LMFDB - Embedded newform 48.5.l.a.43.3

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			43.3
Character	$\chi$	$=$	48.43
Dual form			48.5.l.a.19.3

$q$-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 $\left(\mathbb{Z}/48\mathbb{Z}\right)^\times$.

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

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	0.971948	−	0.235194i	$-0.0755726\pi$
$5$	18.4189	+	18.4189i	0.736754	+	0.736754i	−0.235194	+	0.971948i	$0.575573\pi$
$6$	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	0.362957	−	0.931806i	$-0.381767\pi$
$11$	156.666	−	156.666i	1.29476	−	1.29476i	0.931806	−	0.362957i	$-0.118233\pi$
$12$	42.7197	−	71.3234i	0.296665	−	0.495301i
$13$	−21.7289	+	21.7289i	−0.128573	+	0.128573i	−0.768465	−	0.639892i	$-0.778979\pi$
$13$	−21.7289	+	21.7289i	−0.128573	+	0.128573i	0.639892	+	0.768465i	$0.278979\pi$
$14$	−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	0.865312	−	0.501234i	$-0.167120\pi$
$19$	131.432	+	131.432i	0.364079	+	0.364079i	−0.501234	+	0.865312i	$0.667120\pi$
$20$	−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	−0.0277296	+	0.999615i	$0.508828\pi$
$29$	−863.997	+	863.997i	−1.02735	+	1.02735i	−0.999615	+	0.0277296i	$0.991172\pi$
$30$	−333.022	+	426.863i	−0.370024	+	0.474292i
$31$		−	43.3158i		−	0.0450737i	−0.999746	−	0.0225368i	$-0.992826\pi$
$31$		−	43.3158i		−	0.0450737i	0.999746	−	0.0225368i	$-0.00717431\pi$
$32$	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	0.996671	−	0.0815331i	$-0.0259816\pi$
$37$	1252.82	+	1252.82i	0.915138	+	0.915138i	−0.0815331	+	0.996671i	$0.525982\pi$
$38$	−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	$-0.909327\pi$
$41$		−	944.794i		−	0.562043i	0.959702	−	0.281021i	$-0.0906732\pi$
$42$	12.6215	+	102.203i	0.00715505	+	0.0579382i
$43$	483.569	−	483.569i	0.261530	−	0.261530i	−0.564146	−	0.825675i	$-0.690794\pi$
$43$	483.569	−	483.569i	0.261530	−	0.261530i	0.825675	+	0.564146i	$0.190794\pi$
$44$	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	$-0.628551\pi$
$47$		−	4062.58i		−	1.83911i	0.392967	−	0.919553i	$-0.371449\pi$
$48$	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	0.852654	−	0.522476i	$-0.174992\pi$
$53$	927.469	+	927.469i	0.330178	+	0.330178i	−0.522476	+	0.852654i	$0.674992\pi$
$54$	−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	−0.163628	+	0.986522i	$0.552320\pi$
$59$	−4003.67	+	4003.67i	−1.15015	+	1.15015i	−0.986522	+	0.163628i	$0.947680\pi$
$60$	2100.54	−	526.846i	0.583484	−	0.146346i
$61$	−3184.14	+	3184.14i	−0.855721	+	0.855721i	−0.990831	−	0.135110i	$-0.956861\pi$
$61$	−3184.14	+	3184.14i	−0.855721	+	0.855721i	0.135110	+	0.990831i	$0.456861\pi$
$62$	−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	0.547793	−	0.836614i	$-0.315468\pi$
$67$	−1296.52	−	1296.52i	−0.288822	−	0.288822i	−0.836614	+	0.547793i	$0.815468\pi$
$68$	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	$0.0255147\pi$
$73$			853.396i			0.160142i	−0.996789	+	0.0800709i	$0.974485\pi$
$74$	−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	$0.124104\pi$
$79$			4744.17i			0.760161i	−0.924953	+	0.380081i	$0.875896\pi$
$80$	−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	−0.999917	−	0.0128527i	$-0.995909\pi$
