LMFDB - Embedded newform 1050.3.p.a.451.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1050,3,Mod(451,1050)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1050, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 1]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("1050.451");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	1050.p (of order $6$, degree $2$, 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:	$28.6104277578$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\sqrt{2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 2x^{2} + 4 $ x^4 + 2*x^2 + 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 42)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			451.2
Root			$-0.707107 - 1.22474i$ of defining polynomial
Character	$\chi$	$=$	1050.451
Dual form			1050.3.p.a.901.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 + 1.22474i) q^{2} +(-1.50000 - 0.866025i) q^{3} +(-1.00000 + 1.73205i) q^{4} -2.44949i q^{6} +(6.74264 + 1.88064i) q^{7} -2.82843 q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})$	\(q+(0.707107 + 1.22474i) q^{2} +(-1.50000 - 0.866025i) q^{3} +(-1.00000 + 1.73205i) q^{4} -2.44949i q^{6} +(6.74264 + 1.88064i) q^{7} -2.82843 q^{8} +(1.50000 + 2.59808i) q^{9} +(-3.00000 + 5.19615i) q^{11} +(3.00000 - 1.73205i) q^{12} -17.8639i q^{13} +(2.46447 + 9.58783i) q^{14} +(-2.00000 - 3.46410i) q^{16} +(16.2426 + 9.37769i) q^{17} +(-2.12132 + 3.67423i) q^{18} +(-14.7426 + 8.51167i) q^{19} +(-8.48528 - 8.66025i) q^{21} -8.48528 q^{22} +(6.72792 + 11.6531i) q^{23} +(4.24264 + 2.44949i) q^{24} +(21.8787 - 12.6317i) q^{26} -5.19615i q^{27} +(-10.0000 + 9.79796i) q^{28} +33.9411 q^{29} +(12.7721 + 7.37396i) q^{31} +(2.82843 - 4.89898i) q^{32} +(9.00000 - 5.19615i) q^{33} +26.5241i q^{34} -6.00000 q^{36} +(2.98528 + 5.17066i) q^{37} +(-20.8492 - 12.0373i) q^{38} +(-15.4706 + 26.7958i) q^{39} -35.2354i q^{41} +(4.60660 - 16.5160i) q^{42} -15.4853 q^{43} +(-6.00000 - 10.3923i) q^{44} +(-9.51472 + 16.4800i) q^{46} +(28.7574 - 16.6031i) q^{47} +6.92820i q^{48} +(41.9264 + 25.3609i) q^{49} +(-16.2426 - 28.1331i) q^{51} +(30.9411 + 17.8639i) q^{52} +(-17.2721 + 29.9161i) q^{53} +(6.36396 - 3.67423i) q^{54} +(-19.0711 - 5.31925i) q^{56} +29.4853 q^{57} +(24.0000 + 41.5692i) q^{58} +(23.6985 + 13.6823i) q^{59} +(-34.9706 + 20.1903i) q^{61} +20.8567i q^{62} +(5.22792 + 20.3389i) q^{63} +8.00000 q^{64} +(12.7279 + 7.34847i) q^{66} +(-57.1985 + 99.0707i) q^{67} +(-32.4853 + 18.7554i) q^{68} -23.3062i q^{69} +18.6030 q^{71} +(-4.24264 - 7.34847i) q^{72} +(101.353 + 58.5161i) q^{73} +(-4.22183 + 7.31242i) q^{74} -34.0467i q^{76} +(-30.0000 + 29.3939i) q^{77} -43.7574 q^{78} +(44.1690 + 76.5030i) q^{79} +(-4.50000 + 7.79423i) q^{81} +(43.1543 - 24.9152i) q^{82} +75.7601i q^{83} +(23.4853 - 6.03668i) q^{84} +(-10.9497 - 18.9655i) q^{86} +(-50.9117 - 29.3939i) q^{87} +(8.48528 - 14.6969i) q^{88} +(-18.0000 + 10.3923i) q^{89} +(33.5955 - 120.450i) q^{91} -26.9117 q^{92} +(-12.7721 - 22.1219i) q^{93} +(40.6690 + 23.4803i) q^{94} +(-8.48528 + 4.89898i) q^{96} +30.5826i q^{97} +(-1.41421 + 69.2820i) q^{98} -18.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 6 q^{3} - 4 q^{4} + 10 q^{7} + 6 q^{9}+O(q^{10}) $ 4 * q - 6 * q^3 - 4 * q^4 + 10 * q^7 + 6 * q^9	$ 4 q - 6 q^{3} - 4 q^{4} + 10 q^{7} + 6 q^{9} - 12 q^{11} + 12 q^{12} + 24 q^{14} - 8 q^{16} + 48 q^{17} - 42 q^{19} - 24 q^{23} + 96 q^{26} - 40 q^{28} + 102 q^{31} + 36 q^{33} - 24 q^{36} - 22 q^{37} - 24 q^{38} + 6 q^{39} - 24 q^{42} - 28 q^{43} - 24 q^{44} - 72 q^{46} + 132 q^{47} - 2 q^{49} - 48 q^{51} - 12 q^{52} - 120 q^{53} - 48 q^{56} + 84 q^{57} + 96 q^{58} - 24 q^{59} - 72 q^{61} - 30 q^{63} + 32 q^{64} - 110 q^{67} - 96 q^{68} + 312 q^{71} + 66 q^{73} - 48 q^{74} - 120 q^{77} - 192 q^{78} - 10 q^{79} - 18 q^{81} - 48 q^{82} + 60 q^{84} - 24 q^{86} - 72 q^{89} - 222 q^{91} + 96 q^{92} - 102 q^{93} - 24 q^{94} - 72 q^{99}+O(q^{100}) $ 4 * q - 6 * q^3 - 4 * q^4 + 10 * q^7 + 6 * q^9 - 12 * q^11 + 12 * q^12 + 24 * q^14 - 8 * q^16 + 48 * q^17 - 42 * q^19 - 24 * q^23 + 96 * q^26 - 40 * q^28 + 102 * q^31 + 36 * q^33 - 24 * q^36 - 22 * q^37 - 24 * q^38 + 6 * q^39 - 24 * q^42 - 28 * q^43 - 24 * q^44 - 72 * q^46 + 132 * q^47 - 2 * q^49 - 48 * q^51 - 12 * q^52 - 120 * q^53 - 48 * q^56 + 84 * q^57 + 96 * q^58 - 24 * q^59 - 72 * q^61 - 30 * q^63 + 32 * q^64 - 110 * q^67 - 96 * q^68 + 312 * q^71 + 66 * q^73 - 48 * q^74 - 120 * q^77 - 192 * q^78 - 10 * q^79 - 18 * q^81 - 48 * q^82 + 60 * q^84 - 24 * q^86 - 72 * q^89 - 222 * q^91 + 96 * q^92 - 102 * q^93 - 24 * q^94 - 72 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times$.

$n$	$127$	$451$	$701$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$1$

Coefficient data

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

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

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

$2$	0.707107	+	1.22474i	0.353553	+	0.612372i
$2$	0.707107	+	1.22474i	0.353553	+	0.612372i
$3$	−1.50000	−	0.866025i	−0.500000	−	0.288675i
$3$	−1.50000	−	0.866025i	−0.500000	−	0.288675i
$4$	−1.00000	+	1.73205i	−0.250000	+	0.433013i
$5$		0			0
$5$		0			0
$6$		−	2.44949i		−	0.408248i
$7$	6.74264	+	1.88064i	0.963234	+	0.268662i
$7$	6.74264	+	1.88064i	0.963234	+	0.268662i
$8$	−2.82843			−0.353553
$9$	1.50000	+	2.59808i	0.166667	+	0.288675i
$10$		0			0
$11$	−3.00000	+	5.19615i	−0.272727	+	0.472377i	−0.969559	−	0.244857i	$-0.921259\pi$
$11$	−3.00000	+	5.19615i	−0.272727	+	0.472377i	0.696832	+	0.717234i	$0.254592\pi$
$12$	3.00000	−	1.73205i	0.250000	−	0.144338i
$13$		−	17.8639i		−	1.37414i	−0.726590	−	0.687072i	$-0.758896\pi$
$13$		−	17.8639i		−	1.37414i	0.726590	−	0.687072i	$-0.241104\pi$
$14$	2.46447	+	9.58783i	0.176033	+	0.684845i
$15$		0			0
$16$	−2.00000	−	3.46410i	−0.125000	−	0.216506i
$17$	16.2426	+	9.37769i	0.955449	+	0.551629i	0.894770	−	0.446528i	$-0.147340\pi$
$17$	16.2426	+	9.37769i	0.955449	+	0.551629i	0.0606799	+	0.998157i	$0.480673\pi$
$18$	−2.12132	+	3.67423i	−0.117851	+	0.204124i
$19$	−14.7426	+	8.51167i	−0.775928	+	0.447983i	−0.834985	−	0.550272i	$-0.814524\pi$
$19$	−14.7426	+	8.51167i	−0.775928	+	0.447983i	0.0590569	+	0.998255i	$0.481191\pi$
$20$		0			0
$21$	−8.48528	−	8.66025i	−0.404061	−	0.412393i
$22$	−8.48528			−0.385695
$23$	6.72792	+	11.6531i	0.292518	+	0.506657i	0.974405	−	0.224802i	$-0.0721734\pi$
$23$	6.72792	+	11.6531i	0.292518	+	0.506657i	−0.681886	+	0.731458i	$0.738840\pi$
$24$	4.24264	+	2.44949i	0.176777	+	0.102062i
$25$		0			0
$26$	21.8787	−	12.6317i	0.841488	−	0.485833i
$27$		−	5.19615i		−	0.192450i
$28$	−10.0000	+	9.79796i	−0.357143	+	0.349927i
$29$	33.9411			1.17038			0.585192	−	0.810895i	$-0.301019\pi$
$29$	33.9411			1.17038			0.585192	+	0.810895i	$0.301019\pi$
$30$		0			0
$31$	12.7721	+	7.37396i	0.412003	+	0.237870i	0.691650	−	0.722233i	$-0.256884\pi$
$31$	12.7721	+	7.37396i	0.412003	+	0.237870i	−0.279647	+	0.960103i	$0.590218\pi$
$32$	2.82843	−	4.89898i	0.0883883	−	0.153093i
$33$	9.00000	−	5.19615i	0.272727	−	0.157459i
$34$			26.5241i			0.780121i
$35$		0			0
$36$	−6.00000			−0.166667
$37$	2.98528	+	5.17066i	0.0806833	+	0.139748i	0.903544	−	0.428496i	$-0.140956\pi$
$37$	2.98528	+	5.17066i	0.0806833	+	0.139748i	−0.822860	+	0.568244i	$0.807623\pi$
$38$	−20.8492	−	12.0373i	−0.548664	−	0.316771i
$39$	−15.4706	+	26.7958i	−0.396681	+	0.687072i
$40$		0			0
$41$		−	35.2354i		−	0.859399i	−0.902972	−	0.429700i	$-0.858619\pi$
$41$		−	35.2354i		−	0.859399i	0.902972	−	0.429700i	$-0.141381\pi$
$42$	4.60660	−	16.5160i	0.109681	−	0.393239i
$43$	−15.4853			−0.360123			−0.180061	−	0.983655i	$-0.557630\pi$
$43$	−15.4853			−0.360123			−0.180061	+	0.983655i	$0.557630\pi$
$44$	−6.00000	−	10.3923i	−0.136364	−	0.236189i
$45$		0			0
$46$	−9.51472	+	16.4800i	−0.206842	+	0.358260i
$47$	28.7574	−	16.6031i	0.611859	−	0.353257i	−0.161834	−	0.986818i	$-0.551741\pi$
$47$	28.7574	−	16.6031i	0.611859	−	0.353257i	0.773693	+	0.633561i	$0.218408\pi$
$48$			6.92820i			0.144338i
$49$	41.9264	+	25.3609i	0.855641	+	0.517570i
$50$		0			0
$51$	−16.2426	−	28.1331i	−0.318483	−	0.551629i
$52$	30.9411	+	17.8639i	0.595022	+	0.343536i
$53$	−17.2721	+	29.9161i	−0.325888	+	0.564455i	−0.981692	−	0.190477i	$-0.938997\pi$
