LMFDB - Embedded newform 60.6.j.a.7.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [60,6,Mod(7,60)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(60, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 0, 1]))

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

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

chi := DirichletCharacter("60.7");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 60 = 2^{2} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	60.j (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:	$9.62302918878$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$30$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			7.12
Character	$\chi$	$=$	60.7
Dual form			60.6.j.a.43.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.54160 + 5.05374i) q^{2} +(6.36396 + 6.36396i) q^{3} +(-19.0805 - 25.6892i) q^{4} +(46.5686 + 30.9252i) q^{5} +(-48.3364 + 15.9871i) q^{6} +(-69.0576 + 69.0576i) q^{7} +(178.321 - 31.1362i) q^{8} +81.0000i q^{9} +O(q^{10})$	\(q+(-2.54160 + 5.05374i) q^{2} +(6.36396 + 6.36396i) q^{3} +(-19.0805 - 25.6892i) q^{4} +(46.5686 + 30.9252i) q^{5} +(-48.3364 + 15.9871i) q^{6} +(-69.0576 + 69.0576i) q^{7} +(178.321 - 31.1362i) q^{8} +81.0000i q^{9} +(-274.647 + 156.746i) q^{10} +471.958i q^{11} +(42.0573 - 284.913i) q^{12} +(-137.412 + 137.412i) q^{13} +(-173.482 - 524.516i) q^{14} +(99.5539 + 493.167i) q^{15} +(-295.868 + 980.326i) q^{16} +(-915.632 - 915.632i) q^{17} +(-409.353 - 205.870i) q^{18} -777.207 q^{19} +(-94.1096 - 1786.38i) q^{20} -878.960 q^{21} +(-2385.15 - 1199.53i) q^{22} +(-2138.84 - 2138.84i) q^{23} +(1332.98 + 936.681i) q^{24} +(1212.27 + 2880.28i) q^{25} +(-345.198 - 1043.69i) q^{26} +(-515.481 + 515.481i) q^{27} +(3091.69 + 456.379i) q^{28} +5520.15i q^{29} +(-2745.36 - 750.316i) q^{30} +1274.32i q^{31} +(-4202.33 - 3986.84i) q^{32} +(-3003.52 + 3003.52i) q^{33} +(6954.54 - 2300.19i) q^{34} +(-5351.54 + 1080.30i) q^{35} +(2080.82 - 1545.52i) q^{36} +(5189.86 + 5189.86i) q^{37} +(1975.35 - 3927.80i) q^{38} -1748.97 q^{39} +(9267.07 + 4064.66i) q^{40} +14218.2 q^{41} +(2233.97 - 4442.03i) q^{42} +(4764.67 + 4764.67i) q^{43} +(12124.2 - 9005.21i) q^{44} +(-2504.94 + 3772.05i) q^{45} +(16245.2 - 5373.06i) q^{46} +(19281.3 - 19281.3i) q^{47} +(-8121.65 + 4355.86i) q^{48} +7269.08i q^{49} +(-17637.3 - 1194.07i) q^{50} -11654.1i q^{51} +(6151.90 + 908.110i) q^{52} +(-23446.9 + 23446.9i) q^{53} +(-1294.96 - 3915.25i) q^{54} +(-14595.4 + 21978.4i) q^{55} +(-10164.3 + 14464.7i) q^{56} +(-4946.12 - 4946.12i) q^{57} +(-27897.4 - 14030.0i) q^{58} +12503.5 q^{59} +(10769.5 - 11967.3i) q^{60} +20129.9 q^{61} +(-6440.06 - 3238.81i) q^{62} +(-5593.67 - 5593.67i) q^{63} +(30829.1 - 11104.5i) q^{64} +(-10648.6 + 2149.59i) q^{65} +(-7545.26 - 22812.8i) q^{66} +(-30888.0 + 30888.0i) q^{67} +(-6051.11 + 40992.6i) q^{68} -27223.0i q^{69} +(8141.95 - 29790.9i) q^{70} -56152.6i q^{71} +(2522.03 + 14444.0i) q^{72} +(36983.3 - 36983.3i) q^{73} +(-39418.7 + 13037.6i) q^{74} +(-10615.2 + 26044.8i) q^{75} +(14829.5 + 19965.8i) q^{76} +(-32592.3 - 32592.3i) q^{77} +(4445.19 - 8838.83i) q^{78} +14296.6 q^{79} +(-44094.9 + 36502.6i) q^{80} -6561.00 q^{81} +(-36137.1 + 71855.2i) q^{82} +(56758.8 + 56758.8i) q^{83} +(16771.0 + 22579.8i) q^{84} +(-14323.6 - 70955.8i) q^{85} +(-36189.3 + 11969.5i) q^{86} +(-35130.0 + 35130.0i) q^{87} +(14695.0 + 84160.3i) q^{88} -27861.0i q^{89} +(-12696.4 - 22246.4i) q^{90} -18978.7i q^{91} +(-14134.9 + 95755.3i) q^{92} +(-8109.70 + 8109.70i) q^{93} +(48437.2 + 146448. i) q^{94} +(-36193.4 - 24035.3i) q^{95} +(-1371.38 - 52115.5i) q^{96} +(-104470. - 104470. i) q^{97} +(-36736.0 - 18475.1i) q^{98} -38228.6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q + 180 q^{6} - 492 q^{8}+O(q^{10}) $ 60 * q + 180 * q^6 - 492 * q^8	$ 60 q + 180 q^{6} - 492 q^{8} - 568 q^{10} + 792 q^{12} - 244 q^{13} - 2740 q^{16} - 2020 q^{17} + 6820 q^{20} + 2212 q^{22} + 15580 q^{25} - 11920 q^{26} - 4724 q^{28} + 1368 q^{30} - 25580 q^{32} - 9432 q^{33} + 1620 q^{36} + 3764 q^{37} + 9776 q^{38} + 47032 q^{40} + 19280 q^{41} + 14220 q^{42} - 6156 q^{45} - 25400 q^{46} - 44784 q^{48} - 104816 q^{50} - 61288 q^{52} + 40244 q^{53} + 76480 q^{56} + 242100 q^{58} + 88380 q^{60} - 96160 q^{61} + 83864 q^{62} + 88420 q^{65} - 63720 q^{66} - 346256 q^{68} - 373436 q^{70} - 39852 q^{72} - 72036 q^{73} + 304040 q^{76} + 241008 q^{77} + 151416 q^{78} + 534404 q^{80} - 393660 q^{81} + 497776 q^{82} - 14276 q^{85} - 719680 q^{86} - 600740 q^{88} - 86508 q^{90} - 697064 q^{92} + 1584 q^{93} + 295020 q^{96} + 71580 q^{97} + 1425384 q^{98}+O(q^{100}) $ 60 * q + 180 * q^6 - 492 * q^8 - 568 * q^10 + 792 * q^12 - 244 * q^13 - 2740 * q^16 - 2020 * q^17 + 6820 * q^20 + 2212 * q^22 + 15580 * q^25 - 11920 * q^26 - 4724 * q^28 + 1368 * q^30 - 25580 * q^32 - 9432 * q^33 + 1620 * q^36 + 3764 * q^37 + 9776 * q^38 + 47032 * q^40 + 19280 * q^41 + 14220 * q^42 - 6156 * q^45 - 25400 * q^46 - 44784 * q^48 - 104816 * q^50 - 61288 * q^52 + 40244 * q^53 + 76480 * q^56 + 242100 * q^58 + 88380 * q^60 - 96160 * q^61 + 83864 * q^62 + 88420 * q^65 - 63720 * q^66 - 346256 * q^68 - 373436 * q^70 - 39852 * q^72 - 72036 * q^73 + 304040 * q^76 + 241008 * q^77 + 151416 * q^78 + 534404 * q^80 - 393660 * q^81 + 497776 * q^82 - 14276 * q^85 - 719680 * q^86 - 600740 * q^88 - 86508 * q^90 - 697064 * q^92 + 1584 * q^93 + 295020 * q^96 + 71580 * q^97 + 1425384 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$31$	$37$	$41$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$1$

Coefficient data

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

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

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

$2$	−2.54160	+	5.05374i	−0.449296	+	0.893383i
$2$	−2.54160	+	5.05374i	−0.449296	+	0.893383i
$3$	6.36396	+	6.36396i	0.408248	+	0.408248i
$3$	6.36396	+	6.36396i	0.408248	+	0.408248i
$4$	−19.0805	−	25.6892i	−0.596266	−	0.802787i
$5$	46.5686	+	30.9252i	0.833044	+	0.553207i
$5$	46.5686	+	30.9252i	0.833044	+	0.553207i
$6$	−48.3364	+	15.9871i	−0.548146	+	0.181298i
$7$	−69.0576	+	69.0576i	−0.532680	+	0.532680i	−0.921369	−	0.388689i	$-0.872928\pi$
$7$	−69.0576	+	69.0576i	−0.532680	+	0.532680i	0.388689	+	0.921369i	$0.372928\pi$
$8$	178.321	−	31.1362i	0.985096	−	0.172005i
$9$			81.0000i			0.333333i
$10$	−274.647	+	156.746i	−0.868509	+	0.495674i
$11$			471.958i			1.17604i	0.808847	+	0.588020i	$0.200092\pi$
$11$			471.958i			1.17604i	−0.808847	+	0.588020i	$0.799908\pi$
$12$	42.0573	−	284.913i	0.0843118	−	0.571161i
$13$	−137.412	+	137.412i	−0.225510	+	0.225510i	−0.810814	−	0.585304i	$-0.800975\pi$
$13$	−137.412	+	137.412i	−0.225510	+	0.225510i	0.585304	+	0.810814i	$0.300975\pi$
$14$	−173.482	−	524.516i	−0.236556	−	0.715219i
$15$	99.5539	+	493.167i	0.114243	+	0.565934i
$16$	−295.868	+	980.326i	−0.288934	+	0.957349i
$17$	−915.632	−	915.632i	−0.768420	−	0.768420i	0.209408	−	0.977828i	$-0.432846\pi$
$17$	−915.632	−	915.632i	−0.768420	−	0.768420i	−0.977828	+	0.209408i	$0.932846\pi$
$18$	−409.353	−	205.870i	−0.297794	−	0.149765i
$19$	−777.207			−0.493916			−0.246958	−	0.969026i	$-0.579431\pi$
$19$	−777.207			−0.493916			−0.246958	+	0.969026i	$0.579431\pi$
$20$	−94.1096	−	1786.38i	−0.0526089	−	0.998615i
$21$	−878.960			−0.434932
$22$	−2385.15	−	1199.53i	−1.05065	−	0.528390i
$23$	−2138.84	−	2138.84i	−0.843061	−	0.843061i	0.146195	−	0.989256i	$-0.453297\pi$
$23$	−2138.84	−	2138.84i	−0.843061	−	0.843061i	−0.989256	+	0.146195i	$0.953297\pi$
$24$	1332.98	+	936.681i	0.472385	+	0.331943i
$25$	1212.27	+	2880.28i	0.387925	+	0.921691i
$26$	−345.198	−	1043.69i	−0.100146	−	0.302788i
$27$	−515.481	+	515.481i	−0.136083	+	0.136083i
$28$	3091.69	+	456.379i	0.745248	+	0.110010i
$29$			5520.15i			1.21886i	0.792838	+	0.609432i	$0.208603\pi$
$29$			5520.15i			1.21886i	−0.792838	+	0.609432i	$0.791397\pi$
$30$	−2745.36	−	750.316i	−0.556925	−	0.152209i
$31$			1274.32i			0.238162i	0.992885	+	0.119081i	$0.0379949\pi$
$31$			1274.32i			0.238162i	−0.992885	+	0.119081i	$0.962005\pi$
$32$	−4202.33	−	3986.84i	−0.725463	−	0.688262i
$33$	−3003.52	+	3003.52i	−0.480116	+	0.480116i
$34$	6954.54	−	2300.19i	1.03174	−	0.341245i
$35$	−5351.54	+	1080.30i	−0.738428	+	0.149064i
$36$	2080.82	−	1545.52i	0.267596	−	0.198755i
$37$	5189.86	+	5189.86i	0.623234	+	0.623234i	0.946357	−	0.323123i	$-0.104733\pi$
$37$	5189.86	+	5189.86i	0.623234	+	0.623234i	−0.323123	+	0.946357i	$0.604733\pi$
$38$	1975.35	−	3927.80i	0.221914	−	0.441256i
$39$	−1748.97			−0.184128
$40$	9267.07	+	4064.66i	0.915783	+	0.401674i
$41$	14218.2			1.32095			0.660474	−	0.750849i	$-0.270355\pi$
$41$	14218.2			1.32095			0.660474	+	0.750849i	$0.270355\pi$
$42$	2233.97	−	4442.03i	0.195413	−	0.388561i
$43$	4764.67	+	4764.67i	0.392972	+	0.392972i	0.875746	−	0.482773i	$-0.160370\pi$
$43$	4764.67	+	4764.67i	0.392972	+	0.392972i	−0.482773	+	0.875746i	$0.660370\pi$
$44$	12124.2	−	9005.21i	0.944109	−	0.701232i
$45$	−2504.94	+	3772.05i	−0.184402	+	0.277681i
$46$	16245.2	−	5373.06i	1.13196	−	0.374392i
$47$	19281.3	−	19281.3i	1.27319	−	1.27319i	0.328779	−	0.944407i	$-0.393363\pi$
$47$	19281.3	−	19281.3i	1.27319	−	1.27319i	0.944407	−	0.328779i	$-0.106637\pi$
$48$	−8121.65	+	4355.86i	−0.508793	+	0.272880i
$49$			7269.08i			0.432503i
$50$	−17637.3	−	1194.07i	−0.997716	−	0.0675468i
$51$		−	11654.1i		−	0.627412i
$52$	6151.90	+	908.110i	0.315501	+	0.0465726i
$53$	−23446.9	+	23446.9i	−1.14656	+	1.14656i	−0.159331	+	0.987225i	$0.550934\pi$
