LMFDB - Embedded newform 15.5.f.a.13.2

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			13.2
Root			$-2.08045 + 2.08045i$ of defining polynomial
Character	$\chi$	$=$	15.13
Dual form			15.5.f.a.7.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.08045 + 2.08045i) q^{2} +(3.67423 + 3.67423i) q^{3} +7.34348i q^{4} +(-8.43390 + 23.5344i) q^{5} -15.2881 q^{6} +(65.1093 - 65.1093i) q^{7} +(-48.5649 - 48.5649i) q^{8} +27.0000i q^{9} +O(q^{10})$	\(q+(-2.08045 + 2.08045i) q^{2} +(3.67423 + 3.67423i) q^{3} +7.34348i q^{4} +(-8.43390 + 23.5344i) q^{5} -15.2881 q^{6} +(65.1093 - 65.1093i) q^{7} +(-48.5649 - 48.5649i) q^{8} +27.0000i q^{9} +(-31.4158 - 66.5084i) q^{10} +56.3999 q^{11} +(-26.9817 + 26.9817i) q^{12} +(0.983822 + 0.983822i) q^{13} +270.913i q^{14} +(-117.459 + 55.4829i) q^{15} +84.5776 q^{16} +(159.144 - 159.144i) q^{17} +(-56.1721 - 56.1721i) q^{18} +265.552i q^{19} +(-172.825 - 61.9342i) q^{20} +478.454 q^{21} +(-117.337 + 117.337i) q^{22} +(-185.430 - 185.430i) q^{23} -356.877i q^{24} +(-482.739 - 396.974i) q^{25} -4.09358 q^{26} +(-99.2043 + 99.2043i) q^{27} +(478.129 + 478.129i) q^{28} -544.071i q^{29} +(128.938 - 359.797i) q^{30} -710.805 q^{31} +(601.079 - 601.079i) q^{32} +(207.227 + 207.227i) q^{33} +662.183i q^{34} +(983.184 + 2081.43i) q^{35} -198.274 q^{36} +(-639.026 + 639.026i) q^{37} +(-552.467 - 552.467i) q^{38} +7.22958i q^{39} +(1552.54 - 733.355i) q^{40} -1325.70 q^{41} +(-995.397 + 995.397i) q^{42} +(-22.3358 - 22.3358i) q^{43} +414.172i q^{44} +(-635.430 - 227.715i) q^{45} +771.553 q^{46} +(456.136 - 456.136i) q^{47} +(310.758 + 310.758i) q^{48} -6077.44i q^{49} +(1830.20 - 178.428i) q^{50} +1169.47 q^{51} +(-7.22468 + 7.22468i) q^{52} +(-424.212 - 424.212i) q^{53} -412.779i q^{54} +(-475.672 + 1327.34i) q^{55} -6324.05 q^{56} +(-975.701 + 975.701i) q^{57} +(1131.91 + 1131.91i) q^{58} +3460.30i q^{59} +(-407.437 - 862.559i) q^{60} +4937.82 q^{61} +(1478.79 - 1478.79i) q^{62} +(1757.95 + 1757.95i) q^{63} +3854.27i q^{64} +(-31.4511 + 14.8562i) q^{65} -862.248 q^{66} +(-3801.58 + 3801.58i) q^{67} +(1168.67 + 1168.67i) q^{68} -1362.62i q^{69} +(-6375.78 - 2284.85i) q^{70} +7950.20 q^{71} +(1311.25 - 1311.25i) q^{72} +(-1940.65 - 1940.65i) q^{73} -2658.92i q^{74} +(-315.118 - 3232.27i) q^{75} -1950.08 q^{76} +(3672.16 - 3672.16i) q^{77} +(-15.0408 - 15.0408i) q^{78} +4083.83i q^{79} +(-713.319 + 1990.48i) q^{80} -729.000 q^{81} +(2758.05 - 2758.05i) q^{82} +(-9103.10 - 9103.10i) q^{83} +3513.51i q^{84} +(2403.16 + 5087.58i) q^{85} +92.9369 q^{86} +(1999.04 - 1999.04i) q^{87} +(-2739.06 - 2739.06i) q^{88} +7016.23i q^{89} +(1795.73 - 848.228i) q^{90} +128.112 q^{91} +(1361.70 - 1361.70i) q^{92} +(-2611.66 - 2611.66i) q^{93} +1897.93i q^{94} +(-6249.62 - 2239.64i) q^{95} +4417.01 q^{96} +(2571.87 - 2571.87i) q^{97} +(12643.8 + 12643.8i) q^{98} +1522.80i 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 $

$2$	−2.08045	+	2.08045i	−0.520112	+	0.520112i	−0.917605	−	0.397493i	$-0.869880\pi$
$2$	−2.08045	+	2.08045i	−0.520112	+	0.520112i	0.397493	+	0.917605i	$0.369880\pi$
$3$	3.67423	+	3.67423i	0.408248	+	0.408248i
$3$	3.67423	+	3.67423i	0.408248	+	0.408248i
$4$			7.34348i			0.458968i
$5$	−8.43390	+	23.5344i	−0.337356	+	0.941377i
$5$	−8.43390	+	23.5344i	−0.337356	+	0.941377i
$6$	−15.2881			−0.424669
$7$	65.1093	−	65.1093i	1.32876	−	1.32876i	0.422309	−	0.906452i	$-0.361220\pi$
$7$	65.1093	−	65.1093i	1.32876	−	1.32876i	0.906452	−	0.422309i	$-0.138780\pi$
$8$	−48.5649	−	48.5649i	−0.758826	−	0.758826i
$9$			27.0000i			0.333333i
$10$	−31.4158	−	66.5084i	−0.314158	−	0.665084i
$11$	56.3999			0.466115			0.233058	−	0.972463i	$-0.425127\pi$
$11$	56.3999			0.466115			0.233058	+	0.972463i	$0.425127\pi$
$12$	−26.9817	+	26.9817i	−0.187373	+	0.187373i
$13$	0.983822	+	0.983822i	0.00582143	+	0.00582143i	0.710012	−	0.704190i	$-0.248690\pi$
$13$	0.983822	+	0.983822i	0.00582143	+	0.00582143i	−0.704190	+	0.710012i	$0.748690\pi$
$14$			270.913i			1.38221i
$15$	−117.459	+	55.4829i	−0.522041	+	0.246591i
$16$	84.5776			0.330381
$17$	159.144	−	159.144i	0.550673	−	0.550673i	−0.375962	−	0.926635i	$-0.622688\pi$
$17$	159.144	−	159.144i	0.550673	−	0.550673i	0.926635	+	0.375962i	$0.122688\pi$
$18$	−56.1721	−	56.1721i	−0.173371	−	0.173371i
$19$			265.552i			0.735602i	0.929905	+	0.367801i	$0.119889\pi$
$19$			265.552i			0.735602i	−0.929905	+	0.367801i	$0.880111\pi$
$20$	−172.825	−	61.9342i	−0.432062	−	0.154836i
$21$	478.454			1.08493
$22$	−117.337	+	117.337i	−0.242432	+	0.242432i
$23$	−185.430	−	185.430i	−0.350529	−	0.350529i	0.509778	−	0.860306i	$-0.329728\pi$
$23$	−185.430	−	185.430i	−0.350529	−	0.350529i	−0.860306	+	0.509778i	$0.829728\pi$
$24$		−	356.877i		−	0.619579i
$25$	−482.739	−	396.974i	−0.772382	−	0.635159i
$26$	−4.09358			−0.00605559
$27$	−99.2043	+	99.2043i	−0.136083	+	0.136083i
$28$	478.129	+	478.129i	0.609858	+	0.609858i
$29$		−	544.071i		−	0.646933i	−0.946240	−	0.323467i	$-0.895152\pi$
$29$		−	544.071i		−	0.646933i	0.946240	−	0.323467i	$-0.104848\pi$
$30$	128.938	−	359.797i	0.143265	−	0.399774i
$31$	−710.805			−0.739651			−0.369826	−	0.929101i	$-0.620583\pi$
$31$	−710.805			−0.739651			−0.369826	+	0.929101i	$0.620583\pi$
$32$	601.079	−	601.079i	0.586991	−	0.586991i
$33$	207.227	+	207.227i	0.190291	+	0.190291i
$34$			662.183i			0.572823i
$35$	983.184	+	2081.43i	0.802599	+	1.69913i
$36$	−198.274			−0.152989
$37$	−639.026	+	639.026i	−0.466783	+	0.466783i	−0.900871	−	0.434088i	$-0.857071\pi$
$37$	−639.026	+	639.026i	−0.466783	+	0.466783i	0.434088	+	0.900871i	$0.357071\pi$
$38$	−552.467	−	552.467i	−0.382595	−	0.382595i
$39$			7.22958i			0.00475318i
$40$	1552.54	−	733.355i	0.970336	−	0.458347i
$41$	−1325.70			−0.788638			−0.394319	−	0.918974i	$-0.629019\pi$
$41$	−1325.70			−0.788638			−0.394319	+	0.918974i	$0.629019\pi$
$42$	−995.397	+	995.397i	−0.564284	+	0.564284i
$43$	−22.3358	−	22.3358i	−0.0120799	−	0.0120799i	0.701041	−	0.713121i	$-0.252719\pi$
$43$	−22.3358	−	22.3358i	−0.0120799	−	0.0120799i	−0.713121	+	0.701041i	$0.752719\pi$
$44$			414.172i			0.213932i
$45$	−635.430	−	227.715i	−0.313792	−	0.112452i
$46$	771.553			0.364628
$47$	456.136	−	456.136i	0.206490	−	0.206490i	−0.596284	−	0.802774i	$-0.703357\pi$
$47$	456.136	−	456.136i	0.206490	−	0.206490i	0.802774	+	0.596284i	$0.203357\pi$
$48$	310.758	+	310.758i	0.134878	+	0.134878i
$49$		−	6077.44i		−	2.53121i
$50$	1830.20	−	178.428i	0.732078	−	0.0713713i
$51$	1169.47			0.449622
$52$	−7.22468	+	7.22468i	−0.00267185	+	0.00267185i
$53$	−424.212	−	424.212i	−0.151019	−	0.151019i	0.627554	−	0.778573i	$-0.284056\pi$
$53$	−424.212	−	424.212i	−0.151019	−	0.151019i	−0.778573	+	0.627554i	$0.784056\pi$
$54$		−	412.779i		−	0.141556i
$55$	−475.672	+	1327.34i	−0.157247	+	0.438790i
$56$	−6324.05			−2.01660
$57$	−975.701	+	975.701i	−0.300308	+	0.300308i
$58$	1131.91	+	1131.91i	0.336478	+	0.336478i
$59$			3460.30i			0.994054i	0.867735	+	0.497027i	$0.165575\pi$
$59$			3460.30i			0.994054i	−0.867735	+	0.497027i	$0.834425\pi$
$60$	−407.437	−	862.559i	−0.113177	−	0.239600i
$61$	4937.82			1.32701			0.663507	−	0.748170i	$-0.269067\pi$
$61$	4937.82			1.32701			0.663507	+	0.748170i	$0.269067\pi$
$62$	1478.79	−	1478.79i	0.384701	−	0.384701i
$63$	1757.95	+	1757.95i	0.442920	+	0.442920i
$64$			3854.27i			0.940983i
$65$	−31.4511	+	14.8562i	−0.00744406	+	0.00351627i
$66$	−862.248			−0.197945
$67$	−3801.58	+	3801.58i	−0.846866	+	0.846866i	−0.989741	−	0.142874i	$-0.954366\pi$
$67$	−3801.58	+	3801.58i	−0.846866	+	0.846866i	0.142874	+	0.989741i	$0.454366\pi$
$68$	1168.67	+	1168.67i	0.252741	+	0.252741i
$69$		−	1362.62i		−	0.286206i
$70$	−6375.78	−	2284.85i	−1.30118	−	0.466296i
$71$	7950.20			1.57711			0.788554	−	0.614966i	$-0.210830\pi$
$71$	7950.20			1.57711			0.788554	+	0.614966i	$0.210830\pi$
$72$	1311.25	−	1311.25i	0.252942	−	0.252942i
$73$	−1940.65	−	1940.65i	−0.364168	−	0.364168i	0.501177	−	0.865345i	$-0.332901\pi$
$73$	−1940.65	−	1940.65i	−0.364168	−	0.364168i	−0.865345	+	0.501177i	$0.832901\pi$
$74$		−	2658.92i		−	0.485558i
$75$	−315.118	−	3232.27i	−0.0560211	−	0.574626i
$76$	−1950.08			−0.337617
$77$	3672.16	−	3672.16i	0.619355	−	0.619355i
$78$	−15.0408	−	15.0408i	−0.00247218	−	0.00247218i
