LMFDB - Embedded newform 75.5.d.b.74.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [75,5,Mod(74,75)]

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, 1]))

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

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

chi := DirichletCharacter("75.74");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 75 = 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	75.d (of order $2$, degree $1$, not 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:	$4$
Coefficient field:	$\Q(i, \sqrt{14})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 49 $ x^4 + 49
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2\cdot 5^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			74.4
Root			$-1.87083 + 1.87083i$ of defining polynomial
Character	$\chi$	$=$	75.74
Dual form			75.5.d.b.74.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+3.74166 q^{2} +(-7.48331 + 5.00000i) q^{3} -2.00000 q^{4} +(-28.0000 + 18.7083i) q^{6} -75.0000i q^{7} -67.3498 q^{8} +(31.0000 - 74.8331i) q^{9} +O(q^{10})$	\(q+3.74166 q^{2} +(-7.48331 + 5.00000i) q^{3} -2.00000 q^{4} +(-28.0000 + 18.7083i) q^{6} -75.0000i q^{7} -67.3498 q^{8} +(31.0000 - 74.8331i) q^{9} -37.4166i q^{11} +(14.9666 - 10.0000i) q^{12} -55.0000i q^{13} -280.624i q^{14} -220.000 q^{16} -501.382 q^{17} +(115.991 - 280.000i) q^{18} +347.000 q^{19} +(375.000 + 561.249i) q^{21} -140.000i q^{22} -651.048 q^{23} +(504.000 - 336.749i) q^{24} -205.791i q^{26} +(142.183 + 715.000i) q^{27} +150.000i q^{28} +860.581i q^{29} -3.00000 q^{31} +254.433 q^{32} +(187.083 + 280.000i) q^{33} -1876.00 q^{34} +(-62.0000 + 149.666i) q^{36} -2230.00i q^{37} +1298.36 q^{38} +(275.000 + 411.582i) q^{39} -2207.58i q^{41} +(1403.12 + 2100.00i) q^{42} +1475.00i q^{43} +74.8331i q^{44} -2436.00 q^{46} +1855.86 q^{47} +(1646.33 - 1100.00i) q^{48} -3224.00 q^{49} +(3752.00 - 2506.91i) q^{51} +110.000i q^{52} +546.282 q^{53} +(532.000 + 2675.29i) q^{54} +5051.24i q^{56} +(-2596.71 + 1735.00i) q^{57} +3220.00i q^{58} +2843.66i q^{59} +367.000 q^{61} -11.2250 q^{62} +(-5612.49 - 2325.00i) q^{63} +4472.00 q^{64} +(700.000 + 1047.66i) q^{66} -2235.00i q^{67} +1002.76 q^{68} +(4872.00 - 3255.24i) q^{69} +486.415i q^{71} +(-2087.84 + 5040.00i) q^{72} -6970.00i q^{73} -8343.90i q^{74} -694.000 q^{76} -2806.24 q^{77} +(1028.96 + 1540.00i) q^{78} -4518.00 q^{79} +(-4639.00 - 4639.66i) q^{81} -8260.00i q^{82} -314.299 q^{83} +(-750.000 - 1122.50i) q^{84} +5518.94i q^{86} +(-4302.91 - 6440.00i) q^{87} +2520.00i q^{88} -8081.98i q^{89} -4125.00 q^{91} +1302.10 q^{92} +(22.4499 - 15.0000i) q^{93} +6944.00 q^{94} +(-1904.00 + 1272.16i) q^{96} +4535.00i q^{97} -12063.1 q^{98} +(-2800.00 - 1159.91i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 8 q^{4} - 112 q^{6} + 124 q^{9}+O(q^{10}) $ 4 * q - 8 * q^4 - 112 * q^6 + 124 * q^9	$ 4 q - 8 q^{4} - 112 q^{6} + 124 q^{9} - 880 q^{16} + 1388 q^{19} + 1500 q^{21} + 2016 q^{24} - 12 q^{31} - 7504 q^{34} - 248 q^{36} + 1100 q^{39} - 9744 q^{46} - 12896 q^{49} + 15008 q^{51} + 2128 q^{54} + 1468 q^{61} + 17888 q^{64} + 2800 q^{66} + 19488 q^{69} - 2776 q^{76} - 18072 q^{79} - 18556 q^{81} - 3000 q^{84} - 16500 q^{91} + 27776 q^{94} - 7616 q^{96} - 11200 q^{99}+O(q^{100}) $ 4 * q - 8 * q^4 - 112 * q^6 + 124 * q^9 - 880 * q^16 + 1388 * q^19 + 1500 * q^21 + 2016 * q^24 - 12 * q^31 - 7504 * q^34 - 248 * q^36 + 1100 * q^39 - 9744 * q^46 - 12896 * q^49 + 15008 * q^51 + 2128 * q^54 + 1468 * q^61 + 17888 * q^64 + 2800 * q^66 + 19488 * q^69 - 2776 * q^76 - 18072 * q^79 - 18556 * q^81 - 3000 * q^84 - 16500 * q^91 + 27776 * q^94 - 7616 * q^96 - 11200 * 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 $

$2$	3.74166			0.935414			0.467707	−	0.883883i	$-0.345080\pi$
$2$	3.74166			0.935414			0.467707	+	0.883883i	$0.345080\pi$
$3$	−7.48331	+	5.00000i	−0.831479	+	0.555556i
$3$	−7.48331	+	5.00000i	−0.831479	+	0.555556i
$4$	−2.00000			−0.125000
$5$		0			0
$5$		0			0
$6$	−28.0000	+	18.7083i	−0.777778	+	0.519675i
$7$		−	75.0000i		−	1.53061i	−0.643666	−	0.765306i	$-0.722588\pi$
$7$		−	75.0000i		−	1.53061i	0.643666	−	0.765306i	$-0.277412\pi$
$8$	−67.3498			−1.05234
$9$	31.0000	−	74.8331i	0.382716	−	0.923866i
$10$		0			0
$11$		−	37.4166i		−	0.309228i	−0.987975	−	0.154614i	$-0.950587\pi$
$11$		−	37.4166i		−	0.309228i	0.987975	−	0.154614i	$-0.0494134\pi$
$12$	14.9666	−	10.0000i	0.103935	−	0.0694444i
$13$		−	55.0000i		−	0.325444i	−0.986672	−	0.162722i	$-0.947973\pi$
$13$		−	55.0000i		−	0.325444i	0.986672	−	0.162722i	$-0.0520273\pi$
$14$		−	280.624i		−	1.43176i
$15$		0			0
$16$	−220.000			−0.859375
$17$	−501.382			−1.73489			−0.867443	−	0.497536i	$-0.834238\pi$
$17$	−501.382			−1.73489			−0.867443	+	0.497536i	$0.834238\pi$
$18$	115.991	−	280.000i	0.357998	−	0.864198i
$19$	347.000			0.961219			0.480609	−	0.876935i	$-0.340415\pi$
$19$	347.000			0.961219			0.480609	+	0.876935i	$0.340415\pi$
$20$		0			0
$21$	375.000	+	561.249i	0.850340	+	1.27267i
$22$		−	140.000i		−	0.289256i
$23$	−651.048			−1.23072			−0.615358	−	0.788248i	$-0.710988\pi$
$23$	−651.048			−1.23072			−0.615358	+	0.788248i	$0.710988\pi$
$24$	504.000	−	336.749i	0.875000	−	0.584634i
$25$		0			0
$26$		−	205.791i		−	0.304425i
$27$	142.183	+	715.000i	0.195038	+	0.980796i
$28$			150.000i			0.191327i
$29$			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	$0.500497\pi$
$32$	254.433			0.248469
$33$	187.083	+	280.000i	0.171793	+	0.257117i
$34$	−1876.00			−1.62284
$35$		0			0
$36$	−62.0000	+	149.666i	−0.0478395	+	0.115483i
$37$		−	2230.00i		−	1.62893i	−0.580215	−	0.814463i	$-0.697032\pi$
$37$		−	2230.00i		−	1.62893i	0.580215	−	0.814463i	$-0.302968\pi$
$38$	1298.36			0.899138
$39$	275.000	+	411.582i	0.180802	+	0.270600i
$40$		0			0
$41$		−	2207.58i		−	1.31325i	−0.754216	−	0.656626i	$-0.771983\pi$
$41$		−	2207.58i		−	1.31325i	0.754216	−	0.656626i	$-0.228017\pi$
$42$	1403.12	+	2100.00i	0.795420	+	1.19048i
$43$			1475.00i			0.797729i	0.917010	+	0.398864i	$0.130596\pi$
$43$			1475.00i			0.797729i	−0.917010	+	0.398864i	$0.869404\pi$
$44$			74.8331i			0.0386535i
$45$		0			0
$46$	−2436.00			−1.15123
$47$	1855.86			0.840137			0.420068	−	0.907492i	$-0.362006\pi$
$47$	1855.86			0.840137			0.420068	+	0.907492i	$0.362006\pi$
$48$	1646.33	−	1100.00i	0.714553	−	0.477431i
$49$	−3224.00			−1.34277
