LMFDB - Embedded newform 51.6.h.a.19.2

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			19.2
Character	$\chi$	$=$	51.19
Dual form			51.6.h.a.43.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-6.70687 - 6.70687i) q^{2} +(8.31492 - 3.44415i) q^{3} +57.9642i q^{4} +(14.8469 + 35.8437i) q^{5} +(-78.8665 - 32.6676i) q^{6} +(90.1287 - 217.590i) q^{7} +(174.139 - 174.139i) q^{8} +(57.2756 - 57.2756i) q^{9} +(140.822 - 339.975i) q^{10} +(79.5662 + 32.9574i) q^{11} +(199.638 + 481.968i) q^{12} -516.438i q^{13} +(-2063.83 + 854.866i) q^{14} +(246.902 + 246.902i) q^{15} -480.997 q^{16} +(-1178.08 + 178.873i) q^{17} -768.281 q^{18} +(-952.328 - 952.328i) q^{19} +(-2077.65 + 860.591i) q^{20} -2119.66i q^{21} +(-312.599 - 754.682i) q^{22} +(827.585 + 342.797i) q^{23} +(848.189 - 2047.71i) q^{24} +(1145.37 - 1145.37i) q^{25} +(-3463.68 + 3463.68i) q^{26} +(278.976 - 673.508i) q^{27} +(12612.4 + 5224.24i) q^{28} +(-1603.87 - 3872.10i) q^{29} -3311.88i q^{30} +(-6871.70 + 2846.35i) q^{31} +(-2346.46 - 2346.46i) q^{32} +775.097 q^{33} +(9100.88 + 6701.52i) q^{34} +9137.36 q^{35} +(3319.94 + 3319.94i) q^{36} +(11965.1 - 4956.10i) q^{37} +12774.3i q^{38} +(-1778.69 - 4294.14i) q^{39} +(8827.20 + 3656.35i) q^{40} +(5618.76 - 13564.9i) q^{41} +(-14216.3 + 14216.3i) q^{42} +(-602.213 + 602.213i) q^{43} +(-1910.35 + 4612.00i) q^{44} +(2903.34 + 1202.60i) q^{45} +(-3251.41 - 7849.60i) q^{46} +537.757i q^{47} +(-3999.45 + 1656.63i) q^{48} +(-27337.9 - 27337.9i) q^{49} -15363.7 q^{50} +(-9179.53 + 5544.78i) q^{51} +29934.9 q^{52} +(11927.2 + 11927.2i) q^{53} +(-6388.19 + 2646.07i) q^{54} +3341.26i q^{55} +(-22195.9 - 53585.7i) q^{56} +(-11198.5 - 4638.57i) q^{57} +(-15212.7 + 36726.6i) q^{58} +(-33790.4 + 33790.4i) q^{59} +(-14311.5 + 14311.5i) q^{60} +(4500.95 - 10866.2i) q^{61} +(65177.7 + 26997.5i) q^{62} +(-7300.43 - 17624.8i) q^{63} +46866.7i q^{64} +(18511.0 - 7667.52i) q^{65} +(-5198.48 - 5198.48i) q^{66} +29231.4 q^{67} +(-10368.2 - 68286.2i) q^{68} +8061.94 q^{69} +(-61283.1 - 61283.1i) q^{70} +(55771.1 - 23101.2i) q^{71} -19947.8i q^{72} +(24157.4 + 58321.1i) q^{73} +(-113488. - 47008.4i) q^{74} +(5578.84 - 13468.5i) q^{75} +(55201.0 - 55201.0i) q^{76} +(14342.4 - 14342.4i) q^{77} +(-16870.8 + 40729.7i) q^{78} +(79649.3 + 32991.8i) q^{79} +(-7141.33 - 17240.7i) q^{80} -6561.00i q^{81} +(-128662. + 53293.7i) q^{82} +(20981.3 + 20981.3i) q^{83} +122864. q^{84} +(-23902.3 - 39570.8i) q^{85} +8077.92 q^{86} +(-26672.2 - 26672.2i) q^{87} +(19594.7 - 8116.40i) q^{88} +134357. i q^{89} +(-11406.6 - 27538.0i) q^{90} +(-112372. - 46545.9i) q^{91} +(-19870.0 + 47970.3i) q^{92} +(-47334.4 + 47334.4i) q^{93} +(3606.67 - 3606.67i) q^{94} +(19995.8 - 48274.1i) q^{95} +(-27592.1 - 11429.0i) q^{96} +(-899.810 - 2172.33i) q^{97} +366703. i q^{98} +(6444.87 - 2669.55i) 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 $

$2$	−6.70687	−	6.70687i	−1.18562	−	1.18562i	−0.978266	−	0.207352i	$-0.933515\pi$
$2$	−6.70687	−	6.70687i	−1.18562	−	1.18562i	−0.207352	−	0.978266i	$-0.566485\pi$
$3$	8.31492	−	3.44415i	0.533402	−	0.220942i
$3$	8.31492	−	3.44415i	0.533402	−	0.220942i
$4$			57.9642i			1.81138i
$5$	14.8469	+	35.8437i	0.265590	+	0.641191i	0.999266	−	0.0383085i	$-0.0121970\pi$
$5$	14.8469	+	35.8437i	0.265590	+	0.641191i	−0.733676	+	0.679500i	$0.762197\pi$
$6$	−78.8665	−	32.6676i	−0.894365	−	0.370458i
$7$	90.1287	−	217.590i	0.695213	−	1.67839i	−0.0387900	−	0.999247i	$-0.512350\pi$
$7$	90.1287	−	217.590i	0.695213	−	1.67839i	0.734003	−	0.679146i	$-0.237650\pi$
$8$	174.139	−	174.139i	0.961990	−	0.961990i
$9$	57.2756	−	57.2756i	0.235702	−	0.235702i
$10$	140.822	−	339.975i	0.445320	−	1.07510i
$11$	79.5662	+	32.9574i	0.198265	+	0.0821243i	0.479607	−	0.877484i	$-0.340779\pi$
$11$	79.5662	+	32.9574i	0.198265	+	0.0821243i	−0.281341	+	0.959608i	$0.590779\pi$
$12$	199.638	+	481.968i	0.400211	+	0.966195i
$13$		−	516.438i		−	0.847539i	−0.905770	−	0.423769i	$-0.860707\pi$
$13$		−	516.438i		−	0.847539i	0.905770	−	0.423769i	$-0.139293\pi$
$14$	−2063.83	+	854.866i	−2.81419	+	1.16568i
$15$	246.902	+	246.902i	0.283333	+	0.283333i
$16$	−480.997			−0.469724
$17$	−1178.08	+	178.873i	−0.988669	+	0.150114i
$17$	−1178.08	+	178.873i	−0.988669	+	0.150114i
$18$	−768.281			−0.558906
$19$	−952.328	−	952.328i	−0.605205	−	0.605205i	0.336484	−	0.941689i	$-0.390762\pi$
$19$	−952.328	−	952.328i	−0.605205	−	0.605205i	−0.941689	+	0.336484i	$0.890762\pi$
$20$	−2077.65	+	860.591i	−1.16144	+	0.481085i
$21$		−	2119.66i		−	1.04886i
$22$	−312.599	−	754.682i	−0.137699	−	0.332435i
$23$	827.585	+	342.797i	0.326207	+	0.135119i	0.539776	−	0.841809i	$-0.318509\pi$
$23$	827.585	+	342.797i	0.326207	+	0.135119i	−0.213569	+	0.976928i	$0.568509\pi$
$24$	848.189	−	2047.71i	0.300583	−	0.725672i
$25$	1145.37	−	1145.37i	0.366519	−	0.366519i
$26$	−3463.68	+	3463.68i	−1.00486	+	1.00486i
$27$	278.976	−	673.508i	0.0736475	−	0.177801i
$28$	12612.4	+	5224.24i	3.04021	+	1.25930i
$29$	−1603.87	−	3872.10i	−0.354140	−	0.854971i	−0.996100	−	0.0882320i	$-0.971878\pi$
$29$	−1603.87	−	3872.10i	−0.354140	−	0.854971i	0.641960	−	0.766739i	$-0.278122\pi$
$30$		−	3311.88i		−	0.671849i
$31$	−6871.70	+	2846.35i	−1.28428	+	0.531967i	−0.917276	−	0.398252i	$-0.869617\pi$
$31$	−6871.70	+	2846.35i	−1.28428	+	0.531967i	−0.367005	+	0.930219i	$0.619617\pi$
$32$	−2346.46	−	2346.46i	−0.405077	−	0.405077i
$33$	775.097			0.123900
$34$	9100.88	+	6701.52i	1.35016	+	0.994206i
$35$	9137.36			1.26081
$36$	3319.94	+	3319.94i	0.426947	+	0.426947i
$37$	11965.1	−	4956.10i	1.43685	−	0.595163i	0.477818	−	0.878459i	$-0.341428\pi$
$37$	11965.1	−	4956.10i	1.43685	−	0.595163i	0.959033	+	0.283296i	$0.0914279\pi$
$38$			12774.3i			1.43508i
$39$	−1778.69	−	4294.14i	−0.187257	−	0.452079i
$40$	8827.20	+	3656.35i	0.872314	+	0.361324i
$41$	5618.76	−	13564.9i	0.522013	−	1.26025i	−0.414638	−	0.909986i	$-0.636092\pi$
$41$	5618.76	−	13564.9i	0.522013	−	1.26025i	0.936651	−	0.350264i	$-0.113908\pi$
$42$	−14216.3	+	14216.3i	−1.24355	+	1.24355i
$43$	−602.213	+	602.213i	−0.0496682	+	0.0496682i	−0.731505	−	0.681836i	$-0.761182\pi$
$43$	−602.213	+	602.213i	−0.0496682	+	0.0496682i	0.681836	+	0.731505i	$0.261182\pi$
$44$	−1910.35	+	4612.00i	−0.148758	+	0.359135i
$45$	2903.34	+	1202.60i	0.213730	+	0.0885300i
$46$	−3251.41	−	7849.60i	−0.226557	−	0.546957i
$47$			537.757i			0.0355093i	0.999842	+	0.0177546i	$0.00565177\pi$
$47$			537.757i			0.0355093i	−0.999842	+	0.0177546i	$0.994348\pi$
$48$	−3999.45	+	1656.63i	−0.250552	+	0.103782i
$49$	−27337.9	−	27337.9i	−1.62658	−	1.62658i
$50$	−15363.7			−0.869103
$51$	−9179.53	+	5544.78i	−0.494191	+	0.298510i
$52$	29934.9			1.53522
$53$	11927.2	+	11927.2i	0.583240	+	0.583240i	0.935792	−	0.352552i	$-0.114686\pi$
$53$	11927.2	+	11927.2i	0.583240	+	0.583240i	−0.352552	+	0.935792i	$0.614686\pi$
$54$	−6388.19	+	2646.07i	−0.298122	+	0.123486i
$55$			3341.26i			0.148937i
$56$	−22195.9	−	53585.7i	−0.945809	−	2.28339i
$57$	−11198.5	−	4638.57i	−0.456533	−	0.189102i
$58$	−15212.7	+	36726.6i	−0.593793	+	1.43354i
$59$	−33790.4	+	33790.4i	−1.26376	+	1.26376i	−0.314498	+	0.949258i	$0.601836\pi$
$59$	−33790.4	+	33790.4i	−1.26376	+	1.26376i	−0.949258	+	0.314498i	$0.898164\pi$
$60$	−14311.5	+	14311.5i	−0.513224	+	0.513224i
$61$	4500.95	−	10866.2i	0.154874	−	0.373900i	−0.827330	−	0.561716i	$-0.810141\pi$
$61$	4500.95	−	10866.2i	0.154874	−	0.373900i	0.982204	+	0.187817i	$0.0601412\pi$
$62$	65177.7	+	26997.5i	2.15338	+	0.891958i
$63$	−7300.43	−	17624.8i	−0.231738	−	0.559464i
$64$			46866.7i			1.43026i
$65$	18511.0	−	7667.52i	0.543434	−	0.225098i
$66$	−5198.48	−	5198.48i	−0.146898	−	0.146898i
$67$	29231.4			0.795541			0.397770	−	0.917485i	$-0.369784\pi$
$67$	29231.4			0.795541			0.397770	+	0.917485i	$0.369784\pi$
$68$	−10368.2	−	68286.2i	−0.271914	−	1.79086i
$69$	8061.94			0.203853
$70$	−61283.1	−	61283.1i	−1.49484	−	1.49484i
$71$	55771.1	−	23101.2i	1.31300	−	0.543861i	0.387239	−	0.921979i	$-0.373429\pi$
$71$	55771.1	−	23101.2i	1.31300	−	0.543861i	0.925757	+	0.378118i	$0.123429\pi$
$72$		−	19947.8i		−	0.453486i
$73$	24157.4	+	58321.1i	0.530570	+	1.28091i	0.931146	+	0.364646i	$0.118810\pi$
$73$	24157.4	+	58321.1i	0.530570	+	1.28091i	−0.400577	+	0.916263i	$0.631190\pi$
$74$	−113488.	−	47008.4i	−2.40919	−	0.997920i
$75$	5578.84	−	13468.5i	0.114522	−	0.276482i
$76$	55201.0	−	55201.0i	1.09626	−	1.09626i
$77$	14342.4	−	14342.4i	0.275674	−	0.275674i
$78$	−16870.8	+	40729.7i	−0.313978	+	0.758009i
$79$	79649.3	+	32991.8i	1.43587	+	0.594755i	0.958792	−	0.284108i	$-0.0916973\pi$
$79$	79649.3	+	32991.8i	1.43587	+	0.594755i	0.477074	+	0.878863i	$0.341697\pi$
$80$	−7141.33	−	17240.7i	−0.124754	−	0.301183i
$81$		−	6561.00i		−	0.111111i
$82$	−128662.	+	53293.7i	−2.11308	+	0.875268i
$83$	20981.3	+	20981.3i	0.334301	+	0.334301i	0.854217	−	0.519916i	$-0.174037\pi$
$83$	20981.3	+	20981.3i	0.334301	+	0.334301i	−0.519916	+	0.854217i	$0.674037\pi$
