LMFDB - Embedded newform 126.3.n.a.19.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [126,3,Mod(19,126)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(126, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 5]))

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

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

chi := DirichletCharacter("126.19");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 126 = 2 \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	126.n (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:	$3.43325133094$
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:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 42)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			19.2
Root			$0.707107 - 1.22474i$ of defining polynomial
Character	$\chi$	$=$	126.19
Dual form			126.3.n.a.73.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 1.22474i) q^{2} +(-1.00000 - 1.73205i) q^{4} +(-7.24264 - 4.18154i) q^{5} +(-6.74264 + 1.88064i) q^{7} -2.82843 q^{8} +O(q^{10})$	\(q+(0.707107 - 1.22474i) q^{2} +(-1.00000 - 1.73205i) q^{4} +(-7.24264 - 4.18154i) q^{5} +(-6.74264 + 1.88064i) q^{7} -2.82843 q^{8} +(-10.2426 + 5.91359i) q^{10} +(3.00000 + 5.19615i) q^{11} -17.8639i q^{13} +(-2.46447 + 9.58783i) q^{14} +(-2.00000 + 3.46410i) q^{16} +(16.2426 - 9.37769i) q^{17} +(-14.7426 - 8.51167i) q^{19} +16.7262i q^{20} +8.48528 q^{22} +(6.72792 - 11.6531i) q^{23} +(22.4706 + 38.9202i) q^{25} +(-21.8787 - 12.6317i) q^{26} +(10.0000 + 9.79796i) q^{28} -33.9411 q^{29} +(12.7721 - 7.37396i) q^{31} +(2.82843 + 4.89898i) q^{32} -26.5241i q^{34} +(56.6985 + 14.5738i) q^{35} +(-2.98528 + 5.17066i) q^{37} +(-20.8492 + 12.0373i) q^{38} +(20.4853 + 11.8272i) q^{40} -35.2354i q^{41} +15.4853 q^{43} +(6.00000 - 10.3923i) q^{44} +(-9.51472 - 16.4800i) q^{46} +(28.7574 + 16.6031i) q^{47} +(41.9264 - 25.3609i) q^{49} +63.5563 q^{50} +(-30.9411 + 17.8639i) q^{52} +(-17.2721 - 29.9161i) q^{53} -50.1785i q^{55} +(19.0711 - 5.31925i) q^{56} +(-24.0000 + 41.5692i) q^{58} +(-23.6985 + 13.6823i) q^{59} +(-34.9706 - 20.1903i) q^{61} -20.8567i q^{62} +8.00000 q^{64} +(-74.6985 + 129.382i) q^{65} +(57.1985 + 99.0707i) q^{67} +(-32.4853 - 18.7554i) q^{68} +(57.9411 - 59.1359i) q^{70} -18.6030 q^{71} +(-101.353 + 58.5161i) q^{73} +(4.22183 + 7.31242i) q^{74} +34.0467i q^{76} +(-30.0000 - 29.3939i) q^{77} +(44.1690 - 76.5030i) q^{79} +(28.9706 - 16.7262i) q^{80} +(-43.1543 - 24.9152i) q^{82} -75.7601i q^{83} -156.853 q^{85} +(10.9497 - 18.9655i) q^{86} +(-8.48528 - 14.6969i) q^{88} +(18.0000 + 10.3923i) q^{89} +(33.5955 + 120.450i) q^{91} -26.9117 q^{92} +(40.6690 - 23.4803i) q^{94} +(71.1838 + 123.294i) q^{95} +30.5826i q^{97} +(-1.41421 - 69.2820i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{4} - 12 q^{5} - 10 q^{7}+O(q^{10}) $ 4 * q - 4 * q^4 - 12 * q^5 - 10 * q^7	$ 4 q - 4 q^{4} - 12 q^{5} - 10 q^{7} - 24 q^{10} + 12 q^{11} - 24 q^{14} - 8 q^{16} + 48 q^{17} - 42 q^{19} - 24 q^{23} + 22 q^{25} - 96 q^{26} + 40 q^{28} + 102 q^{31} + 108 q^{35} + 22 q^{37} - 24 q^{38} + 48 q^{40} + 28 q^{43} + 24 q^{44} - 72 q^{46} + 132 q^{47} - 2 q^{49} + 192 q^{50} + 12 q^{52} - 120 q^{53} + 48 q^{56} - 96 q^{58} + 24 q^{59} - 72 q^{61} + 32 q^{64} - 180 q^{65} + 110 q^{67} - 96 q^{68} + 96 q^{70} - 312 q^{71} - 66 q^{73} + 48 q^{74} - 120 q^{77} - 10 q^{79} + 48 q^{80} + 48 q^{82} - 288 q^{85} + 24 q^{86} + 72 q^{89} - 222 q^{91} + 96 q^{92} - 24 q^{94} + 132 q^{95}+O(q^{100}) $ 4 * q - 4 * q^4 - 12 * q^5 - 10 * q^7 - 24 * q^10 + 12 * q^11 - 24 * q^14 - 8 * q^16 + 48 * q^17 - 42 * q^19 - 24 * q^23 + 22 * q^25 - 96 * q^26 + 40 * q^28 + 102 * q^31 + 108 * q^35 + 22 * q^37 - 24 * q^38 + 48 * q^40 + 28 * q^43 + 24 * q^44 - 72 * q^46 + 132 * q^47 - 2 * q^49 + 192 * q^50 + 12 * q^52 - 120 * q^53 + 48 * q^56 - 96 * q^58 + 24 * q^59 - 72 * q^61 + 32 * q^64 - 180 * q^65 + 110 * q^67 - 96 * q^68 + 96 * q^70 - 312 * q^71 - 66 * q^73 + 48 * q^74 - 120 * q^77 - 10 * q^79 + 48 * q^80 + 48 * q^82 - 288 * q^85 + 24 * q^86 + 72 * q^89 - 222 * q^91 + 96 * q^92 - 24 * q^94 + 132 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/126\mathbb{Z}\right)^\times$.

$n$	$29$	$73$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	0.707107	−	1.22474i	0.353553	−	0.612372i
$2$	0.707107	−	1.22474i	0.353553	−	0.612372i
$3$		0			0
$3$		0			0
$4$	−1.00000	−	1.73205i	−0.250000	−	0.433013i
$5$	−7.24264	−	4.18154i	−1.44853	−	0.836308i	−0.450134	−	0.892961i	$-0.648624\pi$
$5$	−7.24264	−	4.18154i	−1.44853	−	0.836308i	−0.998394	+	0.0566528i	$0.981957\pi$
$6$		0			0
$7$	−6.74264	+	1.88064i	−0.963234	+	0.268662i
$7$	−6.74264	+	1.88064i	−0.963234	+	0.268662i
$8$	−2.82843			−0.353553
$9$		0			0
$10$	−10.2426	+	5.91359i	−1.02426	+	0.591359i
$11$	3.00000	+	5.19615i	0.272727	+	0.472377i	0.969559	−	0.244857i	$-0.0787410\pi$
$11$	3.00000	+	5.19615i	0.272727	+	0.472377i	−0.696832	+	0.717234i	$0.745408\pi$
$12$		0			0
$13$		−	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	0.0606799	−	0.998157i	$-0.480673\pi$
$17$	16.2426	−	9.37769i	0.955449	−	0.551629i	0.894770	+	0.446528i	$0.147340\pi$
$18$		0			0
$19$	−14.7426	−	8.51167i	−0.775928	−	0.447983i	0.0590569	−	0.998255i	$-0.481191\pi$
$19$	−14.7426	−	8.51167i	−0.775928	−	0.447983i	−0.834985	+	0.550272i	$0.814524\pi$
$20$			16.7262i			0.836308i
$21$		0			0
$22$	8.48528			0.385695
$23$	6.72792	−	11.6531i	0.292518	−	0.506657i	−0.681886	−	0.731458i	$-0.738840\pi$
$23$	6.72792	−	11.6531i	0.292518	−	0.506657i	0.974405	+	0.224802i	$0.0721734\pi$
$24$		0			0
$25$	22.4706	+	38.9202i	0.898823	+	1.55681i
$26$	−21.8787	−	12.6317i	−0.841488	−	0.485833i
$27$		0			0
$28$	10.0000	+	9.79796i	0.357143	+	0.349927i
$29$	−33.9411			−1.17038			−0.585192	−	0.810895i	$-0.698981\pi$
$29$	−33.9411			−1.17038			−0.585192	+	0.810895i	$0.698981\pi$
$30$		0			0
$31$	12.7721	−	7.37396i	0.412003	−	0.237870i	−0.279647	−	0.960103i	$-0.590218\pi$
$31$	12.7721	−	7.37396i	0.412003	−	0.237870i	0.691650	+	0.722233i	$0.256884\pi$
$32$	2.82843	+	4.89898i	0.0883883	+	0.153093i
$33$		0			0
$34$		−	26.5241i		−	0.780121i
$35$	56.6985	+	14.5738i	1.61996	+	0.416396i
$36$		0			0
$37$	−2.98528	+	5.17066i	−0.0806833	+	0.139748i	−0.903544	−	0.428496i	$-0.859044\pi$
$37$	−2.98528	+	5.17066i	−0.0806833	+	0.139748i	0.822860	+	0.568244i	$0.192377\pi$
$38$	−20.8492	+	12.0373i	−0.548664	+	0.316771i
$39$		0			0
$40$	20.4853	+	11.8272i	0.512132	+	0.295680i
$41$		−	35.2354i		−	0.859399i	−0.902972	−	0.429700i	$-0.858619\pi$
$41$		−	35.2354i		−	0.859399i	0.902972	−	0.429700i	$-0.141381\pi$
$42$		0			0
$43$	15.4853			0.360123			0.180061	−	0.983655i	$-0.442370\pi$
$43$	15.4853			0.360123			0.180061	+	0.983655i	$0.442370\pi$
$44$	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	0.773693	−	0.633561i	$-0.218408\pi$
