LMFDB - Embedded newform 15.5.f.a.13.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [15,5,Mod(7,15)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(15, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("15.7");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 15 = 3 \cdot 5 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	15.f (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:	$1.55054944626$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 60x^{5} + 1973x^{4} - 3300x^{3} + 1800x^{2} + 31560x + 276676 $ x^8 - 60x^5 + 1973x^4 - 3300x^3 + 1800x^2 + 31560*x + 276676
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			13.4
Root			$3.80336 - 3.80336i$ of defining polynomial
Character	$\chi$	$=$	15.13
Dual form			15.5.f.a.7.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.80336 - 3.80336i) q^{2} +(-3.67423 - 3.67423i) q^{3} -12.9311i q^{4} +(6.56915 + 24.1215i) q^{5} -27.9489 q^{6} +(16.6149 - 16.6149i) q^{7} +(11.6720 + 11.6720i) q^{8} +27.0000i q^{9} +O(q^{10})$	\(q+(3.80336 - 3.80336i) q^{2} +(-3.67423 - 3.67423i) q^{3} -12.9311i q^{4} +(6.56915 + 24.1215i) q^{5} -27.9489 q^{6} +(16.6149 - 16.6149i) q^{7} +(11.6720 + 11.6720i) q^{8} +27.0000i q^{9} +(116.728 + 66.7579i) q^{10} -215.278 q^{11} +(-47.5121 + 47.5121i) q^{12} +(-29.9347 - 29.9347i) q^{13} -126.385i q^{14} +(64.4914 - 112.765i) q^{15} +295.684 q^{16} +(-3.97694 + 3.97694i) q^{17} +(102.691 + 102.691i) q^{18} -604.349i q^{19} +(311.919 - 84.9467i) q^{20} -122.094 q^{21} +(-818.782 + 818.782i) q^{22} +(376.379 + 376.379i) q^{23} -85.7710i q^{24} +(-538.692 + 316.916i) q^{25} -227.705 q^{26} +(99.2043 - 99.2043i) q^{27} +(-214.850 - 214.850i) q^{28} +624.166i q^{29} +(-183.601 - 674.169i) q^{30} +263.888 q^{31} +(937.842 - 937.842i) q^{32} +(790.983 + 790.983i) q^{33} +30.2515i q^{34} +(509.922 + 291.630i) q^{35} +349.141 q^{36} +(979.613 - 979.613i) q^{37} +(-2298.56 - 2298.56i) q^{38} +219.974i q^{39} +(-204.870 + 358.220i) q^{40} -1579.25 q^{41} +(-464.368 + 464.368i) q^{42} +(-30.8409 - 30.8409i) q^{43} +2783.80i q^{44} +(-651.280 + 177.367i) q^{45} +2863.01 q^{46} +(1785.16 - 1785.16i) q^{47} +(-1086.41 - 1086.41i) q^{48} +1848.89i q^{49} +(-843.498 + 3254.19i) q^{50} +29.2245 q^{51} +(-387.089 + 387.089i) q^{52} +(707.912 + 707.912i) q^{53} -754.620i q^{54} +(-1414.20 - 5192.84i) q^{55} +387.857 q^{56} +(-2220.52 + 2220.52i) q^{57} +(2373.93 + 2373.93i) q^{58} -1366.84i q^{59} +(-1458.18 - 833.948i) q^{60} -2983.71 q^{61} +(1003.66 - 1003.66i) q^{62} +(448.602 + 448.602i) q^{63} -2402.96i q^{64} +(525.423 - 918.714i) q^{65} +6016.80 q^{66} +(-986.003 + 986.003i) q^{67} +(51.4265 + 51.4265i) q^{68} -2765.81i q^{69} +(3048.59 - 830.242i) q^{70} +68.0686 q^{71} +(-315.143 + 315.143i) q^{72} +(2476.90 + 2476.90i) q^{73} -7451.65i q^{74} +(3143.70 + 814.860i) q^{75} -7814.93 q^{76} +(-3576.83 + 3576.83i) q^{77} +(836.641 + 836.641i) q^{78} +6047.25i q^{79} +(1942.39 + 7132.33i) q^{80} -729.000 q^{81} +(-6006.45 + 6006.45i) q^{82} +(-5158.95 - 5158.95i) q^{83} +1578.82i q^{84} +(-122.055 - 69.8047i) q^{85} -234.598 q^{86} +(2293.33 - 2293.33i) q^{87} +(-2512.72 - 2512.72i) q^{88} +7028.50i q^{89} +(-1802.46 + 3151.65i) q^{90} -994.722 q^{91} +(4867.01 - 4867.01i) q^{92} +(-969.586 - 969.586i) q^{93} -13579.2i q^{94} +(14577.8 - 3970.06i) q^{95} -6891.70 q^{96} +(10869.3 - 10869.3i) q^{97} +(7032.00 + 7032.00i) q^{98} -5812.52i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 84 q^{5} + 36 q^{6} + 20 q^{7} + 180 q^{8}+O(q^{10}) $ 8 * q - 84 * q^5 + 36 * q^6 + 20 * q^7 + 180 * q^8	\( 8 q - 84 q^{5} + 36 q^{6} + 20 q^{7} + 180 q^{8} + 104 q^{10} - 288 q^{11} - 360 q^{12} - 340 q^{13} + 144 q^{15} + 620 q^{16} + 900 q^{17} + 564 q^{20} + 792 q^{21} - 1100 q^{22} - 1560 q^{23} - 1204 q^{25} - 3024 q^{26} + 3580 q^{28} - 2664 q^{30} - 512 q^{31} + 4980 q^{32} + 2700 q^{33} + 6600 q^{35} + 2484 q^{36} - 3820 q^{37} - 7680 q^{38} - 2952 q^{40} - 2712 q^{41} - 7380 q^{42} - 1240 q^{43} - 1944 q^{45} + 13528 q^{46} + 4800 q^{47} + 3600 q^{48} + 3744 q^{50} + 6264 q^{51} - 1240 q^{52} + 1020 q^{53} - 3644 q^{55} - 30720 q^{56} - 5400 q^{57} + 2340 q^{58} - 1044 q^{60} - 4760 q^{61} + 28680 q^{62} + 540 q^{63} - 1212 q^{65} + 10008 q^{66} - 8920 q^{67} - 1920 q^{68} + 7380 q^{70} + 7536 q^{71} - 4860 q^{72} + 11600 q^{73} - 5976 q^{75} + 4344 q^{76} - 360 q^{77} - 4680 q^{78} + 10644 q^{80} - 5832 q^{81} - 27200 q^{82} - 32400 q^{83} - 15628 q^{85} + 14592 q^{86} + 10620 q^{87} - 14340 q^{88} + 8964 q^{90} + 16528 q^{91} - 31800 q^{92} + 14040 q^{93} + 18864 q^{95} - 4068 q^{96} + 58640 q^{97} + 46440 q^{98}+O(q^{100}) \) 8 * q - 84 * q^5 + 36 * q^6 + 20 * q^7 + 180 * q^8 + 104 * q^10 - 288 * q^11 - 360 * q^12 - 340 * q^13 + 144 * q^15 + 620 * q^16 + 900 * q^17 + 564 * q^20 + 792 * q^21 - 1100 * q^22 - 1560 * q^23 - 1204 * q^25 - 3024 * q^26 + 3580 * q^28 - 2664 * q^30 - 512 * q^31 + 4980 * q^32 + 2700 * q^33 + 6600 * q^35 + 2484 * q^36 - 3820 * q^37 - 7680 * q^38 - 2952 * q^40 - 2712 * q^41 - 7380 * q^42 - 1240 * q^43 - 1944 * q^45 + 13528 * q^46 + 4800 * q^47 + 3600 * q^48 + 3744 * q^50 + 6264 * q^51 - 1240 * q^52 + 1020 * q^53 - 3644 * q^55 - 30720 * q^56 - 5400 * q^57 + 2340 * q^58 - 1044 * q^60 - 4760 * q^61 + 28680 * q^62 + 540 * q^63 - 1212 * q^65 + 10008 * q^66 - 8920 * q^67 - 1920 * q^68 + 7380 * q^70 + 7536 * q^71 - 4860 * q^72 + 11600 * q^73 - 5976 * q^75 + 4344 * q^76 - 360 * q^77 - 4680 * q^78 + 10644 * q^80 - 5832 * q^81 - 27200 * q^82 - 32400 * q^83 - 15628 * q^85 + 14592 * q^86 + 10620 * q^87 - 14340 * q^88 + 8964 * q^90 + 16528 * q^91 - 31800 * q^92 + 14040 * q^93 + 18864 * q^95 - 4068 * q^96 + 58640 * q^97 + 46440 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/15\mathbb{Z}\right)^\times$.

$n$	$7$	$11$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	3.80336	−	3.80336i	0.950841	−	0.950841i	−0.0480062	−	0.998847i	$-0.515287\pi$
$2$	3.80336	−	3.80336i	0.950841	−	0.950841i	0.998847	+	0.0480062i	$0.0152867\pi$
$3$	−3.67423	−	3.67423i	−0.408248	−	0.408248i
$3$	−3.67423	−	3.67423i	−0.408248	−	0.408248i
$4$		−	12.9311i		−	0.808197i
$5$	6.56915	+	24.1215i	0.262766	+	0.964860i
$5$	6.56915	+	24.1215i	0.262766	+	0.964860i
$6$	−27.9489			−0.776358
$7$	16.6149	−	16.6149i	0.339079	−	0.339079i	−0.516941	−	0.856021i	$-0.672929\pi$
$7$	16.6149	−	16.6149i	0.339079	−	0.339079i	0.856021	+	0.516941i	$0.172929\pi$
$8$	11.6720	+	11.6720i	0.182374	+	0.182374i
$9$			27.0000i			0.333333i
$10$	116.728	+	66.7579i	1.16728	+	0.667579i
$11$	−215.278			−1.77916			−0.889580	−	0.456779i	$-0.849003\pi$
$11$	−215.278			−1.77916			−0.889580	+	0.456779i	$0.849003\pi$
$12$	−47.5121	+	47.5121i	−0.329945	+	0.329945i
$13$	−29.9347	−	29.9347i	−0.177128	−	0.177128i	0.612975	−	0.790103i	$-0.289973\pi$
$13$	−29.9347	−	29.9347i	−0.177128	−	0.177128i	−0.790103	+	0.612975i	$0.789973\pi$
$14$		−	126.385i		−	0.644821i
$15$	64.4914	−	112.765i	0.286628	−	0.501176i
$16$	295.684			1.15501
$17$	−3.97694	+	3.97694i	−0.0137611	+	0.0137611i	−0.713954	−	0.700193i	$-0.753097\pi$
$17$	−3.97694	+	3.97694i	−0.0137611	+	0.0137611i	0.700193	+	0.713954i	$0.253097\pi$
$18$	102.691	+	102.691i	0.316947	+	0.316947i
$19$		−	604.349i		−	1.67410i	−0.547128	−	0.837049i	$-0.684279\pi$
$19$		−	604.349i		−	1.67410i	0.547128	−	0.837049i	$-0.315721\pi$
$20$	311.919	−	84.9467i	0.779796	−	0.212367i
$21$	−122.094			−0.276857
$22$	−818.782	+	818.782i	−1.69170	+	1.69170i
$23$	376.379	+	376.379i	0.711491	+	0.711491i	0.966847	−	0.255356i	$-0.0821926\pi$
$23$	376.379	+	376.379i	0.711491	+	0.711491i	−0.255356	+	0.966847i	$0.582193\pi$
$24$		−	85.7710i		−	0.148908i
$25$	−538.692	+	316.916i	−0.861908	+	0.507065i
$26$	−227.705			−0.336841
$27$	99.2043	−	99.2043i	0.136083	−	0.136083i
$28$	−214.850	−	214.850i	−0.274043	−	0.274043i
$29$			624.166i			0.742171i	0.928599	+	0.371086i	$0.121014\pi$
$29$			624.166i			0.742171i	−0.928599	+	0.371086i	$0.878986\pi$
$30$	−183.601	−	674.169i	−0.204001	−	0.749077i
$31$	263.888			0.274597			0.137299	−	0.990530i	$-0.456158\pi$
$31$	263.888			0.274597			0.137299	+	0.990530i	$0.456158\pi$
$32$	937.842	−	937.842i	0.915861	−	0.915861i
$33$	790.983	+	790.983i	0.726339	+	0.726339i
$34$			30.2515i			0.0261691i
$35$	509.922	+	291.630i	0.416263	+	0.238065i
$36$	349.141			0.269399
$37$	979.613	−	979.613i	0.715568	−	0.715568i	−0.252126	−	0.967694i	$-0.581130\pi$
$37$	979.613	−	979.613i	0.715568	−	0.715568i	0.967694	+	0.252126i	$0.0811298\pi$
$38$	−2298.56	−	2298.56i	−1.59180	−	1.59180i
$39$			219.974i			0.144625i
$40$	−204.870	+	358.220i	−0.128044	+	0.223887i
$41$	−1579.25			−0.939468			−0.469734	−	0.882808i	$-0.655650\pi$
$41$	−1579.25			−0.939468			−0.469734	+	0.882808i	$0.655650\pi$
$42$	−464.368	+	464.368i	−0.263247	+	0.263247i
$43$	−30.8409	−	30.8409i	−0.0166797	−	0.0166797i	0.698718	−	0.715397i	$-0.253754\pi$
