LMFDB - Embedded newform 49.7.d.e.31.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [49,7,Mod(19,49)] 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("49.19"); S:= CuspForms(chi, 7); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(49, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([5])) N = Newforms(chi, 7, names="a")

Level:	$ N $	$=$	$ 49 = 7^{2} $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	49.d (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [24,-20] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$11.2726500974$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			31.6
Character	$\chi$	$=$	49.31
Dual form			49.7.d.e.19.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.33452 - 4.04351i) q^{2} +(32.1003 + 18.5331i) q^{3} +(21.1000 - 36.5463i) q^{4} +(189.226 - 109.250i) q^{5} -173.064i q^{6} -495.852 q^{8} +(322.454 + 558.506i) q^{9} +(-883.503 - 510.091i) q^{10} +(168.957 - 292.642i) q^{11} +(1354.64 - 782.099i) q^{12} +2480.18i q^{13} +8098.94 q^{15} +(-192.824 - 333.981i) q^{16} +(-5159.10 - 2978.61i) q^{17} +(1505.55 - 2607.69i) q^{18} +(1609.96 - 929.513i) q^{19} -9220.67i q^{20} -1577.73 q^{22} +(5190.93 + 8990.96i) q^{23} +(-15917.0 - 9189.70i) q^{24} +(16058.4 - 27814.0i) q^{25} +(10028.6 - 5790.03i) q^{26} -3117.00i q^{27} -137.033 q^{29} +(-18907.2 - 32748.1i) q^{30} +(20912.7 + 12074.0i) q^{31} +(-16767.6 + 29042.3i) q^{32} +(10847.1 - 6262.60i) q^{33} +27814.5i q^{34} +27215.1 q^{36} +(37443.9 + 64854.7i) q^{37} +(-7516.99 - 4339.93i) q^{38} +(-45965.5 + 79614.5i) q^{39} +(-93828.1 + 54171.7i) q^{40} +13051.8i q^{41} -91089.1 q^{43} +(-7129.99 - 12349.5i) q^{44} +(122033. + 70455.8i) q^{45} +(24236.7 - 41979.2i) q^{46} +(41692.6 - 24071.3i) q^{47} -14294.5i q^{48} -149955. q^{50} +(-110406. - 191229. i) q^{51} +(90641.4 + 52331.8i) q^{52} +(-48053.1 + 83230.4i) q^{53} +(-12603.6 + 7276.70i) q^{54} -73833.8i q^{55} +68907.1 q^{57} +(319.905 + 554.092i) q^{58} +(-142788. - 82438.8i) q^{59} +(170888. - 295987. i) q^{60} +(-107191. + 61886.8i) q^{61} -112748. i q^{62} +131896. q^{64} +(270958. + 469314. i) q^{65} +(-50645.7 - 29240.3i) q^{66} +(-237259. + 410944. i) q^{67} +(-217714. + 125697. i) q^{68} +384817. i q^{69} +444087. q^{71} +(-159889. - 276937. i) q^{72} +(-450655. - 260186. i) q^{73} +(174827. - 302809. i) q^{74} +(1.03096e6 - 595226. i) q^{75} -78451.0i q^{76} +429229. q^{78} +(-97094.1 - 168172. i) q^{79} +(-72974.5 - 42131.8i) q^{80} +(292836. - 507208. i) q^{81} +(52775.2 - 30469.7i) q^{82} +1316.59i q^{83} -1.30165e6 q^{85} +(212649. + 368320. i) q^{86} +(-4398.79 - 2539.64i) q^{87} +(-83777.7 + 145107. i) q^{88} +(196387. - 113384. i) q^{89} -657922. i q^{90} +438115. q^{92} +(447536. + 775156. i) q^{93} +(-194665. - 112390. i) q^{94} +(203098. - 351776. i) q^{95} +(-1.07649e6 + 621511. i) q^{96} +470089. i q^{97} +217923. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 20 q^{2} - 564 q^{4} + 1880 q^{8} + 1252 q^{9} + 3872 q^{11} + 44864 q^{15} - 37908 q^{16} + 19436 q^{18} + 159744 q^{22} - 40032 q^{23} + 28860 q^{25} + 68032 q^{29} - 21192 q^{30} + 82060 q^{32}+ \cdots - 8949984 q^{99}+O(q^{100}) $ 24 * q - 20 * q^2 - 564 * q^4 + 1880 * q^8 + 1252 * q^9 + 3872 * q^11 + 44864 * q^15 - 37908 * q^16 + 19436 * q^18 + 159744 * q^22 - 40032 * q^23 + 28860 * q^25 + 68032 * q^29 - 21192 * q^30 + 82060 * q^32 - 563240 * q^36 + 169632 * q^37 - 492128 * q^39 - 241536 * q^43 + 404312 * q^44 + 118872 * q^46 - 2091048 * q^50 + 539424 * q^51 + 15856 * q^53 + 1853888 * q^57 - 971304 * q^58 + 429912 * q^60 - 11496 * q^64 + 267904 * q^65 - 1508352 * q^67 + 5037248 * q^71 - 2550364 * q^72 + 3876024 * q^74 - 135184 * q^78 - 232224 * q^79 - 528204 * q^81 + 1508256 * q^85 + 1560848 * q^86 - 1812720 * q^88 + 7305776 * q^92 - 164384 * q^93 - 2305600 * q^95 - 8949984 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/49\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−2.33452	−	4.04351i	−0.291815	−	0.505439i	0.682424	−	0.730957i	$-0.260926\pi$
$2$	−2.33452	−	4.04351i	−0.291815	−	0.505439i	−0.974239	+	0.225518i	$0.927593\pi$
$3$	32.1003	+	18.5331i	1.18890	+	0.686412i	0.958057	−	0.286579i	$-0.0925180\pi$
$3$	32.1003	+	18.5331i	1.18890	+	0.686412i	0.230844	+	0.972991i	$0.425851\pi$
$4$	21.1000	−	36.5463i	0.329688	−	0.571036i
$5$	189.226	−	109.250i	1.51381	−	0.873996i	0.513937	−	0.857828i	$-0.328187\pi$
$5$	189.226	−	109.250i	1.51381	−	0.873996i	0.999869	−	0.0161685i	$-0.00514680\pi$
$6$		−	173.064i		−	0.801222i
$7$		0			0
$7$		0			0
$8$	−495.852			−0.968462
$9$	322.454	+	558.506i	0.442323	+	0.766126i
$10$	−883.503	−	510.091i	−0.883503	−	0.510091i
$11$	168.957	−	292.642i	0.126940	−	0.219866i	−0.795550	−	0.605888i	$-0.792818\pi$
$11$	168.957	−	292.642i	0.126940	−	0.219866i	0.922490	+	0.386022i	$0.126151\pi$
$12$	1354.64	−	782.099i	0.783932	−	0.452604i
$13$			2480.18i			1.12889i	0.825469	+	0.564447i	$0.190910\pi$
$13$			2480.18i			1.12889i	−0.825469	+	0.564447i	$0.809090\pi$
$14$		0			0
$15$	8098.94			2.39969
$16$	−192.824	−	333.981i	−0.0470761	−	0.0815382i
$17$	−5159.10	−	2978.61i	−1.05009	−	0.606271i	−0.127417	−	0.991849i	$-0.540669\pi$
$17$	−5159.10	−	2978.61i	−1.05009	−	0.606271i	−0.922675	+	0.385579i	$0.874002\pi$
$18$	1505.55	−	2607.69i	0.258153	−	0.447135i
$19$	1609.96	−	929.513i	0.234723	−	0.135517i	−0.378026	−	0.925795i	$-0.623397\pi$
$19$	1609.96	−	929.513i	0.234723	−	0.135517i	0.612749	+	0.790278i	$0.290064\pi$
$20$		−	9220.67i		−	1.15258i
$21$		0			0
$22$	−1577.73			−0.148172
$23$	5190.93	+	8990.96i	0.426640	+	0.738963i	0.996572	−	0.0827292i	$-0.0263636\pi$
$23$	5190.93	+	8990.96i	0.426640	+	0.738963i	−0.569932	+	0.821692i	$0.693030\pi$
$24$	−15917.0	−	9189.70i	−1.15140	−	0.664764i
$25$	16058.4	−	27814.0i	1.02774	−	1.78010i
$26$	10028.6	−	5790.03i	0.570586	−	0.329428i
$27$		−	3117.00i		−	0.158360i
$28$		0			0
$29$	−137.033			−0.00561862			−0.00280931	−	0.999996i	$-0.500894\pi$
$29$	−137.033			−0.00561862			−0.00280931	+	0.999996i	$0.500894\pi$
$30$	−18907.2	−	32748.1i	−0.700265	−	1.21289i
$31$	20912.7	+	12074.0i	0.701981	+	0.405289i	0.808085	−	0.589066i	$-0.200504\pi$
$31$	20912.7	+	12074.0i	0.701981	+	0.405289i	−0.106104	+	0.994355i	$0.533838\pi$
$32$	−16767.6	+	29042.3i	−0.511706	+	0.886301i
$33$	10847.1	−	6262.60i	0.301838	−	0.174266i
$34$			27814.5i			0.707676i
$35$		0			0
$36$	27215.1			0.583315
$37$	37443.9	+	64854.7i	0.739223	+	1.28037i	0.952846	+	0.303456i	$0.0981405\pi$
$37$	37443.9	+	64854.7i	0.739223	+	1.28037i	−0.213622	+	0.976916i	$0.568526\pi$
$38$	−7516.99	−	4339.93i	−0.136991	−	0.0790920i
$39$	−45965.5	+	79614.5i	−0.774886	+	1.34214i
$40$	−93828.1	+	54171.7i	−1.46606	+	0.846432i
$41$			13051.8i			0.189374i	0.995507	+	0.0946868i	$0.0301850\pi$
$41$			13051.8i			0.189374i	−0.995507	+	0.0946868i	$0.969815\pi$
$42$		0			0
$43$	−91089.1			−1.14567			−0.572837	−	0.819669i	$-0.694157\pi$
$43$	−91089.1			−1.14567			−0.572837	+	0.819669i	$0.694157\pi$
$44$	−7129.99	−	12349.5i	−0.0837010	−	0.144974i
$45$	122033.	+	70455.8i	1.33918	+	0.773178i
$46$	24236.7	−	41979.2i	0.249000	−	0.431281i
$47$	41692.6	−	24071.3i	0.401574	−	0.231849i	−0.285589	−	0.958352i	$-0.592189\pi$
$47$	41692.6	−	24071.3i	0.401574	−	0.231849i	0.687163	+	0.726503i	$0.258856\pi$
$48$		−	14294.5i		−	0.129254i
$49$		0			0
$50$	−149955.			−1.19964
$51$	−110406.	−	191229.i	−0.832303	−	1.44159i
$52$	90641.4	+	52331.8i	0.644639	+	0.372183i
$53$	−48053.1	+	83230.4i	−0.322771	+	0.559055i	−0.981059	−	0.193711i	$-0.937948\pi$
$53$	−48053.1	+	83230.4i	−0.322771	+	0.559055i	0.658288	+	0.752766i	$0.271281\pi$
$54$	−12603.6	+	7276.70i	−0.0800412	+	0.0462118i
$55$		−	73833.8i		−	0.443780i
$56$		0			0
$57$	68907.1			0.372083
$58$	319.905	+	554.092i	0.00163960	+	0.00283987i
$59$	−142788.	−	82438.8i	−0.695242	−	0.401398i	0.110331	−	0.993895i	$-0.464809\pi$
$59$	−142788.	−	82438.8i	−0.695242	−	0.401398i	−0.805573	+	0.592497i	$0.798142\pi$
$60$	170888.	−	295987.i	0.791148	−	1.37031i
$61$	−107191.	+	61886.8i	−0.472247	+	0.272652i	−0.717180	−	0.696888i	$-0.754567\pi$
$61$	−107191.	+	61886.8i	−0.472247	+	0.272652i	0.244933	+	0.969540i	$0.421234\pi$
$62$		−	112748.i		−	0.473077i
$63$		0			0
$64$	131896.			0.503142
$65$	270958.	+	469314.i	0.986649	+	1.70893i
$66$	−50645.7	−	29240.3i	−0.176162	−	0.101707i
$67$	−237259.	+	410944.i	−0.788856	+	1.36634i	0.137812	+	0.990458i	$0.455993\pi$
