LMFDB - Embedded newform 189.3.j.a.44.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [189,3,Mod(44,189)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(189, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5, 2]))

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

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

chi := DirichletCharacter("189.44");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	189.j (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.14987699641$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{6})$
Coefficient field:	6.0.63369648.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + 12x^{4} + 17x^{3} + 118x^{2} + 33x + 9 $ x^6 - x^5 + 12x^4 + 17x^3 + 118x^2 + 33x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			44.1
Root			$-0.140998 + 0.244215i$ of defining polynomial
Character	$\chi$	$=$	189.44
Dual form			189.3.j.a.116.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.09257i q^{2} -5.56399 q^{4} +(5.67824 - 3.27834i) q^{5} +(6.63848 - 2.22048i) q^{7} +4.83675i q^{8} +O(q^{10})$	\(q-3.09257i q^{2} -5.56399 q^{4} +(5.67824 - 3.27834i) q^{5} +(6.63848 - 2.22048i) q^{7} +4.83675i q^{8} +(-10.1385 - 17.5604i) q^{10} +(6.01050 + 3.47017i) q^{11} +(4.39625 - 7.61453i) q^{13} +(-6.86699 - 20.5300i) q^{14} -7.29797 q^{16} +(-28.2614 + 16.3167i) q^{17} +(-1.93601 + 3.35327i) q^{19} +(-31.5937 + 18.2406i) q^{20} +(10.7317 - 18.5879i) q^{22} +(8.88072 - 5.12729i) q^{23} +(8.99497 - 15.5797i) q^{25} +(-23.5485 - 13.5957i) q^{26} +(-36.9365 + 12.3547i) q^{28} +(11.6782 - 6.74244i) q^{29} -7.54298 q^{31} +41.9165i q^{32} +(50.4607 + 87.4005i) q^{34} +(30.4155 - 34.3716i) q^{35} +(-24.1577 + 41.8423i) q^{37} +(10.3702 + 5.98725i) q^{38} +(15.8565 + 27.4642i) q^{40} +(43.6664 + 25.2108i) q^{41} +(-27.3670 - 47.4010i) q^{43} +(-33.4424 - 19.3080i) q^{44} +(-15.8565 - 27.4642i) q^{46} +40.2995i q^{47} +(39.1389 - 29.4812i) q^{49} +(-48.1815 - 27.8176i) q^{50} +(-24.4607 + 42.3672i) q^{52} +(45.7116 - 26.3916i) q^{53} +45.5055 q^{55} +(10.7399 + 32.1087i) q^{56} +(-20.8515 - 36.1158i) q^{58} -56.1270i q^{59} +35.6270 q^{61} +23.3272i q^{62} +100.438 q^{64} -57.6495i q^{65} -62.1910 q^{67} +(157.246 - 90.7862i) q^{68} +(-106.297 - 94.0619i) q^{70} +14.5752i q^{71} +(44.6824 + 77.3921i) q^{73} +(129.400 + 74.7093i) q^{74} +(10.7719 - 18.6575i) q^{76} +(47.6061 + 9.69043i) q^{77} +13.5951 q^{79} +(-41.4397 + 23.9252i) q^{80} +(77.9662 - 135.041i) q^{82} +(-33.1139 + 19.1183i) q^{83} +(-106.984 + 185.301i) q^{85} +(-146.591 + 84.6343i) q^{86} +(-16.7843 + 29.0713i) q^{88} +(75.1559 + 43.3913i) q^{89} +(12.2765 - 60.3107i) q^{91} +(-49.4122 + 28.5282i) q^{92} +124.629 q^{94} +25.3876i q^{95} +(11.9209 + 20.6477i) q^{97} +(-91.1728 - 121.040i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 26 q^{4} + 15 q^{5} - 2 q^{7}+O(q^{10}) $ 6 * q - 26 * q^4 + 15 * q^5 - 2 * q^7	$ 6 q - 26 q^{4} + 15 q^{5} - 2 q^{7} - 19 q^{10} + 9 q^{11} + 11 q^{13} + 24 q^{14} + 94 q^{16} - 33 q^{17} - 19 q^{19} - 45 q^{20} + 65 q^{22} - 15 q^{23} - 26 q^{25} - 81 q^{26} - 42 q^{28} + 51 q^{29} - 92 q^{31} + 93 q^{34} + 57 q^{35} + 7 q^{37} + 21 q^{38} + 57 q^{40} + 27 q^{41} - 99 q^{43} + 273 q^{44} - 57 q^{46} + 6 q^{49} - 294 q^{50} + 63 q^{52} - 45 q^{53} + 166 q^{55} - 360 q^{56} - 7 q^{58} + 44 q^{61} - 138 q^{64} - 196 q^{67} + 567 q^{68} - 257 q^{70} - 101 q^{73} + 411 q^{74} - 99 q^{76} - 105 q^{77} + 180 q^{79} - 93 q^{80} + 151 q^{82} - 99 q^{83} - 159 q^{85} - 249 q^{86} - 495 q^{88} + 243 q^{89} + 177 q^{91} - 147 q^{92} + 888 q^{94} - 161 q^{97} - 360 q^{98}+O(q^{100}) $ 6 * q - 26 * q^4 + 15 * q^5 - 2 * q^7 - 19 * q^10 + 9 * q^11 + 11 * q^13 + 24 * q^14 + 94 * q^16 - 33 * q^17 - 19 * q^19 - 45 * q^20 + 65 * q^22 - 15 * q^23 - 26 * q^25 - 81 * q^26 - 42 * q^28 + 51 * q^29 - 92 * q^31 + 93 * q^34 + 57 * q^35 + 7 * q^37 + 21 * q^38 + 57 * q^40 + 27 * q^41 - 99 * q^43 + 273 * q^44 - 57 * q^46 + 6 * q^49 - 294 * q^50 + 63 * q^52 - 45 * q^53 + 166 * q^55 - 360 * q^56 - 7 * q^58 + 44 * q^61 - 138 * q^64 - 196 * q^67 + 567 * q^68 - 257 * q^70 - 101 * q^73 + 411 * q^74 - 99 * q^76 - 105 * q^77 + 180 * q^79 - 93 * q^80 + 151 * q^82 - 99 * q^83 - 159 * q^85 - 249 * q^86 - 495 * q^88 + 243 * q^89 + 177 * q^91 - 147 * q^92 + 888 * q^94 - 161 * q^97 - 360 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/189\mathbb{Z}\right)^\times$.

$n$	$29$	$136$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$		−	3.09257i		−	1.54629i	−0.634232	−	0.773143i	$-0.718684\pi$
$2$		−	3.09257i		−	1.54629i	0.634232	−	0.773143i	$-0.281316\pi$
$3$		0			0
$3$		0			0
$4$	−5.56399			−1.39100
$5$	5.67824	−	3.27834i	1.13565	−	0.655667i	0.190299	−	0.981726i	$-0.439054\pi$
$5$	5.67824	−	3.27834i	1.13565	−	0.655667i	0.945349	+	0.326059i	$0.105721\pi$
$6$		0			0
$7$	6.63848	−	2.22048i	0.948355	−	0.317212i
$7$	6.63848	−	2.22048i	0.948355	−	0.317212i
$8$			4.83675i			0.604594i
$9$		0			0
$10$	−10.1385	−	17.5604i	−1.01385	−	1.75604i
$11$	6.01050	+	3.47017i	0.546409	+	0.315470i	0.747673	−	0.664068i	$-0.231171\pi$
$11$	6.01050	+	3.47017i	0.546409	+	0.315470i	−0.201263	+	0.979537i	$0.564505\pi$
$12$		0			0
$13$	4.39625	−	7.61453i	0.338173	−	0.585733i	−0.645916	−	0.763408i	$-0.723524\pi$
$13$	4.39625	−	7.61453i	0.338173	−	0.585733i	0.984089	+	0.177676i	$0.0568578\pi$
$14$	−6.86699	−	20.5300i	−0.490499	−	1.46643i
$15$		0			0
$16$	−7.29797			−0.456123
$17$	−28.2614	+	16.3167i	−1.66244	+	0.959809i	−0.690891	+	0.722959i	$0.742782\pi$
$17$	−28.2614	+	16.3167i	−1.66244	+	0.959809i	−0.971546	+	0.236850i	$0.923885\pi$
$18$		0			0
$19$	−1.93601	+	3.35327i	−0.101895	+	0.176488i	−0.912465	−	0.409154i	$-0.865824\pi$
$19$	−1.93601	+	3.35327i	−0.101895	+	0.176488i	0.810570	+	0.585641i	$0.199157\pi$
$20$	−31.5937	+	18.2406i	−1.57968	+	0.912031i
$21$		0			0
$22$	10.7317	−	18.5879i	0.487806	−	0.844905i
$23$	8.88072	−	5.12729i	0.386118	−	0.222925i	−0.294359	−	0.955695i	$-0.595106\pi$
$23$	8.88072	−	5.12729i	0.386118	−	0.222925i	0.680477	+	0.732770i	$0.261773\pi$
$24$		0			0
$25$	8.99497	−	15.5797i	0.359799	−	0.623190i
$26$	−23.5485	−	13.5957i	−0.905710	−	0.522912i
$27$		0			0
$28$	−36.9365	+	12.3547i	−1.31916	+	0.441240i
$29$	11.6782	−	6.74244i	0.402698	−	0.232498i	−0.284949	−	0.958543i	$-0.591977\pi$
$29$	11.6782	−	6.74244i	0.402698	−	0.232498i	0.687647	+	0.726045i	$0.258643\pi$
$30$		0			0
$31$	−7.54298			−0.243322			−0.121661	−	0.992572i	$-0.538822\pi$
$31$	−7.54298			−0.243322			−0.121661	+	0.992572i	$0.538822\pi$
$32$			41.9165i			1.30989i
$33$		0			0
$34$	50.4607	+	87.4005i	1.48414	+	2.57060i
$35$	30.4155	−	34.3716i	0.869013	−	0.982046i
$36$		0			0
$37$	−24.1577	+	41.8423i	−0.652910	+	1.13087i	0.329503	+	0.944155i	$0.393119\pi$
$37$	−24.1577	+	41.8423i	−0.652910	+	1.13087i	−0.982413	+	0.186719i	$0.940214\pi$
$38$	10.3702	+	5.98725i	0.272900	+	0.157559i
$39$		0			0
$40$	15.8565	+	27.4642i	0.396412	+	0.686606i
$41$	43.6664	+	25.2108i	1.06503	+	0.614898i	0.926820	−	0.375505i	$-0.122531\pi$
$41$	43.6664	+	25.2108i	1.06503	+	0.614898i	0.138213	+	0.990402i	$0.455864\pi$
$42$		0			0
$43$	−27.3670	−	47.4010i	−0.636442	−	1.10235i	−0.986208	−	0.165512i	$-0.947072\pi$
$43$	−27.3670	−	47.4010i	−0.636442	−	1.10235i	0.349766	−	0.936837i	$-0.386261\pi$
$44$	−33.4424	−	19.3080i	−0.760054	−	0.438817i
$45$		0			0
$46$	−15.8565	−	27.4642i	−0.344706	−	0.597049i
$47$			40.2995i			0.857436i	0.903438	+	0.428718i	$0.141035\pi$
$47$			40.2995i			0.857436i	−0.903438	+	0.428718i	$0.858965\pi$
$48$		0			0
$49$	39.1389	−	29.4812i	0.798754	−	0.601658i
