LMFDB - Embedded newform 40.6.k.a.3.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [40,6,Mod(3,40)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(40, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 2, 3]))

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

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

chi := DirichletCharacter("40.3");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 40 = 2^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	40.k (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:	$6.41535279252$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$28$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			3.8
Character	$\chi$	$=$	40.3
Dual form			40.6.k.a.27.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.87156 - 4.12444i) q^{2} +(-18.3638 - 18.3638i) q^{3} +(-2.02198 + 31.9361i) q^{4} +(-43.5466 - 35.0528i) q^{5} +(-4.64371 + 146.837i) q^{6} +(-112.979 - 112.979i) q^{7} +(139.546 - 115.303i) q^{8} +431.456i q^{9} +O(q^{10})$	\(q+(-3.87156 - 4.12444i) q^{2} +(-18.3638 - 18.3638i) q^{3} +(-2.02198 + 31.9361i) q^{4} +(-43.5466 - 35.0528i) q^{5} +(-4.64371 + 146.837i) q^{6} +(-112.979 - 112.979i) q^{7} +(139.546 - 115.303i) q^{8} +431.456i q^{9} +(24.0203 + 315.314i) q^{10} +564.643 q^{11} +(623.597 - 549.335i) q^{12} +(181.168 - 181.168i) q^{13} +(-28.5693 + 903.377i) q^{14} +(155.978 + 1443.38i) q^{15} +(-1015.82 - 129.148i) q^{16} +(-994.839 + 994.839i) q^{17} +(1779.51 - 1670.41i) q^{18} -1892.29i q^{19} +(1207.50 - 1319.83i) q^{20} +4149.42i q^{21} +(-2186.05 - 2328.83i) q^{22} +(-781.175 + 781.175i) q^{23} +(-4680.00 - 445.202i) q^{24} +(667.606 + 3052.86i) q^{25} +(-1448.62 - 45.8126i) q^{26} +(3460.76 - 3460.76i) q^{27} +(3836.53 - 3379.65i) q^{28} -4664.12 q^{29} +(5349.25 - 6231.46i) q^{30} -1584.47i q^{31} +(3400.16 + 4689.70i) q^{32} +(-10369.0 - 10369.0i) q^{33} +(7954.74 + 251.569i) q^{34} +(959.616 + 8880.04i) q^{35} +(-13779.0 - 872.394i) q^{36} +(1140.25 + 1140.25i) q^{37} +(-7804.62 + 7326.11i) q^{38} -6653.86 q^{39} +(-10118.5 + 129.556i) q^{40} +3173.58 q^{41} +(17114.0 - 16064.8i) q^{42} +(-2117.52 - 2117.52i) q^{43} +(-1141.69 + 18032.5i) q^{44} +(15123.7 - 18788.4i) q^{45} +(6246.28 + 197.539i) q^{46} +(17005.4 + 17005.4i) q^{47} +(16282.7 + 21026.0i) q^{48} +8721.29i q^{49} +(10006.6 - 14572.8i) q^{50} +36538.0 q^{51} +(5419.48 + 6152.11i) q^{52} +(-12399.1 + 12399.1i) q^{53} +(-27672.2 - 875.135i) q^{54} +(-24588.2 - 19792.3i) q^{55} +(-28792.5 - 2739.00i) q^{56} +(-34749.5 + 34749.5i) q^{57} +(18057.4 + 19236.9i) q^{58} -15914.9i q^{59} +(-46411.2 + 2062.84i) q^{60} +2790.00i q^{61} +(-6535.05 + 6134.38i) q^{62} +(48745.2 - 48745.2i) q^{63} +(6178.45 - 32180.3i) q^{64} +(-14239.7 + 1538.80i) q^{65} +(-2622.04 + 82910.3i) q^{66} +(1758.54 - 1758.54i) q^{67} +(-29759.7 - 33782.8i) q^{68} +28690.6 q^{69} +(32909.9 - 38337.5i) q^{70} -10081.7i q^{71} +(49748.1 + 60208.2i) q^{72} +(-236.094 - 236.094i) q^{73} +(288.339 - 9117.43i) q^{74} +(43802.2 - 68321.7i) q^{75} +(60432.2 + 3826.16i) q^{76} +(-63792.5 - 63792.5i) q^{77} +(25760.8 + 27443.4i) q^{78} -88128.5 q^{79} +(39708.6 + 41231.4i) q^{80} -22261.4 q^{81} +(-12286.7 - 13089.2i) q^{82} +(-43374.7 - 43374.7i) q^{83} +(-132516. - 8390.04i) q^{84} +(78193.7 - 8449.95i) q^{85} +(-535.466 + 16931.7i) q^{86} +(85650.8 + 85650.8i) q^{87} +(78793.9 - 65105.0i) q^{88} +38471.3i q^{89} +(-136044. + 10363.7i) q^{90} -40936.2 q^{91} +(-23368.1 - 26527.2i) q^{92} +(-29096.9 + 29096.9i) q^{93} +(4300.21 - 135975. i) q^{94} +(-66329.9 + 82402.6i) q^{95} +(23680.9 - 148560. i) q^{96} +(82579.2 - 82579.2i) q^{97} +(35970.4 - 33765.0i) q^{98} +243618. i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 2 q^{2} - 4 q^{3} + 176 q^{6} + 244 q^{8}+O(q^{10}) $ 56 * q - 2 * q^2 - 4 * q^3 + 176 * q^6 + 244 * q^8	$ 56 q - 2 q^{2} - 4 q^{3} + 176 q^{6} + 244 q^{8} - 570 q^{10} - 8 q^{11} - 308 q^{12} + 456 q^{16} - 408 q^{17} + 3370 q^{18} + 1360 q^{20} - 3148 q^{22} - 3120 q^{25} - 5084 q^{26} + 968 q^{27} - 10020 q^{28} + 21100 q^{30} + 7968 q^{32} - 976 q^{33} - 4780 q^{35} + 23132 q^{36} - 49524 q^{38} - 58980 q^{40} - 8 q^{41} + 42060 q^{42} + 1308 q^{43} + 42416 q^{46} + 93776 q^{48} - 94010 q^{50} + 20872 q^{51} - 67180 q^{52} - 43384 q^{56} + 968 q^{57} + 86100 q^{58} + 118180 q^{60} + 6240 q^{62} + 17680 q^{65} - 41128 q^{66} + 89252 q^{67} - 158164 q^{68} + 116980 q^{70} + 1180 q^{72} - 25184 q^{73} - 127740 q^{75} + 41592 q^{76} - 161440 q^{78} - 167360 q^{80} - 67792 q^{81} + 23412 q^{82} - 126444 q^{83} - 192704 q^{86} + 100176 q^{88} - 82330 q^{90} + 329432 q^{91} + 226020 q^{92} + 358176 q^{96} + 212576 q^{97} + 65834 q^{98}+O(q^{100}) $ 56 * q - 2 * q^2 - 4 * q^3 + 176 * q^6 + 244 * q^8 - 570 * q^10 - 8 * q^11 - 308 * q^12 + 456 * q^16 - 408 * q^17 + 3370 * q^18 + 1360 * q^20 - 3148 * q^22 - 3120 * q^25 - 5084 * q^26 + 968 * q^27 - 10020 * q^28 + 21100 * q^30 + 7968 * q^32 - 976 * q^33 - 4780 * q^35 + 23132 * q^36 - 49524 * q^38 - 58980 * q^40 - 8 * q^41 + 42060 * q^42 + 1308 * q^43 + 42416 * q^46 + 93776 * q^48 - 94010 * q^50 + 20872 * q^51 - 67180 * q^52 - 43384 * q^56 + 968 * q^57 + 86100 * q^58 + 118180 * q^60 + 6240 * q^62 + 17680 * q^65 - 41128 * q^66 + 89252 * q^67 - 158164 * q^68 + 116980 * q^70 + 1180 * q^72 - 25184 * q^73 - 127740 * q^75 + 41592 * q^76 - 161440 * q^78 - 167360 * q^80 - 67792 * q^81 + 23412 * q^82 - 126444 * q^83 - 192704 * q^86 + 100176 * q^88 - 82330 * q^90 + 329432 * q^91 + 226020 * q^92 + 358176 * q^96 + 212576 * q^97 + 65834 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/40\mathbb{Z}\right)^\times$.

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

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 $

$2$	−3.87156	−	4.12444i	−0.684402	−	0.729105i
$2$	−3.87156	−	4.12444i	−0.684402	−	0.729105i
$3$	−18.3638	−	18.3638i	−1.17804	−	1.17804i	−0.980244	−	0.197792i	$-0.936623\pi$
$3$	−18.3638	−	18.3638i	−1.17804	−	1.17804i	−0.197792	−	0.980244i	$-0.563377\pi$
$4$	−2.02198	+	31.9361i	−0.0631868	+	0.998002i
$5$	−43.5466	−	35.0528i	−0.778985	−	0.627043i
$5$	−43.5466	−	35.0528i	−0.778985	−	0.627043i
$6$	−4.64371	+	146.837i	−0.0526608	+	1.66516i
$7$	−112.979	−	112.979i	−0.871467	−	0.871467i	0.121166	−	0.992632i	$-0.461337\pi$
$7$	−112.979	−	112.979i	−0.871467	−	0.871467i	−0.992632	+	0.121166i	$0.961337\pi$
$8$	139.546	−	115.303i	0.770893	−	0.636965i
$9$			431.456i			1.77554i
$10$	24.0203	+	315.314i	0.0759590	+	0.997111i
$11$	564.643			1.40699			0.703497	−	0.710699i	$-0.251621\pi$
$11$	564.643			1.40699			0.703497	+	0.710699i	$0.251621\pi$
$12$	623.597	−	549.335i	1.25012	−	1.10125i
$13$	181.168	−	181.168i	0.297319	−	0.297319i	−0.542644	−	0.839963i	$-0.682577\pi$
$13$	181.168	−	181.168i	0.297319	−	0.297319i	0.839963	+	0.542644i	$0.182577\pi$
$14$	−28.5693	+	903.377i	−0.0389564	+	1.23182i
$15$	155.978	+	1443.38i	0.178993	+	1.65635i
$16$	−1015.82	−	129.148i	−0.992015	−	0.126121i
$17$	−994.839	+	994.839i	−0.834893	+	0.834893i	−0.988181	−	0.153289i	$-0.951013\pi$
$17$	−994.839	+	994.839i	−0.834893	+	0.834893i	0.153289	+	0.988181i	$0.451013\pi$
$18$	1779.51	−	1670.41i	1.29455	−	1.21518i
$19$		−	1892.29i		−	1.20255i	−0.799042	−	0.601275i	$-0.794660\pi$
$19$		−	1892.29i		−	1.20255i	0.799042	−	0.601275i	$-0.205340\pi$
$20$	1207.50	−	1319.83i	0.675012	−	0.737807i
$21$			4149.42i			2.05324i
$22$	−2186.05	−	2328.83i	−0.962949	−	1.02584i
$23$	−781.175	+	781.175i	−0.307914	+	0.307914i	−0.844100	−	0.536186i	$-0.819865\pi$
$23$	−781.175	+	781.175i	−0.307914	+	0.307914i	0.536186	+	0.844100i	$0.319865\pi$
$24$	−4680.00	−	445.202i	−1.65851	−	0.157772i
$25$	667.606	+	3052.86i	0.213634	+	0.976914i
$26$	−1448.62	−	45.8126i	−0.420263	−	0.0132908i
$27$	3460.76	−	3460.76i	0.913613	−	0.913613i
$28$	3836.53	−	3379.65i	0.924790	−	0.814660i
$29$	−4664.12			−1.02985			−0.514926	−	0.857235i	$-0.672181\pi$
$29$	−4664.12			−1.02985			−0.514926	+	0.857235i	$0.672181\pi$
$30$	5349.25	−	6231.46i	1.08515	−	1.26412i
$31$		−	1584.47i		−	0.296128i	−0.988978	−	0.148064i	$-0.952696\pi$
$31$		−	1584.47i		−	0.296128i	0.988978	−	0.148064i	$-0.0473042\pi$
$32$	3400.16	+	4689.70i	0.586982	+	0.809600i
$33$	−10369.0	−	10369.0i	−1.65749	−	1.65749i
$34$	7954.74	+	251.569i	1.18013	+	0.0373215i
$35$	959.616	+	8880.04i	0.132412	+	1.22531i
$36$	−13779.0	−	872.394i	−1.77199	−	0.112191i
$37$	1140.25	+	1140.25i	0.136929	+	0.136929i	0.772249	−	0.635320i	$-0.219132\pi$
$37$	1140.25	+	1140.25i	0.136929	+	0.136929i	−0.635320	+	0.772249i	$0.719132\pi$
$38$	−7804.62	+	7326.11i	−0.876784	+	0.823028i
$39$	−6653.86			−0.700506
$40$	−10118.5	+	129.556i	−0.999918	+	0.0128029i
$41$	3173.58			0.294842			0.147421	−	0.989074i	$-0.452903\pi$
$41$	3173.58			0.294842			0.147421	+	0.989074i	$0.452903\pi$
$42$	17114.0	−	16064.8i	1.49703	−	1.40524i
$43$	−2117.52	−	2117.52i	−0.174645	−	0.174645i	0.614371	−	0.789017i	$-0.289410\pi$
$43$	−2117.52	−	2117.52i	−0.174645	−	0.174645i	−0.789017	+	0.614371i	$0.789410\pi$
$44$	−1141.69	+	18032.5i	−0.0889034	+	1.40418i
$45$	15123.7	−	18788.4i	1.11334	−	1.38312i
$46$	6246.28	+	197.539i	0.435238	+	0.0137644i
$47$	17005.4	+	17005.4i	1.12290	+	1.12290i	0.991303	+	0.131597i	$0.0420106\pi$
$47$	17005.4	+	17005.4i	1.12290	+	1.12290i	0.131597	+	0.991303i	$0.457989\pi$
$48$	16282.7	+	21026.0i	1.02005	+	1.31720i
$49$			8721.29i			0.518908i
$50$	10006.6	−	14572.8i	0.566061	−	0.824364i
$51$	36538.0			1.96707
$52$	5419.48	+	6152.11i	0.277939	+	0.315512i