$67$	−237259.	+	410944.i	−0.788856	+	1.36634i	−0.926668	+	0.375881i	$0.877340\pi$
$68$	−217714.	+	125697.i	−0.692405	+	0.399760i
$69$			384817.i			1.17140i
$70$		0			0
$71$	444087.			1.24077			0.620387	−	0.784296i	$-0.286976\pi$
$71$	444087.			1.24077			0.620387	+	0.784296i	$0.286976\pi$
$72$	−159889.	−	276937.i	−0.428373	−	0.741964i
$73$	−450655.	−	260186.i	−1.15845	−	0.668829i	−0.207514	−	0.978232i	$-0.566537\pi$
$73$	−450655.	−	260186.i	−1.15845	−	0.668829i	−0.950931	+	0.309403i	$0.899871\pi$
$74$	174827.	−	302809.i	0.431433	−	0.747264i
$75$	1.03096e6	−	595226.i	2.44376	−	1.41091i
$76$		−	78451.0i		−	0.178714i
$77$		0			0
$78$	429229.			0.904494
$79$	−97094.1	−	168172.i	−0.196930	−	0.341093i	0.750602	−	0.660755i	$-0.229764\pi$
$79$	−97094.1	−	168172.i	−0.196930	−	0.341093i	−0.947531	+	0.319663i	$0.896430\pi$
$80$	−72974.5	−	42131.8i	−0.142528	−	0.0822887i
$81$	292836.	−	507208.i	0.551024	−	0.954401i
$82$	52775.2	−	30469.7i	0.0957168	−	0.0552621i
$83$			1316.59i			0.00230259i	0.999999	+	0.00115130i	$0.000366469\pi$
$83$			1316.59i			0.00230259i	−0.999999	+	0.00115130i	$0.999634\pi$
$84$		0			0
$85$	−1.30165e6			−2.11951
$86$	212649.	+	368320.i	0.334325	+	0.579068i
$87$	−4398.79	−	2539.64i	−0.00667998	−	0.00385669i
$88$	−83777.7	+	145107.i	−0.122936	+	0.212932i
$89$	196387.	−	113384.i	0.278575	−	0.160835i	−0.354203	−	0.935168i	$-0.615248\pi$
$89$	196387.	−	113384.i	0.278575	−	0.160835i	0.632778	+	0.774333i	$0.281915\pi$
$90$		−	657922.i		−	0.902500i
$91$		0			0
$92$	438115.			0.562633
$93$	447536.	+	775156.i	0.556390	+	0.963696i
$94$	−194665.	−	112390.i	−0.234371	−	0.135314i
$95$	203098.	−	351776.i	0.236883	−	0.410294i
$96$	−1.07649e6	+	621511.i	−1.21674	+	0.702482i
$97$			470089.i			0.515069i	0.966269	+	0.257534i	$0.0829101\pi$
$97$			470089.i			0.515069i	−0.966269	+	0.257534i	$0.917090\pi$
$98$		0			0
$99$	217923.			0.224594
$100$	−677667.	−	1.17375e6i	−0.677667	−	1.17375i
$101$	1.05389e6	+	608466.i	1.02290	+	0.590571i	0.914942	−	0.403585i	$-0.132236\pi$
$101$	1.05389e6	+	608466.i	1.02290	+	0.590571i	0.107957	+	0.994156i	$0.465569\pi$
$102$	−515490.	+	892854.i	−0.485757	+	0.841356i
$103$	−542406.	+	313158.i	−0.496378	+	0.286584i	−0.727217	−	0.686408i	$-0.759186\pi$
$103$	−542406.	+	313158.i	−0.496378	+	0.286584i	0.230838	+	0.972992i	$0.425853\pi$
$104$		−	1.22980e6i		−	1.09329i
$105$		0			0
$106$	448724.			0.376757
$107$	−592800.	−	1.02676e6i	−0.483902	−	0.838142i	0.515927	−	0.856632i	$-0.327447\pi$
$107$	−592800.	−	1.02676e6i	−0.483902	−	0.838142i	−0.999829	+	0.0184901i	$0.994114\pi$
$108$	−113915.	−	65768.8i	−0.0904293	−	0.0522094i
$109$	−658473.	+	1.14051e6i	−0.508462	+	0.880682i	0.491490	+	0.870883i	$0.336453\pi$
$109$	−658473.	+	1.14051e6i	−0.508462	+	0.880682i	−0.999952	+	0.00979908i	$0.996881\pi$
$110$	−298548.	+	172367.i	−0.224303	+	0.129502i
$111$			2.77581e6i			2.02965i
$112$		0			0
$113$	345360.			0.239352			0.119676	−	0.992813i	$-0.461814\pi$
$113$	345360.			0.239352			0.119676	+	0.992813i	$0.461814\pi$
$114$	−160865.	−	278627.i	−0.108579	−	0.188065i
$115$	1.96452e6	+	1.13421e6i	1.29170	+	0.745765i
$116$	−2891.39	+	5008.03i	−0.00185239	+	0.00320843i
$117$	−1.38520e6	+	799743.i	−0.864875	+	0.499336i
$118$			769820.i			0.468536i
$119$		0			0
$120$	−4.01588e6			−2.32401
$121$	828688.	+	1.43533e6i	0.467773	+	0.810206i
$122$	500479.	+	288952.i	0.275617	+	0.159128i
$123$	−241891.	+	418968.i	−0.129988	+	0.225146i
$124$	882517.	−	509522.i	0.462869	−	0.267238i
$125$		−	3.60346e6i		−	1.84497i
$126$		0			0
$127$	−1.60068e6			−0.781438			−0.390719	−	0.920510i	$-0.627774\pi$
$127$	−1.60068e6			−0.781438			−0.390719	+	0.920510i	$0.627774\pi$
$128$	765212.	+	1.32539e6i	0.364882	+	0.631993i
$129$	−2.92399e6	−	1.68817e6i	−1.36209	−	0.786405i
$130$	1.26512e6	−	2.19125e6i	0.575838	−	0.997381i
$131$	1.99308e6	−	1.15071e6i	0.886565	−	0.511859i	0.0137479	−	0.999905i	$-0.495624\pi$
$131$	1.99308e6	−	1.15071e6i	0.886565	−	0.511859i	0.872817	+	0.488047i	$0.162290\pi$
$132$		−	528564.i		−	0.229814i
$133$		0			0
$134$	2.21554e6			0.920801
$135$	−340531.	−	589817.i	−0.138406	−	0.239726i
$136$	2.55815e6	+	1.47695e6i	1.01697	+	0.587150i
$137$	−1.56791e6	+	2.71571e6i	−0.609762	+	1.05614i	0.381517	+	0.924362i	$0.375402\pi$
$137$	−1.56791e6	+	2.71571e6i	−0.609762	+	1.05614i	−0.991279	+	0.131778i	$0.957932\pi$
$138$	1.55601e6	−	898363.i	0.592073	−	0.341834i
$139$			1.73191e6i			0.644884i	0.946589	+	0.322442i	$0.104504\pi$
$139$			1.73191e6i			0.644884i	−0.946589	+	0.322442i	$0.895496\pi$
$140$		0			0
$141$	1.78446e6			0.636576
$142$	−1.03673e6	−	1.79567e6i	−0.362077	−	0.627135i
$143$	725804.	+	419043.i	0.248205	+	0.143302i
$144$	124353.	−	215387.i	0.0416457	−	0.0721325i
$145$	−25930.1	+	14970.7i	−0.00850550	+	0.00491065i
$146$			2.42964e6i			0.780697i
$147$		0			0
$148$	3.16027e6			0.974852
$149$	−9469.11	−	16401.0i	−0.00286253	−	0.00495805i	0.864591	−	0.502477i	$-0.167578\pi$
$149$	−9469.11	−	16401.0i	−0.00286253	−	0.00495805i	−0.867453	+	0.497519i	$0.834245\pi$
$150$	−4.81360e6	−	2.77913e6i	−1.42625	−	0.823447i
$151$	3.23693e6	−	5.60653e6i	0.940161	−	1.62841i	0.175000	−	0.984568i	$-0.444008\pi$
$151$	3.23693e6	−	5.60653e6i	0.940161	−	1.62841i	0.765162	−	0.643838i	$-0.222659\pi$
$152$	−798304.	+	460901.i	−0.227320	+	0.131243i
$153$		−	3.84185e6i		−	1.07267i
$154$		0			0
$155$	5.27630e6			1.41688
$156$	1.93975e6	+	3.35974e6i	0.510941	+	0.884976i
$157$	−6.29620e6	−	3.63511e6i	−1.62697	−	0.939332i	−0.984990	−	0.172611i	$-0.944780\pi$
$157$	−6.29620e6	−	3.63511e6i	−1.62697	−	0.939332i	−0.641980	−	0.766721i	$-0.721887\pi$
$158$	−453336.	+	785202.i	−0.114934	+	0.199072i
$159$	−3.08504e6	+	1.78115e6i	−0.767484	+	0.443107i
$160$			7.32740e6i			1.78892i
$161$		0			0
$162$	−2.73453e6			−0.643188
$163$	−1.52538e6	−	2.64204e6i	−0.352222	−	0.610066i	0.634417	−	0.772991i	$-0.281240\pi$
$163$	−1.52538e6	−	2.64204e6i	−0.352222	−	0.610066i	−0.986638	+	0.162925i	$0.947907\pi$
$164$	476996.	+	275394.i	0.108139	+	0.0624342i
$165$	1.36837e6	−	2.37009e6i	0.304616	−	0.527610i
$166$	5323.65	−	3073.61i	0.00116382	−	0.000671931i
$167$		−	8.97646e6i		−	1.92733i	−0.267118	−	0.963664i	$-0.586071\pi$
$167$		−	8.97646e6i		−	1.92733i	0.267118	−	0.963664i	$-0.413929\pi$
$168$		0			0
$169$	−1.32448e6			−0.274401
$170$	3.03872e6	+	5.26322e6i	0.618506	+	1.07128i
$171$	1.03828e6	+	599450.i	0.207647	+	0.119885i
$172$	−1.92198e6	+	3.32897e6i	−0.377715	+	0.654221i
$173$	4.39172e6	−	2.53556e6i	0.848197	−	0.489707i	−0.0118452	−	0.999930i	$-0.503771\pi$
$173$	4.39172e6	−	2.53556e6i	0.848197	−	0.489707i	0.860042	+	0.510223i	$0.170437\pi$
$174$			23715.4i			0.00450176i
$175$		0			0
$176$	−130316.			−0.0239033
$177$	−3.05570e6	−	5.29262e6i	−0.551049	−	0.954445i
$178$	−916937.	−	529394.i	−0.162585	−	0.0938683i
$179$	1.06759e6	−	1.84913e6i	0.186143	−	0.322409i	−0.757818	−	0.652466i	$-0.773734\pi$
$179$	1.06759e6	−	1.84913e6i	0.186143	−	0.322409i	0.943961	+	0.330057i	$0.107068\pi$
$180$	5.14980e6	−	2.97324e6i	0.883025	−	0.509815i
$181$		−	3.35610e6i		−	0.565978i	−0.959123	−	0.282989i	$-0.908674\pi$
$181$		−	3.35610e6i		−	0.565978i	0.959123	−	0.282989i	$-0.0913260\pi$
$182$		0			0
$183$	−4.58782e6			−0.748606
$184$	−2.57394e6	−	4.45819e6i	−0.413185	−	0.715657i
$185$	1.41707e7	+	8.18145e6i	2.23808	+	1.29216i
$186$	2.08957e6	−	3.61923e6i	0.324726	−	0.562442i
$187$	−1.74333e6	+	1.00651e6i	−0.266597	+	0.153920i
$188$		−	2.03162e6i		−	0.305751i
$189$		0			0
$190$	−1.89654e6			−0.276504
$191$	3.68708e6	+	6.38620e6i	0.529154	+	0.916522i	0.999422	+	0.0339979i	$0.0108240\pi$
$191$	3.68708e6	+	6.38620e6i	0.529154	+	0.916522i	−0.470268	+	0.882524i	$0.655843\pi$
$192$	4.23389e6	+	2.44444e6i	0.598186	+	0.345363i
$193$	−2.01568e6	+	3.49127e6i	−0.280382	+	0.485636i	−0.971479	−	0.237126i	$-0.923795\pi$
$193$	−2.01568e6	+	3.49127e6i	−0.280382	+	0.485636i	0.691097	+	0.722762i	$0.257128\pi$
$194$	1.90081e6	−	1.09743e6i	0.260336	−	0.150305i
$195$			2.00868e7i			2.70899i
$196$		0			0
$197$	3.14188e6			0.410951			0.205476	−	0.978662i	$-0.434126\pi$
$197$	3.14188e6			0.410951			0.205476	+	0.978662i	$0.434126\pi$
$198$	−508746.	−	881174.i	−0.0655398	−	0.113518i
$199$	−1.34682e7	−	7.77587e6i	−1.70903	−	0.986711i	−0.935760	−	0.352637i	$-0.885285\pi$
$199$	−1.34682e7	−	7.77587e6i	−1.70903	−	0.986711i	−0.773272	−	0.634074i	$-0.781382\pi$
$200$	−7.96261e6	+	1.37916e7i	−0.995326	+	1.72396i
$201$	−1.52322e7	+	8.79430e6i	−1.87574	+	1.08296i
$202$		−	5.68191e6i		−	0.689350i
