LMFDB - Embedded newform 10.5.c.a.7.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [10,5,Mod(3,10)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(10, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("10.3");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 10 = 2 \cdot 5 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	10.c (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:	$1.03369963084$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(i)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} + 1 $ x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			7.1
Root			$1.00000i$ of defining polynomial
Character	$\chi$	$=$	10.7
Dual form			10.5.c.a.3.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.00000 - 2.00000i) q^{2} +(9.00000 - 9.00000i) q^{3} +8.00000i q^{4} +(-15.0000 + 20.0000i) q^{5} -36.0000 q^{6} +(29.0000 + 29.0000i) q^{7} +(16.0000 - 16.0000i) q^{8} -81.0000i q^{9} +(70.0000 - 10.0000i) q^{10} -118.000 q^{11} +(72.0000 + 72.0000i) q^{12} +(69.0000 - 69.0000i) q^{13} -116.000i q^{14} +(45.0000 + 315.000i) q^{15} -64.0000 q^{16} +(-271.000 - 271.000i) q^{17} +(-162.000 + 162.000i) q^{18} +280.000i q^{19} +(-160.000 - 120.000i) q^{20} +522.000 q^{21} +(236.000 + 236.000i) q^{22} +(269.000 - 269.000i) q^{23} -288.000i q^{24} +(-175.000 - 600.000i) q^{25} -276.000 q^{26} +(-232.000 + 232.000i) q^{28} +680.000i q^{29} +(540.000 - 720.000i) q^{30} +202.000 q^{31} +(128.000 + 128.000i) q^{32} +(-1062.00 + 1062.00i) q^{33} +1084.00i q^{34} +(-1015.00 + 145.000i) q^{35} +648.000 q^{36} +(-651.000 - 651.000i) q^{37} +(560.000 - 560.000i) q^{38} -1242.00i q^{39} +(80.0000 + 560.000i) q^{40} +1682.00 q^{41} +(-1044.00 - 1044.00i) q^{42} +(1089.00 - 1089.00i) q^{43} -944.000i q^{44} +(1620.00 + 1215.00i) q^{45} -1076.00 q^{46} +(1269.00 + 1269.00i) q^{47} +(-576.000 + 576.000i) q^{48} -719.000i q^{49} +(-850.000 + 1550.00i) q^{50} -4878.00 q^{51} +(552.000 + 552.000i) q^{52} +(-611.000 + 611.000i) q^{53} +(1770.00 - 2360.00i) q^{55} +928.000 q^{56} +(2520.00 + 2520.00i) q^{57} +(1360.00 - 1360.00i) q^{58} +1160.00i q^{59} +(-2520.00 + 360.000i) q^{60} -5598.00 q^{61} +(-404.000 - 404.000i) q^{62} +(2349.00 - 2349.00i) q^{63} -512.000i q^{64} +(345.000 + 2415.00i) q^{65} +4248.00 q^{66} +(-751.000 - 751.000i) q^{67} +(2168.00 - 2168.00i) q^{68} -4842.00i q^{69} +(2320.00 + 1740.00i) q^{70} +6442.00 q^{71} +(-1296.00 - 1296.00i) q^{72} +(-2951.00 + 2951.00i) q^{73} +2604.00i q^{74} +(-6975.00 - 3825.00i) q^{75} -2240.00 q^{76} +(-3422.00 - 3422.00i) q^{77} +(-2484.00 + 2484.00i) q^{78} +10560.0i q^{79} +(960.000 - 1280.00i) q^{80} +6561.00 q^{81} +(-3364.00 - 3364.00i) q^{82} +(-6231.00 + 6231.00i) q^{83} +4176.00i q^{84} +(9485.00 - 1355.00i) q^{85} -4356.00 q^{86} +(6120.00 + 6120.00i) q^{87} +(-1888.00 + 1888.00i) q^{88} -14480.0i q^{89} +(-810.000 - 5670.00i) q^{90} +4002.00 q^{91} +(2152.00 + 2152.00i) q^{92} +(1818.00 - 1818.00i) q^{93} -5076.00i q^{94} +(-5600.00 - 4200.00i) q^{95} +2304.00 q^{96} +(-7311.00 - 7311.00i) q^{97} +(-1438.00 + 1438.00i) q^{98} +9558.00i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 4 q^{2} + 18 q^{3} - 30 q^{5} - 72 q^{6} + 58 q^{7} + 32 q^{8} + 140 q^{10} - 236 q^{11} + 144 q^{12} + 138 q^{13} + 90 q^{15} - 128 q^{16} - 542 q^{17} - 324 q^{18} - 320 q^{20} + 1044 q^{21} + 472 q^{22}+ \cdots - 2876 q^{98}+O(q^{100}) $ 2 * q - 4 * q^2 + 18 * q^3 - 30 * q^5 - 72 * q^6 + 58 * q^7 + 32 * q^8 + 140 * q^10 - 236 * q^11 + 144 * q^12 + 138 * q^13 + 90 * q^15 - 128 * q^16 - 542 * q^17 - 324 * q^18 - 320 * q^20 + 1044 * q^21 + 472 * q^22 + 538 * q^23 - 350 * q^25 - 552 * q^26 - 464 * q^28 + 1080 * q^30 + 404 * q^31 + 256 * q^32 - 2124 * q^33 - 2030 * q^35 + 1296 * q^36 - 1302 * q^37 + 1120 * q^38 + 160 * q^40 + 3364 * q^41 - 2088 * q^42 + 2178 * q^43 + 3240 * q^45 - 2152 * q^46 + 2538 * q^47 - 1152 * q^48 - 1700 * q^50 - 9756 * q^51 + 1104 * q^52 - 1222 * q^53 + 3540 * q^55 + 1856 * q^56 + 5040 * q^57 + 2720 * q^58 - 5040 * q^60 - 11196 * q^61 - 808 * q^62 + 4698 * q^63 + 690 * q^65 + 8496 * q^66 - 1502 * q^67 + 4336 * q^68 + 4640 * q^70 + 12884 * q^71 - 2592 * q^72 - 5902 * q^73 - 13950 * q^75 - 4480 * q^76 - 6844 * q^77 - 4968 * q^78 + 1920 * q^80 + 13122 * q^81 - 6728 * q^82 - 12462 * q^83 + 18970 * q^85 - 8712 * q^86 + 12240 * q^87 - 3776 * q^88 - 1620 * q^90 + 8004 * q^91 + 4304 * q^92 + 3636 * q^93 - 11200 * q^95 + 4608 * q^96 - 14622 * q^97 - 2876 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/10\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	−2.00000	−	2.00000i	−0.500000	−	0.500000i
$2$	−2.00000	−	2.00000i	−0.500000	−	0.500000i
$3$	9.00000	−	9.00000i	1.00000	−	1.00000i		−	1.00000i	$-0.5\pi$
$3$	9.00000	−	9.00000i	1.00000	−	1.00000i	1.00000			$0$
$4$			8.00000i			0.500000i
$5$	−15.0000	+	20.0000i	−0.600000	+	0.800000i
$5$	−15.0000	+	20.0000i	−0.600000	+	0.800000i
$6$	−36.0000			−1.00000
$7$	29.0000	+	29.0000i	0.591837	+	0.591837i	0.938127	−	0.346291i	$-0.112559\pi$
$7$	29.0000	+	29.0000i	0.591837	+	0.591837i	−0.346291	+	0.938127i	$0.612559\pi$
$8$	16.0000	−	16.0000i	0.250000	−	0.250000i
$9$		−	81.0000i		−	1.00000i
$10$	70.0000	−	10.0000i	0.700000	−	0.100000i
$11$	−118.000			−0.975207			−0.487603	−	0.873065i	$-0.662129\pi$
$11$	−118.000			−0.975207			−0.487603	+	0.873065i	$0.662129\pi$
$12$	72.0000	+	72.0000i	0.500000	+	0.500000i
$13$	69.0000	−	69.0000i	0.408284	−	0.408284i	−0.472856	−	0.881140i	$-0.656777\pi$
$13$	69.0000	−	69.0000i	0.408284	−	0.408284i	0.881140	+	0.472856i	$0.156777\pi$
$14$		−	116.000i		−	0.591837i
$15$	45.0000	+	315.000i	0.200000	+	1.40000i
$16$	−64.0000			−0.250000
$17$	−271.000	−	271.000i	−0.937716	−	0.937716i	0.0604547	−	0.998171i	$-0.480745\pi$
$17$	−271.000	−	271.000i	−0.937716	−	0.937716i	−0.998171	+	0.0604547i	$0.980745\pi$
$18$	−162.000	+	162.000i	−0.500000	+	0.500000i
$19$			280.000i			0.775623i	0.921739	+	0.387812i	$0.126769\pi$
$19$			280.000i			0.775623i	−0.921739	+	0.387812i	$0.873231\pi$
$20$	−160.000	−	120.000i	−0.400000	−	0.300000i
$21$	522.000			1.18367
$22$	236.000	+	236.000i	0.487603	+	0.487603i
$23$	269.000	−	269.000i	0.508507	−	0.508507i	−0.405561	−	0.914068i	$-0.632924\pi$
$23$	269.000	−	269.000i	0.508507	−	0.508507i	0.914068	+	0.405561i	$0.132924\pi$
$24$		−	288.000i		−	0.500000i
$25$	−175.000	−	600.000i	−0.280000	−	0.960000i
$26$	−276.000			−0.408284
$27$		0			0
$28$	−232.000	+	232.000i	−0.295918	+	0.295918i
$29$			680.000i			0.808561i	0.914635	+	0.404281i	$0.132478\pi$
$29$			680.000i			0.808561i	−0.914635	+	0.404281i	$0.867522\pi$
$30$	540.000	−	720.000i	0.600000	−	0.800000i
$31$	202.000			0.210198			0.105099	−	0.994462i	$-0.466484\pi$
