LMFDB - Embedded newform 48.5.l.a.19.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [48,5,Mod(19,48)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(48, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 0]))

N = Newforms(chi, 5, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("48.19");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 48 = 2^{4} \cdot 3 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	48.l (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$4.96175822802$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			19.3
Character	$\chi$	$=$	48.19
Dual form			48.5.l.a.43.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.15376 + 2.46044i) q^{2} +(-3.67423 + 3.67423i) q^{3} +(3.89246 - 15.5193i) q^{4} +(18.4189 - 18.4189i) q^{5} +(2.54743 - 20.6279i) q^{6} +4.95460 q^{7} +(25.9084 + 58.5214i) q^{8} -27.0000i q^{9} +O(q^{10})$	\(q+(-3.15376 + 2.46044i) q^{2} +(-3.67423 + 3.67423i) q^{3} +(3.89246 - 15.5193i) q^{4} +(18.4189 - 18.4189i) q^{5} +(2.54743 - 20.6279i) q^{6} +4.95460 q^{7} +(25.9084 + 58.5214i) q^{8} -27.0000i q^{9} +(-12.7702 + 103.407i) q^{10} +(156.666 + 156.666i) q^{11} +(42.7197 + 71.3234i) q^{12} +(-21.7289 - 21.7289i) q^{13} +(-15.6256 + 12.1905i) q^{14} +135.350i q^{15} +(-225.697 - 120.817i) q^{16} +416.167 q^{17} +(66.4319 + 85.1516i) q^{18} +(131.432 - 131.432i) q^{19} +(-214.153 - 357.542i) q^{20} +(-18.2043 + 18.2043i) q^{21} +(-879.557 - 108.620i) q^{22} +469.559 q^{23} +(-310.215 - 119.828i) q^{24} -53.5084i q^{25} +(121.990 + 15.0652i) q^{26} +(99.2043 + 99.2043i) q^{27} +(19.2856 - 76.8919i) q^{28} +(-863.997 - 863.997i) q^{29} +(-333.022 - 426.863i) q^{30} +43.3158i q^{31} +(1009.06 - 174.288i) q^{32} -1151.26 q^{33} +(-1312.49 + 1023.95i) q^{34} +(91.2580 - 91.2580i) q^{35} +(-419.021 - 105.096i) q^{36} +(1252.82 - 1252.82i) q^{37} +(-91.1252 + 737.888i) q^{38} +159.674 q^{39} +(1555.10 + 600.694i) q^{40} +944.794i q^{41} +(12.6215 - 102.203i) q^{42} +(483.569 + 483.569i) q^{43} +(3041.17 - 1821.53i) q^{44} +(-497.309 - 497.309i) q^{45} +(-1480.88 + 1155.32i) q^{46} +4062.58i q^{47} +(1273.17 - 385.357i) q^{48} -2376.45 q^{49} +(131.654 + 168.753i) q^{50} +(-1529.09 + 1529.09i) q^{51} +(-421.796 + 252.638i) q^{52} +(927.469 - 927.469i) q^{53} +(-556.954 - 68.7807i) q^{54} +5771.23 q^{55} +(128.366 + 289.950i) q^{56} +965.827i q^{57} +(4850.66 + 599.030i) q^{58} +(-4003.67 - 4003.67i) q^{59} +(2100.54 + 526.846i) q^{60} +(-3184.14 - 3184.14i) q^{61} +(-106.576 - 136.608i) q^{62} -133.774i q^{63} +(-2753.51 + 3032.39i) q^{64} -800.443 q^{65} +(3630.79 - 2832.60i) q^{66} +(-1296.52 + 1296.52i) q^{67} +(1619.91 - 6458.61i) q^{68} +(-1725.27 + 1725.27i) q^{69} +(-63.2713 + 512.341i) q^{70} -2348.95 q^{71} +(1580.08 - 699.527i) q^{72} -853.396i q^{73} +(-868.612 + 7033.61i) q^{74} +(196.603 + 196.603i) q^{75} +(-1528.14 - 2551.33i) q^{76} +(776.218 + 776.218i) q^{77} +(-503.575 + 392.869i) q^{78} -4744.17i q^{79} +(-6382.39 + 1931.79i) q^{80} -729.000 q^{81} +(-2324.61 - 2979.66i) q^{82} +(-6976.97 + 6976.97i) q^{83} +(211.659 + 353.378i) q^{84} +(7665.31 - 7665.31i) q^{85} +(-2714.85 - 335.269i) q^{86} +6349.06 q^{87} +(-5109.35 + 13227.3i) q^{88} +9805.15i q^{89} +(2792.00 + 344.796i) q^{90} +(-107.658 - 107.658i) q^{91} +(1827.74 - 7287.23i) q^{92} +(-159.152 - 159.152i) q^{93} +(-9995.75 - 12812.4i) q^{94} -4841.67i q^{95} +(-3067.14 + 4347.90i) q^{96} -40.2349 q^{97} +(7494.77 - 5847.12i) q^{98} +(4229.99 - 4229.99i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 12 q^{4} + 180 q^{8}+O(q^{10}) $ 32 * q + 12 * q^4 + 180 * q^8	$ 32 q + 12 q^{4} + 180 q^{8} + 296 q^{10} - 192 q^{11} + 360 q^{12} - 156 q^{14} + 352 q^{16} - 324 q^{18} + 704 q^{19} - 1200 q^{20} - 1568 q^{22} - 2304 q^{23} + 1188 q^{24} + 2700 q^{26} + 4680 q^{28} - 1728 q^{29} + 1512 q^{30} - 3360 q^{32} - 9312 q^{34} - 5184 q^{35} - 756 q^{36} + 3648 q^{37} - 5880 q^{38} + 5232 q^{40} + 4500 q^{42} + 1088 q^{43} + 18840 q^{44} + 680 q^{46} + 2160 q^{48} + 10976 q^{49} - 25884 q^{50} - 4032 q^{51} - 25584 q^{52} + 960 q^{53} + 972 q^{54} + 11776 q^{55} + 15456 q^{56} + 12624 q^{58} + 13056 q^{59} + 7992 q^{60} + 3776 q^{61} + 21852 q^{62} - 8664 q^{64} + 4032 q^{65} - 8856 q^{66} - 896 q^{67} - 17280 q^{68} - 9792 q^{69} - 18240 q^{70} - 39936 q^{71} + 4860 q^{72} + 24204 q^{74} - 1152 q^{75} + 16776 q^{76} + 9408 q^{77} - 3780 q^{78} - 14232 q^{80} - 23328 q^{81} - 33800 q^{82} + 24000 q^{83} - 11448 q^{84} - 11200 q^{85} - 1200 q^{86} - 11424 q^{88} + 4104 q^{90} + 30528 q^{91} - 11664 q^{92} - 8040 q^{94} + 10080 q^{96} + 52968 q^{98} - 5184 q^{99}+O(q^{100}) $ 32 * q + 12 * q^4 + 180 * q^8 + 296 * q^10 - 192 * q^11 + 360 * q^12 - 156 * q^14 + 352 * q^16 - 324 * q^18 + 704 * q^19 - 1200 * q^20 - 1568 * q^22 - 2304 * q^23 + 1188 * q^24 + 2700 * q^26 + 4680 * q^28 - 1728 * q^29 + 1512 * q^30 - 3360 * q^32 - 9312 * q^34 - 5184 * q^35 - 756 * q^36 + 3648 * q^37 - 5880 * q^38 + 5232 * q^40 + 4500 * q^42 + 1088 * q^43 + 18840 * q^44 + 680 * q^46 + 2160 * q^48 + 10976 * q^49 - 25884 * q^50 - 4032 * q^51 - 25584 * q^52 + 960 * q^53 + 972 * q^54 + 11776 * q^55 + 15456 * q^56 + 12624 * q^58 + 13056 * q^59 + 7992 * q^60 + 3776 * q^61 + 21852 * q^62 - 8664 * q^64 + 4032 * q^65 - 8856 * q^66 - 896 * q^67 - 17280 * q^68 - 9792 * q^69 - 18240 * q^70 - 39936 * q^71 + 4860 * q^72 + 24204 * q^74 - 1152 * q^75 + 16776 * q^76 + 9408 * q^77 - 3780 * q^78 - 14232 * q^80 - 23328 * q^81 - 33800 * q^82 + 24000 * q^83 - 11448 * q^84 - 11200 * q^85 - 1200 * q^86 - 11424 * q^88 + 4104 * q^90 + 30528 * q^91 - 11664 * q^92 - 8040 * q^94 + 10080 * q^96 + 52968 * q^98 - 5184 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/48\mathbb{Z}\right)^\times$.

$n$	$17$	$31$	$37$
$\chi(n)$	$1$	$-1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−3.15376	+	2.46044i	−0.788441	+	0.615110i
$2$	−3.15376	+	2.46044i	−0.788441	+	0.615110i
$3$	−3.67423	+	3.67423i	−0.408248	+	0.408248i
$3$	−3.67423	+	3.67423i	−0.408248	+	0.408248i
$4$	3.89246	−	15.5193i	0.243279	−	0.969956i
$5$	18.4189	−	18.4189i	0.736754	−	0.736754i	−0.235194	−	0.971948i	$-0.575573\pi$
$5$	18.4189	−	18.4189i	0.736754	−	0.736754i	0.971948	+	0.235194i	$0.0755726\pi$
$6$	2.54743	−	20.6279i	0.0707620	−	0.572997i
$7$	4.95460			0.101114			0.0505571	−	0.998721i	$-0.483900\pi$
$7$	4.95460			0.101114			0.0505571	+	0.998721i	$0.483900\pi$
$8$	25.9084	+	58.5214i	0.404819	+	0.914397i
$9$		−	27.0000i		−	0.333333i
$10$	−12.7702	+	103.407i	−0.127702	+	1.03407i
$11$	156.666	+	156.666i	1.29476	+	1.29476i	0.931806	+	0.362957i	$0.118233\pi$
$11$	156.666	+	156.666i	1.29476	+	1.29476i	0.362957	+	0.931806i	$0.381767\pi$
$12$	42.7197	+	71.3234i	0.296665	+	0.495301i
$13$	−21.7289	−	21.7289i	−0.128573	−	0.128573i	0.639892	−	0.768465i	$-0.278979\pi$
$13$	−21.7289	−	21.7289i	−0.128573	−	0.128573i	−0.768465	+	0.639892i	$0.778979\pi$
$14$	−15.6256	+	12.1905i	−0.0797226	+	0.0621964i
$15$			135.350i			0.601557i
$16$	−225.697	−	120.817i	−0.881631	−	0.471940i
$17$	416.167			1.44002			0.720011	−	0.693962i	$-0.244137\pi$
$17$	416.167			1.44002			0.720011	+	0.693962i	$0.244137\pi$
$18$	66.4319	+	85.1516i	0.205037	+	0.262814i
$19$	131.432	−	131.432i	0.364079	−	0.364079i	−0.501234	−	0.865312i	$-0.667120\pi$
$19$	131.432	−	131.432i	0.364079	−	0.364079i	0.865312	+	0.501234i	$0.167120\pi$
$20$	−214.153	−	357.542i	−0.535383	−	0.893856i
$21$	−18.2043	+	18.2043i	−0.0412797	+	0.0412797i
$22$	−879.557	−	108.620i	−1.81727	−	0.224422i
$23$	469.559			0.887636			0.443818	−	0.896117i	$-0.353624\pi$
$23$	469.559			0.887636			0.443818	+	0.896117i	$0.353624\pi$
$24$	−310.215	−	119.828i	−0.538568	−	0.208034i
$25$		−	53.5084i		−	0.0856135i
$26$	121.990	+	15.0652i	0.180459	+	0.0222857i
$27$	99.2043	+	99.2043i	0.136083	+	0.136083i
$28$	19.2856	−	76.8919i	0.0245989	−	0.0980764i
$29$	−863.997	−	863.997i	−1.02735	−	1.02735i	−0.999615	−	0.0277296i	$-0.991172\pi$
$29$	−863.997	−	863.997i	−1.02735	−	1.02735i	−0.0277296	−	0.999615i	$-0.508828\pi$
$30$	−333.022	−	426.863i	−0.370024	−	0.474292i
$31$			43.3158i			0.0450737i	0.999746	+	0.0225368i	$0.00717431\pi$
$31$			43.3158i			0.0450737i	−0.999746	+	0.0225368i	$0.992826\pi$
$32$	1009.06	−	174.288i	0.985409	−	0.170204i
$33$	−1151.26			−1.05717
$34$	−1312.49	+	1023.95i	−1.13537	+	0.885773i
$35$	91.2580	−	91.2580i	0.0744963	−	0.0744963i
$36$	−419.021	−	105.096i	−0.323319	−	0.0810929i
$37$	1252.82	−	1252.82i	0.915138	−	0.915138i	−0.0815331	−	0.996671i	$-0.525982\pi$
$37$	1252.82	−	1252.82i	0.915138	−	0.915138i	0.996671	+	0.0815331i	$0.0259816\pi$
$38$	−91.1252	+	737.888i	−0.0631061	+	0.511003i
$39$	159.674			0.104980
$40$	1555.10	+	600.694i	0.971938	+	0.375434i
$41$			944.794i			0.562043i	0.959702	+	0.281021i	$0.0906732\pi$
$41$			944.794i			0.562043i	−0.959702	+	0.281021i	$0.909327\pi$
$42$	12.6215	−	102.203i	0.00715505	−	0.0579382i
$43$	483.569	+	483.569i	0.261530	+	0.261530i	0.825675	−	0.564146i	$-0.190794\pi$
$43$	483.569	+	483.569i	0.261530	+	0.261530i	−0.564146	+	0.825675i	$0.690794\pi$
$44$	3041.17	−	1821.53i	1.57085	−	0.940875i
$45$	−497.309	−	497.309i	−0.245585	−	0.245585i
$46$	−1480.88	+	1155.32i	−0.699848	+	0.545994i
$47$			4062.58i			1.83911i	0.392967	+	0.919553i	$0.371449\pi$
