LMFDB - Embedded newform 82.6.f.b.25.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [82,6,Mod(23,82)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(82, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([9])) N = Newforms(chi, 6, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("82.23"); S:= CuspForms(chi, 6); N := Newforms(S);

Level:	$ N $	$=$	$ 82 = 2 \cdot 41 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	82.f (of order $10$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [40] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$13.1514732247$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			25.1
Character	$\chi$	$=$	82.25
Dual form			82.6.f.b.23.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.23607 + 3.80423i) q^{2} -27.3707i q^{3} +(-12.9443 - 9.40456i) q^{4} +(80.2757 + 58.3237i) q^{5} +(104.124 + 33.8320i) q^{6} +(108.180 - 35.1500i) q^{7} +(51.7771 - 37.6183i) q^{8} -506.154 q^{9} +(-321.103 + 233.295i) q^{10} +(223.071 + 307.031i) q^{11} +(-257.409 + 354.294i) q^{12} +(13.9510 + 4.53295i) q^{13} +454.991i q^{14} +(1596.36 - 2197.20i) q^{15} +(79.1084 + 243.470i) q^{16} +(101.772 + 140.077i) q^{17} +(625.641 - 1925.52i) q^{18} +(1892.47 - 614.901i) q^{19} +(-490.602 - 1509.92i) q^{20} +(-962.078 - 2960.97i) q^{21} +(-1443.75 + 469.101i) q^{22} +(1280.63 - 3941.38i) q^{23} +(-1029.64 - 1417.17i) q^{24} +(2076.86 + 6391.91i) q^{25} +(-34.4887 + 47.4697i) q^{26} +7202.70i q^{27} +(-1730.89 - 562.399i) q^{28} +(3780.21 - 5203.01i) q^{29} +(6385.44 + 8788.81i) q^{30} +(-3451.48 + 2507.65i) q^{31} -1024.00 q^{32} +(8403.64 - 6105.60i) q^{33} +(-658.681 + 214.018i) q^{34} +(10734.3 + 3487.80i) q^{35} +(6551.80 + 4760.16i) q^{36} +(-9308.37 - 6762.93i) q^{37} +7959.45i q^{38} +(124.070 - 381.848i) q^{39} +6350.48 q^{40} +(-8174.69 + 7002.19i) q^{41} +12453.4 q^{42} +(242.314 - 745.766i) q^{43} -6072.18i q^{44} +(-40631.9 - 29520.8i) q^{45} +(13411.0 + 9743.63i) q^{46} +(-2003.16 - 650.865i) q^{47} +(6663.95 - 2165.25i) q^{48} +(-3129.66 + 2273.83i) q^{49} -26883.4 q^{50} +(3834.00 - 2785.56i) q^{51} +(-137.955 - 189.879i) q^{52} +(18068.5 - 24869.2i) q^{53} +(-27400.7 - 8903.03i) q^{54} +37657.5i q^{55} +(4278.99 - 5889.52i) q^{56} +(-16830.3 - 51798.2i) q^{57} +(15120.8 + 20812.1i) q^{58} +(-3482.68 + 10718.6i) q^{59} +(-41327.4 + 13428.1i) q^{60} +(6703.66 + 20631.7i) q^{61} +(-5273.39 - 16229.8i) q^{62} +(-54756.0 + 17791.3i) q^{63} +(1265.73 - 3895.53i) q^{64} +(855.547 + 1177.56i) q^{65} +(12839.6 + 39516.3i) q^{66} +(3323.88 - 4574.92i) q^{67} -2770.31i q^{68} +(-107878. - 35051.8i) q^{69} +(-26536.8 + 36524.7i) q^{70} +(32078.5 + 44152.3i) q^{71} +(-26207.2 + 19040.6i) q^{72} +77537.7 q^{73} +(37233.5 - 27051.7i) q^{74} +(174951. - 56845.0i) q^{75} +(-30279.5 - 9838.42i) q^{76} +(34924.0 + 25373.8i) q^{77} +(1299.28 + 943.980i) q^{78} +80004.4i q^{79} +(-7849.63 + 24158.7i) q^{80} +74147.5 q^{81} +(-16533.4 - 39753.6i) q^{82} -58471.8 q^{83} +(-15393.2 + 47375.6i) q^{84} +17180.5i q^{85} +(2537.54 + 1843.63i) q^{86} +(-142410. - 103467. i) q^{87} +(23099.9 + 7505.62i) q^{88} +(-129431. + 42054.6i) q^{89} +(162528. - 118083. i) q^{90} +1668.56 q^{91} +(-53643.8 + 38974.5i) q^{92} +(68636.0 + 94469.4i) q^{93} +(4952.07 - 6815.95i) q^{94} +(187783. + 61014.3i) q^{95} +28027.6i q^{96} +(-102254. + 140740. i) q^{97} +(-4781.70 - 14716.5i) q^{98} +(-112908. - 155405. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 40 q^{2} - 160 q^{4} + 24 q^{5} - 100 q^{6} + 640 q^{8} - 4576 q^{9} - 96 q^{10} + 20 q^{11} + 400 q^{12} - 275 q^{13} + 1385 q^{15} - 2560 q^{16} - 105 q^{17} - 2476 q^{18} + 4720 q^{19} + 1424 q^{20}+ \cdots - 537690 q^{99}+O(q^{100}) $ 40 * q + 40 * q^2 - 160 * q^4 + 24 * q^5 - 100 * q^6 + 640 * q^8 - 4576 * q^9 - 96 * q^10 + 20 * q^11 + 400 * q^12 - 275 * q^13 + 1385 * q^15 - 2560 * q^16 - 105 * q^17 - 2476 * q^18 + 4720 * q^19 + 1424 * q^20 + 6961 * q^21 - 4140 * q^22 - 1019 * q^23 + 1600 * q^24 - 2006 * q^25 - 8620 * q^26 - 12525 * q^29 + 5540 * q^30 + 8900 * q^31 - 40960 * q^32 + 17684 * q^33 - 13100 * q^34 - 29955 * q^35 + 26704 * q^36 - 31651 * q^37 - 10104 * q^39 + 14464 * q^40 + 35044 * q^41 + 32776 * q^42 - 15615 * q^43 - 39955 * q^45 - 3224 * q^46 + 8330 * q^47 - 6400 * q^48 + 48406 * q^49 - 135016 * q^50 + 120325 * q^51 - 34480 * q^52 + 145425 * q^53 + 72200 * q^54 + 17600 * q^56 + 31992 * q^57 - 50100 * q^58 + 18978 * q^59 + 1680 * q^60 + 52673 * q^61 + 66140 * q^62 - 88455 * q^63 - 40960 * q^64 + 204480 * q^65 - 17556 * q^66 - 149205 * q^67 - 249735 * q^69 - 49100 * q^70 + 151175 * q^71 - 106816 * q^72 - 107670 * q^73 + 126604 * q^74 + 120180 * q^75 - 75520 * q^76 - 207367 * q^77 - 99284 * q^78 + 22784 * q^80 + 1167568 * q^81 + 84204 * q^82 - 281376 * q^83 + 111376 * q^84 - 131400 * q^86 - 141269 * q^87 + 66240 * q^88 - 277775 * q^89 + 159820 * q^90 - 518682 * q^91 + 12896 * q^92 - 172375 * q^93 + 16320 * q^94 + 149585 * q^95 + 330875 * q^97 - 171004 * q^98 - 537690 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/82\mathbb{Z}\right)^\times$.

$n$	$47$
$\chi(n)$	$e\left(\frac{1}{10}\right)$

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 $

$2$	−1.23607	+	3.80423i	−0.218508	+	0.672499i
$2$	−1.23607	+	3.80423i	−0.218508	+	0.672499i
$3$		−	27.3707i		−	1.75583i	−0.478817	−	0.877915i	$-0.658934\pi$
$3$		−	27.3707i		−	1.75583i	0.478817	−	0.877915i	$-0.341066\pi$
$4$	−12.9443	−	9.40456i	−0.404508	−	0.293893i
$5$	80.2757	+	58.3237i	1.43602	+	1.04333i	0.988856	+	0.148873i	$0.0475644\pi$
$5$	80.2757	+	58.3237i	1.43602	+	1.04333i	0.447160	+	0.894454i	$0.352436\pi$
$6$	104.124	+	33.8320i	1.18079	+	0.383663i
$7$	108.180	−	35.1500i	0.834456	−	0.271131i	0.139535	−	0.990217i	$-0.455439\pi$
$7$	108.180	−	35.1500i	0.834456	−	0.271131i	0.694921	+	0.719086i	$0.255439\pi$
$8$	51.7771	−	37.6183i	0.286031	−	0.207813i
$9$	−506.154			−2.08294
$10$	−321.103	+	233.295i	−1.01542	+	0.737743i
$11$	223.071	+	307.031i	0.555855	+	0.765069i	0.990792	−	0.135392i	$-0.0432295\pi$
$11$	223.071	+	307.031i	0.555855	+	0.765069i	−0.434937	+	0.900461i	$0.643229\pi$
$12$	−257.409	+	354.294i	−0.516025	+	0.710248i
$13$	13.9510	+	4.53295i	0.0228953	+	0.00743914i	0.320442	−	0.947268i	$-0.396168\pi$
$13$	13.9510	+	4.53295i	0.0228953	+	0.00743914i	−0.297547	+	0.954707i	$0.596168\pi$
$14$			454.991i			0.620415i
$15$	1596.36	−	2197.20i	1.83190	−	2.52140i
$16$	79.1084	+	243.470i	0.0772542	+	0.237764i
$17$	101.772	+	140.077i	0.0854093	+	0.117556i	0.849584	−	0.527454i	$-0.176853\pi$
$17$	101.772	+	140.077i	0.0854093	+	0.117556i	−0.764174	+	0.645010i	$0.776853\pi$
$18$	625.641	−	1925.52i	0.455139	−	1.40077i
$19$	1892.47	−	614.901i	1.20267	−	0.390770i	0.361925	−	0.932207i	$-0.382120\pi$
$19$	1892.47	−	614.901i	1.20267	−	0.390770i	0.840741	+	0.541437i	$0.182120\pi$
$20$	−490.602	−	1509.92i	−0.274255	−	0.844069i
$21$	−962.078	−	2960.97i	−0.476060	−	1.46516i
$22$	−1443.75	+	469.101i	−0.635966	+	0.206638i
$23$	1280.63	−	3941.38i	0.504783	−	1.55356i	−0.296351	−	0.955079i	$-0.595770\pi$
$23$	1280.63	−	3941.38i	0.504783	−	1.55356i	0.801135	−	0.598484i	$-0.204230\pi$
$24$	−1029.64	−	1417.17i	−0.364885	−	0.502221i
$25$	2076.86	+	6391.91i	0.664594	+	2.04541i
$26$	−34.4887	+	47.4697i	−0.0100056	+	0.0137716i
$27$			7202.70i			1.90146i
$28$	−1730.89	−	562.399i	−0.417228	−	0.135566i
$29$	3780.21	−	5203.01i	0.834682	−	1.14884i	−0.152352	−	0.988326i	$-0.548685\pi$
$29$	3780.21	−	5203.01i	0.834682	−	1.14884i	0.987033	−	0.160515i	$-0.0513154\pi$
$30$	6385.44	+	8788.81i	1.29535	+	1.78290i
$31$	−3451.48	+	2507.65i	−0.645062	+	0.468665i	−0.861585	−	0.507613i	$-0.830528\pi$
$31$	−3451.48	+	2507.65i	−0.645062	+	0.468665i	0.216524	+	0.976277i	$0.430528\pi$
$32$	−1024.00			−0.176777
$33$	8403.64	−	6105.60i	1.34333	−	0.975986i
$34$	−658.681	+	214.018i	−0.0977187	+	0.0317507i
$35$	10734.3	+	3487.80i	1.48117	+	0.481262i
$36$	6551.80	+	4760.16i	0.842566	+	0.612160i
$37$	−9308.37	−	6762.93i	−1.11781	−	0.812139i	−0.133938	−	0.990990i	$-0.542762\pi$
$37$	−9308.37	−	6762.93i	−1.11781	−	0.812139i	−0.983876	+	0.178850i	$0.942762\pi$
$38$			7959.45i			0.894178i
$39$	124.070	−	381.848i	0.0130619	−	0.0402003i
$40$	6350.48			0.627562
$41$	−8174.69	+	7002.19i	−0.759472	+	0.650540i
$41$	−8174.69	+	7002.19i	−0.759472	+	0.650540i
$42$	12453.4			1.08934
$43$	242.314	−	745.766i	0.0199851	−	0.0615079i	−0.940567	−	0.339609i	$-0.889705\pi$
$43$	242.314	−	745.766i	0.0199851	−	0.0615079i	0.960552	+	0.278101i	$0.0897051\pi$
$44$		−	6072.18i		−	0.472838i
$45$	−40631.9	−	29520.8i	−2.99113	−	2.17319i
$46$	13411.0	+	9743.63i	0.934470	+	0.678932i
$47$	−2003.16	−	650.865i	−0.132273	−	0.0429780i	0.242133	−	0.970243i	$-0.422153\pi$
$47$	−2003.16	−	650.865i	−0.132273	−	0.0429780i	−0.374405	+	0.927265i	$0.622153\pi$
$48$	6663.95	−	2165.25i	0.417473	−	0.135645i
$49$	−3129.66	+	2273.83i	−0.186212	+	0.135291i
$50$	−26883.4			−1.52076
$51$	3834.00	−	2785.56i	0.206408	−	0.149964i
$52$	−137.955	−	189.879i	−0.00707504	−	0.00973796i
$53$	18068.5	−	24869.2i	0.883552	−	1.21611i	−0.0918718	−	0.995771i	$-0.529285\pi$
$53$	18068.5	−	24869.2i	0.883552	−	1.21611i	0.975424	−	0.220335i	$-0.0707150\pi$
$54$	−27400.7	−	8903.03i	−1.27873	−	0.415483i
$55$			37657.5i			1.67859i
$56$	4278.99	−	5889.52i	0.182335	−	0.250963i
$57$	−16830.3	−	51798.2i	−0.686126	−	2.11168i
$58$	15120.8	+	20812.1i	0.590209	+	0.812353i
$59$	−3482.68	+	10718.6i	−0.130252	+	0.400874i	−0.994821	−	0.101640i	$-0.967591\pi$
