LMFDB - Embedded newform 51.6.h.a.19.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [51,6,Mod(19,51)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(51, base_ring=CyclotomicField(8)) chi = DirichletCharacter(H, H._module([0, 7])) N = Newforms(chi, 6, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("51.19"); S:= CuspForms(chi, 6); N := Newforms(S);

Level:	$ N $	$=$	$ 51 = 3 \cdot 17 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	51.h (of order $8$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$8.17957481046$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			19.7
Character	$\chi$	$=$	51.19
Dual form			51.6.h.a.43.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.06332 - 1.06332i) q^{2} +(-8.31492 + 3.44415i) q^{3} -29.7387i q^{4} +(29.0694 + 70.1798i) q^{5} +(12.5037 + 5.17918i) q^{6} +(48.3729 - 116.783i) q^{7} +(-65.6480 + 65.6480i) q^{8} +(57.2756 - 57.2756i) q^{9} +(43.7135 - 105.534i) q^{10} +(-721.222 - 298.740i) q^{11} +(102.425 + 247.275i) q^{12} -565.587i q^{13} +(-175.613 + 72.7413i) q^{14} +(-483.420 - 483.420i) q^{15} -812.029 q^{16} +(999.358 - 648.954i) q^{17} -121.805 q^{18} +(-1387.06 - 1387.06i) q^{19} +(2087.06 - 864.487i) q^{20} +1137.64i q^{21} +(449.234 + 1084.55i) q^{22} +(-1114.32 - 461.567i) q^{23} +(319.756 - 771.959i) q^{24} +(-1870.47 + 1870.47i) q^{25} +(-601.399 + 601.399i) q^{26} +(-278.976 + 673.508i) q^{27} +(-3472.96 - 1438.55i) q^{28} +(451.671 + 1090.43i) q^{29} +1028.06i q^{30} +(-1248.11 + 516.985i) q^{31} +(2964.18 + 2964.18i) q^{32} +7025.81 q^{33} +(-1752.68 - 372.591i) q^{34} +9601.95 q^{35} +(-1703.30 - 1703.30i) q^{36} +(13529.8 - 5604.21i) q^{37} +2949.78i q^{38} +(1947.97 + 4702.80i) q^{39} +(-6515.52 - 2698.81i) q^{40} +(3202.98 - 7732.67i) q^{41} +(1209.68 - 1209.68i) q^{42} +(-12269.0 + 12269.0i) q^{43} +(-8884.14 + 21448.2i) q^{44} +(5684.57 + 2354.62i) q^{45} +(694.086 + 1675.67i) q^{46} +13520.5i q^{47} +(6751.95 - 2796.75i) q^{48} +(586.125 + 586.125i) q^{49} +3977.81 q^{50} +(-6074.48 + 8837.94i) q^{51} -16819.8 q^{52} +(-16507.2 - 16507.2i) q^{53} +(1012.80 - 419.514i) q^{54} -59299.4i q^{55} +(4490.95 + 10842.1i) q^{56} +(16310.5 + 6756.04i) q^{57} +(679.206 - 1639.75i) q^{58} +(15474.8 - 15474.8i) q^{59} +(-14376.3 + 14376.3i) q^{60} +(4601.19 - 11108.3i) q^{61} +(1876.86 + 777.423i) q^{62} +(-3918.21 - 9459.38i) q^{63} +19681.2i q^{64} +(39692.8 - 16441.3i) q^{65} +(-7470.68 - 7470.68i) q^{66} -61678.1 q^{67} +(-19299.0 - 29719.6i) q^{68} +10855.2 q^{69} +(-10209.9 - 10209.9i) q^{70} +(20188.3 - 8362.28i) q^{71} +7520.06i q^{72} +(-10796.4 - 26064.9i) q^{73} +(-20345.5 - 8427.40i) q^{74} +(9110.61 - 21995.0i) q^{75} +(-41249.4 + 41249.4i) q^{76} +(-69775.2 + 69775.2i) q^{77} +(2929.28 - 7071.90i) q^{78} +(71825.3 + 29751.0i) q^{79} +(-23605.2 - 56988.0i) q^{80} -6561.00i q^{81} +(-11628.1 + 4816.51i) q^{82} +(4901.56 + 4901.56i) q^{83} +33831.9 q^{84} +(74594.2 + 51270.0i) q^{85} +26091.6 q^{86} +(-7511.22 - 7511.22i) q^{87} +(66958.5 - 27735.1i) q^{88} +115238. i q^{89} +(-3540.79 - 8548.23i) q^{90} +(-66050.6 - 27359.1i) q^{91} +(-13726.4 + 33138.4i) q^{92} +(8597.38 - 8597.38i) q^{93} +(14376.6 - 14376.6i) q^{94} +(57022.6 - 137665. i) q^{95} +(-34856.0 - 14437.8i) q^{96} +(11124.7 + 26857.4i) q^{97} -1246.48i q^{98} +(-58419.0 + 24197.9i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 88 q^{5} + 360 q^{6} + 1280 q^{10} - 632 q^{11} - 4256 q^{14} - 8192 q^{16} + 6248 q^{17} + 4152 q^{19} - 16384 q^{20} - 19592 q^{22} - 3608 q^{23} + 10440 q^{24} + 30384 q^{25} - 19936 q^{26} + 13624 q^{28}+ \cdots - 51192 q^{99}+O(q^{100}) $ 56 * q - 88 * q^5 + 360 * q^6 + 1280 * q^10 - 632 * q^11 - 4256 * q^14 - 8192 * q^16 + 6248 * q^17 + 4152 * q^19 - 16384 * q^20 - 19592 * q^22 - 3608 * q^23 + 10440 * q^24 + 30384 * q^25 - 19936 * q^26 + 13624 * q^28 - 23424 * q^29 + 2728 * q^31 + 67200 * q^32 + 20376 * q^33 + 11960 * q^34 + 26272 * q^35 + 3240 * q^36 + 32296 * q^37 - 22320 * q^39 - 100184 * q^40 + 6552 * q^41 - 21528 * q^42 - 38152 * q^43 - 26208 * q^44 + 31752 * q^45 + 106368 * q^46 + 9768 * q^49 + 96128 * q^50 - 62720 * q^52 + 65984 * q^53 + 29160 * q^54 - 268304 * q^56 - 28656 * q^57 - 139352 * q^58 - 67312 * q^59 - 109800 * q^60 - 307184 * q^61 + 150704 * q^62 - 696 * q^65 + 54720 * q^66 + 364272 * q^67 + 558960 * q^68 - 81864 * q^69 + 313960 * q^70 + 309808 * q^71 - 268752 * q^73 - 393712 * q^74 - 96624 * q^75 - 228552 * q^76 - 841536 * q^77 - 130824 * q^78 - 57216 * q^79 + 658528 * q^80 - 335992 * q^82 + 406240 * q^83 + 664848 * q^84 + 686840 * q^85 - 842560 * q^86 + 127224 * q^87 + 538248 * q^88 - 103680 * q^90 - 368592 * q^91 + 96752 * q^92 - 113472 * q^93 - 622576 * q^94 - 1143560 * q^95 - 375552 * q^96 - 40424 * q^97 - 51192 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/51\mathbb{Z}\right)^\times$.

$n$	$35$	$37$
$\chi(n)$	$1$	$e\left(\frac{7}{8}\right)$

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 $

$2$	−1.06332	−	1.06332i	−0.187970	−	0.187970i	0.606848	−	0.794818i	$-0.292434\pi$
$2$	−1.06332	−	1.06332i	−0.187970	−	0.187970i	−0.794818	+	0.606848i	$0.792434\pi$
$3$	−8.31492	+	3.44415i	−0.533402	+	0.220942i
$3$	−8.31492	+	3.44415i	−0.533402	+	0.220942i
$4$		−	29.7387i		−	0.929334i
$5$	29.0694	+	70.1798i	0.520010	+	1.25541i	0.937896	+	0.346916i	$0.112771\pi$
$5$	29.0694	+	70.1798i	0.520010	+	1.25541i	−0.417886	+	0.908499i	$0.637229\pi$
$6$	12.5037	+	5.17918i	0.141794	+	0.0587331i
$7$	48.3729	−	116.783i	0.373127	−	0.900809i	−0.620089	−	0.784531i	$-0.712904\pi$
$7$	48.3729	−	116.783i	0.373127	−	0.900809i	0.993217	−	0.116278i	$-0.0370963\pi$
$8$	−65.6480	+	65.6480i	−0.362657	+	0.362657i
$9$	57.2756	−	57.2756i	0.235702	−	0.235702i
$10$	43.7135	−	105.534i	0.138234	−	0.333727i
$11$	−721.222	−	298.740i	−1.79716	−	0.744409i	−0.987522	−	0.157483i	$-0.949662\pi$
$11$	−721.222	−	298.740i	−1.79716	−	0.744409i	−0.809640	−	0.586926i	$-0.800338\pi$
$12$	102.425	+	247.275i	0.205329	+	0.495709i
$13$		−	565.587i		−	0.928198i	−0.885783	−	0.464099i	$-0.846378\pi$
$13$		−	565.587i		−	0.928198i	0.885783	−	0.464099i	$-0.153622\pi$
$14$	−175.613	+	72.7413i	−0.239462	+	0.0991884i
$15$	−483.420	−	483.420i	−0.554749	−	0.554749i
$16$	−812.029			−0.792997
$17$	999.358	−	648.954i	0.838685	−	0.544617i
$17$	999.358	−	648.954i	0.838685	−	0.544617i
$18$	−121.805			−0.0886100
$19$	−1387.06	−	1387.06i	−0.881478	−	0.881478i	0.112207	−	0.993685i	$-0.464208\pi$
$19$	−1387.06	−	1387.06i	−0.881478	−	0.881478i	−0.993685	+	0.112207i	$0.964208\pi$
$20$	2087.06	−	864.487i	1.16670	−	0.483263i
$21$			1137.64i			0.562933i
$22$	449.234	+	1084.55i	0.197886	+	0.477740i
$23$	−1114.32	−	461.567i	−0.439229	−	0.181934i	0.152100	−	0.988365i	$-0.451396\pi$
$23$	−1114.32	−	461.567i	−0.439229	−	0.181934i	−0.591329	+	0.806431i	$0.701396\pi$
$24$	319.756	−	771.959i	0.113316	−	0.273569i
$25$	−1870.47	+	1870.47i	−0.598550	+	0.598550i
$26$	−601.399	+	601.399i	−0.174474	+	0.174474i
$27$	−278.976	+	673.508i	−0.0736475	+	0.177801i
$28$	−3472.96	−	1438.55i	−0.837153	−	0.346760i
$29$	451.671	+	1090.43i	0.0997304	+	0.240770i	0.965868	−	0.259035i	$-0.0834047\pi$
$29$	451.671	+	1090.43i	0.0997304	+	0.240770i	−0.866137	+	0.499806i	$0.833405\pi$
$30$			1028.06i			0.208552i
$31$	−1248.11	+	516.985i	−0.233265	+	0.0966215i	−0.496254	−	0.868177i	$-0.665292\pi$
$31$	−1248.11	+	516.985i	−0.233265	+	0.0966215i	0.262989	+	0.964799i	$0.415292\pi$
$32$	2964.18	+	2964.18i	0.511717	+	0.511717i
$33$	7025.81			1.12308
$34$	−1752.68	−	372.591i	−0.260020	−	0.0552758i
$35$	9601.95			1.32492
$36$	−1703.30	−	1703.30i	−0.219046	−	0.219046i
$37$	13529.8	−	5604.21i	1.62475	−	0.672993i	0.630119	−	0.776498i	$-0.283006\pi$
$37$	13529.8	−	5604.21i	1.62475	−	0.672993i	0.994629	+	0.103505i	$0.0330059\pi$
$38$			2949.78i			0.331383i
$39$	1947.97	+	4702.80i	0.205078	+	0.495103i
$40$	−6515.52	−	2698.81i	−0.643871	−	0.266700i
$41$	3202.98	−	7732.67i	0.297573	−	0.718406i	−0.702405	−	0.711778i	$-0.747890\pi$
$41$	3202.98	−	7732.67i	0.297573	−	0.718406i	0.999978	−	0.00662776i	$-0.00210970\pi$
$42$	1209.68	−	1209.68i	0.105815	−	0.105815i
$43$	−12269.0	+	12269.0i	−1.01190	+	1.01190i	−0.0119686	+	0.999928i	$0.503810\pi$
$43$	−12269.0	+	12269.0i	−1.01190	+	1.01190i	−0.999928	+	0.0119686i	$0.996190\pi$
$44$	−8884.14	+	21448.2i	−0.691805	+	1.67016i
$45$	5684.57	+	2354.62i	0.418472	+	0.173337i
$46$	694.086	+	1675.67i	0.0483636	+	0.116760i
$47$			13520.5i			0.892786i	0.894837	+	0.446393i	$0.147292\pi$
$47$			13520.5i			0.892786i	−0.894837	+	0.446393i	$0.852708\pi$
$48$	6751.95	−	2796.75i	0.422986	−	0.175207i
$49$	586.125	+	586.125i	0.0348738	+	0.0348738i
$50$	3977.81			0.225019
$51$	−6074.48	+	8837.94i	−0.327027	+	0.475801i
$52$	−16819.8			−0.862606
$53$	−16507.2	−	16507.2i	−0.807206	−	0.807206i	0.177004	−	0.984210i	$-0.443360\pi$
$53$	−16507.2	−	16507.2i	−0.807206	−	0.807206i	−0.984210	+	0.177004i	$0.943360\pi$
$54$	1012.80	−	419.514i	0.0472648	−	0.0195777i
$55$		−	59299.4i		−	2.64328i
$56$	4490.95	+	10842.1i	0.191368	+	0.462002i
$57$	16310.5	+	6756.04i	0.664938	+	0.275426i
$58$	679.206	−	1639.75i	0.0265113	−	0.0640040i
$59$	15474.8	−	15474.8i	0.578756	−	0.578756i	−0.355804	−	0.934560i	$-0.615793\pi$
$59$	15474.8	−	15474.8i	0.578756	−	0.578756i	0.934560	+	0.355804i	$0.115793\pi$
$60$	−14376.3	+	14376.3i	−0.515547	+	0.515547i
