LMFDB - Embedded newform 294.4.e.f.79.1

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:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			79.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	294.79
Dual form			294.4.e.f.67.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 - 1.73205i) q^{2} +(-1.50000 - 2.59808i) q^{3} +(-2.00000 - 3.46410i) q^{4} +(-4.00000 + 6.92820i) q^{5} -6.00000 q^{6} -8.00000 q^{8} +(-4.50000 + 7.79423i) q^{9} +O(q^{10})$	\(q+(1.00000 - 1.73205i) q^{2} +(-1.50000 - 2.59808i) q^{3} +(-2.00000 - 3.46410i) q^{4} +(-4.00000 + 6.92820i) q^{5} -6.00000 q^{6} -8.00000 q^{8} +(-4.50000 + 7.79423i) q^{9} +(8.00000 + 13.8564i) q^{10} +(-20.0000 - 34.6410i) q^{11} +(-6.00000 + 10.3923i) q^{12} +4.00000 q^{13} +24.0000 q^{15} +(-8.00000 + 13.8564i) q^{16} +(42.0000 + 72.7461i) q^{17} +(9.00000 + 15.5885i) q^{18} +(-74.0000 + 128.172i) q^{19} +32.0000 q^{20} -80.0000 q^{22} +(-42.0000 + 72.7461i) q^{23} +(12.0000 + 20.7846i) q^{24} +(30.5000 + 52.8275i) q^{25} +(4.00000 - 6.92820i) q^{26} +27.0000 q^{27} +58.0000 q^{29} +(24.0000 - 41.5692i) q^{30} +(68.0000 + 117.779i) q^{31} +(16.0000 + 27.7128i) q^{32} +(-60.0000 + 103.923i) q^{33} +168.000 q^{34} +36.0000 q^{36} +(111.000 - 192.258i) q^{37} +(148.000 + 256.344i) q^{38} +(-6.00000 - 10.3923i) q^{39} +(32.0000 - 55.4256i) q^{40} +420.000 q^{41} -164.000 q^{43} +(-80.0000 + 138.564i) q^{44} +(-36.0000 - 62.3538i) q^{45} +(84.0000 + 145.492i) q^{46} +(-244.000 + 422.620i) q^{47} +48.0000 q^{48} +122.000 q^{50} +(126.000 - 218.238i) q^{51} +(-8.00000 - 13.8564i) q^{52} +(-239.000 - 413.960i) q^{53} +(27.0000 - 46.7654i) q^{54} +320.000 q^{55} +444.000 q^{57} +(58.0000 - 100.459i) q^{58} +(-274.000 - 474.582i) q^{59} +(-48.0000 - 83.1384i) q^{60} +(-346.000 + 599.290i) q^{61} +272.000 q^{62} +64.0000 q^{64} +(-16.0000 + 27.7128i) q^{65} +(120.000 + 207.846i) q^{66} +(454.000 + 786.351i) q^{67} +(168.000 - 290.985i) q^{68} +252.000 q^{69} -524.000 q^{71} +(36.0000 - 62.3538i) q^{72} +(-220.000 - 381.051i) q^{73} +(-222.000 - 384.515i) q^{74} +(91.5000 - 158.483i) q^{75} +592.000 q^{76} -24.0000 q^{78} +(-608.000 + 1053.09i) q^{79} +(-64.0000 - 110.851i) q^{80} +(-40.5000 - 70.1481i) q^{81} +(420.000 - 727.461i) q^{82} -684.000 q^{83} -672.000 q^{85} +(-164.000 + 284.056i) q^{86} +(-87.0000 - 150.688i) q^{87} +(160.000 + 277.128i) q^{88} +(-302.000 + 523.079i) q^{89} -144.000 q^{90} +336.000 q^{92} +(204.000 - 353.338i) q^{93} +(488.000 + 845.241i) q^{94} +(-592.000 - 1025.37i) q^{95} +(48.0000 - 83.1384i) q^{96} -832.000 q^{97} +360.000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} - 3 q^{3} - 4 q^{4} - 8 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 - 8 * q^5 - 12 * q^6 - 16 * q^8 - 9 * q^9	\( 2 q + 2 q^{2} - 3 q^{3} - 4 q^{4} - 8 q^{5} - 12 q^{6} - 16 q^{8} - 9 q^{9} + 16 q^{10} - 40 q^{11} - 12 q^{12} + 8 q^{13} + 48 q^{15} - 16 q^{16} + 84 q^{17} + 18 q^{18} - 148 q^{19} + 64 q^{20} - 160 q^{22} - 84 q^{23} + 24 q^{24} + 61 q^{25} + 8 q^{26} + 54 q^{27} + 116 q^{29} + 48 q^{30} + 136 q^{31} + 32 q^{32} - 120 q^{33} + 336 q^{34} + 72 q^{36} + 222 q^{37} + 296 q^{38} - 12 q^{39} + 64 q^{40} + 840 q^{41} - 328 q^{43} - 160 q^{44} - 72 q^{45} + 168 q^{46} - 488 q^{47} + 96 q^{48} + 244 q^{50} + 252 q^{51} - 16 q^{52} - 478 q^{53} + 54 q^{54} + 640 q^{55} + 888 q^{57} + 116 q^{58} - 548 q^{59} - 96 q^{60} - 692 q^{61} + 544 q^{62} + 128 q^{64} - 32 q^{65} + 240 q^{66} + 908 q^{67} + 336 q^{68} + 504 q^{69} - 1048 q^{71} + 72 q^{72} - 440 q^{73} - 444 q^{74} + 183 q^{75} + 1184 q^{76} - 48 q^{78} - 1216 q^{79} - 128 q^{80} - 81 q^{81} + 840 q^{82} - 1368 q^{83} - 1344 q^{85} - 328 q^{86} - 174 q^{87} + 320 q^{88} - 604 q^{89} - 288 q^{90} + 672 q^{92} + 408 q^{93} + 976 q^{94} - 1184 q^{95} + 96 q^{96} - 1664 q^{97} + 720 q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 - 3 * q^3 - 4 * q^4 - 8 * q^5 - 12 * q^6 - 16 * q^8 - 9 * q^9 + 16 * q^10 - 40 * q^11 - 12 * q^12 + 8 * q^13 + 48 * q^15 - 16 * q^16 + 84 * q^17 + 18 * q^18 - 148 * q^19 + 64 * q^20 - 160 * q^22 - 84 * q^23 + 24 * q^24 + 61 * q^25 + 8 * q^26 + 54 * q^27 + 116 * q^29 + 48 * q^30 + 136 * q^31 + 32 * q^32 - 120 * q^33 + 336 * q^34 + 72 * q^36 + 222 * q^37 + 296 * q^38 - 12 * q^39 + 64 * q^40 + 840 * q^41 - 328 * q^43 - 160 * q^44 - 72 * q^45 + 168 * q^46 - 488 * q^47 + 96 * q^48 + 244 * q^50 + 252 * q^51 - 16 * q^52 - 478 * q^53 + 54 * q^54 + 640 * q^55 + 888 * q^57 + 116 * q^58 - 548 * q^59 - 96 * q^60 - 692 * q^61 + 544 * q^62 + 128 * q^64 - 32 * q^65 + 240 * q^66 + 908 * q^67 + 336 * q^68 + 504 * q^69 - 1048 * q^71 + 72 * q^72 - 440 * q^73 - 444 * q^74 + 183 * q^75 + 1184 * q^76 - 48 * q^78 - 1216 * q^79 - 128 * q^80 - 81 * q^81 + 840 * q^82 - 1368 * q^83 - 1344 * q^85 - 328 * q^86 - 174 * q^87 + 320 * q^88 - 604 * q^89 - 288 * q^90 + 672 * q^92 + 408 * q^93 + 976 * q^94 - 1184 * q^95 + 96 * q^96 - 1664 * q^97 + 720 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	1.00000	−	1.73205i	0.353553	−	0.612372i
$2$	1.00000	−	1.73205i	0.353553	−	0.612372i
$3$	−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
$5$	−4.00000	+	6.92820i	−0.357771	+	0.619677i	−0.987588	−	0.157066i	$-0.949796\pi$
$5$	−4.00000	+	6.92820i	−0.357771	+	0.619677i	0.629817	+	0.776743i	$0.283130\pi$
$6$	−6.00000			−0.408248
$7$		0			0
$7$		0			0
$8$	−8.00000			−0.353553
$9$	−4.50000	+	7.79423i	−0.166667	+	0.288675i
$10$	8.00000	+	13.8564i	0.252982	+	0.438178i
$11$	−20.0000	−	34.6410i	−0.548202	−	0.949514i	−0.998398	−	0.0565844i	$-0.981979\pi$
$11$	−20.0000	−	34.6410i	−0.548202	−	0.949514i	0.450195	−	0.892930i	$-0.351354\pi$
$12$	−6.00000	+	10.3923i	−0.144338	+	0.250000i
$13$	4.00000			0.0853385			0.0426692	−	0.999089i	$-0.486414\pi$
$13$	4.00000			0.0853385			0.0426692	+	0.999089i	$0.486414\pi$
$14$		0			0
$15$	24.0000			0.413118
$16$	−8.00000	+	13.8564i	−0.125000	+	0.216506i
$17$	42.0000	+	72.7461i	0.599206	+	1.03785i	0.992939	+	0.118630i	$0.0378502\pi$
$17$	42.0000	+	72.7461i	0.599206	+	1.03785i	−0.393733	+	0.919225i	$0.628817\pi$
$18$	9.00000	+	15.5885i	0.117851	+	0.204124i
$19$	−74.0000	+	128.172i	−0.893514	+	1.54761i	−0.0578808	+	0.998324i	$0.518434\pi$
$19$	−74.0000	+	128.172i	−0.893514	+	1.54761i	−0.835633	+	0.549288i	$0.814899\pi$
$20$	32.0000			0.357771
$21$		0			0
$22$	−80.0000			−0.775275
$23$	−42.0000	+	72.7461i	−0.380765	+	0.659505i	−0.991172	−	0.132583i	$-0.957673\pi$
$23$	−42.0000	+	72.7461i	−0.380765	+	0.659505i	0.610406	+	0.792088i	$0.291006\pi$
$24$	12.0000	+	20.7846i	0.102062	+	0.176777i
$25$	30.5000	+	52.8275i	0.244000	+	0.422620i
$26$	4.00000	−	6.92820i	0.0301717	−	0.0522589i
$27$	27.0000			0.192450
$28$		0			0
$29$	58.0000			0.371391			0.185695	−	0.982607i	$-0.440546\pi$
$29$	58.0000			0.371391			0.185695	+	0.982607i	$0.440546\pi$
$30$	24.0000	−	41.5692i	0.146059	−	0.252982i
$31$	68.0000	+	117.779i	0.393973	+	0.682381i	0.992970	−	0.118370i	$-0.0377670\pi$
$31$	68.0000	+	117.779i	0.393973	+	0.682381i	−0.598997	+	0.800752i	$0.704434\pi$
$32$	16.0000	+	27.7128i	0.0883883	+	0.153093i
$33$	−60.0000	+	103.923i	−0.316505	+	0.548202i
$34$	168.000			0.847405
$35$		0			0
$36$	36.0000			0.166667
$37$	111.000	−	192.258i	0.493197	−	0.854242i	−0.506772	−	0.862080i	$-0.669162\pi$
$37$	111.000	−	192.258i	0.493197	−	0.854242i	0.999969	+	0.00783774i	$0.00249486\pi$
$38$	148.000	+	256.344i	0.631810	+	1.09433i
$39$	−6.00000	−	10.3923i	−0.0246351	−	0.0426692i
$40$	32.0000	−	55.4256i	0.126491	−	0.219089i
$41$	420.000			1.59983			0.799914	−	0.600114i	$-0.204878\pi$
$41$	420.000			1.59983			0.799914	+	0.600114i	$0.204878\pi$
$42$		0			0
$43$	−164.000			−0.581622			−0.290811	−	0.956780i	$-0.593925\pi$
$43$	−164.000			−0.581622			−0.290811	+	0.956780i	$0.593925\pi$
$44$	−80.0000	+	138.564i	−0.274101	+	0.474757i
$45$	−36.0000	−	62.3538i	−0.119257	−	0.206559i
$46$	84.0000	+	145.492i	0.269242	+	0.466341i
$47$	−244.000	+	422.620i	−0.757257	+	1.31161i	0.186988	+	0.982362i	$0.440127\pi$
$47$	−244.000	+	422.620i	−0.757257	+	1.31161i	−0.944245	+	0.329245i	$0.893206\pi$
$48$	48.0000			0.144338
$49$		0			0
$50$	122.000			0.345068
$51$	126.000	−	218.238i	0.345952	−	0.599206i
$52$	−8.00000	−	13.8564i	−0.0213346	−	0.0369527i
$53$	−239.000	−	413.960i	−0.619418	−	1.07286i	−0.989592	−	0.143902i	$-0.954035\pi$
