LMFDB - Embedded newform 80.6.q.a.29.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [80,6,Mod(29,80)]

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, 3, 2]))

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

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

chi := DirichletCharacter("80.29");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 80 = 2^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	80.q (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:	$116$
Relative dimension:	$58$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			29.11
Character	$\chi$	$=$	80.29
Dual form			80.6.q.a.69.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.74064 - 3.08648i) q^{2} +(-1.81560 + 1.81560i) q^{3} +(12.9473 + 29.2637i) q^{4} +(48.1357 - 28.4245i) q^{5} +(14.2109 - 3.00330i) q^{6} -66.7879 q^{7} +(28.9433 - 178.690i) q^{8} +236.407i q^{9} +O(q^{10})$	\(q+(-4.74064 - 3.08648i) q^{2} +(-1.81560 + 1.81560i) q^{3} +(12.9473 + 29.2637i) q^{4} +(48.1357 - 28.4245i) q^{5} +(14.2109 - 3.00330i) q^{6} -66.7879 q^{7} +(28.9433 - 178.690i) q^{8} +236.407i q^{9} +(-315.926 - 13.8197i) q^{10} +(215.262 - 215.262i) q^{11} +(-76.6384 - 29.6241i) q^{12} +(-631.811 + 631.811i) q^{13} +(316.617 + 206.139i) q^{14} +(-35.7878 + 139.003i) q^{15} +(-688.734 + 757.774i) q^{16} -755.437i q^{17} +(729.665 - 1120.72i) q^{18} +(1909.08 + 1909.08i) q^{19} +(1455.04 + 1040.61i) q^{20} +(121.260 - 121.260i) q^{21} +(-1684.88 + 356.078i) q^{22} +3963.77 q^{23} +(271.881 + 376.980i) q^{24} +(1509.10 - 2736.47i) q^{25} +(4945.26 - 1045.12i) q^{26} +(-870.412 - 870.412i) q^{27} +(-864.724 - 1954.46i) q^{28} +(586.717 + 586.717i) q^{29} +(598.686 - 548.504i) q^{30} +4694.91 q^{31} +(5603.89 - 1466.57i) q^{32} +781.660i q^{33} +(-2331.64 + 3581.26i) q^{34} +(-3214.89 + 1898.41i) q^{35} +(-6918.16 + 3060.84i) q^{36} +(9100.34 + 9100.34i) q^{37} +(-3157.93 - 14942.6i) q^{38} -2294.23i q^{39} +(-3685.97 - 9424.10i) q^{40} +4883.98i q^{41} +(-949.117 + 200.584i) q^{42} +(6120.84 + 6120.84i) q^{43} +(9086.44 + 3512.31i) q^{44} +(6719.75 + 11379.6i) q^{45} +(-18790.8 - 12234.1i) q^{46} +17818.7i q^{47} +(-125.350 - 2626.28i) q^{48} -12346.4 q^{49} +(-15600.1 + 8314.80i) q^{50} +(1371.57 + 1371.57i) q^{51} +(-26669.4 - 10308.9i) q^{52} +(-1181.77 - 1181.77i) q^{53} +(1439.80 + 6812.81i) q^{54} +(4243.09 - 16480.5i) q^{55} +(-1933.06 + 11934.4i) q^{56} -6932.26 q^{57} +(-970.524 - 4592.30i) q^{58} +(16657.6 - 16657.6i) q^{59} +(-4531.10 + 752.428i) q^{60} +(-39024.8 - 39024.8i) q^{61} +(-22256.9 - 14490.7i) q^{62} -15789.1i q^{63} +(-31092.6 - 10343.8i) q^{64} +(-12453.8 + 48371.6i) q^{65} +(2412.58 - 3705.57i) q^{66} +(-5695.24 + 5695.24i) q^{67} +(22106.9 - 9780.89i) q^{68} +(-7196.62 + 7196.62i) q^{69} +(21100.0 + 922.988i) q^{70} +50085.0i q^{71} +(42243.7 + 6842.41i) q^{72} +56678.1 q^{73} +(-15053.4 - 71229.4i) q^{74} +(2228.41 + 7708.25i) q^{75} +(-31149.4 + 80584.4i) q^{76} +(-14376.9 + 14376.9i) q^{77} +(-7081.09 + 10876.1i) q^{78} +48495.1 q^{79} +(-11613.4 + 56052.9i) q^{80} -54286.3 q^{81} +(15074.3 - 23153.2i) q^{82} +(57382.7 - 57382.7i) q^{83} +(5118.52 + 1978.53i) q^{84} +(-21472.9 - 36363.5i) q^{85} +(-10124.9 - 47908.5i) q^{86} -2130.48 q^{87} +(-32234.9 - 44695.7i) q^{88} -41470.4i q^{89} +(3267.07 - 74687.1i) q^{90} +(42197.3 - 42197.3i) q^{91} +(51320.2 + 115995. i) q^{92} +(-8524.07 + 8524.07i) q^{93} +(54996.9 - 84471.9i) q^{94} +(146160. + 37630.4i) q^{95} +(-7511.71 + 12837.1i) q^{96} -5473.40i q^{97} +(58529.7 + 38106.8i) q^{98} +(50889.5 + 50889.5i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 116 q - 4 q^{4} - 2 q^{5} - 4 q^{6}+O(q^{10}) $ 116 * q - 4 * q^4 - 2 * q^5 - 4 * q^6	$ 116 q - 4 q^{4} - 2 q^{5} - 4 q^{6} + 532 q^{10} - 4 q^{11} + 1108 q^{14} - 4 q^{15} + 1216 q^{16} + 2356 q^{19} + 824 q^{20} - 976 q^{21} - 2864 q^{24} - 12104 q^{26} - 4 q^{29} + 736 q^{30} + 23056 q^{31} - 38304 q^{34} - 3864 q^{35} - 20588 q^{36} + 15144 q^{40} - 25536 q^{44} + 6734 q^{45} - 36052 q^{46} + 220884 q^{49} + 56116 q^{50} - 9472 q^{51} - 104360 q^{54} - 2552 q^{56} + 14476 q^{59} + 1008 q^{60} - 48084 q^{61} + 72944 q^{64} - 27692 q^{65} - 56736 q^{66} - 23296 q^{69} + 135260 q^{70} - 186128 q^{74} - 33244 q^{75} - 35824 q^{76} + 427312 q^{79} - 129128 q^{80} - 551132 q^{81} - 418448 q^{84} + 6248 q^{85} + 177516 q^{86} + 449576 q^{90} - 231952 q^{91} + 607356 q^{94} + 38420 q^{95} - 440264 q^{96} + 406924 q^{99}+O(q^{100}) $ 116 * q - 4 * q^4 - 2 * q^5 - 4 * q^6 + 532 * q^10 - 4 * q^11 + 1108 * q^14 - 4 * q^15 + 1216 * q^16 + 2356 * q^19 + 824 * q^20 - 976 * q^21 - 2864 * q^24 - 12104 * q^26 - 4 * q^29 + 736 * q^30 + 23056 * q^31 - 38304 * q^34 - 3864 * q^35 - 20588 * q^36 + 15144 * q^40 - 25536 * q^44 + 6734 * q^45 - 36052 * q^46 + 220884 * q^49 + 56116 * q^50 - 9472 * q^51 - 104360 * q^54 - 2552 * q^56 + 14476 * q^59 + 1008 * q^60 - 48084 * q^61 + 72944 * q^64 - 27692 * q^65 - 56736 * q^66 - 23296 * q^69 + 135260 * q^70 - 186128 * q^74 - 33244 * q^75 - 35824 * q^76 + 427312 * q^79 - 129128 * q^80 - 551132 * q^81 - 418448 * q^84 + 6248 * q^85 + 177516 * q^86 + 449576 * q^90 - 231952 * q^91 + 607356 * q^94 + 38420 * q^95 - 440264 * q^96 + 406924 * 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 $

$2$	−4.74064	−	3.08648i	−0.838035	−	0.545617i
$2$	−4.74064	−	3.08648i	−0.838035	−	0.545617i
$3$	−1.81560	+	1.81560i	−0.116471	+	0.116471i	−0.762940	−	0.646469i	$-0.776245\pi$
$3$	−1.81560	+	1.81560i	−0.116471	+	0.116471i	0.646469	+	0.762940i	$0.276245\pi$
$4$	12.9473	+	29.2637i	0.404604	+	0.914492i
$5$	48.1357	−	28.4245i	0.861078	−	0.508472i
$5$	48.1357	−	28.4245i	0.861078	−	0.508472i
$6$	14.2109	−	3.00330i	0.161155	−	0.0340581i
$7$	−66.7879			−0.515173			−0.257586	−	0.966255i	$-0.582927\pi$
$7$	−66.7879			−0.515173			−0.257586	+	0.966255i	$0.582927\pi$
$8$	28.9433	−	178.690i	0.159891	−	0.987135i
$9$			236.407i			0.972869i
$10$	−315.926	−	13.8197i	−0.999045	−	0.0437017i
$11$	215.262	−	215.262i	0.536397	−	0.536397i	−0.386072	−	0.922469i	$-0.626168\pi$
$11$	215.262	−	215.262i	0.536397	−	0.536397i	0.922469	+	0.386072i	$0.126168\pi$
$12$	−76.6384	−	29.6241i	−0.153636	−	0.0593871i
$13$	−631.811	+	631.811i	−1.03688	+	1.03688i	−0.0375869	+	0.999293i	$0.511967\pi$
$13$	−631.811	+	631.811i	−1.03688	+	1.03688i	−0.999293	+	0.0375869i	$0.988033\pi$
$14$	316.617	+	206.139i	0.431732	+	0.281087i
$15$	−35.7878	+	139.003i	−0.0410683	+	0.159513i
$16$	−688.734	+	757.774i	−0.672592	+	0.740014i
$17$		−	755.437i		−	0.633981i	−0.948429	−	0.316990i	$-0.897328\pi$
$17$		−	755.437i		−	0.633981i	0.948429	−	0.316990i	$-0.102672\pi$
$18$	729.665	−	1120.72i	0.530814	−	0.815298i
$19$	1909.08	+	1909.08i	1.21322	+	1.21322i	0.969960	+	0.243262i	$0.0782176\pi$
$19$	1909.08	+	1909.08i	1.21322	+	1.21322i	0.243262	+	0.969960i	$0.421782\pi$
$20$	1455.04	+	1040.61i	0.813390	+	0.581719i
$21$	121.260	−	121.260i	0.0600026	−	0.0600026i
$22$	−1684.88	+	356.078i	−0.742186	+	0.156852i
$23$	3963.77			1.56239			0.781194	−	0.624288i	$-0.214611\pi$
$23$	3963.77			1.56239			0.781194	+	0.624288i	$0.214611\pi$
$24$	271.881	+	376.980i	0.0963498	+	0.133595i
$25$	1509.10	−	2736.47i	0.482912	−	0.875669i
$26$	4945.26	−	1045.12i	1.43468	−	0.303202i
$27$	−870.412	−	870.412i	−0.229782	−	0.229782i
$28$	−864.724	−	1954.46i	−0.208441	−	0.471121i
$29$	586.717	+	586.717i	0.129549	+	0.129549i	0.768908	−	0.639359i	$-0.220800\pi$
$29$	586.717	+	586.717i	0.129549	+	0.129549i	−0.639359	+	0.768908i	$0.720800\pi$
$30$	598.686	−	548.504i	0.121449	−	0.111270i
$31$	4694.91			0.877451			0.438725	−	0.898621i	$-0.355430\pi$
$31$	4694.91			0.877451			0.438725	+	0.898621i	$0.355430\pi$
$32$	5603.89	−	1466.57i	0.967419	−	0.253180i
$33$			781.660i			0.124949i
$34$	−2331.64	+	3581.26i	−0.345911	+	0.531298i
$35$	−3214.89	+	1898.41i	−0.443604	+	0.261951i
$36$	−6918.16	+	3060.84i	−0.889681	+	0.393626i
$37$	9100.34	+	9100.34i	1.09283	+	1.09283i	0.995225	+	0.0976066i	$0.0311187\pi$
$37$	9100.34	+	9100.34i	1.09283	+	1.09283i	0.0976066	+	0.995225i	$0.468881\pi$
$38$	−3157.93	−	14942.6i	−0.354767	−	1.67868i
$39$		−	2294.23i		−	0.241533i
$40$	−3685.97	−	9424.10i	−0.364252	−	0.931300i
$41$			4883.98i			0.453747i	0.973924	+	0.226874i	$0.0728504\pi$
$41$			4883.98i			0.453747i	−0.973924	+	0.226874i	$0.927150\pi$
$42$	−949.117	+	200.584i	−0.0830226	+	0.0175458i
$43$	6120.84	+	6120.84i	0.504824	+	0.504824i	0.912933	−	0.408109i	$-0.133812\pi$
$43$	6120.84	+	6120.84i	0.504824	+	0.504824i	−0.408109	+	0.912933i	$0.633812\pi$
$44$	9086.44	+	3512.31i	0.707558	+	0.273502i
$45$	6719.75	+	11379.6i	0.494677	+	0.837716i
$46$	−18790.8	−	12234.1i	−1.30934	−	0.852466i
$47$			17818.7i			1.17661i	0.808641	+	0.588303i	$0.200204\pi$
$47$			17818.7i			1.17661i	−0.808641	+	0.588303i	$0.799796\pi$
$48$	−125.350	−	2626.28i	−0.00785272	−	0.164527i
$49$	−12346.4			−0.734597
$50$	−15600.1	+	8314.80i	−0.882477	+	0.470356i
$51$	1371.57	+	1371.57i	0.0738402	+	0.0738402i
$52$	−26669.4	−	10308.9i	−1.36774	−	0.528693i
$53$	−1181.77	−	1181.77i	−0.0577889	−	0.0577889i	0.677622	−	0.735411i	$-0.263011\pi$
$53$	−1181.77	−	1181.77i	−0.0577889	−	0.0577889i	−0.735411	+	0.677622i	$0.763011\pi$
$54$	1439.80	+	6812.81i	0.0671921	+	0.317938i
$55$	4243.09	−	16480.5i	0.189137	−	0.734622i
$56$	−1933.06	+	11934.4i	−0.0823713	+	0.508545i
$57$	−6932.26			−0.282610
$58$	−970.524	−	4592.30i	−0.0378823	−	0.179250i