$47$			4062.58i			1.83911i	−0.392967	+	0.919553i	$0.628551\pi$
$48$	1273.17	−	385.357i	0.552593	−	0.167256i
$49$	−2376.45			−0.989776
$50$	131.654	+	168.753i	0.0526617	+	0.0675012i
$51$	−1529.09	+	1529.09i	−0.587887	+	0.587887i
$52$	−421.796	+	252.638i	−0.155990	+	0.0934314i
$53$	927.469	−	927.469i	0.330178	−	0.330178i	−0.522476	−	0.852654i	$-0.674992\pi$
$53$	927.469	−	927.469i	0.330178	−	0.330178i	0.852654	+	0.522476i	$0.174992\pi$
$54$	−556.954	−	68.7807i	−0.190999	−	0.0235873i
$55$	5771.23			1.90784
$56$	128.366	+	289.950i	0.0409330	+	0.0924585i
$57$			965.827i			0.297269i
$58$	4850.66	+	599.030i	1.44193	+	0.178071i
$59$	−4003.67	−	4003.67i	−1.15015	−	1.15015i	−0.986522	−	0.163628i	$-0.947680\pi$
$59$	−4003.67	−	4003.67i	−1.15015	−	1.15015i	−0.163628	−	0.986522i	$-0.552320\pi$
$60$	2100.54	+	526.846i	0.583484	+	0.146346i
$61$	−3184.14	−	3184.14i	−0.855721	−	0.855721i	0.135110	−	0.990831i	$-0.456861\pi$
$61$	−3184.14	−	3184.14i	−0.855721	−	0.855721i	−0.990831	+	0.135110i	$0.956861\pi$
$62$	−106.576	−	136.608i	−0.0277253	−	0.0355379i
$63$		−	133.774i		−	0.0337047i
$64$	−2753.51	+	3032.39i	−0.672243	+	0.740331i
$65$	−800.443			−0.189454
$66$	3630.79	−	2832.60i	0.833516	−	0.650276i
$67$	−1296.52	+	1296.52i	−0.288822	+	0.288822i	−0.836614	−	0.547793i	$-0.815468\pi$
$67$	−1296.52	+	1296.52i	−0.288822	+	0.288822i	0.547793	+	0.836614i	$0.315468\pi$
$68$	1619.91	−	6458.61i	0.350327	−	1.39676i
$69$	−1725.27	+	1725.27i	−0.362376	+	0.362376i
$70$	−63.2713	+	512.341i	−0.0129125	+	0.104559i
$71$	−2348.95			−0.465970			−0.232985	−	0.972480i	$-0.574849\pi$
$71$	−2348.95			−0.465970			−0.232985	+	0.972480i	$0.574849\pi$
$72$	1580.08	−	699.527i	0.304799	−	0.134940i
$73$		−	853.396i		−	0.160142i	−0.996789	−	0.0800709i	$-0.974485\pi$
$73$		−	853.396i		−	0.160142i	0.996789	−	0.0800709i	$-0.0255147\pi$
$74$	−868.612	+	7033.61i	−0.158622	+	1.28444i
$75$	196.603	+	196.603i	0.0349516	+	0.0349516i
$76$	−1528.14	−	2551.33i	−0.264568	−	0.441713i
$77$	776.218	+	776.218i	0.130919	+	0.130919i
$78$	−503.575	+	392.869i	−0.0827703	+	0.0645741i
$79$		−	4744.17i		−	0.760161i	−0.924953	−	0.380081i	$-0.875896\pi$
$79$		−	4744.17i		−	0.760161i	0.924953	−	0.380081i	$-0.124104\pi$
$80$	−6382.39	+	1931.79i	−0.997249	+	0.301842i
$81$	−729.000			−0.111111
$82$	−2324.61	−	2979.66i	−0.345718	−	0.443137i
$83$	−6976.97	+	6976.97i	−1.01277	+	1.01277i	−0.0128527	+	0.999917i	$0.504091\pi$
$83$	−6976.97	+	6976.97i	−1.01277	+	1.01277i	−0.999917	+	0.0128527i	$0.995909\pi$
$84$	211.659	+	353.378i	0.0299970	+	0.0500820i
$85$	7665.31	−	7665.31i	1.06094	−	1.06094i
$86$	−2714.85	−	335.269i	−0.367071	−	0.0453312i
$87$	6349.06			0.838824
$88$	−5109.35	+	13227.3i	−0.659782	+	1.70807i
$89$			9805.15i			1.23787i	0.785443	+	0.618934i	$0.212435\pi$
$89$			9805.15i			1.23787i	−0.785443	+	0.618934i	$0.787565\pi$
$90$	2792.00	+	344.796i	0.344691	+	0.0425674i
$91$	−107.658	−	107.658i	−0.0130006	−	0.0130006i
$92$	1827.74	−	7287.23i	0.215943	−	0.860968i
$93$	−159.152	−	159.152i	−0.0184013	−	0.0184013i
$94$	−9995.75	−	12812.4i	−1.13125	−	1.45003i
$95$		−	4841.67i		−	0.536473i
$96$	−3067.14	+	4347.90i	−0.332806	+	0.471777i
$97$	−40.2349			−0.00427621			−0.00213811	−	0.999998i	$-0.500681\pi$
$97$	−40.2349			−0.00427621			−0.00213811	+	0.999998i	$0.500681\pi$
$98$	7494.77	−	5847.12i	0.780380	−	0.608821i
$99$	4229.99	−	4229.99i	0.431588	−	0.431588i
$100$	−830.413	−	208.279i	−0.0830413	−	0.0208279i
$101$	2324.71	−	2324.71i	0.227891	−	0.227891i	−0.583920	−	0.811811i	$-0.698482\pi$
$101$	2324.71	−	2324.71i	0.227891	−	0.227891i	0.811811	+	0.583920i	$0.198482\pi$
$102$	1060.16	−	8584.64i	0.101899	−	0.825129i
$103$	9556.17			0.900760			0.450380	−	0.892837i	$-0.351288\pi$
$103$	9556.17			0.900760			0.450380	+	0.892837i	$0.351288\pi$
$104$	708.644	−	1834.57i	0.0655181	−	0.169616i
$105$			670.606i			0.0608260i
$106$	−643.036	+	5207.00i	−0.0572300	+	0.463421i
$107$	−14480.7	−	14480.7i	−1.26480	−	1.26480i	−0.948738	−	0.316064i	$-0.897639\pi$
$107$	−14480.7	−	14480.7i	−1.26480	−	1.26480i	−0.316064	−	0.948738i	$-0.602361\pi$
$108$	1925.73	−	1153.43i	0.165100	−	0.0988883i
$109$	7860.30	+	7860.30i	0.661586	+	0.661586i	0.955754	−	0.294168i	$-0.0950425\pi$
$109$	7860.30	+	7860.30i	0.661586	+	0.661586i	−0.294168	+	0.955754i	$0.595042\pi$
$110$	−18201.1	+	14199.8i	−1.50422	+	1.17353i
$111$			9206.33i			0.747207i
$112$	−1118.24	−	598.597i	−0.0891454	−	0.0477198i
$113$	21490.4			1.68301			0.841507	−	0.540246i	$-0.181669\pi$
$113$	21490.4			1.68301			0.841507	+	0.540246i	$0.181669\pi$
$114$	−2376.36	−	3045.99i	−0.182853	−	0.234379i
$115$	8648.74	−	8648.74i	0.653969	−	0.653969i
$116$	−16771.7	+	10045.6i	−1.24641	+	0.746549i
$117$	−586.680	+	586.680i	−0.0428578	+	0.0428578i
$118$	22477.4	+	2775.84i	1.61430	+	0.199357i
$119$	2061.94			0.145607
$120$	−7920.89	+	3506.72i	−0.550062	+	0.243522i
$121$			34447.6i			2.35282i
$122$	17876.4	+	2207.64i	1.20105	+	0.148323i
$123$	−3471.39	−	3471.39i	−0.229453	−	0.229453i
$124$	672.231	+	168.605i	0.0437195	+	0.0109655i
$125$	10526.2	+	10526.2i	0.673678	+	0.673678i
$126$	329.143	+	421.892i	0.0207321	+	0.0265742i
$127$		−	2411.89i		−	0.149537i	−0.997201	−	0.0747687i	$-0.976178\pi$
$127$		−	2411.89i		−	0.149537i	0.997201	−	0.0747687i	$-0.0238218\pi$
$128$	1222.89	−	16338.3i	0.0746391	−	0.997211i
$129$	−3553.49			−0.213538
$130$	2524.41	−	1969.44i	0.149373	−	0.116535i
$131$	−5633.33	+	5633.33i	−0.328264	+	0.328264i	−0.851926	−	0.523662i	$-0.824565\pi$
$131$	−5633.33	+	5633.33i	−0.328264	+	0.328264i	0.523662	+	0.851926i	$0.324565\pi$
$132$	−4481.22	+	17866.7i	−0.257187	+	1.02541i
$133$	651.194	−	651.194i	0.0368135	−	0.0368135i
$134$	898.908	−	7278.93i	0.0500617	−	0.405376i
$135$	3654.46			0.200519
$136$	10782.2	+	24354.6i	0.582949	+	1.31675i
$137$			625.988i			0.0333522i	0.999861	+	0.0166761i	$0.00530842\pi$
$137$			625.988i			0.0333522i	−0.999861	+	0.0166761i	$0.994692\pi$
$138$	1196.17	−	9686.02i	0.0628109	−	0.508613i
$139$	−3524.37	−	3524.37i	−0.182411	−	0.182411i	0.609994	−	0.792406i	$-0.291172\pi$
$139$	−3524.37	−	3524.37i	−0.182411	−	0.182411i	−0.792406	+	0.609994i	$0.791172\pi$
$140$	−1061.04	−	1771.48i	−0.0541348	−	0.0903815i
$141$	−14926.9	−	14926.9i	−0.750812	−	0.750812i
$142$	7408.05	−	5779.46i	0.367390	−	0.286623i
$143$		−	6808.37i		−	0.332944i
$144$	−3262.05	+	6093.83i	−0.157313	+	0.293877i
$145$	−31827.7			−1.51380
$146$	2099.73	+	2691.41i	0.0985049	+	0.126262i
$147$	8731.64	−	8731.64i	0.404074	−	0.404074i
$148$	−14566.4	−	24319.5i	−0.665010	−	1.11028i
$149$	21169.0	−	21169.0i	0.953517	−	0.953517i	−0.0454500	−	0.998967i	$-0.514472\pi$
$149$	21169.0	−	21169.0i	0.953517	−	0.953517i	0.998967	+	0.0454500i	$0.0144722\pi$
$150$	−1103.77	−	136.309i	−0.0490563	−	0.00605818i
$151$	−37593.7			−1.64878			−0.824388	−	0.566025i	$-0.808481\pi$
$151$	−37593.7			−1.64878			−0.824388	+	0.566025i	$0.808481\pi$
$152$	11096.8	+	4286.40i	0.480298	+	0.185526i
$153$		−	11236.5i		−	0.480008i
$154$	−4357.85	−	538.170i	−0.183751	−	0.0226923i
$155$	797.827	+	797.827i	0.0332082	+	0.0332082i
$156$	621.525	−	2478.03i	0.0255393	−	0.101826i
$157$	−24045.2	−	24045.2i	−0.975503	−	0.975503i	0.0242036	−	0.999707i	$-0.492295\pi$
$157$	−24045.2	−	24045.2i	−0.975503	−	0.975503i	−0.999707	+	0.0242036i	$0.992295\pi$
$158$	11672.7	+	14962.0i	0.467583	+	0.599342i
$159$			6815.48i			0.269589i
$160$	15375.5	−	21795.9i	0.600606	−	0.851402i
$161$	2326.48			0.0897525
$162$	2299.09	−	1793.66i	0.0876046	−	0.0683456i
$163$	−27454.8	+	27454.8i	−1.03334	+	1.03334i	−0.0339160	+	0.999425i	$0.510798\pi$
$163$	−27454.8	+	27454.8i	−1.03334	+	1.03334i	−0.999425	+	0.0339160i	$0.989202\pi$
$164$	14662.5	+	3677.57i	0.545157	+	0.136733i
$165$	−21204.8	+	21204.8i	−0.778874	+	0.778874i
$166$	4837.30	−	39170.2i	0.175544	−	1.42147i
$167$	−21379.2			−0.766582			−0.383291	−	0.923628i	$-0.625209\pi$
$167$	−21379.2			−0.766582			−0.383291	+	0.923628i	$0.625209\pi$
$168$	−1536.99	−	593.698i	−0.0544568	−	0.0210352i
$169$		−	27616.7i		−	0.966938i
$170$	−5314.54	+	43034.6i	−0.183894	+	1.48909i
$171$	−3548.67	−	3548.67i	−0.121360	−	0.121360i
$172$	9386.92	−	5622.38i	0.317297	−	0.190048i
$173$	12932.3	+	12932.3i	0.432098	+	0.432098i	0.889342	−	0.457243i	$-0.151163\pi$
$173$	12932.3	+	12932.3i	0.432098	+	0.432098i	−0.457243	+	0.889342i	$0.651163\pi$
$174$	−20023.4	+	15621.5i	−0.661363	+	0.515969i
$175$		−	265.113i		−	0.00865674i
$176$	−16431.3	−	54287.1i	−0.530453	−	1.75255i
$177$	29420.9			0.939094
$178$	−24125.0	−	30923.1i	−0.761425	−	0.975986i
$179$	16905.3	−	16905.3i	0.527615	−	0.527615i	−0.392246	−	0.919860i	$-0.628302\pi$
$179$	16905.3	−	16905.3i	0.527615	−	0.527615i	0.919860	+	0.392246i	$0.128302\pi$
$180$	−9653.65	+	5782.13i	−0.297952	+	0.178461i
$181$	−21859.9	+	21859.9i	−0.667253	+	0.667253i	−0.957079	−	0.289826i	$-0.906403\pi$
$181$	−21859.9	+	21859.9i	−0.667253	+	0.667253i	0.289826	+	0.957079i	$0.406403\pi$
$182$	604.414	+	74.6418i	0.0182470	+	0.00225340i
$183$	23398.5			0.698693
$184$	12165.5	+	27479.3i	0.359332	+	0.811651i
$185$		−	46151.1i		−	1.34846i
$186$	893.514	+	110.344i	0.0258271	+	0.00318951i
$187$	65199.3	+	65199.3i	1.86449	+	1.86449i
$188$	63048.5	+	15813.4i	1.78385	+	0.447415i
$189$	491.517	+	491.517i	0.0137599	+	0.0137599i