$50$	−48.1815	−	27.8176i	−0.963629	−	0.556352i
$51$		0			0
$52$	−24.4607	+	42.3672i	−0.470398	+	0.814753i
$53$	45.7116	−	26.3916i	0.862483	−	0.497955i	−0.00235973	−	0.999997i	$-0.500751\pi$
$53$	45.7116	−	26.3916i	0.862483	−	0.497955i	0.864843	+	0.502042i	$0.167418\pi$
$54$		0			0
$55$	45.5055			0.827372
$56$	10.7399	+	32.1087i	0.191784	+	0.573369i
$57$		0			0
$58$	−20.8515	−	36.1158i	−0.359508	−	0.622686i
$59$		−	56.1270i		−	0.951305i	−0.879633	−	0.475653i	$-0.842212\pi$
$59$		−	56.1270i		−	0.951305i	0.879633	−	0.475653i	$-0.157788\pi$
$60$		0			0
$61$	35.6270			0.584049			0.292025	−	0.956411i	$-0.405671\pi$
$61$	35.6270			0.584049			0.292025	+	0.956411i	$0.405671\pi$
$62$			23.3272i			0.376245i
$63$		0			0
$64$	100.438			1.56934
$65$		−	57.6495i		−	0.886916i
$66$		0			0
$67$	−62.1910			−0.928224			−0.464112	−	0.885777i	$-0.653626\pi$
$67$	−62.1910			−0.928224			−0.464112	+	0.885777i	$0.653626\pi$
$68$	157.246	−	90.7862i	2.31245	−	1.33509i
$69$		0			0
$70$	−106.297	−	94.0619i	−1.51852	−	1.34374i
$71$			14.5752i			0.205285i	0.994718	+	0.102642i	$0.0327297\pi$
$71$			14.5752i			0.205285i	−0.994718	+	0.102642i	$0.967270\pi$
$72$		0			0
$73$	44.6824	+	77.3921i	0.612087	+	1.06017i	0.990888	+	0.134688i	$0.0430032\pi$
$73$	44.6824	+	77.3921i	0.612087	+	1.06017i	−0.378801	+	0.925478i	$0.623663\pi$
$74$	129.400	+	74.7093i	1.74865	+	1.00959i
$75$		0			0
$76$	10.7719	−	18.6575i	0.141736	−	0.245494i
$77$	47.6061	+	9.69043i	0.618261	+	0.125850i
$78$		0			0
$79$	13.5951			0.172089			0.0860446	−	0.996291i	$-0.472577\pi$
$79$	13.5951			0.172089			0.0860446	+	0.996291i	$0.472577\pi$
$80$	−41.4397	+	23.9252i	−0.517996	+	0.299065i
$81$		0			0
$82$	77.9662	−	135.041i	0.950807	−	1.64685i
$83$	−33.1139	+	19.1183i	−0.398962	+	0.230341i	−0.686036	−	0.727567i	$-0.740651\pi$
$83$	−33.1139	+	19.1183i	−0.398962	+	0.230341i	0.287074	+	0.957908i	$0.407317\pi$
$84$		0			0
$85$	−106.984	+	185.301i	−1.25863	+	2.18001i
$86$	−146.591	+	84.6343i	−1.70455	+	0.984120i
$87$		0			0
$88$	−16.7843	+	29.0713i	−0.190731	+	0.330356i
$89$	75.1559	+	43.3913i	0.844448	+	0.487542i	0.858774	−	0.512355i	$-0.171227\pi$
$89$	75.1559	+	43.3913i	0.844448	+	0.487542i	−0.0143256	+	0.999897i	$0.504560\pi$
$90$		0			0
$91$	12.2765	−	60.3107i	0.134907	−	0.662755i
$92$	−49.4122	+	28.5282i	−0.537089	+	0.310089i
$93$		0			0
$94$	124.629			1.32584
$95$			25.3876i			0.267237i
$96$		0			0
$97$	11.9209	+	20.6477i	0.122896	+	0.212862i	0.920909	−	0.389779i	$-0.127448\pi$
$97$	11.9209	+	20.6477i	0.122896	+	0.212862i	−0.798012	+	0.602641i	$0.794115\pi$
$98$	−91.1728	−	121.040i	−0.930335	−	1.23510i
$99$		0			0
$100$	−50.0479	+	86.6856i	−0.500479	+	0.866856i
$101$	23.3767	+	13.4965i	0.231452	+	0.133629i	0.611242	−	0.791444i	$-0.290670\pi$
$101$	23.3767	+	13.4965i	0.231452	+	0.133629i	−0.379790	+	0.925073i	$0.624004\pi$
$102$		0			0
$103$	75.1317	+	130.132i	0.729434	+	1.26342i	0.957123	+	0.289682i	$0.0935496\pi$
$103$	75.1317	+	130.132i	0.729434	+	1.26342i	−0.227689	+	0.973734i	$0.573117\pi$
$104$	36.8296	+	21.2636i	0.354130	+	0.204457i
$105$		0			0
$106$	−81.6179	−	141.366i	−0.769980	−	1.33365i
$107$	−86.1284	−	49.7263i	−0.804939	−	0.464732i	0.0402565	−	0.999189i	$-0.487182\pi$
$107$	−86.1284	−	49.7263i	−0.804939	−	0.464732i	−0.845195	+	0.534458i	$0.820516\pi$
$108$		0			0
$109$	77.2047	+	133.723i	0.708300	+	1.22681i	0.965487	+	0.260450i	$0.0838710\pi$
$109$	77.2047	+	133.723i	0.708300	+	1.22681i	−0.257187	+	0.966362i	$0.582796\pi$
$110$		−	140.729i		−	1.27935i
$111$		0			0
$112$	−48.4475	+	16.2050i	−0.432567	+	0.144688i
$113$	−78.3541	−	45.2378i	−0.693399	−	0.400334i	0.111485	−	0.993766i	$-0.464439\pi$
$113$	−78.3541	−	45.2378i	−0.693399	−	0.400334i	−0.804884	+	0.593432i	$0.797773\pi$
$114$		0			0
$115$	33.6179	−	58.2280i	0.292330	−	0.506330i
$116$	−64.9776	+	37.5149i	−0.560152	+	0.323404i
$117$		0			0
$118$	−173.577			−1.47099
$119$	−151.382	+	171.072i	−1.27212	+	1.43758i
$120$		0			0
$121$	−36.4159	−	63.0742i	−0.300958	−	0.521274i
$122$		−	110.179i		−	0.903107i
$123$		0			0
$124$	41.9691			0.338460
$125$			45.9626i			0.367701i
$126$		0			0
$127$	−149.428			−1.17660			−0.588298	−	0.808644i	$-0.700202\pi$
$127$	−149.428			−1.17660			−0.588298	+	0.808644i	$0.700202\pi$
$128$		−	142.945i		−	1.11676i
$129$		0			0
$130$	−178.285			−1.37142
$131$	−114.510	+	66.1122i	−0.874120	+	0.504673i	−0.868715	−	0.495312i	$-0.835054\pi$
$131$	−114.510	+	66.1122i	−0.874120	+	0.504673i	−0.00540450	+	0.999985i	$0.501720\pi$
$132$		0			0
$133$	−5.40630	+	26.5595i	−0.0406489	+	0.199695i
$134$			192.330i			1.43530i
$135$		0			0
$136$	−78.9200	−	136.693i	−0.580294	−	1.00510i
$137$	−72.7062	−	41.9769i	−0.530702	−	0.306401i	0.210600	−	0.977572i	$-0.432458\pi$
$137$	−72.7062	−	41.9769i	−0.530702	−	0.306401i	−0.741302	+	0.671171i	$0.765792\pi$
$138$		0			0
$139$	46.3953	−	80.3591i	0.333779	−	0.578123i	−0.649470	−	0.760387i	$-0.725009\pi$
$139$	46.3953	−	80.3591i	0.333779	−	0.578123i	0.983250	+	0.182264i	$0.0583426\pi$
$140$	−169.231	+	191.243i	−1.20879	+	1.36602i
$141$		0			0
$142$	45.0749			0.317429
$143$	52.8473	−	30.5114i	0.369562	−	0.213367i
$144$		0			0
$145$	44.2079	−	76.5704i	0.304882	−	0.528072i
$146$	239.341	−	138.183i	1.63932	−	0.946461i
$147$		0			0
$148$	134.413	−	232.810i	0.908197	−	1.57304i
$149$	231.185	−	133.475i	1.55158	−	0.895803i	0.553563	−	0.832807i	$-0.313268\pi$
$149$	231.185	−	133.475i	1.55158	−	0.895803i	0.998014	−	0.0629964i	$-0.0200657\pi$
$150$		0			0
$151$	11.8511	−	20.5267i	0.0784839	−	0.135938i	−0.824112	−	0.566427i	$-0.808325\pi$
$151$	11.8511	−	20.5267i	0.0784839	−	0.135938i	0.902596	+	0.430489i	$0.141659\pi$
$152$	−16.2189	−	9.36399i	−0.106703	−	0.0616052i
$153$		0			0
$154$	29.9683	−	147.225i	0.194600	−	0.956007i
$155$	−42.8309	+	24.7284i	−0.276328	+	0.159538i
$156$		0			0
$157$	−61.7020			−0.393007			−0.196503	−	0.980503i	$-0.562959\pi$
$157$	−61.7020			−0.393007			−0.196503	+	0.980503i	$0.562959\pi$
$158$		−	42.0437i		−	0.266099i
$159$		0			0
$160$	137.416	+	238.012i	0.858852	+	1.48758i
$161$	47.5695	−	53.7569i	0.295463	−	0.333894i
$162$		0			0
$163$	84.3903	−	146.168i	0.517732	−	0.896738i	−0.482056	−	0.876140i	$-0.660110\pi$
$163$	84.3903	−	146.168i	0.517732	−	0.896738i	0.999788	−	0.0205976i	$-0.00655689\pi$
$164$	−242.959	−	140.273i	−1.48146	−	0.855321i
$165$		0			0
$166$	59.1247	+	102.407i	0.356173	+	0.616909i
$167$	58.3089	+	33.6646i	0.349155	+	0.201585i	0.664313	−	0.747455i	$-0.268724\pi$
$167$	58.3089	+	33.6646i	0.349155	+	0.201585i	−0.315158	+	0.949039i	$0.602058\pi$
$168$		0			0
$169$	45.8460	+	79.4076i	0.271278	+	0.469867i
$170$	573.056	+	330.854i	3.37092	+	1.94620i
$171$		0			0
$172$	152.270	+	263.739i	0.885289	+	1.53337i
$173$			3.10411i			0.0179428i	0.999960	+	0.00897142i	$0.00285573\pi$
$173$			3.10411i			0.0179428i	−0.999960	+	0.00897142i	$0.997144\pi$
$174$		0			0
$175$	25.1184	−	123.399i	0.143534	−	0.705138i
$176$	−43.8645	−	25.3252i	−0.249230	−	0.143893i
$177$		0			0
$178$	134.191	−	232.425i	0.753879	−	1.30576i
$179$	−118.393	+	68.3545i	−0.661416	+	0.381869i	−0.792816	−	0.609461i	$-0.791386\pi$
$179$	−118.393	+	68.3545i	−0.661416	+	0.381869i	0.131401	+	0.991329i	$0.458053\pi$
$180$		0			0
$181$	−245.515			−1.35643			−0.678217	−	0.734862i	$-0.737247\pi$
$181$	−245.515			−1.35643			−0.678217	+	0.734862i	$0.737247\pi$
$182$	−186.515	−	37.9660i	−1.02481	−	0.208604i
$183$		0			0
$184$	24.7994	+	42.9538i	0.134779	+	0.233445i
$185$			316.788i			1.71237i
$186$		0			0
$187$	−226.487			−1.21116
$188$		−	224.226i		−	1.19269i
$189$		0			0
$190$	78.5128			0.413225
$191$		−	52.5230i		−	0.274990i	−0.990502	−	0.137495i	$-0.956095\pi$