$79$			4083.83i			0.654355i	0.944963	+	0.327178i	$0.106098\pi$
$79$			4083.83i			0.654355i	−0.944963	+	0.327178i	$0.893902\pi$
$80$	−713.319	+	1990.48i	−0.111456	+	0.311013i
$81$	−729.000			−0.111111
$82$	2758.05	−	2758.05i	0.410180	−	0.410180i
$83$	−9103.10	−	9103.10i	−1.32140	−	1.32140i	−0.912646	−	0.408750i	$-0.865965\pi$
$83$	−9103.10	−	9103.10i	−1.32140	−	1.32140i	−0.408750	−	0.912646i	$-0.634035\pi$
$84$			3513.51i			0.497947i
$85$	2403.16	+	5087.58i	0.332618	+	0.704164i
$86$	92.9369			0.0125658
$87$	1999.04	−	1999.04i	0.264109	−	0.264109i
$88$	−2739.06	−	2739.06i	−0.353700	−	0.353700i
$89$			7016.23i			0.885775i	0.896577	+	0.442888i	$0.146046\pi$
$89$			7016.23i			0.885775i	−0.896577	+	0.442888i	$0.853954\pi$
$90$	1795.73	−	848.228i	0.221695	−	0.104719i
$91$	128.112			0.0154706
$92$	1361.70	−	1361.70i	0.160881	−	0.160881i
$93$	−2611.66	−	2611.66i	−0.301961	−	0.301961i
$94$			1897.93i			0.214796i
$95$	−6249.62	−	2239.64i	−0.692479	−	0.248160i
$96$	4417.01			0.479276
$97$	2571.87	−	2571.87i	0.273342	−	0.273342i	−0.557102	−	0.830444i	$-0.688087\pi$
$97$	2571.87	−	2571.87i	0.273342	−	0.273342i	0.830444	+	0.557102i	$0.188087\pi$
$98$	12643.8	+	12643.8i	1.31651	+	1.31651i
$99$			1522.80i			0.155372i
$100$	2915.17	−	3544.98i	0.291517	−	0.354498i
$101$	−7459.58			−0.731260			−0.365630	−	0.930760i	$-0.619146\pi$
$101$	−7459.58			−0.731260			−0.365630	+	0.930760i	$0.619146\pi$
$102$	−2433.02	+	2433.02i	−0.233854	+	0.233854i
$103$	4637.29	+	4637.29i	0.437109	+	0.437109i	0.891038	−	0.453929i	$-0.149978\pi$
$103$	4637.29	+	4637.29i	0.437109	+	0.437109i	−0.453929	+	0.891038i	$0.649978\pi$
$104$		−	95.5584i		−	0.00883491i
$105$	−4035.23	+	11260.1i	−0.366007	+	1.02133i
$106$	1765.10			0.157093
$107$	−8804.34	+	8804.34i	−0.769005	+	0.769005i	−0.977931	−	0.208926i	$-0.933003\pi$
$107$	−8804.34	+	8804.34i	−0.769005	+	0.769005i	0.208926	+	0.977931i	$0.433003\pi$
$108$	−728.505	−	728.505i	−0.0624576	−	0.0624576i
$109$		−	7981.01i		−	0.671746i	−0.941907	−	0.335873i	$-0.890969\pi$
$109$		−	7981.01i		−	0.671746i	0.941907	−	0.335873i	$-0.109031\pi$
$110$	−1771.85	−	3751.07i	−0.146434	−	0.310006i
$111$	−4695.86			−0.381126
$112$	5506.78	−	5506.78i	0.438997	−	0.438997i
$113$	1867.37	+	1867.37i	0.146242	+	0.146242i	0.776437	−	0.630195i	$-0.217025\pi$
$113$	1867.37	+	1867.37i	0.146242	+	0.146242i	−0.630195	+	0.776437i	$0.717025\pi$
$114$		−	4059.79i		−	0.312388i
$115$	5927.88	−	2800.09i	0.448233	−	0.211727i
$116$	3995.38			0.296921
$117$	−26.5632	+	26.5632i	−0.00194048	+	0.00194048i
$118$	−7198.98	−	7198.98i	−0.517019	−	0.517019i
$119$		−	20723.6i		−	1.46342i
$120$	8398.91	+	3009.87i	0.583257	+	0.209019i
$121$	−11460.0			−0.782737
$122$	−10272.9	+	10272.9i	−0.690195	+	0.690195i
$123$	−4870.93	−	4870.93i	−0.321960	−	0.321960i
$124$		−	5219.78i		−	0.339476i
$125$	13413.9	−	8012.93i	0.858492	−	0.512828i
$126$	−7314.64			−0.460736
$127$	3139.44	−	3139.44i	0.194646	−	0.194646i	−0.603054	−	0.797700i	$-0.706050\pi$
$127$	3139.44	−	3139.44i	0.194646	−	0.194646i	0.797700	+	0.603054i	$0.206050\pi$
$128$	1598.67	+	1598.67i	0.0975748	+	0.0975748i
$129$		−	164.134i		−	0.00986323i
$130$	34.5248	−	96.3400i	0.00204289	−	0.00570059i
$131$	28716.4			1.67335			0.836676	−	0.547698i	$-0.184496\pi$
$131$	28716.4			1.67335			0.836676	+	0.547698i	$0.184496\pi$
$132$	−1521.76	+	1521.76i	−0.0873373	+	0.0873373i
$133$	17289.9	+	17289.9i	0.977439	+	0.977439i
$134$		−	15818.0i		−	0.880930i
$135$	−1498.04	−	3171.40i	−0.0821968	−	0.174014i
$136$	−15457.7			−0.835730
$137$	−25626.6	+	25626.6i	−1.36537	+	1.36537i	−0.498453	+	0.866917i	$0.666098\pi$
$137$	−25626.6	+	25626.6i	−1.36537	+	1.36537i	−0.866917	+	0.498453i	$0.833902\pi$
$138$	2834.87	+	2834.87i	0.148859	+	0.148859i
$139$			16504.6i			0.854229i	0.904197	+	0.427115i	$0.140470\pi$
$139$			16504.6i			0.854229i	−0.904197	+	0.427115i	$0.859530\pi$
$140$	−15285.0	+	7220.00i	−0.779846	+	0.368367i
$141$	3351.90			0.168598
$142$	−16540.0	+	16540.0i	−0.820272	+	0.820272i
$143$	55.4875	+	55.4875i	0.00271346	+	0.00271346i
$144$			2283.59i			0.110127i
$145$	12804.4	+	4588.64i	0.609008	+	0.218247i
$146$	8074.84			0.378816
$147$	22329.9	−	22329.9i	1.03336	−	1.03336i
$148$	−4692.67	−	4692.67i	−0.214238	−	0.214238i
$149$			10599.1i			0.477413i	0.971092	+	0.238707i	$0.0767235\pi$
$149$			10599.1i			0.477413i	−0.971092	+	0.238707i	$0.923277\pi$
$150$	7380.15	+	6068.98i	0.328007	+	0.269732i
$151$	−30610.3			−1.34250			−0.671248	−	0.741233i	$-0.734242\pi$
$151$	−30610.3			−1.34250			−0.671248	+	0.741233i	$0.734242\pi$
$152$	12896.5	−	12896.5i	0.558194	−	0.558194i
$153$	4296.90	+	4296.90i	0.183558	+	0.183558i
$154$			15279.5i			0.644268i
$155$	5994.86	−	16728.4i	0.249526	−	0.696291i
$156$	−53.0903			−0.00218156
$157$	17506.2	−	17506.2i	0.710220	−	0.710220i	−0.256361	−	0.966581i	$-0.582524\pi$
$157$	17506.2	−	17506.2i	0.710220	−	0.710220i	0.966581	+	0.256361i	$0.0825237\pi$
$158$	−8496.20	−	8496.20i	−0.340338	−	0.340338i
$159$		−	3117.31i		−	0.123306i
$160$	9076.61	+	19215.5i	0.354555	+	0.750605i
$161$	−24146.4			−0.931538
$162$	1516.65	−	1516.65i	0.0577902	−	0.0577902i
$163$	−13776.0	−	13776.0i	−0.518500	−	0.518500i	0.398618	−	0.917117i	$-0.369490\pi$
$163$	−13776.0	−	13776.0i	−0.518500	−	0.518500i	−0.917117	+	0.398618i	$0.869490\pi$
$164$		−	9735.26i		−	0.361959i
$165$	−6624.69	+	3129.23i	−0.243331	+	0.114940i
$166$	37877.0			1.37455
$167$	22076.9	−	22076.9i	0.791598	−	0.791598i	−0.190156	−	0.981754i	$-0.560899\pi$
$167$	22076.9	−	22076.9i	0.791598	−	0.791598i	0.981754	+	0.190156i	$0.0608994\pi$
$168$	−23236.0	−	23236.0i	−0.823272	−	0.823272i
$169$		−	28559.1i		−	0.999932i
$170$	−15584.1	−	5584.79i	−0.539242	−	0.193245i
$171$	−7169.91			−0.245201
$172$	164.023	−	164.023i	0.00554430	−	0.00554430i
$173$	26956.5	+	26956.5i	0.900682	+	0.900682i	0.995495	−	0.0948128i	$-0.0302252\pi$
$173$	26956.5	+	26956.5i	0.900682	+	0.900682i	−0.0948128	+	0.995495i	$0.530225\pi$
$174$			8317.81i			0.274733i
$175$	−57277.5	+	5584.06i	−1.87028	+	0.182337i
$176$	4770.17			0.153996
$177$	−12714.0	+	12714.0i	−0.405821	+	0.405821i
$178$	−14596.9	−	14596.9i	−0.460702	−	0.460702i
$179$			43705.2i			1.36404i	0.731333	+	0.682020i	$0.238898\pi$
$179$			43705.2i			1.36404i	−0.731333	+	0.682020i	$0.761102\pi$
$180$	1672.22	−	4666.27i	0.0516118	−	0.144021i
$181$	30384.4			0.927456			0.463728	−	0.885978i	$-0.346512\pi$
$181$	30384.4			0.927456			0.463728	+	0.885978i	$0.346512\pi$
$182$	−266.530	+	266.530i	−0.00804643	+	0.00804643i
$183$	18142.7	+	18142.7i	0.541751	+	0.541751i
$184$			18010.7i			0.531981i
$185$	−9649.62	−	20428.6i	−0.281947	−	0.596891i
$186$	10866.9			0.314107
$187$	8975.73	−	8975.73i	0.256677	−	0.256677i
$188$	3349.63	+	3349.63i	0.0947722	+	0.0947722i
$189$			12918.2i			0.361643i
$190$	17661.5	−	8342.55i	0.489237	−	0.231096i
$191$	4369.57			0.119777			0.0598883	−	0.998205i	$-0.480926\pi$
$191$	4369.57			0.119777			0.0598883	+	0.998205i	$0.480926\pi$
$192$	−14161.5	+	14161.5i	−0.384155	+	0.384155i
$193$	−5475.99	−	5475.99i	−0.147011	−	0.147011i	0.629771	−	0.776781i	$-0.283149\pi$
$193$	−5475.99	−	5475.99i	−0.147011	−	0.147011i	−0.776781	+	0.629771i	$0.783149\pi$
$194$			10701.3i			0.284337i
$195$	−170.144	−	60.9736i	−0.00447453	−	0.00160351i
$196$	44629.5			1.16174
$197$	−11188.4	+	11188.4i	−0.288295	+	0.288295i	−0.836406	−	0.548111i	$-0.815347\pi$
$197$	−11188.4	+	11188.4i	−0.288295	+	0.288295i	0.548111	+	0.836406i	$0.315347\pi$
$198$	−3168.10	−	3168.10i	−0.0808106	−	0.0808106i
$199$			17995.1i			0.454409i	0.973847	+	0.227205i	$0.0729586\pi$
$199$			17995.1i			0.454409i	−0.973847	+	0.227205i	$0.927041\pi$
$200$	4165.14	+	42723.1i	0.104128	+	1.06808i
$201$	−27935.8			−0.691464
$202$	15519.3	−	15519.3i	0.380337	−	0.380337i
$203$	−35424.1	−	35424.1i	−0.859620	−	0.859620i
$204$			8587.97i			0.206362i
$205$	11180.8	−	31199.6i	0.266052	−	0.742406i
$206$	−19295.3			−0.454691
$207$	5006.60	−	5006.60i	0.116843	−	0.116843i
$208$	83.2093	+	83.2093i	0.00192329	+	0.00192329i
$209$			14977.1i			0.342875i
$210$	−15031.0	−	31821.2i	−0.340839	−	0.721569i
$211$	−12455.8			−0.279774			−0.139887	−	0.990167i	$-0.544674\pi$
