LMFDB - Embedded newform 80.6.l.a.21.2

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			21.2
Character	$\chi$	$=$	80.21
Dual form			80.6.l.a.61.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-5.65514 + 0.139396i) q^{2} +(19.6483 - 19.6483i) q^{3} +(31.9611 - 1.57661i) q^{4} +(-17.6777 - 17.6777i) q^{5} +(-108.375 + 113.853i) q^{6} -152.043i q^{7} +(-180.525 + 13.3712i) q^{8} -529.109i q^{9} +O(q^{10})$	\(q+(-5.65514 + 0.139396i) q^{2} +(19.6483 - 19.6483i) q^{3} +(31.9611 - 1.57661i) q^{4} +(-17.6777 - 17.6777i) q^{5} +(-108.375 + 113.853i) q^{6} -152.043i q^{7} +(-180.525 + 13.3712i) q^{8} -529.109i q^{9} +(102.434 + 97.5054i) q^{10} +(-11.6148 - 11.6148i) q^{11} +(597.003 - 658.959i) q^{12} +(-337.401 + 337.401i) q^{13} +(21.1942 + 859.825i) q^{14} -694.671 q^{15} +(1019.03 - 100.780i) q^{16} +1971.39 q^{17} +(73.7557 + 2992.18i) q^{18} +(-1675.04 + 1675.04i) q^{19} +(-592.869 - 537.128i) q^{20} +(-2987.39 - 2987.39i) q^{21} +(67.3025 + 64.0644i) q^{22} -2713.65i q^{23} +(-3284.28 + 3809.72i) q^{24} +625.000i q^{25} +(1861.01 - 1955.08i) q^{26} +(-5621.55 - 5621.55i) q^{27} +(-239.712 - 4859.47i) q^{28} +(2271.81 - 2271.81i) q^{29} +(3928.46 - 96.8344i) q^{30} -9252.07 q^{31} +(-5748.70 + 711.975i) q^{32} -456.423 q^{33} +(-11148.5 + 274.804i) q^{34} +(-2687.77 + 2687.77i) q^{35} +(-834.197 - 16910.9i) q^{36} +(2728.98 + 2728.98i) q^{37} +(9239.11 - 9706.10i) q^{38} +13258.7i q^{39} +(3427.63 + 2954.89i) q^{40} -9698.90i q^{41} +(17310.5 + 16477.6i) q^{42} +(7983.39 + 7983.39i) q^{43} +(-389.535 - 352.911i) q^{44} +(-9353.41 + 9353.41i) q^{45} +(378.272 + 15346.1i) q^{46} -12393.3 q^{47} +(18042.0 - 22002.3i) q^{48} -6310.14 q^{49} +(-87.1225 - 3534.46i) q^{50} +(38734.4 - 38734.4i) q^{51} +(-10251.8 + 11315.7i) q^{52} +(779.013 + 779.013i) q^{53} +(32574.2 + 31007.0i) q^{54} +410.646i q^{55} +(2033.00 + 27447.6i) q^{56} +65823.4i q^{57} +(-12530.7 + 13164.1i) q^{58} +(-2779.17 - 2779.17i) q^{59} +(-22202.5 + 1095.22i) q^{60} +(16149.2 - 16149.2i) q^{61} +(52321.7 - 1289.70i) q^{62} -80447.4 q^{63} +(32410.4 - 4827.66i) q^{64} +11928.9 q^{65} +(2581.13 - 63.6235i) q^{66} +(27196.6 - 27196.6i) q^{67} +(63007.8 - 3108.10i) q^{68} +(-53318.6 - 53318.6i) q^{69} +(14825.0 - 15574.4i) q^{70} -61737.5i q^{71} +(7074.81 + 95517.3i) q^{72} +18521.1i q^{73} +(-15813.2 - 15052.4i) q^{74} +(12280.2 + 12280.2i) q^{75} +(-50895.4 + 56177.2i) q^{76} +(-1765.96 + 1765.96i) q^{77} +(-1848.21 - 74979.6i) q^{78} +54765.8 q^{79} +(-19795.6 - 16232.5i) q^{80} -92333.9 q^{81} +(1351.99 + 54848.6i) q^{82} +(76036.0 - 76036.0i) q^{83} +(-100190. - 90770.3i) q^{84} +(-34849.5 - 34849.5i) q^{85} +(-46260.0 - 44034.3i) q^{86} -89274.2i q^{87} +(2252.07 + 1941.46i) q^{88} +60590.0i q^{89} +(51591.0 - 54198.7i) q^{90} +(51299.5 + 51299.5i) q^{91} +(-4278.36 - 86731.4i) q^{92} +(-181787. + 181787. i) q^{93} +(70086.0 - 1727.58i) q^{94} +59221.7 q^{95} +(-98962.9 + 126941. i) q^{96} +80405.2 q^{97} +(35684.7 - 879.608i) q^{98} +(-6145.52 + 6145.52i) 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 $\left(\mathbb{Z}/80\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	−5.65514	+	0.139396i	−0.999696	+	0.0246420i
$2$	−5.65514	+	0.139396i	−0.999696	+	0.0246420i
$3$	19.6483	−	19.6483i	1.26044	−	1.26044i	0.309556	−	0.950881i	$-0.399820\pi$
$3$	19.6483	−	19.6483i	1.26044	−	1.26044i	0.950881	−	0.309556i	$-0.100180\pi$
$4$	31.9611	−	1.57661i	0.998786	−	0.0492690i
$5$	−17.6777	−	17.6777i	−0.316228	−	0.316228i
$5$	−17.6777	−	17.6777i	−0.316228	−	0.316228i
$6$	−108.375	+	113.853i	−1.22899	+	1.29111i
$7$		−	152.043i		−	1.17279i	−0.810024	−	0.586397i	$-0.800546\pi$
$7$		−	152.043i		−	1.17279i	0.810024	−	0.586397i	$-0.199454\pi$
$8$	−180.525	+	13.3712i	−0.997268	+	0.0738660i
$9$		−	529.109i		−	2.17740i
$10$	102.434	+	97.5054i	0.323924	+	0.308339i
$11$	−11.6148	−	11.6148i	−0.0289422	−	0.0289422i	0.692488	−	0.721430i	$-0.256515\pi$
$11$	−11.6148	−	11.6148i	−0.0289422	−	0.0289422i	−0.721430	+	0.692488i	$0.756515\pi$
$12$	597.003	−	658.959i	1.19681	−	1.32101i
$13$	−337.401	+	337.401i	−0.553717	+	0.553717i	−0.927511	−	0.373795i	$-0.878056\pi$
$13$	−337.401	+	337.401i	−0.553717	+	0.553717i	0.373795	+	0.927511i	$0.378056\pi$
$14$	21.1942	+	859.825i	0.0289000	+	1.17244i
$15$	−694.671			−0.797170
$16$	1019.03	−	100.780i	0.995145	−	0.0984182i
$17$	1971.39			1.65443			0.827217	−	0.561882i	$-0.189922\pi$
$17$	1971.39			1.65443			0.827217	+	0.561882i	$0.189922\pi$
$18$	73.7557	+	2992.18i	0.0536555	+	2.17674i
$19$	−1675.04	+	1675.04i	−1.06449	+	1.06449i	−0.0667196	+	0.997772i	$0.521253\pi$
$19$	−1675.04	+	1675.04i	−1.06449	+	1.06449i	−0.997772	+	0.0667196i	$0.978747\pi$
$20$	−592.869	−	537.128i	−0.331424	−	0.300264i
$21$	−2987.39	−	2987.39i	−1.47823	−	1.47823i
$22$	67.3025	+	64.0644i	0.0296466	+	0.0282202i
$23$		−	2713.65i		−	1.06963i	−0.844968	−	0.534816i	$-0.820381\pi$
$23$		−	2713.65i		−	1.06963i	0.844968	−	0.534816i	$-0.179619\pi$
$24$	−3284.28	+	3809.72i	−1.16389	+	1.35010i
$25$			625.000i			0.200000i
$26$	1861.01	−	1955.08i	0.539904	−	0.567193i
$27$	−5621.55	−	5621.55i	−1.48404	−	1.48404i
$28$	−239.712	−	4859.47i	−0.0577824	−	1.17137i
$29$	2271.81	−	2271.81i	0.501622	−	0.501622i	−0.410320	−	0.911942i	$-0.634583\pi$
$29$	2271.81	−	2271.81i	0.501622	−	0.501622i	0.911942	+	0.410320i	$0.134583\pi$
$30$	3928.46	−	96.8344i	0.796928	−	0.0196438i
$31$	−9252.07			−1.72916			−0.864579	−	0.502497i	$-0.832415\pi$
$31$	−9252.07			−1.72916			−0.864579	+	0.502497i	$0.832415\pi$
$32$	−5748.70	+	711.975i	−0.992418	+	0.122911i
$33$	−456.423			−0.0729596
$34$	−11148.5	+	274.804i	−1.65393	+	0.0407685i
$35$	−2687.77	+	2687.77i	−0.370870	+	0.370870i
$36$	−834.197	−	16910.9i	−0.107278	−	2.17476i
$37$	2728.98	+	2728.98i	0.327715	+	0.327715i	0.851717	−	0.524002i	$-0.175562\pi$
$37$	2728.98	+	2728.98i	0.327715	+	0.327715i	−0.524002	+	0.851717i	$0.675562\pi$
$38$	9239.11	−	9706.10i	1.03794	−	1.09040i
$39$			13258.7i			1.39585i
$40$	3427.63	+	2954.89i	0.338722	+	0.292005i
$41$		−	9698.90i		−	0.901079i	−0.892757	−	0.450539i	$-0.851232\pi$
$41$		−	9698.90i		−	0.901079i	0.892757	−	0.450539i	$-0.148768\pi$
$42$	17310.5	+	16477.6i	1.51421	+	1.44136i
$43$	7983.39	+	7983.39i	0.658440	+	0.658440i	0.955011	−	0.296571i	$-0.0958432\pi$
$43$	7983.39	+	7983.39i	0.658440	+	0.658440i	−0.296571	+	0.955011i	$0.595843\pi$
$44$	−389.535	−	352.911i	−0.0303330	−	0.0274811i
$45$	−9353.41	+	9353.41i	−0.688555	+	0.688555i
$46$	378.272	+	15346.1i	0.0263578	+	1.06931i
$47$	−12393.3			−0.818359			−0.409179	−	0.912454i	$-0.634185\pi$
$47$	−12393.3			−0.818359			−0.409179	+	0.912454i	$0.634185\pi$
$48$	18042.0	−	22002.3i	1.13027	−	1.37837i
$49$	−6310.14			−0.375447
$50$	−87.1225	−	3534.46i	−0.00492839	−	0.199939i
$51$	38734.4	−	38734.4i	2.08531	−	2.08531i
$52$	−10251.8	+	11315.7i	−0.525763	+	0.580325i
$53$	779.013	+	779.013i	0.0380939	+	0.0380939i	0.725897	−	0.687803i	$-0.241425\pi$
$53$	779.013	+	779.013i	0.0380939	+	0.0380939i	−0.687803	+	0.725897i	$0.741425\pi$
$54$	32574.2	+	31007.0i	1.52016	+	1.44702i
$55$			410.646i			0.0183046i
$56$	2033.00	+	27447.6i	0.0866297	+	1.16959i
$57$			65823.4i			2.68345i
$58$	−12530.7	+	13164.1i	−0.489109	+	0.513831i
$59$	−2779.17	−	2779.17i	−0.103940	−	0.103940i	0.653224	−	0.757165i	$-0.273416\pi$
$59$	−2779.17	−	2779.17i	−0.103940	−	0.103940i	−0.757165	+	0.653224i	$0.773416\pi$
$60$	−22202.5	+	1095.22i	−0.796202	+	0.0392758i
$61$	16149.2	−	16149.2i	0.555682	−	0.555682i	−0.372393	−	0.928075i	$-0.621463\pi$
$61$	16149.2	−	16149.2i	0.555682	−	0.555682i	0.928075	+	0.372393i	$0.121463\pi$
$62$	52321.7	−	1289.70i	1.72863	−	0.0426098i
$63$	−80447.4			−2.55365
$64$	32410.4	−	4827.66i	0.989088	−	0.147328i
$65$	11928.9			0.350201
$66$	2581.13	−	63.6235i	0.0729375	−	0.00179787i
$67$	27196.6	−	27196.6i	0.740164	−	0.740164i	−0.232445	−	0.972609i	$-0.574673\pi$
$67$	27196.6	−	27196.6i	0.740164	−	0.740164i	0.972609	+	0.232445i	$0.0746727\pi$
$68$	63007.8	−	3108.10i	1.65243	−	0.0815123i
$69$	−53318.6	−	53318.6i	−1.34820	−	1.34820i
$70$	14825.0	−	15574.4i	0.361619	−	0.379897i
$71$		−	61737.5i		−	1.45346i	−0.686923	−	0.726730i	$-0.741039\pi$
$71$		−	61737.5i		−	1.45346i	0.686923	−	0.726730i	$-0.258961\pi$
$72$	7074.81	+	95517.3i	0.160836	+	2.17146i
$73$			18521.1i			0.406780i	0.979098	+	0.203390i	$0.0651960\pi$
$73$			18521.1i			0.406780i	−0.979098	+	0.203390i	$0.934804\pi$
$74$	−15813.2	−	15052.4i	−0.335691	−	0.319540i
$75$	12280.2	+	12280.2i	0.252087	+	0.252087i
$76$	−50895.4	+	56177.2i	−1.01075	+	1.11564i
$77$	−1765.96	+	1765.96i	−0.0339432	+	0.0339432i
$78$	−1848.21	−	74979.6i	−0.0343965	−	1.39543i
$79$	54765.8			0.987284			0.493642	−	0.869665i	$-0.335665\pi$
$79$	54765.8			0.987284			0.493642	+	0.869665i	$0.335665\pi$
$80$	−19795.6	−	16232.5i	−0.345815	−	0.283570i
