LMFDB - Embedded newform 189.4.s.a.17.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [189,4,Mod(17,189)]

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, 1]))

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

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

chi := DirichletCharacter("189.17");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	189.s (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:	$11.1513609911$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			17.9
Character	$\chi$	$=$	189.17
Dual form			189.4.s.a.89.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.958607 - 0.553452i) q^{2} +(-3.38738 - 5.86712i) q^{4} -12.4738 q^{5} +(-18.2811 + 2.96677i) q^{7} +16.3542i q^{8} +O(q^{10})$	\(q+(-0.958607 - 0.553452i) q^{2} +(-3.38738 - 5.86712i) q^{4} -12.4738 q^{5} +(-18.2811 + 2.96677i) q^{7} +16.3542i q^{8} +(11.9574 + 6.90363i) q^{10} +3.72145i q^{11} +(68.0440 + 39.2852i) q^{13} +(19.1663 + 7.27374i) q^{14} +(-18.0478 + 31.2597i) q^{16} +(56.8448 - 98.4582i) q^{17} +(33.4526 - 19.3138i) q^{19} +(42.2534 + 73.1851i) q^{20} +(2.05964 - 3.56741i) q^{22} +37.6101i q^{23} +30.5949 q^{25} +(-43.4849 - 75.3181i) q^{26} +(79.3314 + 97.2077i) q^{28} +(144.984 - 83.7067i) q^{29} +(-183.916 + 106.184i) q^{31} +(147.907 - 85.3941i) q^{32} +(-108.984 + 62.9218i) q^{34} +(228.034 - 37.0068i) q^{35} +(132.003 + 228.635i) q^{37} -42.7571 q^{38} -203.999i q^{40} +(-190.215 + 329.461i) q^{41} +(90.2450 + 156.309i) q^{43} +(21.8342 - 12.6060i) q^{44} +(20.8154 - 36.0533i) q^{46} +(-77.0348 + 133.428i) q^{47} +(325.397 - 108.472i) q^{49} +(-29.3284 - 16.9328i) q^{50} -532.296i q^{52} +(162.088 + 93.5816i) q^{53} -46.4205i q^{55} +(-48.5192 - 298.973i) q^{56} -185.311 q^{58} +(234.149 + 405.558i) q^{59} +(308.466 + 178.093i) q^{61} +235.071 q^{62} +99.7183 q^{64} +(-848.765 - 490.035i) q^{65} +(48.3829 + 83.8017i) q^{67} -770.221 q^{68} +(-239.076 - 90.7309i) q^{70} +705.036i q^{71} +(-631.911 - 364.834i) q^{73} -292.228i q^{74} +(-226.633 - 130.847i) q^{76} +(-11.0407 - 68.0322i) q^{77} +(204.962 - 355.005i) q^{79} +(225.124 - 389.926i) q^{80} +(364.682 - 210.549i) q^{82} +(-321.436 - 556.744i) q^{83} +(-709.069 + 1228.14i) q^{85} -199.785i q^{86} -60.8615 q^{88} +(74.4458 + 128.944i) q^{89} +(-1360.47 - 516.306i) q^{91} +(220.663 - 127.400i) q^{92} +(147.692 - 85.2702i) q^{94} +(-417.279 + 240.916i) q^{95} +(-605.085 + 349.346i) q^{97} +(-371.961 - 76.1098i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + 3 q^{2} + 81 q^{4} + 6 q^{5} + 5 q^{7}+O(q^{10}) $ 44 * q + 3 * q^2 + 81 * q^4 + 6 * q^5 + 5 * q^7	$ 44 q + 3 q^{2} + 81 q^{4} + 6 q^{5} + 5 q^{7} - 6 q^{10} + 36 q^{13} - 129 q^{14} - 263 q^{16} - 72 q^{17} - 6 q^{19} + 24 q^{20} + 14 q^{22} + 698 q^{25} - 96 q^{26} - 156 q^{28} + 132 q^{29} + 177 q^{31} + 501 q^{32} - 24 q^{34} + 765 q^{35} + 82 q^{37} + 1746 q^{38} + 618 q^{41} + 82 q^{43} + 603 q^{44} + 266 q^{46} + 201 q^{47} + 515 q^{49} + 1845 q^{50} + 564 q^{53} - 3600 q^{56} - 538 q^{58} - 747 q^{59} - 1209 q^{61} - 2904 q^{62} - 1144 q^{64} + 831 q^{65} + 295 q^{67} - 7008 q^{68} - 390 q^{70} - 6 q^{73} + 144 q^{76} + 1203 q^{77} - 551 q^{79} - 4239 q^{80} + 18 q^{82} + 1830 q^{83} - 237 q^{85} + 1246 q^{88} + 4266 q^{89} - 1140 q^{91} - 7896 q^{92} - 3 q^{94} + 1053 q^{95} + 792 q^{97} + 5667 q^{98}+O(q^{100}) $ 44 * q + 3 * q^2 + 81 * q^4 + 6 * q^5 + 5 * q^7 - 6 * q^10 + 36 * q^13 - 129 * q^14 - 263 * q^16 - 72 * q^17 - 6 * q^19 + 24 * q^20 + 14 * q^22 + 698 * q^25 - 96 * q^26 - 156 * q^28 + 132 * q^29 + 177 * q^31 + 501 * q^32 - 24 * q^34 + 765 * q^35 + 82 * q^37 + 1746 * q^38 + 618 * q^41 + 82 * q^43 + 603 * q^44 + 266 * q^46 + 201 * q^47 + 515 * q^49 + 1845 * q^50 + 564 * q^53 - 3600 * q^56 - 538 * q^58 - 747 * q^59 - 1209 * q^61 - 2904 * q^62 - 1144 * q^64 + 831 * q^65 + 295 * q^67 - 7008 * q^68 - 390 * q^70 - 6 * q^73 + 144 * q^76 + 1203 * q^77 - 551 * q^79 - 4239 * q^80 + 18 * q^82 + 1830 * q^83 - 237 * q^85 + 1246 * q^88 + 4266 * q^89 - 1140 * q^91 - 7896 * q^92 - 3 * q^94 + 1053 * q^95 + 792 * q^97 + 5667 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−0.958607	−	0.553452i	−0.338919	−	0.195675i	0.320875	−	0.947122i	$-0.396023\pi$
$2$	−0.958607	−	0.553452i	−0.338919	−	0.195675i	−0.659794	+	0.751447i	$0.729356\pi$
$3$		0			0
$3$		0			0
$4$	−3.38738	−	5.86712i	−0.423423	−	0.733390i
$5$	−12.4738			−1.11569			−0.557844	−	0.829946i	$-0.688371\pi$
$5$	−12.4738			−1.11569			−0.557844	+	0.829946i	$0.688371\pi$
$6$		0			0
$7$	−18.2811	+	2.96677i	−0.987086	+	0.160190i
$7$	−18.2811	+	2.96677i	−0.987086	+	0.160190i
$8$			16.3542i			0.722762i
$9$		0			0
$10$	11.9574	+	6.90363i	0.378127	+	0.218312i
$11$			3.72145i			0.102005i	0.998699	+	0.0510027i	$0.0162417\pi$
$11$			3.72145i			0.102005i	−0.998699	+	0.0510027i	$0.983758\pi$
$12$		0			0
$13$	68.0440	+	39.2852i	1.45169	+	0.838135i	0.998578	−	0.0533171i	$-0.0169794\pi$
$13$	68.0440	+	39.2852i	1.45169	+	0.838135i	0.453115	+	0.891452i	$0.350313\pi$
$14$	19.1663	+	7.27374i	0.365887	+	0.138856i
$15$		0			0
$16$	−18.0478	+	31.2597i	−0.281996	+	0.488432i
$17$	56.8448	−	98.4582i	0.810994	−	1.40468i	−0.101175	−	0.994869i	$-0.532260\pi$
$17$	56.8448	−	98.4582i	0.810994	−	1.40468i	0.912169	−	0.409814i	$-0.134406\pi$
$18$		0			0
$19$	33.4526	−	19.3138i	0.403923	−	0.233205i	−0.284252	−	0.958750i	$-0.591745\pi$
$19$	33.4526	−	19.3138i	0.403923	−	0.233205i	0.688175	+	0.725544i	$0.258412\pi$
$20$	42.2534	+	73.1851i	0.472408	+	0.818234i
$21$		0			0
$22$	2.05964	−	3.56741i	0.0199599	−	0.0345715i
$23$			37.6101i			0.340967i	0.985361	+	0.170483i	$0.0545329\pi$
$23$			37.6101i			0.340967i	−0.985361	+	0.170483i	$0.945467\pi$
$24$		0			0
$25$	30.5949			0.244759
$26$	−43.4849	−	75.3181i	−0.328004	−	0.568119i
$27$		0			0
$28$	79.3314	+	97.2077i	0.535437	+	0.656091i
$29$	144.984	−	83.7067i	0.928376	−	0.535998i	0.0420787	−	0.999114i	$-0.486602\pi$
$29$	144.984	−	83.7067i	0.928376	−	0.535998i	0.886298	+	0.463116i	$0.153269\pi$
$30$		0			0
$31$	−183.916	+	106.184i	−1.06556	+	0.615201i	−0.926965	−	0.375148i	$-0.877592\pi$
$31$	−183.916	+	106.184i	−1.06556	+	0.615201i	−0.138595	+	0.990349i	$0.544259\pi$
$32$	147.907	−	85.3941i	0.817078	−	0.471740i
$33$		0			0
$34$	−108.984	+	62.9218i	−0.549722	+	0.317382i
$35$	228.034	−	37.0068i	1.10128	−	0.178723i
$36$		0			0
$37$	132.003	+	228.635i	0.586516	+	1.01588i	0.994685	+	0.102969i	$0.0328342\pi$
$37$	132.003	+	228.635i	0.586516	+	1.01588i	−0.408169	+	0.912907i	$0.633832\pi$
$38$	−42.7571			−0.182530
$39$		0			0
$40$		−	203.999i		−	0.806377i
$41$	−190.215	+	329.461i	−0.724549	+	1.25496i	0.234610	+	0.972090i	$0.424619\pi$
$41$	−190.215	+	329.461i	−0.724549	+	1.25496i	−0.959159	+	0.282866i	$0.908715\pi$
$42$		0			0
$43$	90.2450	+	156.309i	0.320052	+	0.554346i	0.980498	−	0.196527i	$-0.0629663\pi$
$43$	90.2450	+	156.309i	0.320052	+	0.554346i	−0.660447	+	0.750873i	$0.729633\pi$
$44$	21.8342	−	12.6060i	0.0748097	−	0.0431914i
$45$		0			0
$46$	20.8154	−	36.0533i	0.0667186	−	0.115560i
$47$	−77.0348	+	133.428i	−0.239078	+	0.414096i	−0.960450	−	0.278452i	$-0.910179\pi$
$47$	−77.0348	+	133.428i	−0.239078	+	0.414096i	0.721372	+	0.692548i	$0.243512\pi$
$48$		0			0
$49$	325.397	−	108.472i	0.948678	−	0.316244i
$50$	−29.3284	−	16.9328i	−0.0829533	−	0.0478931i
$51$		0			0
$52$		−	532.296i		−	1.41954i
$53$	162.088	+	93.5816i	0.420085	+	0.242536i	0.695114	−	0.718900i	$-0.255354\pi$
$53$	162.088	+	93.5816i	0.420085	+	0.242536i	−0.275029	+	0.961436i	$0.588687\pi$
