LMFDB - Embedded newform 80.6.l.a.61.9

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			61.9
Character	$\chi$	$=$	80.61
Dual form			80.6.l.a.21.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.43266 - 3.51447i) q^{2} +(11.6877 + 11.6877i) q^{3} +(7.29694 + 31.1569i) q^{4} +(-17.6777 + 17.6777i) q^{5} +(-10.7314 - 92.8834i) q^{6} -158.930i q^{7} +(77.1554 - 163.753i) q^{8} +30.2029i q^{9} +O(q^{10})$	\(q+(-4.43266 - 3.51447i) q^{2} +(11.6877 + 11.6877i) q^{3} +(7.29694 + 31.1569i) q^{4} +(-17.6777 + 17.6777i) q^{5} +(-10.7314 - 92.8834i) q^{6} -158.930i q^{7} +(77.1554 - 163.753i) q^{8} +30.2029i q^{9} +(140.487 - 16.2314i) q^{10} +(137.400 - 137.400i) q^{11} +(-278.868 + 449.436i) q^{12} +(743.018 + 743.018i) q^{13} +(-558.556 + 704.484i) q^{14} -413.221 q^{15} +(-917.509 + 454.701i) q^{16} +648.336 q^{17} +(106.147 - 133.879i) q^{18} +(1213.14 + 1213.14i) q^{19} +(-679.775 - 421.789i) q^{20} +(1857.52 - 1857.52i) q^{21} +(-1091.94 + 126.159i) q^{22} +2611.61i q^{23} +(2815.66 - 1012.12i) q^{24} -625.000i q^{25} +(-682.228 - 5904.86i) q^{26} +(2487.10 - 2487.10i) q^{27} +(4951.78 - 1159.70i) q^{28} +(2546.27 + 2546.27i) q^{29} +(1831.67 + 1452.26i) q^{30} +1694.67 q^{31} +(5665.04 + 1209.03i) q^{32} +3211.78 q^{33} +(-2873.85 - 2278.56i) q^{34} +(2809.52 + 2809.52i) q^{35} +(-941.031 + 220.389i) q^{36} +(-351.582 + 351.582i) q^{37} +(-1113.89 - 9641.02i) q^{38} +17368.3i q^{39} +(1530.84 + 4258.70i) q^{40} -11567.5i q^{41} +(-14762.0 + 1705.55i) q^{42} +(4162.74 - 4162.74i) q^{43} +(5283.57 + 3278.37i) q^{44} +(-533.917 - 533.917i) q^{45} +(9178.43 - 11576.4i) q^{46} -15044.7 q^{47} +(-16037.9 - 5409.15i) q^{48} -8451.82 q^{49} +(-2196.55 + 2770.41i) q^{50} +(7577.54 + 7577.54i) q^{51} +(-17728.4 + 28571.9i) q^{52} +(-13648.4 + 13648.4i) q^{53} +(-19765.3 + 2283.62i) q^{54} +4857.83i q^{55} +(-26025.3 - 12262.3i) q^{56} +28357.7i q^{57} +(-2337.95 - 20235.6i) q^{58} +(20038.2 - 20038.2i) q^{59} +(-3015.25 - 12874.7i) q^{60} +(8716.26 + 8716.26i) q^{61} +(-7511.89 - 5955.87i) q^{62} +4800.16 q^{63} +(-20862.1 - 25268.9i) q^{64} -26269.7 q^{65} +(-14236.7 - 11287.7i) q^{66} +(47288.8 + 47288.8i) q^{67} +(4730.87 + 20200.2i) q^{68} +(-30523.6 + 30523.6i) q^{69} +(-2579.66 - 22327.6i) q^{70} -80382.1i q^{71} +(4945.82 + 2330.32i) q^{72} +21977.6i q^{73} +(2794.07 - 322.817i) q^{74} +(7304.79 - 7304.79i) q^{75} +(-28945.6 + 46650.1i) q^{76} +(-21837.1 - 21837.1i) q^{77} +(61040.4 - 76987.7i) q^{78} +84815.5 q^{79} +(8181.38 - 24257.5i) q^{80} +65476.1 q^{81} +(-40653.8 + 51275.0i) q^{82} +(-34172.2 - 34172.2i) q^{83} +(71429.0 + 44320.5i) q^{84} +(-11461.1 + 11461.1i) q^{85} +(-33081.8 + 3822.16i) q^{86} +59520.0i q^{87} +(-11898.5 - 33100.9i) q^{88} -121103. i q^{89} +(490.235 + 4243.11i) q^{90} +(118088. - 118088. i) q^{91} +(-81369.7 + 19056.7i) q^{92} +(19806.7 + 19806.7i) q^{93} +(66688.0 + 52874.2i) q^{94} -42891.1 q^{95} +(52080.3 + 80341.8i) q^{96} -132139. q^{97} +(37464.1 + 29703.7i) q^{98} +(4149.89 + 4149.89i) 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 $

$2$	−4.43266	−	3.51447i	−0.783591	−	0.621277i
$2$	−4.43266	−	3.51447i	−0.783591	−	0.621277i
$3$	11.6877	+	11.6877i	0.749764	+	0.749764i	0.974435	−	0.224671i	$-0.0721307\pi$
$3$	11.6877	+	11.6877i	0.749764	+	0.749764i	−0.224671	+	0.974435i	$0.572131\pi$
$4$	7.29694	+	31.1569i	0.228029	+	0.973654i
$5$	−17.6777	+	17.6777i	−0.316228	+	0.316228i
$5$	−17.6777	+	17.6777i	−0.316228	+	0.316228i
$6$	−10.7314	−	92.8834i	−0.121697	−	1.05332i
$7$		−	158.930i		−	1.22592i	−0.790115	−	0.612959i	$-0.789979\pi$
$7$		−	158.930i		−	1.22592i	0.790115	−	0.612959i	$-0.210021\pi$
$8$	77.1554	−	163.753i	0.426227	−	0.904616i
$9$			30.2029i			0.124292i
$10$	140.487	−	16.2314i	0.444258	−	0.0513281i
$11$	137.400	−	137.400i	0.342378	−	0.342378i	−0.514883	−	0.857261i	$-0.672165\pi$
$11$	137.400	−	137.400i	0.342378	−	0.342378i	0.857261	+	0.514883i	$0.172165\pi$
$12$	−278.868	+	449.436i	−0.559043	+	0.900979i
$13$	743.018	+	743.018i	1.21939	+	1.21939i	0.967847	+	0.251538i	$0.0809363\pi$
$13$	743.018	+	743.018i	1.21939	+	1.21939i	0.251538	+	0.967847i	$0.419064\pi$
$14$	−558.556	+	704.484i	−0.761635	+	0.960618i
$15$	−413.221			−0.474192
$16$	−917.509	+	454.701i	−0.896005	+	0.444043i
$17$	648.336			0.544099			0.272050	−	0.962283i	$-0.412299\pi$
$17$	648.336			0.544099			0.272050	+	0.962283i	$0.412299\pi$
$18$	106.147	−	133.879i	0.0772197	−	0.0973940i
$19$	1213.14	+	1213.14i	0.770954	+	0.770954i	0.978273	−	0.207319i	$-0.0664739\pi$
$19$	1213.14	+	1213.14i	0.770954	+	0.770954i	−0.207319	+	0.978273i	$0.566474\pi$
$20$	−679.775	−	421.789i	−0.380006	−	0.235787i
$21$	1857.52	−	1857.52i	0.919149	−	0.919149i
$22$	−1091.94	+	126.159i	−0.480996	+	0.0555726i
$23$			2611.61i			1.02941i	0.857367	+	0.514705i	$0.172099\pi$
$23$			2611.61i			1.02941i	−0.857367	+	0.514705i	$0.827901\pi$
$24$	2815.66	−	1012.12i	0.997818	−	0.358679i
$25$		−	625.000i		−	0.200000i
$26$	−682.228	−	5904.86i	−0.197923	−	1.71308i
$27$	2487.10	−	2487.10i	0.656574	−	0.656574i
$28$	4951.78	−	1159.70i	1.19362	−	0.279545i
$29$	2546.27	+	2546.27i	0.562225	+	0.562225i	0.929939	−	0.367714i	$-0.119859\pi$
$29$	2546.27	+	2546.27i	0.562225	+	0.562225i	−0.367714	+	0.929939i	$0.619859\pi$
$30$	1831.67	+	1452.26i	0.371573	+	0.294605i
$31$	1694.67			0.316724			0.158362	−	0.987381i	$-0.449379\pi$
$31$	1694.67			0.316724			0.158362	+	0.987381i	$0.449379\pi$
$32$	5665.04	+	1209.03i	0.977976	+	0.208719i
$33$	3211.78			0.513405
$34$	−2873.85	−	2278.56i	−0.426351	−	0.338036i
$35$	2809.52	+	2809.52i	0.387669	+	0.387669i
$36$	−941.031	+	220.389i	−0.121017	+	0.0283422i
$37$	−351.582	+	351.582i	−0.0422204	+	0.0422204i	−0.727902	−	0.685681i	$-0.759504\pi$
$37$	−351.582	+	351.582i	−0.0422204	+	0.0422204i	0.685681	+	0.727902i	$0.259504\pi$
$38$	−1113.89	−	9641.02i	−0.125136	−	1.08309i
$39$			17368.3i			1.82850i
$40$	1530.84	+	4258.70i	0.151280	+	0.420850i
$41$		−	11567.5i		−	1.07469i	−0.843364	−	0.537343i	$-0.819428\pi$
$41$		−	11567.5i		−	1.07469i	0.843364	−	0.537343i	$-0.180572\pi$
$42$	−14762.0	+	1705.55i	−1.29128	+	0.149191i
$43$	4162.74	−	4162.74i	0.343327	−	0.343327i	−0.514290	−	0.857617i	$-0.671944\pi$
$43$	4162.74	−	4162.74i	0.343327	−	0.343327i	0.857617	+	0.514290i	$0.171944\pi$
$44$	5283.57	+	3278.37i	0.411430	+	0.255286i
$45$	−533.917	−	533.917i	−0.0393046	−	0.0393046i
$46$	9178.43	−	11576.4i	0.639549	−	0.806636i
$47$	−15044.7			−0.993434			−0.496717	−	0.867913i	$-0.665461\pi$
$47$	−15044.7			−0.993434			−0.496717	+	0.867913i	$0.665461\pi$
$48$	−16037.9	−	5409.15i	−1.00472	−	0.338865i
$49$	−8451.82			−0.502875
$50$	−2196.55	+	2770.41i	−0.124255	+	0.156718i
$51$	7577.54	+	7577.54i	0.407946	+	0.407946i
$52$	−17728.4	+	28571.9i	−0.909204	+	1.46532i
$53$	−13648.4	+	13648.4i	−0.667411	+	0.667411i	−0.957116	−	0.289705i	$-0.906443\pi$
$53$	−13648.4	+	13648.4i	−0.667411	+	0.667411i	0.289705	+	0.957116i	$0.406443\pi$
$54$	−19765.3	+	2283.62i	−0.922400	+	0.106571i
$55$			4857.83i			0.216539i
$56$	−26025.3	−	12262.3i	−1.10899	−	0.522520i
$57$			28357.7i			1.15607i
$58$	−2337.95	−	20235.6i	−0.0912568	−	0.789852i
$59$	20038.2	−	20038.2i	0.749425	−	0.749425i	−0.224946	−	0.974371i	$-0.572221\pi$
$59$	20038.2	−	20038.2i	0.749425	−	0.749425i	0.974371	+	0.224946i	$0.0722207\pi$
$60$	−3015.25	−	12874.7i	−0.108130	−	0.461699i
$61$	8716.26	+	8716.26i	0.299920	+	0.299920i	0.840982	−	0.541062i	$-0.181978\pi$
$61$	8716.26	+	8716.26i	0.299920	+	0.299920i	−0.541062	+	0.840982i	$0.681978\pi$
$62$	−7511.89	−	5955.87i	−0.248182	−	0.196773i
$63$	4800.16			0.152372
$64$	−20862.1	−	25268.9i	−0.636660	−	0.771144i
$65$	−26269.7			−0.771207
$66$	−14236.7	−	11287.7i	−0.402300	−	0.318967i
$67$	47288.8	+	47288.8i	1.28698	+	1.28698i	0.936614	+	0.350363i	$0.113942\pi$
$67$	47288.8	+	47288.8i	1.28698	+	1.28698i	0.350363	+	0.936614i	$0.386058\pi$
$68$	4730.87	+	20200.2i	0.124071	+	0.529765i
$69$	−30523.6	+	30523.6i	−0.771814	+	0.771814i
$70$	−2579.66	−	22327.6i	−0.0629241	−	0.544624i
$71$		−	80382.1i		−	1.89240i	−0.323578	−	0.946202i	$-0.604886\pi$
$71$		−	80382.1i		−	1.89240i	0.323578	−	0.946202i	$-0.395114\pi$
$72$	4945.82	+	2330.32i	0.112436	+	0.0529766i
$73$			21977.6i			0.482696i	0.970439	+	0.241348i	$0.0775896\pi$
$73$			21977.6i			0.482696i	−0.970439	+	0.241348i	$0.922410\pi$
$74$	2794.07	−	322.817i	0.0593141	−	0.00685295i
$75$	7304.79	−	7304.79i	0.149953	−	0.149953i
$76$	−28945.6	+	46650.1i	−0.574843	+	0.926443i
$77$	−21837.1	−	21837.1i	−0.419727	−	0.419727i
$78$	61040.4	−	76987.7i	1.13601	−	1.43280i
$79$	84815.5			1.52900			0.764500	−	0.644623i	$-0.222986\pi$
$79$	84815.5			1.52900			0.764500	+	0.644623i	$0.222986\pi$
$80$	8181.38	−	24257.5i	0.142923	−	0.423761i
$81$	65476.1			1.10884
$82$	−40653.8	+	51275.0i	−0.667677	+	0.842114i