$81$	−92333.9			−1.56368
$82$	1351.99	+	54848.6i	0.0222043	+	0.900805i
$83$	76036.0	−	76036.0i	1.21150	−	1.21150i	0.240969	−	0.970533i	$-0.422535\pi$
$83$	76036.0	−	76036.0i	1.21150	−	1.21150i	0.970533	−	0.240969i	$-0.0774653\pi$
$84$	−100190.	−	90770.3i	−1.54927	−	1.40361i
$85$	−34849.5	−	34849.5i	−0.523178	−	0.523178i
$86$	−46260.0	−	44034.3i	−0.674465	−	0.642015i
$87$		−	89274.2i		−	1.26453i
$88$	2252.07	+	1941.46i	0.0310010	+	0.0267253i
$89$			60590.0i			0.810823i	0.914134	+	0.405412i	$0.132872\pi$
$89$			60590.0i			0.810823i	−0.914134	+	0.405412i	$0.867128\pi$
$90$	51591.0	−	54198.7i	0.671379	−	0.705314i
$91$	51299.5	+	51299.5i	0.649396	+	0.649396i
$92$	−4278.36	−	86731.4i	−0.0526997	−	1.06833i
$93$	−181787.	+	181787.i	−2.17949	+	2.17949i
$94$	70086.0	−	1727.58i	0.818110	−	0.0201660i
$95$	59221.7			0.673243
$96$	−98962.9	+	126941.i	−1.09596	+	1.40580i
$97$	80405.2			0.867670			0.433835	−	0.900992i	$-0.357160\pi$
$97$	80405.2			0.867670			0.433835	+	0.900992i	$0.357160\pi$
$98$	35684.7	−	879.608i	0.375333	−	0.00925175i
$99$	−6145.52	+	6145.52i	−0.0630188	+	0.0630188i
$100$	985.379	+	19975.7i	0.00985379	+	0.199757i
$101$	−19812.4	−	19812.4i	−0.193256	−	0.193256i	0.603845	−	0.797102i	$-0.293634\pi$
$101$	−19812.4	−	19812.4i	−0.193256	−	0.193256i	−0.797102	+	0.603845i	$0.793634\pi$
$102$	−213649.	+	224447.i	−2.03329	+	2.13606i
$103$			130085.i			1.20819i	0.796912	+	0.604095i	$0.206465\pi$
$103$			130085.i			1.20819i	−0.796912	+	0.604095i	$0.793535\pi$
$104$	56397.7	−	65420.6i	0.511303	−	0.593105i
$105$			105620.i			0.934917i
$106$	−4514.02	−	4296.83i	−0.0390210	−	0.0371436i
$107$	141881.	+	141881.i	1.19802	+	1.19802i	0.974759	+	0.223260i	$0.0716700\pi$
$107$	141881.	+	141881.i	1.19802	+	1.19802i	0.223260	+	0.974759i	$0.428330\pi$
$108$	−188534.	−	170808.i	−1.55536	−	1.40912i
$109$	9250.02	−	9250.02i	0.0745721	−	0.0745721i	−0.668837	−	0.743409i	$-0.733208\pi$
$109$	9250.02	−	9250.02i	0.0745721	−	0.0745721i	0.743409	+	0.668837i	$0.233208\pi$
$110$	−57.2425	−	2322.26i	−0.000451062	−	0.0182991i
$111$	107240.			0.826128
$112$	−15323.0	−	154936.i	−0.115424	−	1.16710i
$113$	46485.0			0.342466			0.171233	−	0.985231i	$-0.445225\pi$
$113$	46485.0			0.342466			0.171233	+	0.985231i	$0.445225\pi$
$114$	−9175.52	−	372240.i	−0.0661254	−	2.68263i
$115$	−47971.0	+	47971.0i	−0.338247	+	0.338247i
$116$	69027.8	−	76191.3i	0.476298	−	0.525727i
$117$	178522.	+	178522.i	1.20566	+	1.20566i
$118$	16104.0	+	15329.2i	0.106470	+	0.101348i
$119$		−	299736.i		−	1.94031i
$120$	125405.	−	9288.57i	0.794993	−	0.0588838i
$121$		−	160781.i		−	0.998325i
$122$	−89074.7	+	93577.0i	−0.541820	+	0.569206i
$123$	−190567.	−	190567.i	−1.13575	−	1.13575i
$124$	−295707.	+	14586.9i	−1.72706	+	0.0851938i
$125$	11048.5	−	11048.5i	0.0632456	−	0.0632456i
$126$	454941.	−	11214.1i	2.55287	−	0.0629269i
$127$	−286357.			−1.57543			−0.787714	−	0.616041i	$-0.788736\pi$
$127$	−286357.			−1.57543			−0.787714	+	0.616041i	$0.788736\pi$
$128$	−182612.	+	31819.0i	−0.985157	+	0.171657i
$129$	313719.			1.65984
$130$	−67459.6	+	1662.84i	−0.350095	+	0.00862964i
$131$	117828.	−	117828.i	0.599887	−	0.599887i	−0.340396	−	0.940282i	$-0.610561\pi$
$131$	117828.	−	117828.i	0.599887	−	0.599887i	0.940282	+	0.340396i	$0.110561\pi$
$132$	−14587.8	+	719.599i	−0.0728710	+	0.00359464i
$133$	254679.	+	254679.i	1.24843	+	1.24843i
$134$	−150010.	+	157592.i	−0.721700	+	0.758178i
$135$			198752.i			0.938591i
$136$	−355884.	+	26359.8i	−1.64992	+	0.122207i
$137$		−	82337.9i		−	0.374799i	−0.982284	−	0.187400i	$-0.939994\pi$
$137$		−	82337.9i		−	0.374799i	0.982284	−	0.187400i	$-0.0600059\pi$
$138$	308956.	+	294091.i	1.38102	+	1.31457i
$139$	−214865.	−	214865.i	−0.943255	−	0.943255i	0.0552189	−	0.998474i	$-0.482414\pi$
$139$	−214865.	−	214865.i	−0.943255	−	0.943255i	−0.998474	+	0.0552189i	$0.982414\pi$
$140$	−81666.6	+	90141.7i	−0.352147	+	0.388692i
$141$	−243508.	+	243508.i	−1.03149	+	1.03149i
$142$	8605.96	+	349134.i	0.0358161	+	1.45302i
$143$	7837.71			0.0320515
$144$	−53323.8	−	539177.i	−0.214296	−	2.16683i
$145$	−80320.5			−0.317254
$146$	−2581.77	−	104739.i	−0.0100239	−	0.406657i
$147$	−123983.	+	123983.i	−0.473227	+	0.473227i
$148$	91523.9	+	82918.8i	0.343463	+	0.311171i
$149$	359536.	+	359536.i	1.32671	+	1.32671i	0.908220	+	0.418494i	$0.137442\pi$
$149$	359536.	+	359536.i	1.32671	+	1.32671i	0.418494	+	0.908220i	$0.362558\pi$
$150$	−71157.8	−	67734.2i	−0.258223	−	0.245799i
$151$		−	89139.5i		−	0.318147i	−0.987267	−	0.159073i	$-0.949149\pi$
$151$		−	89139.5i		−	0.318147i	0.987267	−	0.159073i	$-0.0508507\pi$
$152$	279990.	−	324784.i	0.982954	−	1.14021i
$153$		−	1.04308e6i		−	3.60237i
$154$	9740.56	−	10232.9i	0.0330965	−	0.0347694i
$155$	163555.	+	163555.i	0.546808	+	0.546808i
$156$	20903.7	+	423762.i	0.0687721	+	1.39415i
$157$	41880.8	−	41880.8i	0.135602	−	0.135602i	−0.636048	−	0.771650i	$-0.719432\pi$
$157$	41880.8	−	41880.8i	0.135602	−	0.135602i	0.771650	+	0.636048i	$0.219432\pi$
$158$	−309708.	+	7634.14i	−0.986984	+	0.0243286i
$159$	30612.5			0.0960298
$160$	114210.	+	89037.5i	0.352698	+	0.274962i
$161$	−412592.			−1.25446
$162$	522161.	−	12871.0i	1.56321	−	0.0385322i
$163$	119285.	−	119285.i	0.351654	−	0.351654i	−0.509070	−	0.860725i	$-0.670011\pi$
$163$	119285.	−	119285.i	0.351654	−	0.351654i	0.860725	+	0.509070i	$0.170011\pi$
$164$	−15291.3	−	309988.i	−0.0443952	−	0.899984i
$165$	8068.49	+	8068.49i	0.0230719	+	0.0230719i
$166$	−419395.	+	440593.i	−1.18128	+	1.24099i
$167$		−	121470.i		−	0.337036i	−0.985699	−	0.168518i	$-0.946102\pi$
$167$		−	121470.i		−	0.337036i	0.985699	−	0.168518i	$-0.0538982\pi$
$168$	579242.	+	499352.i	1.58339	+	1.36500i
$169$			143615.i			0.386796i
$170$	201937.	+	192221.i	0.535912	+	0.510127i
$171$	886281.	+	886281.i	2.31783	+	2.31783i
$172$	267745.	+	242571.i	0.690081	+	0.625199i
$173$	219318.	−	219318.i	0.557134	−	0.557134i	−0.371356	−	0.928490i	$-0.621107\pi$
$173$	219318.	−	219318.i	0.557134	−	0.557134i	0.928490	+	0.371356i	$0.121107\pi$
$174$	12444.5	+	504858.i	0.0311604	+	1.26414i
$175$	95027.0			0.234559
$176$	−13006.4	−	10665.3i	−0.0316501	−	0.0259532i
$177$	−109212.			−0.262021
$178$	−8446.01	−	342645.i	−0.0199803	−	0.810577i
$179$	−481512.	+	481512.i	−1.12325	+	1.12325i	−0.131996	+	0.991250i	$0.542138\pi$
$179$	−481512.	+	481512.i	−1.12325	+	1.12325i	−0.991250	+	0.131996i	$0.957862\pi$
$180$	−284199.	+	313692.i	−0.653795	+	0.721644i
$181$	−185016.	−	185016.i	−0.419772	−	0.419772i	0.465353	−	0.885125i	$-0.345927\pi$
$181$	−185016.	−	185016.i	−0.419772	−	0.419772i	−0.885125	+	0.465353i	$0.845927\pi$
$182$	−297256.	−	282955.i	−0.665201	−	0.633196i
$183$		−	634607.i		−	1.40080i
$184$	36284.7	+	489881.i	0.0790095	+	1.06671i
$185$		−	96484.1i		−	0.207265i
$186$	1.00269e6	−	1.05337e6i	2.12513	−	2.23254i
$187$	−22897.3	−	22897.3i	−0.0478830	−	0.0478830i
$188$	−396105.	+	19539.4i	−0.817365	+	0.0403197i
$189$	−854718.	+	854718.i	−1.74048	+	1.74048i
$190$	−334907.	+	8255.27i	−0.673039	+	0.0165900i
$191$	144475.			0.286556			0.143278	−	0.989682i	$-0.454236\pi$
$191$	144475.			0.286556			0.143278	+	0.989682i	$0.454236\pi$
$192$	541954.	−	731664.i	1.06098	−	1.43238i
$193$	573446.			1.10815			0.554076	−	0.832466i	$-0.313072\pi$
$193$	573446.			1.10815			0.554076	+	0.832466i	$0.313072\pi$
$194$	−454702.	+	11208.2i	−0.867407	+	0.0213811i
$195$	234383.	−	234383.i	0.441406	−	0.441406i
$196$	−201679.	+	9948.61i	−0.374991	+	0.0184979i
$197$	228983.	+	228983.i	0.420376	+	0.420376i	0.885333	−	0.464957i	$-0.153930\pi$
$197$	228983.	+	228983.i	0.420376	+	0.420376i	−0.464957	+	0.885333i	$0.653930\pi$
$198$	33897.1	−	35610.4i	0.0614468	−	0.0645526i
$199$			455416.i			0.815221i	0.913156	+	0.407611i	$0.133638\pi$
$199$			455416.i			0.815221i	−0.913156	+	0.407611i	$0.866362\pi$
$200$	−8356.99	−	112828.i	−0.0147732	−	0.199454i
$201$		−	1.06873e6i		−	1.86586i
$202$	114804.	+	109280.i	0.197960	+	0.188435i
$203$	−345413.	−	345413.i	−0.588300	−	0.588300i
$204$	1.17693e6	−	1.29906e6i	1.98004	−	2.18552i
$205$	−171454.	+	171454.i	−0.284946	+	0.284946i
$206$	−18133.4	−	735651.i	−0.0297722	−	1.20782i
$207$	−1.43582e6			−2.32902
$208$	−309818.	+	377824.i	−0.496533	+	0.605524i
$209$	38910.7			0.0616174
$210$	−14723.0	−	597296.i	−0.0230382	−	0.934633i
$211$	−375836.	+	375836.i	−0.581156	+	0.581156i	−0.935221	−	0.354065i	$-0.884799\pi$
$211$	−375836.	+	375836.i	−0.581156	+	0.581156i	0.354065	+	0.935221i	$0.384799\pi$
$212$	26126.3	+	23669.9i	0.0399244	+	0.0361708i
$213$	−1.21304e6	−	1.21304e6i	−1.83200	−	1.83200i
$214$	−822132.	−	782577.i	−1.22718	−	1.16813i
$215$		−	282255.i		−	0.416434i
$216$	1.09000e6	+	939662.i	1.58961	+	1.37037i
$217$			1.40671e6i			2.02795i
$218$	−51020.7	+	53599.5i	−0.0727119	+	0.0763871i
$219$	363908.	+	363908.i	0.512721	+	0.512721i
$220$	647.428	+	13124.7i	0.000901851	+	0.0182824i
