LMFDB - Embedded newform 169.4.e.d.147.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [169,4,Mod(23,169)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(169, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("169.23");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 169 = 13^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	169.e (of order $6$, degree $2$, 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:	$9.97132279097$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	no (minimal twist has level 13)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			147.1
Root			$-0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	169.147
Dual form			169.4.e.d.23.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.59808 - 1.50000i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} -9.00000i q^{5} +(-2.59808 + 1.50000i) q^{6} +(-12.9904 + 7.50000i) q^{7} +21.0000i q^{8} +(13.0000 + 22.5167i) q^{9} +O(q^{10})$	\(q+(-2.59808 - 1.50000i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} -9.00000i q^{5} +(-2.59808 + 1.50000i) q^{6} +(-12.9904 + 7.50000i) q^{7} +21.0000i q^{8} +(13.0000 + 22.5167i) q^{9} +(-13.5000 + 23.3827i) q^{10} +(-41.5692 - 24.0000i) q^{11} +1.00000 q^{12} +45.0000 q^{14} +(-7.79423 - 4.50000i) q^{15} +(35.5000 - 61.4878i) q^{16} +(22.5000 + 38.9711i) q^{17} -78.0000i q^{18} +(5.19615 - 3.00000i) q^{19} +(7.79423 - 4.50000i) q^{20} +15.0000i q^{21} +(72.0000 + 124.708i) q^{22} +(-81.0000 + 140.296i) q^{23} +(18.1865 + 10.5000i) q^{24} +44.0000 q^{25} +53.0000 q^{27} +(-12.9904 - 7.50000i) q^{28} +(72.0000 - 124.708i) q^{29} +(13.5000 + 23.3827i) q^{30} +264.000i q^{31} +(-38.9711 + 22.5000i) q^{32} +(-41.5692 + 24.0000i) q^{33} -135.000i q^{34} +(67.5000 + 116.913i) q^{35} +(-13.0000 + 22.5167i) q^{36} +(262.406 + 151.500i) q^{37} -18.0000 q^{38} +189.000 q^{40} +(166.277 + 96.0000i) q^{41} +(22.5000 - 38.9711i) q^{42} +(48.5000 + 84.0045i) q^{43} -48.0000i q^{44} +(202.650 - 117.000i) q^{45} +(420.888 - 243.000i) q^{46} -111.000i q^{47} +(-35.5000 - 61.4878i) q^{48} +(-59.0000 + 102.191i) q^{49} +(-114.315 - 66.0000i) q^{50} +45.0000 q^{51} -414.000 q^{53} +(-137.698 - 79.5000i) q^{54} +(-216.000 + 374.123i) q^{55} +(-157.500 - 272.798i) q^{56} -6.00000i q^{57} +(-374.123 + 216.000i) q^{58} +(-452.065 + 261.000i) q^{59} -9.00000i q^{60} +(-188.000 - 325.626i) q^{61} +(396.000 - 685.892i) q^{62} +(-337.750 - 195.000i) q^{63} -433.000 q^{64} +144.000 q^{66} +(31.1769 + 18.0000i) q^{67} +(-22.5000 + 38.9711i) q^{68} +(81.0000 + 140.296i) q^{69} -405.000i q^{70} +(309.171 - 178.500i) q^{71} +(-472.850 + 273.000i) q^{72} +1098.00i q^{73} +(-454.500 - 787.217i) q^{74} +(22.0000 - 38.1051i) q^{75} +(5.19615 + 3.00000i) q^{76} +720.000 q^{77} -830.000 q^{79} +(-553.390 - 319.500i) q^{80} +(-324.500 + 562.050i) q^{81} +(-288.000 - 498.831i) q^{82} -438.000i q^{83} +(-12.9904 + 7.50000i) q^{84} +(350.740 - 202.500i) q^{85} -291.000i q^{86} +(-72.0000 - 124.708i) q^{87} +(504.000 - 872.954i) q^{88} +(-379.319 - 219.000i) q^{89} -702.000 q^{90} -162.000 q^{92} +(228.631 + 132.000i) q^{93} +(-166.500 + 288.386i) q^{94} +(-27.0000 - 46.7654i) q^{95} +45.0000i q^{96} +(-737.854 + 426.000i) q^{97} +(306.573 - 177.000i) q^{98} -1248.00i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{3} + 2 q^{4} + 52 q^{9}+O(q^{10}) $ 4 * q + 2 * q^3 + 2 * q^4 + 52 * q^9	$ 4 q + 2 q^{3} + 2 q^{4} + 52 q^{9} - 54 q^{10} + 4 q^{12} + 180 q^{14} + 142 q^{16} + 90 q^{17} + 288 q^{22} - 324 q^{23} + 176 q^{25} + 212 q^{27} + 288 q^{29} + 54 q^{30} + 270 q^{35} - 52 q^{36} - 72 q^{38} + 756 q^{40} + 90 q^{42} + 194 q^{43} - 142 q^{48} - 236 q^{49} + 180 q^{51} - 1656 q^{53} - 864 q^{55} - 630 q^{56} - 752 q^{61} + 1584 q^{62} - 1732 q^{64} + 576 q^{66} - 90 q^{68} + 324 q^{69} - 1818 q^{74} + 88 q^{75} + 2880 q^{77} - 3320 q^{79} - 1298 q^{81} - 1152 q^{82} - 288 q^{87} + 2016 q^{88} - 2808 q^{90} - 648 q^{92} - 666 q^{94} - 108 q^{95}+O(q^{100}) $ 4 * q + 2 * q^3 + 2 * q^4 + 52 * q^9 - 54 * q^10 + 4 * q^12 + 180 * q^14 + 142 * q^16 + 90 * q^17 + 288 * q^22 - 324 * q^23 + 176 * q^25 + 212 * q^27 + 288 * q^29 + 54 * q^30 + 270 * q^35 - 52 * q^36 - 72 * q^38 + 756 * q^40 + 90 * q^42 + 194 * q^43 - 142 * q^48 - 236 * q^49 + 180 * q^51 - 1656 * q^53 - 864 * q^55 - 630 * q^56 - 752 * q^61 + 1584 * q^62 - 1732 * q^64 + 576 * q^66 - 90 * q^68 + 324 * q^69 - 1818 * q^74 + 88 * q^75 + 2880 * q^77 - 3320 * q^79 - 1298 * q^81 - 1152 * q^82 - 288 * q^87 + 2016 * q^88 - 2808 * q^90 - 648 * q^92 - 666 * q^94 - 108 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/169\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	−2.59808	−	1.50000i	−0.918559	−	0.530330i	−0.0353837	−	0.999374i	$-0.511265\pi$
$2$	−2.59808	−	1.50000i	−0.918559	−	0.530330i	−0.883175	+	0.469044i	$0.844599\pi$
$3$	0.500000	−	0.866025i	0.0962250	−	0.166667i	−0.813894	−	0.581013i	$-0.802656\pi$
$3$	0.500000	−	0.866025i	0.0962250	−	0.166667i	0.910119	+	0.414346i	$0.135990\pi$
$4$	0.500000	+	0.866025i	0.0625000	+	0.108253i
$5$		−	9.00000i		−	0.804984i	−0.915423	−	0.402492i	$-0.868144\pi$
$5$		−	9.00000i		−	0.804984i	0.915423	−	0.402492i	$-0.131856\pi$
$6$	−2.59808	+	1.50000i	−0.176777	+	0.102062i
$7$	−12.9904	+	7.50000i	−0.701415	+	0.404962i	−0.807874	−	0.589355i	$-0.799382\pi$
$7$	−12.9904	+	7.50000i	−0.701415	+	0.404962i	0.106459	+	0.994317i	$0.466049\pi$
$8$			21.0000i			0.928078i
$9$	13.0000	+	22.5167i	0.481481	+	0.833950i
$10$	−13.5000	+	23.3827i	−0.426907	+	0.739425i
$11$	−41.5692	−	24.0000i	−1.13942	−	0.657843i	−0.193131	−	0.981173i	$-0.561864\pi$
$11$	−41.5692	−	24.0000i	−1.13942	−	0.657843i	−0.946286	+	0.323330i	$0.895198\pi$
$12$	1.00000			0.0240563
$13$		0			0
$13$		0			0
$14$	45.0000			0.859054
$15$	−7.79423	−	4.50000i	−0.134164	−	0.0774597i
$16$	35.5000	−	61.4878i	0.554688	−	0.960747i
$17$	22.5000	+	38.9711i	0.321003	+	0.555994i	0.980695	−	0.195542i	$-0.0626467\pi$
$17$	22.5000	+	38.9711i	0.321003	+	0.555994i	−0.659692	+	0.751536i	$0.729313\pi$
$18$		−	78.0000i		−	1.02138i
$19$	5.19615	−	3.00000i	0.0627410	−	0.0362235i	−0.468301	−	0.883569i	$-0.655134\pi$
$19$	5.19615	−	3.00000i	0.0627410	−	0.0362235i	0.531042	+	0.847345i	$0.321801\pi$
$20$	7.79423	−	4.50000i	0.0871421	−	0.0503115i
$21$			15.0000i			0.155870i
$22$	72.0000	+	124.708i	0.697748	+	1.20853i
$23$	−81.0000	+	140.296i	−0.734333	+	1.27190i	0.220682	+	0.975346i	$0.429172\pi$
$23$	−81.0000	+	140.296i	−0.734333	+	1.27190i	−0.955015	+	0.296557i	$0.904162\pi$
$24$	18.1865	+	10.5000i	0.154680	+	0.0893043i
$25$	44.0000			0.352000
$26$		0			0
$27$	53.0000			0.377772
$28$	−12.9904	−	7.50000i	−0.0876768	−	0.0506202i
$29$	72.0000	−	124.708i	0.461037	−	0.798539i	−0.537976	−	0.842960i	$-0.680811\pi$
$29$	72.0000	−	124.708i	0.461037	−	0.798539i	0.999013	+	0.0444210i	$0.0141443\pi$
$30$	13.5000	+	23.3827i	0.0821584	+	0.142302i
$31$			264.000i			1.52954i	0.644302	+	0.764771i	$0.277148\pi$
$31$			264.000i			1.52954i	−0.644302	+	0.764771i	$0.722852\pi$
$32$	−38.9711	+	22.5000i	−0.215287	+	0.124296i
$33$	−41.5692	+	24.0000i	−0.219281	+	0.126602i
$34$		−	135.000i		−	0.680950i
$35$	67.5000	+	116.913i	0.325988	+	0.564628i
$36$	−13.0000	+	22.5167i	−0.0601852	+	0.104244i
$37$	262.406	+	151.500i	1.16593	+	0.673147i	0.952717	−	0.303860i	$-0.0982754\pi$
$37$	262.406	+	151.500i	1.16593	+	0.673147i	0.213208	+	0.977007i	$0.431609\pi$
$38$	−18.0000			−0.0768417
$39$		0			0
$40$	189.000			0.747088
$41$	166.277	+	96.0000i	0.633368	+	0.365675i	0.782055	−	0.623209i	$-0.214171\pi$
$41$	166.277	+	96.0000i	0.633368	+	0.365675i	−0.148687	+	0.988884i	$0.547505\pi$
$42$	22.5000	−	38.9711i	0.0826625	−	0.143176i
$43$	48.5000	+	84.0045i	0.172004	+	0.297920i	0.939120	−	0.343588i	$-0.111642\pi$
$43$	48.5000	+	84.0045i	0.172004	+	0.297920i	−0.767116	+	0.641508i	$0.778309\pi$
$44$		−	48.0000i		−	0.164461i
$45$	202.650	−	117.000i	0.671317	−	0.387585i
$46$	420.888	−	243.000i	1.34906	−	0.778878i
$47$		−	111.000i		−	0.344490i	−0.985054	−	0.172245i	$-0.944898\pi$
$47$		−	111.000i		−	0.344490i	0.985054	−	0.172245i	$-0.0551020\pi$
$48$	−35.5000	−	61.4878i	−0.106750	−	0.184896i
$49$	−59.0000	+	102.191i	−0.172012	+	0.297933i
$50$	−114.315	−	66.0000i	−0.323333	−	0.186676i
$51$	45.0000			0.123554
$52$		0			0
$53$	−414.000			−1.07297			−0.536484	−	0.843911i	$-0.680248\pi$
$53$	−414.000			−1.07297			−0.536484	+	0.843911i	$0.680248\pi$
$54$	−137.698	−	79.5000i	−0.347006	−	0.200344i
$55$	−216.000	+	374.123i	−0.529553	+	0.917213i
$56$	−157.500	−	272.798i	−0.375836	−	0.650967i
$57$		−	6.00000i		−	0.0139424i
$58$	−374.123	+	216.000i	−0.846979	+	0.489003i
$59$	−452.065	+	261.000i	−0.997523	+	0.575920i	−0.907515	−	0.420021i	$-0.862023\pi$