$53$	−23446.9	+	23446.9i	−1.14656	+	1.14656i	−0.987225	+	0.159331i	$0.949066\pi$
$54$	−1294.96	−	3915.25i	−0.0604326	−	0.182715i
$55$	−14595.4	+	21978.4i	−0.650593	+	0.979693i
$56$	−10164.3	+	14464.7i	−0.433118	+	0.616365i
$57$	−4946.12	−	4946.12i	−0.201640	−	0.201640i
$58$	−27897.4	−	14030.0i	−1.08891	−	0.547631i
$59$	12503.5			0.467629			0.233815	−	0.972281i	$-0.424879\pi$
$59$	12503.5			0.467629			0.233815	+	0.972281i	$0.424879\pi$
$60$	10769.5	−	11967.3i	0.386205	−	0.429160i
$61$	20129.9			0.692656			0.346328	−	0.938113i	$-0.387428\pi$
$61$	20129.9			0.692656			0.346328	+	0.938113i	$0.387428\pi$
$62$	−6440.06	−	3238.81i	−0.212770	−	0.107005i
$63$	−5593.67	−	5593.67i	−0.177560	−	0.177560i
$64$	30829.1	−	11104.5i	0.940829	−	0.338883i
$65$	−10648.6	+	2149.59i	−0.312614	+	0.0631062i
$66$	−7545.26	−	22812.8i	−0.213213	−	0.644642i
$67$	−30888.0	+	30888.0i	−0.840625	+	0.840625i	−0.988940	−	0.148315i	$-0.952615\pi$
$67$	−30888.0	+	30888.0i	−0.840625	+	0.840625i	0.148315	+	0.988940i	$0.452615\pi$
$68$	−6051.11	+	40992.6i	−0.158695	+	1.07506i
$69$		−	27223.0i		−	0.688357i
$70$	8141.95	−	29790.9i	0.198602	−	0.726673i
$71$		−	56152.6i		−	1.32198i	−0.750396	−	0.660989i	$-0.770137\pi$
$71$		−	56152.6i		−	1.32198i	0.750396	−	0.660989i	$-0.229863\pi$
$72$	2522.03	+	14444.0i	0.0573350	+	0.328365i
$73$	36983.3	−	36983.3i	0.812265	−	0.812265i	−0.172708	−	0.984973i	$-0.555252\pi$
$73$	36983.3	−	36983.3i	0.812265	−	0.812265i	0.984973	+	0.172708i	$0.0552516\pi$
$74$	−39418.7	+	13037.6i	−0.836803	+	0.276770i
$75$	−10615.2	+	26044.8i	−0.217909	+	0.534648i
$76$	14829.5	+	19965.8i	0.294505	+	0.396509i
$77$	−32592.3	−	32592.3i	−0.626453	−	0.626453i
$78$	4445.19	−	8838.83i	0.0827282	−	0.164497i
$79$	14296.6			0.257730			0.128865	−	0.991662i	$-0.458867\pi$
$79$	14296.6			0.257730			0.128865	+	0.991662i	$0.458867\pi$
$80$	−44094.9	+	36502.6i	−0.770306	+	0.637674i
$81$	−6561.00			−0.111111
$82$	−36137.1	+	71855.2i	−0.593497	+	1.18011i
$83$	56758.8	+	56758.8i	0.904353	+	0.904353i	0.995809	−	0.0914560i	$-0.0291521\pi$
$83$	56758.8	+	56758.8i	0.904353	+	0.904353i	−0.0914560	+	0.995809i	$0.529152\pi$
$84$	16771.0	+	22579.8i	0.259335	+	0.349157i
$85$	−14323.6	−	70955.8i	−0.215033	−	1.06522i
$86$	−36189.3	+	11969.5i	−0.527636	+	0.174514i
$87$	−35130.0	+	35130.0i	−0.497599	+	0.497599i
$88$	14695.0	+	84160.3i	0.202285	+	1.15851i
$89$		−	27861.0i		−	0.372840i	−0.982470	−	0.186420i	$-0.940312\pi$
$89$		−	27861.0i		−	0.372840i	0.982470	−	0.186420i	$-0.0596885\pi$
$90$	−12696.4	−	22246.4i	−0.165225	−	0.289503i
$91$		−	18978.7i		−	0.240250i
$92$	−14134.9	+	95755.3i	−0.174110	+	1.17949i
$93$	−8109.70	+	8109.70i	−0.0972294	+	0.0972294i
$94$	48437.2	+	146448.i	0.565405	+	1.70948i
$95$	−36193.4	−	24035.3i	−0.411454	−	0.273238i
$96$	−1371.38	−	52115.5i	−0.0151873	−	0.577150i
$97$	−104470.	−	104470.i	−1.12736	−	1.12736i	−0.990605	−	0.136757i	$-0.956332\pi$
$97$	−104470.	−	104470.i	−1.12736	−	1.12736i	−0.136757	−	0.990605i	$-0.543668\pi$
$98$	−36736.0	−	18475.1i	−0.386391	−	0.194322i
$99$	−38228.6			−0.392013
$100$	50861.5	−	86099.4i	0.508615	−	0.860994i
$101$	155457.			1.51638			0.758190	−	0.652033i	$-0.226084\pi$
$101$	155457.			1.51638			0.758190	+	0.652033i	$0.226084\pi$
$102$	58896.7	+	29620.1i	0.560520	+	0.281894i
$103$	51500.2	+	51500.2i	0.478317	+	0.478317i	0.904593	−	0.426276i	$-0.140175\pi$
$103$	51500.2	+	51500.2i	0.478317	+	0.478317i	−0.426276	+	0.904593i	$0.640175\pi$
$104$	−20225.0	+	28782.0i	−0.183360	+	0.260938i
$105$	−40931.9	−	27182.0i	−0.362317	−	0.240607i
$106$	−58901.7	−	178087.i	−0.509170	−	1.53946i
$107$	152974.	−	152974.i	1.29169	−	1.29169i	0.357953	−	0.933740i	$-0.383475\pi$
$107$	152974.	−	152974.i	1.29169	−	1.29169i	0.933740	−	0.357953i	$-0.116525\pi$
$108$	23077.9	+	3406.64i	0.190387	+	0.0281039i
$109$			198019.i			1.59640i	0.602395	+	0.798198i	$0.294213\pi$
$109$			198019.i			1.59640i	−0.602395	+	0.798198i	$0.705787\pi$
$110$	−73977.5	−	129622.i	−0.582932	−	1.02140i
$111$			66056.1i			0.508868i
$112$	−47267.0	−	88130.9i	−0.356052	−	0.663870i
$113$	95751.0	−	95751.0i	0.705419	−	0.705419i	−0.260149	−	0.965568i	$-0.583772\pi$
$113$	95751.0	−	95751.0i	0.705419	−	0.705419i	0.965568	+	0.260149i	$0.0837718\pi$
$114$	37567.4	−	12425.3i	0.270738	−	0.0895458i
$115$	−33458.7	−	165747.i	−0.235920	−	1.16869i
$116$	141808.	−	105327.i	0.978489	−	0.726768i
$117$	−11130.4	−	11130.4i	−0.0751701	−	0.0751701i
$118$	−31778.9	+	63189.4i	−0.210104	+	0.417772i
$119$	126463.			0.818645
$120$	33108.0	+	84842.6i	0.209884	+	0.537849i
$121$	−61693.7			−0.383069
$122$	−51162.3	+	101731.i	−0.311208	+	0.618807i
$123$	90484.3	+	90484.3i	0.539275	+	0.539275i
$124$	32736.2	−	24314.6i	0.191194	−	0.142008i
$125$	−32619.9	+	171620.i	−0.186727	+	0.982412i
$126$	42485.8	−	14052.0i	0.238406	−	0.0788521i
$127$	−122697.	+	122697.i	−0.675033	+	0.675033i	−0.958872	−	0.283839i	$-0.908392\pi$
$127$	−122697.	+	122697.i	−0.675033	+	0.675033i	0.283839	+	0.958872i	$0.408392\pi$
$128$	−22236.0	+	184025.i	−0.119959	+	0.992779i
$129$			60644.4i			0.320861i
$130$	16201.0	−	59278.5i	0.0840782	−	0.307637i
$131$		−	202640.i		−	1.03169i	−0.856683	−	0.515843i	$-0.827479\pi$
$131$		−	202640.i		−	1.03169i	0.856683	−	0.515843i	$-0.172521\pi$
$132$	134467.	+	19849.3i	0.671708	+	0.0991540i
$133$	53672.1	−	53672.1i	0.263099	−	0.263099i
$134$	−77594.8	−	234605.i	−0.373311	−	1.12869i
$135$	−39946.6	+	8063.87i	−0.188645	+	0.0380810i
$136$	−191786.	−	134768.i	−0.889140	−	0.624796i
$137$	25230.9	+	25230.9i	0.114850	+	0.114850i	0.762196	−	0.647346i	$-0.224121\pi$
$137$	25230.9	+	25230.9i	0.114850	+	0.114850i	−0.647346	+	0.762196i	$0.724121\pi$
$138$	137578.	+	69190.1i	0.614966	+	0.309276i
$139$	−61245.1			−0.268865			−0.134432	−	0.990923i	$-0.542921\pi$
$139$	−61245.1			−0.268865			−0.134432	+	0.990923i	$0.542921\pi$
$140$	129862.	+	116864.i	0.559966	+	0.503919i
$141$	245411.			1.03955
$142$	283781.	+	142718.i	1.18103	+	0.593960i
$143$	−64852.8	−	64852.8i	−0.265209	−	0.265209i
$144$	−79406.4	−	23965.3i	−0.319116	−	0.0963112i
$145$	−170712.	+	257065.i	−0.674284	+	1.01537i
$146$	92906.9	+	280900.i	0.360716	+	1.09061i
$147$	−46260.2	+	46260.2i	−0.176569	+	0.176569i
$148$	34298.0	−	232348.i	0.128711	−	0.871937i
$149$			162447.i			0.599442i	0.954027	+	0.299721i	$0.0968935\pi$
$149$			162447.i			0.599442i	−0.954027	+	0.299721i	$0.903106\pi$
$150$	−104644.	−	119842.i	−0.379740	−	0.434892i
$151$			301807.i			1.07718i	0.842569	+	0.538589i	$0.181042\pi$
$151$			301807.i			1.07718i	−0.842569	+	0.538589i	$0.818958\pi$
$152$	−138593.	+	24199.3i	−0.486555	+	0.0849560i
$153$	74166.2	−	74166.2i	0.256140	−	0.256140i
$154$	247550.	−	81876.3i	0.841125	−	0.278200i
$155$	−39408.5	+	59343.1i	−0.131753	+	0.198400i
$156$	33371.2	+	44929.6i	0.109790	+	0.147816i
$157$	−299040.	−	299040.i	−0.968233	−	0.968233i	0.0312779	−	0.999511i	$-0.490042\pi$
$157$	−299040.	−	299040.i	−0.968233	−	0.968233i	−0.999511	+	0.0312779i	$0.990042\pi$
$158$	−36336.3	+	72251.2i	−0.115797	+	0.230252i
$159$	−298430.			−0.936159
$160$	−72402.8	−	315619.i	−0.223591	−	0.974683i
$161$	295407.			0.898164
$162$	16675.5	−	33157.6i	0.0499218	−	0.0992648i
$163$	−131571.	−	131571.i	−0.387874	−	0.387874i	0.486054	−	0.873929i	$-0.338436\pi$
$163$	−131571.	−	131571.i	−0.387874	−	0.387874i	−0.873929	+	0.486054i	$0.838436\pi$
$164$	−271291.	−	365255.i	−0.787637	−	1.06044i
$165$	−232754.	+	46985.3i	−0.665561	+	0.134354i
$166$	−431102.	+	142586.i	−1.21426	+	0.401611i
$167$	−158624.	+	158624.i	−0.440127	+	0.440127i	−0.892055	−	0.451928i	$-0.850737\pi$
$167$	−158624.	+	158624.i	−0.440127	+	0.440127i	0.451928	+	0.892055i	$0.350737\pi$
$168$	−156737.	+	27367.5i	−0.428449	+	0.0748104i
$169$			333529.i			0.898290i
$170$	394997.	+	107954.i	1.04827	+	0.286494i
$171$		−	62953.8i		−	0.164639i
$172$	31488.1	−	213313.i	0.0811570	−	0.549789i
$173$	−331788.	+	331788.i	−0.842840	+	0.842840i	−0.989227	−	0.146387i	$-0.953235\pi$
$173$	−331788.	+	331788.i	−0.842840	+	0.842840i	0.146387	+	0.989227i	$0.453235\pi$
$174$	−88251.3	−	266824.i	−0.220977	−	0.668116i
$175$	−282622.	−	115189.i	−0.697607	−	0.284327i
$176$	−462673.	−	139637.i	−1.12588	−	0.339797i
$177$	79571.8	+	79571.8i	0.190909	+	0.190909i
$178$	140802.	+	70811.7i	0.333089	+	0.167515i
$179$	379062.			0.884256			0.442128	−	0.896952i	$-0.354224\pi$
$179$	379062.			0.884256			0.442128	+	0.896952i	$0.354224\pi$
$180$	144697.	−	7622.88i	0.332872	−	0.0175363i
$181$	32072.4			0.0727670			0.0363835	−	0.999338i	$-0.488416\pi$
$181$	32072.4			0.0727670			0.0363835	+	0.999338i	$0.488416\pi$
$182$	95913.4	+	48236.3i	0.214635	+	0.107943i
$183$	128106.	+	128106.i	0.282776	+	0.282776i
$184$	−447997.	−	314806.i	−0.975507	−	0.685486i
$185$	81186.9	+	402181.i	0.174404	+	0.863958i
$186$	−20372.7	−	61595.9i	−0.0431783	−	0.130548i
$187$	432140.	−	432140.i	0.903692	−	0.903692i
$188$	−863218.	−	127424.i	−1.78125	−	0.262939i
$189$		−	71195.8i		−	0.144977i
$190$	213457.	−	121824.i	0.428970	−	0.244821i
$191$			619462.i			1.22866i	0.789050	+	0.614329i	$0.210573\pi$
$191$			619462.i			1.22866i	−0.789050	+	0.614329i	$0.789427\pi$
$192$	266864.	+	125526.i	0.522440	+	0.245743i
$193$	353159.	−	353159.i	0.682459	−	0.682459i	−0.278095	−	0.960554i	$-0.589703\pi$
$193$	353159.	−	353159.i	0.682459	−	0.682459i	0.960554	+	0.278095i	$0.0897029\pi$
$194$	793487.	−	262443.i	1.51369	−	0.500647i
$195$	−81447.0	−	54087.2i	−0.153387	−	0.101861i
$196$	186737.	−	138698.i	0.347208	−	0.257887i