$221$	−665147.	+	665147.i	−0.916088	+	0.916088i
$222$	−606454.	+	14948.8i	−0.825877	+	0.0203574i
$223$	−372759.			−0.501956			−0.250978	−	0.967993i	$-0.580752\pi$
$223$	−372759.			−0.501956			−0.250978	+	0.967993i	$0.580752\pi$
$224$	108251.	+	874050.i	0.144149	+	1.16390i
$225$	330693.			0.435481
$226$	−262879.	+	6479.83i	−0.342362	+	0.00843902i
$227$	603192.	−	603192.i	0.776946	−	0.776946i	−0.202365	−	0.979310i	$-0.564863\pi$
$227$	603192.	−	603192.i	0.776946	−	0.776946i	0.979310	+	0.202365i	$0.0648626\pi$
$228$	103778.	+	2.10379e6i	0.132211	+	2.68019i
$229$	578307.	+	578307.i	0.728736	+	0.728736i	0.970368	−	0.241632i	$-0.0776828\pi$
$229$	578307.	+	578307.i	0.728736	+	0.728736i	−0.241632	+	0.970368i	$0.577683\pi$
$230$	264596.	−	277970.i	0.329810	−	0.346480i
$231$			69396.0i			0.0855666i
$232$	−379741.	+	440494.i	−0.463199	+	0.537304i
$233$		−	815767.i		−	0.984410i	−0.870479	−	0.492205i	$-0.836191\pi$
$233$		−	815767.i		−	0.984410i	0.870479	−	0.492205i	$-0.163809\pi$
$234$	−1.03445e6	−	984679.i	−1.23501	−	1.17559i
$235$	219085.	+	219085.i	0.258788	+	0.258788i
$236$	−93207.0	−	84443.7i	−0.108935	−	0.0986931i
$237$	1.07605e6	−	1.07605e6i	1.24441	−	1.24441i
$238$	41782.0	+	1.69505e6i	0.0478131	+	1.93972i
$239$	255220.			0.289015			0.144507	−	0.989504i	$-0.453840\pi$
$239$	255220.			0.289015			0.144507	+	0.989504i	$0.453840\pi$
$240$	−707890.	+	70009.2i	−0.793300	+	0.0784561i
$241$	−1.21711e6			−1.34986			−0.674928	−	0.737883i	$-0.735825\pi$
$241$	−1.21711e6			−1.34986			−0.674928	+	0.737883i	$0.735825\pi$
$242$	22412.3	+	909240.i	0.0246007	+	0.998022i
$243$	−448165.	+	448165.i	−0.486880	+	0.486880i
$244$	490686.	−	541607.i	0.527629	−	0.582385i
$245$	111549.	+	111549.i	0.118727	+	0.118727i
$246$	1.10424e6	+	1.05112e6i	1.16340	+	1.10742i
$247$		−	1.13032e6i		−	1.17885i
$248$	1.67023e6	−	123711.i	1.72443	−	0.127726i
$249$		−	2.98795e6i		−	3.05404i
$250$	−60940.9	+	64021.1i	−0.0616679	+	0.0647848i
$251$	−711568.	−	711568.i	−0.712906	−	0.712906i	0.254236	−	0.967142i	$-0.418176\pi$
$251$	−711568.	−	711568.i	−0.712906	−	0.712906i	−0.967142	+	0.254236i	$0.918176\pi$
$252$	−2.57119e6	+	126834.i	−2.55055	+	0.125816i
$253$	−31518.6	+	31518.6i	−0.0309575	+	0.0309575i
$254$	1.61939e6	−	39917.0i	1.57495	−	0.0388217i
$255$	−1.36947e6			−1.31887
$256$	1.02826e6	−	205396.i	0.980628	−	0.195881i
$257$	−394842.			−0.372899			−0.186449	−	0.982465i	$-0.559698\pi$
$257$	−394842.			−0.372899			−0.186449	+	0.982465i	$0.559698\pi$
$258$	−1.77413e6	+	43731.2i	−1.65934	+	0.0409018i
$259$	414923.	−	414923.i	0.384342	−	0.384342i
$260$	381262.	−	18807.2i	0.349776	−	0.0172540i
$261$	−1.20203e6	−	1.20203e6i	−1.09223	−	1.09223i
$262$	−649907.	+	682757.i	−0.584922	+	0.614487i
$263$			446751.i			0.398269i	0.979972	+	0.199134i	$0.0638130\pi$
$263$			446751.i			0.398269i	−0.979972	+	0.199134i	$0.936187\pi$
$264$	82395.7	−	6102.91i	0.0727603	−	0.00538924i
$265$		−	27542.3i		−	0.0240927i
$266$	−1.47575e6	−	1.40474e6i	−1.27881	−	1.21729i
$267$	1.19049e6	+	1.19049e6i	1.02199	+	1.02199i
$268$	826357.	−	912113.i	0.702798	−	0.775732i
$269$	−616974.	+	616974.i	−0.519860	+	0.519860i	−0.917529	−	0.397669i	$-0.869819\pi$
$269$	−616974.	+	616974.i	−0.519860	+	0.519860i	0.397669	+	0.917529i	$0.369819\pi$
$270$	−27705.2	−	1.12397e6i	−0.0231287	−	0.938306i
$271$	−302965.			−0.250593			−0.125297	−	0.992119i	$-0.539988\pi$
$271$	−302965.			−0.250593			−0.125297	+	0.992119i	$0.539988\pi$
$272$	2.00890e6	−	198677.i	1.64640	−	0.162827i
$273$	2.01589e6			1.63705
$274$	11477.6	+	465632.i	0.00923579	+	0.374685i
$275$	7259.27	−	7259.27i	0.00578844	−	0.00578844i
$276$	−1.78818e6	−	1.62006e6i	−1.41299	−	1.28014i
$277$	−754020.	−	754020.i	−0.590450	−	0.590450i	0.347303	−	0.937753i	$-0.387098\pi$
$277$	−754020.	−	754020.i	−0.590450	−	0.590450i	−0.937753	+	0.347303i	$0.887098\pi$
$278$	1.24504e6	+	1.18514e6i	0.966213	+	0.919725i
$279$			4.89535e6i			3.76507i
$280$	449270.	−	521148.i	0.342462	−	0.397252i
$281$			1.82778e6i			1.38088i	0.723388	+	0.690442i	$0.242584\pi$
$281$			1.82778e6i			1.38088i	−0.723388	+	0.690442i	$0.757416\pi$
$282$	1.34312e6	−	1.41101e6i	1.00576	−	1.05659i
$283$	112611.	+	112611.i	0.0835825	+	0.0835825i	0.747662	−	0.664079i	$-0.231176\pi$
$283$	112611.	+	112611.i	0.0835825	+	0.0835825i	−0.664079	+	0.747662i	$0.731176\pi$
$284$	−97335.8	−	1.97320e6i	−0.0716105	−	1.45170i
$285$	1.16360e6	−	1.16360e6i	0.848581	−	0.848581i
$286$	−44323.3	+	1092.54i	−0.0320418	+	0.000789813i
$287$	−1.47465e6			−1.05678
$288$	376712.	+	3.04169e6i	0.267626	+	2.16089i
$289$	2.46651e6			1.73716
$290$	454224.	−	11196.4i	0.317157	−	0.00781775i
$291$	1.57982e6	−	1.57982e6i	1.09364	−	1.09364i
$292$	29200.5	+	591956.i	0.0200416	+	0.406286i
$293$	1.02302e6	+	1.02302e6i	0.696168	+	0.696168i	0.963582	−	0.267414i	$-0.0861691\pi$
$293$	1.02302e6	+	1.02302e6i	0.696168	+	0.696168i	−0.267414	+	0.963582i	$0.586169\pi$
$294$	683860.	−	718425.i	0.461422	−	0.484745i
$295$			98258.4i			0.0657377i
$296$	−529139.	−	456159.i	−0.351027	−	0.302613i
$297$			130587.i			0.0859029i
$298$	−2.08334e6	−	1.98311e6i	−1.35900	−	1.29362i
$299$	915588.	+	915588.i	0.592273	+	0.592273i
$300$	411849.	+	373127.i	0.264201	+	0.239361i
$301$	1.21382e6	−	1.21382e6i	0.772215	−	0.772215i
$302$	12425.7	+	504096.i	0.00783977	+	0.318050i
$303$	−778559.			−0.487175
$304$	−1.53811e6	+	1.87573e6i	−0.954558	+	1.16409i
$305$	−570960.			−0.351444
$306$	145401.	+	5.89875e6i	0.0887695	+	3.60128i
$307$	712045.	−	712045.i	0.431183	−	0.431183i	−0.457848	−	0.889031i	$-0.651379\pi$
$307$	712045.	−	712045.i	0.431183	−	0.431183i	0.889031	+	0.457848i	$0.151379\pi$
$308$	−53657.8	+	59226.2i	−0.0322297	+	0.0355744i
$309$	2.55595e6	+	2.55595e6i	1.52285	+	1.52285i
$310$	−947725.	−	902127.i	−0.560116	−	0.533167i
$311$		−	459793.i		−	0.269564i	−0.990875	−	0.134782i	$-0.956967\pi$
$311$		−	459793.i		−	0.269564i	0.990875	−	0.134782i	$-0.0430334\pi$
$312$	−177284.	−	2.39352e6i	−0.103106	−	1.39204i
$313$			2.11774e6i			1.22183i	0.791696	+	0.610915i	$0.209198\pi$
$313$			2.11774e6i			1.22183i	−0.791696	+	0.610915i	$0.790802\pi$
$314$	−231004.	+	242680.i	−0.132219	+	0.138902i
$315$	1.42212e6	+	1.42212e6i	0.807534	+	0.807534i
$316$	1.75038e6	−	86344.2i	0.986085	−	0.0486424i
$317$	818417.	−	818417.i	0.457432	−	0.457432i	−0.440380	−	0.897812i	$-0.645156\pi$
$317$	818417.	−	818417.i	0.457432	−	0.457432i	0.897812	+	0.440380i	$0.145156\pi$
$318$	−173118.	+	4267.26i	−0.0960007	+	0.00236636i
$319$	−52773.3			−0.0290361
$320$	−658283.	−	487599.i	−0.359366	−	0.266188i
$321$	5.57542e6			3.02006
$322$	2.33327e6	−	57513.7i	1.25408	−	0.0309123i
$323$	−3.30216e6	+	3.30216e6i	−1.76113	+	1.76113i
$324$	−2.95110e6	+	145574.i	−1.56178	+	0.0770410i
$325$	−210875.	−	210875.i	−0.110743	−	0.110743i
$326$	−657944.	+	691199.i	−0.342882	+	0.360213i
$327$		−	363494.i		−	0.187987i
$328$	129686.	+	1.75089e6i	0.0665591	+	0.898617i
$329$			1.88432e6i			0.959766i
$330$	−46753.1	−	44503.7i	−0.0236334	−	0.0224963i
$331$	−930448.	−	930448.i	−0.466790	−	0.466790i	0.434083	−	0.900873i	$-0.357073\pi$
$331$	−930448.	−	930448.i	−0.466790	−	0.466790i	−0.900873	+	0.434083i	$0.857073\pi$
$332$	2.31032e6	−	2.55008e6i	1.15034	−	1.26972i
$333$	1.44393e6	−	1.44393e6i	0.713568	−	0.713568i
$334$	16932.4	+	686928.i	0.00830524	+	0.336934i
$335$	−961546.			−0.468121
$336$	−3.34530e6	−	2.74316e6i	−1.61654	−	1.32557i
$337$	−1.66985e6			−0.800946			−0.400473	−	0.916308i	$-0.631154\pi$
$337$	−1.66985e6			−0.800946			−0.400473	+	0.916308i	$0.631154\pi$
$338$	−20019.3	−	812160.i	−0.00953141	−	0.386679i
$339$	913350.	−	913350.i	0.431656	−	0.431656i
$340$	−1.16877e6	−	1.05889e6i	−0.548319	−	0.496766i
$341$	107461.	+	107461.i	0.0500456	+	0.0500456i
$342$	−5.13558e6	−	4.88849e6i	−2.37424	−	2.26001i
$343$		−	1.59598e6i		−	0.732472i
$344$	−1.54795e6	−	1.33445e6i	−0.705277	−	0.608005i
$345$			1.88510e6i			0.852679i
$346$	−1.20970e6	+	1.27085e6i	−0.543236	+	0.570694i
$347$	2.96486e6	+	2.96486e6i	1.32185	+	1.32185i	0.912281	+	0.409565i	$0.134320\pi$
$347$	2.96486e6	+	2.96486e6i	1.32185	+	1.32185i	0.409565	+	0.912281i	$0.365680\pi$
$348$	−140750.	−	2.85330e6i	−0.0623019	−	1.26299i
$349$	−2.89685e6	+	2.89685e6i	−1.27310	+	1.27310i	−0.328650	+	0.944452i	$0.606594\pi$
$349$	−2.89685e6	+	2.89685e6i	−1.27310	+	1.27310i	−0.944452	+	0.328650i	$0.893406\pi$
$350$	−537391.	+	13246.4i	−0.234488	+	0.00577999i
$351$	3.79343e6			1.64348
$352$	75039.7	+	58500.7i	0.0322800	+	0.0251654i
$353$	−2.14860e6			−0.917740			−0.458870	−	0.888503i	$-0.651746\pi$
$353$	−2.14860e6			−0.917740			−0.458870	+	0.888503i	$0.651746\pi$
$354$	617607.	−	15223.7i	0.261941	−	0.00645670i
$355$	−1.09138e6	+	1.09138e6i	−0.459625	+	0.459625i
$356$	95526.7	+	1.93653e6i	0.0399484	+	0.809839i
$357$	−5.88930e6	−	5.88930e6i	−2.44564	−	2.44564i