$83$	−34172.2	−	34172.2i	−0.544474	−	0.544474i	0.380363	−	0.924837i	$-0.375799\pi$
$83$	−34172.2	−	34172.2i	−0.544474	−	0.544474i	−0.924837	+	0.380363i	$0.875799\pi$
$84$	71429.0	+	44320.5i	1.10453	+	0.685341i
$85$	−11461.1	+	11461.1i	−0.172059	+	0.172059i
$86$	−33081.8	+	3822.16i	−0.482329	+	0.0557267i
$87$			59520.0i			0.843072i
$88$	−11898.5	−	33100.9i	−0.163790	−	0.455651i
$89$		−	121103.i		−	1.62061i	−0.586008	−	0.810305i	$-0.699301\pi$
$89$		−	121103.i		−	1.62061i	0.586008	−	0.810305i	$-0.300699\pi$
$90$	490.235	+	4243.11i	0.00637967	+	0.0552177i
$91$	118088.	−	118088.i	1.49487	−	1.49487i
$92$	−81369.7	+	19056.7i	−1.00229	+	0.234736i
$93$	19806.7	+	19806.7i	0.237468	+	0.237468i
$94$	66688.0	+	52874.2i	0.778446	+	0.617198i
$95$	−42891.1			−0.487594
$96$	52080.3	+	80341.8i	0.576761	+	0.889741i
$97$	−132139.			−1.42595			−0.712973	−	0.701191i	$-0.752652\pi$
$97$	−132139.			−1.42595			−0.712973	+	0.701191i	$0.752652\pi$
$98$	37464.1	+	29703.7i	0.394048	+	0.312425i
$99$	4149.89	+	4149.89i	0.0425548	+	0.0425548i
$100$	19473.1	−	4560.59i	0.194731	−	0.0456059i
$101$	−119734.	+	119734.i	−1.16792	+	1.16792i	−0.185226	+	0.982696i	$0.559302\pi$
$101$	−119734.	+	119734.i	−1.16792	+	1.16792i	−0.982696	+	0.185226i	$0.940698\pi$
$102$	−6957.58	−	60219.7i	−0.0662152	−	0.573110i
$103$			155299.i			1.44237i	0.692743	+	0.721184i	$0.256402\pi$
$103$			155299.i			1.44237i	−0.692743	+	0.721184i	$0.743598\pi$
$104$	178999.	−	64343.6i	1.62281	−	0.583340i
$105$			65673.4i			0.581321i
$106$	108466.	−	12531.8i	0.937625	−	0.108330i
$107$	12010.2	−	12010.2i	0.101412	−	0.101412i	−0.654580	−	0.755993i	$-0.727155\pi$
$107$	12010.2	−	12010.2i	0.101412	−	0.101412i	0.755993	+	0.654580i	$0.227155\pi$
$108$	95638.6	+	59342.2i	0.788995	+	0.489558i
$109$	−168077.	−	168077.i	−1.35501	−	1.35501i	−0.879958	−	0.475052i	$-0.842429\pi$
$109$	−168077.	−	168077.i	−1.35501	−	1.35501i	−0.475052	−	0.879958i	$-0.657571\pi$
$110$	17072.7	−	21533.1i	0.134531	−	0.169678i
$111$	−8218.34			−0.0633106
$112$	72265.7	+	145820.i	0.544361	+	1.09843i
$113$	−81941.5			−0.603682			−0.301841	−	0.953358i	$-0.597601\pi$
$113$	−81941.5			−0.603682			−0.301841	+	0.953358i	$0.597601\pi$
$114$	99662.2	−	125700.i	0.718238	−	0.905884i
$115$	−46167.1	−	46167.1i	−0.325528	−	0.325528i
$116$	−60754.1	+	97914.1i	−0.419209	+	0.675616i
$117$	−22441.3	+	22441.3i	−0.151560	+	0.151560i
$118$	−159246.	+	18398.7i	−1.05284	+	0.121642i
$119$		−	103040.i		−	0.667021i
$120$	−31882.3	+	67666.2i	−0.202114	+	0.428962i
$121$			123293.i			0.765555i
$122$	−8003.14	−	69269.3i	−0.0486811	−	0.421348i
$123$	135197.	−	135197.i	0.805760	−	0.805760i
$124$	12365.9	+	52800.7i	0.0722223	+	0.308379i
$125$	11048.5	+	11048.5i	0.0632456	+	0.0632456i
$126$	−21277.5	−	16870.0i	−0.119397	−	0.0946651i
$127$	−48898.8			−0.269023			−0.134511	−	0.990912i	$-0.542946\pi$
$127$	−48898.8			−0.269023			−0.134511	+	0.990912i	$0.542946\pi$
$128$	3667.77	+	185328.i	0.0197869	+	0.999804i
$129$	97305.3			0.514828
$130$	116444.	+	92324.0i	0.604311	+	0.479133i
$131$	−5646.44	−	5646.44i	−0.0287472	−	0.0287472i	0.692587	−	0.721334i	$-0.256471\pi$
$131$	−5646.44	−	5646.44i	−0.0287472	−	0.0287472i	−0.721334	+	0.692587i	$0.756471\pi$
$132$	23436.1	+	100069.i	0.117071	+	0.499879i
$133$	192805.	−	192805.i	0.945127	−	0.945127i
$134$	−43419.8	−	375810.i	−0.208894	−	1.80803i
$135$			87932.3i			0.415254i
$136$	50022.7	−	106167.i	0.231910	−	0.492201i
$137$		−	125451.i		−	0.571048i	−0.958372	−	0.285524i	$-0.907832\pi$
$137$		−	125451.i		−	0.571048i	0.958372	−	0.285524i	$-0.0921677\pi$
$138$	242575.	−	28026.3i	1.08430	−	0.125276i
$139$	−49824.7	+	49824.7i	−0.218730	+	0.218730i	−0.807963	−	0.589233i	$-0.799430\pi$
$139$	−49824.7	+	49824.7i	−0.218730	+	0.218730i	0.589233	+	0.807963i	$0.299430\pi$
$140$	−67035.1	+	108037.i	−0.289056	+	0.465856i
$141$	−175837.	−	175837.i	−0.744841	−	0.744841i
$142$	−282501.	+	356307.i	−1.17571	+	1.48287i
$143$	204182.			0.834981
$144$	−13733.3	−	27711.5i	−0.0551910	−	0.111366i
$145$	−90024.4			−0.355582
$146$	77239.9	−	97419.4i	0.299888	−	0.378236i
$147$	−98782.1	−	98782.1i	−0.377038	−	0.377038i
$148$	−13519.7	−	8388.74i	−0.0507355	−	0.0314806i
$149$	59822.8	−	59822.8i	0.220750	−	0.220750i	−0.588064	−	0.808814i	$-0.700110\pi$
$149$	59822.8	−	59822.8i	0.220750	−	0.220750i	0.808814	+	0.588064i	$0.200110\pi$
$150$	−58052.1	+	6707.15i	−0.210664	+	0.0243394i
$151$		−	43983.6i		−	0.156981i	−0.996915	−	0.0784907i	$-0.974990\pi$
$151$		−	43983.6i		−	0.156981i	0.996915	−	0.0784907i	$-0.0250101\pi$
$152$	292257.	−	105055.i	1.02602	−	0.368816i
$153$			19581.7i			0.0676271i
$154$	20050.5	+	173542.i	0.0681275	+	0.589661i
$155$	−29957.8	+	29957.8i	−0.100157	+	0.100157i
$156$	−541143.	+	126735.i	−1.78033	+	0.416952i
$157$	−307828.	−	307828.i	−0.996688	−	0.996688i	0.00330636	−	0.999995i	$-0.498948\pi$
$157$	−307828.	−	307828.i	−0.996688	−	0.996688i	−0.999995	+	0.00330636i	$0.998948\pi$
$158$	−375958.	−	298082.i	−1.19811	−	0.949933i
$159$	−319037.			−1.00080
$160$	−121518.	+	78771.9i	−0.375266	+	0.243260i
$161$	415063.			1.26197
$162$	−290233.	−	230114.i	−0.868880	−	0.688899i
$163$	93121.7	+	93121.7i	0.274525	+	0.274525i	0.830919	−	0.556394i	$-0.187815\pi$
$163$	93121.7	+	93121.7i	0.274525	+	0.274525i	−0.556394	+	0.830919i	$0.687815\pi$
$164$	360409.	−	84407.6i	1.04637	−	0.245060i
$165$	−56776.7	+	56776.7i	−0.162353	+	0.162353i
$166$	31376.4	+	271571.i	0.0883756	+	0.764915i
$167$			435223.i			1.20759i	0.797138	+	0.603797i	$0.206346\pi$
$167$			435223.i			1.20759i	−0.797138	+	0.603797i	$0.793654\pi$
$168$	−160857.	−	447493.i	−0.439710	−	1.22324i
$169$			732859.i			1.97380i
$170$	91082.7	−	10523.4i	0.241721	−	0.0279276i
$171$	−36640.5	+	36640.5i	−0.0958234	+	0.0958234i
$172$	160073.	+	99322.9i	0.412570	+	0.255993i
$173$	−330292.	−	330292.i	−0.839039	−	0.839039i	0.149693	−	0.988732i	$-0.452171\pi$
$173$	−330292.	−	330292.i	−0.839039	−	0.839039i	−0.988732	+	0.149693i	$0.952171\pi$
$174$	209181.	−	263832.i	0.523781	−	0.660623i
$175$	−99331.4			−0.245184
$176$	−63590.0	+	188542.i	−0.154742	+	0.458803i
$177$	468399.			1.12378
$178$	−425612.	+	536807.i	−1.00685	+	1.26990i
$179$	−131457.	−	131457.i	−0.306656	−	0.306656i	0.536955	−	0.843611i	$-0.319575\pi$
$179$	−131457.	−	131457.i	−0.306656	−	0.306656i	−0.843611	+	0.536955i	$0.819575\pi$
$180$	12739.3	−	20531.2i	0.0293065	−	0.0472316i
$181$	−252957.	+	252957.i	−0.573918	+	0.573918i	−0.933221	−	0.359303i	$-0.883015\pi$
$181$	−252957.	+	252957.i	−0.573918	+	0.573918i	0.359303	+	0.933221i	$0.383015\pi$
$182$	−938462.	+	108427.i	−2.10009	+	0.242637i
$183$			203745.i			0.449739i
$184$	427659.	+	201500.i	0.931221	+	0.438763i
$185$		−	12430.3i		−	0.0267025i
$186$	−18186.2	−	157407.i	−0.0385443	−	0.333611i
$187$	89081.6	−	89081.6i	0.186288	−	0.186288i
$188$	−109780.	−	468747.i	−0.226532	−	0.967261i
$189$	−395275.	−	395275.i	−0.804906	−	0.804906i
$190$	190122.	+	150740.i	0.382074	+	0.302931i
$191$	156118.			0.309648			0.154824	−	0.987942i	$-0.450519\pi$
$191$	156118.			0.309648			0.154824	+	0.987942i	$0.450519\pi$
$192$	51504.9	−	539163.i	0.100831	−	1.05552i
$193$	879287.			1.69917			0.849586	−	0.527450i	$-0.176852\pi$
$193$	879287.			1.69917			0.849586	+	0.527450i	$0.176852\pi$
$194$	585729.	+	464401.i	1.11736	+	0.885908i
$195$	−307031.	−	307031.i	−0.578223	−	0.578223i
$196$	−61672.5	−	263333.i	−0.114670	−	0.489627i
$197$	−395423.	+	395423.i	−0.725934	+	0.725934i	−0.969807	−	0.243874i	$-0.921582\pi$
$197$	−395423.	+	395423.i	−0.725934	+	0.725934i	0.243874	+	0.969807i	$0.421582\pi$
$198$	−3810.37	−	32979.7i	−0.00690723	−	0.0597839i
$199$			193051.i			0.345573i	0.984959	+	0.172787i	$0.0552771\pi$
$199$			193051.i			0.345573i	−0.984959	+	0.172787i	$0.944723\pi$
$200$	−102346.	−	48222.1i	−0.180923	−	0.0852455i
$201$			1.10539e6i			1.92986i
$202$	951542.	−	109938.i	1.64078	−	0.189570i
$203$	404680.	−	404680.i	0.689242	−	0.689242i
$204$	−180800.	+	291386.i	−0.304175	+	0.490222i
$205$	204487.	+	204487.i	0.339845	+	0.339845i
$206$	545795.	−	688389.i	0.896111	−	1.13023i
$207$	−78878.2			−0.127947
$208$	−1.01958e6	−	343875.i	−1.63404	−	0.551116i
$209$	333373.			0.527915
$210$	230807.	−	291108.i	0.361161	−	0.455518i
$211$	−42750.3	−	42750.3i	−0.0661049	−	0.0661049i	0.673281	−	0.739386i	$-0.264884\pi$
$211$	−42750.3	−	42750.3i	−0.0661049	−	0.0661049i	−0.739386	+	0.673281i	$0.764884\pi$
$212$	−524836.	−	325652.i	−0.802017	−	0.497639i
$213$	939479.	−	939479.i	1.41886	−	1.41886i
$214$	−95446.7	+	11027.6i	−0.142471	+	0.0164606i
$215$			147175.i			0.217139i
$216$	−215377.	−	599163.i	−0.314098	−	0.873798i
$217$		−	269334.i		−	0.388277i
$218$	154326.	+	1.33573e6i	0.219937	+	1.90361i
$219$	−256867.	+	256867.i	−0.361908	+	0.361908i
$220$	−151355.	+	35447.3i	−0.210834	+	0.0493772i
