LMFDB - Embedded newform 15.5.f.a.7.2

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			7.2
Root			$-2.08045 - 2.08045i$ of defining polynomial
Character	$\chi$	$=$	15.7
Dual form			15.5.f.a.13.2

$q$-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 $\left(\mathbb{Z}/15\mathbb{Z}\right)^\times$.

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

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	0.397493	−	0.917605i	$-0.369880\pi$
$2$	−2.08045	−	2.08045i	−0.520112	−	0.520112i	−0.917605	+	0.397493i	$0.869880\pi$
$3$	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	0.906452	+	0.422309i	$0.138780\pi$
$7$	65.1093	+	65.1093i	1.32876	+	1.32876i	0.422309	+	0.906452i	$0.361220\pi$
$8$	−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	−0.704190	−	0.710012i	$-0.748690\pi$
$13$	0.983822	−	0.983822i	0.00582143	−	0.00582143i	0.710012	+	0.704190i	$0.248690\pi$
$14$		−	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	0.926635	−	0.375962i	$-0.122688\pi$
$17$	159.144	+	159.144i	0.550673	+	0.550673i	−0.375962	+	0.926635i	$0.622688\pi$
$18$	−56.1721	+	56.1721i	−0.173371	+	0.173371i
$19$		−	265.552i		−	0.735602i	−0.929905	−	0.367801i	$-0.880111\pi$
$19$		−	265.552i		−	0.735602i	0.929905	−	0.367801i	$-0.119889\pi$
$20$	−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	−0.860306	−	0.509778i	$-0.829728\pi$
$23$	−185.430	+	185.430i	−0.350529	+	0.350529i	0.509778	+	0.860306i	$0.329728\pi$
$24$			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	$0.104848\pi$
$29$			544.071i			0.646933i	−0.946240	+	0.323467i	$0.895152\pi$
$30$	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	0.434088	−	0.900871i	$-0.357071\pi$
$37$	−639.026	−	639.026i	−0.466783	−	0.466783i	−0.900871	+	0.434088i	$0.857071\pi$
$38$	−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	−0.713121	−	0.701041i	$-0.752719\pi$
$43$	−22.3358	+	22.3358i	−0.0120799	+	0.0120799i	0.701041	+	0.713121i	$0.252719\pi$
$44$		−	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	0.802774	−	0.596284i	$-0.203357\pi$
$47$	456.136	+	456.136i	0.206490	+	0.206490i	−0.596284	+	0.802774i	$0.703357\pi$
$48$	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	−0.778573	−	0.627554i	$-0.784056\pi$
$53$	−424.212	+	424.212i	−0.151019	+	0.151019i	0.627554	+	0.778573i	$0.284056\pi$
$54$			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	$-0.834425\pi$
$59$		−	3460.30i		−	0.994054i	0.867735	−	0.497027i	$-0.165575\pi$
$60$	−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	0.142874	−	0.989741i	$-0.454366\pi$
$67$	−3801.58	−	3801.58i	−0.846866	−	0.846866i	−0.989741	+	0.142874i	$0.954366\pi$
$68$	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	−0.865345	−	0.501177i	$-0.832901\pi$
$73$	−1940.65	+	1940.65i	−0.364168	+	0.364168i	0.501177	+	0.865345i	$0.332901\pi$
$74$			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	$-0.893902\pi$
$79$		−	4083.83i		−	0.654355i	0.944963	−	0.327178i	$-0.106098\pi$
$80$	−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	−0.408750	+	0.912646i	$0.634035\pi$
$83$	−9103.10	+	9103.10i	−1.32140	+	1.32140i	−0.912646	+	0.408750i	$0.865965\pi$
$84$		−	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	$-0.853954\pi$
$89$		−	7016.23i		−	0.885775i	0.896577	−	0.442888i	$-0.146046\pi$
