LMFDB - Embedded newform 75.5.c.c.26.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [75,5,Mod(26,75)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(75, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("75.26");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 75 = 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	75.c (of order $2$, degree $1$, 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:	$7.75274723129$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{-14}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} + 14 $ x^2 + 14
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			26.2
Root			$3.74166i$ of defining polynomial
Character	$\chi$	$=$	75.26
Dual form			75.5.c.c.26.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+3.74166i q^{2} +(-5.00000 + 7.48331i) q^{3} +2.00000 q^{4} +(-28.0000 - 18.7083i) q^{6} -75.0000 q^{7} +67.3498i q^{8} +(-31.0000 - 74.8331i) q^{9} +O(q^{10})$	\(q+3.74166i q^{2} +(-5.00000 + 7.48331i) q^{3} +2.00000 q^{4} +(-28.0000 - 18.7083i) q^{6} -75.0000 q^{7} +67.3498i q^{8} +(-31.0000 - 74.8331i) q^{9} +37.4166i q^{11} +(-10.0000 + 14.9666i) q^{12} +55.0000 q^{13} -280.624i q^{14} -220.000 q^{16} -501.382i q^{17} +(280.000 - 115.991i) q^{18} -347.000 q^{19} +(375.000 - 561.249i) q^{21} -140.000 q^{22} +651.048i q^{23} +(-504.000 - 336.749i) q^{24} +205.791i q^{26} +(715.000 + 142.183i) q^{27} -150.000 q^{28} +860.581i q^{29} -3.00000 q^{31} +254.433i q^{32} +(-280.000 - 187.083i) q^{33} +1876.00 q^{34} +(-62.0000 - 149.666i) q^{36} -2230.00 q^{37} -1298.36i q^{38} +(-275.000 + 411.582i) q^{39} +2207.58i q^{41} +(2100.00 + 1403.12i) q^{42} -1475.00 q^{43} +74.8331i q^{44} -2436.00 q^{46} +1855.86i q^{47} +(1100.00 - 1646.33i) q^{48} +3224.00 q^{49} +(3752.00 + 2506.91i) q^{51} +110.000 q^{52} -546.282i q^{53} +(-532.000 + 2675.29i) q^{54} -5051.24i q^{56} +(1735.00 - 2596.71i) q^{57} -3220.00 q^{58} +2843.66i q^{59} +367.000 q^{61} -11.2250i q^{62} +(2325.00 + 5612.49i) q^{63} -4472.00 q^{64} +(700.000 - 1047.66i) q^{66} -2235.00 q^{67} -1002.76i q^{68} +(-4872.00 - 3255.24i) q^{69} -486.415i q^{71} +(5040.00 - 2087.84i) q^{72} +6970.00 q^{73} -8343.90i q^{74} -694.000 q^{76} -2806.24i q^{77} +(-1540.00 - 1028.96i) q^{78} +4518.00 q^{79} +(-4639.00 + 4639.66i) q^{81} -8260.00 q^{82} +314.299i q^{83} +(750.000 - 1122.50i) q^{84} -5518.94i q^{86} +(-6440.00 - 4302.91i) q^{87} -2520.00 q^{88} -8081.98i q^{89} -4125.00 q^{91} +1302.10i q^{92} +(15.0000 - 22.4499i) q^{93} -6944.00 q^{94} +(-1904.00 - 1272.16i) q^{96} +4535.00 q^{97} +12063.1i q^{98} +(2800.00 - 1159.91i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 10 q^{3} + 4 q^{4} - 56 q^{6} - 150 q^{7} - 62 q^{9}+O(q^{10}) $ 2 * q - 10 * q^3 + 4 * q^4 - 56 * q^6 - 150 * q^7 - 62 * q^9	$ 2 q - 10 q^{3} + 4 q^{4} - 56 q^{6} - 150 q^{7} - 62 q^{9} - 20 q^{12} + 110 q^{13} - 440 q^{16} + 560 q^{18} - 694 q^{19} + 750 q^{21} - 280 q^{22} - 1008 q^{24} + 1430 q^{27} - 300 q^{28} - 6 q^{31} - 560 q^{33} + 3752 q^{34} - 124 q^{36} - 4460 q^{37} - 550 q^{39} + 4200 q^{42} - 2950 q^{43} - 4872 q^{46} + 2200 q^{48} + 6448 q^{49} + 7504 q^{51} + 220 q^{52} - 1064 q^{54} + 3470 q^{57} - 6440 q^{58} + 734 q^{61} + 4650 q^{63} - 8944 q^{64} + 1400 q^{66} - 4470 q^{67} - 9744 q^{69} + 10080 q^{72} + 13940 q^{73} - 1388 q^{76} - 3080 q^{78} + 9036 q^{79} - 9278 q^{81} - 16520 q^{82} + 1500 q^{84} - 12880 q^{87} - 5040 q^{88} - 8250 q^{91} + 30 q^{93} - 13888 q^{94} - 3808 q^{96} + 9070 q^{97} + 5600 q^{99}+O(q^{100}) $ 2 * q - 10 * q^3 + 4 * q^4 - 56 * q^6 - 150 * q^7 - 62 * q^9 - 20 * q^12 + 110 * q^13 - 440 * q^16 + 560 * q^18 - 694 * q^19 + 750 * q^21 - 280 * q^22 - 1008 * q^24 + 1430 * q^27 - 300 * q^28 - 6 * q^31 - 560 * q^33 + 3752 * q^34 - 124 * q^36 - 4460 * q^37 - 550 * q^39 + 4200 * q^42 - 2950 * q^43 - 4872 * q^46 + 2200 * q^48 + 6448 * q^49 + 7504 * q^51 + 220 * q^52 - 1064 * q^54 + 3470 * q^57 - 6440 * q^58 + 734 * q^61 + 4650 * q^63 - 8944 * q^64 + 1400 * q^66 - 4470 * q^67 - 9744 * q^69 + 10080 * q^72 + 13940 * q^73 - 1388 * q^76 - 3080 * q^78 + 9036 * q^79 - 9278 * q^81 - 16520 * q^82 + 1500 * q^84 - 12880 * q^87 - 5040 * q^88 - 8250 * q^91 + 30 * q^93 - 13888 * q^94 - 3808 * q^96 + 9070 * q^97 + 5600 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/75\mathbb{Z}\right)^\times$.

$n$	$26$	$52$
$\chi(n)$	$-1$	$1$

Coefficient data

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

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

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

$2$			3.74166i			0.935414i	0.883883	+	0.467707i	$0.154920\pi$
$2$			3.74166i			0.935414i	−0.883883	+	0.467707i	$0.845080\pi$
$3$	−5.00000	+	7.48331i	−0.555556	+	0.831479i
$3$	−5.00000	+	7.48331i	−0.555556	+	0.831479i
$4$	2.00000			0.125000
$5$		0			0
$5$		0			0
$6$	−28.0000	−	18.7083i	−0.777778	−	0.519675i
$7$	−75.0000			−1.53061			−0.765306	−	0.643666i	$-0.777412\pi$
$7$	−75.0000			−1.53061			−0.765306	+	0.643666i	$0.777412\pi$
$8$			67.3498i			1.05234i
$9$	−31.0000	−	74.8331i	−0.382716	−	0.923866i
$10$		0			0
$11$			37.4166i			0.309228i	0.987975	+	0.154614i	$0.0494134\pi$
$11$			37.4166i			0.309228i	−0.987975	+	0.154614i	$0.950587\pi$
$12$	−10.0000	+	14.9666i	−0.0694444	+	0.103935i
$13$	55.0000			0.325444			0.162722	−	0.986672i	$-0.447973\pi$
$13$	55.0000			0.325444			0.162722	+	0.986672i	$0.447973\pi$
$14$		−	280.624i		−	1.43176i
$15$		0			0
$16$	−220.000			−0.859375
$17$		−	501.382i		−	1.73489i	−0.497536	−	0.867443i	$-0.665762\pi$
$17$		−	501.382i		−	1.73489i	0.497536	−	0.867443i	$-0.334238\pi$
$18$	280.000	−	115.991i	0.864198	−	0.357998i
$19$	−347.000			−0.961219			−0.480609	−	0.876935i	$-0.659585\pi$
$19$	−347.000			−0.961219			−0.480609	+	0.876935i	$0.659585\pi$
$20$		0			0
$21$	375.000	−	561.249i	0.850340	−	1.27267i
$22$	−140.000			−0.289256
$23$			651.048i			1.23072i	0.788248	+	0.615358i	$0.210988\pi$
$23$			651.048i			1.23072i	−0.788248	+	0.615358i	$0.789012\pi$
$24$	−504.000	−	336.749i	−0.875000	−	0.584634i
$25$		0			0
$26$			205.791i			0.304425i
$27$	715.000	+	142.183i	0.980796	+	0.195038i
$28$	−150.000			−0.191327
$29$			860.581i			1.02328i	0.859199	+	0.511642i	$0.170962\pi$
$29$			860.581i			1.02328i	−0.859199	+	0.511642i	$0.829038\pi$
$30$		0			0
$31$	−3.00000			−0.00312175			−0.00156087	−	0.999999i	$-0.500497\pi$
$31$	−3.00000			−0.00312175			−0.00156087	+	0.999999i	$0.500497\pi$
$32$			254.433i			0.248469i
$33$	−280.000	−	187.083i	−0.257117	−	0.171793i
$34$	1876.00			1.62284
$35$		0			0
$36$	−62.0000	−	149.666i	−0.0478395	−	0.115483i
$37$	−2230.00			−1.62893			−0.814463	−	0.580215i	$-0.802968\pi$
$37$	−2230.00			−1.62893			−0.814463	+	0.580215i	$0.802968\pi$
$38$		−	1298.36i		−	0.899138i
$39$	−275.000	+	411.582i	−0.180802	+	0.270600i
$40$		0			0
$41$			2207.58i			1.31325i	0.754216	+	0.656626i	$0.228017\pi$
$41$			2207.58i			1.31325i	−0.754216	+	0.656626i	$0.771983\pi$
$42$	2100.00	+	1403.12i	1.19048	+	0.795420i
$43$	−1475.00			−0.797729			−0.398864	−	0.917010i	$-0.630596\pi$
$43$	−1475.00			−0.797729			−0.398864	+	0.917010i	$0.630596\pi$