$59$	16657.6	−	16657.6i	0.622991	−	0.622991i	−0.323304	−	0.946295i	$-0.604794\pi$
$59$	16657.6	−	16657.6i	0.622991	−	0.622991i	0.946295	+	0.323304i	$0.104794\pi$
$60$	−4531.10	+	752.428i	−0.162489	+	0.0269828i
$61$	−39024.8	−	39024.8i	−1.34282	−	1.34282i	−0.893244	−	0.449572i	$-0.851576\pi$
$61$	−39024.8	−	39024.8i	−1.34282	−	1.34282i	−0.449572	−	0.893244i	$-0.648424\pi$
$62$	−22256.9	−	14490.7i	−0.735334	−	0.478752i
$63$		−	15789.1i		−	0.501195i
$64$	−31092.6	−	10343.8i	−0.948870	−	0.315667i
$65$	−12453.8	+	48371.6i	−0.365610	+	1.42006i
$66$	2412.58	−	3705.57i	0.0681743	−	0.104712i
$67$	−5695.24	+	5695.24i	−0.154998	+	0.154998i	−0.780346	−	0.625348i	$-0.784957\pi$
$67$	−5695.24	+	5695.24i	−0.154998	+	0.154998i	0.625348	+	0.780346i	$0.284957\pi$
$68$	22106.9	−	9780.89i	0.579770	−	0.256511i
$69$	−7196.62	+	7196.62i	−0.181973	+	0.181973i
$70$	21100.0	+	922.988i	0.514680	+	0.0225139i
$71$			50085.0i			1.17913i	0.807721	+	0.589565i	$0.200701\pi$
$71$			50085.0i			1.17913i	−0.807721	+	0.589565i	$0.799299\pi$
$72$	42243.7	+	6842.41i	0.960353	+	0.155553i
$73$	56678.1			1.24483			0.622413	−	0.782689i	$-0.286153\pi$
$73$	56678.1			1.24483			0.622413	+	0.782689i	$0.286153\pi$
$74$	−15053.4	−	71229.4i	−0.319563	−	1.51210i
$75$	2228.41	+	7708.25i	0.0457448	+	0.158235i
$76$	−31149.4	+	80584.4i	−0.618608	+	1.60036i
$77$	−14376.9	+	14376.9i	−0.276337	+	0.276337i
$78$	−7081.09	+	10876.1i	−0.131784	+	0.202413i
$79$	48495.1			0.874239			0.437120	−	0.899403i	$-0.355999\pi$
$79$	48495.1			0.874239			0.437120	+	0.899403i	$0.355999\pi$
$80$	−11613.4	+	56052.9i	−0.202877	+	0.979204i
$81$	−54286.3			−0.919343
$82$	15074.3	−	23153.2i	0.247572	−	0.380256i
$83$	57382.7	−	57382.7i	0.914293	−	0.914293i	−0.0823134	−	0.996606i	$-0.526231\pi$
$83$	57382.7	−	57382.7i	0.914293	−	0.914293i	0.996606	+	0.0823134i	$0.0262308\pi$
$84$	5118.52	+	1978.53i	0.0791491	+	0.0305946i
$85$	−21472.9	−	36363.5i	−0.322362	−	0.545907i
$86$	−10124.9	−	47908.5i	−0.147619	−	0.698500i
$87$	−2130.48			−0.0301773
$88$	−32234.9	−	44695.7i	−0.443731	−	0.615260i
$89$		−	41470.4i		−	0.554962i	−0.960731	−	0.277481i	$-0.910501\pi$
$89$		−	41470.4i		−	0.554962i	0.960731	−	0.277481i	$-0.0894995\pi$
$90$	3267.07	−	74687.1i	0.0425160	−	0.971940i
$91$	42197.3	−	42197.3i	0.534172	−	0.534172i
$92$	51320.2	+	115995.i	0.632148	+	1.42879i
$93$	−8524.07	+	8524.07i	−0.102197	+	0.102197i
$94$	54996.9	−	84471.9i	0.641976	−	0.986036i
$95$	146160.	+	37630.4i	1.66157	+	0.427790i
$96$	−7511.71	+	12837.1i	−0.0831881	+	0.142164i
$97$		−	5473.40i		−	0.0590647i	−0.999564	−	0.0295324i	$-0.990598\pi$
$97$		−	5473.40i		−	0.0590647i	0.999564	−	0.0295324i	$-0.00940181\pi$
$98$	58529.7	+	38106.8i	0.615618	+	0.400809i
$99$	50889.5	+	50889.5i	0.521844	+	0.521844i
$100$	99618.0	+	8731.98i	0.996180	+	0.0873198i
$101$	−130838.	+	130838.i	−1.27624	+	1.27624i	−0.333481	+	0.942757i	$0.608223\pi$
$101$	−130838.	+	130838.i	−1.27624	+	1.27624i	−0.942757	+	0.333481i	$0.891777\pi$
$102$	−2268.80	−	10735.5i	−0.0215922	−	0.102169i
$103$	−151457.			−1.40668			−0.703342	−	0.710852i	$-0.748310\pi$
$103$	−151457.			−1.40668			−0.703342	+	0.710852i	$0.748310\pi$
$104$	94611.9	+	131185.i	0.857753	+	1.18933i
$105$	2390.19	−	9283.70i	0.0211573	−	0.0821765i
$106$	1954.85	+	9249.88i	0.0168985	+	0.0799597i
$107$	−109508.	−	109508.i	−0.924669	−	0.924669i	0.0726858	−	0.997355i	$-0.476843\pi$
$107$	−109508.	−	109508.i	−0.924669	−	0.924669i	−0.997355	+	0.0726858i	$0.976843\pi$
$108$	14202.0	−	36741.0i	0.117163	−	0.303104i
$109$	15125.6	+	15125.6i	0.121940	+	0.121940i	0.765443	−	0.643503i	$-0.222520\pi$
$109$	15125.6	+	15125.6i	0.121940	+	0.121940i	−0.643503	+	0.765443i	$0.722520\pi$
$110$	−70981.7	+	65032.0i	−0.559325	+	0.512443i
$111$	−33045.1			−0.254566
$112$	45999.1	−	50610.2i	0.346501	−	0.381235i
$113$			73302.7i			0.540037i	0.962855	+	0.270019i	$0.0870299\pi$
$113$			73302.7i			0.540037i	−0.962855	+	0.270019i	$0.912970\pi$
$114$	32863.3	+	21396.3i	0.236837	+	0.154197i
$115$	190799.	−	112668.i	1.34534	−	0.794432i
$116$	−9573.12	+	24765.9i	−0.0660554	+	0.170887i
$117$	−149365.	−	149365.i	−1.00875	−	1.00875i
$118$	−130381.	+	27554.3i	−0.862003	+	0.182173i
$119$			50454.1i			0.326609i
$120$	23802.6	+	10418.1i	0.150894	+	0.0660445i
$121$			68375.4i			0.424558i
$122$	64553.4	+	305452.i	0.392663	+	1.85799i
$123$	−8867.34	−	8867.34i	−0.0528483	−	0.0528483i
$124$	60786.5	+	137391.i	0.355020	+	0.802422i
$125$	−5141.02	−	174617.i	−0.0294289	−	0.999567i
$126$	−48732.8	+	74850.6i	−0.273461	+	0.420019i
$127$		−	95791.2i		−	0.527007i	−0.964658	−	0.263503i	$-0.915122\pi$
$127$		−	95791.2i		−	0.527007i	0.964658	−	0.263503i	$-0.0848780\pi$
$128$	115473.	+	145003.i	0.622952	+	0.782260i
$129$	−22226.0			−0.117594
$130$	208337.	−	190874.i	1.08120	−	0.990576i
$131$	−58638.1	−	58638.1i	−0.298540	−	0.298540i	0.541902	−	0.840442i	$-0.317704\pi$
$131$	−58638.1	−	58638.1i	−0.298540	−	0.298540i	−0.840442	+	0.541902i	$0.817704\pi$
$132$	−22874.3	+	10120.4i	−0.114265	+	0.0505548i
$133$	−127504.	−	127504.i	−0.625019	−	0.625019i
$134$	44577.3	−	9420.86i	0.214463	−	0.0453240i
$135$	−66638.9	−	17156.9i	−0.314698	−	0.0810223i
$136$	−134989.	−	21864.9i	−0.625824	−	0.101368i
$137$	49131.8			0.223646			0.111823	−	0.993728i	$-0.464331\pi$
$137$	49131.8			0.223646			0.111823	+	0.993728i	$0.464331\pi$
$138$	56328.8	−	11904.4i	0.251787	−	0.0532119i
$139$	34482.0	−	34482.0i	0.151375	−	0.151375i	−0.627357	−	0.778732i	$-0.715863\pi$
$139$	34482.0	−	34482.0i	0.151375	−	0.151375i	0.778732	+	0.627357i	$0.215863\pi$
$140$	−97178.8	−	69500.3i	−0.419036	−	0.299686i
$141$	−32351.6	−	32351.6i	−0.137040	−	0.137040i
$142$	154586.	−	237435.i	0.643354	−	0.988152i
$143$			272010.i			1.11236i
$144$	−179143.	−	162822.i	−0.719937	−	0.654344i
$145$	44919.1	+	11564.9i	0.177424	+	0.0456797i
$146$	−268691.	−	174936.i	−1.04321	−	0.679198i
$147$	22416.1	−	22416.1i	0.0855591	−	0.0855591i
$148$	−148485.	+	384135.i	−0.557222	+	1.44155i
$149$	−114886.	+	114886.i	−0.423938	+	0.423938i	−0.886557	−	0.462619i	$-0.846910\pi$
$149$	−114886.	+	114886.i	−0.423938	+	0.423938i	0.462619	+	0.886557i	$0.346910\pi$
$150$	13227.2	−	43419.9i	0.0480000	−	0.157565i
$151$		−	112578.i		−	0.401800i	−0.979612	−	0.200900i	$-0.935613\pi$
$151$		−	112578.i		−	0.401800i	0.979612	−	0.200900i	$-0.0643867\pi$
$152$	396390.	−	285880.i	1.39160	−	1.00363i
$153$	178591.			0.616780
$154$	112530.	−	23781.7i	0.382354	−	0.0808057i
$155$	225993.	−	133450.i	0.755554	−	0.446159i
$156$	67137.8	−	29704.1i	0.220880	−	0.0977250i
$157$	−218623.	+	218623.i	−0.707860	+	0.707860i	−0.966085	−	0.258225i	$-0.916862\pi$
$157$	−218623.	+	218623.i	−0.707860	+	0.707860i	0.258225	+	0.966085i	$0.416862\pi$
$158$	−229898.	−	149679.i	−0.732643	−	0.477000i
$159$	4291.26			0.0134614
$160$	228061.	−	229882.i	0.704289	−	0.709913i
$161$	−264732.			−0.804900
$162$	257352.	+	167553.i	0.770442	+	0.501610i
$163$	194909.	−	194909.i	0.574596	−	0.574596i	−0.358813	−	0.933409i	$-0.616819\pi$
$163$	194909.	−	194909.i	0.574596	−	0.574596i	0.933409	+	0.358813i	$0.116819\pi$
$164$	−142923.	+	63234.4i	−0.414948	+	0.183588i
$165$	22218.3	+	37625.8i	0.0635331	+	0.107591i
$166$	−449141.	+	94920.2i	−1.26506	+	0.267355i
$167$	−241326.			−0.669596			−0.334798	−	0.942290i	$-0.608668\pi$
$167$	−241326.			−0.669596			−0.334798	+	0.942290i	$0.608668\pi$
$168$	−18158.4	−	25177.7i	−0.0496368	−	0.0688245i
$169$		−	427077.i		−	1.15024i
$170$	−10439.9	+	238662.i	−0.0277060	+	0.633375i
$171$	−451321.	+	451321.i	−1.18031	+	1.18031i
$172$	−99870.2	+	258367.i	−0.257404	+	0.665911i
$173$	−98095.6	+	98095.6i	−0.249192	+	0.249192i	−0.820639	−	0.571447i	$-0.806382\pi$
$173$	−98095.6	+	98095.6i	−0.249192	+	0.249192i	0.571447	+	0.820639i	$0.306382\pi$
$174$	10099.9	+	6575.69i	0.0252896	+	0.0164653i
$175$	−100790.	+	182763.i	−0.248783	+	0.451121i
$176$	14861.8	+	311378.i	0.0361650	+	0.757717i
$177$			60487.0i			0.145121i
$178$	−127997.	+	196596.i	−0.302797	+	0.465077i
$179$	−65528.8	−	65528.8i	−0.152862	−	0.152862i	0.626533	−	0.779395i	$-0.284473\pi$
$179$	−65528.8	−	65528.8i	−0.152862	−	0.152862i	−0.779395	+	0.626533i	$0.784473\pi$
$180$	−246008.	+	343981.i	−0.565937	+	0.791322i
$181$	150608.	−	150608.i	0.341706	−	0.341706i	−0.515303	−	0.857008i	$-0.672320\pi$
$181$	150608.	−	150608.i	0.341706	−	0.341706i	0.857008	+	0.515303i	$0.172320\pi$
$182$	−330283.	+	69801.2i	−0.739108	+	0.156201i
$183$	141707.			0.312798
$184$	114725.	−	708288.i	0.249811	−	1.54229i
$185$	696724.	+	179379.i	1.49669	+	0.385339i
$186$	66718.9	−	14100.2i	0.141406	−	0.0298843i
$187$	−162617.	−	162617.i	−0.340065	−	0.340065i
$188$	−521441.	+	230704.i	−1.07600	+	0.476059i
$189$	58133.0	+	58133.0i	0.118377	+	0.118377i
$190$	−576745.	−	629511.i	−1.15904	−	1.26508i
$191$	432078.			0.856995			0.428498	−	0.903543i	$-0.359043\pi$
$191$	432078.			0.856995			0.428498	+	0.903543i	$0.359043\pi$
$192$	75231.8	−	37671.5i	0.147282	−	0.0737496i
$193$			446187.i			0.862231i	0.902297	+	0.431115i	$0.141880\pi$
$193$			446187.i			0.862231i	−0.902297	+	0.431115i	$0.858120\pi$
$194$	−16893.5	+	25947.4i	−0.0322267	+	0.0494983i
$195$	−65212.3	−	110434.i	−0.122813	−	0.207978i
$196$	−159852.	−	361301.i	−0.297221	−	0.671783i
$197$	−409391.	−	409391.i	−0.751576	−	0.751576i	0.223197	−	0.974773i	$-0.428351\pi$
$197$	−409391.	−	409391.i	−0.751576	−	0.751576i	−0.974773	+	0.223197i	$0.928351\pi$
$198$	−84179.5	−	398318.i	−0.152596	−	0.722050i