$90$	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	0.830444	−	0.557102i	$-0.188087\pi$
$97$	2571.87	+	2571.87i	0.273342	+	0.273342i	−0.557102	+	0.830444i	$0.688087\pi$
$98$	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	−0.453929	−	0.891038i	$-0.649978\pi$
$103$	4637.29	−	4637.29i	0.437109	−	0.437109i	0.891038	+	0.453929i	$0.149978\pi$
$104$			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	0.208926	−	0.977931i	$-0.433003\pi$
$107$	−8804.34	−	8804.34i	−0.769005	−	0.769005i	−0.977931	+	0.208926i	$0.933003\pi$
$108$	−728.505	+	728.505i	−0.0624576	+	0.0624576i
$109$			7981.01i			0.671746i	0.941907	+	0.335873i	$0.109031\pi$
$109$			7981.01i			0.671746i	−0.941907	+	0.335873i	$0.890969\pi$
$110$	−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	−0.630195	−	0.776437i	$-0.717025\pi$
$113$	1867.37	−	1867.37i	0.146242	−	0.146242i	0.776437	+	0.630195i	$0.217025\pi$
$114$			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	0.797700	−	0.603054i	$-0.206050\pi$
$127$	3139.44	+	3139.44i	0.194646	+	0.194646i	−0.603054	+	0.797700i	$0.706050\pi$
$128$	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	−0.866917	−	0.498453i	$-0.833902\pi$
$137$	−25626.6	−	25626.6i	−1.36537	−	1.36537i	−0.498453	−	0.866917i	$-0.666098\pi$
$138$	2834.87	−	2834.87i	0.148859	−	0.148859i
$139$		−	16504.6i		−	0.854229i	−0.904197	−	0.427115i	$-0.859530\pi$
$139$		−	16504.6i		−	0.854229i	0.904197	−	0.427115i	$-0.140470\pi$
$140$	−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	$-0.923277\pi$
$149$		−	10599.1i		−	0.477413i	0.971092	−	0.238707i	$-0.0767235\pi$
$150$	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	0.966581	−	0.256361i	$-0.0825237\pi$
$157$	17506.2	+	17506.2i	0.710220	+	0.710220i	−0.256361	+	0.966581i	$0.582524\pi$
$158$	−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	−0.917117	−	0.398618i	$-0.869490\pi$
$163$	−13776.0	+	13776.0i	−0.518500	+	0.518500i	0.398618	+	0.917117i	$0.369490\pi$
$164$			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	0.981754	−	0.190156i	$-0.0608994\pi$
$167$	22076.9	+	22076.9i	0.791598	+	0.791598i	−0.190156	+	0.981754i	$0.560899\pi$
$168$	−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	−0.0948128	−	0.995495i	$-0.530225\pi$
$173$	26956.5	−	26956.5i	0.900682	−	0.900682i	0.995495	+	0.0948128i	$0.0302252\pi$
$174$		−	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	$-0.761102\pi$
$179$		−	43705.2i		−	1.36404i	0.731333	−	0.682020i	$-0.238898\pi$
$180$	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	−0.776781	−	0.629771i	$-0.783149\pi$
$193$	−5475.99	+	5475.99i	−0.147011	+	0.147011i	0.629771	+	0.776781i	$0.283149\pi$
$194$		−	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	0.548111	−	0.836406i	$-0.315347\pi$
$197$	−11188.4	−	11188.4i	−0.288295	−	0.288295i	−0.836406	+	0.548111i	$0.815347\pi$
$198$	−3168.10	+	3168.10i	−0.0808106	+	0.0808106i
$199$		−	17995.1i		−	0.454409i	−0.973847	−	0.227205i	$-0.927041\pi$
$199$		−	17995.1i		−	0.454409i	0.973847	−	0.227205i	$-0.0729586\pi$
$200$	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	−0.389963	−	0.920830i	$-0.627512\pi$
$223$	26399.5	−	26399.5i	0.530867	−	0.530867i	0.920830	+	0.389963i	$0.127512\pi$
$224$			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	0.947109	−	0.320912i	$-0.103989\pi$
$227$	32267.3	+	32267.3i	0.626197	+	0.626197i	−0.320912	+	0.947109i	$0.603989\pi$