$191$		−	52.5230i		−	0.274990i	0.990502	−	0.137495i	$-0.0439051\pi$
$192$		0			0
$193$	−126.877			−0.657392			−0.328696	−	0.944436i	$-0.606609\pi$
$193$	−126.877			−0.657392			−0.328696	+	0.944436i	$0.606609\pi$
$194$	63.8543	−	36.8663i	0.329146	−	0.190032i
$195$		0			0
$196$	−217.769	+	164.033i	−1.11106	+	0.836905i
$197$		−	262.003i		−	1.32997i	−0.746859	−	0.664983i	$-0.768439\pi$
$197$		−	262.003i		−	1.32997i	0.746859	−	0.664983i	$-0.231561\pi$
$198$		0			0
$199$	−5.96437	−	10.3306i	−0.0299717	−	0.0519125i	0.850650	−	0.525732i	$-0.176208\pi$
$199$	−5.96437	−	10.3306i	−0.0299717	−	0.0519125i	−0.880622	+	0.473819i	$0.842875\pi$
$200$	75.3553	+	43.5064i	0.376777	+	0.217532i
$201$		0			0
$202$	41.7389	−	72.2940i	0.206628	−	0.357891i
$203$	62.5544	−	70.6909i	0.308150	−	0.348231i
$204$		0			0
$205$	330.598			1.61267
$206$	402.442	−	232.350i	1.95360	−	1.12791i
$207$		0			0
$208$	−32.0837	+	55.5706i	−0.154249	+	0.267166i
$209$	−23.2728	+	13.4366i	−0.111353	+	0.0642897i
$210$		0			0
$211$	131.699	−	228.109i	0.624165	−	1.08109i	−0.364536	−	0.931189i	$-0.618773\pi$
$211$	131.699	−	228.109i	0.624165	−	1.08109i	0.988702	−	0.149897i	$-0.0478941\pi$
$212$	−254.339	+	146.843i	−1.19971	+	0.692654i
$213$		0			0
$214$	−153.782	+	266.358i	−0.718607	+	1.24466i
$215$	−310.793	−	179.436i	−1.44555	−	0.834588i
$216$		0			0
$217$	−50.0740	+	16.7490i	−0.230756	+	0.0771846i
$218$	413.546	−	238.761i	1.89700	−	1.09523i
$219$		0			0
$220$	−253.192			−1.15087
$221$			286.930i			1.29833i
$222$		0			0
$223$	−106.127	−	183.817i	−0.475904	−	0.824290i	0.523715	−	0.851894i	$-0.324546\pi$
$223$	−106.127	−	183.817i	−0.475904	−	0.824290i	−0.999619	+	0.0276035i	$0.991212\pi$
$224$	93.0748	+	278.262i	0.415512	+	1.24224i
$225$		0			0
$226$	−139.901	+	242.316i	−0.619031	+	1.07219i
$227$	153.720	+	88.7501i	0.677179	+	0.390970i	0.798791	−	0.601608i	$-0.205473\pi$
$227$	153.720	+	88.7501i	0.677179	+	0.390970i	−0.121612	+	0.992578i	$0.538806\pi$
$228$		0			0
$229$	44.8167	+	77.6247i	0.195706	+	0.338973i	0.947132	−	0.320845i	$-0.103967\pi$
$229$	44.8167	+	77.6247i	0.195706	+	0.338973i	−0.751426	+	0.659818i	$0.770634\pi$
$230$	−180.074	−	103.966i	−0.782931	−	0.452025i
$231$		0			0
$232$	32.6115	+	56.4847i	0.140567	+	0.243469i
$233$	−49.3848	−	28.5123i	−0.211952	−	0.122370i	0.390266	−	0.920702i	$-0.372383\pi$
$233$	−49.3848	−	28.5123i	−0.211952	−	0.122370i	−0.602218	+	0.798332i	$0.705716\pi$
$234$		0			0
$235$	132.115	+	228.830i	0.562192	+	0.973746i
$236$			312.290i			1.32326i
$237$		0			0
$238$	529.054	+	468.160i	2.22291	+	1.96706i
$239$	−334.530	−	193.141i	−1.39971	−	0.808122i	−0.405346	−	0.914163i	$-0.632849\pi$
$239$	−334.530	−	193.141i	−1.39971	−	0.808122i	−0.994362	+	0.106042i	$0.966182\pi$
$240$		0			0
$241$	−49.7423	+	86.1562i	−0.206400	+	0.357495i	−0.950578	−	0.310487i	$-0.899508\pi$
$241$	−49.7423	+	86.1562i	−0.206400	+	0.357495i	0.744178	+	0.667981i	$0.232841\pi$
$242$	−195.061	+	112.619i	−0.806039	+	0.465367i
$243$		0			0
$244$	−198.228			−0.812411
$245$	125.591	−	295.712i	0.512616	−	1.20699i
$246$		0			0
$247$	17.0224	+	29.4836i	0.0689165	+	0.119367i
$248$		−	36.4835i		−	0.147111i
$249$		0			0
$250$	142.143			0.568571
$251$			98.5469i			0.392617i	0.980542	+	0.196309i	$0.0628954\pi$
$251$			98.5469i			0.392617i	−0.980542	+	0.196309i	$0.937105\pi$
$252$		0			0
$253$	71.1701			0.281305
$254$			462.116i			1.81935i
$255$		0			0
$256$	−40.3161			−0.157485
$257$	171.453	−	98.9886i	0.667133	−	0.385169i	−0.127856	−	0.991793i	$-0.540810\pi$
$257$	171.453	−	98.9886i	0.667133	−	0.385169i	0.794989	+	0.606623i	$0.207476\pi$
$258$		0			0
$259$	−67.4603	+	331.411i	−0.260464	+	1.27958i
$260$			320.761i			1.23370i
$261$		0			0
$262$	204.457	+	354.129i	0.780369	+	1.35164i
$263$	114.940	+	66.3606i	0.437034	+	0.252322i	0.702339	−	0.711843i	$-0.252139\pi$
$263$	114.940	+	66.3606i	0.437034	+	0.252322i	−0.265305	+	0.964165i	$0.585473\pi$
$264$		0			0
$265$	173.041	−	299.716i	0.652986	−	1.13100i
$266$	82.1371	+	16.7194i	0.308786	+	0.0628548i
$267$		0			0
$268$	346.030			1.29116
$269$	−152.369	+	87.9704i	−0.566428	+	0.327027i	−0.755721	−	0.654893i	$-0.772714\pi$
$269$	−152.369	+	87.9704i	−0.566428	+	0.327027i	0.189293	+	0.981921i	$0.439380\pi$
$270$		0			0
$271$	−68.1137	+	117.976i	−0.251342	+	0.435337i	−0.963896	−	0.266280i	$-0.914205\pi$
$271$	−68.1137	+	117.976i	−0.251342	+	0.435337i	0.712553	+	0.701618i	$0.247539\pi$
$272$	206.251	−	119.079i	0.758277	−	0.437791i
$273$		0			0
$274$	−129.817	+	224.849i	−0.473783	+	0.820617i
$275$	108.129	−	62.4281i	0.393195	−	0.227011i
$276$		0			0
$277$	67.7609	−	117.365i	0.244624	−	0.423701i	−0.717402	−	0.696660i	$-0.754669\pi$
$277$	67.7609	−	117.365i	0.244624	−	0.423701i	0.962026	+	0.272958i	$0.0880021\pi$
$278$	−248.516	−	143.481i	−0.893943	−	0.516118i
$279$		0			0
$280$	166.247	+	147.112i	0.593739	+	0.525400i
$281$	−115.051	+	66.4246i	−0.409434	+	0.236387i	−0.690546	−	0.723288i	$-0.742630\pi$
$281$	−115.051	+	66.4246i	−0.409434	+	0.236387i	0.281113	+	0.959675i	$0.409296\pi$
$282$		0			0
$283$	−102.904			−0.363618			−0.181809	−	0.983334i	$-0.558195\pi$
$283$	−102.904			−0.363618			−0.181809	+	0.983334i	$0.558195\pi$
$284$		−	81.0963i		−	0.285550i
$285$		0			0
$286$	−94.3587	−	163.434i	−0.329926	−	0.571448i
$287$	345.859	+	70.4011i	1.20508	+	0.245300i
$288$		0			0
$289$	387.973	−	671.988i	1.34247	−	2.32522i
$290$	−236.799	−	136.716i	−0.816550	−	0.471435i
$291$		0			0
$292$	−248.612	−	430.609i	−0.851412	−	1.47469i
$293$	−68.8226	−	39.7347i	−0.234889	−	0.135613i	0.377936	−	0.925832i	$-0.376634\pi$
$293$	−68.8226	−	39.7347i	−0.234889	−	0.135613i	−0.612826	+	0.790218i	$0.709967\pi$
$294$		0			0
$295$	−184.003	−	318.703i	−0.623740	−	1.08035i
$296$	−202.381	−	116.845i	−0.683719	−	0.394745i
$297$		0			0
$298$	−412.780	−	714.956i	−1.38517	−	2.39918i
$299$		−	90.1633i		−	0.301549i
$300$		0			0
$301$	−286.928	−	253.903i	−0.953250	−	0.843532i
$302$	−63.4801	−	36.6503i	−0.210199	−	0.121359i
$303$		0			0
$304$	14.1289	−	24.4721i	0.0464768	−	0.0805002i
$305$	202.299	−	116.797i	0.663275	−	0.382942i
$306$		0			0
$307$	−49.4198			−0.160976			−0.0804882	−	0.996756i	$-0.525648\pi$
$307$	−49.4198			−0.160976			−0.0804882	+	0.996756i	$0.525648\pi$
$308$	−264.880	−	53.9175i	−0.859999	−	0.175057i
$309$		0			0
$310$	76.4744	+	132.458i	0.246692	+	0.427282i
$311$			180.407i			0.580087i	0.957014	+	0.290043i	$0.0936697\pi$
$311$			180.407i			0.580087i	−0.957014	+	0.290043i	$0.906330\pi$
$312$		0			0
$313$	−334.198			−1.06773			−0.533863	−	0.845571i	$-0.679260\pi$
$313$	−334.198			−1.06773			−0.533863	+	0.845571i	$0.679260\pi$
$314$			190.818i			0.607700i
$315$		0			0
$316$	−75.6427			−0.239376
$317$			40.2995i			0.127128i	0.997978	+	0.0635638i	$0.0202466\pi$
$317$			40.2995i			0.127128i	−0.997978	+	0.0635638i	$0.979753\pi$
$318$		0			0
$319$	93.5895			0.293384
$320$	570.310	−	329.269i	1.78222	−	1.02897i
$321$		0			0
$322$	−166.247	−	147.112i	−0.516295	−	0.456869i
$323$		−	126.358i		−	0.391200i
$324$		0			0
$325$	−79.0883	−	136.985i	−0.243349	−	0.421492i
$326$	−452.036	−	260.983i	−1.38661	−	0.800561i
$327$		0			0
$328$	−121.938	+	211.203i	−0.371763	+	0.643913i
$329$	89.4842	+	267.527i	0.271988	+	0.813153i
$330$		0			0
$331$	−609.354			−1.84095			−0.920474	−	0.390804i	$-0.872197\pi$
$331$	−609.354			−1.84095			−0.920474	+	0.390804i	$0.872197\pi$
$332$	184.245	−	106.374i	0.554956	−	0.320404i
$333$		0			0
$334$	104.110	−	180.324i	0.311707	−	0.539893i
$335$	−353.136	+	203.883i	−1.05414	+	0.608606i
$336$		0			0