$199$			153658.i			0.275056i	0.990498	+	0.137528i	$0.0439157\pi$
$199$			153658.i			0.275056i	−0.990498	+	0.137528i	$0.956084\pi$
$200$	−445302.	−	348864.i	−0.787190	−	0.616710i
$201$		−	20680.6i		−	0.0361054i
$202$	1.02409e6	−	216428.i	1.76587	−	0.373194i
$203$	−39185.6	−	39185.6i	−0.0667400	−	0.0667400i
$204$	−22379.1	+	57895.5i	−0.0376503	+	0.0974023i
$205$	138824.	+	235094.i	0.230718	+	0.390712i
$206$	718003.	+	467469.i	1.17885	+	0.767511i
$207$			937064.i			1.52000i
$208$	−43620.4	−	913919.i	−0.0699087	−	1.46470i
$209$	821906.			1.30154
$210$	−39985.0	+	36633.4i	−0.0625674	+	0.0573230i
$211$	−266226.	−	266226.i	−0.411665	−	0.411665i	0.470653	−	0.882318i	$-0.344018\pi$
$211$	−266226.	−	266226.i	−0.411665	−	0.411665i	−0.882318	+	0.470653i	$0.844018\pi$
$212$	19282.3	−	49883.9i	0.0294659	−	0.0762291i
$213$	−90934.3	−	90934.3i	−0.137334	−	0.137334i
$214$	181144.	+	857132.i	0.270389	+	1.27942i
$215$	468613.	+	120649.i	0.691382	+	0.178004i
$216$	−180727.	+	130342.i	−0.263565	+	0.190085i
$217$	−313563.			−0.452039
$218$	−25020.2	−	118390.i	−0.0356573	−	0.168722i
$219$	−102905.	+	102905.i	−0.144986	+	0.144986i
$220$	537218.	−	89209.8i	0.748332	−	0.124267i
$221$	477293.	+	477293.i	0.657362	+	0.657362i
$222$	156655.	+	101993.i	0.213335	+	0.138896i
$223$			976009.i			1.31429i	0.753763	+	0.657146i	$0.228236\pi$
$223$			976009.i			1.31429i	−0.753763	+	0.657146i	$0.771764\pi$
$224$	−374272.	+	97949.3i	−0.498388	+	0.130431i
$225$	646920.	+	356762.i	0.851911	+	0.469810i
$226$	226247.	−	347502.i	0.294654	−	0.452570i
$227$	788265.	−	788265.i	1.01533	−	1.01533i	0.0154498	−	0.999881i	$-0.495082\pi$
$227$	788265.	−	788265.i	1.01533	−	1.01533i	0.999881	−	0.0154498i	$-0.00491801\pi$
$228$	−89754.2	−	202864.i	−0.114345	−	0.258445i
$229$	654476.	−	654476.i	0.824717	−	0.824717i	−0.162063	−	0.986780i	$-0.551815\pi$
$229$	654476.	−	654476.i	0.824717	−	0.824717i	0.986780	+	0.162063i	$0.0518148\pi$
$230$	−1.25226e6	−	54778.1i	−1.56090	−	0.0682790i
$231$		−	52205.4i		−	0.0643703i
$232$	121822.	−	87859.1i	0.148596	−	0.107168i
$233$	1.58630e6			1.91424			0.957118	−	0.289697i	$-0.0935546\pi$
$233$	1.58630e6			1.91424			0.957118	+	0.289697i	$0.0935546\pi$
$234$	247073.	+	1.16909e6i	0.294976	+	1.39576i
$235$	506486.	+	857715.i	0.598271	+	1.01315i
$236$	703134.	+	271792.i	0.821785	+	0.317656i
$237$	−88047.7	+	88047.7i	−0.101823	+	0.101823i
$238$	155725.	−	239185.i	0.178204	−	0.273710i
$239$	−1.41494e6			−1.60229			−0.801147	−	0.598467i	$-0.795777\pi$
$239$	−1.41494e6			−1.60229			−0.801147	+	0.598467i	$0.795777\pi$
$240$	−80684.4	−	122855.i	−0.0904194	−	0.137678i
$241$	857282.			0.950782			0.475391	−	0.879775i	$-0.342307\pi$
$241$	857282.			0.950782			0.475391	+	0.879775i	$0.342307\pi$
$242$	211039.	−	324143.i	0.231646	−	0.355794i
$243$	310072.	−	310072.i	0.336858	−	0.336858i
$244$	636746.	−	1.64728e6i	0.684686	−	1.77130i
$245$	−594302.	+	350939.i	−0.632546	+	0.373522i
$246$	14668.0	+	69405.7i	0.0154538	+	0.0731236i
$247$	−2.41236e6			−2.51593
$248$	135886.	−	838935.i	0.140296	−	0.866162i
$249$			208368.i			0.212977i
$250$	−514580.	+	843665.i	−0.520718	+	0.853728i
$251$	618043.	−	618043.i	0.619205	−	0.619205i	−0.326123	−	0.945327i	$-0.605742\pi$
$251$	618043.	−	618043.i	0.619205	−	0.619205i	0.945327	+	0.326123i	$0.105742\pi$
$252$	462049.	−	204427.i	0.458339	−	0.202786i
$253$	853250.	−	853250.i	0.838060	−	0.838060i
$254$	−295657.	+	454111.i	−0.287544	+	0.441650i
$255$	105008.	+	27035.4i	0.101128	+	0.0260365i
$256$	−99867.4	−	1.04381e6i	−0.0952410	−	0.995454i
$257$			860805.i			0.812965i	0.913659	+	0.406482i	$0.133245\pi$
$257$			860805.i			0.812965i	−0.913659	+	0.406482i	$0.866755\pi$
$258$	105365.	+	68600.0i	0.0985482	+	0.0641616i
$259$	−607793.	−	607793.i	−0.562997	−	0.562997i
$260$	−1.57678e6	+	261838.i	−1.44656	+	0.240214i
$261$	−138704.	+	138704.i	−0.126034	+	0.126034i
$262$	96997.0	+	458968.i	0.0872982	+	0.413075i
$263$	16274.1			0.0145080			0.00725398	−	0.999974i	$-0.497691\pi$
$263$	16274.1			0.0145080			0.00725398	+	0.999974i	$0.497691\pi$
$264$	139675.	+	22623.8i	0.123342	+	0.0199782i
$265$	−90476.8	−	23294.3i	−0.0791449	−	0.0203767i
$266$	210912.	+	997986.i	0.182766	+	0.864809i
$267$	75293.6	+	75293.6i	0.0646368	+	0.0646368i
$268$	−240402.	−	92926.0i	−0.204457	−	0.0790315i
$269$	298521.	+	298521.i	0.251533	+	0.251533i	0.821599	−	0.570066i	$-0.193082\pi$
$269$	298521.	+	298521.i	0.251533	+	0.251533i	−0.570066	+	0.821599i	$0.693082\pi$
$270$	262957.	+	287014.i	0.219520	+	0.239604i
$271$	−228547.			−0.189039			−0.0945196	−	0.995523i	$-0.530132\pi$
$271$	−228547.			−0.189039			−0.0945196	+	0.995523i	$0.530132\pi$
$272$	572451.	+	520295.i	0.469155	+	0.426410i
$273$			153227.i			0.124431i
$274$	−232916.	−	151644.i	−0.187423	−	0.122025i
$275$	−264206.	−	913909.i	−0.210674	−	0.728738i
$276$	−303777.	−	117423.i	−0.240039	−	0.0927857i
$277$	−1.67652e6	−	1.67652e6i	−1.31284	−	1.31284i	−0.919317	−	0.393519i	$-0.871258\pi$
$277$	−1.67652e6	−	1.67652e6i	−1.31284	−	1.31284i	−0.393519	−	0.919317i	$-0.628742\pi$
$278$	−269894.	+	57038.8i	−0.209451	+	0.0442648i
$279$			1.10991e6i			0.853645i
$280$	246179.	+	629416.i	0.187653	+	0.479780i
$281$		−	951097.i		−	0.718553i	−0.933231	−	0.359277i	$-0.883023\pi$
$281$		−	951097.i		−	0.718553i	0.933231	−	0.359277i	$-0.116977\pi$
$282$	53514.8	+	253220.i	0.0400729	+	0.189616i
$283$	−302270.	−	302270.i	−0.224351	−	0.224351i	0.585977	−	0.810328i	$-0.300711\pi$
$283$	−302270.	−	302270.i	−0.224351	−	0.224351i	−0.810328	+	0.585977i	$0.800711\pi$
$284$	−1.46567e6	+	648466.i	−1.07830	+	0.477080i
$285$	−333689.	+	197046.i	−0.243349	+	0.143699i
$286$	839552.	−	1.28950e6i	0.606922	−	0.932194i
$287$		−	326190.i		−	0.233758i
$288$	346708.	+	1.32480e6i	0.246311	+	0.941172i
$289$	849172.			0.598068
$290$	−177251.	−	193467.i	−0.123764	−	0.135087i
$291$	9937.51	+	9937.51i	0.00687931	+	0.00687931i
$292$	733830.	+	1.65861e6i	0.503661	+	1.13838i
$293$	−891830.	−	891830.i	−0.606894	−	0.606894i	0.335239	−	0.942133i	$-0.391183\pi$
$293$	−891830.	−	891830.i	−0.606894	−	0.606894i	−0.942133	+	0.335239i	$0.891183\pi$
$294$	−175453.	+	37079.8i	−0.118384	+	0.0250190i
$295$	328342.	−	1.27531e6i	0.219670	−	0.853218i
$296$	1.88954e6	−	1.36275e6i	1.25351	−	0.904038i
$297$	−374733.			−0.246508
$298$	899229.	−	190041.i	0.586583	−	0.123967i
$299$	−2.50435e6	+	2.50435e6i	−1.62001	+	1.62001i
$300$	−196720.	+	165013.i	−0.126196	+	0.105856i
$301$	−408798.	−	408798.i	−0.260071	−	0.260071i
$302$	−347469.	+	533691.i	−0.219229	+	0.336723i
$303$		−	475100.i		−	0.297289i
$304$	−2.76150e6	+	131804.i	−1.71381	+	0.0817982i
$305$	−2.98775e6	−	769229.i	−1.83905	−	0.473485i
$306$	−846634.	−	551216.i	−0.516883	−	0.336526i
$307$	−1.35818e6	+	1.35818e6i	−0.822451	+	0.822451i	−0.986459	−	0.164008i	$-0.947558\pi$
$307$	−1.35818e6	+	1.35818e6i	−0.822451	+	0.822451i	0.164008	+	0.986459i	$0.447558\pi$
$308$	−606865.	−	234580.i	−0.364515	−	0.140901i
$309$	274985.	−	274985.i	0.163837	−	0.163837i
$310$	−1.48324e6	−	64882.1i	−0.876612	−	0.0383461i
$311$			923803.i			0.541599i	0.962636	+	0.270800i	$0.0872881\pi$
$311$			923803.i			0.541599i	−0.962636	+	0.270800i	$0.912712\pi$
$312$	−409957.	−	66402.6i	−0.238425	−	0.0386188i
$313$	−791901.			−0.456888			−0.228444	−	0.973557i	$-0.573364\pi$
$313$	−791901.			−0.456888			−0.228444	+	0.973557i	$0.573364\pi$
$314$	1.71119e6	−	361638.i	0.979432	−	0.206990i
$315$	−448798.	−	760022.i	−0.254844	−	0.431569i
$316$	627882.	+	1.41915e6i	0.353721	+	0.799485i
$317$	276824.	−	276824.i	0.154723	−	0.154723i	−0.625500	−	0.780224i	$-0.715105\pi$
$317$	276824.	−	276824.i	0.154723	−	0.154723i	0.780224	+	0.625500i	$0.215105\pi$
$318$	−20343.3	−	13244.9i	−0.0112812	−	0.00734479i
$319$	252596.			0.138979
$320$	−1.79068e6	+	385884.i	−0.977559	+	0.210660i
$321$	397645.			0.215394
$322$	1.25500e6	+	817089.i	0.674534	+	0.439167i
$323$	1.44219e6	−	1.44219e6i	0.769160	−	0.769160i
$324$	−702862.	−	1.58862e6i	−0.371970	−	0.840732i
$325$	775464.	+	2.68239e6i	0.407243	+	1.40869i
$326$	−1.52557e6	+	322411.i	−0.795041	+	0.168022i
$327$	−54924.0			−0.0284049
$328$	872720.	+	141358.i	0.447909	+	0.0725499i
$329$		−	1.19007e6i		−	0.606155i
$330$	10802.3	−	246946.i	0.00546048	−	0.124830i
$331$	2.00251e6	−	2.00251e6i	1.00463	−	1.00463i	0.00463803	−	0.999989i	$-0.498524\pi$
$331$	2.00251e6	−	2.00251e6i	1.00463	−	1.00463i	0.999989	−	0.00463803i	$-0.00147634\pi$
$332$	2.42218e6	+	936280.i	1.20604	+	0.466187i
$333$	−2.15139e6	+	2.15139e6i	−1.06318	+	1.06318i
$334$	1.14404e6	+	744847.i	0.561144	+	0.365343i
$335$	−112260.	+	436029.i	−0.0546531	+	0.212277i
$336$	8371.84	+	175404.i	0.00404550	+	0.0847599i
$337$		−	1.19366e6i		−	0.572542i	−0.958149	−	0.286271i	$-0.907584\pi$
$337$		−	1.19366e6i		−	0.572542i	0.958149	−	0.286271i	$-0.0924157\pi$
$338$	−1.31816e6	+	2.02462e6i	−0.627591	+	0.963942i
$339$	−133088.	−	133088.i	−0.0628986	−	0.0628986i
$340$	786117.	−	1.09919e6i	0.368799	−	0.515673i
$341$	1.01064e6	−	1.01064e6i	0.470661	−	0.470661i
$342$	3.53254e6	−	746558.i	1.63313	−	0.345142i
$343$	1.94709e6			0.893617
$344$	1.27089e6	−	916578.i	0.579046	−	0.417612i
$345$	−141855.	+	550975.i	−0.0641646	+	0.249221i
$346$	767806.	−	162266.i	0.344795	−	0.0728681i
$347$	−1.73877e6	−	1.73877e6i	−0.775209	−	0.775209i	0.203803	−	0.979012i	$-0.434670\pi$
$347$	−1.73877e6	−	1.73877e6i	−0.775209	−	0.775209i	−0.979012	+	0.203803i	$0.934670\pi$
$348$	−27584.1	−	62346.0i	−0.0122098	−	0.0275969i
