LMFDB - Embedded newform 189.4.i.a.143.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [189,4,Mod(143,189)]

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([1, 1]))

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

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

chi := DirichletCharacter("189.143");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	189.i (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			143.9
Character	$\chi$	$=$	189.143
Dual form			189.4.i.a.152.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.10690i q^{2} +6.77476 q^{4} +(-6.23688 + 10.8026i) q^{5} +(11.7098 + 14.3485i) q^{7} -16.3542i q^{8} +O(q^{10})$	\(q-1.10690i q^{2} +6.77476 q^{4} +(-6.23688 + 10.8026i) q^{5} +(11.7098 + 14.3485i) q^{7} -16.3542i q^{8} +(11.9574 + 6.90363i) q^{10} +(-3.22287 + 1.86072i) q^{11} +(-68.0440 + 39.2852i) q^{13} +(15.8824 - 12.9617i) q^{14} +36.0955 q^{16} +(-56.8448 + 98.4582i) q^{17} +(33.4526 - 19.3138i) q^{19} +(-42.2534 + 73.1851i) q^{20} +(2.05964 + 3.56741i) q^{22} +(32.5713 + 18.8050i) q^{23} +(-15.2974 - 26.4959i) q^{25} +(43.4849 + 75.3181i) q^{26} +(79.3314 + 97.2077i) q^{28} +(144.984 + 83.7067i) q^{29} -212.368i q^{31} -170.788i q^{32} +(108.984 + 62.9218i) q^{34} +(-228.034 + 37.0068i) q^{35} +(132.003 + 228.635i) q^{37} +(-21.3786 - 37.0288i) q^{38} +(176.668 + 101.999i) q^{40} +(190.215 + 329.461i) q^{41} +(90.2450 - 156.309i) q^{43} +(-21.8342 + 12.6060i) q^{44} +(20.8154 - 36.0533i) q^{46} -154.070 q^{47} +(-68.7592 + 336.037i) q^{49} +(-29.3284 + 16.9328i) q^{50} +(-460.982 + 266.148i) q^{52} +(-162.088 - 93.5816i) q^{53} -46.4205i q^{55} +(234.659 - 191.506i) q^{56} +(92.6553 - 160.484i) q^{58} +468.298 q^{59} -356.186i q^{61} -235.071 q^{62} +99.7183 q^{64} -980.069i q^{65} -96.7659 q^{67} +(-385.110 + 667.031i) q^{68} +(40.9629 + 252.412i) q^{70} -705.036i q^{71} +(-631.911 - 364.834i) q^{73} +(253.077 - 146.114i) q^{74} +(226.633 - 130.847i) q^{76} +(-64.4379 - 24.4546i) q^{77} -409.925 q^{79} +(-225.124 + 389.926i) q^{80} +(364.682 - 210.549i) q^{82} +(321.436 - 556.744i) q^{83} +(-709.069 - 1228.14i) q^{85} +(-173.019 - 99.8925i) q^{86} +(30.4307 + 52.7076i) q^{88} +(-74.4458 - 128.944i) q^{89} +(-1360.47 - 516.306i) q^{91} +(220.663 + 127.400i) q^{92} +170.540i q^{94} +481.833i q^{95} +(605.085 + 349.346i) q^{97} +(371.961 + 76.1098i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - 162 q^{4} + 3 q^{5} + 5 q^{7}+O(q^{10}) $ 44 * q - 162 * q^4 + 3 * q^5 + 5 * q^7	$ 44 q - 162 q^{4} + 3 q^{5} + 5 q^{7} - 6 q^{10} - 9 q^{11} - 36 q^{13} - 54 q^{14} + 526 q^{16} + 72 q^{17} - 6 q^{19} - 24 q^{20} + 14 q^{22} + 285 q^{23} - 349 q^{25} + 96 q^{26} - 156 q^{28} + 132 q^{29} + 24 q^{34} - 765 q^{35} + 82 q^{37} + 873 q^{38} + 420 q^{40} - 618 q^{41} + 82 q^{43} - 603 q^{44} + 266 q^{46} + 402 q^{47} - 79 q^{49} + 1845 q^{50} + 189 q^{52} - 564 q^{53} - 66 q^{56} + 269 q^{58} - 1494 q^{59} + 2904 q^{62} - 1144 q^{64} - 590 q^{67} - 3504 q^{68} - 105 q^{70} - 6 q^{73} - 1515 q^{74} - 144 q^{76} + 4443 q^{77} + 1102 q^{79} + 4239 q^{80} + 18 q^{82} - 1830 q^{83} - 237 q^{85} - 1209 q^{86} - 623 q^{88} - 4266 q^{89} - 1140 q^{91} - 7896 q^{92} - 792 q^{97} - 5667 q^{98}+O(q^{100}) $ 44 * q - 162 * q^4 + 3 * q^5 + 5 * q^7 - 6 * q^10 - 9 * q^11 - 36 * q^13 - 54 * q^14 + 526 * q^16 + 72 * q^17 - 6 * q^19 - 24 * q^20 + 14 * q^22 + 285 * q^23 - 349 * q^25 + 96 * q^26 - 156 * q^28 + 132 * q^29 + 24 * q^34 - 765 * q^35 + 82 * q^37 + 873 * q^38 + 420 * q^40 - 618 * q^41 + 82 * q^43 - 603 * q^44 + 266 * q^46 + 402 * q^47 - 79 * q^49 + 1845 * q^50 + 189 * q^52 - 564 * q^53 - 66 * q^56 + 269 * q^58 - 1494 * q^59 + 2904 * q^62 - 1144 * q^64 - 590 * q^67 - 3504 * q^68 - 105 * q^70 - 6 * q^73 - 1515 * q^74 - 144 * q^76 + 4443 * q^77 + 1102 * q^79 + 4239 * q^80 + 18 * q^82 - 1830 * q^83 - 237 * q^85 - 1209 * q^86 - 623 * q^88 - 4266 * q^89 - 1140 * q^91 - 7896 * q^92 - 792 * q^97 - 5667 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$		−	1.10690i		−	0.391350i	−0.980669	−	0.195675i	$-0.937310\pi$
