LMFDB - Embedded newform 98.4.c.d.79.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [98,4,Mod(67,98)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(98, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4]))

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

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

chi := DirichletCharacter("98.67");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 98 = 2 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	98.c (of order $3$, 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:	$5.78218718056$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 14)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			79.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	98.79
Dual form			98.4.c.d.67.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 - 1.73205i) q^{2} +(-4.00000 - 6.92820i) q^{3} +(-2.00000 - 3.46410i) q^{4} +(7.00000 - 12.1244i) q^{5} -16.0000 q^{6} -8.00000 q^{8} +(-18.5000 + 32.0429i) q^{9} +O(q^{10})$	\(q+(1.00000 - 1.73205i) q^{2} +(-4.00000 - 6.92820i) q^{3} +(-2.00000 - 3.46410i) q^{4} +(7.00000 - 12.1244i) q^{5} -16.0000 q^{6} -8.00000 q^{8} +(-18.5000 + 32.0429i) q^{9} +(-14.0000 - 24.2487i) q^{10} +(14.0000 + 24.2487i) q^{11} +(-16.0000 + 27.7128i) q^{12} +18.0000 q^{13} -112.000 q^{15} +(-8.00000 + 13.8564i) q^{16} +(-37.0000 - 64.0859i) q^{17} +(37.0000 + 64.0859i) q^{18} +(-40.0000 + 69.2820i) q^{19} -56.0000 q^{20} +56.0000 q^{22} +(56.0000 - 96.9948i) q^{23} +(32.0000 + 55.4256i) q^{24} +(-35.5000 - 61.4878i) q^{25} +(18.0000 - 31.1769i) q^{26} +80.0000 q^{27} +190.000 q^{29} +(-112.000 + 193.990i) q^{30} +(-36.0000 - 62.3538i) q^{31} +(16.0000 + 27.7128i) q^{32} +(112.000 - 193.990i) q^{33} -148.000 q^{34} +148.000 q^{36} +(173.000 - 299.645i) q^{37} +(80.0000 + 138.564i) q^{38} +(-72.0000 - 124.708i) q^{39} +(-56.0000 + 96.9948i) q^{40} +162.000 q^{41} -412.000 q^{43} +(56.0000 - 96.9948i) q^{44} +(259.000 + 448.601i) q^{45} +(-112.000 - 193.990i) q^{46} +(-12.0000 + 20.7846i) q^{47} +128.000 q^{48} -142.000 q^{50} +(-296.000 + 512.687i) q^{51} +(-36.0000 - 62.3538i) q^{52} +(-159.000 - 275.396i) q^{53} +(80.0000 - 138.564i) q^{54} +392.000 q^{55} +640.000 q^{57} +(190.000 - 329.090i) q^{58} +(100.000 + 173.205i) q^{59} +(224.000 + 387.979i) q^{60} +(99.0000 - 171.473i) q^{61} -144.000 q^{62} +64.0000 q^{64} +(126.000 - 218.238i) q^{65} +(-224.000 - 387.979i) q^{66} +(358.000 + 620.074i) q^{67} +(-148.000 + 256.344i) q^{68} -896.000 q^{69} +392.000 q^{71} +(148.000 - 256.344i) q^{72} +(-269.000 - 465.922i) q^{73} +(-346.000 - 599.290i) q^{74} +(-284.000 + 491.902i) q^{75} +320.000 q^{76} -288.000 q^{78} +(-120.000 + 207.846i) q^{79} +(112.000 + 193.990i) q^{80} +(179.500 + 310.903i) q^{81} +(162.000 - 280.592i) q^{82} -1072.00 q^{83} -1036.00 q^{85} +(-412.000 + 713.605i) q^{86} +(-760.000 - 1316.36i) q^{87} +(-112.000 - 193.990i) q^{88} +(-405.000 + 701.481i) q^{89} +1036.00 q^{90} -448.000 q^{92} +(-288.000 + 498.831i) q^{93} +(24.0000 + 41.5692i) q^{94} +(560.000 + 969.948i) q^{95} +(128.000 - 221.703i) q^{96} +1354.00 q^{97} -1036.00 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} - 8 q^{3} - 4 q^{4} + 14 q^{5} - 32 q^{6} - 16 q^{8} - 37 q^{9}+O(q^{10}) $ 2 * q + 2 * q^2 - 8 * q^3 - 4 * q^4 + 14 * q^5 - 32 * q^6 - 16 * q^8 - 37 * q^9	\( 2 q + 2 q^{2} - 8 q^{3} - 4 q^{4} + 14 q^{5} - 32 q^{6} - 16 q^{8} - 37 q^{9} - 28 q^{10} + 28 q^{11} - 32 q^{12} + 36 q^{13} - 224 q^{15} - 16 q^{16} - 74 q^{17} + 74 q^{18} - 80 q^{19} - 112 q^{20} + 112 q^{22} + 112 q^{23} + 64 q^{24} - 71 q^{25} + 36 q^{26} + 160 q^{27} + 380 q^{29} - 224 q^{30} - 72 q^{31} + 32 q^{32} + 224 q^{33} - 296 q^{34} + 296 q^{36} + 346 q^{37} + 160 q^{38} - 144 q^{39} - 112 q^{40} + 324 q^{41} - 824 q^{43} + 112 q^{44} + 518 q^{45} - 224 q^{46} - 24 q^{47} + 256 q^{48} - 284 q^{50} - 592 q^{51} - 72 q^{52} - 318 q^{53} + 160 q^{54} + 784 q^{55} + 1280 q^{57} + 380 q^{58} + 200 q^{59} + 448 q^{60} + 198 q^{61} - 288 q^{62} + 128 q^{64} + 252 q^{65} - 448 q^{66} + 716 q^{67} - 296 q^{68} - 1792 q^{69} + 784 q^{71} + 296 q^{72} - 538 q^{73} - 692 q^{74} - 568 q^{75} + 640 q^{76} - 576 q^{78} - 240 q^{79} + 224 q^{80} + 359 q^{81} + 324 q^{82} - 2144 q^{83} - 2072 q^{85} - 824 q^{86} - 1520 q^{87} - 224 q^{88} - 810 q^{89} + 2072 q^{90} - 896 q^{92} - 576 q^{93} + 48 q^{94} + 1120 q^{95} + 256 q^{96} + 2708 q^{97} - 2072 q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 - 8 * q^3 - 4 * q^4 + 14 * q^5 - 32 * q^6 - 16 * q^8 - 37 * q^9 - 28 * q^10 + 28 * q^11 - 32 * q^12 + 36 * q^13 - 224 * q^15 - 16 * q^16 - 74 * q^17 + 74 * q^18 - 80 * q^19 - 112 * q^20 + 112 * q^22 + 112 * q^23 + 64 * q^24 - 71 * q^25 + 36 * q^26 + 160 * q^27 + 380 * q^29 - 224 * q^30 - 72 * q^31 + 32 * q^32 + 224 * q^33 - 296 * q^34 + 296 * q^36 + 346 * q^37 + 160 * q^38 - 144 * q^39 - 112 * q^40 + 324 * q^41 - 824 * q^43 + 112 * q^44 + 518 * q^45 - 224 * q^46 - 24 * q^47 + 256 * q^48 - 284 * q^50 - 592 * q^51 - 72 * q^52 - 318 * q^53 + 160 * q^54 + 784 * q^55 + 1280 * q^57 + 380 * q^58 + 200 * q^59 + 448 * q^60 + 198 * q^61 - 288 * q^62 + 128 * q^64 + 252 * q^65 - 448 * q^66 + 716 * q^67 - 296 * q^68 - 1792 * q^69 + 784 * q^71 + 296 * q^72 - 538 * q^73 - 692 * q^74 - 568 * q^75 + 640 * q^76 - 576 * q^78 - 240 * q^79 + 224 * q^80 + 359 * q^81 + 324 * q^82 - 2144 * q^83 - 2072 * q^85 - 824 * q^86 - 1520 * q^87 - 224 * q^88 - 810 * q^89 + 2072 * q^90 - 896 * q^92 - 576 * q^93 + 48 * q^94 + 1120 * q^95 + 256 * q^96 + 2708 * q^97 - 2072 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/98\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	1.00000	−	1.73205i	0.353553	−	0.612372i
$2$	1.00000	−	1.73205i	0.353553	−	0.612372i
$3$	−4.00000	−	6.92820i	−0.769800	−	1.33333i	−0.937671	−	0.347524i	$-0.887022\pi$
$3$	−4.00000	−	6.92820i	−0.769800	−	1.33333i	0.167871	−	0.985809i	$-0.446311\pi$
$4$	−2.00000	−	3.46410i	−0.250000	−	0.433013i
$5$	7.00000	−	12.1244i	0.626099	−	1.08444i	−0.362228	−	0.932089i	$-0.617984\pi$
$5$	7.00000	−	12.1244i	0.626099	−	1.08444i	0.988327	−	0.152346i	$-0.0486828\pi$
$6$	−16.0000			−1.08866
$7$		0			0
$7$		0			0
$8$	−8.00000			−0.353553
$9$	−18.5000	+	32.0429i	−0.685185	+	1.18678i
$10$	−14.0000	−	24.2487i	−0.442719	−	0.766812i
$11$	14.0000	+	24.2487i	0.383742	+	0.664660i	0.991594	−	0.129390i	$-0.0413020\pi$
$11$	14.0000	+	24.2487i	0.383742	+	0.664660i	−0.607852	+	0.794050i	$0.707969\pi$
$12$	−16.0000	+	27.7128i	−0.384900	+	0.666667i
$13$	18.0000			0.384023			0.192012	−	0.981393i	$-0.438499\pi$
$13$	18.0000			0.384023			0.192012	+	0.981393i	$0.438499\pi$
$14$		0			0
$15$	−112.000			−1.92789
$16$	−8.00000	+	13.8564i	−0.125000	+	0.216506i
$17$	−37.0000	−	64.0859i	−0.527872	−	0.914301i	−0.999472	−	0.0324882i	$-0.989657\pi$