$190$	11912.6	+	15269.5i	0.329990	+	0.422977i
$191$			20413.4i			0.559563i	0.960064	+	0.279781i	$0.0902620\pi$
$191$			20413.4i			0.559563i	−0.960064	+	0.279781i	$0.909738\pi$
$192$	−1024.70	−	21258.8i	−0.0277966	−	0.576681i
$193$	−34286.3			−0.920463			−0.460232	−	0.887799i	$-0.652234\pi$
$193$	−34286.3			−0.920463			−0.460232	+	0.887799i	$0.652234\pi$
$194$	126.891	−	98.9955i	0.00337154	−	0.00263034i
$195$	2941.01	−	2941.01i	0.0773442	−	0.0773442i
$196$	−9250.25	+	36880.9i	−0.240791	+	0.960039i
$197$	−43791.3	+	43791.3i	−1.12838	+	1.12838i	−0.137940	+	0.990441i	$0.544048\pi$
$197$	−43791.3	+	43791.3i	−1.12838	+	1.12838i	−0.990441	+	0.137940i	$0.955952\pi$
$198$	−2932.75	+	23748.0i	−0.0748075	+	0.605755i
$199$	−8358.27			−0.211062			−0.105531	−	0.994416i	$-0.533654\pi$
$199$	−8358.27			−0.211062			−0.105531	+	0.994416i	$0.533654\pi$
$200$	3131.39	−	1386.32i	0.0782847	−	0.0346580i
$201$		−	9527.44i		−	0.235822i
$202$	−1611.78	+	13051.4i	−0.0395005	+	0.319856i
$203$	−4280.76	−	4280.76i	−0.103879	−	0.103879i
$204$	17778.5	+	29682.4i	0.427204	+	0.713245i
$205$	17402.0	+	17402.0i	0.414087	+	0.414087i
$206$	−30137.9	+	23512.4i	−0.710197	+	0.554067i
$207$		−	12678.1i		−	0.295879i
$208$	2278.95	+	7529.37i	0.0526754	+	0.174033i
$209$	41182.0			0.942791
$210$	−1649.99	−	2114.93i	−0.0374147	−	0.0479577i
$211$	10690.9	−	10690.9i	0.240132	−	0.240132i	−0.576772	−	0.816905i	$-0.695688\pi$
$211$	10690.9	−	10690.9i	0.240132	−	0.240132i	0.816905	+	0.576772i	$0.195688\pi$
$212$	−10783.5	−	18003.8i	−0.239933	−	0.400583i
$213$	8630.61	−	8630.61i	0.190231	−	0.190231i
$214$	81297.7	+	10039.8i	1.77521	+	0.219229i
$215$	17813.6			0.385366
$216$	−3235.35	+	8375.80i	−0.0693447	+	0.179523i
$217$			214.612i			0.00455759i
$218$	−44129.4	−	5449.73i	−0.928570	−	0.114673i
$219$	3135.58	+	3135.58i	0.0653776	+	0.0653776i
$220$	22464.3	−	89565.4i	0.464138	−	1.85053i
$221$	−9042.84	−	9042.84i	−0.185149	−	0.185149i
$222$	−22651.6	−	29034.6i	−0.459614	−	0.589128i
$223$		−	67566.3i		−	1.35869i	−0.733819	−	0.679345i	$-0.762264\pi$
$223$		−	67566.3i		−	1.35869i	0.733819	−	0.679345i	$-0.237736\pi$
$224$	4999.48	−	863.528i	0.0996388	−	0.0172100i
$225$	−1444.73			−0.0285378
$226$	−67775.7	+	52875.9i	−1.32696	+	1.03524i
$227$	12332.5	−	12332.5i	0.239331	−	0.239331i	−0.577242	−	0.816573i	$-0.695871\pi$
$227$	12332.5	−	12332.5i	0.239331	−	0.239331i	0.816573	+	0.577242i	$0.195871\pi$
$228$	14989.0	+	3759.44i	0.288338	+	0.0723192i
$229$	51546.1	−	51546.1i	0.982936	−	0.982936i	−0.0169210	−	0.999857i	$-0.505386\pi$
$229$	51546.1	−	51546.1i	0.982936	−	0.982936i	0.999857	+	0.0169210i	$0.00538638\pi$
$230$	−5996.38	+	48555.8i	−0.113353	+	0.917879i
$231$	−5704.01			−0.106895
$232$	28177.5	−	72947.1i	0.523512	−	1.35529i
$233$		−	58015.9i		−	1.06865i	−0.845279	−	0.534325i	$-0.820566\pi$
$233$		−	58015.9i		−	1.06865i	0.845279	−	0.534325i	$-0.179434\pi$
$234$	406.759	−	3293.74i	0.00742858	−	0.0601531i
$235$	74828.1	+	74828.1i	1.35497	+	1.35497i
$236$	−77718.4	+	46550.1i	−1.39540	+	0.835789i
$237$	17431.2	+	17431.2i	0.310335	+	0.310335i
$238$	−6502.86	+	5073.27i	−0.114802	+	0.0895642i
$239$			49682.0i			0.869767i	0.900487	+	0.434884i	$0.143211\pi$
$239$			49682.0i			0.869767i	−0.900487	+	0.434884i	$0.856789\pi$
$240$	16352.6	−	30548.2i	0.283899	−	0.530351i
$241$	−63543.7			−1.09405			−0.547027	−	0.837115i	$-0.684240\pi$
$241$	−63543.7			−1.09405			−0.547027	+	0.837115i	$0.684240\pi$
$242$	−84756.4	−	108640.i	−1.44724	−	1.85506i
$243$	2678.52	−	2678.52i	0.0453609	−	0.0453609i
$244$	−61809.7	+	37021.5i	−1.03819	+	0.621833i
$245$	−43771.5	+	43771.5i	−0.729222	+	0.729222i
$246$	19489.1	+	2406.80i	0.322049	+	0.0397713i
$247$	−5711.76			−0.0936216
$248$	−2534.90	+	1122.24i	−0.0412152	+	0.0182467i
$249$		−	51270.1i		−	0.826923i
$250$	−59096.4	−	7298.08i	−0.945542	−	0.116769i
$251$	18737.6	+	18737.6i	0.297417	+	0.297417i	0.840001	−	0.542584i	$-0.182554\pi$
$251$	18737.6	+	18737.6i	0.297417	+	0.297417i	−0.542584	+	0.840001i	$0.682554\pi$
$252$	−2076.08	−	520.710i	−0.0326921	−	0.00819965i
$253$	73564.1	+	73564.1i	1.14928	+	1.14928i
$254$	5934.31	+	7606.53i	0.0919820	+	0.117901i
$255$			56328.3i			0.866256i
$256$	36342.7	+	54536.0i	0.554546	+	0.832153i
$257$	43815.4			0.663377			0.331688	−	0.943389i	$-0.392382\pi$
$257$	43815.4			0.663377			0.331688	+	0.943389i	$0.392382\pi$
$258$	11206.9	−	8743.15i	0.168362	−	0.131350i
$259$	6207.23	−	6207.23i	0.0925334	−	0.0925334i
$260$	−3115.69	+	12422.3i	−0.0460901	+	0.183762i
$261$	−23327.9	+	23327.9i	−0.342448	+	0.342448i
$262$	3905.72	−	31626.7i	0.0568982	−	0.460735i
$263$	−22420.4			−0.324140			−0.162070	−	0.986779i	$-0.551817\pi$
$263$	−22420.4			−0.324140			−0.162070	+	0.986779i	$0.551817\pi$
$264$	−29827.3	−	67373.2i	−0.427962	−	0.966672i
$265$		−	34165.8i		−	0.486520i
$266$	−451.488	+	3655.94i	−0.00638092	+	0.0516696i
$267$	−36026.4	−	36026.4i	−0.505358	−	0.505358i
$268$	15074.4	+	25167.8i	0.209880	+	0.350409i
$269$	−97320.0	−	97320.0i	−1.34492	−	1.34492i	−0.891083	−	0.453841i	$-0.850053\pi$
$269$	−97320.0	−	97320.0i	−1.34492	−	1.34492i	−0.453841	−	0.891083i	$-0.649947\pi$
$270$	−11525.3	+	8991.58i	−0.158097	+	0.123341i
$271$		−	8004.88i		−	0.108997i	−0.998514	−	0.0544987i	$-0.982644\pi$
$271$		−	8004.88i		−	0.108997i	0.998514	−	0.0544987i	$-0.0173561\pi$
$272$	−93927.7	−	50279.8i	−1.26957	−	0.679604i
$273$	791.121			0.0106149
$274$	−1540.21	−	1974.22i	−0.0205153	−	0.0262963i
$275$	8382.97	−	8382.97i	0.110849	−	0.110849i
$276$	20059.4	+	33490.5i	0.263330	+	0.439647i
$277$	71046.8	−	71046.8i	0.925945	−	0.925945i	−0.0714963	−	0.997441i	$-0.522777\pi$
$277$	71046.8	−	71046.8i	0.925945	−	0.925945i	0.997441	+	0.0714963i	$0.0227774\pi$
$278$	19786.5	+	2443.53i	0.256024	+	0.0316175i
$279$	1169.53			0.0150246
$280$	7704.89	+	2976.19i	0.0982767	+	0.0379617i
$281$			44327.9i			0.561390i	0.959797	+	0.280695i	$0.0905650\pi$
$281$			44327.9i			0.561390i	−0.959797	+	0.280695i	$0.909435\pi$
$282$	83802.6	+	10349.2i	1.05380	+	0.130139i
$283$	−68224.1	−	68224.1i	−0.851854	−	0.851854i	0.138508	−	0.990361i	$-0.455769\pi$
$283$	−68224.1	−	68224.1i	−0.851854	−	0.851854i	−0.990361	+	0.138508i	$0.955769\pi$
$284$	−9143.21	+	36454.1i	−0.113361	+	0.451970i
$285$	17789.4	+	17789.4i	0.219014	+	0.219014i
$286$	16751.6	+	21472.0i	0.204797	+	0.262507i
$287$			4681.07i			0.0568305i
$288$	−4705.79	−	27244.6i	−0.0567345	−	0.328470i
$289$	89673.6			1.07366
$290$	100377.	−	78310.1i	1.19354	−	0.931155i
$291$	147.832	−	147.832i	0.00174576	−	0.00174576i
$292$	−13244.1	−	3321.81i	−0.155331	−	0.0389591i
$293$	−75735.7	+	75735.7i	−0.882197	+	0.882197i	−0.993758	−	0.111560i	$-0.964415\pi$
$293$	−75735.7	+	75735.7i	−0.882197	+	0.882197i	0.111560	+	0.993758i	$0.464415\pi$
$294$	−6053.85	+	49021.2i	−0.0700386	+	0.567139i
$295$	−147486.			−1.69476
$296$	105776.	+	40858.3i	1.20726	+	0.466334i
$297$			31083.9i			0.352390i
$298$	−14677.0	+	118847.i	−0.165274	+	1.33831i
$299$	−10203.0	−	10203.0i	−0.114126	−	0.114126i
$300$	3816.40	−	2285.87i	0.0424045	−	0.0253985i
$301$	2395.89	+	2395.89i	0.0264444	+	0.0264444i
$302$	118562.	−	92497.2i	1.29996	−	1.01418i
$303$			17083.1i			0.186072i
$304$	−45543.2	+	13784.8i	−0.492806	+	0.149160i
$305$	−117296.			−1.26091
$306$	27646.7	+	35437.3i	0.295258	+	0.378458i
$307$	5734.72	−	5734.72i	0.0608465	−	0.0608465i	−0.676029	−	0.736875i	$-0.736301\pi$
$307$	5734.72	−	5734.72i	0.0608465	−	0.0608465i	0.736875	+	0.676029i	$0.236301\pi$
$308$	15067.8	−	9024.96i	0.158835	−	0.0951358i
$309$	−35111.6	+	35111.6i	−0.367734	+	0.367734i
$310$	−4479.17	−	553.153i	−0.0466094	−	0.00575601i
$311$	11081.3			0.114570			0.0572850	−	0.998358i	$-0.481756\pi$
$311$	11081.3			0.114570			0.0572850	+	0.998358i	$0.481756\pi$
$312$	4136.91	+	9344.35i	0.0424978	+	0.0959931i
$313$			104836.i			1.07010i	0.844821	+	0.535049i	$0.179707\pi$
$313$			104836.i			1.07010i	−0.844821	+	0.535049i	$0.820293\pi$
$314$	134995.	+	16671.1i	1.36917	+	0.169085i
$315$	−2463.97	−	2463.97i	−0.0248321	−	0.0248321i
$316$	−73626.2	−	18466.5i	−0.737323	−	0.184931i
$317$	78165.3	+	78165.3i	0.777849	+	0.777849i	0.979465	−	0.201616i	$-0.0646192\pi$
$317$	78165.3	+	78165.3i	0.777849	+	0.777849i	−0.201616	+	0.979465i	$0.564619\pi$
$318$	−16769.1	−	21494.4i	−0.165827	−	0.212555i
$319$		−	270718.i		−	2.66034i
$320$	5136.77	+	106570.i	0.0501638	+	1.04072i
$321$	106411.			1.03271
$322$	−7337.16	+	5724.16i	−0.0707646	+	0.0552077i
$323$	54697.7	−	54697.7i	0.524281	−	0.524281i
$324$	−2837.60	+	11313.6i	−0.0270310	+	0.107773i
$325$	−1162.68	+	1162.68i	−0.0110076	+	0.0110076i
$326$	19035.1	−	154137.i	0.179110	−	1.45035i
$327$	−57761.2			−0.540183
$328$	−55290.6	+	24478.1i	−0.513930	+	0.227526i
$329$			20128.5i			0.185960i
$330$	14701.8	−	119048.i	0.135003	−	1.09319i
$331$	60949.9	+	60949.9i	0.556310	+	0.556310i	0.928255	−	0.371945i	$-0.121309\pi$
$331$	60949.9	+	60949.9i	0.556310	+	0.556310i	−0.371945	+	0.928255i	$0.621309\pi$
$332$	81120.2	+	135435.i	0.735957	+	1.22873i
$333$	−33826.2	−	33826.2i	−0.305046	−	0.305046i
$334$	67424.9	−	52602.2i	0.604404	−	0.471532i
$335$			47760.8i			0.425581i
$336$	6308.06	−	1909.29i	0.0558750	−	0.0169119i
$337$	−36576.3			−0.322062			−0.161031	−	0.986949i	$-0.551482\pi$
$337$	−36576.3			−0.322062			−0.161031	+	0.986949i	$0.551482\pi$