$43$	−30.8409	−	30.8409i	−0.0166797	−	0.0166797i	−0.715397	+	0.698718i	$0.753754\pi$
$44$			2783.80i			1.43791i
$45$	−651.280	+	177.367i	−0.321620	+	0.0875887i
$46$	2863.01			1.35303
$47$	1785.16	−	1785.16i	0.808129	−	0.808129i	−0.176221	−	0.984351i	$-0.556387\pi$
$47$	1785.16	−	1785.16i	0.808129	−	0.808129i	0.984351	+	0.176221i	$0.0563874\pi$
$48$	−1086.41	−	1086.41i	−0.471533	−	0.471533i
$49$			1848.89i			0.770050i
$50$	−843.498	+	3254.19i	−0.337399	+	1.30168i
$51$	29.2245			0.0112359
$52$	−387.089	+	387.089i	−0.143154	+	0.143154i
$53$	707.912	+	707.912i	0.252016	+	0.252016i	0.821797	−	0.569781i	$-0.192972\pi$
$53$	707.912	+	707.912i	0.252016	+	0.252016i	−0.569781	+	0.821797i	$0.692972\pi$
$54$		−	754.620i		−	0.258786i
$55$	−1414.20	−	5192.84i	−0.467503	−	1.71664i
$56$	387.857			0.123679
$57$	−2220.52	+	2220.52i	−0.683448	+	0.683448i
$58$	2373.93	+	2373.93i	0.705687	+	0.705687i
$59$		−	1366.84i		−	0.392657i	−0.980538	−	0.196329i	$-0.937098\pi$
$59$		−	1366.84i		−	0.392657i	0.980538	−	0.196329i	$-0.0629020\pi$
$60$	−1458.18	−	833.948i	−0.405049	−	0.231652i
$61$	−2983.71			−0.801856			−0.400928	−	0.916110i	$-0.631312\pi$
$61$	−2983.71			−0.801856			−0.400928	+	0.916110i	$0.631312\pi$
$62$	1003.66	−	1003.66i	0.261098	−	0.261098i
$63$	448.602	+	448.602i	0.113026	+	0.113026i
$64$		−	2402.96i		−	0.586661i
$65$	525.423	−	918.714i	0.124361	−	0.217447i
$66$	6016.80			1.38127
$67$	−986.003	+	986.003i	−0.219649	+	0.219649i	−0.808350	−	0.588702i	$-0.799639\pi$
$67$	−986.003	+	986.003i	−0.219649	+	0.219649i	0.588702	+	0.808350i	$0.299639\pi$
$68$	51.4265	+	51.4265i	0.0111216	+	0.0111216i
$69$		−	2765.81i		−	0.580930i
$70$	3048.59	−	830.242i	0.622162	−	0.169437i
$71$	68.0686			0.0135030			0.00675150	−	0.999977i	$-0.497851\pi$
$71$	68.0686			0.0135030			0.00675150	+	0.999977i	$0.497851\pi$
$72$	−315.143	+	315.143i	−0.0607914	+	0.0607914i
$73$	2476.90	+	2476.90i	0.464797	+	0.464797i	0.900224	−	0.435427i	$-0.143403\pi$
$73$	2476.90	+	2476.90i	0.464797	+	0.464797i	−0.435427	+	0.900224i	$0.643403\pi$
$74$		−	7451.65i		−	1.36078i
$75$	3143.70	+	814.860i	0.558881	+	0.144864i
$76$	−7814.93			−1.35300
$77$	−3576.83	+	3576.83i	−0.603277	+	0.603277i
$78$	836.641	+	836.641i	0.137515	+	0.137515i
$79$			6047.25i			0.968955i	0.874804	+	0.484478i	$0.160990\pi$
$79$			6047.25i			0.968955i	−0.874804	+	0.484478i	$0.839010\pi$
$80$	1942.39	+	7132.33i	0.303499	+	1.11443i
$81$	−729.000			−0.111111
$82$	−6006.45	+	6006.45i	−0.893285	+	0.893285i
$83$	−5158.95	−	5158.95i	−0.748868	−	0.748868i	0.225398	−	0.974267i	$-0.427632\pi$
$83$	−5158.95	−	5158.95i	−0.748868	−	0.748868i	−0.974267	+	0.225398i	$0.927632\pi$
$84$			1578.82i			0.223755i
$85$	−122.055	−	69.8047i	−0.0168934	−	0.00966154i
$86$	−234.598			−0.0317196
$87$	2293.33	−	2293.33i	0.302990	−	0.302990i
$88$	−2512.72	−	2512.72i	−0.324473	−	0.324473i
$89$			7028.50i			0.887325i	0.896194	+	0.443662i	$0.146321\pi$
$89$			7028.50i			0.887325i	−0.896194	+	0.443662i	$0.853679\pi$
$90$	−1802.46	+	3151.65i	−0.222526	+	0.389092i
$91$	−994.722			−0.120121
$92$	4867.01	−	4867.01i	0.575025	−	0.575025i
$93$	−969.586	−	969.586i	−0.112104	−	0.112104i
$94$		−	13579.2i		−	1.53681i
$95$	14577.8	−	3970.06i	1.61527	−	0.439896i
$96$	−6891.70			−0.747797
$97$	10869.3	−	10869.3i	1.15520	−	1.15520i	0.169703	−	0.985495i	$-0.445719\pi$
$97$	10869.3	−	10869.3i	1.15520	−	1.15520i	0.985495	−	0.169703i	$-0.0542810\pi$
$98$	7032.00	+	7032.00i	0.732195	+	0.732195i
$99$		−	5812.52i		−	0.593054i
$100$	4098.08	+	6965.91i	0.409808	+	0.696591i
$101$	−4043.94			−0.396426			−0.198213	−	0.980159i	$-0.563514\pi$
$101$	−4043.94			−0.396426			−0.198213	+	0.980159i	$0.563514\pi$
$102$	111.151	−	111.151i	0.0106835	−	0.0106835i
$103$	−119.716	−	119.716i	−0.0112844	−	0.0112844i	0.701442	−	0.712726i	$-0.252540\pi$
$103$	−119.716	−	119.716i	−0.0112844	−	0.0112844i	−0.712726	+	0.701442i	$0.752540\pi$
$104$		−	698.792i		−	0.0646073i
$105$	−802.054	−	2945.09i	−0.0727487	−	0.267128i
$106$	5384.89			0.479254
$107$	−8330.41	+	8330.41i	−0.727610	+	0.727610i	−0.970143	−	0.242533i	$-0.922022\pi$
$107$	−8330.41	+	8330.41i	−0.727610	+	0.727610i	0.242533	+	0.970143i	$0.422022\pi$
$108$	−1282.83	−	1282.83i	−0.109982	−	0.109982i
$109$			8380.72i			0.705389i	0.935739	+	0.352694i	$0.114734\pi$
$109$			8380.72i			0.705389i	−0.935739	+	0.352694i	$0.885266\pi$
$110$	−25128.9	−	14371.5i	−2.07677	−	1.18773i
$111$	−7198.66			−0.584259
$112$	4912.75	−	4912.75i	0.391642	−	0.391642i
$113$	968.067	+	968.067i	0.0758139	+	0.0758139i	0.743997	−	0.668183i	$-0.232928\pi$
$113$	968.067	+	968.067i	0.0758139	+	0.0758139i	−0.668183	+	0.743997i	$0.732928\pi$
$114$			16890.9i			1.29970i
$115$	−6606.33	+	11551.3i	−0.499533	+	0.873445i
$116$	8071.19			0.599821
$117$	808.236	−	808.236i	0.0590427	−	0.0590427i
$118$	−5198.59	−	5198.59i	−0.373355	−	0.373355i
$119$			132.153i			0.00933218i
$120$	2068.92	−	563.443i	0.143675	−	0.0391280i
$121$	31703.8			2.16541
$122$	−11348.1	+	11348.1i	−0.762437	+	0.762437i
$123$	5802.52	+	5802.52i	0.383536	+	0.383536i
$124$		−	3412.37i		−	0.221929i
$125$	−11183.2	−	10912.2i	−0.715727	−	0.698381i
$126$	3412.39			0.214940
$127$	−12023.3	+	12023.3i	−0.745446	+	0.745446i	−0.973620	−	0.228174i	$-0.926724\pi$
$127$	−12023.3	+	12023.3i	−0.745446	+	0.745446i	0.228174	+	0.973620i	$0.426724\pi$
$128$	5866.12	+	5866.12i	0.358039	+	0.358039i
$129$			226.633i			0.0136190i
$130$	−1495.83	−	5492.58i	−0.0885105	−	0.325005i
$131$	4866.47			0.283577			0.141789	−	0.989897i	$-0.454715\pi$
$131$	4866.47			0.283577			0.141789	+	0.989897i	$0.454715\pi$
$132$	10228.3	−	10228.3i	0.587025	−	0.587025i
$133$	−10041.2	−	10041.2i	−0.567652	−	0.567652i
$134$			7500.26i			0.417702i
$135$	3044.64	+	1741.27i	0.167059	+	0.0955428i
$136$	−92.8374			−0.00501933
$137$	10167.9	−	10167.9i	0.541736	−	0.541736i	−0.382301	−	0.924038i	$-0.624868\pi$
$137$	10167.9	−	10167.9i	0.541736	−	0.541736i	0.924038	+	0.382301i	$0.124868\pi$
$138$	−10519.4	−	10519.4i	−0.552372	−	0.552372i
$139$			4195.51i			0.217148i	0.994088	+	0.108574i	$0.0346284\pi$
$139$			4195.51i			0.217148i	−0.994088	+	0.108574i	$0.965372\pi$
$140$	3771.11	−	6593.87i	0.192404	−	0.336422i
$141$	−13118.2			−0.659835
$142$	258.890	−	258.890i	0.0128392	−	0.0128392i
$143$	6444.29	+	6444.29i	0.315139	+	0.315139i
$144$			7983.46i			0.385005i
$145$	−15055.8	+	4100.24i	−0.716091	+	0.195018i
$146$	18841.1			0.883895
$147$	6793.26	−	6793.26i	0.314372	−	0.314372i
$148$	−12667.5	−	12667.5i	−0.578320	−	0.578320i
$149$		−	24880.4i		−	1.12069i	−0.828259	−	0.560345i	$-0.810669\pi$
$149$		−	24880.4i		−	1.12069i	0.828259	−	0.560345i	$-0.189331\pi$
$150$	15055.9	−	8857.44i	0.669149	−	0.393664i
$151$	−37791.8			−1.65746			−0.828732	−	0.559645i	$-0.810937\pi$
$151$	−37791.8			−1.65746			−0.828732	+	0.559645i	$0.810937\pi$
$152$	7053.94	−	7053.94i	0.305312	−	0.305312i
$153$	−107.377	−	107.377i	−0.00458702	−	0.00458702i
$154$			27208.0i			1.14724i
$155$	1733.52	+	6365.37i	0.0721548	+	0.264948i
$156$	2844.52			0.116885
$157$	18627.8	−	18627.8i	0.755723	−	0.755723i	−0.219818	−	0.975541i	$-0.570546\pi$
$157$	18627.8	−	18627.8i	0.755723	−	0.755723i	0.975541	+	0.219818i	$0.0705463\pi$
$158$	22999.9	+	22999.9i	0.921322	+	0.921322i
$159$		−	5202.07i		−	0.205770i
$160$	28783.0	+	16461.3i	1.12433	+	0.643020i
$161$	12507.0			0.482504
$162$	−2772.65	+	2772.65i	−0.105649	+	0.105649i
$163$	−280.411	−	280.411i	−0.0105541	−	0.0105541i	0.701810	−	0.712364i	$-0.252376\pi$
$163$	−280.411	−	280.411i	−0.0105541	−	0.0105541i	−0.712364	+	0.701810i	$0.752376\pi$
$164$			20421.5i			0.759275i
$165$	−13883.6	+	24275.8i	−0.509958	+	0.891673i
$166$	−39242.8			−1.42411
$167$	−25855.1	+	25855.1i	−0.927073	+	0.927073i	−0.997516	−	0.0704428i	$-0.977559\pi$
$167$	−25855.1	+	25855.1i	−0.927073	+	0.927073i	0.0704428	+	0.997516i	$0.477559\pi$
$168$	−1425.08	−	1425.08i	−0.0504916	−	0.0504916i
$169$		−	26768.8i		−	0.937251i
$170$	−729.712	+	198.727i	−0.0252495	+	0.00687636i
$171$	16317.4			0.558033
$172$	−398.808	+	398.808i	−0.0134805	+	0.0134805i
$173$	−31991.2	−	31991.2i	−1.06890	−	1.06890i	−0.997443	−	0.0714600i	$-0.977234\pi$
$173$	−31991.2	−	31991.2i	−1.06890	−	1.06890i	−0.0714600	−	0.997443i	$-0.522766\pi$
$174$		−	17444.8i		−	0.576191i
$175$	−3684.80	+	14215.8i	−0.120320	+	0.464190i
$176$	−63654.3			−2.05496
$177$	−5022.09	+	5022.09i	−0.160302	+	0.160302i
$178$	26731.9	+	26731.9i	0.843705	+	0.843705i
$179$		−	17987.8i		−	0.561400i	−0.959796	−	0.280700i	$-0.909433\pi$
$179$		−	17987.8i		−	0.561400i	0.959796	−	0.280700i	$-0.0905666\pi$
$180$	2293.56	+	8421.80i	0.0707889	+	0.259932i
$181$	23072.1			0.704255			0.352127	−	0.935952i	$-0.385458\pi$
$181$	23072.1			0.704255			0.352127	+	0.935952i	$0.385458\pi$
$182$	−3783.29	+	3783.29i	−0.114216	+	0.114216i
$183$	10962.8	+	10962.8i	0.327356	+	0.327356i
$184$			8786.16i			0.259515i