$2$		−	1.10690i		−	0.391350i	0.980669	−	0.195675i	$-0.0626897\pi$
$3$		0			0
$3$		0			0
$4$	6.77476			0.846846
$5$	−6.23688	+	10.8026i	−0.557844	+	0.966214i	0.439832	+	0.898080i	$0.355038\pi$
$5$	−6.23688	+	10.8026i	−0.557844	+	0.966214i	−0.997676	+	0.0681339i	$0.978295\pi$
$6$		0			0
$7$	11.7098	+	14.3485i	0.632272	+	0.774746i
$7$	11.7098	+	14.3485i	0.632272	+	0.774746i
$8$		−	16.3542i		−	0.722762i
$9$		0			0
$10$	11.9574	+	6.90363i	0.378127	+	0.218312i
$11$	−3.22287	+	1.86072i	−0.0883393	+	0.0510027i	−0.543519	−	0.839397i	$-0.682908\pi$
$11$	−3.22287	+	1.86072i	−0.0883393	+	0.0510027i	0.455180	+	0.890400i	$0.349575\pi$
$12$		0			0
$13$	−68.0440	+	39.2852i	−1.45169	+	0.838135i	−0.998578	−	0.0533171i	$-0.983021\pi$
$13$	−68.0440	+	39.2852i	−1.45169	+	0.838135i	−0.453115	+	0.891452i	$0.649687\pi$
$14$	15.8824	−	12.9617i	0.303197	−	0.247439i
$15$		0			0
$16$	36.0955			0.563993
$17$	−56.8448	+	98.4582i	−0.810994	+	1.40468i	0.101175	+	0.994869i	$0.467740\pi$
$17$	−56.8448	+	98.4582i	−0.810994	+	1.40468i	−0.912169	+	0.409814i	$0.865594\pi$
$18$		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
$23$	32.5713	+	18.8050i	0.295286	+	0.170483i	0.640323	−	0.768106i	$-0.278800\pi$
$23$	32.5713	+	18.8050i	0.295286	+	0.170483i	−0.345037	+	0.938589i	$0.612134\pi$
$24$		0			0
$25$	−15.2974	−	26.4959i	−0.122379	−	0.211967i
$26$	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	0.886298	−	0.463116i	$-0.153269\pi$
$29$	144.984	+	83.7067i	0.928376	+	0.535998i	0.0420787	+	0.999114i	$0.486602\pi$
$30$		0			0
$31$		−	212.368i		−	1.23040i	−0.788370	−	0.615201i	$-0.789075\pi$
$31$		−	212.368i		−	1.23040i	0.788370	−	0.615201i	$-0.210925\pi$
$32$		−	170.788i		−	0.943480i
$33$		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	$0.633832\pi$
$38$	−21.3786	−	37.0288i	−0.0912648	−	0.158075i
$39$		0			0
$40$	176.668	+	101.999i	0.698343	+	0.403188i
$41$	190.215	+	329.461i	0.724549	+	1.25496i	0.959159	+	0.282866i	$0.0912853\pi$
$41$	190.215	+	329.461i	0.724549	+	1.25496i	−0.234610	+	0.972090i	$0.575381\pi$
$42$		0			0
$43$	90.2450	−	156.309i	0.320052	−	0.554346i	−0.660447	−	0.750873i	$-0.729633\pi$
$43$	90.2450	−	156.309i	0.320052	−	0.554346i	0.980498	+	0.196527i	$0.0629663\pi$
$44$	−21.8342	+	12.6060i	−0.0748097	+	0.0431914i
$45$		0			0
$46$	20.8154	−	36.0533i	0.0667186	−	0.115560i
$47$	−154.070			−0.478157			−0.239078	−	0.971000i	$-0.576845\pi$
$47$	−154.070			−0.478157			−0.239078	+	0.971000i	$0.576845\pi$
$48$		0			0
$49$	−68.7592	+	336.037i	−0.200464	+	0.979701i
$50$	−29.3284	+	16.9328i	−0.0829533	+	0.0478931i
$51$		0			0
$52$	−460.982	+	266.148i	−1.22936	+	0.709771i
$53$	−162.088	−	93.5816i	−0.420085	−	0.242536i	0.275029	−	0.961436i	$-0.411313\pi$
$53$	−162.088	−	93.5816i	−0.420085	−	0.242536i	−0.695114	+	0.718900i	$0.744646\pi$
$54$		0			0
$55$		−	46.4205i		−	0.113806i
$56$	234.659	−	191.506i	0.559957	−	0.456982i
$57$		0			0
$58$	92.6553	−	160.484i	0.209763	−	0.363320i
$59$	468.298			1.03334			0.516672	−	0.856184i	$-0.327171\pi$
$59$	468.298			1.03334			0.516672	+	0.856184i	$0.327171\pi$