$228$	−7165.05	+	7165.05i	−0.137832	+	0.137832i
$229$			68117.5i			1.29894i	0.760389	+	0.649468i	$0.225008\pi$
$229$			68117.5i			1.29894i	−0.760389	+	0.649468i	$0.774992\pi$
$230$	−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	−0.245019	+	0.969518i	$0.578794\pi$
$233$	−65936.0	+	65936.0i	−1.21454	+	1.21454i	−0.969518	+	0.245019i	$0.921206\pi$
$234$			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	$-0.807950\pi$
$239$		−	64820.9i		−	1.13480i	0.823443	−	0.567400i	$-0.192050\pi$
$240$	−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	0.876562	−	0.481290i	$-0.159832\pi$
$257$	26107.3	+	26107.3i	0.395272	+	0.395272i	−0.481290	+	0.876562i	$0.659832\pi$
$258$	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	−0.496719	−	0.867911i	$-0.665462\pi$
$263$	25675.0	−	25675.0i	0.371192	−	0.371192i	0.867911	+	0.496719i	$0.165462\pi$
$264$			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	$0.198435\pi$
$269$			84488.9i			1.16760i	−0.811896	+	0.583801i	$0.801565\pi$
$270$	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	0.997780	−	0.0665996i	$-0.0212150\pi$
$277$	71448.5	+	71448.5i	0.931180	+	0.931180i	−0.0665996	+	0.997780i	$0.521215\pi$
$278$	−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	−0.306102	−	0.951999i	$-0.599025\pi$
$283$	51729.2	−	51729.2i	0.645896	−	0.645896i	0.951999	+	0.306102i	$0.0990250\pi$
$284$		−	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	−0.988238	−	0.152926i	$-0.951130\pi$
$293$	−71710.7	+	71710.7i	−0.835312	+	0.835312i	0.152926	+	0.988238i	$0.451130\pi$
$294$		−	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	0.814379	−	0.580334i	$-0.197078\pi$
$307$	22058.5	+	22058.5i	0.234045	+	0.234045i	−0.580334	+	0.814379i	$0.697078\pi$
$308$	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	−0.521301	−	0.853373i	$-0.674553\pi$
$313$	32532.8	−	32532.8i	0.332072	−	0.332072i	0.853373	+	0.521301i	$0.174553\pi$
$314$		−	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	0.246080	−	0.969249i	$-0.420857\pi$
$317$	−72670.5	−	72670.5i	−0.723169	−	0.723169i	−0.969249	+	0.246080i	$0.920857\pi$
$318$	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	0.290058	−	0.957009i	$-0.406326\pi$
$337$	−75745.0	−	75745.0i	−0.666952	−	0.666952i	−0.957009	+	0.290058i	$0.906326\pi$
$338$	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	0.883462	−	0.468502i	$-0.155206\pi$
$347$	49964.9	+	49964.9i	0.414960	+	0.414960i	−0.468502	+	0.883462i	$0.655206\pi$
$348$	14679.9	−	14679.9i	0.121218	−	0.121218i
$349$		−	74192.9i		−	0.609132i	−0.952491	−	0.304566i	$-0.901489\pi$
$349$		−	74192.9i		−	0.609132i	0.952491	−	0.304566i	$-0.0985115\pi$
$350$	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	−0.766473	−	0.642276i	$-0.777990\pi$
$353$	−15476.1	+	15476.1i	−0.124198	+	0.124198i	0.642276	+	0.766473i	$0.277990\pi$
$354$			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	$-0.942300\pi$
$359$		−	46469.2i		−	0.360559i	0.983615	−	0.180279i	$-0.0577002\pi$
$360$	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	0.888160	−	0.459535i	$-0.151984\pi$
$367$	57731.0	+	57731.0i	0.428624	+	0.428624i	−0.459535	+	0.888160i	$0.651984\pi$
$368$	−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	0.218634	−	0.975807i	$-0.429840\pi$
