LMFDB - Embedded newform 245.4.e.g.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.g.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	−0.753612	−	0.657320i	$-0.771690\pi$
$3$	1.00000	−	1.73205i	0.192450	−	0.333333i	0.946062	+	0.323987i	$0.105023\pi$
$4$	−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	$-0.367147\pi$
$13$	38.0000			0.810716			0.405358	+	0.914158i	$0.367147\pi$
$14$		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	−0.758266	−	0.651945i	$-0.773953\pi$
$17$	13.0000	−	22.5167i	0.185468	−	0.321241i	0.943734	+	0.330705i	$0.107286\pi$
$18$	−46.0000	+	79.6743i	−0.602350	+	1.04330i
$19$	50.0000	+	86.6025i	0.603726	+	1.04568i	0.992251	+	0.124246i	$0.0396511\pi$
$19$	50.0000	+	86.6025i	0.603726	+	1.04568i	−0.388526	+	0.921438i	$0.627016\pi$
$20$	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	−0.978980	−	0.203954i	$-0.934621\pi$
$31$	−54.0000	+	93.5307i	−0.312861	+	0.541891i	0.666120	+	0.745845i	$0.267954\pi$
$32$	−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	$-0.513341\pi$
$41$	−22.0000			−0.0838006			−0.0419003	+	0.999122i	$0.513341\pi$
$42$		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	$-0.872768\pi$
$47$	−257.000	−	445.137i	−0.797602	−	1.38149i	0.123571	−	0.992336i	$-0.460565\pi$
$48$	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	$-0.647333\pi$
$59$	250.000	−	433.013i	0.551648	−	0.955482i	0.998156	−	0.0607026i	$-0.0193341\pi$
$60$	40.0000	−	69.2820i	0.0860663	−	0.149071i
$61$	−259.000	−	448.601i	−0.543632	−	0.941598i	−0.998692	−	0.0511373i	$-0.983715\pi$
$61$	−259.000	−	448.601i	−0.543632	−	0.941598i	0.455060	−	0.890461i	$-0.349618\pi$
$62$	−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	$0.415204\pi$
$73$	−439.000	+	760.370i	−0.703850	+	1.21910i	−0.967105	+	0.254378i	$0.918129\pi$
$74$	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	$-0.559704\pi$
$83$	−282.000			−0.372934			−0.186467	+	0.982461i	$0.559704\pi$
$84$		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	0.817901	−	0.575360i	$-0.195138\pi$
$89$	−75.0000	−	129.904i	−0.0893257	−	0.154717i	−0.907226	+	0.420643i	$0.861805\pi$
$90$	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	$-0.564751\pi$
$97$	−386.000			−0.404045			−0.202022	+	0.979381i	$0.564751\pi$
$98$		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	−0.639699	−	0.768626i	$-0.720941\pi$
$101$	351.000	−	607.950i	0.345800	−	0.598943i	0.985499	+	0.169682i	$0.0542742\pi$
$102$	104.000	−	180.133i	0.100956	−	0.174861i
$103$	−299.000	−	517.883i	−0.286032	−	0.495423i	0.686827	−	0.726821i	$-0.259003\pi$
$103$	−299.000	−	517.883i	−0.286032	−	0.495423i	−0.972859	+	0.231399i	$0.925670\pi$
$104$		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	$-0.903232\pi$
$131$	−1104.00	−	1912.18i	−0.736312	−	1.27533i	0.217833	−	0.975986i	$-0.430101\pi$
$132$	−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	$-0.431490\pi$
$139$	700.000			0.427146			0.213573	+	0.976927i	$0.431490\pi$
$140$		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	$0.385211\pi$
$157$	−1247.00	+	2159.87i	−0.633894	+	1.09794i	−0.986748	+	0.162259i	$0.948122\pi$
$158$	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	$-0.757811\pi$
$167$	−3126.00			−1.44849			−0.724243	+	0.689545i	$0.757811\pi$
$168$		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	0.857328	−	0.514770i	$-0.172123\pi$