$59$	−452.065	+	261.000i	−0.997523	+	0.575920i	−0.0900089	+	0.995941i	$0.528690\pi$
$60$		−	9.00000i		−	0.0193649i
$61$	−188.000	−	325.626i	−0.394605	−	0.683477i	0.598445	−	0.801164i	$-0.295785\pi$
$61$	−188.000	−	325.626i	−0.394605	−	0.683477i	−0.993051	+	0.117687i	$0.962452\pi$
$62$	396.000	−	685.892i	0.811162	−	1.40497i
$63$	−337.750	−	195.000i	−0.675436	−	0.389963i
$64$	−433.000			−0.845703
$65$		0			0
$66$	144.000			0.268563
$67$	31.1769	+	18.0000i	0.0568488	+	0.0328216i	0.528155	−	0.849148i	$-0.322884\pi$
$67$	31.1769	+	18.0000i	0.0568488	+	0.0328216i	−0.471306	+	0.881970i	$0.656217\pi$
$68$	−22.5000	+	38.9711i	−0.0401254	+	0.0694992i
$69$	81.0000	+	140.296i	0.141323	+	0.244778i
$70$		−	405.000i		−	0.691525i
$71$	309.171	−	178.500i	0.516787	−	0.298367i	−0.218832	−	0.975762i	$-0.570225\pi$
$71$	309.171	−	178.500i	0.516787	−	0.298367i	0.735619	+	0.677396i	$0.236891\pi$
$72$	−472.850	+	273.000i	−0.773971	+	0.446852i
$73$			1098.00i			1.76043i	0.474578	+	0.880214i	$0.342601\pi$
$73$			1098.00i			1.76043i	−0.474578	+	0.880214i	$0.657399\pi$
$74$	−454.500	−	787.217i	−0.713980	−	1.23665i
$75$	22.0000	−	38.1051i	0.0338712	−	0.0586667i
$76$	5.19615	+	3.00000i	0.00784263	+	0.00452794i
$77$	720.000			1.06561
$78$		0			0
$79$	−830.000			−1.18205			−0.591027	−	0.806652i	$-0.701277\pi$
$79$	−830.000			−1.18205			−0.591027	+	0.806652i	$0.701277\pi$
$80$	−553.390	−	319.500i	−0.773386	−	0.446515i
$81$	−324.500	+	562.050i	−0.445130	+	0.770988i
$82$	−288.000	−	498.831i	−0.387857	−	0.671788i
$83$		−	438.000i		−	0.579238i	−0.957142	−	0.289619i	$-0.906471\pi$
$83$		−	438.000i		−	0.579238i	0.957142	−	0.289619i	$-0.0935286\pi$
$84$	−12.9904	+	7.50000i	−0.0168734	+	0.00974187i
$85$	350.740	−	202.500i	0.447566	−	0.258402i
$86$		−	291.000i		−	0.364876i
$87$	−72.0000	−	124.708i	−0.0887266	−	0.153679i
$88$	504.000	−	872.954i	0.610529	−	1.05747i
$89$	−379.319	−	219.000i	−0.451772	−	0.260831i	0.256806	−	0.966463i	$-0.417330\pi$
$89$	−379.319	−	219.000i	−0.451772	−	0.260831i	−0.708578	+	0.705632i	$0.750663\pi$
$90$	−702.000			−0.822192
$91$		0			0
$92$	−162.000			−0.183583
$93$	228.631	+	132.000i	0.254924	+	0.147180i
$94$	−166.500	+	288.386i	−0.182693	+	0.316434i
$95$	−27.0000	−	46.7654i	−0.0291594	−	0.0505055i
$96$			45.0000i			0.0478416i
$97$	−737.854	+	426.000i	−0.772347	+	0.445915i	−0.833711	−	0.552201i	$-0.813788\pi$
$97$	−737.854	+	426.000i	−0.772347	+	0.445915i	0.0613640	+	0.998115i	$0.480455\pi$
$98$	306.573	−	177.000i	0.316006	−	0.182446i
$99$		−	1248.00i		−	1.26696i
$100$	22.0000	+	38.1051i	0.0220000	+	0.0381051i
$101$	−198.000	+	342.946i	−0.195067	+	0.337865i	−0.946922	−	0.321462i	$-0.895826\pi$
$101$	−198.000	+	342.946i	−0.195067	+	0.337865i	0.751856	+	0.659328i	$0.229159\pi$
$102$	−116.913	−	67.5000i	−0.113492	−	0.0655245i
$103$	182.000			0.174107			0.0870534	−	0.996204i	$-0.472255\pi$
$103$	182.000			0.174107			0.0870534	+	0.996204i	$0.472255\pi$
$104$		0			0
$105$	135.000			0.125473
$106$	1075.60	+	621.000i	0.985584	+	0.569027i
$107$	306.000	−	530.008i	0.276469	−	0.478858i	−0.694036	−	0.719940i	$-0.744169\pi$
$107$	306.000	−	530.008i	0.276469	−	0.478858i	0.970505	+	0.241083i	$0.0775025\pi$
$108$	26.5000	+	45.8993i	0.0236108	+	0.0408951i
$109$			1083.00i			0.951675i	0.879533	+	0.475838i	$0.157855\pi$
$109$			1083.00i			0.951675i	−0.879533	+	0.475838i	$0.842145\pi$
$110$	1122.37	−	648.000i	0.972852	−	0.561676i
$111$	262.406	−	151.500i	0.224382	−	0.129547i
$112$			1065.00i			0.898509i
$113$	−45.0000	−	77.9423i	−0.0374623	−	0.0648867i	0.846686	−	0.532092i	$-0.178594\pi$
$113$	−45.0000	−	77.9423i	−0.0374623	−	0.0648867i	−0.884149	+	0.467206i	$0.845261\pi$
$114$	−9.00000	+	15.5885i	−0.00739410	+	0.0128070i
$115$	1262.67	+	729.000i	1.02386	+	0.591127i
$116$	144.000			0.115259
$117$		0			0
$118$	1566.00			1.22171
$119$	−584.567	−	337.500i	−0.450312	−	0.259988i
$120$	94.5000	−	163.679i	0.0718886	−	0.124515i
$121$	486.500	+	842.643i	0.365515	+	0.633090i
$122$			1128.00i			0.837085i
$123$	166.277	−	96.0000i	0.121892	−	0.0703742i
$124$	−228.631	+	132.000i	−0.165578	+	0.0955964i
$125$		−	1521.00i		−	1.08834i
$126$	585.000	+	1013.25i	0.413619	+	0.716408i
$127$	−1043.00	+	1806.53i	−0.728750	+	1.26223i	0.228661	+	0.973506i	$0.426565\pi$
$127$	−1043.00	+	1806.53i	−0.728750	+	1.26223i	−0.957412	+	0.288726i	$0.906768\pi$
$128$	1436.74	+	829.500i	0.992115	+	0.572798i
$129$	97.0000			0.0662044
$130$		0			0
$131$	−1467.00			−0.978415			−0.489208	−	0.872167i	$-0.662714\pi$
$131$	−1467.00			−0.978415			−0.489208	+	0.872167i	$0.662714\pi$
$132$	−41.5692	−	24.0000i	−0.0274101	−	0.0158252i
$133$	−45.0000	+	77.9423i	−0.0293383	+	0.0508154i
$134$	−54.0000	−	93.5307i	−0.0348126	−	0.0602972i
$135$		−	477.000i		−	0.304101i
$136$	−818.394	+	472.500i	−0.516005	+	0.297916i
$137$	358.535	−	207.000i	0.223589	−	0.129089i	−0.384022	−	0.923324i	$-0.625461\pi$
$137$	358.535	−	207.000i	0.223589	−	0.129089i	0.607611	+	0.794235i	$0.292128\pi$
$138$		−	486.000i		−	0.299790i
$139$	1209.50	+	2094.92i	0.738046	+	1.27833i	0.953374	+	0.301792i	$0.0975848\pi$
$139$	1209.50	+	2094.92i	0.738046	+	1.27833i	−0.215327	+	0.976542i	$0.569082\pi$
$140$	−67.5000	+	116.913i	−0.0407485	+	0.0705785i
$141$	−96.1288	−	55.5000i	−0.0574149	−	0.0331485i
$142$	−1071.00			−0.632932
$143$		0			0
$144$	1846.00			1.06829
$145$	−1122.37	−	648.000i	−0.642811	−	0.371127i
$146$	1647.00	−	2852.69i	0.933607	−	1.61706i
$147$	59.0000	+	102.191i	0.0331037	+	0.0573372i
$148$			303.000i			0.168287i
$149$	−805.404	+	465.000i	−0.442827	+	0.255666i	−0.704796	−	0.709410i	$-0.748962\pi$
$149$	−805.404	+	465.000i	−0.442827	+	0.255666i	0.261969	+	0.965076i	$0.415628\pi$
$150$	−114.315	+	66.0000i	−0.0622254	+	0.0359258i
$151$			1683.00i			0.907024i	0.891250	+	0.453512i	$0.149829\pi$
$151$			1683.00i			0.907024i	−0.891250	+	0.453512i	$0.850171\pi$
$152$	63.0000	+	109.119i	0.0336183	+	0.0582285i
$153$	−585.000	+	1013.25i	−0.309114	+	0.535401i
$154$	−1870.61	−	1080.00i	−0.978821	−	0.565123i
$155$	2376.00			1.23126
$156$		0			0
$157$	1874.00			0.952621			0.476310	−	0.879277i	$-0.341974\pi$
$157$	1874.00			0.952621			0.476310	+	0.879277i	$0.341974\pi$
$158$	2156.40	+	1245.00i	1.08579	+	0.626879i
$159$	−207.000	+	358.535i	−0.103246	+	0.178828i
$160$	202.500	+	350.740i	0.100056	+	0.173303i
$161$		−	2430.00i		−	1.18951i
$162$	1686.15	−	973.500i	0.817757	−	0.472132i
$163$	1034.03	−	597.000i	0.496882	−	0.286875i	−0.230543	−	0.973062i	$-0.574050\pi$
$163$	1034.03	−	597.000i	0.496882	−	0.286875i	0.727425	+	0.686187i	$0.240717\pi$
$164$			192.000i			0.0914188i
$165$	216.000	+	374.123i	0.101913	+	0.176518i
$166$	−657.000	+	1137.96i	−0.307187	+	0.532064i
$167$	−2068.07	−	1194.00i	−0.958275	−	0.553260i	−0.0626334	−	0.998037i	$-0.519950\pi$
$167$	−2068.07	−	1194.00i	−0.958275	−	0.553260i	−0.895642	+	0.444776i	$0.853283\pi$
$168$	−315.000			−0.144659
$169$		0			0
$170$	−1215.00			−0.548154
$171$	135.100	+	78.0000i	0.0604173	+	0.0348819i
$172$	−48.5000	+	84.0045i	−0.0215005	+	0.0372400i
$173$	783.000	+	1356.20i	0.344106	+	0.596010i	0.985191	−	0.171461i	$-0.0548486\pi$
$173$	783.000	+	1356.20i	0.344106	+	0.596010i	−0.641085	+	0.767470i	$0.721515\pi$
$174$			432.000i			0.188217i
$175$	−571.577	+	330.000i	−0.246898	+	0.142547i
$176$	−2951.41	+	1704.00i	−1.26404	+	0.729795i
$177$			522.000i			0.221672i
$178$	657.000	+	1137.96i	0.276653	+	0.479177i
$179$	328.500	−	568.979i	0.137169	−	0.237584i	−0.789255	−	0.614066i	$-0.789533\pi$
$179$	328.500	−	568.979i	0.137169	−	0.237584i	0.926424	+	0.376482i	$0.122866\pi$
$180$	202.650	+	117.000i	0.0839146	+	0.0484481i
$181$	−1222.00			−0.501826			−0.250913	−	0.968010i	$-0.580731\pi$
$181$	−1222.00			−0.501826			−0.250913	+	0.968010i	$0.580731\pi$
$182$		0			0
$183$	−376.000			−0.151884
$184$	−2946.22	−	1701.00i	−1.18042	−	0.681518i
$185$	1363.50	−	2361.65i	0.541873	−	0.938552i
$186$	−396.000	−	685.892i	−0.156108	−	0.270387i
$187$		−	2160.00i		−	0.844678i
$188$	96.1288	−	55.5000i	0.0372921	−	0.0215306i
$189$	−688.490	+	397.500i	−0.264975	+	0.152983i
$190$			162.000i			0.0618564i
$191$	−630.000	−	1091.19i	−0.238666	−	0.413382i	0.721666	−	0.692242i	$-0.243377\pi$
$191$	−630.000	−	1091.19i	−0.238666	−	0.413382i	−0.960332	+	0.278860i	$0.910043\pi$
$192$	−216.500	+	374.989i	−0.0813778	+	0.140951i
$193$	296.181	+	171.000i	0.110464	+	0.0637764i	0.554214	−	0.832374i	$-0.313019\pi$
$193$	296.181	+	171.000i	0.110464	+	0.0637764i	−0.443750	+	0.896151i	$0.646352\pi$
$194$	2556.00			0.945928
$195$		0			0
$196$	−118.000			−0.0430029
$197$	−70.1481	−	40.5000i	−0.0253698	−	0.0146472i	0.487261	−	0.873256i	$-0.337996\pi$
