−0.232439	+	0.232439i	−0.813710	−	0.581271i	$-0.802556\pi$
$293$	−341569.	+	341569.i	−0.232439	+	0.232439i	0.581271	+	0.813710i	$0.302556\pi$
$294$	893991.	+	395191.i	0.603205	+	0.266648i
$295$		−	994365.i		−	0.665259i
$296$	92804.8	+	278071.i	0.0615660	+	0.184470i
$297$		−	2.49588e6i		−	1.64184i
$298$	−509298.	+	1.15212e6i	−0.332224	+	0.751549i
$299$	−327432.	+	327432.i	−0.211809	+	0.211809i
$300$	8719.01	−	185169.i	0.00559325	−	0.118786i
$301$	−2.44227e6	−	2.44227e6i	−1.55374	−	1.55374i
$302$	−427125.	−	1.10393e6i	−0.269487	−	0.696507i
$303$	−1.78357e6			−1.11605
$304$	2.05819e6	−	1.70318e6i	1.27732	−	1.05700i
$305$	−417495.			−0.256981
$306$	−236812.	−	612056.i	−0.144577	−	0.373669i
$307$	−942153.	−	942153.i	−0.570526	−	0.570526i	0.361749	−	0.932275i	$-0.382180\pi$
$307$	−942153.	−	942153.i	−0.570526	−	0.570526i	−0.932275	+	0.361749i	$0.882180\pi$
$308$	4.05058e6	+	190729.i	2.43299	+	0.114562i
$309$	1.01433e6	−	1.01433e6i	0.604345	−	0.604345i
$310$	171896.	−	388859.i	0.101593	−	0.229820i
$311$			188120.i			0.110289i	0.998478	+	0.0551446i	$0.0175620\pi$
$311$			188120.i			0.110289i	−0.998478	+	0.0551446i	$0.982438\pi$
$312$	−250852.	−	125310.i	−0.145892	−	0.0728784i
$313$			585670.i			0.337903i	0.985624	+	0.168951i	$0.0540381\pi$
$313$			585670.i			0.337903i	−0.985624	+	0.168951i	$0.945962\pi$
$314$	−1.63310e6	−	721916.i	−0.934735	−	0.413202i
$315$	522853.	−	522853.i	0.296895	−	0.296895i
$316$	574003.	−	522378.i	0.323367	−	0.294284i
$317$	−1.32593e6	−	1.32593e6i	−0.741094	−	0.741094i	0.231695	−	0.972789i	$-0.425573\pi$
$317$	−1.32593e6	−	1.32593e6i	−0.741094	−	0.741094i	−0.972789	+	0.231695i	$0.925573\pi$
$318$	−826841.	+	319915.i	−0.458516	+	0.177405i
$319$	5.48320e6			3.01687
$320$	−811052.	−	115251.i	−0.442766	−	0.0629174i
$321$	1.27086e6			0.688390
$322$	2.75217e6	−	1.06485e6i	1.47923	−	0.572331i
$323$	−1.36238e6	−	1.36238e6i	−0.726595	−	0.726595i
$324$	−89973.4	+	81881.3i	−0.0476159	+	0.0433334i
$325$	73860.6	−	73860.6i	0.0387886	−	0.0387886i
$326$	1.29284e6	+	571504.i	0.673755	+	0.297835i
$327$		−	129931.i		−	0.0671962i
$328$	−1.54911e6	−	773835.i	−0.795053	−	0.397159i
$329$			3.92743e6i			2.00041i
$330$	−356693.	+	806902.i	−0.180306	+	0.407883i
$331$	−2.11251e6	+	2.11251e6i	−1.05981	+	1.05981i	−0.0617168	+	0.998094i	$0.519658\pi$
$331$	−2.11251e6	+	2.11251e6i	−1.05981	+	1.05981i	−0.998094	+	0.0617168i	$0.980342\pi$
$332$	−3.65405e6	−	172057.i	−1.81940	−	0.0856698i
$333$	−179887.	−	179887.i	−0.0888973	−	0.0888973i
$334$	470337.	+	1.21562e6i	0.230698	+	0.596253i
$335$	−293013.			−0.142651
$336$	1.13927e6	+	1.37674e6i	0.550527	+	0.665277i
$337$	−3.64159e6			−1.74669			−0.873346	−	0.487100i	$-0.838055\pi$
$337$	−3.64159e6			−1.74669			−0.873346	+	0.487100i	$0.838055\pi$
$338$	700884.	+	1.81148e6i	0.333699	+	0.862467i
$339$	319886.	+	319886.i	0.151181	+	0.151181i
$340$	−27788.5	+	590155.i	−0.0130367	+	0.276866i
$341$	−1.43076e6	+	1.43076e6i	−0.666316	+	0.666316i
$342$	−937342.	+	2.12043e6i	−0.433344	+	0.980300i
$343$		−	345532.i		−	0.158582i
$344$	−1.05127e6	−	3.14991e6i	−0.478980	−	1.43517i
$345$			642019.i			0.290403i
$346$	2.75131e6	+	1.21622e6i	1.23552	+	0.546164i
$347$	−666657.	+	666657.i	−0.297221	+	0.297221i	−0.839924	−	0.542704i	$-0.817401\pi$
$347$	−666657.	+	666657.i	−0.297221	+	0.297221i	0.542704	+	0.839924i	$0.317401\pi$
$348$	1.62636e6	+	1.78708e6i	0.719892	+	0.791037i
$349$	−626668.	−	626668.i	−0.275406	−	0.275406i	0.555866	−	0.831272i	$-0.312387\pi$
$349$	−626668.	−	626668.i	−0.275406	−	0.275406i	−0.831272	+	0.555866i	$0.812387\pi$
$350$	−620820.	+	240203.i	−0.270892	+	0.104811i
$351$	619763.			0.268509
$352$	3.40194e6	+	1.90438e6i	1.46342	+	0.819212i
$353$	−227754.			−0.0972811			−0.0486406	−	0.998816i	$-0.515489\pi$
$353$	−227754.			−0.0972811			−0.0486406	+	0.998816i	$0.515489\pi$
$354$	−1.94495e6	+	752524.i	−0.824897	+	0.319163i
$355$	−369748.	−	369748.i	−0.155717	−	0.155717i
$356$	1.18210e6	+	1.29892e6i	0.494343	+	0.543197i
$357$	911307.	−	911307.i	0.378437	−	0.378437i
$358$	−120696.	−	53353.8i	−0.0497719	−	0.0220018i
$359$		−	855379.i		−	0.350286i	−0.984543	−	0.175143i	$-0.943961\pi$
$359$		−	855379.i		−	0.350286i	0.984543	−	0.175143i	$-0.0560387\pi$
$360$	674348.	−	225060.i	0.274238	−	0.0915256i
$361$			4.33023e6i			1.74881i
$362$	209455.	−	473825.i	0.0840079	−	0.190041i
$363$	1.91337e6	−	1.91337e6i	0.762135	−	0.762135i
$364$	−47360.8	+	1.00582e6i	−0.0187355	+	0.397893i
$365$	185339.	+	185339.i	0.0728172	+	0.0728172i
$366$	315955.	+	816606.i	0.123288	+	0.318647i
$367$	677534.			0.262583			0.131291	−	0.991344i	$-0.458088\pi$
$367$	677534.			0.262583			0.131291	+	0.991344i	$0.458088\pi$
$368$	2.82464e6	+	266597.i	1.08729	+	0.102621i
$369$	1.50273e6			0.574534
$370$	82641.4	+	213592.i	0.0313829	+	0.0811113i
$371$	2.25117e6	+	2.25117e6i	0.849129	+	0.849129i
$372$	−890686.	−	41939.5i	−0.333708	−	0.0157132i
$373$	16042.9	−	16042.9i	0.00597050	−	0.00597050i	−0.704115	−	0.710086i	$-0.748656\pi$
$373$	16042.9	−	16042.9i	0.00597050	−	0.00597050i	0.710086	+	0.704115i	$0.248656\pi$
$374$	1.13682e6	−	2.57169e6i	0.420255	−	0.950691i
$375$		−	144824.i		−	0.0531816i
$376$	−1.68742e6	+	3.37797e6i	−0.615537	+	1.23222i
$377$			1.36156e6i			0.493382i
$378$	−3.61242e6	−	1.59688e6i	−1.30037	−	0.574834i
$379$	2.12086e6	−	2.12086e6i	0.758426	−	0.758426i	−0.217610	−	0.976036i	$-0.569826\pi$
$379$	2.12086e6	−	2.12086e6i	0.758426	−	0.758426i	0.976036	+	0.217610i	$0.0698261\pi$
$380$	1.54359e6	−	1.40477e6i	0.548371	−	0.499051i
$381$	−402834.	−	402834.i	−0.142172	−	0.142172i
$382$	−2.61944e6	+	1.01349e6i	−0.918438	+	0.355355i
$383$	−4.12055e6			−1.43535			−0.717676	−	0.696377i	$-0.754794\pi$
$383$	−4.12055e6			−1.43535			−0.717676	+	0.696377i	$0.754794\pi$
$384$	388367.	+	1.67361e6i	0.134405	+	0.579198i
$385$	3.16802e6			1.08927
$386$	1.36223e6	−	527063.i	0.465352	−	0.180050i
$387$	2.03771e6	+	2.03771e6i	0.691616	+	0.691616i
$388$	−1.16971e6	+	1.06451e6i	−0.394457	+	0.358981i
$389$	282068.	−	282068.i	0.0945106	−	0.0945106i	−0.658271	−	0.752781i	$-0.728712\pi$
$389$	282068.	−	282068.i	0.0945106	−	0.0945106i	0.752781	+	0.658271i	$0.228712\pi$
$390$	−200366.	−	88572.2i	−0.0667056	−	0.0294874i
$391$		−	2.04619e6i		−	0.676868i
$392$	1.50805e6	−	3.01889e6i	0.495679	−	0.992276i
$393$			461971.i			0.150881i