$59$	−3482.68	+	10718.6i	−0.130252	+	0.400874i	0.864570	+	0.502513i	$0.167591\pi$
$60$	−41327.4	+	13428.1i	−1.48204	+	0.481545i
$61$	6703.66	+	20631.7i	0.230668	+	0.709923i	0.997667	+	0.0682741i	$0.0217492\pi$
$61$	6703.66	+	20631.7i	0.230668	+	0.709923i	−0.766999	+	0.641649i	$0.778251\pi$
$62$	−5273.39	−	16229.8i	−0.174225	−	0.536210i
$63$	−54756.0	+	17791.3i	−1.73812	+	0.564750i
$64$	1265.73	−	3895.53i	0.0386271	−	0.118882i
$65$	855.547	+	1177.56i	0.0251166	+	0.0345700i
$66$	12839.6	+	39516.3i	0.362821	+	1.11665i
$67$	3323.88	−	4574.92i	0.0904603	−	0.124508i	−0.761388	−	0.648296i	$-0.775482\pi$
$67$	3323.88	−	4574.92i	0.0904603	−	0.124508i	0.851848	+	0.523788i	$0.175482\pi$
$68$		−	2770.31i		−	0.0726535i
$69$	−107878.	−	35051.8i	−2.72779	−	0.886314i
$70$	−26536.8	+	36524.7i	−0.647296	+	0.890926i
$71$	32078.5	+	44152.3i	0.755211	+	1.03946i	0.997597	+	0.0692794i	$0.0220700\pi$
$71$	32078.5	+	44152.3i	0.755211	+	1.03946i	−0.242386	+	0.970180i	$0.577930\pi$
$72$	−26207.2	+	19040.6i	−0.595784	+	0.432863i
$73$	77537.7			1.70297			0.851483	−	0.524382i	$-0.175704\pi$
$73$	77537.7			1.70297			0.851483	+	0.524382i	$0.175704\pi$
$74$	37233.5	−	27051.7i	0.790414	−	0.574269i
$75$	174951.	−	56845.0i	3.59139	−	1.16691i
$76$	−30279.5	−	9838.42i	−0.601333	−	0.195385i
$77$	34924.0	+	25373.8i	0.671271	+	0.487707i
$78$	1299.28	+	943.980i	0.0241805	+	0.0175682i
$79$			80004.4i			1.44227i	0.692796	+	0.721134i	$0.256379\pi$
$79$			80004.4i			1.44227i	−0.692796	+	0.721134i	$0.743621\pi$
$80$	−7849.63	+	24158.7i	−0.137127	+	0.422035i
$81$	74147.5			1.25569
$82$	−16533.4	−	39753.6i	−0.271537	−	0.652892i
$83$	−58471.8			−0.931647			−0.465823	−	0.884878i	$-0.654242\pi$
$83$	−58471.8			−0.931647			−0.465823	+	0.884878i	$0.654242\pi$
$84$	−15393.2	+	47375.6i	−0.238030	+	0.732582i
$85$			17180.5i			0.257922i
$86$	2537.54	+	1843.63i	0.0369971	+	0.0268800i
$87$	−142410.	−	103467.i	−2.01717	−	1.46556i
$88$	23099.9	+	7505.62i	0.317983	+	0.103319i
$89$	−129431.	+	42054.6i	−1.73206	+	0.562780i	−0.993745	−	0.111677i	$-0.964378\pi$
$89$	−129431.	+	42054.6i	−1.73206	+	0.562780i	−0.738314	+	0.674457i	$0.764378\pi$
$90$	162528.	−	118083.i	2.11505	−	1.53667i
$91$	1668.56			0.0211221
$92$	−53643.8	+	38974.5i	−0.660770	+	0.480077i
$93$	68636.0	+	94469.4i	0.822896	+	1.13262i
$94$	4952.07	−	6815.95i	0.0578053	−	0.0795621i
$95$	187783.	+	61014.3i	2.13475	+	0.693622i
$96$			28027.6i			0.310390i
$97$	−102254.	+	140740.i	−1.10344	+	1.51876i	−0.272704	+	0.962098i	$0.587918\pi$
$97$	−102254.	+	140740.i	−1.10344	+	1.51876i	−0.830739	+	0.556662i	$0.812082\pi$
$98$	−4781.70	−	14716.5i	−0.0502941	−	0.154789i
$99$	−112908.	−	155405.i	−1.15781	−	1.59359i
$100$	33229.7	−	102271.i	0.332297	−	1.02271i
$101$	45889.1	−	14910.3i	0.447616	−	0.145439i	−0.0765306	−	0.997067i	$-0.524384\pi$
$101$	45889.1	−	14910.3i	0.447616	−	0.145439i	0.524147	+	0.851628i	$0.324384\pi$
$102$	5857.83	+	18028.5i	0.0557489	+	0.171577i
$103$	−33306.8	−	102508.i	−0.309343	−	0.952060i	−0.978021	−	0.208508i	$-0.933139\pi$
$103$	−33306.8	−	102508.i	−0.309343	−	0.952060i	0.668678	−	0.743552i	$-0.266861\pi$
$104$	892.863	−	290.109i	0.00809472	−	0.00263013i
$105$	95463.4	−	293806.i	0.845014	−	2.60068i
$106$	72274.0	+	99476.6i	0.624766	+	0.859917i
$107$	−28237.1	−	86904.8i	−0.238430	−	0.733811i	−0.996648	−	0.0818103i	$-0.973930\pi$
$107$	−28237.1	−	86904.8i	−0.238430	−	0.733811i	0.758218	−	0.652001i	$-0.226070\pi$
$108$	67738.3	−	93233.8i	0.558824	−	0.769155i
$109$		−	70603.6i		−	0.569194i	−0.958647	−	0.284597i	$-0.908140\pi$
$109$		−	70603.6i		−	0.569194i	0.958647	−	0.284597i	$-0.0918598\pi$
$110$	−143258.	−	46547.2i	−1.12885	−	0.366785i
$111$	−185106.	+	254777.i	−1.42598	+	1.96269i
$112$	17116.0	+	23558.1i	0.128931	+	0.177458i
$113$	−74507.6	+	54132.9i	−0.548914	+	0.398809i	−0.827385	−	0.561635i	$-0.810172\pi$
$113$	−74507.6	+	54132.9i	−0.548914	+	0.398809i	0.278471	+	0.960445i	$0.410172\pi$
$114$	217855.			1.57002
$115$	332680.	−	241706.i	2.34575	−	1.70429i
$116$	−97864.1	+	31798.0i	−0.675272	+	0.219409i
$117$	−7061.35	−	2294.37i	−0.0476895	−	0.0154953i
$118$	−36471.1	−	26497.8i	−0.241126	−	0.175188i
$119$	15933.4	+	11576.3i	0.103143	+	0.0749381i
$120$		−	173817.i		−	1.10189i
$121$	5260.21	−	16189.3i	0.0326617	−	0.100523i
$122$	−86773.9			−0.527825
$123$	191655.	+	223747.i	1.14224	+	1.33350i
$124$	68260.2			0.398670
$125$	−110258.	+	339340.i	−0.631155	+	1.94249i
$126$		−	230295.i		−	1.29229i
$127$	125408.	+	91114.4i	0.689948	+	0.501277i	0.876643	−	0.481141i	$-0.159778\pi$
$127$	125408.	+	91114.4i	0.689948	+	0.501277i	−0.186695	+	0.982418i	$0.559778\pi$
$128$	13254.9	+	9630.27i	0.0715077	+	0.0519534i
$129$	−20412.1	−	6632.30i	−0.107997	−	0.0350905i
$130$	−5537.22	+	1799.15i	−0.0287365	+	0.00933704i
$131$	53177.4	−	38635.6i	0.270738	−	0.196702i	−0.444130	−	0.895963i	$-0.646487\pi$
$131$	53177.4	−	38635.6i	0.270738	−	0.196702i	0.714867	+	0.699260i	$0.246487\pi$
$132$	−166200.			−0.830224
$133$	183115.	−	133041.i	0.897623	−	0.652161i
$134$	13295.5	+	18299.7i	0.0639651	+	0.0880404i
$135$	−420089.	+	578202.i	−1.98384	+	2.73052i
$136$	10538.9	+	3424.29i	0.0488594	+	0.0158754i
$137$			10779.0i			0.0490657i	0.999699	+	0.0245329i	$0.00780984\pi$
$137$			10779.0i			0.0490657i	−0.999699	+	0.0245329i	$0.992190\pi$
$138$	266690.	−	367067.i	1.19209	−	1.64077i
$139$	78927.3	+	242913.i	0.346489	+	1.06638i	0.960782	+	0.277306i	$0.0894417\pi$
$139$	78927.3	+	242913.i	0.346489	+	1.06638i	−0.614292	+	0.789079i	$0.710558\pi$
$140$	−106147.	−	146099.i	−0.457707	−	0.629980i
$141$	−17814.6	+	54827.7i	−0.0754620	+	0.232248i
$142$	−207617.	+	67458.7i	−0.864055	+	0.280748i
$143$	1720.30	+	5294.55i	0.00703502	+	0.0216516i
$144$	−40041.0	−	123234.i	−0.160916	−	0.495248i
$145$	606918.	−	197200.i	2.39723	−	0.778908i
$146$	−95841.9	+	294971.i	−0.372112	+	1.14524i
$147$	62236.3	+	85660.9i	0.237548	+	0.326956i
$148$	56887.7	+	175082.i	0.213483	+	0.657035i
$149$	−126643.	+	174309.i	−0.467322	+	0.643214i	−0.976007	−	0.217739i	$-0.930132\pi$
$149$	−126643.	+	174309.i	−0.467322	+	0.643214i	0.508685	+	0.860953i	$0.330132\pi$
$150$			735817.i			2.67019i
$151$	−396471.	−	128821.i	−1.41504	−	0.459775i	−0.501018	−	0.865437i	$-0.667041\pi$
$151$	−396471.	−	128821.i	−1.41504	−	0.459775i	−0.914023	+	0.405662i	$0.867041\pi$
$152$	74855.1	−	103029.i	0.262792	−	0.361703i
$153$	−51512.2	−	70900.5i	−0.177902	−	0.244862i
$154$	−139696.	+	101495.i	−0.474660	+	0.344861i
$155$	−423326.			−1.41529
$156$	−5197.11	+	3775.92i	−0.0170982	+	0.0124226i
$157$	263668.	−	85671.1i	0.853707	−	0.277386i	0.150709	−	0.988578i	$-0.451844\pi$
$157$	263668.	−	85671.1i	0.853707	−	0.277386i	0.702998	+	0.711192i	$0.251844\pi$
$158$	−304355.	−	98890.8i	−0.969923	−	0.315147i
$159$	−680686.	−	494547.i	−2.13527	−	1.55137i
$160$	−82202.4	−	59723.5i	−0.253854	−	0.184436i
$161$		−	471395.i		−	1.43324i
$162$	−91651.3	+	282074.i	−0.274379	+	0.844452i
$163$	−123763.			−0.364858			−0.182429	−	0.983219i	$-0.558396\pi$
$163$	−123763.			−0.364858			−0.182429	+	0.983219i	$0.558396\pi$
$164$	171668.	−	13758.8i	0.498402	−	0.0399458i
$165$	1.03071e6			2.94732
$166$	72275.1	−	222440.i	0.203572	−	0.626531i
$167$		−	243540.i		−	0.675738i	−0.941193	−	0.337869i	$-0.890294\pi$
$167$		−	243540.i		−	0.675738i	0.941193	−	0.337869i	$-0.109706\pi$
$168$	−161200.	−	117119.i	−0.440649	−	0.320150i
$169$	−300208.	−	218114.i	−0.808548	−	0.587445i
$170$	−65358.4	−	21236.2i	−0.173452	−	0.0563580i
$171$	−957882.	+	311235.i	−2.50508	+	0.813950i
$172$	−10150.2	+	7374.54i	−0.0261609	+	0.0190070i
$173$	−28309.1			−0.0719135			−0.0359568	−	0.999353i	$-0.511448\pi$
$173$	−28309.1			−0.0719135			−0.0359568	+	0.999353i	$0.511448\pi$
$174$	569640.	−	413868.i	1.42635	−	1.03631i
$175$	449351.	+	618478.i	1.10915	+	1.52661i
$176$	−57106.2	+	78599.9i	−0.138964	+	0.191267i
$177$	293375.	+	95323.3i	0.703866	+	0.228700i
$178$		−	544366.i		−	1.28778i
$179$	−258584.	+	355910.i	−0.603210	+	0.830247i	−0.995997	−	0.0893823i	$-0.971511\pi$
$179$	−258584.	+	355910.i	−0.603210	+	0.830247i	0.392788	+	0.919629i	$0.371511\pi$
$180$	248320.	+	764250.i	0.571256	+	1.75814i
$181$	−156130.	−	214894.i	−0.354233	−	0.487560i	0.594297	−	0.804245i	$-0.297430\pi$
$181$	−156130.	−	214894.i	−0.354233	−	0.487560i	−0.948531	+	0.316685i	$0.897430\pi$
$182$	−2062.45	+	6347.57i	−0.00461535	+	0.0142046i
$183$	564705.	−	183484.i	1.24650	−	0.405014i
$184$	−81960.5	−	252248.i	−0.178468	−	0.549268i
$185$	−352797.	−	1.08580e6i	−0.757872	−	2.33249i
$186$	−444222.	+	144336.i	−0.941494	+	0.305910i
$187$	−20305.6	+	62494.2i	−0.0424631	+	0.130688i
$188$	19808.3	+	27263.8i	0.0408745	+	0.0562589i
$189$	253175.	+	779192.i	0.515544	+	1.58668i
$190$	−464225.	+	638951.i	−0.932920	+	1.28405i
$191$			123956.i			0.245859i	0.992415	+	0.122929i	$0.0392288\pi$
$191$			123956.i			0.245859i	−0.992415	+	0.122929i	$0.960771\pi$
$192$	−106623.	−	34644.0i	−0.208737	−	0.0678227i
$193$	−28198.8	+	38812.4i	−0.0544927	+	0.0750027i	−0.835394	−	0.549652i	$-0.814760\pi$
$193$	−28198.8	+	38812.4i	−0.0544927	+	0.0750027i	0.780901	+	0.624655i	$0.214760\pi$
$194$	−409015.	−	562961.i	−0.780252	−	1.07393i
$195$	32230.6	−	23416.9i	0.0606991	−	0.0441005i
$196$	61895.6			0.115085
$197$	−592850.	+	430731.i	−1.08838	+	0.790752i	−0.979124	−	0.203262i	$-0.934846\pi$
$197$	−592850.	+	430731.i	−1.08838	+	0.790752i	−0.109253	+	0.994014i	$0.534846\pi$
$198$	730758.	−	237438.i	1.32468	−	0.430414i
$199$	214287.	+	69626.1i	0.383586	+	0.124635i	0.494461	−	0.869200i	$-0.335365\pi$