$203$		0			0
$204$	−9.31827e6			−1.09760
$205$	1.42591e6	+	2.46974e6i	0.165512	+	0.286675i
$206$	2.53252e6	+	1.46215e6i	0.289701	+	0.167259i
$207$	−3.34767e6	+	5.79834e6i	−0.377426	+	0.653721i
$208$	828332.	−	478238.i	0.0920480	−	0.0531439i
$209$		−	628190.i		−	0.0688101i
$210$		0			0
$211$	−8.36559e6			−0.890532			−0.445266	−	0.895398i	$-0.646891\pi$
$211$	−8.36559e6			−0.890532			−0.445266	+	0.895398i	$0.646891\pi$
$212$	2.02784e6	+	3.51233e6i	0.212827	+	0.368627i
$213$	1.42553e7	+	8.23032e6i	1.47516	+	0.851683i
$214$	−2.76781e6	+	4.79399e6i	−0.282420	+	0.489165i
$215$	−1.72364e7	+	9.95145e6i	−1.73433	+	1.00132i
$216$			1.54557e6i			0.153366i
$217$		0			0
$218$	6.14888e6			0.593508
$219$	−9.64411e6	−	1.67041e7i	−0.918184	−	1.59034i
$220$	−2.69835e6	−	1.55790e6i	−0.253414	−	0.146309i
$221$	7.38748e6	−	1.27955e7i	0.684415	−	1.18544i
$222$	1.12240e7	−	6.48018e6i	1.02586	−	0.592282i
$223$		−	593711.i		−	0.0535378i	−0.999642	−	0.0267689i	$-0.991478\pi$
$223$		−	593711.i		−	0.0535378i	0.999642	−	0.0267689i	$-0.00852182\pi$
$224$		0			0
$225$	2.07124e7			1.81837
$226$	−806250.	−	1.39647e6i	−0.0698465	−	0.120978i
$227$	−2.67216e6	−	1.54277e6i	−0.228446	−	0.131894i	0.381409	−	0.924407i	$-0.375439\pi$
$227$	−2.67216e6	−	1.54277e6i	−0.228446	−	0.131894i	−0.609855	+	0.792513i	$0.708772\pi$
$228$	1.45394e6	−	2.51830e6i	0.122671	−	0.212473i
$229$	1.22658e7	−	7.08164e6i	1.02138	−	0.589695i	0.106877	−	0.994272i	$-0.465915\pi$
$229$	1.22658e7	−	7.08164e6i	1.02138	−	0.589695i	0.914504	+	0.404577i	$0.132581\pi$
$230$		−	1.05914e7i		−	0.870501i
$231$		0			0
$232$	67947.9			0.00544142
$233$	4.62614e6	+	8.01271e6i	0.365722	+	0.633449i	0.988892	−	0.148638i	$-0.0474888\pi$
$233$	4.62614e6	+	8.01271e6i	0.365722	+	0.633449i	−0.623170	+	0.782086i	$0.714155\pi$
$234$	6.46753e6	+	3.73403e6i	0.504767	+	0.291428i
$235$	5.25955e6	−	9.10981e6i	0.405270	−	0.701949i
$236$	−6.02567e6	+	3.47892e6i	−0.458426	+	0.264672i
$237$		−	7.19783e6i		−	0.540700i
$238$		0			0
$239$	−2.66050e7			−1.94881			−0.974406	−	0.224797i	$-0.927828\pi$
$239$	−2.66050e7			−1.94881			−0.974406	+	0.224797i	$0.927828\pi$
$240$	−1.56167e6	−	2.70489e6i	−0.112968	−	0.195666i
$241$	2.64296e6	+	1.52592e6i	0.188817	+	0.109013i	0.591428	−	0.806358i	$-0.298564\pi$
$241$	2.64296e6	+	1.52592e6i	0.188817	+	0.109013i	−0.402612	+	0.915371i	$0.631898\pi$
$242$	3.86918e6	−	6.70161e6i	0.273006	−	0.472861i
$243$	1.68324e7	−	9.71821e6i	1.17308	−	0.677278i
$244$			5.22325e6i			0.359560i
$245$		0			0
$246$	2.25880e6			0.151730
$247$	2.30536e6	+	3.99300e6i	0.152985	+	0.264977i
$248$	−1.03696e7	−	5.98690e6i	−0.679841	−	0.392507i
$249$	−24400.6	+	42263.0i	−0.00158053	+	0.00273755i
$250$	−1.45706e7	+	8.41234e6i	−0.932519	+	0.538390i
$251$		−	1.74661e7i		−	1.10452i	−0.833670	−	0.552262i	$-0.813765\pi$
$251$		−	1.74661e7i		−	1.10452i	0.833670	−	0.552262i	$-0.186235\pi$
$252$		0			0
$253$	3.50818e6			0.216631
$254$	3.73683e6	+	6.47238e6i	0.228035	+	0.394969i
$255$	−4.17833e7	−	2.41236e7i	−2.51989	−	1.45486i
$256$	7.79347e6	−	1.34987e7i	0.464527	−	0.804584i
$257$	1.59284e7	−	9.19627e6i	0.938367	−	0.541767i	0.0489192	−	0.998803i	$-0.484422\pi$
$257$	1.59284e7	−	9.19627e6i	0.938367	−	0.541767i	0.889448	+	0.457036i	$0.151089\pi$
$258$			1.57642e7i			0.917939i
$259$		0			0
$260$	2.28689e7			1.30114
$261$	−44186.6	−	76533.5i	−0.00248525	−	0.00430457i
$262$	−9.30577e6	−	5.37269e6i	−0.517426	−	0.298736i
$263$	−1.18171e7	+	2.04677e7i	−0.649594	+	1.12513i	0.333626	+	0.942706i	$0.391728\pi$
$263$	−1.18171e7	+	2.04677e7i	−0.649594	+	1.12513i	−0.983220	+	0.182424i	$0.941606\pi$
$264$	−5.37858e6	+	3.10532e6i	−0.292318	+	0.168770i
$265$			2.09991e7i			1.12840i
$266$		0			0
$267$	8.40543e6			0.441597
$268$	1.00123e7	+	1.73419e7i	0.520153	+	0.900931i
$269$	8.21520e6	+	4.74305e6i	0.422048	+	0.243669i	0.695953	−	0.718087i	$-0.254982\pi$
$269$	8.21520e6	+	4.74305e6i	0.422048	+	0.243669i	−0.273905	+	0.961757i	$0.588316\pi$
$270$	−1.58995e6	+	2.75388e6i	−0.0807780	+	0.139912i
$271$	1.13518e7	−	6.55395e6i	0.570369	−	0.329303i	−0.186928	−	0.982374i	$-0.559853\pi$
$271$	1.13518e7	−	6.55395e6i	0.570369	−	0.329303i	0.757297	+	0.653071i	$0.226520\pi$
$272$			2.29739e6i			0.114163i
$273$		0			0
$274$	1.46413e7			0.711752
$275$	−5.42636e6	−	9.39874e6i	−0.260922	−	0.451930i
$276$	1.40636e7	+	8.11965e6i	0.668915	+	0.386198i
$277$	1.06422e6	−	1.84328e6i	0.0500717	−	0.0867267i	−0.839903	−	0.542736i	$-0.817388\pi$
$277$	1.06422e6	−	1.84328e6i	0.0500717	−	0.0867267i	0.889975	+	0.456009i	$0.150722\pi$
$278$	7.00301e6	−	4.04319e6i	0.325949	−	0.188187i
$279$			1.55732e7i			0.717075i
$280$		0			0
$281$	3.23005e7			1.45576			0.727880	−	0.685705i	$-0.240506\pi$
$281$	3.23005e7			1.45576			0.727880	+	0.685705i	$0.240506\pi$
$282$	−4.16587e6	−	7.21549e6i	−0.185762	−	0.321750i
$283$	1.63068e7	+	9.41471e6i	0.719463	+	0.415382i	0.814555	−	0.580086i	$-0.196981\pi$
$283$	1.63068e7	+	9.41471e6i	0.719463	+	0.415382i	−0.0950922	+	0.995468i	$0.530315\pi$
$284$	9.37024e6	−	1.62297e7i	0.409068	−	0.708527i
$285$	1.30390e7	−	7.52807e6i	0.563261	−	0.325199i
$286$		−	3.91306e6i		−	0.167270i
$287$		0			0
$288$	−2.16271e7			−0.905358
$289$	5.67543e6	+	9.83013e6i	0.235128	+	0.407254i
$290$	121069.	+	69899.0i	0.00496407	+	0.00286601i
$291$	−8.71223e6	+	1.50900e7i	−0.353550	+	0.612366i
$292$	−1.90177e7	+	1.09799e7i	−0.763851	+	0.441009i
$293$		−	2.71896e7i		−	1.08094i	−0.841364	−	0.540468i	$-0.818247\pi$
$293$		−	2.71896e7i		−	1.08094i	0.841364	−	0.540468i	$-0.181753\pi$
$294$		0			0
$295$	−3.60256e7			−1.40328
$296$	−1.85666e7	−	3.21584e7i	−0.715909	−	1.23999i
$297$	−912165.	−	526638.i	−0.0348180	−	0.0201022i
$298$	−44211.7	+	76576.8i	−0.00167066	+	0.00289367i
$299$	−2.22992e7	+	1.28744e7i	−0.834211	+	0.481632i
$300$		−	5.02371e7i		−	1.86063i
$301$		0			0
$302$	−3.02267e7			−1.09741
$303$	2.25536e7	+	3.90639e7i	0.810750	+	1.40426i
$304$	−620879.	−	358464.i	−0.0220997	−	0.0127593i
$305$	−1.35222e7	+	2.34211e7i	−0.476593	+	0.825484i
$306$	−1.55346e7	+	8.96889e6i	−0.542169	+	0.313022i
$307$			2.59826e7i			0.897981i	0.893536	+	0.448991i	$0.148216\pi$
$307$			2.59826e7i			0.897981i	−0.893536	+	0.448991i	$0.851784\pi$
$308$		0			0
$309$	−2.32152e7			−0.786859
$310$	−1.23176e7	−	2.13348e7i	−0.413468	−	0.716148i
$311$	−7.09517e6	−	4.09640e6i	−0.235875	−	0.136182i	0.377404	−	0.926049i	$-0.376817\pi$
$311$	−7.09517e6	−	4.09640e6i	−0.235875	−	0.136182i	−0.613279	+	0.789866i	$0.710150\pi$
$312$	2.27921e7	−	3.94771e7i	0.750448	−	1.29981i
$313$	1.55031e6	−	895071.i	0.0505575	−	0.0291894i	−0.474508	−	0.880251i	$-0.657374\pi$
$313$	1.55031e6	−	895071.i	0.0505575	−	0.0291894i	0.525066	+	0.851062i	$0.324041\pi$
$314$			3.39450e7i			1.09644i
$315$		0			0
$316$	−8.19475e6			−0.259702
$317$	1.85409e6	+	3.21138e6i	0.0582040	+	0.100812i	0.893659	−	0.448746i	$-0.148129\pi$
$317$	1.85409e6	+	3.21138e6i	0.0582040	+	0.100812i	−0.835455	+	0.549559i	$0.814796\pi$
$318$	1.44042e7	+	8.31626e6i	0.447927	+	0.258611i
$319$	−23152.6	+	40101.4i	−0.000713226	+	0.00123534i
$320$	2.49581e7	−	1.44095e7i	0.761659	−	0.439744i
$321$		−	4.39458e7i		−	1.32862i
$322$		0			0
$323$	−1.10746e7			−0.328641
$324$	−1.23577e7	−	2.14042e7i	−0.363332	−	0.629309i
$325$	6.89837e7	+	3.98278e7i	2.00954	+	1.16021i
$326$	−7.12208e6	+	1.23358e7i	−0.205567	+	0.356053i
$327$	−4.22744e7	+	2.44071e7i	−1.20902	+	0.698029i
$328$		−	6.47178e6i		−	0.183401i
$329$		0			0
$330$	−1.27780e7			−0.355566
$331$	−3.12551e7	−	5.41354e7i	−0.861860	−	1.49279i	−0.870131	−	0.492820i	$-0.835966\pi$
$331$	−3.12551e7	−	5.41354e7i	−0.861860	−	1.49279i	0.00827058	−	0.999966i	$-0.497367\pi$
$332$	48116.6	+	27780.1i	0.00131486	+	0.000759137i
$333$	−2.41478e7	+	4.18253e7i	−0.653951	+	1.13268i
$334$	−3.62964e7	+	2.09557e7i	−0.974146	+	0.562423i
$335$			1.03682e8i			2.75783i
$336$		0			0
$337$	6.69875e7			1.75027			0.875134	−	0.483882i	$-0.160773\pi$
$337$	6.69875e7			1.75027			0.875134	+	0.483882i	$0.160773\pi$
$338$	3.09203e6	+	5.35555e6i	0.0800743	+	0.138693i
$339$	1.10862e7	+	6.40060e6i	0.284566	+	0.164294i
$340$	−2.74648e7	+	4.75704e7i	−0.698778	+	1.21032i
$341$	7.06669e6	−	4.07996e6i	0.178219	−	0.102895i
$342$		−	5.59771e6i		−	0.139937i
$343$		0			0
$344$	4.51668e7			1.10954
$345$	4.20411e7	+	7.28173e7i	1.02380	+	1.77328i
$346$	−2.05051e7	−	1.18386e7i	−0.495033	−	0.285808i
$347$	3.43451e7	−	5.94875e7i	0.822009	−	1.42376i	−0.0821743	−	0.996618i	$-0.526186\pi$