$53$	−239.000	−	413.960i	−0.619418	−	1.07286i	0.370174	−	0.928963i	$-0.379298\pi$
$54$	27.0000	−	46.7654i	0.0680414	−	0.117851i
$55$	320.000			0.784523
$56$		0			0
$57$	444.000			1.03174
$58$	58.0000	−	100.459i	0.131306	−	0.227429i
$59$	−274.000	−	474.582i	−0.604606	−	1.04721i	−0.992114	−	0.125342i	$-0.959997\pi$
$59$	−274.000	−	474.582i	−0.604606	−	1.04721i	0.387507	−	0.921867i	$-0.373336\pi$
$60$	−48.0000	−	83.1384i	−0.103280	−	0.178885i
$61$	−346.000	+	599.290i	−0.726242	+	1.25789i	0.232219	+	0.972664i	$0.425401\pi$
$61$	−346.000	+	599.290i	−0.726242	+	1.25789i	−0.958461	+	0.285224i	$0.907932\pi$
$62$	272.000			0.557162
$63$		0			0
$64$	64.0000			0.125000
$65$	−16.0000	+	27.7128i	−0.0305316	+	0.0528823i
$66$	120.000	+	207.846i	0.223803	+	0.387638i
$67$	454.000	+	786.351i	0.827835	+	1.43385i	0.899733	+	0.436440i	$0.143761\pi$
$67$	454.000	+	786.351i	0.827835	+	1.43385i	−0.0718987	+	0.997412i	$0.522906\pi$
$68$	168.000	−	290.985i	0.299603	−	0.518927i
$69$	252.000			0.439670
$70$		0			0
$71$	−524.000			−0.875878			−0.437939	−	0.899005i	$-0.644291\pi$
$71$	−524.000			−0.875878			−0.437939	+	0.899005i	$0.644291\pi$
$72$	36.0000	−	62.3538i	0.0589256	−	0.102062i
$73$	−220.000	−	381.051i	−0.352727	−	0.610941i	0.633999	−	0.773334i	$-0.281412\pi$
$73$	−220.000	−	381.051i	−0.352727	−	0.610941i	−0.986726	+	0.162393i	$0.948079\pi$
$74$	−222.000	−	384.515i	−0.348743	−	0.604040i
$75$	91.5000	−	158.483i	0.140873	−	0.244000i
$76$	592.000			0.893514
$77$		0			0
$78$	−24.0000			−0.0348393
$79$	−608.000	+	1053.09i	−0.865890	+	1.49977i	0.000269874		1.00000i	$0.499914\pi$
$79$	−608.000	+	1053.09i	−0.865890	+	1.49977i	−0.866160	+	0.499766i	$0.833419\pi$
$80$	−64.0000	−	110.851i	−0.0894427	−	0.154919i
$81$	−40.5000	−	70.1481i	−0.0555556	−	0.0962250i
$82$	420.000	−	727.461i	0.565625	−	0.979691i
$83$	−684.000			−0.904563			−0.452282	−	0.891875i	$-0.649390\pi$
$83$	−684.000			−0.904563			−0.452282	+	0.891875i	$0.649390\pi$
$84$		0			0
$85$	−672.000			−0.857513
$86$	−164.000	+	284.056i	−0.205635	+	0.356170i
$87$	−87.0000	−	150.688i	−0.107211	−	0.185695i
$88$	160.000	+	277.128i	0.193819	+	0.335704i
$89$	−302.000	+	523.079i	−0.359685	+	0.622992i	−0.987908	−	0.155041i	$-0.950449\pi$
$89$	−302.000	+	523.079i	−0.359685	+	0.622992i	0.628223	+	0.778033i	$0.283782\pi$
$90$	−144.000			−0.168655
$91$		0			0
$92$	336.000			0.380765
$93$	204.000	−	353.338i	0.227460	−	0.393973i
$94$	488.000	+	845.241i	0.535461	+	0.927446i
$95$	−592.000	−	1025.37i	−0.639347	−	1.10738i
$96$	48.0000	−	83.1384i	0.0510310	−	0.0883883i
$97$	−832.000			−0.870895			−0.435447	−	0.900214i	$-0.643410\pi$
$97$	−832.000			−0.870895			−0.435447	+	0.900214i	$0.643410\pi$
$98$		0			0
$99$	360.000			0.365468
$100$	122.000	−	211.310i	0.122000	−	0.211310i
$101$	−232.000	−	401.836i	−0.228563	−	0.395883i	0.728819	−	0.684706i	$-0.240069\pi$
$101$	−232.000	−	401.836i	−0.228563	−	0.395883i	−0.957382	+	0.288823i	$0.906736\pi$
$102$	−252.000	−	436.477i	−0.244625	−	0.423702i
$103$	316.000	−	547.328i	0.302295	−	0.523591i	−0.674360	−	0.738402i	$-0.735580\pi$
$103$	316.000	−	547.328i	0.302295	−	0.523591i	0.976655	+	0.214812i	$0.0689138\pi$
$104$	−32.0000			−0.0301717
$105$		0			0
$106$	−956.000			−0.875990
$107$	80.0000	−	138.564i	0.0722794	−	0.125192i	−0.827621	−	0.561288i	$-0.810306\pi$
$107$	80.0000	−	138.564i	0.0722794	−	0.125192i	0.899900	+	0.436096i	$0.143639\pi$
$108$	−54.0000	−	93.5307i	−0.0481125	−	0.0833333i
$109$	1099.00	+	1903.52i	0.965735	+	1.67270i	0.707627	+	0.706586i	$0.249766\pi$
$109$	1099.00	+	1903.52i	0.965735	+	1.67270i	0.258108	+	0.966116i	$0.416901\pi$
$110$	320.000	−	554.256i	0.277371	−	0.480421i
$111$	−666.000			−0.569495
$112$		0			0
$113$	770.000			0.641022			0.320511	−	0.947245i	$-0.396145\pi$
$113$	770.000			0.641022			0.320511	+	0.947245i	$0.396145\pi$
$114$	444.000	−	769.031i	0.364776	−	0.631810i
$115$	−336.000	−	581.969i	−0.272454	−	0.471903i
$116$	−116.000	−	200.918i	−0.0928477	−	0.160817i
$117$	−18.0000	+	31.1769i	−0.0142231	+	0.0246351i
$118$	−1096.00			−0.855042
$119$		0			0
$120$	−192.000			−0.146059
$121$	−134.500	+	232.961i	−0.101052	+	0.175027i
$122$	692.000	+	1198.58i	0.513531	+	0.889461i
$123$	−630.000	−	1091.19i	−0.461831	−	0.799914i
$124$	272.000	−	471.118i	0.196986	−	0.341191i
$125$	−1488.00			−1.06473
$126$		0			0
$127$	−184.000			−0.128562			−0.0642809	−	0.997932i	$-0.520475\pi$
$127$	−184.000			−0.128562			−0.0642809	+	0.997932i	$0.520475\pi$
$128$	64.0000	−	110.851i	0.0441942	−	0.0765466i
$129$	246.000	+	426.084i	0.167900	+	0.290811i
$130$	32.0000	+	55.4256i	0.0215891	+	0.0373935i
$131$	726.000	−	1257.47i	0.484205	−	0.838668i	−0.515630	−	0.856811i	$-0.672442\pi$
$131$	726.000	−	1257.47i	0.484205	−	0.838668i	0.999835	+	0.0181429i	$0.00577539\pi$
$132$	480.000			0.316505
$133$		0			0
$134$	1816.00			1.17074
$135$	−108.000	+	187.061i	−0.0688530	+	0.119257i
$136$	−336.000	−	581.969i	−0.211851	−	0.366937i
$137$	−323.000	−	559.452i	−0.201429	−	0.348885i	0.747560	−	0.664194i	$-0.231225\pi$
$137$	−323.000	−	559.452i	−0.201429	−	0.348885i	−0.948989	+	0.315309i	$0.897892\pi$
$138$	252.000	−	436.477i	0.155447	−	0.269242i
$139$	−3012.00			−1.83795			−0.918973	−	0.394320i	$-0.870980\pi$
$139$	−3012.00			−1.83795			−0.918973	+	0.394320i	$0.870980\pi$
$140$		0			0
$141$	1464.00			0.874405
$142$	−524.000	+	907.595i	−0.309670	+	0.536364i
$143$	−80.0000	−	138.564i	−0.0467828	−	0.0810301i
$144$	−72.0000	−	124.708i	−0.0416667	−	0.0721688i
$145$	−232.000	+	401.836i	−0.132873	+	0.230142i
$146$	−880.000			−0.498831
$147$		0			0
$148$	−888.000			−0.493197
$149$	1585.00	−	2745.30i	0.871465	−	1.50942i	0.0109833	−	0.999940i	$-0.496504\pi$
$149$	1585.00	−	2745.30i	0.871465	−	1.50942i	0.860482	−	0.509482i	$-0.170163\pi$
$150$	−183.000	−	316.965i	−0.0996126	−	0.172534i
$151$	940.000	+	1628.13i	0.506597	+	0.877451i	0.999971	+	0.00763414i	$0.00243005\pi$
$151$	940.000	+	1628.13i	0.506597	+	0.877451i	−0.493374	+	0.869817i	$0.664237\pi$
$152$	592.000	−	1025.37i	0.315905	−	0.547163i
$153$	−756.000			−0.399470
$154$		0			0
$155$	−1088.00			−0.563808
$156$	−24.0000	+	41.5692i	−0.0123176	+	0.0213346i
$157$	−302.000	−	523.079i	−0.153517	−	0.265900i	0.779001	−	0.627023i	$-0.215727\pi$
$157$	−302.000	−	523.079i	−0.153517	−	0.265900i	−0.932518	+	0.361123i	$0.882393\pi$
$158$	1216.00	+	2106.17i	0.612277	+	1.06049i
$159$	−717.000	+	1241.88i	−0.357621	+	0.619418i
$160$	−256.000			−0.126491
$161$		0			0
$162$	−162.000			−0.0785674
$163$	−558.000	+	966.484i	−0.268135	+	0.464423i	−0.968380	−	0.249479i	$-0.919741\pi$
$163$	−558.000	+	966.484i	−0.268135	+	0.464423i	0.700246	+	0.713902i	$0.253074\pi$
$164$	−840.000	−	1454.92i	−0.399957	−	0.692746i
$165$	−480.000	−	831.384i	−0.226472	−	0.392262i
$166$	−684.000	+	1184.72i	−0.319811	+	0.553930i
$167$	−1784.00			−0.826647			−0.413324	−	0.910584i	$-0.635632\pi$
$167$	−1784.00			−0.826647			−0.413324	+	0.910584i	$0.635632\pi$
$168$		0			0
$169$	−2181.00			−0.992717
$170$	−672.000	+	1163.94i	−0.303177	+	0.525118i
$171$	−666.000	−	1153.55i	−0.297838	−	0.515870i
$172$	328.000	+	568.113i	0.145406	+	0.251850i
$173$	172.000	−	297.913i	0.0755891	−	0.130924i	−0.825753	−	0.564032i	$-0.809250\pi$
$173$	172.000	−	297.913i	0.0755891	−	0.130924i	0.901342	+	0.433107i	$0.142583\pi$
$174$	−348.000			−0.151620
$175$		0			0
$176$	640.000			0.274101
$177$	−822.000	+	1423.75i	−0.349070	+	0.604606i
$178$	604.000	+	1046.16i	0.254335	+	0.440522i
$179$	−696.000	−	1205.51i	−0.290623	−	0.503373i	0.683334	−	0.730106i	$-0.260529\pi$
$179$	−696.000	−	1205.51i	−0.290623	−	0.503373i	−0.973957	+	0.226732i	$0.927196\pi$
$180$	−144.000	+	249.415i	−0.0596285	+	0.103280i
$181$	4052.00			1.66399			0.831997	−	0.554781i	$-0.187198\pi$
$181$	4052.00			1.66399			0.831997	+	0.554781i	$0.187198\pi$
$182$		0			0
$183$	2076.00			0.838592
$184$	336.000	−	581.969i	0.134621	−	0.233170i
$185$	888.000	+	1538.06i	0.352903	+	0.611246i
$186$	−408.000	−	706.677i	−0.160839	−	0.278581i
$187$	1680.00	−	2909.85i	0.656972	−	1.13791i
$188$	1952.00			0.757257
$189$		0			0
$190$	−2368.00			−0.904173
$191$	1554.00	−	2691.61i	0.588709	−	1.01967i	−0.405692	−	0.914010i	$-0.632970\pi$
$191$	1554.00	−	2691.61i	0.588709	−	1.01967i	0.994402	−	0.105665i	$-0.0336971\pi$
$192$	−96.0000	−	166.277i	−0.0360844	−	0.0625000i
$193$	−25.0000	−	43.3013i	−0.00932404	−	0.0161497i	0.861326	−	0.508053i	$-0.169635\pi$
