LMFDB - Embedded newform 16.5.f.a.3.4

Newspace parameters

Level:	$ N $	$=$	$ 16 = 2^{4} $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	16.f (of order $4$, degree $2$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$1.65391940934$
Analytic rank:	$0$
Dimension:	$14$
Relative dimension:	$7$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
Defining polynomial:	$x^{14} - 4 x^{13} + 15 x^{12} - 34 x^{11} + 62 x^{10} - 312 x^{9} + 1432 x^{8} - 4960 x^{7} + 11456 x^{6} - 19968 x^{5} + 31744 x^{4} - 139264 x^{3} + 491520 x^{2} - 1048576 x + 2097152$
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{21} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			3.4
Root			$-2.15805 - 1.82834i$ of defining polynomial
Character	$\chi$	$=$	16.3
Dual form			16.5.f.a.11.4

$q$-expansion

$f(q)$	$=$	$q+(0.329715 - 3.98639i) q^{2} +(3.91498 - 3.91498i) q^{3} +(-15.7826 - 2.62875i) q^{4} +(4.72348 - 4.72348i) q^{5} +(-14.3158 - 16.8975i) q^{6} +45.3712 q^{7} +(-15.6830 + 62.0487i) q^{8} +50.3458i q^{9} +O(q^{10})$	\(q+(0.329715 - 3.98639i) q^{2} +(3.91498 - 3.91498i) q^{3} +(-15.7826 - 2.62875i) q^{4} +(4.72348 - 4.72348i) q^{5} +(-14.3158 - 16.8975i) q^{6} +45.3712 q^{7} +(-15.6830 + 62.0487i) q^{8} +50.3458i q^{9} +(-17.2722 - 20.3870i) q^{10} +(110.228 + 110.228i) q^{11} +(-72.0800 + 51.4970i) q^{12} +(-157.128 - 157.128i) q^{13} +(14.9596 - 180.867i) q^{14} -36.9847i q^{15} +(242.179 + 82.9768i) q^{16} -378.592 q^{17} +(200.698 + 16.5998i) q^{18} +(203.127 - 203.127i) q^{19} +(-86.9656 + 62.1319i) q^{20} +(177.627 - 177.627i) q^{21} +(475.755 - 403.067i) q^{22} -740.444 q^{23} +(181.521 + 304.318i) q^{24} +580.377i q^{25} +(-678.183 + 574.567i) q^{26} +(514.217 + 514.217i) q^{27} +(-716.074 - 119.269i) q^{28} +(82.6244 + 82.6244i) q^{29} +(-147.435 - 12.1944i) q^{30} -286.217i q^{31} +(410.628 - 938.062i) q^{32} +863.080 q^{33} +(-124.828 + 1509.21i) q^{34} +(214.310 - 214.310i) q^{35} +(132.346 - 794.587i) q^{36} +(1470.39 - 1470.39i) q^{37} +(-742.770 - 876.719i) q^{38} -1230.31 q^{39} +(219.008 + 367.164i) q^{40} +1301.21i q^{41} +(-649.525 - 766.658i) q^{42} +(-366.979 - 366.979i) q^{43} +(-1449.92 - 2029.44i) q^{44} +(237.808 + 237.808i) q^{45} +(-244.136 + 2951.70i) q^{46} -751.307i q^{47} +(1272.98 - 623.275i) q^{48} -342.455 q^{49} +(2313.61 + 191.359i) q^{50} +(-1482.18 + 1482.18i) q^{51} +(2066.84 + 2892.94i) q^{52} +(-1929.33 + 1929.33i) q^{53} +(2219.41 - 1880.32i) q^{54} +1041.32 q^{55} +(-711.555 + 2815.22i) q^{56} -1590.48i q^{57} +(356.616 - 302.130i) q^{58} +(-1357.57 - 1357.57i) q^{59} +(-97.2234 + 583.714i) q^{60} +(-1835.78 - 1835.78i) q^{61} +(-1140.97 - 94.3702i) q^{62} +2284.25i q^{63} +(-3604.09 - 1946.22i) q^{64} -1484.39 q^{65} +(284.571 - 3440.57i) q^{66} +(2205.02 - 2205.02i) q^{67} +(5975.15 + 995.222i) q^{68} +(-2898.83 + 2898.83i) q^{69} +(-783.662 - 924.984i) q^{70} +8970.40 q^{71} +(-3123.90 - 789.572i) q^{72} -9350.46i q^{73} +(-5376.75 - 6346.37i) q^{74} +(2272.17 + 2272.17i) q^{75} +(-3739.84 + 2671.90i) q^{76} +(5001.17 + 5001.17i) q^{77} +(-405.652 + 4904.49i) q^{78} +2860.08i q^{79} +(1535.87 - 751.991i) q^{80} -51.7173 q^{81} +(5187.13 + 429.029i) q^{82} +(-1036.63 + 1036.63i) q^{83} +(-3270.35 + 2336.48i) q^{84} +(-1788.27 + 1788.27i) q^{85} +(-1583.92 + 1341.92i) q^{86} +646.946 q^{87} +(-8568.19 + 5110.80i) q^{88} +5171.06i q^{89} +(1026.40 - 869.585i) q^{90} +(-7129.10 - 7129.10i) q^{91} +(11686.1 + 1946.44i) q^{92} +(-1120.54 - 1120.54i) q^{93} +(-2995.00 - 247.717i) q^{94} -1918.94i q^{95} +(-2064.90 - 5280.10i) q^{96} +8539.92 q^{97} +(-112.913 + 1365.16i) q^{98} +(-5549.51 + 5549.51i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14q - 2q^{2} - 2q^{3} - 8q^{4} - 2q^{5} + 64q^{6} - 4q^{7} - 92q^{8} + O(q^{10}) $	\( 14q - 2q^{2} - 2q^{3} - 8q^{4} - 2q^{5} + 64q^{6} - 4q^{7} - 92q^{8} - 100q^{10} + 94q^{11} - 332q^{12} - 2q^{13} + 44q^{14} - 168q^{16} - 4q^{17} + 1390q^{18} - 706q^{19} + 1900q^{20} - 164q^{21} + 900q^{22} + 1148q^{23} - 1872q^{24} - 3416q^{26} - 1664q^{27} - 3784q^{28} + 862q^{29} - 3740q^{30} + 3208q^{32} - 4q^{33} + 7508q^{34} + 1340q^{35} + 11468q^{36} - 1826q^{37} + 3568q^{38} + 2684q^{39} - 5144q^{40} - 17064q^{42} + 1694q^{43} - 14636q^{44} + 1410q^{45} - 5316q^{46} + 6888q^{48} + 682q^{49} + 20070q^{50} - 3012q^{51} + 20452q^{52} - 482q^{53} + 10784q^{54} - 11780q^{55} - 6952q^{56} - 20456q^{58} - 2786q^{59} - 29920q^{60} - 3778q^{61} - 11472q^{62} + 15808q^{64} - 2020q^{65} + 30148q^{66} + 7998q^{67} + 18032q^{68} + 9628q^{69} + 15296q^{70} + 19964q^{71} - 17708q^{72} - 23780q^{74} + 17570q^{75} - 23996q^{76} - 9508q^{77} - 8052q^{78} + 1384q^{80} + 1454q^{81} + 16016q^{82} - 17282q^{83} + 19624q^{84} + 9948q^{85} - 4796q^{86} - 49284q^{87} + 7288q^{88} - 5416q^{90} - 28036q^{91} - 14632q^{92} + 8896q^{93} + 432q^{94} + 6064q^{96} - 4q^{97} - 12246q^{98} + 49214q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/16\mathbb{Z}\right)^\times$.

$n$	$5$	$15$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$

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 $

$2$	0.329715	−	3.98639i	0.0824289	−	0.996597i
$2$	0.329715	−	3.98639i	0.0824289	−	0.996597i
$3$	3.91498	−	3.91498i	0.434998	−	0.434998i	−0.455327	−	0.890324i	$-0.650477\pi$
$3$	3.91498	−	3.91498i	0.434998	−	0.434998i	0.890324	+	0.455327i	$0.150477\pi$
$4$	−15.7826	−	2.62875i	−0.986411	−	0.164297i
$5$	4.72348	−	4.72348i	0.188939	−	0.188939i	−0.606298	−	0.795237i	$-0.707346\pi$
$5$	4.72348	−	4.72348i	0.188939	−	0.188939i	0.795237	+	0.606298i	$0.207346\pi$
$6$	−14.3158	−	16.8975i	−0.397661	−	0.469374i
$7$	45.3712			0.925943			0.462971	−	0.886373i	$-0.346783\pi$
$7$	45.3712			0.925943			0.462971	+	0.886373i	$0.346783\pi$
$8$	−15.6830	+	62.0487i	−0.245046	+	0.969511i
$9$			50.3458i			0.621554i
$10$	−17.2722	−	20.3870i	−0.172722	−	0.203870i
$11$	110.228	+	110.228i	0.910974	+	0.910974i	0.996349	−	0.0853752i	$-0.0272089\pi$
$11$	110.228	+	110.228i	0.910974	+	0.910974i	−0.0853752	+	0.996349i	$0.527209\pi$
$12$	−72.0800	+	51.4970i	−0.500555	+	0.357618i
$13$	−157.128	−	157.128i	−0.929754	−	0.929754i	0.0679357	−	0.997690i	$-0.478359\pi$
$13$	−157.128	−	157.128i	−0.929754	−	0.929754i	−0.997690	+	0.0679357i	$0.978359\pi$
$14$	14.9596	−	180.867i	0.0763244	−	0.922792i
$15$		−	36.9847i		−	0.164376i
$16$	242.179	+	82.9768i	0.946013	+	0.324128i
$17$	−378.592			−1.31001			−0.655003	−	0.755626i	$-0.727333\pi$
$17$	−378.592			−1.31001			−0.655003	+	0.755626i	$0.727333\pi$
$18$	200.698	+	16.5998i	0.619438	+	0.0512340i
$19$	203.127	−	203.127i	0.562680	−	0.562680i	−0.367388	−	0.930068i	$-0.619748\pi$
$19$	203.127	−	203.127i	0.562680	−	0.562680i	0.930068	+	0.367388i	$0.119748\pi$
$20$	−86.9656	+	62.1319i	−0.217414	+	0.155330i
$21$	177.627	−	177.627i	0.402783	−	0.402783i
$22$	475.755	−	403.067i	0.982964	−	0.832783i
$23$	−740.444			−1.39971			−0.699853	−	0.714287i	$-0.746751\pi$
$23$	−740.444			−1.39971			−0.699853	+	0.714287i	$0.746751\pi$
$24$	181.521	+	304.318i	0.315141	+	0.528330i
$25$			580.377i			0.928604i
$26$	−678.183	+	574.567i	−1.00323	+	0.849951i
$27$	514.217	+	514.217i	0.705372	+	0.705372i
$28$	−716.074	−	119.269i	−0.913360	−	0.152129i