$199$	214287.	+	69626.1i	0.383586	+	0.124635i	−0.110875	+	0.993834i	$0.535365\pi$
$200$	347986.	+	252827.i	0.615158	+	0.446939i
$201$	−125219.	−	90976.8i	−0.218615	−	0.158833i
$202$			193003.i			0.332801i
$203$	226059.	−	695738.i	0.385019	−	1.18497i
$204$	−75825.3			−0.127567
$205$	−1.06462e6	+	85327.2i	−1.76934	+	0.141809i
$206$	431133.			0.707853
$207$	−648197.	+	1.99495e6i	−1.05143	+	3.23598i
$208$			3755.25i			0.00601839i
$209$	610949.	+	443880.i	0.967474	+	0.702911i
$210$	999706.	+	726329.i	1.56431	+	1.13654i
$211$	372147.	+	120918.i	0.575451	+	0.186975i	0.582262	−	0.813002i	$-0.302168\pi$
$211$	372147.	+	120918.i	0.575451	+	0.186975i	−0.00681079	+	0.999977i	$0.502168\pi$
$212$	−467767.	+	151987.i	−0.714809	+	0.232256i
$213$	1.20848e6	−	878011.i	1.82511	−	1.32602i
$214$	365508.			0.545586
$215$	62947.8	−	45734.2i	0.0928719	−	0.0674754i
$216$	270953.	+	372935.i	0.395148	+	0.543875i
$217$	−285239.	+	392598.i	−0.411206	+	0.565977i
$218$	268592.	+	87270.9i	0.382782	+	0.124374i
$219$		−	2.12226e6i		−	2.99012i
$220$	354152.	−	487448.i	0.493325	−	0.679003i
$221$	784.856	+	2415.54i	0.00108096	+	0.00332685i
$222$	−740424.	−	1.01911e6i	−1.00832	−	1.38783i
$223$	−79460.8	+	244555.i	−0.107002	+	0.329317i	−0.990195	−	0.139692i	$-0.955389\pi$
$223$	−79460.8	+	244555.i	−0.107002	+	0.329317i	0.883193	+	0.469009i	$0.155389\pi$
$224$	−110777.	+	35993.6i	−0.147512	+	0.0479297i
$225$	−1.05121e6	−	3.23529e6i	−1.38431	−	4.26047i
$226$	−113837.	−	350356.i	−0.148257	−	0.456287i
$227$	−376966.	+	122484.i	−0.485554	+	0.157766i	−0.541556	−	0.840665i	$-0.682165\pi$
$227$	−376966.	+	122484.i	−0.485554	+	0.157766i	0.0560022	+	0.998431i	$0.482165\pi$
$228$	−269284.	+	828772.i	−0.343063	+	1.05584i
$229$	−170931.	−	235267.i	−0.215393	−	0.296464i	0.687624	−	0.726066i	$-0.258654\pi$
$229$	−170931.	−	235267.i	−0.215393	−	0.296464i	−0.903018	+	0.429603i	$0.858654\pi$
$230$	508290.	+	1.56435e6i	0.633566	+	1.94991i
$231$	694498.	−	955895.i	0.856330	−	1.17864i
$232$		−	411602.i		−	0.502062i
$233$	374188.	+	121581.i	0.451544	+	0.146715i	0.525955	−	0.850512i	$-0.323708\pi$
$233$	374188.	+	121581.i	0.451544	+	0.146715i	−0.0744117	+	0.997228i	$0.523708\pi$
$234$	17456.6	−	24027.0i	0.0208411	−	0.0286853i
$235$	−122844.	−	169080.i	−0.145106	−	0.199721i
$236$	145884.	−	105991.i	0.170502	−	0.123877i
$237$	2.18977e6			2.53238
$238$	−63733.6	+	46305.2i	−0.0729334	+	0.0529892i
$239$	902460.	−	293227.i	1.02196	−	0.332054i	0.250352	−	0.968155i	$-0.419454\pi$
$239$	902460.	−	293227.i	1.02196	−	0.332054i	0.771606	+	0.636101i	$0.219454\pi$
$240$	661239.	+	214850.i	0.741021	+	0.240772i
$241$	510858.	+	371160.i	0.566575	+	0.411641i	0.833860	−	0.551977i	$-0.186126\pi$
$241$	510858.	+	371160.i	0.566575	+	0.411641i	−0.267284	+	0.963618i	$0.586126\pi$
$242$	55085.6	+	40022.0i	0.0604644	+	0.0439299i
$243$		−	279210.i		−	0.303330i
$244$	107258.	−	330108.i	0.115334	−	0.354961i
$245$	−383854.			−0.408556
$246$	−1.08808e6	+	452531.i	−1.14637	+	0.476772i
$247$	29189.2			0.0304424
$248$	−84374.3	+	259677.i	−0.0871126	+	0.268105i
$249$			1.60041e6i			1.63581i
$250$	−1.15464e6	−	838894.i	−1.16841	−	0.848901i
$251$	−458511.	−	333128.i	−0.459373	−	0.333754i	0.333912	−	0.942604i	$-0.391631\pi$
$251$	−458511.	−	333128.i	−0.459373	−	0.333754i	−0.793285	+	0.608850i	$0.791631\pi$
$252$	876095.	+	284661.i	0.869061	+	0.282375i
$253$	1.49580e6	−	486014.i	1.46917	−	0.477362i
$254$	−501633.	+	364457.i	−0.487867	+	0.354456i
$255$	470242.			0.452867
$256$	−53019.7	+	38521.1i	−0.0505636	+	0.0367366i
$257$	−931643.	−	1.28230e6i	−0.879866	−	1.21103i	−0.976458	−	0.215708i	$-0.930794\pi$
$257$	−931643.	−	1.28230e6i	−0.879866	−	1.21103i	0.0965915	−	0.995324i	$-0.469206\pi$
$258$	50461.5	−	69454.3i	0.0471966	−	0.0649606i
$259$	−1.24470e6	−	404428.i	−1.15296	−	0.374621i
$260$		−	23288.7i		−	0.0213654i
$261$	−1.91337e6	+	2.63353e6i	−1.73859	+	2.39296i
$262$	81247.8	+	250055.i	0.0731238	+	0.225052i
$263$	−745509.	−	1.02611e6i	−0.664605	−	0.914751i	0.335018	−	0.942212i	$-0.391258\pi$
$263$	−745509.	−	1.02611e6i	−0.664605	−	0.914751i	−0.999623	+	0.0274612i	$0.991258\pi$
$264$	205434.	−	632261.i	0.181411	−	0.558324i
$265$	2.90092e6	−	942567.i	2.53759	−	0.824513i
$266$	279774.	+	861057.i	0.242440	+	0.746152i
$267$	1.15106e6	+	3.54261e6i	0.988146	+	3.04120i
$268$	−86050.3	+	27959.5i	−0.0731839	+	0.0237789i
$269$	−408427.	+	1.25701e6i	−0.344139	+	1.05915i	0.617904	+	0.786254i	$0.287982\pi$
$269$	−408427.	+	1.25701e6i	−0.344139	+	1.05915i	−0.962043	+	0.272898i	$0.912018\pi$
$270$	−1.68035e6	−	2.31281e6i	−1.40279	−	1.93077i
$271$	361967.	+	1.11402e6i	0.299395	+	0.921444i	0.981709	+	0.190385i	$0.0609737\pi$
$271$	361967.	+	1.11402e6i	0.299395	+	0.921444i	−0.682314	+	0.731059i	$0.739026\pi$
$272$	−26053.6	+	35859.7i	−0.0213523	+	0.0293890i
$273$		−	45669.5i		−	0.0370869i
$274$	−41005.9	−	13323.6i	−0.0329966	−	0.0107213i
$275$	−1.49923e6	+	2.06351e6i	−1.19546	+	1.64541i
$276$	1.06676e6	+	1.46827e6i	0.842934	+	1.16020i
$277$	−1.43506e6	+	1.04263e6i	−1.12375	+	0.816451i	−0.984773	−	0.173844i	$-0.944381\pi$
$277$	−1.43506e6	+	1.04263e6i	−1.12375	+	0.816451i	−0.138976	+	0.990296i	$0.544381\pi$
$278$	−1.02166e6			−0.792853
$279$	1.74698e6	−	1.26926e6i	1.34362	−	0.976200i
$280$	686998.	−	223219.i	0.523673	−	0.170152i
$281$	−1.38915e6	−	451363.i	−1.04950	−	0.341005i	−0.267031	−	0.963688i	$-0.586042\pi$
$281$	−1.38915e6	−	451363.i	−1.04950	−	0.341005i	−0.782474	+	0.622683i	$0.786042\pi$
$282$	−186557.	−	135542.i	−0.139698	−	0.101496i
$283$	674665.	+	490173.i	0.500751	+	0.363817i	0.809304	−	0.587390i	$-0.199845\pi$
$283$	674665.	+	490173.i	0.500751	+	0.363817i	−0.308553	+	0.951207i	$0.599845\pi$
$284$		−	873204.i		−	0.642421i
$285$	1.67000e6	−	5.13974e6i	1.21788	−	3.74826i
$286$	−22268.1			−0.0160979
$287$	−638215.	+	1.04484e6i	−0.457364	+	0.748764i
$288$	518302.			0.368215
$289$	429496.	−	1.32185e6i	0.302492	−	0.930976i
$290$			2.55261e6i			1.78233i
$291$	3.85216e6	+	2.79876e6i	2.66668	+	1.93746i
$292$	−1.00367e6	−	729209.i	−0.688864	−	0.500489i
$293$	−1.12370e6	−	365113.i	−0.764684	−	0.248461i	−0.0993960	−	0.995048i	$-0.531691\pi$
$293$	−1.12370e6	−	365113.i	−0.764684	−	0.248461i	−0.665288	+	0.746587i	$0.731691\pi$
$294$	−402802.	+	130878.i	−0.271784	+	0.0883078i
$295$	−904723.	+	657319.i	−0.605286	+	0.439766i
$296$	−736370.			−0.488503
$297$	−2.21145e6	+	1.60671e6i	−1.45474	+	1.05693i
$298$	−506573.	−	697238.i	−0.330447	−	0.454821i
$299$	35732.2	−	49181.1i	0.0231143	−	0.0318142i
$300$	−2.79921e6	−	909520.i	−1.79570	−	0.583457i
$301$		−	89194.6i		−	0.0567443i
$302$	980131.	−	1.34903e6i	0.618396	−	0.851149i
$303$	−408104.	−	1.25602e6i	−0.255367	−	0.785938i
$304$	299421.	+	412117.i	0.185822	+	0.255762i
$305$	−665179.	+	2.04721e6i	−0.409439	+	1.26012i
$306$	333394.	−	108326.i	0.203542	−	0.0661348i
$307$	−642763.	−	1.97822e6i	−0.389229	−	1.19792i	−0.933366	−	0.358927i	$-0.883143\pi$
$307$	−642763.	−	1.97822e6i	−0.389229	−	1.19792i	0.544137	−	0.838996i	$-0.316857\pi$
$308$	−213437.	−	656891.i	−0.128201	−	0.394563i
$309$	−2.80571e6	+	911631.i	−1.67166	+	0.543154i
$310$	523259.	−	1.61043e6i	0.309252	−	0.951780i
$311$	−789713.	−	1.08695e6i	−0.462987	−	0.637246i	0.512138	−	0.858903i	$-0.328854\pi$
$311$	−789713.	−	1.08695e6i	−0.462987	−	0.637246i	−0.975125	+	0.221657i	$0.928854\pi$
$312$	−7940.48	−	24438.3i	−0.00461807	−	0.0142129i
$313$	524508.	−	721924.i	0.302616	−	0.416515i	−0.630445	−	0.776234i	$-0.717128\pi$
$313$	524508.	−	721924.i	0.302616	−	0.416515i	0.933061	+	0.359719i	$0.117128\pi$
$314$			1.10895e6i			0.634728i
$315$	−5.43323e6	−	1.76536e6i	−3.08519	−	1.00244i
$316$	752406.	−	1.03560e6i	0.423872	−	0.583410i
$317$	1.60942e6	+	2.21517e6i	0.899541	+	1.23811i	0.970614	+	0.240640i	$0.0773574\pi$
$317$	1.60942e6	+	2.21517e6i	0.899541	+	1.23811i	−0.0710737	+	0.997471i	$0.522643\pi$
$318$	2.72274e6	−	1.97819e6i	1.50987	−	1.09698i
$319$	2.44074e6			1.34290
$320$	328809.	−	238894.i	0.179502	−	0.130416i
$321$	−2.37864e6	+	772868.i	−1.28845	+	0.418642i
$322$	1.79329e6	+	582676.i	0.963854	+	0.313175i
$323$	278734.	+	202512.i	0.148656	+	0.108005i
$324$	−959785.	−	697325.i	−0.507939	−	0.369039i
$325$			98587.8i			0.0517743i
$326$	152980.	−	470824.i	0.0797243	−	0.245366i
$327$	−1.93247e6			−0.999408
$328$	−159852.	+	670070.i	−0.0820413	+	0.343903i
$329$	−239580.			−0.122028
$330$	−1.27403e6	+	3.92106e6i	−0.644012	+	1.98207i
$331$		−	185837.i		−	0.0932316i	−0.998913	−	0.0466158i	$-0.985156\pi$
$331$		−	185837.i		−	0.0932316i	0.998913	−	0.0466158i	$-0.0148436\pi$
$332$	756875.	+	549902.i	0.376859	+	0.273804i
$333$	4.71147e6	+	3.42308e6i	2.32834	+	1.69164i
$334$	926479.	+	301031.i	0.454433	+	0.147654i
$335$	533653.	−	173395.i	0.259805	−	0.0844157i
$336$	644801.	−	468475.i	0.311586	−	0.226380i
$337$	−3.52785e6			−1.69214			−0.846068	−	0.533076i	$-0.821036\pi$
$337$	−3.52785e6			−1.69214			−0.846068	+	0.533076i	$0.821036\pi$
$338$	1.20083e6	−	872456.i	0.571730	−	0.415386i
$339$	1.48165e6	+	2.03932e6i	0.700241	+	0.963800i
$340$	161575.	−	222389.i	0.0758013	−	0.104332i
$341$	−1.53985e6	−	500328.i	−0.717121	−	0.233007i
$342$		−	4.02871e6i		−	1.86252i
$343$	−1.38235e6	+	1.90264e6i	−0.634426	+	0.873213i
$344$	−15508.1	−	47729.0i	−0.00706581	−	0.0217463i
$345$	−6.61566e6	−	9.10567e6i	−2.99244	−	4.11874i
$346$	34992.0	−	107694.i	0.0157137	−	0.0483617i
$347$	2.06356e6	−	670492.i	0.920013	−	0.298930i	0.189541	−	0.981873i	$-0.439300\pi$