$358$	2.65590e6	−	2.79014e6i	1.09523	−	1.15058i
$359$		−	2.61006e6i		−	1.06884i	−0.845218	−	0.534421i	$-0.820530\pi$
$359$		−	2.61006e6i		−	1.06884i	0.845218	−	0.534421i	$-0.179470\pi$
$360$	1.56346e6	−	1.81359e6i	0.635814	−	0.737535i
$361$		−	3.13544e6i		−	1.26628i
$362$	1.07208e6	+	1.02050e6i	0.429988	+	0.409300i
$363$	−3.15907e6	−	3.15907e6i	−1.25833	−	1.25833i
$364$	1.72047e6	+	1.55871e6i	0.680602	+	0.616612i
$365$	327410.	−	327410.i	0.128635	−	0.128635i
$366$	88461.7	+	3.58879e6i	0.0345186	+	1.40038i
$367$	−7255.03			−0.00281173			−0.00140587	−	0.999999i	$-0.500448\pi$
$367$	−7255.03			−0.00281173			−0.00140587	+	0.999999i	$0.500448\pi$
$368$	−273483.	−	2.76529e6i	−0.105271	−	1.06444i
$369$	−5.13177e6			−1.96201
$370$	13449.5	+	545631.i	0.00510742	+	0.207202i
$371$	118444.	−	118444.i	0.0446763	−	0.0446763i
$372$	−5.52352e6	+	6.09673e6i	−2.06947	+	2.28423i
$373$	3.28076e6	+	3.28076e6i	1.22096	+	1.22096i	0.967290	+	0.253675i	$0.0816393\pi$
$373$	3.28076e6	+	3.28076e6i	1.22096	+	1.22096i	0.253675	+	0.967290i	$0.418361\pi$
$374$	132679.	+	126296.i	0.0490484	+	0.0466885i
$375$		−	434170.i		−	0.159434i
$376$	2.23730e6	−	165714.i	0.816123	−	0.0604489i
$377$			1.53302e6i			0.555513i
$378$	4.71440e6	−	4.95269e6i	1.69706	−	1.78284i
$379$	−1.97719e6	−	1.97719e6i	−0.707051	−	0.707051i	0.258863	−	0.965914i	$-0.416652\pi$
$379$	−1.97719e6	−	1.97719e6i	−0.707051	−	0.707051i	−0.965914	+	0.258863i	$0.916652\pi$
$380$	1.89279e6	−	93369.4i	0.672426	−	0.0331700i
$381$	−5.62642e6	+	5.62642e6i	−1.98573	+	1.98573i
$382$	−817027.	+	20139.3i	−0.286469	+	0.00706130i
$383$	925457.			0.322374			0.161187	−	0.986924i	$-0.448468\pi$
$383$	925457.			0.322374			0.161187	+	0.986924i	$0.448468\pi$
$384$	−2.96283e6	+	4.21321e6i	−1.02537	+	1.45809i
$385$	62436.0			0.0214676
$386$	−3.24291e6	+	79936.1i	−1.10781	+	0.0273070i
$387$	4.22408e6	−	4.22408e6i	1.43369	−	1.43369i
$388$	2.56984e6	−	126767.i	0.866617	−	0.0427492i
$389$	−1.44312e6	−	1.44312e6i	−0.483536	−	0.483536i	0.422723	−	0.906259i	$-0.361074\pi$
$389$	−1.44312e6	−	1.44312e6i	−0.483536	−	0.483536i	−0.906259	+	0.422723i	$0.861074\pi$
$390$	−1.29279e6	+	1.35814e6i	−0.430395	+	0.452150i
$391$		−	5.34966e6i		−	1.76964i
$392$	1.13914e6	−	84374.0i	0.374421	−	0.0277328i
$393$		−	4.63022e6i		−	1.51224i
$394$	−1.32685e6	−	1.26301e6i	−0.430607	−	0.409889i
$395$	−968132.	−	968132.i	−0.312207	−	0.312207i
$396$	−186729.	+	206107.i	−0.0598374	+	0.0660472i
$397$	2.24787e6	−	2.24787e6i	0.715807	−	0.715807i	−0.251937	−	0.967744i	$-0.581068\pi$
$397$	2.24787e6	−	2.24787e6i	0.715807	−	0.715807i	0.967744	+	0.251937i	$0.0810676\pi$
$398$	−63483.2	−	2.57544e6i	−0.0200887	−	0.814974i
$399$	1.00080e7			3.14713
$400$	62987.7	+	636893.i	0.0196836	+	0.199029i
$401$	−2.69259e6			−0.836200			−0.418100	−	0.908401i	$-0.637304\pi$
$401$	−2.69259e6			−0.836200			−0.418100	+	0.908401i	$0.637304\pi$
$402$	148977.	+	6.04383e6i	0.0459785	+	1.86529i
$403$	3.12165e6	−	3.12165e6i	0.957463	−	0.957463i
$404$	−664463.	−	601990.i	−0.202543	−	0.183500i
$405$	1.63225e6	+	1.63225e6i	0.494480	+	0.494480i
$406$	2.00151e6	+	1.90521e6i	0.602618	+	0.573624i
$407$		−	63393.3i		−	0.0189696i
$408$	−6.47459e6	+	7.51044e6i	−1.92558	+	2.23365i
$409$			625505.i			0.184894i	0.995718	+	0.0924470i	$0.0294689\pi$
$409$			625505.i			0.184894i	−0.995718	+	0.0924470i	$0.970531\pi$
$410$	945695.	−	993495.i	0.277838	−	0.291881i
$411$	−1.61780e6	−	1.61780e6i	−0.472411	−	0.472411i
$412$	205093.	+	4.15768e6i	0.0595263	+	1.20672i
$413$	−422553.	+	422553.i	−0.121901	+	0.121901i
$414$	8.11974e6	−	200147.i	2.32831	−	0.0573916i
$415$	−2.68828e6			−0.766221
$416$	1.69939e6	−	2.17983e6i	0.481460	−	0.617576i
$417$	−8.44346e6			−2.37783
$418$	−220045.	+	5424.00i	−0.0615987	+	0.00151837i
$419$	−3.97089e6	+	3.97089e6i	−1.10497	+	1.10497i	−0.111174	+	0.993801i	$0.535461\pi$
$419$	−3.97089e6	+	3.97089e6i	−1.10497	+	1.10497i	−0.993801	+	0.111174i	$0.964539\pi$
$420$	166521.	+	3.37574e6i	0.0460624	+	0.933782i
$421$	4.47822e6	+	4.47822e6i	1.23140	+	1.23140i	0.963425	+	0.267979i	$0.0863558\pi$
$421$	4.47822e6	+	4.47822e6i	1.23140	+	1.23140i	0.267979	+	0.963425i	$0.413644\pi$
$422$	2.07301e6	−	2.17779e6i	0.566658	−	0.595300i
$423$			6.55743e6i			1.78190i
$424$	−151048.	−	130215.i	−0.0408036	−	0.0351760i
$425$			1.23212e6i			0.330887i
$426$	7.02897e6	+	6.69079e6i	1.87658	+	1.78630i
$427$	−2.45537e6	−	2.45537e6i	−0.651701	−	0.651701i
$428$	4.75836e6	+	4.31098e6i	1.25559	+	1.13754i
$429$	153997.	−	153997.i	0.0403989	−	0.0403989i
$430$	39345.3	+	1.59619e6i	0.0102617	+	0.416307i
$431$	−3.93764e6			−1.02104			−0.510521	−	0.859865i	$-0.670547\pi$
$431$	−3.93764e6			−1.02104			−0.510521	+	0.859865i	$0.670547\pi$
$432$	−6.29506e6	−	5.16198e6i	−1.62290	−	1.33078i
$433$	−3.83172e6			−0.982141			−0.491071	−	0.871120i	$-0.663394\pi$
$433$	−3.83172e6			−0.982141			−0.491071	+	0.871120i	$0.663394\pi$
$434$	−196090.	−	7.95516e6i	−0.0499726	−	2.02733i
$435$	−1.57816e6	+	1.57816e6i	−0.399878	+	0.399878i
$436$	281058.	−	310225.i	0.0708075	−	0.0781556i
$437$	4.54548e6	+	4.54548e6i	1.13861	+	1.13861i
$438$	−2.10868e6	−	2.00722e6i	−0.525200	−	0.499931i
$439$			1.34172e6i			0.332278i	0.986102	+	0.166139i	$0.0531301\pi$
$439$			1.34172e6i			0.332278i	−0.986102	+	0.166139i	$0.946870\pi$
$440$	−5490.83	−	74131.9i	−0.00135209	−	0.0182546i
$441$			3.33875e6i			0.817500i
$442$	3.66878e6	−	3.85422e6i	0.893236	−	0.938384i
$443$	−655716.	−	655716.i	−0.158747	−	0.158747i	0.623264	−	0.782011i	$-0.285806\pi$
$443$	−655716.	−	655716.i	−0.158747	−	0.158747i	−0.782011	+	0.623264i	$0.785806\pi$
$444$	3.42750e6	−	169075.i	0.825125	−	0.0407025i
$445$	1.07109e6	−	1.07109e6i	0.256405	−	0.256405i
$446$	2.10800e6	−	51961.1i	0.501804	−	0.0123692i
$447$	1.41285e7			3.34448
$448$	−734013.	−	4.92778e6i	−0.172786	−	1.16000i
$449$	3.17602e6			0.743476			0.371738	−	0.928338i	$-0.378762\pi$
$449$	3.17602e6			0.743476			0.371738	+	0.928338i	$0.378762\pi$
$450$	−1.87011e6	+	46097.3i	−0.435348	+	0.0107311i
$451$	−112651.	+	112651.i	−0.0260792	+	0.0260792i
$452$	1.48571e6	−	73288.6i	0.342050	−	0.0168729i
$453$	−1.75144e6	−	1.75144e6i	−0.401004	−	0.401004i
$454$	−3.32705e6	+	3.49521e6i	−0.757564	+	0.795855i
$455$		−	1.81371e6i		−	0.410714i
$456$	−880137.	−	1.18828e7i	−0.198216	−	2.67612i
$457$			4.41310e6i			0.988447i	0.869335	+	0.494224i	$0.164548\pi$
$457$			4.41310e6i			0.988447i	−0.869335	+	0.494224i	$0.835452\pi$
$458$	−3.35102e6	−	3.18979e6i	−0.746472	−	0.710557i
$459$	−1.10822e7	−	1.10822e7i	−2.45525	−	2.45525i
$460$	−1.45758e6	+	1.60884e6i	−0.321172	+	0.354502i
$461$	−2.80445e6	+	2.80445e6i	−0.614604	+	0.614604i	−0.944142	−	0.329539i	$-0.893107\pi$
$461$	−2.80445e6	+	2.80445e6i	−0.614604	+	0.614604i	0.329539	+	0.944142i	$0.393107\pi$
$462$	−9673.52	−	392444.i	−0.00210853	−	0.0855407i
$463$	−2.47795e6			−0.537205			−0.268603	−	0.963251i	$-0.586562\pi$
$463$	−2.47795e6			−0.537205			−0.268603	+	0.963251i	$0.586562\pi$
$464$	2.08608e6	−	2.54399e6i	0.449818	−	0.548555i
$465$	6.42714e6			1.37843
$466$	113715.	+	4.61327e6i	0.0242578	+	0.984111i
$467$	−1.18173e6	+	1.18173e6i	−0.250742	+	0.250742i	−0.821275	−	0.570533i	$-0.806737\pi$
$467$	−1.18173e6	+	1.18173e6i	−0.250742	+	0.250742i	0.570533	+	0.821275i	$0.306737\pi$
$468$	5.98722e6	+	5.42430e6i	1.26360	+	1.14480i
$469$	−4.13506e6	−	4.13506e6i	−0.868060	−	0.868060i
$470$	−1.26950e6	−	1.20842e6i	−0.265086	−	0.252332i
$471$		−	1.64577e6i		−	0.341835i
$472$	538869.	+	464548.i	0.111334	+	0.0959788i
$473$		−	185451.i		−	0.0381134i
$474$	−5.93523e6	+	6.23523e6i	−1.21337	+	1.27470i
$475$	−1.04690e6	−	1.04690e6i	−0.212898	−	0.212898i
$476$	−472566.	−	9.57991e6i	−0.0955972	−	1.93796i
$477$	412183.	−	412183.i	0.0829457	−	0.0829457i
$478$	−1.44330e6	+	35576.6i	−0.288927	+	0.00712189i
$479$	9.82296e6			1.95616			0.978078	−	0.208240i	$-0.0667734\pi$
$479$	9.82296e6			1.95616			0.978078	+	0.208240i	$0.0667734\pi$
$480$	3.99345e6	−	494588.i	0.791126	−	0.0979808i
$481$	−1.84152e6			−0.362922
$482$	6.88293e6	−	169660.i	1.34945	−	0.0332631i
$483$	−8.10672e6	+	8.10672e6i	−1.58117	+	1.58117i
$484$	−253489.	−	5.13875e6i	−0.0491864	−	0.997112i
$485$	−1.42138e6	−	1.42138e6i	−0.274381	−	0.274381i
$486$	2.47196e6	−	2.59691e6i	0.474735	−	0.498730i
$487$			2.05462e6i			0.392562i	0.980548	+	0.196281i	$0.0628865\pi$
$487$			2.05462e6i			0.392562i	−0.980548	+	0.196281i	$0.937114\pi$
$488$	−2.69940e6	+	3.13126e6i	−0.513118	+	0.595210i
$489$		−	4.68748e6i		−	0.886476i
$490$	−646372.	−	615273.i	−0.121616	−	0.115765i
$491$	4.27455e6	+	4.27455e6i	0.800178	+	0.800178i	0.983123	−	0.182945i	$-0.0585631\pi$
$491$	4.27455e6	+	4.27455e6i	0.800178	+	0.800178i	−0.182945	+	0.983123i	$0.558563\pi$
$492$	−6.39117e6	−	5.79028e6i	−1.19033	−	1.07842i
$493$	4.47861e6	−	4.47861e6i	0.829901	−	0.829901i