$53$	−12399.1	+	12399.1i	−0.606316	+	0.606316i	−0.941981	−	0.335665i	$-0.891039\pi$
$53$	−12399.1	+	12399.1i	−0.606316	+	0.606316i	0.335665	+	0.941981i	$0.391039\pi$
$54$	−27672.2	−	875.135i	−1.29140	−	0.0408404i
$55$	−24588.2	−	19792.3i	−1.09603	−	0.882245i
$56$	−28792.5	−	2739.00i	−1.22690	−	0.116714i
$57$	−34749.5	+	34749.5i	−1.41665	+	1.41665i
$58$	18057.4	+	19236.9i	0.704833	+	0.750870i
$59$		−	15914.9i		−	0.595216i	−0.954688	−	0.297608i	$-0.903811\pi$
$59$		−	15914.9i		−	0.595216i	0.954688	−	0.297608i	$-0.0961889\pi$
$60$	−46411.2	+	2062.84i	−1.66435	+	0.0739754i
$61$			2790.00i			0.0960020i	0.998847	+	0.0480010i	$0.0152851\pi$
$61$			2790.00i			0.0960020i	−0.998847	+	0.0480010i	$0.984715\pi$
$62$	−6535.05	+	6134.38i	−0.215909	+	0.202671i
$63$	48745.2	−	48745.2i	1.54732	−	1.54732i
$64$	6178.45	−	32180.3i	0.188551	−	0.982063i
$65$	−14239.7	+	1538.80i	−0.418039	+	0.0451752i
$66$	−2622.04	+	82910.3i	−0.0740933	+	2.34287i
$67$	1758.54	−	1758.54i	0.0478593	−	0.0478593i	−0.682772	−	0.730631i	$-0.739226\pi$
$67$	1758.54	−	1758.54i	0.0478593	−	0.0478593i	0.730631	+	0.682772i	$0.239226\pi$
$68$	−29759.7	−	33782.8i	−0.780470	−	0.885978i
$69$	28690.6			0.725467
$70$	32909.9	−	38337.5i	0.802753	−	0.935145i
$71$		−	10081.7i		−	0.237350i	−0.992933	−	0.118675i	$-0.962135\pi$
$71$		−	10081.7i		−	0.237350i	0.992933	−	0.118675i	$-0.0378647\pi$
$72$	49748.1	+	60208.2i	1.13096	+	1.36875i
$73$	−236.094	−	236.094i	−0.00518534	−	0.00518534i	0.704509	−	0.709695i	$-0.251167\pi$
$73$	−236.094	−	236.094i	−0.00518534	−	0.00518534i	−0.709695	+	0.704509i	$0.751167\pi$
$74$	288.339	−	9117.43i	0.00612102	−	0.193550i
$75$	43802.2	−	68321.7i	0.899171	−	1.40251i
$76$	60432.2	+	3826.16i	1.20015	+	0.0759852i
$77$	−63792.5	−	63792.5i	−1.22615	−	1.22615i
$78$	25760.8	+	27443.4i	0.479428	+	0.510742i
$79$	−88128.5			−1.58872			−0.794362	−	0.607445i	$-0.792195\pi$
$79$	−88128.5			−1.58872			−0.794362	+	0.607445i	$0.792195\pi$
$80$	39708.6	+	41231.4i	0.693681	+	0.720282i
$81$	−22261.4			−0.376999
$82$	−12286.7	−	13089.2i	−0.201791	−	0.214971i
$83$	−43374.7	−	43374.7i	−0.691100	−	0.691100i	0.271374	−	0.962474i	$-0.412522\pi$
$83$	−43374.7	−	43374.7i	−0.691100	−	0.691100i	−0.962474	+	0.271374i	$0.912522\pi$
$84$	−132516.	−	8390.04i	−2.04914	−	0.129738i
$85$	78193.7	−	8449.95i	1.17388	−	0.126855i
$86$	−535.466	+	16931.7i	−0.00780703	+	0.246862i
$87$	85650.8	+	85650.8i	1.21320	+	1.21320i
$88$	78793.9	−	65105.0i	1.08464	−	0.896205i
$89$			38471.3i			0.514827i	0.966301	+	0.257414i	$0.0828703\pi$
$89$			38471.3i			0.514827i	−0.966301	+	0.257414i	$0.917130\pi$
$90$	−136044.	+	10363.7i	−1.77041	+	0.134868i
$91$	−40936.2			−0.518208
$92$	−23368.1	−	26527.2i	−0.287842	−	0.326754i
$93$	−29096.9	+	29096.9i	−0.348850	+	0.348850i
$94$	4300.21	−	135975.i	0.0501961	−	1.58723i
$95$	−66329.9	+	82402.6i	−0.754050	+	0.936767i
$96$	23680.9	−	148560.i	0.262252	−	1.64522i
$97$	82579.2	−	82579.2i	0.891131	−	0.891131i	−0.103499	−	0.994630i	$-0.533004\pi$
$97$	82579.2	−	82579.2i	0.891131	−	0.891131i	0.994630	+	0.103499i	$0.0330037\pi$
$98$	35970.4	−	33765.0i	0.378338	−	0.355142i
$99$			243618.i			2.49817i
$100$	−98846.0	+	15147.9i	−0.988460	+	0.151479i
$101$			178258.i			1.73879i	0.494119	+	0.869394i	$0.335491\pi$
$101$			178258.i			1.73879i	−0.494119	+	0.869394i	$0.664509\pi$
$102$	−141459.	−	150699.i	−1.34627	−	1.43420i
$103$	−17025.6	+	17025.6i	−0.158128	+	0.158128i	−0.781737	−	0.623609i	$-0.785666\pi$
$103$	−17025.6	+	17025.6i	−0.158128	+	0.158128i	0.623609	+	0.781737i	$0.285666\pi$
$104$	4392.15	−	46170.6i	0.0398193	−	0.418583i
$105$	145449.	−	180693.i	1.28747	−	1.59944i
$106$	99143.0	+	3135.40i	0.857032	+	0.0271036i
$107$	−148967.	+	148967.i	−1.25786	+	1.25786i	−0.305744	+	0.952114i	$0.598905\pi$
$107$	−148967.	+	148967.i	−1.25786	+	1.25786i	−0.952114	+	0.305744i	$0.901095\pi$
$108$	103525.	+	117521.i	0.854059	+	0.969515i
$109$	−121955.			−0.983179			−0.491589	−	0.870827i	$-0.663584\pi$
$109$	−121955.			−0.983179			−0.491589	+	0.870827i	$0.663584\pi$
$110$	13562.9	+	178040.i	0.106874	+	1.40293i
$111$		−	41878.5i		−	0.322615i
$112$	100175.	+	129357.i	0.754598	+	0.974418i
$113$	8213.03	+	8213.03i	0.0605073	+	0.0605073i	0.736713	−	0.676206i	$-0.236377\pi$
$113$	8213.03	+	8213.03i	0.0605073	+	0.0605073i	−0.676206	+	0.736713i	$0.736377\pi$
$114$	277857.	+	8787.23i	2.00244	+	0.0633272i
$115$	61399.9	−	6635.14i	0.432935	−	0.0467849i
$116$	9430.75	−	148954.i	0.0650731	−	1.02779i
$117$	78166.0	+	78166.0i	0.527902	+	0.527902i
$118$	−65640.1	+	61615.7i	−0.433975	+	0.407367i
$119$	224791.			1.45516
$120$	188192.	+	183434.i	1.19302	+	1.16286i
$121$	157770.			0.979629
$122$	11507.2	−	10801.7i	0.0699955	−	0.0657040i
$123$	−58278.8	−	58278.8i	−0.347335	−	0.347335i
$124$	50601.8	+	3203.77i	0.295537	+	0.0187114i
$125$	77939.1	−	156343.i	0.446149	−	0.894958i
$126$	−389767.	−	12326.4i	−2.18715	−	0.0691687i
$127$	−125043.	−	125043.i	−0.687941	−	0.687941i	0.273835	−	0.961777i	$-0.411708\pi$
$127$	−125043.	−	125043.i	−0.687941	−	0.687941i	−0.961777	+	0.273835i	$0.911708\pi$
$128$	−156646.	+	99105.3i	−0.845072	+	0.534653i
$129$			77771.4i			0.411477i
$130$	61476.6	+	52773.1i	0.319044	+	0.273876i
$131$	−238712.			−1.21533			−0.607666	−	0.794192i	$-0.707894\pi$
$131$	−238712.			−1.21533			−0.607666	+	0.794192i	$0.707894\pi$
$132$	352110.	−	310178.i	1.75891	−	1.54945i
$133$	−213788.	+	213788.i	−1.04798	+	1.04798i
$134$	−14061.3	−	444.689i	−0.0676494	−	0.00213941i
$135$	−272013.	+	29395.0i	−1.28456	+	0.138816i
$136$	−24118.4	+	253534.i	−0.111815	+	1.17541i
$137$	−83771.4	+	83771.4i	−0.381324	+	0.381324i	−0.871579	−	0.490255i	$-0.836904\pi$
$137$	−83771.4	+	83771.4i	−0.381324	+	0.381324i	0.490255	+	0.871579i	$0.336904\pi$
$138$	−111078.	−	118333.i	−0.496511	−	0.528941i
$139$		−	136221.i		−	0.598006i	−0.954252	−	0.299003i	$-0.903346\pi$
$139$		−	136221.i		−	0.598006i	0.954252	−	0.299003i	$-0.0966541\pi$
$140$	−285534.	+	12691.1i	−1.23122	+	0.0547242i
$141$		−	624565.i		−	2.64564i
$142$	−41581.5	+	39032.1i	−0.173053	+	0.162443i
$143$	102295.	−	102295.i	0.418326	−	0.418326i
$144$	55721.7	−	438283.i	0.223933	−	1.76136i
$145$	203106.	+	163490.i	0.802239	+	0.645762i
$146$	−59.7018	+	1887.80i	−0.000231796	+	0.00732951i
$147$	160156.	−	160156.i	0.611293	−	0.611293i
$148$	−38720.6	+	34109.5i	−0.145307	+	0.128003i
$149$	320066.			1.18106			0.590532	−	0.807014i	$-0.298918\pi$
$149$	320066.			1.18106			0.590532	+	0.807014i	$0.298918\pi$
$150$	−451371.	+	83852.5i	−1.63797	+	0.304290i
$151$			316550.i			1.12980i	0.825161	+	0.564898i	$0.191084\pi$
$151$			316550.i			1.12980i	−0.825161	+	0.564898i	$0.808916\pi$
$152$	−218186.	−	264062.i	−0.765982	−	0.927037i
$153$	−429229.	−	429229.i	−1.48238	−	1.48238i
$154$	−16131.4	+	510085.i	−0.0548114	+	1.73317i
$155$	−55540.1	+	68998.3i	−0.185685	+	0.230680i
$156$	13453.9	−	212498.i	0.0442627	−	0.699106i
$157$	−70981.8	−	70981.8i	−0.229825	−	0.229825i	0.582794	−	0.812620i	$-0.301959\pi$
$157$	−70981.8	−	70981.8i	−0.229825	−	0.229825i	−0.812620	+	0.582794i	$0.801959\pi$
$158$	341195.	+	363480.i	1.08733	+	1.15835i
$159$	455387.			1.42853
$160$	16321.8	−	323406.i	0.0504043	−	0.998729i
$161$	176512.			0.536673
$162$	86186.4	+	91815.8i	0.258019	+	0.274872i
$163$	−308350.	−	308350.i	−0.909024	−	0.909024i	0.0871698	−	0.996193i	$-0.472218\pi$
$163$	−308350.	−	308350.i	−0.909024	−	0.909024i	−0.996193	+	0.0871698i	$0.972218\pi$
$164$	−6416.90	+	101352.i	−0.0186301	+	0.294253i
$165$	88071.8	+	814994.i	0.251841	+	2.33048i
$166$	−10968.3	+	346824.i	−0.0308937	+	0.976875i
$167$	−350383.	−	350383.i	−0.972192	−	0.972192i	0.0274317	−	0.999624i	$-0.491267\pi$
$167$	−350383.	−	350383.i	−0.972192	−	0.972192i	−0.999624	+	0.0274317i	$0.991267\pi$
$168$	478441.	+	579037.i	1.30784	+	1.58283i
$169$			305649.i			0.823202i
$170$	−337583.	−	289791.i	−0.895898	−	0.769063i
$171$	816438.			2.13517
$172$	71906.9	−	63343.8i	0.185332	−	0.163261i
$173$	188032.	−	188032.i	0.477657	−	0.477657i	−0.426724	−	0.904382i	$-0.640333\pi$
$173$	188032.	−	188032.i	0.477657	−	0.477657i	0.904382	+	0.426724i	$0.140333\pi$
$174$	21658.8	−	684864.i	0.0542328	−	1.71487i
$175$	269482.	−	420332.i	0.665173	−	1.03752i
$176$	−573577.	−	72922.5i	−1.39576	−	0.177451i
$177$	−292258.	+	292258.i	−0.701186	+	0.701186i
$178$	158672.	−	148944.i	0.375363	−	0.352349i
$179$		−	106396.i		−	0.248194i	−0.992270	−	0.124097i	$-0.960397\pi$
$179$		−	106396.i		−	0.248194i	0.992270	−	0.124097i	$-0.0396034\pi$
$180$	569448.	+	520982.i	1.31001	+	1.19851i
$181$		−	832428.i		−	1.88865i	−0.329021	−	0.944323i	$-0.606719\pi$
$181$		−	832428.i		−	1.88865i	0.329021	−	0.944323i	$-0.393281\pi$
$182$	158487.	+	168839.i	0.354663	+	0.377828i
$183$	51235.0	−	51235.0i	0.113094	−	0.113094i
$184$	−18938.4	+	199082.i	−0.0412382	+	0.433499i
$185$	−9685.03	−	89622.8i	−0.0208052	−	0.192526i
$186$	232659.	+	7357.83i	0.493102	+	0.0155944i
$187$	−561729.	+	561729.i	−1.17469	+	1.17469i
$188$	−577469.	+	508700.i	−1.19161	+	1.04970i
$189$	−781983.			−1.59237
$190$	596665.	−	45453.3i	1.19908	−	0.0913444i
$191$			433612.i			0.860038i	0.902820	+	0.430019i	$0.141493\pi$
$191$			433612.i			0.860038i	−0.902820	+	0.430019i	$0.858507\pi$
$192$	−704410.	+	477491.i	−1.37903	+	0.934786i
$193$	113793.	+	113793.i	0.219899	+	0.219899i	0.808456	−	0.588557i	$-0.200304\pi$
$193$	113793.	+	113793.i	0.219899	+	0.219899i	−0.588557	+	0.808456i	$0.700304\pi$
$194$	−660304.	−	20882.1i	−1.25962	−	0.0398355i
$195$	289753.	+	233236.i	0.545683	+	0.439247i
$196$	−278524.	−	17634.3i	−0.517871	−	0.0327882i