$60$		0			0
$61$		−	356.186i		−	0.747622i	−0.927505	−	0.373811i	$-0.878051\pi$
$61$		−	356.186i		−	0.747622i	0.927505	−	0.373811i	$-0.121949\pi$
$62$	−235.071			−0.481518
$63$		0			0
$64$	99.7183			0.194762
$65$		−	980.069i		−	1.87019i
$66$		0			0
$67$	−96.7659			−0.176445			−0.0882226	−	0.996101i	$-0.528119\pi$
$67$	−96.7659			−0.176445			−0.0882226	+	0.996101i	$0.528119\pi$
$68$	−385.110	+	667.031i	−0.686787	+	1.18955i
$69$		0			0
$70$	40.9629	+	252.412i	0.0699430	+	0.430985i
$71$		−	705.036i		−	1.17848i	−0.807956	−	0.589242i	$-0.799426\pi$
$71$		−	705.036i		−	1.17848i	0.807956	−	0.589242i	$-0.200574\pi$
$72$		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	$0.865548\pi$
$74$	253.077	−	146.114i	0.397562	−	0.229533i
$75$		0			0
$76$	226.633	−	130.847i	0.342061	−	0.197489i
$77$	−64.4379	−	24.4546i	−0.0953686	−	0.0361929i
$78$		0			0
$79$	−409.925			−0.583799			−0.291900	−	0.956449i	$-0.594287\pi$
$79$	−409.925			−0.583799			−0.291900	+	0.956449i	$0.594287\pi$
$80$	−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	$-0.693577\pi$
$83$	321.436	−	556.744i	0.425087	−	0.736272i	0.996429	+	0.0844400i	$0.0269101\pi$
$84$		0			0
$85$	−709.069	−	1228.14i	−0.904816	−	1.56719i
$86$	−173.019	−	99.8925i	−0.216943	−	0.125252i
$87$		0			0
$88$	30.4307	+	52.7076i	0.0368628	+	0.0638483i
$89$	−74.4458	−	128.944i	−0.0886656	−	0.153573i	0.818282	−	0.574817i	$-0.194927\pi$
$89$	−74.4458	−	128.944i	−0.0886656	−	0.153573i	−0.906947	+	0.421244i	$0.861594\pi$
$90$		0			0
$91$	−1360.47	−	516.306i	−1.56721	−	0.594764i
$92$	220.663	+	127.400i	0.250062	+	0.144373i
$93$		0			0
$94$			170.540i			0.187126i
$95$			481.833i			0.520368i
$96$		0			0
$97$	605.085	+	349.346i	0.633372	+	0.365677i	0.782057	−	0.623207i	$-0.214171\pi$
$97$	605.085	+	349.346i	0.633372	+	0.365677i	−0.148685	+	0.988885i	$0.547504\pi$
$98$	371.961	+	76.1098i	0.383406	+	0.0784515i
$99$		0			0
$100$	−103.636	−	179.504i	−0.103636	−	0.179504i
$101$	−298.894	−	517.699i	−0.294466	−	0.510030i	0.680395	−	0.732846i	$-0.261808\pi$
$101$	−298.894	−	517.699i	−0.294466	−	0.510030i	−0.974860	+	0.222816i	$0.928475\pi$
$102$		0			0
$103$	449.222	+	259.359i	0.429740	+	0.248110i	0.699236	−	0.714891i	$-0.253524\pi$
$103$	449.222	+	259.359i	0.429740	+	0.248110i	−0.269496	+	0.963001i	$0.586857\pi$
$104$	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	−0.763523	−	0.645780i	$-0.776532\pi$
$107$	−648.620	+	374.481i	−0.586023	+	0.338341i	0.177500	+	0.984121i	$0.443199\pi$
$108$		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	$0.192399\pi$
$110$	−51.3830			−0.0445380
$111$		0			0
$112$	422.673	+	517.917i	0.356597	+	0.436952i
$113$	1353.78	−	781.605i	1.12702	−	0.650683i	0.183833	−	0.982957i	$-0.441149\pi$
$113$	1353.78	−	781.605i	1.12702	−	0.650683i	0.943183	+	0.332274i	$0.107816\pi$
$114$		0			0
$115$	−406.286	+	234.570i	−0.329447	+	0.190206i
$116$	982.235	+	567.093i	0.786191	+	0.453908i
$117$		0			0
$118$		−	518.361i		−	0.404398i
$119$	−2078.37	+	337.291i	−1.60104	+	0.259827i
$120$		0			0
$121$	−658.575	+	1140.69i	−0.494797	+	0.857014i
$122$	−394.263			−0.292581
$123$		0			0
$124$		−	1438.75i		−	1.04196i
$125$	−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	$0.305145\pi$
$128$		−	1476.68i		−	1.01970i
$129$		0			0
$130$	−1084.84			−0.731899
$131$	1412.68	−	2446.84i	0.942189	−	1.63192i	0.180906	−	0.983500i	$-0.442097\pi$
$131$	1412.68	−	2446.84i	0.942189	−	1.63192i	0.761283	−	0.648420i	$-0.224570\pi$
$132$		0			0
$133$	668.849	+	253.832i	0.436064	+	0.165489i
$134$			107.110i			0.0690518i