$44$			74.8331i			0.0386535i
$45$		0			0
$46$	−2436.00			−1.15123
$47$			1855.86i			0.840137i	0.907492	+	0.420068i	$0.137994\pi$
$47$			1855.86i			0.840137i	−0.907492	+	0.420068i	$0.862006\pi$
$48$	1100.00	−	1646.33i	0.477431	−	0.714553i
$49$	3224.00			1.34277
$50$		0			0
$51$	3752.00	+	2506.91i	1.44252	+	0.963826i
$52$	110.000			0.0406805
$53$		−	546.282i		−	0.194476i	−0.995261	−	0.0972378i	$-0.968999\pi$
$53$		−	546.282i		−	0.194476i	0.995261	−	0.0972378i	$-0.0310007\pi$
$54$	−532.000	+	2675.29i	−0.182442	+	0.917450i
$55$		0			0
$56$		−	5051.24i		−	1.61073i
$57$	1735.00	−	2596.71i	0.534010	−	0.799234i
$58$	−3220.00			−0.957194
$59$			2843.66i			0.816909i	0.912779	+	0.408454i	$0.133932\pi$
$59$			2843.66i			0.816909i	−0.912779	+	0.408454i	$0.866068\pi$
$60$		0			0
$61$	367.000			0.0986294			0.0493147	−	0.998783i	$-0.484296\pi$
$61$	367.000			0.0986294			0.0493147	+	0.998783i	$0.484296\pi$
$62$		−	11.2250i		−	0.00292013i
$63$	2325.00	+	5612.49i	0.585790	+	1.41408i
$64$	−4472.00			−1.09180
$65$		0			0
$66$	700.000	−	1047.66i	0.160698	−	0.240511i
$67$	−2235.00			−0.497884			−0.248942	−	0.968518i	$-0.580083\pi$
$67$	−2235.00			−0.497884			−0.248942	+	0.968518i	$0.580083\pi$
$68$		−	1002.76i		−	0.216861i
$69$	−4872.00	−	3255.24i	−1.02331	−	0.683731i
$70$		0			0
$71$		−	486.415i		−	0.0964919i	−0.998835	−	0.0482459i	$-0.984637\pi$
$71$		−	486.415i		−	0.0964919i	0.998835	−	0.0482459i	$-0.0153631\pi$
$72$	5040.00	−	2087.84i	0.972222	−	0.402748i
$73$	6970.00			1.30794			0.653969	−	0.756521i	$-0.273103\pi$
$73$	6970.00			1.30794			0.653969	+	0.756521i	$0.273103\pi$
$74$		−	8343.90i		−	1.52372i
$75$		0			0
$76$	−694.000			−0.120152
$77$		−	2806.24i		−	0.473308i
$78$	−1540.00	−	1028.96i	−0.253123	−	0.169125i
$79$	4518.00			0.723922			0.361961	−	0.932193i	$-0.382107\pi$
$79$	4518.00			0.723922			0.361961	+	0.932193i	$0.382107\pi$
$80$		0			0
$81$	−4639.00	+	4639.66i	−0.707057	+	0.707157i
$82$	−8260.00			−1.22844
$83$			314.299i			0.0456233i	0.999740	+	0.0228117i	$0.00726181\pi$
$83$			314.299i			0.0456233i	−0.999740	+	0.0228117i	$0.992738\pi$
$84$	750.000	−	1122.50i	0.106293	−	0.159084i
$85$		0			0
$86$		−	5518.94i		−	0.746207i
$87$	−6440.00	−	4302.91i	−0.850839	−	0.568491i
$88$	−2520.00			−0.325413
$89$		−	8081.98i		−	1.02032i	−0.860079	−	0.510162i	$-0.829586\pi$
$89$		−	8081.98i		−	1.02032i	0.860079	−	0.510162i	$-0.170414\pi$
$90$		0			0
$91$	−4125.00			−0.498128
$92$			1302.10i			0.153839i
$93$	15.0000	−	22.4499i	0.00173430	−	0.00259567i
$94$	−6944.00			−0.785876
$95$		0			0
$96$	−1904.00	−	1272.16i	−0.206597	−	0.138039i
$97$	4535.00			0.481985			0.240993	−	0.970527i	$-0.422527\pi$
$97$	4535.00			0.481985			0.240993	+	0.970527i	$0.422527\pi$
$98$			12063.1i			1.25605i
$99$	2800.00	−	1159.91i	0.285685	−	0.118346i
$100$		0			0
$101$			10663.7i			1.04536i	0.852529	+	0.522680i	$0.175068\pi$
$101$			10663.7i			1.04536i	−0.852529	+	0.522680i	$0.824932\pi$
$102$	−9380.00	+	14038.7i	−0.901576	+	1.34936i
$103$	2390.00			0.225280			0.112640	−	0.993636i	$-0.464069\pi$
$103$	2390.00			0.225280			0.112640	+	0.993636i	$0.464069\pi$
$104$			3704.24i			0.342478i
$105$		0			0
$106$	2044.00			0.181915
$107$		−	3345.04i		−	0.292169i	−0.989272	−	0.146084i	$-0.953333\pi$
$107$		−	3345.04i		−	0.292169i	0.989272	−	0.146084i	$-0.0466671\pi$
$108$	1430.00	+	284.366i	0.122599	+	0.0243798i
$109$	−2137.00			−0.179867			−0.0899335	−	0.995948i	$-0.528665\pi$
$109$	−2137.00			−0.179867			−0.0899335	+	0.995948i	$0.528665\pi$
$110$		0			0
$111$	11150.0	−	16687.8i	0.904959	−	1.35442i
$112$	16500.0			1.31537
$113$		−	7618.01i		−	0.596602i	−0.954472	−	0.298301i	$-0.903580\pi$
$113$		−	7618.01i		−	0.596602i	0.954472	−	0.298301i	$-0.0964200\pi$
$114$	9716.00	+	6491.78i	0.747615	+	0.499521i
$115$		0			0
$116$			1721.16i			0.127910i
$117$	−1705.00	−	4115.82i	−0.124553	−	0.300666i
$118$	−10640.0			−0.764148
$119$			37603.7i			2.65544i
$120$		0			0
$121$	13241.0			0.904378
$122$			1373.19i			0.0922594i
$123$	−16520.0	−	11037.9i	−1.09194	−	0.729585i
$124$	−6.00000			−0.000390219
$125$		0			0
$126$	−21000.0	+	8699.35i	−1.32275	+	0.547956i
$127$	26830.0			1.66346			0.831732	−	0.555178i	$-0.187350\pi$
$127$	26830.0			1.66346			0.831732	+	0.555178i	$0.187350\pi$
$128$		−	12661.8i		−	0.772813i
$129$	7375.00	−	11037.9i	0.443183	−	0.663295i
$130$		0			0
$131$			11337.2i			0.660639i	0.943869	+	0.330319i	$0.107156\pi$
$131$			11337.2i			0.660639i	−0.943869	+	0.330319i	$0.892844\pi$
$132$	−560.000	−	374.166i	−0.0321396	−	0.0214742i
$133$	26025.0			1.47125
$134$		−	8362.60i		−	0.465728i
$135$		0			0
$136$	33768.0			1.82569
$137$			6869.68i			0.366012i	0.983112	+	0.183006i	$0.0585828\pi$
$137$			6869.68i			0.366012i	−0.983112	+	0.183006i	$0.941417\pi$
$138$	12180.0	−	18229.4i	0.639572	−	0.957223i
$139$	−4642.00			−0.240257			−0.120128	−	0.992758i	$-0.538331\pi$
$139$	−4642.00			−0.240257			−0.120128	+	0.992758i	$0.538331\pi$
$140$		0			0
$141$	−13888.0	−	9279.31i	−0.698556	−	0.466743i
$142$	1820.00			0.0902599
$143$			2057.91i			0.100636i
$144$	6820.00	+	16463.3i	0.328897	+	0.793947i
$145$		0			0
$146$			26079.4i			1.22346i
$147$	−16120.0	+	24126.2i	−0.745985	+	1.11649i
$148$	−4460.00			−0.203616
$149$		−	11599.1i		−	0.522460i	−0.965277	−	0.261230i	$-0.915872\pi$
$149$		−	11599.1i		−	0.522460i	0.965277	−	0.261230i	$-0.0841281\pi$
$150$		0			0
$151$	−23123.0			−1.01412			−0.507061	−	0.861910i	$-0.669268\pi$
$151$	−23123.0			−1.01412			−0.507061	+	0.861910i	$0.669268\pi$
$152$		−	23370.4i		−	1.01153i
$153$	−37520.0	+	15542.8i	−1.60280	+	0.663969i
$154$	10500.0			0.442739
$155$		0			0
$156$	−550.000	+	823.165i	−0.0226003	+	0.0338250i
$157$	−13225.0			−0.536533			−0.268266	−	0.963345i	$-0.586451\pi$
$157$	−13225.0			−0.536533			−0.268266	+	0.963345i	$0.586451\pi$
$158$			16904.8i			0.677167i
$159$	4088.00	+	2731.41i	0.161702	+	0.108042i
$160$		0			0
$161$		−	48828.6i		−	1.88375i
$162$	−17360.0	−	17357.5i	−0.661485	−	0.661391i
$163$	−24595.0			−0.925703			−0.462851	−	0.886436i	$-0.653174\pi$
$163$	−24595.0			−0.925703			−0.462851	+	0.886436i	$0.653174\pi$
$164$			4415.16i			0.164157i
$165$		0			0
$166$	−1176.00			−0.0426767
$167$			41779.3i			1.49806i	0.662537	+	0.749029i	$0.269480\pi$
$167$			41779.3i			1.49806i	−0.662537	+	0.749029i	$0.730520\pi$
$168$	37800.0	+	25256.2i	1.33929	+	0.894848i
$169$	−25536.0			−0.894086
$170$		0			0
$171$	10757.0	+	25967.1i	0.367874	+	0.888037i
$172$	−2950.00			−0.0997161
$173$			10753.5i			0.359301i	0.983730	+	0.179651i	$0.0574967\pi$
$173$			10753.5i			0.359301i	−0.983730	+	0.179651i	$0.942503\pi$
$174$	16100.0	−	24096.3i	0.531774	−	0.795887i
$175$		0			0
$176$		−	8231.65i		−	0.265743i
$177$	−21280.0	−	14218.3i	−0.679243	−	0.453838i
$178$	30240.0			0.954425
$179$		−	58444.7i		−	1.82406i	−0.410124	−	0.912030i	$-0.634515\pi$
$179$		−	58444.7i		−	1.82406i	0.410124	−	0.912030i	$-0.365485\pi$
$180$		0			0
$181$	−26353.0			−0.804402			−0.402201	−	0.915551i	$-0.631755\pi$
$181$	−26353.0			−0.804402			−0.402201	+	0.915551i	$0.631755\pi$
$182$		−	15434.3i		−	0.465956i