$337$	−250.673	+	434.179i	−0.743837	+	1.28836i	0.206899	+	0.978362i	$0.433663\pi$
$337$	−250.673	+	434.179i	−0.743837	+	1.28836i	−0.950736	+	0.310002i	$0.899670\pi$
$338$	245.573	−	141.782i	0.726549	−	0.419473i
$339$		0			0
$340$	595.255	−	1031.01i	1.75075	−	3.03239i
$341$	−45.3371	−	26.1754i	−0.132953	−	0.0767607i
$342$		0			0
$343$	194.361	−	282.618i	0.566649	−	0.823959i
$344$	229.267	−	132.367i	0.666473	−	0.384789i
$345$		0			0
$346$	9.59968			0.0277447
$347$		−	438.238i		−	1.26293i	−0.775403	−	0.631467i	$-0.782453\pi$
$347$		−	438.238i		−	1.26293i	0.775403	−	0.631467i	$-0.217547\pi$
$348$		0			0
$349$	340.597	+	589.930i	0.975921	+	1.69035i	0.676861	+	0.736111i	$0.263340\pi$
$349$	340.597	+	589.930i	0.975921	+	1.69035i	0.299060	+	0.954234i	$0.403327\pi$
$350$	−381.620	−	77.6806i	−1.09034	−	0.221944i
$351$		0			0
$352$	−145.457	+	251.939i	−0.413231	+	0.715736i
$353$	−285.265	−	164.698i	−0.808117	−	0.466566i	0.0381848	−	0.999271i	$-0.487842\pi$
$353$	−285.265	−	164.698i	−0.808117	−	0.466566i	−0.846301	+	0.532704i	$0.821176\pi$
$354$		0			0
$355$	47.7824	+	82.7616i	0.134598	+	0.233131i
$356$	−418.167	−	241.429i	−1.17463	−	0.678170i
$357$		0			0
$358$	211.391	+	366.140i	0.590478	+	1.02274i
$359$	−232.053	−	133.976i	−0.646387	−	0.373192i	0.140684	−	0.990055i	$-0.455070\pi$
$359$	−232.053	−	133.976i	−0.646387	−	0.373192i	−0.787071	+	0.616863i	$0.788403\pi$
$360$		0			0
$361$	173.004	+	299.651i	0.479235	+	0.830059i
$362$			759.271i			2.09743i
$363$		0			0
$364$	−68.3064	+	335.568i	−0.187655	+	0.921890i
$365$	507.435	+	292.968i	1.39023	+	0.802651i
$366$		0			0
$367$	242.336	−	419.738i	0.660316	−	1.14370i	−0.320216	−	0.947344i	$-0.603756\pi$
$367$	242.336	−	419.738i	0.660316	−	1.14370i	0.980533	−	0.196357i	$-0.0629111\pi$
$368$	−64.8113	+	37.4188i	−0.176118	+	0.101682i
$369$		0			0
$370$	979.689			2.64781
$371$	244.854	−	276.702i	0.659983	−	0.745828i
$372$		0			0
$373$	44.9469	+	77.8504i	0.120501	+	0.208714i	0.919965	−	0.391999i	$-0.128217\pi$
$373$	44.9469	+	77.8504i	0.120501	+	0.208714i	−0.799464	+	0.600714i	$0.794883\pi$
$374$			700.428i			1.87280i
$375$		0			0
$376$	−194.918			−0.518400
$377$		−	118.566i		−	0.314498i
$378$		0			0
$379$	−558.621			−1.47393			−0.736967	−	0.675929i	$-0.763743\pi$
$379$	−558.621			−1.47393			−0.736967	+	0.675929i	$0.763743\pi$
$380$		−	141.256i		−	0.371727i
$381$		0			0
$382$	−162.431			−0.425213
$383$	−17.9175	+	10.3447i	−0.0467819	+	0.0270095i	−0.523209	−	0.852205i	$-0.675265\pi$
$383$	−17.9175	+	10.3447i	−0.0467819	+	0.0270095i	0.476427	+	0.879214i	$0.341932\pi$
$384$		0			0
$385$	302.087	−	101.044i	0.784642	−	0.262452i
$386$			392.375i			1.01652i
$387$		0			0
$388$	−66.3279	−	114.883i	−0.170948	−	0.296091i
$389$	328.312	+	189.551i	0.843991	+	0.487278i	0.858619	−	0.512615i	$-0.171323\pi$
$389$	328.312	+	189.551i	0.843991	+	0.487278i	−0.0146279	+	0.999893i	$0.504656\pi$
$390$		0			0
$391$	−167.321	+	289.809i	−0.427932	+	0.741199i
$392$	142.593	+	189.305i	0.363759	+	0.482921i
$393$		0			0
$394$	−810.263			−2.05651
$395$	77.1960	−	44.5691i	0.195433	−	0.112833i
$396$		0			0
$397$	−135.962	+	235.492i	−0.342473	+	0.593180i	−0.984891	−	0.173174i	$-0.944598\pi$
$397$	−135.962	+	235.492i	−0.342473	+	0.593180i	0.642419	+	0.766354i	$0.277931\pi$
$398$	−31.9481	+	18.4452i	−0.0802716	+	0.0463448i
$399$		0			0
$400$	−65.6451	+	113.701i	−0.164113	+	0.284252i
$401$	−311.346	+	179.756i	−0.776424	+	0.448269i	−0.835161	−	0.550005i	$-0.814626\pi$
$401$	−311.346	+	179.756i	−0.776424	+	0.448269i	0.0587375	+	0.998273i	$0.481293\pi$
$402$		0			0
$403$	−33.1608	+	57.4363i	−0.0822849	+	0.142522i
$404$	−130.068	−	75.0945i	−0.321949	−	0.185878i
$405$		0			0
$406$	−218.616	−	193.454i	−0.538464	−	0.476487i
$407$	−290.400	+	167.662i	−0.713513	+	0.411947i
$408$		0			0
$409$	436.460			1.06714			0.533570	−	0.845756i	$-0.320850\pi$
$409$	436.460			1.06714			0.533570	+	0.845756i	$0.320850\pi$
$410$		−	1022.40i		−	2.49365i
$411$		0			0
$412$	−418.032	−	724.052i	−1.01464	−	1.75741i
$413$	−124.629	−	372.598i	−0.301765	−	0.902175i
$414$		0			0
$415$	−125.352	+	217.117i	−0.302054	+	0.523173i
$416$	319.174	+	184.275i	0.767246	+	0.442970i
$417$		0			0
$418$	41.5535	+	71.9727i	0.0994102	+	0.172184i
$419$	−226.114	−	130.547i	−0.539653	−	0.311569i	0.205285	−	0.978702i	$-0.434188\pi$
$419$	−226.114	−	130.547i	−0.539653	−	0.311569i	−0.744938	+	0.667133i	$0.767521\pi$
$420$		0			0
$421$	185.524	+	321.337i	0.440675	+	0.763272i	0.997740	−	0.0671975i	$-0.0214058\pi$
$421$	185.524	+	321.337i	0.440675	+	0.763272i	−0.557065	+	0.830469i	$0.688072\pi$
$422$	−705.443	−	407.288i	−1.67167	−	0.965137i
$423$		0			0
$424$	127.650	+	221.096i	0.301060	+	0.521452i
$425$			587.075i			1.38135i
$426$		0			0
$427$	236.509	−	79.1091i	0.553886	−	0.185267i
$428$	479.218	+	276.676i	1.11967	+	0.646440i
$429$		0			0
$430$	−554.920	+	961.149i	−1.29051	+	2.23523i
$431$	−261.697	+	151.091i	−0.607185	+	0.350558i	−0.771863	−	0.635789i	$-0.780675\pi$
$431$	−261.697	+	151.091i	−0.607185	+	0.350558i	0.164678	+	0.986347i	$0.447341\pi$
$432$		0			0
$433$	−182.648			−0.421819			−0.210910	−	0.977506i	$-0.567643\pi$
$433$	−182.648			−0.421819			−0.210910	+	0.977506i	$0.567643\pi$
$434$	51.7976	+	154.857i	0.119349	+	0.356814i
$435$		0			0
$436$	−429.566	−	744.031i	−0.985244	−	1.70649i
$437$			39.7059i			0.0908602i
$438$		0			0
$439$	248.056			0.565048			0.282524	−	0.959260i	$-0.408828\pi$
$439$	248.056			0.565048			0.282524	+	0.959260i	$0.408828\pi$
$440$			220.099i			0.500224i
$441$		0			0
$442$	887.351			2.00758
$443$		−	97.9650i		−	0.221140i	−0.993868	−	0.110570i	$-0.964732\pi$
$443$		−	97.9650i		−	0.221140i	0.993868	−	0.110570i	$-0.0352676\pi$
$444$		0			0
$445$	569.005			1.27866
$446$	−568.466	+	328.204i	−1.27459	+	0.735883i
$447$		0			0
$448$	666.755	−	223.020i	1.48829	−	0.497813i
$449$			623.990i			1.38973i	0.719139	+	0.694866i	$0.244536\pi$
$449$			623.990i			1.38973i	−0.719139	+	0.694866i	$0.755464\pi$
$450$		0			0
$451$	174.971	+	303.059i	0.387963	+	0.671972i
$452$	435.961	+	251.702i	0.964516	+	0.556864i
$453$		0			0
$454$	274.466	−	475.389i	0.604551	−	1.04711i
$455$	−128.010	−	382.705i	−0.281340	−	0.841111i
$456$		0			0
$457$	55.9890			0.122514			0.0612571	−	0.998122i	$-0.480489\pi$
$457$	55.9890			0.122514			0.0612571	+	0.998122i	$0.480489\pi$
$458$	240.060	−	138.599i	0.524148	−	0.302617i
$459$		0			0
$460$	−187.050	+	323.980i	−0.406630	+	0.704304i
$461$	−282.323	+	162.999i	−0.612414	+	0.353577i	−0.773910	−	0.633296i	$-0.781702\pi$
$461$	−282.323	+	162.999i	−0.612414	+	0.353577i	0.161496	+	0.986873i	$0.448368\pi$
$462$		0			0
$463$	134.683	−	233.278i	0.290893	−	0.503841i	−0.683128	−	0.730298i	$-0.739381\pi$
$463$	134.683	−	233.278i	0.290893	−	0.503841i	0.974021	+	0.226457i	$0.0727144\pi$
$464$	−85.2275	+	49.2061i	−0.183680	+	0.106048i
$465$		0			0
$466$	−88.1764	+	152.726i	−0.189220	+	0.327738i
$467$	211.178	+	121.924i	0.452201	+	0.261078i	0.708759	−	0.705450i	$-0.249255\pi$
$467$	211.178	+	121.924i	0.452201	+	0.261078i	−0.256558	+	0.966529i	$0.582589\pi$
$468$		0			0
$469$	−412.854	+	138.094i	−0.880286	+	0.294443i
$470$	707.674	−	408.576i	1.50569	−	0.869310i
$471$		0			0
$472$	271.472			0.575153
$473$		−	379.872i		−	0.803112i
$474$		0			0
$475$	34.8287	+	60.3251i	0.0733236	+	0.127000i
$476$	842.288	−	951.845i	1.76951	−	1.99968i
$477$		0			0
$478$	−597.302	+	1034.56i	−1.24959	+	2.16435i
$479$	−501.193	−	289.364i	−1.04633	−	0.604100i	−0.124711	−	0.992193i	$-0.539800\pi$
$479$	−501.193	−	289.364i	−1.04633	−	0.604100i	−0.921620	+	0.388094i	$0.873134\pi$
$480$		0			0
$481$	212.406	+	367.899i	0.441593	+	0.764862i