$50$		0			0
$51$	3752.00	−	2506.91i	1.44252	−	0.963826i
$52$			110.000i			0.0406805i
$53$	546.282			0.194476			0.0972378	−	0.995261i	$-0.468999\pi$
$53$	546.282			0.194476			0.0972378	+	0.995261i	$0.468999\pi$
$54$	532.000	+	2675.29i	0.182442	+	0.917450i
$55$		0			0
$56$			5051.24i			1.61073i
$57$	−2596.71	+	1735.00i	−0.799234	+	0.534010i
$58$			3220.00i			0.957194i
$59$			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	$0.484296\pi$
$62$	−11.2250			−0.00292013
$63$	−5612.49	−	2325.00i	−1.41408	−	0.585790i
$64$	4472.00			1.09180
$65$		0			0
$66$	700.000	+	1047.66i	0.160698	+	0.240511i
$67$		−	2235.00i		−	0.497884i	−0.968518	−	0.248942i	$-0.919917\pi$
$67$		−	2235.00i		−	0.497884i	0.968518	−	0.248942i	$-0.0800828\pi$
$68$	1002.76			0.216861
$69$	4872.00	−	3255.24i	1.02331	−	0.683731i
$70$		0			0
$71$			486.415i			0.0964919i	0.998835	+	0.0482459i	$0.0153631\pi$
$71$			486.415i			0.0964919i	−0.998835	+	0.0482459i	$0.984637\pi$
$72$	−2087.84	+	5040.00i	−0.402748	+	0.972222i
$73$		−	6970.00i		−	1.30794i	−0.756521	−	0.653969i	$-0.773103\pi$
$73$		−	6970.00i		−	1.30794i	0.756521	−	0.653969i	$-0.226897\pi$
$74$		−	8343.90i		−	1.52372i
$75$		0			0
$76$	−694.000			−0.120152
$77$	−2806.24			−0.473308
$78$	1028.96	+	1540.00i	0.169125	+	0.253123i
$79$	−4518.00			−0.723922			−0.361961	−	0.932193i	$-0.617893\pi$
$79$	−4518.00			−0.723922			−0.361961	+	0.932193i	$0.617893\pi$
$80$		0			0
$81$	−4639.00	−	4639.66i	−0.707057	−	0.707157i
$82$		−	8260.00i		−	1.22844i
$83$	−314.299			−0.0456233			−0.0228117	−	0.999740i	$-0.507262\pi$
$83$	−314.299			−0.0456233			−0.0228117	+	0.999740i	$0.507262\pi$
$84$	−750.000	−	1122.50i	−0.106293	−	0.159084i
$85$		0			0
$86$			5518.94i			0.746207i
$87$	−4302.91	−	6440.00i	−0.568491	−	0.850839i
$88$			2520.00i			0.325413i
$89$		−	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
$92$	1302.10			0.153839
$93$	22.4499	−	15.0000i	0.00259567	−	0.00173430i
$94$	6944.00			0.785876
$95$		0			0
$96$	−1904.00	+	1272.16i	−0.206597	+	0.138039i
$97$			4535.00i			0.481985i	0.970527	+	0.240993i	$0.0774730\pi$
$97$			4535.00i			0.481985i	−0.970527	+	0.240993i	$0.922527\pi$
$98$	−12063.1			−1.25605
$99$	−2800.00	−	1159.91i	−0.285685	−	0.118346i
$100$		0			0
$101$		−	10663.7i		−	1.04536i	−0.852529	−	0.522680i	$-0.824932\pi$
$101$		−	10663.7i		−	1.04536i	0.852529	−	0.522680i	$-0.175068\pi$
$102$	14038.7	−	9380.00i	1.34936	−	0.901576i
$103$		−	2390.00i		−	0.225280i	−0.993636	−	0.112640i	$-0.964069\pi$
$103$		−	2390.00i		−	0.225280i	0.993636	−	0.112640i	$-0.0359307\pi$
$104$			3704.24i			0.342478i
$105$		0			0
$106$	2044.00			0.181915
$107$	−3345.04			−0.292169			−0.146084	−	0.989272i	$-0.546667\pi$
$107$	−3345.04			−0.292169			−0.146084	+	0.989272i	$0.546667\pi$
$108$	−284.366	−	1430.00i	−0.0243798	−	0.122599i
$109$	2137.00			0.179867			0.0899335	−	0.995948i	$-0.471335\pi$
$109$	2137.00			0.179867			0.0899335	+	0.995948i	$0.471335\pi$
$110$		0			0
$111$	11150.0	+	16687.8i	0.904959	+	1.35442i
$112$			16500.0i			1.31537i
$113$	7618.01			0.596602			0.298301	−	0.954472i	$-0.403580\pi$
$113$	7618.01			0.596602			0.298301	+	0.954472i	$0.403580\pi$
$114$	−9716.00	+	6491.78i	−0.747615	+	0.499521i
$115$		0			0
$116$		−	1721.16i		−	0.127910i
$117$	−4115.82	−	1705.00i	−0.300666	−	0.124553i
$118$			10640.0i			0.764148i
$119$			37603.7i			2.65544i
$120$		0			0
$121$	13241.0			0.904378
$122$	1373.19			0.0922594
$123$	11037.9	+	16520.0i	0.729585	+	1.09194i
$124$	6.00000			0.000390219
$125$		0			0
$126$	−21000.0	−	8699.35i	−1.32275	−	0.547956i
$127$			26830.0i			1.66346i	0.555178	+	0.831732i	$0.312650\pi$
$127$			26830.0i			1.66346i	−0.555178	+	0.831732i	$0.687350\pi$
$128$	12661.8			0.772813
$129$	−7375.00	−	11037.9i	−0.443183	−	0.663295i
$130$		0			0
$131$		−	11337.2i		−	0.660639i	−0.943869	−	0.330319i	$-0.892844\pi$
$131$		−	11337.2i		−	0.660639i	0.943869	−	0.330319i	$-0.107156\pi$
$132$	−374.166	−	560.000i	−0.0214742	−	0.0321396i
$133$		−	26025.0i		−	1.47125i
$134$		−	8362.60i		−	0.465728i
$135$		0			0
$136$	33768.0			1.82569
$137$	6869.68			0.366012			0.183006	−	0.983112i	$-0.441417\pi$
$137$	6869.68			0.366012			0.183006	+	0.983112i	$0.441417\pi$
$138$	18229.4	−	12180.0i	0.957223	−	0.639572i
$139$	4642.00			0.240257			0.120128	−	0.992758i	$-0.461669\pi$
$139$	4642.00			0.240257			0.120128	+	0.992758i	$0.461669\pi$
$140$		0			0
$141$	−13888.0	+	9279.31i	−0.698556	+	0.466743i
$142$			1820.00i			0.0902599i
$143$	−2057.91			−0.100636
$144$	−6820.00	+	16463.3i	−0.328897	+	0.793947i
$145$		0			0
$146$		−	26079.4i		−	1.22346i
$147$	24126.2	−	16120.0i	1.11649	−	0.745985i
$148$			4460.00i			0.203616i
$149$		−	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	$0.669268\pi$
$152$	−23370.4			−1.01153
$153$	−15542.8	+	37520.0i	−0.663969	+	1.60280i
$154$	−10500.0			−0.442739
$155$		0			0
$156$	−550.000	−	823.165i	−0.0226003	−	0.0338250i
$157$		−	13225.0i		−	0.536533i	−0.963345	−	0.268266i	$-0.913549\pi$
$157$		−	13225.0i		−	0.536533i	0.963345	−	0.268266i	$-0.0864508\pi$
$158$	−16904.8			−0.677167
$159$	−4088.00	+	2731.41i	−0.161702	+	0.108042i
$160$		0			0
$161$			48828.6i			1.88375i
$162$	−17357.5	−	17360.0i	−0.661391	−	0.661485i
$163$			24595.0i			0.925703i	0.886436	+	0.462851i	$0.153174\pi$
$163$			24595.0i			0.925703i	−0.886436	+	0.462851i	$0.846826\pi$
$164$			4415.16i			0.164157i
$165$		0			0
$166$	−1176.00			−0.0426767
$167$	41779.3			1.49806			0.749029	−	0.662537i	$-0.230520\pi$
$167$	41779.3			1.49806			0.749029	+	0.662537i	$0.230520\pi$
$168$	−25256.2	−	37800.0i	−0.894848	−	1.33929i
$169$	25536.0			0.894086
$170$		0			0
$171$	10757.0	−	25967.1i	0.367874	−	0.888037i
$172$		−	2950.00i		−	0.0997161i
$173$	−10753.5			−0.359301			−0.179651	−	0.983730i	$-0.557497\pi$
$173$	−10753.5			−0.359301			−0.179651	+	0.983730i	$0.557497\pi$
$174$	−16100.0	−	24096.3i	−0.531774	−	0.795887i
$175$		0			0
$176$			8231.65i			0.265743i
$177$	−14218.3	−	21280.0i	−0.453838	−	0.679243i
$178$		−	30240.0i		−	0.954425i
$179$		−	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	$0.631755\pi$
$182$	−15434.3			−0.465956
$183$	−2746.38	+	1835.00i	−0.0820083	+	0.0547941i
$184$	43848.0			1.29513
$185$		0			0
$186$	84.0000	−	56.1249i	0.00242803	−	0.00162229i
$187$			18760.0i			0.536475i
$188$	−3711.72			−0.105017
$189$	53625.0	−	10663.7i	1.50122	−	0.298528i