$29$	82.6244	+	82.6244i	0.0982455	+	0.0982455i	0.754521	−	0.656276i	$-0.227869\pi$
$29$	82.6244	+	82.6244i	0.0982455	+	0.0982455i	−0.656276	+	0.754521i	$0.727869\pi$
$30$	−147.435	−	12.1944i	−0.163817	−	0.0135494i
$31$		−	286.217i		−	0.297833i	−0.988850	−	0.148916i	$-0.952421\pi$
$31$		−	286.217i		−	0.297833i	0.988850	−	0.148916i	$-0.0475785\pi$
$32$	410.628	−	938.062i	0.401004	−	0.916076i
$33$	863.080			0.792543
$34$	−124.828	+	1509.21i	−0.107982	+	1.30555i
$35$	214.310	−	214.310i	0.174947	−	0.174947i
$36$	132.346	−	794.587i	0.102119	−	0.613107i
$37$	1470.39	−	1470.39i	1.07406	−	1.07406i	0.0770352	−	0.997028i	$-0.475455\pi$
$37$	1470.39	−	1470.39i	1.07406	−	1.07406i	0.997028	−	0.0770352i	$-0.0245454\pi$
$38$	−742.770	−	876.719i	−0.514384	−	0.607146i
$39$	−1230.31			−0.808882
$40$	219.008	+	367.164i	0.136880	+	0.229478i
$41$			1301.21i			0.774070i	0.922065	+	0.387035i	$0.126501\pi$
$41$			1301.21i			0.774070i	−0.922065	+	0.387035i	$0.873499\pi$
$42$	−649.525	−	766.658i	−0.368212	−	0.434613i
$43$	−366.979	−	366.979i	−0.198474	−	0.198474i	0.600871	−	0.799346i	$-0.294820\pi$
$43$	−366.979	−	366.979i	−0.198474	−	0.198474i	−0.799346	+	0.600871i	$0.794820\pi$
$44$	−1449.92	−	2029.44i	−0.748924	−	1.04826i
$45$	237.808	+	237.808i	0.117436	+	0.117436i
$46$	−244.136	+	2951.70i	−0.115376	+	1.39494i
$47$		−	751.307i		−	0.340112i	−0.985434	−	0.170056i	$-0.945605\pi$
$47$		−	751.307i		−	0.340112i	0.985434	−	0.170056i	$-0.0543948\pi$
$48$	1272.98	−	623.275i	0.552509	−	0.270519i
$49$	−342.455			−0.142630
$50$	2313.61	+	191.359i	0.925444	+	0.0765437i
$51$	−1482.18	+	1482.18i	−0.569850	+	0.569850i
$52$	2066.84	+	2892.94i	0.764364	+	1.06988i
$53$	−1929.33	+	1929.33i	−0.686838	+	0.686838i	−0.961532	−	0.274693i	$-0.911424\pi$
$53$	−1929.33	+	1929.33i	−0.686838	+	0.686838i	0.274693	+	0.961532i	$0.411424\pi$
$54$	2219.41	−	1880.32i	0.761115	−	0.644829i
$55$	1041.32			0.344238
$56$	−711.555	+	2815.22i	−0.226899	+	0.897712i
$57$		−	1590.48i		−	0.489529i
$58$	356.616	−	302.130i	0.106009	−	0.0898129i
$59$	−1357.57	−	1357.57i	−0.389994	−	0.389994i	0.484691	−	0.874685i	$-0.338932\pi$
$59$	−1357.57	−	1357.57i	−0.389994	−	0.389994i	−0.874685	+	0.484691i	$0.838932\pi$
$60$	−97.2234	+	583.714i	−0.0270065	+	0.162143i
$61$	−1835.78	−	1835.78i	−0.493356	−	0.493356i	0.416006	−	0.909362i	$-0.363430\pi$
$61$	−1835.78	−	1835.78i	−0.493356	−	0.493356i	−0.909362	+	0.416006i	$0.863430\pi$
$62$	−1140.97	−	94.3702i	−0.296819	−	0.0245500i
$63$			2284.25i			0.575523i
$64$	−3604.09	−	1946.22i	−0.879905	−	0.475150i
$65$	−1484.39			−0.351334
$66$	284.571	−	3440.57i	0.0653284	−	0.789846i
$67$	2205.02	−	2205.02i	0.491204	−	0.491204i	−0.417481	−	0.908686i	$-0.637087\pi$
$67$	2205.02	−	2205.02i	0.491204	−	0.491204i	0.908686	+	0.417481i	$0.137087\pi$
$68$	5975.15	+	995.222i	1.29220	+	0.215230i
$69$	−2898.83	+	2898.83i	−0.608869	+	0.608869i
$70$	−783.662	−	924.984i	−0.159931	−	0.188772i
$71$	8970.40			1.77949			0.889744	−	0.456460i	$-0.150883\pi$
$71$	8970.40			1.77949			0.889744	+	0.456460i	$0.150883\pi$
$72$	−3123.90	−	789.572i	−0.602603	−	0.152309i
$73$		−	9350.46i		−	1.75464i	−0.479909	−	0.877318i	$-0.659330\pi$
$73$		−	9350.46i		−	1.75464i	0.479909	−	0.877318i	$-0.340670\pi$
$74$	−5376.75	−	6346.37i	−0.981875	−	1.15894i
$75$	2272.17	+	2272.17i	0.403941	+	0.403941i
$76$	−3739.84	+	2671.90i	−0.647480	+	0.462587i
$77$	5001.17	+	5001.17i	0.843509	+	0.843509i
$78$	−405.652	+	4904.49i	−0.0666752	+	0.806129i
$79$			2860.08i			0.458273i	0.973394	+	0.229137i	$0.0735903\pi$
$79$			2860.08i			0.458273i	−0.973394	+	0.229137i	$0.926410\pi$
$80$	1535.87	−	751.991i	0.239980	−	0.117499i
$81$	−51.7173			−0.00788253
$82$	5187.13	+	429.029i	0.771436	+	0.0638057i
$83$	−1036.63	+	1036.63i	−0.150477	+	0.150477i	−0.778331	−	0.627854i	$-0.783933\pi$
$83$	−1036.63	+	1036.63i	−0.150477	+	0.150477i	0.627854	+	0.778331i	$0.283933\pi$
$84$	−3270.35	+	2336.48i	−0.463486	+	0.331134i
$85$	−1788.27	+	1788.27i	−0.247512	+	0.247512i
$86$	−1583.92	+	1341.92i	−0.214159	+	0.181439i
$87$	646.946			0.0854731
$88$	−8568.19	+	5110.80i	−1.10643	+	0.659969i
$89$			5171.06i			0.652830i	0.945227	+	0.326415i	$0.105841\pi$
$89$			5171.06i			0.652830i	−0.945227	+	0.326415i	$0.894159\pi$
$90$	1026.40	−	869.585i	0.126716	−	0.107356i
$91$	−7129.10	−	7129.10i	−0.860899	−	0.860899i
$92$	11686.1	+	1946.44i	1.38068	+	0.229967i
$93$	−1120.54	−	1120.54i	−0.129557	−	0.129557i
$94$	−2995.00	−	247.717i	−0.338954	−	0.0280350i
$95$		−	1918.94i		−	0.212625i
$96$	−2064.90	−	5280.10i	−0.224055	−	0.572927i
$97$	8539.92			0.907633			0.453817	−	0.891095i	$-0.350062\pi$
$97$	8539.92			0.907633			0.453817	+	0.891095i	$0.350062\pi$
$98$	−112.913	+	1365.16i	−0.0117568	+	0.142145i
$99$	−5549.51	+	5549.51i	−0.566219	+	0.566219i
$100$	1525.67	−	9159.85i	0.152567	−	0.915985i
$101$	537.642	−	537.642i	0.0527049	−	0.0527049i	−0.680263	−	0.732968i	$-0.738134\pi$
$101$	537.642	−	537.642i	0.0527049	−	0.0527049i	0.732968	+	0.680263i	$0.238134\pi$
$102$	5419.85	+	6397.24i	0.520939	+	0.614883i
$103$	−5543.86			−0.522562			−0.261281	−	0.965263i	$-0.584145\pi$
$103$	−5543.86			−0.522562			−0.261281	+	0.965263i	$0.584145\pi$
$104$	12213.9	−	7285.38i	1.12924	−	0.673574i
$105$		−	1678.04i		−	0.152203i
$106$	7054.92	+	8327.18i	0.627886	+	0.741116i
$107$	−2989.60	−	2989.60i	−0.261123	−	0.261123i	0.564387	−	0.825510i	$-0.309113\pi$
$107$	−2989.60	−	2989.60i	−0.261123	−	0.261123i	−0.825510	+	0.564387i	$0.809113\pi$
$108$	−6763.92	−	9467.41i	−0.579897	−	0.811677i
$109$	−3353.83	−	3353.83i	−0.282285	−	0.282285i	0.551734	−	0.834020i	$-0.313966\pi$
$109$	−3353.83	−	3353.83i	−0.282285	−	0.282285i	−0.834020	+	0.551734i	$0.813966\pi$
$110$	343.339	−	4151.10i	0.0283751	−	0.343066i
$111$		−	11513.1i		−	0.934431i
$112$	10988.0	+	3764.76i	0.875954	+	0.300124i
$113$	−3193.81			−0.250122			−0.125061	−	0.992149i	$-0.539913\pi$
$113$	−3193.81			−0.250122			−0.125061	+	0.992149i	$0.539913\pi$
$114$	−6340.27	−	524.406i	−0.487863	−	0.0403513i
$115$	−3497.48	+	3497.48i	−0.264459	+	0.264459i
$116$	−1086.83	−	1521.22i	−0.0807690	−	0.113052i
$117$	7910.76	−	7910.76i	0.577892	−	0.577892i
$118$	−5859.41	+	4964.18i	−0.420813	+	0.356520i
$119$	−17177.2			−1.21299
$120$	2294.85	+	580.030i	0.159365	+	0.0402798i
$121$			9659.34i			0.659746i
$122$	−7923.41	+	6712.84i	−0.532344	+	0.451010i
$123$	5094.22	+	5094.22i	0.336719	+	0.336719i
$124$	−752.393	+	4517.24i	−0.0489329	+	0.293785i
$125$	5693.58	+	5693.58i	0.364389	+	0.364389i
$126$	9105.91	+	753.153i	0.573565	+	0.0474397i
$127$			22900.5i			1.41983i	0.704287	+	0.709915i	$0.251267\pi$
$127$			22900.5i			1.41983i	−0.704287	+	0.709915i	$0.748733\pi$
$128$	−8946.69	+	13725.6i	−0.546063	+	0.837744i
$129$	−2873.43			−0.172672
$130$	−489.425	+	5917.34i	−0.0289601	+	0.350139i
$131$	19255.9	−	19255.9i	1.12207	−	1.12207i	0.130644	−	0.991429i	$-0.458296\pi$
$131$	19255.9	−	19255.9i	1.12207	−	1.12207i	0.991429	−	0.130644i	$-0.0417045\pi$
$132$	−13621.6	−	2268.82i	−0.781773	−	0.130212i
$133$	9216.13	−	9216.13i	0.521009	−	0.521009i
$134$	−8063.02	−	9517.08i	−0.449043	−	0.530022i
$135$	4857.79			0.266545
$136$	5937.44	−	23491.1i	0.321012	−	1.27007i
$137$			19938.2i			1.06229i	0.847280	+	0.531147i	$0.178239\pi$
$137$			19938.2i			1.06229i	−0.847280	+	0.531147i	$0.821761\pi$