$54$		0			0
$55$		−	46.4205i		−	0.113806i
$56$	−48.5192	−	298.973i	−0.115780	−	0.713428i
$57$		0			0
$58$	−185.311			−0.419525
$59$	234.149	+	405.558i	0.516672	+	0.894902i	0.999813	+	0.0193590i	$0.00616255\pi$
$59$	234.149	+	405.558i	0.516672	+	0.894902i	−0.483141	+	0.875543i	$0.660504\pi$
$60$		0			0
$61$	308.466	+	178.093i	0.647460	+	0.373811i	0.787482	−	0.616337i	$-0.211384\pi$
$61$	308.466	+	178.093i	0.647460	+	0.373811i	−0.140023	+	0.990148i	$0.544718\pi$
$62$	235.071			0.481518
$63$		0			0
$64$	99.7183			0.194762
$65$	−848.765	−	490.035i	−1.61964	−	0.935097i
$66$		0			0
$67$	48.3829	+	83.8017i	0.0882226	+	0.152806i	0.906760	−	0.421647i	$-0.138548\pi$
$67$	48.3829	+	83.8017i	0.0882226	+	0.152806i	−0.818537	+	0.574453i	$0.805215\pi$
$68$	−770.221			−1.37357
$69$		0			0
$70$	−239.076	−	90.7309i	−0.408216	−	0.154920i
$71$			705.036i			1.17848i	0.807956	+	0.589242i	$0.200574\pi$
$71$			705.036i			1.17848i	−0.807956	+	0.589242i	$0.799426\pi$
$72$		0			0
$73$	−631.911	−	364.834i	−1.01314	−	0.584939i	−0.101034	−	0.994883i	$-0.532215\pi$
$73$	−631.911	−	364.834i	−1.01314	−	0.584939i	−0.912111	+	0.409944i	$0.865548\pi$
$74$		−	292.228i		−	0.459066i
$75$		0			0
$76$	−226.633	−	130.847i	−0.342061	−	0.197489i
$77$	−11.0407	−	68.0322i	−0.0163403	−	0.100688i
$78$		0			0
$79$	204.962	−	355.005i	0.291900	−	0.505585i	−0.682359	−	0.731017i	$-0.739046\pi$
$79$	204.962	−	355.005i	0.291900	−	0.505585i	0.974259	+	0.225432i	$0.0723793\pi$
$80$	225.124	−	389.926i	0.314620	−	0.544938i
$81$		0			0
$82$	364.682	−	210.549i	0.491126	−	0.283552i
$83$	−321.436	−	556.744i	−0.425087	−	0.736272i	0.571341	−	0.820712i	$-0.306423\pi$
$83$	−321.436	−	556.744i	−0.425087	−	0.736272i	−0.996429	+	0.0844400i	$0.973090\pi$
$84$		0			0
$85$	−709.069	+	1228.14i	−0.904816	+	1.56719i
$86$		−	199.785i		−	0.250504i
$87$		0			0
$88$	−60.8615			−0.0737256
$89$	74.4458	+	128.944i	0.0886656	+	0.153573i	0.906947	−	0.421244i	$-0.138406\pi$
$89$	74.4458	+	128.944i	0.0886656	+	0.153573i	−0.818282	+	0.574817i	$0.805073\pi$
$90$		0			0
$91$	−1360.47	−	516.306i	−1.56721	−	0.594764i
$92$	220.663	−	127.400i	0.250062	−	0.144373i
$93$		0			0
$94$	147.692	−	85.2702i	0.162056	−	0.0935632i
$95$	−417.279	+	240.916i	−0.450652	+	0.260184i
$96$		0			0
$97$	−605.085	+	349.346i	−0.633372	+	0.365677i	−0.782057	−	0.623207i	$-0.785829\pi$
$97$	−605.085	+	349.346i	−0.633372	+	0.365677i	0.148685	+	0.988885i	$0.452496\pi$
$98$	−371.961	−	76.1098i	−0.383406	−	0.0784515i
$99$		0			0
$100$	−103.636	−	179.504i	−0.103636	−	0.179504i
$101$	−597.788			−0.588932			−0.294466	−	0.955662i	$-0.595142\pi$
$101$	−597.788			−0.588932			−0.294466	+	0.955662i	$0.595142\pi$
$102$		0			0
$103$		−	518.717i		−	0.496220i	−0.968732	−	0.248110i	$-0.920190\pi$
$103$		−	518.717i		−	0.496220i	0.968732	−	0.248110i	$-0.0798095\pi$
$104$	−642.480	+	1112.81i	−0.605772	+	1.04923i
$105$		0			0
$106$	−103.586	−	179.416i	−0.0949164	−	0.164400i
$107$	648.620	−	374.481i	0.586023	−	0.338341i	−0.177500	−	0.984121i	$-0.556801\pi$
$107$	648.620	−	374.481i	0.586023	−	0.338341i	0.763523	+	0.645780i	$0.223468\pi$
$108$		0			0
$109$	−91.8969	+	159.170i	−0.0807535	+	0.139869i	−0.903574	−	0.428432i	$-0.859066\pi$
$109$	−91.8969	+	159.170i	−0.0807535	+	0.139869i	0.822820	+	0.568302i	$0.192399\pi$
$110$	−25.6915	+	44.4990i	−0.0222690	+	0.0385710i
$111$		0			0
$112$	237.193	−	625.004i	0.200113	−	0.527298i
$113$	1353.78	+	781.605i	1.12702	+	0.650683i	0.943183	−	0.332274i	$-0.107816\pi$
$113$	1353.78	+	781.605i	1.12702	+	0.650683i	0.183833	+	0.982957i	$0.441149\pi$
$114$		0			0
$115$		−	469.139i		−	0.380413i
$116$	−982.235	−	567.093i	−0.786191	−	0.453908i
$117$		0			0
$118$		−	518.361i		−	0.404398i
$119$	−747.083	+	1968.57i	−0.575504	+	1.51646i
$120$		0			0
$121$	1317.15			0.989595
$122$	−197.132	−	341.442i	−0.146291	−	0.253383i
$123$		0			0
$124$	1245.99	+	719.373i	0.902365	+	0.520981i
$125$	1177.59			0.842613
$126$		0			0
$127$	1644.85			1.14926			0.574632	−	0.818412i	$-0.305145\pi$
$127$	1644.85			1.14926			0.574632	+	0.818412i	$0.305145\pi$
$128$	−1278.85	−	738.342i	−0.883087	−	0.509850i
$129$		0			0
$130$	542.421	+	939.501i	0.365950	+	0.633844i
$131$	2825.37			1.88438			0.942189	−	0.335081i	$-0.108764\pi$
$131$	2825.37			1.88438			0.942189	+	0.335081i	$0.108764\pi$
$132$		0			0
$133$	−554.250	+	452.324i	−0.361350	+	0.294898i
$134$		−	107.110i		−	0.0690518i
$135$		0			0
$136$	1610.21	+	929.654i	1.01525	+	0.586156i
$137$		−	777.229i		−	0.484695i	−0.970190	−	0.242347i	$-0.922083\pi$
$137$		−	777.229i		−	0.484695i	0.970190	−	0.242347i	$-0.0779173\pi$
$138$		0			0
$139$	−1472.69	−	850.256i	−0.898645	−	0.518833i	−0.0218847	−	0.999761i	$-0.506967\pi$
$139$	−1472.69	−	850.256i	−0.898645	−	0.518833i	−0.876760	+	0.480928i	$0.840300\pi$
$140$	−989.562	−	1212.55i	−0.597380	−	0.731992i
$141$		0			0
$142$	390.204	−	675.853i	0.230600	−	0.399410i
$143$	−146.198	+	253.222i	−0.0854943	+	0.148080i
$144$		0			0
$145$	−1808.50	+	1044.14i	−1.03578	+	0.598007i
$146$	403.836	+	699.464i	0.228916	+	0.396494i
$147$		0			0
$148$	894.286	−	1548.95i	0.496688	−	0.860290i
$149$		−	870.911i		−	0.478844i	−0.970916	−	0.239422i	$-0.923042\pi$
$149$		−	870.911i		−	0.478844i	0.970916	−	0.239422i	$-0.0769580\pi$
$150$		0			0
$151$	−102.754			−0.0553776			−0.0276888	−	0.999617i	$-0.508815\pi$
$151$	−102.754			−0.0553776			−0.0276888	+	0.999617i	$0.508815\pi$
$152$	315.863	+	547.091i	0.168552	+	0.291940i
$153$		0			0
$154$	−27.0689	+	71.3266i	−0.0141641	+	0.0373225i
$155$	2294.13	−	1324.52i	1.18883	−	0.686373i
$156$		0			0
$157$	697.899	−	402.932i	0.354767	−	0.204825i	−0.312016	−	0.950077i	$-0.601004\pi$
$157$	697.899	−	402.932i	0.354767	−	0.204825i	0.666783	+	0.745252i	$0.267671\pi$
$158$	−392.957	+	226.874i	−0.197860	+	0.114235i
$159$		0			0
$160$	−1844.96	+	1065.19i	−0.911604	+	0.526315i
$161$	−111.580	−	687.553i	−0.0546197	−	0.336564i
$162$		0			0
$163$	46.0094	+	79.6906i	0.0221088	+	0.0382936i	0.876868	−	0.480731i	$-0.159629\pi$
$163$	46.0094	+	79.6906i	0.0221088	+	0.0382936i	−0.854759	+	0.519025i	$0.826295\pi$
$164$	2577.32			1.22716
$165$		0			0
$166$			711.598i			0.332715i
$167$	−1919.63	+	3324.89i	−0.889492	+	1.54065i	−0.0490152	+	0.998798i	$0.515608\pi$
$167$	−1919.63	+	3324.89i	−0.889492	+	1.54065i	−0.840477	+	0.541847i	$0.817725\pi$
$168$		0			0
$169$	1988.15	+	3443.59i	0.904941	+	1.56740i
$170$	1359.44	−	784.871i	0.613318	−	0.354099i
$171$		0			0
$172$	611.389	−	1058.96i	0.271035	−	0.469446i
$173$	39.1096	−	67.7398i	0.0171876	−	0.0297697i	−0.857304	−	0.514811i	$-0.827862\pi$
$173$	39.1096	−	67.7398i	0.0171876	−	0.0297697i	0.874491	+	0.485041i	$0.161195\pi$
$174$		0			0
$175$	−559.307	+	90.7679i	−0.241598	+	0.0392080i
$176$	−116.331	−	67.1639i	−0.0498227	−	0.0287652i
$177$		0			0
$178$		−	164.809i		−	0.0693985i
$179$	213.100	+	123.033i	0.0889823	+	0.0513740i	0.543831	−	0.839195i	$-0.316973\pi$
$179$	213.100	+	123.033i	0.0889823	+	0.0513740i	−0.454849	+	0.890569i	$0.650307\pi$
$180$		0			0
$181$			4214.90i			1.73089i	0.501003	+	0.865446i	$0.332965\pi$
$181$			4214.90i			1.73089i	−0.501003	+	0.865446i	$0.667035\pi$
$182$	1018.40	+	1247.89i	0.414775	+	0.508239i
$183$		0			0
$184$	−615.084			−0.246438
$185$	−1646.57	−	2851.94i	−0.654369	−	1.13340i
$186$		0			0
$187$	366.407	+	211.545i	0.143285	+	0.0827258i
$188$	1043.79			0.404925
$189$		0			0
$190$	533.342			0.203646
$191$	2333.97	+	1347.52i	0.884187	+	0.510486i	0.872037	−	0.489440i	$-0.162799\pi$
$191$	2333.97	+	1347.52i	0.884187	+	0.510486i	0.0121506	+	0.999926i	$0.496132\pi$