$197$	−618420.	−	618420.i	−1.13532	−	1.13532i	−0.989279	−	0.146040i	$-0.953347\pi$
$197$	−618420.	−	618420.i	−1.13532	−	1.13532i	−0.146040	−	0.989279i	$-0.546653\pi$
$198$	97162.0	−	193197.i	0.176130	−	0.350218i
$199$	−58527.6			−0.104768			−0.0523839	−	0.998627i	$-0.516682\pi$
$199$	−58527.6			−0.104768			−0.0523839	+	0.998627i	$0.516682\pi$
$200$	305854.	+	475871.i	0.540679	+	0.841229i
$201$	−393140.			−0.686368
$202$	−395111.	+	785641.i	−0.681304	+	1.35471i
$203$	−381208.	−	381208.i	−0.649265	−	0.649265i
$204$	−299384.	+	222366.i	−0.503678	+	0.374105i
$205$	662123.	+	439702.i	1.10041	+	0.730758i
$206$	−391161.	+	129375.i	−0.642226	+	0.212414i
$207$	173246.	−	173246.i	0.281020	−	0.281020i
$208$	−94052.7	−	175364.i	−0.150735	−	0.281050i
$209$		−	366810.i		−	0.580865i
$210$	241403.	−	137773.i	0.377742	−	0.215584i
$211$			572266.i			0.884894i	0.896795	+	0.442447i	$0.145890\pi$
$211$			572266.i			0.884894i	−0.896795	+	0.442447i	$0.854110\pi$
$212$	1.04971e6	+	154953.i	1.60409	+	0.236788i
$213$	357353.	−	357353.i	0.539695	−	0.539695i
$214$	384292.	+	1.16189e6i	0.573624	+	1.73433i
$215$	74535.7	+	369233.i	0.109968	+	0.544758i
$216$	−75871.2	+	107971.i	−0.110648	+	0.157462i
$217$	−88001.3	−	88001.3i	−0.126864	−	0.126864i
$218$	−1.00074e6	−	503286.i	−1.42619	−	0.717255i
$219$	470720.			0.663212
$220$	843096.	−	44415.8i	1.17441	−	0.0618701i
$221$	251638.			0.346573
$222$	−333830.	−	167888.i	−0.454614	−	0.228633i
$223$	−111998.	−	111998.i	−0.150816	−	0.150816i	0.627666	−	0.778482i	$-0.284010\pi$
$223$	−111998.	−	111998.i	−0.150816	−	0.150816i	−0.778482	+	0.627666i	$0.784010\pi$
$224$	565524.	−	14881.4i	0.753063	−	0.0198163i
$225$	−233303.	+	98193.5i	−0.307230	+	0.129308i
$226$	240539.	+	727261.i	0.313267	+	0.947152i
$227$	739564.	−	739564.i	0.952601	−	0.952601i	−0.0463254	−	0.998926i	$-0.514751\pi$
$227$	739564.	−	739564.i	0.952601	−	0.952601i	0.998926	+	0.0463254i	$0.0147511\pi$
$228$	−32687.2	+	221436.i	−0.0416429	+	0.282105i
$229$		−	544452.i		−	0.686074i	−0.939322	−	0.343037i	$-0.888544\pi$
$229$		−	544452.i		−	0.686074i	0.939322	−	0.343037i	$-0.111456\pi$
$230$	922680.	+	252171.i	1.15009	+	0.314323i
$231$		−	414833.i		−	0.511497i
$232$	171876.	+	984360.i	0.209651	+	1.20070i
$233$	447263.	−	447263.i	0.539726	−	0.539726i	−0.383723	−	0.923448i	$-0.625358\pi$
$233$	447263.	−	447263.i	0.539726	−	0.539726i	0.923448	+	0.383723i	$0.125358\pi$
$234$	84539.0	−	27961.0i	0.100929	−	0.0333821i
$235$	1.49418e6	−	301625.i	1.76496	−	0.356285i
$236$	−238573.	−	321205.i	−0.278831	−	0.375407i
$237$	90983.0	+	90983.0i	0.105218	+	0.105218i
$238$	−321418.	+	639110.i	−0.367814	+	0.731363i
$239$	−1.43125e6			−1.62076			−0.810382	−	0.585901i	$-0.800741\pi$
$239$	−1.43125e6			−1.62076			−0.810382	+	0.585901i	$0.800741\pi$
$240$	−512919.	−	48317.2i	−0.574806	−	0.0541469i
$241$	568815.			0.630853			0.315427	−	0.948950i	$-0.397852\pi$
$241$	568815.			0.630853			0.315427	+	0.948950i	$0.397852\pi$
$242$	156801.	−	311784.i	0.172111	−	0.342227i
$243$	−41753.9	−	41753.9i	−0.0453609	−	0.0453609i
$244$	−384090.	−	517122.i	−0.413007	−	0.556055i
$245$	−224798.	+	338511.i	−0.239264	+	0.360294i
$246$	−687259.	+	227309.i	−0.724073	+	0.239485i
$247$	106798.	−	106798.i	0.111383	−	0.111383i
$248$	39677.4	+	227238.i	0.0409651	+	0.234613i
$249$			722422.i			0.738401i
$250$	−784417.	−	601043.i	−0.793774	−	0.608213i
$251$			371191.i			0.371889i	0.982560	+	0.185944i	$0.0595344\pi$
$251$			371191.i			0.371889i	−0.982560	+	0.185944i	$0.940466\pi$
$252$	−36966.7	+	250427.i	−0.0366699	+	0.248416i
$253$	1.00944e6	−	1.00944e6i	0.991473	−	0.991473i
$254$	−308231.	−	931926.i	−0.299773	−	0.906352i
$255$	360405.	−	542715.i	0.347089	−	0.522662i
$256$	−873500.	−	580094.i	−0.833035	−	0.553221i
$257$	−1.12785e6	−	1.12785e6i	−1.06517	−	1.06517i	−0.997723	−	0.0674499i	$-0.978514\pi$
$257$	−1.12785e6	−	1.12785e6i	−1.06517	−	1.06517i	−0.0674499	−	0.997723i	$-0.521486\pi$
$258$	−306481.	−	154134.i	−0.286651	−	0.144161i
$259$	−716798.			−0.663969
$260$	258402.	+	232538.i	0.237062	+	0.213334i
$261$	−447132.			−0.406288
$262$	1.02409e6	+	515031.i	0.921691	+	0.463532i
$263$	−25656.0	−	25656.0i	−0.0228718	−	0.0228718i	0.695578	−	0.718450i	$-0.255148\pi$
$263$	−25656.0	−	25656.0i	−0.0228718	−	0.0228718i	−0.718450	+	0.695578i	$0.755148\pi$
$264$	−442074.	+	629111.i	−0.390378	+	0.555543i
$265$	−1.81699e6	+	366789.i	−1.58941	+	0.320849i
$266$	134832.	+	407658.i	0.116839	+	0.353258i
$267$	177307.	−	177307.i	0.152211	−	0.152211i
$268$	1.38285e6	+	204128.i	1.17608	+	0.173607i
$269$		−	1.62618e6i		−	1.37022i	−0.728441	−	0.685108i	$-0.759755\pi$
$269$		−	1.62618e6i		−	1.37022i	0.728441	−	0.685108i	$-0.240245\pi$
$270$	60775.6	−	222375.i	0.0507364	−	0.185642i
$271$			785041.i			0.649336i	0.945828	+	0.324668i	$0.105253\pi$
$271$			785041.i			0.649336i	−0.945828	+	0.324668i	$0.894747\pi$
$272$	1.16852e6	−	626711.i	0.957669	−	0.513624i
$273$	120780.	−	120780.i	0.0980816	−	0.0980816i
$274$	−191638.	+	63383.5i	−0.154207	+	0.0510035i
$275$	−1.35937e6	+	572139.i	−1.08395	+	0.456215i
$276$	−699337.	+	519429.i	−0.552604	+	0.410444i
$277$	713367.	+	713367.i	0.558616	+	0.558616i	0.928913	−	0.370297i	$-0.120744\pi$
$277$	713367.	+	713367.i	0.558616	+	0.558616i	−0.370297	+	0.928913i	$0.620744\pi$
$278$	155661.	−	309516.i	0.120800	−	0.240199i
$279$	−103220.			−0.0793875
$280$	−920658.	+	359266.i	−0.701783	+	0.273856i
$281$	204595.			0.154571			0.0772856	−	0.997009i	$-0.475375\pi$
$281$	204595.			0.154571			0.0772856	+	0.997009i	$0.475375\pi$
$282$	−623737.	+	1.24024e6i	−0.467067	+	0.928718i
$283$	762742.	+	762742.i	0.566124	+	0.566124i	0.931040	−	0.364916i	$-0.118902\pi$
$283$	762742.	+	762742.i	0.566124	+	0.566124i	−0.364916	+	0.931040i	$0.618902\pi$
$284$	−1.44252e6	+	1.07142e6i	−1.06127	+	0.788251i
$285$	−77374.0	−	383293.i	−0.0564265	−	0.279524i
$286$	492579.	−	162919.i	0.356091	−	0.117776i
$287$	−981878.	+	981878.i	−0.703643	+	0.703643i
$288$	322934.	−	340389.i	0.229421	−	0.241821i
$289$			256908.i			0.180939i
$290$	−865260.	−	1.51609e6i	−0.604159	−	1.05859i
$291$		−	1.32969e6i		−	0.920487i
$292$	−1.65573e6	−	244410.i	−1.13640	−	0.167750i
$293$	−971098.	+	971098.i	−0.660837	+	0.660837i	−0.955577	−	0.294741i	$-0.904767\pi$
$293$	−971098.	+	971098.i	−0.660837	+	0.660837i	0.294741	+	0.955577i	$0.404767\pi$
$294$	−116212.	−	351362.i	−0.0784119	−	0.237075i
$295$	582270.	+	386673.i	0.389556	+	0.258696i
$296$	1.08706e6	+	763870.i	0.721144	+	0.506746i
$297$	−243285.	−	243285.i	−0.160039	−	0.160039i
$298$	−820966.	−	412877.i	−0.535531	−	0.269327i
$299$	587805.			0.380238
$300$	871614.	−	224253.i	0.559141	−	0.143858i
$301$	−658074.			−0.418657
$302$	−1.52525e6	−	767074.i	−0.962332	−	0.483972i
$303$	989325.	+	989325.i	0.619060	+	0.619060i
$304$	229951.	−	761916.i	0.142709	−	0.472850i
$305$	937423.	+	622522.i	0.577013	+	0.383182i
$306$	186315.	+	563317.i	0.113748	+	0.343914i
$307$	636200.	−	636200.i	0.385255	−	0.385255i	−0.487736	−	0.872991i	$-0.662177\pi$
$307$	636200.	−	636200.i	0.385255	−	0.385255i	0.872991	+	0.487736i	$0.162177\pi$
$308$	−215392.	+	1.45915e6i	−0.129376	+	0.876441i
$309$			655490.i			0.390544i
$310$	−199744.	−	349987.i	−0.118051	−	0.206846i
$311$			1.70228e6i			0.998000i	0.866602	+	0.499000i	$0.166299\pi$
$311$			1.70228e6i			0.998000i	−0.866602	+	0.499000i	$0.833701\pi$
$312$	−311879.	+	54456.3i	−0.181384	+	0.0316710i
$313$	−54907.0	+	54907.0i	−0.0316786	+	0.0316786i	−0.722769	−	0.691090i	$-0.757131\pi$
$313$	−54907.0	+	54907.0i	−0.0316786	+	0.0316786i	0.691090	+	0.722769i	$0.257131\pi$
$314$	2.27131e6	−	751228.i	1.30003	−	0.429979i
$315$	−87503.9	−	433475.i	−0.0496880	−	0.246143i
$316$	−272786.	−	367268.i	−0.153676	−	0.206902i
$317$	554974.	+	554974.i	0.310187	+	0.310187i	0.844982	−	0.534795i	$-0.179611\pi$
$317$	554974.	+	554974.i	0.310187	+	0.310187i	−0.534795	+	0.844982i	$0.679611\pi$
$318$	758490.	−	1.50819e6i	0.420613	−	0.836349i
$319$	−2.60528e6			−1.43343
$320$	1.77908e6	+	436274.i	0.971224	+	0.238168i
$321$	1.94705e6			1.05466
$322$	−750807.	+	1.49291e6i	−0.403542	+	0.802405i
$323$	711636.	+	711636.i	0.379535	+	0.379535i
$324$	125187.	+	168547.i	0.0662518	+	0.0891985i
$325$	−562366.	−	229206.i	−0.295332	−	0.120370i
$326$	999326.	−	330524.i	0.520790	−	0.172250i
$327$	−1.26019e6	+	1.26019e6i	−0.651726	+	0.651726i
$328$	2.53542e6	−	442702.i	1.30126	−	0.227210i
$329$			2.66304e6i			1.35640i
$330$	354118.	−	1.29570e6i	0.179004	−	0.654966i
$331$		−	3.54321e6i		−	1.77757i	−0.458322	−	0.888786i	$-0.651549\pi$
$331$		−	3.54321e6i		−	1.77757i	0.458322	−	0.888786i	$-0.348451\pi$
$332$	375100.	−	2.54107e6i	0.186768	−	1.26524i
$333$	−420378.	+	420378.i	−0.207745	+	0.207745i
$334$	−398485.	−	1.20480e6i	−0.195455	−	0.590949i
$335$	−2.39363e6	+	483193.i	−1.16532	+	0.235238i
$336$	260056.	−	861667.i	0.125666	−	0.416381i
$337$	1.75690e6	+	1.75690e6i	0.842696	+	0.842696i	0.989209	−	0.146512i	$-0.0468048\pi$
$337$	1.75690e6	+	1.75690e6i	0.842696	+	0.842696i	−0.146512	+	0.989209i	$0.546805\pi$
$338$	−1.68557e6	−	847698.i	−0.802517	−	0.403598i
$339$	1.21871e6			0.575972
$340$	−1.54949e6	+	1.72183e6i	−0.726930	+	0.807782i
$341$	−601424.			−0.280088
$342$	318152.	+	160004.i	0.147085	+	0.0739715i
$343$	−1.66264e6	−	1.66264e6i	−0.763066	−	0.763066i
$344$	997998.	+	701290.i	0.454709	+	0.319522i
$345$	841877.	−	1.26774e6i	0.380803	−	0.573431i
$346$	−833496.	−	2.52004e6i	−0.374294	−	1.13166i
$347$	−321428.	+	321428.i	−0.143305	+	0.143305i	−0.775119	−	0.631815i	$-0.782310\pi$