$138$	10600.1	+	12511.6i	0.556609	+	0.656985i
$139$	25175.4	+	25175.4i	1.30301	+	1.30301i	0.926356	+	0.376649i	$0.122924\pi$
$139$	25175.4	+	25175.4i	1.30301	+	1.30301i	0.376649	+	0.926356i	$0.377076\pi$
$140$	−3945.73	+	2819.00i	−0.201313	+	0.143826i
$141$	−2941.35	−	2941.35i	−0.147948	−	0.147948i
$142$	2957.68	−	35759.5i	0.146681	−	1.77343i
$143$		−	34639.8i		−	1.69396i
$144$	−4177.54	+	12192.7i	−0.201463	+	0.587998i
$145$	780.550			0.0371249
$146$	−37274.5	−	3082.99i	−1.74867	−	0.144633i
$147$	−1340.70	+	1340.70i	−0.0620438	+	0.0620438i
$148$	−27071.9	+	19341.3i	−1.23593	+	0.883003i
$149$	−3216.99	+	3216.99i	−0.144903	+	0.144903i	−0.775837	−	0.630934i	$-0.782672\pi$
$149$	−3216.99	+	3216.99i	−0.144903	+	0.144903i	0.630934	+	0.775837i	$0.282672\pi$
$150$	9806.91	−	8308.57i	0.435862	−	0.369270i
$151$	−14770.5			−0.647802			−0.323901	−	0.946091i	$-0.604994\pi$
$151$	−14770.5			−0.647802			−0.323901	+	0.946091i	$0.604994\pi$
$152$	9418.15	+	15789.4i	0.407642	+	0.683407i
$153$		−	19060.5i		−	0.814239i
$154$	21585.6	−	18287.6i	0.910168	−	0.771109i
$155$	−1351.94	−	1351.94i	−0.0562723	−	0.0562723i
$156$	19417.5	+	3234.17i	0.797890	+	0.132897i
$157$	−18014.6	−	18014.6i	−0.730845	−	0.730845i	0.239942	−	0.970787i	$-0.422872\pi$
$157$	−18014.6	−	18014.6i	−0.730845	−	0.730845i	−0.970787	+	0.239942i	$0.922872\pi$
$158$	11401.4	+	943.014i	0.456714	+	0.0377749i
$159$			15106.6i			0.597547i
$160$	−2491.33	−	6370.52i	−0.0973175	−	0.248848i
$161$	−33594.8			−1.29605
$162$	−17.0520	+	206.165i	−0.000649748	+	0.00785571i
$163$	15083.2	−	15083.2i	0.567700	−	0.567700i	−0.363784	−	0.931483i	$-0.618515\pi$
$163$	15083.2	−	15083.2i	0.567700	−	0.567700i	0.931483	+	0.363784i	$0.118515\pi$
$164$	3420.55	−	20536.5i	0.127177	−	0.763551i
$165$	4076.74	−	4076.74i	0.149743	−	0.149743i
$166$	3790.63	+	4474.22i	0.137561	+	0.162368i
$167$	23733.6			0.851001			0.425501	−	0.904958i	$-0.360098\pi$
$167$	23733.6			0.851001			0.425501	+	0.904958i	$0.360098\pi$
$168$	8235.83	+	13807.3i	0.291802	+	0.489203i
$169$			20817.7i			0.728885i
$170$	6539.13	+	7718.37i	0.226267	+	0.267072i
$171$	10226.6	+	10226.6i	0.349736	+	0.349736i
$172$	4827.18	+	6756.57i	0.163169	+	0.228386i
$173$	−12072.3	−	12072.3i	−0.403363	−	0.403363i	0.476053	−	0.879416i	$-0.342067\pi$
$173$	−12072.3	−	12072.3i	−0.403363	−	0.403363i	−0.879416	+	0.476053i	$0.842067\pi$
$174$	213.308	−	2578.98i	0.00704545	−	0.0851823i
$175$			26332.4i			0.859834i
$176$	17548.6	+	35841.3i	0.566521	+	1.15707i
$177$	−10629.7			−0.339293
$178$	20613.9	+	1704.98i	0.650608	+	0.0538120i
$179$	−28111.5	+	28111.5i	−0.877361	+	0.877361i	−0.993261	−	0.115900i	$-0.963025\pi$
$179$	−28111.5	+	28111.5i	−0.877361	+	0.877361i	0.115900	+	0.993261i	$0.463025\pi$
$180$	−3128.08	−	4378.36i	−0.0965458	−	0.135134i
$181$	−15906.7	+	15906.7i	−0.485539	+	0.485539i	−0.906895	−	0.421356i	$-0.861554\pi$
$181$	−15906.7	+	15906.7i	−0.485539	+	0.485539i	0.421356	+	0.906895i	$0.361554\pi$
$182$	−30770.0	+	26068.8i	−0.928932	+	0.787006i
$183$	−14374.1			−0.429218
$184$	11612.4	−	45943.6i	0.342993	−	1.35703i
$185$		−	13890.8i		−	0.405866i
$186$	−4836.34	+	4097.43i	−0.139795	+	0.118437i
$187$	−41731.4	−	41731.4i	−1.19338	−	1.19338i
$188$	−1975.00	+	11857.6i	−0.0558792	+	0.335490i
$189$	23330.6	+	23330.6i	0.653134	+	0.653134i
$190$	−7649.63	−	632.703i	−0.211901	−	0.0175264i
$191$		−	28038.6i		−	0.768581i	−0.923212	−	0.384290i	$-0.874446\pi$
$191$		−	28038.6i		−	0.768581i	0.923212	−	0.384290i	$-0.125554\pi$
$192$	−21729.3	+	6490.54i	−0.589446	+	0.176067i
$193$	56713.1			1.52254			0.761270	−	0.648436i	$-0.224576\pi$
$193$	56713.1			1.52254			0.761270	+	0.648436i	$0.224576\pi$
$194$	2815.74	−	34043.4i	0.0748152	−	0.904544i
$195$	−5811.35	+	5811.35i	−0.152830	+	0.152830i
$196$	5404.82	+	900.227i	0.140692	+	0.0234337i
$197$	−10179.3	+	10179.3i	−0.262292	+	0.262292i	−0.825985	−	0.563692i	$-0.809380\pi$
$197$	−10179.3	+	10179.3i	−0.262292	+	0.262292i	0.563692	+	0.825985i	$0.309380\pi$
$198$	20292.7	+	23952.3i	0.517619	+	0.610965i
$199$	31787.3			0.802689			0.401344	−	0.915927i	$-0.368543\pi$
$199$	31787.3			0.802689			0.401344	+	0.915927i	$0.368543\pi$
$200$	−36011.7	−	9102.04i	−0.900292	−	0.227551i
$201$		−	17265.2i		−	0.427346i
$202$	−1965.98	−	2320.52i	−0.0481811	−	0.0568699i
$203$	3748.77	+	3748.77i	0.0909697	+	0.0909697i
$204$	27288.9	−	19496.3i	0.655731	−	0.468482i
$205$	6146.25	+	6146.25i	0.146252	+	0.146252i
$206$	−1827.89	+	22100.0i	−0.0430742	+	0.520783i
$207$		−	37278.3i		−	0.869992i
$208$	−25015.3	−	51091.3i	−0.578200	−	1.18092i
$209$	44780.6			1.02517
$210$	−6689.32	−	553.276i	−0.151685	−	0.0125459i
$211$	−10699.8	+	10699.8i	−0.240332	+	0.240332i	−0.816988	−	0.576655i	$-0.804358\pi$
$211$	−10699.8	+	10699.8i	−0.240332	+	0.240332i	0.576655	+	0.816988i	$0.304358\pi$
$212$	35521.5	−	25378.1i	0.790350	−	0.564660i
$213$	35118.9	−	35118.9i	0.774073	−	0.774073i
$214$	−12903.4	+	10932.0i	−0.281759	+	0.238711i
$215$	−3466.84			−0.0749992
$216$	−39970.9	+	23842.0i	−0.856716	+	0.511018i
$217$		−	12986.0i		−	0.275776i
$218$	−14475.5	+	12263.9i	−0.304593	+	0.258056i
$219$	−36606.9	−	36606.9i	−0.763263	−	0.763263i
$220$	−16434.7	−	2737.36i	−0.339560	−	0.0565571i
$221$	59487.5	+	59487.5i	1.21798	+	1.21798i
$222$	−45895.8	−	3796.05i	−0.931251	−	0.0770241i
$223$			91700.4i			1.84400i	0.387187	+	0.922001i	$0.373447\pi$
$223$			91700.4i			1.84400i	−0.387187	+	0.922001i	$0.626553\pi$
$224$	18630.7	−	42561.0i	0.371307	−	0.848234i
$225$	−29219.6			−0.577177
$226$	−1053.05	+	12731.8i	−0.0206173	+	0.249271i
$227$	17499.5	−	17499.5i	0.339605	−	0.339605i	−0.516614	−	0.856218i	$-0.672808\pi$
$227$	17499.5	−	17499.5i	0.339605	−	0.339605i	0.856218	+	0.516614i	$0.172808\pi$
$228$	−4180.97	+	25101.9i	−0.0804280	+	0.482877i
$229$	−63859.8	+	63859.8i	−1.21775	+	1.21775i	−0.249326	+	0.968420i	$0.580209\pi$
$229$	−63859.8	+	63859.8i	−1.21775	+	1.21775i	−0.968420	+	0.249326i	$0.919791\pi$
$230$	12789.1	+	15095.5i	0.241760	+	0.285359i
$231$	39159.0			0.733850
$232$	−6422.54	+	3830.94i	−0.119325	+	0.0711754i
$233$		−	63891.7i		−	1.17688i	−0.808540	−	0.588441i	$-0.799742\pi$
$233$		−	63891.7i		−	1.17688i	0.808540	−	0.588441i	$-0.200258\pi$
$234$	−28927.1	−	34143.7i	−0.528290	−	0.623560i
$235$	−3548.79	−	3548.79i	−0.0642605	−	0.0642605i
$236$	17857.2	+	24994.6i	0.320620	+	0.448769i
$237$	11197.2	+	11197.2i	0.199348	+	0.199348i
$238$	−5663.58	+	68474.8i	−0.0999855	+	1.20886i
$239$		−	12096.4i		−	0.211768i	−0.994378	−	0.105884i	$-0.966233\pi$
$239$		−	12096.4i		−	0.211768i	0.994378	−	0.105884i	$-0.0337672\pi$
$240$	3068.87	−	8956.93i	0.0532790	−	0.155502i
$241$	27978.6			0.481717			0.240859	−	0.970560i	$-0.422571\pi$
$241$	27978.6			0.481717			0.240859	+	0.970560i	$0.422571\pi$
$242$	38505.9	+	3184.83i	0.657501	+	0.0543821i
$243$	−41854.0	+	41854.0i	−0.708801	+	0.708801i
$244$	24147.5	+	33799.1i	0.405595	+	0.567709i
$245$	−1617.58	+	1617.58i	−0.0269484	+	0.0269484i
$246$	21987.2	−	18627.9i	0.363328	−	0.307818i
$247$	−63834.2			−1.04631
$248$	17759.4	+	4488.73i	0.288752	+	0.0729828i
$249$			8116.80i			0.130914i
$250$	24574.1	−	20819.6i	0.393185	−	0.333113i
$251$	1996.06	+	1996.06i	0.0316830	+	0.0316830i	0.722771	−	0.691088i	$-0.242868\pi$