$84$	122864.			1.89989
$85$	−23902.3	−	39570.8i	−0.358832	−	0.594057i
$86$	8077.92			0.117775
$87$	−26672.2	−	26672.2i	−0.377798	−	0.377798i
$88$	19594.7	−	8116.40i	0.269732	−	0.111727i
$89$			134357.i			1.79798i	0.437974	+	0.898988i	$0.355696\pi$
$89$			134357.i			1.79798i	−0.437974	+	0.898988i	$0.644304\pi$
$90$	−11406.6	−	27538.0i	−0.148440	−	0.358365i
$91$	−112372.	−	46545.9i	−1.42250	−	0.589220i
$92$	−19870.0	+	47970.3i	−0.244753	+	0.590885i
$93$	−47334.4	+	47334.4i	−0.567504	+	0.567504i
$94$	3606.67	−	3606.67i	0.0421004	−	0.0421004i
$95$	19995.8	−	48274.1i	0.227316	−	0.548789i
$96$	−27592.1	−	11429.0i	−0.305568	−	0.126570i
$97$	−899.810	−	2172.33i	−0.00971005	−	0.0234421i	0.918950	−	0.394374i	$-0.129038\pi$
$97$	−899.810	−	2172.33i	−0.00971005	−	0.0234421i	−0.928660	+	0.370932i	$0.879038\pi$
$98$			366703.i			3.85700i
$99$	6444.87	−	2669.55i	0.0660885	−	0.0273748i
$100$	66390.6	+	66390.6i	0.663906	+	0.663906i
$101$	−9105.12			−0.0888141			−0.0444071	−	0.999014i	$-0.514140\pi$
$101$	−9105.12			−0.0888141			−0.0444071	+	0.999014i	$0.514140\pi$
$102$	98754.1	+	24377.8i	0.939841	+	0.232003i
$103$	27618.1			0.256508			0.128254	−	0.991741i	$-0.459063\pi$
$103$	27618.1			0.256508			0.128254	+	0.991741i	$0.459063\pi$
$104$	−89931.8	−	89931.8i	−0.815324	−	0.815324i
$105$	75976.4	−	31470.4i	0.672520	−	0.278567i
$106$		−	159988.i		−	1.38300i
$107$	−60730.8	−	146617.i	−0.512801	−	1.23801i	−0.942247	−	0.334919i	$-0.891291\pi$
$107$	−60730.8	−	146617.i	−0.512801	−	1.23801i	0.429445	−	0.903093i	$-0.358709\pi$
$108$	39039.4	+	16170.6i	0.322065	+	0.133404i
$109$	8979.89	−	21679.4i	0.0723943	−	0.174775i	−0.883540	−	0.468355i	$-0.844847\pi$
$109$	8979.89	−	21679.4i	0.0723943	−	0.174775i	0.955935	+	0.293580i	$0.0948467\pi$
$110$	22409.4	−	22409.4i	0.176583	−	0.176583i
$111$	82419.1	−	82419.1i	0.634922	−	0.634922i
$112$	−43351.6	+	104660.i	−0.326558	+	0.788381i
$113$	−3363.03	−	1393.01i	−0.0247762	−	0.0102626i	0.370261	−	0.928928i	$-0.379268\pi$
$113$	−3363.03	−	1393.01i	−0.0247762	−	0.0102626i	−0.395037	+	0.918665i	$0.629268\pi$
$114$	43996.6	+	106217.i	0.317071	+	0.765477i
$115$			34753.2i			0.245047i
$116$	224443.	−	92967.4i	1.54868	−	0.641484i
$117$	−29579.3	−	29579.3i	−0.199767	−	0.199767i
$118$	453256.			2.99667
$119$	−67257.5	+	272459.i	−0.435385	+	1.76374i
$120$	85990.4			0.545126
$121$	−108636.	−	108636.i	−0.674542	−	0.674542i
$122$	−103066.	+	42691.2i	−0.626924	+	0.259680i
$123$		−	132143.i		−	0.787555i
$124$	−164987.	−	398313.i	−0.963595	−	2.32632i
$125$	170071.	+	70445.7i	0.973543	+	0.403255i
$126$	−69244.2	+	167170.i	−0.388559	+	0.938064i
$127$	−144513.	+	144513.i	−0.795054	+	0.795054i	−0.982311	−	0.187257i	$-0.940040\pi$
$127$	−144513.	+	144513.i	−0.795054	+	0.795054i	0.187257	+	0.982311i	$0.440040\pi$
$128$	239242.	−	239242.i	1.29066	−	1.29066i
$129$	−2933.24	+	7081.46i	−0.0155193	+	0.0374670i
$130$	−175576.	−	72726.0i	−0.911186	−	0.377426i
$131$	−12510.3	−	30202.6i	−0.0636928	−	0.153768i	0.888829	−	0.458240i	$-0.151520\pi$
$131$	−12510.3	−	30202.6i	−0.0636928	−	0.153768i	−0.952521	+	0.304472i	$0.901520\pi$
$132$			44927.9i			0.224430i
$133$	−293049.	+	121385.i	−1.43652	+	0.595026i
$134$	−196051.	−	196051.i	−0.943208	−	0.943208i
$135$	28282.9			0.133564
$136$	−174000.	+	236297.i	−0.806681	+	1.09550i
$137$	184671.			0.840615			0.420308	−	0.907382i	$-0.361922\pi$
$137$	184671.			0.840615			0.420308	+	0.907382i	$0.361922\pi$
$138$	−54070.4	−	54070.4i	−0.241692	−	0.241692i
$139$	−32634.5	+	13517.7i	−0.143265	+	0.0593423i	−0.453164	−	0.891427i	$-0.649705\pi$
$139$	−32634.5	+	13517.7i	−0.143265	+	0.0593423i	0.309899	+	0.950770i	$0.399705\pi$
$140$			529640.i			2.28381i
$141$	1852.12	+	4471.41i	0.00784550	+	0.0189407i
$142$	−528986.	−	219113.i	−2.20152	−	0.911901i
$143$	17020.5	−	41091.0i	0.0696035	−	0.168038i
$144$	−27549.4	+	27549.4i	−0.110715	+	0.110715i
$145$	114978.	−	114978.i	0.454143	−	0.454143i
$146$	229131.	−	553172.i	0.889616	−	2.14772i
$147$	−321468.	−	133156.i	−1.22700	−	0.508239i
$148$	287277.	+	693547.i	1.07807	+	2.60269i
$149$		−	250448.i		−	0.924171i	−0.886835	−	0.462085i	$-0.847101\pi$
$149$		−	250448.i		−	0.924171i	0.886835	−	0.462085i	$-0.152899\pi$
$150$	−127748.	+	52915.0i	−0.463581	+	0.192022i
$151$	198961.	+	198961.i	0.710110	+	0.710110i	0.966558	−	0.256448i	$-0.0825522\pi$
$151$	198961.	+	198961.i	0.710110	+	0.710110i	−0.256448	+	0.966558i	$0.582552\pi$
$152$	−331675.			−1.16440
$153$	−57230.0	+	77720.1i	−0.197649	+	0.268414i
$154$	−192385.			−0.653687
$155$	−204047.	−	204047.i	−0.682185	−	0.682185i
$156$	248906.	−	103100.i	0.818888	−	0.339195i
$157$			129640.i			0.419750i	0.977728	+	0.209875i	$0.0673057\pi$
$157$			129640.i			0.419750i	−0.977728	+	0.209875i	$0.932694\pi$
$158$	−312926.	−	755469.i	−0.997237	−	2.40754i
$159$	140252.	+	58094.4i	0.439964	+	0.182239i
$160$	49267.9	−	118943.i	0.152147	−	0.367316i
$161$	149178.	−	149178.i	0.453567	−	0.453567i
$162$	−44003.8	+	44003.8i	−0.131735	+	0.131735i
$163$	−242293.	+	584947.i	−0.714286	+	1.72444i	−0.0252824	+	0.999680i	$0.508048\pi$
$163$	−242293.	+	584947.i	−0.714286	+	1.72444i	−0.689003	+	0.724758i	$0.741952\pi$
$164$	786279.	+	325687.i	2.28280	+	0.945565i
$165$	11507.8	+	27782.3i	0.0329066	+	0.0794435i
$166$		−	281438.i		−	0.792708i
$167$	−76129.7	+	31534.0i	−0.211234	+	0.0874958i	−0.485791	−	0.874075i	$-0.661469\pi$
$167$	−76129.7	+	31534.0i	−0.211234	+	0.0874958i	0.274558	+	0.961571i	$0.411469\pi$
$168$	−369115.	−	369115.i	−1.00899	−	1.00899i
$169$	104585.			0.281678
$170$	−105087.	+	425706.i	−0.278886	+	1.12976i
$171$	−109090.			−0.285296
$172$	−34906.8	−	34906.8i	−0.0899681	−	0.0899681i
$173$	−487613.	+	201976.i	−1.23868	+	0.513079i	−0.903302	−	0.429004i	$-0.858864\pi$
$173$	−487613.	+	201976.i	−1.23868	+	0.513079i	−0.335379	+	0.942083i	$0.608864\pi$
$174$			357774.i			0.895850i
$175$	−145990.	−	352452.i	−0.360354	−	0.869972i
$176$	−38271.1	−	15852.4i	−0.0931300	−	0.0385757i
$177$	−164585.	+	397344.i	−0.394873	+	0.953308i
$178$	901112.	−	901112.i	2.13171	−	2.13171i
$179$	177071.	−	177071.i	0.413062	−	0.413062i	−0.469742	−	0.882804i	$-0.655653\pi$
$179$	177071.	−	177071.i	0.413062	−	0.413062i	0.882804	+	0.469742i	$0.155653\pi$
$180$	−69707.9	+	168290.i	−0.160362	+	0.387147i
$181$	416248.	+	172415.i	0.944399	+	0.391183i	0.801123	−	0.598500i	$-0.204236\pi$
$181$	416248.	+	172415.i	0.944399	+	0.391183i	0.143276	+	0.989683i	$0.454236\pi$
$182$	441485.	+	1.06584e6i	0.987956	+	2.38514i
$183$		−	105854.i		−	0.233657i
$184$	203809.	−	84420.4i	0.443791	−	0.183824i
$185$	355290.	+	355290.i	0.763226	+	0.763226i
$186$	634931.			1.34569
$187$	−99630.2	−	24594.1i	−0.208347	−	0.0514312i
$188$	−31170.7			−0.0643208
$189$	−121405.	−	121405.i	−0.247219	−	0.247219i
$190$	−457877.	+	189659.i	−0.920164	+	0.381144i
$191$			280646.i			0.556642i	0.960488	+	0.278321i	$0.0897778\pi$
$191$			280646.i			0.556642i	−0.960488	+	0.278321i	$0.910222\pi$
$192$	161416.	+	389692.i	0.316004	+	0.762902i
$193$	917593.	+	380079.i	1.77320	+	0.734482i	0.994212	+	0.107438i	$0.0342646\pi$
$193$	917593.	+	380079.i	1.77320	+	0.734482i	0.778984	+	0.627044i	$0.215735\pi$
$194$	−8534.65	+	20604.5i	−0.0162810	+	0.0393058i
$195$	127510.	−	127510.i	0.240135	−	0.240135i
$196$	1.58462e6	−	1.58462e6i	2.94635	−	2.94635i
$197$	97722.9	−	235924.i	0.179403	−	0.433118i	−0.808438	−	0.588581i	$-0.799687\pi$
$197$	97722.9	−	235924.i	0.179403	−	0.433118i	0.987842	+	0.155463i	$0.0496869\pi$
$198$	−61129.2	−	25320.5i	−0.110812	−	0.0458997i
$199$	−204321.	−	493275.i	−0.365747	−	0.882992i	−0.994437	−	0.105335i	$-0.966408\pi$
$199$	−204321.	−	493275.i	−0.365747	−	0.882992i	0.628690	−	0.777656i	$-0.283592\pi$
$200$		−	398907.i		−	0.705175i
$201$	243057.	−	100677.i	0.424343	−	0.175769i
$202$	61066.8	+	61066.8i	0.105300	+	0.105300i
$203$	−987084.			−1.68118
$204$	−321399.	−	532085.i	−0.540716	−	0.895169i
$205$	569637.			0.946703
$206$	−185231.	−	185231.i	−0.304121	−	0.304121i
$207$	67034.4	−	27766.5i	0.108736	−	0.0450398i
$208$			248405.i			0.398109i
$209$	−44386.9	−	107159.i	−0.0702893	−	0.169693i
$210$	−720632.	−	298495.i	−1.12763	−	0.467078i
$211$	−158480.	+	382605.i	−0.245058	+	0.591622i	−0.997771	−	0.0667263i	$-0.978745\pi$
$211$	−158480.	+	382605.i	−0.245058	+	0.591622i	0.752714	+	0.658348i	$0.228745\pi$
$212$	−691348.	+	691348.i	−1.05647	+	1.05647i
$213$	384168.	−	384168.i	0.580193	−	0.580193i
$214$	−576028.	+	1.39065e6i	−0.859823	+	2.07580i
$215$	−30526.5	−	12644.5i	−0.0450382	−	0.0186554i
$216$	−68703.3	−	165864.i	−0.100194	−	0.241891i
$217$			1.75175e6i			2.52536i
$218$	−205628.	+	85173.8i	−0.293049	+	0.121385i
$219$	401733.	+	401733.i	0.566014	+	0.566014i
$220$	−193674.			−0.269783
$221$	92376.6	+	608403.i	0.127228	+	0.837935i
$222$	−1.10555e6			−1.50555
$223$	−380077.	−	380077.i	−0.511811	−	0.511811i	0.403270	−	0.915081i	$-0.367874\pi$