$192$		0			0
$193$	−60.7485	−	105.219i	−0.0226568	−	0.0392428i	0.854475	−	0.519493i	$-0.173879\pi$
$193$	−60.7485	−	105.219i	−0.0226568	−	0.0392428i	−0.877132	+	0.480250i	$0.840546\pi$
$194$	773.384			0.286215
$195$		0			0
$196$	−1738.66	−	1541.71i	−0.633622	−	0.561846i
$197$		−	590.988i		−	0.213737i	−0.994273	−	0.106868i	$-0.965918\pi$
$197$		−	590.988i		−	0.213737i	0.994273	−	0.106868i	$-0.0340824\pi$
$198$		0			0
$199$	103.470	+	59.7383i	0.0368582	+	0.0212801i	0.518316	−	0.855189i	$-0.326559\pi$
$199$	103.470	+	59.7383i	0.0368582	+	0.0212801i	−0.481458	+	0.876469i	$0.659892\pi$
$200$			500.356i			0.176902i
$201$		0			0
$202$	573.043	+	330.847i	0.199600	+	0.115239i
$203$	−2402.13	+	1960.39i	−0.830526	+	0.677794i
$204$		0			0
$205$	2372.69	−	4109.62i	0.808371	−	1.40014i
$206$	−287.085	+	497.246i	−0.0970978	+	0.168178i
$207$		0			0
$208$	−2456.08	+	1418.02i	−0.818744	+	0.472702i
$209$	71.8755	+	124.492i	0.0237882	+	0.0412024i
$210$		0			0
$211$	−2357.88	+	4083.96i	−0.769302	+	1.33247i	0.168639	+	0.985678i	$0.446063\pi$
$211$	−2357.88	+	4083.96i	−0.769302	+	1.33247i	−0.937942	+	0.346793i	$0.887271\pi$
$212$		−	1267.99i		−	0.410781i
$213$		0			0
$214$	−829.029			−0.264819
$215$	−1125.69	−	1949.76i	−0.357078	−	0.618477i
$216$		0			0
$217$	3047.17	−	2486.80i	0.953250	−	0.777949i
$218$	176.186	−	101.721i	0.0547377	−	0.0316028i
$219$		0			0
$220$	−272.355	+	157.244i	−0.0834643	+	0.0481881i
$221$	7735.90	−	4466.32i	2.35463	−	1.35945i
$222$		0			0
$223$	−2370.99	+	1368.89i	−0.711988	+	0.411066i	−0.811797	−	0.583940i	$-0.801510\pi$
$223$	−2370.99	+	1368.89i	−0.711988	+	0.411066i	0.0998088	+	0.995007i	$0.468177\pi$
$224$	−2450.56	+	1999.90i	−0.730958	+	0.596536i
$225$		0			0
$226$	−865.161	−	1498.50i	−0.254645	−	0.441057i
$227$	−5075.55			−1.48404			−0.742018	−	0.670380i	$-0.766131\pi$
$227$	−5075.55			−1.48404			−0.742018	+	0.670380i	$0.766131\pi$
$228$		0			0
$229$		−	1841.10i		−	0.531280i	−0.964072	−	0.265640i	$-0.914417\pi$
$229$		−	1841.10i		−	0.531280i	0.964072	−	0.265640i	$-0.0855832\pi$
$230$	−259.646	+	449.720i	−0.0744371	+	0.128929i
$231$		0			0
$232$	1368.96	+	2371.11i	0.387399	+	0.670995i
$233$	−2765.48	+	1596.65i	−0.777566	+	0.448928i	−0.835567	−	0.549388i	$-0.814861\pi$
$233$	−2765.48	+	1596.65i	−0.777566	+	0.448928i	0.0580009	+	0.998317i	$0.481527\pi$
$234$		0			0
$235$	960.915	−	1664.35i	0.266737	−	0.462002i
$236$	1586.31	−	2747.56i	0.437541	−	0.757843i
$237$		0			0
$238$	1805.67	−	1473.61i	0.491781	−	0.401344i
$239$	−388.647	−	224.385i	−0.105186	−	0.0607292i	0.446484	−	0.894792i	$-0.352676\pi$
$239$	−388.647	−	224.385i	−0.105186	−	0.0607292i	−0.551670	+	0.834062i	$0.686009\pi$
$240$		0			0
$241$		−	1103.73i		−	0.295012i	−0.989061	−	0.147506i	$-0.952875\pi$
$241$		−	1103.73i		−	0.295012i	0.989061	−	0.147506i	$-0.0471245\pi$
$242$	−1262.63	−	728.979i	−0.335392	−	0.193639i
$243$		0			0
$244$		−	2413.08i		−	0.633120i
$245$	−4058.92	+	1353.05i	−1.05843	+	0.352829i
$246$		0			0
$247$	3034.99			0.781830
$248$	−1736.56	−	3007.81i	−0.444644	−	0.770146i
$249$		0			0
$250$	−1128.84	−	651.738i	−0.285577	−	0.164878i
$251$	−4137.13			−1.04037			−0.520186	−	0.854053i	$-0.674137\pi$
$251$	−4137.13			−1.04037			−0.520186	+	0.854053i	$0.674137\pi$
$252$		0			0
$253$	−139.964			−0.0347805
$254$	−1576.76	−	910.343i	−0.389507	−	0.224882i
$255$		0			0
$256$	418.400	+	724.691i	0.102149	+	0.176926i
$257$	−1613.81			−0.391699			−0.195849	−	0.980634i	$-0.562746\pi$
$257$	−1613.81			−0.391699			−0.195849	+	0.980634i	$0.562746\pi$
$258$		0			0
$259$	−3091.46	−	3788.08i	−0.741675	−	0.908802i
$260$			6639.74i			1.58377i
$261$		0			0
$262$	−2708.42	−	1563.71i	−0.638651	−	0.368725i
$263$			5800.44i			1.35996i	0.733229	+	0.679982i	$0.238012\pi$
$263$			5800.44i			1.35996i	−0.733229	+	0.679982i	$0.761988\pi$
$264$		0			0
$265$	−2021.85	−	1167.31i	−0.468684	−	0.270595i
$266$	781.647	−	126.851i	0.180172	−	0.0292395i
$267$		0			0
$268$	327.783	−	567.737i	0.0747109	−	0.129403i
$269$	−1625.70	+	2815.80i	−0.368479	+	0.638224i	−0.989328	−	0.145706i	$-0.953455\pi$
$269$	−1625.70	+	2815.80i	−0.368479	+	0.638224i	0.620849	+	0.783930i	$0.286788\pi$
$270$		0			0
$271$	2171.88	−	1253.93i	0.486834	−	0.281074i	−0.236426	−	0.971649i	$-0.575976\pi$
$271$	2171.88	−	1253.93i	0.486834	−	0.281074i	0.723260	+	0.690576i	$0.242643\pi$
$272$	2051.85	+	3553.90i	0.457395	+	0.792231i
$273$		0			0
$274$	−430.159	+	745.057i	−0.0948425	+	0.164272i
$275$			113.857i			0.0249667i
$276$		0			0
$277$	5741.68			1.24543			0.622715	−	0.782449i	$-0.286030\pi$
$277$	5741.68			1.24543			0.622715	+	0.782449i	$0.286030\pi$
$278$	941.152	+	1630.12i	0.203045	+	0.351684i
$279$		0			0
$280$	605.218	+	3729.32i	0.129174	+	0.795963i
$281$	5760.65	−	3325.91i	1.22296	−	0.706076i	0.257412	−	0.966302i	$-0.417130\pi$
$281$	5760.65	−	3325.91i	1.22296	−	0.706076i	0.965548	+	0.260226i	$0.0837970\pi$
$282$		0			0
$283$	−1389.64	+	802.309i	−0.291892	+	0.168524i	−0.638795	−	0.769377i	$-0.720567\pi$
$283$	−1389.64	+	802.309i	−0.291892	+	0.168524i	0.346903	+	0.937901i	$0.387233\pi$
$284$	4136.53	−	2388.23i	0.864289	−	0.498997i
$285$		0			0
$286$	280.293	−	161.827i	0.0579512	−	0.0334582i
$287$	2499.89	−	6587.23i	0.514160	−	1.35482i
$288$		0			0
$289$	−4006.17	−	6938.89i	−0.815423	−	1.41235i
$290$	2311.52			0.468059
$291$		0			0
$292$			4943.33i			0.990707i
$293$	−47.1597	+	81.6830i	−0.00940307	+	0.0162866i	−0.870689	−	0.491835i	$-0.836326\pi$
$293$	−47.1597	+	81.6830i	−0.00940307	+	0.0162866i	0.861286	+	0.508121i	$0.169660\pi$
$294$		0			0
$295$	−2920.72	−	5058.84i	−0.576444	−	0.998431i
$296$	−3739.15	+	2158.80i	−0.734236	+	0.423912i
$297$		0			0
$298$	−482.007	+	834.861i	−0.0936977	+	0.162289i
$299$	−1477.52	+	2559.14i	−0.285776	+	0.494979i
$300$		0			0
$301$	−2113.51	−	2589.76i	−0.404720	−	0.495918i
$302$	98.5008	+	56.8695i	0.0187685	+	0.0108360i
$303$		0			0
$304$			1394.29i			0.263052i
$305$	−3847.73	−	2221.49i	−0.722363	−	0.417056i
$306$		0			0
$307$			4341.53i			0.807115i	0.914954	+	0.403557i	$0.132226\pi$
$307$			4341.53i			0.807115i	−0.914954	+	0.403557i	$0.867774\pi$
$308$	−361.754	+	295.228i	−0.0669248	+	0.0546174i
$309$		0			0
$310$	−2932.22			−0.537223
$311$	619.110	+	1072.33i	0.112883	+	0.195518i	0.916931	−	0.399045i	$-0.130658\pi$
$311$	619.110	+	1072.33i	0.112883	+	0.195518i	−0.804049	+	0.594563i	$0.797325\pi$
$312$		0			0
$313$	370.765	+	214.061i	0.0669549	+	0.0386564i	0.533104	−	0.846050i	$-0.321026\pi$
$313$	370.765	+	214.061i	0.0669549	+	0.0386564i	−0.466149	+	0.884706i	$0.654359\pi$
$314$	−892.015			−0.160316
$315$		0			0
$316$	−2777.14			−0.494388
$317$	−3711.39	−	2142.77i	−0.657578	−	0.379653i	0.133775	−	0.991012i	$-0.457290\pi$
$317$	−3711.39	−	2142.77i	−0.657578	−	0.379653i	−0.791354	+	0.611359i	$0.790623\pi$
$318$		0			0
$319$	311.510	+	539.552i	0.0546747	+	0.0946994i
$320$	−1243.86			−0.217294
$321$		0			0
$322$	−273.566	+	720.847i	−0.0473454	+	0.124755i
$323$		−	4391.57i		−	0.756512i
$324$		0			0
$325$	2081.80	+	1201.93i	0.355315	+	0.205141i
$326$		−	101.856i		−	0.0173045i
$327$		0			0
$328$	−5388.09	−	3110.81i	−0.907035	−	0.523677i
$329$	1012.43	−	2667.76i	0.169657	−	0.447047i
$330$		0			0
$331$	−5180.91	+	8973.60i	−0.860328	+	1.49013i	0.0112839	+	0.999936i	$0.496408\pi$
$331$	−5180.91	+	8973.60i	−0.860328	+	1.49013i	−0.871612	+	0.490196i	$0.836925\pi$
$332$	−2177.66	+	3771.81i	−0.359983	+	0.623509i
$333$		0			0
$334$	3680.33	−	2124.84i	0.602931	−	0.348102i
$335$	−603.517	−	1045.32i	−0.0984289	−	0.170484i