$221$	481726.	+	481726.i	0.663467	+	0.663467i
$222$	36429.1	+	28883.1i	0.0496096	+	0.0393335i
$223$	415872.			0.560012			0.280006	−	0.959998i	$-0.409664\pi$
$223$	415872.			0.560012			0.280006	+	0.959998i	$0.409664\pi$
$224$	192152.	−	900346.i	0.255873	−	1.19892i
$225$	18876.8			0.0248584
$226$	363219.	+	287981.i	0.473039	+	0.375054i
$227$	315776.	+	315776.i	0.406738	+	0.406738i	0.880599	−	0.473861i	$-0.157140\pi$
$227$	315776.	+	315776.i	0.406738	+	0.406738i	−0.473861	+	0.880599i	$0.657140\pi$
$228$	−883538.	+	206924.i	−1.12561	+	0.263617i
$229$	−378838.	+	378838.i	−0.477381	+	0.477381i	−0.904293	−	0.426912i	$-0.859601\pi$
$229$	−378838.	+	378838.i	−0.477381	+	0.477381i	0.426912	+	0.904293i	$0.359601\pi$
$230$	42390.0	+	366896.i	0.0528377	+	0.457324i
$231$		−	510448.i		−	0.629393i
$232$	613419.	−	220501.i	0.748233	−	0.268962i
$233$			30826.5i			0.0371992i	0.999827	+	0.0185996i	$0.00592078\pi$
$233$			30826.5i			0.0371992i	−0.999827	+	0.0185996i	$0.994079\pi$
$234$	178344.	−	20605.3i	0.212921	−	0.0246002i
$235$	265955.	−	265955.i	0.314151	−	0.314151i
$236$	770545.	+	478111.i	0.900572	+	0.558790i
$237$	991295.	+	991295.i	1.14639	+	1.14639i
$238$	−362132.	+	456742.i	−0.414405	+	0.522672i
$239$	−1.41615e6			−1.60367			−0.801836	−	0.597544i	$-0.796143\pi$
$239$	−1.41615e6			−1.60367			−0.801836	+	0.597544i	$0.796143\pi$
$240$	379134.	−	187892.i	0.424879	−	0.210562i
$241$	479173.			0.531434			0.265717	−	0.964051i	$-0.414391\pi$
$241$	479173.			0.531434			0.265717	+	0.964051i	$0.414391\pi$
$242$	433311.	−	546517.i	0.475622	−	0.599882i
$243$	160897.	+	160897.i	0.174796	+	0.174796i
$244$	−207970.	+	335174.i	−0.223628	+	0.360409i
$245$	149409.	−	149409.i	0.159023	−	0.159023i
$246$	−1.07443e6	+	124136.i	−1.13199	+	0.130786i
$247$			1.80278e6i			1.88018i
$248$	130753.	−	277507.i	0.134996	−	0.286513i
$249$		−	798786.i		−	0.816454i
$250$	−10144.6	−	87804.3i	−0.0102656	−	0.0888517i
$251$	1.07714e6	−	1.07714e6i	1.07917	−	1.07917i	0.0825809	−	0.996584i	$-0.473684\pi$
$251$	1.07714e6	−	1.07714e6i	1.07917	−	1.07917i	0.996584	−	0.0825809i	$-0.0263163\pi$
$252$	35026.5	+	149558.i	0.0347452	+	0.148357i
$253$	358835.	+	358835.i	0.352447	+	0.352447i
$254$	216752.	+	171854.i	0.210804	+	0.167138i
$255$	−267906.			−0.258008
$256$	635071.	−	834384.i	0.605651	−	0.795731i
$257$	−687917.			−0.649685			−0.324843	−	0.945768i	$-0.605311\pi$
$257$	−687917.			−0.649685			−0.324843	+	0.945768i	$0.605311\pi$
$258$	−431321.	−	341977.i	−0.403415	−	0.319851i
$259$	55877.0	+	55877.0i	0.0517587	+	0.0517587i
$260$	−191688.	−	818482.i	−0.175858	−	0.750889i
$261$	−76904.9	+	76904.9i	−0.0698800	+	0.0698800i
$262$	5184.47	+	44873.0i	0.00466607	+	0.0403861i
$263$			742587.i			0.662000i	0.943631	+	0.331000i	$0.107386\pi$
$263$			742587.i			0.662000i	−0.943631	+	0.331000i	$0.892614\pi$
$264$	247806.	−	525938.i	0.218827	−	0.464435i
$265$		−	482546.i		−	0.422108i
$266$	−1.53225e6	+	177031.i	−1.32778	+	0.153407i
$267$	1.41541e6	−	1.41541e6i	1.21508	−	1.21508i
$268$	−1.12831e6	+	1.81844e6i	−0.959602	+	1.54654i
$269$	−1.01173e6	−	1.01173e6i	−0.852481	−	0.852481i	0.137957	−	0.990438i	$-0.455946\pi$
$269$	−1.01173e6	−	1.01173e6i	−0.852481	−	0.852481i	−0.990438	+	0.137957i	$0.955946\pi$
$270$	309036.	−	389774.i	0.257988	−	0.325389i
$271$	−539293.			−0.446068			−0.223034	−	0.974811i	$-0.571596\pi$
$271$	−539293.			−0.446068			−0.223034	+	0.974811i	$0.571596\pi$
$272$	−594855.	+	294799.i	−0.487516	+	0.241604i
$273$	2.76035e6			2.24159
$274$	−440894.	+	556082.i	−0.354779	+	0.447468i
$275$	−85875.1	−	85875.1i	−0.0684756	−	0.0684756i
$276$	−1.17375e6	−	728293.i	−0.927477	−	0.575484i
$277$	1.64818e6	−	1.64818e6i	1.29064	−	1.29064i	0.356249	−	0.934391i	$-0.384056\pi$
$277$	1.64818e6	−	1.64818e6i	1.29064	−	1.29064i	0.934391	−	0.356249i	$-0.115944\pi$
$278$	395964.	−	45748.3i	0.307286	−	0.0355028i
$279$			51183.9i			0.0393662i
$280$	676836.	−	243297.i	0.515927	−	0.185457i
$281$		−	899791.i		−	0.679792i	−0.940463	−	0.339896i	$-0.889608\pi$
$281$		−	899791.i		−	0.679792i	0.940463	−	0.339896i	$-0.110392\pi$
$282$	161451.	+	1.39740e6i	0.120898	+	1.04640i
$283$	−1.75527e6	+	1.75527e6i	−1.30280	+	1.30280i	−0.376301	+	0.926498i	$0.622804\pi$
$283$	−1.75527e6	+	1.75527e6i	−1.30280	+	1.30280i	−0.926498	+	0.376301i	$0.877196\pi$
$284$	2.50446e6	−	586544.i	1.84255	−	0.431523i
$285$	−501297.	−	501297.i	−0.365581	−	0.365581i
$286$	−905068.	−	717591.i	−0.654284	−	0.518755i
$287$	−1.83843e6			−1.31748
$288$	−36516.3	+	171101.i	−0.0259421	+	0.121554i
$289$	−999517.			−0.703956
$290$	399047.	+	316388.i	0.278631	+	0.220915i
$291$	−1.54440e6	−	1.54440e6i	−1.06912	−	1.06912i
$292$	−684756.	+	160370.i	−0.469979	+	0.110069i
$293$	−1.45385e6	+	1.45385e6i	−0.989350	+	0.989350i	−0.999944	−	0.0105935i	$-0.996628\pi$
$293$	−1.45385e6	+	1.45385e6i	−0.989350	+	0.989350i	0.0105935	+	0.999944i	$0.496628\pi$
$294$	90700.2	+	785034.i	0.0611984	+	0.529688i
$295$			708456.i			0.473978i
$296$	30446.1	+	84699.0i	0.0201977	+	0.0561887i
$297$		−	683456.i		−	0.449593i
$298$	−475420.	+	54928.4i	−0.310125	+	0.0358308i
$299$	−1.94047e6	+	1.94047e6i	−1.25525	+	1.25525i
$300$	280897.	+	174292.i	0.180196	+	0.111809i
$301$	−661585.	−	661585.i	−0.420891	−	0.420891i
$302$	−154579.	+	194964.i	−0.0975289	+	0.123009i
$303$	−2.79882e6			−1.75133
$304$	−1.66469e6	−	561454.i	−1.03312	−	0.348442i
$305$	−308166.			−0.189686
$306$	68819.3	−	86798.8i	0.0420152	−	0.0529920i
$307$	−763222.	−	763222.i	−0.462173	−	0.462173i	0.437194	−	0.899367i	$-0.355972\pi$
$307$	−763222.	−	763222.i	−0.462173	−	0.462173i	−0.899367	+	0.437194i	$0.855972\pi$
$308$	521032.	−	839719.i	0.312959	−	0.504379i
$309$	−1.81508e6	+	1.81508e6i	−1.08144	+	1.08144i
$310$	238079.	−	27506.8i	0.140707	−	0.0162568i
$311$			1.47977e6i			0.867549i	0.901021	+	0.433775i	$0.142819\pi$
$311$			1.47977e6i			0.867549i	−0.901021	+	0.433775i	$0.857181\pi$
$312$	2.84411e6	+	1.34006e6i	1.65409	+	0.779358i
$313$		−	1.66057e6i		−	0.958067i	−0.877797	−	0.479034i	$-0.840987\pi$
$313$		−	1.66057e6i		−	0.958067i	0.877797	−	0.479034i	$-0.159013\pi$
$314$	282643.	+	2.44635e6i	0.161776	+	1.40022i
$315$	−84855.6	+	84855.6i	−0.0481842	+	0.0481842i
$316$	618894.	+	2.64259e6i	0.348657	+	1.48872i
$317$	827202.	+	827202.i	0.462342	+	0.462342i	0.899423	−	0.437080i	$-0.143987\pi$
$317$	827202.	+	827202.i	0.462342	+	0.462342i	−0.437080	+	0.899423i	$0.643987\pi$
$318$	1.41418e6	+	1.12125e6i	0.784219	+	0.621775i
$319$	699717.			0.384987
$320$	815488.	+	77901.5i	0.445187	+	0.0425276i
$321$	280742.			0.152071
$322$	−1.83983e6	−	1.45873e6i	−0.988870	−	0.784034i
$323$	786526.	+	786526.i	0.419476	+	0.419476i
$324$	477775.	+	2.04003e6i	0.252849	+	1.07963i
$325$	464386.	−	464386.i	0.243877	−	0.243877i
$326$	−85503.0	−	740051.i	−0.0445592	−	0.385672i
$327$		−	3.92886e6i		−	2.03187i
$328$	−1.89422e6	−	892498.i	−0.972178	−	0.458060i
$329$			2.39106e6i			1.21787i
$330$	451212.	−	52131.5i	0.228085	−	0.0263521i
$331$	980690.	−	980690.i	0.491996	−	0.491996i	−0.416938	−	0.908935i	$-0.636897\pi$
$331$	980690.	−	980690.i	0.491996	−	0.491996i	0.908935	+	0.416938i	$0.136897\pi$
$332$	815348.	−	1.31405e6i	0.405974	−	0.654286i
$333$	−10618.8	−	10618.8i	−0.00524765	−	0.00524765i
$334$	1.52958e6	−	1.92920e6i	0.750250	−	0.946259i
$335$	−1.67191e6			−0.813956
$336$	−859678.	+	2.54891e6i	−0.415420	+	1.23170i
$337$	−3.61743e6			−1.73510			−0.867551	−	0.497349i	$-0.834307\pi$
$337$	−3.61743e6			−1.73510			−0.867551	+	0.497349i	$0.834307\pi$
$338$	2.57561e6	−	3.24851e6i	1.22628	−	1.54665i
$339$	−957705.	−	957705.i	−0.452619	−	0.452619i
$340$	−440723.	−	273461.i	−0.206761	−	0.128292i
$341$	232848.	−	232848.i	0.108439	−	0.108439i
$342$	291187.	−	33642.8i	0.134619	−	0.0155534i
$343$		−	1.32789e6i		−	0.609434i
$344$	−360483.	−	1.00284e6i	−0.164244	−	0.456914i
$345$		−	1.07917e6i		−	0.488138i
$346$	303269.	+	2.62487e6i	0.136188	+	1.17874i
$347$	2.91142e6	−	2.91142e6i	1.29802	−	1.29802i	0.368322	−	0.929698i	$-0.379932\pi$
$347$	2.91142e6	−	2.91142e6i	1.29802	−	1.29802i	0.929698	−	0.368322i	$-0.120068\pi$
$348$	−1.85446e6	+	434314.i	−0.820861	+	0.192245i
$349$	−1.50734e6	−	1.50734e6i	−0.662440	−	0.662440i	0.293515	−	0.955955i	$-0.405175\pi$
$349$	−1.50734e6	−	1.50734e6i	−0.662440	−	0.662440i	−0.955955	+	0.293515i	$0.905175\pi$
$350$	440302.	+	349098.i	0.192124	+	0.152327i
$351$	3.69592e6			1.60123
$352$	944499.	−	612257.i	0.406298	−	0.263376i
$353$	1.04810e6			0.447677			0.223839	−	0.974626i	$-0.428141\pi$
$353$	1.04810e6			0.447677			0.223839	+	0.974626i	$0.428141\pi$
$354$	−2.07625e6	−	1.64618e6i	−0.880586	−	0.698181i
$355$	1.42097e6	+	1.42097e6i	0.598430	+	0.598430i
$356$	3.77319e6	−	883679.i	1.57791	−	0.369547i
$357$	1.20430e6	−	1.20430e6i	0.500108	−	0.500108i
$358$	120702.	+	1.04471e6i	0.0497746	+	0.430812i