$482$	266.444	+	153.832i	0.552788	+	0.319153i
$483$		0			0
$484$	202.618	+	350.944i	0.418632	+	0.725091i
$485$	135.380	+	78.1616i	0.279134	+	0.161158i
$486$		0			0
$487$	−438.856	−	760.120i	−0.901141	−	1.56082i	−0.826015	−	0.563648i	$-0.809397\pi$
$487$	−438.856	−	760.120i	−0.901141	−	1.56082i	−0.0751259	−	0.997174i	$-0.523936\pi$
$488$			172.319i			0.353113i
$489$		0			0
$490$	−914.511	−	388.399i	−1.86635	−	0.792651i
$491$	−193.388	−	111.653i	−0.393867	−	0.227399i	0.289968	−	0.957036i	$-0.406355\pi$
$491$	−193.388	−	111.653i	−0.393867	−	0.227399i	−0.683834	+	0.729637i	$0.739689\pi$
$492$		0			0
$493$	−220.029	+	381.102i	−0.446307	+	0.773026i
$494$	91.1801	−	52.6429i	0.184575	−	0.106564i
$495$		0			0
$496$	55.0485			0.110985
$497$	32.3640	+	96.7573i	0.0651187	+	0.194683i
$498$		0			0
$499$	−34.9560	−	60.5456i	−0.0700521	−	0.121334i	0.828872	−	0.559439i	$-0.188983\pi$
$499$	−34.9560	−	60.5456i	−0.0700521	−	0.121334i	−0.898924	+	0.438105i	$0.855650\pi$
$500$		−	255.736i		−	0.511471i
$501$		0			0
$502$	304.763			0.607098
$503$			884.758i			1.75896i	0.475934	+	0.879481i	$0.342110\pi$
$503$			884.758i			1.75896i	−0.475934	+	0.879481i	$0.657890\pi$
$504$		0			0
$505$	176.985			0.350464
$506$		−	220.099i		−	0.434977i
$507$		0			0
$508$	831.415			1.63664
$509$	77.3961	−	44.6847i	0.152055	−	0.0877891i	−0.422042	−	0.906576i	$-0.638687\pi$
$509$	77.3961	−	44.6847i	0.152055	−	0.0877891i	0.574097	+	0.818787i	$0.305353\pi$
$510$		0			0
$511$	468.471	+	414.550i	0.916773	+	0.811253i
$512$		−	447.099i		−	0.873241i
$513$		0			0
$514$	−306.129	−	530.231i	−0.595582	−	1.03158i
$515$	853.232	+	492.614i	1.65676	+	0.956531i
$516$		0			0
$517$	−139.846	+	242.220i	−0.270495	+	0.468511i
$518$	1024.91	+	208.626i	1.97860	+	0.402752i
$519$		0			0
$520$	278.836			0.536224
$521$	−148.371	+	85.6622i	−0.284782	+	0.164419i	−0.635586	−	0.772030i	$-0.719242\pi$
$521$	−148.371	+	85.6622i	−0.284782	+	0.164419i	0.350804	+	0.936449i	$0.385908\pi$
$522$		0			0
$523$	222.657	−	385.654i	0.425731	−	0.737388i	−0.570757	−	0.821119i	$-0.693350\pi$
$523$	222.657	−	385.654i	0.425731	−	0.737388i	0.996488	+	0.0837307i	$0.0266835\pi$
$524$	637.131	−	367.848i	1.21590	−	0.701999i
$525$		0			0
$526$	205.225	−	355.460i	0.390161	−	0.675780i
$527$	213.176	−	123.077i	0.404508	−	0.233543i
$528$		0			0
$529$	−211.922	+	367.059i	−0.400609	+	0.693874i
$530$	−926.893	−	535.142i	−1.74885	−	1.00970i
$531$		0			0
$532$	30.0806	−	147.777i	0.0565425	−	0.277776i
$533$	383.937	−	221.666i	0.720331	−	0.415884i
$534$		0			0
$535$	−652.078			−1.21884
$536$		−	300.802i		−	0.561198i
$537$		0			0
$538$	272.055	+	471.212i	0.505678	+	0.875859i
$539$	337.550	−	41.3786i	0.626251	−	0.0767691i
$540$		0			0
$541$	329.857	−	571.329i	0.609717	−	1.05606i	−0.381570	−	0.924340i	$-0.624616\pi$
$541$	329.857	−	571.329i	0.609717	−	1.05606i	0.991287	−	0.131721i	$-0.0420503\pi$
$542$	364.850	+	210.646i	0.673156	+	0.388647i
$543$		0			0
$544$	−683.941	−	1184.62i	−1.25724	−	2.17761i
$545$	876.775	+	506.206i	1.60876	+	0.928818i
$546$		0			0
$547$	140.018	+	242.518i	0.255974	+	0.443360i	0.965160	−	0.261662i	$-0.0842706\pi$
$547$	140.018	+	242.518i	0.255974	+	0.443360i	−0.709186	+	0.705022i	$0.750937\pi$
$548$	404.537	+	233.559i	0.738205	+	0.426203i
$549$		0			0
$550$	−193.063	−	334.395i	−0.351024	−	0.607992i
$551$			52.2137i			0.0947617i
$552$		0			0
$553$	90.2505	−	30.1875i	0.163202	−	0.0545887i
$554$	−362.960	−	209.555i	−0.655163	−	0.378258i
$555$		0			0
$556$	−258.143	+	447.117i	−0.464286	+	0.804168i
$557$	352.694	−	203.628i	0.633203	−	0.365580i	−0.148789	−	0.988869i	$-0.547537\pi$
$557$	352.694	−	203.628i	0.633203	−	0.365580i	0.781991	+	0.623289i	$0.214204\pi$
$558$		0			0
$559$	−481.248			−0.860910
$560$	−221.971	+	250.843i	−0.396377	+	0.447934i
$561$		0			0
$562$	205.423	+	355.803i	0.365521	+	0.633101i
$563$		−	392.798i		−	0.697688i	−0.937181	−	0.348844i	$-0.886574\pi$
$563$		−	392.798i		−	0.697688i	0.937181	−	0.348844i	$-0.113426\pi$
$564$		0			0
$565$	−593.218			−1.04994
$566$			318.238i			0.562258i
$567$		0			0
$568$	−70.4966			−0.124114
$569$		−	835.581i		−	1.46851i	−0.678875	−	0.734254i	$-0.737532\pi$
$569$		−	835.581i		−	1.46851i	0.678875	−	0.734254i	$-0.262468\pi$
$570$		0			0
$571$	865.024			1.51493			0.757464	−	0.652877i	$-0.226438\pi$
$571$	865.024			1.51493			0.757464	+	0.652877i	$0.226438\pi$
$572$	−294.042	+	169.765i	−0.514060	+	0.296792i
$573$		0			0
$574$	217.720	−	1069.59i	0.379304	−	1.86340i
$575$		−	184.479i		−	0.320833i
$576$		0			0
$577$	395.014	+	684.185i	0.684600	+	1.18576i	0.973562	+	0.228422i	$0.0733566\pi$
$577$	395.014	+	684.185i	0.684600	+	1.18576i	−0.288962	+	0.957341i	$0.593310\pi$
$578$	−2078.17	−	1199.83i	−3.59545	−	2.07583i
$579$		0			0
$580$	−245.973	+	426.037i	−0.424091	+	0.734547i
$581$	−177.374	+	200.445i	−0.305291	+	0.345000i
$582$		0			0
$583$	366.333			0.628359
$584$	−374.326	+	216.117i	−0.640970	+	0.370064i
$585$		0			0
$586$	−122.882	+	212.839i	−0.209697	+	0.363206i
$587$	−252.042	+	145.517i	−0.429373	+	0.247899i	−0.699080	−	0.715044i	$-0.746407\pi$
$587$	−252.042	+	145.517i	−0.429373	+	0.247899i	0.269706	+	0.962943i	$0.413073\pi$
$588$		0			0
$589$	14.6033	−	25.2936i	0.0247934	−	0.0429434i
$590$	−985.611	+	569.043i	−1.67053	+	0.964479i
$591$		0			0
$592$	176.302	−	305.364i	0.297808	−	0.515818i
$593$	1015.69	+	586.410i	1.71280	+	0.988887i	0.930735	+	0.365694i	$0.119168\pi$
$593$	1015.69	+	586.410i	1.71280	+	0.988887i	0.782068	+	0.623194i	$0.214165\pi$
$594$		0			0
$595$	−298.751	+	1467.67i	−0.502103	+	2.46668i
$596$	−1286.31	+	742.652i	−2.15824	+	1.24606i
$597$		0			0
$598$	−278.836			−0.466281
$599$		−	3.44849i		−	0.00575708i	−0.999996	−	0.00287854i	$-0.999084\pi$
$599$		−	3.44849i		−	0.00575708i	0.999996	−	0.00287854i	$-0.000916269\pi$
$600$		0			0
$601$	−575.547	−	996.876i	−0.957649	−	1.65870i	−0.728187	−	0.685379i	$-0.759637\pi$
$601$	−575.547	−	996.876i	−0.957649	−	1.65870i	−0.229462	−	0.973318i	$-0.573697\pi$
$602$	−785.213	+	887.346i	−1.30434	+	1.47400i
$603$		0			0
$604$	−65.9393	+	114.210i	−0.109171	+	0.189090i
$605$	−413.557	−	238.767i	−0.683565	−	0.394656i
$606$		0			0
$607$	−378.598	−	655.751i	−0.623720	−	1.08031i	−0.988787	−	0.149333i	$-0.952287\pi$
$607$	−378.598	−	655.751i	−0.623720	−	1.08031i	0.365067	−	0.930981i	$-0.381046\pi$
$608$	−140.557	−	81.1507i	−0.231180	−	0.133472i
$609$		0			0
$610$	−361.204	−	625.623i	−0.592137	−	1.02561i
$611$	306.861	+	177.167i	0.502228	+	0.289962i
$612$		0			0
$613$	−265.964	−	460.664i	−0.433874	−	0.751491i	0.563329	−	0.826232i	$-0.309520\pi$
$613$	−265.964	−	460.664i	−0.433874	−	0.751491i	−0.997203	+	0.0747414i	$0.976187\pi$
$614$			152.834i			0.248916i
$615$		0			0
$616$	−46.8702	+	230.259i	−0.0760880	+	0.373796i
$617$	−725.294	−	418.749i	−1.17552	−	0.678685i	−0.220544	−	0.975377i	$-0.570783\pi$
$617$	−725.294	−	418.749i	−1.17552	−	0.678685i	−0.954973	+	0.296692i	$0.904117\pi$
$618$		0			0
$619$	291.851	−	505.500i	0.471488	−	0.816640i	−0.527980	−	0.849257i	$-0.677051\pi$
$619$	291.851	−	505.500i	0.471488	−	0.816640i	0.999468	+	0.0326162i	$0.0103839\pi$
$620$	238.311	−	137.589i	0.384372	−	0.221917i
$621$		0			0
$622$	557.921			0.896979
$623$	595.271	+	121.170i	0.955490	+	0.194494i
$624$		0			0
$625$	375.555	+	650.481i	0.600888	+	1.04077i
$626$			1033.53i			1.65101i
$627$		0			0
$628$	343.309			0.546671
$629$		−	1576.70i		−	2.50668i
$630$		0			0
$631$	654.982			1.03801			0.519003	−	0.854772i	$-0.326303\pi$
$631$	654.982			1.03801			0.519003	+	0.854772i	$0.326303\pi$
$632$			65.7559i			0.104044i
$633$		0			0
$634$	124.629			0.196576
