LMFDB - Embedded newform 98.7.d.c.19.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [98,7,Mod(19,98)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("98.19"); S:= CuspForms(chi, 7); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(98, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([5])) N = Newforms(chi, 7, names="a")

Level:	$ N $	$=$	$ 98 = 2 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	98.d (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,0,-128,336,0,0,0,756] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(9)] == traces)

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

Self dual:	no
Analytic conductor:	$22.5453001947$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} + 285x^{6} + 282x^{5} + 62091x^{4} + 29260x^{3} + 4838750x^{2} + 2401000x + 294122500 $ x^8 - 2x^7 + 285x^6 + 282x^5 + 62091x^4 + 29260x^3 + 4838750x^2 + 2401000*x + 294122500
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{6}\cdot 3^{2} $
Twist minimal:	no (minimal twist has level 14)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			19.3
Root			$7.51287 - 13.0127i$ of defining polynomial
Character	$\chi$	$=$	98.19
Dual form			98.7.d.c.31.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.82843 - 4.89898i) q^{2} +(-21.8891 + 12.6377i) q^{3} +(-16.0000 - 27.7128i) q^{4} +(10.7486 + 6.20573i) q^{5} +142.979i q^{6} -181.019 q^{8} +(-45.0775 + 78.0766i) q^{9} +(60.8035 - 35.1049i) q^{10} +(774.831 + 1342.05i) q^{11} +(700.452 + 404.406i) q^{12} -2770.09i q^{13} -313.705 q^{15} +(-512.000 + 886.810i) q^{16} +(109.615 - 63.2864i) q^{17} +(254.997 + 441.668i) q^{18} +(1147.81 + 662.687i) q^{19} -397.167i q^{20} +8766.21 q^{22} +(7119.76 - 12331.8i) q^{23} +(3962.35 - 2287.67i) q^{24} +(-7735.48 - 13398.2i) q^{25} +(-13570.6 - 7835.01i) q^{26} -20704.5i q^{27} -7479.03 q^{29} +(-887.290 + 1536.83i) q^{30} +(49241.9 - 28429.8i) q^{31} +(2896.31 + 5016.55i) q^{32} +(-33920.8 - 19584.2i) q^{33} -716.004i q^{34} +2884.96 q^{36} +(45005.7 - 77952.2i) q^{37} +(6492.98 - 3748.72i) q^{38} +(35007.6 + 60634.9i) q^{39} +(-1945.71 - 1123.36i) q^{40} +35783.9i q^{41} -79422.8 q^{43} +(24794.6 - 42945.5i) q^{44} +(-969.044 + 559.478i) q^{45} +(-40275.4 - 69759.1i) q^{46} +(-126334. - 72939.0i) q^{47} -25882.0i q^{48} -87516.9 q^{50} +(-1599.59 + 2770.57i) q^{51} +(-76767.1 + 44321.5i) q^{52} +(85090.3 + 147381. i) q^{53} +(-101431. - 58561.0i) q^{54} +19233.6i q^{55} -33499.3 q^{57} +(-21153.9 + 36639.6i) q^{58} +(187919. - 108495. i) q^{59} +(5019.27 + 8693.64i) q^{60} +(172492. + 99588.5i) q^{61} -321647. i q^{62} +32768.0 q^{64} +(17190.5 - 29774.8i) q^{65} +(-191885. + 110785. i) q^{66} +(-72219.0 - 125087. i) q^{67} +(-3507.69 - 2025.16i) q^{68} +359909. i q^{69} +407591. q^{71} +(8159.90 - 14133.4i) q^{72} +(161733. - 93376.3i) q^{73} +(-254591. - 440964. i) q^{74} +(338646. + 195517. i) q^{75} -42411.9i q^{76} +396066. q^{78} +(-41929.3 + 72623.6i) q^{79} +(-11006.6 + 6354.67i) q^{80} +(228795. + 396285. i) q^{81} +(175305. + 101212. i) q^{82} +162495. i q^{83} +1570.95 q^{85} +(-224642. + 389091. i) q^{86} +(163709. - 94517.7i) q^{87} +(-140259. - 242936. i) q^{88} +(439806. + 253922. i) q^{89} +6329.77i q^{90} -455665. q^{92} +(-718575. + 1.24461e6i) q^{93} +(-714653. + 412605. i) q^{94} +(8224.91 + 14246.0i) q^{95} +(-126795. - 73205.3i) q^{96} -509740. i q^{97} -139710. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 128 q^{4} + 336 q^{5} + 756 q^{9} + 2016 q^{10} - 1356 q^{11} + 27144 q^{15} - 4096 q^{16} + 17304 q^{17} - 6816 q^{18} + 32004 q^{19} + 25248 q^{22} - 4128 q^{23} - 10752 q^{24} + 4664 q^{25} + 4704 q^{26}+ \cdots - 4625928 q^{99}+O(q^{100}) $ 8 * q - 128 * q^4 + 336 * q^5 + 756 * q^9 + 2016 * q^10 - 1356 * q^11 + 27144 * q^15 - 4096 * q^16 + 17304 * q^17 - 6816 * q^18 + 32004 * q^19 + 25248 * q^22 - 4128 * q^23 - 10752 * q^24 + 4664 * q^25 + 4704 * q^26 - 30312 * q^29 + 9648 * q^30 + 3108 * q^31 - 3276 * q^33 - 48384 * q^36 - 6124 * q^37 - 155568 * q^38 + 100764 * q^39 - 64512 * q^40 - 297376 * q^43 - 43392 * q^44 + 172116 * q^45 - 194064 * q^46 - 313908 * q^47 + 38784 * q^50 + 253692 * q^51 - 255360 * q^52 + 278484 * q^53 - 386064 * q^54 - 81288 * q^57 - 169824 * q^58 + 835464 * q^59 - 434304 * q^60 + 995316 * q^61 + 262144 * q^64 + 8316 * q^65 - 1673280 * q^66 + 648808 * q^67 - 553728 * q^68 + 190128 * q^71 - 218112 * q^72 + 1617084 * q^73 - 1158144 * q^74 + 2042208 * q^75 + 1122432 * q^78 + 70096 * q^79 - 344064 * q^80 + 1177920 * q^81 - 66528 * q^82 + 2190984 * q^85 - 573024 * q^86 + 2057076 * q^87 - 403968 * q^88 - 739116 * q^89 + 264192 * q^92 - 23364 * q^93 - 3795120 * q^94 + 725640 * q^95 + 344064 * q^96 - 4625928 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/98\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	2.82843	−	4.89898i	0.353553	−	0.612372i
$2$	2.82843	−	4.89898i	0.353553	−	0.612372i
$3$	−21.8891	+	12.6377i	−0.810708	+	0.468063i	−0.847202	−	0.531271i	$-0.821715\pi$
$3$	−21.8891	+	12.6377i	−0.810708	+	0.468063i	0.0364935	+	0.999334i	$0.488381\pi$
$4$	−16.0000	−	27.7128i	−0.250000	−	0.433013i
$5$	10.7486	+	6.20573i	0.0859892	+	0.0496459i	0.542378	−	0.840135i	$-0.317524\pi$
$5$	10.7486	+	6.20573i	0.0859892	+	0.0496459i	−0.456389	+	0.889780i	$0.650857\pi$
$6$			142.979i			0.661941i
$7$		0			0
$7$		0			0
$8$	−181.019			−0.353553
$9$	−45.0775	+	78.0766i	−0.0618347	+	0.107101i
$10$	60.8035	−	35.1049i	0.0608035	−	0.0351049i
$11$	774.831	+	1342.05i	0.582142	+	1.00830i	0.995225	+	0.0976064i	$0.0311186\pi$
$11$	774.831	+	1342.05i	0.582142	+	1.00830i	−0.413083	+	0.910693i	$0.635548\pi$
$12$	700.452	+	404.406i	0.405354	+	0.234031i
$13$		−	2770.09i		−	1.26085i	−0.776249	−	0.630427i	$-0.782880\pi$
$13$		−	2770.09i		−	1.26085i	0.776249	−	0.630427i	$-0.217120\pi$
$14$		0			0
$15$	−313.705			−0.0929495
$16$	−512.000	+	886.810i	−0.125000	+	0.216506i
$17$	109.615	−	63.2864i	0.0223113	−	0.0128814i	−0.488803	−	0.872394i	$-0.662566\pi$
$17$	109.615	−	63.2864i	0.0223113	−	0.0128814i	0.511114	+	0.859513i	$0.329233\pi$
$18$	254.997	+	441.668i	0.0437238	+	0.0757318i
$19$	1147.81	+	662.687i	0.167343	+	0.0966156i	0.581332	−	0.813666i	$-0.302532\pi$
$19$	1147.81	+	662.687i	0.167343	+	0.0966156i	−0.413989	+	0.910282i	$0.635865\pi$
$20$		−	397.167i		−	0.0496459i
$21$		0			0
$22$	8766.21			0.823273
$23$	7119.76	−	12331.8i	0.585170	−	1.01354i	−0.409685	−	0.912227i	$-0.634361\pi$
$23$	7119.76	−	12331.8i	0.585170	−	1.01354i	0.994854	−	0.101316i	$-0.0323055\pi$
$24$	3962.35	−	2287.67i	0.286629	−	0.165485i
$25$	−7735.48	−	13398.2i	−0.495071	−	0.857487i
$26$	−13570.6	−	7835.01i	−0.772112	−	0.445779i
$27$		−	20704.5i		−	1.05190i
$28$		0			0
$29$	−7479.03			−0.306656			−0.153328	−	0.988175i	$-0.548999\pi$
$29$	−7479.03			−0.306656			−0.153328	+	0.988175i	$0.548999\pi$
$30$	−887.290	+	1536.83i	−0.0328626	+	0.0569197i
$31$	49241.9	−	28429.8i	1.65291	−	0.954309i	0.677046	−	0.735941i	$-0.263260\pi$
$31$	49241.9	−	28429.8i	1.65291	−	0.954309i	0.975866	−	0.218369i	$-0.0700735\pi$
$32$	2896.31	+	5016.55i	0.0883883	+	0.153093i
$33$	−33920.8	−	19584.2i	−0.943895	−	0.544958i
$34$		−	716.004i		−	0.0182171i
$35$		0			0
$36$	2884.96			0.0618347
$37$	45005.7	−	77952.2i	0.888511	−	1.53895i	0.0468752	−	0.998901i	$-0.485074\pi$
$37$	45005.7	−	77952.2i	0.888511	−	1.53895i	0.841636	−	0.540046i	$-0.181593\pi$
$38$	6492.98	−	3748.72i	0.118329	−	0.0683176i
$39$	35007.6	+	60634.9i	0.590158	+	1.02218i
$40$	−1945.71	−	1123.36i	−0.0304018	−	0.0175525i
$41$			35783.9i			0.519202i	0.965716	+	0.259601i	$0.0835910\pi$
$41$			35783.9i			0.519202i	−0.965716	+	0.259601i	$0.916409\pi$
$42$		0			0
$43$	−79422.8			−0.998942			−0.499471	−	0.866331i	$-0.666472\pi$
$43$	−79422.8			−0.998942			−0.499471	+	0.866331i	$0.666472\pi$
$44$	24794.6	−	42945.5i	0.291071	−	0.504150i
$45$	−969.044	+	559.478i	−0.0106342	+	0.00613968i
$46$	−40275.4	−	69759.1i	−0.413777	−	0.716684i
$47$	−126334.	−	72939.0i	−1.21682	−	0.702532i	−0.252585	−	0.967575i	$-0.581281\pi$
$47$	−126334.	−	72939.0i	−1.21682	−	0.702532i	−0.964237	+	0.265043i	$0.914614\pi$
$48$		−	25882.0i		−	0.234031i
$49$		0			0
$50$	−87516.9			−0.700136
$51$	−1599.59	+	2770.57i	−0.0120586	+	0.0208861i
$52$	−76767.1	+	44321.5i	−0.545966	+	0.315213i
$53$	85090.3	+	147381.i	0.571547	+	0.989949i	0.996407	+	0.0846900i	$0.0269900\pi$
$53$	85090.3	+	147381.i	0.571547	+	0.989949i	−0.424860	+	0.905259i	$0.639677\pi$
$54$	−101431.	−	58561.0i	−0.644152	−	0.371901i
$55$			19233.6i			0.115604i
$56$		0			0
$57$	−33499.3			−0.180889
$58$	−21153.9	+	36639.6i	−0.108419	+	0.187788i