$61$	4601.19	−	11108.3i	0.158324	−	0.382227i	−0.824735	−	0.565520i	$-0.808676\pi$
$61$	4601.19	−	11108.3i	0.158324	−	0.382227i	0.983058	+	0.183293i	$0.0586756\pi$
$62$	1876.86	+	777.423i	0.0620088	+	0.0256849i
$63$	−3918.21	−	9459.38i	−0.124376	−	0.300270i
$64$			19681.2i			0.600622i
$65$	39692.8	−	16441.3i	1.16527	−	0.482672i
$66$	−7470.68	−	7470.68i	−0.211106	−	0.211106i
$67$	−61678.1			−1.67859			−0.839294	−	0.543678i	$-0.817031\pi$
$67$	−61678.1			−1.67859			−0.839294	+	0.543678i	$0.817031\pi$
$68$	−19299.0	−	29719.6i	−0.506132	−	0.779418i
$69$	10855.2			0.274482
$70$	−10209.9	−	10209.9i	−0.249045	−	0.249045i
$71$	20188.3	−	8362.28i	0.475286	−	0.196870i	−0.132164	−	0.991228i	$-0.542193\pi$
$71$	20188.3	−	8362.28i	0.475286	−	0.196870i	0.607450	+	0.794358i	$0.292193\pi$
$72$			7520.06i			0.170958i
$73$	−10796.4	−	26064.9i	−0.237123	−	0.572465i	0.759860	−	0.650087i	$-0.225267\pi$
$73$	−10796.4	−	26064.9i	−0.237123	−	0.572465i	−0.996983	+	0.0776215i	$0.975267\pi$
$74$	−20345.5	−	8427.40i	−0.431907	−	0.178902i
$75$	9110.61	−	21995.0i	0.187023	−	0.451513i
$76$	−41249.4	+	41249.4i	−0.819187	+	0.819187i
$77$	−69775.2	+	69775.2i	−1.34114	+	1.34114i
$78$	2929.28	−	7071.90i	0.0545160	−	0.131613i
$79$	71825.3	+	29751.0i	1.29482	+	0.536332i	0.920419	−	0.390934i	$-0.127848\pi$
$79$	71825.3	+	29751.0i	1.29482	+	0.536332i	0.374402	+	0.927266i	$0.377848\pi$
$80$	−23605.2	−	56988.0i	−0.412366	−	0.995540i
$81$		−	6561.00i		−	0.111111i
$82$	−11628.1	+	4816.51i	−0.190974	+	0.0791039i
$83$	4901.56	+	4901.56i	0.0780979	+	0.0780979i	0.745077	−	0.666979i	$-0.232413\pi$
$83$	4901.56	+	4901.56i	0.0780979	+	0.0780979i	−0.666979	+	0.745077i	$0.732413\pi$
$84$	33831.9			0.523153
$85$	74594.2	+	51270.0i	1.11985	+	0.769691i
$86$	26091.6			0.380413
$87$	−7511.22	−	7511.22i	−0.106393	−	0.106393i
$88$	66958.5	−	27735.1i	0.921719	−	0.381789i
$89$			115238.i			1.54213i	0.636756	+	0.771066i	$0.280276\pi$
$89$			115238.i			1.54213i	−0.636756	+	0.771066i	$0.719724\pi$
$90$	−3540.79	−	8548.23i	−0.0460781	−	0.111242i
$91$	−66050.6	−	27359.1i	−0.836129	−	0.346336i
$92$	−13726.4	+	33138.4i	−0.169078	+	0.408190i
$93$	8597.38	−	8597.38i	0.103076	−	0.103076i
$94$	14376.6	−	14376.6i	0.167817	−	0.167817i
$95$	57022.6	−	137665.i	0.648243	−	1.56500i
$96$	−34856.0	−	14437.8i	−0.386011	−	0.159891i
$97$	11124.7	+	26857.4i	0.120049	+	0.289824i	0.972468	−	0.233035i	$-0.0748656\pi$
$97$	11124.7	+	26857.4i	0.120049	+	0.289824i	−0.852419	+	0.522859i	$0.824866\pi$
$98$		−	1246.48i		−	0.0131105i
$99$	−58419.0	+	24197.9i	−0.599054	+	0.248136i
$100$	55625.3	+	55625.3i	0.556253	+	0.556253i
$101$	5974.83			0.0582803			0.0291402	−	0.999575i	$-0.490723\pi$
$101$	5974.83			0.0582803			0.0291402	+	0.999575i	$0.490723\pi$
$102$	15856.7	−	2938.44i	0.150908	−	0.0279651i
$103$	66567.5			0.618258			0.309129	−	0.951020i	$-0.399963\pi$
$103$	66567.5			0.618258			0.309129	+	0.951020i	$0.399963\pi$
$104$	37129.6	+	37129.6i	0.336618	+	0.336618i
$105$	−79839.4	+	33070.6i	−0.706715	+	0.292731i
$106$			35104.9i			0.303461i
$107$	30294.2	+	73136.7i	0.255800	+	0.617556i	0.998652	−	0.0518996i	$-0.0165276\pi$
$107$	30294.2	+	73136.7i	0.255800	+	0.617556i	−0.742852	+	0.669455i	$0.766528\pi$
$108$	20029.3	+	8296.39i	0.165236	+	0.0684431i
$109$	25598.4	−	61800.0i	0.206370	−	0.498221i	−0.786476	−	0.617620i	$-0.788097\pi$
$109$	25598.4	−	61800.0i	0.206370	−	0.498221i	0.992846	+	0.119399i	$0.0380968\pi$
$110$	−63054.3	+	63054.3i	−0.496859	+	0.496859i
$111$	−93197.1	+	93197.1i	−0.717952	+	0.717952i
$112$	−39280.2	+	94830.8i	−0.295889	+	0.714339i
$113$	−53919.5	−	22334.2i	−0.397237	−	0.164541i	0.175117	−	0.984548i	$-0.443970\pi$
$113$	−53919.5	−	22334.2i	−0.397237	−	0.164541i	−0.572354	+	0.820007i	$0.693970\pi$
$114$	−10159.5	−	24527.2i	−0.0732166	−	0.176760i
$115$		−	91620.3i		−	0.646022i
$116$	32428.0	−	13432.1i	0.223756	−	0.0926829i
$117$	−32394.3	−	32394.3i	−0.218778	−	0.218778i
$118$	−32909.4			−0.217578
$119$	−27444.6	−	148099.i	−0.177660	−	0.958706i
$120$	63471.1			0.402367
$121$	317035.	+	317035.i	1.96854	+	1.96854i
$122$	−16704.2	+	6919.09i	−0.101607	+	0.0420872i
$123$			75328.0i			0.448946i
$124$	15374.5	+	37117.3i	0.0897937	+	0.216781i
$125$	33669.4	+	13946.3i	0.192735	+	0.0798334i
$126$	−5892.05	+	14224.7i	−0.0330628	+	0.0798207i
$127$	223706.	−	223706.i	1.23075	−	1.23075i	0.267069	−	0.963677i	$-0.413945\pi$
$127$	223706.	−	223706.i	1.23075	−	1.23075i	0.963677	−	0.267069i	$-0.0860551\pi$
$128$	115781.	−	115781.i	0.624616	−	0.624616i
$129$	59759.2	−	144271.i	0.316177	−	0.763319i
$130$	−59688.5	−	24723.8i	−0.309765	−	0.128309i
$131$	−80644.5	−	194693.i	−0.410579	−	0.991225i	−0.984983	−	0.172653i	$-0.944766\pi$
$131$	−80644.5	−	194693.i	−0.410579	−	0.991225i	0.574404	−	0.818572i	$-0.305234\pi$
$132$		−	208938.i		−	1.04372i
$133$	−229081.	+	94888.3i	−1.12295	+	0.465140i
$134$	65583.6	+	65583.6i	0.315524	+	0.315524i
$135$	−55376.4			−0.261511
$136$	−23003.3	+	108208.i	−0.106646	+	0.501665i
$137$	−392735.			−1.78772			−0.893858	−	0.448350i	$-0.852012\pi$
$137$	−392735.			−1.78772			−0.893858	+	0.448350i	$0.852012\pi$
$138$	−11542.5	−	11542.5i	−0.0515945	−	0.0515945i
$139$	−103906.	+	43039.3i	−0.456146	+	0.188942i	−0.598912	−	0.800814i	$-0.704400\pi$
$139$	−103906.	+	43039.3i	−0.456146	+	0.188942i	0.142766	+	0.989756i	$0.454400\pi$
$140$		−	285550.i		−	1.23129i
$141$	−46566.5	−	112422.i	−0.197254	−	0.476214i
$142$	−30358.4	−	12574.9i	−0.126345	−	0.0523339i
$143$	−168963.	+	407913.i	−0.690959	+	1.66812i
$144$	−46509.5	+	46509.5i	−0.186911	+	0.186911i
$145$	−63396.4	+	63396.4i	−0.250406	+	0.250406i
$146$	−16235.3	+	39195.4i	−0.0630344	+	0.152178i
$147$	−6892.28	−	2854.87i	−0.0263069	−	0.0108967i
$148$	−166662.	−	402358.i	−0.625435	−	1.50993i
$149$			9949.43i			0.0367141i	0.999831	+	0.0183570i	$0.00584355\pi$
$149$			9949.43i			0.0367141i	−0.999831	+	0.0183570i	$0.994156\pi$
$150$	−33075.2	+	13700.2i	−0.120026	+	0.0497162i
$151$	29453.9	+	29453.9i	0.105124	+	0.105124i	0.757712	−	0.652589i	$-0.226317\pi$
$151$	29453.9	+	29453.9i	0.105124	+	0.105124i	−0.652589	+	0.757712i	$0.726317\pi$
$152$	182115.			0.639349
$153$	20069.6	−	94408.1i	0.0693123	−	0.326047i
$154$	148387.			0.504189
$155$	−72563.9	−	72563.9i	−0.242600	−	0.242600i
$156$	139855.	−	57930.0i	0.460116	−	0.190586i
$157$		−	491950.i		−	1.59284i	−0.604746	−	0.796419i	$-0.706725\pi$
$157$		−	491950.i		−	1.59284i	0.604746	−	0.796419i	$-0.293275\pi$
$158$	−44738.4	−	108008.i	−0.142573	−	0.344202i
$159$	194110.	+	80402.9i	0.608912	+	0.252219i
$160$	−121859.	+	294193.i	−0.376319	+	0.908515i
$161$	−107806.	+	107806.i	−0.327776	+	0.327776i
$162$	−6976.44	+	6976.44i	−0.0208856	+	0.0208856i
$163$	92749.8	−	223918.i	0.273429	−	0.660115i	−0.726197	−	0.687487i	$-0.758714\pi$
$163$	92749.8	−	223918.i	0.273429	−	0.660115i	0.999625	+	0.0273718i	$0.00871382\pi$
$164$	−229959.	−	95252.3i	−0.667639	−	0.276545i
$165$	204236.	+	493070.i	0.584014	+	1.40993i
$166$		−	10423.9i		−	0.0293601i
$167$	−43753.8	+	18123.4i	−0.121402	+	0.0502862i	−0.442557	−	0.896740i	$-0.645929\pi$
$167$	−43753.8	+	18123.4i	−0.121402	+	0.0502862i	0.321156	+	0.947026i	$0.395929\pi$
$168$	−74683.8	−	74683.8i	−0.204152	−	0.204152i
$169$	51404.9			0.138448
$170$	−24801.1	−	133834.i	−0.0658186	−	0.355176i
$171$	−158890.			−0.415533
$172$	364863.	+	364863.i	0.940391	+	0.940391i
$173$	127932.	−	52991.0i	0.324985	−	0.134613i	−0.214226	−	0.976784i	$-0.568723\pi$
$173$	127932.	−	52991.0i	0.324985	−	0.134613i	0.539210	+	0.842171i	$0.318723\pi$
$174$			15973.7i			0.0399974i
$175$	127958.	+	308918.i	0.315844	+	0.762514i
$176$	585653.	+	242585.i	1.42514	+	0.590314i
$177$	−75374.2	+	181969.i	−0.180838	+	0.436581i
$178$	122535.	−	122535.i	0.289875	−	0.289875i
$179$	−104592.	+	104592.i	−0.243986	+	0.243986i	−0.818497	−	0.574511i	$-0.805192\pi$
$179$	−104592.	+	104592.i	−0.243986	+	0.243986i	0.574511	+	0.818497i	$0.305192\pi$
$180$	70023.5	−	169052.i	0.161088	−	0.388900i
$181$	−506965.	−	209992.i	−1.15022	−	0.476437i	−0.275614	−	0.961268i	$-0.588881\pi$
$181$	−506965.	−	209992.i	−1.15022	−	0.476437i	−0.874608	+	0.484831i	$0.838881\pi$
$182$	41141.5	+	99324.4i	0.0920665	+	0.222268i
$183$			108211.i			0.238861i
$184$	103454.	−	42852.0i	0.225269	−	0.0933096i
$185$	786606.	+	786606.i	1.68977	+	1.68977i
$186$	−18283.5			−0.0387505
$187$	−914627.	+	169492.i	−1.91267	+	0.354442i
$188$	402081.			0.829697
$189$	65159.1	+	65159.1i	0.132685	+	0.132685i
$190$	−207015.	+	85748.4i	−0.416023	+	0.172322i
$191$		−	164802.i		−	0.326873i	−0.986554	−	0.163437i	$-0.947742\pi$
$191$		−	164802.i		−	0.326873i	0.986554	−	0.163437i	$-0.0522580\pi$
$192$	−67784.9	−	163647.i	−0.132703	−	0.320373i
$193$	−133823.	−	55431.3i	−0.258605	−	0.107118i	0.249614	−	0.968345i	$-0.419696\pi$
$193$	−133823.	−	55431.3i	−0.258605	−	0.107118i	−0.508220	+	0.861228i	$0.669696\pi$
$194$	16728.9	−	40387.1i	0.0319126	−	0.0770439i
$195$	−273416.	+	273416.i	−0.514917	+	0.514917i
$196$	17430.6	−	17430.6i	0.0324095	−	0.0324095i
$197$	194065.	−	468514.i	0.356271	−	0.860115i	−0.639546	−	0.768753i	$-0.720878\pi$
$197$	194065.	−	468514.i	0.356271	−	0.860115i	0.995818	−	0.0913628i	$-0.0291223\pi$
$198$	87848.2	+	36387.9i	0.159247	+	0.0659621i
$199$	−66040.3	−	159435.i	−0.118216	−	0.285399i	0.853685	−	0.520790i	$-0.174363\pi$