$347$	3.43451e7	−	5.94875e7i	0.822009	−	1.42376i	0.904184	−	0.427144i	$-0.140480\pi$
$348$	−185629.	+	107173.i	−0.00440462	+	0.00254301i
$349$		−	5.59039e7i		−	1.31512i	−0.753402	−	0.657561i	$-0.771588\pi$
$349$		−	5.59039e7i		−	1.31512i	0.753402	−	0.657561i	$-0.228412\pi$
$350$		0			0
$351$	7.73072e6			0.178772
$352$	5.66600e6	+	9.81379e6i	0.129912	+	0.225014i
$353$	−2.35854e7	−	1.36170e7i	−0.536190	−	0.309570i	0.207343	−	0.978268i	$-0.433518\pi$
$353$	−2.35854e7	−	1.36170e7i	−0.536190	−	0.309570i	−0.743534	+	0.668699i	$0.766852\pi$
$354$	−1.42672e7	+	2.47115e7i	−0.321609	+	0.557043i
$355$	8.40327e7	−	4.85163e7i	1.87829	−	1.08443i
$356$		−	9.56961e6i		−	0.212102i
$357$		0			0
$358$	−9.96928e6			−0.217278
$359$	−1.55148e6	−	2.68723e6i	−0.0335322	−	0.0580794i	0.848772	−	0.528759i	$-0.177342\pi$
$359$	−1.55148e6	−	2.68723e6i	−0.0335322	−	0.0580794i	−0.882304	+	0.470679i	$0.844009\pi$
$360$	−6.05104e7	−	3.49357e7i	−1.29695	−	0.748793i
$361$	−2.17950e7	+	3.77500e7i	−0.463270	+	0.802407i
$362$	−1.35704e7	+	7.83489e6i	−0.286067	+	0.165161i
$363$			6.14327e7i			1.28434i
$364$		0			0
$365$	−1.13701e8			−2.33822
$366$	1.07104e7	+	1.85509e7i	0.218455	+	0.378374i
$367$	1.09551e7	+	6.32491e6i	0.221624	+	0.127955i	0.606702	−	0.794929i	$-0.292492\pi$
$367$	1.09551e7	+	6.32491e6i	0.221624	+	0.127955i	−0.385078	+	0.922884i	$0.625825\pi$
$368$	2.00187e6	−	3.46734e6i	0.0401692	−	0.0695750i
$369$	−7.28952e6	+	4.20861e6i	−0.145084	+	0.0837644i
$370$		−	7.63991e7i		−	1.50828i
$371$		0			0
$372$	3.77721e7			0.733740
$373$	1.82028e7	+	3.15282e7i	0.350762	+	0.607537i	0.986383	−	0.164464i	$-0.0525893\pi$
$373$	1.82028e7	+	3.15282e7i	0.350762	+	0.607537i	−0.635621	+	0.772001i	$0.719256\pi$
$374$	8.13968e6	+	4.69945e6i	0.155594	+	0.0898322i
$375$	6.67833e7	−	1.15672e8i	1.26641	−	2.19349i
$376$	−2.06734e7	+	1.19358e7i	−0.388909	+	0.224537i
$377$		−	339865.i		−	0.00634282i
$378$		0			0
$379$	6.04753e6			0.111086			0.0555431	−	0.998456i	$-0.482311\pi$
$379$	6.04753e6			0.111086			0.0555431	+	0.998456i	$0.482311\pi$
$380$	−8.57073e6	−	1.48449e7i	−0.156195	−	0.270538i
$381$	−5.13825e7	−	2.96657e7i	−0.929052	−	0.536389i
$382$	1.72151e7	−	2.98175e7i	0.308830	−	0.534910i
$383$	7.21667e7	−	4.16655e7i	1.28452	−	0.741617i	0.306848	−	0.951759i	$-0.400726\pi$
$383$	7.21667e7	−	4.16655e7i	1.28452	−	0.741617i	0.977671	+	0.210141i	$0.0673924\pi$
$384$			5.67271e7i			1.00184i
$385$		0			0
$386$	1.88226e7			0.327279
$387$	−2.93720e7	−	5.08738e7i	−0.506758	−	0.877731i
$388$	1.71800e7	+	9.91890e6i	0.294123	+	0.169812i
$389$	3.11160e7	−	5.38945e7i	0.528609	−	0.915578i	−0.470834	−	0.882222i	$-0.656047\pi$
$389$	3.11160e7	−	5.38945e7i	0.528609	−	0.915578i	0.999444	−	0.0333566i	$-0.0106197\pi$
$390$	8.12213e7	−	4.68931e7i	1.36923	−	0.790525i
$391$		−	6.18470e7i		−	1.03464i
$392$		0			0
$393$	8.53047e7			1.40538
$394$	−7.33477e6	−	1.27042e7i	−0.119922	−	0.207711i
$395$	−3.67454e7	−	2.12150e7i	−0.596227	−	0.344232i
$396$	4.59818e6	−	7.96428e6i	0.0740458	−	0.128251i
$397$	−2.93369e7	+	1.69377e7i	−0.468859	+	0.270696i	−0.715762	−	0.698344i	$-0.753920\pi$
$397$	−2.93369e7	+	1.69377e7i	−0.468859	+	0.270696i	0.246903	+	0.969040i	$0.420587\pi$
$398$			7.26117e7i			1.15175i
$399$		0			0
$400$	−1.23858e7			−0.193528
$401$	−4.41730e7	−	7.65099e7i	−0.685053	−	1.18655i	−0.973420	−	0.229027i	$-0.926446\pi$
$401$	−4.41730e7	−	7.65099e7i	−0.685053	−	1.18655i	0.288367	−	0.957520i	$-0.406888\pi$
$402$	7.11196e7	+	4.10609e7i	1.09474	+	0.632049i
$403$	−2.99456e7	+	5.18673e7i	−0.457528	+	0.792462i
$404$	4.44744e7	−	2.56773e7i	0.674475	−	0.389408i
$405$		−	1.27969e8i		−	1.92637i
$406$		0			0
$407$	2.53056e7			0.375347
$408$	5.47450e7	+	9.48211e7i	0.806054	+	1.39613i
$409$	−9.02983e7	−	5.21337e7i	−1.31980	−	0.761989i	−0.336107	−	0.941824i	$-0.609110\pi$
$409$	−9.02983e7	−	5.21337e7i	−1.31980	−	0.761989i	−0.983697	+	0.179835i	$0.942444\pi$
$410$	6.65761e6	−	1.15313e7i	0.0965977	−	0.167312i
$411$	−1.00661e8	+	5.81167e7i	−1.44989	+	0.837097i
$412$			2.64306e7i			0.377933i
$413$		0			0
$414$	3.12608e7			0.440554
$415$	143837.	+	249133.i	0.00201246	+	0.00348568i
$416$	−7.20301e7	−	4.15866e7i	−1.00054	−	0.577662i
$417$	−3.20978e7	+	5.55950e7i	−0.442656	+	0.766704i
$418$	−2.54009e6	+	1.46652e6i	−0.0347793	+	0.0200798i
$419$			3.90828e7i			0.531304i	0.964069	+	0.265652i	$0.0855873\pi$
$419$			3.90828e7i			0.531304i	−0.964069	+	0.265652i	$0.914413\pi$
$420$		0			0
$421$	4.83618e7			0.648121			0.324061	−	0.946036i	$-0.394952\pi$
$421$	4.83618e7			0.648121			0.324061	+	0.946036i	$0.394952\pi$
$422$	1.95296e7	+	3.38263e7i	0.259871	+	0.450109i
$423$	2.68879e7	+	1.55237e7i	0.355251	+	0.205104i
$424$	2.38273e7	−	4.12700e7i	0.312591	−	0.541423i
$425$	−1.65694e8	+	9.56635e7i	−2.15844	+	1.24618i
$426$		−	7.68554e7i		−	0.994135i
$427$		0			0
$428$	−5.00324e7			−0.638146
$429$	1.55324e7	+	2.69028e7i	0.196728	+	0.340743i
$430$	8.04775e7	+	4.64637e7i	1.01221	+	0.584398i
$431$	−4.15193e7	+	7.19135e7i	−0.518583	+	0.898211i	0.481184	+	0.876619i	$0.340207\pi$
$431$	−4.15193e7	+	7.19135e7i	−0.518583	+	0.898211i	−0.999767	+	0.0215919i	$0.993127\pi$
$432$	−1.04102e6	+	601032.i	−0.0129124	+	0.00745497i
$433$			1.19303e8i			1.46956i	0.678306	+	0.734779i	$0.262714\pi$
$433$			1.19303e8i			1.46956i	−0.678306	+	0.734779i	$0.737286\pi$
$434$		0			0
$435$	−1.10982e6			−0.0134829
$436$	2.77876e7	+	4.81296e7i	0.335268	+	0.580701i
$437$	1.67144e7	+	9.65008e6i	0.200284	+	0.115634i
$438$	−4.50288e7	+	7.79921e7i	−0.535880	+	0.928171i
$439$	6.28400e6	−	3.62807e6i	0.0742750	−	0.0428827i	−0.462403	−	0.886670i	$-0.653012\pi$
$439$	6.28400e6	−	3.62807e6i	0.0742750	−	0.0428827i	0.536678	+	0.843787i	$0.319679\pi$
$440$			3.66107e7i			0.429784i
$441$		0			0
$442$	−6.89849e7			−0.798891
$443$	−6.48058e7	−	1.12247e8i	−0.745423	−	1.29111i	−0.949997	−	0.312259i	$-0.898914\pi$
$443$	−6.48058e7	−	1.12247e8i	−0.745423	−	1.29111i	0.204574	−	0.978851i	$-0.434419\pi$
$444$	1.01446e8	+	5.85696e7i	1.15900	+	0.669150i
$445$	2.47743e7	−	4.29103e7i	0.281139	−	0.486947i
$446$	−2.40068e6	+	1.38603e6i	−0.0270601	+	0.0156231i
$447$		−	701969.i		−	0.00785951i
$448$		0			0
$449$	−1.01683e8			−1.12333			−0.561666	−	0.827364i	$-0.689839\pi$
$449$	−1.01683e8			−1.12333			−0.561666	+	0.827364i	$0.689839\pi$
$450$	−4.83535e7	−	8.37508e7i	−0.530629	−	0.919076i
$451$	3.81951e6	+	2.20519e6i	0.0416369	+	0.0240390i
$452$	7.28711e6	−	1.26216e7i	0.0789114	−	0.136679i
$453$	2.07813e8	−	1.19981e8i	2.23552	−	1.29068i
$454$			1.44065e7i			0.153954i
$455$		0			0
$456$	−3.41678e7			−0.360348
$457$	5.53580e7	+	9.58828e7i	0.580005	+	1.00460i	0.995478	+	0.0949923i	$0.0302826\pi$
$457$	5.53580e7	+	9.58828e7i	0.580005	+	1.00460i	−0.415473	+	0.909605i	$0.636384\pi$
$458$	−5.72693e7	−	3.30645e7i	−0.596109	−	0.344164i
$459$	−9.28432e6	+	1.60809e7i	−0.0960090	+	0.166293i
$460$	8.29027e7	−	4.78639e7i	0.851717	−	0.491739i
$461$		−	6.62027e7i		−	0.675730i	−0.941195	−	0.337865i	$-0.890295\pi$
$461$		−	6.62027e7i		−	0.675730i	0.941195	−	0.337865i	$-0.109705\pi$
$462$		0			0
$463$	−5.93183e7			−0.597649			−0.298824	−	0.954308i	$-0.596594\pi$
$463$	−5.93183e7			−0.597649			−0.298824	+	0.954308i	$0.596594\pi$
$464$	26423.1	+	45766.2i	0.000264503	+	0.000458132i
$465$	1.69371e8	+	9.77863e7i	1.68453	+	0.972566i
$466$	2.15996e7	−	3.74117e7i	0.213446	−	0.369700i
$467$	−1.18679e8	+	6.85194e7i	−1.16526	+	0.672764i	−0.952559	−	0.304353i	$-0.901560\pi$
$467$	−1.18679e8	+	6.85194e7i	−1.16526	+	0.672764i	−0.212703	+	0.977117i	$0.568227\pi$
$468$			6.74984e7i			0.658500i
$469$		0			0
$470$	−4.91141e7			−0.473056
$471$	−1.34740e8	−	2.33377e8i	−1.28954	−	2.23354i
$472$	7.08019e7	+	4.08775e7i	0.673316	+	0.388739i
$473$	−1.53901e7	+	2.66565e7i	−0.145432	+	0.251895i
$474$	−2.91045e7	+	1.68035e7i	−0.273291	+	0.157784i
$475$		−	5.97061e7i		−	0.557106i
$476$		0			0
$477$	−6.19796e7			−0.571076
$478$	6.21100e7	+	1.07578e8i	0.568693	+	0.985004i
$479$	1.28847e7	+	7.43898e6i	0.117238	+	0.0676872i	0.557472	−	0.830196i	$-0.311771\pi$
$479$	1.28847e7	+	7.43898e6i	0.117238	+	0.0676872i	−0.440234	+	0.897883i	$0.645105\pi$
$480$	−1.35800e8	+	2.35212e8i	−1.22793	+	2.12684i
$481$	−1.60851e8	+	9.28675e7i	−1.44540	+	0.834504i
$482$		−	1.42491e7i		−	0.127247i
$483$		0			0
$484$	6.99413e7			0.616876
$485$	5.13571e7	+	8.89530e7i	0.450168	+	0.779714i
$486$	−7.85913e7	−	4.53747e7i	−0.684645	−	0.395280i