$190$		0			0
$191$			22487.4i			0.616413i	0.951319	+	0.308206i	$0.0997288\pi$
$191$			22487.4i			0.616413i	−0.951319	+	0.308206i	$0.900271\pi$
$192$	−33465.4	+	22360.0i	−0.907807	+	0.606554i
$193$		−	14375.0i		−	0.385916i	−0.981207	−	0.192958i	$-0.938192\pi$
$193$		−	14375.0i		−	0.385916i	0.981207	−	0.192958i	$-0.0618082\pi$
$194$			16968.4i			0.450856i
$195$		0			0
$196$	6448.00			0.167847
$197$	−35560.7			−0.916301			−0.458150	−	0.888875i	$-0.651488\pi$
$197$	−35560.7			−0.916301			−0.458150	+	0.888875i	$0.651488\pi$
$198$	−10476.6	−	4340.00i	−0.267234	−	0.110703i
$199$	−43573.0			−1.10030			−0.550150	−	0.835066i	$-0.685430\pi$
$199$	−43573.0			−1.10030			−0.550150	+	0.835066i	$0.685430\pi$
$200$		0			0
$201$	11175.0	+	16725.2i	0.276602	+	0.413980i
$202$		−	39900.0i		−	0.977845i
$203$	64543.6			1.56625
$204$	−7504.00	+	5013.82i	−0.180315	+	0.120478i
$205$		0			0
$206$		−	8942.56i		−	0.210731i
$207$	−20182.5	+	48720.0i	−0.471014	+	1.13702i
$208$			12100.0i			0.279678i
$209$		−	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	$0.442792\pi$
$212$	−1092.56			−0.0243095
$213$	−2432.08	−	3640.00i	−0.0536066	−	0.0802310i
$214$	−12516.0			−0.273299
$215$		0			0
$216$	−9576.00	−	48155.1i	−0.205247	−	1.03213i
$217$			225.000i			0.00477819i
$218$	7995.92			0.168250
$219$	34850.0	+	52158.7i	0.726632	+	1.08752i
$220$		0			0
$221$			27576.0i			0.564608i
$222$	41719.5	+	62440.0i	0.846512	+	1.26694i
$223$		−	40445.0i		−	0.813308i	−0.913582	−	0.406654i	$-0.866695\pi$
$223$		−	40445.0i		−	0.813308i	0.913582	−	0.406654i	$-0.133305\pi$
$224$		−	19082.5i		−	0.380310i
$225$		0			0
$226$	28504.0			0.558070
$227$	46119.7			0.895024			0.447512	−	0.894278i	$-0.352310\pi$
$227$	46119.7			0.895024			0.447512	+	0.894278i	$0.352310\pi$
$228$	5193.42	−	3470.00i	0.0999042	−	0.0667513i
$229$	−36543.0			−0.696840			−0.348420	−	0.937338i	$-0.613282\pi$
$229$	−36543.0			−0.696840			−0.348420	+	0.937338i	$0.613282\pi$
$230$		0			0
$231$	21000.0	−	14031.2i	0.393546	−	0.262949i
$232$		−	57960.0i		−	1.07684i
$233$	−83940.3			−1.54618			−0.773088	−	0.634299i	$-0.781289\pi$
$233$	−83940.3			−1.54618			−0.773088	+	0.634299i	$0.781289\pi$
$234$	−15400.0	−	6379.53i	−0.281248	−	0.116508i
$235$		0			0
$236$		−	5687.32i		−	0.102114i
$237$	33809.6	−	22590.0i	0.601927	−	0.402179i
$238$			140700.i			2.48393i
$239$			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	$0.845311\pi$
$242$	49543.3			0.845968
$243$	57913.4	+	11525.0i	0.980768	+	0.195177i
$244$	−734.000			−0.0123287
$245$		0			0
$246$	41300.0	+	61812.2i	0.682464	+	1.02142i
$247$		−	19085.0i		−	0.312823i
$248$	202.049			0.00328514
$249$	2352.00	−	1571.50i	0.0379349	−	0.0253463i
$250$		0			0
$251$		−	72962.3i		−	1.15811i	−0.815287	−	0.579057i	$-0.803421\pi$
$251$		−	72962.3i		−	1.15811i	0.815287	−	0.579057i	$-0.196579\pi$
$252$	11225.0	+	4650.00i	0.176760	+	0.0732237i
$253$			24360.0i			0.380571i
$254$			100389.i			1.55603i
$255$		0			0
$256$	−24176.0			−0.368896
$257$	−55541.2			−0.840908			−0.420454	−	0.907314i	$-0.638129\pi$
$257$	−55541.2			−0.840908			−0.420454	+	0.907314i	$0.638129\pi$
$258$	−27594.7	−	41300.0i	−0.414559	−	0.620456i
$259$	−167250.			−2.49325
$260$		0			0
$261$	64400.0	+	26678.0i	0.945377	+	0.391627i
$262$		−	42420.0i		−	0.617971i
$263$	106585.			1.54093			0.770467	−	0.637480i	$-0.220023\pi$
$263$	106585.			1.54093			0.770467	+	0.637480i	$0.220023\pi$
$264$	−12600.0	−	18858.0i	−0.180785	−	0.270574i
$265$		0			0
$266$		−	97376.6i		−	1.37623i
$267$	40409.9	+	60480.0i	0.566846	+	0.848378i
$268$			4470.00i			0.0622355i
$269$		−	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.			1.49092
$273$	30868.7	−	20625.0i	0.414183	−	0.276738i
$274$	25704.0			0.342373
$275$		0			0
$276$	−9744.00	+	6510.48i	−0.127914	+	0.0854663i
$277$			50055.0i			0.652361i	0.945308	+	0.326180i	$0.105762\pi$
$277$			50055.0i			0.652361i	−0.945308	+	0.326180i	$0.894238\pi$
$278$	17368.8			0.224740
$279$	−93.0000	+	224.499i	−0.00119474	+	0.00288408i
$280$		0			0
$281$		−	42767.1i		−	0.541624i	−0.962632	−	0.270812i	$-0.912708\pi$
$281$		−	42767.1i		−	0.541624i	0.962632	−	0.270812i	$-0.0872921\pi$
$282$	−51964.1	+	34720.0i	−0.653440	+	0.436598i
$283$		−	33885.0i		−	0.423092i	−0.977368	−	0.211546i	$-0.932150\pi$
$283$		−	33885.0i		−	0.423092i	0.977368	−	0.211546i	$-0.0678498\pi$
$284$		−	972.831i		−	0.0120615i
$285$		0			0
$286$	−7700.00			−0.0941366
$287$	−165568.			−2.01008
$288$	7887.41	−	19040.0i	0.0950932	−	0.229552i
$289$	167863.			2.00983
$290$		0			0
$291$	−22675.0	−	33936.8i	−0.267770	−	0.400761i
$292$			13940.0i			0.163492i
$293$	−132993.			−1.54916			−0.774578	−	0.632479i	$-0.782038\pi$
$293$	−132993.			−1.54916			−0.774578	+	0.632479i	$0.782038\pi$
$294$	90272.0	−	60315.5i	1.04438	−	0.697806i
$295$		0			0
$296$			150190.i			1.71419i
$297$	26752.9	−	5320.00i	0.303289	−	0.0603113i
$298$		−	43400.0i		−	0.488717i
$299$			35807.7i			0.400529i
$300$		0			0
$301$	110625.			1.22101
$302$	−86518.3			−0.948624
$303$	53318.6	+	79800.0i	0.580756	+	0.869196i
$304$	−76340.0			−0.826047
$305$		0			0
$306$	−58156.0	+	140387.i	−0.621086	+	1.49928i
$307$		−	135875.i		−	1.44166i	−0.693112	−	0.720830i	$-0.743761\pi$
$307$		−	135875.i		−	1.44166i	0.693112	−	0.720830i	$-0.256239\pi$
$308$	5612.49			0.0591635
$309$	11950.0	+	17885.1i	0.125156	+	0.187316i
$310$		0			0
$311$		−	28286.9i		−	0.292459i	−0.989251	−	0.146230i	$-0.953286\pi$
$311$		−	28286.9i		−	0.292459i	0.989251	−	0.146230i	$-0.0467138\pi$
$312$	−18521.2	−	27720.0i	−0.190265	−	0.284763i
$313$		−	170255.i		−	1.73785i	−0.494948	−	0.868923i	$-0.664813\pi$
$313$		−	170255.i		−	1.73785i	0.494948	−	0.868923i	$-0.335187\pi$
$314$		−	49483.4i		−	0.501881i
$315$		0			0
$316$	9036.00			0.0904903
$317$	−10790.9			−0.107384			−0.0536921	−	0.998558i	$-0.517099\pi$
$317$	−10790.9			−0.107384			−0.0536921	+	0.998558i	$0.517099\pi$
$318$	−15295.9	+	10220.0i	−0.151259	+	0.101064i
$319$	32200.0			0.316428
$320$		0			0
$321$	25032.0	−	16725.2i	0.242932	−	0.162316i
$322$			182700.i			1.76208i
$323$	−173980.			−1.66761
$324$	9278.00	+	9279.31i	0.0883821	+	0.0883946i
$325$		0			0
$326$			92026.1i			0.865916i
$327$	−15991.8	+	10685.0i	−0.149556	+	0.0999261i
$328$			148680.i			1.38199i
$329$		−	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	$0.535486\pi$
$332$	628.598			0.00570292