$17$	−37.0000	−	64.0859i	−0.527872	−	0.914301i	0.471600	−	0.881812i	$-0.343676\pi$
$18$	37.0000	+	64.0859i	0.484499	+	0.839177i
$19$	−40.0000	+	69.2820i	−0.482980	+	0.836547i	−0.999809	−	0.0195422i	$-0.993779\pi$
$19$	−40.0000	+	69.2820i	−0.482980	+	0.836547i	0.516829	+	0.856089i	$0.327112\pi$
$20$	−56.0000			−0.626099
$21$		0			0
$22$	56.0000			0.542693
$23$	56.0000	−	96.9948i	0.507687	−	0.879340i	−0.492273	−	0.870441i	$-0.663834\pi$
$23$	56.0000	−	96.9948i	0.507687	−	0.879340i	0.999960	−	0.00889936i	$-0.00283279\pi$
$24$	32.0000	+	55.4256i	0.272166	+	0.471405i
$25$	−35.5000	−	61.4878i	−0.284000	−	0.491902i
$26$	18.0000	−	31.1769i	0.135773	−	0.235165i
$27$	80.0000			0.570222
$28$		0			0
$29$	190.000			1.21662			0.608312	−	0.793698i	$-0.291847\pi$
$29$	190.000			1.21662			0.608312	+	0.793698i	$0.291847\pi$
$30$	−112.000	+	193.990i	−0.681610	+	1.18058i
$31$	−36.0000	−	62.3538i	−0.208574	−	0.361261i	0.742692	−	0.669634i	$-0.233549\pi$
$31$	−36.0000	−	62.3538i	−0.208574	−	0.361261i	−0.951266	+	0.308373i	$0.900216\pi$
$32$	16.0000	+	27.7128i	0.0883883	+	0.153093i
$33$	112.000	−	193.990i	0.590809	−	1.02331i
$34$	−148.000			−0.746523
$35$		0			0
$36$	148.000			0.685185
$37$	173.000	−	299.645i	0.768676	−	1.33139i	−0.169605	−	0.985512i	$-0.554249\pi$
$37$	173.000	−	299.645i	0.768676	−	1.33139i	0.938281	−	0.345874i	$-0.112418\pi$
$38$	80.0000	+	138.564i	0.341519	+	0.591528i
$39$	−72.0000	−	124.708i	−0.295621	−	0.512031i
$40$	−56.0000	+	96.9948i	−0.221359	+	0.383406i
$41$	162.000			0.617077			0.308538	−	0.951212i	$-0.400160\pi$
$41$	162.000			0.617077			0.308538	+	0.951212i	$0.400160\pi$
$42$		0			0
$43$	−412.000			−1.46115			−0.730575	−	0.682833i	$-0.760748\pi$
$43$	−412.000			−1.46115			−0.730575	+	0.682833i	$0.760748\pi$
$44$	56.0000	−	96.9948i	0.191871	−	0.332330i
$45$	259.000	+	448.601i	0.857988	+	1.48608i
$46$	−112.000	−	193.990i	−0.358989	−	0.621787i
$47$	−12.0000	+	20.7846i	−0.0372421	+	0.0645053i	−0.884046	−	0.467401i	$-0.845191\pi$
$47$	−12.0000	+	20.7846i	−0.0372421	+	0.0645053i	0.846804	+	0.531906i	$0.178524\pi$
$48$	128.000			0.384900
$49$		0			0
$50$	−142.000			−0.401637
$51$	−296.000	+	512.687i	−0.812712	+	1.40766i
$52$	−36.0000	−	62.3538i	−0.0960058	−	0.166287i
$53$	−159.000	−	275.396i	−0.412082	−	0.713746i	0.583036	−	0.812447i	$-0.301865\pi$
$53$	−159.000	−	275.396i	−0.412082	−	0.713746i	−0.995117	+	0.0987002i	$0.968532\pi$
$54$	80.0000	−	138.564i	0.201604	−	0.349189i
$55$	392.000			0.961041
$56$		0			0
$57$	640.000			1.48719
$58$	190.000	−	329.090i	0.430142	−	0.745027i
$59$	100.000	+	173.205i	0.220659	+	0.382193i	0.955008	−	0.296579i	$-0.0958458\pi$
$59$	100.000	+	173.205i	0.220659	+	0.382193i	−0.734349	+	0.678772i	$0.762512\pi$
$60$	224.000	+	387.979i	0.481971	+	0.834799i
$61$	99.0000	−	171.473i	0.207798	−	0.359916i	−0.743223	−	0.669044i	$-0.766704\pi$
$61$	99.0000	−	171.473i	0.207798	−	0.359916i	0.951020	+	0.309128i	$0.100037\pi$
$62$	−144.000			−0.294968
$63$		0			0
$64$	64.0000			0.125000
$65$	126.000	−	218.238i	0.240437	−	0.416448i
$66$	−224.000	−	387.979i	−0.417765	−	0.723590i
$67$	358.000	+	620.074i	0.652786	+	1.13066i	0.982444	+	0.186558i	$0.0597332\pi$
$67$	358.000	+	620.074i	0.652786	+	1.13066i	−0.329658	+	0.944100i	$0.606933\pi$
$68$	−148.000	+	256.344i	−0.263936	+	0.457150i
$69$	−896.000			−1.56327
$70$		0			0
$71$	392.000			0.655237			0.327619	−	0.944810i	$-0.393754\pi$
$71$	392.000			0.655237			0.327619	+	0.944810i	$0.393754\pi$
$72$	148.000	−	256.344i	0.242250	−	0.419589i
$73$	−269.000	−	465.922i	−0.431289	−	0.747014i	0.565696	−	0.824614i	$-0.308608\pi$
$73$	−269.000	−	465.922i	−0.431289	−	0.747014i	−0.996985	+	0.0776001i	$0.975274\pi$
$74$	−346.000	−	599.290i	−0.543536	−	0.941432i
$75$	−284.000	+	491.902i	−0.437247	+	0.757333i
$76$	320.000			0.482980
$77$		0			0
$78$	−288.000			−0.418072
$79$	−120.000	+	207.846i	−0.170899	+	0.296006i	−0.938735	−	0.344641i	$-0.888001\pi$
$79$	−120.000	+	207.846i	−0.170899	+	0.296006i	0.767835	+	0.640647i	$0.221334\pi$
$80$	112.000	+	193.990i	0.156525	+	0.271109i
$81$	179.500	+	310.903i	0.246228	+	0.426479i
$82$	162.000	−	280.592i	0.218170	−	0.377881i
$83$	−1072.00			−1.41768			−0.708839	−	0.705370i	$-0.750781\pi$
$83$	−1072.00			−1.41768			−0.708839	+	0.705370i	$0.750781\pi$
$84$		0			0
$85$	−1036.00			−1.32200
$86$	−412.000	+	713.605i	−0.516594	+	0.894767i
$87$	−760.000	−	1316.36i	−0.936558	−	1.62217i
$88$	−112.000	−	193.990i	−0.135673	−	0.234993i
$89$	−405.000	+	701.481i	−0.482359	+	0.835470i	−0.999795	−	0.0202521i	$-0.993553\pi$
$89$	−405.000	+	701.481i	−0.482359	+	0.835470i	0.517436	+	0.855722i	$0.326886\pi$
$90$	1036.00			1.21338
$91$		0			0
$92$	−448.000			−0.507687
$93$	−288.000	+	498.831i	−0.321121	+	0.556197i
$94$	24.0000	+	41.5692i	0.0263342	+	0.0456121i
$95$	560.000	+	969.948i	0.604787	+	1.04752i
$96$	128.000	−	221.703i	0.136083	−	0.235702i
$97$	1354.00			1.41730			0.708649	−	0.705561i	$-0.249305\pi$
$97$	1354.00			1.41730			0.708649	+	0.705561i	$0.249305\pi$
$98$		0			0
$99$	−1036.00			−1.05174
$100$	−142.000	+	245.951i	−0.142000	+	0.245951i
$101$	679.000	+	1176.06i	0.668941	+	1.15864i	0.978201	+	0.207662i	$0.0665854\pi$
$101$	679.000	+	1176.06i	0.668941	+	1.15864i	−0.309260	+	0.950978i	$0.600081\pi$
$102$	592.000	+	1025.37i	0.574674	+	0.995364i
$103$	416.000	−	720.533i	0.397958	−	0.689284i	−0.595516	−	0.803344i	$-0.703052\pi$
$103$	416.000	−	720.533i	0.397958	−	0.689284i	0.993474	+	0.114060i	$0.0363856\pi$
$104$	−144.000			−0.135773
$105$		0			0
$106$	−636.000			−0.582772
$107$	−222.000	+	384.515i	−0.200575	+	0.347406i	−0.948714	−	0.316136i	$-0.897614\pi$
$107$	−222.000	+	384.515i	−0.200575	+	0.347406i	0.748139	+	0.663542i	$0.230948\pi$
$108$	−160.000	−	277.128i	−0.142556	−	0.246914i
$109$	−935.000	−	1619.47i	−0.821622	−	1.42309i	−0.904474	−	0.426529i	$-0.859736\pi$
$109$	−935.000	−	1619.47i	−0.821622	−	1.42309i	0.0828525	−	0.996562i	$-0.473597\pi$
$110$	392.000	−	678.964i	0.339779	−	0.588515i
$111$	−2768.00			−2.36691
$112$		0			0
$113$	1378.00			1.14718			0.573590	−	0.819143i	$-0.305550\pi$
$113$	1378.00			1.14718			0.573590	+	0.819143i	$0.305550\pi$
$114$	640.000	−	1108.51i	0.525803	−	0.910717i
$115$	−784.000	−	1357.93i	−0.635725	−	1.10111i
$116$	−380.000	−	658.179i	−0.304156	−	0.526814i
$117$	−333.000	+	576.773i	−0.263127	+	0.455749i
$118$	400.000			0.312059
$119$		0			0
$120$	896.000			0.681610
$121$	273.500	−	473.716i	0.205485	−	0.355910i
$122$	−198.000	−	342.946i	−0.146935	−	0.254499i
$123$	−648.000	−	1122.37i	−0.475026	−	0.822769i
$124$	−144.000	+	249.415i	−0.104287	+	0.180630i
$125$	756.000			0.540950
$126$		0			0
$127$	1944.00			1.35828			0.679142	−	0.734007i	$-0.262352\pi$
$127$	1944.00			1.35828			0.679142	+	0.734007i	$0.262352\pi$
$128$	64.0000	−	110.851i	0.0441942	−	0.0765466i
