LMFDB - Embedded newform 189.4.f.b.64.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [189,4,Mod(64,189)]

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([2, 0]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("189.64");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	189.f (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$11.1513609911$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 3 x^{15} + 58 x^{14} - 129 x^{13} + 2107 x^{12} - 4455 x^{11} + 42901 x^{10} - 76404 x^{9} + \cdots + 21307456 $ x^16 - 3x^15 + 58x^14 - 129x^13 + 2107x^12 - 4455x^11 + 42901x^10 - 76404x^9 + 599392x^8 - 1089732x^7 + 4808401x^6 - 7939134x^5 + 26225236x^4 - 39450864x^3 + 62254768x^2 - 39660672*x + 21307456
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{14} $
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			64.7
Root			$2.28179 + 3.95218i$ of defining polynomial
Character	$\chi$	$=$	189.64
Dual form			189.4.f.b.127.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.28179 + 3.95218i) q^{2} +(-6.41313 + 11.1079i) q^{4} +(10.3955 - 18.0055i) q^{5} +(3.50000 + 6.06218i) q^{7} -22.0250 q^{8} +O(q^{10})$	\(q+(2.28179 + 3.95218i) q^{2} +(-6.41313 + 11.1079i) q^{4} +(10.3955 - 18.0055i) q^{5} +(3.50000 + 6.06218i) q^{7} -22.0250 q^{8} +94.8813 q^{10} +(22.6993 + 39.3163i) q^{11} +(-14.6521 + 25.3782i) q^{13} +(-15.9725 + 27.6652i) q^{14} +(1.04863 + 1.81629i) q^{16} +98.0555 q^{17} +31.1554 q^{19} +(133.335 + 230.943i) q^{20} +(-103.590 + 179.423i) q^{22} +(4.19596 - 7.26761i) q^{23} +(-153.632 - 266.099i) q^{25} -133.732 q^{26} -89.7838 q^{28} +(-36.1332 - 62.5845i) q^{29} +(15.4299 - 26.7254i) q^{31} +(-92.8855 + 160.882i) q^{32} +(223.742 + 387.533i) q^{34} +145.537 q^{35} -196.369 q^{37} +(71.0900 + 123.131i) q^{38} +(-228.961 + 396.571i) q^{40} +(106.336 - 184.180i) q^{41} +(-118.438 - 205.141i) q^{43} -582.293 q^{44} +38.2972 q^{46} +(-110.018 - 190.557i) q^{47} +(-24.5000 + 42.4352i) q^{49} +(701.114 - 1214.36i) q^{50} +(-187.932 - 325.507i) q^{52} -55.9028 q^{53} +943.880 q^{55} +(-77.0874 - 133.519i) q^{56} +(164.897 - 285.609i) q^{58} +(-327.326 + 566.946i) q^{59} +(-174.391 - 302.055i) q^{61} +140.831 q^{62} -831.002 q^{64} +(304.632 + 527.638i) q^{65} +(-105.247 + 182.293i) q^{67} +(-628.842 + 1089.19i) q^{68} +(332.085 + 575.187i) q^{70} +548.252 q^{71} -266.888 q^{73} +(-448.073 - 776.086i) q^{74} +(-199.803 + 346.070i) q^{76} +(-158.895 + 275.214i) q^{77} +(134.946 + 233.733i) q^{79} +43.6042 q^{80} +970.550 q^{82} +(312.634 + 541.499i) q^{83} +(1019.34 - 1765.54i) q^{85} +(540.503 - 936.178i) q^{86} +(-499.951 - 865.941i) q^{88} -1605.63 q^{89} -205.129 q^{91} +(53.8184 + 93.2162i) q^{92} +(502.076 - 869.621i) q^{94} +(323.875 - 560.969i) q^{95} +(145.549 + 252.099i) q^{97} -223.615 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 3 q^{2} - 43 q^{4} + 30 q^{5} + 56 q^{7} - 12 q^{8}+O(q^{10}) $ 16 * q + 3 * q^2 - 43 * q^4 + 30 * q^5 + 56 * q^7 - 12 * q^8	$ 16 q + 3 q^{2} - 43 q^{4} + 30 q^{5} + 56 q^{7} - 12 q^{8} - 28 q^{10} + 24 q^{11} - 68 q^{13} - 21 q^{14} - 103 q^{16} - 336 q^{17} + 352 q^{19} + 330 q^{20} - 151 q^{22} + 228 q^{23} - 244 q^{25} - 1590 q^{26} - 602 q^{28} + 618 q^{29} - 72 q^{31} + 786 q^{32} + 261 q^{34} + 420 q^{35} + 420 q^{37} + 1032 q^{38} + 375 q^{40} + 420 q^{41} + 2 q^{43} - 774 q^{44} + 804 q^{46} + 570 q^{47} - 392 q^{49} + 1110 q^{50} + 431 q^{52} - 1056 q^{53} - 1676 q^{55} - 42 q^{56} - 37 q^{58} - 150 q^{59} - 578 q^{61} - 2340 q^{62} - 224 q^{64} - 366 q^{65} + 898 q^{67} + 2526 q^{68} - 98 q^{70} - 1764 q^{71} + 1944 q^{73} - 222 q^{74} - 1423 q^{76} - 168 q^{77} + 158 q^{79} - 4950 q^{80} - 422 q^{82} + 2958 q^{83} + 774 q^{85} - 114 q^{86} - 1317 q^{88} - 8760 q^{89} - 952 q^{91} + 4629 q^{92} + 3234 q^{94} + 930 q^{95} + 60 q^{97} - 294 q^{98}+O(q^{100}) $ 16 * q + 3 * q^2 - 43 * q^4 + 30 * q^5 + 56 * q^7 - 12 * q^8 - 28 * q^10 + 24 * q^11 - 68 * q^13 - 21 * q^14 - 103 * q^16 - 336 * q^17 + 352 * q^19 + 330 * q^20 - 151 * q^22 + 228 * q^23 - 244 * q^25 - 1590 * q^26 - 602 * q^28 + 618 * q^29 - 72 * q^31 + 786 * q^32 + 261 * q^34 + 420 * q^35 + 420 * q^37 + 1032 * q^38 + 375 * q^40 + 420 * q^41 + 2 * q^43 - 774 * q^44 + 804 * q^46 + 570 * q^47 - 392 * q^49 + 1110 * q^50 + 431 * q^52 - 1056 * q^53 - 1676 * q^55 - 42 * q^56 - 37 * q^58 - 150 * q^59 - 578 * q^61 - 2340 * q^62 - 224 * q^64 - 366 * q^65 + 898 * q^67 + 2526 * q^68 - 98 * q^70 - 1764 * q^71 + 1944 * q^73 - 222 * q^74 - 1423 * q^76 - 168 * q^77 + 158 * q^79 - 4950 * q^80 - 422 * q^82 + 2958 * q^83 + 774 * q^85 - 114 * q^86 - 1317 * q^88 - 8760 * q^89 - 952 * q^91 + 4629 * q^92 + 3234 * q^94 + 930 * q^95 + 60 * q^97 - 294 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	2.28179	+	3.95218i	0.806734	+	1.39730i	0.915114	+	0.403195i	$0.132100\pi$
$2$	2.28179	+	3.95218i	0.806734	+	1.39730i	−0.108380	+	0.994110i	$0.534566\pi$
$3$		0			0
$3$		0			0
$4$	−6.41313	+	11.1079i	−0.801641	+	1.38848i
$5$	10.3955	−	18.0055i	0.929801	−	1.61046i	0.146149	−	0.989263i	$-0.453312\pi$
$5$	10.3955	−	18.0055i	0.929801	−	1.61046i	0.783652	−	0.621200i	$-0.213355\pi$
$6$		0			0
$7$	3.50000	+	6.06218i	0.188982	+	0.327327i
$7$	3.50000	+	6.06218i	0.188982	+	0.327327i
$8$	−22.0250			−0.973376
$9$		0			0
$10$	94.8813			3.00041
$11$	22.6993	+	39.3163i	0.622190	+	1.07766i	0.989077	+	0.147399i	$0.0470901\pi$
$11$	22.6993	+	39.3163i	0.622190	+	1.07766i	−0.366887	+	0.930265i	$0.619577\pi$
$12$		0			0
$13$	−14.6521	+	25.3782i	−0.312597	+	0.541434i	−0.978924	−	0.204226i	$-0.934532\pi$
$13$	−14.6521	+	25.3782i	−0.312597	+	0.541434i	0.666327	+	0.745660i	$0.267866\pi$
$14$	−15.9725	+	27.6652i	−0.304917	+	0.528132i
$15$		0			0
$16$	1.04863	+	1.81629i	0.0163849	+	0.0283795i
$17$	98.0555			1.39894			0.699469	−	0.714663i	$-0.253420\pi$
$17$	98.0555			1.39894			0.699469	+	0.714663i	$0.253420\pi$
$18$		0			0
$19$	31.1554			0.376186			0.188093	−	0.982151i	$-0.439769\pi$
$19$	31.1554			0.376186			0.188093	+	0.982151i	$0.439769\pi$
$20$	133.335	+	230.943i	1.49073	+	2.58202i
$21$		0			0
$22$	−103.590	+	179.423i	−1.00388	+	1.73878i
$23$	4.19596	−	7.26761i	0.0380399	−	0.0658870i	−0.846379	−	0.532582i	$-0.821222\pi$
$23$	4.19596	−	7.26761i	0.0380399	−	0.0658870i	0.884419	+	0.466695i	$0.154555\pi$
$24$		0			0
$25$	−153.632	−	266.099i	−1.22906	−	2.12879i
$26$	−133.732			−1.00873
$27$		0			0
$28$	−89.7838			−0.605983
$29$	−36.1332	−	62.5845i	−0.231371	−	0.400747i	0.726841	−	0.686806i	$-0.240988\pi$
$29$	−36.1332	−	62.5845i	−0.231371	−	0.400747i	−0.958212	+	0.286059i	$0.907655\pi$
$30$		0			0
$31$	15.4299	−	26.7254i	0.0893965	−	0.154839i	−0.817860	−	0.575418i	$-0.804840\pi$
$31$	15.4299	−	26.7254i	0.0893965	−	0.154839i	0.907256	+	0.420578i	$0.138173\pi$
$32$	−92.8855	+	160.882i	−0.513125	+	0.888758i
$33$		0			0
$34$	223.742	+	387.533i	1.12857	+	1.95474i
$35$	145.537			0.702863
$36$		0			0
$37$	−196.369			−0.872511			−0.436255	−	0.899823i	$-0.643696\pi$
$37$	−196.369			−0.872511			−0.436255	+	0.899823i	$0.643696\pi$
$38$	71.0900	+	123.131i	0.303482	+	0.525646i
$39$		0			0
$40$	−228.961	+	396.571i	−0.905046	+	1.56759i
$41$	106.336	−	184.180i	0.405048	−	0.701564i	−0.589279	−	0.807930i	$-0.700588\pi$
$41$	106.336	−	184.180i	0.405048	−	0.701564i	0.994327	+	0.106366i	$0.0339215\pi$
$42$		0			0
$43$	−118.438	−	205.141i	−0.420039	−	0.727529i	0.575904	−	0.817517i	$-0.304650\pi$