$197$	497139.	+	497139.i	0.912666	+	0.912666i	0.996481	−	0.0838152i	$-0.0267106\pi$
$197$	497139.	+	497139.i	0.912666	+	0.912666i	−0.0838152	+	0.996481i	$0.526711\pi$
$198$	1.00479e6	−	943184.i	1.82143	−	1.70975i
$199$	−339239.			−0.607258			−0.303629	−	0.952790i	$-0.598198\pi$
$199$	−339239.			−0.607258			−0.303629	+	0.952790i	$0.598198\pi$
$200$	445165.	+	349038.i	0.786949	+	0.617018i
$201$	−64587.0			−0.112760
$202$	735216.	−	690139.i	1.26776	−	1.19003i
$203$	526946.	+	526946.i	0.897482	+	0.897482i
$204$	−73879.0	+	1.16688e6i	−0.124293	+	1.96314i
$205$	−138198.	−	111243.i	−0.229677	−	0.184879i
$206$	136137.	+	4305.32i	0.223515	+	0.00706866i
$207$	−337043.	−	337043.i	−0.546713	−	0.546713i
$208$	−207432.	+	160637.i	−0.332443	+	0.257447i
$209$		−	1.06847e6i		−	1.69198i
$210$	−1.30837e6	+	99670.5i	−2.04731	+	0.155962i
$211$	253328.			0.391721			0.195861	−	0.980632i	$-0.437250\pi$
$211$	253328.			0.391721			0.195861	+	0.980632i	$0.437250\pi$
$212$	−370907.	−	421048.i	−0.566794	−	0.643416i
$213$	−185139.	+	185139.i	−0.279607	+	0.279607i
$214$	1.19114e6	+	37669.9i	1.77799	+	0.0562290i
$215$	17985.8	+	166436.i	0.0265359	+	0.245556i
$216$	83901.0	−	881973.i	0.122358	−	1.28624i
$217$	−179011.	+	179011.i	−0.258066	+	0.258066i
$218$	472156.	+	502995.i	0.672890	+	0.716840i
$219$			8671.13i			0.0122170i
$220$	681805.	−	745232.i	0.949737	−	1.03809i
$221$			360466.i			0.496459i
$222$	−172725.	+	162135.i	−0.235220	+	0.220798i
$223$	−111660.	+	111660.i	−0.150361	+	0.150361i	−0.778279	−	0.627918i	$-0.783907\pi$
$223$	−111660.	+	111660.i	−0.150361	+	0.150361i	0.627918	+	0.778279i	$0.283907\pi$
$224$	145691.	−	913981.i	0.194004	−	1.21707i
$225$	−1.31717e6	+	288043.i	−1.73455	+	0.379315i
$226$	2076.86	−	65671.4i	0.00270480	−	0.0855274i
$227$	917106.	−	917106.i	1.18129	−	1.18129i	0.201874	−	0.979411i	$-0.435297\pi$
$227$	917106.	−	917106.i	1.18129	−	1.18129i	0.979411	−	0.201874i	$-0.0647032\pi$
$228$	−1.03950e6	−	1.18003e6i	−1.32430	−	1.50333i
$229$	−806085.			−1.01576			−0.507881	−	0.861427i	$-0.669571\pi$
$229$	−806085.			−1.01576			−0.507881	+	0.861427i	$0.669571\pi$
$230$	−265080.	−	227552.i	−0.330413	−	0.283635i
$231$			2.34294e6i			2.88889i
$232$	−650862.	+	537787.i	−0.793906	+	0.655980i
$233$	534768.	+	534768.i	0.645321	+	0.645321i	0.951858	−	0.306538i	$-0.0991706\pi$
$233$	534768.	+	534768.i	0.645321	+	0.645321i	−0.306538	+	0.951858i	$0.599171\pi$
$234$	19766.1	−	625016.i	0.0235984	−	0.746193i
$235$	−144440.	−	1.33661e6i	−0.170615	−	1.57883i
$236$	508260.	+	32179.6i	0.594027	+	0.0376098i
$237$	1.61837e6	+	1.61837e6i	1.87157	+	1.87157i
$238$	−870293.	−	927136.i	−0.995916	−	1.06097i
$239$	1.43507e6			1.62509			0.812546	−	0.582897i	$-0.198081\pi$
$239$	1.43507e6			1.62509			0.812546	+	0.582897i	$0.198081\pi$
$240$	27963.6	−	1.48636e6i	0.0313375	−	1.66570i
$241$	−1.11920e6			−1.24126			−0.620631	−	0.784103i	$-0.713124\pi$
$241$	−1.11920e6			−1.24126			−0.620631	+	0.784103i	$0.713124\pi$
$242$	−610818.	−	650714.i	−0.670461	−	0.714252i
$243$	−432161.	−	432161.i	−0.469494	−	0.469494i
$244$	−89101.7	−	5641.32i	−0.0958101	−	0.00606606i
$245$	305706.	−	379782.i	0.325378	−	0.404222i
$246$	−14737.2	+	465998.i	−0.0155266	+	0.490960i
$247$	−342822.	−	342822.i	−0.357541	−	0.357541i
$248$	−182694.	−	221107.i	−0.188623	−	0.228283i
$249$			1.59304e6i			1.62828i
$250$	−946572.	+	283836.i	−0.957864	+	0.287222i
$251$	−429663.			−0.430471			−0.215235	−	0.976562i	$-0.569052\pi$
$251$	−429663.			−0.430471			−0.215235	+	0.976562i	$0.569052\pi$
$252$	1.45817e6	+	1.65529e6i	1.44646	+	1.64200i
$253$	−441085.	+	441085.i	−0.433232	+	0.433232i
$254$	−31620.2	+	999847.i	−0.0307524	+	0.972409i
$255$	−1.59110e6	−	1.28076e6i	−1.53232	−	1.23344i
$256$	1.01522e6	+	262383.i	0.968187	+	0.250228i
$257$	697777.	−	697777.i	0.658997	−	0.658997i	−0.296146	−	0.955143i	$-0.595701\pi$
$257$	697777.	−	697777.i	0.658997	−	0.658997i	0.955143	+	0.296146i	$0.0957014\pi$
$258$	320763.	−	301097.i	0.300010	−	0.281616i
$259$		−	257647.i		−	0.238658i
$260$	−20351.0	−	457871.i	−0.0186703	−	0.420058i
$261$		−	2.01236e6i		−	1.82854i
$262$	924187.	+	984551.i	0.831777	+	0.886105i
$263$	187532.	−	187532.i	0.167181	−	0.167181i	−0.618558	−	0.785739i	$-0.712283\pi$
$263$	187532.	−	187532.i	0.167181	−	0.167181i	0.785739	+	0.618558i	$0.212283\pi$
$264$	−2.64253e6	−	251380.i	−2.33351	−	0.221984i
$265$	974558.	−	105315.i	0.852498	−	0.0921246i
$266$	1.70945e6	+	54061.3i	1.48133	+	0.0468470i
$267$	706478.	−	706478.i	0.606485	−	0.606485i
$268$	52605.2	+	59716.7i	0.0447396	+	0.0507877i
$269$	−1.61456e6			−1.36043			−0.680213	−	0.733015i	$-0.738113\pi$
$269$	−1.61456e6			−1.36043			−0.680213	+	0.733015i	$0.738113\pi$
$270$	1.17436e6	+	1.00810e6i	0.980370	+	0.841576i
$271$		−	986263.i		−	0.815774i	−0.913033	−	0.407887i	$-0.866266\pi$
$271$		−	986263.i		−	0.815774i	0.913033	−	0.407887i	$-0.133734\pi$
$272$	1.13906e6	−	882099.i	0.933523	−	0.722928i
$273$	751743.	+	751743.i	0.610468	+	0.610468i
$274$	669836.	+	21183.6i	0.539004	+	0.0170460i
$275$	376959.	+	1.72377e6i	0.300582	+	1.37451i
$276$	−58011.8	+	916266.i	−0.0458399	+	0.724017i
$277$	−1.15208e6	−	1.15208e6i	−0.902160	−	0.902160i	0.0934628	−	0.995623i	$-0.470206\pi$
$277$	−1.15208e6	−	1.15208e6i	−0.902160	−	0.902160i	−0.995623	+	0.0934628i	$0.970206\pi$
$278$	−561833.	+	527387.i	−0.436009	+	0.409277i
$279$	683630.			0.525788
$280$	1.15781e6	+	1.12853e6i	0.882553	+	0.860238i
$281$	−2.08579e6			−1.57582			−0.787908	−	0.615793i	$-0.788836\pi$
$281$	−2.08579e6			−1.57582			−0.787908	+	0.615793i	$0.788836\pi$
$282$	−2.57598e6	+	2.41804e6i	−1.92894	+	1.81068i
$283$	1.17348e6	+	1.17348e6i	0.870980	+	0.870980i	0.992579	−	0.121599i	$-0.0388023\pi$
$283$	1.17348e6	+	1.17348e6i	0.870980	+	0.870980i	−0.121599	+	0.992579i	$0.538802\pi$
$284$	321971.	+	20385.1i	0.236876	+	0.0149974i
$285$	2.73129e6	−	295155.i	1.99184	−	0.215247i
$286$	−817953.	−	25867.8i	−0.591307	−	0.0187001i
$287$	−358546.	−	358546.i	−0.256945	−	0.256945i
$288$	−2.02340e6	+	1.46702e6i	−1.43748	+	1.04221i
$289$		−	559553.i		−	0.394091i
$290$	−112034.	−	1.47066e6i	−0.0782265	−	1.02688i
$291$	−3.03293e6			−2.09957
$292$	8017.27	−	7062.52i	0.00550262	−	0.00484733i
$293$	−197657.	+	197657.i	−0.134506	+	0.134506i	−0.771154	−	0.636648i	$-0.780320\pi$
$293$	−197657.	+	197657.i	−0.134506	+	0.134506i	0.636648	+	0.771154i	$0.280320\pi$
$294$	−1.28061e6	−	40499.2i	−0.864067	−	0.0273261i
$295$	−557862.	+	693041.i	−0.373226	+	0.463664i
$296$	290592.	+	27643.7i	0.192777	+	0.0183386i
$297$	1.95409e6	−	1.95409e6i	1.28545	−	1.28545i
$298$	−1.23915e6	−	1.32009e6i	−0.808323	−	0.861119i
$299$			283048.i			0.183097i
$300$	2.09336e6	+	1.53701e6i	1.34289	+	0.985994i
$301$			478469.i			0.304395i
$302$	1.30559e6	−	1.22554e6i	0.823739	−	0.773235i
$303$	3.27350e6	−	3.27350e6i	2.04836	−	2.04836i
$304$	−244385.	+	1.92223e6i	−0.151667	+	1.19295i
$305$	97797.3	−	121495.i	0.0601974	−	0.0747840i
$306$	−108541.	+	3.43212e6i	−0.0662658	+	2.09536i
$307$	−989520.	+	989520.i	−0.599210	+	0.599210i	−0.940102	−	0.340893i	$-0.889271\pi$
$307$	−989520.	+	989520.i	−0.599210	+	0.599210i	0.340893	+	0.940102i	$0.389271\pi$
$308$	2.16627e6	−	1.90829e6i	1.30117	−	1.14622i
$309$	625307.			0.372561
$310$	499606.	−	38059.5i	0.295273	−	0.0224936i
$311$			1.75736e6i			1.03029i	0.857102	+	0.515146i	$0.172262\pi$
$311$			1.75736e6i			1.03029i	−0.857102	+	0.515146i	$0.827738\pi$
$312$	−928522.	+	767209.i	−0.540015	+	0.446198i
$313$	627444.	+	627444.i	0.362005	+	0.362005i	0.864551	−	0.502546i	$-0.167603\pi$
$313$	627444.	+	627444.i	0.362005	+	0.362005i	−0.502546	+	0.864551i	$0.667603\pi$
$314$	−17949.4	+	567570.i	−0.0102737	+	0.324860i
$315$	−3.83134e6	+	414032.i	−2.17558	+	0.235103i
$316$	178194.	−	2.81448e6i	0.100386	−	1.58555i
$317$	92320.6	+	92320.6i	0.0516001	+	0.0516001i	0.732436	−	0.680836i	$-0.238383\pi$
$317$	92320.6	+	92320.6i	0.0516001	+	0.0516001i	−0.680836	+	0.732436i	$0.738383\pi$
$318$	−1.76306e6	−	1.87822e6i	−0.977686	−	1.04154i
$319$	−2.63356e6			−1.44899
$320$	−1.39706e6	+	1.18477e6i	−0.762675	+	0.646782i
$321$	5.47120e6			2.96360
$322$	−683378.	−	728013.i	−0.367300	−	0.391291i
$323$	1.88252e6	+	1.88252e6i	1.00400	+	1.00400i
$324$	45012.1	−	710941.i	0.0238213	−	0.376245i
$325$	674029.	+	432131.i	0.353973	+	0.226938i
$326$	−77973.6	+	2.46557e6i	−0.0406353	+	1.28491i
$327$	2.23955e6	+	2.23955e6i	1.15822	+	1.15822i
$328$	442862.	−	365923.i	0.227292	−	0.187804i
$329$		−	3.84248e6i		−	1.95714i
$330$	3.02042e6	−	3.51855e6i	1.52680	−	1.77860i
$331$	−135099.			−0.0677772			−0.0338886	−	0.999426i	$-0.510789\pi$
$331$	−135099.			−0.0677772			−0.0338886	+	0.999426i	$0.510789\pi$
$332$	1.47292e6	−	1.29751e6i	0.733387	−	0.646051i
$333$	−491967.	+	491967.i	−0.243123	+	0.243123i
$334$	−88602.6	+	2.80166e6i	−0.0434591	+	1.37420i
$335$	−138220.	+	14936.7i	−0.0672915	+	0.00727181i
$336$	535890.	−	4.21508e6i	0.258957	−	2.03684i
$337$	−848072.	+	848072.i	−0.406779	+	0.406779i	−0.880614	−	0.473835i	$-0.842869\pi$
$337$	−848072.	+	848072.i	−0.406779	+	0.406779i	0.473835	+	0.880614i	$0.342869\pi$
$338$	1.26063e6	−	1.18334e6i	0.600201	−	0.563402i
$339$		−	301644.i		−	0.142559i
$340$	111752.	+	2.51428e6i	0.0524275	+	1.17955i
$341$		−	894660.i		−	0.416651i
$342$	−3.16089e6	−	3.36735e6i	−1.46132	−	1.55676i
$343$	−913511.	+	913511.i	−0.419255	+	0.419255i
$344$	−539650.	−	51336.2i	−0.245876	−	0.0233899i
$345$	−1.24938e6	−	1.00569e6i	−0.565127	−	0.454899i
$346$	−1.50350e6	−	47548.3i	−0.675172	−	0.0213523i
$347$	−561469.	+	561469.i	−0.250324	+	0.250324i	−0.821103	−	0.570779i	$-0.806641\pi$