$83$	−6976.97	−	6976.97i	−1.01277	−	1.01277i	−0.0128527	−	0.999917i	$-0.504091\pi$
$84$	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	$-0.787565\pi$
$89$		−	9805.15i		−	1.23787i	0.785443	−	0.618934i	$-0.212435\pi$
$90$	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	0.811811	−	0.583920i	$-0.198482\pi$
$101$	2324.71	+	2324.71i	0.227891	+	0.227891i	−0.583920	+	0.811811i	$0.698482\pi$
$102$	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	−0.316064	+	0.948738i	$0.602361\pi$
$107$	−14480.7	+	14480.7i	−1.26480	+	1.26480i	−0.948738	+	0.316064i	$0.897639\pi$
$108$	1925.73	+	1153.43i	0.165100	+	0.0988883i
$109$	7860.30	−	7860.30i	0.661586	−	0.661586i	−0.294168	−	0.955754i	$-0.595042\pi$
$109$	7860.30	−	7860.30i	0.661586	−	0.661586i	0.955754	+	0.294168i	$0.0950425\pi$
$110$	−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	$0.0238218\pi$
$127$			2411.89i			0.149537i	−0.997201	+	0.0747687i	$0.976178\pi$
$128$	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	0.523662	−	0.851926i	$-0.324565\pi$
$131$	−5633.33	−	5633.33i	−0.328264	−	0.328264i	−0.851926	+	0.523662i	$0.824565\pi$
$132$	−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	$-0.994692\pi$
$137$		−	625.988i		−	0.0333522i	0.999861	−	0.0166761i	$-0.00530842\pi$
$138$	1196.17	+	9686.02i	0.0628109	+	0.508613i
$139$	−3524.37	+	3524.37i	−0.182411	+	0.182411i	−0.792406	−	0.609994i	$-0.791172\pi$
$139$	−3524.37	+	3524.37i	−0.182411	+	0.182411i	0.609994	+	0.792406i	$0.291172\pi$
$140$	−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	0.998967	−	0.0454500i	$-0.0144722\pi$
$149$	21169.0	+	21169.0i	0.953517	+	0.953517i	−0.0454500	+	0.998967i	$0.514472\pi$
$150$	−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	−0.999707	−	0.0242036i	$-0.992295\pi$
$157$	−24045.2	+	24045.2i	−0.975503	+	0.975503i	0.0242036	+	0.999707i	$0.492295\pi$
$158$	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	−0.999425	−	0.0339160i	$-0.989202\pi$
$163$	−27454.8	−	27454.8i	−1.03334	−	1.03334i	−0.0339160	−	0.999425i	$-0.510798\pi$
$164$	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	−0.457243	−	0.889342i	$-0.651163\pi$
$173$	12932.3	−	12932.3i	0.432098	−	0.432098i	0.889342	+	0.457243i	$0.151163\pi$
$174$	−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	0.919860	−	0.392246i	$-0.128302\pi$
$179$	16905.3	+	16905.3i	0.527615	+	0.527615i	−0.392246	+	0.919860i	$0.628302\pi$
$180$	−9653.65	−	5782.13i	−0.297952	−	0.178461i
$181$	−21859.9	−	21859.9i	−0.667253	−	0.667253i	0.289826	−	0.957079i	$-0.406403\pi$
$181$	−21859.9	−	21859.9i	−0.667253	−	0.667253i	−0.957079	+	0.289826i	$0.906403\pi$
$182$	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	$-0.909738\pi$
$191$		−	20413.4i		−	0.559563i	0.960064	−	0.279781i	$-0.0902620\pi$
$192$	−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	−0.990441	−	0.137940i	$-0.955952\pi$
$197$	−43791.3	−	43791.3i	−1.12838	−	1.12838i	−0.137940	−	0.990441i	$-0.544048\pi$
$198$	−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	0.816905	−	0.576772i	$-0.195688\pi$
$211$	10690.9	+	10690.9i	0.240132	+	0.240132i	−0.576772	+	0.816905i	$0.695688\pi$
$212$	−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	$0.237736\pi$
$223$			67566.3i			1.35869i	−0.733819	+	0.679345i	$0.762264\pi$