$373$	166181.	−	166181.i	1.19444	−	1.19444i	0.975807	−	0.218634i	$-0.0701600\pi$
$374$		−	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	$0.0459380\pi$
$379$			41316.4i			0.287636i	−0.989604	+	0.143818i	$0.954062\pi$
$380$	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	−0.417009	−	0.908902i	$-0.636922\pi$
$383$	72155.3	−	72155.3i	0.491893	−	0.491893i	0.908902	+	0.417009i	$0.136922\pi$
$384$		−	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	$0.219007\pi$
$389$			192183.i			1.27004i	−0.772497	+	0.635018i	$0.780993\pi$
$390$	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	−0.991194	−	0.132416i	$-0.957726\pi$
$397$	−177091.	−	177091.i	−1.12361	−	1.12361i	−0.132416	−	0.991194i	$-0.542274\pi$
$398$	−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	$0.292147\pi$
$409$			265733.i			1.58854i	−0.607563	+	0.794271i	$0.707853\pi$
$410$	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	$0.116450\pi$
$419$			125608.i			0.715467i	−0.933824	+	0.357734i	$0.883550\pi$
$420$	−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	−0.945218	−	0.326440i	$-0.894151\pi$
$433$	−116014.	+	116014.i	−0.618777	+	0.618777i	0.326440	+	0.945218i	$0.394151\pi$
$434$			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	$0.139582\pi$
$439$			163656.i			0.849184i	−0.905385	+	0.424592i	$0.860418\pi$
$440$	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	−0.939720	−	0.341945i	$-0.888914\pi$
$443$	−117313.	+	117313.i	−0.597775	+	0.597775i	0.341945	+	0.939720i	$0.388914\pi$
$444$			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	$-0.676859\pi$
$449$		−	342550.i		−	1.69915i	0.527468	−	0.849575i	$-0.323141\pi$
$450$	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	0.200221	−	0.979751i	$-0.435834\pi$
$457$	−162804.	−	162804.i	−0.779530	−	0.779530i	−0.979751	+	0.200221i	$0.935834\pi$
$458$	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	−0.782126	−	0.623120i	$-0.785865\pi$
$463$	−34085.9	+	34085.9i	−0.159006	+	0.159006i	0.623120	+	0.782126i	$0.285865\pi$
$464$			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	0.359889	−	0.932995i	$-0.382815\pi$
$467$	−124988.	−	124988.i	−0.573107	−	0.573107i	−0.932995	+	0.359889i	$0.882815\pi$
$468$	−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	$-0.817953\pi$
$479$		−	248368.i		−	1.08249i	0.840864	−	0.541247i	$-0.182047\pi$
$480$	−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	0.286190	−	0.958173i	$-0.407611\pi$
$487$	−159374.	−	159374.i	−0.671983	−	0.671983i	−0.958173	+	0.286190i	$0.907611\pi$
$488$	−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	$-0.866750\pi$
$499$		−	202437.i		−	0.812998i	0.913651	−	0.406499i	$-0.133250\pi$
$500$	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	−0.770166	−	0.637844i	$-0.779827\pi$
$503$	−33478.6	+	33478.6i	−0.132322	+	0.132322i	0.637844	+	0.770166i	$0.279827\pi$
$504$			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	$0.0356022\pi$
$509$			57834.5i			0.223229i	−0.993752	+	0.111615i	$0.964398\pi$
$510$	−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	−0.209825	−	0.977739i	$-0.567289\pi$
$523$	210047.	−	210047.i	0.767914	−	0.767914i	0.977739	+	0.209825i	$0.0672894\pi$
$524$		−	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	0.398182	−	0.917306i	$-0.369641\pi$
$547$	−155327.	−	155327.i	−0.519125	−	0.519125i	−0.917306	+	0.398182i	$0.869641\pi$