$59$	187919.	−	108495.i	0.914989	−	0.528269i	0.0329557	−	0.999457i	$-0.489508\pi$
$59$	187919.	−	108495.i	0.914989	−	0.528269i	0.882033	+	0.471188i	$0.156175\pi$
$60$	5019.27	+	8693.64i	0.0232374	+	0.0402483i
$61$	172492.	+	99588.5i	0.759942	+	0.438753i	0.829275	−	0.558841i	$-0.188754\pi$
$61$	172492.	+	99588.5i	0.759942	+	0.438753i	−0.0693329	+	0.997594i	$0.522087\pi$
$62$		−	321647.i		−	1.34960i
$63$		0			0
$64$	32768.0			0.125000
$65$	17190.5	−	29774.8i	0.0625962	−	0.108420i
$66$	−191885.	+	110785.i	−0.667434	+	0.385343i
$67$	−72219.0	−	125087.i	−0.240119	−	0.415899i	0.720629	−	0.693321i	$-0.243853\pi$
$67$	−72219.0	−	125087.i	−0.240119	−	0.415899i	−0.960748	+	0.277422i	$0.910520\pi$
$68$	−3507.69	−	2025.16i	−0.0111556	−	0.00644071i
$69$			359909.i			1.09558i
$70$		0			0
$71$	407591.			1.13880			0.569402	−	0.822059i	$-0.307175\pi$
$71$	407591.			1.13880			0.569402	+	0.822059i	$0.307175\pi$
$72$	8159.90	−	14133.4i	0.0218619	−	0.0378659i
$73$	161733.	−	93376.3i	0.415747	−	0.240032i	−0.277509	−	0.960723i	$-0.589509\pi$
$73$	161733.	−	93376.3i	0.415747	−	0.240032i	0.693256	+	0.720691i	$0.256176\pi$
$74$	−254591.	−	440964.i	−0.628272	−	1.08820i
$75$	338646.	+	195517.i	0.802716	+	0.463448i
$76$		−	42411.9i		−	0.0966156i
$77$		0			0
$78$	396066.			0.834610
$79$	−41929.3	+	72623.6i	−0.0850425	+	0.147298i	−0.905409	−	0.424540i	$-0.860436\pi$
$79$	−41929.3	+	72623.6i	−0.0850425	+	0.147298i	0.820367	+	0.571838i	$0.193769\pi$
$80$	−11006.6	+	6354.67i	−0.0214973	+	0.0124115i
$81$	228795.	+	396285.i	0.430518	+	0.745679i
$82$	175305.	+	101212.i	0.317945	+	0.183565i
$83$			162495.i			0.284188i	0.989853	+	0.142094i	$0.0453836\pi$
$83$			162495.i			0.284188i	−0.989853	+	0.142094i	$0.954616\pi$
$84$		0			0
$85$	1570.95			0.00255804
$86$	−224642.	+	389091.i	−0.353179	+	0.611724i
$87$	163709.	−	94517.7i	0.248609	−	0.143534i
$88$	−140259.	−	242936.i	−0.205818	−	0.356488i
$89$	439806.	+	253922.i	0.623866	+	0.360189i	0.778373	−	0.627803i	$-0.216046\pi$
$89$	439806.	+	253922.i	0.623866	+	0.360189i	−0.154507	+	0.987992i	$0.549379\pi$
$90$			6329.77i			0.00868281i
$91$		0			0
$92$	−455665.			−0.585170
$93$	−718575.	+	1.24461e6i	−0.893353	+	1.54733i
$94$	−714653.	+	412605.i	−0.860423	+	0.496765i
$95$	8224.91	+	14246.0i	0.00959313	+	0.0166158i
$96$	−126795.	−	73205.3i	−0.143314	−	0.0827426i
$97$		−	509740.i		−	0.558514i	−0.960216	−	0.279257i	$-0.909912\pi$
$97$		−	509740.i		−	0.558514i	0.960216	−	0.279257i	$-0.0900881\pi$
$98$		0			0
$99$	−139710.			−0.143986
$100$	−247535.	+	428744.i	−0.247535	+	0.428744i
$101$	−1.35057e6	+	779754.i	−1.31085	+	0.756821i	−0.982237	−	0.187642i	$-0.939915\pi$
$101$	−1.35057e6	+	779754.i	−1.31085	+	0.756821i	−0.328616	+	0.944464i	$0.606582\pi$
$102$	9048.63	+	15672.7i	0.00852673	+	0.0147687i
$103$	629819.	+	363626.i	0.576374	+	0.332769i	0.759691	−	0.650284i	$-0.225350\pi$
$103$	629819.	+	363626.i	0.576374	+	0.332769i	−0.183317	+	0.983054i	$0.558684\pi$
$104$			501441.i			0.445779i
$105$		0			0
$106$	962686.			0.808290
$107$	874822.	−	1.51524e6i	0.714116	−	1.23688i	−0.249184	−	0.968456i	$-0.580162\pi$
$107$	874822.	−	1.51524e6i	0.714116	−	1.23688i	0.963300	−	0.268428i	$-0.0865043\pi$
$108$	−573779.	+	331271.i	−0.455484	+	0.262974i
$109$	386426.	+	669309.i	0.298392	+	0.516830i	0.975768	−	0.218807i	$-0.0702165\pi$
$109$	386426.	+	669309.i	0.298392	+	0.516830i	−0.677376	+	0.735637i	$0.736883\pi$
$110$	94224.9	+	54400.8i	0.0707926	+	0.0408721i
$111$			2.27508e6i			1.66352i
$112$		0			0
$113$	−2.26586e6			−1.57035			−0.785176	−	0.619273i	$-0.787428\pi$
$113$	−2.26586e6			−1.57035			−0.785176	+	0.619273i	$0.787428\pi$
$114$	−94750.4	+	164112.i	−0.0639538	+	0.110771i
$115$	153056.	−	88366.7i	0.100637	−	0.0581025i
$116$	119665.	+	207265.i	0.0766640	+	0.132786i
$117$	216279.	+	124869.i	0.135039	+	0.0779645i
$118$		−	1.22748e6i		−	0.747085i
$119$		0			0
$120$	56786.6			0.0328626
$121$	−314946.	+	545503.i	−0.177779	+	0.307922i
$122$	975764.	−	563358.i	0.537360	−	0.310245i
$123$	−452226.	−	783278.i	−0.243019	−	0.420921i
$124$	−1.57574e6	−	909755.i	−0.826456	−	0.477155i
$125$		−	385946.i		−	0.197605i
$126$		0			0
$127$	813391.			0.397089			0.198545	−	0.980092i	$-0.436379\pi$
$127$	813391.			0.397089			0.198545	+	0.980092i	$0.436379\pi$
$128$	92681.9	−	160530.i	0.0441942	−	0.0765466i
$129$	1.73850e6	−	1.00372e6i	0.809850	−	0.467567i
$130$	−97244.0	−	168432.i	−0.0442622	−	0.0766643i
$131$	−2.65677e6	−	1.53389e6i	−1.18179	−	0.682307i	−0.225362	−	0.974275i	$-0.572357\pi$
$131$	−2.65677e6	−	1.53389e6i	−1.18179	−	0.682307i	−0.956428	+	0.291968i	$0.905690\pi$
$132$			1.25339e6i			0.544958i
$133$		0			0
$134$	−817064.			−0.339580
$135$	128486.	−	222545.i	0.0522223	−	0.0904516i
$136$	−19842.5	+	11456.1i	−0.00788822	+	0.00455427i
$137$	314000.	+	543865.i	0.122115	+	0.211509i	0.920601	−	0.390503i	$-0.127699\pi$
$137$	314000.	+	543865.i	0.122115	+	0.211509i	−0.798487	+	0.602013i	$0.794366\pi$
$138$	1.76319e6	+	1.01798e6i	0.670906	+	0.387348i
$139$		−	2.79572e6i		−	1.04100i	−0.853863	−	0.520498i	$-0.825746\pi$
$139$		−	2.79572e6i		−	1.04100i	0.853863	−	0.520498i	$-0.174254\pi$
$140$		0			0
$141$	3.68712e6			1.31532
$142$	1.15284e6	−	1.99678e6i	0.402628	−	0.697373i
$143$	3.71760e6	−	2.14636e6i	1.27132	−	0.733996i
$144$	−46159.4	−	79950.4i	−0.0154587	−	0.0267752i
$145$	−80389.5	−	46412.9i	−0.0263691	−	0.0152242i
$146$		−	1.05643e6i		−	0.339456i
$147$		0			0
$148$	−2.88037e6			−0.888511
$149$	2.04538e6	−	3.54271e6i	0.618324	−	1.07097i	−0.371468	−	0.928446i	$-0.621145\pi$
$149$	2.04538e6	−	3.54271e6i	0.618324	−	1.07097i	0.989792	−	0.142522i	$-0.0455212\pi$
$150$	1.91567e6	−	1.10601e6i	0.567606	−	0.327707i
$151$	−819369.	−	1.41919e6i	−0.237985	−	0.412201i	0.722151	−	0.691735i	$-0.243153\pi$
$151$	−819369.	−	1.41919e6i	−0.237985	−	0.412201i	−0.960136	+	0.279534i	$0.909820\pi$
$152$	−207775.	−	119959.i	−0.0591647	−	0.0341588i
$153$			11411.2i			0.00318607i
$154$		0			0
$155$	705712.			0.189510
$156$	1.12024e6	−	1.94032e6i	0.295079	−	0.511092i
$157$	−4.98347e6	+	2.87721e6i	−1.28775	+	0.743485i	−0.978253	−	0.207414i	$-0.933495\pi$
$157$	−4.98347e6	+	2.87721e6i	−1.28775	+	0.743485i	−0.309501	+	0.950899i	$0.600162\pi$
$158$	237188.	+	410821.i	0.0601341	+	0.104155i
$159$	−3.72510e6	−	2.15069e6i	−0.926716	−	0.535040i
$160$			71894.9i			0.0175525i
$161$		0			0
$162$	2.58852e6			0.608845
$163$	−478970.	+	829600.i	−0.110597	+	0.191560i	−0.916011	−	0.401152i	$-0.868610\pi$
$163$	−478970.	+	829600.i	−0.110597	+	0.191560i	0.805414	+	0.592713i	$0.201943\pi$
$164$	991672.	−	572542.i	0.224821	−	0.129800i
$165$	−243068.	−	421006.i	−0.0541098	−	0.0937210i
$166$	796061.	+	459606.i	0.174029	+	0.100476i
$167$		−	6.70923e6i		−	1.44053i	−0.693698	−	0.720266i	$-0.744020\pi$
$167$		−	6.70923e6i		−	1.44053i	0.693698	−	0.720266i	$-0.255980\pi$
$168$		0			0
$169$	−2.84662e6			−0.589751
$170$	4443.33	−	7696.07i	0.000904402	−	0.00156647i
$171$	−103481.	+	59744.5i	−0.0206952	+	0.0119484i
$172$	1.27077e6	+	2.20103e6i	0.249735	+	0.432554i
$173$	300592.	+	173547.i	0.0580550	+	0.0335181i	0.528747	−	0.848780i	$-0.322662\pi$
$173$	300592.	+	173547.i	0.0580550	+	0.0335181i	−0.470692	+	0.882298i	$0.655996\pi$
$174$		−	1.06935e6i		−	0.202988i
$175$		0			0
$176$	−1.58685e6			−0.291071
$177$	−2.74226e6	+	4.74974e6i	−0.494526	+	0.856544i
$178$	2.48792e6	−	1.43640e6i	0.441140	−	0.254692i
$179$	1.47270e6	+	2.55079e6i	0.256777	+	0.444750i	0.965377	−	0.260860i	$-0.0840062\pi$
$179$	1.47270e6	+	2.55079e6i	0.256777	+	0.444750i	−0.708600	+	0.705611i	$0.750673\pi$
$180$	31009.4	+	17903.3i	0.00531712	+	0.00306984i
$181$			2.88805e6i			0.487046i	0.969895	+	0.243523i	$0.0783031\pi$
$181$			2.88805e6i			0.487046i	−0.969895	+	0.243523i	$0.921697\pi$
$182$		0			0
$183$	−5.03428e6			−0.821455
$184$	−1.28881e6	+	2.23229e6i	−0.206889	+	0.358342i
$185$	967502.	−	558587.i	0.152805	−	0.0882218i
$186$	4.06487e6	+	7.04057e6i	0.631696	+	1.09413i
$187$	169867.	+	98072.5i	0.0259767	+	0.0149976i
$188$			4.66810e6i			0.702532i
$189$		0			0
$190$	93054.3			0.0135667
$191$	2.83365e6	−	4.90802e6i	0.406674	−	0.704379i	−0.587841	−	0.808976i	$-0.700022\pi$
$191$	2.83365e6	−	4.90802e6i	0.406674	−	0.704379i	0.994515	+	0.104597i	$0.0333553\pi$
$192$	−717263.	+	414112.i	−0.101339	+	0.0585078i
$193$	−6.54313e6	−	1.13330e7i	−0.910152	−	1.57643i	−0.813848	−	0.581078i	$-0.802631\pi$
$193$	−6.54313e6	−	1.13330e7i	−0.910152	−	1.57643i	−0.0963038	−	0.995352i	$-0.530702\pi$
$194$	−2.49721e6	−	1.44176e6i	−0.342018	−	0.197464i
$195$			868991.i			0.117196i
$196$		0			0
$197$	4.47088e6			0.584783			0.292391	−	0.956299i	$-0.405549\pi$