$183$	−1835.00	+	2746.38i	−0.0547941	+	0.0820083i
$184$	−43848.0			−1.29513
$185$		0			0
$186$	84.0000	+	56.1249i	0.00242803	+	0.00162229i
$187$	18760.0			0.536475
$188$			3711.72i			0.105017i
$189$	−53625.0	−	10663.7i	−1.50122	−	0.298528i
$190$		0			0
$191$		−	22487.4i		−	0.616413i	−0.951319	−	0.308206i	$-0.900271\pi$
$191$		−	22487.4i		−	0.616413i	0.951319	−	0.308206i	$-0.0997288\pi$
$192$	22360.0	−	33465.4i	0.606554	−	0.907807i
$193$	14375.0			0.385916			0.192958	−	0.981207i	$-0.438192\pi$
$193$	14375.0			0.385916			0.192958	+	0.981207i	$0.438192\pi$
$194$			16968.4i			0.450856i
$195$		0			0
$196$	6448.00			0.167847
$197$		−	35560.7i		−	0.916301i	−0.888875	−	0.458150i	$-0.848512\pi$
$197$		−	35560.7i		−	0.916301i	0.888875	−	0.458150i	$-0.151488\pi$
$198$	4340.00	+	10476.6i	0.110703	+	0.267234i
$199$	43573.0			1.10030			0.550150	−	0.835066i	$-0.314570\pi$
$199$	43573.0			1.10030			0.550150	+	0.835066i	$0.314570\pi$
$200$		0			0
$201$	11175.0	−	16725.2i	0.276602	−	0.413980i
$202$	−39900.0			−0.977845
$203$		−	64543.6i		−	1.56625i
$204$	7504.00	+	5013.82i	0.180315	+	0.120478i
$205$		0			0
$206$			8942.56i			0.210731i
$207$	48720.0	−	20182.5i	1.13702	−	0.471014i
$208$	−12100.0			−0.279678
$209$		−	12983.6i		−	0.297236i
$210$		0			0
$211$	15917.0			0.357517			0.178758	−	0.983893i	$-0.442792\pi$
$211$	15917.0			0.357517			0.178758	+	0.983893i	$0.442792\pi$
$212$		−	1092.56i		−	0.0243095i
$213$	3640.00	+	2432.08i	0.0802310	+	0.0536066i
$214$	12516.0			0.273299
$215$		0			0
$216$	−9576.00	+	48155.1i	−0.205247	+	1.03213i
$217$	225.000			0.00477819
$218$		−	7995.92i		−	0.168250i
$219$	−34850.0	+	52158.7i	−0.726632	+	1.08752i
$220$		0			0
$221$		−	27576.0i		−	0.564608i
$222$	62440.0	+	41719.5i	1.26694	+	0.846512i
$223$	40445.0			0.813308			0.406654	−	0.913582i	$-0.366695\pi$
$223$	40445.0			0.813308			0.406654	+	0.913582i	$0.366695\pi$
$224$		−	19082.5i		−	0.380310i
$225$		0			0
$226$	28504.0			0.558070
$227$			46119.7i			0.895024i	0.894278	+	0.447512i	$0.147690\pi$
$227$			46119.7i			0.895024i	−0.894278	+	0.447512i	$0.852310\pi$
$228$	3470.00	−	5193.42i	0.0667513	−	0.0999042i
$229$	36543.0			0.696840			0.348420	−	0.937338i	$-0.386718\pi$
$229$	36543.0			0.696840			0.348420	+	0.937338i	$0.386718\pi$
$230$		0			0
$231$	21000.0	+	14031.2i	0.393546	+	0.262949i
$232$	−57960.0			−1.07684
$233$			83940.3i			1.54618i	0.634299	+	0.773088i	$0.281289\pi$
$233$			83940.3i			1.54618i	−0.634299	+	0.773088i	$0.718711\pi$
$234$	15400.0	−	6379.53i	0.281248	−	0.116508i
$235$		0			0
$236$			5687.32i			0.102114i
$237$	−22590.0	+	33809.6i	−0.402179	+	0.601927i
$238$	−140700.			−2.48393
$239$			91633.2i			1.60419i	0.597193	+	0.802097i	$0.296282\pi$
$239$			91633.2i			1.60419i	−0.597193	+	0.802097i	$0.703718\pi$
$240$		0			0
$241$	−102713.			−1.76844			−0.884222	−	0.467067i	$-0.845311\pi$
$241$	−102713.			−1.76844			−0.884222	+	0.467067i	$0.845311\pi$
$242$			49543.3i			0.845968i
$243$	−11525.0	−	57913.4i	−0.195177	−	0.980768i
$244$	734.000			0.0123287
$245$		0			0
$246$	41300.0	−	61812.2i	0.682464	−	1.02142i
$247$	−19085.0			−0.312823
$248$		−	202.049i		−	0.00328514i
$249$	−2352.00	−	1571.50i	−0.0379349	−	0.0253463i
$250$		0			0
$251$			72962.3i			1.15811i	0.815287	+	0.579057i	$0.196579\pi$
$251$			72962.3i			1.15811i	−0.815287	+	0.579057i	$0.803421\pi$
$252$	4650.00	+	11225.0i	0.0732237	+	0.176760i
$253$	−24360.0			−0.380571
$254$			100389.i			1.55603i
$255$		0			0
$256$	−24176.0			−0.368896
$257$		−	55541.2i		−	0.840908i	−0.907314	−	0.420454i	$-0.861871\pi$
$257$		−	55541.2i		−	0.840908i	0.907314	−	0.420454i	$-0.138129\pi$
$258$	41300.0	+	27594.7i	0.620456	+	0.414559i
$259$	167250.			2.49325
$260$		0			0
$261$	64400.0	−	26678.0i	0.945377	−	0.391627i
$262$	−42420.0			−0.617971
$263$		−	106585.i		−	1.54093i	−0.637480	−	0.770467i	$-0.720023\pi$
$263$		−	106585.i		−	1.54093i	0.637480	−	0.770467i	$-0.279977\pi$
$264$	12600.0	−	18858.0i	0.180785	−	0.270574i
$265$		0			0
$266$			97376.6i			1.37623i
$267$	60480.0	+	40409.9i	0.848378	+	0.566846i
$268$	−4470.00			−0.0622355
$269$		−	88415.4i		−	1.22186i	−0.791683	−	0.610932i	$-0.790795\pi$
$269$		−	88415.4i		−	1.22186i	0.791683	−	0.610932i	$-0.209205\pi$
$270$		0			0
$271$	−13418.0			−0.182704			−0.0913522	−	0.995819i	$-0.529119\pi$
$271$	−13418.0			−0.182704			−0.0913522	+	0.995819i	$0.529119\pi$
$272$			110304.i			1.49092i
$273$	20625.0	−	30868.7i	0.276738	−	0.414183i
$274$	−25704.0			−0.342373
$275$		0			0
$276$	−9744.00	−	6510.48i	−0.127914	−	0.0854663i
$277$	50055.0			0.652361			0.326180	−	0.945308i	$-0.394238\pi$
$277$	50055.0			0.652361			0.326180	+	0.945308i	$0.394238\pi$
$278$		−	17368.8i		−	0.224740i
$279$	93.0000	+	224.499i	0.00119474	+	0.00288408i
$280$		0			0
$281$			42767.1i			0.541624i	0.962632	+	0.270812i	$0.0872921\pi$
$281$			42767.1i			0.541624i	−0.962632	+	0.270812i	$0.912708\pi$
$282$	34720.0	−	51964.1i	0.436598	−	0.653440i
$283$	33885.0			0.423092			0.211546	−	0.977368i	$-0.432150\pi$
$283$	33885.0			0.423092			0.211546	+	0.977368i	$0.432150\pi$
$284$		−	972.831i		−	0.0120615i
$285$		0			0
$286$	−7700.00			−0.0941366
$287$		−	165568.i		−	2.01008i
$288$	19040.0	−	7887.41i	0.229552	−	0.0950932i
$289$	−167863.			−2.00983
$290$		0			0
$291$	−22675.0	+	33936.8i	−0.267770	+	0.400761i
$292$	13940.0			0.163492
$293$			132993.i			1.54916i	0.632479	+	0.774578i	$0.282038\pi$
$293$			132993.i			1.54916i	−0.632479	+	0.774578i	$0.717962\pi$
$294$	−90272.0	−	60315.5i	−1.04438	−	0.697806i
$295$		0			0
$296$		−	150190.i		−	1.71419i
$297$	−5320.00	+	26752.9i	−0.0603113	+	0.303289i
$298$	43400.0			0.488717
$299$			35807.7i			0.400529i
$300$		0			0
$301$	110625.			1.22101
$302$		−	86518.3i		−	0.948624i
$303$	−79800.0	−	53318.6i	−0.869196	−	0.580756i
$304$	76340.0			0.826047
$305$		0			0
$306$	−58156.0	−	140387.i	−0.621086	−	1.49928i
$307$	−135875.			−1.44166			−0.720830	−	0.693112i	$-0.756239\pi$
$307$	−135875.			−1.44166			−0.720830	+	0.693112i	$0.756239\pi$
$308$		−	5612.49i		−	0.0591635i
$309$	−11950.0	+	17885.1i	−0.125156	+	0.187316i
$310$		0			0
$311$			28286.9i			0.292459i	0.989251	+	0.146230i	$0.0467138\pi$
$311$			28286.9i			0.292459i	−0.989251	+	0.146230i	$0.953286\pi$
$312$	−27720.0	−	18521.2i	−0.284763	−	0.190265i
$313$	170255.			1.73785			0.868923	−	0.494948i	$-0.164813\pi$
$313$	170255.			1.73785			0.868923	+	0.494948i	$0.164813\pi$
$314$		−	49483.4i		−	0.501881i
$315$		0			0
$316$	9036.00			0.0904903
$317$		−	10790.9i		−	0.107384i	−0.998558	−	0.0536921i	$-0.982901\pi$
$317$		−	10790.9i		−	0.107384i	0.998558	−	0.0536921i	$-0.0170990\pi$
$318$	−10220.0	+	15295.9i	−0.101064	+	0.151259i
$319$	−32200.0			−0.316428
$320$		0			0
$321$	25032.0	+	16725.2i	0.242932	+	0.162316i
$322$	182700.			1.76208
$323$			173980.i			1.66761i
$324$	−9278.00	+	9279.31i	−0.0883821	+	0.0883946i
$325$		0			0
$326$		−	92026.1i		−	0.865916i
$327$	10685.0	−	15991.8i	0.0999261	−	0.149556i
$328$	−148680.			−1.38199
$329$		−	139190.i		−	1.28592i
$330$		0			0
$331$	−24378.0			−0.222506			−0.111253	−	0.993792i	$-0.535486\pi$