$173$	−39.0000	−	67.5500i	−0.0171394	−	0.0296863i	−0.874468	+	0.485083i	$0.838789\pi$
$174$	−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	$-0.616434\pi$
$181$	−1742.00			−0.715369			−0.357685	+	0.933842i	$0.616434\pi$
$182$		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	−0.999113	−	0.0421099i	$-0.986592\pi$
$199$	−1300.00	+	2251.67i	−0.463088	+	0.802092i	0.536025	+	0.844202i	$0.319925\pi$
$200$		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	$-0.0746262\pi$
$223$	6478.00			1.94529			0.972643	+	0.232303i	$0.0746262\pi$
$224$		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	−0.814934	−	0.579554i	$-0.803227\pi$
$227$	323.000	−	559.452i	0.0944417	−	0.163578i	0.909375	+	0.415976i	$0.136560\pi$
$228$	−800.000	+	1385.64i	−0.232374	+	0.402484i
$229$	1875.00	+	3247.60i	0.541063	+	0.937149i	0.998843	+	0.0480836i	$0.0153114\pi$
$229$	1875.00	+	3247.60i	0.541063	+	0.937149i	−0.457780	+	0.889065i	$0.651355\pi$
$230$	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	−0.590321	−	0.807168i	$-0.700999\pi$
$241$	1511.00	−	2617.13i	0.403867	−	0.699519i	0.994189	+	0.107649i	$0.0343323\pi$
$242$	−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	$-0.449844\pi$
$251$	1248.00			0.313837			0.156918	+	0.987612i	$0.449844\pi$
$252$		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	0.965053	−	0.262054i	$-0.0843999\pi$
$257$	1053.00	+	1823.85i	0.255581	+	0.442679i	−0.709472	+	0.704734i	$0.751067\pi$
$258$	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	$0.432935\pi$
$269$	−3275.00	+	5672.47i	−0.742306	+	1.28571i	−0.951443	+	0.307825i	$0.900399\pi$
$270$	1000.00	−	1732.05i	0.225400	−	0.390405i
$271$	−2194.00	−	3800.12i	−0.491793	−	0.851811i	0.508162	−	0.861262i	$-0.330325\pi$
$271$	−2194.00	−	3800.12i	−0.491793	−	0.851811i	−0.999955	+	0.00945040i	$0.996992\pi$
$272$	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	$-0.404892\pi$
$283$	4641.00	−	8038.45i	0.974837	−	1.68847i	0.680473	−	0.732774i	$-0.261775\pi$
$284$	−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	$-0.660350\pi$
$293$	−4842.00			−0.965436			−0.482718	+	0.875776i	$0.660350\pi$
$294$		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	$-0.422485\pi$
$307$	2594.00			0.482239			0.241120	+	0.970495i	$0.422485\pi$
$308$		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	$-0.600303\pi$
$311$	3666.00	−	6349.70i	0.668424	−	1.15774i	0.978345	−	0.206982i	$-0.0663640\pi$
$312$		0			0
$313$	781.000	+	1352.73i	0.141037	+	0.244284i	0.927888	−	0.372860i	$-0.121623\pi$
$313$	781.000	+	1352.73i	0.141037	+	0.244284i	−0.786850	+	0.617144i	$0.788290\pi$
$314$	−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	$-0.528109\pi$
$349$	−1150.00			−0.176384			−0.0881921	+	0.996103i	$0.528109\pi$
$350$		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	−0.982818	−	0.184577i	$-0.940909\pi$
$353$	−2199.00	+	3808.78i	−0.331561	+	0.574280i	0.651257	+	0.758857i	$0.274242\pi$
$354$	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	−0.995712	−	0.0925111i	$-0.970511\pi$
$367$	−2937.00	+	5087.03i	−0.417739	+	0.723545i	0.577973	+	0.816056i	$0.303844\pi$
$368$	−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	$-0.999447\pi$
$383$	−3759.00	−	6510.78i	−0.501504	−	0.868630i	0.498495	−	0.866893i	$-0.333886\pi$
$384$		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	$0.170127\pi$