$53$	−17.2721	+	29.9161i	−0.325888	+	0.564455i	0.655803	+	0.754932i	$0.272330\pi$
$54$	6.36396	−	3.67423i	0.117851	−	0.0680414i
$55$		0			0
$56$	−19.0711	−	5.31925i	−0.340555	−	0.0949865i
$57$	29.4853			0.517286
$58$	24.0000	+	41.5692i	0.413793	+	0.716711i
$59$	23.6985	+	13.6823i	0.401669	+	0.231904i	0.687204	−	0.726465i	$-0.258838\pi$
$59$	23.6985	+	13.6823i	0.401669	+	0.231904i	−0.285535	+	0.958368i	$0.592171\pi$
$60$		0			0
$61$	−34.9706	+	20.1903i	−0.573288	+	0.330988i	−0.758461	−	0.651718i	$-0.774049\pi$
$61$	−34.9706	+	20.1903i	−0.573288	+	0.330988i	0.185174	+	0.982706i	$0.440715\pi$
$62$			20.8567i			0.336399i
$63$	5.22792	+	20.3389i	0.0829829	+	0.322839i
$64$	8.00000			0.125000
$65$		0			0
$66$	12.7279	+	7.34847i	0.192847	+	0.111340i
$67$	−57.1985	+	99.0707i	−0.853709	+	1.47867i	0.0241291	+	0.999709i	$0.492319\pi$
$67$	−57.1985	+	99.0707i	−0.853709	+	1.47867i	−0.877838	+	0.478958i	$0.841015\pi$
$68$	−32.4853	+	18.7554i	−0.477725	+	0.275814i
$69$		−	23.3062i		−	0.337771i
$70$		0			0
$71$	18.6030			0.262015			0.131007	−	0.991381i	$-0.458179\pi$
$71$	18.6030			0.262015			0.131007	+	0.991381i	$0.458179\pi$
$72$	−4.24264	−	7.34847i	−0.0589256	−	0.102062i
$73$	101.353	+	58.5161i	1.38839	+	0.801590i	0.993134	−	0.116979i	$-0.0373210\pi$
$73$	101.353	+	58.5161i	1.38839	+	0.801590i	0.395260	+	0.918569i	$0.370654\pi$
$74$	−4.22183	+	7.31242i	−0.0570517	+	0.0988164i
$75$		0			0
$76$		−	34.0467i		−	0.447983i
$77$	−30.0000	+	29.3939i	−0.389610	+	0.381739i
$78$	−43.7574			−0.560992
$79$	44.1690	+	76.5030i	0.559102	+	0.968393i	0.997572	+	0.0696469i	$0.0221873\pi$
$79$	44.1690	+	76.5030i	0.559102	+	0.968393i	−0.438470	+	0.898746i	$0.644479\pi$
$80$		0			0
$81$	−4.50000	+	7.79423i	−0.0555556	+	0.0962250i
$82$	43.1543	−	24.9152i	0.526272	−	0.303843i
$83$			75.7601i			0.912772i	0.889782	+	0.456386i	$0.150856\pi$
$83$			75.7601i			0.912772i	−0.889782	+	0.456386i	$0.849144\pi$
$84$	23.4853	−	6.03668i	0.279587	−	0.0718653i
$85$		0			0
$86$	−10.9497	−	18.9655i	−0.127323	−	0.220529i
$87$	−50.9117	−	29.3939i	−0.585192	−	0.337861i
$88$	8.48528	−	14.6969i	0.0964237	−	0.167011i
$89$	−18.0000	+	10.3923i	−0.202247	+	0.116767i	−0.597703	−	0.801717i	$-0.703920\pi$
$89$	−18.0000	+	10.3923i	−0.202247	+	0.116767i	0.395456	+	0.918485i	$0.370587\pi$
$90$		0			0
$91$	33.5955	−	120.450i	0.369181	−	1.32362i
$92$	−26.9117			−0.292518
$93$	−12.7721	−	22.1219i	−0.137334	−	0.237870i
$94$	40.6690	+	23.4803i	0.432649	+	0.249790i
$95$		0			0
$96$	−8.48528	+	4.89898i	−0.0883883	+	0.0510310i
$97$			30.5826i			0.315284i	0.987496	+	0.157642i	$0.0503892\pi$
$97$			30.5826i			0.315284i	−0.987496	+	0.157642i	$0.949611\pi$
$98$	−1.41421	+	69.2820i	−0.0144308	+	0.706960i
$99$	−18.0000			−0.181818
$100$		0			0
$101$	110.823	+	63.9839i	1.09726	+	0.633504i	0.935500	−	0.353326i	$-0.114949\pi$
$101$	110.823	+	63.9839i	1.09726	+	0.633504i	0.161761	+	0.986830i	$0.448283\pi$
$102$	22.9706	−	39.7862i	0.225202	−	0.390061i
$103$	70.1102	−	40.4781i	0.680681	−	0.392992i	−0.119430	−	0.992843i	$-0.538107\pi$
$103$	70.1102	−	40.4781i	0.680681	−	0.392992i	0.800112	+	0.599851i	$0.204774\pi$
$104$			50.5266i			0.485833i
$105$		0			0
$106$	−48.8528			−0.460876
$107$	84.7279	+	146.753i	0.791850	+	1.37152i	0.924820	+	0.380404i	$0.124215\pi$
$107$	84.7279	+	146.753i	0.791850	+	1.37152i	−0.132971	+	0.991120i	$0.542452\pi$
$108$	9.00000	+	5.19615i	0.0833333	+	0.0481125i
$109$	−89.4706	+	154.968i	−0.820831	+	1.42172i	0.0842335	+	0.996446i	$0.473156\pi$
$109$	−89.4706	+	154.968i	−0.820831	+	1.42172i	−0.905064	+	0.425275i	$0.860177\pi$
$110$		0			0
$111$		−	10.3413i		−	0.0931650i
$112$	−6.97056	−	27.1185i	−0.0622372	−	0.242129i
$113$	17.3970			0.153955			0.0769777	−	0.997033i	$-0.475473\pi$
$113$	17.3970			0.153955			0.0769777	+	0.997033i	$0.475473\pi$
$114$	20.8492	+	36.1119i	0.182888	+	0.316771i
$115$		0			0
$116$	−33.9411	+	58.7878i	−0.292596	+	0.506791i
$117$	46.4117	−	26.7958i	0.396681	−	0.229024i
$118$			38.6995i			0.327962i
$119$	91.8823	+	93.7769i	0.772120	+	0.788041i
$120$		0			0
$121$	42.5000	+	73.6122i	0.351240	+	0.608365i
$122$	−49.4558	−	28.5533i	−0.405376	−	0.234044i
$123$	−30.5147	+	52.8530i	−0.248087	+	0.429700i
$124$	−25.5442	+	14.7479i	−0.206001	+	0.118935i
$125$		0			0
$126$	−21.2132	+	20.7846i	−0.168359	+	0.164957i
$127$	−167.426			−1.31832			−0.659159	−	0.752004i	$-0.729088\pi$
$127$	−167.426			−1.31832			−0.659159	+	0.752004i	$0.729088\pi$
$128$	5.65685	+	9.79796i	0.0441942	+	0.0765466i
$129$	23.2279	+	13.4106i	0.180061	+	0.103959i
$130$		0			0
$131$	−1.54416	+	0.891519i	−0.0117874	+	0.00680549i	−0.505882	−	0.862603i	$-0.668833\pi$
$131$	−1.54416	+	0.891519i	−0.0117874	+	0.00680549i	0.494095	+	0.869408i	$0.335500\pi$
$132$			20.7846i			0.157459i
$133$	−115.412	+	29.6656i	−0.867757	+	0.223049i
$134$	−161.782			−1.20733
$135$		0			0
$136$	−45.9411	−	26.5241i	−0.337802	−	0.195030i
$137$	50.4853	−	87.4431i	0.368506	−	0.638271i	−0.620826	−	0.783948i	$-0.713203\pi$
$137$	50.4853	−	87.4431i	0.368506	−	0.638271i	0.989332	+	0.145677i	$0.0465362\pi$
$138$	28.5442	−	16.4800i	0.206842	−	0.119420i
$139$			140.542i			1.01110i	0.862799	+	0.505548i	$0.168710\pi$
$139$			140.542i			1.01110i	−0.862799	+	0.505548i	$0.831290\pi$
$140$		0			0
$141$	−57.5147			−0.407906
$142$	13.1543	+	22.7840i	0.0926361	+	0.160450i
$143$	92.8234	+	53.5916i	0.649115	+	0.374766i
$144$	6.00000	−	10.3923i	0.0416667	−	0.0721688i
$145$		0			0
$146$			165.508i			1.13362i
$147$	−40.9264	−	74.3507i	−0.278411	−	0.505787i
$148$	−11.9411			−0.0806833
$149$	−91.4558	−	158.406i	−0.613798	−	1.06313i	−0.990594	−	0.136833i	$-0.956308\pi$
$149$	−91.4558	−	158.406i	−0.613798	−	1.06313i	0.376797	−	0.926296i	$-0.377026\pi$
$150$		0			0
$151$	144.397	−	250.103i	0.956271	−	1.65631i	0.224840	−	0.974396i	$-0.427814\pi$
$151$	144.397	−	250.103i	0.956271	−	1.65631i	0.731432	−	0.681915i	$-0.238852\pi$
$152$	41.6985	−	24.0746i	0.274332	−	0.158386i
$153$			56.2662i			0.367753i
$154$	−57.2132	−	15.9577i	−0.371514	−	0.103622i
$155$		0			0
$156$	−30.9411	−	53.5916i	−0.198341	−	0.343536i
$157$	−162.000	−	93.5307i	−1.03185	−	0.595737i	−0.114334	−	0.993442i	$-0.536473\pi$
$157$	−162.000	−	93.5307i	−1.03185	−	0.595737i	−0.917513	+	0.397705i	$0.869807\pi$
$158$	−62.4645	+	108.192i	−0.395345	+	0.684757i
$159$	51.8162	−	29.9161i	0.325888	−	0.188152i
$160$		0			0
$161$	23.4487	+	91.2255i	0.145644	+	0.566618i
$162$	−12.7279			−0.0785674
$163$	8.02944	+	13.9074i	0.0492604	+	0.0853214i	0.889604	−	0.456732i	$-0.150980\pi$
$163$	8.02944	+	13.9074i	0.0492604	+	0.0853214i	−0.840344	+	0.542054i	$0.817647\pi$
$164$	61.0294	+	35.2354i	0.372131	+	0.214850i
$165$		0			0
$166$	−92.7868	+	53.5705i	−0.558957	+	0.322714i
$167$		−	176.117i		−	1.05459i	−0.849681	−	0.527297i	$-0.823206\pi$
$167$		−	176.117i		−	1.05459i	0.849681	−	0.527297i	$-0.176794\pi$
$168$	24.0000	+	24.4949i	0.142857	+	0.145803i
$169$	−150.118			−0.888271
$170$		0			0
$171$	−44.2279	−	25.5350i	−0.258643	−	0.149328i
$172$	15.4853	−	26.8213i	0.0900307	−	0.155938i
$173$	200.184	−	115.576i	1.15713	−	0.668070i	0.206517	−	0.978443i	$-0.433787\pi$
$173$	200.184	−	115.576i	1.15713	−	0.668070i	0.950615	+	0.310373i	$0.100454\pi$
$174$		−	83.1384i		−	0.477807i
$175$		0			0
$176$	24.0000			0.136364
$177$	−23.6985	−	41.0470i	−0.133890	−	0.231904i
$178$	−25.4558	−	14.6969i	−0.143010	−	0.0825671i
$179$	42.6396	−	73.8540i	0.238210	−	0.412592i	−0.721991	−	0.691903i	$-0.756773\pi$
$179$	42.6396	−	73.8540i	0.238210	−	0.412592i	0.960201	+	0.279311i	$0.0901060\pi$
$180$		0			0
$181$			5.58655i			0.0308649i	0.999881	+	0.0154325i	$0.00491250\pi$
$181$			5.58655i			0.0308649i	−0.999881	+	0.0154325i	$0.995087\pi$
$182$	171.276	−	44.0249i	0.941075	−	0.241895i
$183$	69.9411			0.382192
$184$	−19.0294	−	32.9600i	−0.103421	−	0.179130i
$185$		0			0
$186$	18.0624	−	31.2851i	0.0971099	−	0.168199i
$187$	−97.4558	+	56.2662i	−0.521154	+	0.300889i
$188$			66.4123i			0.353257i
$189$	9.77208	−	35.0358i	0.0517041	−	0.185375i
$190$		0			0
$191$	−92.6985	−	160.558i	−0.485332	−	0.840620i	0.514526	−	0.857475i	$-0.327968\pi$
$191$	−92.6985	−	160.558i	−0.485332	−	0.840620i	−0.999858	+	0.0168547i	$0.994635\pi$
$192$	−12.0000	−	6.92820i	−0.0625000	−	0.0360844i
$193$	113.897	−	197.275i	0.590140	−	1.02215i	−0.404073	−	0.914727i	$-0.632406\pi$