$223$	−380077.	−	380077.i	−0.511811	−	0.511811i	−0.915081	+	0.403270i	$0.867874\pi$
$224$	−722048.	+	299082.i	−0.961493	+	0.398264i
$225$		−	131204.i		−	0.172779i
$226$	13212.7	+	31898.2i	0.0172076	+	0.0415427i
$227$	−321048.	−	132983.i	−0.413529	−	0.171289i	0.166212	−	0.986090i	$-0.446846\pi$
$227$	−321048.	−	132983.i	−0.413529	−	0.171289i	−0.579741	+	0.814801i	$0.696846\pi$
$228$	268871.	−	649112.i	0.342536	−	0.826956i
$229$	−1.06860e6	+	1.06860e6i	−1.34656	+	1.34656i	−0.457186	+	0.889371i	$0.651143\pi$
$229$	−1.06860e6	+	1.06860e6i	−1.34656	+	1.34656i	−0.889371	+	0.457186i	$0.848857\pi$
$230$	233085.	−	233085.i	0.290532	−	0.290532i
$231$	69858.5	−	168653.i	0.0861369	−	0.207953i
$232$	−953579.	−	394985.i	−1.16315	−	0.481794i
$233$	−420283.	−	1.01465e6i	−0.507168	−	1.22441i	−0.945507	−	0.325602i	$-0.894433\pi$
$233$	−420283.	−	1.01465e6i	−0.507168	−	1.22441i	0.438339	−	0.898810i	$-0.355567\pi$
$234$			396769.i			0.473695i
$235$	−19275.2	+	7984.05i	−0.0227682	+	0.00943091i
$236$	−1.95863e6	−	1.95863e6i	−2.28915	−	2.28915i
$237$	775906.			0.897301
$238$	2.27843e6	−	1.37626e6i	2.60732	−	1.57492i
$239$	−242486.			−0.274595			−0.137297	−	0.990530i	$-0.543842\pi$
$239$	−242486.			−0.274595			−0.137297	+	0.990530i	$0.543842\pi$
$240$	−118759.	−	118759.i	−0.133088	−	0.133088i
$241$	893426.	−	370069.i	0.990869	−	0.410431i	0.172428	−	0.985022i	$-0.444839\pi$
$241$	893426.	−	370069.i	0.990869	−	0.410431i	0.818441	+	0.574591i	$0.194839\pi$
$242$			1.45721e6i			1.59950i
$243$	−22597.1	−	54554.2i	−0.0245492	−	0.0592669i
$244$	629854.	+	260894.i	0.677275	+	0.280536i
$245$	574006.	−	1.38577e6i	0.610944	−	1.47495i
$246$	−886265.	+	886265.i	−0.933740	+	0.933740i
$247$	−491818.	+	491818.i	−0.512935	+	0.512935i
$248$	−700970.	+	1.69229e6i	−0.723719	+	1.74721i
$249$	246721.	+	102195.i	0.252178	+	0.104456i
$250$	−668174.	−	1.61311e6i	−0.676145	−	1.63236i
$251$		−	1.60237e6i		−	1.60538i	−0.596393	−	0.802692i	$-0.703400\pi$
$251$		−	1.60237e6i		−	1.60538i	0.596393	−	0.802692i	$-0.296600\pi$
$252$	1.02161e6	−	423164.i	1.01340	−	0.419766i
$253$	54550.1	+	54550.1i	0.0535790	+	0.0535790i
$254$	1.93846e6			1.88526
$255$	−335033.	−	246705.i	−0.322654	−	0.237590i
$256$	−1.70940e6			−1.63021
$257$	406184.	+	406184.i	0.383610	+	0.383610i	0.872401	−	0.488791i	$-0.162562\pi$
$257$	406184.	+	406184.i	0.383610	+	0.383610i	−0.488791	+	0.872401i	$0.662562\pi$
$258$	67167.3	−	27821.6i	0.0628215	−	0.0260215i
$259$		−	3.05017e6i		−	2.82537i
$260$	444442.	+	1.07298e6i	0.407738	+	0.984367i
$261$	−313640.	−	129914.i	−0.284990	−	0.118047i
$262$	−118660.	+	286470.i	−0.106795	+	0.257825i
$263$	509577.	−	509577.i	0.454276	−	0.454276i	−0.442495	−	0.896771i	$-0.645906\pi$
$263$	509577.	−	509577.i	0.454276	−	0.454276i	0.896771	+	0.442495i	$0.145906\pi$
$264$	134974.	−	134974.i	0.119191	−	0.119191i
$265$	−250431.	+	604595.i	−0.219065	+	0.528871i
$266$	2.77956e6	+	1.15133e6i	2.40864	+	0.997690i
$267$	462744.	+	1.11716e6i	0.397249	+	0.959044i
$268$			1.69438e6i			1.44103i
$269$	1.35899e6	−	562914.i	1.14508	−	0.474309i	0.272201	−	0.962240i	$-0.412248\pi$
$269$	1.35899e6	−	562914.i	1.14508	−	0.474309i	0.872882	+	0.487932i	$0.162248\pi$
$270$	−189690.	−	189690.i	−0.158356	−	0.158356i
$271$	−540724.			−0.447252			−0.223626	−	0.974675i	$-0.571789\pi$
$271$	−540724.			−0.447252			−0.223626	+	0.974675i	$0.571789\pi$
$272$	566651.	−	86037.2i	0.464401	−	0.0705122i
$273$	−1.09467e6			−0.888950
$274$	−1.23856e6	−	1.23856e6i	−0.996649	−	0.996649i
$275$	128881.	−	53384.4i	0.102768	−	0.0425680i
$276$			467304.i			0.369256i
$277$	556262.	+	1.34293e6i	0.435592	+	1.05161i	0.977455	+	0.211145i	$0.0677191\pi$
$277$	556262.	+	1.34293e6i	0.435592	+	1.05161i	−0.541863	+	0.840467i	$0.682281\pi$
$278$	309537.	+	128214.i	0.240215	+	0.0995003i
$279$	−230555.	+	556608.i	−0.177322	+	0.428094i
$280$	1.59117e6	−	1.59117e6i	1.21289	−	1.21289i
$281$	−1.29872e6	+	1.29872e6i	−0.981184	+	0.981184i	−0.999826	−	0.0186420i	$-0.994066\pi$
$281$	−1.29872e6	+	1.29872e6i	−0.981184	+	0.981184i	0.0186420	+	0.999826i	$0.494066\pi$
$282$	17567.2	−	42411.1i	0.0131547	−	0.0317582i
$283$	643858.	+	266695.i	0.477886	+	0.197947i	0.608606	−	0.793473i	$-0.291729\pi$
$283$	643858.	+	266695.i	0.477886	+	0.197947i	−0.130720	+	0.991419i	$0.541729\pi$
$284$	1.33904e6	+	3.23273e6i	0.985140	+	2.37834i
$285$		−	470264.i		−	0.342949i
$286$	−389746.	+	161438.i	−0.281752	+	0.116705i
$287$	−2.44517e6	−	2.44517e6i	−1.75229	−	1.75229i
$288$	−268790.			−0.190955
$289$	1.35587e6	−	421451.i	0.954931	−	0.296826i
$290$	−1.54228e6			−1.07688
$291$	−14963.7	−	14963.7i	−0.0103587	−	0.0103587i
$292$	−3.38054e6	+	1.40026e6i	−2.32022	+	0.961065i
$293$		−	1.05482e6i		−	0.717808i	−0.933374	−	0.358904i	$-0.883151\pi$
$293$		−	1.05482e6i		−	0.717808i	0.933374	−	0.358904i	$-0.116849\pi$
$294$	1.26298e6	+	3.04910e6i	0.852174	+	2.05733i
$295$	−1.71286e6	−	709488.i	−1.14595	−	0.474668i
$296$	1.22054e6	−	2.94663e6i	0.809695	−	1.95478i
$297$	44394.2	−	44394.2i	0.0292035	−	0.0292035i
$298$	−1.67972e6	+	1.67972e6i	−1.09571	+	1.09571i
$299$	177033.	−	427396.i	0.114519	−	0.276473i
$300$	780691.	+	323373.i	0.500814	+	0.207444i
$301$	76758.8	+	185312.i	0.0488328	+	0.117893i
$302$		−	2.66881e6i		−	1.68384i
$303$	−75708.3	+	31359.4i	−0.0473736	+	0.0196228i
$304$	458067.	+	458067.i	0.284279	+	0.284279i
$305$	456311.			0.280874
$306$	905093.	−	137424.i	0.552573	−	0.0838997i
$307$	1.20536e6			0.729914			0.364957	−	0.931024i	$-0.381084\pi$
$307$	1.20536e6			0.729914			0.364957	+	0.931024i	$0.381084\pi$
$308$	831347.	+	831347.i	0.499350	+	0.499350i
$309$	229643.	−	95121.0i	0.136822	−	0.0566735i
$310$			2.73704e6i			1.61762i
$311$	1.01944e6	+	2.46115e6i	0.597670	+	1.44290i	0.875949	+	0.482403i	$0.160236\pi$
$311$	1.01944e6	+	2.46115e6i	0.597670	+	1.44290i	−0.278279	+	0.960500i	$0.589764\pi$
$312$	−1.05751e6	−	438037.i	−0.615035	−	0.254756i
$313$	1.04647e6	−	2.52640e6i	0.603763	−	1.45761i	−0.265917	−	0.963996i	$-0.585675\pi$
$313$	1.04647e6	−	2.52640e6i	0.603763	−	1.45761i	0.869680	−	0.493616i	$-0.164325\pi$
$314$	869480.	−	869480.i	0.497663	−	0.497663i
$315$	523348.	−	523348.i	0.297176	−	0.297176i
$316$	−1.91235e6	+	4.61681e6i	−1.07733	+	2.60090i
$317$	−63929.6	−	26480.5i	−0.0357317	−	0.0148006i	0.364746	−	0.931107i	$-0.381156\pi$
$317$	−63929.6	−	26480.5i	−0.0357317	−	0.0148006i	−0.400478	+	0.916306i	$0.631156\pi$
$318$	−551022.	−	1.33028e6i	−0.305563	−	0.737695i
$319$		−	360948.i		−	0.198595i
$320$	−1.67987e6	+	695826.i	−0.917068	+	0.379862i
$321$	−1.00994e6	−	1.00994e6i	−0.547059	−	0.547059i
$322$	−2.00104e6			−1.07551
$323$	1.29226e6	+	951569.i	0.689197	+	0.507498i
$324$	380303.			0.201265
$325$	−591513.	−	591513.i	−0.310639	−	0.310639i
$326$	5.54819e6	−	2.29814e6i	2.89140	−	1.19766i
$327$		−	211190.i		−	0.109221i
$328$	−1.38373e6	−	3.34062e6i	−0.710177	−	1.71452i
$329$	117011.	+	48467.4i	0.0595985	+	0.0246865i
$330$	109151.	−	263514.i	0.0551751	−	0.133204i
$331$	325791.	−	325791.i	0.163444	−	0.163444i	−0.620646	−	0.784091i	$-0.713130\pi$
$331$	325791.	−	325791.i	0.163444	−	0.163444i	0.784091	+	0.620646i	$0.213130\pi$
$332$	−1.21617e6	+	1.21617e6i	−0.605547	+	0.605547i
$333$	401444.	−	969172.i	0.198388	−	0.478950i
$334$	722087.	+	299098.i	0.354179	+	0.146706i
$335$	433997.	+	1.04776e6i	0.211288	+	0.510094i
$336$			1.01955e6i			0.492675i
$337$	2.59229e6	−	1.07376e6i	1.24340	−	0.515031i	0.338621	−	0.940923i	$-0.390039\pi$
$337$	2.59229e6	−	1.07376e6i	1.24340	−	0.515031i	0.904774	+	0.425891i	$0.140039\pi$
$338$	−701438.	−	701438.i	−0.333962	−	0.333962i
$339$	−32761.1			−0.0154831
$340$	2.29369e6	−	1.38548e6i	1.07606	−	0.649983i
$341$	−640564.			−0.298316
$342$	731655.	+	731655.i	0.338253	+	0.338253i
$343$	−4.75534e6	+	1.96972e6i	−2.18246	+	0.904004i
$344$			209737.i			0.0955607i
$345$	119695.	+	288970.i	0.0541413	+	0.130709i
$346$	4.62498e6	+	1.91573e6i	2.07692	+	0.860288i
$347$	−739200.	+	1.78459e6i	−0.329563	+	0.795635i	0.669062	+	0.743207i	$0.266696\pi$
$347$	−739200.	+	1.78459e6i	−0.329563	+	0.795635i	−0.998625	+	0.0524283i	$0.983304\pi$
$348$	1.54603e6	−	1.54603e6i	0.684337	−	0.684337i
$349$	−1.27140e6	+	1.27140e6i	−0.558749	+	0.558749i	−0.928951	−	0.370202i	$-0.879288\pi$
$349$	−1.27140e6	+	1.27140e6i	−0.558749	+	0.558749i	0.370202	+	0.928951i	$0.379288\pi$
$350$	−1.38471e6	+	3.34299e6i	−0.604212	+	1.45870i
$351$	−347825.	−	144074.i	−0.150693	−	0.0624191i
$352$	−109366.	−	264032.i	−0.0470461	−	0.113579i
$353$			272811.i			0.116526i	0.998301	+	0.0582632i	$0.0185563\pi$
$353$			272811.i			0.116526i	−0.998301	+	0.0582632i	$0.981444\pi$
$354$	3.76878e6	−	1.56108e6i	1.59843	−	0.662090i
$355$	1.65606e6	+	1.65606e6i	0.697437	+	0.697437i
$356$	−7.78787e6			−3.25682
$357$	379149.	+	2.49712e6i	0.157449	+	1.03698i
$358$	−2.37519e6			−0.979468
$359$	831442.	+	831442.i	0.340483	+	0.340483i	0.856549	−	0.516066i	$-0.172604\pi$