$197$	−70.1481	−	40.5000i	−0.0253698	−	0.0146472i	−0.512631	+	0.858609i	$0.671329\pi$
$198$	−1872.00	+	3242.40i	−0.671905	+	1.16377i
$199$	−998.000	−	1728.59i	−0.355509	−	0.615760i	0.631696	−	0.775216i	$-0.282359\pi$
$199$	−998.000	−	1728.59i	−0.355509	−	0.615760i	−0.987205	+	0.159456i	$0.949026\pi$
$200$			924.000i			0.326683i
$201$	31.1769	−	18.0000i	0.0109405	−	0.00631653i
$202$	1028.84	−	594.000i	0.358360	−	0.206899i
$203$			2160.00i			0.746809i
$204$	22.5000	+	38.9711i	0.00772213	+	0.0133751i
$205$	864.000	−	1496.49i	0.294363	−	0.509851i
$206$	−472.850	−	273.000i	−0.159927	−	0.0923340i
$207$	−4212.00			−1.41427
$208$		0			0
$209$	−288.000			−0.0953176
$210$	−350.740	−	202.500i	−0.115254	−	0.0665420i
$211$	−1416.50	+	2453.45i	−0.462161	+	0.800486i	−0.999068	−	0.0431553i	$-0.986259\pi$
$211$	−1416.50	+	2453.45i	−0.462161	+	0.800486i	0.536908	+	0.843641i	$0.319592\pi$
$212$	−207.000	−	358.535i	−0.0670605	−	0.116152i
$213$		−	357.000i		−	0.114841i
$214$	−1590.02	+	918.000i	−0.507905	+	0.293239i
$215$	756.040	−	436.500i	0.239821	−	0.138461i
$216$			1113.00i			0.350602i
$217$	−1980.00	−	3429.46i	−0.619406	−	1.07284i
$218$	1624.50	−	2813.72i	0.504702	−	0.874169i
$219$	950.896	+	549.000i	0.293405	+	0.169397i
$220$	−432.000			−0.132388
$221$		0			0
$222$	−909.000			−0.274811
$223$	3037.15	+	1753.50i	0.912030	+	0.526561i	0.881084	−	0.472960i	$-0.156815\pi$
$223$	3037.15	+	1753.50i	0.912030	+	0.526561i	0.0309462	+	0.999521i	$0.490148\pi$
$224$	337.500	−	584.567i	0.100670	−	0.174366i
$225$	572.000	+	990.733i	0.169481	+	0.293551i
$226$			270.000i			0.0794696i
$227$	−197.454	+	114.000i	−0.0577333	+	0.0333324i	−0.528589	−	0.848878i	$-0.677279\pi$
$227$	−197.454	+	114.000i	−0.0577333	+	0.0333324i	0.470855	+	0.882210i	$0.343945\pi$
$228$	5.19615	−	3.00000i	0.00150931	−	0.000871403i
$229$		−	5493.00i		−	1.58510i	−0.609808	−	0.792549i	$-0.708753\pi$
$229$		−	5493.00i		−	1.58510i	0.609808	−	0.792549i	$-0.291247\pi$
$230$	−2187.00	−	3788.00i	−0.626985	−	1.08597i
$231$	360.000	−	623.538i	0.102538	−	0.177601i
$232$	2618.86	+	1512.00i	0.741106	+	0.427878i
$233$	3627.00			1.01980			0.509898	−	0.860235i	$-0.329683\pi$
$233$	3627.00			1.01980			0.509898	+	0.860235i	$0.329683\pi$
$234$		0			0
$235$	−999.000			−0.277309
$236$	−452.065	−	261.000i	−0.124690	−	0.0719901i
$237$	−415.000	+	718.801i	−0.113743	+	0.197009i
$238$	1012.50	+	1753.70i	0.275759	+	0.477628i
$239$			6075.00i			1.64418i	0.569357	+	0.822090i	$0.307192\pi$
$239$			6075.00i			1.64418i	−0.569357	+	0.822090i	$0.692808\pi$
$240$	−553.390	+	319.500i	−0.148838	+	0.0859318i
$241$	−181.865	+	105.000i	−0.0486099	+	0.0280649i	−0.524108	−	0.851652i	$-0.675601\pi$
$241$	−181.865	+	105.000i	−0.0486099	+	0.0280649i	0.475498	+	0.879717i	$0.342268\pi$
$242$		−	2919.00i		−	0.775374i
$243$	1040.00	+	1801.33i	0.274552	+	0.475537i
$244$	188.000	−	325.626i	0.0493257	−	0.0854346i
$245$	919.719	+	531.000i	0.239831	+	0.138467i
$246$	−576.000			−0.149286
$247$		0			0
$248$	−5544.00			−1.41953
$249$	−379.319	−	219.000i	−0.0965397	−	0.0557372i
$250$	−2281.50	+	3951.67i	−0.577179	+	0.999703i
$251$	−3546.00	−	6141.85i	−0.891719	−	1.54450i	−0.837813	−	0.545957i	$-0.816166\pi$
$251$	−3546.00	−	6141.85i	−0.891719	−	1.54450i	−0.0539061	−	0.998546i	$-0.517167\pi$
$252$		−	390.000i		−	0.0974908i
$253$	6734.21	−	3888.00i	1.67342	−	0.966152i
$254$	5419.59	−	3129.00i	1.33880	−	0.772956i
$255$		−	405.000i		−	0.0994592i
$256$	−756.500	−	1310.30i	−0.184692	−	0.319897i
$257$	2902.50	−	5027.28i	0.704486	−	1.22021i	−0.262390	−	0.964962i	$-0.584511\pi$
$257$	2902.50	−	5027.28i	0.704486	−	1.22021i	0.966877	−	0.255244i	$-0.0821559\pi$
$258$	−252.013	−	145.500i	−0.0608127	−	0.0351102i
$259$	−4545.00			−1.09040
$260$		0			0
$261$	3744.00			0.887923
$262$	3811.38	+	2200.50i	0.898732	+	0.518883i
$263$	−396.000	+	685.892i	−0.0928457	+	0.160813i	−0.908707	−	0.417434i	$-0.862930\pi$
$263$	−396.000	+	685.892i	−0.0928457	+	0.160813i	0.815862	+	0.578247i	$0.196263\pi$
$264$	−504.000	−	872.954i	−0.117496	−	0.203510i
$265$			3726.00i			0.863722i
$266$	233.827	−	135.000i	0.0538979	−	0.0311180i
$267$	−379.319	+	219.000i	−0.0869436	+	0.0501969i
$268$			36.0000i			0.00820541i
$269$	−2736.00	−	4738.89i	−0.620137	−	1.07411i	−0.989460	−	0.144808i	$-0.953744\pi$
$269$	−2736.00	−	4738.89i	−0.620137	−	1.07411i	0.369323	−	0.929301i	$-0.379590\pi$
$270$	−715.500	+	1239.28i	−0.161274	+	0.279335i
$271$	2018.71	+	1165.50i	0.452500	+	0.261251i	0.708886	−	0.705323i	$-0.249198\pi$
$271$	2018.71	+	1165.50i	0.452500	+	0.261251i	−0.256385	+	0.966575i	$0.582532\pi$
$272$	3195.00			0.712225
$273$		0			0
$274$	−1242.00			−0.273839
$275$	−1829.05	−	1056.00i	−0.401075	−	0.231561i
$276$	−81.0000	+	140.296i	−0.0176653	+	0.0305972i
$277$	692.000	+	1198.58i	0.150102	+	0.259984i	0.931265	−	0.364343i	$-0.118706\pi$
$277$	692.000	+	1198.58i	0.150102	+	0.259984i	−0.781163	+	0.624327i	$0.785373\pi$
$278$		−	7257.00i		−	1.56563i
$279$	−5944.40	+	3432.00i	−1.27556	+	0.736446i
$280$	−2455.18	+	1417.50i	−0.524019	+	0.302542i
$281$			4062.00i			0.862344i	0.902270	+	0.431172i	$0.141900\pi$
$281$			4062.00i			0.862344i	−0.902270	+	0.431172i	$0.858100\pi$
$282$	166.500	+	288.386i	0.0351593	+	0.0608977i
$283$	1882.00	−	3259.72i	0.395312	−	0.684700i	−0.597829	−	0.801624i	$-0.703970\pi$
$283$	1882.00	−	3259.72i	0.395312	−	0.684700i	0.993141	+	0.116923i	$0.0373032\pi$
$284$	309.171	+	178.500i	0.0645983	+	0.0372959i
$285$	−54.0000			−0.0112235
$286$		0			0
$287$	−2880.00			−0.592338
$288$	−1013.25	−	585.000i	−0.207314	−	0.119693i
$289$	1444.00	−	2501.08i	0.293914	−	0.509074i
$290$	1944.00	+	3367.11i	0.393640	+	0.681805i
$291$			852.000i			0.171633i
$292$	−950.896	+	549.000i	−0.190572	+	0.110027i
$293$	−3660.69	+	2113.50i	−0.729897	+	0.421406i	−0.818384	−	0.574671i	$-0.805130\pi$
$293$	−3660.69	+	2113.50i	−0.729897	+	0.421406i	0.0884876	+	0.996077i	$0.471797\pi$
$294$		−	354.000i		−	0.0702235i
$295$	2349.00	+	4068.59i	0.463607	+	0.802991i
$296$	−3181.50	+	5510.52i	−0.624733	+	1.08207i
$297$	−2203.17	−	1272.00i	−0.430440	−	0.248515i
$298$	2790.00			0.542350
$299$		0			0
$300$	44.0000			0.00846780
$301$	−1260.07	−	727.500i	−0.241293	−	0.139310i
$302$	2524.50	−	4372.56i	0.481022	−	0.833155i
$303$	198.000	+	342.946i	0.0375406	+	0.0650222i
$304$		−	426.000i		−	0.0803710i
$305$	−2930.63	+	1692.00i	−0.550188	+	0.317651i
$306$	3039.75	−	1755.00i	0.567879	−	0.327865i
$307$		−	306.000i		−	0.0568871i	−0.999595	−	0.0284436i	$-0.990945\pi$
$307$		−	306.000i		−	0.0568871i	0.999595	−	0.0284436i	$-0.00905509\pi$
$308$	360.000	+	623.538i	0.0666003	+	0.115355i
$309$	91.0000	−	157.617i	0.0167534	−	0.0290178i
$310$	−6173.03	−	3564.00i	−1.13098	−	0.652973i
$311$	−2106.00			−0.383988			−0.191994	−	0.981396i	$-0.561495\pi$
$311$	−2106.00			−0.383988			−0.191994	+	0.981396i	$0.561495\pi$
$312$		0			0
$313$	10051.0			1.81507			0.907534	−	0.419979i	$-0.137963\pi$
$313$	10051.0			1.81507			0.907534	+	0.419979i	$0.137963\pi$
$314$	−4868.79	−	2811.00i	−0.875038	−	0.505204i
$315$	−1755.00	+	3039.75i	−0.313914	+	0.543716i
$316$	−415.000	−	718.801i	−0.0738784	−	0.127961i
$317$		−	2154.00i		−	0.381643i	−0.981625	−	0.190821i	$-0.938885\pi$
$317$		−	2154.00i		−	0.381643i	0.981625	−	0.190821i	$-0.0611151\pi$
$318$	1075.60	−	621.000i	0.189676	−	0.109509i
$319$	−5985.97	+	3456.00i	−1.05063	+	0.606579i
$320$			3897.00i			0.680778i
$321$	−306.000	−	530.008i	−0.0532064	−	0.0921562i
$322$	−3645.00	+	6313.33i	−0.630832	+	1.09263i
$323$	233.827	+	135.000i	0.0402801	+	0.0232557i
$324$	−649.000			−0.111283
$325$		0			0
$326$	−3582.00			−0.608554
$327$	937.906	+	541.500i	0.158613	+	0.0915750i
$328$	−2016.00	+	3491.81i	−0.339375	+	0.587815i
$329$	832.500	+	1441.93i	0.139505	+	0.241630i
$330$		−	1296.00i		−	0.216189i
$331$	9327.09	−	5385.00i	1.54883	−	0.894219i	0.550601	−	0.834769i	$-0.314399\pi$
$331$	9327.09	−	5385.00i	1.54883	−	0.894219i	0.998231	−	0.0594500i	$-0.0189347\pi$
$332$	379.319	−	219.000i	0.0627043	−	0.0362024i
$333$			7878.00i			1.29643i
$334$	3582.00	+	6204.21i	0.586821	+	1.01640i
$335$	162.000	−	280.592i	0.0264209	−	0.0457624i
$336$	922.317	+	532.500i	0.149752	+	0.0864591i
$337$	−2171.00			−0.350926			−0.175463	−	0.984486i	$-0.556142\pi$
$337$	−2171.00			−0.350926			−0.175463	+	0.984486i	$0.556142\pi$
$338$		0			0
$339$	−90.0000			−0.0144193
$340$	350.740	+	202.500i	0.0559458	+	0.0323003i
$341$	6336.00	−	10974.3i	1.00620	−	1.74279i
$342$	−234.000	−	405.300i	−0.0369979	−	0.0640822i
$343$		−	6915.00i		−	1.08856i
$344$	−1764.09	+	1018.50i	−0.276493	+	0.159633i
$345$	1262.67	−	729.000i	0.197042	−	0.113762i
$346$		−	4698.00i		−	0.729960i
$347$	3523.50	+	6102.88i	0.545105	+	0.944149i	0.998600	+	0.0528907i	$0.0168435\pi$
