LMFDB - Embedded newform 245.4.e.f.116.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [245,4,Mod(116,245)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(245, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("245.116");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 245 = 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	245.e (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:	$14.4554679514$
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:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 5)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			116.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	245.116
Dual form			245.4.e.f.226.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.00000 + 3.46410i) q^{2} +(-1.00000 + 1.73205i) q^{3} +(-4.00000 + 6.92820i) q^{4} +(2.50000 + 4.33013i) q^{5} -8.00000 q^{6} +(11.5000 + 19.9186i) q^{9} +O(q^{10})$	\(q+(2.00000 + 3.46410i) q^{2} +(-1.00000 + 1.73205i) q^{3} +(-4.00000 + 6.92820i) q^{4} +(2.50000 + 4.33013i) q^{5} -8.00000 q^{6} +(11.5000 + 19.9186i) q^{9} +(-10.0000 + 17.3205i) q^{10} +(-16.0000 + 27.7128i) q^{11} +(-8.00000 - 13.8564i) q^{12} -38.0000 q^{13} -10.0000 q^{15} +(32.0000 + 55.4256i) q^{16} +(-13.0000 + 22.5167i) q^{17} +(-46.0000 + 79.6743i) q^{18} +(-50.0000 - 86.6025i) q^{19} -40.0000 q^{20} -128.000 q^{22} +(39.0000 + 67.5500i) q^{23} +(-12.5000 + 21.6506i) q^{25} +(-76.0000 - 131.636i) q^{26} -100.000 q^{27} -50.0000 q^{29} +(-20.0000 - 34.6410i) q^{30} +(54.0000 - 93.5307i) q^{31} +(-128.000 + 221.703i) q^{32} +(-32.0000 - 55.4256i) q^{33} -104.000 q^{34} -184.000 q^{36} +(-133.000 - 230.363i) q^{37} +(200.000 - 346.410i) q^{38} +(38.0000 - 65.8179i) q^{39} +22.0000 q^{41} +442.000 q^{43} +(-128.000 - 221.703i) q^{44} +(-57.5000 + 99.5929i) q^{45} +(-156.000 + 270.200i) q^{46} +(257.000 + 445.137i) q^{47} -128.000 q^{48} -100.000 q^{50} +(-26.0000 - 45.0333i) q^{51} +(152.000 - 263.272i) q^{52} +(-1.00000 + 1.73205i) q^{53} +(-200.000 - 346.410i) q^{54} -160.000 q^{55} +200.000 q^{57} +(-100.000 - 173.205i) q^{58} +(-250.000 + 433.013i) q^{59} +(40.0000 - 69.2820i) q^{60} +(259.000 + 448.601i) q^{61} +432.000 q^{62} -512.000 q^{64} +(-95.0000 - 164.545i) q^{65} +(128.000 - 221.703i) q^{66} +(-63.0000 + 109.119i) q^{67} +(-104.000 - 180.133i) q^{68} -156.000 q^{69} +412.000 q^{71} +(439.000 - 760.370i) q^{73} +(532.000 - 921.451i) q^{74} +(-25.0000 - 43.3013i) q^{75} +800.000 q^{76} +304.000 q^{78} +(-300.000 - 519.615i) q^{79} +(-160.000 + 277.128i) q^{80} +(-210.500 + 364.597i) q^{81} +(44.0000 + 76.2102i) q^{82} +282.000 q^{83} -130.000 q^{85} +(884.000 + 1531.13i) q^{86} +(50.0000 - 86.6025i) q^{87} +(75.0000 + 129.904i) q^{89} -460.000 q^{90} -624.000 q^{92} +(108.000 + 187.061i) q^{93} +(-1028.00 + 1780.55i) q^{94} +(250.000 - 433.013i) q^{95} +(-256.000 - 443.405i) q^{96} +386.000 q^{97} -736.000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 4 q^{2} - 2 q^{3} - 8 q^{4} + 5 q^{5} - 16 q^{6} + 23 q^{9}+O(q^{10}) $ 2 * q + 4 * q^2 - 2 * q^3 - 8 * q^4 + 5 * q^5 - 16 * q^6 + 23 * q^9	$ 2 q + 4 q^{2} - 2 q^{3} - 8 q^{4} + 5 q^{5} - 16 q^{6} + 23 q^{9} - 20 q^{10} - 32 q^{11} - 16 q^{12} - 76 q^{13} - 20 q^{15} + 64 q^{16} - 26 q^{17} - 92 q^{18} - 100 q^{19} - 80 q^{20} - 256 q^{22} + 78 q^{23} - 25 q^{25} - 152 q^{26} - 200 q^{27} - 100 q^{29} - 40 q^{30} + 108 q^{31} - 256 q^{32} - 64 q^{33} - 208 q^{34} - 368 q^{36} - 266 q^{37} + 400 q^{38} + 76 q^{39} + 44 q^{41} + 884 q^{43} - 256 q^{44} - 115 q^{45} - 312 q^{46} + 514 q^{47} - 256 q^{48} - 200 q^{50} - 52 q^{51} + 304 q^{52} - 2 q^{53} - 400 q^{54} - 320 q^{55} + 400 q^{57} - 200 q^{58} - 500 q^{59} + 80 q^{60} + 518 q^{61} + 864 q^{62} - 1024 q^{64} - 190 q^{65} + 256 q^{66} - 126 q^{67} - 208 q^{68} - 312 q^{69} + 824 q^{71} + 878 q^{73} + 1064 q^{74} - 50 q^{75} + 1600 q^{76} + 608 q^{78} - 600 q^{79} - 320 q^{80} - 421 q^{81} + 88 q^{82} + 564 q^{83} - 260 q^{85} + 1768 q^{86} + 100 q^{87} + 150 q^{89} - 920 q^{90} - 1248 q^{92} + 216 q^{93} - 2056 q^{94} + 500 q^{95} - 512 q^{96} + 772 q^{97} - 1472 q^{99}+O(q^{100}) $ 2 * q + 4 * q^2 - 2 * q^3 - 8 * q^4 + 5 * q^5 - 16 * q^6 + 23 * q^9 - 20 * q^10 - 32 * q^11 - 16 * q^12 - 76 * q^13 - 20 * q^15 + 64 * q^16 - 26 * q^17 - 92 * q^18 - 100 * q^19 - 80 * q^20 - 256 * q^22 + 78 * q^23 - 25 * q^25 - 152 * q^26 - 200 * q^27 - 100 * q^29 - 40 * q^30 + 108 * q^31 - 256 * q^32 - 64 * q^33 - 208 * q^34 - 368 * q^36 - 266 * q^37 + 400 * q^38 + 76 * q^39 + 44 * q^41 + 884 * q^43 - 256 * q^44 - 115 * q^45 - 312 * q^46 + 514 * q^47 - 256 * q^48 - 200 * q^50 - 52 * q^51 + 304 * q^52 - 2 * q^53 - 400 * q^54 - 320 * q^55 + 400 * q^57 - 200 * q^58 - 500 * q^59 + 80 * q^60 + 518 * q^61 + 864 * q^62 - 1024 * q^64 - 190 * q^65 + 256 * q^66 - 126 * q^67 - 208 * q^68 - 312 * q^69 + 824 * q^71 + 878 * q^73 + 1064 * q^74 - 50 * q^75 + 1600 * q^76 + 608 * q^78 - 600 * q^79 - 320 * q^80 - 421 * q^81 + 88 * q^82 + 564 * q^83 - 260 * q^85 + 1768 * q^86 + 100 * q^87 + 150 * q^89 - 920 * q^90 - 1248 * q^92 + 216 * q^93 - 2056 * q^94 + 500 * q^95 - 512 * q^96 + 772 * q^97 - 1472 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/245\mathbb{Z}\right)^\times$.

$n$	$101$	$197$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	2.00000	+	3.46410i	0.707107	+	1.22474i	0.965926	+	0.258819i	$0.0833333\pi$
$2$	2.00000	+	3.46410i	0.707107	+	1.22474i	−0.258819	+	0.965926i	$0.583333\pi$
$3$	−1.00000	+	1.73205i	−0.192450	+	0.333333i	−0.946062	−	0.323987i	$-0.894977\pi$
$3$	−1.00000	+	1.73205i	−0.192450	+	0.333333i	0.753612	+	0.657320i	$0.228310\pi$
$4$	−4.00000	+	6.92820i	−0.500000	+	0.866025i
$5$	2.50000	+	4.33013i	0.223607	+	0.387298i
$5$	2.50000	+	4.33013i	0.223607	+	0.387298i
$6$	−8.00000			−0.544331
$7$		0			0
$7$		0			0
$8$		0			0
$9$	11.5000	+	19.9186i	0.425926	+	0.737725i
$10$	−10.0000	+	17.3205i	−0.316228	+	0.547723i
$11$	−16.0000	+	27.7128i	−0.438562	+	0.759612i	−0.997579	−	0.0695447i	$-0.977845\pi$
$11$	−16.0000	+	27.7128i	−0.438562	+	0.759612i	0.559017	+	0.829156i	$0.311179\pi$
$12$	−8.00000	−	13.8564i	−0.192450	−	0.333333i
$13$	−38.0000			−0.810716			−0.405358	−	0.914158i	$-0.632853\pi$
$13$	−38.0000			−0.810716			−0.405358	+	0.914158i	$0.632853\pi$
$14$		0			0
$15$	−10.0000			−0.172133
$16$	32.0000	+	55.4256i	0.500000	+	0.866025i
$17$	−13.0000	+	22.5167i	−0.185468	+	0.321241i	−0.943734	−	0.330705i	$-0.892714\pi$
$17$	−13.0000	+	22.5167i	−0.185468	+	0.321241i	0.758266	+	0.651945i	$0.226047\pi$
$18$	−46.0000	+	79.6743i	−0.602350	+	1.04330i
$19$	−50.0000	−	86.6025i	−0.603726	−	1.04568i	−0.992251	−	0.124246i	$-0.960349\pi$
$19$	−50.0000	−	86.6025i	−0.603726	−	1.04568i	0.388526	−	0.921438i	$-0.372984\pi$
$20$	−40.0000			−0.447214
$21$		0			0
$22$	−128.000			−1.24044
$23$	39.0000	+	67.5500i	0.353568	+	0.612398i	0.986872	−	0.161506i	$-0.0516350\pi$
$23$	39.0000	+	67.5500i	0.353568	+	0.612398i	−0.633304	+	0.773903i	$0.718302\pi$
$24$		0			0
$25$	−12.5000	+	21.6506i	−0.100000	+	0.173205i
$26$	−76.0000	−	131.636i	−0.573263	−	0.992920i
$27$	−100.000			−0.712778
$28$		0			0
$29$	−50.0000			−0.320164			−0.160082	−	0.987104i	$-0.551176\pi$
$29$	−50.0000			−0.320164			−0.160082	+	0.987104i	$0.551176\pi$
$30$	−20.0000	−	34.6410i	−0.121716	−	0.210819i
$31$	54.0000	−	93.5307i	0.312861	−	0.541891i	−0.666120	−	0.745845i	$-0.732046\pi$
$31$	54.0000	−	93.5307i	0.312861	−	0.541891i	0.978980	+	0.203954i	$0.0653793\pi$
$32$	−128.000	+	221.703i	−0.707107	+	1.22474i
$33$	−32.0000	−	55.4256i	−0.168803	−	0.292375i
$34$	−104.000			−0.524584
$35$		0			0
$36$	−184.000			−0.851852
$37$	−133.000	−	230.363i	−0.590948	−	1.02355i	−0.994105	−	0.108421i	$-0.965421\pi$
$37$	−133.000	−	230.363i	−0.590948	−	1.02355i	0.403157	−	0.915131i	$-0.367913\pi$
$38$	200.000	−	346.410i	0.853797	−	1.47882i
$39$	38.0000	−	65.8179i	0.156022	−	0.270239i
$40$		0			0
$41$	22.0000			0.0838006			0.0419003	−	0.999122i	$-0.486659\pi$
$41$	22.0000			0.0838006			0.0419003	+	0.999122i	$0.486659\pi$
$42$		0			0
$43$	442.000			1.56754			0.783772	−	0.621049i	$-0.213293\pi$
$43$	442.000			1.56754			0.783772	+	0.621049i	$0.213293\pi$
$44$	−128.000	−	221.703i	−0.438562	−	0.759612i
$45$	−57.5000	+	99.5929i	−0.190480	+	0.329921i
$46$	−156.000	+	270.200i	−0.500021	+	0.866061i
$47$	257.000	+	445.137i	0.797602	+	1.38149i	0.921174	+	0.389152i	$0.127232\pi$