$359$		−	2.43835e6i		−	0.998528i	−0.866450	−	0.499264i	$-0.833604\pi$
$359$		−	2.43835e6i		−	0.998528i	0.866450	−	0.499264i	$-0.166396\pi$
$360$	−128625.	+	46236.0i	−0.0523082	+	0.0188029i
$361$			467341.i			0.188741i
$362$	2.01028e6	−	232261.i	0.806279	−	0.0931548i
$363$	−1.44101e6	+	1.44101e6i	−0.573985	+	0.573985i
$364$	4.54094e6	+	2.81758e6i	1.79636	+	1.11461i
$365$	−388514.	−	388514.i	−0.152642	−	0.152642i
$366$	716058.	−	903134.i	0.279412	−	0.352411i
$367$	2.50919e6			0.972451			0.486225	−	0.873833i	$-0.338373\pi$
$367$	2.50919e6			0.972451			0.486225	+	0.873833i	$0.338373\pi$
$368$	−1.18750e6	−	2.39617e6i	−0.457103	−	0.922357i
$369$	349374.			0.133575
$370$	−43686.0	+	55099.3i	−0.0165897	+	0.0209238i
$371$	2.16915e6	+	2.16915e6i	0.818192	+	0.818192i
$372$	−472588.	+	761645.i	−0.177062	+	0.285361i
$373$	2.21861e6	−	2.21861e6i	0.825675	−	0.825675i	−0.161240	−	0.986915i	$-0.551549\pi$
$373$	2.21861e6	−	2.21861e6i	0.825675	−	0.825675i	0.986915	+	0.161240i	$0.0515493\pi$
$374$	−707943.	+	81793.4i	−0.261709	+	0.0302370i
$375$			258263.i			0.0948385i
$376$	−1.16078e6	+	2.46361e6i	−0.423429	+	0.898676i
$377$			3.78385e6i			1.37114i
$378$	362936.	+	3.14131e6i	0.130647	+	1.13079i
$379$	−753371.	+	753371.i	−0.269408	+	0.269408i	−0.828862	−	0.559454i	$-0.811011\pi$
$379$	−753371.	+	753371.i	−0.269408	+	0.269408i	0.559454	+	0.828862i	$0.311011\pi$
$380$	−312974.	−	1.33636e6i	−0.111186	−	0.474748i
$381$	−571513.	−	571513.i	−0.201703	−	0.201703i
$382$	−692017.	−	548672.i	−0.242638	−	0.192378i
$383$	2.85916e6			0.995958			0.497979	−	0.867189i	$-0.334076\pi$
$383$	2.85916e6			0.995958			0.497979	+	0.867189i	$0.334076\pi$
$384$	−2.12318e6	+	2.20891e6i	−0.734782	+	0.764453i
$385$	772056.			0.265459
$386$	−3.89758e6	−	3.09023e6i	−1.33146	−	1.05566i
$387$	125727.	+	125727.i	0.0426728	+	0.0426728i
$388$	−964214.	−	4.11706e6i	−0.325158	−	1.38838i
$389$	−1.16610e6	+	1.16610e6i	−0.390715	+	0.390715i	−0.874942	−	0.484227i	$-0.839101\pi$
$389$	−1.16610e6	+	1.16610e6i	−0.390715	+	0.390715i	0.484227	+	0.874942i	$0.339101\pi$
$390$	281911.	+	2.44002e6i	0.0938536	+	0.812327i
$391$			1.69320e6i			0.560101i
$392$	−652104.	+	1.38401e6i	−0.214339	+	0.454909i
$393$		−	131987.i		−	0.0431073i
$394$	3.14248e6	−	363072.i	1.01984	−	0.117829i
$395$	−1.49934e6	+	1.49934e6i	−0.483513	+	0.483513i
$396$	−99016.4	+	159579.i	−0.0317299	+	0.0511374i
$397$	3.45127e6	+	3.45127e6i	1.09901	+	1.09901i	0.994526	+	0.104485i	$0.0333196\pi$
$397$	3.45127e6	+	3.45127e6i	1.09901	+	1.09901i	0.104485	+	0.994526i	$0.466680\pi$
$398$	678474.	−	855731.i	0.214697	−	0.270788i
$399$	4.50689e6			1.41724
$400$	284188.	+	573443.i	0.0888087	+	0.179201i
$401$	−4.27920e6			−1.32893			−0.664465	−	0.747320i	$-0.731340\pi$
$401$	−4.27920e6			−1.32893			−0.664465	+	0.747320i	$0.731340\pi$
$402$	3.88486e6	−	4.89982e6i	1.19898	−	1.51222i
$403$	1.25917e6	+	1.25917e6i	0.386208	+	0.386208i
$404$	−4.60423e6	−	2.85685e6i	−1.40347	−	0.870832i
$405$	−1.15746e6	+	1.15746e6i	−0.350647	+	0.350647i
$406$	−3.21605e6	+	371571.i	−0.968294	+	0.111873i
$407$			96614.9i			0.0289107i
$408$	1.82549e6	−	656196.i	0.542912	−	0.195157i
$409$			939276.i			0.277642i	0.990317	+	0.138821i	$0.0443312\pi$
$409$			939276.i			0.277642i	−0.990317	+	0.138821i	$0.955669\pi$
$410$	−187757.	−	1.62509e6i	−0.0551616	−	0.477438i
$411$	1.46623e6	−	1.46623e6i	0.428151	−	0.428151i
$412$	−4.83865e6	+	1.13321e6i	−1.40437	+	0.328902i
$413$	−3.18467e6	−	3.18467e6i	−0.918733	−	0.918733i
$414$	349640.	+	277215.i	0.100258	+	0.0794907i
$415$	1.20817e6			0.344356
$416$	3.31090e6	+	5.10756e6i	0.938020	+	1.44704i
$417$	−1.16467e6			−0.327991
$418$	−1.47773e6	−	1.17163e6i	−0.413670	−	0.327982i
$419$	801198.	+	801198.i	0.222949	+	0.222949i	0.809739	−	0.586790i	$-0.199609\pi$
$419$	801198.	+	801198.i	0.222949	+	0.222949i	−0.586790	+	0.809739i	$0.699609\pi$
$420$	−2.04618e6	+	479215.i	−0.566006	+	0.132558i
$421$	−3.09877e6	+	3.09877e6i	−0.852088	+	0.852088i	−0.990390	−	0.138302i	$-0.955835\pi$
$421$	−3.09877e6	+	3.09877e6i	−0.852088	+	0.852088i	0.138302	+	0.990390i	$0.455835\pi$
$422$	39252.7	+	339743.i	0.0107297	+	0.0928686i
$423$		−	454394.i		−	0.123476i
$424$	1.18192e6	+	3.28803e6i	0.319282	+	0.888220i
$425$		−	405210.i		−	0.108820i
$426$	−7.46617e6	+	862616.i	−1.99331	+	0.230300i
$427$	1.38528e6	−	1.38528e6i	0.367677	−	0.367677i
$428$	461839.	+	286563.i	0.121866	+	0.0756156i
$429$	2.38641e6	+	2.38641e6i	0.626039	+	0.626039i
$430$	517243.	−	652376.i	0.134903	−	0.170148i
$431$	3.88577e6			1.00759			0.503795	−	0.863823i	$-0.331937\pi$
$431$	3.88577e6			1.00759			0.503795	+	0.863823i	$0.331937\pi$
$432$	−1.15105e6	+	3.41282e6i	−0.296746	+	0.879842i
$433$	−3.66645e6			−0.939780			−0.469890	−	0.882725i	$-0.655706\pi$
$433$	−3.66645e6			−0.939780			−0.469890	+	0.882725i	$0.655706\pi$
$434$	−946568.	+	1.19387e6i	−0.241228	+	0.304250i
$435$	−1.05217e6	−	1.05217e6i	−0.266603	−	0.266603i
$436$	4.01032e6	−	6.46322e6i	1.01033	−	1.62829i
$437$	−3.16826e6	+	3.16826e6i	−0.793628	+	0.793628i
$438$	2.04136e6	−	235852.i	0.508433	−	0.0587427i
$439$		−	5.04597e6i		−	1.24964i	−0.780770	−	0.624818i	$-0.785173\pi$
$439$		−	5.04597e6i		−	1.24964i	0.780770	−	0.624818i	$-0.214827\pi$
$440$	795484.	+	374808.i	0.195884	+	0.0922948i
$441$		−	255270.i		−	0.0625033i
$442$	−442313.	−	3.82834e6i	−0.107690	−	0.932083i
$443$	−4.20429e6	+	4.20429e6i	−1.01785	+	1.01785i	−0.0180102	+	0.999838i	$0.505733\pi$
$443$	−4.20429e6	+	4.20429e6i	−1.01785	+	1.01785i	−0.999838	+	0.0180102i	$0.994267\pi$
$444$	−59968.7	−	256058.i	−0.0144367	−	0.0616427i
$445$	2.14081e6	+	2.14081e6i	0.512482	+	0.512482i
$446$	−1.84342e6	−	1.46157e6i	−0.438820	−	0.347922i
$447$	1.39838e6			0.331021
$448$	−4.01599e6	+	3.31562e6i	−0.945360	+	0.780493i
$449$	−859414.			−0.201181			−0.100590	−	0.994928i	$-0.532073\pi$
$449$	−859414.			−0.201181			−0.100590	+	0.994928i	$0.532073\pi$
$450$	−83674.6	−	66342.2i	−0.0194788	−	0.0154439i
$451$	−1.58938e6	−	1.58938e6i	−0.367949	−	0.367949i
$452$	−597922.	−	2.55305e6i	−0.137657	−	0.587777i
$453$	514065.	−	514065.i	0.117699	−	0.117699i
$454$	−289941.	−	2.50952e6i	−0.0660192	−	0.571413i
$455$			4.17504e6i			0.945437i
$456$	4.64365e6	+	2.18795e6i	1.04580	+	0.492748i
$457$		−	1.05972e6i		−	0.237357i	−0.992933	−	0.118679i	$-0.962134\pi$
$457$		−	1.05972e6i		−	0.237357i	0.992933	−	0.118679i	$-0.0378658\pi$
$458$	3.01068e6	−	347844.i	0.670657	−	0.0774855i
$459$	1.61248e6	−	1.61248e6i	0.357242	−	0.357242i
$460$	1.10155e6	−	1.77531e6i	0.242722	−	0.391182i
$461$	2.46745e6	+	2.46745e6i	0.540750	+	0.540750i	0.923749	−	0.382999i	$-0.125109\pi$
$461$	2.46745e6	+	2.46745e6i	0.540750	+	0.540750i	−0.382999	+	0.923749i	$0.625109\pi$
$462$	−1.79396e6	+	2.26264e6i	−0.391027	+	0.493186i
$463$	1.06094e6			0.230006			0.115003	−	0.993365i	$-0.463312\pi$
$463$	1.06094e6			0.230006			0.115003	+	0.993365i	$0.463312\pi$
$464$	−3.49402e6	−	1.17844e6i	−0.753409	−	0.254104i
$465$	−700273.			−0.150188
$466$	108339.	−	136643.i	0.0231110	−	0.0291490i
$467$	−1.62579e6	−	1.62579e6i	−0.344963	−	0.344963i	0.513266	−	0.858229i	$-0.328435\pi$
$467$	−1.62579e6	−	1.62579e6i	−0.344963	−	0.344963i	−0.858229	+	0.513266i	$0.828435\pi$
$468$	−862956.	−	535450.i	−0.182127	−	0.113007i
$469$	7.51561e6	−	7.51561e6i	1.57773	−	1.57773i
$470$	−2.11358e6	+	244196.i	−0.441341	+	0.0509911i
$471$		−	7.19559e6i		−	1.49456i
$472$	−1.73526e6	−	4.82736e6i	−0.358516	−	0.997367i
$473$		−	1.14392e6i		−	0.235095i
$474$	−910193.	−	7.87796e6i	−0.186075	−	1.61053i
$475$	758215.	−	758215.i	0.154191	−	0.154191i
$476$	3.21042e6	−	751879.i	0.649448	−	0.152100i
$477$	−412223.	−	412223.i	−0.0829538	−	0.0829538i
$478$	6.27732e6	+	4.97703e6i	1.25662	+	0.996325i
$479$	−2.23239e6			−0.444560			−0.222280	−	0.974983i	$-0.571350\pi$
$479$	−2.23239e6			−0.444560			−0.222280	+	0.974983i	$0.571350\pi$
$480$	−2.34092e6	−	499597.i	−0.463749	−	0.0989730i
$481$	−522463.			−0.102966
$482$	−2.12401e6	−	1.68404e6i	−0.416427	−	0.330168i
$483$	4.85112e6	+	4.85112e6i	0.946181	+	0.946181i
$484$	−3.84144e6	+	899664.i	−0.745386	+	0.174569i
$485$	2.33592e6	−	2.33592e6i	0.450924	−	0.450924i
$486$	−147733.	−	1.27867e6i	−0.0283719	−	0.245566i
$487$			453105.i			0.0865718i	0.999063	+	0.0432859i	$0.0137826\pi$
$487$			453105.i			0.0865718i	−0.999063	+	0.0432859i	$0.986217\pi$
$488$	2.09982e6	−	754807.i	0.399147	−	0.143478i
$489$			2.17675e6i			0.411658i
$490$	−1.18737e6	+	137185.i	−0.223407	+	0.0258116i
$491$	−4.56248e6	+	4.56248e6i	−0.854077	+	0.854077i	−0.990632	−	0.136555i	$-0.956397\pi$
$491$	−4.56248e6	+	4.56248e6i	−0.854077	+	0.854077i	0.136555	+	0.990632i	$0.456397\pi$
$492$	5.19887e6	+	3.22581e6i	0.968269	+	0.600795i
$493$	1.65084e6	+	1.65084e6i	0.305906	+	0.305906i
$494$	6.33581e6	−	7.99110e6i	1.16811	−	1.47329i
$495$	−146721.			−0.0269140