$347$	2.06356e6	−	670492.i	0.920013	−	0.298930i	0.730472	+	0.682943i	$0.239300\pi$
$348$	870332.	+	2.67861e6i	0.385245	+	1.18566i
$349$	−269433.	−	829228.i	−0.118410	−	0.364427i	0.874233	−	0.485506i	$-0.161365\pi$
$349$	−269433.	−	829228.i	−0.118410	−	0.364427i	−0.992643	+	0.121079i	$0.961365\pi$
$350$	−2.90826e6	+	944951.i	−1.26900	+	0.412324i
$351$	−32649.5	+	100485.i	−0.0141452	+	0.0435344i
$352$	−228425.	−	314400.i	−0.0982622	−	0.135246i
$353$	934728.	+	2.87680e6i	0.399253	+	1.22878i	0.925599	+	0.378505i	$0.123562\pi$
$353$	934728.	+	2.87680e6i	0.399253	+	1.22878i	−0.526346	+	0.850271i	$0.676438\pi$
$354$	−725263.	+	998239.i	−0.307601	+	0.423376i
$355$			5.41530e6i			2.28061i
$356$	2.07089e6	+	672874.i	0.866029	+	0.281390i
$357$	316851.	−	436108.i	0.131578	−	0.181102i
$358$	−1.03433e6	−	1.42364e6i	−0.426534	−	0.587073i
$359$	1.66899e6	−	1.21259e6i	0.683467	−	0.496568i	−0.191039	−	0.981582i	$-0.561186\pi$
$359$	1.66899e6	−	1.21259e6i	0.683467	−	0.496568i	0.874506	+	0.485015i	$0.161186\pi$
$360$	−3.21432e6			−1.30717
$361$	1.20014e6	−	871951.i	0.484689	−	0.352147i
$362$	1.01049e6	−	328329.i	0.405286	−	0.131686i
$363$	−443111.	−	143975.i	−0.176500	−	0.0573485i
$364$	−21598.3	−	15692.1i	−0.00854408	−	0.00620764i
$365$	6.22440e6	+	4.52229e6i	2.44549	+	1.77675i
$366$			2.37506e6i			0.926771i
$367$	−983548.	+	3.02705e6i	−0.381180	+	1.17315i	0.558033	+	0.829819i	$0.311556\pi$
$367$	−983548.	+	3.02705e6i	−0.381180	+	1.17315i	−0.939214	+	0.343333i	$0.888444\pi$
$368$	1.06092e6			0.408378
$369$	4.13765e6	−	3.54419e6i	1.58193	−	1.35504i
$370$	4.56670e6			1.73420
$371$	1.08051e6	−	3.32546e6i	0.407562	−	1.25435i
$372$		−	1.86833e6i		−	0.699997i
$373$	131300.	+	95395.1i	0.0488644	+	0.0355021i	0.611949	−	0.790897i	$-0.290386\pi$
$373$	131300.	+	95395.1i	0.0488644	+	0.0355021i	−0.563085	+	0.826399i	$0.690386\pi$
$374$	−212643.	−	154494.i	−0.0786089	−	0.0571127i
$375$	9.28796e6	+	3.01784e6i	3.41069	+	1.10820i
$376$	−128202.	+	41655.3i	−0.0467655	+	0.0151950i
$377$	76322.7	−	55451.7i	0.0276567	−	0.0200938i
$378$	−3.27716e6			−1.17969
$379$	730809.	−	530964.i	0.261340	−	0.189875i	−0.449398	−	0.893332i	$-0.648361\pi$
$379$	730809.	−	530964.i	0.261340	−	0.189875i	0.710738	+	0.703457i	$0.248361\pi$
$380$	−1.85690e6	−	2.55580e6i	−0.659674	−	0.907963i
$381$	2.49386e6	−	3.43251e6i	0.880157	−	1.21143i
$382$	−471558.	−	153219.i	−0.165340	−	0.0537221i
$383$		−	2.11878e6i		−	0.738054i	−0.929419	−	0.369027i	$-0.879691\pi$
$383$		−	2.11878e6i		−	0.738054i	0.929419	−	0.369027i	$-0.120309\pi$
$384$	263587.	−	362797.i	0.0912213	−	0.125555i
$385$	1.32366e6	+	4.07380e6i	0.455118	+	1.40071i
$386$	−112795.	−	155250.i	−0.0385321	−	0.0530349i
$387$	−122648.	+	377472.i	−0.0416278	+	0.128117i
$388$	2.64720e6	−	860128.i	0.892705	−	0.290057i
$389$	717876.	+	2.20940e6i	0.240534	+	0.740286i	0.996339	+	0.0854900i	$0.0272456\pi$
$389$	717876.	+	2.20940e6i	0.240534	+	0.740286i	−0.755805	+	0.654796i	$0.772754\pi$
$390$	49244.0	+	151557.i	0.0163943	+	0.0504563i
$391$	682429.	−	221735.i	0.225744	−	0.0733485i
$392$	−76507.1	+	235465.i	−0.0251470	+	0.0773946i
$393$	−1.05748e6	−	1.45550e6i	−0.345376	−	0.475369i
$394$	−905795.	−	2.78775e6i	−0.293961	−	0.904718i
$395$	−4.66615e6	+	6.42241e6i	−1.50476	+	2.07112i
$396$			3.07346e6i			0.984893i
$397$	680394.	+	221073.i	0.216663	+	0.0703979i	0.415337	−	0.909668i	$-0.363664\pi$
$397$	680394.	+	221073.i	0.216663	+	0.0703979i	−0.198674	+	0.980066i	$0.563664\pi$
$398$	−529747.	+	729134.i	−0.167633	+	0.230728i
$399$	−3.64141e6	−	5.01197e6i	−1.14508	−	1.57607i
$400$	−1.39194e6	+	1.01131e6i	−0.434983	+	0.316033i
$401$	−2.14484e6			−0.666091			−0.333045	−	0.942911i	$-0.608076\pi$
$401$	−2.14484e6			−0.666091			−0.333045	+	0.942911i	$0.608076\pi$
$402$	500875.	−	363907.i	0.154584	−	0.112312i
$403$	−59518.6	+	19338.8i	−0.0182554	+	0.00593152i
$404$	−734225.	−	238564.i	−0.223808	−	0.0727197i
$405$	5.95224e6	+	4.32456e6i	1.80320	+	1.31010i
$406$	2.36732e6	+	1.71996e6i	0.712758	+	0.517849i
$407$		−	4.36657e6i		−	1.30664i
$408$	93725.3	−	288457.i	0.0278744	−	0.0857887i
$409$	−2.48342e6			−0.734077			−0.367038	−	0.930206i	$-0.619628\pi$
$409$	−2.48342e6			−0.734077			−0.367038	+	0.930206i	$0.619628\pi$
$410$	991342.	−	4.15554e6i	0.291249	−	1.22086i
$411$	295029.			0.0861511
$412$	−532909.	+	1.64013e6i	−0.154672	+	0.476030i
$413$			1.28196e6i			0.369827i
$414$	−6.78801e6	−	4.93178e6i	−1.94644	−	1.41417i
$415$	−4.69387e6	−	3.41030e6i	−1.33786	−	0.972012i
$416$	−14285.8	−	4641.74i	−0.00404736	−	0.00131507i
$417$	6.64870e6	−	2.16029e6i	1.87239	−	0.608377i
$418$	−2.44380e6	+	1.77552e6i	−0.684107	+	0.497033i
$419$	−2.05108e6			−0.570753			−0.285376	−	0.958416i	$-0.592119\pi$
$419$	−2.05108e6			−0.570753			−0.285376	+	0.958416i	$0.592119\pi$
$420$	−3.99882e6	+	2.90532e6i	−1.10614	+	0.803656i
$421$	−757549.	−	1.04268e6i	−0.208308	−	0.286711i	0.692061	−	0.721839i	$-0.256703\pi$
$421$	−757549.	−	1.04268e6i	−0.208308	−	0.286711i	−0.900368	+	0.435128i	$0.856703\pi$
$422$	−919998.	+	1.26627e6i	−0.251481	+	0.346134i
$423$	1.01391e6	+	329438.i	0.275516	+	0.0895205i
$424$		−	1.96736e6i		−	0.531458i
$425$	−683993.	+	941436.i	−0.183687	+	0.252824i
$426$	1.84639e6	+	5.68261e6i	0.492946	+	1.51713i
$427$	1.45041e6	+	1.99632e6i	0.384965	+	0.529858i
$428$	−451793.	+	1.39048e6i	−0.119215	+	0.366906i
$429$	144916.	−	47085.9i	0.0380165	−	0.0123523i
$430$	96175.6	+	295998.i	0.0250838	+	0.0772001i
$431$	−1.85709e6	−	5.71554e6i	−0.481548	−	1.48205i	−0.836919	−	0.547327i	$-0.815645\pi$
$431$	−1.85709e6	−	5.71554e6i	−0.481548	−	1.48205i	0.355370	−	0.934726i	$-0.384355\pi$
$432$	−1.75365e6	+	569794.i	−0.452098	+	0.146896i
$433$	−337768.	+	1.03954e6i	−0.0865763	+	0.266454i	−0.984967	−	0.172743i	$-0.944737\pi$
$433$	−337768.	+	1.03954e6i	−0.0865763	+	0.266454i	0.898391	+	0.439197i	$0.144737\pi$
$434$	−1.14096e6	−	1.57039e6i	−0.290767	−	0.400206i
$435$	−5.39749e6	−	1.66118e7i	−1.36763	−	4.20913i
$436$	−663996.	+	913912.i	−0.167282	+	0.230244i
$437$		−	8.24641e6i		−	2.06567i
$438$	8.07356e6	+	2.62326e6i	2.01085	+	0.653365i
$439$	2.53448e6	−	3.48841e6i	0.627664	−	0.863905i	−0.370219	−	0.928945i	$-0.620717\pi$
$439$	2.53448e6	−	3.48841e6i	0.627664	−	0.863905i	0.997883	+	0.0650395i	$0.0207174\pi$
$440$	1.41661e6	+	1.94979e6i	0.348833	+	0.480128i
$441$	1.58409e6	−	1.15091e6i	0.387868	−	0.281802i
$442$	−10159.4			−0.00247350
$443$	5.40086e6	−	3.92396e6i	1.30754	−	0.949981i	0.307537	−	0.951536i	$-0.400495\pi$
$443$	5.40086e6	−	3.92396e6i	1.30754	−	0.949981i	0.999999	+	0.00155536i	$0.000495085\pi$
$444$	4.79212e6	−	1.55706e6i	1.15364	−	0.374841i
$445$	−1.28429e7	−	4.17292e6i	−3.07443	−	0.998942i
$446$	−832124.	−	604573.i	−0.198085	−	0.143917i
$447$	4.77097e6	+	3.46631e6i	1.12937	+	0.820538i
$448$		−	465910.i		−	0.109675i
$449$	771951.	−	2.37582e6i	0.180707	−	0.556157i	−0.819142	−	0.573591i	$-0.805550\pi$
$449$	771951.	−	2.37582e6i	0.180707	−	0.556157i	0.999848	+	0.0174340i	$0.00554971\pi$
$450$	1.36071e7			3.16764
$451$	−3.97342e6	−	947898.i	−0.919864	−	0.219442i
$452$	1.47354e6			0.339248
$453$	−3.52593e6	+	1.08517e7i	−0.807287	+	2.48457i
$454$		−	1.58546e6i		−	0.361007i
$455$	133945.	+	97316.5i	0.0303317	+	0.0220373i
$456$	−2.81998e6	−	2.04884e6i	−0.635088	−	0.461419i
$457$	4.16346e6	+	1.35279e6i	0.932533	+	0.302998i	0.735598	−	0.677418i	$-0.236901\pi$
$457$	4.16346e6	+	1.35279e6i	0.932533	+	0.302998i	0.196935	+	0.980417i	$0.436901\pi$
$458$	1.10629e6	−	359455.i	0.246437	−	0.0800721i
$459$	−1.00893e6	+	733032.i	−0.223527	+	0.162402i
$460$	−6.57944e6			−1.44975
$461$	4.20841e6	−	3.05759e6i	0.922286	−	0.670080i	−0.0218062	−	0.999762i	$-0.506942\pi$
$461$	4.20841e6	−	3.05759e6i	0.922286	−	0.670080i	0.944092	+	0.329682i	$0.106942\pi$
$462$	2.77799e6	+	3.82358e6i	0.605517	+	0.833422i
$463$	−5.12040e6	+	7.04763e6i	−1.11007	+	1.52788i	−0.288765	+	0.957400i	$0.593244\pi$
$463$	−5.12040e6	+	7.04763e6i	−1.11007	+	1.52788i	−0.821308	+	0.570484i	$0.806756\pi$
$464$	1.56583e6	+	508768.i	0.337636	+	0.109705i
$465$			1.15867e7i			2.48501i
$466$	−925043.	+	1.27321e6i	−0.197332	+	0.271604i
$467$	−122527.	−	377099.i	−0.0259979	−	0.0800134i	0.937216	−	0.348750i	$-0.113394\pi$
$467$	−122527.	−	377099.i	−0.0259979	−	0.0800134i	−0.963214	+	0.268737i	$0.913394\pi$
$468$	69826.5	+	96107.9i	0.0147369	+	0.0202836i
$469$	198770.	−	611751.i	0.0417272	−	0.128423i
$470$	795063.	−	258332.i	0.166019	−	0.0539427i
$471$	−2.34488e6	−	7.21678e6i	−0.487043	−	1.49896i
$472$	222891.	+	685989.i	0.0460509	+	0.141730i
$473$	283026.	−	91960.8i	0.0581666	−	0.0188995i
$474$	−2.70671e6	+	8.33039e6i	−0.553345	+	1.70302i
$475$	7.86079e6	+	1.08194e7i	1.59857	+	2.20024i
$476$	−97376.3	−	299694.i	−0.0196986	−	0.0606262i
$477$	−9.14544e6	+	1.25876e7i	−1.84039	+	2.53307i
$478$			3.79561e6i			0.759822i
$479$	−4.84578e6	−	1.57449e6i	−0.964994	−	0.313545i	−0.216200	−	0.976349i	$-0.569366\pi$
$479$	−4.84578e6	−	1.57449e6i	−0.964994	−	0.313545i	−0.748793	+	0.662804i	$0.769366\pi$
$480$	−1.63467e6	+	2.24993e6i	−0.323838	+	0.445725i
$481$	−99205.0	−	136544.i	−0.0195511	−	0.0269098i
$482$	−2.04343e6	+	1.48464e6i	−0.400629	+	0.291074i
$483$	−1.29024e7			−2.51653
$484$	−220342.	+	160088.i	−0.0427548	+	0.0310632i
$485$	−1.64170e7	+	5.33421e6i	−3.16913	+	1.02971i
$486$	1.06218e6	+	345122.i	0.203989	+	0.0662799i
$487$	7.18796e6	+	5.22236e6i	1.37336	+	0.997802i	0.997467	+	0.0711371i	$0.0226628\pi$
$487$	7.18796e6	+	5.22236e6i	1.37336	+	0.997802i	0.375890	+	0.926664i	$0.377337\pi$