$333$	−166878.	−	69130.0i	−1.50491	−	0.623416i
$334$	156324.			1.40131
$335$		0			0
$336$	−82500.0	−	123475.i	−0.730761	−	1.09370i
$337$		−	81905.0i		−	0.721192i	−0.932722	−	0.360596i	$-0.882573\pi$
$337$		−	81905.0i		−	0.721192i	0.932722	−	0.360596i	$-0.117427\pi$
$338$	95547.0			0.836341
$339$	−57008.0	+	38090.1i	−0.496063	+	0.331446i
$340$		0			0
$341$			112.250i			0.000965332i
$342$	40249.0	−	97160.0i	0.344115	−	0.830683i
$343$			61725.0i			0.524654i
$344$		−	99341.0i		−	0.839483i
$345$		0			0
$346$	−40236.0			−0.336095
$347$	210640.			1.74937			0.874687	−	0.484688i	$-0.161067\pi$
$347$	210640.			1.74937			0.874687	+	0.484688i	$0.161067\pi$
$348$	8605.81	+	12880.0i	0.0710613	+	0.106355i
$349$	−9298.00			−0.0763376			−0.0381688	−	0.999271i	$-0.512152\pi$
$349$	−9298.00			−0.0763376			−0.0381688	+	0.999271i	$0.512152\pi$
$350$		0			0
$351$	39325.0	−	7820.06i	0.319194	−	0.0634740i
$352$		−	9520.00i		−	0.0768337i
$353$	55922.8			0.448786			0.224393	−	0.974499i	$-0.427960\pi$
$353$	55922.8			0.448786			0.224393	+	0.974499i	$0.427960\pi$
$354$	−53200.0	−	79622.5i	−0.424527	−	0.635374i
$355$		0			0
$356$			16164.0i			0.127540i
$357$	−188018.	−	281400.i	−1.47524	−	2.20794i
$358$		−	218680.i		−	1.70625i
$359$			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
$362$	−98603.9			−0.752449
$363$	−99086.6	+	66205.0i	−0.751972	+	0.502432i
$364$	8250.00			0.0622660
$365$		0			0
$366$	−10276.0	+	6865.94i	−0.0767118	+	0.0512552i
$367$			142965.i			1.06145i	0.847546	+	0.530723i	$0.178079\pi$
$367$			142965.i			1.06145i	−0.847546	+	0.530723i	$0.821921\pi$
$368$	143231.			1.05765
$369$	−165200.	−	68434.9i	−1.21327	−	0.502603i
$370$		0			0
$371$		−	40971.1i		−	0.297667i
$372$	−44.8999	+	30.0000i	−0.000324459	+	0.000216788i
$373$			134705.i			0.968202i	0.875012	+	0.484101i	$0.160853\pi$
$373$			134705.i			0.968202i	−0.875012	+	0.484101i	$0.839147\pi$
$374$			70193.5i			0.501827i
$375$		0			0
$376$	−124992.			−0.884110
$377$	47332.0			0.333021
$378$	200646.	−	39900.0i	1.40426	−	0.279248i
$379$	−18493.0			−0.128745			−0.0643723	−	0.997926i	$-0.520505\pi$
$379$	−18493.0			−0.128745			−0.0643723	+	0.997926i	$0.520505\pi$
$380$		0			0
$381$	−134150.	−	200777.i	−0.924146	−	1.38314i
$382$			84140.0i			0.576602i
$383$	101833.			0.694210			0.347105	−	0.937826i	$-0.387165\pi$
$383$	101833.			0.694210			0.347105	+	0.937826i	$0.387165\pi$
$384$	−94752.0	+	63308.8i	−0.642578	+	0.429341i
$385$		0			0
$386$		−	53786.3i		−	0.360992i
$387$	110379.	+	45725.0i	0.736994	+	0.305304i
$388$		−	9070.00i		−	0.0602482i
$389$			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.			1.41306
$393$	56686.1	+	84840.0i	0.367022	+	0.549308i
$394$	−133056.			−0.857121
$395$		0			0
$396$	5600.00	+	2319.83i	0.0357106	+	0.0147933i
$397$			244735.i			1.55280i	0.630241	+	0.776399i	$0.282956\pi$
$397$			244735.i			1.55280i	−0.630241	+	0.776399i	$0.717044\pi$
$398$	−163035.			−1.02924
$399$	130125.	+	194753.i	0.817363	+	1.22332i
$400$		0			0
$401$			201488.i			1.25303i	0.779410	+	0.626514i	$0.215519\pi$
$401$			201488.i			1.25303i	−0.779410	+	0.626514i	$0.784481\pi$
$402$	41813.0	+	62580.0i	0.258738	+	0.387243i
$403$			165.000i			0.00101595i
$404$			21327.4i			0.130670i
$405$		0			0
$406$	241500.			1.46509
$407$	−83439.0			−0.503709
$408$	−252697.	+	168840.i	−1.51803	+	1.01427i
$409$	203737.			1.21793			0.608966	−	0.793196i	$-0.291584\pi$
$409$	203737.			1.21793			0.608966	+	0.793196i	$0.291584\pi$
$410$		0			0
$411$	−51408.0	+	34348.4i	−0.304332	+	0.203340i
$412$			4780.00i			0.0281601i
$413$	213274.			1.25037
$414$	−75516.0	+	182294.i	−0.440594	+	1.06358i
$415$		0			0
$416$		−	13993.8i		−	0.0808628i
$417$	−34737.5	+	23210.0i	−0.199769	+	0.133476i
$418$		−	48580.0i		−	0.278039i
$419$			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	$0.468085\pi$
$422$	59556.0			0.334426
$423$	57531.7	−	138880.i	0.321534	−	0.776174i
$424$	−36792.0			−0.204655
$425$		0			0
$426$	−9100.00	−	13619.6i	−0.0501444	−	0.0750492i
$427$		−	27525.0i		−	0.150963i
$428$	6690.08			0.0365211
$429$	15400.0	−	10289.6i	0.0836770	−	0.0559091i
$430$		0			0
$431$			38052.7i			0.204847i	0.994741	+	0.102424i	$0.0326597\pi$
$431$			38052.7i			0.204847i	−0.994741	+	0.102424i	$0.967340\pi$
$432$	−31280.3	−	157300.i	−0.167611	−	0.842871i
$433$			43265.0i			0.230760i	0.993321	+	0.115380i	$0.0368086\pi$
$433$			43265.0i			0.230760i	−0.993321	+	0.115380i	$0.963191\pi$
$434$			841.873i			0.00446958i
$435$		0			0
$436$	−4274.00			−0.0224834
$437$	−225914.			−1.18299
$438$	130397.	+	195160.i	0.679702	+	1.01728i
$439$	−89533.0			−0.464573			−0.232287	−	0.972647i	$-0.574621\pi$
$439$	−89533.0			−0.464573			−0.232287	+	0.972647i	$0.574621\pi$
$440$		0			0
$441$	−99944.0	+	241262.i	−0.513901	+	1.24054i
$442$			103180.i			0.528142i
$443$	−161056.			−0.820671			−0.410336	−	0.911935i	$-0.634588\pi$
$443$	−161056.			−0.820671			−0.410336	+	0.911935i	$0.634588\pi$
$444$	−22300.0	−	33375.6i	−0.113120	−	0.169302i
$445$		0			0
$446$		−	151331.i		−	0.760780i
$447$	57995.7	+	86800.0i	0.290256	+	0.434415i
$448$		−	335400.i		−	1.67112i
$449$			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
$452$	−15236.0			−0.0745753
$453$	173037.	−	115615.i	0.843222	−	0.563401i
$454$	172564.			0.837218
$455$		0			0
$456$	174888.	−	116852.i	0.841066	−	0.561961i
$457$			63850.0i			0.305723i	0.988248	+	0.152862i	$0.0488489\pi$
$457$			63850.0i			0.305723i	−0.988248	+	0.152862i	$0.951151\pi$
$458$	−136731.			−0.651834
$459$	−71288.0	−	358488.i	−0.338369	−	1.70157i
$460$		0			0
$461$		−	281410.i		−	1.32415i	−0.749437	−	0.662076i	$-0.769676\pi$
$461$		−	281410.i		−	1.32415i	0.749437	−	0.662076i	$-0.230324\pi$
$462$	78574.8	−	52500.0i	0.368128	−	0.245966i
$463$			307770.i			1.43570i	0.696197	+	0.717851i	$0.254874\pi$
$463$			307770.i			1.43570i	−0.696197	+	0.717851i	$0.745126\pi$
$464$		−	189328.i		−	0.879384i
$465$		0			0
$466$	−314076.			−1.44632
$467$	274885.			1.26042			0.630212	−	0.776423i	$-0.282968\pi$
$467$	274885.			1.26042			0.630212	+	0.776423i	$0.282968\pi$
$468$	8231.65	+	3410.00i	0.0375833	+	0.0155691i
$469$	−167625.			−0.762067
$470$		0			0
$471$	66125.0	+	98966.8i	0.298074	+	0.446116i
$472$		−	191520.i		−	0.859667i
$473$	55189.4			0.246680
$474$	126504.	−	84524.0i	0.563051	−	0.376204i
$475$		0			0
$476$		−	75207.3i		−	0.331930i