$193$	−25.0000	−	43.3013i	−0.00932404	−	0.0161497i	−0.870650	+	0.491903i	$0.836301\pi$
$194$	−832.000	+	1441.07i	−0.307908	+	0.533312i
$195$	96.0000			0.0352549
$196$		0			0
$197$	−162.000			−0.0585889			−0.0292945	−	0.999571i	$-0.509326\pi$
$197$	−162.000			−0.0585889			−0.0292945	+	0.999571i	$0.509326\pi$
$198$	360.000	−	623.538i	0.129213	−	0.223803i
$199$	−772.000	−	1337.14i	−0.275003	−	0.476319i	0.695133	−	0.718881i	$-0.255346\pi$
$199$	−772.000	−	1337.14i	−0.275003	−	0.476319i	−0.970136	+	0.242562i	$0.922012\pi$
$200$	−244.000	−	422.620i	−0.0862670	−	0.149419i
$201$	1362.00	−	2359.05i	0.477951	−	0.827835i
$202$	−928.000			−0.323237
$203$		0			0
$204$	−1008.00			−0.345952
$205$	−1680.00	+	2909.85i	−0.572372	+	0.991378i
$206$	−632.000	−	1094.66i	−0.213755	−	0.370234i
$207$	−378.000	−	654.715i	−0.126922	−	0.219835i
$208$	−32.0000	+	55.4256i	−0.0106673	+	0.0184763i
$209$	5920.00			1.95931
$210$		0			0
$211$	−1204.00			−0.392828			−0.196414	−	0.980521i	$-0.562930\pi$
$211$	−1204.00			−0.392828			−0.196414	+	0.980521i	$0.562930\pi$
$212$	−956.000	+	1655.84i	−0.309709	+	0.536432i
$213$	786.000	+	1361.39i	0.252844	+	0.437939i
$214$	−160.000	−	277.128i	−0.0511092	−	0.0885238i
$215$	656.000	−	1136.23i	0.208088	−	0.360418i
$216$	−216.000			−0.0680414
$217$		0			0
$218$	4396.00			1.36576
$219$	−660.000	+	1143.15i	−0.203647	+	0.352727i
$220$	−640.000	−	1108.51i	−0.196131	−	0.339709i
$221$	168.000	+	290.985i	0.0511353	+	0.0885690i
$222$	−666.000	+	1153.55i	−0.201347	+	0.348743i
$223$	2000.00			0.600583			0.300291	−	0.953848i	$-0.402916\pi$
$223$	2000.00			0.600583			0.300291	+	0.953848i	$0.402916\pi$
$224$		0			0
$225$	−549.000			−0.162667
$226$	770.000	−	1333.68i	0.226636	−	0.392544i
$227$	−194.000	−	336.018i	−0.0567235	−	0.0982480i	0.836269	−	0.548319i	$-0.184732\pi$
$227$	−194.000	−	336.018i	−0.0567235	−	0.0982480i	−0.892993	+	0.450071i	$0.851399\pi$
$228$	−888.000	−	1538.06i	−0.257935	−	0.446757i
$229$	−2090.00	+	3619.99i	−0.603105	+	1.04461i	0.389243	+	0.921135i	$0.372737\pi$
$229$	−2090.00	+	3619.99i	−0.603105	+	1.04461i	−0.992348	+	0.123474i	$0.960597\pi$
$230$	−1344.00			−0.385308
$231$		0			0
$232$	−464.000			−0.131306
$233$	661.000	−	1144.89i	0.185852	−	0.321905i	−0.758011	−	0.652242i	$-0.773829\pi$
$233$	661.000	−	1144.89i	0.185852	−	0.321905i	0.943863	+	0.330336i	$0.107162\pi$
$234$	36.0000	+	62.3538i	0.0100572	+	0.0174196i
$235$	−1952.00	−	3380.96i	−0.541849	−	0.938509i
$236$	−1096.00	+	1898.33i	−0.302303	+	0.523604i
$237$	3648.00			0.999844
$238$		0			0
$239$	2412.00			0.652800			0.326400	−	0.945232i	$-0.394164\pi$
$239$	2412.00			0.652800			0.326400	+	0.945232i	$0.394164\pi$
$240$	−192.000	+	332.554i	−0.0516398	+	0.0894427i
$241$	2168.00	+	3755.09i	0.579474	+	1.00368i	0.995540	+	0.0943434i	$0.0300752\pi$
$241$	2168.00	+	3755.09i	0.579474	+	1.00368i	−0.416066	+	0.909334i	$0.636591\pi$
$242$	269.000	+	465.922i	0.0714544	+	0.123763i
$243$	−121.500	+	210.444i	−0.0320750	+	0.0555556i
$244$	2768.00			0.726242
$245$		0			0
$246$	−2520.00			−0.653127
$247$	−296.000	+	512.687i	−0.0762511	+	0.132071i
$248$	−544.000	−	942.236i	−0.139290	−	0.241258i
$249$	1026.00	+	1777.08i	0.261125	+	0.452282i
$250$	−1488.00	+	2577.29i	−0.376438	+	0.652009i
$251$	764.000			0.192125			0.0960623	−	0.995375i	$-0.469375\pi$
$251$	764.000			0.192125			0.0960623	+	0.995375i	$0.469375\pi$
$252$		0			0
$253$	3360.00			0.834946
$254$	−184.000	+	318.697i	−0.0454535	+	0.0787278i
$255$	1008.00	+	1745.91i	0.247543	+	0.428757i
$256$	−128.000	−	221.703i	−0.0312500	−	0.0541266i
$257$	−2150.00	+	3723.91i	−0.521842	+	0.903856i	0.477835	+	0.878449i	$0.341421\pi$
$257$	−2150.00	+	3723.91i	−0.521842	+	0.903856i	−0.999677	+	0.0254070i	$0.991912\pi$
$258$	984.000			0.237446
$259$		0			0
$260$	128.000			0.0305316
$261$	−261.000	+	452.065i	−0.0618984	+	0.107211i
$262$	−1452.00	−	2514.94i	−0.342385	−	0.593028i
$263$	1930.00	+	3342.86i	0.452505	+	0.783762i	0.998541	−	0.0539998i	$-0.0171970\pi$
$263$	1930.00	+	3342.86i	0.452505	+	0.783762i	−0.546036	+	0.837762i	$0.683864\pi$
$264$	480.000	−	831.384i	0.111901	−	0.193819i
$265$	3824.00			0.886439
$266$		0			0
$267$	1812.00			0.415328
$268$	1816.00	−	3145.40i	0.413917	−	0.716926i
$269$	1400.00	+	2424.87i	0.317322	+	0.549617i	0.979928	−	0.199350i	$-0.0638832\pi$
$269$	1400.00	+	2424.87i	0.317322	+	0.549617i	−0.662607	+	0.748968i	$0.730550\pi$
$270$	216.000	+	374.123i	0.0486864	+	0.0843274i
$271$	2440.00	−	4226.20i	0.546935	−	0.947320i	−0.451547	−	0.892247i	$-0.649128\pi$
$271$	2440.00	−	4226.20i	0.546935	−	0.947320i	0.998482	−	0.0550723i	$-0.0175389\pi$
$272$	−1344.00			−0.299603
$273$		0			0
$274$	−1292.00			−0.284863
$275$	1220.00	−	2113.10i	0.267523	−	0.463363i
$276$	−504.000	−	872.954i	−0.109918	−	0.190383i
$277$	3337.00	+	5779.85i	0.723830	+	1.25371i	0.959454	+	0.281866i	$0.0909533\pi$
$277$	3337.00	+	5779.85i	0.723830	+	1.25371i	−0.235624	+	0.971844i	$0.575713\pi$
$278$	−3012.00	+	5216.94i	−0.649812	+	1.12551i
$279$	−1224.00			−0.262649
$280$		0			0
$281$	−9402.00			−1.99600			−0.998001	−	0.0632056i	$-0.979868\pi$
$281$	−9402.00			−1.99600			−0.998001	+	0.0632056i	$0.979868\pi$
$282$	1464.00	−	2535.72i	0.309149	−	0.535461i
$283$	4550.00	+	7880.83i	0.955722	+	1.65536i	0.732706	+	0.680545i	$0.238257\pi$
$283$	4550.00	+	7880.83i	0.955722	+	1.65536i	0.223016	+	0.974815i	$0.428410\pi$
$284$	1048.00	+	1815.19i	0.218970	+	0.379266i
$285$	−1776.00	+	3076.12i	−0.369127	+	0.639347i
$286$	−320.000			−0.0661608
$287$		0			0
$288$	−288.000			−0.0589256
$289$	−1071.50	+	1855.89i	−0.218095	+	0.377751i
$290$	464.000	+	803.672i	0.0939552	+	0.162735i
$291$	1248.00	+	2161.60i	0.251406	+	0.435447i
$292$	−880.000	+	1524.20i	−0.176363	+	0.305470i
$293$	5952.00			1.18676			0.593378	−	0.804924i	$-0.297794\pi$
$293$	5952.00			1.18676			0.593378	+	0.804924i	$0.297794\pi$
$294$		0			0
$295$	4384.00			0.865242
$296$	−888.000	+	1538.06i	−0.174371	+	0.302020i
$297$	−540.000	−	935.307i	−0.105502	−	0.182734i
$298$	−3170.00	−	5490.60i	−0.616219	−	1.06732i
$299$	−168.000	+	290.985i	−0.0324939	+	0.0562812i
$300$	−732.000			−0.140873
$301$		0			0
$302$	3760.00			0.716436
$303$	−696.000	+	1205.51i	−0.131961	+	0.228563i
$304$	−1184.00	−	2050.75i	−0.223378	−	0.386903i
$305$	−2768.00	−	4794.32i	−0.519656	−	0.900071i
$306$	−756.000	+	1309.43i	−0.141234	+	0.244625i
$307$	−3004.00			−0.558460			−0.279230	−	0.960224i	$-0.590079\pi$
$307$	−3004.00			−0.558460			−0.279230	+	0.960224i	$0.590079\pi$
$308$		0			0
$309$	−1896.00			−0.349060
$310$	−1088.00	+	1884.47i	−0.199336	+	0.345261i
$311$	−344.000	−	595.825i	−0.0627217	−	0.108637i	0.832959	−	0.553334i	$-0.186645\pi$
$311$	−344.000	−	595.825i	−0.0627217	−	0.108637i	−0.895681	+	0.444697i	$0.853311\pi$
$312$	48.0000	+	83.1384i	0.00870982	+	0.0150859i
$313$	−2796.00	+	4842.81i	−0.504918	+	0.874543i	0.495066	+	0.868855i	$0.335144\pi$
$313$	−2796.00	+	4842.81i	−0.504918	+	0.874543i	−0.999984	+	0.00568790i	$0.998189\pi$
$314$	−1208.00			−0.217106
$315$		0			0
$316$	4864.00			0.865890
$317$	1461.00	−	2530.53i	0.258858	−	0.448355i	−0.707078	−	0.707135i	$-0.749987\pi$
$317$	1461.00	−	2530.53i	0.258858	−	0.448355i	0.965936	+	0.258780i	$0.0833205\pi$
$318$	1434.00	+	2483.76i	0.252876	+	0.437995i
$319$	−1160.00	−	2009.18i	−0.203597	−	0.352641i
$320$	−256.000	+	443.405i	−0.0447214	+	0.0774597i
$321$	−480.000			−0.0834610
$322$		0			0
$323$	−12432.0			−2.14159
$324$	−162.000	+	280.592i	−0.0277778	+	0.0481125i
$325$	122.000	+	211.310i	0.0208226	+	0.0360658i
$326$	1116.00	+	1932.97i	0.189600	+	0.328396i
$327$	3297.00	−	5710.57i	0.557567	−	0.965735i
$328$	−3360.00			−0.565625
$329$		0			0
$330$	−1920.00			−0.320280
$331$	3746.00	−	6488.26i	0.622051	−	1.07742i	−0.367053	−	0.930200i	$-0.619633\pi$
$331$	3746.00	−	6488.26i	0.622051	−	1.07742i	0.989103	−	0.147223i	$-0.0470336\pi$
$332$	1368.00	+	2369.45i	0.226141	+	0.391687i
$333$	999.000	+	1730.32i	0.164399	+	0.284747i
$334$	−1784.00	+	3089.98i	−0.292264	+	0.506216i
$335$	−7264.00			−1.18470
$336$		0			0
$337$	10766.0			1.74024			0.870121	−	0.492839i	$-0.164041\pi$
$337$	10766.0			1.74024			0.870121	+	0.492839i	$0.164041\pi$
$338$	−2181.00	+	3777.60i	−0.350979	+	0.607913i
$339$	−1155.00	−	2000.52i	−0.185047	−	0.320511i
$340$	1344.00	+	2327.88i	0.214378	+	0.371314i
$341$	2720.00	−	4711.18i	0.431954	−	0.748166i