$193$	113.897	−	197.275i	0.590140	−	1.02215i	0.994213	−	0.107425i	$-0.0342607\pi$
$194$	−37.4558	+	21.6251i	−0.193071	+	0.111470i
$195$		0			0
$196$	−85.8528	+	47.2577i	−0.438025	+	0.241111i
$197$	−123.161			−0.625185			−0.312593	−	0.949887i	$-0.601197\pi$
$197$	−123.161			−0.625185			−0.312593	+	0.949887i	$0.601197\pi$
$198$	−12.7279	−	22.0454i	−0.0642824	−	0.111340i
$199$	5.39697	+	3.11594i	0.0271205	+	0.0156580i	0.513499	−	0.858090i	$-0.328349\pi$
$199$	5.39697	+	3.11594i	0.0271205	+	0.0156580i	−0.486378	+	0.873748i	$0.661682\pi$
$200$		0			0
$201$	171.595	−	99.0707i	0.853709	−	0.492889i
$202$			180.974i			0.895910i
$203$	228.853	+	63.8309i	1.12735	+	0.314438i
$204$	64.9706			0.318483
$205$		0			0
$206$	99.1508	+	57.2447i	0.481314	+	0.277887i
$207$	−20.1838	+	34.9593i	−0.0975061	+	0.168886i
$208$	−61.8823	+	35.7277i	−0.297511	+	0.171768i
$209$		−	102.140i		−	0.488708i
$210$		0			0
$211$	−124.912			−0.591999			−0.295999	−	0.955188i	$-0.595653\pi$
$211$	−124.912			−0.591999			−0.295999	+	0.955188i	$0.595653\pi$
$212$	−34.5442	−	59.8322i	−0.162944	−	0.282228i
$213$	−27.9045	−	16.1107i	−0.131007	−	0.0756371i
$214$	−119.823	+	207.540i	−0.559922	+	0.969814i
$215$		0			0
$216$			14.6969i			0.0680414i
$217$	72.2498	+	73.7396i	0.332948	+	0.339814i
$218$	−253.061			−1.16083
$219$	−101.353	−	175.548i	−0.462798	−	0.801590i
$220$		0			0
$221$	167.522	−	290.156i	0.758017	−	1.31292i
$222$	12.6655	−	7.31242i	0.0570517	−	0.0329388i
$223$		−	228.631i		−	1.02525i	−0.858613	−	0.512625i	$-0.828673\pi$
$223$		−	228.631i		−	1.02525i	0.858613	−	0.512625i	$-0.171327\pi$
$224$	28.2843	−	27.7128i	0.126269	−	0.123718i
$225$		0			0
$226$	12.3015	+	21.3068i	0.0544315	+	0.0942781i
$227$	146.823	+	84.7685i	0.646799	+	0.373430i	0.787229	−	0.616661i	$-0.211515\pi$
$227$	146.823	+	84.7685i	0.646799	+	0.373430i	−0.140430	+	0.990091i	$0.544848\pi$
$228$	−29.4853	+	51.0700i	−0.129321	+	0.223991i
$229$	30.0442	−	17.3460i	0.131197	−	0.0757467i	−0.432965	−	0.901411i	$-0.642533\pi$
$229$	30.0442	−	17.3460i	0.131197	−	0.0757467i	0.564162	+	0.825664i	$0.309199\pi$
$230$		0			0
$231$	70.4558	−	18.1101i	0.305004	−	0.0783985i
$232$	−96.0000			−0.413793
$233$	−127.243	−	220.391i	−0.546106	−	0.945883i	−0.998536	−	0.0540833i	$-0.982776\pi$
$233$	−127.243	−	220.391i	−0.546106	−	0.945883i	0.452431	−	0.891800i	$-0.350557\pi$
$234$	65.6360	+	37.8950i	0.280496	+	0.161944i
$235$		0			0
$236$	−47.3970	+	27.3647i	−0.200835	+	0.115952i
$237$		−	153.006i		−	0.645595i
$238$	−49.8823	+	178.843i	−0.209589	+	0.751440i
$239$	197.147			0.824884			0.412442	−	0.910984i	$-0.364676\pi$
$239$	197.147			0.824884			0.412442	+	0.910984i	$0.364676\pi$
$240$		0			0
$241$	76.6173	+	44.2350i	0.317914	+	0.183548i	0.650462	−	0.759538i	$-0.274575\pi$
$241$	76.6173	+	44.2350i	0.317914	+	0.183548i	−0.332548	+	0.943086i	$0.607908\pi$
$242$	−60.1041	+	104.103i	−0.248364	+	0.430179i
$243$	13.5000	−	7.79423i	0.0555556	−	0.0320750i
$244$		−	80.7611i		−	0.330988i
$245$		0			0
$246$	−86.3087			−0.350848
$247$	152.051	+	263.361i	0.615592	+	1.06624i
$248$	−36.1249	−	20.8567i	−0.145665	−	0.0840997i
$249$	65.6102	−	113.640i	0.263495	−	0.456386i
$250$		0			0
$251$			215.903i			0.860172i	0.902788	+	0.430086i	$0.141517\pi$
$251$			215.903i			0.860172i	−0.902788	+	0.430086i	$0.858483\pi$
$252$	−40.4558	−	11.2838i	−0.160539	−	0.0447771i
$253$	−80.7351			−0.319111
$254$	−118.388	−	205.055i	−0.466096	−	0.807302i
$255$		0			0
$256$	−8.00000	+	13.8564i	−0.0312500	+	0.0541266i
$257$	3.72792	−	2.15232i	0.0145055	−	0.00837477i	−0.492730	−	0.870182i	$-0.664001\pi$
$257$	3.72792	−	2.15232i	0.0145055	−	0.00837477i	0.507235	+	0.861808i	$0.330668\pi$
$258$			37.9310i			0.147020i
$259$	10.4045	+	40.4781i	0.0401720	+	0.156286i
$260$		0			0
$261$	50.9117	+	88.1816i	0.195064	+	0.337861i
$262$	−2.18377	−	1.26080i	−0.00833499	−	0.00481221i
$263$	141.338	−	244.805i	0.537407	−	0.930817i	−0.461635	−	0.887070i	$-0.652737\pi$
$263$	141.338	−	244.805i	0.537407	−	0.930817i	0.999043	−	0.0437468i	$-0.0139295\pi$
$264$	−25.4558	+	14.6969i	−0.0964237	+	0.0556702i
$265$		0			0
$266$	−117.941	−	120.373i	−0.443388	−	0.452531i
$267$	36.0000			0.134831
$268$	−114.397	−	198.141i	−0.426854	−	0.739333i
$269$	−330.765	−	190.967i	−1.22961	−	0.709914i	−0.262660	−	0.964888i	$-0.584600\pi$
$269$	−330.765	−	190.967i	−1.22961	−	0.709914i	−0.966948	+	0.254974i	$0.917933\pi$
$270$		0			0
$271$	−73.0294	+	42.1636i	−0.269481	+	0.155585i	−0.628652	−	0.777687i	$-0.716393\pi$
$271$	−73.0294	+	42.1636i	−0.269481	+	0.155585i	0.359171	+	0.933272i	$0.383060\pi$
$272$		−	75.0215i		−	0.275814i
$273$	−154.706	+	151.580i	−0.566687	+	0.555238i
$274$	142.794			0.521146
$275$		0			0
$276$	40.3675	+	23.3062i	0.146259	+	0.0844428i
$277$	−68.5589	+	118.747i	−0.247505	+	0.428691i	−0.962833	−	0.270098i	$-0.912944\pi$
$277$	−68.5589	+	118.747i	−0.247505	+	0.428691i	0.715328	+	0.698789i	$0.246277\pi$
$278$	−172.128	+	99.3784i	−0.619167	+	0.357476i
$279$			44.2438i			0.158580i
$280$		0			0
$281$	−325.103			−1.15695			−0.578474	−	0.815701i	$-0.696352\pi$
$281$	−325.103			−1.15695			−0.578474	+	0.815701i	$0.696352\pi$
$282$	−40.6690	−	70.4409i	−0.144216	−	0.249790i
$283$	−168.507	−	97.2876i	−0.595432	−	0.343773i	0.171811	−	0.985130i	$-0.445038\pi$
$283$	−168.507	−	97.2876i	−0.595432	−	0.343773i	−0.767242	+	0.641357i	$0.778372\pi$
$284$	−18.6030	+	32.2214i	−0.0655036	+	0.113456i
$285$		0			0
$286$			151.580i			0.530000i
$287$	66.2649	−	237.579i	0.230888	−	0.827803i
$288$	16.9706			0.0589256
$289$	31.3823	+	54.3557i	0.108589	+	0.188082i
$290$		0			0
$291$	26.4853	−	45.8739i	0.0910147	−	0.157642i
$292$	−202.706	+	117.032i	−0.694197	+	0.400795i
$293$		−	239.702i		−	0.818095i	−0.912513	−	0.409048i	$-0.865861\pi$
$293$		−	239.702i		−	0.818095i	0.912513	−	0.409048i	$-0.134139\pi$
$294$	62.1213	−	102.698i	0.211297	−	0.349314i
$295$		0			0
$296$	−8.44365	−	14.6248i	−0.0285258	−	0.0494082i
$297$	27.0000	+	15.5885i	0.0909091	+	0.0524864i
$298$	129.338	−	224.020i	0.434020	−	0.751745i
$299$	208.169	−	120.187i	0.696219	−	0.401962i
$300$		0			0
$301$	−104.412	−	29.1222i	−0.346883	−	0.0967515i
$302$	408.416			1.35237
$303$	−110.823	−	191.952i	−0.365754	−	0.633504i
$304$	58.9706	+	34.0467i	0.193982	+	0.111996i
$305$		0			0
$306$	−68.9117	+	39.7862i	−0.225202	+	0.130020i
$307$			540.272i			1.75984i	0.475120	+	0.879921i	$0.342405\pi$
$307$			540.272i			1.75984i	−0.475120	+	0.879921i	$0.657595\pi$
$308$	−20.9117	−	81.3554i	−0.0678951	−	0.264141i
$309$	−140.220			−0.453788
$310$		0			0
$311$	350.044	+	202.098i	1.12554	+	0.649832i	0.942810	−	0.333330i	$-0.108172\pi$
$311$	350.044	+	202.098i	1.12554	+	0.649832i	0.182732	+	0.983163i	$0.441506\pi$
$312$	43.7574	−	75.7900i	0.140248	−	0.242917i
$313$	113.706	−	65.6482i	0.363278	−	0.209739i	−0.307240	−	0.951632i	$-0.599405\pi$
$313$	113.706	−	65.6482i	0.363278	−	0.209739i	0.670518	+	0.741893i	$0.266072\pi$
$314$		−	264.545i		−	0.842500i
$315$		0			0
$316$	−176.676			−0.559102
$317$	−46.9706	−	81.3554i	−0.148172	−	0.256642i	0.782380	−	0.622802i	$-0.214006\pi$
$317$	−46.9706	−	81.3554i	−0.148172	−	0.256642i	−0.930552	+	0.366160i	$0.880672\pi$
$318$	73.2792	+	42.3078i	0.230438	+	0.133043i
$319$	−101.823	+	176.363i	−0.319196	+	0.552863i
$320$		0			0
$321$		−	293.506i		−	0.914349i
$322$	−95.1472	+	93.2248i	−0.295488	+	0.289518i
$323$	−319.279			−0.988481
$324$	−9.00000	−	15.5885i	−0.0277778	−	0.0481125i
$325$		0			0
$326$	−11.3553	+	19.6680i	−0.0348323	+	0.0603314i
$327$	268.412	−	154.968i	0.820831	−	0.473907i
$328$			99.6607i			0.303843i
$329$	225.125	−	57.8664i	0.684270	−	0.175886i
$330$		0			0
$331$	130.684	+	226.351i	0.394815	+	0.683840i	0.993078	−	0.117460i	$-0.0374754\pi$
$331$	130.684	+	226.351i	0.394815	+	0.683840i	−0.598263	+	0.801300i	$0.704142\pi$
$332$	−131.220	−	75.7601i	−0.395242	−	0.228193i
$333$	−8.95584	+	15.5120i	−0.0268944	+	0.0465825i
$334$	215.698	−	124.534i	0.645804	−	0.372855i
$335$		0			0
$336$	−13.0294	+	46.7144i	−0.0387781	+	0.139031i
$337$	−136.265			−0.404347			−0.202173	−	0.979350i	$-0.564800\pi$
$337$	−136.265			−0.404347			−0.202173	+	0.979350i	$0.564800\pi$
$338$	−106.149	−	183.856i	−0.314051	−	0.543952i
$339$	−26.0955	−	15.0662i	−0.0769777	−	0.0444431i
$340$		0			0
$341$	−76.6325	+	44.2438i	−0.224729	+	0.129747i