$331$	−24378.0			−0.222506			−0.111253	+	0.993792i	$0.535486\pi$
$332$			628.598i			0.00570292i
$333$	69130.0	+	166878.i	0.623416	+	1.50491i
$334$	−156324.			−1.40131
$335$		0			0
$336$	−82500.0	+	123475.i	−0.730761	+	1.09370i
$337$	−81905.0			−0.721192			−0.360596	−	0.932722i	$-0.617427\pi$
$337$	−81905.0			−0.721192			−0.360596	+	0.932722i	$0.617427\pi$
$338$		−	95547.0i		−	0.836341i
$339$	57008.0	+	38090.1i	0.496063	+	0.331446i
$340$		0			0
$341$		−	112.250i		−	0.000965332i
$342$	−97160.0	+	40249.0i	−0.830683	+	0.344115i
$343$	−61725.0			−0.524654
$344$		−	99341.0i		−	0.839483i
$345$		0			0
$346$	−40236.0			−0.336095
$347$			210640.i			1.74937i	0.484688	+	0.874687i	$0.338933\pi$
$347$			210640.i			1.74937i	−0.484688	+	0.874687i	$0.661067\pi$
$348$	−12880.0	−	8605.81i	−0.106355	−	0.0710613i
$349$	9298.00			0.0763376			0.0381688	−	0.999271i	$-0.487848\pi$
$349$	9298.00			0.0763376			0.0381688	+	0.999271i	$0.487848\pi$
$350$		0			0
$351$	39325.0	+	7820.06i	0.319194	+	0.0634740i
$352$	−9520.00			−0.0768337
$353$		−	55922.8i		−	0.448786i	−0.974499	−	0.224393i	$-0.927960\pi$
$353$		−	55922.8i		−	0.448786i	0.974499	−	0.224393i	$-0.0720400\pi$
$354$	53200.0	−	79622.5i	0.424527	−	0.635374i
$355$		0			0
$356$		−	16164.0i		−	0.127540i
$357$	−281400.	−	188018.i	−2.20794	−	1.47524i
$358$	218680.			1.70625
$359$			70380.6i			0.546090i	0.962001	+	0.273045i	$0.0880307\pi$
$359$			70380.6i			0.546090i	−0.962001	+	0.273045i	$0.911969\pi$
$360$		0			0
$361$	−9912.00			−0.0760583
$362$		−	98603.9i		−	0.752449i
$363$	−66205.0	+	99086.6i	−0.502432	+	0.751972i
$364$	−8250.00			−0.0622660
$365$		0			0
$366$	−10276.0	−	6865.94i	−0.0767118	−	0.0512552i
$367$	142965.			1.06145			0.530723	−	0.847546i	$-0.321921\pi$
$367$	142965.			1.06145			0.530723	+	0.847546i	$0.321921\pi$
$368$		−	143231.i		−	1.05765i
$369$	165200.	−	68434.9i	1.21327	−	0.502603i
$370$		0			0
$371$			40971.1i			0.297667i
$372$	30.0000	−	44.8999i	0.000216788	−	0.000324459i
$373$	−134705.			−0.968202			−0.484101	−	0.875012i	$-0.660853\pi$
$373$	−134705.			−0.968202			−0.484101	+	0.875012i	$0.660853\pi$
$374$			70193.5i			0.501827i
$375$		0			0
$376$	−124992.			−0.884110
$377$			47332.0i			0.333021i
$378$	39900.0	−	200646.i	0.279248	−	1.40426i
$379$	18493.0			0.128745			0.0643723	−	0.997926i	$-0.479495\pi$
$379$	18493.0			0.128745			0.0643723	+	0.997926i	$0.479495\pi$
$380$		0			0
$381$	−134150.	+	200777.i	−0.924146	+	1.38314i
$382$	84140.0			0.576602
$383$		−	101833.i		−	0.694210i	−0.937826	−	0.347105i	$-0.887165\pi$
$383$		−	101833.i		−	0.694210i	0.937826	−	0.347105i	$-0.112835\pi$
$384$	94752.0	+	63308.8i	0.642578	+	0.429341i
$385$		0			0
$386$			53786.3i			0.360992i
$387$	45725.0	+	110379.i	0.305304	+	0.736994i
$388$	9070.00			0.0602482
$389$			74421.6i			0.491813i	0.969294	+	0.245906i	$0.0790855\pi$
$389$			74421.6i			0.491813i	−0.969294	+	0.245906i	$0.920914\pi$
$390$		0			0
$391$	326424.			2.13515
$392$			217136.i			1.41306i
$393$	−84840.0	−	56686.1i	−0.549308	−	0.367022i
$394$	133056.			0.857121
$395$		0			0
$396$	5600.00	−	2319.83i	0.0357106	−	0.0147933i
$397$	244735.			1.55280			0.776399	−	0.630241i	$-0.217044\pi$
$397$	244735.			1.55280			0.776399	+	0.630241i	$0.217044\pi$
$398$			163035.i			1.02924i
$399$	−130125.	+	194753.i	−0.817363	+	1.22332i
$400$		0			0
$401$		−	201488.i		−	1.25303i	−0.779410	−	0.626514i	$-0.784481\pi$
$401$		−	201488.i		−	1.25303i	0.779410	−	0.626514i	$-0.215519\pi$
$402$	62580.0	+	41813.0i	0.387243	+	0.258738i
$403$	−165.000			−0.00101595
$404$			21327.4i			0.130670i
$405$		0			0
$406$	241500.			1.46509
$407$		−	83439.0i		−	0.503709i
$408$	−168840.	+	252697.i	−1.01427	+	1.51803i
$409$	−203737.			−1.21793			−0.608966	−	0.793196i	$-0.708416\pi$
$409$	−203737.			−1.21793			−0.608966	+	0.793196i	$0.708416\pi$
$410$		0			0
$411$	−51408.0	−	34348.4i	−0.304332	−	0.203340i
$412$	4780.00			0.0281601
$413$		−	213274.i		−	1.25037i
$414$	75516.0	+	182294.i	0.440594	+	1.06358i
$415$		0			0
$416$			13993.8i			0.0808628i
$417$	23210.0	−	34737.5i	0.133476	−	0.199769i
$418$	48580.0			0.278039
$419$			165643.i			0.943508i	0.881730	+	0.471754i	$0.156379\pi$
$419$			165643.i			0.943508i	−0.881730	+	0.471754i	$0.843621\pi$
$420$		0			0
$421$	35482.0			0.200191			0.100095	−	0.994978i	$-0.468085\pi$
$421$	35482.0			0.200191			0.100095	+	0.994978i	$0.468085\pi$
$422$			59556.0i			0.334426i
$423$	138880.	−	57531.7i	0.776174	−	0.321534i
$424$	36792.0			0.204655
$425$		0			0
$426$	−9100.00	+	13619.6i	−0.0501444	+	0.0750492i
$427$	−27525.0			−0.150963
$428$		−	6690.08i		−	0.0365211i
$429$	−15400.0	−	10289.6i	−0.0836770	−	0.0559091i
$430$		0			0
$431$		−	38052.7i		−	0.204847i	−0.994741	−	0.102424i	$-0.967340\pi$
$431$		−	38052.7i		−	0.204847i	0.994741	−	0.102424i	$-0.0326597\pi$
$432$	−157300.	−	31280.3i	−0.842871	−	0.167611i
$433$	−43265.0			−0.230760			−0.115380	−	0.993321i	$-0.536809\pi$
$433$	−43265.0			−0.230760			−0.115380	+	0.993321i	$0.536809\pi$
$434$			841.873i			0.00446958i
$435$		0			0
$436$	−4274.00			−0.0224834
$437$		−	225914.i		−	1.18299i
$438$	−195160.	−	130397.i	−1.01728	−	0.679702i
$439$	89533.0			0.464573			0.232287	−	0.972647i	$-0.425379\pi$
$439$	89533.0			0.464573			0.232287	+	0.972647i	$0.425379\pi$
$440$		0			0
$441$	−99944.0	−	241262.i	−0.513901	−	1.24054i
$442$	103180.			0.528142
$443$			161056.i			0.820671i	0.911935	+	0.410336i	$0.134588\pi$
$443$			161056.i			0.820671i	−0.911935	+	0.410336i	$0.865412\pi$
$444$	22300.0	−	33375.6i	0.113120	−	0.169302i
$445$		0			0
$446$			151331.i			0.760780i
$447$	86800.0	+	57995.7i	0.434415	+	0.290256i
$448$	335400.			1.67112
$449$			114869.i			0.569783i	0.958560	+	0.284892i	$0.0919576\pi$
$449$			114869.i			0.569783i	−0.958560	+	0.284892i	$0.908042\pi$
$450$		0			0
$451$	−82600.0			−0.406094
$452$		−	15236.0i		−	0.0745753i
$453$	115615.	−	173037.i	0.563401	−	0.843222i
$454$	−172564.			−0.837218
$455$		0			0
$456$	174888.	+	116852.i	0.841066	+	0.561961i
$457$	63850.0			0.305723			0.152862	−	0.988248i	$-0.451151\pi$
$457$	63850.0			0.305723			0.152862	+	0.988248i	$0.451151\pi$
$458$			136731.i			0.651834i
$459$	71288.0	−	358488.i	0.338369	−	1.70157i
$460$		0			0
$461$			281410.i			1.32415i	0.749437	+	0.662076i	$0.230324\pi$
$461$			281410.i			1.32415i	−0.749437	+	0.662076i	$0.769676\pi$
$462$	−52500.0	+	78574.8i	−0.245966	+	0.368128i
$463$	−307770.			−1.43570			−0.717851	−	0.696197i	$-0.754874\pi$
$463$	−307770.			−1.43570			−0.717851	+	0.696197i	$0.754874\pi$
$464$		−	189328.i		−	0.879384i
$465$		0			0
$466$	−314076.			−1.44632
$467$			274885.i			1.26042i	0.776423	+	0.630212i	$0.217032\pi$
$467$			274885.i			1.26042i	−0.776423	+	0.630212i	$0.782968\pi$
$468$	−3410.00	−	8231.65i	−0.0155691	−	0.0375833i
$469$	167625.			0.762067
$470$		0			0
$471$	66125.0	−	98966.8i	0.298074	−	0.446116i
$472$	−191520.			−0.859667
$473$		−	55189.4i		−	0.246680i
$474$	−126504.	−	84524.0i	−0.563051	−	0.376204i
$475$		0			0
$476$			75207.3i			0.331930i
$477$	−40880.0	+	16934.7i	−0.179669	+	0.0744289i
$478$	−342860.			−1.50059
$479$		−	178926.i		−	0.779835i	−0.920850	−	0.389917i	$-0.872504\pi$
