LMFDB - Embedded newform 126.3.n.a.73.1

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			73.1
Root			$-0.707107 - 1.22474i$ of defining polynomial
Character	$\chi$	$=$	126.73
Dual form			126.3.n.a.19.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 - 1.22474i) q^{2} +(-1.00000 + 1.73205i) q^{4} +(1.24264 - 0.717439i) q^{5} +(1.74264 - 6.77962i) q^{7} +2.82843 q^{8} +O(q^{10})$	\(q+(-0.707107 - 1.22474i) q^{2} +(-1.00000 + 1.73205i) q^{4} +(1.24264 - 0.717439i) q^{5} +(1.74264 - 6.77962i) q^{7} +2.82843 q^{8} +(-1.75736 - 1.01461i) q^{10} +(3.00000 - 5.19615i) q^{11} -21.3280i q^{13} +(-9.53553 + 2.65962i) q^{14} +(-2.00000 - 3.46410i) q^{16} +(7.75736 + 4.47871i) q^{17} +(-6.25736 + 3.61269i) q^{19} +2.86976i q^{20} -8.48528 q^{22} +(-18.7279 - 32.4377i) q^{23} +(-11.4706 + 19.8676i) q^{25} +(-26.1213 + 15.0812i) q^{26} +(10.0000 + 9.79796i) q^{28} +33.9411 q^{29} +(38.2279 + 22.0709i) q^{31} +(-2.82843 + 4.89898i) q^{32} -12.6677i q^{34} +(-2.69848 - 9.67487i) q^{35} +(13.9853 + 24.2232i) q^{37} +(8.84924 + 5.10911i) q^{38} +(3.51472 - 2.02922i) q^{40} +54.8313i q^{41} -1.48528 q^{43} +(6.00000 + 10.3923i) q^{44} +(-26.4853 + 45.8739i) q^{46} +(37.2426 - 21.5020i) q^{47} +(-42.9264 - 23.6289i) q^{49} +32.4437 q^{50} +(36.9411 + 21.3280i) q^{52} +(-42.7279 + 74.0069i) q^{53} -8.60927i q^{55} +(4.92893 - 19.1757i) q^{56} +(-24.0000 - 41.5692i) q^{58} +(35.6985 + 20.6105i) q^{59} +(-1.02944 + 0.594346i) q^{61} -62.4259i q^{62} +8.00000 q^{64} +(-15.3015 - 26.5030i) q^{65} +(-2.19848 + 3.80789i) q^{67} +(-15.5147 + 8.95743i) q^{68} +(-9.94113 + 10.1461i) q^{70} -137.397 q^{71} +(68.3528 + 39.4635i) q^{73} +(19.7782 - 34.2568i) q^{74} -14.4508i q^{76} +(-30.0000 - 29.3939i) q^{77} +(-49.1690 - 85.1633i) q^{79} +(-4.97056 - 2.86976i) q^{80} +(67.1543 - 38.7716i) q^{82} -110.401i q^{83} +12.8528 q^{85} +(1.05025 + 1.81909i) q^{86} +(8.48528 - 14.6969i) q^{88} +(18.0000 - 10.3923i) q^{89} +(-144.595 - 37.1670i) q^{91} +74.9117 q^{92} +(-52.6690 - 30.4085i) q^{94} +(-5.18377 + 8.97855i) q^{95} -10.9867i q^{97} +(1.41421 + 69.2820i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/126\mathbb{Z}\right)^\times$.

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

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
$5$	1.24264	−	0.717439i	0.248528	−	0.143488i	−0.370562	−	0.928808i	$-0.620835\pi$
$5$	1.24264	−	0.717439i	0.248528	−	0.143488i	0.619090	+	0.785320i	$0.287502\pi$
$6$		0			0
$7$	1.74264	−	6.77962i	0.248949	−	0.968517i
$7$	1.74264	−	6.77962i	0.248949	−	0.968517i
$8$	2.82843			0.353553
$9$		0			0
$10$	−1.75736	−	1.01461i	−0.175736	−	0.101461i
$11$	3.00000	−	5.19615i	0.272727	−	0.472377i	−0.696832	−	0.717234i	$-0.745408\pi$
$11$	3.00000	−	5.19615i	0.272727	−	0.472377i	0.969559	+	0.244857i	$0.0787410\pi$
$12$		0			0
$13$		−	21.3280i		−	1.64061i	−0.571924	−	0.820306i	$-0.693803\pi$
$13$		−	21.3280i		−	1.64061i	0.571924	−	0.820306i	$-0.306197\pi$
$14$	−9.53553	+	2.65962i	−0.681110	+	0.189973i
$15$		0			0
$16$	−2.00000	−	3.46410i	−0.125000	−	0.216506i
$17$	7.75736	+	4.47871i	0.456315	+	0.263454i	0.710494	−	0.703704i	$-0.248472\pi$
$17$	7.75736	+	4.47871i	0.456315	+	0.263454i	−0.254178	+	0.967157i	$0.581805\pi$
$18$		0			0
$19$	−6.25736	+	3.61269i	−0.329335	+	0.190141i	−0.655546	−	0.755156i	$-0.727561\pi$
$19$	−6.25736	+	3.61269i	−0.329335	+	0.190141i	0.326211	+	0.945297i	$0.394228\pi$
$20$			2.86976i			0.143488i
$21$		0			0
$22$	−8.48528			−0.385695
$23$	−18.7279	−	32.4377i	−0.814257	−	1.41034i	−0.909860	−	0.414916i	$-0.863811\pi$
$23$	−18.7279	−	32.4377i	−0.814257	−	1.41034i	0.0956024	−	0.995420i	$-0.469522\pi$
$24$		0			0
$25$	−11.4706	+	19.8676i	−0.458823	+	0.794704i
$26$	−26.1213	+	15.0812i	−1.00467	+	0.580044i
$27$		0			0
$28$	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
$31$	38.2279	+	22.0709i	1.23316	+	0.711965i	0.967687	−	0.252154i	$-0.0811390\pi$
$31$	38.2279	+	22.0709i	1.23316	+	0.711965i	0.265472	+	0.964119i	$0.414472\pi$
$32$	−2.82843	+	4.89898i	−0.0883883	+	0.153093i
$33$		0			0
$34$		−	12.6677i		−	0.372580i
$35$	−2.69848	−	9.67487i	−0.0770996	−	0.276425i
$36$		0			0
$37$	13.9853	+	24.2232i	0.377981	+	0.654682i	0.990768	−	0.135566i	$-0.0432853\pi$
$37$	13.9853	+	24.2232i	0.377981	+	0.654682i	−0.612788	+	0.790248i	$0.709952\pi$
$38$	8.84924	+	5.10911i	0.232875	+	0.134450i
$39$		0			0
$40$	3.51472	−	2.02922i	0.0878680	−	0.0507306i
$41$			54.8313i			1.33735i	0.743556	+	0.668674i	$0.233138\pi$
$41$			54.8313i			1.33735i	−0.743556	+	0.668674i	$0.766862\pi$
$42$		0			0
$43$	−1.48528			−0.0345414			−0.0172707	−	0.999851i	$-0.505498\pi$
$43$	−1.48528			−0.0345414			−0.0172707	+	0.999851i	$0.505498\pi$
$44$	6.00000	+	10.3923i	0.136364	+	0.236189i
$45$		0			0
$46$	−26.4853	+	45.8739i	−0.575767	+	0.997258i
$47$	37.2426	−	21.5020i	0.792397	−	0.457490i	−0.0484090	−	0.998828i	$-0.515415\pi$
$47$	37.2426	−	21.5020i	0.792397	−	0.457490i	0.840806	+	0.541337i	$0.182082\pi$
$48$		0			0
$49$	−42.9264	−	23.6289i	−0.876049	−	0.482222i
$50$	32.4437			0.648873
$51$		0			0
$52$	36.9411	+	21.3280i	0.710406	+	0.410153i
$53$	−42.7279	+	74.0069i	−0.806187	+	1.39636i	0.109299	+	0.994009i	$0.465139\pi$
$53$	−42.7279	+	74.0069i	−0.806187	+	1.39636i	−0.915487	+	0.402348i	$0.868194\pi$
$54$		0			0
$55$		−	8.60927i		−	0.156532i
$56$	4.92893	−	19.1757i	0.0880166	−	0.342422i
$57$		0			0
$58$	−24.0000	−	41.5692i	−0.413793	−	0.716711i
$59$	35.6985	+	20.6105i	0.605059	+	0.349331i	0.771029	−	0.636800i	$-0.219742\pi$
$59$	35.6985	+	20.6105i	0.605059	+	0.349331i	−0.165970	+	0.986131i	$0.553076\pi$
$60$		0			0
$61$	−1.02944	+	0.594346i	−0.0168760	+	0.00974337i	−0.508414	−	0.861113i	$-0.669768\pi$
$61$	−1.02944	+	0.594346i	−0.0168760	+	0.00974337i	0.491538	+	0.870856i	$0.336435\pi$
$62$		−	62.4259i		−	1.00687i
$63$		0			0
$64$	8.00000			0.125000
$65$	−15.3015	−	26.5030i	−0.235408	−	0.407738i
$66$		0			0
$67$	−2.19848	+	3.80789i	−0.0328132	+	0.0568341i	−0.881966	−	0.471314i	$-0.843780\pi$
$67$	−2.19848	+	3.80789i	−0.0328132	+	0.0568341i	0.849152	+	0.528148i	$0.177113\pi$
$68$	−15.5147	+	8.95743i	−0.228158	+	0.131727i
$69$		0			0
$70$	−9.94113	+	10.1461i	−0.142016	+	0.144945i
$71$	−137.397			−1.93517			−0.967584	−	0.252548i	$-0.918731\pi$
$71$	−137.397			−1.93517			−0.967584	+	0.252548i	$0.918731\pi$
$72$		0			0
$73$	68.3528	+	39.4635i	0.936340	+	0.540596i	0.888811	−	0.458274i	$-0.151532\pi$
$73$	68.3528	+	39.4635i	0.936340	+	0.540596i	0.0475288	+	0.998870i	$0.484865\pi$
$74$	19.7782	−	34.2568i	0.267273	−	0.462930i
$75$		0			0
$76$		−	14.4508i		−	0.190141i
$77$	−30.0000	−	29.3939i	−0.389610	−	0.381739i
$78$		0			0
$79$	−49.1690	−	85.1633i	−0.622393	−	1.07802i	−0.989039	−	0.147656i	$-0.952827\pi$
$79$	−49.1690	−	85.1633i	−0.622393	−	1.07802i	0.366646	−	0.930361i	$-0.380506\pi$
$80$	−4.97056	−	2.86976i	−0.0621320	−	0.0358719i
$81$		0			0
$82$	67.1543	−	38.7716i	0.818955	−	0.472824i
$83$		−	110.401i		−	1.33013i	−0.746784	−	0.665067i	$-0.768403\pi$
$83$		−	110.401i		−	1.33013i	0.746784	−	0.665067i	$-0.231597\pi$
$84$		0			0
$85$	12.8528			0.151210
$86$	1.05025	+	1.81909i	0.0122122	+	0.0211522i
$87$		0			0
$88$	8.48528	−	14.6969i	0.0964237	−	0.167011i