$43$	−118.438	−	205.141i	−0.420039	−	0.727529i	−0.995943	+	0.0899887i	$0.971317\pi$
$44$	−582.293			−1.99509
$45$		0			0
$46$	38.2972			0.122752
$47$	−110.018	−	190.557i	−0.341442	−	0.591395i	0.643259	−	0.765649i	$-0.277582\pi$
$47$	−110.018	−	190.557i	−0.341442	−	0.591395i	−0.984701	+	0.174254i	$0.944249\pi$
$48$		0			0
$49$	−24.5000	+	42.4352i	−0.0714286	+	0.123718i
$50$	701.114	−	1214.36i	1.98305	−	3.43474i
$51$		0			0
$52$	−187.932	−	325.507i	−0.501181	−	0.868071i
$53$	−55.9028			−0.144884			−0.0724419	−	0.997373i	$-0.523079\pi$
$53$	−55.9028			−0.144884			−0.0724419	+	0.997373i	$0.523079\pi$
$54$		0			0
$55$	943.880			2.31405
$56$	−77.0874	−	133.519i	−0.183951	−	0.318612i
$57$		0			0
$58$	164.897	−	285.609i	0.373310	−	0.646592i
$59$	−327.326	+	566.946i	−0.722275	+	1.25102i	0.237810	+	0.971312i	$0.423570\pi$
$59$	−327.326	+	566.946i	−0.722275	+	1.25102i	−0.960086	+	0.279706i	$0.909763\pi$
$60$		0			0
$61$	−174.391	−	302.055i	−0.366041	−	0.634002i	0.622901	−	0.782300i	$-0.285954\pi$
$61$	−174.391	−	302.055i	−0.366041	−	0.634002i	−0.988943	+	0.148298i	$0.952620\pi$
$62$	140.831			0.288477
$63$		0			0
$64$	−831.002			−1.62305
$65$	304.632	+	527.638i	0.581306	+	1.00685i
$66$		0			0
$67$	−105.247	+	182.293i	−0.191910	+	0.332398i	−0.945883	−	0.324507i	$-0.894802\pi$
$67$	−105.247	+	182.293i	−0.191910	+	0.332398i	0.753973	+	0.656905i	$0.228135\pi$
$68$	−628.842	+	1089.19i	−1.12145	+	1.94240i
$69$		0			0
$70$	332.085	+	575.187i	0.567024	+	0.982115i
$71$	548.252			0.916416			0.458208	−	0.888845i	$-0.348492\pi$
$71$	548.252			0.916416			0.458208	+	0.888845i	$0.348492\pi$
$72$		0			0
$73$	−266.888			−0.427902			−0.213951	−	0.976844i	$-0.568633\pi$
$73$	−266.888			−0.427902			−0.213951	+	0.976844i	$0.568633\pi$
$74$	−448.073	−	776.086i	−0.703884	−	1.21916i
$75$		0			0
$76$	−199.803	+	346.070i	−0.301566	+	0.522328i
$77$	−158.895	+	275.214i	−0.235166	+	0.407319i
$78$		0			0
$79$	134.946	+	233.733i	0.192185	+	0.332874i	0.945974	−	0.324242i	$-0.105109\pi$
$79$	134.946	+	233.733i	0.192185	+	0.332874i	−0.753789	+	0.657116i	$0.771776\pi$
$80$	43.6042			0.0609388
$81$		0			0
$82$	970.550			1.30706
$83$	312.634	+	541.499i	0.413447	+	0.716111i	0.995264	−	0.0972088i	$-0.0309915\pi$
$83$	312.634	+	541.499i	0.413447	+	0.716111i	−0.581817	+	0.813320i	$0.697658\pi$
$84$		0			0
$85$	1019.34	−	1765.54i	1.30073	−	2.25294i
$86$	540.503	−	936.178i	0.677720	−	1.17384i
$87$		0			0
$88$	−499.951	−	865.941i	−0.605625	−	1.04897i
$89$	−1605.63			−1.91232			−0.956162	−	0.292838i	$-0.905400\pi$
$89$	−1605.63			−1.91232			−0.956162	+	0.292838i	$0.905400\pi$
$90$		0			0
$91$	−205.129			−0.236301
$92$	53.8184	+	93.2162i	0.0609887	+	0.105635i
$93$		0			0
$94$	502.076	−	869.621i	0.550906	−	0.954198i
$95$	323.875	−	560.969i	0.349778	−	0.605833i
$96$		0			0
$97$	145.549	+	252.099i	0.152354	+	0.263884i	0.932092	−	0.362221i	$-0.117981\pi$
$97$	145.549	+	252.099i	0.152354	+	0.263884i	−0.779739	+	0.626105i	$0.784648\pi$
$98$	−223.615			−0.230496
$99$		0			0
$100$	3941.06			3.94106
$101$	−726.307	−	1258.00i	−0.715547	−	1.23936i	−0.962748	−	0.270399i	$-0.912844\pi$
$101$	−726.307	−	1258.00i	−0.715547	−	1.23936i	0.247201	−	0.968964i	$-0.420489\pi$
$102$		0			0
$103$	28.1341	−	48.7296i	0.0269139	−	0.0466162i	−0.852255	−	0.523127i	$-0.824765\pi$
$103$	28.1341	−	48.7296i	0.0269139	−	0.0466162i	0.879169	+	0.476511i	$0.158099\pi$
$104$	322.712	−	558.954i	0.304275	−	0.527019i
$105$		0			0
$106$	−127.558	−	220.938i	−0.116883	−	0.202447i
$107$	300.124			0.271160			0.135580	−	0.990766i	$-0.456710\pi$
$107$	300.124			0.271160			0.135580	+	0.990766i	$0.456710\pi$
$108$		0			0
$109$	−936.906			−0.823296			−0.411648	−	0.911343i	$-0.635047\pi$
$109$	−936.906			−0.823296			−0.411648	+	0.911343i	$0.635047\pi$
$110$	2153.74	+	3730.38i	1.86682	+	3.23343i
$111$		0			0
$112$	−7.34044	+	12.7140i	−0.00619291	+	0.0107264i
$113$	697.297	−	1207.75i	0.580498	−	1.00545i	−0.414923	−	0.909857i	$-0.636191\pi$
$113$	697.297	−	1207.75i	0.580498	−	1.00545i	0.995420	−	0.0955946i	$-0.0304753\pi$
$114$		0			0
$115$	−87.2381	−	151.101i	−0.0707391	−	0.122524i
$116$	926.907			0.741906
$117$		0			0
$118$	−2987.56			−2.33074
$119$	343.194	+	594.430i	0.264375	+	0.457910i
$120$		0			0
$121$	−365.014	+	632.222i	−0.274240	+	0.474998i
$122$	795.849	−	1378.45i	0.590596	−	1.02294i
$123$		0			0
$124$	197.908	+	342.786i	0.143328	+	0.248251i
$125$	−3789.47			−2.71152
$126$		0			0
$127$	−2387.37			−1.66807			−0.834034	−	0.551714i	$-0.813974\pi$
$127$	−2387.37			−1.66807			−0.834034	+	0.551714i	$0.813974\pi$
$128$	−1153.09	−	1997.21i	−0.796247	−	1.37914i
$129$		0			0
$130$	−1390.21	+	2407.92i	−0.937920	+	1.62452i
$131$	1060.00	−	1835.97i	0.706963	−	1.22450i	−0.259015	−	0.965873i	$-0.583398\pi$
$131$	1060.00	−	1835.97i	0.706963	−	1.22450i	0.965978	−	0.258623i	$-0.0832688\pi$
$132$		0			0
$133$	109.044	+	188.869i	0.0710925	+	0.123136i
$134$	−960.606			−0.619282
$135$		0			0
$136$	−2159.67			−1.36169
$137$	−32.9508	−	57.0725i	−0.0205487	−	0.0355915i	0.855568	−	0.517690i	$-0.173208\pi$
$137$	−32.9508	−	57.0725i	−0.0205487	−	0.0355915i	−0.876117	+	0.482099i	$0.839875\pi$
$138$		0			0
$139$	981.641	−	1700.25i	0.599005	−	1.03751i	−0.393963	−	0.919126i	$-0.628896\pi$
$139$	981.641	−	1700.25i	0.599005	−	1.03751i	0.992968	−	0.118381i	$-0.0377705\pi$
$140$	−933.346	+	1616.60i	−0.563444	+	0.975914i
$141$		0			0
$142$	1251.00	+	2166.79i	0.739304	+	1.28051i
$143$	−1330.37			−0.777979
$144$		0			0
$145$	−1502.49			−0.860517
$146$	−608.982	−	1054.79i	−0.345203	−	0.597910i
$147$		0			0
$148$	1259.34	−	2181.24i	0.699440	−	1.21147i
$149$	−1316.91	+	2280.95i	−0.724063	+	1.25411i	0.235296	+	0.971924i	$0.424394\pi$
$149$	−1316.91	+	2280.95i	−0.724063	+	1.25411i	−0.959359	+	0.282190i	$0.908939\pi$
$150$		0			0
$151$	368.737	+	638.671i	0.198724	+	0.344200i	0.948115	−	0.317927i	$-0.102987\pi$
$151$	368.737	+	638.671i	0.198724	+	0.344200i	−0.749391	+	0.662128i	$0.769654\pi$
$152$	−686.197			−0.366170
$153$		0			0
$154$	−1450.26			−0.758865
$155$	−320.803	−	555.646i	−0.166242	−	0.287939i
$156$		0			0
$157$	−1173.36	+	2032.32i	−0.596462	+	1.03310i	0.396877	+	0.917872i	$0.370094\pi$
$157$	−1173.36	+	2032.32i	−0.596462	+	1.03310i	−0.993339	+	0.115230i	$0.963239\pi$
$158$	−615.837	+	1066.66i	−0.310084	+	0.537082i
$159$		0			0
$160$	1931.18	+	3344.90i	0.954207	+	1.65274i
$161$	58.7434			0.0287555
$162$		0			0
$163$	−572.002			−0.274863			−0.137431	−	0.990511i	$-0.543885\pi$
$163$	−572.002			−0.274863			−0.137431	+	0.990511i	$0.543885\pi$
$164$	1363.90	+	2362.34i	0.649406	+	1.12480i
$165$		0			0
$166$	−1426.73	+	2471.17i	−0.667083	+	1.15542i
$167$	271.886	−	470.920i	0.125983	−	0.218209i	−0.796134	−	0.605121i	$-0.793125\pi$
$167$	271.886	−	470.920i	0.125983	−	0.218209i	0.922117	+	0.386912i	$0.126458\pi$
$168$		0			0
$169$	669.132	+	1158.97i	0.304566	+	0.527524i
$170$	9303.63			4.19739
$171$		0			0
$172$	3038.24			1.34688
$173$	1017.23	+	1761.89i	0.447042	+	0.774299i	0.998192	−	0.0601072i	$-0.0191443\pi$
$173$	1017.23	+	1761.89i	0.447042	+	0.774299i	−0.551150	+	0.834406i	$0.685811\pi$
$174$		0			0
$175$	1075.43	−	1862.69i	0.464541	−	0.804608i
$176$	−47.6064	+	82.4568i	−0.0203890	+	0.0353148i
$177$		0			0
$178$	−3663.72	−	6345.75i	−1.54274	−	2.67210i
$179$	931.218			0.388841			0.194420	−	0.980918i	$-0.437717\pi$
$179$	931.218			0.388841			0.194420	+	0.980918i	$0.437717\pi$
$180$		0			0
$181$	1002.74			0.411785			0.205892	−	0.978575i	$-0.433990\pi$