$496$	−1.55487e6	+	770566.i	−0.283786	+	0.140639i
$497$	−1.27752e7			−2.31993
$498$	−2.80731e6	+	3.54075e6i	−0.507244	+	0.639766i
$499$	2.47751e6	+	2.47751e6i	0.445413	+	0.445413i	0.893826	−	0.448413i	$-0.148011\pi$
$499$	2.47751e6	+	2.47751e6i	0.445413	+	0.445413i	−0.448413	+	0.893826i	$0.648011\pi$
$500$	−263618.	+	424859.i	−0.0471575	+	0.0760011i
$501$	−5.08674e6	+	5.08674e6i	−0.905410	+	0.905410i
$502$	−8.56018e6	+	989014.i	−1.51608	+	0.175163i
$503$			2.63380e6i			0.464155i	0.972697	+	0.232077i	$0.0745523\pi$
$503$			2.63380e6i			0.464155i	−0.972697	+	0.232077i	$0.925448\pi$
$504$	370358.	−	786041.i	0.0649450	−	0.137838i
$505$		−	4.23323e6i		−	0.738659i
$506$	−329477.	−	2.85171e6i	−0.0572070	−	0.495142i
$507$	−8.56541e6	+	8.56541e6i	−1.47989	+	1.47989i
$508$	−356812.	−	1.52354e6i	−0.0613451	−	0.261935i
$509$	4.14738e6	+	4.14738e6i	0.709544	+	0.709544i	0.966439	−	0.256895i	$-0.0826995\pi$
$509$	4.14738e6	+	4.14738e6i	0.709544	+	0.709544i	−0.256895	+	0.966439i	$0.582700\pi$
$510$	1.18754e6	+	941550.i	0.202172	+	0.160294i
$511$	3.49291e6			0.591746
$512$	−5.74747e6	+	1.46660e6i	−0.968952	+	0.247250i
$513$	6.03442e6			1.01238
$514$	3.04930e6	+	2.41767e6i	0.509087	+	0.403635i
$515$	−2.74533e6	−	2.74533e6i	−0.456117	−	0.456117i
$516$	710031.	+	3.03174e6i	0.117396	+	0.501265i
$517$	−2.06715e6	+	2.06715e6i	−0.340130	+	0.340130i
$518$	−51305.4	−	444062.i	−0.00840115	−	0.0727142i
$519$		−	7.72067e6i		−	1.25816i
$520$	−2.02685e6	+	4.30173e6i	−0.328710	+	0.697646i
$521$			4.21798e6i			0.680785i	0.940284	+	0.340392i	$0.110560\pi$
$521$			4.21798e6i			0.680785i	−0.940284	+	0.340392i	$0.889440\pi$
$522$	611174.	−	70613.0i	0.0981722	−	0.0113425i
$523$	−3.72307e6	+	3.72307e6i	−0.595179	+	0.595179i	−0.939026	−	0.343847i	$-0.888270\pi$
$523$	−3.72307e6	+	3.72307e6i	−0.595179	+	0.595179i	0.343847	+	0.939026i	$0.388270\pi$
$524$	134724.	−	217127.i	0.0214347	−	0.0345451i
$525$	−1.16095e6	−	1.16095e6i	−0.183830	−	0.183830i
$526$	2.60980e6	−	3.29164e6i	0.411286	−	0.518737i
$527$	1.09872e6			0.172329
$528$	−2.94683e6	+	1.46040e6i	−0.460014	+	0.227974i
$529$	−384150.			−0.0596846
$530$	−1.69589e6	+	2.13896e6i	−0.262246	+	0.330760i
$531$	605212.	+	605212.i	0.0931474	+	0.0931474i
$532$	7.41411e6	+	4.60034e6i	1.13574	+	0.704710i
$533$	8.59489e6	−	8.59489e6i	1.31046	−	1.31046i
$534$	−1.12484e7	+	1.29961e6i	−1.70702	+	0.197223i
$535$			424625.i			0.0641388i
$536$	1.13923e7	−	4.09509e6i	1.71277	−	0.615675i
$537$		−	3.07286e6i		−	0.459840i
$538$	928957.	+	8.04037e6i	0.138369	+	1.19762i
$539$	−1.16128e6	+	1.16128e6i	−0.172173	+	0.172173i
$540$	−2.73970e6	+	641636.i	−0.404314	+	0.0946901i
$541$	−9.06672e6	−	9.06672e6i	−1.33186	−	1.33186i	−0.903710	−	0.428146i	$-0.859167\pi$
$541$	−9.06672e6	−	9.06672e6i	−1.33186	−	1.33186i	−0.428146	−	0.903710i	$-0.640833\pi$
$542$	2.39050e6	+	1.89533e6i	0.349535	+	0.277132i
$543$	−5.91295e6			−0.860606
$544$	3.67285e6	+	783859.i	0.532116	+	0.113564i
$545$	5.94242e6			0.856983
$546$	−1.22357e7	−	9.70117e6i	−1.75649	−	1.39265i
$547$	4.89258e6	+	4.89258e6i	0.699148	+	0.699148i	0.964227	−	0.265079i	$-0.0853979\pi$
$547$	4.89258e6	+	4.89258e6i	0.699148	+	0.699148i	−0.265079	+	0.964227i	$0.585398\pi$
$548$	3.90867e6	−	915409.i	0.556004	−	0.130216i
$549$	−263257.	+	263257.i	−0.0372776	+	0.0372776i
$550$	78849.3	+	682461.i	0.0111145	+	0.0961992i
$551$			6.17800e6i			0.866899i
$552$	2.64327e6	+	7.35339e6i	0.369227	+	1.02716i
$553$		−	1.34798e7i		−	1.87443i
$554$	−1.30983e7	+	1.51333e6i	−1.81318	+	0.209489i
$555$	145281.	−	145281.i	0.0200206	−	0.0200206i
$556$	−1.91595e6	−	1.18882e6i	−0.262844	−	0.163090i
$557$	9.38556e6	+	9.38556e6i	1.28181	+	1.28181i	0.939639	+	0.342167i	$0.111161\pi$
$557$	9.38556e6	+	9.38556e6i	1.28181	+	1.28181i	0.342167	+	0.939639i	$0.388839\pi$
$558$	179885.	−	226881.i	0.0244573	−	0.0308470i
$559$	6.18598e6			0.837296
$560$	−3.85525e6	−	1.30027e6i	−0.519496	−	0.175212i
$561$	2.08231e6			0.279343
$562$	−3.16229e6	+	3.98847e6i	−0.422339	+	0.532679i
$563$	−9.63950e6	−	9.63950e6i	−1.28169	−	1.28169i	−0.939705	−	0.341987i	$-0.888900\pi$
$563$	−9.63950e6	−	9.63950e6i	−1.28169	−	1.28169i	−0.341987	−	0.939705i	$-0.611100\pi$
$564$	4.19548e6	−	6.76163e6i	0.555372	−	0.895063i
$565$	1.44854e6	−	1.44854e6i	0.190901	−	0.190901i
$566$	1.39493e7	−	1.61166e6i	1.83026	−	0.211462i
$567$		−	1.04061e7i		−	1.35935i
$568$	−1.31628e7	−	6.20192e6i	−1.71190	−	0.806594i
$569$		−	5.64345e6i		−	0.730742i	−0.930862	−	0.365371i	$-0.880942\pi$
$569$		−	5.64345e6i		−	0.730742i	0.930862	−	0.365371i	$-0.119058\pi$
$570$	460284.	+	3.98388e6i	0.0593387	+	0.513592i
$571$	9.76836e6	−	9.76836e6i	1.25381	−	1.25381i	0.299810	−	0.953999i	$-0.403077\pi$
$571$	9.76836e6	−	9.76836e6i	1.25381	−	1.25381i	0.953999	−	0.299810i	$-0.0969234\pi$
$572$	1.48990e6	+	6.36168e6i	0.190400	+	0.812983i
$573$	1.82465e6	+	1.82465e6i	0.232163	+	0.232163i
$574$	8.14914e6	+	6.46112e6i	1.03236	+	0.818518i
$575$	1.63225e6			0.205882
$576$	763194.	−	630096.i	0.0958470	−	0.0791317i
$577$	−380585.			−0.0475896			−0.0237948	−	0.999717i	$-0.507575\pi$
$577$	−380585.			−0.0475896			−0.0237948	+	0.999717i	$0.507575\pi$
$578$	4.43052e6	+	3.51278e6i	0.551614	+	0.437352i
$579$	1.02768e7	+	1.02768e7i	1.27398	+	1.27398i
$580$	−656902.	−	2.80488e6i	−0.0810832	−	0.346214i
$581$	−5.43099e6	+	5.43099e6i	−0.667481	+	0.667481i
$582$	1.41805e6	+	1.22736e7i	0.173533	+	1.50198i
$583$			3.75060e6i			0.457014i
$584$	3.59891e6	+	1.69569e6i	0.436655	+	0.205738i
$585$		−	793421.i		−	0.0958548i
$586$	1.15539e7	−	1.33490e6i	1.38991	−	0.160585i
$587$	−616594.	+	616594.i	−0.0738591	+	0.0738591i	−0.743071	−	0.669212i	$-0.766632\pi$
$587$	−616594.	+	616594.i	−0.0738591	+	0.0738591i	0.669212	+	0.743071i	$0.266632\pi$
$588$	2.35694e6	−	3.79855e6i	0.281129	−	0.453080i
$589$	2.05588e6	+	2.05588e6i	0.244179	+	0.244179i
$590$	2.48985e6	−	3.14035e6i	0.294472	−	0.371405i
$591$	−9.24315e6			−1.08856
$592$	162715.	−	482444.i	0.0190820	−	0.0565774i
$593$	−8.64591e6			−1.00966			−0.504829	−	0.863220i	$-0.668444\pi$
$593$	−8.64591e6			−1.00966			−0.504829	+	0.863220i	$0.668444\pi$
$594$	−2.40199e6	+	3.02953e6i	−0.279322	+	0.352297i
$595$	1.82151e6	+	1.82151e6i	0.210931	+	0.210931i
$596$	2.30042e6	+	1.42737e6i	0.265272	+	0.164597i
$597$	−2.25632e6	+	2.25632e6i	−0.259098	+	0.259098i
$598$	1.54212e7	−	1.78171e6i	1.76346	−	0.203744i
$599$		−	1.88849e6i		−	0.215054i	−0.994202	−	0.107527i	$-0.965707\pi$
$599$		−	1.88849e6i		−	0.215054i	0.994202	−	0.107527i	$-0.0342932\pi$
$600$	−632577.	−	1.75979e6i	−0.0717357	−	0.199564i
$601$		−	5.80779e6i		−	0.655881i	−0.944698	−	0.327940i	$-0.893646\pi$
$601$		−	5.80779e6i		−	0.655881i	0.944698	−	0.327940i	$-0.106354\pi$
$602$	607457.	+	5.25770e6i	0.0683163	+	0.591296i
$603$	−1.42826e6	+	1.42826e6i	−0.159961	+	0.159961i
$604$	1.37039e6	−	320945.i	0.152846	−	0.0357964i
$605$	−2.17954e6	−	2.17954e6i	−0.242090	−	0.242090i
$606$	1.24062e7	+	9.83638e6i	1.37233	+	1.08806i
$607$	−1.31092e7			−1.44413			−0.722064	−	0.691827i	$-0.756806\pi$
$607$	−1.31092e7			−1.44413			−0.722064	+	0.691827i	$0.756806\pi$
$608$	5.40578e6	+	8.33924e6i	0.593061	+	0.914887i
$609$	9.45952e6			1.03354
$610$	1.36600e6	+	1.08304e6i	0.148636	+	0.117848i
$611$	−1.11785e7	−	1.11785e7i	−1.21138	−	1.21138i
$612$	−610105.	+	142886.i	−0.0658454	+	0.0154210i
$613$	5.27786e6	−	5.27786e6i	0.567292	−	0.567292i	−0.364077	−	0.931369i	$-0.618615\pi$
$613$	5.27786e6	−	5.27786e6i	0.567292	−	0.567292i	0.931369	+	0.364077i	$0.118615\pi$
$614$	700779.	+	6.06542e6i	0.0750170	+	0.649292i
$615$			4.77995e6i			0.509608i
$616$	−5.26073e6	+	1.89104e6i	−0.558591	+	0.200793i
$617$			1.36911e7i			1.44786i	0.689874	+	0.723929i	$0.257666\pi$
$617$			1.36911e7i			1.44786i	−0.689874	+	0.723929i	$0.742334\pi$
$618$	1.44247e7	−	1.66658e6i	1.51927	−	0.175532i
$619$	4.17112e6	−	4.17112e6i	0.437548	−	0.437548i	−0.453638	−	0.891186i	$-0.649874\pi$
$619$	4.17112e6	−	4.17112e6i	0.437548	−	0.437548i	0.891186	+	0.453638i	$0.149874\pi$
$620$	−1.15199e6	−	714793.i	−0.120357	−	0.0746794i
$621$	6.49533e6	+	6.49533e6i	0.675884	+	0.675884i
$622$	5.20062e6	−	6.55933e6i	0.538989	−	0.679804i
$623$	−1.92469e7			−1.98674
$624$	−7.89737e6	−	1.59356e7i	−0.811935	−	1.63835i
$625$	−390625.			−0.0400000
$626$	−5.83603e6	+	7.36074e6i	−0.595225	+	0.750733i
$627$	3.89635e6	+	3.89635e6i	0.395812	+	0.395812i
$628$	7.34478e6	−	1.18372e7i	0.743156	−	1.19770i
$629$	−227943.	+	227943.i	−0.0229721	+	0.0229721i
$630$	674359.	−	77913.2i	0.0676924	−	0.00782095i
$631$		−	8.20739e6i		−	0.820601i	−0.911950	−	0.410300i	$-0.865424\pi$
$631$		−	8.20739e6i		−	0.820601i	0.911950	−	0.410300i	$-0.134576\pi$
$632$	6.54398e6	−	1.38888e7i	0.651702	−	1.38316i
$633$		−	999303.i		−	0.0991261i
$634$	−759525.	−	6.57389e6i	−0.0750445	−	0.649530i
$635$	864417.	−	864417.i	0.0850724	−	0.0850724i