$89$	18.0000	−	10.3923i	0.202247	−	0.116767i	−0.395456	−	0.918485i	$-0.629413\pi$
$89$	18.0000	−	10.3923i	0.202247	−	0.116767i	0.597703	+	0.801717i	$0.296080\pi$
$90$		0			0
$91$	−144.595	−	37.1670i	−1.58896	−	0.408428i
$92$	74.9117			0.814257
$93$		0			0
$94$	−52.6690	−	30.4085i	−0.560309	−	0.323495i
$95$	−5.18377	+	8.97855i	−0.0545660	+	0.0945110i
$96$		0			0
$97$		−	10.9867i		−	0.113264i	−0.998395	−	0.0566322i	$-0.981964\pi$
$97$		−	10.9867i		−	0.113264i	0.998395	−	0.0566322i	$-0.0180362\pi$
$98$	1.41421	+	69.2820i	0.0144308	+	0.706960i
$99$		0			0
$100$	−22.9411	−	39.7352i	−0.229411	−	0.397352i
$101$	92.8234	+	53.5916i	0.919043	+	0.530610i	0.883330	−	0.468752i	$-0.155296\pi$
$101$	92.8234	+	53.5916i	0.919043	+	0.530610i	0.0357136	+	0.999362i	$0.488630\pi$
$102$		0			0
$103$	91.1102	−	52.6025i	0.884565	−	0.510704i	0.0124040	−	0.999923i	$-0.496052\pi$
$103$	91.1102	−	52.6025i	0.884565	−	0.510704i	0.872161	+	0.489219i	$0.162718\pi$
$104$		−	60.3246i		−	0.580044i
$105$		0			0
$106$	120.853			1.14012
$107$	59.2721	+	102.662i	0.553945	+	0.959460i	0.997985	+	0.0634534i	$0.0202114\pi$
$107$	59.2721	+	102.662i	0.553945	+	0.959460i	−0.444040	+	0.896007i	$0.646455\pi$
$108$		0			0
$109$	−55.5294	+	96.1798i	−0.509444	+	0.882384i	0.490496	+	0.871444i	$0.336816\pi$
$109$	−55.5294	+	96.1798i	−0.509444	+	0.882384i	−0.999940	+	0.0109400i	$0.996518\pi$
$110$	−10.5442	+	6.08767i	−0.0958560	+	0.0553425i
$111$		0			0
$112$	−26.9706	+	7.52255i	−0.240809	+	0.0671656i
$113$	−101.397			−0.897318			−0.448659	−	0.893703i	$-0.648098\pi$
$113$	−101.397			−0.897318			−0.448659	+	0.893703i	$0.648098\pi$
$114$		0			0
$115$	−46.5442	−	26.8723i	−0.404732	−	0.233672i
$116$	−33.9411	+	58.7878i	−0.292596	+	0.506791i
$117$		0			0
$118$		−	58.2954i		−	0.494029i
$119$	43.8823	−	44.7871i	0.368758	−	0.376362i
$120$		0			0
$121$	42.5000	+	73.6122i	0.351240	+	0.608365i
$122$	1.45584	+	0.840532i	0.0119331	+	0.00688961i
$123$		0			0
$124$	−76.4558	+	44.1418i	−0.616579	+	0.355982i
$125$			68.7897i			0.550317i
$126$		0			0
$127$	82.5736			0.650186			0.325093	−	0.945682i	$-0.394604\pi$
$127$	82.5736			0.650186			0.325093	+	0.945682i	$0.394604\pi$
$128$	−5.65685	−	9.79796i	−0.0441942	−	0.0765466i
$129$		0			0
$130$	−21.6396	+	37.4809i	−0.166459	+	0.288315i
$131$	52.4558	−	30.2854i	0.400426	−	0.231186i	−0.286242	−	0.958157i	$-0.592406\pi$
$131$	52.4558	−	30.2854i	0.400426	−	0.231186i	0.686668	+	0.726971i	$0.259073\pi$
$132$		0			0
$133$	13.5883	+	48.7181i	0.102168	+	0.366302i
$134$	6.21825			0.0464049
$135$		0			0
$136$	21.9411	+	12.6677i	0.161332	+	0.0931450i
$137$	33.5147	−	58.0492i	0.244633	−	0.423717i	−0.717395	−	0.696666i	$-0.754666\pi$
$137$	33.5147	−	58.0492i	0.244633	−	0.423717i	0.962028	+	0.272949i	$0.0879992\pi$
$138$		0			0
$139$			91.5525i			0.658651i	0.944216	+	0.329326i	$0.106821\pi$
$139$			91.5525i			0.658651i	−0.944216	+	0.329326i	$0.893179\pi$
$140$	19.4558	+	5.00095i	0.138970	+	0.0357211i
$141$		0			0
$142$	97.1543	+	168.276i	0.684185	+	1.18504i
$143$	−110.823	−	63.9839i	−0.774989	−	0.447440i
$144$		0			0
$145$	42.1766	−	24.3507i	0.290873	−	0.167936i
$146$		−	111.620i		−	0.764518i
$147$		0			0
$148$	−55.9411			−0.377981
$149$	40.5442	+	70.2245i	0.272108	+	0.471306i	0.969402	−	0.245480i	$-0.0789457\pi$
$149$	40.5442	+	70.2245i	0.272108	+	0.471306i	−0.697293	+	0.716786i	$0.745612\pi$
$150$		0			0
$151$	25.6030	−	44.3457i	0.169556	−	0.293680i	−0.768708	−	0.639600i	$-0.779100\pi$
$151$	25.6030	−	44.3457i	0.169556	−	0.293680i	0.938264	+	0.345920i	$0.112433\pi$
$152$	−17.6985	+	10.2182i	−0.116437	+	0.0672252i
$153$		0			0
$154$	−14.7868	+	57.5270i	−0.0960182	+	0.373552i
$155$	63.3381			0.408633
$156$		0			0
$157$	162.000	+	93.5307i	1.03185	+	0.595737i	0.917513	−	0.397705i	$-0.130193\pi$
$157$	162.000	+	93.5307i	1.03185	+	0.595737i	0.114334	+	0.993442i	$0.463527\pi$
$158$	−69.5355	+	120.439i	−0.440098	+	0.762273i
$159$		0			0
$160$			8.11689i			0.0507306i
$161$	−252.551	+	70.4409i	−1.56864	+	0.437521i
$162$		0			0
$163$	−41.9706	−	72.6951i	−0.257488	−	0.445982i	0.708080	−	0.706132i	$-0.249561\pi$
$163$	−41.9706	−	72.6951i	−0.257488	−	0.445982i	−0.965568	+	0.260149i	$0.916228\pi$
$164$	−94.9706	−	54.8313i	−0.579089	−	0.334337i
$165$		0			0
$166$	−135.213	+	78.0654i	−0.814537	+	0.470273i
$167$			127.620i			0.764190i	0.924123	+	0.382095i	$0.124797\pi$
$167$			127.620i			0.764190i	−0.924123	+	0.382095i	$0.875203\pi$
$168$		0			0
$169$	−285.882			−1.69161
$170$	−9.08831	−	15.7414i	−0.0534607	−	0.0925966i
$171$		0			0
$172$	1.48528	−	2.57258i	0.00863536	−	0.0149569i
$173$	123.816	−	71.4853i	0.715701	−	0.413210i	−0.0974675	−	0.995239i	$-0.531074\pi$
$173$	123.816	−	71.4853i	0.715701	−	0.413210i	0.813168	+	0.582029i	$0.197741\pi$
$174$		0			0
$175$	114.706	+	112.388i	0.655461	+	0.642218i
$176$	−24.0000			−0.136364
$177$		0			0
$178$	−25.4558	−	14.6969i	−0.143010	−	0.0825671i
$179$	84.6396	−	146.600i	0.472847	−	0.818995i	−0.526670	−	0.850070i	$-0.676560\pi$
$179$	84.6396	−	146.600i	0.472847	−	0.818995i	0.999517	+	0.0310748i	$0.00989300\pi$
$180$		0			0
$181$		−	209.969i		−	1.16005i	−0.814600	−	0.580024i	$-0.803043\pi$
$181$		−	209.969i		−	1.16005i	0.814600	−	0.580024i	$-0.196957\pi$
$182$	56.7244	+	203.374i	0.311672	+	1.11744i
$183$		0			0
$184$	−52.9706	−	91.7477i	−0.287883	−	0.498629i
$185$	34.7574	+	20.0672i	0.187878	+	0.108471i
$186$		0			0
$187$	46.5442	−	26.8723i	0.248899	−	0.143702i
$188$			86.0082i			0.457490i
$189$		0			0
$190$	14.6619			0.0771679
$191$	33.3015	+	57.6799i	0.174353	+	0.301989i	0.939937	−	0.341347i	$-0.110883\pi$
$191$	33.3015	+	57.6799i	0.174353	+	0.301989i	−0.765584	+	0.643336i	$0.777550\pi$
$192$		0			0
$193$	4.89697	−	8.48180i	0.0253729	−	0.0439472i	−0.853060	−	0.521813i	$-0.825256\pi$
$193$	4.89697	−	8.48180i	0.0253729	−	0.0439472i	0.878433	+	0.477865i	$0.158589\pi$
$194$	−13.4558	+	7.76874i	−0.0693600	+	0.0400450i
$195$		0			0
$196$	83.8528	−	50.7218i	0.427820	−	0.258785i
$197$	267.161			1.35615			0.678075	−	0.734993i	$-0.262815\pi$
$197$	267.161			1.35615			0.678075	+	0.734993i	$0.262815\pi$
$198$		0			0
$199$	−113.397	−	65.4698i	−0.569834	−	0.328994i	0.187249	−	0.982312i	$-0.440043\pi$
$199$	−113.397	−	65.4698i	−0.569834	−	0.328994i	−0.757083	+	0.653319i	$0.773376\pi$
$200$	−32.4437	+	56.1941i	−0.162218	+	0.280970i
$201$		0			0
$202$		−	151.580i		−	0.750396i
$203$	59.1472	−	230.108i	0.291365	−	1.13354i
$204$		0			0
$205$	39.3381	+	68.1356i	0.191893	+	0.332369i
$206$	−128.849	−	74.3911i	−0.625482	−	0.361122i
$207$		0			0
$208$	−73.8823	+	42.6559i	−0.355203	+	0.205077i
$209$			43.3523i			0.207427i
$210$		0			0
$211$	−23.0883			−0.109423			−0.0547116	−	0.998502i	$-0.517424\pi$
$211$	−23.0883			−0.109423			−0.0547116	+	0.998502i	$0.517424\pi$
$212$	−85.4558	−	148.014i	−0.403094	−	0.698179i
$213$		0			0
$214$	83.8234	−	145.186i	0.391698	−	0.678441i
$215$	−1.84567	+	1.06560i	−0.00858452	+	0.00495627i
$216$		0			0
$217$	216.250	−	220.709i	0.996543	−	1.01709i
$218$	157.061			0.720463
$219$		0			0
$220$	14.9117	+	8.60927i	0.0677804	+	0.0391330i
$221$	95.5219	−	165.449i	0.432226	−	0.748637i
$222$		0			0
$223$			228.631i			1.02525i	0.858613	+	0.512625i	$0.171327\pi$