$477$	16934.7	−	40880.0i	0.0744289	−	0.179669i
$478$			342860.i			1.50059i
$479$		−	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.			−1.65423
$483$	−244143.	−	365400.i	−1.04653	−	1.56630i
$484$	−26482.0			−0.113047
$485$		0			0
$486$	216692.	+	43122.6i	0.917425	+	0.182571i
$487$		−	349555.i		−	1.47386i	−0.675967	−	0.736932i	$-0.736274\pi$
$487$		−	349555.i		−	1.47386i	0.675967	−	0.736932i	$-0.263726\pi$
$488$	−24717.4			−0.103792
$489$	−122975.	−	184052.i	−0.514279	−	0.769703i
$490$		0			0
$491$			130808.i			0.542591i	0.962496	+	0.271295i	$0.0874520\pi$
$491$			130808.i			0.542591i	−0.962496	+	0.271295i	$0.912548\pi$
$492$	−22075.8	−	33040.0i	−0.0911981	−	0.136493i
$493$		−	431480.i		−	1.77528i
$494$		−	71409.5i		−	0.292619i
$495$		0			0
$496$	660.000			0.00268275
$497$	36481.2			0.147692
$498$	8800.38	−	5880.00i	0.0354848	−	0.0237093i
$499$	212027.			0.851511			0.425755	−	0.904838i	$-0.360008\pi$
$499$	212027.			0.851511			0.425755	+	0.904838i	$0.360008\pi$
$500$		0			0
$501$	−312648.	+	208897.i	−1.24560	+	0.832255i
$502$		−	273000.i		−	1.08332i
$503$	77624.4			0.306805			0.153402	−	0.988164i	$-0.450977\pi$
$503$	77624.4			0.306805			0.153402	+	0.988164i	$0.450977\pi$
$504$	378000.	+	156588.i	1.48810	+	0.616451i
$505$		0			0
$506$			91146.8i			0.355992i
$507$	−191094.	+	127680.i	−0.743414	+	0.496715i
$508$		−	53660.0i		−	0.207933i
$509$		−	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.			−1.11788
$513$	49337.5	+	248105.i	0.187475	+	0.942759i
$514$	−207816.			−0.786598
$515$		0			0
$516$	14750.0	+	22075.8i	0.0553978	+	0.0829119i
$517$		−	69440.0i		−	0.259794i
$518$	−625792.			−2.33223
$519$	80472.0	−	53767.6i	0.298751	−	0.199612i
$520$		0			0
$521$		−	166766.i		−	0.614372i	−0.951650	−	0.307186i	$-0.900613\pi$
$521$		−	166766.i		−	0.614372i	0.951650	−	0.307186i	$-0.0993873\pi$
$522$	240963.	+	99820.0i	0.884319	+	0.366333i
$523$			307355.i			1.12367i	0.827251	+	0.561833i	$0.189903\pi$
$523$			307355.i			1.12367i	−0.827251	+	0.561833i	$0.810097\pi$
$524$			22674.4i			0.0825798i
$525$		0			0
$526$	398804.			1.44141
$527$	1504.15			0.00541588
$528$	−41158.2	−	61600.0i	−0.147635	−	0.220960i
$529$	144023.			0.514660
$530$		0			0
$531$	212800.	+	88153.4i	0.754714	+	0.312644i
$532$			52050.0i			0.183907i
$533$	−121417.			−0.427390
$534$	151200.	+	226295.i	0.530236	+	0.793585i
$535$		0			0
$536$			150527.i			0.523944i
$537$	292223.	+	437360.i	1.01337	+	1.51667i
$538$		−	330820.i		−	1.14295i
$539$			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	$0.103845\pi$
$542$	−50205.6			−0.170904
$543$	197208.	−	131765.i	0.668843	−	0.446890i
$544$	−127568.			−0.431066
$545$		0			0
$546$	115500.	−	77171.7i	0.387433	−	0.258865i
$547$		−	96290.0i		−	0.321815i	−0.986969	−	0.160908i	$-0.948558\pi$
$547$		−	96290.0i		−	0.321815i	0.986969	−	0.160908i	$-0.0514421\pi$
$548$	−13739.4			−0.0457515
$549$	11377.0	−	27463.8i	0.0377471	−	0.0911204i
$550$		0			0
$551$			298622.i			0.983599i
$552$	−328128.	+	219240.i	−1.07688	+	0.719518i
$553$			338850.i			1.10804i
$554$			187289.i			0.610228i
$555$		0			0
$556$	−9284.00			−0.0300321
$557$	350803.			1.13071			0.565357	−	0.824846i	$-0.308738\pi$
$557$	350803.			1.13071			0.565357	+	0.824846i	$0.308738\pi$
$558$	−347.974	+	840.000i	−0.00111758	+	0.00269781i
$559$	81125.0			0.259616
$560$		0			0
$561$	−93800.0	−	140387.i	−0.298042	−	0.446068i
$562$		−	160020.i		−	0.506643i
$563$	438470.			1.38332			0.691660	−	0.722223i	$-0.256879\pi$
$563$	438470.			1.38332			0.691660	+	0.722223i	$0.256879\pi$
$564$	27776.0	−	18558.6i	0.0873196	−	0.0583428i
$565$		0			0
$566$		−	126786.i		−	0.395766i
$567$	−347974.	+	347925.i	−1.08238	+	1.08223i
$568$		−	32760.0i		−	0.101542i
$569$		−	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	$0.829204\pi$
$572$	4115.82			0.0125795
$573$	−112437.	−	168280.i	−0.342452	−	0.512535i
$574$	−619500.			−1.88026
$575$		0			0
$576$	138632.	−	334654.i	0.417848	−	1.00867i
$577$		−	42745.0i		−	0.128391i	−0.997937	−	0.0641954i	$-0.979552\pi$
$577$		−	42745.0i		−	0.128391i	0.997937	−	0.0641954i	$-0.0204481\pi$
$578$	628086.			1.88002
$579$	71875.0	+	107573.i	0.214398	+	0.320882i
$580$		0			0
$581$			23572.4i			0.0698316i
$582$	−84842.1	−	126980.i	−0.250476	−	0.374877i
$583$		−	20440.0i		−	0.0601373i
$584$			469428.i			1.37640i
$585$		0			0
$586$	−497616.			−1.44910
$587$	−214824.			−0.623456			−0.311728	−	0.950171i	$-0.600908\pi$
$587$	−214824.			−0.623456			−0.311728	+	0.950171i	$0.600908\pi$
$588$	−48252.4	+	32240.0i	−0.139561	+	0.0932482i
$589$	−1041.00			−0.00300068
$590$		0			0
$591$	266112.	−	177804.i	0.761885	−	0.509056i
$592$			490600.i			1.39986i
$593$	459498.			1.30669			0.653347	−	0.757058i	$-0.273364\pi$
$593$	459498.			1.30669			0.653347	+	0.757058i	$0.273364\pi$
$594$	100100.	−	19905.6i	0.283701	−	0.0564161i
$595$		0			0
$596$			23198.3i			0.0653075i
$597$	326070.	−	217865.i	0.914877	−	0.611278i
$598$			133980.i			0.374660i
$599$		−	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.			1.14215
$603$	−167252.	−	69285.0i	−0.459978	−	0.190548i
$604$	46246.0			0.126765
$605$		0			0
$606$	199500.	+	298584.i	0.543247	+	0.813058i
$607$		−	291050.i		−	0.789933i	−0.918696	−	0.394966i	$-0.870756\pi$
$607$		−	291050.i		−	0.789933i	0.918696	−	0.394966i	$-0.129244\pi$
$608$	88288.1			0.238834
$609$	−483000.	+	322718.i	−1.30230	+	0.870139i
$610$		0			0
$611$		−	102072.i		−	0.273417i
$612$	31085.7	−	75040.0i	0.0829961	−	0.200350i
$613$			415670.i			1.10618i	0.833120	+	0.553092i	$0.186552\pi$
$613$			415670.i			1.10618i	−0.833120	+	0.553092i	$0.813448\pi$
$614$		−	508398.i		−	1.34855i
$615$		0			0
$616$	189000.			0.498081
$617$	671500.			1.76391			0.881954	−	0.471336i	$-0.156228\pi$
$617$	671500.			1.76391			0.881954	+	0.471336i	$0.156228\pi$
$618$	44712.8	+	66920.0i	0.117073	+	0.175218i
$619$	−373853.			−0.975707			−0.487854	−	0.872925i	$-0.662220\pi$
$619$	−373853.			−0.975707			−0.487854	+	0.872925i	$0.662220\pi$
$620$		0			0
$621$	−92568.0	−	465500.i	−0.240037	−	1.20708i
$622$		−	105840.i		−	0.273570i
$623$	−606148.			−1.56172
$624$	−60500.0	−	90548.1i	−0.155377	−	0.232547i
$625$		0			0
$626$		−	637036.i		−	1.62561i
$627$	64917.8	+	97160.0i	0.165131	+	0.247145i
$628$			26450.0i			0.0670666i
$629$			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.			0.761813