$47$	28.7574	+	16.6031i	0.611859	+	0.353257i	−0.161834	+	0.986818i	$0.551741\pi$
$48$		0			0
$49$	41.9264	−	25.3609i	0.855641	−	0.517570i
$50$	63.5563			1.27113
$51$		0			0
$52$	−30.9411	+	17.8639i	−0.595022	+	0.343536i
$53$	−17.2721	−	29.9161i	−0.325888	−	0.564455i	0.655803	−	0.754932i	$-0.272330\pi$
$53$	−17.2721	−	29.9161i	−0.325888	−	0.564455i	−0.981692	+	0.190477i	$0.938997\pi$
$54$		0			0
$55$		−	50.1785i		−	0.912336i
$56$	19.0711	−	5.31925i	0.340555	−	0.0949865i
$57$		0			0
$58$	−24.0000	+	41.5692i	−0.413793	+	0.716711i
$59$	−23.6985	+	13.6823i	−0.401669	+	0.231904i	−0.687204	−	0.726465i	$-0.741162\pi$
$59$	−23.6985	+	13.6823i	−0.401669	+	0.231904i	0.285535	+	0.958368i	$0.407829\pi$
$60$		0			0
$61$	−34.9706	−	20.1903i	−0.573288	−	0.330988i	0.185174	−	0.982706i	$-0.440715\pi$
$61$	−34.9706	−	20.1903i	−0.573288	−	0.330988i	−0.758461	+	0.651718i	$0.774049\pi$
$62$		−	20.8567i		−	0.336399i
$63$		0			0
$64$	8.00000			0.125000
$65$	−74.6985	+	129.382i	−1.14921	+	1.99049i
$66$		0			0
$67$	57.1985	+	99.0707i	0.853709	+	1.47867i	0.877838	+	0.478958i	$0.158985\pi$
$67$	57.1985	+	99.0707i	0.853709	+	1.47867i	−0.0241291	+	0.999709i	$0.507681\pi$
$68$	−32.4853	−	18.7554i	−0.477725	−	0.275814i
$69$		0			0
$70$	57.9411	−	59.1359i	0.827730	−	0.844799i
$71$	−18.6030			−0.262015			−0.131007	−	0.991381i	$-0.541821\pi$
$71$	−18.6030			−0.262015			−0.131007	+	0.991381i	$0.541821\pi$
$72$		0			0
$73$	−101.353	+	58.5161i	−1.38839	+	0.801590i	−0.993134	−	0.116979i	$-0.962679\pi$
$73$	−101.353	+	58.5161i	−1.38839	+	0.801590i	−0.395260	+	0.918569i	$0.629346\pi$
$74$	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
$78$		0			0
$79$	44.1690	−	76.5030i	0.559102	−	0.968393i	−0.438470	−	0.898746i	$-0.644479\pi$
$79$	44.1690	−	76.5030i	0.559102	−	0.968393i	0.997572	−	0.0696469i	$-0.0221873\pi$
$80$	28.9706	−	16.7262i	0.362132	−	0.209077i
$81$		0			0
$82$	−43.1543	−	24.9152i	−0.526272	−	0.303843i
$83$		−	75.7601i		−	0.912772i	−0.889782	−	0.456386i	$-0.849144\pi$
$83$		−	75.7601i		−	0.912772i	0.889782	−	0.456386i	$-0.150856\pi$
$84$		0			0
$85$	−156.853			−1.84533
$86$	10.9497	−	18.9655i	0.127323	−	0.220529i
$87$		0			0
$88$	−8.48528	−	14.6969i	−0.0964237	−	0.167011i
$89$	18.0000	+	10.3923i	0.202247	+	0.116767i	0.597703	−	0.801717i	$-0.296080\pi$
$89$	18.0000	+	10.3923i	0.202247	+	0.116767i	−0.395456	+	0.918485i	$0.629413\pi$
$90$		0			0
$91$	33.5955	+	120.450i	0.369181	+	1.32362i
$92$	−26.9117			−0.292518
$93$		0			0
$94$	40.6690	−	23.4803i	0.432649	−	0.249790i
$95$	71.1838	+	123.294i	0.749303	+	1.29783i
$96$		0			0
$97$			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
$99$		0			0
$100$	44.9411	−	77.8403i	0.449411	−	0.778403i
$101$	−110.823	+	63.9839i	−1.09726	+	0.633504i	−0.935500	−	0.353326i	$-0.885051\pi$
$101$	−110.823	+	63.9839i	−1.09726	+	0.633504i	−0.161761	+	0.986830i	$0.551717\pi$
$102$		0			0
$103$	−70.1102	−	40.4781i	−0.680681	−	0.392992i	0.119430	−	0.992843i	$-0.461893\pi$
$103$	−70.1102	−	40.4781i	−0.680681	−	0.392992i	−0.800112	+	0.599851i	$0.795226\pi$
$104$			50.5266i			0.485833i
$105$		0			0
$106$	−48.8528			−0.460876
$107$	84.7279	−	146.753i	0.791850	−	1.37152i	−0.132971	−	0.991120i	$-0.542452\pi$
$107$	84.7279	−	146.753i	0.791850	−	1.37152i	0.924820	−	0.380404i	$-0.124215\pi$
$108$		0			0
$109$	−89.4706	−	154.968i	−0.820831	−	1.42172i	−0.905064	−	0.425275i	$-0.860177\pi$
$109$	−89.4706	−	154.968i	−0.820831	−	1.42172i	0.0842335	−	0.996446i	$-0.473156\pi$
$110$	−61.4558	−	35.4815i	−0.558689	−	0.322560i
$111$		0			0
$112$	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	$0.475473\pi$
$114$		0			0
$115$	−97.4558	+	56.2662i	−0.847442	+	0.489271i
$116$	33.9411	+	58.7878i	0.292596	+	0.506791i
$117$		0			0
$118$			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
$123$		0			0
$124$	−25.5442	−	14.7479i	−0.206001	−	0.118935i
$125$		−	166.769i		−	1.33415i
$126$		0			0
$127$	167.426			1.31832			0.659159	−	0.752004i	$-0.270912\pi$
$127$	167.426			1.31832			0.659159	+	0.752004i	$0.270912\pi$
$128$	5.65685	−	9.79796i	0.0441942	−	0.0765466i
$129$		0			0
$130$	105.640	+	182.973i	0.812612	+	1.40749i
$131$	1.54416	+	0.891519i	0.0117874	+	0.00680549i	0.505882	−	0.862603i	$-0.331167\pi$
$131$	1.54416	+	0.891519i	0.0117874	+	0.00680549i	−0.494095	+	0.869408i	$0.664500\pi$
$132$		0			0
$133$	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	0.989332	−	0.145677i	$-0.0465362\pi$
$137$	50.4853	+	87.4431i	0.368506	+	0.638271i	−0.620826	+	0.783948i	$0.713203\pi$
$138$		0			0
$139$		−	140.542i		−	1.01110i	−0.862799	−	0.505548i	$-0.831290\pi$
$139$		−	140.542i		−	1.01110i	0.862799	−	0.505548i	$-0.168710\pi$
$140$	−31.4558	−	112.779i	−0.224685	−	0.805561i
$141$		0			0
$142$	−13.1543	+	22.7840i	−0.0926361	+	0.160450i
$143$	92.8234	−	53.5916i	0.649115	−	0.374766i
$144$		0			0
$145$	245.823	+	141.926i	1.69533	+	0.978801i
$146$			165.508i			1.13362i
$147$		0			0
$148$	11.9411			0.0806833
$149$	91.4558	−	158.406i	0.613798	−	1.06313i	−0.376797	−	0.926296i	$-0.622974\pi$
$149$	91.4558	−	158.406i	0.613798	−	1.06313i	0.990594	−	0.136833i	$-0.0436922\pi$
$150$		0			0
$151$	144.397	+	250.103i	0.956271	+	1.65631i	0.731432	+	0.681915i	$0.238852\pi$
$151$	144.397	+	250.103i	0.956271	+	1.65631i	0.224840	+	0.974396i	$0.427814\pi$
$152$	41.6985	+	24.0746i	0.274332	+	0.158386i
$153$		0			0
$154$	−57.2132	+	15.9577i	−0.371514	+	0.103622i
$155$	−123.338			−0.795730
$156$		0			0
$157$	162.000	−	93.5307i	1.03185	−	0.595737i	0.114334	−	0.993442i	$-0.463527\pi$
$157$	162.000	−	93.5307i	1.03185	−	0.595737i	0.917513	+	0.397705i	$0.130193\pi$
$158$	−62.4645	−	108.192i	−0.395345	−	0.684757i
$159$		0			0
$160$		−	47.3087i		−	0.295680i
$161$	−23.4487	+	91.2255i	−0.145644	+	0.566618i
$162$		0			0
$163$	−8.02944	+	13.9074i	−0.0492604	+	0.0853214i	−0.889604	−	0.456732i	$-0.849020\pi$
$163$	−8.02944	+	13.9074i	−0.0492604	+	0.0853214i	0.840344	+	0.542054i	$0.182353\pi$
$164$	−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	$0.176794\pi$
$167$			176.117i			1.05459i	−0.849681	+	0.527297i	$0.823206\pi$
$168$		0			0
$169$	−150.118			−0.888271
$170$	−110.912	+	192.105i	−0.652422	+	1.13003i
$171$		0			0
$172$	−15.4853	−	26.8213i	−0.0900307	−	0.155938i
$173$	200.184	+	115.576i	1.15713	+	0.668070i	0.950615	−	0.310373i	$-0.100454\pi$
$173$	200.184	+	115.576i	1.15713	+	0.668070i	0.206517	+	0.978443i	$0.433787\pi$
$174$		0			0
$175$	−224.706	−	220.166i	−1.28403	−	1.25809i
$176$	−24.0000			−0.136364
$177$		0			0
$178$	25.4558	−	14.6969i	0.143010	−	0.0825671i
$179$	−42.6396	−	73.8540i	−0.238210	−	0.412592i	0.721991	−	0.691903i	$-0.243227\pi$
$179$	−42.6396	−	73.8540i	−0.238210	−	0.412592i	−0.960201	+	0.279311i	$0.909894\pi$
