LMFDB - Embedded newform 294.4.e.i.67.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [294,4,Mod(67,294)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(294, 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("294.67");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 294 = 2 \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	294.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:	$17.3465615417$
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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 42)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			67.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	294.67
Dual form			294.4.e.i.79.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 + 1.73205i) q^{2} +(1.50000 - 2.59808i) q^{3} +(-2.00000 + 3.46410i) q^{4} +(-3.00000 - 5.19615i) q^{5} +6.00000 q^{6} -8.00000 q^{8} +(-4.50000 - 7.79423i) q^{9} +O(q^{10})$	\(q+(1.00000 + 1.73205i) q^{2} +(1.50000 - 2.59808i) q^{3} +(-2.00000 + 3.46410i) q^{4} +(-3.00000 - 5.19615i) q^{5} +6.00000 q^{6} -8.00000 q^{8} +(-4.50000 - 7.79423i) q^{9} +(6.00000 - 10.3923i) q^{10} +(15.0000 - 25.9808i) q^{11} +(6.00000 + 10.3923i) q^{12} -53.0000 q^{13} -18.0000 q^{15} +(-8.00000 - 13.8564i) q^{16} +(-42.0000 + 72.7461i) q^{17} +(9.00000 - 15.5885i) q^{18} +(-48.5000 - 84.0045i) q^{19} +24.0000 q^{20} +60.0000 q^{22} +(-42.0000 - 72.7461i) q^{23} +(-12.0000 + 20.7846i) q^{24} +(44.5000 - 77.0763i) q^{25} +(-53.0000 - 91.7987i) q^{26} -27.0000 q^{27} -180.000 q^{29} +(-18.0000 - 31.1769i) q^{30} +(89.5000 - 155.019i) q^{31} +(16.0000 - 27.7128i) q^{32} +(-45.0000 - 77.9423i) q^{33} -168.000 q^{34} +36.0000 q^{36} +(72.5000 + 125.574i) q^{37} +(97.0000 - 168.009i) q^{38} +(-79.5000 + 137.698i) q^{39} +(24.0000 + 41.5692i) q^{40} -126.000 q^{41} -325.000 q^{43} +(60.0000 + 103.923i) q^{44} +(-27.0000 + 46.7654i) q^{45} +(84.0000 - 145.492i) q^{46} +(-183.000 - 316.965i) q^{47} -48.0000 q^{48} +178.000 q^{50} +(126.000 + 218.238i) q^{51} +(106.000 - 183.597i) q^{52} +(384.000 - 665.108i) q^{53} +(-27.0000 - 46.7654i) q^{54} -180.000 q^{55} -291.000 q^{57} +(-180.000 - 311.769i) q^{58} +(-132.000 + 228.631i) q^{59} +(36.0000 - 62.3538i) q^{60} +(409.000 + 708.409i) q^{61} +358.000 q^{62} +64.0000 q^{64} +(159.000 + 275.396i) q^{65} +(90.0000 - 155.885i) q^{66} +(261.500 - 452.931i) q^{67} +(-168.000 - 290.985i) q^{68} -252.000 q^{69} -342.000 q^{71} +(36.0000 + 62.3538i) q^{72} +(-21.5000 + 37.2391i) q^{73} +(-145.000 + 251.147i) q^{74} +(-133.500 - 231.229i) q^{75} +388.000 q^{76} -318.000 q^{78} +(585.500 + 1014.12i) q^{79} +(-48.0000 + 83.1384i) q^{80} +(-40.5000 + 70.1481i) q^{81} +(-126.000 - 218.238i) q^{82} +810.000 q^{83} +504.000 q^{85} +(-325.000 - 562.917i) q^{86} +(-270.000 + 467.654i) q^{87} +(-120.000 + 207.846i) q^{88} +(-300.000 - 519.615i) q^{89} -108.000 q^{90} +336.000 q^{92} +(-268.500 - 465.056i) q^{93} +(366.000 - 633.931i) q^{94} +(-291.000 + 504.027i) q^{95} +(-48.0000 - 83.1384i) q^{96} -386.000 q^{97} -270.000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} + 3 q^{3} - 4 q^{4} - 6 q^{5} + 12 q^{6} - 16 q^{8} - 9 q^{9}+O(q^{10}) $ 2 * q + 2 * q^2 + 3 * q^3 - 4 * q^4 - 6 * q^5 + 12 * q^6 - 16 * q^8 - 9 * q^9	\( 2 q + 2 q^{2} + 3 q^{3} - 4 q^{4} - 6 q^{5} + 12 q^{6} - 16 q^{8} - 9 q^{9} + 12 q^{10} + 30 q^{11} + 12 q^{12} - 106 q^{13} - 36 q^{15} - 16 q^{16} - 84 q^{17} + 18 q^{18} - 97 q^{19} + 48 q^{20} + 120 q^{22} - 84 q^{23} - 24 q^{24} + 89 q^{25} - 106 q^{26} - 54 q^{27} - 360 q^{29} - 36 q^{30} + 179 q^{31} + 32 q^{32} - 90 q^{33} - 336 q^{34} + 72 q^{36} + 145 q^{37} + 194 q^{38} - 159 q^{39} + 48 q^{40} - 252 q^{41} - 650 q^{43} + 120 q^{44} - 54 q^{45} + 168 q^{46} - 366 q^{47} - 96 q^{48} + 356 q^{50} + 252 q^{51} + 212 q^{52} + 768 q^{53} - 54 q^{54} - 360 q^{55} - 582 q^{57} - 360 q^{58} - 264 q^{59} + 72 q^{60} + 818 q^{61} + 716 q^{62} + 128 q^{64} + 318 q^{65} + 180 q^{66} + 523 q^{67} - 336 q^{68} - 504 q^{69} - 684 q^{71} + 72 q^{72} - 43 q^{73} - 290 q^{74} - 267 q^{75} + 776 q^{76} - 636 q^{78} + 1171 q^{79} - 96 q^{80} - 81 q^{81} - 252 q^{82} + 1620 q^{83} + 1008 q^{85} - 650 q^{86} - 540 q^{87} - 240 q^{88} - 600 q^{89} - 216 q^{90} + 672 q^{92} - 537 q^{93} + 732 q^{94} - 582 q^{95} - 96 q^{96} - 772 q^{97} - 540 q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 + 3 * q^3 - 4 * q^4 - 6 * q^5 + 12 * q^6 - 16 * q^8 - 9 * q^9 + 12 * q^10 + 30 * q^11 + 12 * q^12 - 106 * q^13 - 36 * q^15 - 16 * q^16 - 84 * q^17 + 18 * q^18 - 97 * q^19 + 48 * q^20 + 120 * q^22 - 84 * q^23 - 24 * q^24 + 89 * q^25 - 106 * q^26 - 54 * q^27 - 360 * q^29 - 36 * q^30 + 179 * q^31 + 32 * q^32 - 90 * q^33 - 336 * q^34 + 72 * q^36 + 145 * q^37 + 194 * q^38 - 159 * q^39 + 48 * q^40 - 252 * q^41 - 650 * q^43 + 120 * q^44 - 54 * q^45 + 168 * q^46 - 366 * q^47 - 96 * q^48 + 356 * q^50 + 252 * q^51 + 212 * q^52 + 768 * q^53 - 54 * q^54 - 360 * q^55 - 582 * q^57 - 360 * q^58 - 264 * q^59 + 72 * q^60 + 818 * q^61 + 716 * q^62 + 128 * q^64 + 318 * q^65 + 180 * q^66 + 523 * q^67 - 336 * q^68 - 504 * q^69 - 684 * q^71 + 72 * q^72 - 43 * q^73 - 290 * q^74 - 267 * q^75 + 776 * q^76 - 636 * q^78 + 1171 * q^79 - 96 * q^80 - 81 * q^81 - 252 * q^82 + 1620 * q^83 + 1008 * q^85 - 650 * q^86 - 540 * q^87 - 240 * q^88 - 600 * q^89 - 216 * q^90 + 672 * q^92 - 537 * q^93 + 732 * q^94 - 582 * q^95 - 96 * q^96 - 772 * q^97 - 540 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/294\mathbb{Z}\right)^\times$.

$n$	$197$	$199$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	1.00000	+	1.73205i	0.353553	+	0.612372i
$2$	1.00000	+	1.73205i	0.353553	+	0.612372i
$3$	1.50000	−	2.59808i	0.288675	−	0.500000i
$3$	1.50000	−	2.59808i	0.288675	−	0.500000i
$4$	−2.00000	+	3.46410i	−0.250000	+	0.433013i
$5$	−3.00000	−	5.19615i	−0.268328	−	0.464758i	0.700102	−	0.714043i	$-0.253138\pi$
$5$	−3.00000	−	5.19615i	−0.268328	−	0.464758i	−0.968430	+	0.249285i	$0.919804\pi$
$6$	6.00000			0.408248
$7$		0			0
$7$		0			0
$8$	−8.00000			−0.353553
$9$	−4.50000	−	7.79423i	−0.166667	−	0.288675i
$10$	6.00000	−	10.3923i	0.189737	−	0.328634i
$11$	15.0000	−	25.9808i	0.411152	−	0.712136i	−0.583864	−	0.811851i	$-0.698460\pi$
$11$	15.0000	−	25.9808i	0.411152	−	0.712136i	0.995016	+	0.0997155i	$0.0317933\pi$
$12$	6.00000	+	10.3923i	0.144338	+	0.250000i
$13$	−53.0000			−1.13074			−0.565368	−	0.824839i	$-0.691266\pi$
$13$	−53.0000			−1.13074			−0.565368	+	0.824839i	$0.691266\pi$
$14$		0			0
$15$	−18.0000			−0.309839
$16$	−8.00000	−	13.8564i	−0.125000	−	0.216506i
$17$	−42.0000	+	72.7461i	−0.599206	+	1.03785i	0.393733	+	0.919225i	$0.371183\pi$
$17$	−42.0000	+	72.7461i	−0.599206	+	1.03785i	−0.992939	+	0.118630i	$0.962150\pi$
$18$	9.00000	−	15.5885i	0.117851	−	0.204124i
$19$	−48.5000	−	84.0045i	−0.585614	−	1.01431i	−0.994799	−	0.101861i	$-0.967520\pi$
$19$	−48.5000	−	84.0045i	−0.585614	−	1.01431i	0.409185	−	0.912452i	$-0.365813\pi$
$20$	24.0000			0.268328
$21$		0			0
$22$	60.0000			0.581456
$23$	−42.0000	−	72.7461i	−0.380765	−	0.659505i	0.610406	−	0.792088i	$-0.291006\pi$
$23$	−42.0000	−	72.7461i	−0.380765	−	0.659505i	−0.991172	+	0.132583i	$0.957673\pi$
$24$	−12.0000	+	20.7846i	−0.102062	+	0.176777i
$25$	44.5000	−	77.0763i	0.356000	−	0.616610i
$26$	−53.0000	−	91.7987i	−0.399775	−	0.692431i
$27$	−27.0000			−0.192450
$28$		0			0
$29$	−180.000			−1.15259			−0.576296	−	0.817241i	$-0.695502\pi$
$29$	−180.000			−1.15259			−0.576296	+	0.817241i	$0.695502\pi$
$30$	−18.0000	−	31.1769i	−0.109545	−	0.189737i
$31$	89.5000	−	155.019i	0.518538	−	0.898134i	−0.481230	−	0.876594i	$-0.659810\pi$
$31$	89.5000	−	155.019i	0.518538	−	0.898134i	0.999768	−	0.0215397i	$-0.00685682\pi$
$32$	16.0000	−	27.7128i	0.0883883	−	0.153093i
$33$	−45.0000	−	77.9423i	−0.237379	−	0.411152i
$34$	−168.000			−0.847405
$35$		0			0
$36$	36.0000			0.166667
$37$	72.5000	+	125.574i	0.322133	+	0.557951i	0.980928	−	0.194372i	$-0.0622668\pi$
$37$	72.5000	+	125.574i	0.322133	+	0.557951i	−0.658795	+	0.752323i	$0.728933\pi$
$38$	97.0000	−	168.009i	0.414092	−	0.717228i
$39$	−79.5000	+	137.698i	−0.326415	+	0.565368i
$40$	24.0000	+	41.5692i	0.0948683	+	0.164317i
$41$	−126.000			−0.479949			−0.239974	−	0.970779i	$-0.577139\pi$
$41$	−126.000			−0.479949			−0.239974	+	0.970779i	$0.577139\pi$
$42$		0			0
$43$	−325.000			−1.15261			−0.576303	−	0.817236i	$-0.695505\pi$
$43$	−325.000			−1.15261			−0.576303	+	0.817236i	$0.695505\pi$