$211$	−12455.8			−0.279774			−0.139887	+	0.990167i	$0.544674\pi$
$212$	3115.19	−	3115.19i	0.0693128	−	0.0693128i
$213$	29210.9	+	29210.9i	0.643852	+	0.643852i
$214$		−	36633.9i		−	0.799937i
$215$	714.039	−	337.282i	0.0154470	−	0.00729654i
$216$	9635.69			0.206526
$217$	−46280.0	+	46280.0i	−0.982820	+	0.982820i
$218$	16604.1	+	16604.1i	0.349383	+	0.349383i
$219$		−	14260.8i		−	0.297342i
$220$	−9747.30	−	3493.09i	−0.201390	−	0.0721712i
$221$	313.140			0.00641141
$222$	9769.49	−	9769.49i	0.198228	−	0.198228i
$223$	26399.5	+	26399.5i	0.530867	+	0.530867i	0.920830	−	0.389963i	$-0.127512\pi$
$223$	26399.5	+	26399.5i	0.530867	+	0.530867i	−0.389963	+	0.920830i	$0.627512\pi$
$224$		−	78271.6i		−	1.55994i
$225$	10718.3	−	13033.9i	0.211720	−	0.257461i
$226$	−7769.92			−0.152125
$227$	32267.3	−	32267.3i	0.626197	−	0.626197i	−0.320912	−	0.947109i	$-0.603989\pi$
$227$	32267.3	−	32267.3i	0.626197	−	0.626197i	0.947109	+	0.320912i	$0.103989\pi$
$228$	−7165.05	−	7165.05i	−0.137832	−	0.137832i
$229$		−	68117.5i		−	1.29894i	−0.760389	−	0.649468i	$-0.774992\pi$
$229$		−	68117.5i		−	1.29894i	0.760389	−	0.649468i	$-0.225008\pi$
$230$	−6507.21	+	18158.1i	−0.123010	+	0.343253i
$231$	26984.7			0.505702
$232$	−26422.7	+	26422.7i	−0.490910	+	0.490910i
$233$	−65936.0	−	65936.0i	−1.21454	−	1.21454i	−0.969518	−	0.245019i	$-0.921206\pi$
$233$	−65936.0	−	65936.0i	−1.21454	−	1.21454i	−0.245019	−	0.969518i	$-0.578794\pi$
$234$		−	110.527i		−	0.00201853i
$235$	6887.90	+	14581.9i	0.124724	+	0.264045i
$236$	−25410.7			−0.456239
$237$	−15005.0	+	15005.0i	−0.267139	+	0.267139i
$238$	43114.3	+	43114.3i	0.761144	+	0.761144i
$239$			64820.9i			1.13480i	0.823443	+	0.567400i	$0.192050\pi$
$239$			64820.9i			1.13480i	−0.823443	+	0.567400i	$0.807950\pi$
$240$	−9934.41	+	4692.61i	−0.172472	+	0.0814689i
$241$	−59597.9			−1.02612			−0.513058	−	0.858354i	$-0.671488\pi$
$241$	−59597.9			−1.02612			−0.513058	+	0.858354i	$0.671488\pi$
$242$	23842.0	−	23842.0i	0.407111	−	0.407111i
$243$	−2678.52	−	2678.52i	−0.0453609	−	0.0453609i
$244$			36260.8i			0.609056i
$245$	143029.	+	51256.5i	2.38282	+	0.853919i
$246$	20267.4			0.334910
$247$	−261.256	+	261.256i	−0.00428226	+	0.00428226i
$248$	34520.1	+	34520.1i	0.561267	+	0.561267i
$249$		−	66893.9i		−	1.07892i
$250$	−11236.5	+	44577.5i	−0.179784	+	0.713239i
$251$	−33922.6			−0.538445			−0.269223	−	0.963078i	$-0.586767\pi$
$251$	−33922.6			−0.538445			−0.269223	+	0.963078i	$0.586767\pi$
$252$	−12909.5	+	12909.5i	−0.203286	+	0.203286i
$253$	−10458.2	−	10458.2i	−0.163387	−	0.163387i
$254$			13062.9i			0.202475i
$255$	−9863.18	+	27522.8i	−0.151683	+	0.423264i
$256$	−68320.1			−1.04248
$257$	26107.3	−	26107.3i	0.395272	−	0.395272i	−0.481290	−	0.876562i	$-0.659832\pi$
$257$	26107.3	−	26107.3i	0.395272	−	0.395272i	0.876562	+	0.481290i	$0.159832\pi$
$258$	341.472	+	341.472i	0.00512998	+	0.00512998i
$259$			83213.0i			1.24049i
$260$	−109.096	−	230.961i	−0.00161385	−	0.00341658i
$261$	14689.9			0.215644
$262$	−59743.0	+	59743.0i	−0.870330	+	0.870330i
$263$	25675.0	+	25675.0i	0.371192	+	0.371192i	0.867911	−	0.496719i	$-0.165462\pi$
$263$	25675.0	+	25675.0i	0.371192	+	0.371192i	−0.496719	+	0.867911i	$0.665462\pi$
$264$		−	20127.9i		−	0.288795i
$265$	13561.4	−	6405.83i	0.193113	−	0.0912186i
$266$	−71941.5			−1.01675
$267$	−25779.3	+	25779.3i	−0.361616	+	0.361616i
$268$	−27916.9	−	27916.9i	−0.388684	−	0.388684i
$269$		−	84488.9i		−	1.16760i	−0.811896	−	0.583801i	$-0.801565\pi$
$269$		−	84488.9i		−	1.16760i	0.811896	−	0.583801i	$-0.198435\pi$
$270$	9714.51	+	3481.34i	0.133258	+	0.0477549i
$271$	105918.			1.44222			0.721109	−	0.692821i	$-0.243633\pi$
$271$	105918.			1.44222			0.721109	+	0.692821i	$0.243633\pi$
$272$	13460.0	−	13460.0i	0.181932	−	0.181932i
$273$	470.713	+	470.713i	0.00631584	+	0.00631584i
$274$		−	106630.i		−	1.42029i
$275$	−27226.4	−	22389.3i	−0.360019	−	0.296057i
$276$	10006.4			0.131359
$277$	71448.5	−	71448.5i	0.931180	−	0.931180i	−0.0665996	−	0.997780i	$-0.521215\pi$
$277$	71448.5	−	71448.5i	0.931180	−	0.931180i	0.997780	+	0.0665996i	$0.0212150\pi$
$278$	−34336.9	−	34336.9i	−0.444295	−	0.444295i
$279$		−	19191.7i		−	0.246550i
$280$	53336.4	−	148833.i	0.680311	−	1.89838i
$281$	6316.20			0.0799914			0.0399957	−	0.999200i	$-0.487266\pi$
$281$	6316.20			0.0799914			0.0399957	+	0.999200i	$0.487266\pi$
$282$	−6973.46	+	6973.46i	−0.0876899	+	0.0876899i
$283$	51729.2	+	51729.2i	0.645896	+	0.645896i	0.951999	−	0.306102i	$-0.0990250\pi$
$283$	51729.2	+	51729.2i	0.645896	+	0.645896i	−0.306102	+	0.951999i	$0.599025\pi$
$284$			58382.2i			0.723841i
$285$	−14733.6	−	31191.5i	−0.181392	−	0.384014i
$286$	−230.878			−0.00282260
$287$	−86315.4	+	86315.4i	−1.04791	+	1.04791i
$288$	16229.1	+	16229.1i	0.195664	+	0.195664i
$289$			32867.1i			0.393519i
$290$	−36185.3	+	17092.4i	−0.430265	+	0.203240i
$291$	18899.3			0.223183
$292$	14251.1	−	14251.1i	0.167141	−	0.167141i
$293$	−71710.7	−	71710.7i	−0.835312	−	0.835312i	0.152926	−	0.988238i	$-0.451130\pi$
$293$	−71710.7	−	71710.7i	−0.835312	−	0.835312i	−0.988238	+	0.152926i	$0.951130\pi$
$294$			92912.4i			1.07493i
$295$	−81436.3	−	29183.9i	−0.935780	−	0.335350i
$296$	62068.4			0.708414
$297$	−5595.12	+	5595.12i	−0.0634302	+	0.0634302i
$298$	−22050.8	−	22050.8i	−0.248308	−	0.248308i
$299$		−	364.860i		−	0.00408116i
$300$	23736.1	−	2314.07i	0.263735	−	0.0257118i
$301$	−2908.54			−0.0321027
$302$	63683.0	−	63683.0i	0.698248	−	0.698248i
$303$	−27408.2	−	27408.2i	−0.298535	−	0.298535i
$304$			22459.8i			0.243029i
$305$	−41645.1	+	116209.i	−0.447676	+	1.24922i
$306$	−17878.9			−0.190941
$307$	22058.5	−	22058.5i	0.234045	−	0.234045i	−0.580334	−	0.814379i	$-0.697078\pi$
$307$	22058.5	−	22058.5i	0.234045	−	0.234045i	0.814379	+	0.580334i	$0.197078\pi$
$308$	26966.4	+	26966.4i	0.284264	+	0.284264i
$309$			34076.9i			0.356898i
$310$	22330.5	+	47274.5i	0.232368	+	0.491930i
$311$	100432.			1.03837			0.519184	−	0.854663i	$-0.326236\pi$
$311$	100432.			1.03837			0.519184	+	0.854663i	$0.326236\pi$
$312$	351.104	−	351.104i	0.00360684	−	0.00360684i
$313$	32532.8	+	32532.8i	0.332072	+	0.332072i	0.853373	−	0.521301i	$-0.174553\pi$
$313$	32532.8	+	32532.8i	0.332072	+	0.332072i	−0.521301	+	0.853373i	$0.674553\pi$
$314$			72841.4i			0.738787i
$315$	−56198.7	+	26546.0i	−0.566377	+	0.267533i
$316$	−29989.5			−0.300328
$317$	−72670.5	+	72670.5i	−0.723169	+	0.723169i	−0.969249	−	0.246080i	$-0.920857\pi$
$317$	−72670.5	+	72670.5i	−0.723169	+	0.723169i	0.246080	+	0.969249i	$0.420857\pi$
$318$	6485.40	+	6485.40i	0.0641331	+	0.0641331i
$319$		−	30685.6i		−	0.301545i
$320$	−90707.9	−	32506.5i	−0.885820	−	0.317446i
$321$	−64698.4			−0.627890
$322$	50235.3	−	50235.3i	0.484504	−	0.484504i
$323$	42261.2	+	42261.2i	0.405076	+	0.405076i
$324$		−	5353.40i		−	0.0509964i
$325$	−84.3769	−	865.481i	−0.000798834	−	0.00819390i
$326$	57320.5			0.539355
$327$	29324.1	−	29324.1i	0.274239	−	0.274239i
$328$	64382.5	+	64382.5i	0.598439	+	0.598439i
$329$		−	59397.4i		−	0.548751i
$330$	7272.11	−	20292.5i	0.0667779	−	0.186341i
$331$	114400.			1.04417			0.522085	−	0.852893i	$-0.325154\pi$
$331$	114400.			1.04417			0.522085	+	0.852893i	$0.325154\pi$
$332$	66848.5	−	66848.5i	0.606478	−	0.606478i
$333$	−17253.7	−	17253.7i	−0.155594	−	0.155594i
$334$			91859.5i			0.823439i
$335$	−57405.9	−	121530.i	−0.511525	−	1.08292i
$336$	40466.4			0.358440
$337$	−75745.0	+	75745.0i	−0.666952	+	0.666952i	−0.957009	−	0.290058i	$-0.906326\pi$
$337$	−75745.0	+	75745.0i	−0.666952	+	0.666952i	0.290058	+	0.957009i	$0.406326\pi$
$338$	59415.6	+	59415.6i	0.520076	+	0.520076i
$339$			13722.3i			0.119406i
$340$	−37360.6	+	17647.6i	−0.323188	+	0.152661i
$341$	−40089.3			−0.344763
$342$	14916.6	−	14916.6i	0.127532	−	0.127532i
$343$	−239370.	−	239370.i	−2.03461	−	2.03461i
$344$			2169.47i			0.0183332i
$345$	32068.6	+	11492.2i	0.269427	+	0.0965532i
$346$	−112163.			−0.936911
$347$	49964.9	−	49964.9i	0.414960	−	0.414960i	−0.468502	−	0.883462i	$-0.655206\pi$
$347$	49964.9	−	49964.9i	0.414960	−	0.414960i	0.883462	+	0.468502i	$0.155206\pi$
$348$	14679.9	+	14679.9i	0.121218	+	0.121218i
$349$			74192.9i			0.609132i	0.952491	+	0.304566i	$0.0985115\pi$
$349$			74192.9i			0.609132i	−0.952491	+	0.304566i	$0.901489\pi$