$342$		−	72.2239i		−	0.211181i
$343$	235.000	+	249.848i	0.685131	+	0.728420i
$344$	43.7990			0.127323
$345$		0			0
$346$	283.103	+	163.449i	0.818216	+	0.472397i
$347$	−161.095	+	279.026i	−0.464252	+	0.804108i	−0.999167	−	0.0407975i	$-0.987010\pi$
$347$	−161.095	+	279.026i	−0.464252	+	0.804108i	0.534915	+	0.844906i	$0.320343\pi$
$348$	101.823	−	58.7878i	0.292596	−	0.168930i
$349$		−	346.495i		−	0.992821i	−0.868088	−	0.496411i	$-0.834651\pi$
$349$		−	346.495i		−	0.992821i	0.868088	−	0.496411i	$-0.165349\pi$
$350$		0			0
$351$	−92.8234			−0.264454
$352$	16.9706	+	29.3939i	0.0482118	+	0.0835053i
$353$	537.448	+	310.296i	1.52252	+	0.879025i	0.999646	+	0.0266116i	$0.00847174\pi$
$353$	537.448	+	310.296i	1.52252	+	0.879025i	0.522869	+	0.852413i	$0.324862\pi$
$354$	33.5147	−	58.0492i	0.0946743	−	0.163981i
$355$		0			0
$356$		−	41.5692i		−	0.116767i
$357$	−56.6102	−	220.238i	−0.158572	−	0.616912i
$358$	120.603			0.336880
$359$	−10.1177	−	17.5245i	−0.0281831	−	0.0488146i	0.851590	−	0.524209i	$-0.175639\pi$
$359$	−10.1177	−	17.5245i	−0.0281831	−	0.0488146i	−0.879773	+	0.475394i	$0.842305\pi$
$360$		0			0
$361$	−35.6030	+	61.6663i	−0.0986234	+	0.170821i
$362$	−6.84210	+	3.95029i	−0.0189008	+	0.0109124i
$363$		−	147.224i		−	0.405577i
$364$	175.029	+	178.639i	0.480850	+	0.490766i
$365$		0			0
$366$	49.4558	+	85.6600i	0.135125	+	0.234044i
$367$	269.831	+	155.787i	0.735234	+	0.424488i	0.820334	−	0.571885i	$-0.193788\pi$
$367$	269.831	+	155.787i	0.735234	+	0.424488i	−0.0850998	+	0.996372i	$0.527121\pi$
$368$	26.9117	−	46.6124i	0.0731296	−	0.126664i
$369$	91.5442	−	52.8530i	0.248087	−	0.143233i
$370$		0			0
$371$	−172.721	+	169.231i	−0.465555	+	0.456149i
$372$	51.0883			0.137334
$373$	−340.691	−	590.094i	−0.913380	−	1.58202i	−0.809255	−	0.587457i	$-0.800129\pi$
$373$	−340.691	−	590.094i	−0.913380	−	1.58202i	−0.104125	−	0.994564i	$-0.533204\pi$
$374$	−137.823	−	79.5724i	−0.368512	−	0.212760i
$375$		0			0
$376$	−81.3381	+	46.9606i	−0.216325	+	0.124895i
$377$		−	606.320i		−	1.60828i
$378$	49.8198	−	12.8057i	0.131798	−	0.0338776i
$379$	−624.779			−1.64849			−0.824246	−	0.566231i	$-0.808401\pi$
$379$	−624.779			−1.64849			−0.824246	+	0.566231i	$0.808401\pi$
$380$		0			0
$381$	251.140	+	144.996i	0.659159	+	0.380566i
$382$	131.095	−	227.064i	0.343182	−	0.594408i
$383$	−119.772	+	69.1502i	−0.312720	+	0.180549i	−0.648143	−	0.761519i	$-0.724454\pi$
$383$	−119.772	+	69.1502i	−0.312720	+	0.180549i	0.335423	+	0.942068i	$0.391121\pi$
$384$		−	19.5959i		−	0.0510310i
$385$		0			0
$386$	322.149			0.834584
$387$	−23.2279	−	40.2319i	−0.0600205	−	0.103959i
$388$	−52.9706	−	30.5826i	−0.136522	−	0.0788211i
$389$	281.787	−	488.069i	0.724388	−	1.25468i	−0.234838	−	0.972035i	$-0.575456\pi$
$389$	281.787	−	488.069i	0.724388	−	1.25468i	0.959226	−	0.282642i	$-0.0912107\pi$
$390$		0			0
$391$			252.370i			0.645446i
$392$	−118.586	−	71.7315i	−0.302515	−	0.182989i
$393$	3.08831			0.00785830
$394$	−87.0883	−	150.841i	−0.221036	−	0.382846i
$395$		0			0
$396$	18.0000	−	31.1769i	0.0454545	−	0.0787296i
$397$	392.603	−	226.669i	0.988923	−	0.570955i	0.0839711	−	0.996468i	$-0.473240\pi$
$397$	392.603	−	226.669i	0.988923	−	0.570955i	0.904952	+	0.425513i	$0.139906\pi$
$398$			8.81321i			0.0221438i
$399$	198.809	+	55.4511i	0.498267	+	0.138975i
$400$		0			0
$401$	137.875	+	238.807i	0.343828	+	0.595528i	0.985140	−	0.171752i	$-0.0549429\pi$
$401$	137.875	+	238.807i	0.343828	+	0.595528i	−0.641312	+	0.767280i	$0.721610\pi$
$402$	242.673	+	140.107i	0.603663	+	0.348525i
$403$	131.727	−	228.159i	0.326867	−	0.566151i
$404$	−221.647	+	127.968i	−0.548631	+	0.316752i
$405$		0			0
$406$	83.6468	+	325.422i	0.206026	+	0.801531i
$407$	−35.8234			−0.0880181
$408$	45.9411	+	79.5724i	0.112601	+	0.195030i
$409$	−377.441	−	217.916i	−0.922839	−	0.532801i	−0.0382993	−	0.999266i	$-0.512194\pi$
$409$	−377.441	−	217.916i	−0.922839	−	0.532801i	−0.884540	+	0.466465i	$0.845527\pi$
$410$		0			0
$411$	−151.456	+	87.4431i	−0.368506	+	0.212757i
$412$			161.913i			0.392992i
$413$	134.059	+	136.823i	0.324598	+	0.331291i
$414$	−57.0883			−0.137894
$415$		0			0
$416$	−87.5147	−	50.5266i	−0.210372	−	0.121458i
$417$	121.713	−	210.813i	0.291878	−	0.505548i
$418$	125.095	−	72.2239i	0.299271	−	0.172784i
$419$			301.257i			0.718991i	0.933147	+	0.359496i	$0.117051\pi$
$419$			301.257i			0.718991i	−0.933147	+	0.359496i	$0.882949\pi$
$420$		0			0
$421$	−203.794			−0.484071			−0.242036	−	0.970267i	$-0.577815\pi$
$421$	−203.794			−0.484071			−0.242036	+	0.970267i	$0.577815\pi$
$422$	−88.3259	−	152.985i	−0.209303	−	0.362524i
$423$	86.2721	+	49.8092i	0.203953	+	0.117752i
$424$	48.8528	−	84.6156i	0.115219	−	0.199565i
$425$		0			0
$426$		−	45.5679i		−	0.106967i
$427$	−273.765	+	70.3688i	−0.641135	+	0.164798i
$428$	−338.912			−0.791850
$429$	−92.8234	−	160.775i	−0.216372	−	0.374766i
$430$		0			0
$431$	197.860	−	342.703i	0.459072	−	0.795136i	−0.539840	−	0.841767i	$-0.681515\pi$
$431$	197.860	−	342.703i	0.459072	−	0.795136i	0.998912	+	0.0466317i	$0.0148487\pi$
$432$	−18.0000	+	10.3923i	−0.0416667	+	0.0240563i
$433$		−	44.2685i		−	0.102237i	−0.998693	−	0.0511184i	$-0.983721\pi$
$433$		−	44.2685i		−	0.102237i	0.998693	−	0.0511184i	$-0.0162786\pi$
$434$	−39.2239	+	140.629i	−0.0903777	+	0.324031i
$435$		0			0
$436$	−178.941	−	309.935i	−0.410415	−	0.710860i
$437$	−198.375	−	114.532i	−0.453947	−	0.262086i
$438$	143.335	−	248.263i	0.327248	−	0.566810i
$439$	344.558	−	198.931i	0.784871	−	0.453146i	−0.0532827	−	0.998579i	$-0.516968\pi$
$439$	344.558	−	198.931i	0.784871	−	0.453146i	0.838154	+	0.545434i	$0.183635\pi$
$440$		0			0
$441$	−3.00000	+	146.969i	−0.00680272	+	0.333264i
$442$	473.823			1.07200
$443$	−59.2721	−	102.662i	−0.133797	−	0.231743i	0.791340	−	0.611376i	$-0.209384\pi$
$443$	−59.2721	−	102.662i	−0.133797	−	0.231743i	−0.925137	+	0.379633i	$0.876050\pi$
$444$	17.9117	+	10.3413i	0.0403416	+	0.0232913i
$445$		0			0
$446$	280.014	−	161.666i	0.627835	−	0.362481i
$447$			316.812i			0.708752i
$448$	53.9411	+	15.0451i	0.120404	+	0.0335828i
$449$	713.897			1.58997			0.794985	−	0.606629i	$-0.207479\pi$
$449$	713.897			1.58997			0.794985	+	0.606629i	$0.207479\pi$
$450$		0			0
$451$	183.088	+	105.706i	0.405961	+	0.234382i
$452$	−17.3970	+	30.1324i	−0.0384889	+	0.0666647i
$453$	−433.191	+	250.103i	−0.956271	+	0.552104i
$454$			239.762i			0.528109i
$455$		0			0
$456$	−83.3970			−0.182888
$457$	−62.5883	−	108.406i	−0.136955	−	0.237213i	0.789388	−	0.613895i	$-0.210398\pi$
$457$	−62.5883	−	108.406i	−0.136955	−	0.237213i	−0.926342	+	0.376682i	$0.877065\pi$
$458$	42.4889	+	24.5310i	0.0927704	+	0.0535610i
$459$	48.7279	−	84.3992i	0.106161	−	0.183876i
$460$		0			0
$461$		−	655.767i		−	1.42249i	−0.702945	−	0.711244i	$-0.748132\pi$
$461$		−	655.767i		−	1.42249i	0.702945	−	0.711244i	$-0.251868\pi$
$462$	72.0000	+	73.4847i	0.155844	+	0.159058i
$463$	−869.396			−1.87775			−0.938873	−	0.344265i	$-0.888128\pi$
$463$	−869.396			−1.87775			−0.938873	+	0.344265i	$0.888128\pi$
$464$	−67.8823	−	117.576i	−0.146298	−	0.253395i
$465$		0			0
$466$	179.948	−	311.680i	0.386155	−	0.668840i
$467$	231.551	−	133.686i	0.495827	−	0.286266i	−0.231162	−	0.972915i	$-0.574253\pi$
$467$	231.551	−	133.686i	0.495827	−	0.286266i	0.726989	+	0.686649i	$0.240919\pi$
$468$			107.183i			0.229024i
$469$	−571.985	+	560.428i	−1.21958	+	1.19494i
$470$		0			0
$471$	162.000	+	280.592i	0.343949	+	0.595737i
$472$	−67.0294	−	38.6995i	−0.142012	−	0.0819904i
$473$	46.4558	−	80.4639i	0.0982153	−	0.170114i
$474$	187.393	−	108.192i	0.395345	−	0.228252i
$475$		0			0
$476$	−254.309	+	65.3678i	−0.534262	+	0.137327i
$477$	−103.632			−0.217259
$478$	139.404	+	241.455i	0.291640	+	0.505136i
$479$	235.331	+	135.868i	0.491296	+	0.283650i	0.725112	−	0.688631i	$-0.241788\pi$
$479$	235.331	+	135.868i	0.491296	+	0.283650i	−0.233816	+	0.972281i	$0.575121\pi$
$480$		0			0
$481$	92.3680	−	53.3287i	0.192033	−	0.110870i
$482$			125.116i			0.259576i
$483$	43.8305	−	157.145i	0.0907464	−	0.325353i
$484$	−170.000			−0.351240
$485$		0			0
$486$	19.0919	+	11.0227i	0.0392837	+	0.0226805i
$487$	−280.757	+	486.285i	−0.576503	+	0.998532i	0.419374	+	0.907814i	$0.362250\pi$
$487$	−280.757	+	486.285i	−0.576503	+	0.998532i	−0.995877	+	0.0907186i	$0.971084\pi$