$342$	−2664.00			−0.421206
$343$		0			0
$344$	1312.00			0.205635
$345$	−1008.00	+	1745.91i	−0.157301	+	0.272454i
$346$	−344.000	−	595.825i	−0.0534496	−	0.0925774i
$347$	1992.00	+	3450.25i	0.308173	+	0.533772i	0.977963	−	0.208779i	$-0.0669490\pi$
$347$	1992.00	+	3450.25i	0.308173	+	0.533772i	−0.669789	+	0.742551i	$0.733616\pi$
$348$	−348.000	+	602.754i	−0.0536056	+	0.0928477i
$349$	−180.000			−0.0276080			−0.0138040	−	0.999905i	$-0.504394\pi$
$349$	−180.000			−0.0276080			−0.0138040	+	0.999905i	$0.504394\pi$
$350$		0			0
$351$	108.000			0.0164234
$352$	640.000	−	1108.51i	0.0969094	−	0.167852i
$353$	5214.00	+	9030.91i	0.786156	+	1.36166i	0.928306	+	0.371818i	$0.121265\pi$
$353$	5214.00	+	9030.91i	0.786156	+	1.36166i	−0.142149	+	0.989845i	$0.545401\pi$
$354$	1644.00	+	2847.49i	0.246829	+	0.427521i
$355$	2096.00	−	3630.38i	0.313364	−	0.542762i
$356$	2416.00			0.359685
$357$		0			0
$358$	−2784.00			−0.411003
$359$	−4342.00	+	7520.56i	−0.638334	+	1.10563i	0.347464	+	0.937693i	$0.387043\pi$
$359$	−4342.00	+	7520.56i	−0.638334	+	1.10563i	−0.985798	+	0.167934i	$0.946290\pi$
$360$	288.000	+	498.831i	0.0421637	+	0.0730297i
$361$	−7522.50	−	13029.4i	−1.09673	−	1.89960i
$362$	4052.00	−	7018.27i	0.588310	−	1.01898i
$363$	807.000			0.116685
$364$		0			0
$365$	3520.00			0.504781
$366$	2076.00	−	3595.74i	0.296487	−	0.513531i
$367$	−2824.00	−	4891.31i	−0.401666	−	0.695707i	0.592261	−	0.805746i	$-0.298236\pi$
$367$	−2824.00	−	4891.31i	−0.401666	−	0.695707i	−0.993927	+	0.110040i	$0.964902\pi$
$368$	−672.000	−	1163.94i	−0.0951914	−	0.164876i
$369$	−1890.00	+	3273.58i	−0.266638	+	0.461831i
$370$	3552.00			0.499080
$371$		0			0
$372$	−1632.00			−0.227460
$373$	1273.00	−	2204.90i	0.176712	−	0.306074i	−0.764041	−	0.645168i	$-0.776787\pi$
$373$	1273.00	−	2204.90i	0.176712	−	0.306074i	0.940752	+	0.339095i	$0.110121\pi$
$374$	−3360.00	−	5819.69i	−0.464549	−	0.804623i
$375$	2232.00	+	3865.94i	0.307360	+	0.532363i
$376$	1952.00	−	3380.96i	0.267731	−	0.463723i
$377$	232.000			0.0316939
$378$		0			0
$379$	8268.00			1.12058			0.560288	−	0.828298i	$-0.310690\pi$
$379$	8268.00			1.12058			0.560288	+	0.828298i	$0.310690\pi$
$380$	−2368.00	+	4101.50i	−0.319673	+	0.553690i
$381$	276.000	+	478.046i	0.0371126	+	0.0642809i
$382$	−3108.00	−	5383.21i	−0.416280	−	0.721019i
$383$	5436.00	−	9415.43i	0.725239	−	1.25615i	−0.233636	−	0.972324i	$-0.575062\pi$
$383$	5436.00	−	9415.43i	0.725239	−	1.25615i	0.958875	−	0.283827i	$-0.0916042\pi$
$384$	−384.000			−0.0510310
$385$		0			0
$386$	−100.000			−0.0131862
$387$	738.000	−	1278.25i	0.0969371	−	0.167900i
$388$	1664.00	+	2882.13i	0.217724	+	0.377109i
$389$	−5217.00	−	9036.11i	−0.679980	−	1.17776i	−0.974986	−	0.222265i	$-0.928655\pi$
$389$	−5217.00	−	9036.11i	−0.679980	−	1.17776i	0.295006	−	0.955495i	$-0.404678\pi$
$390$	96.0000	−	166.277i	0.0124645	−	0.0215891i
$391$	−7056.00			−0.912627
$392$		0			0
$393$	−4356.00			−0.559112
$394$	−162.000	+	280.592i	−0.0207143	+	0.0358783i
$395$	−4864.00	−	8424.70i	−0.619581	−	1.07315i
$396$	−720.000	−	1247.08i	−0.0913671	−	0.158252i
$397$	1522.00	−	2636.18i	0.192411	−	0.333265i	−0.753638	−	0.657290i	$-0.771703\pi$
$397$	1522.00	−	2636.18i	0.192411	−	0.333265i	0.946049	+	0.324025i	$0.105036\pi$
$398$	−3088.00			−0.388913
$399$		0			0
$400$	−976.000			−0.122000
$401$	−4455.00	+	7716.29i	−0.554793	+	0.960930i	0.443126	+	0.896459i	$0.353869\pi$
$401$	−4455.00	+	7716.29i	−0.554793	+	0.960930i	−0.997920	+	0.0644709i	$0.979464\pi$
$402$	−2724.00	−	4718.11i	−0.337962	−	0.585368i
$403$	272.000	+	471.118i	0.0336211	+	0.0582334i
$404$	−928.000	+	1607.34i	−0.114281	+	0.197941i
$405$	648.000			0.0795046
$406$		0			0
$407$	−8880.00			−1.08149
$408$	−1008.00	+	1745.91i	−0.122312	+	0.211851i
$409$	−2808.00	−	4863.60i	−0.339478	−	0.587994i	0.644856	−	0.764304i	$-0.276917\pi$
$409$	−2808.00	−	4863.60i	−0.339478	−	0.587994i	−0.984335	+	0.176310i	$0.943584\pi$
$410$	3360.00	+	5819.69i	0.404728	+	0.701010i
$411$	−969.000	+	1678.36i	−0.116295	+	0.201429i
$412$	−2528.00			−0.302295
$413$		0			0
$414$	−1512.00			−0.179495
$415$	2736.00	−	4738.89i	0.323626	−	0.560537i
$416$	64.0000	+	110.851i	0.00754293	+	0.0130647i
$417$	4518.00	+	7825.41i	0.530569	+	0.918973i
$418$	5920.00	−	10253.7i	0.692719	−	1.19983i
$419$	−8932.00			−1.04142			−0.520712	−	0.853732i	$-0.674334\pi$
$419$	−8932.00			−1.04142			−0.520712	+	0.853732i	$0.674334\pi$
$420$		0			0
$421$	−5538.00			−0.641106			−0.320553	−	0.947231i	$-0.603869\pi$
$421$	−5538.00			−0.641106			−0.320553	+	0.947231i	$0.603869\pi$
$422$	−1204.00	+	2085.39i	−0.138886	+	0.240557i
$423$	−2196.00	−	3803.58i	−0.252419	−	0.437202i
$424$	1912.00	+	3311.68i	0.218997	+	0.379315i
$425$	−2562.00	+	4437.51i	−0.292412	+	0.506473i
$426$	3144.00			0.357576
$427$		0			0
$428$	−640.000			−0.0722794
$429$	−240.000	+	415.692i	−0.0270100	+	0.0467828i
$430$	−1312.00	−	2272.45i	−0.147140	−	0.254854i
$431$	3350.00	+	5802.37i	0.374394	+	0.648469i	0.990236	−	0.139400i	$-0.0445174\pi$
$431$	3350.00	+	5802.37i	0.374394	+	0.648469i	−0.615842	+	0.787870i	$0.711184\pi$
$432$	−216.000	+	374.123i	−0.0240563	+	0.0416667i
$433$	−5048.00			−0.560257			−0.280129	−	0.959962i	$-0.590377\pi$
$433$	−5048.00			−0.560257			−0.280129	+	0.959962i	$0.590377\pi$
$434$		0			0
$435$	1392.00			0.153428
$436$	4396.00	−	7614.10i	0.482867	−	0.836351i
$437$	−6216.00	−	10766.4i	−0.680438	−	1.17855i
$438$	1320.00	+	2286.31i	0.144000	+	0.249415i
$439$	672.000	−	1163.94i	0.0730588	−	0.126542i	−0.827182	−	0.561935i	$-0.810057\pi$
$439$	672.000	−	1163.94i	0.0730588	−	0.126542i	0.900240	+	0.435393i	$0.143391\pi$
$440$	−2560.00			−0.277371
$441$		0			0
$442$	672.000			0.0723162
$443$	2196.00	−	3803.58i	0.235519	−	0.407932i	−0.723904	−	0.689901i	$-0.757654\pi$
$443$	2196.00	−	3803.58i	0.235519	−	0.407932i	0.959424	+	0.281969i	$0.0909875\pi$
$444$	1332.00	+	2307.09i	0.142374	+	0.246598i
$445$	−2416.00	−	4184.63i	−0.257369	−	0.445777i
$446$	2000.00	−	3464.10i	0.212338	−	0.367780i
$447$	−9510.00			−1.00628
$448$		0			0
$449$	3666.00			0.385321			0.192661	−	0.981265i	$-0.438288\pi$
$449$	3666.00			0.385321			0.192661	+	0.981265i	$0.438288\pi$
$450$	−549.000	+	950.896i	−0.0575114	+	0.0996126i
$451$	−8400.00	−	14549.2i	−0.877030	−	1.51906i
$452$	−1540.00	−	2667.36i	−0.160256	−	0.277571i
$453$	2820.00	−	4884.38i	0.292484	−	0.506597i
$454$	−776.000			−0.0802191
$455$		0			0
$456$	−3552.00			−0.364776
$457$	−13.0000	+	22.5167i	−0.00133067	+	0.00230478i	−0.866690	−	0.498847i	$-0.833757\pi$
$457$	−13.0000	+	22.5167i	−0.00133067	+	0.00230478i	0.865359	+	0.501152i	$0.167090\pi$
$458$	4180.00	+	7239.97i	0.426460	+	0.738650i
$459$	1134.00	+	1964.15i	0.115317	+	0.199735i
$460$	−1344.00	+	2327.88i	−0.136227	+	0.235952i
$461$	7656.00			0.773483			0.386741	−	0.922188i	$-0.373601\pi$
$461$	7656.00			0.773483			0.386741	+	0.922188i	$0.373601\pi$
$462$		0			0
$463$	12608.0			1.26554			0.632768	−	0.774341i	$-0.281919\pi$
$463$	12608.0			1.26554			0.632768	+	0.774341i	$0.281919\pi$
$464$	−464.000	+	803.672i	−0.0464238	+	0.0804084i
$465$	1632.00	+	2826.71i	0.162757	+	0.281904i
$466$	−1322.00	−	2289.77i	−0.131417	−	0.227621i
$467$	1534.00	−	2656.97i	0.152002	−	0.263276i	−0.779961	−	0.625828i	$-0.784761\pi$
$467$	1534.00	−	2656.97i	0.152002	−	0.263276i	0.931963	+	0.362552i	$0.118095\pi$
$468$	144.000			0.0142231
$469$		0			0
$470$	−7808.00			−0.766290
$471$	−906.000	+	1569.24i	−0.0886333	+	0.153517i
$472$	2192.00	+	3796.66i	0.213761	+	0.370244i
$473$	3280.00	+	5681.13i	0.318847	+	0.552259i
$474$	3648.00	−	6318.52i	0.353498	−	0.612277i
$475$	−9028.00			−0.872070
$476$		0			0
$477$	4302.00			0.412946
$478$	2412.00	−	4177.71i	0.230800	−	0.399757i
$479$	−3228.00	−	5591.06i	−0.307915	−	0.533324i	0.669991	−	0.742369i	$-0.266298\pi$
$479$	−3228.00	−	5591.06i	−0.307915	−	0.533324i	−0.977906	+	0.209045i	$0.932964\pi$
$480$	384.000	+	665.108i	0.0365148	+	0.0632456i
$481$	444.000	−	769.031i	0.0420887	−	0.0728997i
$482$	8672.00			0.819500
$483$		0			0
$484$	1076.00			0.101052
$485$	3328.00	−	5764.27i	0.311581	−	0.539674i
$486$	243.000	+	420.888i	0.0226805	+	0.0392837i
$487$	−5948.00	−	10302.2i	−0.553449	−	0.958602i	−0.998022	−	0.0628592i	$-0.979978\pi$
$487$	−5948.00	−	10302.2i	−0.553449	−	0.958602i	0.444574	−	0.895742i	$-0.353355\pi$
$488$	2768.00	−	4794.32i	0.256765	−	0.444731i
$489$	3348.00			0.309615
$490$		0			0