$487$	2.82488e7	−	4.89283e7i	0.244576	−	0.423617i	−0.717437	−	0.696624i	$-0.754685\pi$
$487$	2.82488e7	−	4.89283e7i	0.244576	−	0.423617i	0.962012	+	0.273006i	$0.0880180\pi$
$488$	5.31509e7	−	3.06867e7i	0.457353	−	0.264053i
$489$		−	1.13080e8i		−	0.967077i
$490$		0			0
$491$	−5.45185e7			−0.460574			−0.230287	−	0.973123i	$-0.573966\pi$
$491$	−5.45185e7			−0.460574			−0.230287	+	0.973123i	$0.573966\pi$
$492$	1.02078e7	+	1.76805e7i	0.0857112	+	0.148456i
$493$	706965.	+	408166.i	0.00590007	+	0.00340640i
$494$	1.07638e7	−	1.86435e7i	0.0892864	−	0.154649i
$495$	4.12367e7	−	2.38080e7i	0.339991	−	0.196294i
$496$		−	9.31258e6i		−	0.0763177i
$497$		0			0
$498$	227855.			0.00184489
$499$	1.03544e8	+	1.79343e8i	0.833339	+	1.44339i	0.895375	+	0.445312i	$0.146907\pi$
$499$	1.03544e8	+	1.79343e8i	0.833339	+	1.44339i	−0.0620362	+	0.998074i	$0.519759\pi$
$500$	−1.31693e8	−	7.60330e7i	−1.05354	−	0.608264i
$501$	1.66362e8	−	2.88147e8i	1.32294	−	2.29140i
$502$	−7.06244e7	+	4.07750e7i	−0.558269	+	0.322317i
$503$			6.02477e7i			0.473409i	0.971582	+	0.236705i	$0.0760673\pi$
$503$			6.02477e7i			0.473409i	−0.971582	+	0.236705i	$0.923933\pi$
$504$		0			0
$505$	2.65899e8			2.06463
$506$	−8.18991e6	−	1.41853e7i	−0.0632161	−	0.109493i
$507$	−4.25162e7	−	2.45468e7i	−0.326235	−	0.188352i
$508$	−3.37745e7	+	5.84991e7i	−0.257631	+	0.446229i
$509$	−4.33827e7	+	2.50470e7i	−0.328976	+	0.189934i	−0.655386	−	0.755294i	$-0.727494\pi$
$509$	−4.33827e7	+	2.50470e7i	−0.328976	+	0.189934i	0.326411	+	0.945228i	$0.394161\pi$
$510$			2.25268e8i			1.69820i
$511$		0			0
$512$	2.51711e7			0.187539
$513$	−2.89729e6	−	5.01826e6i	−0.0214605	−	0.0371707i
$514$	−7.43704e7	−	4.29378e7i	−0.547660	−	0.316191i
$515$	−6.84248e7	+	1.18515e8i	−0.500947	+	0.867666i
$516$	−1.23393e8	+	7.12407e7i	−0.898131	+	0.518536i
$517$		−	1.62680e7i		−	0.117723i
$518$		0			0
$519$	1.87968e8			1.34456
$520$	−1.34355e8	−	2.32710e8i	−0.955532	−	1.65503i
$521$	1.12365e8	+	6.48737e7i	0.794541	+	0.458728i	0.841559	−	0.540166i	$-0.181638\pi$
$521$	1.12365e8	+	6.48737e7i	0.794541	+	0.458728i	−0.0470178	+	0.998894i	$0.514972\pi$
$522$	−206309.	+	357338.i	−0.00145046	+	0.00251228i
$523$	1.58592e8	−	9.15633e7i	1.10860	−	0.640053i	0.170137	−	0.985420i	$-0.445579\pi$
$523$	1.58592e8	−	9.15633e7i	1.10860	−	0.640053i	0.938468	+	0.345367i	$0.112246\pi$
$524$		−	9.71196e7i		−	0.675015i
$525$		0			0
$526$	1.10349e8			0.758245
$527$	−7.19272e7	−	1.24582e8i	−0.491429	−	0.851181i
$528$	−4.18317e6	−	2.41516e6i	−0.0284187	−	0.0164075i
$529$	2.01263e7	−	3.48598e7i	0.135956	−	0.235482i
$530$	8.49101e7	−	4.90229e7i	0.570338	−	0.329285i
$531$		−	1.06331e8i		−	0.710191i
$532$		0			0
$533$	−3.23709e7			−0.213783
$534$	−1.96227e7	−	3.39874e7i	−0.128865	−	0.223200i
$535$	−2.24346e8	−	1.29526e8i	−1.46507	−	0.845857i
$536$	1.17645e8	−	2.03768e8i	0.763977	−	1.32325i
$537$	6.85402e7	−	3.95717e7i	0.442612	−	0.255542i
$538$		−	4.42910e7i		−	0.284426i
$539$		0			0
$540$	−2.87408e7			−0.182523
$541$	−2.62933e7	−	4.55414e7i	−0.166056	−	0.287617i	0.770974	−	0.636867i	$-0.219770\pi$
$541$	−2.62933e7	−	4.55414e7i	−0.166056	−	0.287617i	−0.937030	+	0.349250i	$0.886437\pi$
$542$	−5.30019e7	−	3.06007e7i	−0.332884	−	0.192191i
$543$	6.21991e7	−	1.07732e8i	0.388494	−	0.672892i
$544$	1.73011e8	−	9.98881e7i	1.07468	−	0.620465i
$545$			2.87752e8i			1.77758i
$546$		0			0
$547$	−2.12491e8			−1.29831			−0.649154	−	0.760657i	$-0.724877\pi$
$547$	−2.12491e8			−1.29831			−0.649154	+	0.760657i	$0.724877\pi$
$548$	6.61661e7	+	1.14603e8i	0.402063	+	0.696393i
$549$	−6.91283e7	−	3.99112e7i	−0.417771	−	0.241200i
$550$	−2.53359e7	+	4.38831e7i	−0.152282	+	0.263760i
$551$	−220617.	+	127373.i	−0.00131882	+	0.000761420i
$552$		−	1.90812e8i		−	1.13446i
$553$		0			0
$554$	−9.93778e6			−0.0584467
$555$	3.03256e8	+	5.25254e8i	1.77390	+	3.07249i
$556$	6.32951e7	+	3.65434e7i	0.368252	+	0.212611i
$557$	−8.87221e6	+	1.53671e7i	−0.0513412	+	0.0889256i	−0.890554	−	0.454878i	$-0.849683\pi$
$557$	−8.87221e6	+	1.53671e7i	−0.0513412	+	0.0889256i	0.839213	+	0.543803i	$0.183016\pi$
$558$	6.29702e7	−	3.63559e7i	0.362437	−	0.209253i
$559$		−	2.25917e8i		−	1.29334i
$560$		0			0
$561$	−7.46153e7			−0.422610
$562$	−7.54061e7	−	1.30607e8i	−0.424813	−	0.735797i
$563$	6.61180e7	+	3.81733e7i	0.370506	+	0.213911i	0.673679	−	0.739024i	$-0.264713\pi$
$563$	6.61180e7	+	3.81733e7i	0.370506	+	0.213911i	−0.303174	+	0.952935i	$0.598046\pi$
$564$	3.76522e7	−	6.52155e7i	0.209871	−	0.363508i
$565$	6.53510e7	−	3.77304e7i	0.362332	−	0.209193i
$566$		−	8.79153e7i		−	0.484859i
$567$		0			0
$568$	−2.20202e8			−1.20164
$569$	−2.21456e7	−	3.83573e7i	−0.120213	−	0.208215i	0.799639	−	0.600481i	$-0.205024\pi$
$569$	−2.21456e7	−	3.83573e7i	−0.120213	−	0.208215i	−0.919852	+	0.392267i	$0.871691\pi$
$570$	−6.08797e7	−	3.51489e7i	−0.328736	−	0.189796i
$571$	2.41163e7	−	4.17707e7i	0.129540	−	0.224369i	−0.793959	−	0.607972i	$-0.791983\pi$
$571$	2.41163e7	−	4.17707e7i	0.129540	−	0.224369i	0.923498	+	0.383602i	$0.125317\pi$
$572$	3.06290e7	−	1.76836e7i	0.163661	−	0.0944895i
$573$			2.73332e8i			1.45287i
$574$		0			0
$575$	3.33433e8			1.75390
$576$	4.25302e7	+	7.36645e7i	0.222551	+	0.385470i
$577$	−1.91662e8	−	1.10656e8i	−0.997719	−	0.576033i	−0.0901463	−	0.995929i	$-0.528733\pi$
$577$	−1.91662e8	−	1.10656e8i	−0.997719	−	0.576033i	−0.907573	+	0.419895i	$0.862067\pi$
$578$	2.64988e7	−	4.58973e7i	0.137228	−	0.237686i
$579$	−1.29408e8	+	7.47139e7i	−0.666693	+	0.384916i
$580$			1.26353e6i			0.00647593i
$581$		0			0
$582$	8.13555e7			0.412684
$583$	1.62378e7	+	2.81247e7i	0.0819448	+	0.141933i
$584$	2.23458e8	+	1.29014e8i	1.12191	+	0.647735i
$585$	−1.74743e8	+	3.02664e8i	−0.872836	+	1.51180i
$586$	−1.09941e8	+	6.34747e7i	−0.546347	+	0.315434i
$587$		−	6.64788e7i		−	0.328676i	−0.986404	−	0.164338i	$-0.947451\pi$
$587$		−	6.64788e7i		−	0.328676i	0.986404	−	0.164338i	$-0.0525488\pi$
$588$		0			0
$589$	4.48916e7			0.219694
$590$	8.41025e7	+	1.45670e8i	0.409499	+	0.709273i
$591$	1.00855e8	+	5.82288e7i	0.488580	+	0.282082i
$592$	1.44401e7	−	2.50111e7i	0.0695995	−	0.120550i
$593$	2.46435e8	−	1.42279e8i	1.18178	−	0.682303i	0.225358	−	0.974276i	$-0.427645\pi$
$593$	2.46435e8	−	1.42279e8i	1.18178	−	0.682303i	0.956427	+	0.291973i	$0.0943117\pi$
$594$			4.91779e6i			0.0234645i
$595$		0			0
$596$	−799194.			−0.00377497
$597$	−2.88222e8	−	4.99216e8i	−1.35458	−	2.34620i
$598$	1.04116e8	+	6.01113e7i	0.486871	+	0.281095i
$599$	−2.10134e8	+	3.63963e8i	−0.977724	+	1.69347i	−0.307087	+	0.951681i	$0.599354\pi$
$599$	−2.10134e8	+	3.63963e8i	−0.977724	+	1.69347i	−0.670637	+	0.741786i	$0.733979\pi$
$600$	−5.11205e8	+	2.95144e8i	−2.36669	+	1.36641i
$601$			2.99194e8i			1.37825i	0.724641	+	0.689127i	$0.242006\pi$
$601$			2.99194e8i			1.37825i	−0.724641	+	0.689127i	$0.757994\pi$
$602$		0			0
$603$	−3.06020e8			−1.39572
$604$	−1.36599e8	−	2.36596e8i	−0.619920	−	1.07373i
$605$	3.13618e8	+	1.81068e8i	1.41623	+	0.817663i
$606$	1.05303e8	−	1.82391e8i	0.473178	−	0.819569i
$607$	3.62825e7	−	2.09477e7i	0.162230	−	0.0936636i	−0.416687	−	0.909050i	$-0.636809\pi$
$607$	3.62825e7	−	2.09477e7i	0.162230	−	0.0936636i	0.578917	+	0.815386i	$0.303476\pi$
$608$			6.23427e7i			0.277380i
$609$		0			0
$610$	1.26271e8			0.556309
$611$	5.97010e7	+	1.03405e8i	0.261733	+	0.453335i
$612$	−1.40406e8	−	8.10632e7i	−0.612534	−	0.353647i
$613$	−2.02482e8	+	3.50710e8i	−0.879034	+	1.52253i	−0.0266322	+	0.999645i	$0.508478\pi$
$613$	−2.02482e8	+	3.50710e8i	−0.879034	+	1.52253i	−0.852402	+	0.522887i	$0.824855\pi$
$614$	1.05061e8	−	6.06569e7i	0.453874	−	0.262045i
$615$			1.05706e8i			0.454438i
$616$		0			0
$617$	9.28527e7			0.395311			0.197655	−	0.980272i	$-0.436667\pi$
$617$	9.28527e7			0.395311			0.197655	+	0.980272i	$0.436667\pi$
$618$	5.41964e7	+	9.38709e7i	0.229617	+	0.397709i
$619$	2.28969e6	+	1.32195e6i	0.00965394	+	0.00557370i	0.504819	−	0.863225i	$-0.331559\pi$
$619$	2.28969e6	+	1.32195e6i	0.00965394	+	0.00557370i	−0.495165	+	0.868799i	$0.664892\pi$
$620$	1.11330e8	−	1.92829e8i	0.467129	−	0.809092i
$621$	2.80248e7	−	1.61801e7i	0.117022	−	0.0675628i
$622$			3.82525e7i			0.158960i
$623$		0			0
$624$	3.54530e7			0.145915
$625$	−1.42763e8	−	2.47273e8i	−0.584757	−	1.01283i
$626$	−7.23846e6	−	4.17912e6i	−0.0295069	−	0.0170358i
$627$	1.16423e7	−	2.01651e7i	0.0472321	−	0.0818084i
$628$	−2.65700e8	+	1.53402e8i	−1.07278	+	0.619373i
$629$		−	4.46123e8i		−	1.79268i
$630$		0			0
$631$	−9.99099e7			−0.397668			−0.198834	−	0.980033i	$-0.563715\pi$