$181$	1002.74			0.411785			0.205892	+	0.978575i	$0.433990\pi$
$182$	−468.062	−	810.708i	−0.190632	−	0.330185i
$183$		0			0
$184$	−92.4159	+	160.069i	−0.0370271	+	0.0641328i
$185$	−2041.35	+	3535.73i	−0.811261	+	1.40515i
$186$		0			0
$187$	2225.79	+	3855.18i	0.870405	+	1.50759i
$188$	2822.24			1.09486
$189$		0			0
$190$	2956.06			1.12871
$191$	−1921.54	−	3328.21i	−0.727947	−	1.26084i	−0.957750	−	0.287604i	$-0.907141\pi$
$191$	−1921.54	−	3328.21i	−0.727947	−	1.26084i	0.229803	−	0.973237i	$-0.426192\pi$
$192$		0			0
$193$	1733.05	−	3001.73i	0.646361	−	1.11953i	−0.337624	−	0.941281i	$-0.609623\pi$
$193$	1733.05	−	3001.73i	0.646361	−	1.11953i	0.983985	−	0.178250i	$-0.0570435\pi$
$194$	−664.227	+	1150.47i	−0.245818	+	0.425769i
$195$		0			0
$196$	−314.243	−	544.285i	−0.114520	−	0.198355i
$197$	3691.99			1.33525			0.667623	−	0.744500i	$-0.267312\pi$
$197$	3691.99			1.33525			0.667623	+	0.744500i	$0.267312\pi$
$198$		0			0
$199$	−481.783			−0.171622			−0.0858108	−	0.996311i	$-0.527348\pi$
$199$	−481.783			−0.171622			−0.0858108	+	0.996311i	$0.527348\pi$
$200$	3383.75	+	5860.83i	1.19634	+	2.07212i
$201$		0			0
$202$	3314.56	−	5740.98i	1.15451	−	1.99967i
$203$	252.932	−	438.092i	0.0874501	−	0.151468i
$204$		0			0
$205$	−2210.84	−	3829.29i	−0.753228	−	1.30463i
$206$	256.784			0.0868494
$207$		0			0
$208$	−61.4588			−0.0204875
$209$	707.204	+	1224.91i	0.234059	+	0.405402i
$210$		0			0
$211$	−574.892	+	995.742i	−0.187570	+	0.324880i	−0.944439	−	0.328686i	$-0.893394\pi$
$211$	−574.892	+	995.742i	−0.187570	+	0.324880i	0.756870	+	0.653566i	$0.226728\pi$
$212$	358.512	−	620.960i	0.116145	−	0.201169i
$213$		0			0
$214$	684.820	+	1186.14i	0.218754	+	0.378893i
$215$	−4924.90			−1.56221
$216$		0			0
$217$	216.018			0.0675774
$218$	−2137.82	−	3702.82i	−0.664182	−	1.15040i
$219$		0			0
$220$	−6053.22	+	10484.5i	−1.85504	+	3.21302i
$221$	−1436.72	+	2488.47i	−0.437304	+	0.757433i
$222$		0			0
$223$	1007.98	+	1745.87i	0.302687	+	0.524269i	0.976744	−	0.214411i	$-0.0687830\pi$
$223$	1007.98	+	1745.87i	0.302687	+	0.524269i	−0.674057	+	0.738680i	$0.735450\pi$
$224$	−1300.40			−0.387886
$225$		0			0
$226$	6364.34			1.87323
$227$	1521.10	+	2634.62i	0.444753	+	0.770335i	0.998035	−	0.0626590i	$-0.0199581\pi$
$227$	1521.10	+	2634.62i	0.444753	+	0.770335i	−0.553282	+	0.832994i	$0.686625\pi$
$228$		0			0
$229$	−2040.67	+	3534.54i	−0.588870	+	1.01995i	0.405511	+	0.914090i	$0.367094\pi$
$229$	−2040.67	+	3534.54i	−0.588870	+	1.01995i	−0.994381	+	0.105863i	$0.966240\pi$
$230$	398.118	−	689.560i	0.114135	−	0.197688i
$231$		0			0
$232$	795.833	+	1378.42i	0.225211	+	0.390077i
$233$	−2667.57			−0.750035			−0.375017	−	0.927018i	$-0.622363\pi$
$233$	−2667.57			−0.750035			−0.375017	+	0.927018i	$0.622363\pi$
$234$		0			0
$235$	−4574.77			−1.26989
$236$	−4198.37	−	7271.79i	−1.15801	−	2.00573i
$237$		0			0
$238$	−1566.19	+	2712.73i	−0.426560	+	0.738824i
$239$	−2986.31	+	5172.45i	−0.808237	+	1.39991i	0.105848	+	0.994382i	$0.466244\pi$
$239$	−2986.31	+	5172.45i	−0.808237	+	1.39991i	−0.914084	+	0.405525i	$0.867089\pi$
$240$		0			0
$241$	1320.63	+	2287.40i	0.352984	+	0.611387i	0.986771	−	0.162121i	$-0.0518336\pi$
$241$	1320.63	+	2287.40i	0.352984	+	0.611387i	−0.633787	+	0.773508i	$0.718500\pi$
$242$	−3331.54			−0.884956
$243$		0			0
$244$	4473.57			1.17373
$245$	509.379	+	882.270i	0.132829	+	0.230066i
$246$		0			0
$247$	−456.492	+	790.667i	−0.117595	+	0.203680i
$248$	−339.843	+	588.626i	−0.0870164	+	0.150717i
$249$		0			0
$250$	−8646.77	−	14976.6i	−2.18748	−	3.78882i
$251$	7001.16			1.76060			0.880298	−	0.474422i	$-0.157343\pi$
$251$	7001.16			1.76060			0.880298	+	0.474422i	$0.157343\pi$
$252$		0			0
$253$	380.981			0.0946721
$254$	−5447.47	−	9435.29i	−1.34569	−	2.33080i
$255$		0			0
$256$	1938.20	−	3357.06i	0.473193	−	0.819595i
$257$	2893.85	−	5012.30i	0.702388	−	1.21657i	−0.265239	−	0.964183i	$-0.585451\pi$
$257$	2893.85	−	5012.30i	0.702388	−	1.21657i	0.967626	−	0.252388i	$-0.0812159\pi$
$258$		0			0
$259$	−687.292	−	1190.43i	−0.164889	−	0.285596i
$260$	−7814.57			−1.86400
$261$		0			0
$262$	9674.74			2.28133
$263$	−3743.32	−	6483.62i	−0.877653	−	1.52014i	−0.853909	−	0.520422i	$-0.825775\pi$
$263$	−3743.32	−	6483.62i	−0.877653	−	1.52014i	−0.0237442	−	0.999718i	$-0.507559\pi$
$264$		0			0
$265$	−581.137	+	1006.56i	−0.134713	+	0.233330i
$266$	−497.630	+	861.920i	−0.114705	+	0.198676i
$267$		0			0
$268$	−1349.93	−	2338.14i	−0.307686	−	0.532928i
$269$	3249.42			0.736508			0.368254	−	0.929725i	$-0.379956\pi$
$269$	3249.42			0.736508			0.368254	+	0.929725i	$0.379956\pi$
$270$		0			0
$271$	−3946.32			−0.884581			−0.442291	−	0.896872i	$-0.645834\pi$
$271$	−3946.32			−0.884581			−0.442291	+	0.896872i	$0.645834\pi$
$272$	102.824	+	178.097i	0.0229215	+	0.0397012i
$273$		0			0
$274$	150.374	−	260.455i	0.0331547	−	0.0574257i
$275$	6974.69	−	12080.5i	1.52942	−	2.64903i
$276$		0			0
$277$	−2327.13	−	4030.71i	−0.504779	−	0.874303i	−0.999985	−	0.00552735i	$-0.998241\pi$
$277$	−2327.13	−	4030.71i	−0.504779	−	0.874303i	0.495206	−	0.868776i	$-0.335093\pi$
$278$	8959.60			1.93295
$279$		0			0
$280$	−3205.45			−0.684150
$281$	3223.44	+	5583.17i	0.684322	+	1.18528i	0.973649	+	0.228051i	$0.0732352\pi$
$281$	3223.44	+	5583.17i	0.684322	+	1.18528i	−0.289327	+	0.957230i	$0.593431\pi$
$282$		0			0
$283$	1819.23	−	3151.00i	0.382127	−	0.661864i	−0.609239	−	0.792987i	$-0.708525\pi$
$283$	1819.23	−	3151.00i	0.382127	−	0.661864i	0.991366	+	0.131123i	$0.0418583\pi$
$284$	−3516.01	+	6089.91i	−0.734636	+	1.27243i
$285$		0			0
$286$	−3035.62	−	5257.85i	−0.627622	−	1.08707i
$287$	1488.71			0.306187
$288$		0			0
$289$	4701.88			0.957029
$290$	−3428.36	−	5938.10i	−0.694208	−	1.20240i
$291$		0			0
$292$	1711.59	−	2964.55i	0.343024	−	0.594135i
$293$	3163.73	−	5479.74i	0.630809	−	1.09259i	−0.356578	−	0.934266i	$-0.616056\pi$
$293$	3163.73	−	5479.74i	0.630809	−	1.09259i	0.987387	−	0.158328i	$-0.0506102\pi$
$294$		0			0
$295$	6805.43	+	11787.4i	1.34314	+	2.32639i
$296$	4325.03			0.849281
$297$		0			0
$298$	−12019.6			−2.33651
$299$	122.959	+	212.972i	0.0237823	+	0.0411922i
$300$		0			0
$301$	829.068	−	1435.99i	0.158760	−	0.274980i
$302$	−1682.76	+	2914.62i	−0.320635	+	0.555357i
$303$		0			0
$304$	32.6706	+	56.5871i	0.00616377	+	0.0106760i
$305$	−7251.53			−1.36138
$306$		0			0
$307$	2712.80			0.504324			0.252162	−	0.967685i	$-0.418858\pi$
$307$	2712.80			0.504324			0.252162	+	0.967685i	$0.418858\pi$
$308$	−2038.03	−	3529.96i	−0.377037	−	0.653047i
$309$		0			0
$310$	1464.01	−	2535.74i	0.268226	−	0.464581i
$311$	1523.04	−	2637.98i	0.277696	−	0.480983i	−0.693116	−	0.720826i	$-0.743763\pi$
$311$	1523.04	−	2637.98i	0.277696	−	0.480983i	0.970812	+	0.239843i	$0.0770959\pi$
$312$		0			0
$313$	−2190.26	−	3793.65i	−0.395531	−	0.685079i	0.597638	−	0.801766i	$-0.296106\pi$
$313$	−2190.26	−	3793.65i	−0.395531	−	0.685079i	−0.993169	+	0.116687i	$0.962773\pi$
$314$	−10709.5			−1.92475
$315$		0			0
$316$	−3461.70			−0.616253
$317$	3453.12	+	5980.99i	0.611820	+	1.05970i	0.990934	+	0.134353i	$0.0428955\pi$
$317$	3453.12	+	5980.99i	0.611820	+	1.05970i	−0.379114	+	0.925350i	$0.623771\pi$
$318$		0			0
$319$	1640.39	−	2841.25i	0.287914	−	0.498681i
$320$	−8638.67	+	14962.6i	−1.50911	+	2.61386i
$321$		0			0
$322$	134.040	+	232.164i	0.0231980	+	0.0401801i
$323$	3054.96			0.526261
$324$		0			0
$325$	9004.16			1.53680
$326$	−1305.19	−	2260.65i	−0.221741	−	0.384067i
$327$		0			0
$328$	−2342.06	+	4056.57i	−0.394264	+	0.682885i