$223$			228.631i			1.02525i	−0.858613	+	0.512625i	$0.828673\pi$
$224$	28.2843	+	27.7128i	0.126269	+	0.123718i
$225$		0			0
$226$	71.6985	+	124.185i	0.317250	+	0.549493i
$227$	−56.8234	−	32.8070i	−0.250323	−	0.144524i	0.369589	−	0.929195i	$-0.379498\pi$
$227$	−56.8234	−	32.8070i	−0.250323	−	0.144524i	−0.619912	+	0.784671i	$0.712832\pi$
$228$		0			0
$229$	80.9558	−	46.7399i	0.353519	−	0.204104i	−0.312715	−	0.949847i	$-0.601239\pi$
$229$	80.9558	−	46.7399i	0.353519	−	0.204104i	0.666234	+	0.745743i	$0.267905\pi$
$230$			76.0063i			0.330462i
$231$		0			0
$232$	96.0000			0.413793
$233$	−118.757	−	205.694i	−0.509688	−	0.882806i	−0.999937	−	0.0112234i	$-0.996427\pi$
$233$	−118.757	−	205.694i	−0.509688	−	0.882806i	0.490249	−	0.871583i	$-0.336906\pi$
$234$		0			0
$235$	30.8528	−	53.4386i	0.131289	−	0.227398i
$236$	−71.3970	+	41.2211i	−0.302530	+	0.174666i
$237$		0			0
$238$	−85.8823	−	22.0753i	−0.360850	−	0.0927533i
$239$	−366.853			−1.53495			−0.767475	−	0.641079i	$-0.778487\pi$
$239$	−366.853			−1.53495			−0.767475	+	0.641079i	$0.778487\pi$
$240$		0			0
$241$	−364.617	−	210.512i	−1.51293	−	0.873493i	−0.999885	−	0.0151343i	$-0.995182\pi$
$241$	−364.617	−	210.512i	−1.51293	−	0.873493i	−0.513049	−	0.858359i	$-0.671484\pi$
$242$	60.1041	−	104.103i	0.248364	−	0.430179i
$243$		0			0
$244$		−	2.37738i		−	0.00974337i
$245$	−70.2944	+	1.43488i	−0.286916	+	0.00585664i
$246$		0			0
$247$	77.0513	+	133.457i	0.311949	+	0.540311i
$248$	108.125	+	62.4259i	0.435987	+	0.251717i
$249$		0			0
$250$	84.2498	−	48.6416i	0.336999	−	0.194567i
$251$			146.621i			0.584148i	0.956396	+	0.292074i	$0.0943454\pi$
$251$			146.621i			0.584148i	−0.956396	+	0.292074i	$0.905655\pi$
$252$		0			0
$253$	−224.735			−0.888281
$254$	−58.3883	−	101.132i	−0.229875	−	0.398156i
$255$		0			0
$256$	−8.00000	+	13.8564i	−0.0312500	+	0.0541266i
$257$	−21.7279	+	12.5446i	−0.0845444	+	0.0488118i	−0.541676	−	0.840587i	$-0.682210\pi$
$257$	−21.7279	+	12.5446i	−0.0845444	+	0.0488118i	0.457132	+	0.889399i	$0.348877\pi$
$258$		0			0
$259$	188.595	−	52.6025i	0.728168	−	0.203098i
$260$	61.2061			0.235408
$261$		0			0
$262$	−74.1838	−	42.8300i	−0.283144	−	0.163473i
$263$	−45.3381	+	78.5279i	−0.172388	+	0.298585i	−0.939254	−	0.343222i	$-0.888482\pi$
$263$	−45.3381	+	78.5279i	−0.172388	+	0.298585i	0.766866	+	0.641807i	$0.221815\pi$
$264$		0			0
$265$			122.619i			0.462712i
$266$	50.0589	−	51.0911i	0.188191	−	0.192072i
$267$		0			0
$268$	−4.39697	−	7.61577i	−0.0164066	−	0.0284171i
$269$	59.2355	+	34.1996i	0.220206	+	0.127136i	0.606046	−	0.795430i	$-0.292755\pi$
$269$	59.2355	+	34.1996i	0.220206	+	0.127136i	−0.385839	+	0.922566i	$0.626088\pi$
$270$		0			0
$271$	−106.971	+	61.7595i	−0.394725	+	0.227895i	−0.684206	−	0.729289i	$-0.739851\pi$
$271$	−106.971	+	61.7595i	−0.394725	+	0.227895i	0.289480	+	0.957184i	$0.406518\pi$
$272$		−	35.8297i		−	0.131727i
$273$		0			0
$274$	−94.7939			−0.345963
$275$	68.8234	+	119.206i	0.250267	+	0.433475i
$276$		0			0
$277$	136.441	−	236.323i	0.492567	−	0.853151i	−0.507396	−	0.861713i	$-0.669392\pi$
$277$	136.441	−	236.323i	0.492567	−	0.853151i	0.999963	+	0.00856145i	$0.00272523\pi$
$278$	112.128	−	64.7374i	0.403340	−	0.232868i
$279$		0			0
$280$	−7.63247	−	27.3647i	−0.0272588	−	0.0977309i
$281$	−133.103			−0.473675			−0.236837	−	0.971549i	$-0.576111\pi$
$281$	−133.103			−0.473675			−0.236837	+	0.971549i	$0.576111\pi$
$282$		0			0
$283$	−111.507	−	64.3787i	−0.394018	−	0.227486i	0.289882	−	0.957063i	$-0.406384\pi$
$283$	−111.507	−	64.3787i	−0.394018	−	0.227486i	−0.683900	+	0.729576i	$0.739717\pi$
$284$	137.397	−	237.979i	0.483792	−	0.837953i
$285$		0			0
$286$			180.974i			0.632776i
$287$	371.735	+	95.5512i	1.29524	+	0.332931i
$288$		0			0
$289$	−104.382	−	180.795i	−0.361184	−	0.625589i
$290$	−59.6468	−	34.4371i	−0.205678	−	0.118749i
$291$		0			0
$292$	−136.706	+	78.9270i	−0.468170	+	0.270298i
$293$			308.984i			1.05455i	0.849694	+	0.527276i	$0.176787\pi$
$293$			308.984i			1.05455i	−0.849694	+	0.527276i	$0.823213\pi$
$294$		0			0
$295$	59.1472			0.200499
$296$	39.5563	+	68.5136i	0.133636	+	0.231465i
$297$		0			0
$298$	57.3381	−	99.3125i	0.192410	−	0.333263i
$299$	−691.831	+	399.429i	−2.31381	+	1.33588i
$300$		0			0
$301$	−2.58831	+	10.0696i	−0.00859904	+	0.0334539i
$302$	−72.4163			−0.239789
$303$		0			0
$304$	25.0294	+	14.4508i	0.0823337	+	0.0475354i
$305$	−0.852814	+	1.47712i	−0.00279611	+	0.00484301i
$306$		0			0
$307$			606.090i			1.97423i	0.160003	+	0.987117i	$0.448850\pi$
$307$			606.090i			1.97423i	−0.160003	+	0.987117i	$0.551150\pi$
$308$	80.9117	−	22.5676i	0.262700	−	0.0732716i
$309$		0			0
$310$	−44.7868	−	77.5730i	−0.144474	−	0.250236i
$311$	176.044	+	101.639i	0.566057	+	0.326813i	0.755573	−	0.655064i	$-0.227359\pi$
$311$	176.044	+	101.639i	0.566057	+	0.326813i	−0.189516	+	0.981878i	$0.560692\pi$
$312$		0			0
$313$	−351.294	+	202.820i	−1.12234	+	0.647986i	−0.941999	−	0.335617i	$-0.891055\pi$
$313$	−351.294	+	202.820i	−1.12234	+	0.647986i	−0.180346	+	0.983603i	$0.557722\pi$
$314$		−	264.545i		−	0.842500i
$315$		0			0
$316$	196.676			0.622393
$317$	−13.0294	−	22.5676i	−0.0411023	−	0.0711913i	0.844742	−	0.535173i	$-0.179754\pi$
$317$	−13.0294	−	22.5676i	−0.0411023	−	0.0711913i	−0.885845	+	0.463982i	$0.846420\pi$
$318$		0			0
$319$	101.823	−	176.363i	0.319196	−	0.552863i
$320$	9.94113	−	5.73951i	0.0310660	−	0.0179360i
$321$		0			0
$322$	264.853	+	259.502i	0.822524	+	0.805906i
$323$	−64.7208			−0.200374
$324$		0			0
$325$	423.735	+	244.644i	1.30380	+	0.752750i
$326$	−59.3553	+	102.806i	−0.182072	+	0.315357i
$327$		0			0
$328$			155.086i			0.472824i
$329$	−80.8751	−	289.961i	−0.245821	−	0.881341i
$330$		0			0
$331$	54.3162	+	94.0785i	0.164097	+	0.284225i	0.936334	−	0.351110i	$-0.114196\pi$
$331$	54.3162	+	94.0785i	0.164097	+	0.284225i	−0.772237	+	0.635335i	$0.780862\pi$
$332$	191.220	+	110.401i	0.575965	+	0.332533i
$333$		0			0
$334$	156.302	−	90.2407i	0.467969	−	0.270182i
$335$			6.30911i			0.0188332i
$336$		0			0
$337$	441.735			1.31079			0.655393	−	0.755288i	$-0.272503\pi$
$337$	441.735			1.31079			0.655393	+	0.755288i	$0.272503\pi$
$338$	202.149	+	350.133i	0.598075	+	1.03590i
$339$		0			0
$340$	−12.8528	+	22.2617i	−0.0378024	+	0.0654757i
$341$	229.368	−	132.425i	0.672632	−	0.388344i
$342$		0			0
$343$	−235.000	+	249.848i	−0.685131	+	0.728420i
$344$	−4.20101			−0.0122122
$345$		0			0
$346$	−175.103	−	101.096i	−0.506077	−	0.292184i
$347$	17.0955	−	29.6102i	0.0492664	−	0.0853320i	−0.840341	−	0.542059i	$-0.817645\pi$
$347$	17.0955	−	29.6102i	0.0492664	−	0.0853320i	0.889607	+	0.456727i	$0.150978\pi$
$348$		0			0
$349$			221.787i			0.635493i	0.948176	+	0.317746i	$0.102926\pi$
$349$			221.787i			0.635493i	−0.948176	+	0.317746i	$0.897074\pi$
$350$	56.5376	−	219.956i	0.161536	−	0.628444i
$351$		0			0
$352$	16.9706	+	29.3939i	0.0482118	+	0.0835053i
$353$	−387.448	−	223.693i	−1.09759	−	0.633692i	−0.162000	−	0.986791i	$-0.551794\pi$
$353$	−387.448	−	223.693i	−1.09759	−	0.633692i	−0.935586	+	0.353099i	$0.885128\pi$
$354$		0			0
$355$	−170.735	+	98.5739i	−0.480944	+	0.277673i
$356$			41.5692i			0.116767i
$357$		0			0
$358$	−239.397			−0.668707