$494$	157562.	+	6.39212e6i	0.0290492	+	1.17849i
$495$	217277.			0.0398566
$496$	−9.42812e6	+	932426.i	−1.72076	+	0.170181i
$497$	−9.38677e6			−1.70461
$498$	416509.	+	1.68973e7i	0.0752576	+	3.05312i
$499$	−2.64763e6	+	2.64763e6i	−0.475999	+	0.475999i	−0.903850	−	0.427850i	$-0.859271\pi$
$499$	−2.64763e6	+	2.64763e6i	−0.475999	+	0.475999i	0.427850	+	0.903850i	$0.359271\pi$
$500$	335705.	−	370543.i	0.0600527	−	0.0662848i
$501$	−2.38667e6	−	2.38667e6i	−0.424813	−	0.424813i
$502$	4.12320e6	+	3.92483e6i	0.730257	+	0.695122i
$503$			475460.i			0.0837904i	0.999122	+	0.0418952i	$0.0133396\pi$
$503$			475460.i			0.0837904i	−0.999122	+	0.0418952i	$0.986660\pi$
$504$	1.45228e7	−	1.07568e6i	2.54667	−	0.188628i
$505$			700474.i			0.122226i
$506$	173849.	−	182636.i	0.0301852	−	0.0317110i
$507$	2.82178e6	+	2.82178e6i	0.487532	+	0.487532i
$508$	−9.15230e6	+	451473.i	−1.57352	+	0.0776197i
$509$	2.26623e6	−	2.26623e6i	0.387712	−	0.387712i	−0.486159	−	0.873870i	$-0.661602\pi$
$509$	2.26623e6	−	2.26623e6i	0.387712	−	0.387712i	0.873870	+	0.486159i	$0.161602\pi$
$510$	7.74452e6	−	190898.i	1.31847	−	0.0324995i
$511$	2.81601e6			0.477070
$512$	−5.78633e6	+	1.30488e6i	−0.975503	+	0.219986i
$513$	1.88327e7			3.15950
$514$	2.23289e6	−	55039.4i	0.372785	−	0.00918895i
$515$	2.29961e6	−	2.29961e6i	0.382063	−	0.382063i
$516$	1.00268e7	−	494612.i	1.65783	−	0.0817788i
$517$	143947.	+	143947.i	0.0236851	+	0.0236851i
$518$	−2.28861e6	+	2.40429e6i	−0.374755	+	0.393697i
$519$		−	8.61845e6i		−	1.40447i
$520$	−2.15346e6	+	159504.i	−0.349244	+	0.0258680i
$521$			5.50679e6i			0.888801i	0.895828	+	0.444401i	$0.146583\pi$
$521$			5.50679e6i			0.888801i	−0.895828	+	0.444401i	$0.853417\pi$
$522$	6.96522e6	+	6.63011e6i	1.11882	+	1.06499i
$523$	4.02488e6	+	4.02488e6i	0.643426	+	0.643426i	0.951396	−	0.307970i	$-0.0996496\pi$
$523$	4.02488e6	+	4.02488e6i	0.643426	+	0.643426i	−0.307970	+	0.951396i	$0.599650\pi$
$524$	3.58014e6	−	3.95168e6i	0.569602	−	0.628714i
$525$	1.86712e6	−	1.86712e6i	0.295647	−	0.295647i
$526$	−62275.3	−	2.52644e6i	−0.00981412	−	0.398148i
$527$	−1.82394e7			−2.86078
$528$	−465108.	+	45998.4i	−0.0726054	+	0.00718056i
$529$	−927561.			−0.144113
$530$	3839.28	+	155755.i	0.000593691	+	0.0240854i
$531$	−1.47048e6	+	1.47048e6i	−0.226320	+	0.226320i
$532$	8.54136e6	+	7.73830e6i	1.30842	+	1.18540i
$533$	3.27241e6	+	3.27241e6i	0.498942	+	0.498942i
$534$	−6.89833e6	−	6.56643e6i	−1.04687	−	0.996497i
$535$		−	5.01624e6i		−	0.757694i
$536$	−4.54601e6	+	5.27332e6i	−0.683469	+	0.792815i
$537$			1.89218e7i			2.83156i
$538$	3.40307e6	−	3.57508e6i	0.506892	−	0.532513i
$539$	73291.2	+	73291.2i	0.0108663	+	0.0108663i
$540$	313353.	+	6.35233e6i	0.0462434	+	0.937451i
$541$	7.20318e6	−	7.20318e6i	1.05811	−	1.05811i	0.0599075	−	0.998204i	$-0.480919\pi$
$541$	7.20318e6	−	7.20318e6i	1.05811	−	1.05811i	0.998204	−	0.0599075i	$-0.0190806\pi$
$542$	1.71331e6	−	42232.1i	0.250517	−	0.00617511i
$543$	−7.27049e6			−1.05819
$544$	−1.13329e7	+	1.40358e6i	−1.64189	+	0.203348i
$545$	−327038.			−0.0471635
$546$	−1.14001e7	+	281007.i	−1.63655	+	0.0403400i
$547$	579264.	−	579264.i	0.0827767	−	0.0827767i	−0.664506	−	0.747283i	$-0.731358\pi$
$547$	579264.	−	579264.i	0.0827767	−	0.0827767i	0.747283	+	0.664506i	$0.231358\pi$
$548$	−129815.	−	2.63161e6i	−0.0184660	−	0.374344i
$549$	−8.54468e6	−	8.54468e6i	−1.20994	−	1.20994i
$550$	−40040.3	+	42064.1i	−0.00564404	+	0.00592932i
$551$			7.61075e6i			1.06794i
$552$	1.03383e7	+	8.91239e6i	1.44411	+	1.24493i
$553$		−	8.32677e6i		−	1.15788i
$554$	4.36919e6	+	4.15898e6i	0.604821	+	0.575721i
$555$	−1.89574e6	−	1.89574e6i	−0.261245	−	0.261245i
$556$	−7.20610e6	−	6.52858e6i	−0.988583	−	0.895637i
$557$	1.06112e6	−	1.06112e6i	0.144920	−	0.144920i	−0.630925	−	0.775844i	$-0.717324\pi$
$557$	1.06112e6	−	1.06112e6i	0.144920	−	0.144920i	0.775844	+	0.630925i	$0.217324\pi$
$558$	−682392.	−	2.76839e7i	−0.0927788	−	3.76393i
$559$	−5.38720e6			−0.729178
$560$	−2.46804e6	+	3.00979e6i	−0.332569	+	0.405570i
$561$	−899786.			−0.120707
$562$	−254785.	−	1.03363e7i	−0.0340277	−	1.38046i
$563$	5.65144e6	−	5.65144e6i	0.751429	−	0.751429i	−0.223317	−	0.974746i	$-0.571688\pi$
$563$	5.65144e6	−	5.65144e6i	0.751429	−	0.751429i	0.974746	+	0.223317i	$0.0716885\pi$
$564$	−7.39887e6	+	8.16670e6i	−0.979416	+	1.08106i
$565$	−821747.	−	821747.i	−0.108297	−	0.108297i
$566$	−652529.	−	621134.i	−0.0856168	−	0.0814975i
$567$			1.40387e7i			1.83388i
$568$	825504.	+	1.11452e7i	0.107361	+	1.44949i
$569$			5.69200e6i			0.737028i	0.929622	+	0.368514i	$0.120133\pi$
$569$			5.69200e6i			0.737028i	−0.929622	+	0.368514i	$0.879867\pi$
$570$	−6.41814e6	+	6.74255e6i	−0.827413	+	0.869234i
$571$	−500996.	−	500996.i	−0.0643049	−	0.0643049i	0.674223	−	0.738528i	$-0.264479\pi$
$571$	−500996.	−	500996.i	−0.0643049	−	0.0643049i	−0.738528	+	0.674223i	$0.764479\pi$
$572$	250502.	−	12357.0i	0.0320126	−	0.00157915i
$573$	2.83869e6	−	2.83869e6i	0.361186	−	0.361186i
$574$	8.33936e6	−	205561.i	1.05646	−	0.0260411i
$575$	1.69603e6			0.213926
$576$	−2.55436e6	−	1.71486e7i	−0.320794	−	2.15364i
$577$	4.96081e6			0.620316			0.310158	−	0.950685i	$-0.399618\pi$
$577$	4.96081e6			0.620316			0.310158	+	0.950685i	$0.399618\pi$
$578$	−1.39485e7	+	343822.i	−1.73663	+	0.0428069i
$579$	1.12672e7	−	1.12672e7i	1.39676	−	1.39676i
$580$	−2.56714e6	+	126634.i	−0.316868	+	0.0156308i
$581$	−1.15608e7	−	1.15608e7i	−1.42084	−	1.42084i
$582$	−8.71389e6	+	9.15434e6i	−1.06636	+	1.12026i
$583$		−	18096.2i		−	0.00220504i
$584$	−247649.	−	3.34352e6i	−0.0300473	−	0.405669i
$585$		−	6.31170e6i		−	0.762529i
$586$	−5.92791e6	−	5.64270e6i	−0.713111	−	0.678802i
$587$	−2.22699e6	−	2.22699e6i	−0.266761	−	0.266761i	0.561032	−	0.827794i	$-0.310404\pi$
$587$	−2.22699e6	−	2.22699e6i	−0.266761	−	0.266761i	−0.827794	+	0.561032i	$0.810404\pi$
$588$	−3.76717e6	+	4.15812e6i	−0.449337	+	0.495968i
$589$	1.54976e7	−	1.54976e7i	1.84067	−	1.84067i
$590$	−13696.8	−	555664.i	−0.00161991	−	0.0657177i
$591$	8.99824e6			1.05971
$592$	3.05594e6	+	2.50588e6i	0.358377	+	0.293871i
$593$	−749550.			−0.0875314			−0.0437657	−	0.999042i	$-0.513936\pi$
$593$	−749550.			−0.0875314			−0.0437657	+	0.999042i	$0.513936\pi$
$594$	−18203.3	−	738486.i	−0.00211682	−	0.0858768i
$595$	−5.29864e6	+	5.29864e6i	−0.613581	+	0.613581i
$596$	1.20580e7	+	1.09243e7i	1.39047	+	1.25974i
$597$	8.94814e6	+	8.94814e6i	1.02754	+	1.02754i
$598$	−5.30540e6	−	5.05014e6i	−0.606688	−	0.577498i
$599$			1.24336e7i			1.41589i	0.706267	+	0.707946i	$0.250378\pi$
$599$			1.24336e7i			1.41589i	−0.706267	+	0.707946i	$0.749622\pi$
$600$	−2.38108e6	−	2.05267e6i	−0.270019	−	0.232778i
$601$			1.06573e7i			1.20354i	0.798668	+	0.601772i	$0.205538\pi$
$601$			1.06573e7i			1.20354i	−0.798668	+	0.601772i	$0.794462\pi$
$602$	−6.69511e6	+	7.03352e6i	−0.752951	+	0.791009i
$603$	−1.43900e7	−	1.43900e7i	−1.61164	−	1.61164i
$604$	−140538.	−	2.84900e6i	−0.0156748	−	0.317761i
$605$	−2.84224e6	+	2.84224e6i	−0.315698	+	0.315698i
$606$	4.40286e6	−	108528.i	0.487027	−	0.0120049i
$607$	1.21466e7			1.33808			0.669039	−	0.743228i	$-0.266706\pi$
$607$	1.21466e7			1.33808			0.669039	+	0.743228i	$0.266706\pi$
$608$	8.43673e6	−	1.08219e7i	0.925583	−	1.18726i
$609$	−1.35735e7			−1.48303
$610$	3.22886e6	−	79589.5i	0.351337	−	0.00866027i
$611$	4.18152e6	−	4.18152e6i	0.453139	−	0.453139i
$612$	−1.64453e6	−	3.33380e7i	−0.177485	−	3.59800i
$613$	189949.	+	189949.i	0.0204168	+	0.0204168i	0.717241	−	0.696825i	$-0.245404\pi$
$613$	189949.	+	189949.i	0.0204168	+	0.0204168i	−0.696825	+	0.717241i	$0.745404\pi$
$614$	−3.92746e6	+	4.12597e6i	−0.420427	+	0.441677i
$615$			6.73755e6i			0.718313i
$616$	295186.	−	342412.i	0.0313433	−	0.0363578i
$617$		−	1.08751e7i		−	1.15006i	−0.818133	−	0.575028i	$-0.804991\pi$
$617$		−	1.08751e7i		−	1.15006i	0.818133	−	0.575028i	$-0.195009\pi$
$618$	−1.48106e7	−	1.40980e7i	−1.55991	−	1.48486i
$619$	1.32235e7	+	1.32235e7i	1.38714	+	1.38714i	0.831277	+	0.555859i	$0.187611\pi$
$619$	1.32235e7	+	1.32235e7i	1.38714	+	1.38714i	0.555859	+	0.831277i	$0.312389\pi$
$620$	5.48527e6	+	4.96954e6i	0.573084	+	0.519203i
$621$	−1.52549e7	+	1.52549e7i	−1.58738	+	1.58738i
$622$	64093.3	+	2.60019e6i	0.00664258	+	0.269482i
$623$	9.21230e6			0.950929
$624$	1.33621e6	+	1.35110e7i	0.137377	+	1.38907i
$625$	−390625.			−0.0400000
$626$	−295204.	−	1.19761e7i	−0.0301083	−	1.22146i
$627$	764528.	−	764528.i	0.0776649	−	0.0776649i
$628$	1.27253e6	−	1.40459e6i	0.128756	−	0.142118i
$629$	5.37988e6	+	5.37988e6i	0.542183	+	0.542183i
$630$	−8.24054e6	−	7.84406e6i	−0.827188	−	0.787390i
$631$		−	1.12988e7i		−	1.12969i	−0.825197	−	0.564845i	$-0.808936\pi$
$631$		−	1.12988e7i		−	1.12969i	0.825197	−	0.564845i	$-0.191064\pi$
$632$	−9.88659e6	+	732284.i	−0.984587	+	0.0729267i
$633$			1.47691e7i			1.46502i
$634$	−4.51418e6	+	4.74235e6i	−0.446021	+	0.468565i