$180$		0			0
$181$		−	5.58655i		−	0.0308649i	−0.999881	−	0.0154325i	$-0.995087\pi$
$181$		−	5.58655i		−	0.0308649i	0.999881	−	0.0154325i	$-0.00491250\pi$
$182$	171.276	+	44.0249i	0.941075	+	0.241895i
$183$		0			0
$184$	−19.0294	+	32.9600i	−0.103421	+	0.179130i
$185$	43.2426	−	24.9662i	0.233744	−	0.134952i
$186$		0			0
$187$	97.4558	+	56.2662i	0.521154	+	0.300889i
$188$		−	66.4123i		−	0.353257i
$189$		0			0
$190$	201.338			1.05967
$191$	92.6985	−	160.558i	0.485332	−	0.840620i	−0.514526	−	0.857475i	$-0.672032\pi$
$191$	92.6985	−	160.558i	0.485332	−	0.840620i	0.999858	+	0.0168547i	$0.00536527\pi$
$192$		0			0
$193$	−113.897	−	197.275i	−0.590140	−	1.02215i	−0.994213	−	0.107425i	$-0.965739\pi$
$193$	−113.897	−	197.275i	−0.590140	−	1.02215i	0.404073	−	0.914727i	$-0.367594\pi$
$194$	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	$0.601197\pi$
$198$		0			0
$199$	5.39697	−	3.11594i	0.0271205	−	0.0156580i	−0.486378	−	0.873748i	$-0.661682\pi$
$199$	5.39697	−	3.11594i	0.0271205	−	0.0156580i	0.513499	+	0.858090i	$0.328349\pi$
$200$	−63.5563	−	110.083i	−0.317782	−	0.550414i
$201$		0			0
$202$			180.974i			0.895910i
$203$	228.853	−	63.8309i	1.12735	−	0.314438i
$204$		0			0
$205$	−147.338	+	255.197i	−0.718722	+	1.24486i
$206$	−99.1508	+	57.2447i	−0.481314	+	0.277887i
$207$		0			0
$208$	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
$213$		0			0
$214$	−119.823	−	207.540i	−0.559922	−	0.969814i
$215$	−112.154	−	64.7523i	−0.521648	−	0.301174i
$216$		0			0
$217$	−72.2498	+	73.7396i	−0.332948	+	0.339814i
$218$	−253.061			−1.16083
$219$		0			0
$220$	−86.9117	+	50.1785i	−0.395053	+	0.228084i
$221$	−167.522	−	290.156i	−0.758017	−	1.31292i
$222$		0			0
$223$		−	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	−0.140430	−	0.990091i	$-0.544848\pi$
$227$	146.823	−	84.7685i	0.646799	−	0.373430i	0.787229	+	0.616661i	$0.211515\pi$
$228$		0			0
$229$	30.0442	+	17.3460i	0.131197	+	0.0757467i	0.564162	−	0.825664i	$-0.309199\pi$
$229$	30.0442	+	17.3460i	0.131197	+	0.0757467i	−0.432965	+	0.901411i	$0.642533\pi$
$230$			159.145i			0.691934i
$231$		0			0
$232$	96.0000			0.413793
$233$	−127.243	+	220.391i	−0.546106	+	0.945883i	0.452431	+	0.891800i	$0.350557\pi$
$233$	−127.243	+	220.391i	−0.546106	+	0.945883i	−0.998536	+	0.0540833i	$0.982776\pi$
$234$		0			0
$235$	−138.853	−	240.500i	−0.590863	−	1.02340i
$236$	47.3970	+	27.3647i	0.200835	+	0.115952i
$237$		0			0
$238$	49.8823	+	178.843i	0.209589	+	0.751440i
$239$	−197.147			−0.824884			−0.412442	−	0.910984i	$-0.635324\pi$
$239$	−197.147			−0.824884			−0.412442	+	0.910984i	$0.635324\pi$
$240$		0			0
$241$	76.6173	−	44.2350i	0.317914	−	0.183548i	−0.332548	−	0.943086i	$-0.607908\pi$
$241$	76.6173	−	44.2350i	0.317914	−	0.183548i	0.650462	+	0.759538i	$0.274575\pi$
$242$	−60.1041	−	104.103i	−0.248364	−	0.430179i
$243$		0			0
$244$			80.7611i			0.330988i
$245$	−409.706	+	8.36308i	−1.67227	+	0.0341350i
$246$		0			0
$247$	−152.051	+	263.361i	−0.615592	+	1.06624i
$248$	−36.1249	+	20.8567i	−0.145665	+	0.0840997i
$249$		0			0
$250$	−204.250	−	117.924i	−0.816999	−	0.471695i
$251$			215.903i			0.860172i	0.902788	+	0.430086i	$0.141517\pi$
$251$			215.903i			0.860172i	−0.902788	+	0.430086i	$0.858483\pi$
$252$		0			0
$253$	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	0.507235	−	0.861808i	$-0.330668\pi$
$257$	3.72792	+	2.15232i	0.0145055	+	0.00837477i	−0.492730	+	0.870182i	$0.664001\pi$
$258$		0			0
$259$	10.4045	−	40.4781i	0.0401720	−	0.156286i
$260$	298.794			1.14921
$261$		0			0
$262$	2.18377	−	1.26080i	0.00833499	−	0.00481221i
$263$	141.338	+	244.805i	0.537407	+	0.930817i	0.999043	+	0.0437468i	$0.0139295\pi$
$263$	141.338	+	244.805i	0.537407	+	0.930817i	−0.461635	+	0.887070i	$0.652737\pi$
$264$		0			0
$265$			288.896i			1.09017i
$266$	117.941	−	120.373i	0.443388	−	0.452531i
$267$		0			0
$268$	114.397	−	198.141i	0.426854	−	0.739333i
$269$	330.765	−	190.967i	1.22961	−	0.709914i	0.262660	−	0.964888i	$-0.415400\pi$
$269$	330.765	−	190.967i	1.22961	−	0.709914i	0.966948	+	0.254974i	$0.0820669\pi$
$270$		0			0
$271$	−73.0294	−	42.1636i	−0.269481	−	0.155585i	0.359171	−	0.933272i	$-0.383060\pi$
$271$	−73.0294	−	42.1636i	−0.269481	−	0.155585i	−0.628652	+	0.777687i	$0.716393\pi$
$272$			75.0215i			0.275814i
$273$		0			0
$274$	142.794			0.521146
$275$	−134.823	+	233.521i	−0.490267	+	0.849167i
$276$		0			0
$277$	68.5589	+	118.747i	0.247505	+	0.428691i	0.962833	−	0.270098i	$-0.0870560\pi$
$277$	68.5589	+	118.747i	0.247505	+	0.428691i	−0.715328	+	0.698789i	$0.753723\pi$
$278$	−172.128	−	99.3784i	−0.619167	−	0.357476i
$279$		0			0
$280$	−160.368	−	41.2211i	−0.572741	−	0.147218i
$281$	325.103			1.15695			0.578474	−	0.815701i	$-0.303648\pi$
$281$	325.103			1.15695			0.578474	+	0.815701i	$0.303648\pi$
$282$		0			0
$283$	168.507	−	97.2876i	0.595432	−	0.343773i	−0.171811	−	0.985130i	$-0.554962\pi$
$283$	168.507	−	97.2876i	0.595432	−	0.343773i	0.767242	+	0.641357i	$0.221628\pi$
$284$	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
$288$		0			0
$289$	31.3823	−	54.3557i	0.108589	−	0.188082i
$290$	347.647	−	200.714i	1.19878	−	0.692117i
$291$		0			0
$292$	202.706	+	117.032i	0.694197	+	0.400795i
$293$			239.702i			0.818095i	0.912513	+	0.409048i	$0.134139\pi$
$293$			239.702i			0.818095i	−0.912513	+	0.409048i	$0.865861\pi$
$294$		0			0
$295$	228.853			0.775772
$296$	8.44365	−	14.6248i	0.0285258	−	0.0494082i
$297$		0			0
$298$	−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
$303$		0			0
$304$	58.9706	−	34.0467i	0.193982	−	0.111996i
$305$	168.853	+	292.462i	0.553616	+	0.958891i
$306$		0			0
$307$			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
$309$		0			0
$310$	−87.2132	+	151.058i	−0.281333	+	0.487283i
$311$	−350.044	+	202.098i	−1.12554	+	0.649832i	−0.942810	−	0.333330i	$-0.891828\pi$
$311$	−350.044	+	202.098i	−1.12554	+	0.649832i	−0.182732	+	0.983163i	$0.558494\pi$
$312$		0			0
$313$	−113.706	−	65.6482i	−0.363278	−	0.209739i	0.307240	−	0.951632i	$-0.400595\pi$
$313$	−113.706	−	65.6482i	−0.363278	−	0.209739i	−0.670518	+	0.741893i	$0.733928\pi$
$314$		−	264.545i		−	0.842500i
$315$		0			0
$316$	−176.676			−0.559102
$317$	−46.9706	+	81.3554i	−0.148172	+	0.256642i	−0.930552	−	0.366160i	$-0.880672\pi$
$317$	−46.9706	+	81.3554i	−0.148172	+	0.256642i	0.782380	+	0.622802i	$0.214006\pi$
$318$		0			0
$319$	−101.823	−	176.363i	−0.319196	−	0.552863i
$320$	−57.9411	−	33.4523i	−0.181066	−	0.104539i
$321$		0			0
$322$	95.1472	+	93.2248i	0.295488	+	0.289518i
$323$	−319.279			−0.988481
$324$		0			0
$325$	695.265	−	401.411i	2.13928	−	1.23511i
$326$	11.3553	+	19.6680i	0.0348323	+	0.0603314i
$327$		0			0
$328$			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	−0.598263	−	0.801300i	$-0.704142\pi$