$31$	202.000			0.210198			0.105099	+	0.994462i	$0.466484\pi$
$32$	128.000	+	128.000i	0.125000	+	0.125000i
$33$	−1062.00	+	1062.00i	−0.975207	+	0.975207i
$34$			1084.00i			0.937716i
$35$	−1015.00	+	145.000i	−0.828571	+	0.118367i
$36$	648.000			0.500000
$37$	−651.000	−	651.000i	−0.475530	−	0.475530i	0.428169	−	0.903699i	$-0.359159\pi$
$37$	−651.000	−	651.000i	−0.475530	−	0.475530i	−0.903699	+	0.428169i	$0.859159\pi$
$38$	560.000	−	560.000i	0.387812	−	0.387812i
$39$		−	1242.00i		−	0.816568i
$40$	80.0000	+	560.000i	0.0500000	+	0.350000i
$41$	1682.00			1.00059			0.500297	−	0.865854i	$-0.333224\pi$
$41$	1682.00			1.00059			0.500297	+	0.865854i	$0.333224\pi$
$42$	−1044.00	−	1044.00i	−0.591837	−	0.591837i
$43$	1089.00	−	1089.00i	0.588967	−	0.588967i	−0.348385	−	0.937352i	$-0.613270\pi$
$43$	1089.00	−	1089.00i	0.588967	−	0.588967i	0.937352	+	0.348385i	$0.113270\pi$
$44$		−	944.000i		−	0.487603i
$45$	1620.00	+	1215.00i	0.800000	+	0.600000i
$46$	−1076.00			−0.508507
$47$	1269.00	+	1269.00i	0.574468	+	0.574468i	0.933374	−	0.358906i	$-0.116850\pi$
$47$	1269.00	+	1269.00i	0.574468	+	0.574468i	−0.358906	+	0.933374i	$0.616850\pi$
$48$	−576.000	+	576.000i	−0.250000	+	0.250000i
$49$		−	719.000i		−	0.299459i
$50$	−850.000	+	1550.00i	−0.340000	+	0.620000i
$51$	−4878.00			−1.87543
$52$	552.000	+	552.000i	0.204142	+	0.204142i
$53$	−611.000	+	611.000i	−0.217515	+	0.217515i	−0.807450	−	0.589935i	$-0.799153\pi$
$53$	−611.000	+	611.000i	−0.217515	+	0.217515i	0.589935	+	0.807450i	$0.299153\pi$
$54$		0			0
$55$	1770.00	−	2360.00i	0.585124	−	0.780165i
$56$	928.000			0.295918
$57$	2520.00	+	2520.00i	0.775623	+	0.775623i
$58$	1360.00	−	1360.00i	0.404281	−	0.404281i
$59$			1160.00i			0.333238i	0.986021	+	0.166619i	$0.0532849\pi$
$59$			1160.00i			0.333238i	−0.986021	+	0.166619i	$0.946715\pi$
$60$	−2520.00	+	360.000i	−0.700000	+	0.100000i
$61$	−5598.00			−1.50443			−0.752217	−	0.658915i	$-0.771016\pi$
$61$	−5598.00			−1.50443			−0.752217	+	0.658915i	$0.771016\pi$
$62$	−404.000	−	404.000i	−0.105099	−	0.105099i
$63$	2349.00	−	2349.00i	0.591837	−	0.591837i
$64$		−	512.000i		−	0.125000i
$65$	345.000	+	2415.00i	0.0816568	+	0.571598i
$66$	4248.00			0.975207
$67$	−751.000	−	751.000i	−0.167298	−	0.167298i	0.618493	−	0.785791i	$-0.287744\pi$
$67$	−751.000	−	751.000i	−0.167298	−	0.167298i	−0.785791	+	0.618493i	$0.787744\pi$
$68$	2168.00	−	2168.00i	0.468858	−	0.468858i
$69$		−	4842.00i		−	1.01701i
$70$	2320.00	+	1740.00i	0.473469	+	0.355102i
$71$	6442.00			1.27792			0.638961	−	0.769240i	$-0.279365\pi$
$71$	6442.00			1.27792			0.638961	+	0.769240i	$0.279365\pi$
$72$	−1296.00	−	1296.00i	−0.250000	−	0.250000i
$73$	−2951.00	+	2951.00i	−0.553762	+	0.553762i	−0.927525	−	0.373762i	$-0.878068\pi$
$73$	−2951.00	+	2951.00i	−0.553762	+	0.553762i	0.373762	+	0.927525i	$0.378068\pi$
$74$			2604.00i			0.475530i
$75$	−6975.00	−	3825.00i	−1.24000	−	0.680000i
$76$	−2240.00			−0.387812
$77$	−3422.00	−	3422.00i	−0.577163	−	0.577163i
$78$	−2484.00	+	2484.00i	−0.408284	+	0.408284i
$79$			10560.0i			1.69204i	0.533154	+	0.846018i	$0.321007\pi$
$79$			10560.0i			1.69204i	−0.533154	+	0.846018i	$0.678993\pi$
$80$	960.000	−	1280.00i	0.150000	−	0.200000i
$81$	6561.00			1.00000
$82$	−3364.00	−	3364.00i	−0.500297	−	0.500297i
$83$	−6231.00	+	6231.00i	−0.904485	+	0.904485i	−0.995820	−	0.0913348i	$-0.970887\pi$
$83$	−6231.00	+	6231.00i	−0.904485	+	0.904485i	0.0913348	+	0.995820i	$0.470887\pi$
$84$			4176.00i			0.591837i
$85$	9485.00	−	1355.00i	1.31280	−	0.187543i
$86$	−4356.00			−0.588967
$87$	6120.00	+	6120.00i	0.808561	+	0.808561i
$88$	−1888.00	+	1888.00i	−0.243802	+	0.243802i
$89$		−	14480.0i		−	1.82805i	−0.405656	−	0.914026i	$-0.632957\pi$
$89$		−	14480.0i		−	1.82805i	0.405656	−	0.914026i	$-0.367043\pi$
$90$	−810.000	−	5670.00i	−0.100000	−	0.700000i
$91$	4002.00			0.483275
$92$	2152.00	+	2152.00i	0.254253	+	0.254253i
$93$	1818.00	−	1818.00i	0.210198	−	0.210198i
$94$		−	5076.00i		−	0.574468i
$95$	−5600.00	−	4200.00i	−0.620499	−	0.465374i
$96$	2304.00			0.250000
$97$	−7311.00	−	7311.00i	−0.777022	−	0.777022i	0.202301	−	0.979323i	$-0.435158\pi$
$97$	−7311.00	−	7311.00i	−0.777022	−	0.777022i	−0.979323	+	0.202301i	$0.935158\pi$
$98$	−1438.00	+	1438.00i	−0.149729	+	0.149729i
$99$			9558.00i			0.975207i
$100$	4800.00	−	1400.00i	0.480000	−	0.140000i
$101$	−878.000			−0.0860700			−0.0430350	−	0.999074i	$-0.513703\pi$
$101$	−878.000			−0.0860700			−0.0430350	+	0.999074i	$0.513703\pi$
$102$	9756.00	+	9756.00i	0.937716	+	0.937716i
$103$	10429.0	−	10429.0i	0.983033	−	0.983033i	−0.0168252	−	0.999858i	$-0.505356\pi$
$103$	10429.0	−	10429.0i	0.983033	−	0.983033i	0.999858	+	0.0168252i	$0.00535587\pi$
$104$		−	2208.00i		−	0.204142i
$105$	−7830.00	+	10440.0i	−0.710204	+	0.946939i
$106$	2444.00			0.217515
$107$	−4711.00	−	4711.00i	−0.411477	−	0.411477i	0.470776	−	0.882253i	$-0.343974\pi$
$107$	−4711.00	−	4711.00i	−0.411477	−	0.411477i	−0.882253	+	0.470776i	$0.843974\pi$
$108$		0			0
$109$			22040.0i			1.85506i	0.373745	+	0.927531i	$0.378073\pi$
$109$			22040.0i			1.85506i	−0.373745	+	0.927531i	$0.621927\pi$
$110$	−8260.00	+	1180.00i	−0.682645	+	0.0975207i
$111$	−11718.0			−0.951059
$112$	−1856.00	−	1856.00i	−0.147959	−	0.147959i
$113$	−2111.00	+	2111.00i	−0.165322	+	0.165322i	−0.784920	−	0.619597i	$-0.787296\pi$
$113$	−2111.00	+	2111.00i	−0.165322	+	0.165322i	0.619597	+	0.784920i	$0.287296\pi$
$114$		−	10080.0i		−	0.775623i
$115$	1345.00	+	9415.00i	0.101701	+	0.711909i
$116$	−5440.00			−0.404281
$117$	−5589.00	−	5589.00i	−0.408284	−	0.408284i
$118$	2320.00	−	2320.00i	0.166619	−	0.166619i
$119$		−	15718.0i		−	1.10995i
$120$	5760.00	+	4320.00i	0.400000	+	0.300000i
$121$	−717.000			−0.0489721
$122$	11196.0	+	11196.0i	0.752217	+	0.752217i
$123$	15138.0	−	15138.0i	1.00059	−	1.00059i
$124$			1616.00i			0.105099i
$125$	14625.0	+	5500.00i	0.936000	+	0.352000i
$126$	−9396.00			−0.591837
$127$	5909.00	+	5909.00i	0.366359	+	0.366359i	0.866147	−	0.499789i	$-0.166589\pi$
$127$	5909.00	+	5909.00i	0.366359	+	0.366359i	−0.499789	+	0.866147i	$0.666589\pi$
$128$	−1024.00	+	1024.00i	−0.0625000	+	0.0625000i
$129$		−	19602.0i		−	1.17793i
$130$	4140.00	−	5520.00i	0.244970	−	0.326627i
$131$	−6358.00			−0.370491			−0.185246	−	0.982692i	$-0.559308\pi$
$131$	−6358.00			−0.370491			−0.185246	+	0.982692i	$0.559308\pi$
$132$	−8496.00	−	8496.00i	−0.487603	−	0.487603i
$133$	−8120.00	+	8120.00i	−0.459042	+	0.459042i
$134$			3004.00i			0.167298i
$135$		0			0
$136$	−8672.00			−0.468858
$137$	20409.0	+	20409.0i	1.08738	+	1.08738i	0.995798	+	0.0915804i	$0.0291919\pi$
$137$	20409.0	+	20409.0i	1.08738	+	1.08738i	0.0915804	+	0.995798i	$0.470808\pi$
$138$	−9684.00	+	9684.00i	−0.508507	+	0.508507i
$139$		−	9400.00i		−	0.486517i	−0.969961	−	0.243259i	$-0.921784\pi$