$199$	−66040.3	−	159435.i	−0.118216	−	0.285399i	−0.971901	+	0.235392i	$0.924363\pi$
$200$		−	245585.i		−	0.434137i
$201$	512848.	−	212429.i	0.895362	−	0.370871i
$202$	−6353.15	−	6353.15i	−0.0109550	−	0.0109550i
$203$	149192.			0.254100
$204$	262829.	+	180647.i	0.442178	+	0.303917i
$205$	635786.			1.05664
$206$	−70782.6	−	70782.6i	−0.116214	−	0.116214i
$207$	−90260.0	+	37386.9i	−0.146410	+	0.0606448i
$208$			459273.i			0.736058i
$209$	586008.	+	1.41475e6i	0.927978	+	2.24034i
$210$	120059.	+	49730.2i	0.187866	+	0.0778166i
$211$	431925.	−	1.04276e6i	0.667885	−	1.61242i	−0.117256	−	0.993102i	$-0.537410\pi$
$211$	431925.	−	1.04276e6i	0.667885	−	1.61242i	0.785142	−	0.619316i	$-0.212590\pi$
$212$	−490904.	+	490904.i	−0.750165	+	0.750165i
$213$	−139063.	+	139063.i	−0.210021	+	0.210021i
$214$	45555.3	−	109980.i	0.0679993	−	0.164165i
$215$	−1.21768e6	−	504381.i	−1.79655	−	0.744154i
$216$	−25900.2	−	62528.7i	−0.0377719	−	0.0911895i
$217$			170766.i			0.246179i
$218$	−92932.5	+	38493.9i	−0.132442	+	0.0548593i
$219$	179543.	+	179543.i	0.252964	+	0.252964i
$220$	−1.76349e6			−2.45650
$221$	−367040.	−	565223.i	−0.505513	−	0.778465i
$222$	198197.			0.269907
$223$	−220587.	−	220587.i	−0.297043	−	0.297043i	0.542812	−	0.839854i	$-0.317360\pi$
$223$	−220587.	−	220587.i	−0.297043	−	0.297043i	−0.839854	+	0.542812i	$0.817360\pi$
$224$	489551.	−	202779.i	0.651895	−	0.270024i
$225$			214265.i			0.282159i
$226$	33585.3	+	81082.1i	0.0437399	+	0.105598i
$227$	−248410.	−	102895.i	−0.319966	−	0.132534i	0.216919	−	0.976190i	$-0.430399\pi$
$227$	−248410.	−	102895.i	−0.319966	−	0.132534i	−0.536885	+	0.843655i	$0.680399\pi$
$228$	200916.	−	485054.i	0.255963	−	0.617950i
$229$	665781.	−	665781.i	0.838962	−	0.838962i	−0.149760	−	0.988722i	$-0.547850\pi$
$229$	665781.	−	665781.i	0.838962	−	0.838962i	0.988722	+	0.149760i	$0.0478501\pi$
$230$	−97421.7	+	97421.7i	−0.121433	+	0.121433i
$231$	339859.	−	820491.i	0.419052	−	1.01168i
$232$	−101236.	−	41933.3i	−0.123485	−	0.0511492i
$233$	171884.	+	414964.i	0.207417	+	0.500749i	0.993015	−	0.117988i	$-0.0376445\pi$
$233$	171884.	+	414964.i	0.207417	+	0.500749i	−0.785598	+	0.618737i	$0.787644\pi$
$234$			68891.1i			0.0822476i
$235$	−948865.	+	393033.i	−1.12082	+	0.464257i
$236$	−460201.	−	460201.i	−0.537858	−	0.537858i
$237$	−699688.			−0.809159
$238$	−128294.	+	186659.i	−0.146813	+	0.213603i
$239$	1.55229e6			1.75784			0.878918	−	0.476972i	$-0.158266\pi$
$239$	1.55229e6			1.75784			0.878918	+	0.476972i	$0.158266\pi$
$240$	392551.	+	392551.i	0.439914	+	0.439914i
$241$	376979.	−	156150.i	0.418095	−	0.173181i	−0.163711	−	0.986508i	$-0.552346\pi$
$241$	376979.	−	156150.i	0.418095	−	0.173181i	0.581806	+	0.813328i	$0.302346\pi$
$242$		−	674220.i		−	0.740054i
$243$	22597.1	+	54554.2i	0.0245492	+	0.0592669i
$244$	−330345.	−	136833.i	−0.355217	−	0.147136i
$245$	−24095.8	+	58172.4i	−0.0256464	+	0.0619159i
$246$	80097.8	−	80097.8i	0.0843884	−	0.0843884i
$247$	−784503.	+	784503.i	−0.818186	+	0.818186i
$248$	47997.1	−	115875.i	0.0495548	−	0.119636i
$249$	−57637.8	−	23874.3i	−0.0589127	−	0.0244024i
$250$	−20971.9	−	50630.8i	−0.0212221	−	0.0512347i
$251$		−	310870.i		−	0.311454i	−0.987800	−	0.155727i	$-0.950228\pi$
$251$		−	310870.i		−	0.311454i	0.987800	−	0.155727i	$-0.0497720\pi$
$252$	−281310.	+	116522.i	−0.279051	+	0.115587i
$253$	665784.	+	665784.i	0.653931	+	0.653931i
$254$	−475742.			−0.462687
$255$	−796827.	−	169392.i	−0.767385	−	0.163133i
$256$	383573.			0.365803
$257$	175714.	+	175714.i	0.165949	+	0.165949i	0.785196	−	0.619247i	$-0.212562\pi$
$257$	175714.	+	175714.i	0.165949	+	0.165949i	−0.619247	+	0.785196i	$0.712562\pi$
$258$	−216950.	+	89863.5i	−0.202913	+	0.0840493i
$259$		−	1.85113e6i		−	1.71470i
$260$	−488942.	−	1.18041e6i	−0.448564	−	1.08293i
$261$	88324.9	+	36585.4i	0.0802568	+	0.0332435i
$262$	−121270.	+	292772.i	−0.109144	+	0.263497i
$263$	−295905.	+	295905.i	−0.263792	+	0.263792i	−0.826593	−	0.562800i	$-0.809724\pi$
$263$	−295905.	+	295905.i	−0.263792	+	0.263792i	0.562800	+	0.826593i	$0.309724\pi$
$264$	−461230.	+	461230.i	−0.407294	+	0.407294i
$265$	678619.	−	1.63833e6i	0.593624	−	1.43313i
$266$	344482.	+	142689.i	0.298513	+	0.123648i
$267$	−396898.	−	958196.i	−0.340722	−	0.822576i
$268$			1.83423e6i			1.55997i
$269$	−578349.	+	239560.i	−0.487314	+	0.201852i	−0.612792	−	0.790244i	$-0.709954\pi$
$269$	−578349.	+	239560.i	−0.487314	+	0.201852i	0.125478	+	0.992096i	$0.459954\pi$
$270$	58882.8	+	58882.8i	0.0491563	+	0.0491563i
$271$	620351.			0.513115			0.256557	−	0.966529i	$-0.417412\pi$
$271$	620351.			0.513115			0.256557	+	0.966529i	$0.417412\pi$
$272$	−811507.	+	526969.i	−0.665074	+	0.431880i
$273$	643434.			0.522513
$274$	417603.	+	417603.i	0.336037	+	0.336037i
$275$	1.90781e6	−	790239.i	1.52126	−	0.630125i
$276$		−	322819.i		−	0.255086i
$277$	−192999.	−	465940.i	−0.151131	−	0.364863i	0.830123	−	0.557580i	$-0.188270\pi$
$277$	−192999.	−	465940.i	−0.151131	−	0.364863i	−0.981254	+	0.192717i	$0.938270\pi$
$278$	156250.	+	64720.9i	0.121257	+	0.0502264i
$279$	−41875.8	+	101097.i	−0.0322072	+	0.0777550i
$280$	−630349.	+	630349.i	−0.480492	+	0.480492i
$281$	−1.46824e6	+	1.46824e6i	−1.10926	+	1.10926i	−0.116008	+	0.993248i	$0.537010\pi$
$281$	−1.46824e6	+	1.46824e6i	−1.10926	+	1.10926i	−0.993248	+	0.116008i	$0.962990\pi$
$282$	−70025.0	+	169055.i	−0.0524361	+	0.126592i
$283$	1.56304e6	+	647431.i	1.16012	+	0.480537i	0.877915	−	0.478817i	$-0.158934\pi$
$283$	1.56304e6	+	647431.i	1.16012	+	0.480537i	0.282205	+	0.959354i	$0.408934\pi$
$284$	−248683.	−	600375.i	−0.182958	−	0.441699i
$285$			1.34106e6i			0.977997i
$286$	613405.	−	254080.i	0.443437	−	0.183678i
$287$	−748103.	−	748103.i	−0.536113	−	0.536113i
$288$	339551.			0.241226
$289$	577575.	−	1.29707e6i	0.406784	−	0.913525i
$290$	134821.			0.0941377
$291$	−185002.	−	185002.i	−0.128069	−	0.128069i
$292$	−775136.	+	321072.i	−0.532012	+	0.220366i
$293$		−	1.03867e6i		−	0.706820i	−0.935468	−	0.353410i	$-0.885022\pi$
$293$		−	1.03867e6i		−	0.706820i	0.935468	−	0.353410i	$-0.114978\pi$
$294$	4293.05	+	10364.3i	0.00289666	+	0.00699316i
$295$	1.53586e6	+	636176.i	1.02754	+	0.425620i
$296$	−520297.	+	1.25611e6i	−0.345161	+	0.833293i
$297$	402408.	−	402408.i	0.264713	−	0.264713i
$298$	10579.4	−	10579.4i	0.00690115	−	0.00690115i
$299$	−261056.	+	630245.i	−0.168871	+	0.407691i
$300$	−654101.	−	270938.i	−0.419606	−	0.173807i
$301$	839314.	+	2.02628e6i	0.533960	+	1.28909i
$302$		−	62637.9i		−	0.0395203i
$303$	−49680.2	+	20578.2i	−0.0310869	+	0.0128766i
$304$	1.12633e6	+	1.12633e6i	0.699009	+	0.699009i
$305$	913330.			0.562183
$306$	−121726.	+	79045.6i	−0.0743158	+	0.0482586i
$307$	489848.			0.296630			0.148315	−	0.988940i	$-0.452615\pi$
$307$	489848.			0.296630			0.148315	+	0.988940i	$0.452615\pi$
$308$	2.07502e6	+	2.07502e6i	1.24637	+	1.24637i
$309$	−553503.	+	229269.i	−0.329780	+	0.136599i
$310$			154317.i			0.0912032i
$311$	365509.	+	882417.i	0.214288	+	0.517336i	0.994073	−	0.108710i	$-0.0346721\pi$
$311$	365509.	+	882417.i	0.214288	+	0.517336i	−0.779786	+	0.626046i	$0.784672\pi$
$312$	−436610.	−	180850.i	−0.253926	−	0.105180i
$313$	−605240.	+	1.46118e6i	−0.349194	+	0.843029i	0.647521	+	0.762047i	$0.275806\pi$
$313$	−605240.	+	1.46118e6i	−0.349194	+	0.843029i	−0.996716	+	0.0809821i	$0.974194\pi$
$314$	−523100.	+	523100.i	−0.299406	+	0.299406i
$315$	549958.	−	549958.i	0.312286	−	0.312286i
$316$	884757.	−	2.13599e6i	0.498432	−	1.20332i
$317$	−874661.	−	362297.i	−0.488868	−	0.202496i	0.124613	−	0.992205i	$-0.460231\pi$
$317$	−874661.	−	362297.i	−0.488868	−	0.202496i	−0.613481	+	0.789710i	$0.710231\pi$
$318$	−120907.	−	291895.i	−0.0670475	−	0.161867i
$319$		−	921375.i		−	0.506944i
$320$	−1.38122e6	+	572121.i	−0.754030	+	0.312329i
$321$	−503788.	−	503788.i	−0.272888	−	0.272888i
$322$	229264.			0.123224
$323$	−2.28631e6	−	486031.i	−1.21935	−	0.259214i
$324$	−195116.			−0.103259
$325$	1.05791e6	+	1.05791e6i	0.555573	+	0.555573i
$326$	−336719.	+	139474.i	−0.175478	+	0.0726855i
$327$			602027.i			0.311348i
$328$	297365.	+	717903.i	0.152618	+	0.368452i
$329$	1.57895e6	+	654025.i	0.804229	+	0.333123i
$330$	307123.	−	741459.i	0.155248	−	0.374803i
$331$	−2.24049e6	+	2.24049e6i	−1.12402	+	1.12402i	−0.132884	+	0.991132i	$0.542424\pi$
$331$	−2.24049e6	+	2.24049e6i	−1.12402	+	1.12402i	−0.991132	+	0.132884i	$0.957576\pi$
$332$	145766.	−	145766.i	0.0725790	−	0.0725790i
$333$	453941.	−	1.09591e6i	0.224331	−	0.541583i
$334$	65795.3	+	27253.3i	0.0322722	+	0.0133676i
$335$	−1.79295e6	−	4.32856e6i	−0.872882	−	2.10732i
$336$		−	923797.i		−	0.446404i
$337$	−2.11594e6	+	876452.i	−1.01491	+	0.420391i	−0.827245	−	0.561841i	$-0.810093\pi$
$337$	−2.11594e6	+	876452.i	−1.01491	+	0.420391i	−0.187669	+	0.982232i	$0.560093\pi$
$338$	−54659.8	−	54659.8i	−0.0260241	−	0.0260241i
$339$	525259.			0.248241
$340$	1.52470e6	−	2.21834e6i	0.715300	−	1.04071i
$341$	1.05461e6			0.491141
$342$	168950.	+	168950.i	0.0781077	+	0.0781077i
$343$	2.05957e6	−	853100.i	0.945236	−	0.391530i
$344$		−	1.61086e6i		−	0.733944i
$345$	315554.	+	761815.i	0.142734	+	0.344589i
$346$	−192379.	−	79685.9i	−0.0863907	−	0.0357842i
$347$	−108749.	+	262542.i	−0.0484842	+	0.117051i	−0.946266	−	0.323389i	$-0.895178\pi$
$347$	−108749.	+	262542.i	−0.0484842	+	0.117051i	0.897782	+	0.440440i	$0.145178\pi$
$348$	−223374.	+	223374.i	−0.0988745	+	0.0988745i