$44$	60.0000	+	103.923i	0.205576	+	0.356068i
$45$	−27.0000	+	46.7654i	−0.0894427	+	0.154919i
$46$	84.0000	−	145.492i	0.269242	−	0.466341i
$47$	−183.000	−	316.965i	−0.567942	−	0.983705i	−0.996769	−	0.0803184i	$-0.974406\pi$
$47$	−183.000	−	316.965i	−0.567942	−	0.983705i	0.428827	−	0.903387i	$-0.358927\pi$
$48$	−48.0000			−0.144338
$49$		0			0
$50$	178.000			0.503460
$51$	126.000	+	218.238i	0.345952	+	0.599206i
$52$	106.000	−	183.597i	0.282684	−	0.489623i
$53$	384.000	−	665.108i	0.995216	−	1.72376i	0.413000	−	0.910731i	$-0.364481\pi$
$53$	384.000	−	665.108i	0.995216	−	1.72376i	0.582217	−	0.813034i	$-0.302186\pi$
$54$	−27.0000	−	46.7654i	−0.0680414	−	0.117851i
$55$	−180.000			−0.441294
$56$		0			0
$57$	−291.000			−0.676209
$58$	−180.000	−	311.769i	−0.407503	−	0.705815i
$59$	−132.000	+	228.631i	−0.291270	+	0.504495i	−0.974110	−	0.226073i	$-0.927411\pi$
$59$	−132.000	+	228.631i	−0.291270	+	0.504495i	0.682840	+	0.730568i	$0.260745\pi$
$60$	36.0000	−	62.3538i	0.0774597	−	0.134164i
$61$	409.000	+	708.409i	0.858477	+	1.48693i	0.873382	+	0.487036i	$0.161922\pi$
$61$	409.000	+	708.409i	0.858477	+	1.48693i	−0.0149048	+	0.999889i	$0.504745\pi$
$62$	358.000			0.733323
$63$		0			0
$64$	64.0000			0.125000
$65$	159.000	+	275.396i	0.303408	+	0.525518i
$66$	90.0000	−	155.885i	0.167852	−	0.290728i
$67$	261.500	−	452.931i	0.476826	−	0.825886i	−0.522822	−	0.852442i	$-0.675121\pi$
$67$	261.500	−	452.931i	0.476826	−	0.825886i	0.999647	+	0.0265560i	$0.00845402\pi$
$68$	−168.000	−	290.985i	−0.299603	−	0.518927i
$69$	−252.000			−0.439670
$70$		0			0
$71$	−342.000			−0.571661			−0.285831	−	0.958280i	$-0.592269\pi$
$71$	−342.000			−0.571661			−0.285831	+	0.958280i	$0.592269\pi$
$72$	36.0000	+	62.3538i	0.0589256	+	0.102062i
$73$	−21.5000	+	37.2391i	−0.0344710	+	0.0597056i	−0.882746	−	0.469850i	$-0.844308\pi$
$73$	−21.5000	+	37.2391i	−0.0344710	+	0.0597056i	0.848275	+	0.529556i	$0.177641\pi$
$74$	−145.000	+	251.147i	−0.227783	+	0.394531i
$75$	−133.500	−	231.229i	−0.205537	−	0.356000i
$76$	388.000			0.585614
$77$		0			0
$78$	−318.000			−0.461621
$79$	585.500	+	1014.12i	0.833847	+	1.44427i	0.894966	+	0.446135i	$0.147200\pi$
$79$	585.500	+	1014.12i	0.833847	+	1.44427i	−0.0611191	+	0.998130i	$0.519467\pi$
$80$	−48.0000	+	83.1384i	−0.0670820	+	0.116190i
$81$	−40.5000	+	70.1481i	−0.0555556	+	0.0962250i
$82$	−126.000	−	218.238i	−0.169687	−	0.293907i
$83$	810.000			1.07119			0.535597	−	0.844474i	$-0.320087\pi$
$83$	810.000			1.07119			0.535597	+	0.844474i	$0.320087\pi$
$84$		0			0
$85$	504.000			0.643135
$86$	−325.000	−	562.917i	−0.407508	−	0.705824i
$87$	−270.000	+	467.654i	−0.332725	+	0.576296i
$88$	−120.000	+	207.846i	−0.145364	+	0.251778i
$89$	−300.000	−	519.615i	−0.357303	−	0.618866i	0.630207	−	0.776428i	$-0.282970\pi$
$89$	−300.000	−	519.615i	−0.357303	−	0.618866i	−0.987509	+	0.157561i	$0.949637\pi$
$90$	−108.000			−0.126491
$91$		0			0
$92$	336.000			0.380765
$93$	−268.500	−	465.056i	−0.299378	−	0.518538i
$94$	366.000	−	633.931i	0.401596	−	0.695585i
$95$	−291.000	+	504.027i	−0.314273	+	0.544337i
$96$	−48.0000	−	83.1384i	−0.0510310	−	0.0883883i
$97$	−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
$99$	−270.000			−0.274101
$100$	178.000	+	308.305i	0.178000	+	0.308305i
$101$	309.000	−	535.204i	0.304422	−	0.527275i	−0.672710	−	0.739906i	$-0.734870\pi$
$101$	309.000	−	535.204i	0.304422	−	0.527275i	0.977133	+	0.212631i	$0.0682033\pi$
$102$	−252.000	+	436.477i	−0.244625	+	0.423702i
$103$	737.500	+	1277.39i	0.705515	+	1.22199i	0.966505	+	0.256646i	$0.0826175\pi$
$103$	737.500	+	1277.39i	0.705515	+	1.22199i	−0.260991	+	0.965341i	$0.584049\pi$
$104$	424.000			0.399775
$105$		0			0
$106$	1536.00			1.40745
$107$	−942.000	−	1631.59i	−0.851090	−	1.47413i	−0.880226	−	0.474555i	$-0.842609\pi$
$107$	−942.000	−	1631.59i	−0.851090	−	1.47413i	0.0291364	−	0.999575i	$-0.490724\pi$
$108$	54.0000	−	93.5307i	0.0481125	−	0.0833333i
$109$	−206.500	+	357.668i	−0.181460	+	0.314298i	−0.942378	−	0.334550i	$-0.891416\pi$
$109$	−206.500	+	357.668i	−0.181460	+	0.314298i	0.760918	+	0.648848i	$0.224749\pi$
$110$	−180.000	−	311.769i	−0.156021	−	0.270237i
$111$	435.000			0.371967
$112$		0			0
$113$	−882.000			−0.734262			−0.367131	−	0.930169i	$-0.619660\pi$
$113$	−882.000			−0.734262			−0.367131	+	0.930169i	$0.619660\pi$
$114$	−291.000	−	504.027i	−0.239076	−	0.414092i
$115$	−252.000	+	436.477i	−0.204340	+	0.353928i
$116$	360.000	−	623.538i	0.288148	−	0.499087i
$117$	238.500	+	413.094i	0.188456	+	0.326415i
$118$	−528.000			−0.411918
$119$		0			0
$120$	144.000			0.109545
$121$	215.500	+	373.257i	0.161908	+	0.280433i
$122$	−818.000	+	1416.82i	−0.607035	+	1.05142i
$123$	−189.000	+	327.358i	−0.138549	+	0.239974i
$124$	358.000	+	620.074i	0.259269	+	0.449067i
$125$	−1284.00			−0.918756
$126$		0			0
$127$	2483.00			1.73489			0.867443	−	0.497536i	$-0.165762\pi$
$127$	2483.00			1.73489			0.867443	+	0.497536i	$0.165762\pi$
$128$	64.0000	+	110.851i	0.0441942	+	0.0765466i
$129$	−487.500	+	844.375i	−0.332729	+	0.576303i
$130$	−318.000	+	550.792i	−0.214542	+	0.371597i
$131$	1059.00	+	1834.24i	0.706300	+	1.22335i	0.966220	+	0.257717i	$0.0829702\pi$
$131$	1059.00	+	1834.24i	0.706300	+	1.22335i	−0.259921	+	0.965630i	$0.583696\pi$
$132$	360.000			0.237379
$133$		0			0
$134$	1046.00			0.674333
$135$	81.0000	+	140.296i	0.0516398	+	0.0894427i
$136$	336.000	−	581.969i	0.211851	−	0.366937i
$137$	−1506.00	+	2608.47i	−0.939170	+	1.62669i	−0.172146	+	0.985071i	$0.555070\pi$
$137$	−1506.00	+	2608.47i	−0.939170	+	1.62669i	−0.767024	+	0.641618i	$0.778263\pi$
$138$	−252.000	−	436.477i	−0.155447	−	0.269242i
$139$	37.0000			0.0225777			0.0112888	−	0.999936i	$-0.496407\pi$
$139$	37.0000			0.0225777			0.0112888	+	0.999936i	$0.496407\pi$
$140$		0			0
$141$	−1098.00			−0.655803
$142$	−342.000	−	592.361i	−0.202113	−	0.350069i
$143$	−795.000	+	1376.98i	−0.464904	+	0.805237i
$144$	−72.0000	+	124.708i	−0.0416667	+	0.0721688i
$145$	540.000	+	935.307i	0.309273	+	0.535676i
$146$	−86.0000			−0.0487494
$147$		0			0
$148$	−580.000			−0.322133
$149$	822.000	+	1423.75i	0.451952	+	0.782804i	0.998507	−	0.0546191i	$-0.0173945\pi$
$149$	822.000	+	1423.75i	0.451952	+	0.782804i	−0.546555	+	0.837423i	$0.684061\pi$
$150$	267.000	−	462.458i	0.145336	−	0.251730i
$151$	−544.000	+	942.236i	−0.293179	+	0.507802i	−0.974560	−	0.224128i	$-0.928047\pi$
$151$	−544.000	+	942.236i	−0.293179	+	0.507802i	0.681380	+	0.731930i	$0.261380\pi$
$152$	388.000	+	672.036i	0.207046	+	0.358614i
$153$	756.000			0.399470
$154$		0			0
$155$	−1074.00			−0.556553
$156$	−318.000	−	550.792i	−0.163208	−	0.282684i
$157$	253.000	−	438.209i	0.128609	−	0.222757i	−0.794529	−	0.607226i	$-0.792282\pi$
$157$	253.000	−	438.209i	0.128609	−	0.222757i	0.923138	+	0.384469i	$0.125615\pi$
$158$	−1171.00	+	2028.23i	−0.589619	+	1.02125i
$159$	−1152.00	−	1995.32i	−0.574588	−	0.995216i
$160$	−192.000			−0.0948683
$161$		0			0
$162$	−162.000			−0.0785674
$163$	−922.000	−	1596.95i	−0.443047	−	0.767379i	0.554867	−	0.831939i	$-0.312769\pi$
$163$	−922.000	−	1596.95i	−0.443047	−	0.767379i	−0.997914	+	0.0645596i	$0.979436\pi$
$164$	252.000	−	436.477i	0.119987	−	0.207824i
$165$	−270.000	+	467.654i	−0.127391	+	0.220647i
$166$	810.000	+	1402.96i	0.378724	+	0.655969i
$167$	−162.000			−0.0750655			−0.0375327	−	0.999295i	$-0.511950\pi$
$167$	−162.000			−0.0750655			−0.0375327	+	0.999295i	$0.511950\pi$
$168$		0			0
$169$	612.000			0.278562
$170$	504.000	+	872.954i	0.227383	+	0.393838i
$171$	−436.500	+	756.040i	−0.195205	+	0.338104i
$172$	650.000	−	1125.83i	0.288151	−	0.499093i
$173$	−1362.00	−	2359.05i	−0.598560	−	1.03674i	−0.993034	−	0.117830i	$-0.962406\pi$
$173$	−1362.00	−	2359.05i	−0.598560	−	1.03674i	0.394473	−	0.918907i	$-0.370927\pi$
$174$	−1080.00			−0.470544
$175$		0			0
$176$	−480.000			−0.205576
$177$	396.000	+	685.892i	0.168165	+	0.291270i
$178$	600.000	−	1039.23i	0.252651	−	0.437605i
$179$	627.000	−	1086.00i	0.261811	−	0.453470i	−0.704912	−	0.709295i	$-0.749014\pi$
$179$	627.000	−	1086.00i	0.261811	−	0.453470i	0.966723	+	0.255825i	$0.0823469\pi$
$180$	−108.000	−	187.061i	−0.0447214	−	0.0774597i
$181$	1807.00			0.742062			0.371031	−	0.928620i	$-0.379004\pi$
$181$	1807.00			0.742062			0.371031	+	0.928620i	$0.379004\pi$
$182$		0			0
$183$	2454.00			0.991284
$184$	336.000	+	581.969i	0.134621	+	0.233170i
$185$	435.000	−	753.442i	0.172875	−	0.299428i
$186$	537.000	−	930.111i	0.211692	−	0.366662i