$636$	−2.32799e6	−	9.94021e6i	−0.228212	−	0.974435i
$637$	−6.27986e6	−	6.27986e6i	−0.613199	−	0.613199i
$638$	−3.10161e6	−	2.45914e6i	−0.301672	−	0.239183i
$639$	2.42778e6			0.235210
$640$	−3.34100e6	−	3.21132e6i	−0.322423	−	0.309909i
$641$	7.38569e6			0.709980			0.354990	−	0.934870i	$-0.384484\pi$
$641$	7.38569e6			0.709980			0.354990	+	0.934870i	$0.384484\pi$
$642$	−1.24444e6	−	986662.i	−0.119161	−	0.0944780i
$643$	−8.17794e6	−	8.17794e6i	−0.780039	−	0.780039i	0.199798	−	0.979837i	$-0.435971\pi$
$643$	−8.17794e6	−	8.17794e6i	−0.780039	−	0.780039i	−0.979837	+	0.199798i	$0.935971\pi$
$644$	3.02869e6	+	1.29321e7i	0.287767	+	1.22872i
$645$	−1.72013e6	+	1.72013e6i	−0.162803	+	0.162803i
$646$	−722176.	−	6.25063e6i	−0.0680866	−	0.589308i
$647$		−	1.75318e7i		−	1.64651i	−0.567670	−	0.823256i	$-0.692155\pi$
$647$		−	1.75318e7i		−	1.64651i	0.567670	−	0.823256i	$-0.307845\pi$
$648$	5.05183e6	−	1.07219e7i	0.472620	−	1.00308i
$649$		−	5.50650e6i		−	0.513173i
$650$	−3.69054e6	+	426393.i	−0.342615	+	0.0395846i
$651$	3.14789e6	−	3.14789e6i	0.291116	−	0.291116i
$652$	−2.22188e6	+	3.58089e6i	−0.204693	+	0.329892i
$653$	6.90508e6	+	6.90508e6i	0.633703	+	0.633703i	0.948995	−	0.315292i	$-0.102102\pi$
$653$	6.90508e6	+	6.90508e6i	0.633703	+	0.633703i	−0.315292	+	0.948995i	$0.602102\pi$
$654$	−1.38079e7	+	1.74153e7i	−1.26236	+	1.59216i
$655$	199632.			0.0181814
$656$	5.25977e6	+	1.06133e7i	0.477207	+	0.962924i
$657$	−663789.			−0.0599953
$658$	8.40331e6	−	1.05987e7i	0.756634	−	0.954311i
$659$	−5.69848e6	−	5.69848e6i	−0.511147	−	0.511147i	0.403731	−	0.914878i	$-0.367713\pi$
$659$	−5.69848e6	−	5.69848e6i	−0.511147	−	0.511147i	−0.914878	+	0.403731i	$0.867713\pi$
$660$	−2.18328e6	−	1.35469e6i	−0.195097	−	0.121054i
$661$	−9.53996e6	+	9.53996e6i	−0.849265	+	0.849265i	−0.990041	−	0.140777i	$-0.955040\pi$
$661$	−9.53996e6	+	9.53996e6i	−0.849265	+	0.849265i	0.140777	+	0.990041i	$0.455040\pi$
$662$	−7.79368e6	+	900455.i	−0.691190	+	0.0798578i
$663$			1.12605e7i			0.994887i
$664$	−8.23236e6	+	2.95923e6i	−0.724610	+	0.260470i
$665$			6.81670e6i			0.597751i
$666$	9750.03	+	84389.1i	0.000851766	+	0.00737226i
$667$	−6.64987e6	+	6.64987e6i	−0.578760	+	0.578760i
$668$	−1.35602e7	+	3.17580e6i	−1.17578	+	0.275367i
$669$	4.86057e6	+	4.86057e6i	0.419877	+	0.419877i
$670$	7.41101e6	+	5.87588e6i	0.637808	+	0.505692i
$671$	2.39523e6			0.205372
$672$	1.27687e7	−	8.27714e6i	1.09075	−	0.707061i
$673$	−1.77045e7			−1.50677			−0.753384	−	0.657580i	$-0.771580\pi$
$673$	−1.77045e7			−1.50677			−0.753384	+	0.657580i	$0.771580\pi$
$674$	1.60348e7	+	1.27134e7i	1.35961	+	1.07798i
$675$	−1.55444e6	−	1.55444e6i	−0.131315	−	0.131315i
$676$	−2.28336e7	+	5.34763e6i	−1.92180	+	0.450085i
$677$	1.22868e7	−	1.22868e7i	1.03030	−	1.03030i	0.0307780	−	0.999526i	$-0.490201\pi$
$677$	1.22868e7	−	1.22868e7i	1.03030	−	1.03030i	0.999526	−	0.0307780i	$-0.00979850\pi$
$678$	879350.	+	7.61101e6i	0.0734662	+	0.635870i
$679$			2.10010e7i			1.74809i
$680$	992502.	+	2.76107e6i	0.0823112	+	0.228984i
$681$			7.38137e6i			0.609915i
$682$	−1.85047e6	+	213797.i	−0.152343	+	0.0176012i
$683$	4.08331e6	−	4.08331e6i	0.334935	−	0.334935i	−0.519522	−	0.854457i	$-0.673890\pi$
$683$	4.08331e6	−	4.08331e6i	0.334935	−	0.334935i	0.854457	+	0.519522i	$0.173890\pi$
$684$	−1.40897e6	−	874243.i	−0.115149	−	0.0714483i
$685$	2.21768e6	+	2.21768e6i	0.180581	+	0.180581i
$686$	−4.66684e6	+	5.88608e6i	−0.378628	+	0.477547i
$687$	−8.85547e6			−0.715846
$688$	−1.92655e6	+	5.71215e6i	−0.155171	+	0.460075i
$689$	−2.02821e7			−1.62766
$690$	−3.79272e6	+	4.78360e6i	−0.303269	+	0.382501i
$691$	−1.18293e7	−	1.18293e7i	−0.942463	−	0.942463i	0.0559699	−	0.998432i	$-0.482175\pi$
$691$	−1.18293e7	−	1.18293e7i	−0.942463	−	0.942463i	−0.998432	+	0.0559699i	$0.982175\pi$
$692$	7.88076e6	−	1.27010e7i	0.625609	−	1.00826i
$693$	659543.	−	659543.i	0.0521687	−	0.0521687i
$694$	−2.31375e7	+	2.67322e6i	−1.82355	+	0.210687i
$695$		−	1.76157e6i		−	0.138337i
$696$	9.74657e6	+	4.59229e6i	0.762656	+	0.359340i
$697$		−	7.49966e6i		−	0.584735i
$698$	1.38401e6	+	1.19790e7i	0.107523	+	0.930640i
$699$	−360289.	+	360289.i	−0.0278906	+	0.0278906i
$700$	−724815.	−	3.09486e6i	−0.0559091	−	0.238724i
$701$	5.74616e6	+	5.74616e6i	0.441654	+	0.441654i	0.892568	−	0.450913i	$-0.148902\pi$
$701$	5.74616e6	+	5.74616e6i	0.441654	+	0.441654i	−0.450913	+	0.892568i	$0.648902\pi$
$702$	−1.63828e7	−	1.29892e7i	−1.25471	−	0.994810i
$703$	−853039.			−0.0651000
$704$	−6.33840e6	−	605492.i	−0.482001	−	0.0460444i
$705$	6.21679e6			0.471079
$706$	−4.64586e6	−	3.68351e6i	−0.350796	−	0.278132i
$707$	1.90293e7	+	1.90293e7i	1.43178	+	1.43178i
$708$	3.41788e6	+	1.45939e7i	0.256256	+	1.09418i
$709$	1.34563e7	−	1.34563e7i	1.00534	−	1.00534i	0.00535047	−	0.999986i	$-0.498297\pi$
$709$	1.34563e7	−	1.34563e7i	1.00534	−	1.00534i	0.999986	−	0.00535047i	$-0.00170312\pi$
$710$	−1.30471e6	−	1.12926e7i	−0.0971335	−	0.840716i
$711$			2.56168e6i			0.190042i
$712$	−1.98309e7	−	9.34373e6i	−1.46603	−	0.690749i
$713$			4.42581e6i			0.326038i
$714$	−9.57073e6	+	1.10577e6i	−0.702586	+	0.0811744i
$715$	−3.60946e6	+	3.60946e6i	−0.264044	+	0.264044i
$716$	3.13657e6	−	5.05504e6i	0.228651	−	0.368504i
$717$	−1.65515e7	−	1.65515e7i	−1.20238	−	1.20238i
$718$	−8.56952e6	+	1.08084e7i	−0.620362	+	0.782437i
$719$	686917.			0.0495544			0.0247772	−	0.999693i	$-0.492112\pi$
$719$	686917.			0.0495544			0.0247772	+	0.999693i	$0.492112\pi$
$720$	732647.	+	247102.i	0.0526700	+	0.0177642i
$721$	2.46817e7			1.76823
$722$	1.64246e6	−	2.07156e6i	0.117260	−	0.147895i
$723$	5.60041e6	+	5.60041e6i	0.398450	+	0.398450i
$724$	−9.72717e6	−	6.03555e6i	−0.689668	−	0.427928i
$725$	1.59142e6	−	1.59142e6i	0.112445	−	0.112445i
$726$	1.14519e7	−	1.32311e6i	0.806374	−	0.0931657i
$727$			7.82015e6i			0.548756i	0.961622	+	0.274378i	$0.0884719\pi$
$727$			7.82015e6i			0.548756i	−0.961622	+	0.274378i	$0.911528\pi$
$728$	−1.02261e7	−	2.84484e7i	−0.715127	−	1.98943i
$729$		−	1.21497e7i		−	0.846731i
$730$	356727.	+	3.08757e6i	0.0247759	+	0.214442i
$731$	2.69885e6	−	2.69885e6i	0.186804	−	0.186804i
$732$	−6.34808e6	+	1.48672e6i	−0.437890	+	0.102554i
$733$	−7.11806e6	−	7.11806e6i	−0.489330	−	0.489330i	0.418765	−	0.908095i	$-0.362463\pi$
$733$	−7.11806e6	−	7.11806e6i	−0.489330	−	0.489330i	−0.908095	+	0.418765i	$0.862463\pi$
$734$	−1.11224e7	−	8.81847e6i	−0.762004	−	0.604162i
$735$	3.49247e6			0.238460
$736$	−3.15751e6	+	1.47949e7i	−0.214858	+	1.00674i
$737$	1.29950e7			0.881265
$738$	−1.54865e6	−	1.22786e6i	−0.104668	−	0.0829869i
$739$	−892506.	−	892506.i	−0.0601174	−	0.0601174i	0.676409	−	0.736526i	$-0.263535\pi$
$739$	−892506.	−	892506.i	−0.0601174	−	0.0601174i	−0.736526	+	0.676409i	$0.763535\pi$
$740$	387290.	−	90703.1i	0.0259990	−	0.00608896i
$741$	−2.10702e7	+	2.10702e7i	−1.40969	+	1.40969i
$742$	−1.99168e6	−	1.72385e7i	−0.132804	−	1.14945i
$743$			1.42088e7i			0.944249i	0.881532	+	0.472124i	$0.156513\pi$
$743$			1.42088e7i			0.944249i	−0.881532	+	0.472124i	$0.843487\pi$
$744$	4.77160e6	−	1.71521e6i	0.316033	−	0.113602i
$745$			2.11506e6i			0.139615i
$746$	−1.76316e7	+	2.03710e6i	−1.15997	+	0.134018i
$747$	1.03210e6	−	1.03210e6i	0.0676738	−	0.0676738i
$748$	3.42553e6	+	2.12549e6i	0.223859	+	0.138901i
$749$	−1.90878e6	−	1.90878e6i	−0.124323	−	0.124323i
$750$	907660.	−	1.14479e6i	0.0589210	−	0.0743146i
$751$	−1.10742e6			−0.0716494			−0.0358247	−	0.999358i	$-0.511406\pi$
$751$	−1.10742e6			−0.0716494			−0.0358247	+	0.999358i	$0.511406\pi$
$752$	1.38037e7	−	6.84083e6i	0.890122	−	0.441128i
$753$	2.51785e7			1.61824
$754$	1.32983e7	−	1.67725e7i	0.851857	−	1.07441i
$755$	777527.	+	777527.i	0.0496419	+	0.0496419i
$756$	9.43127e6	−	1.51999e7i	0.600158	−	0.967243i
$757$	1.91836e7	−	1.91836e7i	1.21672	−	1.21672i	0.247946	−	0.968774i	$-0.420245\pi$
$757$	1.91836e7	−	1.91836e7i	1.21672	−	1.21672i	0.968774	−	0.247946i	$-0.0797554\pi$
$758$	5.98714e6	−	691734.i	0.378483	−	0.0437286i
$759$			8.38790e6i			0.528504i
$760$	−3.30928e6	+	7.02355e6i	−0.207826	+	0.441086i
$761$			1.49440e7i			0.935417i	0.883883	+	0.467708i	$0.154920\pi$
$761$			1.49440e7i			0.935417i	−0.883883	+	0.467708i	$0.845080\pi$
$762$	524754.	+	4.54189e6i	0.0327392	+	0.283367i
$763$	−2.67125e7	+	2.67125e7i	−1.66113	+	1.66113i
$764$	1.13918e6	+	4.86415e6i	0.0706089	+	0.301491i
$765$	−346158.	−	346158.i	−0.0213856	−	0.0213856i
$766$	−1.26737e7	−	1.00484e7i	−0.780423	−	0.618766i
$767$	2.97774e7			1.82768
$768$	1.71745e7	−	2.32951e6i	1.05071	−	0.142515i
$769$	2.21878e7			1.35300			0.676500	−	0.736442i	$-0.263496\pi$
$769$	2.21878e7			1.35300			0.676500	+	0.736442i	$0.263496\pi$
$770$	−3.42226e6	−	2.71337e6i	−0.208011	−	0.164924i
$771$	−8.04014e6	−	8.04014e6i	−0.487111	−	0.487111i
$772$	6.41611e6	+	2.73959e7i	0.387461	+	1.65441i