$349$	−2.31533e6	+	2.31533e6i	−1.01754	+	1.01754i	−0.0176926	+	0.999843i	$0.505632\pi$
$349$	−2.31533e6	+	2.31533e6i	−1.01754	+	1.01754i	−0.999843	+	0.0176926i	$0.994368\pi$
$350$	192418.	−	464539.i	0.0839607	−	0.202699i
$351$	380927.	+	157785.i	0.165034	+	0.0683594i
$352$	−1.25231e6	−	3.02335e6i	−0.538712	−	1.30057i
$353$		−	1.32334e6i		−	0.565241i	−0.959232	−	0.282621i	$-0.908796\pi$
$353$		−	1.32334e6i		−	0.565241i	0.959232	−	0.282621i	$-0.0912038\pi$
$354$	273639.	−	113345.i	0.116056	−	0.0480721i
$355$	1.17373e6	+	1.17373e6i	0.494306	+	0.494306i
$356$	3.42703e6			1.43316
$357$	738276.	+	1.13691e6i	0.306583	+	0.472123i
$358$	222429.			0.0917242
$359$	−496769.	−	496769.i	−0.203431	−	0.203431i	0.598037	−	0.801468i	$-0.295948\pi$
$359$	−496769.	−	496769.i	−0.203431	−	0.203431i	−0.801468	+	0.598037i	$0.795948\pi$
$360$	−527757.	+	218604.i	−0.214624	+	0.0889000i
$361$			1.37177e6i			0.554006i
$362$	315777.	+	762354.i	0.126651	+	0.305763i
$363$	−3.72804e6	−	1.54420e6i	−1.48496	−	0.615089i
$364$	−813623.	+	1.96426e6i	−0.321862	+	0.777044i
$365$	1.51538e6	−	1.51538e6i	0.595375	−	0.595375i
$366$	115063.	−	115063.i	0.0448988	−	0.0448988i
$367$	516168.	−	1.24614e6i	0.200044	−	0.482950i	−0.791742	−	0.610856i	$-0.790826\pi$
$367$	516168.	−	1.24614e6i	0.200044	−	0.482950i	0.991786	+	0.127906i	$0.0408256\pi$
$368$	904860.	+	374805.i	0.348307	+	0.144273i
$369$	−259441.	−	626346.i	−0.0991911	−	0.239469i
$370$		−	1.67283e6i		−	0.635253i
$371$	−2.72626e6	+	1.12925e6i	−1.02833	+	0.425948i
$372$	−255675.	−	255675.i	−0.0957923	−	0.0957923i
$373$	1.36285e6			0.507197			0.253598	−	0.967310i	$-0.418386\pi$
$373$	1.36285e6			0.507197			0.253598	+	0.967310i	$0.418386\pi$
$374$	1.15277e6	+	792317.i	0.426149	+	0.292901i
$375$	−327992.			−0.120444
$376$	−887592.	−	887592.i	−0.323775	−	0.323775i
$377$	616733.	−	255459.i	0.223483	−	0.0925696i
$378$		−	138570.i		−	0.0498815i
$379$	−1.72671e6	−	4.16865e6i	−0.617478	−	1.49072i	−0.854622	−	0.519250i	$-0.826211\pi$
$379$	−1.72671e6	−	4.16865e6i	−0.617478	−	1.49072i	0.237144	−	0.971475i	$-0.423789\pi$
$380$	−4.09397e6	−	1.69578e6i	−1.45441	−	0.602435i
$381$	−1.08962e6	+	2.63057e6i	−0.384559	+	0.928407i
$382$	−175237.	+	175237.i	−0.0614425	+	0.0614425i
$383$	2.11831e6	−	2.11831e6i	0.737891	−	0.737891i	−0.234279	−	0.972169i	$-0.575273\pi$
$383$	2.11831e6	−	2.11831e6i	0.737891	−	0.737891i	0.972169	+	0.234279i	$0.0752728\pi$
$384$	−563943.	+	1.36148e6i	−0.195167	+	0.471176i
$385$	−6.92514e6	−	2.86849e6i	−2.38109	−	0.986282i
$386$	83355.4	+	201238.i	0.0284751	+	0.0687450i
$387$			1.40542e6i			0.477013i
$388$	798704.	−	330834.i	0.269343	−	0.111566i
$389$	3.06258e6	+	3.06258e6i	1.02616	+	1.02616i	0.999649	+	0.0265092i	$0.00843912\pi$
$389$	3.06258e6	+	3.06258e6i	1.02616	+	1.02616i	0.0265092	+	0.999649i	$0.491561\pi$
$390$	581457.			0.193578
$391$	−1.41314e6	+	261872.i	−0.467459	+	0.0866259i
$392$	−76955.8			−0.0252945
$393$	1.34110e6	+	1.34110e6i	0.438007	+	0.438007i
$394$	−704533.	+	291827.i	−0.228644	+	0.0947076i
$395$			5.90553e6i			1.90444i
$396$	719615.	+	1.73730e6i	0.230602	+	0.556722i
$397$	−369342.	−	152986.i	−0.117612	−	0.0487165i	0.323101	−	0.946364i	$-0.395275\pi$
$397$	−369342.	−	152986.i	−0.117612	−	0.0487165i	−0.440713	+	0.897648i	$0.645275\pi$
$398$	−99308.9	+	239753.i	−0.0314254	+	0.0758676i
$399$	1.57798e6	−	1.57798e6i	0.496213	−	0.496213i
$400$	1.51887e6	−	1.51887e6i	0.474648	−	0.474648i
$401$	687396.	−	1.65952e6i	0.213475	−	0.515373i	−0.780478	−	0.625183i	$-0.785024\pi$
$401$	687396.	−	1.65952e6i	0.213475	−	0.515373i	0.993953	+	0.109810i	$0.0350242\pi$
$402$	−771202.	−	319442.i	−0.238014	−	0.0985887i
$403$	292400.	+	705916.i	0.0896839	+	0.216516i
$404$		−	177684.i		−	0.0541619i
$405$	460450.	−	190725.i	0.139491	−	0.0577789i
$406$	−158639.	−	158639.i	−0.0477633	−	0.0477633i
$407$	−1.14322e7			−3.42092
$408$	−181415.	−	978970.i	−0.0539540	−	0.291152i
$409$	2.73980e6			0.809862			0.404931	−	0.914347i	$-0.367295\pi$
$409$	2.73980e6			0.809862			0.404931	+	0.914347i	$0.367295\pi$
$410$	−676044.	−	676044.i	−0.198616	−	0.198616i
$411$	3.26556e6	−	1.35264e6i	0.953572	−	0.394982i
$412$		−	1.97963e6i		−	0.574568i
$413$	−1.05863e6	−	2.55575e6i	−0.305399	−	0.737298i
$414$	135729.	+	56221.0i	0.0389200	+	0.0161212i
$415$	−201505.	+	486476.i	−0.0574336	+	0.138657i
$416$	1.67650e6	−	1.67650e6i	0.474975	−	0.474975i
$417$	715737.	−	715737.i	0.201564	−	0.201564i
$418$	881216.	−	2.12744e6i	0.246684	−	0.595549i
$419$	5.67394e6	+	2.35022e6i	1.57888	+	0.653994i	0.988236	−	0.152936i	$-0.0488729\pi$
$419$	5.67394e6	+	2.35022e6i	1.57888	+	0.653994i	0.590646	+	0.806931i	$0.298873\pi$
$420$	983476.	+	2.37432e6i	0.272045	+	0.656774i
$421$			1.97211e6i			0.542284i	0.962539	+	0.271142i	$0.0874013\pi$
$421$			1.97211e6i			0.542284i	−0.962539	+	0.271142i	$0.912599\pi$
$422$	−1.56806e6	+	649512.i	−0.428629	+	0.177544i
$423$	774394.	+	774394.i	0.210432	+	0.210432i
$424$	2.16733e6			0.585479
$425$	−655419.	+	3.08311e6i	−0.176014	+	0.827975i
$426$	295738.			0.0789556
$427$	−1.07468e6	−	1.07468e6i	−0.285239	−	0.285239i
$428$	2.17499e6	−	900911.i	0.573916	−	0.237724i
$429$		−	3.97370e6i		−	1.04244i
$430$	758469.	+	1.83111e6i	0.197818	+	0.477576i
$431$	6.89781e6	+	2.85717e6i	1.78862	+	0.740870i	0.990353	+	0.138565i	$0.0442491\pi$
$431$	6.89781e6	+	2.85717e6i	1.78862	+	0.740870i	0.798266	+	0.602305i	$0.205751\pi$
$432$	226537.	−	546908.i	0.0584022	−	0.140995i
$433$	−601246.	+	601246.i	−0.154111	+	0.154111i	−0.779951	−	0.625840i	$-0.784756\pi$
$433$	−601246.	+	601246.i	−0.154111	+	0.154111i	0.625840	+	0.779951i	$0.284756\pi$
$434$	181579.	−	181579.i	0.0462744	−	0.0462744i
$435$	308789.	−	745483.i	0.0782418	−	0.188892i
$436$	−1.83785e6	−	761263.i	−0.463014	−	0.191787i
$437$	905409.	+	2.18585e6i	0.226799	+	0.547541i
$438$		−	381823.i		−	0.0950992i
$439$	4.91259e6	−	2.03486e6i	1.21660	−	0.503934i	0.320275	−	0.947325i	$-0.396225\pi$
$439$	4.91259e6	−	2.03486e6i	1.21660	−	0.503934i	0.896328	+	0.443391i	$0.146225\pi$
$440$	3.89289e6	+	3.89289e6i	0.958606	+	0.958606i
$441$	67141.3			0.0164397
$442$	−210733.	+	991294.i	−0.0513069	+	0.241350i
$443$	−3.11704e6			−0.754628			−0.377314	−	0.926085i	$-0.623152\pi$
$443$	−3.11704e6			−0.754628			−0.377314	+	0.926085i	$0.623152\pi$
$444$	2.77156e6	+	2.77156e6i	0.667217	+	0.667217i
$445$	−8.08740e6	+	3.34991e6i	−1.93601	+	0.801924i
$446$			469110.i			0.111670i
$447$	−34267.3	−	82728.6i	−0.00811169	−	0.0195834i
$448$	2.29842e6	+	952036.i	0.541046	+	0.224108i
$449$	619962.	−	1.49672e6i	0.145127	−	0.350368i	−0.834555	−	0.550925i	$-0.814275\pi$
$449$	619962.	−	1.49672e6i	0.145127	−	0.350368i	0.979682	+	0.200557i	$0.0642750\pi$
$450$	227832.	−	227832.i	0.0530375	−	0.0530375i
$451$	−4.62011e6	+	4.62011e6i	−1.06957	+	1.06957i
$452$	−664190.	+	1.60350e6i	−0.152914	+	0.369166i
$453$	−346351.	−	143463.i	−0.0792995	−	0.0328469i
$454$	154729.	+	373549.i	0.0352316	+	0.0850566i
$455$		−	5.43073e6i		−	1.22979i
$456$	−1.51427e6	+	627233.i	−0.341030	+	0.141259i
$457$	−1.58237e6	−	1.58237e6i	−0.354420	−	0.354420i	0.507331	−	0.861751i	$-0.330632\pi$
$457$	−1.58237e6	−	1.58237e6i	−0.354420	−	0.354420i	−0.861751	+	0.507331i	$0.830632\pi$
$458$	−1.41588e6			−0.315400
$459$	158279.	+	854118.i	0.0350664	+	0.189228i
$460$	−2.72467e6			−0.600370
$461$	1.28233e6	+	1.28233e6i	0.281026	+	0.281026i	0.833518	−	0.552492i	$-0.186323\pi$
$461$	1.28233e6	+	1.28233e6i	0.281026	+	0.281026i	−0.552492	+	0.833518i	$0.686323\pi$
$462$	−1.23382e6	+	511066.i	−0.268935	+	0.111397i
$463$			4.16371e6i			0.902667i	0.892355	+	0.451334i	$0.149052\pi$
$463$			4.16371e6i			0.902667i	−0.892355	+	0.451334i	$0.850948\pi$
$464$	−366770.	−	885461.i	−0.0790859	−	0.190930i
$465$	853284.	+	353442.i	0.183004	+	0.0758028i
$466$	258472.	−	624006.i	0.0551377	−	0.133114i
$467$	−4.09741e6	+	4.09741e6i	−0.869396	+	0.869396i	−0.992405	−	0.123010i	$-0.960745\pi$
$467$	−4.09741e6	+	4.09741e6i	−0.869396	+	0.869396i	0.123010	+	0.992405i	$0.460745\pi$
$468$	−963366.	+	963366.i	−0.203318	+	0.203318i
$469$	−2.98355e6	+	7.20293e6i	−0.626327	+	1.51209i
$470$	1.42687e6	+	591027.i	0.297947	+	0.123414i
$471$	1.69435e6	+	4.09052e6i	0.351925	+	0.849623i
$472$			2.03178e6i			0.419780i
$473$	1.25139e7	−	5.18341e6i	2.57181	−	1.06528i
$474$	743993.	+	743993.i	0.152098	+	0.152098i
$475$	5.18890e6			1.05522
$476$	−4.40428e6	+	816168.i	−0.890959	+	0.165106i
$477$	−1.89093e6			−0.380521
$478$	−1.65058e6	−	1.65058e6i	−0.330421	−	0.330421i
$479$	2.48617e6	−	1.02980e6i	0.495099	−	0.205077i	−0.121141	−	0.992635i	$-0.538655\pi$
$479$	2.48617e6	−	1.02980e6i	0.495099	−	0.205077i	0.616240	+	0.787559i	$0.288655\pi$
$480$		−	2.86589e6i		−	0.567749i
$481$	−3.16967e6	−	7.65226e6i	−0.624671	−	1.50809i
$482$	−566887.	−	234812.i	−0.111142	−	0.0460366i
$483$	525097.	−	1.26770e6i	0.102417	−	0.247256i
$484$	9.42822e6	−	9.42822e6i	1.82943	−	1.82943i
$485$	−1.56146e6	+	1.56146e6i	−0.301423	+	0.301423i
$486$	33980.6	−	82036.4i	0.00652590	−	0.0157549i
$487$	−2.00311e6	−	829717.i	−0.382722	−	0.158529i	0.183024	−	0.983109i	$-0.441412\pi$
$487$	−2.00311e6	−	829717.i	−0.382722	−	0.158529i	−0.565746	+	0.824580i	$0.691412\pi$
$488$	427176.	+	1.03129e6i	0.0812002	+	0.196035i
$489$			2.18130e6i			0.412519i
$490$	87477.5	−	36234.4i	0.0164591	−	0.00681758i
$491$	−4.08744e6	−	4.08744e6i	−0.765151	−	0.765151i	0.212097	−	0.977249i	$-0.431971\pi$