$129$	1648.00	+	2854.42i	1.12479	+	1.94820i
$130$	−252.000	−	436.477i	−0.170014	−	0.294473i
$131$	424.000	−	734.390i	0.282787	−	0.489801i	−0.689283	−	0.724492i	$-0.742074\pi$
$131$	424.000	−	734.390i	0.282787	−	0.489801i	0.972070	+	0.234691i	$0.0754078\pi$
$132$	−896.000			−0.590809
$133$		0			0
$134$	1432.00			0.923179
$135$	560.000	−	969.948i	0.357016	−	0.618369i
$136$	296.000	+	512.687i	0.186631	+	0.323254i
$137$	1483.00	+	2568.63i	0.924827	+	1.60185i	0.791840	+	0.610729i	$0.209123\pi$
$137$	1483.00	+	2568.63i	0.924827	+	1.60185i	0.132987	+	0.991118i	$0.457543\pi$
$138$	−896.000	+	1551.92i	−0.552700	+	0.957304i
$139$	2800.00			1.70858			0.854291	−	0.519795i	$-0.173992\pi$
$139$	2800.00			1.70858			0.854291	+	0.519795i	$0.173992\pi$
$140$		0			0
$141$	192.000			0.114676
$142$	392.000	−	678.964i	0.231661	−	0.401249i
$143$	252.000	+	436.477i	0.147366	+	0.255245i
$144$	−296.000	−	512.687i	−0.171296	−	0.296694i
$145$	1330.00	−	2303.63i	0.761728	−	1.31935i
$146$	−1076.00			−0.609934
$147$		0			0
$148$	−1384.00			−0.768676
$149$	−255.000	+	441.673i	−0.140204	+	0.242841i	−0.927573	−	0.373641i	$-0.878109\pi$
$149$	−255.000	+	441.673i	−0.140204	+	0.242841i	0.787369	+	0.616482i	$0.211443\pi$
$150$	568.000	+	983.805i	0.309180	+	0.535516i
$151$	−296.000	−	512.687i	−0.159524	−	0.276304i	0.775173	−	0.631749i	$-0.217663\pi$
$151$	−296.000	−	512.687i	−0.159524	−	0.276304i	−0.934697	+	0.355445i	$0.884329\pi$
$152$	320.000	−	554.256i	0.170759	−	0.295764i
$153$	2738.00			1.44676
$154$		0			0
$155$	−1008.00			−0.522352
$156$	−288.000	+	498.831i	−0.147811	+	0.256015i
$157$	1343.00	+	2326.14i	0.682695	+	1.18246i	0.974155	+	0.225879i	$0.0725254\pi$
$157$	1343.00	+	2326.14i	0.682695	+	1.18246i	−0.291461	+	0.956583i	$0.594141\pi$
$158$	240.000	+	415.692i	0.120844	+	0.209308i
$159$	−1272.00	+	2203.17i	−0.634441	+	1.09888i
$160$	448.000			0.221359
$161$		0			0
$162$	718.000			0.348219
$163$	506.000	−	876.418i	0.243147	−	0.421143i	−0.718462	−	0.695566i	$-0.755154\pi$
$163$	506.000	−	876.418i	0.243147	−	0.421143i	0.961609	+	0.274423i	$0.0884869\pi$
$164$	−324.000	−	561.184i	−0.154269	−	0.267202i
$165$	−1568.00	−	2715.86i	−0.739810	−	1.28139i
$166$	−1072.00	+	1856.76i	−0.501225	+	0.868147i
$167$	544.000			0.252072			0.126036	−	0.992026i	$-0.459775\pi$
$167$	544.000			0.252072			0.126036	+	0.992026i	$0.459775\pi$
$168$		0			0
$169$	−1873.00			−0.852526
$170$	−1036.00	+	1794.40i	−0.467397	+	0.809556i
$171$	−1480.00	−	2563.44i	−0.661862	−	1.14638i
$172$	824.000	+	1427.21i	0.365287	+	0.632696i
$173$	−929.000	+	1609.08i	−0.408269	+	0.707143i	−0.994696	−	0.102859i	$-0.967201\pi$
$173$	−929.000	+	1609.08i	−0.408269	+	0.707143i	0.586427	+	0.810002i	$0.300534\pi$
$174$	−3040.00			−1.32449
$175$		0			0
$176$	−448.000			−0.191871
$177$	800.000	−	1385.64i	0.339727	−	0.588424i
$178$	810.000	+	1402.96i	0.341079	+	0.590766i
$179$	150.000	+	259.808i	0.0626342	+	0.108486i	0.895642	−	0.444775i	$-0.146717\pi$
$179$	150.000	+	259.808i	0.0626342	+	0.108486i	−0.833008	+	0.553261i	$0.813383\pi$
$180$	1036.00	−	1794.40i	0.428994	−	0.743039i
$181$	−2358.00			−0.968336			−0.484168	−	0.874975i	$-0.660878\pi$
$181$	−2358.00			−0.968336			−0.484168	+	0.874975i	$0.660878\pi$
$182$		0			0
$183$	−1584.00			−0.639851
$184$	−448.000	+	775.959i	−0.179495	+	0.310894i
$185$	−2422.00	−	4195.03i	−0.962535	−	1.66716i
$186$	576.000	+	997.661i	0.227067	+	0.393291i
$187$	1036.00	−	1794.40i	0.405133	−	0.701710i
$188$	96.0000			0.0372421
$189$		0			0
$190$	2240.00			0.855298
$191$	−696.000	+	1205.51i	−0.263669	+	0.456688i	−0.967214	−	0.253962i	$-0.918266\pi$
$191$	−696.000	+	1205.51i	−0.263669	+	0.456688i	0.703545	+	0.710651i	$0.251599\pi$
$192$	−256.000	−	443.405i	−0.0962250	−	0.166667i
$193$	−889.000	−	1539.79i	−0.331563	−	0.574284i	0.651256	−	0.758858i	$-0.274243\pi$
$193$	−889.000	−	1539.79i	−0.331563	−	0.574284i	−0.982818	+	0.184575i	$0.940909\pi$
$194$	1354.00	−	2345.20i	0.501090	−	0.867914i
$195$	−2016.00			−0.740353
$196$		0			0
$197$	1214.00			0.439055			0.219528	−	0.975606i	$-0.429548\pi$
$197$	1214.00			0.439055			0.219528	+	0.975606i	$0.429548\pi$
$198$	−1036.00	+	1794.40i	−0.371845	+	0.644054i
$199$	−520.000	−	900.666i	−0.185235	−	0.320837i	0.758420	−	0.651766i	$-0.225971\pi$
$199$	−520.000	−	900.666i	−0.185235	−	0.320837i	−0.943656	+	0.330929i	$0.892638\pi$
$200$	284.000	+	491.902i	0.100409	+	0.173914i
$201$	2864.00	−	4960.59i	1.00503	−	1.74076i
$202$	2716.00			0.946025
$203$		0			0
$204$	2368.00			0.812712
$205$	1134.00	−	1964.15i	0.386351	−	0.669180i
$206$	−832.000	−	1441.07i	−0.281399	−	0.487397i
$207$	2072.00	+	3588.81i	0.695720	+	1.20502i
$208$	−144.000	+	249.415i	−0.0480029	+	0.0831435i
$209$	−2240.00			−0.741359
$210$		0			0
$211$	−3868.00			−1.26201			−0.631005	−	0.775779i	$-0.717357\pi$
$211$	−3868.00			−1.26201			−0.631005	+	0.775779i	$0.717357\pi$
$212$	−636.000	+	1101.58i	−0.206041	+	0.356873i
$213$	−1568.00	−	2715.86i	−0.504402	−	0.873650i
$214$	444.000	+	769.031i	0.141828	+	0.245653i
$215$	−2884.00	+	4995.23i	−0.914824	+	1.58452i
$216$	−640.000			−0.201604
$217$		0			0
$218$	−3740.00			−1.16195
$219$	−2152.00	+	3727.37i	−0.664012	+	1.15010i
$220$	−784.000	−	1357.93i	−0.240260	−	0.416143i
$221$	−666.000	−	1153.55i	−0.202715	−	0.351113i
$222$	−2768.00	+	4794.32i	−0.836829	+	1.44943i
$223$	3968.00			1.19156			0.595778	−	0.803149i	$-0.296844\pi$
$223$	3968.00			1.19156			0.595778	+	0.803149i	$0.296844\pi$
$224$		0			0
$225$	2627.00			0.778370
$226$	1378.00	−	2386.77i	0.405589	−	0.702501i
$227$	1968.00	+	3408.68i	0.575422	+	0.996660i	0.995996	+	0.0894015i	$0.0284954\pi$
$227$	1968.00	+	3408.68i	0.575422	+	0.996660i	−0.420574	+	0.907258i	$0.638171\pi$
$228$	−1280.00	−	2217.03i	−0.371799	−	0.643974i
$229$	−2405.00	+	4165.58i	−0.694004	+	1.20205i	0.276512	+	0.961011i	$0.410822\pi$
$229$	−2405.00	+	4165.58i	−0.694004	+	1.20205i	−0.970515	+	0.241039i	$0.922512\pi$
$230$	−3136.00			−0.899051
$231$		0			0
$232$	−1520.00			−0.430142
$233$	1091.00	−	1889.67i	0.306754	−	0.531314i	−0.670896	−	0.741551i	$-0.734090\pi$
$233$	1091.00	−	1889.67i	0.306754	−	0.531314i	0.977650	+	0.210237i	$0.0674236\pi$
$234$	666.000	+	1153.55i	0.186059	+	0.322263i
$235$	168.000	+	290.985i	0.0466345	+	0.0807734i
$236$	400.000	−	692.820i	0.110330	−	0.191096i
$237$	1920.00			0.526234
$238$		0			0
$239$	−3000.00			−0.811941			−0.405970	−	0.913886i	$-0.633066\pi$
$239$	−3000.00			−0.811941			−0.405970	+	0.913886i	$0.633066\pi$
$240$	896.000	−	1551.92i	0.240986	−	0.417399i
$241$	−1021.00	−	1768.42i	−0.272898	−	0.472673i	0.696705	−	0.717358i	$-0.254649\pi$
$241$	−1021.00	−	1768.42i	−0.272898	−	0.472673i	−0.969603	+	0.244685i	$0.921315\pi$
$242$	−547.000	−	947.432i	−0.145300	−	0.251666i
$243$	2516.00	−	4357.84i	0.664204	−	1.15043i