$347$	−561469.	+	561469.i	−0.250324	+	0.250324i	0.570779	+	0.821103i	$0.306641\pi$
$348$	−2.90853e6	+	2.56217e6i	−1.28744	+	1.13412i
$349$	1.98231e6			0.871181			0.435590	−	0.900145i	$-0.356540\pi$
$349$	1.98231e6			0.871181			0.435590	+	0.900145i	$0.356540\pi$
$350$	−2.77695e6	+	515882.i	−1.21171	+	0.225102i
$351$		−	1.25396e6i		−	0.543269i
$352$	1.91988e6	+	2.64801e6i	0.825879	+	1.13910i
$353$	−2.08346e6	−	2.08346e6i	−0.889913	−	0.889913i	0.104601	−	0.994514i	$-0.466643\pi$
$353$	−2.08346e6	−	2.08346e6i	−0.889913	−	0.889913i	−0.994514	+	0.104601i	$0.966643\pi$
$354$	2.33690e6	+	73904.3i	0.991132	+	0.0313445i
$355$	−353393.	+	439025.i	−0.148829	+	0.184892i
$356$	−1.22862e6	−	77788.1i	−0.513799	−	0.0325303i
$357$	−4.12801e6	−	4.12801e6i	−1.71423	−	1.71423i
$358$	−438822.	+	411917.i	−0.180959	+	0.169864i
$359$	−2.12642e6			−0.870788			−0.435394	−	0.900240i	$-0.643391\pi$
$359$	−2.12642e6			−0.870788			−0.435394	+	0.900240i	$0.643391\pi$
$360$	−55897.9	−	4.36567e6i	−0.0227321	−	1.77539i
$361$	−1.10465e6			−0.446125
$362$	−3.43330e6	+	3.22280e6i	−1.37702	+	1.29259i
$363$	−2.89726e6	−	2.89726e6i	−1.15404	−	1.15404i
$364$	82772.1	−	1.30734e6i	0.0327439	−	0.517172i
$365$	2005.33	+	18556.8i	0.000787868	+	0.00729073i
$366$	−409675.	−	12956.0i	−0.159859	−	0.00505554i
$367$	392979.	+	392979.i	0.152301	+	0.152301i	0.779145	−	0.626844i	$-0.215654\pi$
$367$	392979.	+	392979.i	0.152301	+	0.152301i	−0.626844	+	0.779145i	$0.715654\pi$
$368$	894423.	−	692649.i	0.344289	−	0.266620i
$369$			1.36926e6i			0.523503i
$370$	−332147.	+	386926.i	−0.126132	+	0.146934i
$371$	2.80166e6			1.05677
$372$	−870406.	−	988072.i	−0.326110	−	0.370196i
$373$	−3.04357e6	+	3.04357e6i	−1.13269	+	1.13269i	−0.142964	+	0.989728i	$0.545663\pi$
$373$	−3.04357e6	+	3.04357e6i	−1.13269	+	1.13269i	−0.989728	+	0.142964i	$0.954337\pi$
$374$	4.49158e6	+	142046.i	1.66043	+	0.0525111i
$375$	−4.30230e6	+	1.43979e6i	−1.57987	+	0.528713i
$376$	4.33381e6	+	412270.i	1.58088	+	0.150388i
$377$	−844990.	+	844990.i	−0.306195	+	0.306195i
$378$	3.02750e6	+	3.22524e6i	1.08982	+	1.16100i
$379$		−	5.21265e6i		−	1.86406i	−0.362376	−	0.932032i	$-0.618034\pi$
$379$		−	5.21265e6i		−	1.86406i	0.362376	−	0.932032i	$-0.381966\pi$
$380$	−2.49750e6	−	2.28493e6i	−0.887249	−	0.811735i
$381$			4.59253e6i			1.62084i
$382$	1.78841e6	−	1.67876e6i	0.627058	−	0.588612i
$383$	1.54346e6	−	1.54346e6i	0.537648	−	0.537648i	−0.385190	−	0.922837i	$-0.625864\pi$
$383$	1.54346e6	−	1.54346e6i	0.537648	−	0.537648i	0.922837	+	0.385190i	$0.125864\pi$
$384$	4.69655e6	+	1.05666e6i	1.62537	+	0.365685i
$385$	541840.	+	5.01405e6i	0.186303	+	1.72400i
$386$	28775.3	−	909891.i	0.00982995	−	0.310829i
$387$	913618.	−	913618.i	0.310090	−	0.310090i
$388$	2.47028e6	+	2.80423e6i	0.833043	+	0.945658i
$389$	2.38261e6			0.798325			0.399162	−	0.916880i	$-0.369301\pi$
$389$	2.38261e6			0.798325			0.399162	+	0.916880i	$0.369301\pi$
$390$	−159828.	−	2.09805e6i	−0.0532097	−	0.698482i
$391$		−	1.55429e6i		−	0.514150i
$392$	1.00559e6	+	1.21703e6i	0.330526	+	0.400023i
$393$	4.38364e6	+	4.38364e6i	1.43171	+	1.43171i
$394$	125713.	−	3.97512e6i	0.0407981	−	1.29006i
$395$	3.83769e6	+	3.08915e6i	1.23759	+	0.996198i
$396$	−7.78021e6	−	492591.i	−2.49318	−	0.157851i
$397$	2.63572e6	+	2.63572e6i	0.839311	+	0.839311i	0.988768	−	0.149457i	$-0.0477526\pi$
$397$	2.63572e6	+	2.63572e6i	0.839311	+	0.839311i	−0.149457	+	0.988768i	$0.547753\pi$
$398$	1.31339e6	+	1.39917e6i	0.415609	+	0.442755i
$399$	7.85190e6			2.46912
$400$	−283900.	−	3.18738e6i	−0.0887187	−	0.996057i
$401$	−725347.			−0.225261			−0.112630	−	0.993637i	$-0.535928\pi$
$401$	−725347.			−0.225261			−0.112630	+	0.993637i	$0.535928\pi$
$402$	250053.	+	266385.i	0.0771732	+	0.0822138i
$403$	−287056.	−	287056.i	−0.0880447	−	0.0880447i
$404$	−5.69287e6	−	360435.i	−1.73531	−	0.109868i
$405$	969407.	+	780324.i	0.293676	+	0.236394i
$406$	133251.	−	4.21346e6i	0.0401194	−	1.26860i
$407$	643833.	+	643833.i	0.192658	+	0.192658i
$408$	5.09875e6	−	4.21294e6i	1.51640	−	1.25295i
$409$			1.53906e6i			0.454932i	0.973786	+	0.227466i	$0.0730440\pi$
$409$			1.53906e6i			0.454932i	−0.973786	+	0.227466i	$0.926956\pi$
$410$	76230.4	+	1.00067e6i	0.0223959	+	0.293990i
$411$	3.07672e6			0.898427
$412$	−509304.	−	578155.i	−0.147820	−	0.167804i
$413$	−1.79805e6	+	1.79805e6i	−0.518711	+	0.518711i
$414$	−85229.2	+	2.69499e6i	−0.0244392	+	0.772782i
$415$	368415.	+	3.40922e6i	0.105007	+	0.971706i
$416$	1.46563e6	+	233624.i	0.415231	+	0.0661887i
$417$	−2.50152e6	+	2.50152e6i	−0.704473	+	0.704473i
$418$	−4.40682e6	+	4.13663e6i	−1.23363	+	1.15799i
$419$			2.90192e6i			0.807514i	0.914866	+	0.403757i	$0.132296\pi$
$419$			2.90192e6i			0.807514i	−0.914866	+	0.403757i	$0.867704\pi$
$420$	5.47653e6	+	5.01042e6i	1.51489	+	1.38596i
$421$		−	4.02303e6i		−	1.10624i	−0.833103	−	0.553118i	$-0.813438\pi$
$421$		−	4.02303e6i		−	1.10624i	0.833103	−	0.553118i	$-0.186562\pi$
$422$	−980776.	−	1.04484e6i	−0.268095	−	0.285606i
$423$	−7.33706e6	+	7.33706e6i	−1.99375	+	1.99375i
$424$	−300597.	+	3.15990e6i	−0.0812026	+	0.853607i
$425$	−3.70126e6	−	2.37294e6i	−0.993979	−	0.637257i
$426$	1.48037e6	+	46816.7i	0.395227	+	0.0124990i
$427$	315210.	−	315210.i	0.0836625	−	0.0836625i
$428$	−4.45622e6	−	5.05864e6i	−1.17586	−	1.33482i
$429$	−3.75705e6			−0.985607
$430$	616822.	−	718549.i	0.160875	−	0.187407i
$431$		−	3.83756e6i		−	0.995089i	−0.867439	−	0.497544i	$-0.834235\pi$
$431$		−	3.83756e6i		−	0.995089i	0.867439	−	0.497544i	$-0.165765\pi$
$432$	−3.96247e6	+	3.06857e6i	−1.02154	+	0.791091i
$433$	−3.70645e6	−	3.70645e6i	−0.950031	−	0.950031i	0.0487783	−	0.998810i	$-0.484467\pi$
$433$	−3.70645e6	−	3.70645e6i	−0.950031	−	0.950031i	−0.998810	+	0.0487783i	$0.984467\pi$
$434$	1.43137e6	+	45267.2i	0.364778	+	0.0115361i
$435$	−727500.	−	6.73210e6i	−0.184336	−	1.70580i
$436$	246590.	−	3.89475e6i	0.0621239	−	0.981214i
$437$	1.47821e6	+	1.47821e6i	0.370281	+	0.370281i
$438$	35763.5	−	33570.8i	0.00890749	−	0.00836136i
$439$	2.21409e6			0.548320			0.274160	−	0.961684i	$-0.411600\pi$
$439$	2.21409e6			0.548320			0.274160	+	0.961684i	$0.411600\pi$
$440$	−5.71331e6	+	73153.1i	−1.40688	+	0.0180136i
$441$	−3.76285e6			−0.921342
$442$	1.48672e6	−	1.39557e6i	0.361971	−	0.339778i
$443$	2.11417e6	+	2.11417e6i	0.511835	+	0.511835i	0.915088	−	0.403253i	$-0.132121\pi$
$443$	2.11417e6	+	2.11417e6i	0.511835	+	0.511835i	−0.403253	+	0.915088i	$0.632121\pi$
$444$	1.33744e6	+	84677.5i	0.321970	+	0.0203850i
$445$	1.34852e6	−	1.67529e6i	0.322819	−	0.401043i
$446$	892832.	+	28235.8i	0.212536	+	0.00672145i
$447$	−5.87761e6	−	5.87761e6i	−1.39134	−	1.39134i
$448$	−4.33371e6	+	2.93765e6i	−1.02015	+	0.691519i
$449$		−	4.58602e6i		−	1.07354i	−0.843727	−	0.536772i	$-0.819644\pi$
$449$		−	4.58602e6i		−	1.07354i	0.843727	−	0.536772i	$-0.180356\pi$
$450$	6.28753e6	+	4.31742e6i	1.46369	+	1.00506i
$451$	1.79194e6			0.414841
$452$	−278898.	+	245685.i	−0.0642096	+	0.0565631i
$453$	5.81305e6	−	5.81305e6i	1.33094	−	1.33094i
$454$	−7.33318e6	−	231912.i	−1.66976	−	0.0528060i
$455$	1.78263e6	+	1.43493e6i	0.403676	+	0.324939i
$456$	−842451.	+	8.85589e6i	−0.189728	+	1.99444i
$457$	2.58042e6	−	2.58042e6i	0.577962	−	0.577962i	−0.356379	−	0.934341i	$-0.615989\pi$
$457$	2.58042e6	−	2.58042e6i	0.577962	−	0.577962i	0.934341	+	0.356379i	$0.115989\pi$
$458$	3.12081e6	+	3.32465e6i	0.695191	+	0.740597i
$459$			6.88580e6i			1.52554i
$460$	87751.0	+	1.97429e6i	0.0193356	+	0.435026i
$461$		−	4.39818e6i		−	0.963875i	−0.876206	−	0.481937i	$-0.839933\pi$
$461$		−	4.39818e6i		−	0.963875i	0.876206	−	0.481937i	$-0.160067\pi$
$462$	9.66331e6	−	9.07085e6i	2.10630	−	1.97716i
$463$	6.05182e6	−	6.05182e6i	1.31200	−	1.31200i	0.392059	−	0.919940i	$-0.371763\pi$
$463$	6.05182e6	−	6.05182e6i	1.31200	−	1.31200i	0.919940	−	0.392059i	$-0.128237\pi$
$464$	4.73792e6	+	602362.i	1.02163	+	0.129886i
$465$	2.28699e6	−	247143.i	0.490493	−	0.0530048i
$466$	135229.	−	4.27601e6i	0.0288472	−	0.912165i
$467$	−1.85830e6	+	1.85830e6i	−0.394297	+	0.394297i	−0.876216	−	0.481919i	$-0.839940\pi$
$467$	−1.85830e6	+	1.85830e6i	−0.394297	+	0.394297i	0.481919	+	0.876216i	$0.339940\pi$
$468$	−2.65436e6	+	2.33826e6i	−0.560204	+	0.493491i
$469$	−397355.			−0.0834156
$470$	−4.95356e6	+	5.77051e6i	−1.03436	+	1.20495i
$471$			2.60699e6i			0.541485i
$472$	−1.83504e6	−	2.22087e6i	−0.379132	−	0.458848i
$473$	−1.19564e6	−	1.19564e6i	−0.245725	−	0.245725i
$474$	409243.	−	1.29405e7i	0.0836634	−	2.64548i
$475$	5.77688e6	−	1.26330e6i	1.17479	−	0.256905i
$476$	−454522.	+	7.17894e6i	−0.0919470	+	1.45225i
$477$	−5.34965e6	−	5.34965e6i	−1.07654	−	1.07654i
$478$	−5.55596e6	−	5.91885e6i	−1.11222	−	1.18486i
$479$	−7.21535e6			−1.43687			−0.718437	−	0.695593i	$-0.755142\pi$
$479$	−7.21535e6			−1.43687			−0.718437	+	0.695593i	$0.755142\pi$
$480$	−6.23867e6	+	5.63922e6i	−1.23592	+	1.11716i
$481$	413153.			0.0814233
$482$	4.33304e6	+	4.61605e6i	0.849523	+	0.905010i
$483$	−3.24143e6	−	3.24143e6i	−0.632220	−	0.632220i
$484$	−319008.	+	5.03856e6i	−0.0618996	+	0.977672i
$485$	−6.49067e6	+	701411.i	−1.25295	+	0.135400i
$486$	−109282.	+	3.45556e6i	−0.0209874	+	0.663634i
$487$	1.44227e6	+	1.44227e6i	0.275566	+	0.275566i	0.831336	−	0.555770i	$-0.187577\pi$
$487$	1.44227e6	+	1.44227e6i	0.275566	+	0.275566i	−0.555770	+	0.831336i	$0.687577\pi$
$488$	321696.	+	389335.i	0.0611499	+	0.0740072i
$489$			1.13249e7i			2.14173i
$490$	−2.74995e6	+	209488.i	−0.517409	+	0.0394157i
$491$	−8.71746e6			−1.63187			−0.815936	−	0.578142i	$-0.803778\pi$
$491$	−8.71746e6			−1.63187			−0.815936	+	0.578142i	$0.803778\pi$