$224$	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	0.816573	−	0.577242i	$-0.195871\pi$
$227$	12332.5	+	12332.5i	0.239331	+	0.239331i	−0.577242	+	0.816573i	$0.695871\pi$
$228$	14989.0	−	3759.44i	0.288338	−	0.0723192i
$229$	51546.1	+	51546.1i	0.982936	+	0.982936i	0.999857	−	0.0169210i	$-0.00538638\pi$
$229$	51546.1	+	51546.1i	0.982936	+	0.982936i	−0.0169210	+	0.999857i	$0.505386\pi$
$230$	−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	$0.179434\pi$
$233$			58015.9i			1.06865i	−0.845279	+	0.534325i	$0.820566\pi$
$234$	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	$-0.856789\pi$
$239$		−	49682.0i		−	0.869767i	0.900487	−	0.434884i	$-0.143211\pi$
$240$	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	−0.542584	−	0.840001i	$-0.682554\pi$
$251$	18737.6	−	18737.6i	0.297417	−	0.297417i	0.840001	+	0.542584i	$0.182554\pi$
$252$	−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	−0.453841	+	0.891083i	$0.649947\pi$
$269$	−97320.0	+	97320.0i	−1.34492	+	1.34492i	−0.891083	+	0.453841i	$0.850053\pi$
$270$	−11525.3	−	8991.58i	−0.158097	−	0.123341i
$271$			8004.88i			0.108997i	0.998514	+	0.0544987i	$0.0173561\pi$
$271$			8004.88i			0.108997i	−0.998514	+	0.0544987i	$0.982644\pi$
$272$	−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	0.997441	−	0.0714963i	$-0.0227774\pi$
$277$	71046.8	+	71046.8i	0.925945	+	0.925945i	−0.0714963	+	0.997441i	$0.522777\pi$
$278$	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	$-0.909435\pi$
$281$		−	44327.9i		−	0.561390i	0.959797	−	0.280695i	$-0.0905650\pi$
$282$	83802.6	−	10349.2i	1.05380	−	0.130139i
$283$	−68224.1	+	68224.1i	−0.851854	+	0.851854i	−0.990361	−	0.138508i	$-0.955769\pi$
$283$	−68224.1	+	68224.1i	−0.851854	+	0.851854i	0.138508	+	0.990361i	$0.455769\pi$
$284$	−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	0.111560	−	0.993758i	$-0.464415\pi$
$293$	−75735.7	−	75735.7i	−0.882197	−	0.882197i	−0.993758	+	0.111560i	$0.964415\pi$
$294$	−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	0.736875	−	0.676029i	$-0.236301\pi$
$307$	5734.72	+	5734.72i	0.0608465	+	0.0608465i	−0.676029	+	0.736875i	$0.736301\pi$
$308$	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	$-0.820293\pi$
$313$		−	104836.i		−	1.07010i	0.844821	−	0.535049i	$-0.179707\pi$
$314$	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	−0.201616	−	0.979465i	$-0.564619\pi$
$317$	78165.3	−	78165.3i	0.777849	−	0.777849i	0.979465	+	0.201616i	$0.0646192\pi$
$318$	−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	−0.371945	−	0.928255i	$-0.621309\pi$
$331$	60949.9	−	60949.9i	0.556310	−	0.556310i	0.928255	+	0.371945i	$0.121309\pi$
$332$	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	−0.785735	−	0.618563i	$-0.787715\pi$
$347$	−20129.0	+	20129.0i	−0.167172	+	0.167172i	0.618563	+	0.785735i	$0.287715\pi$
$348$	24713.5	+	98532.9i	0.204068	+	0.813622i
$349$	−5475.74	+	5475.74i	−0.0449565	+	0.0449565i	−0.729228	−	0.684271i	$-0.760120\pi$
$349$	−5475.74	+	5475.74i	−0.0449565	+	0.0449565i	0.684271	+	0.729228i	$0.260120\pi$
$350$	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	$-0.903125\pi$
$367$		−	80723.3i		−	0.599331i	0.954044	−	0.299666i	$-0.0968751\pi$
$368$	−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	0.986529	−	0.163589i	$-0.0523071\pi$