$488$	1.12323e6	+	816071.i	0.213510	+	0.155124i
$489$			3.38749e6i			0.640628i
$490$	474470.	−	1.46027e6i	0.0892727	−	0.274753i
$491$	4.80965e6			0.900346			0.450173	−	0.892941i	$-0.351362\pi$
$491$	4.80965e6			0.900346			0.450173	+	0.892941i	$0.351362\pi$
$492$	−376588.	−	4.69867e6i	−0.0701381	−	0.875109i
$493$	1.11354e6			0.206342
$494$	−36079.8	+	111042.i	−0.00665191	+	0.0204725i
$495$		−	1.90605e7i		−	3.49640i
$496$	−883579.	−	641958.i	−0.161265	−	0.117166i
$497$	5.02222e6	+	3.64886e6i	0.912021	+	0.662622i
$498$	−6.08833e6	−	1.97822e6i	−1.10008	−	0.357438i
$499$	−56743.5	+	18437.1i	−0.0102015	+	0.00331467i	−0.314113	−	0.949386i	$-0.601707\pi$
$499$	−56743.5	+	18437.1i	−0.0102015	+	0.00331467i	0.303912	+	0.952700i	$0.401707\pi$
$500$	4.61856e6	−	3.35558e6i	0.826192	−	0.600264i
$501$	−6.66584e6			−1.18648
$502$	1.83404e6	−	1.33251e6i	0.324826	−	0.236000i
$503$	3.26021e6	+	4.48730e6i	0.574547	+	0.790797i	0.993084	−	0.117403i	$-0.0374570\pi$
$503$	3.26021e6	+	4.48730e6i	0.574547	+	0.790797i	−0.418537	+	0.908200i	$0.637457\pi$
$504$	−2.16583e6	+	2.98101e6i	−0.379793	+	0.522741i
$505$	4.55340e6	+	1.47949e6i	0.794525	+	0.258157i
$506$			6.29110e6i			1.09232i
$507$	−5.96993e6	+	8.21690e6i	−1.03145	+	1.41967i
$508$	−766426.	−	2.35882e6i	−0.131768	−	0.405541i
$509$	−1.36894e6	−	1.88419e6i	−0.234202	−	0.322351i	0.675699	−	0.737178i	$-0.263842\pi$
$509$	−1.36894e6	−	1.88419e6i	−0.234202	−	0.322351i	−0.909900	+	0.414827i	$0.863842\pi$
$510$	−581250.	+	1.78891e6i	−0.0989550	+	0.304552i
$511$	8.38807e6	−	2.72545e6i	1.42105	−	0.461727i
$512$	−81007.0	−	249314.i	−0.0136568	−	0.0420312i
$513$	4.42895e6	+	1.36309e7i	0.743032	+	2.28682i
$514$	6.02972e6	−	1.95917e6i	1.00668	−	0.327089i
$515$	3.30491e6	−	1.01715e7i	0.549088	−	1.68992i
$516$	201846.	+	277817.i	0.0333731	+	0.0459341i
$517$	−247010.	−	760220.i	−0.0406433	−	0.125087i
$518$	3.07707e6	−	4.23522e6i	0.503863	−	0.693509i
$519$			774839.i			0.126268i
$520$	88595.5	+	28786.4i	0.0143682	+	0.00466852i
$521$	2.27338e6	−	3.12903e6i	0.366925	−	0.505029i	−0.585137	−	0.810934i	$-0.698959\pi$
$521$	2.27338e6	−	3.12903e6i	0.366925	−	0.505029i	0.952062	+	0.305906i	$0.0989593\pi$
$522$	−7.65347e6	−	1.05341e7i	−1.22937	−	1.69208i
$523$	−1.80587e6	+	1.31204e6i	−0.288691	+	0.209746i	−0.722699	−	0.691163i	$-0.757099\pi$
$523$	−1.80587e6	+	1.31204e6i	−0.288691	+	0.209746i	0.434008	+	0.900909i	$0.357099\pi$
$524$	−1.05169e6			−0.167325
$525$	1.69282e7	−	1.22990e7i	2.68047	−	1.94748i
$526$	4.82504e6	−	1.56775e6i	0.760390	−	0.247066i
$527$	−702527.	−	228265.i	−0.110189	−	0.0358024i
$528$	2.15133e6	+	1.56303e6i	0.335833	+	0.243997i
$529$	−8.68736e6	−	6.31174e6i	−1.34974	−	0.980641i
$530$			1.22008e7i			1.88669i
$531$	1.76277e6	−	5.42526e6i	0.271306	−	0.834995i
$532$	−3.62147e6			−0.554761
$533$	−145786.	+	60632.0i	−0.0222278	+	0.00924450i
$534$	−1.48997e7			−2.26112
$535$	2.80186e6	−	8.62324e6i	0.423216	−	1.30252i
$536$		−	361915.i		−	0.0544120i
$537$	9.74149e6	+	7.07761e6i	1.45777	+	1.05913i
$538$	−4.27711e6	−	3.10750e6i	−0.637081	−	0.462866i
$539$	−1.39627e6	−	453677.i	−0.207013	−	0.0672627i
$540$	1.08755e7	−	3.53366e6i	1.60496	−	0.521483i
$541$	−3.42524e6	+	2.48858e6i	−0.503151	+	0.365560i	−0.810219	−	0.586127i	$-0.800652\pi$
$541$	−3.42524e6	+	2.48858e6i	−0.503151	+	0.365560i	0.307068	+	0.951687i	$0.400652\pi$
$542$	−4.68539e6			−0.685090
$543$	−5.88180e6	+	4.27338e6i	−0.856073	+	0.621973i
$544$	−104214.	−	143439.i	−0.0150984	−	0.0207811i
$545$	4.11787e6	−	5.66776e6i	0.593856	−	0.817372i
$546$	173737.	+	56450.7i	0.0249409	+	0.00810378i
$547$		−	2.63321e6i		−	0.376286i	−0.982142	−	0.188143i	$-0.939753\pi$
$547$		−	2.63321e6i		−	0.376286i	0.982142	−	0.188143i	$-0.0602468\pi$
$548$	101372.	−	139527.i	0.0144201	−	0.0198475i
$549$	−3.39308e6	−	1.04428e7i	−0.480467	−	1.47873i
$550$	−5.99691e6	−	8.25404e6i	−0.845319	−	1.16348i
$551$	3.95460e6	−	1.21710e7i	0.554911	−	1.70784i
$552$	−6.90421e6	+	2.24331e6i	−0.964420	+	0.313359i
$553$	2.81215e6	+	8.65491e6i	0.391044	+	1.20351i
$554$	−2.19257e6	−	6.74804e6i	−0.303514	−	0.934121i
$555$	−2.97190e7	+	9.65630e6i	−4.09546	+	1.33069i
$556$	1.26284e6	−	3.88661e6i	0.173245	−	0.533192i
$557$	−4.70413e6	−	6.47467e6i	−0.642452	−	0.884260i	0.356291	−	0.934375i	$-0.384041\pi$
$557$	−4.70413e6	−	6.47467e6i	−0.642452	−	0.884260i	−0.998743	+	0.0501152i	$0.984041\pi$
$558$	2.66915e6	+	8.21480e6i	0.362900	+	1.11689i
$559$	6761.04	−	9305.77i	0.000915132	−	0.00125957i
$560$			2.88941e6i			0.389349i
$561$	1.71051e6	+	555778.i	0.229466	+	0.0745579i
$562$	3.43418e6	−	4.72674e6i	0.458650	−	0.631278i
$563$	836966.	+	1.15198e6i	0.111285	+	0.153171i	0.861026	−	0.508560i	$-0.169822\pi$
$563$	836966.	+	1.15198e6i	0.111285	+	0.153171i	−0.749741	+	0.661731i	$0.769822\pi$
$564$	746228.	−	542166.i	0.0987811	−	0.0717687i
$565$	−9.13839e6			−1.20434
$566$	−2.69866e6	+	1.96069e6i	−0.354084	+	0.257257i
$567$	8.02131e6	−	2.60628e6i	1.04782	−	0.340458i
$568$	3.32187e6	+	1.07934e6i	0.432027	+	0.140374i
$569$	−3.48785e6	−	2.53407e6i	−0.451624	−	0.328124i	0.338613	−	0.940926i	$-0.390042\pi$
$569$	−3.48785e6	−	2.53407e6i	−0.451624	−	0.328124i	−0.790237	+	0.612802i	$0.790042\pi$
$570$	1.74885e7	+	1.27061e7i	2.25458	+	1.63805i
$571$			996266.i			0.127875i	0.997954	+	0.0639374i	$0.0203658\pi$
$571$			996266.i			0.127875i	−0.997954	+	0.0639374i	$0.979634\pi$
$572$	27524.9	−	84712.9i	0.00351751	−	0.0108258i
$573$	3.39277e6			0.431686
$574$	−3.18593e6	−	3.71941e6i	−0.403605	−	0.471188i
$575$	2.78527e7			3.51315
$576$	−640656.	+	1.97174e6i	−0.0804579	+	0.247624i
$577$			5.80417e6i			0.725773i	0.931833	+	0.362887i	$0.118209\pi$
$577$			5.80417e6i			0.725773i	−0.931833	+	0.362887i	$0.881791\pi$
$578$	4.49774e6	+	3.26780e6i	0.559983	+	0.406851i
$579$	1.06232e6	+	771822.i	0.131692	+	0.0956798i
$580$	−9.71069e6	−	3.15520e6i	−1.19862	−	0.389454i
$581$	−6.32551e6	+	2.05528e6i	−0.777419	+	0.252599i
$582$	−1.54086e7	+	1.11950e7i	−1.88563	+	1.36999i
$583$	1.16662e7			1.42153
$584$	4.01468e6	−	2.91683e6i	0.487101	−	0.353899i
$585$	−433039.	−	596027.i	−0.0523163	−	0.0720072i
$586$	2.77794e6	−	3.82351e6i	0.334179	−	0.459958i
$587$	8.33265e6	+	2.70744e6i	0.998132	+	0.324313i	0.762119	−	0.647437i	$-0.224159\pi$
$587$	8.33265e6	+	2.70744e6i	0.998132	+	0.324313i	0.236013	+	0.971750i	$0.424159\pi$
$588$		−	1.69412e6i		−	0.202070i
$589$	−4.98987e6	+	6.86797e6i	−0.592654	+	0.815718i
$590$	−1.38229e6	−	4.25426e6i	−0.163482	−	0.503146i
$591$	1.17894e7	+	1.62267e7i	1.38843	+	1.91101i
$592$	910204.	−	2.80132e6i	0.106742	−	0.328517i
$593$	−1.09282e7	+	3.55079e6i	−1.27618	+	0.414657i	−0.867234	−	0.497901i	$-0.834104\pi$
$593$	−1.09282e7	+	3.55079e6i	−1.27618	+	0.414657i	−0.408948	+	0.912558i	$0.634104\pi$
$594$	−3.37880e6	−	1.03989e7i	−0.392913	−	1.20926i
$595$	603893.	+	1.85859e6i	0.0699307	+	0.215225i
$596$	3.27861e6	−	1.06528e6i	0.378072	−	0.122843i
$597$	1.90571e6	−	5.86518e6i	0.218837	−	0.673512i
$598$	142929.	+	196725.i	0.0163443	+	0.0224960i
$599$	1.48637e6	+	4.57459e6i	0.169262	+	0.520936i	0.999325	−	0.0367338i	$-0.0116954\pi$
$599$	1.48637e6	+	4.57459e6i	0.169262	+	0.520936i	−0.830063	+	0.557670i	$0.811695\pi$
$600$	6.92004e6	−	9.52462e6i	0.784748	−	1.08011i
$601$			3.50419e6i			0.395732i	0.980229	+	0.197866i	$0.0634011\pi$
$601$			3.50419e6i			0.395732i	−0.980229	+	0.197866i	$0.936599\pi$
$602$	339316.	+	110251.i	0.0381604	+	0.0123991i
$603$	−1.68239e6	+	2.31562e6i	−0.188423	+	0.259342i
$604$	3.92052e6	+	5.39614e6i	0.437272	+	0.601853i
$605$	1.36648e6	−	992809.i	0.151781	−	0.110275i
$606$	5.28261e6			0.584342
$607$	4.98908e6	−	3.62478e6i	0.549603	−	0.399310i	−0.278036	−	0.960571i	$-0.589683\pi$
$607$	4.98908e6	−	3.62478e6i	0.549603	−	0.399310i	0.827639	+	0.561261i	$0.189683\pi$
$608$	−1.93789e6	+	629659.i	−0.212603	+	0.0690790i
$609$	−1.90428e7	−	6.18739e6i	−2.08060	−	0.676027i
$610$	−6.96584e6	−	5.06098e6i	−0.757965	−	0.550694i
$611$	−24995.7	−	18160.4i	−0.00270871	−	0.00196799i
$612$			1.40220e6i			0.151333i
$613$	2.82549e6	−	8.69595e6i	0.303698	−	0.934687i	−0.676462	−	0.736478i	$-0.736488\pi$
$613$	2.82549e6	−	8.69595e6i	0.303698	−	0.934687i	0.980160	−	0.198209i	$-0.0635124\pi$
$614$	8.32010e6			0.890651
$615$	2.33546e6	+	2.91395e7i	0.248992	+	3.10666i
$616$	2.76278e6			0.293356
$617$	5.56030e6	−	1.71129e7i	0.588011	−	1.80971i	0.00118465	−	0.999999i	$-0.499623\pi$
$617$	5.56030e6	−	1.71129e7i	0.588011	−	1.80971i	0.586826	−	0.809713i	$-0.300377\pi$
$618$		−	1.18004e7i		−	1.24287i
$619$	1.41431e7	+	1.02755e7i	1.48360	+	1.07790i	0.976374	+	0.216086i	$0.0693292\pi$
$619$	1.41431e7	+	1.02755e7i	1.48360	+	1.07790i	0.507226	+	0.861813i	$0.330671\pi$
$620$	5.47964e6	+	3.98119e6i	0.572497	+	0.415943i
$621$	2.83886e7	+	9.22402e6i	2.95403	+	0.959823i
$622$	5.11113e6	−	1.66071e6i	0.529713	−	0.172114i
$623$	−1.25237e7	+	9.09897e6i	−1.29274	+	0.939231i
$624$	102784.			0.0105673
$625$	−1.16511e7	+	8.46503e6i	−1.19307	+	0.866819i
$626$	2.09803e6	+	2.88769e6i	0.213982	+	0.294520i
$627$	1.21493e7	−	1.67221e7i	1.23419	−	1.69872i
$628$	−4.21869e6	−	1.37074e6i	−0.426854	−	0.138693i
$629$		−	1.99216e6i		−	0.200770i
$630$	1.34317e7	−	1.84871e7i	1.34828	−	1.85574i
$631$	−346577.	−	1.06665e6i	−0.0346519	−	0.106647i	0.932235	−	0.361855i	$-0.117856\pi$
$631$	−346577.	−	1.06665e6i	−0.0346519	−	0.106647i	−0.966886	+	0.255207i	$0.917856\pi$
$632$	3.00962e6	+	4.14239e6i	0.299723	+	0.412533i
$633$	3.30960e6	−	1.01859e7i	0.328297	−	1.01039i