$47$	257.000	+	445.137i	0.797602	+	1.38149i	−0.123571	+	0.992336i	$0.539435\pi$
$48$	−128.000			−0.384900
$49$		0			0
$50$	−100.000			−0.282843
$51$	−26.0000	−	45.0333i	−0.0713868	−	0.123646i
$52$	152.000	−	263.272i	0.405358	−	0.702100i
$53$	−1.00000	+	1.73205i	−0.00259171	+	0.00448897i	−0.867318	−	0.497754i	$-0.834158\pi$
$53$	−1.00000	+	1.73205i	−0.00259171	+	0.00448897i	0.864727	+	0.502243i	$0.167492\pi$
$54$	−200.000	−	346.410i	−0.504010	−	0.872971i
$55$	−160.000			−0.392262
$56$		0			0
$57$	200.000			0.464748
$58$	−100.000	−	173.205i	−0.226390	−	0.392120i
$59$	−250.000	+	433.013i	−0.551648	+	0.955482i	0.446508	+	0.894780i	$0.352667\pi$
$59$	−250.000	+	433.013i	−0.551648	+	0.955482i	−0.998156	+	0.0607026i	$0.980666\pi$
$60$	40.0000	−	69.2820i	0.0860663	−	0.149071i
$61$	259.000	+	448.601i	0.543632	+	0.941598i	0.998692	+	0.0511373i	$0.0162846\pi$
$61$	259.000	+	448.601i	0.543632	+	0.941598i	−0.455060	+	0.890461i	$0.650382\pi$
$62$	432.000			0.884904
$63$		0			0
$64$	−512.000			−1.00000
$65$	−95.0000	−	164.545i	−0.181282	−	0.313989i
$66$	128.000	−	221.703i	0.238723	−	0.413480i
$67$	−63.0000	+	109.119i	−0.114876	+	0.198971i	−0.917730	−	0.397205i	$-0.869980\pi$
$67$	−63.0000	+	109.119i	−0.114876	+	0.198971i	0.802854	+	0.596175i	$0.203314\pi$
$68$	−104.000	−	180.133i	−0.185468	−	0.321241i
$69$	−156.000			−0.272177
$70$		0			0
$71$	412.000			0.688668			0.344334	−	0.938847i	$-0.388105\pi$
$71$	412.000			0.688668			0.344334	+	0.938847i	$0.388105\pi$
$72$		0			0
$73$	439.000	−	760.370i	0.703850	−	1.21910i	−0.263255	−	0.964726i	$-0.584796\pi$
$73$	439.000	−	760.370i	0.703850	−	1.21910i	0.967105	−	0.254378i	$-0.0818707\pi$
$74$	532.000	−	921.451i	0.835726	−	1.44752i
$75$	−25.0000	−	43.3013i	−0.0384900	−	0.0666667i
$76$	800.000			1.20745
$77$		0			0
$78$	304.000			0.441298
$79$	−300.000	−	519.615i	−0.427249	−	0.740016i	0.569379	−	0.822075i	$-0.307184\pi$
$79$	−300.000	−	519.615i	−0.427249	−	0.740016i	−0.996627	+	0.0820590i	$0.973850\pi$
$80$	−160.000	+	277.128i	−0.223607	+	0.387298i
$81$	−210.500	+	364.597i	−0.288752	+	0.500133i
$82$	44.0000	+	76.2102i	0.0592559	+	0.102634i
$83$	282.000			0.372934			0.186467	−	0.982461i	$-0.440296\pi$
$83$	282.000			0.372934			0.186467	+	0.982461i	$0.440296\pi$
$84$		0			0
$85$	−130.000			−0.165888
$86$	884.000	+	1531.13i	1.10842	+	1.91984i
$87$	50.0000	−	86.6025i	0.0616157	−	0.106721i
$88$		0			0
$89$	75.0000	+	129.904i	0.0893257	+	0.154717i	0.907226	−	0.420643i	$-0.138195\pi$
$89$	75.0000	+	129.904i	0.0893257	+	0.154717i	−0.817901	+	0.575360i	$0.804862\pi$
$90$	−460.000			−0.538758
$91$		0			0
$92$	−624.000			−0.707136
$93$	108.000	+	187.061i	0.120420	+	0.208574i
$94$	−1028.00	+	1780.55i	−1.12798	+	1.95372i
$95$	250.000	−	433.013i	0.269994	−	0.467644i
$96$	−256.000	−	443.405i	−0.272166	−	0.471405i
$97$	386.000			0.404045			0.202022	−	0.979381i	$-0.435249\pi$
$97$	386.000			0.404045			0.202022	+	0.979381i	$0.435249\pi$
$98$		0			0
$99$	−736.000			−0.747180
$100$	−100.000	−	173.205i	−0.100000	−	0.173205i
$101$	−351.000	+	607.950i	−0.345800	+	0.598943i	−0.985499	−	0.169682i	$-0.945726\pi$
$101$	−351.000	+	607.950i	−0.345800	+	0.598943i	0.639699	+	0.768626i	$0.279059\pi$
$102$	104.000	−	180.133i	0.100956	−	0.174861i
$103$	299.000	+	517.883i	0.286032	+	0.495423i	0.972859	−	0.231399i	$-0.0743301\pi$
$103$	299.000	+	517.883i	0.286032	+	0.495423i	−0.686827	+	0.726821i	$0.740997\pi$
$104$		0			0
$105$		0			0
$106$	−8.00000			−0.00733046
$107$	597.000	+	1034.03i	0.539385	+	0.934242i	0.998937	+	0.0460912i	$0.0146765\pi$
$107$	597.000	+	1034.03i	0.539385	+	0.934242i	−0.459552	+	0.888151i	$0.651990\pi$
$108$	400.000	−	692.820i	0.356389	−	0.617284i
$109$	275.000	−	476.314i	0.241653	−	0.418556i	−0.719532	−	0.694459i	$-0.755644\pi$
$109$	275.000	−	476.314i	0.241653	−	0.418556i	0.961185	+	0.275903i	$0.0889770\pi$
$110$	−320.000	−	554.256i	−0.277371	−	0.480421i
$111$	532.000			0.454912
$112$		0			0
$113$	1562.00			1.30036			0.650180	−	0.759781i	$-0.274694\pi$
$113$	1562.00			1.30036			0.650180	+	0.759781i	$0.274694\pi$
$114$	400.000	+	692.820i	0.328627	+	0.569198i
$115$	−195.000	+	337.750i	−0.158120	+	0.273873i
$116$	200.000	−	346.410i	0.160082	−	0.277270i
$117$	−437.000	−	756.906i	−0.345305	−	0.598085i
$118$	−2000.00			−1.56030
$119$		0			0
$120$		0			0
$121$	153.500	+	265.870i	0.115327	+	0.199752i
$122$	−1036.00	+	1794.40i	−0.768812	+	1.33162i
$123$	−22.0000	+	38.1051i	−0.0161274	+	0.0279335i
$124$	432.000	+	748.246i	0.312861	+	0.541891i
$125$	−125.000			−0.0894427
$126$		0			0
$127$	1846.00			1.28981			0.644906	−	0.764262i	$-0.276897\pi$
$127$	1846.00			1.28981			0.644906	+	0.764262i	$0.276897\pi$
$128$		0			0
$129$	−442.000	+	765.566i	−0.301674	+	0.522514i
$130$	380.000	−	658.179i	0.256371	−	0.444047i
$131$	1104.00	+	1912.18i	0.736312	+	1.27533i	0.954145	+	0.299344i	$0.0967680\pi$
$131$	1104.00	+	1912.18i	0.736312	+	1.27533i	−0.217833	+	0.975986i	$0.569899\pi$
$132$	512.000			0.337605
$133$		0			0
$134$	−504.000			−0.324918
$135$	−250.000	−	433.013i	−0.159382	−	0.276058i
$136$		0			0
$137$	1167.00	−	2021.30i	0.727763	−	1.26052i	−0.230064	−	0.973176i	$-0.573893\pi$
$137$	1167.00	−	2021.30i	0.727763	−	1.26052i	0.957827	−	0.287347i	$-0.0927733\pi$
$138$	−312.000	−	540.400i	−0.192458	−	0.333347i
$139$	−700.000			−0.427146			−0.213573	−	0.976927i	$-0.568510\pi$
$139$	−700.000			−0.427146			−0.213573	+	0.976927i	$0.568510\pi$
$140$		0			0
$141$	−1028.00			−0.613994
$142$	824.000	+	1427.21i	0.486962	+	0.843442i
$143$	608.000	−	1053.09i	0.355549	−	0.615829i
$144$	−736.000	+	1274.79i	−0.425926	+	0.737725i
$145$	−125.000	−	216.506i	−0.0715909	−	0.123999i
$146$	3512.00			1.99079
$147$		0			0
$148$	2128.00			1.18190
$149$	−1025.00	−	1775.35i	−0.563566	−	0.976124i	−0.997182	−	0.0750264i	$-0.976096\pi$
$149$	−1025.00	−	1775.35i	−0.563566	−	0.976124i	0.433616	−	0.901098i	$-0.357237\pi$
$150$	100.000	−	173.205i	0.0544331	−	0.0942809i
$151$	−926.000	+	1603.88i	−0.499052	+	0.864383i	−0.999999	−	0.00109462i	$-0.999652\pi$
$151$	−926.000	+	1603.88i	−0.499052	+	0.864383i	0.500948	+	0.865478i	$0.332985\pi$
$152$		0			0
$153$	−598.000			−0.315983
$154$		0			0
$155$	540.000			0.279831
$156$	304.000	+	526.543i	0.156022	+	0.270239i
$157$	1247.00	−	2159.87i	0.633894	−	1.09794i	−0.352854	−	0.935678i	$-0.614789\pi$
$157$	1247.00	−	2159.87i	0.633894	−	1.09794i	0.986748	−	0.162259i	$-0.0518780\pi$
$158$	1200.00	−	2078.46i	0.604221	−	1.04654i
$159$	−2.00000	−	3.46410i	−0.000997549	−	0.00172781i
$160$	−1280.00			−0.632456
$161$		0			0
$162$	−1684.00			−0.816713
$163$	−1381.00	−	2391.96i	−0.663609	−	1.14940i	−0.979660	−	0.200662i	$-0.935691\pi$
$163$	−1381.00	−	2391.96i	−0.663609	−	1.14940i	0.316051	−	0.948742i	$-0.397643\pi$
$164$	−88.0000	+	152.420i	−0.0419003	+	0.0725734i
$165$	160.000	−	277.128i	0.0754908	−	0.130754i
$166$	564.000	+	976.877i	0.263704	+	0.456749i
$167$	3126.00			1.44849			0.724243	−	0.689545i	$-0.242189\pi$
$167$	3126.00			1.44849			0.724243	+	0.689545i	$0.242189\pi$
$168$		0			0
$169$	−753.000			−0.342740
$170$	−260.000	−	450.333i	−0.117301	−	0.203170i
$171$	1150.00	−	1991.86i	0.514285	−	0.890767i
$172$	−1768.00	+	3062.27i	−0.783772	+	1.35753i
$173$	39.0000	+	67.5500i	0.0171394	+	0.0296863i	0.874468	−	0.485083i	$-0.161211\pi$
$173$	39.0000	+	67.5500i	0.0171394	+	0.0296863i	−0.857328	+	0.514770i	$0.827877\pi$
$174$	400.000			0.174275
$175$		0			0
$176$	−2048.00			−0.877124
$177$	−500.000	−	866.025i	−0.212329	−	0.367765i
$178$	−300.000	+	519.615i	−0.126326	+	0.218802i
$179$	650.000	−	1125.83i	0.271415	−	0.470105i	−0.697809	−	0.716283i	$-0.745842\pi$
$179$	650.000	−	1125.83i	0.271415	−	0.470105i	0.969224	+	0.246179i	$0.0791751\pi$
$180$	−460.000	−	796.743i	−0.190480	−	0.329921i
$181$	1742.00			0.715369			0.357685	−	0.933842i	$-0.383566\pi$
$181$	1742.00			0.715369			0.357685	+	0.933842i	$0.383566\pi$
$182$		0			0
$183$	−1036.00			−0.418488
$184$		0			0
$185$	665.000	−	1151.81i	0.264280	−	0.457746i
$186$	−432.000	+	748.246i	−0.170300	+	0.294968i
$187$	−416.000	−	720.533i	−0.162679	−	0.281768i
$188$	−4112.00			−1.59520
$189$		0			0
$190$	2000.00			0.763659
$191$	−1886.00	−	3266.65i	−0.714483	−	1.23752i	−0.963159	−	0.268933i	$-0.913329\pi$
$191$	−1886.00	−	3266.65i	−0.714483	−	1.23752i	0.248676	−	0.968587i	$-0.420004\pi$