$338$	67949.3	+	87096.6i	0.594773	+	0.762374i
$339$	−78960.8	+	78960.8i	−0.687088	+	0.687088i
$340$	−89123.4	−	148797.i	−0.770963	−	1.28717i
$341$	−6786.13	+	6786.13i	−0.0583597	+	0.0583597i
$342$	19923.0	+	2460.38i	0.170334	+	0.0210354i
$343$	−23670.3			−0.201195
$344$	−15770.6	+	40827.6i	−0.133270	+	0.345014i
$345$			63555.0i			0.533964i
$346$	−72604.4	−	8966.25i	−0.606472	−	0.0748960i
$347$	−20129.0	−	20129.0i	−0.167172	−	0.167172i	0.618563	−	0.785735i	$-0.287715\pi$
$347$	−20129.0	−	20129.0i	−0.167172	−	0.167172i	−0.785735	+	0.618563i	$0.787715\pi$
$348$	24713.5	−	98532.9i	0.204068	−	0.813622i
$349$	−5475.74	−	5475.74i	−0.0449565	−	0.0449565i	0.684271	−	0.729228i	$-0.260120\pi$
$349$	−5475.74	−	5475.74i	−0.0449565	−	0.0449565i	−0.729228	+	0.684271i	$0.760120\pi$
$350$	652.294	+	836.103i	0.00532485	+	0.00682533i
$351$		−	4311.20i		−	0.0349932i
$352$	185391.	+	130780.i	1.49624	+	1.05550i
$353$	59714.9			0.479219			0.239609	−	0.970869i	$-0.422981\pi$
$353$	59714.9			0.479219			0.239609	+	0.970869i	$0.422981\pi$
$354$	−92786.5	+	72388.3i	−0.740420	+	0.577646i
$355$	−43265.0	+	43265.0i	−0.343305	+	0.343305i
$356$	152169.	+	38166.2i	1.20068	+	0.301147i
$357$	−7576.04	+	7576.04i	−0.0594437	+	0.0594437i
$358$	−11720.8	+	94909.8i	−0.0914519	+	0.740534i
$359$	110853.			0.860118			0.430059	−	0.902801i	$-0.358493\pi$
$359$	110853.			0.860118			0.430059	+	0.902801i	$0.358493\pi$
$360$	16218.7	−	41987.7i	0.125145	−	0.323979i
$361$			95772.1i			0.734894i
$362$	15156.0	−	122726.i	0.115656	−	0.936524i
$363$	−126569.	−	126569.i	−0.960535	−	0.960535i
$364$	−2089.83	+	1251.72i	−0.0157728	+	0.00944724i
$365$	−15718.6	−	15718.6i	−0.117985	−	0.117985i
$366$	−73793.5	+	57570.7i	−0.550878	+	0.429773i
$367$			80723.3i			0.599331i	0.954044	+	0.299666i	$0.0968751\pi$
$367$			80723.3i			0.599331i	−0.954044	+	0.299666i	$0.903125\pi$
$368$	−105978.	−	56730.5i	−0.782567	−	0.418910i
$369$	25509.4			0.187348
$370$	113552.	+	145550.i	0.829453	+	1.06318i
$371$	4595.23	−	4595.23i	0.0333856	−	0.0333856i
$372$	−3089.43	+	1850.44i	−0.0223250	+	0.0133718i
$373$	114495.	−	114495.i	0.822940	−	0.822940i	−0.163589	−	0.986529i	$-0.552307\pi$
$373$	114495.	−	114495.i	0.822940	−	0.822940i	0.986529	+	0.163589i	$0.0523071\pi$
$374$	−366042.	−	45204.2i	−2.61690	−	0.323173i
$375$	−77351.6			−0.550056
$376$	−237748.	+	105255.i	−1.68167	+	0.744505i
$377$			37547.4i			0.264178i
$378$	−2759.48	−	340.781i	−0.0193127	−	0.00238502i
$379$	−83672.7	−	83672.7i	−0.582513	−	0.582513i	0.353080	−	0.935593i	$-0.385134\pi$
$379$	−83672.7	−	83672.7i	−0.582513	−	0.582513i	−0.935593	+	0.353080i	$0.885134\pi$
$380$	−75139.3	−	18846.0i	−0.520355	−	0.130512i
$381$	8861.84	+	8861.84i	0.0610484	+	0.0610484i
$382$	−50226.0	−	64379.1i	−0.344193	−	0.441182i
$383$			24350.8i			0.166003i	0.996549	+	0.0830014i	$0.0264506\pi$
$383$			24350.8i			0.166003i	−0.996549	+	0.0830014i	$0.973549\pi$
$384$	55537.6	+	64523.9i	0.376638	+	0.437581i
$385$	28594.1			0.192910
$386$	108131.	−	84359.5i	0.725731	−	0.566186i
$387$	13056.4	−	13056.4i	0.0871766	−	0.0871766i
$388$	−156.613	+	624.417i	−0.00104031	+	0.00414774i
$389$	97431.5	−	97431.5i	0.643873	−	0.643873i	−0.307632	−	0.951505i	$-0.599537\pi$
$389$	97431.5	−	97431.5i	0.643873	−	0.643873i	0.951505	+	0.307632i	$0.0995367\pi$
$390$	−2039.07	+	16511.5i	−0.0134061	+	0.108557i
$391$	195415.			1.27822
$392$	−61570.1	−	139073.i	−0.400680	−	0.905048i
$393$		−	41396.4i		−	0.268026i
$394$	30361.6	−	245854.i	0.195583	−	1.58374i
$395$	−87382.1	−	87382.1i	−0.560052	−	0.560052i
$396$	−49181.4	−	82111.6i	−0.313625	−	0.523617i
$397$	−80501.7	−	80501.7i	−0.510768	−	0.510768i	0.403994	−	0.914762i	$-0.367622\pi$
$397$	−80501.7	−	80501.7i	−0.510768	−	0.510768i	−0.914762	+	0.403994i	$0.867622\pi$
$398$	26360.0	−	20565.0i	0.166410	−	0.129826i
$399$			4785.28i			0.0300581i
$400$	−6464.70	+	12076.7i	−0.0404044	+	0.0754795i
$401$	−222598.			−1.38431			−0.692154	−	0.721750i	$-0.743338\pi$
$401$	−222598.			−1.38431			−0.692154	+	0.721750i	$0.743338\pi$
$402$	23441.7	+	30047.3i	0.145056	+	0.185932i
$403$	941.205	−	941.205i	0.00579527	−	0.00579527i
$404$	−27029.1	−	45126.8i	−0.165603	−	0.276485i
$405$	−13427.3	+	13427.3i	−0.0818616	+	0.0818616i
$406$	24033.0	+	2967.95i	0.145800	+	0.0180055i
$407$	392550.			2.36977
$408$	−129101.	−	49868.3i	−0.775550	−	0.299574i
$409$		−	30247.2i		−	0.180817i	−0.995905	−	0.0904083i	$-0.971183\pi$
$409$		−	30247.2i		−	0.180817i	0.995905	−	0.0904083i	$-0.0288172\pi$
$410$	−97698.5	−	12065.2i	−0.581193	−	0.0717741i
$411$	−2300.03	−	2300.03i	−0.0136160	−	0.0136160i
$412$	37197.0	−	148305.i	0.219136	−	0.873698i
$413$	−19836.6	−	19836.6i	−0.116297	−	0.116297i
$414$	31193.7	+	39983.7i	0.181998	+	0.233283i
$415$			257016.i			1.49233i
$416$	−25712.8	−	18138.6i	−0.148581	−	0.104814i
$417$	25898.7			0.148938
$418$	−129878.	+	101326.i	−0.743335	+	0.579920i
$419$	−73262.6	+	73262.6i	−0.417305	+	0.417305i	−0.884274	−	0.466968i	$-0.845346\pi$
$419$	−73262.6	+	73262.6i	−0.417305	+	0.417305i	0.466968	+	0.884274i	$0.345346\pi$
$420$	10407.3	+	2610.31i	0.0589985	+	0.0147977i
$421$	108612.	−	108612.i	0.612790	−	0.612790i	−0.330882	−	0.943672i	$-0.607346\pi$
$421$	108612.	−	108612.i	0.612790	−	0.612790i	0.943672	+	0.330882i	$0.107346\pi$
$422$	−7412.28	+	60021.1i	−0.0416224	+	0.337038i
$423$	109690.			0.613035
$424$	78306.0	+	30247.5i	0.435576	+	0.168251i
$425$		−	22268.4i		−	0.123285i
$426$	−5983.80	+	48454.0i	−0.0329730	+	0.266999i
$427$	−15776.1	−	15776.1i	−0.0865255	−	0.0865255i
$428$	−281096.	+	168365.i	−1.53450	+	0.919103i
$429$	25015.6	+	25015.6i	0.135924	+	0.135924i
$430$	−56179.8	+	43829.2i	−0.303839	+	0.237043i
$431$		−	208370.i		−	1.12171i	−0.827915	−	0.560854i	$-0.810473\pi$
$431$		−	208370.i		−	1.12171i	0.827915	−	0.560854i	$-0.189527\pi$
$432$	−10404.6	−	34375.7i	−0.0557519	−	0.184198i
$433$	−111006.			−0.592064			−0.296032	−	0.955178i	$-0.595664\pi$
$433$	−111006.			−0.592064			−0.296032	+	0.955178i	$0.595664\pi$
$434$	−528.041	−	676.836i	−0.00280342	−	0.00359339i
$435$	116942.	−	116942.i	0.618007	−	0.618007i
$436$	152582.	−	91390.5i	0.802659	−	0.480760i
$437$	61715.3	−	61715.3i	0.323169	−	0.323169i
$438$	−17603.8	−	2173.97i	−0.0917609	−	0.0113320i
$439$	−36220.6			−0.187943			−0.0939716	−	0.995575i	$-0.529956\pi$
$439$	−36220.6			−0.187943			−0.0939716	+	0.995575i	$0.529956\pi$
$440$	149523.	+	337740.i	0.772332	+	1.74453i
$441$			64164.2i			0.329925i
$442$	50768.4	+	6269.61i	0.259865	+	0.0320920i
$443$	181195.	+	181195.i	0.923293	+	0.923293i	0.997261	−	0.0739673i	$-0.0235660\pi$
$443$	181195.	+	181195.i	0.923293	+	0.923293i	−0.0739673	+	0.997261i	$0.523566\pi$
$444$	142876.	+	35835.3i	0.724758	+	0.181780i
$445$	180600.	+	180600.i	0.912005	+	0.912005i
$446$	166243.	+	213088.i	0.835744	+	1.07125i
$447$			155560.i			0.778543i
$448$	−13642.5	+	15024.3i	−0.0679733	+	0.0748579i
$449$	−8225.59			−0.0408014			−0.0204007	−	0.999792i	$-0.506494\pi$
$449$	−8225.59			−0.0408014			−0.0204007	+	0.999792i	$0.506494\pi$
$450$	4556.33	−	3554.67i	0.0225004	−	0.0175539i
$451$	−148017.	+	148017.i	−0.727712	+	0.727712i
$452$	83650.6	−	333516.i	0.409442	−	1.63245i
$453$	138128.	−	138128.i	0.673110	−	0.673110i
$454$	−8550.39	+	69237.0i	−0.0414834	+	0.335913i
$455$	−3965.87			−0.0191565
$456$	−56521.5	+	25023.0i	−0.271822	+	0.120340i
$457$			129406.i			0.619613i	0.950800	+	0.309807i	$0.100264\pi$
$457$			129406.i			0.619613i	−0.950800	+	0.309807i	$0.899736\pi$
$458$	−35738.2	+	289391.i	−0.170373	+	1.37960i
$459$	41285.5	+	41285.5i	0.195962	+	0.195962i
$460$	−100558.	−	167887.i	−0.475225	−	0.793418i
$461$	−154534.	−	154534.i	−0.727147	−	0.727147i	0.242903	−	0.970051i	$-0.421900\pi$
$461$	−154534.	−	154534.i	−0.727147	−	0.727147i	−0.970051	+	0.242903i	$0.921900\pi$
$462$	17989.1	−	14034.4i	0.0842803	−	0.0657521i
$463$			52826.9i			0.246430i	0.992380	+	0.123215i	$0.0393204\pi$
$463$			52826.9i			0.246430i	−0.992380	+	0.123215i	$0.960680\pi$
$464$	90616.8	+	299387.i	0.420894	+	1.39058i
$465$	−5862.81			−0.0271144
$466$	142745.	+	182968.i	0.657337	+	0.842567i
$467$	−216028.	+	216028.i	−0.990551	+	0.990551i	−0.999956	−	0.00940448i	$-0.997006\pi$
$467$	−216028.	+	216028.i	−0.990551	+	0.990551i	0.00940448	+	0.999956i	$0.497006\pi$
$468$	6821.24	+	11388.5i	0.0311438	+	0.0519966i
$469$	−6423.73	+	6423.73i	−0.0292040	+	0.0292040i
$470$	−420101.	−	51880.1i	−1.90177	−	0.234858i
$471$	176695.			0.796495
$472$	130572.	−	338029.i	0.586091	−	1.51730i
$473$			151518.i			0.677238i
$474$	−97862.2	−	12085.4i	−0.435570	−	0.0537906i
$475$	−7032.74	−	7032.74i	−0.0311700	−	0.0311700i
$476$	8026.01	−	31999.8i	0.0354230	−	0.141232i
$477$	−25041.7	−	25041.7i	−0.110059	−	0.110059i
$478$	−122240.	−	156685.i	−0.535003	−	0.685760i
$479$			207031.i			0.902329i	0.892441	+	0.451165i	$0.148991\pi$
$479$			207031.i			0.902329i	−0.892441	+	0.451165i	$0.851009\pi$
$480$	23590.0	+	136576.i	0.102387	+	0.592780i
$481$	−54444.9			−0.235325
$482$	200402.	−	156346.i	0.862596	−	0.672963i
$483$	−8548.02	+	8548.02i	−0.0366413	+	0.0366413i
$484$	534603.	+	134086.i	2.28213	+	0.572391i
$485$	−741.080	+	741.080i	−0.00315052	+	0.00315052i
$486$	−1857.08	+	15037.7i	−0.00786245	+	0.0636664i