$135$		0			0
$136$	1610.21	+	929.654i	1.01525	+	0.586156i
$137$	673.100	−	388.614i	0.419758	−	0.242347i	−0.275216	−	0.961382i	$-0.588749\pi$
$137$	673.100	−	388.614i	0.419758	−	0.242347i	0.694974	+	0.719035i	$0.255416\pi$
$138$		0			0
$139$	1472.69	−	850.256i	0.898645	−	0.518833i	0.0218847	−	0.999761i	$-0.493033\pi$
$139$	1472.69	−	850.256i	0.898645	−	0.518833i	0.876760	+	0.480928i	$0.159700\pi$
$140$	−1544.88	+	250.712i	−0.932614	+	0.151350i
$141$		0			0
$142$	−780.407			−0.461199
$143$	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
$149$	−754.231	−	435.455i	−0.414691	−	0.239422i	0.278112	−	0.960549i	$-0.410291\pi$
$149$	−754.231	−	435.455i	−0.414691	−	0.239422i	−0.692803	+	0.721127i	$0.743625\pi$
$150$		0			0
$151$	51.3771	+	88.9877i	0.0276888	+	0.0479584i	0.879538	−	0.475829i	$-0.157852\pi$
$151$	51.3771	+	88.9877i	0.0276888	+	0.0479584i	−0.851849	+	0.523787i	$0.824519\pi$
$152$	−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
$157$			805.865i			0.409650i	0.978799	+	0.204825i	$0.0656625\pi$
$157$			805.865i			0.409650i	−0.978799	+	0.204825i	$0.934338\pi$
$158$			453.747i			0.228470i
$159$		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	$0.826295\pi$
$164$	1288.66	+	2232.02i	0.613581	+	1.06275i
$165$		0			0
$166$	−616.262	−	355.799i	−0.288140	−	0.166358i
$167$	1919.63	+	3324.89i	0.889492	+	1.54065i	0.840477	+	0.541847i	$0.182275\pi$
$167$	1919.63	+	3324.89i	0.889492	+	1.54065i	0.0490152	+	0.998798i	$0.484392\pi$
$168$		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
$173$	78.2192			0.0343751			0.0171876	−	0.999852i	$-0.494529\pi$
$173$	78.2192			0.0343751			0.0171876	+	0.999852i	$0.494529\pi$
$174$		0			0
$175$	201.046	−	529.758i	0.0868439	−	0.228834i
$176$	−116.331	+	67.1639i	−0.0498227	+	0.0287652i
$177$		0			0
$178$	−142.728	+	82.4043i	−0.0601008	+	0.0346992i
$179$	−213.100	−	123.033i	−0.0889823	−	0.0513740i	0.454849	−	0.890569i	$-0.349693\pi$
$179$	−213.100	−	123.033i	−0.0889823	−	0.0513740i	−0.543831	+	0.839195i	$0.683027\pi$
$180$		0			0
$181$			4214.90i			1.73089i	0.501003	+	0.865446i	$0.332965\pi$
$181$			4214.90i			1.73089i	−0.501003	+	0.865446i	$0.667035\pi$
$182$	−571.501	+	1505.91i	−0.232761	+	0.613326i
$183$		0			0
$184$	307.542	−	532.678i	0.123219	−	0.213422i
$185$	−3293.14			−1.30874
$186$		0			0
$187$		−	423.090i		−	0.165452i
$188$	−1043.79			−0.404925
$189$		0			0
$190$	533.342			0.203646
$191$			2695.03i			1.02097i	0.859886	+	0.510486i	$0.170534\pi$
$191$			2695.03i			1.02097i	−0.859886	+	0.510486i	$0.829466\pi$
$192$		0			0
$193$	121.497			0.0453137			0.0226568	−	0.999743i	$-0.492787\pi$
$193$	121.497			0.0453137			0.0226568	+	0.999743i	$0.492787\pi$
$194$	386.692	−	669.771i	0.143108	−	0.247870i
$195$		0			0
$196$	−465.827	+	2276.57i	−0.169762	+	0.829655i
$197$			590.988i			0.213737i	0.994273	+	0.106868i	$0.0340824\pi$
$197$			590.988i			0.213737i	−0.994273	+	0.106868i	$0.965918\pi$
$198$		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	$0.659892\pi$
$200$	−433.321	+	250.178i	−0.153202	+	0.0884512i
$201$		0			0
$202$	−573.043	+	330.847i	−0.199600	+	0.115239i
$203$	496.677	+	3060.50i	0.171724	+	1.05815i
$204$		0			0
$205$	−4745.38			−1.61674
$206$	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	−0.937942	−	0.346793i	$-0.887271\pi$
$211$	−2357.88	−	4083.96i	−0.769302	−	1.33247i	0.168639	−	0.985678i	$-0.446063\pi$
$212$	−1098.11	−	633.993i	−0.355747	−	0.205391i
$213$		0			0
$214$	414.514	+	717.960i	0.132409	+	0.229340i
$215$	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
$220$		−	314.488i		−	0.0963762i