$336$		0			0
$337$	900.566	−	1559.83i	0.145570	−	0.252134i	−0.784016	−	0.620741i	$-0.786832\pi$
$337$	900.566	−	1559.83i	0.145570	−	0.252134i	0.929585	+	0.368607i	$0.120165\pi$
$338$		−	4401.39i		−	0.708296i
$339$		0			0
$340$	9607.55			1.53248
$341$	−395.159	−	684.436i	−0.0627539	−	0.108693i
$342$		0			0
$343$	−5626.79	+	2948.35i	−0.885768	+	0.464129i
$344$	−2556.31	+	1475.89i	−0.400660	+	0.231321i
$345$		0			0
$346$	−74.9815	+	43.2906i	−0.0116504	+	0.00672635i
$347$	−2749.86	+	1587.63i	−0.425419	+	0.245615i	−0.697393	−	0.716689i	$-0.745657\pi$
$347$	−2749.86	+	1587.63i	−0.425419	+	0.245615i	0.271974	+	0.962304i	$0.412323\pi$
$348$		0			0
$349$	6434.98	−	3715.24i	0.986981	−	0.569834i	0.0826105	−	0.996582i	$-0.473674\pi$
$349$	6434.98	−	3715.24i	0.986981	−	0.569834i	0.904370	+	0.426748i	$0.140341\pi$
$350$	586.391	+	222.539i	0.0895541	+	0.0339863i
$351$		0			0
$352$	317.790	+	550.428i	0.0481200	+	0.0833464i
$353$	6095.40			0.919052			0.459526	−	0.888164i	$-0.348019\pi$
$353$	6095.40			0.919052			0.459526	+	0.888164i	$0.348019\pi$
$354$		0			0
$355$		−	8794.46i		−	1.31482i
$356$	504.353	−	873.565i	0.0750861	−	0.130053i
$357$		0			0
$358$	−136.186	−	235.881i	−0.0201052	−	0.0348232i
$359$	7038.53	−	4063.70i	1.03476	−	0.597420i	0.116416	−	0.993200i	$-0.462859\pi$
$359$	7038.53	−	4063.70i	1.03476	−	0.597420i	0.918345	+	0.395781i	$0.129526\pi$
$360$		0			0
$361$	−2683.45	+	4647.87i	−0.391231	+	0.677631i
$362$	2332.75	−	4040.44i	0.338692	−	0.586631i
$363$		0			0
$364$	1579.20	+	9730.95i	0.227397	+	1.40121i
$365$	7882.31	+	4550.85i	1.13035	+	0.652610i
$366$		0			0
$367$			169.168i			0.0240614i	0.999928	+	0.0120307i	$0.00382958\pi$
$367$			169.168i			0.0240614i	−0.999928	+	0.0120307i	$0.996170\pi$
$368$	−1175.68	−	678.778i	−0.166539	−	0.0961515i
$369$		0			0
$370$			3645.19i			0.512174i
$371$	−3240.78	−	1229.90i	−0.453512	−	0.172111i
$372$		0			0
$373$	13664.6			1.89685			0.948424	−	0.317003i	$-0.102677\pi$
$373$	13664.6			1.89685			0.948424	+	0.317003i	$0.102677\pi$
$374$	−234.160	−	405.577i	−0.0323747	−	0.0560746i
$375$		0			0
$376$	−2182.12	−	1259.85i	−0.299293	−	0.172797i
$377$	13153.7			1.79696
$378$		0			0
$379$	4708.21			0.638112			0.319056	−	0.947736i	$-0.396634\pi$
$379$	4708.21			0.638112			0.319056	+	0.947736i	$0.396634\pi$
$380$	2826.97	+	1632.15i	0.381633	+	0.220336i
$381$		0			0
$382$	−1491.57	−	2583.47i	−0.199778	−	0.346026i
$383$	−12369.3			−1.65024			−0.825120	−	0.564957i	$-0.808893\pi$
$383$	−12369.3			−1.65024			−0.825120	+	0.564957i	$0.808893\pi$
$384$		0			0
$385$	137.719	+	848.617i	0.0182307	+	0.112336i
$386$			134.485i			0.0177335i
$387$		0			0
$388$	4099.31	+	2366.74i	0.536368	+	0.309672i
$389$			9022.85i			1.17603i	0.808849	+	0.588016i	$0.200091\pi$
$389$			9022.85i			1.17603i	−0.808849	+	0.588016i	$0.799909\pi$
$390$		0			0
$391$	3703.02	+	2137.94i	0.478950	+	0.276522i
$392$	1773.97	+	5321.61i	0.228569	+	0.685669i
$393$		0			0
$394$	−327.083	+	566.525i	−0.0418229	+	0.0724394i
$395$	−2556.65	+	4428.25i	−0.325669	+	0.564075i
$396$		0			0
$397$	5716.84	−	3300.62i	0.722720	−	0.417263i	−0.0930329	−	0.995663i	$-0.529656\pi$
$397$	5716.84	−	3300.62i	0.722720	−	0.417263i	0.815753	+	0.578400i	$0.196323\pi$
$398$	−66.1245	−	114.531i	−0.00832794	−	0.0144244i
$399$		0			0
$400$	−552.169	+	956.385i	−0.0690211	+	0.119548i
$401$		−	702.295i		−	0.0874586i	−0.999043	−	0.0437293i	$-0.986076\pi$
$401$		−	702.295i		−	0.0874586i	0.999043	−	0.0437293i	$-0.0139239\pi$
$402$		0			0
$403$	−16685.9			−2.06249
$404$	2024.94	+	3507.29i	0.249367	+	0.431916i
$405$		0			0
$406$	3387.68	−	549.774i	0.414108	−	0.0672040i
$407$	−850.854	+	491.241i	−0.103625	+	0.0598278i
$408$		0			0
$409$	4197.60	−	2423.48i	0.507476	−	0.292992i	−0.224319	−	0.974516i	$-0.572016\pi$
$409$	4197.60	−	2423.48i	0.507476	−	0.292992i	0.731796	+	0.681524i	$0.238683\pi$
$410$	−4548.96	+	2626.34i	−0.547944	+	0.316355i
$411$		0			0
$412$	−3043.37	+	1757.09i	−0.363923	+	0.210111i
$413$	−5483.70	−	6719.38i	−0.653354	−	0.800579i
$414$		0			0
$415$	4009.52	+	6944.70i	0.474264	+	0.821450i
$416$	13418.9			1.58153
$417$		0			0
$418$		−	159.118i		−	0.0186190i
$419$	−2902.78	+	5027.77i	−0.338449	+	0.586211i	−0.984141	−	0.177387i	$-0.943236\pi$
$419$	−2902.78	+	5027.77i	−0.338449	+	0.586211i	0.645692	+	0.763598i	$0.276569\pi$
$420$		0			0
$421$	4730.66	+	8193.74i	0.547644	+	0.948547i	0.998435	+	0.0559179i	$0.0178085\pi$
$421$	4730.66	+	8193.74i	0.547644	+	0.948547i	−0.450791	+	0.892629i	$0.648858\pi$
$422$	4520.55	−	2609.94i	0.521462	−	0.301066i
$423$		0			0
$424$	−1530.46	+	2650.83i	−0.175296	+	0.303622i
$425$	1739.16	−	3012.31i	0.198498	−	0.343809i
$426$		0			0
$427$	−6167.46	−	2340.59i	−0.698979	−	0.265267i
$428$	−4394.25	−	2537.02i	−0.496271	−	0.286522i
$429$		0			0
$430$			2492.07i			0.279485i
$431$	4423.48	+	2553.90i	0.494365	+	0.285422i	0.726384	−	0.687289i	$-0.241200\pi$
$431$	4423.48	+	2553.90i	0.494365	+	0.285422i	−0.232018	+	0.972711i	$0.574533\pi$
$432$		0			0
$433$		−	15003.8i		−	1.66521i	−0.553866	−	0.832606i	$-0.686848\pi$
$433$		−	15003.8i		−	1.66521i	0.553866	−	0.832606i	$-0.313152\pi$
$434$	−4297.36	+	697.402i	−0.475299	+	0.0771345i
$435$		0			0
$436$	1245.16			0.136771
$437$	726.395	+	1258.15i	0.0795153	+	0.137725i
$438$		0			0
$439$	4808.09	+	2775.95i	0.522728	+	0.301797i	0.738050	−	0.674746i	$-0.235747\pi$
$439$	4808.09	+	2775.95i	0.522728	+	0.301797i	−0.215322	+	0.976543i	$0.569080\pi$
$440$	759.172			0.0822548
$441$		0			0
$442$	−9887.58			−1.06404
$443$	−6333.33	−	3656.55i	−0.679245	−	0.392162i	0.120325	−	0.992735i	$-0.461606\pi$
$443$	−6333.33	−	3656.55i	−0.679245	−	0.392162i	−0.799571	+	0.600572i	$0.794940\pi$
$444$		0			0
$445$	−928.619	−	1608.42i	−0.0989231	−	0.171340i
$446$	3030.46			0.321741
$447$		0			0
$448$	−1822.96	+	295.841i	−0.192247	+	0.0311991i
$449$		−	15920.2i		−	1.67332i	−0.547720	−	0.836662i	$-0.684504\pi$
$449$		−	15920.2i		−	1.67332i	0.547720	−	0.836662i	$-0.315496\pi$
$450$		0			0
$451$	−1226.07	−	707.874i	−0.128012	−	0.0739079i
$452$		−	10590.4i		−	1.10206i
$453$		0			0
$454$	4865.46	+	2809.07i	0.502967	+	0.290388i
$455$	16970.2	+	6440.28i	1.74851	+	0.663571i
$456$		0			0
$457$	−7796.81	+	13504.5i	−0.798073	+	1.38230i	0.122797	+	0.992432i	$0.460814\pi$
$457$	−7796.81	+	13504.5i	−0.798073	+	1.38230i	−0.920870	+	0.389871i	$0.872520\pi$
$458$	−1018.96	+	1764.89i	−0.103958	+	0.180061i
$459$		0			0
$460$	−2752.49	+	1589.15i	−0.278991	+	0.161075i
$461$	−5142.24	−	8906.62i	−0.519518	−	0.899832i	−0.999743	−	0.0226865i	$-0.992778\pi$
$461$	−5142.24	−	8906.62i	−0.519518	−	0.899832i	0.480224	−	0.877146i	$-0.340555\pi$
$462$		0			0
$463$	5144.96	−	8911.33i	0.516429	−	0.894481i	−0.483389	−	0.875405i	$-0.660594\pi$
$463$	5144.96	−	8911.33i	0.516429	−	0.894481i	0.999818	−	0.0190753i	$-0.00607223\pi$
$464$			6042.88i			0.604599i
$465$		0			0
$466$	3534.68			0.351376
$467$	5970.25	+	10340.8i	0.591585	+	1.02465i	0.994019	+	0.109206i	$0.0348308\pi$
$467$	5970.25	+	10340.8i	0.591585	+	1.02465i	−0.402435	+	0.915449i	$0.631836\pi$
$468$		0			0
$469$	−1133.11	−	1388.45i	−0.111561	−	0.136700i
$470$	−1842.28	+	1063.64i	−0.180804	+	0.104387i
$471$		0			0
$472$	−6632.60	+	3829.33i	−0.646801	+	0.373431i
$473$	−581.696	+	335.842i	−0.0565463	+	0.0326470i
$474$		0			0
$475$	1023.48	−	590.904i	0.0988638	−	0.0570790i
$476$	14080.5	−	2285.07i	1.35584	−	0.220033i
$477$		0			0
$478$	248.373	+	430.194i	0.0237663	+	0.0411645i
$479$	6528.18			0.622714			0.311357	−	0.950293i	$-0.399217\pi$