$359$	145.882	+	252.675i	0.406357	+	0.703831i	0.994478	−	0.104941i	$-0.0334655\pi$
$359$	145.882	+	252.675i	0.406357	+	0.703831i	−0.588121	+	0.808773i	$0.700132\pi$
$360$		0			0
$361$	−154.397	+	267.423i	−0.427692	+	0.740785i
$362$	−257.158	+	148.470i	−0.710381	+	0.410139i
$363$		0			0
$364$	208.971	−	213.280i	0.574095	−	0.585933i
$365$	113.251			0.310276
$366$		0			0
$367$	−363.169	−	209.676i	−0.989561	−	0.571324i	−0.0844183	−	0.996430i	$-0.526903\pi$
$367$	−363.169	−	209.676i	−0.989561	−	0.571324i	−0.905143	+	0.425107i	$0.860237\pi$
$368$	−74.9117	+	129.751i	−0.203564	+	0.352584i
$369$		0			0
$370$		−	56.7585i		−	0.153401i
$371$	427.279	+	418.646i	1.15170	+	1.12843i
$372$		0			0
$373$	−15.6909	−	27.1775i	−0.0420668	−	0.0728618i	0.844225	−	0.535988i	$-0.180061\pi$
$373$	−15.6909	−	27.1775i	−0.0420668	−	0.0728618i	−0.886292	+	0.463127i	$0.846728\pi$
$374$	−65.8234	−	38.0031i	−0.175998	−	0.101613i
$375$		0			0
$376$	105.338	−	60.8170i	0.280155	−	0.161747i
$377$		−	723.895i		−	1.92015i
$378$		0			0
$379$	206.779			0.545590			0.272795	−	0.962072i	$-0.412052\pi$
$379$	206.779			0.545590			0.272795	+	0.962072i	$0.412052\pi$
$380$	−10.3675	−	17.9571i	−0.0272830	−	0.0472555i
$381$		0			0
$382$	47.0955	−	81.5717i	0.123287	−	0.213539i
$383$	431.772	−	249.283i	1.12734	−	0.650871i	0.184076	−	0.982912i	$-0.441071\pi$
$383$	431.772	−	249.283i	1.12734	−	0.650871i	0.943265	+	0.332041i	$0.107737\pi$
$384$		0			0
$385$	−58.3675	−	15.0029i	−0.151604	−	0.0389685i
$386$	−13.8507			−0.0358827
$387$		0			0
$388$	19.0294	+	10.9867i	0.0490449	+	0.0283161i
$389$	−324.213	+	561.554i	−0.833453	+	1.44358i	0.0618308	+	0.998087i	$0.480306\pi$
$389$	−324.213	+	561.554i	−0.833453	+	1.44358i	−0.895284	+	0.445496i	$0.853027\pi$
$390$		0			0
$391$		−	335.508i		−	0.858077i
$392$	−121.414	−	66.8325i	−0.309730	−	0.170491i
$393$		0			0
$394$	−188.912	−	327.205i	−0.479471	−	0.830469i
$395$	−122.199	−	70.5516i	−0.309364	−	0.178612i
$396$		0			0
$397$	65.6026	−	37.8757i	0.165246	−	0.0954047i	−0.415096	−	0.909777i	$-0.636252\pi$
$397$	65.6026	−	37.8757i	0.165246	−	0.0954047i	0.580342	+	0.814373i	$0.302919\pi$
$398$			185.176i			0.465268i
$399$		0			0
$400$	91.7645			0.229411
$401$	−282.125	−	488.655i	−0.703553	−	1.21859i	−0.967211	−	0.253974i	$-0.918262\pi$
$401$	−282.125	−	488.655i	−0.703553	−	1.21859i	0.263658	−	0.964616i	$-0.415071\pi$
$402$		0			0
$403$	470.727	−	815.324i	1.16806	−	2.02314i
$404$	−185.647	+	107.183i	−0.459522	+	0.265305i
$405$		0			0
$406$	−323.647	+	90.2706i	−0.797159	+	0.222341i
$407$	167.823			0.412342
$408$		0			0
$409$	−309.559	−	178.724i	−0.756868	−	0.436978i	0.0713023	−	0.997455i	$-0.477284\pi$
$409$	−309.559	−	178.724i	−0.756868	−	0.436978i	−0.828170	+	0.560477i	$0.810618\pi$
$410$	55.6325	−	96.3583i	0.135689	−	0.235020i
$411$		0			0
$412$			210.410i			0.510704i
$413$	201.941	−	206.105i	0.488962	−	0.499044i
$414$		0			0
$415$	−79.2061	−	137.189i	−0.190858	−	0.330576i
$416$	104.485	+	60.3246i	0.251167	+	0.145011i
$417$		0			0
$418$	53.0955	−	30.6547i	0.127023	−	0.0733365i
$419$			502.175i			1.19851i	0.800559	+	0.599254i	$0.204536\pi$
$419$			502.175i			1.19851i	−0.800559	+	0.599254i	$0.795464\pi$
$420$		0			0
$421$	33.7939			0.0802706			0.0401353	−	0.999194i	$-0.487221\pi$
$421$	33.7939			0.0802706			0.0401353	+	0.999194i	$0.487221\pi$
$422$	16.3259	+	28.2773i	0.0386870	+	0.0670078i
$423$		0			0
$424$	−120.853	+	209.323i	−0.285030	+	0.493687i
$425$	−177.963	+	102.747i	−0.418735	+	0.241757i
$426$		0			0
$427$	2.23550	+	8.01492i	0.00523536	+	0.0187703i
$428$	−237.088			−0.553945
$429$		0			0
$430$	2.61017	+	1.50698i	0.00607017	+	0.00350461i
$431$	251.860	−	436.234i	0.584362	−	1.01214i	−0.410593	−	0.911819i	$-0.634678\pi$
$431$	251.860	−	436.234i	0.584362	−	1.01214i	0.994955	−	0.100326i	$-0.0319884\pi$
$432$		0			0
$433$		−	837.548i		−	1.93429i	−0.254224	−	0.967145i	$-0.581820\pi$
$433$		−	837.548i		−	1.93429i	0.254224	−	0.967145i	$-0.418180\pi$
$434$	−423.224	−	108.786i	−0.975170	−	0.250659i
$435$		0			0
$436$	−111.059	−	192.360i	−0.254722	−	0.441192i
$437$	234.375	+	135.316i	0.536326	+	0.309648i
$438$		0			0
$439$	−164.558	+	95.0079i	−0.374848	+	0.216419i	−0.675575	−	0.737292i	$-0.736104\pi$
$439$	−164.558	+	95.0079i	−0.374848	+	0.216419i	0.300726	+	0.953711i	$0.402771\pi$
$440$		−	24.3507i		−	0.0553425i
$441$		0			0
$442$	−270.177			−0.611259
$443$	−84.7279	−	146.753i	−0.191259	−	0.331271i	0.754408	−	0.656405i	$-0.227924\pi$
$443$	−84.7279	−	146.753i	−0.191259	−	0.331271i	−0.945668	+	0.325134i	$0.894591\pi$
$444$		0			0
$445$	14.9117	−	25.8278i	0.0335094	−	0.0580400i
$446$	280.014	−	161.666i	0.627835	−	0.362481i
$447$		0			0
$448$	13.9411	−	54.2369i	0.0311186	−	0.121065i
$449$	−18.1035			−0.0403195			−0.0201598	−	0.999797i	$-0.506417\pi$
$449$	−18.1035			−0.0403195			−0.0201598	+	0.999797i	$0.506417\pi$
$450$		0			0
$451$	284.912	+	164.494i	0.631733	+	0.364731i
$452$	101.397	−	175.625i	0.224330	−	0.388550i
$453$		0			0
$454$			92.7922i			0.204388i
$455$	−206.345	+	57.5532i	−0.453506	+	0.126491i
$456$		0			0
$457$	164.412	+	284.769i	0.359763	+	0.623128i	0.987921	−	0.154958i	$-0.0495242\pi$
$457$	164.412	+	284.769i	0.359763	+	0.623128i	−0.628158	+	0.778086i	$0.716191\pi$
$458$	−114.489	−	66.1002i	−0.249976	−	0.144324i
$459$		0			0
$460$	93.0883	−	53.7446i	0.202366	−	0.116836i
$461$		−	794.331i		−	1.72306i	−0.507706	−	0.861530i	$-0.669506\pi$
$461$		−	794.331i		−	1.72306i	0.507706	−	0.861530i	$-0.330494\pi$
$462$		0			0
$463$	−403.396			−0.871266			−0.435633	−	0.900124i	$-0.643475\pi$
$463$	−403.396			−0.871266			−0.435633	+	0.900124i	$0.643475\pi$
$464$	−67.8823	−	117.576i	−0.146298	−	0.253395i
$465$		0			0
$466$	−167.948	+	290.895i	−0.360404	+	0.624238i
$467$	2.44870	−	1.41376i	0.00524347	−	0.00302732i	−0.497376	−	0.867535i	$-0.665703\pi$
$467$	2.44870	−	1.41376i	0.00524347	−	0.00302732i	0.502619	+	0.864508i	$0.332370\pi$
$468$		0			0
$469$	21.9848	+	21.5407i	0.0468760	+	0.0459289i
$470$	−87.2649			−0.185670
$471$		0			0
$472$	100.971	+	58.2954i	0.213921	+	0.123507i
$473$	−4.45584	+	7.71775i	−0.00942039	+	0.0163166i
$474$		0			0
$475$		−	165.758i		−	0.348965i
$476$	33.6913	+	120.793i	0.0707801	+	0.253768i
$477$		0			0
$478$	259.404	+	449.301i	0.542686	+	0.939960i
$479$	−328.669	−	189.757i	−0.686157	−	0.396153i	0.116014	−	0.993248i	$-0.462988\pi$
$479$	−328.669	−	189.757i	−0.686157	−	0.396153i	−0.802171	+	0.597095i	$0.796322\pi$
$480$		0			0
$481$	516.632	−	298.278i	1.07408	−	0.620120i
$482$			595.418i			1.23531i
$483$		0			0
$484$	−170.000			−0.351240
$485$	−7.88225	−	13.6525i	−0.0162521	−	0.0281494i
$486$		0			0
$487$	−287.757	+	498.410i	−0.590877	+	1.02343i	0.403238	+	0.915095i	$0.367885\pi$
$487$	−287.757	+	498.410i	−0.590877	+	1.02343i	−0.994115	+	0.108333i	$0.965449\pi$
$488$	−2.91169	+	1.68106i	−0.00596657	+	0.00344480i
$489$		0			0
$490$	51.4630	+	85.0781i	0.105027	+	0.173629i
$491$	−238.441			−0.485623			−0.242811	−	0.970074i	$-0.578070\pi$
$491$	−238.441			−0.485623			−0.242811	+	0.970074i	$0.578070\pi$
$492$		0			0
$493$	263.294	+	152.013i	0.534064	+	0.308342i
$494$	108.967	−	188.736i	0.220581	−	0.382057i
$495$		0			0
$496$		−	176.567i		−	0.355982i