$349$	−717557.	−	717557.i	−0.315350	−	0.315350i	0.531628	−	0.846978i	$-0.321580\pi$
$349$	−717557.	−	717557.i	−0.315350	−	0.315350i	−0.846978	+	0.531628i	$0.821580\pi$
$350$	1.04190e6	−	555328.i	0.454628	−	0.242315i
$351$	1.09987e6			0.476512
$352$	890608.	−	1.52200e6i	0.383116	−	0.654725i
$353$		−	3.03453e6i		−	1.29615i	−0.761578	−	0.648074i	$-0.775575\pi$
$353$		−	3.03453e6i		−	1.29615i	0.761578	−	0.648074i	$-0.224425\pi$
$354$	186692.	−	286747.i	0.0791803	−	0.121616i
$355$	1.42364e6	+	2.41088e6i	0.599555	+	1.01532i
$356$	1.21358e6	−	536930.i	0.507508	−	0.224539i
$357$	−91604.4	−	91604.4i	−0.0380405	−	0.0380405i
$358$	108395.	+	512902.i	0.0446995	+	0.211508i
$359$		−	512652.i		−	0.209936i	−0.994476	−	0.104968i	$-0.966526\pi$
$359$		−	512652.i		−	0.209936i	0.994476	−	0.104968i	$-0.0334740\pi$
$360$	2.22792e6	−	871391.i	0.906033	−	0.354370i
$361$			4.81309e6i			1.94382i
$362$	−1.17883e6	+	249130.i	−0.472802	+	0.0999207i
$363$	−124142.	−	124142.i	−0.0494486	−	0.0494486i
$364$	1.78119e6	+	688509.i	0.704624	+	0.272368i
$365$	2.72824e6	−	1.61105e6i	1.07189	−	0.632959i
$366$	−671782.	−	437375.i	−0.262135	−	0.170668i
$367$		−	2.92644e6i		−	1.13416i	−0.823663	−	0.567080i	$-0.808073\pi$
$367$		−	2.92644e6i		−	1.13416i	0.823663	−	0.567080i	$-0.191927\pi$
$368$	−2.72998e6	+	3.00364e6i	−1.05085	+	1.15619i
$369$	−1.15461e6			−0.441436
$370$	−2.74927e6	−	3.00079e6i	−1.04403	−	1.13955i
$371$	78928.2	+	78928.2i	0.0297713	+	0.0297713i
$372$	−359810.	−	139082.i	−0.134808	−	0.0521092i
$373$	2.04904e6	+	2.04904e6i	0.762567	+	0.762567i	0.976786	−	0.214219i	$-0.0687205\pi$
$373$	2.04904e6	+	2.04904e6i	0.762567	+	0.762567i	−0.214219	+	0.976786i	$0.568720\pi$
$374$	268995.	+	1.27282e6i	0.0994409	+	0.470532i
$375$	326369.	+	307701.i	0.119848	+	0.112993i
$376$	3.18403e6	+	515732.i	1.16147	+	0.188128i
$377$	−741388.			−0.268653
$378$	−96161.4	−	455014.i	−0.0346155	−	0.163793i
$379$	−265407.	+	265407.i	−0.0949106	+	0.0949106i	−0.752968	−	0.658057i	$-0.771378\pi$
$379$	−265407.	+	265407.i	−0.0949106	+	0.0949106i	0.658057	+	0.752968i	$0.271378\pi$
$380$	791169.	+	4.76439e6i	0.281067	+	1.69258i
$381$	173918.	+	173918.i	0.0613809	+	0.0613809i
$382$	−2.04832e6	−	1.33360e6i	−0.718192	−	0.467591i
$383$			865077.i			0.301341i	0.988584	+	0.150670i	$0.0481432\pi$
$383$			865077.i			0.301341i	−0.988584	+	0.150670i	$0.951857\pi$
$384$	−472919.	−	53614.5i	−0.163666	−	0.0185547i
$385$	−283387.	+	1.10070e6i	−0.0974380	+	0.378457i
$386$	1.37715e6	−	2.11521e6i	0.470448	−	0.722579i
$387$	−1.44701e6	+	1.44701e6i	−0.491127	+	0.491127i
$388$	160172.	−	70865.9i	0.0540142	−	0.0238978i
$389$	2.34562e6	−	2.34562e6i	0.785928	−	0.785928i	−0.194896	−	0.980824i	$-0.562437\pi$
$389$	2.34562e6	−	2.34562e6i	0.785928	−	0.785928i	0.980824	+	0.194896i	$0.0624368\pi$
$390$	−31705.5	+	724806.i	−0.0105554	+	0.241302i
$391$		−	2.99438e6i		−	0.990524i
$392$	−357345.	+	2.20618e6i	−0.117455	+	0.725146i
$393$	212927.			0.0695423
$394$	677200.	+	3.20435e6i	0.219774	+	1.03992i
$395$	2.33435e6	−	1.37845e6i	0.752789	−	0.444527i
$396$	−830335.	+	2.14810e6i	−0.266082	+	0.688362i
$397$	42359.3	−	42359.3i	0.0134888	−	0.0134888i	−0.700330	−	0.713819i	$-0.746964\pi$
$397$	42359.3	−	42359.3i	0.0134888	−	0.0134888i	0.713819	+	0.700330i	$0.246964\pi$
$398$	474261.	−	728435.i	0.150075	−	0.230507i
$399$	462991.			0.145593
$400$	1.03426e6	+	3.02825e6i	0.323205	+	0.946329i
$401$	−1.38642e6			−0.430561			−0.215280	−	0.976552i	$-0.569067\pi$
$401$	−1.38642e6			−0.430561			−0.215280	+	0.976552i	$0.569067\pi$
$402$	−63830.1	+	98039.1i	−0.0196997	+	0.0302576i
$403$	−2.96629e6	+	2.96629e6i	−0.909811	+	0.909811i
$404$	−5.52283e6	−	2.13481e6i	−1.68348	−	0.650739i
$405$	−2.61311e6	+	1.54306e6i	−0.791627	+	0.467461i
$406$	64819.3	+	306710.i	0.0195159	+	0.0923449i
$407$	3.91792e6			1.17238
$408$	284785.	−	205389.i	0.0846966	−	0.0610839i
$409$		−	2.44842e6i		−	0.723732i	−0.932230	−	0.361866i	$-0.882140\pi$
$409$		−	2.44842e6i		−	0.723732i	0.932230	−	0.361866i	$-0.117860\pi$
$410$	67495.0	−	1.54297e6i	0.0198295	−	0.453314i
$411$	−89203.7	+	89203.7i	−0.0260482	+	0.0260482i
$412$	−1.96096e6	−	4.43220e6i	−0.569149	−	1.28640i
$413$	−1.11253e6	+	1.11253e6i	−0.320948	+	0.320948i
$414$	2.89223e6	−	4.44228e6i	0.829338	−	1.27381i
$415$	1.13108e6	−	4.39323e6i	0.322385	−	1.25217i
$416$	−2.61400e6	+	4.46719e6i	−0.740581	+	1.26561i
$417$			125211.i			0.0352616i
$418$	−3.89636e6	−	2.53679e6i	−1.09073	−	0.710141i
$419$	3.79954e6	+	3.79954e6i	1.05730	+	1.05730i	0.998256	+	0.0590396i	$0.0188038\pi$
$419$	3.79954e6	+	3.79954e6i	1.05730	+	1.05730i	0.0590396	+	0.998256i	$0.481196\pi$
$420$	302622.	−	50253.1i	0.0837101	−	0.0139008i
$421$	−3.49666e6	+	3.49666e6i	−0.961498	+	0.961498i	−0.999286	−	0.0377883i	$-0.987969\pi$
$421$	−3.49666e6	+	3.49666e6i	−0.961498	+	0.961498i	0.0377883	+	0.999286i	$0.487969\pi$
$422$	440380.	+	2.08378e6i	0.120378	+	0.569601i
$423$	−4.21246e6			−1.14468
$424$	−245376.	+	176967.i	−0.0662854	+	0.0478055i
$425$	−2.06723e6	−	1.14003e6i	−0.555157	−	0.306157i
$426$	150420.	+	711753.i	0.0401589	+	0.190023i
$427$	2.60639e6	+	2.60639e6i	0.691782	+	0.691782i
$428$	1.78678e6	−	4.62245e6i	0.471478	−	1.21973i
$429$	−493861.	−	493861.i	−0.129557	−	0.129557i
$430$	−1.84914e6	−	2.01832e6i	−0.482280	−	0.526403i
$431$	3.95495e6			1.02553			0.512765	−	0.858529i	$-0.328621\pi$
$431$	3.95495e6			1.02553			0.512765	+	0.858529i	$0.328621\pi$
$432$	1.25906e6	−	60093.5i	0.324591	−	0.0154924i
$433$			4.20674e6i			1.07827i	0.842221	+	0.539133i	$0.181248\pi$
$433$			4.20674e6i			1.07827i	−0.842221	+	0.539133i	$0.818752\pi$
$434$	1.48649e6	+	967805.i	0.378824	+	0.246640i
$435$	−102552.	+	60557.9i	−0.0259850	+	0.0153443i
$436$	−246795.	+	638467.i	−0.0621757	+	0.160850i
$437$	7.56717e6	+	7.56717e6i	1.89553	+	1.89553i
$438$	805448.	−	170221.i	0.200610	−	0.0423963i
$439$			4.79154e6i			1.18663i	0.804972	+	0.593313i	$0.202180\pi$
$439$			4.79154e6i			1.18663i	−0.804972	+	0.593313i	$0.797820\pi$
$440$	−2.82210e6	−	1.23520e6i	−0.694930	−	0.304163i
$441$		−	2.91877e6i		−	0.714667i
$442$	−789521.	−	3.73583e6i	−0.192224	−	0.909560i
$443$	2.31516e6	+	2.31516e6i	0.560494	+	0.560494i	0.929448	−	0.368954i	$-0.120284\pi$
$443$	2.31516e6	+	2.31516e6i	0.560494	+	0.560494i	−0.368954	+	0.929448i	$0.620284\pi$
$444$	−427846.	−	967025.i	−0.102998	−	0.232799i
$445$	−1.17877e6	−	1.99621e6i	−0.282183	−	0.477865i
$446$	3.01243e6	−	4.62691e6i	0.717100	−	1.10142i
$447$		−	417175.i		−	0.0987529i
$448$	2.07661e6	+	690840.i	0.488832	+	0.162623i
$449$	2.66476e6			0.623796			0.311898	−	0.950116i	$-0.399035\pi$
$449$	2.66476e6			0.623796			0.311898	+	0.950116i	$0.399035\pi$
$450$	−1.96568e6	−	3.68798e6i	−0.457595	−	0.858534i
$451$	1.05133e6	+	1.05133e6i	0.243388	+	0.243388i
$452$	−2.14511e6	+	949073.i	−0.493860	+	0.218501i
$453$	204396.	+	204396.i	0.0467980	+	0.0467980i
$454$	−6.16984e6	+	1.30392e6i	−1.40486	+	0.296900i
$455$	831763.	−	3.23064e6i	0.188352	−	0.731576i
$456$	−200643.	+	1.23873e6i	−0.0451867	+	0.278974i
$457$	−5.79281e6			−1.29747			−0.648737	−	0.761012i	$-0.724703\pi$
$457$	−5.79281e6			−1.29747			−0.648737	+	0.761012i	$0.724703\pi$
$458$	−5.12266e6	+	1.08261e6i	−1.14112	+	0.241162i
$459$	−657541.	+	657541.i	−0.145677	+	0.145677i
$460$	5.76743e6	+	4.12475e6i	1.27083	+	0.908872i
$461$	−3.54518e6	−	3.54518e6i	−0.776937	−	0.776937i	0.202372	−	0.979309i	$-0.435135\pi$
$461$	−3.54518e6	−	3.54518e6i	−0.776937	−	0.776937i	−0.979309	+	0.202372i	$0.935135\pi$
$462$	−161131.	+	247487.i	−0.0351216	+	0.0539446i
$463$		−	279304.i		−	0.0605515i	−0.999542	−	0.0302758i	$-0.990361\pi$
$463$		−	279304.i		−	0.0605515i	0.999542	−	0.0302758i	$-0.00963855\pi$
$464$	−848690.	+	40507.1i	−0.183001	+	0.00873446i
$465$	−168020.	+	652605.i	−0.0360354	+	0.139964i
$466$	−7.52008e6	−	4.89608e6i	−1.60420	−	1.04444i
$467$	1.25030e6	−	1.25030e6i	0.265291	−	0.265291i	−0.561909	−	0.827199i	$-0.689933\pi$
$467$	1.25030e6	−	1.25030e6i	0.265291	−	0.265291i	0.827199	+	0.561909i	$0.189933\pi$
$468$	2.43710e6	−	6.30484e6i	0.514349	−	1.33064i
$469$	380373.	−	380373.i	0.0798506	−	0.0798506i
$470$	246248.	−	5.62938e6i	0.0514196	−	1.17548i
$471$		−	793865.i		−	0.164890i
$472$	−2.49443e6	−	3.45868e6i	−0.515366	−	0.714587i
$473$	2.63517e6			0.541571
$474$	689160.	−	145645.i	0.140888	−	0.0297749i
$475$	8.10513e6	−	2.34315e6i	1.64826	−	0.476502i
$476$	−1.47648e6	+	653245.i	−0.298682	+	0.132147i
$477$	279380.	−	279380.i	0.0562211	−	0.0562211i
$478$	6.70771e6	+	4.36717e6i	1.34278	+	0.874240i
$479$	−4.94907e6			−0.985564			−0.492782	−	0.870153i	$-0.664020\pi$
$479$	−4.94907e6			−0.985564			−0.492782	+	0.870153i	$0.664020\pi$
$480$	3306.81	+	831441.i	0.000655097	+	0.164713i
$481$	−1.14994e7			−2.26627
$482$	−4.06406e6	−	2.64598e6i	−0.796788	−	0.518763i
$483$	480647.	−	480647.i	0.0937473	−	0.0937473i
$484$	−2.00092e6	+	885278.i	−0.388255	+	0.171778i
$485$	−155579.	−	263466.i	−0.0300328	−	0.0508593i
$486$	−2.42697e6	+	512910.i	−0.466095	+	0.0985032i
$487$	3.34367e6			0.638853			0.319427	−	0.947611i	$-0.396510\pi$
$487$	3.34367e6			0.638853			0.319427	+	0.947611i	$0.396510\pi$
$488$	−8.10288e6	+	5.84386e6i	−1.54024	+	1.11084i
$489$			707753.i			0.133847i
$490$	3.90054e6	+	170623.i	0.733895	+	0.0321031i
$491$	−990957.	+	990957.i	−0.185503	+	0.185503i	−0.793749	−	0.608246i	$-0.791874\pi$
$491$	−990957.	+	990957.i	−0.185503	+	0.185503i	0.608246	+	0.793749i	$0.291874\pi$