$479$	6528.18			0.622714			0.311357	+	0.950293i	$0.399217\pi$
$480$		0			0
$481$			20743.0i			1.96632i
$482$	−610.864	+	1058.05i	−0.0577263	+	0.0999849i
$483$		0			0
$484$	−4461.69	−	7727.88i	−0.419017	−	0.725759i
$485$	7547.69	−	4357.66i	0.706645	−	0.407982i
$486$		0			0
$487$	1624.66	−	2814.00i	0.151172	−	0.261837i	−0.780487	−	0.625172i	$-0.785029\pi$
$487$	1624.66	−	2814.00i	0.151172	−	0.261837i	0.931658	+	0.363335i	$0.118362\pi$
$488$	−2912.57	+	5044.73i	−0.270176	+	0.467959i
$489$		0			0
$490$	4639.76	+	949.376i	0.427761	+	0.0875274i
$491$	−9629.30	−	5559.48i	−0.885059	−	0.510989i	−0.0127359	−	0.999919i	$-0.504054\pi$
$491$	−9629.30	−	5559.48i	−0.885059	−	0.510989i	−0.872323	+	0.488930i	$0.837387\pi$
$492$		0			0
$493$		−	19033.2i		−	1.73877i
$494$	−2909.36	−	1679.72i	−0.264977	−	0.152984i
$495$		0			0
$496$		−	7665.55i		−	0.693938i
$497$	−2091.68	−	12888.8i	−0.188782	−	1.16327i
$498$		0			0
$499$	−8160.84			−0.732123			−0.366062	−	0.930591i	$-0.619294\pi$
$499$	−8160.84			−0.732123			−0.366062	+	0.930591i	$0.619294\pi$
$500$	−3988.94	−	6909.05i	−0.356782	−	0.617964i
$501$		0			0
$502$	3965.88	+	2289.70i	0.352601	+	0.203574i
$503$	−6103.08			−0.541000			−0.270500	−	0.962720i	$-0.587189\pi$
$503$	−6103.08			−0.541000			−0.270500	+	0.962720i	$0.587189\pi$
$504$		0			0
$505$	7456.66			0.657064
$506$	134.170	+	77.4633i	0.0117877	+	0.00680566i
$507$		0			0
$508$	−5571.72	−	9650.51i	−0.486625	−	0.842859i
$509$	332.400			0.0289458			0.0144729	−	0.999895i	$-0.495393\pi$
$509$	332.400			0.0289458			0.0144729	+	0.999895i	$0.495393\pi$
$510$		0			0
$511$	12634.4	+	4794.83i	1.09376	+	0.415089i
$512$			10887.2i			0.939749i
$513$		0			0
$514$	1547.01	+	893.165i	0.132754	+	0.0766455i
$515$			6470.35i			0.553627i
$516$		0			0
$517$	−496.547	−	286.681i	−0.0422400	−	0.0243873i
$518$	866.974	+	5342.25i	0.0735379	+	0.453137i
$519$		0			0
$520$	8014.14	−	13880.9i	0.675853	−	1.17061i
$521$	−5203.98	+	9013.56i	−0.437602	+	0.757948i	−0.997504	−	0.0706102i	$-0.977505\pi$
$521$	−5203.98	+	9013.56i	−0.437602	+	0.757948i	0.559902	+	0.828559i	$0.310839\pi$
$522$		0			0
$523$	−11845.6	+	6839.04i	−0.990384	+	0.571798i	−0.905389	−	0.424583i	$-0.860421\pi$
$523$	−11845.6	+	6839.04i	−0.990384	+	0.571798i	−0.0849946	+	0.996381i	$0.527087\pi$
$524$	−9570.60	−	16576.8i	−0.797889	−	1.38198i
$525$		0			0
$526$	3210.26	−	5560.34i	0.266111	−	0.460917i
$527$			24144.1i			1.99570i
$528$		0			0
$529$	10752.5			0.883742
$530$	1292.10	+	2237.99i	0.105897	+	0.183419i
$531$		0			0
$532$	4531.29	+	1719.65i	0.369279	+	0.140144i
$533$	−25885.9	+	14945.2i	−2.10365	+	1.21454i
$534$		0			0
$535$	−8090.74	+	4671.19i	−0.653819	+	0.377483i
$536$	−1370.51	+	791.266i	−0.110442	+	0.0637640i
$537$		0			0
$538$	3116.82	−	1799.49i	0.249769	−	0.144204i
$539$	403.671	+	1210.95i	0.0322585	+	0.0967703i
$540$		0			0
$541$	−28.6719	−	49.6612i	−0.00227856	−	0.00394658i	0.864884	−	0.501972i	$-0.167392\pi$
$541$	−28.6719	−	49.6612i	−0.00227856	−	0.00394658i	−0.867162	+	0.498025i	$0.834059\pi$
$542$	−2775.97			−0.219996
$543$		0			0
$544$		−	19416.9i		−	1.53031i
$545$	1146.30	−	1985.45i	0.0900956	−	0.156050i
$546$		0			0
$547$	−9099.49	−	15760.8i	−0.711272	−	1.23196i	−0.964380	−	0.264522i	$-0.914786\pi$
$547$	−9099.49	−	15760.8i	−0.711272	−	1.23196i	0.253107	−	0.967438i	$-0.418547\pi$
$548$	−4560.09	+	2632.77i	−0.355470	+	0.205231i
$549$		0			0
$550$	63.0145	−	109.144i	0.00488536	−	0.00846169i
$551$	3233.40	−	5600.41i	0.249995	−	0.433004i
$552$		0			0
$553$	−2693.72	+	7097.96i	−0.207140	+	0.545816i
$554$	−5504.01	−	3177.74i	−0.422099	−	0.243699i
$555$		0			0
$556$			11520.6i			0.878743i
$557$	−16522.7	−	9539.40i	−1.25689	−	0.725668i	−0.284425	−	0.958698i	$-0.591803\pi$
$557$	−16522.7	−	9539.40i	−1.25689	−	0.725668i	−0.972470	+	0.233030i	$0.925136\pi$
$558$		0			0
$559$			14181.2i			1.07299i
$560$	−2958.69	+	7796.16i	−0.223263	+	0.588300i
$561$		0			0
$562$	−7362.93			−0.552645
$563$	−10787.3	−	18684.2i	−0.807516	−	1.39866i	−0.914579	−	0.404407i	$-0.867478\pi$
$563$	−10787.3	−	18684.2i	−0.807516	−	1.39866i	0.107063	−	0.994252i	$-0.465855\pi$
$564$		0			0
$565$	−16886.7	−	9749.55i	−1.25740	−	0.725959i
$566$	1776.16			0.131904
$567$		0			0
$568$	−11530.3			−0.851764
$569$	2644.80	+	1526.98i	0.194861	+	0.112503i	0.594256	−	0.804276i	$-0.297447\pi$
$569$	2644.80	+	1526.98i	0.194861	+	0.112503i	−0.399395	+	0.916779i	$0.630780\pi$
$570$		0			0
$571$	−3506.26	−	6073.01i	−0.256974	−	0.445092i	0.708456	−	0.705755i	$-0.249392\pi$
$571$	−3506.26	−	6073.01i	−0.256974	−	0.445092i	−0.965430	+	0.260663i	$0.916059\pi$
$572$	1980.91			0.144801
$573$		0			0
$574$	−6042.13	+	4930.99i	−0.439362	+	0.358564i
$575$			1150.67i			0.0834547i
$576$		0			0
$577$	−18180.1	−	10496.3i	−1.31169	−	0.757305i	−0.329315	−	0.944220i	$-0.606818\pi$
$577$	−18180.1	−	10496.3i	−1.31169	−	0.757305i	−0.982376	+	0.186915i	$0.940151\pi$
$578$			8868.89i			0.638231i
$579$		0			0
$580$	12252.2	+	7073.79i	0.877144	+	0.506419i
$581$	7527.94	+	9224.26i	0.537541	+	0.658669i
$582$		0			0
$583$	−348.259	+	603.203i	−0.0247400	+	0.0428509i
$584$	5966.58	−	10334.4i	0.422772	−	0.732263i
$585$		0			0
$586$	90.4152	−	52.2012i	0.00637375	−	0.00367988i
$587$	−6537.09	−	11322.6i	−0.459650	−	0.796137i	0.539292	−	0.842119i	$-0.318692\pi$
$587$	−6537.09	−	11322.6i	−0.459650	−	0.796137i	−0.998942	+	0.0459813i	$0.985359\pi$
$588$		0			0
$589$	−4101.65	+	7104.27i	−0.286936	+	0.496988i
$590$			6465.92i			0.451182i
$591$		0			0
$592$	−9529.41			−0.661582
$593$	555.269	+	961.755i	0.0384523	+	0.0666013i	0.884611	−	0.466330i	$-0.154424\pi$
$593$	555.269	+	961.755i	0.0384523	+	0.0666013i	−0.846159	+	0.532931i	$0.821091\pi$
$594$		0			0
$595$	9318.94	−	24555.5i	0.642083	−	1.69189i
$596$	−5109.74	+	2950.11i	−0.351179	+	0.202754i
$597$		0			0
$598$	2832.72	−	1635.47i	0.193710	−	0.111838i
$599$	16879.0	−	9745.10i	1.15135	−	0.664731i	0.202133	−	0.979358i	$-0.435213\pi$
$599$	16879.0	−	9745.10i	1.15135	−	0.664731i	0.949215	+	0.314627i	$0.101879\pi$
$600$		0			0
$601$	18365.6	−	10603.4i	1.24650	−	0.719669i	0.276093	−	0.961131i	$-0.410960\pi$
$601$	18365.6	−	10603.4i	1.24650	−	0.719669i	0.970410	+	0.241462i	$0.0776270\pi$
$602$	592.716	+	3652.29i	0.0401284	+	0.247269i
$603$		0			0
$604$	348.067	+	602.871i	0.0234481	+	0.0406133i
$605$	−16429.8			−1.10408
$606$		0			0
$607$			6606.80i			0.441782i	0.975298	+	0.220891i	$0.0708966\pi$
$607$			6606.80i			0.441782i	−0.975298	+	0.220891i	$0.929103\pi$
$608$	3298.58	−	5713.30i	0.220025	−	0.381094i
$609$		0			0
$610$	2458.98	+	4259.07i	0.163215	+	0.282696i
$611$	−10483.5	+	6052.66i	−0.694137	+	0.400760i
$612$		0			0
$613$	−4381.85	+	7589.58i	−0.288713	+	0.500066i	−0.973503	−	0.228675i	$-0.926561\pi$
$613$	−4381.85	+	7589.58i	−0.288713	+	0.500066i	0.684790	+	0.728741i	$0.259894\pi$
$614$	2402.83	−	4161.82i	0.157932	−	0.273546i
$615$		0			0
$616$	1112.61	−	180.562i	0.0727735	−	0.0118101i
$617$	10903.4	+	6295.11i	0.711436	+	0.410748i	0.811593	−	0.584224i	$-0.198601\pi$
$617$	10903.4	+	6295.11i	0.711436	+	0.410748i	−0.100156	+	0.994972i	$0.531934\pi$
$618$		0			0
$619$			14475.9i			0.939962i	0.882677	+	0.469981i	$0.155739\pi$
$619$			14475.9i			0.939962i	−0.882677	+	0.469981i	$0.844261\pi$
$620$	−15542.2	−	8973.29i	−1.00676	−	0.581252i
$621$		0			0
$622$		−	1370.59i		−	0.0883531i
$623$	−1743.50	−	2136.37i	−0.112122	−	0.137387i
$624$		0			0
$625$	−18513.3			−1.18485
$626$	−236.945	−	410.401i	−0.0151282	−	0.0262028i
$627$		0			0
$628$	−4728.10	−	2729.77i	−0.300433	−	0.173455i