$373$	114495.	+	114495.i	0.822940	+	0.822940i	−0.163589	+	0.986529i	$0.552307\pi$
$374$	−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	−0.935593	−	0.353080i	$-0.885134\pi$
$379$	−83672.7	+	83672.7i	−0.582513	+	0.582513i	0.353080	+	0.935593i	$0.385134\pi$
$380$	−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	$-0.973549\pi$
$383$		−	24350.8i		−	0.166003i	0.996549	−	0.0830014i	$-0.0264506\pi$
$384$	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	0.951505	−	0.307632i	$-0.0995367\pi$
$389$	97431.5	+	97431.5i	0.643873	+	0.643873i	−0.307632	+	0.951505i	$0.599537\pi$
$390$	−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	−0.914762	−	0.403994i	$-0.867622\pi$
$397$	−80501.7	+	80501.7i	−0.510768	+	0.510768i	0.403994	+	0.914762i	$0.367622\pi$
$398$	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	$0.0288172\pi$
$409$			30247.2i			0.180817i	−0.995905	+	0.0904083i	$0.971183\pi$
$410$	−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	0.466968	−	0.884274i	$-0.345346\pi$
$419$	−73262.6	−	73262.6i	−0.417305	−	0.417305i	−0.884274	+	0.466968i	$0.845346\pi$
$420$	10407.3	−	2610.31i	0.0589985	−	0.0147977i
$421$	108612.	+	108612.i	0.612790	+	0.612790i	0.943672	−	0.330882i	$-0.107346\pi$
$421$	108612.	+	108612.i	0.612790	+	0.612790i	−0.330882	+	0.943672i	$0.607346\pi$
$422$	−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	$0.189527\pi$
$431$			208370.i			1.12171i	−0.827915	+	0.560854i	$0.810473\pi$
$432$	−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	−0.0739673	−	0.997261i	$-0.523566\pi$
$443$	181195.	−	181195.i	0.923293	−	0.923293i	0.997261	+	0.0739673i	$0.0235660\pi$
$444$	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	$-0.899736\pi$
$457$		−	129406.i		−	0.619613i	0.950800	−	0.309807i	$-0.100264\pi$
$458$	−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	−0.970051	−	0.242903i	$-0.921900\pi$
$461$	−154534.	+	154534.i	−0.727147	+	0.727147i	0.242903	+	0.970051i	$0.421900\pi$
$462$	17989.1	+	14034.4i	0.0842803	+	0.0657521i
$463$		−	52826.9i		−	0.246430i	−0.992380	−	0.123215i	$-0.960680\pi$
$463$		−	52826.9i		−	0.246430i	0.992380	−	0.123215i	$-0.0393204\pi$
$464$	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	0.00940448	−	0.999956i	$-0.497006\pi$
$467$	−216028.	−	216028.i	−0.990551	−	0.990551i	−0.999956	+	0.00940448i	$0.997006\pi$
$468$	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	$-0.851009\pi$
$479$		−	207031.i		−	0.902329i	0.892441	−	0.451165i	$-0.148991\pi$
$480$	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	−0.624007	−	0.781418i	$-0.714497\pi$
$491$	37948.8	−	37948.8i	0.157411	−	0.157411i	0.781418	+	0.624007i	$0.214497\pi$
$492$	−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	0.898625	−	0.438718i	$-0.144567\pi$
$499$	114517.	+	114517.i	0.459907	+	0.459907i	−0.438718	+	0.898625i	$0.644567\pi$
$500$	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	−0.934097	−	0.357019i	$-0.883793\pi$
$509$	−149510.	+	149510.i	−0.577077	+	0.577077i	0.357019	+	0.934097i	$0.383793\pi$
$510$	−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	$0.257395\pi$
$521$			392690.i			1.44668i	−0.690490	+	0.723342i	$0.742605\pi$
$522$	16173.8	+	130968.i	0.0593569	+	0.480644i
$523$	−131519.	+	131519.i	−0.480825	+	0.480825i	−0.905395	−	0.424570i	$-0.860425\pi$