$347$	−321428.	+	321428.i	−0.143305	+	0.143305i	0.631815	+	0.775119i	$0.282310\pi$
$348$	1.57276e6	+	232162.i	0.696168	+	0.102765i
$349$			1.56837e6i			0.689262i	0.938738	+	0.344631i	$0.111996\pi$
$349$			1.56837e6i			0.689262i	−0.938738	+	0.344631i	$0.888004\pi$
$350$	1.30045e6	−	1.13553e6i	0.567445	−	0.495483i
$351$		−	141667.i		−	0.0613761i
$352$	1.88162e6	−	1.98332e6i	0.809423	−	0.853173i
$353$	−1.63918e6	+	1.63918e6i	−0.700149	+	0.700149i	−0.964442	−	0.264294i	$-0.914861\pi$
$353$	−1.63918e6	+	1.63918e6i	−0.700149	+	0.700149i	0.264294	+	0.964442i	$0.414861\pi$
$354$	−604375.	+	199895.i	−0.256329	+	0.0847801i
$355$	1.73653e6	−	2.61495e6i	0.731327	−	1.10127i
$356$	−715727.	+	531603.i	−0.299311	+	0.222312i
$357$	804804.	+	804804.i	0.334210	+	0.334210i
$358$	−963426.	+	1.91568e6i	−0.397293	+	0.789980i
$359$	3.50207e6			1.43413			0.717065	−	0.697006i	$-0.245485\pi$
$359$	3.50207e6			1.43413			0.717065	+	0.697006i	$0.245485\pi$
$360$	−329237.	+	750633.i	−0.133891	+	0.305261i
$361$	−1.87205e6			−0.756047
$362$	−81515.2	+	162085.i	−0.0326939	+	0.0650088i
$363$	−392616.	−	392616.i	−0.156387	−	0.156387i
$364$	−487547.	+	362123.i	−0.192869	+	0.143253i
$365$	2.86597e6	−	578543.i	1.12600	−	0.227302i
$366$	−973010.	+	321820.i	−0.379677	+	0.125577i
$367$	350065.	−	350065.i	0.135670	−	0.135670i	−0.636010	−	0.771680i	$-0.719416\pi$
$367$	350065.	−	350065.i	0.135670	−	0.135670i	0.771680	+	0.636010i	$0.219416\pi$
$368$	2.72958e6	−	1.46395e6i	1.05069	−	0.563515i
$369$			1.15168e6i			0.440316i
$370$	−2.23886e6	−	611888.i	−0.850205	−	0.232363i
$371$		−	3.23837e6i		−	1.22150i
$372$	363069.	+	53594.3i	0.136029	+	0.0200799i
$373$	−1.45117e6	+	1.45117e6i	−0.540067	+	0.540067i	−0.923548	−	0.383482i	$-0.874725\pi$
$373$	−1.45117e6	+	1.45117e6i	−0.540067	+	0.540067i	0.383482	+	0.923548i	$0.374725\pi$
$374$	1.08559e6	+	3.28225e6i	0.401318	+	1.21337i
$375$	−1.29978e6	+	884593.i	−0.477299	+	0.324837i
$376$	2.83792e6	−	4.03862e6i	1.03522	−	1.47320i
$377$	−758534.	−	758534.i	−0.274867	−	0.274867i
$378$	359805.	+	180951.i	0.129520	+	0.0651377i
$379$	1.47016e6			0.525734			0.262867	−	0.964832i	$-0.415332\pi$
$379$	1.47016e6			0.525734			0.262867	+	0.964832i	$0.415332\pi$
$380$	73142.7	+	1.38839e6i	0.0259844	+	0.493232i
$381$	−1.56168e6			−0.551162
$382$	−3.13060e6	−	1.57443e6i	−1.09766	−	0.552031i
$383$	−617148.	−	617148.i	−0.214977	−	0.214977i	0.591401	−	0.806378i	$-0.298575\pi$
$383$	−617148.	−	617148.i	−0.214977	−	0.214977i	−0.806378	+	0.591401i	$0.798575\pi$
$384$	−1.31264e6	+	1.02962e6i	−0.454273	+	0.356327i
$385$	−509854.	−	2.52570e6i	−0.175305	−	0.868421i
$386$	887182.	+	2.68236e6i	0.303071	+	0.916323i
$387$	−385939.	+	385939.i	−0.130991	+	0.130991i
$388$	−690409.	+	4.67710e6i	−0.232824	+	1.57724i
$389$		−	1.44183e6i		−	0.483102i	−0.970388	−	0.241551i	$-0.922344\pi$
$389$		−	1.44183e6i		−	0.483102i	0.970388	−	0.241551i	$-0.0776561\pi$
$390$	480349.	−	274144.i	0.159917	−	0.0912676i
$391$			3.91679e6i			1.29565i
$392$	226332.	+	1.29623e6i	0.0743927	+	0.426057i
$393$	1.28959e6	−	1.28959e6i	0.421184	−	0.421184i
$394$	4.69711e6	−	1.55355e6i	1.52437	−	0.504180i
$395$	665772.	+	442125.i	0.214700	+	0.142578i
$396$	729422.	+	982062.i	0.233744	+	0.314703i
$397$	1.22840e6	+	1.22840e6i	0.391169	+	0.391169i	0.875104	−	0.483935i	$-0.160793\pi$
$397$	1.22840e6	+	1.22840e6i	0.391169	+	0.391169i	−0.483935	+	0.875104i	$0.660793\pi$
$398$	148754.	−	295783.i	0.0470718	−	0.0935977i
$399$	683135.			0.214820
$400$	−3.18229e6	+	336230.i	−0.994465	+	0.105072i
$401$	2.17553e6			0.675622			0.337811	−	0.941214i	$-0.390314\pi$
$401$	2.17553e6			0.675622			0.337811	+	0.941214i	$0.390314\pi$
$402$	999205.	−	1.98683e6i	0.308382	−	0.613189i
$403$	−175107.	−	175107.i	−0.0537081	−	0.0537081i
$404$	−2.96621e6	−	3.99358e6i	−0.904166	−	1.21733i
$405$	−305536.	−	202900.i	−0.0925605	−	0.0614674i
$406$	2.89541e6	−	957646.i	0.871755	−	0.288330i
$407$	−2.44940e6	+	2.44940e6i	−0.732948	+	0.732948i
$408$	−362864.	−	2.07817e6i	−0.107918	−	0.618062i
$409$		−	4.78991e6i		−	1.41585i	−0.706285	−	0.707927i	$-0.749630\pi$
$409$		−	4.78991e6i		−	1.41585i	0.706285	−	0.707927i	$-0.250370\pi$
$410$	−3.90499e6	+	2.22865e6i	−1.14726	+	0.654760i
$411$			321137.i			0.0937748i
$412$	340347.	−	2.30565e6i	0.0987823	−	0.669190i
$413$	−863463.	+	863463.i	−0.249097	+	0.249097i
$414$	435218.	+	1.31586e6i	0.124797	+	0.377320i
$415$	887900.	+	4.39845e6i	0.253072	+	1.25366i
$416$	1.12529e6	−	29611.2i	0.318809	−	0.00838923i
$417$	−389761.	−	389761.i	−0.109764	−	0.109764i
$418$	1.85376e6	+	932284.i	0.518935	+	0.260980i
$419$	4.63600e6			1.29005			0.645027	−	0.764160i	$-0.276846\pi$
$419$	4.63600e6			1.29005			0.645027	+	0.764160i	$0.276846\pi$
$420$	82718.6	+	1.57015e6i	0.0228813	+	0.434329i
$421$	−1.00776e6			−0.277110			−0.138555	−	0.990355i	$-0.544246\pi$
$421$	−1.00776e6			−0.277110			−0.138555	+	0.990355i	$0.544246\pi$
$422$	−2.89208e6	−	1.45447e6i	−0.790550	−	0.397580i
$423$	1.56179e6	+	1.56179e6i	0.424395	+	0.424395i
$424$	−3.45103e6	+	4.91113e6i	−0.932255	+	1.32668i
$425$	1.52729e6	−	3.74727e6i	0.410157	−	1.00634i
$426$	897719.	+	2.71422e6i	0.239672	+	0.724638i
$427$	−1.39013e6	+	1.39013e6i	−0.368964	+	0.368964i
$428$	−6.84861e6	−	1.01096e6i	−1.80715	−	0.266761i
$429$		−	825441.i		−	0.216542i
$430$	−2.05544e6	−	561759.i	−0.536086	−	0.146514i
$431$		−	4.72894e6i		−	1.22623i	−0.789995	−	0.613114i	$-0.789917\pi$
$431$		−	4.72894e6i		−	1.22623i	0.789995	−	0.613114i	$-0.210083\pi$
$432$	−352825.	−	657853.i	−0.0909598	−	0.169598i
$433$	−1.99872e6	+	1.99872e6i	−0.512309	+	0.512309i	−0.915233	−	0.402925i	$-0.867994\pi$
$433$	−1.99872e6	+	1.99872e6i	−0.512309	+	0.512309i	0.402925	+	0.915233i	$0.367994\pi$
$434$	668400.	−	221071.i	0.170338	−	0.0563388i
$435$	−2.72236e6	+	549552.i	−0.689798	+	0.139247i
$436$	5.08695e6	−	3.77831e6i	1.28157	−	0.951877i
$437$	1.66232e6	+	1.66232e6i	0.416401	+	0.416401i
$438$	−1.19638e6	+	2.37890e6i	−0.297979	+	0.592502i
$439$	−3.01924e6			−0.747715			−0.373857	−	0.927486i	$-0.621965\pi$
$439$	−3.01924e6			−0.747715			−0.373857	+	0.927486i	$0.621965\pi$
$440$	−1.91835e6	+	4.37367e6i	−0.472385	+	1.07700i
$441$	−588796.			−0.144168
$442$	−639563.	+	1.27171e6i	−0.155714	+	0.309623i
$443$	−1.81042e6	−	1.81042e6i	−0.438299	−	0.438299i	0.453140	−	0.891439i	$-0.350304\pi$
$443$	−1.81042e6	−	1.81042e6i	−0.438299	−	0.438299i	−0.891439	+	0.453140i	$0.850304\pi$
$444$	1.69693e6	−	1.26038e6i	0.408513	−	0.303421i
$445$	861608.	−	1.29745e6i	0.206257	−	0.310592i
$446$	850662.	−	281354.i	0.202498	−	0.0669754i
$447$	−1.03381e6	+	1.03381e6i	−0.244721	+	0.244721i
$448$	−1.36213e6	+	2.89583e6i	−0.320645	+	0.681677i
$449$		−	5.24473e6i		−	1.22774i	−0.789406	−	0.613872i	$-0.789611\pi$
$449$		−	5.24473e6i		−	1.22774i	0.789406	−	0.613872i	$-0.210389\pi$
$450$	96719.6	−	1.42862e6i	0.0225156	−	0.332572i
$451$			6.71041e6i			1.55349i
$452$	−4.28674e6	−	632787.i	−0.986919	−	0.145684i
$453$	−1.92069e6	+	1.92069e6i	−0.439756	+	0.439756i
$454$	1.85788e6	+	5.61724e6i	0.423038	+	1.27904i
$455$	586920.	−	883811.i	0.132908	−	0.200139i
$456$	−1.03600e6	−	727996.i	−0.233318	−	0.163952i
$457$	−3.15839e6	−	3.15839e6i	−0.707417	−	0.707417i	0.258574	−	0.965991i	$-0.416747\pi$
$457$	−3.15839e6	−	3.15839e6i	−0.707417	−	0.707417i	−0.965991	+	0.258574i	$0.916747\pi$
$458$	2.75152e6	+	1.38378e6i	0.612927	+	0.308250i
$459$	943982.			0.209137
$460$	−3.61949e6	+	4.02206e6i	−0.797541	+	0.886246i
$461$	−27448.9			−0.00601552			−0.00300776	−	0.999995i	$-0.500957\pi$
$461$	−27448.9			−0.00601552			−0.00300776	+	0.999995i	$0.500957\pi$
$462$	2.09646e6	+	1.05434e6i	0.456963	+	0.229814i
$463$	−1.97887e6	−	1.97887e6i	−0.429007	−	0.429007i	0.459283	−	0.888290i	$-0.348106\pi$
$463$	−1.97887e6	−	1.97887e6i	−0.429007	−	0.429007i	−0.888290	+	0.459283i	$0.848106\pi$
$464$	−5.41154e6	−	1.63323e6i	−1.16688	−	0.352171i
$465$	−628451.	+	126863.i	−0.134784	+	0.0272084i
$466$	1.12358e6	+	3.39711e6i	0.239685	+	0.724678i
$467$	4.43077e6	−	4.43077e6i	0.940129	−	0.940129i	−0.0581772	−	0.998306i	$-0.518529\pi$
$467$	4.43077e6	−	4.43077e6i	0.940129	−	0.940129i	0.998306	+	0.0581772i	$0.0185288\pi$
$468$	−73556.9	+	498304.i	−0.0155242	+	0.105167i
$469$		−	4.26610e6i		−	0.895569i
$470$	−2.27328e6	+	8.31781e6i	−0.474688	+	1.73686i
$471$		−	3.80615e6i		−	0.790559i
$472$	2.22964e6	−	389312.i	0.460660	−	0.0804345i
$473$	−2.24873e6	+	2.24873e6i	−0.462151	+	0.462151i
$474$	−691047.	+	228561.i	−0.141274	+	0.0467259i
$475$	−942181.	−	2.23858e6i	−0.191602	−	0.455238i
$476$	−2.41298e6	−	3.24873e6i	−0.488130	−	0.657197i
$477$	−1.89920e6	−	1.89920e6i	−0.382185	−	0.382185i
$478$	3.63766e6	−	7.23315e6i	0.728203	−	1.44796i
$479$	3.26374e6			0.649946			0.324973	−	0.945723i	$-0.394645\pi$
$479$	3.26374e6			0.649946			0.324973	+	0.945723i	$0.394645\pi$
$480$	1.54782e6	−	2.46936e6i	0.306632	−	0.489193i
$481$	−1.42630e6			−0.281091
$482$	−1.44570e6	+	2.87464e6i	−0.283440	+	0.563593i
$483$	1.87996e6	+	1.87996e6i	0.366674	+	0.366674i
$484$	1.17715e6	+	1.58486e6i	0.228411	+	0.307523i
$485$	−1.63427e6	−	8.09579e6i	−0.315478	−	1.56281i
$486$	317135.	−	104892.i	0.0609052	−	0.0201442i
$487$	2.24714e6	−	2.24714e6i	0.429345	−	0.429345i	−0.459060	−	0.888405i	$-0.651814\pi$
$487$	2.24714e6	−	2.24714e6i	0.429345	−	0.429345i	0.888405	+	0.459060i	$0.151814\pi$
$488$	3.58960e6	−	626770.i	0.682333	−	0.119140i
$489$		−	1.67462e6i		−	0.316698i
$490$	−1.13940e6	−	1.99643e6i	−0.214381	−	0.375633i
$491$		−	7.53200e6i		−	1.40996i	−0.709228	−	0.704979i	$-0.750956\pi$