$329$	770.126	−	1333.90i	0.129053	−	0.223526i
$330$		0			0
$331$	−2851.26	−	4938.52i	−0.473472	−	0.820078i	0.526067	−	0.850443i	$-0.323666\pi$
$331$	−2851.26	−	4938.52i	−0.473472	−	0.820078i	−0.999539	+	0.0303654i	$0.990333\pi$
$332$	−8019.85			−1.32574
$333$		0			0
$334$	2481.54			0.406539
$335$	2188.19	+	3790.06i	0.356876	+	0.618128i
$336$		0			0
$337$	−614.807	+	1064.88i	−0.0993788	+	0.172129i	−0.911428	−	0.411460i	$-0.865019\pi$
$337$	−614.807	+	1064.88i	−0.0993788	+	0.172129i	0.812049	+	0.583589i	$0.198352\pi$
$338$	−3053.63	+	5289.05i	−0.491408	+	0.851143i
$339$		0			0
$340$	13074.3	+	22645.3i	2.08544	+	3.61209i
$341$	1400.99			0.222486
$342$		0			0
$343$	−343.000			−0.0539949
$344$	2608.60	+	4518.23i	0.408856	+	0.708159i
$345$		0			0
$346$	−4642.19	+	8040.50i	−0.721288	+	1.24931i
$347$	2192.74	−	3797.94i	0.339229	−	0.587562i	−0.645059	−	0.764133i	$-0.723167\pi$
$347$	2192.74	−	3797.94i	0.339229	−	0.587562i	0.984288	+	0.176571i	$0.0565005\pi$
$348$		0			0
$349$	−1460.02	−	2528.82i	−0.223934	−	0.387865i	0.732065	−	0.681235i	$-0.238557\pi$
$349$	−1460.02	−	2528.82i	−0.223934	−	0.387865i	−0.955999	+	0.293370i	$0.905223\pi$
$350$	9815.59			1.49904
$351$		0			0
$352$	−8433.73			−1.27704
$353$	5565.95	+	9640.52i	0.839223	+	1.45358i	0.890545	+	0.454895i	$0.150323\pi$
$353$	5565.95	+	9640.52i	0.839223	+	1.45358i	−0.0513214	+	0.998682i	$0.516343\pi$
$354$		0			0
$355$	5699.35	−	9871.56i	0.852084	−	1.47585i
$356$	10297.1	−	17835.2i	1.53300	−	2.65523i
$357$		0			0
$358$	2124.84	+	3680.34i	0.313691	+	0.543329i
$359$	−7640.81			−1.12330			−0.561652	−	0.827373i	$-0.689834\pi$
$359$	−7640.81			−1.12330			−0.561652	+	0.827373i	$0.689834\pi$
$360$		0			0
$361$	−5888.34			−0.858484
$362$	2288.04	+	3963.00i	0.332201	+	0.575389i
$363$		0			0
$364$	1315.52	−	2278.55i	0.189429	−	0.328100i
$365$	−2774.43	+	4805.45i	−0.397864	+	0.689121i
$366$		0			0
$367$	−2204.25	−	3817.87i	−0.313518	−	0.543028i	0.665604	−	0.746305i	$-0.268174\pi$
$367$	−2204.25	−	3817.87i	−0.313518	−	0.543028i	−0.979121	+	0.203277i	$0.934841\pi$
$368$	17.6001			0.00249312
$369$		0			0
$370$	−18631.8			−2.61789
$371$	−195.660	−	338.893i	−0.0273804	−	0.0474243i
$372$		0			0
$373$	−2302.17	+	3987.47i	−0.319575	+	0.553521i	−0.980399	−	0.197020i	$-0.936874\pi$
$373$	−2302.17	+	3987.47i	−0.319575	+	0.553521i	0.660824	+	0.750541i	$0.270207\pi$
$374$	−10157.6	+	17593.4i	−1.40437	+	2.43244i
$375$		0			0
$376$	2423.15	+	4197.01i	0.332352	+	0.575650i
$377$	2117.71			0.289304
$378$		0			0
$379$	14679.5			1.98954			0.994770	−	0.102143i	$-0.0325700\pi$
$379$	14679.5			1.98954			0.994770	+	0.102143i	$0.0325700\pi$
$380$	4154.11	+	7195.13i	0.560793	+	0.971321i
$381$		0			0
$382$	8769.10	−	15188.5i	1.17452	−	2.03433i
$383$	911.873	−	1579.41i	0.121657	−	0.210716i	−0.798764	−	0.601644i	$-0.794513\pi$
$383$	911.873	−	1579.41i	0.121657	−	0.210716i	0.920421	+	0.390928i	$0.127846\pi$
$384$		0			0
$385$	3303.58	+	5721.97i	0.437314	+	0.757451i
$386$	15817.8			2.08577
$387$		0			0
$388$	−3733.71			−0.488532
$389$	4306.80	+	7459.59i	0.561345	+	0.972278i	0.997379	+	0.0723480i	$0.0230492\pi$
$389$	4306.80	+	7459.59i	0.561345	+	0.972278i	−0.436035	+	0.899930i	$0.643617\pi$
$390$		0			0
$391$	411.437	−	712.629i	0.0532155	−	0.0921719i
$392$	539.612	−	934.636i	0.0695269	−	0.120424i
$393$		0			0
$394$	8424.34	+	14591.4i	1.07719	+	1.86575i
$395$	5611.32			0.714775
$396$		0			0
$397$	−5497.04			−0.694933			−0.347467	−	0.937692i	$-0.612958\pi$
$397$	−5497.04			−0.694933			−0.347467	+	0.937692i	$0.612958\pi$
$398$	−1099.33	−	1904.09i	−0.138453	−	0.239808i
$399$		0			0
$400$	322.208	−	558.081i	0.0402760	−	0.0697602i
$401$	−4310.52	+	7466.04i	−0.536801	+	0.929767i	0.462273	+	0.886738i	$0.347034\pi$
$401$	−4310.52	+	7466.04i	−0.536801	+	0.929767i	−0.999074	+	0.0430288i	$0.986299\pi$
$402$		0			0
$403$	452.161	+	783.165i	0.0558902	+	0.0968046i
$404$	18631.6			2.29445
$405$		0			0
$406$	2308.55			0.282196
$407$	−4457.44	−	7720.51i	−0.542867	−	0.940274i
$408$		0			0
$409$	−4699.45	+	8139.69i	−0.568149	+	0.984063i	0.428600	+	0.903494i	$0.359007\pi$
$409$	−4699.45	+	8139.69i	−0.568149	+	0.984063i	−0.996749	+	0.0805684i	$0.974326\pi$
$410$	10089.3	−	17475.3i	1.21531	−	2.10498i
$411$		0			0
$412$	360.854	+	625.018i	0.0431505	+	0.0747389i
$413$	−4582.57			−0.545989
$414$		0			0
$415$	13000.0			1.53769
$416$	−2721.94	−	4714.53i	−0.320803	−	0.555646i
$417$		0			0
$418$	−3227.38	+	5589.99i	−0.377647	+	0.654104i
$419$	−297.363	+	515.048i	−0.0346710	+	0.0600519i	−0.882840	−	0.469673i	$-0.844372\pi$
$419$	−297.363	+	515.048i	−0.0346710	+	0.0600519i	0.848169	+	0.529725i	$0.177705\pi$
$420$		0			0
$421$	−1558.89	−	2700.07i	−0.180464	−	0.312574i	0.761574	−	0.648078i	$-0.224427\pi$
$421$	−1558.89	−	2700.07i	−0.180464	−	0.312574i	−0.942039	+	0.335504i	$0.891093\pi$
$422$	−5247.13			−0.605276
$423$		0			0
$424$	1231.26			0.141026
$425$	−15064.5	−	26092.5i	−1.71938	−	2.97805i
$426$		0			0
$427$	1220.74	−	2114.38i	0.138351	−	0.239630i
$428$	−1924.73	+	3333.73i	−0.217373	+	0.376500i
$429$		0			0
$430$	−11237.6	−	19464.1i	−1.26029	−	2.18288i
$431$	8465.93			0.946148			0.473074	−	0.881023i	$-0.343144\pi$
$431$	8465.93			0.946148			0.473074	+	0.881023i	$0.343144\pi$
$432$		0			0
$433$	5368.98			0.595881			0.297941	−	0.954584i	$-0.403700\pi$
$433$	5368.98			0.595881			0.297941	+	0.954584i	$0.403700\pi$
$434$	492.909	+	853.743i	0.0545170	+	0.0944262i
$435$		0			0
$436$	6008.50	−	10407.0i	0.659988	−	1.14313i
$437$	130.727	−	226.425i	0.0143101	−	0.0247858i
$438$		0			0
$439$	8896.36	+	15408.9i	0.967198	+	1.67524i	0.703589	+	0.710607i	$0.251580\pi$
$439$	8896.36	+	15408.9i	0.967198	+	1.67524i	0.263609	+	0.964630i	$0.415087\pi$
$440$	−20788.9			−2.25244
$441$		0			0
$442$	−13113.2			−1.41115
$443$	4431.80	+	7676.10i	0.475307	+	0.823256i	0.999600	−	0.0282821i	$-0.00900368\pi$
$443$	4431.80	+	7676.10i	0.475307	+	0.823256i	−0.524293	+	0.851538i	$0.675670\pi$
$444$		0			0
$445$	−16691.4	+	28910.3i	−1.77808	+	3.07973i
$446$	−4599.99	+	7967.41i	−0.488376	+	0.845892i
$447$		0			0
$448$	−2908.51	−	5037.68i	−0.306728	−	0.531268i
$449$	−114.115			−0.0119943			−0.00599714	−	0.999982i	$-0.501909\pi$
$449$	−114.115			−0.0119943			−0.00599714	+	0.999982i	$0.501909\pi$
$450$		0			0
$451$	9655.04			1.00807
$452$	8943.71	+	15491.0i	0.930701	+	1.61202i
$453$		0			0
$454$	−6941.66	+	12023.3i	−0.717595	+	1.24291i
$455$	−2132.42	+	3693.46i	−0.219713	+	0.380554i
$456$		0			0
$457$	−4031.28	−	6982.39i	−0.412638	−	0.714710i	0.582540	−	0.812802i	$-0.302059\pi$
$457$	−4031.28	−	6982.39i	−0.412638	−	0.714710i	−0.995177	+	0.0980929i	$0.968726\pi$
$458$	−18625.5			−1.90025
$459$		0			0
$460$	2237.87			0.226829
$461$	2064.94	+	3576.57i	0.208620	+	0.361340i	0.951280	−	0.308329i	$-0.0997696\pi$
$461$	2064.94	+	3576.57i	0.208620	+	0.361340i	−0.742660	+	0.669668i	$0.766436\pi$
$462$		0			0
$463$	−5909.24	+	10235.1i	−0.593144	+	1.02736i	0.400662	+	0.916226i	$0.368780\pi$
$463$	−5909.24	+	10235.1i	−0.593144	+	1.02736i	−0.993806	+	0.111130i	$0.964553\pi$
$464$	75.7810	−	131.256i	0.00758199	−	0.0131324i
$465$		0			0
$466$	−6086.83	−	10542.7i	−0.605079	−	1.04803i
$467$	−1590.26			−0.157577			−0.0787884	−	0.996891i	$-0.525105\pi$
$467$	−1590.26			−0.157577			−0.0787884	+	0.996891i	$0.525105\pi$
$468$		0			0
$469$	−1473.46			−0.145070
$470$	−10438.7	−	18080.3i	−1.02447	−	1.77443i
$471$		0			0
$472$	7209.35	−	12487.0i	0.703045	−	1.21771i