$773$	−1.04659e7	+	1.04659e7i	−0.629979	+	0.629979i	−0.948063	−	0.318084i	$-0.896961\pi$
$773$	−1.04659e7	+	1.04659e7i	−0.629979	+	0.629979i	0.318084	+	0.948063i	$0.396961\pi$
$774$	−115441.	−	999168.i	−0.00692637	−	0.0599496i
$775$		−	1.05917e6i		−	0.0633447i
$776$	−1.01953e7	+	2.16382e7i	−0.607778	+	1.28993i
$777$			1.30614e6i			0.0776137i
$778$	9.26712e6	−	1.07069e6i	0.548903	−	0.0634185i
$779$	1.40331e7	−	1.40331e7i	0.828533	−	0.828533i
$780$	7.32576e6	−	1.18065e7i	0.431138	−	0.694841i
$781$	−1.10445e7	−	1.10445e7i	−0.647917	−	0.647917i
$782$	5.95071e6	−	7.50538e6i	0.347978	−	0.438890i
$783$	1.26657e7			0.738285
$784$	7.75463e6	−	3.84305e6i	0.450579	−	0.223298i
$785$	1.08834e7			0.630361
$786$	−463866.	+	585055.i	−0.0267816	+	0.0337785i
$787$	3.23376e6	+	3.23376e6i	0.186111	+	0.186111i	0.794012	−	0.607902i	$-0.207989\pi$
$787$	3.23376e6	+	3.23376e6i	0.186111	+	0.186111i	−0.607902	+	0.794012i	$0.707989\pi$
$788$	−1.52056e7	−	9.43480e6i	−0.872342	−	0.541274i
$789$	−8.67911e6	+	8.67911e6i	−0.496344	+	0.496344i
$790$	1.19155e7	−	1.37667e6i	0.679271	−	0.0784807i
$791$			1.30230e7i			0.740064i
$792$	999743.	−	359370.i	0.0566338	−	0.0203577i
$793$			1.29527e7i			0.731436i
$794$	−3.16890e6	−	2.74277e7i	−0.178385	−	1.54397i
$795$	5.63983e6	−	5.63983e6i	0.316481	−	0.316481i
$796$	−6.01489e6	+	1.40868e6i	−0.336469	+	0.0788008i
$797$	−8.02312e6	−	8.02312e6i	−0.447401	−	0.447401i	0.447088	−	0.894490i	$-0.352461\pi$
$797$	−8.02312e6	−	8.02312e6i	−0.447401	−	0.447401i	−0.894490	+	0.447088i	$0.852461\pi$
$798$	−1.99775e7	−	1.58393e7i	−1.11054	−	0.880501i
$799$	−9.75403e6			−0.540526
$800$	755644.	−	3.54065e6i	0.0417438	−	0.195595i
$801$	3.65766e6			0.201429
$802$	1.89682e7	+	1.50391e7i	1.04134	+	0.825633i
$803$	3.01973e6	+	3.01973e6i	0.165265	+	0.165265i
$804$	−3.44406e7	+	8.06596e6i	−1.87901	+	0.440064i
$805$	−7.33735e6	+	7.33735e6i	−0.399071	+	0.399071i
$806$	−1.15615e6	−	1.00068e7i	−0.0626869	−	0.542571i
$807$		−	2.36496e7i		−	1.27832i
$808$	1.03687e7	+	2.88449e7i	0.558721	+	1.55432i
$809$			3.07979e7i			1.65443i	0.561883	+	0.827217i	$0.310077\pi$
$809$			3.07979e7i			1.65443i	−0.561883	+	0.827217i	$0.689923\pi$
$810$	9.19853e6	−	1.06277e6i	0.492613	−	0.0569148i
$811$	1.90142e7	−	1.90142e7i	1.01514	−	1.01514i	0.0152577	−	0.999884i	$-0.495143\pi$
$811$	1.90142e7	−	1.90142e7i	1.01514	−	1.01514i	0.999884	−	0.0152577i	$-0.00485686\pi$
$812$	1.55615e7	+	9.65566e6i	0.828250	+	0.513916i
$813$	−6.30307e6	−	6.30307e6i	−0.334446	−	0.334446i
$814$	339550.	−	428261.i	0.0179615	−	0.0226541i
$815$	−3.29235e6			−0.173625
$816$	−1.03980e7	−	3.50695e6i	−0.546667	−	0.184376i
$817$	1.01000e7			0.529379
$818$	3.30106e6	−	4.16349e6i	0.172493	−	0.217558i
$819$	3.56661e6	+	3.56661e6i	0.185800	+	0.185800i
$820$	−4.87906e6	+	7.86332e6i	−0.253397	+	0.408387i
$821$	6.78079e6	−	6.78079e6i	0.351093	−	0.351093i	−0.509423	−	0.860516i	$-0.670141\pi$
$821$	6.78079e6	−	6.78079e6i	0.351093	−	0.351093i	0.860516	+	0.509423i	$0.170141\pi$
$822$	−1.16523e7	+	1.34627e6i	−0.601496	+	0.0694948i
$823$			1.61025e6i			0.0828692i	0.999141	+	0.0414346i	$0.0131928\pi$
$823$			1.61025e6i			0.0828692i	−0.999141	+	0.0414346i	$0.986807\pi$
$824$	2.54307e7	+	1.19822e7i	1.30479	+	0.614777i
$825$		−	2.00736e6i		−	0.102681i
$826$	2.92412e6	+	2.53090e7i	0.149123	+	1.29070i
$827$	−6.09944e6	+	6.09944e6i	−0.310117	+	0.310117i	−0.844955	−	0.534838i	$-0.820373\pi$
$827$	−6.09944e6	+	6.09944e6i	−0.310117	+	0.310117i	0.534838	+	0.844955i	$0.320373\pi$
$828$	−575569.	−	2.45760e6i	−0.0291757	−	0.124576i
$829$	7.67020e6	+	7.67020e6i	0.387633	+	0.387633i	0.873842	−	0.486209i	$-0.161621\pi$
$829$	7.67020e6	+	7.67020e6i	0.387633	+	0.387633i	−0.486209	+	0.873842i	$0.661621\pi$
$830$	−5.35540e6	−	4.24608e6i	−0.269834	−	0.213940i
$831$	3.85267e7			1.93535
$832$	3.27431e6	−	3.42761e7i	0.163988	−	1.71666i
$833$	−5.47963e6			−0.273614
$834$	5.16258e6	+	4.09320e6i	0.257011	+	0.203774i
$835$	−7.69373e6	−	7.69373e6i	−0.381875	−	0.381875i
$836$	2.43260e6	+	1.03869e7i	0.120380	+	0.514007i
$837$	4.21481e6	−	4.21481e6i	0.207953	−	0.207953i
$838$	−735648.	−	6.36723e6i	−0.0361876	−	0.313213i
$839$		−	1.29839e7i		−	0.636798i	−0.947957	−	0.318399i	$-0.896855\pi$
$839$		−	1.29839e7i		−	0.636798i	0.947957	−	0.318399i	$-0.103145\pi$
$840$	1.07542e7	+	5.06706e6i	0.525872	+	0.247775i
$841$		−	7.54413e6i		−	0.367806i
$842$	2.46264e7	−	2.84525e6i	1.19707	−	0.138306i
$843$	1.05165e7	−	1.05165e7i	0.509683	−	0.509683i
$844$	1.02002e6	−	1.64392e6i	0.0492894	−	0.0794371i
$845$	−1.29552e7	−	1.29552e7i	−0.624171	−	0.624171i
$846$	−1.59696e6	+	2.01417e6i	−0.0767127	+	0.0967545i
$847$	1.95950e7			0.938507
$848$	6.31662e6	−	1.87285e7i	0.301644	−	0.894364i
$849$	−4.10299e7			−1.95358
$850$	−1.42410e6	+	1.79616e6i	−0.0676073	+	0.0852702i
$851$	−918194.	−	918194.i	−0.0434621	−	0.0434621i
$852$	3.61266e7	+	2.24160e7i	1.70502	+	1.05793i
$853$	−5.74188e6	+	5.74188e6i	−0.270198	+	0.270198i	−0.829180	−	0.558982i	$-0.811192\pi$
$853$	−5.74188e6	+	5.74188e6i	−0.270198	+	0.270198i	0.558982	+	0.829180i	$0.311192\pi$
$854$	−1.10090e7	+	1.27194e6i	−0.516538	+	0.0596791i
$855$		−	1.29544e6i		−	0.0606040i
$856$	−1.04005e6	−	2.89336e6i	−0.0485145	−	0.134964i
$857$			3.10244e7i			1.44295i	0.692440	+	0.721476i	$0.256536\pi$
$857$			3.10244e7i			1.44295i	−0.692440	+	0.721476i	$0.743464\pi$
$858$	−2.19116e6	−	1.89651e7i	−0.101615	−	0.879502i
$859$	−1.18811e7	+	1.18811e7i	−0.549381	+	0.549381i	−0.926262	−	0.376881i	$-0.876997\pi$
$859$	−1.18811e7	+	1.18811e7i	−0.549381	+	0.549381i	0.376881	+	0.926262i	$0.376997\pi$
$860$	−4.58552e6	+	1.07393e6i	−0.211418	+	0.0495141i
$861$	−2.14870e7	−	2.14870e7i	−0.987796	−	0.987796i
$862$	−1.72243e7	−	1.36564e7i	−0.789538	−	0.625992i
$863$	−2.24369e7			−1.02550			−0.512751	−	0.858537i	$-0.671374\pi$
$863$	−2.24369e7			−1.02550			−0.512751	+	0.858537i	$0.671374\pi$
$864$	1.70965e7	−	1.10825e7i	0.779153	−	0.505074i
$865$	1.16776e7			0.530655
$866$	1.62521e7	+	1.28856e7i	0.736403	+	0.583864i
$867$	−1.16820e7	−	1.16820e7i	−0.527801	−	0.527801i
$868$	8.39162e6	−	1.96531e6i	0.378048	−	0.0885386i
$869$	1.16537e7	−	1.16537e7i	0.523496	−	0.523496i
$870$	966091.	+	8.36177e6i	0.0432733	+	0.374542i
$871$			7.02728e7i			3.13864i
$872$	−4.04912e7	+	1.45551e7i	−1.80331	+	0.648221i
$873$		−	3.99100e6i		−	0.177234i
$874$	2.51786e7	−	2.90905e6i	1.11494	−	0.128817i
$875$	1.75595e6	−	1.75595e6i	0.0775339	−	0.0775339i
$876$	−9.87754e6	−	6.12885e6i	−0.434899	−	0.269848i
$877$	5.96970e6	+	5.96970e6i	0.262092	+	0.262092i	0.825904	−	0.563812i	$-0.190666\pi$
$877$	5.96970e6	+	5.96970e6i	0.262092	+	0.262092i	−0.563812	+	0.825904i	$0.690666\pi$
$878$	−1.77339e7	+	2.23671e7i	−0.776371	+	0.979204i
$879$	−3.39842e7			−1.48356
$880$	−2.20886e6	−	4.45711e6i	−0.0961526	−	0.194020i
$881$	2.25643e7			0.979451			0.489726	−	0.871877i	$-0.337097\pi$
$881$	2.25643e7			0.979451			0.489726	+	0.871877i	$0.337097\pi$
$882$	−897140.	+	1.13152e6i	−0.0388319	+	0.0489770i
$883$	2.29266e7	+	2.29266e7i	0.989551	+	0.989551i	0.999946	−	0.0103945i	$-0.00330872\pi$
$883$	2.29266e7	+	2.29266e7i	0.989551	+	0.989551i	−0.0103945	+	0.999946i	$0.503309\pi$
$884$	−1.14940e7	+	1.85242e7i	−0.494697	+	0.797277i
$885$	−8.28020e6	+	8.28020e6i	−0.355372	+	0.355372i
$886$	3.34120e7	−	3.86031e6i	1.42994	−	0.165211i
$887$		−	3.63690e7i		−	1.55211i	−0.630666	−	0.776054i	$-0.717218\pi$
$887$		−	3.63690e7i		−	1.55211i	0.630666	−	0.776054i	$-0.282782\pi$
$888$	−634089.	+	1.34578e6i	−0.0269847	+	0.0572718i
$889$			7.77150e6i			0.329800i
$890$	−1.96566e6	−	1.70133e7i	−0.0831829	−	0.719970i
$891$	8.99643e6	−	8.99643e6i	0.379644	−	0.379644i
$892$	3.03459e6	+	1.29573e7i	0.127699	+	0.545258i
$893$	−1.82514e7	−	1.82514e7i	−0.765892	−	0.765892i
$894$	−6.19853e6	−	4.91456e6i	−0.259385	−	0.205656i
$895$	4.64772e6			0.193947
$896$	2.94541e7	−	582919.i	1.22568	−	0.0242571i
$897$	−4.53592e7			−1.88228
$898$	3.80949e6	+	3.02039e6i	0.157643	+	0.124989i
$899$	4.31509e6	+	4.31509e6i	0.178070	+	0.178070i
$900$	137743.	+	588144.i	0.00566844	+	0.0242035i
$901$	−8.84879e6	+	8.84879e6i	−0.363138	+	0.363138i
$902$	1.45935e6	+	1.26310e7i	0.0597231	+	0.516919i
$903$		−	1.54648e7i		−	0.631137i
$904$	−6.32223e6	+	1.34182e7i	−0.257306	+	0.546100i
$905$		−	8.94337e6i		−	0.362978i
$906$	−4.08534e6	+	472007.i	−0.165352	+	0.0191042i
$907$	6.72038e6	−	6.72038e6i	0.271254	−	0.271254i	−0.558351	−	0.829605i	$-0.688566\pi$
$907$	6.72038e6	−	6.72038e6i	0.271254	−	0.271254i	0.829605	+	0.558351i	$0.188566\pi$
$908$	−7.53442e6	+	1.21428e7i	−0.303274	+	0.488770i
$909$	−3.61632e6	−	3.61632e6i	−0.145163	−	0.145163i
$910$	1.46731e7	−	1.85065e7i	0.587378	−	0.740836i
$911$	−3.10619e7			−1.24003			−0.620015	−	0.784590i	$-0.712874\pi$
$911$	−3.10619e7			−1.24003			−0.620015	+	0.784590i	$0.712874\pi$
$912$	−1.28942e7	−	2.60184e7i	−0.513344	−	1.03584i