$491$	−264.000			−0.0242651			−0.0121325	−	0.999926i	$-0.503862\pi$
$491$	−264.000			−0.0242651			−0.0121325	+	0.999926i	$0.503862\pi$
$492$	−2520.00	+	4364.77i	−0.230915	+	0.399957i
$493$	2436.00	+	4219.28i	0.222539	+	0.385450i
$494$	592.000	+	1025.37i	0.0539177	+	0.0933882i
$495$	−1440.00	+	2494.15i	−0.130754	+	0.226472i
$496$	−2176.00			−0.196986
$497$		0			0
$498$	4104.00			0.369286
$499$	1314.00	−	2275.91i	0.117881	−	0.204176i	−0.801047	−	0.598602i	$-0.795723\pi$
$499$	1314.00	−	2275.91i	0.117881	−	0.204176i	0.918928	+	0.394426i	$0.129056\pi$
$500$	2976.00	+	5154.58i	0.266182	+	0.461040i
$501$	2676.00	+	4634.97i	0.238632	+	0.413324i
$502$	764.000	−	1323.29i	0.0679263	−	0.117652i
$503$	−13568.0			−1.20272			−0.601359	−	0.798979i	$-0.705374\pi$
$503$	−13568.0			−1.20272			−0.601359	+	0.798979i	$0.705374\pi$
$504$		0			0
$505$	3712.00			0.327093
$506$	3360.00	−	5819.69i	0.295198	−	0.511298i
$507$	3271.50	+	5666.40i	0.286573	+	0.496359i
$508$	368.000	+	637.395i	0.0321405	+	0.0556689i
$509$	−10328.0	+	17888.6i	−0.899372	+	1.55776i	−0.0710743	+	0.997471i	$0.522643\pi$
$509$	−10328.0	+	17888.6i	−0.899372	+	1.55776i	−0.828298	+	0.560288i	$0.810691\pi$
$510$	4032.00			0.350078
$511$		0			0
$512$	−512.000			−0.0441942
$513$	−1998.00	+	3460.64i	−0.171957	+	0.297838i
$514$	4300.00	+	7447.82i	0.368998	+	0.639123i
$515$	2528.00	+	4378.62i	0.216305	+	0.374651i
$516$	984.000	−	1704.34i	0.0839500	−	0.145406i
$517$	19520.0			1.66052
$518$		0			0
$519$	−1032.00			−0.0872828
$520$	128.000	−	221.703i	0.0107946	−	0.0186967i
$521$	−1814.00	−	3141.94i	−0.152539	−	0.264205i	0.779621	−	0.626251i	$-0.215412\pi$
$521$	−1814.00	−	3141.94i	−0.152539	−	0.264205i	−0.932160	+	0.362046i	$0.882078\pi$
$522$	522.000	+	904.131i	0.0437688	+	0.0758098i
$523$	−2426.00	+	4201.96i	−0.202833	+	0.351317i	−0.949440	−	0.313948i	$-0.898348\pi$
$523$	−2426.00	+	4201.96i	−0.202833	+	0.351317i	0.746607	+	0.665265i	$0.231681\pi$
$524$	−5808.00			−0.484205
$525$		0			0
$526$	7720.00			0.639939
$527$	−5712.00	+	9893.47i	−0.472142	+	0.817773i
$528$	−960.000	−	1662.77i	−0.0791262	−	0.137051i
$529$	2555.50	+	4426.26i	0.210035	+	0.363792i
$530$	3824.00	−	6623.36i	0.313404	−	0.542831i
$531$	4932.00			0.403071
$532$		0			0
$533$	1680.00			0.136527
$534$	1812.00	−	3138.48i	0.146841	−	0.254335i
$535$	640.000	+	1108.51i	0.0517189	+	0.0895798i
$536$	−3632.00	−	6290.81i	−0.292684	−	0.506943i
$537$	−2088.00	+	3616.52i	−0.167791	+	0.290623i
$538$	5600.00			0.448760
$539$		0			0
$540$	864.000			0.0688530
$541$	3565.00	−	6174.76i	0.283311	−	0.490709i	−0.688887	−	0.724869i	$-0.741900\pi$
$541$	3565.00	−	6174.76i	0.283311	−	0.490709i	0.972198	+	0.234159i	$0.0752338\pi$
$542$	−4880.00	−	8452.41i	−0.386742	−	0.669856i
$543$	−6078.00	−	10527.4i	−0.480353	−	0.831997i
$544$	−1344.00	+	2327.88i	−0.105926	+	0.183469i
$545$	−17584.0			−1.38205
$546$		0			0
$547$	−12788.0			−0.999589			−0.499795	−	0.866144i	$-0.666591\pi$
$547$	−12788.0			−0.999589			−0.499795	+	0.866144i	$0.666591\pi$
$548$	−1292.00	+	2237.81i	−0.100714	+	0.174443i
$549$	−3114.00	−	5393.61i	−0.242081	−	0.419296i
$550$	−2440.00	−	4226.20i	−0.189167	−	0.327647i
$551$	−4292.00	+	7433.96i	−0.331843	+	0.574768i
$552$	−2016.00			−0.155447
$553$		0			0
$554$	13348.0			1.02365
$555$	2664.00	−	4614.18i	0.203749	−	0.352903i
$556$	6024.00	+	10433.9i	0.459487	+	0.795854i
$557$	−1203.00	−	2083.66i	−0.0915130	−	0.158505i	0.816635	−	0.577155i	$-0.195837\pi$
$557$	−1203.00	−	2083.66i	−0.0915130	−	0.158505i	−0.908148	+	0.418649i	$0.862504\pi$
$558$	−1224.00	+	2120.03i	−0.0928603	+	0.160839i
$559$	−656.000			−0.0496348
$560$		0			0
$561$	−10080.0			−0.758606
$562$	−9402.00	+	16284.7i	−0.705693	+	1.22230i
$563$	12706.0	+	22007.4i	0.951144	+	1.64743i	0.742955	+	0.669341i	$0.233423\pi$
$563$	12706.0	+	22007.4i	0.951144	+	1.64743i	0.208189	+	0.978089i	$0.433243\pi$
$564$	−2928.00	−	5071.44i	−0.218601	−	0.378628i
$565$	−3080.00	+	5334.72i	−0.229339	+	0.397227i
$566$	18200.0			1.35160
$567$		0			0
$568$	4192.00			0.309670
$569$	4845.00	−	8391.79i	0.356965	−	0.618281i	−0.630487	−	0.776199i	$-0.717145\pi$
$569$	4845.00	−	8391.79i	0.356965	−	0.618281i	0.987452	+	0.157918i	$0.0504783\pi$
$570$	3552.00	+	6152.24i	0.261012	+	0.452086i
$571$	−2802.00	−	4853.21i	−0.205359	−	0.355692i	0.744888	−	0.667190i	$-0.232503\pi$
$571$	−2802.00	−	4853.21i	−0.205359	−	0.355692i	−0.950247	+	0.311497i	$0.899170\pi$
$572$	−320.000	+	554.256i	−0.0233914	+	0.0405151i
$573$	−9324.00			−0.679783
$574$		0			0
$575$	−5124.00			−0.371627
$576$	−288.000	+	498.831i	−0.0208333	+	0.0360844i
$577$	10784.0	+	18678.4i	0.778066	+	1.34765i	0.933055	+	0.359733i	$0.117132\pi$
$577$	10784.0	+	18678.4i	0.778066	+	1.34765i	−0.154990	+	0.987916i	$0.549534\pi$
$578$	2143.00	+	3711.78i	0.154216	+	0.267111i
$579$	−75.0000	+	129.904i	−0.00538324	+	0.00932404i
$580$	1856.00			0.132873
$581$		0			0
$582$	4992.00			0.355541
$583$	−9560.00	+	16558.4i	−0.679133	+	1.17629i
$584$	1760.00	+	3048.41i	0.124708	+	0.216000i
$585$	−144.000	−	249.415i	−0.0101772	−	0.0176274i
$586$	5952.00	−	10309.2i	0.419582	−	0.726737i
$587$	20300.0			1.42738			0.713689	−	0.700463i	$-0.247023\pi$
$587$	20300.0			1.42738			0.713689	+	0.700463i	$0.247023\pi$
$588$		0			0
$589$	−20128.0			−1.40808
$590$	4384.00	−	7593.31i	0.305909	−	0.529850i
$591$	243.000	+	420.888i	0.0169132	+	0.0292945i
$592$	1776.00	+	3076.12i	0.123299	+	0.213561i
$593$	−6906.00	+	11961.5i	−0.478238	+	0.828333i	−0.999689	−	0.0249483i	$-0.992058\pi$
$593$	−6906.00	+	11961.5i	−0.478238	+	0.828333i	0.521450	+	0.853282i	$0.325391\pi$
$594$	−2160.00			−0.149202
$595$		0			0
$596$	−12680.0			−0.871465
$597$	−2316.00	+	4011.43i	−0.158773	+	0.275003i
$598$	336.000	+	581.969i	0.0229767	+	0.0397968i
$599$	10998.0	+	19049.1i	0.750194	+	1.29937i	0.947728	+	0.319078i	$0.103373\pi$
$599$	10998.0	+	19049.1i	0.750194	+	1.29937i	−0.197535	+	0.980296i	$0.563294\pi$
$600$	−732.000	+	1267.86i	−0.0498063	+	0.0862670i
$601$	8368.00			0.567950			0.283975	−	0.958832i	$-0.408347\pi$
$601$	8368.00			0.567950			0.283975	+	0.958832i	$0.408347\pi$
$602$		0			0
$603$	−8172.00			−0.551890
$604$	3760.00	−	6512.51i	0.253298	−	0.438726i
$605$	−1076.00	−	1863.69i	−0.0723068	−	0.125239i
$606$	1392.00	+	2411.01i	0.0933105	+	0.161618i
$607$	−10752.0	+	18623.0i	−0.718962	+	1.24528i	0.242449	+	0.970164i	$0.422049\pi$
$607$	−10752.0	+	18623.0i	−0.718962	+	1.24528i	−0.961411	+	0.275115i	$0.911284\pi$
$608$	−4736.00			−0.315905
$609$		0			0
$610$	−11072.0			−0.734905
$611$	−976.000	+	1690.48i	−0.0646231	+	0.111931i
$612$	1512.00	+	2618.86i	0.0998676	+	0.172976i
$613$	5135.00	+	8894.08i	0.338337	+	0.586017i	0.984120	−	0.177504i	$-0.0568022\pi$
$613$	5135.00	+	8894.08i	0.338337	+	0.586017i	−0.645783	+	0.763521i	$0.723469\pi$
$614$	−3004.00	+	5203.08i	−0.197446	+	0.341986i
$615$	10080.0			0.660918
$616$		0			0
$617$	28358.0			1.85032			0.925162	−	0.379572i	$-0.123929\pi$
$617$	28358.0			1.85032			0.925162	+	0.379572i	$0.123929\pi$
$618$	−1896.00	+	3283.97i	−0.123411	+	0.213755i
$619$	−8146.00	−	14109.3i	−0.528942	−	0.916155i	−0.999430	−	0.0337488i	$-0.989255\pi$
$619$	−8146.00	−	14109.3i	−0.528942	−	0.916155i	0.470488	−	0.882406i	$-0.344078\pi$
$620$	2176.00	+	3768.94i	0.140952	+	0.244136i
$621$	−1134.00	+	1964.15i	−0.0732783	+	0.126922i
$622$	−1376.00			−0.0887019
$623$		0			0
$624$	192.000			0.0123176
$625$	2139.50	−	3705.72i	0.136928	−	0.237166i
$626$	5592.00	+	9685.63i	0.357031	+	0.618395i
$627$	−8880.00	−	15380.6i	−0.565603	−	0.979653i
$628$	−1208.00	+	2092.32i	−0.0767587	+	0.132950i
$629$	18648.0			1.18211
$630$		0			0
$631$	11256.0			0.710134			0.355067	−	0.934841i	$-0.384458\pi$
$631$	11256.0			0.710134			0.355067	+	0.934841i	$0.384458\pi$
$632$	4864.00	−	8424.70i	0.306138	−	0.530247i
$633$	1806.00	+	3128.08i	0.113400	+	0.196414i
$634$	−2922.00	−	5061.05i	−0.183040	−	0.317035i
$635$	736.000	−	1274.79i	0.0459957	−	0.0796669i
$636$	5736.00			0.357621
$637$		0			0
$638$	−4640.00			−0.287930
$639$	2358.00	−	4084.18i	0.145980	−	0.252844i
$640$	512.000	+	886.810i	0.0316228	+	0.0547723i
$641$	−7759.00	−	13439.0i	−0.478100	−	0.828093i	0.521585	−	0.853199i	$-0.325341\pi$
$641$	−7759.00	−	13439.0i	−0.478100	−	0.828093i	−0.999685	+	0.0251060i	$0.992008\pi$
$642$	−480.000	+	831.384i	−0.0295079	+	0.0511092i
$643$	−10452.0			−0.641037			−0.320518	−	0.947242i	$-0.603857\pi$