$479$		−	178926.i		−	0.779835i	0.920850	−	0.389917i	$-0.127496\pi$
$480$		0			0
$481$	−122650.			−0.530124
$482$		−	384317.i		−	1.65423i
$483$	365400.	+	244143.i	1.56630	+	1.04653i
$484$	26482.0			0.113047
$485$		0			0
$486$	216692.	−	43122.6i	0.917425	−	0.182571i
$487$	−349555.			−1.47386			−0.736932	−	0.675967i	$-0.763726\pi$
$487$	−349555.			−1.47386			−0.736932	+	0.675967i	$0.763726\pi$
$488$			24717.4i			0.103792i
$489$	122975.	−	184052.i	0.514279	−	0.769703i
$490$		0			0
$491$		−	130808.i		−	0.542591i	−0.962496	−	0.271295i	$-0.912548\pi$
$491$		−	130808.i		−	0.542591i	0.962496	−	0.271295i	$-0.0874520\pi$
$492$	−33040.0	−	22075.8i	−0.136493	−	0.0911981i
$493$	431480.			1.77528
$494$		−	71409.5i		−	0.292619i
$495$		0			0
$496$	660.000			0.00268275
$497$			36481.2i			0.147692i
$498$	5880.00	−	8800.38i	0.0237093	−	0.0354848i
$499$	−212027.			−0.851511			−0.425755	−	0.904838i	$-0.639992\pi$
$499$	−212027.			−0.851511			−0.425755	+	0.904838i	$0.639992\pi$
$500$		0			0
$501$	−312648.	−	208897.i	−1.24560	−	0.832255i
$502$	−273000.			−1.08332
$503$		−	77624.4i		−	0.306805i	−0.988164	−	0.153402i	$-0.950977\pi$
$503$		−	77624.4i		−	0.306805i	0.988164	−	0.153402i	$-0.0490231\pi$
$504$	−378000.	+	156588.i	−1.48810	+	0.616451i
$505$		0			0
$506$		−	91146.8i		−	0.355992i
$507$	127680.	−	191094.i	0.496715	−	0.743414i
$508$	53660.0			0.207933
$509$		−	222778.i		−	0.859879i	−0.902858	−	0.429939i	$-0.858535\pi$
$509$		−	222778.i		−	0.859879i	0.902858	−	0.429939i	$-0.141465\pi$
$510$		0			0
$511$	−522750.			−2.00195
$512$		−	293047.i		−	1.11788i
$513$	−248105.	−	49337.5i	−0.942759	−	0.187475i
$514$	207816.			0.786598
$515$		0			0
$516$	14750.0	−	22075.8i	0.0553978	−	0.0829119i
$517$	−69440.0			−0.259794
$518$			625792.i			2.33223i
$519$	−80472.0	−	53767.6i	−0.298751	−	0.199612i
$520$		0			0
$521$			166766.i			0.614372i	0.951650	+	0.307186i	$0.0993873\pi$
$521$			166766.i			0.614372i	−0.951650	+	0.307186i	$0.900613\pi$
$522$	99820.0	+	240963.i	0.366333	+	0.884319i
$523$	−307355.			−1.12367			−0.561833	−	0.827251i	$-0.689903\pi$
$523$	−307355.			−1.12367			−0.561833	+	0.827251i	$0.689903\pi$
$524$			22674.4i			0.0825798i
$525$		0			0
$526$	398804.			1.44141
$527$			1504.15i			0.00541588i
$528$	61600.0	+	41158.2i	0.220960	+	0.147635i
$529$	−144023.			−0.514660
$530$		0			0
$531$	212800.	−	88153.4i	0.754714	−	0.312644i
$532$	52050.0			0.183907
$533$			121417.i			0.427390i
$534$	−151200.	+	226295.i	−0.530236	+	0.793585i
$535$		0			0
$536$		−	150527.i		−	0.523944i
$537$	437360.	+	292223.i	1.51667	+	1.01337i
$538$	330820.			1.14295
$539$			120631.i			0.415223i
$540$		0			0
$541$	554487.			1.89451			0.947255	−	0.320481i	$-0.103845\pi$
$541$	554487.			1.89451			0.947255	+	0.320481i	$0.103845\pi$
$542$		−	50205.6i		−	0.170904i
$543$	131765.	−	197208.i	0.446890	−	0.668843i
$544$	127568.			0.431066
$545$		0			0
$546$	115500.	+	77171.7i	0.387433	+	0.258865i
$547$	−96290.0			−0.321815			−0.160908	−	0.986969i	$-0.551442\pi$
$547$	−96290.0			−0.321815			−0.160908	+	0.986969i	$0.551442\pi$
$548$			13739.4i			0.0457515i
$549$	−11377.0	−	27463.8i	−0.0377471	−	0.0911204i
$550$		0			0
$551$		−	298622.i		−	0.983599i
$552$	219240.	−	328128.i	0.719518	−	1.07688i
$553$	−338850.			−1.10804
$554$			187289.i			0.610228i
$555$		0			0
$556$	−9284.00			−0.0300321
$557$			350803.i			1.13071i	0.824846	+	0.565357i	$0.191262\pi$
$557$			350803.i			1.13071i	−0.824846	+	0.565357i	$0.808738\pi$
$558$	−840.000	+	347.974i	−0.00269781	+	0.00111758i
$559$	−81125.0			−0.259616
$560$		0			0
$561$	−93800.0	+	140387.i	−0.298042	+	0.446068i
$562$	−160020.			−0.506643
$563$		−	438470.i		−	1.38332i	−0.722223	−	0.691660i	$-0.756879\pi$
$563$		−	438470.i		−	1.38332i	0.722223	−	0.691660i	$-0.243121\pi$
$564$	−27776.0	−	18558.6i	−0.0873196	−	0.0583428i
$565$		0			0
$566$			126786.i			0.395766i
$567$	347925.	−	347974.i	1.08223	−	1.08238i
$568$	32760.0			0.101542
$569$		−	6847.23i		−	0.0211490i	−0.999944	−	0.0105745i	$-0.996634\pi$
$569$		−	6847.23i		−	0.0211490i	0.999944	−	0.0105745i	$-0.00336604\pi$
$570$		0			0
$571$	−560443.			−1.71893			−0.859467	−	0.511191i	$-0.829204\pi$
$571$	−560443.			−1.71893			−0.859467	+	0.511191i	$0.829204\pi$
$572$			4115.82i			0.0125795i
$573$	168280.	+	112437.i	0.512535	+	0.342452i
$574$	619500.			1.88026
$575$		0			0
$576$	138632.	+	334654.i	0.417848	+	1.00867i
$577$	−42745.0			−0.128391			−0.0641954	−	0.997937i	$-0.520448\pi$
$577$	−42745.0			−0.128391			−0.0641954	+	0.997937i	$0.520448\pi$
$578$		−	628086.i		−	1.88002i
$579$	−71875.0	+	107573.i	−0.214398	+	0.320882i
$580$		0			0
$581$		−	23572.4i		−	0.0698316i
$582$	−126980.	−	84842.1i	−0.374877	−	0.250476i
$583$	20440.0			0.0601373
$584$			469428.i			1.37640i
$585$		0			0
$586$	−497616.			−1.44910
$587$		−	214824.i		−	0.623456i	−0.950171	−	0.311728i	$-0.899092\pi$
$587$		−	214824.i		−	0.623456i	0.950171	−	0.311728i	$-0.100908\pi$
$588$	−32240.0	+	48252.4i	−0.0932482	+	0.139561i
$589$	1041.00			0.00300068
$590$		0			0
$591$	266112.	+	177804.i	0.761885	+	0.509056i
$592$	490600.			1.39986
$593$		−	459498.i		−	1.30669i	−0.757058	−	0.653347i	$-0.773364\pi$
$593$		−	459498.i		−	1.30669i	0.757058	−	0.653347i	$-0.226636\pi$
$594$	−100100.	−	19905.6i	−0.283701	−	0.0564161i
$595$		0			0
$596$		−	23198.3i		−	0.0653075i
$597$	−217865.	+	326070.i	−0.611278	+	0.914877i
$598$	−133980.			−0.374660
$599$		−	259671.i		−	0.723719i	−0.932233	−	0.361859i	$-0.882142\pi$
$599$		−	259671.i		−	0.723719i	0.932233	−	0.361859i	$-0.117858\pi$
$600$		0			0
$601$	247127.			0.684181			0.342091	−	0.939667i	$-0.388865\pi$
$601$	247127.			0.684181			0.342091	+	0.939667i	$0.388865\pi$
$602$			413921.i			1.14215i
$603$	69285.0	+	167252.i	0.190548	+	0.459978i
$604$	−46246.0			−0.126765
$605$		0			0
$606$	199500.	−	298584.i	0.543247	−	0.813058i
$607$	−291050.			−0.789933			−0.394966	−	0.918696i	$-0.629244\pi$
$607$	−291050.			−0.789933			−0.394966	+	0.918696i	$0.629244\pi$
$608$		−	88288.1i		−	0.238834i
$609$	483000.	+	322718.i	1.30230	+	0.870139i
$610$		0			0
$611$			102072.i			0.273417i
$612$	−75040.0	+	31085.7i	−0.200350	+	0.0829961i
$613$	−415670.			−1.10618			−0.553092	−	0.833120i	$-0.686552\pi$
$613$	−415670.			−1.10618			−0.553092	+	0.833120i	$0.686552\pi$
$614$		−	508398.i		−	1.34855i
$615$		0			0
$616$	189000.			0.498081
$617$			671500.i			1.76391i	0.471336	+	0.881954i	$0.343772\pi$
$617$			671500.i			1.76391i	−0.471336	+	0.881954i	$0.656228\pi$
$618$	−66920.0	−	44712.8i	−0.175218	−	0.117073i
$619$	373853.			0.975707			0.487854	−	0.872925i	$-0.337780\pi$
$619$	373853.			0.975707			0.487854	+	0.872925i	$0.337780\pi$
$620$		0			0
$621$	−92568.0	+	465500.i	−0.240037	+	1.20708i
$622$	−105840.			−0.273570
$623$			606148.i			1.56172i
$624$	60500.0	−	90548.1i	0.155377	−	0.232547i
$625$		0			0
$626$			637036.i			1.62561i
$627$	97160.0	+	64917.8i	0.247145	+	0.165131i
$628$	−26450.0			−0.0670666
$629$			1.11808e6i			2.82600i
$630$		0			0
$631$	−27203.0			−0.0683216			−0.0341608	−	0.999416i	$-0.510876\pi$
$631$	−27203.0			−0.0683216			−0.0341608	+	0.999416i	$0.510876\pi$