$635$	−848.487	+	489.874i	−1.33620	+	0.771456i
$636$		0			0
$637$	−52.4213	−	427.631i	−0.0822940	−	0.671321i
$638$		−	289.432i		−	0.453655i
$639$		0			0
$640$	−468.622	−	811.676i	−0.732221	−	1.26824i
$641$	−231.146	−	133.452i	−0.360601	−	0.208193i	0.308743	−	0.951145i	$-0.400092\pi$
$641$	−231.146	−	133.452i	−0.360601	−	0.208193i	−0.669345	+	0.742952i	$0.733425\pi$
$642$		0			0
$643$	−145.484	+	251.986i	−0.226259	+	0.391892i	−0.956696	−	0.291088i	$-0.905983\pi$
$643$	−145.484	+	251.986i	−0.226259	+	0.391892i	0.730438	+	0.682979i	$0.239316\pi$
$644$	−264.676	+	299.103i	−0.410988	+	0.464445i
$645$		0			0
$646$	−390.770			−0.604906
$647$	−407.474	+	235.255i	−0.629791	+	0.363610i	−0.780671	−	0.624942i	$-0.785122\pi$
$647$	−407.474	+	235.255i	−0.629791	+	0.363610i	0.150880	+	0.988552i	$0.451789\pi$
$648$		0			0
$649$	194.770	−	337.352i	0.300108	−	0.519802i
$650$	−423.635	+	244.586i	−0.651747	+	0.376286i
$651$		0			0
$652$	−469.547	+	813.279i	−0.720164	+	1.24736i
$653$	−225.654	+	130.281i	−0.345565	+	0.199512i	−0.662730	−	0.748858i	$-0.730602\pi$
$653$	−225.654	+	130.281i	−0.345565	+	0.199512i	0.317165	+	0.948370i	$0.397269\pi$
$654$		0			0
$655$	−433.476	+	750.802i	−0.661795	+	1.14626i
$656$	−318.676	−	183.988i	−0.485787	−	0.280469i
$657$		0			0
$658$	827.347	−	276.736i	1.25737	−	0.420572i
$659$	993.568	−	573.637i	1.50769	−	0.870465i	0.507730	−	0.861516i	$-0.330485\pi$
$659$	993.568	−	573.637i	1.50769	−	0.870465i	0.999960	−	0.00894898i	$-0.00284859\pi$
$660$		0			0
$661$	262.625			0.397315			0.198658	−	0.980069i	$-0.436342\pi$
$661$	262.625			0.397315			0.198658	+	0.980069i	$0.436342\pi$
$662$			1884.47i			2.84663i
$663$		0			0
$664$	−92.4704	−	160.163i	−0.139263	−	0.241210i
$665$	56.3726	+	168.535i	0.0847708	+	0.253436i
$666$		0			0
$667$	69.1408	−	119.755i	0.103659	−	0.179543i
$668$	−324.430	−	187.310i	−0.485674	−	0.280404i
$669$		0			0
$670$	630.522	+	1092.10i	0.941078	+	1.63000i
$671$	214.136	+	123.632i	0.319130	+	0.184250i
$672$		0			0
$673$	−242.749	−	420.453i	−0.360696	−	0.624744i	0.627379	−	0.778714i	$-0.284128\pi$
$673$	−242.749	−	420.453i	−0.360696	−	0.624744i	−0.988076	+	0.153970i	$0.950794\pi$
$674$	1342.73	+	775.224i	1.99218	+	1.15018i
$675$		0			0
$676$	−255.087	−	441.823i	−0.377347	−	0.653584i
$677$		−	602.276i		−	0.889625i	−0.895624	−	0.444812i	$-0.853270\pi$
$677$		−	602.276i		−	0.889625i	0.895624	−	0.444812i	$-0.146730\pi$
$678$		0			0
$679$	124.985	+	110.599i	0.184072	+	0.162885i
$680$	−896.254	−	517.453i	−1.31802	−	0.760960i
$681$		0			0
$682$	−80.9493	+	140.208i	−0.118694	+	0.205584i
$683$	−584.817	+	337.644i	−0.856247	+	0.494354i	−0.862754	−	0.505625i	$-0.831262\pi$
$683$	−584.817	+	337.644i	−0.856247	+	0.494354i	0.00650687	+	0.999979i	$0.497929\pi$
$684$		0			0
$685$	−550.458			−0.803589
$686$	−874.016	−	601.074i	−1.27408	−	0.876201i
$687$		0			0
$688$	199.724	+	345.931i	0.290296	+	0.502807i
$689$		−	464.096i		−	0.673580i
$690$		0			0
$691$	822.364			1.19011			0.595054	−	0.803686i	$-0.297131\pi$
$691$	822.364			1.19011			0.595054	+	0.803686i	$0.297131\pi$
$692$		−	17.2712i		−	0.0249584i
$693$		0			0
$694$	−1355.28			−1.95285
$695$		−	608.398i		−	0.875393i
$696$		0			0
$697$	−1645.43			−2.36074
$698$	1824.40	−	1053.32i	2.61376	−	1.50905i
$699$		0			0
$700$	−139.759	+	686.591i	−0.199655	+	0.980845i
$701$			835.836i			1.19235i	0.802855	+	0.596174i	$0.203313\pi$
$701$			835.836i			1.19235i	−0.802855	+	0.596174i	$0.796687\pi$
$702$		0			0
$703$	−93.5390	−	162.014i	−0.133057	−	0.230461i
$704$	603.682	+	348.536i	0.857502	+	0.495079i
$705$		0			0
$706$	−509.340	+	882.203i	−0.721445	+	1.24958i
$707$	185.154	+	37.6890i	0.261887	+	0.0533084i
$708$		0			0
$709$	−680.531			−0.959847			−0.479923	−	0.877310i	$-0.659336\pi$
$709$	−680.531			−0.959847			−0.479923	+	0.877310i	$0.659336\pi$
$710$	255.946	−	147.771i	0.360487	−	0.208128i
$711$		0			0
$712$	−209.873	+	363.510i	−0.294765	+	0.510548i
$713$	−66.9871	+	38.6750i	−0.0939511	+	0.0542427i
$714$		0			0
$715$	200.053	−	346.503i	0.279795	−	0.484619i
$716$	658.740	−	380.324i	0.920028	−	0.531178i
$717$		0			0
$718$	−414.330	+	717.640i	−0.577061	+	0.999498i
$719$	−582.541	−	336.330i	−0.810210	−	0.467775i	0.0368191	−	0.999322i	$-0.488277\pi$
$719$	−582.541	−	336.330i	−0.810210	−	0.467775i	−0.847029	+	0.531547i	$0.821611\pi$
$720$		0			0
$721$	787.715	+	697.050i	1.09253	+	0.966782i
$722$	926.693	−	535.026i	1.28351	−	0.741033i
$723$		0			0
$724$	1366.04			1.88680
$725$		−	242.592i		−	0.334610i
$726$		0			0
$727$	−386.881	−	670.098i	−0.532161	−	0.921730i	−0.999295	−	0.0375436i	$-0.988047\pi$
$727$	−386.881	−	670.098i	−0.532161	−	0.921730i	0.467134	−	0.884187i	$-0.345287\pi$
$728$	291.708	+	59.3784i	0.400697	+	0.0815638i
$729$		0			0
$730$	906.023	−	1569.28i	1.24113	−	2.14970i
$731$	1546.86	+	893.081i	2.11609	+	1.22172i
$732$		0			0
$733$	−205.889	−	356.611i	−0.280886	−	0.486509i	0.690717	−	0.723125i	$-0.257295\pi$
$733$	−205.889	−	356.611i	−0.280886	−	0.486509i	−0.971603	+	0.236616i	$0.923962\pi$
$734$	−1298.07	−	749.441i	−1.76849	−	1.02104i
$735$		0			0
$736$	214.918	+	372.249i	0.292008	+	0.505773i
$737$	−373.799	−	215.813i	−0.507190	−	0.292826i
$738$		0			0
$739$	416.075	+	720.664i	0.563025	+	0.975188i	0.997230	+	0.0743737i	$0.0236958\pi$
$739$	416.075	+	720.664i	0.563025	+	0.975188i	−0.434206	+	0.900814i	$0.642971\pi$
$740$		−	1762.61i		−	2.38190i
$741$		0			0
$742$	−855.721	−	757.227i	−1.15326	−	1.02052i
$743$	730.532	+	421.773i	0.983219	+	0.567662i	0.903240	−	0.429135i	$-0.141182\pi$
$743$	730.532	+	421.773i	0.983219	+	0.567662i	0.0799785	+	0.996797i	$0.474515\pi$
$744$		0			0
$745$	875.150	−	1515.80i	1.17470	−	2.03464i
$746$	240.758	−	139.002i	0.322732	−	0.186329i
$747$		0			0
$748$	1260.17			1.68472
$749$	−682.178	−	138.861i	−0.910786	−	0.185395i
$750$		0			0
$751$	−305.563	−	529.251i	−0.406875	−	0.704729i	0.587663	−	0.809106i	$-0.300048\pi$
$751$	−305.563	−	529.251i	−0.406875	−	0.704729i	−0.994538	+	0.104378i	$0.966715\pi$
$752$		−	294.105i		−	0.391096i
$753$		0			0
$754$	−366.673			−0.486304
$755$		−	155.407i		−	0.205837i
$756$		0			0
$757$	38.7326			0.0511659			0.0255829	−	0.999673i	$-0.491856\pi$
$757$	38.7326			0.0511659			0.0255829	+	0.999673i	$0.491856\pi$
$758$			1727.57i			2.27912i
$759$		0			0
$760$	−122.793			−0.161570
$761$	570.745	−	329.519i	0.749993	−	0.433009i	−0.0756985	−	0.997131i	$-0.524119\pi$
$761$	570.745	−	329.519i	0.749993	−	0.433009i	0.825691	+	0.564122i	$0.190785\pi$
$762$		0			0
$763$	809.451	+	716.283i	1.06088	+	0.938772i
$764$			292.238i			0.382510i
$765$		0			0
$766$	31.9916	+	55.4110i	0.0417644	+	0.0723381i
$767$	−427.381	−	246.748i	−0.557211	−	0.321706i
$768$		0			0
$769$	153.720	−	266.251i	0.199896	−	0.346231i	−0.748598	−	0.663024i	$-0.769273\pi$
$769$	153.720	−	266.251i	0.199896	−	0.346231i	0.948495	+	0.316793i	$0.102606\pi$
$770$	−312.486	−	934.226i	−0.405826	−	1.21328i
$771$		0			0
$772$	705.940			0.914431
$773$	90.6280	−	52.3241i	0.117242	−	0.0676896i	−0.440232	−	0.897884i	$-0.645104\pi$
$773$	90.6280	−	52.3241i	0.117242	−	0.0676896i	0.557474	+	0.830194i	$0.311771\pi$
$774$		0			0
$775$	−67.8489	+	117.518i	−0.0875470	+	0.151636i
$776$	−99.8675	+	57.6585i	−0.128695	+	0.0743022i
$777$		0			0
$778$	586.201	−	1015.33i	0.753471	−	1.30505i
$779$	−169.077	+	97.6167i	−0.217044	+	0.125310i
$780$		0			0
$781$	−50.5784	+	87.6044i	−0.0647611	+	0.112169i
$782$	896.254	+	517.453i	1.14611	+	0.661704i
$783$		0			0
$784$	−285.635	+	215.153i	−0.364330	+	0.274430i
$785$	−350.359	+	202.280i	−0.446317	+	0.257681i
$786$		0			0