$350$	107545.	−	130780.i	0.877921	−	1.06759i
$351$	−195.199			−0.00158439
$352$	33900.8	−	33900.8i	0.273605	−	0.273605i
$353$	−15476.1	−	15476.1i	−0.124198	−	0.124198i	0.642276	−	0.766473i	$-0.277990\pi$
$353$	−15476.1	−	15476.1i	−0.124198	−	0.124198i	−0.766473	+	0.642276i	$0.777990\pi$
$354$		−	52901.5i		−	0.422145i
$355$	−67051.2	+	187103.i	−0.532047	+	1.48465i
$356$	−51523.5			−0.406542
$357$	76143.2	−	76143.2i	0.597441	−	0.597441i
$358$	−90926.4	−	90926.4i	−0.709453	−	0.709453i
$359$			46469.2i			0.360559i	0.983615	+	0.180279i	$0.0577002\pi$
$359$			46469.2i			0.360559i	−0.983615	+	0.180279i	$0.942300\pi$
$360$	19800.6	+	41918.5i	0.152782	+	0.323445i
$361$	59803.0			0.458890
$362$	−63213.1	+	63213.1i	−0.482381	+	0.482381i
$363$	−42106.9	−	42106.9i	−0.319551	−	0.319551i
$364$			940.787i			0.00710049i
$365$	62039.4	−	29304.9i	0.465674	−	0.219965i
$366$	−75489.8			−0.563542
$367$	57731.0	−	57731.0i	0.428624	−	0.428624i	−0.459535	−	0.888160i	$-0.651984\pi$
$367$	57731.0	−	57731.0i	0.428624	−	0.428624i	0.888160	+	0.459535i	$0.151984\pi$
$368$	−15683.2	−	15683.2i	−0.115808	−	0.115808i
$369$		−	35793.9i		−	0.262879i
$370$	62576.1	+	22425.1i	0.457093	+	0.163806i
$371$	−55240.3			−0.401336
$372$	19178.7	−	19178.7i	0.138590	−	0.138590i
$373$	166181.	+	166181.i	1.19444	+	1.19444i	0.975807	+	0.218634i	$0.0701600\pi$
$373$	166181.	+	166181.i	1.19444	+	1.19444i	0.218634	+	0.975807i	$0.429840\pi$
$374$			37347.1i			0.267001i
$375$	78727.3	+	19844.5i	0.559839	+	0.141117i
$376$	−44304.4			−0.313380
$377$	535.269	−	535.269i	0.00376608	−	0.00376608i
$378$	−26875.7	−	26875.7i	−0.188095	−	0.188095i
$379$		−	41316.4i		−	0.287636i	−0.989604	−	0.143818i	$-0.954062\pi$
$379$		−	41316.4i		−	0.287636i	0.989604	−	0.143818i	$-0.0459380\pi$
$380$	16446.8	−	45894.0i	0.113897	−	0.317825i
$381$	23070.1			0.158928
$382$	−9090.66	+	9090.66i	−0.0622972	+	0.0622972i
$383$	72155.3	+	72155.3i	0.491893	+	0.491893i	0.908902	−	0.417009i	$-0.136922\pi$
$383$	72155.3	+	72155.3i	0.491893	+	0.491893i	−0.417009	+	0.908902i	$0.636922\pi$
$384$			11747.7i			0.0796695i
$385$	55451.5	+	117393.i	0.374104	+	0.791990i
$386$	22785.0			0.152924
$387$	603.067	−	603.067i	0.00402665	−	0.00402665i
$388$	18886.5	+	18886.5i	0.125455	+	0.125455i
$389$		−	192183.i		−	1.27004i	−0.772497	−	0.635018i	$-0.780993\pi$
$389$		−	192183.i		−	1.27004i	0.772497	−	0.635018i	$-0.219007\pi$
$390$	480.828	−	227.123i	0.00316126	−	0.00149325i
$391$	−59020.2			−0.386053
$392$	−295150.	+	295150.i	−1.92075	+	1.92075i
$393$	105511.	+	105511.i	0.683143	+	0.683143i
$394$		−	46553.9i		−	0.299891i
$395$	−96110.7	−	34442.6i	−0.615995	−	0.220751i
$396$	−11182.6			−0.0713106
$397$	−177091.	+	177091.i	−1.12361	+	1.12361i	−0.132416	+	0.991194i	$0.542274\pi$
$397$	−177091.	+	177091.i	−1.12361	+	1.12361i	−0.991194	+	0.132416i	$0.957726\pi$
$398$	−37437.8	−	37437.8i	−0.236344	−	0.236344i
$399$			127054.i			0.798076i
$400$	−40828.8	−	33575.1i	−0.255180	−	0.209844i
$401$	208300.			1.29539			0.647694	−	0.761900i	$-0.275733\pi$
$401$	208300.			1.29539			0.647694	+	0.761900i	$0.275733\pi$
$402$	58119.0	−	58119.0i	0.359638	−	0.359638i
$403$	−699.305	−	699.305i	−0.00430583	−	0.00430583i
$404$		−	54779.3i		−	0.335624i
$405$	6148.32	−	17156.6i	0.0374840	−	0.104597i
$406$	147396.			0.894197
$407$	−36041.0	+	36041.0i	−0.217574	+	0.217574i
$408$	−56795.1	−	56795.1i	−0.341185	−	0.341185i
$409$		−	265733.i		−	1.58854i	−0.607563	−	0.794271i	$-0.707853\pi$
$409$		−	265733.i		−	1.58854i	0.607563	−	0.794271i	$-0.292147\pi$
$410$	41648.0	+	88170.2i	0.247757	+	0.524511i
$411$	−188316.			−1.11482
$412$	−34053.8	+	34053.8i	−0.200619	+	0.200619i
$413$	225298.	+	225298.i	1.32086	+	1.32086i
$414$			20831.9i			0.121543i
$415$	291011.	−	137462.i	1.68971	−	0.798151i
$416$	1182.71			0.00683426
$417$	−60641.6	+	60641.6i	−0.348738	+	0.348738i
$418$	−31159.1	−	31159.1i	−0.178333	−	0.178333i
$419$		−	125608.i		−	0.715467i	−0.933824	−	0.357734i	$-0.883550\pi$
$419$		−	125608.i		−	0.715467i	0.933824	−	0.357734i	$-0.116450\pi$
$420$	−82688.6	−	29632.6i	−0.468756	−	0.167986i
$421$	−278634.			−1.57206			−0.786031	−	0.618187i	$-0.787868\pi$
$421$	−278634.			−1.57206			−0.786031	+	0.618187i	$0.787868\pi$
$422$	25913.7	−	25913.7i	0.145514	−	0.145514i
$423$	12315.7	+	12315.7i	0.0688300	+	0.0688300i
$424$			41203.6i			0.229194i
$425$	−140001.	+	13648.9i	−0.775094	+	0.0755650i
$426$	−121543.			−0.669750
$427$	321498.	−	321498.i	1.76328	−	1.76328i
$428$	−64654.5	−	64654.5i	−0.352948	−	0.352948i
$429$			407.748i			0.00221553i
$430$	−783.821	+	2187.22i	−0.00423916	+	0.0118292i
$431$	100603.			0.541575			0.270787	−	0.962639i	$-0.412716\pi$
$431$	100603.			0.541575			0.270787	+	0.962639i	$0.412716\pi$
$432$	−8390.46	+	8390.46i	−0.0449592	+	0.0449592i
$433$	−116014.	−	116014.i	−0.618777	−	0.618777i	0.326440	−	0.945218i	$-0.394151\pi$
$433$	−116014.	−	116014.i	−0.618777	−	0.618777i	−0.945218	+	0.326440i	$0.894151\pi$
$434$		−	192566.i		−	1.02235i
$435$	30186.6	+	63906.1i	0.159528	+	0.337726i
$436$	58608.4			0.308310
$437$	49241.3	−	49241.3i	0.257850	−	0.257850i
$438$	29668.9	+	29668.9i	0.154651	+	0.154651i
$439$		−	163656.i		−	0.849184i	−0.905385	−	0.424592i	$-0.860418\pi$
$439$		−	163656.i		−	0.849184i	0.905385	−	0.424592i	$-0.139582\pi$
$440$	87563.0	−	41361.2i	0.452288	−	0.213642i
$441$	164091.			0.843737
$442$	−651.470	+	651.470i	−0.00333465	+	0.00333465i
$443$	−117313.	−	117313.i	−0.597775	−	0.597775i	0.341945	−	0.939720i	$-0.388914\pi$
$443$	−117313.	−	117313.i	−0.597775	−	0.597775i	−0.939720	+	0.341945i	$0.888914\pi$
$444$		−	34484.0i		−	0.174925i
$445$	−165123.	−	59174.2i	−0.833849	−	0.298822i
$446$	−109845.			−0.552220
$447$	−38943.4	+	38943.4i	−0.194903	+	0.194903i
$448$	250948.	+	250948.i	1.25034	+	1.25034i
$449$			342550.i			1.69915i	0.527468	+	0.849575i	$0.323141\pi$
$449$			342550.i			1.69915i	−0.527468	+	0.849575i	$0.676859\pi$
$450$	4817.56	+	49415.3i	0.0237904	+	0.244026i
$451$	−74769.4			−0.367596
$452$	−13713.0	+	13713.0i	−0.0671204	+	0.0671204i
$453$	−112469.	−	112469.i	−0.548072	−	0.548072i
$454$			134261.i			0.651385i
$455$	−1080.48	+	3015.04i	−0.00521909	+	0.0145636i
$456$	94769.6			0.455763
$457$	−162804.	+	162804.i	−0.779530	+	0.779530i	−0.979751	−	0.200221i	$-0.935834\pi$
$457$	−162804.	+	162804.i	−0.779530	+	0.779530i	0.200221	+	0.979751i	$0.435834\pi$
$458$	141715.	+	141715.i	0.675592	+	0.675592i
$459$			31575.6i			0.149874i
$460$	20562.4	+	43531.3i	0.0971757	+	0.205724i
$461$	−283688.			−1.33487			−0.667436	−	0.744667i	$-0.732608\pi$
$461$	−283688.			−1.33487			−0.667436	+	0.744667i	$0.732608\pi$
$462$	−56140.3	+	56140.3i	−0.263021	+	0.263021i
$463$	−34085.9	−	34085.9i	−0.159006	−	0.159006i	0.623120	−	0.782126i	$-0.285865\pi$
$463$	−34085.9	−	34085.9i	−0.159006	−	0.159006i	−0.782126	+	0.623120i	$0.785865\pi$
$464$		−	46016.2i		−	0.213735i
$465$	83490.5	−	39437.5i	0.386128	−	0.182391i
$466$	274353.			1.26339
$467$	−124988.	+	124988.i	−0.573107	+	0.573107i	−0.932995	−	0.359889i	$-0.882815\pi$
$467$	−124988.	+	124988.i	−0.573107	+	0.573107i	0.359889	+	0.932995i	$0.382815\pi$
$468$	−195.066	−	195.066i	−0.000890616	−	0.000890616i
$469$			495037.i			2.25057i
$470$	−44666.8	−	16007.0i	−0.202204	−	0.0724626i
$471$	128644.			0.579892
$472$	168049.	−	168049.i	0.754314	−	0.754314i
$473$	−1259.74	−	1259.74i	−0.00563064	−	0.00563064i
$474$		−	62434.0i		−	0.277885i
$475$	105417.	−	128192.i	0.467224	−	0.568165i
$476$	152183.			0.671665
$477$	11453.7	−	11453.7i	0.0503396	−	0.0503396i
$478$	−134856.	−	134856.i	−0.590222	−	0.590222i
$479$			248368.i			1.08249i	0.840864	+	0.541247i	$0.182047\pi$
$479$			248368.i			1.08249i	−0.840864	+	0.541247i	$0.817953\pi$
$480$	−37252.6	+	103952.i	−0.161687	+	0.451180i
$481$	−1257.37			−0.00543469
$482$	123990.	−	123990.i	0.533695	−	0.533695i
$483$	−88719.5	−	88719.5i	−0.380299	−	0.380299i
$484$		−	84156.7i		−	0.359251i
$485$	38836.6	+	82218.5i	0.165104	+	0.349531i
$486$	11145.0			0.0471855
$487$	−159374.	+	159374.i	−0.671983	+	0.671983i	−0.958173	−	0.286190i	$-0.907611\pi$
$487$	−159374.	+	159374.i	−0.671983	+	0.671983i	0.286190	+	0.958173i	$0.407611\pi$