$488$	98.9117	−	57.1067i	0.202688	−	0.117022i
$489$		−	27.8148i		−	0.0568810i
$490$		0			0
$491$	−406.441			−0.827781			−0.413891	−	0.910327i	$-0.635830\pi$
$491$	−406.441			−0.827781			−0.413891	+	0.910327i	$0.635830\pi$
$492$	−61.0294	−	105.706i	−0.124044	−	0.214850i
$493$	551.294	+	318.289i	1.11824	+	0.645618i
$494$	−215.033	+	372.448i	−0.435289	+	0.753944i
$495$		0			0
$496$		−	58.9917i		−	0.118935i
$497$	125.434	+	34.9856i	0.252381	+	0.0703935i
$498$	185.574			0.372638
$499$	185.713	+	321.665i	0.372171	+	0.644619i	0.989899	−	0.141773i	$-0.0452802\pi$
$499$	185.713	+	321.665i	0.372171	+	0.644619i	−0.617728	+	0.786391i	$0.711947\pi$
$500$		0			0
$501$	−152.522	+	264.176i	−0.304435	+	0.527297i
$502$	−264.426	+	152.667i	−0.526746	+	0.304117i
$503$			64.6292i			0.128488i	0.997934	+	0.0642438i	$0.0204635\pi$
$503$			64.6292i			0.128488i	−0.997934	+	0.0642438i	$0.979536\pi$
$504$	−14.7868	−	57.5270i	−0.0293389	−	0.114141i
$505$		0			0
$506$	−57.0883	−	98.8799i	−0.112823	−	0.195415i
$507$	225.177	+	130.006i	0.444135	+	0.256422i
$508$	167.426	−	289.991i	0.329580	−	0.570849i
$509$	871.889	−	503.385i	1.71294	−	0.988969i	0.782410	−	0.622764i	$-0.213990\pi$
$509$	871.889	−	503.385i	1.71294	−	0.988969i	0.930534	−	0.366205i	$-0.119343\pi$
$510$		0			0
$511$	573.338	+	585.161i	1.12199	+	1.14513i
$512$	−22.6274			−0.0441942
$513$	44.2279	+	76.6050i	0.0862143	+	0.149328i
$514$	5.27208	+	3.04384i	0.0102570	+	0.00592186i
$515$		0			0
$516$	−46.4558	+	26.8213i	−0.0900307	+	0.0519793i
$517$			199.237i			0.385371i
$518$	−42.2183	+	41.3653i	−0.0815024	+	0.0798557i
$519$	−400.368			−0.771421
$520$		0			0
$521$	−322.294	−	186.077i	−0.618607	−	0.357153i	0.157719	−	0.987484i	$-0.449586\pi$
$521$	−322.294	−	186.077i	−0.618607	−	0.357153i	−0.776327	+	0.630331i	$0.782919\pi$
$522$	−72.0000	+	124.708i	−0.137931	+	0.238904i
$523$	551.904	−	318.642i	1.05527	−	0.609258i	0.131147	−	0.991363i	$-0.458134\pi$
$523$	551.904	−	318.642i	1.05527	−	0.609258i	0.924119	+	0.382105i	$0.124801\pi$
$524$		−	3.56608i		−	0.00680549i
$525$		0			0
$526$	399.765			0.760009
$527$	138.302	+	239.545i	0.262432	+	0.454545i
$528$	−36.0000	−	20.7846i	−0.0681818	−	0.0393648i
$529$	173.970	−	301.325i	0.328866	−	0.569613i
$530$		0			0
$531$			82.0940i			0.154603i
$532$	64.0294	−	229.564i	0.120356	−	0.431512i
$533$	−629.440			−1.18094
$534$	25.4558	+	44.0908i	0.0476701	+	0.0825671i
$535$		0			0
$536$	161.782	−	280.214i	0.301832	−	0.522788i
$537$	−127.919	+	73.8540i	−0.238210	+	0.137531i
$538$		−	540.136i		−	1.00397i
$539$	−257.558	+	141.773i	−0.477845	+	0.263030i
$540$		0			0
$541$	−110.412	−	191.239i	−0.204088	−	0.353491i	0.745754	−	0.666222i	$-0.232090\pi$
$541$	−110.412	−	191.239i	−0.204088	−	0.353491i	−0.949842	+	0.312731i	$0.898756\pi$
$542$	−103.279	−	59.6283i	−0.190552	−	0.110015i
$543$	4.83810	−	8.37983i	0.00890994	−	0.0154325i
$544$	91.8823	−	53.0482i	0.168901	−	0.0975152i
$545$		0			0
$546$	−295.040	−	82.2917i	−0.540367	−	0.150717i
$547$	160.676			0.293741			0.146870	−	0.989156i	$-0.453080\pi$
$547$	160.676			0.293741			0.146870	+	0.989156i	$0.453080\pi$
$548$	100.971	+	174.886i	0.184253	+	0.319135i
$549$	−104.912	−	60.5708i	−0.191096	−	0.110329i
$550$		0			0
$551$	−500.382	+	288.896i	−0.908134	+	0.524311i
$552$			65.9199i			0.119420i
$553$	153.942	+	598.898i	0.278375	+	1.08300i
$554$	−193.914			−0.350025
$555$		0			0
$556$	−243.426	−	140.542i	−0.437817	−	0.252774i
$557$	−237.177	+	410.802i	−0.425811	+	0.737526i	−0.996496	−	0.0836431i	$-0.973344\pi$
$557$	−237.177	+	410.802i	−0.425811	+	0.737526i	0.570685	+	0.821169i	$0.306678\pi$
$558$	−54.1873	+	31.2851i	−0.0971099	+	0.0560664i
$559$			276.627i			0.494860i
$560$		0			0
$561$	194.912			0.347436
$562$	−229.882	−	398.168i	−0.409043	−	0.708484i
$563$	430.301	+	248.434i	0.764300	+	0.441269i	0.830837	−	0.556515i	$-0.187862\pi$
$563$	430.301	+	248.434i	0.764300	+	0.441269i	−0.0665378	+	0.997784i	$0.521195\pi$
$564$	57.5147	−	99.6184i	0.101976	−	0.176628i
$565$		0			0
$566$		−	275.171i		−	0.486168i
$567$	−45.0000	+	44.0908i	−0.0793651	+	0.0777616i
$568$	−52.6173			−0.0926361
$569$	−392.647	−	680.084i	−0.690065	−	1.19523i	−0.971816	−	0.235740i	$-0.924249\pi$
$569$	−392.647	−	680.084i	−0.690065	−	1.19523i	0.281752	−	0.959487i	$-0.409085\pi$
$570$		0			0
$571$	357.521	−	619.245i	0.626132	−	1.08449i	−0.362189	−	0.932105i	$-0.617970\pi$
$571$	357.521	−	619.245i	0.626132	−	1.08449i	0.988321	−	0.152388i	$-0.0486963\pi$
$572$	−185.647	+	107.183i	−0.324557	+	0.187383i
$573$			321.117i			0.560414i
$574$	337.831	−	86.8364i	0.588555	−	0.151283i
$575$		0			0
$576$	12.0000	+	20.7846i	0.0208333	+	0.0360844i
$577$	−669.117	−	386.315i	−1.15965	−	0.669524i	−0.208429	−	0.978038i	$-0.566835\pi$
$577$	−669.117	−	386.315i	−1.15965	−	0.669524i	−0.951220	+	0.308514i	$0.900168\pi$
$578$	−44.3812	+	76.8705i	−0.0767841	+	0.132994i
$579$	−341.691	+	197.275i	−0.590140	+	0.340717i
$580$		0			0
$581$	−142.477	+	510.823i	−0.245228	+	0.879214i
$582$	74.9117			0.128714
$583$	−103.632	−	179.497i	−0.177757	−	0.307885i
$584$	−286.669	−	165.508i	−0.490872	−	0.283405i
$585$		0			0
$586$	293.574	−	169.495i	0.500979	−	0.289240i
$587$		−	436.477i		−	0.743572i	−0.928318	−	0.371786i	$-0.878746\pi$
$587$		−	436.477i		−	0.743572i	0.928318	−	0.371786i	$-0.121254\pi$
$588$	169.706	+	3.46410i	0.288615	+	0.00589133i
$589$	−251.059			−0.426246
$590$		0			0
$591$	184.742	+	106.661i	0.312593	+	0.180475i
$592$	11.9411	−	20.6826i	0.0201708	−	0.0349369i
$593$	−722.397	+	417.076i	−1.21821	+	0.703332i	−0.964534	−	0.263958i	$-0.914972\pi$
$593$	−722.397	+	417.076i	−1.21821	+	0.703332i	−0.253673	+	0.967290i	$0.581639\pi$
$594$			44.0908i			0.0742270i
$595$		0			0
$596$	365.823			0.613798
$597$	−5.39697	−	9.34783i	−0.00904015	−	0.0156580i
$598$	294.396	+	169.970i	0.492301	+	0.284230i
$599$	−436.794	+	756.549i	−0.729205	+	1.26302i	0.228014	+	0.973658i	$0.426777\pi$
$599$	−436.794	+	756.549i	−0.729205	+	1.26302i	−0.957220	+	0.289363i	$0.906557\pi$
$600$		0			0
$601$		−	198.982i		−	0.331085i	−0.986203	−	0.165542i	$-0.947063\pi$
$601$		−	198.982i		−	0.331085i	0.986203	−	0.165542i	$-0.0529375\pi$
$602$	−38.1630	−	148.470i	−0.0633936	−	0.246628i
$603$	−343.191			−0.569139
$604$	288.794	+	500.206i	0.478136	+	0.828155i
$605$		0			0
$606$	156.728	−	271.461i	0.258627	−	0.447955i
$607$	−137.654	+	79.4748i	−0.226778	+	0.130930i	−0.609085	−	0.793105i	$-0.708463\pi$
$607$	−137.654	+	79.4748i	−0.226778	+	0.130930i	0.382307	+	0.924035i	$0.375130\pi$
$608$			96.2985i			0.158386i
$609$	−288.000	−	293.939i	−0.472906	−	0.482658i
$610$		0			0
$611$	−296.595	−	513.718i	−0.485426	−	0.840782i
$612$	−97.4558	−	56.2662i	−0.159242	−	0.0919382i
$613$	−357.368	+	618.979i	−0.582981	+	1.00975i	0.412143	+	0.911119i	$0.364781\pi$
$613$	−357.368	+	618.979i	−0.582981	+	1.00975i	−0.995124	+	0.0986338i	$0.968553\pi$
$614$	−661.695	+	382.030i	−1.07768	+	0.622198i
$615$		0			0
$616$	84.8528	−	83.1384i	0.137748	−	0.134965i
$617$	639.381			1.03627			0.518137	−	0.855298i	$-0.326626\pi$
$617$	639.381			1.03627			0.518137	+	0.855298i	$0.326626\pi$
$618$	−99.1508	−	171.734i	−0.160438	−	0.277887i
$619$	148.978	+	86.0126i	0.240676	+	0.138954i	0.615487	−	0.788147i	$-0.288959\pi$
$619$	148.978	+	86.0126i	0.240676	+	0.138954i	−0.374812	+	0.927101i	$0.622293\pi$
$620$		0			0
$621$	60.5513	−	34.9593i	0.0975061	−	0.0562952i
$622$			571.619i			0.919002i
$623$	−140.912	+	36.2201i	−0.226182	+	0.0581382i
$624$	123.765			0.198341
$625$		0			0
$626$	160.805	+	92.8406i	0.256876	+	0.148308i
$627$	−88.4558	+	153.210i	−0.141078	+	0.244354i
$628$	324.000	−	187.061i	0.515924	−	0.297869i
$629$			111.980i			0.178029i
$630$		0			0
$631$	−1141.06			−1.80833			−0.904166	−	0.427180i	$-0.859507\pi$
$631$	−1141.06			−1.80833			−0.904166	+	0.427180i	$0.859507\pi$
$632$	−124.929	−	216.383i	−0.197672	−	0.342379i
$633$	187.368	+	108.177i	0.295999	+	0.170895i
$634$	66.4264	−	115.054i	0.104774	−	0.181473i
$635$		0			0
$636$			119.664i			0.188152i
$637$	453.044	−	748.968i	0.711215	−	1.17577i
$638$	−288.000			−0.451411
$639$	27.9045	+	48.3321i	0.0436691	+	0.0756371i
$640$		0			0
$641$	−114.551	+	198.409i	−0.178707	+	0.309530i	−0.941438	−	0.337186i	$-0.890525\pi$
$641$	−114.551	+	198.409i	−0.178707	+	0.309530i	0.762731	+	0.646716i	$0.223858\pi$