$634$	−1.04164e7	+	3.38449e6i	−1.02918	+	0.334402i
$635$	4.75310e6	+	1.46285e7i	0.467781	+	1.43968i
$636$	4.15998e6	+	1.28031e7i	0.407801	+	1.25508i
$637$	−53969.0	+	17535.6i	−0.00526982	+	0.00171227i
$638$	−3.01692e6	+	9.28513e6i	−0.293435	+	0.903101i
$639$	−1.62367e7	−	2.23479e7i	−1.57306	−	2.16513i
$640$	502376.	+	1.54615e6i	0.0484818	+	0.149212i
$641$	1.08101e6	−	1.48789e6i	0.103917	−	0.143029i	−0.753892	−	0.656999i	$-0.771826\pi$
$641$	1.08101e6	−	1.48789e6i	0.103917	−	0.143029i	0.857808	+	0.513970i	$0.171826\pi$
$642$		−	1.00042e7i		−	0.957956i
$643$	−7.30483e6	−	2.37348e6i	−0.696760	−	0.226391i	−0.0608414	−	0.998147i	$-0.519378\pi$
$643$	−7.30483e6	−	2.37348e6i	−0.696760	−	0.226391i	−0.635918	+	0.771757i	$0.719378\pi$
$644$	−4.43326e6	+	6.10186e6i	−0.421220	+	0.579759i
$645$	−1.25178e6	−	1.72292e6i	−0.118475	−	0.163067i
$646$	−1.11493e6	+	810047.i	−0.105116	+	0.0763711i
$647$	7.71478e6			0.724541			0.362270	−	0.932073i	$-0.382002\pi$
$647$	7.71478e6			0.724541			0.362270	+	0.932073i	$0.382002\pi$
$648$	3.83914e6	−	2.78930e6i	0.359167	−	0.260950i
$649$	−4.06782e6	+	1.32172e6i	−0.379097	+	0.123176i
$650$	−375050.	−	121861.i	−0.0348182	−	0.0113131i
$651$	1.07457e7	+	7.80719e6i	0.993759	+	0.722008i
$652$	1.60203e6	+	1.16394e6i	0.147588	+	0.107229i
$653$		−	1.61408e7i		−	1.48130i	−0.671890	−	0.740651i	$-0.734517\pi$
$653$		−	1.61408e7i		−	1.48130i	0.671890	−	0.740651i	$-0.265483\pi$
$654$	2.38866e6	−	7.35155e6i	0.218379	−	0.672101i
$655$	6.52223e6			0.594009
$656$	−2.35151e6	−	1.43636e6i	−0.213348	−	0.130318i
$657$	−3.92460e7			−3.54717
$658$	296137.	−	911417.i	0.0266642	−	0.0820640i
$659$		−	5.73005e6i		−	0.513979i	−0.966414	−	0.256989i	$-0.917269\pi$
$659$		−	5.73005e6i		−	0.513979i	0.966414	−	0.256989i	$-0.0827306\pi$
$660$	−1.33418e7	−	9.69338e6i	−1.19221	−	0.866195i
$661$	6.72999e6	+	4.88962e6i	0.599116	+	0.435283i	0.845565	−	0.533873i	$-0.179264\pi$
$661$	6.72999e6	+	4.88962e6i	0.599116	+	0.435283i	−0.246449	+	0.969156i	$0.579264\pi$
$662$	706967.	+	229708.i	0.0626981	+	0.0203718i
$663$	66114.9	−	21482.0i	0.00584138	−	0.00189798i
$664$	−3.02750e6	+	2.19961e6i	−0.266480	+	0.193609i
$665$	2.24591e7			1.96942
$666$	−1.88459e7	+	1.36923e7i	−1.64638	+	1.19617i
$667$	−1.56660e7	−	2.15624e7i	−1.36346	−	1.87665i
$668$	−2.29038e6	+	3.15244e6i	−0.198594	+	0.273342i
$669$	6.69364e6	+	2.17490e6i	0.578225	+	0.187877i
$670$			2.24447e6i			0.193164i
$671$	−4.83919e6	+	6.66057e6i	−0.414922	+	0.571091i
$672$	985168.	+	3.03204e6i	0.0841564	+	0.259007i
$673$	1.09334e7	+	1.50485e7i	0.930502	+	1.28073i	0.959664	+	0.281151i	$0.0907162\pi$
$673$	1.09334e7	+	1.50485e7i	0.930502	+	1.28073i	−0.0291618	+	0.999575i	$0.509284\pi$
$674$	4.36066e6	−	1.34207e7i	0.369745	−	1.13796i
$675$	−4.60390e7	+	1.49590e7i	−3.88926	+	1.26370i
$676$	1.83471e6	+	5.64666e6i	0.154419	+	0.475253i
$677$	−939392.	−	2.89115e6i	−0.0787726	−	0.242437i	0.903914	−	0.427715i	$-0.140681\pi$
$677$	−939392.	−	2.89115e6i	−0.0787726	−	0.242437i	−0.982686	+	0.185278i	$0.940681\pi$
$678$	−9.58947e6	+	3.11581e6i	−0.801162	+	0.260313i
$679$	−6.11485e6	+	1.88196e7i	−0.508992	+	1.56652i
$680$	646300.	+	889555.i	0.0535996	+	0.0737736i
$681$	3.35246e6	+	1.03178e7i	0.277010	+	0.852550i
$682$	3.80672e6	−	5.23950e6i	0.313394	−	0.431349i
$683$			1.63568e7i			1.34167i	0.741606	+	0.670836i	$0.234064\pi$
$683$			1.63568e7i			1.34167i	−0.741606	+	0.670836i	$0.765936\pi$
$684$	1.53261e7	+	4.97976e6i	1.25254	+	0.406975i
$685$	−628673.	+	865294.i	−0.0511916	+	0.0704592i
$686$	−5.52938e6	−	7.61054e6i	−0.448607	−	0.617455i
$687$	−6.43940e6	+	4.67850e6i	−0.520540	+	0.378194i
$688$	200741.			0.0161683
$689$	364804.	−	265046.i	0.0292760	−	0.0212703i
$690$	4.28174e7	−	1.39122e7i	3.42372	−	1.11243i
$691$	8.47600e6	+	2.75402e6i	0.675298	+	0.219418i	0.626536	−	0.779393i	$-0.284472\pi$
$691$	8.47600e6	+	2.75402e6i	0.675298	+	0.219418i	0.0487626	+	0.998810i	$0.484472\pi$
$692$	366441.	+	266235.i	0.0290896	+	0.0211349i
$693$	−1.76769e7	−	1.28431e7i	−1.39822	−	1.01586i
$694$			8.67903e6i			0.684026i
$695$	−7.83166e6	+	2.41034e7i	−0.615023	+	1.89285i
$696$	−1.12658e7			−0.881535
$697$	−1.81280e6	−	432460.i	−0.141341	−	0.0337182i
$698$	3.48761e6			0.270950
$699$	3.32775e6	−	1.02418e7i	0.257607	−	0.792834i
$700$		−	1.22317e7i		−	0.943499i
$701$	−1.64827e7	−	1.19753e7i	−1.26687	−	0.920435i	−0.267797	−	0.963475i	$-0.586296\pi$
$701$	−1.64827e7	−	1.19753e7i	−1.26687	−	0.920435i	−0.999073	+	0.0430406i	$0.986296\pi$
$702$	−341910.	−	248412.i	−0.0261860	−	0.0190252i
$703$	−2.17744e7	−	7.07492e6i	−1.66172	−	0.539925i
$704$	1.47840e6	−	480360.i	0.112424	−	0.0365288i
$705$	−4.62784e6	+	3.36232e6i	−0.350676	+	0.254781i
$706$	−1.20994e7			−0.913590
$707$	4.44021e6	−	3.22600e6i	0.334083	−	0.242726i
$708$	−2.90105e6	−	3.99295e6i	−0.217507	−	0.299372i
$709$	−7.15095e6	+	9.84244e6i	−0.534255	+	0.735338i	−0.987771	−	0.155909i	$-0.950169\pi$
$709$	−7.15095e6	+	9.84244e6i	−0.534255	+	0.735338i	0.453517	+	0.891248i	$0.350169\pi$
$710$	−2.06010e7	−	6.69368e6i	−1.53371	−	0.498332i
$711$		−	4.04945e7i		−	3.00416i
$712$	−5.11953e6	+	7.04643e6i	−0.378469	+	0.520917i
$713$	5.46352e6	+	1.68150e7i	0.402484	+	1.23872i
$714$	1.26740e6	+	1.74443e6i	0.0930400	+	0.128059i
$715$	−170699.	+	525359.i	−0.0124873	+	0.0384318i
$716$	6.69435e6	−	2.17513e6i	0.488007	−	0.158563i
$717$	−8.02582e6	−	2.47009e7i	−0.583031	−	1.79438i
$718$	2.54999e6	+	7.84806e6i	0.184598	+	0.568134i
$719$	1.35204e7	−	4.39305e6i	0.975366	−	0.316916i	0.222386	−	0.974959i	$-0.428616\pi$
$719$	1.35204e7	−	4.39305e6i	0.975366	−	0.316916i	0.752980	+	0.658043i	$0.228616\pi$
$720$	3.97312e6	−	1.22280e7i	0.285628	−	0.879072i
$721$	−7.20630e6	−	9.91862e6i	−0.516267	−	0.710580i
$722$	1.83365e6	+	5.64338e6i	0.130910	+	0.402899i
$723$	1.01589e7	−	1.39825e7i	0.722772	−	0.994810i
$724$			4.24998e6i			0.301329i
$725$	4.11082e7	+	1.33568e7i	2.90458	+	0.943754i
$726$	1.09543e6	−	1.50773e6i	0.0771335	−	0.106165i
$727$	6.19078e6	+	8.52088e6i	0.434419	+	0.597927i	0.968961	−	0.247215i	$-0.0795155\pi$
$727$	6.19078e6	+	8.52088e6i	0.434419	+	0.597927i	−0.534541	+	0.845142i	$0.679516\pi$
$728$	86393.0	−	62768.2i	0.00604158	−	0.00438946i
$729$	1.03757e7			0.723099
$730$	−2.48976e7	+	1.80892e7i	−1.72922	+	1.25635i
$731$	129125.	−	41955.3i	0.00893753	−	0.00290398i
$732$	−9.03527e6	−	2.93574e6i	−0.623252	−	0.202507i
$733$	−2.32500e6	−	1.68921e6i	−0.159832	−	0.116125i	0.504995	−	0.863122i	$-0.331494\pi$
$733$	−2.32500e6	−	1.68921e6i	−0.159832	−	0.116125i	−0.664826	+	0.746998i	$0.731494\pi$
$734$	−1.02998e7	−	7.48328e6i	−0.705652	−	0.512686i
$735$			1.05064e7i			0.717354i
$736$	−1.31137e6	+	4.03598e6i	−0.0892339	+	0.274634i
$737$	2.14610e6			0.145540
$738$	8.36846e6	+	2.01214e7i	0.565594	+	1.35993i
$739$	2.31565e7			1.55978			0.779888	−	0.625919i	$-0.215276\pi$
$739$	2.31565e7			1.55978			0.779888	+	0.625919i	$0.215276\pi$
$740$	−5.64476e6	+	1.73728e7i	−0.378936	+	1.16625i
$741$		−	798927.i		−	0.0534517i
$742$	1.13152e7	+	8.22100e6i	0.754490	+	0.548169i
$743$	1.66231e6	+	1.20774e6i	0.110469	+	0.0802605i	0.641648	−	0.766999i	$-0.278251\pi$
$743$	1.66231e6	+	1.20774e6i	0.110469	+	0.0802605i	−0.531179	+	0.847260i	$0.678251\pi$
$744$	7.10755e6	+	2.30938e6i	0.470747	+	0.152955i
$745$	−2.03328e7	+	6.60651e6i	−1.34216	+	0.436096i
$746$	−525200.	+	381580.i	−0.0345524	+	0.0251038i
$747$	2.95957e7			1.94056
$748$	850571.	−	617976.i	0.0555849	−	0.0403848i
$749$	−6.10940e6	−	8.40887e6i	−0.397918	−	0.547688i
$750$	−2.29611e7	+	3.16032e7i	−1.49053	+	2.05153i
$751$	1.29738e7	+	4.21546e6i	0.839400	+	0.272738i	0.697000	−	0.717072i	$-0.254518\pi$
$751$	1.29738e7	+	4.21546e6i	0.839400	+	0.272738i	0.142400	+	0.989809i	$0.454518\pi$
$752$		−	539198.i		−	0.0347699i
$753$	−9.11793e6	+	1.25498e7i	−0.586015	+	0.806580i
$754$	116611.	+	358891.i	0.00746982	+	0.0229897i
$755$	−2.43137e7	−	3.34649e7i	−1.55233	−	2.13659i
$756$	4.05080e6	−	1.24671e7i	0.257772	−	0.793341i
$757$	2.01515e7	−	6.54762e6i	1.27811	−	0.415283i	0.410195	−	0.911998i	$-0.365461\pi$
$757$	2.01515e7	−	6.54762e6i	1.27811	−	0.415283i	0.867914	+	0.496715i	$0.165461\pi$
$758$	1.11658e6	+	3.43647e6i	0.0705855	+	0.217240i
$759$	−1.33025e7	−	4.09410e7i	−0.838166	−	2.57961i
$760$	1.20181e7	−	3.90492e6i	0.754748	−	0.245232i
$761$	1.13377e6	−	3.48939e6i	0.0709681	−	0.218417i	−0.909281	−	0.416182i	$-0.863368\pi$
$761$	1.13377e6	−	3.48939e6i	0.0709681	−	0.218417i	0.980250	+	0.197764i	$0.0633680\pi$
$762$	9.97545e6	+	1.37300e7i	0.622365	+	0.856611i
$763$	−2.48171e6	−	7.63793e6i	−0.154326	−	0.474968i
$764$	1.16576e6	−	1.60453e6i	0.0722560	−	0.0994519i
$765$		−	8.69597e6i		−	0.537235i
$766$	8.06030e6	+	2.61895e6i	0.496340	+	0.161271i
$767$	−97173.7	+	133748.i	−0.00596431	+	0.00820917i
$768$	1.05435e6	+	1.45119e6i	0.0645032	+	0.0887810i
$769$	−4.54925e6	+	3.30523e6i	−0.277411	+	0.201551i	−0.717788	−	0.696262i	$-0.754845\pi$
$769$	−4.54925e6	+	3.30523e6i	−0.277411	+	0.201551i	0.440376	+	0.897813i	$0.354845\pi$
$770$	−1.71338e7			−1.04142
$771$	−3.50973e7	+	2.54997e7i	−2.12637	+	1.54490i
$772$	730027.	−	237200.i	0.0440855	−	0.0143242i
$773$	−3.51407e6	−	1.14179e6i	−0.211525	−	0.0687287i	0.201338	−	0.979522i	$-0.435471\pi$
$773$	−3.51407e6	−	1.14179e6i	−0.211525	−	0.0687287i	−0.412863	+	0.910793i	$0.635471\pi$
$774$	−1.28439e6	−	933163.i	−0.0770626	−	0.0559893i
$775$	−2.31969e7	−	1.68535e7i	−1.38732	−	1.00794i
$776$			1.11337e7i			0.663722i
$777$	−1.10695e7	+	3.40683e7i	−0.657770	+	2.02441i
$778$	−9.29239e6			−0.550400