$359$	831442.	+	831442.i	0.340483	+	0.340483i	−0.516066	+	0.856549i	$0.672604\pi$
$360$	715003.	−	296164.i	0.290771	−	0.120441i
$361$		−	662241.i		−	0.267453i
$362$	−1.63535e6	−	3.94809e6i	−0.655903	−	1.58349i
$363$	−1.27745e6	−	529139.i	−0.508837	−	0.210767i
$364$	2.69800e6	−	6.51354e6i	1.06730	−	2.57670i
$365$	−1.73178e6	+	1.73178e6i	−0.680393	+	0.680393i
$366$	−709948.	+	709948.i	−0.277028	+	0.277028i
$367$	−327332.	+	790250.i	−0.126860	+	0.306266i	−0.974530	−	0.224257i	$-0.928005\pi$
$367$	−327332.	+	790250.i	−0.126860	+	0.306266i	0.847670	+	0.530523i	$0.178005\pi$
$368$	−398066.	−	164884.i	−0.153227	−	0.0634687i
$369$	−455120.	−	1.09876e6i	−0.174004	−	0.420084i
$370$		−	4.76576e6i		−	1.80979i
$371$	3.67021e6	−	1.52025e6i	1.38438	−	0.573430i
$372$	−2.74370e6	−	2.74370e6i	−1.02797	−	1.02797i
$373$	759968.			0.282829			0.141414	−	0.989951i	$-0.454835\pi$
$373$	759968.			0.282829			0.141414	+	0.989951i	$0.454835\pi$
$374$	503258.	+	833156.i	0.186042	+	0.307998i
$375$	1.65675e6			0.608386
$376$	93644.4	+	93644.4i	0.0341595	+	0.0341595i
$377$	−1.99970e6	+	828302.i	−0.724621	+	0.300148i
$378$			1.62849e6i			0.586214i
$379$	−886292.	−	2.13970e6i	−0.316941	−	0.765164i	−0.999413	−	0.0342521i	$-0.989095\pi$
$379$	−886292.	−	2.13970e6i	−0.316941	−	0.765164i	0.682472	−	0.730912i	$-0.260905\pi$
$380$	2.79817e6	+	1.15904e6i	0.994066	+	0.411756i
$381$	−703887.	+	1.69933e6i	−0.248422	+	0.599745i
$382$	1.88226e6	−	1.88226e6i	0.659965	−	0.659965i
$383$	368600.	−	368600.i	0.128398	−	0.128398i	−0.639987	−	0.768385i	$-0.721060\pi$
$383$	368600.	−	368600.i	0.128398	−	0.128398i	0.768385	+	0.639987i	$0.221060\pi$
$384$	1.16529e6	−	2.81326e6i	0.403280	−	0.973604i
$385$	727025.	+	301144.i	0.249976	+	0.103543i
$386$	−3.60503e6	−	8.70332e6i	−1.23152	−	2.97315i
$387$			68984.2i			0.0234138i
$388$	125918.	−	52156.8i	0.0424627	−	0.0175886i
$389$	1.74821e6	+	1.74821e6i	0.585760	+	0.585760i	0.936480	−	0.350720i	$-0.114063\pi$
$389$	1.74821e6	+	1.74821e6i	0.585760	+	0.585760i	−0.350720	+	0.936480i	$0.614063\pi$
$390$	−1.71038e6			−0.569418
$391$	−1.03627e6	−	255808.i	−0.342794	−	0.0846199i
$392$	−9.52116e6			−3.12950
$393$	−208044.	−	208044.i	−0.0679477	−	0.0679477i
$394$	−2.23773e6	+	926896.i	−0.726217	+	0.300809i
$395$			3.34475e6i			1.07863i
$396$	154738.	+	373572.i	0.0495861	+	0.119712i
$397$	−3.18176e6	−	1.31793e6i	−1.01319	−	0.419677i	−0.186572	−	0.982441i	$-0.559738\pi$
$397$	−3.18176e6	−	1.31793e6i	−1.01319	−	0.419677i	−0.826617	+	0.562764i	$0.809738\pi$
$398$	−1.93798e6	+	4.67869e6i	−0.613255	+	1.48053i
$399$	−2.01861e6	+	2.01861e6i	−0.634776	+	0.634776i
$400$	−550920.	+	550920.i	−0.172163	+	0.172163i
$401$	−295803.	+	714133.i	−0.0918634	+	0.221778i	−0.963132	−	0.269028i	$-0.913298\pi$
$401$	−295803.	+	714133.i	−0.0918634	+	0.221778i	0.871269	+	0.490806i	$0.163298\pi$
$402$	−2.30538e6	−	954919.i	−0.711504	−	0.294714i
$403$	1.46996e6	+	3.54881e6i	0.450863	+	1.08848i
$404$		−	527771.i		−	0.160876i
$405$	235170.	−	97410.7i	0.0712434	−	0.0295100i
$406$	6.62025e6	+	6.62025e6i	1.99324	+	1.99324i
$407$	1.11536e6			0.333755
$408$	−632951.	+	2.56407e6i	−0.188243	+	0.762571i
$409$	233484.			0.0690159			0.0345080	−	0.999404i	$-0.489014\pi$
$409$	233484.			0.0690159			0.0345080	+	0.999404i	$0.489014\pi$
$410$	−3.82048e6	−	3.82048e6i	−1.12243	−	1.12243i
$411$	1.53552e6	−	636035.i	0.448386	−	0.185727i
$412$			1.60086e6i			0.464635i
$413$	4.30697e6	+	1.03979e7i	1.24250	+	2.99966i
$414$	−635818.	−	263364.i	−0.182319	−	0.0755190i
$415$	−440540.	+	1.06356e6i	−0.125564	+	0.303138i
$416$	−1.21180e6	+	1.21180e6i	−0.343319	+	0.343319i
$417$	−224796.	+	224796.i	−0.0633066	+	0.0633066i
$418$	−421007.	+	1.01640e6i	−0.117855	+	0.284528i
$419$	−5.02383e6	−	2.08094e6i	−1.39798	−	0.579061i	−0.448751	−	0.893657i	$-0.648131\pi$
$419$	−5.02383e6	−	2.08094e6i	−1.39798	−	0.579061i	−0.949226	+	0.314596i	$0.898131\pi$
$420$	1.82416e6	+	4.40391e6i	0.504591	+	1.21819i
$421$		−	2.89157e6i		−	0.795111i	−0.917578	−	0.397556i	$-0.869859\pi$
$421$		−	2.89157e6i		−	0.795111i	0.917578	−	0.397556i	$-0.130141\pi$
$422$	3.62899e6	−	1.50318e6i	0.991983	−	0.410893i
$423$	30800.4	+	30800.4i	0.00836961	+	0.00836961i
$424$	4.15396e6			1.12214
$425$	−1.14446e6	+	1.55421e6i	−0.307346	+	0.417385i
$426$	−5.15313e6			−1.37578
$427$	−1.95872e6	−	1.95872e6i	−0.519880	−	0.519880i
$428$	8.49854e6	−	3.52021e6i	2.24251	−	0.928880i
$429$		−	400289.i		−	0.105010i
$430$	119932.	+	289542.i	0.0312799	+	0.0755164i
$431$	−252602.	−	104631.i	−0.0655003	−	0.0271311i	0.349693	−	0.936864i	$-0.386286\pi$
$431$	−252602.	−	104631.i	−0.0655003	−	0.0271311i	−0.415193	+	0.909733i	$0.636286\pi$
$432$	−134187.	+	323955.i	−0.0345939	+	0.0835172i
$433$	3.49616e6	−	3.49616e6i	0.896132	−	0.896132i	−0.0989591	−	0.995092i	$-0.531551\pi$
$433$	3.49616e6	−	3.49616e6i	0.896132	−	0.896132i	0.995092	+	0.0989591i	$0.0315513\pi$
$434$	1.17488e7	−	1.17488e7i	2.99411	−	2.99411i
$435$	560028.	−	1.35203e6i	0.141901	−	0.342580i
$436$	1.25663e6	+	520512.i	0.316585	+	0.131134i
$437$	−461677.	−	1.11459e6i	−0.115647	−	0.279197i
$438$		−	5.38874e6i		−	1.34215i
$439$	−3.79162e6	+	1.57054e6i	−0.938996	+	0.388945i	−0.799084	−	0.601219i	$-0.794682\pi$
$439$	−3.79162e6	+	1.57054e6i	−0.938996	+	0.388945i	−0.139912	+	0.990164i	$0.544682\pi$
$440$	581843.	+	581843.i	0.143276	+	0.143276i
$441$	−3.13159e6			−0.766775
$442$	3.46092e6	−	4.70004e6i	0.842628	−	1.14431i
$443$	2.06287e6			0.499417			0.249708	−	0.968321i	$-0.419665\pi$
$443$	2.06287e6			0.499417			0.249708	+	0.968321i	$0.419665\pi$
$444$	4.77736e6	+	4.77736e6i	1.15009	+	1.15009i
$445$	−4.81583e6	+	1.99478e6i	−1.15285	+	0.477524i
$446$			5.09826e6i			1.21363i
$447$	−862581.	−	2.08246e6i	−0.204188	−	0.492955i
$448$	1.01977e7	+	4.22403e6i	2.40053	+	0.994334i
$449$	−508320.	+	1.22719e6i	−0.118993	+	0.287275i	−0.972142	−	0.234393i	$-0.924690\pi$
$449$	−508320.	+	1.22719e6i	−0.118993	+	0.287275i	0.853149	+	0.521667i	$0.174690\pi$
$450$	−879967.	+	879967.i	−0.204850	+	0.204850i
$451$	894128.	−	894128.i	0.206994	−	0.206994i
$452$	80745.0	−	194936.i	0.0185896	−	0.0448792i
$453$	2.33960e6	+	969092.i	0.535668	+	0.221881i
$454$	1.26133e6	+	3.04513e6i	0.287204	+	0.693371i
$455$		−	4.71888e6i		−	1.06859i
$456$	−2.75785e6	+	1.14234e6i	−0.621095	+	0.257266i
$457$	4.58189e6	+	4.58189e6i	1.02625	+	1.02625i	0.999646	+	0.0266056i	$0.00846983\pi$
$457$	4.58189e6	+	4.58189e6i	1.02625	+	1.02625i	0.0266056	+	0.999646i	$0.491530\pi$
$458$	1.43339e7			3.19301
$459$	−208183.	+	843345.i	−0.0461225	+	0.186842i
$460$	−2.01444e6			−0.443874
$461$	−2.21185e6	−	2.21185e6i	−0.484733	−	0.484733i	0.421906	−	0.906639i	$-0.361361\pi$
$461$	−2.21185e6	−	2.21185e6i	−0.484733	−	0.484733i	−0.906639	+	0.421906i	$0.861361\pi$
$462$	−1.59967e6	+	662604.i	−0.348678	+	0.144427i
$463$		−	3.64764e6i		−	0.790788i	−0.918512	−	0.395394i	$-0.870608\pi$
$463$		−	3.64764e6i		−	0.790788i	0.918512	−	0.395394i	$-0.129392\pi$
$464$	771459.	+	1.86247e6i	0.166348	+	0.401600i
$465$	−2.39941e6	−	993867.i	−0.514602	−	0.213155i
$466$	−3.98636e6	+	9.62393e6i	−0.850378	+	2.05299i
$467$	4.37008e6	−	4.37008e6i	0.927250	−	0.927250i	−0.0702777	−	0.997527i	$-0.522389\pi$
$467$	4.37008e6	−	4.37008e6i	0.927250	−	0.927250i	0.997527	+	0.0702777i	$0.0223885\pi$
$468$	1.71454e6	−	1.71454e6i	0.361854	−	0.361854i
$469$	2.63459e6	−	6.36046e6i	0.553071	−	1.33523i
$470$	182824.	+	75728.3i	0.0381759	+	0.0158130i
$471$	446500.	+	1.07795e6i	0.0927405	+	0.223895i
$472$			1.17684e7i			2.43144i
$473$	−67763.2	+	28068.4i	−0.0139265	+	0.00576853i
$474$	−5.20390e6	−	5.20390e6i	−1.06386	−	1.06386i
$475$	−2.18154e6			−0.443638
$476$	−1.57929e7	−	3.89853e6i	−3.19480	−	0.788649i
$477$	1.36627e6			0.274942
$478$	1.62632e6	+	1.62632e6i	0.325565	+	0.325565i
$479$	−3.62026e6	+	1.49956e6i	−0.720943	+	0.298624i	−0.712824	−	0.701343i	$-0.752584\pi$
$479$	−3.62026e6	+	1.49956e6i	−0.720943	+	0.298624i	−0.00811856	+	0.999967i	$0.502584\pi$
$480$		−	1.15869e6i		−	0.229543i
$481$	−2.55952e6	−	6.17922e6i	−0.504424	−	1.21779i
$482$	−8.47410e6	−	3.51009e6i	−1.66141	−	0.688177i
$483$	726612.	−	1.75420e6i	0.141721	−	0.342145i
$484$	6.29698e6	−	6.29698e6i	1.22185	−	1.22185i
$485$	64505.0	−	64505.0i	0.0124520	−	0.0124520i
$486$	−214332.	+	517443.i	−0.0411620	+	0.0993739i
$487$	−2.24201e6	−	928672.i	−0.428367	−	0.177435i	0.158074	−	0.987427i	$-0.449471\pi$
$487$	−2.24201e6	−	928672.i	−0.428367	−	0.177435i	−0.586441	+	0.809992i	$0.699471\pi$
$488$	−1.10845e6	−	2.67602e6i	−0.210700	−	0.508675i
$489$			5.69828e6i			1.07764i
$490$	−1.31440e7	+	5.44442e6i	−2.47307	+	1.02438i
$491$	4.38665e6	+	4.38665e6i	0.821163	+	0.821163i	0.986275	−	0.165112i	$-0.0527984\pi$
$491$	4.38665e6	+	4.38665e6i	0.821163	+	0.821163i	−0.165112	+	0.986275i	$0.552798\pi$
$492$	7.65956e6			1.42656
$493$	2.58210e6	+	4.27473e6i	0.478471	+	0.792121i
$494$	6.59712e6			1.21629