$347$	3523.50	+	6102.88i	0.545105	+	0.944149i	−0.453495	+	0.891259i	$0.649823\pi$
$348$	72.0000	−	124.708i	0.0110908	−	0.0192099i
$349$	−5952.19	−	3436.50i	−0.912933	−	0.527082i	−0.0315592	−	0.999502i	$-0.510047\pi$
$349$	−5952.19	−	3436.50i	−0.912933	−	0.527082i	−0.881374	+	0.472420i	$0.843381\pi$
$350$	1980.00			0.302387
$351$		0			0
$352$	2160.00			0.327069
$353$	8069.62	+	4659.00i	1.21672	+	0.702475i	0.964215	−	0.265121i	$-0.0854118\pi$
$353$	8069.62	+	4659.00i	1.21672	+	0.702475i	0.252507	+	0.967595i	$0.418745\pi$
$354$	783.000	−	1356.20i	0.117559	−	0.203619i
$355$	−1606.50	−	2782.54i	−0.240181	−	0.416005i
$356$		−	438.000i		−	0.0652077i
$357$	−584.567	+	337.500i	−0.0866627	+	0.0500347i
$358$	−1706.94	+	985.500i	−0.251995	+	0.145490i
$359$		−	4128.00i		−	0.606873i	−0.952852	−	0.303437i	$-0.901866\pi$
$359$		−	4128.00i		−	0.606873i	0.952852	−	0.303437i	$-0.0981341\pi$
$360$	2457.00	+	4255.65i	0.359709	+	0.623034i
$361$	−3411.50	+	5908.89i	−0.497376	+	0.861480i
$362$	3174.85	+	1833.00i	0.460957	+	0.266134i
$363$	973.000			0.140687
$364$		0			0
$365$	9882.00			1.41712
$366$	976.877	+	564.000i	0.139514	+	0.0805485i
$367$	1268.00	−	2196.24i	0.180352	−	0.312378i	−0.761649	−	0.647990i	$-0.775610\pi$
$367$	1268.00	−	2196.24i	0.180352	−	0.312378i	0.942000	+	0.335612i	$0.108943\pi$
$368$	5751.00	+	9961.02i	0.814651	+	1.41102i
$369$			4992.00i			0.704263i
$370$	−7084.95	+	4090.50i	−0.995484	+	0.574743i
$371$	5378.02	−	3105.00i	0.752595	−	0.434511i
$372$			264.000i			0.0367951i
$373$	46.0000	+	79.6743i	0.00638550	+	0.0110600i	0.869200	−	0.494460i	$-0.164634\pi$
$373$	46.0000	+	79.6743i	0.00638550	+	0.0110600i	−0.862815	+	0.505520i	$0.831301\pi$
$374$	−3240.00	+	5611.84i	−0.447958	+	0.775887i
$375$	−1317.22	−	760.500i	−0.181390	−	0.104725i
$376$	2331.00			0.319713
$377$		0			0
$378$	2385.00			0.324527
$379$	−8817.87	−	5091.00i	−1.19510	−	0.689992i	−0.235643	−	0.971840i	$-0.575719\pi$
$379$	−8817.87	−	5091.00i	−1.19510	−	0.689992i	−0.959459	+	0.281847i	$0.909053\pi$
$380$	27.0000	−	46.7654i	0.00364492	−	0.00631319i
$381$	1043.00	+	1806.53i	0.140248	+	0.242917i
$382$			3780.00i			0.506287i
$383$	−501.429	+	289.500i	−0.0668977	+	0.0386234i	−0.533076	−	0.846068i	$-0.678964\pi$
$383$	−501.429	+	289.500i	−0.0668977	+	0.0386234i	0.466178	+	0.884691i	$0.345631\pi$
$384$	1436.74	−	829.500i	0.190933	−	0.110235i
$385$		−	6480.00i		−	0.857796i
$386$	−513.000	−	888.542i	−0.0676451	−	0.117165i
$387$	−1261.00	+	2184.12i	−0.165634	+	0.286886i
$388$	−737.854	−	426.000i	−0.0965434	−	0.0557394i
$389$	2106.00			0.274495			0.137247	−	0.990537i	$-0.456174\pi$
$389$	2106.00			0.274495			0.137247	+	0.990537i	$0.456174\pi$
$390$		0			0
$391$	−7290.00			−0.942893
$392$	−2146.01	−	1239.00i	−0.276505	−	0.159640i
$393$	−733.500	+	1270.46i	−0.0941480	+	0.163069i
$394$	121.500	+	210.444i	0.0155357	+	0.0269087i
$395$			7470.00i			0.951535i
$396$	1080.80	−	624.000i	0.137152	−	0.0791848i
$397$	1709.53	−	987.000i	0.216119	−	0.124776i	−0.388033	−	0.921645i	$-0.626845\pi$
$397$	1709.53	−	987.000i	0.216119	−	0.124776i	0.604152	+	0.796869i	$0.293512\pi$
$398$			5988.00i			0.754149i
$399$	45.0000	+	77.9423i	0.00564616	+	0.00977944i
$400$	1562.00	−	2705.46i	0.195250	−	0.338183i
$401$	10293.6	+	5943.00i	1.28189	+	0.740098i	0.977193	−	0.212352i	$-0.0681125\pi$
$401$	10293.6	+	5943.00i	1.28189	+	0.740098i	0.304694	+	0.952450i	$0.401446\pi$
$402$	−108.000			−0.0133994
$403$		0			0
$404$	−396.000			−0.0487667
$405$	5058.45	+	2920.50i	0.620634	+	0.358323i
$406$	3240.00	−	5611.84i	0.396055	−	0.685988i
$407$	−7272.00	−	12595.5i	−0.885650	−	1.53399i
$408$			945.000i			0.114668i
$409$	1086.00	−	627.000i	0.131293	−	0.0758023i	−0.432915	−	0.901435i	$-0.642515\pi$
$409$	1086.00	−	627.000i	0.131293	−	0.0758023i	0.564208	+	0.825633i	$0.309182\pi$
$410$	−4489.48	+	2592.00i	−0.540779	+	0.312219i
$411$		−	414.000i		−	0.0496864i
$412$	91.0000	+	157.617i	0.0108817	+	0.0188476i
$413$	3915.00	−	6780.98i	0.466452	−	0.807918i
$414$	10943.1	+	6318.00i	1.29909	+	0.750031i
$415$	−3942.00			−0.466278
$416$		0			0
$417$	2419.00			0.284074
$418$	748.246	+	432.000i	0.0875548	+	0.0505498i
$419$	−2911.50	+	5042.87i	−0.339466	+	0.587972i	−0.984332	−	0.176323i	$-0.943580\pi$
$419$	−2911.50	+	5042.87i	−0.339466	+	0.587972i	0.644867	+	0.764295i	$0.276913\pi$
$420$	67.5000	+	116.913i	0.00784205	+	0.0135828i
$421$		−	7341.00i		−	0.849830i	−0.905233	−	0.424915i	$-0.860304\pi$
$421$		−	7341.00i		−	0.849830i	0.905233	−	0.424915i	$-0.139696\pi$
$422$	7360.35	−	4249.50i	0.849043	−	0.490195i
$423$	2499.35	−	1443.00i	0.287287	−	0.165865i
$424$		−	8694.00i		−	0.995797i
$425$	990.000	+	1714.73i	0.112993	+	0.195710i
$426$	−535.500	+	927.513i	−0.0609039	+	0.105489i
$427$	4884.38	+	2820.00i	0.553564	+	0.319600i
$428$	612.000			0.0691171
$429$		0			0
$430$	−2619.00			−0.293720
$431$	6482.20	+	3742.50i	0.724447	+	0.418260i	0.816387	−	0.577505i	$-0.195974\pi$
$431$	6482.20	+	3742.50i	0.724447	+	0.418260i	−0.0919403	+	0.995765i	$0.529307\pi$
$432$	1881.50	−	3258.85i	0.209546	−	0.362944i
$433$	7601.50	+	13166.2i	0.843660	+	1.46126i	0.886780	+	0.462192i	$0.152937\pi$
$433$	7601.50	+	13166.2i	0.843660	+	1.46126i	−0.0431199	+	0.999070i	$0.513730\pi$
$434$			11880.0i			1.31396i
$435$	−1122.37	+	648.000i	−0.123709	+	0.0714235i
$436$	−937.906	+	541.500i	−0.103022	+	0.0594797i
$437$			972.000i			0.106401i
$438$	−1647.00	−	2852.69i	−0.179673	−	0.311202i
$439$	881.000	−	1525.94i	0.0957809	−	0.165897i	−0.814153	−	0.580650i	$-0.802799\pi$
$439$	881.000	−	1525.94i	0.0957809	−	0.165897i	0.909934	+	0.414752i	$0.136132\pi$
$440$	−7856.58	−	4536.00i	−0.851245	−	0.491467i
$441$	−3068.00			−0.331282
$442$		0			0
$443$	−7317.00			−0.784743			−0.392372	−	0.919807i	$-0.628345\pi$
$443$	−7317.00			−0.784743			−0.392372	+	0.919807i	$0.628345\pi$
$444$	262.406	+	151.500i	0.0280478	+	0.0161934i
$445$	−1971.00	+	3413.87i	−0.209965	+	0.363670i
$446$	−5260.50	−	9111.45i	−0.558502	−	0.967354i
$447$			930.000i			0.0984060i
$448$	5624.83	−	3247.50i	0.593189	−	0.342478i
$449$	4343.98	−	2508.00i	0.456582	−	0.263608i	−0.254024	−	0.967198i	$-0.581754\pi$
$449$	4343.98	−	2508.00i	0.456582	−	0.263608i	0.710606	+	0.703590i	$0.248421\pi$
$450$		−	3432.00i		−	0.359525i
$451$	−4608.00	−	7981.29i	−0.481114	−	0.833313i
$452$	45.0000	−	77.9423i	0.00468279	−	0.00811083i
$453$	1457.52	+	841.500i	0.151171	+	0.0872784i
$454$	684.000			0.0707086
$455$		0			0
$456$	126.000			0.0129397
$457$	−8547.67	−	4935.00i	−0.874930	−	0.505141i	−0.00594684	−	0.999982i	$-0.501893\pi$
$457$	−8547.67	−	4935.00i	−0.874930	−	0.505141i	−0.868984	+	0.494841i	$0.835226\pi$
$458$	−8239.50	+	14271.2i	−0.840626	+	1.45601i
$459$	1192.50	+	2065.47i	0.121266	+	0.210039i
$460$			1458.00i			0.147782i
$461$	−12592.9	+	7270.50i	−1.27225	+	0.734536i	−0.975412	−	0.220391i	$-0.929267\pi$
$461$	−12592.9	+	7270.50i	−1.27225	+	0.734536i	−0.296842	+	0.954927i	$0.595933\pi$
$462$	−1870.61	+	1080.00i	−0.188374	+	0.108758i
$463$			2112.00i			0.211993i	0.994366	+	0.105997i	$0.0338033\pi$
$463$			2112.00i			0.211993i	−0.994366	+	0.105997i	$0.966197\pi$
$464$	−5112.00	−	8854.24i	−0.511463	−	0.885879i
$465$	1188.00	−	2057.68i	0.118478	−	0.205210i
$466$	−9423.22	−	5440.50i	−0.936743	−	0.540829i
$467$	3276.00			0.324615			0.162307	−	0.986740i	$-0.448106\pi$
$467$	3276.00			0.324615			0.162307	+	0.986740i	$0.448106\pi$
$468$		0			0
$469$	−540.000			−0.0531661
$470$	2595.48	+	1498.50i	0.254724	+	0.147065i
$471$	937.000	−	1622.93i	0.0916660	−	0.158770i
$472$	−5481.00	−	9493.37i	−0.534499	−	0.925779i
$473$		−	4656.00i		−	0.452607i
$474$	2156.40	−	1245.00i	0.208960	−	0.120643i
$475$	228.631	−	132.000i	0.0220848	−	0.0127507i
$476$		−	675.000i		−	0.0649970i
$477$	−5382.00	−	9321.90i	−0.516614	−	0.894802i
$478$	9112.50	−	15783.3i	0.871958	−	1.51028i
$479$	−13382.7	−	7726.50i	−1.27656	−	0.737020i	−0.300343	−	0.953831i	$-0.597101\pi$
$479$	−13382.7	−	7726.50i	−1.27656	−	0.737020i	−0.976214	+	0.216811i	$0.930435\pi$
$480$	405.000			0.0385117
$481$		0			0
$482$	630.000			0.0595347
$483$	−2104.44	−	1215.00i	−0.198251	−	0.114460i
$484$	−486.500	+	842.643i	−0.0456893	+	0.0791362i
$485$	3834.00	+	6640.68i	0.358955	+	0.621728i
$486$		−	6240.00i		−	0.582412i
$487$	−3169.65	+	1830.00i	−0.294930	+	0.170278i	−0.640163	−	0.768239i	$-0.721133\pi$
$487$	−3169.65	+	1830.00i	−0.294930	+	0.170278i	0.345233	+	0.938517i	$0.387800\pi$
$488$	6838.14	−	3948.00i	0.634319	−	0.366225i
$489$		−	1194.00i		−	0.110418i
$490$	−1593.00	−	2759.16i	−0.146866	−	0.254380i
$491$	−373.500	+	646.921i	−0.0343296	+	0.0594606i	−0.882680	−	0.469975i	$-0.844263\pi$
$491$	−373.500	+	646.921i	−0.0343296	+	0.0594606i	0.848350	+	0.529436i	$0.177596\pi$