$397$	6893.00	+	11939.0i	0.871410	+	1.50933i	0.0108715	+	0.999941i	$0.496539\pi$
$398$	−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	$-0.597908\pi$
$409$	5575.00	−	9656.18i	0.674000	−	1.16740i	0.976760	−	0.214335i	$-0.0687586\pi$
$410$	−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	$-0.205535\pi$
$419$	13700.0			1.59735			0.798674	+	0.601764i	$0.205535\pi$
$420$		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	$-0.480239\pi$
$433$	1118.00			0.124082			0.0620412	+	0.998074i	$0.480239\pi$
$434$		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	0.786665	−	0.617380i	$-0.211806\pi$
$439$	−1300.00	−	2251.67i	−0.141334	−	0.244798i	−0.927999	+	0.372582i	$0.878472\pi$
$440$		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	$-0.304310\pi$
$461$	11418.0			1.15356			0.576778	+	0.816901i	$0.304310\pi$
$462$		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	0.981172	−	0.193134i	$-0.0618653\pi$
$467$	3263.00	+	5651.68i	0.323327	+	0.560019i	−0.657845	+	0.753153i	$0.728532\pi$
$468$	−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	$-0.521741\pi$
$479$	8700.00	−	15068.8i	0.829881	−	1.43740i	0.898131	−	0.439728i	$-0.144925\pi$
$480$	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	$-0.536791\pi$
$503$	−2602.00			−0.230651			−0.115325	+	0.993328i	$0.536791\pi$
$504$		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	0.999861	−	0.0166899i	$-0.00531281\pi$
$509$	5575.00	+	9656.18i	0.485476	+	0.840870i	−0.514384	+	0.857560i	$0.671979\pi$
$510$	−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	−0.932314	−	0.361650i	$-0.882214\pi$
$521$	−1819.00	+	3150.60i	−0.152959	+	0.264933i	0.779355	+	0.626583i	$0.215547\pi$
$522$	2300.00	−	3983.72i	0.192851	−	0.334028i
$523$	−1039.00	−	1799.60i	−0.0868686	−	0.150461i	0.819317	−	0.573340i	$-0.194353\pi$
$523$	−1039.00	−	1799.60i	−0.0868686	−	0.150461i	−0.906186	+	0.422879i	$0.861019\pi$
$524$	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	$0.553209\pi$
$563$	−12519.0	+	21683.5i	−0.937146	+	1.62318i	−0.770763	+	0.637123i	$0.780125\pi$
$564$	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	−0.999963	−	0.00856059i	$-0.997275\pi$
$577$	−6827.00	+	11824.7i	−0.492568	+	0.853153i	0.507395	+	0.861713i	$0.330608\pi$
$578$	−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	$-0.665945\pi$
$587$	−14166.0			−0.996071			−0.498035	+	0.867157i	$0.665945\pi$
$588$		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	$0.0452998\pi$
$593$	8921.00	+	15451.6i	0.617777	+	1.07002i	−0.372114	+	0.928187i	$0.621367\pi$
$594$	−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	$-0.877211\pi$
$601$	−27302.0			−1.85303			−0.926516	+	0.376256i	$0.877211\pi$
$602$		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	0.795606	−	0.605815i	$-0.207153\pi$
$607$	−1897.00	−	3285.70i	−0.126848	−	0.219708i	−0.922454	+	0.386107i	$0.873819\pi$
$608$	−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	−0.699254	−	0.714873i	$-0.746484\pi$
$619$	4150.00	−	7188.01i	0.269471	−	0.466738i	0.968725	+	0.248135i	$0.0798178\pi$
$620$	−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	$-0.517990\pi$
$643$	−1842.00			−0.112973			−0.0564863	+	0.998403i	$0.517990\pi$
$644$		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	−0.977767	−	0.209696i	$-0.932753\pi$