$139$		−	9400.00i		−	0.486517i	0.969961	−	0.243259i	$-0.0782164\pi$
$140$	−1160.00	−	8120.00i	−0.0591837	−	0.414286i
$141$	22842.0			1.14894
$142$	−12884.0	−	12884.0i	−0.638961	−	0.638961i
$143$	−8142.00	+	8142.00i	−0.398161	+	0.398161i
$144$			5184.00i			0.250000i
$145$	−13600.0	−	10200.0i	−0.646849	−	0.485137i
$146$	11804.0			0.553762
$147$	−6471.00	−	6471.00i	−0.299459	−	0.299459i
$148$	5208.00	−	5208.00i	0.237765	−	0.237765i
$149$			13800.0i			0.621594i	0.950476	+	0.310797i	$0.100596\pi$
$149$			13800.0i			0.621594i	−0.950476	+	0.310797i	$0.899404\pi$
$150$	6300.00	+	21600.0i	0.280000	+	0.960000i
$151$	−18998.0			−0.833209			−0.416605	−	0.909088i	$-0.636780\pi$
$151$	−18998.0			−0.833209			−0.416605	+	0.909088i	$0.636780\pi$
$152$	4480.00	+	4480.00i	0.193906	+	0.193906i
$153$	−21951.0	+	21951.0i	−0.937716	+	0.937716i
$154$			13688.0i			0.577163i
$155$	−3030.00	+	4040.00i	−0.126119	+	0.168158i
$156$	9936.00			0.408284
$157$	−16371.0	−	16371.0i	−0.664165	−	0.664165i	0.292194	−	0.956359i	$-0.405615\pi$
$157$	−16371.0	−	16371.0i	−0.664165	−	0.664165i	−0.956359	+	0.292194i	$0.905615\pi$
$158$	21120.0	−	21120.0i	0.846018	−	0.846018i
$159$			10998.0i			0.435030i
$160$	−4480.00	+	640.000i	−0.175000	+	0.0250000i
$161$	15602.0			0.601906
$162$	−13122.0	−	13122.0i	−0.500000	−	0.500000i
$163$	20009.0	−	20009.0i	0.753096	−	0.753096i	−0.221960	−	0.975056i	$-0.571245\pi$
$163$	20009.0	−	20009.0i	0.753096	−	0.753096i	0.975056	+	0.221960i	$0.0712455\pi$
$164$			13456.0i			0.500297i
$165$	−5310.00	−	37170.0i	−0.195041	−	1.36529i
$166$	24924.0			0.904485
$167$	1549.00	+	1549.00i	0.0555416	+	0.0555416i	0.734332	−	0.678790i	$-0.237496\pi$
$167$	1549.00	+	1549.00i	0.0555416	+	0.0555416i	−0.678790	+	0.734332i	$0.737496\pi$
$168$	8352.00	−	8352.00i	0.295918	−	0.295918i
$169$			19039.0i			0.666608i
$170$	−21680.0	−	16260.0i	−0.750173	−	0.562630i
$171$	22680.0			0.775623
$172$	8712.00	+	8712.00i	0.294484	+	0.294484i
$173$	2789.00	−	2789.00i	0.0931872	−	0.0931872i	−0.658976	−	0.752164i	$-0.729010\pi$
$173$	2789.00	−	2789.00i	0.0931872	−	0.0931872i	0.752164	+	0.658976i	$0.229010\pi$
$174$		−	24480.0i		−	0.808561i
$175$	12325.0	−	22475.0i	0.402449	−	0.733878i
$176$	7552.00			0.243802
$177$	10440.0	+	10440.0i	0.333238	+	0.333238i
$178$	−28960.0	+	28960.0i	−0.914026	+	0.914026i
$179$		−	2600.00i		−	0.0811460i	−0.999177	−	0.0405730i	$-0.987082\pi$
$179$		−	2600.00i		−	0.0811460i	0.999177	−	0.0405730i	$-0.0129183\pi$
$180$	−9720.00	+	12960.0i	−0.300000	+	0.400000i
$181$	−44398.0			−1.35521			−0.677604	−	0.735427i	$-0.736982\pi$
$181$	−44398.0			−1.35521			−0.677604	+	0.735427i	$0.736982\pi$
$182$	−8004.00	−	8004.00i	−0.241637	−	0.241637i
$183$	−50382.0	+	50382.0i	−1.50443	+	1.50443i
$184$		−	8608.00i		−	0.254253i
$185$	22785.0	−	3255.00i	0.665741	−	0.0951059i
$186$	−7272.00			−0.210198
$187$	31978.0	+	31978.0i	0.914467	+	0.914467i
$188$	−10152.0	+	10152.0i	−0.287234	+	0.287234i
$189$		0			0
$190$	2800.00	+	19600.0i	0.0775623	+	0.542936i
$191$	−14678.0			−0.402346			−0.201173	−	0.979556i	$-0.564475\pi$
$191$	−14678.0			−0.402346			−0.201173	+	0.979556i	$0.564475\pi$
$192$	−4608.00	−	4608.00i	−0.125000	−	0.125000i
$193$	42849.0	−	42849.0i	1.15034	−	1.15034i	0.163855	−	0.986484i	$-0.447607\pi$
$193$	42849.0	−	42849.0i	1.15034	−	1.15034i	0.986484	−	0.163855i	$-0.0523930\pi$
$194$			29244.0i			0.777022i
$195$	24840.0	+	18630.0i	0.653254	+	0.489941i
$196$	5752.00			0.149729
$197$	−10971.0	−	10971.0i	−0.282692	−	0.282692i	0.551490	−	0.834182i	$-0.314060\pi$
$197$	−10971.0	−	10971.0i	−0.282692	−	0.282692i	−0.834182	+	0.551490i	$0.814060\pi$
$198$	19116.0	−	19116.0i	0.487603	−	0.487603i
$199$		−	38160.0i		−	0.963612i	−0.876278	−	0.481806i	$-0.839981\pi$
$199$		−	38160.0i		−	0.963612i	0.876278	−	0.481806i	$-0.160019\pi$
$200$	−12400.0	−	6800.00i	−0.310000	−	0.170000i
$201$	−13518.0			−0.334596
$202$	1756.00	+	1756.00i	0.0430350	+	0.0430350i
$203$	−19720.0	+	19720.0i	−0.478536	+	0.478536i
$204$		−	39024.0i		−	0.937716i
$205$	−25230.0	+	33640.0i	−0.600357	+	0.800476i
$206$	−41716.0			−0.983033
$207$	−21789.0	−	21789.0i	−0.508507	−	0.508507i
$208$	−4416.00	+	4416.00i	−0.102071	+	0.102071i
$209$		−	33040.0i		−	0.756393i
$210$	36540.0	−	5220.00i	0.828571	−	0.118367i
$211$	72842.0			1.63613			0.818063	−	0.575128i	$-0.195048\pi$
$211$	72842.0			1.63613			0.818063	+	0.575128i	$0.195048\pi$
$212$	−4888.00	−	4888.00i	−0.108758	−	0.108758i
$213$	57978.0	−	57978.0i	1.27792	−	1.27792i
$214$			18844.0i			0.411477i
$215$	5445.00	+	38115.0i	0.117793	+	0.824554i
$216$		0			0
$217$	5858.00	+	5858.00i	0.124403	+	0.124403i
$218$	44080.0	−	44080.0i	0.927531	−	0.927531i
$219$			53118.0i			1.10752i
$220$	18880.0	+	14160.0i	0.390083	+	0.292562i
$221$	−37398.0			−0.765709
$222$	23436.0	+	23436.0i	0.475530	+	0.475530i
$223$	−30891.0	+	30891.0i	−0.621187	+	0.621187i	−0.945835	−	0.324648i	$-0.894754\pi$
$223$	−30891.0	+	30891.0i	−0.621187	+	0.621187i	0.324648	+	0.945835i	$0.394754\pi$
$224$			7424.00i			0.147959i
$225$	−48600.0	+	14175.0i	−0.960000	+	0.280000i
$226$	8444.00			0.165322
$227$	−54911.0	−	54911.0i	−1.06563	−	1.06563i	−0.997689	−	0.0679438i	$-0.978356\pi$
$227$	−54911.0	−	54911.0i	−1.06563	−	1.06563i	−0.0679438	−	0.997689i	$-0.521644\pi$
$228$	−20160.0	+	20160.0i	−0.387812	+	0.387812i
$229$		−	50280.0i		−	0.958792i	−0.877599	−	0.479396i	$-0.840856\pi$
$229$		−	50280.0i		−	0.958792i	0.877599	−	0.479396i	$-0.159144\pi$
$230$	16140.0	−	21520.0i	0.305104	−	0.406805i
$231$	−61596.0			−1.15433
$232$	10880.0	+	10880.0i	0.202140	+	0.202140i
$233$	−2391.00	+	2391.00i	−0.0440421	+	0.0440421i	−0.728785	−	0.684743i	$-0.759915\pi$
$233$	−2391.00	+	2391.00i	−0.0440421	+	0.0440421i	0.684743	+	0.728785i	$0.259915\pi$
$234$			22356.0i			0.408284i
$235$	−44415.0	+	6345.00i	−0.804255	+	0.114894i
$236$	−9280.00			−0.166619
$237$	95040.0	+	95040.0i	1.69204	+	1.69204i
$238$	−31436.0	+	31436.0i	−0.554975	+	0.554975i
$239$		−	17760.0i		−	0.310919i	−0.987842	−	0.155459i	$-0.950314\pi$
$239$		−	17760.0i		−	0.310919i	0.987842	−	0.155459i	$-0.0496858\pi$
$240$	−2880.00	−	20160.0i	−0.0500000	−	0.350000i
$241$	−28238.0			−0.486183			−0.243092	−	0.970003i	$-0.578162\pi$
$241$	−28238.0			−0.486183			−0.243092	+	0.970003i	$0.578162\pi$
$242$	1434.00	+	1434.00i	0.0244860	+	0.0244860i
$243$	59049.0	−	59049.0i	1.00000	−	1.00000i
$244$		−	44784.0i		−	0.752217i
$245$	14380.0	+	10785.0i	0.239567	+	0.179675i
$246$	−60552.0			−1.00059
$247$	19320.0	+	19320.0i	0.316675	+	0.316675i
$248$	3232.00	−	3232.00i	0.0525494	−	0.0525494i
$249$			112158.i			1.80897i
$250$	−18250.0	−	40250.0i	−0.292000	−	0.644000i
$251$	121002.			1.92064			0.960318	−	0.278907i	$-0.0899722\pi$