$787$	−1512.06			−1.92130			−0.960650	−	0.277762i	$-0.910407\pi$
$787$	−1512.06			−1.92130			−0.960650	+	0.277762i	$0.910407\pi$
$788$			1457.78i			1.84998i
$789$		0			0
$790$	−137.833	−	238.734i	−0.174472	−	0.302195i
$791$	−620.602	−	126.326i	−0.784579	−	0.159705i
$792$		0			0
$793$	156.625	−	271.283i	0.197510	−	0.342097i
$794$	728.277	+	420.471i	0.917226	+	0.529560i
$795$		0			0
$796$	33.1857	+	57.4793i	0.0416906	+	0.0722102i
$797$	−689.122	−	397.865i	−0.864645	−	0.499203i	0.000920235	−	1.00000i	$-0.499707\pi$
$797$	−689.122	−	397.865i	−0.864645	−	0.499203i	−0.865565	+	0.500797i	$0.833040\pi$
$798$		0			0
$799$	−657.556	−	1138.92i	−0.822974	−	1.42543i
$800$	653.048	+	377.038i	0.816311	+	0.471297i
$801$		0			0
$802$	555.907	+	962.859i	0.693151	+	1.20057i
$803$			620.221i			0.772380i
$804$		0			0
$805$	93.8780	−	461.193i	0.116619	−	0.572911i
$806$	177.626	+	102.552i	0.220379	+	0.127236i
$807$		0			0
$808$	−65.2793	+	113.067i	−0.0807912	+	0.139934i
$809$	780.748	−	450.765i	0.965077	−	0.557188i	0.0673454	−	0.997730i	$-0.478547\pi$
$809$	780.748	−	450.765i	0.965077	−	0.557188i	0.897732	+	0.440542i	$0.145214\pi$
$810$		0			0
$811$	1340.86			1.65334			0.826668	−	0.562690i	$-0.190233\pi$
$811$	1340.86			1.65334			0.826668	+	0.562690i	$0.190233\pi$
$812$	−348.052	+	393.323i	−0.428635	+	0.484388i
$813$		0			0
$814$	518.508	+	898.081i	0.636987	+	1.10329i
$815$		−	1106.64i		−	1.35784i
$816$		0			0
$817$	211.931			0.259402
$818$		−	1349.78i		−	1.65010i
$819$		0			0
$820$	−1839.44			−2.24322
$821$			488.403i			0.594888i	0.954739	+	0.297444i	$0.0961341\pi$
$821$			488.403i			0.594888i	−0.954739	+	0.297444i	$0.903866\pi$
$822$		0			0
$823$	357.790			0.434739			0.217369	−	0.976089i	$-0.430252\pi$
$823$	357.790			0.434739			0.217369	+	0.976089i	$0.430252\pi$
$824$	−629.415	+	363.393i	−0.763853	+	0.441011i
$825$		0			0
$826$	−1152.29	+	385.424i	−1.39502	+	0.466615i
$827$			1214.55i			1.46862i	0.678816	+	0.734308i	$0.262493\pi$
$827$			1214.55i			1.46862i	−0.678816	+	0.734308i	$0.737507\pi$
$828$		0			0
$829$	−318.243	−	551.213i	−0.383888	−	0.664914i	0.607726	−	0.794147i	$-0.292082\pi$
$829$	−318.243	−	551.213i	−0.383888	−	0.664914i	−0.991614	+	0.129233i	$0.958748\pi$
$830$	671.449	+	387.661i	0.808974	+	0.467062i
$831$		0			0
$832$	441.550	−	764.786i	0.530709	−	0.919214i
$833$	−625.084	+	1471.80i	−0.750401	+	1.76687i
$834$		0			0
$835$	441.456			0.528690
$836$	129.490	−	74.7608i	0.154892	−	0.0894268i
$837$		0			0
$838$	−403.727	+	699.275i	−0.481774	+	0.834457i
$839$	912.315	−	526.725i	1.08738	−	0.627801i	0.154505	−	0.987992i	$-0.450622\pi$
$839$	912.315	−	526.725i	1.08738	−	0.627801i	0.932879	+	0.360191i	$0.117288\pi$
$840$		0			0
$841$	−329.579	+	570.848i	−0.391890	+	0.678773i
$842$	993.758	−	573.747i	1.18024	−	0.681409i
$843$		0			0
$844$	−732.771	+	1269.20i	−0.868212	+	1.50379i
$845$	520.649	+	300.597i	0.616153	+	0.355736i
$846$		0			0
$847$	−381.801	−	337.856i	−0.450769	−	0.398886i
$848$	−333.602	+	192.605i	−0.393399	+	0.227129i
$849$		0			0
$850$	1815.57			2.13596
$851$			495.453i			0.582201i
$852$		0			0
$853$	193.907	+	335.856i	0.227323	+	0.393735i	0.957014	−	0.290042i	$-0.0936693\pi$
$853$	193.907	+	335.856i	0.227323	+	0.393735i	−0.729691	+	0.683777i	$0.760336\pi$
$854$	−244.650	−	731.422i	−0.286476	−	0.856466i
$855$		0			0
$856$	240.514	−	416.582i	0.280974	−	0.486661i
$857$	−469.976	−	271.341i	−0.548397	−	0.316617i	0.200078	−	0.979780i	$-0.435880\pi$
$857$	−469.976	−	271.341i	−0.548397	−	0.316617i	−0.748475	+	0.663163i	$0.769214\pi$
$858$		0			0
$859$	366.499	+	634.795i	0.426658	+	0.738994i	0.996574	−	0.0827097i	$-0.0263574\pi$
$859$	366.499	+	634.795i	0.426658	+	0.738994i	−0.569916	+	0.821703i	$0.693024\pi$
$860$	1729.25	+	998.382i	2.01075	+	1.16091i
$861$		0			0
$862$	467.258	+	809.315i	0.542063	+	0.938880i
$863$	29.8544	+	17.2365i	0.0345938	+	0.0199727i	0.517197	−	0.855866i	$-0.326975\pi$
$863$	29.8544	+	17.2365i	0.0345938	+	0.0199727i	−0.482603	+	0.875839i	$0.660309\pi$
$864$		0			0
$865$	10.1763	+	17.6259i	0.0117645	+	0.0203768i
$866$			564.851i			0.652253i
$867$		0			0
$868$	278.611	−	93.1915i	0.320981	−	0.107364i
$869$	81.7131	+	47.1771i	0.0940312	+	0.0542889i
$870$		0			0
$871$	−273.407	+	473.555i	−0.313900	+	0.543691i
$872$	−646.782	+	373.420i	−0.741723	+	0.428234i
$873$		0			0
$874$	122.793			0.140496
$875$	102.059	+	305.122i	0.116639	+	0.348711i
$876$		0			0
$877$	−161.259	−	279.309i	−0.183876	−	0.318482i	0.759321	−	0.650716i	$-0.225531\pi$
$877$	−161.259	−	279.309i	−0.183876	−	0.318482i	−0.943197	+	0.332234i	$0.892198\pi$
$878$		−	767.131i		−	0.873726i
$879$		0			0
$880$	−332.098			−0.377384
$881$		−	93.0003i		−	0.105562i	−0.998606	−	0.0527811i	$-0.983191\pi$
$881$		−	93.0003i		−	0.105562i	0.998606	−	0.0527811i	$-0.0168086\pi$
$882$		0			0
$883$	1694.12			1.91859			0.959296	−	0.282404i	$-0.0911318\pi$
$883$	1694.12			1.91859			0.959296	+	0.282404i	$0.0911318\pi$
$884$		−	1596.48i		−	1.80597i
$885$		0			0
$886$	−302.964			−0.341945
$887$	−262.854	+	151.759i	−0.296341	+	0.171092i	−0.640798	−	0.767710i	$-0.721396\pi$
$887$	−262.854	+	151.759i	−0.296341	+	0.171092i	0.344457	+	0.938802i	$0.388063\pi$
$888$		0			0
$889$	−991.974	+	331.801i	−1.11583	+	0.373230i
$890$		−	1759.69i		−	1.97718i
$891$		0			0
$892$	590.487	+	1022.75i	0.661981	+	1.14659i
$893$	−135.135	−	78.0202i	−0.151327	−	0.0873686i
$894$		0			0
$895$	−448.178	+	776.267i	−0.500757	+	0.867337i
$896$	−317.407	−	948.938i	−0.354248	−	1.05908i
$897$		0			0
$898$	1929.73			2.14892
$899$	−88.0888	+	50.8581i	−0.0979853	+	0.0565719i
$900$		0			0
$901$	−861.251	+	1491.73i	−0.955883	+	1.65564i
$902$	937.232	−	541.111i	1.03906	−	0.599901i
$903$		0			0
$904$	218.804	−	378.979i	0.242040	−	0.419225i
$905$	−1394.09	+	804.879i	−1.54043	+	0.889369i
$906$		0			0
$907$	−67.4876	+	116.892i	−0.0744075	+	0.128878i	−0.900828	−	0.434175i	$-0.857040\pi$
$907$	−67.4876	+	116.892i	−0.0744075	+	0.128878i	0.826421	+	0.563053i	$0.190373\pi$
$908$	−855.295	−	493.805i	−0.941955	−	0.543838i
$909$		0			0
$910$	−1183.54	+	395.879i	−1.30060	+	0.435032i
$911$	−126.154	+	72.8353i	−0.138479	+	0.0799509i	−0.567639	−	0.823278i	$-0.692143\pi$
$911$	−126.154	+	72.8353i	−0.138479	+	0.0799509i	0.429160	+	0.903229i	$0.358810\pi$
$912$		0			0
$913$	−265.375			−0.290662
$914$		−	173.150i		−	0.189442i
$915$		0			0
$916$	−249.359	−	431.903i	−0.272226	−	0.471510i
$917$	−613.370	+	693.151i	−0.668887	+	0.755890i
$918$		0			0
$919$	131.948	−	228.541i	0.143578	−	0.248684i	−0.785264	−	0.619162i	$-0.787473\pi$
$919$	131.948	−	228.541i	0.143578	−	0.248684i	0.928841	+	0.370478i	$0.120806\pi$
$920$	281.634	+	162.601i	0.306124	+	0.176741i
$921$		0			0
$922$	504.086	+	873.103i	0.546731	+	0.946966i
$923$	110.983	+	64.0763i	0.120242	+	0.0694217i
$924$		0			0
$925$	434.595	+	752.741i	0.469833	+	0.813774i
$926$	−721.429	−	416.517i	−0.779081	−	0.449803i
$927$		0			0
$928$	282.619	+	489.511i	0.304547	+	0.527490i
$929$		−	1522.21i		−	1.63855i	−0.573403	−	0.819273i	$-0.694377\pi$
$929$		−	1522.21i		−	1.63855i	0.573403	−	0.819273i	$-0.305623\pi$
$930$		0			0
$931$	23.0852	+	188.319i	0.0247961	+	0.202276i
$932$	274.776	+	158.642i	0.294825	+	0.170217i
$933$		0			0
$934$	377.057	−	653.082i	0.403702	−	0.699232i
$935$	−1286.05	+	742.501i	−1.37545	+	0.794119i
$936$		0			0
$937$	−891.293			−0.951220			−0.475610	−	0.879656i	$-0.657773\pi$
$937$	−891.293			−0.951220			−0.475610	+	0.879656i	$0.657773\pi$
$938$	427.065	+	1276.78i	0.455293	+	1.36117i
$939$		0			0
$940$	−735.088	−	1273.21i	−0.782008	−	1.35448i
$941$		−	305.368i		−	0.324515i	−0.986748	−	0.162257i	$-0.948123\pi$