$192$	512.000	−	886.810i	0.192450	−	0.333333i
$193$	179.000	−	310.037i	0.0667601	−	0.115632i	−0.830713	−	0.556700i	$-0.812067\pi$
$193$	179.000	−	310.037i	0.0667601	−	0.115632i	0.897473	+	0.441069i	$0.145400\pi$
$194$	772.000	+	1337.14i	0.285703	+	0.494852i
$195$	380.000			0.139551
$196$		0			0
$197$	−2214.00			−0.800716			−0.400358	−	0.916359i	$-0.631114\pi$
$197$	−2214.00			−0.800716			−0.400358	+	0.916359i	$0.631114\pi$
$198$	−1472.00	−	2549.58i	−0.528336	−	0.915104i
$199$	1300.00	−	2251.67i	0.463088	−	0.802092i	−0.536025	−	0.844202i	$-0.680075\pi$
$199$	1300.00	−	2251.67i	0.463088	−	0.802092i	0.999113	+	0.0421099i	$0.0134080\pi$
$200$		0			0
$201$	−126.000	−	218.238i	−0.0442157	−	0.0765838i
$202$	−2808.00			−0.978070
$203$		0			0
$204$	416.000			0.142774
$205$	55.0000	+	95.2628i	0.0187384	+	0.0324558i
$206$	−1196.00	+	2071.53i	−0.404511	+	0.700634i
$207$	−897.000	+	1553.65i	−0.301187	+	0.521672i
$208$	−1216.00	−	2106.17i	−0.405358	−	0.702100i
$209$	3200.00			1.05908
$210$		0			0
$211$	−1168.00			−0.381083			−0.190541	−	0.981679i	$-0.561024\pi$
$211$	−1168.00			−0.381083			−0.190541	+	0.981679i	$0.561024\pi$
$212$	−8.00000	−	13.8564i	−0.00259171	−	0.00448897i
$213$	−412.000	+	713.605i	−0.132534	+	0.229556i
$214$	−2388.00	+	4136.14i	−0.762805	+	1.32122i
$215$	1105.00	+	1913.92i	0.350513	+	0.607107i
$216$		0			0
$217$		0			0
$218$	2200.00			0.683499
$219$	878.000	+	1520.74i	0.270912	+	0.469233i
$220$	640.000	−	1108.51i	0.196131	−	0.339709i
$221$	494.000	−	855.633i	0.150362	−	0.260435i
$222$	1064.00	+	1842.90i	0.321671	+	0.557151i
$223$	−6478.00			−1.94529			−0.972643	−	0.232303i	$-0.925374\pi$
$223$	−6478.00			−1.94529			−0.972643	+	0.232303i	$0.925374\pi$
$224$		0			0
$225$	−575.000			−0.170370
$226$	3124.00	+	5410.93i	0.919493	+	1.59261i
$227$	−323.000	+	559.452i	−0.0944417	+	0.163578i	−0.909375	−	0.415976i	$-0.863440\pi$
$227$	−323.000	+	559.452i	−0.0944417	+	0.163578i	0.814934	+	0.579554i	$0.196773\pi$
$228$	−800.000	+	1385.64i	−0.232374	+	0.402484i
$229$	−1875.00	−	3247.60i	−0.541063	−	0.937149i	−0.998843	−	0.0480836i	$-0.984689\pi$
$229$	−1875.00	−	3247.60i	−0.541063	−	0.937149i	0.457780	−	0.889065i	$-0.348645\pi$
$230$	−1560.00			−0.447232
$231$		0			0
$232$		0			0
$233$	−741.000	−	1283.45i	−0.208346	−	0.360865i	0.742848	−	0.669460i	$-0.233475\pi$
$233$	−741.000	−	1283.45i	−0.208346	−	0.360865i	−0.951194	+	0.308595i	$0.900141\pi$
$234$	1748.00	−	3027.62i	0.488335	−	0.845821i
$235$	−1285.00	+	2225.69i	−0.356699	+	0.617820i
$236$	−2000.00	−	3464.10i	−0.551648	−	0.955482i
$237$	1200.00			0.328896
$238$		0			0
$239$	1400.00			0.378906			0.189453	−	0.981890i	$-0.439329\pi$
$239$	1400.00			0.378906			0.189453	+	0.981890i	$0.439329\pi$
$240$	−320.000	−	554.256i	−0.0860663	−	0.149071i
$241$	−1511.00	+	2617.13i	−0.403867	+	0.699519i	−0.994189	−	0.107649i	$-0.965668\pi$
$241$	−1511.00	+	2617.13i	−0.403867	+	0.699519i	0.590321	+	0.807168i	$0.299001\pi$
$242$	−614.000	+	1063.48i	−0.163097	+	0.282492i
$243$	−1771.00	−	3067.46i	−0.467530	−	0.809785i
$244$	−4144.00			−1.08726
$245$		0			0
$246$	−176.000			−0.0456152
$247$	1900.00	+	3290.90i	0.489450	+	0.847752i
$248$		0			0
$249$	−282.000	+	488.438i	−0.0717712	+	0.124311i
$250$	−250.000	−	433.013i	−0.0632456	−	0.109545i
$251$	−1248.00			−0.313837			−0.156918	−	0.987612i	$-0.550156\pi$
$251$	−1248.00			−0.313837			−0.156918	+	0.987612i	$0.550156\pi$
$252$		0			0
$253$	−2496.00			−0.620246
$254$	3692.00	+	6394.73i	0.912034	+	1.57969i
$255$	130.000	−	225.167i	0.0319252	−	0.0552960i
$256$	−2048.00	+	3547.24i	−0.500000	+	0.866025i
$257$	−1053.00	−	1823.85i	−0.255581	−	0.442679i	0.709472	−	0.704734i	$-0.248933\pi$
$257$	−1053.00	−	1823.85i	−0.255581	−	0.442679i	−0.965053	+	0.262054i	$0.915600\pi$
$258$	−3536.00			−0.853263
$259$		0			0
$260$	1520.00			0.362563
$261$	−575.000	−	995.929i	−0.136366	−	0.236193i
$262$	−4416.00	+	7648.74i	−1.04130	+	1.80359i
$263$	1819.00	−	3150.60i	0.426480	−	0.738686i	−0.570077	−	0.821591i	$-0.693087\pi$
$263$	1819.00	−	3150.60i	0.426480	−	0.738686i	0.996557	+	0.0829055i	$0.0264200\pi$
$264$		0			0
$265$	−10.0000			−0.00231809
$266$		0			0
$267$	−300.000			−0.0687629
$268$	−504.000	−	872.954i	−0.114876	−	0.198971i
$269$	3275.00	−	5672.47i	0.742306	−	1.28571i	−0.209137	−	0.977886i	$-0.567065\pi$
$269$	3275.00	−	5672.47i	0.742306	−	1.28571i	0.951443	−	0.307825i	$-0.0996012\pi$
$270$	1000.00	−	1732.05i	0.225400	−	0.390405i
$271$	2194.00	+	3800.12i	0.491793	+	0.851811i	0.999955	−	0.00945040i	$-0.00300820\pi$
$271$	2194.00	+	3800.12i	0.491793	+	0.851811i	−0.508162	+	0.861262i	$0.669675\pi$
$272$	−1664.00			−0.370937
$273$		0			0
$274$	9336.00			2.05842
$275$	−400.000	−	692.820i	−0.0877124	−	0.151922i
$276$	624.000	−	1080.80i	0.136088	−	0.235712i
$277$	−273.000	+	472.850i	−0.0592165	+	0.102566i	−0.894114	−	0.447840i	$-0.852194\pi$
$277$	−273.000	+	472.850i	−0.0592165	+	0.102566i	0.834897	+	0.550406i	$0.185527\pi$
$278$	−1400.00	−	2424.87i	−0.302037	−	0.523144i
$279$	2484.00			0.533022
$280$		0			0
$281$	−6858.00			−1.45592			−0.727961	−	0.685619i	$-0.759532\pi$
$281$	−6858.00			−1.45592			−0.727961	+	0.685619i	$0.759532\pi$
$282$	−2056.00	−	3561.10i	−0.434160	−	0.751987i
$283$	−4641.00	+	8038.45i	−0.974837	+	1.68847i	−0.294364	+	0.955693i	$0.595108\pi$
$283$	−4641.00	+	8038.45i	−0.974837	+	1.68847i	−0.680473	+	0.732774i	$0.738225\pi$
$284$	−1648.00	+	2854.42i	−0.344334	+	0.596404i
$285$	500.000	+	866.025i	0.103921	+	0.179996i
$286$	4864.00			1.00564
$287$		0			0
$288$	−5888.00			−1.20470
$289$	2118.50	+	3669.35i	0.431203	+	0.746865i
$290$	500.000	−	866.025i	0.101245	−	0.175361i
$291$	−386.000	+	668.572i	−0.0777585	+	0.134682i
$292$	3512.00	+	6082.96i	0.703850	+	1.21910i
$293$	4842.00			0.965436			0.482718	−	0.875776i	$-0.339650\pi$
$293$	4842.00			0.965436			0.482718	+	0.875776i	$0.339650\pi$
$294$		0			0
$295$	−2500.00			−0.493409
$296$		0			0
$297$	1600.00	−	2771.28i	0.312597	−	0.541435i
$298$	4100.00	−	7101.41i	0.797002	−	1.38045i
$299$	−1482.00	−	2566.90i	−0.286643	−	0.496480i
$300$	400.000			0.0769800
$301$		0			0
$302$	−7408.00			−1.41153
$303$	−702.000	−	1215.90i	−0.133099	−	0.230533i
$304$	3200.00	−	5542.56i	0.603726	−	1.04568i
$305$	−1295.00	+	2243.01i	−0.243120	+	0.421096i
$306$	−1196.00	−	2071.53i	−0.223434	−	0.386999i
$307$	−2594.00			−0.482239			−0.241120	−	0.970495i	$-0.577515\pi$
$307$	−2594.00			−0.482239			−0.241120	+	0.970495i	$0.577515\pi$
$308$		0			0
$309$	−1196.00			−0.220188
$310$	1080.00	+	1870.61i	0.197871	+	0.342722i
$311$	−3666.00	+	6349.70i	−0.668424	+	1.15774i	0.309921	+	0.950762i	$0.399697\pi$
$311$	−3666.00	+	6349.70i	−0.668424	+	1.15774i	−0.978345	+	0.206982i	$0.933636\pi$
$312$		0			0
$313$	−781.000	−	1352.73i	−0.141037	−	0.244284i	0.786850	−	0.617144i	$-0.211710\pi$
$313$	−781.000	−	1352.73i	−0.141037	−	0.244284i	−0.927888	+	0.372860i	$0.878377\pi$
$314$	9976.00			1.79292
$315$		0			0
$316$	4800.00			0.854497
$317$	−713.000	−	1234.95i	−0.126328	−	0.218807i	0.795923	−	0.605398i	$-0.206986\pi$
$317$	−713.000	−	1234.95i	−0.126328	−	0.218807i	−0.922251	+	0.386591i	$0.873653\pi$
$318$	8.00000	−	13.8564i	0.00141075	−	0.00244349i
$319$	800.000	−	1385.64i	0.140412	−	0.243201i
$320$	−1280.00	−	2217.03i	−0.223607	−	0.387298i
$321$	−2388.00			−0.415219
$322$		0			0
$323$	2600.00			0.447888
$324$	−1684.00	−	2916.77i	−0.288752	−	0.500133i
$325$	475.000	−	822.724i	0.0810716	−	0.140420i
$326$	5524.00	−	9567.85i	0.938485	−	1.62550i
$327$	550.000	+	952.628i	0.0930124	+	0.161102i
$328$		0			0
$329$		0			0
$330$	1280.00			0.213520
$331$	2004.00	+	3471.03i	0.332779	+	0.576390i	0.983056	−	0.183308i	$-0.0586804\pi$
$331$	2004.00	+	3471.03i	0.332779	+	0.576390i	−0.650277	+	0.759697i	$0.725347\pi$
$332$	−1128.00	+	1953.75i	−0.186467	+	0.322970i
$333$	3059.00	−	5298.34i	0.503400	−	0.871914i
$334$	6252.00	+	10828.8i	1.02423	+	1.77403i
$335$	−630.000			−0.102748
$336$		0			0
$337$	8866.00			1.43312			0.716561	−	0.697525i	$-0.245715\pi$
$337$	8866.00			1.43312			0.716561	+	0.697525i	$0.245715\pi$
$338$	−1506.00	−	2608.47i	−0.242354	−	0.419769i
$339$	−1562.00	+	2705.46i	−0.250254	+	0.433453i
$340$	520.000	−	900.666i	0.0829440	−	0.143663i
$341$	1728.00	+	2992.98i	0.274418	+	0.475305i
$342$	9200.00			1.45462
$343$		0			0
$344$		0			0
$345$	−390.000	−	675.500i	−0.0608606	−	0.105414i