$492$	166.277	+	96.0000i	0.0152365	+	0.00879678i
$493$	6480.00			0.591977
$494$		0			0
$495$	−11232.0			−1.01988
$496$	16232.8	+	9372.00i	1.46950	+	0.848418i
$497$	−2677.50	+	4637.57i	−0.241655	+	0.418558i
$498$	657.000	+	1137.96i	0.0591182	+	0.102396i
$499$		−	15804.0i		−	1.41780i	−0.705307	−	0.708902i	$-0.749191\pi$
$499$		−	15804.0i		−	1.41780i	0.705307	−	0.708902i	$-0.250809\pi$
$500$	1317.22	−	760.500i	0.117816	−	0.0680212i
$501$	−2068.07	+	1194.00i	−0.184420	+	0.106475i
$502$			21276.0i			1.89162i
$503$	6039.00	+	10459.9i	0.535319	+	0.927201i	0.999148	+	0.0412754i	$0.0131421\pi$
$503$	6039.00	+	10459.9i	0.535319	+	0.927201i	−0.463828	+	0.885925i	$0.653525\pi$
$504$	4095.00	−	7092.75i	0.361916	−	0.626857i
$505$	3086.51	+	1782.00i	0.271976	+	0.157026i
$506$	−23328.0			−2.04952
$507$		0			0
$508$	−2086.00			−0.182188
$509$	−13951.7	−	8055.00i	−1.21493	−	0.701437i	−0.251097	−	0.967962i	$-0.580791\pi$
$509$	−13951.7	−	8055.00i	−1.21493	−	0.701437i	−0.963828	+	0.266525i	$0.914125\pi$
$510$	−607.500	+	1052.22i	−0.0527462	+	0.0913591i
$511$	−8235.00	−	14263.4i	−0.712906	−	1.23479i
$512$		−	8733.00i		−	0.753804i
$513$	275.396	−	159.000i	0.0237018	−	0.0136843i
$514$	−15081.8	+	8707.50i	−1.29422	+	0.747221i
$515$		−	1638.00i		−	0.140153i
$516$	48.5000	+	84.0045i	0.00413778	+	0.00716684i
$517$	−2664.00	+	4614.18i	−0.226620	+	0.392518i
$518$	11808.3	+	6817.50i	1.00159	+	0.578270i
$519$	1566.00			0.132447
$520$		0			0
$521$	3915.00			0.329212			0.164606	−	0.986359i	$-0.447365\pi$
$521$	3915.00			0.329212			0.164606	+	0.986359i	$0.447365\pi$
$522$	−9727.20	−	5616.00i	−0.815609	−	0.470892i
$523$	−8092.00	+	14015.8i	−0.676555	+	1.17183i	0.299456	+	0.954110i	$0.403195\pi$
$523$	−8092.00	+	14015.8i	−0.676555	+	1.17183i	−0.976012	+	0.217718i	$0.930139\pi$
$524$	−733.500	−	1270.46i	−0.0611509	−	0.105917i
$525$			660.000i			0.0548662i
$526$	2057.68	−	1188.00i	0.170568	−	0.0984777i
$527$	−10288.4	+	5940.00i	−0.850415	+	0.490988i
$528$			3408.00i			0.280898i
$529$	−7038.50	−	12191.0i	−0.578491	−	1.00198i
$530$	5589.00	−	9680.43i	0.458058	−	0.793379i
$531$	−11753.7	−	6786.00i	−0.960578	−	0.554590i
$532$	−90.0000			−0.00733458
$533$		0			0
$534$	1314.00			0.106484
$535$	−4770.07	−	2754.00i	−0.385473	−	0.222553i
$536$	−378.000	+	654.715i	−0.0304610	+	0.0527601i
$537$	−328.500	−	568.979i	−0.0263982	−	0.0457230i
$538$			16416.0i			1.31551i
$539$	4905.17	−	2832.00i	0.391986	−	0.226313i
$540$	413.094	−	238.500i	0.0329199	−	0.0190063i
$541$			7923.00i			0.629642i	0.949151	+	0.314821i	$0.101945\pi$
$541$			7923.00i			0.629642i	−0.949151	+	0.314821i	$0.898055\pi$
$542$	−3496.50	−	6056.12i	−0.277099	−	0.479949i
$543$	−611.000	+	1058.28i	−0.0482882	+	0.0836377i
$544$	−1753.70	−	1012.50i	−0.138216	−	0.0797989i
$545$	9747.00			0.766084
$546$		0			0
$547$	−14389.0			−1.12473			−0.562367	−	0.826888i	$-0.690109\pi$
$547$	−14389.0			−1.12473			−0.562367	+	0.826888i	$0.690109\pi$
$548$	358.535	+	207.000i	0.0279486	+	0.0161361i
$549$	4888.00	−	8466.26i	0.379990	−	0.658163i
$550$	3168.00	+	5487.14i	0.245607	+	0.425404i
$551$		−	864.000i		−	0.0668015i
$552$	−2946.22	+	1701.00i	−0.227173	+	0.131158i
$553$	10782.0	−	6225.00i	0.829110	−	0.478687i
$554$		−	4152.00i		−	0.318414i
$555$	−1363.50	−	2361.65i	−0.104284	−	0.180624i
$556$	−1209.50	+	2094.92i	−0.0922558	+	0.159792i
$557$	−8991.94	−	5191.50i	−0.684023	−	0.394921i	0.117346	−	0.993091i	$-0.462561\pi$
$557$	−8991.94	−	5191.50i	−0.684023	−	0.394921i	−0.801369	+	0.598170i	$0.795895\pi$
$558$	20592.0			1.56224
$559$		0			0
$560$	9585.00			0.723286
$561$	−1870.61	−	1080.00i	−0.140780	−	0.0812792i
$562$	6093.00	−	10553.4i	0.457327	−	0.792113i
$563$	8212.50	+	14224.5i	0.614770	+	1.06481i	0.990425	+	0.138053i	$0.0440846\pi$
$563$	8212.50	+	14224.5i	0.614770	+	1.06481i	−0.375655	+	0.926760i	$0.622582\pi$
$564$		−	111.000i		−	0.00828713i
$565$	−701.481	+	405.000i	−0.0522328	+	0.0301566i
$566$	−9779.16	+	5646.00i	−0.726234	+	0.419292i
$567$		−	9735.00i		−	0.721043i
$568$	3748.50	+	6492.59i	0.276908	+	0.479618i
$569$	−6106.50	+	10576.8i	−0.449908	+	0.779264i	−0.998380	−	0.0569054i	$-0.981877\pi$
$569$	−6106.50	+	10576.8i	−0.449908	+	0.779264i	0.548471	+	0.836169i	$0.315210\pi$
$570$	140.296	+	81.0000i	0.0103094	+	0.00595213i
$571$	−6383.00			−0.467811			−0.233906	−	0.972259i	$-0.575151\pi$
$571$	−6383.00			−0.467811			−0.233906	+	0.972259i	$0.575151\pi$
$572$		0			0
$573$	−1260.00			−0.0918626
$574$	7482.46	+	4320.00i	0.544097	+	0.314135i
$575$	−3564.00	+	6173.03i	−0.258485	+	0.447710i
$576$	−5629.00	−	9749.71i	−0.407190	−	0.705274i
$577$			6426.00i			0.463636i	0.972759	+	0.231818i	$0.0744674\pi$
$577$			6426.00i			0.463636i	−0.972759	+	0.231818i	$0.925533\pi$
$578$	−7503.24	+	4332.00i	−0.539955	+	0.311743i
$579$	296.181	−	171.000i	0.0212588	−	0.0122738i
$580$		−	1296.00i		−	0.0927818i
$581$	3285.00	+	5689.79i	0.234569	+	0.406286i
$582$	1278.00	−	2213.56i	0.0910220	−	0.157655i
$583$	17209.7	+	9936.00i	1.22256	+	0.705844i
$584$	−23058.0			−1.63381
$585$		0			0
$586$	12681.0			0.893937
$587$	18472.3	+	10665.0i	1.29887	+	0.749901i	0.980208	−	0.197969i	$-0.0634346\pi$
$587$	18472.3	+	10665.0i	1.29887	+	0.749901i	0.318658	+	0.947870i	$0.396768\pi$
$588$	−59.0000	+	102.191i	−0.00413796	+	0.00716715i
$589$	792.000	+	1371.78i	0.0554054	+	0.0959650i
$590$		−	14094.0i		−	0.983459i
$591$	−70.1481	+	40.5000i	−0.00488241	+	0.00281886i
$592$	18630.8	−	10756.5i	1.29345	−	0.746773i
$593$		−	12084.0i		−	0.836813i	−0.908260	−	0.418407i	$-0.862589\pi$
$593$		−	12084.0i		−	0.836813i	0.908260	−	0.418407i	$-0.137411\pi$
$594$	3816.00	+	6609.51i	0.263590	+	0.456551i
$595$	−3037.50	+	5261.10i	−0.209286	+	0.362495i
$596$	−805.404	−	465.000i	−0.0553534	−	0.0319583i
$597$	−1996.00			−0.136836
$598$		0			0
$599$	2394.00			0.163299			0.0816496	−	0.996661i	$-0.473981\pi$
$599$	2394.00			0.163299			0.0816496	+	0.996661i	$0.473981\pi$
$600$	800.207	+	462.000i	0.0544472	+	0.0314351i
$601$	10985.5	−	19027.4i	0.745604	−	1.29142i	−0.204308	−	0.978907i	$-0.565495\pi$
$601$	10985.5	−	19027.4i	0.745604	−	1.29142i	0.949912	−	0.312517i	$-0.101172\pi$
$602$	2182.50	+	3780.20i	0.147761	+	0.255929i
$603$			936.000i			0.0632121i
$604$	−1457.52	+	841.500i	−0.0981882	+	0.0566890i
$605$	7583.78	−	4378.50i	0.509628	−	0.294234i
$606$		−	1188.00i		−	0.0796356i
$607$	7703.00	+	13342.0i	0.515083	+	0.892149i	0.999847	+	0.0175043i	$0.00557208\pi$
$607$	7703.00	+	13342.0i	0.515083	+	0.892149i	−0.484764	+	0.874645i	$0.661095\pi$
$608$	−135.000	+	233.827i	−0.00900489	+	0.0155969i
$609$	1870.61	+	1080.00i	0.124468	+	0.0718618i
$610$	10152.0			0.673840
$611$		0			0
$612$	−1170.00			−0.0772785
$613$	8339.82	+	4815.00i	0.549498	+	0.317253i	0.748920	−	0.662661i	$-0.230573\pi$
$613$	8339.82	+	4815.00i	0.549498	+	0.317253i	−0.199421	+	0.979914i	$0.563906\pi$
$614$	−459.000	+	795.011i	−0.0301689	+	0.0522541i
$615$	−864.000	−	1496.49i	−0.0566502	−	0.0981209i
$616$			15120.0i			0.988965i
$617$	12772.1	−	7374.00i	0.833366	−	0.481144i	−0.0216375	−	0.999766i	$-0.506888\pi$
$617$	12772.1	−	7374.00i	0.833366	−	0.481144i	0.855004	+	0.518622i	$0.173555\pi$
$618$	−472.850	+	273.000i	−0.0307780	+	0.0177697i
$619$			3672.00i			0.238433i	0.992868	+	0.119217i	$0.0380383\pi$
$619$			3672.00i			0.238433i	−0.992868	+	0.119217i	$0.961962\pi$
$620$	1188.00	+	2057.68i	0.0769536	+	0.133288i
$621$	−4293.00	+	7435.69i	−0.277411	+	0.480490i
$622$	5471.55	+	3159.00i	0.352716	+	0.203640i
$623$	6570.00			0.422506
$624$		0			0
$625$	−8189.00			−0.524096
$626$	−26113.3	−	15076.5i	−1.66725	−	0.962585i
$627$	−144.000	+	249.415i	−0.00917194	+	0.0158863i
$628$	937.000	+	1622.93i	0.0595388	+	0.103124i
$629$			13635.0i			0.864329i
$630$	9119.25	−	5265.00i	0.576698	−	0.332957i
$631$	17212.3	−	9937.50i	1.08591	−	0.626950i	0.153425	−	0.988160i	$-0.450970\pi$
$631$	17212.3	−	9937.50i	1.08591	−	0.626950i	0.932485	+	0.361210i	$0.117636\pi$
$632$		−	17430.0i		−	1.09704i
$633$	1416.50	+	2453.45i	0.0889428	+	0.154054i
$634$	−3231.00	+	5596.26i	−0.202397	+	0.350561i
$635$	16258.8	+	9387.00i	1.01608	+	0.586633i
$636$	−414.000			−0.0258116
$637$		0			0
$638$	20736.0			1.28675
$639$	8038.45	+	4641.00i	0.497646	+	0.287316i
$640$	7465.50	−	12930.6i	0.461093	−	0.798637i
$641$	−855.000	−	1480.90i	−0.0526840	−	0.0912514i	0.838481	−	0.544931i	$-0.183444\pi$
$641$	−855.000	−	1480.90i	−0.0526840	−	0.0912514i	−0.891165	+	0.453680i	$0.850111\pi$
$642$			1836.00i			0.112868i
$643$	−14247.8	+	8226.00i	−0.873842	+	0.504513i	−0.868623	−	0.495474i	$-0.834995\pi$
$643$	−14247.8	+	8226.00i	−0.873842	+	0.504513i	−0.00521887	+	0.999986i	$0.501661\pi$
$644$	2104.44	−	1215.00i	0.128768	−	0.0743443i