$473$	5376.93	−	9313.11i	0.522688	−	0.905322i
$474$		0			0
$475$	−4786.48	−	8290.42i	−0.462355	−	0.800822i
$476$	−8803.79			−0.847734
$477$		0			0
$478$	−27256.6			−2.60813
$479$	6567.28	+	11374.9i	0.626444	+	1.08503i	0.988260	+	0.152783i	$0.0488235\pi$
$479$	6567.28	+	11374.9i	0.626444	+	1.08503i	−0.361816	+	0.932249i	$0.617843\pi$
$480$		0			0
$481$	2877.22	−	4983.50i	0.272744	−	0.472407i
$482$	−6026.80	+	10438.7i	−0.569529	+	0.986453i
$483$		0			0
$484$	−4681.76	−	8109.04i	−0.439684	−	0.761555i
$485$	6052.23			0.566635
$486$		0			0
$487$	−18337.9			−1.70631			−0.853153	−	0.521661i	$-0.825313\pi$
$487$	−18337.9			−1.70631			−0.853153	+	0.521661i	$0.825313\pi$
$488$	3840.97	+	6652.75i	0.356296	+	0.617122i
$489$		0			0
$490$	−2324.59	+	4026.31i	−0.214315	+	0.371204i
$491$	−4048.59	+	7012.36i	−0.372119	+	0.644528i	−0.989891	−	0.141828i	$-0.954702\pi$
$491$	−4048.59	+	7012.36i	−0.372119	+	0.644528i	0.617773	+	0.786357i	$0.288035\pi$
$492$		0			0
$493$	−3543.06	−	6136.76i	−0.323674	−	0.560620i
$494$	−4166.47			−0.379471
$495$		0			0
$496$	64.7212			0.00585901
$497$	1918.88	+	3323.60i	0.173186	+	0.299968i
$498$		0			0
$499$	301.177	−	521.655i	0.0270191	−	0.0467985i	−0.852200	−	0.523217i	$-0.824732\pi$
$499$	301.177	−	521.655i	0.0270191	−	0.0467985i	0.879219	+	0.476418i	$0.158065\pi$
$500$	24302.3	−	42092.9i	2.17367	−	3.76490i
$501$		0			0
$502$	15975.2	+	27669.8i	1.42033	+	2.46009i
$503$	−11416.3			−1.01198			−0.505992	−	0.862538i	$-0.668874\pi$
$503$	−11416.3			−1.01198			−0.505992	+	0.862538i	$0.668874\pi$
$504$		0			0
$505$	−30201.3			−2.66126
$506$	869.317	+	1505.70i	0.0763752	+	0.132286i
$507$		0			0
$508$	15310.5	−	26518.5i	1.33719	−	2.31608i
$509$	6406.07	−	11095.6i	0.557847	−	0.966220i	−0.439829	−	0.898082i	$-0.644961\pi$
$509$	6406.07	−	11095.6i	0.557847	−	0.966220i	0.997676	−	0.0681380i	$-0.0217058\pi$
$510$		0			0
$511$	−934.108	−	1617.92i	−0.0808659	−	0.140064i
$512$	−759.150			−0.0655273
$513$		0			0
$514$	26412.7			2.26656
$515$	−584.935	−	1013.14i	−0.0500491	−	0.0866876i
$516$		0			0
$517$	4994.66	−	8651.00i	0.424884	−	0.735920i
$518$	3136.51	−	5432.60i	0.266043	−	0.460801i
$519$		0			0
$520$	−6709.51	−	11621.2i	−0.565830	−	0.980046i
$521$	−3033.32			−0.255071			−0.127536	−	0.991834i	$-0.540707\pi$
$521$	−3033.32			−0.255071			−0.127536	+	0.991834i	$0.540707\pi$
$522$		0			0
$523$	12789.3			1.06928			0.534642	−	0.845078i	$-0.320446\pi$
$523$	12789.3			1.06928			0.534642	+	0.845078i	$0.320446\pi$
$524$	13595.8	+	23548.6i	1.13346	+	1.96321i
$525$		0			0
$526$	17082.9	−	29588.5i	1.41607	−	2.45270i
$527$	1512.99	−	2620.57i	0.125060	−	0.216611i
$528$		0			0
$529$	6048.29	+	10475.9i	0.497106	+	0.861013i
$530$	−5304.13			−0.434711
$531$		0			0
$532$	−2797.25			−0.227962
$533$	3116.11	+	5397.25i	0.253234	+	0.438614i
$534$		0			0
$535$	3119.94	−	5403.89i	0.252124	−	0.436692i
$536$	2318.06	−	4015.01i	0.186801	−	0.323548i
$537$		0			0
$538$	7414.49	+	12842.3i	0.594166	+	1.02913i
$539$	−2224.53			−0.177768
$540$		0			0
$541$	3836.05			0.304851			0.152426	−	0.988315i	$-0.451292\pi$
$541$	3836.05			0.304851			0.152426	+	0.988315i	$0.451292\pi$
$542$	−9004.66	−	15596.5i	−0.713622	−	1.23603i
$543$		0			0
$544$	−9107.93	+	15775.4i	−0.717830	+	1.24332i
$545$	−9739.60	+	16869.5i	−0.765502	+	1.32589i
$546$		0			0
$547$	−2438.27	−	4223.20i	−0.190590	−	0.330112i	0.754856	−	0.655891i	$-0.227707\pi$
$547$	−2438.27	−	4223.20i	−0.190590	−	0.330112i	−0.945446	+	0.325779i	$0.894373\pi$
$548$	845.271			0.0658908
$549$		0			0
$550$	63659.1			4.93533
$551$	−1125.74	−	1949.84i	−0.0870386	−	0.150755i
$552$		0			0
$553$	−944.622	+	1636.13i	−0.0726391	+	0.125815i
$554$	10620.1	−	18394.5i	0.814445	−	1.41066i
$555$		0			0
$556$	12590.8	+	21807.9i	0.960374	+	1.66342i
$557$	−26004.6			−1.97819			−0.989095	−	0.147276i	$-0.952949\pi$
$557$	−26004.6			−1.97819			−0.989095	+	0.147276i	$0.952949\pi$
$558$		0			0
$559$	6941.48			0.525212
$560$	152.615	+	264.337i	0.0115163	+	0.0199469i
$561$		0			0
$562$	−14710.4	+	25479.2i	−1.10413	+	1.91241i
$563$	7675.11	−	13293.7i	0.574542	−	0.995137i	−0.421549	−	0.906806i	$-0.638513\pi$
$563$	7675.11	−	13293.7i	0.574542	−	0.995137i	0.996091	−	0.0883309i	$-0.0281533\pi$
$564$		0			0
$565$	−14497.5	−	25110.4i	−1.07949	−	1.86974i
$566$	16604.4			1.23310
$567$		0			0
$568$	−12075.2			−0.892017
$569$	−10436.7	−	18077.0i	−0.768947	−	1.33186i	−0.938134	−	0.346272i	$-0.887448\pi$
$569$	−10436.7	−	18077.0i	−0.768947	−	1.33186i	0.169187	−	0.985584i	$-0.445886\pi$
$570$		0			0
$571$	3.53471	−	6.12229i	0.000259059	−	0.000448704i	−0.865896	−	0.500224i	$-0.833251\pi$
$571$	3.53471	−	6.12229i	0.000259059	−	0.000448704i	0.866155	+	0.499776i	$0.166584\pi$
$572$	8531.82	−	14777.5i	0.623660	−	1.08021i
$573$		0			0
$574$	3396.92	+	5883.64i	0.247012	+	0.427837i
$575$	−2578.54			−0.187013
$576$		0			0
$577$	−13121.5			−0.946715			−0.473357	−	0.880870i	$-0.656958\pi$
$577$	−13121.5			−0.946715			−0.473357	+	0.880870i	$0.656958\pi$
$578$	10728.7	+	18582.7i	0.772068	+	1.33726i
$579$		0			0
$580$	9635.65	−	16689.4i	0.689825	−	1.19481i
$581$	−2188.44	+	3790.49i	−0.156268	+	0.270664i
$582$		0			0
$583$	−1268.95	−	2197.89i	−0.0901452	−	0.156136i
$584$	5878.20			0.416510
$585$		0			0
$586$	28875.9			2.03558
$587$	−1918.15	−	3322.34i	−0.134873	−	0.233607i	0.790676	−	0.612235i	$-0.209729\pi$
$587$	−1918.15	−	3322.34i	−0.134873	−	0.233607i	−0.925549	+	0.378628i	$0.876396\pi$
$588$		0			0
$589$	480.724	−	832.638i	0.0336297	−	0.0582483i
$590$	−31057.1	+	53792.5i	−2.16712	+	3.75357i
$591$		0			0
$592$	−205.919	−	356.663i	−0.0142960	−	0.0247614i
$593$	−2999.00			−0.207680			−0.103840	−	0.994594i	$-0.533113\pi$
$593$	−2999.00			−0.207680			−0.103840	+	0.994594i	$0.533113\pi$
$594$		0			0
$595$	14270.7			0.983263
$596$	−16891.0	−	29256.1i	−1.16088	−	2.01070i
$597$		0			0
$598$	−561.134	+	971.913i	−0.0383720	+	0.0664623i
$599$	4181.01	−	7241.73i	0.285195	−	0.493972i	−0.687462	−	0.726221i	$-0.741275\pi$
$599$	4181.01	−	7241.73i	0.285195	−	0.493972i	0.972656	+	0.232249i	$0.0746084\pi$
$600$		0			0
$601$	7265.07	+	12583.5i	0.493092	+	0.854061i	0.999968	−	0.00795794i	$-0.00253312\pi$
$601$	7265.07	+	12583.5i	0.493092	+	0.854061i	−0.506876	+	0.862019i	$0.669200\pi$
$602$	7567.04			0.512308
$603$		0			0
$604$	−9459.02			−0.637222
$605$	7588.99	+	13144.5i	0.509977	+	0.883307i
$606$		0			0
$607$	6504.64	−	11266.4i	0.434951	−	0.753357i	−0.562341	−	0.826906i	$-0.690099\pi$
$607$	6504.64	−	11266.4i	0.434951	−	0.753357i	0.997292	+	0.0735487i	$0.0234324\pi$
$608$	−2893.88	+	5012.35i	−0.193030	+	0.334338i
$609$		0			0
$610$	−16546.5	−	28659.3i	−1.09827	−	1.90227i
$611$	6447.98			0.426935
$612$		0			0
$613$	3740.67			0.246467			0.123233	−	0.992378i	$-0.460674\pi$
$613$	3740.67			0.246467			0.123233	+	0.992378i	$0.460674\pi$
$614$	6190.03	+	10721.5i	0.406856	+	0.704695i
$615$		0			0
$616$	3499.66	−	6061.58i	0.228905	−	0.396474i
$617$	11342.8	−	19646.3i	0.740104	−	1.28190i	−0.212344	−	0.977195i	$-0.568110\pi$
$617$	11342.8	−	19646.3i	0.740104	−	1.28190i	0.952448	−	0.304703i	$-0.0985570\pi$
$618$		0			0
$619$	594.523	+	1029.74i	0.0386040	+	0.0668641i	0.884682	−	0.466195i	$-0.154376\pi$
$619$	594.523	+	1029.74i	0.0386040	+	0.0668641i	−0.846078	+	0.533059i	$0.821042\pi$
$620$	8229.39			0.533065
$621$		0			0
$622$	13901.0			0.896107
$623$	−5619.72	−	9733.64i	−0.361395	−	0.625955i
$624$		0			0
$625$	−20189.3	+	34968.9i	−1.29212	+	2.23801i
$626$	9995.45	−	17312.6i	0.638176	−	1.10535i