$487$	280857.			1.18420			0.592102	−	0.805863i	$-0.298298\pi$
$487$	280857.			1.18420			0.592102	+	0.805863i	$0.298298\pi$
$488$	103844.	−	268836.i	0.436056	−	1.12888i
$489$		−	201751.i		−	0.843719i
$490$	30347.8	−	245742.i	0.126397	−	1.02350i
$491$	37948.8	+	37948.8i	0.157411	+	0.157411i	0.781418	−	0.624007i	$-0.214497\pi$
$491$	37948.8	+	37948.8i	0.157411	+	0.157411i	−0.624007	+	0.781418i	$0.714497\pi$
$492$	−67385.9	+	40361.3i	−0.278380	+	0.166738i
$493$	−359567.	−	359567.i	−1.47940	−	1.47940i
$494$	18013.5	−	14053.5i	0.0738151	−	0.0575876i
$495$		−	155823.i		−	0.635948i
$496$	5233.27	−	9776.27i	0.0212721	−	0.0397383i
$497$	−11638.1			−0.0471162
$498$	126147.	+	161694.i	0.508649	+	0.651980i
$499$	114517.	−	114517.i	0.459907	−	0.459907i	−0.438718	−	0.898625i	$-0.644567\pi$
$499$	114517.	−	114517.i	0.459907	−	0.459907i	0.898625	+	0.438718i	$0.144567\pi$
$500$	204332.	−	122387.i	0.817330	−	0.489547i
$501$	78552.2	−	78552.2i	0.312956	−	0.312956i
$502$	−105197.	−	12991.2i	−0.417440	−	0.0515516i
$503$	−294757.			−1.16501			−0.582504	−	0.812828i	$-0.697927\pi$
$503$	−294757.			−1.16501			−0.582504	+	0.812828i	$0.697927\pi$
$504$	7828.64	−	3465.88i	0.0308195	−	0.0136443i
$505$		−	85637.1i		−	0.335799i
$506$	−413004.	−	51003.7i	−1.61307	−	0.199205i
$507$	101470.	+	101470.i	0.394751	+	0.394751i
$508$	−37430.8	−	9388.18i	−0.145045	−	0.0363793i
$509$	−149510.	−	149510.i	−0.577077	−	0.577077i	0.357019	−	0.934097i	$-0.383793\pi$
$509$	−149510.	−	149510.i	−0.577077	−	0.577077i	−0.934097	+	0.357019i	$0.883793\pi$
$510$	−138592.	−	177646.i	−0.532843	−	0.682992i
$511$		−	4228.23i		−	0.0161926i
$512$	−248799.	−	82574.5i	−0.949093	−	0.314997i
$513$	26077.3			0.0990896
$514$	−138183.	+	107805.i	−0.523034	+	0.408050i
$515$	176014.	−	176014.i	0.663639	−	0.663639i
$516$	−13831.8	+	55147.7i	−0.0519493	+	0.207123i
$517$	−636470.	+	636470.i	−2.38121	+	2.38121i
$518$	−4303.62	+	34848.7i	−0.0160389	+	0.129875i
$519$	−95032.4			−0.352807
$520$	−20738.2	−	46843.0i	−0.0766946	−	0.173236i
$521$		−	392690.i		−	1.44668i	−0.690490	−	0.723342i	$-0.742605\pi$
$521$		−	392690.i		−	1.44668i	0.690490	−	0.723342i	$-0.257395\pi$
$522$	16173.8	−	130968.i	0.0593569	−	0.480644i
$523$	−131519.	−	131519.i	−0.480825	−	0.480825i	0.424570	−	0.905395i	$-0.360425\pi$
$523$	−131519.	−	131519.i	−0.480825	−	0.480825i	−0.905395	+	0.424570i	$0.860425\pi$
$524$	65497.9	+	109353.i	0.238542	+	0.398261i
$525$	974.086	+	974.086i	0.00353410	+	0.00353410i
$526$	70708.7	−	55164.1i	0.255565	−	0.199382i
$527$			18026.6i			0.0649071i
$528$	259836.	+	139091.i	0.932033	+	0.498920i
$529$	−59355.1			−0.212103
$530$	84063.0	+	107751.i	0.299263	+	0.383592i
$531$	−108099.	+	108099.i	−0.383384	+	0.383384i
$532$	−7571.33	−	12640.8i	−0.0267516	−	0.0446634i
$533$	20529.3	−	20529.3i	0.0722637	−	0.0722637i
$534$	202260.	+	24978.0i	0.709295	+	0.0875941i
$535$	−533436.			−1.86370
$536$	−109465.	−	42283.4i	−0.381018	−	0.147177i
$537$			124228.i			0.430796i
$538$	546375.	+	67474.3i	1.88767	+	0.233117i
$539$	−372310.	−	372310.i	−1.28152	−	1.28152i
$540$	14224.8	−	56714.7i	0.0487820	−	0.194495i
$541$	115208.	+	115208.i	0.393629	+	0.393629i	0.875979	−	0.482350i	$-0.160217\pi$
$541$	115208.	+	115208.i	0.393629	+	0.393629i	−0.482350	+	0.875979i	$0.660217\pi$
$542$	19695.5	+	25245.5i	0.0670455	+	0.0859381i
$543$		−	160637.i		−	0.544810i
$544$	419936.	−	72533.0i	1.41901	−	0.245097i
$545$	289556.			0.974852
$546$	−2495.01	+	1946.51i	−0.00836925	+	0.00652936i
$547$	−155634.	+	155634.i	−0.520151	+	0.520151i	−0.917617	−	0.397466i	$-0.869890\pi$
$547$	−155634.	+	155634.i	−0.520151	+	0.520151i	0.397466	+	0.917617i	$0.369890\pi$
$548$	9714.89	+	2436.63i	0.0323502	+	0.00811389i
$549$	−85971.7	+	85971.7i	−0.285240	+	0.285240i
$550$	−5812.11	+	47063.7i	−0.0192136	+	0.155582i
$551$	−227114.			−0.748069
$552$	−145664.	−	56266.2i	−0.478052	−	0.184659i
$553$		−	23505.4i		−	0.0768631i
$554$	−49258.4	+	398871.i	−0.160495	+	1.29961i
$555$	169570.	+	169570.i	0.550508	+	0.550508i
$556$	−68414.2	+	40977.3i	−0.221308	+	0.132554i
$557$	136688.	+	136688.i	0.440576	+	0.440576i	0.892206	−	0.451629i	$-0.149157\pi$
$557$	136688.	+	136688.i	0.440576	+	0.440576i	−0.451629	+	0.892206i	$0.649157\pi$
$558$	−3688.41	+	2877.55i	−0.0118460	+	0.00924176i
$559$		−	21014.8i		−	0.0672515i
$560$	−31622.2	+	9571.22i	−0.100836	+	0.0305205i
$561$	−479115.			−1.52235
$562$	−109066.	−	139800.i	−0.345317	−	0.442623i
$563$	257500.	−	257500.i	0.812383	−	0.812383i	−0.172607	−	0.984991i	$-0.555219\pi$
$563$	257500.	−	257500.i	0.812383	−	0.812383i	0.984991	+	0.172607i	$0.0552192\pi$
$564$	−289757.	+	173553.i	−0.910911	+	0.545598i
$565$	395829.	−	395829.i	1.23997	−	1.23997i
$566$	383024.	+	47301.4i	1.19562	+	0.147653i
$567$	−3611.90			−0.0112349
$568$	−60857.7	−	137464.i	−0.188633	−	0.426081i
$569$			441198.i			1.36273i	0.731946	+	0.681363i	$0.238612\pi$
$569$			441198.i			1.36273i	−0.731946	+	0.681363i	$0.761388\pi$
$570$	−99873.5	−	12333.8i	−0.307398	−	0.0379619i
$571$	138592.	+	138592.i	0.425076	+	0.425076i	0.886947	−	0.461871i	$-0.152822\pi$
$571$	138592.	+	138592.i	0.425076	+	0.425076i	−0.461871	+	0.886947i	$0.652822\pi$
$572$	−105661.	−	26501.3i	−0.322941	−	0.0809982i
$573$	−75003.7	−	75003.7i	−0.228441	−	0.228441i
$574$	−11517.5	−	14763.0i	−0.0349570	−	0.0448075i
$575$		−	25125.4i		−	0.0759936i
$576$	81874.6	+	74344.7i	0.246777	+	0.224081i
$577$	192821.			0.579166			0.289583	−	0.957153i	$-0.406483\pi$
$577$	192821.			0.579166			0.289583	+	0.957153i	$0.406483\pi$
$578$	−282809.	+	220637.i	−0.846522	+	0.660422i
$579$	125976.	−	125976.i	0.375778	−	0.375778i
$580$	−123888.	+	493943.i	−0.368276	+	1.46832i
$581$	−34568.1	+	34568.1i	−0.102405	+	0.102405i
$582$	−102.496	+	829.961i	−0.000302593	+	0.00245026i
$583$	290606.			0.855003
$584$	49941.9	−	22110.1i	0.146433	−	0.0648285i
$585$			21612.0i			0.0631513i
$586$	52509.4	−	425196.i	0.152912	−	1.23821i
$587$	228595.	+	228595.i	0.663422	+	0.663422i	0.956185	−	0.292763i	$-0.0945747\pi$
$587$	228595.	+	228595.i	0.663422	+	0.663422i	−0.292763	+	0.956185i	$0.594575\pi$
$588$	−101521.	−	169497.i	−0.293632	−	0.490237i
$589$	5693.10	+	5693.10i	0.0164104	+	0.0164104i
$590$	465137.	−	362881.i	1.33622	−	1.04246i
$591$		−	321799.i		−	0.921319i
$592$	−434121.	+	131397.i	−1.23870	+	0.374924i
$593$	48036.1			0.136602			0.0683012	−	0.997665i	$-0.478242\pi$
$593$	48036.1			0.136602			0.0683012	+	0.997665i	$0.478242\pi$
$594$	−76480.2	−	98031.4i	−0.216759	−	0.277839i
$595$	37978.5	−	37978.5i	0.107276	−	0.107276i
$596$	−246129.	−	410928.i	−0.692899	−	1.15684i
$597$	30710.2	−	30710.2i	0.0861657	−	0.0861657i
$598$	57281.8	+	7073.98i	0.160182	+	0.0197816i
$599$	−244831.			−0.682360			−0.341180	−	0.939998i	$-0.610826\pi$
$599$	−244831.			−0.682360			−0.341180	+	0.939998i	$0.610826\pi$
$600$	−6411.79	+	16599.1i	−0.0178105	+	0.0461086i
$601$			81370.9i			0.225279i	0.993636	+	0.112639i	$0.0359305\pi$
$601$			81370.9i			0.225279i	−0.993636	+	0.112639i	$0.964070\pi$
$602$	−13451.0	−	1661.12i	−0.0371160	−	0.00458363i
$603$	35006.1	+	35006.1i	0.0962739	+	0.0962739i
$604$	−146332.	+	583429.i	−0.401112	+	1.59924i
$605$	634486.	+	634486.i	1.73345	+	1.73345i
$606$	−42031.9	−	53876.0i	−0.114455	−	0.146707i
$607$			278722.i			0.756474i	0.925709	+	0.378237i	$0.123470\pi$
$607$			278722.i			0.756474i	−0.925709	+	0.378237i	$0.876530\pi$
$608$	109716.	−	155530.i	0.296799	−	0.420734i
$609$	31457.0			0.0848170
$610$	369925.	−	288601.i	0.994155	−	0.775600i
$611$	88275.5	−	88275.5i	0.236460	−	0.236460i
$612$	−174383.	−	43737.6i	−0.465586	−	0.116776i
$613$	−347109.	+	347109.i	−0.923729	+	0.923729i	−0.997291	−	0.0735612i	$-0.976564\pi$
$613$	−347109.	+	347109.i	−0.923729	+	0.923729i	0.0735612	+	0.997291i	$0.476564\pi$
$614$	−3976.01	+	32195.9i	−0.0105466	+	0.0854011i
$615$	−127878.			−0.338101
$616$	−25314.8	+	65535.9i	−0.0667133	+	0.172710i
$617$		−	62919.7i		−	0.165279i	−0.996580	−	0.0826393i	$-0.973665\pi$
$617$		−	62919.7i		−	0.165279i	0.996580	−	0.0826393i	$-0.0263349\pi$
$618$	24343.7	−	197124.i	0.0637396	−	0.516133i
$619$	81462.2	+	81462.2i	0.212606	+	0.212606i	0.805373	−	0.592768i	$-0.201965\pi$
$619$	81462.2	+	81462.2i	0.212606	+	0.212606i	−0.592768	+	0.805373i	$0.701965\pi$
$620$	15487.2	−	9276.21i	0.0402894	−	0.0241317i
$621$	46582.3	+	46582.3i	0.120792	+	0.120792i
$622$	−34947.9	+	27264.9i	−0.0903316	+	0.0704731i
$623$			48580.6i			0.125166i
$624$	−36038.1	−	19291.3i	−0.0925534	−	0.0495441i
$625$	421205.			1.07828
$626$	−257944.	−	330629.i	−0.658228	−	0.843709i
$627$	−151312.	+	151312.i	−0.384893	+	0.384893i
$628$	−466759.	+	279570.i	−1.18352	+	0.708877i
$629$	521383.	−	521383.i	1.31782	−	1.31782i
$630$	13833.2	+	1708.33i	0.0348531	+	0.00430417i
$631$	421857.			1.05951			0.529757	−	0.848150i	$-0.322283\pi$
$631$	421857.			1.05951			0.529757	+	0.848150i	$0.322283\pi$
$632$	277635.	−	122914.i	0.695089	−	0.307728i
$633$			78562.0i			0.196067i
$634$	−438836.	−	54193.8i	−1.09175	−	0.134825i
$635$	−44424.2	−	44424.2i	−0.110172	−	0.110172i
$636$	105771.	+	26529.0i	0.261489	+	0.0655853i
$637$	51637.7	+	51637.7i	0.127259	+	0.127259i
$638$	666087.	+	853782.i	1.63640	+	2.09752i
$639$			63421.8i			0.155323i
$640$	−278409.	−	323457.i	−0.679708	−	0.789690i
$641$	591311.			1.43913			0.719564	−	0.694426i	$-0.244342\pi$