$497$	−239.434	+	931.499i	−0.481758	+	1.87424i
$498$		0			0
$499$	143.287	+	248.180i	0.287148	+	0.497355i	0.973128	−	0.230266i	$-0.0739595\pi$
$499$	143.287	+	248.180i	0.287148	+	0.497355i	−0.685980	+	0.727620i	$0.740626\pi$
$500$	−119.147	−	68.7897i	−0.238294	−	0.137579i
$501$		0			0
$502$	179.574	−	103.677i	0.357716	−	0.206528i
$503$			25.4374i			0.0505714i	0.999680	+	0.0252857i	$0.00804954\pi$
$503$			25.4374i			0.0505714i	−0.999680	+	0.0252857i	$0.991950\pi$
$504$		0			0
$505$	153.795			0.304544
$506$	158.912	+	275.243i	0.314055	+	0.543959i
$507$		0			0
$508$	−82.5736	+	143.022i	−0.162546	+	0.281539i
$509$	697.889	−	402.926i	1.37110	−	0.791603i	0.380031	−	0.924974i	$-0.375913\pi$
$509$	697.889	−	402.926i	1.37110	−	0.791603i	0.991066	+	0.133370i	$0.0425800\pi$
$510$		0			0
$511$	386.662	−	394.635i	0.756677	−	0.772280i
$512$	22.6274			0.0441942
$513$		0			0
$514$	30.7279	+	17.7408i	0.0597819	+	0.0345151i
$515$	75.4781	−	130.732i	0.146559	−	0.253848i
$516$		0			0
$517$		−	258.025i		−	0.499080i
$518$	−197.782	−	193.786i	−0.381818	−	0.374104i
$519$		0			0
$520$	−43.2792	−	74.9618i	−0.0832293	−	0.144157i
$521$	661.706	+	382.036i	1.27007	+	0.733274i	0.975001	−	0.222202i	$-0.0713244\pi$
$521$	661.706	+	382.036i	1.27007	+	0.733274i	0.295068	+	0.955476i	$0.404658\pi$
$522$		0			0
$523$	−153.096	+	88.3900i	−0.292726	+	0.169006i	−0.639171	−	0.769065i	$-0.720722\pi$
$523$	−153.096	+	88.3900i	−0.292726	+	0.169006i	0.346444	+	0.938071i	$0.387389\pi$
$524$			121.142i			0.231186i
$525$		0			0
$526$	128.235			0.243794
$527$	197.698	+	342.424i	0.375139	+	0.649761i
$528$		0			0
$529$	−436.970	+	756.854i	−0.826030	+	1.43073i
$530$	150.177	−	86.7045i	0.283352	−	0.163593i
$531$		0			0
$532$	−97.9706	−	25.1825i	−0.184155	−	0.0473355i
$533$	1169.44			2.19407
$534$		0			0
$535$	147.308	+	85.0482i	0.275342	+	0.158969i
$536$	−6.21825	+	10.7703i	−0.0116012	+	0.0200939i
$537$		0			0
$538$		−	96.7312i		−	0.179798i
$539$	−251.558	+	152.166i	−0.466713	+	0.282311i
$540$		0			0
$541$	−8.58831	−	14.8754i	−0.0158749	−	0.0274961i	0.857979	−	0.513685i	$-0.171720\pi$
$541$	−8.58831	−	14.8754i	−0.0158749	−	0.0274961i	−0.873854	+	0.486189i	$0.838387\pi$
$542$	151.279	+	87.3411i	0.279113	+	0.161146i
$543$		0			0
$544$	−43.8823	+	25.3354i	−0.0806659	+	0.0465725i
$545$			159.356i			0.292396i
$546$		0			0
$547$	212.676			0.388805			0.194402	−	0.980922i	$-0.437723\pi$
$547$	212.676			0.388805			0.194402	+	0.980922i	$0.437723\pi$
$548$	67.0294	+	116.098i	0.122316	+	0.211858i
$549$		0			0
$550$	97.3310	−	168.582i	0.176965	−	0.306513i
$551$	−212.382	+	122.619i	−0.385448	+	0.222538i
$552$		0			0
$553$	−663.058	+	184.938i	−1.19902	+	0.334427i
$554$	−385.914			−0.696595
$555$		0			0
$556$	−158.574	−	91.5525i	−0.285204	−	0.164663i
$557$	−440.823	+	763.528i	−0.791424	+	1.37079i	0.133661	+	0.991027i	$0.457327\pi$
$557$	−440.823	+	763.528i	−0.791424	+	1.37079i	−0.925085	+	0.379760i	$0.876007\pi$
$558$		0			0
$559$			31.6780i			0.0566691i
$560$	−28.1177	+	28.6976i	−0.0502103	+	0.0512456i
$561$		0			0
$562$	94.1177	+	163.017i	0.167469	+	0.290065i
$563$	−664.301	−	383.534i	−1.17993	−	0.681233i	−0.223932	−	0.974605i	$-0.571889\pi$
$563$	−664.301	−	383.534i	−1.17993	−	0.681233i	−0.955998	+	0.293372i	$0.905223\pi$
$564$		0			0
$565$	−126.000	+	72.7461i	−0.223009	+	0.128754i
$566$			182.090i			0.321714i
$567$		0			0
$568$	−388.617			−0.684185
$569$	−14.6468	−	25.3689i	−0.0257412	−	0.0445851i	0.852868	−	0.522127i	$-0.174861\pi$
$569$	−14.6468	−	25.3689i	−0.0257412	−	0.0445851i	−0.878609	+	0.477542i	$0.841528\pi$
$570$		0			0
$571$	−482.521	+	835.752i	−0.845046	+	1.46366i	0.0405347	+	0.999178i	$0.487094\pi$
$571$	−482.521	+	835.752i	−0.845046	+	1.46366i	−0.885581	+	0.464485i	$0.846239\pi$
$572$	221.647	−	127.968i	0.387494	−	0.223720i
$573$		0			0
$574$	−145.831	−	522.846i	−0.254060	−	0.910881i
$575$	859.279			1.49440
$576$		0			0
$577$	227.883	+	131.568i	0.394944	+	0.228021i	0.684300	−	0.729201i	$-0.260108\pi$
$577$	227.883	+	131.568i	0.394944	+	0.228021i	−0.289356	+	0.957222i	$0.593441\pi$
$578$	−147.619	+	255.683i	−0.255396	+	0.442359i
$579$		0			0
$580$			97.4027i			0.167936i
$581$	−748.477	−	192.389i	−1.28826	−	0.331135i
$582$		0			0
$583$	256.368	+	444.042i	0.439738	+	0.761649i
$584$	193.331	+	111.620i	0.331046	+	0.191130i
$585$		0			0
$586$	378.426	−	218.485i	0.645779	−	0.372841i
$587$		−	436.477i		−	0.743572i	−0.928318	−	0.371786i	$-0.878746\pi$
$587$		−	436.477i		−	0.743572i	0.928318	−	0.371786i	$-0.121254\pi$
$588$		0			0
$589$	−318.941			−0.541496
$590$	−41.8234	−	72.4402i	−0.0708871	−	0.122780i
$591$		0			0
$592$	55.9411	−	96.8929i	0.0944951	−	0.163670i
$593$	−603.603	+	348.490i	−1.01788	+	0.587673i	−0.913489	−	0.406863i	$-0.866623\pi$
$593$	−603.603	+	348.490i	−1.01788	+	0.587673i	−0.104391	+	0.994536i	$0.533289\pi$
$594$		0			0
$595$	22.3978	−	87.1372i	0.0376434	−	0.146449i
$596$	−162.177			−0.272108
$597$		0			0
$598$	978.396	+	564.877i	1.63611	+	0.944611i
$599$	199.206	−	345.035i	0.332564	−	0.576018i	−0.650450	−	0.759549i	$-0.725419\pi$
$599$	199.206	−	345.035i	0.332564	−	0.576018i	0.983014	+	0.183531i	$0.0587528\pi$
$600$		0			0
$601$			36.1691i			0.0601816i	0.999547	+	0.0300908i	$0.00957964\pi$
$601$			36.1691i			0.0601816i	−0.999547	+	0.0300908i	$0.990420\pi$
$602$	14.1630	−	3.95029i	0.0235265	−	0.00656194i
$603$		0			0
$604$	51.2061	+	88.6915i	0.0847782	+	0.146840i
$605$	105.624	+	60.9823i	0.174586	+	0.100797i
$606$		0			0
$607$	27.3457	−	15.7880i	0.0450505	−	0.0260099i	−0.477306	−	0.878737i	$-0.658387\pi$
$607$	27.3457	−	15.7880i	0.0450505	−	0.0260099i	0.522356	+	0.852727i	$0.325053\pi$
$608$		−	40.8729i		−	0.0672252i
$609$		0			0
$610$	2.41212			0.00395430
$611$	−458.595	−	794.310i	−0.750565	−	1.30002i
$612$		0			0
$613$	204.632	−	354.434i	0.333821	−	0.578195i	−0.649436	−	0.760416i	$-0.724995\pi$
$613$	204.632	−	354.434i	0.333821	−	0.578195i	0.983258	+	0.182220i	$0.0583285\pi$
$614$	742.305	−	428.570i	1.20897	−	0.697997i
$615$		0			0
$616$	−84.8528	−	83.1384i	−0.137748	−	0.134965i
$617$	−1227.38			−1.98927			−0.994636	−	0.103436i	$-0.967016\pi$
$617$	−1227.38			−1.98927			−0.994636	+	0.103436i	$0.967016\pi$
$618$		0			0
$619$	412.022	+	237.881i	0.665625	+	0.384299i	0.794417	−	0.607373i	$-0.207777\pi$
$619$	412.022	+	237.881i	0.665625	+	0.384299i	−0.128792	+	0.991672i	$0.541110\pi$
$620$	−63.3381	+	109.705i	−0.102158	+	0.176943i
$621$		0			0
$622$		−	287.478i		−	0.462184i
$623$	−39.0883	−	140.143i	−0.0627421	−	0.224949i
$624$		0			0
$625$	−237.412	−	411.209i	−0.379859	−	0.657935i
$626$	496.805	+	286.830i	0.793618	+	0.458195i
$627$		0			0
$628$	−324.000	+	187.061i	−0.515924	+	0.297869i
$629$			250.544i			0.398322i
$630$		0			0
$631$	−54.9420			−0.0870713			−0.0435357	−	0.999052i	$-0.513862\pi$
$631$	−54.9420			−0.0870713			−0.0435357	+	0.999052i	$0.513862\pi$
$632$	−139.071	−	240.878i	−0.220049	−	0.381136i
$633$		0			0
$634$	−18.4264	+	31.9155i	−0.0290637	+	0.0503399i
$635$	102.609	−	59.2415i	0.161589	−	0.0932937i
$636$		0			0
$637$	−503.956	+	915.533i	−0.791139	+	1.43726i
$638$	−288.000			−0.451411
$639$		0			0
$640$	−14.0589	−	8.11689i	−0.0219670	−	0.0126826i