$492$	144683.	−	374300.i	0.0269467	−	0.0697119i
$493$	443228.	−	443228.i	0.0821314	−	0.0821314i
$494$	1.14361e7	+	7.44569e6i	2.10844	+	1.37274i
$495$	3.89611e6	+	1.00310e6i	0.714691	+	0.184005i
$496$	−3.23354e6	+	3.55768e6i	−0.590166	+	0.649326i
$497$		−	3.34507e6i		−	0.607455i
$498$	643123.	−	987797.i	0.116204	−	0.178482i
$499$	−3.21493e6	−	3.21493e6i	−0.577990	−	0.577990i	0.356359	−	0.934349i	$-0.384018\pi$
$499$	−3.21493e6	−	3.21493e6i	−0.577990	−	0.577990i	−0.934349	+	0.356359i	$0.884018\pi$
$500$	5.04339e6	−	2.41127e6i	0.902189	−	0.431341i
$501$	438151.	−	438151.i	0.0779883	−	0.0779883i
$502$	−4.83749e6	+	1.02234e6i	−0.856764	+	0.181066i
$503$	8.67311e6			1.52846			0.764231	−	0.644942i	$-0.223119\pi$
$503$	8.67311e6			1.52846			0.764231	+	0.644942i	$0.223119\pi$
$504$	−2.82137e6	−	456990.i	−0.494747	−	0.0801365i
$505$	−2.57899e6	+	1.00170e7i	−0.450009	+	1.74787i
$506$	−6.67849e6	+	1.41141e6i	−1.15958	+	0.245063i
$507$	775400.	+	775400.i	0.133970	+	0.133970i
$508$	2.80321e6	−	1.24024e6i	0.481943	−	0.213229i
$509$	−2.71092e6	−	2.71092e6i	−0.463792	−	0.463792i	0.436104	−	0.899896i	$-0.356358\pi$
$509$	−2.71092e6	−	2.71092e6i	−0.463792	−	0.463792i	−0.899896	+	0.436104i	$0.856358\pi$
$510$	−414360.	−	452269.i	−0.0705427	−	0.0769966i
$511$	−3.78541e6			−0.641300
$512$	−2.74826e6	+	5.25656e6i	−0.463322	+	0.886190i
$513$		−	3.32337e6i		−	0.557553i
$514$	2.65685e6	−	4.08076e6i	0.443568	−	0.681293i
$515$	−7.29050e6	+	4.30509e6i	−1.21126	+	0.715260i
$516$	−287767.	−	650416.i	−0.0475792	−	0.107539i
$517$	3.83569e6	+	3.83569e6i	0.631127	+	0.631127i
$518$	1.00539e6	+	4.75726e6i	0.164630	+	0.778992i
$519$		−	356205.i		−	0.0580472i
$520$	8.28308e6	+	3.62541e6i	1.34333	+	0.587961i
$521$		−	1.54053e6i		−	0.248643i	−0.992242	−	0.124321i	$-0.960325\pi$
$521$		−	1.54053e6i		−	0.248643i	0.992242	−	0.124321i	$-0.0396754\pi$
$522$	1.08565e6	−	229439.i	0.174387	−	0.0368545i
$523$	−8.81069e6	−	8.81069e6i	−1.40850	−	1.40850i	−0.767770	−	0.640726i	$-0.778633\pi$
$523$	−8.81069e6	−	8.81069e6i	−1.40850	−	1.40850i	−0.640726	−	0.767770i	$-0.721367\pi$
$524$	956765.	−	2.47518e6i	0.152222	−	0.393802i
$525$	−148831.	−	514818.i	−0.0235665	−	0.0815183i
$526$	−77149.4	−	50229.5i	−0.0121582	−	0.00791580i
$527$		−	3.54671e6i		−	0.556287i
$528$	−592322.	−	538356.i	−0.0924640	−	0.0840397i
$529$	9.27515e6			1.44106
$530$	357021.	+	389684.i	0.0552082	+	0.0602592i
$531$	3.93797e6	+	3.93797e6i	0.606089	+	0.606089i
$532$	2.08040e6	−	5.38206e6i	0.318690	−	0.824460i
$533$	−3.08575e6	−	3.08575e6i	−0.470481	−	0.470481i
$534$	−124548.	−	589332.i	−0.0189009	−	0.0894348i
$535$	−8.38395e6	−	2.15854e6i	−1.26638	−	0.326044i
$536$	852847.	+	1.18253e6i	0.128221	+	0.177786i
$537$	237948.			0.0356079
$538$	−493802.	−	2.33656e6i	−0.0735525	−	0.348033i
$539$	−2.65771e6	+	2.65771e6i	−0.394035	+	0.394035i
$540$	−360719.	−	2.17224e6i	−0.0532335	−	0.320570i
$541$	6.94709e6	+	6.94709e6i	1.02049	+	1.02049i	0.999786	+	0.0207067i	$0.00659161\pi$
$541$	6.94709e6	+	6.94709e6i	1.02049	+	1.02049i	0.0207067	+	0.999786i	$0.493408\pi$
$542$	1.08346e6	+	705405.i	0.158421	+	0.103143i
$543$			546889.i			0.0795975i
$544$	−1.10790e6	−	4.23339e6i	−0.160511	−	0.613325i
$545$	1.15802e6	+	298144.i	0.167003	+	0.0429967i
$546$	472931.	−	726393.i	0.0678917	−	0.104277i
$547$	−6.35931e6	+	6.35931e6i	−0.908744	+	0.908744i	−0.996171	−	0.0874266i	$-0.972136\pi$
$547$	−6.35931e6	+	6.35931e6i	−0.908744	+	0.908744i	0.0874266	+	0.996171i	$0.472136\pi$
$548$	636125.	+	1.43778e6i	0.0904880	+	0.204523i
$549$	9.22575e6	−	9.22575e6i	1.30638	−	1.30638i
$550$	−1.56826e6	+	5.14798e6i	−0.221060	+	0.725655i
$551$			2.24018e6i			0.314343i
$552$	1.07767e6	+	1.49426e6i	0.150536	+	0.208727i
$553$	−3.23889e6			−0.450384
$554$	2.77324e6	+	1.31223e7i	0.383896	+	1.81651i
$555$	−1.59065e6	+	939291.i	−0.219201	+	0.129440i
$556$	1.45552e6	+	562623.i	0.199679	+	0.0771845i
$557$	2.49577e6	−	2.49577e6i	0.340853	−	0.340853i	−0.515835	−	0.856688i	$-0.672518\pi$
$557$	2.49577e6	−	2.49577e6i	0.340853	−	0.340853i	0.856688	+	0.515835i	$0.172518\pi$
$558$	3.42571e6	−	5.26168e6i	0.465763	−	0.715384i
$559$	−7.73442e6			−1.04688
$560$	775633.	−	3.74366e6i	0.104517	−	0.504459i
$561$	590495.			0.0792153
$562$	−2.93554e6	+	4.50881e6i	−0.392055	+	0.602172i
$563$	589467.	−	589467.i	0.0783769	−	0.0783769i	−0.666832	−	0.745208i	$-0.732350\pi$
$563$	589467.	−	589467.i	0.0783769	−	0.0783769i	0.745208	+	0.666832i	$0.232350\pi$
$564$	527862.	−	1.36559e6i	0.0698752	−	0.180769i
$565$	2.08359e6	+	3.52848e6i	0.274594	+	0.465014i
$566$	500003.	+	2.36590e6i	0.0656042	+	0.310424i
$567$	3.62567e6			0.473621
$568$	8.94971e6	+	1.44963e6i	1.16396	+	0.188532i
$569$		−	6.22577e6i		−	0.806143i	−0.915168	−	0.403072i	$-0.867943\pi$
$569$		−	6.22577e6i		−	0.806143i	0.915168	−	0.403072i	$-0.132057\pi$
$570$	2.19008e6	+	95801.6i	0.282340	+	0.0123505i
$571$	−1.42937e6	+	1.42937e6i	−0.183466	+	0.183466i	−0.792864	−	0.609398i	$-0.791411\pi$
$571$	−1.42937e6	+	1.42937e6i	−0.183466	+	0.183466i	0.609398	+	0.792864i	$0.291411\pi$
$572$	−7.96003e6	+	3.52180e6i	−1.01724	+	0.450064i
$573$	−784480.	+	784480.i	−0.0998149	+	0.0998149i
$574$	−1.00678e6	+	1.54635e6i	−0.127542	+	0.195897i
$575$	5.98172e6	−	1.08467e7i	0.754496	−	1.36814i
$576$	2.44535e6	−	7.35051e6i	0.307103	−	0.923126i
$577$		−	4.63591e6i		−	0.579689i	−0.957074	−	0.289845i	$-0.906396\pi$
$577$		−	4.63591e6i		−	0.579689i	0.957074	−	0.289845i	$-0.0936036\pi$
$578$	−4.02562e6	−	2.62095e6i	−0.501202	−	0.326316i
$579$	−810097.	−	810097.i	−0.100425	−	0.100425i
$580$	243149.	+	1.46424e6i	0.0300126	+	0.180735i
$581$	−3.83247e6	+	3.83247e6i	−0.471019	+	0.471019i
$582$	−16438.2	−	77782.0i	−0.00201163	−	0.00951857i
$583$	−508782.			−0.0619956
$584$	1.64045e6	−	1.01278e7i	0.199036	−	1.22881i
$585$	−1.14354e7	−	2.94417e6i	−1.38153	−	0.355691i
$586$	1.47523e6	+	6.98046e6i	0.177466	+	0.839730i
$587$	6.80452e6	+	6.80452e6i	0.815084	+	0.815084i	0.985391	−	0.170307i	$-0.0544761\pi$
$587$	6.80452e6	+	6.80452e6i	0.815084	+	0.815084i	−0.170307	+	0.985391i	$0.554476\pi$
$588$	946207.	+	365750.i	0.112861	+	0.0436256i
$589$	8.96296e6	+	8.96296e6i	1.06454	+	1.06454i
$590$	−5.49276e6	+	5.03236e6i	−0.649622	+	0.595170i
$591$	1.48658e6			0.175073
$592$	−1.31637e7	+	628290.i	−1.54374	+	0.0736811i
$593$		−	1.35010e7i		−	1.57663i	−0.615272	−	0.788315i	$-0.710954\pi$
$593$		−	1.35010e7i		−	1.57663i	0.615272	−	0.788315i	$-0.289046\pi$
$594$	1.77648e6	+	1.15661e6i	0.206582	+	0.134499i
$595$	1.43413e6	+	2.42864e6i	0.166072	+	0.281236i
$596$	−4.84948e6	−	1.87454e6i	−0.559216	−	0.216161i
$597$	−278981.	−	278981.i	−0.0320360	−	0.0320360i
$598$	1.96019e7	−	4.14261e6i	2.24153	−	0.473719i
$599$			6.16972e6i			0.702584i	0.936266	+	0.351292i	$0.114258\pi$
$599$			6.16972e6i			0.702584i	−0.936266	+	0.351292i	$0.885742\pi$
$600$	1.44189e6	−	175093.i	0.163513	−	0.0198560i
$601$			1.36129e7i			1.53732i	0.639660	+	0.768658i	$0.279075\pi$
$601$			1.36129e7i			1.53732i	−0.639660	+	0.768658i	$0.720925\pi$
$602$	676218.	+	3.19971e6i	0.0760494	+	0.359848i
$603$	−1.34640e6	−	1.34640e6i	−0.150793	−	0.150793i
$604$	3.29445e6	−	1.45758e6i	0.367443	−	0.162570i
$605$	1.94354e6	+	3.29130e6i	0.215876	+	0.365577i
$606$	−1.46639e6	+	2.25228e6i	−0.162206	+	0.249138i
$607$		−	7.08789e6i		−	0.780810i	−0.920643	−	0.390405i	$-0.872335\pi$
$607$		−	7.08789e6i		−	0.780810i	0.920643	−	0.390405i	$-0.127665\pi$
$608$	1.34981e7	+	7.89848e6i	1.48086	+	0.866532i
$609$	142291.			0.0155465
$610$	1.17896e7	+	1.28683e7i	1.28285	+	1.40022i
$611$	−1.12580e7	−	1.12580e7i	−1.22000	−	1.22000i
$612$	2.31227e6	+	5.22624e6i	0.249552	+	0.564041i
$613$	−2.71263e6	−	2.71263e6i	−0.291568	−	0.291568i	0.546132	−	0.837699i	$-0.316100\pi$
$613$	−2.71263e6	−	2.71263e6i	−0.291568	−	0.291568i	−0.837699	+	0.546132i	$0.816100\pi$
$614$	1.06306e7	−	2.24664e6i	1.13799	−	0.240499i
$615$	−678886.	−	174787.i	−0.0723784	−	0.0186346i
$616$	2.15290e6	+	2.98513e6i	0.228598	+	0.316965i
$617$	8.70638e6			0.920714			0.460357	−	0.887734i	$-0.347721\pi$
$617$	8.70638e6			0.920714			0.460357	+	0.887734i	$0.347721\pi$
$618$	−2.15234e6	+	454870.i	−0.226694	+	0.0479089i
$619$	−6.09748e6	+	6.09748e6i	−0.639623	+	0.639623i	−0.950462	−	0.310840i	$-0.899390\pi$
$619$	−6.09748e6	+	6.09748e6i	−0.639623	+	0.639623i	0.310840	+	0.950462i	$0.399390\pi$
$620$	6.83125e6	+	4.88557e6i	0.713709	+	0.510430i
$621$	−3.45011e6	−	3.45011e6i	−0.359008	−	0.359008i
$622$	2.85130e6	−	4.37941e6i	0.295506	−	0.453879i
$623$			2.76972e6i			0.285901i
$624$	1.73851e6	+	1.58011e6i	0.178737	+	0.162453i
$625$	−5.21087e6	−	8.25919e6i	−0.533593	−	0.845742i
$626$	3.75412e6	+	2.44418e6i	0.382888	+	0.249286i
$627$	−1.49225e6	+	1.49225e6i	−0.151591	+	0.151591i
$628$	−9.22832e6	−	3.56715e6i	−0.933735	−	0.360930i
$629$	6.87473e6	−	6.87473e6i	0.692834	−	0.692834i
$630$	−218201.	+	4.98820e6i	−0.0219031	+	0.500717i
$631$		−	9.47327e6i		−	0.947167i	−0.880749	−	0.473583i	$-0.842960\pi$
$631$		−	9.47327e6i		−	0.947167i	0.880749	−	0.473583i	$-0.157040\pi$
$632$	1.40361e6	−	8.66562e6i	0.139783	−	0.862992i
$633$	966719.			0.0958939
$634$	−2.16673e6	+	457912.i	−0.214083	+	0.0452438i
$635$	−2.72281e6	−	4.61098e6i	−0.267968	−	0.453794i
$636$	55560.3	+	125578.i	0.00544655	+	0.0123104i
$637$	7.80057e6	−	7.80057e6i	0.761689	−	0.761689i
$638$	−1.19747e6	−	779631.i	−0.116469	−	0.0758294i
$639$	−1.18404e7			−1.14714
$640$	9.67999e6	+	3.69756e6i	0.934168	+	0.356833i
$641$	1.17360e7			1.12817			0.564085	−	0.825717i	$-0.309229\pi$