$645$		−	873.000i		−	0.0532936i
$646$	−405.000	−	701.481i	−0.0246664	−	0.0427235i
$647$	−12951.0	+	22431.8i	−0.786950	+	1.36304i	0.140878	+	0.990027i	$0.455007\pi$
$647$	−12951.0	+	22431.8i	−0.786950	+	1.36304i	−0.927827	+	0.373010i	$0.878326\pi$
$648$	−11803.1	−	6814.50i	−0.715537	−	0.413115i
$649$	25056.0			1.51546
$650$		0			0
$651$	−3960.00			−0.238410
$652$	1034.03	+	597.000i	0.0621103	+	0.0358594i
$653$	−9054.00	+	15682.0i	−0.542589	+	0.939791i	0.456166	+	0.889895i	$0.349222\pi$
$653$	−9054.00	+	15682.0i	−0.542589	+	0.939791i	−0.998754	+	0.0498963i	$0.984111\pi$
$654$	−1624.50	−	2813.72i	−0.0971299	−	0.168234i
$655$			13203.0i			0.787609i
$656$	11805.7	−	6816.00i	0.702643	−	0.405671i
$657$	−24723.3	+	14274.0i	−1.46811	+	0.847613i
$658$		−	4995.00i		−	0.295935i
$659$	16452.0	+	28495.7i	0.972502	+	1.68442i	0.687943	+	0.725765i	$0.258514\pi$
$659$	16452.0	+	28495.7i	0.972502	+	1.68442i	0.284559	+	0.958658i	$0.408153\pi$
$660$	−216.000	+	374.123i	−0.0127391	+	0.0220647i
$661$	13265.8	+	7659.00i	0.780604	+	0.450682i	0.836644	−	0.547747i	$-0.184514\pi$
$661$	13265.8	+	7659.00i	0.780604	+	0.450682i	−0.0560406	+	0.998428i	$0.517848\pi$
$662$	−32310.0			−1.89692
$663$		0			0
$664$	9198.00			0.537578
$665$	701.481	+	405.000i	0.0409056	+	0.0236169i
$666$	11817.0	−	20467.6i	0.687537	−	1.19085i
$667$	11664.0	+	20202.6i	0.677109	+	1.17279i
$668$		−	2388.00i		−	0.138315i
$669$	3037.15	−	1753.50i	0.175520	−	0.101337i
$670$	−841.777	+	486.000i	−0.0485383	+	0.0280236i
$671$			18048.0i			1.03835i
$672$	−337.500	−	584.567i	−0.0193740	−	0.0335568i
$673$	3864.50	−	6693.51i	0.221346	−	0.383382i	−0.733871	−	0.679289i	$-0.762288\pi$
$673$	3864.50	−	6693.51i	0.221346	−	0.383382i	0.955217	+	0.295907i	$0.0956218\pi$
$674$	5640.42	+	3256.50i	0.322346	+	0.186106i
$675$	2332.00			0.132976
$676$		0			0
$677$	19242.0			1.09236			0.546182	−	0.837667i	$-0.316081\pi$
$677$	19242.0			1.09236			0.546182	+	0.837667i	$0.316081\pi$
$678$	233.827	+	135.000i	0.0132449	+	0.00764697i
$679$	6390.00	−	11067.8i	0.361157	−	0.625543i
$680$	4252.50	+	7365.55i	0.239818	+	0.415376i
$681$			228.000i			0.0128296i
$682$	−32922.8	+	19008.0i	−1.84850	+	1.06723i
$683$	−19501.2	+	11259.0i	−1.09252	+	0.630767i	−0.934246	−	0.356629i	$-0.883926\pi$
$683$	−19501.2	+	11259.0i	−1.09252	+	0.630767i	−0.158274	+	0.987395i	$0.550593\pi$
$684$			156.000i			0.00872048i
$685$	−1863.00	−	3226.81i	−0.103915	−	0.179986i
$686$	−10372.5	+	17965.7i	−0.577294	+	0.999903i
$687$	−4757.08	−	2746.50i	−0.264183	−	0.152526i
$688$	6887.00			0.381634
$689$		0			0
$690$	−4374.00			−0.241327
$691$	−7939.72	−	4584.00i	−0.437107	−	0.252364i	0.265262	−	0.964176i	$-0.414541\pi$
$691$	−7939.72	−	4584.00i	−0.437107	−	0.252364i	−0.702370	+	0.711812i	$0.747875\pi$
$692$	−783.000	+	1356.20i	−0.0430133	+	0.0745012i
$693$	9360.00	+	16212.0i	0.513069	+	0.888662i
$694$		−	21141.0i		−	1.15634i
$695$	18854.2	−	10885.5i	1.02904	−	0.594116i
$696$	2618.86	−	1512.00i	0.142626	−	0.0823451i
$697$			8640.00i			0.469531i
$698$	10309.5	+	17856.6i	0.559055	+	0.968312i
$699$	1813.50	−	3141.07i	0.0981300	−	0.169966i
$700$	−571.577	−	330.000i	−0.0308622	−	0.0178183i
$701$	1170.00			0.0630389			0.0315195	−	0.999503i	$-0.489965\pi$
$701$	1170.00			0.0630389			0.0315195	+	0.999503i	$0.489965\pi$
$702$		0			0
$703$	1818.00			0.0975351
$704$	17999.5	+	10392.0i	0.963609	+	0.556340i
$705$	−499.500	+	865.159i	−0.0266841	+	0.0462181i
$706$	−13977.0	−	24208.9i	−0.745087	−	1.29053i
$707$		−	5940.00i		−	0.315978i
$708$	−452.065	+	261.000i	−0.0239967	+	0.0138545i
$709$	1439.33	−	831.000i	0.0762417	−	0.0440181i	−0.461395	−	0.887195i	$-0.652651\pi$
$709$	1439.33	−	831.000i	0.0762417	−	0.0440181i	0.537636	+	0.843177i	$0.319317\pi$
$710$			9639.00i			0.509500i
$711$	−10790.0	−	18688.8i	−0.569137	−	0.985775i
$712$	4599.00	−	7965.70i	0.242071	−	0.419280i
$713$	−37038.2	−	21384.0i	−1.94543	−	1.12319i
$714$	2025.00			0.106140
$715$		0			0
$716$	657.000			0.0342922
$717$	5261.10	+	3037.50i	0.274030	+	0.158211i
$718$	−6192.00	+	10724.9i	−0.321843	+	0.557449i
$719$	−15480.0	−	26812.1i	−0.802930	−	1.39072i	−0.917680	−	0.397321i	$-0.869940\pi$
$719$	−15480.0	−	26812.1i	−0.802930	−	1.39072i	0.114750	−	0.993394i	$-0.463393\pi$
$720$		−	16614.0i		−	0.859954i
$721$	−2364.25	+	1365.00i	−0.122121	+	0.0705066i
$722$	17726.7	−	10234.5i	0.913738	−	0.527547i
$723$			210.000i			0.0108022i
$724$	−611.000	−	1058.28i	−0.0313641	−	0.0543243i
$725$	3168.00	−	5487.14i	0.162285	−	0.281086i
$726$	−2527.93	−	1459.50i	−0.129229	−	0.0746104i
$727$	−8372.00			−0.427098			−0.213549	−	0.976932i	$-0.568502\pi$
$727$	−8372.00			−0.427098			−0.213549	+	0.976932i	$0.568502\pi$
$728$		0			0
$729$	−15443.0			−0.784586
$730$	−25674.2	−	14823.0i	−1.30170	−	0.751540i
$731$	−2182.50	+	3780.20i	−0.110428	+	0.191266i
$732$	−188.000	−	325.626i	−0.00949273	−	0.0164419i
$733$		−	2739.00i		−	0.138018i	−0.997616	−	0.0690091i	$-0.978016\pi$
$733$		−	2739.00i		−	0.138018i	0.997616	−	0.0690091i	$-0.0219837\pi$
$734$	−6588.72	+	3804.00i	−0.331327	+	0.191292i
$735$	919.719	−	531.000i	0.0461556	−	0.0266479i
$736$		−	7290.00i		−	0.365099i
$737$	−864.000	−	1496.49i	−0.0431830	−	0.0747951i
$738$	7488.00	−	12969.6i	0.373492	−	0.646907i
$739$	−5850.87	−	3378.00i	−0.291242	−	0.168148i	0.347260	−	0.937769i	$-0.387112\pi$
$739$	−5850.87	−	3378.00i	−0.291242	−	0.168148i	−0.638502	+	0.769620i	$0.720445\pi$
$740$	2727.00			0.135468
$741$		0			0
$742$	−18630.0			−0.921737
$743$	−25671.6	−	14821.5i	−1.26756	−	0.731828i	−0.293037	−	0.956101i	$-0.594666\pi$
$743$	−25671.6	−	14821.5i	−1.26756	−	0.731828i	−0.974526	+	0.224273i	$0.927999\pi$
$744$	−2772.00	+	4801.24i	−0.136595	+	0.236589i
$745$	4185.00	+	7248.63i	0.205807	+	0.356469i
$746$		−	276.000i		−	0.0135457i
$747$	9862.30	−	5694.00i	0.483056	−	0.278892i
$748$	1870.61	−	1080.00i	0.0914391	−	0.0527924i
$749$			9180.00i			0.447837i
$750$	2281.50	+	3951.67i	0.111078	+	0.192393i
$751$	−9064.00	+	15699.3i	−0.440413	+	0.762817i	−0.997720	−	0.0674890i	$-0.978501\pi$
$751$	−9064.00	+	15699.3i	−0.440413	+	0.762817i	0.557307	+	0.830306i	$0.311835\pi$
$752$	−6825.15	−	3940.50i	−0.330967	−	0.191084i
$753$	−7092.00			−0.343223
$754$		0			0
$755$	15147.0			0.730140
$756$	−688.490	−	397.500i	−0.0331219	−	0.0191229i
$757$	3205.00	−	5551.22i	0.153881	−	0.266529i	−0.778770	−	0.627309i	$-0.784156\pi$
$757$	3205.00	−	5551.22i	0.153881	−	0.266529i	0.932651	+	0.360780i	$0.117490\pi$
$758$	15273.0	+	26453.6i	0.731847	+	1.26760i
$759$		−	7776.00i		−	0.371872i
$760$	982.073	−	567.000i	0.0468731	−	0.0270622i
$761$	−24499.9	+	14145.0i	−1.16704	+	0.673792i	−0.952982	−	0.303028i	$-0.902002\pi$
$761$	−24499.9	+	14145.0i	−1.16704	+	0.673792i	−0.214061	+	0.976820i	$0.568669\pi$
$762$		−	6258.00i		−	0.297511i
$763$	−8122.50	−	14068.6i	−0.385392	−	0.667519i
$764$	630.000	−	1091.19i	0.0298332	−	0.0516727i
$765$	9119.25	+	5265.00i	0.430990	+	0.248832i
$766$	1737.00			0.0819326
$767$		0			0
$768$	−1513.00			−0.0710881
$769$	24214.1	+	13980.0i	1.13548	+	0.655568i	0.945307	−	0.326183i	$-0.105763\pi$
$769$	24214.1	+	13980.0i	1.13548	+	0.655568i	0.190170	+	0.981751i	$0.439096\pi$
$770$	−9720.00	+	16835.5i	−0.454915	+	0.787936i
$771$	−2902.50	−	5027.28i	−0.135578	−	0.234829i
$772$			342.000i			0.0159441i
$773$	−4892.18	+	2824.50i	−0.227632	+	0.131423i	−0.609479	−	0.792802i	$-0.708621\pi$
$773$	−4892.18	+	2824.50i	−0.227632	+	0.131423i	0.381847	+	0.924225i	$0.375288\pi$
$774$	6552.35	−	3783.00i	0.304288	−	0.175681i
$775$			11616.0i			0.538399i
$776$	−8946.00	−	15494.9i	−0.413844	−	0.716798i
$777$	−2272.50	+	3936.09i	−0.104923	+	0.181733i
$778$	−5471.55	−	3159.00i	−0.252139	−	0.145573i
$779$	1152.00			0.0529842
$780$		0			0
$781$	−17136.0			−0.785114
$782$	18940.0	+	10935.0i	0.866102	+	0.500045i
$783$	3816.00	−	6609.51i	0.174167	−	0.301666i
$784$	4189.00	+	7255.56i	0.190825	+	0.330519i
$785$		−	16866.0i		−	0.766845i
$786$	3811.38	−	2200.50i	0.172961	−	0.0998591i
$787$	−654.715	+	378.000i	−0.0296545	+	0.0171210i	−0.514754	−	0.857338i	$-0.672117\pi$
$787$	−654.715	+	378.000i	−0.0296545	+	0.0171210i	0.485099	+	0.874459i	$0.338783\pi$
$788$		−	81.0000i		−	0.00366181i
$789$	396.000	+	685.892i	0.0178682	+	0.0309486i
$790$	11205.0	−	19407.6i	0.504628	−	0.874041i
$791$	1169.13	+	675.000i	0.0525533	+	0.0303416i
$792$	26208.0			1.17583
$793$		0			0
$794$	−5922.00			−0.264690
$795$	3226.81	+	1863.00i	0.143954	+	0.0831117i
$796$	998.000	−	1728.59i	0.0444387	−	0.0769700i
$797$	−15597.0	−	27014.8i	−0.693192	−	1.20064i	−0.970786	−	0.239945i	$-0.922870\pi$
$797$	−15597.0	−	27014.8i	−0.693192	−	1.20064i	0.277594	−	0.960698i	$-0.410463\pi$
$798$		−	270.000i		−	0.0119773i
$799$	4325.80	−	2497.50i	0.191534	−	0.110582i