$491$	−4.08744e6	−	4.08744e6i	−0.765151	−	0.765151i	−0.977249	+	0.212097i	$0.931971\pi$
$492$	2.24016e6			0.417221
$493$	1.15902e6	+	796617.i	0.214770	+	0.147616i
$494$	1.66835e6			0.307589
$495$	−3.39641e6	−	3.39641e6i	−0.623028	−	0.623028i
$496$	1.01350e6	−	419807.i	0.184978	−	0.0766206i
$497$		−	2.76215e6i		−	0.501599i
$498$	35901.3	+	86673.5i	0.00648690	+	0.0156608i
$499$	5.24863e6	+	2.17405e6i	0.943614	+	0.390858i	0.800827	−	0.598896i	$-0.204394\pi$
$499$	5.24863e6	+	2.17405e6i	0.943614	+	0.390858i	0.142787	+	0.989753i	$0.454394\pi$
$500$	414746.	−	1.00128e6i	0.0741920	−	0.179115i
$501$	301389.	−	301389.i	0.0536455	−	0.0536455i
$502$	−330554.	+	330554.i	−0.0585441	+	0.0585441i
$503$	1.13806e6	−	2.74753e6i	0.200561	−	0.484197i	−0.791315	−	0.611409i	$-0.790603\pi$
$503$	1.13806e6	−	2.74753e6i	0.200561	−	0.484197i	0.991875	+	0.127212i	$0.0406030\pi$
$504$	878212.	+	363767.i	0.154001	+	0.0637892i
$505$	173685.	+	419312.i	0.0303064	+	0.0731660i
$506$		−	1.41588e6i		−	0.245839i
$507$	−427427.	+	177046.i	−0.0738486	+	0.0305891i
$508$	−6.65273e6	−	6.65273e6i	−1.14377	−	1.14377i
$509$	−7.90755e6			−1.35284			−0.676421	−	0.736515i	$-0.736470\pi$
$509$	−7.90755e6			−1.35284			−0.676421	+	0.736515i	$0.736470\pi$
$510$	667164.	+	1.02740e6i	0.113581	+	0.174910i
$511$	−3.56618e6			−0.604159
$512$	−4.11286e6	−	4.11286e6i	−0.693376	−	0.693376i
$513$	1.32115e6	−	547240.i	0.221646	−	0.0918087i
$514$		−	373681.i		−	0.0623868i
$515$	1.93508e6	+	4.67170e6i	0.321500	+	0.776170i
$516$	−4.29044e6	−	1.77716e6i	−0.709379	−	0.293834i
$517$	4.03911e6	−	9.75126e6i	0.664598	−	1.60448i
$518$	−1.96835e6	+	1.96835e6i	−0.322312	+	0.322312i
$519$	−881232.	+	881232.i	−0.143606	+	0.143606i
$520$	−1.52641e6	+	3.68509e6i	−0.247550	+	0.597640i
$521$	−864894.	−	358251.i	−0.139595	−	0.0578220i	0.311792	−	0.950150i	$-0.399071\pi$
$521$	−864894.	−	358251.i	−0.139595	−	0.0578220i	−0.451387	+	0.892328i	$0.649071\pi$
$522$	−55015.7	−	132820.i	−0.00883711	−	0.0213347i
$523$			3.42476e6i			0.547490i	0.961802	+	0.273745i	$0.0882624\pi$
$523$			3.42476e6i			0.547490i	−0.961802	+	0.273745i	$0.911738\pi$
$524$	−5.78992e6	+	2.39826e6i	−0.921180	+	0.381565i
$525$	−2.12792e6	−	2.12792e6i	−0.336943	−	0.336943i
$526$	629282.			0.0991702
$527$	−911812.	+	1.32662e6i	−0.143014	+	0.208075i
$528$	−5.70516e6			−0.890600
$529$	−3.52252e6	−	3.52252e6i	−0.547285	−	0.547285i
$530$	−2.46366e6	+	1.02048e6i	−0.380970	+	0.157803i
$531$		−	1.77266e6i		−	0.272828i
$532$	2.82185e6	+	6.81256e6i	0.432270	+	1.04359i
$533$	−4.37349e6	−	1.81156e6i	−0.666823	−	0.276207i
$534$	−596839.	+	1.44090e6i	−0.0905742	+	0.218665i
$535$	−4.25209e6	+	4.25209e6i	−0.642270	+	0.642270i
$536$	4.04904e6	−	4.04904e6i	0.608752	−	0.608752i
$537$	509442.	−	1.22990e6i	0.0762358	−	0.184050i
$538$	869699.	+	360241.i	0.129543	+	0.0536584i
$539$	−247627.	−	597825.i	−0.0367135	−	0.0886343i
$540$			1.64682e6i			0.243031i
$541$	260559.	−	107927.i	0.0382747	−	0.0158539i	−0.363464	−	0.931608i	$-0.618406\pi$
$541$	260559.	−	107927.i	0.0382747	−	0.0158539i	0.401739	+	0.915754i	$0.368406\pi$
$542$	−659632.	−	659632.i	−0.0964502	−	0.0964502i
$543$	4.93861e6			0.718796
$544$	4.88590e6	+	1.03866e6i	0.707859	+	0.150479i
$545$	5.08125e6			0.732789
$546$	−684176.	−	684176.i	−0.0982169	−	0.0982169i
$547$	2.61786e6	−	1.08435e6i	0.374091	−	0.154954i	−0.187713	−	0.982224i	$-0.560107\pi$
$547$	2.61786e6	−	1.08435e6i	0.374091	−	0.154954i	0.561804	+	0.827270i	$0.310107\pi$
$548$			1.16794e7i			1.66139i
$549$	−372696.	−	899769.i	−0.0527745	−	0.127409i
$550$	−2.86889e6	−	1.18833e6i	−0.404396	−	0.167506i
$551$	885998.	−	2.13899e6i	0.124324	−	0.300144i
$552$	−712621.	+	712621.i	−0.0995431	+	0.0995431i
$553$	6.94880e6	−	6.94880e6i	0.966266	−	0.966266i
$554$	−290224.	+	700662.i	−0.0401753	+	0.0969916i
$555$	−9.24975e6	−	3.83137e6i	−1.27467	−	0.527985i
$556$	1.27993e6	+	3.09003e6i	0.175590	+	0.423912i
$557$		−	5.12501e6i		−	0.699933i	−0.936762	−	0.349966i	$-0.886193\pi$
$557$		−	5.12501e6i		−	0.699933i	0.936762	−	0.349966i	$-0.113807\pi$
$558$	152026.	−	62971.2i	0.0206696	−	0.00856163i
$559$	6.93915e6	+	6.93915e6i	0.939241	+	0.939241i
$560$	−7.79706e6			−1.05066
$561$	7.02129e6	−	4.55942e6i	0.941911	−	0.611650i
$562$	3.12242e6			0.417014
$563$	−3.52617e6	−	3.52617e6i	−0.468848	−	0.468848i	0.432693	−	0.901541i	$-0.357563\pi$
$563$	−3.52617e6	−	3.52617e6i	−0.468848	−	0.468848i	−0.901541	+	0.432693i	$0.857563\pi$
$564$	−3.34327e6	+	1.38483e6i	−0.442562	+	0.183315i
$565$		−	4.43330e6i		−	0.584260i
$566$	−973581.	−	2.35043e6i	−0.127741	−	0.308395i
$567$	−766210.	−	317375.i	−0.100090	−	0.0414586i
$568$	−776357.	+	1.87429e6i	−0.100970	+	0.243762i
$569$	1.81923e6	−	1.81923e6i	0.235563	−	0.235563i	−0.579447	−	0.815010i	$-0.696731\pi$
$569$	1.81923e6	−	1.81923e6i	0.235563	−	0.235563i	0.815010	+	0.579447i	$0.196731\pi$
$570$	1.42598e6	−	1.42598e6i	0.183834	−	0.183834i
$571$	−1.43183e6	+	3.45674e6i	−0.183781	+	0.443687i	−0.988740	−	0.149644i	$-0.952187\pi$
$571$	−1.43183e6	+	3.45674e6i	−0.183781	+	0.443687i	0.804959	+	0.593331i	$0.202187\pi$
$572$	1.21308e7	+	5.02475e6i	1.55024	+	0.642132i
$573$	567604.	+	1.37032e6i	0.0722202	+	0.174355i
$574$			1.59095e6i			0.201547i
$575$	2.94765e6	−	1.22096e6i	0.371797	−	0.154003i
$576$	1.12725e6	+	1.12725e6i	0.141568	+	0.141568i
$577$	9.07211e6			1.13441			0.567204	−	0.823578i	$-0.308025\pi$
$577$	9.07211e6			1.13441			0.567204	+	0.823578i	$0.308025\pi$
$578$	−1.99335e6	+	765058.i	−0.248179	+	0.0952522i
$579$	1.30364e6			0.161607
$580$	1.88533e6	+	1.88533e6i	0.232711	+	0.232711i
$581$	809519.	−	335314.i	0.0994917	−	0.0412108i
$582$			393432.i			0.0481462i
$583$	6.97401e6	+	1.68367e7i	0.849789	+	2.05157i
$584$	2.41987e6	+	1.00234e6i	0.293603	+	0.121614i
$585$	1.33174e6	−	3.21511e6i	0.160891	−	0.388425i
$586$	−1.10444e6	+	1.10444e6i	−0.132861	+	0.132861i
$587$	7.81057e6	−	7.81057e6i	0.935594	−	0.935594i	−0.0624540	−	0.998048i	$-0.519893\pi$
$587$	7.81057e6	−	7.81057e6i	0.935594	−	0.935594i	0.998048	+	0.0624540i	$0.0198927\pi$
$588$	−84900.3	+	204967.i	−0.0101266	+	0.0244479i
$589$	2.44830e6	+	1.01412e6i	0.290788	+	0.120448i
$590$	−956657.	−	2.30957e6i	−0.113143	−	0.273150i
$591$			4.56404e6i			0.537503i
$592$	−1.09866e7	+	4.55078e6i	−1.28842	+	0.533681i
$593$	−1.07205e7	−	1.07205e7i	−1.25192	−	1.25192i	−0.954857	−	0.297066i	$-0.903992\pi$
$593$	−1.07205e7	−	1.07205e7i	−1.25192	−	1.25192i	−0.297066	−	0.954857i	$-0.596008\pi$
$594$	−855776.			−0.0995162
$595$	9.59578e6	−	6.23122e6i	1.11119	−	0.721574i
$596$	295883.			0.0341196
$597$	1.09824e6	+	1.09824e6i	0.126113	+	0.126113i
$598$	947738.	−	392566.i	0.108377	−	0.0448910i
$599$			5.25191e6i			0.598067i	0.954243	+	0.299033i	$0.0966642\pi$
$599$			5.25191e6i			0.598067i	−0.954243	+	0.299033i	$0.903336\pi$
$600$	845832.	+	2.04202e6i	0.0959192	+	0.231570i
$601$	−1.25203e7	−	5.18608e6i	−1.41393	−	0.585670i	−0.460604	−	0.887606i	$-0.652367\pi$
$601$	−1.25203e7	−	5.18608e6i	−1.41393	−	0.585670i	−0.953328	+	0.301936i	$0.902367\pi$
$602$	1.26213e6	−	3.04705e6i	0.141942	−	0.342679i
$603$	−3.53265e6	+	3.53265e6i	−0.395647	+	0.395647i
$604$	875922.	−	875922.i	0.0976951	−	0.0976951i
$605$	−1.30334e7	+	3.14655e7i	−1.44767	+	3.49500i
$606$	74707.2	+	30944.7i	0.00826382	+	0.00342299i
$607$	4.00903e6	+	9.67865e6i	0.441639	+	1.06621i	0.975374	+	0.220559i	$0.0707882\pi$
$607$	4.00903e6	+	9.67865e6i	0.441639	+	1.06621i	−0.533734	+	0.845652i	$0.679212\pi$
$608$		−	8.22300e6i		−	0.902134i
$609$	−1.24052e6	+	513840.i	−0.135538	+	0.0561415i
$610$	−971162.	−	971162.i	−0.105674	−	0.105674i
$611$	7.64700e6			0.828682
$612$	−2.80757e6	−	596844.i	−0.303007	−	0.0644143i
$613$	−8.23298e6			−0.884924			−0.442462	−	0.896787i	$-0.645895\pi$
$613$	−8.23298e6			−0.884924			−0.442462	+	0.896787i	$0.645895\pi$
$614$	−520865.	−	520865.i	−0.0557577	−	0.0557577i
$615$	−5.28651e6	+	2.18974e6i	−0.563613	+	0.233456i
$616$		−	9.16120e6i		−	0.972749i
$617$	−1.81164e6	−	4.37370e6i	−0.191584	−	0.462525i	0.798675	−	0.601763i	$-0.205535\pi$
$617$	−1.81164e6	−	4.37370e6i	−0.191584	−	0.462525i	−0.990259	+	0.139238i	$0.955535\pi$
$618$	832337.	+	344765.i	0.0876654	+	0.0363122i
$619$	1.16908e6	−	2.82241e6i	0.122636	−	0.296069i	−0.850625	−	0.525773i	$-0.823776\pi$
$619$	1.16908e6	−	2.82241e6i	0.122636	−	0.296069i	0.973260	+	0.229704i	$0.0737760\pi$
$620$	−2.15796e6	+	2.15796e6i	−0.225457	+	0.225457i
$621$	621738.	−	621738.i	0.0646961	−	0.0646961i
$622$	549638.	−	1.32694e6i	0.0569641	−	0.137523i
$623$	1.34578e7	+	5.57441e6i	1.38917	+	0.575411i
$624$	−1.58180e6	−	3.81881e6i	−0.162626	−	0.392615i
$625$			1.10347e7i			1.12995i
$626$	2.19727e6	−	910137.i	0.224102	−	0.0928263i
$627$	−9.74521e6	−	9.74521e6i	−0.989971	−	0.989971i
$628$	−1.46299e7			−1.48028
$629$	9.88420e6	−	1.43808e7i	0.996128	−	1.44930i
$630$	−1.16956e6			−0.117401
$631$	1.14489e7	+	1.14489e7i	1.14469	+	1.14469i	0.987581	+	0.157113i	$0.0502188\pi$
$631$	1.14489e7	+	1.14489e7i	1.14469	+	1.14469i	0.157113	+	0.987581i	$0.449781\pi$
$632$	−6.66828e6	+	2.76209e6i	−0.664081	+	0.275071i
$633$			1.01581e7i			1.00763i
$634$	544808.	+	1.31528e6i	0.0538295	+	0.129956i
$635$	2.22027e7	+	9.19665e6i	2.18510	+	0.905097i
$636$	2.39108e6	−	5.77257e6i	0.234396	−	0.565883i
$637$	331504.	−	331504.i	0.0323698	−	0.0323698i