$244$	−792.000			−0.207798
$245$		0			0
$246$	−2592.00			−0.671788
$247$	−720.000	+	1247.08i	−0.185476	+	0.321253i
$248$	288.000	+	498.831i	0.0737420	+	0.127725i
$249$	4288.00	+	7427.03i	1.09133	+	1.89024i
$250$	756.000	−	1309.43i	0.191255	−	0.331263i
$251$	−528.000			−0.132777			−0.0663886	−	0.997794i	$-0.521148\pi$
$251$	−528.000			−0.132777			−0.0663886	+	0.997794i	$0.521148\pi$
$252$		0			0
$253$	3136.00			0.779283
$254$	1944.00	−	3367.11i	0.480226	−	0.831776i
$255$	4144.00	+	7177.62i	1.01768	+	1.76267i
$256$	−128.000	−	221.703i	−0.0312500	−	0.0541266i
$257$	−2817.00	+	4879.19i	−0.683734	+	1.18426i	0.290099	+	0.956997i	$0.406312\pi$
$257$	−2817.00	+	4879.19i	−0.683734	+	1.18426i	−0.973833	+	0.227265i	$0.927022\pi$
$258$	6592.00			1.59070
$259$		0			0
$260$	−1008.00			−0.240437
$261$	−3515.00	+	6088.16i	−0.833613	+	1.44386i
$262$	−848.000	−	1468.78i	−0.199960	−	0.346342i
$263$	−84.0000	−	145.492i	−0.0196945	−	0.0341119i	0.856010	−	0.516959i	$-0.172936\pi$
$263$	−84.0000	−	145.492i	−0.0196945	−	0.0341119i	−0.875705	+	0.482847i	$0.839603\pi$
$264$	−896.000	+	1551.92i	−0.208883	+	0.361795i
$265$	−4452.00			−1.03202
$266$		0			0
$267$	6480.00			1.48528
$268$	1432.00	−	2480.30i	0.326393	−	0.565329i
$269$	655.000	+	1134.49i	0.148461	+	0.257142i	0.930659	−	0.365888i	$-0.119235\pi$
$269$	655.000	+	1134.49i	0.148461	+	0.257142i	−0.782198	+	0.623030i	$0.785901\pi$
$270$	−1120.00	−	1939.90i	−0.252448	−	0.437253i
$271$	1104.00	−	1912.18i	0.247466	−	0.428623i	−0.715356	−	0.698760i	$-0.753736\pi$
$271$	1104.00	−	1912.18i	0.247466	−	0.428623i	0.962822	+	0.270137i	$0.0870689\pi$
$272$	1184.00			0.263936
$273$		0			0
$274$	5932.00			1.30790
$275$	994.000	−	1721.66i	0.217965	−	0.377527i
$276$	1792.00	+	3103.84i	0.390818	+	0.676916i
$277$	−2647.00	−	4584.74i	−0.574162	−	0.994477i	−0.996132	−	0.0878678i	$-0.971995\pi$
$277$	−2647.00	−	4584.74i	−0.574162	−	0.994477i	0.421970	−	0.906610i	$-0.361339\pi$
$278$	2800.00	−	4849.74i	0.604075	−	1.04629i
$279$	2664.00			0.571647
$280$		0			0
$281$	3242.00			0.688262			0.344131	−	0.938922i	$-0.388174\pi$
$281$	3242.00			0.688262			0.344131	+	0.938922i	$0.388174\pi$
$282$	192.000	−	332.554i	0.0405441	−	0.0702244i
$283$	796.000	+	1378.71i	0.167199	+	0.289597i	0.937434	−	0.348163i	$-0.113194\pi$
$283$	796.000	+	1378.71i	0.167199	+	0.289597i	−0.770235	+	0.637760i	$0.779861\pi$
$284$	−784.000	−	1357.93i	−0.163809	−	0.283726i
$285$	4480.00	−	7759.59i	0.931131	−	1.61277i
$286$	1008.00			0.208407
$287$		0			0
$288$	−1184.00			−0.242250
$289$	−281.500	+	487.572i	−0.0572970	+	0.0992413i
$290$	−2660.00	−	4607.26i	−0.538623	−	0.932922i
$291$	−5416.00	−	9380.79i	−1.09104	−	1.88973i
$292$	−1076.00	+	1863.69i	−0.215644	+	0.373507i
$293$	−5022.00			−1.00133			−0.500663	−	0.865642i	$-0.666910\pi$
$293$	−5022.00			−1.00133			−0.500663	+	0.865642i	$0.666910\pi$
$294$		0			0
$295$	2800.00			0.552618
$296$	−1384.00	+	2397.16i	−0.271768	+	0.470716i
$297$	1120.00	+	1939.90i	0.218818	+	0.379004i
$298$	510.000	+	883.346i	0.0991393	+	0.171714i
$299$	1008.00	−	1745.91i	0.194964	−	0.337687i
$300$	2272.00			0.437247
$301$		0			0
$302$	−1184.00			−0.225601
$303$	5432.00	−	9408.50i	1.02990	−	1.78384i
$304$	−640.000	−	1108.51i	−0.120745	−	0.209137i
$305$	−1386.00	−	2400.62i	−0.260204	−	0.450686i
$306$	2738.00	−	4742.36i	0.511507	−	0.885956i
$307$	−9536.00			−1.77280			−0.886398	−	0.462924i	$-0.846800\pi$
$307$	−9536.00			−1.77280			−0.886398	+	0.462924i	$0.846800\pi$
$308$		0			0
$309$	−6656.00			−1.22539
$310$	−1008.00	+	1745.91i	−0.184679	+	0.319874i
$311$	484.000	+	838.313i	0.0882480	+	0.152850i	0.906771	−	0.421624i	$-0.138540\pi$
$311$	484.000	+	838.313i	0.0882480	+	0.152850i	−0.818523	+	0.574474i	$0.805207\pi$
$312$	576.000	+	997.661i	0.104518	+	0.181030i
$313$	−1529.00	+	2648.31i	−0.276116	+	0.478246i	−0.970416	−	0.241439i	$-0.922381\pi$
$313$	−1529.00	+	2648.31i	−0.276116	+	0.478246i	0.694300	+	0.719685i	$0.255714\pi$
$314$	5372.00			0.965476
$315$		0			0
$316$	960.000			0.170899
$317$	2493.00	−	4318.00i	0.441706	−	0.765057i	−0.556110	−	0.831109i	$-0.687707\pi$
$317$	2493.00	−	4318.00i	0.441706	−	0.765057i	0.997816	+	0.0660512i	$0.0210401\pi$
$318$	2544.00	+	4406.34i	0.448618	+	0.777029i
$319$	2660.00	+	4607.26i	0.466870	+	0.808642i
$320$	448.000	−	775.959i	0.0782624	−	0.135554i
$321$	3552.00			0.617612
$322$		0			0
$323$	5920.00			1.01981
$324$	718.000	−	1243.61i	0.123114	−	0.213239i
$325$	−639.000	−	1106.78i	−0.109063	−	0.188902i
$326$	−1012.00	−	1752.84i	−0.171931	−	0.297793i
$327$	−7480.00	+	12955.7i	−1.26497	+	2.19099i
$328$	−1296.00			−0.218170
$329$		0			0
$330$	−6272.00			−1.04625
$331$	−4306.00	+	7458.21i	−0.715043	+	1.23849i	0.247900	+	0.968786i	$0.420259\pi$
$331$	−4306.00	+	7458.21i	−0.715043	+	1.23849i	−0.962943	+	0.269705i	$0.913074\pi$
$332$	2144.00	+	3713.52i	0.354420	+	0.613873i
$333$	6401.00	+	11086.9i	1.05337	+	1.82449i
$334$	544.000	−	942.236i	0.0891208	−	0.154362i
$335$	10024.0			1.63483
$336$		0			0
$337$	−10206.0			−1.64972			−0.824861	−	0.565336i	$-0.808747\pi$
$337$	−10206.0			−1.64972			−0.824861	+	0.565336i	$0.808747\pi$
$338$	−1873.00	+	3244.13i	−0.301414	+	0.522064i
$339$	−5512.00	−	9547.06i	−0.883100	−	1.52957i
$340$	2072.00	+	3588.81i	0.330500	+	0.572443i
$341$	1008.00	−	1745.91i	0.160077	−	0.277262i
$342$	−5920.00			−0.936014
$343$		0			0
$344$	3296.00			0.516594
$345$	−6272.00	+	10863.4i	−0.978763	+	1.69527i
$346$	1858.00	+	3218.15i	0.288690	+	0.500026i
$347$	−1002.00	−	1735.51i	−0.155015	−	0.268494i	0.778050	−	0.628203i	$-0.216209\pi$
$347$	−1002.00	−	1735.51i	−0.155015	−	0.268494i	−0.933064	+	0.359709i	$0.882876\pi$
$348$	−3040.00	+	5265.43i	−0.468279	+	0.811083i
$349$	1330.00			0.203992			0.101996	−	0.994785i	$-0.467477\pi$
$349$	1330.00			0.203992			0.101996	+	0.994785i	$0.467477\pi$
$350$		0			0
$351$	1440.00			0.218979
$352$	−448.000	+	775.959i	−0.0678366	+	0.117496i
$353$	−489.000	−	846.973i	−0.0737304	−	0.127705i	0.826803	−	0.562492i	$-0.190157\pi$
$353$	−489.000	−	846.973i	−0.0737304	−	0.127705i	−0.900533	+	0.434787i	$0.856824\pi$
$354$	−1600.00	−	2771.28i	−0.240223	−	0.416079i
$355$	2744.00	−	4752.75i	0.410243	−	0.710562i
$356$	3240.00			0.482359
$357$		0			0
$358$	600.000			0.0885782
$359$	4840.00	−	8383.13i	0.711547	−	1.23244i	−0.252729	−	0.967537i	$-0.581328\pi$
$359$	4840.00	−	8383.13i	0.711547	−	1.23244i	0.964276	−	0.264899i	$-0.0853385\pi$
$360$	−2072.00	−	3588.81i	−0.303344	−	0.525408i
$361$	229.500	+	397.506i	0.0334597	+	0.0579539i
$362$	−2358.00	+	4084.18i	−0.342358	+	0.592982i
$363$	−4376.00			−0.632728
$364$		0			0
$365$	−7532.00			−1.08012
$366$	−1584.00	+	2743.57i	−0.226221	+	0.391827i
$367$	4328.00	+	7496.32i	0.615585	+	1.06622i	0.990282	+	0.139077i	$0.0444136\pi$