$394$	1.57400e6	−	3.56066e6i	0.510815	−	1.15555i
$395$	428748.	−	428748.i	0.138264	−	0.138264i
$396$	−3.37960e6	−	159134.i	−1.08300	−	0.0509948i
$397$	2.09410e6	+	2.09410e6i	0.666839	+	0.666839i	0.956983	−	0.290144i	$-0.0937032\pi$
$397$	2.09410e6	+	2.09410e6i	0.666839	+	0.666839i	−0.290144	+	0.956983i	$0.593703\pi$
$398$	−391232.	−	1.01116e6i	−0.123802	−	0.319974i
$399$	−4.55280e6			−1.43168
$400$	−637168.	−	60137.7i	−0.199115	−	0.0187930i
$401$	3.84199e6			1.19315			0.596575	−	0.802557i	$-0.296528\pi$
$401$	3.84199e6			1.19315			0.596575	+	0.802557i	$0.296528\pi$
$402$	221749.	+	573124.i	0.0684378	+	0.176882i
$403$	−355278.	−	355278.i	−0.108970	−	0.108970i
$404$	−289626.	+	6.15091e6i	−0.0882846	+	1.87493i
$405$	−67205.1	+	67205.1i	−0.0203594	+	0.0203594i
$406$	3.50818e6	−	7.93613e6i	1.05625	−	2.38943i
$407$		−	1.08995e6i		−	0.326153i
$408$	1.17535e6	−	392269.i	0.349557	−	0.116663i
$409$		−	1.40769e6i		−	0.416100i	−0.978118	−	0.208050i	$-0.933288\pi$
$409$		−	1.40769e6i		−	0.416100i	0.978118	−	0.208050i	$-0.0667117\pi$
$410$	−1.23733e6	−	546967.i	−0.363519	−	0.160695i
$411$	1.96501e6	−	1.96501e6i	0.573800	−	0.573800i
$412$	−3.33338e6	−	3.66281e6i	−0.967479	−	1.06309i
$413$	5.29534e6	+	5.29534e6i	1.52763	+	1.52763i
$414$	−2.29627e6	+	888454.i	−0.658449	+	0.254762i
$415$	−2.85789e6			−0.814564
$416$	−472885.	+	844753.i	−0.133975	+	0.239330i
$417$	−1.72789e6			−0.486604
$418$	−9.26369e6	+	3.58423e6i	−2.59324	+	1.00336i
$419$	−1.09349e6	−	1.09349e6i	−0.304284	−	0.304284i	0.538403	−	0.842687i	$-0.319028\pi$
$419$	−1.09349e6	−	1.09349e6i	−0.304284	−	0.304284i	−0.842687	+	0.538403i	$0.819028\pi$
$420$	939658.	+	1.03252e6i	0.259924	+	0.285612i
$421$	249622.	−	249622.i	0.0686399	−	0.0686399i	−0.671953	−	0.740593i	$-0.734545\pi$
$421$	249622.	−	249622.i	0.0686399	−	0.0686399i	0.740593	+	0.671953i	$0.234545\pi$
$422$	979307.	+	432905.i	0.267694	+	0.118335i
$423$		−	3.27685e6i		−	0.890443i
$424$	969009.	+	2.90344e6i	0.261766	+	0.784329i
$425$			461569.i			0.123955i
$426$	−443394.	+	1.00304e6i	−0.118377	+	0.267789i
$427$	2.22330e6	−	2.22330e6i	0.590105	−	0.590105i
$428$	206370.	−	4.38275e6i	0.0544548	−	1.15648i
$429$	737220.	+	737220.i	0.193399	+	0.193399i
$430$	−936140.	−	2.41952e6i	−0.244157	−	0.631041i
$431$	−1.20518e6			−0.312506			−0.156253	−	0.987717i	$-0.549941\pi$
$431$	−1.20518e6			−0.312506			−0.156253	+	0.987717i	$0.549941\pi$
$432$	−2.42093e6	−	2.92554e6i	−0.624126	−	0.754218i
$433$	−1.67409e6			−0.429101			−0.214550	−	0.976713i	$-0.568829\pi$
$433$	−1.67409e6			−0.429101			−0.214550	+	0.976713i	$0.568829\pi$
$434$	1.15541e6	+	2.98622e6i	0.294449	+	0.761023i
$435$	1.33485e6	+	1.33485e6i	0.338228	+	0.338228i
$436$	−448089.	−	21099.0i	−0.112888	−	0.00531553i
$437$	−5.11129e6	+	5.11129e6i	−1.28034	+	1.28034i
$438$	222255.	−	502779.i	0.0553561	−	0.125225i
$439$			315411.i			0.0781117i	0.999237	+	0.0390559i	$0.0124350\pi$
$439$			315411.i			0.0781117i	−0.999237	+	0.0390559i	$0.987565\pi$
$440$	2.72480e6	+	1.36114e6i	0.670971	+	0.335175i
$441$			2.92852e6i			0.717054i
$442$	638589.	+	282290.i	0.155477	+	0.0687289i
$443$	3.90144e6	−	3.90144e6i	0.944530	−	0.944530i	−0.0540105	−	0.998540i	$-0.517200\pi$
$443$	3.90144e6	−	3.90144e6i	0.944530	−	0.944530i	0.998540	+	0.0540105i	$0.0172004\pi$
$444$	355238.	−	323288.i	0.0855188	−	0.0778274i
$445$	970222.	+	970222.i	0.232258	+	0.232258i
$446$	−445903.	+	172525.i	−0.106146	+	0.0410692i
$447$	2.06396e6			0.488576
$448$	4.93289e6	−	3.70538e6i	1.16120	−	0.872244i
$449$	−5.37209e6			−1.25756			−0.628779	−	0.777584i	$-0.716445\pi$
$449$	−5.37209e6			−1.25756			−0.628779	+	0.777584i	$0.716445\pi$
$450$	517981.	−	200413.i	0.120582	−	0.0466547i
$451$	4.55261e6	+	4.55261e6i	1.05395	+	1.05395i
$452$	1.15512e6	−	1.05123e6i	0.265939	−	0.242020i
$453$	−1.37140e6	+	1.37140e6i	−0.313992	+	0.313992i
$454$	−4.50698e6	−	1.99232e6i	−1.02623	−	0.453649i
$455$			786667.i			0.178140i
$456$	−3.91585e6	−	1.95611e6i	−0.881889	−	0.440536i
$457$		−	2.77078e6i		−	0.620600i	−0.950639	−	0.310300i	$-0.899570\pi$
$457$		−	2.77078e6i		−	0.620600i	0.950639	−	0.310300i	$-0.100430\pi$
$458$	−174069.	+	393775.i	−0.0387755	+	0.0877171i
$459$	−1.93651e6	+	1.93651e6i	−0.429031	+	0.429031i
$460$	2.21410e6	+	104255.i	0.487869	+	0.0229722i
$461$	−5.30157e6	−	5.30157e6i	−1.16186	−	1.16186i	−0.984069	−	0.177788i	$-0.943106\pi$
$461$	−5.30157e6	−	5.30157e6i	−1.16186	−	1.16186i	−0.177788	−	0.984069i	$-0.556894\pi$
$462$	−2.39752e6	−	6.19655e6i	−0.522586	−	1.35066i
$463$	6.65061e6			1.44181			0.720906	−	0.693032i	$-0.243726\pi$
$463$	6.65061e6			1.44181			0.720906	+	0.693032i	$0.243726\pi$
$464$	6.42713e6	−	5.31854e6i	1.38587	−	1.14683i
$465$	−696619.			−0.149404
$466$	−216104.	−	558535.i	−0.0460996	−	0.119148i
$467$	3.66531e6	+	3.66531e6i	0.777712	+	0.777712i	0.979441	−	0.201730i	$-0.0646562\pi$
$467$	3.66531e6	+	3.66531e6i	0.777712	+	0.777712i	−0.201730	+	0.979441i	$0.564656\pi$
$468$	39515.4	−	839205.i	0.00833973	−	0.177114i
$469$	1.56040e6	−	1.56040e6i	0.327569	−	0.327569i
$470$	−1.19271e6	+	2.69813e6i	−0.249053	+	0.563401i
$471$			2.92560e6i			0.607664i
$472$	2.27936e6	+	6.82965e6i	0.470932	+	1.41105i
$473$			1.23467e7i			2.53745i
$474$	−1.16309e6	−	514146.i	−0.237775	−	0.105109i
$475$	1.15298e6	−	1.15298e6i	0.234470	−	0.234470i
$476$	−2.99480e6	−	3.29077e6i	−0.605829	−	0.665702i
$477$	−1.87826e6	−	1.87826e6i	−0.377973	−	0.377973i
$478$	−7.11583e6	+	2.75320e6i	−1.42448	+	0.551148i
$479$	−6.25752e6			−1.24613			−0.623065	−	0.782170i	$-0.714113\pi$
$479$	−6.25752e6			−1.24613			−0.623065	+	0.782170i	$0.714113\pi$
$480$	364574.	+	1.29179e6i	0.0722242	+	0.255911i
$481$	270652.			0.0533394
$482$	3.09220e6	−	1.19641e6i	0.606247	−	0.234564i
$483$	−3.41898e6	−	3.41898e6i	−0.666851	−	0.666851i
$484$	−6.28784e6	−	6.90925e6i	−1.22008	−	1.34066i
$485$	−873711.	+	873711.i	−0.168661	+	0.168661i
$486$	4.84462e6	+	2.14158e6i	0.930398	+	0.411285i
$487$			2.88481e6i			0.551181i	0.961275	+	0.275590i	$0.0888734\pi$
$487$			2.88481e6i			0.551181i	−0.961275	+	0.275590i	$0.911127\pi$
$488$	2.86750e6	−	957014.i	0.545072	−	0.181915i
$489$		−	2.31605e6i		−	0.438002i
$490$	1.06593e6	−	2.41131e6i	0.200557	−	0.453695i
$491$	4.39193e6	−	4.39193e6i	0.822151	−	0.822151i	−0.164265	−	0.986416i	$-0.552525\pi$