$221$		−	8932.65i		−	2.71889i
$222$		0			0
$223$	2370.99	+	1368.89i	0.711988	+	0.411066i	0.811797	−	0.583940i	$-0.198490\pi$
$223$	2370.99	+	1368.89i	0.711988	+	0.411066i	−0.0998088	+	0.995007i	$0.531823\pi$
$224$	2450.56	−	1999.90i	0.730958	−	0.596536i
$225$		0			0
$226$	−865.161	−	1498.50i	−0.254645	−	0.441057i
$227$	−2537.77	−	4395.55i	−0.742018	−	1.28521i	−0.951575	−	0.307416i	$-0.900536\pi$
$227$	−2537.77	−	4395.55i	−0.742018	−	1.28521i	0.209558	−	0.977796i	$-0.432798\pi$
$228$		0			0
$229$	1594.44	+	920.549i	0.460102	+	0.265640i	0.712087	−	0.702091i	$-0.247750\pi$
$229$	1594.44	+	920.549i	0.460102	+	0.265640i	−0.251985	+	0.967731i	$0.581083\pi$
$230$	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	−0.0580009	−	0.998317i	$-0.518473\pi$
$233$	2765.48	−	1596.65i	0.777566	−	0.448928i	0.835567	+	0.549388i	$0.185139\pi$
$234$		0			0
$235$	960.915	−	1664.35i	0.266737	−	0.462002i
$236$	3172.61			0.875082
$237$		0			0
$238$	373.349	+	2300.56i	0.101683	+	0.626567i
$239$	−388.647	+	224.385i	−0.105186	+	0.0607292i	−0.551670	−	0.834062i	$-0.686009\pi$
$239$	−388.647	+	224.385i	−0.105186	+	0.0607292i	0.446484	+	0.894792i	$0.352676\pi$
$240$		0			0
$241$	−955.862	+	551.867i	−0.255488	+	0.147506i	−0.622274	−	0.782799i	$-0.713791\pi$
$241$	−955.862	+	551.867i	−0.255488	+	0.147506i	0.366787	+	0.930305i	$0.380458\pi$
$242$	1262.63	+	728.979i	0.335392	+	0.193639i
$243$		0			0
$244$		−	2413.08i		−	0.633120i
$245$	−3201.23	−	2838.60i	−0.834773	−	0.740211i
$246$		0			0
$247$	−1517.50	+	2628.38i	−0.390915	+	0.677085i
$248$	−3473.12			−0.889288
$249$		0			0
$250$			1303.48i			0.329756i
$251$	4137.13			1.04037			0.520186	−	0.854053i	$-0.325863\pi$
$251$	4137.13			1.04037			0.520186	+	0.854053i	$0.325863\pi$
$252$		0			0
$253$	−139.964			−0.0347805
$254$		−	1820.69i		−	0.449764i
$255$		0			0
$256$	−836.801			−0.204297
$257$	−806.904	+	1397.60i	−0.195849	+	0.339221i	−0.947179	−	0.320707i	$-0.896080\pi$
$257$	−806.904	+	1397.60i	−0.195849	+	0.339221i	0.751329	+	0.659927i	$0.229413\pi$
$258$		0			0
$259$	−1734.84	+	4571.32i	−0.416208	+	1.09671i
$260$		−	6639.74i		−	1.58377i
$261$		0			0
$262$	−2708.42	−	1563.71i	−0.638651	−	0.368725i
$263$	−5023.33	+	2900.22i	−1.17776	+	0.679982i	−0.955496	−	0.295004i	$-0.904679\pi$
$263$	−5023.33	+	2900.22i	−1.17776	+	0.679982i	−0.222267	+	0.974986i	$0.571346\pi$
$264$		0			0
$265$	2021.85	−	1167.31i	0.468684	−	0.270595i
$266$	280.968	−	740.351i	0.0647640	−	0.170654i
$267$		0			0
$268$	−655.566			−0.149422
$269$	1625.70	−	2815.80i	0.368479	−	0.638224i	−0.620849	−	0.783930i	$-0.713212\pi$
$269$	1625.70	−	2815.80i	0.368479	−	0.638224i	0.989328	+	0.145706i	$0.0465454\pi$
$270$		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
$275$	98.6032	+	56.9286i	0.0216218	+	0.0124834i
$276$		0			0
$277$	−2870.84	−	4972.44i	−0.622715	−	1.07857i	−0.988978	−	0.148062i	$-0.952696\pi$
$277$	−2870.84	−	4972.44i	−0.622715	−	1.07857i	0.366263	−	0.930511i	$-0.380637\pi$
$278$	−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	0.965548	−	0.260226i	$-0.0837970\pi$
$281$	5760.65	+	3325.91i	1.22296	+	0.706076i	0.257412	+	0.966302i	$0.417130\pi$
$282$		0			0
$283$		−	1604.62i		−	0.337048i	−0.985698	−	0.168524i	$-0.946100\pi$
$283$		−	1604.62i		−	0.337048i	0.985698	−	0.168524i	$-0.0539001\pi$
$284$		−	4776.46i		−	0.997995i
$285$		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
$290$	1155.76	+	2001.84i	0.234030	+	0.405351i
$291$		0			0
$292$	−4281.05	−	2471.66i	−0.857977	−	0.495353i
$293$	47.1597	+	81.6830i	0.00940307	+	0.0162866i	0.870689	−	0.491835i	$-0.163674\pi$