$647$	−5057.00	+	8758.98i	−0.307282	+	0.532227i	0.670485	+	0.741923i	$0.266086\pi$
$648$		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	−0.951533	−	0.307546i	$-0.900492\pi$
$661$	−3559.00	+	6164.37i	−0.209424	+	0.362732i	0.742109	+	0.670279i	$0.233825\pi$
$662$	−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	$-0.841399\pi$
$677$	−15027.0	−	26027.5i	−0.853079	−	1.47758i	0.0253367	−	0.999679i	$-0.491934\pi$
$678$	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	$0.131576\pi$
$691$	14636.0	+	25350.3i	0.805759	+	1.39562i	−0.110018	+	0.993930i	$0.535091\pi$
$692$	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	0.949265	−	0.314476i	$-0.101829\pi$
$719$	3900.00	+	6755.00i	0.202289	+	0.350374i	−0.746977	+	0.664850i	$0.768495\pi$
$720$	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	$-0.429984\pi$
$727$	8554.00			0.436383			0.218191	+	0.975906i	$0.429984\pi$
$728$		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	0.900045	−	0.435796i	$-0.143533\pi$
$733$	1441.00	+	2495.89i	0.0726119	+	0.125768i	−0.827433	+	0.561564i	$0.810200\pi$
$734$	−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	0.807194	−	0.590287i	$-0.200985\pi$
$761$	−2259.00	−	3912.70i	−0.107607	−	0.186380i	−0.914800	+	0.403907i	$0.867652\pi$
$762$	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	$-0.122111\pi$
$769$	39550.0			1.85463			0.927314	+	0.374283i	$0.122111\pi$
$770$		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	$-0.661249\pi$
$773$	11061.0	−	19158.2i	0.514666	−	0.891427i	0.999855	−	0.0170180i	$-0.00541726\pi$
$774$	−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	−0.990581	−	0.136928i	$-0.956277\pi$
$787$	−8317.00	+	14405.5i	−0.376708	+	0.652477i	0.613873	+	0.789405i	$0.289611\pi$
$788$	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	$-0.710044\pi$
$797$	−27586.0			−1.22603			−0.613015	+	0.790071i	$0.710044\pi$
$798$		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	$-0.569687\pi$
$811$	−10032.0			−0.434366			−0.217183	+	0.976131i	$0.569687\pi$
$812$		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	$0.344860\pi$
$829$	−12675.0	+	21953.7i	−0.531026	+	0.919765i	−0.999344	+	0.0362048i	$0.988473\pi$
$830$	−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	$-0.895331\pi$
$839$	−46000.0			−1.89284			−0.946422	+	0.322932i	$0.895331\pi$
$840$		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	$-0.389184\pi$
$853$	16998.0			0.682298			0.341149	+	0.940009i	$0.389184\pi$
$854$		0			0
$855$	11500.0			0.459990
$856$		0			0
$857$	−13247.0	+	22944.5i	−0.528015	+	0.914549i	0.471452	+	0.881892i	$0.343730\pi$
$857$	−13247.0	+	22944.5i	−0.528015	+	0.914549i	−0.999467	+	0.0326569i	$0.989603\pi$
$858$	−4864.00	+	8424.70i	−0.193536	+	0.335215i
$859$	−10750.0	−	18619.5i	−0.426991	−	0.739570i	0.569613	−	0.821913i	$-0.307093\pi$
$859$	−10750.0	−	18619.5i	−0.426991	−	0.739570i	−0.996604	+	0.0823429i	$0.973760\pi$
$860$	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	$-0.716895\pi$
$881$	−32942.0			−1.25976			−0.629878	+	0.776694i	$0.716895\pi$
$882$		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	$-0.905613\pi$
$887$	−19317.0	−	33458.0i	−0.731230	−	1.26653i	0.225127	−	0.974329i	$-0.427720\pi$
$888$		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	$-0.837708\pi$