$187$	1260.00	+	2182.38i	0.492729	+	0.853432i
$188$	1464.00			0.567942
$189$		0			0
$190$	−1164.00			−0.444450
$191$	−357.000	−	618.342i	−0.135244	−	0.234250i	0.790447	−	0.612531i	$-0.209849\pi$
$191$	−357.000	−	618.342i	−0.135244	−	0.234250i	−0.925691	+	0.378281i	$0.876515\pi$
$192$	96.0000	−	166.277i	0.0360844	−	0.0625000i
$193$	1854.50	−	3212.09i	0.691657	−	1.19799i	−0.279637	−	0.960106i	$-0.590214\pi$
$193$	1854.50	−	3212.09i	0.691657	−	1.19799i	0.971295	−	0.237880i	$-0.0764524\pi$
$194$	−386.000	−	668.572i	−0.142851	−	0.247426i
$195$	954.000			0.350345
$196$		0			0
$197$	−1044.00			−0.377573			−0.188787	−	0.982018i	$-0.560455\pi$
$197$	−1044.00			−0.377573			−0.188787	+	0.982018i	$0.560455\pi$
$198$	−270.000	−	467.654i	−0.0969094	−	0.167852i
$199$	−68.0000	+	117.779i	−0.0242231	+	0.0419556i	−0.877883	−	0.478875i	$-0.841045\pi$
$199$	−68.0000	+	117.779i	−0.0242231	+	0.0419556i	0.853660	+	0.520831i	$0.174378\pi$
$200$	−356.000	+	616.610i	−0.125865	+	0.218005i
$201$	−784.500	−	1358.79i	−0.275295	−	0.476826i
$202$	1236.00			0.430518
$203$		0			0
$204$	−1008.00			−0.345952
$205$	378.000	+	654.715i	0.128784	+	0.223060i
$206$	−1475.00	+	2554.77i	−0.498874	+	0.864076i
$207$	−378.000	+	654.715i	−0.126922	+	0.219835i
$208$	424.000	+	734.390i	0.141342	+	0.244811i
$209$	−2910.00			−0.963105
$210$		0			0
$211$	1484.00			0.484184			0.242092	−	0.970253i	$-0.422166\pi$
$211$	1484.00			0.484184			0.242092	+	0.970253i	$0.422166\pi$
$212$	1536.00	+	2660.43i	0.497608	+	0.861882i
$213$	−513.000	+	888.542i	−0.165024	+	0.285831i
$214$	1884.00	−	3263.18i	0.601811	−	1.04237i
$215$	975.000	+	1688.75i	0.309277	+	0.535683i
$216$	216.000			0.0680414
$217$		0			0
$218$	−826.000			−0.256623
$219$	64.5000	+	111.717i	0.0199019	+	0.0344710i
$220$	360.000	−	623.538i	0.110324	−	0.191086i
$221$	2226.00	−	3855.55i	0.677543	−	1.17354i
$222$	435.000	+	753.442i	0.131510	+	0.227783i
$223$	2032.00			0.610192			0.305096	−	0.952322i	$-0.401311\pi$
$223$	2032.00			0.610192			0.305096	+	0.952322i	$0.401311\pi$
$224$		0			0
$225$	−801.000			−0.237333
$226$	−882.000	−	1527.67i	−0.259601	−	0.449642i
$227$	3099.00	−	5367.63i	0.906114	−	1.56944i	0.0866989	−	0.996235i	$-0.472368\pi$
$227$	3099.00	−	5367.63i	0.906114	−	1.56944i	0.819415	−	0.573201i	$-0.194298\pi$
$228$	582.000	−	1008.05i	0.169052	−	0.292807i
$229$	−2295.50	−	3975.92i	−0.662406	−	1.14732i	−0.979982	−	0.199088i	$-0.936202\pi$
$229$	−2295.50	−	3975.92i	−0.662406	−	1.14732i	0.317576	−	0.948233i	$-0.397131\pi$
$230$	−1008.00			−0.288981
$231$		0			0
$232$	1440.00			0.407503
$233$	−2265.00	−	3923.10i	−0.636846	−	1.10305i	−0.986121	−	0.166029i	$-0.946905\pi$
$233$	−2265.00	−	3923.10i	−0.636846	−	1.10305i	0.349275	−	0.937020i	$-0.386428\pi$
$234$	−477.000	+	826.188i	−0.133258	+	0.230810i
$235$	−1098.00	+	1901.79i	−0.304790	+	0.527912i
$236$	−528.000	−	914.523i	−0.145635	−	0.252247i
$237$	3513.00			0.962843
$238$		0			0
$239$	1530.00			0.414090			0.207045	−	0.978331i	$-0.433615\pi$
$239$	1530.00			0.414090			0.207045	+	0.978331i	$0.433615\pi$
$240$	144.000	+	249.415i	0.0387298	+	0.0670820i
$241$	2767.00	−	4792.58i	0.739577	−	1.28099i	−0.213108	−	0.977029i	$-0.568359\pi$
$241$	2767.00	−	4792.58i	0.739577	−	1.28099i	0.952686	−	0.303957i	$-0.0983079\pi$
$242$	−431.000	+	746.514i	−0.114486	+	0.198296i
$243$	121.500	+	210.444i	0.0320750	+	0.0555556i
$244$	−3272.00			−0.858477
$245$		0			0
$246$	−756.000			−0.195938
$247$	2570.50	+	4452.24i	0.662174	+	1.14692i
$248$	−716.000	+	1240.15i	−0.183331	+	0.317538i
$249$	1215.00	−	2104.44i	0.309227	−	0.535597i
$250$	−1284.00	−	2223.95i	−0.324829	−	0.562621i
$251$	468.000			0.117689			0.0588444	−	0.998267i	$-0.481258\pi$
$251$	468.000			0.117689			0.0588444	+	0.998267i	$0.481258\pi$
$252$		0			0
$253$	−2520.00			−0.626210
$254$	2483.00	+	4300.68i	0.613375	+	1.06240i
$255$	756.000	−	1309.43i	0.185657	−	0.321568i
$256$	−128.000	+	221.703i	−0.0312500	+	0.0541266i
$257$	−1245.00	−	2156.40i	−0.302183	−	0.523396i	0.674447	−	0.738323i	$-0.264382\pi$
$257$	−1245.00	−	2156.40i	−0.302183	−	0.523396i	−0.976630	+	0.214927i	$0.931049\pi$
$258$	−1950.00			−0.470549
$259$		0			0
$260$	−1272.00			−0.303408
$261$	810.000	+	1402.96i	0.192099	+	0.332725i
$262$	−2118.00	+	3668.48i	−0.499429	+	0.865037i
$263$	−786.000	+	1361.39i	−0.184285	+	0.319190i	−0.943335	−	0.331841i	$-0.892330\pi$
$263$	−786.000	+	1361.39i	−0.184285	+	0.319190i	0.759051	+	0.651032i	$0.225663\pi$
$264$	360.000	+	623.538i	0.0839260	+	0.145364i
$265$	−4608.00			−1.06818
$266$		0			0
$267$	−1800.00			−0.412578
$268$	1046.00	+	1811.73i	0.238413	+	0.412943i
$269$	903.000	−	1564.04i	0.204672	−	0.354503i	−0.745356	−	0.666667i	$-0.767720\pi$
$269$	903.000	−	1564.04i	0.204672	−	0.354503i	0.950028	+	0.312164i	$0.101054\pi$
$270$	−162.000	+	280.592i	−0.0365148	+	0.0632456i
$271$	−3056.00	−	5293.15i	−0.685014	−	1.18648i	−0.973432	−	0.228975i	$-0.926463\pi$
$271$	−3056.00	−	5293.15i	−0.685014	−	1.18648i	0.288418	−	0.957504i	$-0.406871\pi$
$272$	1344.00			0.299603
$273$		0			0
$274$	−6024.00			−1.32819
$275$	−1335.00	−	2312.29i	−0.292740	−	0.507041i
$276$	504.000	−	872.954i	0.109918	−	0.190383i
$277$	2115.50	−	3664.15i	0.458874	−	0.794793i	−0.540028	−	0.841647i	$-0.681586\pi$
$277$	2115.50	−	3664.15i	0.458874	−	0.794793i	0.998902	+	0.0468542i	$0.0149196\pi$
$278$	37.0000	+	64.0859i	0.00798242	+	0.0138260i
$279$	−1611.00			−0.345692
$280$		0			0
$281$	−3816.00			−0.810119			−0.405060	−	0.914290i	$-0.632749\pi$
$281$	−3816.00			−0.810119			−0.405060	+	0.914290i	$0.632749\pi$
$282$	−1098.00	−	1901.79i	−0.231862	−	0.401596i
$283$	−1998.50	+	3461.50i	−0.419783	+	0.727085i	−0.995917	−	0.0902699i	$-0.971227\pi$
$283$	−1998.50	+	3461.50i	−0.419783	+	0.727085i	0.576135	+	0.817355i	$0.304560\pi$
$284$	684.000	−	1184.72i	0.142915	−	0.247536i
$285$	873.000	+	1512.08i	0.181446	+	0.314273i
$286$	−3180.00			−0.657473
$287$		0			0
$288$	−288.000			−0.0589256
$289$	−1071.50	−	1855.89i	−0.218095	−	0.377751i
$290$	−1080.00	+	1870.61i	−0.218689	+	0.378780i
$291$	−579.000	+	1002.86i	−0.116638	+	0.202022i
$292$	−86.0000	−	148.956i	−0.0172355	−	0.0298528i
$293$	−4608.00			−0.918779			−0.459389	−	0.888235i	$-0.651932\pi$
$293$	−4608.00			−0.918779			−0.459389	+	0.888235i	$0.651932\pi$
$294$		0			0
$295$	1584.00			0.312624
$296$	−580.000	−	1004.59i	−0.113891	−	0.197265i
$297$	−405.000	+	701.481i	−0.0791262	+	0.137051i
$298$	−1644.00	+	2847.49i	−0.319578	+	0.553526i
$299$	2226.00	+	3855.55i	0.430545	+	0.745726i
$300$	1068.00			0.205537
$301$		0			0
$302$	−2176.00			−0.414618
$303$	−927.000	−	1605.61i	−0.175758	−	0.304422i
$304$	−776.000	+	1344.07i	−0.146403	+	0.253578i
$305$	2454.00	−	4250.45i	0.460707	−	0.797968i
$306$	756.000	+	1309.43i	0.141234	+	0.244625i
$307$	631.000			0.117306			0.0586532	−	0.998278i	$-0.481319\pi$
$307$	631.000			0.117306			0.0586532	+	0.998278i	$0.481319\pi$
$308$		0			0
$309$	4425.00			0.814658
$310$	−1074.00	−	1860.22i	−0.196771	−	0.340818i
$311$	1947.00	−	3372.30i	0.354998	−	0.614874i	−0.632120	−	0.774871i	$-0.717815\pi$
$311$	1947.00	−	3372.30i	0.354998	−	0.614874i	0.987118	+	0.159997i	$0.0511484\pi$
$312$	636.000	−	1101.58i	0.115405	−	0.199888i
$313$	−1092.50	−	1892.27i	−0.197290	−	0.341716i	0.750359	−	0.661031i	$-0.229881\pi$
$313$	−1092.50	−	1892.27i	−0.197290	−	0.341716i	−0.947649	+	0.319314i	$0.896547\pi$
$314$	1012.00			0.181880
$315$		0			0
$316$	−4684.00			−0.833847
$317$	−1752.00	−	3034.55i	−0.310417	−	0.537658i	0.668036	−	0.744129i	$-0.267135\pi$
$317$	−1752.00	−	3034.55i	−0.310417	−	0.537658i	−0.978453	+	0.206471i	$0.933802\pi$
$318$	2304.00	−	3990.65i	0.406295	−	0.703724i
$319$	−2700.00	+	4676.54i	−0.473890	+	0.820802i
$320$	−192.000	−	332.554i	−0.0335410	−	0.0580948i
$321$	−5652.00			−0.982754
$322$		0			0
$323$	8148.00			1.40361
$324$	−162.000	−	280.592i	−0.0277778	−	0.0481125i
$325$	−2358.50	+	4085.04i	−0.402542	+	0.697223i
$326$	1844.00	−	3193.90i	0.313281	−	0.542619i
$327$	619.500	+	1073.01i	0.104766	+	0.181460i
$328$	1008.00			0.169687
$329$		0			0
$330$	−1080.00			−0.180158
$331$	−1472.50	−	2550.44i	−0.244519	−	0.423520i	0.717477	−	0.696582i	$-0.245297\pi$
$331$	−1472.50	−	2550.44i	−0.244519	−	0.423520i	−0.961996	+	0.273062i	$0.911964\pi$
$332$	−1620.00	+	2805.92i	−0.267798	+	0.463840i
$333$	652.500	−	1130.16i	0.107378	−	0.185984i
$334$	−162.000	−	280.592i	−0.0265397	−	0.0459680i
$335$	−3138.00			−0.511783
$336$		0			0