$632$			304287.i			0.761813i
$633$	−79585.0	+	119112.i	−0.198620	+	0.297268i
$634$	40376.0			0.100449
$635$		0			0
$636$	8176.00	+	5462.82i	0.0202128	+	0.0135053i
$637$	177320.			0.436997
$638$		−	120481.i		−	0.295991i
$639$	−36400.0	+	15078.9i	−0.0891455	+	0.0369290i
$640$		0			0
$641$		−	780360.i		−	1.89924i	−0.313409	−	0.949618i	$-0.601471\pi$
$641$		−	780360.i		−	1.89924i	0.313409	−	0.949618i	$-0.398529\pi$
$642$	−62580.0	+	93661.2i	−0.151833	+	0.227242i
$643$	−288450.			−0.697668			−0.348834	−	0.937185i	$-0.613422\pi$
$643$	−288450.			−0.697668			−0.348834	+	0.937185i	$0.613422\pi$
$644$		−	97657.3i		−	0.235468i
$645$		0			0
$646$	−650972.			−1.55990
$647$		−	320301.i		−	0.765155i	−0.923923	−	0.382578i	$-0.875036\pi$
$647$		−	320301.i		−	0.765155i	0.923923	−	0.382578i	$-0.124964\pi$
$648$	−312480.	−	312436.i	−0.744170	−	0.744065i
$649$	−106400.			−0.252611
$650$		0			0
$651$	−1125.00	+	1683.75i	−0.00265455	+	0.00397296i
$652$	−49190.0			−0.115713
$653$			356221.i			0.835397i	0.908586	+	0.417698i	$0.137163\pi$
$653$			356221.i			0.835397i	−0.908586	+	0.417698i	$0.862837\pi$
$654$	59836.0	+	39979.6i	0.139897	+	0.0934723i
$655$		0			0
$656$		−	485667.i		−	1.12858i
$657$	−216070.	−	521587.i	−0.500569	−	1.20836i
$658$	520800.			1.20287
$659$		−	637541.i		−	1.46804i	−0.679129	−	0.734019i	$-0.737642\pi$
$659$		−	637541.i		−	1.46804i	0.679129	−	0.734019i	$-0.262358\pi$
$660$		0			0
$661$	830842.			1.90158			0.950792	−	0.309830i	$-0.100272\pi$
$661$	830842.			1.90158			0.950792	+	0.309830i	$0.100272\pi$
$662$		−	91214.1i		−	0.208135i
$663$	206360.	+	137880.i	0.469460	+	0.313671i
$664$	−21168.0			−0.0480113
$665$		0			0
$666$	−624400.	+	258661.i	−1.40771	+	0.583152i
$667$	−560280.			−1.25937
$668$			83558.7i			0.187257i
$669$	−202225.	+	302663.i	−0.451838	+	0.676249i
$670$		0			0
$671$			13731.9i			0.0304990i
$672$	142800.	+	95412.3i	0.316220	+	0.211284i
$673$	203370.			0.449011			0.224505	−	0.974473i	$-0.427923\pi$
$673$	203370.			0.449011			0.224505	+	0.974473i	$0.427923\pi$
$674$		−	306460.i		−	0.674613i
$675$		0			0
$676$	−51072.0			−0.111761
$677$		−	554042.i		−	1.20883i	−0.796669	−	0.604415i	$-0.793407\pi$
$677$		−	554042.i		−	1.20883i	0.796669	−	0.604415i	$-0.206593\pi$
$678$	−142520.	+	213304.i	−0.310039	+	0.464024i
$679$	−340125.			−0.737733
$680$		0			0
$681$	−345128.	−	230598.i	−0.744194	−	0.497235i
$682$	420.000			0.000902985
$683$		−	55810.6i		−	0.119640i	−0.998209	−	0.0598198i	$-0.980947\pi$
$683$		−	55810.6i		−	0.119640i	0.998209	−	0.0598198i	$-0.0190526\pi$
$684$	21514.0	+	51934.2i	0.0459842	+	0.111005i
$685$		0			0
$686$		−	230954.i		−	0.490769i
$687$	−182715.	+	273463.i	−0.387133	+	0.579408i
$688$	324500.			0.685548
$689$		−	30045.5i		−	0.0632909i
$690$		0			0
$691$	655462.			1.37275			0.686375	−	0.727248i	$-0.259201\pi$
$691$	655462.			1.37275			0.686375	+	0.727248i	$0.259201\pi$
$692$			21507.0i			0.0449126i
$693$	−210000.	+	86993.5i	−0.437273	+	0.181143i
$694$	−788144.			−1.63639
$695$		0			0
$696$	289800.	−	433733.i	0.598246	−	0.895373i
$697$	1.10684e6			2.27834
$698$			34789.9i			0.0714073i
$699$	−628152.	−	419702.i	−1.28561	−	0.858987i
$700$		0			0
$701$			901552.i			1.83466i	0.398131	+	0.917329i	$0.369659\pi$
$701$			901552.i			1.83466i	−0.398131	+	0.917329i	$0.630341\pi$
$702$	−29260.0	+	147141.i	−0.0593745	+	0.298578i
$703$	773810.			1.56575
$704$		−	167327.i		−	0.337614i
$705$		0			0
$706$	209244.			0.419801
$707$		−	799779.i		−	1.60004i
$708$	−42560.0	−	28436.6i	−0.0849054	−	0.0567298i
$709$	−176537.			−0.351191			−0.175595	−	0.984462i	$-0.556185\pi$
$709$	−176537.			−0.351191			−0.175595	+	0.984462i	$0.556185\pi$
$710$		0			0
$711$	−140058.	−	338096.i	−0.277057	−	0.668807i
$712$	544320.			1.07373
$713$		−	1953.15i		−	0.00384198i
$714$	703500.	−	1.05290e6i	1.37996	−	2.06534i
$715$		0			0
$716$		−	116889.i		−	0.228007i
$717$	−685720.	−	458166.i	−1.33385	−	0.891219i
$718$	−263340.			−0.510820
$719$		−	357066.i		−	0.690703i	−0.938473	−	0.345351i	$-0.887760\pi$
$719$		−	357066.i		−	0.690703i	0.938473	−	0.345351i	$-0.112240\pi$
$720$		0			0
$721$	−179250.			−0.344817
$722$		−	37087.3i		−	0.0711461i
$723$	513565.	−	768634.i	0.982469	−	1.47042i
$724$	−52706.0			−0.100550
$725$		0			0
$726$	−370748.	−	247716.i	−0.703405	−	0.469982i
$727$	207605.			0.392798			0.196399	−	0.980524i	$-0.437075\pi$
$727$	207605.			0.392798			0.196399	+	0.980524i	$0.437075\pi$
$728$		−	277818.i		−	0.524201i
$729$	491009.	+	203322.i	0.923920	+	0.382586i
$730$		0			0
$731$			739539.i			1.38397i
$732$	−3670.00	+	5492.75i	−0.00684926	+	0.0102510i
$733$	−186190.			−0.346536			−0.173268	−	0.984875i	$-0.555433\pi$
$733$	−186190.			−0.346536			−0.173268	+	0.984875i	$0.555433\pi$
$734$			534926.i			0.992891i
$735$		0			0
$736$	−165648.			−0.305795
$737$		−	83626.0i		−	0.153960i
$738$	256060.	+	618122.i	0.470142	+	1.13491i
$739$	−471242.			−0.862889			−0.431445	−	0.902139i	$-0.641996\pi$
$739$	−471242.			−0.862889			−0.431445	+	0.902139i	$0.641996\pi$
$740$		0			0
$741$	95425.0	−	142819.i	0.173790	−	0.260106i
$742$	−153300.			−0.278442
$743$			568897.i			1.03052i	0.857034	+	0.515259i	$0.172304\pi$
$743$			568897.i			1.03052i	−0.857034	+	0.515259i	$0.827696\pi$
$744$	1512.00	+	1010.25i	0.00273153	+	0.00182508i
$745$		0			0
$746$		−	504020.i		−	0.905670i
$747$	23520.0	−	9743.28i	0.0421499	−	0.0174608i
$748$	37520.0			0.0670594
$749$			250878.i			0.447197i
$750$		0			0
$751$	−486098.			−0.861874			−0.430937	−	0.902382i	$-0.641817\pi$
$751$	−486098.			−0.861874			−0.430937	+	0.902382i	$0.641817\pi$
$752$		−	408290.i		−	0.721993i
$753$	−546000.	−	364812.i	−0.962948	−	0.643396i
$754$	−177100.			−0.311513
$755$		0			0
$756$	−107250.	−	21327.4i	−0.187652	−	0.0373160i
$757$	−89825.0			−0.156749			−0.0783746	−	0.996924i	$-0.524973\pi$
$757$	−89825.0			−0.156749			−0.0783746	+	0.996924i	$0.524973\pi$
$758$			69194.5i			0.120430i
$759$	121800.	−	182294.i	0.211429	−	0.316437i
$760$		0			0
$761$		−	477959.i		−	0.825319i	−0.910885	−	0.412659i	$-0.864600\pi$
$761$		−	477959.i		−	0.825319i	0.910885	−	0.412659i	$-0.135400\pi$
$762$	−751240.	−	501943.i	−1.29380	−	0.864460i
$763$	160275.			0.275307
$764$		−	44974.7i		−	0.0770516i
$765$		0			0
$766$	381024.			0.649374
$767$			156401.i			0.265858i
$768$	120880.	−	180917.i	0.204942	−	0.306730i
$769$	257903.			0.436118			0.218059	−	0.975936i	$-0.430028\pi$
$769$	257903.			0.436118			0.218059	+	0.975936i	$0.430028\pi$
$770$		0			0
$771$	415632.	+	277706.i	0.699198	+	0.467171i
$772$	28750.0			0.0482396
$773$			934569.i			1.56406i	0.623243	+	0.782028i	$0.285815\pi$
$773$			934569.i			1.56406i	−0.623243	+	0.782028i	$0.714185\pi$
$774$	−413000.	+	171087.i	−0.689395	+	0.285585i
$775$		0			0
$776$			305431.i			0.507213i
$777$	−836250.	+	1.25158e6i	−1.38514	+	2.07309i
$778$	−278460.			−0.460049
$779$		−	766030.i		−	1.26232i
$780$		0			0
$781$	18200.0			0.0298380
$782$			1.22137e6i			1.99725i
$783$	−122360.	+	615316.i	−0.199580	+	1.00363i
$784$	−709280.			−1.15395
$785$		0			0
$786$	212100.	−	317442.i	0.343317	−	0.513830i