$627$		0			0
$628$	−15049.8	−	26067.1i	−0.956296	−	1.65635i
$629$	−19255.1			−1.22059
$630$		0			0
$631$	23574.4			1.48729			0.743646	−	0.668574i	$-0.233095\pi$
$631$	23574.4			1.48729			0.743646	+	0.668574i	$0.233095\pi$
$632$	−2972.18	−	5147.97i	−0.187068	−	0.324012i
$633$		0			0
$634$	−15758.6	+	27294.7i	−0.987152	+	1.70980i
$635$	−24817.8	+	42985.8i	−1.55097	+	2.68636i
$636$		0			0
$637$	−717.953	−	1243.53i	−0.0446567	−	0.0773477i
$638$	14972.1			0.929079
$639$		0			0
$640$	−47947.7			−2.96140
$641$	−6996.33	−	12118.0i	−0.431105	−	0.746696i	0.565863	−	0.824499i	$-0.308543\pi$
$641$	−6996.33	−	12118.0i	−0.431105	−	0.746696i	−0.996969	+	0.0778026i	$0.975210\pi$
$642$		0			0
$643$	−5948.33	+	10302.8i	−0.364820	+	0.631886i	−0.988747	−	0.149596i	$-0.952203\pi$
$643$	−5948.33	+	10302.8i	−0.364820	+	0.631886i	0.623927	+	0.781482i	$0.285536\pi$
$644$	−376.729	+	652.513i	−0.0230515	+	0.0399264i
$645$		0			0
$646$	6970.77	+	12073.7i	0.424553	+	0.735347i
$647$	5011.63			0.304525			0.152262	−	0.988340i	$-0.451344\pi$
$647$	5011.63			0.304525			0.152262	+	0.988340i	$0.451344\pi$
$648$		0			0
$649$	−29720.3			−1.79757
$650$	20545.6	+	35586.0i	1.23979	+	2.14738i
$651$		0			0
$652$	3668.32	−	6353.72i	0.220341	−	0.381642i
$653$	−6238.61	+	10805.6i	−0.373868	+	0.647558i	−0.990157	−	0.139962i	$-0.955302\pi$
$653$	−6238.61	+	10805.6i	−0.373868	+	0.647558i	0.616289	+	0.787520i	$0.288635\pi$
$654$		0			0
$655$	−22038.3	−	38171.5i	−1.31467	−	2.27708i
$656$	446.032			0.0265467
$657$		0			0
$658$	7029.06			0.416446
$659$	14463.6	+	25051.6i	0.854962	+	1.48084i	0.876680	+	0.481073i	$0.159753\pi$
$659$	14463.6	+	25051.6i	0.854962	+	1.48084i	−0.0217183	+	0.999764i	$0.506914\pi$
$660$		0			0
$661$	12339.9	−	21373.3i	0.726121	−	1.25768i	−0.232389	−	0.972623i	$-0.574654\pi$
$661$	12339.9	−	21373.3i	0.726121	−	1.25768i	0.958511	−	0.285056i	$-0.0920123\pi$
$662$	13011.9	−	22537.3i	0.763933	−	1.32317i
$663$		0			0
$664$	−6885.77	−	11926.5i	−0.402439	−	0.697045i
$665$	4534.26			0.264407
$666$		0			0
$667$	−606.453			−0.0352053
$668$	3487.28	+	6040.14i	0.201986	+	0.349850i
$669$		0			0
$670$	−9985.98	+	17296.2i	−0.575809	+	0.997330i
$671$	7917.11	−	13712.8i	0.455494	−	0.788939i
$672$		0			0
$673$	537.810	+	931.515i	0.0308040	+	0.0533540i	0.881016	−	0.473086i	$-0.156860\pi$
$673$	537.810	+	931.515i	0.0308040	+	0.0533540i	−0.850212	+	0.526440i	$0.823527\pi$
$674$	−5611.44			−0.320689
$675$		0			0
$676$	−17164.9			−0.976610
$677$	11518.6	+	19950.8i	0.653908	+	1.13260i	0.982166	+	0.188013i	$0.0602048\pi$
$677$	11518.6	+	19950.8i	0.653908	+	1.13260i	−0.328259	+	0.944588i	$0.606462\pi$
$678$		0			0
$679$	−1018.85	+	1764.69i	−0.0575843	+	0.0997389i
$680$	−22450.8	+	38886.0i	−1.26610	+	2.19296i
$681$		0			0
$682$	3196.76	+	5536.95i	0.179487	+	0.310881i
$683$	1233.44			0.0691015			0.0345508	−	0.999403i	$-0.489000\pi$
$683$	1233.44			0.0691015			0.0345508	+	0.999403i	$0.489000\pi$
$684$		0			0
$685$	−1370.16			−0.0764249
$686$	−782.654	−	1355.60i	−0.0435596	−	0.0754474i
$687$		0			0
$688$	248.397	−	430.236i	0.0137646	−	0.0238410i
$689$	819.093	−	1418.71i	0.0452902	−	0.0784450i
$690$		0			0
$691$	15214.0	+	26351.4i	0.837578	+	1.45073i	0.891914	+	0.452205i	$0.149363\pi$
$691$	15214.0	+	26351.4i	0.837578	+	1.45073i	−0.0543356	+	0.998523i	$0.517304\pi$
$692$	−26094.4			−1.43347
$693$		0			0
$694$	20013.5			1.09467
$695$	−20409.3	−	35349.9i	−1.11391	−	1.92935i
$696$		0			0
$697$	10426.9	−	18059.9i	0.566637	−	0.981444i
$698$	6662.90	−	11540.5i	0.361310	−	0.625808i
$699$		0			0
$700$	13793.7	+	23891.4i	0.744790	+	1.29001i
$701$	−359.627			−0.0193765			−0.00968825	−	0.999953i	$-0.503084\pi$
$701$	−359.627			−0.0193765			−0.00968825	+	0.999953i	$0.503084\pi$
$702$		0			0
$703$	−6117.96			−0.328226
$704$	−18863.1	−	32671.9i	−1.00985	−	1.74910i
$705$		0			0
$706$	−25400.7	+	43995.3i	−1.35406	+	2.34530i
$707$	5084.15	−	8806.00i	0.270451	−	0.468435i
$708$		0			0
$709$	−16634.0	−	28810.9i	−0.881103	−	1.52611i	−0.850116	−	0.526595i	$-0.823469\pi$
$709$	−16634.0	−	28810.9i	−0.881103	−	1.52611i	−0.0309861	−	0.999520i	$-0.509865\pi$
$710$	52018.8			2.74962
$711$		0			0
$712$	35364.1			1.86141
$713$	−129.486	−	224.277i	−0.00680126	−	0.0117801i
$714$		0			0
$715$	−13829.8	+	23954.0i	−0.723366	+	1.25291i
$716$	−5972.02	+	10343.8i	−0.311711	+	0.539899i
$717$		0			0
$718$	−17434.7	−	30197.8i	−0.906209	−	1.56960i
$719$	8882.66			0.460733			0.230367	−	0.973104i	$-0.426007\pi$
$719$	8882.66			0.460733			0.230367	+	0.973104i	$0.426007\pi$
$720$		0			0
$721$	393.877			0.0203450
$722$	−13436.0	−	23271.8i	−0.692569	−	1.19956i
$723$		0			0
$724$	−6430.69	+	11138.3i	−0.330103	+	0.571756i
$725$	−11102.5	+	19230.0i	−0.568738	+	0.985083i
$726$		0			0
$727$	8494.42	+	14712.8i	0.433343	+	0.750573i	0.997159	−	0.0753280i	$-0.0240004\pi$
$727$	8494.42	+	14712.8i	0.433343	+	0.750573i	−0.563815	+	0.825901i	$0.690667\pi$
$728$	4517.97			0.230010
$729$		0			0
$730$	−25322.7			−1.28388
$731$	−11613.5	−	20115.2i	−0.587609	−	1.01777i
$732$		0			0
$733$	10991.9	−	19038.5i	0.553882	−	0.959351i	−0.444108	−	0.895973i	$-0.646479\pi$
$733$	10991.9	−	19038.5i	0.553882	−	0.959351i	0.997990	−	0.0633778i	$-0.0201873\pi$
$734$	10059.3	−	17423.2i	0.505851	−	0.876159i
$735$		0			0
$736$	779.487	+	1350.11i	0.0390384	+	0.0676165i
$737$	−9556.12			−0.477618
$738$		0			0
$739$	18909.8			0.941284			0.470642	−	0.882324i	$-0.344022\pi$
$739$	18909.8			0.941284			0.470642	+	0.882324i	$0.344022\pi$
$740$	−26182.9	−	45350.2i	−1.30068	−	2.25284i
$741$		0			0
$742$	892.909	−	1546.56i	0.0441775	−	0.0765177i
$743$	−5004.66	+	8668.33i	−0.247111	+	0.428008i	−0.962723	−	0.270489i	$-0.912814\pi$
$743$	−5004.66	+	8668.33i	−0.247111	+	0.428008i	0.715612	+	0.698498i	$0.246148\pi$
$744$		0			0
$745$	27379.8	+	47423.2i	1.34647	+	2.33215i
$746$	−21012.2			−1.03125
$747$		0			0
$748$	−57097.0			−2.79101
$749$	1050.43	+	1819.40i	0.0512443	+	0.0887578i
$750$		0			0
$751$	14626.9	−	25334.5i	0.710708	−	1.23098i	−0.253884	−	0.967235i	$-0.581708\pi$
$751$	14626.9	−	25334.5i	0.710708	−	1.23098i	0.964592	−	0.263747i	$-0.0849585\pi$
$752$	230.737	−	399.649i	0.0111890	−	0.0193799i
$753$		0			0
$754$	4832.17	+	8369.56i	0.233391	+	0.404246i
$755$	15332.8			0.739096
$756$		0			0
$757$	−20805.2			−0.998912			−0.499456	−	0.866339i	$-0.666467\pi$
$757$	−20805.2			−0.998912			−0.499456	+	0.866339i	$0.666467\pi$
$758$	33495.5	+	58016.0i	1.60503	+	2.77999i
$759$		0			0
$760$	−7133.35	+	12355.3i	−0.340466	+	0.589704i
$761$	5062.52	−	8768.54i	0.241151	−	0.417687i	−0.719891	−	0.694087i	$-0.755808\pi$
$761$	5062.52	−	8768.54i	0.241151	−	0.417687i	0.961043	+	0.276400i	$0.0891416\pi$
$762$		0			0
$763$	−3279.17	−	5679.69i	−0.155588	−	0.269487i
$764$	49292.3			2.33421
$765$		0			0
$766$	8322.81			0.392579
$767$	−9592.04	−	16613.9i	−0.451562	−	0.782129i
$768$		0			0
$769$	18632.4	−	32272.3i	0.873735	−	1.51335i	0.0156305	−	0.999878i	$-0.495024\pi$
$769$	18632.4	−	32272.3i	0.873735	−	1.51335i	0.858104	−	0.513475i	$-0.171642\pi$
$770$	−15076.2	+	26112.7i	−0.705593	+	1.22212i
$771$		0			0
$772$	22228.6	+	38501.0i	1.03630	+	1.79492i
$773$	−16637.3			−0.774130			−0.387065	−	0.922052i	$-0.626511\pi$
$773$	−16637.3			−0.774130			−0.387065	+	0.922052i	$0.626511\pi$
$774$		0			0
$775$	−9482.13			−0.439494
$776$	−3205.73	−	5552.48i	−0.148297	−	0.256859i
$777$		0			0
$778$	−19654.4	+	34042.4i	−0.905713	+	1.56874i
$779$	3312.95	−	5738.20i	0.152373	−	0.263918i