$337$	4277.00			0.691344			0.345672	−	0.938355i	$-0.387651\pi$
$337$	4277.00			0.691344			0.345672	+	0.938355i	$0.387651\pi$
$338$	612.000	+	1060.02i	0.0984864	+	0.170583i
$339$	−1323.00	+	2291.50i	−0.211963	+	0.367131i
$340$	−1008.00	+	1745.91i	−0.160784	+	0.278486i
$341$	−2685.00	−	4650.56i	−0.426396	−	0.738539i
$342$	−1746.00			−0.276061
$343$		0			0
$344$	2600.00			0.407508
$345$	756.000	+	1309.43i	0.117976	+	0.204340i
$346$	2724.00	−	4718.11i	0.423246	−	0.733084i
$347$	−3594.00	+	6224.99i	−0.556012	+	0.963040i	0.441812	+	0.897107i	$0.354336\pi$
$347$	−3594.00	+	6224.99i	−0.556012	+	0.963040i	−0.997824	+	0.0659329i	$0.978998\pi$
$348$	−1080.00	−	1870.61i	−0.166362	−	0.288148i
$349$	9406.00			1.44267			0.721335	−	0.692587i	$-0.243529\pi$
$349$	9406.00			1.44267			0.721335	+	0.692587i	$0.243529\pi$
$350$		0			0
$351$	1431.00			0.217610
$352$	−480.000	−	831.384i	−0.0726821	−	0.125889i
$353$	1695.00	−	2935.83i	0.255569	−	0.442658i	−0.709481	−	0.704724i	$-0.751071\pi$
$353$	1695.00	−	2935.83i	0.255569	−	0.442658i	0.965050	+	0.262066i	$0.0844040\pi$
$354$	−792.000	+	1371.78i	−0.118911	+	0.205959i
$355$	1026.00	+	1777.08i	0.153393	+	0.265684i
$356$	2400.00			0.357303
$357$		0			0
$358$	2508.00			0.370257
$359$	2406.00	+	4167.31i	0.353715	+	0.612653i	0.986897	−	0.161350i	$-0.0515848\pi$
$359$	2406.00	+	4167.31i	0.353715	+	0.612653i	−0.633182	+	0.774003i	$0.718251\pi$
$360$	216.000	−	374.123i	0.0316228	−	0.0547723i
$361$	−1275.00	+	2208.36i	−0.185887	+	0.321966i
$362$	1807.00	+	3129.82i	0.262359	+	0.454418i
$363$	1293.00			0.186956
$364$		0			0
$365$	258.000			0.0369982
$366$	2454.00	+	4250.45i	0.350472	+	0.607035i
$367$	−3549.50	+	6147.91i	−0.504857	+	0.874437i	0.495128	+	0.868820i	$0.335121\pi$
$367$	−3549.50	+	6147.91i	−0.504857	+	0.874437i	−0.999984	+	0.00561709i	$0.998212\pi$
$368$	−672.000	+	1163.94i	−0.0951914	+	0.164876i
$369$	567.000	+	982.073i	0.0799914	+	0.138549i
$370$	1740.00			0.244482
$371$		0			0
$372$	2148.00			0.299378
$373$	−1481.50	−	2566.03i	−0.205655	−	0.356204i	0.744687	−	0.667414i	$-0.232599\pi$
$373$	−1481.50	−	2566.03i	−0.205655	−	0.356204i	−0.950341	+	0.311210i	$0.899266\pi$
$374$	−2520.00	+	4364.77i	−0.348412	+	0.603467i
$375$	−1926.00	+	3335.93i	−0.265222	+	0.459378i
$376$	1464.00	+	2535.72i	0.200798	+	0.347792i
$377$	9540.00			1.30328
$378$		0			0
$379$	−11899.0			−1.61269			−0.806346	−	0.591444i	$-0.798558\pi$
$379$	−11899.0			−1.61269			−0.806346	+	0.591444i	$0.798558\pi$
$380$	−1164.00	−	2016.11i	−0.157137	−	0.272169i
$381$	3724.50	−	6451.02i	0.500819	−	0.867443i
$382$	714.000	−	1236.68i	0.0956320	−	0.165639i
$383$	1284.00	+	2223.95i	0.171304	+	0.296707i	0.938876	−	0.344256i	$-0.111869\pi$
$383$	1284.00	+	2223.95i	0.171304	+	0.296707i	−0.767572	+	0.640963i	$0.778535\pi$
$384$	384.000			0.0510310
$385$		0			0
$386$	7418.00			0.978151
$387$	1462.50	+	2533.12i	0.192101	+	0.332729i
$388$	772.000	−	1337.14i	0.101011	−	0.174957i
$389$	5073.00	−	8786.69i	0.661212	−	1.14525i	−0.319086	−	0.947726i	$-0.603376\pi$
$389$	5073.00	−	8786.69i	0.661212	−	1.14525i	0.980298	−	0.197526i	$-0.0632908\pi$
$390$	954.000	+	1652.38i	0.123866	+	0.214542i
$391$	7056.00			0.912627
$392$		0			0
$393$	6354.00			0.815565
$394$	−1044.00	−	1808.26i	−0.133492	−	0.231215i
$395$	3513.00	−	6084.69i	0.447489	−	0.775074i
$396$	540.000	−	935.307i	0.0685253	−	0.118689i
$397$	−3114.50	−	5394.47i	−0.393734	−	0.681967i	0.599205	−	0.800596i	$-0.295483\pi$
$397$	−3114.50	−	5394.47i	−0.393734	−	0.681967i	−0.992939	+	0.118629i	$0.962150\pi$
$398$	−272.000			−0.0342566
$399$		0			0
$400$	−1424.00			−0.178000
$401$	1236.00	+	2140.81i	0.153922	+	0.266601i	0.932666	−	0.360741i	$-0.117476\pi$
$401$	1236.00	+	2140.81i	0.153922	+	0.266601i	−0.778744	+	0.627342i	$0.784143\pi$
$402$	1569.00	−	2717.59i	0.194663	−	0.337167i
$403$	−4743.50	+	8215.98i	−0.586329	+	1.01555i
$404$	1236.00	+	2140.81i	0.152211	+	0.263637i
$405$	486.000			0.0596285
$406$		0			0
$407$	4350.00			0.529783
$408$	−1008.00	−	1745.91i	−0.122312	−	0.211851i
$409$	−3537.50	+	6127.13i	−0.427673	+	0.740751i	−0.996666	−	0.0815915i	$-0.974000\pi$
$409$	−3537.50	+	6127.13i	−0.427673	+	0.740751i	0.568993	+	0.822342i	$0.307333\pi$
$410$	−756.000	+	1309.43i	−0.0910639	+	0.157727i
$411$	4518.00	+	7825.41i	0.542230	+	0.939170i
$412$	−5900.00			−0.705515
$413$		0			0
$414$	−1512.00			−0.179495
$415$	−2430.00	−	4208.88i	−0.287431	−	0.497846i
$416$	−848.000	+	1468.78i	−0.0999438	+	0.173108i
$417$	55.5000	−	96.1288i	0.00651762	−	0.0112888i
$418$	−2910.00	−	5040.27i	−0.340509	−	0.589779i
$419$	4158.00			0.484801			0.242400	−	0.970176i	$-0.422065\pi$
$419$	4158.00			0.484801			0.242400	+	0.970176i	$0.422065\pi$
$420$		0			0
$421$	−6595.00			−0.763469			−0.381735	−	0.924272i	$-0.624673\pi$
$421$	−6595.00			−0.763469			−0.381735	+	0.924272i	$0.624673\pi$
$422$	1484.00	+	2570.36i	0.171185	+	0.296501i
$423$	−1647.00	+	2852.69i	−0.189314	+	0.327902i
$424$	−3072.00	+	5320.86i	−0.351862	+	0.609443i
$425$	3738.00	+	6474.41i	0.426634	+	0.738953i
$426$	−2052.00			−0.233380
$427$		0			0
$428$	7536.00			0.851090
$429$	2385.00	+	4130.94i	0.268412	+	0.464904i
$430$	−1950.00	+	3377.50i	−0.218692	+	0.378785i
$431$	−759.000	+	1314.63i	−0.0848254	+	0.146922i	−0.905317	−	0.424737i	$-0.860367\pi$
$431$	−759.000	+	1314.63i	−0.0848254	+	0.146922i	0.820491	+	0.571659i	$0.193700\pi$
$432$	216.000	+	374.123i	0.0240563	+	0.0416667i
$433$	−8567.00			−0.950817			−0.475408	−	0.879765i	$-0.657700\pi$
$433$	−8567.00			−0.950817			−0.475408	+	0.879765i	$0.657700\pi$
$434$		0			0
$435$	3240.00			0.357117
$436$	−826.000	−	1430.67i	−0.0907299	−	0.157149i
$437$	−4074.00	+	7056.37i	−0.445963	+	0.772431i
$438$	−129.000	+	223.435i	−0.0140727	+	0.0243747i
$439$	5320.00	+	9214.51i	0.578382	+	1.00179i	0.995665	+	0.0930106i	$0.0296491\pi$
$439$	5320.00	+	9214.51i	0.578382	+	1.00179i	−0.417283	+	0.908777i	$0.637018\pi$
$440$	1440.00			0.156021
$441$		0			0
$442$	8904.00			0.958190
$443$	−3516.00	−	6089.89i	−0.377088	−	0.653136i	0.613549	−	0.789657i	$-0.289741\pi$
$443$	−3516.00	−	6089.89i	−0.377088	−	0.653136i	−0.990637	+	0.136520i	$0.956408\pi$
$444$	−870.000	+	1506.88i	−0.0929918	+	0.161067i
$445$	−1800.00	+	3117.69i	−0.191749	+	0.332119i
$446$	2032.00	+	3519.53i	0.215735	+	0.373665i
$447$	4932.00			0.521869
$448$		0			0
$449$	−14814.0			−1.55705			−0.778525	−	0.627613i	$-0.784032\pi$
$449$	−14814.0			−1.55705			−0.778525	+	0.627613i	$0.784032\pi$
$450$	−801.000	−	1387.37i	−0.0839100	−	0.145336i
$451$	−1890.00	+	3273.58i	−0.197332	+	0.341789i
$452$	1764.00	−	3055.34i	0.183565	−	0.317945i
$453$	1632.00	+	2826.71i	0.169267	+	0.293179i
$454$	12396.0			1.28144
$455$		0			0
$456$	2328.00			0.239076
$457$	5625.50	+	9743.65i	0.575820	+	0.997350i	0.995952	+	0.0898866i	$0.0286505\pi$
$457$	5625.50	+	9743.65i	0.575820	+	0.997350i	−0.420132	+	0.907463i	$0.638016\pi$
$458$	4591.00	−	7951.85i	0.468392	−	0.811278i
$459$	1134.00	−	1964.15i	0.115317	−	0.199735i
$460$	−1008.00	−	1745.91i	−0.102170	−	0.176964i
$461$	3852.00			0.389166			0.194583	−	0.980886i	$-0.437665\pi$
$461$	3852.00			0.389166			0.194583	+	0.980886i	$0.437665\pi$
$462$		0			0
$463$	−475.000			−0.0476784			−0.0238392	−	0.999716i	$-0.507589\pi$
$463$	−475.000			−0.0476784			−0.0238392	+	0.999716i	$0.507589\pi$
$464$	1440.00	+	2494.15i	0.144074	+	0.249543i
$465$	−1611.00	+	2790.33i	−0.160663	+	0.278277i
$466$	4530.00	−	7846.19i	0.450318	−	0.779974i
$467$	2967.00	+	5138.99i	0.293997	+	0.509217i	0.974751	−	0.223295i	$-0.0716812\pi$
$467$	2967.00	+	5138.99i	0.293997	+	0.509217i	−0.680754	+	0.732512i	$0.738348\pi$
$468$	−1908.00			−0.188456
$469$		0			0
$470$	−4392.00			−0.431038
$471$	−759.000	−	1314.63i	−0.0742524	−	0.128609i
$472$	1056.00	−	1829.05i	0.102980	−	0.178366i
$473$	−4875.00	+	8443.75i	−0.473896	+	0.820812i
$474$	3513.00	+	6084.69i	0.340417	+	0.589619i
$475$	−8633.00			−0.833914
$476$		0			0
$477$	−6912.00			−0.663477
$478$	1530.00	+	2650.04i	0.146403	+	0.253577i
$479$	−6684.00	+	11577.0i	−0.637578	+	1.10432i	0.348385	+	0.937352i	$0.386730\pi$
$479$	−6684.00	+	11577.0i	−0.637578	+	1.10432i	−0.985963	+	0.166966i	$0.946603\pi$
$480$	−288.000	+	498.831i	−0.0273861	+	0.0474342i
$481$	−3842.50	−	6655.41i	−0.364247	−	0.630895i
$482$	11068.0			1.04592
$483$		0			0
$484$	−1724.00			−0.161908
$485$	1158.00	+	2005.71i	0.108417	+	0.187783i
$486$	−243.000	+	420.888i	−0.0226805	+	0.0392837i