$779$	−1.11647e7	+	1.82781e7i	−0.659180	+	1.07916i
$780$	−637428.			−0.0375141
$781$	−6.40033e6	+	1.96982e7i	−0.375470	+	1.15558i
$782$			2.87019e6i			0.167839i
$783$	3.74758e7	+	2.72277e7i	2.18447	+	1.58711i
$784$	−801193.	−	582101.i	−0.0465529	−	0.0338227i
$785$	2.61628e7	+	8.50082e6i	1.51534	+	0.492364i
$786$	6.84418e6	−	2.22381e6i	0.395153	−	0.128393i
$787$	−312636.	+	227143.i	−0.0179929	+	0.0130726i	−0.596745	−	0.802431i	$-0.703540\pi$
$787$	−312636.	+	227143.i	−0.0179929	+	0.0130726i	0.578752	+	0.815503i	$0.303540\pi$
$788$	1.17249e7			0.672654
$789$	−2.80852e7	+	2.04051e7i	−1.60615	+	1.16693i
$790$	−1.86646e7	−	2.56896e7i	−1.06402	−	1.46450i
$791$	−6.15749e6	+	8.47506e6i	−0.349915	+	0.481617i
$792$	−1.16921e7	−	3.79900e6i	−0.662339	−	0.215207i
$793$			318220.i			0.0179699i
$794$	−1.68203e6	+	2.31511e6i	−0.0946850	+	0.130323i
$795$	−2.57987e7	−	7.94003e7i	−1.44771	−	4.45558i
$796$	−2.11899e6	−	2.91654e6i	−0.118535	−	0.163149i
$797$	−1.68029e6	+	5.17140e6i	−0.0936998	+	0.288378i	−0.986913	−	0.161256i	$-0.948446\pi$
$797$	−1.68029e6	+	5.17140e6i	−0.0936998	+	0.288378i	0.893213	+	0.449634i	$0.148446\pi$
$798$	2.35677e7	−	7.65761e6i	1.31012	−	0.425683i
$799$	−112694.	−	346835.i	−0.00624500	−	0.0192201i
$800$	−2.12670e6	−	6.54532e6i	−0.117485	−	0.361581i
$801$	6.55119e7	−	2.12861e7i	3.60777	−	1.17224i
$802$	2.65116e6	−	8.15944e6i	0.145546	−	0.447945i
$803$	1.72964e7	+	2.38065e7i	0.946602	+	1.30289i
$804$	765269.	+	2.35526e6i	0.0417517	+	0.128498i
$805$	2.74935e7	−	3.78416e7i	1.49534	−	2.05816i
$806$		−	250326.i		−	0.0135728i
$807$	3.44052e7	+	1.11789e7i	1.85969	+	0.604250i
$808$	1.81510e6	−	2.49828e6i	0.0978077	−	0.134621i
$809$	817341.	+	1.12497e6i	0.0439068	+	0.0604325i	0.830406	−	0.557159i	$-0.188109\pi$
$809$	817341.	+	1.12497e6i	0.0439068	+	0.0604325i	−0.786499	+	0.617591i	$0.788109\pi$
$810$	−2.38090e7	+	1.72982e7i	−1.27505	+	0.926380i
$811$	−1.92221e7			−1.02624			−0.513119	−	0.858318i	$-0.671510\pi$
$811$	−1.92221e7			−1.02624			−0.513119	+	0.858318i	$0.671510\pi$
$812$	−9.46929e6	+	6.87984e6i	−0.503996	+	0.366175i
$813$	3.04914e7	−	9.90727e6i	1.61790	−	0.525687i
$814$	1.66114e7	+	5.39738e6i	0.878711	+	0.285510i
$815$	−9.93520e6	−	7.21835e6i	−0.523941	−	0.380666i
$816$	981504.	+	713104.i	0.0516020	+	0.0374910i
$817$		−	1.56034e6i		−	0.0817831i
$818$	3.06967e6	−	9.44748e6i	0.160402	−	0.493665i
$819$	−844547.			−0.0439961
$820$	1.45832e7	+	8.90782e6i	0.757390	+	0.462633i
$821$	−2.54148e7			−1.31592			−0.657959	−	0.753053i	$-0.728580\pi$
$821$	−2.54148e7			−1.31592			−0.657959	+	0.753053i	$0.728580\pi$
$822$	−364676.	+	1.12236e6i	−0.0188247	+	0.0579365i
$823$		−	3.17043e7i		−	1.63162i	−0.578321	−	0.815809i	$-0.696292\pi$
$823$		−	3.17043e7i		−	1.63162i	0.578321	−	0.815809i	$-0.303708\pi$
$824$	−5.58070e6	−	4.05462e6i	−0.286333	−	0.208033i
$825$	5.64796e7	+	4.10349e7i	2.88906	+	2.09903i
$826$	−4.87686e6	−	1.58459e6i	−0.248708	−	0.0808101i
$827$	−1.05695e7	+	3.43423e6i	−0.537389	+	0.174608i	−0.565122	−	0.825007i	$-0.691171\pi$
$827$	−1.05695e7	+	3.43423e6i	−0.537389	+	0.174608i	0.0277333	+	0.999615i	$0.491171\pi$
$828$	2.71520e7	−	1.97271e7i	1.37634	−	0.999972i
$829$	−3.89731e6			−0.196960			−0.0984802	−	0.995139i	$-0.531398\pi$
$829$	−3.89731e6			−0.196960			−0.0984802	+	0.995139i	$0.531398\pi$
$830$	1.87755e7	−	1.36412e7i	0.946010	−	0.687316i
$831$	2.85375e7	+	3.92784e7i	1.43355	+	1.97311i
$832$	35316.5	−	48609.0i	0.00176876	−	0.00243449i
$833$	−637022.	−	206981.i	−0.0318084	−	0.0103352i
$834$			2.79634e7i			1.39211i
$835$	1.42041e7	−	1.95503e7i	0.705015	−	0.970371i
$836$	−3.73379e6	−	1.14914e7i	−0.184771	−	0.568667i
$837$	−1.80618e7	−	2.48600e7i	−0.891145	−	1.22656i
$838$	2.53528e6	−	7.80278e6i	0.124714	−	0.383830i
$839$	−3.55419e6	+	1.15483e6i	−0.174315	+	0.0566385i	−0.394874	−	0.918735i	$-0.629212\pi$
$839$	−3.55419e6	+	1.15483e6i	−0.174315	+	0.0566385i	0.220559	+	0.975374i	$0.429212\pi$
$840$	−6.10966e6	−	1.88036e7i	−0.298757	−	0.919481i
$841$	−6.44306e6	−	1.98297e7i	−0.314125	−	0.966777i
$842$	4.90296e6	−	1.59307e6i	0.238330	−	0.0774380i
$843$	−1.23541e7	+	3.80221e7i	−0.598746	+	1.84275i
$844$	−3.67999e6	−	5.06507e6i	−0.177824	−	0.244754i
$845$	−1.13782e7	−	3.50185e7i	−0.548191	−	1.68716i
$846$	−2.50651e6	+	3.44992e6i	−0.120405	+	0.165723i
$847$		−	1.93626e6i		−	0.0927373i
$848$	7.48427e6	+	2.43179e6i	0.357404	+	0.116128i
$849$	1.34164e7	−	1.84660e7i	0.638801	−	0.879234i
$850$	−2.73597e6	−	3.76574e6i	−0.129887	−	0.178774i
$851$	−3.85759e7	+	2.80270e7i	−1.82596	+	1.32664i
$852$	−2.39002e7			−1.12798
$853$	1.10120e7	−	8.00070e6i	0.518197	−	0.376492i	−0.297727	−	0.954651i	$-0.596229\pi$
$853$	1.10120e7	−	8.00070e6i	0.518197	−	0.376492i	0.815924	+	0.578159i	$0.196229\pi$
$854$	−9.38724e6	+	3.05010e6i	−0.440447	+	0.143110i
$855$	−9.50470e7	−	3.08827e7i	−4.44655	−	1.44477i
$856$	−4.73124e6	−	3.43745e6i	−0.220694	−	0.160344i
$857$	1.09515e7	+	7.95675e6i	0.509357	+	0.370070i	0.812580	−	0.582850i	$-0.198063\pi$
$857$	1.09515e7	+	7.95675e6i	0.509357	+	0.370070i	−0.303222	+	0.952920i	$0.598063\pi$
$858$			609493.i			0.0282651i
$859$	6.42232e6	−	1.97659e7i	0.296968	−	0.913972i	−0.685586	−	0.727992i	$-0.740454\pi$
$859$	6.42232e6	−	1.97659e7i	0.296968	−	0.913972i	0.982553	−	0.185980i	$-0.0595461\pi$
$860$	−1.24492e6			−0.0573980
$861$	2.85980e7	+	1.74684e7i	1.31470	+	0.803054i
$862$	2.40387e7			1.10190
$863$	2.65861e6	−	8.18237e6i	0.121514	−	0.373983i	−0.871735	−	0.489977i	$-0.837005\pi$
$863$	2.65861e6	−	8.18237e6i	0.121514	−	0.373983i	0.993250	+	0.115994i	$0.0370052\pi$
$864$		−	7.37557e6i		−	0.336133i
$865$	−2.27253e6	−	1.65109e6i	−0.103269	−	0.0750293i
$866$	−3.53715e6	−	2.56989e6i	−0.160273	−	0.116445i
$867$	−3.61800e7	−	1.17556e7i	−1.63464	−	0.531125i
$868$	7.38442e6	−	2.39934e6i	0.332673	−	0.108092i
$869$	−2.45638e7	+	1.78467e7i	−1.10343	+	0.801692i
$870$	6.98666e7			3.12947
$871$	67109.3	−	48757.8i	0.00299735	−	0.00217770i
$872$	−2.65598e6	−	3.65565e6i	−0.118286	−	0.162807i
$873$	5.17562e7	−	7.12363e7i	2.29840	−	3.16348i
$874$	3.13712e7	+	1.01931e7i	1.38916	+	0.451366i
$875$			4.05855e7i			1.79205i
$876$	−1.99589e7	+	2.74711e7i	−0.878774	+	1.20953i
$877$	1.24799e7	+	3.84093e7i	0.547915	+	1.68631i	0.713957	+	0.700190i	$0.246901\pi$
$877$	1.24799e7	+	3.84093e7i	0.547915	+	1.68631i	−0.166042	+	0.986119i	$0.553099\pi$
$878$	1.01379e7	+	1.39536e7i	0.443825	+	0.610873i
$879$	−9.99338e6	+	3.07565e7i	−0.436255	+	1.34265i
$880$	−9.16848e6	+	2.97902e6i	−0.399108	+	0.129678i
$881$	−1.24048e7	−	3.81782e7i	−0.538458	−	1.65720i	−0.736057	−	0.676919i	$-0.763315\pi$
$881$	−1.24048e7	−	3.81782e7i	−0.538458	−	1.65720i	0.197600	−	0.980283i	$-0.436685\pi$
$882$	2.42028e6	+	7.44884e6i	0.104759	+	0.322416i
$883$	2.66600e7	−	8.66237e6i	1.15069	−	0.373883i	0.329288	−	0.944229i	$-0.393191\pi$
$883$	2.66600e7	−	8.66237e6i	1.15069	−	0.373883i	0.821404	+	0.570347i	$0.193191\pi$
$884$	12557.7	−	38648.6i	0.000540479	−	0.00166342i
$885$	1.79913e7	+	2.47629e7i	0.772154	+	1.06278i
$886$	8.25178e6	+	2.53964e7i	0.353153	+	1.08689i
$887$	4.37133e6	−	6.01662e6i	0.186554	−	0.256769i	−0.705488	−	0.708722i	$-0.749272\pi$
$887$	4.37133e6	−	6.01662e6i	0.186554	−	0.256769i	0.892042	+	0.451952i	$0.149272\pi$
$888$			2.01550e7i			0.857727i
$889$	1.67694e7	+	5.44870e6i	0.711643	+	0.231227i
$890$	3.17495e7	−	4.36994e7i	1.34357	−	1.84927i
$891$	1.65402e7	+	2.27656e7i	0.697984	+	0.960692i
$892$	3.32850e6	−	2.41829e6i	0.140067	−	0.101765i
$893$	−4.19113e6			−0.175874
$894$	−1.90839e7	+	1.38652e7i	−0.798588	+	0.580208i
$895$	−4.15160e7	+	1.34894e7i	−1.73244	+	0.562903i
$896$	1.77243e6	+	575897.i	0.0737562	+	0.0239648i
$897$	−1.34612e6	−	978014.i	−0.0558603	−	0.0405849i
$898$	8.08397e6	+	5.87335e6i	0.334529	+	0.243050i
$899$			2.74375e7i			1.13226i
$900$	−1.68194e7	+	5.17647e7i	−0.692155	+	2.13023i
$901$	5.32246e6			0.218424
$902$	8.51744e6	−	1.39441e7i	0.348572	−	0.570657i
$903$	−2.44132e6			−0.0996333
$904$	−1.82140e6	+	5.60569e6i	−0.0741283	+	0.228143i
$905$		−	2.63569e7i		−	1.06973i
$906$	−3.69240e7	−	2.68268e7i	−1.49447	−	1.08580i
$907$	1.18079e6	+	857895.i	0.0476601	+	0.0346271i	0.611360	−	0.791352i	$-0.290623\pi$
$907$	1.18079e6	+	857895.i	0.0476601	+	0.0346271i	−0.563700	+	0.825979i	$0.690623\pi$
$908$	6.03145e6	+	1.95974e6i	0.242777	+	0.0788830i
$909$	−2.32269e7	+	7.54689e6i	−0.932357	+	0.302941i
$910$	−535779.	+	389266.i	−0.0214478	+	0.0155827i
$911$	2.06498e7			0.824366			0.412183	−	0.911101i	$-0.364766\pi$
$911$	2.06498e7			0.824366			0.412183	+	0.911101i	$0.364766\pi$
$912$	1.12799e7	−	8.19534e6i	0.449075	−	0.326272i
$913$	−1.30434e7	−	1.79527e7i	−0.517860	−	0.712774i
$914$	−1.02926e7	+	1.41666e7i	−0.407532	+	0.560919i
$915$	5.60335e7	+	1.82064e7i	2.21256	+	0.718905i
$916$			4.65289e6i			0.183225i
$917$	4.39471e6	−	6.04880e6i	0.172587	−	0.237545i
$918$	−1.54151e6	−	4.74428e6i	−0.0603726	−	0.185808i
$919$	−2.02177e7	−	2.78273e7i	−0.789667	−	1.08688i	−0.994150	−	0.108013i	$-0.965551\pi$
$919$	−2.02177e7	−	2.78273e7i	−0.789667	−	1.08688i	0.204483	−	0.978870i	$-0.434449\pi$
$920$	8.13263e6	−	2.50297e7i	0.316783	−	0.974957i
$921$	−5.41453e7	+	1.75929e7i	−2.10335	+	0.683419i
$922$	6.42987e6	+	1.97891e7i	0.249101	+	0.766654i
$923$	247387.	+	761379.i	0.00955812	+	0.0294169i
$924$	−1.79795e7	+	5.84191e6i	−0.692785	+	0.225100i
$925$	2.38959e7	−	7.35439e7i	0.918266	−	2.82613i
$926$	−2.04816e7	−	2.81905e7i	−0.784940	−	1.08038i
$927$	1.68584e7	+	5.18848e7i	0.644343	+	1.98308i