$495$	191373.	+	191373.i	0.0351049	+	0.0351049i
$496$	3.30527e6	−	1.36909e6i	0.603257	−	0.249877i
$497$		−	1.42173e7i		−	2.58182i
$498$	−969316.	−	2.34014e6i	−0.175143	−	0.422832i
$499$	−1.11516e6	−	461913.i	−0.200486	−	0.0830441i	0.280181	−	0.959947i	$-0.409605\pi$
$499$	−1.11516e6	−	461913.i	−0.200486	−	0.0830441i	−0.480667	+	0.876903i	$0.659605\pi$
$500$	−4.08333e6	+	9.85804e6i	−0.730449	+	1.76346i
$501$	−524405.	+	524405.i	−0.0933409	+	0.0933409i
$502$	−1.07469e7	+	1.07469e7i	−1.90337	+	1.90337i
$503$	−3.71290e6	+	8.96374e6i	−0.654325	+	1.57968i	0.152114	+	0.988363i	$0.451392\pi$
$503$	−3.71290e6	+	8.96374e6i	−0.654325	+	1.57968i	−0.806439	+	0.591317i	$0.798608\pi$
$504$	−4.34045e6	−	1.79787e6i	−0.761128	−	0.315270i
$505$	−135183.	−	326361.i	−0.0235881	−	0.0569468i
$506$		−	731721.i		−	0.127048i
$507$	869615.	−	360206.i	0.150247	−	0.0622345i
$508$	−8.37657e6	−	8.37657e6i	−1.44015	−	1.44015i
$509$	−1.04833e6			−0.179350			−0.0896750	−	0.995971i	$-0.528583\pi$
$509$	−1.04833e6			−0.179350			−0.0896750	+	0.995971i	$0.528583\pi$
$510$	592405.	+	3.90164e6i	0.100854	+	0.664236i
$511$	1.48673e7			2.51873
$512$	3.80896e6	+	3.80896e6i	0.642143	+	0.642143i
$513$	−907078.	+	375724.i	−0.152178	+	0.0630341i
$514$		−	5.44844e6i		−	0.909629i
$515$	410045.	+	989935.i	0.0681260	+	0.164471i
$516$	−410471.	−	170023.i	−0.0678670	−	0.0281114i
$517$	−17723.1	+	42787.3i	−0.00291617	+	0.00704026i
$518$	−2.04571e7	+	2.04571e7i	−3.34981	+	3.34981i
$519$	−3.35882e6	+	3.35882e6i	−0.547355	+	0.547355i
$520$	1.88828e6	−	4.55870e6i	0.306236	−	0.739320i
$521$	663048.	+	274644.i	0.107017	+	0.0443277i	0.435549	−	0.900165i	$-0.356554\pi$
$521$	663048.	+	274644.i	0.107017	+	0.0443277i	−0.328533	+	0.944493i	$0.606554\pi$
$522$	1.23223e6	+	2.97486e6i	0.197931	+	0.477848i
$523$		−	4.67685e6i		−	0.747652i	−0.927499	−	0.373826i	$-0.878046\pi$
$523$		−	4.67685e6i		−	0.747652i	0.927499	−	0.373826i	$-0.121954\pi$
$524$	1.75067e6	−	725151.i	0.278532	−	0.115372i
$525$	−2.42780e6	−	2.42780e6i	−0.384427	−	0.384427i
$526$	−6.83533e6			−1.07720
$527$	7.58625e6	−	4.58238e6i	1.18987	−	0.718728i
$528$	−372819.			−0.0581987
$529$	−3.98379e6	−	3.98379e6i	−0.618953	−	0.618953i
$530$	5.73455e6	−	2.37533e6i	0.886767	−	0.367311i
$531$			3.87073e6i			0.595740i
$532$	−7.03599e6	−	1.69864e7i	−1.07782	−	2.60209i
$533$	−7.00543e6	−	2.90174e6i	−1.06811	−	0.442426i
$534$	4.38910e6	−	1.05962e7i	0.666074	−	1.60805i
$535$	4.35363e6	−	4.35363e6i	0.657607	−	0.657607i
$536$	5.09032e6	−	5.09032e6i	0.765302	−	0.765302i
$537$	862472.	−	2.08219e6i	0.129065	−	0.311591i
$538$	−1.28900e7	−	5.33921e6i	−1.91998	−	0.795282i
$539$	−1.27419e6	−	3.07616e6i	−0.188913	−	0.456075i
$540$			1.63940e6i			0.241936i
$541$	−9.79886e6	+	4.05882e6i	−1.43940	+	0.596220i	−0.959654	−	0.281185i	$-0.909273\pi$
$541$	−9.79886e6	+	4.05882e6i	−1.43940	+	0.596220i	−0.479750	+	0.877405i	$0.659273\pi$
$542$	3.62657e6	+	3.62657e6i	0.530271	+	0.530271i
$543$	4.05489e6			0.590173
$544$	3.18402e6	+	2.34459e6i	0.461295	+	0.339679i
$545$	910392.			0.131292
$546$	7.34182e6	+	7.34182e6i	1.05396	+	1.05396i
$547$	−6.54859e6	+	2.71252e6i	−0.935793	+	0.387618i	−0.797873	−	0.602825i	$-0.794042\pi$
$547$	−6.54859e6	+	2.71252e6i	−0.935793	+	0.387618i	−0.137920	+	0.990443i	$0.544042\pi$
$548$			1.07043e7i			1.52268i
$549$	−364577.	−	880166.i	−0.0516248	−	0.124633i
$550$	−1.22243e6	−	506348.i	−0.172313	−	0.0713745i
$551$	−2.16009e6	+	5.21492e6i	−0.303105	+	0.731760i
$552$	1.40390e6	−	1.40390e6i	0.196104	−	0.196104i
$553$	1.43574e7	−	1.43574e7i	1.99647	−	1.99647i
$554$	5.27611e6	−	1.27377e7i	0.730364	−	1.76326i
$555$	4.17788e6	+	1.73053e6i	0.575735	+	0.238477i
$556$	−783541.	−	1.89164e6i	−0.107492	−	0.259508i
$557$			3.17968e6i			0.434256i	0.976143	+	0.217128i	$0.0696689\pi$
$557$			3.17968e6i			0.434256i	−0.976143	+	0.217128i	$0.930331\pi$
$558$	5.27940e6	−	2.18680e6i	0.717792	−	0.297319i
$559$	311005.	+	311005.i	0.0420958	+	0.0420958i
$560$	−4.39504e6			−0.592233
$561$	−913123.	+	138644.i	−0.122496	+	0.0185991i
$562$	1.74207e7			2.32662
$563$	−2.94804e6	−	2.94804e6i	−0.391978	−	0.391978i	0.483414	−	0.875392i	$-0.339397\pi$
$563$	−2.94804e6	−	2.94804e6i	−0.391978	−	0.391978i	−0.875392	+	0.483414i	$0.839397\pi$
$564$	−259182.	+	107357.i	−0.0343089	+	0.0142112i
$565$		−	141225.i		−	0.0186119i
$566$	−2.52958e6	−	6.10696e6i	−0.331901	−	0.801279i
$567$	−1.42761e6	−	591334.i	−0.186488	−	0.0772459i
$568$	5.68911e6	−	1.37347e7i	0.739900	−	1.78628i
$569$	−5.91743e6	+	5.91743e6i	−0.766218	+	0.766218i	−0.977438	−	0.211220i	$-0.932256\pi$
$569$	−5.91743e6	+	5.91743e6i	−0.766218	+	0.766218i	0.211220	+	0.977438i	$0.432256\pi$
$570$	−3.15400e6	+	3.15400e6i	−0.406606	+	0.406606i
$571$	−3.35336e6	+	8.09574e6i	−0.430418	+	1.03912i	0.548735	+	0.835996i	$0.315110\pi$
$571$	−3.35336e6	+	8.09574e6i	−0.430418	+	1.03912i	−0.979153	+	0.203125i	$0.934890\pi$
$572$	2.38181e6	+	986578.i	0.304381	+	0.126079i
$573$	966588.	+	2.33355e6i	0.122986	+	0.296914i
$574$			3.27989e7i			4.15509i
$575$	1.34052e6	−	555262.i	0.169085	−	0.0700372i
$576$	2.68432e6	+	2.68432e6i	0.337115	+	0.337115i
$577$	4.04584e6			0.505906			0.252953	−	0.967479i	$-0.418598\pi$
$577$	4.04584e6			0.505906			0.252953	+	0.967479i	$0.418598\pi$
$578$	−1.19202e7	−	6.26700e6i	−1.48411	−	0.780262i
$579$	8.93876e6			1.10810
$580$	6.66458e6	+	6.66458e6i	0.822627	+	0.822627i
$581$	6.45635e6	−	2.67431e6i	0.793500	−	0.328678i
$582$			200719.i			0.0245630i
$583$	555911.	+	1.34209e6i	0.0677382	+	0.163534i
$584$	1.43627e7	+	5.94922e6i	1.74262	+	0.721818i
$585$	621069.	−	1.49939e6i	0.0750326	−	0.181145i
$586$	−7.07453e6	+	7.07453e6i	−0.851047	+	0.851047i
$587$	−7.05373e6	+	7.05373e6i	−0.844935	+	0.844935i	−0.989496	−	0.144561i	$-0.953823\pi$
$587$	−7.05373e6	+	7.05373e6i	−0.844935	+	0.844935i	0.144561	+	0.989496i	$0.453823\pi$
$588$	7.71830e6	−	1.86336e7i	0.920616	−	2.22256i
$589$	9.25478e6	+	3.83346e6i	1.09920	+	0.455305i
$590$	6.72946e6	+	1.62463e7i	0.795884	+	1.92143i
$591$		−	2.29826e6i		−	0.270664i
$592$	−5.75517e6	+	2.38387e6i	−0.674922	+	0.279562i
$593$	−8.97604e6	−	8.97604e6i	−1.04821	−	1.04821i	−0.998778	−	0.0494316i	$-0.984259\pi$
$593$	−8.97604e6	−	8.97604e6i	−1.04821	−	1.04821i	−0.0494316	−	0.998778i	$-0.515741\pi$
$594$	−595492.			−0.0692484
$595$	−1.07645e7	+	1.63442e6i	−1.24653	+	0.189266i
$596$	1.45170e7			1.67403
$597$	−3.39783e6	−	3.39783e6i	−0.390181	−	0.390181i
$598$	−4.05383e6	+	1.67915e6i	−0.463567	+	0.192016i
$599$		−	8.26218e6i		−	0.940866i	−0.882436	−	0.470433i	$-0.844098\pi$
$599$		−	8.26218e6i		−	0.940866i	0.882436	−	0.470433i	$-0.155902\pi$
$600$	−1.37390e6	−	3.31688e6i	−0.155803	−	0.376142i
$601$	9.31830e6	+	3.85976e6i	1.05233	+	0.435888i	0.840722	−	0.541468i	$-0.182131\pi$
$601$	9.31830e6	+	3.85976e6i	1.05233	+	0.435888i	0.211604	+	0.977355i	$0.432131\pi$
$602$	728053.	−	1.75767e6i	0.0818788	−	0.197673i
$603$	1.67425e6	−	1.67425e6i	0.187511	−	0.187511i
$604$	−1.15326e7	+	1.15326e7i	−1.28628	+	1.28628i
$605$	2.28099e6	−	5.50681e6i	0.253359	−	0.611662i
$606$	718089.	+	297442.i	0.0794322	+	0.0329019i
$607$	121164.	+	292516.i	0.0133476	+	0.0322239i	0.930413	−	0.366513i	$-0.119449\pi$
$607$	121164.	+	292516.i	0.0133476	+	0.0322239i	−0.917065	+	0.398737i	$0.869449\pi$
$608$			4.46919e6i			0.490309i
$609$	−8.20752e6	+	3.39967e6i	−0.896745	+	0.371444i
$610$	−3.06042e6	−	3.06042e6i	−0.333010	−	0.333010i
$611$	277718.			0.0300955
$612$	−4.50498e6	−	3.31729e6i	−0.486200	−	0.358018i
$613$	−6.40739e6			−0.688699			−0.344350	−	0.938841i	$-0.611901\pi$
$613$	−6.40739e6			−0.688699			−0.344350	+	0.938841i	$0.611901\pi$
$614$	−8.08421e6	−	8.08421e6i	−0.865399	−	0.865399i
$615$	4.73649e6	−	1.96192e6i	0.504973	−	0.209167i
$616$		−	4.99514e6i		−	0.530390i
$617$	3.97562e6	+	9.59800e6i	0.420428	+	1.01500i	0.982221	+	0.187726i	$0.0601117\pi$
$617$	3.97562e6	+	9.59800e6i	0.420428	+	1.01500i	−0.561793	+	0.827278i	$0.689888\pi$
$618$	−2.17815e6	−	902218.i	−0.229412	−	0.0950255i
$619$	−988005.	+	2.38525e6i	−0.103641	+	0.250212i	−0.967190	−	0.254053i	$-0.918236\pi$
$619$	−988005.	+	2.38525e6i	−0.103641	+	0.250212i	0.863549	+	0.504265i	$0.168236\pi$
$620$	1.18275e7	−	1.18275e7i	1.23570	−	1.23570i
$621$	461753.	−	461753.i	0.0480486	−	0.0480486i
$622$	9.66936e6	−	2.33439e7i	1.00212	−	2.41934i
$623$	2.92346e7	+	1.21094e7i	3.01771	+	1.24998i
$624$	855544.	+	2.06547e6i	0.0879592	+	0.212352i
$625$			2.08000e6i			0.212992i
$626$	−2.39628e7	+	9.92572e6i	−2.44400	+	1.01234i
$627$	−738147.	−	738147.i	−0.0749849	−	0.0749849i
$628$	−7.51450e6			−0.760328
$629$	−1.32093e7	+	7.97889e6i	−1.33123	+	0.804110i
$630$	−7.02006e6			−0.704676
$631$	1.04127e6	+	1.04127e6i	0.104110	+	0.104110i	0.757243	−	0.653133i	$-0.226546\pi$
$631$	1.04127e6	+	1.04127e6i	0.104110	+	0.104110i	−0.653133	+	0.757243i	$0.726546\pi$
$632$	1.96152e7	−	8.12487e6i	1.95344	−	0.809140i
$633$			3.72716e6i			0.369716i