$913$	−9.39053e6			−0.372832
$914$	−3.72437e6	+	4.69740e6i	−0.147465	+	0.185991i
$915$	−3.60174e6	−	3.60174e6i	−0.142220	−	0.142220i
$916$	−1.45678e7	−	9.03908e6i	−0.573661	−	0.355947i
$917$	−897390.	+	897390.i	−0.0352418	+	0.0352418i
$918$	−1.28146e7	+	1.48055e6i	−0.501877	+	0.0579852i
$919$			9.82341e6i			0.383684i	0.981426	+	0.191842i	$0.0614461\pi$
$919$			9.82341e6i			0.383684i	−0.981426	+	0.191842i	$0.938554\pi$
$920$	−1.11221e7	+	3.99796e6i	−0.433227	+	0.155729i
$921$		−	1.78406e7i		−	0.693042i
$922$	−2.26558e6	−	1.96092e7i	−0.0877712	−	0.759683i
$923$	5.97254e7	−	5.97254e7i	2.30757	−	2.30757i
$924$	1.59040e7	−	3.72471e6i	0.612811	−	0.143520i
$925$	219739.	+	219739.i	0.00844408	+	0.00844408i
$926$	−4.70280e6	−	3.72866e6i	−0.180231	−	0.142898i
$927$	−4.69049e6			−0.179275
$928$	1.13462e7	+	1.75033e7i	0.432495	+	0.667189i
$929$	−2.84167e7			−1.08028			−0.540138	−	0.841577i	$-0.681628\pi$
$929$	−2.84167e7			−1.08028			−0.540138	+	0.841577i	$0.681628\pi$
$930$	3.10407e6	+	2.46109e6i	0.117686	+	0.0933083i
$931$	−1.02533e7	−	1.02533e7i	−0.387694	−	0.387694i
$932$	−960459.	+	224939.i	−0.0362192	+	0.00848252i
$933$	−1.72951e7	+	1.72951e7i	−0.650457	+	0.650457i
$934$	1.49278e6	+	1.29204e7i	0.0559923	+	0.484628i
$935$			3.14951e6i			0.117819i
$936$	1.94336e6	+	5.40630e6i	0.0725045	+	0.201702i
$937$		−	4.24273e6i		−	0.157869i	−0.996880	−	0.0789345i	$-0.974848\pi$
$937$		−	4.24273e6i		−	0.157869i	0.996880	−	0.0789345i	$-0.0251518\pi$
$938$	−5.97276e7	+	6.90072e6i	−2.21650	+	0.256087i
$939$	1.94082e7	−	1.94082e7i	0.718324	−	0.718324i
$940$	1.02270e7	+	6.34569e6i	0.377510	+	0.234239i
$941$	−9.79250e6	−	9.79250e6i	−0.360512	−	0.360512i	0.503490	−	0.864001i	$-0.332049\pi$
$941$	−9.79250e6	−	9.79250e6i	−0.360512	−	0.360512i	−0.864001	+	0.503490i	$0.832049\pi$
$942$	−2.52887e7	+	3.18956e7i	−0.928537	+	1.17112i
$943$	3.02099e7			1.10629
$944$	−9.27384e6	+	2.74966e7i	−0.338711	+	1.00427i
$945$	1.39751e7			0.509067
$946$	−4.02028e6	+	5.07062e6i	−0.146059	+	0.184218i
$947$	−1.97791e6	−	1.97791e6i	−0.0716690	−	0.0716690i	0.670364	−	0.742033i	$-0.266138\pi$
$947$	−1.97791e6	−	1.97791e6i	−0.0716690	−	0.0716690i	−0.742033	+	0.670364i	$0.766138\pi$
$948$	−2.36523e7	+	3.81192e7i	−0.854777	+	1.37760i
$949$	−1.63298e7	+	1.63298e7i	−0.588593	+	0.588593i
$950$	−6.02564e6	+	696182.i	−0.216618	+	0.0250273i
$951$			1.93361e7i			0.693295i
$952$	−1.68732e7	−	7.95011e6i	−0.603398	−	0.284303i
$953$		−	3.23728e6i		−	0.115465i	−0.998332	−	0.0577323i	$-0.981613\pi$
$953$		−	3.23728e6i		−	0.115465i	0.998332	−	0.0577323i	$-0.0183870\pi$
$954$	378497.	+	3.27599e6i	0.0134645	+	0.116539i
$955$	−2.75980e6	+	2.75980e6i	−0.0979195	+	0.0979195i
$956$	−1.03336e7	−	4.41230e7i	−0.365684	−	1.56142i
$957$	8.17806e6	+	8.17806e6i	0.288649	+	0.288649i
$958$	9.89541e6	+	7.84567e6i	0.348353	+	0.276195i
$959$	−1.99380e7			−0.700058
$960$	8.62066e6	+	1.04416e7i	0.301899	+	0.365671i
$961$	−2.57573e7			−0.899686
$962$	2.31590e6	+	1.83618e6i	0.0806831	+	0.0639703i
$963$	362743.	+	362743.i	0.0126047	+	0.0126047i
$964$	3.49650e6	+	1.49296e7i	0.121183	+	0.517433i
$965$	−1.55437e7	+	1.55437e7i	−0.537326	+	0.537326i
$966$	−4.45423e6	−	3.85525e7i	−0.153578	−	1.32926i
$967$			3.37290e7i			1.15995i	0.814636	+	0.579973i	$0.196937\pi$
$967$			3.37290e7i			1.15995i	−0.814636	+	0.579973i	$0.803063\pi$
$968$	2.01897e7	+	9.51275e6i	0.692533	+	0.326300i
$969$			1.83853e7i			0.629015i
$970$	−1.85639e7	+	2.14481e6i	−0.633489	+	0.0731911i
$971$	2.88322e7	−	2.88322e7i	0.981364	−	0.981364i	−0.0184652	−	0.999830i	$-0.505878\pi$
$971$	2.88322e7	−	2.88322e7i	0.981364	−	0.981364i	0.999830	+	0.0184652i	$0.00587798\pi$
$972$	−3.83901e6	+	6.18712e6i	−0.130333	+	0.210050i
$973$	7.91865e6	+	7.91865e6i	0.268145	+	0.268145i
$974$	1.59243e6	−	2.00846e6i	0.0537851	−	0.0678369i
$975$	1.08552e7			0.365700
$976$	−1.19605e7	−	4.03396e6i	−0.401908	−	0.135552i
$977$	8.82833e6			0.295898			0.147949	−	0.988995i	$-0.452733\pi$
$977$	8.82833e6			0.295898			0.147949	+	0.988995i	$0.452733\pi$
$978$	7.65014e6	−	9.64880e6i	0.255754	−	0.322571i
$979$	−1.66395e7	−	1.66395e7i	−0.554861	−	0.554861i
$980$	5.74534e6	+	3.56489e6i	0.191095	+	0.118572i
$981$	5.07642e6	−	5.07642e6i	0.168417	−	0.168417i
$982$	3.62586e7	−	4.18920e6i	1.19987	−	0.138628i
$983$		−	5.82183e7i		−	1.92166i	−0.277142	−	0.960829i	$-0.589387\pi$
$983$		−	5.82183e7i		−	1.92166i	0.277142	−	0.960829i	$-0.410613\pi$
$984$	−1.17078e7	−	3.25702e7i	−0.385467	−	1.07234i
$985$		−	1.39803e7i		−	0.459121i
$986$	−1.51578e6	−	1.31195e7i	−0.0496528	−	0.429758i
$987$	−2.79459e7	+	2.79459e7i	−0.913114	+	0.913114i
$988$	−5.61690e7	+	1.31548e7i	−1.83065	+	0.428736i
$989$	1.08714e7	+	1.08714e7i	0.353424	+	0.353424i
$990$	650363.	+	515646.i	0.0210896	+	0.0167211i
$991$	−1.58713e6			−0.0513367			−0.0256684	−	0.999671i	$-0.508171\pi$
$991$	−1.58713e6			−0.0513367			−0.0256684	+	0.999671i	$0.508171\pi$
$992$	9.60036e6	+	2.04891e6i	0.309748	+	0.0661063i
$993$	2.29240e7			0.737762
$994$	5.66279e7	+	4.48980e7i	1.81788	+	1.44132i
$995$	−3.41270e6	−	3.41270e6i	−0.109280	−	0.109280i
$996$	2.48877e7	−	5.82869e6i	0.794944	−	0.186176i
$997$	−3.58570e7	+	3.58570e7i	−1.14245	+	1.14245i	−0.154444	+	0.988002i	$0.549359\pi$
$997$	−3.58570e7	+	3.58570e7i	−1.14245	+	1.14245i	−0.988002	+	0.154444i	$0.950641\pi$
$998$	−2.27481e6	−	1.96891e7i	−0.0722967	−	0.625747i
$999$			1.74884e6i			0.0554416i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	80.6.l.a.61.9	yes	80
4.3	odd	2		320.6.l.a.81.9		80
16.5	even	4	inner	80.6.l.a.21.9	✓	80
16.11	odd	4		320.6.l.a.241.9		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.6.l.a.21.9	✓	80	16.5	even	4	inner
80.6.l.a.61.9	yes	80	1.1	even	1	trivial
320.6.l.a.81.9		80	4.3	odd	2
320.6.l.a.241.9		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)

\(f(q)\)	\(=\)	\(q+(-4.43266 - 3.51447i) q^{2} +(11.6877 + 11.6877i) q^{3} +(7.29694 + 31.1569i) q^{4} +(-17.6777 + 17.6777i) q^{5} +(-10.7314 - 92.8834i) q^{6} -158.930i q^{7} +(77.1554 - 163.753i) q^{8} +30.2029i q^{9} +O(q^{10})\)	\(q+(-4.43266 - 3.51447i) q^{2} +(11.6877 + 11.6877i) q^{3} +(7.29694 + 31.1569i) q^{4} +(-17.6777 + 17.6777i) q^{5} +(-10.7314 - 92.8834i) q^{6} -158.930i q^{7} +(77.1554 - 163.753i) q^{8} +30.2029i q^{9} +(140.487 - 16.2314i) q^{10} +(137.400 - 137.400i) q^{11} +(-278.868 + 449.436i) q^{12} +(743.018 + 743.018i) q^{13} +(-558.556 + 704.484i) q^{14} -413.221 q^{15} +(-917.509 + 454.701i) q^{16} +648.336 q^{17} +(106.147 - 133.879i) q^{18} +(1213.14 + 1213.14i) q^{19} +(-679.775 - 421.789i) q^{20} +(1857.52 - 1857.52i) q^{21} +(-1091.94 + 126.159i) q^{22} +2611.61i q^{23} +(2815.66 - 1012.12i) q^{24} -625.000i q^{25} +(-682.228 - 5904.86i) q^{26} +(2487.10 - 2487.10i) q^{27} +(4951.78 - 1159.70i) q^{28} +(2546.27 + 2546.27i) q^{29} +(1831.67 + 1452.26i) q^{30} +1694.67 q^{31} +(5665.04 + 1209.03i) q^{32} +3211.78 q^{33} +(-2873.85 - 2278.56i) q^{34} +(2809.52 + 2809.52i) q^{35} +(-941.031 + 220.389i) q^{36} +(-351.582 + 351.582i) q^{37} +(-1113.89 - 9641.02i) q^{38} +17368.3i q^{39} +(1530.84 + 4258.70i) q^{40} -11567.5i q^{41} +(-14762.0 + 1705.55i) q^{42} +(4162.74 - 4162.74i) q^{43} +(5283.57 + 3278.37i) q^{44} +(-533.917 - 533.917i) q^{45} +(9178.43 - 11576.4i) q^{46} -15044.7 q^{47} +(-16037.9 - 5409.15i) q^{48} -8451.82 q^{49} +(-2196.55 + 2770.41i) q^{50} +(7577.54 + 7577.54i) q^{51} +(-17728.4 + 28571.9i) q^{52} +(-13648.4 + 13648.4i) q^{53} +(-19765.3 + 2283.62i) q^{54} +4857.83i q^{55} +(-26025.3 - 12262.3i) q^{56} +28357.7i q^{57} +(-2337.95 - 20235.6i) q^{58} +(20038.2 - 20038.2i) q^{59} +(-3015.25 - 12874.7i) q^{60} +(8716.26 + 8716.26i) q^{61} +(-7511.89 - 5955.87i) q^{62} +4800.16 q^{63} +(-20862.1 - 25268.9i) q^{64} -26269.7 q^{65} +(-14236.7 - 11287.7i) q^{66} +(47288.8 + 47288.8i) q^{67} +(4730.87 + 20200.2i) q^{68} +(-30523.6 + 30523.6i) q^{69} +(-2579.66 - 22327.6i) q^{70} -80382.1i q^{71} +(4945.82 + 2330.32i) q^{72} +21977.6i q^{73} +(2794.07 - 322.817i) q^{74} +(7304.79 - 7304.79i) q^{75} +(-28945.6 + 46650.1i) q^{76} +(-21837.1 - 21837.1i) q^{77} +(61040.4 - 76987.7i) q^{78} +84815.5 q^{79} +(8181.38 - 24257.5i) q^{80} +65476.1 q^{81} +(-40653.8 + 51275.0i) q^{82} +(-34172.2 - 34172.2i) q^{83} +(71429.0 + 44320.5i) q^{84} +(-11461.1 + 11461.1i) q^{85} +(-33081.8 + 3822.16i) q^{86} +59520.0i q^{87} +(-11898.5 - 33100.9i) q^{88} -121103. i q^{89} +(490.235 + 4243.11i) q^{90} +(118088. - 118088. i) q^{91} +(-81369.7 + 19056.7i) q^{92} +(19806.7 + 19806.7i) q^{93} +(66688.0 + 52874.2i) q^{94} -42891.1 q^{95} +(52080.3 + 80341.8i) q^{96} -132139. q^{97} +(37464.1 + 29703.7i) q^{98} +(4149.89 + 4149.89i) 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

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more