$331$	130.684	−	226.351i	0.394815	−	0.683840i	0.993078	+	0.117460i	$0.0374754\pi$
$332$	−131.220	+	75.7601i	−0.395242	+	0.228193i
$333$		0			0
$334$	215.698	+	124.534i	0.645804	+	0.372855i
$335$		−	956.711i		−	2.85585i
$336$		0			0
$337$	136.265			0.404347			0.202173	−	0.979350i	$-0.435200\pi$
$337$	136.265			0.404347			0.202173	+	0.979350i	$0.435200\pi$
$338$	−106.149	+	183.856i	−0.314051	+	0.543952i
$339$		0			0
$340$	156.853	+	271.677i	0.461332	+	0.799050i
$341$	76.6325	+	44.2438i	0.224729	+	0.129747i
$342$		0			0
$343$	−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	0.534915	−	0.844906i	$-0.320343\pi$
$347$	−161.095	−	279.026i	−0.464252	−	0.804108i	−0.999167	+	0.0407975i	$0.987010\pi$
$348$		0			0
$349$			346.495i			0.992821i	0.868088	+	0.496411i	$0.165349\pi$
$349$			346.495i			0.992821i	−0.868088	+	0.496411i	$0.834651\pi$
$350$	−428.538	+	119.526i	−1.22439	+	0.341504i
$351$		0			0
$352$	−16.9706	+	29.3939i	−0.0482118	+	0.0835053i
$353$	537.448	−	310.296i	1.52252	−	0.879025i	0.522869	−	0.852413i	$-0.324862\pi$
$353$	537.448	−	310.296i	1.52252	−	0.879025i	0.999646	−	0.0266116i	$-0.00847174\pi$
$354$		0			0
$355$	134.735	+	77.7893i	0.379535	+	0.219125i
$356$		−	41.5692i		−	0.116767i
$357$		0			0
$358$	−120.603			−0.336880
$359$	10.1177	−	17.5245i	0.0281831	−	0.0488146i	−0.851590	−	0.524209i	$-0.824361\pi$
$359$	10.1177	−	17.5245i	0.0281831	−	0.0488146i	0.879773	+	0.475394i	$0.157695\pi$
$360$		0			0
$361$	−35.6030	−	61.6663i	−0.0986234	−	0.170821i
$362$	−6.84210	−	3.95029i	−0.0189008	−	0.0109124i
$363$		0			0
$364$	175.029	−	178.639i	0.480850	−	0.490766i
$365$	978.749			2.68151
$366$		0			0
$367$	−269.831	+	155.787i	−0.735234	+	0.424488i	−0.820334	−	0.571885i	$-0.806212\pi$
$367$	−269.831	+	155.787i	−0.735234	+	0.424488i	0.0850998	+	0.996372i	$0.472879\pi$
$368$	26.9117	+	46.6124i	0.0731296	+	0.126664i
$369$		0			0
$370$		−	70.6149i		−	0.190851i
$371$	172.721	+	169.231i	0.465555	+	0.456149i
$372$		0			0
$373$	340.691	−	590.094i	0.913380	−	1.58202i	0.104125	−	0.994564i	$-0.466796\pi$
$373$	340.691	−	590.094i	0.913380	−	1.58202i	0.809255	−	0.587457i	$-0.199871\pi$
$374$	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
$378$		0			0
$379$	−624.779			−1.64849			−0.824246	−	0.566231i	$-0.808401\pi$
$379$	−624.779			−1.64849			−0.824246	+	0.566231i	$0.808401\pi$
$380$	142.368	−	246.588i	0.374651	−	0.648915i
$381$		0			0
$382$	−131.095	−	227.064i	−0.343182	−	0.594408i
$383$	−119.772	−	69.1502i	−0.312720	−	0.180549i	0.335423	−	0.942068i	$-0.391121\pi$
$383$	−119.772	−	69.1502i	−0.312720	−	0.180549i	−0.648143	+	0.761519i	$0.724454\pi$
$384$		0			0
$385$	94.3675	+	338.336i	0.245110	+	0.878794i
$386$	−322.149			−0.834584
$387$		0			0
$388$	52.9706	−	30.5826i	0.136522	−	0.0788211i
$389$	−281.787	−	488.069i	−0.724388	−	1.25468i	−0.959226	−	0.282642i	$-0.908789\pi$
$389$	−281.787	−	488.069i	−0.724388	−	1.25468i	0.234838	−	0.972035i	$-0.424544\pi$
$390$		0			0
$391$		−	252.370i		−	0.645446i
$392$	−118.586	+	71.7315i	−0.302515	+	0.182989i
$393$		0			0
$394$	−87.0883	+	150.841i	−0.221036	+	0.382846i
$395$	−639.801	+	369.389i	−1.61975	+	0.935163i
$396$		0			0
$397$	−392.603	−	226.669i	−0.988923	−	0.570955i	−0.0839711	−	0.996468i	$-0.526760\pi$
$397$	−392.603	−	226.669i	−0.988923	−	0.570955i	−0.904952	+	0.425513i	$0.860094\pi$
$398$		−	8.81321i		−	0.0221438i
$399$		0			0
$400$	−179.765			−0.449411
$401$	−137.875	+	238.807i	−0.343828	+	0.595528i	−0.985140	−	0.171752i	$-0.945057\pi$
$401$	−137.875	+	238.807i	−0.343828	+	0.595528i	0.641312	+	0.767280i	$0.278390\pi$
$402$		0			0
$403$	−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
$408$		0			0
$409$	−377.441	+	217.916i	−0.922839	+	0.532801i	−0.884540	−	0.466465i	$-0.845527\pi$
$409$	−377.441	+	217.916i	−0.922839	+	0.532801i	−0.0382993	+	0.999266i	$0.512194\pi$
$410$	208.368	+	360.903i	0.508213	+	0.880252i
$411$		0			0
$412$			161.913i			0.392992i
$413$	134.059	−	136.823i	0.324598	−	0.331291i
$414$		0			0
$415$	−316.794	+	548.703i	−0.763359	+	1.32218i
$416$	87.5147	−	50.5266i	0.210372	−	0.121458i
$417$		0			0
$418$	−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
$423$		0			0
$424$	48.8528	+	84.6156i	0.115219	+	0.199565i
$425$	729.963	+	421.444i	1.71756	+	0.991633i
$426$		0			0
$427$	273.765	+	70.3688i	0.641135	+	0.164798i
$428$	−338.912			−0.791850
$429$		0			0
$430$	−158.610	+	91.5736i	−0.368861	+	0.212962i
$431$	−197.860	−	342.703i	−0.459072	−	0.795136i	0.539840	−	0.841767i	$-0.318485\pi$
$431$	−197.860	−	342.703i	−0.459072	−	0.795136i	−0.998912	+	0.0466317i	$0.985151\pi$
$432$		0			0
$433$		−	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
$438$		0			0
$439$	344.558	+	198.931i	0.784871	+	0.453146i	0.838154	−	0.545434i	$-0.183635\pi$
$439$	344.558	+	198.931i	0.784871	+	0.453146i	−0.0532827	+	0.998579i	$0.516968\pi$
$440$			141.926i			0.322560i
$441$		0			0
$442$	−473.823			−1.07200
$443$	−59.2721	+	102.662i	−0.133797	+	0.231743i	−0.925137	−	0.379633i	$-0.876050\pi$
$443$	−59.2721	+	102.662i	−0.133797	+	0.231743i	0.791340	+	0.611376i	$0.209384\pi$
$444$		0			0
$445$	−86.9117	−	150.535i	−0.195307	−	0.338282i
$446$	−280.014	−	161.666i	−0.627835	−	0.362481i
$447$		0			0
$448$	−53.9411	+	15.0451i	−0.120404	+	0.0335828i
$449$	−713.897			−1.58997			−0.794985	−	0.606629i	$-0.792521\pi$
$449$	−713.897			−1.58997			−0.794985	+	0.606629i	$0.792521\pi$
$450$		0			0
$451$	183.088	−	105.706i	0.405961	−	0.234382i
$452$	−17.3970	−	30.1324i	−0.0384889	−	0.0666647i
$453$		0			0
$454$		−	239.762i		−	0.528109i
$455$	260.345	−	1012.85i	0.572187	−	2.22605i
$456$		0			0
$457$	62.5883	−	108.406i	0.136955	−	0.237213i	−0.789388	−	0.613895i	$-0.789602\pi$
$457$	62.5883	−	108.406i	0.136955	−	0.237213i	0.926342	+	0.376682i	$0.122935\pi$
$458$	42.4889	−	24.5310i	0.0927704	−	0.0535610i
$459$		0			0
$460$	194.912	+	112.532i	0.423721	+	0.244635i
$461$		−	655.767i		−	1.42249i	−0.702945	−	0.711244i	$-0.748132\pi$
$461$		−	655.767i		−	1.42249i	0.702945	−	0.711244i	$-0.251868\pi$
$462$		0			0
$463$	869.396			1.87775			0.938873	−	0.344265i	$-0.111872\pi$
$463$	869.396			1.87775			0.938873	+	0.344265i	$0.111872\pi$
$464$	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	0.726989	−	0.686649i	$-0.240919\pi$
$467$	231.551	+	133.686i	0.495827	+	0.286266i	−0.231162	+	0.972915i	$0.574253\pi$
$468$		0			0
$469$	−571.985	−	560.428i	−1.21958	−	1.19494i
$470$	−392.735			−0.835607
$471$		0			0
$472$	67.0294	−	38.6995i	0.142012	−	0.0819904i
$473$	46.4558	+	80.4639i	0.0982153	+	0.170114i
$474$		0			0
$475$		−	765.048i		−	1.61063i
$476$	254.309	+	65.3678i	0.534262	+	0.137327i
$477$		0			0
$478$	−139.404	+	241.455i	−0.291640	+	0.505136i
$479$	−235.331	+	135.868i	−0.491296	+	0.283650i	−0.725112	−	0.688631i	$-0.758212\pi$