$642$	359.470	−	207.540i	0.559922	−	0.323271i
$643$			707.670i			1.10058i	0.834975	+	0.550288i	$0.185482\pi$
$643$			707.670i			1.10058i	−0.834975	+	0.550288i	$0.814518\pi$
$644$	−181.456	−	50.6111i	−0.281764	−	0.0785887i
$645$		0			0
$646$	−225.765	−	391.036i	−0.349481	−	0.605318i
$647$	−1021.37	−	589.687i	−1.57862	−	0.911417i	−0.995052	−	0.0993530i	$-0.968323\pi$
$647$	−1021.37	−	589.687i	−1.57862	−	0.911417i	−0.583568	−	0.812064i	$-0.698344\pi$
$648$	12.7279	−	22.0454i	0.0196419	−	0.0340207i
$649$	−142.191	+	82.0940i	−0.219092	+	0.126493i
$650$		0			0
$651$	−44.5143	−	173.180i	−0.0683783	−	0.266021i
$652$	−32.1177			−0.0492604
$653$	−77.3818	−	134.029i	−0.118502	−	0.205252i	0.800672	−	0.599103i	$-0.204476\pi$
$653$	−77.3818	−	134.029i	−0.118502	−	0.205252i	−0.919174	+	0.393851i	$0.871143\pi$
$654$	379.591	+	219.157i	0.580415	+	0.335103i
$655$		0			0
$656$	−122.059	+	70.4707i	−0.186065	+	0.107425i
$657$			351.096i			0.534393i
$658$	230.059	+	234.803i	0.349634	+	0.356843i
$659$	591.308			0.897280			0.448640	−	0.893712i	$-0.351908\pi$
$659$	591.308			0.897280			0.448640	+	0.893712i	$0.351908\pi$
$660$		0			0
$661$	140.441	+	81.0837i	0.212468	+	0.122668i	0.602458	−	0.798151i	$-0.294188\pi$
$661$	140.441	+	81.0837i	0.212468	+	0.122668i	−0.389990	+	0.920819i	$0.627522\pi$
$662$	−184.815	+	320.109i	−0.279176	+	0.483548i
$663$	−502.566	+	290.156i	−0.758017	+	0.437642i
$664$		−	214.282i		−	0.322714i
$665$		0			0
$666$	−25.3310			−0.0380345
$667$	228.353	+	395.519i	0.342359	+	0.592983i
$668$	305.044	+	176.117i	0.456652	+	0.263648i
$669$	−198.000	+	342.946i	−0.295964	+	0.512625i
$670$		0			0
$671$		−	242.283i		−	0.361078i
$672$	−66.4264	+	17.0743i	−0.0988488	+	0.0254082i
$673$	−42.3238			−0.0628883			−0.0314441	−	0.999506i	$-0.510011\pi$
$673$	−42.3238			−0.0628883			−0.0314441	+	0.999506i	$0.510011\pi$
$674$	−96.3539	−	166.890i	−0.142958	−	0.247611i
$675$		0			0
$676$	150.118	−	260.012i	0.222068	−	0.384632i
$677$	−430.721	+	248.677i	−0.636220	+	0.367322i	−0.783157	−	0.621824i	$-0.786392\pi$
$677$	−430.721	+	248.677i	−0.636220	+	0.367322i	0.146937	+	0.989146i	$0.453059\pi$
$678$		−	42.6137i		−	0.0628521i
$679$	−57.5147	+	206.207i	−0.0847050	+	0.303693i
$680$		0			0
$681$	−146.823	−	254.306i	−0.215600	−	0.373430i
$682$	−108.375	−	62.5701i	−0.158907	−	0.0917451i
$683$	608.080	−	1053.23i	0.890308	−	1.54206i	0.0508015	−	0.998709i	$-0.483822\pi$
$683$	608.080	−	1053.23i	0.890308	−	1.54206i	0.839506	−	0.543350i	$-0.182844\pi$
$684$	88.4558	−	51.0700i	0.129321	−	0.0746638i
$685$		0			0
$686$	−139.830	+	464.484i	−0.203834	+	0.677091i
$687$	−60.0883			−0.0874648
$688$	30.9706	+	53.6426i	0.0450154	+	0.0779689i
$689$	534.418	+	308.546i	0.775642	+	0.447817i
$690$		0			0
$691$	−932.182	+	538.196i	−1.34903	+	0.778865i	−0.988113	−	0.153731i	$-0.950871\pi$
$691$	−932.182	+	538.196i	−1.34903	+	0.778865i	−0.360921	+	0.932596i	$0.617538\pi$
$692$			462.305i			0.668070i
$693$	−121.368	−	33.8515i	−0.175134	−	0.0488477i
$694$	−455.647			−0.656552
$695$		0			0
$696$	144.000	+	83.1384i	0.206897	+	0.119452i
$697$	330.426	−	572.315i	0.474069	−	0.821112i
$698$	424.368	−	245.009i	0.607976	−	0.351015i
$699$			440.781i			0.630589i
$700$		0			0
$701$	−695.897			−0.992720			−0.496360	−	0.868117i	$-0.665330\pi$
$701$	−695.897			−0.992720			−0.496360	+	0.868117i	$0.665330\pi$
$702$	−65.6360	−	113.685i	−0.0934986	−	0.161944i
$703$	−88.0219	−	50.8194i	−0.125209	−	0.0722894i
$704$	−24.0000	+	41.5692i	−0.0340909	+	0.0590472i
$705$		0			0
$706$			877.649i			1.24313i
$707$	626.912	+	639.839i	0.886721	+	0.905006i
$708$	94.7939			0.133890
$709$	−127.412	−	220.684i	−0.179707	−	0.311261i	0.762073	−	0.647491i	$-0.224182\pi$
$709$	−127.412	−	220.684i	−0.179707	−	0.311261i	−0.941780	+	0.336229i	$0.890848\pi$
$710$		0			0
$711$	−132.507	+	229.509i	−0.186367	+	0.322798i
$712$	50.9117	−	29.3939i	0.0715052	−	0.0412835i
$713$			198.446i			0.278325i
$714$	229.706	−	225.065i	0.321717	−	0.315217i
$715$		0			0
$716$	85.2792	+	147.708i	0.119105	+	0.206296i
$717$	−295.721	−	170.734i	−0.412442	−	0.238123i
$718$	14.3087	−	24.7833i	0.0199285	−	0.0345172i
$719$	−964.925	+	557.100i	−1.34204	+	0.774826i	−0.987106	−	0.160066i	$-0.948829\pi$
$719$	−964.925	+	557.100i	−1.34204	+	0.774826i	−0.354931	+	0.934892i	$0.615496\pi$
$720$		0			0
$721$	548.852	−	141.078i	0.761238	−	0.195669i
$722$	−100.701			−0.139474
$723$	−76.6173	−	132.705i	−0.105971	−	0.183548i
$724$	−9.67619	−	5.58655i	−0.0133649	−	0.00771623i
$725$		0			0
$726$	180.312	−	104.103i	0.248364	−	0.143393i
$727$		−	398.345i		−	0.547930i	−0.961740	−	0.273965i	$-0.911665\pi$
$727$		−	398.345i		−	0.547930i	0.961740	−	0.273965i	$-0.0883353\pi$
$728$	−95.0223	+	340.683i	−0.130525	+	0.467971i
$729$	−27.0000			−0.0370370
$730$		0			0
$731$	−251.522	−	145.216i	−0.344079	−	0.198654i
$732$	−69.9411	+	121.142i	−0.0955480	+	0.165494i
$733$	−818.514	+	472.569i	−1.11666	+	0.644706i	−0.940547	−	0.339663i	$-0.889687\pi$
$733$	−818.514	+	472.569i	−1.11666	+	0.644706i	−0.176116	+	0.984369i	$0.556354\pi$
$734$			440.632i			0.600316i
$735$		0			0
$736$	76.1177			0.103421
$737$	−343.191	−	594.424i	−0.465659	−	0.806546i
$738$	129.463	+	74.7455i	0.175424	+	0.101281i
$739$	−96.3162	+	166.825i	−0.130333	+	0.225744i	−0.923805	−	0.382863i	$-0.874938\pi$
$739$	−96.3162	+	166.825i	−0.130333	+	0.225744i	0.793472	+	0.608607i	$0.208271\pi$
$740$		0			0
$741$		−	526.721i		−	0.710825i
$742$	−329.397	−	91.8744i	−0.443931	−	0.123820i
$743$	911.616			1.22694			0.613470	−	0.789718i	$-0.289773\pi$
$743$	911.616			1.22694			0.613470	+	0.789718i	$0.289773\pi$
$744$	36.1249	+	62.5701i	0.0485550	+	0.0840997i
$745$		0			0
$746$	481.810	−	834.519i	0.645858	−	1.11866i
$747$	−196.831	+	113.640i	−0.263495	+	0.152129i
$748$		−	225.065i		−	0.300889i
$749$	295.301	+	1148.85i	0.394260	+	1.53384i
$750$		0			0
$751$	195.831	+	339.189i	0.260760	+	0.451650i	0.966444	−	0.256877i	$-0.0826935\pi$
$751$	195.831	+	339.189i	0.260760	+	0.451650i	−0.705684	+	0.708527i	$0.749360\pi$
$752$	−115.029	−	66.4123i	−0.152965	−	0.0883142i
$753$	186.978	−	323.855i	0.248310	−	0.430086i
$754$	742.587	−	428.733i	0.984863	−	0.568611i
$755$		0			0
$756$	50.9117	+	51.9615i	0.0673435	+	0.0687322i
$757$	152.823			0.201879			0.100940	−	0.994893i	$-0.467815\pi$
$757$	152.823			0.201879			0.100940	+	0.994893i	$0.467815\pi$
$758$	−441.785	−	765.195i	−0.582830	−	1.00949i
$759$	121.103	+	69.9186i	0.159555	+	0.0921194i
$760$		0			0
$761$	−109.331	+	63.1223i	−0.143667	+	0.0829465i	−0.570111	−	0.821568i	$-0.693100\pi$
$761$	−109.331	+	63.1223i	−0.143667	+	0.0829465i	0.426443	+	0.904514i	$0.359766\pi$
$762$			410.109i			0.538201i
$763$	−894.706	+	876.629i	−1.17262	+	1.14892i
$764$	370.794			0.485332
$765$		0			0
$766$	−169.383	−	97.7931i	−0.221126	−	0.127667i
$767$	244.419	−	423.347i	0.318669	−	0.551951i
$768$	24.0000	−	13.8564i	0.0312500	−	0.0180422i
$769$			369.148i			0.480037i	0.970768	+	0.240018i	$0.0771535\pi$
$769$			369.148i			0.480037i	−0.970768	+	0.240018i	$0.922847\pi$
$770$		0			0
$771$	−7.45584			−0.00967036
$772$	227.794	+	394.551i	0.295070	+	0.511076i
$773$	1215.65	+	701.853i	1.57263	+	0.907961i	0.995845	+	0.0910674i	$0.0290279\pi$
$773$	1215.65	+	701.853i	1.57263	+	0.907961i	0.576789	+	0.816893i	$0.304305\pi$
$774$	32.8492	−	56.8966i	0.0424409	−	0.0735098i
$775$		0			0
$776$		−	86.5006i		−	0.111470i
$777$	19.4483	−	69.7278i	0.0250299	−	0.0897398i
$778$	797.013			1.02444
$779$	299.912	+	519.462i	0.384996	+	0.666832i
$780$		0			0
$781$	−55.8091	+	96.6642i	−0.0714585	+	0.123770i
$782$	−309.088	+	178.452i	−0.395254	+	0.228200i
$783$		−	176.363i		−	0.225240i
$784$	4.00000	−	195.959i	0.00510204	−	0.249948i
$785$		0			0
$786$	2.18377	+	3.78239i	0.00277833	+	0.00481221i
$787$	−196.161	−	113.253i	−0.249251	−	0.143905i	0.370170	−	0.928964i	$-0.379299\pi$
$787$	−196.161	−	113.253i	−0.249251	−	0.143905i	−0.619421	+	0.785059i	$0.712633\pi$
$788$	123.161	−	213.322i	0.156296	−	0.270713i
$789$	−424.014	+	244.805i	−0.537407	+	0.310272i
$790$		0			0
$791$	117.302	+	32.7174i	0.148295	+	0.0413621i
$792$	50.9117			0.0642824
$793$	360.676	+	624.709i	0.454825	+	0.787780i
$794$	555.224	+	320.559i	0.699274	+	0.403726i
$795$		0			0
$796$	−10.7939	+	6.23188i	−0.0135602	+	0.00782900i