$491$	4.39193e6	−	4.39193e6i	0.822151	−	0.822151i	0.986416	+	0.164265i	$0.0525253\pi$
$492$	−133450.	+	2.83412e6i	−0.0248545	+	0.527845i
$493$	−4.25433e6	−	4.25433e6i	−0.788340	−	0.788340i
$494$	−890019.	−	2.30031e6i	−0.164090	−	0.424101i
$495$	−2.64324e6			−0.484868
$496$	−289270.	+	3.06486e6i	−0.0527957	+	0.559379i
$497$	3.93807e6			0.715143
$498$	2.16282e6	+	5.58994e6i	0.390792	+	1.01003i
$499$	3.90280e6	+	3.90280e6i	0.701657	+	0.701657i	0.964766	−	0.263109i	$-0.0847480\pi$
$499$	3.90280e6	+	3.90280e6i	0.701657	+	0.701657i	−0.263109	+	0.964766i	$0.584748\pi$
$500$	−499447.	−	23517.3i	−0.0893437	−	0.00420691i
$501$	1.51014e6	−	1.51014e6i	0.268797	−	0.268797i
$502$	2.29464e6	−	5.19088e6i	0.406402	−	0.919352i
$503$		−	4.35740e6i		−	0.767905i	−0.923353	−	0.383952i	$-0.874563\pi$
$503$		−	4.35740e6i		−	0.767905i	0.923353	−	0.383952i	$-0.125437\pi$
$504$	−2.39261e6	+	4.78966e6i	−0.419562	+	0.839902i
$505$			4.81072e6i			0.839425i
$506$	−9.64829e6	−	4.26505e6i	−1.67523	−	0.740539i
$507$	2.25038e6	−	2.25038e6i	0.388809	−	0.388809i
$508$	−1.45465e6	+	1.32382e6i	−0.250092	+	0.227599i
$509$	−3.41041e6	−	3.41041e6i	−0.583462	−	0.583462i	0.352391	−	0.935853i	$-0.385369\pi$
$509$	−3.41041e6	−	3.41041e6i	−0.583462	−	0.583462i	−0.935853	+	0.352391i	$0.885369\pi$
$510$	902815.	−	349310.i	0.153700	−	0.0594683i
$511$	−1.97399e6			−0.334420
$512$	5.83478e6	−	1.06757e6i	0.983670	−	0.179979i
$513$	9.67463e6			1.62308
$514$	335833.	−	129938.i	0.0560680	−	0.0216934i
$515$	−2.73591e6	−	2.73591e6i	−0.454552	−	0.454552i
$516$	−4.02404e6	+	3.66212e6i	−0.665331	+	0.605492i
$517$	9.92740e6	−	9.92740e6i	1.63346	−	1.63346i
$518$	−1.57755e6	−	697359.i	−0.258320	−	0.114191i
$519$		−	4.92881e6i		−	0.803200i
$520$	−337991.	+	676610.i	−0.0548147	+	0.109731i
$521$		−	6.70842e6i		−	1.08274i	−0.840783	−	0.541372i	$-0.817905\pi$
$521$		−	6.70842e6i		−	1.08274i	0.840783	−	0.541372i	$-0.182095\pi$
$522$	−2.92705e6	+	6.62150e6i	−0.470169	+	1.06360i
$523$	−4.05929e6	+	4.05929e6i	−0.648928	+	0.648928i	−0.952734	−	0.303806i	$-0.901742\pi$
$523$	−4.05929e6	+	4.05929e6i	−0.648928	+	0.648928i	0.303806	+	0.952734i	$0.401742\pi$
$524$	1.59318e6	+	75017.6i	0.253476	+	0.0119353i
$525$	771237.	+	771237.i	0.122121	+	0.122121i
$526$	253670.	+	655627.i	0.0399765	+	0.103322i
$527$	2.22021e6			0.348230
$528$	600248.	−	6.35973e6i	0.0937014	−	0.992781i
$529$	−1.24041e6			−0.192720
$530$	862890.	+	2.23020e6i	0.133434	+	0.344868i
$531$	−4.41817e6	−	4.41817e6i	−0.679995	−	0.679995i
$532$	−739311.	+	1.57010e7i	−0.113253	+	2.40519i
$533$	−1.13048e6	+	1.13048e6i	−0.172364	+	0.172364i
$534$	1.16347e6	−	2.63198e6i	0.176564	−	0.399419i
$535$		−	3.42782e6i		−	0.517766i
$536$	2.01252e6	−	671668.i	0.302571	−	0.100982i
$537$			216219.i			0.0323563i
$538$	148807.	+	65780.5i	0.0221650	+	0.00979809i
$539$	−8.87212e6	+	8.87212e6i	−1.31539	+	1.31539i
$540$	−1.99676e6	−	2.19409e6i	−0.294674	−	0.323795i
$541$	−6.54418e6	−	6.54418e6i	−0.961307	−	0.961307i	0.0379721	−	0.999279i	$-0.487910\pi$
$541$	−6.54418e6	−	6.54418e6i	−0.961307	−	0.961307i	−0.999279	+	0.0379721i	$0.987910\pi$
$542$	2.96463e6	−	1.14705e6i	0.433483	−	0.167720i
$543$	−848830.			−0.123544
$544$	−1.16194e6	−	4.11709e6i	−0.168340	−	0.596476i
$545$	−350457.			−0.0505410
$546$	1.53870e6	−	595340.i	0.220888	−	0.0854641i
$547$	2.32882e6	+	2.32882e6i	0.332788	+	0.332788i	0.853644	−	0.520856i	$-0.174387\pi$
$547$	2.32882e6	+	2.32882e6i	0.332788	+	0.332788i	−0.520856	+	0.853644i	$0.674387\pi$
$548$	−6.45756e6	−	7.09574e6i	−0.918580	−	1.00936i
$549$	−1.85501e6	+	1.85501e6i	−0.262673	+	0.262673i
$550$	2.17641e6	+	962089.i	0.306785	+	0.135615i
$551$			2.12542e7i			2.98240i
$552$	−1.47169e6	−	4.40962e6i	−0.205574	−	0.615961i
$553$			4.56647e6i			0.634991i
$554$	215075.	−	486537.i	0.0297725	−	0.0673506i
$555$	265343.	−	265343.i	0.0365658	−	0.0365658i
$556$	−280585.	+	5.95889e6i	−0.0384926	+	0.817483i
$557$	5.03610e6	+	5.03610e6i	0.687790	+	0.687790i	0.961743	−	0.273953i	$-0.0883313\pi$
$557$	5.03610e6	+	5.03610e6i	0.687790	+	0.687790i	−0.273953	+	0.961743i	$0.588331\pi$
$558$	−964012.	−	2.49155e6i	−0.131068	−	0.338754i
$559$	−3.06587e6			−0.414977
$560$	3.71340e6	−	3.07289e6i	0.500382	−	0.414073i
$561$	−4.60703e6			−0.618037
$562$	4.26688e6	+	1.10280e7i	0.569862	+	1.47285i
$563$	−1.07805e6	−	1.07805e6i	−0.143340	−	0.143340i	0.631795	−	0.775135i	$-0.282318\pi$
$563$	−1.07805e6	−	1.07805e6i	−0.143340	−	0.143340i	−0.775135	+	0.631795i	$0.782318\pi$
$564$	6.18008e6	+	291000.i	0.818081	+	0.0385208i
$565$	862811.	−	862811.i	0.113709	−	0.113709i
$566$	−2.20627e6	+	4.99098e6i	−0.289480	+	0.654854i
$567$		−	715782.i		−	0.0935025i
$568$	3.38712e6	+	1.69199e6i	0.440515	+	0.220053i
$569$			1.47166e7i			1.90558i	0.303626	+	0.952791i	$0.401803\pi$
$569$			1.47166e7i			1.90558i	−0.303626	+	0.952791i	$0.598197\pi$
$570$	−3.12775e6	−	1.38263e6i	−0.403223	−	0.178246i
$571$	8.20240e6	−	8.20240e6i	1.05281	−	1.05281i	0.0542867	−	0.998525i	$-0.482712\pi$
$571$	8.20240e6	−	8.20240e6i	1.05281	−	1.05281i	0.998525	−	0.0542867i	$-0.0172885\pi$
$572$	2.66213e6	−	2.42270e6i	0.340204	−	0.309606i
$573$	3.25409e6	+	3.25409e6i	0.414041	+	0.414041i
$574$	9.50203e6	−	3.67645e6i	1.20375	−	0.465746i
$575$	1.73168e6			0.218423
$576$	−4.11576e6	+	3.09159e6i	−0.516884	+	0.388262i
$577$	−3.37411e6			−0.421910			−0.210955	−	0.977496i	$-0.567657\pi$
$577$	−3.37411e6			−0.421910			−0.210955	+	0.977496i	$0.567657\pi$
$578$	4.61341e6	−	1.78498e6i	0.574384	−	0.222236i
$579$	−1.69228e6	−	1.69228e6i	−0.209785	−	0.209785i
$580$	4.82021e6	−	4.38668e6i	0.594971	−	0.541460i
$581$	1.52193e7	−	1.52193e7i	1.87048	−	1.87048i
$582$	2.37017e6	+	1.04774e6i	0.290049	+	0.128217i
$583$		−	1.13806e7i		−	1.38674i
$584$	−1.69782e6	−	848124.i	−0.205996	−	0.102903i
$585$		−	656355.i		−	0.0792957i
$586$	1.10480e6	−	2.49925e6i	0.132904	−	0.300653i
$587$	−5.42676e6	+	5.42676e6i	−0.650048	+	0.650048i	−0.953004	−	0.302957i	$-0.902026\pi$
$587$	−5.42676e6	+	5.42676e6i	−0.650048	+	0.650048i	0.302957	+	0.953004i	$0.402026\pi$
$588$	−5.52314e6	−	260066.i	−0.658783	−	0.0310199i
$589$	−5.54597e6	−	5.54597e6i	−0.658702	−	0.658702i
$590$	2.02974e6	+	5.24600e6i	0.240055	+	0.620438i
$591$	−6.37872e6			−0.751215
$592$	−1.05722e6	−	1.27759e6i	−0.123983	−	0.149826i
$593$	2.28164e6			0.266447			0.133224	−	0.991086i	$-0.457467\pi$