$491$		−	7.53200e6i		−	1.40996i	0.709228	−	0.704979i	$-0.249044\pi$
$492$	597980.	−	4.05095e6i	0.111372	−	0.754474i
$493$	5.05442e6	−	5.05442e6i	0.936600	−	0.936600i
$494$	268290.	+	811165.i	0.0494638	+	0.149552i
$495$	−1.78025e6	−	1.18223e6i	−0.326564	−	0.216864i
$496$	−1.24925e6	−	377030.i	−0.228005	−	0.0688131i
$497$	3.87777e6	+	3.87777e6i	0.704192	+	0.704192i
$498$	−3.65093e6	−	1.83611e6i	−0.659675	−	0.331761i
$499$	−2.13951e6			−0.384648			−0.192324	−	0.981332i	$-0.561602\pi$
$499$	−2.13951e6			−0.384648			−0.192324	+	0.981332i	$0.561602\pi$
$500$	5.03119e6	−	2.43663e6i	0.900006	−	0.435877i
$501$	−2.01896e6			−0.359362
$502$	−1.87590e6	−	943420.i	−0.332239	−	0.167088i
$503$	3.44136e6	+	3.44136e6i	0.606471	+	0.606471i	0.942022	−	0.335551i	$-0.108923\pi$
$503$	3.44136e6	+	3.44136e6i	0.606471	+	0.606471i	−0.335551	+	0.942022i	$0.608923\pi$
$504$	−1.17164e6	−	823305.i	−0.205455	−	0.144373i
$505$	7.23943e6	+	4.80755e6i	1.26321	+	0.838872i
$506$	2.53586e6	+	7.66707e6i	0.440300	+	1.33123i
$507$	−2.12256e6	+	2.12256e6i	−0.366725	+	0.366725i
$508$	5.49311e6	+	810864.i	0.944407	+	0.139408i
$509$			8.34787e6i			1.42817i	0.700057	+	0.714087i	$0.253158\pi$
$509$			8.34787e6i			1.42817i	−0.700057	+	0.714087i	$0.746842\pi$
$510$	1.82673e6	+	3.20076e6i	0.310992	+	0.544913i
$511$			5.10795e6i			0.865356i
$512$	5.15173e6	−	2.94007e6i	0.868517	−	0.495659i
$513$	400636.	−	400636.i	0.0672134	−	0.0672134i
$514$	8.56643e6	−	2.83332e6i	1.43018	−	0.473029i
$515$	805637.	+	3.99094e6i	0.133851	+	0.663067i
$516$	1.55791e6	−	1.15713e6i	0.257583	−	0.191318i
$517$	9.09998e6	+	9.09998e6i	1.49732	+	1.49732i
$518$	1.82182e6	−	3.62251e6i	0.298319	−	0.593178i
$519$	−4.22297e6			−0.688176
$520$	−1.83194e6	+	714874.i	−0.297100	+	0.115937i
$521$	−3.08444e6			−0.497832			−0.248916	−	0.968525i	$-0.580074\pi$
$521$	−3.08444e6			−0.497832			−0.248916	+	0.968525i	$0.580074\pi$
$522$	1.13643e6	−	2.25969e6i	0.182544	−	0.362971i
$523$	−1.54735e6	−	1.54735e6i	−0.247362	−	0.247362i	0.572525	−	0.819887i	$-0.305964\pi$
$523$	−1.54735e6	−	1.54735e6i	−0.247362	−	0.247362i	−0.819887	+	0.572525i	$0.805964\pi$
$524$	−5.20566e6	+	3.86648e6i	−0.828224	+	0.615159i
$525$	−1.06553e6	−	2.53166e6i	−0.168721	−	0.400873i
$526$	194866.	−	64451.3i	0.0307094	−	0.0101571i
$527$	1.16681e6	−	1.16681e6i	0.183009	−	0.183009i
$528$	−2.05578e6	−	3.83308e6i	−0.320917	−	0.598360i
$529$			2.71295e6i			0.421505i
$530$	2.76441e6	−	1.01148e7i	0.427476	−	1.56411i
$531$			1.01278e6i			0.155876i
$532$	−2.40288e6	−	354701.i	−0.368090	−	0.0543355i
$533$	−1.95376e6	+	1.95376e6i	−0.297888	+	0.297888i
$534$	445418.	+	1.34670e6i	0.0675950	+	0.204371i
$535$	1.18546e7	−	2.39304e6i	1.79061	−	0.361464i
$536$	−4.54625e6	+	6.46972e6i	−0.683505	+	0.972688i
$537$	2.41234e6	+	2.41234e6i	0.360996	+	0.360996i
$538$	8.21831e6	+	4.13311e6i	1.22413	+	0.615633i
$539$	−3.43070e6			−0.508641
$540$	969355.	+	872332.i	0.143053	+	0.128735i
$541$	−3.08532e6			−0.453218			−0.226609	−	0.973986i	$-0.572764\pi$
$541$	−3.08532e6			−0.453218			−0.226609	+	0.973986i	$0.572764\pi$
$542$	−3.96739e6	−	1.99526e6i	−0.580105	−	0.291744i
$543$	204107.	+	204107.i	0.0297070	+	0.0297070i
$544$	197311.	+	7.49826e6i	0.0285861	+	1.08633i
$545$	−6.12378e6	+	9.22147e6i	−0.883137	+	1.32987i
$546$	303415.	+	917363.i	0.0435567	+	0.131692i
$547$	−4.61986e6	+	4.61986e6i	−0.660177	+	0.660177i	−0.955422	−	0.295245i	$-0.904599\pi$
$547$	−4.61986e6	+	4.61986e6i	−0.660177	+	0.660177i	0.295245	+	0.955422i	$0.404599\pi$
$548$	166743.	−	1.12958e6i	0.0237190	−	0.160682i
$549$			1.63052e6i			0.230885i
$550$	563551.	−	8.32407e6i	0.0794377	−	1.17335i
$551$		−	4.29030e6i		−	0.602017i
$552$	−847622.	−	4.85445e6i	−0.118401	−	0.678097i
$553$	−987289.	+	987289.i	−0.137288	+	0.137288i
$554$	−5.41826e6	+	1.79207e6i	−0.750042	+	0.248074i
$555$	−2.04280e6	+	3.07614e6i	−0.281509	+	0.423910i
$556$	1.16859e6	+	1.57334e6i	0.160315	+	0.215841i
$557$	3.81379e6	+	3.81379e6i	0.520857	+	0.520857i	0.917830	−	0.396973i	$-0.129939\pi$
$557$	3.81379e6	+	3.81379e6i	0.520857	+	0.520857i	−0.396973	+	0.917830i	$0.629939\pi$
$558$	262343.	−	521645.i	0.0356685	−	0.0709234i
$559$	−1.30945e6			−0.177239
$560$	524307.	−	5.56587e6i	0.0706506	−	0.750003i
$561$	5.50025e6			0.737862
$562$	−519998.	+	1.03397e6i	−0.0694482	+	0.138091i
$563$	4.95676e6	+	4.95676e6i	0.659063	+	0.659063i	0.955158	−	0.296095i	$-0.0956846\pi$
$563$	4.95676e6	+	4.95676e6i	0.659063	+	0.659063i	−0.296095	+	0.955158i	$0.595685\pi$
$564$	−4.68257e6	−	6.30441e6i	−0.619850	−	0.834539i
$565$	7.42011e6	−	1.49787e6i	0.977888	−	0.197403i
$566$	−5.79329e6	+	1.91611e6i	−0.760123	+	0.251408i
$567$	453087.	−	453087.i	0.0591867	−	0.0591867i
$568$	−1.74838e6	−	1.00132e7i	−0.227387	−	1.30228i
$569$			4.58186e6i			0.593282i	0.954989	+	0.296641i	$0.0958665\pi$
$569$			4.58186e6i			0.593282i	−0.954989	+	0.296641i	$0.904134\pi$
$570$	2.13372e6	+	583151.i	0.275074	+	0.0751786i
$571$			4.18507e6i			0.537170i	0.963256	+	0.268585i	$0.0865561\pi$
$571$			4.18507e6i			0.537170i	−0.963256	+	0.268585i	$0.913444\pi$
$572$	−428590.	+	2.90344e6i	−0.0547712	+	0.371042i
$573$	−3.94223e6	+	3.94223e6i	−0.501598	+	0.501598i
$574$	−2.46661e6	−	7.45769e6i	−0.312479	−	0.944767i
$575$	3.56763e6	−	8.75332e6i	0.449998	−	1.10409i
$576$	899465.	+	2.49715e6i	0.112961	+	0.313610i
$577$	−4.60755e6	−	4.60755e6i	−0.576144	−	0.576144i	0.357695	−	0.933839i	$-0.383563\pi$
$577$	−4.60755e6	−	4.60755e6i	−0.576144	−	0.576144i	−0.933839	+	0.357695i	$0.883563\pi$
$578$	−1.29834e6	−	652957.i	−0.161648	−	0.0812952i
$579$	4.49497e6			0.557225
$580$	9.86106e6	−	519499.i	1.21718	−	0.0641231i
$581$	−7.83926e6			−0.963462
$582$	6.71990e6	+	3.37954e6i	0.822347	+	0.413571i
$583$	−1.10659e7	−	1.10659e7i	−1.34840	−	1.34840i
$584$	5.44339e6	−	7.74643e6i	0.660446	−	0.939873i
$585$	−174117.	−	862535.i	−0.0210354	−	0.104205i
$586$	−2.43953e6	−	7.37582e6i	−0.293469	−	0.887291i
$587$	−6.72437e6	+	6.72437e6i	−0.805483	+	0.805483i	−0.983947	−	0.178463i	$-0.942887\pi$
$587$	−6.72437e6	+	6.72437e6i	−0.805483	+	0.805483i	0.178463	+	0.983947i	$0.442887\pi$
$588$	2.07105e6	+	305718.i	0.247029	+	0.0364651i
$589$		−	990409.i		−	0.117632i
$590$	−3.43405e6	+	1.95987e6i	−0.406140	+	0.231792i
$591$		−	7.87120e6i		−	0.926984i
$592$	−6.62326e6	+	3.55224e6i	−0.776725	+	0.416579i
$593$	9.64858e6	−	9.64858e6i	1.12675	−	1.12675i	0.136045	−	0.990703i	$-0.456561\pi$
$593$	9.64858e6	−	9.64858e6i	1.12675	−	1.12675i	0.990703	−	0.136045i	$-0.0434390\pi$
$594$	1.84784e6	−	611166.i	0.214881	−	0.0710711i
$595$	5.88919e6	+	3.91089e6i	0.681967	+	0.452880i
$596$	4.17314e6	−	3.09958e6i	0.481224	−	0.357427i
$597$	−372467.	−	372467.i	−0.0427713	−	0.0427713i
$598$	−1.49397e6	+	2.97061e6i	−0.170839	+	0.339698i
$599$	−1.04667e7			−1.19191			−0.595954	−	0.803018i	$-0.703226\pi$
$599$	−1.04667e7			−1.19191			−0.595954	+	0.803018i	$0.703226\pi$
$600$	−1.08198e6	+	4.97487e6i	−0.122699	+	0.564162i
$601$	−1.49944e7			−1.69333			−0.846665	−	0.532126i	$-0.821393\pi$
$601$	−1.49944e7			−1.69333			−0.846665	+	0.532126i	$0.821393\pi$
$602$	1.67256e6	−	3.32574e6i	0.188101	−	0.374021i
$603$	−2.50193e6	−	2.50193e6i	−0.280208	−	0.280208i
$604$	7.75318e6	−	5.75864e6i	0.864744	−	0.642284i
$605$	−2.87299e6	−	1.90789e6i	−0.319113	−	0.211916i
$606$	−7.51426e6	+	2.48532e6i	−0.831199	+	0.274916i
$607$	4.60259e6	−	4.60259e6i	0.507027	−	0.507027i	−0.406586	−	0.913613i	$-0.633281\pi$
$607$	4.60259e6	−	4.60259e6i	0.507027	−	0.507027i	0.913613	+	0.406586i	$0.133281\pi$
$608$	3.26608e6	+	3.09860e6i	0.358318	+	0.339943i
$609$		−	4.85199e6i		−	0.530123i
$610$	−5.52862e6	+	3.15528e6i	−0.601578	+	0.343332i
$611$			5.29897e6i			0.574233i
$612$	−3.32040e6	−	490140.i	−0.358353	−	0.0528983i
$613$	−5.64782e6	+	5.64782e6i	−0.607058	+	0.607058i	−0.942176	−	0.335118i	$-0.891224\pi$
$613$	−5.64782e6	+	5.64782e6i	−0.607058	+	0.607058i	0.335118	+	0.942176i	$0.391224\pi$
$614$	1.59822e6	+	4.83216e6i	0.171086	+	0.517273i
$615$	1.41548e6	+	7.01197e6i	0.150909	+	0.747570i
$616$	−6.82671e6	−	4.79711e6i	−0.724870	−	0.509364i
$617$	5.62216e6	+	5.62216e6i	0.594552	+	0.594552i	0.938858	−	0.344305i	$-0.111886\pi$
$617$	5.62216e6	+	5.62216e6i	0.594552	+	0.594552i	−0.344305	+	0.938858i	$0.611886\pi$
$618$	−3.31267e6	−	1.66599e6i	−0.348905	−	0.175470i
$619$	−1.70562e7			−1.78919			−0.894593	−	0.446882i	$-0.852535\pi$
$619$	−1.70562e7			−1.78919			−0.894593	+	0.446882i	$0.852535\pi$
$620$	2.27641e6	−	119925.i	0.237833	−	0.0125295i
$621$	2.20506e6			0.229452
$622$	−8.60289e6	−	4.32653e6i	−0.891596	−	0.448398i
$623$	1.92402e6	+	1.92402e6i	0.198604	+	0.198604i
$624$	517464.	−	1.71456e6i	0.0532009	−	0.176275i
$625$	−6.82645e6	+	6.98334e6i	−0.699029	+	0.715094i
$626$	−137934.	−	417037.i	−0.0140681	−	0.0425343i
$627$	2.33436e6	−	2.33436e6i	0.237137	−	0.237137i
$628$	−1.97625e6	+	1.33879e7i	−0.199960	+	1.35461i
$629$		−	9.50400e6i		−	0.957811i
$630$	2.41307e6	+	659498.i	0.242224	+	0.0662006i
$631$			1.83840e7i			1.83808i	0.394159	+	0.919042i	$0.371036\pi$
$631$			1.83840e7i			1.83808i	−0.394159	+	0.919042i	$0.628964\pi$
$632$	2.54939e6	−	445142.i	0.253889	−	0.0443308i
$633$	−3.64188e6	+	3.64188e6i	−0.361257	+	0.361257i
$634$	−4.21521e6	+	1.39417e6i	−0.416482	+	0.137750i
$635$	−9.50826e6	+	1.91940e6i	−0.935765	+	0.188899i
$636$	5.69420e6	+	7.66642e6i	0.558200	+	0.751536i
$637$	−998860.	−	998860.i	−0.0975340	−	0.0975340i
$638$	6.62158e6	−	1.31664e7i	0.644036	−	1.28060i
$639$	4.54836e6			0.440659
$640$	−6.72651e6	+	7.88214e6i	−0.649143	+	0.760667i