$197$	4.47088e6			0.584783			0.292391	+	0.956299i	$0.405549\pi$
$198$	−395159.	+	684436.i	−0.0509069	+	0.0881733i
$199$	−6.97809e6	+	4.02880e6i	−0.885477	+	0.511230i	−0.872460	−	0.488685i	$-0.837477\pi$
$199$	−6.97809e6	+	4.02880e6i	−0.885477	+	0.511230i	−0.0130165	+	0.999915i	$0.504143\pi$
$200$	1.40027e6	+	2.42534e6i	0.175034	+	0.303168i
$201$	3.16162e6	+	1.82536e6i	0.389333	+	0.224782i
$202$			8.82191e6i			1.07031i
$203$		0			0
$204$	102374.			0.0120586
$205$	−222065.	+	384628.i	−0.0257762	+	0.0446457i
$206$	3.56279e6	−	2.05698e6i	0.407558	−	0.235304i
$207$	641882.	+	1.11177e6i	0.0723676	+	0.125344i
$208$	2.45655e6	+	1.41829e6i	0.272983	+	0.157607i
$209$			2.05388e6i			0.224976i
$210$		0			0
$211$	421809.			0.0449023			0.0224511	−	0.999748i	$-0.492853\pi$
$211$	421809.			0.0449023			0.0224511	+	0.999748i	$0.492853\pi$
$212$	2.72289e6	−	4.71618e6i	0.285774	−	0.494975i
$213$	−8.92180e6	+	5.15101e6i	−0.923238	+	0.533032i
$214$	−4.94874e6	−	8.57147e6i	−0.504956	−	0.874610i
$215$	−853688.	−	492877.i	−0.0858981	−	0.0495933i
$216$			3.74791e6i			0.371901i
$217$		0			0
$218$	4.37191e6			0.421990
$219$	−2.36012e6	+	4.08785e6i	−0.224700	+	0.389191i
$220$	533017.	−	307737.i	0.0500579	−	0.0289009i
$221$	−175309.	−	303645.i	−0.0162416	−	0.0281312i
$222$	1.11455e7	+	6.43488e6i	1.01869	+	0.588141i
$223$		−	4.49399e6i		−	0.405245i	−0.979257	−	0.202622i	$-0.935054\pi$
$223$		−	4.49399e6i		−	0.405245i	0.979257	−	0.202622i	$-0.0649464\pi$
$224$		0			0
$225$	1.39478e6			0.122450
$226$	−6.40881e6	+	1.11004e7i	−0.555203	+	0.961640i
$227$	3.37074e6	−	1.94610e6i	0.288169	−	0.166375i	−0.348947	−	0.937143i	$-0.613461\pi$
$227$	3.37074e6	−	1.94610e6i	0.288169	−	0.166375i	0.637116	+	0.770768i	$0.280127\pi$
$228$	535989.	+	928360.i	0.0452222	+	0.0783271i
$229$	2.13533e6	+	1.23283e6i	0.177811	+	0.102659i	0.586264	−	0.810120i	$-0.300598\pi$
$229$	2.13533e6	+	1.23283e6i	0.177811	+	0.102659i	−0.408453	+	0.912779i	$0.633932\pi$
$230$		−	999755.i		−	0.0821694i
$231$		0			0
$232$	1.35385e6			0.108419
$233$	−1.13486e7	+	1.96564e7i	−0.897170	+	1.55394i	−0.0660751	+	0.997815i	$0.521048\pi$
$233$	−1.13486e7	+	1.96564e7i	−0.897170	+	1.55394i	−0.831095	+	0.556130i	$0.812286\pi$
$234$	1.22346e6	−	706366.i	0.0954867	−	0.0551293i
$235$	−905280.	−	1.56799e6i	−0.0697556	−	0.120820i
$236$	−6.01342e6	−	3.47185e6i	−0.457494	−	0.264134i
$237$		−	2.11956e6i		−	0.159221i
$238$		0			0
$239$	−3.91448e6			−0.286734			−0.143367	−	0.989670i	$-0.545793\pi$
$239$	−3.91448e6			−0.286734			−0.143367	+	0.989670i	$0.545793\pi$
$240$	160617.	−	278196.i	0.0116187	−	0.0201242i
$241$	−8.50987e6	+	4.91317e6i	−0.607955	+	0.351003i	−0.772165	−	0.635422i	$-0.780826\pi$
$241$	−8.50987e6	+	4.91317e6i	−0.607955	+	0.351003i	0.164209	+	0.986425i	$0.447493\pi$
$242$	1.78161e6	+	3.08583e6i	0.125709	+	0.217734i
$243$	3.05515e6	+	1.76389e6i	0.212919	+	0.122929i
$244$		−	6.37367e6i		−	0.438753i
$245$		0			0
$246$	−5.11635e6			−0.343681
$247$	1.83570e6	−	3.17953e6i	0.121818	−	0.210995i
$248$	−8.91374e6	+	5.14635e6i	−0.584393	+	0.337399i
$249$	−2.05356e6	−	3.55688e6i	−0.133018	−	0.230394i
$250$	−1.89074e6	−	1.09162e6i	−0.121008	−	0.0698638i
$251$			1.12666e7i			0.712477i	0.934395	+	0.356238i	$0.115941\pi$
$251$			1.12666e7i			0.712477i	−0.934395	+	0.356238i	$0.884059\pi$
$252$		0			0
$253$	2.20664e7			1.36261
$254$	2.30062e6	−	3.98479e6i	0.140392	−	0.243167i
$255$	−34386.8	+	19853.2i	−0.00207382	+	0.00119732i
$256$	−524288.	−	908093.i	−0.0312500	−	0.0541266i
$257$	2.70095e7	+	1.55940e7i	1.59117	+	0.918665i	0.993106	+	0.117219i	$0.0373979\pi$
$257$	2.70095e7	+	1.55940e7i	1.59117	+	0.918665i	0.598067	+	0.801446i	$0.295935\pi$
$258$		−	1.13558e7i		−	0.661240i
$259$		0			0
$260$	−1.10019e6			−0.0625962
$261$	337136.	−	583937.i	0.0189620	−	0.0328431i
$262$	−1.50290e7	+	8.67698e6i	−0.835652	+	0.482464i
$263$	6.75928e6	+	1.17074e7i	0.371564	+	0.643567i	0.989806	−	0.142420i	$-0.0454884\pi$
$263$	6.75928e6	+	1.17074e7i	0.371564	+	0.643567i	−0.618243	+	0.785987i	$0.712155\pi$
$264$	6.14031e6	+	3.54511e6i	0.333717	+	0.192672i
$265$			2.11219e6i			0.113500i
$266$		0			0
$267$	−1.28360e7			−0.674364
$268$	−2.31101e6	+	4.00278e6i	−0.120060	+	0.207949i
$269$	2.25818e7	−	1.30376e7i	1.16011	−	0.669792i	0.208783	−	0.977962i	$-0.433050\pi$
$269$	2.25818e7	−	1.30376e7i	1.16011	−	0.669792i	0.951331	+	0.308170i	$0.0997164\pi$
$270$	−726828.	−	1.25890e6i	−0.0369267	−	0.0639589i
$271$	−9.56566e6	−	5.52274e6i	−0.480626	−	0.277490i	0.240051	−	0.970760i	$-0.422836\pi$
$271$	−9.56566e6	−	5.52274e6i	−0.480626	−	0.277490i	−0.720677	+	0.693271i	$0.756169\pi$
$272$			129611.i			0.00644071i
$273$		0			0
$274$	3.55251e6			0.172696
$275$	1.19874e7	−	2.07627e7i	0.576403	−	0.998359i
$276$	9.97410e6	−	5.75855e6i	0.474402	−	0.273896i
$277$	7.97353e6	+	1.38106e7i	0.375155	+	0.649788i	0.990350	−	0.138587i	$-0.0442560\pi$
$277$	7.97353e6	+	1.38106e7i	0.375155	+	0.649788i	−0.615195	+	0.788375i	$0.710923\pi$
$278$	−1.36962e7	−	7.90748e6i	−0.637477	−	0.368047i
$279$			5.12618e6i			0.236038i
$280$		0			0
$281$	−1.25628e6			−0.0566198			−0.0283099	−	0.999599i	$-0.509013\pi$
$281$	−1.25628e6			−0.0566198			−0.0283099	+	0.999599i	$0.509013\pi$
$282$	1.04288e7	−	1.80631e7i	0.465034	−	0.805463i
$283$	−292144.	+	168669.i	−0.0128896	+	0.00744179i	−0.506431	−	0.862281i	$-0.669035\pi$
$283$	−292144.	+	168669.i	−0.0128896	+	0.00744179i	0.493541	+	0.869722i	$0.335702\pi$
$284$	−6.52145e6	−	1.12955e7i	−0.284701	−	0.493117i
$285$	−360072.	−	207888.i	−0.0155545	−	0.00898037i
$286$		−	2.42832e7i		−	1.03803i
$287$		0			0
$288$	−522234.			−0.0218619
$289$	−1.20608e7	+	2.08899e7i	−0.499668	+	0.865451i
$290$	−454751.	+	262551.i	−0.0186458	+	0.0107651i
$291$	6.44194e6	+	1.11578e7i	0.261419	+	0.452792i
$292$	−5.17544e6	−	2.98804e6i	−0.207873	−	0.120016i
$293$			1.30355e7i			0.518233i	0.965846	+	0.259117i	$0.0834314\pi$
$293$			1.30355e7i			0.518233i	−0.965846	+	0.259117i	$0.916569\pi$
$294$		0			0
$295$	2.69317e6			0.104905
$296$	−8.14691e6	+	1.41109e7i	−0.314136	+	0.544100i
$297$	2.77864e7	−	1.60425e7i	1.06063	−	0.612353i
$298$	−1.15704e7	−	2.00406e7i	−0.437221	−	0.757289i
$299$	−3.41602e7	−	1.97224e7i	−1.27793	−	0.737813i
$300$		−	1.25131e7i		−	0.463448i
$301$		0			0
$302$	−9.27010e6			−0.336561
$303$	1.97086e7	−	3.41363e7i	0.708480	−	1.22712i
$304$	−1.17535e6	+	678591.i	−0.0418358	+	0.0241539i
$305$	1.23604e6	+	2.14088e6i	0.0435645	+	0.0754560i
$306$	55903.1	+	32275.7i	0.00195106	+	0.00112645i
$307$		−	3.48621e7i		−	1.20487i	−0.798170	−	0.602433i	$-0.794198\pi$
$307$		−	3.48621e7i		−	1.20487i	0.798170	−	0.602433i	$-0.205802\pi$
$308$		0			0
$309$	−1.83816e7			−0.623028
$310$	1.99605e6	−	3.45727e6i	0.0670019	−	0.116051i
$311$	3.81969e7	−	2.20530e7i	1.26983	−	0.733139i	0.294877	−	0.955535i	$-0.404721\pi$
$311$	3.81969e7	−	2.20530e7i	1.26983	−	0.733139i	0.974956	+	0.222397i	$0.0713880\pi$
$312$	−6.33705e6	−	1.09761e7i	−0.208652	−	0.361397i
$313$	−3.77077e7	−	2.17706e7i	−1.22970	−	0.709965i	−0.262729	−	0.964870i	$-0.584623\pi$
$313$	−3.77077e7	−	2.17706e7i	−1.22970	−	0.709965i	−0.966966	+	0.254905i	$0.917956\pi$
$314$			3.25519e7i			1.05145i
$315$		0			0
$316$	2.68347e6			0.0850425
$317$	1.63697e7	−	2.83531e7i	0.513880	−	0.890067i	−0.485990	−	0.873964i	$-0.661541\pi$
$317$	1.63697e7	−	2.83531e7i	0.513880	−	0.890067i	0.999870	−	0.0161023i	$-0.00512574\pi$
$318$	−2.10724e7	+	1.21661e7i	−0.655287	+	0.378330i
$319$	−5.79499e6	−	1.00372e7i	−0.178517	−	0.309201i
$320$	352212.	+	203349.i	0.0107486	+	0.00620573i
$321$			4.42229e7i			1.33700i
$322$		0			0
$323$	167756.			0.00497818
$324$	7.32144e6	−	1.26811e7i	0.215259	−	0.372840i
$325$	−3.71144e7	+	2.14280e7i	−1.08117	+	0.624211i
$326$	2.70946e6	+	4.69293e6i	0.0782042	+	0.135454i
$327$	−1.69170e7	−	9.76706e6i	−0.483817	−	0.279332i
$328$		−	6.47758e6i		−	0.183565i
$329$		0			0
$330$	−2.75000e6			−0.0765228
$331$	1.58127e7	−	2.73884e7i	0.436036	−	0.755236i	−0.561344	−	0.827583i	$-0.689715\pi$
$331$	1.58127e7	−	2.73884e7i	0.436036	−	0.755236i	0.997380	+	0.0723465i	$0.0230487\pi$
$332$	4.50320e6	−	2.59992e6i	0.123057	−	0.0710471i
$333$	4.05750e6	+	7.02779e6i	0.109882	+	0.190321i
$334$	−3.28684e7	−	1.89766e7i	−0.882143	−	0.509305i
$335$		−	1.79269e6i		−	0.0476837i
$336$		0			0
$337$	−8.23591e6			−0.215190			−0.107595	−	0.994195i	$-0.534315\pi$
$337$	−8.23591e6			−0.215190			−0.107595	+	0.994195i	$0.534315\pi$
$338$	−8.05145e6	+	1.39455e7i	−0.208509	+	0.361147i
$339$	4.95976e7	−	2.86352e7i	1.27310	−	0.735023i
$340$	−25135.3	−	43535.5i	−0.000639509	−	0.00110766i
$341$	7.63083e7	+	4.40566e7i	1.92446	+	1.11109i
$342$			675932.i			0.0168976i