$797$		−	688.414i		−	0.863756i	−0.901932	−	0.431878i	$-0.857851\pi$
$797$		−	688.414i		−	0.863756i	0.901932	−	0.431878i	$-0.142149\pi$
$798$	72.6655	+	282.700i	0.0910595	+	0.354260i
$799$	622.794			0.779467
$800$		0			0
$801$	−54.0000	−	31.1769i	−0.0674157	−	0.0389225i
$802$	−194.985	+	337.724i	−0.243123	+	0.421102i
$803$	−608.117	+	351.096i	−0.757306	+	0.437231i
$804$			396.283i			0.492889i
$805$		0			0
$806$	372.582			0.462260
$807$	330.765	+	572.901i	0.409869	+	0.709914i
$808$	−313.456	−	180.974i	−0.387940	−	0.223977i
$809$	−12.6396	+	21.8924i	−0.0156237	+	0.0270611i	−0.873732	−	0.486408i	$-0.838307\pi$
$809$	−12.6396	+	21.8924i	−0.0156237	+	0.0270611i	0.858108	+	0.513470i	$0.171640\pi$
$810$		0			0
$811$		−	1527.62i		−	1.88362i	−0.336145	−	0.941810i	$-0.609123\pi$
$811$		−	1527.62i		−	1.88362i	0.336145	−	0.941810i	$-0.390877\pi$
$812$	−339.411	+	332.554i	−0.417994	+	0.409549i
$813$	146.059			0.179654
$814$	−25.3310	−	43.8745i	−0.0311191	−	0.0538999i
$815$		0			0
$816$	−64.9706	+	112.532i	−0.0796208	+	0.137907i
$817$	228.294	−	131.806i	0.279430	−	0.161329i
$818$		−	616.359i		−	0.753495i
$819$	363.331	−	93.3909i	0.443627	−	0.114030i
$820$		0			0
$821$	58.3310	+	101.032i	0.0710487	+	0.123060i	0.899361	−	0.437206i	$-0.144032\pi$
$821$	58.3310	+	101.032i	0.0710487	+	0.123060i	−0.828312	+	0.560266i	$0.810699\pi$
$822$	−214.191	−	123.663i	−0.260573	−	0.150442i
$823$	62.9554	−	109.042i	0.0764950	−	0.132493i	−0.825240	−	0.564782i	$-0.808960\pi$
$823$	62.9554	−	109.042i	0.0764950	−	0.132493i	0.901735	+	0.432288i	$0.142294\pi$
$824$	−198.302	+	114.489i	−0.240657	+	0.138943i
$825$		0			0
$826$	−72.7797	+	260.937i	−0.0881110	+	0.315904i
$827$	1434.40			1.73446			0.867229	−	0.497910i	$-0.165899\pi$
$827$	1434.40			1.73446			0.867229	+	0.497910i	$0.165899\pi$
$828$	−40.3675	−	69.9186i	−0.0487531	−	0.0844428i
$829$	−32.3225	−	18.6614i	−0.0389898	−	0.0225107i	0.480378	−	0.877061i	$-0.340499\pi$
$829$	−32.3225	−	18.6614i	−0.0389898	−	0.0225107i	−0.519368	+	0.854551i	$0.673833\pi$
$830$		0			0
$831$	205.677	−	118.747i	0.247505	−	0.142897i
$832$		−	142.911i		−	0.171768i
$833$	443.169	+	805.101i	0.532015	+	0.966508i
$834$	344.257			0.412778
$835$		0			0
$836$	176.912	+	102.140i	0.211617	+	0.122177i
$837$	38.3162	−	66.3657i	0.0457781	−	0.0792899i
$838$	−368.963	+	213.021i	−0.440290	+	0.254202i
$839$		−	3.07370i		−	0.00366353i	−0.999998	−	0.00183177i	$-0.999417\pi$
$839$		−	3.07370i		−	0.00366353i	0.999998	−	0.00183177i	$-0.000583069\pi$
$840$		0			0
$841$	311.000			0.369798
$842$	−144.104	−	249.596i	−0.171145	−	0.296432i
$843$	487.654	+	281.547i	0.578474	+	0.333982i
$844$	124.912	−	216.353i	0.148000	−	0.256343i
$845$		0			0
$846$			140.882i			0.166527i
$847$	148.124	+	576.267i	0.174881	+	0.680363i
$848$	138.177			0.162944
$849$	168.507	+	291.863i	0.198477	+	0.343773i
$850$		0			0
$851$	−40.1695	+	69.5756i	−0.0472027	+	0.0817574i
$852$	55.8091	−	32.2214i	0.0655036	−	0.0378185i
$853$		−	155.257i		−	0.182013i	−0.995850	−	0.0910063i	$-0.970992\pi$
$853$		−	155.257i		−	0.182013i	0.995850	−	0.0910063i	$-0.0290083\pi$
$854$	−279.765	−	285.533i	−0.327593	−	0.334348i
$855$		0			0
$856$	−239.647	−	415.080i	−0.279961	−	0.484907i
$857$	1388.98	+	801.931i	1.62075	+	0.935742i	0.986719	+	0.162436i	$0.0519352\pi$
$857$	1388.98	+	801.931i	1.62075	+	0.935742i	0.634033	+	0.773306i	$0.281398\pi$
$858$	131.272	−	227.370i	0.152998	−	0.265000i
$859$	545.367	−	314.868i	0.634886	−	0.366551i	−0.147756	−	0.989024i	$-0.547205\pi$
$859$	545.367	−	314.868i	0.634886	−	0.366551i	0.782642	+	0.622472i	$0.213872\pi$
$860$		0			0
$861$	−305.147	+	298.982i	−0.354410	+	0.347250i
$862$	559.632			0.649226
$863$	514.706	+	891.496i	0.596414	+	1.03302i	0.993346	+	0.115172i	$0.0367418\pi$
$863$	514.706	+	891.496i	0.596414	+	1.03302i	−0.396931	+	0.917848i	$0.629925\pi$
$864$	−25.4558	−	14.6969i	−0.0294628	−	0.0170103i
$865$		0			0
$866$	54.2176	−	31.3026i	0.0626070	−	0.0361462i
$867$		−	108.711i		−	0.125388i
$868$	−199.971	+	51.4007i	−0.230381	+	0.0592174i
$869$	−530.029			−0.609929
$870$		0			0
$871$	1769.79	+	1021.79i	2.03190	+	1.17312i
$872$	253.061	−	438.314i	0.290208	−	0.502654i
$873$	−79.4558	+	45.8739i	−0.0910147	+	0.0525474i
$874$		−	323.944i		−	0.370646i
$875$		0			0
$876$	405.411			0.462798
$877$	324.220	+	561.566i	0.369693	+	0.640326i	0.989517	−	0.144414i	$-0.0461297\pi$
$877$	324.220	+	561.566i	0.369693	+	0.640326i	−0.619825	+	0.784740i	$0.712796\pi$
$878$	487.279	+	281.331i	0.554988	+	0.320422i
$879$	−207.588	+	359.553i	−0.236164	+	0.409048i
$880$		0			0
$881$			363.857i			0.413005i	0.978446	+	0.206502i	$0.0662082\pi$
$881$			363.857i			0.413005i	−0.978446	+	0.206502i	$0.933792\pi$
$882$	−182.121	+	100.249i	−0.206487	+	0.113661i
$883$	−1536.16			−1.73971			−0.869853	−	0.493312i	$-0.835786\pi$
$883$	−1536.16			−1.73971			−0.869853	+	0.493312i	$0.835786\pi$
$884$	335.044	+	580.313i	0.379009	+	0.656462i
$885$		0			0
$886$	83.8234	−	145.186i	0.0946088	−	0.163867i
$887$	−974.720	+	562.755i	−1.09890	+	0.634447i	−0.935931	−	0.352185i	$-0.885439\pi$
$887$	−974.720	+	562.755i	−1.09890	+	0.634447i	−0.162964	+	0.986632i	$0.552106\pi$
$888$			29.2497i			0.0329388i
$889$	−1128.90	−	314.868i	−1.26985	−	0.354183i
$890$		0			0
$891$	−27.0000	−	46.7654i	−0.0303030	−	0.0524864i
$892$	396.000	+	228.631i	0.443946	+	0.256312i
$893$	−282.640	+	489.546i	−0.316506	+	0.548204i
$894$	−388.014	+	224.020i	−0.434020	+	0.250582i
$895$		0			0
$896$	19.7157	+	76.7026i	0.0220042	+	0.0856056i
$897$	−416.339			−0.464146
$898$	504.801	+	874.341i	0.562139	+	0.973654i
$899$	433.499	+	250.281i	0.482201	+	0.278399i
$900$		0			0
$901$	−561.088	+	323.944i	−0.622740	+	0.359539i
$902$			298.982i			0.331466i
$903$	131.397	+	134.106i	0.145512	+	0.148512i
$904$	−49.2061			−0.0544315
$905$		0			0
$906$	−612.624	−	353.699i	−0.676186	−	0.390396i
$907$	117.448	−	203.426i	0.129491	−	0.224285i	−0.793989	−	0.607933i	$-0.791999\pi$
$907$	117.448	−	203.426i	0.129491	−	0.224285i	0.923479	+	0.383648i	$0.125332\pi$
$908$	−293.647	+	169.537i	−0.323400	+	0.186715i
$909$			383.903i			0.422336i
$910$		0			0
$911$	224.278			0.246189			0.123095	−	0.992395i	$-0.460718\pi$
$911$	224.278			0.246189			0.123095	+	0.992395i	$0.460718\pi$
$912$	−58.9706	−	102.140i	−0.0646607	−	0.111996i
$913$	−393.661	−	227.280i	−0.431173	−	0.248938i
$914$	88.5132	−	153.309i	0.0968416	−	0.167735i
$915$		0			0
$916$			69.3840i			0.0757467i
$917$	−12.0883	+	3.10719i	−0.0131825	+	0.00338843i
$918$	137.823			0.150134
$919$	466.081	+	807.276i	0.507161	+	0.878428i	0.999966	+	0.00828836i	$0.00263830\pi$
$919$	466.081	+	807.276i	0.507161	+	0.878428i	−0.492805	+	0.870140i	$0.664028\pi$
$920$		0			0
$921$	467.889	−	810.407i	0.508023	−	0.879921i
$922$	803.147	−	463.697i	0.871092	−	0.502925i
$923$		−	332.322i		−	0.360046i
$924$	−39.0883	+	140.143i	−0.0423034	+	0.151670i
$925$		0			0
$926$	−614.756	−	1064.79i	−0.663883	−	1.14988i
$927$	210.331	+	121.434i	0.226894	+	0.130997i
$928$	96.0000	−	166.277i	0.103448	−	0.179178i
$929$	−618.390	+	357.028i	−0.665651	+	0.384314i	−0.794427	−	0.607360i	$-0.792229\pi$
$929$	−618.390	+	357.028i	−0.665651	+	0.384314i	0.128776	+	0.991674i	$0.458895\pi$
$930$		0			0
$931$	−833.970	−	17.0233i	−0.895778	−	0.0182850i
$932$	508.971			0.546106
$933$	−350.044	−	606.294i	−0.375181	−	0.649832i
$934$	327.463	+	189.061i	0.350603	+	0.202421i
$935$		0			0
$936$	−131.272	+	75.7900i	−0.140248	+	0.0809722i
$937$		−	1723.25i		−	1.83912i	−0.392952	−	0.919559i	$-0.628546\pi$
$937$		−	1723.25i		−	1.83912i	0.392952	−	0.919559i	$-0.371454\pi$
$938$	−1090.84	−	304.253i	−1.16294	−	0.324363i
$939$	−227.412			−0.242185
$940$		0			0
$941$	835.508	+	482.381i	0.887893	+	0.512625i	0.873253	−	0.487267i	$-0.162006\pi$
$941$	835.508	+	482.381i	0.887893	+	0.512625i	0.0146405	+	0.999893i	$0.495340\pi$
$942$	−229.103	+	396.817i	−0.243209	+	0.421250i
$943$	410.601	−	237.061i	0.435420	−	0.251390i
$944$		−	109.459i		−	0.115952i
$945$		0			0
$946$	131.397			0.138897
$947$	725.881	+	1257.26i	0.766506	+	1.32763i	0.939447	+	0.342695i	$0.111340\pi$
$947$	725.881	+	1257.26i	0.766506	+	1.32763i	−0.172940	+	0.984932i	$0.555327\pi$
$948$	265.014	+	153.006i	0.279551	+	0.161399i
$949$	1045.32	−	1810.55i	1.10150	−	1.90785i
$950$		0			0
$951$			162.711i			0.171094i