$641$	7.16035e6			0.688318			0.344159	−	0.938911i	$-0.388164\pi$
$641$	7.16035e6			0.688318			0.344159	+	0.938911i	$0.388164\pi$
$642$	−4.94862e6	+	9.83985e6i	−0.473856	+	0.942217i
$643$	−3.04044e6	−	3.04044e6i	−0.290007	−	0.290007i	0.547076	−	0.837083i	$-0.315741\pi$
$643$	−3.04044e6	−	3.04044e6i	−0.290007	−	0.290007i	−0.837083	+	0.547076i	$0.815741\pi$
$644$	−5.63651e6	−	7.58876e6i	−0.535545	−	0.721035i
$645$	−1.87544e6	+	2.82412e6i	−0.177502	+	0.267291i
$646$	−5.40512e6	+	1.78773e6i	−0.509594	+	0.168546i
$647$	1.95944e6	−	1.95944e6i	0.184023	−	0.184023i	−0.609083	−	0.793106i	$-0.708462\pi$
$647$	1.95944e6	−	1.95944e6i	0.184023	−	0.184023i	0.793106	+	0.609083i	$0.208462\pi$
$648$	−1.16997e6	+	204285.i	−0.109455	+	0.0191117i
$649$			5.90113e6i			0.549951i
$650$	2.58766e6	−	2.25950e6i	0.240228	−	0.209763i
$651$		−	1.12007e6i		−	0.103584i
$652$	−869508.	+	5.89039e6i	−0.0801041	+	0.542656i
$653$	6.77033e6	−	6.77033e6i	0.621336	−	0.621336i	−0.324537	−	0.945873i	$-0.605208\pi$
$653$	6.77033e6	−	6.77033e6i	0.621336	−	0.621336i	0.945873	+	0.324537i	$0.105208\pi$
$654$	−3.16576e6	−	9.57154e6i	−0.289423	−	0.875059i
$655$	6.26669e6	−	9.43667e6i	0.570736	−	0.859440i
$656$	−4.20672e6	+	1.39385e7i	−0.381666	+	1.26461i
$657$	2.99564e6	+	2.99564e6i	0.270755	+	0.270755i
$658$	−1.34583e7	−	6.76840e6i	−1.21179	−	0.609426i
$659$	−7.90626e6			−0.709182			−0.354591	−	0.935022i	$-0.615380\pi$
$659$	−7.90626e6			−0.709182			−0.354591	+	0.935022i	$0.615380\pi$
$660$	5.64809e6	+	5.08277e6i	0.504710	+	0.454193i
$661$	1.14433e7			1.01870			0.509351	−	0.860559i	$-0.329885\pi$
$661$	1.14433e7			1.01870			0.509351	+	0.860559i	$0.329885\pi$
$662$	1.79065e7	+	9.00544e6i	1.58805	+	0.798656i
$663$	1.60141e6	+	1.60141e6i	0.141488	+	0.141488i
$664$	1.18886e7	+	8.35406e6i	1.04643	+	0.735322i
$665$	4.15925e6	−	839614.i	0.364722	−	0.0736250i
$666$	−1.05605e6	−	3.19292e6i	−0.0922566	−	0.278934i
$667$	1.18067e7	−	1.18067e7i	1.02758	−	1.02758i
$668$	7.10155e6	+	1.04829e6i	0.615761	+	0.0908954i
$669$		−	1.42550e6i		−	0.123141i
$670$	3.64172e6	−	1.33248e7i	0.313415	−	1.14677i
$671$			9.50049e6i			0.814591i
$672$	3.69368e6	+	3.50427e6i	0.315527	+	0.299347i
$673$	4.01002e6	−	4.01002e6i	0.341279	−	0.341279i	−0.515569	−	0.856848i	$-0.672419\pi$
$673$	4.01002e6	−	4.01002e6i	0.341279	−	0.341279i	0.856848	+	0.515569i	$0.172419\pi$
$674$	−1.33442e7	+	4.41356e6i	−1.13147	+	0.374230i
$675$	−2.10963e6	−	859832.i	−0.178216	−	0.0726364i
$676$	8.56808e6	−	6.36390e6i	0.721136	−	0.535620i
$677$	−8.01600e6	−	8.01600e6i	−0.672181	−	0.672181i	0.286038	−	0.958218i	$-0.407662\pi$
$677$	−8.01600e6	−	8.01600e6i	−0.672181	−	0.672181i	−0.958218	+	0.286038i	$0.907662\pi$
$678$	−3.09748e6	+	6.15905e6i	−0.258782	+	0.514564i
$679$	1.44289e7			1.20105
$680$	−4.76350e6	−	1.22070e7i	−0.395051	−	1.01236i
$681$	9.41311e6			0.777795
$682$	1.52858e6	−	3.03944e6i	0.125843	−	0.250226i
$683$	7.03576e6	+	7.03576e6i	0.577111	+	0.577111i	0.934106	−	0.356996i	$-0.116199\pi$
$683$	7.03576e6	+	7.03576e6i	0.577111	+	0.577111i	−0.356996	+	0.934106i	$0.616199\pi$
$684$	−1.61723e6	+	1.20119e6i	−0.132170	+	0.0981684i
$685$	394697.	+	1.95524e6i	0.0321394	+	0.159211i
$686$	1.26283e7	−	4.17677e6i	1.02455	−	0.338868i
$687$	3.46487e6	−	3.46487e6i	0.280088	−	0.280088i
$688$	−6.08065e6	+	3.26122e6i	−0.489755	+	0.262669i
$689$		−	6.44377e6i		−	0.517120i
$690$	4.26709e6	+	7.47671e6i	0.341200	+	0.597844i
$691$			1.75155e6i			0.139549i	0.997563	+	0.0697745i	$0.0222280\pi$
$691$			1.75155e6i			0.139549i	−0.997563	+	0.0697745i	$0.977772\pi$
$692$	1.48540e7	+	2.19268e6i	1.17918	+	0.174064i
$693$	2.63998e6	−	2.63998e6i	0.208818	−	0.208818i
$694$	−807470.	−	2.44135e6i	−0.0636397	−	0.192412i
$695$	−2.85210e6	−	1.89402e6i	−0.223976	−	0.148738i
$696$	−5.17062e6	+	7.35824e6i	−0.404594	+	0.575773i
$697$	−1.30187e7	−	1.30187e7i	−1.01504	−	1.01504i
$698$	−7.92611e6	−	3.98616e6i	−0.615774	−	0.309682i
$699$	5.69273e6			0.440684
$700$	2.43345e6	+	9.45820e6i	0.187705	+	0.729564i
$701$	−4.80355e6			−0.369205			−0.184602	−	0.982813i	$-0.559100\pi$
$701$	−4.80355e6			−0.369205			−0.184602	+	0.982813i	$0.559100\pi$
$702$	715946.	+	360060.i	0.0548324	+	0.0275761i
$703$	−4.03359e6	−	4.03359e6i	−0.307825	−	0.307825i
$704$	5.24087e6	+	1.45500e7i	0.398539	+	1.10645i
$705$	1.14284e7	+	7.58938e6i	0.865993	+	0.575087i
$706$	−4.11784e6	−	1.24501e7i	−0.310927	−	0.940075i
$707$	−1.07355e7	+	1.07355e7i	−0.807746	+	0.807746i
$708$	525864.	−	3.56241e6i	0.0394267	−	0.267092i
$709$		−	1.19995e7i		−	0.896492i	−0.893910	−	0.448246i	$-0.852049\pi$
$709$		−	1.19995e7i		−	0.896492i	0.893910	−	0.448246i	$-0.147951\pi$
$710$	8.80169e6	+	1.54221e7i	0.655270	+	1.14815i
$711$			1.15802e6i			0.0859100i
$712$	−867487.	−	4.96822e6i	−0.0641303	−	0.367283i
$713$	2.72556e6	−	2.72556e6i	0.200786	−	0.200786i
$714$	−6.11276e6	+	2.02178e6i	−0.448737	+	0.148418i
$715$	−1.01452e6	−	5.02569e6i	−0.0742154	−	0.367646i
$716$	−7.23271e6	−	9.73780e6i	−0.527252	−	0.709869i
$717$	−9.10840e6	−	9.10840e6i	−0.661674	−	0.661674i
$718$	−8.90087e6	+	1.76985e7i	−0.644349	+	1.28123i
$719$	1.19772e7			0.864040			0.432020	−	0.901864i	$-0.357801\pi$
$719$	1.19772e7			0.864040			0.432020	+	0.901864i	$0.357801\pi$
$720$	−2.95671e6	−	3.57169e6i	−0.212558	−	0.256769i
$721$	−7.11296e6			−0.509580
$722$	4.75800e6	−	9.46084e6i	0.339689	−	0.675440i
$723$	3.61992e6	+	3.61992e6i	0.257545	+	0.257545i
$724$	−611957.	−	823913.i	−0.0433885	−	0.0584164i
$725$	−1.58996e7	+	6.69188e6i	−1.12342	+	0.472828i
$726$	2.98205e6	−	986304.i	0.209978	−	0.0694495i
$727$	1.54863e7	−	1.54863e7i	1.08670	−	1.08670i	0.0908375	−	0.995866i	$-0.471046\pi$
$727$	1.54863e7	−	1.54863e7i	1.08670	−	1.08670i	0.995866	−	0.0908375i	$-0.0289544\pi$
$728$	−590925.	−	3.38431e6i	−0.0413242	−	0.236669i
$729$		−	531441.i		−	0.0370370i
$730$	−4.36036e6	+	1.59543e7i	−0.302841	+	1.10808i
$731$		−	8.72538e6i		−	0.603936i
$732$	846611.	−	5.73527e6i	0.0583991	−	0.395618i
$733$	1.22893e7	−	1.22893e7i	0.844824	−	0.844824i	−0.144658	−	0.989482i	$-0.546208\pi$
$733$	1.22893e7	−	1.22893e7i	0.844824	−	0.844824i	0.989482	+	0.144658i	$0.0462082\pi$
$734$	879411.	+	2.65886e6i	0.0602493	+	0.182161i
$735$	−3.58487e6	+	723666.i	−0.244769	+	0.0494105i
$736$	460903.	+	1.75153e7i	0.0313628	+	1.19186i
$737$	−1.45778e7	−	1.45778e7i	−0.988609	−	0.988609i
$738$	−5.82027e6	−	2.92710e6i	−0.393371	−	0.197832i
$739$	2.88388e7			1.94252			0.971262	−	0.238012i	$-0.0764958\pi$
$739$	2.88388e7			1.94252			0.971262	+	0.238012i	$0.0764958\pi$
$740$	8.78262e6	−	9.75946e6i	0.589583	−	0.655158i
$741$	1.35931e6			0.0909439
$742$	1.63659e7	+	8.23065e6i	1.09126	+	0.548813i
$743$	−1.12409e6	−	1.12409e6i	−0.0747011	−	0.0747011i	0.668769	−	0.743470i	$-0.266821\pi$
$743$	−1.12409e6	−	1.12409e6i	−0.0747011	−	0.0747011i	−0.743470	+	0.668769i	$0.766821\pi$
$744$	−1.19363e6	+	1.69864e6i	−0.0790564	+	0.112504i
$745$	−5.02372e6	+	7.56494e6i	−0.331615	+	0.499361i
$746$	−3.64554e6	−	1.10222e7i	−0.239837	−	0.725136i
$747$	−4.59746e6	+	4.59746e6i	−0.301451	+	0.301451i
$748$	−1.93468e7	−	2.85587e6i	−1.26431	−	0.186631i
$749$			2.11281e7i			1.37612i
$750$	−1.16699e6	−	8.81701e6i	−0.0757552	−	0.572359i
$751$		−	1.79452e7i		−	1.16104i	−0.814246	−	0.580521i	$-0.802849\pi$
$751$		−	1.79452e7i		−	1.16104i	0.814246	−	0.580521i	$-0.197151\pi$
$752$	1.31972e7	+	2.46067e7i	0.851017	+	1.58675i
$753$	−2.36224e6	+	2.36224e6i	−0.151823	+	0.151823i
$754$	5.76133e6	−	1.90554e6i	0.369058	−	0.122065i
$755$	−9.33345e6	+	1.40547e7i	−0.595902	+	0.897336i
$756$	−1.82896e6	+	1.35845e6i	−0.116386	+	0.0864450i
$757$	−1.53680e6	−	1.53680e6i	−0.0974714	−	0.0974714i	0.656690	−	0.754161i	$-0.271956\pi$
$757$	−1.53680e6	−	1.53680e6i	−0.0974714	−	0.0974714i	−0.754161	+	0.656690i	$0.771956\pi$
$758$	−3.73656e6	+	7.42979e6i	−0.236210	+	0.469682i
$759$	1.28481e7			0.809535
$760$	−7.20244e6	−	3.15908e6i	−0.452320	−	0.198393i
$761$	2.96990e7			1.85900			0.929502	−	0.368816i	$-0.120237\pi$
$761$	2.96990e7			1.85900			0.929502	+	0.368816i	$0.120237\pi$
$762$	3.96917e6	−	7.89231e6i	0.247635	−	0.492399i
$763$	−1.36747e7	−	1.36747e7i	−0.850369	−	0.850369i
$764$	1.59135e7	−	1.18196e7i	0.986350	−	0.732607i
$765$	5.74742e6	−	1.16021e6i	0.355074	−	0.0716776i
$766$	4.68745e6	−	1.55036e6i	0.288645	−	0.0954685i
$767$	−1.71813e6	+	1.71813e6i	−0.105455	+	0.105455i
$768$	−1.86723e6	−	9.25062e6i	−0.114234	−	0.565936i
$769$			1.15427e7i			0.703866i	0.936025	+	0.351933i	$0.114475\pi$
$769$			1.15427e7i			0.703866i	−0.936025	+	0.351933i	$0.885525\pi$
$770$	1.40601e7	+	3.84266e6i	0.854596	+	0.233564i
$771$		−	1.43552e7i		−	0.869710i
$772$	−1.58108e7	−	2.33391e6i	−0.954796	−	0.140942i
$773$	−3.27124e6	+	3.27124e6i	−0.196908	+	0.196908i	−0.798673	−	0.601765i	$-0.794464\pi$
$773$	−3.27124e6	+	3.27124e6i	−0.196908	+	0.196908i	0.601765	+	0.798673i	$0.294464\pi$
$774$	−969530.	−	2.93134e6i	−0.0581713	−	0.175879i
$775$	−3.67040e6	+	1.54481e6i	−0.219512	+	0.0923891i
$776$	−2.18821e7	−	1.53765e7i	−1.30447	−	0.916648i
$777$	−4.56168e6	−	4.56168e6i	−0.271064	−	0.271064i
$778$	7.28661e6	+	3.66455e6i	0.431595	+	0.217056i
$779$	−1.10505e7			−0.652437
$780$	164595.	+	3.12432e6i	0.00968679	+	0.183873i
$781$	2.65017e7			1.55470
$782$	−1.97944e7	−	9.95491e6i	−1.15751	−	0.582131i
$783$	−2.84553e6	−	2.84553e6i	−0.165866	−	0.165866i
$784$	−7.12607e6	−	2.15069e6i	−0.414057	−	0.124965i
$785$	−4.67799e6	−	2.31737e7i	−0.270948	−	1.34221i
$786$	3.23964e6	+	9.79491e6i	0.187042	+	0.565515i