$251$	121002.			1.92064			0.960318	+	0.278907i	$0.0899722\pi$
$252$	18792.0	+	18792.0i	0.295918	+	0.295918i
$253$	−31742.0	+	31742.0i	−0.495899	+	0.495899i
$254$		−	23636.0i		−	0.366359i
$255$	73170.0	−	97560.0i	1.12526	−	1.50035i
$256$	4096.00			0.0625000
$257$	−72431.0	−	72431.0i	−1.09663	−	1.09663i	−0.994803	−	0.101823i	$-0.967533\pi$
$257$	−72431.0	−	72431.0i	−1.09663	−	1.09663i	−0.101823	−	0.994803i	$-0.532467\pi$
$258$	−39204.0	+	39204.0i	−0.588967	+	0.588967i
$259$		−	37758.0i		−	0.562872i
$260$	−19320.0	+	2760.00i	−0.285799	+	0.0408284i
$261$	55080.0			0.808561
$262$	12716.0	+	12716.0i	0.185246	+	0.185246i
$263$	−14771.0	+	14771.0i	−0.213549	+	0.213549i	−0.805773	−	0.592224i	$-0.798250\pi$
$263$	−14771.0	+	14771.0i	−0.213549	+	0.213549i	0.592224	+	0.805773i	$0.298250\pi$
$264$			33984.0i			0.487603i
$265$	−3055.00	−	21385.0i	−0.0435030	−	0.304521i
$266$	32480.0			0.459042
$267$	−130320.	−	130320.i	−1.82805	−	1.82805i
$268$	6008.00	−	6008.00i	0.0836489	−	0.0836489i
$269$			89720.0i			1.23989i	0.784644	+	0.619947i	$0.212846\pi$
$269$			89720.0i			1.23989i	−0.784644	+	0.619947i	$0.787154\pi$
$270$		0			0
$271$	68202.0			0.928664			0.464332	−	0.885661i	$-0.346294\pi$
$271$	68202.0			0.928664			0.464332	+	0.885661i	$0.346294\pi$
$272$	17344.0	+	17344.0i	0.234429	+	0.234429i
$273$	36018.0	−	36018.0i	0.483275	−	0.483275i
$274$		−	81636.0i		−	1.08738i
$275$	20650.0	+	70800.0i	0.273058	+	0.936198i
$276$	38736.0			0.508507
$277$	18549.0	+	18549.0i	0.241747	+	0.241747i	0.817573	−	0.575826i	$-0.195319\pi$
$277$	18549.0	+	18549.0i	0.241747	+	0.241747i	−0.575826	+	0.817573i	$0.695319\pi$
$278$	−18800.0	+	18800.0i	−0.243259	+	0.243259i
$279$		−	16362.0i		−	0.210198i
$280$	−13920.0	+	18560.0i	−0.177551	+	0.236735i
$281$	2322.00			0.0294069			0.0147035	−	0.999892i	$-0.495320\pi$
$281$	2322.00			0.0294069			0.0147035	+	0.999892i	$0.495320\pi$
$282$	−45684.0	−	45684.0i	−0.574468	−	0.574468i
$283$	−91711.0	+	91711.0i	−1.14511	+	1.14511i	−0.157613	+	0.987501i	$0.550380\pi$
$283$	−91711.0	+	91711.0i	−1.14511	+	1.14511i	−0.987501	+	0.157613i	$0.949620\pi$
$284$			51536.0i			0.638961i
$285$	−88200.0	+	12600.0i	−1.08587	+	0.155125i
$286$	32568.0			0.398161
$287$	48778.0	+	48778.0i	0.592189	+	0.592189i
$288$	10368.0	−	10368.0i	0.125000	−	0.125000i
$289$			63361.0i			0.758624i
$290$	6800.00	+	47600.0i	0.0808561	+	0.565993i
$291$	−131598.			−1.55404
$292$	−23608.0	−	23608.0i	−0.276881	−	0.276881i
$293$	−4851.00	+	4851.00i	−0.0565062	+	0.0565062i	−0.734795	−	0.678289i	$-0.762722\pi$
$293$	−4851.00	+	4851.00i	−0.0565062	+	0.0565062i	0.678289	+	0.734795i	$0.262722\pi$
$294$			25884.0i			0.299459i
$295$	−23200.0	−	17400.0i	−0.266590	−	0.199943i
$296$	−20832.0			−0.237765
$297$		0			0
$298$	27600.0	−	27600.0i	0.310797	−	0.310797i
$299$		−	37122.0i		−	0.415230i
$300$	30600.0	−	55800.0i	0.340000	−	0.620000i
$301$	63162.0			0.697145
$302$	37996.0	+	37996.0i	0.416605	+	0.416605i
$303$	−7902.00	+	7902.00i	−0.0860700	+	0.0860700i
$304$		−	17920.0i		−	0.193906i
$305$	83970.0	−	111960.i	0.902661	−	1.20355i
$306$	87804.0			0.937716
$307$	42849.0	+	42849.0i	0.454636	+	0.454636i	0.896890	−	0.442254i	$-0.145821\pi$
$307$	42849.0	+	42849.0i	0.454636	+	0.454636i	−0.442254	+	0.896890i	$0.645821\pi$
$308$	27376.0	−	27376.0i	0.288582	−	0.288582i
$309$		−	187722.i		−	1.96607i
$310$	14140.0	−	2020.00i	0.147138	−	0.0210198i
$311$	−72278.0			−0.747283			−0.373642	−	0.927573i	$-0.621891\pi$
$311$	−72278.0			−0.747283			−0.373642	+	0.927573i	$0.621891\pi$
$312$	−19872.0	−	19872.0i	−0.204142	−	0.204142i
$313$	18249.0	−	18249.0i	0.186273	−	0.186273i	−0.607810	−	0.794083i	$-0.707952\pi$
$313$	18249.0	−	18249.0i	0.186273	−	0.186273i	0.794083	+	0.607810i	$0.207952\pi$
$314$			65484.0i			0.664165i
$315$	11745.0	+	82215.0i	0.118367	+	0.828571i
$316$	−84480.0			−0.846018
$317$	25149.0	+	25149.0i	0.250266	+	0.250266i	0.821080	−	0.570814i	$-0.193372\pi$
$317$	25149.0	+	25149.0i	0.250266	+	0.250266i	−0.570814	+	0.821080i	$0.693372\pi$
$318$	21996.0	−	21996.0i	0.217515	−	0.217515i
$319$		−	80240.0i		−	0.788514i
$320$	10240.0	+	7680.00i	0.100000	+	0.0750000i
$321$	−84798.0			−0.822954
$322$	−31204.0	−	31204.0i	−0.300953	−	0.300953i
$323$	75880.0	−	75880.0i	0.727315	−	0.727315i
$324$			52488.0i			0.500000i
$325$	−53475.0	−	29325.0i	−0.506272	−	0.277633i
$326$	−80036.0			−0.753096
$327$	198360.	+	198360.i	1.85506	+	1.85506i
$328$	26912.0	−	26912.0i	0.250149	−	0.250149i
$329$			73602.0i			0.679983i
$330$	−63720.0	+	84960.0i	−0.585124	+	0.780165i
$331$	−54038.0			−0.493223			−0.246611	−	0.969114i	$-0.579317\pi$
$331$	−54038.0			−0.493223			−0.246611	+	0.969114i	$0.579317\pi$
$332$	−49848.0	−	49848.0i	−0.452243	−	0.452243i
$333$	−52731.0	+	52731.0i	−0.475530	+	0.475530i
$334$		−	6196.00i		−	0.0555416i
$335$	26285.0	−	3755.00i	0.234217	−	0.0334596i
$336$	−33408.0			−0.295918
$337$	8529.00	+	8529.00i	0.0750997	+	0.0750997i	0.743659	−	0.668559i	$-0.233089\pi$
$337$	8529.00	+	8529.00i	0.0750997	+	0.0750997i	−0.668559	+	0.743659i	$0.733089\pi$
$338$	38078.0	−	38078.0i	0.333304	−	0.333304i
$339$			37998.0i			0.330645i
$340$	10840.0	+	75880.0i	0.0937716	+	0.656401i
$341$	−23836.0			−0.204986
$342$	−45360.0	−	45360.0i	−0.387812	−	0.387812i
$343$	90480.0	−	90480.0i	0.769067	−	0.769067i
$344$		−	34848.0i		−	0.294484i
$345$	96840.0	+	72630.0i	0.813611	+	0.610208i
$346$	−11156.0			−0.0931872
$347$	−56551.0	−	56551.0i	−0.469658	−	0.469658i	0.432146	−	0.901804i	$-0.357756\pi$
$347$	−56551.0	−	56551.0i	−0.469658	−	0.469658i	−0.901804	+	0.432146i	$0.857756\pi$
$348$	−48960.0	+	48960.0i	−0.404281	+	0.404281i
$349$		−	22520.0i		−	0.184892i	−0.995718	−	0.0924459i	$-0.970531\pi$
$349$		−	22520.0i		−	0.184892i	0.995718	−	0.0924459i	$-0.0294685\pi$
$350$	−69600.0	+	20300.0i	−0.568163	+	0.165714i
$351$		0			0
$352$	−15104.0	−	15104.0i	−0.121901	−	0.121901i
$353$	−44511.0	+	44511.0i	−0.357205	+	0.357205i	−0.862782	−	0.505576i	$-0.831280\pi$
$353$	−44511.0	+	44511.0i	−0.357205	+	0.357205i	0.505576	+	0.862782i	$0.331280\pi$
$354$		−	41760.0i		−	0.333238i
$355$	−96630.0	+	128840.i	−0.766753	+	1.02234i
$356$	115840.			0.914026
$357$	−141462.	−	141462.i	−1.10995	−	1.10995i
$358$	−5200.00	+	5200.00i	−0.0405730	+	0.0405730i
$359$		−	9680.00i		−	0.0751080i	−0.999295	−	0.0375540i	$-0.988043\pi$
$359$		−	9680.00i		−	0.0751080i	0.999295	−	0.0375540i	$-0.0119566\pi$
$360$	45360.0	−	6480.00i	0.350000	−	0.0500000i
$361$	51921.0			0.398409
$362$	88796.0	+	88796.0i	0.677604	+	0.677604i
$363$	−6453.00	+	6453.00i	−0.0489721	+	0.0489721i
$364$			32016.0i			0.241637i
$365$	−14755.0	−	103285.i	−0.110752	−	0.775267i
$366$	201528.			1.50443
$367$	−14971.0	−	14971.0i	−0.111152	−	0.111152i	0.649343	−	0.760496i	$-0.275044\pi$