$523$	−131519.	+	131519.i	−0.480825	+	0.480825i	0.424570	+	0.905395i	$0.360425\pi$
$524$	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	−0.482350	−	0.875979i	$-0.660217\pi$
$541$	115208.	−	115208.i	0.393629	−	0.393629i	0.875979	+	0.482350i	$0.160217\pi$
$542$	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	0.397466	−	0.917617i	$-0.369890\pi$
$547$	−155634.	−	155634.i	−0.520151	−	0.520151i	−0.917617	+	0.397466i	$0.869890\pi$
$548$	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	−0.451629	−	0.892206i	$-0.649157\pi$
$557$	136688.	−	136688.i	0.440576	−	0.440576i	0.892206	+	0.451629i	$0.149157\pi$
$558$	−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	0.984991	−	0.172607i	$-0.0552192\pi$
$563$	257500.	+	257500.i	0.812383	+	0.812383i	−0.172607	+	0.984991i	$0.555219\pi$
$564$	−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	$-0.761388\pi$
$569$		−	441198.i		−	1.36273i	0.731946	−	0.681363i	$-0.238612\pi$
$570$	−99873.5	+	12333.8i	−0.307398	+	0.0379619i
$571$	138592.	−	138592.i	0.425076	−	0.425076i	−0.461871	−	0.886947i	$-0.652822\pi$
$571$	138592.	−	138592.i	0.425076	−	0.425076i	0.886947	+	0.461871i	$0.152822\pi$
$572$	−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	−0.292763	−	0.956185i	$-0.594575\pi$
$587$	228595.	−	228595.i	0.663422	−	0.663422i	0.956185	+	0.292763i	$0.0945747\pi$
$588$	−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	$-0.964070\pi$
$601$		−	81370.9i		−	0.225279i	0.993636	−	0.112639i	$-0.0359305\pi$
$602$	−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	$-0.876530\pi$
$607$		−	278722.i		−	0.756474i	0.925709	−	0.378237i	$-0.123470\pi$
$608$	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	0.0735612	−	0.997291i	$-0.476564\pi$
$613$	−347109.	−	347109.i	−0.923729	−	0.923729i	−0.997291	+	0.0735612i	$0.976564\pi$
$614$	−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	$0.0263349\pi$
$617$			62919.7i			0.165279i	−0.996580	+	0.0826393i	$0.973665\pi$
$618$	24343.7	+	197124.i	0.0637396	+	0.516133i
$619$	81462.2	−	81462.2i	0.212606	−	0.212606i	−0.592768	−	0.805373i	$-0.701965\pi$
$619$	81462.2	−	81462.2i	0.212606	−	0.212606i	0.805373	+	0.592768i	$0.201965\pi$
$620$	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	0.843426	+	0.537245i	$0.180535\pi$
$643$	570837.	+	570837.i	1.38067	+	1.38067i	0.537245	+	0.843426i	$0.319465\pi$
$644$	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	−0.450558	−	0.892747i	$-0.648775\pi$
$653$	188553.	−	188553.i	0.442189	−	0.442189i	0.892747	+	0.450558i	$0.148775\pi$
$654$	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	−0.986760	−	0.162188i	$-0.948145\pi$
$659$	−498966.	−	498966.i	−1.14895	−	1.14895i	−0.162188	−	0.986760i	$-0.551855\pi$
$660$	246545.	−	411623.i	0.565990	−	0.944957i
$661$	−481399.	−	481399.i	−1.10180	−	1.10180i	−0.994194	−	0.107606i	$-0.965682\pi$
$661$	−481399.	−	481399.i	−1.10180	−	1.10180i	−0.107606	−	0.994194i	$-0.534318\pi$
$662$	−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	0.122493	−	0.992469i	$-0.460911\pi$
$677$	−398735.	−	398735.i	−0.869976	−	0.869976i	−0.992469	+	0.122493i	$0.960911\pi$
$678$	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	−0.417234	−	0.908799i	$-0.637001\pi$
$683$	229310.	−	229310.i	0.491565	−	0.491565i	0.908799	+	0.417234i	$0.137001\pi$