$487$	−3326.50	+	5761.67i	−0.309524	+	0.536111i	−0.978258	−	0.207390i	$-0.933503\pi$
$487$	−3326.50	+	5761.67i	−0.309524	+	0.536111i	0.668734	+	0.743501i	$0.266836\pi$
$488$	−3272.00	−	5667.27i	−0.303517	−	0.525708i
$489$	−5532.00			−0.511586
$490$		0			0
$491$	15444.0			1.41951			0.709754	−	0.704450i	$-0.248806\pi$
$491$	15444.0			1.41951			0.709754	+	0.704450i	$0.248806\pi$
$492$	−756.000	−	1309.43i	−0.0692746	−	0.119987i
$493$	7560.00	−	13094.3i	0.690640	−	1.19622i
$494$	−5141.00	+	8904.47i	−0.468228	+	0.810994i
$495$	810.000	+	1402.96i	0.0735491	+	0.127391i
$496$	−2864.00			−0.259269
$497$		0			0
$498$	4860.00			0.437313
$499$	−341.500	−	591.495i	−0.0306366	−	0.0530641i	0.850301	−	0.526297i	$-0.176420\pi$
$499$	−341.500	−	591.495i	−0.0306366	−	0.0530641i	−0.880937	+	0.473233i	$0.843087\pi$
$500$	2568.00	−	4447.91i	0.229689	−	0.397833i
$501$	−243.000	+	420.888i	−0.0216695	+	0.0375327i
$502$	468.000	+	810.600i	0.0416093	+	0.0720694i
$503$	−9882.00			−0.875977			−0.437989	−	0.898980i	$-0.644309\pi$
$503$	−9882.00			−0.875977			−0.437989	+	0.898980i	$0.644309\pi$
$504$		0			0
$505$	−3708.00			−0.326740
$506$	−2520.00	−	4364.77i	−0.221399	−	0.383474i
$507$	918.000	−	1590.02i	0.0804138	−	0.139281i
$508$	−4966.00	+	8601.36i	−0.433722	+	0.751228i
$509$	2103.00	+	3642.50i	0.183131	+	0.317193i	0.942945	−	0.332948i	$-0.108043\pi$
$509$	2103.00	+	3642.50i	0.183131	+	0.317193i	−0.759814	+	0.650141i	$0.774710\pi$
$510$	3024.00			0.262559
$511$		0			0
$512$	−512.000			−0.0441942
$513$	1309.50	+	2268.12i	0.112701	+	0.195205i
$514$	2490.00	−	4312.81i	0.213675	−	0.370097i
$515$	4425.00	−	7664.32i	0.378619	−	0.655787i
$516$	−1950.00	−	3377.50i	−0.166364	−	0.288151i
$517$	−10980.0			−0.934042
$518$		0			0
$519$	−8172.00			−0.691158
$520$	−1272.00	−	2203.17i	−0.107271	−	0.185799i
$521$	4530.00	−	7846.19i	0.380927	−	0.659785i	−0.610268	−	0.792195i	$-0.708938\pi$
$521$	4530.00	−	7846.19i	0.380927	−	0.659785i	0.991195	+	0.132410i	$0.0422716\pi$
$522$	−1620.00	+	2805.92i	−0.135834	+	0.235272i
$523$	−7839.50	−	13578.4i	−0.655444	−	1.13526i	−0.981782	−	0.190010i	$-0.939148\pi$
$523$	−7839.50	−	13578.4i	−0.655444	−	1.13526i	0.326338	−	0.945253i	$-0.394185\pi$
$524$	−8472.00			−0.706300
$525$		0			0
$526$	−3144.00			−0.260618
$527$	7518.00	+	13021.6i	0.621422	+	1.07633i
$528$	−720.000	+	1247.08i	−0.0593447	+	0.102788i
$529$	2555.50	−	4426.26i	0.210035	−	0.363792i
$530$	−4608.00	−	7981.29i	−0.377658	−	0.654123i
$531$	2376.00			0.194180
$532$		0			0
$533$	6678.00			0.542695
$534$	−1800.00	−	3117.69i	−0.145868	−	0.252651i
$535$	−5652.00	+	9789.55i	−0.456743	+	0.791101i
$536$	−2092.00	+	3623.45i	−0.168583	+	0.291995i
$537$	−1881.00	−	3257.99i	−0.151157	−	0.261811i
$538$	3612.00			0.289451
$539$		0			0
$540$	−648.000			−0.0516398
$541$	3855.50	+	6677.92i	0.306397	+	0.530696i	0.977571	−	0.210604i	$-0.0675431\pi$
$541$	3855.50	+	6677.92i	0.306397	+	0.530696i	−0.671174	+	0.741300i	$0.734210\pi$
$542$	6112.00	−	10586.3i	0.484378	−	0.838967i
$543$	2710.50	−	4694.72i	0.214215	−	0.371031i
$544$	1344.00	+	2327.88i	0.105926	+	0.183469i
$545$	2478.00			0.194763
$546$		0			0
$547$	4292.00			0.335489			0.167745	−	0.985830i	$-0.446352\pi$
$547$	4292.00			0.335489			0.167745	+	0.985830i	$0.446352\pi$
$548$	−6024.00	−	10433.9i	−0.469585	−	0.813345i
$549$	3681.00	−	6375.68i	0.286159	−	0.495642i
$550$	2670.00	−	4624.58i	0.206999	−	0.358532i
$551$	8730.00	+	15120.8i	0.674974	+	1.16909i
$552$	2016.00			0.155447
$553$		0			0
$554$	8462.00			0.648946
$555$	−1305.00	−	2260.33i	−0.0998093	−	0.172875i
$556$	−74.0000	+	128.172i	−0.00564442	+	0.00977643i
$557$	4929.00	−	8537.28i	0.374952	−	0.649436i	−0.615368	−	0.788240i	$-0.710992\pi$
$557$	4929.00	−	8537.28i	0.374952	−	0.649436i	0.990320	+	0.138804i	$0.0443258\pi$
$558$	−1611.00	−	2790.33i	−0.122221	−	0.211692i
$559$	17225.0			1.30329
$560$		0			0
$561$	7560.00			0.568954
$562$	−3816.00	−	6609.51i	−0.286420	−	0.496095i
$563$	−6945.00	+	12029.1i	−0.519888	+	0.900472i	0.479845	+	0.877353i	$0.340693\pi$
$563$	−6945.00	+	12029.1i	−0.519888	+	0.900472i	−0.999733	+	0.0231188i	$0.992640\pi$
$564$	2196.00	−	3803.58i	0.163951	−	0.283971i
$565$	2646.00	+	4583.01i	0.197023	+	0.341254i
$566$	−7994.00			−0.593662
$567$		0			0
$568$	2736.00			0.202113
$569$	−9519.00	−	16487.4i	−0.701331	−	1.21474i	−0.967999	−	0.250952i	$-0.919256\pi$
$569$	−9519.00	−	16487.4i	−0.701331	−	1.21474i	0.266669	−	0.963788i	$-0.414077\pi$
$570$	−1746.00	+	3024.16i	−0.128302	+	0.222225i
$571$	4026.50	−	6974.10i	0.295103	−	0.511133i	−0.679906	−	0.733299i	$-0.737979\pi$
$571$	4026.50	−	6974.10i	0.295103	−	0.511133i	0.975009	+	0.222166i	$0.0713127\pi$
$572$	−3180.00	−	5507.92i	−0.232452	−	0.402618i
$573$	−2142.00			−0.156166
$574$		0			0
$575$	−7476.00			−0.542210
$576$	−288.000	−	498.831i	−0.0208333	−	0.0360844i
$577$	−8568.50	+	14841.1i	−0.618217	+	1.07078i	0.371594	+	0.928395i	$0.378811\pi$
$577$	−8568.50	+	14841.1i	−0.618217	+	1.07078i	−0.989811	+	0.142388i	$0.954522\pi$
$578$	2143.00	−	3711.78i	0.154216	−	0.267111i
$579$	−5563.50	−	9636.26i	−0.399328	−	0.691657i
$580$	−4320.00			−0.309273
$581$		0			0
$582$	−2316.00			−0.164951
$583$	−11520.0	−	19953.2i	−0.818370	−	1.41746i
$584$	172.000	−	297.913i	0.0121873	−	0.0211091i
$585$	1431.00	−	2478.56i	0.101136	−	0.175173i
$586$	−4608.00	−	7981.29i	−0.324837	−	0.562635i
$587$	−18144.0			−1.27578			−0.637890	−	0.770127i	$-0.720193\pi$
$587$	−18144.0			−1.27578			−0.637890	+	0.770127i	$0.720193\pi$
$588$		0			0
$589$	−17363.0			−1.21465
$590$	1584.00	+	2743.57i	0.110529	+	0.191442i
$591$	−1566.00	+	2712.39i	−0.108996	+	0.188787i
$592$	1160.00	−	2009.18i	0.0805333	−	0.139488i
$593$	−12351.0	−	21392.6i	−0.855303	−	1.48143i	−0.876363	−	0.481650i	$-0.840038\pi$
$593$	−12351.0	−	21392.6i	−0.855303	−	1.48143i	0.0210603	−	0.999778i	$-0.493296\pi$
$594$	−1620.00			−0.111901
$595$		0			0
$596$	−6576.00			−0.451952
$597$	204.000	+	353.338i	0.0139852	+	0.0242231i
$598$	−4452.00	+	7711.09i	−0.304441	+	0.527308i
$599$	1086.00	−	1881.01i	0.0740781	−	0.128307i	−0.826607	−	0.562780i	$-0.809732\pi$
$599$	1086.00	−	1881.01i	0.0740781	−	0.128307i	0.900685	+	0.434473i	$0.143065\pi$
$600$	1068.00	+	1849.83i	0.0726682	+	0.125865i
$601$	−4175.00			−0.283364			−0.141682	−	0.989912i	$-0.545251\pi$
$601$	−4175.00			−0.283364			−0.141682	+	0.989912i	$0.545251\pi$
$602$		0			0
$603$	−4707.00			−0.317884
$604$	−2176.00	−	3768.94i	−0.146590	−	0.253901i
$605$	1293.00	−	2239.54i	0.0868891	−	0.150496i
$606$	1854.00	−	3211.22i	0.124280	−	0.215259i
$607$	1130.50	+	1958.08i	0.0755940	+	0.130933i	0.901344	−	0.433103i	$-0.142581\pi$
$607$	1130.50	+	1958.08i	0.0755940	+	0.130933i	−0.825750	+	0.564036i	$0.809248\pi$
$608$	−3104.00			−0.207046
$609$		0			0
$610$	9816.00			0.651538
$611$	9699.00	+	16799.2i	0.642192	+	1.11231i
$612$	−1512.00	+	2618.86i	−0.0998676	+	0.172976i
$613$	8159.00	−	14131.8i	0.537584	−	0.931123i	−0.461450	−	0.887166i	$-0.652670\pi$
$613$	8159.00	−	14131.8i	0.537584	−	0.931123i	0.999033	−	0.0439561i	$-0.0139962\pi$
$614$	631.000	+	1092.92i	0.0414741	+	0.0718352i
$615$	2268.00			0.148707
$616$		0			0
$617$	−26550.0			−1.73235			−0.866177	−	0.499737i	$-0.833430\pi$
$617$	−26550.0			−1.73235			−0.866177	+	0.499737i	$0.833430\pi$
$618$	4425.00	+	7664.32i	0.288025	+	0.498874i
$619$	9962.50	−	17255.6i	0.646893	−	1.12045i	−0.336968	−	0.941516i	$-0.609401\pi$
$619$	9962.50	−	17255.6i	0.646893	−	1.12045i	0.983861	−	0.178935i	$-0.0572652\pi$
$620$	2148.00	−	3720.45i	0.139138	−	0.240995i
$621$	1134.00	+	1964.15i	0.0732783	+	0.126922i
$622$	7788.00			0.502042
$623$		0			0
$624$	2544.00			0.163208
$625$	−1710.50	−	2962.67i	−0.109472	−	0.189611i
$626$	2185.00	−	3784.53i	0.139505	−	0.241630i
$627$	−4365.00	+	7560.40i	−0.278024	+	0.481552i
$628$	1012.00	+	1752.84i	0.0643045	+	0.111379i
$629$	−12180.0			−0.772096
$630$		0			0
$631$	−6832.00			−0.431026			−0.215513	−	0.976501i	$-0.569142\pi$
$631$	−6832.00			−0.431026			−0.215513	+	0.976501i	$0.569142\pi$
$632$	−4684.00	−	8112.93i	−0.294809	−	0.510625i
$633$	2226.00	−	3855.55i	0.139772	−	0.242092i
$634$	3504.00	−	6069.11i	0.219498	−	0.380181i
$635$	−7449.00	−	12902.0i	−0.465519	−	0.806303i
$636$	9216.00			0.574588
$637$		0			0
$638$	−10800.0			−0.670182
$639$	1539.00	+	2665.63i	0.0952768	+	0.165024i
$640$	384.000	−	665.108i	0.0237171	−	0.0410792i
$641$	−5106.00	+	8843.85i	−0.314625	+	0.544947i	−0.979358	−	0.202134i	$-0.935212\pi$