$593$	2.28164e6			0.266447			0.133224	+	0.991086i	$0.457467\pi$
$594$	5.09469e6	+	1.31676e7i	0.592450	+	1.53123i
$595$	−2.45802e6	−	2.45802e6i	−0.284638	−	0.284638i
$596$	335158.	−	7.11788e6i	0.0386486	−	0.820796i
$597$	−1.25616e6	+	1.25616e6i	−0.144247	+	0.144247i
$598$	1.05908e6	−	2.39581e6i	0.121108	−	0.273968i
$599$			6.49203e6i			0.739288i	0.929173	+	0.369644i	$0.120520\pi$
$599$			6.49203e6i			0.739288i	−0.929173	+	0.369644i	$0.879480\pi$
$600$	331976.	+	994699.i	0.0376469	+	0.112801i
$601$		−	6.88707e6i		−	0.777765i	−0.921287	−	0.388883i	$-0.872861\pi$
$601$		−	6.88707e6i		−	0.777765i	0.921287	−	0.388883i	$-0.127139\pi$
$602$	1.78700e7	+	7.89950e6i	2.00972	+	0.888399i
$603$	−1.30192e6	+	1.30192e6i	−0.145811	+	0.145811i
$604$	4.50679e6	+	4.95219e6i	0.502661	+	0.552338i
$605$	−5.16082e6	−	5.16082e6i	−0.573232	−	0.573232i
$606$	9.40963e6	−	3.64070e6i	1.04086	−	0.402720i
$607$	3.80516e6			0.419180			0.209590	−	0.977789i	$-0.432787\pi$
$607$	3.80516e6			0.419180			0.209590	+	0.977789i	$0.432787\pi$
$608$	−7.38183e6	+	1.31868e7i	−0.809851	+	1.44670i
$609$	−1.42171e7			−1.55335
$610$	2.20259e6	−	852208.i	0.239667	−	0.0927302i
$611$	2.46512e6	+	2.46512e6i	0.267138	+	0.267138i
$612$	2.49871e6	+	2.74565e6i	0.269673	+	0.296324i
$613$	3.28114e6	−	3.28114e6i	0.352675	−	0.352675i	−0.508429	−	0.861104i	$-0.669774\pi$
$613$	3.28114e6	−	3.28114e6i	0.352675	−	0.352675i	0.861104	+	0.508429i	$0.169774\pi$
$614$	6.89371e6	+	3.04738e6i	0.737959	+	0.326216i
$615$			2.21661e6i			0.236321i
$616$	−2.17591e7	+	7.26199e6i	−2.31041	+	0.771088i
$617$		−	8.55203e6i		−	0.904391i	−0.891919	−	0.452196i	$-0.850641\pi$
$617$		−	8.55203e6i		−	0.904391i	0.891919	−	0.452196i	$-0.149359\pi$
$618$	−3.28085e6	+	7.42186e6i	−0.345554	+	0.781703i
$619$	4.94184e6	−	4.94184e6i	0.518396	−	0.518396i	−0.398690	−	0.917086i	$-0.630535\pi$
$619$	4.94184e6	−	4.94184e6i	0.518396	−	0.518396i	0.917086	+	0.398690i	$0.130535\pi$
$620$	−113121.	+	2.40240e6i	−0.0118186	+	0.250996i
$621$	7.26527e6	+	7.26527e6i	0.756002	+	0.756002i
$622$	−383998.	−	992468.i	−0.0397972	−	0.102859i
$623$	−1.03335e7			−1.06667
$624$	1.57922e6	+	149051.i	0.162360	+	0.0153240i
$625$	−390625.			−0.0400000
$626$	−1.19549e6	−	3.08983e6i	−0.121930	−	0.315137i
$627$	1.15082e7	+	1.15082e7i	1.16906	+	1.16906i
$628$	1.00894e7	+	475077.i	1.02086	+	0.0480690i
$629$	−845678.	+	845678.i	−0.0852272	+	0.0852272i
$630$	−1.69116e6	+	3.82570e6i	−0.169759	+	0.384025i
$631$			1.29565e7i			1.29543i	0.761883	+	0.647714i	$0.224275\pi$
$631$			1.29565e7i			1.29543i	−0.761883	+	0.647714i	$0.775725\pi$
$632$	−1.96198e6	+	3.92760e6i	−0.195390	+	0.391142i
$633$		−	1.75437e6i		−	0.174025i
$634$	9.70181e6	+	4.28871e6i	0.958583	+	0.423744i
$635$	−1.08654e6	+	1.08654e6i	−0.106933	+	0.106933i
$636$	3.70917e6	−	3.37557e6i	0.363608	−	0.330906i
$637$	−2.20308e6	−	2.20308e6i	−0.215120	−	0.215120i
$638$	−2.89279e7	+	1.11925e7i	−2.81361	+	1.08862i
$639$	−3.28573e6			−0.318332
$640$	4.51415e6	−	1.04752e6i	0.435638	−	0.101091i
$641$	−1.14049e7			−1.09634			−0.548170	−	0.836367i	$-0.684675\pi$
$641$	−1.14049e7			−1.09634			−0.548170	+	0.836367i	$0.684675\pi$
$642$	−6.70471e6	+	2.59413e6i	−0.642011	+	0.248402i
$643$	3.99894e6	+	3.99894e6i	0.381432	+	0.381432i	0.871618	−	0.490186i	$-0.163071\pi$
$643$	3.99894e6	+	3.99894e6i	0.381432	+	0.381432i	−0.490186	+	0.871618i	$0.663071\pi$
$644$	−1.23461e7	+	1.12357e7i	−1.17304	+	1.06754i
$645$	−3.00573e6	+	3.00573e6i	−0.284480	+	0.284480i
$646$	9.96850e6	+	4.40660e6i	0.939829	+	0.415453i
$647$		−	7.77701e6i		−	0.730386i	−0.930932	−	0.365193i	$-0.881003\pi$
$647$		−	7.77701e6i		−	0.730386i	0.930932	−	0.365193i	$-0.118997\pi$
$648$	307536.	−	615641.i	0.0287712	−	0.0575957i
$649$		−	2.67701e7i		−	2.49482i
$650$	−238901.	+	540436.i	−0.0221786	+	0.0501719i
$651$	3.70974e6	−	3.70974e6i	0.343077	−	0.343077i
$652$	−7.98727e6	−	376094.i	−0.735833	−	0.0346480i
$653$	4.22723e6	+	4.22723e6i	0.387948	+	0.387948i	0.873955	−	0.486007i	$-0.161547\pi$
$653$	4.22723e6	+	4.22723e6i	0.387948	+	0.387948i	−0.486007	+	0.873955i	$0.661547\pi$
$654$	265222.	+	685483.i	0.0242474	+	0.0626689i
$655$	1.24605e6			0.113483
$656$	9.75225e6	+	920444.i	0.884800	+	0.0835098i
$657$	1.64700e6			0.148860
$658$	−8.01685e6	−	2.07201e7i	−0.721837	−	1.86564i
$659$	−1.35510e7	−	1.35510e7i	−1.21551	−	1.21551i	−0.969188	−	0.246321i	$-0.920778\pi$
$659$	−1.35510e7	−	1.35510e7i	−1.21551	−	1.21551i	−0.246321	−	0.969188i	$-0.579222\pi$
$660$	234732.	−	4.98509e6i	0.0209755	−	0.445465i
$661$	−9.65407e6	+	9.65407e6i	−0.859423	+	0.859423i	−0.991270	−	0.131847i	$-0.957909\pi$
$661$	−9.65407e6	+	9.65407e6i	−0.859423	+	0.859423i	0.131847	+	0.991270i	$0.457909\pi$
$662$	6.83287e6	−	1.54572e7i	0.605980	−	1.37083i
$663$		−	1.14400e6i		−	0.101074i
$664$	1.96290e7	−	6.55108e6i	1.72774	−	0.576624i
$665$			1.22800e7i			1.07683i
$666$	1.31623e6	+	581841.i	0.114986	+	0.0508299i
$667$	−1.59611e7	+	1.59611e7i	−1.38915	+	1.38915i
$668$	−4.96274e6	−	5.45319e6i	−0.430309	−	0.472835i
$669$	553940.	+	553940.i	0.0478517	+	0.0478517i
$670$	1.54586e6	−	598111.i	0.133040	−	0.0514748i
$671$	−1.12397e7			−0.963717
$672$	−8.82073e6	−	4.93777e6i	−0.753497	−	0.421801i
$673$	1.70638e7			1.45224			0.726120	−	0.687568i	$-0.241322\pi$
$673$	1.70638e7			1.45224			0.726120	+	0.687568i	$0.241322\pi$
$674$	1.92120e7	−	7.43337e6i	1.62901	−	0.630284i
$675$	−1.63886e6	−	1.63886e6i	−0.138447	−	0.138447i
$676$	−7.39535e6	−	8.12621e6i	−0.622432	−	0.683945i
$677$	2.10965e6	−	2.10965e6i	0.176904	−	0.176904i	−0.613101	−	0.790005i	$-0.710078\pi$
$677$	2.10965e6	−	2.10965e6i	0.176904	−	0.176904i	0.790005	+	0.613101i	$0.210078\pi$
$678$	−2.34060e6	−	1.03467e6i	−0.195548	−	0.0864422i
$679$		−	9.30564e6i		−	0.774590i
$680$	−1.05805e6	−	3.17022e6i	−0.0877470	−	0.262916i
$681$			8.07400e6i			0.667146i
$682$	4.62776e6	−	1.04688e7i	0.380987	−	0.861860i
$683$	−842946.	+	842946.i	−0.0691430	+	0.0691430i	−0.740833	−	0.671690i	$-0.765569\pi$
$683$	−842946.	+	842946.i	−0.0691430	+	0.0691430i	0.671690	+	0.740833i	$0.265569\pi$
$684$	616844.	−	1.31002e7i	0.0504121	−	1.07062i
$685$	−5.30012e6	−	5.30012e6i	−0.431578	−	0.431578i
$686$	705315.	+	1.82293e6i	0.0572233	+	0.147897i
$687$	705425.			0.0570241
$688$	1.19759e7	+	1.44722e7i	0.964581	+	1.16564i