$684$	−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	0.925139	−	0.379627i	$-0.123948\pi$
$691$	260472.	+	260472.i	0.545512	+	0.545512i	−0.379627	+	0.925139i	$0.623948\pi$
$692$	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	−0.675547	−	0.737317i	$-0.736093\pi$
$701$	30353.7	−	30353.7i	0.0617697	−	0.0617697i	0.737317	+	0.675547i	$0.236093\pi$
$702$	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	0.523964	−	0.851740i	$-0.324453\pi$
$709$	−164767.	−	164767.i	−0.327776	−	0.327776i	−0.851740	+	0.523964i	$0.824453\pi$
$710$	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	$0.118269\pi$
$719$			375380.i			0.726127i	−0.931764	+	0.363064i	$0.881731\pi$
$720$	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	−0.494605	−	0.869118i	$-0.664687\pi$
$733$	201222.	−	201222.i	0.374513	−	0.374513i	0.869118	+	0.494605i	$0.164687\pi$
$734$	−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	0.758851	−	0.651264i	$-0.225761\pi$
$739$	58755.9	+	58755.9i	0.107588	+	0.107588i	−0.651264	+	0.758851i	$0.725761\pi$
$740$	−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	$0.0844260\pi$
$751$			295687.i			0.524267i	−0.965032	+	0.262133i	$0.915574\pi$
$752$	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	0.762747	−	0.646697i	$-0.223850\pi$
$757$	66501.9	+	66501.9i	0.116049	+	0.116049i	−0.646697	+	0.762747i	$0.723850\pi$
$758$	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	$-0.990227\pi$
$761$		−	35555.3i		−	0.0613954i	0.999529	−	0.0306977i	$-0.00977291\pi$
$762$	−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	0.247764	−	0.968820i	$-0.420304\pi$
$773$	−430852.	−	430852.i	−0.721056	−	0.721056i	−0.968820	+	0.247764i	$0.920304\pi$
$774$	−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	0.723506	−	0.690318i	$-0.242529\pi$
$787$	20555.3	+	20555.3i	0.0331876	+	0.0331876i	−0.690318	+	0.723506i	$0.742529\pi$
$788$	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	−0.866592	−	0.499017i	$-0.833695\pi$
$797$	−233487.	+	233487.i	−0.367575	+	0.367575i	0.499017	+	0.866592i	$0.333695\pi$
$798$	−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	$0.238063\pi$
$809$			890223.i			1.36020i	−0.733121	+	0.680098i	$0.761937\pi$
$810$	9309.49	+	75383.9i	0.0141891	+	0.114897i
$811$	−6506.48	+	6506.48i	−0.00989246	+	0.00989246i	−0.712036	−	0.702143i	$-0.752227\pi$
$811$	−6506.48	+	6506.48i	−0.00989246	+	0.00989246i	0.702143	+	0.712036i	$0.252227\pi$
$812$	−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	0.968029	+	0.250840i	$0.0807069\pi$
$821$	821567.	+	821567.i	1.21887	+	1.21887i	0.250840	+	0.968029i	$0.419293\pi$
$822$	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	−0.717931	−	0.696114i	$-0.754911\pi$
$827$	−14921.5	+	14921.5i	−0.0218173	+	0.0218173i	0.696114	+	0.717931i	$0.254911\pi$
$828$	−196755.	+	49349.0i	−0.286989	+	0.0719810i
$829$	−616162.	+	616162.i	−0.896574	+	0.896574i	−0.995131	−	0.0985573i	$-0.968577\pi$
$829$	−616162.	+	616162.i	−0.896574	+	0.896574i	0.0985573	+	0.995131i	$0.468577\pi$
$830$	−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	0.638256	−	0.769824i	$-0.279656\pi$
$853$	−95729.9	−	95729.9i	−0.131568	−	0.131568i	−0.769824	+	0.638256i	$0.779656\pi$
$854$	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	$-0.808981\pi$