$548$	−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	0.900088	−	0.435707i	$-0.143502\pi$
$557$	144074.	+	144074.i	0.464381	+	0.464381i	−0.435707	+	0.900088i	$0.643502\pi$
$558$	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	0.105970	−	0.994369i	$-0.466205\pi$
$563$	348774.	−	348774.i	1.10034	−	1.10034i	0.994369	−	0.105970i	$-0.0337948\pi$
$564$		−	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	$-0.908691\pi$
$569$		−	183209.i		−	0.565878i	0.959138	−	0.282939i	$-0.0913095\pi$
$570$	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	0.913346	−	0.407184i	$-0.133489\pi$
$577$	168516.	+	168516.i	0.506161	+	0.506161i	−0.407184	+	0.913346i	$0.633489\pi$
$578$	−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	0.493040	−	0.870007i	$-0.335886\pi$
$587$	−129891.	−	129891.i	−0.376966	−	0.376966i	−0.870007	+	0.493040i	$0.835886\pi$
$588$	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	−0.990510	−	0.137438i	$-0.956113\pi$
$593$	−299982.	+	299982.i	−0.853072	+	0.853072i	0.137438	+	0.990510i	$0.456113\pi$
$594$			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	$0.352935\pi$
$599$			642365.i			1.79031i	−0.445754	+	0.895155i	$0.647065\pi$
$600$	−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	0.502909	−	0.864340i	$-0.332263\pi$
$607$	−133169.	−	133169.i	−0.361431	−	0.361431i	−0.864340	+	0.502909i	$0.832263\pi$
$608$	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	−0.0513978	+	0.998678i	$0.516368\pi$
$613$	−394586.	+	394586.i	−1.05008	+	1.05008i	−0.998678	+	0.0513978i	$0.983632\pi$
$614$		−	91783.0i		−	0.243459i
$615$	155716.	+	73553.7i	0.411701	+	0.194471i
$616$	−356676.			−0.939966
$617$	246284.	+	246284.i	0.646942	+	0.646942i	0.952253	−	0.305311i	$-0.0987603\pi$
$617$	246284.	+	246284.i	0.646942	+	0.646942i	−0.305311	+	0.952253i	$0.598760\pi$
$618$	−70895.3	+	70895.3i	−0.185627	+	0.185627i
$619$		−	135789.i		−	0.354391i	−0.984176	−	0.177195i	$-0.943298\pi$
$619$		−	135789.i		−	0.354391i	0.984176	−	0.177195i	$-0.0567025\pi$
$620$	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	−0.299265	−	0.954170i	$-0.596741\pi$
$643$	270770.	−	270770.i	0.654905	−	0.654905i	0.954170	+	0.299265i	$0.0967415\pi$
$644$			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	0.733044	−	0.680181i	$-0.238099\pi$
$647$	22129.0	+	22129.0i	0.0528632	+	0.0528632i	−0.680181	+	0.733044i	$0.738099\pi$
$648$	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	−0.876613	−	0.481195i	$-0.840203\pi$
$653$	−168610.	+	168610.i	−0.395418	+	0.395418i	0.481195	+	0.876613i	$0.340203\pi$
$654$		−	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	$-0.961044\pi$
$659$		−	106032.i		−	0.244155i	0.992521	−	0.122078i	$-0.0389557\pi$
$660$	−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	−0.872932	−	0.487842i	$-0.837784\pi$
$673$	−174418.	+	174418.i	−0.385090	+	0.385090i	0.487842	+	0.872932i	$0.337784\pi$
$674$			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	0.824803	−	0.565421i	$-0.191286\pi$
$677$	118882.	+	118882.i	0.259382	+	0.259382i	−0.565421	+	0.824803i	$0.691286\pi$
$678$	−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	−0.999990	−	0.00453640i	$-0.998556\pi$
$683$	−464368.	+	464368.i	−0.995453	+	0.995453i	0.00453640	+	0.999990i	$0.498556\pi$