$343$		0			0
$344$	1.43771e7			0.353179
$345$	−2.23350e6	+	3.86854e6i	−0.0543912	+	0.0942084i
$346$	1.70041e6	−	981731.i	0.0410511	−	0.0237009i
$347$	3.12505e7	+	5.41274e7i	0.747943	+	1.29547i	0.948807	+	0.315856i	$0.102292\pi$
$347$	3.12505e7	+	5.41274e7i	0.747943	+	1.29547i	−0.200864	+	0.979619i	$0.564375\pi$
$348$	−5.23870e6	−	3.02457e6i	−0.124304	−	0.0717671i
$349$		−	2.49010e7i		−	0.585788i	−0.956145	−	0.292894i	$-0.905382\pi$
$349$		−	2.49010e7i		−	0.585788i	0.956145	−	0.292894i	$-0.0946183\pi$
$350$		0			0
$351$	−5.73533e7			−1.32629
$352$	−4.48830e6	+	7.77397e6i	−0.102909	+	0.178244i
$353$	−5.99767e7	+	3.46276e7i	−1.36351	+	0.787224i	−0.990089	−	0.140438i	$-0.955149\pi$
$353$	−5.99767e7	+	3.46276e7i	−1.36351	+	0.787224i	−0.373422	+	0.927662i	$0.621816\pi$
$354$	1.55126e7	+	2.68686e7i	0.349683	+	0.605668i
$355$	4.38105e6	+	2.52940e6i	0.0979249	+	0.0565369i
$356$		−	1.62510e7i		−	0.360189i
$357$		0			0
$358$	1.66617e7			0.363137
$359$	−1.50466e7	+	2.60615e7i	−0.325204	+	0.563270i	−0.981554	−	0.191187i	$-0.938766\pi$
$359$	−1.50466e7	+	2.60615e7i	−0.325204	+	0.563270i	0.656350	+	0.754457i	$0.272100\pi$
$360$	175416.	−	101276.i	0.00375977	−	0.00217070i
$361$	−2.26446e7	−	3.92217e7i	−0.481331	−	0.833689i
$362$	1.41485e7	+	8.16865e6i	0.298253	+	0.172197i
$363$		−	1.59208e7i		−	0.332847i
$364$		0			0
$365$	2.31787e6			0.0476663
$366$	−1.42391e7	+	2.46628e7i	−0.290428	+	0.503036i
$367$	1.83705e7	−	1.06062e7i	0.371640	−	0.214566i	−0.302535	−	0.953138i	$-0.597833\pi$
$367$	1.83705e7	−	1.06062e7i	0.371640	−	0.214566i	0.674175	+	0.738572i	$0.264500\pi$
$368$	7.29063e6	+	1.26277e7i	0.146292	+	0.253386i
$369$	−2.79388e6	−	1.61305e6i	−0.0556070	−	0.0321047i
$370$		−	6.31969e6i		−	0.124764i
$371$		0			0
$372$	4.59888e7			0.893353
$373$	−2.44206e7	+	4.22977e7i	−0.470575	+	0.815060i	−0.999434	−	0.0336496i	$-0.989287\pi$
$373$	−2.44206e7	+	4.22977e7i	−0.470575	+	0.815060i	0.528858	+	0.848710i	$0.322620\pi$
$374$	960911.	−	554782.i	0.0183683	−	0.0106049i
$375$	4.87747e6	+	8.44803e6i	0.0924913	+	0.160200i
$376$	2.28689e7	+	1.32034e7i	0.430211	+	0.248383i
$377$			2.07176e7i			0.386648i
$378$		0			0
$379$	8.40563e6			0.154402			0.0772009	−	0.997016i	$-0.475402\pi$
$379$	8.40563e6			0.154402			0.0772009	+	0.997016i	$0.475402\pi$
$380$	263197.	−	455871.i	0.00479657	−	0.00830790i
$381$	−1.78044e7	+	1.02794e7i	−0.321924	+	0.185863i
$382$	−1.60295e7	−	2.77640e7i	−0.287562	−	0.498071i
$383$	−1.47384e7	−	8.50922e6i	−0.262334	−	0.151458i	0.363065	−	0.931764i	$-0.381730\pi$
$383$	−1.47384e7	−	8.50922e6i	−0.262334	−	0.151458i	−0.625399	+	0.780305i	$0.715064\pi$
$384$			4.68514e6i			0.0827426i
$385$		0			0
$386$	−7.40271e7			−1.28715
$387$	3.58019e6	−	6.20106e6i	0.0617693	−	0.106988i
$388$	−1.41263e7	+	8.15585e6i	−0.241844	+	0.139628i
$389$	−2.99145e6	−	5.18135e6i	−0.0508199	−	0.0880226i	0.839496	−	0.543365i	$-0.182850\pi$
$389$	−2.99145e6	−	5.18135e6i	−0.0508199	−	0.0880226i	−0.890316	+	0.455343i	$0.849517\pi$
$390$	4.25717e6	+	2.45788e6i	0.0717674	+	0.0414349i
$391$		−	1.80234e6i		−	0.0301513i
$392$		0			0
$393$	7.75392e7			1.27745
$394$	1.26456e7	−	2.19028e7i	0.206752	−	0.358105i
$395$	−901366.	+	520404.i	−0.0146255	+	0.00844402i
$396$	2.23536e6	+	3.87175e6i	0.0359966	+	0.0623479i
$397$	9.15067e7	+	5.28314e7i	1.46245	+	0.844346i	0.999124	−	0.0418414i	$-0.0133224\pi$
$397$	9.15067e7	+	5.28314e7i	1.46245	+	0.844346i	0.463326	+	0.886188i	$0.346656\pi$
$398$			4.55807e7i			0.722989i
$399$		0			0
$400$	1.58423e7			0.247535
$401$	−3.06343e7	+	5.30601e7i	−0.475089	+	0.822877i	−0.999593	−	0.0285303i	$-0.990917\pi$
$401$	−3.06343e7	+	5.30601e7i	−0.475089	+	0.822877i	0.524504	+	0.851408i	$0.324251\pi$
$402$	1.78848e7	−	1.03258e7i	0.275300	−	0.158945i
$403$	−7.87533e7	−	1.36405e8i	−1.20324	−	2.08408i
$404$	4.32183e7	+	2.49521e7i	0.655427	+	0.378411i
$405$			5.67936e6i			0.0854938i
$406$		0			0
$407$	1.39487e8			2.06896
$408$	289556.	−	501526.i	0.00426336	−	0.00738436i
$409$	−9.47417e7	+	5.46991e7i	−1.38475	+	0.799486i	−0.992717	−	0.120466i	$-0.961561\pi$
$409$	−9.47417e7	+	5.46991e7i	−1.38475	+	0.799486i	−0.392032	+	0.919951i	$0.628228\pi$
$410$	1.25619e6	+	2.17579e6i	0.0182265	+	0.0315693i
$411$	−1.37464e7	−	7.93648e6i	−0.197999	−	0.114315i
$412$		−	2.32721e7i		−	0.332769i
$413$		0			0
$414$	7.26207e6			0.102343
$415$	−1.00840e6	+	1.74660e6i	−0.0141088	+	0.0244371i
$416$	1.38963e7	−	8.02305e6i	0.193028	−	0.111445i
$417$	3.53314e7	+	6.11958e7i	0.487251	+	0.843943i
$418$	1.00619e7	+	5.80925e6i	0.137769	+	0.0795411i
$419$		−	2.04457e7i		−	0.277946i	−0.990296	−	0.138973i	$-0.955620\pi$
$419$		−	2.04457e7i		−	0.277946i	0.990296	−	0.138973i	$-0.0443802\pi$
$420$		0			0
$421$	−3.19255e7			−0.427850			−0.213925	−	0.976850i	$-0.568625\pi$
$421$	−3.19255e7			−0.427850			−0.213925	+	0.976850i	$0.568625\pi$
$422$	1.19306e6	−	2.06643e6i	0.0158754	−	0.0274969i
$423$	1.13897e7	−	6.57582e6i	0.150484	−	0.0868818i
$424$	−1.54030e7	−	2.66787e7i	−0.202073	−	0.350000i
$425$	−1.69585e6	−	979101.i	−0.0220913	−	0.0127544i
$426$			5.82770e7i			0.753821i
$427$		0			0
$428$	−5.59886e7			−0.714116
$429$	−5.42500e7	+	9.39637e7i	−0.687112	+	1.19011i
$430$	−4.82919e6	+	2.78813e6i	−0.0607392	+	0.0350678i
$431$	−155642.	−	269579.i	−0.00194399	−	0.00336709i	0.865052	−	0.501683i	$-0.167285\pi$
$431$	−155642.	−	269579.i	−0.00194399	−	0.00336709i	−0.866996	+	0.498316i	$0.833952\pi$
$432$	1.83609e7	+	1.06007e7i	0.227742	+	0.131487i
$433$		−	5.06252e7i		−	0.623596i	−0.950148	−	0.311798i	$-0.899069\pi$
$433$		−	5.06252e7i		−	0.623596i	0.950148	−	0.311798i	$-0.100931\pi$
$434$		0			0
$435$	2.34621e6			0.0285035
$436$	1.23656e7	−	2.14179e7i	0.149196	−	0.258415i
$437$	1.63442e7	−	9.43634e6i	0.195848	−	0.113073i
$438$	1.33509e7	+	2.31244e7i	0.158887	+	0.275200i
$439$	−7.01109e7	−	4.04786e7i	−0.828690	−	0.478445i	0.0247137	−	0.999695i	$-0.492133\pi$
$439$	−7.01109e7	−	4.04786e7i	−0.828690	−	0.478445i	−0.853404	+	0.521250i	$0.825466\pi$
$440$		−	3.48165e6i		−	0.0408721i
$441$		0			0
$442$	−1.98340e6			−0.0229691
$443$	1.28372e6	−	2.22346e6i	0.0147658	−	0.0255752i	−0.858548	−	0.512733i	$-0.828633\pi$
$443$	1.28372e6	−	2.22346e6i	0.0147658	−	0.0255752i	0.873314	+	0.487158i	$0.161966\pi$
$444$	6.30487e7	−	3.64012e7i	0.720323	−	0.415879i
$445$	3.15155e6	+	5.45864e6i	0.0357638	+	0.0619447i
$446$	−2.20160e7	−	1.27109e7i	−0.248161	−	0.143276i
$447$			1.03396e8i			1.15766i
$448$		0			0
$449$	−6.11330e7			−0.675362			−0.337681	−	0.941261i	$-0.609643\pi$
$449$	−6.11330e7			−0.675362			−0.337681	+	0.941261i	$0.609643\pi$
$450$	3.94505e6	−	6.83302e6i	0.0432927	−	0.0749851i
$451$	−4.80237e7	+	2.77265e7i	−0.523511	+	0.302249i
$452$	3.62537e7	+	6.27932e7i	0.392588	+	0.679982i
$453$	3.58705e7	+	2.07099e7i	0.385872	+	0.222783i
$454$		−	2.20176e7i		−	0.235289i
$455$		0			0
$456$	6.06402e6			0.0639538
$457$	−4.79859e6	+	8.31141e6i	−0.0502765	+	0.0870815i	−0.890068	−	0.455827i	$-0.849344\pi$
$457$	−4.79859e6	+	8.31141e6i	−0.0502765	+	0.0870815i	0.839792	+	0.542908i	$0.182677\pi$
$458$	1.20792e7	−	6.97395e6i	0.125731	−	0.0725910i
$459$	−1.31031e6	−	2.26952e6i	−0.0135499	−	0.0234691i
$460$	−4.89778e6	−	2.82773e6i	−0.0503183	−	0.0290513i
$461$			6.04509e7i			0.617021i	0.951221	+	0.308510i	$0.0998304\pi$
$461$			6.04509e7i			0.617021i	−0.951221	+	0.308510i	$0.900170\pi$
$462$		0			0
$463$	−1.14757e8			−1.15621			−0.578104	−	0.815963i	$-0.696207\pi$
$463$	−1.14757e8			−1.15621			−0.578104	+	0.815963i	$0.696207\pi$
$464$	3.82926e6	−	6.63248e6i	0.0383320	−	0.0663930i
$465$	−1.54474e7	+	8.91857e6i	−0.153637	+	0.0887026i
$466$	6.41974e7	+	1.11193e8i	0.634395	+	1.09880i
$467$	5.93604e7	+	3.42717e7i	0.582836	+	0.336500i	0.762259	−	0.647272i	$-0.224090\pi$
$467$	5.93604e7	+	3.42717e7i	0.582836	+	0.336500i	−0.179424	+	0.983772i	$0.557423\pi$
$468$		−	7.99162e6i		−	0.0779645i
$469$		0			0
$470$	−1.02421e7			−0.0986493
$471$	7.27226e7	−	1.25959e8i	0.695995	−	1.20550i
$472$	−3.40171e7	+	1.96398e7i	−0.323497	+	0.186771i
$473$	−6.15393e7	−	1.06589e8i	−0.581526	−	1.00723i
$474$	−1.03837e7	−	5.99501e6i	−0.0975025	−	0.0562931i
$475$		−	2.05048e7i		−	0.191326i
$476$		0			0
$477$	−1.53426e7			−0.141366
$478$	−1.10718e7	+	1.91769e7i	−0.101376	+	0.175588i
$479$	−8.46880e7	+	4.88946e7i	−0.770576	+	0.444892i	−0.833080	−	0.553153i	$-0.813425\pi$
$479$	−8.46880e7	+	4.88946e7i	−0.770576	+	0.444892i	0.0625041	+	0.998045i	$0.480091\pi$
$480$	−908585.	−	1.57372e6i	−0.00821565	−	0.0142299i
$481$	−2.15935e8	−	1.24670e8i	−1.94039	−	1.12028i
$482$			5.55862e7i			0.496393i
$483$		0			0
$484$	2.01566e7			0.177779