$633$	−119112.	+	79585.0i	−0.297268	+	0.198620i
$634$	−40376.0			−0.100449
$635$		0			0
$636$	8176.00	−	5462.82i	0.0202128	−	0.0135053i
$637$			177320.i			0.436997i
$638$	120481.			0.295991
$639$	36400.0	+	15078.9i	0.0891455	+	0.0369290i
$640$		0			0
$641$			780360.i			1.89924i	0.313409	+	0.949618i	$0.398529\pi$
$641$			780360.i			1.89924i	−0.313409	+	0.949618i	$0.601471\pi$
$642$	93661.2	−	62580.0i	0.227242	−	0.151833i
$643$			288450.i			0.697668i	0.937185	+	0.348834i	$0.113422\pi$
$643$			288450.i			0.697668i	−0.937185	+	0.348834i	$0.886578\pi$
$644$		−	97657.3i		−	0.235468i
$645$		0			0
$646$	−650972.			−1.55990
$647$	−320301.			−0.765155			−0.382578	−	0.923923i	$-0.624964\pi$
$647$	−320301.			−0.765155			−0.382578	+	0.923923i	$0.624964\pi$
$648$	312436.	+	312480.i	0.744065	+	0.744170i
$649$	106400.			0.252611
$650$		0			0
$651$	−1125.00	−	1683.75i	−0.00265455	−	0.00397296i
$652$		−	49190.0i		−	0.115713i
$653$	−356221.			−0.835397			−0.417698	−	0.908586i	$-0.637163\pi$
$653$	−356221.			−0.835397			−0.417698	+	0.908586i	$0.637163\pi$
$654$	−59836.0	+	39979.6i	−0.139897	+	0.0934723i
$655$		0			0
$656$			485667.i			1.12858i
$657$	−521587.	−	216070.i	−1.20836	−	0.500569i
$658$		−	520800.i		−	1.20287i
$659$		−	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	$0.100272\pi$
$662$	−91214.1			−0.208135
$663$	−137880.	−	206360.i	−0.313671	−	0.469460i
$664$	21168.0			0.0480113
$665$		0			0
$666$	−624400.	−	258661.i	−1.40771	−	0.583152i
$667$		−	560280.i		−	1.25937i
$668$	−83558.7			−0.187257
$669$	202225.	+	302663.i	0.451838	+	0.676249i
$670$		0			0
$671$		−	13731.9i		−	0.0304990i
$672$	95412.3	+	142800.i	0.211284	+	0.316220i
$673$		−	203370.i		−	0.449011i	−0.974473	−	0.224505i	$-0.927923\pi$
$673$		−	203370.i		−	0.449011i	0.974473	−	0.224505i	$-0.0720766\pi$
$674$		−	306460.i		−	0.674613i
$675$		0			0
$676$	−51072.0			−0.111761
$677$	−554042.			−1.20883			−0.604415	−	0.796669i	$-0.706593\pi$
$677$	−554042.			−1.20883			−0.604415	+	0.796669i	$0.706593\pi$
$678$	−213304.	+	142520.i	−0.464024	+	0.310039i
$679$	340125.			0.737733
$680$		0			0
$681$	−345128.	+	230598.i	−0.744194	+	0.497235i
$682$			420.000i			0.000902985i
$683$	55810.6			0.119640			0.0598198	−	0.998209i	$-0.480947\pi$
$683$	55810.6			0.119640			0.0598198	+	0.998209i	$0.480947\pi$
$684$	−21514.0	+	51934.2i	−0.0459842	+	0.111005i
$685$		0			0
$686$			230954.i			0.490769i
$687$	273463.	−	182715.i	0.579408	−	0.387133i
$688$		−	324500.i		−	0.685548i
$689$		−	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	$0.259201\pi$
$692$	21507.0			0.0449126
$693$	−86993.5	+	210000.i	−0.181143	+	0.437273i
$694$	788144.			1.63639
$695$		0			0
$696$	289800.	+	433733.i	0.598246	+	0.895373i
$697$			1.10684e6i			2.27834i
$698$	−34789.9			−0.0714073
$699$	628152.	−	419702.i	1.28561	−	0.858987i
$700$		0			0
$701$		−	901552.i		−	1.83466i	−0.398131	−	0.917329i	$-0.630341\pi$
$701$		−	901552.i		−	1.83466i	0.398131	−	0.917329i	$-0.369659\pi$
$702$	147141.	−	29260.0i	0.298578	−	0.0593745i
$703$		−	773810.i		−	1.56575i
$704$		−	167327.i		−	0.337614i
$705$		0			0
$706$	209244.			0.419801
$707$	−799779.			−1.60004
$708$	28436.6	+	42560.0i	0.0567298	+	0.0849054i
$709$	176537.			0.351191			0.175595	−	0.984462i	$-0.443815\pi$
$709$	176537.			0.351191			0.175595	+	0.984462i	$0.443815\pi$
$710$		0			0
$711$	−140058.	+	338096.i	−0.277057	+	0.668807i
$712$			544320.i			1.07373i
$713$	1953.15			0.00384198
$714$	−703500.	−	1.05290e6i	−1.37996	−	2.06534i
$715$		0			0
$716$			116889.i			0.228007i
$717$	−458166.	−	685720.i	−0.891219	−	1.33385i
$718$			263340.i			0.510820i
$719$		−	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
$722$	−37087.3			−0.0711461
$723$	768634.	−	513565.i	1.47042	−	0.982469i
$724$	52706.0			0.100550
$725$		0			0
$726$	−370748.	+	247716.i	−0.703405	+	0.469982i
$727$			207605.i			0.392798i	0.980524	+	0.196399i	$0.0629247\pi$
$727$			207605.i			0.392798i	−0.980524	+	0.196399i	$0.937075\pi$
$728$	277818.			0.524201
$729$	−491009.	+	203322.i	−0.923920	+	0.382586i
$730$		0			0
$731$		−	739539.i		−	1.38397i
$732$	5492.75	−	3670.00i	0.0102510	−	0.00684926i
$733$			186190.i			0.346536i	0.984875	+	0.173268i	$0.0554327\pi$
$733$			186190.i			0.346536i	−0.984875	+	0.173268i	$0.944567\pi$
$734$			534926.i			0.992891i
$735$		0			0
$736$	−165648.			−0.305795
$737$	−83626.0			−0.153960
$738$	−618122.	−	256060.i	−1.13491	−	0.470142i
$739$	471242.			0.862889			0.431445	−	0.902139i	$-0.358004\pi$
$739$	471242.			0.862889			0.431445	+	0.902139i	$0.358004\pi$
$740$		0			0
$741$	95425.0	+	142819.i	0.173790	+	0.260106i
$742$		−	153300.i		−	0.278442i
$743$	−568897.			−1.03052			−0.515259	−	0.857034i	$-0.672304\pi$
$743$	−568897.			−1.03052			−0.515259	+	0.857034i	$0.672304\pi$
$744$	−1512.00	+	1010.25i	−0.00273153	+	0.00182508i
$745$		0			0
$746$			504020.i			0.905670i
$747$	−9743.28	+	23520.0i	−0.0174608	+	0.0421499i
$748$		−	37520.0i		−	0.0670594i
$749$			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.			−0.721993
$753$	364812.	+	546000.i	0.643396	+	0.962948i
$754$	177100.			0.311513
$755$		0			0
$756$	−107250.	+	21327.4i	−0.187652	+	0.0373160i
$757$		−	89825.0i		−	0.156749i	−0.996924	−	0.0783746i	$-0.975027\pi$
$757$		−	89825.0i		−	0.156749i	0.996924	−	0.0783746i	$-0.0249730\pi$
$758$	−69194.5			−0.120430
$759$	−121800.	−	182294.i	−0.211429	−	0.316437i
$760$		0			0
$761$			477959.i			0.825319i	0.910885	+	0.412659i	$0.135400\pi$
$761$			477959.i			0.825319i	−0.910885	+	0.412659i	$0.864600\pi$
$762$	−501943.	−	751240.i	−0.864460	−	1.29380i
$763$		−	160275.i		−	0.275307i
$764$		−	44974.7i		−	0.0770516i
$765$		0			0
$766$	381024.			0.649374
$767$	156401.			0.265858
$768$	180917.	−	120880.i	0.306730	−	0.204942i
$769$	−257903.			−0.436118			−0.218059	−	0.975936i	$-0.569972\pi$
$769$	−257903.			−0.436118			−0.218059	+	0.975936i	$0.569972\pi$
$770$		0			0
$771$	415632.	−	277706.i	0.699198	−	0.467171i
$772$			28750.0i			0.0482396i
$773$	−934569.			−1.56406			−0.782028	−	0.623243i	$-0.785815\pi$
$773$	−934569.			−1.56406			−0.782028	+	0.623243i	$0.785815\pi$
$774$	413000.	+	171087.i	0.689395	+	0.285585i
$775$		0			0
$776$		−	305431.i		−	0.507213i
$777$	1.25158e6	−	836250.i	2.07309	−	1.38514i
$778$			278460.i			0.460049i
$779$		−	766030.i		−	1.26232i
$780$		0			0
$781$	18200.0			0.0298380