$488$	−239804.	−	239804.i	−1.00697	−	1.00697i
$489$		−	101233.i		−	0.423353i
$490$	−404201.	+	190928.i	−1.68347	+	0.795201i
$491$	−16577.9			−0.0687647			−0.0343823	−	0.999409i	$-0.510946\pi$
$491$	−16577.9			−0.0687647			−0.0343823	+	0.999409i	$0.510946\pi$
$492$	35769.6	−	35769.6i	0.147769	−	0.147769i
$493$	−86585.9	−	86585.9i	−0.356249	−	0.356249i
$494$		−	1087.06i		−	0.00445450i
$495$	−35838.2	−	12843.1i	−0.146263	−	0.0524156i
$496$	−60118.1			−0.244367
$497$	517632.	−	517632.i	2.09560	−	2.09560i
$498$	139169.	+	139169.i	0.561157	+	0.561157i
$499$			202437.i			0.812998i	0.913651	+	0.406499i	$0.133250\pi$
$499$			202437.i			0.812998i	−0.913651	+	0.406499i	$0.866750\pi$
$500$	58842.8	+	98505.0i	0.235371	+	0.394020i
$501$	162231.			0.646337
$502$	70574.2	−	70574.2i	0.280052	−	0.280052i
$503$	−33478.6	−	33478.6i	−0.132322	−	0.132322i	0.637844	−	0.770166i	$-0.279827\pi$
$503$	−33478.6	−	33478.6i	−0.132322	−	0.132322i	−0.770166	+	0.637844i	$0.779827\pi$
$504$		−	170749.i		−	0.672199i
$505$	62913.4	−	175557.i	0.246695	−	0.688391i
$506$	43515.5			0.169959
$507$	104933.	−	104933.i	0.408221	−	0.408221i
$508$	23054.4	+	23054.4i	0.0893361	+	0.0893361i
$509$		−	57834.5i		−	0.223229i	−0.993752	−	0.111615i	$-0.964398\pi$
$509$		−	57834.5i		−	0.223229i	0.993752	−	0.111615i	$-0.0356022\pi$
$510$	−36739.8	−	77779.5i	−0.141253	−	0.299037i
$511$	−252709.			−0.967784
$512$	116558.	−	116558.i	0.444633	−	0.444633i
$513$	−26343.9	−	26343.9i	−0.100103	−	0.100103i
$514$			108630.i			0.411171i
$515$	−148246.	+	70025.4i	−0.558945	+	0.264023i
$516$	1205.32			0.00452690
$517$	25726.0	−	25726.0i	0.0962481	−	0.0962481i
$518$	−173120.	−	173120.i	−0.645191	−	0.645191i
$519$			198089.i			0.735404i
$520$	2248.91	+	805.930i	0.00831698	+	0.00298051i
$521$	−56237.4			−0.207181			−0.103591	−	0.994620i	$-0.533033\pi$
$521$	−56237.4			−0.207181			−0.103591	+	0.994620i	$0.533033\pi$
$522$	−30561.6	+	30561.6i	−0.112159	+	0.112159i
$523$	210047.	+	210047.i	0.767914	+	0.767914i	0.977739	−	0.209825i	$-0.0672894\pi$
$523$	210047.	+	210047.i	0.767914	+	0.767914i	−0.209825	+	0.977739i	$0.567289\pi$
$524$			210878.i			0.768015i
$525$	−230968.	−	189934.i	−0.837979	−	0.689102i
$526$	−106831.			−0.386123
$527$	−113121.	+	113121.i	−0.407306	+	0.407306i
$528$	17526.7	+	17526.7i	0.0628684	+	0.0628684i
$529$		−	211073.i		−	0.754259i
$530$	−14886.7	+	41540.7i	−0.0529964	+	0.147884i
$531$	−93428.2			−0.331351
$532$	−126968.	+	126968.i	−0.448613	+	0.448613i
$533$	−1304.25	−	1304.25i	−0.00459100	−	0.00459100i
$534$		−	107265.i		−	0.376162i
$535$	−132950.	−	281460.i	−0.464495	−	0.983352i
$536$	369247.			1.28525
$537$	−160583.	+	160583.i	−0.556867	+	0.556867i
$538$	175775.	+	175775.i	0.607284	+	0.607284i
$539$		−	342767.i		−	1.17984i
$540$	23289.1	−	11000.8i	0.0798666	−	0.0377257i
$541$	263561.			0.900505			0.450252	−	0.892901i	$-0.351334\pi$
$541$	263561.			0.900505			0.450252	+	0.892901i	$0.351334\pi$
$542$	−220357.	+	220357.i	−0.750115	+	0.750115i
$543$	111639.	+	111639.i	0.378632	+	0.378632i
$544$		−	191317.i		−	0.646480i
$545$	187829.	+	67311.1i	0.632366	+	0.226618i
$546$	−1958.59			−0.00656988
$547$	−155327.	+	155327.i	−0.519125	+	0.519125i	−0.917306	−	0.398182i	$-0.869641\pi$
$547$	−155327.	+	155327.i	−0.519125	+	0.519125i	0.398182	+	0.917306i	$0.369641\pi$
$548$	−188189.	−	188189.i	−0.626660	−	0.626660i
$549$			133321.i			0.442338i
$550$	103223.	−	10063.3i	0.341233	−	0.0332672i
$551$	144479.			0.475885
$552$	−66175.7	+	66175.7i	−0.217180	+	0.217180i
$553$	265895.	+	265895.i	0.869482	+	0.869482i
$554$			297290.i			0.968635i
$555$	39604.4	−	110514.i	0.128575	−	0.358784i
$556$	−121201.			−0.392064
$557$	144074.	−	144074.i	0.464381	−	0.464381i	−0.435707	−	0.900088i	$-0.643502\pi$
$557$	144074.	−	144074.i	0.464381	−	0.464381i	0.900088	+	0.435707i	$0.143502\pi$
$558$	39927.4	+	39927.4i	0.128234	+	0.128234i
$559$		−	43.9489i		−	0.000140645i
$560$	83155.3	+	176043.i	0.265164	+	0.561361i
$561$	65957.9			0.209576
$562$	−13140.5	+	13140.5i	−0.0416044	+	0.0416044i
$563$	348774.	+	348774.i	1.10034	+	1.10034i	0.994369	+	0.105970i	$0.0337948\pi$
$563$	348774.	+	348774.i	1.10034	+	1.10034i	0.105970	+	0.994369i	$0.466205\pi$
$564$			24614.6i			0.0773812i
$565$	−59696.6	+	28198.2i	−0.187005	+	0.0883334i
$566$	−215240.			−0.671876
$567$	−47464.7	+	47464.7i	−0.147640	+	0.147640i
$568$	−386101.	−	386101.i	−1.19675	−	1.19675i
$569$			183209.i			0.565878i	0.959138	+	0.282939i	$0.0913095\pi$
$569$			183209.i			0.565878i	−0.959138	+	0.282939i	$0.908691\pi$
$570$	95544.8	+	34239.9i	0.294075	+	0.105386i
$571$	363497.			1.11488			0.557440	−	0.830217i	$-0.311784\pi$
$571$	363497.			1.11488			0.557440	+	0.830217i	$0.311784\pi$
$572$	−407.471	+	407.471i	−0.00124539	+	0.00124539i
$573$	16054.8	+	16054.8i	0.0488986	+	0.0488986i
$574$		−	359149.i		−	1.09006i
$575$	15903.3	+	163125.i	0.0481006	+	0.493383i
$576$	−104065.			−0.313661
$577$	168516.	−	168516.i	0.506161	−	0.506161i	−0.407184	−	0.913346i	$-0.633489\pi$
$577$	168516.	−	168516.i	0.506161	−	0.506161i	0.913346	+	0.407184i	$0.133489\pi$
$578$	−68378.2	−	68378.2i	−0.204674	−	0.204674i
$579$		−	40240.2i		−	0.120034i
$580$	−33696.6	+	94028.9i	−0.100168	+	0.279515i
$581$	−1.18539e6			−3.51164
$582$	−39319.0	+	39319.0i	−0.116080	+	0.116080i
$583$	−23925.5	−	23925.5i	−0.0703922	−	0.0703922i
$584$			188495.i			0.552680i
$585$	−401.118	−	849.181i	−0.00117209	−	0.00248135i
$586$	298380.			0.868911
$587$	−129891.	+	129891.i	−0.376966	+	0.376966i	−0.870007	−	0.493040i	$-0.835886\pi$
$587$	−129891.	+	129891.i	−0.376966	+	0.376966i	0.493040	+	0.870007i	$0.335886\pi$
$588$	163979.	+	163979.i	0.474280	+	0.474280i
$589$		−	188756.i		−	0.544089i
$590$	230139.	−	108708.i	0.661130	−	0.312291i
$591$	−82217.9			−0.235392
$592$	−54047.2	+	54047.2i	−0.154216	+	0.154216i
$593$	−299982.	−	299982.i	−0.853072	−	0.853072i	0.137438	−	0.990510i	$-0.456113\pi$
$593$	−299982.	−	299982.i	−0.853072	−	0.853072i	−0.990510	+	0.137438i	$0.956113\pi$
$594$		−	23280.7i		−	0.0659816i
$595$	487717.	+	174780.i	1.37763	+	0.493695i
$596$	−77834.0			−0.219117
$597$	−66118.1	+	66118.1i	−0.185512	+	0.185512i
$598$	759.071	+	759.071i	0.00212266	+	0.00212266i
$599$		−	642365.i		−	1.79031i	−0.445754	−	0.895155i	$-0.647065\pi$
$599$		−	642365.i		−	1.79031i	0.445754	−	0.895155i	$-0.352935\pi$
$600$	−141671.	+	172279.i	−0.393531	+	0.478551i
$601$	624794.			1.72977			0.864884	−	0.501971i	$-0.167392\pi$
$601$	624794.			1.72977			0.864884	+	0.501971i	$0.167392\pi$
$602$	6051.06	−	6051.06i	0.0166970	−	0.0166970i
$603$	−102643.	−	102643.i	−0.282289	−	0.282289i
$604$		−	224786.i		−	0.616163i
$605$	96652.9	−	269706.i	0.264061	−	0.736850i
$606$	114043.			0.310544
$607$	−133169.	+	133169.i	−0.361431	+	0.361431i	−0.864340	−	0.502909i	$-0.832263\pi$
$607$	−133169.	+	133169.i	−0.361431	+	0.361431i	0.502909	+	0.864340i	$0.332263\pi$
$608$	159618.	+	159618.i	0.431792	+	0.431792i
$609$		−	260313.i		−	0.701877i
$610$	−155126.	−	328406.i	−0.416892	−	0.882575i
$611$	897.513			0.00240413
$612$	−31554.2	+	31554.2i	−0.0842470	+	0.0842470i
$613$	−394586.	−	394586.i	−1.05008	−	1.05008i	−0.998678	−	0.0513978i	$-0.983632\pi$
$613$	−394586.	−	394586.i	−1.05008	−	1.05008i	−0.0513978	−	0.998678i	$-0.516368\pi$
$614$			91783.0i			0.243459i
$615$	155716.	−	73553.7i	0.411701	−	0.194471i
$616$	−356676.			−0.939966
$617$	246284.	−	246284.i	0.646942	−	0.646942i	−0.305311	−	0.952253i	$-0.598760\pi$
$617$	246284.	−	246284.i	0.646942	−	0.646942i	0.952253	+	0.305311i	$0.0987603\pi$
$618$	−70895.3	−	70895.3i	−0.185627	−	0.185627i
$619$			135789.i			0.354391i	0.984176	+	0.177195i	$0.0567025\pi$
$619$			135789.i			0.354391i	−0.984176	+	0.177195i	$0.943298\pi$
$620$	122845.	+	44023.1i	0.319575	+	0.114524i
$621$	36790.9			0.0954018
$622$	−208943.	+	208943.i	−0.540067	+	0.540067i
$623$	456821.	+	456821.i	1.17698	+	1.17698i
$624$			611.461i			0.00157036i
$625$	75448.0	+	383269.i	0.193147	+	0.981170i
$626$	−135365.			−0.345429
$627$	−55029.5	+	55029.5i	−0.139978	+	0.139978i
$628$	128556.	+	128556.i	0.325968	+	0.325968i
$629$			203395.i			0.514089i
$630$	61691.0	−	172146.i	0.155432	−	0.433726i
$631$	−566102.			−1.42179			−0.710896	−	0.703297i	$-0.751710\pi$