$485$	3.16331e6	−	5.47902e6i	0.0277279	−	0.0480261i
$486$	1.72826e7	−	9.97809e6i	0.150556	−	0.0869237i
$487$	−1.14091e7	−	1.97612e7i	−0.0987794	−	0.171091i	0.812400	−	0.583100i	$-0.198160\pi$
$487$	−1.14091e7	−	1.97612e7i	−0.0987794	−	0.171091i	−0.911180	+	0.412009i	$0.864827\pi$
$488$	−3.12245e7	−	1.80275e7i	−0.268680	−	0.155123i
$489$		−	2.42123e7i		−	0.207066i
$490$		0			0
$491$	1.11615e7			0.0942930			0.0471465	−	0.998888i	$-0.484987\pi$
$491$	1.11615e7			0.0942930			0.0471465	+	0.998888i	$0.484987\pi$
$492$	−1.44712e7	+	2.50649e7i	−0.121509	+	0.210461i
$493$	−819816.	+	473321.i	−0.00684188	+	0.00395016i
$494$	−1.03843e7	−	1.79862e7i	−0.0861384	−	0.149196i
$495$	−1.50169e6	−	867002.i	−0.0123813	−	0.00714833i
$496$			5.82243e7i			0.477155i
$497$		0			0
$498$	−2.32334e7			−0.188116
$499$	2.16628e7	−	3.75211e7i	0.174347	−	0.301977i	−0.765588	−	0.643331i	$-0.777552\pi$
$499$	2.16628e7	−	3.75211e7i	0.174347	−	0.301977i	0.939935	+	0.341354i	$0.110885\pi$
$500$	−1.06957e7	+	6.17514e6i	−0.0855653	+	0.0494011i
$501$	8.47892e7	+	1.46859e8i	0.674260	+	1.16785i
$502$	5.51947e7	+	3.18667e7i	0.436301	+	0.251899i
$503$		−	2.32014e8i		−	1.82310i	−0.411192	−	0.911549i	$-0.634887\pi$
$503$		−	2.32014e8i		−	1.82310i	0.411192	−	0.911549i	$-0.365113\pi$
$504$		0			0
$505$	−1.93558e7			−0.150292
$506$	6.24133e7	−	1.08103e8i	0.481755	−	0.834424i
$507$	6.23100e7	−	3.59747e7i	0.478116	−	0.276041i
$508$	−1.30143e7	−	2.25414e7i	−0.0992723	−	0.171945i
$509$	1.02119e8	+	5.89587e7i	0.774382	+	0.447089i	0.834435	−	0.551106i	$-0.185794\pi$
$509$	1.02119e8	+	5.89587e7i	0.774382	+	0.447089i	−0.0600538	+	0.998195i	$0.519127\pi$
$510$			224614.i			0.00169327i
$511$		0			0
$512$	−5.93164e6			−0.0441942
$513$	1.37206e7	−	2.37647e7i	0.101630	−	0.176028i
$514$	1.52789e8	−	8.82127e7i	1.12513	−	0.649594i
$515$	4.51313e6	+	7.81698e6i	0.0330412	+	0.0572291i
$516$	−5.56319e7	−	3.21191e7i	−0.404925	−	0.233784i
$517$		−	2.26062e8i		−	1.63589i
$518$		0			0
$519$	−8.77294e6			−0.0627542
$520$	−3.11181e6	+	5.38981e6i	−0.0221311	+	0.0383322i
$521$	1.94107e8	−	1.12068e8i	1.37255	−	0.792443i	0.381303	−	0.924450i	$-0.375475\pi$
$521$	1.94107e8	−	1.12068e8i	1.37255	−	0.792443i	0.991249	+	0.132007i	$0.0421422\pi$
$522$	−1.90713e6	−	3.30325e6i	−0.0134082	−	0.0232236i
$523$	−1.57711e8	−	9.10546e7i	−1.10245	−	0.636497i	−0.165584	−	0.986196i	$-0.552951\pi$
$523$	−1.57711e8	−	9.10546e7i	−1.10245	−	0.636497i	−0.936862	+	0.349698i	$0.886284\pi$
$524$			9.81688e7i			0.682307i
$525$		0			0
$526$	7.64725e7			0.525470
$527$	3.59844e6	−	6.23268e6i	0.0245857	−	0.0425837i
$528$	3.47348e7	−	2.00542e7i	0.235974	−	0.136239i
$529$	−2.73640e7	−	4.73959e7i	−0.184847	−	0.320165i
$530$	1.03476e7	+	5.97417e6i	0.0695042	+	0.0401283i
$531$			1.95628e7i			0.130661i
$532$		0			0
$533$	9.91248e7			0.654637
$534$	−3.63056e7	+	6.28831e7i	−0.238424	+	0.412962i
$535$	1.88063e7	−	1.08578e7i	0.122812	−	0.0709058i
$536$	1.30730e7	+	2.26432e7i	0.0848950	+	0.147042i
$537$	−6.44723e7	−	3.72231e7i	−0.416342	−	0.240375i
$538$		−	1.47503e8i		−	0.947229i
$539$		0			0
$540$	−8.22312e6			−0.0522223
$541$	1.22675e8	−	2.12480e8i	0.774756	−	1.34192i	−0.160176	−	0.987089i	$-0.551206\pi$
$541$	1.22675e8	−	2.12480e8i	0.774756	−	1.34192i	0.934932	−	0.354828i	$-0.115461\pi$
$542$	−5.41116e7	+	3.12413e7i	−0.339854	+	0.196215i
$543$	−3.64983e7	−	6.32170e7i	−0.227968	−	0.394852i
$544$	634959.	+	366594.i	0.00394411	+	0.00227713i
$545$			9.59222e6i			0.0592556i
$546$		0			0
$547$	1.02069e8			0.623637			0.311819	−	0.950142i	$-0.399062\pi$
$547$	1.02069e8			0.623637			0.311819	+	0.950142i	$0.399062\pi$
$548$	1.00480e7	−	1.74037e7i	0.0610574	−	0.105755i
$549$	−1.55511e7	+	8.97841e6i	−0.0939816	+	0.0542603i
$550$	−6.78109e7	−	1.17452e8i	−0.407578	−	0.705947i
$551$	−8.58449e6	−	4.95625e6i	−0.0513168	−	0.0296278i
$552$		−	6.51505e7i		−	0.387348i
$553$		0			0
$554$	9.02102e7			0.530550
$555$	−1.41185e7	+	2.44540e7i	−0.0825866	+	0.143044i
$556$	−7.74772e7	+	4.47315e7i	−0.450764	+	0.260249i
$557$	−9.57059e7	−	1.65768e8i	−0.553826	−	0.959255i	−0.997994	−	0.0633110i	$-0.979834\pi$
$557$	−9.57059e7	−	1.65768e8i	−0.553826	−	0.959255i	0.444168	−	0.895944i	$-0.353499\pi$
$558$	2.51131e7	+	1.44990e7i	0.144543	+	0.0834520i
$559$			2.20009e8i			1.25952i
$560$		0			0
$561$	−4.95764e6			−0.0280793
$562$	−3.55330e6	+	6.15450e6i	−0.0200181	+	0.0346724i
$563$	1.66748e8	−	9.62718e7i	0.934403	−	0.539478i	0.0462018	−	0.998932i	$-0.485288\pi$
$563$	1.66748e8	−	9.62718e7i	0.934403	−	0.539478i	0.888202	+	0.459454i	$0.151955\pi$
$564$	−5.89939e7	−	1.02181e8i	−0.328829	−	0.569549i
$565$	−2.43549e7	−	1.40613e7i	−0.135033	−	0.0779615i
$566$			1.90828e6i			0.0105243i
$567$		0			0
$568$	−7.37818e7			−0.402628
$569$	2.99208e7	−	5.18243e7i	0.162419	−	0.281317i	−0.773317	−	0.634020i	$-0.781404\pi$
$569$	2.99208e7	−	5.18243e7i	0.162419	−	0.281317i	0.935736	+	0.352702i	$0.114737\pi$
$570$	−2.03688e6	+	1.17599e6i	−0.0109987	+	0.00635008i
$571$	1.27846e8	+	2.21435e8i	0.686716	+	1.18943i	0.972894	+	0.231251i	$0.0742819\pi$
$571$	1.27846e8	+	2.21435e8i	0.686716	+	1.18943i	−0.286178	+	0.958177i	$0.592385\pi$
$572$	−1.18963e8	−	6.86834e7i	−0.635659	−	0.366998i
$573$			1.43243e8i			0.761395i
$574$		0			0
$575$	−2.20299e8			−1.15880
$576$	−1.47710e6	+	2.55841e6i	−0.00772934	+	0.0133876i
$577$	2.79824e7	−	1.61556e7i	0.145666	−	0.0841001i	−0.425396	−	0.905007i	$-0.639865\pi$
$577$	2.79824e7	−	1.61556e7i	0.145666	−	0.0841001i	0.571061	+	0.820907i	$0.306532\pi$
$578$	6.82260e7	+	1.18171e8i	0.353319	+	0.611966i
$579$	2.86447e8	+	1.65380e8i	1.47574	+	0.852016i
$580$			2.97042e6i			0.0152242i
$581$		0			0
$582$	7.28822e7			0.369703
$583$	−1.31861e8	+	2.28390e8i	−0.665444	+	1.15258i
$584$	−2.92767e7	+	1.69029e7i	−0.146989	+	0.0848640i
$585$	1.54981e6	+	2.68435e6i	0.00774123	+	0.0134082i
$586$	6.38607e7	+	3.68700e7i	0.317352	+	0.183223i
$587$		−	9.56070e7i		−	0.472689i	−0.971669	−	0.236344i	$-0.924051\pi$
$587$		−	9.56070e7i		−	0.472689i	0.971669	−	0.236344i	$-0.0759493\pi$
$588$		0			0
$589$	7.53603e7			0.368805
$590$	7.61744e6	−	1.31938e7i	0.0370897	−	0.0642412i
$591$	−9.78637e7	+	5.65016e7i	−0.474088	+	0.273715i
$592$	4.60859e7	+	7.98231e7i	0.222128	+	0.384737i
$593$	1.00699e8	+	5.81386e7i	0.482905	+	0.278805i	0.721626	−	0.692283i	$-0.243395\pi$
$593$	1.00699e8	+	5.81386e7i	0.482905	+	0.278805i	−0.238722	+	0.971088i	$0.576728\pi$
$594$		−	1.81500e8i		−	0.865997i
$595$		0			0
$596$	−1.30905e8			−0.618324
$597$	1.01829e8	−	1.76374e8i	0.478576	−	0.828917i
$598$	−1.93239e8	+	1.11567e8i	−0.903633	+	0.521713i
$599$	1.79992e8	+	3.11756e8i	0.837477	+	1.45055i	0.891997	+	0.452041i	$0.149304\pi$
$599$	1.79992e8	+	3.11756e8i	0.837477	+	1.45055i	−0.0545197	+	0.998513i	$0.517363\pi$
$600$	−6.13014e7	−	3.53924e7i	−0.283803	−	0.163854i
$601$			3.47560e8i			1.60105i	0.599297	+	0.800527i	$0.295447\pi$
$601$			3.47560e8i			1.60105i	−0.599297	+	0.800527i	$0.704553\pi$
$602$		0			0
$603$	1.30218e7			0.0593908
$604$	−2.62198e7	+	4.54140e7i	−0.118992	+	0.206101i
$605$	−6.77049e6	+	3.90895e6i	−0.0305741	+	0.0176520i
$606$	−1.11489e8	−	1.93104e8i	−0.500971	−	0.867707i
$607$	1.84155e8	+	1.06322e8i	0.823414	+	0.475398i	0.851592	−	0.524205i	$-0.175637\pi$
$607$	1.84155e8	+	1.06322e8i	0.823414	+	0.475398i	−0.0281785	+	0.999603i	$0.508971\pi$
$608$			7.67738e6i			0.0341588i
$609$		0			0
$610$	1.39842e7			0.0616095
$611$	−2.02048e8	+	3.49957e8i	−0.885790	+	1.53423i
$612$	316236.	−	182579.i	0.00137961	−	0.000796519i
$613$	3.94274e7	+	6.82903e7i	0.171166	+	0.296468i	0.938828	−	0.344387i	$-0.111913\pi$
$613$	3.94274e7	+	6.82903e7i	0.171166	+	0.296468i	−0.767662	+	0.640855i	$0.778580\pi$
$614$	−1.70789e8	−	9.86049e7i	−0.737826	−	0.425984i
$615$		−	1.12256e7i		−	0.0482595i
$616$		0			0
$617$	4.19908e6			0.0178772			0.00893859	−	0.999960i	$-0.497155\pi$
$617$	4.19908e6			0.0178772			0.00893859	+	0.999960i	$0.497155\pi$
$618$	−5.19910e7	+	9.00510e7i	−0.220274	+	0.381525i
$619$	−2.30232e8	+	1.32925e8i	−0.970721	+	0.560446i	−0.899456	−	0.437011i	$-0.856037\pi$
$619$	−2.30232e8	+	1.32925e8i	−0.970721	+	0.560446i	−0.0712651	+	0.997457i	$0.522704\pi$
$620$	−1.12914e7	−	1.95573e7i	−0.0473775	−	0.0820603i
$621$	−2.55323e8	−	1.47411e8i	−1.06614	−	0.615537i
$622$		−	2.49501e8i		−	1.03681i
$623$		0			0
$624$	−7.16956e7			−0.295079
$625$	−1.18472e8	+	2.05199e8i	−0.485260	+	0.840496i
$626$	−2.13307e8	+	1.23153e8i	−0.869526	+	0.502021i
$627$	−2.59563e7	−	4.49577e7i	−0.105303	−	0.182390i
$628$	1.59471e8	+	9.20707e7i	0.643877	+	0.371743i
$629$		−	1.13930e7i		−	0.0457811i
$630$		0			0
$631$	−2.02533e8			−0.806135			−0.403068	−	0.915170i	$-0.632056\pi$