$782$	1.22137e6			1.99725
$783$	−615316.	+	122360.i	−1.00363	+	0.199580i
$784$	709280.			1.15395
$785$		0			0
$786$	212100.	+	317442.i	0.343317	+	0.513830i
$787$		−	304355.i		−	0.491395i	−0.969347	−	0.245698i	$-0.920983\pi$
$787$		−	304355.i		−	0.491395i	0.969347	−	0.245698i	$-0.0790170\pi$
$788$	71121.4			0.114538
$789$	−797608.	+	532924.i	−1.28125	+	0.856074i
$790$		0			0
$791$		−	571351.i		−	0.913167i
$792$	188580.	+	78120.0i	0.300638	+	0.124541i
$793$		−	20185.0i		−	0.0320983i
$794$			915715.i			1.45251i
$795$		0			0
$796$	87146.0			0.137538
$797$	92029.8			0.144881			0.0724406	−	0.997373i	$-0.476921\pi$
$797$	92029.8			0.144881			0.0724406	+	0.997373i	$0.476921\pi$
$798$	486883.	+	728700.i	0.764573	+	1.14431i
$799$	−930496.			−1.45754
$800$		0			0
$801$	−604800.	−	250541.i	−0.942642	−	0.390494i
$802$			753900.i			1.17210i
$803$	−260794.			−0.404451
$804$	−22350.0	−	33450.4i	−0.0345753	−	0.0517475i
$805$		0			0
$806$			617.373i			0.000950338i
$807$	442077.	+	661640.i	0.678814	+	1.01596i
$808$			718200.i			1.10008i
$809$			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.			−0.195781
$813$	100411.	−	67090.0i	0.151915	−	0.101502i
$814$	−312200.			−0.471177
$815$		0			0
$816$	−825440.	+	551520.i	−1.23967	+	0.828288i
$817$			511825.i			0.766792i
$818$	762314.			1.13927
$819$	−127875.	+	308687.i	−0.190642	+	0.460204i
$820$		0			0
$821$		−	948959.i		−	1.40787i	−0.710267	−	0.703933i	$-0.751426\pi$
$821$		−	948959.i		−	1.40787i	0.710267	−	0.703933i	$-0.248574\pi$
$822$	−192351.	+	128520.i	−0.284676	+	0.190207i
$823$		−	672845.i		−	0.993380i	−0.867928	−	0.496690i	$-0.834549\pi$
$823$		−	672845.i		−	0.993380i	0.867928	−	0.496690i	$-0.165451\pi$
$824$			160966.i			0.237072i
$825$		0			0
$826$	798000.			1.16961
$827$	−530096.			−0.775074			−0.387537	−	0.921854i	$-0.626674\pi$
$827$	−530096.			−0.775074			−0.387537	+	0.921854i	$0.626674\pi$
$828$	40365.0	−	97440.0i	0.0588768	−	0.142127i
$829$	−951018.			−1.38382			−0.691910	−	0.721984i	$-0.743231\pi$
$829$	−951018.			−1.38382			−0.691910	+	0.721984i	$0.743231\pi$
$830$		0			0
$831$	−250275.	−	374577.i	−0.362423	−	0.542425i
$832$		−	245960.i		−	0.355319i
$833$	1.61646e6			2.32956
$834$	−129976.	+	86843.9i	−0.186866	+	0.124855i
$835$		0			0
$836$			25967.1i			0.0371545i
$837$	−426.549	−	2145.00i	−0.000608861	−	0.00306180i
$838$			619780.i			0.882571i
$839$			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.			0.187261
$843$	213836.	+	320040.i	0.300902	+	0.450349i
$844$	−31834.0			−0.0446896
$845$		0			0
$846$	215264.	−	519641.i	0.300767	−	0.726044i
$847$		−	993075.i		−	1.38425i
$848$	−120182.			−0.167127
$849$	169425.	+	253572.i	0.235051	+	0.351792i
$850$		0			0
$851$			1.45184e6i			2.00474i
$852$	4864.15	+	7280.00i	0.00670082	+	0.0100289i
$853$		−	1.09802e6i		−	1.50907i	−0.656258	−	0.754536i	$-0.727862\pi$
$853$		−	1.09802e6i		−	1.50907i	0.656258	−	0.754536i	$-0.272138\pi$
$854$		−	102989.i		−	0.141213i
$855$		0			0
$856$	225288.			0.307461
$857$	657619.			0.895391			0.447695	−	0.894186i	$-0.352245\pi$
$857$	657619.			0.895391			0.447695	+	0.894186i	$0.352245\pi$
$858$	57621.5	−	38500.0i	0.0782727	−	0.0522981i
$859$	401162.			0.543668			0.271834	−	0.962344i	$-0.412370\pi$
$859$	401162.			0.543668			0.271834	+	0.962344i	$0.412370\pi$
$860$		0			0
$861$	1.23900e6	−	827842.i	1.67134	−	1.11671i
$862$			142380.i			0.191617i
$863$	246336.			0.330755			0.165377	−	0.986230i	$-0.447116\pi$
$863$	246336.			0.330755			0.165377	+	0.986230i	$0.447116\pi$
$864$	36176.0	+	181919.i	0.0484611	+	0.243698i
$865$		0			0
$866$			161883.i			0.215856i
$867$	−1.25617e6	+	839315.i	−1.67113	+	1.11657i
$868$		−	450.000i		−	0.000597273i
$869$			169048.i			0.223857i
$870$		0			0
$871$	−122925.			−0.162033
$872$	−143927.			−0.189281
$873$	339368.	+	140585.i	0.445290	+	0.184464i
$874$	−845292.			−1.10658
$875$		0			0
$876$	−69700.0	−	104317.i	−0.0908290	−	0.135940i
$877$			1.20146e6i			1.56210i	0.624470	+	0.781049i	$0.285315\pi$
$877$			1.20146e6i			1.56210i	−0.624470	+	0.781049i	$0.714685\pi$
$878$	−335002.			−0.434568
$879$	995232.	−	664967.i	1.28809	−	0.860642i
$880$		0			0
$881$			161714.i			0.208352i	0.994559	+	0.104176i	$0.0332205\pi$
$881$			161714.i			0.208352i	−0.994559	+	0.104176i	$0.966780\pi$
$882$	−373956.	+	902720.i	−0.480710	+	1.16042i
$883$			378715.i			0.485726i	0.970061	+	0.242863i	$0.0780865\pi$
$883$			378715.i			0.485726i	−0.970061	+	0.242863i	$0.921913\pi$
$884$		−	55152.0i		−	0.0705760i
$885$		0			0
$886$	−602616.			−0.767668
$887$	1.19559e6			1.51963			0.759813	−	0.650142i	$-0.225291\pi$
$887$	1.19559e6			1.51963			0.759813	+	0.650142i	$0.225291\pi$
$888$	−750951.	−	1.12392e6i	−0.952326	−	1.42531i
$889$	2.01225e6			2.54612
$890$		0			0
$891$	−173600.	+	173575.i	−0.218673	+	0.218642i
$892$			80890.0i			0.101664i
$893$	643984.			0.807555
$894$	217000.	+	324776.i	0.271509	+	0.406358i
$895$		0			0
$896$		−	949633.i		−	1.18288i
$897$	−179038.	−	267960.i	−0.222516	−	0.333031i
$898$			429800.i			0.532983i
$899$		−	2581.74i		−	0.00319443i
$900$		0			0
$901$	−273896.			−0.337393
$902$	−309061.			−0.379866
$903$	−827842.	+	553125.i	−1.01525	+	0.678341i
$904$	−513072.			−0.627829
$905$		0			0
$906$	647444.	−	432592.i	0.788762	−	0.527014i
$907$		−	407850.i		−	0.495776i	−0.968789	−	0.247888i	$-0.920263\pi$
$907$		−	407850.i		−	0.495776i	0.968789	−	0.247888i	$-0.0797366\pi$
$908$	−92239.3			−0.111878
$909$	−798000.	−	330575.i	−0.965773	−	0.400076i
$910$		0			0
$911$			790762.i			0.952816i	0.879224	+	0.476408i	$0.158061\pi$
$911$			790762.i			0.952816i	−0.879224	+	0.476408i	$0.841939\pi$
$912$	571276.	−	381700.i	0.686841	−	0.458915i
$913$			11760.0i			0.0141080i
$914$			238905.i			0.285978i
$915$		0			0
$916$	73086.0			0.0871050
$917$	−850292.			−1.01118
$918$	−266735.	−	1.34134e6i	−0.316516	−	1.59167i
$919$	−1.29805e6			−1.53696			−0.768478	−	0.639876i	$-0.778986\pi$
$919$	−1.29805e6			−1.53696			−0.768478	+	0.639876i	$0.778986\pi$
$920$		0			0
$921$	679375.	+	1.01680e6i	0.800922	+	1.19871i
$922$		−	1.05294e6i		−	1.23863i
$923$	26752.9			0.0314027
$924$	−42000.0	+	28062.4i	−0.0491932	+	0.0328686i
$925$		0			0
$926$			1.15157e6i			1.34298i
$927$	−178851.	−	74090.0i	−0.208129	−	0.0862184i
$928$			218960.i			0.254255i
$929$		−	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.			0.193272