$635$	5.06213e6	+	5.06213e6i	0.498194	+	0.498194i
$636$	978411.	−	48263.9i	0.0959132	−	0.00473129i
$637$	2.12904e6	−	2.12904e6i	0.207891	−	0.207891i
$638$	298440.	−	7356.39i	0.0290273	−	0.000715506i
$639$	−3.26659e7			−3.16477
$640$	3.79065e6	+	2.66568e6i	0.365817	+	0.257251i
$641$	−1.29242e7			−1.24239			−0.621195	−	0.783656i	$-0.713352\pi$
$641$	−1.29242e7			−1.24239			−0.621195	+	0.783656i	$0.713352\pi$
$642$	−3.15298e7	+	777191.i	−3.01914	+	0.0744201i
$643$	−816087.	+	816087.i	−0.0778411	+	0.0778411i	−0.744955	−	0.667114i	$-0.767529\pi$
$643$	−816087.	+	816087.i	−0.0778411	+	0.0778411i	0.667114	+	0.744955i	$0.267529\pi$
$644$	−1.31869e7	+	650496.i	−1.25294	+	0.0618059i
$645$	−5.54583e6	−	5.54583e6i	−0.524889	−	0.524889i
$646$	1.82139e7	−	1.91345e7i	1.71720	−	1.80399i
$647$			1.14750e7i			1.07769i	0.842406	+	0.538844i	$0.181139\pi$
$647$			1.14750e7i			1.07769i	−0.842406	+	0.538844i	$0.818861\pi$
$648$	1.66686e7	−	1.23461e6i	1.55941	−	0.115503i
$649$			64559.1i			0.00601653i
$650$	1.22192e6	+	1.16313e6i	0.113439	+	0.107981i
$651$	2.76395e7	+	2.76395e7i	2.55610	+	2.55610i
$652$	3.62441e6	−	4.00054e6i	0.333902	−	0.368553i
$653$	5.60167e6	−	5.60167e6i	0.514084	−	0.514084i	−0.401691	−	0.915775i	$-0.631577\pi$
$653$	5.60167e6	−	5.60167e6i	0.514084	−	0.514084i	0.915775	+	0.401691i	$0.131577\pi$
$654$	50669.6	+	2.05561e6i	0.00463237	+	0.187930i
$655$	−4.16584e6			−0.379402
$656$	−977458.	−	9.88346e6i	−0.0886826	−	0.896704i
$657$	9.79969e6			0.885725
$658$	−262667.	−	1.06561e7i	−0.0236505	−	0.959475i
$659$	3.61020e6	−	3.61020e6i	0.323831	−	0.323831i	−0.526404	−	0.850235i	$-0.676460\pi$
$659$	3.61020e6	−	3.61020e6i	0.323831	−	0.323831i	0.850235	+	0.526404i	$0.176460\pi$
$660$	270599.	+	245157.i	0.0241806	+	0.0219071i
$661$	4.16305e6	+	4.16305e6i	0.370602	+	0.370602i	0.867696	−	0.497094i	$-0.165600\pi$
$661$	4.16305e6	+	4.16305e6i	0.370602	+	0.370602i	−0.497094	+	0.867696i	$0.665600\pi$
$662$	5.39151e6	+	5.13211e6i	0.478151	+	0.455146i
$663$			2.61380e7i			2.30934i
$664$	−1.27097e7	+	1.47431e7i	−1.11870	+	1.29768i
$665$		−	9.00426e6i		−	0.789576i
$666$	−7.96434e6	+	8.36689e6i	−0.695767	+	0.730935i
$667$	−6.16489e6	−	6.16489e6i	−0.536551	−	0.536551i
$668$	−191510.	−	3.88231e6i	−0.0166054	−	0.336627i
$669$	−7.32406e6	+	7.32406e6i	−0.632684	+	0.632684i
$670$	5.43767e6	−	134036.i	0.467979	−	0.0115354i
$671$	−375140.			−0.0321653
$672$	1.93005e7	+	1.50466e7i	1.64872	+	1.28533i
$673$	2.21199e7			1.88255			0.941273	−	0.337645i	$-0.109630\pi$
$673$	2.21199e7			1.88255			0.941273	+	0.337645i	$0.109630\pi$
$674$	9.44324e6	−	232771.i	0.800703	−	0.0197369i
$675$	3.51347e6	−	3.51347e6i	0.296809	−	0.296809i
$676$	226424.	+	4.59009e6i	0.0190570	+	0.386326i
$677$	−5.09252e6	−	5.09252e6i	−0.427033	−	0.427033i	0.460584	−	0.887616i	$-0.347640\pi$
$677$	−5.09252e6	−	5.09252e6i	−0.427033	−	0.427033i	−0.887616	+	0.460584i	$0.847640\pi$
$678$	−5.03780e6	+	5.29244e6i	−0.420888	+	0.442162i
$679$		−	1.22251e7i		−	1.01760i
$680$	6.75719e6	+	5.82523e6i	0.560394	+	0.483104i
$681$		−	2.37033e7i		−	1.95858i
$682$	−622688.	−	592728.i	−0.0512636	−	0.0487972i
$683$	5.69497e6	+	5.69497e6i	0.467132	+	0.467132i	0.900984	−	0.433852i	$-0.142846\pi$
$683$	5.69497e6	+	5.69497e6i	0.467132	+	0.467132i	−0.433852	+	0.900984i	$0.642846\pi$
$684$	2.97239e7	+	2.69292e7i	2.42921	+	2.20082i
$685$	−1.45554e6	+	1.45554e6i	−0.118522	+	0.118522i
$686$	222473.	+	9.02546e6i	0.0180496	+	0.732250i
$687$	2.27255e7			1.83705
$688$	8.93987e6	+	7.33073e6i	0.720046	+	0.590441i
$689$	−525679.			−0.0421864
$690$	−262775.	−	1.06605e7i	−0.0210117	−	0.852420i
$691$	−2.98475e6	+	2.98475e6i	−0.237801	+	0.237801i	−0.815939	−	0.578138i	$-0.803779\pi$
$691$	−2.98475e6	+	2.98475e6i	−0.237801	+	0.237801i	0.578138	+	0.815939i	$0.303779\pi$
$692$	6.66389e6	−	7.35544e6i	0.529008	−	0.583907i
$693$	934384.	+	934384.i	0.0739081	+	0.0739081i
$694$	−1.71800e7	−	1.63534e7i	−1.35402	−	1.28887i
$695$			7.59664e6i			0.596567i
$696$	1.19370e6	+	1.61162e7i	0.0934055	+	1.26107i
$697$		−	1.91203e7i		−	1.49078i
$698$	1.59783e7	−	1.67859e7i	1.24134	−	1.30409i
$699$	−1.60284e7	−	1.60284e7i	−1.24079	−	1.24079i
$700$	3.03717e6	−	149820.i	0.234274	−	0.0115565i
$701$	−9.70805e6	+	9.70805e6i	−0.746169	+	0.746169i	−0.973757	−	0.227589i	$-0.926916\pi$
$701$	−9.70805e6	+	9.70805e6i	−0.746169	+	0.746169i	0.227589	+	0.973757i	$0.426916\pi$
$702$	−2.14524e7	+	528789.i	−1.64298	+	0.0404985i
$703$	−9.14233e6			−0.697699
$704$	−432514.	−	320369.i	−0.0328904	−	0.0243624i
$705$	8.60929e6			0.652371
$706$	1.21506e7	−	299507.i	0.917461	−	0.0226149i
$707$	−3.01234e6	+	3.01234e6i	−0.226650	+	0.226650i
$708$	−3.49053e6	+	172184.i	−0.261702	+	0.0129095i
$709$	1.00421e7	+	1.00421e7i	0.750256	+	0.750256i	0.974527	−	0.224270i	$-0.0719999\pi$
$709$	1.00421e7	+	1.00421e7i	0.750256	+	0.750256i	−0.224270	+	0.974527i	$0.572000\pi$
$710$	6.01974e6	−	6.32401e6i	0.448159	−	0.470811i
$711$		−	2.89771e7i		−	2.14972i
$712$	−810160.	−	1.09380e7i	−0.0598923	−	0.808608i
$713$			2.51069e7i			1.84956i
$714$	3.41257e7	+	3.24838e7i	2.50516	+	2.38463i
$715$	−138552.	−	138552.i	−0.0101356	−	0.0101356i
$716$	−1.46305e7	+	1.61488e7i	−1.06654	+	1.17722i
$717$	5.01463e6	−	5.01463e6i	0.364285	−	0.364285i
$718$	363831.	+	1.47602e7i	0.0263384	+	1.06852i
$719$	−3.73707e6			−0.269593			−0.134796	−	0.990873i	$-0.543038\pi$
$719$	−3.73707e6			−0.269593			−0.134796	+	0.990873i	$0.543038\pi$
$720$	−8.58876e6	+	1.04740e7i	−0.617446	+	0.752979i
$721$	1.97786e7			1.41696
$722$	437068.	+	1.77314e7i	0.0312037	+	1.26590i
$723$	−2.39141e7	+	2.39141e7i	−1.70141	+	1.70141i
$724$	−6.20502e6	−	5.62163e6i	−0.439943	−	0.398580i
$725$	1.41988e6	+	1.41988e6i	0.100324	+	0.100324i
$726$	1.83053e7	+	1.74246e7i	1.28895	+	1.22694i
$727$		−	2.73870e7i		−	1.92180i	−0.276894	−	0.960900i	$-0.589305\pi$
$727$		−	2.73870e7i		−	1.92180i	0.276894	−	0.960900i	$-0.410695\pi$
$728$	−9.94676e6	−	8.57489e6i	−0.695590	−	0.599653i
$729$		−	4.82580e6i		−	0.336318i
$730$	−1.80591e6	+	1.89719e6i	−0.125426	+	0.131766i
$731$	1.57383e7	+	1.57383e7i	1.08935	+	1.08935i
$732$	−1.00053e6	−	2.02828e7i	−0.0690161	−	1.39910i
$733$	−1.05278e6	+	1.05278e6i	−0.0723728	+	0.0723728i	−0.742367	−	0.669994i	$-0.766297\pi$
$733$	−1.05278e6	+	1.05278e6i	−0.0723728	+	0.0723728i	0.669994	+	0.742367i	$0.266297\pi$
$734$	41028.2	−	1011.32i	0.00281088	−	6.92866e-5i
$735$	4.38347e6			0.299295
$736$	1.93205e6	+	1.56000e7i	0.131469	+	1.06152i
$737$	−631769.			−0.0428439
$738$	2.90209e7	−	715349.i	1.96142	−	0.0483478i
$739$	−1.09564e6	+	1.09564e6i	−0.0737998	+	0.0737998i	−0.743043	−	0.669243i	$-0.766618\pi$
$739$	−1.09564e6	+	1.09564e6i	−0.0737998	+	0.0737998i	0.669243	+	0.743043i	$0.266618\pi$
$740$	−152117.	−	3.08374e6i	−0.0102117	−	0.207013i
$741$	−2.22089e7	−	2.22089e7i	−1.48587	−	1.48587i
$742$	−653304.	+	686326.i	−0.0435618	+	0.0457636i
$743$		−	4.23113e6i		−	0.281180i	−0.990068	−	0.140590i	$-0.955100\pi$
$743$		−	4.23113e6i		−	0.281180i	0.990068	−	0.140590i	$-0.0448999\pi$
$744$	3.03864e7	−	3.52478e7i	2.01255	−	2.33453i
$745$		−	1.27115e7i		−	0.839087i
$746$	−1.90105e7	−	1.80958e7i	−1.25068	−	1.19051i
$747$	−4.02313e7	−	4.02313e7i	−2.63793	−	2.63793i
$748$	−767925.	−	695725.i	−0.0501840	−	0.0454657i
$749$	2.15720e7	−	2.15720e7i	1.40503	−	1.40503i
$750$	60521.5	+	2.45529e6i	0.00392877	+	0.159386i
$751$	1.15236e7			0.745568			0.372784	−	0.927918i	$-0.378403\pi$
$751$	1.15236e7			0.745568			0.372784	+	0.927918i	$0.378403\pi$
$752$	−1.26292e7	+	1.24900e6i	−0.814386	+	0.0805414i
$753$	−2.79622e7			−1.79715
$754$	−213697.	−	8.66943e6i	−0.0136889	−	0.555344i
$755$	−1.57578e6	+	1.57578e6i	−0.100607	+	0.100607i
$756$	−2.59702e7	+	2.86653e7i	−1.65261	+	1.82412i
$757$	−3.45229e6	−	3.45229e6i	−0.218962	−	0.218962i	0.589099	−	0.808061i	$-0.299483\pi$
$757$	−3.45229e6	−	3.45229e6i	−0.218962	−	0.218962i	−0.808061	+	0.589099i	$0.799483\pi$
$758$	1.14569e7	+	1.09057e7i	0.724260	+	0.689414i
$759$			1.23857e6i			0.0780400i
$760$	−1.06910e7	+	791865.i	−0.671404	+	0.0497298i
$761$		−	1.60302e7i		−	1.00341i	−0.865040	−	0.501703i	$-0.832707\pi$
$761$		−	1.60302e7i		−	1.00341i	0.865040	−	0.501703i	$-0.167293\pi$
$762$	3.10339e7	−	3.26025e7i	1.93619	−	2.03406i
$763$	−1.40640e6	−	1.40640e6i	−0.0874578	−	0.0874578i
$764$	4.61759e6	−	227780.i	0.286208	−	0.0141183i
$765$	−1.84392e7	+	1.84392e7i	−1.13917	+	1.13917i
$766$	−5.23359e6	+	129005.i	−0.322276	+	0.00794392i
$767$	1.87538e6			0.115107
$768$	1.61679e7	−	2.42393e7i	0.989124	−	1.48292i
$769$	−1.30895e7			−0.798189			−0.399095	−	0.916910i	$-0.630675\pi$
$769$	−1.30895e7			−0.798189			−0.399095	+	0.916910i	$0.630675\pi$
$770$	−353084.	+	8703.33i	−0.0214611	+	0.000529004i
$771$	−7.75797e6	+	7.75797e6i	−0.470015	+	0.470015i
$772$	1.83280e7	−	904099.i	1.10681	−	0.0545975i