$780$		0			0
$781$	12444.9	+	21555.2i	0.570185	+	0.987589i
$782$	3755.25			0.171723
$783$		0			0
$784$	−102.766			−0.00468140
$785$	24395.4	+	42254.0i	1.10918	+	1.92116i
$786$		0			0
$787$	−6559.92	+	11362.1i	−0.297123	+	0.514633i	−0.975477	−	0.220103i	$-0.929361\pi$
$787$	−6559.92	+	11362.1i	−0.297123	+	0.514633i	0.678353	+	0.734736i	$0.262694\pi$
$788$	−23677.2	+	41010.1i	−1.07039	+	1.85397i
$789$		0			0
$790$	12803.9	+	22176.9i	0.576634	+	0.998759i
$791$	9762.16			0.438815
$792$		0			0
$793$	10220.8			0.457694
$794$	−12543.1	−	21725.3i	−0.560626	−	0.971033i
$795$		0			0
$796$	3089.74	−	5351.58i	0.137579	−	0.238294i
$797$	−191.253	+	331.260i	−0.00850004	+	0.0147225i	−0.870244	−	0.492621i	$-0.836039\pi$
$797$	−191.253	+	331.260i	−0.00850004	+	0.0147225i	0.861744	+	0.507343i	$0.169372\pi$
$798$		0			0
$799$	−10787.9	−	18685.1i	−0.477657	−	0.827325i
$800$	57080.9			2.52264
$801$		0			0
$802$	−39342.8			−1.73222
$803$	−6058.16	−	10493.0i	−0.266236	−	0.461135i
$804$		0			0
$805$	610.666	−	1057.71i	0.0267368	−	0.0463096i
$806$	−2063.47	+	3574.04i	−0.0901770	+	0.156191i
$807$		0			0
$808$	15996.9	+	27707.4i	0.696496	+	1.20637i
$809$	−2590.19			−0.112566			−0.0562831	−	0.998415i	$-0.517925\pi$
$809$	−2590.19			−0.112566			−0.0562831	+	0.998415i	$0.517925\pi$
$810$		0			0
$811$	−20167.1			−0.873199			−0.436599	−	0.899656i	$-0.643817\pi$
$811$	−20167.1			−0.873199			−0.436599	+	0.899656i	$0.643817\pi$
$812$	3244.17	+	5619.07i	0.140207	+	0.242846i
$813$		0			0
$814$	20341.9	−	35233.1i	0.875899	−	1.51710i
$815$	−5946.24	+	10299.2i	−0.255568	+	0.442656i
$816$		0			0
$817$	−3689.99	−	6391.25i	−0.158013	−	0.273686i
$818$	−42892.6			−1.83338
$819$		0			0
$820$	56713.6			2.41527
$821$	14806.3	+	25645.2i	0.629407	+	1.09016i	0.987671	+	0.156544i	$0.0500355\pi$
$821$	14806.3	+	25645.2i	0.629407	+	1.09016i	−0.358264	+	0.933620i	$0.616631\pi$
$822$		0			0
$823$	−5118.30	+	8865.16i	−0.216784	+	0.375480i	−0.953823	−	0.300370i	$-0.902890\pi$
$823$	−5118.30	+	8865.16i	−0.216784	+	0.375480i	0.737039	+	0.675850i	$0.236223\pi$
$824$	−619.652	+	1073.27i	−0.0261973	+	0.0453751i
$825$		0			0
$826$	−10456.5	−	18111.1i	−0.440468	−	0.762913i
$827$	8733.00			0.367202			0.183601	−	0.983001i	$-0.441225\pi$
$827$	8733.00			0.367202			0.183601	+	0.983001i	$0.441225\pi$
$828$		0			0
$829$	10394.4			0.435481			0.217741	−	0.976007i	$-0.430131\pi$
$829$	10394.4			0.435481			0.217741	+	0.976007i	$0.430131\pi$
$830$	29663.1	+	51378.1i	1.24051	+	2.14863i
$831$		0			0
$832$	12175.9	−	21089.3i	0.507361	−	0.878775i
$833$	−2402.36	+	4161.01i	−0.0999242	+	0.173074i
$834$		0			0
$835$	−5652.77	−	9790.89i	−0.234278	−	0.405782i
$836$	−18141.6			−0.750525
$837$		0			0
$838$	−2714.08			−0.111881
$839$	−14344.8	−	24846.0i	−0.590272	−	1.02238i	−0.994196	−	0.107588i	$-0.965687\pi$
$839$	−14344.8	−	24846.0i	−0.590272	−	1.02238i	0.403924	−	0.914793i	$-0.367646\pi$
$840$		0			0
$841$	9583.28	−	16598.7i	0.392935	−	0.680583i
$842$	7114.11	−	12322.0i	0.291174	−	0.504328i
$843$		0			0
$844$	−7373.71	−	12771.6i	−0.300727	−	0.520874i
$845$	27823.8			1.13274
$846$		0			0
$847$	−5110.19			−0.207306
$848$	−58.6215	−	101.535i	−0.00237391	−	0.00411172i
$849$		0			0
$850$	68748.1	−	119075.i	2.77416	−	4.80499i
$851$	−823.957	+	1427.13i	−0.0331902	+	0.0574871i
$852$		0			0
$853$	−11064.3	−	19163.9i	−0.444120	−	0.769239i	0.553870	−	0.832603i	$-0.313150\pi$
$853$	−11064.3	−	19163.9i	−0.444120	−	0.769239i	−0.997990	+	0.0633642i	$0.979817\pi$
$854$	11141.9			0.446449
$855$		0			0
$856$	−6610.22			−0.263940
$857$	2393.76	+	4146.11i	0.0954132	+	0.165261i	0.909781	−	0.415089i	$-0.136249\pi$
$857$	2393.76	+	4146.11i	0.0954132	+	0.165261i	−0.814368	+	0.580349i	$0.802916\pi$
$858$		0			0
$859$	−5787.93	+	10025.0i	−0.229897	+	0.398194i	−0.957777	−	0.287511i	$-0.907172\pi$
$859$	−5787.93	+	10025.0i	−0.229897	+	0.398194i	0.727880	+	0.685704i	$0.240506\pi$
$860$	31584.0	−	54705.1i	1.25233	−	2.16910i
$861$		0			0
$862$	19317.5	+	33458.8i	0.763290	+	1.32206i
$863$	−4683.61			−0.184741			−0.0923707	−	0.995725i	$-0.529444\pi$
$863$	−4683.61			−0.184741			−0.0923707	+	0.995725i	$0.529444\pi$
$864$		0			0
$865$	42298.2			1.66264
$866$	12250.9	+	21219.1i	0.480718	+	0.832628i
$867$		0			0
$868$	−1385.35	+	2399.50i	−0.0541728	+	0.0938300i
$869$	−6126.35	+	10611.2i	−0.239151	+	0.414222i
$870$		0			0
$871$	−3084.18	−	5341.96i	−0.119981	−	0.207813i
$872$	20635.3			0.801377
$873$		0			0
$874$	1193.16			0.0461777
$875$	−13263.1	−	22972.4i	−0.512429	−	0.887554i
$876$		0			0
$877$	11435.6	−	19807.1i	0.440313	−	0.762644i	−0.557400	−	0.830244i	$-0.688201\pi$
$877$	11435.6	−	19807.1i	0.440313	−	0.762644i	0.997712	+	0.0676002i	$0.0215342\pi$
$878$	−40599.2	+	70319.9i	−1.56054	+	2.70294i
$879$		0			0
$880$	989.785	+	1714.36i	0.0379155	+	0.0656716i
$881$	20712.8			0.792091			0.396045	−	0.918231i	$-0.370382\pi$
$881$	20712.8			0.792091			0.396045	+	0.918231i	$0.370382\pi$
$882$		0			0
$883$	−21641.0			−0.824775			−0.412388	−	0.911008i	$-0.635305\pi$
$883$	−21641.0			−0.824775			−0.412388	+	0.911008i	$0.635305\pi$
$884$	−18427.7	−	31917.8i	−0.701122	−	1.21438i
$885$		0			0
$886$	−20224.9	+	35030.5i	−0.766893	+	1.32830i
$887$	13479.5	−	23347.1i	0.510255	−	0.883787i	−0.489675	−	0.871905i	$-0.662884\pi$
$887$	13479.5	−	23347.1i	0.510255	−	0.883787i	0.999929	−	0.0118818i	$-0.00378217\pi$
$888$		0			0
$889$	−8355.78	−	14472.6i	−0.315235	−	0.546003i
$890$	−152345.			−5.73776
$891$		0			0
$892$	−25857.1			−0.970585
$893$	−3427.65	−	5936.87i	−0.128446	−	0.222475i
$894$		0			0
$895$	9680.47	−	16767.1i	0.361545	−	0.626214i
$896$	8071.62	−	13980.5i	0.300953	−	0.521266i
$897$		0			0
$898$	−260.387	−	451.003i	−0.00967620	−	0.0167597i
$899$	−2230.12			−0.0827351
$900$		0			0
$901$	−5481.58			−0.202683
$902$	22030.8	+	38158.4i	0.813242	+	1.40858i
$903$		0			0
$904$	−15358.0	+	26600.8i	−0.565042	+	0.978682i
$905$	10424.0	−	18054.8i	0.382878	−	0.663164i
$906$		0			0
$907$	10184.2	+	17639.5i	0.372833	+	0.645765i	0.990000	−	0.141067i	$-0.0450532\pi$
$907$	10184.2	+	17639.5i	0.372833	+	0.645765i	−0.617167	+	0.786832i	$0.711720\pi$
$908$	−39020.0			−1.42613
$909$		0			0
$910$	−19462.9			−0.709001
$911$	10750.9	+	18621.1i	0.390991	+	0.677217i	0.992581	−	0.121589i	$-0.0387989\pi$
$911$	10750.9	+	18621.1i	0.390991	+	0.677217i	−0.601589	+	0.798806i	$0.705466\pi$
$912$		0			0
$913$	−14193.1	+	24583.2i	−0.514485	+	0.891113i
$914$	18397.1	−	31864.7i	0.665778	−	1.15316i
$915$		0			0
$916$	−26174.2	−	45335.0i	−0.944125	−	1.63527i
$917$	14839.9			0.534414
$918$		0			0
$919$	−2461.02			−0.0883369			−0.0441685	−	0.999024i	$-0.514064\pi$
$919$	−2461.02			−0.0883369			−0.0441685	+	0.999024i	$0.514064\pi$
$920$	1921.42	+	3327.99i	0.0688557	+	0.119262i
$921$		0			0
$922$	−9423.50	+	16322.0i	−0.336601	+	0.583010i
$923$	−8033.04	+	13913.6i	−0.286469	+	0.496179i
$924$		0			0
$925$	30168.7	+	52253.7i	1.07237	+	1.85740i
$926$	−53934.6			−1.91404
$927$		0			0
$928$	13425.0			0.474889
$929$	866.047	+	1500.04i	0.0305857	+	0.0529759i	0.880913	−	0.473278i	$-0.156929\pi$
$929$	866.047	+	1500.04i	0.0305857	+	0.0529759i	−0.850327	+	0.526254i	$0.823596\pi$
$930$		0			0
$931$	−763.307	+	1322.09i	−0.0268704	+	0.0465409i
$932$	17107.4	−	29631.0i	0.601259	−	1.04141i
$933$		0			0
$934$	−3628.63	−	6284.97i	−0.127123	−	0.220183i
$935$	92552.7			3.23721
$936$		0			0
$937$	35120.9			1.22449			0.612247	−	0.790667i	$-0.290266\pi$