$367$	−14971.0	−	14971.0i	−0.111152	−	0.111152i	−0.760496	+	0.649343i	$0.775044\pi$
$368$	−17216.0	+	17216.0i	−0.127127	+	0.127127i
$369$		−	136242.i		−	1.00059i
$370$	−52080.0	−	39060.0i	−0.380424	−	0.285318i
$371$	−35438.0			−0.257467
$372$	14544.0	+	14544.0i	0.105099	+	0.105099i
$373$	−13811.0	+	13811.0i	−0.0992676	+	0.0992676i	−0.754996	−	0.655729i	$-0.772361\pi$
$373$	−13811.0	+	13811.0i	−0.0992676	+	0.0992676i	0.655729	+	0.754996i	$0.272361\pi$
$374$		−	127912.i		−	0.914467i
$375$	181125.	−	82125.0i	1.28800	−	0.584000i
$376$	40608.0			0.287234
$377$	46920.0	+	46920.0i	0.330123	+	0.330123i
$378$		0			0
$379$			251080.i			1.74797i	0.485954	+	0.873984i	$0.338472\pi$
$379$			251080.i			1.74797i	−0.485954	+	0.873984i	$0.661528\pi$
$380$	33600.0	−	44800.0i	0.232687	−	0.310249i
$381$	106362.			0.732717
$382$	29356.0	+	29356.0i	0.201173	+	0.201173i
$383$	−86091.0	+	86091.0i	−0.586895	+	0.586895i	−0.936789	−	0.349894i	$-0.886217\pi$
$383$	−86091.0	+	86091.0i	−0.586895	+	0.586895i	0.349894	+	0.936789i	$0.386217\pi$
$384$			18432.0i			0.125000i
$385$	119770.	−	17110.0i	0.808028	−	0.115433i
$386$	−171396.			−1.15034
$387$	−88209.0	−	88209.0i	−0.588967	−	0.588967i
$388$	58488.0	−	58488.0i	0.388511	−	0.388511i
$389$		−	75000.0i		−	0.495635i	−0.968807	−	0.247818i	$-0.920287\pi$
$389$		−	75000.0i		−	0.495635i	0.968807	−	0.247818i	$-0.0797134\pi$
$390$	−12420.0	−	86940.0i	−0.0816568	−	0.571598i
$391$	−145798.			−0.953670
$392$	−11504.0	−	11504.0i	−0.0748646	−	0.0748646i
$393$	−57222.0	+	57222.0i	−0.370491	+	0.370491i
$394$			43884.0i			0.282692i
$395$	−211200.	−	158400.i	−1.35363	−	1.01522i
$396$	−76464.0			−0.487603
$397$	29149.0	+	29149.0i	0.184945	+	0.184945i	0.793507	−	0.608562i	$-0.208253\pi$
$397$	29149.0	+	29149.0i	0.184945	+	0.184945i	−0.608562	+	0.793507i	$0.708253\pi$
$398$	−76320.0	+	76320.0i	−0.481806	+	0.481806i
$399$			146160.i			0.918085i
$400$	11200.0	+	38400.0i	0.0700000	+	0.240000i
$401$	−45918.0			−0.285558			−0.142779	−	0.989755i	$-0.545604\pi$
$401$	−45918.0			−0.285558			−0.142779	+	0.989755i	$0.545604\pi$
$402$	27036.0	+	27036.0i	0.167298	+	0.167298i
$403$	13938.0	−	13938.0i	0.0858204	−	0.0858204i
$404$		−	7024.00i		−	0.0430350i
$405$	−98415.0	+	131220.i	−0.600000	+	0.800000i
$406$	78880.0			0.478536
$407$	76818.0	+	76818.0i	0.463740	+	0.463740i
$408$	−78048.0	+	78048.0i	−0.468858	+	0.468858i
$409$			78720.0i			0.470585i	0.971925	+	0.235293i	$0.0756049\pi$
$409$			78720.0i			0.470585i	−0.971925	+	0.235293i	$0.924395\pi$
$410$	117740.	−	16820.0i	0.700416	−	0.100059i
$411$	367362.			2.17476
$412$	83432.0	+	83432.0i	0.491517	+	0.491517i
$413$	−33640.0	+	33640.0i	−0.197222	+	0.197222i
$414$			87156.0i			0.508507i
$415$	−31155.0	−	218085.i	−0.180897	−	1.26628i
$416$	17664.0			0.102071
$417$	−84600.0	−	84600.0i	−0.486517	−	0.486517i
$418$	−66080.0	+	66080.0i	−0.378196	+	0.378196i
$419$		−	14760.0i		−	0.0840733i	−0.999116	−	0.0420367i	$-0.986615\pi$
$419$		−	14760.0i		−	0.0840733i	0.999116	−	0.0420367i	$-0.0133846\pi$
$420$	−83520.0	−	62640.0i	−0.473469	−	0.355102i
$421$	221282.			1.24848			0.624240	−	0.781232i	$-0.285409\pi$
$421$	221282.			1.24848			0.624240	+	0.781232i	$0.285409\pi$
$422$	−145684.	−	145684.i	−0.818063	−	0.818063i
$423$	102789.	−	102789.i	0.574468	−	0.574468i
$424$			19552.0i			0.108758i
$425$	−115175.	+	210025.i	−0.637647	+	1.16277i
$426$	−231912.			−1.27792
$427$	−162342.	−	162342.i	−0.890379	−	0.890379i
$428$	37688.0	−	37688.0i	0.205738	−	0.205738i
$429$			146556.i			0.796323i
$430$	65340.0	−	87120.0i	0.353380	−	0.471174i
$431$	212522.			1.14406			0.572031	−	0.820232i	$-0.306156\pi$
$431$	212522.			1.14406			0.572031	+	0.820232i	$0.306156\pi$
$432$		0			0
$433$	145409.	−	145409.i	0.775560	−	0.775560i	−0.203512	−	0.979072i	$-0.565236\pi$
$433$	145409.	−	145409.i	0.775560	−	0.775560i	0.979072	+	0.203512i	$0.0652357\pi$
$434$		−	23432.0i		−	0.124403i
$435$	−214200.	+	30600.0i	−1.13199	+	0.161712i
$436$	−176320.			−0.927531
$437$	75320.0	+	75320.0i	0.394410	+	0.394410i
$438$	106236.	−	106236.i	0.553762	−	0.553762i
$439$		−	299440.i		−	1.55375i	−0.629656	−	0.776874i	$-0.716804\pi$
$439$		−	299440.i		−	1.55375i	0.629656	−	0.776874i	$-0.283196\pi$
$440$	−9440.00	−	66080.0i	−0.0487603	−	0.341322i
$441$	−58239.0			−0.299459
$442$	74796.0	+	74796.0i	0.382855	+	0.382855i
$443$	240609.	−	240609.i	1.22604	−	1.22604i	0.260590	−	0.965450i	$-0.416083\pi$
$443$	240609.	−	240609.i	1.22604	−	1.22604i	0.965450	−	0.260590i	$-0.0839170\pi$
$444$		−	93744.0i		−	0.475530i
$445$	289600.	+	217200.i	1.46244	+	1.09683i
$446$	123564.			0.621187
$447$	124200.	+	124200.i	0.621594	+	0.621594i
$448$	14848.0	−	14848.0i	0.0739796	−	0.0739796i
$449$		−	82480.0i		−	0.409125i	−0.978854	−	0.204562i	$-0.934423\pi$
$449$		−	82480.0i		−	0.409125i	0.978854	−	0.204562i	$-0.0655772\pi$
$450$	125550.	+	68850.0i	0.620000	+	0.340000i
$451$	−198476.			−0.975787
$452$	−16888.0	−	16888.0i	−0.0826611	−	0.0826611i
$453$	−170982.	+	170982.i	−0.833209	+	0.833209i
$454$			219644.i			1.06563i
$455$	−60030.0	+	80040.0i	−0.289965	+	0.386620i
$456$	80640.0			0.387812
$457$	−188151.	−	188151.i	−0.900895	−	0.900895i	0.0946187	−	0.995514i	$-0.469837\pi$
$457$	−188151.	−	188151.i	−0.900895	−	0.900895i	−0.995514	+	0.0946187i	$0.969837\pi$
$458$	−100560.	+	100560.i	−0.479396	+	0.479396i
$459$		0			0
$460$	−75320.0	+	10760.0i	−0.355955	+	0.0508507i
$461$	−326158.			−1.53471			−0.767355	−	0.641223i	$-0.778427\pi$
$461$	−326158.			−1.53471			−0.767355	+	0.641223i	$0.778427\pi$
$462$	123192.	+	123192.i	0.577163	+	0.577163i
$463$	−218731.	+	218731.i	−1.02035	+	1.02035i	−0.0205595	+	0.999789i	$0.506545\pi$
$463$	−218731.	+	218731.i	−1.02035	+	1.02035i	−0.999789	+	0.0205595i	$0.993455\pi$
$464$		−	43520.0i		−	0.202140i
$465$	9090.00	+	63630.0i	0.0420395	+	0.294277i
$466$	9564.00			0.0440421
$467$	59249.0	+	59249.0i	0.271673	+	0.271673i	0.829774	−	0.558100i	$-0.188470\pi$
$467$	59249.0	+	59249.0i	0.271673	+	0.271673i	−0.558100	+	0.829774i	$0.688470\pi$
$468$	44712.0	−	44712.0i	0.204142	−	0.204142i
$469$		−	43558.0i		−	0.198026i
$470$	101520.	+	76140.0i	0.459574	+	0.344681i
$471$	−294678.			−1.32833
$472$	18560.0	+	18560.0i	0.0833094	+	0.0833094i
$473$	−128502.	+	128502.i	−0.574365	+	0.574365i
$474$		−	380160.i		−	1.69204i
$475$	168000.	−	49000.0i	0.744598	−	0.217175i
$476$	125744.			0.554975
$477$	49491.0	+	49491.0i	0.217515	+	0.217515i
$478$	−35520.0	+	35520.0i	−0.155459	+	0.155459i
$479$			273440.i			1.19177i	0.803071	+	0.595883i	$0.203198\pi$
$479$			273440.i			1.19177i	−0.803071	+	0.595883i	$0.796802\pi$
$480$	−34560.0	+	46080.0i	−0.150000	+	0.200000i
$481$	−89838.0			−0.388302
$482$	56476.0	+	56476.0i	0.243092	+	0.243092i