$367$	4328.00	+	7496.32i	0.615585	+	1.06622i	−0.374696	+	0.927148i	$0.622253\pi$
$368$	896.000	+	1551.92i	0.126922	+	0.219835i
$369$	−2997.00	+	5190.96i	−0.422812	+	0.732332i
$370$	−9688.00			−1.36123
$371$		0			0
$372$	2304.00			0.321121
$373$	−2639.00	+	4570.88i	−0.366333	+	0.634508i	−0.988989	−	0.147988i	$-0.952720\pi$
$373$	−2639.00	+	4570.88i	−0.366333	+	0.634508i	0.622656	+	0.782496i	$0.286054\pi$
$374$	−2072.00	−	3588.81i	−0.286472	−	0.496184i
$375$	−3024.00	−	5237.72i	−0.416423	−	0.721266i
$376$	96.0000	−	166.277i	0.0131671	−	0.0228061i
$377$	3420.00			0.467212
$378$		0			0
$379$	6340.00			0.859272			0.429636	−	0.903002i	$-0.358642\pi$
$379$	6340.00			0.859272			0.429636	+	0.903002i	$0.358642\pi$
$380$	2240.00	−	3879.79i	0.302394	−	0.523761i
$381$	−7776.00	−	13468.4i	−1.04561	−	1.81105i
$382$	1392.00	+	2411.01i	0.186442	+	0.322927i
$383$	3116.00	−	5397.07i	0.415718	−	0.720045i	−0.579785	−	0.814769i	$-0.696864\pi$
$383$	3116.00	−	5397.07i	0.415718	−	0.720045i	0.995504	+	0.0947240i	$0.0301968\pi$
$384$	−1024.00			−0.136083
$385$		0			0
$386$	−3556.00			−0.468901
$387$	7622.00	−	13201.7i	1.00116	−	1.73406i
$388$	−2708.00	−	4690.39i	−0.354324	−	0.613708i
$389$	7405.00	+	12825.8i	0.965163	+	1.67171i	0.709177	+	0.705031i	$0.249067\pi$
$389$	7405.00	+	12825.8i	0.965163	+	1.67171i	0.255986	+	0.966680i	$0.417600\pi$
$390$	−2016.00	+	3491.81i	−0.261754	+	0.453372i
$391$	−8288.00			−1.07197
$392$		0			0
$393$	−6784.00			−0.870757
$394$	1214.00	−	2102.71i	0.155230	−	0.268865i
$395$	1680.00	+	2909.85i	0.214000	+	0.370659i
$396$	2072.00	+	3588.81i	0.262934	+	0.455415i
$397$	−2577.00	+	4463.49i	−0.325783	+	0.564273i	−0.981671	−	0.190586i	$-0.938961\pi$
$397$	−2577.00	+	4463.49i	−0.325783	+	0.564273i	0.655887	+	0.754859i	$0.272295\pi$
$398$	−2080.00			−0.261962
$399$		0			0
$400$	1136.00			0.142000
$401$	−1641.00	+	2842.30i	−0.204358	+	0.353959i	−0.949928	−	0.312469i	$-0.898844\pi$
$401$	−1641.00	+	2842.30i	−0.204358	+	0.353959i	0.745570	+	0.666427i	$0.232177\pi$
$402$	−5728.00	−	9921.19i	−0.710663	−	1.23091i
$403$	−648.000	−	1122.37i	−0.0800972	−	0.138732i
$404$	2716.00	−	4704.25i	0.334470	−	0.579320i
$405$	5026.00			0.616652
$406$		0			0
$407$	9688.00			1.17989
$408$	2368.00	−	4101.50i	0.287337	−	0.497682i
$409$	−2905.00	−	5031.61i	−0.351205	−	0.608306i	0.635256	−	0.772302i	$-0.280895\pi$
$409$	−2905.00	−	5031.61i	−0.351205	−	0.608306i	−0.986461	+	0.163996i	$0.947561\pi$
$410$	−2268.00	−	3928.29i	−0.273192	−	0.473182i
$411$	11864.0	−	20549.1i	1.42386	−	2.46620i
$412$	−3328.00			−0.397958
$413$		0			0
$414$	8288.00			0.983896
$415$	−7504.00	+	12997.3i	−0.887607	+	1.53738i
$416$	288.000	+	498.831i	0.0339432	+	0.0587913i
$417$	−11200.0	−	19399.0i	−1.31527	−	2.27811i
$418$	−2240.00	+	3879.79i	−0.262110	+	0.453988i
$419$	13560.0			1.58102			0.790512	−	0.612446i	$-0.209814\pi$
$419$	13560.0			1.58102			0.790512	+	0.612446i	$0.209814\pi$
$420$		0			0
$421$	−738.000			−0.0854345			−0.0427172	−	0.999087i	$-0.513601\pi$
$421$	−738.000			−0.0854345			−0.0427172	+	0.999087i	$0.513601\pi$
$422$	−3868.00	+	6699.57i	−0.446188	+	0.772820i
$423$	−444.000	−	769.031i	−0.0510355	−	0.0883961i
$424$	1272.00	+	2203.17i	0.145693	+	0.252347i
$425$	−2627.00	+	4550.10i	−0.299831	+	0.519323i
$426$	−6272.00			−0.713332
$427$		0			0
$428$	1776.00			0.200575
$429$	2016.00	−	3491.81i	0.226884	−	0.392975i
$430$	5768.00	+	9990.47i	0.646878	+	1.12043i
$431$	−636.000	−	1101.58i	−0.0710790	−	0.123112i	0.828295	−	0.560292i	$-0.189311\pi$
$431$	−636.000	−	1101.58i	−0.0710790	−	0.123112i	−0.899374	+	0.437179i	$0.855978\pi$
$432$	−640.000	+	1108.51i	−0.0712778	+	0.123457i
$433$	−5062.00			−0.561811			−0.280906	−	0.959735i	$-0.590635\pi$
$433$	−5062.00			−0.561811			−0.280906	+	0.959735i	$0.590635\pi$
$434$		0			0
$435$	−21280.0			−2.34551
$436$	−3740.00	+	6477.87i	−0.410811	+	0.711545i
$437$	4480.00	+	7759.59i	0.490406	+	0.849408i
$438$	4304.00	+	7454.75i	0.469528	+	0.813246i
$439$	−2820.00	+	4884.38i	−0.306586	+	0.531023i	−0.977613	−	0.210410i	$-0.932520\pi$
$439$	−2820.00	+	4884.38i	−0.306586	+	0.531023i	0.671027	+	0.741433i	$0.265853\pi$
$440$	−3136.00			−0.339779
$441$		0			0
$442$	−2664.00			−0.286682
$443$	−6694.00	+	11594.3i	−0.717927	+	1.24349i	0.243893	+	0.969802i	$0.421575\pi$
$443$	−6694.00	+	11594.3i	−0.717927	+	1.24349i	−0.961820	+	0.273683i	$0.911758\pi$
$444$	5536.00	+	9588.63i	0.591727	+	1.02490i
$445$	5670.00	+	9820.73i	0.604008	+	1.04617i
$446$	3968.00	−	6872.78i	0.421279	−	0.729676i
$447$	4080.00			0.431717
$448$		0			0
$449$	−3230.00			−0.339495			−0.169747	−	0.985488i	$-0.554295\pi$
$449$	−3230.00			−0.339495			−0.169747	+	0.985488i	$0.554295\pi$
$450$	2627.00	−	4550.10i	0.275195	−	0.476653i
$451$	2268.00	+	3928.29i	0.236798	+	0.410146i
$452$	−2756.00	−	4773.53i	−0.286795	−	0.496743i
$453$	−2368.00	+	4101.50i	−0.245603	+	0.425398i
$454$	7872.00			0.813769
$455$		0			0
$456$	−5120.00			−0.525803
$457$	5323.00	−	9219.71i	0.544857	−	0.943719i	−0.453759	−	0.891124i	$-0.649917\pi$
$457$	5323.00	−	9219.71i	0.544857	−	0.943719i	0.998616	−	0.0525950i	$-0.0167492\pi$
$458$	4810.00	+	8331.16i	0.490735	+	0.849978i
$459$	−2960.00	−	5126.87i	−0.301004	−	0.521355i
$460$	−3136.00	+	5431.71i	−0.317863	+	0.550554i
$461$	7282.00			0.735698			0.367849	−	0.929886i	$-0.380094\pi$
$461$	7282.00			0.735698			0.367849	+	0.929886i	$0.380094\pi$
$462$		0			0
$463$	12688.0			1.27357			0.636783	−	0.771043i	$-0.280265\pi$
$463$	12688.0			1.27357			0.636783	+	0.771043i	$0.280265\pi$
$464$	−1520.00	+	2632.72i	−0.152078	+	0.263407i
$465$	4032.00	+	6983.63i	0.402107	+	0.696469i
$466$	−2182.00	−	3779.33i	−0.216908	−	0.375696i
$467$	1408.00	−	2438.73i	0.139517	−	0.241651i	−0.787797	−	0.615935i	$-0.788778\pi$
$467$	1408.00	−	2438.73i	0.139517	−	0.241651i	0.927314	+	0.374285i	$0.122112\pi$
$468$	2664.00			0.263127
$469$		0			0
$470$	672.000			0.0659512
$471$	10744.0	−	18609.2i	1.05108	−	1.82052i
$472$	−800.000	−	1385.64i	−0.0780148	−	0.135126i
$473$	−5768.00	−	9990.47i	−0.560704	−	0.971168i
$474$	1920.00	−	3325.54i	0.186052	−	0.322251i
$475$	5680.00			0.548666
$476$		0			0
$477$	11766.0			1.12941
$478$	−3000.00	+	5196.15i	−0.287064	+	0.497210i
$479$	1580.00	+	2736.64i	0.150714	+	0.261044i	0.931490	−	0.363766i	$-0.118509\pi$
$479$	1580.00	+	2736.64i	0.150714	+	0.261044i	−0.780776	+	0.624811i	$0.785176\pi$
$480$	−1792.00	−	3103.84i	−0.170403	−	0.295146i
$481$	3114.00	−	5393.61i	0.295190	−	0.511283i
$482$	−4084.00			−0.385936
$483$		0			0
$484$	−2188.00			−0.205485
$485$	9478.00	−	16416.4i	0.887369	−	1.53697i
$486$	−5032.00	−	8715.68i	−0.469663	−	0.813480i
$487$	7088.00	+	12276.8i	0.659523	+	1.14233i	0.980739	+	0.195322i	$0.0625752\pi$
$487$	7088.00	+	12276.8i	0.659523	+	1.14233i	−0.321216	+	0.947006i	$0.604091\pi$
$488$	−792.000	+	1371.78i	−0.0734675	+	0.127249i