$787$	−304355.			−0.491395			−0.245698	−	0.969347i	$-0.579017\pi$
$787$	−304355.			−0.491395			−0.245698	+	0.969347i	$0.579017\pi$
$788$		−	71121.4i		−	0.114538i
$789$	797608.	+	532924.i	1.28125	+	0.856074i
$790$		0			0
$791$			571351.i			0.913167i
$792$	78120.0	+	188580.i	0.124541	+	0.300638i
$793$	20185.0			0.0320983
$794$			915715.i			1.45251i
$795$		0			0
$796$	87146.0			0.137538
$797$			92029.8i			0.144881i	0.997373	+	0.0724406i	$0.0230788\pi$
$797$			92029.8i			0.144881i	−0.997373	+	0.0724406i	$0.976921\pi$
$798$	−728700.	−	486883.i	−1.14431	−	0.764573i
$799$	930496.			1.45754
$800$		0			0
$801$	−604800.	+	250541.i	−0.942642	+	0.390494i
$802$	753900.			1.17210
$803$			260794.i			0.404451i
$804$	22350.0	−	33450.4i	0.0345753	−	0.0517475i
$805$		0			0
$806$		−	617.373i		−	0.000950338i
$807$	661640.	+	442077.i	1.01596	+	0.678814i
$808$	−718200.			−1.10008
$809$			9391.56i			0.0143496i	0.999974	+	0.00717481i	$0.00228383\pi$
$809$			9391.56i			0.0143496i	−0.999974	+	0.00717481i	$0.997716\pi$
$810$		0			0
$811$	90117.0			0.137014			0.0685070	−	0.997651i	$-0.478176\pi$
$811$	90117.0			0.137014			0.0685070	+	0.997651i	$0.478176\pi$
$812$		−	129087.i		−	0.195781i
$813$	67090.0	−	100411.i	0.101502	−	0.151915i
$814$	312200.			0.471177
$815$		0			0
$816$	−825440.	−	551520.i	−1.23967	−	0.828288i
$817$	511825.			0.766792
$818$		−	762314.i		−	1.13927i
$819$	127875.	+	308687.i	0.190642	+	0.460204i
$820$		0			0
$821$			948959.i			1.40787i	0.710267	+	0.703933i	$0.248574\pi$
$821$			948959.i			1.40787i	−0.710267	+	0.703933i	$0.751426\pi$
$822$	128520.	−	192351.i	0.190207	−	0.284676i
$823$	672845.			0.993380			0.496690	−	0.867928i	$-0.334549\pi$
$823$	672845.			0.993380			0.496690	+	0.867928i	$0.334549\pi$
$824$			160966.i			0.237072i
$825$		0			0
$826$	798000.			1.16961
$827$		−	530096.i		−	0.775074i	−0.921854	−	0.387537i	$-0.873326\pi$
$827$		−	530096.i		−	0.775074i	0.921854	−	0.387537i	$-0.126674\pi$
$828$	97440.0	−	40365.0i	0.142127	−	0.0588768i
$829$	951018.			1.38382			0.691910	−	0.721984i	$-0.256769\pi$
$829$	951018.			1.38382			0.691910	+	0.721984i	$0.256769\pi$
$830$		0			0
$831$	−250275.	+	374577.i	−0.362423	+	0.542425i
$832$	−245960.			−0.355319
$833$		−	1.61646e6i		−	2.32956i
$834$	129976.	+	86843.9i	0.186866	+	0.124855i
$835$		0			0
$836$		−	25967.1i		−	0.0371545i
$837$	−2145.00	−	426.549i	−0.00306180	−	0.000608861i
$838$	−619780.			−0.882571
$839$			675706.i			0.959917i	0.877291	+	0.479959i	$0.159348\pi$
$839$			675706.i			0.959917i	−0.877291	+	0.479959i	$0.840652\pi$
$840$		0			0
$841$	−33319.0			−0.0471086
$842$			132761.i			0.187261i
$843$	−320040.	−	213836.i	−0.450349	−	0.300902i
$844$	31834.0			0.0446896
$845$		0			0
$846$	215264.	+	519641.i	0.300767	+	0.726044i
$847$	−993075.			−1.38425
$848$			120182.i			0.167127i
$849$	−169425.	+	253572.i	−0.235051	+	0.351792i
$850$		0			0
$851$		−	1.45184e6i		−	2.00474i
$852$	7280.00	+	4864.15i	0.0100289	+	0.00670082i
$853$	1.09802e6			1.50907			0.754536	−	0.656258i	$-0.227862\pi$
$853$	1.09802e6			1.50907			0.754536	+	0.656258i	$0.227862\pi$
$854$		−	102989.i		−	0.141213i
$855$		0			0
$856$	225288.			0.307461
$857$			657619.i			0.895391i	0.894186	+	0.447695i	$0.147755\pi$
$857$			657619.i			0.895391i	−0.894186	+	0.447695i	$0.852245\pi$
$858$	38500.0	−	57621.5i	0.0522981	−	0.0782727i
$859$	−401162.			−0.543668			−0.271834	−	0.962344i	$-0.587630\pi$
$859$	−401162.			−0.543668			−0.271834	+	0.962344i	$0.587630\pi$
$860$		0			0
$861$	1.23900e6	+	827842.i	1.67134	+	1.11671i
$862$	142380.			0.191617
$863$		−	246336.i		−	0.330755i	−0.986230	−	0.165377i	$-0.947116\pi$
$863$		−	246336.i		−	0.330755i	0.986230	−	0.165377i	$-0.0528842\pi$
$864$	−36176.0	+	181919.i	−0.0484611	+	0.243698i
$865$		0			0
$866$		−	161883.i		−	0.215856i
$867$	839315.	−	1.25617e6i	1.11657	−	1.67113i
$868$	450.000			0.000597273
$869$			169048.i			0.223857i
$870$		0			0
$871$	−122925.			−0.162033
$872$		−	143927.i		−	0.189281i
$873$	−140585.	−	339368.i	−0.184464	−	0.445290i
$874$	845292.			1.10658
$875$		0			0
$876$	−69700.0	+	104317.i	−0.0908290	+	0.135940i
$877$	1.20146e6			1.56210			0.781049	−	0.624470i	$-0.214685\pi$
$877$	1.20146e6			1.56210			0.781049	+	0.624470i	$0.214685\pi$
$878$			335002.i			0.434568i
$879$	−995232.	−	664967.i	−1.28809	−	0.860642i
$880$		0			0
$881$		−	161714.i		−	0.208352i	−0.994559	−	0.104176i	$-0.966780\pi$
$881$		−	161714.i		−	0.208352i	0.994559	−	0.104176i	$-0.0332205\pi$
$882$	902720.	−	373956.i	1.16042	−	0.480710i
$883$	−378715.			−0.485726			−0.242863	−	0.970061i	$-0.578087\pi$
$883$	−378715.			−0.485726			−0.242863	+	0.970061i	$0.578087\pi$
$884$		−	55152.0i		−	0.0705760i
$885$		0			0
$886$	−602616.			−0.767668
$887$			1.19559e6i			1.51963i	0.650142	+	0.759813i	$0.274709\pi$
$887$			1.19559e6i			1.51963i	−0.650142	+	0.759813i	$0.725291\pi$
$888$	1.12392e6	+	750951.i	1.42531	+	0.952326i
$889$	−2.01225e6			−2.54612
$890$		0			0
$891$	−173600.	−	173575.i	−0.218673	−	0.218642i
$892$	80890.0			0.101664
$893$		−	643984.i		−	0.807555i
$894$	−217000.	+	324776.i	−0.271509	+	0.406358i
$895$		0			0
$896$			949633.i			1.18288i
$897$	−267960.	−	179038.i	−0.333031	−	0.222516i
$898$	−429800.			−0.532983
$899$		−	2581.74i		−	0.00319443i
$900$		0			0
$901$	−273896.			−0.337393
$902$		−	309061.i		−	0.379866i
$903$	−553125.	+	827842.i	−0.678341	+	1.01525i
$904$	513072.			0.627829
$905$		0			0
$906$	647444.	+	432592.i	0.788762	+	0.527014i
$907$	−407850.			−0.495776			−0.247888	−	0.968789i	$-0.579737\pi$
$907$	−407850.			−0.495776			−0.247888	+	0.968789i	$0.579737\pi$
$908$			92239.3i			0.111878i
$909$	798000.	−	330575.i	0.965773	−	0.400076i
$910$		0			0
$911$		−	790762.i		−	0.952816i	−0.879224	−	0.476408i	$-0.841939\pi$
$911$		−	790762.i		−	0.952816i	0.879224	−	0.476408i	$-0.158061\pi$
$912$	−381700.	+	571276.i	−0.458915	+	0.686841i
$913$	−11760.0			−0.0141080
$914$			238905.i			0.285978i
$915$		0			0
$916$	73086.0			0.0871050
$917$		−	850292.i		−	1.01118i
$918$	1.34134e6	+	266735.i	1.59167	+	0.316516i
$919$	1.29805e6			1.53696			0.768478	−	0.639876i	$-0.221014\pi$
$919$	1.29805e6			1.53696			0.768478	+	0.639876i	$0.221014\pi$
$920$		0			0
$921$	679375.	−	1.01680e6i	0.800922	−	1.19871i
$922$	−1.05294e6			−1.23863
$923$		−	26752.9i		−	0.0314027i
$924$	42000.0	+	28062.4i	0.0491932	+	0.0328686i
$925$		0			0
$926$		−	1.15157e6i		−	1.34298i
$927$	−74090.0	−	178851.i	−0.0862184	−	0.208129i
$928$	−218960.			−0.254255
$929$		−	899382.i		−	1.04211i	−0.853524	−	0.521054i	$-0.825539\pi$
$929$		−	899382.i		−	1.04211i	0.853524	−	0.521054i	$-0.174461\pi$
$930$		0			0
$931$	−1.11873e6			−1.29070
$932$			167881.i			0.193272i
$933$	−211680.	−	141435.i	−0.243174	−	0.162477i
$934$	−1.02852e6			−1.17902
$935$		0			0
$936$	277200.	−	114831.i	0.316404	−	0.131072i
$937$	696495.			0.793302			0.396651	−	0.917969i	$-0.370172\pi$
$937$	696495.			0.793302			0.396651	+	0.917969i	$0.370172\pi$
$938$			627195.i			0.712848i
$939$	−851275.	+	1.27407e6i	−0.965470	+	1.44498i
$940$		0			0
$941$		−	47743.5i		−	0.0539182i	−0.999637	−	0.0269591i	$-0.991418\pi$