$629$	30014.7			1.90264
$630$		0			0
$631$	4746.41			0.299448			0.149724	−	0.988728i	$-0.452162\pi$
$631$	4746.41			0.299448			0.149724	+	0.988728i	$0.452162\pi$
$632$	5805.84	+	3352.00i	0.365418	+	0.210974i
$633$		0			0
$634$	2371.84	+	4108.15i	0.148577	+	0.257343i
$635$	−20517.4			−1.28222
$636$		0			0
$637$	26402.6	+	5402.44i	1.64224	+	0.336032i
$638$		−	689.624i		−	0.0427938i
$639$		0			0
$640$	15952.0	+	9209.91i	0.985249	+	0.568834i
$641$			16884.3i			1.04039i	0.854047	+	0.520195i	$0.174141\pi$
$641$			16884.3i			1.04039i	−0.854047	+	0.520195i	$0.825859\pi$
$642$		0			0
$643$	7268.42	+	4196.42i	0.445783	+	0.257373i	0.706048	−	0.708164i	$-0.250476\pi$
$643$	7268.42	+	4196.42i	0.445783	+	0.257373i	−0.260265	+	0.965537i	$0.583810\pi$
$644$	−3655.99	+	2983.66i	−0.223705	+	0.182566i
$645$		0			0
$646$	−2430.52	+	4209.79i	−0.148030	+	0.256396i
$647$	1835.83	−	3179.75i	0.111552	−	0.193213i	−0.804844	−	0.593486i	$-0.797751\pi$
$647$	1835.83	−	3179.75i	0.111552	−	0.193213i	0.916396	+	0.400273i	$0.131085\pi$
$648$		0			0
$649$	−1509.26	+	871.374i	−0.0912848	+	0.0527033i
$650$	−1330.42	−	2304.35i	−0.0802818	−	0.139052i
$651$		0			0
$652$	311.703	−	539.885i	0.0187227	−	0.0324287i
$653$			6596.57i			0.395319i	0.980271	+	0.197660i	$0.0633341\pi$
$653$			6596.57i			0.395319i	−0.980271	+	0.197660i	$0.936666\pi$
$654$		0			0
$655$	−35243.0			−2.10238
$656$	−6865.90	−	11892.1i	−0.408641	−	0.707786i
$657$		0			0
$658$	−2447.00	+	1997.00i	−0.144976	+	0.118315i
$659$	21380.3	−	12343.9i	1.26382	−	0.729666i	0.290008	−	0.957024i	$-0.406342\pi$
$659$	21380.3	−	12343.9i	1.26382	−	0.729666i	0.973811	+	0.227358i	$0.0730087\pi$
$660$		0			0
$661$	−384.039	+	221.725i	−0.0225982	+	0.0130471i	−0.511257	−	0.859428i	$-0.670820\pi$
$661$	−384.039	+	221.725i	−0.0225982	+	0.0130471i	0.488658	+	0.872475i	$0.337486\pi$
$662$	9932.91	−	5734.77i	0.583163	−	0.336689i
$663$		0			0
$664$	9105.13	−	5256.85i	0.532150	−	0.307237i
$665$	6913.58	−	5642.19i	0.403154	−	0.329014i
$666$		0			0
$667$	3148.22	+	5452.87i	0.182758	+	0.316546i
$668$	26010.0			1.50652
$669$		0			0
$670$			1336.07i			0.0770402i
$671$	−662.764	+	1147.94i	−0.0381307	+	0.0660444i
$672$		0			0
$673$	−12123.6	−	20998.6i	−0.694397	−	1.20273i	−0.970383	−	0.241570i	$-0.922338\pi$
$673$	−12123.6	−	20998.6i	−0.694397	−	1.20273i	0.275986	−	0.961162i	$-0.410996\pi$
$674$	−1726.58	+	996.840i	−0.0986725	+	0.0569686i
$675$		0			0
$676$	13469.3	−	23329.5i	0.766345	−	1.32735i
$677$	12638.5	−	21890.5i	0.717485	−	1.24272i	−0.244509	−	0.969647i	$-0.578627\pi$
$677$	12638.5	−	21890.5i	0.717485	−	1.24272i	0.961993	−	0.273073i	$-0.0880400\pi$
$678$		0			0
$679$	10025.2	−	8181.57i	0.566614	−	0.462415i
$680$	−20085.4	−	11596.3i	−1.13270	−	0.653967i
$681$		0			0
$682$			874.806i			0.0491174i
$683$	15251.8	+	8805.63i	0.854457	+	0.493321i	0.862152	−	0.506650i	$-0.169116\pi$
$683$	15251.8	+	8805.63i	0.854457	+	0.493321i	−0.00769531	+	0.999970i	$0.502450\pi$
$684$		0			0
$685$			9694.97i			0.540768i
$686$	7025.65	+	287.847i	0.391021	+	0.0160205i
$687$		0			0
$688$	−6514.89			−0.361014
$689$	7352.74	+	12735.3i	0.406556	+	0.704176i
$690$		0			0
$691$	25261.4	+	14584.7i	1.39072	+	0.802934i	0.993395	−	0.114743i	$-0.0366045\pi$
$691$	25261.4	+	14584.7i	1.39072	+	0.802934i	0.397327	+	0.917677i	$0.369938\pi$
$692$	−529.917			−0.0291104
$693$		0			0
$694$	3514.71			0.192243
$695$	18370.0	+	10605.9i	1.00261	+	0.578856i
$696$		0			0
$697$	21625.4	+	37456.3i	1.17521	+	2.03552i
$698$	−8224.81			−0.446008
$699$		0			0
$700$	2427.13	+	2974.06i	0.131053	+	0.160584i
$701$			21991.9i			1.18491i	0.805603	+	0.592456i	$0.201841\pi$
$701$			21991.9i			1.18491i	−0.805603	+	0.592456i	$0.798159\pi$
$702$		0			0
$703$	8831.65	+	5098.95i	0.473815	+	0.273557i
$704$			371.097i			0.0198668i
$705$		0			0
$706$	−5843.09	−	3373.51i	−0.311484	−	0.179835i
$707$	10928.2	−	1773.50i	0.581326	−	0.0943412i
$708$		0			0
$709$	−8680.05	+	15034.3i	−0.459783	+	0.796367i	−0.998949	−	0.0458321i	$-0.985406\pi$
$709$	−8680.05	+	15034.3i	−0.459783	+	0.796367i	0.539166	+	0.842199i	$0.318739\pi$
$710$	−4867.31	+	8430.43i	−0.257277	+	0.445617i
$711$		0			0
$712$	−2108.78	+	1217.50i	−0.110997	+	0.0640841i
$713$	−3993.59	−	6917.11i	−0.209763	−	0.363321i
$714$		0			0
$715$	1823.64	−	3158.63i	0.0953849	−	0.165212i
$716$		−	1667.04i		−	0.0870116i
$717$		0			0
$718$	−8996.24			−0.467600
$719$	12003.3	+	20790.4i	0.622599	+	1.07837i	0.989000	+	0.147916i	$0.0472565\pi$
$719$	12003.3	+	20790.4i	0.622599	+	1.07837i	−0.366401	+	0.930457i	$0.619410\pi$
$720$		0			0
$721$	1538.91	+	9482.71i	0.0794898	+	0.489812i
$722$	5144.75	−	2970.32i	0.265191	−	0.153108i
$723$		0			0
$724$	24729.3	−	14277.5i	1.26942	−	0.732899i
$725$	4435.77	−	2561.00i	0.227228	−	0.131190i
$726$		0			0
$727$	−16384.0	+	9459.32i	−0.835831	+	0.482568i	−0.855845	−	0.517232i	$-0.826962\pi$
$727$	−16384.0	+	9459.32i	−0.835831	+	0.482568i	0.0200136	+	0.999800i	$0.493629\pi$
$728$	8443.79	−	22249.4i	0.429873	−	1.13272i
$729$		0			0
$730$	−5037.36	−	8724.96i	−0.255398	−	0.442363i
$731$	20519.8			1.03824
$732$		0			0
$733$		−	34371.7i		−	1.73199i	−0.500056	−	0.865993i	$-0.666687\pi$
$733$		−	34371.7i		−	1.73199i	0.500056	−	0.865993i	$-0.333313\pi$
$734$	93.6265	−	162.166i	0.00470820	−	0.00815484i
$735$		0			0
$736$	3211.68	+	5562.79i	0.160848	+	0.278597i
$737$	−311.864	+	180.055i	−0.0155870	+	0.00899918i
$738$		0			0
$739$	−10959.7	+	18982.8i	−0.545549	+	0.944919i	0.453023	+	0.891499i	$0.350346\pi$
$739$	−10959.7	+	18982.8i	−0.545549	+	0.944919i	−0.998572	+	0.0534199i	$0.982988\pi$
$740$	−11155.1	+	19321.2i	−0.554149	+	0.959815i
$741$		0			0
$742$	2425.95	+	2972.60i	0.120026	+	0.147072i
$743$	−32847.1	−	18964.3i	−1.62186	−	0.936382i	−0.986422	−	0.164231i	$-0.947486\pi$
$743$	−32847.1	−	18964.3i	−1.62186	−	0.936382i	−0.635439	−	0.772151i	$-0.719181\pi$
$744$		0			0
$745$			10863.5i			0.534241i
$746$	−13098.9	−	7562.68i	−0.642877	−	0.371165i
$747$		0			0
$748$		−	2866.34i		−	0.140112i
$749$	−10746.5	+	8770.23i	−0.524257	+	0.427847i
$750$		0			0
$751$	−14761.9			−0.717269			−0.358635	−	0.933478i	$-0.616758\pi$
$751$	−14761.9			−0.717269			−0.358635	+	0.933478i	$0.616758\pi$
$752$	−2780.62	−	4816.17i	−0.134839	−	0.233547i
$753$		0			0
$754$	−12609.3	−	7279.96i	−0.609022	−	0.351619i
$755$	1281.73			0.0617841
$756$		0			0
$757$	32881.1			1.57871			0.789355	−	0.613937i	$-0.210415\pi$
$757$	32881.1			1.57871			0.789355	+	0.613937i	$0.210415\pi$
$758$	−4513.32	−	2605.77i	−0.216268	−	0.124862i
$759$		0			0
$760$	−3940.00	−	6824.29i	−0.188051	−	0.325714i
$761$	25237.9			1.20220			0.601099	−	0.799174i	$-0.294730\pi$
$761$	25237.9			1.20220			0.601099	+	0.799174i	$0.294730\pi$
$762$		0			0
$763$	1207.75	−	3182.44i	0.0573049	−	0.150999i
$764$		−	18258.2i		−	0.864605i
$765$		0			0
$766$	11857.3	+	6845.81i	0.559297	+	0.322910i
$767$			36794.4i			1.73216i
$768$		0			0
$769$	−2558.83	−	1477.34i	−0.119992	−	0.0692775i	0.438803	−	0.898583i	$-0.355403\pi$
$769$	−2558.83	−	1477.34i	−0.119992	−	0.0692775i	−0.558795	+	0.829306i	$0.688736\pi$
$770$	337.651	−	889.711i	0.0158027	−	0.0416402i
$771$		0			0
$772$	−411.557	+	712.837i	−0.0191868	+	0.0332326i
$773$	−15778.4	+	27329.0i	−0.734165	+	1.27161i	0.220924	+	0.975291i	$0.429093\pi$
$773$	−15778.4	+	27329.0i	−0.734165	+	1.27161i	−0.955089	+	0.296319i	$0.904241\pi$
$774$		0			0
$775$	−5626.90	+	3248.69i	−0.260805	+	0.150576i
$776$	−5713.29	−	9895.70i	−0.264298	−	0.457777i
$777$		0			0
$778$	4993.71	−	8649.36i	0.230120	−	0.398579i