$641$	−5106.00	+	8843.85i	−0.314625	+	0.544947i	0.664732	+	0.747082i	$0.268546\pi$
$642$	−5652.00	−	9789.55i	−0.347456	−	0.601811i
$643$	−3779.00			−0.231772			−0.115886	−	0.993263i	$-0.536971\pi$
$643$	−3779.00			−0.231772			−0.115886	+	0.993263i	$0.536971\pi$
$644$		0			0
$645$	5850.00			0.357122
$646$	8148.00	+	14112.7i	0.496252	+	0.859534i
$647$	8499.00	−	14720.7i	0.516430	−	0.894483i	−0.483388	−	0.875406i	$-0.660594\pi$
$647$	8499.00	−	14720.7i	0.516430	−	0.894483i	0.999818	−	0.0190767i	$-0.00607268\pi$
$648$	324.000	−	561.184i	0.0196419	−	0.0340207i
$649$	3960.00	+	6858.92i	0.239512	+	0.414848i
$650$	−9434.00			−0.569280
$651$		0			0
$652$	7376.00			0.443047
$653$	10875.0	+	18836.1i	0.651718	+	1.12881i	0.982706	+	0.185173i	$0.0592846\pi$
$653$	10875.0	+	18836.1i	0.651718	+	1.12881i	−0.330988	+	0.943635i	$0.607382\pi$
$654$	−1239.00	+	2146.01i	−0.0740806	+	0.128311i
$655$	6354.00	−	11005.5i	0.379040	−	0.656517i
$656$	1008.00	+	1745.91i	0.0599936	+	0.103912i
$657$	387.000			0.0229807
$658$		0			0
$659$	−10944.0			−0.646916			−0.323458	−	0.946243i	$-0.604845\pi$
$659$	−10944.0			−0.646916			−0.323458	+	0.946243i	$0.604845\pi$
$660$	−1080.00	−	1870.61i	−0.0636954	−	0.110324i
$661$	5477.50	−	9487.31i	0.322315	−	0.558266i	−0.658650	−	0.752449i	$-0.728872\pi$
$661$	5477.50	−	9487.31i	0.322315	−	0.558266i	0.980965	+	0.194184i	$0.0622057\pi$
$662$	2945.00	−	5100.89i	0.172901	−	0.299474i
$663$	−6678.00	−	11566.6i	−0.391180	−	0.677543i
$664$	−6480.00			−0.378724
$665$		0			0
$666$	2610.00			0.151855
$667$	7560.00	+	13094.3i	0.438867	+	0.760140i
$668$	324.000	−	561.184i	0.0187664	−	0.0325043i
$669$	3048.00	−	5279.29i	0.176147	−	0.305096i
$670$	−3138.00	−	5435.18i	−0.180943	−	0.313402i
$671$	24540.0			1.41186
$672$		0			0
$673$	25103.0			1.43782			0.718908	−	0.695106i	$-0.244642\pi$
$673$	25103.0			1.43782			0.718908	+	0.695106i	$0.244642\pi$
$674$	4277.00	+	7407.98i	0.244427	+	0.423360i
$675$	−1201.50	+	2081.06i	−0.0685122	+	0.118667i
$676$	−1224.00	+	2120.03i	−0.0696404	+	0.120621i
$677$	−2802.00	−	4853.21i	−0.159069	−	0.275515i	0.775464	−	0.631391i	$-0.217516\pi$
$677$	−2802.00	−	4853.21i	−0.159069	−	0.275515i	−0.934533	+	0.355876i	$0.884183\pi$
$678$	−5292.00			−0.299761
$679$		0			0
$680$	−4032.00			−0.227383
$681$	−9297.00	−	16102.9i	−0.523145	−	0.906114i
$682$	5370.00	−	9301.11i	0.301507	−	0.522226i
$683$	−5484.00	+	9498.57i	−0.307232	+	0.532141i	−0.977756	−	0.209747i	$-0.932736\pi$
$683$	−5484.00	+	9498.57i	−0.307232	+	0.532141i	0.670524	+	0.741888i	$0.266069\pi$
$684$	−1746.00	−	3024.16i	−0.0976023	−	0.169052i
$685$	18072.0			1.00802
$686$		0			0
$687$	−13773.0			−0.764880
$688$	2600.00	+	4503.33i	0.144076	+	0.249546i
$689$	−20352.0	+	35250.7i	−1.12533	+	1.94912i
$690$	−1512.00	+	2618.86i	−0.0834215	+	0.144490i
$691$	4202.50	+	7278.94i	0.231361	+	0.400729i	0.958209	−	0.286069i	$-0.0923487\pi$
$691$	4202.50	+	7278.94i	0.231361	+	0.400729i	−0.726848	+	0.686799i	$0.759015\pi$
$692$	10896.0			0.598560
$693$		0			0
$694$	−14376.0			−0.786319
$695$	−111.000	−	192.258i	−0.00605823	−	0.0104932i
$696$	2160.00	−	3741.23i	0.117636	−	0.203751i
$697$	5292.00	−	9166.01i	0.287588	−	0.498117i
$698$	9406.00	+	16291.7i	0.510061	+	0.883451i
$699$	−13590.0			−0.735366
$700$		0			0
$701$	468.000			0.0252156			0.0126078	−	0.999921i	$-0.495987\pi$
$701$	468.000			0.0252156			0.0126078	+	0.999921i	$0.495987\pi$
$702$	1431.00	+	2478.56i	0.0769368	+	0.133258i
$703$	7032.50	−	12180.6i	0.377291	−	0.653488i
$704$	960.000	−	1662.77i	0.0513940	−	0.0890170i
$705$	3294.00	+	5705.38i	0.175971	+	0.304790i
$706$	6780.00			0.361429
$707$		0			0
$708$	−3168.00			−0.168165
$709$	12533.0	+	21707.8i	0.663874	+	1.14986i	0.979589	+	0.201010i	$0.0644222\pi$
$709$	12533.0	+	21707.8i	0.663874	+	1.14986i	−0.315715	+	0.948854i	$0.602244\pi$
$710$	−2052.00	+	3554.17i	−0.108465	+	0.187867i
$711$	5269.50	−	9127.04i	0.277949	−	0.481422i
$712$	2400.00	+	4156.92i	0.126326	+	0.218802i
$713$	−15036.0			−0.789765
$714$		0			0
$715$	9540.00			0.498987
$716$	2508.00	+	4343.98i	0.130906	+	0.226735i
$717$	2295.00	−	3975.06i	0.119537	−	0.207045i
$718$	−4812.00	+	8334.63i	−0.250115	+	0.433211i
$719$	5541.00	+	9597.29i	0.287405	+	0.497801i	0.973190	−	0.230004i	$-0.0738740\pi$
$719$	5541.00	+	9597.29i	0.287405	+	0.497801i	−0.685784	+	0.727805i	$0.740541\pi$
$720$	864.000			0.0447214
$721$		0			0
$722$	−5100.00			−0.262884
$723$	−8301.00	−	14377.8i	−0.426995	−	0.739577i
$724$	−3614.00	+	6259.63i	−0.185516	+	0.321322i
$725$	−8010.00	+	13873.7i	−0.410323	+	0.710700i
$726$	1293.00	+	2239.54i	0.0660988	+	0.114486i
$727$	−13481.0			−0.687734			−0.343867	−	0.939018i	$-0.611737\pi$
$727$	−13481.0			−0.687734			−0.343867	+	0.939018i	$0.611737\pi$
$728$		0			0
$729$	729.000			0.0370370
$730$	258.000	+	446.869i	0.0130808	+	0.0226567i
$731$	13650.0	−	23642.5i	0.690648	−	1.19624i
$732$	−4908.00	+	8500.91i	−0.247821	+	0.429238i
$733$	12158.5	+	21059.1i	0.612666	+	1.06117i	0.990789	+	0.135414i	$0.0432364\pi$
$733$	12158.5	+	21059.1i	0.612666	+	1.06117i	−0.378123	+	0.925755i	$0.623430\pi$
$734$	−14198.0			−0.713975
$735$		0			0
$736$	−2688.00			−0.134621
$737$	−7845.00	−	13587.9i	−0.392095	−	0.679129i
$738$	−1134.00	+	1964.15i	−0.0565625	+	0.0979691i
$739$	9108.50	−	15776.4i	0.453399	−	0.785309i	−0.545196	−	0.838309i	$-0.683545\pi$
$739$	9108.50	−	15776.4i	0.453399	−	0.785309i	0.998595	+	0.0529992i	$0.0168781\pi$
$740$	1740.00	+	3013.77i	0.0864374	+	0.149714i
$741$	15423.0			0.764613
$742$		0			0
$743$	19782.0			0.976758			0.488379	−	0.872632i	$-0.337588\pi$
$743$	19782.0			0.976758			0.488379	+	0.872632i	$0.337588\pi$
$744$	2148.00	+	3720.45i	0.105846	+	0.183331i
$745$	4932.00	−	8542.47i	0.242543	−	0.420097i
$746$	2963.00	−	5132.07i	0.145420	−	0.251874i
$747$	−3645.00	−	6313.33i	−0.178532	−	0.309227i
$748$	−10080.0			−0.492729
$749$		0			0
$750$	−7704.00			−0.375080
$751$	2460.50	+	4261.71i	0.119554	+	0.207073i	0.919591	−	0.392877i	$-0.128520\pi$
$751$	2460.50	+	4261.71i	0.119554	+	0.207073i	−0.800037	+	0.599951i	$0.795187\pi$
$752$	−2928.00	+	5071.44i	−0.141986	+	0.245926i
$753$	702.000	−	1215.90i	0.0339738	−	0.0588444i
$754$	9540.00	+	16523.8i	0.460778	+	0.798090i
$755$	6528.00			0.314673
$756$		0			0
$757$	18098.0			0.868934			0.434467	−	0.900688i	$-0.356937\pi$
$757$	18098.0			0.868934			0.434467	+	0.900688i	$0.356937\pi$
$758$	−11899.0	−	20609.7i	−0.570173	−	0.987569i
$759$	−3780.00	+	6547.15i	−0.180771	+	0.313105i
$760$	2328.00	−	4032.21i	0.111112	−	0.192452i
$761$	−12234.0	−	21189.9i	−0.582762	−	1.00937i	−0.995150	−	0.0983657i	$-0.968639\pi$
$761$	−12234.0	−	21189.9i	−0.582762	−	1.00937i	0.412388	−	0.911008i	$-0.364695\pi$
$762$	14898.0			0.708265
$763$		0			0
$764$	2856.00			0.135244
$765$	−2268.00	−	3928.29i	−0.107189	−	0.185657i
$766$	−2568.00	+	4447.91i	−0.121130	+	0.209803i
$767$	6996.00	−	12117.4i	0.329349	−	0.570450i
$768$	384.000	+	665.108i	0.0180422	+	0.0312500i
$769$	−21719.0			−1.01847			−0.509237	−	0.860626i	$-0.670072\pi$
$769$	−21719.0			−1.01847			−0.509237	+	0.860626i	$0.670072\pi$
$770$		0			0
$771$	−7470.00			−0.348931
$772$	7418.00	+	12848.4i	0.345829	+	0.598993i
$773$	−15153.0	+	26245.8i	−0.705065	+	1.22121i	0.261603	+	0.965176i	$0.415749\pi$
$773$	−15153.0	+	26245.8i	−0.705065	+	1.22121i	−0.966668	+	0.256033i	$0.917584\pi$
$774$	−2925.00	+	5066.25i	−0.135836	+	0.235275i
$775$	−7965.50	−	13796.7i	−0.369199	−	0.639471i
$776$	3088.00			0.142851
$777$		0			0
$778$	20292.0			0.935094
$779$	6111.00	+	10584.6i	0.281065	+	0.486818i
$780$	−1908.00	+	3304.75i	−0.0875864	+	0.151704i
$781$	−5130.00	+	8885.42i	−0.235039	+	0.407100i
$782$	7056.00	+	12221.4i	0.322662	+	0.558868i
$783$	4860.00			0.221816
$784$		0			0
$785$	−3036.00			−0.138038
$786$	6354.00	+	11005.5i	0.288346	+	0.499429i
$787$	13648.0	−	23639.0i	0.618169	−	1.07070i	−0.371651	−	0.928372i	$-0.621208\pi$
$787$	13648.0	−	23639.0i	0.618169	−	1.07070i	0.989820	−	0.142327i	$-0.0454584\pi$
$788$	2088.00	−	3616.52i	0.0943933	−	0.163494i
$789$	2358.00	+	4084.18i	0.106397	+	0.184285i
$790$	14052.0			0.632845
$791$		0			0
$792$	2160.00			0.0969094
$793$	−21677.0	−	37545.7i	−0.970710	−	1.68132i
$794$	6229.00	−	10788.9i	0.278412	−	0.482223i
$795$	−6912.00	+	11971.9i	−0.308356	+	0.534089i
$796$	−272.000	−	471.118i	−0.0121115	−	0.0209778i
$797$	35100.0			1.55998			0.779991	−	0.625791i	$-0.215224\pi$
$797$	35100.0			1.55998			0.779991	+	0.625791i	$0.215224\pi$
$798$		0			0