$643$	−10452.0			−0.641037			−0.320518	+	0.947242i	$0.603857\pi$
$644$		0			0
$645$	−3936.00			−0.240279
$646$	−12432.0	+	21532.9i	−0.757168	+	1.31145i
$647$	−36.0000	−	62.3538i	−0.00218749	−	0.00378884i	0.864930	−	0.501893i	$-0.167363\pi$
$647$	−36.0000	−	62.3538i	−0.00218749	−	0.00378884i	−0.867117	+	0.498104i	$0.834030\pi$
$648$	324.000	+	561.184i	0.0196419	+	0.0340207i
$649$	−10960.0	+	18983.3i	−0.662893	+	1.14816i
$650$	488.000			0.0294476
$651$		0			0
$652$	4464.00			0.268135
$653$	−5981.00	+	10359.4i	−0.358430	+	0.620819i	−0.987699	−	0.156369i	$-0.950021\pi$
$653$	−5981.00	+	10359.4i	−0.358430	+	0.620819i	0.629269	+	0.777188i	$0.283354\pi$
$654$	−6594.00	−	11421.1i	−0.394260	−	0.682878i
$655$	5808.00	+	10059.8i	0.346469	+	0.600102i
$656$	−3360.00	+	5819.69i	−0.199979	+	0.346373i
$657$	3960.00			0.235151
$658$		0			0
$659$	−6016.00			−0.355615			−0.177807	−	0.984065i	$-0.556900\pi$
$659$	−6016.00			−0.355615			−0.177807	+	0.984065i	$0.556900\pi$
$660$	−1920.00	+	3325.54i	−0.113236	+	0.196131i
$661$	−13034.0	−	22575.6i	−0.766965	−	1.32842i	−0.939201	−	0.343367i	$-0.888433\pi$
$661$	−13034.0	−	22575.6i	−0.766965	−	1.32842i	0.172236	−	0.985056i	$-0.444901\pi$
$662$	−7492.00	−	12976.5i	−0.439856	−	0.761853i
$663$	504.000	−	872.954i	0.0295230	−	0.0511353i
$664$	5472.00			0.319811
$665$		0			0
$666$	3996.00			0.232495
$667$	−2436.00	+	4219.28i	−0.141413	+	0.244934i
$668$	3568.00	+	6179.96i	0.206662	+	0.357949i
$669$	−3000.00	−	5196.15i	−0.173373	−	0.300291i
$670$	−7264.00	+	12581.6i	−0.418855	+	0.725478i
$671$	27680.0			1.59251
$672$		0			0
$673$	−20530.0			−1.17589			−0.587945	−	0.808901i	$-0.700063\pi$
$673$	−20530.0			−1.17589			−0.587945	+	0.808901i	$0.700063\pi$
$674$	10766.0	−	18647.3i	0.615268	−	1.06568i
$675$	823.500	+	1426.34i	0.0469578	+	0.0813333i
$676$	4362.00	+	7555.21i	0.248179	+	0.429859i
$677$	5028.00	−	8708.75i	0.285438	−	0.494394i	−0.687277	−	0.726395i	$-0.741194\pi$
$677$	5028.00	−	8708.75i	0.285438	−	0.494394i	0.972715	+	0.232002i	$0.0745275\pi$
$678$	−4620.00			−0.261696
$679$		0			0
$680$	5376.00			0.303177
$681$	−582.000	+	1008.05i	−0.0327493	+	0.0567235i
$682$	−5440.00	−	9422.36i	−0.305437	−	0.529033i
$683$	−3076.00	−	5327.79i	−0.172328	−	0.298480i	0.766905	−	0.641760i	$-0.221795\pi$
$683$	−3076.00	−	5327.79i	−0.172328	−	0.298480i	−0.939233	+	0.343280i	$0.888462\pi$
$684$	−2664.00	+	4614.18i	−0.148919	+	0.257935i
$685$	5168.00			0.288262
$686$		0			0
$687$	12540.0			0.696406
$688$	1312.00	−	2272.45i	0.0727028	−	0.125925i
$689$	−956.000	−	1655.84i	−0.0528602	−	0.0915566i
$690$	2016.00	+	3491.81i	0.111229	+	0.192654i
$691$	7358.00	−	12744.4i	0.405082	−	0.701622i	−0.589249	−	0.807951i	$-0.700576\pi$
$691$	7358.00	−	12744.4i	0.405082	−	0.701622i	0.994331	+	0.106329i	$0.0339097\pi$
$692$	−1376.00			−0.0755891
$693$		0			0
$694$	7968.00			0.435823
$695$	12048.0	−	20867.7i	0.657564	−	1.13893i
$696$	696.000	+	1205.51i	0.0379049	+	0.0656532i
$697$	17640.0	+	30553.4i	0.958626	+	1.66039i
$698$	−180.000	+	311.769i	−0.00976089	+	0.0169064i
$699$	−3966.00			−0.214604
$700$		0			0
$701$	28202.0			1.51951			0.759754	−	0.650211i	$-0.225319\pi$
$701$	28202.0			1.51951			0.759754	+	0.650211i	$0.225319\pi$
$702$	108.000	−	187.061i	0.00580655	−	0.0100572i
$703$	16428.0	+	28454.1i	0.881357	+	1.52655i
$704$	−1280.00	−	2217.03i	−0.0685253	−	0.118689i
$705$	−5856.00	+	10142.9i	−0.312836	+	0.541849i
$706$	20856.0			1.11179
$707$		0			0
$708$	6576.00			0.349070
$709$	−11057.0	+	19151.3i	−0.585690	+	1.01445i	0.409099	+	0.912490i	$0.365843\pi$
$709$	−11057.0	+	19151.3i	−0.585690	+	1.01445i	−0.994789	+	0.101955i	$0.967490\pi$
$710$	−4192.00	−	7260.76i	−0.221582	−	0.383791i
$711$	−5472.00	−	9477.78i	−0.288630	−	0.499922i
$712$	2416.00	−	4184.63i	0.127168	−	0.220261i
$713$	−11424.0			−0.600045
$714$		0			0
$715$	1280.00			0.0669501
$716$	−2784.00	+	4822.03i	−0.145311	+	0.251687i
$717$	−3618.00	−	6266.56i	−0.188447	−	0.326400i
$718$	8684.00	+	15041.1i	0.451370	+	0.781797i
$719$	4644.00	−	8043.64i	0.240879	−	0.417215i	−0.720086	−	0.693885i	$-0.755898\pi$
$719$	4644.00	−	8043.64i	0.240879	−	0.417215i	0.960965	+	0.276670i	$0.0892310\pi$
$720$	1152.00			0.0596285
$721$		0			0
$722$	−30090.0			−1.55102
$723$	6504.00	−	11265.3i	0.334559	−	0.579474i
$724$	−8104.00	−	14036.5i	−0.415998	−	0.720530i
$725$	1769.00	+	3064.00i	0.0906193	+	0.156957i
$726$	807.000	−	1397.77i	0.0412542	−	0.0714544i
$727$	23848.0			1.21661			0.608304	−	0.793704i	$-0.291850\pi$
$727$	23848.0			1.21661			0.608304	+	0.793704i	$0.291850\pi$
$728$		0			0
$729$	729.000			0.0370370
$730$	3520.00	−	6096.82i	0.178467	−	0.309114i
$731$	−6888.00	−	11930.4i	−0.348511	−	0.603640i
$732$	−4152.00	−	7191.47i	−0.209648	−	0.363121i
$733$	17378.0	−	30099.6i	0.875677	−	1.51672i	0.0196367	−	0.999807i	$-0.493749\pi$
$733$	17378.0	−	30099.6i	0.875677	−	1.51672i	0.856040	−	0.516909i	$-0.172918\pi$
$734$	−11296.0			−0.568042
$735$		0			0
$736$	−2688.00			−0.134621
$737$	18160.0	−	31454.0i	0.907642	−	1.57208i
$738$	3780.00	+	6547.15i	0.188542	+	0.326564i
$739$	−13022.0	−	22554.8i	−0.648203	−	1.12272i	−0.983552	−	0.180626i	$-0.942187\pi$
$739$	−13022.0	−	22554.8i	−0.648203	−	1.12272i	0.335349	−	0.942094i	$-0.391146\pi$
$740$	3552.00	−	6152.24i	0.176452	−	0.305623i
$741$	1776.00			0.0880472
$742$		0			0
$743$	36204.0			1.78761			0.893806	−	0.448454i	$-0.148025\pi$
$743$	36204.0			1.78761			0.893806	+	0.448454i	$0.148025\pi$
$744$	−1632.00	+	2826.71i	−0.0804194	+	0.139290i
$745$	12680.0	+	21962.4i	0.623569	+	1.08005i
$746$	−2546.00	−	4409.80i	−0.124954	−	0.216427i
$747$	3078.00	−	5331.25i	0.150761	−	0.261125i
$748$	−13440.0			−0.656972
$749$		0			0
$750$	8928.00			0.434673
$751$	5712.00	−	9893.47i	0.277542	−	0.480716i	−0.693232	−	0.720715i	$-0.743814\pi$
$751$	5712.00	−	9893.47i	0.277542	−	0.480716i	0.970773	+	0.239999i	$0.0771470\pi$
$752$	−3904.00	−	6761.93i	−0.189314	−	0.327902i
$753$	−1146.00	−	1984.93i	−0.0554616	−	0.0960623i
$754$	232.000	−	401.836i	0.0112055	−	0.0194085i
$755$	−15040.0			−0.724982
$756$		0			0
$757$	−16622.0			−0.798067			−0.399034	−	0.916936i	$-0.630654\pi$
$757$	−16622.0			−0.798067			−0.399034	+	0.916936i	$0.630654\pi$
$758$	8268.00	−	14320.6i	0.396184	−	0.686210i
$759$	−5040.00	−	8729.54i	−0.241028	−	0.417473i
$760$	4736.00	+	8202.99i	0.226043	+	0.391518i
$761$	19262.0	−	33362.8i	0.917539	−	1.58922i	0.114397	−	0.993435i	$-0.463506\pi$
$761$	19262.0	−	33362.8i	0.917539	−	1.58922i	0.803141	−	0.595789i	$-0.203160\pi$
$762$	1104.00			0.0524852
$763$		0			0
$764$	−12432.0			−0.588709
$765$	3024.00	−	5237.72i	0.142919	−	0.247543i
$766$	−10872.0	−	18830.9i	−0.512822	−	0.888233i
$767$	−1096.00	−	1898.33i	−0.0515962	−	0.0893672i
$768$	−384.000	+	665.108i	−0.0180422	+	0.0312500i
$769$	−18440.0			−0.864712			−0.432356	−	0.901703i	$-0.642318\pi$
$769$	−18440.0			−0.864712			−0.432356	+	0.901703i	$0.642318\pi$
$770$		0			0
$771$	12900.0			0.602571
$772$	−100.000	+	173.205i	−0.00466202	+	0.00807485i
$773$	6984.00	+	12096.6i	0.324964	+	0.562854i	0.981505	−	0.191436i	$-0.0613145\pi$
$773$	6984.00	+	12096.6i	0.324964	+	0.562854i	−0.656541	+	0.754290i	$0.727981\pi$
$774$	−1476.00	−	2556.51i	−0.0685449	−	0.118723i
$775$	−4148.00	+	7184.55i	−0.192259	+	0.333002i
$776$	6656.00			0.307908
$777$		0			0
$778$	−20868.0			−0.961638
$779$	−31080.0	+	53832.1i	−1.42947	+	2.47591i
$780$	−192.000	−	332.554i	−0.00881372	−	0.0152658i
$781$	10480.0	+	18151.9i	0.480159	+	0.831659i
$782$	−7056.00	+	12221.4i	−0.322662	+	0.558868i
$783$	1566.00			0.0714742
$784$		0			0
$785$	4832.00			0.219696
$786$	−4356.00	+	7544.81i	−0.197676	+	0.342385i
$787$	−5458.00	−	9453.53i	−0.247213	−	0.428186i	0.715538	−	0.698573i	$-0.246181\pi$
$787$	−5458.00	−	9453.53i	−0.247213	−	0.428186i	−0.962752	+	0.270388i	$0.912848\pi$
$788$	324.000	+	561.184i	0.0146472	+	0.0253698i
$789$	5790.00	−	10028.6i	0.261254	−	0.452505i
$790$	−19456.0			−0.876220
$791$		0			0
$792$	−2880.00			−0.129213
$793$	−1384.00	+	2397.16i	−0.0619764	+	0.107346i
$794$	−3044.00	−	5272.36i	−0.136055	−	0.235654i
$795$	−5736.00	−	9935.04i	−0.255893	−	0.443220i
$796$	−3088.00	+	5348.57i	−0.137502	+	0.238160i
$797$	12360.0			0.549327			0.274664	−	0.961540i	$-0.411434\pi$
$797$	12360.0			0.549327			0.274664	+	0.961540i	$0.411434\pi$
$798$		0			0
$799$	−40992.0			−1.81501