$346$	−156.000	+	270.200i	−0.0242388	+	0.0419828i
$347$	857.000	−	1484.37i	0.132583	−	0.229640i	−0.792089	−	0.610406i	$-0.791006\pi$
$347$	857.000	−	1484.37i	0.132583	−	0.229640i	0.924671	+	0.380766i	$0.124340\pi$
$348$	400.000	+	692.820i	0.0616157	+	0.106721i
$349$	1150.00			0.176384			0.0881921	−	0.996103i	$-0.471891\pi$
$349$	1150.00			0.176384			0.0881921	+	0.996103i	$0.471891\pi$
$350$		0			0
$351$	3800.00			0.577860
$352$	−4096.00	−	7094.48i	−0.620220	−	1.07425i
$353$	2199.00	−	3808.78i	0.331561	−	0.574280i	−0.651257	−	0.758857i	$-0.725758\pi$
$353$	2199.00	−	3808.78i	0.331561	−	0.574280i	0.982818	+	0.184577i	$0.0590915\pi$
$354$	2000.00	−	3464.10i	0.300279	−	0.520099i
$355$	1030.00	+	1784.01i	0.153991	+	0.266720i
$356$	−1200.00			−0.178651
$357$		0			0
$358$	5200.00			0.767677
$359$	−900.000	−	1558.85i	−0.132312	−	0.229172i	0.792255	−	0.610190i	$-0.208907\pi$
$359$	−900.000	−	1558.85i	−0.132312	−	0.229172i	−0.924568	+	0.381018i	$0.875574\pi$
$360$		0			0
$361$	−1570.50	+	2720.19i	−0.228969	+	0.396586i
$362$	3484.00	+	6034.47i	0.505842	+	0.876145i
$363$	−614.000			−0.0887786
$364$		0			0
$365$	4390.00			0.629543
$366$	−2072.00	−	3588.81i	−0.295916	−	0.512541i
$367$	2937.00	−	5087.03i	0.417739	−	0.723545i	−0.577973	−	0.816056i	$-0.696156\pi$
$367$	2937.00	−	5087.03i	0.417739	−	0.723545i	0.995712	+	0.0925111i	$0.0294894\pi$
$368$	−2496.00	+	4323.20i	−0.353568	+	0.612398i
$369$	253.000	+	438.209i	0.0356928	+	0.0618218i
$370$	5320.00			0.747496
$371$		0			0
$372$	−1728.00			−0.240840
$373$	1039.00	+	1799.60i	0.144229	+	0.249812i	0.929085	−	0.369866i	$-0.120597\pi$
$373$	1039.00	+	1799.60i	0.144229	+	0.249812i	−0.784856	+	0.619678i	$0.787263\pi$
$374$	1664.00	−	2882.13i	0.230063	−	0.398480i
$375$	125.000	−	216.506i	0.0172133	−	0.0298142i
$376$		0			0
$377$	1900.00			0.259562
$378$		0			0
$379$	7900.00			1.07070			0.535351	−	0.844630i	$-0.320179\pi$
$379$	7900.00			1.07070			0.535351	+	0.844630i	$0.320179\pi$
$380$	2000.00	+	3464.10i	0.269994	+	0.467644i
$381$	−1846.00	+	3197.37i	−0.248224	+	0.429937i
$382$	7544.00	−	13066.6i	1.01043	−	1.75012i
$383$	3759.00	+	6510.78i	0.501504	+	0.868630i	0.999998	+	0.00173723i	$0.000552976\pi$
$383$	3759.00	+	6510.78i	0.501504	+	0.868630i	−0.498495	+	0.866893i	$0.666114\pi$
$384$		0			0
$385$		0			0
$386$	1432.00			0.188826
$387$	5083.00	+	8804.01i	0.667657	+	1.15642i
$388$	−1544.00	+	2674.29i	−0.202022	+	0.349913i
$389$	975.000	−	1688.75i	0.127081	−	0.220111i	−0.795464	−	0.606001i	$-0.792773\pi$
$389$	975.000	−	1688.75i	0.127081	−	0.220111i	0.922544	+	0.385891i	$0.126106\pi$
$390$	760.000	+	1316.36i	0.0986772	+	0.170914i
$391$	−2028.00			−0.262303
$392$		0			0
$393$	−4416.00			−0.566814
$394$	−4428.00	−	7669.52i	−0.566191	−	0.980672i
$395$	1500.00	−	2598.08i	0.191071	−	0.330945i
$396$	2944.00	−	5099.16i	0.373590	−	0.647077i
$397$	−6893.00	−	11939.0i	−0.871410	−	1.50933i	−0.860538	−	0.509385i	$-0.829873\pi$
$397$	−6893.00	−	11939.0i	−0.871410	−	1.50933i	−0.0108715	−	0.999941i	$-0.503461\pi$
$398$	10400.0			1.30981
$399$		0			0
$400$	−1600.00			−0.200000
$401$	−3201.00	−	5544.29i	−0.398629	−	0.690446i	0.594928	−	0.803779i	$-0.297181\pi$
$401$	−3201.00	−	5544.29i	−0.398629	−	0.690446i	−0.993557	+	0.113333i	$0.963847\pi$
$402$	504.000	−	872.954i	0.0625304	−	0.108306i
$403$	−2052.00	+	3554.17i	−0.253641	+	0.439319i
$404$	−2808.00	−	4863.60i	−0.345800	−	0.598943i
$405$	−2105.00			−0.258267
$406$		0			0
$407$	8512.00			1.03667
$408$		0			0
$409$	−5575.00	+	9656.18i	−0.674000	+	1.16740i	0.302760	+	0.953067i	$0.402092\pi$
$409$	−5575.00	+	9656.18i	−0.674000	+	1.16740i	−0.976760	+	0.214335i	$0.931241\pi$
$410$	−220.000	+	381.051i	−0.0265001	+	0.0458995i
$411$	2334.00	+	4042.61i	0.280116	+	0.485175i
$412$	−4784.00			−0.572065
$413$		0			0
$414$	−7176.00			−0.851887
$415$	705.000	+	1221.10i	0.0833906	+	0.144437i
$416$	4864.00	−	8424.70i	0.573263	−	0.992920i
$417$	700.000	−	1212.44i	0.0822042	−	0.142382i
$418$	6400.00	+	11085.1i	0.748886	+	1.29711i
$419$	−13700.0			−1.59735			−0.798674	−	0.601764i	$-0.794465\pi$
$419$	−13700.0			−1.59735			−0.798674	+	0.601764i	$0.794465\pi$
$420$		0			0
$421$	−5438.00			−0.629529			−0.314765	−	0.949170i	$-0.601926\pi$
$421$	−5438.00			−0.629529			−0.314765	+	0.949170i	$0.601926\pi$
$422$	−2336.00	−	4046.07i	−0.269466	−	0.466729i
$423$	−5911.00	+	10238.2i	−0.679439	+	1.17682i
$424$		0			0
$425$	−325.000	−	562.917i	−0.0370937	−	0.0642481i
$426$	−3296.00			−0.374863
$427$		0			0
$428$	−9552.00			−1.07877
$429$	1216.00	+	2106.17i	0.136851	+	0.237033i
$430$	−4420.00	+	7655.66i	−0.495701	+	0.858579i
$431$	−3846.00	+	6661.47i	−0.429827	+	0.744482i	−0.996858	−	0.0792149i	$-0.974759\pi$
$431$	−3846.00	+	6661.47i	−0.429827	+	0.744482i	0.567031	+	0.823697i	$0.308092\pi$
$432$	−3200.00	−	5542.56i	−0.356389	−	0.617284i
$433$	−1118.00			−0.124082			−0.0620412	−	0.998074i	$-0.519761\pi$
$433$	−1118.00			−0.124082			−0.0620412	+	0.998074i	$0.519761\pi$
$434$		0			0
$435$	500.000			0.0551107
$436$	2200.00	+	3810.51i	0.241653	+	0.418556i
$437$	3900.00	−	6755.00i	0.426916	−	0.739440i
$438$	−3512.00	+	6082.96i	−0.383128	+	0.663596i
$439$	1300.00	+	2251.67i	0.141334	+	0.244798i	0.927999	−	0.372582i	$-0.121528\pi$
$439$	1300.00	+	2251.67i	0.141334	+	0.244798i	−0.786665	+	0.617380i	$0.788194\pi$
$440$		0			0
$441$		0			0
$442$	3952.00			0.425288
$443$	5979.00	+	10355.9i	0.641243	+	1.11067i	0.985155	+	0.171664i	$0.0549145\pi$
$443$	5979.00	+	10355.9i	0.641243	+	1.11067i	−0.343912	+	0.939002i	$0.611752\pi$
$444$	−2128.00	+	3685.80i	−0.227456	+	0.393965i
$445$	−375.000	+	649.519i	−0.0399477	+	0.0691914i
$446$	−12956.0	−	22440.5i	−1.37553	−	2.38248i
$447$	4100.00			0.433833
$448$		0			0
$449$	−17050.0			−1.79207			−0.896035	−	0.443984i	$-0.853565\pi$
$449$	−17050.0			−1.79207			−0.896035	+	0.443984i	$0.853565\pi$
$450$	−1150.00	−	1991.86i	−0.120470	−	0.208660i
$451$	−352.000	+	609.682i	−0.0367517	+	0.0636559i
$452$	−6248.00	+	10821.9i	−0.650180	+	1.12614i
$453$	−1852.00	−	3207.76i	−0.192085	−	0.332701i
$454$	−2584.00			−0.267121
$455$		0			0
$456$		0			0
$457$	4747.00	+	8222.05i	0.485898	+	0.841600i	0.999869	−	0.0162080i	$-0.00515939\pi$
$457$	4747.00	+	8222.05i	0.485898	+	0.841600i	−0.513971	+	0.857808i	$0.671826\pi$
$458$	7500.00	−	12990.4i	0.765179	−	1.32533i
$459$	1300.00	−	2251.67i	0.132198	−	0.228973i
$460$	−1560.00	−	2702.00i	−0.158120	−	0.273873i
$461$	−11418.0			−1.15356			−0.576778	−	0.816901i	$-0.695690\pi$
$461$	−11418.0			−1.15356			−0.576778	+	0.816901i	$0.695690\pi$
$462$		0			0
$463$	7962.00			0.799191			0.399596	−	0.916692i	$-0.369151\pi$
$463$	7962.00			0.799191			0.399596	+	0.916692i	$0.369151\pi$
$464$	−1600.00	−	2771.28i	−0.160082	−	0.277270i
$465$	−540.000	+	935.307i	−0.0538535	+	0.0932771i
$466$	2964.00	−	5133.80i	0.294645	−	0.510340i
$467$	−3263.00	−	5651.68i	−0.323327	−	0.560019i	0.657845	−	0.753153i	$-0.271468\pi$
$467$	−3263.00	−	5651.68i	−0.323327	−	0.560019i	−0.981172	+	0.193134i	$0.938135\pi$
$468$	6992.00			0.690610
$469$		0			0
$470$	−10280.0			−1.00890
$471$	2494.00	+	4319.73i	0.243986	+	0.422596i
$472$		0			0
$473$	−7072.00	+	12249.1i	−0.687465	+	1.19072i
$474$	2400.00	+	4156.92i	0.232565	+	0.402814i
$475$	2500.00			0.241490
$476$		0			0
$477$	−46.0000			−0.00441550
$478$	2800.00	+	4849.74i	0.267927	+	0.464063i
$479$	−8700.00	+	15068.8i	−0.829881	+	1.43740i	0.0682495	+	0.997668i	$0.478259\pi$
$479$	−8700.00	+	15068.8i	−0.829881	+	1.43740i	−0.898131	+	0.439728i	$0.855075\pi$
$480$	1280.00	−	2217.03i	0.121716	−	0.210819i
$481$	5054.00	+	8753.78i	0.479091	+	0.829809i
$482$	−12088.0			−1.14231
$483$		0			0
$484$	−2456.00			−0.230654
$485$	965.000	+	1671.43i	0.0903472	+	0.156486i
$486$	7084.00	−	12269.8i	0.661187	−	1.14521i
$487$	−583.000	+	1009.79i	−0.0542469	+	0.0939584i	−0.891874	−	0.452285i	$-0.850609\pi$
$487$	−583.000	+	1009.79i	−0.0542469	+	0.0939584i	0.837627	+	0.546243i	$0.183942\pi$
$488$		0			0
$489$	5524.00			0.510846
$490$		0			0
$491$	7072.00			0.650010			0.325005	−	0.945712i	$-0.394634\pi$
$491$	7072.00			0.650010			0.325005	+	0.945712i	$0.394634\pi$
$492$	−176.000	−	304.841i	−0.0161274	−	0.0279335i
$493$	650.000	−	1125.83i	0.0593804	−	0.102850i
$494$	−7600.00	+	13163.6i	−0.692187	+	1.19890i
$495$	−1840.00	−	3186.97i	−0.167074	−	0.289381i
$496$	6912.00			0.625722
$497$		0			0