$799$	30744.0			1.36126
$800$	−1424.00	−	2466.44i	−0.0629325	−	0.109002i
$801$	−2700.00	+	4676.54i	−0.119101	+	0.206289i
$802$	−2472.00	+	4281.63i	−0.108840	+	0.188516i
$803$	645.000	+	1117.17i	0.0283456	+	0.0490961i
$804$	6276.00			0.275295
$805$		0			0
$806$	−18974.0			−0.829194
$807$	−2709.00	−	4692.13i	−0.118168	−	0.204672i
$808$	−2472.00	+	4281.63i	−0.107630	+	0.186420i
$809$	−22197.0	+	38446.3i	−0.964654	+	1.67083i	−0.254112	+	0.967175i	$0.581783\pi$
$809$	−22197.0	+	38446.3i	−0.964654	+	1.67083i	−0.710542	+	0.703655i	$0.751550\pi$
$810$	486.000	+	841.777i	0.0210819	+	0.0365148i
$811$	8584.00			0.371671			0.185835	−	0.982581i	$-0.440501\pi$
$811$	8584.00			0.371671			0.185835	+	0.982581i	$0.440501\pi$
$812$		0			0
$813$	−18336.0			−0.790986
$814$	4350.00	+	7534.42i	0.187306	+	0.324424i
$815$	−5532.00	+	9581.71i	−0.237764	+	0.411819i
$816$	2016.00	−	3491.81i	0.0864879	−	0.149801i
$817$	15762.5	+	27301.5i	0.674982	+	1.16910i
$818$	−14150.0			−0.604820
$819$		0			0
$820$	−3024.00			−0.128784
$821$	4917.00	+	8516.49i	0.209019	+	0.362031i	0.951406	−	0.307940i	$-0.0996397\pi$
$821$	4917.00	+	8516.49i	0.209019	+	0.362031i	−0.742387	+	0.669971i	$0.766306\pi$
$822$	−9036.00	+	15650.8i	−0.383414	+	0.664093i
$823$	−21928.0	+	37980.4i	−0.928751	+	1.60864i	−0.143336	+	0.989674i	$0.545783\pi$
$823$	−21928.0	+	37980.4i	−0.928751	+	1.60864i	−0.785415	+	0.618970i	$0.787550\pi$
$824$	−5900.00	−	10219.1i	−0.249437	−	0.432038i
$825$	−8010.00			−0.338027
$826$		0			0
$827$	13266.0			0.557804			0.278902	−	0.960320i	$-0.410030\pi$
$827$	13266.0			0.557804			0.278902	+	0.960320i	$0.410030\pi$
$828$	−1512.00	−	2618.86i	−0.0634609	−	0.109918i
$829$	8726.50	−	15114.7i	0.365602	−	0.633241i	−0.623271	−	0.782006i	$-0.714197\pi$
$829$	8726.50	−	15114.7i	0.365602	−	0.633241i	0.988873	+	0.148765i	$0.0475299\pi$
$830$	4860.00	−	8417.77i	0.203245	−	0.352030i
$831$	−6346.50	−	10992.5i	−0.264931	−	0.458874i
$832$	−3392.00			−0.141342
$833$		0			0
$834$	222.000			0.00921730
$835$	486.000	+	841.777i	0.0201422	+	0.0348873i
$836$	5820.00	−	10080.5i	0.240776	−	0.417037i
$837$	−2416.50	+	4185.50i	−0.0997927	+	0.172846i
$838$	4158.00	+	7201.87i	0.171403	+	0.296879i
$839$	35172.0			1.44729			0.723643	−	0.690175i	$-0.242466\pi$
$839$	35172.0			1.44729			0.723643	+	0.690175i	$0.242466\pi$
$840$		0			0
$841$	8011.00			0.328468
$842$	−6595.00	−	11422.9i	−0.269927	−	0.467528i
$843$	−5724.00	+	9914.26i	−0.233861	+	0.405060i
$844$	−2968.00	+	5140.73i	−0.121046	+	0.209658i
$845$	−1836.00	−	3180.05i	−0.0747459	−	0.129464i
$846$	−6588.00			−0.267731
$847$		0			0
$848$	−12288.0			−0.497608
$849$	5995.50	+	10384.5i	0.242362	+	0.419783i
$850$	−7476.00	+	12948.8i	−0.301676	+	0.522518i
$851$	6090.00	−	10548.2i	0.245314	−	0.424897i
$852$	−2052.00	−	3554.17i	−0.0825122	−	0.142915i
$853$	−3503.00			−0.140610			−0.0703051	−	0.997526i	$-0.522397\pi$
$853$	−3503.00			−0.140610			−0.0703051	+	0.997526i	$0.522397\pi$
$854$		0			0
$855$	5238.00			0.209516
$856$	7536.00	+	13052.7i	0.300906	+	0.521184i
$857$	11424.0	−	19786.9i	0.455352	−	0.788692i	−0.543357	−	0.839502i	$-0.682847\pi$
$857$	11424.0	−	19786.9i	0.455352	−	0.788692i	0.998708	+	0.0508097i	$0.0161802\pi$
$858$	−4770.00	+	8261.88i	−0.189796	+	0.328737i
$859$	−6728.00	−	11653.2i	−0.267237	−	0.462868i	0.700910	−	0.713249i	$-0.252777\pi$
$859$	−6728.00	−	11653.2i	−0.267237	−	0.462868i	−0.968147	+	0.250382i	$0.919444\pi$
$860$	−7800.00			−0.309277
$861$		0			0
$862$	−3036.00			−0.119961
$863$	−20355.0	−	35255.9i	−0.802888	−	1.39064i	−0.917708	−	0.397256i	$-0.869962\pi$
$863$	−20355.0	−	35255.9i	−0.802888	−	1.39064i	0.114820	−	0.993386i	$-0.463371\pi$
$864$	−432.000	+	748.246i	−0.0170103	+	0.0294628i
$865$	−8172.00	+	14154.3i	−0.321221	+	0.556371i
$866$	−8567.00	−	14838.5i	−0.336165	−	0.582254i
$867$	−6429.00			−0.251834
$868$		0			0
$869$	35130.0			1.37135
$870$	3240.00	+	5611.84i	0.126260	+	0.218689i
$871$	−13859.5	+	24005.4i	−0.539163	+	0.933858i
$872$	1652.00	−	2861.35i	0.0641557	−	0.111121i
$873$	1737.00	+	3008.57i	0.0673408	+	0.116638i
$874$	−16296.0			−0.630687
$875$		0			0
$876$	−516.000			−0.0199019
$877$	−1453.00	−	2516.67i	−0.0559456	−	0.0969007i	0.836696	−	0.547667i	$-0.184484\pi$
$877$	−1453.00	−	2516.67i	−0.0559456	−	0.0969007i	−0.892642	+	0.450767i	$0.851151\pi$
$878$	−10640.0	+	18429.0i	−0.408978	+	0.708371i
$879$	−6912.00	+	11971.9i	−0.265229	+	0.459389i
$880$	1440.00	+	2494.15i	0.0551618	+	0.0955431i
$881$	19188.0			0.733780			0.366890	−	0.930264i	$-0.380423\pi$
$881$	19188.0			0.733780			0.366890	+	0.930264i	$0.380423\pi$
$882$		0			0
$883$	−17251.0			−0.657466			−0.328733	−	0.944423i	$-0.606622\pi$
$883$	−17251.0			−0.657466			−0.328733	+	0.944423i	$0.606622\pi$
$884$	8904.00	+	15422.2i	0.338771	+	0.586769i
$885$	2376.00	−	4115.35i	0.0902467	−	0.156312i
$886$	7032.00	−	12179.8i	0.266642	−	0.461837i
$887$	−1047.00	−	1813.46i	−0.0396334	−	0.0686471i	0.845528	−	0.533931i	$-0.179286\pi$
$887$	−1047.00	−	1813.46i	−0.0396334	−	0.0686471i	−0.885162	+	0.465284i	$0.845952\pi$
$888$	−3480.00			−0.131510
$889$		0			0
$890$	−7200.00			−0.271174
$891$	1215.00	+	2104.44i	0.0456835	+	0.0791262i
$892$	−4064.00	+	7039.05i	−0.152548	+	0.264221i
$893$	−17751.0	+	30745.6i	−0.665190	+	1.15214i
$894$	4932.00	+	8542.47i	0.184509	+	0.319578i
$895$	−7524.00			−0.281005
$896$		0			0
$897$	13356.0			0.497150
$898$	−14814.0	−	25658.6i	−0.550501	−	0.953495i
$899$	−16110.0	+	27903.3i	−0.597662	+	1.03518i
$900$	1602.00	−	2774.75i	0.0593333	−	0.102768i
$901$	32256.0	+	55869.0i	1.19268	+	2.06578i
$902$	−7560.00			−0.279069
$903$		0			0
$904$	7056.00			0.259601
$905$	−5421.00	−	9389.45i	−0.199116	−	0.344879i
$906$	−3264.00	+	5653.41i	−0.119690	+	0.207309i
$907$	20133.5	−	34872.2i	0.737069	−	1.27664i	−0.216740	−	0.976229i	$-0.569542\pi$
$907$	20133.5	−	34872.2i	0.737069	−	1.27664i	0.953809	−	0.300412i	$-0.0971242\pi$
$908$	12396.0	+	21470.5i	0.453057	+	0.784718i
$909$	−5562.00			−0.202948
$910$		0			0
$911$	17604.0			0.640227			0.320113	−	0.947379i	$-0.396279\pi$
$911$	17604.0			0.640227			0.320113	+	0.947379i	$0.396279\pi$
$912$	2328.00	+	4032.21i	0.0845261	+	0.146403i
$913$	12150.0	−	21044.4i	0.440423	−	0.762835i
$914$	−11251.0	+	19487.3i	−0.407166	+	0.705233i
$915$	−7362.00	−	12751.4i	−0.265989	−	0.460707i
$916$	18364.0			0.662406
$917$		0			0
$918$	4536.00			0.163083
$919$	−1754.50	−	3038.88i	−0.0629767	−	0.109079i	0.832818	−	0.553547i	$-0.186726\pi$
$919$	−1754.50	−	3038.88i	−0.0629767	−	0.109079i	−0.895795	+	0.444468i	$0.853393\pi$
$920$	2016.00	−	3491.81i	0.0722452	−	0.125132i
$921$	946.500	−	1639.39i	0.0338634	−	0.0586532i
$922$	3852.00	+	6671.86i	0.137591	+	0.238315i
$923$	18126.0			0.646397
$924$		0			0
$925$	12905.0			0.458718
$926$	−475.000	−	822.724i	−0.0168569	−	0.0291970i
$927$	6637.50	−	11496.5i	0.235172	−	0.407329i
$928$	−2880.00	+	4988.31i	−0.101876	+	0.176454i
$929$	−17319.0	−	29997.4i	−0.611645	−	1.05940i	−0.990963	−	0.134134i	$-0.957175\pi$
$929$	−17319.0	−	29997.4i	−0.611645	−	1.05940i	0.379319	−	0.925266i	$-0.376158\pi$
$930$	−6444.00			−0.227212
$931$		0			0
$932$	18120.0			0.636846
$933$	−5841.00	−	10116.9i	−0.204958	−	0.354998i
$934$	−5934.00	+	10278.0i	−0.207887	+	0.360071i
$935$	7560.00	−	13094.3i	0.264426	−	0.458000i
$936$	−1908.00	−	3304.75i	−0.0666292	−	0.115405i
$937$	17353.0			0.605014			0.302507	−	0.953147i	$-0.402176\pi$
$937$	17353.0			0.605014			0.302507	+	0.953147i	$0.402176\pi$
$938$		0			0
$939$	−6555.00			−0.227811
$940$	−4392.00	−	7607.17i	−0.152395	−	0.263956i
$941$	−23460.0	+	40633.9i	−0.812725	+	1.40768i	0.0982252	+	0.995164i	$0.468683\pi$
$941$	−23460.0	+	40633.9i	−0.812725	+	1.40768i	−0.910950	+	0.412517i	$0.864650\pi$
$942$	1518.00	−	2629.25i	0.0525044	−	0.0909402i
$943$	5292.00	+	9166.01i	0.182748	+	0.316529i
$944$	4224.00			0.145635
$945$		0			0
$946$	−19500.0			−0.670190
$947$	−9177.00	−	15895.0i	−0.314902	−	0.545427i	0.664514	−	0.747275i	$-0.268638\pi$
$947$	−9177.00	−	15895.0i	−0.314902	−	0.545427i	−0.979417	+	0.201849i	$0.935305\pi$
$948$	−7026.00	+	12169.4i	−0.240711	+	0.416923i
$949$	1139.50	−	1973.67i	0.0389776	−	0.0675112i
$950$	−8633.00	−	14952.8i	−0.294833	−	0.510666i
$951$	−10512.0			−0.358438
$952$		0			0
$953$	35568.0			1.20898			0.604491	−	0.796612i	$-0.293376\pi$
$953$	35568.0			1.20898			0.604491	+	0.796612i	$0.293376\pi$
$954$	−6912.00	−	11971.9i	−0.234575	−	0.406295i