$631$	−9.99099e7			−0.397668			−0.198834	+	0.980033i	$0.563715\pi$
$632$	4.81443e7	+	8.33885e7i	0.190719	+	0.330335i
$633$	−2.68538e8	−	1.55041e8i	−1.05875	−	0.611272i
$634$	8.65682e6	−	1.49941e7i	0.0339696	−	0.0588371i
$635$	−3.02891e8	+	1.74874e8i	−1.18295	+	0.682974i
$636$			1.50329e8i			0.584348i
$637$		0			0
$638$	216201.			0.000832521
$639$	1.43197e8	+	2.48025e8i	0.548823	+	0.950590i
$640$	2.89596e8	+	1.67198e8i	1.10472	+	0.637810i
$641$	1.22357e8	−	2.11929e8i	0.464574	−	0.804666i	−0.534608	−	0.845100i	$-0.679541\pi$
$641$	1.22357e8	−	2.11929e8i	0.464574	−	0.804666i	0.999182	+	0.0404343i	$0.0128741\pi$
$642$	−1.77695e8	+	1.02592e8i	−0.671538	+	0.387713i
$643$			1.10620e8i			0.416103i	0.978118	+	0.208051i	$0.0667122\pi$
$643$			1.10620e8i			0.416103i	−0.978118	+	0.208051i	$0.933288\pi$
$644$		0			0
$645$	−7.37726e8			−2.74926
$646$	2.58539e7	+	4.47803e7i	0.0959023	+	0.166108i
$647$	2.61172e8	+	1.50787e8i	0.964302	+	0.556740i	0.897494	−	0.441026i	$-0.145385\pi$
$647$	2.61172e8	+	1.50787e8i	0.964302	+	0.556740i	0.0668075	+	0.997766i	$0.478719\pi$
$648$	−1.45204e8	+	2.51500e8i	−0.533645	+	0.924301i
$649$	−4.82501e7	+	2.78572e7i	−0.176508	+	0.101907i
$650$		−	3.71915e8i		−	1.35427i
$651$		0			0
$652$	−1.28742e8			−0.464493
$653$	4.50335e7	+	7.80003e7i	0.161732	+	0.280128i	0.935490	−	0.353353i	$-0.114959\pi$
$653$	4.50335e7	+	7.80003e7i	0.161732	+	0.280128i	−0.773758	+	0.633481i	$0.781625\pi$
$654$	1.97381e8	+	1.13958e8i	0.705622	+	0.407391i
$655$	2.51428e8	−	4.35486e8i	0.894725	−	1.54971i
$656$	4.35905e6	−	2.51670e6i	0.0154412	−	0.00891498i
$657$		−	3.35591e8i		−	1.18335i
$658$		0			0
$659$	−2.22075e8			−0.775967			−0.387984	−	0.921666i	$-0.626828\pi$
$659$	−2.22075e8			−0.775967			−0.387984	+	0.921666i	$0.626828\pi$
$660$	−5.77454e7	−	1.00018e8i	−0.200856	−	0.347893i
$661$	9.27734e7	+	5.35627e7i	0.321232	+	0.185463i	0.651942	−	0.758269i	$-0.273955\pi$
$661$	9.27734e7	+	5.35627e7i	0.321232	+	0.185463i	−0.330710	+	0.943733i	$0.607288\pi$
$662$	−1.45931e8	+	2.52761e8i	−0.503008	+	0.871235i
$663$	4.74281e8	−	2.73826e8i	1.62740	−	0.939582i
$664$		−	652836.i		−	0.00222997i
$665$		0			0
$666$	2.25494e8			0.763331
$667$	−711327.	−	1.23205e6i	−0.00239713	−	0.00415195i
$668$	−3.28056e8	−	1.89404e8i	−1.10057	−	0.635417i
$669$	1.10033e7	−	1.90583e7i	0.0367490	−	0.0636511i
$670$	4.19238e8	−	2.42047e8i	1.39391	−	0.804777i
$671$			4.18248e7i			0.138441i
$672$		0			0
$673$	1.25072e8			0.410314			0.205157	−	0.978729i	$-0.434230\pi$
$673$	1.25072e8			0.410314			0.205157	+	0.978729i	$0.434230\pi$
$674$	−1.56384e8	−	2.70865e8i	−0.510754	−	0.884652i
$675$	−8.66963e7	−	5.00541e7i	−0.281896	−	0.162753i
$676$	−2.79466e7	+	4.84049e7i	−0.0904666	+	0.156693i
$677$	2.86440e8	−	1.65376e8i	0.923141	−	0.532976i	0.0385052	−	0.999258i	$-0.487740\pi$
$677$	2.86440e8	−	1.65376e8i	0.923141	−	0.532976i	0.884636	+	0.466283i	$0.154407\pi$
$678$		−	5.97694e7i		−	0.191774i
$679$		0			0
$680$	6.45425e8			2.05267
$681$	−5.71847e7	−	9.90469e7i	−0.181067	−	0.313617i
$682$	−3.29947e7	−	1.90495e7i	−0.104014	−	0.0600524i
$683$	−1.66737e8	+	2.88797e8i	−0.523323	+	0.906422i	0.476308	+	0.879278i	$0.341975\pi$
$683$	−1.66737e8	+	2.88797e8i	−0.523323	+	0.906422i	−0.999632	+	0.0271439i	$0.991359\pi$
$684$	4.38154e7	−	2.52968e7i	0.136917	−	0.0790492i
$685$			6.85176e8i			2.13172i
$686$		0			0
$687$	5.24980e8			1.61909
$688$	1.75641e7	+	3.04220e7i	0.0539339	+	0.0934162i
$689$	−2.06426e8	−	1.19180e8i	−0.631114	−	0.364374i
$690$	1.96292e8	−	3.39987e8i	0.597523	−	1.03494i
$691$	−2.71338e8	+	1.56657e8i	−0.822386	+	0.474805i	−0.851239	−	0.524779i	$-0.824148\pi$
$691$	−2.71338e8	+	1.56657e8i	−0.822386	+	0.474805i	0.0288523	+	0.999584i	$0.490815\pi$
$692$		−	2.14002e8i		−	0.645801i
$693$		0			0
$694$	−3.20718e8			−0.959499
$695$	1.89211e8	+	3.27723e8i	0.563627	+	0.976230i
$696$	2.18115e6	+	1.25929e6i	0.00646931	+	0.00373506i
$697$	3.88763e7	−	6.73357e7i	0.114812	−	0.198860i
$698$	−2.26048e8	+	1.30509e8i	−0.664713	+	0.383772i
$699$			3.42947e8i			1.00414i
$700$		0			0
$701$	1.96801e8			0.571313			0.285656	−	0.958332i	$-0.407788\pi$
$701$	1.96801e8			0.571313			0.285656	+	0.958332i	$0.407788\pi$
$702$	−1.80475e7	−	3.12592e7i	−0.0521682	−	0.0903581i
$703$	1.20567e8	+	6.96091e7i	0.347025	+	0.200355i
$704$	2.22847e7	−	3.85982e7i	0.0638687	−	0.110624i
$705$	3.37666e8	−	1.94952e8i	0.963653	−	0.556365i
$706$			1.27157e8i			0.361348i
$707$		0			0
$708$	−2.57901e8			−0.726697
$709$	1.61735e8	+	2.80134e8i	0.453802	+	0.786007i	0.998618	−	0.0525477i	$-0.0167342\pi$
$709$	1.61735e8	+	2.80134e8i	0.453802	+	0.786007i	−0.544817	+	0.838555i	$0.683401\pi$
$710$	−3.92352e8	−	2.26525e8i	−1.09623	−	0.632907i
$711$	6.26167e7	−	1.08455e8i	0.174213	−	0.301746i
$712$	−9.73788e7	+	5.62217e7i	−0.269789	+	0.155763i
$713$			2.50700e8i			0.691650i
$714$		0			0
$715$	1.83121e8			0.500980
$716$	−4.50525e7	−	7.80333e7i	−0.122738	−	0.212589i
$717$	−8.54029e8	−	4.93074e8i	−2.31694	−	1.33769i
$718$	−7.24390e6	+	1.25468e7i	−0.0195704	+	0.0338969i
$719$	−1.69566e8	+	9.78988e7i	−0.456196	+	0.263385i	−0.710443	−	0.703754i	$-0.751506\pi$
$719$	−1.69566e8	+	9.78988e7i	−0.456196	+	0.263385i	0.254248	+	0.967139i	$0.418172\pi$
$720$		−	5.43422e7i		−	0.145593i
$721$		0			0
$722$	2.03523e8			0.540757
$723$	5.65600e7	+	9.79647e7i	0.149656	+	0.259212i
$724$	−1.22653e8	−	7.08139e7i	−0.323194	−	0.186596i
$725$	−2.20053e6	+	3.81142e6i	−0.00577448	+	0.0100017i
$726$	2.48404e8	−	1.43416e8i	0.649155	−	0.374790i
$727$		−	4.17769e8i		−	1.08726i	−0.839326	−	0.543629i	$-0.817050\pi$
$727$		−	4.17769e8i		−	1.08726i	0.839326	−	0.543629i	$-0.182950\pi$
$728$		0			0
$729$	2.93479e8			0.757522
$730$	2.65437e8	+	4.59750e8i	0.682327	+	1.18182i
$731$	4.69938e8	+	2.71319e8i	1.20306	+	0.694589i
$732$	−9.68032e7	+	1.67668e8i	−0.246806	+	0.427481i
$733$	−4.17083e8	+	2.40803e8i	−1.05904	+	0.611434i	−0.925165	−	0.379565i	$-0.876074\pi$
$733$	−4.17083e8	+	2.40803e8i	−1.05904	+	0.611434i	−0.133870	+	0.990999i	$0.542740\pi$
$734$		−	5.90625e7i		−	0.149356i
$735$		0			0
$736$	−3.48158e8			−0.873258
$737$	8.01730e7	+	1.38864e8i	0.200275	+	0.346886i
$738$	3.40351e7	+	1.96502e7i	0.0846755	+	0.0488874i
$739$	2.47054e7	−	4.27910e7i	0.0612150	−	0.106028i	−0.833794	−	0.552076i	$-0.813836\pi$
$739$	2.47054e7	−	4.27910e7i	0.0612150	−	0.106028i	0.895009	+	0.446049i	$0.147169\pi$
$740$	5.98004e8	−	3.45258e8i	1.47574	−	0.852017i
$741$			1.70902e8i			0.420042i
$742$		0			0
$743$	3.93297e8			0.958857			0.479428	−	0.877581i	$-0.340844\pi$
$743$	3.93297e8			0.958857			0.479428	+	0.877581i	$0.340844\pi$
$744$	−2.21912e8	−	3.84363e8i	−0.538843	−	0.933303i
$745$	−3.58360e6	−	2.06899e6i	−0.00866664	−	0.00500369i
$746$	8.49898e7	−	1.47207e8i	0.204715	−	0.354577i
$747$	−735325.	+	424540.i	−0.00176408	+	0.00101849i
$748$			8.49498e7i			0.202982i
$749$		0			0
$750$	−6.23628e8			−1.47823
$751$	−1.30097e8	−	2.25335e8i	−0.307148	−	0.531995i	0.670589	−	0.741829i	$-0.266041\pi$
$751$	−1.30097e8	−	2.25335e8i	−0.307148	−	0.531995i	−0.977737	+	0.209833i	$0.932708\pi$
$752$	−1.60787e7	−	9.28302e6i	−0.0378091	−	0.0218291i
$753$	3.23702e8	−	5.60668e8i	0.758159	−	1.31317i
$754$	−1.37425e6	+	793422.i	−0.00320591	+	0.00185093i
$755$		−	1.41453e9i		−	3.28679i
$756$		0			0
$757$	−2.20999e7			−0.0509452			−0.0254726	−	0.999676i	$-0.508109\pi$
$757$	−2.20999e7			−0.0509452			−0.0254726	+	0.999676i	$0.508109\pi$
$758$	−1.41181e7	−	2.44532e7i	−0.0324166	−	0.0561473i
$759$	1.12614e8	+	6.50175e7i	0.257552	+	0.148698i
$760$	−1.00707e8	+	1.74429e8i	−0.229412	+	0.397354i
$761$	−4.70527e8	+	2.71659e8i	−1.06765	+	0.616410i	−0.927539	−	0.373725i	$-0.878080\pi$
$761$	−4.70527e8	+	2.71659e8i	−1.06765	+	0.616410i	−0.140114	+	0.990135i	$0.544747\pi$
$762$			2.77021e8i			0.626105i
$763$		0			0
$764$	3.11190e8			0.697823
$765$	−4.19721e8	−	7.26978e8i	−0.937510	−	1.62382i
$766$	−3.36949e8	−	1.94538e8i	−0.749684	−	0.432830i
$767$	2.04463e8	−	3.54140e8i	0.453136	−	0.784854i
$768$	5.00346e8	−	2.88875e8i	1.10455	−	0.637714i
$769$			1.01672e8i			0.223576i	0.993732	+	0.111788i	$0.0356577\pi$
$769$			1.01672e8i			0.223576i	−0.993732	+	0.111788i	$0.964342\pi$
$770$		0			0
$771$	6.81742e8			1.48750
$772$	8.50620e7	+	1.47332e8i	0.184877	+	0.320217i
$773$	5.23095e8	+	3.02009e8i	1.13251	+	0.653855i	0.944565	−	0.328325i	$-0.106484\pi$
$773$	5.23095e8	+	3.02009e8i	1.13251	+	0.653855i	0.187944	+	0.982180i	$0.439817\pi$