$251$	1996.06	+	1996.06i	0.0316830	+	0.0316830i	−0.691088	+	0.722771i	$0.742868\pi$
$252$	6004.72	−	36051.4i	0.0945565	−	0.567702i
$253$	−81617.5	−	81617.5i	−1.27509	−	1.27509i
$254$	91290.1	+	7550.63i	1.41500	+	0.117035i
$255$			14002.1i			0.215334i
$256$	51765.7	+	40190.5i	0.789882	+	0.613259i
$257$	−73510.4			−1.11297			−0.556484	−	0.830859i	$-0.687850\pi$
$257$	−73510.4			−1.11297			−0.556484	+	0.830859i	$0.687850\pi$
$258$	−947.415	+	11454.6i	−0.0142331	+	0.172084i
$259$	66713.5	−	66713.5i	0.994521	−	0.994521i
$260$	23427.5	+	3902.08i	0.346560	+	0.0577231i
$261$	−4159.80	+	4159.80i	−0.0610648	+	0.0610648i
$262$	−70412.5	−	83110.5i	−1.02576	−	1.21075i
$263$	68109.3			0.984680			0.492340	−	0.870403i	$-0.336142\pi$
$263$	68109.3			0.984680			0.492340	+	0.870403i	$0.336142\pi$
$264$	−13535.6	+	53553.0i	−0.194210	+	0.768380i
$265$			18226.3i			0.259542i
$266$	−33700.4	−	39777.8i	−0.476290	−	0.562182i
$267$	20244.6	+	20244.6i	0.283980	+	0.283980i
$268$	−40597.3	+	29004.4i	−0.565232	+	0.403826i
$269$	−15056.1	−	15056.1i	−0.208069	−	0.208069i	0.595377	−	0.803446i	$-0.297003\pi$
$269$	−15056.1	−	15056.1i	−0.208069	−	0.208069i	−0.803446	+	0.595377i	$0.797003\pi$
$270$	1601.69	−	19365.0i	0.0219710	−	0.265638i
$271$		−	104320.i		−	1.42046i	−0.703968	−	0.710232i	$-0.748590\pi$
$271$		−	104320.i		−	1.42046i	0.703968	−	0.710232i	$-0.251410\pi$
$272$	−91687.1	−	31414.3i	−1.23928	−	0.424610i
$273$	−55820.6			−0.748979
$274$	79481.4	+	6573.93i	1.05868	+	0.0875637i
$275$	−63973.7	+	63973.7i	−0.845934	+	0.845934i
$276$	53371.2	−	38130.6i	0.700630	−	0.500560i
$277$	2136.36	−	2136.36i	0.0278430	−	0.0278430i	−0.693048	−	0.720891i	$-0.743733\pi$
$277$	2136.36	−	2136.36i	0.0278430	−	0.0278430i	0.720891	+	0.693048i	$0.243733\pi$
$278$	108659.	−	92058.1i	1.40598	−	1.19117i
$279$	14409.8			0.185119
$280$	9936.65	+	16658.7i	0.126743	+	0.212483i
$281$			36783.7i			0.465846i	0.972495	+	0.232923i	$0.0748290\pi$
$281$			36783.7i			0.465846i	−0.972495	+	0.232923i	$0.925171\pi$
$282$	−12695.2	+	10755.6i	−0.159640	+	0.135249i
$283$	14172.0	+	14172.0i	0.176953	+	0.176953i	0.790026	−	0.613073i	$-0.210067\pi$
$283$	14172.0	+	14172.0i	0.176953	+	0.176953i	−0.613073	+	0.790026i	$0.710067\pi$
$284$	−141576.	−	23580.9i	−1.75531	−	0.292364i
$285$	−7512.60	−	7512.60i	−0.0924913	−	0.0924913i
$286$	−138088.	−	11421.3i	−1.68820	−	0.139631i
$287$			59037.5i			0.716744i
$288$	47227.5	+	20673.4i	0.569391	+	0.249245i
$289$	59810.8			0.716117
$290$	257.359	−	3111.58i	0.00306016	−	0.0369985i
$291$	33433.6	−	33433.6i	0.394819	−	0.394819i
$292$	−24580.0	+	147574.i	−0.288281	+	1.73079i
$293$	80721.8	−	80721.8i	0.940276	−	0.940276i	−0.0580384	−	0.998314i	$-0.518485\pi$
$293$	80721.8	−	80721.8i	0.940276	−	0.940276i	0.998314	+	0.0580384i	$0.0184846\pi$
$294$	4902.52	+	5786.62i	0.0567185	+	0.0669469i
$295$	−12824.9			−0.147370
$296$	68175.9	+	114296.i	0.778122	+	1.30451i
$297$			113362.i			1.28515i
$298$	11763.5	+	13884.9i	0.132466	+	0.156354i
$299$	116345.	+	116345.i	1.30138	+	1.30138i
$300$	−29887.7	−	41833.6i	−0.332085	−	0.464818i
$301$	−16650.3	−	16650.3i	−0.183776	−	0.183776i
$302$	−4870.07	+	58881.1i	−0.0533976	+	0.645598i
$303$		−	4209.72i		−	0.0458530i
$304$	66048.1	−	32338.4i	0.714683	−	0.349922i
$305$	−17342.5			−0.186429
$306$	−75982.7	−	6284.55i	−0.811468	−	0.0671168i
$307$	113714.	−	113714.i	1.20653	−	1.20653i	0.234389	−	0.972143i	$-0.424691\pi$
$307$	113714.	−	113714.i	1.20653	−	1.20653i	0.972143	−	0.234389i	$-0.0753090\pi$
$308$	−65784.5	−	92078.1i	−0.693461	−	0.970633i
$309$	−21704.1	+	21704.1i	−0.227313	+	0.227313i
$310$	−5835.12	+	4943.61i	−0.0607193	+	0.0514424i
$311$	−93801.8			−0.969819			−0.484909	−	0.874564i	$-0.661147\pi$
$311$	−93801.8			−0.969819			−0.484909	+	0.874564i	$0.661147\pi$
$312$	19294.9	−	76339.2i	0.198214	−	0.784220i
$313$			9229.52i			0.0942086i	0.998890	+	0.0471043i	$0.0149993\pi$
$313$			9229.52i			0.0942086i	−0.998890	+	0.0471043i	$0.985001\pi$
$314$	−77752.9	+	65873.5i	−0.788601	+	0.668115i
$315$	10789.6	+	10789.6i	0.108739	+	0.108739i
$316$	7518.44	−	45139.5i	0.0752928	−	0.452046i
$317$	−8447.44	−	8447.44i	−0.0840634	−	0.0840634i	0.663825	−	0.747888i	$-0.268932\pi$
$317$	−8447.44	−	8447.44i	−0.0840634	−	0.0840634i	−0.747888	+	0.663825i	$0.768932\pi$
$318$	60220.7	+	4980.87i	0.595513	+	0.0492551i
$319$			18215.0i			0.178998i
$320$	−26216.8	+	7830.94i	−0.256023	+	0.0764740i
$321$	−23408.5			−0.227176
$322$	−11076.7	+	133922.i	−0.106832	+	1.29164i
$323$	−76902.4	+	76902.4i	−0.737114	+	0.737114i
$324$	816.232	+	135.952i	0.00777542	+	0.00129507i
$325$	91193.8	−	91193.8i	0.863373	−	0.863373i
$326$	−55154.4	−	65100.7i	−0.518973	−	0.612562i
$327$	−26260.4			−0.245587
$328$	−80738.5	−	20406.8i	−0.750469	−	0.189683i
$329$		−	34087.7i		−	0.314924i
$330$	−14907.3	−	17595.6i	−0.136890	−	0.161576i
$331$	−46092.1	−	46092.1i	−0.420698	−	0.420698i	0.464746	−	0.885444i	$-0.346146\pi$
$331$	−46092.1	−	46092.1i	−0.420698	−	0.420698i	−0.885444	+	0.464746i	$0.846146\pi$
$332$	19085.8	−	13635.7i	0.173155	−	0.123709i
$333$	74028.2	+	74028.2i	0.667588	+	0.667588i
$334$	7825.33	−	94611.2i	0.0701471	−	0.848105i
$335$		−	20830.7i		−	0.185616i
$336$	57756.6	−	28278.7i	0.511592	−	0.250485i
$337$	39317.8			0.346201			0.173101	−	0.984904i	$-0.444621\pi$
$337$	39317.8			0.346201			0.173101	+	0.984904i	$0.444621\pi$
$338$	82987.4	+	6863.91i	0.726405	+	0.0600812i
$339$	−12503.7	+	12503.7i	−0.108803	+	0.108803i
$340$	32924.5	−	23522.6i	0.284814	−	0.203483i
$341$	31549.1	−	31549.1i	0.271318	−	0.271318i
$342$	44139.1	−	37395.4i	0.377374	−	0.319717i
$343$	−124474.			−1.05801
$344$	28525.9	−	17015.3i	0.241059	−	0.143788i
$345$			27385.1i			0.230079i
$346$	−52105.1	+	44144.3i	−0.435239	+	0.368742i
$347$	−67694.0	−	67694.0i	−0.562201	−	0.562201i	0.367731	−	0.929932i	$-0.380135\pi$
$347$	−67694.0	−	67694.0i	−0.562201	−	0.562201i	−0.929932	+	0.367731i	$0.880135\pi$
$348$	−10210.5	−	1700.66i	−0.0843116	−	0.0140430i
$349$	−7662.83	−	7662.83i	−0.0629127	−	0.0629127i	0.674950	−	0.737863i	$-0.264165\pi$
$349$	−7662.83	−	7662.83i	−0.0629127	−	0.0629127i	−0.737863	+	0.674950i	$0.764165\pi$
$350$	104971.	+	8682.20i	0.856908	+	0.0708751i
$351$		−	161596.i		−	1.31165i
$352$	148663.	−	58137.9i	1.19983	−	0.469217i
$353$	70618.0			0.566716			0.283358	−	0.959014i	$-0.408551\pi$
$353$	70618.0			0.566716			0.283358	+	0.959014i	$0.408551\pi$
$354$	−3504.78	+	42374.2i	−0.0279675	+	0.338138i
$355$	42371.5	−	42371.5i	0.336215	−	0.336215i
$356$	13593.4	−	81612.7i	0.107258	−	0.643958i
$357$	−67248.3	+	67248.3i	−0.527649	+	0.527649i
$358$	102795.	+	121332.i	0.802055	+	0.946695i
$359$	−168144.			−1.30465			−0.652323	−	0.757941i	$-0.726206\pi$
$359$	−168144.			−1.30465			−0.652323	+	0.757941i	$0.726206\pi$
$360$	−18485.2	+	11026.1i	−0.142633	+	0.0850782i
$361$			47799.6i			0.366783i
$362$	58165.8	+	68655.2i	0.443864	+	0.523909i
$363$	37816.1	+	37816.1i	0.286988	+	0.286988i
$364$	93775.0	+	131256.i	0.707757	+	0.990643i
$365$	−44166.7	−	44166.7i	−0.331520	−	0.331520i
$366$	−4739.35	+	57300.6i	−0.0353799	+	0.427757i
$367$			82596.4i			0.613238i	0.951832	+	0.306619i	$0.0991977\pi$
$367$			82596.4i			0.613238i	−0.951832	+	0.306619i	$0.900802\pi$