$684$			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	$-0.933169\pi$
$709$		−	209535.i		−	0.416835i	0.978040	−	0.208418i	$-0.0668313\pi$
$710$	−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	$0.189438\pi$
$719$			579641.i			1.12125i	−0.828071	+	0.560623i	$0.810562\pi$
$720$	−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	0.950460	+	0.310848i	$0.100613\pi$
$727$	666638.	+	666638.i	1.26131	+	1.26131i	0.310848	+	0.950460i	$0.399387\pi$
$728$	−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	−0.514387	−	0.857558i	$-0.671981\pi$
$733$	184382.	−	184382.i	0.343171	−	0.343171i	0.857558	+	0.514387i	$0.171981\pi$
$734$		−	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	$-0.948731\pi$
$739$		−	175164.i		−	0.320742i	0.987057	−	0.160371i	$-0.0512691\pi$
$740$	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	−0.0207283	−	0.999785i	$-0.506598\pi$
$743$	540487.	−	540487.i	0.979057	−	0.979057i	0.999785	+	0.0207283i	$0.00659849\pi$
$744$		−	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	0.992265	−	0.124139i	$-0.0396168\pi$
$757$	497479.	+	497479.i	0.868126	+	0.868126i	−0.124139	+	0.992265i	$0.539617\pi$
$758$	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	$0.0171782\pi$
$769$			63796.8i			0.107881i	−0.998544	+	0.0539406i	$0.982822\pi$
$770$	−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	−0.578013	−	0.816028i	$-0.696172\pi$
$773$	142221.	−	142221.i	0.238015	−	0.238015i	0.816028	+	0.578013i	$0.196172\pi$
$774$		−	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	0.555150	−	0.831751i	$-0.312661\pi$
$787$	−171318.	−	171318.i	−0.276601	−	0.276601i	−0.831751	+	0.555150i	$0.812661\pi$
$788$	−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	0.322010	−	0.946736i	$-0.395642\pi$
$797$	−396832.	−	396832.i	−0.624727	−	0.624727i	−0.946736	+	0.322010i	$0.895642\pi$
$798$	−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	$0.143914\pi$
$809$			571851.i			0.873748i	−0.899523	+	0.436874i	$0.856086\pi$
$810$	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	−0.101231	+	0.994863i	$0.532278\pi$
$823$	−742417.	+	742417.i	−1.09609	+	1.09609i	−0.994863	+	0.101231i	$0.967722\pi$
$824$			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	0.327689	−	0.944786i	$-0.393730\pi$
$827$	−422050.	−	422050.i	−0.617097	−	0.617097i	−0.944786	+	0.327689i	$0.893730\pi$
$828$	36765.9	−	36765.9i	0.0536271	−	0.0536271i
$829$		−	310239.i		−	0.451427i	−0.974194	−	0.225713i	$-0.927529\pi$
$829$		−	310239.i		−	0.451427i	0.974194	−	0.225713i	$-0.0724712\pi$
$830$	−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	$0.326812\pi$
$839$			1.20455e6i			1.71120i	−0.517636	+	0.855601i	$0.673188\pi$
$840$	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	−0.316402	−	0.948625i	$-0.602475\pi$
$853$	460012.	−	460012.i	0.632224	−	0.632224i	0.948625	+	0.316402i	$0.102475\pi$
$854$		−	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	0.381855	−	0.924222i	$-0.375285\pi$
$857$	−398341.	−	398341.i	−0.542367	−	0.542367i	−0.924222	+	0.381855i	$0.875285\pi$
$858$	−848.298	+	848.298i	−0.00115232	+	0.00115232i
$859$		−	323065.i		−	0.437828i	−0.975744	−	0.218914i	$-0.929749\pi$
$859$		−	323065.i		−	0.437828i	0.975744	−	0.218914i	$-0.0702514\pi$
$860$	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	−0.371309	−	0.928509i	$-0.621091\pi$