$800$	−1714.73	+	990.000i	−0.0757811	+	0.0437522i
$801$		−	11388.0i		−	0.502341i
$802$	−17829.0	−	30880.7i	−0.784992	−	1.35965i
$803$	26352.0	−	45643.0i	1.15808	−	2.00586i
$804$	31.1769	+	18.0000i	0.00136757	+	0.000789566i
$805$	−21870.0			−0.957536
$806$		0			0
$807$	−5472.00			−0.238691
$808$	−7201.87	−	4158.00i	−0.313565	−	0.181037i
$809$	−8527.50	+	14770.1i	−0.370594	+	0.641888i	−0.989657	−	0.143453i	$-0.954179\pi$
$809$	−8527.50	+	14770.1i	−0.370594	+	0.641888i	0.619063	+	0.785342i	$0.287513\pi$
$810$	−8761.50	−	15175.4i	−0.380059	−	0.658281i
$811$			35520.0i			1.53795i	0.639280	+	0.768974i	$0.279232\pi$
$811$			35520.0i			1.53795i	−0.639280	+	0.768974i	$0.720768\pi$
$812$	−1870.61	+	1080.00i	−0.0808445	+	0.0466756i
$813$	2018.71	−	1165.50i	0.0870837	−	0.0502778i
$814$			43632.0i			1.87875i
$815$	−5373.00	−	9306.31i	−0.230930	−	0.399983i
$816$	1597.50	−	2766.95i	0.0685339	−	0.118704i
$817$	504.027	+	291.000i	0.0215834	+	0.0124612i
$818$	−3762.00			−0.160801
$819$		0			0
$820$	1728.00			0.0735907
$821$	−948.298	−	547.500i	−0.0403116	−	0.0232739i	0.479709	−	0.877428i	$-0.340742\pi$
$821$	−948.298	−	547.500i	−0.0403116	−	0.0232739i	−0.520020	+	0.854154i	$0.674076\pi$
$822$	−621.000	+	1075.60i	−0.0263502	+	0.0456399i
$823$	1277.00	+	2211.83i	0.0540868	+	0.0936811i	0.891801	−	0.452428i	$-0.149442\pi$
$823$	1277.00	+	2211.83i	0.0540868	+	0.0936811i	−0.837714	+	0.546109i	$0.816109\pi$
$824$			3822.00i			0.161585i
$825$	−1829.05	+	1056.00i	−0.0771869	+	0.0445639i
$826$	−20342.9	+	11745.0i	−0.856927	+	0.494747i
$827$		−	21522.0i		−	0.904950i	−0.891777	−	0.452475i	$-0.850541\pi$
$827$		−	21522.0i		−	0.904950i	0.891777	−	0.452475i	$-0.149459\pi$
$828$	−2106.00	−	3647.70i	−0.0883920	−	0.153099i
$829$	6562.00	−	11365.7i	0.274919	−	0.476173i	−0.695196	−	0.718820i	$-0.744682\pi$
$829$	6562.00	−	11365.7i	0.274919	−	0.476173i	0.970115	+	0.242647i	$0.0780157\pi$
$830$	10241.6	+	5913.00i	0.428303	+	0.247281i
$831$	1384.00			0.0577743
$832$		0			0
$833$	−5310.00			−0.220865
$834$	−6284.75	−	3628.50i	−0.260939	−	0.150653i
$835$	−10746.0	+	18612.6i	−0.445366	+	0.771397i
$836$	−144.000	−	249.415i	−0.00595735	−	0.0103184i
$837$			13992.0i			0.577819i
$838$	15128.6	−	8734.50i	0.623638	−	0.360058i
$839$	20285.8	−	11712.0i	0.834735	−	0.481935i	−0.0207360	−	0.999785i	$-0.506601\pi$
$839$	20285.8	−	11712.0i	0.834735	−	0.481935i	0.855471	+	0.517850i	$0.173268\pi$
$840$			2835.00i			0.116449i
$841$	1826.50	+	3163.59i	0.0748903	+	0.129714i
$842$	−11011.5	+	19072.5i	−0.450690	+	0.780619i
$843$	3517.80	+	2031.00i	0.143724	+	0.0829791i
$844$	−2833.00			−0.115540
$845$		0			0
$846$	−8658.00			−0.351854
$847$	−12639.6	−	7297.50i	−0.512755	−	0.296039i
$848$	−14697.0	+	25456.0i	−0.595162	+	1.03085i
$849$	−1882.00	−	3259.72i	−0.0760778	−	0.131771i
$850$		−	5940.00i		−	0.239694i
$851$	−42509.7	+	24543.0i	−1.71236	+	0.988629i
$852$	309.171	−	178.500i	0.0124320	−	0.00717759i
$853$		−	31077.0i		−	1.24743i	−0.781653	−	0.623714i	$-0.785623\pi$
$853$		−	31077.0i		−	1.24743i	0.781653	−	0.623714i	$-0.214377\pi$
$854$	−8460.00	−	14653.1i	−0.338987	−	0.587143i
$855$	702.000	−	1215.90i	0.0280794	−	0.0486350i
$856$	11130.2	+	6426.00i	0.444417	+	0.256584i
$857$	−19422.0			−0.774146			−0.387073	−	0.922049i	$-0.626514\pi$
$857$	−19422.0			−0.774146			−0.387073	+	0.922049i	$0.626514\pi$
$858$		0			0
$859$	1744.00			0.0692718			0.0346359	−	0.999400i	$-0.488973\pi$
$859$	1744.00			0.0692718			0.0346359	+	0.999400i	$0.488973\pi$
$860$	756.040	+	436.500i	0.0299776	+	0.0173076i
$861$	−1440.00	+	2494.15i	−0.0569978	+	0.0987230i
$862$	−11227.5	−	19446.6i	−0.443631	−	0.768392i
$863$			19179.0i			0.756501i	0.925703	+	0.378251i	$0.123474\pi$
$863$			19179.0i			0.756501i	−0.925703	+	0.378251i	$0.876526\pi$
$864$	−2065.47	+	1192.50i	−0.0813296	+	0.0469556i
$865$	12205.8	−	7047.00i	0.479778	−	0.277000i
$866$		−	45609.0i		−	1.78967i
$867$	−1444.00	−	2501.08i	−0.0565638	−	0.0979714i
$868$	1980.00	−	3429.46i	0.0774258	−	0.134105i
$869$	34502.5	+	19920.0i	1.34685	+	0.777606i
$870$	3888.00			0.151512
$871$		0			0
$872$	−22743.0			−0.883228
$873$	−19184.2	−	11076.0i	−0.743742	−	0.429400i
$874$	1458.00	−	2525.33i	0.0564274	−	0.0977352i
$875$	11407.5	+	19758.4i	0.440736	+	0.763377i
$876$			1098.00i			0.0423493i
$877$	25302.7	−	14608.5i	0.974242	−	0.562479i	0.0737152	−	0.997279i	$-0.476514\pi$
$877$	25302.7	−	14608.5i	0.974242	−	0.562479i	0.900527	+	0.434800i	$0.143181\pi$
$878$	−4577.81	+	2643.00i	−0.175961	+	0.101591i
$879$			4227.00i			0.162199i
$880$	15336.0	+	26562.7i	0.587473	+	1.01753i
$881$	7816.50	−	13538.6i	0.298916	−	0.517737i	−0.676973	−	0.736008i	$-0.736708\pi$
$881$	7816.50	−	13538.6i	0.298916	−	0.517737i	0.975888	+	0.218271i	$0.0700418\pi$
$882$	7970.90	+	4602.00i	0.304302	+	0.175689i
$883$	30589.0			1.16580			0.582900	−	0.812544i	$-0.301918\pi$
$883$	30589.0			1.16580			0.582900	+	0.812544i	$0.301918\pi$
$884$		0			0
$885$	4698.00			0.178442
$886$	19010.1	+	10975.5i	0.720832	+	0.416173i
$887$	12942.0	−	22416.2i	0.489910	−	0.848548i	−0.510023	−	0.860161i	$-0.670363\pi$
$887$	12942.0	−	22416.2i	0.489910	−	0.848548i	0.999933	+	0.0116124i	$0.00369644\pi$
$888$	3181.50	+	5510.52i	0.120230	+	0.208244i
$889$		−	31290.0i		−	1.18046i
$890$	10241.6	−	5913.00i	0.385730	−	0.222701i
$891$	26978.4	−	15576.0i	1.01438	−	0.585652i
$892$			3507.00i			0.131640i
$893$	−333.000	−	576.773i	−0.0124786	−	0.0216136i
$894$	1395.00	−	2416.21i	0.0521877	−	0.0903917i
$895$	−5120.81	−	2956.50i	−0.191251	−	0.110419i
$896$	−24885.0			−0.927845
$897$		0			0
$898$	−15048.0			−0.559196
$899$	32922.8	+	19008.0i	1.22140	+	0.705175i
$900$	−572.000	+	990.733i	−0.0211852	+	0.0366938i
$901$	−9315.00	−	16134.1i	−0.344426	−	0.596563i
$902$			27648.0i			1.02060i
$903$	−1260.07	+	727.500i	−0.0464368	+	0.0268103i
$904$	1636.79	−	945.000i	0.0602199	−	0.0347680i
$905$			10998.0i			0.403962i
$906$	−2524.50	−	4372.56i	−0.0925727	−	0.160341i
$907$	6152.50	−	10656.4i	0.225237	−	0.390123i	−0.731153	−	0.682213i	$-0.761018\pi$
$907$	6152.50	−	10656.4i	0.225237	−	0.390123i	0.956391	+	0.292091i	$0.0943509\pi$
$908$	−197.454	−	114.000i	−0.00721667	−	0.00416655i
$909$	−10296.0			−0.375684
$910$		0			0
$911$	29772.0			1.08276			0.541378	−	0.840779i	$-0.317903\pi$
$911$	29772.0			1.08276			0.541378	+	0.840779i	$0.317903\pi$
$912$	−368.927	−	213.000i	−0.0133952	−	0.00773370i
$913$	−10512.0	+	18207.3i	−0.381048	+	0.659994i
$914$	14805.0	+	25643.0i	0.535783	+	0.928004i
$915$			3384.00i			0.122264i
$916$	4757.08	−	2746.50i	0.171592	−	0.0990687i
$917$	19056.9	−	11002.5i	0.686275	−	0.396221i
$918$		−	7155.00i		−	0.257244i
$919$	−23822.0	−	41260.9i	−0.855076	−	1.48104i	−0.876574	−	0.481267i	$-0.840177\pi$
$919$	−23822.0	−	41260.9i	−0.855076	−	1.48104i	0.0214976	−	0.999769i	$-0.493157\pi$
$920$	−15309.0	+	26516.0i	−0.548612	+	0.950223i
$921$	−265.004	−	153.000i	−0.00948118	−	0.00547396i
$922$	43623.0			1.55819
$923$		0			0
$924$	720.000			0.0256345
$925$	11545.9	+	6666.00i	0.410406	+	0.236948i
$926$	3168.00	−	5487.14i	0.112427	−	0.194728i
$927$	2366.00	+	4098.03i	0.0838292	+	0.145196i
$928$			6480.00i			0.229220i
$929$	18986.7	−	10962.0i	0.670543	−	0.387138i	−0.125739	−	0.992063i	$-0.540130\pi$
$929$	18986.7	−	10962.0i	0.670543	−	0.387138i	0.796282	+	0.604925i	$0.206797\pi$
$930$	−6173.03	+	3564.00i	−0.217658	+	0.125665i
$931$			708.000i			0.0249235i
$932$	1813.50	+	3141.07i	0.0637373	+	0.110396i
$933$	−1053.00	+	1823.85i	−0.0369493	+	0.0639980i
$934$	−8511.30	−	4914.00i	−0.298178	−	0.172153i
$935$	−19440.0			−0.679953
$936$		0			0
$937$	32398.0			1.12956			0.564779	−	0.825242i	$-0.308961\pi$
$937$	32398.0			1.12956			0.564779	+	0.825242i	$0.308961\pi$
$938$	1402.96	+	810.000i	0.0488361	+	0.0281956i
$939$	5025.50	−	8704.42i	0.174655	−	0.302511i
$940$	−499.500	−	865.159i	−0.0173318	−	0.0300196i
$941$			2097.00i			0.0726464i	0.999340	+	0.0363232i	$0.0115646\pi$
$941$			2097.00i			0.0726464i	−0.999340	+	0.0363232i	$0.988435\pi$
$942$	−4868.79	+	2811.00i	−0.168401	+	0.0972265i
$943$	−26936.9	+	15552.0i	−0.930206	+	0.537055i
$944$			37062.0i			1.27782i
$945$	3577.50	+	6196.41i	0.123149	+	0.213301i
$946$	−6984.00	+	12096.6i	−0.240031	+	0.415746i
$947$	−17334.4	−	10008.0i	−0.594816	−	0.343417i	0.172183	−	0.985065i	$-0.444918\pi$
$947$	−17334.4	−	10008.0i	−0.594816	−	0.343417i	−0.767000	+	0.641648i	$0.778251\pi$
$948$	−830.000			−0.0284358
$949$		0			0
$950$	−792.000			−0.0270483
$951$	−1865.42	−	1077.00i	−0.0636071	−	0.0367236i
$952$	7087.50	−	12275.9i	0.241289	−	0.417925i
$953$	−12496.5	−	21644.6i	−0.424765	−	0.735715i	0.571633	−	0.820509i	$-0.306310\pi$
$953$	−12496.5	−	21644.6i	−0.424765	−	0.735715i	−0.996398	+	0.0847942i	$0.972977\pi$