$185$	30065.0	+	17194.5i	0.878450	+	0.502396i
$186$	−7375.38			−0.213186
$187$	856.150	−	856.150i	0.0244831	−	0.0244831i
$188$	−23084.1	−	23084.1i	−0.653128	−	0.653128i
$189$		−	3296.54i		−	0.0922857i
$190$	40345.1	−	70544.3i	1.11759	−	1.95414i
$191$	51892.0			1.42244			0.711220	−	0.702970i	$-0.248143\pi$
$191$	51892.0			1.42244			0.711220	+	0.702970i	$0.248143\pi$
$192$	−8829.06	+	8829.06i	−0.239503	+	0.239503i
$193$	50542.0	+	50542.0i	1.35687	+	1.35687i	0.877751	+	0.479118i	$0.159043\pi$
$193$	50542.0	+	50542.0i	1.35687	+	1.35687i	0.479118	+	0.877751i	$0.340957\pi$
$194$		−	82679.5i		−	2.19682i
$195$	−5306.10	+	1445.04i	−0.139542	+	0.0380024i
$196$	23908.3			0.622352
$197$	−22327.7	+	22327.7i	−0.575323	+	0.575323i	−0.933611	−	0.358288i	$-0.883360\pi$
$197$	−22327.7	+	22327.7i	−0.575323	+	0.575323i	0.358288	+	0.933611i	$0.383360\pi$
$198$	−22107.1	−	22107.1i	−0.563900	−	0.563900i
$199$		−	57027.8i		−	1.44006i	−0.693943	−	0.720030i	$-0.744128\pi$
$199$		−	57027.8i		−	1.44006i	0.693943	−	0.720030i	$-0.255872\pi$
$200$	−9986.62	−	2588.57i	−0.249665	−	0.0647143i
$201$	7245.61			0.179342
$202$	−15380.6	+	15380.6i	−0.376938	+	0.376938i
$203$	10370.5	+	10370.5i	0.251655	+	0.251655i
$204$		−	377.906i		−	0.00908078i
$205$	−10374.3	−	38093.8i	−0.246860	−	0.906455i
$206$	−910.647			−0.0214593
$207$	−10162.2	+	10162.2i	−0.237164	+	0.237164i
$208$	−8851.19	−	8851.19i	−0.204586	−	0.204586i
$209$			130103.i			2.97849i
$210$	−14251.7	−	8150.74i	−0.323169	−	0.184824i
$211$	−50695.3			−1.13868			−0.569341	−	0.822101i	$-0.692802\pi$
$211$	−50695.3			−1.13868			−0.569341	+	0.822101i	$0.692802\pi$
$212$	9154.12	−	9154.12i	0.203678	−	0.203678i
$213$	−250.100	−	250.100i	−0.00551258	−	0.00551258i
$214$			63367.1i			1.38368i
$215$	541.329	−	946.526i	0.0117107	−	0.0204765i
$216$	2315.82			0.0496360
$217$	4384.47	−	4384.47i	0.0931102	−	0.0931102i
$218$	31874.9	+	31874.9i	0.670712	+	0.670712i
$219$		−	18201.4i		−	0.379505i
$220$	−67149.3	+	18287.2i	−1.38738	+	0.377835i
$221$	238.097			0.00487494
$222$	−27379.1	+	27379.1i	−0.555537	+	0.555537i
$223$	−18991.4	−	18991.4i	−0.381898	−	0.381898i	0.489888	−	0.871786i	$-0.337038\pi$
$223$	−18991.4	−	18991.4i	−0.381898	−	0.381898i	−0.871786	+	0.489888i	$0.837038\pi$
$224$		−	31164.3i		−	0.621099i
$225$	−8556.72	−	14544.7i	−0.169022	−	0.287303i
$226$	7363.82			0.144174
$227$	24016.1	−	24016.1i	0.466069	−	0.466069i	−0.434570	−	0.900638i	$-0.643100\pi$
$227$	24016.1	−	24016.1i	0.466069	−	0.466069i	0.900638	+	0.434570i	$0.143100\pi$
$228$	28713.9	+	28713.9i	0.552360	+	0.552360i
$229$			4953.50i			0.0944586i	0.998884	+	0.0472293i	$0.0150391\pi$
$229$			4953.50i			0.0944586i	−0.998884	+	0.0472293i	$0.984961\pi$
$230$	18807.6	+	69060.1i	0.355530	+	1.30548i
$231$	26284.2			0.492573
$232$	−7285.24	+	7285.24i	−0.135353	+	0.135353i
$233$	−60878.5	−	60878.5i	−1.12138	−	1.12138i	−0.991534	−	0.129844i	$-0.958552\pi$
$233$	−60878.5	−	60878.5i	−1.12138	−	1.12138i	−0.129844	−	0.991534i	$-0.541448\pi$
$234$		−	6148.03i		−	0.112280i
$235$	54787.6	+	31333.7i	0.992080	+	0.567382i
$236$	−17674.8			−0.317345
$237$	22219.0	−	22219.0i	0.395574	−	0.395574i
$238$	502.626	+	502.626i	0.00887342	+	0.00887342i
$239$		−	40609.0i		−	0.710929i	−0.934690	−	0.355464i	$-0.884323\pi$
$239$		−	40609.0i		−	0.710929i	0.934690	−	0.355464i	$-0.115677\pi$
$240$	19069.1	−	33342.7i	0.331060	−	0.578866i
$241$	24443.6			0.420854			0.210427	−	0.977610i	$-0.432515\pi$
$241$	24443.6			0.420854			0.210427	+	0.977610i	$0.432515\pi$
$242$	120581.	−	120581.i	2.05896	−	2.05896i
$243$	2678.52	+	2678.52i	0.0453609	+	0.0453609i
$244$			38582.7i			0.648057i
$245$	−44598.0	+	12145.6i	−0.742990	+	0.202343i
$246$	44138.2			0.729364
$247$	−18091.0	+	18091.0i	−0.296530	+	0.296530i
$248$	3080.09	+	3080.09i	0.0500795	+	0.0500795i
$249$			37910.4i			0.611448i
$250$	−84036.9	+	1030.83i	−1.34459	+	0.0164932i
$251$	−71951.0			−1.14206			−0.571030	−	0.820929i	$-0.693456\pi$
$251$	−71951.0			−1.14206			−0.571030	+	0.820929i	$0.693456\pi$
$252$	5800.94	−	5800.94i	0.0913476	−	0.0913476i
$253$	−81026.3	−	81026.3i	−1.26586	−	1.26586i
$254$			91457.9i			1.41760i
$255$	191.980	+	704.937i	0.00295240	+	0.0108410i
$256$	83069.4			1.26754
$257$	33507.3	−	33507.3i	0.507310	−	0.507310i	−0.406390	−	0.913700i	$-0.633213\pi$
$257$	33507.3	−	33507.3i	0.507310	−	0.507310i	0.913700	+	0.406390i	$0.133213\pi$
$258$	861.968	+	861.968i	0.0129495	+	0.0129495i
$259$		−	32552.3i		−	0.485269i
$260$	−11880.0	−	6794.32i	−0.175740	−	0.100508i
$261$	−16852.5			−0.247390
$262$	18508.9	−	18508.9i	0.269637	−	0.269637i
$263$	−18051.0	−	18051.0i	−0.260969	−	0.260969i	0.564479	−	0.825448i	$-0.309077\pi$
$263$	−18051.0	−	18051.0i	−0.260969	−	0.260969i	−0.825448	+	0.564479i	$0.809077\pi$
$264$			18464.6i			0.264931i
$265$	−12425.5	+	21726.3i	−0.176939	+	0.309381i
$266$	−76380.6			−1.07949
$267$	25824.4	−	25824.4i	0.362249	−	0.362249i
$268$	12750.2	+	12750.2i	0.177519	+	0.177519i
$269$			90057.7i			1.24456i	0.782794	+	0.622281i	$0.213794\pi$
$269$			90057.7i			1.24456i	−0.782794	+	0.622281i	$0.786206\pi$
$270$	18202.6	−	4957.22i	0.249692	−	0.0680002i
$271$	28019.1			0.381518			0.190759	−	0.981637i	$-0.438905\pi$
$271$	28019.1			0.381518			0.190759	+	0.981637i	$0.438905\pi$
$272$	−1175.92	+	1175.92i	−0.0158942	+	0.0158942i
$273$	3654.84	+	3654.84i	0.0490392	+	0.0490392i
$274$		−	77344.1i		−	1.03021i
$275$	115969.	−	68225.1i	1.53347	−	0.902150i
$276$	−35765.1			−0.469506
$277$	−77139.7	+	77139.7i	−1.00535	+	1.00535i	−0.00536651	+	0.999986i	$0.501708\pi$
$277$	−77139.7	+	77139.7i	−1.00535	+	1.00535i	−0.999986	+	0.00536651i	$0.998292\pi$
$278$	15957.1	+	15957.1i	0.206473	+	0.206473i
$279$			7124.97i			0.0915324i
$280$	2547.89	+	9355.68i	0.0324986	+	0.119333i
$281$	59704.3			0.756125			0.378062	−	0.925780i	$-0.376591\pi$
$281$	59704.3			0.756125			0.378062	+	0.925780i	$0.376591\pi$
$282$	−49893.2	+	49893.2i	−0.627398	+	0.627398i
$283$	71516.3	+	71516.3i	0.892960	+	0.892960i	0.994801	−	0.101841i	$-0.0324733\pi$
$283$	71516.3	+	71516.3i	0.892960	+	0.892960i	−0.101841	+	0.994801i	$0.532473\pi$
$284$		−	880.205i		−	0.0109131i
$285$	−68149.2	−	38975.3i	−0.839018	−	0.479844i
$286$	49019.9			0.599295
$287$	−26239.0	+	26239.0i	−0.318554	+	0.318554i
$288$	25321.7	+	25321.7i	0.305287	+	0.305287i
$289$			83489.4i			0.999621i
$290$	−41668.0	+	72857.5i	−0.495458	+	0.866319i
$291$	−79872.5			−0.943216
$292$	32029.2	−	32029.2i	0.375647	−	0.375647i
$293$	2048.52	+	2048.52i	0.0238619	+	0.0238619i	0.718937	−	0.695075i	$-0.244629\pi$
$293$	2048.52	+	2048.52i	0.0238619	+	0.0238619i	−0.695075	+	0.718937i	$0.744629\pi$
$294$		−	51674.5i		−	0.597835i
$295$	32970.2	−	8978.99i	0.378859	−	0.103177i
$296$	22868.0			0.261003
$297$	−21356.6	+	21356.6i	−0.242113	+	0.242113i
$298$	−94629.4	−	94629.4i	−1.06560	−	1.06560i
$299$		−	22533.5i		−	0.252050i
$300$	10537.1	−	40651.7i	0.117079	−	0.451686i
$301$	−1024.83			−0.0113115
$302$	−143736.	+	143736.i	−1.57598	+	1.57598i
$303$	14858.4	+	14858.4i	0.161840	+	0.161840i
$304$		−	178696.i		−	1.93361i
$305$	−19600.4	−	71971.4i	−0.210701	−	0.773678i
$306$	−816.791			−0.00872305
$307$	−28977.5	+	28977.5i	−0.307457	+	0.307457i	−0.843922	−	0.536465i	$-0.819759\pi$
$307$	−28977.5	+	28977.5i	−0.307457	+	0.307457i	0.536465	+	0.843922i	$0.319759\pi$
$308$	46252.5	+	46252.5i	0.487566	+	0.487566i
$309$			879.729i			0.00921366i
$310$	30803.0	+	17616.6i	0.320531	+	0.183315i
$311$	−20134.0			−0.208166			−0.104083	−	0.994569i	$-0.533191\pi$
$311$	−20134.0			−0.208166			−0.104083	+	0.994569i	$0.533191\pi$
$312$	−2567.53	+	2567.53i	−0.0263758	+	0.0263758i
$313$	115839.	+	115839.i	1.18240	+	1.18240i	0.979120	+	0.203283i	$0.0651611\pi$
$313$	115839.	+	115839.i	1.18240	+	1.18240i	0.203283	+	0.979120i	$0.434839\pi$
$314$		−	141697.i		−	1.43715i
$315$	−7874.01	+	13767.9i	−0.0793551	+	0.138754i
$316$	78197.9			0.783106
$317$	56563.1	−	56563.1i	0.562879	−	0.562879i	−0.367245	−	0.930124i	$-0.619699\pi$
$317$	56563.1	−	56563.1i	0.562879	−	0.562879i	0.930124	+	0.367245i	$0.119699\pi$
$318$	−19785.4	−	19785.4i	−0.195655	−	0.195655i
$319$		−	134370.i		−	1.32044i
$320$	57963.1	−	15785.4i	0.566046	−	0.154155i
$321$	61215.7			0.594091
$322$	47568.6	−	47568.6i	0.458785	−	0.458785i
$323$	2403.46	+	2403.46i	0.0230373	+	0.0230373i
$324$			9426.81i			0.0897996i
$325$	25612.3	+	6638.82i	0.242484	+	0.0628527i
$326$	−2133.01			−0.0200705
$327$	30792.7	−	30792.7i	0.287974	−	0.287974i
$328$	−18432.9	−	18432.9i	−0.171335	−	0.171335i
$329$		−	59320.4i		−	0.548040i
$330$	39525.3	+	145134.i	0.362950	+	1.33273i
$331$	−76249.8			−0.695958			−0.347979	−	0.937502i	$-0.613132\pi$
$331$	−76249.8			−0.695958			−0.347979	+	0.937502i	$0.613132\pi$
$332$	−66711.2	+	66711.2i	−0.605233	+	0.605233i
$333$	26449.6	+	26449.6i	0.238523	+	0.238523i
$334$			196673.i			1.76300i