$779$			14695.1i			0.675875i
$780$		0			0
$781$	−2623.76			−0.120212
$782$	−2366.49	−	4098.88i	−0.108217	−	0.187437i
$783$		0			0
$784$	−2481.90	+	12129.5i	−0.113060	+	0.552544i
$785$	−8705.43	+	5026.08i	−0.395809	+	0.228521i
$786$		0			0
$787$	−8734.13	+	5042.65i	−0.395601	+	0.228401i	−0.684584	−	0.728934i	$-0.740016\pi$
$787$	−8734.13	+	5042.65i	−0.395601	+	0.228401i	0.288983	+	0.957334i	$0.406683\pi$
$788$	−3467.40	+	2001.90i	−0.156752	+	0.0905010i
$789$		0			0
$790$	4901.65	−	2829.97i	0.220750	−	0.127450i
$791$	−27067.4	−	10272.2i	−1.21670	−	0.461743i
$792$		0			0
$793$	13992.8	+	24236.3i	0.626608	+	1.08532i
$794$	−7306.93			−0.326591
$795$		0			0
$796$		−	809.425i		−	0.0360419i
$797$	17563.1	−	30420.2i	0.780573	−	1.35199i	−0.151036	−	0.988528i	$-0.548261\pi$
$797$	17563.1	−	30420.2i	0.780573	−	1.35199i	0.931609	−	0.363463i	$-0.118406\pi$
$798$		0			0
$799$	8758.07	+	15169.4i	0.387782	+	0.671659i
$800$	4525.19	−	2612.62i	0.199987	−	0.115463i
$801$		0			0
$802$	−388.686	+	673.224i	−0.0171134	+	0.0296414i
$803$	1357.71	−	2351.62i	0.0596670	−	0.103346i
$804$		0			0
$805$	1391.83	+	8576.38i	0.0609385	+	0.375500i
$806$	15995.2	+	9234.82i	0.699015	+	0.403577i
$807$		0			0
$808$		−	9776.36i		−	0.425657i
$809$	−17101.2	−	9873.35i	−0.743195	−	0.429084i	0.0800351	−	0.996792i	$-0.474497\pi$
$809$	−17101.2	−	9873.35i	−0.743195	−	0.429084i	−0.823230	+	0.567708i	$0.807830\pi$
$810$		0			0
$811$		−	32458.3i		−	1.40538i	−0.711494	−	0.702692i	$-0.751981\pi$
$811$		−	32458.3i		−	1.40538i	0.711494	−	0.702692i	$-0.248019\pi$
$812$	19638.8	+	7453.02i	0.848750	+	0.322106i
$813$		0			0
$814$	1087.51			0.0468272
$815$	−573.911	−	994.042i	−0.0246665	−	0.0427237i
$816$		0			0
$817$	6037.85	+	3485.96i	0.258553	+	0.149276i
$818$	−5365.13			−0.229324
$819$		0			0
$820$	−32148.9			−1.36913
$821$	30882.9	+	17830.3i	1.31282	+	0.757955i	0.982562	−	0.185937i	$-0.0595321\pi$
$821$	30882.9	+	17830.3i	1.31282	+	0.757955i	0.330254	+	0.943892i	$0.392865\pi$
$822$		0			0
$823$	−475.381	−	823.384i	−0.0201346	−	0.0348741i	0.855783	−	0.517336i	$-0.173076\pi$
$823$	−475.381	−	823.384i	−0.0201346	−	0.0348741i	−0.875917	+	0.482462i	$0.839743\pi$
$824$	8483.22			0.358649
$825$		0			0
$826$	1537.86	+	9476.21i	0.0647808	+	0.399176i
$827$			18206.6i			0.765545i	0.923843	+	0.382772i	$0.125031\pi$
$827$			18206.6i			0.765545i	−0.923843	+	0.382772i	$0.874969\pi$
$828$		0			0
$829$	−35013.3	−	20214.9i	−1.46690	−	0.846916i	−0.467587	−	0.883947i	$-0.654877\pi$
$829$	−35013.3	−	20214.9i	−1.46690	−	0.846916i	−0.999314	+	0.0370311i	$0.988210\pi$
$830$		−	8876.31i		−	0.371206i
$831$		0			0
$832$	6785.23	+	3917.45i	0.282735	+	0.163237i
$833$	7817.21	−	38204.0i	0.325150	−	1.58906i
$834$		0			0
$835$	23945.0	−	41473.9i	0.992395	−	1.71888i
$836$	486.940	−	843.404i	0.0201449	−	0.0348920i
$837$		0			0
$838$	5565.25	−	3213.10i	0.229413	−	0.132452i
$839$	6782.34	+	11747.4i	0.279085	+	0.483390i	0.971158	−	0.238438i	$-0.0766355\pi$
$839$	6782.34	+	11747.4i	0.279085	+	0.483390i	−0.692072	+	0.721828i	$0.743302\pi$
$840$		0			0
$841$	1819.14	−	3150.84i	0.0745884	−	0.129191i
$842$		−	10472.8i		−	0.428640i
$843$		0			0
$844$	31948.1			1.30296
$845$	−24799.8	−	42954.5i	−1.00963	−	1.74873i
$846$		0			0
$847$	−24079.0	+	3907.68i	−0.976815	+	0.158524i
$848$	−5850.66	+	3377.88i	−0.236925	+	0.136789i
$849$		0			0
$850$	−3334.34	+	1925.08i	−0.134549	+	0.0776821i
$851$	−8598.98	+	4964.63i	−0.346380	+	0.199983i
$852$		0			0
$853$	658.326	−	380.085i	0.0264252	−	0.0152566i	−0.486729	−	0.873553i	$-0.661810\pi$
$853$	658.326	−	380.085i	0.0264252	−	0.0152566i	0.513154	+	0.858296i	$0.328477\pi$
$854$	4616.76	+	5657.09i	0.184991	+	0.226676i
$855$		0			0
$856$	6124.35	+	10607.7i	0.244540	+	0.423555i
$857$	26318.6			1.04904			0.524519	−	0.851399i	$-0.324245\pi$
$857$	26318.6			1.04904			0.524519	+	0.851399i	$0.324245\pi$
$858$		0			0
$859$			18320.3i			0.727683i	0.931461	+	0.363841i	$0.118535\pi$
$859$			18320.3i			0.727683i	−0.931461	+	0.363841i	$0.881465\pi$
$860$	−7626.32	+	13209.2i	−0.302390	+	0.523755i
$861$		0			0
$862$	−2826.92	−	4896.36i	−0.111700	−	0.193470i
$863$	11719.7	−	6766.36i	0.462274	−	0.266894i	−0.250726	−	0.968058i	$-0.580669\pi$
$863$	11719.7	−	6766.36i	0.462274	−	0.266894i	0.713000	+	0.701164i	$0.247336\pi$
$864$		0			0
$865$	−487.844	+	844.971i	−0.0191760	+	0.0332137i
$866$	−8303.88	+	14382.7i	−0.325840	+	0.564371i
$867$		0			0
$868$	−24912.3	−	9454.36i	−0.974168	−	0.369702i
$869$	1321.13	+	762.757i	0.0515724	+	0.0297753i
$870$		0			0
$871$			7602.93i			0.295770i
$872$	−2603.11	−	1502.90i	−0.101092	−	0.0583655i
$873$		0			0
$874$		−	1608.10i		−	0.0622365i
$875$	−21527.6	+	3493.63i	−0.831732	+	0.134979i
$876$		0			0
$877$	14407.4			0.554735			0.277368	−	0.960764i	$-0.410538\pi$
$877$	14407.4			0.554735			0.277368	+	0.960764i	$0.410538\pi$
$878$	−3072.71	−	5322.09i	−0.118108	−	0.204569i
$879$		0			0
$880$	1451.09	+	837.787i	0.0555866	+	0.0320929i
$881$	10256.6			0.392229			0.196115	−	0.980581i	$-0.437168\pi$
$881$	10256.6			0.392229			0.196115	+	0.980581i	$0.437168\pi$
$882$		0			0
$883$	−41832.5			−1.59431			−0.797155	−	0.603774i	$-0.793663\pi$
$883$	−41832.5			−1.59431			−0.797155	+	0.603774i	$0.793663\pi$
$884$	−52408.9	−	30258.3i	−1.99401	−	1.15124i
$885$		0			0
$886$	4047.45	+	7010.39i	0.153473	+	0.265822i
$887$	−7923.30			−0.299930			−0.149965	−	0.988691i	$-0.547916\pi$
$887$	−7923.30			−0.299930			−0.149965	+	0.988691i	$0.547916\pi$
$888$		0			0
$889$	−30069.6	+	4879.88i	−1.13442	+	0.184101i
$890$			2055.78i			0.0774270i
$891$		0			0
$892$	16062.9	+	9273.92i	0.602944	+	0.348110i
$893$			5951.36i			0.223017i
$894$		0			0
$895$	−2658.16	−	1534.69i	−0.0992765	−	0.0573173i
$896$	25569.2	+	9703.66i	0.953356	+	0.361804i
$897$		0			0
$898$	−8811.08	+	15261.2i	−0.327427	+	0.567121i
$899$	−17776.7	+	30790.1i	−0.659494	+	1.14228i
$900$		0			0
$901$	18427.7	−	10639.3i	0.681373	−	0.393391i
$902$	783.548	+	1357.14i	0.0289238	+	0.0500975i
$903$		0			0
$904$	−12782.6	+	22140.0i	−0.470289	+	0.814565i
$905$		−	52575.7i		−	1.93113i
$906$		0			0
$907$	22184.9			0.812169			0.406085	−	0.913835i	$-0.366894\pi$
$907$	22184.9			0.812169			0.406085	+	0.913835i	$0.366894\pi$
$908$	17192.8	+	29778.8i	0.628374	+	1.08838i
$909$		0			0
$910$	−12703.3	−	15565.9i	−0.462760	−	0.567036i
$911$	32277.9	−	18635.6i	1.17389	−	0.677746i	0.219297	−	0.975658i	$-0.429624\pi$
$911$	32277.9	−	18635.6i	1.17389	−	0.677746i	0.954593	+	0.297913i	$0.0962904\pi$
$912$		0			0
$913$	2071.90	−	1196.21i	0.0751038	−	0.0433612i
$914$	14948.1	−	8630.31i	0.540963	−	0.312325i
$915$		0			0
$916$	−10801.9	+	6236.50i	−0.389635	+	0.224956i
$917$	−51650.8	+	8382.22i	−1.86004	+	0.301860i
$918$		0			0
$919$	−6591.09	−	11416.1i	−0.236583	−	0.409774i	0.723148	−	0.690693i	$-0.242694\pi$
$919$	−6591.09	−	11416.1i	−0.236583	−	0.409774i	−0.959732	+	0.280918i	$0.909361\pi$
$920$	7672.41			0.274948
$921$		0			0
$922$			11383.9i			0.406627i
$923$	−27697.5	+	47973.5i	−0.987730	+	1.71080i
$924$		0			0
$925$	4038.60	+	6995.06i	0.143555	+	0.248645i
$926$	−9863.98	+	5694.97i	−0.350055	+	0.202104i
$927$		0			0
$928$	14296.1	−	24761.6i	0.505704	−	0.875905i
$929$	−7377.21	+	12777.7i	−0.260537	+	0.451263i	−0.966385	−	0.257101i	$-0.917233\pi$
$929$	−7377.21	+	12777.7i	−0.260537	+	0.451263i	0.705848	+	0.708363i	$0.250566\pi$
$930$		0			0
$931$	8790.35	−	9913.31i	0.309444	−	0.348975i
$932$	18735.5	+	10816.9i	0.658478	+	0.380173i
$933$		0			0
$934$		−	13217.0i		−	0.463033i
$935$	−4570.48	−	2638.77i	−0.159862	−	0.0922961i