$634$	251166.	+	606369.i	0.0248164	+	0.0599120i
$635$	−7.32543e6	−	3.03429e6i	−0.720940	−	0.298623i
$636$	−3.36740e6	+	8.12961e6i	−0.330104	+	0.796942i
$637$	−1.41183e7	+	1.41183e7i	−1.37859	+	1.37859i
$638$	−2.42083e6	+	2.42083e6i	−0.235458	+	0.235458i
$639$	1.87119e6	−	4.51746e6i	0.181287	−	0.437665i
$640$	1.21273e7	+	5.02330e6i	1.17035	+	0.484774i
$641$	−7.04643e6	−	1.70116e7i	−0.677367	−	1.63531i	−0.768795	−	0.639496i	$-0.779143\pi$
$641$	−7.04643e6	−	1.70116e7i	−0.677367	−	1.63531i	0.0914279	−	0.995812i	$-0.470857\pi$
$642$			1.35471e7i			1.29721i
$643$	1.17746e7	−	4.87718e6i	1.12310	−	0.465202i	0.257668	−	0.966234i	$-0.417046\pi$
$643$	1.17746e7	−	4.87718e6i	1.12310	−	0.465202i	0.865429	+	0.501032i	$0.167046\pi$
$644$	8.64701e6	+	8.64701e6i	0.821582	+	0.821582i
$645$	−297375.			−0.0281453
$646$	−2.28497e6	−	1.50491e7i	−0.215427	−	1.41882i
$647$	1.39153e7			1.30687			0.653433	−	0.756984i	$-0.273328\pi$
$647$	1.39153e7			1.30687			0.653433	+	0.756984i	$0.273328\pi$
$648$	−1.14252e6	−	1.14252e6i	−0.106888	−	0.106888i
$649$	−3.80222e6	+	1.57493e6i	−0.354344	+	0.146774i
$650$			7.93441e6i			0.736599i
$651$	6.03330e6	+	1.45657e7i	0.557959	+	1.34703i
$652$	−3.39060e7	−	1.40443e7i	−3.12362	−	1.29384i
$653$	486005.	−	1.17332e6i	0.0446024	−	0.107680i	−0.900008	−	0.435873i	$-0.856440\pi$
$653$	486005.	−	1.17332e6i	0.0446024	−	0.107680i	0.944611	+	0.328193i	$0.106440\pi$
$654$	−1.41643e6	+	1.41643e6i	−0.129494	+	0.129494i
$655$	896831.	−	896831.i	0.0816784	−	0.0816784i
$656$	−2.70261e6	+	6.52467e6i	−0.245202	+	0.591969i
$657$	4.72401e6	+	1.95675e6i	0.426970	+	0.176857i
$658$	−459710.	−	1.10984e6i	−0.0413923	−	0.0999299i
$659$		−	7.85611e6i		−	0.704683i	−0.935871	−	0.352342i	$-0.885386\pi$
$659$		−	7.85611e6i		−	0.704683i	0.935871	−	0.352342i	$-0.114614\pi$
$660$	−1.61038e6	+	667042.i	−0.143903	+	0.0596064i
$661$	8.37860e6	+	8.37860e6i	0.745878	+	0.745878i	0.973702	−	0.227824i	$-0.0731611\pi$
$661$	8.37860e6	+	8.37860e6i	0.745878	+	0.745878i	−0.227824	+	0.973702i	$0.573161\pi$
$662$	−4.37008e6			−0.387565
$663$	2.86353e6	+	4.74066e6i	0.252999	+	0.418846i
$664$	7.30733e6			0.643189
$665$	−8.70176e6	−	8.70176e6i	−0.763050	−	0.763050i
$666$	−9.19255e6	+	3.80768e6i	−0.803064	+	0.332640i
$667$		−	3.75429e6i		−	0.326748i
$668$	−1.82784e6	−	4.41280e6i	−0.158488	−	0.382625i
$669$	−4.46935e6	−	1.85127e6i	−0.386082	−	0.159920i
$670$	4.11643e6	−	9.93795e6i	0.354270	−	0.855283i
$671$	716247.	−	716247.i	0.0614124	−	0.0614124i
$672$	−4.97369e6	+	4.97369e6i	−0.424869	+	0.424869i
$673$	1.80159e6	−	4.34943e6i	0.153327	−	0.370164i	−0.828487	−	0.560008i	$-0.810798\pi$
$673$	1.80159e6	−	4.34943e6i	0.153327	−	0.370164i	0.981814	+	0.189844i	$0.0607981\pi$
$674$	−2.45878e7	−	1.01846e7i	−2.08482	−	0.863562i
$675$	−451886.	−	1.09095e6i	−0.0381741	−	0.0921605i
$676$			6.06219e6i			0.510226i
$677$	1.58741e6	−	657528.i	0.133112	−	0.0551369i	−0.315133	−	0.949048i	$-0.602049\pi$
$677$	1.58741e6	−	657528.i	0.133112	−	0.0551369i	0.448245	+	0.893911i	$0.352049\pi$
$678$	219724.	+	219724.i	0.0183571	+	0.0183571i
$679$	−553776.			−0.0460957
$680$	−1.10531e7	−	2.72851e6i	−0.916670	−	0.226283i
$681$	−3.12750e6			−0.258422
$682$	4.29618e6	+	4.29618e6i	0.353689	+	0.353689i
$683$	4.80354e6	−	1.98969e6i	0.394012	−	0.163205i	−0.176876	−	0.984233i	$-0.556599\pi$
$683$	4.80354e6	−	1.98969e6i	0.394012	−	0.163205i	0.570888	+	0.821028i	$0.306599\pi$
$684$		−	6.32334e6i		−	0.516781i
$685$	2.74180e6	+	6.61928e6i	0.223259	+	0.538995i
$686$	4.51041e7	+	1.86827e7i	3.65937	+	1.51576i
$687$	−5.20488e6	+	1.25657e7i	−0.420745	+	1.01577i
$688$	289662.	−	289662.i	0.0233303	−	0.0233303i
$689$	6.15963e6	−	6.15963e6i	0.494318	−	0.494318i
$690$	1.13530e6	−	2.74086e6i	0.0907797	−	0.219162i
$691$	−9.18439e6	−	3.80430e6i	−0.731737	−	0.303095i	−0.0144715	−	0.999895i	$-0.504607\pi$
$691$	−9.18439e6	−	3.80430e6i	−0.731737	−	0.303095i	−0.717266	+	0.696800i	$0.754607\pi$
$692$	−1.17074e7	−	2.82641e7i	−0.929382	−	2.24373i
$693$		−	1.64294e6i		−	0.129954i
$694$	1.69267e7	−	7.01127e6i	1.33406	−	0.552584i
$695$	−969045.	−	969045.i	−0.0760995	−	0.0760995i
$696$	−9.28932e6			−0.726877
$697$	−4.19294e6	+	1.69855e7i	−0.326916	+	1.32433i
$698$	1.70542e7			1.32493
$699$	−6.98923e6	−	6.98923e6i	−0.541049	−	0.541049i
$700$	2.04296e7	−	8.46223e6i	1.57585	−	0.652739i
$701$		−	4.33741e6i		−	0.333377i	−0.986010	−	0.166689i	$-0.946693\pi$
$701$		−	4.33741e6i		−	0.333377i	0.986010	−	0.166689i	$-0.0533075\pi$
$702$	1.36653e6	+	3.29910e6i	0.104659	+	0.252670i
$703$	−1.61145e7	−	6.67485e6i	−1.22979	−	0.509394i
$704$	−1.54460e6	+	3.72900e6i	−0.117459	+	0.283571i
$705$	−132773.	+	132773.i	−0.0100609	+	0.0100609i
$706$	1.82970e6	−	1.82970e6i	0.138156	−	0.138156i
$707$	−820632.	+	1.98118e6i	−0.0617448	+	0.149065i
$708$	−2.30317e7	−	9.54005e6i	−1.72680	−	0.715266i
$709$	−3.46381e6	−	8.36237e6i	−0.258784	−	0.624761i	0.740074	−	0.672525i	$-0.234790\pi$
$709$	−3.46381e6	−	8.36237e6i	−0.258784	−	0.624761i	−0.998859	+	0.0477645i	$0.984790\pi$
$710$		−	2.22140e7i		−	1.65379i
$711$	6.45159e6	−	2.67234e6i	0.478622	−	0.198252i
$712$	2.33967e7	+	2.33967e7i	1.72963	+	1.72963i
$713$	−6.66264e6			−0.490820
$714$	1.42049e7	−	1.92908e7i	1.04278	−	1.41613i
$715$	1.72555e6			0.126230
$716$	1.02638e7	+	1.02638e7i	0.748213	+	0.748213i
$717$	−2.01625e6	+	835159.i	−0.146469	+	0.0606696i
$718$		−	1.11527e7i		−	0.807366i
$719$	−2.48615e6	−	6.00209e6i	−0.179351	−	0.432993i	0.808479	−	0.588524i	$-0.200291\pi$
$719$	−2.48615e6	−	6.00209e6i	−0.179351	−	0.432993i	−0.987831	+	0.155532i	$0.950291\pi$
$720$	−1.39650e6	−	578448.i	−0.100394	−	0.0415846i
$721$	2.48919e6	−	6.00943e6i	0.178328	−	0.430522i
$722$	−4.44156e6	+	4.44156e6i	−0.317098	+	0.317098i
$723$	6.15419e6	−	6.15419e6i	0.437850	−	0.437850i
$724$	−9.99393e6	+	2.41275e7i	−0.708582	+	1.71067i
$725$	−6.27202e6	−	2.59796e6i	−0.443162	−	0.183564i
$726$	5.01885e6	+	1.21166e7i	0.353397	+	0.853176i
$727$		−	1.16975e7i		−	0.820839i	−0.911897	−	0.410420i	$-0.865382\pi$
$727$		−	1.16975e7i		−	0.820839i	0.911897	−	0.410420i	$-0.134618\pi$
$728$	−2.76737e7	+	1.14628e7i	−1.93526	+	0.801610i
$729$	−375786.	−	375786.i	−0.0261891	−	0.0261891i
$730$	2.32296e7			1.61337
$731$	601732.	−	817171.i	0.0416495	−	0.0565613i
$732$	6.13574e6			0.423242
$733$	2.03924e7	+	2.03924e7i	1.40187	+	1.40187i	0.794158	+	0.607712i	$0.207912\pi$
$733$	2.03924e7	+	2.03924e7i	1.40187	+	1.40187i	0.607712	+	0.794158i	$0.292088\pi$
$734$	7.49548e6	−	3.10473e6i	0.513522	−	0.212708i
$735$		−	1.34995e7i		−	0.921724i
$736$	−1.13753e6	−	2.74625e6i	−0.0774051	−	0.186873i
$737$	2.32583e6	+	963391.i	0.157728	+	0.0653332i
$738$	−4.31679e6	+	1.04217e7i	−0.291756	+	0.704361i
$739$	−6.02602e6	+	6.02602e6i	−0.405900	+	0.405900i	−0.880306	−	0.474406i	$-0.842663\pi$
$739$	−6.02602e6	+	6.02602e6i	−0.405900	+	0.405900i	0.474406	+	0.880306i	$0.342663\pi$
$740$	−2.05941e7	+	2.05941e7i	−1.38249	+	1.38249i
$741$	−2.39553e6	+	5.78332e6i	−0.160272	+	0.386930i
$742$	−3.48117e7	−	1.44195e7i	−2.32122	−	0.961480i
$743$	5.12256e6	+	1.23670e7i	0.340420	+	0.821847i	0.997673	+	0.0681769i	$0.0217182\pi$
$743$	5.12256e6	+	1.23670e7i	0.340420	+	0.821847i	−0.657253	+	0.753670i	$0.728282\pi$
$744$			1.64855e7i			1.09187i
$745$	8.97698e6	−	3.71839e6i	0.592570	−	0.245451i
$746$	−5.09701e6	−	5.09701e6i	−0.335327	−	0.335327i
$747$	2.40344e6			0.157591
$748$	1.42558e6	−	5.77499e6i	0.0931616	−	0.377396i
$749$	−3.73760e7			−2.43438
$750$	−1.11116e7	−	1.11116e7i	−0.721314	−	0.721314i
$751$	−4.85864e6	+	2.01251e6i	−0.314351	+	0.130208i	−0.534280	−	0.845307i	$-0.679417\pi$
$751$	−4.85864e6	+	2.01251e6i	−0.314351	+	0.130208i	0.219929	+	0.975516i	$0.429417\pi$
$752$		−	258660.i		−	0.0166795i
$753$	−5.51881e6	−	1.33236e7i	−0.354697	−	0.856315i
$754$	1.89670e7	+	7.85640e6i	1.21498	+	0.503263i
$755$	−4.17753e6	+	1.00855e7i	−0.266718	+	0.643914i
$756$	7.03714e6	−	7.03714e6i	0.447808	−	0.447808i
$757$	−1.97185e6	+	1.97185e6i	−0.125065	+	0.125065i	−0.766869	−	0.641804i	$-0.778186\pi$
$757$	−1.97185e6	+	1.97185e6i	−0.125065	+	0.125065i	0.641804	+	0.766869i	$0.278186\pi$
$758$	−8.40643e6	+	2.02949e7i	−0.531421	+	1.28296i
$759$	641458.	+	265701.i	0.0404170	+	0.0167413i
$760$	−4.92435e6	−	1.18884e7i	−0.309254	−	0.746604i
$761$		−	2.17747e7i		−	1.36298i	−0.731826	−	0.681492i	$-0.761331\pi$
$761$		−	2.17747e7i		−	1.36298i	0.731826	−	0.681492i	$-0.238669\pi$
$762$	1.61181e7	−	6.67633e6i	1.00560	−	0.416534i
$763$	−3.90787e6	−	3.90787e6i	−0.243012	−	0.243012i
$764$	−1.62674e7			−1.00829
$765$	−3.63546e6	−	897428.i	−0.224598	−	0.0554429i
$766$	−4.94431e6			−0.304463
$767$	1.74506e7	+	1.74506e7i	1.07108	+	1.07108i
$768$	−1.42135e7	+	5.88742e6i	−0.869557	+	0.360182i
$769$		−	2.01069e7i		−	1.22611i	−0.790041	−	0.613054i	$-0.789941\pi$
$769$		−	2.01069e7i		−	1.22611i	0.790041	−	0.613054i	$-0.210059\pi$
$770$	−2.85633e6	−	6.89580e6i	−0.173613	−	0.419139i