$483$	140418.	−	140418.i	0.601906	−	0.601906i
$484$		−	5736.00i		−	0.0244860i
$485$	255885.	−	36555.0i	1.08783	−	0.155404i
$486$	−236196.			−1.00000
$487$	−123651.	−	123651.i	−0.521362	−	0.521362i	0.396620	−	0.917983i	$-0.370183\pi$
$487$	−123651.	−	123651.i	−0.521362	−	0.521362i	−0.917983	+	0.396620i	$0.870183\pi$
$488$	−89568.0	+	89568.0i	−0.376109	+	0.376109i
$489$		−	360162.i		−	1.50619i
$490$	−7190.00	−	50330.0i	−0.0299459	−	0.209621i
$491$	198442.			0.823134			0.411567	−	0.911379i	$-0.364982\pi$
$491$	198442.			0.823134			0.411567	+	0.911379i	$0.364982\pi$
$492$	121104.	+	121104.i	0.500297	+	0.500297i
$493$	184280.	−	184280.i	0.758201	−	0.758201i
$494$		−	77280.0i		−	0.316675i
$495$	−191160.	−	143370.i	−0.780165	−	0.585124i
$496$	−12928.0			−0.0525494
$497$	186818.	+	186818.i	0.756321	+	0.756321i
$498$	224316.	−	224316.i	0.904485	−	0.904485i
$499$			269240.i			1.08128i	0.841254	+	0.540640i	$0.181818\pi$
$499$			269240.i			1.08128i	−0.841254	+	0.540640i	$0.818182\pi$
$500$	−44000.0	+	117000.i	−0.176000	+	0.468000i
$501$	27882.0			0.111083
$502$	−242004.	−	242004.i	−0.960318	−	0.960318i
$503$	109869.	−	109869.i	0.434249	−	0.434249i	−0.455822	−	0.890071i	$-0.650655\pi$
$503$	109869.	−	109869.i	0.434249	−	0.434249i	0.890071	+	0.455822i	$0.150655\pi$
$504$		−	75168.0i		−	0.295918i
$505$	13170.0	−	17560.0i	0.0516420	−	0.0688560i
$506$	126968.			0.495899
$507$	171351.	+	171351.i	0.666608	+	0.666608i
$508$	−47272.0	+	47272.0i	−0.183179	+	0.183179i
$509$		−	211000.i		−	0.814417i	−0.913335	−	0.407209i	$-0.866502\pi$
$509$		−	211000.i		−	0.814417i	0.913335	−	0.407209i	$-0.133498\pi$
$510$	−341460.	+	48780.0i	−1.31280	+	0.187543i
$511$	−171158.			−0.655474
$512$	−8192.00	−	8192.00i	−0.0312500	−	0.0312500i
$513$		0			0
$514$			289724.i			1.09663i
$515$	52145.0	+	365015.i	0.196607	+	1.37625i
$516$	156816.			0.588967
$517$	−149742.	−	149742.i	−0.560225	−	0.560225i
$518$	−75516.0	+	75516.0i	−0.281436	+	0.281436i
$519$		−	50202.0i		−	0.186374i
$520$	44160.0	+	33120.0i	0.163314	+	0.122485i
$521$	297282.			1.09520			0.547600	−	0.836740i	$-0.315542\pi$
$521$	297282.			1.09520			0.547600	+	0.836740i	$0.315542\pi$
$522$	−110160.	−	110160.i	−0.404281	−	0.404281i
$523$	−25071.0	+	25071.0i	−0.0916576	+	0.0916576i	−0.751449	−	0.659791i	$-0.770645\pi$
$523$	−25071.0	+	25071.0i	−0.0916576	+	0.0916576i	0.659791	+	0.751449i	$0.270645\pi$
$524$		−	50864.0i		−	0.185246i
$525$	−91350.0	−	313200.i	−0.331429	−	1.13633i
$526$	59084.0			0.213549
$527$	−54742.0	−	54742.0i	−0.197106	−	0.197106i
$528$	67968.0	−	67968.0i	0.243802	−	0.243802i
$529$			135119.i			0.482842i
$530$	−36660.0	+	48880.0i	−0.130509	+	0.174012i
$531$	93960.0			0.333238
$532$	−64960.0	−	64960.0i	−0.229521	−	0.229521i
$533$	116058.	−	116058.i	0.408527	−	0.408527i
$534$			521280.i			1.82805i
$535$	164885.	−	23555.0i	0.576068	−	0.0822954i
$536$	−24032.0			−0.0836489
$537$	−23400.0	−	23400.0i	−0.0811460	−	0.0811460i
$538$	179440.	−	179440.i	0.619947	−	0.619947i
$539$			84842.0i			0.292034i
$540$		0			0
$541$	−142478.			−0.486803			−0.243402	−	0.969926i	$-0.578263\pi$
$541$	−142478.			−0.486803			−0.243402	+	0.969926i	$0.578263\pi$
$542$	−136404.	−	136404.i	−0.464332	−	0.464332i
$543$	−399582.	+	399582.i	−1.35521	+	1.35521i
$544$		−	69376.0i		−	0.234429i
$545$	−440800.	−	330600.i	−1.48405	−	1.11304i
$546$	−144072.			−0.483275
$547$	291009.	+	291009.i	0.972594	+	0.972594i	0.999634	−	0.0270399i	$-0.00860813\pi$
$547$	291009.	+	291009.i	0.972594	+	0.972594i	−0.0270399	+	0.999634i	$0.508608\pi$
$548$	−163272.	+	163272.i	−0.543689	+	0.543689i
$549$			453438.i			1.50443i
$550$	100300.	−	182900.i	0.331570	−	0.604628i
$551$	−190400.			−0.627139
$552$	−77472.0	−	77472.0i	−0.254253	−	0.254253i
$553$	−306240.	+	306240.i	−1.00141	+	1.00141i
$554$		−	74196.0i		−	0.241747i
$555$	175770.	−	234360.i	0.570636	−	0.760847i
$556$	75200.0			0.243259
$557$	−83091.0	−	83091.0i	−0.267820	−	0.267820i	0.560401	−	0.828221i	$-0.310647\pi$
$557$	−83091.0	−	83091.0i	−0.267820	−	0.267820i	−0.828221	+	0.560401i	$0.810647\pi$
$558$	−32724.0	+	32724.0i	−0.105099	+	0.105099i
$559$		−	150282.i		−	0.480932i
$560$	64960.0	−	9280.00i	0.207143	−	0.0295918i
$561$	575604.			1.82893
$562$	−4644.00	−	4644.00i	−0.0147035	−	0.0147035i
$563$	43449.0	−	43449.0i	0.137076	−	0.137076i	−0.635239	−	0.772316i	$-0.719098\pi$
$563$	43449.0	−	43449.0i	0.137076	−	0.137076i	0.772316	+	0.635239i	$0.219098\pi$
$564$			182736.i			0.574468i
$565$	−10555.0	−	73885.0i	−0.0330645	−	0.231451i
$566$	366844.			1.14511
$567$	190269.	+	190269.i	0.591837	+	0.591837i
$568$	103072.	−	103072.i	0.319480	−	0.319480i
$569$		−	270560.i		−	0.835678i	−0.908521	−	0.417839i	$-0.862788\pi$
$569$		−	270560.i		−	0.835678i	0.908521	−	0.417839i	$-0.137212\pi$
$570$	201600.	+	151200.i	0.620499	+	0.465374i
$571$	57482.0			0.176303			0.0881515	−	0.996107i	$-0.471904\pi$
$571$	57482.0			0.176303			0.0881515	+	0.996107i	$0.471904\pi$
$572$	−65136.0	−	65136.0i	−0.199081	−	0.199081i
$573$	−132102.	+	132102.i	−0.402346	+	0.402346i
$574$		−	195112.i		−	0.592189i
$575$	−208475.	−	114325.i	−0.630548	−	0.345784i
$576$	−41472.0			−0.125000
$577$	195889.	+	195889.i	0.588381	+	0.588381i	0.937193	−	0.348812i	$-0.113415\pi$
$577$	195889.	+	195889.i	0.588381	+	0.588381i	−0.348812	+	0.937193i	$0.613415\pi$
$578$	126722.	−	126722.i	0.379312	−	0.379312i
$579$		−	771282.i		−	2.30068i
$580$	81600.0	−	108800.i	0.242568	−	0.323424i
$581$	−361398.			−1.07062
$582$	263196.	+	263196.i	0.777022	+	0.777022i
$583$	72098.0	−	72098.0i	0.212122	−	0.212122i
$584$			94432.0i			0.276881i
$585$	195615.	−	27945.0i	0.571598	−	0.0816568i
$586$	19404.0			0.0565062
$587$	−404631.	−	404631.i	−1.17431	−	1.17431i	−0.981171	−	0.193139i	$-0.938133\pi$
$587$	−404631.	−	404631.i	−1.17431	−	1.17431i	−0.193139	−	0.981171i	$-0.561867\pi$
$588$	51768.0	−	51768.0i	0.149729	−	0.149729i
$589$			56560.0i			0.163034i
$590$	11600.0	+	81200.0i	0.0333238	+	0.233266i
$591$	−197478.			−0.565384
$592$	41664.0	+	41664.0i	0.118882	+	0.118882i
$593$	−210991.	+	210991.i	−0.600005	+	0.600005i	−0.940314	−	0.340309i	$-0.889468\pi$
$593$	−210991.	+	210991.i	−0.600005	+	0.600005i	0.340309	+	0.940314i	$0.389468\pi$
$594$		0			0
$595$	314360.	+	235770.i	0.887960	+	0.665970i
$596$	−110400.			−0.310797
$597$	−343440.	−	343440.i	−0.963612	−	0.963612i
$598$	−74244.0	+	74244.0i	−0.207615	+	0.207615i
$599$			300560.i			0.837679i	0.908060	+	0.418839i	$0.137563\pi$
$599$			300560.i			0.837679i	−0.908060	+	0.418839i	$0.862437\pi$
$600$	−172800.	+	50400.0i	−0.480000	+	0.140000i
$601$	367442.			1.01728			0.508639	−	0.860980i	$-0.330149\pi$
$601$	367442.			1.01728			0.508639	+	0.860980i	$0.330149\pi$
$602$	−126324.	−	126324.i	−0.348572	−	0.348572i