$774$	−1.37139e8	+	2.37532e8i	−0.295759	+	0.512270i
$775$	6.71650e8	−	3.87778e8i	1.44291	−	0.833062i
$776$		−	2.33095e8i		−	0.498824i
$777$		0			0
$778$	−2.90564e8			−0.617025
$779$	1.21318e7	+	2.10130e7i	0.0256634	+	0.0444503i
$780$	7.34100e8	+	4.23833e8i	1.54693	+	0.893122i
$781$	7.50315e7	−	1.29958e8i	0.157504	−	0.272804i
$782$	−2.50079e8	+	1.44383e8i	−0.522946	+	0.301923i
$783$			427130.i			0.000889764i
$784$		0			0
$785$	−1.58854e9			−3.28389
$786$	−1.99145e8	−	3.44930e8i	−0.410112	−	0.710335i
$787$	2.32603e8	+	1.34294e8i	0.477191	+	0.275506i	0.719245	−	0.694757i	$-0.244488\pi$
$787$	2.32603e8	+	1.34294e8i	0.477191	+	0.275506i	−0.242054	+	0.970263i	$0.577821\pi$
$788$	6.62937e7	−	1.14824e8i	0.135486	−	0.234668i
$789$	−7.58662e8	+	4.38014e8i	−1.54461	+	0.891778i
$790$			1.98107e8i			0.401808i
$791$		0			0
$792$	−1.08058e8			−0.217510
$793$	−1.53490e8	−	2.65853e8i	−0.307795	−	0.533116i
$794$	1.36975e8	+	7.90826e7i	0.273640	+	0.157986i
$795$	−3.89179e8	+	6.74079e8i	−0.774548	+	1.34156i
$796$	−5.68359e8	+	3.28142e8i	−1.12689	+	0.650613i
$797$			7.25063e8i			1.43219i	0.698003	+	0.716095i	$0.254072\pi$
$797$			7.25063e8i			1.43219i	−0.698003	+	0.716095i	$0.745928\pi$
$798$		0			0
$799$	−2.86795e8			−0.562253
$800$	5.38522e8	+	9.32748e8i	1.05180	+	1.82177i
$801$	1.26651e8	+	7.31221e7i	0.246440	+	0.142282i
$802$	−2.06246e8	+	3.57228e8i	−0.399818	+	0.692504i
$803$	−1.52282e8	+	8.79203e7i	−0.294106	+	0.169802i
$804$			7.42239e8i			1.42816i
$805$		0			0
$806$	2.79634e8			0.534054
$807$	1.75807e8	+	3.04507e8i	0.334515	+	0.579397i
$808$	−5.22576e8	−	3.01709e8i	−0.990639	−	0.571946i
$809$	−2.11007e8	+	3.65475e8i	−0.398522	+	0.690260i	−0.993544	−	0.113450i	$-0.963810\pi$
$809$	−2.11007e8	+	3.65475e8i	−0.398522	+	0.690260i	0.595022	+	0.803709i	$0.297143\pi$
$810$	−5.17444e8	+	2.98746e8i	−0.973662	+	0.562144i
$811$		−	5.33775e8i		−	1.00068i	−0.865828	−	0.500341i	$-0.833208\pi$
$811$		−	5.33775e8i		−	1.00068i	0.865828	−	0.500341i	$-0.166792\pi$
$812$		0			0
$813$	4.85861e8			0.904149
$814$	−5.90764e7	−	1.02323e8i	−0.109532	−	0.189715i
$815$	−5.77283e8	−	3.33295e8i	−1.06639	−	0.615681i
$816$	−4.25777e7	+	7.37468e7i	−0.0783632	+	0.135729i
$817$	−1.46650e8	+	8.46685e7i	−0.268916	+	0.155259i
$818$			4.86829e8i			0.889440i
$819$		0			0
$820$	1.20347e8			0.218269
$821$	2.94325e8	+	5.09787e8i	0.531861	+	0.921211i	0.999308	+	0.0371896i	$0.0118406\pi$
$821$	2.94325e8	+	5.09787e8i	0.531861	+	0.921211i	−0.467447	+	0.884021i	$0.654826\pi$
$822$	4.69991e8	+	2.71349e8i	0.846202	+	0.488555i
$823$	−2.64832e8	+	4.58702e8i	−0.475084	+	0.822870i	−0.999593	−	0.0285354i	$-0.990916\pi$
$823$	−2.64832e8	+	4.58702e8i	−0.475084	+	0.822870i	0.524509	+	0.851405i	$0.324249\pi$
$824$	2.68953e8	−	1.55280e8i	0.480723	−	0.277546i
$825$		−	4.02270e8i		−	0.716400i
$826$		0			0
$827$	−2.30019e8			−0.406674			−0.203337	−	0.979109i	$-0.565179\pi$
$827$	−2.30019e8			−0.406674			−0.203337	+	0.979109i	$0.565179\pi$
$828$	1.41272e8	+	2.44690e8i	0.248866	+	0.431048i
$829$	−4.31467e8	−	2.49107e8i	−0.757327	−	0.437243i	0.0710081	−	0.997476i	$-0.477378\pi$
$829$	−4.31467e8	−	2.49107e8i	−0.757327	−	0.437243i	−0.828335	+	0.560233i	$0.810712\pi$
$830$	671582.	−	1.16321e6i	0.00117453	−	0.00203435i
$831$	6.83236e7	−	3.94467e7i	0.119061	−	0.0687396i
$832$			3.27125e8i			0.567994i
$833$		0			0
$834$	2.99732e8			0.516695
$835$	−9.80674e8	−	1.69858e9i	−1.68448	−	2.91760i
$836$	−2.29580e7	−	1.32548e7i	−0.0392931	−	0.0226859i
$837$	3.76345e7	−	6.51849e7i	0.0641815	−	0.111166i
$838$	1.58032e8	−	9.12396e7i	0.268542	−	0.155043i
$839$		−	1.16451e8i		−	0.197178i	−0.995128	−	0.0985891i	$-0.968567\pi$
$839$		−	1.16451e8i		−	0.197178i	0.995128	−	0.0985891i	$-0.0314330\pi$
$840$		0			0
$841$	−5.94805e8			−0.999968
$842$	−1.12902e8	−	1.95551e8i	−0.189132	−	0.327586i
$843$	1.03686e9	+	5.98629e8i	1.73075	+	0.999251i
$844$	−1.76514e8	+	3.05732e8i	−0.293597	+	0.508526i
$845$	−2.50626e8	+	1.44699e8i	−0.415390	+	0.239825i
$846$		−	1.44962e8i		−	0.239410i
$847$		0			0
$848$	3.70631e7			0.0607791
$849$	3.48968e8	+	6.04430e8i	0.570246	+	0.987696i
$850$	7.73633e8	+	4.46657e8i	1.25973	+	0.727306i
$851$	−3.88737e8	+	6.73313e8i	−0.630765	+	1.09252i
$852$	6.01576e8	−	3.47320e8i	0.972683	−	0.561579i
$853$		−	8.54702e8i		−	1.37711i	−0.725186	−	0.688553i	$-0.758246\pi$
$853$		−	8.54702e8i		−	1.37711i	0.725186	−	0.688553i	$-0.241754\pi$
$854$		0			0
$855$	2.61958e8			0.419116
$856$	2.93942e8	+	5.09122e8i	0.468640	+	0.811709i
$857$	5.40048e8	+	3.11797e8i	0.858005	+	0.495370i	0.863344	−	0.504616i	$-0.168366\pi$
$857$	5.40048e8	+	3.11797e8i	0.858005	+	0.495370i	−0.00533854	+	0.999986i	$0.501699\pi$
$858$	7.25213e7	−	1.25611e8i	0.114816	−	0.198868i
$859$	4.19221e8	−	2.42037e8i	0.661399	−	0.381859i	−0.131411	−	0.991328i	$-0.541951\pi$
$859$	4.19221e8	−	2.42037e8i	0.661399	−	0.381859i	0.792810	+	0.609469i	$0.208617\pi$
$860$			8.39903e8i			1.32049i
$861$		0			0
$862$	3.87710e8			0.605321
$863$	−2.79678e8	−	4.84416e8i	−0.435136	−	0.753678i	0.562170	−	0.827021i	$-0.309966\pi$
$863$	−2.79678e8	−	4.84416e8i	−0.435136	−	0.753678i	−0.997307	+	0.0733432i	$0.976633\pi$
$864$	9.05248e7	+	5.22645e7i	0.140355	+	0.0810337i
$865$	5.54018e8	−	9.59588e8i	0.856004	−	1.48264i
$866$	4.82402e8	−	2.78515e8i	0.742772	−	0.428839i
$867$			4.20734e8i			0.645580i
$868$		0			0
$869$	−6.56189e7			−0.0999929
$870$	2.59089e6	+	4.48756e6i	0.00393452	+	0.00681479i
$871$	−1.01922e9	−	5.88444e8i	−1.54245	−	0.890535i
$872$	3.26506e8	−	5.65524e8i	0.492426	−	0.852907i
$873$	−2.62548e8	+	1.51582e8i	−0.394608	+	0.227827i
$874$		−	9.01133e7i		−	0.134975i
$875$		0			0
$876$	−8.13964e8			−1.21086
$877$	4.94076e8	+	8.55765e8i	0.732479	+	1.26869i	0.955820	+	0.293951i	$0.0949703\pi$
$877$	4.94076e8	+	8.55765e8i	0.732479	+	1.26869i	−0.223341	+	0.974740i	$0.571696\pi$
$878$	−2.93403e7	−	1.69396e7i	−0.0433491	−	0.0250276i
$879$	5.03909e8	−	8.72795e8i	0.741968	−	1.28513i
$880$	−2.46591e7	+	1.42369e7i	−0.0361850	+	0.0208914i
$881$		−	1.56990e8i		−	0.229586i	−0.993389	−	0.114793i	$-0.963380\pi$
$881$		−	1.56990e8i		−	0.229586i	0.993389	−	0.114793i	$-0.0366205\pi$
$882$		0			0
$883$	8.84759e8			1.28512			0.642559	−	0.766236i	$-0.277873\pi$
$883$	8.84759e8			1.28512			0.642559	+	0.766236i	$0.277873\pi$
$884$	−3.11752e8	−	5.39971e8i	−0.451287	−	0.781652i
$885$	−1.15643e9	−	6.67667e8i	−1.66836	−	0.963230i
$886$	−3.02581e8	+	5.24086e8i	−0.435051	+	0.753531i
$887$	−3.16641e7	+	1.82813e7i	−0.0453729	+	0.0261961i	−0.522515	−	0.852630i	$-0.675006\pi$
$887$	−3.16641e7	+	1.82813e7i	−0.0453729	+	0.0261961i	0.477142	+	0.878826i	$0.341673\pi$
$888$		−	1.37639e9i		−	1.96564i
$889$		0			0
$890$	−2.31344e8			−0.328162
$891$	−9.89535e7	−	1.71392e8i	−0.139894	−	0.242303i
$892$	−2.16980e7	−	1.25273e7i	−0.0305720	−	0.0176508i
$893$	4.47491e7	−	7.75077e7i	0.0628391	−	0.108840i
$894$	−2.83842e6	+	1.63876e6i	−0.00397250	+	0.00229352i
$895$		−	4.66537e8i		−	0.650754i
$896$		0			0
$897$	−9.54415e8			−1.32239
$898$	2.37380e8	+	4.11155e8i	0.327805	+	0.567775i
$899$	−2.86572e6	−	1.65452e6i	−0.00394416	−	0.00227716i
$900$	4.37032e8	−	7.56962e8i	0.599495	−	1.03836i
$901$	4.95822e8	−	2.86263e8i	0.677877	−	0.391373i
$902$		−	2.05923e7i		−	0.0280598i
$903$		0			0
$904$	−1.71248e8			−0.231803
$905$	−3.66653e8	−	6.35061e8i	−0.494663	−	0.856781i
$906$	−9.70287e8	−	5.60195e8i	−1.30471	−	0.753278i
$907$	3.57136e8	−	6.18577e8i	0.478643	−	0.829034i	−0.521057	−	0.853522i	$-0.674462\pi$
$907$	3.57136e8	−	6.18577e8i	0.478643	−	0.829034i	0.999700	+	0.0244881i	$0.00779559\pi$
$908$	−1.12765e8	+	6.51050e7i	−0.150632	+	0.0869675i
$909$			7.84808e8i			1.04489i
$910$		0			0
$911$	3.82999e8			0.506574			0.253287	−	0.967391i	$-0.418488\pi$
$911$	3.82999e8			0.506574			0.253287	+	0.967391i	$0.418488\pi$
$912$	−1.32869e7	−	2.30136e7i	−0.0175162	−	0.0303390i
$913$	385290.	+	222447.i	0.000506262	+	0.000292291i
$914$	2.58469e8	−	4.47681e8i	0.338508	−	0.586314i
$915$	−8.68134e8	+	5.01218e8i	−1.13324	+	0.654279i
$916$		−	5.97691e8i		−	0.777661i
$917$		0			0
$918$	8.66978e7			0.112068
$919$	5.31812e8	+	9.21126e8i	0.685191	+	1.18679i	0.973377	+	0.229212i	$0.0736148\pi$
$919$	5.31812e8	+	9.21126e8i	0.685191	+	1.18679i	−0.288185	+	0.957575i	$0.593052\pi$
$920$	−9.74111e8	−	5.62403e8i	−1.25096	−	0.722244i
$921$	−4.81539e8	+	8.34050e8i	−0.616385	+	1.06761i
$922$	−2.67691e8	+	1.54552e8i	−0.341540	+	0.197188i
$923$			1.10141e9i			1.40070i
$924$		0			0
$925$	2.40516e9			3.03892