$941$		−	305.368i		−	0.324515i	0.986748	−	0.162257i	$-0.0518775\pi$
$942$		0			0
$943$	517.052			0.548305
$944$			409.614i			0.433913i
$945$		0			0
$946$	−1174.78			−1.24184
$947$			1457.18i			1.53873i	0.638806	+	0.769367i	$0.279428\pi$
$947$			1457.18i			1.53873i	−0.638806	+	0.769367i	$0.720572\pi$
$948$		0			0
$949$	785.739			0.827965
$950$	186.560	−	107.710i	0.196379	−	0.113379i
$951$		0			0
$952$	−827.434	−	732.197i	−0.869154	−	0.769115i
$953$		−	1041.41i		−	1.09277i	−0.837535	−	0.546383i	$-0.816004\pi$
$953$		−	1041.41i		−	1.09277i	0.837535	−	0.546383i	$-0.183996\pi$
$954$		0			0
$955$	−172.188	−	298.239i	−0.180302	−	0.312292i
$956$	1861.32	+	1074.63i	1.94699	+	1.12410i
$957$		0			0
$958$	−894.877	+	1549.97i	−0.934110	+	1.61793i
$959$	−575.868	−	117.221i	−0.600488	−	0.122232i
$960$		0			0
$961$	−904.103			−0.940794
$962$	1137.75	−	656.882i	1.18269	−	0.682829i
$963$		0			0
$964$	276.766	−	479.372i	0.287101	−	0.497274i
$965$	−720.437	+	415.944i	−0.746566	+	0.431030i
$966$		0			0
$967$	−142.789	+	247.318i	−0.147662	+	0.255758i	−0.930363	−	0.366640i	$-0.880508\pi$
$967$	−142.789	+	247.318i	−0.147662	+	0.255758i	0.782701	+	0.622398i	$0.213841\pi$
$968$	305.074	−	176.135i	0.315159	−	0.181957i
$969$		0			0
$970$	241.720	−	418.672i	0.249196	−	0.431620i
$971$	111.068	+	64.1253i	0.114385	+	0.0660405i	0.556101	−	0.831115i	$-0.312297\pi$
$971$	111.068	+	64.1253i	0.114385	+	0.0660405i	−0.441716	+	0.897155i	$0.645630\pi$
$972$		0			0
$973$	129.559	−	636.482i	0.133154	−	0.654144i
$974$	−2350.73	+	1357.19i	−2.41348	+	1.39342i
$975$		0			0
$976$	−260.005			−0.266399
$977$			236.136i			0.241695i	0.992671	+	0.120848i	$0.0385612\pi$
$977$			236.136i			0.241695i	−0.992671	+	0.120848i	$0.961439\pi$
$978$		0			0
$979$	301.150	+	521.607i	0.307610	+	0.532795i
$980$	−698.787	+	1645.34i	−0.713048	+	1.67892i
$981$		0			0
$982$	−345.294	+	598.067i	−0.351624	+	0.609030i
$983$	−1425.07	−	822.764i	−1.44971	−	0.836993i	−0.451250	−	0.892398i	$-0.649022\pi$
$983$	−1425.07	−	822.764i	−1.44971	−	0.836993i	−0.998464	+	0.0554052i	$0.982355\pi$
$984$		0			0
$985$	−858.934	−	1487.72i	−0.872015	−	1.51037i
$986$	1178.58	+	680.456i	1.19532	+	0.690118i
$987$		0			0
$988$	−94.7123	−	164.046i	−0.0958626	−	0.166039i
$989$	−486.077	−	280.637i	−0.491483	−	0.283758i
$990$		0			0
$991$	−687.312	−	1190.46i	−0.693554	−	1.20127i	−0.970666	−	0.240433i	$-0.922711\pi$
$991$	−687.312	−	1190.46i	−0.693554	−	1.20127i	0.277112	−	0.960838i	$-0.410623\pi$
$992$		−	316.175i		−	0.318725i
$993$		0			0
$994$	299.229	−	100.088i	0.301035	−	0.100692i
$995$	−67.7343	−	39.1064i	−0.0680747	−	0.0393029i
$996$		0			0
$997$	535.928	−	928.254i	0.537540	−	0.931047i	−0.461496	−	0.887143i	$-0.652687\pi$
$997$	535.928	−	928.254i	0.537540	−	0.931047i	0.999036	−	0.0439044i	$-0.0139797\pi$
$998$	−187.241	+	108.104i	−0.187617	+	0.108321i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.3.j.a.44.1		6
3.2	odd	2		63.3.j.a.23.3	yes	6
7.4	even	3		189.3.n.a.179.3		6
9.2	odd	6		189.3.n.a.170.3		6
9.7	even	3		63.3.n.a.2.1	yes	6
21.2	odd	6		441.3.r.b.50.3		6
21.5	even	6		441.3.r.c.50.3		6
21.11	odd	6		63.3.n.a.32.1	yes	6
21.17	even	6		441.3.n.c.410.1		6
21.20	even	2		441.3.j.c.275.3		6
63.11	odd	6	inner	189.3.j.a.116.3		6
63.16	even	3		441.3.r.b.344.3		6
63.25	even	3		63.3.j.a.11.1	✓	6
63.34	odd	6		441.3.n.c.128.1		6
63.52	odd	6		441.3.j.c.263.1		6
63.61	odd	6		441.3.r.c.344.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.3.j.a.11.1	✓	6	63.25	even	3
63.3.j.a.23.3	yes	6	3.2	odd	2
63.3.n.a.2.1	yes	6	9.7	even	3
63.3.n.a.32.1	yes	6	21.11	odd	6
189.3.j.a.44.1		6	1.1	even	1	trivial
189.3.j.a.116.3		6	63.11	odd	6	inner
189.3.n.a.170.3		6	9.2	odd	6
189.3.n.a.179.3		6	7.4	even	3
441.3.j.c.263.1		6	63.52	odd	6
441.3.j.c.275.3		6	21.20	even	2
441.3.n.c.128.1		6	63.34	odd	6
441.3.n.c.410.1		6	21.17	even	6
441.3.r.b.50.3		6	21.2	odd	6
441.3.r.b.344.3		6	63.16	even	3
441.3.r.c.50.3		6	21.5	even	6
441.3.r.c.344.3		6	63.61	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:	\( N \)	\(=\)	\( 189 = 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	189.j (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-3.09257i q^{2} -5.56399 q^{4} +(5.67824 - 3.27834i) q^{5} +(6.63848 - 2.22048i) q^{7} +4.83675i q^{8} +O(q^{10})\)	\(q-3.09257i q^{2} -5.56399 q^{4} +(5.67824 - 3.27834i) q^{5} +(6.63848 - 2.22048i) q^{7} +4.83675i q^{8} +(-10.1385 - 17.5604i) q^{10} +(6.01050 + 3.47017i) q^{11} +(4.39625 - 7.61453i) q^{13} +(-6.86699 - 20.5300i) q^{14} -7.29797 q^{16} +(-28.2614 + 16.3167i) q^{17} +(-1.93601 + 3.35327i) q^{19} +(-31.5937 + 18.2406i) q^{20} +(10.7317 - 18.5879i) q^{22} +(8.88072 - 5.12729i) q^{23} +(8.99497 - 15.5797i) q^{25} +(-23.5485 - 13.5957i) q^{26} +(-36.9365 + 12.3547i) q^{28} +(11.6782 - 6.74244i) q^{29} -7.54298 q^{31} +41.9165i q^{32} +(50.4607 + 87.4005i) q^{34} +(30.4155 - 34.3716i) q^{35} +(-24.1577 + 41.8423i) q^{37} +(10.3702 + 5.98725i) q^{38} +(15.8565 + 27.4642i) q^{40} +(43.6664 + 25.2108i) q^{41} +(-27.3670 - 47.4010i) q^{43} +(-33.4424 - 19.3080i) q^{44} +(-15.8565 - 27.4642i) q^{46} +40.2995i q^{47} +(39.1389 - 29.4812i) q^{49} +(-48.1815 - 27.8176i) q^{50} +(-24.4607 + 42.3672i) q^{52} +(45.7116 - 26.3916i) q^{53} +45.5055 q^{55} +(10.7399 + 32.1087i) q^{56} +(-20.8515 - 36.1158i) q^{58} -56.1270i q^{59} +35.6270 q^{61} +23.3272i q^{62} +100.438 q^{64} -57.6495i q^{65} -62.1910 q^{67} +(157.246 - 90.7862i) q^{68} +(-106.297 - 94.0619i) q^{70} +14.5752i q^{71} +(44.6824 + 77.3921i) q^{73} +(129.400 + 74.7093i) q^{74} +(10.7719 - 18.6575i) q^{76} +(47.6061 + 9.69043i) q^{77} +13.5951 q^{79} +(-41.4397 + 23.9252i) q^{80} +(77.9662 - 135.041i) q^{82} +(-33.1139 + 19.1183i) q^{83} +(-106.984 + 185.301i) q^{85} +(-146.591 + 84.6343i) q^{86} +(-16.7843 + 29.0713i) q^{88} +(75.1559 + 43.3913i) q^{89} +(12.2765 - 60.3107i) q^{91} +(-49.4122 + 28.5282i) q^{92} +124.629 q^{94} +25.3876i q^{95} +(11.9209 + 20.6477i) q^{97} +(-91.1728 - 121.040i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 26 q^{4} + 15 q^{5} - 2 q^{7}+O(q^{10}) \) 6 * q - 26 * q^4 + 15 * q^5 - 2 * q^7	\( 6 q - 26 q^{4} + 15 q^{5} - 2 q^{7} - 19 q^{10} + 9 q^{11} + 11 q^{13} + 24 q^{14} + 94 q^{16} - 33 q^{17} - 19 q^{19} - 45 q^{20} + 65 q^{22} - 15 q^{23} - 26 q^{25} - 81 q^{26} - 42 q^{28} + 51 q^{29} - 92 q^{31} + 93 q^{34} + 57 q^{35} + 7 q^{37} + 21 q^{38} + 57 q^{40} + 27 q^{41} - 99 q^{43} + 273 q^{44} - 57 q^{46} + 6 q^{49} - 294 q^{50} + 63 q^{52} - 45 q^{53} + 166 q^{55} - 360 q^{56} - 7 q^{58} + 44 q^{61} - 138 q^{64} - 196 q^{67} + 567 q^{68} - 257 q^{70} - 101 q^{73} + 411 q^{74} - 99 q^{76} - 105 q^{77} + 180 q^{79} - 93 q^{80} + 151 q^{82} - 99 q^{83} - 159 q^{85} - 249 q^{86} - 495 q^{88} + 243 q^{89} + 177 q^{91} - 147 q^{92} + 888 q^{94} - 161 q^{97} - 360 q^{98}+O(q^{100}) \) 6 * q - 26 * q^4 + 15 * q^5 - 2 * q^7 - 19 * q^10 + 9 * q^11 + 11 * q^13 + 24 * q^14 + 94 * q^16 - 33 * q^17 - 19 * q^19 - 45 * q^20 + 65 * q^22 - 15 * q^23 - 26 * q^25 - 81 * q^26 - 42 * q^28 + 51 * q^29 - 92 * q^31 + 93 * q^34 + 57 * q^35 + 7 * q^37 + 21 * q^38 + 57 * q^40 + 27 * q^41 - 99 * q^43 + 273 * q^44 - 57 * q^46 + 6 * q^49 - 294 * q^50 + 63 * q^52 - 45 * q^53 + 166 * q^55 - 360 * q^56 - 7 * q^58 + 44 * q^61 - 138 * q^64 - 196 * q^67 + 567 * q^68 - 257 * q^70 - 101 * q^73 + 411 * q^74 - 99 * q^76 - 105 * q^77 + 180 * q^79 - 93 * q^80 + 151 * q^82 - 99 * q^83 - 159 * q^85 - 249 * q^86 - 495 * q^88 + 243 * q^89 + 177 * q^91 - 147 * q^92 + 888 * q^94 - 161 * q^97 - 360 * q^98

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