$489$	−8096.00			−0.748699
$490$		0			0
$491$	−11268.0			−1.03568			−0.517839	−	0.855478i	$-0.673263\pi$
$491$	−11268.0			−1.03568			−0.517839	+	0.855478i	$0.673263\pi$
$492$	−2592.00	+	4489.48i	−0.237513	+	0.411385i
$493$	−7030.00	−	12176.3i	−0.642222	−	1.11236i
$494$	1440.00	+	2494.15i	0.131151	+	0.227160i
$495$	−7252.00	+	12560.8i	−0.658491	+	1.14054i
$496$	1152.00			0.104287
$497$		0			0
$498$	17152.0			1.54337
$499$	2230.00	−	3862.47i	0.200057	−	0.346509i	−0.748489	−	0.663147i	$-0.769221\pi$
$499$	2230.00	−	3862.47i	0.200057	−	0.346509i	0.948547	+	0.316638i	$0.102554\pi$
$500$	−1512.00	−	2618.86i	−0.135237	−	0.234238i
$501$	−2176.00	−	3768.94i	−0.194045	−	0.336096i
$502$	−528.000	+	914.523i	−0.0469438	+	0.0813091i
$503$	−1512.00			−0.134029			−0.0670147	−	0.997752i	$-0.521347\pi$
$503$	−1512.00			−0.134029			−0.0670147	+	0.997752i	$0.521347\pi$
$504$		0			0
$505$	19012.0			1.67529
$506$	3136.00	−	5431.71i	0.275518	−	0.477212i
$507$	7492.00	+	12976.5i	0.656275	+	1.13670i
$508$	−3888.00	−	6734.21i	−0.339571	−	0.588154i
$509$	5895.00	−	10210.4i	0.513342	−	0.889135i	−0.486538	−	0.873660i	$-0.661740\pi$
$509$	5895.00	−	10210.4i	0.513342	−	0.889135i	0.999880	−	0.0154756i	$-0.00492624\pi$
$510$	16576.0			1.43921
$511$		0			0
$512$	−512.000			−0.0441942
$513$	−3200.00	+	5542.56i	−0.275406	+	0.477018i
$514$	5634.00	+	9758.37i	0.483473	+	0.837400i
$515$	−5824.00	−	10087.5i	−0.498323	−	0.863120i
$516$	6592.00	−	11417.7i	0.562397	−	0.974099i
$517$	−672.000			−0.0571654
$518$		0			0
$519$	14864.0			1.25714
$520$	−1008.00	+	1745.91i	−0.0850072	+	0.147237i
$521$	−681.000	−	1179.53i	−0.0572652	−	0.0991862i	0.835972	−	0.548773i	$-0.184905\pi$
$521$	−681.000	−	1179.53i	−0.0572652	−	0.0991862i	−0.893237	+	0.449586i	$0.851571\pi$
$522$	7030.00	+	12176.3i	0.589454	+	1.02096i
$523$	−3484.00	+	6034.47i	−0.291290	+	0.504529i	−0.974115	−	0.226053i	$-0.927418\pi$
$523$	−3484.00	+	6034.47i	−0.291290	+	0.504529i	0.682825	+	0.730582i	$0.260751\pi$
$524$	−3392.00			−0.282787
$525$		0			0
$526$	−336.000			−0.0278523
$527$	−2664.00	+	4614.18i	−0.220200	+	0.381398i
$528$	1792.00	+	3103.84i	0.147702	+	0.255828i
$529$	−188.500	−	326.492i	−0.0154927	−	0.0268342i
$530$	−4452.00	+	7711.09i	−0.364873	+	0.631978i
$531$	−7400.00			−0.604770
$532$		0			0
$533$	2916.00			0.236972
$534$	6480.00	−	11223.7i	0.525126	−	0.909544i
$535$	3108.00	+	5383.21i	0.251160	+	0.435022i
$536$	−2864.00	−	4960.59i	−0.230795	−	0.399748i
$537$	1200.00	−	2078.46i	0.0964317	−	0.167025i
$538$	2620.00			0.209956
$539$		0			0
$540$	−4480.00			−0.357016
$541$	−3531.00	+	6115.87i	−0.280609	+	0.486029i	−0.971535	−	0.236896i	$-0.923870\pi$
$541$	−3531.00	+	6115.87i	−0.280609	+	0.486029i	0.690926	+	0.722926i	$0.257203\pi$
$542$	−2208.00	−	3824.37i	−0.174985	−	0.303082i
$543$	9432.00	+	16336.7i	0.745425	+	1.29111i
$544$	1184.00	−	2050.75i	0.0933154	−	0.161627i
$545$	−26180.0			−2.05767
$546$		0			0
$547$	−8196.00			−0.640650			−0.320325	−	0.947308i	$-0.603792\pi$
$547$	−8196.00			−0.640650			−0.320325	+	0.947308i	$0.603792\pi$
$548$	5932.00	−	10274.5i	0.462413	−	0.800923i
$549$	3663.00	+	6344.50i	0.284760	+	0.493218i
$550$	−1988.00	−	3443.32i	−0.154125	−	0.266952i
$551$	−7600.00	+	13163.6i	−0.587606	+	1.01776i
$552$	7168.00			0.552700
$553$		0			0
$554$	−10588.0			−0.811987
$555$	−19376.0	+	33560.2i	−1.48192	+	2.56676i
$556$	−5600.00	−	9699.48i	−0.427146	−	0.739838i
$557$	3733.00	+	6465.75i	0.283972	+	0.491854i	0.972359	−	0.233490i	$-0.0750145\pi$
$557$	3733.00	+	6465.75i	0.283972	+	0.491854i	−0.688388	+	0.725343i	$0.741681\pi$
$558$	2664.00	−	4614.18i	0.202108	−	0.350061i
$559$	−7416.00			−0.561115
$560$		0			0
$561$	−16576.0			−1.24749
$562$	3242.00	−	5615.31i	0.243337	−	0.421472i
$563$	−12484.0	−	21622.9i	−0.934526	−	1.61865i	−0.775478	−	0.631375i	$-0.782491\pi$
$563$	−12484.0	−	21622.9i	−0.934526	−	1.61865i	−0.159048	−	0.987271i	$-0.550842\pi$
$564$	−384.000	−	665.108i	−0.0286690	−	0.0496562i
$565$	9646.00	−	16707.4i	0.718248	−	1.24404i
$566$	3184.00			0.236455
$567$		0			0
$568$	−3136.00			−0.231661
$569$	−7125.00	+	12340.9i	−0.524948	+	0.909237i	0.474630	+	0.880186i	$0.342582\pi$
$569$	−7125.00	+	12340.9i	−0.524948	+	0.909237i	−0.999578	+	0.0290514i	$0.990751\pi$
$570$	−8960.00	−	15519.2i	−0.658409	−	1.14040i
$571$	−3186.00	−	5518.31i	−0.233503	−	0.404438i	0.725334	−	0.688397i	$-0.241685\pi$
$571$	−3186.00	−	5518.31i	−0.233503	−	0.404438i	−0.958836	+	0.283959i	$0.908352\pi$
$572$	1008.00	−	1745.91i	0.0736829	−	0.127622i
$573$	11136.0			0.811890
$574$		0			0
$575$	−7952.00			−0.576733
$576$	−1184.00	+	2050.75i	−0.0856481	+	0.148347i
$577$	4183.00	+	7245.17i	0.301803	+	0.522739i	0.976545	−	0.215316i	$-0.0690780\pi$
$577$	4183.00	+	7245.17i	0.301803	+	0.522739i	−0.674741	+	0.738055i	$0.735745\pi$
$578$	563.000	+	975.145i	0.0405151	+	0.0701742i
$579$	−7112.00	+	12318.3i	−0.510474	+	0.884167i
$580$	−10640.0			−0.761728
$581$		0			0
$582$	−21664.0			−1.54296
$583$	4452.00	−	7711.09i	0.316266	−	0.547789i
$584$	2152.00	+	3727.37i	0.152484	+	0.264109i
$585$	4662.00	+	8074.82i	0.329487	+	0.570688i
$586$	−5022.00	+	8698.36i	−0.354022	+	0.613184i
$587$	20384.0			1.43328			0.716642	−	0.697441i	$-0.245678\pi$
$587$	20384.0			1.43328			0.716642	+	0.697441i	$0.245678\pi$
$588$		0			0
$589$	5760.00			0.402948
$590$	2800.00	−	4849.74i	0.195380	−	0.338408i
$591$	−4856.00	−	8410.84i	−0.337985	−	0.585407i
$592$	2768.00	+	4794.32i	0.192169	+	0.332847i
$593$	−4689.00	+	8121.59i	−0.324712	+	0.562417i	−0.981454	−	0.191698i	$-0.938601\pi$
$593$	−4689.00	+	8121.59i	−0.324712	+	0.562417i	0.656742	+	0.754115i	$0.271934\pi$
$594$	4480.00			0.309456
$595$		0			0
$596$	2040.00			0.140204
$597$	−4160.00	+	7205.33i	−0.285188	+	0.493961i
$598$	−2016.00	−	3491.81i	−0.137860	−	0.238781i
$599$	4500.00	+	7794.23i	0.306953	+	0.531659i	0.977694	−	0.210033i	$-0.0673571\pi$
$599$	4500.00	+	7794.23i	0.306953	+	0.531659i	−0.670741	+	0.741692i	$0.734024\pi$
$600$	2272.00	−	3935.22i	0.154590	−	0.267758i
$601$	7562.00			0.513245			0.256623	−	0.966512i	$-0.417390\pi$
$601$	7562.00			0.513245			0.256623	+	0.966512i	$0.417390\pi$
$602$		0			0
$603$	−26492.0			−1.78912
$604$	−1184.00	+	2050.75i	−0.0797620	+	0.138152i
$605$	−3829.00	−	6632.02i	−0.257307	−	0.445670i
$606$	−10864.0	−	18817.0i	−0.728251	−	1.26137i
$607$	1488.00	−	2577.29i	0.0994993	−	0.172338i	−0.811978	−	0.583688i	$-0.801609\pi$
$607$	1488.00	−	2577.29i	0.0994993	−	0.172338i	0.911478	+	0.411350i	$0.134943\pi$
$608$	−2560.00			−0.170759
$609$		0			0
$610$	−5544.00			−0.367984
$611$	−216.000	+	374.123i	−0.0143018	+	0.0247715i
$612$	−5476.00	−	9484.71i	−0.361690	−	0.626465i
$613$	−2139.00	−	3704.86i	−0.140935	−	0.244107i	0.786914	−	0.617063i	$-0.211678\pi$
$613$	−2139.00	−	3704.86i	−0.140935	−	0.244107i	−0.927849	+	0.372956i	$0.878344\pi$