$479$	−235.331	+	135.868i	−0.491296	+	0.283650i	0.233816	+	0.972281i	$0.424879\pi$
$480$		0			0
$481$	92.3680	+	53.3287i	0.192033	+	0.110870i
$482$		−	125.116i		−	0.259576i
$483$		0			0
$484$	−170.000			−0.351240
$485$	127.882	−	221.499i	0.263675	−	0.456698i
$486$		0			0
$487$	280.757	+	486.285i	0.576503	+	0.998532i	0.995877	+	0.0907186i	$0.0289164\pi$
$487$	280.757	+	486.285i	0.576503	+	0.998532i	−0.419374	+	0.907814i	$0.637750\pi$
$488$	98.9117	+	57.1067i	0.202688	+	0.117022i
$489$		0			0
$490$	−279.463	+	507.698i	−0.570333	+	1.03612i
$491$	406.441			0.827781			0.413891	−	0.910327i	$-0.364170\pi$
$491$	406.441			0.827781			0.413891	+	0.910327i	$0.364170\pi$
$492$		0			0
$493$	−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
$498$		0			0
$499$	185.713	−	321.665i	0.372171	−	0.644619i	−0.617728	−	0.786391i	$-0.711947\pi$
$499$	185.713	−	321.665i	0.372171	−	0.644619i	0.989899	+	0.141773i	$0.0452802\pi$
$500$	−288.853	+	166.769i	−0.577706	+	0.333538i
$501$		0			0
$502$	264.426	+	152.667i	0.526746	+	0.304117i
$503$		−	64.6292i		−	0.128488i	−0.997934	−	0.0642438i	$-0.979536\pi$
$503$		−	64.6292i		−	0.128488i	0.997934	−	0.0642438i	$-0.0204635\pi$
$504$		0			0
$505$	1070.21			2.11922
$506$	57.0883	−	98.8799i	0.112823	−	0.195415i
$507$		0			0
$508$	−167.426	−	289.991i	−0.329580	−	0.570849i
$509$	−871.889	−	503.385i	−1.71294	−	0.988969i	−0.930534	−	0.366205i	$-0.880657\pi$
$509$	−871.889	−	503.385i	−1.71294	−	0.988969i	−0.782410	−	0.622764i	$-0.786010\pi$
$510$		0			0
$511$	573.338	−	585.161i	1.12199	−	1.14513i
$512$	−22.6274			−0.0441942
$513$		0			0
$514$	5.27208	−	3.04384i	0.0102570	−	0.00592186i
$515$	338.522	+	586.337i	0.657324	+	1.13852i
$516$		0			0
$517$			199.237i			0.385371i
$518$	−42.2183	−	41.3653i	−0.0815024	−	0.0798557i
$519$		0			0
$520$	211.279	−	365.946i	0.406306	−	0.703743i
$521$	322.294	−	186.077i	0.618607	−	0.357153i	−0.157719	−	0.987484i	$-0.550414\pi$
$521$	322.294	−	186.077i	0.618607	−	0.357153i	0.776327	+	0.630331i	$0.217081\pi$
$522$		0			0
$523$	−551.904	−	318.642i	−1.05527	−	0.609258i	−0.131147	−	0.991363i	$-0.541866\pi$
$523$	−551.904	−	318.642i	−1.05527	−	0.609258i	−0.924119	+	0.382105i	$0.875199\pi$
$524$		−	3.56608i		−	0.00680549i
$525$		0			0
$526$	399.765			0.760009
$527$	138.302	−	239.545i	0.262432	−	0.454545i
$528$		0			0
$529$	173.970	+	301.325i	0.328866	+	0.569613i
$530$	353.823	+	204.280i	0.667591	+	0.385434i
$531$		0			0
$532$	−64.0294	−	229.564i	−0.120356	−	0.431512i
$533$	−629.440			−1.18094
$534$		0			0
$535$	−1227.31	+	708.586i	−2.29403	+	1.32446i
$536$	−161.782	−	280.214i	−0.301832	−	0.522788i
$537$		0			0
$538$		−	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	−0.949842	−	0.312731i	$-0.898756\pi$
$541$	−110.412	+	191.239i	−0.204088	+	0.353491i	0.745754	+	0.666222i	$0.232090\pi$
$542$	−103.279	+	59.6283i	−0.190552	+	0.110015i
$543$		0			0
$544$	91.8823	+	53.0482i	0.168901	+	0.0975152i
$545$			1496.50i			2.74587i
$546$		0			0
$547$	−160.676			−0.293741			−0.146870	−	0.989156i	$-0.546920\pi$
$547$	−160.676			−0.293741			−0.146870	+	0.989156i	$0.546920\pi$
$548$	100.971	−	174.886i	0.184253	−	0.319135i
$549$		0			0
$550$	190.669	+	330.248i	0.346671	+	0.600452i
$551$	500.382	+	288.896i	0.908134	+	0.524311i
$552$		0			0
$553$	−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	0.570685	−	0.821169i	$-0.306678\pi$
$557$	−237.177	−	410.802i	−0.425811	−	0.737526i	−0.996496	+	0.0836431i	$0.973344\pi$
$558$		0			0
$559$		−	276.627i		−	0.494860i
$560$	−163.882	+	167.262i	−0.292647	+	0.298681i
$561$		0			0
$562$	229.882	−	398.168i	0.409043	−	0.708484i
$563$	430.301	−	248.434i	0.764300	−	0.441269i	−0.0665378	−	0.997784i	$-0.521195\pi$
$563$	430.301	−	248.434i	0.764300	−	0.441269i	0.830837	+	0.556515i	$0.187862\pi$
$564$		0			0
$565$	−126.000	−	72.7461i	−0.223009	−	0.128754i
$566$		−	275.171i		−	0.486168i
$567$		0			0
$568$	52.6173			0.0926361
$569$	392.647	−	680.084i	0.690065	−	1.19523i	−0.281752	−	0.959487i	$-0.590915\pi$
$569$	392.647	−	680.084i	0.690065	−	1.19523i	0.971816	−	0.235740i	$-0.0757512\pi$
$570$		0			0
$571$	357.521	+	619.245i	0.626132	+	1.08449i	0.988321	+	0.152388i	$0.0486963\pi$
$571$	357.521	+	619.245i	0.626132	+	1.08449i	−0.362189	+	0.932105i	$0.617970\pi$
$572$	−185.647	−	107.183i	−0.324557	−	0.187383i
$573$		0			0
$574$	337.831	+	86.8364i	0.588555	+	0.151283i
$575$	604.721			1.05169
$576$		0			0
$577$	669.117	−	386.315i	1.15965	−	0.669524i	0.208429	−	0.978038i	$-0.433165\pi$
$577$	669.117	−	386.315i	1.15965	−	0.669524i	0.951220	+	0.308514i	$0.0998317\pi$
$578$	−44.3812	−	76.8705i	−0.0767841	−	0.132994i
$579$		0			0
$580$		−	567.705i		−	0.978801i
$581$	142.477	+	510.823i	0.245228	+	0.879214i
$582$		0			0
$583$	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	$0.121254\pi$
$587$			436.477i			0.743572i	−0.928318	+	0.371786i	$0.878746\pi$
$588$		0			0
$589$	−251.059			−0.426246
$590$	161.823	−	280.286i	0.274277	−	0.475062i
$591$		0			0
$592$	−11.9411	−	20.6826i	−0.0201708	−	0.0349369i
$593$	−722.397	−	417.076i	−1.21821	−	0.703332i	−0.253673	−	0.967290i	$-0.581639\pi$
$593$	−722.397	−	417.076i	−1.21821	−	0.703332i	−0.964534	+	0.263958i	$0.914972\pi$
$594$		0			0
$595$	1057.60	−	294.983i	1.77748	−	0.495770i
$596$	−365.823			−0.613798
$597$		0			0
$598$	−294.396	+	169.970i	−0.492301	+	0.284230i
$599$	436.794	+	756.549i	0.729205	+	1.26302i	0.957220	+	0.289363i	$0.0934434\pi$
$599$	436.794	+	756.549i	0.729205	+	1.26302i	−0.228014	+	0.973658i	$0.573223\pi$
$600$		0			0
$601$			198.982i			0.331085i	0.986203	+	0.165542i	$0.0529375\pi$
$601$			198.982i			0.331085i	−0.986203	+	0.165542i	$0.947063\pi$
$602$	−38.1630	+	148.470i	−0.0633936	+	0.246628i
$603$		0			0
$604$	288.794	−	500.206i	0.478136	−	0.828155i
$605$	−615.624	+	355.431i	−1.01756	+	0.587489i
$606$		0			0
$607$	137.654	+	79.4748i	0.226778	+	0.130930i	0.609085	−	0.793105i	$-0.291537\pi$
$607$	137.654	+	79.4748i	0.226778	+	0.130930i	−0.382307	+	0.924035i	$0.624870\pi$
$608$		−	96.2985i		−	0.158386i
$609$		0			0
$610$	477.588			0.782931
$611$	296.595	−	513.718i	0.485426	−	0.840782i
$612$		0			0
$613$	357.368	+	618.979i	0.582981	+	1.00975i	0.995124	+	0.0986338i	$0.0314473\pi$
$613$	357.368	+	618.979i	0.582981	+	1.00975i	−0.412143	+	0.911119i	$0.635219\pi$
$614$	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	$0.326626\pi$
$618$		0			0
$619$	148.978	−	86.0126i	0.240676	−	0.138954i	−0.374812	−	0.927101i	$-0.622293\pi$
$619$	148.978	−	86.0126i	0.240676	−	0.138954i	0.615487	+	0.788147i	$0.288959\pi$
$620$	123.338	+	213.628i	0.198932	+	0.344561i
$621$		0			0
$622$			571.619i			0.919002i
$623$	−140.912	−	36.2201i	−0.226182	−	0.0581382i
$624$		0			0
$625$	−135.588	+	234.846i	−0.216941	+	0.375753i
$626$	−160.805	+	92.8406i	−0.256876	+	0.148308i