$368$	−179320.	−	61439.7i	−1.32414	−	0.453684i
$369$	−65510.6			−0.481126
$370$	−55373.9	−	4580.00i	−0.404485	−	0.0334550i
$371$	−87536.0	+	87536.0i	−0.635973	+	0.635973i
$372$	14739.3	+	20630.5i	0.106510	+	0.149082i
$373$	−76631.0	+	76631.0i	−0.550791	+	0.550791i	−0.926669	−	0.375878i	$-0.877341\pi$
$373$	−76631.0	+	76631.0i	−0.550791	+	0.550791i	0.375878	+	0.926669i	$0.377341\pi$
$374$	−180117.	+	152598.i	−1.28769	+	1.09095i
$375$	44580.5			0.317017
$376$	46617.6	+	11782.7i	0.329742	+	0.0833431i
$377$		−	25965.3i		−	0.182688i
$378$	100697.	−	85312.4i	0.704749	−	0.597075i
$379$	−95935.8	−	95935.8i	−0.667886	−	0.667886i	0.289340	−	0.957226i	$-0.406564\pi$
$379$	−95935.8	−	95935.8i	−0.667886	−	0.667886i	−0.957226	+	0.289340i	$0.906564\pi$
$380$	−5044.40	+	30285.8i	−0.0349335	+	0.209735i
$381$	89654.8	+	89654.8i	0.617623	+	0.617623i
$382$	−111773.	−	9244.76i	−0.765965	−	0.0633532i
$383$			168708.i			1.15011i	0.818116	+	0.575054i	$0.195019\pi$
$383$			168708.i			1.15011i	−0.818116	+	0.575054i	$0.804981\pi$
$384$	18709.3	+	88761.6i	0.126881	+	0.601953i
$385$	47245.9			0.318744
$386$	18699.2	−	226080.i	0.125501	−	1.51736i
$387$	18475.9	−	18475.9i	0.123362	−	0.123362i
$388$	−134782.	−	22449.3i	−0.895299	−	0.149121i
$389$	66490.0	−	66490.0i	0.439397	−	0.439397i	−0.452412	−	0.891809i	$-0.649436\pi$
$389$	66490.0	−	66490.0i	0.439397	−	0.439397i	0.891809	+	0.452412i	$0.149436\pi$
$390$	21250.2	+	25082.4i	0.139712	+	0.164907i
$391$	280326.			1.83362
$392$	5370.71	−	21248.9i	0.0349510	−	0.138282i
$393$		−	150773.i		−	0.976199i
$394$	37222.4	+	43934.9i	0.239779	+	0.283020i
$395$	13509.6	+	13509.6i	0.0865859	+	0.0865859i
$396$	102174.	−	72997.3i	0.651552	−	0.465497i
$397$	18578.8	+	18578.8i	0.117879	+	0.117879i	0.763586	−	0.645706i	$-0.223437\pi$
$397$	18578.8	+	18578.8i	0.117879	+	0.117879i	−0.645706	+	0.763586i	$0.723437\pi$
$398$	10480.8	−	126716.i	0.0661647	−	0.799957i
$399$		−	72162.0i		−	0.453276i
$400$	−48157.9	+	140555.i	−0.300987	+	0.878471i
$401$	−129108.			−0.802908			−0.401454	−	0.915879i	$-0.631495\pi$
$401$	−129108.			−0.802908			−0.401454	+	0.915879i	$0.631495\pi$
$402$	−68825.7	−	5692.60i	−0.425891	−	0.0352256i
$403$	−44972.9	+	44972.9i	−0.276911	+	0.276911i
$404$	−9898.70	+	7072.05i	−0.0606479	+	0.0433294i
$405$	−244.286	+	244.286i	−0.00148932	+	0.00148932i
$406$	16180.1	−	13708.0i	0.0981586	−	0.0831616i
$407$	324156.			1.95689
$408$	−68722.4	−	115212.i	−0.412836	−	0.692116i
$409$			17952.4i			0.107319i	0.998559	+	0.0536594i	$0.0170885\pi$
$409$			17952.4i			0.107319i	−0.998559	+	0.0536594i	$0.982911\pi$
$410$	26527.8	−	22474.8i	0.157810	−	0.133699i
$411$	78057.7	+	78057.7i	0.462096	+	0.462096i
$412$	87496.3	+	14573.4i	0.515461	+	0.0858551i
$413$	−61594.5	−	61594.5i	−0.361112	−	0.361112i
$414$	−148606.	−	12291.2i	−0.867031	−	0.0717124i
$415$			9793.04i			0.0568619i
$416$	−211918.	+	82874.9i	−1.22456	+	0.478891i
$417$	197122.			1.13361
$418$	14764.8	−	178513.i	0.0845038	−	1.02168i
$419$	56887.3	−	56887.3i	0.324031	−	0.324031i	−0.526280	−	0.850311i	$-0.676414\pi$
$419$	56887.3	−	56887.3i	0.324031	−	0.324031i	0.850311	+	0.526280i	$0.176414\pi$
$420$	−4411.14	+	26483.8i	−0.0250065	+	0.150135i
$421$	−144162.	+	144162.i	−0.813365	+	0.813365i	−0.985137	−	0.171772i	$-0.945051\pi$
$421$	−144162.	+	144162.i	−0.813365	+	0.813365i	0.171772	+	0.985137i	$0.445051\pi$
$422$	39125.8	+	46181.6i	0.219704	+	0.259325i
$423$	37825.2			0.211398
$424$	−89454.8	−	149970.i	−0.497590	−	0.834205i
$425$		−	219726.i		−	1.21648i
$426$	−128418.	−	151577.i	−0.707633	−	0.835245i
$427$	−83291.4	−	83291.4i	−0.456819	−	0.456819i
$428$	39324.7	+	55042.5i	0.214673	+	0.300477i
$429$	−135614.	−	135614.i	−0.736870	−	0.736870i
$430$	−1143.07	+	13820.2i	−0.00618210	+	0.0747440i
$431$		−	18641.5i		−	0.100352i	−0.998740	−	0.0501760i	$-0.984022\pi$
$431$		−	18641.5i		−	0.100352i	0.998740	−	0.0501760i	$-0.0159782\pi$
$432$	81864.6	+	167201.i	0.438661	+	0.895923i
$433$	2193.97			0.0117019			0.00585094	−	0.999983i	$-0.498138\pi$
$433$	2193.97			0.0117019			0.00585094	+	0.999983i	$0.498138\pi$
$434$	−51767.3	−	4281.69i	−0.274838	−	0.0227319i
$435$	3055.84	−	3055.84i	0.0161492	−	0.0161492i
$436$	44115.7	+	61748.5i	0.232071	+	0.324828i
$437$	−150404.	+	150404.i	−0.787586	+	0.787586i
$438$	−157999.	+	133859.i	−0.823581	+	0.697751i
$439$	118115.			0.612880			0.306440	−	0.951890i	$-0.400862\pi$
$439$	118115.			0.612880			0.306440	+	0.951890i	$0.400862\pi$
$440$	−16331.0	+	64612.5i	−0.0843541	+	0.333742i
$441$		−	17241.2i		−	0.0886523i
$442$	256754.	−	217526.i	1.31424	−	1.11344i
$443$	37885.8	+	37885.8i	0.193050	+	0.193050i	0.797013	−	0.603963i	$-0.206412\pi$
$443$	37885.8	+	37885.8i	0.193050	+	0.193050i	−0.603963	+	0.797013i	$0.706412\pi$
$444$	−30265.1	+	181707.i	−0.153524	+	0.921733i
$445$	24425.4	+	24425.4i	0.123345	+	0.123345i
$446$	365553.	+	30235.0i	1.83773	+	0.151999i
$447$			25188.9i			0.126065i
$448$	−163522.	−	88302.1i	−0.814741	−	0.439962i
$449$	−85186.6			−0.422550			−0.211275	−	0.977427i	$-0.567762\pi$
$449$	−85186.6			−0.422550			−0.211275	+	0.977427i	$0.567762\pi$
$450$	−9634.15	+	116481.i	−0.0475760	+	0.575213i
$451$	−143430.	+	143430.i	−0.705157	+	0.705157i
$452$	50406.5	+	8395.71i	0.246723	+	0.0410942i
$453$	−57826.4	+	57826.4i	−0.281793	+	0.281793i
$454$	−63989.9	−	75529.6i	−0.310456	−	0.366442i
$455$	−67348.4			−0.325315
$456$	98687.2	+	24943.4i	0.474604	+	0.119957i
$457$			96935.7i			0.464142i	0.972699	+	0.232071i	$0.0745502\pi$
$457$			96935.7i			0.464142i	−0.972699	+	0.232071i	$0.925450\pi$
$458$	233514.	+	275625.i	1.11322	+	1.31398i
$459$	−194678.	−	194678.i	−0.924042	−	0.924042i
$460$	64393.2	−	46005.2i	0.304315	−	0.217416i
$461$	295014.	+	295014.i	1.38816	+	1.38816i	0.829176	+	0.558988i	$0.188810\pi$
$461$	295014.	+	295014.i	1.38816	+	1.38816i	0.558988	+	0.829176i	$0.311190\pi$
$462$	12911.3	−	156103.i	0.0604904	−	0.731352i
$463$			224348.i			1.04655i	0.852164	+	0.523275i	$0.175290\pi$
$463$			224348.i			1.04655i	−0.852164	+	0.523275i	$0.824710\pi$
$464$	13154.0	+	26865.8i	0.0610974	+	0.124786i
$465$	−10585.7			−0.0489567
$466$	−254697.	−	21066.1i	−1.17288	−	0.0970090i
$467$	189556.	−	189556.i	0.869168	−	0.869168i	−0.123212	−	0.992380i	$-0.539320\pi$
$467$	189556.	−	189556.i	0.869168	−	0.869168i	0.992380	+	0.123212i	$0.0393196\pi$
$468$	−145648.	+	104057.i	−0.664985	+	0.475093i
$469$	100044.	−	100044.i	0.454827	−	0.454827i
$470$	−15316.9	+	12976.7i	−0.0693387	+	0.0587449i
$471$	−141054.			−0.635832
$472$	105526.	−	62944.7i	0.473670	−	0.282537i
$473$		−	80902.6i		−	0.361610i
$474$	48328.2	−	40944.4i	0.215102	−	0.182238i
$475$	117891.	+	117891.i	0.522506	+	0.522506i
$476$	271100.	+	45154.4i	1.19651	+	0.199290i
$477$	−97133.7	−	97133.7i	−0.426907	−	0.426907i
$478$	−48221.0	−	3988.37i	−0.211047	−	0.0174558i
$479$		−	132796.i		−	0.578781i	−0.957211	−	0.289390i	$-0.906547\pi$
$479$		−	132796.i		−	0.578781i	0.957211	−	0.289390i	$-0.0934526\pi$
$480$	−34693.9	−	15187.0i	−0.150581	−	0.0659156i
$481$	−462081.			−1.99723
$482$	9224.98	−	111534.i	0.0397074	−	0.480078i
$483$	−131523.	+	131523.i	−0.563778	+	0.563778i
$484$	25392.0	−	152449.i	0.108394	−	0.650781i
$485$	40338.2	−	40338.2i	0.171488	−	0.171488i