$641$	591311.			1.43913			0.719564	+	0.694426i	$0.244342\pi$
$642$	−335596.	+	261818.i	−0.814228	+	0.635228i
$643$	570837.	−	570837.i	1.38067	−	1.38067i	0.537245	−	0.843426i	$-0.319465\pi$
$643$	570837.	−	570837.i	1.38067	−	1.38067i	0.843426	−	0.537245i	$-0.180535\pi$
$644$	9055.72	−	36105.3i	0.0218349	−	0.0870561i
$645$	−65451.2	+	65451.2i	−0.157325	+	0.157325i
$646$	−37923.2	+	307084.i	−0.0908742	+	0.735856i
$647$	−669599.			−1.59958			−0.799791	−	0.600279i	$-0.795056\pi$
$647$	−669599.			−1.59958			−0.799791	+	0.600279i	$0.795056\pi$
$648$	−18887.2	−	42662.1i	−0.0449799	−	0.101600i
$649$		−	1.25448e6i		−	2.97834i
$650$	806.113	−	6527.52i	0.00190796	−	0.0154498i
$651$	−788.536	−	788.536i	−0.00186063	−	0.00186063i
$652$	319213.	+	532947.i	0.750906	+	1.25369i
$653$	188553.	+	188553.i	0.442189	+	0.442189i	0.892747	−	0.450558i	$-0.148775\pi$
$653$	188553.	+	188553.i	0.442189	+	0.442189i	−0.450558	+	0.892747i	$0.648775\pi$
$654$	182165.	−	142118.i	0.425902	−	0.332272i
$655$			207519.i			0.483699i
$656$	114147.	−	213238.i	0.265250	−	0.495514i
$657$	−23041.7			−0.0533806
$658$	−49524.9	−	63480.4i	−0.114386	−	0.146618i
$659$	−498966.	+	498966.i	−1.14895	+	1.14895i	−0.162188	+	0.986760i	$0.551855\pi$
$659$	−498966.	+	498966.i	−1.14895	+	1.14895i	−0.986760	+	0.162188i	$0.948145\pi$
$660$	246545.	+	411623.i	0.565990	+	0.944957i
$661$	−481399.	+	481399.i	−1.10180	+	1.10180i	−0.107606	+	0.994194i	$0.534318\pi$
$661$	−481399.	+	481399.i	−1.10180	+	1.10180i	−0.994194	+	0.107606i	$0.965682\pi$
$662$	−342185.	−	42258.0i	−0.780810	−	0.0964257i
$663$	66451.0			0.151173
$664$	−589065.	−	227540.i	−1.33606	−	0.516085i
$665$		−	23988.5i		−	0.0542450i
$666$	189907.	+	23452.5i	0.428148	+	0.0528739i
$667$	−405698.	−	405698.i	−0.911908	−	0.911908i
$668$	−83217.7	+	331790.i	−0.186493	+	0.743551i
$669$	248254.	+	248254.i	0.554683	+	0.554683i
$670$	−117513.	−	150626.i	−0.261779	−	0.335546i
$671$		−	997694.i		−	2.21591i
$672$	−15196.4	+	21542.1i	−0.0336514	+	0.0477033i
$673$	129459.			0.285826			0.142913	−	0.989735i	$-0.454353\pi$
$673$	129459.			0.285826			0.142913	+	0.989735i	$0.454353\pi$
$674$	115353.	−	89993.8i	0.253927	−	0.198104i
$675$	5308.27	−	5308.27i	0.0116505	−	0.0116505i
$676$	−428592.	−	107497.i	−0.937887	−	0.235235i
$677$	−398735.	+	398735.i	−0.869976	+	0.869976i	−0.992469	−	0.122493i	$-0.960911\pi$
$677$	−398735.	+	398735.i	−0.869976	+	0.869976i	0.122493	+	0.992469i	$0.460911\pi$
$678$	54745.4	−	443302.i	0.119093	−	0.964363i
$679$	−199.348			−0.000432386
$680$	647181.	+	249989.i	1.39961	+	0.540633i
$681$			90624.7i			0.195413i
$682$	4704.98	−	38098.7i	0.0101155	−	0.0819108i
$683$	229310.	+	229310.i	0.491565	+	0.491565i	0.908799	−	0.417234i	$-0.137001\pi$
$683$	229310.	+	229310.i	0.491565	+	0.491565i	−0.417234	+	0.908799i	$0.637001\pi$
$684$	−68886.0	+	41259.9i	−0.147238	+	0.0881892i
$685$	11530.0	+	11530.0i	0.0245724	+	0.0245724i
$686$	74650.7	−	58239.5i	0.158630	−	0.123757i
$687$			378785.i			0.802564i
$688$	−50717.1	−	167563.i	−0.107146	−	0.353999i
$689$	−40305.8			−0.0849041
$690$	−156373.	−	200438.i	−0.328446	−	0.420999i
$691$	260472.	−	260472.i	0.545512	−	0.545512i	−0.379627	−	0.925139i	$-0.623948\pi$
$691$	260472.	−	260472.i	0.545512	−	0.545512i	0.925139	+	0.379627i	$0.123948\pi$
$692$	251038.	−	150361.i	0.524237	−	0.313996i
$693$	20957.9	−	20957.9i	0.0436396	−	0.0436396i
$694$	113008.	+	13955.9i	0.234634	+	0.0289760i
$695$	−129830.			−0.268785
$696$	164494.	+	371556.i	0.339572	+	0.767018i
$697$			393191.i			0.809354i
$698$	30741.9	+	3796.46i	0.0630987	+	0.00779234i
$699$	213164.	+	213164.i	0.436274	+	0.436274i
$700$	−4114.36	−	1031.94i	−0.00839666	−	0.00210600i
$701$	30353.7	+	30353.7i	0.0617697	+	0.0617697i	0.737317	−	0.675547i	$-0.236093\pi$
$701$	30353.7	+	30353.7i	0.0617697	+	0.0617697i	−0.675547	+	0.737317i	$0.736093\pi$
$702$	10607.5	+	13596.5i	0.0215247	+	0.0275901i
$703$		−	329323.i		−	0.666364i
$704$	−906456.	+	43692.1i	−1.82895	+	0.0881573i
$705$	−549872.			−1.10633
$706$	−188327.	+	146925.i	−0.377836	+	0.294772i
$707$	11518.0	−	11518.0i	0.0230430	−	0.0230430i
$708$	114520.	−	456591.i	0.228462	−	0.910880i
$709$	−164767.	+	164767.i	−0.327776	+	0.327776i	−0.851740	−	0.523964i	$-0.824453\pi$
$709$	−164767.	+	164767.i	−0.327776	+	0.327776i	0.523964	+	0.851740i	$0.324453\pi$
$710$	29996.7	−	242899.i	0.0595054	−	0.481846i
$711$	−128092.			−0.253387
$712$	−573811.	+	254036.i	−1.13190	+	0.501113i
$713$			20339.3i			0.0400090i
$714$	5252.65	−	42533.4i	0.0103034	−	0.0834323i
$715$	−125402.	−	125402.i	−0.245298	−	0.245298i
$716$	−196555.	−	328162.i	−0.383406	−	0.640121i
$717$	−182543.	−	182543.i	−0.355081	−	0.355081i
$718$	−349604.	+	272747.i	−0.678153	+	0.529068i
$719$		−	375380.i		−	0.726127i	−0.931764	−	0.363064i	$-0.881731\pi$
$719$		−	375380.i		−	0.726127i	0.931764	−	0.363064i	$-0.118269\pi$
$720$	52158.2	+	172325.i	0.100614	+	0.332416i
$721$	47346.9			0.0910797
$722$	−235642.	−	302043.i	−0.452041	−	0.579420i
$723$	233474.	−	233474.i	0.446645	−	0.446645i
$724$	254161.	+	424339.i	0.484878	+	0.809535i
$725$	−46231.1	+	46231.1i	−0.0879546	+	0.0879546i
$726$	710583.	+	87753.1i	1.34816	+	0.166490i
$727$	−308080.			−0.582901			−0.291451	−	0.956586i	$-0.594138\pi$
$727$	−308080.			−0.582901			−0.291451	+	0.956586i	$0.594138\pi$
$728$	3511.04	−	9089.54i	0.00662481	−	0.0171506i
$729$			19683.0i			0.0370370i
$730$	88247.3	+	10898.1i	0.165598	+	0.0204505i
$731$	201245.	+	201245.i	0.376609	+	0.376609i
$732$	91077.9	−	363129.i	0.169977	−	0.677702i
$733$	201222.	+	201222.i	0.374513	+	0.374513i	0.869118	−	0.494605i	$-0.164687\pi$
$733$	201222.	+	201222.i	0.374513	+	0.374513i	−0.494605	+	0.869118i	$0.664687\pi$
$734$	−198615.	−	254582.i	−0.368655	−	0.472537i
$735$		−	321654.i		−	0.595407i
$736$	473813.	−	81838.7i	0.874684	−	0.151079i
$737$	−406242.			−0.747911
$738$	−80450.7	+	62764.4i	−0.147712	+	0.115239i
$739$	58755.9	−	58755.9i	0.107588	−	0.107588i	−0.651264	−	0.758851i	$-0.725761\pi$
$739$	58755.9	−	58755.9i	0.107588	−	0.107588i	0.758851	+	0.651264i	$0.225761\pi$
$740$	−716233.	−	179642.i	−1.30795	−	0.328052i
$741$	20986.3	−	20986.3i	0.0382209	−	0.0382209i
$742$	−3185.98	+	25798.6i	−0.00578676	+	0.0468585i
$743$	−84874.1			−0.153744			−0.0768719	−	0.997041i	$-0.524493\pi$
$743$	−84874.1			−0.153744			−0.0768719	+	0.997041i	$0.524493\pi$
$744$	5190.43	−	13437.2i	0.00937687	−	0.0242752i
$745$		−	779818.i		−	1.40501i
$746$	−79381.9	+	642797.i	−0.142641	+	1.15504i
$747$	188378.	+	188378.i	0.337590	+	0.337590i
$748$	1.26563e6	−	758061.i	2.26206	−	1.35488i
$749$	−71746.1	−	71746.1i	−0.127889	−	0.127889i
$750$	243949.	−	190319.i	0.433687	−	0.338345i
$751$		−	295687.i		−	0.524267i	−0.965032	−	0.262133i	$-0.915574\pi$
$751$		−	295687.i		−	0.524267i	0.965032	−	0.262133i	$-0.0844260\pi$
$752$	490827.	−	916915.i	0.867947	−	1.62141i
$753$	−137692.			−0.242840
$754$	−92383.2	−	118416.i	−0.162499	−	0.208289i
$755$	−692434.	+	692434.i	−1.21474	+	1.21474i
$756$	9541.22	−	5714.79i	0.0166940	−	0.00999901i
$757$	66501.9	−	66501.9i	0.116049	−	0.116049i	−0.646697	−	0.762747i	$-0.723850\pi$
$757$	66501.9	−	66501.9i	0.116049	−	0.116049i	0.762747	+	0.646697i	$0.223850\pi$
$758$	469756.	+	58012.3i	0.817587	+	0.100967i
$759$	−540583.			−0.938381
$760$	283341.	−	125440.i	0.490549	−	0.217174i
$761$			35555.3i			0.0613954i	0.999529	+	0.0306977i	$0.00977291\pi$
$761$			35555.3i			0.0613954i	−0.999529	+	0.0306977i	$0.990227\pi$
$762$	−49752.2	−	6144.12i	−0.0856845	−	0.0105816i
$763$	38944.6	+	38944.6i	0.0668957	+	0.0668957i
$764$	316802.	+	79458.4i	0.542752	+	0.136130i
$765$	−206963.	−	206963.i	−0.353648	−	0.353648i
$766$	−59913.6	−	76796.6i	−0.102110	−	0.130883i
$767$			173991.i			0.295757i
$768$	−333910.	−	66846.3i	−0.566118	−	0.113333i
$769$	828418.			1.40087			0.700433	−	0.713718i	$-0.252990\pi$
$769$	828418.			1.40087			0.700433	+	0.713718i	$0.252990\pi$
$770$	−90179.0	+	70354.1i	−0.152098	+	0.118661i
$771$	−160988.	+	160988.i	−0.270822	+	0.270822i
$772$	−133458.	+	532100.i	−0.223929	+	0.892809i
$773$	−430852.	+	430852.i	−0.721056	+	0.721056i	−0.968820	−	0.247764i	$-0.920304\pi$
$773$	−430852.	+	430852.i	−0.721056	+	0.721056i	0.247764	+	0.968820i	$0.420304\pi$
$774$	−9052.28	+	73301.0i	−0.0151104	+	0.122357i
$775$	2317.76			0.00385891
$776$	−1042.42	−	2354.60i	−0.00173109	−	0.00391015i
$777$			45613.7i			0.0755532i
$778$	−67551.5	+	547000.i	−0.111603	+	0.903709i
$779$	124176.	+	124176.i	0.204628	+	0.204628i
$780$	−34194.7	−	57090.3i	−0.0562043	−	0.0938368i
$781$	−368002.	−	368002.i	−0.603320	−	0.603320i
$782$	−616292.	+	480807.i	−1.00780	+	0.786243i
$783$		−	171425.i		−	0.279608i
$784$	536359.	+	287115.i	0.872617	+	0.467115i
$785$	−885770.			−1.43741
$786$	101853.	+	130554.i	0.164866	+	0.211323i
$787$	20555.3	−	20555.3i	0.0331876	−	0.0331876i	−0.690318	−	0.723506i	$-0.742529\pi$
$787$	20555.3	−	20555.3i	0.0331876	−	0.0331876i	0.723506	+	0.690318i	$0.242529\pi$
$788$	509155.	+	850067.i	0.819969	+	1.36899i
$789$	82377.9	−	82377.9i	0.132329	−	0.132329i
$790$	490581.	+	60584.1i	0.786062	+	0.0970743i
$791$	106476.			0.170177
$792$	357137.	+	137953.i	0.569357	+	0.219927i
$793$			138376.i			0.220046i
$794$	451953.	+	55813.7i	0.716890	+	0.0885319i