$641$	−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	$0.223858\pi$
$642$		0			0
$643$		−	854.640i		−	1.32914i	−0.747224	−	0.664572i	$-0.768614\pi$
$643$		−	854.640i		−	1.32914i	0.747224	−	0.664572i	$-0.231386\pi$
$644$	130.544	−	507.873i	0.202708	−	0.788622i
$645$		0			0
$646$	45.7645	+	79.2664i	0.0708429	+	0.122703i
$647$	−868.632	−	501.505i	−1.34255	−	0.775124i	−0.355372	−	0.934725i	$-0.615646\pi$
$647$	−868.632	−	501.505i	−1.34255	−	0.775124i	−0.987182	+	0.159601i	$0.948979\pi$
$648$		0			0
$649$	214.191	−	123.663i	0.330032	−	0.190544i
$650$		−	691.957i		−	1.06455i
$651$		0			0
$652$	167.882			0.257488
$653$	635.382	+	1100.51i	0.973020	+	1.68532i	0.686321	+	0.727299i	$0.259224\pi$
$653$	635.382	+	1100.51i	0.973020	+	1.68532i	0.286698	+	0.958021i	$0.407442\pi$
$654$		0			0
$655$	43.4558	−	75.2677i	0.0663448	−	0.114913i
$656$	189.941	−	109.663i	0.289544	−	0.167169i
$657$		0			0
$658$	−297.941	+	304.085i	−0.452798	+	0.462135i
$659$	783.308			1.18863			0.594315	−	0.804232i	$-0.297423\pi$
$659$	783.308			1.18863			0.594315	+	0.804232i	$0.297423\pi$
$660$		0			0
$661$	72.5589	+	41.8919i	0.109771	+	0.0633765i	0.553881	−	0.832596i	$-0.313146\pi$
$661$	72.5589	+	41.8919i	0.109771	+	0.0633765i	−0.444109	+	0.895973i	$0.646480\pi$
$662$	76.8148	−	133.047i	0.116034	−	0.200977i
$663$		0			0
$664$		−	312.262i		−	0.470273i
$665$	51.8377	+	50.7903i	0.0779514	+	0.0763764i
$666$		0			0
$667$	−635.647	−	1100.97i	−0.952994	−	1.65063i
$668$	−221.044	−	127.620i	−0.330904	−	0.191047i
$669$		0			0
$670$	7.72706	−	4.46122i	0.0115329	−	0.00665853i
$671$			7.13215i			0.0106291i
$672$		0			0
$673$	415.676			0.617647			0.308823	−	0.951119i	$-0.400065\pi$
$673$	415.676			0.617647			0.308823	+	0.951119i	$0.400065\pi$
$674$	−312.354	−	541.013i	−0.463433	−	0.802690i
$675$		0			0
$676$	285.882	−	495.163i	0.422903	−	0.732489i
$677$	−685.279	+	395.646i	−1.01223	+	0.584411i	−0.911844	−	0.410538i	$-0.865341\pi$
$677$	−685.279	+	395.646i	−1.01223	+	0.584411i	−0.100386	+	0.994949i	$0.532008\pi$
$678$		0			0
$679$	−74.4853	−	19.1458i	−0.109698	−	0.0281970i
$680$	36.3532			0.0534607
$681$		0			0
$682$	−324.375	−	187.278i	−0.475623	−	0.274601i
$683$	−164.080	+	284.195i	−0.240235	+	0.416099i	−0.960781	−	0.277308i	$-0.910558\pi$
$683$	−164.080	+	284.195i	−0.240235	+	0.416099i	0.720546	+	0.693407i	$0.243891\pi$
$684$		0			0
$685$		−	96.1791i		−	0.140407i
$686$	472.170	+	111.146i	0.688295	+	0.162020i
$687$		0			0
$688$	2.97056	+	5.14517i	0.00431768	+	0.00747844i
$689$	1578.42	+	911.300i	2.29088	+	1.32264i
$690$		0			0
$691$	875.182	−	505.287i	1.26654	−	0.731240i	0.292212	−	0.956353i	$-0.405609\pi$
$691$	875.182	−	505.287i	1.26654	−	0.731240i	0.974333	+	0.225113i	$0.0722753\pi$
$692$			285.941i			0.413210i
$693$		0			0
$694$	−48.3532			−0.0696733
$695$	65.6833	+	113.767i	0.0945084	+	0.163693i
$696$		0			0
$697$	−245.574	+	425.346i	−0.352329	+	0.610252i
$698$	271.632	−	156.827i	0.389158	−	0.224681i
$699$		0			0
$700$	−309.368	+	86.2879i	−0.441954	+	0.123268i
$701$	0.103464			0.000147594			7.37972e−5	−	1.00000i	$-0.499977\pi$
$701$	0.103464			0.000147594			7.37972e−5		1.00000i	$0.499977\pi$
$702$		0			0
$703$	−175.022	−	101.049i	−0.248964	−	0.143740i
$704$	24.0000	−	41.5692i	0.0340909	−	0.0590472i
$705$		0			0
$706$			632.700i			0.896175i
$707$	525.088	−	535.916i	0.742699	−	0.758014i
$708$		0			0
$709$	−602.588	−	1043.71i	−0.849912	−	1.47209i	−0.881286	−	0.472584i	$-0.843321\pi$
$709$	−602.588	−	1043.71i	−0.849912	−	1.47209i	0.0313734	−	0.999508i	$-0.490012\pi$
$710$	241.456	+	139.405i	0.340079	+	0.196345i
$711$		0			0
$712$	50.9117	−	29.3939i	0.0715052	−	0.0412835i
$713$		−	1653.37i		−	2.31889i
$714$		0			0
$715$	−183.618			−0.256809
$716$	169.279	+	293.200i	0.236423	+	0.409498i
$717$		0			0
$718$	206.309	−	357.337i	0.287338	−	0.497684i
$719$	−850.925	+	491.282i	−1.18348	+	0.683285i	−0.956818	−	0.290688i	$-0.906116\pi$
$719$	−850.925	+	491.282i	−1.18348	+	0.683285i	−0.226666	+	0.973973i	$0.572783\pi$
$720$		0			0
$721$	−197.852	−	709.359i	−0.274414	−	0.983855i
$722$	436.701			0.604848
$723$		0			0
$724$	363.676	+	209.969i	0.502315	+	0.290012i
$725$	−389.324	+	674.329i	−0.536998	+	0.930108i
$726$		0			0
$727$		−	630.440i		−	0.867181i	−0.901110	−	0.433590i	$-0.857247\pi$
$727$		−	630.440i		−	0.867181i	0.901110	−	0.433590i	$-0.142753\pi$
$728$	−408.978	−	105.124i	−0.561783	−	0.144401i
$729$		0			0
$730$	−80.0803	−	138.703i	−0.109699	−	0.190004i
$731$	−11.5219	−	6.65215i	−0.0157618	−	0.00910007i
$732$		0			0
$733$	258.486	−	149.237i	0.352641	−	0.203597i	−0.313207	−	0.949685i	$-0.601403\pi$
$733$	258.486	−	149.237i	0.352641	−	0.203597i	0.665848	+	0.746088i	$0.268070\pi$
$734$			593.053i			0.807974i
$735$		0			0
$736$	211.882			0.287883
$737$	13.1909	+	22.8473i	0.0178981	+	0.0310004i
$738$		0			0
$739$	−172.684	+	299.097i	−0.233672	+	0.404732i	−0.958886	−	0.283792i	$-0.908408\pi$
$739$	−172.684	+	299.097i	−0.233672	+	0.404732i	0.725214	+	0.688524i	$0.241741\pi$
$740$	−69.5147	+	40.1343i	−0.0939388	+	0.0542356i
$741$		0			0
$742$	210.603	−	819.336i	0.283832	−	1.10423i
$743$	−683.616			−0.920076			−0.460038	−	0.887899i	$-0.652164\pi$
$743$	−683.616			−0.920076			−0.460038	+	0.887899i	$0.652164\pi$
$744$		0			0
$745$	100.764	+	58.1759i	0.135253	+	0.0780885i
$746$	−22.1903	+	38.4347i	−0.0297457	+	0.0515211i
$747$		0			0
$748$			107.489i			0.143702i
$749$	799.301	−	222.939i	1.06716	−	0.297648i
$750$		0			0
$751$	289.169	+	500.855i	0.385045	+	0.666918i	0.991775	−	0.127990i	$-0.0408525\pi$
$751$	289.169	+	500.855i	0.385045	+	0.666918i	−0.606730	+	0.794908i	$0.707519\pi$
$752$	−148.971	−	86.0082i	−0.198099	−	0.114373i
$753$		0			0
$754$	−886.587	+	511.871i	−1.17584	+	0.678874i
$755$		−	73.4744i		−	0.0973171i
$756$		0			0
$757$	1204.82			1.59158			0.795788	−	0.605576i	$-0.207057\pi$
$757$	1204.82			1.59158			0.795788	+	0.605576i	$0.207057\pi$
$758$	−146.215	−	253.251i	−0.192895	−	0.334105i
$759$		0			0
$760$	−14.6619	+	25.3952i	−0.0192920	+	0.0334147i
$761$	202.669	−	117.011i	0.266319	−	0.153760i	−0.360894	−	0.932607i	$-0.617529\pi$
$761$	202.669	−	117.011i	0.266319	−	0.153760i	0.627214	+	0.778847i	$0.284195\pi$
$762$		0			0
$763$	555.294	+	544.075i	0.727778	+	0.713074i
$764$	−133.206			−0.174353
$765$		0			0
$766$	−610.617	−	352.540i	−0.797151	−	0.460235i
$767$	439.581	−	761.376i	0.573117	−	0.992668i
$768$		0			0
$769$			1290.16i			1.67771i	0.544358	+	0.838853i	$0.316774\pi$
$769$			1290.16i			1.67771i	−0.544358	+	0.838853i	$0.683226\pi$
$770$	22.8974	+	82.0940i	0.0297369	+	0.106616i
$771$		0			0
$772$	9.79394	+	16.9636i	0.0126864	+	0.0219736i
$773$	−345.646	−	199.559i	−0.447149	−	0.258161i	0.259477	−	0.965749i	$-0.416450\pi$
$773$	−345.646	−	199.559i	−0.447149	−	0.258161i	−0.706625	+	0.707588i	$0.749783\pi$
$774$		0			0
$775$	−876.992	+	506.331i	−1.13160	+	0.653331i
$776$		−	31.0749i		−	0.0400450i
$777$		0			0
$778$	917.013			1.17868
$779$	−198.088	−	343.099i	−0.254285	−	0.440435i
$780$		0			0
$781$	−412.191	+	713.936i	−0.527773	+	0.914130i
$782$	−410.912	+	237.240i	−0.525463	+	0.303376i
$783$		0			0
$784$	4.00000	+	195.959i	0.00510204	+	0.249948i
$785$	268.410			0.341924