$627$		0			0
$628$	−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
$633$		0			0
$634$	66.4264	+	115.054i	0.104774	+	0.181473i
$635$	−1212.61	−	700.100i	−1.90962	−	1.10252i
$636$		0			0
$637$	−453.044	−	748.968i	−0.711215	−	1.17577i
$638$	−288.000			−0.451411
$639$		0			0
$640$	−81.9411	+	47.3087i	−0.128033	+	0.0739199i
$641$	114.551	+	198.409i	0.178707	+	0.309530i	0.941438	−	0.337186i	$-0.109475\pi$
$641$	114.551	+	198.409i	0.178707	+	0.309530i	−0.762731	+	0.646716i	$0.776142\pi$
$642$		0			0
$643$			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	−0.583568	+	0.812064i	$0.698344\pi$
$647$	−1021.37	+	589.687i	−1.57862	+	0.911417i	−0.995052	+	0.0993530i	$0.968323\pi$
$648$		0			0
$649$	−142.191	−	82.0940i	−0.219092	−	0.126493i
$650$		−	1135.36i		−	1.74671i
$651$		0			0
$652$	32.1177			0.0492604
$653$	−77.3818	+	134.029i	−0.118502	+	0.205252i	−0.919174	−	0.393851i	$-0.871143\pi$
$653$	−77.3818	+	134.029i	−0.118502	+	0.205252i	0.800672	+	0.599103i	$0.204476\pi$
$654$		0			0
$655$	−7.45584	−	12.9139i	−0.0113830	−	0.0197159i
$656$	122.059	+	70.4707i	0.186065	+	0.107425i
$657$		0			0
$658$	−230.059	+	234.803i	−0.349634	+	0.356843i
$659$	−591.308			−0.897280			−0.448640	−	0.893712i	$-0.648092\pi$
$659$	−591.308			−0.897280			−0.448640	+	0.893712i	$0.648092\pi$
$660$		0			0
$661$	140.441	−	81.0837i	0.212468	−	0.122668i	−0.389990	−	0.920819i	$-0.627522\pi$
$661$	140.441	−	81.0837i	0.212468	−	0.122668i	0.602458	+	0.798151i	$0.294188\pi$
$662$	−184.815	−	320.109i	−0.279176	−	0.483548i
$663$		0			0
$664$			214.282i			0.322714i
$665$	−711.838	−	697.456i	−1.07043	−	1.04881i
$666$		0			0
$667$	−228.353	+	395.519i	−0.342359	+	0.592983i
$668$	305.044	−	176.117i	0.456652	−	0.263648i
$669$		0			0
$670$	−1171.73	−	676.497i	−1.74885	−	1.00970i
$671$		−	242.283i		−	0.361078i
$672$		0			0
$673$	42.3238			0.0628883			0.0314441	−	0.999506i	$-0.489989\pi$
$673$	42.3238			0.0628883			0.0314441	+	0.999506i	$0.489989\pi$
$674$	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	0.146937	−	0.989146i	$-0.453059\pi$
$677$	−430.721	−	248.677i	−0.636220	−	0.367322i	−0.783157	+	0.621824i	$0.786392\pi$
$678$		0			0
$679$	−57.5147	−	206.207i	−0.0847050	−	0.303693i
$680$	443.647			0.652422
$681$		0			0
$682$	108.375	−	62.5701i	0.158907	−	0.0917451i
$683$	608.080	+	1053.23i	0.890308	+	1.54206i	0.839506	+	0.543350i	$0.182844\pi$
$683$	608.080	+	1053.23i	0.890308	+	1.54206i	0.0508015	+	0.998709i	$0.483822\pi$
$684$		0			0
$685$		−	844.425i		−	1.23274i
$686$	139.830	+	464.484i	0.203834	+	0.677091i
$687$		0			0
$688$	−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	−0.360921	−	0.932596i	$-0.617538\pi$
$691$	−932.182	−	538.196i	−1.34903	−	0.778865i	−0.988113	+	0.153731i	$0.950871\pi$
$692$		−	462.305i		−	0.668070i
$693$		0			0
$694$	−455.647			−0.656552
$695$	−587.683	+	1017.90i	−0.845588	+	1.46460i
$696$		0			0
$697$	−330.426	−	572.315i	−0.474069	−	0.821112i
$698$	424.368	+	245.009i	0.607976	+	0.351015i
$699$		0			0
$700$	−156.632	+	609.367i	−0.223761	+	0.870525i
$701$	695.897			0.992720			0.496360	−	0.868117i	$-0.334670\pi$
$701$	695.897			0.992720			0.496360	+	0.868117i	$0.334670\pi$
$702$		0			0
$703$	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
$708$		0			0
$709$	−127.412	+	220.684i	−0.179707	+	0.311261i	−0.941780	−	0.336229i	$-0.890848\pi$
$709$	−127.412	+	220.684i	−0.179707	+	0.311261i	0.762073	+	0.647491i	$0.224182\pi$
$710$	190.544	−	110.011i	0.268372	−	0.154945i
$711$		0			0
$712$	−50.9117	−	29.3939i	−0.0715052	−	0.0412835i
$713$		−	198.446i		−	0.278325i
$714$		0			0
$715$	−896.382			−1.25368
$716$	−85.2792	+	147.708i	−0.119105	+	0.206296i
$717$		0			0
$718$	−14.3087	−	24.7833i	−0.0199285	−	0.0345172i
$719$	964.925	+	557.100i	1.34204	+	0.774826i	0.987106	−	0.160066i	$-0.0511709\pi$
$719$	964.925	+	557.100i	1.34204	+	0.774826i	0.354931	+	0.934892i	$0.384504\pi$
$720$		0			0
$721$	548.852	+	141.078i	0.761238	+	0.195669i
$722$	−100.701			−0.139474
$723$		0			0
$724$	−9.67619	+	5.58655i	−0.0133649	+	0.00771623i
$725$	−762.676	−	1320.99i	−1.05197	−	1.82206i
$726$		0			0
$727$		−	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
$729$		0			0
$730$	692.080	−	1198.72i	0.948055	−	1.64208i
$731$	251.522	−	145.216i	0.344079	−	0.198654i
$732$		0			0
$733$	818.514	+	472.569i	1.11666	+	0.644706i	0.940547	−	0.339663i	$-0.110313\pi$
$733$	818.514	+	472.569i	1.11666	+	0.644706i	0.176116	+	0.984369i	$0.443646\pi$
$734$			440.632i			0.600316i
$735$		0			0
$736$	76.1177			0.103421
$737$	−343.191	+	594.424i	−0.465659	+	0.806546i
$738$		0			0
$739$	−96.3162	−	166.825i	−0.130333	−	0.225744i	0.793472	−	0.608607i	$-0.208271\pi$
$739$	−96.3162	−	166.825i	−0.130333	−	0.225744i	−0.923805	+	0.382863i	$0.874938\pi$
$740$	−86.4853	−	49.9323i	−0.116872	−	0.0674761i
$741$		0			0
$742$	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	$0.289773\pi$
$744$		0			0
$745$	−1324.76	+	764.853i	−1.77821	+	1.02665i
$746$	−481.810	−	834.519i	−0.645858	−	1.11866i
$747$		0			0
$748$		−	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	−0.705684	−	0.708527i	$-0.749360\pi$
$751$	195.831	−	339.189i	0.260760	−	0.451650i	0.966444	+	0.256877i	$0.0826935\pi$
$752$	−115.029	+	66.4123i	−0.152965	+	0.0883142i
$753$		0			0
$754$	742.587	+	428.733i	0.984863	+	0.568611i
$755$		−	2415.21i		−	3.19895i
$756$		0			0
$757$	−152.823			−0.201879			−0.100940	−	0.994893i	$-0.532185\pi$
$757$	−152.823			−0.201879			−0.100940	+	0.994893i	$0.532185\pi$
$758$	−441.785	+	765.195i	−0.582830	+	1.00949i
$759$		0			0
$760$	−201.338	−	348.728i	−0.264919	−	0.458852i
$761$	109.331	+	63.1223i	0.143667	+	0.0829465i	0.570111	−	0.821568i	$-0.306900\pi$
$761$	109.331	+	63.1223i	0.143667	+	0.0829465i	−0.426443	+	0.904514i	$0.640234\pi$
$762$		0			0
$763$	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
$768$		0			0
$769$		−	369.148i		−	0.480037i	−0.970768	−	0.240018i	$-0.922847\pi$
$769$		−	369.148i		−	0.480037i	0.970768	−	0.240018i	$-0.0771535\pi$
$770$	481.103	+	123.663i	0.624809	+	0.160602i
$771$		0			0
$772$	−227.794	+	394.551i	−0.295070	+	0.511076i
$773$	1215.65	−	701.853i	1.57263	−	0.907961i	0.576789	−	0.816893i	$-0.304305\pi$
$773$	1215.65	−	701.853i	1.57263	−	0.907961i	0.995845	−	0.0910674i	$-0.0290279\pi$
$774$		0			0
$775$	573.992	+	331.394i	0.740634	+	0.427605i
$776$		−	86.5006i		−	0.111470i
$777$		0			0
$778$	−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
$783$		0			0
$784$	4.00000	+	195.959i	0.00510204	+	0.249948i
$785$	−1564.41			−1.99288
$786$		0			0
$787$	196.161	−	113.253i	0.249251	−	0.143905i	−0.370170	−	0.928964i	$-0.620701\pi$
$787$	196.161	−	113.253i	0.249251	−	0.143905i	0.619421	+	0.785059i	$0.287367\pi$
$788$	123.161	+	213.322i	0.156296	+	0.270713i
$789$		0			0