$641$	1.17360e7			1.12817			0.564085	+	0.825717i	$0.309229\pi$
$642$	−1.88509e6	−	1.22732e6i	−0.180507	−	0.117523i
$643$	4.50231e6	−	4.50231e6i	0.429445	−	0.429445i	−0.458994	−	0.888439i	$-0.651790\pi$
$643$	4.50231e6	−	4.50231e6i	0.429445	−	0.429445i	0.888439	+	0.458994i	$0.151790\pi$
$644$	−3.42757e6	−	7.74705e6i	−0.325665	−	0.736075i
$645$	−1.06986e6	+	631762.i	−0.101258	+	0.0597935i
$646$	−1.12882e7	+	2.38562e6i	−1.06425	+	0.224916i
$647$	6.46776e6			0.607426			0.303713	−	0.952764i	$-0.401774\pi$
$647$	6.46776e6			0.607426			0.303713	+	0.952764i	$0.401774\pi$
$648$	−1.57123e6	+	9.70045e6i	−0.146994	+	0.907516i
$649$		−	7.17150e6i		−	0.668341i
$650$	4.60295e6	−	1.51097e7i	0.427320	−	1.40273i
$651$	569305.	−	569305.i	0.0526493	−	0.0526493i
$652$	8.22731e6	+	3.18022e6i	0.757947	+	0.292980i
$653$	−6.64073e6	+	6.64073e6i	−0.609442	+	0.609442i	−0.942800	−	0.333358i	$-0.891818\pi$
$653$	−6.64073e6	+	6.64073e6i	−0.609442	+	0.609442i	0.333358	+	0.942800i	$0.391818\pi$
$654$	260375.	+	169522.i	0.0238043	+	0.0154982i
$655$	−4.48935e6	−	1.15583e6i	−0.408865	−	0.105267i
$656$	−3.70095e6	−	3.36376e6i	−0.335779	−	0.305186i
$657$			1.33991e7i			1.21105i
$658$	−3.67313e6	+	5.64170e6i	−0.330728	+	0.507979i
$659$	8.98947e6	+	8.98947e6i	0.806345	+	0.806345i	0.984079	−	0.177734i	$-0.0568767\pi$
$659$	8.98947e6	+	8.98947e6i	0.806345	+	0.806345i	−0.177734	+	0.984079i	$0.556877\pi$
$660$	−813404.	+	1.13734e6i	−0.0726853	+	0.101632i
$661$	4.02666e6	−	4.02666e6i	0.358460	−	0.358460i	−0.504785	−	0.863245i	$-0.668428\pi$
$661$	4.02666e6	−	4.02666e6i	0.358460	−	0.358460i	0.863245	+	0.504785i	$0.168428\pi$
$662$	−1.56739e7	+	3.31248e6i	−1.39005	+	0.293770i
$663$	−1.73315e6			−0.153127
$664$	−8.59289e6	−	1.19146e7i	−0.756343	−	1.04872i
$665$	−9.76170e6	−	2.51326e6i	−0.855996	−	0.220385i
$666$	1.68391e7	−	3.55874e6i	1.47107	−	0.310893i
$667$	2.32561e6	+	2.32561e6i	0.202406	+	0.202406i
$668$	−3.12452e6	−	7.06210e6i	−0.270921	−	0.612340i
$669$	−1.77204e6	−	1.77204e6i	−0.153077	−	0.153077i
$670$	1.87798e6	−	1.72057e6i	0.161623	−	0.148076i
$671$	−1.68011e7			−1.44056
$672$	501692.	−	857365.i	0.0428562	−	0.0732390i
$673$			9.88304e6i			0.841111i	0.907267	+	0.420555i	$0.138165\pi$
$673$			9.88304e6i			0.841111i	−0.907267	+	0.420555i	$0.861835\pi$
$674$	−3.68422e6	+	5.65873e6i	−0.312389	+	0.479810i
$675$	−3.69539e6	+	1.06831e6i	−0.312177	+	0.0902485i
$676$	1.24979e7	−	5.52950e6i	1.05189	−	0.465392i
$677$	−1.24254e6	−	1.24254e6i	−0.104193	−	0.104193i	0.653088	−	0.757282i	$-0.273473\pi$
$677$	−1.24254e6	−	1.24254e6i	−0.104193	−	0.104193i	−0.757282	+	0.653088i	$0.773473\pi$
$678$	220150.	+	1.04170e6i	0.0183926	+	0.0870297i
$679$			365557.i			0.0304285i
$680$	−7.11931e6	+	2.78452e6i	−0.590426	+	0.230929i
$681$			2.86235e6i			0.236513i
$682$	−7.91036e6	+	1.67176e6i	−0.651232	+	0.137630i
$683$	−1.39418e7	−	1.39418e7i	−1.14359	−	1.14359i	−0.987789	−	0.155796i	$-0.950206\pi$
$683$	−1.39418e7	−	1.39418e7i	−1.14359	−	1.14359i	−0.155796	−	0.987789i	$-0.549794\pi$
$684$	−1.90507e7	−	7.36394e6i	−1.55694	−	0.601825i
$685$	2.36500e6	−	1.39655e6i	0.192577	−	0.113718i
$686$	−9.23047e6	−	6.00966e6i	−0.748882	−	0.487573i
$687$			2.37653e6i			0.192111i
$688$	−8.85384e6	+	422585.i	−0.713117	+	0.0340363i
$689$	1.49331e6			0.119840
$690$	2.37305e6	−	2.17414e6i	0.189751	−	0.173846i
$691$	1.13415e6	+	1.13415e6i	0.0903601	+	0.0903601i	0.750842	−	0.660482i	$-0.229648\pi$
$691$	1.13415e6	+	1.13415e6i	0.0903601	+	0.0903601i	−0.660482	+	0.750842i	$0.729648\pi$
$692$	−4.14072e6	−	1.60057e6i	−0.328708	−	0.127060i
$693$	−3.39880e6	−	3.39880e6i	−0.268840	−	0.268840i
$694$	2.87621e6	+	1.36096e7i	0.226685	+	1.07262i
$695$	679683.	−	2.63995e6i	0.0533758	−	0.207316i
$696$	−61663.3	+	380697.i	−0.00482507	+	0.0297891i
$697$	3.68954e6			0.287667
$698$	1.18696e6	+	5.61640e6i	0.0922138	+	0.436335i
$699$	−2.88009e6	+	2.88009e6i	−0.222953	+	0.222953i
$700$	−6.65328e6	−	583191.i	−0.513205	−	0.0449848i
$701$	−7.25781e6	−	7.25781e6i	−0.557841	−	0.557841i	0.370851	−	0.928692i	$-0.379066\pi$
$701$	−7.25781e6	−	7.25781e6i	−0.557841	−	0.557841i	−0.928692	+	0.370851i	$0.879066\pi$
$702$	−5.21409e6	−	3.39473e6i	−0.399334	−	0.259993i
$703$			3.47466e7i			2.65170i
$704$	−8.91968e6	+	4.46643e6i	−0.678293	+	0.339648i
$705$	−2.47684e6	−	637691.i	−0.187683	−	0.0483212i
$706$	−9.36600e6	+	1.43856e7i	−0.707200	+	1.08622i
$707$	8.73842e6	−	8.73842e6i	0.657483	−	0.657483i
$708$	−1.77008e6	+	783145.i	−0.132712	+	0.0587163i
$709$	−1.09625e7	+	1.09625e7i	−0.819018	+	0.819018i	−0.985966	−	0.166948i	$-0.946609\pi$
$709$	−1.09625e7	+	1.09625e7i	−0.819018	+	0.819018i	0.166948	+	0.985966i	$0.446609\pi$
$710$	692159.	−	1.58231e7i	0.0515299	−	1.17800i
$711$			1.14646e7i			0.850520i
$712$	−7.41036e6	−	1.20029e6i	−0.547822	−	0.0887332i
$713$	1.86095e7			1.37092
$714$	151529.	+	716998.i	0.0111237	+	0.0526348i
$715$	7.73174e6	+	1.30934e7i	0.565603	+	0.957827i
$716$	1.06920e6	−	2.76604e6i	0.0779426	−	0.201640i
$717$	2.56896e6	−	2.56896e6i	0.186621	−	0.186621i
$718$	−1.58229e6	+	2.43030e6i	−0.114545	+	0.175933i
$719$	7.66850e6			0.553208			0.276604	−	0.960984i	$-0.410791\pi$
$719$	7.66850e6			0.553208			0.276604	+	0.960984i	$0.410791\pi$
$720$	−1.32513e7	−	2.74549e6i	−0.952637	−	0.197373i
$721$	1.01155e7			0.724685
$722$	1.48555e7	−	2.28171e7i	1.06058	−	1.62899i
$723$	−1.55648e6	+	1.55648e6i	−0.110738	+	0.110738i
$724$	6.35733e6	+	2.45739e6i	0.450743	+	0.174232i
$725$	2.49094e6	−	720117.i	0.176002	−	0.0508813i
$726$	205352.	+	971677.i	0.0144596	+	0.0684196i
$727$	−1.70309e7			−1.19509			−0.597547	−	0.801834i	$-0.703858\pi$
$727$	−1.70309e7			−1.19509			−0.597547	+	0.801834i	$0.703858\pi$
$728$	−6.31893e6	−	8.76159e6i	−0.441891	−	0.612709i
$729$		−	1.20656e7i		−	0.840875i
$730$	−1.79061e7	−	783274.i	−1.24364	−	0.0544009i
$731$	4.62391e6	−	4.62391e6i	0.320049	−	0.320049i
$732$	1.83473e6	+	4.14688e6i	0.126559	+	0.286051i
$733$	−1.66431e7	+	1.66431e7i	−1.14413	+	1.14413i	−0.156440	+	0.987687i	$0.550002\pi$
$733$	−1.66431e7	+	1.66431e7i	−1.14413	+	1.14413i	−0.987687	+	0.156440i	$0.949998\pi$
$734$	−9.03238e6	+	1.38732e7i	−0.618817	+	0.950465i
$735$	441849.	−	1.71618e6i	0.0301686	−	0.117178i
$736$	2.22125e7	−	5.81316e6i	1.51148	−	0.395565i
$737$			2.45194e6i			0.166280i
$738$	5.47357e6	+	3.56367e6i	0.369939	+	0.240855i
$739$	−2.01511e7	−	2.01511e7i	−1.35733	−	1.35733i	−0.877188	−	0.480147i	$-0.840583\pi$
$739$	−2.01511e7	−	2.01511e7i	−1.35733	−	1.35733i	−0.480147	−	0.877188i	$-0.659417\pi$
$740$	3.77140e6	+	2.27112e7i	0.253176	+	1.52462i
$741$	4.37988e6	−	4.37988e6i	0.293033	−	0.293033i
$742$	−130560.	−	617780.i	−0.00870563	−	0.0411931i
$743$	−7.81496e6			−0.519343			−0.259672	−	0.965697i	$-0.583614\pi$
$743$	−7.81496e6			−0.519343			−0.259672	+	0.965697i	$0.583614\pi$
$744$	1.27646e6	+	1.76989e6i	0.0845422	+	0.117223i
$745$	−2.26456e6	+	8.79573e6i	−0.149483	+	0.580605i
$746$	−3.38944e6	−	1.60381e7i	−0.222988	−	1.05513i
$747$	1.35657e7	+	1.35657e7i	0.889488	+	0.889488i
$748$	2.65333e6	−	6.86424e6i	0.173395	−	0.448578i
$749$	7.31381e6	+	7.31381e6i	0.476364	+	0.476364i
$750$	−597486.	−	2.46603e6i	−0.0387859	−	0.160083i
$751$	2.06823e7			1.33814			0.669068	−	0.743202i	$-0.266694\pi$
$751$	2.06823e7			1.33814			0.669068	+	0.743202i	$0.266694\pi$
$752$	−1.35025e7	−	1.22723e7i	−0.870704	−	0.791375i
$753$			2.24424e6i			0.144239i
$754$	3.51465e6	+	2.28828e6i	0.225141	+	0.146582i
$755$	−3.19996e6	−	5.41901e6i	−0.204304	−	0.345982i
$756$	−948522.	+	2.45385e6i	−0.0603592	+	0.156151i
$757$	−2.04197e6	−	2.04197e6i	−0.129512	−	0.129512i	0.639379	−	0.768891i	$-0.279191\pi$
$757$	−2.04197e6	−	2.04197e6i	−0.129512	−	0.129512i	−0.768891	+	0.639379i	$0.779191\pi$
$758$	2.07737e6	−	439027.i	0.131323	−	0.0277535i
$759$			3.09832e6i			0.195219i
$760$	1.09545e7	−	2.50282e7i	0.687956	−	1.57179i
$761$		−	1.34863e7i		−	0.844175i	−0.906555	−	0.422088i	$-0.861297\pi$
$761$		−	1.34863e7i		−	0.844175i	0.906555	−	0.422088i	$-0.138703\pi$
$762$	−287689.	−	1.36128e6i	−0.0179488	−	0.0849298i
$763$	−1.01021e6	−	1.01021e6i	−0.0628201	−	0.0628201i
$764$	5.59425e6	+	1.26442e7i	0.346743	+	0.783715i
$765$	8.59660e6	−	5.07635e6i	0.531096	−	0.313616i
$766$	2.67004e6	−	4.10102e6i	0.164417	−	0.252534i
$767$			2.10489e7i			1.29193i
$768$	2.07646e6	+	1.71382e6i	0.127034	+	0.104849i
$769$	2.62996e6			0.160374			0.0801869	−	0.996780i	$-0.474448\pi$
$769$	2.62996e6			0.160374			0.0801869	+	0.996780i	$0.474448\pi$
$770$	4.74072e6	−	4.34335e6i	0.288149	−	0.263996i
$771$	−1.56288e6	−	1.56288e6i	−0.0946867	−	0.0946867i
$772$	−1.30571e7	+	5.77692e6i	−0.788503	+	0.348862i
$773$	−1.09101e7	−	1.09101e7i	−0.656720	−	0.656720i	0.297882	−	0.954603i	$-0.403720\pi$
$773$	−1.09101e7	−	1.09101e7i	−0.656720	−	0.656720i	−0.954603	+	0.297882i	$0.903720\pi$
$774$	1.13259e7	−	2.39359e6i	0.679549	−	0.143614i
$775$	7.08508e6	−	1.28475e7i	0.423731	−	0.768356i
$776$	−978045.	−	158418.i	−0.0583048	−	0.00944390i
$777$	2.20702e6			0.131145
$778$	−1.83594e7	+	3.88003e6i	−1.08745	+	0.229819i
$779$	−9.32391e6	+	9.32391e6i	−0.550496	+	0.550496i
$780$	2.38740e6	−	3.33819e6i	0.140504	−	0.196460i
$781$	1.07814e7	+	1.07814e7i	0.632481	+	0.632481i
$782$	−9.24209e6	+	1.41953e7i	−0.540447	+	0.830094i
$783$		−	1.02137e6i		−	0.0595359i
$784$	8.50337e6	−	9.35576e6i	0.494084	−	0.543612i
$785$	−4.30934e6	+	1.67378e7i	−0.249596	+	0.969450i
$786$	−1.00941e6	−	657194.i	−0.0582788	−	0.0379435i