$795$	125533.	+	125533.i	0.198621	+	0.198621i
$796$	−32534.2	+	129714.i	−0.0513469	+	0.204721i
$797$	−233487.	−	233487.i	−0.367575	−	0.367575i	0.499017	−	0.866592i	$-0.333695\pi$
$797$	−233487.	−	233487.i	−0.367575	−	0.367575i	−0.866592	+	0.499017i	$0.833695\pi$
$798$	−11773.9	−	15091.6i	−0.0184890	−	0.0236990i
$799$			1.69071e6i			2.64835i
$800$	−9325.90	−	53993.1i	−0.0145717	−	0.0843643i
$801$	264739.			0.412623
$802$	702022.	−	547690.i	1.09145	−	0.851502i
$803$	133698.	−	133698.i	0.207346	−	0.207346i
$804$	−147859.	−	37085.2i	−0.228737	−	0.0573705i
$805$	42851.0	−	42851.0i	0.0661256	−	0.0661256i
$806$	−652.559	+	5284.12i	−0.00100450	+	0.00813396i
$807$	715153.			1.09813
$808$	196275.	+	75815.8i	0.300637	+	0.116128i
$809$		−	890223.i		−	1.36020i	−0.733121	−	0.680098i	$-0.761937\pi$
$809$		−	890223.i		−	1.36020i	0.733121	−	0.680098i	$-0.238063\pi$
$810$	9309.49	−	75383.9i	0.0141891	−	0.114897i
$811$	−6506.48	−	6506.48i	−0.00989246	−	0.00989246i	0.702143	−	0.712036i	$-0.252227\pi$
$811$	−6506.48	−	6506.48i	−0.00989246	−	0.00989246i	−0.712036	+	0.702143i	$0.752227\pi$
$812$	−83097.0	+	49771.7i	−0.126030	+	0.0754867i
$813$	29411.8	+	29411.8i	0.0444980	+	0.0444980i
$814$	−1.23801e6	+	965847.i	−1.86843	+	1.45767i
$815$			1.01137e6i			1.52264i
$816$	529852.	−	160373.i	0.795746	−	0.240852i
$817$	127113.			0.190435
$818$	74421.4	+	95392.5i	0.111222	+	0.142563i
$819$	−2906.76	+	2906.76i	−0.00433353	+	0.00433353i
$820$	337804.	−	202330.i	0.502385	−	0.300908i
$821$	821567.	−	821567.i	1.21887	−	1.21887i	0.250840	−	0.968029i	$-0.419293\pi$
$821$	821567.	−	821567.i	1.21887	−	1.21887i	0.968029	−	0.250840i	$-0.0807069\pi$
$822$	12912.8	+	1594.66i	0.0191107	+	0.00236007i
$823$	1.23284e6			1.82014			0.910072	−	0.414450i	$-0.136026\pi$
$823$	1.23284e6			1.82014			0.910072	+	0.414450i	$0.136026\pi$
$824$	247585.	+	559240.i	0.364645	+	0.823653i
$825$			61602.0i			0.0905079i
$826$	111367.	+	13753.2i	0.163228	+	0.0201578i
$827$	−14921.5	−	14921.5i	−0.0218173	−	0.0218173i	0.696114	−	0.717931i	$-0.254911\pi$
$827$	−14921.5	−	14921.5i	−0.0218173	−	0.0218173i	−0.717931	+	0.696114i	$0.754911\pi$
$828$	−196755.	−	49349.0i	−0.286989	−	0.0719810i
$829$	−616162.	−	616162.i	−0.896574	−	0.896574i	0.0985573	−	0.995131i	$-0.468577\pi$
$829$	−616162.	−	616162.i	−0.896574	−	0.896574i	−0.995131	+	0.0985573i	$0.968577\pi$
$830$	−632372.	−	810567.i	−0.917945	−	1.17661i
$831$			522085.i			0.756031i
$832$	125721.	−	6059.90i	0.181619	−	0.00875425i
$833$	−989000.			−1.42530
$834$	−81678.4	+	63722.3i	−0.117429	+	0.0916134i
$835$	−393780.	+	393780.i	−0.564782	+	0.564782i
$836$	160299.	−	639116.i	0.229361	−	0.914466i
$837$	−4297.12	+	4297.12i	−0.00613375	+	0.00613375i
$838$	50794.7	−	411311.i	0.0723319	−	0.585710i
$839$	−6191.93			−0.00879634			−0.00439817	−	0.999990i	$-0.501400\pi$
$839$	−6191.93			−0.00879634			−0.00439817	+	0.999990i	$0.501400\pi$
$840$	−39244.8	+	17374.4i	−0.0556191	+	0.0246235i
$841$			785701.i			1.11088i
$842$	−75302.9	+	609767.i	−0.106215	+	0.860082i
$843$	−162871.	−	162871.i	−0.229187	−	0.229187i
$844$	−124302.	−	207530.i	−0.174499	−	0.291337i
$845$	−508668.	−	508668.i	−0.712395	−	0.712395i
$846$	−345936.	+	269885.i	−0.483342	+	0.377084i
$847$			170674.i			0.237904i
$848$	−321381.	+	97273.8i	−0.446919	+	0.135271i
$849$	501343.			0.695536
$850$	54790.1	+	70229.3i	0.0758341	+	0.0972032i
$851$	588275.	−	588275.i	0.812309	−	0.812309i
$852$	−100347.	−	167535.i	−0.138237	−	0.230795i
$853$	−95729.9	+	95729.9i	−0.131568	+	0.131568i	−0.769824	−	0.638256i	$-0.779656\pi$
$853$	−95729.9	+	95729.9i	−0.131568	+	0.131568i	0.638256	+	0.769824i	$0.279656\pi$
$854$	88570.3	+	10937.9i	0.121443	+	0.0149975i
$855$	−130725.			−0.178824
$856$	472259.	−	1.22260e6i	0.644515	−	1.66855i
$857$			829527.i			1.12945i	0.825278	+	0.564727i	$0.191019\pi$
$857$			829527.i			1.12945i	−0.825278	+	0.564727i	$0.808981\pi$
$858$	−140442.	−	17343.9i	−0.190776	−	0.0235598i
$859$	−371817.	−	371817.i	−0.503898	−	0.503898i	0.408749	−	0.912647i	$-0.365965\pi$
$859$	−371817.	−	371817.i	−0.503898	−	0.503898i	−0.912647	+	0.408749i	$0.865965\pi$
$860$	69338.6	−	276454.i	0.0937515	−	0.373789i
$861$	−17199.3	−	17199.3i	−0.0232009	−	0.0232009i
$862$	512681.	+	657149.i	0.689974	+	0.884401i
$863$			111658.i			0.149923i	0.997186	+	0.0749617i	$0.0238835\pi$
$863$			111658.i			0.149923i	−0.997186	+	0.0749617i	$0.976117\pi$
$864$	117393.	+	82812.8i	0.157259	+	0.110935i
$865$	476395.			0.636700
$866$	350085.	−	273123.i	0.466808	−	0.364185i
$867$	−329482.	+	329482.i	−0.438322	+	0.438322i
$868$	3330.63	+	835.370i	0.00442066	+	0.00110876i
$869$	743251.	−	743251.i	0.984228	−	0.984228i
$870$	−81078.9	+	656538.i	−0.107120	+	0.867404i
$871$	56343.9			0.0742696
$872$	−256348.	+	663644.i	−0.337129	+	0.872775i
$873$			1086.34i			0.00142540i
$874$	−42788.7	+	346482.i	−0.0560152	+	0.453584i
$875$	52153.2	+	52153.2i	0.0681184	+	0.0681184i
$876$	60867.1	−	36456.9i	0.0793184	−	0.0475085i
$877$	118994.	+	118994.i	0.154713	+	0.154713i	0.780219	−	0.625506i	$-0.215107\pi$
$877$	118994.	+	118994.i	0.154713	+	0.154713i	−0.625506	+	0.780219i	$0.715107\pi$
$878$	114231.	−	89118.6i	0.148182	−	0.115606i
$879$		−	556542.i		−	0.720311i
$880$	−1.30255e6	−	697260.i	−1.68201	−	0.900387i
$881$	−735033.			−0.947011			−0.473505	−	0.880791i	$-0.657012\pi$
$881$	−735033.			−0.947011			−0.473505	+	0.880791i	$0.657012\pi$
$882$	−157872.	−	202359.i	−0.202940	−	0.260127i
$883$	177393.	−	177393.i	0.227518	−	0.227518i	−0.584137	−	0.811655i	$-0.698567\pi$
$883$	177393.	−	177393.i	0.227518	−	0.227518i	0.811655	+	0.584137i	$0.198567\pi$
$884$	−175537.	+	105140.i	−0.224629	+	0.134543i
$885$	541899.	−	541899.i	0.691881	−	0.691881i
$886$	−1.01727e6	−	125627.i	−1.29589	−	0.160035i
$887$	432025.			0.549113			0.274557	−	0.961571i	$-0.411469\pi$
$887$	432025.			0.549113			0.274557	+	0.961571i	$0.411469\pi$
$888$	−538767.	+	238522.i	−0.683243	+	0.302484i
$889$		−	11949.9i		−	0.0151203i
$890$	−1.01392e6	−	125214.i	−1.28005	−	0.158079i
$891$	−114210.	−	114210.i	−0.143863	−	0.143863i
$892$	−1.04858e6	−	262999.i	−1.31787	−	0.330540i
$893$	533955.	+	533955.i	0.669579	+	0.669579i
$894$	−382746.	−	490599.i	−0.478890	−	0.613835i
$895$		−	622753.i		−	0.777445i
$896$	6058.91	−	80949.7i	0.00754707	−	0.100832i
$897$	74976.5			0.0931837
$898$	25941.6	−	20238.6i	0.0321695	−	0.0250973i
$899$	37424.7	−	37424.7i	0.0463062	−	0.0463062i
$900$	−5623.55	+	22421.2i	−0.00694265	+	0.0276804i
$901$	385982.	−	385982.i	0.475463	−	0.475463i
$902$	102624.	−	830999.i	0.126135	−	1.02138i
$903$	−17606.1			−0.0215917
$904$	556783.	+	1.25765e6i	0.681316	+	1.53894i
$905$			805268.i			0.983204i
$906$	−95767.6	+	775480.i	−0.116671	+	0.944745i
$907$	−179624.	−	179624.i	−0.218348	−	0.218348i	0.589454	−	0.807802i	$-0.299343\pi$
$907$	−179624.	−	179624.i	−0.218348	−	0.218348i	−0.807802	+	0.589454i	$0.799343\pi$
$908$	−143388.	−	239395.i	−0.173916	−	0.290364i
$909$	−62767.2	−	62767.2i	−0.0759636	−	0.0759636i
$910$	12507.4	−	9757.79i	0.0151038	−	0.0117833i
$911$		−	373405.i		−	0.449929i	−0.974367	−	0.224964i	$-0.927773\pi$
$911$		−	373405.i		−	0.449929i	0.974367	−	0.224964i	$-0.0722266\pi$
$912$	116688.	−	217985.i	0.140293	−	0.262081i
$913$	−2.18611e6			−2.62259
$914$	−318395.	−	408115.i	−0.381131	−	0.488529i
$915$	430974.	−	430974.i	0.514765	−	0.514765i
$916$	−599319.	−	1.00060e6i	−0.714277	−	1.19253i
$917$	−27910.9	+	27910.9i	−0.0331921	+	0.0331921i
$918$	−231785.	−	28624.2i	−0.275043	−	0.0339663i
$919$	−663639.			−0.785779			−0.392890	−	0.919586i	$-0.628525\pi$
$919$	−663639.			−0.785779			−0.392890	+	0.919586i	$0.628525\pi$
$920$	730212.	+	282061.i	0.862727	+	0.333248i
$921$			42141.4i			0.0496809i
$922$	867586.	+	107142.i	1.02059	+	0.126037i
$923$	51040.2	+	51040.2i	0.0599113	+	0.0599113i
$924$	−22202.6	+	88522.3i	−0.0260052	+	0.103683i
$925$	−67036.6	−	67036.6i	−0.0783481	−	0.0783481i
$926$	−129977.	−	166603.i	−0.151581	−	0.194295i
$927$		−	258017.i		−	0.300253i
$928$	−1.02241e6	−	721239.i	−1.18721	−	0.837497i
$929$	1.65629e6			1.91913			0.959564	−	0.281489i	$-0.0908284\pi$
$929$	1.65629e6			1.91913			0.959564	+	0.281489i	$0.0908284\pi$
$930$	18489.9	−	14425.1i	0.0213781	−	0.0166783i
$931$	−312343.	+	312343.i	−0.360356	+	0.360356i
$932$	−900366.	−	225825.i	−1.03654	−	0.259980i
$933$	−40715.4	+	40715.4i	−0.0467730	+	0.0467730i
$934$	149778.	−	1.21283e6i	0.171693	−	1.39029i
$935$	2.40179e6			2.74734
$936$	−49533.3	−	19133.4i	−0.0565387	−	0.0218394i
$937$			156421.i			0.178163i	0.996024	+	0.0890813i	$0.0283931\pi$
$937$			156421.i			0.178163i	−0.996024	+	0.0890813i	$0.971607\pi$
$938$	4453.73	−	36064.2i	0.00506195	−	0.0409893i
$939$	−385193.	−	385193.i	−0.436865	−	0.436865i
$940$	1.45255e6	−	870015.i	1.64390	−	0.984625i
$941$	−898327.	−	898327.i	−1.01451	−	1.01451i	−0.999893	−	0.0146141i	$-0.995348\pi$
$941$	−898327.	−	898327.i	−1.01451	−	1.01451i	−0.0146141	−	0.999893i	$-0.504652\pi$
$942$	−557255.	+	434748.i	−0.627990	+	0.489932i
$943$			443637.i			0.498889i
$944$	419909.	+	1.38733e6i	0.471207	+	1.55681i
$945$	18106.4			0.0202753
$946$	−372801.	−	477851.i	−0.416576	−	0.533962i
$947$	727102.	−	727102.i	0.810766	−	0.810766i	−0.173983	−	0.984749i	$-0.555664\pi$
$947$	727102.	−	727102.i	0.810766	−	0.810766i	0.984749	+	0.173983i	$0.0556638\pi$