$941$		−	47743.5i		−	0.0539182i	0.999637	−	0.0269591i	$-0.00858239\pi$
$942$	370300.	+	247417.i	0.417303	+	0.278823i
$943$	−1.43724e6			−1.61624
$944$		−	625605.i		−	0.702031i
$945$		0			0
$946$	206500.			0.230748
$947$		−	633290.i		−	0.706160i	−0.935593	−	0.353080i	$-0.885134\pi$
$947$		−	633290.i		−	0.706160i	0.935593	−	0.353080i	$-0.114866\pi$
$948$	−45180.0	+	67619.2i	−0.0502724	+	0.0752408i
$949$	383350.			0.425660
$950$		0			0
$951$	80752.0	+	53954.7i	0.0892878	+	0.0596579i
$952$	−2.53260e6			−2.79443
$953$			1.25497e6i			1.38180i	0.722948	+	0.690902i	$0.242786\pi$
$953$			1.25497e6i			1.38180i	−0.722948	+	0.690902i	$0.757214\pi$
$954$	−63364.0	−	152959.i	−0.0696219	−	0.168065i
$955$		0			0
$956$			183266.i			0.200524i
$957$	161000.	−	240963.i	0.175793	−	0.263103i
$958$	669480.			0.729469
$959$		−	515226.i		−	0.560223i
$960$		0			0
$961$	−923512.			−0.999990
$962$		−	458914.i		−	0.495886i
$963$	−250320.	+	103696.i	−0.269925	+	0.111818i
$964$	−205426.			−0.221056
$965$		0			0
$966$	−913500.	+	1.36720e6i	−0.978936	+	1.46514i
$967$	−1.54201e6			−1.64905			−0.824526	−	0.565824i	$-0.808558\pi$
$967$	−1.54201e6			−1.64905			−0.824526	+	0.565824i	$0.808558\pi$
$968$			891779.i			0.951714i
$969$	−1.30194e6	−	869898.i	−1.38658	−	0.926447i
$970$		0			0
$971$		−	1.69677e6i		−	1.79963i	−0.436270	−	0.899816i	$-0.643701\pi$
$971$		−	1.69677e6i		−	1.79963i	0.436270	−	0.899816i	$-0.356299\pi$
$972$	−23050.0	−	115827.i	−0.0243971	−	0.122596i
$973$	348150.			0.367740
$974$		−	1.30792e6i		−	1.37867i
$975$		0			0
$976$	−80740.0			−0.0847596
$977$			1.20136e6i			1.25859i	0.777168	+	0.629293i	$0.216655\pi$
$977$			1.20136e6i			1.25859i	−0.777168	+	0.629293i	$0.783345\pi$
$978$	688660.	+	460130.i	0.719991	+	0.481064i
$979$	302400.			0.315512
$980$		0			0
$981$	66247.0	+	159918.i	0.0688380	+	0.166173i
$982$	489440.			0.507547
$983$		−	478992.i		−	0.495703i	−0.968798	−	0.247851i	$-0.920276\pi$
$983$		−	478992.i		−	0.495703i	0.968798	−	0.247851i	$-0.0797244\pi$
$984$	743400.	−	1.11262e6i	0.767772	−	1.14910i
$985$		0			0
$986$			1.61445e6i			1.66062i
$987$	1.04160e6	+	695948.i	1.06922	+	0.714402i
$988$	−38170.0			−0.0391028
$989$		−	960296.i		−	0.981777i
$990$		0			0
$991$	−972163.			−0.989901			−0.494951	−	0.868921i	$-0.664814\pi$
$991$	−972163.			−0.989901			−0.494951	+	0.868921i	$0.664814\pi$
$992$		−	763.298i		−	0.000775659i
$993$	121890.	−	182428.i	0.123615	−	0.185009i
$994$	−136500.			−0.138153
$995$		0			0
$996$	−4704.00	−	3142.99i	−0.00474186	−	0.00316829i
$997$	−1.00299e6			−1.00904			−0.504518	−	0.863401i	$-0.668330\pi$
$997$	−1.00299e6			−1.00904			−0.504518	+	0.863401i	$0.668330\pi$
$998$		−	793332.i		−	0.796515i
$999$	−1.59445e6	−	317068.i	−1.59764	−	0.317703i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	75.5.c.c.26.2	yes	2
3.2	odd	2	inner	75.5.c.c.26.1	✓	2
5.2	odd	4		75.5.d.b.74.2		4
5.3	odd	4		75.5.d.b.74.3		4
5.4	even	2		75.5.c.g.26.1	yes	2
15.2	even	4		75.5.d.b.74.4		4
15.8	even	4		75.5.d.b.74.1		4
15.14	odd	2		75.5.c.g.26.2	yes	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.5.c.c.26.1	✓	2	3.2	odd	2	inner
75.5.c.c.26.2	yes	2	1.1	even	1	trivial
75.5.c.g.26.1	yes	2	5.4	even	2
75.5.c.g.26.2	yes	2	15.14	odd	2
75.5.d.b.74.1		4	15.8	even	4
75.5.d.b.74.2		4	5.2	odd	4
75.5.d.b.74.3		4	5.3	odd	4
75.5.d.b.74.4		4	15.2	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:	\( N \)	\(=\)	\( 75 = 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	75.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+3.74166i q^{2} +(-5.00000 + 7.48331i) q^{3} +2.00000 q^{4} +(-28.0000 - 18.7083i) q^{6} -75.0000 q^{7} +67.3498i q^{8} +(-31.0000 - 74.8331i) q^{9} +O(q^{10})\)	\(q+3.74166i q^{2} +(-5.00000 + 7.48331i) q^{3} +2.00000 q^{4} +(-28.0000 - 18.7083i) q^{6} -75.0000 q^{7} +67.3498i q^{8} +(-31.0000 - 74.8331i) q^{9} +37.4166i q^{11} +(-10.0000 + 14.9666i) q^{12} +55.0000 q^{13} -280.624i q^{14} -220.000 q^{16} -501.382i q^{17} +(280.000 - 115.991i) q^{18} -347.000 q^{19} +(375.000 - 561.249i) q^{21} -140.000 q^{22} +651.048i q^{23} +(-504.000 - 336.749i) q^{24} +205.791i q^{26} +(715.000 + 142.183i) q^{27} -150.000 q^{28} +860.581i q^{29} -3.00000 q^{31} +254.433i q^{32} +(-280.000 - 187.083i) q^{33} +1876.00 q^{34} +(-62.0000 - 149.666i) q^{36} -2230.00 q^{37} -1298.36i q^{38} +(-275.000 + 411.582i) q^{39} +2207.58i q^{41} +(2100.00 + 1403.12i) q^{42} -1475.00 q^{43} +74.8331i q^{44} -2436.00 q^{46} +1855.86i q^{47} +(1100.00 - 1646.33i) q^{48} +3224.00 q^{49} +(3752.00 + 2506.91i) q^{51} +110.000 q^{52} -546.282i q^{53} +(-532.000 + 2675.29i) q^{54} -5051.24i q^{56} +(1735.00 - 2596.71i) q^{57} -3220.00 q^{58} +2843.66i q^{59} +367.000 q^{61} -11.2250i q^{62} +(2325.00 + 5612.49i) q^{63} -4472.00 q^{64} +(700.000 - 1047.66i) q^{66} -2235.00 q^{67} -1002.76i q^{68} +(-4872.00 - 3255.24i) q^{69} -486.415i q^{71} +(5040.00 - 2087.84i) q^{72} +6970.00 q^{73} -8343.90i q^{74} -694.000 q^{76} -2806.24i q^{77} +(-1540.00 - 1028.96i) q^{78} +4518.00 q^{79} +(-4639.00 + 4639.66i) q^{81} -8260.00 q^{82} +314.299i q^{83} +(750.000 - 1122.50i) q^{84} -5518.94i q^{86} +(-6440.00 - 4302.91i) q^{87} -2520.00 q^{88} -8081.98i q^{89} -4125.00 q^{91} +1302.10i q^{92} +(15.0000 - 22.4499i) q^{93} -6944.00 q^{94} +(-1904.00 - 1272.16i) q^{96} +4535.00 q^{97} +12063.1i q^{98} +(2800.00 - 1159.91i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 10 q^{3} + 4 q^{4} - 56 q^{6} - 150 q^{7} - 62 q^{9}+O(q^{10}) \) 2 * q - 10 * q^3 + 4 * q^4 - 56 * q^6 - 150 * q^7 - 62 * q^9	\( 2 q - 10 q^{3} + 4 q^{4} - 56 q^{6} - 150 q^{7} - 62 q^{9} - 20 q^{12} + 110 q^{13} - 440 q^{16} + 560 q^{18} - 694 q^{19} + 750 q^{21} - 280 q^{22} - 1008 q^{24} + 1430 q^{27} - 300 q^{28} - 6 q^{31} - 560 q^{33} + 3752 q^{34} - 124 q^{36} - 4460 q^{37} - 550 q^{39} + 4200 q^{42} - 2950 q^{43} - 4872 q^{46} + 2200 q^{48} + 6448 q^{49} + 7504 q^{51} + 220 q^{52} - 1064 q^{54} + 3470 q^{57} - 6440 q^{58} + 734 q^{61} + 4650 q^{63} - 8944 q^{64} + 1400 q^{66} - 4470 q^{67} - 9744 q^{69} + 10080 q^{72} + 13940 q^{73} - 1388 q^{76} - 3080 q^{78} + 9036 q^{79} - 9278 q^{81} - 16520 q^{82} + 1500 q^{84} - 12880 q^{87} - 5040 q^{88} - 8250 q^{91} + 30 q^{93} - 13888 q^{94} - 3808 q^{96} + 9070 q^{97} + 5600 q^{99}+O(q^{100}) \) 2 * q - 10 * q^3 + 4 * q^4 - 56 * q^6 - 150 * q^7 - 62 * q^9 - 20 * q^12 + 110 * q^13 - 440 * q^16 + 560 * q^18 - 694 * q^19 + 750 * q^21 - 280 * q^22 - 1008 * q^24 + 1430 * q^27 - 300 * q^28 - 6 * q^31 - 560 * q^33 + 3752 * q^34 - 124 * q^36 - 4460 * q^37 - 550 * q^39 + 4200 * q^42 - 2950 * q^43 - 4872 * q^46 + 2200 * q^48 + 6448 * q^49 + 7504 * q^51 + 220 * q^52 - 1064 * q^54 + 3470 * q^57 - 6440 * q^58 + 734 * q^61 + 4650 * q^63 - 8944 * q^64 + 1400 * q^66 - 4470 * q^67 - 9744 * q^69 + 10080 * q^72 + 13940 * q^73 - 1388 * q^76 - 3080 * q^78 + 9036 * q^79 - 9278 * q^81 - 16520 * q^82 + 1500 * q^84 - 12880 * q^87 - 5040 * q^88 - 8250 * q^91 + 30 * q^93 - 13888 * q^94 - 3808 * q^96 + 9070 * q^97 + 5600 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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