$335$	−30261.1	−	17306.7i	−0.269646	−	0.154214i
$336$	−36101.2			−0.319774
$337$	88861.9	−	88861.9i	0.782448	−	0.782448i	−0.197795	−	0.980243i	$-0.563378\pi$
$337$	88861.9	−	88861.9i	0.782448	−	0.782448i	0.980243	+	0.197795i	$0.0633780\pi$
$338$	−101812.	−	101812.i	−0.891177	−	0.891177i
$339$		−	7113.81i		−	0.0619018i
$340$	−902.654	+	1578.31i	−0.00780843	+	0.0136532i
$341$	−56809.4			−0.488552
$342$	62061.1	−	62061.1i	0.530600	−	0.530600i
$343$	70611.5	+	70611.5i	0.600188	+	0.600188i
$344$		−	719.946i		−	0.00608392i
$345$	66715.4	−	18169.0i	0.560516	−	0.152649i
$346$	−243348.			−2.03271
$347$	−41523.5	+	41523.5i	−0.344854	+	0.344854i	−0.858189	−	0.513334i	$-0.828410\pi$
$347$	−41523.5	+	41523.5i	−0.344854	+	0.344854i	0.513334	+	0.858189i	$0.328410\pi$
$348$	−29655.4	−	29655.4i	−0.244876	−	0.244876i
$349$			94995.3i			0.779922i	0.920831	+	0.389961i	$0.127511\pi$
$349$			94995.3i			0.779922i	−0.920831	+	0.389961i	$0.872489\pi$
$350$	40053.3	+	68082.6i	0.326966	+	0.555776i
$351$	−5939.30			−0.0482082
$352$	−201897.	+	201897.i	−1.62946	+	1.62946i
$353$	54491.3	+	54491.3i	0.437298	+	0.437298i	0.891102	−	0.453804i	$-0.149933\pi$
$353$	54491.3	+	54491.3i	0.437298	+	0.437298i	−0.453804	+	0.891102i	$0.649933\pi$
$354$			38201.7i			0.304843i
$355$	447.153	+	1641.92i	0.00354813	+	0.0130285i
$356$	90886.6			0.717133
$357$	485.561	−	485.561i	0.00380985	−	0.00380985i
$358$	−68414.2	−	68414.2i	−0.533802	−	0.533802i
$359$			60457.0i			0.469092i	0.972105	+	0.234546i	$0.0753603\pi$
$359$			60457.0i			0.469092i	−0.972105	+	0.234546i	$0.924640\pi$
$360$	−9671.94	−	5531.49i	−0.0746291	−	0.0426813i
$361$	−234917.			−1.80260
$362$	87751.6	−	87751.6i	0.669634	−	0.669634i
$363$	−116487.	−	116487.i	−0.884026	−	0.884026i
$364$			12862.9i			0.0970814i
$365$	−43475.4	+	76017.7i	−0.326331	+	0.570596i
$366$	83391.3			0.622527
$367$	84336.6	−	84336.6i	0.626158	−	0.626158i	−0.320941	−	0.947099i	$-0.603999\pi$
$367$	84336.6	−	84336.6i	0.626158	−	0.626158i	0.947099	+	0.320941i	$0.103999\pi$
$368$	111289.	+	111289.i	0.821783	+	0.821783i
$369$		−	42639.7i		−	0.313156i
$370$	179745.	−	48951.0i	1.31296	−	0.357568i
$371$	23523.8			0.170907
$372$	−12537.9	+	12537.9i	−0.0906020	+	0.0906020i
$373$	−67604.9	−	67604.9i	−0.485915	−	0.485915i	0.421099	−	0.907015i	$-0.361644\pi$
$373$	−67604.9	−	67604.9i	−0.485915	−	0.485915i	−0.907015	+	0.421099i	$0.861644\pi$
$374$		−	6512.50i		−	0.0465591i
$375$	995.828	+	81183.8i	0.00708145	+	0.577307i
$376$	41672.6			0.294764
$377$	18684.2	−	18684.2i	0.131459	−	0.131459i
$378$	−12537.9	−	12537.9i	−0.0877490	−	0.0877490i
$379$			128651.i			0.895645i	0.894123	+	0.447822i	$0.147800\pi$
$379$			128651.i			0.895645i	−0.894123	+	0.447822i	$0.852200\pi$
$380$	−51337.5	−	188508.i	−0.355523	−	1.30546i
$381$	88352.8			0.608654
$382$	197364.	−	197364.i	1.35251	−	1.35251i
$383$	147476.	+	147476.i	1.00536	+	1.00536i	0.999986	+	0.00537910i	$0.00171223\pi$
$383$	147476.	+	147476.i	1.00536	+	1.00536i	0.00537910	+	0.999986i	$0.498288\pi$
$384$		−	43107.0i		−	0.292338i
$385$	−109775.	−	62781.7i	−0.740598	−	0.423557i
$386$	384459.			2.58033
$387$	832.703	−	832.703i	0.00555992	−	0.00555992i
$388$	−140552.	−	140552.i	−0.933628	−	0.933628i
$389$		−	175663.i		−	1.16086i	−0.814309	−	0.580432i	$-0.802884\pi$
$389$		−	175663.i		−	1.16086i	0.814309	−	0.580432i	$-0.197116\pi$
$390$	−14685.0	+	25677.0i	−0.0965483	+	0.168817i
$391$	−2993.68			−0.0195817
$392$	−21580.2	+	21580.2i	−0.140437	+	0.140437i
$393$	−17880.5	−	17880.5i	−0.115770	−	0.115770i
$394$			169841.i			1.09408i
$395$	−145869.	+	39725.3i	−0.934906	+	0.254609i
$396$	−75162.5			−0.479304
$397$	59199.8	−	59199.8i	0.375612	−	0.375612i	−0.493904	−	0.869516i	$-0.664431\pi$
$397$	59199.8	−	59199.8i	0.375612	−	0.375612i	0.869516	+	0.493904i	$0.164431\pi$
$398$	−216897.	−	216897.i	−1.36927	−	1.36927i
$399$			73787.4i			0.463486i
$400$	−159283.	+	93706.8i	−0.995516	+	0.585667i
$401$	81929.2			0.509507			0.254753	−	0.967006i	$-0.418006\pi$
$401$	81929.2			0.509507			0.254753	+	0.967006i	$0.418006\pi$
$402$	27557.7	−	27557.7i	0.170526	−	0.170526i
$403$	−7899.39	−	7899.39i	−0.0486389	−	0.0486389i
$404$			52292.8i			0.320390i
$405$	−4788.91	−	17584.6i	−0.0291962	−	0.107207i
$406$	78885.2			0.478568
$407$	−210890.	+	210890.i	−1.27311	+	1.27311i
$408$	341.107	+	341.107i	0.00204913	+	0.00204913i
$409$		−	107251.i		−	0.641145i	−0.947224	−	0.320573i	$-0.896125\pi$
$409$		−	107251.i		−	0.641145i	0.947224	−	0.320573i	$-0.103875\pi$
$410$	−184342.	−	105427.i	−1.09662	−	0.627170i
$411$	−74718.1			−0.442326
$412$	−1548.07	+	1548.07i	−0.00912000	+	0.00912000i
$413$	−22709.9	−	22709.9i	−0.133142	−	0.133142i
$414$			77301.3i			0.451010i
$415$	90551.7	−	158332.i	0.525775	−	0.919330i
$416$	−56147.9			−0.324449
$417$	15415.3	−	15415.3i	0.0886502	−	0.0886502i
$418$	494830.	+	494830.i	2.83207	+	2.83207i
$419$			25226.4i			0.143690i	0.997416	+	0.0718451i	$0.0228887\pi$
$419$			25226.4i			0.143690i	−0.997416	+	0.0718451i	$0.977111\pi$
$420$	−38083.4	+	10371.5i	−0.215892	+	0.0587953i
$421$	165855.			0.935762			0.467881	−	0.883792i	$-0.345018\pi$
$421$	165855.			0.935762			0.467881	+	0.883792i	$0.345018\pi$
$422$	−192813.	+	192813.i	−1.08271	+	1.08271i
$423$	48199.3	+	48199.3i	0.269376	+	0.269376i
$424$			16525.4i			0.0919224i
$425$	881.994	−	3402.70i	0.00488301	−	0.0188385i
$426$	−1902.44			−0.0104832
$427$	−49573.9	+	49573.9i	−0.271893	+	0.271893i
$428$	107722.	+	107722.i	0.588052	+	0.588052i
$429$		−	47355.6i		−	0.257310i
$430$	−1541.11	−	5658.85i	−0.00833483	−	0.0306049i
$431$	−181899.			−0.979210			−0.489605	−	0.871944i	$-0.662859\pi$
$431$	−181899.			−0.979210			−0.489605	+	0.871944i	$0.662859\pi$
$432$	29333.1	−	29333.1i	0.157178	−	0.157178i
$433$	−178342.	−	178342.i	−0.951214	−	0.951214i	0.0476501	−	0.998864i	$-0.484827\pi$
$433$	−178342.	−	178342.i	−0.951214	−	0.951214i	−0.998864	+	0.0476501i	$0.984827\pi$
$434$		−	33351.5i		−	0.177066i
$435$	70383.9	+	40253.3i	0.371959	+	0.212727i
$436$	108372.			0.570093
$437$	227464.	−	227464.i	1.19111	−	1.19111i
$438$	−69226.7	−	69226.7i	−0.360849	−	0.360849i
$439$		−	24924.4i		−	0.129329i	−0.997907	−	0.0646645i	$-0.979402\pi$
$439$		−	24924.4i		−	0.129329i	0.997907	−	0.0646645i	$-0.0205977\pi$
$440$	44104.1	−	77117.0i	0.227811	−	0.398332i
$441$	−49920.1			−0.256683
$442$	905.569	−	905.569i	0.00463529	−	0.00463529i
$443$	−75101.4	−	75101.4i	−0.382684	−	0.382684i	0.489384	−	0.872068i	$-0.337222\pi$
$443$	−75101.4	−	75101.4i	−0.382684	−	0.382684i	−0.872068	+	0.489384i	$0.837222\pi$
$444$			93086.9i			0.472196i
$445$	−169538.	+	46171.3i	−0.856144	+	0.233159i
$446$	−144462.			−0.726248
$447$	−91416.6	+	91416.6i	−0.457520	+	0.457520i
$448$	−39925.0	−	39925.0i	−0.198925	−	0.198925i
$449$			226867.i			1.12533i	0.826687	+	0.562663i	$0.190223\pi$
$449$			226867.i			1.12533i	−0.826687	+	0.562663i	$0.809777\pi$
$450$	−87863.1	−	22774.5i	−0.433892	−	0.112466i
$451$	339978.			1.67147
$452$	12518.2	−	12518.2i	0.0612725	−	0.0612725i
$453$	138856.	+	138856.i	0.676657	+	0.676657i
$454$		−	182684.i		−	0.886314i
$455$	−6534.48	−	23994.2i	−0.0315637	−	0.115900i
$456$	−51835.7			−0.249287
$457$	−3272.88	+	3272.88i	−0.0156710	+	0.0156710i	−0.714899	−	0.699228i	$-0.753527\pi$
$457$	−3272.88	+	3272.88i	−0.0156710	+	0.0156710i	0.699228	+	0.714899i	$0.253527\pi$
$458$	18840.0	+	18840.0i	0.0898151	+	0.0898151i
$459$			789.060i			0.00374528i
$460$	149372.	+	85427.4i	0.705915	+	0.403721i
$461$	94982.0			0.446930			0.223465	−	0.974712i	$-0.428263\pi$
$461$	94982.0			0.446930			0.223465	+	0.974712i	$0.428263\pi$
$462$	99968.4	−	99968.4i	0.468359	−	0.468359i
$463$	−216080.	−	216080.i	−1.00798	−	1.00798i	−0.999968	−	0.00801234i	$-0.997450\pi$
$463$	−216080.	−	216080.i	−1.00798	−	1.00798i	−0.00801234	−	0.999968i	$-0.502550\pi$
$464$			184556.i			0.857219i
$465$	17018.5	−	29757.2i	0.0787074	−	0.137622i
$466$	−463086.			−2.13250
$467$	7732.59	−	7732.59i	0.0354561	−	0.0354561i	−0.689156	−	0.724613i	$-0.742019\pi$
$467$	7732.59	−	7732.59i	0.0354561	−	0.0354561i	0.724613	+	0.689156i	$0.242019\pi$
$468$	−10451.4	−	10451.4i	−0.0477181	−	0.0477181i
$469$			32764.7i			0.148957i
$470$	327551.	−	89203.9i	1.48280	−	0.403820i
$471$	−136886.			−0.617045
$472$	15953.7	−	15953.7i	0.0716106	−	0.0716106i
$473$	6639.37	+	6639.37i	0.0296759	+	0.0296759i
$474$		−	169014.i		−	0.752256i
$475$	191528.	+	325558.i	0.848876	+	1.44292i
$476$	1708.89			0.00754224
$477$	−19113.6	+	19113.6i	−0.0840052	+	0.0840052i
$478$	−154451.	−	154451.i	−0.675980	−	0.675980i
$479$		−	320749.i		−	1.39796i	−0.715142	−	0.698980i	$-0.753638\pi$
$479$		−	320749.i		−	1.39796i	0.715142	−	0.698980i	$-0.246362\pi$
$480$	−45272.6	−	166238.i	−0.196496	−	0.721519i
$481$	−58648.8			−0.253495
$482$	92967.9	−	92967.9i	0.400165	−	0.400165i
$483$	−45953.6	−	45953.6i	−0.196981	−	0.196981i
$484$		−	409967.i		−	1.75008i