$486$	153046.	+	180646.i	0.647964	+	0.764815i
$487$	−283936.			−1.19719			−0.598595	−	0.801052i	$-0.704274\pi$
$487$	−283936.			−1.19719			−0.598595	+	0.801052i	$0.704274\pi$
$488$	142698.	−	85117.3i	0.599209	−	0.357419i
$489$		−	118101.i		−	0.493896i
$490$	5914.96	+	6981.64i	0.0246354	+	0.0290781i
$491$	−111725.	−	111725.i	−0.463435	−	0.463435i	0.436345	−	0.899780i	$-0.356273\pi$
$491$	−111725.	−	111725.i	−0.463435	−	0.463435i	−0.899780	+	0.436345i	$0.856273\pi$
$492$	−67008.5	−	93791.3i	−0.276821	−	0.387465i
$493$	−31280.9	−	31280.9i	−0.128702	−	0.128702i
$494$	−21047.1	+	254468.i	−0.0862459	+	1.04275i
$495$			52426.1i			0.213962i
$496$	23749.4	−	69315.9i	0.0965359	−	0.281754i
$497$	406998.			1.64770
$498$	32356.7	+	2676.23i	0.130468	+	0.0107911i
$499$	61595.1	−	61595.1i	0.247369	−	0.247369i	−0.572521	−	0.819890i	$-0.694035\pi$
$499$	61595.1	−	61595.1i	0.247369	−	0.247369i	0.819890	+	0.572521i	$0.194035\pi$
$500$	−74892.4	−	104826.i	−0.299570	−	0.419305i
$501$	92916.5	−	92916.5i	0.370184	−	0.370184i
$502$	8615.21	−	7298.95i	0.0341868	−	0.0289636i
$503$	−70874.1			−0.280125			−0.140062	−	0.990143i	$-0.544730\pi$
$503$	−70874.1			−0.280125			−0.140062	+	0.990143i	$0.544730\pi$
$504$	−141735.	−	35823.8i	−0.557976	−	0.141030i
$505$		−	5079.09i		−	0.0199160i
$506$	−352270.	+	298449.i	−1.37586	+	1.16565i
$507$	81500.9	+	81500.9i	0.317064	+	0.317064i
$508$	60199.5	−	361428.i	0.233274	−	1.40054i
$509$	−128181.	−	128181.i	−0.494754	−	0.494754i	0.415046	−	0.909800i	$-0.363765\pi$
$509$	−128181.	−	128181.i	−0.494754	−	0.494754i	−0.909800	+	0.415046i	$0.863765\pi$
$510$	55817.8	+	4616.71i	0.214601	+	0.0177498i
$511$		−	424241.i		−	1.62469i
$512$	177283.	−	193107.i	0.676281	−	0.736644i
$513$	208903.			0.793797
$514$	−24237.5	+	293041.i	−0.0917406	+	1.10918i
$515$	−26186.3	+	26186.3i	−0.0987324	+	0.0987324i
$516$	45350.2	+	7553.53i	0.170325	+	0.0283694i
$517$	82814.9	−	82814.9i	0.309833	−	0.309833i
$518$	−243949.	−	287942.i	−0.909160	−	1.07311i
$519$	−94525.3			−0.350924
$520$	23279.6	−	92104.3i	0.0860932	−	0.340623i
$521$			494250.i			1.82084i	0.413688	+	0.910419i	$0.364241\pi$
$521$			494250.i			1.82084i	−0.413688	+	0.910419i	$0.635759\pi$
$522$	15211.0	+	17954.1i	0.0558235	+	0.0658905i
$523$	179670.	+	179670.i	0.656859	+	0.656859i	0.954636	−	0.297776i	$-0.0962450\pi$
$523$	179670.	+	179670.i	0.656859	+	0.656859i	−0.297776	+	0.954636i	$0.596245\pi$
$524$	−354527.	+	253289.i	−1.29118	+	0.922473i
$525$	103091.	+	103091.i	0.374026	+	0.374026i
$526$	22456.7	−	271510.i	0.0811660	−	0.981329i
$527$			108360.i			0.390163i
$528$	209020.	+	71615.6i	0.749756	+	0.256886i
$529$	268417.			0.959175
$530$	72657.1	+	6009.50i	0.258658	+	0.0213937i
$531$	68347.9	−	68347.9i	0.242402	−	0.242402i
$532$	−169681.	+	121227.i	−0.599529	+	0.428329i
$533$	204457.	−	204457.i	0.719694	−	0.719694i
$534$	87377.9	−	74027.9i	0.306421	−	0.259605i
$535$	−28242.7			−0.0986729
$536$	102237.	+	171400.i	0.355860	+	0.596596i
$537$			220112.i			0.763300i
$538$	−64983.7	+	55055.2i	−0.224512	+	0.190210i
$539$	−37748.1	−	37748.1i	−0.129932	−	0.129932i
$540$	−76668.4	−	12769.9i	−0.262923	−	0.0437925i
$541$	300961.	+	300961.i	1.02829	+	1.02829i	0.999588	+	0.0287034i	$0.00913784\pi$
$541$	300961.	+	300961.i	1.02829	+	1.02829i	0.0287034	+	0.999588i	$0.490862\pi$
$542$	−415861.	−	34396.0i	−1.41563	−	0.117087i
$543$			124549.i			0.422417i
$544$	−155460.	+	355143.i	−0.525318	+	1.20007i
$545$	−31683.6			−0.106670
$546$	−18404.9	+	222523.i	−0.0617374	+	0.746430i
$547$	−159057.	+	159057.i	−0.531591	+	0.531591i	−0.921046	−	0.389455i	$-0.872663\pi$
$547$	−159057.	+	159057.i	−0.531591	+	0.531591i	0.389455	+	0.921046i	$0.372663\pi$
$548$	52412.5	−	314676.i	0.174531	−	1.04786i
$549$	92423.8	−	92423.8i	0.306647	−	0.306647i
$550$	233931.	+	276117.i	0.773326	+	0.912784i
$551$	33566.6			0.110561
$552$	−134406.	−	225331.i	−0.441104	−	0.739506i
$553$			129765.i			0.424335i
$554$	−7811.98	−	9220.76i	−0.0254532	−	0.0300433i
$555$	−54382.0	−	54382.0i	−0.176551	−	0.176551i
$556$	−331152.	−	463512.i	−1.07122	−	1.49938i
$557$	−394524.	−	394524.i	−1.27164	−	1.27164i	−0.945229	−	0.326409i	$-0.894161\pi$
$557$	−394524.	−	394524.i	−1.27164	−	1.27164i	−0.326409	−	0.945229i	$-0.605839\pi$
$558$	4751.15	−	57443.2i	0.0152591	−	0.184489i
$559$			115326.i			0.369065i
$560$	69684.2	−	34118.7i	0.222207	−	0.108797i
$561$	−326755.			−1.03824
$562$	146634.	+	12128.1i	0.464261	+	0.0383992i
$563$	169317.	−	169317.i	0.534177	−	0.534177i	−0.387636	−	0.921813i	$-0.626708\pi$
$563$	169317.	−	169317.i	0.534177	−	0.534177i	0.921813	+	0.387636i	$0.126708\pi$
$564$	38690.0	+	54154.2i	0.121630	+	0.170245i
$565$	−15085.9	+	15085.9i	−0.0472579	+	0.0472579i
$566$	61167.9	−	51822.4i	0.190937	−	0.161765i
$567$	−2346.48			−0.00729877
$568$	−140682.	+	556602.i	−0.436057	+	1.72523i
$569$			165645.i			0.511626i	0.966726	+	0.255813i	$0.0823432\pi$
$569$			165645.i			0.511626i	−0.966726	+	0.255813i	$0.917657\pi$
$570$	−32425.2	+	27471.1i	−0.0998005	+	0.0845526i
$571$	335641.	+	335641.i	1.02945	+	1.02945i	0.999553	+	0.0298925i	$0.00951651\pi$
$571$	335641.	+	335641.i	1.02945	+	1.02945i	0.0298925	+	0.999553i	$0.490483\pi$
$572$	−91059.4	+	546706.i	−0.278312	+	1.67094i
$573$	−109771.	−	109771.i	−0.334331	−	0.334331i
$574$	235346.	+	19465.6i	0.714305	+	0.0590804i
$575$		−	429737.i		−	1.29977i
$576$	97983.9	−	181451.i	0.295331	−	0.546908i
$577$	−99615.9			−0.299211			−0.149605	−	0.988746i	$-0.547800\pi$
$577$	−99615.9			−0.299211			−0.149605	+	0.988746i	$0.547800\pi$
$578$	19720.5	−	238429.i	0.0590287	−	0.713680i
$579$	222031.	−	222031.i	0.662301	−	0.662301i
$580$	−12319.1	−	2051.87i	−0.0366204	−	0.00609949i
$581$	−47033.3	+	47033.3i	−0.139333	+	0.139333i
$582$	−122256.	−	144303.i	−0.360930	−	0.426019i
$583$	−425331.			−1.25138
$584$	580184.	+	146643.i	1.70114	+	0.429967i
$585$		−	74732.7i		−	0.218373i
$586$	−295173.	−	348403.i	−0.859570	−	1.01458i
$587$	−45023.9	−	45023.9i	−0.130667	−	0.130667i	0.638748	−	0.769416i	$-0.279452\pi$
$587$	−45023.9	−	45023.9i	−0.130667	−	0.130667i	−0.769416	+	0.638748i	$0.779452\pi$
$588$	24684.1	−	17635.4i	0.0713943	−	0.0510071i
$589$	−58138.5	−	58138.5i	−0.167584	−	0.167584i
$590$	−4228.57	+	51125.1i	−0.0121476	+	0.146869i
$591$			79703.6i			0.228193i
$592$	478107.	−	234090.i	1.36421	−	0.667944i
$593$	−385101.			−1.09513			−0.547564	−	0.836764i	$-0.684445\pi$
$593$	−385101.			−1.09513			−0.547564	+	0.836764i	$0.684445\pi$
$594$	451905.	+	37377.2i	1.28078	+	0.105934i
$595$	−81136.1	+	81136.1i	−0.229182	+	0.229182i
$596$	59229.0	−	42315.7i	0.166741	−	0.119127i
$597$	124447.	−	124447.i	0.349168	−	0.349168i
$598$	502156.	−	425435.i	1.40422	−	1.18968i
$599$	209331.			0.583417			0.291709	−	0.956507i	$-0.405776\pi$
$599$	209331.			0.583417			0.291709	+	0.956507i	$0.405776\pi$
$600$	−176619.	+	105351.i	−0.490609	+	0.292641i
$601$		−	515555.i		−	1.42734i	−0.700484	−	0.713668i	$-0.747033\pi$
$601$		−	515555.i		−	1.42734i	0.700484	−	0.713668i	$-0.252967\pi$
$602$	−71864.3	+	60884.6i	−0.198299	+	0.168002i
$603$	111013.	+	111013.i	0.305310	+	0.305310i
$604$	233117.	+	38828.0i	0.638999	+	0.106432i
$605$	45625.7	+	45625.7i	0.124652	+	0.124652i
$606$	−16781.6	−	1388.01i	−0.0456970	−	0.00377961i