$689$	2.82597e6			0.226788
$690$	−1.31052e6	−	3.38712e6i	−0.104790	−	0.270837i
$691$	1.59221e7	+	1.59221e7i	1.26854	+	1.26854i	0.946842	+	0.321700i	$0.104254\pi$
$691$	1.59221e7	+	1.59221e7i	1.26854	+	1.26854i	0.321700	+	0.946842i	$0.395746\pi$
$692$	−1.69978e7	−	800370.i	−1.34936	−	0.0635368i
$693$	1.40762e7	−	1.40762e7i	1.11340	−	1.11340i
$694$	2.15629e6	−	4.87791e6i	0.169945	−	0.384446i
$695$			4.66054e6i			0.365995i
$696$	−1.22281e7	−	6.10838e6i	−0.956831	−	0.477973i
$697$		−	7.06460e6i		−	0.550815i
$698$	4.58531e6	+	2.02695e6i	0.356230	+	0.157472i
$699$	−693860.	+	693860.i	−0.0537129	+	0.0537129i
$700$	2.78497e6	−	2.53449e6i	0.214820	−	0.195499i
$701$	−1.68894e7	−	1.68894e7i	−1.29813	−	1.29813i	−0.929624	−	0.368509i	$-0.879868\pi$
$701$	−1.68894e7	−	1.68894e7i	−1.29813	−	1.29813i	−0.368509	−	0.929624i	$-0.620132\pi$
$702$	−3.26970e6	+	1.26509e6i	−0.250418	+	0.0968898i
$703$	4.22493e6			0.322427
$704$	−2.18350e7	−	3.10278e6i	−1.66044	−	0.235950i
$705$	4.83354e6			0.366262
$706$	1.20157e6	−	464901.i	0.0907269	−	0.0351033i
$707$	−2.56188e7	−	2.56188e7i	−1.92757	−	1.92757i
$708$	8.72493e6	−	7.94022e6i	0.654152	−	0.595319i
$709$	−1.49066e7	+	1.49066e7i	−1.11369	+	1.11369i	−0.121038	+	0.992648i	$0.538622\pi$
$709$	−1.49066e7	+	1.49066e7i	−1.11369	+	1.11369i	−0.992648	+	0.121038i	$0.961378\pi$
$710$	2.70544e6	+	1.19594e6i	0.201415	+	0.0890359i
$711$		−	3.81003e6i		−	0.282654i
$712$	−8.88784e6	−	4.43981e6i	−0.657047	−	0.328219i
$713$		−	8.32962e6i		−	0.613622i
$714$	−2.94761e6	+	6.66801e6i	−0.216384	+	0.489498i
$715$	1.98846e6	−	1.98846e6i	0.145463	−	0.145463i
$716$	745666.	+	35111.0i	0.0543578	+	0.00255953i
$717$	8.83990e6	+	8.83990e6i	0.642169	+	0.642169i
$718$	1.74604e6	+	4.51275e6i	0.126399	+	0.326686i
$719$	2.09230e7			1.50939			0.754697	−	0.656074i	$-0.227784\pi$
$719$	2.09230e7			1.50939			0.754697	+	0.656074i	$0.227784\pi$
$720$	−3.09827e6	+	2.56387e6i	−0.222735	+	0.184316i
$721$	2.91394e7			2.08758
$722$	−8.83905e6	−	2.28451e7i	−0.631048	−	1.63099i
$723$	−3.84139e6	−	3.84139e6i	−0.273302	−	0.273302i
$724$	−137838.	+	2.92732e6i	−0.00977288	+	0.207551i
$725$	3.60043e6	−	3.60043e6i	0.254395	−	0.254395i
$726$	−6.18876e6	+	1.40001e7i	−0.435775	+	0.985799i
$727$		−	1.67529e6i		−	0.117558i	−0.998271	−	0.0587791i	$-0.981279\pi$
$727$		−	1.67529e6i		−	0.117558i	0.998271	−	0.0587791i	$-0.0187207\pi$
$728$	−1.80326e6	−	5.40311e6i	−0.126104	−	0.377846i
$729$		−	7.75504e6i		−	0.540462i
$730$	−1.35612e6	−	599476.i	−0.0941869	−	0.0416355i
$731$	9.57961e6	−	9.57961e6i	0.663063	−	0.663063i
$732$	−3.33378e6	−	3.66325e6i	−0.229964	−	0.252691i
$733$	9.15341e6	+	9.15341e6i	0.629249	+	0.629249i	0.947879	−	0.318630i	$-0.103223\pi$
$733$	9.15341e6	+	9.15341e6i	0.629249	+	0.629249i	−0.318630	+	0.947879i	$0.603223\pi$
$734$	−3.57449e6	+	1.38301e6i	−0.244891	+	0.0947514i
$735$	−4.31973e6			−0.294943
$736$	−1.54462e7	+	4.35928e6i	−1.05106	+	0.296634i
$737$	−7.88845e6			−0.534962
$738$	−7.92801e6	+	3.06744e6i	−0.535826	+	0.207317i
$739$	1.40631e7	+	1.40631e7i	0.947264	+	0.947264i	0.998677	−	0.0514130i	$-0.0163725\pi$
$739$	1.40631e7	+	1.40631e7i	0.947264	+	0.947264i	−0.0514130	+	0.998677i	$0.516372\pi$
$740$	−871988.	−	958164.i	−0.0585371	−	0.0643221i
$741$	−2.85765e6	+	2.85765e6i	−0.191189	+	0.191189i
$742$	−1.64718e7	−	7.28138e6i	−1.09832	−	0.485517i
$743$			7.51352e6i			0.499312i	0.968335	+	0.249656i	$0.0803175\pi$
$743$			7.51352e6i			0.499312i	−0.968335	+	0.249656i	$0.919683\pi$
$744$	4.78463e6	−	1.59685e6i	0.316895	−	0.105762i
$745$		−	5.56701e6i		−	0.367478i
$746$	−51890.5	+	117385.i	−0.00341382	+	0.00772267i
$747$	−1.26982e7	+	1.26982e7i	−0.832607	+	0.832607i
$748$	−748117.	+	1.58881e7i	−0.0488895	+	1.03829i
$749$	1.82543e7	+	1.82543e7i	1.18895	+	1.18895i
$750$	295620.	+	764050.i	0.0191903	+	0.0495985i
$751$	2.28474e7			1.47821			0.739106	−	0.673589i	$-0.235248\pi$
$751$	2.28474e7			1.47821			0.739106	+	0.673589i	$0.235248\pi$
$752$	2.00712e6	−	2.12657e7i	0.129428	−	1.37131i
$753$	−9.29917e6			−0.597663
$754$	−2.77928e6	−	7.18322e6i	−0.178034	−	0.460141i
$755$	3.69901e6	+	3.69901e6i	0.236166	+	0.236166i
$756$	2.23178e7	+	1.05087e6i	1.42019	+	0.0668720i
$757$	3.31030e6	−	3.31030e6i	0.209956	−	0.209956i	−0.594293	−	0.804249i	$-0.702568\pi$
$757$	3.31030e6	−	3.31030e6i	0.209956	−	0.209956i	0.804249	+	0.594293i	$0.202568\pi$
$758$	−6.85988e6	+	1.55182e7i	−0.433654	+	0.981001i
$759$			1.72844e7i			1.08905i
$760$	−5.27612e6	+	1.05620e7i	−0.331345	+	0.663304i
$761$		−	6.71250e6i		−	0.420167i	−0.977683	−	0.210084i	$-0.932626\pi$
$761$		−	6.71250e6i		−	0.420167i	0.977683	−	0.210084i	$-0.0673737\pi$
$762$	2.94753e6	+	1.30296e6i	0.183895	+	0.0812913i
$763$	1.86631e6	−	1.86631e6i	0.116057	−	0.116057i
$764$	1.17507e7	−	1.06938e7i	0.728331	−	0.662826i
$765$	2.05085e6	+	2.05085e6i	0.126701	+	0.126701i
$766$	2.17389e7	−	8.41105e6i	1.33865	−	0.517939i
$767$	6.64743e6			0.408005
$768$	−5.46517e6	−	8.03678e6i	−0.334349	−	0.491676i
$769$	1.46852e6			0.0895494			0.0447747	−	0.998997i	$-0.485743\pi$
$769$	1.46852e6			0.0895494			0.0447747	+	0.998997i	$0.485743\pi$
$770$	−1.67136e7	+	6.46671e6i	−1.01588	+	0.393058i
$771$	−417200.	−	417200.i	−0.0252760	−	0.0252760i
$772$	−6.11088e6	+	5.56128e6i	−0.369029	+	0.335839i
$773$	−9.89528e6	+	9.89528e6i	−0.595634	+	0.595634i	−0.939148	−	0.343514i	$-0.888383\pi$
$773$	−9.89528e6	+	9.89528e6i	−0.595634	+	0.595634i	0.343514	+	0.939148i	$0.388383\pi$
$774$	−1.49099e7	−	6.59094e6i	−0.894584	−	0.395453i
$775$			1.87895e6i			0.112373i
$776$	3.99817e6	−	8.00374e6i	0.238345	−	0.477132i
$777$			2.82609e6i			0.167932i
$778$	−912346.	+	2.06389e6i	−0.0540394	+	0.122247i
$779$	−1.76470e7	+	1.76470e7i	−1.04191	+	1.04191i
$780$	1.23787e6	+	58287.4i	0.0728517	+	0.00343035i
$781$	−9.95430e6	−	9.95430e6i	−0.583960	−	0.583960i
$782$	4.17677e6	+	1.07951e7i	0.244244	+	0.631265i
$783$	3.02111e7			1.76101
$784$	−1.79376e6	+	1.90052e7i	−0.104225	+	1.10429i
$785$	7.89108e6			0.457048
$786$	−942996.	−	2.43724e6i	−0.0544444	−	0.140715i
$787$	−5.82244e6	−	5.82244e6i	−0.335095	−	0.335095i	0.519423	−	0.854518i	$-0.326147\pi$
$787$	−5.82244e6	−	5.82244e6i	−0.335095	−	0.335095i	−0.854518	+	0.519423i	$0.826147\pi$
$788$	−1.03581e6	+	2.19980e7i	−0.0594246	+	1.26202i
$789$	814476.	−	814476.i	0.0465785	−	0.0465785i