$787$	2.05531e7	−	2.05531e7i	1.18288	−	1.18288i	0.203883	−	0.978995i	$-0.434644\pi$
$787$	2.05531e7	−	2.05531e7i	1.18288	−	1.18288i	0.978995	−	0.203883i	$-0.0653561\pi$
$788$	6.67980e6	−	1.72808e7i	0.383220	−	0.991401i
$789$	−29547.2	+	29547.2i	−0.00168975	+	0.00168975i
$790$	−1.53209e7	−	670187.i	−0.873404	−	0.0382057i
$791$		−	4.89573e6i		−	0.278212i
$792$	1.05664e7	−	7.62056e6i	0.598568	−	0.431692i
$793$	4.93126e7			2.78468
$794$	−331551.	+	70069.2i	−0.0186638	+	0.00394435i
$795$	206563.	−	121977.i	0.0115914	−	0.00684477i
$796$	−4.49660e6	+	1.98945e6i	−0.251537	+	0.111289i
$797$	6.47404e6	−	6.47404e6i	0.361019	−	0.361019i	−0.503169	−	0.864188i	$-0.667833\pi$
$797$	6.47404e6	−	6.47404e6i	0.361019	−	0.361019i	0.864188	+	0.503169i	$0.167833\pi$
$798$	−2.19487e6	−	1.42901e6i	−0.122012	−	0.0794380i
$799$	1.34609e7			0.745945
$800$	4.44360e6	−	1.75481e7i	0.245476	−	0.969403i
$801$	9.80389e6			0.539905
$802$	6.57253e6	+	4.27916e6i	0.360825	+	0.234921i
$803$	1.22007e7	−	1.22007e7i	0.667720	−	0.667720i
$804$	605191.	−	267758.i	0.0330181	−	0.0146084i
$805$	−1.27431e7	+	7.52487e6i	−0.693082	+	0.409269i
$806$	2.32175e7	−	4.90673e6i	1.25886	−	0.266045i
$807$	−1.08399e6			−0.0585924
$808$	1.95927e7	+	2.71665e7i	1.05576	+	1.46388i
$809$			2.49006e7i			1.33764i	0.743426	+	0.668819i	$0.233200\pi$
$809$			2.49006e7i			1.33764i	−0.743426	+	0.668819i	$0.766800\pi$
$810$	1.71504e7	+	750220.i	0.918465	+	0.0401768i
$811$	2.14240e7	−	2.14240e7i	1.14380	−	1.14380i	0.156046	−	0.987750i	$-0.450125\pi$
$811$	2.14240e7	−	2.14240e7i	1.14380	−	1.14380i	0.987750	−	0.156046i	$-0.0498749\pi$
$812$	639369.	−	1.65406e6i	0.0340299	−	0.0880364i
$813$	414950.	−	414950.i	0.0220175	−	0.0220175i
$814$	−1.85734e7	−	1.20926e7i	−0.982497	−	0.639672i
$815$	3.84190e6	−	1.49223e7i	0.202606	−	0.786938i
$816$	−1.98399e6	+	94693.8i	−0.104307	+	0.00497847i
$817$			2.33704e7i			1.22493i
$818$	−7.55699e6	+	1.16071e7i	−0.394880	+	0.606512i
$819$	9.97575e6	+	9.97575e6i	0.519680	+	0.519680i
$820$	−5.08232e6	+	7.10636e6i	−0.263953	+	0.369073i
$821$	−1.37591e7	+	1.37591e7i	−0.712411	+	0.712411i	−0.967039	−	0.254628i	$-0.918047\pi$
$821$	−1.37591e7	+	1.37591e7i	−0.712411	+	0.712411i	0.254628	+	0.967039i	$0.418047\pi$
$822$	698208.	−	147557.i	0.0360417	−	0.00761695i
$823$	−6.26045e6			−0.322185			−0.161093	−	0.986939i	$-0.551502\pi$
$823$	−6.26045e6			−0.322185			−0.161093	+	0.986939i	$0.551502\pi$
$824$	−4.38367e6	+	2.70639e7i	−0.224916	+	1.38859i
$825$	2.13899e6	+	1.17960e6i	0.109414	+	0.0603393i
$826$	8.70786e6	−	1.84030e6i	0.444080	−	0.0938508i
$827$	−467092.	−	467092.i	−0.0237486	−	0.0237486i	0.695133	−	0.718881i	$-0.255346\pi$
$827$	−467092.	−	467092.i	−0.0237486	−	0.0237486i	−0.718881	+	0.695133i	$0.755346\pi$
$828$	−2.74220e7	+	1.21325e7i	−1.39003	+	0.614998i
$829$	−1.12199e7	−	1.12199e7i	−0.567027	−	0.567027i	0.364267	−	0.931294i	$-0.381320\pi$
$829$	−1.12199e7	−	1.12199e7i	−0.567027	−	0.567027i	−0.931294	+	0.364267i	$0.881320\pi$
$830$	−1.89217e7	+	1.73356e7i	−0.953376	+	0.873463i
$831$	6.08779e6			0.305814
$832$	2.61799e7	−	1.31093e7i	1.31117	−	0.656555i
$833$			9.32691e6i			0.465720i
$834$	386461.	−	593580.i	0.0192393	−	0.0295504i
$835$	−1.16164e7	+	6.85956e6i	−0.576574	+	0.340471i
$836$	1.06415e7	+	2.40521e7i	0.526607	+	1.19025i
$837$	−4.08650e6	−	4.08650e6i	−0.201622	−	0.201622i
$838$	−6.28506e6	−	2.97395e7i	−0.309171	−	1.46293i
$839$			1.09176e7i			0.535456i	0.963495	+	0.267728i	$0.0862729\pi$
$839$			1.09176e7i			0.535456i	−0.963495	+	0.267728i	$0.913727\pi$
$840$	−1.58973e6	−	695805.i	−0.0777365	−	0.0340243i
$841$		−	1.98227e7i		−	0.966434i
$842$	2.73688e7	−	5.78404e6i	1.33038	−	0.281159i
$843$	1.72681e6	+	1.72681e6i	0.0836904	+	0.0836904i
$844$	4.34385e6	−	1.12377e7i	0.209903	−	0.543025i
$845$	−1.21394e7	−	2.05576e7i	−0.584866	−	0.990448i
$846$	1.99698e7	+	1.30017e7i	0.959284	+	0.624559i
$847$		−	4.56665e6i		−	0.218720i
$848$	1.70944e6	−	81590.0i	0.0816329	−	0.00389626i
$849$	1.09760e6			0.0522608
$850$	6.28131e6	+	1.17849e7i	0.298197	+	0.559473i
$851$	3.60717e7	+	3.60717e7i	1.70743	+	1.70743i
$852$	1.48372e6	−	3.83843e6i	0.0700251	−	0.181157i
$853$	−2.06739e7	−	2.06739e7i	−0.972857	−	0.972857i	0.0267845	−	0.999641i	$-0.491473\pi$
$853$	−2.06739e7	−	2.06739e7i	−0.972857	−	0.972857i	−0.999641	+	0.0267845i	$0.991473\pi$
$854$	−4.31139e6	−	2.04005e7i	−0.202289	−	0.957185i
$855$	−8.89610e6	+	3.45532e7i	−0.416183	+	1.61649i
$856$	−2.27376e7	+	1.63985e7i	−1.06062	+	0.764927i
$857$	−3.02567e7			−1.40724			−0.703622	−	0.710574i	$-0.748435\pi$
$857$	−3.02567e7			−1.40724			−0.703622	+	0.710574i	$0.748435\pi$
$858$	816926.	+	3.86551e6i	0.0378848	+	0.179262i
$859$	1.73141e7	−	1.73141e7i	0.800602	−	0.800602i	−0.182588	−	0.983190i	$-0.558447\pi$
$859$	1.73141e7	−	1.73141e7i	0.800602	−	0.800602i	0.983190	+	0.182588i	$0.0584473\pi$
$860$	2.53662e6	+	1.52755e7i	0.116953	+	0.704284i
$861$	592231.	+	592231.i	0.0272260	+	0.0272260i
$862$	−1.87490e7	−	1.22069e7i	−0.859429	−	0.559547i
$863$			3.74063e7i			1.70969i	0.518881	+	0.854846i	$0.326349\pi$
$863$			3.74063e7i			1.70969i	−0.518881	+	0.854846i	$0.673651\pi$
$864$	−6.15421e6	−	3.60117e6i	−0.280471	−	0.164119i
$865$	−1.93359e6	+	7.51022e6i	−0.0878666	+	0.341281i
$866$	1.29840e7	−	1.99426e7i	0.588320	−	0.903624i
$867$	−1.54176e6	+	1.54176e6i	−0.0696575	+	0.0696575i
$868$	−4.05980e6	−	9.17603e6i	−0.182896	−	0.413386i
$869$	1.04392e7	−	1.04392e7i	0.468939	−	0.468939i
$870$	673075.	+	29442.6i	0.0301485	+	0.00131880i
$871$		−	7.19663e6i		−	0.321428i
$872$	3.14058e6	−	2.26501e6i	0.139868	−	0.100874i
$873$	1.29395e6			0.0574622
$874$	−1.25173e7	−	5.92291e7i	−0.554285	−	2.62275i
$875$	343358.	+	1.16623e7i	0.0151610	+	0.514949i
$876$	−4.34372e6	−	1.67904e6i	−0.191250	−	0.0739266i
$877$	−9.59743e6	+	9.59743e6i	−0.421362	+	0.421362i	−0.885673	−	0.464310i	$-0.846302\pi$
$877$	−9.59743e6	+	9.59743e6i	−0.421362	+	0.421362i	0.464310	+	0.885673i	$0.346302\pi$
$878$	1.47890e7	−	2.27149e7i	0.647443	−	0.994433i
$879$	3.23841e6			0.141371
$880$	9.56615e6	+	1.45660e7i	0.416419	+	0.634064i
$881$	−3.76176e7			−1.63287			−0.816435	−	0.577437i	$-0.804053\pi$
$881$	−3.76176e7			−1.63287			−0.816435	+	0.577437i	$0.804053\pi$
$882$	−9.00872e6	+	1.38368e7i	−0.389935	+	0.598916i
$883$	3.00876e7	−	3.00876e7i	1.29863	−	1.29863i	0.369336	−	0.929296i	$-0.379585\pi$
$883$	3.00876e7	−	3.00876e7i	1.29863	−	1.29863i	0.929296	−	0.369336i	$-0.120415\pi$
$884$	−7.78772e6	+	2.01471e7i	−0.335181	+	0.867124i
$885$	1.71931e6	+	2.91159e6i	0.0737898	+	0.124960i
$886$	−3.82965e6	−	1.81210e7i	−0.163898	−	0.775529i
$887$	−1.25457e7			−0.535411			−0.267706	−	0.963501i	$-0.586265\pi$
$887$	−1.25457e7			−0.535411			−0.267706	+	0.963501i	$0.586265\pi$
$888$	−956436.	+	5.90485e6i	−0.0407027	+	0.251291i
$889$			6.39769e6i			0.271499i
$890$	−573107.	+	1.31016e7i	−0.0242527	+	0.554431i
$891$	−1.16858e7	+	1.16858e7i	−0.493133	+	0.493133i
$892$	−2.85617e7	+	1.26367e7i	−1.20191	+	0.531767i
$893$	−3.40173e7	+	3.40173e7i	−1.42748	+	1.42748i
$894$	−1.28760e6	+	1.97768e6i	−0.0538813	+	0.0827583i
$895$	−5.01690e6	−	1.29166e6i	−0.209352	−	0.0539001i
$896$	−7.71219e6	−	9.68443e6i	−0.320928	−	0.402999i
$897$		−	9.09381e6i		−	0.377368i
$898$	−1.26327e7	−	8.22473e6i	−0.522763	−	0.340354i
$899$	2.75458e6	+	2.75458e6i	0.113673	+	0.113673i
$900$	−2.06430e6	+	2.35504e7i	−0.0849508	+	0.969153i
$901$	−892756.	+	892756.i	−0.0366371	+	0.0366371i
$902$	−1.73908e6	−	8.22892e6i	−0.0711710	−	0.336765i
$903$	1.48443e6			0.0605814
$904$	1.30985e7	+	2.12162e6i	0.533090	+	0.0863470i
$905$	2.96868e6	−	1.15306e7i	0.120487	−	0.467983i
$906$	−338104.	−	1.59983e6i	−0.0136845	−	0.0647521i
$907$	−3.03269e7	−	3.03269e7i	−1.22408	−	1.22408i	−0.966169	−	0.257910i	$-0.916966\pi$
$907$	−3.03269e7	−	3.03269e7i	−1.22408	−	1.22408i	−0.257910	−	0.966169i	$-0.583034\pi$
$908$	3.32735e7	+	1.28617e7i	1.33932	+	0.517705i
$909$	−3.09311e7	−	3.09311e7i	−1.24161	−	1.24161i
$910$	−1.39144e7	+	1.27481e7i	−0.557006	+	0.510318i
$911$	3.68788e7			1.47225			0.736124	−	0.676847i	$-0.236654\pi$
$911$	3.68788e7			1.47225			0.736124	+	0.676847i	$0.236654\pi$
$912$	4.77448e6	−	5.25309e6i	0.190081	−	0.209135i
$913$		−	2.47046e7i		−	0.980847i
$914$	2.74616e7	+	1.78794e7i	1.08733	+	0.707924i
$915$	6.82117e6	−	4.02795e6i	0.269343	−	0.159049i
$916$	2.76261e7	+	1.06787e7i	1.08788	+	0.420514i
$917$	3.91632e6	+	3.91632e6i	0.153799	+	0.153799i
$918$	5.14665e6	−	1.08768e6i	0.201566	−	0.0425985i
$919$		−	2.76164e7i		−	1.07864i	−0.842100	−	0.539322i	$-0.818681\pi$
$919$		−	2.76164e7i		−	1.07864i	0.842100	−	0.539322i	$-0.181319\pi$
$920$	−1.46104e7	−	3.73550e7i	−0.569104	−	1.45505i
$921$		−	4.93181e6i		−	0.191583i
$922$	5.86430e6	+	2.77485e7i	0.227190	+	1.07501i
$923$	−3.16442e7	−	3.16442e7i	−1.22262	−	1.22262i
$924$	1.52773e6	−	675920.i	0.0588662	−	0.0260445i
$925$	3.86361e7	−	1.11695e7i	1.48470	−	0.429218i
$926$	−862066.	+	1.32408e6i	−0.0330380	+	0.0507443i
$927$		−	3.58055e7i		−	1.36852i
$928$	4.14836e6	+	2.42743e6i	0.158127	+	0.0925289i
$929$	−3.13644e7			−1.19233			−0.596166	−	0.802861i	$-0.703310\pi$
$929$	−3.13644e7			−1.19233			−0.596166	+	0.802861i	$0.703310\pi$
$930$	2.81077e6	−	2.57517e6i	0.106566	−	0.0976335i
$931$	−2.35702e7	−	2.35702e7i	−0.891230	−	0.891230i
$932$	2.05383e7	+	4.64211e7i	0.774507	+	1.75055i
$933$	−1.67726e6	−	1.67726e6i	−0.0630805	−	0.0630805i
$934$	−9.78624e6	+	2.06820e6i	−0.367070	+	0.0775755i