$485$	333585.	+	190781.i	1.41815	+	0.811057i
$486$	20374.7			0.0862620
$487$	5262.88	−	5262.88i	0.0221904	−	0.0221904i	−0.695925	−	0.718115i	$-0.745005\pi$
$487$	5262.88	−	5262.88i	0.0221904	−	0.0221904i	0.718115	+	0.695925i	$0.245005\pi$
$488$	−34825.7	−	34825.7i	−0.146238	−	0.146238i
$489$			2060.59i			0.00861737i
$490$	−123428.	+	215817.i	−0.514070	+	0.898862i
$491$	191704.			0.795183			0.397592	−	0.917562i	$-0.369846\pi$
$491$	191704.			0.795183			0.397592	+	0.917562i	$0.369846\pi$
$492$	75033.3	−	75033.3i	0.309973	−	0.309973i
$493$	−2482.27	−	2482.27i	−0.0102131	−	0.0102131i
$494$			137613.i			0.563905i
$495$	140207.	−	38183.3i	0.572213	−	0.155834i
$496$	78027.4			0.317164
$497$	1130.95	−	1130.95i	0.00457859	−	0.00457859i
$498$	144187.	+	144187.i	0.581390	+	0.581390i
$499$			261730.i			1.05112i	0.850756	+	0.525561i	$0.176145\pi$
$499$			261730.i			1.05112i	−0.850756	+	0.525561i	$0.823855\pi$
$500$	−141107.	+	144612.i	−0.564429	+	0.578448i
$501$	189996.			0.756952
$502$	−273656.	+	273656.i	−1.08592	+	1.08592i
$503$	206538.	+	206538.i	0.816328	+	0.816328i	0.985574	−	0.169245i	$-0.0541331\pi$
$503$	206538.	+	206538.i	0.816328	+	0.816328i	−0.169245	+	0.985574i	$0.554133\pi$
$504$			10472.1i			0.0412263i
$505$	−26565.3	−	97545.8i	−0.104167	−	0.382495i
$506$	−616345.			−2.40726
$507$	−98355.0	+	98355.0i	−0.382631	+	0.382631i
$508$	155475.	+	155475.i	0.602467	+	0.602467i
$509$		−	44082.3i		−	0.170149i	−0.996375	−	0.0850743i	$-0.972887\pi$
$509$		−	44082.3i		−	0.170149i	0.996375	−	0.0850743i	$-0.0271128\pi$
$510$	3411.30	+	1950.96i	0.0131153	+	0.00750082i
$511$	82306.9			0.315206
$512$	222085.	−	222085.i	0.847188	−	0.847188i
$513$	−59954.1	−	59954.1i	−0.227816	−	0.227816i
$514$		−	254881.i		−	0.964741i
$515$	2101.30	−	3674.16i	0.00792269	−	0.0138530i
$516$	2930.63			0.0110068
$517$	−384306.	+	384306.i	−1.43779	+	1.43779i
$518$	−123808.	−	123808.i	−0.461414	−	0.461414i
$519$			235086.i			0.872756i
$520$	16855.9	−	4590.47i	0.0623369	−	0.0169766i
$521$	−507981.			−1.87142			−0.935712	−	0.352764i	$-0.885242\pi$
$521$	−507981.			−1.87142			−0.935712	+	0.352764i	$0.885242\pi$
$522$	−64096.1	+	64096.1i	−0.235229	+	0.235229i
$523$	−119838.	−	119838.i	−0.438119	−	0.438119i	0.453260	−	0.891378i	$-0.350261\pi$
$523$	−119838.	−	119838.i	−0.438119	−	0.438119i	−0.891378	+	0.453260i	$0.850261\pi$
$524$		−	62929.0i		−	0.229186i
$525$	65771.1	−	38693.5i	0.238625	−	0.140385i
$526$	−137309.			−0.496280
$527$	−1049.47	+	1049.47i	−0.00377875	+	0.00377875i
$528$	233881.	+	233881.i	0.838933	+	0.838933i
$529$			3481.11i			0.0124396i
$530$	35374.2	+	129892.i	0.125932	+	0.462413i
$531$	36904.7			0.130886
$532$	−129844.	+	129844.i	−0.458775	+	0.458775i
$533$	47274.2	+	47274.2i	0.166406	+	0.166406i
$534$		−	196439.i		−	0.688882i
$535$	−255666.	−	146218.i	−0.893233	−	0.510850i
$536$	−23017.2			−0.0801166
$537$	−66091.5	+	66091.5i	−0.229191	+	0.229191i
$538$	342522.	+	342522.i	1.18338	+	1.18338i
$539$		−	398026.i		−	1.37004i
$540$	22516.6	−	39370.8i	0.0772174	−	0.135016i
$541$	509491.			1.74077			0.870387	−	0.492368i	$-0.163869\pi$
$541$	509491.			1.74077			0.870387	+	0.492368i	$0.163869\pi$
$542$	106567.	−	106567.i	0.362763	−	0.362763i
$543$	−84772.3	−	84772.3i	−0.287511	−	0.287511i
$544$			7459.49i			0.0252064i
$545$	−202156.	+	55054.3i	−0.680601	+	0.185352i
$546$	27801.4			0.0932569
$547$	376658.	−	376658.i	1.25885	−	1.25885i	0.307204	−	0.951644i	$-0.400607\pi$
$547$	376658.	−	376658.i	1.25885	−	1.25885i	0.951644	−	0.307204i	$-0.0993933\pi$
$548$	−131482.	−	131482.i	−0.437830	−	0.437830i
$549$		−	80560.0i		−	0.267285i
$550$	181587.	−	700557.i	0.600288	−	2.31589i
$551$	377214.			1.24247
$552$	32282.4	−	32282.4i	0.105947	−	0.105947i
$553$	100474.	+	100474.i	0.328553	+	0.328553i
$554$			586780.i			1.91186i
$555$	−47289.1	−	173642.i	−0.153523	−	0.563728i
$556$	54252.8			0.175498
$557$	−76108.6	+	76108.6i	−0.245315	+	0.245315i	−0.819045	−	0.573730i	$-0.805496\pi$
$557$	−76108.6	+	76108.6i	−0.245315	+	0.245315i	0.573730	+	0.819045i	$0.305496\pi$
$558$	27098.9	+	27098.9i	0.0870327	+	0.0870327i
$559$			1846.42i			0.00590891i
$560$	150776.	+	86230.3i	0.480789	+	0.274969i
$561$	−6291.39			−0.0199904
$562$	227077.	−	227077.i	0.718954	−	0.718954i
$563$	−242876.	−	242876.i	−0.766244	−	0.766244i	0.211199	−	0.977443i	$-0.432263\pi$
$563$	−242876.	−	242876.i	−0.766244	−	0.766244i	−0.977443	+	0.211199i	$0.932263\pi$
$564$			169633.i			0.533276i
$565$	−16991.8	+	29710.6i	−0.0532284	+	0.0930711i
$566$	544005.			1.69813
$567$	−12112.3	+	12112.3i	−0.0376755	+	0.0376755i
$568$	794.494	+	794.494i	0.00246260	+	0.00246260i
$569$		−	285859.i		−	0.882934i	−0.897278	−	0.441467i	$-0.854458\pi$
$569$		−	285859.i		−	0.882934i	0.897278	−	0.441467i	$-0.145542\pi$
$570$	−407434.	+	110959.i	−1.25403	+	0.341517i
$571$	−28753.2			−0.0881890			−0.0440945	−	0.999027i	$-0.514040\pi$
$571$	−28753.2			−0.0881890			−0.0440945	+	0.999027i	$0.514040\pi$
$572$	83332.0	−	83332.0i	0.254695	−	0.254695i
$573$	−190663.	−	190663.i	−0.580708	−	0.580708i
$574$			199593.i			0.605789i
$575$	−322033.	−	83472.2i	−0.974012	−	0.252468i
$576$	64880.0			0.195554
$577$	−429650.	+	429650.i	−1.29052	+	1.29052i	−0.356048	+	0.934467i	$0.615876\pi$
$577$	−429650.	+	429650.i	−1.29052	+	1.29052i	−0.934467	+	0.356048i	$0.884124\pi$
$578$	317540.	+	317540.i	0.950481	+	0.950481i
$579$		−	371406.i		−	1.10788i
$580$	53020.9	+	194689.i	0.157613	+	0.578743i
$581$	−171431.			−0.507852
$582$	−303784.	+	303784.i	−0.896848	+	0.896848i
$583$	−152398.	−	152398.i	−0.448376	−	0.448376i
$584$			57820.6i			0.169534i
$585$	24805.3	+	14186.4i	0.0724824	+	0.0414535i
$586$	15582.6			0.0453778
$587$	−116615.	+	116615.i	−0.338436	+	0.338436i	−0.855778	−	0.517343i	$-0.826921\pi$
$587$	−116615.	+	116615.i	−0.338436	+	0.338436i	0.517343	+	0.855778i	$0.326921\pi$
$588$	−87844.6	−	87844.6i	−0.254074	−	0.254074i
$589$		−	159480.i		−	0.459703i
$590$	91247.4	−	159548.i	0.262130	−	0.458340i
$591$	164074.			0.469749
$592$	289656.	−	289656.i	0.826492	−	0.826492i
$593$	−80973.9	−	80973.9i	−0.230269	−	0.230269i	0.582536	−	0.812805i	$-0.302061\pi$
$593$	−80973.9	−	80973.9i	−0.230269	−	0.230269i	−0.812805	+	0.582536i	$0.802061\pi$
$594$			162453.i			0.460422i
$595$	−3187.73	+	868.133i	−0.00900424	+	0.00245218i
$596$	−321733.			−0.905738
$597$	−209533.	+	209533.i	−0.587902	+	0.587902i
$598$	−85703.3	−	85703.3i	−0.239660	−	0.239660i
$599$			683966.i			1.90626i	0.302569	+	0.953128i	$0.402156\pi$
$599$			683966.i			1.90626i	−0.302569	+	0.953128i	$0.597844\pi$
$600$	27182.2	+	46204.2i	0.0755060	+	0.128345i
$601$	−211089.			−0.584408			−0.292204	−	0.956356i	$-0.594389\pi$
$601$	−211089.			−0.584408			−0.292204	+	0.956356i	$0.594389\pi$
$602$	−3897.82	+	3897.82i	−0.0107555	+	0.0107555i
$603$	−26622.1	−	26622.1i	−0.0732162	−	0.0732162i
$604$			488692.i			1.33956i
$605$	208267.	+	764743.i	0.568997	+	2.08932i
$606$	113024.			0.307768
$607$	502579.	−	502579.i	1.36404	−	1.36404i	0.495340	−	0.868699i	$-0.335044\pi$
$607$	502579.	−	502579.i	1.36404	−	1.36404i	0.868699	−	0.495340i	$-0.164956\pi$
$608$	−566784.	−	566784.i	−1.53324	−	1.53324i
$609$		−	76207.0i		−	0.205475i
$610$	−348281.	−	199186.i	−0.935987	−	0.535302i
$611$	−106876.			−0.286285
$612$	−1388.51	+	1388.51i	−0.00370721	+	0.00370721i
$613$	402276.	+	402276.i	1.07054	+	1.07054i	0.997316	+	0.0732238i	$0.0233287\pi$
$613$	402276.	+	402276.i	1.07054	+	1.07054i	0.0732238	+	0.997316i	$0.476671\pi$
$614$			220424.i			0.584685i
$615$	−101848.	+	178083.i	−0.269278	+	0.470839i
$616$	−83497.2			−0.220044
$617$	439415.	−	439415.i	1.15426	−	1.15426i	0.168574	−	0.985689i	$-0.446084\pi$
$617$	439415.	−	439415.i	1.15426	−	1.15426i	0.985689	−	0.168574i	$-0.0539163\pi$
$618$	3345.93	+	3345.93i	0.00876072	+	0.00876072i
$619$			555813.i			1.45060i	0.688434	+	0.725299i	$0.258299\pi$
$619$			555813.i			1.45060i	−0.688434	+	0.725299i	$0.741701\pi$
$620$	82311.5	−	22416.4i	0.214130	−	0.0583153i
$621$	74676.8			0.193643
$622$	−76576.9	+	76576.9i	−0.197932	+	0.197932i
$623$	116778.	+	116778.i	0.300874	+	0.300874i
$624$			65042.7i			0.167043i
$625$	189754.	−	341440.i	0.485771	−	0.874086i
$626$	881154.			2.24855
$627$	478030.	−	478030.i	1.21596	−	1.21596i
$628$	−240879.	−	240879.i	−0.610773	−	0.610773i
$629$			7791.73i			0.0196939i
$630$	22416.5	+	82312.0i	0.0564791	+	0.207387i
$631$	−448846.			−1.12730			−0.563648	−	0.826015i	$-0.690603\pi$
$631$	−448846.			−1.12730			−0.563648	+	0.826015i	$0.690603\pi$
$632$	−70583.2	+	70583.2i	−0.176713	+	0.176713i
$633$	186266.	+	186266.i	0.464865	+	0.464865i
$634$		−	430260.i		−	1.07042i
$635$	−369003.	−	211037.i	−0.915128	−	0.523373i
$636$	−67268.7			−0.166303
$637$	55345.9	−	55345.9i	0.136398	−	0.136398i
$638$	−511056.	−	511056.i	−1.25553	−	1.25553i
$639$			1837.85i			0.00450100i
$640$	−102964.	+	180035.i	−0.251377	+	0.439538i