$293$	47.1597	+	81.6830i	0.00940307	+	0.0162866i	−0.861286	+	0.508121i	$0.830340\pi$
$294$		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
$299$	−2955.04			−0.571553
$300$		0			0
$301$	3299.55	−	535.472i	0.631838	−	0.102539i
$302$	98.5008	−	56.8695i	0.0187685	−	0.0108360i
$303$		0			0
$304$	1207.49	−	697.144i	0.227810	−	0.131526i
$305$	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	$0.867774\pi$
$308$	−436.552	−	165.674i	−0.0807625	−	0.0306498i
$309$		0			0
$310$	1466.11	−	2539.38i	0.268612	−	0.465249i
$311$	1238.22			0.225765			0.112883	−	0.993608i	$-0.463992\pi$
$311$	1238.22			0.225765			0.112883	+	0.993608i	$0.463992\pi$
$312$		0			0
$313$		−	428.122i		−	0.0773128i	−0.999253	−	0.0386564i	$-0.987692\pi$
$313$		−	428.122i		−	0.0773128i	0.999253	−	0.0386564i	$-0.0123078\pi$
$314$	892.015			0.160316
$315$		0			0
$316$	−2777.14			−0.494388
$317$		−	4285.54i		−	0.759306i	−0.925129	−	0.379653i	$-0.876043\pi$
$317$		−	4285.54i		−	0.759306i	0.925129	−	0.379653i	$-0.123957\pi$
$318$		0			0
$319$	−623.021			−0.109349
$320$	−621.931	+	1077.22i	−0.108647	+	0.188182i
$321$		0			0
$322$	761.055	−	123.509i	0.131714	−	0.0213754i
$323$			4391.57i			0.756512i
$324$		0			0
$325$	2081.80	+	1201.93i	0.355315	+	0.205141i
$326$	88.2098	−	50.9280i	0.0149862	−	0.00865227i
$327$		0			0
$328$	5388.09	−	3110.81i	0.907035	−	0.523677i
$329$	−1804.13	−	2210.67i	−0.302325	−	0.370450i
$330$		0			0
$331$	10361.8			1.72066			0.860328	−	0.509740i	$-0.170259\pi$
$331$	10361.8			1.72066			0.860328	+	0.509740i	$0.170259\pi$
$332$	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	0.929585	−	0.368607i	$-0.120165\pi$
$337$	900.566	+	1559.83i	0.145570	+	0.252134i	−0.784016	+	0.620741i	$0.786832\pi$
$338$	−3811.72	−	2200.70i	−0.613403	−	0.354148i
$339$		0			0
$340$	−4803.78	−	8320.39i	−0.766239	−	1.32717i
$341$	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
$346$		−	86.5812i		−	0.0134527i
$347$			3175.26i			0.491231i	0.969367	+	0.245615i	$0.0789901\pi$
$347$			3175.26i			0.491231i	−0.969367	+	0.245615i	$0.921010\pi$
$348$		0			0
$349$	−6434.98	−	3715.24i	−0.986981	−	0.569834i	−0.0826105	−	0.996582i	$-0.526326\pi$
$349$	−6434.98	−	3715.24i	−0.986981	−	0.569834i	−0.904370	+	0.426748i	$0.859659\pi$
$350$	−586.391	−	222.539i	−0.0895541	−	0.0339863i
$351$		0			0
$352$	317.790	+	550.428i	0.0481200	+	0.0833464i
$353$	3047.70	+	5278.77i	0.459526	+	0.795922i	0.998936	−	0.0461211i	$-0.0146860\pi$
$353$	3047.70	+	5278.77i	0.459526	+	0.795922i	−0.539410	+	0.842043i	$0.681353\pi$
$354$		0			0
$355$	7616.23	+	4397.23i	1.13867	+	0.657411i
$356$	−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	−0.918345	−	0.395781i	$-0.870474\pi$
$359$	−7038.53	+	4063.70i	−1.03476	+	0.597420i	−0.116416	+	0.993200i	$0.537141\pi$
$360$		0			0
$361$	−2683.45	+	4647.87i	−0.391231	+	0.677631i
$362$	4665.49			0.677384
$363$		0			0
$364$	−9216.85	−	3497.85i	−1.32718	−	0.503673i
$365$	7882.31	−	4550.85i	1.13035	−	0.652610i
$366$		0			0
$367$	146.504	−	84.5842i	0.0208377	−	0.0120307i	−0.489545	−	0.871978i	$-0.662837\pi$
$367$	146.504	−	84.5842i	0.0208377	−	0.0120307i	0.510383	+	0.859947i	$0.329504\pi$
$368$	1175.68	+	678.778i	0.166539	+	0.0961515i
$369$		0			0
$370$			3645.19i			0.512174i
$371$	−555.270	−	3421.55i	−0.0777040	−	0.478808i
$372$		0			0
$373$	−6832.29	+	11833.9i	−0.948424	+	1.64272i	−0.199679	+	0.979861i	$0.563990\pi$
$373$	−6832.29	+	11833.9i	−0.948424	+	1.64272i	−0.748745	+	0.662858i	$0.769343\pi$
$374$	−468.320			−0.0647494
$375$		0			0
$376$			2519.69i			0.345594i