$631$	−2.02533e8			−0.806135			−0.403068	+	0.915170i	$0.632056\pi$
$632$	7.59001e6	−	1.31463e7i	0.0300671	−	0.0520777i
$633$	−9.23303e6	+	5.33069e6i	−0.0364027	+	0.0210171i
$634$	−9.26008e7	−	1.60389e8i	−0.363368	−	0.629372i
$635$	8.74285e6	+	5.04769e6i	0.0341454	+	0.0197138i
$636$			1.37644e8i			0.535040i
$637$		0			0
$638$	−6.55628e7			−0.252462
$639$	−1.83732e7	+	3.18233e7i	−0.0704177	+	0.121967i
$640$	1.99241e6	−	1.15032e6i	0.00760044	−	0.00438812i
$641$	1.15943e7	+	2.00819e7i	0.0440221	+	0.0762484i	0.887197	−	0.461391i	$-0.152649\pi$
$641$	1.15943e7	+	2.00819e7i	0.0440221	+	0.0762484i	−0.843175	+	0.537640i	$0.819316\pi$
$642$	2.16647e8	+	1.25081e8i	0.818744	+	0.472702i
$643$			3.10031e8i			1.16620i	0.812401	+	0.583100i	$0.198160\pi$
$643$			3.10031e8i			1.16620i	−0.812401	+	0.583100i	$0.801840\pi$
$644$		0			0
$645$	2.49153e7			0.0928511
$646$	474486.	−	821834.i	0.00176005	−	0.00304850i
$647$	−1.29013e8	+	7.44859e7i	−0.476345	+	0.275018i	−0.718892	−	0.695122i	$-0.755350\pi$
$647$	−1.29013e8	+	7.44859e7i	−0.476345	+	0.275018i	0.242547	+	0.970140i	$0.422017\pi$
$648$	−4.14163e7	−	7.17352e7i	−0.152211	−	0.263637i
$649$	2.91212e8	+	1.68131e8i	1.06531	+	0.615055i
$650$			2.42430e8i			0.882768i
$651$		0			0
$652$	3.06541e7			0.110597
$653$	1.15112e8	−	1.99379e8i	0.413408	−	0.716044i	−0.581851	−	0.813295i	$-0.697672\pi$
$653$	1.15112e8	−	1.99379e8i	0.413408	−	0.716044i	0.995260	+	0.0972506i	$0.0310048\pi$
$654$	−9.56973e7	+	5.52508e7i	−0.342110	+	0.197518i
$655$	−1.90378e7	−	3.29744e7i	−0.0677474	−	0.117342i
$656$	−3.17335e7	−	1.83214e7i	−0.112410	−	0.0649002i
$657$			1.68367e7i			0.0593691i
$658$		0			0
$659$	4.63051e8			1.61798			0.808989	−	0.587824i	$-0.200015\pi$
$659$	4.63051e8			1.61798			0.808989	+	0.587824i	$0.200015\pi$
$660$	−7.77818e6	+	1.34722e7i	−0.0270549	+	0.0468605i
$661$	2.85316e8	−	1.64727e8i	0.987920	−	0.570376i	0.0832680	−	0.996527i	$-0.473464\pi$
$661$	2.85316e8	−	1.64727e8i	0.987920	−	0.570376i	0.904652	+	0.426151i	$0.140131\pi$
$662$	−8.94502e7	−	1.54932e8i	−0.308324	−	0.534033i
$663$	7.67473e6	+	4.43101e6i	0.0263344	+	0.0152041i
$664$		−	2.94148e7i		−	0.100476i
$665$		0			0
$666$	4.59053e7			0.155396
$667$	−5.32489e7	+	9.22298e7i	−0.179446	+	0.310809i
$668$	−1.85932e8	+	1.07348e8i	−0.623769	+	0.360133i
$669$	5.67936e7	+	9.83694e7i	0.189680	+	0.328535i
$670$	−8.78233e6	−	5.07048e6i	−0.0292002	−	0.0168587i
$671$			3.08657e8i			1.02167i
$672$		0			0
$673$	−8.50491e7			−0.279013			−0.139506	−	0.990221i	$-0.544552\pi$
$673$	−8.50491e7			−0.279013			−0.139506	+	0.990221i	$0.544552\pi$
$674$	−2.32947e7	+	4.03476e7i	−0.0760812	+	0.131776i
$675$	−2.77403e8	+	1.60159e8i	−0.901987	+	0.520762i
$676$	4.55459e7	+	7.88878e7i	0.147438	+	0.255370i
$677$	−3.43079e8	−	1.98077e8i	−1.10568	−	0.638362i	−0.167970	−	0.985792i	$-0.553721\pi$
$677$	−3.43079e8	−	1.98077e8i	−1.10568	−	0.638362i	−0.937706	+	0.347430i	$0.887055\pi$
$678$		−	3.23970e8i		−	1.03948i
$679$		0			0
$680$	−284373.			−0.000904402
$681$	−4.91883e7	+	8.51967e7i	−0.155747	+	0.269762i
$682$	4.31665e8	−	2.49222e8i	1.36080	−	0.785657i
$683$	−1.61680e8	−	2.80039e8i	−0.507452	−	0.878933i	−0.999963	−	0.00862666i	$-0.997254\pi$
$683$	−1.61680e8	−	2.80039e8i	−0.507452	−	0.878933i	0.492510	−	0.870307i	$-0.336079\pi$
$684$	3.31138e6	+	1.91183e6i	0.0103476	+	0.00597420i
$685$			7.79441e6i			0.0242500i
$686$		0			0
$687$	−6.23206e7			−0.192204
$688$	4.06645e7	−	7.04330e7i	0.124868	−	0.216277i
$689$	4.08258e8	−	2.35708e8i	1.24818	−	0.720637i
$690$	1.26346e7	+	2.18838e7i	0.0384604	+	0.0666154i
$691$	4.13643e8	+	2.38817e8i	1.25369	+	0.723821i	0.971841	−	0.235637i	$-0.0757175\pi$
$691$	4.13643e8	+	2.38817e8i	1.25369	+	0.723821i	0.281853	+	0.959458i	$0.409051\pi$
$692$		−	1.11070e7i		−	0.0335181i
$693$		0			0
$694$	3.53559e8			1.05775
$695$	1.73495e7	−	3.00502e7i	0.0516811	−	0.0895143i
$696$	−2.96346e7	+	1.71095e7i	−0.0878964	+	0.0507470i
$697$	2.26463e6	+	3.92246e6i	0.00668805	+	0.0115840i
$698$	−1.21989e8	−	7.04306e7i	−0.358720	−	0.207107i
$699$		−	5.73681e8i		−	1.67973i
$700$		0			0
$701$	1.25339e7			0.0363859			0.0181929	−	0.999834i	$-0.494209\pi$
$701$	1.25339e7			0.0363859			0.0181929	+	0.999834i	$0.494209\pi$
$702$	−1.62220e8	+	2.80973e8i	−0.468913	+	0.812181i
$703$	1.03316e8	−	5.96494e7i	0.297373	−	0.171688i
$704$	2.53897e7	+	4.39762e7i	0.0727678	+	0.126037i
$705$	3.96316e7	+	2.28813e7i	0.113103	+	0.0653000i
$706$			3.91766e8i			1.11330i
$707$		0			0
$708$	1.75505e8			0.494526
$709$	9.71988e7	−	1.68353e8i	0.272723	−	0.472371i	−0.696835	−	0.717232i	$-0.745409\pi$
$709$	9.71988e7	−	1.68353e8i	0.272723	−	0.472371i	0.969558	+	0.244861i	$0.0787423\pi$
$710$	2.47829e7	−	1.43084e7i	0.0692433	−	0.0399777i
$711$	−3.78013e6	−	6.54739e6i	−0.0105172	−	0.0182163i
$712$	−7.96134e7	−	4.59648e7i	−0.220570	−	0.127346i
$713$		−	8.09654e8i		−	2.23373i
$714$		0			0
$715$	5.32788e7			0.145759
$716$	4.71265e7	−	8.16254e7i	0.128388	−	0.222375i
$717$	8.56844e7	−	4.94699e7i	0.232458	−	0.134210i
$718$	8.51166e7	+	1.47426e8i	0.229954	+	0.398292i
$719$	2.09066e8	+	1.20704e8i	0.562467	+	0.324741i	0.754135	−	0.656719i	$-0.228056\pi$
$719$	2.09066e8	+	1.20704e8i	0.562467	+	0.324741i	−0.191668	+	0.981460i	$0.561390\pi$
$720$		−	1.14581e6i		−	0.00306984i
$721$		0			0
$722$	−2.56195e8			−0.680705
$723$	1.24182e8	−	2.15090e8i	0.328583	−	0.569122i
$724$	8.00361e7	−	4.62089e7i	0.210897	−	0.121761i
$725$	5.78539e7	+	1.00206e8i	0.151816	+	0.262954i
$726$	−7.79956e7	−	4.50308e7i	−0.203826	−	0.117679i
$727$			3.89703e8i			1.01422i	0.861882	+	0.507109i	$0.169286\pi$
$727$			3.89703e8i			1.01422i	−0.861882	+	0.507109i	$0.830714\pi$
$728$		0			0
$729$	−4.22749e8			−1.09119
$730$	6.55594e6	−	1.13552e7i	0.0168526	−	0.0291895i
$731$	−8.70595e6	+	5.02638e6i	−0.0222876	+	0.0128678i
$732$	8.05484e7	+	1.39514e8i	0.205364	+	0.355700i
$733$	−1.51751e8	−	8.76135e7i	−0.385319	−	0.222464i	0.294811	−	0.955556i	$-0.404743\pi$
$733$	−1.51751e8	−	8.76135e7i	−0.385319	−	0.222464i	−0.680130	+	0.733092i	$0.738077\pi$
$734$		−	1.19995e8i		−	0.303442i
$735$		0			0
$736$	8.24841e7			0.206889
$737$	1.11915e8	−	1.93843e8i	0.279567	−	0.484224i
$738$	−1.58046e7	+	9.12478e6i	−0.0393201	+	0.0227014i
$739$	−3.83128e6	−	6.63597e6i	−0.00949315	−	0.0164426i	0.861240	−	0.508199i	$-0.169688\pi$
$739$	−3.83128e6	−	6.63597e6i	−0.00949315	−	0.0164426i	−0.870733	+	0.491756i	$0.836355\pi$
$740$	−3.09601e7	−	1.78748e7i	−0.0764023	−	0.0441109i
$741$			9.27963e7i			0.228074i
$742$		0			0
$743$	4.78399e8			1.16634			0.583169	−	0.812351i	$-0.301813\pi$
$743$	4.78399e8			1.16634			0.583169	+	0.812351i	$0.301813\pi$
$744$	1.30076e8	−	2.25298e8i	0.315848	−	0.547065i
$745$	4.39702e7	−	2.53862e7i	0.106338	−	0.0613944i
$746$	1.38144e8	+	2.39272e8i	0.332747	+	0.576335i
$747$	−1.26871e7	−	7.32488e6i	−0.0304368	−	0.0175727i
$748$		−	6.27664e6i		−	0.0149976i
$749$		0			0
$750$	5.51823e7			0.130802
$751$	3.50940e7	−	6.07847e7i	0.0828540	−	0.143507i	−0.821621	−	0.570035i	$-0.806930\pi$
$751$	3.50940e7	−	6.07847e7i	0.0828540	−	0.143507i	0.904475	+	0.426527i	$0.140263\pi$
$752$	1.29366e8	−	7.46895e7i	0.304205	−	0.175633i
$753$	−1.42384e8	−	2.46615e8i	−0.333484	−	0.577611i
$754$	1.01495e8	+	5.85983e7i	0.236773	+	0.136701i
$755$		−	2.03391e7i		−	0.0472598i
$756$		0			0
$757$	−5.44271e7			−0.125466			−0.0627332	−	0.998030i	$-0.519982\pi$
$757$	−5.44271e7			−0.125466			−0.0627332	+	0.998030i	$0.519982\pi$
$758$	2.37747e7	−	4.11790e7i	0.0545893	−	0.0945514i
$759$	−4.83015e8	+	2.78869e8i	−1.10468	+	0.637786i
$760$	−1.48887e6	−	2.57880e6i	−0.00339168	−	0.00587457i
$761$	−4.83017e8	−	2.78870e8i	−1.09599	−	0.632773i	−0.160829	−	0.986982i	$-0.551417\pi$
$761$	−4.83017e8	−	2.78870e8i	−1.09599	−	0.632773i	−0.935166	+	0.354210i	$0.884750\pi$
$762$			1.16298e8i			0.262850i
$763$		0			0
$764$	−1.81354e8			−0.406674
$765$	−70814.7	+	122655.i	−0.000158175	+	0.000273968i
$766$	−8.33729e7	+	4.81354e7i	−0.185498	+	0.107097i
$767$	−3.00542e8	−	5.20555e8i	−0.666070	−	1.15367i
$768$	2.29524e7	+	1.32516e7i	0.0506693	+	0.0292539i
$769$		−	3.50325e8i		−	0.770356i	−0.922842	−	0.385178i	$-0.874140\pi$
$769$		−	3.50325e8i		−	0.770356i	0.922842	−	0.385178i	$-0.125860\pi$
$770$		0			0
$771$	−7.88286e8			−1.71997
$772$	−2.09380e8	+	3.62657e8i	−0.455076	+	0.788215i
$773$	−4.94039e8	+	2.85234e8i	−1.06960	+	0.617536i	−0.928073	−	0.372398i	$-0.878536\pi$
$773$	−4.94039e8	+	2.85234e8i	−1.06960	+	0.617536i	−0.141530	+	0.989934i	$0.545202\pi$
$774$	−2.02526e7	−	3.50785e7i	−0.0436775	−	0.0756516i
$775$	−7.61819e8	−	4.39837e8i	−1.63662	−	0.944901i
$776$			9.22729e7i			0.197464i
$777$		0			0