$863$	414986.	−	414986.i	0.557200	−	0.557200i	0.928509	+	0.371309i	$0.121091\pi$
$864$		−	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	0.519899	−	0.854228i	$-0.325969\pi$
$877$	−257142.	−	257142.i	−0.334328	−	0.334328i	−0.854228	+	0.519899i	$0.825969\pi$
$878$	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	0.182601	−	0.983187i	$-0.441548\pi$
$883$	908952.	−	908952.i	1.16579	−	1.16579i	0.983187	−	0.182601i	$-0.0584518\pi$
$884$		−	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	0.645450	−	0.763802i	$-0.276670\pi$
$887$	−93115.5	−	93115.5i	−0.118352	−	0.118352i	−0.763802	+	0.645450i	$0.776670\pi$
$888$	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	0.668182	−	0.743998i	$-0.267073\pi$
$907$	−62370.3	−	62370.3i	−0.0758164	−	0.0758164i	−0.743998	+	0.668182i	$0.767073\pi$
$908$	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	$0.151379\pi$
$919$			773358.i			0.915692i	−0.889031	+	0.457846i	$0.848621\pi$
$920$	−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	$-0.829461\pi$
$929$		−	881163.i		−	1.02100i	0.859878	−	0.510499i	$-0.170539\pi$
$930$	−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	0.990014	+	0.140967i	$0.0450212\pi$
$937$	992967.	+	992967.i	1.13098	+	1.13098i	0.140967	+	0.990014i	$0.454979\pi$
$938$	−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	0.581331	−	0.813667i	$-0.302532\pi$
$947$	−208361.	−	208361.i	−0.232336	−	0.232336i	−0.813667	+	0.581331i	$0.802532\pi$
$948$	−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	−0.988593	−	0.150610i	$-0.951876\pi$
$953$	−761064.	+	761064.i	−0.837983	+	0.837983i	0.150610	+	0.988593i	$0.451876\pi$
$954$		−	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	0.907895	−	0.419197i	$-0.137688\pi$
$967$	456976.	+	456976.i	0.488698	+	0.488698i	−0.419197	+	0.907895i	$0.637688\pi$
$968$	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	0.767606	−	0.640922i	$-0.221448\pi$
$977$	120924.	+	120924.i	0.126684	+	0.126684i	−0.640922	+	0.767606i	$0.721448\pi$
$978$	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	−0.947771	−	0.318952i	$-0.896669\pi$
$983$	−607621.	+	607621.i	−0.628819	+	0.628819i	0.318952	+	0.947771i	$0.396669\pi$
$984$		−	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	0.798882	−	0.601487i	$-0.205425\pi$
$997$	196213.	+	196213.i	0.197395	+	0.197395i	−0.601487	+	0.798882i	$0.705425\pi$
$998$	−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.7.2	✓	8
3.2	odd	2		45.5.g.e.37.3		8
4.3	odd	2		240.5.bg.c.97.2		8
5.2	odd	4		75.5.f.e.43.3		8
5.3	odd	4	inner	15.5.f.a.13.2	yes	8
5.4	even	2		75.5.f.e.7.3		8
15.2	even	4		225.5.g.m.118.2		8
15.8	even	4		45.5.g.e.28.3		8
15.14	odd	2		225.5.g.m.82.2		8
20.3	even	4		240.5.bg.c.193.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
15.5.f.a.7.2	✓	8	1.1	even	1	trivial
15.5.f.a.13.2	yes	8	5.3	odd	4	inner
45.5.g.e.28.3		8	15.8	even	4
45.5.g.e.37.3		8	3.2	odd	2
75.5.f.e.7.3		8	5.4	even	2
75.5.f.e.43.3		8	5.2	odd	4
225.5.g.m.82.2		8	15.14	odd	2
225.5.g.m.118.2		8	15.2	even	4
240.5.bg.c.97.2		8	4.3	odd	2
240.5.bg.c.193.2		8	20.3	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 15 = 3 \cdot 5 \)
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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Representations

Groups

Database

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