$790$	−1.38678e6	+	3.13714e6i	−0.0790569	+	0.178841i
$791$			9.18954e6i			0.522219i
$792$	1.81547e7	−	6.05904e6i	1.02843	−	0.343234i
$793$		−	2.79099e6i		−	0.157607i
$794$	−1.53225e7	−	6.77334e6i	−0.862537	−	0.381286i
$795$	2.77054e6	−	2.77054e6i	0.155470	−	0.155470i
$796$	4.12807e6	+	4.53603e6i	0.230921	+	0.253743i
$797$	1.89992e7	+	1.89992e7i	1.05947	+	1.05947i	0.998116	+	0.0613557i	$0.0195424\pi$
$797$	1.89992e7	+	1.89992e7i	1.05947	+	1.05947i	0.0613557	+	0.998116i	$0.480458\pi$
$798$	2.40194e7	−	9.29338e6i	1.33522	−	0.516615i
$799$	−1.54050e7			−0.853681
$800$	3.48428e6	−	983346.i	0.192481	−	0.0543227i
$801$	8.62179e6			0.474806
$802$	−2.02693e7	+	7.84244e6i	−1.11276	+	0.430542i
$803$	4.98966e6	+	4.98966e6i	0.273075	+	0.273075i
$804$	−2.33977e6	−	2.57101e6i	−0.127654	−	0.140269i
$805$	−9.22183e6	+	9.22183e6i	−0.501565	+	0.501565i
$806$	2.59956e6	+	1.14914e6i	0.140949	+	0.0623070i
$807$		−	266579.i		−	0.0144093i
$808$	−1.10275e7	−	3.30418e7i	−0.594223	−	1.78047i
$809$		−	6.12178e6i		−	0.328857i	−0.986389	−	0.164428i	$-0.947422\pi$
$809$		−	6.12178e6i		−	0.328857i	0.986389	−	0.164428i	$-0.0525779\pi$
$810$	217374.	−	491738.i	0.0116411	−	0.0263343i
$811$	−7.75891e6	+	7.75891e6i	−0.414237	+	0.414237i	−0.883212	−	0.468975i	$-0.844623\pi$
$811$	−7.75891e6	+	7.75891e6i	−0.414237	+	0.414237i	0.468975	+	0.883212i	$0.344623\pi$
$812$	−2.30866e6	+	4.90299e7i	−0.122877	+	2.60958i
$813$	−3.68292e6	−	3.68292e6i	−0.195418	−	0.195418i
$814$	2.22486e6	+	5.75030e6i	0.117691	+	0.304179i
$815$	−6.24697e6			−0.329439
$816$	−5.40014e6	+	4.46869e6i	−0.283909	+	0.234939i
$817$	−4.78589e7			−2.50846
$818$	2.87343e6	+	7.42658e6i	0.150147	+	0.388066i
$819$	3.49532e6	+	3.49532e6i	0.182086	+	0.182086i
$820$	7.64433e6	+	359947.i	0.397013	+	0.0186941i
$821$	−1.44650e7	+	1.44650e7i	−0.748963	+	0.748963i	−0.974284	−	0.225322i	$-0.927657\pi$
$821$	−1.44650e7	+	1.44650e7i	−0.748963	+	0.748963i	0.225322	+	0.974284i	$0.427657\pi$
$822$	−6.35581e6	+	1.43779e7i	−0.328089	+	0.742194i
$823$		−	2.50801e6i		−	0.129072i	−0.997915	−	0.0645358i	$-0.979443\pi$
$823$		−	2.50801e6i		−	0.129072i	0.997915	−	0.0645358i	$-0.0205567\pi$
$824$	2.50627e7	+	1.25197e7i	1.28591	+	0.642358i
$825$		−	3.89892e6i		−	0.199439i
$826$	−3.87459e7	−	1.71277e7i	−1.97595	−	0.873473i
$827$	−1.45690e6	+	1.45690e6i	−0.0740740	+	0.0740740i	−0.743173	−	0.669099i	$-0.766680\pi$
$827$	−1.45690e6	+	1.45690e6i	−0.0740740	+	0.0740740i	0.669099	+	0.743173i	$0.266680\pi$
$828$	1.03009e7	−	9.37449e6i	0.522157	−	0.475195i
$829$	2.34139e7	+	2.34139e7i	1.18328	+	1.18328i	0.978889	+	0.204393i	$0.0655219\pi$
$829$	2.34139e7	+	2.34139e7i	1.18328	+	1.18328i	0.204393	+	0.978889i	$0.434478\pi$
$830$	1.50774e7	−	5.83365e6i	0.759683	−	0.293931i
$831$	−871602.			−0.0437840
$832$	770467.	−	5.42196e6i	0.0385874	−	0.271549i
$833$	1.37675e7			0.687451
$834$	9.11588e6	−	3.52704e6i	0.453820	−	0.175588i
$835$	−4.07323e6	−	4.07323e6i	−0.202173	−	0.202173i
$836$	4.15564e7	−	3.78189e7i	2.05647	−	1.87151i
$837$	−7.88314e6	+	7.88314e6i	−0.388943	+	0.388943i
$838$	8.00103e6	+	3.53687e6i	0.393582	+	0.173984i
$839$		−	1.27228e7i		−	0.623988i	−0.950084	−	0.311994i	$-0.899003\pi$
$839$		−	1.27228e7i		−	0.623988i	0.950084	−	0.311994i	$-0.100997\pi$
$840$	−7.06501e6	−	3.52923e6i	−0.345474	−	0.172577i
$841$			4.58597e7i			2.23584i
$842$	−807397.	+	1.82647e6i	−0.0392471	+	0.0887837i
$843$	1.37000e7	−	1.37000e7i	0.663974	−	0.663974i
$844$	−6.05023e6	−	284885.i	−0.292358	−	0.0137662i
$845$	−6.06983e6	−	6.06983e6i	−0.292439	−	0.292439i
$846$	6.68886e6	+	1.72878e7i	0.321311	+	0.830450i
$847$	5.49664e7			2.63262
$848$	−1.10389e7	−	1.33398e7i	−0.527150	−	0.637029i
$849$	8.94105e6			0.425715
$850$	−942176.	−	2.43512e6i	−0.0447285	−	0.115604i
$851$	3.17276e6	+	3.17276e6i	0.150180	+	0.150180i
$852$	291788.	−	6.19682e6i	0.0137711	−	0.292462i
$853$	−2.49305e7	+	2.49305e7i	−1.17316	+	1.17316i	−0.191714	+	0.981451i	$0.561404\pi$
$853$	−2.49305e7	+	2.49305e7i	−1.17316	+	1.17316i	−0.981451	+	0.191714i	$0.938596\pi$
$854$	−7.19125e6	+	1.62679e7i	−0.337411	+	0.763283i
$855$		−	1.02458e7i		−	0.479328i
$856$	7.85752e6	+	2.35435e7i	0.366523	+	1.09821i
$857$		−	3.21684e7i		−	1.49616i	−0.663609	−	0.748080i	$-0.730976\pi$
$857$		−	3.21684e7i		−	1.49616i	0.663609	−	0.748080i	$-0.269024\pi$
$858$	−5.39422e6	−	2.38453e6i	−0.250156	−	0.110582i
$859$	6.87332e6	−	6.87332e6i	0.317822	−	0.317822i	−0.530108	−	0.847930i	$-0.677849\pi$
$859$	6.87332e6	−	6.87332e6i	0.317822	−	0.317822i	0.847930	+	0.530108i	$0.177849\pi$
$860$	9.87765e6	+	1.08538e7i	0.455415	+	0.500422i
$861$	−1.18042e7	−	1.18042e7i	−0.542663	−	0.542663i
$862$	6.35819e6	−	2.46006e6i	0.291451	−	0.112766i
$863$	−2.29465e6			−0.104879			−0.0524397	−	0.998624i	$-0.516700\pi$
$863$	−2.29465e6			−0.104879			−0.0524397	+	0.998624i	$0.516700\pi$
$864$	1.87439e7	+	1.04927e7i	0.854232	+	0.478191i
$865$	−1.32942e7			−0.604119
$866$	8.83205e6	−	3.41723e6i	0.400190	−	0.154839i
$867$	−5.73117e6	−	5.73117e6i	−0.258938	−	0.258938i
$868$	−1.21912e7	−	1.33960e7i	−0.549221	−	0.603499i
$869$	1.15427e7	−	1.15427e7i	0.518511	−	0.518511i
$870$	−9.76708e6	−	4.31756e6i	−0.437488	−	0.193393i
$871$		−	1.95882e6i		−	0.0874882i
$872$	2.40706e6	−	803345.i	0.107200	−	0.0357776i
$873$			7.76415e6i			0.344793i
$874$	1.65324e7	−	3.73991e7i	0.732077	−	1.65609i
$875$	2.08022e6	−	2.08022e6i	0.0918519	−	0.0918519i
$876$	−146261.	+	3.10620e6i	−0.00643973	+	0.136763i
$877$	−2.21503e7	−	2.21503e7i	−0.972479	−	0.972479i	0.0271522	−	0.999631i	$-0.491356\pi$
$877$	−2.21503e7	−	2.21503e7i	−0.972479	−	0.972479i	−0.999631	+	0.0271522i	$0.991356\pi$
$878$	−643832.	−	1.66403e6i	−0.0281862	−	0.0728490i
$879$	−4.47727e6			−0.195452
$880$	−1.71537e7	−	1.61902e6i	−0.746711	−	0.0704766i
$881$	4.56902e7			1.98328			0.991638	−	0.129054i	$-0.0411940\pi$
$881$	4.56902e7			1.98328			0.991638	+	0.129054i	$0.0411940\pi$
$882$	−5.97783e6	−	1.54501e7i	−0.258745	−	0.668744i
$883$	−7.48521e6	−	7.48521e6i	−0.323074	−	0.323074i	0.526871	−	0.849945i	$-0.323365\pi$
$883$	−7.48521e6	−	7.48521e6i	−0.323074	−	0.323074i	−0.849945	+	0.526871i	$0.823365\pi$
$884$	−3.94524e6	−	185769.i	−0.169802	−	0.00799543i
$885$	6.51704e6	−	6.51704e6i	0.279700	−	0.279700i
$886$	−1.26192e7	+	2.85467e7i	−0.540065	+	1.22172i
$887$		−	3.52196e7i		−	1.50306i	−0.659701	−	0.751528i	$-0.729317\pi$