$498$	−2256.00			−0.203000
$499$	−50.0000	−	86.6025i	−0.00448559	−	0.00776926i	0.863774	−	0.503880i	$-0.168094\pi$
$499$	−50.0000	−	86.6025i	−0.00448559	−	0.00776926i	−0.868259	+	0.496110i	$0.834761\pi$
$500$	500.000	−	866.025i	0.0447214	−	0.0774597i
$501$	−3126.00	+	5414.39i	−0.278761	+	0.482829i
$502$	−2496.00	−	4323.20i	−0.221916	−	0.384370i
$503$	2602.00			0.230651			0.115325	−	0.993328i	$-0.463209\pi$
$503$	2602.00			0.230651			0.115325	+	0.993328i	$0.463209\pi$
$504$		0			0
$505$	−3510.00			−0.309293
$506$	−4992.00	−	8646.40i	−0.438580	−	0.759643i
$507$	753.000	−	1304.23i	0.0659604	−	0.114247i
$508$	−7384.00	+	12789.5i	−0.644906	+	1.11701i
$509$	−5575.00	−	9656.18i	−0.485476	−	0.840870i	0.514384	−	0.857560i	$-0.328021\pi$
$509$	−5575.00	−	9656.18i	−0.485476	−	0.840870i	−0.999861	+	0.0166899i	$0.994687\pi$
$510$	1040.00			0.0902980
$511$		0			0
$512$	−16384.0			−1.41421
$513$	5000.00	+	8660.25i	0.430322	+	0.745340i
$514$	4212.00	−	7295.40i	0.361446	−	0.626043i
$515$	−1495.00	+	2589.42i	−0.127918	+	0.221560i
$516$	−3536.00	−	6124.53i	−0.301674	−	0.522514i
$517$	−16448.0			−1.39919
$518$		0			0
$519$	−156.000			−0.0131939
$520$		0			0
$521$	1819.00	−	3150.60i	0.152959	−	0.264933i	−0.779355	−	0.626583i	$-0.784453\pi$
$521$	1819.00	−	3150.60i	0.152959	−	0.264933i	0.932314	+	0.361650i	$0.117786\pi$
$522$	2300.00	−	3983.72i	0.192851	−	0.334028i
$523$	1039.00	+	1799.60i	0.0868686	+	0.150461i	0.906186	−	0.422879i	$-0.138981\pi$
$523$	1039.00	+	1799.60i	0.0868686	+	0.150461i	−0.819317	+	0.573340i	$0.805647\pi$
$524$	−17664.0			−1.47262
$525$		0			0
$526$	14552.0			1.20627
$527$	1404.00	+	2431.80i	0.116052	+	0.201007i
$528$	2048.00	−	3547.24i	0.168803	−	0.292375i
$529$	3041.50	−	5268.03i	0.249979	−	0.432977i
$530$	−20.0000	−	34.6410i	−0.00163914	−	0.00283907i
$531$	−11500.0			−0.939845
$532$		0			0
$533$	−836.000			−0.0679384
$534$	−600.000	−	1039.23i	−0.0486227	−	0.0842170i
$535$	−2985.00	+	5170.17i	−0.241220	+	0.417806i
$536$		0			0
$537$	1300.00	+	2251.67i	0.104468	+	0.180943i
$538$	26200.0			2.09956
$539$		0			0
$540$	4000.00			0.318764
$541$	−2811.00	−	4868.79i	−0.223391	−	0.386924i	0.732445	−	0.680826i	$-0.238379\pi$
$541$	−2811.00	−	4868.79i	−0.223391	−	0.386924i	−0.955835	+	0.293903i	$0.905046\pi$
$542$	−8776.00	+	15200.5i	−0.695501	+	1.20464i
$543$	−1742.00	+	3017.23i	−0.137673	+	0.238456i
$544$	−3328.00	−	5764.27i	−0.262292	−	0.454303i
$545$	2750.00			0.216141
$546$		0			0
$547$	16486.0			1.28865			0.644324	−	0.764753i	$-0.277139\pi$
$547$	16486.0			1.28865			0.644324	+	0.764753i	$0.277139\pi$
$548$	9336.00	+	16170.4i	0.727763	+	1.26052i
$549$	−5957.00	+	10317.8i	−0.463094	+	0.802102i
$550$	1600.00	−	2771.28i	0.124044	−	0.214851i
$551$	2500.00	+	4330.13i	0.193291	+	0.334791i
$552$		0			0
$553$		0			0
$554$	−2184.00			−0.167490
$555$	1330.00	+	2303.63i	0.101721	+	0.176187i
$556$	2800.00	−	4849.74i	0.213573	−	0.369919i
$557$	−5853.00	+	10137.7i	−0.445242	+	0.771181i	−0.998069	−	0.0621147i	$-0.980216\pi$
$557$	−5853.00	+	10137.7i	−0.445242	+	0.771181i	0.552827	+	0.833296i	$0.313549\pi$
$558$	4968.00	+	8604.83i	0.376904	+	0.652816i
$559$	−16796.0			−1.27083
$560$		0			0
$561$	1664.00			0.125230
$562$	−13716.0	−	23756.8i	−1.02949	−	1.78313i
$563$	12519.0	−	21683.5i	0.937146	−	1.62318i	0.166383	−	0.986061i	$-0.446791\pi$
$563$	12519.0	−	21683.5i	0.937146	−	1.62318i	0.770763	−	0.637123i	$-0.219875\pi$
$564$	4112.00	−	7122.19i	0.306997	−	0.531735i
$565$	3905.00	+	6763.66i	0.290769	+	0.503627i
$566$	−37128.0			−2.75725
$567$		0			0
$568$		0			0
$569$	−8775.00	−	15198.7i	−0.646515	−	1.11980i	−0.983949	−	0.178448i	$-0.942892\pi$
$569$	−8775.00	−	15198.7i	−0.646515	−	1.11980i	0.337434	−	0.941349i	$-0.390441\pi$
$570$	−2000.00	+	3464.10i	−0.146966	+	0.254553i
$571$	−5356.00	+	9276.86i	−0.392542	+	0.679903i	−0.992784	−	0.119915i	$-0.961738\pi$
$571$	−5356.00	+	9276.86i	−0.392542	+	0.679903i	0.600242	+	0.799819i	$0.295071\pi$
$572$	4864.00	+	8424.70i	0.355549	+	0.615829i
$573$	7544.00			0.550009
$574$		0			0
$575$	−1950.00			−0.141427
$576$	−5888.00	−	10198.3i	−0.425926	−	0.737725i
$577$	6827.00	−	11824.7i	0.492568	−	0.853153i	−0.507395	−	0.861713i	$-0.669392\pi$
$577$	6827.00	−	11824.7i	0.492568	−	0.853153i	0.999963	+	0.00856059i	$0.00272495\pi$
$578$	−8474.00	+	14677.4i	−0.609813	+	1.05623i
$579$	358.000	+	620.074i	0.0256960	+	0.0445067i
$580$	2000.00			0.143182
$581$		0			0
$582$	−3088.00			−0.219934
$583$	−32.0000	−	55.4256i	−0.00227325	−	0.00393738i
$584$		0			0
$585$	2185.00	−	3784.53i	0.154425	−	0.267472i
$586$	9684.00	+	16773.2i	0.682666	+	1.18241i
$587$	14166.0			0.996071			0.498035	−	0.867157i	$-0.334055\pi$
$587$	14166.0			0.996071			0.498035	+	0.867157i	$0.334055\pi$
$588$		0			0
$589$	−10800.0			−0.755528
$590$	−5000.00	−	8660.25i	−0.348893	−	0.604300i
$591$	2214.00	−	3834.76i	0.154098	−	0.266905i
$592$	8512.00	−	14743.2i	0.590948	−	1.02355i
$593$	−8921.00	−	15451.6i	−0.617777	−	1.07002i	−0.989891	−	0.141833i	$-0.954700\pi$
$593$	−8921.00	−	15451.6i	−0.617777	−	1.07002i	0.372114	−	0.928187i	$-0.378633\pi$
$594$	12800.0			0.884159
$595$		0			0
$596$	16400.0			1.12713
$597$	2600.00	+	4503.33i	0.178243	+	0.308725i
$598$	5928.00	−	10267.6i	0.405374	−	0.702129i
$599$	8800.00	−	15242.0i	0.600264	−	1.03969i	−0.392517	−	0.919745i	$-0.628395\pi$
$599$	8800.00	−	15242.0i	0.600264	−	1.03969i	0.992781	−	0.119943i	$-0.0382712\pi$
$600$		0			0
$601$	27302.0			1.85303			0.926516	−	0.376256i	$-0.122789\pi$
$601$	27302.0			1.85303			0.926516	+	0.376256i	$0.122789\pi$
$602$		0			0
$603$	−2898.00			−0.195714
$604$	−7408.00	−	12831.0i	−0.499052	−	0.864383i
$605$	−767.500	+	1329.35i	−0.0515757	+	0.0893318i
$606$	2808.00	−	4863.60i	0.188230	−	0.326023i
$607$	1897.00	+	3285.70i	0.126848	+	0.219708i	0.922454	−	0.386107i	$-0.126181\pi$
$607$	1897.00	+	3285.70i	0.126848	+	0.219708i	−0.795606	+	0.605815i	$0.792847\pi$
$608$	25600.0			1.70759
$609$		0			0
$610$	−10360.0			−0.687646
$611$	−9766.00	−	16915.2i	−0.646629	−	1.11999i
$612$	2392.00	−	4143.07i	0.157992	−	0.273650i
$613$	6619.00	−	11464.4i	0.436116	−	0.755374i	−0.561270	−	0.827633i	$-0.689687\pi$
$613$	6619.00	−	11464.4i	0.436116	−	0.755374i	0.997386	+	0.0722581i	$0.0230205\pi$
$614$	−5188.00	−	8985.88i	−0.340995	−	0.590620i
$615$	−220.000			−0.0144248
$616$		0			0
$617$	−11574.0			−0.755189			−0.377595	−	0.925971i	$-0.623249\pi$
$617$	−11574.0			−0.755189			−0.377595	+	0.925971i	$0.623249\pi$
$618$	−2392.00	−	4143.07i	−0.155696	−	0.269674i
$619$	−4150.00	+	7188.01i	−0.269471	+	0.466738i	−0.968725	−	0.248135i	$-0.920182\pi$
$619$	−4150.00	+	7188.01i	−0.269471	+	0.466738i	0.699254	+	0.714873i	$0.253516\pi$
$620$	−2160.00	+	3741.23i	−0.139916	+	0.242341i
$621$	−3900.00	−	6755.00i	−0.252015	−	0.436504i
$622$	−29328.0			−1.89059
$623$		0			0
$624$	4864.00			0.312045
$625$	−312.500	−	541.266i	−0.0200000	−	0.0346410i
$626$	3124.00	−	5410.93i	0.199457	−	0.345470i
$627$	−3200.00	+	5542.56i	−0.203821	+	0.353028i
$628$	9976.00	+	17278.9i	0.633894	+	1.09794i
$629$	6916.00			0.438409
$630$		0			0
$631$	−7508.00			−0.473675			−0.236837	−	0.971549i	$-0.576111\pi$
$631$	−7508.00			−0.473675			−0.236837	+	0.971549i	$0.576111\pi$
$632$		0			0
$633$	1168.00	−	2023.04i	0.0733394	−	0.127028i
$634$	2852.00	−	4939.81i	0.178655	−	0.309440i
$635$	4615.00	+	7993.41i	0.288411	+	0.499542i
$636$	32.0000			0.00199510
$637$		0			0
$638$	6400.00			0.397145
$639$	4738.00	+	8206.46i	0.293321	+	0.508048i
$640$		0			0
$641$	13689.0	−	23710.0i	0.843499	−	1.46098i	−0.0434190	−	0.999057i	$-0.513825\pi$
$641$	13689.0	−	23710.0i	0.843499	−	1.46098i	0.886918	−	0.461927i	$-0.152842\pi$
$642$	−4776.00	−	8272.27i	−0.293604	−	0.508537i
$643$	1842.00			0.112973			0.0564863	−	0.998403i	$-0.482010\pi$
$643$	1842.00			0.112973			0.0564863	+	0.998403i	$0.482010\pi$
$644$		0			0
$645$	−4420.00			−0.269825
$646$	5200.00	+	9006.66i	0.316705	+	0.548549i
$647$	5057.00	−	8758.98i	0.307282	−	0.532227i	−0.670485	−	0.741923i	$-0.733914\pi$
$647$	5057.00	−	8758.98i	0.307282	−	0.532227i	0.977767	+	0.209696i	$0.0672473\pi$
$648$		0			0
$649$	−8000.00	−	13856.4i	−0.483864	−	0.838076i
$650$	3800.00			0.229305
$651$		0			0
$652$	22096.0			1.32722
$653$	−5201.00	−	9008.40i	−0.311686	−	0.539856i	0.667042	−	0.745020i	$-0.267560\pi$
$653$	−5201.00	−	9008.40i	−0.311686	−	0.539856i	−0.978727	+	0.205165i	$0.934227\pi$