$614$	−9536.00	+	16516.8i	−0.626778	+	1.08561i
$615$	−18144.0			−1.18965
$616$		0			0
$617$	18794.0			1.22629			0.613143	−	0.789972i	$-0.289905\pi$
$617$	18794.0			1.22629			0.613143	+	0.789972i	$0.289905\pi$
$618$	−6656.00	+	11528.5i	−0.433242	+	0.750397i
$619$	−9020.00	−	15623.1i	−0.585694	−	1.01445i	−0.994789	−	0.101959i	$-0.967489\pi$
$619$	−9020.00	−	15623.1i	−0.585694	−	1.01445i	0.409095	−	0.912492i	$-0.365845\pi$
$620$	2016.00	+	3491.81i	0.130588	+	0.226185i
$621$	4480.00	−	7759.59i	0.289495	−	0.501420i
$622$	1936.00			0.124801
$623$		0			0
$624$	2304.00			0.147811
$625$	9729.50	−	16852.0i	0.622688	−	1.07853i
$626$	3058.00	+	5296.61i	0.195243	+	0.338171i
$627$	8960.00	+	15519.2i	0.570698	+	0.988479i
$628$	5372.00	−	9304.58i	0.341347	−	0.591231i
$629$	−25604.0			−1.62305
$630$		0			0
$631$	−21688.0			−1.36828			−0.684141	−	0.729350i	$-0.739823\pi$
$631$	−21688.0			−1.36828			−0.684141	+	0.729350i	$0.739823\pi$
$632$	960.000	−	1662.77i	0.0604221	−	0.104654i
$633$	15472.0	+	26798.3i	0.971496	+	1.68268i
$634$	−4986.00	−	8636.01i	−0.312333	−	0.540977i
$635$	13608.0	−	23569.7i	0.850420	−	1.47297i
$636$	10176.0			0.634441
$637$		0			0
$638$	10640.0			0.660253
$639$	−7252.00	+	12560.8i	−0.448959	+	0.777619i
$640$	−896.000	−	1551.92i	−0.0553399	−	0.0958514i
$641$	5279.00	+	9143.50i	0.325285	+	0.563411i	0.981570	−	0.191102i	$-0.0612063\pi$
$641$	5279.00	+	9143.50i	0.325285	+	0.563411i	−0.656285	+	0.754513i	$0.727873\pi$
$642$	3552.00	−	6152.24i	0.218359	−	0.378208i
$643$	−26152.0			−1.60394			−0.801971	−	0.597363i	$-0.796215\pi$
$643$	−26152.0			−1.60394			−0.801971	+	0.597363i	$0.796215\pi$
$644$		0			0
$645$	46144.0			2.81693
$646$	5920.00	−	10253.7i	0.360556	−	0.624502i
$647$	−12792.0	−	22156.4i	−0.777288	−	1.34630i	−0.933499	−	0.358579i	$-0.883261\pi$
$647$	−12792.0	−	22156.4i	−0.777288	−	1.34630i	0.156211	−	0.987724i	$-0.450072\pi$
$648$	−1436.00	−	2487.22i	−0.0870546	−	0.150783i
$649$	−2800.00	+	4849.74i	−0.169352	+	0.293327i
$650$	−2556.00			−0.154238
$651$		0			0
$652$	−4048.00			−0.243147
$653$	−7599.00	+	13161.9i	−0.455393	+	0.788764i	−0.998711	−	0.0507630i	$-0.983835\pi$
$653$	−7599.00	+	13161.9i	−0.455393	+	0.788764i	0.543317	+	0.839527i	$0.317168\pi$
$654$	14960.0	+	25911.5i	0.894468	+	1.54926i
$655$	−5936.00	−	10281.5i	−0.354105	−	0.613328i
$656$	−1296.00	+	2244.74i	−0.0771346	+	0.133601i
$657$	19906.0			1.18205
$658$		0			0
$659$	−6100.00			−0.360580			−0.180290	−	0.983613i	$-0.557704\pi$
$659$	−6100.00			−0.360580			−0.180290	+	0.983613i	$0.557704\pi$
$660$	−6272.00	+	10863.4i	−0.369905	+	0.640694i
$661$	1159.00	+	2007.45i	0.0681995	+	0.118125i	0.898109	−	0.439773i	$-0.144941\pi$
$661$	1159.00	+	2007.45i	0.0681995	+	0.118125i	−0.829909	+	0.557898i	$0.811608\pi$
$662$	8612.00	+	14916.4i	0.505612	+	0.875745i
$663$	−5328.00	+	9228.37i	−0.312100	+	0.540573i
$664$	8576.00			0.501225
$665$		0			0
$666$	25604.0			1.48969
$667$	10640.0	−	18429.0i	0.617665	−	1.06983i
$668$	−1088.00	−	1884.47i	−0.0630179	−	0.109150i
$669$	−15872.0	−	27491.1i	−0.917260	−	1.58874i
$670$	10024.0	−	17362.1i	0.578001	−	1.00113i
$671$	5544.00			0.318962
$672$		0			0
$673$	−10222.0			−0.585482			−0.292741	−	0.956192i	$-0.594567\pi$
$673$	−10222.0			−0.585482			−0.292741	+	0.956192i	$0.594567\pi$
$674$	−10206.0	+	17677.3i	−0.583265	+	1.01024i
$675$	−2840.00	−	4919.02i	−0.161943	−	0.280494i
$676$	3746.00	+	6488.26i	0.213132	+	0.369155i
$677$	−12717.0	+	22026.5i	−0.721941	+	1.25044i	0.238280	+	0.971197i	$0.423416\pi$
$677$	−12717.0	+	22026.5i	−0.721941	+	1.25044i	−0.960221	+	0.279242i	$0.909917\pi$
$678$	−22048.0			−1.24889
$679$		0			0
$680$	8288.00			0.467397
$681$	15744.0	−	27269.4i	0.885920	−	1.53446i
$682$	−2016.00	−	3491.81i	−0.113192	−	0.196053i
$683$	4266.00	+	7388.93i	0.238996	+	0.413952i	0.960426	−	0.278534i	$-0.0898485\pi$
$683$	4266.00	+	7388.93i	0.238996	+	0.413952i	−0.721431	+	0.692487i	$0.756515\pi$
$684$	−5920.00	+	10253.7i	−0.330931	+	0.573189i
$685$	41524.0			2.31613
$686$		0			0
$687$	38480.0			2.13698
$688$	3296.00	−	5708.84i	0.182644	−	0.316348i
$689$	−2862.00	−	4957.13i	−0.158249	−	0.274095i
$690$	12544.0	+	21726.8i	0.692090	+	1.19873i
$691$	−10336.0	+	17902.5i	−0.569030	+	0.985589i	0.427632	+	0.903953i	$0.359348\pi$
$691$	−10336.0	+	17902.5i	−0.569030	+	0.985589i	−0.996662	+	0.0816365i	$0.973985\pi$
$692$	7432.00			0.408269
$693$		0			0
$694$	−4008.00			−0.219224
$695$	19600.0	−	33948.2i	1.06974	−	1.85285i
$696$	6080.00	+	10530.9i	0.331123	+	0.573522i
$697$	−5994.00	−	10381.9i	−0.325737	−	0.564194i
$698$	1330.00	−	2303.63i	0.0721221	−	0.124919i
$699$	−17456.0			−0.944559
$700$		0			0
$701$	−21458.0			−1.15614			−0.578072	−	0.815985i	$-0.696195\pi$
$701$	−21458.0			−1.15614			−0.578072	+	0.815985i	$0.696195\pi$
$702$	1440.00	−	2494.15i	0.0774207	−	0.134097i
$703$	13840.0	+	23971.6i	0.742511	+	1.28607i
$704$	896.000	+	1551.92i	0.0479677	+	0.0830825i
$705$	1344.00	−	2327.88i	0.0717985	−	0.124359i
$706$	−1956.00			−0.104271
$707$		0			0
$708$	−6400.00			−0.339727
$709$	4925.00	−	8530.35i	0.260878	−	0.451853i	−0.705598	−	0.708613i	$-0.749321\pi$
$709$	4925.00	−	8530.35i	0.260878	−	0.451853i	0.966475	+	0.256759i	$0.0826547\pi$
$710$	−5488.00	−	9505.49i	−0.290086	−	0.502443i
$711$	−4440.00	−	7690.31i	−0.234196	−	0.405639i
$712$	3240.00	−	5611.84i	0.170540	−	0.295383i
$713$	−8064.00			−0.423561
$714$		0			0
$715$	7056.00			0.369062
$716$	600.000	−	1039.23i	0.0313171	−	0.0542428i
$717$	12000.0	+	20784.6i	0.625032	+	1.08259i
$718$	−9680.00	−	16766.3i	−0.503140	−	0.871464i
$719$	9420.00	−	16315.9i	0.488605	−	0.846288i	−0.511309	−	0.859397i	$-0.670839\pi$
$719$	9420.00	−	16315.9i	0.488605	−	0.846288i	0.999914	+	0.0131086i	$0.00417273\pi$
$720$	−8288.00			−0.428994
$721$		0			0
$722$	918.000			0.0473191
$723$	−8168.00	+	14147.4i	−0.420154	+	0.727728i
$724$	4716.00	+	8168.35i	0.242084	+	0.419302i
$725$	−6745.00	−	11682.7i	−0.345521	−	0.598461i
$726$	−4376.00	+	7579.45i	−0.223703	+	0.387465i
$727$	37504.0			1.91327			0.956634	−	0.291291i	$-0.0940849\pi$
$727$	37504.0			1.91327			0.956634	+	0.291291i	$0.0940849\pi$
$728$		0			0
$729$	−30563.0			−1.55276
$730$	−7532.00	+	13045.8i	−0.381879	+	0.661434i
$731$	15244.0	+	26403.4i	0.771299	+	1.33593i
$732$	3168.00	+	5487.14i	0.159963	+	0.277063i
$733$	−6669.00	+	11551.0i	−0.336051	+	0.582057i	−0.983686	−	0.179894i	$-0.942425\pi$
$733$	−6669.00	+	11551.0i	−0.336051	+	0.582057i	0.647635	+	0.761950i	$0.275758\pi$
$734$	17312.0			0.870569
$735$		0			0
$736$	3584.00			0.179495
$737$	−10024.0	+	17362.1i	−0.501002	+	0.867762i
$738$	5994.00	+	10381.9i	0.298973	+	0.517837i
$739$	−8550.00	−	14809.0i	−0.425598	−	0.737157i	0.570878	−	0.821035i	$-0.306603\pi$
$739$	−8550.00	−	14809.0i	−0.425598	−	0.737157i	−0.996476	+	0.0838776i	$0.973270\pi$