$887$		−	3.52196e7i		−	1.50306i	0.659701	−	0.751528i	$-0.270683\pi$
$888$	−1.21423e6	+	2.43071e6i	−0.0516735	+	0.103443i
$889$		−	1.15725e7i		−	0.491101i
$890$	−7.09909e6	−	3.13817e6i	−0.300419	−	0.132801i
$891$	−1.80929e6	+	1.80929e6i	−0.0763507	+	0.0763507i
$892$	2.00030e6	−	1.82039e6i	0.0841749	−	0.0766043i
$893$	3.84811e7	+	3.84811e7i	1.61480	+	1.61480i
$894$	−1.08889e7	+	4.21304e6i	−0.455659	+	0.176300i
$895$	583197.			0.0243365
$896$	−1.84610e7	+	2.96178e7i	−0.768220	+	1.23249i
$897$	−4.29196e6			−0.178104
$898$	2.83417e7	−	1.09658e7i	1.17283	−	0.453782i
$899$	−1.73185e7	−	1.73185e7i	−0.714678	−	0.714678i
$900$	−2.32364e6	+	2.11465e6i	−0.0956229	+	0.0870227i
$901$	−8.83004e6	+	8.83004e6i	−0.362369	+	0.362369i
$902$	−3.33113e7	−	1.47254e7i	−1.36325	−	0.602628i
$903$		−	3.20132e7i		−	1.30650i
$904$	−3.94829e6	+	7.90389e6i	−0.160690	+	0.321677i
$905$			2.28950e6i			0.0929223i
$906$	4.43578e6	−	1.00345e7i	0.179535	−	0.406140i
$907$	−9.49461e6	+	9.49461e6i	−0.383230	+	0.383230i	−0.872264	−	0.489035i	$-0.837349\pi$
$907$	−9.49461e6	+	9.49461e6i	−0.383230	+	0.383230i	0.489035	+	0.872264i	$0.337349\pi$
$908$	2.78444e7	+	1.31110e6i	1.12079	+	0.0527743i
$909$	2.13750e7	+	2.13750e7i	0.858019	+	0.858019i
$910$	−1.60578e6	−	4.15024e6i	−0.0642810	−	0.166138i
$911$	−1.63769e7			−0.653786			−0.326893	−	0.945061i	$-0.606002\pi$
$911$	−1.63769e7			−0.653786			−0.326893	+	0.945061i	$0.606002\pi$
$912$	2.46519e7	+	2.32671e6i	0.981438	+	0.0926308i
$913$	−7.69396e7			−3.05473
$914$	5.65584e6	+	1.46179e7i	0.223940	+	0.578788i
$915$	−2.73625e6	−	2.73625e6i	−0.108044	−	0.108044i
$916$	114551.	−	2.43277e6i	0.00451087	−	0.0957991i
$917$	−6.63566e6	+	6.63566e6i	−0.260592	+	0.260592i
$918$	6.26362e6	−	1.41694e7i	0.245312	−	0.554939i
$919$		−	2.54182e7i		−	0.992786i	−0.868098	−	0.496393i	$-0.834658\pi$
$919$		−	2.54182e7i		−	0.992786i	0.868098	−	0.496393i	$-0.165342\pi$
$920$	−1.18938e7	+	3.96950e6i	−0.463289	+	0.154620i
$921$		−	1.23497e7i		−	0.479741i
$922$	3.87915e7	+	1.71479e7i	1.50283	+	0.664328i
$923$	2.47180e6	−	2.47180e6i	0.0955013	−	0.0955013i
$924$	2.52973e7	+	2.77974e7i	0.974754	+	1.07109i
$925$	−715695.	−	715695.i	−0.0275026	−	0.0275026i
$926$	−3.50868e7	+	1.35755e7i	−1.34467	+	0.520270i
$927$	−2.43124e7			−0.929242
$928$	−2.30514e7	+	4.11785e7i	−0.878672	+	1.56964i
$929$	9.02959e6			0.343264			0.171632	−	0.985161i	$-0.445096\pi$
$929$	9.02959e6			0.343264			0.171632	+	0.985161i	$0.445096\pi$
$930$	3.67517e6	−	1.42197e6i	0.139338	−	0.0539117i
$931$	−3.43905e7	−	3.43905e7i	−1.30036	−	1.30036i
$932$	2.28021e6	+	2.50556e6i	0.0859875	+	0.0944853i
$933$	−1.23293e6	+	1.23293e6i	−0.0463697	+	0.0463697i
$934$	−2.68190e7	−	1.18554e7i	−1.00595	−	0.444681i
$935$			1.24263e7i			0.464850i
$936$	1.50455e6	+	4.50808e6i	0.0561328	+	0.168191i
$937$			3.55819e7i			1.32398i	0.749514	+	0.661989i	$0.230287\pi$
$937$			3.55819e7i			1.32398i	−0.749514	+	0.661989i	$0.769713\pi$
$938$	−5.04708e6	+	1.14174e7i	−0.187298	+	0.423701i
$939$	−3.83846e6	+	3.83846e6i	−0.142067	+	0.142067i
$940$	784898.	−	1.66692e7i	0.0289730	−	0.615312i
$941$	−2.27733e7	−	2.27733e7i	−0.838402	−	0.838402i	0.150246	−	0.988649i	$-0.451993\pi$
$941$	−2.27733e7	−	2.27733e7i	−0.838402	−	0.838402i	−0.988649	+	0.150246i	$0.951993\pi$
$942$	−5.97187e6	−	1.54347e7i	−0.219272	−	0.566723i
$943$	−2.65045e7			−0.970600
$944$	−2.59663e7	−	3.13787e7i	−0.948374	−	1.14605i
$945$	1.74551e7			0.635831
$946$	−2.52026e7	−	6.51378e7i	−0.915626	−	2.36649i
$947$	−5.65143e6	−	5.65143e6i	−0.204778	−	0.204778i	0.597265	−	0.802044i	$-0.296254\pi$
$947$	−5.65143e6	−	5.65143e6i	−0.204778	−	0.204778i	−0.802044	+	0.597265i	$0.796254\pi$
$948$	7.18564e6	+	338348.i	0.259684	+	0.0122277i
$949$	−1.23901e6	+	1.23901e6i	−0.0446589	+	0.0446589i
$950$	−3.72929e6	+	8.43632e6i	−0.134066	+	0.303280i
$951$		−	1.73802e7i		−	0.623167i
$952$	2.25170e7	+	1.12481e7i	0.805227	+	0.402241i
$953$		−	5.34530e7i		−	1.90651i	−0.302162	−	0.953257i	$-0.597708\pi$
$953$		−	5.34530e7i		−	1.90651i	0.302162	−	0.953257i	$-0.402292\pi$
$954$	1.37432e7	+	6.07522e6i	0.488897	+	0.216118i
$955$	8.77709e6	−	8.77709e6i	0.311417	−	0.311417i
$956$	3.19212e7	−	2.90503e7i	1.12963	−	1.02803i
$957$	3.59367e7	+	3.59367e7i	1.26841	+	1.26841i
$958$	3.30130e7	−	1.27731e7i	1.16217	−	0.449659i
$959$	5.64500e7			1.98206
$960$	−4.56026e6	−	6.07096e6i	−0.159702	−	0.212608i
$961$	−1.95912e7			−0.684308
$962$	−1.42789e6	+	552466.i	−0.0497457	+	0.0192472i
$963$	−1.52305e7	−	1.52305e7i	−0.529235	−	0.529235i
$964$	−1.38714e7	+	1.26238e7i	−0.480760	+	0.437521i
$965$	−4.56449e6	+	4.56449e6i	−0.157788	+	0.157788i
$966$	2.50166e7	+	1.10586e7i	0.862552	+	0.381293i
$967$		−	1.41593e7i		−	0.486940i	−0.969908	−	0.243470i	$-0.921714\pi$
$967$		−	1.41593e7i		−	0.486940i	0.969908	−	0.243470i	$-0.0782858\pi$
$968$	4.72764e7	+	2.36163e7i	1.62165	+	0.810072i
$969$		−	1.78580e7i		−	0.610975i
$970$	2.82601e6	−	6.39292e6i	0.0964370	−	0.218157i
$971$	3.08632e7	−	3.08632e7i	1.05049	−	1.05049i	0.0518352	−	0.998656i	$-0.483493\pi$
$971$	3.08632e7	−	3.08632e7i	1.05049	−	1.05049i	0.998656	−	0.0518352i	$-0.0165070\pi$
$972$	−2.99304e7	−	1.40932e6i	−1.01612	−	0.0478459i
$973$	−2.48190e7	−	2.48190e7i	−0.840432	−	0.840432i
$974$	−5.88859e6	−	1.52195e7i	−0.198891	−	0.514046i
$975$	968160.			0.0326164
$976$	−1.31747e7	+	1.09022e7i	−0.442705	+	0.366345i
$977$	4.45007e7			1.49153			0.745763	−	0.666211i	$-0.232085\pi$
$977$	4.45007e7			1.49153			0.745763	+	0.666211i	$0.232085\pi$
$978$	4.72763e6	+	1.22189e7i	0.158051	+	0.408492i
$979$	2.61202e7	+	2.61202e7i	0.871002	+	0.871002i
$980$	−701463.	+	1.48973e7i	−0.0233313	+	0.495497i
$981$	−1.55715e6	+	1.55715e6i	−0.0516605	+	0.0516605i
$982$	−1.42056e7	+	3.21356e7i	−0.470091	+	1.06343i
$983$			5.78980e7i			1.91108i	0.294856	+	0.955542i	$0.404728\pi$
$983$			5.78980e7i			1.91108i	−0.294856	+	0.955542i	$0.595272\pi$
$984$	−5.08110e6	−	1.52245e7i	−0.167290	−	0.501250i
$985$			1.72050e7i			0.565019i
$986$	3.11288e7	+	1.37606e7i	1.01969	+	0.450758i
$987$	−2.57403e7	+	2.57403e7i	−0.841047	+	0.841047i
$988$	9.39099e6	+	1.03191e7i	0.306069	+	0.336317i
$989$	−3.59401e7	−	3.59401e7i	−1.16839	−	1.16839i
$990$	1.39450e7	−	5.39549e6i	0.452200	−	0.174962i
$991$	−4.73284e7			−1.53087			−0.765434	−	0.643514i	$-0.777476\pi$