$786$		0			0
$787$	−1348.16	−	778.361i	−1.71304	−	0.989023i	−0.930401	−	0.366544i	$-0.880541\pi$
$787$	−1348.16	−	778.361i	−1.71304	−	0.989023i	−0.782637	−	0.622478i	$-0.786126\pi$
$788$	−267.161	+	462.737i	−0.339037	+	0.587230i
$789$		0			0
$790$			199.550i			0.252595i
$791$	−176.698	+	687.433i	−0.223386	+	0.869068i
$792$		0			0
$793$	12.6762	+	21.9558i	0.0159851	+	0.0276870i
$794$	−92.7761	−	53.5643i	−0.116846	−	0.0674613i
$795$		0			0
$796$	226.794	−	130.940i	0.284917	−	0.164497i
$797$		−	600.232i		−	0.753114i	−0.926393	−	0.376557i	$-0.877108\pi$
$797$		−	600.232i		−	0.753114i	0.926393	−	0.376557i	$-0.122892\pi$
$798$		0			0
$799$	385.206			0.482110
$800$	−64.8873	−	112.388i	−0.0811091	−	0.140485i
$801$		0			0
$802$	−398.985	+	691.062i	−0.497487	+	0.861673i
$803$	410.117	−	236.781i	0.510731	−	0.294871i
$804$		0			0
$805$	−263.294	+	268.723i	−0.327073	+	0.333817i
$806$	−1331.42			−1.65188
$807$		0			0
$808$	262.544	+	151.580i	0.324931	+	0.187599i
$809$	−114.640	+	198.562i	−0.141705	+	0.245441i	−0.928139	−	0.372234i	$-0.878592\pi$
$809$	−114.640	+	198.562i	−0.141705	+	0.245441i	0.786434	+	0.617675i	$0.211925\pi$
$810$		0			0
$811$			529.955i			0.653459i	0.945118	+	0.326729i	$0.105947\pi$
$811$			529.955i			0.653459i	−0.945118	+	0.326729i	$0.894053\pi$
$812$	339.411	+	332.554i	0.417994	+	0.409549i
$813$		0			0
$814$	−118.669	−	205.541i	−0.145785	−	0.252507i
$815$	−104.309	−	60.2226i	−0.127986	−	0.0738928i
$816$		0			0
$817$	9.29394	−	5.36586i	0.0113757	−	0.00656776i
$818$			505.508i			0.617980i
$819$		0			0
$820$	−157.352			−0.191893
$821$	−151.669	−	262.698i	−0.184737	−	0.319974i	0.758751	−	0.651381i	$-0.225810\pi$
$821$	−151.669	−	262.698i	−0.184737	−	0.319974i	−0.943488	+	0.331407i	$0.892477\pi$
$822$		0			0
$823$	564.955	−	978.531i	0.686459	−	1.18898i	−0.286517	−	0.958075i	$-0.592498\pi$
$823$	564.955	−	978.531i	0.686459	−	1.18898i	0.972976	−	0.230906i	$-0.0741690\pi$
$824$	257.698	−	148.782i	0.312741	−	0.180561i
$825$		0			0
$826$	−395.220	−	101.588i	−0.478475	−	0.122988i
$827$	161.604			0.195410			0.0977049	−	0.995215i	$-0.468850\pi$
$827$	161.604			0.195410			0.0977049	+	0.995215i	$0.468850\pi$
$828$		0			0
$829$	1325.32	+	765.175i	1.59870	+	0.923010i	0.991738	+	0.128279i	$0.0409454\pi$
$829$	1325.32	+	765.175i	1.59870	+	0.923010i	0.606962	+	0.794731i	$0.292388\pi$
$830$	−112.014	+	194.014i	−0.134957	+	0.233752i
$831$		0			0
$832$		−	170.624i		−	0.205077i
$833$	−227.169	−	375.553i	−0.272711	−	0.450844i
$834$		0			0
$835$	91.5593	+	158.585i	0.109652	+	0.189923i
$836$	−75.0883	−	43.3523i	−0.0898186	−	0.0518568i
$837$		0			0
$838$	615.037	−	355.092i	0.733934	−	0.423737i
$839$			218.629i			0.260583i	0.991476	+	0.130291i	$0.0415913\pi$
$839$			218.629i			0.260583i	−0.991476	+	0.130291i	$0.958409\pi$
$840$		0			0
$841$	311.000			0.369798
$842$	−23.8959	−	41.3890i	−0.0283800	−	0.0491555i
$843$		0			0
$844$	23.0883	−	39.9901i	0.0273558	−	0.0473817i
$845$	−355.249	+	205.103i	−0.420413	+	0.242726i
$846$		0			0
$847$	573.124	−	159.854i	0.676652	−	0.188730i
$848$	341.823			0.403094
$849$		0			0
$850$	251.677	+	145.306i	0.296091	+	0.170948i
$851$	523.831	−	907.301i	0.615547	−	1.06616i
$852$		0			0
$853$			762.730i			0.894174i	0.894491	+	0.447087i	$0.147539\pi$
$853$			762.730i			0.894174i	−0.894491	+	0.447087i	$0.852461\pi$
$854$	8.23550	−	8.40532i	0.00964344	−	0.00984230i
$855$		0			0
$856$	167.647	+	290.373i	0.195849	+	0.339220i
$857$	795.015	+	459.002i	0.927672	+	0.535592i	0.886075	−	0.463543i	$-0.153422\pi$
$857$	795.015	+	459.002i	0.927672	+	0.535592i	0.0415977	+	0.999134i	$0.486755\pi$
$858$		0			0
$859$	−761.367	+	439.575i	−0.886341	+	0.511729i	−0.872744	−	0.488179i	$-0.837661\pi$
$859$	−761.367	+	439.575i	−0.886341	+	0.511729i	−0.0135969	+	0.999908i	$0.504328\pi$
$860$		−	4.26239i		−	0.00495627i
$861$		0			0
$862$	−712.368			−0.826412
$863$	175.294	+	303.619i	0.203122	+	0.351818i	0.949533	−	0.313668i	$-0.101558\pi$
$863$	175.294	+	303.619i	0.203122	+	0.351818i	−0.746411	+	0.665486i	$0.768224\pi$
$864$		0			0
$865$	102.573	−	177.661i	0.118581	−	0.205389i
$866$	−1025.78	+	592.236i	−1.18451	+	0.683875i
$867$		0			0
$868$	166.029	+	595.265i	0.191278	+	0.685789i
$869$	−590.029			−0.678974
$870$		0			0
$871$	81.2145	+	46.8892i	0.0932428	+	0.0538338i
$872$	−157.061	+	272.038i	−0.180116	+	0.311970i
$873$		0			0
$874$		−	382.732i		−	0.437909i
$875$	466.368	+	119.876i	0.532991	+	0.137001i
$876$		0			0
$877$	−1.77965	−	3.08245i	−0.00202925	−	0.00351477i	0.865009	−	0.501756i	$-0.167313\pi$
$877$	−1.77965	−	3.08245i	−0.00202925	−	0.00351477i	−0.867038	+	0.498242i	$0.833979\pi$
$878$	232.721	+	134.361i	0.265058	+	0.153031i
$879$		0			0
$880$	−29.8234	+	17.2185i	−0.0338902	+	0.0195665i
$881$			488.565i			0.554557i	0.960790	+	0.277279i	$0.0894325\pi$
$881$			488.565i			0.554557i	−0.960790	+	0.277279i	$0.910567\pi$
$882$		0			0
$883$	−1162.16			−1.31615			−0.658075	−	0.752953i	$-0.728629\pi$
$883$	−1162.16			−1.31615			−0.658075	+	0.752953i	$0.728629\pi$
$884$	191.044	+	330.897i	0.216113	+	0.374318i
$885$		0			0
$886$	−119.823	+	207.540i	−0.135241	+	0.234244i
$887$	−75.2801	+	43.4630i	−0.0848704	+	0.0490000i	−0.541835	−	0.840485i	$-0.682270\pi$
$887$	−75.2801	+	43.4630i	−0.0848704	+	0.0490000i	0.456964	+	0.889485i	$0.348937\pi$
$888$		0			0
$889$	143.896	−	559.817i	0.161863	−	0.629716i
$890$	−42.1766			−0.0473895
$891$		0			0
$892$	−396.000	−	228.631i	−0.443946	−	0.256312i
$893$	−155.360	+	269.092i	−0.173976	+	0.301335i
$894$		0			0
$895$		−	242.895i		−	0.271391i
$896$	−76.2843	+	21.2770i	−0.0851387	+	0.0237466i
$897$		0			0
$898$	12.8011	+	22.1721i	0.0142551	+	0.0246906i
$899$	1297.50	+	749.111i	1.44327	+	0.833272i
$900$		0			0
$901$	−662.912	+	382.732i	−0.735751	+	0.424786i
$902$		−	465.259i		−	0.515808i
$903$		0			0
$904$	−286.794			−0.317250
$905$	−150.640	−	260.915i	−0.166453	−	0.288304i
$906$		0			0
$907$	230.448	−	399.148i	0.254077	−	0.440075i	−0.710567	−	0.703629i	$-0.751562\pi$
$907$	230.448	−	399.148i	0.254077	−	0.440075i	0.964645	+	0.263554i	$0.0848948\pi$
$908$	113.647	−	65.6140i	0.125162	−	0.0722621i
$909$		0			0
$910$	216.396	+	212.024i	0.237798	+	0.232993i
$911$	1184.28			1.29998			0.649988	−	0.759944i	$-0.274774\pi$
$911$	1184.28			1.29998			0.649988	+	0.759944i	$0.274774\pi$
$912$		0			0
$913$	−573.661	−	331.203i	−0.628325	−	0.362764i
$914$	232.513	−	402.725i	0.254391	−	0.440618i
$915$		0			0
$916$			186.960i			0.204104i
$917$	−113.912	−	408.407i	−0.124222	−	0.445373i
$918$		0			0
$919$	270.919	+	469.246i	0.294798	+	0.510605i	0.974938	−	0.222477i	$-0.0714143\pi$
$919$	270.919	+	469.246i	0.294798	+	0.510605i	−0.680140	+	0.733082i	$0.738081\pi$
$920$	−131.647	−	76.0063i	−0.143094	−	0.0826155i
$921$		0			0
$922$	−972.853	+	561.677i	−1.05515	+	0.609194i
$923$			2930.40i			3.17486i
$924$		0			0
$925$	−641.676			−0.693704
$926$	285.244	+	494.057i	0.308039	+	0.533539i
$927$		0			0
$928$	−96.0000	+	166.277i	−0.103448	+	0.179178i
$929$	779.610	−	450.108i	0.839193	−	0.484508i	−0.0177969	−	0.999842i	$-0.505665\pi$
$929$	779.610	−	450.108i	0.839193	−	0.484508i	0.856990	+	0.515333i	$0.172332\pi$
$930$		0			0
$931$	353.970	−	7.22538i	0.380204	−	0.00776088i