$773$	4.93181e6	+	4.93181e6i	0.296864	+	0.296864i	0.839784	−	0.542920i	$-0.182681\pi$
$773$	4.93181e6	+	4.93181e6i	0.296864	+	0.296864i	−0.542920	+	0.839784i	$0.682681\pi$
$774$	−2.32989e7	+	2.44766e7i	−1.39792	+	1.46858i
$775$		−	5.78254e6i		−	0.345831i
$776$	−1.45151e7	+	1.07511e6i	−0.865300	+	0.0640914i
$777$		−	1.63050e7i		−	0.968879i
$778$	8.36222e6	+	7.95989e6i	0.495305	+	0.471474i
$779$	1.62461e7	+	1.62461e7i	0.959191	+	0.959191i
$780$	7.12160e6	−	7.86066e6i	0.419123	−	0.462618i
$781$	−717071.	+	717071.i	−0.0420663	+	0.0420663i
$782$	745721.	+	3.02530e7i	0.0436073	+	1.76910i
$783$	−2.55422e7			−1.48886
$784$	−6.43021e6	+	635938.i	−0.373624	+	0.0369508i
$785$	−1.48071e6			−0.0857622
$786$	645434.	+	2.61845e7i	0.0372645	+	1.51178i
$787$	−2.31058e7	+	2.31058e7i	−1.32979	+	1.32979i	−0.424242	+	0.905549i	$0.639460\pi$
$787$	−2.31058e7	+	2.31058e7i	−1.32979	+	1.32979i	−0.905549	+	0.424242i	$0.860540\pi$
$788$	7.67957e6	+	6.95754e6i	0.440577	+	0.399154i
$789$	8.77788e6	+	8.77788e6i	0.501993	+	0.501993i
$790$	5.60987e6	+	5.33997e6i	0.319805	+	0.304418i
$791$		−	7.06773e6i		−	0.401642i
$792$	1.02725e6	−	1.19159e6i	0.0581917	−	0.0675016i
$793$			1.08975e7i			0.615380i
$794$	−1.23987e7	+	1.30254e7i	−0.697950	+	0.733228i
$795$	−541158.	−	541158.i	−0.0303673	−	0.0303673i
$796$	718012.	+	1.45556e7i	0.0401651	+	0.814231i
$797$	−9.91730e6	+	9.91730e6i	−0.553029	+	0.553029i	−0.927314	−	0.374285i	$-0.877888\pi$
$797$	−9.91730e6	+	9.91730e6i	−0.553029	+	0.553029i	0.374285	+	0.927314i	$0.377888\pi$
$798$	−5.65966e7	+	1.39508e6i	−3.14618	+	0.0775516i
$799$	−2.44321e7			−1.35392
$800$	−444984.	−	3.59294e6i	−0.0245821	−	0.198484i
$801$	3.20587e7			1.76549
$802$	1.52270e7	−	375337.i	0.835946	−	0.0206056i
$803$	215120.	−	215120.i	0.0117731	−	0.0117731i
$804$	−1.68497e6	−	3.41579e7i	−0.0919290	−	1.86359i
$805$	7.29367e6	+	7.29367e6i	0.396695	+	0.396695i
$806$	−1.72182e7	+	1.80885e7i	−0.933579	+	0.980766i
$807$			2.42450e7i			1.31050i
$808$	3.84154e6	+	3.31171e6i	0.207003	+	0.178453i
$809$		−	1.84026e7i		−	0.988569i	−0.869300	−	0.494284i	$-0.835430\pi$
$809$		−	1.84026e7i		−	0.988569i	0.869300	−	0.494284i	$-0.164570\pi$
$810$	−9.45811e6	−	9.00306e6i	−0.506515	−	0.482145i
$811$	6.67819e6	+	6.67819e6i	0.356539	+	0.356539i	0.862535	−	0.505997i	$-0.168875\pi$
$811$	6.67819e6	+	6.67819e6i	0.356539	+	0.356539i	−0.505997	+	0.862535i	$0.668875\pi$
$812$	−1.15844e7	−	1.04952e7i	−0.616570	−	0.558600i
$813$	−5.95274e6	+	5.95274e6i	−0.315857	+	0.315857i
$814$	8836.78	+	358498.i	0.000467448	+	0.0189638i
$815$	−4.21735e6			−0.222406
$816$	3.55678e7	−	4.33751e7i	1.86995	−	2.28042i
$817$	−2.67450e7			−1.40181
$818$	−87192.9	−	3.53732e6i	−0.00455615	−	0.184838i
$819$	2.71430e7	−	2.71430e7i	1.41400	−	1.41400i
$820$	−5.20955e6	+	5.75018e6i	−0.270561	+	0.298639i
$821$	4.76725e6	+	4.76725e6i	0.246837	+	0.246837i	0.819671	−	0.572834i	$-0.194156\pi$
$821$	4.76725e6	+	4.76725e6i	0.246837	+	0.246837i	−0.572834	+	0.819671i	$0.694156\pi$
$822$	9.37438e6	+	8.92336e6i	0.483908	+	0.460626i
$823$		−	1.24864e7i		−	0.642593i	−0.946979	−	0.321297i	$-0.895881\pi$
$823$		−	1.24864e7i		−	0.642593i	0.946979	−	0.321297i	$-0.104119\pi$
$824$	−1.73940e6	−	2.34836e7i	−0.0892443	−	1.20489i
$825$		−	285264.i		−	0.0145919i
$826$	2.33069e6	−	2.44850e6i	0.118860	−	0.124868i
$827$	−1.97584e7	−	1.97584e7i	−1.00459	−	1.00459i	−0.999989	−	0.00459995i	$-0.998536\pi$
$827$	−1.97584e7	−	1.97584e7i	−1.00459	−	1.00459i	−0.00459995	−	0.999989i	$-0.501464\pi$
$828$	−4.58904e7	+	2.26372e6i	−2.32619	+	0.114748i
$829$	−1.04021e7	+	1.04021e7i	−0.525695	+	0.525695i	−0.919286	−	0.393591i	$-0.871233\pi$
$829$	−1.04021e7	+	1.04021e7i	−0.525695	+	0.525695i	0.393591	+	0.919286i	$0.371233\pi$
$830$	1.52026e7	−	374735.i	0.765988	−	0.0188812i
$831$	−2.96304e7			−1.48845
$832$	−9.30644e6	+	1.25642e7i	−0.466096	+	0.629252i
$833$	−1.24397e7			−0.621153
$834$	4.77489e7	−	1.17698e6i	2.37711	−	0.0585944i
$835$	−2.14730e6	+	2.14730e6i	−0.106580	+	0.106580i
$836$	1.24363e6	−	61346.9i	0.0615426	−	0.00303583i
$837$	5.20109e7	+	5.20109e7i	2.56614	+	2.56614i
$838$	2.19024e7	−	2.30094e7i	1.07741	−	1.13187i
$839$		−	5.97699e6i		−	0.293142i	−0.989200	−	0.146571i	$-0.953176\pi$
$839$		−	5.97699e6i		−	0.293142i	0.989200	−	0.146571i	$-0.0468237\pi$
$840$	−1.41226e6	−	1.90670e7i	−0.0690586	−	0.932363i
$841$			1.01889e7i			0.496751i
$842$	−2.59492e7	−	2.47007e7i	−1.26137	−	1.20069i
$843$	3.59126e7	+	3.59126e7i	1.74052	+	1.74052i
$844$	−1.14196e7	+	1.26047e7i	−0.551817	+	0.609083i
$845$	2.53877e6	−	2.53877e6i	0.122316	−	0.122316i
$846$	−914079.	−	3.70831e7i	−0.0439094	−	1.78136i
$847$	−2.44457e7			−1.17083
$848$	872346.	+	715327.i	0.0416581	+	0.0341598i
$849$	4.42523e6			0.210701
$850$	−171752.	−	6.96779e6i	−0.00815370	−	0.330787i
$851$	7.40550e6	−	7.40550e6i	0.350534	−	0.350534i
$852$	−4.06825e7	−	3.68575e7i	−1.92003	−	1.73951i
$853$	17875.4	+	17875.4i	0.000841170	+	0.000841170i	0.707527	−	0.706686i	$-0.249811\pi$
$853$	17875.4	+	17875.4i	0.000841170	+	0.000841170i	−0.706686	+	0.707527i	$0.749811\pi$
$854$	1.42277e7	+	1.35432e7i	0.667562	+	0.635443i
$855$		−	3.13348e7i		−	1.46592i
$856$	−2.75101e7	−	2.37159e7i	−1.28324	−	1.10625i
$857$		−	1.76443e7i		−	0.820640i	−0.911942	−	0.410320i	$-0.865417\pi$
$857$		−	1.76443e7i		−	0.820640i	0.911942	−	0.410320i	$-0.134583\pi$
$858$	−849410.	+	892343.i	−0.0393912	+	0.0413822i
$859$	920994.	+	920994.i	0.0425867	+	0.0425867i	0.728079	−	0.685493i	$-0.240413\pi$
$859$	920994.	+	920994.i	0.0425867	+	0.0425867i	−0.685493	+	0.728079i	$0.740413\pi$
$860$	−445006.	−	9.02120e6i	−0.0205173	−	0.415928i
$861$	−2.89744e7	+	2.89744e7i	−1.33201	+	1.33201i
$862$	2.22679e7	−	548892.i	1.02073	−	0.0251605i
$863$	1.98421e7			0.906901			0.453450	−	0.891281i	$-0.350193\pi$
$863$	1.98421e7			0.906901			0.453450	+	0.891281i	$0.350193\pi$
$864$	3.63190e7	+	2.83142e7i	1.65520	+	1.29039i
$865$	−7.75408e6			−0.352363
$866$	2.16689e7	−	534126.i	0.981843	−	0.0242019i
$867$	4.84627e7	−	4.84627e7i	2.18957	−	2.18957i
$868$	2.21783e6	+	4.49602e7i	0.0999148	+	2.02548i
$869$	−636096.	−	636096.i	−0.0285742	−	0.0285742i
$870$	8.70472e6	−	9.14470e6i	0.389903	−	0.409611i
$871$			1.83523e7i			0.819682i
$872$	−1.54617e6	+	1.79354e6i	−0.0688600	+	0.0798767i
$873$		−	4.25431e7i		−	1.88927i
$874$	−2.63390e7	−	2.50717e7i	−1.16633	−	1.11021i
$875$	−1.67986e6	−	1.67986e6i	−0.0741740	−	0.0741740i
$876$	1.22046e7	+	1.10572e7i	0.537360	+	0.486837i
$877$	−2.55034e7	+	2.55034e7i	−1.11969	+	1.11969i	−0.127905	+	0.991786i	$0.540825\pi$
$877$	−2.55034e7	+	2.55034e7i	−1.11969	+	1.11969i	−0.991786	+	0.127905i	$0.959175\pi$
$878$	−187031.	−	7.58763e6i	−0.00818799	−	0.332177i
$879$	4.02010e7			1.75495
$880$	41385.1	+	418461.i	0.00180151	+	0.0182158i
$881$	−3.12202e7			−1.35518			−0.677588	−	0.735442i	$-0.736975\pi$
$881$	−3.12202e7			−1.35518			−0.677588	+	0.735442i	$0.736975\pi$
$882$	−465409.	−	1.88811e7i	−0.0201448	−	0.817252i
$883$	−751066.	+	751066.i	−0.0324173	+	0.0324173i	−0.723130	−	0.690712i	$-0.757297\pi$
$883$	−751066.	+	751066.i	−0.0324173	+	0.0324173i	0.690712	+	0.723130i	$0.257297\pi$
$884$	−2.02102e7	+	2.23075e7i	−0.869841	+	0.960110i
$885$	1.93061e6	+	1.93061e6i	0.0828582	+	0.0828582i
$886$	3.79957e6	+	3.61676e6i	0.162611	+	0.154787i
$887$			1.33534e6i			0.0569878i	0.999594	+	0.0284939i	$0.00907112\pi$
$887$			1.33534e6i			0.0569878i	−0.999594	+	0.0284939i	$0.990929\pi$
$888$	−1.93594e7	+	1.43392e6i	−0.823871	+	0.0610228i
$889$			4.35387e7i			1.84765i
$890$	−5.90786e6	+	6.20647e6i	−0.250009	+	0.262645i
$891$	1.07244e6	+	1.07244e6i	0.0452564	+	0.0452564i
$892$	−1.19138e7	+	587694.i	−0.501346	+	0.0247309i
$893$	2.07594e7	−	2.07594e7i	0.871136	−	0.871136i
$894$	−7.98988e7	+	1.96946e6i	−3.34346	+	0.0824145i
$895$	1.70240e7			0.710403
$896$	4.83786e6	+	2.77650e7i	0.201318	+	1.15539i
$897$	3.59794e7			1.49305
$898$	−1.79608e7	+	442724.i	−0.743250	+	0.0183207i
$899$	−2.10189e7	+	2.10189e7i	−0.867383	+	0.867383i
$900$	1.05693e7	−	521373.i	0.434952	−	0.0214557i
$901$	1.53574e6	+	1.53574e6i	0.0630238	+	0.0630238i
$902$	621354.	−	652761.i	0.0254286	−	0.0267139i
$903$		−	4.76989e7i		−	1.94666i
$904$	−8.39170e6	+	621560.i	−0.341530	+	0.0252966i
$905$			6.54131e6i			0.265487i
$906$	1.01488e7	+	9.66047e6i	0.410764	+	0.391001i
$907$	−1.98474e7	−	1.98474e7i	−0.801098	−	0.801098i	0.182169	−	0.983267i	$-0.441688\pi$
$907$	−1.98474e7	−	1.98474e7i	−0.801098	−	0.801098i	−0.983267	+	0.182169i	$0.941688\pi$
$908$	1.83277e7	−	2.02297e7i	0.737723	−	0.814281i
$909$	−1.04829e7	+	1.04829e7i	−0.420797	+	0.420797i
$910$	252824.	+	1.02568e7i	0.0101208	+	0.410589i
$911$	1.80547e7			0.720767			0.360383	−	0.932804i	$-0.382646\pi$
$911$	1.80547e7			0.720767			0.360383	+	0.932804i	$0.382646\pi$
$912$	6.63370e6	+	6.70760e7i	0.264100	+	2.67042i
$913$	−1.76629e6			−0.0701270