$377$	−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	$0.396634\pi$
$380$			3264.30i			0.440672i
$381$		0			0
$382$	2983.14			0.399557
$383$	−6184.65	+	10712.1i	−0.825120	+	1.42915i	0.0767074	+	0.997054i	$0.475559\pi$
$383$	−6184.65	+	10712.1i	−0.825120	+	1.42915i	−0.901827	+	0.432096i	$0.857774\pi$
$384$		0			0
$385$	666.065	−	543.577i	0.0881709	−	0.0719564i
$386$		−	134.485i		−	0.0177335i
$387$		0			0
$388$	4099.31	+	2366.74i	0.536368	+	0.309672i
$389$	−7814.02	+	4511.43i	−1.01847	+	0.588016i	−0.913662	−	0.406476i	$-0.866758\pi$
$389$	−7814.02	+	4511.43i	−1.01847	+	0.588016i	−0.104813	+	0.994492i	$0.533424\pi$
$390$		0			0
$391$	−3703.02	+	2137.94i	−0.478950	+	0.276522i
$392$	5495.64	+	1124.50i	0.708091	+	0.144888i
$393$		0			0
$394$	654.167			0.0836458
$395$	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
$401$	−608.205	−	351.147i	−0.0757414	−	0.0437293i	0.461651	−	0.887062i	$-0.347257\pi$
$401$	−608.205	−	351.147i	−0.0757414	−	0.0437293i	−0.537392	+	0.843332i	$0.680591\pi$
$402$		0			0
$403$	8342.94	+	14450.4i	1.03124	+	1.78617i
$404$	−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
$409$			4846.97i			0.585983i	0.956115	+	0.292992i	$0.0946508\pi$
$409$			4846.97i			0.585983i	−0.956115	+	0.292992i	$0.905349\pi$
$410$			5252.68i			0.632711i
$411$		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
$416$	6709.45	+	11621.1i	0.790764	+	1.36964i
$417$		0			0
$418$	137.801	+	79.5592i	0.0161245	+	0.00930950i
$419$	2902.78	+	5027.77i	0.338449	+	0.586211i	0.984141	−	0.177387i	$-0.0567644\pi$
$419$	2902.78	+	5027.77i	0.338449	+	0.586211i	−0.645692	+	0.763598i	$0.723431\pi$
$420$		0			0
$421$	4730.66	−	8193.74i	0.547644	−	0.948547i	−0.450791	−	0.892629i	$-0.648858\pi$
$421$	4730.66	−	8193.74i	0.547644	−	0.948547i	0.998435	−	0.0559179i	$-0.0178085\pi$
$422$	−4520.55	+	2609.94i	−0.521462	+	0.301066i
$423$		0			0
$424$	−1530.46	+	2650.83i	−0.175296	+	0.303622i
$425$	3478.32			0.396996
$426$		0			0
$427$	5110.74	−	4170.88i	0.579217	−	0.472700i
$428$	−4394.25	+	2537.02i	−0.496271	+	0.286522i
$429$		0			0
$430$	2158.20	−	1246.04i	0.242041	−	0.139742i
$431$	−4423.48	−	2553.90i	−0.494365	−	0.285422i	0.232018	−	0.972711i	$-0.425467\pi$
$431$	−4423.48	−	2553.90i	−0.494365	−	0.285422i	−0.726384	+	0.687289i	$0.758800\pi$
$432$		0			0
$433$		−	15003.8i		−	1.66521i	−0.553866	−	0.832606i	$-0.686848\pi$
$433$		−	15003.8i		−	1.66521i	0.553866	−	0.832606i	$-0.313152\pi$
$434$	−2752.65	−	3372.92i	−0.304450	−	0.373054i
$435$		0			0
$436$	−622.580	+	1078.34i	−0.0683857	+	0.118448i
$437$	1452.79			0.159031
$438$		0			0
$439$		−	5551.91i		−	0.603595i	−0.953372	−	0.301797i	$-0.902413\pi$
$439$		−	5551.91i		−	0.603595i	0.953372	−	0.301797i	$-0.0975866\pi$
$440$	−759.172			−0.0822548
$441$		0			0
$442$	−9887.58			−1.06404
$443$		−	7313.10i		−	0.784325i	−0.919896	−	0.392162i	$-0.871727\pi$
$443$		−	7313.10i		−	0.784325i	0.919896	−	0.392162i	$-0.128273\pi$
$444$		0			0
$445$	1857.24			0.197846
$446$	1515.23	−	2624.46i	0.160871	−	0.278636i
$447$		0			0
$448$	1167.69	+	1430.81i	0.123143	+	0.150891i
$449$			15920.2i			1.67332i	0.547720	+	0.836662i	$0.315496\pi$
$449$			15920.2i			1.67332i	−0.547720	+	0.836662i	$0.684504\pi$
$450$		0			0
$451$	−1226.07	−	707.874i	−0.128012	−	0.0739079i
$452$	9171.53	−	5295.19i	0.954409	−	0.551028i
$453$		0			0
$454$	−4865.46	+	2809.07i	−0.502967	+	0.290388i
$455$	14062.5	−	11476.5i	1.44893	−	1.18247i
$456$		0			0
$457$	15593.6			1.59615			0.798073	−	0.602561i	$-0.205853\pi$
$457$	15593.6			1.59615			0.798073	+	0.602561i	$0.205853\pi$