$641$	−579776.			−1.41106			−0.705528	−	0.708682i	$-0.749290\pi$
$641$	−579776.			−1.41106			−0.705528	+	0.708682i	$0.749290\pi$
$642$	232826.	−	232826.i	0.564886	−	0.564886i
$643$	485382.	+	485382.i	1.17398	+	1.17398i	0.981252	+	0.192731i	$0.0617344\pi$
$643$	485382.	+	485382.i	1.17398	+	1.17398i	0.192731	+	0.981252i	$0.438266\pi$
$644$		−	161730.i		−	0.389958i
$645$	−5466.73	+	1488.79i	−0.0131404	+	0.00357860i
$646$	18282.5			0.0438097
$647$	227180.	−	227180.i	0.542703	−	0.542703i	−0.381618	−	0.924320i	$-0.624633\pi$
$647$	227180.	−	227180.i	0.542703	−	0.542703i	0.924320	+	0.381618i	$0.124633\pi$
$648$	−8508.86	−	8508.86i	−0.0202638	−	0.0202638i
$649$			294251.i			0.698601i
$650$	122663.	−	72163.2i	0.290326	−	0.170800i
$651$	−32219.1			−0.0760242
$652$	−3626.04	+	3626.04i	−0.00852977	+	0.00852977i
$653$	51532.9	+	51532.9i	0.120853	+	0.120853i	0.764947	−	0.644093i	$-0.222765\pi$
$653$	51532.9	+	51532.9i	0.120853	+	0.120853i	−0.644093	+	0.764947i	$0.722765\pi$
$654$		−	234232.i		−	0.547634i
$655$	31968.6	+	117386.i	0.0745145	+	0.273612i
$656$	−466958.			−1.08510
$657$	−66876.3	+	66876.3i	−0.154932	+	0.154932i
$658$	−225617.	−	225617.i	−0.521099	−	0.521099i
$659$		−	447720.i		−	1.03095i	−0.856906	−	0.515473i	$-0.827616\pi$
$659$		−	447720.i		−	1.03095i	0.856906	−	0.515473i	$-0.172384\pi$
$660$	313914.	+	179531.i	0.720647	+	0.412146i
$661$	−99640.8			−0.228052			−0.114026	−	0.993478i	$-0.536375\pi$
$661$	−99640.8			−0.228052			−0.114026	+	0.993478i	$0.536375\pi$
$662$	−290006.	+	290006.i	−0.661745	+	0.661745i
$663$	−874.824	−	874.824i	−0.00199019	−	0.00199019i
$664$		−	120430.i		−	0.273149i
$665$	176246.	−	308171.i	0.398545	−	0.696864i
$666$	201195.			0.453594
$667$	−234923.	+	234923.i	−0.528048	+	0.528048i
$668$	334337.	+	334337.i	0.749257	+	0.749257i
$669$			139558.i			0.311818i
$670$	−180917.	+	49270.3i	−0.403024	+	0.109758i
$671$	642327.			1.42663
$672$	−114505.	+	114505.i	−0.253563	+	0.253563i
$673$	−170652.	−	170652.i	−0.376774	−	0.376774i	0.493163	−	0.869937i	$-0.335841\pi$
$673$	−170652.	−	170652.i	−0.376774	−	0.376774i	−0.869937	+	0.493163i	$0.835841\pi$
$674$		−	675948.i		−	1.48797i
$675$	−22001.2	+	84880.0i	−0.0482880	+	0.186294i
$676$	−346152.			−0.757483
$677$	−178335.	+	178335.i	−0.389099	+	0.389099i	−0.874366	−	0.485267i	$-0.838722\pi$
$677$	−178335.	+	178335.i	−0.389099	+	0.389099i	0.485267	+	0.874366i	$0.338722\pi$
$678$	−27056.4	−	27056.4i	−0.0588587	−	0.0588587i
$679$		−	361183.i		−	0.783408i
$680$	−609.863	−	2239.38i	−0.00131891	−	0.00484294i
$681$	−176481.			−0.380543
$682$	−216067.	+	216067.i	−0.464536	+	0.464536i
$683$	621359.	+	621359.i	1.33199	+	1.33199i	0.903588	+	0.428402i	$0.140923\pi$
$683$	621359.	+	621359.i	1.33199	+	1.33199i	0.428402	+	0.903588i	$0.359077\pi$
$684$		−	211003.i		−	0.451000i
$685$	312058.	+	178470.i	0.665049	+	0.380350i
$686$	537122.			1.14137
$687$	18200.3	−	18200.3i	0.0385626	−	0.0385626i
$688$	−9119.14	−	9119.14i	−0.0192654	−	0.0192654i
$689$		−	42382.2i		−	0.0892782i
$690$	184640.	−	322846.i	0.387817	−	0.678106i
$691$	−142980.			−0.299446			−0.149723	−	0.988728i	$-0.547838\pi$
$691$	−142980.			−0.299446			−0.149723	+	0.988728i	$0.547838\pi$
$692$	−413683.	+	413683.i	−0.863884	+	0.863884i
$693$	−96574.3	−	96574.3i	−0.201092	−	0.201092i
$694$			315858.i			0.655803i
$695$	−101202.	+	27561.0i	−0.209517	+	0.0570591i
$696$	53535.4			0.110515
$697$	6280.57	−	6280.57i	0.0129281	−	0.0129281i
$698$	361301.	+	361301.i	0.741582	+	0.741582i
$699$			447364.i			0.915601i
$700$	183827.	+	47648.7i	0.375157	+	0.0972422i
$701$	248096.			0.504876			0.252438	−	0.967613i	$-0.418768\pi$
$701$	248096.			0.504876			0.252438	+	0.967613i	$0.418768\pi$
$702$	−22589.3	+	22589.3i	−0.0458383	+	0.0458383i
$703$	−592028.	−	592028.i	−1.19793	−	1.19793i
$704$			517306.i			1.04376i
$705$	−86175.3	−	316430.i	−0.173382	−	0.636648i
$706$	414500.			0.831602
$707$	−67189.6	+	67189.6i	−0.134420	+	0.134420i
$708$	64941.4	+	64941.4i	0.129555	+	0.129555i
$709$		−	669146.i		−	1.33115i	−0.746329	−	0.665577i	$-0.768186\pi$
$709$		−	669146.i		−	1.33115i	0.746329	−	0.665577i	$-0.231814\pi$
$710$	7945.49	+	4544.12i	0.0157617	+	0.00901432i
$711$	−163276.			−0.322985
$712$	−82036.4	+	82036.4i	−0.161825	+	0.161825i
$713$	99321.8	+	99321.8i	0.195373	+	0.195373i
$714$		−	3693.53i		−	0.00724511i
$715$	−113112.	+	197779.i	−0.221257	+	0.386873i
$716$	−232603.			−0.453722
$717$	−149207.	+	149207.i	−0.290235	+	0.290235i
$718$	229940.	+	229940.i	0.446031	+	0.446031i
$719$		−	244719.i		−	0.473380i	−0.971585	−	0.236690i	$-0.923937\pi$
$719$		−	244719.i		−	0.473380i	0.971585	−	0.236690i	$-0.0760626\pi$
$720$	−192573.	+	52444.6i	−0.371476	+	0.101166i
$721$	−3978.14			−0.00765260
$722$	−893475.	+	893475.i	−1.71399	+	1.71399i
$723$	−89811.5	−	89811.5i	−0.171813	−	0.171813i
$724$		−	298349.i		−	0.569177i
$725$	−197808.	−	336234.i	−0.376329	−	0.639683i
$726$	−886086.			−1.68114
$727$	−515647.	+	515647.i	−0.975626	+	0.975626i	−0.999710	−	0.0240837i	$-0.992333\pi$
$727$	−515647.	+	515647.i	−0.975626	+	0.975626i	0.0240837	+	0.999710i	$0.492333\pi$
$728$	−11610.4	−	11610.4i	−0.0219070	−	0.0219070i
$729$		−	19683.0i		−	0.0370370i
$730$	123770.	+	454476.i	0.232258	+	0.852835i
$731$	245.305			0.000459062
$732$	141762.	−	141762.i	0.264568	−	0.264568i
$733$	98009.3	+	98009.3i	0.182414	+	0.182414i	0.792407	−	0.609993i	$-0.208828\pi$
$733$	98009.3	+	98009.3i	0.182414	+	0.182414i	−0.609993	+	0.792407i	$0.708828\pi$
$734$		−	641526.i		−	1.19075i
$735$	208489.	+	119238.i	0.385931	+	0.220718i
$736$	705967.			1.30325
$737$	212265.	−	212265.i	0.390790	−	0.390790i
$738$	−162174.	−	162174.i	−0.297762	−	0.297762i
$739$			31323.0i			0.0573554i	0.999589	+	0.0286777i	$0.00912965\pi$
$739$			31323.0i			0.0573554i	−0.999589	+	0.0286777i	$0.990870\pi$
$740$	222345.	−	388774.i	0.406035	−	0.709961i
$741$	132941.			0.242116
$742$	89469.4	−	89469.4i	0.162505	−	0.162505i
$743$	46804.2	+	46804.2i	0.0847828	+	0.0847828i	0.748226	−	0.663444i	$-0.230906\pi$
$743$	46804.2	+	46804.2i	0.0847828	+	0.0847828i	−0.663444	+	0.748226i	$0.730906\pi$
$744$		−	22633.9i		−	0.0408897i
$745$	600153.	−	163443.i	1.08131	−	0.294479i
$746$	−514252.			−0.924056
$747$	139292.	−	139292.i	0.249623	−	0.249623i
$748$	−11071.0	−	11071.0i	−0.0197872	−	0.0197872i
$749$			276818.i			0.493435i
$750$	312559.	+	304984.i	0.555660	+	0.542194i
$751$	−186.753			−0.000331121			−0.000165561	−	1.00000i	$-0.500053\pi$
$751$	−186.753			−0.000331121			−0.000165561		1.00000i	$0.500053\pi$
$752$	527842.	−	527842.i	0.933401	−	0.933401i
$753$	264365.	+	264365.i	0.466244	+	0.466244i
$754$		−	142126.i		−	0.249994i
$755$	−248260.	−	911596.i	−0.435525	−	1.59922i
$756$	−42628.0			−0.0745850
$757$	596186.	−	596186.i	1.04037	−	1.04037i	0.0412248	−	0.999150i	$-0.486874\pi$
$757$	596186.	−	596186.i	1.04037	−	1.04037i	0.999150	−	0.0412248i	$-0.0131260\pi$
$758$	489308.	+	489308.i	0.851616	+	0.851616i
$759$			595419.i			1.03357i
$760$	216490.	+	123813.i	0.374809	+	0.214358i
$761$	−1.04441e6			−1.80344			−0.901722	−	0.432315i	$-0.857697\pi$
$761$	−1.04441e6			−1.80344			−0.901722	+	0.432315i	$0.857697\pi$
$762$	336038.	−	336038.i	0.578733	−	0.578733i
$763$	139245.	+	139245.i	0.239183	+	0.239183i
$764$		−	671023.i		−	1.14961i
$765$	1884.73	−	3295.48i	0.00322051	−	0.00563114i
$766$	1.12181e6			1.91188
$767$	−40915.9	+	40915.9i	−0.0695507	+	0.0695507i
$768$	−305216.	−	305216.i	−0.517470	−	0.517470i
$769$		−	577158.i		−	0.975982i	−0.872849	−	0.487991i	$-0.837730\pi$
$769$		−	577158.i		−	0.975982i	0.872849	−	0.487991i	$-0.162270\pi$
$770$	−656296.	+	178733.i	−1.10693	+	0.301456i
$771$	−246227.			−0.414217
$772$	653566.	−	653566.i	1.09662	−	1.09662i
$773$	−414104.	−	414104.i	−0.693027	−	0.693027i	0.269870	−	0.962897i	$-0.413019\pi$
$773$	−414104.	−	414104.i	−0.693027	−	0.693027i	−0.962897	+	0.269870i	$0.913019\pi$
$774$		−	6334.14i		−	0.0105732i
$775$	−142154.	+	83630.2i	−0.236677	+	0.139239i
$776$	253731.			0.421357
$777$	−119605.	+	119605.i	−0.198110	+	0.198110i
$778$	−668111.	−	668111.i	−1.10380	−	1.10380i
$779$			954417.i			1.57276i
$780$	18686.1	+	68613.9i	0.0307134	+	0.112778i
$781$	−14653.7			−0.0240240
$782$	−11386.0	+	11386.0i	−0.0186191	+	0.0186191i
$783$	61920.0	+	61920.0i	0.100997	+	0.100997i
$784$			546687.i			0.889419i
$785$	571700.	+	326962.i	0.927745	+	0.530588i
$786$	−136012.			−0.220157
$787$	−337250.	+	337250.i	−0.544505	+	0.544505i	−0.924846	−	0.380341i	$-0.875807\pi$
$787$	−337250.	+	337250.i	−0.544505	+	0.544505i	0.380341	+	0.924846i	$0.375807\pi$
$788$	288723.	+	288723.i	0.464974	+	0.464974i
$789$			132647.i			0.213080i
$790$	−403702.	+	705881.i	−0.646854	+	1.13104i
$791$	32168.7			0.0514138
$792$	67843.5	−	67843.5i	0.108158	−	0.108158i
$793$	89316.2	+	89316.2i	0.142031	+	0.142031i
$794$		−	450317.i		−	0.714294i
$795$	125482.	−	34173.2i	0.198539	−	0.0540694i