$771$	4.77634e6	+	1.97842e6i	0.289374	+	0.119863i
$772$	−2.20310e7	+	5.31876e7i	−1.33043	+	3.21194i
$773$	−5.68786e6	+	5.68786e6i	−0.342373	+	0.342373i	−0.857259	−	0.514886i	$-0.827834\pi$
$773$	−5.68786e6	+	5.68786e6i	−0.342373	+	0.342373i	0.514886	+	0.857259i	$0.327834\pi$
$774$	462668.	−	462668.i	0.0277599	−	0.0277599i
$775$	−4.61052e6	+	1.11308e7i	−0.275738	+	0.665689i
$776$	−534979.	−	221596.i	−0.0318921	−	0.0132101i
$777$	−1.05052e7	−	2.53619e7i	−0.624243	−	1.50706i
$778$		−	2.34500e7i		−	1.38898i
$779$	−1.82691e7	+	7.56733e6i	−1.07864	+	0.446785i
$780$	7.39099e6	+	7.39099e6i	0.434977	+	0.434977i
$781$	5.19885e6			0.304986
$782$	5.23448e6	+	8.66583e6i	0.306096	+	0.506749i
$783$	−3.05533e6			−0.178096
$784$	1.31494e7	+	1.31494e7i	0.764041	+	0.764041i
$785$	−4.64678e6	+	1.92476e6i	−0.269140	+	0.111481i
$786$			2.79065e6i			0.161120i
$787$	9.94186e6	+	2.40018e7i	0.572178	+	1.38136i	0.899697	+	0.436515i	$0.143787\pi$
$787$	9.94186e6	+	2.40018e7i	0.572178	+	1.38136i	−0.327519	+	0.944844i	$0.606213\pi$
$788$	1.36751e7	+	5.66443e6i	0.784542	+	0.324968i
$789$	2.48203e6	−	5.99215e6i	0.141943	−	0.342681i
$790$	2.24328e7	−	2.24328e7i	1.27884	−	1.27884i
$791$	−606211.	+	606211.i	−0.0344495	+	0.0344495i
$792$	657429.	−	1.58717e6i	0.0372422	−	0.0899107i
$793$	−5.61174e6	−	2.32446e6i	−0.316894	−	0.131262i
$794$	1.25005e7	+	3.01788e7i	0.703680	+	1.69883i
$795$			5.88968e6i			0.330502i
$796$	2.85923e7	−	1.18433e7i	1.59944	−	0.662508i
$797$	1.74442e7	+	1.74442e7i	0.972761	+	0.972761i	0.999639	−	0.0268775i	$-0.00855639\pi$
$797$	1.74442e7	+	1.74442e7i	0.972761	+	0.972761i	−0.0268775	+	0.999639i	$0.508556\pi$
$798$	2.70771e7			1.50520
$799$	−96190.1	−	633519.i	−0.00533044	−	0.0351069i
$800$	−5.37513e6			−0.296937
$801$	7.69536e6	+	7.69536e6i	0.423787	+	0.423787i
$802$	6.77351e6	−	2.80568e6i	0.371859	−	0.154029i
$803$			5.43655e6i			0.297533i
$804$	5.83568e6	+	1.40886e7i	0.318384	+	0.768648i
$805$	7.56194e6	+	3.13226e6i	0.411286	+	0.170360i
$806$	1.39425e7	−	3.36603e7i	0.755969	−	1.82507i
$807$	9.36116e6	−	9.36116e6i	0.505995	−	0.505995i
$808$	−1.58555e6	+	1.58555e6i	−0.0854383	+	0.0854383i
$809$	4.25328e6	−	1.02683e7i	0.228483	−	0.551606i	−0.767510	−	0.641036i	$-0.778505\pi$
$809$	4.25328e6	−	1.02683e7i	0.228483	−	0.551606i	0.995993	+	0.0894306i	$0.0285047\pi$
$810$	−2.23058e6	−	923936.i	−0.119455	−	0.0494799i
$811$	5.71584e6	+	1.37993e7i	0.305160	+	0.736722i	0.999848	+	0.0174112i	$0.00554245\pi$
$811$	5.71584e6	+	1.37993e7i	0.305160	+	0.736722i	−0.694688	+	0.719311i	$0.744458\pi$
$812$		−	5.72156e7i		−	3.04526i
$813$	−4.49608e6	+	1.86234e6i	−0.238565	+	0.0988170i
$814$	−7.48056e6	−	7.48056e6i	−0.395706	−	0.395706i
$815$	−2.45640e7			−1.29540
$816$	4.41533e6	−	2.66702e6i	0.232133	−	0.140217i
$817$	1.14701e6			0.0601189
$818$	−1.56595e6	−	1.56595e6i	−0.0818265	−	0.0818265i
$819$	−9.10211e6	+	3.77022e6i	−0.474168	+	0.196407i
$820$			3.30186e7i			1.71484i
$821$	−4.42917e6	−	1.06930e7i	−0.229332	−	0.553656i	0.766764	−	0.641929i	$-0.221865\pi$
$821$	−4.42917e6	−	1.06930e7i	−0.229332	−	0.553656i	−0.996096	+	0.0882723i	$0.971865\pi$
$822$	−1.45644e7	−	6.03276e6i	−0.751816	−	0.311413i
$823$	−31313.2	+	75596.7i	−0.00161149	+	0.00389048i	−0.924683	−	0.380737i	$-0.875670\pi$
$823$	−31313.2	+	75596.7i	−0.00161149	+	0.00389048i	0.923072	+	0.384628i	$0.125670\pi$
$824$	4.80939e6	−	4.80939e6i	0.246758	−	0.246758i
$825$	887774.	−	887774.i	0.0454117	−	0.0454117i
$826$	4.08514e7	−	9.86239e7i	2.08332	−	5.02958i
$827$	1.24271e7	+	5.14747e6i	0.631838	+	0.261716i	0.675534	−	0.737329i	$-0.263913\pi$
$827$	1.24271e7	+	5.14747e6i	0.631838	+	0.261716i	−0.0436957	+	0.999045i	$0.513913\pi$
$828$	1.60947e6	+	3.88560e6i	0.0815842	+	0.196962i
$829$			1.72287e6i			0.0870697i	0.999052	+	0.0435349i	$0.0138620\pi$
$829$			1.72287e6i			0.0870697i	−0.999052	+	0.0435349i	$0.986138\pi$
$830$	1.00878e7	−	4.17850e6i	0.508277	−	0.210535i
$831$	9.25054e6	+	9.25054e6i	0.464691	+	0.464691i
$832$	2.42037e7			1.21220
$833$	3.70961e7	+	2.73161e7i	1.85232	+	1.36397i
$834$	3.01536e6			0.150115
$835$	−2.26059e6	−	2.26059e6i	−0.112203	−	0.112203i
$836$	6.21142e6	−	2.57285e6i	0.307380	−	0.127321i
$837$			5.42221e6i			0.267524i
$838$	1.97376e7	+	4.76508e7i	0.970922	+	2.34401i
$839$	1.16136e7	+	4.81053e6i	0.569591	+	0.235932i	0.648843	−	0.760922i	$-0.275253\pi$
$839$	1.16136e7	+	4.81053e6i	0.569591	+	0.235932i	−0.0792518	+	0.996855i	$0.525253\pi$
$840$	7.75021e6	−	1.87107e7i	0.378979	−	0.914936i
$841$	2.08286e6	−	2.08286e6i	0.101548	−	0.101548i
$842$	−1.93934e7	+	1.93934e7i	−0.942699	+	0.942699i
$843$	−6.32577e6	+	1.52718e7i	−0.306581	+	0.740151i
$844$	−2.21774e7	−	9.18618e6i	−1.07165	−	0.443893i
$845$	1.55277e6	+	3.74871e6i	0.0748108	+	0.180609i
$846$		−	413149.i		−	0.0198463i
$847$	−3.34292e7	+	1.38468e7i	−1.60110	+	0.663196i
$848$	−5.73692e6	−	5.73692e6i	−0.273961	−	0.273961i
$849$	6.27216e6			0.298640
$850$	1.80996e7	−	2.74815e6i	0.859255	−	0.130465i
$851$	1.16011e7			0.549128
$852$	2.22680e7	+	2.22680e7i	1.05095	+	1.05095i
$853$	−5.74739e6	+	2.38065e6i	−0.270457	+	0.112027i	−0.513790	−	0.857916i	$-0.671759\pi$
$853$	−5.74739e6	+	2.38065e6i	−0.270457	+	0.112027i	0.243333	+	0.969943i	$0.421759\pi$
$854$			2.62738e7i			1.23276i
$855$	−1.61966e6	−	3.91020e6i	−0.0757719	−	0.182930i
$856$	−3.61073e7	−	1.49561e7i	−1.68427	−	0.697645i
$857$	−1.95811e6	+	4.72729e6i	−0.0910718	+	0.219867i	−0.962852	−	0.270031i	$-0.912966\pi$
$857$	−1.95811e6	+	4.72729e6i	−0.0910718	+	0.219867i	0.871780	+	0.489898i	$0.162966\pi$
$858$	−2.68469e6	+	2.68469e6i	−0.124502	+	0.124502i
$859$	5.76496e6	−	5.76496e6i	0.266571	−	0.266571i	−0.561146	−	0.827717i	$-0.689639\pi$
$859$	5.76496e6	−	5.76496e6i	0.266571	−	0.266571i	0.827717	+	0.561146i	$0.189639\pi$
$860$	732929.	−	1.76945e6i	0.0337921	−	0.0815814i
$861$	−2.87530e7	−	1.19099e7i	−1.32183	−	0.547519i
$862$	992420.	+	2.39591e6i	0.0454912	+	0.109825i
$863$			4.90379e6i			0.224132i	0.993701	+	0.112066i	$0.0357469\pi$
$863$			4.90379e6i			0.224132i	−0.993701	+	0.112066i	$0.964253\pi$
$864$	−2.23496e6	+	925752.i	−0.101856	+	0.0421901i
$865$	−1.44791e7	−	1.44791e7i	−0.657963	−	0.657963i
$866$	−4.68967e7			−2.12494
$867$	9.82237e6	−	8.17414e6i	0.443781	−	0.369313i
$868$	−1.01539e8			−4.57439
$869$	5.25007e6	+	5.25007e6i	0.235839	+	0.235839i
$870$	−1.28239e7	+	5.31184e6i	−0.574411	+	0.237929i
$871$		−	1.50962e7i		−	0.674252i
$872$	−2.21147e6	−	5.33896e6i	−0.0984895	−	0.237775i
$873$	−175959.	−	72884.6i	−0.00781404	−	0.00323668i
$874$	−4.37898e6	+	1.05718e7i	−0.193908	+	0.468134i
$875$	3.06566e7	−	3.06566e7i	1.35364	−	1.35364i
$876$	−2.32861e7	+	2.32861e7i	−1.02527	+	1.02527i
$877$	−935379.	+	2.25820e6i	−0.0410666	+	0.0991435i	−0.943082	−	0.332560i	$-0.892087\pi$
$877$	−935379.	+	2.25820e6i	−0.0410666	+	0.0991435i	0.902015	+	0.431704i	$0.142087\pi$
$878$	3.59633e7	+	1.48965e7i	1.57443	+	0.652151i
$879$	−3.63295e6	−	8.77072e6i	−0.158594	−	0.382880i
$880$		−	1.60714e6i		−	0.0699594i
$881$	1.53703e7	−	6.36657e6i	0.667178	−	0.276354i	−0.0232777	−	0.999729i	$-0.507410\pi$
$881$	1.53703e7	−	6.36657e6i	0.667178	−	0.276354i	0.690455	+	0.723375i	$0.257410\pi$
$882$	2.10032e7	+	2.10032e7i	0.909103	+	0.909103i
$883$	−2.06968e7			−0.893307			−0.446654	−	0.894707i	$-0.647384\pi$
$883$	−2.06968e7			−0.893307			−0.446654	+	0.894707i	$0.647384\pi$
$884$	−3.52656e7	+	5.35454e6i	−1.51782	+	0.230458i
$885$	−1.66858e7			−0.716127
$886$	−1.38354e7	−	1.38354e7i	−0.592118	−	0.592118i
$887$	−1.78812e7	+	7.40662e6i	−0.763109	+	0.316090i	−0.730078	−	0.683364i	$-0.760516\pi$
$887$	−1.78812e7	+	7.40662e6i	−0.763109	+	0.316090i	−0.0330312	+	0.999454i	$0.510516\pi$
$888$		−	2.87047e7i		−	1.22158i
$889$	1.84198e7	+	4.44692e7i	0.781681	+	1.88715i
$890$	4.56779e7	+	1.89204e7i	1.93300	+	0.800673i
$891$	216234.	−	522034.i	0.00912492	−	0.0220295i
$892$	2.20309e7	−	2.20309e7i	0.927085	−	0.927085i
$893$	512121.	−	512121.i	0.0214904	−	0.0214904i
$894$	−8.18154e6	+	1.97520e7i	−0.342366	+	0.826546i
$895$	8.97585e6	+	3.71792e6i	0.374557	+	0.155147i
$896$	−3.04941e7	−	7.36192e7i	−1.26895	−	3.06352i
$897$		−	4.16349e6i		−	0.172773i
$898$	1.16399e7	−	4.82139e6i	0.481679	−	0.199518i
$899$	2.20427e7	+	2.20427e7i	0.909632	+	0.909632i
$900$	7.60513e6			0.312968
$901$	−1.61845e7	−	1.19176e7i	−0.664183	−	0.489078i
$902$	−1.19936e7			−0.490833
$903$	1.27649e6	+	1.27649e6i	0.0520950	+	0.0520950i
$904$	−828212.	+	343057.i	−0.0337070	+	0.0139619i
$905$			1.74797e7i			0.709434i
$906$	−9.19179e6	−	2.21909e7i	−0.372031	−	0.898163i
$907$	−2.52486e7	−	1.04583e7i	−1.01910	−	0.422127i	−0.190336	−	0.981719i	$-0.560958\pi$
$907$	−2.52486e7	−	1.04583e7i	−1.01910	−	0.422127i	−0.828768	+	0.559592i	$0.810958\pi$
$908$	7.70823e6	−	1.86093e7i	0.310270	−	0.749059i
$909$	−521501.	+	521501.i	−0.0209337	+	0.0209337i
$910$	−3.16489e7	+	3.16489e7i	−1.26694	+	1.26694i