$492$	1.97903e6	−	1.74336e6i	0.368587	−	0.324694i
$493$	4.64005e6	−	4.64005e6i	0.859816	−	0.859816i
$494$	−86690.6	+	2.74120e6i	−0.0159829	+	0.505387i
$495$	8.53950e6	−	1.06087e7i	1.56646	−	1.94604i
$496$	−204631.	+	1.60954e6i	−0.0373480	+	0.293764i
$497$	−1.13902e6	+	1.13902e6i	−0.206843	+	0.206843i
$498$	6.57041e6	−	6.16757e6i	1.18719	−	1.11440i
$499$		−	2.31575e6i		−	0.416333i	−0.978093	−	0.208167i	$-0.933250\pi$
$499$		−	2.31575e6i		−	0.416333i	0.978093	−	0.208167i	$-0.0667496\pi$
$500$	4.83538e6	+	2.80519e6i	0.864979	+	0.501807i
$501$			1.28687e7i			2.29055i
$502$	1.66347e6	+	1.77212e6i	0.294615	+	0.313858i
$503$	2.57811e6	−	2.57811e6i	0.454340	−	0.454340i	−0.442452	−	0.896792i	$-0.645891\pi$
$503$	2.57811e6	−	2.57811e6i	0.454340	−	0.454340i	0.896792	+	0.442452i	$0.145891\pi$
$504$	1.18176e6	−	1.24227e7i	0.207230	−	2.17841i
$505$	6.24845e6	−	7.76254e6i	1.09029	−	1.35449i
$506$	3.52692e6	+	111539.i	0.612377	+	0.0193664i
$507$	5.61287e6	−	5.61287e6i	0.969762	−	0.969762i
$508$	4.24623e6	−	3.74056e6i	0.730035	−	0.643098i
$509$	6.05440e6			1.03580			0.517901	−	0.855440i	$-0.326713\pi$
$509$	6.05440e6			1.03580			0.517901	+	0.855440i	$0.326713\pi$
$510$	877655.	+	1.15209e7i	0.149416	+	1.96138i
$511$			53347.0i			0.00903770i
$512$	−2.84830e6	−	5.20303e6i	−0.480187	−	0.877166i
$513$	−6.54875e6	−	6.54875e6i	−1.09866	−	1.09866i
$514$	−5.57942e6	−	176449.i	−0.931497	−	0.0294586i
$515$	1.33820e6	−	144612.i	0.222332	−	0.0240262i
$516$	−2.48371e6	−	157252.i	−0.410655	−	0.0259999i
$517$	9.60195e6	+	9.60195e6i	1.57991	+	1.57991i
$518$	−1.06265e6	+	997498.i	−0.174007	+	0.163338i
$519$	−6.90595e6			−1.12540
$520$	−1.80967e6	+	1.85661e6i	−0.293488	+	0.301102i
$521$	−1.03013e7			−1.66265			−0.831323	−	0.555790i	$-0.812416\pi$
$521$	−1.03013e7			−1.66265			−0.831323	+	0.555790i	$0.812416\pi$
$522$	−8.29987e6	+	7.79099e6i	−1.33320	+	1.25146i
$523$	−927010.	−	927010.i	−0.148194	−	0.148194i	0.629117	−	0.777311i	$-0.283417\pi$
$523$	−927010.	−	927010.i	−0.148194	−	0.148194i	−0.777311	+	0.629117i	$0.783417\pi$
$524$	482669.	−	7.62350e6i	0.0767930	−	1.21290i
$525$	−1.26676e7	+	2.77018e6i	−2.00584	+	0.438642i
$526$	−1.49951e6	−	47422.0i	−0.236311	−	0.00747335i
$527$	1.57629e6	+	1.57629e6i	0.247235	+	0.247235i
$528$	9.19390e6	+	1.18722e7i	1.43521	+	1.85330i
$529$			5.21587e6i			0.810378i
$530$	−4.20743e6	−	3.61177e6i	−0.650620	−	0.558510i
$531$	6.86659e6			1.05683
$532$	−6.39526e6	−	7.25981e6i	−0.979669	−	1.11211i
$533$	574951.	−	574951.i	0.0876623	−	0.0876623i
$534$	−5.64900e6	−	178649.i	−0.857271	−	0.0271112i
$535$	1.17087e7	−	1.26530e6i	1.76858	−	0.191121i
$536$	42633.3	−	448164.i	0.00640969	−	0.0673791i
$537$	−1.95382e6	+	1.95382e6i	−0.292381	+	0.292381i
$538$	6.25089e6	+	6.65917e6i	0.931078	+	0.991892i
$539$			4.92441e6i			0.730100i
$540$	−388754.	−	8.74647e6i	−0.0573708	−	1.29077i
$541$		−	7.84634e6i		−	1.15259i	−0.817242	−	0.576294i	$-0.804498\pi$
$541$		−	7.84634e6i		−	1.15259i	0.817242	−	0.576294i	$-0.195502\pi$
$542$	−4.06778e6	+	3.81838e6i	−0.594784	+	0.558317i
$543$	−1.52865e7	+	1.52865e7i	−2.22489	+	2.22489i
$544$	−8.04812e6	−	1.28289e6i	−1.16600	−	0.185862i
$545$	5.31071e6	+	4.27485e6i	0.765881	+	0.616495i
$546$	190096.	−	6.01094e6i	0.0272892	−	0.862900i
$547$	−2.75454e6	+	2.75454e6i	−0.393624	+	0.393624i	−0.875977	−	0.482353i	$-0.839782\pi$
$547$	−2.75454e6	+	2.75454e6i	−0.393624	+	0.393624i	0.482353	+	0.875977i	$0.339782\pi$
$548$	−2.50594e6	−	2.84471e6i	−0.356467	−	0.404657i
$549$	−1.20376e6			−0.170455
$550$	5.65017e6	−	8.22844e6i	0.796443	−	1.15987i
$551$			8.82586e6i			1.23845i
$552$	4.00368e6	−	3.30812e6i	0.559257	−	0.462097i
$553$	9.95662e6	+	9.95662e6i	1.38452	+	1.38452i
$554$	−291331.	+	9.21204e6i	−0.0403285	+	1.27521i
$555$	−1.46796e6	+	1.82367e6i	−0.202293	+	0.251312i
$556$	4.35035e6	+	275435.i	0.596811	+	0.0377861i
$557$	−3.87209e6	−	3.87209e6i	−0.528819	−	0.528819i	0.391401	−	0.920220i	$-0.371991\pi$
$557$	−3.87209e6	−	3.87209e6i	−0.528819	−	0.528819i	−0.920220	+	0.391401i	$0.871991\pi$
$558$	−2.64672e6	−	2.81959e6i	−0.359850	−	0.383354i
$559$	−767255.			−0.103851
$560$	172039.	−	9.14448e6i	0.0231823	−	1.23222i
$561$	2.06309e7			2.76765
$562$	8.07528e6	+	8.60272e6i	1.07849	+	1.14893i
$563$	161996.	+	161996.i	0.0215393	+	0.0215393i	0.717794	−	0.696255i	$-0.245152\pi$
$563$	161996.	+	161996.i	0.0215393	+	0.0215393i	−0.696255	+	0.717794i	$0.745152\pi$
$564$	1.99461e7	+	1.26286e6i	2.64035	+	0.167169i
$565$	−69759.8	−	645539.i	−0.00919356	−	0.0850749i
$566$	296741.	−	9.38312e6i	0.0389347	−	1.23114i
$567$	2.51506e6	+	2.51506e6i	0.328542	+	0.328542i
$568$	−1.16245e6	−	1.40687e6i	−0.151184	−	0.182972i
$569$			3.86832e6i			0.500889i	0.968131	+	0.250444i	$0.0805767\pi$
$569$			3.86832e6i			0.500889i	−0.968131	+	0.250444i	$0.919423\pi$
$570$	−1.17917e7	−	1.01223e7i	−1.52016	−	1.30495i
$571$	−8.11445e6			−1.04152			−0.520761	−	0.853702i	$-0.674352\pi$
$571$	−8.11445e6			−1.04152			−0.520761	+	0.853702i	$0.674352\pi$
$572$	3.06007e6	+	3.47374e6i	0.391058	+	0.443923i
$573$	7.96275e6	−	7.96275e6i	1.01316	−	1.01316i
$574$	−90666.8	+	2.86694e6i	−0.0114860	+	0.363194i
$575$	−2.90633e6	−	1.86330e6i	−0.366586	−	0.235024i
$576$	1.38844e7	+	2.66573e6i	1.74369	+	0.334780i
$577$	−6.64442e6	+	6.64442e6i	−0.830840	+	0.830840i	−0.987632	−	0.156792i	$-0.949885\pi$
$577$	−6.64442e6	+	6.64442e6i	−0.830840	+	0.830840i	0.156792	+	0.987632i	$0.449885\pi$
$578$	−2.30784e6	+	2.16635e6i	−0.287334	+	0.269717i
$579$		−	4.17934e6i		−	0.518098i
$580$	−5.63192e6	+	6.15585e6i	−0.695162	+	0.759832i
$581$			9.80081e6i			1.20454i
$582$	1.17422e7	+	1.25091e7i	1.43695	+	1.53081i
$583$	−7.00104e6	+	7.00104e6i	−0.853083	+	0.853083i
$584$	−60168.3	−	5723.74i	−0.00730022	−	0.000694461i
$585$	−663926.	−	6.14380e6i	−0.0802102	−	0.742245i
$586$	1.58046e6	+	49982.1i	0.190125	+	0.00601272i
$587$	−3.99962e6	+	3.99962e6i	−0.479097	+	0.479097i	−0.904843	−	0.425746i	$-0.860012\pi$
$587$	−3.99962e6	+	3.99962e6i	−0.479097	+	0.479097i	0.425746	+	0.904843i	$0.360012\pi$
$588$	4.79091e6	+	5.43858e6i	0.571446	+	0.648697i
$589$	−2.99827e6			−0.356109
$590$	5.01820e6	−	382282.i	0.593497	−	0.0452120i
$591$		−	1.82587e7i		−	2.15031i
$592$	−1.01103e6	−	1.30555e6i	−0.118566	−	0.153105i
$593$	−1.09039e7	−	1.09039e7i	−1.27334	−	1.27334i	−0.944322	−	0.329023i	$-0.893281\pi$
$593$	−1.09039e7	−	1.09039e7i	−1.27334	−	1.27334i	−0.329023	−	0.944322i	$-0.606719\pi$
$594$	−1.56249e7	−	494138.i	−1.81699	−	0.0574622i
$595$	−9.78887e6	−	7.87955e6i	−1.13355	−	0.912449i
$596$	−647165.	+	1.02216e7i	−0.0746276	+	1.17870i
$597$	6.22971e6	+	6.22971e6i	0.715372	+	0.715372i
$598$	1.16741e6	−	1.09584e6i	0.133497	−	0.125312i
$599$	1.29839e6			0.147856			0.0739281	−	0.997264i	$-0.476446\pi$
$599$	1.29839e6			0.147856			0.0739281	+	0.997264i	$0.476446\pi$
$600$	−1.76526e6	−	1.45846e7i	−0.200184	−	1.65392i
$601$	8.50221e6			0.960165			0.480082	−	0.877223i	$-0.340607\pi$
$601$	8.50221e6			0.960165			0.480082	+	0.877223i	$0.340607\pi$
$602$	1.97342e6	−	1.85243e6i	0.221936	−	0.208329i
$603$	758734.	+	758734.i	0.0849760	+	0.0849760i
$604$	−1.01094e7	−	640057.i	−1.12754	−	0.0713882i
$605$	−6.87035e6	−	5.53029e6i	−0.763116	−	0.614270i
$606$	−2.61749e7	−	827781.i	−2.89536	−	0.0915659i
$607$	4.11444e6	+	4.11444e6i	0.453251	+	0.453251i	0.896432	−	0.443181i	$-0.146150\pi$
$607$	4.11444e6	+	4.11444e6i	0.453251	+	0.453251i	−0.443181	+	0.896432i	$0.646150\pi$
$608$	8.87427e6	−	6.43408e6i	0.973584	−	0.705875i
$609$		−	1.93534e7i		−	2.11453i
$610$	−879727.	+	67016.8i	−0.0957246	+	0.00729221i
$611$	6.16166e6			0.667720
$612$	1.45758e7	−	1.28400e7i	1.57309	−	1.38575i
$613$	−8.31731e6	+	8.31731e6i	−0.893988	+	0.893988i	−0.994896	−	0.100907i	$-0.967825\pi$
$613$	−8.31731e6	+	8.31731e6i	−0.893988	+	0.893988i	0.100907	+	0.994896i	$0.467825\pi$
$614$	7.91221e6	+	250224.i	0.846987	+	0.0267860i
$615$	495008.	+	4.58068e6i	0.0527745	+	0.488362i
$616$	−1.62575e7	−	1.54655e6i	−1.72624	−	0.164215i
$617$	1.22008e7	−	1.22008e7i	1.29025	−	1.29025i	0.355624	−	0.934629i	$-0.384268\pi$
$617$	1.22008e7	−	1.22008e7i	1.29025	−	1.29025i	0.934629	−	0.355624i	$-0.115732\pi$
$618$	−2.42092e6	−	2.57904e6i	−0.254982	−	0.271636i
$619$			1.46475e6i			0.153651i	0.997045	+	0.0768256i	$0.0244785\pi$
$619$			1.46475e6i			0.153651i	−0.997045	+	0.0768256i	$0.975522\pi$
$620$	−2.09123e6	−	1.91325e6i	−0.218486	−	0.199890i
$621$			5.40692e6i			0.562628i
$622$	7.24813e6	−	6.80374e6i	0.751191	−	0.705134i
$623$	4.34643e6	−	4.34643e6i	0.448655	−	0.448655i
$624$	6.75914e6	+	859332.i	0.694912	+	0.0883486i
$625$	−8.87423e6	+	4.07621e6i	−0.908721	+	0.417404i
$626$	158664.	−	5.01705e6i	0.0161824	−	0.511696i
$627$	−1.96211e7	+	1.96211e7i	−1.99321	+	1.99321i
$628$	2.41040e6	−	2.12335e6i	0.243888	−	0.214844i
$629$	−2.26873e6			−0.228642
$630$	1.65409e7	+	1.41992e7i	1.66039	+	1.42532i
$631$			1.24491e6i			0.124470i	0.998062	+	0.0622349i	$0.0198228\pi$
$631$			1.24491e6i			0.124470i	−0.998062	+	0.0622349i	$0.980177\pi$
$632$	−1.22980e7	+	1.01615e7i	−1.22474	+	1.01196i
$633$	−4.65206e6	−	4.65206e6i	−0.461462	−	0.461462i
$634$	23345.4	−	738196.i	0.00230664	−	0.0729371i
$635$	1.06209e6	+	9.82832e6i	0.104527	+	0.967264i
$636$	−920783.	+	1.45433e7i	−0.0902639	+	1.42567i
$637$	1.58002e6	+	1.58002e6i	0.154282	+	0.154282i
$638$	1.01960e7	+	1.08620e7i	0.991696	+	1.05647i
$639$	4.34983e6			0.421425
$640$	1.02953e7	+	1.17517e6i	0.993548	+	0.113410i
$641$	1.52939e7			1.47019			0.735093	−	0.677966i	$-0.237139\pi$
$641$	1.52939e7			1.47019			0.735093	+	0.677966i	$0.237139\pi$