$796$	−737435.			−1.16385
$797$	−365276.	+	365276.i	−0.575048	+	0.575048i	−0.933535	−	0.358487i	$-0.883293\pi$
$797$	−365276.	+	365276.i	−0.575048	+	0.575048i	0.358487	+	0.933535i	$0.383293\pi$
$798$	280640.	+	280640.i	0.440701	+	0.440701i
$799$			14198.9i			0.0222414i
$800$	−207992.	+	802425.i	−0.324987	+	1.25379i
$801$	−189770.			−0.295775
$802$	311606.	−	311606.i	0.484460	−	0.484460i
$803$	−533223.	−	533223.i	−0.826948	−	0.826948i
$804$		−	93694.1i		−	0.144944i
$805$	82160.3	+	301687.i	0.126786	+	0.465549i
$806$	−60088.5			−0.0924957
$807$	330893.	−	330893.i	0.508090	−	0.508090i
$808$	−47200.7	−	47200.7i	−0.0722979	−	0.0722979i
$809$			1.04908e6i			1.60292i	0.598051	+	0.801458i	$0.295942\pi$
$809$			1.04908e6i			1.60292i	−0.598051	+	0.801458i	$0.704058\pi$
$810$	−85094.5	−	48666.5i	−0.129697	−	0.0741755i
$811$	−882064.			−1.34109			−0.670546	−	0.741868i	$-0.733940\pi$
$811$	−882064.			−1.34109			−0.670546	+	0.741868i	$0.733940\pi$
$812$	134102.	−	134102.i	0.203387	−	0.203387i
$813$	−102949.	−	102949.i	−0.155754	−	0.155754i
$814$			1.60418e6i			2.42105i
$815$	4921.87	−	8606.00i	0.00740995	−	0.0129565i
$816$	8641.20			0.0129776
$817$	−18638.6	+	18638.6i	−0.0279235	+	0.0279235i
$818$	−407916.	−	407916.i	−0.609627	−	0.609627i
$819$		−	26857.5i		−	0.0400403i
$820$	−492596.	+	134152.i	−0.732594	+	0.199512i
$821$	1.11452e6			1.65348			0.826742	−	0.562581i	$-0.190191\pi$
$821$	1.11452e6			1.65348			0.826742	+	0.562581i	$0.190191\pi$
$822$	−284180.	+	284180.i	−0.420582	+	0.420582i
$823$	−258025.	−	258025.i	−0.380945	−	0.380945i	0.490497	−	0.871443i	$-0.336815\pi$
$823$	−258025.	−	258025.i	−0.380945	−	0.380945i	−0.871443	+	0.490497i	$0.836815\pi$
$824$		−	2794.64i		−	0.00411596i
$825$	−676772.	−	175422.i	−0.994339	−	0.257736i
$826$	−172748.			−0.253194
$827$	−55607.8	+	55607.8i	−0.0813063	+	0.0813063i	−0.746590	−	0.665284i	$-0.768310\pi$
$827$	−55607.8	+	55607.8i	−0.0813063	+	0.0813063i	0.665284	+	0.746590i	$0.268310\pi$
$828$	131409.	+	131409.i	0.191675	+	0.191675i
$829$		−	1.03445e6i		−	1.50522i	−0.658468	−	0.752609i	$-0.728795\pi$
$829$		−	1.03445e6i		−	1.50522i	0.658468	−	0.752609i	$-0.271205\pi$
$830$	−257792.	−	946594.i	−0.374208	−	1.37407i
$831$	566858.			0.820867
$832$	−71931.9	+	71931.9i	−0.103914	+	0.103914i
$833$	−7352.94	−	7352.94i	−0.0105967	−	0.0105967i
$834$		−	117260.i		−	0.168584i
$835$	−793511.	−	453818.i	−1.13810	−	0.650892i
$836$	1.68239e6			2.40720
$837$	26178.8	−	26178.8i	0.0373679	−	0.0373679i
$838$	95945.1	+	95945.1i	0.136626	+	0.136626i
$839$			426954.i			0.606537i	0.952905	+	0.303268i	$0.0980778\pi$
$839$			426954.i			0.606537i	−0.952905	+	0.303268i	$0.901922\pi$
$840$	25013.4	−	43736.5i	0.0354498	−	0.0619848i
$841$	317698.			0.449182
$842$	630808.	−	630808.i	0.889761	−	0.889761i
$843$	−219368.	−	219368.i	−0.308687	−	0.308687i
$844$			655548.i			0.920279i
$845$	645704.	−	175849.i	0.904316	−	0.246278i
$846$	366639.			0.512268
$847$	526755.	−	526755.i	0.734247	−	0.734247i
$848$	209318.	+	209318.i	0.291082	+	0.291082i
$849$		−	525535.i		−	0.729099i
$850$	−9587.18	−	16296.3i	−0.0132695	−	0.0225554i
$851$	737411.			1.01824
$852$	−3234.08	+	3234.08i	−0.00445525	+	0.00445525i
$853$	−63890.0	−	63890.0i	−0.0878081	−	0.0878081i	0.661838	−	0.749647i	$-0.269776\pi$
$853$	−63890.0	−	63890.0i	−0.0878081	−	0.0878081i	−0.749647	+	0.661838i	$0.769776\pi$
$854$			377095.i			0.517053i
$855$	107192.	+	393601.i	0.146632	+	0.538423i
$856$	−194464.			−0.265395
$857$	−104328.	+	104328.i	−0.142049	+	0.142049i	−0.774555	−	0.632506i	$-0.782026\pi$
$857$	−104328.	+	104328.i	−0.142049	+	0.142049i	0.632506	+	0.774555i	$0.282026\pi$
$858$	−180111.	−	180111.i	−0.244661	−	0.244661i
$859$			1.25585e6i			1.70196i	0.525196	+	0.850982i	$0.323992\pi$
$859$			1.25585e6i			1.70196i	−0.525196	+	0.850982i	$0.676008\pi$
$860$	−12239.7	−	7000.01i	−0.0165490	−	0.00946458i
$861$	192817.			0.260099
$862$	−691828.	+	691828.i	−0.931073	+	0.931073i
$863$	618705.	+	618705.i	0.830734	+	0.830734i	0.987617	−	0.156883i	$-0.0501446\pi$
$863$	618705.	+	618705.i	0.830734	+	0.830734i	−0.156883	+	0.987617i	$0.550145\pi$
$864$		−	186076.i		−	0.249266i
$865$	561520.	−	981831.i	0.750470	−	1.31221i
$866$	−1.35660e6			−1.80891
$867$	306760.	−	306760.i	0.408094	−	0.408094i
$868$	−56696.2	−	56696.2i	−0.0752514	−	0.0752514i
$869$		−	1.30184e6i		−	1.72393i
$870$	420794.	−	114597.i	0.555943	−	0.151403i
$871$	59031.3			0.0778119
$872$	−97819.4	+	97819.4i	−0.128645	+	0.128645i
$873$	293470.	+	293470.i	0.385066	+	0.385066i
$874$		−	1.73026e6i		−	2.26510i
$875$	−367113.	+	4503.14i	−0.479495	+	0.00588165i
$876$	−235365.			−0.306715
$877$	−446207.	+	446207.i	−0.580146	+	0.580146i	−0.934943	−	0.354797i	$-0.884550\pi$
$877$	−446207.	+	446207.i	−0.580146	+	0.580146i	0.354797	+	0.934943i	$0.384550\pi$
$878$	−94796.6	−	94796.6i	−0.122971	−	0.122971i
$879$		−	15053.5i		−	0.0194832i
$880$	−418155.	−	1.53544e6i	−0.539973	−	1.98274i
$881$	−226795.			−0.292201			−0.146101	−	0.989270i	$-0.546672\pi$
$881$	−226795.			−0.292201			−0.146101	+	0.989270i	$0.546672\pi$
$882$	−189864.	+	189864.i	−0.244065	+	0.244065i
$883$	235051.	+	235051.i	0.301467	+	0.301467i	0.841588	−	0.540121i	$-0.181621\pi$
$883$	235051.	+	235051.i	0.301467	+	0.301467i	−0.540121	+	0.841588i	$0.681621\pi$
$884$		−	3078.87i		−	0.00393991i
$885$	−154131.	−	88149.5i	−0.196791	−	0.112547i
$886$	−571276.			−0.727744
$887$	−789601.	+	789601.i	−1.00360	+	1.00360i	−0.00360590	+	0.999993i	$0.501148\pi$
$887$	−789601.	+	789601.i	−1.00360	+	1.00360i	−0.999993	+	0.00360590i	$0.998852\pi$
$888$	−84022.4	−	84022.4i	−0.106554	−	0.106554i
$889$			399531.i			0.505531i
$890$	−469208.	+	820421.i	−0.592360	+	1.03575i
$891$	156938.			0.197685
$892$	−245581.	+	245581.i	−0.308649	+	0.308649i
$893$	−1.07886e6	−	1.07886e6i	−1.35289	−	1.35289i
$894$			695381.i			0.870057i
$895$	433893.	−	118165.i	0.541672	−	0.147517i
$896$	194930.			0.242808
$897$	−82793.5	+	82793.5i	−0.102899	+	0.102899i
$898$	862857.	+	862857.i	1.07001	+	1.07001i
$899$			164710.i			0.203798i
$900$	−188080.	+	110648.i	−0.232197	+	0.136603i
$901$	−5630.65			−0.00693600
$902$	1.29306e6	−	1.29306e6i	1.58930	−	1.58930i
$903$	3765.48	+	3765.48i	0.00461791	+	0.00461791i
$904$			22598.5i			0.0276530i
$905$	151564.	+	556533.i	0.185054	+	0.679507i
$906$	1.05624e6			1.28679
$907$	−36080.2	+	36080.2i	−0.0438585	+	0.0438585i	−0.728696	−	0.684837i	$-0.759873\pi$
$907$	−36080.2	+	36080.2i	−0.0438585	+	0.0438585i	0.684837	+	0.728696i	$0.259873\pi$
$908$	−310555.	−	310555.i	−0.376675	−	0.376675i
$909$		−	109186.i		−	0.132142i
$910$	−116112.	−	66405.6i	−0.140214	−	0.0801903i
$911$	216456.			0.260815			0.130407	−	0.991460i	$-0.458371\pi$
$911$	216456.			0.260815			0.130407	+	0.991460i	$0.458371\pi$
$912$	−656572.	+	656572.i	−0.789392	+	0.789392i
$913$	1.11061e6	+	1.11061e6i	1.33236	+	1.33236i
$914$			24895.9i			0.0298013i
$915$	−192423.	+	336456.i	−0.229835	+	0.401871i
$916$	64054.5			0.0763411
$917$	80855.8	−	80855.8i	0.0961552	−	0.0961552i
$918$	3001.08	+	3001.08i	0.00356117	+	0.00356117i
$919$			358123.i			0.424034i	0.977266	+	0.212017i	$0.0680032\pi$
$919$			358123.i			0.424034i	−0.977266	+	0.212017i	$0.931997\pi$
$920$	−211935.	+	57717.6i	−0.250396	+	0.0681919i
$921$	212940.			0.251037
$922$	361251.	−	361251.i	0.424959	−	0.424959i
$923$	−2037.61	−	2037.61i	−0.00239176	−	0.00239176i
$924$		−	339885.i		−	0.398096i
$925$	−217256.	+	838165.i	−0.253914	+	0.979594i
$926$	−1.64366e6			−1.91686
$927$	3232.33	−	3232.33i	0.00376146	−	0.00376146i
$928$	585369.	+	585369.i	0.679726	+	0.679726i
$929$		−	12991.3i		−	0.0150530i	−0.999972	−	0.00752649i	$-0.997604\pi$
$929$		−	12991.3i		−	0.0150530i	0.999972	−	0.00752649i	$-0.00239578\pi$
$930$	−48450.0	−	177905.i	−0.0560180	−	0.205694i
$931$	1.11738e6			1.28914
$932$	−787229.	+	787229.i	−0.906294	+	0.906294i
$933$	73977.0	+	73977.0i	0.0849832	+	0.0849832i
$934$		−	58819.7i		−	0.0674262i
$935$	26275.8	+	15027.4i	0.0300561	+	0.0171894i
$936$	18867.4			0.0215358
$937$	253354.	−	253354.i	0.288568	−	0.288568i	−0.547946	−	0.836514i	$-0.684590\pi$
$937$	253354.	−	253354.i	0.288568	−	0.288568i	0.836514	+	0.547946i	$0.184590\pi$
$938$	124616.	+	124616.i	0.141634	+	0.141634i
$939$		−	851238.i		−	0.965428i
$940$	405181.	−	708467.i	0.458557	−	0.801796i
$941$	−1.24657e6			−1.40779			−0.703893	−	0.710306i	$-0.748557\pi$
$941$	−1.24657e6			−1.40779			−0.703893	+	0.710306i	$0.748557\pi$
$942$	−520627.	+	520627.i	−0.586712	+	0.586712i
$943$	−594395.	−	594395.i	−0.668424	−	0.668424i
$944$		−	404153.i		−	0.453525i
$945$	79517.4	−	21655.5i	0.0890428	−	0.0242496i
$946$	50503.9			0.0564342
$947$	550159.	−	550159.i	0.613462	−	0.613462i	−0.330384	−	0.943847i	$-0.607178\pi$
$947$	550159.	−	550159.i	0.613462	−	0.613462i	0.943847	+	0.330384i	$0.107178\pi$
$948$	−287317.	−	287317.i	−0.319702	−	0.319702i