$857$		−	829527.i		−	1.12945i	0.825278	−	0.564727i	$-0.191019\pi$
$858$	−140442.	+	17343.9i	−0.190776	+	0.0235598i
$859$	−371817.	+	371817.i	−0.503898	+	0.503898i	−0.912647	−	0.408749i	$-0.865965\pi$
$859$	−371817.	+	371817.i	−0.503898	+	0.503898i	0.408749	+	0.912647i	$0.365965\pi$
$860$	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	$-0.976117\pi$
$863$		−	111658.i		−	0.149923i	0.997186	−	0.0749617i	$-0.0238835\pi$
$864$	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	−0.625506	−	0.780219i	$-0.715107\pi$
$877$	118994.	−	118994.i	0.154713	−	0.154713i	0.780219	+	0.625506i	$0.215107\pi$
$878$	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	0.811655	−	0.584137i	$-0.198567\pi$
$883$	177393.	+	177393.i	0.227518	+	0.227518i	−0.584137	+	0.811655i	$0.698567\pi$
$884$	−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	−0.807802	−	0.589454i	$-0.799343\pi$
$907$	−179624.	+	179624.i	−0.218348	+	0.218348i	0.589454	+	0.807802i	$0.299343\pi$
$908$	−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	$0.0722266\pi$
$911$			373405.i			0.449929i	−0.974367	+	0.224964i	$0.927773\pi$
$912$	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	$-0.971607\pi$
$937$		−	156421.i		−	0.178163i	0.996024	−	0.0890813i	$-0.0283931\pi$
$938$	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	−0.0146141	+	0.999893i	$0.504652\pi$
$941$	−898327.	+	898327.i	−1.01451	+	1.01451i	−0.999893	+	0.0146141i	$0.995348\pi$
$942$	−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	0.984749	−	0.173983i	$-0.0556638\pi$
$947$	727102.	+	727102.i	0.810766	+	0.810766i	−0.173983	+	0.984749i	$0.555664\pi$
$948$	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	$0.000809130\pi$
$953$			4617.25i			0.00508391i	−0.999997	+	0.00254196i	$0.999191\pi$
$954$	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	−0.725068	−	0.688677i	$-0.758192\pi$
$971$	−34311.3	+	34311.3i	−0.0363914	+	0.0363914i	0.688677	+	0.725068i	$0.258192\pi$
$972$	−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	$-0.943265\pi$
$991$		−	348237.i		−	0.354591i	0.984158	−	0.177295i	$-0.0567348\pi$
$992$	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	0.741799	−	0.670623i	$-0.233973\pi$
$997$	70749.7	+	70749.7i	0.0711761	+	0.0711761i	−0.670623	+	0.741799i	$0.733973\pi$
$998$	−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.43.3	yes	32
3.2	odd	2		144.5.m.c.91.14		32
4.3	odd	2		192.5.l.a.79.14		32
8.3	odd	2		384.5.l.a.31.3		32
8.5	even	2		384.5.l.b.31.14		32
12.11	even	2		576.5.m.b.271.4		32
16.3	odd	4	inner	48.5.l.a.19.3	✓	32
16.5	even	4		384.5.l.a.223.3		32
16.11	odd	4		384.5.l.b.223.14		32
16.13	even	4		192.5.l.a.175.14		32
48.29	odd	4		576.5.m.b.559.4		32
48.35	even	4		144.5.m.c.19.14		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
48.5.l.a.19.3	✓	32	16.3	odd	4	inner
48.5.l.a.43.3	yes	32	1.1	even	1	trivial
144.5.m.c.19.14		32	48.35	even	4
144.5.m.c.91.14		32	3.2	odd	2
192.5.l.a.79.14		32	4.3	odd	2
192.5.l.a.175.14		32	16.13	even	4
384.5.l.a.31.3		32	8.3	odd	2
384.5.l.a.223.3		32	16.5	even	4
384.5.l.b.31.14		32	8.5	even	2
384.5.l.b.223.14		32	16.11	odd	4
576.5.m.b.271.4		32	12.11	even	2
576.5.m.b.559.4		32	48.29	odd	4

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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