$928$	−3.87094e6	+	5.32788e6i	−0.147552	+	0.203088i
$929$		−	1.93069e7i		−	0.733961i	−0.930229	−	0.366981i	$-0.880392\pi$
$929$		−	1.93069e7i		−	0.733961i	0.930229	−	0.366981i	$-0.119608\pi$
$930$	−4.40785e7	−	1.43220e7i	−1.67116	−	0.542994i
$931$	−4.52461e6	+	6.22759e6i	−0.171083	+	0.235476i
$932$	−3.70017e6	−	5.09285e6i	−0.139535	−	0.192053i
$933$	−2.97505e7	+	2.16150e7i	−1.11890	+	0.812926i
$934$	1.58602e6			0.0594897
$935$	−5.27494e6	+	3.83247e6i	−0.197328	+	0.143367i
$936$	−451926.	+	146840.i	−0.0168608	+	0.00547840i
$937$	−2.98765e7	−	9.70746e6i	−1.11168	−	0.361207i	−0.305094	−	0.952322i	$-0.598688\pi$
$937$	−2.98765e7	−	9.70746e6i	−1.11168	−	0.361207i	−0.806587	+	0.591115i	$0.798688\pi$
$938$	2.08155e6	+	1.51233e6i	0.0772466	+	0.0561229i
$939$	−1.97595e7	−	1.43561e7i	−0.731329	−	0.531342i
$940$			3.34391e6i			0.123434i
$941$	−1.27299e7	+	3.91785e7i	−0.468651	+	1.44236i	0.385681	+	0.922632i	$0.373967\pi$
$941$	−1.27299e7	+	3.91785e7i	−0.468651	+	1.44236i	−0.854332	+	0.519727i	$0.826033\pi$
$942$	3.03527e7			1.11447
$943$	1.71295e7	+	4.11868e7i	0.627287	+	1.50827i
$944$	−2.88517e6			−0.105376
$945$	−2.51216e7	+	7.73163e7i	−0.915098	+	2.81638i
$946$			1.19037e6i			0.0432467i
$947$	−1.77495e7	−	1.28958e7i	−0.643149	−	0.467275i	0.217782	−	0.975997i	$-0.430118\pi$
$947$	−1.77495e7	−	1.28958e7i	−0.643149	−	0.467275i	−0.860930	+	0.508723i	$0.830118\pi$
$948$	−2.83450e7	−	2.05939e7i	−1.02437	−	0.744247i
$949$	1.08173e6	+	351475.i	0.0389899	+	0.0126686i
$950$	−5.08761e7	+	1.65306e7i	−1.82896	+	0.594266i
$951$	6.06308e7	−	4.40509e7i	2.17391	−	1.57944i
$952$	1.26047e6			0.0450753
$953$	2.48815e6	−	1.80775e6i	0.0887452	−	0.0644772i	−0.542528	−	0.840038i	$-0.682533\pi$
$953$	2.48815e6	−	1.80775e6i	0.0887452	−	0.0644772i	0.631273	+	0.775561i	$0.282533\pi$
$954$	−3.65818e7	−	5.03505e7i	−1.30135	−	1.79115i
$955$	−7.22960e6	+	9.95069e6i	−0.256511	+	0.353057i
$956$	−1.44394e7	−	4.69163e6i	−0.510979	−	0.166027i
$957$		−	6.68047e7i		−	2.35791i
$958$	1.19794e7	−	1.64883e7i	0.421718	−	0.580445i
$959$	378882.	+	1.16608e6i	0.0133033	+	0.0409432i
$960$	−6.53869e6	−	8.99974e6i	−0.228988	−	0.315175i
$961$	−3.22247e6	+	9.91774e6i	−0.112559	+	0.346421i
$962$	642068.	−	208621.i	0.0223688	−	0.00726808i
$963$	1.42923e7	+	4.39872e7i	0.496634	+	1.52848i
$964$	−3.12209e6	−	9.60880e6i	−0.108206	−	0.333025i
$965$	−4.52737e6	+	1.47103e6i	−0.156505	+	0.0508515i
$966$	1.59482e7	−	4.90836e7i	0.549882	−	1.69236i
$967$	2.45442e7	+	3.37823e7i	0.844080	+	1.16178i	0.985136	+	0.171775i	$0.0549501\pi$
$967$	2.45442e7	+	3.37823e7i	0.844080	+	1.16178i	−0.141056	+	0.990002i	$0.545050\pi$
$968$	−336653.	−	1.03611e6i	−0.0115477	−	0.0355401i
$969$	5.54289e6	−	7.62913e6i	0.189638	−	0.261015i
$970$		−	6.90474e7i		−	2.35623i
$971$	5.15328e6	+	1.67440e6i	0.175402	+	0.0569917i	0.395402	−	0.918508i	$-0.370605\pi$
$971$	5.15328e6	+	1.67440e6i	0.175402	+	0.0569917i	−0.219999	+	0.975500i	$0.570605\pi$
$972$	−2.62584e6	+	3.61416e6i	−0.0891463	+	0.122699i
$973$	1.70768e7	+	2.35042e7i	0.578261	+	0.795908i
$974$	−2.87518e7	+	2.08894e7i	−0.971109	+	0.705552i
$975$	2.69841e6			0.0909069
$976$	−4.49290e6	+	3.26428e6i	−0.150974	+	0.109689i
$977$	−1.62695e7	+	5.28628e6i	−0.545303	+	0.177180i	−0.568698	−	0.822547i	$-0.692553\pi$
$977$	−1.62695e7	+	5.28628e6i	−0.545303	+	0.177180i	0.0233946	+	0.999726i	$0.492553\pi$
$978$	−1.28868e7	−	4.18717e6i	−0.430821	−	0.139982i
$979$	−4.17843e7	−	3.03581e7i	−1.39334	−	1.01232i
$980$	4.96871e6	+	3.60998e6i	0.165264	+	0.120071i
$981$			3.57363e7i			1.18560i
$982$	−5.94505e6	+	1.82970e7i	−0.196733	+	0.605482i
$983$	3.47171e7			1.14593			0.572967	−	0.819579i	$-0.305792\pi$
$983$	3.47171e7			1.14593			0.572967	+	0.819579i	$0.305792\pi$
$984$	1.83403e7	+	4.37525e6i	0.603835	+	0.144051i
$985$	−7.27133e7			−2.38794
$986$	−1.37641e6	+	4.23616e6i	−0.0450875	+	0.138765i
$987$			6.55747e6i			0.214261i
$988$	−377832.	−	274511.i	−0.0123142	−	0.00894680i
$989$	−2.62903e6	−	1.91010e6i	−0.0854683	−	0.0620964i
$990$	7.25104e7	+	2.35600e7i	2.35132	+	0.763991i
$991$	3.71302e7	−	1.20643e7i	1.20100	−	0.390229i	0.360872	−	0.932615i	$-0.382479\pi$
$991$	3.71302e7	−	1.20643e7i	1.20100	−	0.390229i	0.840129	+	0.542387i	$0.182479\pi$
$992$	3.53432e6	−	2.56783e6i	0.114032	−	0.0828490i
$993$	−5.08649e6			−0.163699
$994$	−2.00889e7	+	1.45954e7i	−0.644896	+	0.468545i
$995$	1.31412e7	+	1.80873e7i	0.420801	+	0.579184i
$996$	1.50512e7	−	2.07162e7i	0.480754	−	0.661700i
$997$	7.71436e6	+	2.50655e6i	0.245789	+	0.0798616i	0.429321	−	0.903152i	$-0.358753\pi$
$997$	7.71436e6	+	2.50655e6i	0.245789	+	0.0798616i	−0.183532	+	0.983014i	$0.558753\pi$
$998$		−	238654.i		−	0.00758478i
$999$	4.87114e7	−	6.70455e7i	1.54425	−	2.12547i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	82.6.f.b.25.1	yes	40
41.23	even	10	inner	82.6.f.b.23.10	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
82.6.f.b.23.10	✓	40	41.23	even	10	inner
82.6.f.b.25.1	yes	40	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 82 = 2 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	82.f (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.23607 + 3.80423i) q^{2} -27.3707i q^{3} +(-12.9443 - 9.40456i) q^{4} +(80.2757 + 58.3237i) q^{5} +(104.124 + 33.8320i) q^{6} +(108.180 - 35.1500i) q^{7} +(51.7771 - 37.6183i) q^{8} -506.154 q^{9} +(-321.103 + 233.295i) q^{10} +(223.071 + 307.031i) q^{11} +(-257.409 + 354.294i) q^{12} +(13.9510 + 4.53295i) q^{13} +454.991i q^{14} +(1596.36 - 2197.20i) q^{15} +(79.1084 + 243.470i) q^{16} +(101.772 + 140.077i) q^{17} +(625.641 - 1925.52i) q^{18} +(1892.47 - 614.901i) q^{19} +(-490.602 - 1509.92i) q^{20} +(-962.078 - 2960.97i) q^{21} +(-1443.75 + 469.101i) q^{22} +(1280.63 - 3941.38i) q^{23} +(-1029.64 - 1417.17i) q^{24} +(2076.86 + 6391.91i) q^{25} +(-34.4887 + 47.4697i) q^{26} +7202.70i q^{27} +(-1730.89 - 562.399i) q^{28} +(3780.21 - 5203.01i) q^{29} +(6385.44 + 8788.81i) q^{30} +(-3451.48 + 2507.65i) q^{31} -1024.00 q^{32} +(8403.64 - 6105.60i) q^{33} +(-658.681 + 214.018i) q^{34} +(10734.3 + 3487.80i) q^{35} +(6551.80 + 4760.16i) q^{36} +(-9308.37 - 6762.93i) q^{37} +7959.45i q^{38} +(124.070 - 381.848i) q^{39} +6350.48 q^{40} +(-8174.69 + 7002.19i) q^{41} +12453.4 q^{42} +(242.314 - 745.766i) q^{43} -6072.18i q^{44} +(-40631.9 - 29520.8i) q^{45} +(13411.0 + 9743.63i) q^{46} +(-2003.16 - 650.865i) q^{47} +(6663.95 - 2165.25i) q^{48} +(-3129.66 + 2273.83i) q^{49} -26883.4 q^{50} +(3834.00 - 2785.56i) q^{51} +(-137.955 - 189.879i) q^{52} +(18068.5 - 24869.2i) q^{53} +(-27400.7 - 8903.03i) q^{54} +37657.5i q^{55} +(4278.99 - 5889.52i) q^{56} +(-16830.3 - 51798.2i) q^{57} +(15120.8 + 20812.1i) q^{58} +(-3482.68 + 10718.6i) q^{59} +(-41327.4 + 13428.1i) q^{60} +(6703.66 + 20631.7i) q^{61} +(-5273.39 - 16229.8i) q^{62} +(-54756.0 + 17791.3i) q^{63} +(1265.73 - 3895.53i) q^{64} +(855.547 + 1177.56i) q^{65} +(12839.6 + 39516.3i) q^{66} +(3323.88 - 4574.92i) q^{67} -2770.31i q^{68} +(-107878. - 35051.8i) q^{69} +(-26536.8 + 36524.7i) q^{70} +(32078.5 + 44152.3i) q^{71} +(-26207.2 + 19040.6i) q^{72} +77537.7 q^{73} +(37233.5 - 27051.7i) q^{74} +(174951. - 56845.0i) q^{75} +(-30279.5 - 9838.42i) q^{76} +(34924.0 + 25373.8i) q^{77} +(1299.28 + 943.980i) q^{78} +80004.4i q^{79} +(-7849.63 + 24158.7i) q^{80} +74147.5 q^{81} +(-16533.4 - 39753.6i) q^{82} -58471.8 q^{83} +(-15393.2 + 47375.6i) q^{84} +17180.5i q^{85} +(2537.54 + 1843.63i) q^{86} +(-142410. - 103467. i) q^{87} +(23099.9 + 7505.62i) q^{88} +(-129431. + 42054.6i) q^{89} +(162528. - 118083. i) q^{90} +1668.56 q^{91} +(-53643.8 + 38974.5i) q^{92} +(68636.0 + 94469.4i) q^{93} +(4952.07 - 6815.95i) q^{94} +(187783. + 61014.3i) q^{95} +28027.6i q^{96} +(-102254. + 140740. i) q^{97} +(-4781.70 - 14716.5i) q^{98} +(-112908. - 155405. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 40 q^{2} - 160 q^{4} + 24 q^{5} - 100 q^{6} + 640 q^{8} - 4576 q^{9} - 96 q^{10} + 20 q^{11} + 400 q^{12} - 275 q^{13} + 1385 q^{15} - 2560 q^{16} - 105 q^{17} - 2476 q^{18} + 4720 q^{19} + 1424 q^{20}+ \cdots - 537690 q^{99}+O(q^{100}) \) 40 * q + 40 * q^2 - 160 * q^4 + 24 * q^5 - 100 * q^6 + 640 * q^8 - 4576 * q^9 - 96 * q^10 + 20 * q^11 + 400 * q^12 - 275 * q^13 + 1385 * q^15 - 2560 * q^16 - 105 * q^17 - 2476 * q^18 + 4720 * q^19 + 1424 * q^20 + 6961 * q^21 - 4140 * q^22 - 1019 * q^23 + 1600 * q^24 - 2006 * q^25 - 8620 * q^26 - 12525 * q^29 + 5540 * q^30 + 8900 * q^31 - 40960 * q^32 + 17684 * q^33 - 13100 * q^34 - 29955 * q^35 + 26704 * q^36 - 31651 * q^37 - 10104 * q^39 + 14464 * q^40 + 35044 * q^41 + 32776 * q^42 - 15615 * q^43 - 39955 * q^45 - 3224 * q^46 + 8330 * q^47 - 6400 * q^48 + 48406 * q^49 - 135016 * q^50 + 120325 * q^51 - 34480 * q^52 + 145425 * q^53 + 72200 * q^54 + 17600 * q^56 + 31992 * q^57 - 50100 * q^58 + 18978 * q^59 + 1680 * q^60 + 52673 * q^61 + 66140 * q^62 - 88455 * q^63 - 40960 * q^64 + 204480 * q^65 - 17556 * q^66 - 149205 * q^67 - 249735 * q^69 - 49100 * q^70 + 151175 * q^71 - 106816 * q^72 - 107670 * q^73 + 126604 * q^74 + 120180 * q^75 - 75520 * q^76 - 207367 * q^77 - 99284 * q^78 + 22784 * q^80 + 1167568 * q^81 + 84204 * q^82 - 281376 * q^83 + 111376 * q^84 - 131400 * q^86 - 141269 * q^87 + 66240 * q^88 - 277775 * q^89 + 159820 * q^90 - 518682 * q^91 + 12896 * q^92 - 172375 * q^93 + 16320 * q^94 + 149585 * q^95 + 330875 * q^97 - 171004 * q^98 - 537690 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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