$631$	−566102.			−1.42179			−0.710896	+	0.703297i	$0.751710\pi$
$632$	198331.	−	198331.i	0.496542	−	0.496542i
$633$	−45765.6	−	45765.6i	−0.114217	−	0.114217i
$634$		−	302374.i		−	0.752257i
$635$	47407.2	+	100363.i	0.117570	+	0.248900i
$636$	22891.9			0.0565937
$637$	5979.11	−	5979.11i	0.0147353	−	0.0147353i
$638$	63839.7	+	63839.7i	0.156837	+	0.156837i
$639$			214655.i			0.525703i
$640$	−51106.7	+	24140.7i	−0.124772	+	0.0589372i
$641$	398483.			0.969826			0.484913	−	0.874562i	$-0.338851\pi$
$641$	398483.			0.969826			0.484913	+	0.874562i	$0.338851\pi$
$642$	134602.	−	134602.i	0.326573	−	0.326573i
$643$	270770.	+	270770.i	0.654905	+	0.654905i	0.954170	−	0.299265i	$-0.0967415\pi$
$643$	270770.	+	270770.i	0.654905	+	0.654905i	−0.299265	+	0.954170i	$0.596741\pi$
$644$		−	177319.i		−	0.427546i
$645$	3862.80	+	1384.29i	0.00928502	+	0.00332742i
$646$	−175844.			−0.421370
$647$	22129.0	−	22129.0i	0.0528632	−	0.0528632i	−0.680181	−	0.733044i	$-0.738099\pi$
$647$	22129.0	−	22129.0i	0.0528632	−	0.0528632i	0.733044	+	0.680181i	$0.238099\pi$
$648$	35403.8	+	35403.8i	0.0843140	+	0.0843140i
$649$			195161.i			0.463344i
$650$	1976.13	+	1625.04i	0.00467723	+	0.00384626i
$651$	−340087.			−0.802469
$652$	101164.	−	101164.i	0.237974	−	0.237974i
$653$	−168610.	−	168610.i	−0.395418	−	0.395418i	0.481195	−	0.876613i	$-0.340203\pi$
$653$	−168610.	−	168610.i	−0.395418	−	0.395418i	−0.876613	+	0.481195i	$0.840203\pi$
$654$			122014.i			0.285270i
$655$	−242191.	+	675824.i	−0.564516	+	1.57526i
$656$	−112125.			−0.260551
$657$	52397.6	−	52397.6i	0.121389	−	0.121389i
$658$	123573.	+	123573.i	0.285412	+	0.285412i
$659$			106032.i			0.244155i	0.992521	+	0.122078i	$0.0389557\pi$
$659$			106032.i			0.244155i	−0.992521	+	0.122078i	$0.961044\pi$
$660$	−22979.4	−	48648.3i	−0.0527535	−	0.111681i
$661$	−360211.			−0.824432			−0.412216	−	0.911086i	$-0.635245\pi$
$661$	−360211.			−0.824432			−0.412216	+	0.911086i	$0.635245\pi$
$662$	−238004.	+	238004.i	−0.543085	+	0.543085i
$663$	1150.55	+	1150.55i	0.00261745	+	0.00261745i
$664$			884182.i			2.00542i
$665$	−552730.	+	261087.i	−1.24988	+	0.590394i
$666$	71790.8			0.161853
$667$	−100887.	+	100887.i	−0.226769	+	0.226769i
$668$	162121.	+	162121.i	0.363318	+	0.363318i
$669$			193996.i			0.433451i
$670$	372267.	+	133407.i	0.829288	+	0.297187i
$671$	278492.			0.618541
$672$	287588.	−	287588.i	0.636843	−	0.636843i
$673$	−174418.	−	174418.i	−0.385090	−	0.385090i	0.487842	−	0.872932i	$-0.337784\pi$
$673$	−174418.	−	174418.i	−0.385090	−	0.385090i	−0.872932	+	0.487842i	$0.837784\pi$
$674$		−	315167.i		−	0.693779i
$675$	87271.3	−	8508.20i	0.191542	−	0.0186737i
$676$	209723.			0.458937
$677$	118882.	−	118882.i	0.259382	−	0.259382i	−0.565421	−	0.824803i	$-0.691286\pi$
$677$	118882.	−	118882.i	0.259382	−	0.259382i	0.824803	+	0.565421i	$0.191286\pi$
$678$	−28548.5	−	28548.5i	−0.0621046	−	0.0621046i
$679$		−	334906.i		−	0.726412i
$680$	130368.	−	363787.i	0.281939	−	0.786737i
$681$	237115.			0.511288
$682$	83403.7	−	83403.7i	0.179315	−	0.179315i
$683$	−464368.	−	464368.i	−0.995453	−	0.995453i	0.00453640	−	0.999990i	$-0.498556\pi$
$683$	−464368.	−	464368.i	−0.995453	−	0.995453i	−0.999990	+	0.00453640i	$0.998556\pi$
$684$		−	52652.1i		−	0.112539i
$685$	−386975.	−	819240.i	−0.824712	−	1.74594i
$686$	995993.			2.11645
$687$	250280.	−	250280.i	0.530288	−	0.530288i
$688$	−1889.11	−	1889.11i	−0.00399098	−	0.00399098i
$689$		−	834.698i		−	0.00175829i
$690$	−90626.0	+	42808.0i	−0.190351	+	0.0899139i
$691$	112733.			0.236099			0.118050	−	0.993008i	$-0.462336\pi$
$691$	112733.			0.236099			0.118050	+	0.993008i	$0.462336\pi$
$692$	−197955.	+	197955.i	−0.413384	+	0.413384i
$693$	99148.3	+	99148.3i	0.206452	+	0.206452i
$694$			207899.i			0.431651i
$695$	−388425.	−	139198.i	−0.804152	−	0.288179i
$696$	−194167.			−0.400826
$697$	−210978.	+	210978.i	−0.434282	+	0.434282i
$698$	−154354.	−	154354.i	−0.316817	−	0.316817i
$699$		−	484529.i		−	0.991665i
$700$	−41006.4	−	420616.i	−0.0836866	−	0.858400i
$701$	540863.			1.10065			0.550327	−	0.834949i	$-0.314503\pi$
$701$	540863.			1.10065			0.550327	+	0.834949i	$0.314503\pi$
$702$	406.101	−	406.101i	0.000824061	−	0.000824061i
$703$	−169695.	−	169695.i	−0.343366	−	0.343366i
$704$			217380.i			0.438606i
$705$	−28269.6	+	78885.1i	−0.0568777	+	0.158715i
$706$	64394.5			0.129193
$707$	−485688.	+	485688.i	−0.971669	+	0.971669i
$708$	−93364.8	−	93364.8i	−0.186259	−	0.186259i
$709$			209535.i			0.416835i	0.978040	+	0.208418i	$0.0668313\pi$
$709$			209535.i			0.416835i	−0.978040	+	0.208418i	$0.933169\pi$
$710$	−249762.	−	528755.i	−0.495462	−	1.04891i
$711$	−110263.			−0.218118
$712$	340742.	−	340742.i	0.672150	−	0.672150i
$713$	131804.	+	131804.i	0.259269	+	0.259269i
$714$			316824.i			0.621472i
$715$	−1773.84	+	837.890i	−0.00346979	+	0.00163898i
$716$	−320948.			−0.626050
$717$	−238167.	+	238167.i	−0.463280	+	0.463280i
$718$	−96676.7	−	96676.7i	−0.187531	−	0.187531i
$719$		−	579641.i		−	1.12125i	−0.828071	−	0.560623i	$-0.810562\pi$
$719$		−	579641.i		−	1.12125i	0.828071	−	0.560623i	$-0.189438\pi$
$720$	−53743.1	−	19259.6i	−0.103671	−	0.0371520i
$721$	603861.			1.16163
$722$	−124417.	+	124417.i	−0.238674	+	0.238674i
$723$	−218977.	−	218977.i	−0.418910	−	0.418910i
$724$			223127.i			0.425672i
$725$	−215982.	+	262644.i	−0.410905	+	0.499680i
$726$	175202.			0.332404
$727$	666638.	−	666638.i	1.26131	−	1.26131i	0.310848	−	0.950460i	$-0.399387\pi$
$727$	666638.	−	666638.i	1.26131	−	1.26131i	0.950460	−	0.310848i	$-0.100613\pi$
$728$	−6221.74	−	6221.74i	−0.0117395	−	0.0117395i
$729$		−	19683.0i		−	0.0370370i
$730$	−68102.5	+	190037.i	−0.127796	+	0.356609i
$731$	−7109.24			−0.0133042
$732$	−133231.	+	133231.i	−0.248646	+	0.248646i
$733$	184382.	+	184382.i	0.343171	+	0.343171i	0.857558	−	0.514387i	$-0.171981\pi$
$733$	184382.	+	184382.i	0.343171	+	0.343171i	−0.514387	+	0.857558i	$0.671981\pi$
$734$			240212.i			0.445865i
$735$	337194.	+	713850.i	0.624172	+	1.32139i
$736$	−222916.			−0.411514
$737$	−214409.	+	214409.i	−0.394737	+	0.394737i
$738$	74467.3	+	74467.3i	0.136727	+	0.136727i
$739$			175164.i			0.320742i	0.987057	+	0.160371i	$0.0512691\pi$
$739$			175164.i			0.320742i	−0.987057	+	0.160371i	$0.948731\pi$
$740$	150017.	−	70861.8i	0.273953	−	0.129404i
$741$	−1919.83			−0.00349645
$742$	114924.	−	114924.i	0.208740	−	0.208740i
$743$	540487.	+	540487.i	0.979057	+	0.979057i	0.999785	−	0.0207283i	$-0.00659849\pi$
$743$	540487.	+	540487.i	0.979057	+	0.979057i	−0.0207283	+	0.999785i	$0.506598\pi$
$744$			253670.i			0.458272i
$745$	−249443.	−	89391.4i	−0.449426	−	0.161058i
$746$	−691463.			−1.24249
$747$	245784.	−	245784.i	0.440465	−	0.440465i
$748$	65913.1	+	65913.1i	0.117806	+	0.117806i
$749$			1.14649e6i			2.04365i
$750$	−205073.	+	122503.i	−0.364575	+	0.217782i
$751$	−588360.			−1.04319			−0.521595	−	0.853193i	$-0.674663\pi$
$751$	−588360.			−1.04319			−0.521595	+	0.853193i	$0.674663\pi$
$752$	38578.9	−	38578.9i	0.0682204	−	0.0682204i
$753$	−124640.	−	124640.i	−0.219819	−	0.219819i
$754$			2227.20i			0.00391756i
$755$	258164.	−	720395.i	0.452899	−	1.26380i
$756$	−94864.9			−0.165982
$757$	497479.	−	497479.i	0.868126	−	0.868126i	−0.124139	−	0.992265i	$-0.539617\pi$
$757$	497479.	−	497479.i	0.868126	−	0.868126i	0.992265	+	0.124139i	$0.0396168\pi$
$758$	85956.5	+	85956.5i	0.149603	+	0.149603i
$759$		−	76851.9i		−	0.133405i
$760$	194744.	+	412280.i	0.337161	+	0.713781i
$761$	968464.			1.67230			0.836150	−	0.548501i	$-0.184801\pi$
$761$	968464.			1.67230			0.836150	+	0.548501i	$0.184801\pi$
$762$	−47996.1	+	47996.1i	−0.0826601	+	0.0826601i
$763$	−519638.	−	519638.i	−0.892589	−	0.892589i
$764$			32087.9i			0.0549736i
$765$	−137365.	+	64885.4i	−0.234721	+	0.110873i
$766$	−300231.			−0.511679
$767$	−3404.32	+	3404.32i	−0.00578682	+	0.00578682i
$768$	−251024.	−	251024.i	−0.425592	−	0.425592i
$769$		−	63796.8i		−	0.107881i	−0.998544	−	0.0539406i	$-0.982822\pi$
$769$		−	63796.8i		−	0.107881i	0.998544	−	0.0539406i	$-0.0171782\pi$
$770$	−359593.	−	128865.i	−0.606499	−	0.217348i
$771$	191849.			0.322738
$772$	40212.9	−	40212.9i	0.0674731	−	0.0674731i
$773$	142221.	+	142221.i	0.238015	+	0.238015i	0.816028	−	0.578013i	$-0.196172\pi$