$778$	−3.38444e7			−0.0718702
$779$	−2.37135e7	+	4.10730e7i	−0.0501630	+	0.0868848i
$780$	2.40822e7	−	1.39039e7i	0.0507472	−	0.0292989i
$781$	3.15814e8	+	5.47006e8i	0.662946	+	1.14826i
$782$	−8.82960e6	−	5.09777e6i	−0.0184638	−	0.0106601i
$783$			1.54849e8i			0.322570i
$784$		0			0
$785$	−7.14208e7			−0.147644
$786$	2.19314e8	−	3.79863e8i	0.451647	−	0.782275i
$787$	6.46413e8	−	3.73207e8i	1.32613	−	0.765641i	0.341431	−	0.939907i	$-0.389089\pi$
$787$	6.46413e8	−	3.73207e8i	1.32613	−	0.765641i	0.984699	+	0.174266i	$0.0557553\pi$
$788$	−7.15341e7	−	1.23901e8i	−0.146196	−	0.253218i
$789$	−2.95909e8	−	1.70843e8i	−0.602459	−	0.347830i
$790$			5.88770e6i			0.0119416i
$791$		0			0
$792$	2.52902e7			0.0509069
$793$	2.75870e8	−	4.77820e8i	0.553203	−	0.958175i
$794$	5.17640e8	−	2.98860e8i	1.03411	−	0.597043i
$795$	−2.66932e7	−	4.62340e7i	−0.0531250	−	0.0920153i
$796$	2.23299e8	+	1.28922e8i	0.442738	+	0.255615i
$797$		−	8.52897e8i		−	1.68470i	−0.538934	−	0.842348i	$-0.681173\pi$
$797$		−	8.52897e8i		−	1.68470i	0.538934	−	0.842348i	$-0.318827\pi$
$798$		0			0
$799$	−1.84642e7			−0.0361984
$800$	4.48087e7	−	7.76109e7i	0.0875169	−	0.151584i
$801$	−3.96507e7	+	2.28924e7i	−0.0771532	+	0.0445444i
$802$	1.73294e8	+	3.00153e8i	0.335938	+	0.581862i
$803$	2.50631e8	+	1.44702e8i	0.484047	+	0.279465i
$804$		−	1.16823e8i		−	0.224782i
$805$		0			0
$806$	−8.90992e8			−1.70164
$807$	−3.29530e8	+	5.70762e8i	−0.627010	+	1.08601i
$808$	2.44480e8	−	1.41151e8i	0.463457	−	0.267577i
$809$	2.68931e8	+	4.65802e8i	0.507920	+	0.879744i	0.999958	+	0.00916987i	$0.00291890\pi$
$809$	2.68931e8	+	4.65802e8i	0.507920	+	0.879744i	−0.492038	+	0.870574i	$0.663748\pi$
$810$	2.78231e7	+	1.60637e7i	0.0523540	+	0.0302266i
$811$		−	546840.i		−	0.00102517i	−1.00000		0.000512587i	$-0.999837\pi$
$811$		−	546840.i		−	0.00102517i	1.00000		0.000512587i	$-0.000163162\pi$
$812$		0			0
$813$	2.79179e8			0.519530
$814$	3.94530e8	−	6.83346e8i	0.731487	−	1.26697i
$815$	−1.02965e7	+	5.94472e6i	−0.0190204	+	0.0109814i
$816$	−1.63798e6	−	2.83706e6i	−0.00301465	−	0.00522153i
$817$	−9.11621e7	−	5.26325e7i	−0.167166	−	0.0965134i
$818$			6.18850e8i			1.13064i
$819$		0			0
$820$	1.42122e7			0.0257762
$821$	2.66538e7	−	4.61657e7i	0.0481648	−	0.0834238i	−0.840938	−	0.541132i	$-0.817996\pi$
$821$	2.66538e7	−	4.61657e7i	0.0481648	−	0.0834238i	0.889103	+	0.457708i	$0.151329\pi$
$822$	−7.77613e7	+	4.48955e7i	−0.140006	+	0.0808328i
$823$	3.83179e8	+	6.63686e8i	0.687389	+	1.19059i	0.972680	+	0.232151i	$0.0745764\pi$
$823$	3.83179e8	+	6.63686e8i	0.687389	+	1.19059i	−0.285291	+	0.958441i	$0.592090\pi$
$824$	−1.14009e8	−	6.58234e7i	−0.203779	−	0.117652i
$825$			6.05971e8i			1.07917i
$826$		0			0
$827$	1.00353e9			1.77425			0.887127	−	0.461526i	$-0.152698\pi$
$827$	1.00353e9			1.77425			0.887127	+	0.461526i	$0.152698\pi$
$828$	2.05402e7	−	3.55767e7i	0.0361838	−	0.0626722i
$829$	1.28437e8	−	7.41532e7i	0.225438	−	0.130157i	−0.383028	−	0.923737i	$-0.625119\pi$
$829$	1.28437e8	−	7.41532e7i	0.225438	−	0.130157i	0.608466	+	0.793580i	$0.291785\pi$
$830$	5.70438e6	+	9.88028e6i	0.00997641	+	0.0172796i
$831$	−3.49067e8	−	2.01534e8i	−0.608283	−	0.351192i
$832$		−	9.07705e7i		−	0.157607i
$833$		0			0
$834$	3.99729e8			0.689077
$835$	4.16357e7	−	7.21151e7i	0.0715165	−	0.123870i
$836$	5.69188e7	−	3.28621e7i	0.0974175	−	0.0562440i
$837$	−5.88624e8	−	1.01953e9i	−1.00383	−	1.73869i
$838$	−1.00163e8	−	5.78293e7i	−0.170207	−	0.0982688i
$839$			2.21066e8i			0.374315i	0.982330	+	0.187157i	$0.0599274\pi$
$839$			2.21066e8i			0.374315i	−0.982330	+	0.187157i	$0.940073\pi$
$840$		0			0
$841$	−5.38887e8			−0.905962
$842$	−9.02991e7	+	1.56403e8i	−0.151268	+	0.262004i
$843$	2.74989e7	−	1.58765e7i	0.0459021	−	0.0265016i
$844$	−6.74895e6	−	1.16895e7i	−0.0112256	−	0.0194433i
$845$	−3.05973e7	−	1.76653e7i	−0.0507122	−	0.0292787i
$846$		−	7.43969e7i		−	0.122869i
$847$		0			0
$848$	−1.74265e8			−0.285774
$849$	4.26319e6	−	7.38405e6i	0.00696645	−	0.0120662i
$850$	−9.59319e6	+	5.53863e6i	−0.0156209	+	0.00901873i
$851$	−6.40860e8	−	1.11000e9i	−1.03986	−	1.80109i
$852$	2.85498e8	+	1.64832e8i	0.461619	+	0.266516i
$853$			9.10570e8i			1.46712i	0.679624	+	0.733561i	$0.262143\pi$
$853$			9.10570e8i			1.46712i	−0.679624	+	0.733561i	$0.737857\pi$
$854$		0			0
$855$	−1.48303e6			−0.00237276
$856$	−1.58360e8	+	2.74287e8i	−0.252478	+	0.437305i
$857$	−1.68169e8	+	9.70924e7i	−0.267180	+	0.154256i	−0.627605	−	0.778532i	$-0.715965\pi$
$857$	−1.68169e8	+	9.70924e7i	−0.267180	+	0.154256i	0.360426	+	0.932788i	$0.382631\pi$
$858$	3.06884e8	+	5.31539e8i	0.485862	+	0.841537i
$859$	6.25498e8	+	3.61132e8i	0.986840	+	0.569752i	0.904328	−	0.426838i	$-0.140372\pi$
$859$	6.25498e8	+	3.61132e8i	0.986840	+	0.569752i	0.0825118	+	0.996590i	$0.473706\pi$
$860$			3.15441e7i			0.0495933i
$861$		0			0
$862$	−1.76088e6			−0.00274922
$863$	9.71379e7	−	1.68248e8i	0.151132	−	0.261768i	−0.780512	−	0.625141i	$-0.785042\pi$
$863$	9.71379e7	−	1.68248e8i	0.151132	−	0.261768i	0.931644	+	0.363373i	$0.118375\pi$
$864$	1.03865e8	−	5.99665e7i	0.161038	−	0.0929753i
$865$	2.15397e6	+	3.73079e6i	0.00332807	+	0.00576438i
$866$	−2.48012e8	−	1.43190e8i	−0.381873	−	0.220475i
$867$		−	6.09681e8i		−	0.935504i
$868$		0			0
$869$	−1.29952e8			−0.198027
$870$	6.63607e6	−	1.14940e7i	0.0100775	−	0.0174548i
$871$	−3.46503e8	+	2.00053e8i	−0.524387	+	0.302755i
$872$	−6.99506e7	−	1.21158e8i	−0.105497	−	0.182727i
$873$	3.97988e7	+	2.29778e7i	0.0598173	+	0.0345355i
$874$		−	1.06760e8i		−	0.159909i
$875$		0			0
$876$	1.51048e8			0.224700
$877$	−2.48367e8	+	4.30184e8i	−0.368210	+	0.637758i	−0.989286	−	0.145992i	$-0.953362\pi$
$877$	−2.48367e8	+	4.30184e8i	−0.368210	+	0.637758i	0.621076	+	0.783750i	$0.286696\pi$
$878$	−3.96607e8	+	2.28981e8i	−0.585973	+	0.338311i
$879$	−1.64739e8	−	2.85336e8i	−0.242566	−	0.420136i
$880$	−1.70565e7	−	9.84759e6i	−0.0250290	−	0.0144505i
$881$			8.63809e7i			0.126325i	0.998003	+	0.0631626i	$0.0201187\pi$
$881$			8.63809e7i			0.126325i	−0.998003	+	0.0631626i	$0.979881\pi$
$882$		0			0
$883$	6.49219e8			0.942994			0.471497	−	0.881868i	$-0.343714\pi$
$883$	6.49219e8			0.942994			0.471497	+	0.881868i	$0.343714\pi$
$884$	−5.60990e6	+	9.71663e6i	−0.00812079	+	0.0140656i
$885$	−5.89512e7	+	3.40355e7i	−0.0850477	+	0.0491023i
$886$	−7.26180e6	−	1.25778e7i	−0.0104410	−	0.0180844i
$887$	6.17373e8	+	3.56441e8i	0.884661	+	0.510759i	0.872192	−	0.489163i	$-0.162698\pi$
$887$	6.17373e8	+	3.56441e8i	0.884661	+	0.510759i	0.0124685	+	0.999922i	$0.496031\pi$
$888$		−	4.11833e8i		−	0.588141i
$889$		0			0
$890$	3.56557e7			0.0505776
$891$	−3.54555e8	+	6.14107e8i	−0.501246	+	0.868183i
$892$	−1.24541e8	+	7.19038e7i	−0.175476	+	0.101311i
$893$	−9.66714e7	−	1.67440e8i	−0.135751	−	0.235128i
$894$	5.06533e8	+	2.92447e8i	0.708917	+	0.409293i
$895$			3.65568e7i			0.0509916i
$896$		0			0
$897$	9.96983e8			1.38137
$898$	−1.72910e8	+	2.99489e8i	−0.238777	+	0.413573i
$899$	−3.68282e8	+	2.12628e8i	−0.506875	+	0.292645i
$900$	−2.23166e7	−	3.86534e7i	−0.0306126	−	0.0530225i
$901$	1.86544e7	+	1.07701e7i	0.0255039	+	0.0147247i
$902$			3.13689e8i			0.427445i
$903$		0			0
$904$	4.10164e8			0.555203
$905$	−1.79225e7	+	3.10427e7i	−0.0241798	+	0.0418806i
$906$	2.02914e8	−	1.17153e8i	0.272853	−	0.157532i
$907$	4.14206e8	+	7.17425e8i	0.555129	+	0.961512i	0.997893	+	0.0648738i	$0.0206645\pi$
$907$	4.14206e8	+	7.17425e8i	0.555129	+	0.961512i	−0.442764	+	0.896638i	$0.646002\pi$
$908$	−1.07864e8	−	6.22751e7i	−0.144085	−	0.0831873i
$909$		−	1.40597e8i		−	0.187191i
$910$		0			0
$911$	−1.17587e9			−1.55526			−0.777631	−	0.628721i	$-0.783579\pi$
$911$	−1.17587e9			−1.55526			−0.777631	+	0.628721i	$0.783579\pi$
$912$	1.71516e7	−	2.97075e7i	0.0226111	−	0.0391635i
$913$	−2.18076e8	+	1.25906e8i	−0.286547	+	0.165438i
$914$	2.71449e7	+	4.70164e7i	0.0355509	+	0.0615759i
$915$	−5.41116e7	−	3.12414e7i	−0.0706362	−	0.0407818i
$916$		−	7.89013e7i		−	0.102659i
$917$		0			0
$918$	−1.48245e7			−0.0191625
$919$	−2.25460e8	+	3.90508e8i	−0.290485	+	0.503134i	−0.973924	−	0.226873i	$-0.927150\pi$
$919$	−2.25460e8	+	3.90508e8i	−0.290485	+	0.503134i	0.683440	+	0.730007i	$0.260483\pi$
$920$	−2.77060e7	+	1.59961e7i	−0.0355804	+	0.0205423i
$921$	4.40576e8	+	7.63101e8i	0.563952	+	0.976794i
$922$	2.96147e8	+	1.70981e8i	0.377846	+	0.218150i
$923$		−	1.12907e9i		−	1.43587i
$924$		0			0
$925$	−1.39256e9			−1.75950
$926$	−3.24582e8	+	5.62192e8i	−0.408781	+	0.708030i
$927$	−5.67813e7	+	3.27827e7i	−0.0712798	+	0.0411534i
$928$	−2.16616e7	−	3.75190e7i	−0.0271048	−	0.0469469i
$929$	1.03420e9	+	5.97094e8i	1.28990	+	0.744725i	0.978636	−	0.205599i	$-0.0659142\pi$