$929$	−24325.0	−	42132.1i	−0.859071	−	1.48796i	0.0137443	−	0.999906i	$-0.495625\pi$
$930$	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	$-0.436692\pi$
$937$	11334.0			0.395161			0.197580	+	0.980287i	$0.436692\pi$
$938$		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	$0.348261\pi$
$941$	−15589.0	+	27000.9i	−0.540050	+	0.935394i	−0.998901	+	0.0468803i	$0.985072\pi$
$942$	−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	0.993938	−	0.109943i	$-0.0350668\pi$
$971$	12156.0	+	21054.8i	0.401756	+	0.695861i	−0.592182	+	0.805804i	$0.701733\pi$
$972$	−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	$-0.592718\pi$
$983$	21141.0	−	36617.3i	0.685954	−	1.18811i	0.973136	−	0.230232i	$-0.0739484\pi$
$984$		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	$0.334113\pi$
$997$	−15807.0	+	27378.5i	−0.502119	+	0.869696i	−0.999997	+	0.00244862i	$0.999221\pi$
$998$	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.g.116.1		2
7.2	even	3	inner	245.4.e.g.226.1		2
7.3	odd	6		5.4.a.a.1.1	✓	1
7.4	even	3		245.4.a.a.1.1		1
7.5	odd	6		245.4.e.f.226.1		2
7.6	odd	2		245.4.e.f.116.1		2
21.11	odd	6		2205.4.a.q.1.1		1
21.17	even	6		45.4.a.d.1.1		1
28.3	even	6		80.4.a.d.1.1		1
35.3	even	12		25.4.b.a.24.2		2
35.4	even	6		1225.4.a.k.1.1		1
35.17	even	12		25.4.b.a.24.1		2
35.24	odd	6		25.4.a.c.1.1		1
56.3	even	6		320.4.a.h.1.1		1
56.45	odd	6		320.4.a.g.1.1		1
63.31	odd	6		405.4.e.l.136.1		2
63.38	even	6		405.4.e.c.271.1		2
63.52	odd	6		405.4.e.l.271.1		2
63.59	even	6		405.4.e.c.136.1		2
77.10	even	6		605.4.a.d.1.1		1
84.59	odd	6		720.4.a.u.1.1		1
91.38	odd	6		845.4.a.b.1.1		1
105.17	odd	12		225.4.b.c.199.2		2
105.38	odd	12		225.4.b.c.199.1		2
105.59	even	6		225.4.a.b.1.1		1
112.3	even	12		1280.4.d.l.641.1		2
112.45	odd	12		1280.4.d.e.641.2		2
112.59	even	12		1280.4.d.l.641.2		2
112.101	odd	12		1280.4.d.e.641.1		2
119.101	odd	6		1445.4.a.a.1.1		1
133.94	even	6		1805.4.a.h.1.1		1
140.3	odd	12		400.4.c.k.49.1		2
140.59	even	6		400.4.a.m.1.1		1
140.87	odd	12		400.4.c.k.49.2		2
280.59	even	6		1600.4.a.s.1.1		1
280.269	odd	6		1600.4.a.bi.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5.4.a.a.1.1	✓	1	7.3	odd	6
25.4.a.c.1.1		1	35.24	odd	6
25.4.b.a.24.1		2	35.17	even	12
25.4.b.a.24.2		2	35.3	even	12
45.4.a.d.1.1		1	21.17	even	6
80.4.a.d.1.1		1	28.3	even	6
225.4.a.b.1.1		1	105.59	even	6
225.4.b.c.199.1		2	105.38	odd	12
225.4.b.c.199.2		2	105.17	odd	12
245.4.a.a.1.1		1	7.4	even	3
245.4.e.f.116.1		2	7.6	odd	2
245.4.e.f.226.1		2	7.5	odd	6
245.4.e.g.116.1		2	1.1	even	1	trivial
245.4.e.g.226.1		2	7.2	even	3	inner
320.4.a.g.1.1		1	56.45	odd	6
320.4.a.h.1.1		1	56.3	even	6
400.4.a.m.1.1		1	140.59	even	6
400.4.c.k.49.1		2	140.3	odd	12
400.4.c.k.49.2		2	140.87	odd	12
405.4.e.c.136.1		2	63.59	even	6
405.4.e.c.271.1		2	63.38	even	6
405.4.e.l.136.1		2	63.31	odd	6
405.4.e.l.271.1		2	63.52	odd	6
605.4.a.d.1.1		1	77.10	even	6
720.4.a.u.1.1		1	84.59	odd	6
845.4.a.b.1.1		1	91.38	odd	6
1225.4.a.k.1.1		1	35.4	even	6
1280.4.d.e.641.1		2	112.101	odd	12
1280.4.d.e.641.2		2	112.45	odd	12
1280.4.d.l.641.1		2	112.3	even	12
1280.4.d.l.641.2		2	112.59	even	12
1445.4.a.a.1.1		1	119.101	odd	6
1600.4.a.s.1.1		1	280.59	even	6
1600.4.a.bi.1.1		1	280.269	odd	6
1805.4.a.h.1.1		1	133.94	even	6
2205.4.a.q.1.1		1	21.11	odd	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

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