$607$		−	30292.7i		−	0.0822167i	−0.999155	−	0.0411084i	$-0.986911\pi$
$607$		−	30292.7i		−	0.0822167i	0.999155	−	0.0411084i	$-0.0130889\pi$
$608$	−107136.	−	273956.i	−0.289821	−	0.741094i
$609$	29352.7			0.0791432
$610$	−5718.10	+	69134.1i	−0.0153671	+	0.185794i
$611$	−118052.	+	118052.i	−0.316220	+	0.316220i
$612$	−50105.3	+	300824.i	−0.133777	+	0.803175i
$613$	−99803.4	+	99803.4i	−0.265598	+	0.265598i	−0.827324	−	0.561726i	$-0.810138\pi$
$613$	−99803.4	+	99803.4i	−0.265598	+	0.265598i	0.561726	+	0.827324i	$0.310138\pi$
$614$	−415816.	−	490803.i	−1.10297	−	1.30188i
$615$	48124.9			0.127239
$616$	−388749.	+	231883.i	−1.02449	+	0.611093i
$617$			102196.i			0.268451i	0.990951	+	0.134226i	$0.0428547\pi$
$617$			102196.i			0.268451i	−0.990951	+	0.134226i	$0.957145\pi$
$618$	79364.8	+	93677.1i	0.207802	+	0.245277i
$619$	−105904.	−	105904.i	−0.276395	−	0.276395i	0.555273	−	0.831668i	$-0.312614\pi$
$619$	−105904.	−	105904.i	−0.276395	−	0.276395i	−0.831668	+	0.555273i	$0.812614\pi$
$620$	17783.2	+	24891.0i	0.0462623	+	0.0647530i
$621$	−380749.	−	380749.i	−0.987314	−	0.987314i
$622$	−30927.9	+	373930.i	−0.0799410	+	0.966518i
$623$			234617.i			0.604483i
$624$	−297956.	−	102087.i	−0.765213	−	0.262181i
$625$	−308949.			−0.790909
$626$	36792.5	+	3043.12i	0.0938880	+	0.00776551i
$627$	175315.	−	175315.i	0.445948	−	0.445948i
$628$	236961.	+	331673.i	0.600838	+	0.840989i
$629$	−556679.	+	556679.i	−1.40703	+	1.40703i
$630$	46569.1	−	39454.1i	0.117332	−	0.0994057i
$631$	692480.			1.73920			0.869598	−	0.493760i	$-0.164378\pi$
$631$	692480.			1.73920			0.869598	+	0.493760i	$0.164378\pi$
$632$	−177465.	−	44854.6i	−0.444301	−	0.112298i
$633$			83779.3i			0.209088i
$634$	−36460.0	+	30889.5i	−0.0907065	+	0.0768481i
$635$	108170.	+	108170.i	0.268262	+	0.268262i
$636$	39711.4	−	238421.i	0.0981749	−	0.589427i
$637$	53809.4	+	53809.4i	0.132611	+	0.132611i
$638$	72612.1	+	6005.77i	0.178389	+	0.0147546i
$639$			451622.i			1.10605i
$640$	22573.1	+	107092.i	0.0551101	+	0.261456i
$641$	49519.0			0.120519			0.0602595	−	0.998183i	$-0.480807\pi$
$641$	49519.0			0.120519			0.0602595	+	0.998183i	$0.480807\pi$
$642$	−7718.13	+	93315.2i	−0.0187259	+	0.226403i
$643$	−165494.	+	165494.i	−0.400276	+	0.400276i	−0.878330	−	0.478054i	$-0.841342\pi$
$643$	−165494.	+	165494.i	−0.400276	+	0.400276i	0.478054	+	0.878330i	$0.341342\pi$
$644$	530213.	+	88312.3i	1.27844	+	0.212936i
$645$	−13572.6	+	13572.6i	−0.0326245	+	0.0326245i
$646$	281207.	+	331919.i	0.673846	+	0.795365i
$647$	−666565.			−1.59233			−0.796166	−	0.605078i	$-0.793142\pi$
$647$	−666565.			−1.59233			−0.796166	+	0.605078i	$0.793142\pi$
$648$	811.080	−	3208.99i	0.00193159	−	0.00764221i
$649$		−	299284.i		−	0.710548i
$650$	−333466.	−	393602.i	−0.789268	−	0.931602i
$651$	−50840.0	−	50840.0i	−0.119962	−	0.119962i
$652$	−277702.	+	198402.i	−0.653256	+	0.466714i
$653$	461118.	+	461118.i	1.08140	+	1.08140i	0.996379	+	0.0850198i	$0.0270954\pi$
$653$	461118.	+	461118.i	1.08140	+	1.08140i	0.0850198	+	0.996379i	$0.472905\pi$
$654$	−8658.45	+	104684.i	−0.0202435	+	0.244751i
$655$		−	181910.i		−	0.424008i
$656$	−107970.	+	315127.i	−0.250898	+	0.732280i
$657$	470757.			1.09060
$658$	−135887.	−	11239.2i	−0.313852	−	0.0259588i
$659$	326883.	−	326883.i	0.752698	−	0.752698i	−0.222284	−	0.974982i	$-0.571351\pi$
$659$	326883.	−	326883.i	0.752698	−	0.752698i	0.974982	+	0.222284i	$0.0713511\pi$
$660$	−75058.2	+	53624.8i	−0.172310	+	0.123106i
$661$	549615.	−	549615.i	1.25793	−	1.25793i	0.305848	−	0.952080i	$-0.401060\pi$
$661$	549615.	−	549615.i	1.25793	−	1.25793i	0.952080	−	0.305848i	$-0.0989401\pi$
$662$	−198938.	+	168544.i	−0.453944	+	0.384589i
$663$	465785.			1.05964
$664$	−48064.3	−	80579.2i	−0.109015	−	0.182762i
$665$		−	87064.5i		−	0.196878i
$666$	319513.	−	270697.i	0.720345	−	0.610288i
$667$	−61178.8	−	61178.8i	−0.137515	−	0.137515i
$668$	−374577.	−	62389.6i	−0.839437	−	0.139817i
$669$	359005.	+	359005.i	0.802137	+	0.802137i
$670$	−83039.3	−	6868.21i	−0.184984	−	0.0153001i
$671$		−	404708.i		−	0.898869i
$672$	−93686.8	−	239564.i	−0.207463	−	0.530498i
$673$	191664.			0.423166			0.211583	−	0.977360i	$-0.432138\pi$
$673$	191664.			0.423166			0.211583	+	0.977360i	$0.432138\pi$
$674$	12963.7	−	156736.i	0.0285370	−	0.345023i
$675$	−298440.	+	298440.i	−0.655012	+	0.655012i
$676$	54724.4	−	328557.i	0.119753	−	0.718980i
$677$	−544201.	+	544201.i	−1.18736	+	1.18736i	−0.209564	+	0.977795i	$0.567204\pi$
$677$	−544201.	+	544201.i	−1.18736	+	1.18736i	−0.977795	+	0.209564i	$0.932796\pi$
$678$	45721.9	+	53967.3i	0.0994638	+	0.117401i
$679$	387466.			0.840416
$680$	−82914.6	−	139005.i	−0.179314	−	0.300617i
$681$		−	137020.i		−	0.295455i
$682$	−115365.	−	136169.i	−0.248030	−	0.292759i
$683$	−570769.	−	570769.i	−1.22354	−	1.22354i	−0.966364	−	0.257179i	$-0.917207\pi$
$683$	−570769.	−	570769.i	−1.22354	−	1.22354i	−0.257179	−	0.966364i	$-0.582793\pi$
$684$	−134519.	−	188286.i	−0.287523	−	0.402443i
$685$	94177.8	+	94177.8i	0.200709	+	0.200709i
$686$	−41040.9	+	496201.i	−0.0872106	+	1.05441i
$687$			500020.i			1.05943i
$688$	−58424.0	−	119325.i	−0.123428	−	0.252090i
$689$	606305.			1.27718
$690$	109168.	+	9029.29i	0.229296	+	0.0189651i
$691$	−333477.	+	333477.i	−0.698409	+	0.698409i	−0.964067	−	0.265658i	$-0.914411\pi$
$691$	−333477.	+	333477.i	−0.698409	+	0.698409i	0.265658	+	0.964067i	$0.414411\pi$
$692$	158796.	+	222266.i	0.331611	+	0.464153i
$693$	−251788.	+	251788.i	−0.524286	+	0.524286i
$694$	−292174.	+	247535.i	−0.606629	+	0.513946i
$695$	237831.			0.492378
$696$	−10146.0	+	40142.2i	−0.0209449	+	0.0828672i
$697$		−	492628.i		−	1.01404i
$698$	−33073.6	+	28020.5i	−0.0678845	+	0.0575128i
$699$	−250135.	−	250135.i	−0.511941	−	0.511941i
$700$	69221.3	−	415593.i	0.141268	−	0.848150i
$701$	31503.2	+	31503.2i	0.0641089	+	0.0641089i	0.738434	−	0.674325i	$-0.235565\pi$
$701$	31503.2	+	31503.2i	0.0641089	+	0.0641089i	−0.674325	+	0.738434i	$0.735565\pi$
$702$	−644185.	−	53280.7i	−1.30718	−	0.108117i
$703$		−	597354.i		−	1.20871i
$704$	−182744.	−	611798.i	−0.368720	−	1.23442i
$705$	−27786.9			−0.0559064
$706$	23283.8	−	281511.i	0.0467138	−	0.564788i
$707$	24393.5	−	24393.5i	0.0488017	−	0.0488017i
$708$	167764.	+	27942.8i	0.334682	+	0.0557447i
$709$	609708.	−	609708.i	1.21291	−	1.21291i	0.242847	−	0.970064i	$-0.421919\pi$
$709$	609708.	−	609708.i	1.21291	−	1.21291i	0.970064	−	0.242847i	$-0.0780815\pi$
$710$	−154939.	−	182880.i	−0.307357	−	0.362785i
$711$	−143993.			−0.284841
$712$	−320858.	−	81097.6i	−0.632926	−	0.159973i
$713$			211928.i			0.416878i
$714$	245905.	+	290251.i	0.482359	+	0.569346i
$715$	−163621.	−	163621.i	−0.320056	−	0.320056i
$716$	517570.	−	369774.i	1.00959	−	0.721291i
$717$	−47357.2	−	47357.2i	−0.0921187	−	0.0921187i
$718$	−55439.7	+	670288.i	−0.107541	+	1.30021i
$719$			720908.i			1.39451i	0.716823	+	0.697256i	$0.245596\pi$
$719$			720908.i			1.39451i	−0.716823	+	0.697256i	$0.754404\pi$
$720$	37859.6	+	77324.7i	0.0730317	+	0.149160i
$721$	−251531.			−0.483862
$722$	190548.	+	15760.3i	0.365535	+	0.0302335i
$723$	109536.	−	109536.i	0.209546	−	0.209546i
$724$	292864.	−	209235.i	0.558714	−	0.399169i
$725$	−47953.4	+	47953.4i	−0.0912311	+	0.0912311i
$726$	163218.	−	138281.i	0.309668	−	0.262355i