$603$	−60831.0	+	60831.0i	−0.167298	+	0.167298i
$604$		−	151984.i		−	0.416605i
$605$	10755.0	−	14340.0i	0.0293832	−	0.0391777i
$606$	31608.0			0.0860700
$607$	146469.	+	146469.i	0.397529	+	0.397529i	0.877360	−	0.479832i	$-0.159302\pi$
$607$	146469.	+	146469.i	0.397529	+	0.397529i	−0.479832	+	0.877360i	$0.659302\pi$
$608$	−35840.0	+	35840.0i	−0.0969529	+	0.0969529i
$609$			354960.i			0.957072i
$610$	−391860.	+	55980.0i	−1.05310	+	0.150443i
$611$	175122.			0.469092
$612$	−175608.	−	175608.i	−0.468858	−	0.468858i
$613$	160989.	−	160989.i	0.428425	−	0.428425i	−0.459666	−	0.888092i	$-0.652031\pi$
$613$	160989.	−	160989.i	0.428425	−	0.428425i	0.888092	+	0.459666i	$0.152031\pi$
$614$		−	171396.i		−	0.454636i
$615$	75690.0	+	529830.i	0.200119	+	1.40083i
$616$	−109504.			−0.288582
$617$	320409.	+	320409.i	0.841656	+	0.841656i	0.989074	−	0.147419i	$-0.0470965\pi$
$617$	320409.	+	320409.i	0.841656	+	0.841656i	−0.147419	+	0.989074i	$0.547096\pi$
$618$	−375444.	+	375444.i	−0.983033	+	0.983033i
$619$			341160.i			0.890383i	0.895435	+	0.445191i	$0.146864\pi$
$619$			341160.i			0.890383i	−0.895435	+	0.445191i	$0.853136\pi$
$620$	−32320.0	−	24240.0i	−0.0840791	−	0.0630593i
$621$		0			0
$622$	144556.	+	144556.i	0.373642	+	0.373642i
$623$	419920.	−	419920.i	1.08191	−	1.08191i
$624$			79488.0i			0.204142i
$625$	−329375.	+	210000.i	−0.843200	+	0.537600i
$626$	−72996.0			−0.186273
$627$	−297360.	−	297360.i	−0.756393	−	0.756393i
$628$	130968.	−	130968.i	0.332082	−	0.332082i
$629$			352842.i			0.891824i
$630$	140940.	−	187920.i	0.355102	−	0.473469i
$631$	−390998.			−0.982010			−0.491005	−	0.871157i	$-0.663370\pi$
$631$	−390998.			−0.982010			−0.491005	+	0.871157i	$0.663370\pi$
$632$	168960.	+	168960.i	0.423009	+	0.423009i
$633$	655578.	−	655578.i	1.63613	−	1.63613i
$634$		−	100596.i		−	0.250266i
$635$	−206815.	+	29545.0i	−0.512902	+	0.0732717i
$636$	−87984.0			−0.217515
$637$	−49611.0	−	49611.0i	−0.122264	−	0.122264i
$638$	−160480.	+	160480.i	−0.394257	+	0.394257i
$639$		−	521802.i		−	1.27792i
$640$	−5120.00	−	35840.0i	−0.0125000	−	0.0875000i
$641$	−585038.			−1.42386			−0.711931	−	0.702249i	$-0.752179\pi$
$641$	−585038.			−1.42386			−0.711931	+	0.702249i	$0.752179\pi$
$642$	169596.	+	169596.i	0.411477	+	0.411477i
$643$	−31911.0	+	31911.0i	−0.0771824	+	0.0771824i	−0.744644	−	0.667462i	$-0.767381\pi$
$643$	−31911.0	+	31911.0i	−0.0771824	+	0.0771824i	0.667462	+	0.744644i	$0.267381\pi$
$644$			124816.i			0.300953i
$645$	392040.	+	294030.i	0.942347	+	0.706760i
$646$	−303520.			−0.727315
$647$	−280931.	−	280931.i	−0.671106	−	0.671106i	0.286865	−	0.957971i	$-0.407387\pi$
$647$	−280931.	−	280931.i	−0.671106	−	0.671106i	−0.957971	+	0.286865i	$0.907387\pi$
$648$	104976.	−	104976.i	0.250000	−	0.250000i
$649$		−	136880.i		−	0.324975i
$650$	48300.0	+	165600.i	0.114320	+	0.391953i
$651$	105444.			0.248805
$652$	160072.	+	160072.i	0.376548	+	0.376548i
$653$	523989.	−	523989.i	1.22884	−	1.22884i	0.264439	−	0.964402i	$-0.414813\pi$
$653$	523989.	−	523989.i	1.22884	−	1.22884i	0.964402	−	0.264439i	$-0.0851867\pi$
$654$		−	793440.i		−	1.85506i
$655$	95370.0	−	127160.i	0.222295	−	0.296393i
$656$	−107648.			−0.250149
$657$	239031.	+	239031.i	0.553762	+	0.553762i
$658$	147204.	−	147204.i	0.339991	−	0.339991i
$659$		−	404360.i		−	0.931102i	−0.885021	−	0.465551i	$-0.845856\pi$
$659$		−	404360.i		−	0.931102i	0.885021	−	0.465551i	$-0.154144\pi$
$660$	297360.	−	42480.0i	0.682645	−	0.0975207i
$661$	−5278.00			−0.0120800			−0.00603999	−	0.999982i	$-0.501923\pi$
$661$	−5278.00			−0.0120800			−0.00603999	+	0.999982i	$0.501923\pi$
$662$	108076.	+	108076.i	0.246611	+	0.246611i
$663$	−336582.	+	336582.i	−0.765709	+	0.765709i
$664$			199392.i			0.452243i
$665$	−40600.0	−	284200.i	−0.0918085	−	0.642659i
$666$	210924.			0.475530
$667$	182920.	+	182920.i	0.411159	+	0.411159i
$668$	−12392.0	+	12392.0i	−0.0277708	+	0.0277708i
$669$			556038.i			1.24237i
$670$	−60080.0	−	45060.0i	−0.133838	−	0.100379i
$671$	660564.			1.46713
$672$	66816.0	+	66816.0i	0.147959	+	0.147959i
$673$	−332111.	+	332111.i	−0.733252	+	0.733252i	−0.971263	−	0.238011i	$-0.923505\pi$
$673$	−332111.	+	332111.i	−0.733252	+	0.733252i	0.238011	+	0.971263i	$0.423505\pi$
$674$		−	34116.0i		−	0.0750997i
$675$		0			0
$676$	−152312.			−0.333304
$677$	578309.	+	578309.i	1.26178	+	1.26178i	0.950231	+	0.311546i	$0.100847\pi$
$677$	578309.	+	578309.i	1.26178	+	1.26178i	0.311546	+	0.950231i	$0.399153\pi$
$678$	75996.0	−	75996.0i	0.165322	−	0.165322i
$679$		−	424038.i		−	0.919740i
$680$	130080.	−	173440.i	0.281315	−	0.375087i
$681$	−988398.			−2.13127
$682$	47672.0	+	47672.0i	0.102493	+	0.102493i
$683$	−349311.	+	349311.i	−0.748809	+	0.748809i	−0.974255	−	0.225447i	$-0.927616\pi$
$683$	−349311.	+	349311.i	−0.748809	+	0.748809i	0.225447	+	0.974255i	$0.427616\pi$
$684$			181440.i			0.387812i
$685$	−714315.	+	102045.i	−1.52233	+	0.217476i
$686$	−361920.			−0.769067
$687$	−452520.	−	452520.i	−0.958792	−	0.958792i
$688$	−69696.0	+	69696.0i	−0.147242	+	0.147242i
$689$			84318.0i			0.177616i
$690$	−48420.0	−	338940.i	−0.101701	−	0.711909i
$691$	282762.			0.592195			0.296098	−	0.955158i	$-0.404315\pi$
$691$	282762.			0.592195			0.296098	+	0.955158i	$0.404315\pi$
$692$	22312.0	+	22312.0i	0.0465936	+	0.0465936i
$693$	−277182.	+	277182.i	−0.577163	+	0.577163i
$694$			226204.i			0.469658i
$695$	188000.	+	141000.i	0.389214	+	0.291910i
$696$	195840.			0.404281
$697$	−455822.	−	455822.i	−0.938274	−	0.938274i
$698$	−45040.0	+	45040.0i	−0.0924459	+	0.0924459i
$699$			43038.0i			0.0880841i
$700$	179800.	+	98600.0i	0.366939	+	0.201224i
$701$	270242.			0.549942			0.274971	−	0.961453i	$-0.411332\pi$
$701$	270242.			0.549942			0.274971	+	0.961453i	$0.411332\pi$
$702$		0			0
$703$	182280.	−	182280.i	0.368832	−	0.368832i
$704$			60416.0i			0.121901i
$705$	−342630.	+	456840.i	−0.689362	+	0.919149i
$706$	178044.			0.357205
$707$	−25462.0	−	25462.0i	−0.0509394	−	0.0509394i
$708$	−83520.0	+	83520.0i	−0.166619	+	0.166619i
$709$		−	297800.i		−	0.592423i	−0.955122	−	0.296212i	$-0.904277\pi$
$709$		−	297800.i		−	0.592423i	0.955122	−	0.296212i	$-0.0957234\pi$
$710$	450940.	−	64420.0i	0.894545	−	0.127792i
$711$	855360.			1.69204
$712$	−231680.	−	231680.i	−0.457013	−	0.457013i
$713$	54338.0	−	54338.0i	0.106887	−	0.106887i
$714$			565848.i			1.10995i
$715$	−40710.0	−	284970.i	−0.0796323	−	0.557426i
$716$	20800.0			0.0405730
$717$	−159840.	−	159840.i	−0.310919	−	0.310919i
$718$	−19360.0	+	19360.0i	−0.0375540	+	0.0375540i
$719$			913760.i			1.76756i	0.467902	+	0.883780i	$0.345010\pi$
$719$			913760.i			1.76756i	−0.467902	+	0.883780i	$0.654990\pi$
$720$	−103680.	−	77760.0i	−0.200000	−	0.150000i
$721$	604882.			1.16359