$654$	−2200.00	+	3810.51i	−0.131539	+	0.227833i
$655$	−5520.00	+	9560.92i	−0.329289	+	0.570345i
$656$	704.000	+	1219.36i	0.0419003	+	0.0725734i
$657$	20194.0			1.19915
$658$		0			0
$659$	7100.00			0.419692			0.209846	−	0.977734i	$-0.432704\pi$
$659$	7100.00			0.419692			0.209846	+	0.977734i	$0.432704\pi$
$660$	1280.00	+	2217.03i	0.0754908	+	0.130754i
$661$	3559.00	−	6164.37i	0.209424	−	0.362732i	−0.742109	−	0.670279i	$-0.766175\pi$
$661$	3559.00	−	6164.37i	0.209424	−	0.362732i	0.951533	+	0.307546i	$0.0995079\pi$
$662$	−8016.00	+	13884.1i	−0.470620	+	0.815138i
$663$	988.000	+	1711.27i	0.0578744	+	0.100241i
$664$		0			0
$665$		0			0
$666$	24472.0			1.42383
$667$	−1950.00	−	3377.50i	−0.113200	−	0.196068i
$668$	−12504.0	+	21657.6i	−0.724243	+	1.25443i
$669$	6478.00	−	11220.2i	0.374371	−	0.648429i
$670$	−1260.00	−	2182.38i	−0.0726538	−	0.125840i
$671$	−16576.0			−0.953665
$672$		0			0
$673$	−31278.0			−1.79150			−0.895749	−	0.444560i	$-0.853360\pi$
$673$	−31278.0			−1.79150			−0.895749	+	0.444560i	$0.853360\pi$
$674$	17732.0	+	30712.7i	1.01337	+	1.75521i
$675$	1250.00	−	2165.06i	0.0712778	−	0.123457i
$676$	3012.00	−	5216.94i	0.171370	−	0.296822i
$677$	15027.0	+	26027.5i	0.853079	+	1.47758i	0.878416	+	0.477897i	$0.158601\pi$
$677$	15027.0	+	26027.5i	0.853079	+	1.47758i	−0.0253367	+	0.999679i	$0.508066\pi$
$678$	−12496.0			−0.707826
$679$		0			0
$680$		0			0
$681$	−646.000	−	1118.90i	−0.0363506	−	0.0629611i
$682$	−6912.00	+	11971.9i	−0.388085	+	0.672183i
$683$	2259.00	−	3912.70i	0.126557	−	0.219203i	−0.795784	−	0.605581i	$-0.792941\pi$
$683$	2259.00	−	3912.70i	0.126557	−	0.219203i	0.922340	+	0.386378i	$0.126274\pi$
$684$	9200.00	+	15934.9i	0.514285	+	0.890767i
$685$	11670.0			0.650931
$686$		0			0
$687$	7500.00			0.416511
$688$	14144.0	+	24498.1i	0.783772	+	1.35753i
$689$	38.0000	−	65.8179i	0.00210114	−	0.00363928i
$690$	1560.00	−	2702.00i	0.0860698	−	0.149077i
$691$	−14636.0	−	25350.3i	−0.805759	−	1.39562i	−0.915777	−	0.401686i	$-0.868424\pi$
$691$	−14636.0	−	25350.3i	−0.805759	−	1.39562i	0.110018	−	0.993930i	$-0.464909\pi$
$692$	−624.000			−0.0342788
$693$		0			0
$694$	6856.00			0.375000
$695$	−1750.00	−	3031.09i	−0.0955126	−	0.165433i
$696$		0			0
$697$	−286.000	+	495.367i	−0.0155424	+	0.0269202i
$698$	2300.00	+	3983.72i	0.124722	+	0.216026i
$699$	2964.00			0.160385
$700$		0			0
$701$	−5798.00			−0.312393			−0.156196	−	0.987726i	$-0.549923\pi$
$701$	−5798.00			−0.312393			−0.156196	+	0.987726i	$0.549923\pi$
$702$	7600.00	+	13163.6i	0.408609	+	0.707732i
$703$	−13300.0	+	23036.3i	−0.713541	+	1.23589i
$704$	8192.00	−	14189.0i	0.438562	−	0.759612i
$705$	−2570.00	−	4451.37i	−0.137293	−	0.237799i
$706$	17592.0			0.937796
$707$		0			0
$708$	8000.00			0.424659
$709$	−4475.00	−	7750.93i	−0.237041	−	0.410567i	0.722823	−	0.691033i	$-0.242844\pi$
$709$	−4475.00	−	7750.93i	−0.237041	−	0.410567i	−0.959864	+	0.280466i	$0.909511\pi$
$710$	−4120.00	+	7136.05i	−0.217776	+	0.377199i
$711$	6900.00	−	11951.2i	0.363952	−	0.630384i
$712$		0			0
$713$	8424.00			0.442470
$714$		0			0
$715$	6080.00			0.318013
$716$	5200.00	+	9006.66i	0.271415	+	0.470105i
$717$	−1400.00	+	2424.87i	−0.0729204	+	0.126302i
$718$	3600.00	−	6235.38i	0.187118	−	0.324098i
$719$	−3900.00	−	6755.00i	−0.202289	−	0.350374i	0.746977	−	0.664850i	$-0.231505\pi$
$719$	−3900.00	−	6755.00i	−0.202289	−	0.350374i	−0.949265	+	0.314476i	$0.898171\pi$
$720$	−7360.00			−0.380960
$721$		0			0
$722$	−12564.0			−0.647623
$723$	−3022.00	−	5234.26i	−0.155449	−	0.269245i
$724$	−6968.00	+	12068.9i	−0.357685	+	0.619528i
$725$	625.000	−	1082.53i	0.0320164	−	0.0554541i
$726$	−1228.00	−	2126.96i	−0.0627760	−	0.108731i
$727$	−8554.00			−0.436383			−0.218191	−	0.975906i	$-0.570016\pi$
$727$	−8554.00			−0.436383			−0.218191	+	0.975906i	$0.570016\pi$
$728$		0			0
$729$	−4283.00			−0.217599
$730$	8780.00	+	15207.4i	0.445154	+	0.771029i
$731$	−5746.00	+	9952.36i	−0.290730	+	0.503559i
$732$	4144.00	−	7177.62i	0.209244	−	0.362421i
$733$	−1441.00	−	2495.89i	−0.0726119	−	0.125768i	0.827433	−	0.561564i	$-0.189800\pi$
$733$	−1441.00	−	2495.89i	−0.0726119	−	0.125768i	−0.900045	+	0.435796i	$0.856467\pi$
$734$	23496.0			1.18154
$735$		0			0
$736$	−19968.0			−1.00004
$737$	−2016.00	−	3491.81i	−0.100760	−	0.174522i
$738$	−1012.00	+	1752.84i	−0.0504773	+	0.0874292i
$739$	−9350.00	+	16194.7i	−0.465420	+	0.806131i	−0.999220	−	0.0394795i	$-0.987430\pi$
$739$	−9350.00	+	16194.7i	−0.465420	+	0.806131i	0.533800	+	0.845610i	$0.320763\pi$
$740$	5320.00	+	9214.51i	0.264280	+	0.457746i
$741$	−7600.00			−0.376779
$742$		0			0
$743$	12242.0			0.604462			0.302231	−	0.953235i	$-0.402269\pi$
$743$	12242.0			0.604462			0.302231	+	0.953235i	$0.402269\pi$
$744$		0			0
$745$	5125.00	−	8876.76i	0.252034	−	0.436536i
$746$	−4156.00	+	7198.40i	−0.203970	+	0.353287i
$747$	3243.00	+	5617.04i	0.158842	+	0.275123i
$748$	6656.00			0.325358
$749$		0			0
$750$	1000.00			0.0486864
$751$	15574.0	+	26975.0i	0.756729	+	1.31069i	0.944510	+	0.328482i	$0.106537\pi$
$751$	15574.0	+	26975.0i	0.756729	+	1.31069i	−0.187781	+	0.982211i	$0.560130\pi$
$752$	−16448.0	+	28488.8i	−0.797602	+	1.38149i
$753$	1248.00	−	2161.60i	0.0603979	−	0.104612i
$754$	3800.00	+	6581.79i	0.183538	+	0.317898i
$755$	−9260.00			−0.446365
$756$		0			0
$757$	−7694.00			−0.369410			−0.184705	−	0.982794i	$-0.559133\pi$
$757$	−7694.00			−0.369410			−0.184705	+	0.982794i	$0.559133\pi$
$758$	15800.0	+	27366.4i	0.757100	+	1.31134i
$759$	2496.00	−	4323.20i	0.119366	−	0.206749i
$760$		0			0
$761$	2259.00	+	3912.70i	0.107607	+	0.186380i	0.914800	−	0.403907i	$-0.132348\pi$
$761$	2259.00	+	3912.70i	0.107607	+	0.186380i	−0.807194	+	0.590287i	$0.799015\pi$
$762$	−14768.0			−0.702084
$763$		0			0
$764$	30176.0			1.42897
$765$	−1495.00	−	2589.42i	−0.0706560	−	0.122380i
$766$	−15036.0	+	26043.1i	−0.709233	+	1.22843i
$767$	9500.00	−	16454.5i	0.447230	−	0.774624i
$768$	−4096.00	−	7094.48i	−0.192450	−	0.333333i
$769$	−39550.0			−1.85463			−0.927314	−	0.374283i	$-0.877889\pi$
$769$	−39550.0			−1.85463			−0.927314	+	0.374283i	$0.877889\pi$
$770$		0			0
$771$	4212.00			0.196746
$772$	1432.00	+	2480.30i	0.0667601	+	0.115632i
$773$	−11061.0	+	19158.2i	−0.514666	+	0.891427i	0.485190	+	0.874409i	$0.338751\pi$
$773$	−11061.0	+	19158.2i	−0.514666	+	0.891427i	−0.999855	+	0.0170180i	$0.994583\pi$
$774$	−20332.0	+	35216.1i	−0.944210	+	1.63542i
$775$	1350.00	+	2338.27i	0.0625722	+	0.108378i
$776$		0			0
$777$		0			0
$778$	7800.00			0.359439
$779$	−1100.00	−	1905.26i	−0.0505925	−	0.0876289i
$780$	−1520.00	+	2632.72i	−0.0697753	+	0.120854i
$781$	−6592.00	+	11417.7i	−0.302023	+	0.523120i
$782$	−4056.00	−	7025.20i	−0.185476	−	0.321254i
$783$	5000.00			0.228206
$784$		0			0
$785$	12470.0			0.566972
$786$	−8832.00	−	15297.5i	−0.400798	−	0.694202i
$787$	8317.00	−	14405.5i	0.376708	−	0.652477i	−0.613873	−	0.789405i	$-0.710389\pi$
$787$	8317.00	−	14405.5i	0.376708	−	0.652477i	0.990581	+	0.136928i	$0.0437228\pi$
$788$	8856.00	−	15339.0i	0.400358	−	0.693440i
$789$	3638.00	+	6301.20i	0.164152	+	0.284320i
$790$	12000.0			0.540431
$791$		0			0
$792$		0			0
$793$	−9842.00	−	17046.8i	−0.440731	−	0.763368i
$794$	27572.0	−	47756.1i	1.23236	−	2.13451i
$795$	10.0000	−	17.3205i	0.000446118	−	0.000772698i
$796$	10400.0	+	18013.3i	0.463088	+	0.802092i
$797$	27586.0			1.22603			0.613015	−	0.790071i	$-0.289956\pi$
$797$	27586.0			1.22603			0.613015	+	0.790071i	$0.289956\pi$
$798$		0			0
$799$	−13364.0			−0.591720
$800$	−3200.00	−	5542.56i	−0.141421	−	0.244949i
$801$	−1725.00	+	2987.79i	−0.0760922	+	0.131796i
$802$	12804.0	−	22177.2i	0.563747	−	0.976438i
$803$	14048.0	+	24331.8i	0.617364	+	1.06931i
$804$	2016.00			0.0884314
$805$		0			0
$806$	−16416.0			−0.717406
$807$	6550.00	+	11344.9i	0.285714	+	0.494871i
$808$		0			0
$809$	−1925.00	+	3334.20i	−0.0836581	+	0.144900i	−0.904819	−	0.425797i	$-0.859994\pi$
$809$	−1925.00	+	3334.20i	−0.0836581	+	0.144900i	0.821161	+	0.570697i	$0.193327\pi$
$810$	−4210.00	−	7291.93i	−0.182623	−	0.316312i
$811$	10032.0			0.434366			0.217183	−	0.976131i	$-0.430313\pi$
$811$	10032.0			0.434366			0.217183	+	0.976131i	$0.430313\pi$
$812$		0			0
$813$	−8776.00			−0.378583
$814$	17024.0	+	29486.4i	0.733035	+	1.26965i
$815$	6905.00	−	11959.8i	0.296775	−	0.514029i
$816$	1664.00	−	2882.13i	0.0713868	−	0.123646i
$817$	−22100.0	−	38278.3i	−0.946366	−	1.63915i