$933$	141435.	+	211680.i	0.162477	+	0.243174i
$934$	1.02852e6			1.17902
$935$		0			0
$936$	277200.	+	114831.i	0.316404	+	0.131072i
$937$			696495.i			0.793302i	0.917969	+	0.396651i	$0.129828\pi$
$937$			696495.i			0.793302i	−0.917969	+	0.396651i	$0.870172\pi$
$938$	−627195.			−0.712848
$939$	851275.	+	1.27407e6i	0.965470	+	1.44498i
$940$		0			0
$941$			47743.5i			0.0539182i	0.999637	+	0.0269591i	$0.00858239\pi$
$941$			47743.5i			0.0539182i	−0.999637	+	0.0269591i	$0.991418\pi$
$942$	247417.	+	370300.i	0.278823	+	0.417303i
$943$			1.43724e6i			1.61624i
$944$		−	625605.i		−	0.702031i
$945$		0			0
$946$	206500.			0.230748
$947$	−633290.			−0.706160			−0.353080	−	0.935593i	$-0.614866\pi$
$947$	−633290.			−0.706160			−0.353080	+	0.935593i	$0.614866\pi$
$948$	−67619.2	+	45180.0i	−0.0752408	+	0.0502724i
$949$	−383350.			−0.425660
$950$		0			0
$951$	80752.0	−	53954.7i	0.0892878	−	0.0596579i
$952$		−	2.53260e6i		−	2.79443i
$953$	−1.25497e6			−1.38180			−0.690902	−	0.722948i	$-0.742786\pi$
$953$	−1.25497e6			−1.38180			−0.690902	+	0.722948i	$0.742786\pi$
$954$	63364.0	−	152959.i	0.0696219	−	0.168065i
$955$		0			0
$956$		−	183266.i		−	0.200524i
$957$	−240963.	+	161000.i	−0.263103	+	0.175793i
$958$		−	669480.i		−	0.729469i
$959$		−	515226.i		−	0.560223i
$960$		0			0
$961$	−923512.			−0.999990
$962$	−458914.			−0.495886
$963$	−103696.	+	250320.i	−0.111818	+	0.269925i
$964$	205426.			0.221056
$965$		0			0
$966$	−913500.	−	1.36720e6i	−0.978936	−	1.46514i
$967$		−	1.54201e6i		−	1.64905i	−0.565824	−	0.824526i	$-0.691442\pi$
$967$		−	1.54201e6i		−	1.64905i	0.565824	−	0.824526i	$-0.308558\pi$
$968$	−891779.			−0.951714
$969$	1.30194e6	−	869898.i	1.38658	−	0.926447i
$970$		0			0
$971$			1.69677e6i			1.79963i	0.436270	+	0.899816i	$0.356299\pi$
$971$			1.69677e6i			1.79963i	−0.436270	+	0.899816i	$0.643701\pi$
$972$	−115827.	−	23050.0i	−0.122596	−	0.0243971i
$973$		−	348150.i		−	0.367740i
$974$		−	1.30792e6i		−	1.37867i
$975$		0			0
$976$	−80740.0			−0.0847596
$977$	1.20136e6			1.25859			0.629293	−	0.777168i	$-0.283345\pi$
$977$	1.20136e6			1.25859			0.629293	+	0.777168i	$0.283345\pi$
$978$	−460130.	−	688660.i	−0.481064	−	0.719991i
$979$	−302400.			−0.315512
$980$		0			0
$981$	66247.0	−	159918.i	0.0688380	−	0.166173i
$982$			489440.i			0.507547i
$983$	478992.			0.495703			0.247851	−	0.968798i	$-0.420276\pi$
$983$	478992.			0.495703			0.247851	+	0.968798i	$0.420276\pi$
$984$	−743400.	−	1.11262e6i	−0.767772	−	1.14910i
$985$		0			0
$986$		−	1.61445e6i		−	1.66062i
$987$	695948.	+	1.04160e6i	0.714402	+	1.06922i
$988$			38170.0i			0.0391028i
$989$		−	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	$0.664814\pi$
$992$	−763.298			−0.000775659
$993$	182428.	−	121890.i	0.185009	−	0.123615i
$994$	136500.			0.138153
$995$		0			0
$996$	−4704.00	+	3142.99i	−0.00474186	+	0.00316829i
$997$		−	1.00299e6i		−	1.00904i	−0.863401	−	0.504518i	$-0.831670\pi$
$997$		−	1.00299e6i		−	1.00904i	0.863401	−	0.504518i	$-0.168330\pi$
$998$	793332.			0.796515
$999$	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.d.b.74.4		4
3.2	odd	2	inner	75.5.d.b.74.2		4
5.2	odd	4		75.5.c.g.26.2	yes	2
5.3	odd	4		75.5.c.c.26.1	✓	2
5.4	even	2	inner	75.5.d.b.74.1		4
15.2	even	4		75.5.c.g.26.1	yes	2
15.8	even	4		75.5.c.c.26.2	yes	2
15.14	odd	2	inner	75.5.d.b.74.3		4

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

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.d (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+3.74166 q^{2} +(-7.48331 + 5.00000i) q^{3} -2.00000 q^{4} +(-28.0000 + 18.7083i) q^{6} -75.0000i q^{7} -67.3498 q^{8} +(31.0000 - 74.8331i) q^{9} +O(q^{10})\)	\(q+3.74166 q^{2} +(-7.48331 + 5.00000i) q^{3} -2.00000 q^{4} +(-28.0000 + 18.7083i) q^{6} -75.0000i q^{7} -67.3498 q^{8} +(31.0000 - 74.8331i) q^{9} -37.4166i q^{11} +(14.9666 - 10.0000i) q^{12} -55.0000i q^{13} -280.624i q^{14} -220.000 q^{16} -501.382 q^{17} +(115.991 - 280.000i) q^{18} +347.000 q^{19} +(375.000 + 561.249i) q^{21} -140.000i q^{22} -651.048 q^{23} +(504.000 - 336.749i) q^{24} -205.791i q^{26} +(142.183 + 715.000i) q^{27} +150.000i q^{28} +860.581i q^{29} -3.00000 q^{31} +254.433 q^{32} +(187.083 + 280.000i) q^{33} -1876.00 q^{34} +(-62.0000 + 149.666i) q^{36} -2230.00i q^{37} +1298.36 q^{38} +(275.000 + 411.582i) q^{39} -2207.58i q^{41} +(1403.12 + 2100.00i) q^{42} +1475.00i q^{43} +74.8331i q^{44} -2436.00 q^{46} +1855.86 q^{47} +(1646.33 - 1100.00i) q^{48} -3224.00 q^{49} +(3752.00 - 2506.91i) q^{51} +110.000i q^{52} +546.282 q^{53} +(532.000 + 2675.29i) q^{54} +5051.24i q^{56} +(-2596.71 + 1735.00i) q^{57} +3220.00i q^{58} +2843.66i q^{59} +367.000 q^{61} -11.2250 q^{62} +(-5612.49 - 2325.00i) q^{63} +4472.00 q^{64} +(700.000 + 1047.66i) q^{66} -2235.00i q^{67} +1002.76 q^{68} +(4872.00 - 3255.24i) q^{69} +486.415i q^{71} +(-2087.84 + 5040.00i) q^{72} -6970.00i q^{73} -8343.90i q^{74} -694.000 q^{76} -2806.24 q^{77} +(1028.96 + 1540.00i) q^{78} -4518.00 q^{79} +(-4639.00 - 4639.66i) q^{81} -8260.00i q^{82} -314.299 q^{83} +(-750.000 - 1122.50i) q^{84} +5518.94i q^{86} +(-4302.91 - 6440.00i) q^{87} +2520.00i q^{88} -8081.98i q^{89} -4125.00 q^{91} +1302.10 q^{92} +(22.4499 - 15.0000i) q^{93} +6944.00 q^{94} +(-1904.00 + 1272.16i) q^{96} +4535.00i q^{97} -12063.1 q^{98} +(-2800.00 - 1159.91i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 8 q^{4} - 112 q^{6} + 124 q^{9}+O(q^{10}) \) 4 * q - 8 * q^4 - 112 * q^6 + 124 * q^9	\( 4 q - 8 q^{4} - 112 q^{6} + 124 q^{9} - 880 q^{16} + 1388 q^{19} + 1500 q^{21} + 2016 q^{24} - 12 q^{31} - 7504 q^{34} - 248 q^{36} + 1100 q^{39} - 9744 q^{46} - 12896 q^{49} + 15008 q^{51} + 2128 q^{54} + 1468 q^{61} + 17888 q^{64} + 2800 q^{66} + 19488 q^{69} - 2776 q^{76} - 18072 q^{79} - 18556 q^{81} - 3000 q^{84} - 16500 q^{91} + 27776 q^{94} - 7616 q^{96} - 11200 q^{99}+O(q^{100}) \) 4 * q - 8 * q^4 - 112 * q^6 + 124 * q^9 - 880 * q^16 + 1388 * q^19 + 1500 * q^21 + 2016 * q^24 - 12 * q^31 - 7504 * q^34 - 248 * q^36 + 1100 * q^39 - 9744 * q^46 - 12896 * q^49 + 15008 * q^51 + 2128 * q^54 + 1468 * q^61 + 17888 * q^64 + 2800 * q^66 + 19488 * q^69 - 2776 * q^76 - 18072 * q^79 - 18556 * q^81 - 3000 * q^84 - 16500 * q^91 + 27776 * q^94 - 7616 * q^96 - 11200 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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