$954$			32292.0i			1.09590i
$955$	−9820.73	+	5670.00i	−0.332766	+	0.192122i
$956$	−5261.10	+	3037.50i	−0.177988	+	0.102761i
$957$			6912.00i			0.233473i
$958$	23179.5	+	40148.1i	0.781728	+	1.35399i
$959$	−3105.00	+	5378.02i	−0.104552	+	0.181090i
$960$	3374.90	+	1948.50i	0.113463	+	0.0655079i
$961$	−39905.0			−1.33950
$962$		0			0
$963$	15912.0			0.532458
$964$	−181.865	−	105.000i	−0.00607623	−	0.00350811i
$965$	1539.00	−	2665.63i	0.0513390	−	0.0889218i
$966$	3645.00	+	6313.33i	0.121404	+	0.210277i
$967$		−	40959.0i		−	1.36210i	−0.732236	−	0.681051i	$-0.761523\pi$
$967$		−	40959.0i		−	1.36210i	0.732236	−	0.681051i	$-0.238477\pi$
$968$	−17695.5	+	10216.5i	−0.587557	+	0.339226i
$969$	233.827	−	135.000i	0.00775191	−	0.00447557i
$970$		−	23004.0i		−	0.761458i
$971$	24466.5	+	42377.2i	0.808617	+	1.40057i	0.913822	+	0.406116i	$0.133117\pi$
$971$	24466.5	+	42377.2i	0.808617	+	1.40057i	−0.105204	+	0.994451i	$0.533550\pi$
$972$	−1040.00	+	1801.33i	−0.0343189	+	0.0594422i
$973$	−31423.7	−	18142.5i	−1.03535	−	0.597761i
$974$	10980.0			0.361213
$975$		0			0
$976$	−26696.0			−0.875531
$977$	−41039.2	−	23694.0i	−1.34387	−	0.775884i	−0.356497	−	0.934297i	$-0.616029\pi$
$977$	−41039.2	−	23694.0i	−1.34387	−	0.775884i	−0.987373	+	0.158413i	$0.949362\pi$
$978$	−1791.00	+	3102.10i	−0.0585581	+	0.101426i
$979$	10512.0	+	18207.3i	0.343172	+	0.594391i
$980$			1062.00i			0.0346167i
$981$	−24385.5	+	14079.0i	−0.793650	+	0.458214i
$982$	1940.76	−	1120.50i	0.0630674	−	0.0364120i
$983$		−	16803.0i		−	0.545201i	−0.962127	−	0.272600i	$-0.912116\pi$
$983$		−	16803.0i		−	0.545201i	0.962127	−	0.272600i	$-0.0878837\pi$
$984$	2016.00	+	3491.81i	0.0653127	+	0.113125i
$985$	−364.500	+	631.333i	−0.0117908	+	0.0204223i
$986$	−16835.5	−	9720.00i	−0.543765	−	0.313943i
$987$	1665.00			0.0536956
$988$		0			0
$989$	−15714.0			−0.505234
$990$	29181.6	+	16848.0i	0.936820	+	0.540873i
$991$	28763.0	−	49819.0i	0.921985	−	1.59692i	0.125644	−	0.992075i	$-0.459900\pi$
$991$	28763.0	−	49819.0i	0.921985	−	1.59692i	0.796340	−	0.604849i	$-0.206767\pi$
$992$	−5940.00	−	10288.4i	−0.190116	−	0.329291i
$993$		−	10770.0i		−	0.344185i
$994$	13912.7	−	8032.50i	0.443948	−	0.256313i
$995$	−15557.3	+	8982.00i	−0.495677	+	0.286179i
$996$		−	438.000i		−	0.0139343i
$997$	12500.0	+	21650.6i	0.397070	+	0.687746i	0.993363	−	0.115021i	$-0.0366936\pi$
$997$	12500.0	+	21650.6i	0.397070	+	0.687746i	−0.596293	+	0.802767i	$0.703360\pi$
$998$	−23706.0	+	41060.0i	−0.751904	+	1.30234i
$999$	13907.5	+	8029.50i	0.440454	+	0.254296i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	169.4.e.d.147.1		4
13.2	odd	12		169.4.c.b.146.1		2
13.3	even	3	inner	169.4.e.d.23.2		4
13.4	even	6		13.4.b.a.12.1	✓	2
13.5	odd	4		169.4.c.b.22.1		2
13.6	odd	12		169.4.a.c.1.1		1
13.7	odd	12		169.4.a.b.1.1		1
13.8	odd	4		169.4.c.c.22.1		2
13.9	even	3		13.4.b.a.12.2	yes	2
13.10	even	6	inner	169.4.e.d.23.1		4
13.11	odd	12		169.4.c.c.146.1		2
13.12	even	2	inner	169.4.e.d.147.2		4
39.17	odd	6		117.4.b.a.64.2		2
39.20	even	12		1521.4.a.i.1.1		1
39.32	even	12		1521.4.a.d.1.1		1
39.35	odd	6		117.4.b.a.64.1		2
52.35	odd	6		208.4.f.b.129.1		2
52.43	odd	6		208.4.f.b.129.2		2
65.4	even	6		325.4.c.b.51.2		2
65.9	even	6		325.4.c.b.51.1		2
65.17	odd	12		325.4.d.b.324.2		2
65.22	odd	12		325.4.d.a.324.2		2
65.43	odd	12		325.4.d.a.324.1		2
65.48	odd	12		325.4.d.b.324.1		2
104.35	odd	6		832.4.f.c.129.2		2
104.43	odd	6		832.4.f.c.129.1		2
104.61	even	6		832.4.f.e.129.2		2
104.69	even	6		832.4.f.e.129.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
13.4.b.a.12.1	✓	2	13.4	even	6
13.4.b.a.12.2	yes	2	13.9	even	3
117.4.b.a.64.1		2	39.35	odd	6
117.4.b.a.64.2		2	39.17	odd	6
169.4.a.b.1.1		1	13.7	odd	12
169.4.a.c.1.1		1	13.6	odd	12
169.4.c.b.22.1		2	13.5	odd	4
169.4.c.b.146.1		2	13.2	odd	12
169.4.c.c.22.1		2	13.8	odd	4
169.4.c.c.146.1		2	13.11	odd	12
169.4.e.d.23.1		4	13.10	even	6	inner
169.4.e.d.23.2		4	13.3	even	3	inner
169.4.e.d.147.1		4	1.1	even	1	trivial
169.4.e.d.147.2		4	13.12	even	2	inner
208.4.f.b.129.1		2	52.35	odd	6
208.4.f.b.129.2		2	52.43	odd	6
325.4.c.b.51.1		2	65.9	even	6
325.4.c.b.51.2		2	65.4	even	6
325.4.d.a.324.1		2	65.43	odd	12
325.4.d.a.324.2		2	65.22	odd	12
325.4.d.b.324.1		2	65.48	odd	12
325.4.d.b.324.2		2	65.17	odd	12
832.4.f.c.129.1		2	104.43	odd	6
832.4.f.c.129.2		2	104.35	odd	6
832.4.f.e.129.1		2	104.69	even	6
832.4.f.e.129.2		2	104.61	even	6
1521.4.a.d.1.1		1	39.32	even	12
1521.4.a.i.1.1		1	39.20	even	12

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:	\( N \)	\(=\)	\( 169 = 13^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	169.e (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.59808 - 1.50000i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} -9.00000i q^{5} +(-2.59808 + 1.50000i) q^{6} +(-12.9904 + 7.50000i) q^{7} +21.0000i q^{8} +(13.0000 + 22.5167i) q^{9} +O(q^{10})\)	\(q+(-2.59808 - 1.50000i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} -9.00000i q^{5} +(-2.59808 + 1.50000i) q^{6} +(-12.9904 + 7.50000i) q^{7} +21.0000i q^{8} +(13.0000 + 22.5167i) q^{9} +(-13.5000 + 23.3827i) q^{10} +(-41.5692 - 24.0000i) q^{11} +1.00000 q^{12} +45.0000 q^{14} +(-7.79423 - 4.50000i) q^{15} +(35.5000 - 61.4878i) q^{16} +(22.5000 + 38.9711i) q^{17} -78.0000i q^{18} +(5.19615 - 3.00000i) q^{19} +(7.79423 - 4.50000i) q^{20} +15.0000i q^{21} +(72.0000 + 124.708i) q^{22} +(-81.0000 + 140.296i) q^{23} +(18.1865 + 10.5000i) q^{24} +44.0000 q^{25} +53.0000 q^{27} +(-12.9904 - 7.50000i) q^{28} +(72.0000 - 124.708i) q^{29} +(13.5000 + 23.3827i) q^{30} +264.000i q^{31} +(-38.9711 + 22.5000i) q^{32} +(-41.5692 + 24.0000i) q^{33} -135.000i q^{34} +(67.5000 + 116.913i) q^{35} +(-13.0000 + 22.5167i) q^{36} +(262.406 + 151.500i) q^{37} -18.0000 q^{38} +189.000 q^{40} +(166.277 + 96.0000i) q^{41} +(22.5000 - 38.9711i) q^{42} +(48.5000 + 84.0045i) q^{43} -48.0000i q^{44} +(202.650 - 117.000i) q^{45} +(420.888 - 243.000i) q^{46} -111.000i q^{47} +(-35.5000 - 61.4878i) q^{48} +(-59.0000 + 102.191i) q^{49} +(-114.315 - 66.0000i) q^{50} +45.0000 q^{51} -414.000 q^{53} +(-137.698 - 79.5000i) q^{54} +(-216.000 + 374.123i) q^{55} +(-157.500 - 272.798i) q^{56} -6.00000i q^{57} +(-374.123 + 216.000i) q^{58} +(-452.065 + 261.000i) q^{59} -9.00000i q^{60} +(-188.000 - 325.626i) q^{61} +(396.000 - 685.892i) q^{62} +(-337.750 - 195.000i) q^{63} -433.000 q^{64} +144.000 q^{66} +(31.1769 + 18.0000i) q^{67} +(-22.5000 + 38.9711i) q^{68} +(81.0000 + 140.296i) q^{69} -405.000i q^{70} +(309.171 - 178.500i) q^{71} +(-472.850 + 273.000i) q^{72} +1098.00i q^{73} +(-454.500 - 787.217i) q^{74} +(22.0000 - 38.1051i) q^{75} +(5.19615 + 3.00000i) q^{76} +720.000 q^{77} -830.000 q^{79} +(-553.390 - 319.500i) q^{80} +(-324.500 + 562.050i) q^{81} +(-288.000 - 498.831i) q^{82} -438.000i q^{83} +(-12.9904 + 7.50000i) q^{84} +(350.740 - 202.500i) q^{85} -291.000i q^{86} +(-72.0000 - 124.708i) q^{87} +(504.000 - 872.954i) q^{88} +(-379.319 - 219.000i) q^{89} -702.000 q^{90} -162.000 q^{92} +(228.631 + 132.000i) q^{93} +(-166.500 + 288.386i) q^{94} +(-27.0000 - 46.7654i) q^{95} +45.0000i q^{96} +(-737.854 + 426.000i) q^{97} +(306.573 - 177.000i) q^{98} -1248.00i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{3} + 2 q^{4} + 52 q^{9}+O(q^{10}) \) 4 * q + 2 * q^3 + 2 * q^4 + 52 * q^9	\( 4 q + 2 q^{3} + 2 q^{4} + 52 q^{9} - 54 q^{10} + 4 q^{12} + 180 q^{14} + 142 q^{16} + 90 q^{17} + 288 q^{22} - 324 q^{23} + 176 q^{25} + 212 q^{27} + 288 q^{29} + 54 q^{30} + 270 q^{35} - 52 q^{36} - 72 q^{38} + 756 q^{40} + 90 q^{42} + 194 q^{43} - 142 q^{48} - 236 q^{49} + 180 q^{51} - 1656 q^{53} - 864 q^{55} - 630 q^{56} - 752 q^{61} + 1584 q^{62} - 1732 q^{64} + 576 q^{66} - 90 q^{68} + 324 q^{69} - 1818 q^{74} + 88 q^{75} + 2880 q^{77} - 3320 q^{79} - 1298 q^{81} - 1152 q^{82} - 288 q^{87} + 2016 q^{88} - 2808 q^{90} - 648 q^{92} - 666 q^{94} - 108 q^{95}+O(q^{100}) \) 4 * q + 2 * q^3 + 2 * q^4 + 52 * q^9 - 54 * q^10 + 4 * q^12 + 180 * q^14 + 142 * q^16 + 90 * q^17 + 288 * q^22 - 324 * q^23 + 176 * q^25 + 212 * q^27 + 288 * q^29 + 54 * q^30 + 270 * q^35 - 52 * q^36 - 72 * q^38 + 756 * q^40 + 90 * q^42 + 194 * q^43 - 142 * q^48 - 236 * q^49 + 180 * q^51 - 1656 * q^53 - 864 * q^55 - 630 * q^56 - 752 * q^61 + 1584 * q^62 - 1732 * q^64 + 576 * q^66 - 90 * q^68 + 324 * q^69 - 1818 * q^74 + 88 * q^75 + 2880 * q^77 - 3320 * q^79 - 1298 * q^81 - 1152 * q^82 - 288 * q^87 + 2016 * q^88 - 2808 * q^90 - 648 * q^92 - 666 * q^94 - 108 * q^95

Introduction

L-functions

Modular forms

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Database

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