$818$	−44600.0			−1.90636
$819$		0			0
$820$	−880.000			−0.0374767
$821$	−10281.0	−	17807.2i	−0.437039	−	0.756975i	0.560420	−	0.828208i	$-0.310640\pi$
$821$	−10281.0	−	17807.2i	−0.437039	−	0.756975i	−0.997460	+	0.0712339i	$0.977306\pi$
$822$	−9336.00	+	16170.4i	−0.396144	+	0.686142i
$823$	−5161.00	+	8939.11i	−0.218592	+	0.378612i	−0.954378	−	0.298602i	$-0.903480\pi$
$823$	−5161.00	+	8939.11i	−0.218592	+	0.378612i	0.735786	+	0.677214i	$0.236813\pi$
$824$		0			0
$825$	1600.00			0.0675210
$826$		0			0
$827$	8846.00			0.371954			0.185977	−	0.982554i	$-0.440455\pi$
$827$	8846.00			0.371954			0.185977	+	0.982554i	$0.440455\pi$
$828$	−7176.00	−	12429.2i	−0.301187	−	0.521672i
$829$	12675.0	−	21953.7i	0.531026	−	0.919765i	−0.468318	−	0.883560i	$-0.655140\pi$
$829$	12675.0	−	21953.7i	0.531026	−	0.919765i	0.999344	−	0.0362048i	$-0.0115269\pi$
$830$	−2820.00	+	4884.38i	−0.117932	+	0.204264i
$831$	−546.000	−	945.700i	−0.0227925	−	0.0394777i
$832$	19456.0			0.810716
$833$		0			0
$834$	5600.00			0.232509
$835$	7815.00	+	13536.0i	0.323891	+	0.560996i
$836$	−12800.0	+	22170.3i	−0.529542	+	0.917194i
$837$	−5400.00	+	9353.07i	−0.223000	+	0.386248i
$838$	−27400.0	−	47458.2i	−1.12950	−	1.95634i
$839$	46000.0			1.89284			0.946422	−	0.322932i	$-0.104669\pi$
$839$	46000.0			1.89284			0.946422	+	0.322932i	$0.104669\pi$
$840$		0			0
$841$	−21889.0			−0.897495
$842$	−10876.0	−	18837.8i	−0.445145	−	0.771013i
$843$	6858.00	−	11878.4i	0.280192	−	0.485307i
$844$	4672.00	−	8092.14i	0.190541	−	0.330027i
$845$	−1882.50	−	3260.59i	−0.0766390	−	0.132743i
$846$	−47288.0			−1.92174
$847$		0			0
$848$	−128.000			−0.00518342
$849$	−9282.00	−	16076.9i	−0.375215	−	0.649891i
$850$	1300.00	−	2251.67i	0.0524584	−	0.0908606i
$851$	10374.0	−	17968.3i	0.417880	−	0.723790i
$852$	−3296.00	−	5708.84i	−0.132534	−	0.229556i
$853$	−16998.0			−0.682298			−0.341149	−	0.940009i	$-0.610816\pi$
$853$	−16998.0			−0.682298			−0.341149	+	0.940009i	$0.610816\pi$
$854$		0			0
$855$	11500.0			0.459990
$856$		0			0
$857$	13247.0	−	22944.5i	0.528015	−	0.914549i	−0.471452	−	0.881892i	$-0.656270\pi$
$857$	13247.0	−	22944.5i	0.528015	−	0.914549i	0.999467	−	0.0326569i	$-0.0103969\pi$
$858$	−4864.00	+	8424.70i	−0.193536	+	0.335215i
$859$	10750.0	+	18619.5i	0.426991	+	0.739570i	0.996604	−	0.0823429i	$-0.0262403\pi$
$859$	10750.0	+	18619.5i	0.426991	+	0.739570i	−0.569613	+	0.821913i	$0.692907\pi$
$860$	−17680.0			−0.701027
$861$		0			0
$862$	−30768.0			−1.21573
$863$	−12881.0	−	22310.5i	−0.508082	−	0.880023i	−0.999956	−	0.00935699i	$-0.997022\pi$
$863$	−12881.0	−	22310.5i	−0.508082	−	0.880023i	0.491875	−	0.870666i	$-0.336312\pi$
$864$	12800.0	−	22170.3i	0.504010	−	0.872971i
$865$	−195.000	+	337.750i	−0.00766497	+	0.0132761i
$866$	−2236.00	−	3872.87i	−0.0877395	−	0.151969i
$867$	−8474.00			−0.331940
$868$		0			0
$869$	19200.0			0.749500
$870$	1000.00	+	1732.05i	0.0389692	+	0.0674966i
$871$	2394.00	−	4146.53i	0.0931316	−	0.161309i
$872$		0			0
$873$	4439.00	+	7688.57i	0.172093	+	0.298074i
$874$	31200.0			1.20750
$875$		0			0
$876$	−14048.0			−0.541824
$877$	−15273.0	−	26453.6i	−0.588064	−	1.01856i	−0.994486	−	0.104872i	$-0.966557\pi$
$877$	−15273.0	−	26453.6i	−0.588064	−	1.01856i	0.406421	−	0.913686i	$-0.366777\pi$
$878$	−5200.00	+	9006.66i	−0.199876	+	0.346196i
$879$	−4842.00	+	8386.59i	−0.185798	+	0.321812i
$880$	−5120.00	−	8868.10i	−0.196131	−	0.339709i
$881$	32942.0			1.25976			0.629878	−	0.776694i	$-0.283105\pi$
$881$	32942.0			1.25976			0.629878	+	0.776694i	$0.283105\pi$
$882$		0			0
$883$	−27118.0			−1.03351			−0.516757	−	0.856132i	$-0.672861\pi$
$883$	−27118.0			−1.03351			−0.516757	+	0.856132i	$0.672861\pi$
$884$	3952.00	+	6845.06i	0.150362	+	0.260435i
$885$	2500.00	−	4330.13i	0.0949566	−	0.164470i
$886$	−23916.0	+	41423.7i	−0.906855	+	1.57072i
$887$	19317.0	+	33458.0i	0.731230	+	1.26653i	0.956358	+	0.292199i	$0.0943869\pi$
$887$	19317.0	+	33458.0i	0.731230	+	1.26653i	−0.225127	+	0.974329i	$0.572280\pi$
$888$		0			0
$889$		0			0
$890$	−3000.00			−0.112989
$891$	−6736.00	−	11667.1i	−0.253271	−	0.438678i
$892$	25912.0	−	44880.9i	0.972643	−	1.68467i
$893$	25700.0	−	44513.7i	0.963066	−	1.66808i
$894$	8200.00	+	14202.8i	0.306766	+	0.531335i
$895$	6500.00			0.242761
$896$		0			0
$897$	5928.00			0.220658
$898$	−34100.0	−	59062.9i	−1.26718	−	2.19483i
$899$	−2700.00	+	4676.54i	−0.100167	+	0.173494i
$900$	2300.00	−	3983.72i	0.0851852	−	0.147545i
$901$	−26.0000	−	45.0333i	−0.000961360	−	0.00166512i
$902$	−2816.00			−0.103950
$903$		0			0
$904$		0			0
$905$	4355.00	+	7543.08i	0.159961	+	0.277061i
$906$	7408.00	−	12831.0i	0.271649	−	0.470510i
$907$	897.000	−	1553.65i	0.0328384	−	0.0568777i	−0.849139	−	0.528169i	$-0.822879\pi$
$907$	897.000	−	1553.65i	0.0328384	−	0.0568777i	0.881978	+	0.471291i	$0.156212\pi$
$908$	−2584.00	−	4475.62i	−0.0944417	−	0.163578i
$909$	−16146.0			−0.589141
$910$		0			0
$911$	41732.0			1.51772			0.758860	−	0.651254i	$-0.225757\pi$
$911$	41732.0			1.51772			0.758860	+	0.651254i	$0.225757\pi$
$912$	6400.00	+	11085.1i	0.232374	+	0.402484i
$913$	−4512.00	+	7815.01i	−0.163555	+	0.283285i
$914$	−18988.0	+	32888.2i	−0.687163	+	1.19020i
$915$	−2590.00	−	4486.01i	−0.0935768	−	0.162080i
$916$	30000.0			1.08213
$917$		0			0
$918$	10400.0			0.373912
$919$	−14600.0	−	25287.9i	−0.524058	−	0.907696i	−0.999608	−	0.0280066i	$-0.991084\pi$
$919$	−14600.0	−	25287.9i	−0.524058	−	0.907696i	0.475549	−	0.879689i	$-0.342249\pi$
$920$		0			0
$921$	2594.00	−	4492.94i	0.0928070	−	0.160746i
$922$	−22836.0	−	39553.1i	−0.815687	−	1.41281i
$923$	−15656.0			−0.558314
$924$		0			0
$925$	6650.00			0.236379
$926$	15924.0	+	27581.2i	0.565114	+	0.978805i
$927$	−6877.00	+	11911.3i	−0.243657	+	0.422027i
$928$	6400.00	−	11085.1i	0.226390	−	0.392120i
$929$	24325.0	+	42132.1i	0.859071	+	1.48796i	0.872816	+	0.488050i	$0.162292\pi$
$929$	24325.0	+	42132.1i	0.859071	+	1.48796i	−0.0137443	+	0.999906i	$0.504375\pi$
$930$	−4320.00			−0.152321
$931$		0			0
$932$	11856.0			0.416691
$933$	−7332.00	−	12699.4i	−0.257276	−	0.445616i
$934$	13052.0	−	22606.7i	0.457253	−	0.791986i
$935$	2080.00	−	3602.67i	0.0727522	−	0.126010i
$936$		0			0
$937$	−11334.0			−0.395161			−0.197580	−	0.980287i	$-0.563308\pi$
$937$	−11334.0			−0.395161			−0.197580	+	0.980287i	$0.563308\pi$
$938$		0			0
$939$	3124.00			0.108571
$940$	−10280.0	−	17805.5i	−0.356699	−	0.617820i
$941$	15589.0	−	27000.9i	0.540050	−	0.935394i	−0.458851	−	0.888513i	$-0.651739\pi$
$941$	15589.0	−	27000.9i	0.540050	−	0.935394i	0.998901	−	0.0468803i	$-0.0149279\pi$
$942$	−9976.00	+	17278.9i	−0.345048	+	0.597641i
$943$	858.000	+	1486.10i	0.0296292	+	0.0513193i
$944$	−32000.0			−1.10330
$945$		0			0
$946$	−56576.0			−1.94444
$947$	−2343.00	−	4058.20i	−0.0803984	−	0.139254i	0.823023	−	0.568008i	$-0.192286\pi$
$947$	−2343.00	−	4058.20i	−0.0803984	−	0.139254i	−0.903421	+	0.428754i	$0.858953\pi$
$948$	−4800.00	+	8313.84i	−0.164448	+	0.284832i
$949$	−16682.0	+	28894.1i	−0.570622	+	0.988347i
$950$	5000.00	+	8660.25i	0.170759	+	0.295764i
$951$	2852.00			0.0972476
$952$		0			0
$953$	−598.000			−0.0203265			−0.0101632	−	0.999948i	$-0.503235\pi$
$953$	−598.000			−0.0203265			−0.0101632	+	0.999948i	$0.503235\pi$
$954$	−92.0000	−	159.349i	−0.00312223	−	0.00540787i
$955$	9430.00	−	16333.2i	0.319526	−	0.553436i
$956$	−5600.00	+	9699.48i	−0.189453	+	0.328142i
$957$	1600.00	+	2771.28i	0.0540446	+	0.0936079i
$958$	−69600.0			−2.34726
$959$		0			0
$960$	5120.00			0.172133
$961$	9063.50	+	15698.4i	0.304236	+	0.526953i
$962$	−20216.0	+	35015.1i	−0.677536	+	1.17353i
$963$	−13731.0	+	23782.8i	−0.459476	+	0.795836i
$964$	−12088.0	−	20937.0i	−0.403867	−	0.699519i
$965$	1790.00			0.0597121
$966$		0			0
$967$	41726.0			1.38761			0.693804	−	0.720163i	$-0.255933\pi$
$967$	41726.0			1.38761			0.693804	+	0.720163i	$0.255933\pi$
$968$		0			0
$969$	−2600.00	+	4503.33i	−0.0861961	+	0.149296i
$970$	−3860.00	+	6685.72i	−0.127770	+	0.221305i
$971$	−12156.0	−	21054.8i	−0.401756	−	0.695861i	0.592182	−	0.805804i	$-0.298267\pi$
$971$	−12156.0	−	21054.8i	−0.401756	−	0.695861i	−0.993938	+	0.109943i	$0.964933\pi$
$972$	28336.0			0.935059
$973$		0			0
$974$	−4664.00			−0.153433
$975$	950.000	+	1645.45i	0.0312045	+	0.0540477i
$976$	−16576.0	+	28710.5i	−0.543632	+	0.941598i
$977$	−20473.0	+	35460.3i	−0.670409	+	1.16118i	0.307380	+	0.951587i	$0.400548\pi$