$642$	−2.11821e7	−	2.25656e7i	−2.02830	−	2.16078i
$643$	−6.51059e6	−	6.51059e6i	−0.621001	−	0.621001i	0.324786	−	0.945788i	$-0.394708\pi$
$643$	−6.51059e6	−	6.51059e6i	−0.621001	−	0.621001i	−0.945788	+	0.324786i	$0.894708\pi$
$644$	−356903.	+	5.63710e6i	−0.0339106	+	0.535601i
$645$	2.72610e6	−	3.38668e6i	0.258014	−	0.320534i
$646$	476040.	−	1.50526e7i	0.0448809	−	1.41916i
$647$	−1.22615e7	−	1.22615e7i	−1.15155	−	1.15155i	−0.986241	−	0.165311i	$-0.947137\pi$
$647$	−1.22615e7	−	1.22615e7i	−1.15155	−	1.15155i	−0.165311	−	0.986241i	$-0.552863\pi$
$648$	−3.10650e6	+	2.56681e6i	−0.290626	+	0.240135i
$649$		−	8.98625e6i		−	0.837465i
$650$	−827248.	−	4.45301e6i	−0.0767985	−	0.413400i
$651$	6.57464e6			0.608022
$652$	1.04710e7	−	9.22401e6i	0.964646	−	0.849769i
$653$	−748828.	+	748828.i	−0.0687225	+	0.0687225i	−0.740633	−	0.671910i	$-0.765474\pi$
$653$	−748828.	+	748828.i	−0.0687225	+	0.0687225i	0.671910	+	0.740633i	$0.265474\pi$
$654$	566323.	−	1.79074e7i	0.0517749	−	1.63715i
$655$	1.03951e7	+	8.36750e6i	0.946725	+	0.762066i
$656$	−3.22379e6	−	409861.i	−0.292488	−	0.0371858i
$657$	101864.	−	101864.i	0.00920676	−	0.00920676i
$658$	−1.58481e7	+	1.48764e7i	−1.42696	+	1.33947i
$659$			1.12652e7i			1.01047i	0.862981	+	0.505236i	$0.168595\pi$
$659$			1.12652e7i			1.01047i	−0.862981	+	0.505236i	$0.831405\pi$
$660$	−2.62058e7	+	1.16477e6i	−2.34173	+	0.104083i
$661$			4.35068e6i			0.387305i	0.981070	+	0.193653i	$0.0620335\pi$
$661$			4.35068e6i			0.387305i	−0.981070	+	0.193653i	$0.937967\pi$
$662$	523046.	+	557209.i	0.0463869	+	0.0494167i
$663$	6.61952e6	−	6.61952e6i	0.584847	−	0.584847i
$664$	−1.10540e7	−	1.05155e6i	−0.972970	−	0.0925575i
$665$	1.68036e7	−	1.81587e6i	1.47349	−	0.159232i
$666$	3.93377e6	+	124405.i	0.343656	+	0.0108681i
$667$	3.64350e6	−	3.64350e6i	0.317106	−	0.317106i
$668$	1.18983e7	−	1.04814e7i	1.03168	−	0.908820i
$669$	4.10099e6			0.354261
$670$	596735.	+	512253.i	0.0513564	+	0.0440857i
$671$			1.57535e6i			0.135074i
$672$	−1.94596e7	+	1.41087e7i	−1.66230	+	1.20521i
$673$	1.26868e7	+	1.26868e7i	1.07973	+	1.07973i	0.996533	+	0.0831954i	$0.0265126\pi$
$673$	1.26868e7	+	1.26868e7i	1.07973	+	1.07973i	0.0831954	+	0.996533i	$0.473487\pi$
$674$	6.78119e6	+	214455.i	0.574984	+	0.0181839i
$675$	1.28756e7	+	8.25478e6i	1.08770	+	0.697342i
$676$	−9.76123e6	−	618016.i	−0.821557	−	0.0520155i
$677$	−9.11245e6	−	9.11245e6i	−0.764123	−	0.764123i	0.212942	−	0.977065i	$-0.431696\pi$
$677$	−9.11245e6	−	9.11245e6i	−0.764123	−	0.764123i	−0.977065	+	0.212942i	$0.931696\pi$
$678$	−1.24411e6	+	1.16784e6i	−0.103941	+	0.0975681i
$679$	−1.86594e7			−1.55318
$680$	9.93735e6	−	1.01951e7i	0.824135	−	0.845513i
$681$	−3.36830e7			−2.78319
$682$	−3.68997e6	+	3.46373e6i	−0.303782	+	0.285157i
$683$	−1.41156e7	−	1.41156e7i	−1.15784	−	1.15784i	−0.984939	−	0.172900i	$-0.944686\pi$
$683$	−1.41156e7	−	1.41156e7i	−1.15784	−	1.15784i	−0.172900	−	0.984939i	$-0.555314\pi$
$684$	−1.65082e6	+	2.60738e7i	−0.134915	+	2.13091i
$685$	6.58437e6	−	711536.i	0.536152	−	0.0579389i
$686$	7.30444e6	+	231003.i	0.592620	+	0.0187416i
$687$	1.48028e7	+	1.48028e7i	1.19661	+	1.19661i
$688$	1.87756e6	+	2.42450e6i	0.151224	+	0.195277i
$689$			4.49263e6i			0.360539i
$690$	689159.	+	9.04657e6i	0.0551057	+	0.723371i
$691$	−1.99531e6			−0.158970			−0.0794852	−	0.996836i	$-0.525328\pi$
$691$	−1.99531e6			−0.158970			−0.0794852	+	0.996836i	$0.525328\pi$
$692$	5.62480e6	+	6.38520e6i	0.446521	+	0.506885i
$693$	2.75236e7	−	2.75236e7i	2.17707	−	2.17707i
$694$	4.48951e6	+	141981.i	0.353835	+	0.0111900i
$695$	−4.77491e6	+	5.93194e6i	−0.374976	+	0.465838i
$696$	2.18281e7	+	2.07648e6i	1.70802	+	0.162482i
$697$	−3.15720e6	+	3.15720e6i	−0.246161	+	0.246161i
$698$	−7.67464e6	−	8.17592e6i	−0.596238	−	0.635182i
$699$		−	1.96407e7i		−	1.52042i
$700$	1.28789e7	+	9.45609e6i	0.993419	+	0.729401i
$701$			1.00792e7i			0.774699i	0.921933	+	0.387349i	$0.126609\pi$
$701$			1.00792e7i			0.774699i	−0.921933	+	0.387349i	$0.873391\pi$
$702$	−5.17187e6	+	4.85478e6i	−0.396100	+	0.371815i
$703$	2.15768e6	−	2.15768e6i	0.164664	−	0.164664i
$704$	3.48862e6	−	1.81703e7i	0.265290	−	1.38176i
$705$	−2.18927e7	+	2.71977e7i	−1.65893	+	2.06091i
$706$	−526851.	+	1.66593e7i	−0.0397810	+	1.25790i
$707$	2.01394e7	−	2.01394e7i	1.51530	−	1.51530i
$708$	−8.74263e6	−	9.92451e6i	−0.655479	−	0.744091i
$709$	1.12397e7			0.839732			0.419866	−	0.907586i	$-0.362077\pi$
$709$	1.12397e7			0.839732			0.419866	+	0.907586i	$0.362077\pi$
$710$	3.17892e6	−	242167.i	0.236665	−	0.0180289i
$711$		−	3.80235e7i		−	2.82084i
$712$	4.43585e6	+	5.36853e6i	0.327927	+	0.396877i
$713$	1.23775e6	+	1.23775e6i	0.0911820	+	0.0911820i
$714$	−1.04386e6	+	3.30076e7i	−0.0766299	+	2.42308i
$715$	−8.04033e6	+	868874.i	−0.588178	+	0.0635611i
$716$	3.39786e6	+	215130.i	0.247698	+	0.0156826i
$717$	−2.63533e7	−	2.63533e7i	−1.91442	−	1.91442i
$718$	8.23256e6	+	8.77027e6i	0.595969	+	0.634895i
$719$	988101.			0.0712819			0.0356410	−	0.999365i	$-0.488653\pi$
$719$	988101.			0.0712819			0.0356410	+	0.999365i	$0.488653\pi$
$720$	−1.77895e7	+	1.71325e7i	−1.27889	+	1.23166i
$721$	3.84705e6			0.275607
$722$	4.27672e6	+	4.55606e6i	0.305329	+	0.325272i
$723$	2.05527e7	+	2.05527e7i	1.46225	+	1.46225i
$724$	2.65845e7	+	1.68315e6i	1.88487	+	0.119337i
$725$	−3.11380e6	−	1.42389e7i	−0.220011	−	1.00608i
$726$	−732640.	+	2.31665e7i	−0.0515880	+	1.63124i
$727$	5.50085e6	+	5.50085e6i	0.386006	+	0.386006i	0.873260	−	0.487254i	$-0.162002\pi$
$727$	5.50085e6	+	5.50085e6i	0.386006	+	0.386006i	−0.487254	+	0.873260i	$0.662002\pi$
$728$	−5.71250e6	+	4.72007e6i	−0.399483	+	0.330080i
$729$			2.12817e7i			1.48316i
$730$	68772.6	−	80114.7i	0.00477648	−	0.00556423i
$731$	4.21319e6			0.291620
$732$	1.53265e6	+	1.73984e6i	0.105722	+	0.120014i
$733$	−1.53053e7	+	1.53053e7i	−1.05216	+	1.05216i	−0.0536011	+	0.998562i	$0.517070\pi$
$733$	−1.53053e7	+	1.53053e7i	−1.05216	+	1.05216i	−0.998562	+	0.0536011i	$0.982930\pi$
$734$	99374.0	−	3.14226e6i	0.00680820	−	0.215279i
$735$	−1.25881e7	+	1.36033e6i	−0.859495	+	0.0928808i
$736$	−6.31960e6	−	1.00736e6i	−0.430027	−	0.0685472i
$737$	992949.	−	992949.i	0.0673377	−	0.0673377i
$738$	5.64742e6	−	5.30117e6i	0.381689	−	0.358287i
$739$			3.32605e6i			0.224036i	0.993706	+	0.112018i	$0.0357314\pi$
$739$			3.32605e6i			0.224036i	−0.993706	+	0.112018i	$0.964269\pi$
$740$	2.88178e6	−	128086.i	0.193456	−	0.00859852i
$741$			1.25910e7i			0.842393i
$742$	−1.08468e7	−	1.15553e7i	−0.723255	−	0.770495i
$743$	−1.06346e6	+	1.06346e6i	−0.0706726	+	0.0706726i	−0.741560	−	0.670887i	$-0.765914\pi$
$743$	−1.06346e6	+	1.06346e6i	−0.0706726	+	0.0706726i	0.670887	+	0.741560i	$0.265914\pi$
$744$	−705411.	+	7.41532e6i	−0.0467207	+	0.491131i
$745$	−1.39378e7	−	1.12192e7i	−0.920030	−	0.740578i
$746$	2.43364e7	+	769640.i	1.60107	+	0.0506338i
$747$	1.87143e7	−	1.87143e7i	1.22707	−	1.22707i
$748$	−1.68036e7	−	1.90752e7i	−1.09812	−	1.24657i
$749$	3.36602e7			2.19236
$750$	2.25949e7	+	1.21703e7i	1.46676	+	0.790040i
$751$		−	1.17292e7i		−	0.758872i	−0.925218	−	0.379436i	$-0.876118\pi$
$751$		−	1.17292e7i		−	0.758872i	0.925218	−	0.379436i	$-0.123882\pi$
$752$	−1.50782e7	−	1.94707e7i	−0.972313	−	1.25556i
$753$	7.89023e6	+	7.89023e6i	0.507110	+	0.507110i
$754$	6.75654e6	+	213676.i	0.432809	+	0.0136876i
$755$	1.10960e7	−	1.37847e7i	0.708430	−	0.880093i
$756$	1.58115e6	−	2.49735e7i	0.100617	−	1.58918i
$757$	−1.45096e7	−	1.45096e7i	−0.920273	−	0.920273i	0.0767755	−	0.997048i	$-0.475538\pi$
$757$	−1.45096e7	−	1.45096e7i	−0.920273	−	0.920273i	−0.997048	+	0.0767755i	$0.975538\pi$
$758$	−2.14993e7	+	2.01811e7i	−1.35910	+	1.27577i
$759$	1.62000e7			1.02073
$760$	245158.	+	1.91470e7i	0.0153961	+	1.20245i
$761$	−2.07005e7			−1.29574			−0.647871	−	0.761750i	$-0.724341\pi$
$761$	−2.07005e7			−1.29574			−0.647871	+	0.761750i	$0.724341\pi$
$762$	1.89416e7	−	1.77803e7i	1.18176	−	1.10931i
$763$	1.37783e7	+	1.37783e7i	0.856807	+	0.856807i
$764$	−1.38479e7	−	876754.i	−0.858320	−	0.0543431i
$765$	3.64578e6	+	3.37371e7i	0.225236	+	2.08427i
$766$	−1.23415e7	−	390300.i	−0.759969	−	0.0240340i
$767$	−2.88328e6	−	2.88328e6i	−0.176969	−	0.176969i
$768$	−1.38249e7	−	2.34616e7i	−0.845782	−	1.43534i
$769$		−	2.00528e7i		−	1.22281i	−0.791317	−	0.611406i	$-0.790604\pi$
$769$		−	2.00528e7i		−	1.22281i	0.791317	−	0.611406i	$-0.209396\pi$
$770$	1.85824e7	−	2.16470e7i	1.12947	−	1.31574i
$771$	−2.56276e7			−1.55265
$772$	−3.86419e6	+	3.40402e6i	−0.233354	+	0.205565i
$773$	−1.94185e7	+	1.94185e7i	−1.16887	+	1.16887i	−0.186397	+	0.982475i	$0.559681\pi$
$773$	−1.94185e7	+	1.94185e7i	−1.16887	+	1.16887i	−0.982475	+	0.186397i	$0.940319\pi$
$774$	−7.30529e6	−	231030.i	−0.438314	−	0.0138617i
$775$	4.83716e6	−	1.05780e6i	0.289292	−	0.0632631i
$776$	2.00201e6	−	2.10453e7i	0.119347	−	1.25459i
$777$	−4.73137e6	+	4.73137e6i	−0.281148	+	0.281148i
$778$	−9.22444e6	−	9.82694e6i	−0.546375	−	0.582062i
$779$		−	6.00532e6i		−	0.354562i
$780$	−8.03451e6	+	8.78195e6i	−0.472850	+	0.516838i
$781$		−	5.69258e6i		−	0.333950i
$782$	−6.41056e6	+	6.01752e6i	−0.374869	+	0.351885i
$783$	−1.61414e7	+	1.61414e7i	−0.940886	+	0.940886i
$784$	1.12634e6	−	8.85929e6i	0.0654453	−	0.514765i
$785$	602904.	+	5.57912e6i	0.0349200	+	0.323141i
$786$	1.10851e6	−	3.50516e7i	0.0640003	−	2.02373i
$787$	6.19306e6	−	6.19306e6i	0.356425	−	0.356425i	−0.506068	−	0.862493i	$-0.668902\pi$
$787$	6.19306e6	−	6.19306e6i	0.356425	−	0.356425i	0.862493	+	0.506068i	$0.168902\pi$
$788$	−1.68818e7	+	1.48714e7i	−0.968511	+	0.853174i
$789$	−6.88760e6			−0.393891