$790$			1044.79i			1.32252i
$791$	−117.302	+	32.7174i	−0.148295	+	0.0413621i
$792$		0			0
$793$	−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	$0.142149\pi$
$797$			688.414i			0.863756i	−0.901932	+	0.431878i	$0.857851\pi$
$798$		0			0
$799$	622.794			0.779467
$800$	−127.113	+	220.166i	−0.158891	+	0.275207i
$801$		0			0
$802$	194.985	+	337.724i	0.243123	+	0.421102i
$803$	−608.117	−	351.096i	−0.757306	−	0.437231i
$804$		0			0
$805$	551.294	−	562.662i	0.684837	−	0.698958i
$806$	−372.582			−0.462260
$807$		0			0
$808$	313.456	−	180.974i	0.387940	−	0.223977i
$809$	12.6396	+	21.8924i	0.0156237	+	0.0270611i	0.873732	−	0.486408i	$-0.161693\pi$
$809$	12.6396	+	21.8924i	0.0156237	+	0.0270611i	−0.858108	+	0.513470i	$0.828360\pi$
$810$		0			0
$811$			1527.62i			1.88362i	0.336145	+	0.941810i	$0.390877\pi$
$811$			1527.62i			1.88362i	−0.336145	+	0.941810i	$0.609123\pi$
$812$	−339.411	−	332.554i	−0.417994	−	0.409549i
$813$		0			0
$814$	−25.3310	+	43.8745i	−0.0311191	+	0.0538999i
$815$	116.309	−	67.1508i	0.142710	−	0.0823937i
$816$		0			0
$817$	−228.294	−	131.806i	−0.279430	−	0.161329i
$818$			616.359i			0.753495i
$819$		0			0
$820$	589.352			0.718722
$821$	−58.3310	+	101.032i	−0.0710487	+	0.123060i	−0.899361	−	0.437206i	$-0.855968\pi$
$821$	−58.3310	+	101.032i	−0.0710487	+	0.123060i	0.828312	+	0.560266i	$0.189301\pi$
$822$		0			0
$823$	−62.9554	−	109.042i	−0.0764950	−	0.132493i	0.825240	−	0.564782i	$-0.191040\pi$
$823$	−62.9554	−	109.042i	−0.0764950	−	0.132493i	−0.901735	+	0.432288i	$0.857706\pi$
$824$	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	$0.165899\pi$
$828$		0			0
$829$	−32.3225	+	18.6614i	−0.0389898	+	0.0225107i	−0.519368	−	0.854551i	$-0.673833\pi$
$829$	−32.3225	+	18.6614i	−0.0389898	+	0.0225107i	0.480378	+	0.877061i	$0.340499\pi$
$830$	448.014	+	775.984i	0.539776	+	0.934920i
$831$		0			0
$832$		−	142.911i		−	0.171768i
$833$	443.169	−	805.101i	0.532015	−	0.966508i
$834$		0			0
$835$	736.441	−	1275.55i	0.881965	−	1.52761i
$836$	−176.912	+	102.140i	−0.211617	+	0.122177i
$837$		0			0
$838$	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
$843$		0			0
$844$	124.912	+	216.353i	0.148000	+	0.256343i
$845$	1087.25	+	627.723i	1.28669	+	0.742868i
$846$		0			0
$847$	−148.124	+	576.267i	−0.174881	+	0.680363i
$848$	138.177			0.162944
$849$		0			0
$850$	1032.32	−	596.012i	1.21450	−	0.701191i
$851$	40.1695	+	69.5756i	0.0472027	+	0.0817574i
$852$		0			0
$853$		−	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	0.634033	−	0.773306i	$-0.281398\pi$
$857$	1388.98	−	801.931i	1.62075	−	0.935742i	0.986719	−	0.162436i	$-0.0519352\pi$
$858$		0			0
$859$	545.367	+	314.868i	0.634886	+	0.366551i	0.782642	−	0.622472i	$-0.213872\pi$
$859$	545.367	+	314.868i	0.634886	+	0.366551i	−0.147756	+	0.989024i	$0.547205\pi$
$860$			259.009i			0.301174i
$861$		0			0
$862$	−559.632			−0.649226
$863$	514.706	−	891.496i	0.596414	−	1.03302i	−0.396931	−	0.917848i	$-0.629925\pi$
$863$	514.706	−	891.496i	0.596414	−	1.03302i	0.993346	−	0.115172i	$-0.0367418\pi$
$864$		0			0
$865$	−966.573	−	1674.15i	−1.11743	−	1.93544i
$866$	−54.2176	−	31.3026i	−0.0626070	−	0.0361462i
$867$		0			0
$868$	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
$873$		0			0
$874$			323.944i			0.370646i
$875$	313.632	+	1124.47i	0.358437	+	1.28510i
$876$		0			0
$877$	−324.220	+	561.566i	−0.369693	+	0.640326i	−0.989517	−	0.144414i	$-0.953870\pi$
$877$	−324.220	+	561.566i	−0.369693	+	0.640326i	0.619825	+	0.784740i	$0.287204\pi$
$878$	487.279	−	281.331i	0.554988	−	0.320422i
$879$		0			0
$880$	173.823	+	100.357i	0.197527	+	0.114042i
$881$			363.857i			0.413005i	0.978446	+	0.206502i	$0.0662082\pi$
$881$			363.857i			0.413005i	−0.978446	+	0.206502i	$0.933792\pi$
$882$		0			0
$883$	1536.16			1.73971			0.869853	−	0.493312i	$-0.164214\pi$
$883$	1536.16			1.73971			0.869853	+	0.493312i	$0.164214\pi$
$884$	−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	−0.162964	−	0.986632i	$-0.552106\pi$
$887$	−974.720	−	562.755i	−1.09890	−	0.634447i	−0.935931	+	0.352185i	$0.885439\pi$
$888$		0			0
$889$	−1128.90	+	314.868i	−1.26985	+	0.354183i
$890$	−245.823			−0.276206
$891$		0			0
$892$	−396.000	+	228.631i	−0.443946	+	0.256312i
$893$	−282.640	−	489.546i	−0.316506	−	0.548204i
$894$		0			0
$895$			713.197i			0.796868i
$896$	−19.7157	+	76.7026i	−0.0220042	+	0.0856056i
$897$		0			0
$898$	−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
$903$		0			0
$904$	−49.2061			−0.0544315
$905$	−23.3604	+	40.4614i	−0.0258126	+	0.0447087i
$906$		0			0
$907$	−117.448	−	203.426i	−0.129491	−	0.224285i	0.793989	−	0.607933i	$-0.208001\pi$
$907$	−117.448	−	203.426i	−0.129491	−	0.224285i	−0.923479	+	0.383648i	$0.874668\pi$
$908$	−293.647	−	169.537i	−0.323400	−	0.186715i
$909$		0			0
$910$	−1056.40	−	1035.05i	−1.16087	−	1.13742i
$911$	−224.278			−0.246189			−0.123095	−	0.992395i	$-0.539282\pi$
$911$	−224.278			−0.246189			−0.123095	+	0.992395i	$0.539282\pi$
$912$		0			0
$913$	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
$918$		0			0
$919$	466.081	−	807.276i	0.507161	−	0.878428i	−0.492805	−	0.870140i	$-0.664028\pi$
$919$	466.081	−	807.276i	0.507161	−	0.878428i	0.999966	−	0.00828836i	$-0.00263830\pi$
$920$	275.647	−	159.145i	0.299616	−	0.172983i
$921$		0			0
$922$	−803.147	−	463.697i	−0.871092	−	0.502925i
$923$			332.322i			0.360046i
$924$		0			0
$925$	−268.324			−0.290080
$926$	614.756	−	1064.79i	0.663883	−	1.14988i
$927$		0			0
$928$	−96.0000	−	166.277i	−0.103448	−	0.179178i
$929$	618.390	+	357.028i	0.665651	+	0.384314i	0.794427	−	0.607360i	$-0.207771\pi$
$929$	618.390	+	357.028i	0.665651	+	0.384314i	−0.128776	+	0.991674i	$0.541105\pi$
$930$		0			0
$931$	−833.970	+	17.0233i	−0.895778	+	0.0182850i
$932$	508.971			0.546106
$933$		0			0
$934$	327.463	−	189.061i	0.350603	−	0.202421i
$935$	−470.558	−	815.031i	−0.503271	−	0.871691i
$936$		0			0
$937$		−	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
$939$		0			0
$940$	−277.706	+	481.000i	−0.295432	+	0.511702i
$941$	−835.508	+	482.381i	−0.887893	+	0.512625i	−0.873253	−	0.487267i	$-0.837994\pi$
$941$	−835.508	+	482.381i	−0.887893	+	0.512625i	−0.0146405	+	0.999893i	$0.504660\pi$
$942$		0			0
$943$	−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	−0.172940	−	0.984932i	$-0.555327\pi$
$947$	725.881	−	1257.26i	0.766506	−	1.32763i	0.939447	−	0.342695i	$-0.111340\pi$
$948$		0			0
$949$	1045.32	+	1810.55i	1.10150	+	1.90785i
$950$	−936.988	−	540.971i	−0.986304	−	0.569443i
$951$		0			0
$952$	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	$0.705632\pi$
$954$		0			0
$955$	−1342.76	+	775.245i	−1.40604	+	0.811775i
$956$	197.147	+	341.469i	0.206221	+	0.357185i
$957$		0			0
$958$			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
$963$		0			0