$638$	−979717.	+	979717.i	−0.0952903	+	0.0952903i
$639$	677345.	−	1.63526e6i	0.0656233	−	0.158429i
$640$	1.14912e7	+	4.75981e6i	1.10896	+	0.459346i
$641$	−3.76637e6	−	9.09282e6i	−0.362058	−	0.874085i	−0.994999	−	0.0998852i	$-0.968152\pi$
$641$	−3.76637e6	−	9.09282e6i	−0.362058	−	0.874085i	0.632941	−	0.774200i	$-0.281848\pi$
$642$			1.07138e6i			0.102590i
$643$	9.69890e6	−	4.01741e6i	0.925113	−	0.383194i	0.131291	−	0.991344i	$-0.458088\pi$
$643$	9.69890e6	−	4.01741e6i	0.925113	−	0.383194i	0.793822	+	0.608150i	$0.208088\pi$
$644$	3.20601e6	+	3.20601e6i	0.304614	+	0.304614i
$645$	1.18621e7			1.12270
$646$	1.91427e6	+	2.94788e6i	0.180477	+	0.277926i
$647$	−1.65127e7			−1.55081			−0.775404	−	0.631465i	$-0.782454\pi$
$647$	−1.65127e7			−1.55081			−0.775404	+	0.631465i	$0.782454\pi$
$648$	430716.	+	430716.i	0.0402953	+	0.0402953i
$649$	−1.57837e7	+	6.53783e6i	−1.47095	+	0.609287i
$650$		−	2.24980e6i		−	0.208862i
$651$	−588143.	−	1.41990e6i	−0.0543915	−	0.131313i
$652$	−6.65903e6	−	2.75826e6i	−0.613468	−	0.254107i
$653$	−5.33230e6	+	1.28733e7i	−0.489364	+	1.18143i	0.465677	+	0.884955i	$0.345811\pi$
$653$	−5.33230e6	+	1.28733e7i	−0.489364	+	1.18143i	−0.955041	+	0.296474i	$0.904189\pi$
$654$	640147.	−	640147.i	0.0585242	−	0.0585242i
$655$	1.13192e7	−	1.13192e7i	1.03089	−	1.03089i
$656$	−2.60091e6	+	6.27915e6i	−0.235975	+	0.569693i
$657$	−2.11126e6	−	874511.i	−0.190822	−	0.0790409i
$658$	−983497.	−	2.37437e6i	−0.0885540	−	0.213788i
$659$		−	9.95561e6i		−	0.893006i	−0.894782	−	0.446503i	$-0.852669\pi$
$659$		−	9.95561e6i		−	0.893006i	0.894782	−	0.446503i	$-0.147331\pi$
$660$	1.46633e7	−	6.07372e6i	1.31030	−	0.542744i
$661$	−3.86473e6	−	3.86473e6i	−0.344046	−	0.344046i	0.513840	−	0.857886i	$-0.328222\pi$
$661$	−3.86473e6	−	3.86473e6i	−0.344046	−	0.344046i	−0.857886	+	0.513840i	$0.828222\pi$
$662$	4.76471e6			0.422563
$663$	4.99862e6	+	3.43564e6i	0.441638	+	0.303546i
$664$	−643555.			−0.0566455
$665$	−1.33185e7	−	1.33185e7i	−1.16789	−	1.16789i
$666$	−1.64799e6	+	682620.i	−0.143969	+	0.0596339i
$667$		−	1.42357e6i		−	0.123898i
$668$	538967.	+	1.30118e6i	0.0467327	+	0.112823i
$669$	2.59390e6	+	1.07443e6i	0.224072	+	0.0928138i
$670$	−2.69617e6	+	6.50912e6i	−0.232038	+	0.560190i
$671$	−6.63696e6	+	6.63696e6i	−0.569066	+	0.569066i
$672$	−3.37217e6	+	3.37217e6i	−0.288062	+	0.288062i
$673$	2.79689e6	−	6.75230e6i	0.238034	−	0.574664i	−0.759046	−	0.651037i	$-0.774334\pi$
$673$	2.79689e6	−	6.75230e6i	0.238034	−	0.574664i	0.997079	+	0.0763735i	$0.0243341\pi$
$674$	3.18187e6	+	1.31797e6i	0.269794	+	0.111753i
$675$	−737959.	−	1.78159e6i	−0.0623409	−	0.150504i
$676$		−	1.52871e6i		−	0.128665i
$677$	−1.12768e7	+	4.67100e6i	−0.945614	+	0.391686i	−0.801581	−	0.597887i	$-0.796007\pi$
$677$	−1.12768e7	+	4.67100e6i	−0.945614	+	0.391686i	−0.144034	+	0.989573i	$0.546007\pi$
$678$	−558518.	−	558518.i	−0.0466619	−	0.0466619i
$679$	3.67461e6			0.305870
$680$	−8.26274e6	+	1.53119e6i	−0.685254	+	0.126986i
$681$	2.41989e6			0.199953
$682$	−1.12139e6	−	1.12139e6i	−0.0923199	−	0.0923199i
$683$	1.05231e7	−	4.35883e6i	0.863164	−	0.357534i	0.0932200	−	0.995646i	$-0.470284\pi$
$683$	1.05231e7	−	4.35883e6i	0.863164	−	0.357534i	0.769944	+	0.638111i	$0.220284\pi$
$684$			4.72517e6i			0.386169i
$685$	−1.14166e7	−	2.75621e7i	−0.929630	−	2.24433i
$686$	−3.09710e6	−	1.28286e6i	−0.251272	−	0.104080i
$687$	−3.24286e6	+	7.82896e6i	−0.262142	+	0.632867i
$688$	9.96274e6	−	9.96274e6i	0.802431	−	0.802431i
$689$	−9.33627e6	+	9.33627e6i	−0.749248	+	0.749248i
$690$	474518.	−	1.14559e6i	0.0379429	−	0.0916022i
$691$	1.01657e7	+	4.21078e6i	0.809921	+	0.335480i	0.748923	−	0.662657i	$-0.230571\pi$
$691$	1.01657e7	+	4.21078e6i	0.809921	+	0.335480i	0.0609986	+	0.998138i	$0.480571\pi$
$692$	−1.57588e6	−	3.80452e6i	−0.125101	−	0.302019i
$693$			7.99284e6i			0.632220i
$694$	394801.	−	163532.i	0.0311157	−	0.0128885i
$695$	−6.04098e6	−	6.04098e6i	−0.474401	−	0.474401i
$696$	986193.			0.0771683
$697$	−1.81723e6	−	9.80628e6i	−0.141686	−	0.764579i
$698$	4.92388e6			0.382533
$699$	−2.85840e6	−	2.85840e6i	−0.221273	−	0.221273i
$700$	9.18682e6	−	3.80530e6i	0.708631	−	0.293524i
$701$			2.19319e7i			1.68570i	0.538146	+	0.842852i	$0.319125\pi$
$701$			2.19319e7i			1.68570i	−0.538146	+	0.842852i	$0.680875\pi$
$702$	−237271.	−	572824.i	−0.0181720	−	0.0438711i
$703$	−2.65400e7	−	1.09932e7i	−2.02541	−	0.838951i
$704$	5.87955e6	−	1.41945e7i	0.447108	−	1.07941i
$705$	6.53607e6	−	6.53607e6i	0.495272	−	0.495272i
$706$	−1.40713e6	+	1.40713e6i	−0.106249	+	0.106249i
$707$	289020.	−	697756.i	0.0217460	−	0.0524995i
$708$	5.41153e6	+	2.24153e6i	0.405730	+	0.168059i
$709$	627259.	+	1.51434e6i	0.0468632	+	0.113138i	0.945578	−	0.325397i	$-0.105498\pi$
$709$	627259.	+	1.51434e6i	0.0468632	+	0.113138i	−0.898714	+	0.438534i	$0.855498\pi$
$710$		−	2.49610e6i		−	0.185830i
$711$	5.81785e6	−	2.40983e6i	0.431607	−	0.178777i
$712$	−7.56516e6	−	7.56516e6i	−0.559265	−	0.559265i
$713$	1.62942e6			0.120035
$714$	423875.	−	1.99392e6i	0.0311166	−	0.146374i
$715$	−3.35390e7			−2.45349
$716$	3.11042e6	+	3.11042e6i	0.226745	+	0.226745i
$717$	−1.29072e7	+	5.34633e6i	−0.937634	+	0.388381i
$718$			1.05645e6i			0.0764781i
$719$	−6.36327e6	−	1.53623e7i	−0.459048	−	1.10824i	−0.968783	−	0.247909i	$-0.920257\pi$
$719$	−6.36327e6	−	1.53623e7i	−0.459048	−	1.10824i	0.509735	−	0.860331i	$-0.329743\pi$
$720$	−4.61603e6	−	1.91202e6i	−0.331847	−	0.137455i
$721$	3.22007e6	−	7.77392e6i	0.230689	−	0.556932i
$722$	1.45863e6	−	1.45863e6i	0.104137	−	0.104137i
$723$	−2.59675e6	+	2.59675e6i	−0.184750	+	0.184750i
$724$	−6.24488e6	+	1.50765e7i	−0.442770	+	1.06894i
$725$	−2.88445e6	−	1.19478e6i	−0.203807	−	0.0844195i
$726$	2.32212e6	+	5.60608e6i	0.163509	+	0.394746i
$727$			3.19049e6i			0.223883i	0.993715	+	0.111942i	$0.0357069\pi$
$727$			3.19049e6i			0.223883i	−0.993715	+	0.111942i	$0.964293\pi$
$728$	6.13216e6	−	2.54002e6i	0.428830	−	0.177627i
$729$	−375786.	−	375786.i	−0.0261891	−	0.0261891i
$730$	−3.22268e6			−0.223826
$731$	−4.29909e6	+	2.02231e7i	−0.297566	+	1.39976i
$732$	3.21807e6			0.221982
$733$	−8.97654e6	−	8.97654e6i	−0.617091	−	0.617091i	0.327693	−	0.944784i	$-0.393729\pi$
$733$	−8.97654e6	−	8.97654e6i	−0.617091	−	0.617091i	−0.944784	+	0.327693i	$0.893729\pi$
$734$	−1.87390e6	+	776194.i	−0.128383	+	0.0531778i
$735$		−	566688.i		−	0.0386924i
$736$	−1.93488e6	−	4.67122e6i	−0.131662	−	0.317860i
$737$	4.44836e7	+	1.84257e7i	3.01669	+	1.24956i
$738$	−390137.	+	941875.i	−0.0263680	+	0.0636579i
$739$	4.91022e6	−	4.91022e6i	0.330742	−	0.330742i	−0.522126	−	0.852868i	$-0.674861\pi$
$739$	4.91022e6	−	4.91022e6i	0.330742	−	0.330742i	0.852868	+	0.522126i	$0.174861\pi$
$740$	2.33926e7	−	2.33926e7i	1.57036	−	1.57036i
$741$	3.82113e6	−	9.22502e6i	0.255650	−	0.617194i
$742$	4.09964e6	+	1.69813e6i	0.273361	+	0.113230i
$743$	1.73838e6	+	4.19682e6i	0.115524	+	0.278900i	0.971057	−	0.238849i	$-0.0767702\pi$
$743$	1.73838e6	+	4.19682e6i	0.115524	+	0.278900i	−0.855533	+	0.517749i	$0.826770\pi$
$744$			1.12880e6i			0.0747627i
$745$	−698249.	+	289224.i	−0.0460914	+	0.0190917i
$746$	−1.44915e6	−	1.44915e6i	−0.0953379	−	0.0953379i
$747$	561480.			0.0368157
$748$	5.04047e6	+	2.71998e7i	0.329395	+	1.77751i
$749$	1.00065e7			0.651746
$750$	348760.	+	348760.i	0.0226398	+	0.0226398i
$751$	−1.26476e7	+	5.23880e6i	−0.818290	+	0.338947i	−0.752256	−	0.658870i	$-0.771035\pi$
$751$	−1.26476e7	+	5.23880e6i	−0.818290	+	0.338947i	−0.0660338	+	0.997817i	$0.521035\pi$
$752$		−	1.09790e7i		−	0.707976i
$753$	1.07068e6	+	2.58485e6i	0.0688134	+	0.166130i
$754$	−927420.	−	384150.i	−0.0594084	−	0.0246078i
$755$	−1.21086e6	+	2.92328e6i	−0.0773086	+	0.186639i
$756$	1.93775e6	−	1.93775e6i	0.123308	−	0.123308i
$757$	5.14986e6	−	5.14986e6i	0.326630	−	0.326630i	−0.524674	−	0.851303i	$-0.675813\pi$
$757$	5.14986e6	−	5.14986e6i	0.326630	−	0.326630i	0.851303	+	0.524674i	$0.175813\pi$
$758$	−2.59656e6	+	6.26866e6i	−0.164144	+	0.396279i
$759$	−7.82900e6	−	3.24288e6i	−0.493289	−	0.204327i
$760$	5.29399e6	+	1.27808e7i	0.332468	+	0.802648i
$761$		−	2.36295e7i		−	1.47908i	−0.673111	−	0.739542i	$-0.735042\pi$
$761$		−	2.36295e7i		−	1.47908i	0.673111	−	0.739542i	$-0.264958\pi$
$762$	3.95576e6	−	1.63853e6i	0.246798	−	0.102227i
$763$	−5.97889e6	−	5.97889e6i	−0.371800	−	0.371800i
$764$	−4.90100e6			−0.303775
$765$	7.20896e6	−	1.33591e6i	0.445368	−	0.0825322i
$766$	−4.50488e6			−0.277403
$767$	−8.75235e6	−	8.75235e6i	−0.537200	−	0.537200i
$768$	−3.18937e6	+	1.32108e6i	−0.195120	+	0.0808215i
$769$			1.49539e7i			0.911884i	0.890009	+	0.455942i	$0.150698\pi$
$769$			1.49539e7i			0.911884i	−0.890009	+	0.455942i	$0.849302\pi$
$770$	4.31352e6	+	1.04138e7i	0.262183	+	0.632966i
$771$	−2.06623e6	−	855862.i	−0.125182	−	0.0518523i
$772$	−1.64845e6	+	3.97972e6i	−0.0995483	+	0.240331i
$773$	−8.94785e6	+	8.94785e6i	−0.538604	+	0.538604i	−0.923119	−	0.384515i	$-0.874369\pi$
$773$	−8.94785e6	+	8.94785e6i	−0.538604	+	0.538604i	0.384515	+	0.923119i	$0.374369\pi$
$774$	1.49442e6	−	1.49442e6i	0.0896642	−	0.0896642i
$775$	1.36755e6	−	3.30156e6i	0.0817879	−	0.197454i
$776$	−2.49345e6	−	1.03282e6i	−0.148643	−	0.0615701i
$777$	6.37558e6	+	1.53920e7i	0.378850	+	0.914625i
$778$		−	6.51302e6i		−	0.385774i
$779$	−1.51684e7	+	6.28295e6i	−0.895563	+	0.370954i
$780$	8.13103e6	+	8.13103e6i	0.478530	+	0.478530i
$781$	−1.70584e7			−1.00072