$932$	475.029			0.509688
$933$		0			0
$934$	−3.46299	−	1.99936i	−0.00370769	−	0.00214064i
$935$	38.5584	−	66.7852i	0.0412390	−	0.0714280i
$936$		0			0
$937$			233.964i			0.249695i	0.992176	+	0.124847i	$0.0398441\pi$
$937$			233.964i			0.249695i	−0.992176	+	0.124847i	$0.960156\pi$
$938$	10.8362	−	42.1574i	0.0115524	−	0.0449439i
$939$		0			0
$940$	61.7056	+	106.877i	0.0656443	+	0.113699i
$941$	−1132.49	−	653.845i	−1.20350	−	0.694840i	−0.242167	−	0.970234i	$-0.577858\pi$
$941$	−1132.49	−	653.845i	−1.20350	−	0.694840i	−0.961331	+	0.275394i	$0.911192\pi$
$942$		0			0
$943$	1778.60	−	1026.88i	1.88611	−	1.08895i
$944$		−	164.884i		−	0.174666i
$945$		0			0
$946$	12.6030			0.0133224
$947$	−563.881	−	976.671i	−0.595440	−	1.03133i	−0.993485	−	0.113966i	$-0.963645\pi$
$947$	−563.881	−	976.671i	−0.595440	−	1.03133i	0.398045	−	0.917366i	$-0.369689\pi$
$948$		0			0
$949$	841.677	−	1457.83i	0.886909	−	1.53617i
$950$	−203.012	+	117.209i	−0.213696	+	0.123378i
$951$		0			0
$952$	124.118	−	126.677i	0.130376	−	0.133064i
$953$	91.4255			0.0959345			0.0479672	−	0.998849i	$-0.484726\pi$
$953$	91.4255			0.0959345			0.0479672	+	0.998849i	$0.484726\pi$
$954$		0			0
$955$	82.7636	+	47.7836i	0.0866635	+	0.0500352i
$956$	366.853	−	635.408i	0.383737	−	0.664652i
$957$		0			0
$958$			536.714i			0.560245i
$959$	−335.147	−	328.376i	−0.349476	−	0.342415i
$960$		0			0
$961$	493.749	+	855.199i	0.513787	+	0.889905i
$962$	−730.628	−	421.828i	−0.759489	−	0.438491i
$963$		0			0
$964$	729.235	−	421.024i	0.756467	−	0.436747i
$965$		−	14.0531i		−	0.0145628i
$966$		0			0
$967$	−1098.19			−1.13567			−0.567834	−	0.823143i	$-0.692218\pi$
$967$	−1098.19			−1.13567			−0.567834	+	0.823143i	$0.692218\pi$
$968$	120.208	+	208.207i	0.124182	+	0.215089i
$969$		0			0
$970$	−11.1472	+	19.3075i	−0.0114919	+	0.0199046i
$971$	−114.405	+	66.0517i	−0.117822	+	0.0680245i	−0.557753	−	0.830007i	$-0.688336\pi$
$971$	−114.405	+	66.0517i	−0.117822	+	0.0680245i	0.439931	+	0.898032i	$0.355003\pi$
$972$		0			0
$973$	620.691	+	159.543i	0.637915	+	0.163970i
$974$	813.899			0.835626
$975$		0			0
$976$	4.11775	+	2.37738i	0.00421901	+	0.00243584i
$977$	224.117	−	388.182i	0.229393	−	0.397320i	−0.728235	−	0.685327i	$-0.759659\pi$
$977$	224.117	−	388.182i	0.229393	−	0.397320i	0.957628	+	0.288007i	$0.0929926\pi$
$978$		0			0
$979$		−	124.708i		−	0.127383i
$980$	67.8091	−	123.188i	0.0691930	−	0.125702i
$981$		0			0
$982$	168.603	+	292.029i	0.171694	+	0.297382i
$983$	−1426.14	−	823.382i	−1.45080	−	0.837621i	−0.452276	−	0.891878i	$-0.649388\pi$
$983$	−1426.14	−	823.382i	−1.45080	−	0.837621i	−0.998527	+	0.0542567i	$0.982721\pi$
$984$		0			0
$985$	331.986	−	191.672i	0.337041	−	0.194591i
$986$		−	429.956i		−	0.436061i
$987$		0			0
$988$	−308.205			−0.311949
$989$	27.8162	+	48.1791i	0.0281256	+	0.0487150i
$990$		0			0
$991$	314.448	−	544.640i	0.317304	−	0.549587i	−0.662621	−	0.748955i	$-0.730556\pi$
$991$	314.448	−	544.640i	0.317304	−	0.549587i	0.979925	+	0.199369i	$0.0638891\pi$
$992$	−216.250	+	124.852i	−0.217994	+	0.125859i
$993$		0			0
$994$	1310.15	−	365.424i	1.31806	−	0.367630i
$995$	−187.882			−0.188826
$996$		0			0
$997$	−869.645	−	502.090i	−0.872262	−	0.503601i	−0.00416289	−	0.999991i	$-0.501325\pi$
$997$	−869.645	−	502.090i	−0.872262	−	0.503601i	−0.868099	+	0.496390i	$0.834658\pi$
$998$	202.638	−	350.980i	0.203044	−	0.351683i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	126.3.n.a.73.1		4
3.2	odd	2		42.3.g.a.31.2	yes	4
4.3	odd	2		1008.3.cg.h.577.2		4
7.2	even	3		882.3.n.e.19.1		4
7.3	odd	6		882.3.c.b.685.3		4
7.4	even	3		882.3.c.b.685.4		4
7.5	odd	6	inner	126.3.n.a.19.1		4
7.6	odd	2		882.3.n.e.325.1		4
12.11	even	2		336.3.bh.e.241.1		4
15.2	even	4		1050.3.q.a.199.2		8
15.8	even	4		1050.3.q.a.199.3		8
15.14	odd	2		1050.3.p.a.451.1		4
21.2	odd	6		294.3.g.a.19.2		4
21.5	even	6		42.3.g.a.19.2	✓	4
21.11	odd	6		294.3.c.a.97.1		4
21.17	even	6		294.3.c.a.97.2		4
21.20	even	2		294.3.g.a.31.2		4
28.19	even	6		1008.3.cg.h.145.2		4
84.11	even	6		2352.3.f.e.97.3		4
84.47	odd	6		336.3.bh.e.145.1		4
84.59	odd	6		2352.3.f.e.97.2		4
105.47	odd	12		1050.3.q.a.649.3		8
105.68	odd	12		1050.3.q.a.649.2		8
105.89	even	6		1050.3.p.a.901.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.3.g.a.19.2	✓	4	21.5	even	6
42.3.g.a.31.2	yes	4	3.2	odd	2
126.3.n.a.19.1		4	7.5	odd	6	inner
126.3.n.a.73.1		4	1.1	even	1	trivial
294.3.c.a.97.1		4	21.11	odd	6
294.3.c.a.97.2		4	21.17	even	6
294.3.g.a.19.2		4	21.2	odd	6
294.3.g.a.31.2		4	21.20	even	2
336.3.bh.e.145.1		4	84.47	odd	6
336.3.bh.e.241.1		4	12.11	even	2
882.3.c.b.685.3		4	7.3	odd	6
882.3.c.b.685.4		4	7.4	even	3
882.3.n.e.19.1		4	7.2	even	3
882.3.n.e.325.1		4	7.6	odd	2
1008.3.cg.h.145.2		4	28.19	even	6
1008.3.cg.h.577.2		4	4.3	odd	2
1050.3.p.a.451.1		4	15.14	odd	2
1050.3.p.a.901.1		4	105.89	even	6
1050.3.q.a.199.2		8	15.2	even	4
1050.3.q.a.199.3		8	15.8	even	4
1050.3.q.a.649.2		8	105.68	odd	12
1050.3.q.a.649.3		8	105.47	odd	12
2352.3.f.e.97.2		4	84.59	odd	6
2352.3.f.e.97.3		4	84.11	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	126.n (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 1.22474i) q^{2} +(-1.00000 + 1.73205i) q^{4} +(1.24264 - 0.717439i) q^{5} +(1.74264 - 6.77962i) q^{7} +2.82843 q^{8} +O(q^{10})\)	\(q+(-0.707107 - 1.22474i) q^{2} +(-1.00000 + 1.73205i) q^{4} +(1.24264 - 0.717439i) q^{5} +(1.74264 - 6.77962i) q^{7} +2.82843 q^{8} +(-1.75736 - 1.01461i) q^{10} +(3.00000 - 5.19615i) q^{11} -21.3280i q^{13} +(-9.53553 + 2.65962i) q^{14} +(-2.00000 - 3.46410i) q^{16} +(7.75736 + 4.47871i) q^{17} +(-6.25736 + 3.61269i) q^{19} +2.86976i q^{20} -8.48528 q^{22} +(-18.7279 - 32.4377i) q^{23} +(-11.4706 + 19.8676i) q^{25} +(-26.1213 + 15.0812i) q^{26} +(10.0000 + 9.79796i) q^{28} +33.9411 q^{29} +(38.2279 + 22.0709i) q^{31} +(-2.82843 + 4.89898i) q^{32} -12.6677i q^{34} +(-2.69848 - 9.67487i) q^{35} +(13.9853 + 24.2232i) q^{37} +(8.84924 + 5.10911i) q^{38} +(3.51472 - 2.02922i) q^{40} +54.8313i q^{41} -1.48528 q^{43} +(6.00000 + 10.3923i) q^{44} +(-26.4853 + 45.8739i) q^{46} +(37.2426 - 21.5020i) q^{47} +(-42.9264 - 23.6289i) q^{49} +32.4437 q^{50} +(36.9411 + 21.3280i) q^{52} +(-42.7279 + 74.0069i) q^{53} -8.60927i q^{55} +(4.92893 - 19.1757i) q^{56} +(-24.0000 - 41.5692i) q^{58} +(35.6985 + 20.6105i) q^{59} +(-1.02944 + 0.594346i) q^{61} -62.4259i q^{62} +8.00000 q^{64} +(-15.3015 - 26.5030i) q^{65} +(-2.19848 + 3.80789i) q^{67} +(-15.5147 + 8.95743i) q^{68} +(-9.94113 + 10.1461i) q^{70} -137.397 q^{71} +(68.3528 + 39.4635i) q^{73} +(19.7782 - 34.2568i) q^{74} -14.4508i q^{76} +(-30.0000 - 29.3939i) q^{77} +(-49.1690 - 85.1633i) q^{79} +(-4.97056 - 2.86976i) q^{80} +(67.1543 - 38.7716i) q^{82} -110.401i q^{83} +12.8528 q^{85} +(1.05025 + 1.81909i) q^{86} +(8.48528 - 14.6969i) q^{88} +(18.0000 - 10.3923i) q^{89} +(-144.595 - 37.1670i) q^{91} +74.9117 q^{92} +(-52.6690 - 30.4085i) q^{94} +(-5.18377 + 8.97855i) q^{95} -10.9867i q^{97} +(1.41421 + 69.2820i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{4} - 12 q^{5} - 10 q^{7}+O(q^{10}) \) 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

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