$977$	−20473.0	+	35460.3i	−0.670409	+	1.16118i	−0.977788	+	0.209595i	$0.932785\pi$
$978$	11048.0	+	19135.7i	0.361223	+	0.625657i
$979$	−4800.00			−0.156699
$980$		0			0
$981$	12650.0			0.411706
$982$	14144.0	+	24498.1i	0.459626	+	0.796096i
$983$	−21141.0	+	36617.3i	−0.685954	+	1.18811i	0.287181	+	0.957876i	$0.407282\pi$
$983$	−21141.0	+	36617.3i	−0.685954	+	1.18811i	−0.973136	+	0.230232i	$0.926052\pi$
$984$		0			0
$985$	−5535.00	−	9586.90i	−0.179045	−	0.310116i
$986$	5200.00			0.167953
$987$		0			0
$988$	−30400.0			−0.978900
$989$	17238.0	+	29857.1i	0.554233	+	0.959960i
$990$	7360.00	−	12747.9i	0.236279	−	0.409247i
$991$	−586.000	+	1014.98i	−0.0187840	+	0.0325348i	−0.875265	−	0.483644i	$-0.839313\pi$
$991$	−586.000	+	1014.98i	−0.0187840	+	0.0325348i	0.856481	+	0.516179i	$0.172646\pi$
$992$	13824.0	+	23943.9i	0.442452	+	0.766349i
$993$	−8016.00			−0.256173
$994$		0			0
$995$	13000.0			0.414199
$996$	−2256.00	−	3907.51i	−0.0717712	−	0.124311i
$997$	15807.0	−	27378.5i	0.502119	−	0.869696i	−0.497878	−	0.867247i	$-0.665887\pi$
$997$	15807.0	−	27378.5i	0.502119	−	0.869696i	0.999997	−	0.00244862i	$-0.000779421\pi$
$998$	200.000	−	346.410i	0.00634358	−	0.0109874i
$999$	13300.0	+	23036.3i	0.421215	+	0.729565i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	245.4.e.f.116.1		2
7.2	even	3	inner	245.4.e.f.226.1		2
7.3	odd	6		245.4.a.a.1.1		1
7.4	even	3		5.4.a.a.1.1	✓	1
7.5	odd	6		245.4.e.g.226.1		2
7.6	odd	2		245.4.e.g.116.1		2
21.11	odd	6		45.4.a.d.1.1		1
21.17	even	6		2205.4.a.q.1.1		1
28.11	odd	6		80.4.a.d.1.1		1
35.4	even	6		25.4.a.c.1.1		1
35.18	odd	12		25.4.b.a.24.2		2
35.24	odd	6		1225.4.a.k.1.1		1
35.32	odd	12		25.4.b.a.24.1		2
56.11	odd	6		320.4.a.h.1.1		1
56.53	even	6		320.4.a.g.1.1		1
63.4	even	3		405.4.e.l.136.1		2
63.11	odd	6		405.4.e.c.271.1		2
63.25	even	3		405.4.e.l.271.1		2
63.32	odd	6		405.4.e.c.136.1		2
77.32	odd	6		605.4.a.d.1.1		1
84.11	even	6		720.4.a.u.1.1		1
91.25	even	6		845.4.a.b.1.1		1
105.32	even	12		225.4.b.c.199.2		2
105.53	even	12		225.4.b.c.199.1		2
105.74	odd	6		225.4.a.b.1.1		1
112.11	odd	12		1280.4.d.l.641.2		2
112.53	even	12		1280.4.d.e.641.1		2
112.67	odd	12		1280.4.d.l.641.1		2
112.109	even	12		1280.4.d.e.641.2		2
119.67	even	6		1445.4.a.a.1.1		1
133.18	odd	6		1805.4.a.h.1.1		1
140.39	odd	6		400.4.a.m.1.1		1
140.67	even	12		400.4.c.k.49.2		2
140.123	even	12		400.4.c.k.49.1		2
280.109	even	6		1600.4.a.bi.1.1		1
280.179	odd	6		1600.4.a.s.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5.4.a.a.1.1	✓	1	7.4	even	3
25.4.a.c.1.1		1	35.4	even	6
25.4.b.a.24.1		2	35.32	odd	12
25.4.b.a.24.2		2	35.18	odd	12
45.4.a.d.1.1		1	21.11	odd	6
80.4.a.d.1.1		1	28.11	odd	6
225.4.a.b.1.1		1	105.74	odd	6
225.4.b.c.199.1		2	105.53	even	12
225.4.b.c.199.2		2	105.32	even	12
245.4.a.a.1.1		1	7.3	odd	6
245.4.e.f.116.1		2	1.1	even	1	trivial
245.4.e.f.226.1		2	7.2	even	3	inner
245.4.e.g.116.1		2	7.6	odd	2
245.4.e.g.226.1		2	7.5	odd	6
320.4.a.g.1.1		1	56.53	even	6
320.4.a.h.1.1		1	56.11	odd	6
400.4.a.m.1.1		1	140.39	odd	6
400.4.c.k.49.1		2	140.123	even	12
400.4.c.k.49.2		2	140.67	even	12
405.4.e.c.136.1		2	63.32	odd	6
405.4.e.c.271.1		2	63.11	odd	6
405.4.e.l.136.1		2	63.4	even	3
405.4.e.l.271.1		2	63.25	even	3
605.4.a.d.1.1		1	77.32	odd	6
720.4.a.u.1.1		1	84.11	even	6
845.4.a.b.1.1		1	91.25	even	6
1225.4.a.k.1.1		1	35.24	odd	6
1280.4.d.e.641.1		2	112.53	even	12
1280.4.d.e.641.2		2	112.109	even	12
1280.4.d.l.641.1		2	112.67	odd	12
1280.4.d.l.641.2		2	112.11	odd	12
1445.4.a.a.1.1		1	119.67	even	6
1600.4.a.s.1.1		1	280.179	odd	6
1600.4.a.bi.1.1		1	280.109	even	6
1805.4.a.h.1.1		1	133.18	odd	6
2205.4.a.q.1.1		1	21.17	even	6

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:	\( N \)	\(=\)	\( 245 = 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	245.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.00000 + 3.46410i) q^{2} +(-1.00000 + 1.73205i) q^{3} +(-4.00000 + 6.92820i) q^{4} +(2.50000 + 4.33013i) q^{5} -8.00000 q^{6} +(11.5000 + 19.9186i) q^{9} +O(q^{10})\)	\(q+(2.00000 + 3.46410i) q^{2} +(-1.00000 + 1.73205i) q^{3} +(-4.00000 + 6.92820i) q^{4} +(2.50000 + 4.33013i) q^{5} -8.00000 q^{6} +(11.5000 + 19.9186i) q^{9} +(-10.0000 + 17.3205i) q^{10} +(-16.0000 + 27.7128i) q^{11} +(-8.00000 - 13.8564i) q^{12} -38.0000 q^{13} -10.0000 q^{15} +(32.0000 + 55.4256i) q^{16} +(-13.0000 + 22.5167i) q^{17} +(-46.0000 + 79.6743i) q^{18} +(-50.0000 - 86.6025i) q^{19} -40.0000 q^{20} -128.000 q^{22} +(39.0000 + 67.5500i) q^{23} +(-12.5000 + 21.6506i) q^{25} +(-76.0000 - 131.636i) q^{26} -100.000 q^{27} -50.0000 q^{29} +(-20.0000 - 34.6410i) q^{30} +(54.0000 - 93.5307i) q^{31} +(-128.000 + 221.703i) q^{32} +(-32.0000 - 55.4256i) q^{33} -104.000 q^{34} -184.000 q^{36} +(-133.000 - 230.363i) q^{37} +(200.000 - 346.410i) q^{38} +(38.0000 - 65.8179i) q^{39} +22.0000 q^{41} +442.000 q^{43} +(-128.000 - 221.703i) q^{44} +(-57.5000 + 99.5929i) q^{45} +(-156.000 + 270.200i) q^{46} +(257.000 + 445.137i) q^{47} -128.000 q^{48} -100.000 q^{50} +(-26.0000 - 45.0333i) q^{51} +(152.000 - 263.272i) q^{52} +(-1.00000 + 1.73205i) q^{53} +(-200.000 - 346.410i) q^{54} -160.000 q^{55} +200.000 q^{57} +(-100.000 - 173.205i) q^{58} +(-250.000 + 433.013i) q^{59} +(40.0000 - 69.2820i) q^{60} +(259.000 + 448.601i) q^{61} +432.000 q^{62} -512.000 q^{64} +(-95.0000 - 164.545i) q^{65} +(128.000 - 221.703i) q^{66} +(-63.0000 + 109.119i) q^{67} +(-104.000 - 180.133i) q^{68} -156.000 q^{69} +412.000 q^{71} +(439.000 - 760.370i) q^{73} +(532.000 - 921.451i) q^{74} +(-25.0000 - 43.3013i) q^{75} +800.000 q^{76} +304.000 q^{78} +(-300.000 - 519.615i) q^{79} +(-160.000 + 277.128i) q^{80} +(-210.500 + 364.597i) q^{81} +(44.0000 + 76.2102i) q^{82} +282.000 q^{83} -130.000 q^{85} +(884.000 + 1531.13i) q^{86} +(50.0000 - 86.6025i) q^{87} +(75.0000 + 129.904i) q^{89} -460.000 q^{90} -624.000 q^{92} +(108.000 + 187.061i) q^{93} +(-1028.00 + 1780.55i) q^{94} +(250.000 - 433.013i) q^{95} +(-256.000 - 443.405i) q^{96} +386.000 q^{97} -736.000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 4 q^{2} - 2 q^{3} - 8 q^{4} + 5 q^{5} - 16 q^{6} + 23 q^{9}+O(q^{10}) \) 2 * q + 4 * q^2 - 2 * q^3 - 8 * q^4 + 5 * q^5 - 16 * q^6 + 23 * q^9	\( 2 q + 4 q^{2} - 2 q^{3} - 8 q^{4} + 5 q^{5} - 16 q^{6} + 23 q^{9} - 20 q^{10} - 32 q^{11} - 16 q^{12} - 76 q^{13} - 20 q^{15} + 64 q^{16} - 26 q^{17} - 92 q^{18} - 100 q^{19} - 80 q^{20} - 256 q^{22} + 78 q^{23} - 25 q^{25} - 152 q^{26} - 200 q^{27} - 100 q^{29} - 40 q^{30} + 108 q^{31} - 256 q^{32} - 64 q^{33} - 208 q^{34} - 368 q^{36} - 266 q^{37} + 400 q^{38} + 76 q^{39} + 44 q^{41} + 884 q^{43} - 256 q^{44} - 115 q^{45} - 312 q^{46} + 514 q^{47} - 256 q^{48} - 200 q^{50} - 52 q^{51} + 304 q^{52} - 2 q^{53} - 400 q^{54} - 320 q^{55} + 400 q^{57} - 200 q^{58} - 500 q^{59} + 80 q^{60} + 518 q^{61} + 864 q^{62} - 1024 q^{64} - 190 q^{65} + 256 q^{66} - 126 q^{67} - 208 q^{68} - 312 q^{69} + 824 q^{71} + 878 q^{73} + 1064 q^{74} - 50 q^{75} + 1600 q^{76} + 608 q^{78} - 600 q^{79} - 320 q^{80} - 421 q^{81} + 88 q^{82} + 564 q^{83} - 260 q^{85} + 1768 q^{86} + 100 q^{87} + 150 q^{89} - 920 q^{90} - 1248 q^{92} + 216 q^{93} - 2056 q^{94} + 500 q^{95} - 512 q^{96} + 772 q^{97} - 1472 q^{99}+O(q^{100}) \) 2 * q + 4 * q^2 - 2 * q^3 - 8 * q^4 + 5 * q^5 - 16 * q^6 + 23 * q^9 - 20 * q^10 - 32 * q^11 - 16 * q^12 - 76 * q^13 - 20 * q^15 + 64 * q^16 - 26 * q^17 - 92 * q^18 - 100 * q^19 - 80 * q^20 - 256 * q^22 + 78 * q^23 - 25 * q^25 - 152 * q^26 - 200 * q^27 - 100 * q^29 - 40 * q^30 + 108 * q^31 - 256 * q^32 - 64 * q^33 - 208 * q^34 - 368 * q^36 - 266 * q^37 + 400 * q^38 + 76 * q^39 + 44 * q^41 + 884 * q^43 - 256 * q^44 - 115 * q^45 - 312 * q^46 + 514 * q^47 - 256 * q^48 - 200 * q^50 - 52 * q^51 + 304 * q^52 - 2 * q^53 - 400 * q^54 - 320 * q^55 + 400 * q^57 - 200 * q^58 - 500 * q^59 + 80 * q^60 + 518 * q^61 + 864 * q^62 - 1024 * q^64 - 190 * q^65 + 256 * q^66 - 126 * q^67 - 208 * q^68 - 312 * q^69 + 824 * q^71 + 878 * q^73 + 1064 * q^74 - 50 * q^75 + 1600 * q^76 + 608 * q^78 - 600 * q^79 - 320 * q^80 - 421 * q^81 + 88 * q^82 + 564 * q^83 - 260 * q^85 + 1768 * q^86 + 100 * q^87 + 150 * q^89 - 920 * q^90 - 1248 * q^92 + 216 * q^93 - 2056 * q^94 + 500 * q^95 - 512 * q^96 + 772 * q^97 - 1472 * q^99

Introduction

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