$800$	−976.000	+	1690.48i	−0.0431335	+	0.0747094i
$801$	−2718.00	−	4707.71i	−0.119895	−	0.207664i
$802$	8910.00	+	15432.6i	0.392298	+	0.679480i
$803$	−8800.00	+	15242.0i	−0.386731	+	0.669838i
$804$	−10896.0			−0.477951
$805$		0			0
$806$	1088.00			0.0475474
$807$	4200.00	−	7274.61i	0.183206	−	0.317322i
$808$	1856.00	+	3214.69i	0.0808092	+	0.139966i
$809$	−1701.00	−	2946.22i	−0.0739233	−	0.128039i	0.826694	−	0.562651i	$-0.190219\pi$
$809$	−1701.00	−	2946.22i	−0.0739233	−	0.128039i	−0.900618	+	0.434612i	$0.856885\pi$
$810$	648.000	−	1122.37i	0.0281091	−	0.0486864i
$811$	292.000			0.0126430			0.00632152	−	0.999980i	$-0.497988\pi$
$811$	292.000			0.0126430			0.00632152	+	0.999980i	$0.497988\pi$
$812$		0			0
$813$	−14640.0			−0.631546
$814$	−8880.00	+	15380.6i	−0.382363	+	0.662273i
$815$	−4464.00	−	7731.87i	−0.191861	−	0.332314i
$816$	2016.00	+	3491.81i	0.0864879	+	0.149801i
$817$	12136.0	−	21020.2i	0.519688	−	0.900126i
$818$	−11232.0			−0.480095
$819$		0			0
$820$	13440.0			0.572372
$821$	−3455.00	+	5984.24i	−0.146870	+	0.254386i	−0.930069	−	0.367385i	$-0.880253\pi$
$821$	−3455.00	+	5984.24i	−0.146870	+	0.254386i	0.783199	+	0.621771i	$0.213587\pi$
$822$	1938.00	+	3356.71i	0.0822330	+	0.142432i
$823$	−284.000	−	491.902i	−0.0120287	−	0.0208343i	0.859948	−	0.510381i	$-0.170496\pi$
$823$	−284.000	−	491.902i	−0.0120287	−	0.0208343i	−0.871977	+	0.489547i	$0.837162\pi$
$824$	−2528.00	+	4378.62i	−0.106877	+	0.185117i
$825$	−7320.00			−0.308909
$826$		0			0
$827$	−12144.0			−0.510627			−0.255313	−	0.966858i	$-0.582179\pi$
$827$	−12144.0			−0.510627			−0.255313	+	0.966858i	$0.582179\pi$
$828$	−1512.00	+	2618.86i	−0.0634609	+	0.109918i
$829$	−7414.00	−	12841.4i	−0.310614	−	0.537999i	0.667882	−	0.744268i	$-0.267201\pi$
$829$	−7414.00	−	12841.4i	−0.310614	−	0.537999i	−0.978495	+	0.206269i	$0.933868\pi$
$830$	−5472.00	−	9477.78i	−0.228838	−	0.396360i
$831$	10011.0	−	17339.6i	0.417903	−	0.723830i
$832$	256.000			0.0106673
$833$		0			0
$834$	18072.0			0.750338
$835$	7136.00	−	12359.9i	0.295750	−	0.512254i
$836$	−11840.0	−	20507.5i	−0.489827	−	0.848404i
$837$	1836.00	+	3180.05i	0.0758201	+	0.131324i
$838$	−8932.00	+	15470.7i	−0.368199	+	0.637739i
$839$	−22824.0			−0.939180			−0.469590	−	0.882885i	$-0.655598\pi$
$839$	−22824.0			−0.939180			−0.469590	+	0.882885i	$0.655598\pi$
$840$		0			0
$841$	−21025.0			−0.862069
$842$	−5538.00	+	9592.10i	−0.226665	+	0.392596i
$843$	14103.0	+	24427.1i	0.576196	+	0.998001i
$844$	2408.00	+	4170.78i	0.0982071	+	0.170100i
$845$	8724.00	−	15110.4i	0.355165	−	0.615164i
$846$	−8784.00			−0.356974
$847$		0			0
$848$	7648.00			0.309709
$849$	13650.0	−	23642.5i	0.551787	−	0.955722i
$850$	5124.00	+	8875.03i	0.206767	+	0.358131i
$851$	9324.00	+	16149.6i	0.375585	+	0.650532i
$852$	3144.00	−	5445.57i	0.126422	−	0.218970i
$853$	−41780.0			−1.67705			−0.838523	−	0.544866i	$-0.816580\pi$
$853$	−41780.0			−1.67705			−0.838523	+	0.544866i	$0.816580\pi$
$854$		0			0
$855$	10656.0			0.426231
$856$	−640.000	+	1108.51i	−0.0255546	+	0.0442619i
$857$	10710.0	+	18550.3i	0.426892	+	0.739399i	0.996595	−	0.0824518i	$-0.0262750\pi$
$857$	10710.0	+	18550.3i	0.426892	+	0.739399i	−0.569703	+	0.821851i	$0.692942\pi$
$858$	480.000	+	831.384i	0.0190990	+	0.0330804i
$859$	9066.00	−	15702.8i	0.360102	−	0.623716i	−0.627875	−	0.778314i	$-0.716075\pi$
$859$	9066.00	−	15702.8i	0.360102	−	0.623716i	0.987977	+	0.154599i	$0.0494084\pi$
$860$	−5248.00			−0.208088
$861$		0			0
$862$	13400.0			0.529473
$863$	−12018.0	+	20815.8i	−0.474041	+	0.821063i	−0.999558	−	0.0297197i	$-0.990539\pi$
$863$	−12018.0	+	20815.8i	−0.474041	+	0.821063i	0.525517	+	0.850783i	$0.323872\pi$
$864$	432.000	+	748.246i	0.0170103	+	0.0294628i
$865$	1376.00	+	2383.30i	0.0540872	+	0.0936817i
$866$	−5048.00	+	8743.39i	−0.198081	+	0.343086i
$867$	6429.00			0.251834
$868$		0			0
$869$	48640.0			1.89873
$870$	1392.00	−	2411.01i	0.0542451	−	0.0939552i
$871$	1816.00	+	3145.40i	0.0706462	+	0.122363i
$872$	−8792.00	−	15228.2i	−0.341439	−	0.591389i
$873$	3744.00	−	6484.80i	0.145149	−	0.251406i
$874$	−24864.0			−0.962285
$875$		0			0
$876$	5280.00			0.203647
$877$	2187.00	−	3788.00i	0.0842072	−	0.145851i	−0.820846	−	0.571150i	$-0.806498\pi$
$877$	2187.00	−	3788.00i	0.0842072	−	0.145851i	0.905053	+	0.425299i	$0.139831\pi$
$878$	−1344.00	−	2327.88i	−0.0516604	−	0.0894784i
$879$	−8928.00	−	15463.7i	−0.342587	−	0.593378i
$880$	−2560.00	+	4434.05i	−0.0980654	+	0.169854i
$881$	−46348.0			−1.77242			−0.886211	−	0.463282i	$-0.846672\pi$
$881$	−46348.0			−1.77242			−0.886211	+	0.463282i	$0.846672\pi$
$882$		0			0
$883$	−20660.0			−0.787389			−0.393694	−	0.919241i	$-0.628803\pi$
$883$	−20660.0			−0.787389			−0.393694	+	0.919241i	$0.628803\pi$
$884$	672.000	−	1163.94i	0.0255677	−	0.0442845i
$885$	−6576.00	−	11390.0i	−0.249774	−	0.432621i
$886$	−4392.00	−	7607.17i	−0.166537	−	0.288451i
$887$	900.000	−	1558.85i	0.0340688	−	0.0590089i	−0.848488	−	0.529214i	$-0.822487\pi$
$887$	900.000	−	1558.85i	0.0340688	−	0.0590089i	0.882557	+	0.470205i	$0.155820\pi$
$888$	5328.00			0.201347
$889$		0			0
$890$	−9664.00			−0.363975
$891$	−1620.00	+	2805.92i	−0.0609114	+	0.105502i
$892$	−4000.00	−	6928.20i	−0.150146	−	0.260060i
$893$	−36112.0	−	62547.8i	−1.35324	−	2.34388i
$894$	−9510.00	+	16471.8i	−0.355774	+	0.616219i
$895$	11136.0			0.415906
$896$		0			0
$897$	1008.00			0.0375208
$898$	3666.00	−	6349.70i	0.136232	−	0.235960i
$899$	3944.00	+	6831.21i	0.146318	+	0.253430i
$900$	1098.00	+	1901.79i	0.0406667	+	0.0704367i
$901$	20076.0	−	34772.7i	0.742318	−	1.28573i
$902$	−33600.0			−1.24031
$903$		0			0
$904$	−6160.00			−0.226636
$905$	−16208.0	+	28073.1i	−0.595328	+	1.03114i
$906$	−5640.00	−	9768.77i	−0.206817	−	0.358218i
$907$	20998.0	+	36369.6i	0.768718	+	1.33146i	0.938258	+	0.345935i	$0.112438\pi$
$907$	20998.0	+	36369.6i	0.768718	+	1.33146i	−0.169540	+	0.985523i	$0.554228\pi$
$908$	−776.000	+	1344.07i	−0.0283617	+	0.0491240i
$909$	4176.00			0.152375
$910$		0			0
$911$	−41308.0			−1.50230			−0.751150	−	0.660132i	$-0.770500\pi$
$911$	−41308.0			−1.50230			−0.751150	+	0.660132i	$0.770500\pi$
$912$	−3552.00	+	6152.24i	−0.128968	+	0.223378i
$913$	13680.0	+	23694.5i	0.495884	+	0.858896i
$914$	26.0000	+	45.0333i	0.000940923	+	0.00162973i
$915$	−8304.00	+	14382.9i	−0.300024	+	0.519656i
$916$	16720.0			0.603105
$917$		0			0
$918$	4536.00			0.163083
$919$	−1968.00	+	3408.68i	−0.0706402	+	0.122352i	−0.899182	−	0.437575i	$-0.855838\pi$
$919$	−1968.00	+	3408.68i	−0.0706402	+	0.122352i	0.828542	+	0.559927i	$0.189171\pi$
$920$	2688.00	+	4655.75i	0.0963269	+	0.166843i
$921$	4506.00	+	7804.62i	0.161214	+	0.279230i
$922$	7656.00	−	13260.6i	0.273467	−	0.473659i
$923$	−2096.00			−0.0747461
$924$		0			0
$925$	13542.0			0.481360
$926$	12608.0	−	21837.7i	0.447435	−	0.774980i
$927$	2844.00	+	4925.95i	0.100765	+	0.174530i
$928$	928.000	+	1607.34i	0.0328266	+	0.0568574i
$929$	3606.00	−	6245.78i	0.127351	−	0.220578i	−0.795299	−	0.606218i	$-0.792686\pi$
$929$	3606.00	−	6245.78i	0.127351	−	0.220578i	0.922649	+	0.385640i	$0.126019\pi$
$930$	6528.00			0.230174
$931$		0			0
$932$	−5288.00			−0.185852
$933$	−1032.00	+	1787.48i	−0.0362124	+	0.0627217i
$934$	−3068.00	−	5313.93i	−0.107482	−	0.186164i
$935$	13440.0	+	23278.8i	0.470091	+	0.814221i
$936$	144.000	−	249.415i	0.00502862	−	0.00870982i
$937$	−38976.0			−1.35890			−0.679451	−	0.733721i	$-0.737782\pi$
$937$	−38976.0			−1.35890			−0.679451	+	0.733721i	$0.737782\pi$
$938$		0			0
$939$	16776.0			0.583029
$940$	−7808.00	+	13523.9i	−0.270924	+	0.469255i
$941$	−26772.0	−	46370.5i	−0.927463	−	1.60641i	−0.787552	−	0.616248i	$-0.788652\pi$
$941$	−26772.0	−	46370.5i	−0.927463	−	1.60641i	−0.139910	−	0.990164i	$-0.544681\pi$
$942$	1812.00	+	3138.48i	0.0626732	+	0.108553i
$943$	−17640.0	+	30553.4i	−0.609160	+	1.05510i
$944$	8768.00			0.302303
$945$		0			0
$946$	13120.0			0.450918
$947$	10696.0	−	18526.0i	0.367026	−	0.635707i	−0.622073	−	0.782959i	$-0.713709\pi$
$947$	10696.0	−	18526.0i	0.367026	−	0.635707i	0.989099	+	0.147252i	$0.0470428\pi$
$948$	−7296.00	−	12637.0i	−0.249961	−	0.432945i
$949$	−880.000	−	1524.20i	−0.0301012	−	0.0521368i
$950$	−9028.00	+	15637.0i	−0.308323	+	0.534031i
$951$	−8766.00			−0.298903
$952$		0			0
$953$	21162.0			0.719312			0.359656	−	0.933085i	$-0.382894\pi$
$953$	21162.0			0.719312			0.359656	+	0.933085i	$0.382894\pi$