$964$	−153.235	−	88.4701i	−0.158957	−	0.0917739i
$965$			1905.06i			1.97415i
$966$		0			0
$967$	412.190			0.426257			0.213128	−	0.977024i	$-0.431635\pi$
$967$	412.190			0.426257			0.213128	+	0.977024i	$0.431635\pi$
$968$	−120.208	+	208.207i	−0.124182	+	0.215089i
$969$		0			0
$970$	−180.853	−	313.246i	−0.186446	−	0.322934i
$971$	−869.595	−	502.061i	−0.895566	−	0.517056i	−0.0198073	−	0.999804i	$-0.506305\pi$
$971$	−869.595	−	502.061i	−0.895566	−	0.517056i	−0.875759	+	0.482748i	$0.839639\pi$
$972$		0			0
$973$	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	−0.910889	−	0.412652i	$-0.864603\pi$
$977$	−794.117	−	1375.45i	−0.812812	−	1.40783i	0.0980772	−	0.995179i	$-0.468731\pi$
$978$		0			0
$979$			124.708i			0.127383i
$980$	424.191	+	701.268i	0.432848	+	0.715579i
$981$		0			0
$982$	287.397	−	497.786i	0.292665	−	0.506911i
$983$	−721.861	+	416.767i	−0.734345	+	0.423974i	−0.820009	−	0.572350i	$-0.806032\pi$
$983$	−721.861	+	416.767i	−0.734345	+	0.423974i	0.0856648	+	0.996324i	$0.472699\pi$
$984$		0			0
$985$	892.014	+	515.005i	0.905598	+	0.522847i
$986$			900.259i			0.913041i
$987$		0			0
$988$	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	0.848656	−	0.528945i	$-0.177412\pi$
$991$	−33.4483	−	57.9341i	−0.0337520	−	0.0584602i	−0.882408	+	0.470485i	$0.844079\pi$
$992$	72.2498	+	41.7134i	0.0728324	+	0.0420498i
$993$		0			0
$994$	45.8465	−	178.363i	0.0461233	−	0.179439i
$995$	−52.1177			−0.0523796
$996$		0			0
$997$	1268.65	−	732.453i	1.27246	−	0.734657i	0.297012	−	0.954874i	$-0.404010\pi$
$997$	1268.65	−	732.453i	1.27246	−	0.734657i	0.975451	+	0.220217i	$0.0706765\pi$
$998$	−262.638	−	454.903i	−0.263164	−	0.455814i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	126.3.n.a.19.2		4
3.2	odd	2		42.3.g.a.19.1	✓	4
4.3	odd	2		1008.3.cg.h.145.1		4
7.2	even	3		882.3.c.b.685.2		4
7.3	odd	6	inner	126.3.n.a.73.2		4
7.4	even	3		882.3.n.e.325.2		4
7.5	odd	6		882.3.c.b.685.1		4
7.6	odd	2		882.3.n.e.19.2		4
12.11	even	2		336.3.bh.e.145.2		4
15.2	even	4		1050.3.q.a.649.1		8
15.8	even	4		1050.3.q.a.649.4		8
15.14	odd	2		1050.3.p.a.901.2		4
21.2	odd	6		294.3.c.a.97.4		4
21.5	even	6		294.3.c.a.97.3		4
21.11	odd	6		294.3.g.a.31.1		4
21.17	even	6		42.3.g.a.31.1	yes	4
21.20	even	2		294.3.g.a.19.1		4
28.3	even	6		1008.3.cg.h.577.1		4
84.23	even	6		2352.3.f.e.97.1		4
84.47	odd	6		2352.3.f.e.97.4		4
84.59	odd	6		336.3.bh.e.241.2		4
105.17	odd	12		1050.3.q.a.199.4		8
105.38	odd	12		1050.3.q.a.199.1		8
105.59	even	6		1050.3.p.a.451.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.3.g.a.19.1	✓	4	3.2	odd	2
42.3.g.a.31.1	yes	4	21.17	even	6
126.3.n.a.19.2		4	1.1	even	1	trivial
126.3.n.a.73.2		4	7.3	odd	6	inner
294.3.c.a.97.3		4	21.5	even	6
294.3.c.a.97.4		4	21.2	odd	6
294.3.g.a.19.1		4	21.20	even	2
294.3.g.a.31.1		4	21.11	odd	6
336.3.bh.e.145.2		4	12.11	even	2
336.3.bh.e.241.2		4	84.59	odd	6
882.3.c.b.685.1		4	7.5	odd	6
882.3.c.b.685.2		4	7.2	even	3
882.3.n.e.19.2		4	7.6	odd	2
882.3.n.e.325.2		4	7.4	even	3
1008.3.cg.h.145.1		4	4.3	odd	2
1008.3.cg.h.577.1		4	28.3	even	6
1050.3.p.a.451.2		4	105.59	even	6
1050.3.p.a.901.2		4	15.14	odd	2
1050.3.q.a.199.1		8	105.38	odd	12
1050.3.q.a.199.4		8	105.17	odd	12
1050.3.q.a.649.1		8	15.2	even	4
1050.3.q.a.649.4		8	15.8	even	4
2352.3.f.e.97.1		4	84.23	even	6
2352.3.f.e.97.4		4	84.47	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:	\( N \)	\(=\)	\( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	126.n (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 - 1.22474i) q^{2} +(-1.00000 - 1.73205i) q^{4} +(-7.24264 - 4.18154i) q^{5} +(-6.74264 + 1.88064i) q^{7} -2.82843 q^{8} +O(q^{10})\)	\(q+(0.707107 - 1.22474i) q^{2} +(-1.00000 - 1.73205i) q^{4} +(-7.24264 - 4.18154i) q^{5} +(-6.74264 + 1.88064i) q^{7} -2.82843 q^{8} +(-10.2426 + 5.91359i) q^{10} +(3.00000 + 5.19615i) q^{11} -17.8639i q^{13} +(-2.46447 + 9.58783i) q^{14} +(-2.00000 + 3.46410i) q^{16} +(16.2426 - 9.37769i) q^{17} +(-14.7426 - 8.51167i) q^{19} +16.7262i q^{20} +8.48528 q^{22} +(6.72792 - 11.6531i) q^{23} +(22.4706 + 38.9202i) q^{25} +(-21.8787 - 12.6317i) q^{26} +(10.0000 + 9.79796i) q^{28} -33.9411 q^{29} +(12.7721 - 7.37396i) q^{31} +(2.82843 + 4.89898i) q^{32} -26.5241i q^{34} +(56.6985 + 14.5738i) q^{35} +(-2.98528 + 5.17066i) q^{37} +(-20.8492 + 12.0373i) q^{38} +(20.4853 + 11.8272i) q^{40} -35.2354i q^{41} +15.4853 q^{43} +(6.00000 - 10.3923i) q^{44} +(-9.51472 - 16.4800i) q^{46} +(28.7574 + 16.6031i) q^{47} +(41.9264 - 25.3609i) q^{49} +63.5563 q^{50} +(-30.9411 + 17.8639i) q^{52} +(-17.2721 - 29.9161i) q^{53} -50.1785i q^{55} +(19.0711 - 5.31925i) q^{56} +(-24.0000 + 41.5692i) q^{58} +(-23.6985 + 13.6823i) q^{59} +(-34.9706 - 20.1903i) q^{61} -20.8567i q^{62} +8.00000 q^{64} +(-74.6985 + 129.382i) q^{65} +(57.1985 + 99.0707i) q^{67} +(-32.4853 - 18.7554i) q^{68} +(57.9411 - 59.1359i) q^{70} -18.6030 q^{71} +(-101.353 + 58.5161i) q^{73} +(4.22183 + 7.31242i) q^{74} +34.0467i q^{76} +(-30.0000 - 29.3939i) q^{77} +(44.1690 - 76.5030i) q^{79} +(28.9706 - 16.7262i) q^{80} +(-43.1543 - 24.9152i) q^{82} -75.7601i q^{83} -156.853 q^{85} +(10.9497 - 18.9655i) q^{86} +(-8.48528 - 14.6969i) q^{88} +(18.0000 + 10.3923i) q^{89} +(33.5955 + 120.450i) q^{91} -26.9117 q^{92} +(40.6690 - 23.4803i) q^{94} +(71.1838 + 123.294i) q^{95} +30.5826i q^{97} +(-1.41421 - 69.2820i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{4} - 12 q^{5} - 10 q^{7}+O(q^{10}) \) 4 * q - 4 * q^4 - 12 * q^5 - 10 * q^7	\( 4 q - 4 q^{4} - 12 q^{5} - 10 q^{7} - 24 q^{10} + 12 q^{11} - 24 q^{14} - 8 q^{16} + 48 q^{17} - 42 q^{19} - 24 q^{23} + 22 q^{25} - 96 q^{26} + 40 q^{28} + 102 q^{31} + 108 q^{35} + 22 q^{37} - 24 q^{38} + 48 q^{40} + 28 q^{43} + 24 q^{44} - 72 q^{46} + 132 q^{47} - 2 q^{49} + 192 q^{50} + 12 q^{52} - 120 q^{53} + 48 q^{56} - 96 q^{58} + 24 q^{59} - 72 q^{61} + 32 q^{64} - 180 q^{65} + 110 q^{67} - 96 q^{68} + 96 q^{70} - 312 q^{71} - 66 q^{73} + 48 q^{74} - 120 q^{77} - 10 q^{79} + 48 q^{80} + 48 q^{82} - 288 q^{85} + 24 q^{86} + 72 q^{89} - 222 q^{91} + 96 q^{92} - 24 q^{94} + 132 q^{95}+O(q^{100}) \) 4 * q - 4 * q^4 - 12 * q^5 - 10 * q^7 - 24 * q^10 + 12 * q^11 - 24 * q^14 - 8 * q^16 + 48 * q^17 - 42 * q^19 - 24 * q^23 + 22 * q^25 - 96 * q^26 + 40 * q^28 + 102 * q^31 + 108 * q^35 + 22 * q^37 - 24 * q^38 + 48 * q^40 + 28 * q^43 + 24 * q^44 - 72 * q^46 + 132 * q^47 - 2 * q^49 + 192 * q^50 + 12 * q^52 - 120 * q^53 + 48 * q^56 - 96 * q^58 + 24 * q^59 - 72 * q^61 + 32 * q^64 - 180 * q^65 + 110 * q^67 - 96 * q^68 + 96 * q^70 - 312 * q^71 - 66 * q^73 + 48 * q^74 - 120 * q^77 - 10 * q^79 + 48 * q^80 + 48 * q^82 - 288 * q^85 + 24 * q^86 + 72 * q^89 - 222 * q^91 + 96 * q^92 - 24 * q^94 + 132 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more