$949$		−	148290.i		−	0.164657i
$950$	1.96667e6	+	509768.i	2.17913	+	0.564839i
$951$	−415652.			−0.459589
$952$	−1542.48	+	1542.48i	−0.00170195	+	0.00170195i
$953$	457502.	+	457502.i	0.503741	+	0.503741i	0.912598	−	0.408858i	$-0.134073\pi$
$953$	457502.	+	457502.i	0.503741	+	0.503741i	−0.408858	+	0.912598i	$0.634073\pi$
$954$			145392.i			0.159751i
$955$	340887.	+	1.25171e6i	0.373769	+	1.37245i
$956$	−525121.			−0.574570
$957$	−493705.	+	493705.i	−0.539068	+	0.539068i
$958$	−1.21993e6	−	1.21993e6i	−1.32924	−	1.32924i
$959$		−	337875.i		−	0.367383i
$960$	−270969.	−	154971.i	−0.294021	−	0.168154i
$961$	−853884.			−0.924596
$962$	−223063.	+	223063.i	−0.241033	+	0.241033i
$963$	−224921.	−	224921.i	−0.242537	−	0.242537i
$964$		−	316084.i		−	0.340133i
$965$	−887130.	+	1.55117e6i	−0.952648	+	1.66573i
$966$	−349557.			−0.374596
$967$	72229.7	−	72229.7i	0.0772437	−	0.0772437i	−0.667429	−	0.744673i	$-0.732605\pi$
$967$	72229.7	−	72229.7i	0.0772437	−	0.0772437i	0.744673	+	0.667429i	$0.232605\pi$
$968$	370045.	+	370045.i	0.394916	+	0.394916i
$969$		−	17661.8i		−	0.0188099i
$970$	1.99435e6	−	543134.i	2.11962	−	0.577250i
$971$	864636.			0.917054			0.458527	−	0.888680i	$-0.348377\pi$
$971$	864636.			0.917054			0.458527	+	0.888680i	$0.348377\pi$
$972$	34636.3	−	34636.3i	0.0366606	−	0.0366606i
$973$	69708.0	+	69708.0i	0.0736303	+	0.0736303i
$974$		−	40033.3i		−	0.0421992i
$975$	−69713.1	−	118498.i	−0.0733340	−	0.124653i
$976$	−882233.			−0.926155
$977$	838896.	−	838896.i	0.878859	−	0.878859i	−0.114558	−	0.993417i	$-0.536545\pi$
$977$	838896.	−	838896.i	0.878859	−	0.878859i	0.993417	+	0.114558i	$0.0365451\pi$
$978$	7837.19	+	7837.19i	0.00819374	+	0.00819374i
$979$		−	1.51308e6i		−	1.57869i
$980$	157057.	+	576703.i	0.163533	+	0.600482i
$981$	−226280.			−0.235130
$982$	729119.	−	729119.i	0.756093	−	0.756093i
$983$	−1.04189e6	−	1.04189e6i	−1.07823	−	1.07823i	−0.996668	−	0.0815669i	$-0.974008\pi$
$983$	−1.04189e6	−	1.04189e6i	−1.07823	−	1.07823i	−0.0815669	−	0.996668i	$-0.525992\pi$
$984$			135454.i			0.139894i
$985$	−685251.	−	391903.i	−0.706281	−	0.403930i
$986$	−18882.0			−0.0194220
$987$	−217957.	+	217957.i	−0.223736	+	0.223736i
$988$	233937.	+	233937.i	0.239654	+	0.239654i
$989$		−	23215.7i		−	0.0237350i
$990$	388032.	−	678482.i	0.395910	−	0.692258i
$991$	−1.02008e6			−1.03869			−0.519347	−	0.854564i	$-0.673825\pi$
$991$	−1.02008e6			−1.03869			−0.519347	+	0.854564i	$0.673825\pi$
$992$	247485.	−	247485.i	0.251493	−	0.251493i
$993$	280160.	+	280160.i	0.284124	+	0.284124i
$994$		−	8602.85i		−	0.00870702i
$995$	1.37560e6	−	374624.i	1.38945	−	0.378399i
$996$	490225.			0.494171
$997$	−398909.	+	398909.i	−0.401313	+	0.401313i	−0.878696	−	0.477382i	$-0.841586\pi$
$997$	−398909.	+	398909.i	−0.401313	+	0.401313i	0.477382	+	0.878696i	$0.341586\pi$
$998$	995456.	+	995456.i	0.999450	+	0.999450i
$999$		−	194364.i		−	0.194753i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	15.5.f.a.13.4	yes	8
3.2	odd	2		45.5.g.e.28.1		8
4.3	odd	2		240.5.bg.c.193.4		8
5.2	odd	4	inner	15.5.f.a.7.4	✓	8
5.3	odd	4		75.5.f.e.7.1		8
5.4	even	2		75.5.f.e.43.1		8
15.2	even	4		45.5.g.e.37.1		8
15.8	even	4		225.5.g.m.82.4		8
15.14	odd	2		225.5.g.m.118.4		8
20.7	even	4		240.5.bg.c.97.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
15.5.f.a.7.4	✓	8	5.2	odd	4	inner
15.5.f.a.13.4	yes	8	1.1	even	1	trivial
45.5.g.e.28.1		8	3.2	odd	2
45.5.g.e.37.1		8	15.2	even	4
75.5.f.e.7.1		8	5.3	odd	4
75.5.f.e.43.1		8	5.4	even	2
225.5.g.m.82.4		8	15.8	even	4
225.5.g.m.118.4		8	15.14	odd	2
240.5.bg.c.97.4		8	20.7	even	4
240.5.bg.c.193.4		8	4.3	odd	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:	\( N \)	\(=\)	\( 15 = 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	15.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(3.80336 - 3.80336i) q^{2} +(-3.67423 - 3.67423i) q^{3} -12.9311i q^{4} +(6.56915 + 24.1215i) q^{5} -27.9489 q^{6} +(16.6149 - 16.6149i) q^{7} +(11.6720 + 11.6720i) q^{8} +27.0000i q^{9} +O(q^{10})\)	\(q+(3.80336 - 3.80336i) q^{2} +(-3.67423 - 3.67423i) q^{3} -12.9311i q^{4} +(6.56915 + 24.1215i) q^{5} -27.9489 q^{6} +(16.6149 - 16.6149i) q^{7} +(11.6720 + 11.6720i) q^{8} +27.0000i q^{9} +(116.728 + 66.7579i) q^{10} -215.278 q^{11} +(-47.5121 + 47.5121i) q^{12} +(-29.9347 - 29.9347i) q^{13} -126.385i q^{14} +(64.4914 - 112.765i) q^{15} +295.684 q^{16} +(-3.97694 + 3.97694i) q^{17} +(102.691 + 102.691i) q^{18} -604.349i q^{19} +(311.919 - 84.9467i) q^{20} -122.094 q^{21} +(-818.782 + 818.782i) q^{22} +(376.379 + 376.379i) q^{23} -85.7710i q^{24} +(-538.692 + 316.916i) q^{25} -227.705 q^{26} +(99.2043 - 99.2043i) q^{27} +(-214.850 - 214.850i) q^{28} +624.166i q^{29} +(-183.601 - 674.169i) q^{30} +263.888 q^{31} +(937.842 - 937.842i) q^{32} +(790.983 + 790.983i) q^{33} +30.2515i q^{34} +(509.922 + 291.630i) q^{35} +349.141 q^{36} +(979.613 - 979.613i) q^{37} +(-2298.56 - 2298.56i) q^{38} +219.974i q^{39} +(-204.870 + 358.220i) q^{40} -1579.25 q^{41} +(-464.368 + 464.368i) q^{42} +(-30.8409 - 30.8409i) q^{43} +2783.80i q^{44} +(-651.280 + 177.367i) q^{45} +2863.01 q^{46} +(1785.16 - 1785.16i) q^{47} +(-1086.41 - 1086.41i) q^{48} +1848.89i q^{49} +(-843.498 + 3254.19i) q^{50} +29.2245 q^{51} +(-387.089 + 387.089i) q^{52} +(707.912 + 707.912i) q^{53} -754.620i q^{54} +(-1414.20 - 5192.84i) q^{55} +387.857 q^{56} +(-2220.52 + 2220.52i) q^{57} +(2373.93 + 2373.93i) q^{58} -1366.84i q^{59} +(-1458.18 - 833.948i) q^{60} -2983.71 q^{61} +(1003.66 - 1003.66i) q^{62} +(448.602 + 448.602i) q^{63} -2402.96i q^{64} +(525.423 - 918.714i) q^{65} +6016.80 q^{66} +(-986.003 + 986.003i) q^{67} +(51.4265 + 51.4265i) q^{68} -2765.81i q^{69} +(3048.59 - 830.242i) q^{70} +68.0686 q^{71} +(-315.143 + 315.143i) q^{72} +(2476.90 + 2476.90i) q^{73} -7451.65i q^{74} +(3143.70 + 814.860i) q^{75} -7814.93 q^{76} +(-3576.83 + 3576.83i) q^{77} +(836.641 + 836.641i) q^{78} +6047.25i q^{79} +(1942.39 + 7132.33i) q^{80} -729.000 q^{81} +(-6006.45 + 6006.45i) q^{82} +(-5158.95 - 5158.95i) q^{83} +1578.82i q^{84} +(-122.055 - 69.8047i) q^{85} -234.598 q^{86} +(2293.33 - 2293.33i) q^{87} +(-2512.72 - 2512.72i) q^{88} +7028.50i q^{89} +(-1802.46 + 3151.65i) q^{90} -994.722 q^{91} +(4867.01 - 4867.01i) q^{92} +(-969.586 - 969.586i) q^{93} -13579.2i q^{94} +(14577.8 - 3970.06i) q^{95} -6891.70 q^{96} +(10869.3 - 10869.3i) q^{97} +(7032.00 + 7032.00i) q^{98} -5812.52i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 84 q^{5} + 36 q^{6} + 20 q^{7} + 180 q^{8}+O(q^{10}) \) 8 * q - 84 * q^5 + 36 * q^6 + 20 * q^7 + 180 * q^8	\( 8 q - 84 q^{5} + 36 q^{6} + 20 q^{7} + 180 q^{8} + 104 q^{10} - 288 q^{11} - 360 q^{12} - 340 q^{13} + 144 q^{15} + 620 q^{16} + 900 q^{17} + 564 q^{20} + 792 q^{21} - 1100 q^{22} - 1560 q^{23} - 1204 q^{25} - 3024 q^{26} + 3580 q^{28} - 2664 q^{30} - 512 q^{31} + 4980 q^{32} + 2700 q^{33} + 6600 q^{35} + 2484 q^{36} - 3820 q^{37} - 7680 q^{38} - 2952 q^{40} - 2712 q^{41} - 7380 q^{42} - 1240 q^{43} - 1944 q^{45} + 13528 q^{46} + 4800 q^{47} + 3600 q^{48} + 3744 q^{50} + 6264 q^{51} - 1240 q^{52} + 1020 q^{53} - 3644 q^{55} - 30720 q^{56} - 5400 q^{57} + 2340 q^{58} - 1044 q^{60} - 4760 q^{61} + 28680 q^{62} + 540 q^{63} - 1212 q^{65} + 10008 q^{66} - 8920 q^{67} - 1920 q^{68} + 7380 q^{70} + 7536 q^{71} - 4860 q^{72} + 11600 q^{73} - 5976 q^{75} + 4344 q^{76} - 360 q^{77} - 4680 q^{78} + 10644 q^{80} - 5832 q^{81} - 27200 q^{82} - 32400 q^{83} - 15628 q^{85} + 14592 q^{86} + 10620 q^{87} - 14340 q^{88} + 8964 q^{90} + 16528 q^{91} - 31800 q^{92} + 14040 q^{93} + 18864 q^{95} - 4068 q^{96} + 58640 q^{97} + 46440 q^{98}+O(q^{100}) \) 8 * q - 84 * q^5 + 36 * q^6 + 20 * q^7 + 180 * q^8 + 104 * q^10 - 288 * q^11 - 360 * q^12 - 340 * q^13 + 144 * q^15 + 620 * q^16 + 900 * q^17 + 564 * q^20 + 792 * q^21 - 1100 * q^22 - 1560 * q^23 - 1204 * q^25 - 3024 * q^26 + 3580 * q^28 - 2664 * q^30 - 512 * q^31 + 4980 * q^32 + 2700 * q^33 + 6600 * q^35 + 2484 * q^36 - 3820 * q^37 - 7680 * q^38 - 2952 * q^40 - 2712 * q^41 - 7380 * q^42 - 1240 * q^43 - 1944 * q^45 + 13528 * q^46 + 4800 * q^47 + 3600 * q^48 + 3744 * q^50 + 6264 * q^51 - 1240 * q^52 + 1020 * q^53 - 3644 * q^55 - 30720 * q^56 - 5400 * q^57 + 2340 * q^58 - 1044 * q^60 - 4760 * q^61 + 28680 * q^62 + 540 * q^63 - 1212 * q^65 + 10008 * q^66 - 8920 * q^67 - 1920 * q^68 + 7380 * q^70 + 7536 * q^71 - 4860 * q^72 + 11600 * q^73 - 5976 * q^75 + 4344 * q^76 - 360 * q^77 - 4680 * q^78 + 10644 * q^80 - 5832 * q^81 - 27200 * q^82 - 32400 * q^83 - 15628 * q^85 + 14592 * q^86 + 10620 * q^87 - 14340 * q^88 + 8964 * q^90 + 16528 * q^91 - 31800 * q^92 + 14040 * q^93 + 18864 * q^95 - 4068 * q^96 + 58640 * q^97 + 46440 * q^98

Introduction

L-functions

Modular forms

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Database

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