$926$	1.38480e8	+	2.39854e8i	0.174403	+	0.302075i
$927$	−3.49802e8	−	2.01958e8i	−0.439119	−	0.253526i
$928$	2.29770e6	−	3.97974e6i	0.00287508	−	0.00497979i
$929$	5.17735e8	−	2.98914e8i	0.645744	−	0.372820i	−0.141080	−	0.989998i	$-0.545057\pi$
$929$	5.17735e8	−	2.98914e8i	0.645744	−	0.372820i	0.786824	+	0.617178i	$0.211724\pi$
$930$		−	9.13137e8i		−	1.13524i
$931$		0			0
$932$	3.90447e8			0.482296
$933$	−1.51838e8	−	2.62991e8i	−0.186955	−	0.323815i
$934$	5.54118e8	+	3.19920e8i	0.680082	+	0.392646i
$935$	−2.19922e8	+	3.80916e8i	−0.269051	+	0.466009i
$936$	6.86853e8	−	3.96554e8i	0.837599	−	0.483588i
$937$			1.16470e9i			1.41578i	0.706322	+	0.707891i	$0.250353\pi$
$937$			1.16470e9i			1.41578i	−0.706322	+	0.707891i	$0.749647\pi$
$938$		0			0
$939$	6.63539e7			0.0801437
$940$	−2.21953e8	−	3.84434e8i	−0.267225	−	0.462848i
$941$	−3.29623e7	−	1.90308e7i	−0.0395593	−	0.0228396i	0.480090	−	0.877219i	$-0.340604\pi$
$941$	−3.29623e7	−	1.90308e7i	−0.0395593	−	0.0228396i	−0.519649	+	0.854380i	$0.673937\pi$
$942$	−6.29107e8	+	1.08965e9i	−0.752613	+	1.30356i
$943$	−1.17348e8	+	6.77512e7i	−0.139940	+	0.0807945i
$944$			6.35846e7i			0.0755851i
$945$		0			0
$946$	1.43714e8			0.169757
$947$	−3.30356e8	−	5.72193e8i	−0.388984	−	0.673741i	0.603329	−	0.797493i	$-0.293841\pi$
$947$	−3.30356e8	−	5.72193e8i	−0.388984	−	0.673741i	−0.992313	+	0.123752i	$0.960507\pi$
$948$	−2.63054e8	−	1.51874e8i	−0.308759	−	0.178262i
$949$	6.45307e8	−	1.11770e9i	0.755036	−	1.30776i
$950$	−2.41422e8	+	1.39385e8i	−0.281583	+	0.162572i
$951$			1.37448e8i			0.159808i
$952$		0			0
$953$	5.86917e7			0.0678106			0.0339053	−	0.999425i	$-0.489206\pi$
$953$	5.86917e7			0.0678106			0.0339053	+	0.999425i	$0.489206\pi$
$954$	1.44693e8	+	2.50615e8i	0.166649	+	0.288644i
$955$	1.39538e9	+	8.05623e8i	1.60207	+	0.924957i
$956$	−5.61366e8	+	9.72315e8i	−0.642499	+	1.11284i
$957$	−1.48641e6	+	858179.i	−0.00169591	+	0.000979134i
$958$		−	6.94658e7i		−	0.0790086i
$959$		0			0
$960$	1.06822e9			1.20738
$961$	−1.52191e8	−	2.63603e8i	−0.171482	−	0.297016i
$962$	7.51021e8	+	4.33602e8i	0.843581	+	0.487042i
$963$	3.82301e8	−	6.62165e8i	0.428082	−	0.741460i
$964$	1.11533e8	−	6.43937e7i	0.124501	−	0.0718807i
$965$			8.80850e8i			0.980212i
$966$		0			0
$967$	−314380.			−0.000347677			−0.000173838	−	1.00000i	$-0.500055\pi$
$967$	−314380.			−0.000347677			−0.000173838		1.00000i	$0.500055\pi$
$968$	−4.10907e8	−	7.11711e8i	−0.453020	−	0.784653i
$969$	−3.55499e8	−	2.05247e8i	−0.390721	−	0.225583i
$970$	2.39788e8	−	4.15325e8i	0.262732	−	0.455065i
$971$	8.40872e8	−	4.85478e8i	0.918486	−	0.530288i	0.0353341	−	0.999376i	$-0.488750\pi$
$971$	8.40872e8	−	4.85478e8i	0.918486	−	0.530288i	0.883152	+	0.469088i	$0.155417\pi$
$972$		−	8.20218e8i		−	0.893162i
$973$		0			0
$974$	−2.63790e8			−0.285483
$975$	1.47627e9	+	2.55697e9i	1.59276	+	2.75875i
$976$	4.13380e7	+	2.38665e7i	0.0444631	+	0.0256708i
$977$	1.86120e8	−	3.22370e8i	0.199577	−	0.345677i	−0.748814	−	0.662780i	$-0.769377\pi$
$977$	1.86120e8	−	3.22370e8i	0.199577	−	0.345677i	0.948391	+	0.317102i	$0.102710\pi$
$978$	−4.57242e8	+	2.63989e8i	−0.488798	+	0.282208i
$979$		−	7.66279e7i		−	0.0816656i
$980$		0			0
$981$	−8.49309e8			−0.899619
$982$	1.27275e8	+	2.20446e8i	0.134402	+	0.232792i
$983$	−7.32520e8	−	4.22921e8i	−0.771186	−	0.445244i	0.0621117	−	0.998069i	$-0.480216\pi$
$983$	−7.32520e8	−	4.22921e8i	−0.771186	−	0.445244i	−0.833297	+	0.552825i	$0.813550\pi$
$984$	1.19942e8	−	2.07746e8i	0.125889	−	0.218046i
$985$	5.94524e8	−	3.43249e8i	0.622101	−	0.359170i
$986$		−	3.81149e6i		−	0.00397616i
$987$		0			0
$988$	1.94573e8			0.201749
$989$	−4.72838e8	−	8.18979e8i	−0.488791	−	0.846611i
$990$	−1.92536e8	−	1.11161e8i	−0.198429	−	0.114563i
$991$	−5.17042e8	+	8.95543e8i	−0.531257	+	0.920165i	0.468077	+	0.883688i	$0.344947\pi$
$991$	−5.17042e8	+	8.95543e8i	−0.531257	+	0.920165i	−0.999334	+	0.0364773i	$0.988386\pi$
$992$	−7.01311e8	+	4.04902e8i	−0.718415	+	0.414777i
$993$		−	2.31702e9i		−	2.36637i
$994$		0			0
$995$	−3.39804e9			−3.44953
$996$	1.02971e6	+	1.78350e6i	0.00104216	+	0.00180508i
$997$	2.41714e8	+	1.39553e8i	0.243902	+	0.140817i	0.616969	−	0.786987i	$-0.288360\pi$
$997$	2.41714e8	+	1.39553e8i	0.243902	+	0.140817i	−0.373067	+	0.927805i	$0.621694\pi$
$998$	4.83450e8	−	8.37359e8i	0.486362	−	0.842404i
$999$	2.02152e8	−	1.16713e8i	0.202760	−	0.117063i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	49.7.d.e.31.6		24
7.2	even	3	inner	49.7.d.e.19.5		24
7.3	odd	6		49.7.b.c.48.8	yes	12
7.4	even	3		49.7.b.c.48.7	✓	12
7.5	odd	6	inner	49.7.d.e.19.6		24
7.6	odd	2	inner	49.7.d.e.31.5		24
21.11	odd	6		441.7.d.e.244.5		12
21.17	even	6		441.7.d.e.244.6		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
49.7.b.c.48.7	✓	12	7.4	even	3
49.7.b.c.48.8	yes	12	7.3	odd	6
49.7.d.e.19.5		24	7.2	even	3	inner
49.7.d.e.19.6		24	7.5	odd	6	inner
49.7.d.e.31.5		24	7.6	odd	2	inner
49.7.d.e.31.6		24	1.1	even	1	trivial
441.7.d.e.244.5		12	21.11	odd	6
441.7.d.e.244.6		12	21.17	even	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:	\( N \)	\(=\)	\( 49 = 7^{2} \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	49.d (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.33452 - 4.04351i) q^{2} +(32.1003 + 18.5331i) q^{3} +(21.1000 - 36.5463i) q^{4} +(189.226 - 109.250i) q^{5} -173.064i q^{6} -495.852 q^{8} +(322.454 + 558.506i) q^{9} +(-883.503 - 510.091i) q^{10} +(168.957 - 292.642i) q^{11} +(1354.64 - 782.099i) q^{12} +2480.18i q^{13} +8098.94 q^{15} +(-192.824 - 333.981i) q^{16} +(-5159.10 - 2978.61i) q^{17} +(1505.55 - 2607.69i) q^{18} +(1609.96 - 929.513i) q^{19} -9220.67i q^{20} -1577.73 q^{22} +(5190.93 + 8990.96i) q^{23} +(-15917.0 - 9189.70i) q^{24} +(16058.4 - 27814.0i) q^{25} +(10028.6 - 5790.03i) q^{26} -3117.00i q^{27} -137.033 q^{29} +(-18907.2 - 32748.1i) q^{30} +(20912.7 + 12074.0i) q^{31} +(-16767.6 + 29042.3i) q^{32} +(10847.1 - 6262.60i) q^{33} +27814.5i q^{34} +27215.1 q^{36} +(37443.9 + 64854.7i) q^{37} +(-7516.99 - 4339.93i) q^{38} +(-45965.5 + 79614.5i) q^{39} +(-93828.1 + 54171.7i) q^{40} +13051.8i q^{41} -91089.1 q^{43} +(-7129.99 - 12349.5i) q^{44} +(122033. + 70455.8i) q^{45} +(24236.7 - 41979.2i) q^{46} +(41692.6 - 24071.3i) q^{47} -14294.5i q^{48} -149955. q^{50} +(-110406. - 191229. i) q^{51} +(90641.4 + 52331.8i) q^{52} +(-48053.1 + 83230.4i) q^{53} +(-12603.6 + 7276.70i) q^{54} -73833.8i q^{55} +68907.1 q^{57} +(319.905 + 554.092i) q^{58} +(-142788. - 82438.8i) q^{59} +(170888. - 295987. i) q^{60} +(-107191. + 61886.8i) q^{61} -112748. i q^{62} +131896. q^{64} +(270958. + 469314. i) q^{65} +(-50645.7 - 29240.3i) q^{66} +(-237259. + 410944. i) q^{67} +(-217714. + 125697. i) q^{68} +384817. i q^{69} +444087. q^{71} +(-159889. - 276937. i) q^{72} +(-450655. - 260186. i) q^{73} +(174827. - 302809. i) q^{74} +(1.03096e6 - 595226. i) q^{75} -78451.0i q^{76} +429229. q^{78} +(-97094.1 - 168172. i) q^{79} +(-72974.5 - 42131.8i) q^{80} +(292836. - 507208. i) q^{81} +(52775.2 - 30469.7i) q^{82} +1316.59i q^{83} -1.30165e6 q^{85} +(212649. + 368320. i) q^{86} +(-4398.79 - 2539.64i) q^{87} +(-83777.7 + 145107. i) q^{88} +(196387. - 113384. i) q^{89} -657922. i q^{90} +438115. q^{92} +(447536. + 775156. i) q^{93} +(-194665. - 112390. i) q^{94} +(203098. - 351776. i) q^{95} +(-1.07649e6 + 621511. i) q^{96} +470089. i q^{97} +217923. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 20 q^{2} - 564 q^{4} + 1880 q^{8} + 1252 q^{9} + 3872 q^{11} + 44864 q^{15} - 37908 q^{16} + 19436 q^{18} + 159744 q^{22} - 40032 q^{23} + 28860 q^{25} + 68032 q^{29} - 21192 q^{30} + 82060 q^{32}+ \cdots - 8949984 q^{99}+O(q^{100}) \) 24 * q - 20 * q^2 - 564 * q^4 + 1880 * q^8 + 1252 * q^9 + 3872 * q^11 + 44864 * q^15 - 37908 * q^16 + 19436 * q^18 + 159744 * q^22 - 40032 * q^23 + 28860 * q^25 + 68032 * q^29 - 21192 * q^30 + 82060 * q^32 - 563240 * q^36 + 169632 * q^37 - 492128 * q^39 - 241536 * q^43 + 404312 * q^44 + 118872 * q^46 - 2091048 * q^50 + 539424 * q^51 + 15856 * q^53 + 1853888 * q^57 - 971304 * q^58 + 429912 * q^60 - 11496 * q^64 + 267904 * q^65 - 1508352 * q^67 + 5037248 * q^71 - 2550364 * q^72 + 3876024 * q^74 - 135184 * q^78 - 232224 * q^79 - 528204 * q^81 + 1508256 * q^85 + 1560848 * q^86 - 1812720 * q^88 + 7305776 * q^92 - 164384 * q^93 - 2305600 * q^95 - 8949984 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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