$948$	338370.	−	202670.i	0.376509	−	0.225513i
$949$	−18543.4	+	18543.4i	−0.0205900	+	0.0205900i
$950$	39483.2	+	4875.96i	0.0437487	+	0.00540273i
$951$	−574395.			−0.635111
$952$	53421.5	+	120667.i	0.0589444	+	0.133142i
$953$		−	4617.25i		−	0.00508391i	−0.999997	−	0.00254196i	$-0.999191\pi$
$953$		−	4617.25i		−	0.00508391i	0.999997	−	0.00254196i	$-0.000809130\pi$
$954$	140589.	+	17362.0i	0.154474	+	0.0190767i
$955$	375992.	+	375992.i	0.412260	+	0.412260i
$956$	771030.	+	193385.i	0.843637	+	0.211596i
$957$	994683.	+	994683.i	1.08608	+	1.08608i
$958$	−509388.	−	652928.i	−0.555032	−	0.711433i
$959$			3101.52i			0.00337238i
$960$	−410436.	−	372688.i	−0.445351	−	0.404393i
$961$	921645.			0.997968
$962$	171707.	−	133959.i	0.185540	−	0.144751i
$963$	−390979.	+	390979.i	−0.421601	+	0.421601i
$964$	−247341.	+	986154.i	−0.266160	+	1.06118i
$965$	−631515.	+	631515.i	−0.678155	+	0.678155i
$966$	5926.54	−	47990.3i	0.00635107	−	0.0514280i
$967$	−193818.			−0.207272			−0.103636	−	0.994615i	$-0.533048\pi$
$967$	−193818.			−0.207272			−0.103636	+	0.994615i	$0.533048\pi$
$968$	−2.01592e6	+	892484.i	−2.15141	+	0.952467i
$969$			401945.i			0.428074i
$970$	513.809	−	4160.58i	0.000546082	−	0.00442191i
$971$	−34311.3	−	34311.3i	−0.0363914	−	0.0363914i	0.688677	−	0.725068i	$-0.258192\pi$
$971$	−34311.3	−	34311.3i	−0.0363914	−	0.0363914i	−0.725068	+	0.688677i	$0.758192\pi$
$972$	−31142.7	−	51994.7i	−0.0329628	−	0.0550335i
$973$	−17461.8	−	17461.8i	−0.0184444	−	0.0184444i
$974$	−885756.	+	691031.i	−0.933675	+	0.728416i
$975$		−	8543.91i		−	0.00898768i
$976$	333955.	+	1.10335e6i	0.350581	+	1.15828i
$977$	1.66218e6			1.74136			0.870680	−	0.491849i	$-0.163679\pi$
$977$	1.66218e6			1.74136			0.870680	+	0.491849i	$0.163679\pi$
$978$	496396.	+	636275.i	0.518980	+	0.665223i
$979$	−1.53614e6	+	1.53614e6i	−1.60275	+	1.60275i
$980$	508925.	+	849682.i	0.529909	+	0.884717i
$981$	212228.	−	212228.i	0.220529	−	0.220529i
$982$	−213052.	−	26310.8i	−0.220934	−	0.0272842i
$983$	1.27450e6			1.31897			0.659483	−	0.751719i	$-0.270775\pi$
$983$	1.27450e6			1.31897			0.659483	+	0.751719i	$0.270775\pi$
$984$	113212.	−	293089.i	0.116924	−	0.302698i
$985$			1.61317e6i			1.66268i
$986$	2.01868e6	+	249296.i	2.07641	+	0.256426i
$987$	−73956.7	−	73956.7i	−0.0759177	−	0.0759177i
$988$	−22232.8	+	88642.5i	−0.0227762	+	0.0908089i
$989$	227064.	+	227064.i	0.232143	+	0.232143i
$990$	383394.	+	491429.i	0.391178	+	0.501407i
$991$			348237.i			0.354591i	0.984158	+	0.177295i	$0.0567348\pi$
$991$			348237.i			0.354591i	−0.984158	+	0.177295i	$0.943265\pi$
$992$	7549.44	+	43708.2i	0.00767170	+	0.0444160i
$993$	−447888.			−0.454225
$994$	36703.9	−	28634.9i	0.0371483	−	0.0289816i
$995$	−153950.	+	153950.i	−0.155501	+	0.155501i
$996$	−795676.	−	199567.i	−0.802080	−	0.201173i
$997$	70749.7	−	70749.7i	0.0711761	−	0.0711761i	−0.670623	−	0.741799i	$-0.733973\pi$
$997$	70749.7	−	70749.7i	0.0711761	−	0.0711761i	0.741799	+	0.670623i	$0.233973\pi$
$998$	−79397.5	+	642923.i	−0.0797160	+	0.645503i
$999$	248571.			0.249069

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	48.5.l.a.19.3	✓	32
3.2	odd	2		144.5.m.c.19.14		32
4.3	odd	2		192.5.l.a.175.14		32
8.3	odd	2		384.5.l.a.223.3		32
8.5	even	2		384.5.l.b.223.14		32
12.11	even	2		576.5.m.b.559.4		32
16.3	odd	4		384.5.l.b.31.14		32
16.5	even	4		192.5.l.a.79.14		32
16.11	odd	4	inner	48.5.l.a.43.3	yes	32
16.13	even	4		384.5.l.a.31.3		32
48.5	odd	4		576.5.m.b.271.4		32
48.11	even	4		144.5.m.c.91.14		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
48.5.l.a.19.3	✓	32	1.1	even	1	trivial
48.5.l.a.43.3	yes	32	16.11	odd	4	inner
144.5.m.c.19.14		32	3.2	odd	2
144.5.m.c.91.14		32	48.11	even	4
192.5.l.a.79.14		32	16.5	even	4
192.5.l.a.175.14		32	4.3	odd	2
384.5.l.a.31.3		32	16.13	even	4
384.5.l.a.223.3		32	8.3	odd	2
384.5.l.b.31.14		32	16.3	odd	4
384.5.l.b.223.14		32	8.5	even	2
576.5.m.b.271.4		32	48.5	odd	4
576.5.m.b.559.4		32	12.11	even	2

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:	\( N \)	\(=\)	\( 48 = 2^{4} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	48.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.15376 + 2.46044i) q^{2} +(-3.67423 + 3.67423i) q^{3} +(3.89246 - 15.5193i) q^{4} +(18.4189 - 18.4189i) q^{5} +(2.54743 - 20.6279i) q^{6} +4.95460 q^{7} +(25.9084 + 58.5214i) q^{8} -27.0000i q^{9} +O(q^{10})\)	\(q+(-3.15376 + 2.46044i) q^{2} +(-3.67423 + 3.67423i) q^{3} +(3.89246 - 15.5193i) q^{4} +(18.4189 - 18.4189i) q^{5} +(2.54743 - 20.6279i) q^{6} +4.95460 q^{7} +(25.9084 + 58.5214i) q^{8} -27.0000i q^{9} +(-12.7702 + 103.407i) q^{10} +(156.666 + 156.666i) q^{11} +(42.7197 + 71.3234i) q^{12} +(-21.7289 - 21.7289i) q^{13} +(-15.6256 + 12.1905i) q^{14} +135.350i q^{15} +(-225.697 - 120.817i) q^{16} +416.167 q^{17} +(66.4319 + 85.1516i) q^{18} +(131.432 - 131.432i) q^{19} +(-214.153 - 357.542i) q^{20} +(-18.2043 + 18.2043i) q^{21} +(-879.557 - 108.620i) q^{22} +469.559 q^{23} +(-310.215 - 119.828i) q^{24} -53.5084i q^{25} +(121.990 + 15.0652i) q^{26} +(99.2043 + 99.2043i) q^{27} +(19.2856 - 76.8919i) q^{28} +(-863.997 - 863.997i) q^{29} +(-333.022 - 426.863i) q^{30} +43.3158i q^{31} +(1009.06 - 174.288i) q^{32} -1151.26 q^{33} +(-1312.49 + 1023.95i) q^{34} +(91.2580 - 91.2580i) q^{35} +(-419.021 - 105.096i) q^{36} +(1252.82 - 1252.82i) q^{37} +(-91.1252 + 737.888i) q^{38} +159.674 q^{39} +(1555.10 + 600.694i) q^{40} +944.794i q^{41} +(12.6215 - 102.203i) q^{42} +(483.569 + 483.569i) q^{43} +(3041.17 - 1821.53i) q^{44} +(-497.309 - 497.309i) q^{45} +(-1480.88 + 1155.32i) q^{46} +4062.58i q^{47} +(1273.17 - 385.357i) q^{48} -2376.45 q^{49} +(131.654 + 168.753i) q^{50} +(-1529.09 + 1529.09i) q^{51} +(-421.796 + 252.638i) q^{52} +(927.469 - 927.469i) q^{53} +(-556.954 - 68.7807i) q^{54} +5771.23 q^{55} +(128.366 + 289.950i) q^{56} +965.827i q^{57} +(4850.66 + 599.030i) q^{58} +(-4003.67 - 4003.67i) q^{59} +(2100.54 + 526.846i) q^{60} +(-3184.14 - 3184.14i) q^{61} +(-106.576 - 136.608i) q^{62} -133.774i q^{63} +(-2753.51 + 3032.39i) q^{64} -800.443 q^{65} +(3630.79 - 2832.60i) q^{66} +(-1296.52 + 1296.52i) q^{67} +(1619.91 - 6458.61i) q^{68} +(-1725.27 + 1725.27i) q^{69} +(-63.2713 + 512.341i) q^{70} -2348.95 q^{71} +(1580.08 - 699.527i) q^{72} -853.396i q^{73} +(-868.612 + 7033.61i) q^{74} +(196.603 + 196.603i) q^{75} +(-1528.14 - 2551.33i) q^{76} +(776.218 + 776.218i) q^{77} +(-503.575 + 392.869i) q^{78} -4744.17i q^{79} +(-6382.39 + 1931.79i) q^{80} -729.000 q^{81} +(-2324.61 - 2979.66i) q^{82} +(-6976.97 + 6976.97i) q^{83} +(211.659 + 353.378i) q^{84} +(7665.31 - 7665.31i) q^{85} +(-2714.85 - 335.269i) q^{86} +6349.06 q^{87} +(-5109.35 + 13227.3i) q^{88} +9805.15i q^{89} +(2792.00 + 344.796i) q^{90} +(-107.658 - 107.658i) q^{91} +(1827.74 - 7287.23i) q^{92} +(-159.152 - 159.152i) q^{93} +(-9995.75 - 12812.4i) q^{94} -4841.67i q^{95} +(-3067.14 + 4347.90i) q^{96} -40.2349 q^{97} +(7494.77 - 5847.12i) q^{98} +(4229.99 - 4229.99i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 12 q^{4} + 180 q^{8}+O(q^{10}) \) 32 * q + 12 * q^4 + 180 * q^8	\( 32 q + 12 q^{4} + 180 q^{8} + 296 q^{10} - 192 q^{11} + 360 q^{12} - 156 q^{14} + 352 q^{16} - 324 q^{18} + 704 q^{19} - 1200 q^{20} - 1568 q^{22} - 2304 q^{23} + 1188 q^{24} + 2700 q^{26} + 4680 q^{28} - 1728 q^{29} + 1512 q^{30} - 3360 q^{32} - 9312 q^{34} - 5184 q^{35} - 756 q^{36} + 3648 q^{37} - 5880 q^{38} + 5232 q^{40} + 4500 q^{42} + 1088 q^{43} + 18840 q^{44} + 680 q^{46} + 2160 q^{48} + 10976 q^{49} - 25884 q^{50} - 4032 q^{51} - 25584 q^{52} + 960 q^{53} + 972 q^{54} + 11776 q^{55} + 15456 q^{56} + 12624 q^{58} + 13056 q^{59} + 7992 q^{60} + 3776 q^{61} + 21852 q^{62} - 8664 q^{64} + 4032 q^{65} - 8856 q^{66} - 896 q^{67} - 17280 q^{68} - 9792 q^{69} - 18240 q^{70} - 39936 q^{71} + 4860 q^{72} + 24204 q^{74} - 1152 q^{75} + 16776 q^{76} + 9408 q^{77} - 3780 q^{78} - 14232 q^{80} - 23328 q^{81} - 33800 q^{82} + 24000 q^{83} - 11448 q^{84} - 11200 q^{85} - 1200 q^{86} - 11424 q^{88} + 4104 q^{90} + 30528 q^{91} - 11664 q^{92} - 8040 q^{94} + 10080 q^{96} + 52968 q^{98} - 5184 q^{99}+O(q^{100}) \) 32 * q + 12 * q^4 + 180 * q^8 + 296 * q^10 - 192 * q^11 + 360 * q^12 - 156 * q^14 + 352 * q^16 - 324 * q^18 + 704 * q^19 - 1200 * q^20 - 1568 * q^22 - 2304 * q^23 + 1188 * q^24 + 2700 * q^26 + 4680 * q^28 - 1728 * q^29 + 1512 * q^30 - 3360 * q^32 - 9312 * q^34 - 5184 * q^35 - 756 * q^36 + 3648 * q^37 - 5880 * q^38 + 5232 * q^40 + 4500 * q^42 + 1088 * q^43 + 18840 * q^44 + 680 * q^46 + 2160 * q^48 + 10976 * q^49 - 25884 * q^50 - 4032 * q^51 - 25584 * q^52 + 960 * q^53 + 972 * q^54 + 11776 * q^55 + 15456 * q^56 + 12624 * q^58 + 13056 * q^59 + 7992 * q^60 + 3776 * q^61 + 21852 * q^62 - 8664 * q^64 + 4032 * q^65 - 8856 * q^66 - 896 * q^67 - 17280 * q^68 - 9792 * q^69 - 18240 * q^70 - 39936 * q^71 + 4860 * q^72 + 24204 * q^74 - 1152 * q^75 + 16776 * q^76 + 9408 * q^77 - 3780 * q^78 - 14232 * q^80 - 23328 * q^81 - 33800 * q^82 + 24000 * q^83 - 11448 * q^84 - 11200 * q^85 - 1200 * q^86 - 11424 * q^88 + 4104 * q^90 + 30528 * q^91 - 11664 * q^92 - 8040 * q^94 + 10080 * q^96 + 52968 * q^98 - 5184 * q^99

Introduction

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