$935$	−1.24500e7	−	3.20539e6i	−0.465736	−	0.119909i
$936$	−3.10131e7	+	2.23669e7i	−1.15706	+	0.834481i
$937$	1.05413e7			0.392235			0.196117	−	0.980580i	$-0.437167\pi$
$937$	1.05413e7			0.392235			0.196117	+	0.980580i	$0.437167\pi$
$938$	−2.97723e6	+	629199.i	−0.110485	+	0.0233497i
$939$	1.43777e6	−	1.43777e6i	0.0532141	−	0.0532141i
$940$	−1.85423e7	+	2.59268e7i	−0.684454	+	0.957038i
$941$	5.52171e6	+	5.52171e6i	0.203282	+	0.203282i	0.801405	−	0.598122i	$-0.204086\pi$
$941$	5.52171e6	+	5.52171e6i	0.203282	+	0.203282i	−0.598122	+	0.801405i	$0.704086\pi$
$942$	−2.45025e6	+	3.76343e6i	−0.0899668	+	0.138184i
$943$			1.93590e7i			0.708929i
$944$	1.15005e6	+	2.40953e7i	0.0420034	+	0.880041i
$945$	4.45067e6	+	1.14587e6i	0.162124	+	0.0417405i
$946$	−1.24924e7	−	8.13339e6i	−0.453856	−	0.295491i
$947$	−2.82181e7	+	2.82181e7i	−1.02248	+	1.02248i	−0.0227346	+	0.999742i	$0.507237\pi$
$947$	−2.82181e7	+	2.82181e7i	−1.02248	+	1.02248i	−0.999742	+	0.0227346i	$0.992763\pi$
$948$	−3.71659e6	−	1.43662e6i	−0.134315	−	0.0519185i
$949$	−3.58098e7	+	3.58098e7i	−1.29073	+	1.29073i
$950$	−4.56556e7	−	1.39083e7i	−1.64129	−	0.499994i
$951$			1.00520e6i			0.0360415i
$952$	9.01566e6	+	1.46031e6i	0.322408	+	0.0522218i
$953$	2.94278e7			1.04960			0.524802	−	0.851225i	$-0.324139\pi$
$953$	2.94278e7			1.04960			0.524802	+	0.851225i	$0.324139\pi$
$954$	−2.18674e6	+	462139.i	−0.0777904	+	0.0164400i
$955$	2.07984e7	−	1.22816e7i	0.737940	−	0.435758i
$956$	−1.83196e7	−	4.14064e7i	−0.648294	−	1.46529i
$957$	−458613.	+	458613.i	−0.0161870	+	0.0161870i
$958$	2.34617e7	+	1.52752e7i	0.825936	+	0.537741i
$959$	−3.28141e6			−0.115216
$960$	2.55055e6	−	3.95177e6i	0.0893214	−	0.138393i
$961$	−6.58701e6			−0.230080
$962$	5.45144e7	+	3.54926e7i	1.89921	+	1.23652i
$963$	2.58885e7	−	2.58885e7i	0.899582	−	0.899582i
$964$	1.10995e7	+	2.50873e7i	0.384690	+	0.869483i
$965$	1.26826e7	+	2.14775e7i	0.438421	+	0.742448i
$966$	−3.76208e6	+	795069.i	−0.129714	+	0.0274133i
$967$	−5.42564e6			−0.186588			−0.0932942	−	0.995639i	$-0.529740\pi$
$967$	−5.42564e6			−0.186588			−0.0932942	+	0.995639i	$0.529740\pi$
$968$	1.22180e7	+	1.97901e6i	0.419096	+	0.0678828i
$969$			5.23689e6i			0.179169i
$970$	−75640.7	+	1.72919e6i	−0.00258123	+	0.0590083i
$971$	−3.06009e7	+	3.06009e7i	−1.04157	+	1.04157i	−0.0424682	+	0.999098i	$0.513522\pi$
$971$	−3.06009e7	+	3.06009e7i	−1.04157	+	1.04157i	−0.999098	+	0.0424682i	$0.986478\pi$
$972$	1.30885e7	+	5.05927e6i	0.444348	+	0.171760i
$973$	−2.30298e6	+	2.30298e6i	−0.0779844	+	0.0779844i
$974$	−1.58511e7	−	1.03202e7i	−0.535381	−	0.348569i
$975$	−6.27808e6	−	3.46222e6i	−0.211503	−	0.116639i
$976$	5.64497e7	−	2.69429e6i	1.89687	−	0.0905356i
$977$		−	2.60257e7i		−	0.872302i	−0.899874	−	0.436151i	$-0.856341\pi$
$977$		−	2.60257e7i		−	0.872302i	0.899874	−	0.436151i	$-0.143659\pi$
$978$	2.18446e6	−	3.35520e6i	0.0730294	−	0.112169i
$979$	−8.92700e6	−	8.92700e6i	−0.297679	−	0.297679i
$980$	−1.79644e7	−	1.28478e7i	−0.597514	−	0.427329i
$981$	−3.57580e6	+	3.57580e6i	−0.118632	+	0.118632i
$982$	7.75633e6	−	1.63920e6i	0.256672	−	0.0542443i
$983$	3.63283e7			1.19912			0.599558	−	0.800331i	$-0.295343\pi$
$983$	3.63283e7			1.19912			0.599558	+	0.800331i	$0.295343\pi$
$984$	−1.84116e6	+	1.32786e6i	−0.0606183	+	0.0437184i
$985$	−3.13431e7	−	8.06962e6i	−1.02932	−	0.265010i
$986$	−3.46919e6	+	733170.i	−0.113641	+	0.0240167i
$987$	2.16069e6	+	2.16069e6i	0.0705993	+	0.0705993i
$988$	−3.12336e7	−	7.05946e7i	−1.01796	−	2.30080i
$989$	2.42616e7	+	2.42616e7i	0.788731	+	0.788731i
$990$	−1.53740e7	−	1.67806e7i	−0.498540	−	0.544150i
$991$	−4.31692e7			−1.39634			−0.698168	−	0.715934i	$-0.746001\pi$
$991$	−4.31692e7			−1.39634			−0.698168	+	0.715934i	$0.746001\pi$
$992$	2.63097e7	−	6.88542e6i	0.848863	−	0.222153i
$993$			7.27152e6i			0.234019i
$994$	−1.03245e7	+	1.58578e7i	−0.331438	+	0.509069i
$995$	4.36764e6	+	7.39642e6i	0.139859	+	0.236845i
$996$	−6.09763e6	+	2.69781e6i	−0.194766	+	0.0861712i
$997$	−2.50823e7	−	2.50823e7i	−0.799152	−	0.799152i	0.183810	−	0.982962i	$-0.441157\pi$
$997$	−2.50823e7	−	2.50823e7i	−0.799152	−	0.799152i	−0.982962	+	0.183810i	$0.941157\pi$
$998$	5.31802e6	+	2.51637e7i	0.169014	+	0.799737i
$999$		−	1.58421e7i		−	0.502225i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	80.6.q.a.29.11	✓	116
5.4	even	2	inner	80.6.q.a.29.48	yes	116
16.5	even	4	inner	80.6.q.a.69.48	yes	116
80.69	even	4	inner	80.6.q.a.69.11	yes	116

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.6.q.a.29.11	✓	116	1.1	even	1	trivial
80.6.q.a.29.48	yes	116	5.4	even	2	inner
80.6.q.a.69.11	yes	116	80.69	even	4	inner
80.6.q.a.69.48	yes	116	16.5	even	4	inner

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.q (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-4.74064 - 3.08648i) q^{2} +(-1.81560 + 1.81560i) q^{3} +(12.9473 + 29.2637i) q^{4} +(48.1357 - 28.4245i) q^{5} +(14.2109 - 3.00330i) q^{6} -66.7879 q^{7} +(28.9433 - 178.690i) q^{8} +236.407i q^{9} +O(q^{10})\)	\(q+(-4.74064 - 3.08648i) q^{2} +(-1.81560 + 1.81560i) q^{3} +(12.9473 + 29.2637i) q^{4} +(48.1357 - 28.4245i) q^{5} +(14.2109 - 3.00330i) q^{6} -66.7879 q^{7} +(28.9433 - 178.690i) q^{8} +236.407i q^{9} +(-315.926 - 13.8197i) q^{10} +(215.262 - 215.262i) q^{11} +(-76.6384 - 29.6241i) q^{12} +(-631.811 + 631.811i) q^{13} +(316.617 + 206.139i) q^{14} +(-35.7878 + 139.003i) q^{15} +(-688.734 + 757.774i) q^{16} -755.437i q^{17} +(729.665 - 1120.72i) q^{18} +(1909.08 + 1909.08i) q^{19} +(1455.04 + 1040.61i) q^{20} +(121.260 - 121.260i) q^{21} +(-1684.88 + 356.078i) q^{22} +3963.77 q^{23} +(271.881 + 376.980i) q^{24} +(1509.10 - 2736.47i) q^{25} +(4945.26 - 1045.12i) q^{26} +(-870.412 - 870.412i) q^{27} +(-864.724 - 1954.46i) q^{28} +(586.717 + 586.717i) q^{29} +(598.686 - 548.504i) q^{30} +4694.91 q^{31} +(5603.89 - 1466.57i) q^{32} +781.660i q^{33} +(-2331.64 + 3581.26i) q^{34} +(-3214.89 + 1898.41i) q^{35} +(-6918.16 + 3060.84i) q^{36} +(9100.34 + 9100.34i) q^{37} +(-3157.93 - 14942.6i) q^{38} -2294.23i q^{39} +(-3685.97 - 9424.10i) q^{40} +4883.98i q^{41} +(-949.117 + 200.584i) q^{42} +(6120.84 + 6120.84i) q^{43} +(9086.44 + 3512.31i) q^{44} +(6719.75 + 11379.6i) q^{45} +(-18790.8 - 12234.1i) q^{46} +17818.7i q^{47} +(-125.350 - 2626.28i) q^{48} -12346.4 q^{49} +(-15600.1 + 8314.80i) q^{50} +(1371.57 + 1371.57i) q^{51} +(-26669.4 - 10308.9i) q^{52} +(-1181.77 - 1181.77i) q^{53} +(1439.80 + 6812.81i) q^{54} +(4243.09 - 16480.5i) q^{55} +(-1933.06 + 11934.4i) q^{56} -6932.26 q^{57} +(-970.524 - 4592.30i) q^{58} +(16657.6 - 16657.6i) q^{59} +(-4531.10 + 752.428i) q^{60} +(-39024.8 - 39024.8i) q^{61} +(-22256.9 - 14490.7i) q^{62} -15789.1i q^{63} +(-31092.6 - 10343.8i) q^{64} +(-12453.8 + 48371.6i) q^{65} +(2412.58 - 3705.57i) q^{66} +(-5695.24 + 5695.24i) q^{67} +(22106.9 - 9780.89i) q^{68} +(-7196.62 + 7196.62i) q^{69} +(21100.0 + 922.988i) q^{70} +50085.0i q^{71} +(42243.7 + 6842.41i) q^{72} +56678.1 q^{73} +(-15053.4 - 71229.4i) q^{74} +(2228.41 + 7708.25i) q^{75} +(-31149.4 + 80584.4i) q^{76} +(-14376.9 + 14376.9i) q^{77} +(-7081.09 + 10876.1i) q^{78} +48495.1 q^{79} +(-11613.4 + 56052.9i) q^{80} -54286.3 q^{81} +(15074.3 - 23153.2i) q^{82} +(57382.7 - 57382.7i) q^{83} +(5118.52 + 1978.53i) q^{84} +(-21472.9 - 36363.5i) q^{85} +(-10124.9 - 47908.5i) q^{86} -2130.48 q^{87} +(-32234.9 - 44695.7i) q^{88} -41470.4i q^{89} +(3267.07 - 74687.1i) q^{90} +(42197.3 - 42197.3i) q^{91} +(51320.2 + 115995. i) q^{92} +(-8524.07 + 8524.07i) q^{93} +(54996.9 - 84471.9i) q^{94} +(146160. + 37630.4i) q^{95} +(-7511.71 + 12837.1i) q^{96} -5473.40i q^{97} +(58529.7 + 38106.8i) q^{98} +(50889.5 + 50889.5i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 116 q - 4 q^{4} - 2 q^{5} - 4 q^{6}+O(q^{10}) \) 116 * q - 4 * q^4 - 2 * q^5 - 4 * q^6	\( 116 q - 4 q^{4} - 2 q^{5} - 4 q^{6} + 532 q^{10} - 4 q^{11} + 1108 q^{14} - 4 q^{15} + 1216 q^{16} + 2356 q^{19} + 824 q^{20} - 976 q^{21} - 2864 q^{24} - 12104 q^{26} - 4 q^{29} + 736 q^{30} + 23056 q^{31} - 38304 q^{34} - 3864 q^{35} - 20588 q^{36} + 15144 q^{40} - 25536 q^{44} + 6734 q^{45} - 36052 q^{46} + 220884 q^{49} + 56116 q^{50} - 9472 q^{51} - 104360 q^{54} - 2552 q^{56} + 14476 q^{59} + 1008 q^{60} - 48084 q^{61} + 72944 q^{64} - 27692 q^{65} - 56736 q^{66} - 23296 q^{69} + 135260 q^{70} - 186128 q^{74} - 33244 q^{75} - 35824 q^{76} + 427312 q^{79} - 129128 q^{80} - 551132 q^{81} - 418448 q^{84} + 6248 q^{85} + 177516 q^{86} + 449576 q^{90} - 231952 q^{91} + 607356 q^{94} + 38420 q^{95} - 440264 q^{96} + 406924 q^{99}+O(q^{100}) \) 116 * q - 4 * q^4 - 2 * q^5 - 4 * q^6 + 532 * q^10 - 4 * q^11 + 1108 * q^14 - 4 * q^15 + 1216 * q^16 + 2356 * q^19 + 824 * q^20 - 976 * q^21 - 2864 * q^24 - 12104 * q^26 - 4 * q^29 + 736 * q^30 + 23056 * q^31 - 38304 * q^34 - 3864 * q^35 - 20588 * q^36 + 15144 * q^40 - 25536 * q^44 + 6734 * q^45 - 36052 * q^46 + 220884 * q^49 + 56116 * q^50 - 9472 * q^51 - 104360 * q^54 - 2552 * q^56 + 14476 * q^59 + 1008 * q^60 - 48084 * q^61 + 72944 * q^64 - 27692 * q^65 - 56736 * q^66 - 23296 * q^69 + 135260 * q^70 - 186128 * q^74 - 33244 * q^75 - 35824 * q^76 + 427312 * q^79 - 129128 * q^80 - 551132 * q^81 - 418448 * q^84 + 6248 * q^85 + 177516 * q^86 + 449576 * q^90 - 231952 * q^91 + 607356 * q^94 + 38420 * q^95 - 440264 * q^96 + 406924 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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