$740$	−9688.00	+	16780.1i	−0.481268	+	0.833580i
$741$	11520.0			0.571117
$742$		0			0
$743$	−19632.0			−0.969352			−0.484676	−	0.874694i	$-0.661062\pi$
$743$	−19632.0			−0.969352			−0.484676	+	0.874694i	$0.661062\pi$
$744$	2304.00	−	3990.65i	0.113533	−	0.196645i
$745$	3570.00	+	6183.42i	0.175563	+	0.304085i
$746$	5278.00	+	9141.76i	0.259037	+	0.448665i
$747$	19832.0	−	34350.0i	0.971372	−	1.68247i
$748$	−8288.00			−0.405133
$749$		0			0
$750$	−12096.0			−0.588911
$751$	−16956.0	+	29368.7i	−0.823879	+	1.42700i	0.0788938	+	0.996883i	$0.474861\pi$
$751$	−16956.0	+	29368.7i	−0.823879	+	1.42700i	−0.902773	+	0.430117i	$0.858472\pi$
$752$	−192.000	−	332.554i	−0.00931053	−	0.0161263i
$753$	2112.00	+	3658.09i	0.102212	+	0.177036i
$754$	3420.00	−	5923.61i	0.165184	−	0.286108i
$755$	−8288.00			−0.399512
$756$		0			0
$757$	−31386.0			−1.50693			−0.753463	−	0.657490i	$-0.771618\pi$
$757$	−31386.0			−1.50693			−0.753463	+	0.657490i	$0.771618\pi$
$758$	6340.00	−	10981.2i	0.303798	−	0.526194i
$759$	−12544.0	−	21726.8i	−0.599892	−	1.03904i
$760$	−4480.00	−	7759.59i	−0.213825	−	0.370355i
$761$	17279.0	−	29928.1i	0.823079	−	1.42561i	−0.0802993	−	0.996771i	$-0.525588\pi$
$761$	17279.0	−	29928.1i	0.823079	−	1.42561i	0.903378	−	0.428844i	$-0.141079\pi$
$762$	−31104.0			−1.47871
$763$		0			0
$764$	5568.00			0.263669
$765$	19166.0	−	33196.5i	0.905815	−	1.56892i
$766$	−6232.00	−	10794.1i	−0.293957	−	0.509149i
$767$	1800.00	+	3117.69i	0.0847382	+	0.146771i
$768$	−1024.00	+	1773.62i	−0.0481125	+	0.0833333i
$769$	39130.0			1.83493			0.917467	−	0.397812i	$-0.130231\pi$
$769$	39130.0			1.83493			0.917467	+	0.397812i	$0.130231\pi$
$770$		0			0
$771$	45072.0			2.10535
$772$	−3556.00	+	6159.17i	−0.165781	+	0.287142i
$773$	12991.0	+	22501.1i

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:	\( N \)	\(=\)	\( 98 = 2 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	98.c (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 - 1.73205i) q^{2} +(-4.00000 - 6.92820i) q^{3} +(-2.00000 - 3.46410i) q^{4} +(7.00000 - 12.1244i) q^{5} -16.0000 q^{6} -8.00000 q^{8} +(-18.5000 + 32.0429i) q^{9} +O(q^{10})\)	\(q+(1.00000 - 1.73205i) q^{2} +(-4.00000 - 6.92820i) q^{3} +(-2.00000 - 3.46410i) q^{4} +(7.00000 - 12.1244i) q^{5} -16.0000 q^{6} -8.00000 q^{8} +(-18.5000 + 32.0429i) q^{9} +(-14.0000 - 24.2487i) q^{10} +(14.0000 + 24.2487i) q^{11} +(-16.0000 + 27.7128i) q^{12} +18.0000 q^{13} -112.000 q^{15} +(-8.00000 + 13.8564i) q^{16} +(-37.0000 - 64.0859i) q^{17} +(37.0000 + 64.0859i) q^{18} +(-40.0000 + 69.2820i) q^{19} -56.0000 q^{20} +56.0000 q^{22} +(56.0000 - 96.9948i) q^{23} +(32.0000 + 55.4256i) q^{24} +(-35.5000 - 61.4878i) q^{25} +(18.0000 - 31.1769i) q^{26} +80.0000 q^{27} +190.000 q^{29} +(-112.000 + 193.990i) q^{30} +(-36.0000 - 62.3538i) q^{31} +(16.0000 + 27.7128i) q^{32} +(112.000 - 193.990i) q^{33} -148.000 q^{34} +148.000 q^{36} +(173.000 - 299.645i) q^{37} +(80.0000 + 138.564i) q^{38} +(-72.0000 - 124.708i) q^{39} +(-56.0000 + 96.9948i) q^{40} +162.000 q^{41} -412.000 q^{43} +(56.0000 - 96.9948i) q^{44} +(259.000 + 448.601i) q^{45} +(-112.000 - 193.990i) q^{46} +(-12.0000 + 20.7846i) q^{47} +128.000 q^{48} -142.000 q^{50} +(-296.000 + 512.687i) q^{51} +(-36.0000 - 62.3538i) q^{52} +(-159.000 - 275.396i) q^{53} +(80.0000 - 138.564i) q^{54} +392.000 q^{55} +640.000 q^{57} +(190.000 - 329.090i) q^{58} +(100.000 + 173.205i) q^{59} +(224.000 + 387.979i) q^{60} +(99.0000 - 171.473i) q^{61} -144.000 q^{62} +64.0000 q^{64} +(126.000 - 218.238i) q^{65} +(-224.000 - 387.979i) q^{66} +(358.000 + 620.074i) q^{67} +(-148.000 + 256.344i) q^{68} -896.000 q^{69} +392.000 q^{71} +(148.000 - 256.344i) q^{72} +(-269.000 - 465.922i) q^{73} +(-346.000 - 599.290i) q^{74} +(-284.000 + 491.902i) q^{75} +320.000 q^{76} -288.000 q^{78} +(-120.000 + 207.846i) q^{79} +(112.000 + 193.990i) q^{80} +(179.500 + 310.903i) q^{81} +(162.000 - 280.592i) q^{82} -1072.00 q^{83} -1036.00 q^{85} +(-412.000 + 713.605i) q^{86} +(-760.000 - 1316.36i) q^{87} +(-112.000 - 193.990i) q^{88} +(-405.000 + 701.481i) q^{89} +1036.00 q^{90} -448.000 q^{92} +(-288.000 + 498.831i) q^{93} +(24.0000 + 41.5692i) q^{94} +(560.000 + 969.948i) q^{95} +(128.000 - 221.703i) q^{96} +1354.00 q^{97} -1036.00 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} - 8 q^{3} - 4 q^{4} + 14 q^{5} - 32 q^{6} - 16 q^{8} - 37 q^{9}+O(q^{10}) \) 2 * q + 2 * q^2 - 8 * q^3 - 4 * q^4 + 14 * q^5 - 32 * q^6 - 16 * q^8 - 37 * q^9	\( 2 q + 2 q^{2} - 8 q^{3} - 4 q^{4} + 14 q^{5} - 32 q^{6} - 16 q^{8} - 37 q^{9} - 28 q^{10} + 28 q^{11} - 32 q^{12} + 36 q^{13} - 224 q^{15} - 16 q^{16} - 74 q^{17} + 74 q^{18} - 80 q^{19} - 112 q^{20} + 112 q^{22} + 112 q^{23} + 64 q^{24} - 71 q^{25} + 36 q^{26} + 160 q^{27} + 380 q^{29} - 224 q^{30} - 72 q^{31} + 32 q^{32} + 224 q^{33} - 296 q^{34} + 296 q^{36} + 346 q^{37} + 160 q^{38} - 144 q^{39} - 112 q^{40} + 324 q^{41} - 824 q^{43} + 112 q^{44} + 518 q^{45} - 224 q^{46} - 24 q^{47} + 256 q^{48} - 284 q^{50} - 592 q^{51} - 72 q^{52} - 318 q^{53} + 160 q^{54} + 784 q^{55} + 1280 q^{57} + 380 q^{58} + 200 q^{59} + 448 q^{60} + 198 q^{61} - 288 q^{62} + 128 q^{64} + 252 q^{65} - 448 q^{66} + 716 q^{67} - 296 q^{68} - 1792 q^{69} + 784 q^{71} + 296 q^{72} - 538 q^{73} - 692 q^{74} - 568 q^{75} + 640 q^{76} - 576 q^{78} - 240 q^{79} + 224 q^{80} + 359 q^{81} + 324 q^{82} - 2144 q^{83} - 2072 q^{85} - 824 q^{86} - 1520 q^{87} - 224 q^{88} - 810 q^{89} + 2072 q^{90} - 896 q^{92} - 576 q^{93} + 48 q^{94} + 1120 q^{95} + 256 q^{96} + 2708 q^{97} - 2072 q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 - 8 * q^3 - 4 * q^4 + 14 * q^5 - 32 * q^6 - 16 * q^8 - 37 * q^9 - 28 * q^10 + 28 * q^11 - 32 * q^12 + 36 * q^13 - 224 * q^15 - 16 * q^16 - 74 * q^17 + 74 * q^18 - 80 * q^19 - 112 * q^20 + 112 * q^22 + 112 * q^23 + 64 * q^24 - 71 * q^25 + 36 * q^26 + 160 * q^27 + 380 * q^29 - 224 * q^30 - 72 * q^31 + 32 * q^32 + 224 * q^33 - 296 * q^34 + 296 * q^36 + 346 * q^37 + 160 * q^38 - 144 * q^39 - 112 * q^40 + 324 * q^41 - 824 * q^43 + 112 * q^44 + 518 * q^45 - 224 * q^46 - 24 * q^47 + 256 * q^48 - 284 * q^50 - 592 * q^51 - 72 * q^52 - 318 * q^53 + 160 * q^54 + 784 * q^55 + 1280 * q^57 + 380 * q^58 + 200 * q^59 + 448 * q^60 + 198 * q^61 - 288 * q^62 + 128 * q^64 + 252 * q^65 - 448 * q^66 + 716 * q^67 - 296 * q^68 - 1792 * q^69 + 784 * q^71 + 296 * q^72 - 538 * q^73 - 692 * q^74 - 568 * q^75 + 640 * q^76 - 576 * q^78 - 240 * q^79 + 224 * q^80 + 359 * q^81 + 324 * q^82 - 2144 * q^83 - 2072 * q^85 - 824 * q^86 - 1520 * q^87 - 224 * q^88 - 810 * q^89 + 2072 * q^90 - 896 * q^92 - 576 * q^93 + 48 * q^94 + 1120 * q^95 + 256 * q^96 + 2708 * q^97 - 2072 * q^99

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