$790$	−2.11687e6	−	2.77882e7i	−0.120678	−	1.58413i
$791$		−	1.85579e6i		−	0.105460i
$792$	2.80899e7	+	3.39961e7i	1.59125	+	1.92582i
$793$	505459.	+	505459.i	0.0285432	+	0.0285432i
$794$	666504.	−	2.10752e7i	0.0375190	−	1.18637i
$795$	−1.98305e7	−	1.59626e7i	−1.11280	−	0.895747i
$796$	685934.	−	1.08340e7i	0.0383707	−	0.606045i
$797$	2.08333e7	+	2.08333e7i	1.16175	+	1.16175i	0.984093	+	0.177653i	$0.0568505\pi$
$797$	2.08333e7	+	2.08333e7i	1.16175	+	1.16175i	0.177653	+	0.984093i	$0.443150\pi$
$798$	−3.03991e7	−	3.23847e7i	−1.68987	−	1.80025i
$799$	−3.38352e7			−1.87500
$800$	−1.20470e7	+	1.35111e7i	−0.665510	+	0.746389i
$801$	−1.65987e7			−0.914096
$802$	2.80823e6	+	2.99165e6i	0.154169	+	0.164238i
$803$	−133308.	−	133308.i	−0.00729573	−	0.00729573i
$804$	130593.	−	2.06265e6i	0.00712494	−	0.112535i
$805$	−7.68649e6	−	6.18724e6i	−0.418060	−	0.336517i
$806$	−72588.8	+	2.29530e6i	−0.00393579	+	0.124452i
$807$	2.96495e7	+	2.96495e7i	1.60263	+	1.60263i
$808$	2.05537e7	+	2.48753e7i	1.10755	+	1.34042i
$809$			2.04829e7i			1.10032i	0.835058	+	0.550161i	$0.185434\pi$
$809$			2.04829e7i			1.10032i	−0.835058	+	0.550161i	$0.814566\pi$
$810$	−534726.	−	7.01934e6i	−0.0286364	−	0.375910i
$811$	7.29990e6			0.389731			0.194866	−	0.980830i	$-0.437573\pi$
$811$	7.29990e6			0.389731			0.194866	+	0.980830i	$0.437573\pi$
$812$	−1.78940e7	+	1.57631e7i	−0.952397	+	0.838979i
$813$	−1.81115e7	+	1.81115e7i	−0.961011	+	0.961011i
$814$	162808.	−	5.14809e6i	0.00861223	−	0.272324i
$815$	2.61906e6	+	2.42361e7i	0.138118	+	1.27811i
$816$	−3.71161e7	−	4.71881e6i	−1.95136	−	0.248089i
$817$	−4.00696e6	+	4.00696e6i	−0.210020	+	0.210020i
$818$	6.34774e6	−	5.95856e6i	0.331693	−	0.311356i
$819$		−	1.76622e7i		−	0.920098i
$820$	3.83209e6	−	4.18858e6i	0.199022	−	0.217537i
$821$		−	1.41337e7i		−	0.731810i	−0.930652	−	0.365905i	$-0.880759\pi$
$821$		−	1.41337e7i		−	0.731810i	0.930652	−	0.365905i	$-0.119241\pi$
$822$	−1.19117e7	−	1.26897e7i	−0.614886	−	0.655047i
$823$	1.37689e7	−	1.37689e7i	0.708597	−	0.708597i	−0.257643	−	0.966240i	$-0.582946\pi$
$823$	1.37689e7	−	1.37689e7i	0.708597	−	0.708597i	0.966240	+	0.257643i	$0.0829458\pi$
$824$	−412760.	+	4.33896e6i	−0.0211777	+	0.222622i
$825$	2.47326e7	−	3.85773e7i	1.26513	−	1.97332i
$826$	1.43772e7	+	454678.i	0.733202	+	0.0231875i
$827$	−1.07298e7	+	1.07298e7i	−0.545543	+	0.545543i	−0.925148	−	0.379605i	$-0.876060\pi$
$827$	−1.07298e7	+	1.07298e7i	−0.545543	+	0.545543i	0.379605	+	0.925148i	$0.376060\pi$
$828$	1.14453e7	−	1.00823e7i	0.580165	−	0.511075i
$829$	3.03082e7			1.53170			0.765851	−	0.643018i	$-0.222318\pi$
$829$	3.03082e7			1.53170			0.765851	+	0.643018i	$0.222318\pi$
$830$	1.26348e7	−	1.47185e7i	0.636608	−	0.741599i
$831$			4.23131e7i			2.12555i
$832$	−4.71070e6	−	6.94937e6i	−0.235927	−	0.348046i
$833$	−8.67628e6	−	8.67628e6i	−0.433233	−	0.433233i
$834$	2.00022e7	+	632569.i	0.995777	+	0.0314915i
$835$	2.97608e6	+	2.75399e7i	0.147716	+	1.36693i
$836$	3.41226e7	+	2.16041e6i	1.68860	+	0.106911i
$837$	−5.48348e6	−	5.48348e6i	−0.270547	−	0.270547i
$838$	1.19688e7	−	1.12350e7i	0.588762	−	0.552664i
$839$	1.88656e7			0.925263			0.462632	−	0.886551i	$-0.346905\pi$
$839$	1.88656e7			0.925263			0.462632	+	0.886551i	$0.346905\pi$
$840$	−537584.	−	4.19858e7i	−0.0262874	−	2.05307i
$841$	1.24288e6			0.0605955
$842$	−1.65927e7	+	1.55754e7i	−0.806562	+	0.757111i
$843$	3.83030e7	+	3.83030e7i	1.85637	+	1.85637i
$844$	−512224.	+	8.09030e6i	−0.0247516	+	0.390938i
$845$	1.07139e7	−	1.33100e7i	0.516183	−	0.641262i
$846$	5.86672e7	+	1.85535e6i	2.81818	+	0.0891251i
$847$	−1.78247e7	−	1.78247e7i	−0.853714	−	0.853714i
$848$	1.41966e7	−	1.09939e7i	0.677944	−	0.525006i
$849$		−	4.30989e7i		−	2.05209i
$850$	4.54263e6	+	2.44526e7i	0.215655	+	1.16085i
$851$	−1.78147e6			−0.0843246
$852$	−5.53826e6	−	6.28695e6i	−0.261381	−	0.296716i
$853$	−2.97901e6	+	2.97901e6i	−0.140184	+	0.140184i	−0.773716	−	0.633532i	$-0.781604\pi$
$853$	−2.97901e6	+	2.97901e6i	−0.140184	+	0.140184i	0.633532	+	0.773716i	$0.281604\pi$
$854$	−2.52042e6	−	79708.4i	−0.118258	−	0.00373989i
$855$	−3.55531e7	−	2.86184e7i	−1.66327	−	1.33885i
$856$	−3.61149e6	+	3.79642e7i	−0.168462	+	1.77088i
$857$	1.86612e7	−	1.86612e7i	0.867934	−	0.867934i	−0.124309	−	0.992244i	$-0.539671\pi$
$857$	1.86612e7	−	1.86612e7i	0.867934	−	0.867934i	0.992244	+	0.124309i	$0.0396714\pi$
$858$	1.45457e7	+	1.54957e7i	0.674552	+	0.718611i
$859$			9.47597e6i			0.438168i	0.975706	+	0.219084i	$0.0703069\pi$
$859$			9.47597e6i			0.438168i	−0.975706	+	0.219084i	$0.929693\pi$
$860$	−5.35168e6	+	237866.i	−0.246742	+	0.0109669i
$861$			1.31685e7i			0.605381i
$862$	−1.58278e7	+	1.48574e7i	−0.725524	+	0.681041i
$863$	1.10084e7	−	1.10084e7i	0.503150	−	0.503150i	−0.409265	−	0.912415i	$-0.634215\pi$
$863$	1.10084e7	−	1.10084e7i	0.503150	−	0.503150i	0.912415	+	0.409265i	$0.134215\pi$
$864$	2.79971e7	+	4.46280e6i	1.27593	+	0.203387i
$865$	−1.47792e7	+	1.59710e6i	−0.671600	+	0.0725760i
$866$	−937262.	+	2.96368e7i	−0.0424684	+	1.34288i
$867$	−1.02755e7	+	1.02755e7i	−0.464254	+	0.464254i
$868$	−5.35496e6	−	6.07887e6i	−0.241244	−	0.273857i
$869$	−4.97611e7			−2.23532
$870$	−2.49496e7	+	2.90643e7i	−1.11754	+	1.30185i
$871$		−	637184.i		−	0.0284590i
$872$	−1.70184e7	+	1.40617e7i	−0.757925	+	0.626250i
$873$	3.56293e7	+	3.56293e7i	1.58224	+	1.58224i
$874$	373800.	−	1.18198e7i	0.0165524	−	0.523395i
$875$	−2.64688e7	+	8.85794e6i	−1.16873	+	0.391122i
$876$	−276922.	−	17532.8i	−0.0121926	−	0.000771955i
$877$	2.89957e6	+	2.89957e6i	0.127302	+	0.127302i	0.767887	−	0.640585i	$-0.221308\pi$
$877$	2.89957e6	+	2.89957e6i	0.127302	+	0.127302i	−0.640585	+	0.767887i	$0.721308\pi$
$878$	−8.57199e6	−	9.13188e6i	−0.375271	−	0.399783i
$879$	7.25944e6			0.316906
$880$	2.24212e7	+	2.32810e7i	0.976004	+	1.01343i
$881$	1.40093e7			0.608101			0.304050	−	0.952656i	$-0.401661\pi$
$881$	1.40093e7			0.608101			0.304050	+	0.952656i	$0.401661\pi$
$882$	1.45681e7	+	1.55197e7i	0.630569	+	0.671755i
$883$	−1.69111e7	−	1.69111e7i	−0.729910	−	0.729910i	0.240692	−	0.970602i	$-0.422626\pi$
$883$	−1.69111e7	−	1.69111e7i	−0.729910	−	0.729910i	−0.970602	+	0.240692i	$0.922626\pi$
$884$	−1.15119e7	−	728854.i	−0.495467	−	0.0313697i
$885$	2.29713e7	−	2.48238e6i	0.985887	−	0.106539i
$886$	534617.	−	1.69049e7i	0.0228801	−	0.723482i
$887$	−2.40592e7	−	2.40592e7i	−1.02677	−	1.02677i	−0.999632	−	0.0271360i	$-0.991361\pi$
$887$	−2.40592e7	−	2.40592e7i	−1.02677	−	1.02677i	−0.0271360	−	0.999632i	$-0.508639\pi$
$888$	−4.82872e6	−	5.84400e6i	−0.205494	−	0.248701i
$889$			2.82544e7i			1.19904i
$890$	−1.21305e7	+	924093.i	−0.513340	+	0.0391057i
$891$	−1.25697e7			−0.530435
$892$	−3.34020e6	−	3.79175e6i	−0.140560	−	0.159561i
$893$	3.21790e7	−	3.21790e7i	1.35034	−	1.35034i
$894$	−1.48629e6	+	4.69974e7i	−0.0621957	+	1.96666i
$895$	−3.72946e6	+	4.63316e6i	−0.155628	+	0.193339i
$896$	2.88944e7	+	6.50083e6i	1.20238	+	0.270520i
$897$	5.19783e6	−	5.19783e6i	0.215695	−	0.215695i
$898$	−1.89147e7	+	1.77551e7i	−0.782726	+	0.734736i
$899$			7.39017e6i			0.304969i
$900$	−6.53565e6	−	4.26477e7i	−0.268957	−	1.75505i
$901$		−	2.46702e7i		−	1.01242i
$902$	−6.93760e6	−	7.39073e6i	−0.283918	−	0.302462i
$903$	8.78650e6	−	8.78650e6i	0.358589	−	0.358589i
$904$	2.09309e6	+	199113.i	0.0851856	+	0.00810360i
$905$	−2.91789e7	+	3.62494e7i	−1.18426	+	1.47123i
$906$	−4.64811e7	−	1.46997e6i	−1.88129	−	0.0594959i
$907$	5.04627e6	−	5.04627e6i	0.203682	−	0.203682i	−0.597894	−	0.801575i	$-0.703996\pi$
$907$	5.04627e6	−	5.04627e6i	0.203682	−	0.203682i	0.801575	+	0.597894i	$0.203996\pi$
$908$	2.74344e7	+	3.11431e7i	1.10428	+	1.25357i
$909$	−7.69106e7			−3.08729
$910$	−983301.	−	1.29078e7i	−0.0393625	−	0.516711i
$911$			3.08614e7i			1.23202i	0.787737	+	0.616012i	$0.211253\pi$
$911$			3.08614e7i			1.23202i	−0.787737	+	0.616012i	$0.788747\pi$
$912$	3.97872e7	−	3.08115e7i	1.58400	−	1.22667i
$913$	−2.44912e7	−	2.44912e7i	−0.972373	−	0.972373i
$914$	−2.06330e7	−	652519.i	−0.816953	−	0.0258361i
$915$	−4.02703e6	+	435179.i	−0.159013	+	0.0171836i
$916$	1.62989e6	−	2.57432e7i	0.0641828	−	1.01373i
$917$	2.69693e7	+	2.69693e7i	1.05912	+	1.05912i
$918$	2.84001e7	−	2.66588e7i	1.11228	−	1.04408i
$919$	1.46484e7			0.572141			0.286070	−	0.958209i	$-0.407651\pi$
$919$	1.46484e7			0.572141			0.286070	+	0.958209i	$0.407651\pi$
$920$	7.80308e6	−	8.00550e6i	0.303946	−	0.311831i
$921$	3.63426e7			1.41178
$922$	−1.81400e7	+	1.70278e7i	−0.702765	+	0.659678i
$923$	−1.82649e6	−	1.82649e6i	−0.0705688	−	0.0705688i
$924$	−7.48243e7	−	4.73737e6i	−2.88312	−	0.182540i
$925$	−2.71978e6	+	4.24225e6i	−0.104515	+	0.163020i
$926$	−4.83904e7	−	1.53035e6i	−1.85452	−	0.0586492i
$927$	−7.34578e6	−	7.34578e6i	−0.280762	−	0.280762i
$928$	−1.58588e7	−	2.18734e7i	−0.604505	−	0.833768i
$929$			1.85132e7i			0.703787i	0.936040	+	0.351893i	$0.114462\pi$
$929$			1.85132e7i			0.703787i	−0.936040	+	0.351893i	$0.885538\pi$
$930$	−9.87357e6	−	8.47574e6i	−0.374341	−	0.321344i
$931$	1.65032e7			0.624013
$932$	−1.81597e7	+	1.59971e7i	−0.684807	+	0.603255i
$933$	3.22718e7	−	3.22718e7i	1.21372	−	1.21372i
$934$	1.48590e7	+	469915.i	0.557342	+	0.0176259i
$935$	4.41515e7	−	4.77120e6i	1.65164	−	0.178484i
$936$	1.99206e7	+	1.89502e6i	0.743211	+	0.0707008i
$937$	−8.18860e6	+	8.18860e6i	−0.304692	+	0.304692i	−0.842846	−	0.538154i	$-0.819122\pi$
$937$	−8.18860e6	+	8.18860e6i	−0.304692	+	0.304692i	0.538154	+	0.842846i	$0.319122\pi$
$938$	1.53839e6	+	1.63887e6i	0.0570898	+	0.0608187i
$939$		−	2.30445e7i		−	0.852910i
$940$	4.29781e7	−	1.91025e6i	1.58645	−	0.0705131i