$773$	142221.	+	142221.i	0.238015	+	0.238015i	−0.578013	+	0.816028i	$0.696172\pi$
$774$			2509.30i			0.00418861i
$775$	343133.	+	282171.i	0.571293	+	0.469796i
$776$	−249805.			−0.414838
$777$	−305744.	+	305744.i	−0.506426	+	0.506426i
$778$	399827.	+	399827.i	0.660561	+	0.660561i
$779$		−	352043.i		−	0.580124i
$780$	447.759	−	1249.45i	0.000735961	−	0.00205367i
$781$	448391.			0.735114
$782$	122788.	−	122788.i	0.200791	−	0.200791i
$783$	53974.2	+	53974.2i	0.0880365	+	0.0880365i
$784$		−	514015.i		−	0.836264i
$785$	264353.	+	559644.i	0.428988	+	0.908181i
$786$	−439019.			−0.710622
$787$	−171318.	+	171318.i	−0.276601	+	0.276601i	−0.831751	−	0.555150i	$-0.812661\pi$
$787$	−171318.	+	171318.i	−0.276601	+	0.276601i	0.555150	+	0.831751i	$0.312661\pi$
$788$	−82162.1	−	82162.1i	−0.132318	−	0.132318i
$789$			188672.i			0.303077i
$790$	271609.	−	128297.i	0.435201	−	0.205571i
$791$	243166.			0.388642
$792$	73954.5	−	73954.5i	0.117900	−	0.117900i
$793$	4857.93	+	4857.93i	0.00772512	+	0.00772512i
$794$		−	736857.i		−	1.16881i
$795$	73364.1	+	26291.1i	0.116078	+	0.0415982i
$796$	−132146.			−0.208559
$797$	−396832.	+	396832.i	−0.624727	+	0.624727i	−0.946736	−	0.322010i	$-0.895642\pi$
$797$	−396832.	+	396832.i	−0.624727	+	0.624727i	0.322010	+	0.946736i	$0.395642\pi$
$798$	−264330.	−	264330.i	−0.415088	−	0.415088i
$799$		−	145183.i		−	0.227417i
$800$	−528777.	+	51551.2i	−0.826214	+	0.0805487i
$801$	−189438.			−0.295258
$802$	−433357.	+	433357.i	−0.673747	+	0.673747i
$803$	−109453.	−	109453.i	−0.169744	−	0.169744i
$804$		−	205146.i		−	0.317359i
$805$	203648.	−	568271.i	0.314260	−	0.876928i
$806$	2909.74			0.00447902
$807$	310432.	−	310432.i	0.476672	−	0.476672i
$808$	362274.	+	362274.i	0.554899	+	0.554899i
$809$		−	571851.i		−	0.873748i	−0.899523	−	0.436874i	$-0.856086\pi$
$809$		−	571851.i		−	0.873748i	0.899523	−	0.436874i	$-0.143914\pi$
$810$	22902.1	+	48484.6i	0.0349065	+	0.0738982i
$811$	−851039.			−1.29392			−0.646960	−	0.762524i	$-0.723960\pi$
$811$	−851039.			−1.29392			−0.646960	+	0.762524i	$0.723960\pi$
$812$	260136.	−	260136.i	0.394538	−	0.394538i
$813$	389167.	+	389167.i	0.588783	+	0.588783i
$814$		−	149963.i		−	0.226326i
$815$	440396.	−	208025.i	0.663023	−	0.313185i
$816$	98910.8			0.148547
$817$	5931.33	−	5931.33i	0.00888603	−	0.00888603i
$818$	552843.	+	552843.i	0.826220	+	0.826220i
$819$			3459.02i			0.00515686i
$820$	229114.	+	82106.2i	0.340740	+	0.122109i
$821$	−422213.			−0.626391			−0.313195	−	0.949689i	$-0.601399\pi$
$821$	−422213.			−0.626391			−0.313195	+	0.949689i	$0.601399\pi$
$822$	391782.	−	391782.i	0.579831	−	0.579831i
$823$	−742417.	−	742417.i	−1.09609	−	1.09609i	−0.994863	−	0.101231i	$-0.967722\pi$
$823$	−742417.	−	742417.i	−1.09609	−	1.09609i	−0.101231	−	0.994863i	$-0.532278\pi$
$824$		−	450418.i		−	0.663379i
$825$	−17772.7	−	182300.i	−0.0261123	−	0.267842i
$826$	−937440.			−1.37399
$827$	−422050.	+	422050.i	−0.617097	+	0.617097i	−0.944786	−	0.327689i	$-0.893730\pi$
$827$	−422050.	+	422050.i	−0.617097	+	0.617097i	0.327689	+	0.944786i	$0.393730\pi$
$828$	36765.9	+	36765.9i	0.0536271	+	0.0536271i
$829$			310239.i			0.451427i	0.974194	+	0.225713i	$0.0724712\pi$
$829$			310239.i			0.451427i	−0.974194	+	0.225713i	$0.927529\pi$
$830$	−319451.	+	891414.i	−0.463712	+	1.29397i
$831$	525037.			0.760305
$832$	−3791.91	+	3791.91i	−0.00547787	+	0.00547787i
$833$	−967190.	−	967190.i	−1.39387	−	1.39387i
$834$		−	252323.i		−	0.362765i
$835$	333372.	+	705761.i	0.478142	+	1.01224i
$836$	−109984.			−0.157369
$837$	70514.9	−	70514.9i	0.100654	−	0.100654i
$838$	261321.	+	261321.i	0.372123	+	0.372123i
$839$		−	1.20455e6i		−	1.71120i	−0.517636	−	0.855601i	$-0.673188\pi$
$839$		−	1.20455e6i		−	1.71120i	0.517636	−	0.855601i	$-0.326812\pi$
$840$	742817.	−	350876.i	1.05275	−	0.497274i
$841$	411268.			0.581477
$842$	579683.	−	579683.i	0.817648	−	0.817648i
$843$	23207.2	+	23207.2i	0.0326563	+	0.0326563i
$844$		−	91469.1i		−	0.128407i
$845$	672121.	+	240864.i	0.941313	+	0.337333i
$846$	−51244.2			−0.0715985
$847$	−746155.	+	746155.i	−1.04007	+	1.04007i
$848$	−35878.8	−	35878.8i	−0.0498938	−	0.0498938i
$849$			380130.i			0.527372i
$850$	262870.	−	319661.i	0.363833	−	0.442438i
$851$	236989.			0.327242
$852$	−214510.	+	214510.i	−0.295507	+	0.295507i
$853$	460012.	+	460012.i	0.632224	+	0.632224i	0.948625	−	0.316402i	$-0.102475\pi$
$853$	460012.	+	460012.i	0.632224	+	0.632224i	−0.316402	+	0.948625i	$0.602475\pi$
$854$			1.33772e6i			1.83421i
$855$	60470.3	−	168740.i	0.0827199	−	0.230826i
$856$	855163.			1.16708
$857$	−398341.	+	398341.i	−0.542367	+	0.542367i	−0.924222	−	0.381855i	$-0.875285\pi$
$857$	−398341.	+	398341.i	−0.542367	+	0.542367i	0.381855	+	0.924222i	$0.375285\pi$
$858$	−848.298	−	848.298i	−0.00115232	−	0.00115232i
$859$			323065.i			0.437828i	0.975744	+	0.218914i	$0.0702514\pi$
$859$			323065.i			0.437828i	−0.975744	+	0.218914i	$0.929749\pi$
$860$	2476.83	+	5243.53i	0.00334887	+	0.00708968i
$861$	−634286.			−0.855616
$862$	−209300.	+	209300.i	−0.281679	+	0.281679i
$863$	414986.	+	414986.i	0.557200	+	0.557200i	0.928509	−	0.371309i	$-0.121091\pi$
$863$	414986.	+	414986.i	0.557200	+	0.557200i	−0.371309	+	0.928509i	$0.621091\pi$
$864$			119259.i			0.159759i
$865$	−861755.	+	407058.i	−1.15173	+	0.544031i
$866$	482722.			0.643667
$867$	−120761.	+	120761.i	−0.160653	+	0.160653i
$868$	−339856.	−	339856.i	−0.451082	−	0.451082i
$869$			230328.i			0.305005i
$870$	−195755.	−	70151.6i	−0.258627	−	0.0926828i
$871$	−7480.16			−0.00985995
$872$	−387597.	+	387597.i	−0.509738	+	0.509738i
$873$	69440.6	+	69440.6i	0.0911139	+	0.0911139i
$874$			204888.i			0.268221i
$875$	351655.	−	1.39509e6i	0.459304	−	1.82216i
$876$	104724.			0.136470
$877$	−257142.	+	257142.i	−0.334328	+	0.334328i	−0.854228	−	0.519899i	$-0.825969\pi$
$877$	−257142.	+	257142.i	−0.334328	+	0.334328i	0.519899	+	0.854228i	$0.325969\pi$
$878$	340477.	+	340477.i	0.441671	+	0.441671i
$879$		−	526964.i		−	0.682029i
$880$	−40231.1	+	112263.i	−0.0519514	+	0.144968i
$881$	−831152.			−1.07085			−0.535425	−	0.844583i	$-0.679848\pi$
$881$	−831152.			−1.07085			−0.535425	+	0.844583i	$0.679848\pi$
$882$	−341382.	+	341382.i	−0.438837	+	0.438837i
$883$	908952.	+	908952.i	1.16579	+	1.16579i	0.983187	+	0.182601i	$0.0584518\pi$
$883$	908952.	+	908952.i	1.16579	+	1.16579i	0.182601	+	0.983187i	$0.441548\pi$
$884$			2299.53i			0.00294263i
$885$	−191988.	−	406444.i	−0.245124	−	0.518937i
$886$	488126.			0.621820
$887$	−93115.5	+	93115.5i	−0.118352	+	0.118352i	−0.763802	−	0.645450i	$-0.776670\pi$
$887$	−93115.5	+	93115.5i	−0.118352	+	0.118352i	0.645450	+	0.763802i	$0.276670\pi$
$888$	228054.	+	228054.i	0.289209	+	0.289209i
$889$		−	408814.i		−	0.517276i
$890$	466638.	−	220421.i	0.589115	−	0.278274i
$891$	−41115.5			−0.0517906
$892$	−193864.	+	193864.i	−0.243651	+	0.243651i
$893$	121128.	+	121128.i	0.151894	+	0.151894i
$894$		−	162039.i		−	0.202743i
$895$	−1.02858e6	−	368606.i	−1.28408	−	0.460167i
$896$	208176.			0.259307
$897$	1340.58	−	1340.58i	0.00166613	−	0.00166613i
$898$	−712658.	−	712658.i	−0.883748	−	0.883748i
$899$			386728.i			0.478505i
$900$	95714.5	+	78709.7i	0.118166	+	0.0971724i
$901$	−135022.			−0.166324
$902$	155554.	−	155554.i	0.191191	−	0.191191i
$903$	−10686.6	−	10686.6i	−0.0131059	−	0.0131059i
$904$		−	181377.i		−	0.221945i
$905$	−256259.	+	715079.i	−0.312883	+	0.873086i
$906$	467973.			0.570117
$907$	−62370.3	+	62370.3i	−0.0758164	+	0.0758164i	−0.743998	−	0.668182i	$-0.767073\pi$
$907$	−62370.3	+	62370.3i	−0.0758164	+	0.0758164i	0.668182	+	0.743998i	$0.267073\pi$
$908$	236954.	+	236954.i	0.287404	+	0.287404i
$909$		−	201409.i		−	0.243753i
$910$	−4024.74	−	8520.52i	−0.00486021	−	0.0102892i
$911$	−1.18436e6			−1.42708			−0.713540	−	0.700615i	$-0.752909\pi$
$911$	−1.18436e6			−1.42708			−0.713540	+	0.700615i	$0.752909\pi$
$912$	−82522.4	+	82522.4i	−0.0992162	+	0.0992162i
$913$	−513414.	−	513414.i	−0.615923	−	0.615923i
$914$		−	677411.i		−	0.810886i
$915$	−579992.	+	273964.i	−0.692755	+	0.327229i
$916$	500220.			0.596170
$917$	1.86970e6	−	1.86970e6i	2.22349	−	2.22349i
$918$	−65691.4	−	65691.4i	−0.0779513	−	0.0779513i