$782$	1.78107e6	+	1.22417e6i	0.104151	+	0.0715852i
$783$	−860420.			−0.0501540
$784$	−475950.	−	475950.i	−0.0276548	−	0.0276548i
$785$	3.45249e7	−	1.43007e7i	1.99967	−	0.828291i
$786$		−	2.85205e6i		−	0.164665i
$787$	1.11628e7	+	2.69494e7i	0.642446	+	1.55100i	0.823370	+	0.567505i	$0.192091\pi$
$787$	1.11628e7	+	2.69494e7i	0.642446	+	1.55100i	−0.180923	+	0.983497i	$0.557909\pi$
$788$	−1.39330e7	−	5.77123e6i	−0.799335	−	0.331095i
$789$	1.44128e6	−	3.47956e6i	0.0824245	−	0.198990i
$790$	6.27947e6	−	6.27947e6i	0.357977	−	0.357977i
$791$	−5.21649e6	+	5.21649e6i	−0.296440	+	0.296440i
$792$	2.24654e6	−	5.42363e6i	0.127263	−	0.307240i
$793$	−6.28268e6	−	2.60237e6i	−0.354782	−	0.146956i
$794$	230055.	+	555402.i	0.0129503	+	0.0312648i
$795$			1.59598e7i			0.895594i
$796$	−4.74140e6	+	1.96395e6i	−0.265231	+	0.109862i
$797$	1.73499e7	+	1.73499e7i	0.967503	+	0.967503i	0.999488	−	0.0319856i	$-0.0101831\pi$
$797$	1.73499e7	+	1.73499e7i	0.967503	+	0.967503i	−0.0319856	+	0.999488i	$0.510183\pi$
$798$	−3.35579e6			−0.186546
$799$	8.77416e6	+	1.35118e7i	0.486227	+	0.748766i
$800$	−1.10888e7			−0.612576
$801$	6.60034e6	+	6.60034e6i	0.363484	+	0.363484i
$802$	−2.49552e6	+	1.03368e6i	−0.137002	+	0.0567479i
$803$			2.20239e7i			1.20533i
$804$	−6.31735e6	−	1.52514e7i	−0.344663	−	0.832091i
$805$	−1.06997e7	−	4.43194e6i	−0.581942	−	0.241048i
$806$	439700.	−	1.06153e6i	0.0238407	−	0.0575565i
$807$	3.98384e6	−	3.98384e6i	0.215337	−	0.215337i
$808$	−392236.	+	392236.i	−0.0211358	+	0.0211358i
$809$	−8.72936e6	+	2.10745e7i	−0.468933	+	1.13210i	0.495697	+	0.868496i	$0.334913\pi$
$809$	−8.72936e6	+	2.10745e7i	−0.468933	+	1.13210i	−0.964630	+	0.263609i	$0.915087\pi$
$810$	−692407.	−	286804.i	−0.0370808	−	0.0153594i
$811$	1.83989e6	+	4.44189e6i	0.0982290	+	0.237146i	0.965353	−	0.260946i	$-0.0840344\pi$
$811$	1.83989e6	+	4.44189e6i	0.0982290	+	0.237146i	−0.867124	+	0.498092i	$0.834034\pi$
$812$		−	4.43677e6i		−	0.236144i
$813$	−5.15817e6	+	2.13658e6i	−0.273696	+	0.113369i
$814$	1.21561e7	+	1.21561e7i	0.643031	+	0.643031i
$815$	1.84107e7			0.970904
$816$	4.93265e6	−	7.17666e6i	0.259331	−	0.377309i
$817$	3.40355e7			1.78393
$818$	−2.91329e6	−	2.91329e6i	−0.152230	−	0.152230i
$819$	−5.35010e6	+	2.21608e6i	−0.278710	+	0.115445i
$820$		−	1.89074e7i		−	0.981970i
$821$	2.68025e6	+	6.47069e6i	0.138777	+	0.335037i	0.977954	−	0.208822i	$-0.0669628\pi$
$821$	2.68025e6	+	6.47069e6i	0.138777	+	0.335037i	−0.839177	+	0.543859i	$0.816963\pi$
$822$	−4.91063e6	−	2.03405e6i	−0.253488	−	0.104998i
$823$	1.01217e7	−	2.44360e7i	0.520900	−	1.25756i	−0.416446	−	0.909161i	$-0.636724\pi$
$823$	1.01217e7	−	2.44360e7i	0.520900	−	1.25756i	0.937345	−	0.348402i	$-0.113276\pi$
$824$	−4.37003e6	+	4.37003e6i	−0.224216	+	0.224216i
$825$	−1.31415e7	+	1.31415e7i	−0.672220	+	0.672220i
$826$	−1.59192e6	+	3.84324e6i	−0.0811842	+	0.195996i
$827$	−7.89284e6	−	3.26932e6i	−0.401300	−	0.166224i	0.172899	−	0.984940i	$-0.444687\pi$
$827$	−7.89284e6	−	3.26932e6i	−0.401300	−	0.166224i	−0.574199	+	0.818715i	$0.694687\pi$
$828$	1.11184e6	+	2.68421e6i	0.0563593	+	0.136063i
$829$			6.15620e6i			0.311119i	0.987827	+	0.155559i	$0.0497180\pi$
$829$			6.15620e6i			0.311119i	−0.987827	+	0.155559i	$0.950282\pi$
$830$	731544.	−	303016.i	0.0368592	−	0.0152676i
$831$	3.20953e6	+	3.20953e6i	0.161228	+	0.161228i
$832$	1.11314e7			0.557496
$833$	966116.	+	205380.i	0.0482410	+	0.0102552i
$834$	−1.52211e6			−0.0757761
$835$	−2.54380e6	−	2.54380e6i	−0.126260	−	0.126260i
$836$	4.20728e7	−	1.74271e7i	2.08202	−	0.862402i
$837$		−	984841.i		−	0.0485906i
$838$	−3.53418e6	−	8.53225e6i	−0.173851	−	0.419714i
$839$	−2.95307e7	−	1.22320e7i	−1.44834	−	0.599921i	−0.486533	−	0.873662i	$-0.661739\pi$
$839$	−2.95307e7	−	1.22320e7i	−1.44834	−	0.599921i	−0.961803	+	0.273741i	$0.911739\pi$
$840$	3.07028e6	−	7.41231e6i	0.150134	−	0.362456i
$841$	1.35185e7	−	1.35185e7i	0.659083	−	0.659083i
$842$	2.09699e6	−	2.09699e6i	0.101933	−	0.101933i
$843$	7.15146e6	−	1.72652e7i	0.346598	−	0.836761i
$844$	−3.10103e7	−	1.28449e7i	−1.49848	−	0.620689i
$845$	1.49431e6	+	3.60758e6i	0.0719944	+	0.173810i
$846$		−	1.64686e6i		−	0.0791097i
$847$	5.23601e7	−	2.16883e7i	2.50779	−	1.03876i
$848$	1.34043e7	+	1.34043e7i	0.640112	+	0.640112i
$849$	−1.52264e7			−0.724982
$850$	3.97526e6	−	2.58142e6i	0.188720	−	0.122549i
$851$	−1.76632e7			−0.836076
$852$	4.13556e6	+	4.13556e6i	0.195180	+	0.195180i
$853$	−1.60889e7	+	6.66424e6i	−0.757101	+	0.313602i	−0.727635	−	0.685964i	$-0.759381\pi$
$853$	−1.60889e7	+	6.66424e6i	−0.757101	+	0.313602i	−0.0294659	+	0.999566i	$0.509381\pi$
$854$			2.28545e6i			0.107233i
$855$	−4.61883e6	−	1.11508e7i	−0.216081	−	0.521666i
$856$	−6.79004e6	−	2.81252e6i	−0.316729	−	0.131193i
$857$	−9.02017e6	+	2.17766e7i	−0.419530	+	1.01283i	0.562955	+	0.826488i	$0.309665\pi$
$857$	−9.02017e6	+	2.17766e7i	−0.419530	+	1.01283i	−0.982484	+	0.186346i	$0.940335\pi$
$858$	−4.22532e6	+	4.22532e6i	−0.195948	+	0.195948i
$859$	−1.55268e7	+	1.55268e7i	−0.717959	+	0.717959i	−0.968187	−	0.250228i	$-0.919495\pi$
$859$	−1.55268e7	+	1.55268e7i	−0.717959	+	0.717959i	0.250228	+	0.968187i	$0.419495\pi$
$860$	−1.49996e7	+	3.62124e7i	−0.691568	+	1.66959i
$861$	8.79699e6	+	3.64383e6i	0.404414	+	0.167514i
$862$	−4.29650e6	−	1.03727e7i	−0.196946	−	0.475469i
$863$		−	3.25851e7i		−	1.48933i	−0.667436	−	0.744667i	$-0.732608\pi$
$863$		−	3.25851e7i		−	1.48933i	0.667436	−	0.744667i	$-0.267392\pi$
$864$	−2.82334e6	+	1.16946e6i	−0.128670	+	0.0532970i
$865$	7.43780e6	+	7.43780e6i	0.337991	+	0.337991i
$866$	1.27863e6			0.0579364
$867$	−335164.	+	1.27743e7i	−0.0151429	+	0.577152i
$868$	5.07835e6			0.228783
$869$	−4.29142e7	−	4.29142e7i	−1.92775	−	1.92775i
$870$	−1.12103e6	+	464345.i	−0.0502133	+	0.0207990i
$871$			3.48843e7i			1.55806i
$872$	2.37656e6	+	5.73753e6i	0.105842	+	0.255525i
$873$	2.17545e6	+	901100.i	0.0966080	+	0.0400163i
$874$	1.36152e6	−	3.28700e6i	0.0602900	−	0.145553i
$875$	3.25737e6	−	3.25737e6i	0.143829	−	0.143829i
$876$	5.33937e6	−	5.33937e6i	0.235088	−	0.235088i
$877$	8.21514e6	−	1.98331e7i	0.360675	−	0.870747i	−0.634527	−	0.772901i	$-0.718805\pi$
$877$	8.21514e6	−	1.98331e7i	0.360675	−	0.870747i	0.995202	−	0.0978455i	$-0.0311951\pi$
$878$	−7.38736e6	−	3.05994e6i	−0.323410	−	0.133961i
$879$	3.57734e6	+	8.63646e6i	0.156167	+	0.377020i
$880$			4.81529e7i			2.09612i
$881$	−5.12280e6	+	2.12193e6i	−0.222366	+	0.0921068i	−0.491085	−	0.871112i	$-0.663400\pi$
$881$	−5.12280e6	+	2.12193e6i	−0.222366	+	0.0921068i	0.268719	+	0.963218i	$0.413400\pi$
$882$	−71392.7	−	71392.7i	−0.00309017	−	0.00309017i
$883$	4.34574e7			1.87569			0.937846	−	0.347051i	$-0.112817\pi$
$883$	4.34574e7			1.87569			0.937846	+	0.347051i	$0.112817\pi$
$884$	−1.68090e7	+	1.09153e7i	−0.723455	+	0.469791i
$885$	−1.49617e7			−0.642128
$886$	3.31441e6	+	3.31441e6i	0.141848	+	0.141848i
$887$	−2.92899e7	+	1.21323e7i	−1.25000	+	0.517766i	−0.906825	−	0.421507i	$-0.861501\pi$
$887$	−2.92899e7	+	1.21323e7i	−1.25000	+	0.517766i	−0.343171	+	0.939273i	$0.611501\pi$
$888$		−	1.22364e7i		−	0.520741i
$889$	−1.53036e7	−	3.69463e7i	−0.649442	−	1.56789i
$890$	1.21615e7	+	5.03746e6i	0.514651	+	0.213175i
$891$	−1.96003e6	+	4.73194e6i	−0.0827121	+	0.199685i
$892$	−6.55998e6	+	6.55998e6i	−0.276052	+	0.276052i
$893$	1.87537e7	−	1.87537e7i	0.786971	−	0.786971i
$894$	−51529.9	+	124404.i	−0.00215633	+	0.00520584i
$895$	−1.03807e7	−	4.29981e6i	−0.433179	−	0.179429i
$896$	−7.92055e6	−	1.91219e7i	−0.329599	−	0.795721i
$897$		−	6.13955e6i		−	0.254774i
$898$	−2.25071e6	+	932275.i	−0.0931384	+	0.0385792i
$899$	−1.12747e6	−	1.12747e6i	−0.0465272	−	0.0465272i
$900$	6.37195e6			0.262220
$901$	−2.72091e7	−	5.78420e6i	−1.11661	−	0.237373i
$902$	9.82532e6			0.402096
$903$	−1.39577e7	−	1.39577e7i	−0.569630	−	0.569630i
$904$	5.00590e6	−	2.07351e6i	0.203733	−	0.0843890i
$905$		−	4.16831e7i		−	1.69176i
$906$	215734.	+	520829.i	0.00873170	+	0.0210802i
$907$	4.37397e7	+	1.81176e7i	1.76546	+	0.731277i	0.995668	+	0.0929817i	$0.0296398\pi$
$907$	4.37397e7	+	1.81176e7i	1.76546	+	0.731277i	0.769791	+	0.638296i	$0.220360\pi$
$908$	−3.05995e6	+	7.38738e6i	−0.123169	+	0.297355i
$909$	342212.	−	342212.i	0.0137368	−	0.0137368i
$910$	−5.77461e6	+	5.77461e6i	−0.231163	+	0.231163i
$911$	7.74294e6	−	1.86931e7i	0.309108	−	0.746252i	−0.690627	−	0.723211i	$-0.742665\pi$
$911$	7.74294e6	−	1.86931e7i	0.309108	−	0.746252i	0.999735	−	0.0230408i	$-0.00733475\pi$
$912$	−1.32446e7	−	5.48610e6i	−0.527294	−	0.218412i
$913$	−2.07082e6	−	4.99940e6i	−0.0822178	−	0.198491i
$914$			3.36514e6i			0.133241i
$915$	−7.59426e6	+	3.14564e6i	−0.299870	+	0.124210i
$916$	−1.97995e7	−	1.97995e7i	−0.779677	−	0.779677i
$917$	−2.66378e7			−1.04610
$918$	739900.	−	1.07650e6i	0.0289779	−	0.0421607i
$919$	9.65423e6			0.377076			0.188538	−	0.982066i	$-0.439625\pi$
$919$	9.65423e6			0.377076			0.188538	+	0.982066i	$0.439625\pi$
$920$	6.01469e6	+	6.01469e6i	0.234285	+	0.234285i
$921$	−4.07305e6	+	1.68711e6i	−0.158223	+	0.0655382i
$922$		−	2.72705e6i		−	0.105649i
$923$	−4.72960e6	−	1.14183e7i	−0.182734	−	0.441159i
$924$	−2.44003e7	−	1.01070e7i	−0.940191	−	0.389440i
$925$	−1.48245e7	+	3.57895e7i	−0.569673	+	1.37531i
$926$	4.42735e6	−	4.42735e6i	0.169675	−	0.169675i
$927$	3.81270e6	−	3.81270e6i	0.145725	−	0.145725i
$928$	−1.89340e6	+	4.57107e6i	−0.0721726	+	0.174240i