$937$	35120.9			1.22449			0.612247	+	0.790667i	$0.290266\pi$
$938$	−3362.12	−	5823.37i	−0.117033	−	0.202708i
$939$		0			0
$940$	29338.6	−	50815.9i	1.01800	−	1.76322i
$941$	−6463.99	+	11196.0i	−0.223932	+	0.387862i	−0.955999	−	0.293371i	$-0.905223\pi$
$941$	−6463.99	+	11196.0i	−0.223932	+	0.387862i	0.732066	+	0.681233i	$0.238556\pi$
$942$		0			0
$943$	−892.366	−	1545.62i	−0.0308160	−	0.0533748i
$944$	−1372.98			−0.0473376
$945$		0			0
$946$	49076.1			1.68668
$947$	−1601.47	−	2773.83i	−0.0549533	−	0.0951819i	0.837240	−	0.546835i	$-0.184168\pi$
$947$	−1601.47	−	2773.83i	−0.0549533	−	0.0951819i	−0.892193	+	0.451654i	$0.850834\pi$
$948$		0			0
$949$	3910.47	−	6773.13i	0.133761	−	0.231681i
$950$	21843.5	−	37834.0i	0.745995	−	1.29210i
$951$		0			0
$952$	−7558.85	−	13092.3i	−0.257336	−	0.445719i
$953$	36827.2			1.25178			0.625891	−	0.779910i	$-0.284735\pi$
$953$	36827.2			1.25178			0.625891	+	0.779910i	$0.284735\pi$
$954$		0			0
$955$	−79901.5			−2.70738
$956$	−38303.2	−	66343.1i	−1.29583	−	2.24444i
$957$		0			0
$958$	−29970.3	+	51910.1i	−1.01075	+	1.75067i
$959$	230.656	−	399.507i	0.00776669	−	0.0134523i
$960$		0			0
$961$	14419.3	+	24975.0i	0.484017	+	0.838341i
$962$	26260.9			0.880129
$963$		0			0
$964$	−33877.5			−1.13187
$965$	−36031.8	−	62409.0i	−1.20197	−	2.08188i
$966$		0			0
$967$	−490.524	+	849.612i	−0.0163125	+	0.0282541i	−0.874066	−	0.485806i	$-0.838526\pi$
$967$	−490.524	+	849.612i	−0.0163125	+	0.0282541i	0.857754	+	0.514061i	$0.171859\pi$
$968$	8039.42	−	13924.7i	0.266939	−	0.462351i
$969$		0			0
$970$	13809.9	+	23919.5i	0.457124	+	0.791761i
$971$	−35299.7			−1.16666			−0.583328	−	0.812237i	$-0.698250\pi$
$971$	−35299.7			−1.16666			−0.583328	+	0.812237i	$0.698250\pi$
$972$		0			0
$973$	13743.0			0.452805
$974$	−41843.3	−	72474.7i	−1.37654	−	2.38423i
$975$		0			0
$976$	365.745	−	633.489i	0.0119951	−	0.0207761i
$977$	−19802.8	+	34299.4i	−0.648462	+	1.12317i	0.335029	+	0.942208i	$0.391254\pi$
$977$	−19802.8	+	34299.4i	−0.648462	+	1.12317i	−0.983490	+	0.180961i	$0.942079\pi$
$978$		0			0
$979$	−36446.7	−	63127.6i	−1.18983	−	2.06084i
$980$	−13066.8			−0.425924
$981$		0			0
$982$	−36952.1			−1.20080
$983$	−5834.71	−	10106.0i	−0.189317	−	0.327906i	0.755706	−	0.654911i	$-0.227294\pi$
$983$	−5834.71	−	10106.0i	−0.189317	−	0.327906i	−0.945023	+	0.327005i	$0.893961\pi$
$984$		0			0
$985$	38380.0	−	66476.2i	1.24151	−	2.15036i
$986$	16169.0	−	28005.6i	0.522238	−	0.904543i
$987$		0			0
$988$	−5855.08	−	10141.3i	−0.188537	−	0.326556i
$989$	−1987.85			−0.0639129
$990$		0			0
$991$	37428.6			1.19976			0.599879	−	0.800091i	$-0.295215\pi$
$991$	37428.6			1.19976			0.599879	+	0.800091i	$0.295215\pi$
$992$	2866.42	+	4964.79i	0.0917430	+	0.158904i
$993$		0			0
$994$	−8756.97	+	15167.5i	−0.279431	+	0.483988i
$995$	−5008.37	+	8674.76i	−0.159574	+	0.276390i
$996$		0			0
$997$	−5306.23	−	9190.66i	−0.168556	−	0.291947i	0.769357	−	0.638820i	$-0.220577\pi$
$997$	−5306.23	−	9190.66i	−0.168556	−	0.291947i	−0.937912	+	0.346873i	$0.887244\pi$
$998$	2748.89			0.0871891
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.4.f.b.64.7		16
3.2	odd	2		63.4.f.b.22.2	✓	16
9.2	odd	6		63.4.f.b.43.2	yes	16
9.4	even	3		567.4.a.g.1.2		8
9.5	odd	6		567.4.a.i.1.7		8
9.7	even	3	inner	189.4.f.b.127.7		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.4.f.b.22.2	✓	16	3.2	odd	2
63.4.f.b.43.2	yes	16	9.2	odd	6
189.4.f.b.64.7		16	1.1	even	1	trivial
189.4.f.b.127.7		16	9.7	even	3	inner
567.4.a.g.1.2		8	9.4	even	3
567.4.a.i.1.7		8	9.5	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:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	189.f (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.28179 + 3.95218i) q^{2} +(-6.41313 + 11.1079i) q^{4} +(10.3955 - 18.0055i) q^{5} +(3.50000 + 6.06218i) q^{7} -22.0250 q^{8} +O(q^{10})\)	\(q+(2.28179 + 3.95218i) q^{2} +(-6.41313 + 11.1079i) q^{4} +(10.3955 - 18.0055i) q^{5} +(3.50000 + 6.06218i) q^{7} -22.0250 q^{8} +94.8813 q^{10} +(22.6993 + 39.3163i) q^{11} +(-14.6521 + 25.3782i) q^{13} +(-15.9725 + 27.6652i) q^{14} +(1.04863 + 1.81629i) q^{16} +98.0555 q^{17} +31.1554 q^{19} +(133.335 + 230.943i) q^{20} +(-103.590 + 179.423i) q^{22} +(4.19596 - 7.26761i) q^{23} +(-153.632 - 266.099i) q^{25} -133.732 q^{26} -89.7838 q^{28} +(-36.1332 - 62.5845i) q^{29} +(15.4299 - 26.7254i) q^{31} +(-92.8855 + 160.882i) q^{32} +(223.742 + 387.533i) q^{34} +145.537 q^{35} -196.369 q^{37} +(71.0900 + 123.131i) q^{38} +(-228.961 + 396.571i) q^{40} +(106.336 - 184.180i) q^{41} +(-118.438 - 205.141i) q^{43} -582.293 q^{44} +38.2972 q^{46} +(-110.018 - 190.557i) q^{47} +(-24.5000 + 42.4352i) q^{49} +(701.114 - 1214.36i) q^{50} +(-187.932 - 325.507i) q^{52} -55.9028 q^{53} +943.880 q^{55} +(-77.0874 - 133.519i) q^{56} +(164.897 - 285.609i) q^{58} +(-327.326 + 566.946i) q^{59} +(-174.391 - 302.055i) q^{61} +140.831 q^{62} -831.002 q^{64} +(304.632 + 527.638i) q^{65} +(-105.247 + 182.293i) q^{67} +(-628.842 + 1089.19i) q^{68} +(332.085 + 575.187i) q^{70} +548.252 q^{71} -266.888 q^{73} +(-448.073 - 776.086i) q^{74} +(-199.803 + 346.070i) q^{76} +(-158.895 + 275.214i) q^{77} +(134.946 + 233.733i) q^{79} +43.6042 q^{80} +970.550 q^{82} +(312.634 + 541.499i) q^{83} +(1019.34 - 1765.54i) q^{85} +(540.503 - 936.178i) q^{86} +(-499.951 - 865.941i) q^{88} -1605.63 q^{89} -205.129 q^{91} +(53.8184 + 93.2162i) q^{92} +(502.076 - 869.621i) q^{94} +(323.875 - 560.969i) q^{95} +(145.549 + 252.099i) q^{97} -223.615 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 3 q^{2} - 43 q^{4} + 30 q^{5} + 56 q^{7} - 12 q^{8}+O(q^{10}) \) 16 * q + 3 * q^2 - 43 * q^4 + 30 * q^5 + 56 * q^7 - 12 * q^8	\( 16 q + 3 q^{2} - 43 q^{4} + 30 q^{5} + 56 q^{7} - 12 q^{8} - 28 q^{10} + 24 q^{11} - 68 q^{13} - 21 q^{14} - 103 q^{16} - 336 q^{17} + 352 q^{19} + 330 q^{20} - 151 q^{22} + 228 q^{23} - 244 q^{25} - 1590 q^{26} - 602 q^{28} + 618 q^{29} - 72 q^{31} + 786 q^{32} + 261 q^{34} + 420 q^{35} + 420 q^{37} + 1032 q^{38} + 375 q^{40} + 420 q^{41} + 2 q^{43} - 774 q^{44} + 804 q^{46} + 570 q^{47} - 392 q^{49} + 1110 q^{50} + 431 q^{52} - 1056 q^{53} - 1676 q^{55} - 42 q^{56} - 37 q^{58} - 150 q^{59} - 578 q^{61} - 2340 q^{62} - 224 q^{64} - 366 q^{65} + 898 q^{67} + 2526 q^{68} - 98 q^{70} - 1764 q^{71} + 1944 q^{73} - 222 q^{74} - 1423 q^{76} - 168 q^{77} + 158 q^{79} - 4950 q^{80} - 422 q^{82} + 2958 q^{83} + 774 q^{85} - 114 q^{86} - 1317 q^{88} - 8760 q^{89} - 952 q^{91} + 4629 q^{92} + 3234 q^{94} + 930 q^{95} + 60 q^{97} - 294 q^{98}+O(q^{100}) \) 16 * q + 3 * q^2 - 43 * q^4 + 30 * q^5 + 56 * q^7 - 12 * q^8 - 28 * q^10 + 24 * q^11 - 68 * q^13 - 21 * q^14 - 103 * q^16 - 336 * q^17 + 352 * q^19 + 330 * q^20 - 151 * q^22 + 228 * q^23 - 244 * q^25 - 1590 * q^26 - 602 * q^28 + 618 * q^29 - 72 * q^31 + 786 * q^32 + 261 * q^34 + 420 * q^35 + 420 * q^37 + 1032 * q^38 + 375 * q^40 + 420 * q^41 + 2 * q^43 - 774 * q^44 + 804 * q^46 + 570 * q^47 - 392 * q^49 + 1110 * q^50 + 431 * q^52 - 1056 * q^53 - 1676 * q^55 - 42 * q^56 - 37 * q^58 - 150 * q^59 - 578 * q^61 - 2340 * q^62 - 224 * q^64 - 366 * q^65 + 898 * q^67 + 2526 * q^68 - 98 * q^70 - 1764 * q^71 + 1944 * q^73 - 222 * q^74 - 1423 * q^76 - 168 * q^77 + 158 * q^79 - 4950 * q^80 - 422 * q^82 + 2958 * q^83 + 774 * q^85 - 114 * q^86 - 1317 * q^88 - 8760 * q^89 - 952 * q^91 + 4629 * q^92 + 3234 * q^94 + 930 * q^95 + 60 * q^97 - 294 * q^98

Introduction

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