$936$		0			0
$937$		−	15866.9i		−	0.553200i	−0.960985	−	0.276600i	$-0.910792\pi$
$937$		−	15866.9i		−	0.553200i	0.960985	−	0.276600i	$-0.0892076\pi$
$938$	317.772	+	1958.10i	0.0110614	+	0.0681600i
$939$		0			0
$940$	−13019.9			−0.451770
$941$	−22983.8	−	39809.2i	−0.796229	−	1.37911i	−0.922056	−	0.387057i	$-0.873492\pi$
$941$	−22983.8	−	39809.2i	−0.796229	−	1.37911i	0.125827	−	0.992052i	$-0.459842\pi$
$942$		0			0
$943$	−12391.1	−	7153.98i	−0.427899	−	0.247047i
$944$	−16903.5			−0.582798
$945$		0			0
$946$	743.490			0.0255528
$947$	−36095.5	−	20839.7i	−1.23859	−	0.715101i	−0.269785	−	0.962921i	$-0.586953\pi$
$947$	−36095.5	−	20839.7i	−1.23859	−	0.715101i	−0.968806	+	0.247819i	$0.920286\pi$
$948$		0			0
$949$	−28665.2	−	49649.5i	−0.980516	−	1.69830i
$950$	−1308.15			−0.0446757
$951$		0			0
$952$	−32194.4	−	12218.0i	−1.09604	−	0.415953i
$953$		−	8368.68i		−	0.284458i	−0.989834	−	0.142229i	$-0.954573\pi$
$953$		−	8368.68i		−	0.284458i	0.989834	−	0.142229i	$-0.0454269\pi$
$954$		0			0
$955$	−29113.3	−	16808.6i	−0.986477	−	0.569543i
$956$			3040.31i			0.102856i
$957$		0			0
$958$	−6257.95	−	3613.03i	−0.211049	−	0.121849i
$959$	2305.86	+	14208.6i	0.0776434	+	0.478435i
$960$		0			0
$961$	7654.66	−	13258.3i	0.256945	−	0.445043i
$962$	11480.2	−	19884.4i	0.384759	−	0.666422i
$963$		0			0
$964$	−6475.74	+	3738.77i	−0.216358	+	0.124915i
$965$	757.762	+	1312.48i	0.0252780	+	0.0437827i
$966$		0			0
$967$	11424.7	−	19788.2i	0.379932	−	0.658061i	−0.611120	−	0.791538i	$-0.709281\pi$
$967$	11424.7	−	19788.2i	0.379932	−	0.658061i	0.991052	+	0.133477i	$0.0426142\pi$
$968$			21541.0i			0.715242i
$969$		0			0
$970$	−9647.02			−0.319327
$971$	3871.68	+	6705.94i	0.127959	+	0.221631i	0.922886	−	0.385074i	$-0.125824\pi$
$971$	3871.68	+	6705.94i	0.127959	+	0.221631i	−0.794927	+	0.606705i	$0.792491\pi$
$972$		0			0
$973$	29444.8	+	11174.5i	0.970152	+	0.368178i
$974$	−3114.83	+	1798.35i	−0.102470	+	0.0591609i
$975$		0			0
$976$	−11134.3	+	6428.36i	−0.365163	+	0.210827i
$977$	10502.5	−	6063.63i	0.343915	−	0.198560i	−0.318087	−	0.948062i	$-0.603040\pi$
$977$	10502.5	−	6063.63i	0.343915	−	0.198560i	0.662002	+	0.749502i	$0.269707\pi$
$978$		0			0
$979$	−479.858	+	277.046i	−0.0156653	+	0.00904437i
$980$	21687.6	+	19230.9i	0.706924	+	0.626845i
$981$		0			0
$982$	6153.80	+	10658.7i	0.199975	+	0.346367i
$983$	−35224.9			−1.14293			−0.571465	−	0.820627i	$-0.693625\pi$
$983$	−35224.9			−1.14293			−0.571465	+	0.820627i	$0.693625\pi$
$984$		0			0
$985$			7371.85i			0.238464i
$986$	−10534.0	+	18245.3i	−0.340233	+	0.589300i
$987$		0			0
$988$	−10280.7	−	17806.7i	−0.331045	−	0.573386i
$989$	−5878.79	+	3394.12i	−0.189014	+	0.109127i
$990$		0			0
$991$	2330.71	−	4036.90i	0.0747097	−	0.129401i	−0.826250	−	0.563303i	$-0.809530\pi$
$991$	2330.71	−	4036.90i	0.0747097	−	0.129401i	0.900960	+	0.433902i	$0.142864\pi$
$992$	−18135.0	+	31410.8i	−0.580430	+	1.00534i
$993$		0			0
$994$	−5128.25	+	13513.0i	−0.163640	+	0.431192i
$995$	−1290.66	−	745.161i	−0.0411222	−	0.0237419i
$996$		0			0
$997$		−	2849.75i		−	0.0905240i	−0.998975	−	0.0452620i	$-0.985588\pi$
$997$		−	2849.75i		−	0.0905240i	0.998975	−	0.0452620i	$-0.0144123\pi$
$998$	7823.04	+	4516.63i	0.248130	+	0.143258i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.4.s.a.17.9		44
3.2	odd	2		63.4.s.a.59.14	yes	44
7.5	odd	6		189.4.i.a.152.14		44
9.2	odd	6		189.4.i.a.143.9		44
9.7	even	3		63.4.i.a.38.14	yes	44
21.5	even	6		63.4.i.a.5.9	✓	44
63.47	even	6	inner	189.4.s.a.89.9		44
63.61	odd	6		63.4.s.a.47.14	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.4.i.a.5.9	✓	44	21.5	even	6
63.4.i.a.38.14	yes	44	9.7	even	3
63.4.s.a.47.14	yes	44	63.61	odd	6
63.4.s.a.59.14	yes	44	3.2	odd	2
189.4.i.a.143.9		44	9.2	odd	6
189.4.i.a.152.14		44	7.5	odd	6
189.4.s.a.17.9		44	1.1	even	1	trivial
189.4.s.a.89.9		44	63.47	even	6	inner

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.s (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.958607 - 0.553452i) q^{2} +(-3.38738 - 5.86712i) q^{4} -12.4738 q^{5} +(-18.2811 + 2.96677i) q^{7} +16.3542i q^{8} +O(q^{10})\)	\(q+(-0.958607 - 0.553452i) q^{2} +(-3.38738 - 5.86712i) q^{4} -12.4738 q^{5} +(-18.2811 + 2.96677i) q^{7} +16.3542i q^{8} +(11.9574 + 6.90363i) q^{10} +3.72145i q^{11} +(68.0440 + 39.2852i) q^{13} +(19.1663 + 7.27374i) q^{14} +(-18.0478 + 31.2597i) q^{16} +(56.8448 - 98.4582i) q^{17} +(33.4526 - 19.3138i) q^{19} +(42.2534 + 73.1851i) q^{20} +(2.05964 - 3.56741i) q^{22} +37.6101i q^{23} +30.5949 q^{25} +(-43.4849 - 75.3181i) q^{26} +(79.3314 + 97.2077i) q^{28} +(144.984 - 83.7067i) q^{29} +(-183.916 + 106.184i) q^{31} +(147.907 - 85.3941i) q^{32} +(-108.984 + 62.9218i) q^{34} +(228.034 - 37.0068i) q^{35} +(132.003 + 228.635i) q^{37} -42.7571 q^{38} -203.999i q^{40} +(-190.215 + 329.461i) q^{41} +(90.2450 + 156.309i) q^{43} +(21.8342 - 12.6060i) q^{44} +(20.8154 - 36.0533i) q^{46} +(-77.0348 + 133.428i) q^{47} +(325.397 - 108.472i) q^{49} +(-29.3284 - 16.9328i) q^{50} -532.296i q^{52} +(162.088 + 93.5816i) q^{53} -46.4205i q^{55} +(-48.5192 - 298.973i) q^{56} -185.311 q^{58} +(234.149 + 405.558i) q^{59} +(308.466 + 178.093i) q^{61} +235.071 q^{62} +99.7183 q^{64} +(-848.765 - 490.035i) q^{65} +(48.3829 + 83.8017i) q^{67} -770.221 q^{68} +(-239.076 - 90.7309i) q^{70} +705.036i q^{71} +(-631.911 - 364.834i) q^{73} -292.228i q^{74} +(-226.633 - 130.847i) q^{76} +(-11.0407 - 68.0322i) q^{77} +(204.962 - 355.005i) q^{79} +(225.124 - 389.926i) q^{80} +(364.682 - 210.549i) q^{82} +(-321.436 - 556.744i) q^{83} +(-709.069 + 1228.14i) q^{85} -199.785i q^{86} -60.8615 q^{88} +(74.4458 + 128.944i) q^{89} +(-1360.47 - 516.306i) q^{91} +(220.663 - 127.400i) q^{92} +(147.692 - 85.2702i) q^{94} +(-417.279 + 240.916i) q^{95} +(-605.085 + 349.346i) q^{97} +(-371.961 - 76.1098i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 3 q^{2} + 81 q^{4} + 6 q^{5} + 5 q^{7}+O(q^{10}) \) 44 * q + 3 * q^2 + 81 * q^4 + 6 * q^5 + 5 * q^7	\( 44 q + 3 q^{2} + 81 q^{4} + 6 q^{5} + 5 q^{7} - 6 q^{10} + 36 q^{13} - 129 q^{14} - 263 q^{16} - 72 q^{17} - 6 q^{19} + 24 q^{20} + 14 q^{22} + 698 q^{25} - 96 q^{26} - 156 q^{28} + 132 q^{29} + 177 q^{31} + 501 q^{32} - 24 q^{34} + 765 q^{35} + 82 q^{37} + 1746 q^{38} + 618 q^{41} + 82 q^{43} + 603 q^{44} + 266 q^{46} + 201 q^{47} + 515 q^{49} + 1845 q^{50} + 564 q^{53} - 3600 q^{56} - 538 q^{58} - 747 q^{59} - 1209 q^{61} - 2904 q^{62} - 1144 q^{64} + 831 q^{65} + 295 q^{67} - 7008 q^{68} - 390 q^{70} - 6 q^{73} + 144 q^{76} + 1203 q^{77} - 551 q^{79} - 4239 q^{80} + 18 q^{82} + 1830 q^{83} - 237 q^{85} + 1246 q^{88} + 4266 q^{89} - 1140 q^{91} - 7896 q^{92} - 3 q^{94} + 1053 q^{95} + 792 q^{97} + 5667 q^{98}+O(q^{100}) \) 44 * q + 3 * q^2 + 81 * q^4 + 6 * q^5 + 5 * q^7 - 6 * q^10 + 36 * q^13 - 129 * q^14 - 263 * q^16 - 72 * q^17 - 6 * q^19 + 24 * q^20 + 14 * q^22 + 698 * q^25 - 96 * q^26 - 156 * q^28 + 132 * q^29 + 177 * q^31 + 501 * q^32 - 24 * q^34 + 765 * q^35 + 82 * q^37 + 1746 * q^38 + 618 * q^41 + 82 * q^43 + 603 * q^44 + 266 * q^46 + 201 * q^47 + 515 * q^49 + 1845 * q^50 + 564 * q^53 - 3600 * q^56 - 538 * q^58 - 747 * q^59 - 1209 * q^61 - 2904 * q^62 - 1144 * q^64 + 831 * q^65 + 295 * q^67 - 7008 * q^68 - 390 * q^70 - 6 * q^73 + 144 * q^76 + 1203 * q^77 - 551 * q^79 - 4239 * q^80 + 18 * q^82 + 1830 * q^83 - 237 * q^85 + 1246 * q^88 + 4266 * q^89 - 1140 * q^91 - 7896 * q^92 - 3 * q^94 + 1053 * q^95 + 792 * q^97 + 5667 * q^98

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