$787$	−1.72301e7	+	1.72301e7i	−0.991636	+	0.991636i	−0.999965	−	0.00832964i	$-0.997349\pi$
$787$	−1.72301e7	+	1.72301e7i	−0.991636	+	0.991636i	0.00832964	+	0.999965i	$0.497349\pi$
$788$	−4.08693e6	+	2.76865e7i	−0.234467	+	1.58837i
$789$		−	326548.i		−	0.0186747i
$790$	−3.92651e6	+	2.24093e6i	−0.223841	+	0.127750i
$791$			1.32247e7i			0.751526i
$792$	−6.81698e6	+	1.19029e6i	−0.386171	+	0.0674282i
$793$	−2.76610e6	+	2.76610e6i	−0.156201	+	0.156201i
$794$	−9.33014e6	+	3.08591e6i	−0.525215	+	0.173713i
$795$	−1.38975e7	−	9.22900e6i	−0.779862	−	0.517889i
$796$	1.11674e6	+	1.50353e6i	0.0624695	+	0.0841062i
$797$	−1.37249e7	−	1.37249e7i	−0.765358	−	0.765358i	0.211928	−	0.977285i	$-0.432026\pi$
$797$	−1.37249e7	−	1.37249e7i	−0.765358	−	0.765358i	−0.977285	+	0.211928i	$0.932026\pi$
$798$	−1.73626e6	+	3.45238e6i	−0.0965176	+	0.191916i
$799$	−3.53092e7			−1.95668
$800$	6.38889e6	−	1.69370e7i	0.352940	−	0.935646i
$801$	2.25674e6			0.124280
$802$	−5.52932e6	+	1.09945e7i	−0.303554	+	0.603589i
$803$	1.74546e7	+	1.74546e7i	0.955256	+	0.955256i
$804$	7.50131e6	+	1.00994e7i	0.409258	+	0.551007i
$805$	1.37567e7	+	9.13551e6i	0.748210	+	0.496870i
$806$	1.32999e6	−	439891.i	0.0721127	−	0.0238511i
$807$	1.03490e7	−	1.03490e7i	0.559388	−	0.559388i
$808$	2.77214e7	−	4.84036e6i	1.49378	−	0.260825i
$809$			2.49085e7i			1.33806i	0.743235	+	0.669031i	$0.233291\pi$
$809$			2.49085e7i			1.33806i	−0.743235	+	0.669031i	$0.766709\pi$
$810$	1.80196e6	−	1.02841e6i	0.0965010	−	0.0550749i
$811$			2.76389e7i			1.47560i	0.675019	+	0.737801i	$0.264136\pi$
$811$			2.76389e7i			1.47560i	−0.675019	+	0.737801i	$0.735864\pi$
$812$	−2.51928e6	+	1.70666e7i	−0.134087	+	0.908356i
$813$	−4.99597e6	+	4.99597e6i	−0.265090	+	0.265090i
$814$	−6.15321e6	−	1.86040e7i	−0.325492	−	0.984113i
$815$	−2.05821e6	−	1.01959e7i	−0.108542	−	0.537691i
$816$	1.14248e7	+	3.44807e6i	0.600653	+	0.181281i
$817$	−3.70314e6	−	3.70314e6i	−0.194095	−	0.194095i
$818$	2.42069e7	+	1.21740e7i	1.26490	+	0.636138i
$819$	1.53728e6			0.0800833
$820$	−1.33807e6	−	2.53991e7i	−0.0694936	−	1.31912i
$821$	−1.01822e7			−0.527210			−0.263605	−	0.964631i	$-0.584912\pi$
$821$	−1.01822e7			−0.527210			−0.263605	+	0.964631i	$0.584912\pi$
$822$	−1.62294e6	−	816204.i	−0.0837768	−	0.0421327i
$823$	2.36956e7	+	2.36956e7i	1.21946	+	1.21946i	0.967820	+	0.251642i	$0.0809706\pi$
$823$	2.36956e7	+	2.36956e7i	1.21946	+	1.21946i	0.251642	+	0.967820i	$0.419029\pi$
$824$	1.07871e7	+	7.58006e6i	0.553461	+	0.388915i
$825$	−1.22921e7	−	5.00994e6i	−0.628768	−	0.256270i
$826$	−2.16913e6	−	6.55829e6i	−0.110621	−	0.334457i
$827$	−1.42104e7	+	1.42104e7i	−0.722510	+	0.722510i	−0.969116	−	0.246606i	$-0.920685\pi$
$827$	−1.42104e7	+	1.42104e7i	−0.722510	+	0.722510i	0.246606	+	0.969116i	$0.420685\pi$
$828$	−7.75618e6	−	1.14493e6i	−0.393162	−	0.0580366i
$829$			2.98645e6i			0.150928i	0.997149	+	0.0754639i	$0.0240438\pi$
$829$			2.98645e6i			0.150928i	−0.997149	+	0.0754639i	$0.975956\pi$
$830$	−2.44853e7	−	6.69191e6i	−1.23370	−	0.337175i
$831$			9.07967e6i			0.456108i
$832$	−2.71039e6	+	5.76218e6i	−0.135745	+	0.288588i
$833$	6.65581e6	−	6.65581e6i	0.332344	−	0.332344i
$834$	2.96037e6	−	979133.i	0.147377	−	0.0487446i
$835$	−1.22924e7	+	2.48142e6i	−0.610126	+	0.123164i
$836$	−9.42304e6	+	6.99891e6i	−0.466310	+	0.346350i
$837$	−656886.	−	656886.i	−0.0324098	−	0.0324098i
$838$	−1.17829e7	+	2.34291e7i	−0.579616	+	1.15251i
$839$	1.76991e7			0.868055			0.434027	−	0.900900i	$-0.357092\pi$
$839$	1.76991e7			0.868055			0.434027	+	0.900900i	$0.357092\pi$
$840$	−8.14539e6	−	3.57267e6i	−0.398303	−	0.174701i
$841$	−9.96085e6			−0.485631
$842$	2.56133e6	−	5.09296e6i	0.124504	−	0.247565i
$843$	1.30203e6	+	1.30203e6i	0.0631034	+	0.0631034i
$844$	1.47010e7	−	1.09191e7i	0.710382	−	0.527633i
$845$	−1.03144e7	+	1.55320e7i	−0.496940	+	0.748315i
$846$	−1.18623e7	+	3.92342e6i	−0.569827	+	0.188468i
$847$	4.26042e6	−	4.26042e6i	0.204053	−	0.204053i
$848$	−1.60484e7	−	2.99227e7i	−0.766376	−	1.42893i
$849$			9.70812e6i			0.462239i
$850$	1.50559e7	+	1.72426e7i	0.714761	+	0.818569i
$851$		−	2.22006e7i		−	1.05085i
$852$	−1.59986e7	−	2.36163e6i	−0.755062	−	0.111458i
$853$	9.00605e6	−	9.00605e6i	0.423801	−	0.423801i	−0.462709	−	0.886510i	$-0.653123\pi$
$853$	9.00605e6	−	9.00605e6i	0.423801	−	0.423801i	0.886510	+	0.462709i	$0.153123\pi$
$854$	−3.49218e6	−	1.05585e7i	−0.163852	−	0.495401i
$855$	1.94686e6	−	2.93167e6i	0.0910792	−	0.137151i
$856$	2.25156e7	−	3.20416e7i	1.05026	−	1.49462i
$857$	1.14865e7	+	1.14865e7i	0.534240	+	0.534240i	0.921831	−	0.387592i	$-0.126693\pi$
$857$	1.14865e7	+	1.14865e7i	0.534240	+	0.534240i	−0.387592	+	0.921831i	$0.626693\pi$
$858$	4.17156e6	+	2.09794e6i	0.193455	+	0.0972916i
$859$	−1.94363e7			−0.898734			−0.449367	−	0.893347i	$-0.648350\pi$
$859$	−1.94363e7			−0.898734			−0.449367	+	0.893347i	$0.648350\pi$
$860$	8.06310e6	−	8.95991e6i	0.371754	−	0.413102i
$861$	−1.24973e7			−0.574522
$862$	2.38988e7	+	1.20191e7i	1.09549	+	0.550939i
$863$	−2.09970e7	−	2.09970e7i	−0.959688	−	0.959688i	0.0395305	−	0.999218i	$-0.487414\pi$
$863$	−2.09970e7	−	2.09970e7i	−0.959688	−	0.959688i	−0.999218	+	0.0395305i	$0.987414\pi$
$864$	4.22136e6	−	111082.i	0.192383	−	0.00506243i
$865$	−2.57115e7	+	5.19029e6i	−1.16839	+	0.235858i
$866$	−5.02105e6	−	1.51809e7i	−0.227510	−	0.687866i
$867$	−1.63495e6	+	1.63495e6i	−0.0738680	+	0.0738680i
$868$	−581571.	+	3.93979e6i	−0.0262001	+	0.177490i
$869$			6.74740e6i			0.303101i
$870$	4.14185e6	−	1.51548e7i	0.185523	−	0.678816i
$871$		−	8.48876e6i		−	0.379139i
$872$	6.16556e6	+	3.53110e7i	0.274588	+	1.57260i
$873$	8.46209e6	−	8.46209e6i	0.375787	−	0.375787i
$874$	−1.26259e7	+	4.17598e6i	−0.559093	+	0.184918i
$875$	−9.59904e6	−	1.41043e7i	−0.423846	−	0.622777i
$876$	−8.98158e6	−	1.20924e7i	−0.395451	−	0.532418i
$877$	1.52653e7	+	1.52653e7i	0.670204	+	0.670204i	0.957763	−	0.287559i	$-0.0928438\pi$
$877$	1.52653e7	+	1.52653e7i	0.670204	+	0.670204i	−0.287559	+	0.957763i	$0.592844\pi$
$878$	7.67370e6	−	1.52584e7i	0.335945	−	0.667996i
$879$	−1.23601e7			−0.539571
$880$	−1.72277e7	−	2.08110e7i	−0.749930	−	0.905911i
$881$	−3.46641e6			−0.150466			−0.0752332	−	0.997166i	$-0.523970\pi$
$881$	−3.46641e6			−0.150466			−0.0752332	+	0.997166i	$0.523970\pi$
$882$	1.49648e6	−	2.97562e6i	0.0647740	−	0.128797i
$883$	2.99116e7	+	2.99116e7i	1.29103	+	1.29103i	0.934149	+	0.356884i	$0.116161\pi$
$883$	2.99116e7	+	2.99116e7i	1.29103	+	1.29103i	0.356884	+	0.934149i	$0.383839\pi$
$884$	−4.80138e6	−	6.46437e6i	−0.206650	−	0.278225i
$885$	1.24477e6	+	6.16632e6i	0.0534234	+	0.264648i
$886$	1.37508e7	−	4.54802e6i	0.588495	−	0.194643i
$887$	4.67199e6	−	4.67199e6i	0.199385	−	0.199385i	−0.600351	−	0.799736i	$-0.704973\pi$
$887$	4.67199e6	−	4.67199e6i	0.199385	−	0.199385i	0.799736	+	0.600351i	$0.204973\pi$
$888$	2.05674e6	+	1.17792e7i	0.0875278	+	0.501284i
$889$		−	1.69463e7i		−	0.719153i
$890$	4.36710e6	+	7.65194e6i	0.184807	+	0.323815i
$891$		−	3.09652e6i		−	0.130671i
$892$	−740157.	+	5.01411e6i	−0.0311467	+	0.211000i
$893$	−1.49856e7	+	1.49856e7i	−0.628847	+	0.628847i
$894$	−2.59707e6	−	7.85213e6i	−0.108677	−	0.328582i
$895$	1.76524e7	+	1.17226e7i	0.736625	+	0.489177i
$896$	−1.11728e7	−	1.42439e7i	−0.464934	−	0.592733i
$897$	3.74077e6	+	3.74077e6i	0.155232	+	0.155232i
$898$	2.65055e7	+	1.33300e7i	1.09684	+	0.551620i
$899$	−7.03441e6			−0.290288
$900$	6.97405e6	+	4.11978e6i	0.286998	+	0.169538i
$901$	4.29374e7			1.76207
$902$	−3.39127e7	−	1.70552e7i	−1.38786	−	0.697976i
$903$	−4.18796e6	−	4.18796e6i	−0.170916	−	0.170916i
$904$	1.40931e7	−	2.00558e7i	0.573570	−	0.816241i
$905$	1.49356e6	+	991844.i	0.0606181	+	0.0402552i
$906$	−4.82503e6	−	1.45883e7i	−0.195290	−	0.590451i
$907$	5.54805e6	−	5.54805e6i	0.223935	−	0.223935i	−0.586218	−	0.810153i	$-0.699384\pi$
$907$	5.54805e6	−	5.54805e6i	0.223935	−	0.223935i	0.810153	+	0.586218i	$0.199384\pi$
$908$	−3.31100e7	−	4.88753e6i	−1.33274	−	0.196732i
$909$			1.25921e7i			0.505460i
$910$	2.97483e6	+	5.21244e6i	0.119086	+	0.208659i
$911$		−	2.98034e7i		−	1.18979i	−0.803803	−	0.594895i	$-0.797194\pi$
$911$		−	2.98034e7i		−	1.18979i	0.803803	−	0.594895i	$-0.202806\pi$
$912$	6.31220e6	−	3.38541e6i	0.251301	−	0.134780i
$913$	−2.67878e7	+	2.67878e7i	−1.06356	+	1.06356i
$914$	2.39891e7	−	7.93430e6i	0.949834	−	0.314155i
$915$	2.00401e6	+	9.92743e6i	0.0791312	+	0.391998i
$916$	−1.39865e7	+	1.03884e7i	−0.550771	+	0.409082i
$917$	1.39939e7	+	1.39939e7i	0.549559	+	0.549559i
$918$	−2.39923e6	+	4.77064e6i	−0.0939646	+	0.186840i
$919$	2.99891e6			0.117132			0.0585658	−	0.998284i	$-0.481347\pi$
$919$	2.99891e6			0.117132			0.0585658	+	0.998284i	$0.481347\pi$
$920$	−1.11271e7	−	2.85145e7i	−0.433425	−	1.11070i
$921$	8.09750e6			0.314559
$922$	69764.2	−	138720.i	0.00270275	−	0.00537416i
$923$	7.71605e6	+	7.71605e6i	0.298120	+	0.298120i
$924$	−1.06567e7	+	7.91522e6i	−0.410623	+	0.304988i
$925$	−8.65678e6	+	2.12397e7i	−0.332661	+	0.816197i
$926$	1.50302e7	−	4.97118e6i	0.576018	−	0.190516i
$927$	−4.17151e6	+	4.17151e6i	−0.159439	+	0.159439i
$928$	2.20079e7	−	2.31975e7i	0.838898	−	0.884241i
$929$			3.05933e6i			0.116302i	0.998308	+	0.0581510i	$0.0185205\pi$
$929$			3.05933e6i			0.116302i	−0.998308	+	0.0581510i	$0.981480\pi$
$930$	956140.	−	3.49846e6i	0.0362505	−	0.132639i
$931$		−	5.64959e6i		−	0.213620i
$932$	−2.00238e7	−	2.95581e6i	−0.755105	−	0.111465i
$933$	−1.08333e7	+	1.08333e7i	−0.407432	+	0.407432i
$934$	1.11307e7	+	3.36532e7i	0.417499	+	1.26229i
$935$	3.34882e7	−	6.76014e6i	1.25274	−	0.252887i
$936$	−2.33134e6	−	1.63823e6i	−0.0869794	−	0.0611202i