$919$		−	773358.i		−	0.915692i	−0.889031	−	0.457846i	$-0.848621\pi$
$919$		−	773358.i		−	0.915692i	0.889031	−	0.457846i	$-0.151379\pi$
$920$	−423872.	−	151901.i	−0.500794	−	0.179467i
$921$	162096.			0.191097
$922$	590199.	−	590199.i	0.694283	−	0.694283i
$923$	7821.58	+	7821.58i	0.00918103	+	0.00918103i
$924$			198162.i			0.232101i
$925$	562159.	−	54805.6i	0.657016	−	0.0640533i
$926$	141828.			0.165401
$927$	−125207.	+	125207.i	−0.145703	+	0.145703i
$928$	−327030.	−	327030.i	−0.379744	−	0.379744i
$929$			881163.i			1.02100i	0.859878	+	0.510499i	$0.170539\pi$
$929$			881163.i			1.02100i	−0.859878	+	0.510499i	$0.829461\pi$
$930$	−91650.0	+	255745.i	−0.105966	+	0.295693i
$931$	1.61388e6			1.86196
$932$	484200.	−	484200.i	0.557433	−	0.557433i
$933$	369010.	+	369010.i	0.423912	+	0.423912i
$934$		−	520063.i		−	0.596159i
$935$	135538.	+	286939.i	0.155038	+	0.328221i
$936$	2580.08			0.00294497
$937$	992967.	−	992967.i	1.13098	−	1.13098i	0.140967	−	0.990014i	$-0.454979\pi$
$937$	992967.	−	992967.i	1.13098	−	1.13098i	0.990014	−	0.140967i	$-0.0450212\pi$
$938$	−1.02990e6	−	1.02990e6i	−1.17055	−	1.17055i
$939$			239066.i			0.271136i
$940$	−107082.	+	50581.1i	−0.121188	+	0.0572444i
$941$	−1.13615e6			−1.28309			−0.641545	−	0.767085i	$-0.721706\pi$
$941$	−1.13615e6			−1.28309			−0.641545	+	0.767085i	$0.721706\pi$
$942$	−267637.	+	267637.i	−0.301609	+	0.301609i
$943$	245824.	+	245824.i	0.276440	+	0.276440i
$944$			292664.i			0.328417i
$945$	−304023.	−	108951.i	−0.340442	−	0.122002i
$946$	5241.64			0.00585713
$947$	−208361.	+	208361.i	−0.232336	+	0.232336i	−0.813667	−	0.581331i	$-0.802532\pi$
$947$	−208361.	+	208361.i	−0.232336	+	0.232336i	0.581331	+	0.813667i	$0.302532\pi$
$948$	−110189.	−	110189.i	−0.122608	−	0.122608i
$949$		−	3818.51i		−	0.00423996i
$950$	47382.0	+	486013.i	0.0525009	+	0.538518i
$951$	−534017.			−0.590465
$952$	−1.00644e6	+	1.00644e6i	−1.11049	+	1.11049i
$953$	−761064.	−	761064.i	−0.837983	−	0.837983i	0.150610	−	0.988593i	$-0.451876\pi$
$953$	−761064.	−	761064.i	−0.837983	−	0.837983i	−0.988593	+	0.150610i	$0.951876\pi$
$954$			47657.7i			0.0523645i
$955$	−36852.6	+	102835.i	−0.0404074	+	0.112755i
$956$	−476011.			−0.520836
$957$	112746.	−	112746.i	0.123105	−	0.123105i
$958$	−516717.	−	516717.i	−0.563018	−	0.563018i
$959$			3.33706e6i			3.62850i
$960$	−213846.	−	452719.i	−0.232037	−	0.491231i
$961$	−418277.			−0.452916
$962$	2615.90	−	2615.90i	0.00282664	−	0.00282664i
$963$	−237717.	−	237717.i	−0.256335	−	0.256335i
$964$		−	437656.i		−	0.470954i
$965$	175058.	−	82690.4i	0.187987	−	0.0887974i
$966$	369152.			0.395596
$967$	456976.	−	456976.i	0.488698	−	0.488698i	−0.419197	−	0.907895i	$-0.637688\pi$
$967$	456976.	−	456976.i	0.488698	−	0.488698i	0.907895	+	0.419197i	$0.137688\pi$
$968$	556556.	+	556556.i	0.593961	+	0.593961i
$969$			310555.i			0.330743i
$970$	−251849.	−	90253.6i	−0.267668	−	0.0959227i
$971$	1.23029e6			1.30488			0.652439	−	0.757841i	$-0.273746\pi$
$971$	1.23029e6			1.30488			0.652439	+	0.757841i	$0.273746\pi$
$972$	19669.6	−	19669.6i	0.0208192	−	0.0208192i
$973$	1.07460e6	+	1.07460e6i	1.13507	+	1.13507i
$974$		−	663136.i		−	0.699012i
$975$	2869.96	−	3490.00i	0.00301902	−	0.00367127i
$976$	417628.			0.438420
$977$	120924.	−	120924.i	0.126684	−	0.126684i	−0.640922	−	0.767606i	$-0.721448\pi$
$977$	120924.	−	120924.i	0.126684	−	0.126684i	0.767606	+	0.640922i	$0.221448\pi$
$978$	210609.	+	210609.i	0.220191	+	0.220191i
$979$			395715.i			0.412873i
$980$	−376401.	+	1.05033e6i	−0.391921	+	1.09364i
$981$	215487.			0.223915
$982$	34489.4	−	34489.4i	0.0357653	−	0.0357653i
$983$	−607621.	−	607621.i	−0.628819	−	0.628819i	0.318952	−	0.947771i	$-0.396669\pi$
$983$	−607621.	−	607621.i	−0.628819	−	0.628819i	−0.947771	+	0.318952i	$0.896669\pi$
$984$			473113.i			0.488624i
$985$	−168951.	−	357676.i	−0.174136	−	0.368652i
$986$	360275.			0.370578
$987$	218240.	−	218240.i	0.224027	−	0.224027i
$988$	−1918.53	−	1918.53i	−0.00196542	−	0.00196542i
$989$			8283.45i			0.00846873i
$990$	101279.	−	47840.0i	0.103335	−	0.0488113i
$991$	−32696.1			−0.0332927			−0.0166464	−	0.999861i	$-0.505299\pi$
$991$	−32696.1			−0.0332927			−0.0166464	+	0.999861i	$0.505299\pi$
$992$	−427250.	+	427250.i	−0.434169	+	0.434169i
$993$	420334.	+	420334.i	0.426281	+	0.426281i
$994$			2.15381e6i			2.17989i
$995$	−423504.	−	151769.i	−0.427771	−	0.153298i
$996$	491234.			0.495187
$997$	196213.	−	196213.i	0.197395	−	0.197395i	−0.601487	−	0.798882i	$-0.705425\pi$
$997$	196213.	−	196213.i	0.197395	−	0.197395i	0.798882	+	0.601487i	$0.205425\pi$
$998$	−421160.	−	421160.i	−0.422850	−	0.422850i
$999$		−	126788.i		−	0.127042i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	15.5.f.a.13.2	yes	8
3.2	odd	2		45.5.g.e.28.3		8
4.3	odd	2		240.5.bg.c.193.2		8
5.2	odd	4	inner	15.5.f.a.7.2	✓	8
5.3	odd	4		75.5.f.e.7.3		8
5.4	even	2		75.5.f.e.43.3		8
15.2	even	4		45.5.g.e.37.3		8
15.8	even	4		225.5.g.m.82.2		8
15.14	odd	2		225.5.g.m.118.2		8
20.7	even	4		240.5.bg.c.97.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
15.5.f.a.7.2	✓	8	5.2	odd	4	inner
15.5.f.a.13.2	yes	8	1.1	even	1	trivial
45.5.g.e.28.3		8	3.2	odd	2
45.5.g.e.37.3		8	15.2	even	4
75.5.f.e.7.3		8	5.3	odd	4
75.5.f.e.43.3		8	5.4	even	2
225.5.g.m.82.2		8	15.8	even	4
225.5.g.m.118.2		8	15.14	odd	2
240.5.bg.c.97.2		8	20.7	even	4
240.5.bg.c.193.2		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)

\(f(q)\)	\(=\)	\(q+(-2.08045 + 2.08045i) q^{2} +(3.67423 + 3.67423i) q^{3} +7.34348i q^{4} +(-8.43390 + 23.5344i) q^{5} -15.2881 q^{6} +(65.1093 - 65.1093i) q^{7} +(-48.5649 - 48.5649i) q^{8} +27.0000i q^{9} +O(q^{10})\)	\(q+(-2.08045 + 2.08045i) q^{2} +(3.67423 + 3.67423i) q^{3} +7.34348i q^{4} +(-8.43390 + 23.5344i) q^{5} -15.2881 q^{6} +(65.1093 - 65.1093i) q^{7} +(-48.5649 - 48.5649i) q^{8} +27.0000i q^{9} +(-31.4158 - 66.5084i) q^{10} +56.3999 q^{11} +(-26.9817 + 26.9817i) q^{12} +(0.983822 + 0.983822i) q^{13} +270.913i q^{14} +(-117.459 + 55.4829i) q^{15} +84.5776 q^{16} +(159.144 - 159.144i) q^{17} +(-56.1721 - 56.1721i) q^{18} +265.552i q^{19} +(-172.825 - 61.9342i) q^{20} +478.454 q^{21} +(-117.337 + 117.337i) q^{22} +(-185.430 - 185.430i) q^{23} -356.877i q^{24} +(-482.739 - 396.974i) q^{25} -4.09358 q^{26} +(-99.2043 + 99.2043i) q^{27} +(478.129 + 478.129i) q^{28} -544.071i q^{29} +(128.938 - 359.797i) q^{30} -710.805 q^{31} +(601.079 - 601.079i) q^{32} +(207.227 + 207.227i) q^{33} +662.183i q^{34} +(983.184 + 2081.43i) q^{35} -198.274 q^{36} +(-639.026 + 639.026i) q^{37} +(-552.467 - 552.467i) q^{38} +7.22958i q^{39} +(1552.54 - 733.355i) q^{40} -1325.70 q^{41} +(-995.397 + 995.397i) q^{42} +(-22.3358 - 22.3358i) q^{43} +414.172i q^{44} +(-635.430 - 227.715i) q^{45} +771.553 q^{46} +(456.136 - 456.136i) q^{47} +(310.758 + 310.758i) q^{48} -6077.44i q^{49} +(1830.20 - 178.428i) q^{50} +1169.47 q^{51} +(-7.22468 + 7.22468i) q^{52} +(-424.212 - 424.212i) q^{53} -412.779i q^{54} +(-475.672 + 1327.34i) q^{55} -6324.05 q^{56} +(-975.701 + 975.701i) q^{57} +(1131.91 + 1131.91i) q^{58} +3460.30i q^{59} +(-407.437 - 862.559i) q^{60} +4937.82 q^{61} +(1478.79 - 1478.79i) q^{62} +(1757.95 + 1757.95i) q^{63} +3854.27i q^{64} +(-31.4511 + 14.8562i) q^{65} -862.248 q^{66} +(-3801.58 + 3801.58i) q^{67} +(1168.67 + 1168.67i) q^{68} -1362.62i q^{69} +(-6375.78 - 2284.85i) q^{70} +7950.20 q^{71} +(1311.25 - 1311.25i) q^{72} +(-1940.65 - 1940.65i) q^{73} -2658.92i q^{74} +(-315.118 - 3232.27i) q^{75} -1950.08 q^{76} +(3672.16 - 3672.16i) q^{77} +(-15.0408 - 15.0408i) q^{78} +4083.83i q^{79} +(-713.319 + 1990.48i) q^{80} -729.000 q^{81} +(2758.05 - 2758.05i) q^{82} +(-9103.10 - 9103.10i) q^{83} +3513.51i q^{84} +(2403.16 + 5087.58i) q^{85} +92.9369 q^{86} +(1999.04 - 1999.04i) q^{87} +(-2739.06 - 2739.06i) q^{88} +7016.23i q^{89} +(1795.73 - 848.228i) q^{90} +128.112 q^{91} +(1361.70 - 1361.70i) q^{92} +(-2611.66 - 2611.66i) q^{93} +1897.93i q^{94} +(-6249.62 - 2239.64i) q^{95} +4417.01 q^{96} +(2571.87 - 2571.87i) q^{97} +(12643.8 + 12643.8i) q^{98} +1522.80i 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

Varieties

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Database

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