$954$	4302.00	−	7451.28i	0.145998	−	0.252876i
$955$	12432.0	+	21532.9i	0.421246	+	0.729620i
$956$	−4824.00	−	8355.41i	−0.163200	−	0.282671i
$957$	−3480.00	+	6027.54i	−0.117547	+	0.203597i
$958$	−12912.0			−0.435457
$959$		0			0
$960$	1536.00			0.0516398
$961$	5647.50	−	9781.76i	0.189571	−	0.328346i
$962$	−888.000	−	1538.06i	−0.0297612	−	0.0515479i
$963$	720.000	+	1247.08i	0.0240931	+	0.0417305i
$964$	8672.00	−	15020.3i	0.289737	−	0.501839i
$965$	400.000			0.0133435
$966$		0			0
$967$	8224.00			0.273491			0.136746	−	0.990606i	$-0.456336\pi$
$967$	8224.00			0.273491			0.136746	+	0.990606i	$0.456336\pi$
$968$	1076.00	−	1863.69i	0.0357272	−	0.0618814i
$969$	18648.0	+	32299.3i	0.618225	+	1.07080i
$970$	−6656.00	−	11528.5i	−0.220321	−	0.381607i
$971$	4070.00	−	7049.45i	0.134513	−	0.232984i	−0.790898	−	0.611948i	$-0.790386\pi$
$971$	4070.00	−	7049.45i	0.134513	−	0.232984i	0.925411	+	0.378964i	$0.123720\pi$
$972$	972.000			0.0320750
$973$		0			0
$974$	−23792.0			−0.782695
$975$	366.000	−	633.931i	0.0120219	−	0.0208226i
$976$	−5536.00	−	9588.63i	−0.181560	−	0.314472i
$977$	−16079.0	−	27849.6i	−0.526523	−	0.911964i	−0.999522	−	0.0309016i	$-0.990162\pi$
$977$	−16079.0	−	27849.6i	−0.526523	−	0.911964i	0.473000	−	0.881063i	$-0.343171\pi$
$978$	3348.00	−	5798.91i	0.109465	−	0.189600i
$979$	24160.0			0.788720
$980$		0			0
$981$	−19782.0			−0.643823
$982$	−264.000	+	457.261i	−0.00857900	+	0.0148593i
$983$	20708.0	+	35867.3i	0.671905	+	1.16377i	0.977363	+	0.211568i	$0.0678570\pi$
$983$	20708.0	+	35867.3i	0.671905	+	1.16377i	−0.305458	+	0.952205i	$0.598810\pi$
$984$	5040.00	+	8729.54i	0.163282	+	0.282812i
$985$	648.000	−	1122.37i	0.0209614	−	0.0363062i
$986$	9744.00			0.314718
$987$		0			0
$988$	2368.00			0.0762511
$989$	6888.00	−	11930.4i	0.221462	−	0.383583i
$990$	2880.00	+	4988.31i	0.0924570	+	0.160140i
$991$	−6148.00	−	10648.6i	−0.197071	−	0.341338i	0.750506	−	0.660863i	$-0.229810\pi$
$991$	−6148.00	−	10648.6i	−0.197071	−	0.341338i	−0.947578	+	0.319526i	$0.896476\pi$
$992$	−2176.00	+	3768.94i	−0.0696452	+	0.120629i
$993$	−22476.0			−0.718282
$994$		0			0
$995$	12352.0			0.393552
$996$	4104.00	−	7108.34i	0.130562	−	0.226141i
$997$	−28826.0	−	49928.1i	−0.915676	−	1.58600i	−0.805909	−	0.592039i	$-0.798323\pi$
$997$	−28826.0	−	49928.1i	−0.915676	−	1.58600i	−0.109766	−	0.993957i	$-0.535010\pi$
$998$	−2628.00	−	4551.83i	−0.0833546	−	0.144374i
$999$	2997.00	−	5190.96i	0.0949158	−	0.164399i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	294.4.e.f.79.1		2
3.2	odd	2		882.4.g.j.667.1		2
7.2	even	3		294.4.a.f.1.1	yes	1
7.3	odd	6		294.4.e.j.67.1		2
7.4	even	3	inner	294.4.e.f.67.1		2
7.5	odd	6		294.4.a.b.1.1	✓	1
7.6	odd	2		294.4.e.j.79.1		2
21.2	odd	6		882.4.a.j.1.1		1
21.5	even	6		882.4.a.q.1.1		1
21.11	odd	6		882.4.g.j.361.1		2
21.17	even	6		882.4.g.c.361.1		2
21.20	even	2		882.4.g.c.667.1		2
28.19	even	6		2352.4.a.z.1.1		1
28.23	odd	6		2352.4.a.m.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
294.4.a.b.1.1	✓	1	7.5	odd	6
294.4.a.f.1.1	yes	1	7.2	even	3
294.4.e.f.67.1		2	7.4	even	3	inner
294.4.e.f.79.1		2	1.1	even	1	trivial
294.4.e.j.67.1		2	7.3	odd	6
294.4.e.j.79.1		2	7.6	odd	2
882.4.a.j.1.1		1	21.2	odd	6
882.4.a.q.1.1		1	21.5	even	6
882.4.g.c.361.1		2	21.17	even	6
882.4.g.c.667.1		2	21.20	even	2
882.4.g.j.361.1		2	21.11	odd	6
882.4.g.j.667.1		2	3.2	odd	2
2352.4.a.m.1.1		1	28.23	odd	6
2352.4.a.z.1.1		1	28.19	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 294 = 2 \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	294.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 - 1.73205i) q^{2} +(-1.50000 - 2.59808i) q^{3} +(-2.00000 - 3.46410i) q^{4} +(-4.00000 + 6.92820i) q^{5} -6.00000 q^{6} -8.00000 q^{8} +(-4.50000 + 7.79423i) q^{9} +O(q^{10})\)	\(q+(1.00000 - 1.73205i) q^{2} +(-1.50000 - 2.59808i) q^{3} +(-2.00000 - 3.46410i) q^{4} +(-4.00000 + 6.92820i) q^{5} -6.00000 q^{6} -8.00000 q^{8} +(-4.50000 + 7.79423i) q^{9} +(8.00000 + 13.8564i) q^{10} +(-20.0000 - 34.6410i) q^{11} +(-6.00000 + 10.3923i) q^{12} +4.00000 q^{13} +24.0000 q^{15} +(-8.00000 + 13.8564i) q^{16} +(42.0000 + 72.7461i) q^{17} +(9.00000 + 15.5885i) q^{18} +(-74.0000 + 128.172i) q^{19} +32.0000 q^{20} -80.0000 q^{22} +(-42.0000 + 72.7461i) q^{23} +(12.0000 + 20.7846i) q^{24} +(30.5000 + 52.8275i) q^{25} +(4.00000 - 6.92820i) q^{26} +27.0000 q^{27} +58.0000 q^{29} +(24.0000 - 41.5692i) q^{30} +(68.0000 + 117.779i) q^{31} +(16.0000 + 27.7128i) q^{32} +(-60.0000 + 103.923i) q^{33} +168.000 q^{34} +36.0000 q^{36} +(111.000 - 192.258i) q^{37} +(148.000 + 256.344i) q^{38} +(-6.00000 - 10.3923i) q^{39} +(32.0000 - 55.4256i) q^{40} +420.000 q^{41} -164.000 q^{43} +(-80.0000 + 138.564i) q^{44} +(-36.0000 - 62.3538i) q^{45} +(84.0000 + 145.492i) q^{46} +(-244.000 + 422.620i) q^{47} +48.0000 q^{48} +122.000 q^{50} +(126.000 - 218.238i) q^{51} +(-8.00000 - 13.8564i) q^{52} +(-239.000 - 413.960i) q^{53} +(27.0000 - 46.7654i) q^{54} +320.000 q^{55} +444.000 q^{57} +(58.0000 - 100.459i) q^{58} +(-274.000 - 474.582i) q^{59} +(-48.0000 - 83.1384i) q^{60} +(-346.000 + 599.290i) q^{61} +272.000 q^{62} +64.0000 q^{64} +(-16.0000 + 27.7128i) q^{65} +(120.000 + 207.846i) q^{66} +(454.000 + 786.351i) q^{67} +(168.000 - 290.985i) q^{68} +252.000 q^{69} -524.000 q^{71} +(36.0000 - 62.3538i) q^{72} +(-220.000 - 381.051i) q^{73} +(-222.000 - 384.515i) q^{74} +(91.5000 - 158.483i) q^{75} +592.000 q^{76} -24.0000 q^{78} +(-608.000 + 1053.09i) q^{79} +(-64.0000 - 110.851i) q^{80} +(-40.5000 - 70.1481i) q^{81} +(420.000 - 727.461i) q^{82} -684.000 q^{83} -672.000 q^{85} +(-164.000 + 284.056i) q^{86} +(-87.0000 - 150.688i) q^{87} +(160.000 + 277.128i) q^{88} +(-302.000 + 523.079i) q^{89} -144.000 q^{90} +336.000 q^{92} +(204.000 - 353.338i) q^{93} +(488.000 + 845.241i) q^{94} +(-592.000 - 1025.37i) q^{95} +(48.0000 - 83.1384i) q^{96} -832.000 q^{97} +360.000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} - 3 q^{3} - 4 q^{4} - 8 q^{5} - 12 q^{6} - 16 q^{8} - 9 q^{9}+O(q^{10}) \) 2 * q + 2 * q^2 - 3 * q^3 - 4 * q^4 - 8 * q^5 - 12 * q^6 - 16 * q^8 - 9 * q^9	\( 2 q + 2 q^{2} - 3 q^{3} - 4 q^{4} - 8 q^{5} - 12 q^{6} - 16 q^{8} - 9 q^{9} + 16 q^{10} - 40 q^{11} - 12 q^{12} + 8 q^{13} + 48 q^{15} - 16 q^{16} + 84 q^{17} + 18 q^{18} - 148 q^{19} + 64 q^{20} - 160 q^{22} - 84 q^{23} + 24 q^{24} + 61 q^{25} + 8 q^{26} + 54 q^{27} + 116 q^{29} + 48 q^{30} + 136 q^{31} + 32 q^{32} - 120 q^{33} + 336 q^{34} + 72 q^{36} + 222 q^{37} + 296 q^{38} - 12 q^{39} + 64 q^{40} + 840 q^{41} - 328 q^{43} - 160 q^{44} - 72 q^{45} + 168 q^{46} - 488 q^{47} + 96 q^{48} + 244 q^{50} + 252 q^{51} - 16 q^{52} - 478 q^{53} + 54 q^{54} + 640 q^{55} + 888 q^{57} + 116 q^{58} - 548 q^{59} - 96 q^{60} - 692 q^{61} + 544 q^{62} + 128 q^{64} - 32 q^{65} + 240 q^{66} + 908 q^{67} + 336 q^{68} + 504 q^{69} - 1048 q^{71} + 72 q^{72} - 440 q^{73} - 444 q^{74} + 183 q^{75} + 1184 q^{76} - 48 q^{78} - 1216 q^{79} - 128 q^{80} - 81 q^{81} + 840 q^{82} - 1368 q^{83} - 1344 q^{85} - 328 q^{86} - 174 q^{87} + 320 q^{88} - 604 q^{89} - 288 q^{90} + 672 q^{92} + 408 q^{93} + 976 q^{94} - 1184 q^{95} + 96 q^{96} - 1664 q^{97} + 720 q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 - 3 * q^3 - 4 * q^4 - 8 * q^5 - 12 * q^6 - 16 * q^8 - 9 * q^9 + 16 * q^10 - 40 * q^11 - 12 * q^12 + 8 * q^13 + 48 * q^15 - 16 * q^16 + 84 * q^17 + 18 * q^18 - 148 * q^19 + 64 * q^20 - 160 * q^22 - 84 * q^23 + 24 * q^24 + 61 * q^25 + 8 * q^26 + 54 * q^27 + 116 * q^29 + 48 * q^30 + 136 * q^31 + 32 * q^32 - 120 * q^33 + 336 * q^34 + 72 * q^36 + 222 * q^37 + 296 * q^38 - 12 * q^39 + 64 * q^40 + 840 * q^41 - 328 * q^43 - 160 * q^44 - 72 * q^45 + 168 * q^46 - 488 * q^47 + 96 * q^48 + 244 * q^50 + 252 * q^51 - 16 * q^52 - 478 * q^53 + 54 * q^54 + 640 * q^55 + 888 * q^57 + 116 * q^58 - 548 * q^59 - 96 * q^60 - 692 * q^61 + 544 * q^62 + 128 * q^64 - 32 * q^65 + 240 * q^66 + 908 * q^67 + 336 * q^68 + 504 * q^69 - 1048 * q^71 + 72 * q^72 - 440 * q^73 - 444 * q^74 + 183 * q^75 + 1184 * q^76 - 48 * q^78 - 1216 * q^79 - 128 * q^80 - 81 * q^81 + 840 * q^82 - 1368 * q^83 - 1344 * q^85 - 328 * q^86 - 174 * q^87 + 320 * q^88 - 604 * q^89 - 288 * q^90 + 672 * q^92 + 408 * q^93 + 976 * q^94 - 1184 * q^95 + 96 * q^96 - 1664 * q^97 + 720 * q^99

Introduction

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