$929$	4.64733e7	+	1.92499e7i	1.76670	+	0.731793i	0.995452	+	0.0952632i	$0.0303693\pi$
$929$	4.64733e7	+	1.92499e7i	1.76670	+	0.731793i	0.771252	+	0.636530i	$0.219631\pi$
$930$	−531492.	−	1.28313e6i	−0.0201507	−	0.0486480i
$931$		−	1.62598e6i		−	0.0614810i
$932$	1.23405e7	−	5.11160e6i	0.465364	−	0.192760i
$933$	−6.07835e6	−	6.07835e6i	−0.228603	−	0.228603i
$934$	8.71372e6			0.326841
$935$	−3.84826e7	−	5.92614e7i	−1.43958	−	2.21688i
$936$	4.25325e6			0.158683
$937$	1.57324e7	+	1.57324e7i	0.585389	+	0.585389i	0.936379	−	0.350990i	$-0.114155\pi$
$937$	1.57324e7	+	1.57324e7i	0.585389	+	0.585389i	−0.350990	+	0.936379i	$0.614155\pi$
$938$	1.08315e7	−	4.48655e6i	0.401958	−	0.166496i
$939$		−	1.42341e7i		−	0.526825i
$940$	1.16883e7	+	2.82180e7i	0.431450	+	1.04161i
$941$	2.51283e7	+	1.04085e7i	0.925101	+	0.383189i	0.793818	−	0.608156i	$-0.208090\pi$
$941$	2.51283e7	+	1.04085e7i	0.925101	+	0.383189i	0.131283	+	0.991345i	$0.458090\pi$
$942$	2.54790e6	−	6.15117e6i	0.0935523	−	0.225855i
$943$	−7.13828e6	+	7.13828e6i	−0.261405	+	0.261405i
$944$	−1.25660e7	+	1.25660e7i	−0.458952	+	0.458952i
$945$	−2.67872e6	+	6.46699e6i	−0.0975769	+	0.235572i
$946$	−1.88179e7	−	7.79462e6i	−0.683664	−	0.283183i
$947$	−643292.	−	1.55304e6i	−0.0233095	−	0.0562742i	0.911796	−	0.410643i	$-0.134696\pi$
$947$	−643292.	−	1.55304e6i	−0.0233095	−	0.0562742i	−0.935106	+	0.354369i	$0.884696\pi$
$948$			2.08078e7i			0.751979i
$949$	−1.47420e7	+	6.10632e6i	−0.531361	+	0.220097i
$950$	−5.51746e6	−	5.51746e6i	−0.198349	−	0.198349i
$951$	8.52054e6			0.305503
$952$	1.15241e7	+	7.92074e6i	0.412112	+	0.283252i
$953$	1.90510e7			0.679495			0.339747	−	0.940517i	$-0.389658\pi$
$953$	1.90510e7			0.679495			0.339747	+	0.940517i	$0.389658\pi$
$954$	2.01066e6	+	2.01066e6i	0.0715266	+	0.0715266i
$955$	1.15658e7	−	4.79071e6i	0.410362	−	0.169977i
$956$		−	4.61631e7i		−	1.63362i
$957$	3.17335e6	+	7.66116e6i	0.112005	+	0.270405i
$958$	−3.73860e6	−	1.54858e6i	−0.131612	−	0.0545155i
$959$	−1.89977e7	+	4.58646e7i	−0.667046	+	1.61039i
$960$	9.51427e6	−	9.51427e6i	0.333194	−	0.333194i
$961$	−1.89534e7	+	1.89534e7i	−0.662030	+	0.662030i
$962$	−4.76643e6	+	1.15072e7i	−0.166056	+	0.400895i
$963$	5.92408e6	+	2.45383e6i	0.205852	+	0.0852667i
$964$	−4.64370e6	−	1.12109e7i	−0.160943	−	0.388550i
$965$		−	1.10030e7i		−	0.380359i
$966$	−1.90631e6	+	789620.i	−0.0657281	+	0.0272255i
$967$	−2.40765e7	−	2.40765e7i	−0.827996	−	0.827996i	0.159244	−	0.987239i	$-0.449094\pi$
$967$	−2.40765e7	−	2.40765e7i	−0.827996	−	0.827996i	−0.987239	+	0.159244i	$0.949094\pi$
$968$	−4.16255e7			−1.42781
$969$	2.06844e7	−	3.83308e6i	0.707675	−	0.131141i
$970$	3.32066e6			0.113317
$971$	2.81412e7	+	2.81412e7i	0.957843	+	0.957843i	0.999147	−	0.0413036i	$-0.0131511\pi$
$971$	2.81412e7	+	2.81412e7i	0.957843	+	0.957843i	−0.0413036	+	0.999147i	$0.513151\pi$
$972$	1.62237e6	−	672008.i	0.0550788	−	0.0228144i
$973$			1.42164e7i			0.481400i
$974$	1.24770e6	+	3.01221e6i	0.0421417	+	0.101739i
$975$	−1.24401e7	−	5.15284e6i	−0.419093	−	0.173594i
$976$	−3.73630e6	+	9.02022e6i	−0.125550	+	0.303105i
$977$	−2.37167e7	+	2.37167e7i	−0.794909	+	0.794909i	−0.982288	−	0.187378i	$-0.940001\pi$
$977$	−2.37167e7	+	2.37167e7i	−0.794909	+	0.794909i	0.187378	+	0.982288i	$0.440001\pi$
$978$	2.31942e6	−	2.31942e6i	0.0775412	−	0.0775412i
$979$	3.44262e7	−	8.31123e7i	1.14798	−	2.77146i
$980$	1.72997e6	+	716578.i	0.0575406	+	0.0238341i
$981$	−2.07347e6	−	5.00580e6i	−0.0687900	−	0.166074i
$982$			8.69251e6i			0.287651i
$983$	−1.93129e7	+	7.99967e6i	−0.637476	+	0.264051i	−0.677926	−	0.735130i	$-0.737121\pi$
$983$	−1.93129e7	+	7.99967e6i	−0.637476	+	0.264051i	0.0404496	+	0.999182i	$0.487121\pi$
$984$	−4.94513e6	−	4.94513e6i	−0.162813	−	0.162813i
$985$	3.85216e7			1.26507
$986$	−385351.	−	2.07947e6i	−0.0126231	−	0.0681177i
$987$	−1.53814e7			−0.502579
$988$	2.33301e7	+	2.33301e7i	0.760368	+	0.760368i
$989$	1.93345e7	−	8.00860e6i	0.628553	−	0.260355i
$990$			7.22295e6i			0.234221i
$991$	7.97669e6	+	1.92574e7i	0.258011	+	0.622894i	0.998807	−	0.0488362i	$-0.0155512\pi$
$991$	7.97669e6	+	1.92574e7i	0.258011	+	0.622894i	−0.740795	+	0.671731i	$0.765551\pi$
$992$	−5.23207e6	−	2.16720e6i	−0.168809	−	0.0699228i
$993$	1.09129e7	−	2.63460e7i	0.351210	−	0.847895i
$994$	−2.93705e6	+	2.93705e6i	−0.0942857	+	0.0942857i
$995$	9.26940e6	−	9.26940e6i	0.296820	−	0.296820i
$996$	−709992.	+	1.71407e6i	−0.0226780	+	0.0547496i
$997$	2.63472e7	+	1.09134e7i	0.839454	+	0.347713i	0.760638	−	0.649176i	$-0.224886\pi$
$997$	2.63472e7	+	1.09134e7i	0.839454	+	0.347713i	0.0788159	+	0.996889i	$0.474886\pi$
$998$	−3.26926e6	−	7.89268e6i	−0.103902	−	0.250841i
$999$			1.06759e7i			0.338446i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	51.6.h.a.19.7	✓	56
17.3	odd	16		867.6.a.t.1.13		28
17.9	even	8	inner	51.6.h.a.43.7	yes	56
17.14	odd	16		867.6.a.u.1.13		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
51.6.h.a.19.7	✓	56	1.1	even	1	trivial
51.6.h.a.43.7	yes	56	17.9	even	8	inner
867.6.a.t.1.13		28	17.3	odd	16
867.6.a.u.1.13		28	17.14	odd	16

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 51 = 3 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	51.h (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.06332 - 1.06332i) q^{2} +(-8.31492 + 3.44415i) q^{3} -29.7387i q^{4} +(29.0694 + 70.1798i) q^{5} +(12.5037 + 5.17918i) q^{6} +(48.3729 - 116.783i) q^{7} +(-65.6480 + 65.6480i) q^{8} +(57.2756 - 57.2756i) q^{9} +(43.7135 - 105.534i) q^{10} +(-721.222 - 298.740i) q^{11} +(102.425 + 247.275i) q^{12} -565.587i q^{13} +(-175.613 + 72.7413i) q^{14} +(-483.420 - 483.420i) q^{15} -812.029 q^{16} +(999.358 - 648.954i) q^{17} -121.805 q^{18} +(-1387.06 - 1387.06i) q^{19} +(2087.06 - 864.487i) q^{20} +1137.64i q^{21} +(449.234 + 1084.55i) q^{22} +(-1114.32 - 461.567i) q^{23} +(319.756 - 771.959i) q^{24} +(-1870.47 + 1870.47i) q^{25} +(-601.399 + 601.399i) q^{26} +(-278.976 + 673.508i) q^{27} +(-3472.96 - 1438.55i) q^{28} +(451.671 + 1090.43i) q^{29} +1028.06i q^{30} +(-1248.11 + 516.985i) q^{31} +(2964.18 + 2964.18i) q^{32} +7025.81 q^{33} +(-1752.68 - 372.591i) q^{34} +9601.95 q^{35} +(-1703.30 - 1703.30i) q^{36} +(13529.8 - 5604.21i) q^{37} +2949.78i q^{38} +(1947.97 + 4702.80i) q^{39} +(-6515.52 - 2698.81i) q^{40} +(3202.98 - 7732.67i) q^{41} +(1209.68 - 1209.68i) q^{42} +(-12269.0 + 12269.0i) q^{43} +(-8884.14 + 21448.2i) q^{44} +(5684.57 + 2354.62i) q^{45} +(694.086 + 1675.67i) q^{46} +13520.5i q^{47} +(6751.95 - 2796.75i) q^{48} +(586.125 + 586.125i) q^{49} +3977.81 q^{50} +(-6074.48 + 8837.94i) q^{51} -16819.8 q^{52} +(-16507.2 - 16507.2i) q^{53} +(1012.80 - 419.514i) q^{54} -59299.4i q^{55} +(4490.95 + 10842.1i) q^{56} +(16310.5 + 6756.04i) q^{57} +(679.206 - 1639.75i) q^{58} +(15474.8 - 15474.8i) q^{59} +(-14376.3 + 14376.3i) q^{60} +(4601.19 - 11108.3i) q^{61} +(1876.86 + 777.423i) q^{62} +(-3918.21 - 9459.38i) q^{63} +19681.2i q^{64} +(39692.8 - 16441.3i) q^{65} +(-7470.68 - 7470.68i) q^{66} -61678.1 q^{67} +(-19299.0 - 29719.6i) q^{68} +10855.2 q^{69} +(-10209.9 - 10209.9i) q^{70} +(20188.3 - 8362.28i) q^{71} +7520.06i q^{72} +(-10796.4 - 26064.9i) q^{73} +(-20345.5 - 8427.40i) q^{74} +(9110.61 - 21995.0i) q^{75} +(-41249.4 + 41249.4i) q^{76} +(-69775.2 + 69775.2i) q^{77} +(2929.28 - 7071.90i) q^{78} +(71825.3 + 29751.0i) q^{79} +(-23605.2 - 56988.0i) q^{80} -6561.00i q^{81} +(-11628.1 + 4816.51i) q^{82} +(4901.56 + 4901.56i) q^{83} +33831.9 q^{84} +(74594.2 + 51270.0i) q^{85} +26091.6 q^{86} +(-7511.22 - 7511.22i) q^{87} +(66958.5 - 27735.1i) q^{88} +115238. i q^{89} +(-3540.79 - 8548.23i) q^{90} +(-66050.6 - 27359.1i) q^{91} +(-13726.4 + 33138.4i) q^{92} +(8597.38 - 8597.38i) q^{93} +(14376.6 - 14376.6i) q^{94} +(57022.6 - 137665. i) q^{95} +(-34856.0 - 14437.8i) q^{96} +(11124.7 + 26857.4i) q^{97} -1246.48i q^{98} +(-58419.0 + 24197.9i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 88 q^{5} + 360 q^{6} + 1280 q^{10} - 632 q^{11} - 4256 q^{14} - 8192 q^{16} + 6248 q^{17} + 4152 q^{19} - 16384 q^{20} - 19592 q^{22} - 3608 q^{23} + 10440 q^{24} + 30384 q^{25} - 19936 q^{26} + 13624 q^{28}+ \cdots - 51192 q^{99}+O(q^{100}) \) 56 * q - 88 * q^5 + 360 * q^6 + 1280 * q^10 - 632 * q^11 - 4256 * q^14 - 8192 * q^16 + 6248 * q^17 + 4152 * q^19 - 16384 * q^20 - 19592 * q^22 - 3608 * q^23 + 10440 * q^24 + 30384 * q^25 - 19936 * q^26 + 13624 * q^28 - 23424 * q^29 + 2728 * q^31 + 67200 * q^32 + 20376 * q^33 + 11960 * q^34 + 26272 * q^35 + 3240 * q^36 + 32296 * q^37 - 22320 * q^39 - 100184 * q^40 + 6552 * q^41 - 21528 * q^42 - 38152 * q^43 - 26208 * q^44 + 31752 * q^45 + 106368 * q^46 + 9768 * q^49 + 96128 * q^50 - 62720 * q^52 + 65984 * q^53 + 29160 * q^54 - 268304 * q^56 - 28656 * q^57 - 139352 * q^58 - 67312 * q^59 - 109800 * q^60 - 307184 * q^61 + 150704 * q^62 - 696 * q^65 + 54720 * q^66 + 364272 * q^67 + 558960 * q^68 - 81864 * q^69 + 313960 * q^70 + 309808 * q^71 - 268752 * q^73 - 393712 * q^74 - 96624 * q^75 - 228552 * q^76 - 841536 * q^77 - 130824 * q^78 - 57216 * q^79 + 658528 * q^80 - 335992 * q^82 + 406240 * q^83 + 664848 * q^84 + 686840 * q^85 - 842560 * q^86 + 127224 * q^87 + 538248 * q^88 - 103680 * q^90 - 368592 * q^91 + 96752 * q^92 - 113472 * q^93 - 622576 * q^94 - 1143560 * q^95 - 375552 * q^96 - 40424 * q^97 - 51192 * q^99

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