$911$	4.23949e6	−	1.02350e7i	0.169246	−	0.408595i	−0.816385	−	0.577507i	$-0.804025\pi$
$911$	4.23949e6	−	1.02350e7i	0.169246	−	0.408595i	0.985631	+	0.168912i	$0.0540255\pi$
$912$	5.38644e6	+	2.23114e6i	0.214444	+	0.0888258i
$913$	977916.	+	2.36090e6i	0.0388262	+	0.0937347i
$914$		−	6.14602e7i		−	2.43349i
$915$	3.79419e6	−	1.57161e6i	0.149819	−	0.0620570i
$916$	−6.19403e7	−	6.19403e7i	−2.43913	−	2.43913i
$917$	−7.69932e6			−0.302363
$918$	7.05246e6	−	4.25995e6i	0.276206	−	0.166839i
$919$	−2.17512e7			−0.849560			−0.424780	−	0.905297i	$-0.639649\pi$
$919$	−2.17512e7			−0.849560			−0.424780	+	0.905297i	$0.639649\pi$
$920$	6.05187e6	+	6.05187e6i	0.235733	+	0.235733i
$921$	1.00225e7	−	4.15145e6i	0.389337	−	0.161269i
$922$			2.96691e7i			1.14942i
$923$	−1.19303e7	−	2.88023e7i	−0.460943	−	1.11282i
$924$	9.77586e6	+	4.04929e6i	0.376682	+	0.156027i
$925$	8.02789e6	−	1.93810e7i	0.308494	−	0.744771i
$926$	−2.44643e7	+	2.44643e7i	−0.937573	+	0.937573i
$927$	1.58185e6	−	1.58185e6i	0.0604596	−	0.0604596i
$928$	−5.32228e6	+	1.28491e7i	−0.202875	+	0.489783i
$929$	−913962.	−	378576.i	−0.0347447	−	0.0143917i	0.365243	−	0.930912i	$-0.380986\pi$
$929$	−913962.	−	378576.i	−0.0347447	−	0.0143917i	−0.399988	+	0.916520i	$0.630986\pi$
$930$	9.42678e6	+	2.27583e7i	0.357401	+	0.862843i
$931$			5.20692e7i			1.96882i
$932$	5.88136e7	−	2.43614e7i	2.21788	−	0.918675i
$933$	1.69532e7	+	1.69532e7i	0.637597	+	0.637597i
$934$	−5.86191e7			−2.19873
$935$	−597661.	−	3.93626e6i	−0.0223576	−	0.147250i
$936$	−1.03018e7			−0.384347
$937$	1.24923e7	+	1.24923e7i	0.464829	+	0.464829i	0.900234	−	0.435406i	$-0.143395\pi$
$937$	1.24923e7	+	1.24923e7i	0.464829	+	0.464829i	−0.435406	+	0.900234i	$0.643395\pi$
$938$	−6.03286e7	+	2.49889e7i	−2.23880	+	0.927343i
$939$		−	2.46110e7i		−	0.910890i
$940$	−462789.	−	1.11727e6i	−0.0170830	−	0.0412420i
$941$	−2.07643e7	−	8.60086e6i	−0.764440	−	0.316642i	−0.0338223	−	0.999428i	$-0.510768\pi$
$941$	−2.07643e7	−	8.60086e6i	−0.764440	−	0.316642i	−0.730618	+	0.682786i	$0.760768\pi$
$942$	4.23503e6	−	1.02243e7i	0.155500	−	0.375410i
$943$	9.30001e6	−	9.30001e6i	0.340568	−	0.340568i
$944$	1.62531e7	−	1.62531e7i	0.593616	−	0.593616i
$945$	2.54911e6	−	6.15408e6i	0.0928556	−	0.224173i
$946$	642730.	+	266227.i	0.0233507	+	0.00967220i
$947$	−1.37892e7	−	3.32902e7i	−0.499650	−	1.20626i	−0.949673	−	0.313244i	$-0.898584\pi$
$947$	−1.37892e7	−	3.32902e7i	−0.499650	−	1.20626i	0.450023	−	0.893017i	$-0.351416\pi$
$948$			4.49748e7i			1.62536i
$949$	3.01192e7	−	1.24758e7i	1.08562	−	0.449679i
$950$	1.46313e7	+	1.46313e7i	0.525986	+	0.525986i
$951$	−622772.			−0.0223295
$952$	3.57335e7	+	5.91578e7i	1.27786	+	2.11553i
$953$	4.65755e7			1.66121			0.830607	−	0.556859i	$-0.187994\pi$
$953$	4.65755e7			1.66121			0.830607	+	0.556859i	$0.187994\pi$
$954$	−9.16340e6	−	9.16340e6i	−0.325976	−	0.325976i
$955$	−1.00594e7	+	4.16673e6i	−0.356914	+	0.147838i
$956$		−	1.40555e7i		−	0.497396i
$957$	−1.24316e6	−	3.00125e6i	−0.0438780	−	0.105931i
$958$	3.43380e7	+	1.42232e7i	1.20882	+	0.500709i
$959$	1.66442e7	−	4.01825e7i	0.584407	−	1.41088i
$960$	−1.15715e7	+	1.15715e7i	−0.405238	+	0.405238i
$961$	1.88747e7	−	1.88747e7i	0.659283	−	0.659283i
$962$	−2.42769e7	+	5.86096e7i	−0.845776	+	2.04188i
$963$	−1.18760e7	−	4.91919e6i	−0.412671	−	0.170934i
$964$	2.14508e7	+	5.17868e7i	0.743448	+	1.79484i
$965$			3.85329e7i			1.33203i
$966$	−1.66385e7	+	6.89188e6i	−0.573681	+	0.237627i
$967$	−2.53139e7	−	2.53139e7i	−0.870547	−	0.870547i	0.121985	−	0.992532i	$-0.461074\pi$
$967$	−2.53139e7	−	2.53139e7i	−0.870547	−	0.870547i	−0.992532	+	0.121985i	$0.961074\pi$
$968$	−3.78354e7			−1.29781
$969$	1.40224e7	+	3.46148e6i	0.479747	+	0.118427i
$970$	−865253.			−0.0295266
$971$	3.78730e7	+	3.78730e7i	1.28908	+	1.28908i	0.935343	+	0.353741i	$0.115091\pi$
$971$	3.78730e7	+	3.78730e7i	1.28908	+	1.28908i	0.353741	+	0.935343i	$0.384909\pi$
$972$	3.16219e6	−	1.30982e6i	0.107355	−	0.0444679i
$973$			8.31927e6i			0.281711i
$974$	8.80841e6	+	2.12654e7i	0.297509	+	0.718250i
$975$	−6.95564e6	−	2.88112e6i	−0.234329	−	0.0970622i
$976$	−2.16494e6	+	5.22663e6i	−0.0727481	+	0.175629i
$977$	7.67147e6	−	7.67147e6i	0.257124	−	0.257124i	−0.566760	−	0.823883i	$-0.691803\pi$
$977$	7.67147e6	−	7.67147e6i	0.257124	−	0.257124i	0.823883	+	0.566760i	$0.191803\pi$
$978$	3.82176e7	−	3.82176e7i	1.27766	−	1.27766i
$979$	−4.42804e6	+	1.06902e7i	−0.147657	+	0.356476i
$980$	8.03252e7	+	3.32718e7i	2.67170	+	1.10665i
$981$	−727371.	−	1.75603e6i	−0.0241314	−	0.0582585i
$982$		−	5.88414e7i		−	1.94717i
$983$	−1.53412e6	+	635452.i	−0.0506378	+	0.0209748i	−0.407859	−	0.913045i	$-0.633724\pi$
$983$	−1.53412e6	+	635452.i	−0.0506378	+	0.0209748i	0.357221	+	0.934020i	$0.383724\pi$
$984$	−2.30112e7	−	2.30112e7i	−0.757620	−	0.757620i
$985$	9.90726e6			0.325359
$986$	1.13523e7	−	4.59879e7i	0.371870	−	1.50644i
$987$	1.13986e6			0.0372443
$988$	−2.85079e7	−	2.85079e7i	−0.929121	−	0.929121i
$989$	−704819.	+	291945.i	−0.0229132	+	0.00949098i
$990$		−	2.56703e6i		−	0.0832420i
$991$	7.58645e6	+	1.83153e7i	0.245389	+	0.592421i	0.997802	−	0.0662710i	$-0.0211102\pi$
$991$	7.58645e6	+	1.83153e7i	0.245389	+	0.592421i	−0.752413	+	0.658692i	$0.771110\pi$
$992$	2.28030e7	+	9.44531e6i	0.735720	+	0.304745i
$993$	1.58685e6	−	3.83100e6i	0.0510697	−	0.123293i
$994$	−9.53537e7	+	9.53537e7i	−3.06106	+	3.06106i
$995$	1.46473e7	−	1.46473e7i	0.469028	−	0.469028i
$996$	−5.92367e6	+	1.43010e7i	−0.189209	+	0.456791i
$997$	2.79928e7	+	1.15950e7i	0.891884	+	0.369430i	0.781094	−	0.624413i	$-0.214662\pi$
$997$	2.79928e7	+	1.15950e7i	0.891884	+	0.369430i	0.110790	+	0.993844i	$0.464662\pi$
$998$	4.38122e6	+	1.05772e7i	0.139241	+	0.336159i
$999$		−	9.44122e6i		−	0.299305i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	51.6.h.a.19.2	✓	56
17.3	odd	16		867.6.a.u.1.3		28
17.9	even	8	inner	51.6.h.a.43.2	yes	56
17.14	odd	16		867.6.a.t.1.3		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
51.6.h.a.19.2	✓	56	1.1	even	1	trivial
51.6.h.a.43.2	yes	56	17.9	even	8	inner
867.6.a.t.1.3		28	17.14	odd	16
867.6.a.u.1.3		28	17.3	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+(-6.70687 - 6.70687i) q^{2} +(8.31492 - 3.44415i) q^{3} +57.9642i q^{4} +(14.8469 + 35.8437i) q^{5} +(-78.8665 - 32.6676i) q^{6} +(90.1287 - 217.590i) q^{7} +(174.139 - 174.139i) q^{8} +(57.2756 - 57.2756i) q^{9} +(140.822 - 339.975i) q^{10} +(79.5662 + 32.9574i) q^{11} +(199.638 + 481.968i) q^{12} -516.438i q^{13} +(-2063.83 + 854.866i) q^{14} +(246.902 + 246.902i) q^{15} -480.997 q^{16} +(-1178.08 + 178.873i) q^{17} -768.281 q^{18} +(-952.328 - 952.328i) q^{19} +(-2077.65 + 860.591i) q^{20} -2119.66i q^{21} +(-312.599 - 754.682i) q^{22} +(827.585 + 342.797i) q^{23} +(848.189 - 2047.71i) q^{24} +(1145.37 - 1145.37i) q^{25} +(-3463.68 + 3463.68i) q^{26} +(278.976 - 673.508i) q^{27} +(12612.4 + 5224.24i) q^{28} +(-1603.87 - 3872.10i) q^{29} -3311.88i q^{30} +(-6871.70 + 2846.35i) q^{31} +(-2346.46 - 2346.46i) q^{32} +775.097 q^{33} +(9100.88 + 6701.52i) q^{34} +9137.36 q^{35} +(3319.94 + 3319.94i) q^{36} +(11965.1 - 4956.10i) q^{37} +12774.3i q^{38} +(-1778.69 - 4294.14i) q^{39} +(8827.20 + 3656.35i) q^{40} +(5618.76 - 13564.9i) q^{41} +(-14216.3 + 14216.3i) q^{42} +(-602.213 + 602.213i) q^{43} +(-1910.35 + 4612.00i) q^{44} +(2903.34 + 1202.60i) q^{45} +(-3251.41 - 7849.60i) q^{46} +537.757i q^{47} +(-3999.45 + 1656.63i) q^{48} +(-27337.9 - 27337.9i) q^{49} -15363.7 q^{50} +(-9179.53 + 5544.78i) q^{51} +29934.9 q^{52} +(11927.2 + 11927.2i) q^{53} +(-6388.19 + 2646.07i) q^{54} +3341.26i q^{55} +(-22195.9 - 53585.7i) q^{56} +(-11198.5 - 4638.57i) q^{57} +(-15212.7 + 36726.6i) q^{58} +(-33790.4 + 33790.4i) q^{59} +(-14311.5 + 14311.5i) q^{60} +(4500.95 - 10866.2i) q^{61} +(65177.7 + 26997.5i) q^{62} +(-7300.43 - 17624.8i) q^{63} +46866.7i q^{64} +(18511.0 - 7667.52i) q^{65} +(-5198.48 - 5198.48i) q^{66} +29231.4 q^{67} +(-10368.2 - 68286.2i) q^{68} +8061.94 q^{69} +(-61283.1 - 61283.1i) q^{70} +(55771.1 - 23101.2i) q^{71} -19947.8i q^{72} +(24157.4 + 58321.1i) q^{73} +(-113488. - 47008.4i) q^{74} +(5578.84 - 13468.5i) q^{75} +(55201.0 - 55201.0i) q^{76} +(14342.4 - 14342.4i) q^{77} +(-16870.8 + 40729.7i) q^{78} +(79649.3 + 32991.8i) q^{79} +(-7141.33 - 17240.7i) q^{80} -6561.00i q^{81} +(-128662. + 53293.7i) q^{82} +(20981.3 + 20981.3i) q^{83} +122864. q^{84} +(-23902.3 - 39570.8i) q^{85} +8077.92 q^{86} +(-26672.2 - 26672.2i) q^{87} +(19594.7 - 8116.40i) q^{88} +134357. i q^{89} +(-11406.6 - 27538.0i) q^{90} +(-112372. - 46545.9i) q^{91} +(-19870.0 + 47970.3i) q^{92} +(-47334.4 + 47334.4i) q^{93} +(3606.67 - 3606.67i) q^{94} +(19995.8 - 48274.1i) q^{95} +(-27592.1 - 11429.0i) q^{96} +(-899.810 - 2172.33i) q^{97} +366703. i q^{98} +(6444.87 - 2669.55i) 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

Introduction

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