$722$	−103842.	−	103842.i	−0.199204	−	0.199204i
$723$	−254142.	+	254142.i	−0.486183	+	0.486183i
$724$		−	355184.i		−	0.677604i
$725$	408000.	−	119000.i	0.776219	−	0.226397i
$726$	25812.0			0.0489721
$727$	−417651.	−	417651.i	−0.790214	−	0.790214i	0.191315	−	0.981529i	$-0.438725\pi$
$727$	−417651.	−	417651.i	−0.790214	−	0.790214i	−0.981529	+	0.191315i	$0.938725\pi$
$728$	64032.0	−	64032.0i	0.120819	−	0.120819i
$729$		−	531441.i		−	1.00000i
$730$	−177060.	+	236080.i	−0.332257	+	0.443010i
$731$	−590238.			−1.10457
$732$	−403056.	−	403056.i	−0.752217	−	0.752217i
$733$	394549.	−	394549.i	0.734333	−	0.734333i	−0.237142	−	0.971475i	$-0.576211\pi$
$733$	394549.	−	394549.i	0.734333	−	0.734333i	0.971475	+	0.237142i	$0.0762107\pi$
$734$			59884.0i			0.111152i
$735$	226485.	−	32355.0i	0.419242	−	0.0598917i
$736$	68864.0			0.127127
$737$	88618.0	+	88618.0i	0.163150	+	0.163150i
$738$	−272484.	+	272484.i	−0.500297	+	0.500297i
$739$			109880.i			0.201201i	0.994927	+	0.100600i	$0.0320764\pi$
$739$			109880.i			0.201201i	−0.994927	+	0.100600i	$0.967924\pi$
$740$	26040.0	+	182280.i	0.0475530	+	0.332871i
$741$	347760.			0.633349
$742$	70876.0	+	70876.0i	0.128733	+	0.128733i
$743$	−466451.	+	466451.i	−0.844945	+	0.844945i	−0.989497	−	0.144552i	$-0.953826\pi$
$743$	−466451.	+	466451.i	−0.844945	+	0.844945i	0.144552	+	0.989497i	$0.453826\pi$
$744$		−	58176.0i		−	0.105099i
$745$	−276000.	−	207000.i	−0.497275	−	0.372956i
$746$	55244.0			0.0992676
$747$	504711.	+	504711.i	0.904485	+	0.904485i
$748$	−255824.	+	255824.i	−0.457234	+	0.457234i
$749$		−	273238.i		−	0.487054i
$750$	−526500.	−	198000.i	−0.936000	−	0.352000i
$751$	1.01092e6			1.79241			0.896206	−	0.443638i	$-0.146313\pi$
$751$	1.01092e6			1.79241			0.896206	+	0.443638i	$0.146313\pi$
$752$	−81216.0	−	81216.0i	−0.143617	−	0.143617i
$753$	1.08902e6	−	1.08902e6i	1.92064	−	1.92064i
$754$		−	187680.i		−	0.330123i
$755$	284970.	−	379960.i	0.499925	−	0.666567i
$756$		0			0
$757$	313269.	+	313269.i	0.546671	+	0.546671i	0.925476	−	0.378806i	$-0.123665\pi$
$757$	313269.	+	313269.i	0.546671	+	0.546671i	−0.378806	+	0.925476i	$0.623665\pi$
$758$	502160.	−	502160.i	0.873984	−	0.873984i
$759$			571356.i			0.991798i
$760$	−156800.	+	22400.0i	−0.271468	+	0.0387812i
$761$	142082.			0.245341			0.122670	−	0.992447i	$-0.460854\pi$
$761$	142082.			0.245341			0.122670	+	0.992447i	$0.460854\pi$
$762$	−212724.	−	212724.i	−0.366359	−	0.366359i
$763$	−639160.	+	639160.i	−1.09789	+	1.09789i
$764$		−	117424.i		−	0.201173i
$765$	−109755.	−	768285.i	−0.187543	−	1.31280i
$766$	344364.			0.586895
$767$	80040.0	+	80040.0i	0.136056	+	0.136056i
$768$	36864.0	−	36864.0i	0.0625000	−	0.0625000i
$769$			13280.0i			0.0224567

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:	\( N \)	\(=\)	\( 10 = 2 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	10.c (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.00000 - 2.00000i) q^{2} +(9.00000 - 9.00000i) q^{3} +8.00000i q^{4} +(-15.0000 + 20.0000i) q^{5} -36.0000 q^{6} +(29.0000 + 29.0000i) q^{7} +(16.0000 - 16.0000i) q^{8} -81.0000i q^{9} +(70.0000 - 10.0000i) q^{10} -118.000 q^{11} +(72.0000 + 72.0000i) q^{12} +(69.0000 - 69.0000i) q^{13} -116.000i q^{14} +(45.0000 + 315.000i) q^{15} -64.0000 q^{16} +(-271.000 - 271.000i) q^{17} +(-162.000 + 162.000i) q^{18} +280.000i q^{19} +(-160.000 - 120.000i) q^{20} +522.000 q^{21} +(236.000 + 236.000i) q^{22} +(269.000 - 269.000i) q^{23} -288.000i q^{24} +(-175.000 - 600.000i) q^{25} -276.000 q^{26} +(-232.000 + 232.000i) q^{28} +680.000i q^{29} +(540.000 - 720.000i) q^{30} +202.000 q^{31} +(128.000 + 128.000i) q^{32} +(-1062.00 + 1062.00i) q^{33} +1084.00i q^{34} +(-1015.00 + 145.000i) q^{35} +648.000 q^{36} +(-651.000 - 651.000i) q^{37} +(560.000 - 560.000i) q^{38} -1242.00i q^{39} +(80.0000 + 560.000i) q^{40} +1682.00 q^{41} +(-1044.00 - 1044.00i) q^{42} +(1089.00 - 1089.00i) q^{43} -944.000i q^{44} +(1620.00 + 1215.00i) q^{45} -1076.00 q^{46} +(1269.00 + 1269.00i) q^{47} +(-576.000 + 576.000i) q^{48} -719.000i q^{49} +(-850.000 + 1550.00i) q^{50} -4878.00 q^{51} +(552.000 + 552.000i) q^{52} +(-611.000 + 611.000i) q^{53} +(1770.00 - 2360.00i) q^{55} +928.000 q^{56} +(2520.00 + 2520.00i) q^{57} +(1360.00 - 1360.00i) q^{58} +1160.00i q^{59} +(-2520.00 + 360.000i) q^{60} -5598.00 q^{61} +(-404.000 - 404.000i) q^{62} +(2349.00 - 2349.00i) q^{63} -512.000i q^{64} +(345.000 + 2415.00i) q^{65} +4248.00 q^{66} +(-751.000 - 751.000i) q^{67} +(2168.00 - 2168.00i) q^{68} -4842.00i q^{69} +(2320.00 + 1740.00i) q^{70} +6442.00 q^{71} +(-1296.00 - 1296.00i) q^{72} +(-2951.00 + 2951.00i) q^{73} +2604.00i q^{74} +(-6975.00 - 3825.00i) q^{75} -2240.00 q^{76} +(-3422.00 - 3422.00i) q^{77} +(-2484.00 + 2484.00i) q^{78} +10560.0i q^{79} +(960.000 - 1280.00i) q^{80} +6561.00 q^{81} +(-3364.00 - 3364.00i) q^{82} +(-6231.00 + 6231.00i) q^{83} +4176.00i q^{84} +(9485.00 - 1355.00i) q^{85} -4356.00 q^{86} +(6120.00 + 6120.00i) q^{87} +(-1888.00 + 1888.00i) q^{88} -14480.0i q^{89} +(-810.000 - 5670.00i) q^{90} +4002.00 q^{91} +(2152.00 + 2152.00i) q^{92} +(1818.00 - 1818.00i) q^{93} -5076.00i q^{94} +(-5600.00 - 4200.00i) q^{95} +2304.00 q^{96} +(-7311.00 - 7311.00i) q^{97} +(-1438.00 + 1438.00i) q^{98} +9558.00i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 4 q^{2} + 18 q^{3} - 30 q^{5} - 72 q^{6} + 58 q^{7} + 32 q^{8} + 140 q^{10} - 236 q^{11} + 144 q^{12} + 138 q^{13} + 90 q^{15} - 128 q^{16} - 542 q^{17} - 324 q^{18} - 320 q^{20} + 1044 q^{21} + 472 q^{22}+ \cdots - 2876 q^{98}+O(q^{100}) \) 2 * q - 4 * q^2 + 18 * q^3 - 30 * q^5 - 72 * q^6 + 58 * q^7 + 32 * q^8 + 140 * q^10 - 236 * q^11 + 144 * q^12 + 138 * q^13 + 90 * q^15 - 128 * q^16 - 542 * q^17 - 324 * q^18 - 320 * q^20 + 1044 * q^21 + 472 * q^22 + 538 * q^23 - 350 * q^25 - 552 * q^26 - 464 * q^28 + 1080 * q^30 + 404 * q^31 + 256 * q^32 - 2124 * q^33 - 2030 * q^35 + 1296 * q^36 - 1302 * q^37 + 1120 * q^38 + 160 * q^40 + 3364 * q^41 - 2088 * q^42 + 2178 * q^43 + 3240 * q^45 - 2152 * q^46 + 2538 * q^47 - 1152 * q^48 - 1700 * q^50 - 9756 * q^51 + 1104 * q^52 - 1222 * q^53 + 3540 * q^55 + 1856 * q^56 + 5040 * q^57 + 2720 * q^58 - 5040 * q^60 - 11196 * q^61 - 808 * q^62 + 4698 * q^63 + 690 * q^65 + 8496 * q^66 - 1502 * q^67 + 4336 * q^68 + 4640 * q^70 + 12884 * q^71 - 2592 * q^72 - 5902 * q^73 - 13950 * q^75 - 4480 * q^76 - 6844 * q^77 - 4968 * q^78 + 1920 * q^80 + 13122 * q^81 - 6728 * q^82 - 12462 * q^83 + 18970 * q^85 - 8712 * q^86 + 12240 * q^87 - 3776 * q^88 - 1620 * q^90 + 8004 * q^91 + 4304 * q^92 + 3636 * q^93 - 11200 * q^95 + 4608 * q^96 - 14622 * q^97 - 2876 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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