$952$	−259.882	−	265.241i	−0.272986	−	0.278615i
$953$	−1147.43			−1.20401			−0.602007	−	0.798491i	$-0.705632\pi$
$953$	−1147.43			−1.20401			−0.602007	+	0.798491i	$0.705632\pi$
$954$	−73.2792	−	126.923i	−0.0768126	−	0.133043i
$955$		0			0
$956$	−197.147	+	341.469i	−0.206221	+	0.357185i
$957$	305.470	−	176.363i	0.319196	−	0.184288i
$958$			384.294i			0.401142i
$959$	504.853	−	494.653i	0.526437	−	0.515801i
$960$		0			0
$961$	−371.749	−	643.889i	−0.386836	−	0.670020i
$962$	130.628	+	75.4181i	0.135788	+	0.0783972i
$963$	−254.184	+	440.259i	−0.263950	+	0.457175i
$964$	−153.235	+	88.4701i	−0.158957	+	0.0917739i
$965$		0			0
$966$	223.456	−	57.4374i	0.231321	−	0.0594590i
$967$	−412.190			−0.426257			−0.213128	−	0.977024i	$-0.568365\pi$
$967$	−412.190			−0.426257			−0.213128	+	0.977024i	$0.568365\pi$
$968$	−120.208	−	208.207i	−0.124182	−	0.215089i
$969$	478.919	+	276.504i	0.494240	+	0.285350i
$970$		0			0
$971$	869.595	−	502.061i	0.895566	−	0.517056i	0.0198073	−	0.999804i	$-0.493695\pi$
$971$	869.595	−	502.061i	0.895566	−	0.517056i	0.875759	+	0.482748i	$0.160361\pi$
$972$			31.1769i			0.0320750i
$973$	−264.309	+	947.626i	−0.271643	+	0.973922i
$974$	−794.101			−0.815298
$975$		0			0
$976$	139.882	+	80.7611i	0.143322	+	0.0827470i
$977$	−794.117	+	1375.45i	−0.812812	+	1.40783i	0.0980772	+	0.995179i	$0.468731\pi$
$977$	−794.117	+	1375.45i	−0.812812	+	1.40783i	−0.910889	+	0.412652i	$0.864603\pi$
$978$	34.0660	−	19.6680i	0.0348323	−	0.0201105i
$979$		−	124.708i		−	0.127383i
$980$		0			0
$981$	−536.823			−0.547221
$982$	−287.397	−	497.786i	−0.292665	−	0.506911i
$983$	−721.861	−	416.767i	−0.734345	−	0.423974i	0.0856648	−	0.996324i	$-0.472699\pi$
$983$	−721.861	−	416.767i	−0.734345	−	0.423974i	−0.820009	+	0.572350i	$0.806032\pi$
$984$	86.3087	−	149.491i	0.0877121	−	0.151922i
$985$		0			0
$986$			900.259i			0.913041i
$987$	−387.801	−	108.164i	−0.392909	−	0.109589i
$988$	−608.205			−0.615592
$989$	−104.184	−	180.452i	−0.105343	−	0.182459i
$990$		0			0
$991$	−33.4483	+	57.9341i	−0.0337520	+	0.0584602i	−0.882408	−	0.470485i	$-0.844079\pi$
$991$	−33.4483	+	57.9341i	−0.0337520	+	0.0584602i	0.848656	+	0.528945i	$0.177412\pi$
$992$	72.2498	−	41.7134i	0.0728324	−	0.0420498i
$993$		−	452.702i		−	0.455893i
$994$	45.8465	+	178.363i	0.0461233	+	0.179439i
$995$		0			0
$996$	131.220	+	227.280i	0.131747	+	0.228193i
$997$	−1268.65	−	732.453i	−1.27246	−	0.734657i	−0.297012	−	0.954874i	$-0.595990\pi$
$997$	−1268.65	−	732.453i	−1.27246	−	0.734657i	−0.975451	+	0.220217i	$0.929323\pi$
$998$	−262.638	+	454.903i	−0.263164	+	0.455814i
$999$	26.8675	−	15.5120i	0.0268944	−	0.0155275i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1050.3.p.a.451.2		4
5.2	odd	4		1050.3.q.a.199.1		8
5.3	odd	4		1050.3.q.a.199.4		8
5.4	even	2		42.3.g.a.31.1	yes	4
7.5	odd	6	inner	1050.3.p.a.901.2		4
15.14	odd	2		126.3.n.a.73.2		4
20.19	odd	2		336.3.bh.e.241.2		4
35.4	even	6		294.3.c.a.97.3		4
35.9	even	6		294.3.g.a.19.1		4
35.12	even	12		1050.3.q.a.649.4		8
35.19	odd	6		42.3.g.a.19.1	✓	4
35.24	odd	6		294.3.c.a.97.4		4
35.33	even	12		1050.3.q.a.649.1		8
35.34	odd	2		294.3.g.a.31.1		4
60.59	even	2		1008.3.cg.h.577.1		4
105.44	odd	6		882.3.n.e.19.2		4
105.59	even	6		882.3.c.b.685.2		4
105.74	odd	6		882.3.c.b.685.1		4
105.89	even	6		126.3.n.a.19.2		4
105.104	even	2		882.3.n.e.325.2		4
140.19	even	6		336.3.bh.e.145.2		4
140.39	odd	6		2352.3.f.e.97.4		4
140.59	even	6		2352.3.f.e.97.1		4
420.299	odd	6		1008.3.cg.h.145.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.3.g.a.19.1	✓	4	35.19	odd	6
42.3.g.a.31.1	yes	4	5.4	even	2
126.3.n.a.19.2		4	105.89	even	6
126.3.n.a.73.2		4	15.14	odd	2
294.3.c.a.97.3		4	35.4	even	6
294.3.c.a.97.4		4	35.24	odd	6
294.3.g.a.19.1		4	35.9	even	6
294.3.g.a.31.1		4	35.34	odd	2
336.3.bh.e.145.2		4	140.19	even	6
336.3.bh.e.241.2		4	20.19	odd	2
882.3.c.b.685.1		4	105.74	odd	6
882.3.c.b.685.2		4	105.59	even	6
882.3.n.e.19.2		4	105.44	odd	6
882.3.n.e.325.2		4	105.104	even	2
1008.3.cg.h.145.1		4	420.299	odd	6
1008.3.cg.h.577.1		4	60.59	even	2
1050.3.p.a.451.2		4	1.1	even	1	trivial
1050.3.p.a.901.2		4	7.5	odd	6	inner
1050.3.q.a.199.1		8	5.2	odd	4
1050.3.q.a.199.4		8	5.3	odd	4
1050.3.q.a.649.1		8	35.33	even	12
1050.3.q.a.649.4		8	35.12	even	12
2352.3.f.e.97.1		4	140.59	even	6
2352.3.f.e.97.4		4	140.39	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:	\( N \)	\(=\)	\( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1050.p (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 + 1.22474i) q^{2} +(-1.50000 - 0.866025i) q^{3} +(-1.00000 + 1.73205i) q^{4} -2.44949i q^{6} +(6.74264 + 1.88064i) q^{7} -2.82843 q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})\)	\(q+(0.707107 + 1.22474i) q^{2} +(-1.50000 - 0.866025i) q^{3} +(-1.00000 + 1.73205i) q^{4} -2.44949i q^{6} +(6.74264 + 1.88064i) q^{7} -2.82843 q^{8} +(1.50000 + 2.59808i) q^{9} +(-3.00000 + 5.19615i) q^{11} +(3.00000 - 1.73205i) q^{12} -17.8639i q^{13} +(2.46447 + 9.58783i) q^{14} +(-2.00000 - 3.46410i) q^{16} +(16.2426 + 9.37769i) q^{17} +(-2.12132 + 3.67423i) q^{18} +(-14.7426 + 8.51167i) q^{19} +(-8.48528 - 8.66025i) q^{21} -8.48528 q^{22} +(6.72792 + 11.6531i) q^{23} +(4.24264 + 2.44949i) q^{24} +(21.8787 - 12.6317i) q^{26} -5.19615i q^{27} +(-10.0000 + 9.79796i) q^{28} +33.9411 q^{29} +(12.7721 + 7.37396i) q^{31} +(2.82843 - 4.89898i) q^{32} +(9.00000 - 5.19615i) q^{33} +26.5241i q^{34} -6.00000 q^{36} +(2.98528 + 5.17066i) q^{37} +(-20.8492 - 12.0373i) q^{38} +(-15.4706 + 26.7958i) q^{39} -35.2354i q^{41} +(4.60660 - 16.5160i) q^{42} -15.4853 q^{43} +(-6.00000 - 10.3923i) q^{44} +(-9.51472 + 16.4800i) q^{46} +(28.7574 - 16.6031i) q^{47} +6.92820i q^{48} +(41.9264 + 25.3609i) q^{49} +(-16.2426 - 28.1331i) q^{51} +(30.9411 + 17.8639i) q^{52} +(-17.2721 + 29.9161i) q^{53} +(6.36396 - 3.67423i) q^{54} +(-19.0711 - 5.31925i) q^{56} +29.4853 q^{57} +(24.0000 + 41.5692i) q^{58} +(23.6985 + 13.6823i) q^{59} +(-34.9706 + 20.1903i) q^{61} +20.8567i q^{62} +(5.22792 + 20.3389i) q^{63} +8.00000 q^{64} +(12.7279 + 7.34847i) q^{66} +(-57.1985 + 99.0707i) q^{67} +(-32.4853 + 18.7554i) q^{68} -23.3062i q^{69} +18.6030 q^{71} +(-4.24264 - 7.34847i) q^{72} +(101.353 + 58.5161i) q^{73} +(-4.22183 + 7.31242i) q^{74} -34.0467i q^{76} +(-30.0000 + 29.3939i) q^{77} -43.7574 q^{78} +(44.1690 + 76.5030i) q^{79} +(-4.50000 + 7.79423i) q^{81} +(43.1543 - 24.9152i) q^{82} +75.7601i q^{83} +(23.4853 - 6.03668i) q^{84} +(-10.9497 - 18.9655i) q^{86} +(-50.9117 - 29.3939i) q^{87} +(8.48528 - 14.6969i) q^{88} +(-18.0000 + 10.3923i) q^{89} +(33.5955 - 120.450i) q^{91} -26.9117 q^{92} +(-12.7721 - 22.1219i) q^{93} +(40.6690 + 23.4803i) q^{94} +(-8.48528 + 4.89898i) q^{96} +30.5826i q^{97} +(-1.41421 + 69.2820i) q^{98} -18.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 6 q^{3} - 4 q^{4} + 10 q^{7} + 6 q^{9}+O(q^{10}) \) 4 * q - 6 * q^3 - 4 * q^4 + 10 * q^7 + 6 * q^9	\( 4 q - 6 q^{3} - 4 q^{4} + 10 q^{7} + 6 q^{9} - 12 q^{11} + 12 q^{12} + 24 q^{14} - 8 q^{16} + 48 q^{17} - 42 q^{19} - 24 q^{23} + 96 q^{26} - 40 q^{28} + 102 q^{31} + 36 q^{33} - 24 q^{36} - 22 q^{37} - 24 q^{38} + 6 q^{39} - 24 q^{42} - 28 q^{43} - 24 q^{44} - 72 q^{46} + 132 q^{47} - 2 q^{49} - 48 q^{51} - 12 q^{52} - 120 q^{53} - 48 q^{56} + 84 q^{57} + 96 q^{58} - 24 q^{59} - 72 q^{61} - 30 q^{63} + 32 q^{64} - 110 q^{67} - 96 q^{68} + 312 q^{71} + 66 q^{73} - 48 q^{74} - 120 q^{77} - 192 q^{78} - 10 q^{79} - 18 q^{81} - 48 q^{82} + 60 q^{84} - 24 q^{86} - 72 q^{89} - 222 q^{91} + 96 q^{92} - 102 q^{93} - 24 q^{94} - 72 q^{99}+O(q^{100}) \) 4 * q - 6 * q^3 - 4 * q^4 + 10 * q^7 + 6 * q^9 - 12 * q^11 + 12 * q^12 + 24 * q^14 - 8 * q^16 + 48 * q^17 - 42 * q^19 - 24 * q^23 + 96 * q^26 - 40 * q^28 + 102 * q^31 + 36 * q^33 - 24 * q^36 - 22 * q^37 - 24 * q^38 + 6 * q^39 - 24 * q^42 - 28 * q^43 - 24 * q^44 - 72 * q^46 + 132 * q^47 - 2 * q^49 - 48 * q^51 - 12 * q^52 - 120 * q^53 - 48 * q^56 + 84 * q^57 + 96 * q^58 - 24 * q^59 - 72 * q^61 - 30 * q^63 + 32 * q^64 - 110 * q^67 - 96 * q^68 + 312 * q^71 + 66 * q^73 - 48 * q^74 - 120 * q^77 - 192 * q^78 - 10 * q^79 - 18 * q^81 - 48 * q^82 + 60 * q^84 - 24 * q^86 - 72 * q^89 - 222 * q^91 + 96 * q^92 - 102 * q^93 - 24 * q^94 - 72 * q^99

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