$929$	1.03420e9	+	5.97094e8i	1.28990	+	0.744725i	0.311264	+	0.950323i	$0.399248\pi$
$930$			1.00902e8i			0.125444i
$931$		0			0
$932$	7.26311e8			0.897170
$933$	−5.57398e8	+	9.65441e8i	−0.686310	+	1.18872i
$934$	3.35793e8	−	1.93870e8i	0.412127	−	0.237942i
$935$	1.21722e6	+	2.10829e6i	0.00148914	+	0.00257927i
$936$	−3.91508e7	−	2.26037e7i	−0.0477433	−	0.0275646i
$937$		−	5.57908e8i		−	0.678178i	−0.940754	−	0.339089i	$-0.889881\pi$
$937$		−	5.57908e8i		−	0.678178i	0.940754	−	0.339089i	$-0.110119\pi$
$938$		0			0
$939$	1.10052e9			1.32923
$940$	−2.89690e7	+	5.01757e7i	−0.0348778	+	0.0604101i
$941$	−9.18066e8	+	5.30046e8i	−1.10181	+	0.636128i	−0.936695	−	0.350147i	$-0.886132\pi$
$941$	−9.18066e8	+	5.30046e8i	−1.10181	+	0.636128i	−0.165111	+	0.986275i	$0.552798\pi$
$942$	−4.11381e8	−	7.12533e8i	−0.492143	−	0.852417i
$943$	4.41279e8	+	2.54773e8i	0.526234	+	0.303821i
$944$			2.22198e8i			0.264134i
$945$		0			0
$946$	−6.96238e8			−0.822402
$947$	−4.08434e8	+	7.07429e8i	−0.480919	+	0.832977i	−0.999760	−	0.0218939i	$-0.993030\pi$
$947$	−4.08434e8	+	7.07429e8i	−0.480919	+	0.832977i	0.518841	+	0.854871i	$0.326364\pi$
$948$	−5.87389e7	+	3.39129e7i	−0.0689447	+	0.0398052i
$949$	−2.58661e8	−	4.48015e8i	−0.302645	−	0.524196i
$950$	−1.00453e8	−	5.79963e7i	−0.117163	−	0.0676440i
$951$			8.27499e8i			0.962112i
$952$		0			0
$953$	1.23336e9			1.42499			0.712494	−	0.701678i	$-0.247565\pi$
$953$	1.23336e9			1.42499			0.712494	+	0.701678i	$0.247565\pi$
$954$	−4.33955e7	+	7.51632e7i	−0.0499804	+	0.0865686i
$955$	6.09158e7	−	3.51697e7i	0.0699390	−	0.0403793i
$956$	6.26316e7	+	1.08481e8i	0.0716836	+	0.124160i
$957$	2.53694e8	+	1.46471e8i	0.289451	+	0.167115i
$958$			5.53180e8i			0.629173i
$959$		0			0
$960$	−1.02795e7			−0.0116187
$961$	1.17276e9	−	2.03128e9i	1.32141	−	2.28875i
$962$	−1.22151e9	+	7.05241e8i	−1.37206	+	0.792159i
$963$	7.88697e7	+	1.36606e8i	0.0883143	+	0.152965i
$964$	2.72316e8	+	1.57222e8i	0.303978	+	0.175502i
$965$		−	1.62420e8i		−	0.180741i
$966$		0			0
$967$	−5.82431e8			−0.644118			−0.322059	−	0.946720i	$-0.604375\pi$
$967$	−5.82431e8			−0.644118			−0.322059	+	0.946720i	$0.604375\pi$
$968$	5.70114e7	−	9.87466e7i	0.0628544	−	0.108867i
$969$	−3.67203e6	+	2.12005e6i	−0.00403585	+	0.00233010i
$970$	−1.78944e7	−	3.09940e7i	−0.0196066	−	0.0339596i
$971$	−2.97824e7	−	1.71949e7i	−0.0325314	−	0.0187820i	0.483646	−	0.875264i	$-0.339312\pi$
$971$	−2.97824e7	−	1.71949e7i	−0.0325314	−	0.0187820i	−0.516177	+	0.856482i	$0.672646\pi$
$972$		−	1.12889e8i		−	0.122929i
$973$		0			0
$974$	−1.29080e8			−0.139695
$975$	5.41601e8	−	9.38081e8i	0.584340	−	1.01211i
$976$	−1.76632e8	+	1.01979e8i	−0.189986	+	0.109688i
$977$	2.60603e8	+	4.51377e8i	0.279444	+	0.484012i	0.971247	−	0.238075i	$-0.0765164\pi$
$977$	2.60603e8	+	4.51377e8i	0.279444	+	0.484012i	−0.691802	+	0.722087i	$0.743183\pi$
$978$	−1.18615e8	−	6.84827e7i	−0.126802	−	0.0732090i
$979$			7.86987e8i			0.838725i
$980$		0			0
$981$	−6.96765e7			−0.0738039
$982$	3.15696e7	−	5.46802e7i	0.0333376	−	0.0577425i
$983$	5.40048e8	−	3.11797e8i	0.568554	−	0.328255i	−0.188018	−	0.982166i	$-0.560206\pi$
$983$	5.40048e8	−	3.11797e8i	0.568554	−	0.328255i	0.756572	+	0.653911i	$0.226873\pi$
$984$	8.18616e7	+	1.41788e8i	0.0859201	+	0.148818i
$985$	4.80559e7	+	2.77451e7i	0.0502850	+	0.0290320i
$986$			5.35501e6i			0.00558637i
$987$		0			0
$988$	−1.17485e8			−0.121818
$989$	−5.65472e8	+	9.79426e8i	−0.584550	+	1.01247i
$990$	−8.49485e6	+	4.90450e6i	−0.00875488	+	0.00505463i
$991$	−6.99332e7	−	1.21128e8i	−0.0718559	−	0.124458i	0.827859	−	0.560937i	$-0.189559\pi$
$991$	−6.99332e7	−	1.21128e8i	−0.0718559	−	0.124458i	−0.899715	+	0.436478i	$0.856226\pi$
$992$	2.85240e8	+	1.64683e8i	0.292196	+	0.168700i
$993$			7.99344e8i			0.816368i
$994$		0			0
$995$	−1.00007e8			−0.101522
$996$	−6.57140e7	+	1.13820e8i	−0.0665090	+	0.115197i
$997$	1.68279e9	−	9.71557e8i	1.69802	−	0.980353i	0.750386	−	0.661000i	$-0.229868\pi$
$997$	1.68279e9	−	9.71557e8i	1.69802	−	0.980353i	0.947636	−	0.319354i	$-0.103466\pi$
$998$	−1.22543e8	−	2.12252e8i	−0.123282	−	0.213530i
$999$	−1.61396e9	−	9.31820e8i	−1.61881	−	0.934621i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	98.7.d.c.19.3		8
7.2	even	3		98.7.b.c.97.2		8
7.3	odd	6	inner	98.7.d.c.31.3		8
7.4	even	3		14.7.d.a.3.4	✓	8
7.5	odd	6		98.7.b.c.97.3		8
7.6	odd	2		14.7.d.a.5.4	yes	8
21.11	odd	6		126.7.n.c.73.1		8
21.20	even	2		126.7.n.c.19.1		8
28.11	odd	6		112.7.s.c.17.2		8
28.27	even	2		112.7.s.c.33.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
14.7.d.a.3.4	✓	8	7.4	even	3
14.7.d.a.5.4	yes	8	7.6	odd	2
98.7.b.c.97.2		8	7.2	even	3
98.7.b.c.97.3		8	7.5	odd	6
98.7.d.c.19.3		8	1.1	even	1	trivial
98.7.d.c.31.3		8	7.3	odd	6	inner
112.7.s.c.17.2		8	28.11	odd	6
112.7.s.c.33.2		8	28.27	even	2
126.7.n.c.19.1		8	21.20	even	2
126.7.n.c.73.1		8	21.11	odd	6

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:	\( N \)	\(=\)	\( 98 = 2 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	98.d (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.82843 - 4.89898i) q^{2} +(-21.8891 + 12.6377i) q^{3} +(-16.0000 - 27.7128i) q^{4} +(10.7486 + 6.20573i) q^{5} +142.979i q^{6} -181.019 q^{8} +(-45.0775 + 78.0766i) q^{9} +(60.8035 - 35.1049i) q^{10} +(774.831 + 1342.05i) q^{11} +(700.452 + 404.406i) q^{12} -2770.09i q^{13} -313.705 q^{15} +(-512.000 + 886.810i) q^{16} +(109.615 - 63.2864i) q^{17} +(254.997 + 441.668i) q^{18} +(1147.81 + 662.687i) q^{19} -397.167i q^{20} +8766.21 q^{22} +(7119.76 - 12331.8i) q^{23} +(3962.35 - 2287.67i) q^{24} +(-7735.48 - 13398.2i) q^{25} +(-13570.6 - 7835.01i) q^{26} -20704.5i q^{27} -7479.03 q^{29} +(-887.290 + 1536.83i) q^{30} +(49241.9 - 28429.8i) q^{31} +(2896.31 + 5016.55i) q^{32} +(-33920.8 - 19584.2i) q^{33} -716.004i q^{34} +2884.96 q^{36} +(45005.7 - 77952.2i) q^{37} +(6492.98 - 3748.72i) q^{38} +(35007.6 + 60634.9i) q^{39} +(-1945.71 - 1123.36i) q^{40} +35783.9i q^{41} -79422.8 q^{43} +(24794.6 - 42945.5i) q^{44} +(-969.044 + 559.478i) q^{45} +(-40275.4 - 69759.1i) q^{46} +(-126334. - 72939.0i) q^{47} -25882.0i q^{48} -87516.9 q^{50} +(-1599.59 + 2770.57i) q^{51} +(-76767.1 + 44321.5i) q^{52} +(85090.3 + 147381. i) q^{53} +(-101431. - 58561.0i) q^{54} +19233.6i q^{55} -33499.3 q^{57} +(-21153.9 + 36639.6i) q^{58} +(187919. - 108495. i) q^{59} +(5019.27 + 8693.64i) q^{60} +(172492. + 99588.5i) q^{61} -321647. i q^{62} +32768.0 q^{64} +(17190.5 - 29774.8i) q^{65} +(-191885. + 110785. i) q^{66} +(-72219.0 - 125087. i) q^{67} +(-3507.69 - 2025.16i) q^{68} +359909. i q^{69} +407591. q^{71} +(8159.90 - 14133.4i) q^{72} +(161733. - 93376.3i) q^{73} +(-254591. - 440964. i) q^{74} +(338646. + 195517. i) q^{75} -42411.9i q^{76} +396066. q^{78} +(-41929.3 + 72623.6i) q^{79} +(-11006.6 + 6354.67i) q^{80} +(228795. + 396285. i) q^{81} +(175305. + 101212. i) q^{82} +162495. i q^{83} +1570.95 q^{85} +(-224642. + 389091. i) q^{86} +(163709. - 94517.7i) q^{87} +(-140259. - 242936. i) q^{88} +(439806. + 253922. i) q^{89} +6329.77i q^{90} -455665. q^{92} +(-718575. + 1.24461e6i) q^{93} +(-714653. + 412605. i) q^{94} +(8224.91 + 14246.0i) q^{95} +(-126795. - 73205.3i) q^{96} -509740. i q^{97} -139710. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 128 q^{4} + 336 q^{5} + 756 q^{9} + 2016 q^{10} - 1356 q^{11} + 27144 q^{15} - 4096 q^{16} + 17304 q^{17} - 6816 q^{18} + 32004 q^{19} + 25248 q^{22} - 4128 q^{23} - 10752 q^{24} + 4664 q^{25} + 4704 q^{26}+ \cdots - 4625928 q^{99}+O(q^{100}) \) 8 * q - 128 * q^4 + 336 * q^5 + 756 * q^9 + 2016 * q^10 - 1356 * q^11 + 27144 * q^15 - 4096 * q^16 + 17304 * q^17 - 6816 * q^18 + 32004 * q^19 + 25248 * q^22 - 4128 * q^23 - 10752 * q^24 + 4664 * q^25 + 4704 * q^26 - 30312 * q^29 + 9648 * q^30 + 3108 * q^31 - 3276 * q^33 - 48384 * q^36 - 6124 * q^37 - 155568 * q^38 + 100764 * q^39 - 64512 * q^40 - 297376 * q^43 - 43392 * q^44 + 172116 * q^45 - 194064 * q^46 - 313908 * q^47 + 38784 * q^50 + 253692 * q^51 - 255360 * q^52 + 278484 * q^53 - 386064 * q^54 - 81288 * q^57 - 169824 * q^58 + 835464 * q^59 - 434304 * q^60 + 995316 * q^61 + 262144 * q^64 + 8316 * q^65 - 1673280 * q^66 + 648808 * q^67 - 553728 * q^68 + 190128 * q^71 - 218112 * q^72 + 1617084 * q^73 - 1158144 * q^74 + 2042208 * q^75 + 1122432 * q^78 + 70096 * q^79 - 344064 * q^80 + 1177920 * q^81 - 66528 * q^82 + 2190984 * q^85 - 573024 * q^86 + 2057076 * q^87 - 403968 * q^88 - 739116 * q^89 + 264192 * q^92 - 23364 * q^93 - 3795120 * q^94 + 725640 * q^95 + 344064 * q^96 - 4625928 * q^99

Introduction

L-functions

Modular forms

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