$914$	−615169.	−	2.49567e7i	−0.0243573	−	0.988147i
$915$	−1.12184e7	+	1.12184e7i	−0.442973	+	0.442973i
$916$	1.93951e7	+	1.75716e7i	0.763755	+	0.691947i
$917$	−1.79149e7	−	1.79149e7i	−0.703544	−	0.703544i
$918$	6.42165e7	+	6.11268e7i	2.51501	+	2.39400i
$919$			2.96410e7i			1.15772i	0.815426	+	0.578861i	$0.196503\pi$
$919$			2.96410e7i			1.15772i	−0.815426	+	0.578861i	$0.803497\pi$
$920$	8.01853e6	−	9.30139e6i	0.312338	−	0.362308i
$921$		−	2.79809e7i		−	1.08696i
$922$	1.54686e7	−	1.62505e7i	0.599272	−	0.629562i
$923$	2.08303e7	+	2.08303e7i	0.804805	+	0.804805i
$924$	109410.	+	2.21798e6i	0.00421578	+	0.0854627i
$925$	−1.70561e6	+	1.70561e6i	−0.0655430	+	0.0655430i
$926$	1.40131e7	−	345416.i	0.537042	−	0.0132378i
$927$	6.88294e7			2.63072
$928$	−1.14425e7	+	1.46774e7i	−0.436164	+	0.559473i
$929$	−8.63963e6			−0.328440			−0.164220	−	0.986424i	$-0.552511\pi$
$929$	−8.63963e6			−0.328440			−0.164220	+	0.986424i	$0.552511\pi$
$930$	−3.63464e7	+	895918.i	−1.37801	+	0.0339673i
$931$	1.05698e7	−	1.05698e7i	0.399660	−	0.399660i
$932$	−1.28614e6	−	2.60728e7i	−0.0485009	−	0.983215i
$933$	−9.03414e6	−	9.03414e6i	−0.339768	−	0.339768i
$934$	6.51813e6	−	6.84759e6i	0.244487	−	0.256845i
$935$			809543.i			0.0302838i
$936$	−3.46146e7	−	2.98406e7i	−1.29143	−	1.11331i
$937$			1.12375e7i			0.418138i	0.977901	+	0.209069i	$0.0670434\pi$
$937$			1.12375e7i			0.418138i	−0.977901	+	0.209069i	$0.932957\pi$
$938$	2.39608e7	+	2.28079e7i	0.889188	+	0.846406i
$939$	4.16098e7	+	4.16098e7i	1.54004	+	1.54004i
$940$	7.34763e6	+	6.65680e6i	0.271224	+	0.245723i
$941$	−2.30935e7	+	2.30935e7i	−0.850190	+	0.850190i	−0.990156	−	0.139966i	$-0.955301\pi$
$941$	−2.30935e7	+	2.30935e7i	−0.850190	+	0.850190i	0.139966	+	0.990156i	$0.455301\pi$
$942$	229414.	+	9.30706e6i	0.00842349	+	0.341732i
$943$	−2.63194e7			−0.963823
$944$	−3.11213e6	−	2.55196e6i	−0.113665	−	0.0932062i
$945$	3.02189e7			1.10077
$946$	25851.2	+	1.04875e6i	0.000939188	+	0.0381018i
$947$	1.68224e7	−	1.68224e7i	0.609557	−	0.609557i	−0.333274	−	0.942830i	$-0.608153\pi$
$947$	1.68224e7	−	1.68224e7i	0.609557	−	0.609557i	0.942830	+	0.333274i	$0.108153\pi$
$948$	3.26954e7	−	3.60884e7i	1.18159	−	1.30421i
$949$	−6.24904e6	−	6.24904e6i	−0.225241	−	0.225241i
$950$	6.06631e6	+	5.77444e6i	0.218080	+	0.207587i
$951$		−	3.21610e7i		−	1.15313i
$952$	4.00783e6	+	5.41098e7i	0.143323	+	1.93501i
$953$		−	2.32202e7i		−	0.828199i	−0.910232	−	0.414099i	$-0.864097\pi$
$953$		−	2.32202e7i		−	0.828199i	0.910232	−	0.414099i	$-0.135903\pi$
$954$	−2.27349e6	+	2.38841e6i	−0.0808766	+	0.0849645i
$955$	−2.55398e6	−	2.55398e6i	−0.0906170	−	0.0906170i
$956$	8.15712e6	−	402382.i	0.288664	−	0.0142395i
$957$	−1.03691e6	+	1.03691e6i	−0.0365981	+	0.0365981i
$958$	−5.55502e7	+	1.36928e6i	−1.95556	+	0.0482035i
$959$	−1.25189e7			−0.439562
$960$	−2.25146e7	+	3.35364e6i	−0.788471	+	0.117446i
$961$	5.69716e7			1.98999
$962$	1.04140e7	−	256701.i	0.362812	−	0.00894312i
$963$	7.50703e7	−	7.50703e7i	2.60857	−	2.60857i
$964$	−3.89003e7	+	1.91891e6i	−1.34822	+	0.0665060i
$965$	−1.01372e7	−	1.01372e7i	−0.350428	−	0.350428i
$966$	4.47146e7	−	4.69747e7i	1.54172	−	1.61965i
$967$			4.77137e7i			1.64088i	0.571731	+	0.820441i	$0.306272\pi$
$967$			4.77137e7i			1.64088i	−0.571731	+	0.820441i	$0.693728\pi$
$968$	2.14983e6	+	2.90250e7i	0.0737423	+	0.995597i
$969$			1.29763e8i			4.43959i
$970$	8.23621e6	+	7.83994e6i	0.281059	+	0.267537i
$971$	−2.29107e7	−	2.29107e7i	−0.779813	−	0.779813i	0.199986	−	0.979799i	$-0.435910\pi$
$971$	−2.29107e7	−	2.29107e7i	−0.779813	−	0.779813i	−0.979799	+	0.199986i	$0.935910\pi$
$972$	−1.36173e7	+	1.50304e7i	−0.462301	+	0.510277i
$973$	−3.26688e7	+	3.26688e7i	−1.10624	+	1.10624i
$974$	−286405.	−	1.16191e7i	−0.00967349	−	0.392443i
$975$	−8.28667e6			−0.279170
$976$	1.48290e7	−	1.80840e7i	0.498295	−	0.607673i
$977$	−5.07357e7			−1.70050			−0.850251	−	0.526377i	$-0.823550\pi$
$977$	−5.07357e7			−1.70050			−0.850251	+	0.526377i	$0.823550\pi$
$978$	653416.	+	2.65083e7i	0.0218445	+	0.886207i
$979$	703743.	−	703743.i	0.0234670	−	0.0234670i
$980$	3.74109e6	+	3.38935e6i	0.124432	+	0.112733i
$981$	−4.89427e6	−	4.89427e6i	−0.162374	−	0.162374i
$982$	−2.47690e7	−	2.35773e7i	−0.819653	−	0.780217i
$983$		−	6.51198e6i		−	0.214946i	−0.994208	−	0.107473i	$-0.965724\pi$
$983$		−	6.51198e6i		−	0.214946i	0.994208	−	0.107473i	$-0.0342759\pi$
$984$	3.69501e7	+	3.18539e7i	1.21654	+	1.04876i
$985$		−	8.09577e6i		−	0.265869i
$986$	−2.47029e7	+	2.59515e7i	−0.809199	+	0.850099i
$987$	3.70237e7	+	3.70237e7i	1.20973	+	1.20973i
$988$	−1.78207e6	−	3.61264e7i	−0.0580809	−	1.17742i
$989$	2.16641e7	−	2.16641e7i	0.704288	−	0.704288i
$990$	−1.22873e6	+	30287.5i	−0.0398445	+	0.000982145i
$991$	−5.04162e7			−1.63074			−0.815372	−	0.578938i	$-0.803467\pi$
$991$	−5.04162e7			−1.63074			−0.815372	+	0.578938i	$0.803467\pi$
$992$	5.31873e7	−	6.58724e6i	1.71605	−	0.212532i
$993$	−3.65634e7			−1.17672
$994$	5.30835e7	−	1.30848e6i	1.70409	−	0.0420050i
$995$	8.05069e6	−	8.05069e6i	0.257796	−	0.257796i
$996$	−4.71083e6	−	9.54984e7i	−0.150470	−	3.05034i
$997$	1.83995e7	+	1.83995e7i	0.586229	+	0.586229i	0.936608	−	0.350379i	$-0.113947\pi$
$997$	1.83995e7	+	1.83995e7i	0.586229	+	0.586229i	−0.350379	+	0.936608i	$0.613947\pi$
$998$	1.46037e7	−	1.53418e7i	0.464125	−	0.487584i
$999$		−	3.06822e7i		−	0.972686i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	80.6.l.a.21.2	✓	80
4.3	odd	2		320.6.l.a.241.3		80
16.3	odd	4		320.6.l.a.81.3		80
16.13	even	4	inner	80.6.l.a.61.2	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.6.l.a.21.2	✓	80	1.1	even	1	trivial
80.6.l.a.61.2	yes	80	16.13	even	4	inner
320.6.l.a.81.3		80	16.3	odd	4
320.6.l.a.241.3		80	4.3	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:	\( N \)	\(=\)	\( 80 = 2^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	80.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-5.65514 + 0.139396i) q^{2} +(19.6483 - 19.6483i) q^{3} +(31.9611 - 1.57661i) q^{4} +(-17.6777 - 17.6777i) q^{5} +(-108.375 + 113.853i) q^{6} -152.043i q^{7} +(-180.525 + 13.3712i) q^{8} -529.109i q^{9} +O(q^{10})\)	\(q+(-5.65514 + 0.139396i) q^{2} +(19.6483 - 19.6483i) q^{3} +(31.9611 - 1.57661i) q^{4} +(-17.6777 - 17.6777i) q^{5} +(-108.375 + 113.853i) q^{6} -152.043i q^{7} +(-180.525 + 13.3712i) q^{8} -529.109i q^{9} +(102.434 + 97.5054i) q^{10} +(-11.6148 - 11.6148i) q^{11} +(597.003 - 658.959i) q^{12} +(-337.401 + 337.401i) q^{13} +(21.1942 + 859.825i) q^{14} -694.671 q^{15} +(1019.03 - 100.780i) q^{16} +1971.39 q^{17} +(73.7557 + 2992.18i) q^{18} +(-1675.04 + 1675.04i) q^{19} +(-592.869 - 537.128i) q^{20} +(-2987.39 - 2987.39i) q^{21} +(67.3025 + 64.0644i) q^{22} -2713.65i q^{23} +(-3284.28 + 3809.72i) q^{24} +625.000i q^{25} +(1861.01 - 1955.08i) q^{26} +(-5621.55 - 5621.55i) q^{27} +(-239.712 - 4859.47i) q^{28} +(2271.81 - 2271.81i) q^{29} +(3928.46 - 96.8344i) q^{30} -9252.07 q^{31} +(-5748.70 + 711.975i) q^{32} -456.423 q^{33} +(-11148.5 + 274.804i) q^{34} +(-2687.77 + 2687.77i) q^{35} +(-834.197 - 16910.9i) q^{36} +(2728.98 + 2728.98i) q^{37} +(9239.11 - 9706.10i) q^{38} +13258.7i q^{39} +(3427.63 + 2954.89i) q^{40} -9698.90i q^{41} +(17310.5 + 16477.6i) q^{42} +(7983.39 + 7983.39i) q^{43} +(-389.535 - 352.911i) q^{44} +(-9353.41 + 9353.41i) q^{45} +(378.272 + 15346.1i) q^{46} -12393.3 q^{47} +(18042.0 - 22002.3i) q^{48} -6310.14 q^{49} +(-87.1225 - 3534.46i) q^{50} +(38734.4 - 38734.4i) q^{51} +(-10251.8 + 11315.7i) q^{52} +(779.013 + 779.013i) q^{53} +(32574.2 + 31007.0i) q^{54} +410.646i q^{55} +(2033.00 + 27447.6i) q^{56} +65823.4i q^{57} +(-12530.7 + 13164.1i) q^{58} +(-2779.17 - 2779.17i) q^{59} +(-22202.5 + 1095.22i) q^{60} +(16149.2 - 16149.2i) q^{61} +(52321.7 - 1289.70i) q^{62} -80447.4 q^{63} +(32410.4 - 4827.66i) q^{64} +11928.9 q^{65} +(2581.13 - 63.6235i) q^{66} +(27196.6 - 27196.6i) q^{67} +(63007.8 - 3108.10i) q^{68} +(-53318.6 - 53318.6i) q^{69} +(14825.0 - 15574.4i) q^{70} -61737.5i q^{71} +(7074.81 + 95517.3i) q^{72} +18521.1i q^{73} +(-15813.2 - 15052.4i) q^{74} +(12280.2 + 12280.2i) q^{75} +(-50895.4 + 56177.2i) q^{76} +(-1765.96 + 1765.96i) q^{77} +(-1848.21 - 74979.6i) q^{78} +54765.8 q^{79} +(-19795.6 - 16232.5i) q^{80} -92333.9 q^{81} +(1351.99 + 54848.6i) q^{82} +(76036.0 - 76036.0i) q^{83} +(-100190. - 90770.3i) q^{84} +(-34849.5 - 34849.5i) q^{85} +(-46260.0 - 44034.3i) q^{86} -89274.2i q^{87} +(2252.07 + 1941.46i) q^{88} +60590.0i q^{89} +(51591.0 - 54198.7i) q^{90} +(51299.5 + 51299.5i) q^{91} +(-4278.36 - 86731.4i) q^{92} +(-181787. + 181787. i) q^{93} +(70086.0 - 1727.58i) q^{94} +59221.7 q^{95} +(-98962.9 + 126941. i) q^{96} +80405.2 q^{97} +(35684.7 - 879.608i) q^{98} +(-6145.52 + 6145.52i) 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

Introduction

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