$941$			1.27802e7i			0.470503i	0.971935	+	0.235251i	$0.0755913\pi$
$941$			1.27802e7i			0.470503i	−0.971935	+	0.235251i	$0.924409\pi$
$942$	1.07523e7	−	1.00931e7i	0.394799	−	0.370594i
$943$	−2.47912e6	+	2.47912e6i	−0.0907859	+	0.0907859i
$944$	−2.05538e6	+	1.61668e7i	−0.0750693	+	0.590463i
$945$	3.40527e7	+	2.74107e7i	1.24043	+	0.998482i
$946$	−302347.	+	9.56037e6i	−0.0109844	+	0.347334i
$947$	1.83592e7	−	1.83592e7i	0.665239	−	0.665239i	−0.291371	−	0.956610i	$-0.594111\pi$
$947$	1.83592e7	−	1.83592e7i	0.665239	−	0.665239i	0.956610	+	0.291371i	$0.0941114\pi$
$948$	−5.49567e7	+	4.84121e7i	−1.98609	+	1.74958i
$949$	−85545.2			−0.00308340
$950$	−2.75760e7	−	1.89354e7i	−0.991338	−	0.680716i
$951$		−	3.39071e6i		−	0.121574i
$952$	3.13688e7	−	2.59191e7i	1.12177	−	0.926887i
$953$	−2.05931e6	−	2.05931e6i	−0.0734497	−	0.0734497i	0.669428	−	0.742877i	$-0.266539\pi$
$953$	−2.05931e6	−	2.05931e6i	−0.0734497	−	0.0734497i	−0.742877	+	0.669428i	$0.766539\pi$
$954$	−1.35279e6	+	4.27758e7i	−0.0481236	+	1.52169i
$955$	1.51993e7	−	1.88823e7i	0.539281	−	0.669957i
$956$	−2.90168e6	+	4.58304e7i	−0.102684	+	1.62184i
$957$	4.83621e7	+	4.83621e7i	1.70697	+	1.70697i
$958$	2.79347e7	+	2.97592e7i	0.983399	+	1.04763i
$959$	1.89287e7			0.664622
$960$	4.74120e7	+	3.89844e6i	1.66039	+	0.136525i
$961$	2.61186e7			0.912308
$962$	−1.59955e6	−	1.70403e6i	−0.0557263	−	0.0593661i
$963$	−6.42728e7	−	6.42728e7i	−2.23338	−	2.23338i
$964$	2.26299e6	−	3.57427e7i	0.0784314	−	1.23878i
$965$	−966535.	−	8.94407e6i	−0.0334118	−	0.309184i
$966$	−819671.	+	2.59185e7i	−0.0282616	+	0.893648i
$967$	−2.60853e7	−	2.60853e7i	−0.897078	−	0.897078i	0.0980983	−	0.995177i	$-0.468724\pi$
$967$	−2.60853e7	−	2.60853e7i	−0.897078	−	0.897078i	−0.995177	+	0.0980983i	$0.968724\pi$
$968$	2.20163e7	−	1.81914e7i	0.755189	−	0.623990i
$969$		−	6.91403e7i		−	2.36550i
$970$	2.80220e7	+	2.40548e7i	0.956246	+	0.820867i
$971$	−1.27949e7			−0.435500			−0.217750	−	0.976005i	$-0.569872\pi$
$971$	−1.27949e7			−0.435500			−0.217750	+	0.976005i	$0.569872\pi$
$972$	1.46754e7	−	1.29277e7i	0.498222	−	0.438890i
$973$	−1.53900e7	+	1.53900e7i	−0.521142	+	0.521142i
$974$	364713.	−	1.15324e7i	0.0123184	−	0.389514i
$975$	−4.44215e6	−	2.03133e7i	−0.149652	−	0.684334i
$976$	360323.	−	2.83415e6i	0.0121079	−	0.0952354i
$977$	−2.24653e6	+	2.24653e6i	−0.0752967	+	0.0752967i	−0.743752	−	0.668455i	$-0.766956\pi$
$977$	−2.24653e6	+	2.24653e6i	−0.0752967	+	0.0752967i	0.668455	+	0.743752i	$0.266956\pi$
$978$	4.67090e7	−	4.38452e7i	1.56154	−	1.46580i
$979$			2.17225e7i			0.724358i
$980$	1.15106e7	+	1.05309e7i	0.382854	+	0.350269i
$981$		−	5.26181e7i		−	1.74567i
$982$	3.37502e7	+	3.59546e7i	1.11686	+	1.18981i
$983$	1.08719e6	−	1.08719e6i	0.0358857	−	0.0358857i	−0.688936	−	0.724822i	$-0.741922\pi$
$983$	1.08719e6	−	1.08719e6i	0.0358857	−	0.0358857i	0.724822	+	0.688936i	$0.241922\pi$
$984$	−1.48523e7	−	1.41288e6i	−0.488998	−	0.0465178i
$985$	−4.22259e6	−	3.90748e7i	−0.138672	−	1.28323i
$986$	−3.71019e7	−	1.17335e6i	−1.21536	−	0.0384356i
$987$	−7.05624e7	+	7.05624e7i	−2.30558	+	2.30558i
$988$	1.16416e7	−	1.02552e7i	0.379419	−	0.334235i
$989$	3.30831e6			0.107551
$990$	−7.68163e7	+	5.85179e6i	−2.49095	+	0.189758i
$991$			3.55052e7i			1.14844i	0.818701	+	0.574220i	$0.194695\pi$
$991$			3.55052e7i			1.14844i	−0.818701	+	0.574220i	$0.805305\pi$
$992$	7.43070e6	−	5.38746e6i	0.239746	−	0.173822i
$993$	2.48093e6	+	2.48093e6i	0.0798440	+	0.0798440i
$994$	9.10761e6	+	288028.i	0.292374	+	0.00924632i
$995$	1.47727e7	+	1.18913e7i	0.473045	+	0.380777i
$996$	−5.08755e7	−	3.22110e6i	−1.62503	−	0.102886i
$997$	−2.35703e7	−	2.35703e7i	−0.750979	−	0.750979i	0.223683	−	0.974662i	$-0.428192\pi$
$997$	−2.35703e7	−	2.35703e7i	−0.750979	−	0.750979i	−0.974662	+	0.223683i	$0.928192\pi$
$998$	−9.55118e6	+	8.96559e6i	−0.303550	+	0.284939i
$999$	7.89226e6			0.250200

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	40.6.k.a.3.8	✓	56
4.3	odd	2		160.6.o.a.143.28		56
5.2	odd	4	inner	40.6.k.a.27.22	yes	56
8.3	odd	2	inner	40.6.k.a.3.22	yes	56
8.5	even	2		160.6.o.a.143.27		56
20.7	even	4		160.6.o.a.47.27		56
40.27	even	4	inner	40.6.k.a.27.8	yes	56
40.37	odd	4		160.6.o.a.47.28		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
40.6.k.a.3.8	✓	56	1.1	even	1	trivial
40.6.k.a.3.22	yes	56	8.3	odd	2	inner
40.6.k.a.27.8	yes	56	40.27	even	4	inner
40.6.k.a.27.22	yes	56	5.2	odd	4	inner
160.6.o.a.47.27		56	20.7	even	4
160.6.o.a.47.28		56	40.37	odd	4
160.6.o.a.143.27		56	8.5	even	2
160.6.o.a.143.28		56	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 40 = 2^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	40.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.87156 - 4.12444i) q^{2} +(-18.3638 - 18.3638i) q^{3} +(-2.02198 + 31.9361i) q^{4} +(-43.5466 - 35.0528i) q^{5} +(-4.64371 + 146.837i) q^{6} +(-112.979 - 112.979i) q^{7} +(139.546 - 115.303i) q^{8} +431.456i q^{9} +O(q^{10})\)	\(q+(-3.87156 - 4.12444i) q^{2} +(-18.3638 - 18.3638i) q^{3} +(-2.02198 + 31.9361i) q^{4} +(-43.5466 - 35.0528i) q^{5} +(-4.64371 + 146.837i) q^{6} +(-112.979 - 112.979i) q^{7} +(139.546 - 115.303i) q^{8} +431.456i q^{9} +(24.0203 + 315.314i) q^{10} +564.643 q^{11} +(623.597 - 549.335i) q^{12} +(181.168 - 181.168i) q^{13} +(-28.5693 + 903.377i) q^{14} +(155.978 + 1443.38i) q^{15} +(-1015.82 - 129.148i) q^{16} +(-994.839 + 994.839i) q^{17} +(1779.51 - 1670.41i) q^{18} -1892.29i q^{19} +(1207.50 - 1319.83i) q^{20} +4149.42i q^{21} +(-2186.05 - 2328.83i) q^{22} +(-781.175 + 781.175i) q^{23} +(-4680.00 - 445.202i) q^{24} +(667.606 + 3052.86i) q^{25} +(-1448.62 - 45.8126i) q^{26} +(3460.76 - 3460.76i) q^{27} +(3836.53 - 3379.65i) q^{28} -4664.12 q^{29} +(5349.25 - 6231.46i) q^{30} -1584.47i q^{31} +(3400.16 + 4689.70i) q^{32} +(-10369.0 - 10369.0i) q^{33} +(7954.74 + 251.569i) q^{34} +(959.616 + 8880.04i) q^{35} +(-13779.0 - 872.394i) q^{36} +(1140.25 + 1140.25i) q^{37} +(-7804.62 + 7326.11i) q^{38} -6653.86 q^{39} +(-10118.5 + 129.556i) q^{40} +3173.58 q^{41} +(17114.0 - 16064.8i) q^{42} +(-2117.52 - 2117.52i) q^{43} +(-1141.69 + 18032.5i) q^{44} +(15123.7 - 18788.4i) q^{45} +(6246.28 + 197.539i) q^{46} +(17005.4 + 17005.4i) q^{47} +(16282.7 + 21026.0i) q^{48} +8721.29i q^{49} +(10006.6 - 14572.8i) q^{50} +36538.0 q^{51} +(5419.48 + 6152.11i) q^{52} +(-12399.1 + 12399.1i) q^{53} +(-27672.2 - 875.135i) q^{54} +(-24588.2 - 19792.3i) q^{55} +(-28792.5 - 2739.00i) q^{56} +(-34749.5 + 34749.5i) q^{57} +(18057.4 + 19236.9i) q^{58} -15914.9i q^{59} +(-46411.2 + 2062.84i) q^{60} +2790.00i q^{61} +(-6535.05 + 6134.38i) q^{62} +(48745.2 - 48745.2i) q^{63} +(6178.45 - 32180.3i) q^{64} +(-14239.7 + 1538.80i) q^{65} +(-2622.04 + 82910.3i) q^{66} +(1758.54 - 1758.54i) q^{67} +(-29759.7 - 33782.8i) q^{68} +28690.6 q^{69} +(32909.9 - 38337.5i) q^{70} -10081.7i q^{71} +(49748.1 + 60208.2i) q^{72} +(-236.094 - 236.094i) q^{73} +(288.339 - 9117.43i) q^{74} +(43802.2 - 68321.7i) q^{75} +(60432.2 + 3826.16i) q^{76} +(-63792.5 - 63792.5i) q^{77} +(25760.8 + 27443.4i) q^{78} -88128.5 q^{79} +(39708.6 + 41231.4i) q^{80} -22261.4 q^{81} +(-12286.7 - 13089.2i) q^{82} +(-43374.7 - 43374.7i) q^{83} +(-132516. - 8390.04i) q^{84} +(78193.7 - 8449.95i) q^{85} +(-535.466 + 16931.7i) q^{86} +(85650.8 + 85650.8i) q^{87} +(78793.9 - 65105.0i) q^{88} +38471.3i q^{89} +(-136044. + 10363.7i) q^{90} -40936.2 q^{91} +(-23368.1 - 26527.2i) q^{92} +(-29096.9 + 29096.9i) q^{93} +(4300.21 - 135975. i) q^{94} +(-66329.9 + 82402.6i) q^{95} +(23680.9 - 148560. i) q^{96} +(82579.2 - 82579.2i) q^{97} +(35970.4 - 33765.0i) q^{98} +243618. i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 2 q^{2} - 4 q^{3} + 176 q^{6} + 244 q^{8}+O(q^{10}) \) 56 * q - 2 * q^2 - 4 * q^3 + 176 * q^6 + 244 * q^8	\( 56 q - 2 q^{2} - 4 q^{3} + 176 q^{6} + 244 q^{8} - 570 q^{10} - 8 q^{11} - 308 q^{12} + 456 q^{16} - 408 q^{17} + 3370 q^{18} + 1360 q^{20} - 3148 q^{22} - 3120 q^{25} - 5084 q^{26} + 968 q^{27} - 10020 q^{28} + 21100 q^{30} + 7968 q^{32} - 976 q^{33} - 4780 q^{35} + 23132 q^{36} - 49524 q^{38} - 58980 q^{40} - 8 q^{41} + 42060 q^{42} + 1308 q^{43} + 42416 q^{46} + 93776 q^{48} - 94010 q^{50} + 20872 q^{51} - 67180 q^{52} - 43384 q^{56} + 968 q^{57} + 86100 q^{58} + 118180 q^{60} + 6240 q^{62} + 17680 q^{65} - 41128 q^{66} + 89252 q^{67} - 158164 q^{68} + 116980 q^{70} + 1180 q^{72} - 25184 q^{73} - 127740 q^{75} + 41592 q^{76} - 161440 q^{78} - 167360 q^{80} - 67792 q^{81} + 23412 q^{82} - 126444 q^{83} - 192704 q^{86} + 100176 q^{88} - 82330 q^{90} + 329432 q^{91} + 226020 q^{92} + 358176 q^{96} + 212576 q^{97} + 65834 q^{98}+O(q^{100}) \) 56 * q - 2 * q^2 - 4 * q^3 + 176 * q^6 + 244 * q^8 - 570 * q^10 - 8 * q^11 - 308 * q^12 + 456 * q^16 - 408 * q^17 + 3370 * q^18 + 1360 * q^20 - 3148 * q^22 - 3120 * q^25 - 5084 * q^26 + 968 * q^27 - 10020 * q^28 + 21100 * q^30 + 7968 * q^32 - 976 * q^33 - 4780 * q^35 + 23132 * q^36 - 49524 * q^38 - 58980 * q^40 - 8 * q^41 + 42060 * q^42 + 1308 * q^43 + 42416 * q^46 + 93776 * q^48 - 94010 * q^50 + 20872 * q^51 - 67180 * q^52 - 43384 * q^56 + 968 * q^57 + 86100 * q^58 + 118180 * q^60 + 6240 * q^62 + 17680 * q^65 - 41128 * q^66 + 89252 * q^67 - 158164 * q^68 + 116980 * q^70 + 1180 * q^72 - 25184 * q^73 - 127740 * q^75 + 41592 * q^76 - 161440 * q^78 - 167360 * q^80 - 67792 * q^81 + 23412 * q^82 - 126444 * q^83 - 192704 * q^86 + 100176 * q^88 - 82330 * q^90 + 329432 * q^91 + 226020 * q^92 + 358176 * q^96 + 212576 * q^97 + 65834 * q^98

Introduction

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