$937$	4.55386e6	+	4.55386e6i	0.169446	+	0.169446i	0.786736	−	0.617290i	$-0.211769\pi$
$937$	4.55386e6	+	4.55386e6i	0.169446	+	0.169446i	−0.617290	+	0.786736i	$0.711769\pi$
$938$	2.15598e7	+	1.08427e7i	0.800086	+	0.402376i
$939$	−698852.			−0.0258655
$940$	−3.62582e7	−	3.26291e7i	−1.33840	−	1.20444i
$941$	−2.39452e6			−0.0881545			−0.0440773	−	0.999028i	$-0.514035\pi$
$941$	−2.39452e6			−0.0881545			−0.0440773	+	0.999028i	$0.514035\pi$
$942$	1.92353e7	+	9.67373e6i	0.706272	+	0.355195i
$943$	−3.04106e7	−	3.04106e7i	−1.11364	−	1.11364i
$944$	−3.69939e6	+	1.22575e7i	−0.135114	+	0.447685i
$945$	2.20174e6	−	3.31549e6i	0.0802024	−	0.120772i
$946$	−5.64911e6	−	1.70799e7i	−0.205235	−	0.620521i
$947$	1.03647e7	−	1.03647e7i	0.375561	−	0.375561i	−0.493937	−	0.869498i	$-0.664443\pi$
$947$	1.03647e7	−	1.03647e7i	0.375561	−	0.375561i	0.869498	+	0.493937i	$0.164443\pi$
$948$	601276.	−	4.07328e6i	0.0217297	−	0.147205i
$949$			1.01639e7i			0.366349i
$950$	1.37078e7	+	928040.i	0.492788	+	0.0333624i
$951$			7.06366e6i			0.253267i
$952$	2.25510e7	−	3.93757e6i	0.806444	−	0.140811i
$953$	2.18085e7	−	2.18085e7i	0.777847	−	0.777847i	−0.201617	−	0.979464i	$-0.564620\pi$
$953$	2.18085e7	−	2.18085e7i	0.777847	−	0.777847i	0.979464	+	0.201617i	$0.0646198\pi$
$954$	1.44250e7	−	4.77104e6i	0.513152	−	0.169723i
$955$	−1.91570e7	+	2.88474e7i	−0.679702	+	1.02353i
$956$	2.73089e7	+	3.67676e7i	0.966407	+	1.30113i
$957$	−1.65799e7	−	1.65799e7i	−0.585197	−	0.585197i
$958$	−8.29514e6	+	1.64941e7i	−0.292018	+	0.580651i
$959$	−3.48478e6			−0.122357
$960$	8.54554e6	+	1.40984e7i	0.299269	+	0.493732i
$961$	2.70053e7			0.943279
$962$	3.62508e6	−	7.20813e6i	0.126293	−	0.251122i
$963$	1.23909e7	+	1.23909e7i	0.430564	+	0.430564i
$964$	−1.08533e7	−	1.46124e7i	−0.376156	−	0.506441i
$965$	2.73676e7	−	5.52460e6i	0.946059	−	0.190978i
$966$	−1.42789e7	+	4.72271e6i	−0.492326	+	0.162835i
$967$	−41825.4	+	41825.4i	−0.00143838	+	0.00143838i	−0.707826	−	0.706387i	$-0.750324\pi$
$967$	−41825.4	+	41825.4i	−0.00143838	+	0.00143838i	0.706387	+	0.707826i	$0.250324\pi$
$968$	−1.10013e7	+	1.92091e6i	−0.377360	+	0.0658898i
$969$			9.05765e6i			0.309889i
$970$	4.50677e7	+	1.23171e7i	1.53793	+	0.420320i
$971$		−	2.28447e7i		−	0.777565i	−0.921330	−	0.388782i	$-0.872896\pi$
$971$		−	2.28447e7i		−	0.777565i	0.921330	−	0.388782i	$-0.127104\pi$
$972$	−275938.	+	1.86931e6i	−0.00936798	+	0.0634623i
$973$	4.22944e6	−	4.22944e6i	0.143219	−	0.143219i
$974$	5.64511e6	+	1.70678e7i	0.190667	+	0.576473i
$975$	−2.12022e6	−	5.03753e6i	−0.0714280	−	0.169710i
$976$	−5.95580e6	+	1.97339e7i	−0.200132	+	0.663114i
$977$	−1.13711e7	−	1.13711e7i	−0.381123	−	0.381123i	0.490384	−	0.871507i	$-0.336857\pi$
$977$	−1.13711e7	−	1.13711e7i	−0.381123	−	0.381123i	−0.871507	+	0.490384i	$0.836857\pi$
$978$	8.46311e6	+	4.25623e6i	0.282933	+	0.142291i
$979$	1.31492e7			0.438474
$980$	1.29853e7	−	684090.i	0.431904	−	0.0227535i
$981$	−1.60395e7			−0.532132
$982$	3.80647e7	+	1.91433e7i	1.25963	+	0.633489i
$983$	1.66636e7	+	1.66636e7i	0.550028	+	0.550028i	0.926449	−	0.376421i	$-0.122845\pi$
$983$	1.66636e7	+	1.66636e7i	0.550028	+	0.550028i	−0.376421	+	0.926449i	$0.622845\pi$
$984$	1.89526e7	+	1.33179e7i	0.623996	+	0.438480i
$985$	−9.67418e6	−	4.79237e7i	−0.317705	−	1.57384i
$986$	1.26974e7	+	3.83901e7i	0.415932	+	1.25755i
$987$	−1.69475e7	+	1.69475e7i	−0.553749	+	0.553749i
$988$	−4.78130e6	−	705790.i	−0.155831	−	0.0230029i
$989$		−	2.03818e7i		−	0.662600i
$990$	1.04994e7	−	5.99218e6i	0.340467	−	0.194311i
$991$			1.62483e6i			0.0525563i	0.999655	+	0.0262781i	$0.00836556\pi$
$991$			1.62483e6i			0.0525563i	−0.999655	+	0.0262781i	$0.991634\pi$
$992$	5.08049e6	−	5.35510e6i	0.163918	−	0.172778i
$993$	2.25489e7	−	2.25489e7i	0.725691	−	0.725691i
$994$	−2.94530e7	+	9.74148e6i	−0.945503	+	0.312722i
$995$	−2.72555e6	−	1.80998e6i	−0.0872762	−	0.0579582i
$996$	1.85584e7	−	1.37842e7i	0.592779	−	0.440284i
$997$	−1.48046e7	−	1.48046e7i	−0.471693	−	0.471693i	0.430769	−	0.902462i	$-0.358242\pi$
$997$	−1.48046e7	−	1.48046e7i	−0.471693	−	0.471693i	−0.902462	+	0.430769i	$0.858242\pi$
$998$	5.43779e6	−	1.08125e7i	0.172821	−	0.343638i
$999$	−5.35054e6			−0.169623

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	60.6.j.a.7.12	✓	60
4.3	odd	2	inner	60.6.j.a.7.27	yes	60
5.3	odd	4	inner	60.6.j.a.43.27	yes	60
20.3	even	4	inner	60.6.j.a.43.12	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
60.6.j.a.7.12	✓	60	1.1	even	1	trivial
60.6.j.a.7.27	yes	60	4.3	odd	2	inner
60.6.j.a.43.12	yes	60	20.3	even	4	inner
60.6.j.a.43.27	yes	60	5.3	odd	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:	\( N \)	\(=\)	\( 60 = 2^{2} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	60.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.54160 + 5.05374i) q^{2} +(6.36396 + 6.36396i) q^{3} +(-19.0805 - 25.6892i) q^{4} +(46.5686 + 30.9252i) q^{5} +(-48.3364 + 15.9871i) q^{6} +(-69.0576 + 69.0576i) q^{7} +(178.321 - 31.1362i) q^{8} +81.0000i q^{9} +O(q^{10})\)	\(q+(-2.54160 + 5.05374i) q^{2} +(6.36396 + 6.36396i) q^{3} +(-19.0805 - 25.6892i) q^{4} +(46.5686 + 30.9252i) q^{5} +(-48.3364 + 15.9871i) q^{6} +(-69.0576 + 69.0576i) q^{7} +(178.321 - 31.1362i) q^{8} +81.0000i q^{9} +(-274.647 + 156.746i) q^{10} +471.958i q^{11} +(42.0573 - 284.913i) q^{12} +(-137.412 + 137.412i) q^{13} +(-173.482 - 524.516i) q^{14} +(99.5539 + 493.167i) q^{15} +(-295.868 + 980.326i) q^{16} +(-915.632 - 915.632i) q^{17} +(-409.353 - 205.870i) q^{18} -777.207 q^{19} +(-94.1096 - 1786.38i) q^{20} -878.960 q^{21} +(-2385.15 - 1199.53i) q^{22} +(-2138.84 - 2138.84i) q^{23} +(1332.98 + 936.681i) q^{24} +(1212.27 + 2880.28i) q^{25} +(-345.198 - 1043.69i) q^{26} +(-515.481 + 515.481i) q^{27} +(3091.69 + 456.379i) q^{28} +5520.15i q^{29} +(-2745.36 - 750.316i) q^{30} +1274.32i q^{31} +(-4202.33 - 3986.84i) q^{32} +(-3003.52 + 3003.52i) q^{33} +(6954.54 - 2300.19i) q^{34} +(-5351.54 + 1080.30i) q^{35} +(2080.82 - 1545.52i) q^{36} +(5189.86 + 5189.86i) q^{37} +(1975.35 - 3927.80i) q^{38} -1748.97 q^{39} +(9267.07 + 4064.66i) q^{40} +14218.2 q^{41} +(2233.97 - 4442.03i) q^{42} +(4764.67 + 4764.67i) q^{43} +(12124.2 - 9005.21i) q^{44} +(-2504.94 + 3772.05i) q^{45} +(16245.2 - 5373.06i) q^{46} +(19281.3 - 19281.3i) q^{47} +(-8121.65 + 4355.86i) q^{48} +7269.08i q^{49} +(-17637.3 - 1194.07i) q^{50} -11654.1i q^{51} +(6151.90 + 908.110i) q^{52} +(-23446.9 + 23446.9i) q^{53} +(-1294.96 - 3915.25i) q^{54} +(-14595.4 + 21978.4i) q^{55} +(-10164.3 + 14464.7i) q^{56} +(-4946.12 - 4946.12i) q^{57} +(-27897.4 - 14030.0i) q^{58} +12503.5 q^{59} +(10769.5 - 11967.3i) q^{60} +20129.9 q^{61} +(-6440.06 - 3238.81i) q^{62} +(-5593.67 - 5593.67i) q^{63} +(30829.1 - 11104.5i) q^{64} +(-10648.6 + 2149.59i) q^{65} +(-7545.26 - 22812.8i) q^{66} +(-30888.0 + 30888.0i) q^{67} +(-6051.11 + 40992.6i) q^{68} -27223.0i q^{69} +(8141.95 - 29790.9i) q^{70} -56152.6i q^{71} +(2522.03 + 14444.0i) q^{72} +(36983.3 - 36983.3i) q^{73} +(-39418.7 + 13037.6i) q^{74} +(-10615.2 + 26044.8i) q^{75} +(14829.5 + 19965.8i) q^{76} +(-32592.3 - 32592.3i) q^{77} +(4445.19 - 8838.83i) q^{78} +14296.6 q^{79} +(-44094.9 + 36502.6i) q^{80} -6561.00 q^{81} +(-36137.1 + 71855.2i) q^{82} +(56758.8 + 56758.8i) q^{83} +(16771.0 + 22579.8i) q^{84} +(-14323.6 - 70955.8i) q^{85} +(-36189.3 + 11969.5i) q^{86} +(-35130.0 + 35130.0i) q^{87} +(14695.0 + 84160.3i) q^{88} -27861.0i q^{89} +(-12696.4 - 22246.4i) q^{90} -18978.7i q^{91} +(-14134.9 + 95755.3i) q^{92} +(-8109.70 + 8109.70i) q^{93} +(48437.2 + 146448. i) q^{94} +(-36193.4 - 24035.3i) q^{95} +(-1371.38 - 52115.5i) q^{96} +(-104470. - 104470. i) q^{97} +(-36736.0 - 18475.1i) q^{98} -38228.6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q + 180 q^{6} - 492 q^{8}+O(q^{10}) \) 60 * q + 180 * q^6 - 492 * q^8	\( 60 q + 180 q^{6} - 492 q^{8} - 568 q^{10} + 792 q^{12} - 244 q^{13} - 2740 q^{16} - 2020 q^{17} + 6820 q^{20} + 2212 q^{22} + 15580 q^{25} - 11920 q^{26} - 4724 q^{28} + 1368 q^{30} - 25580 q^{32} - 9432 q^{33} + 1620 q^{36} + 3764 q^{37} + 9776 q^{38} + 47032 q^{40} + 19280 q^{41} + 14220 q^{42} - 6156 q^{45} - 25400 q^{46} - 44784 q^{48} - 104816 q^{50} - 61288 q^{52} + 40244 q^{53} + 76480 q^{56} + 242100 q^{58} + 88380 q^{60} - 96160 q^{61} + 83864 q^{62} + 88420 q^{65} - 63720 q^{66} - 346256 q^{68} - 373436 q^{70} - 39852 q^{72} - 72036 q^{73} + 304040 q^{76} + 241008 q^{77} + 151416 q^{78} + 534404 q^{80} - 393660 q^{81} + 497776 q^{82} - 14276 q^{85} - 719680 q^{86} - 600740 q^{88} - 86508 q^{90} - 697064 q^{92} + 1584 q^{93} + 295020 q^{96} + 71580 q^{97} + 1425384 q^{98}+O(q^{100}) \) 60 * q + 180 * q^6 - 492 * q^8 - 568 * q^10 + 792 * q^12 - 244 * q^13 - 2740 * q^16 - 2020 * q^17 + 6820 * q^20 + 2212 * q^22 + 15580 * q^25 - 11920 * q^26 - 4724 * q^28 + 1368 * q^30 - 25580 * q^32 - 9432 * q^33 + 1620 * q^36 + 3764 * q^37 + 9776 * q^38 + 47032 * q^40 + 19280 * q^41 + 14220 * q^42 - 6156 * q^45 - 25400 * q^46 - 44784 * q^48 - 104816 * q^50 - 61288 * q^52 + 40244 * q^53 + 76480 * q^56 + 242100 * q^58 + 88380 * q^60 - 96160 * q^61 + 83864 * q^62 + 88420 * q^65 - 63720 * q^66 - 346256 * q^68 - 373436 * q^70 - 39852 * q^72 - 72036 * q^73 + 304040 * q^76 + 241008 * q^77 + 151416 * q^78 + 534404 * q^80 - 393660 * q^81 + 497776 * q^82 - 14276 * q^85 - 719680 * q^86 - 600740 * q^88 - 86508 * q^90 - 697064 * q^92 + 1584 * q^93 + 295020 * q^96 + 71580 * q^97 + 1425384 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more