$727$	−279904.			−0.529591			−0.264796	−	0.964305i	$-0.585304\pi$
$727$	−279904.			−0.529591			−0.264796	+	0.964305i	$0.585304\pi$
$728$	554157.	−	330546.i	1.04561	−	0.623691i
$729$			323526.i			0.608772i
$730$	−190628.	+	161503.i	−0.357718	+	0.303065i
$731$	138935.	+	138935.i	0.260003	+	0.260003i
$732$	226860.	+	37785.8i	0.423385	+	0.0705191i
$733$	−266306.	−	266306.i	−0.495648	−	0.495648i	0.414432	−	0.910080i	$-0.363980\pi$
$733$	−266306.	−	266306.i	−0.495648	−	0.495648i	−0.910080	+	0.414432i	$0.863980\pi$
$734$	329261.	+	27233.3i	0.611151	+	0.0505485i
$735$			12665.6i			0.0234450i
$736$	−304047.	+	694583.i	−0.561287	+	1.28224i
$737$	486108.			0.894948
$738$	−21599.8	+	261151.i	−0.0396587	+	0.479489i
$739$	−594958.	+	594958.i	−1.08943	+	1.08943i	−0.0938378	+	0.995587i	$0.529914\pi$
$739$	−594958.	+	594958.i	−1.08943	+	1.08943i	−0.995587	+	0.0938378i	$0.970086\pi$
$740$	−36515.3	+	219232.i	−0.0666824	+	0.400350i
$741$	−249910.	+	249910.i	−0.455142	+	0.455142i
$742$	320090.	+	377814.i	0.581386	+	0.686231i
$743$	289367.			0.524170			0.262085	−	0.965045i	$-0.415590\pi$
$743$	289367.			0.524170			0.262085	+	0.965045i	$0.415590\pi$
$744$	87101.1	−	51954.5i	0.157354	−	0.0938592i
$745$			30390.8i			0.0547557i
$746$	280214.	+	330747.i	0.503515	+	0.594317i
$747$	−52190.2	−	52190.2i	−0.0935293	−	0.0935293i
$748$	548927.	+	768329.i	0.981096	+	1.37323i
$749$	−135642.	−	135642.i	−0.241785	−	0.241785i
$750$	14698.9	−	177715.i	0.0261314	−	0.315938i
$751$		−	935795.i		−	1.65921i	−0.558352	−	0.829604i	$-0.688566\pi$
$751$		−	935795.i		−	1.65921i	0.558352	−	0.829604i	$-0.311434\pi$
$752$	62341.0	−	181951.i	0.110240	−	0.321750i
$753$	15629.1			0.0275641
$754$	−103508.	−	8561.16i	−0.182067	−	0.0150588i
$755$	−69768.4	+	69768.4i	−0.122395	+	0.122395i
$756$	−306887.	−	429547.i	−0.536951	−	0.751567i
$757$	−626956.	+	626956.i	−1.09407	+	1.09407i	−0.0989818	+	0.995089i	$0.531559\pi$
$757$	−626956.	+	626956.i	−1.09407	+	1.09407i	−0.995089	+	0.0989818i	$0.968441\pi$
$758$	−414069.	+	350806.i	−0.720666	+	0.610560i
$759$	−639062.			−1.10933
$760$	119068.	+	30094.6i	0.206142	+	0.0521029i
$761$		−	253505.i		−	0.437741i	−0.975754	−	0.218871i	$-0.929763\pi$
$761$		−	253505.i		−	0.437741i	0.975754	−	0.218871i	$-0.0702372\pi$
$762$	386960.	−	327838.i	0.666432	−	0.564612i
$763$	−152167.	−	152167.i	−0.261380	−	0.261380i
$764$	−73706.4	+	442521.i	−0.126275	+	0.758137i
$765$	−90032.1	−	90032.1i	−0.153842	−	0.153842i
$766$	672536.	+	55625.7i	1.14619	+	0.0948021i
$767$			426625.i			0.725197i
$768$	360007.	−	45316.6i	0.610363	−	0.0768306i
$769$	−740462.			−1.25213			−0.626066	−	0.779770i	$-0.715336\pi$
$769$	−740462.			−1.25213			−0.626066	+	0.779770i	$0.715336\pi$
$770$	15577.7	−	188340.i	0.0262737	−	0.317660i
$771$	−287792.	+	287792.i	−0.484138

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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 16 = 2^{4} \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	16.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.329715 - 3.98639i) q^{2} +(3.91498 - 3.91498i) q^{3} +(-15.7826 - 2.62875i) q^{4} +(4.72348 - 4.72348i) q^{5} +(-14.3158 - 16.8975i) q^{6} +45.3712 q^{7} +(-15.6830 + 62.0487i) q^{8} +50.3458i q^{9} +O(q^{10})\)	\(q+(0.329715 - 3.98639i) q^{2} +(3.91498 - 3.91498i) q^{3} +(-15.7826 - 2.62875i) q^{4} +(4.72348 - 4.72348i) q^{5} +(-14.3158 - 16.8975i) q^{6} +45.3712 q^{7} +(-15.6830 + 62.0487i) q^{8} +50.3458i q^{9} +(-17.2722 - 20.3870i) q^{10} +(110.228 + 110.228i) q^{11} +(-72.0800 + 51.4970i) q^{12} +(-157.128 - 157.128i) q^{13} +(14.9596 - 180.867i) q^{14} -36.9847i q^{15} +(242.179 + 82.9768i) q^{16} -378.592 q^{17} +(200.698 + 16.5998i) q^{18} +(203.127 - 203.127i) q^{19} +(-86.9656 + 62.1319i) q^{20} +(177.627 - 177.627i) q^{21} +(475.755 - 403.067i) q^{22} -740.444 q^{23} +(181.521 + 304.318i) q^{24} +580.377i q^{25} +(-678.183 + 574.567i) q^{26} +(514.217 + 514.217i) q^{27} +(-716.074 - 119.269i) q^{28} +(82.6244 + 82.6244i) q^{29} +(-147.435 - 12.1944i) q^{30} -286.217i q^{31} +(410.628 - 938.062i) q^{32} +863.080 q^{33} +(-124.828 + 1509.21i) q^{34} +(214.310 - 214.310i) q^{35} +(132.346 - 794.587i) q^{36} +(1470.39 - 1470.39i) q^{37} +(-742.770 - 876.719i) q^{38} -1230.31 q^{39} +(219.008 + 367.164i) q^{40} +1301.21i q^{41} +(-649.525 - 766.658i) q^{42} +(-366.979 - 366.979i) q^{43} +(-1449.92 - 2029.44i) q^{44} +(237.808 + 237.808i) q^{45} +(-244.136 + 2951.70i) q^{46} -751.307i q^{47} +(1272.98 - 623.275i) q^{48} -342.455 q^{49} +(2313.61 + 191.359i) q^{50} +(-1482.18 + 1482.18i) q^{51} +(2066.84 + 2892.94i) q^{52} +(-1929.33 + 1929.33i) q^{53} +(2219.41 - 1880.32i) q^{54} +1041.32 q^{55} +(-711.555 + 2815.22i) q^{56} -1590.48i q^{57} +(356.616 - 302.130i) q^{58} +(-1357.57 - 1357.57i) q^{59} +(-97.2234 + 583.714i) q^{60} +(-1835.78 - 1835.78i) q^{61} +(-1140.97 - 94.3702i) q^{62} +2284.25i q^{63} +(-3604.09 - 1946.22i) q^{64} -1484.39 q^{65} +(284.571 - 3440.57i) q^{66} +(2205.02 - 2205.02i) q^{67} +(5975.15 + 995.222i) q^{68} +(-2898.83 + 2898.83i) q^{69} +(-783.662 - 924.984i) q^{70} +8970.40 q^{71} +(-3123.90 - 789.572i) q^{72} -9350.46i q^{73} +(-5376.75 - 6346.37i) q^{74} +(2272.17 + 2272.17i) q^{75} +(-3739.84 + 2671.90i) q^{76} +(5001.17 + 5001.17i) q^{77} +(-405.652 + 4904.49i) q^{78} +2860.08i q^{79} +(1535.87 - 751.991i) q^{80} -51.7173 q^{81} +(5187.13 + 429.029i) q^{82} +(-1036.63 + 1036.63i) q^{83} +(-3270.35 + 2336.48i) q^{84} +(-1788.27 + 1788.27i) q^{85} +(-1583.92 + 1341.92i) q^{86} +646.946 q^{87} +(-8568.19 + 5110.80i) q^{88} +5171.06i q^{89} +(1026.40 - 869.585i) q^{90} +(-7129.10 - 7129.10i) q^{91} +(11686.1 + 1946.44i) q^{92} +(-1120.54 - 1120.54i) q^{93} +(-2995.00 - 247.717i) q^{94} -1918.94i q^{95} +(-2064.90 - 5280.10i) q^{96} +8539.92 q^{97} +(-112.913 + 1365.16i) q^{98} +(-5549.51 + 5549.51i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14q - 2q^{2} - 2q^{3} - 8q^{4} - 2q^{5} + 64q^{6} - 4q^{7} - 92q^{8} + O(q^{10}) \)	\( 14q - 2q^{2} - 2q^{3} - 8q^{4} - 2q^{5} + 64q^{6} - 4q^{7} - 92q^{8} - 100q^{10} + 94q^{11} - 332q^{12} - 2q^{13} + 44q^{14} - 168q^{16} - 4q^{17} + 1390q^{18} - 706q^{19} + 1900q^{20} - 164q^{21} + 900q^{22} + 1148q^{23} - 1872q^{24} - 3416q^{26} - 1664q^{27} - 3784q^{28} + 862q^{29} - 3740q^{30} + 3208q^{32} - 4q^{33} + 7508q^{34} + 1340q^{35} + 11468q^{36} - 1826q^{37} + 3568q^{38} + 2684q^{39} - 5144q^{40} - 17064q^{42} + 1694q^{43} - 14636q^{44} + 1410q^{45} - 5316q^{46} + 6888q^{48} + 682q^{49} + 20070q^{50} - 3012q^{51} + 20452q^{52} - 482q^{53} + 10784q^{54} - 11780q^{55} - 6952q^{56} - 20456q^{58} - 2786q^{59} - 29920q^{60} - 3778q^{61} - 11472q^{62} + 15808q^{64} - 2020q^{65} + 30148q^{66} + 7998q^{67} + 18032q^{68} + 9628q^{69} + 15296q^{70} + 19964q^{71} - 17708q^{72} - 23780q^{74} + 17570q^{75} - 23996q^{76} - 9508q^{77} - 8052q^{78} + 1384q^{80} + 1454q^{81} + 16016q^{82} - 17282q^{83} + 19624q^{84} + 9948q^{85} - 4796q^{86} - 49284q^{87} + 7288q^{88} - 5416q^{90} - 28036q^{91} - 14632q^{92} + 8896q^{93} + 432q^{94} + 6064q^{96} - 4q^{97} - 12246q^{98} + 49214q^{99} + O(q^{100}) \)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Properties

Related objects

Downloads

Learn more about