$955$	−2142.00	+	3710.05i	−0.0725796	+	0.125712i
$956$	−3060.00	+	5300.08i	−0.103522	+	0.179306i
$957$	8100.00	+	14029.6i	0.273601	+	0.473890i
$958$	−26736.0			−0.901671
$959$		0			0
$960$	−1152.00			−0.0387298
$961$	−1125.00	−	1948.56i	−0.0377631	−	0.0654076i
$962$	7685.00	−	13310.8i	0.257562	−	0.446110i
$963$	−8478.00	+	14684.3i	−0.283697	+	0.491377i
$964$	11068.0	+	19170.3i	0.369789	+	0.640493i
$965$	−22254.0			−0.742364
$966$		0			0
$967$	−27343.0			−0.909298			−0.454649	−	0.890671i	$-0.650235\pi$
$967$	−27343.0			−0.909298			−0.454649	+	0.890671i	$0.650235\pi$
$968$	−1724.00	−	2986.06i	−0.0572432	−	0.0991482i
$969$	12222.0	−	21169.1i	0.405188	−	0.701806i
$970$	−2316.00	+	4011.43i	−0.0766621	+	0.132783i
$971$	25512.0	+	44188.1i	0.843171	+	1.46042i	0.887200	+	0.461385i	$0.152647\pi$
$971$	25512.0	+	44188.1i	0.843171	+	1.46042i	−0.0440291	+	0.999030i	$0.514019\pi$
$972$	−972.000			−0.0320750
$973$		0			0
$974$	−13306.0			−0.437733
$975$	7075.50	+	12255.1i	0.232408	+	0.402542i
$976$	6544.00	−	11334.5i	0.214619	−	0.371731i
$977$	1113.00	−	1927.77i	0.0364463	−	0.0631268i	−0.847227	−	0.531231i	$-0.821730\pi$
$977$	1113.00	−	1927.77i	0.0364463	−	0.0631268i	0.883673	+	0.468104i	$0.155063\pi$
$978$	−5532.00	−	9581.71i	−0.180873	−	0.313281i
$979$	−18000.0			−0.587623
$980$		0			0
$981$	3717.00			0.120973
$982$	15444.0	+	26749.8i	0.501872	+	0.869267i
$983$	17652.0	−	30574.2i	0.572748	−	0.992029i	−0.423534	−	0.905880i	$-0.639211\pi$
$983$	17652.0	−	30574.2i	0.572748	−	0.992029i	0.996282	−	0.0861487i	$-0.0274560\pi$
$984$	1512.00	−	2618.86i	0.0489846	−	0.0848437i
$985$	3132.00	+	5424.78i	0.101314	+	0.175480i
$986$	30240.0			0.976712
$987$		0			0
$988$	−20564.0			−0.662174
$989$	13650.0	+	23642.5i	0.438872	+	0.760149i
$990$	−1620.00	+	2805.92i	−0.0520071	+	0.0900789i
$991$	1170.50	−	2027.37i	0.0375198	−	0.0649863i	−0.846656	−	0.532141i	$-0.821388\pi$
$991$	1170.50	−	2027.37i	0.0375198	−	0.0649863i	0.884176	+	0.467155i	$0.154721\pi$
$992$	−2864.00	−	4960.59i	−0.0916654	−	0.158769i
$993$	−8835.00			−0.282347
$994$		0			0
$995$	816.000			0.0259989
$996$	4860.00	+	8417.77i	0.154613	+	0.267798i
$997$	14507.5	−	25127.7i	0.460840	−	0.798198i	−0.538163	−	0.842841i	$-0.680882\pi$
$997$	14507.5	−	25127.7i	0.460840	−	0.798198i	0.999003	+	0.0446429i	$0.0142150\pi$
$998$	683.000	−	1182.99i	0.0216633	−	0.0375220i
$999$	−1957.50	−	3390.49i	−0.0619946	−	0.107378i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	294.4.e.i.67.1		2
3.2	odd	2		882.4.g.g.361.1		2
7.2	even	3	inner	294.4.e.i.79.1		2
7.3	odd	6		294.4.a.d.1.1		1
7.4	even	3		294.4.a.c.1.1		1
7.5	odd	6		42.4.e.a.37.1	yes	2
7.6	odd	2		42.4.e.a.25.1	✓	2
21.2	odd	6		882.4.g.g.667.1		2
21.5	even	6		126.4.g.b.37.1		2
21.11	odd	6		882.4.a.l.1.1		1
21.17	even	6		882.4.a.o.1.1		1
21.20	even	2		126.4.g.b.109.1		2
28.3	even	6		2352.4.a.f.1.1		1
28.11	odd	6		2352.4.a.bf.1.1		1
28.19	even	6		336.4.q.f.289.1		2
28.27	even	2		336.4.q.f.193.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.4.e.a.25.1	✓	2	7.6	odd	2
42.4.e.a.37.1	yes	2	7.5	odd	6
126.4.g.b.37.1		2	21.5	even	6
126.4.g.b.109.1		2	21.20	even	2
294.4.a.c.1.1		1	7.4	even	3
294.4.a.d.1.1		1	7.3	odd	6
294.4.e.i.67.1		2	1.1	even	1	trivial
294.4.e.i.79.1		2	7.2	even	3	inner
336.4.q.f.193.1		2	28.27	even	2
336.4.q.f.289.1		2	28.19	even	6
882.4.a.l.1.1		1	21.11	odd	6
882.4.a.o.1.1		1	21.17	even	6
882.4.g.g.361.1		2	3.2	odd	2
882.4.g.g.667.1		2	21.2	odd	6
2352.4.a.f.1.1		1	28.3	even	6
2352.4.a.bf.1.1		1	28.11	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:	\( N \)	\(=\)	\( 294 = 2 \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	294.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 + 1.73205i) q^{2} +(1.50000 - 2.59808i) q^{3} +(-2.00000 + 3.46410i) q^{4} +(-3.00000 - 5.19615i) q^{5} +6.00000 q^{6} -8.00000 q^{8} +(-4.50000 - 7.79423i) q^{9} +O(q^{10})\)	\(q+(1.00000 + 1.73205i) q^{2} +(1.50000 - 2.59808i) q^{3} +(-2.00000 + 3.46410i) q^{4} +(-3.00000 - 5.19615i) q^{5} +6.00000 q^{6} -8.00000 q^{8} +(-4.50000 - 7.79423i) q^{9} +(6.00000 - 10.3923i) q^{10} +(15.0000 - 25.9808i) q^{11} +(6.00000 + 10.3923i) q^{12} -53.0000 q^{13} -18.0000 q^{15} +(-8.00000 - 13.8564i) q^{16} +(-42.0000 + 72.7461i) q^{17} +(9.00000 - 15.5885i) q^{18} +(-48.5000 - 84.0045i) q^{19} +24.0000 q^{20} +60.0000 q^{22} +(-42.0000 - 72.7461i) q^{23} +(-12.0000 + 20.7846i) q^{24} +(44.5000 - 77.0763i) q^{25} +(-53.0000 - 91.7987i) q^{26} -27.0000 q^{27} -180.000 q^{29} +(-18.0000 - 31.1769i) q^{30} +(89.5000 - 155.019i) q^{31} +(16.0000 - 27.7128i) q^{32} +(-45.0000 - 77.9423i) q^{33} -168.000 q^{34} +36.0000 q^{36} +(72.5000 + 125.574i) q^{37} +(97.0000 - 168.009i) q^{38} +(-79.5000 + 137.698i) q^{39} +(24.0000 + 41.5692i) q^{40} -126.000 q^{41} -325.000 q^{43} +(60.0000 + 103.923i) q^{44} +(-27.0000 + 46.7654i) q^{45} +(84.0000 - 145.492i) q^{46} +(-183.000 - 316.965i) q^{47} -48.0000 q^{48} +178.000 q^{50} +(126.000 + 218.238i) q^{51} +(106.000 - 183.597i) q^{52} +(384.000 - 665.108i) q^{53} +(-27.0000 - 46.7654i) q^{54} -180.000 q^{55} -291.000 q^{57} +(-180.000 - 311.769i) q^{58} +(-132.000 + 228.631i) q^{59} +(36.0000 - 62.3538i) q^{60} +(409.000 + 708.409i) q^{61} +358.000 q^{62} +64.0000 q^{64} +(159.000 + 275.396i) q^{65} +(90.0000 - 155.885i) q^{66} +(261.500 - 452.931i) q^{67} +(-168.000 - 290.985i) q^{68} -252.000 q^{69} -342.000 q^{71} +(36.0000 + 62.3538i) q^{72} +(-21.5000 + 37.2391i) q^{73} +(-145.000 + 251.147i) q^{74} +(-133.500 - 231.229i) q^{75} +388.000 q^{76} -318.000 q^{78} +(585.500 + 1014.12i) q^{79} +(-48.0000 + 83.1384i) q^{80} +(-40.5000 + 70.1481i) q^{81} +(-126.000 - 218.238i) q^{82} +810.000 q^{83} +504.000 q^{85} +(-325.000 - 562.917i) q^{86} +(-270.000 + 467.654i) q^{87} +(-120.000 + 207.846i) q^{88} +(-300.000 - 519.615i) q^{89} -108.000 q^{90} +336.000 q^{92} +(-268.500 - 465.056i) q^{93} +(366.000 - 633.931i) q^{94} +(-291.000 + 504.027i) q^{95} +(-48.0000 - 83.1384i) q^{96} -386.000 q^{97} -270.000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} + 3 q^{3} - 4 q^{4} - 6 q^{5} + 12 q^{6} - 16 q^{8} - 9 q^{9}+O(q^{10}) \) 2 * q + 2 * q^2 + 3 * q^3 - 4 * q^4 - 6 * q^5 + 12 * q^6 - 16 * q^8 - 9 * q^9	\( 2 q + 2 q^{2} + 3 q^{3} - 4 q^{4} - 6 q^{5} + 12 q^{6} - 16 q^{8} - 9 q^{9} + 12 q^{10} + 30 q^{11} + 12 q^{12} - 106 q^{13} - 36 q^{15} - 16 q^{16} - 84 q^{17} + 18 q^{18} - 97 q^{19} + 48 q^{20} + 120 q^{22} - 84 q^{23} - 24 q^{24} + 89 q^{25} - 106 q^{26} - 54 q^{27} - 360 q^{29} - 36 q^{30} + 179 q^{31} + 32 q^{32} - 90 q^{33} - 336 q^{34} + 72 q^{36} + 145 q^{37} + 194 q^{38} - 159 q^{39} + 48 q^{40} - 252 q^{41} - 650 q^{43} + 120 q^{44} - 54 q^{45} + 168 q^{46} - 366 q^{47} - 96 q^{48} + 356 q^{50} + 252 q^{51} + 212 q^{52} + 768 q^{53} - 54 q^{54} - 360 q^{55} - 582 q^{57} - 360 q^{58} - 264 q^{59} + 72 q^{60} + 818 q^{61} + 716 q^{62} + 128 q^{64} + 318 q^{65} + 180 q^{66} + 523 q^{67} - 336 q^{68} - 504 q^{69} - 684 q^{71} + 72 q^{72} - 43 q^{73} - 290 q^{74} - 267 q^{75} + 776 q^{76} - 636 q^{78} + 1171 q^{79} - 96 q^{80} - 81 q^{81} - 252 q^{82} + 1620 q^{83} + 1008 q^{85} - 650 q^{86} - 540 q^{87} - 240 q^{88} - 600 q^{89} - 216 q^{90} + 672 q^{92} - 537 q^{93} + 732 q^{94} - 582 q^{95} - 96 q^{96} - 772 q^{97} - 540 q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 + 3 * q^3 - 4 * q^4 - 6 * q^5 + 12 * q^6 - 16 * q^8 - 9 * q^9 + 12 * q^10 + 30 * q^11 + 12 * q^12 - 106 * q^13 - 36 * q^15 - 16 * q^16 - 84 * q^17 + 18 * q^18 - 97 * q^19 + 48 * q^20 + 120 * q^22 - 84 * q^23 - 24 * q^24 + 89 * q^25 - 106 * q^26 - 54 * q^27 - 360 * q^29 - 36 * q^30 + 179 * q^31 + 32 * q^32 - 90 * q^33 - 336 * q^34 + 72 * q^36 + 145 * q^37 + 194 * q^38 - 159 * q^39 + 48 * q^40 - 252 * q^41 - 650 * q^43 + 120 * q^44 - 54 * q^45 + 168 * q^46 - 366 * q^47 - 96 * q^48 + 356 * q^50 + 252 * q^51 + 212 * q^52 + 768 * q^53 - 54 * q^54 - 360 * q^55 - 582 * q^57 - 360 * q^58 - 264 * q^59 + 72 * q^60 + 818 * q^61 + 716 * q^62 + 128 * q^64 + 318 * q^65 + 180 * q^66 + 523 * q^67 - 336 * q^68 - 504 * q^69 - 684 * q^71 + 72 * q^72 - 43 * q^73 - 290 * q^74 - 267 * q^75 + 776 * q^76 - 636 * q^78 + 1171 * q^79 - 96 * q^80 - 81 * q^81 - 252 * q^82 + 1620 * q^83 + 1008 * q^85 - 650 * q^86 - 540 * q^87 - 240 * q^88 - 600 * q^89 - 216 * q^90 + 672 * q^92 - 537 * q^93 + 732 * q^94 - 582 * q^95 - 96 * q^96 - 772 * q^97 - 540 * q^99

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