$991$	−4.73284e7			−1.53087			−0.765434	+	0.643514i	$0.777476\pi$
$992$	−4.73001e6	−	1.67598e7i	−0.152610	−	0.540742i
$993$	−2.76906e7			−0.891168
$994$	−2.07762e7	+	8.03857e6i	−0.666961	+	0.258055i
$995$	3.38816e6	+	3.38816e6i	0.108494	+	0.108494i
$996$	−2.28209e7	−	2.50762e7i	−0.728926	−	0.800964i
$997$	−514849.	+	514849.i	−0.0164037	+	0.0164037i	−0.715261	−	0.698857i	$-0.753692\pi$
$997$	−514849.	+	514849.i	−0.0164037	+	0.0164037i	0.698857	+	0.715261i	$0.253692\pi$
$998$	−2.85567e7	−	1.26235e7i	−0.907572	−	0.401194i
$999$		−	6.00539e6i		−	0.190383i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	80.6.l.a.61.6	yes	80
4.3	odd	2		320.6.l.a.81.14		80
16.5	even	4	inner	80.6.l.a.21.6	✓	80
16.11	odd	4		320.6.l.a.241.14		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.6.l.a.21.6	✓	80	16.5	even	4	inner
80.6.l.a.61.6	yes	80	1.1	even	1	trivial
320.6.l.a.81.14		80	4.3	odd	2
320.6.l.a.241.14		80	16.11	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:	\( N \)	\(=\)	\( 80 = 2^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	80.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-5.27573 + 2.04124i) q^{2} +(6.55397 + 6.55397i) q^{3} +(23.6666 - 21.5381i) q^{4} +(17.6777 - 17.6777i) q^{5} +(-47.9552 - 21.1987i) q^{6} +188.280i q^{7} +(-80.8943 + 161.939i) q^{8} -157.091i q^{9} +O(q^{10})\)	\(q+(-5.27573 + 2.04124i) q^{2} +(6.55397 + 6.55397i) q^{3} +(23.6666 - 21.5381i) q^{4} +(17.6777 - 17.6777i) q^{5} +(-47.9552 - 21.1987i) q^{6} +188.280i q^{7} +(-80.8943 + 161.939i) q^{8} -157.091i q^{9} +(-57.1782 + 129.347i) q^{10} +(475.916 - 475.916i) q^{11} +(296.270 + 13.9504i) q^{12} +(118.177 + 118.177i) q^{13} +(-384.325 - 993.312i) q^{14} +231.718 q^{15} +(96.2203 - 1019.47i) q^{16} -738.511 q^{17} +(320.661 + 828.770i) q^{18} +(1844.77 + 1844.77i) q^{19} +(37.6277 - 799.115i) q^{20} +(-1233.98 + 1233.98i) q^{21} +(-1539.34 + 3482.26i) q^{22} +2770.70i q^{23} +(-1591.52 + 531.162i) q^{24} -625.000i q^{25} +(-864.698 - 382.242i) q^{26} +(2622.18 - 2622.18i) q^{27} +(4055.19 + 4455.95i) q^{28} +(5760.68 + 5760.68i) q^{29} +(-1222.48 + 472.992i) q^{30} -3006.33 q^{31} +(1573.35 + 5574.85i) q^{32} +6238.27 q^{33} +(3896.19 - 1507.48i) q^{34} +(3328.34 + 3328.34i) q^{35} +(-3383.44 - 3717.82i) q^{36} +(1145.11 - 1145.11i) q^{37} +(-13498.1 - 5966.87i) q^{38} +1549.06i q^{39} +(1432.67 + 4292.72i) q^{40} +9566.00i q^{41} +(3991.29 - 9028.99i) q^{42} +(-12971.5 + 12971.5i) q^{43} +(1013.01 - 21513.6i) q^{44} +(-2777.00 - 2777.00i) q^{45} +(-5655.67 - 14617.4i) q^{46} +20859.6 q^{47} +(7312.19 - 6050.94i) q^{48} -18642.2 q^{49} +(1275.78 + 3297.33i) q^{50} +(-4840.18 - 4840.18i) q^{51} +(5342.16 + 251.545i) q^{52} +(11956.5 - 11956.5i) q^{53} +(-8481.42 + 19186.4i) q^{54} -16826.2i q^{55} +(-30489.7 - 15230.7i) q^{56} +24181.1i q^{57} +(-42150.8 - 18632.8i) q^{58} +(28124.9 - 28124.9i) q^{59} +(5483.98 - 4990.76i) q^{60} +(-11808.5 - 11808.5i) q^{61} +(15860.6 - 6136.65i) q^{62} +29577.0 q^{63} +(-19680.2 - 26199.8i) q^{64} +4178.19 q^{65} +(-32911.4 + 12733.8i) q^{66} +(-8287.66 - 8287.66i) q^{67} +(-17478.1 + 15906.1i) q^{68} +(-18159.1 + 18159.1i) q^{69} +(-24353.4 - 10765.5i) q^{70} -20916.1i q^{71} +(25439.1 + 12707.8i) q^{72} +10484.3i q^{73} +(-3703.85 + 8378.75i) q^{74} +(4096.23 - 4096.23i) q^{75} +(83392.2 + 3926.67i) q^{76} +(89605.2 + 89605.2i) q^{77} +(-3162.00 - 8172.40i) q^{78} +24253.7 q^{79} +(-16320.9 - 19722.8i) q^{80} -3801.70 q^{81} +(-19526.5 - 50467.6i) q^{82} +(-80833.3 - 80833.3i) q^{83} +(-2626.58 + 55781.7i) q^{84} +(-13055.2 + 13055.2i) q^{85} +(41956.2 - 94912.3i) q^{86} +75510.6i q^{87} +(38570.2 + 115568. i) q^{88} +54884.0i q^{89} +(20319.3 + 8982.18i) q^{90} +(-22250.3 + 22250.3i) q^{91} +(59675.5 + 65573.1i) q^{92} +(-19703.4 - 19703.4i) q^{93} +(-110050. + 42579.5i) q^{94} +65222.3 q^{95} +(-26225.7 + 46849.1i) q^{96} -49424.6 q^{97} +(98351.2 - 38053.3i) q^{98} +(-74762.1 - 74762.1i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 44 q^{4} - 228 q^{6}+O(q^{10}) \) 80 * q + 44 * q^4 - 228 * q^6	\( 80 q + 44 q^{4} - 228 q^{6} - 100 q^{10} + 1208 q^{11} + 1572 q^{12} - 916 q^{14} - 1800 q^{15} + 2960 q^{16} + 6400 q^{18} + 2360 q^{19} - 3800 q^{20} - 3260 q^{22} - 13880 q^{24} - 880 q^{26} - 7464 q^{27} + 18764 q^{28} - 8144 q^{29} + 22400 q^{32} - 7440 q^{34} + 27948 q^{36} + 21296 q^{37} - 34820 q^{38} - 7260 q^{42} + 32072 q^{43} + 64392 q^{44} + 149268 q^{46} - 88360 q^{47} + 94040 q^{48} - 192080 q^{49} + 2500 q^{50} - 5920 q^{51} - 55016 q^{52} - 49456 q^{53} - 250784 q^{54} - 250352 q^{56} - 115988 q^{58} + 44984 q^{59} + 7700 q^{60} + 48080 q^{61} + 444328 q^{62} + 158760 q^{63} + 218096 q^{64} + 253440 q^{66} + 61160 q^{67} - 119792 q^{68} - 22320 q^{69} - 66200 q^{70} - 629480 q^{72} - 156664 q^{74} + 223232 q^{76} - 14896 q^{77} + 516176 q^{78} + 177680 q^{79} + 48400 q^{80} - 524880 q^{81} + 254476 q^{82} - 329240 q^{83} - 173248 q^{84} + 132400 q^{85} - 765740 q^{86} - 390400 q^{88} + 71100 q^{90} + 364832 q^{91} + 333532 q^{92} - 362352 q^{93} + 537844 q^{94} + 288800 q^{95} + 1151112 q^{96} + 52420 q^{98} + 659000 q^{99}+O(q^{100}) \) 80 * q + 44 * q^4 - 228 * q^6 - 100 * q^10 + 1208 * q^11 + 1572 * q^12 - 916 * q^14 - 1800 * q^15 + 2960 * q^16 + 6400 * q^18 + 2360 * q^19 - 3800 * q^20 - 3260 * q^22 - 13880 * q^24 - 880 * q^26 - 7464 * q^27 + 18764 * q^28 - 8144 * q^29 + 22400 * q^32 - 7440 * q^34 + 27948 * q^36 + 21296 * q^37 - 34820 * q^38 - 7260 * q^42 + 32072 * q^43 + 64392 * q^44 + 149268 * q^46 - 88360 * q^47 + 94040 * q^48 - 192080 * q^49 + 2500 * q^50 - 5920 * q^51 - 55016 * q^52 - 49456 * q^53 - 250784 * q^54 - 250352 * q^56 - 115988 * q^58 + 44984 * q^59 + 7700 * q^60 + 48080 * q^61 + 444328 * q^62 + 158760 * q^63 + 218096 * q^64 + 253440 * q^66 + 61160 * q^67 - 119792 * q^68 - 22320 * q^69 - 66200 * q^70 - 629480 * q^72 - 156664 * q^74 + 223232 * q^76 - 14896 * q^77 + 516176 * q^78 + 177680 * q^79 + 48400 * q^80 - 524880 * q^81 + 254476 * q^82 - 329240 * q^83 - 173248 * q^84 + 132400 * q^85 - 765740 * q^86 - 390400 * q^88 + 71100 * q^90 + 364832 * q^91 + 333532 * q^92 - 362352 * q^93 + 537844 * q^94 + 288800 * q^95 + 1151112 * q^96 + 52420 * q^98 + 659000 * q^99

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