$458$	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	−0.480224	−	0.877146i	$-0.659445\pi$
$461$	5142.24	−	8906.62i	0.519518	−	0.899832i	0.999743	−	0.0226865i	$-0.00722196\pi$
$462$		0			0
$463$	5144.96	+	8911.33i	0.516429	+	0.894481i	0.999818	+	0.0190753i	$0.00607223\pi$
$463$	5144.96	+	8911.33i	0.516429	+	0.894481i	−0.483389	+	0.875405i	$0.660594\pi$
$464$	5233.29	+	3021.44i	0.523598	+	0.302299i
$465$		0			0
$466$	−1767.34	−	3061.12i	−0.175688	−	0.304300i
$467$	−5970.25	−	10340.8i	−0.591585	−	1.02465i	−0.994019	−	0.109206i	$-0.965169\pi$
$467$	−5970.25	−	10340.8i	−0.591585	−	1.02465i	0.402435	−	0.915449i	$-0.368164\pi$
$468$		0			0
$469$	−1133.11	−	1388.45i	−0.111561	−	0.136700i
$470$	−1842.28	−	1063.64i	−0.180804	−	0.104387i
$471$		0			0
$472$		−	7658.66i		−	0.746861i
$473$			671.684i			0.0652940i
$474$		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
$479$	3264.09	+	5653.57i	0.311357	+	0.539286i	0.978656	−	0.205503i	$-0.0658832\pi$
$479$	3264.09	+	5653.57i	0.311357	+	0.539286i	−0.667299	+	0.744790i	$0.732550\pi$
$480$		0			0
$481$	−17964.0	−	10371.5i	−1.70288	−	0.983159i
$482$	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	$0.118362\pi$
$488$	−5825.15			−0.540353
$489$		0			0
$490$	−3142.06	+	3543.46i	−0.289681	+	0.326688i
$491$	−9629.30	+	5559.48i	−0.885059	+	0.510989i	−0.872323	−	0.488930i	$-0.837387\pi$
$491$	−9629.30	+	5559.48i	−0.885059	+	0.510989i	−0.0127359	+	0.999919i	$0.504054\pi$
$492$		0			0
$493$	−16483.2	+	9516.59i	−1.50582	+	0.869383i
$494$	2909.36	+	1679.72i	0.264977	+	0.152984i
$495$		0			0
$496$		−	7665.55i		−	0.693938i
$497$	10116.2	−	8255.87i	0.913027	−	0.745123i
$498$		0			0
$499$	4080.42	−	7067.50i	0.366062	−	0.634037i	−0.622884	−	0.782314i	$-0.714039\pi$
$499$	4080.42	−	7067.50i	0.366062	−	0.634037i	0.988946	+	0.148277i	$0.0473726\pi$
$500$	−7977.88			−0.713563
$501$		0			0
$502$		−	4579.40i		−	0.407149i
$503$	6103.08			0.541000			0.270500	−	0.962720i	$-0.412811\pi$
$503$	6103.08			0.541000			0.270500	+	0.962720i	$0.412811\pi$
$504$		0			0
$505$	7456.66			0.657064
$506$			154.927i			0.0136113i
$507$		0			0
$508$	11143.4			0.973249
$509$	166.200	−	287.867i	0.0144729	−	0.0250678i	−0.858698	−	0.512482i	$-0.828726\pi$
$509$	166.200	−	287.867i	0.0144729	−	0.0250678i	0.873171	+	0.487414i	$0.162060\pi$
$510$		0			0
$511$	−2164.76	−	13339.1i	−0.187403	−	1.15477i
$512$		−	10887.2i		−	0.939749i
$513$		0			0
$514$	1547.01	+	893.165i	0.132754	+	0.0766455i
$515$	−5603.49	+	3235.18i	−0.479455	+	0.276813i
$516$		0			0
$517$	496.547	−	286.681i	0.0422400	−	0.0243873i
$518$	5060.01	+	1920.30i	0.429197	+	0.162883i
$519$		0			0
$520$	−16028.3			−1.35171
$521$	5203.98	−	9013.56i	0.437602	−	0.757948i	−0.559902	−	0.828559i	$-0.689161\pi$
$521$	5203.98	−	9013.56i	0.437602	−	0.757948i	0.997504	+	0.0706102i	$0.0224947\pi$
$522$		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
$527$	20909.4	+	12072.0i	1.72833	+	0.997849i
$528$		0			0
$529$	−5376.24	−	9311.92i	−0.441871	−	0.765343i
$530$	−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
$535$		−	9342.38i		−	0.754965i
$536$			1582.53i			0.127528i
$537$		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	$0.834059\pi$
$542$	−1387.98	−	2404.06i	−0.109998	−	0.190522i
$543$		0			0
$544$	16815.5	+	9708.43i	1.32529	+	0.765157i
$545$	−1146.30	−	1985.45i	−0.0900956	−	0.156050i
$546$		0			0
$547$	−9099.49	+	15760.8i	−0.711272	+	1.23196i	0.253107	+	0.967438i	$0.418547\pi$
$547$	−9099.49	+	15760.8i	−0.711272	+	1.23196i	−0.964380	+	0.264522i	$0.914786\pi$
$548$	4560.09	−	2632.77i	0.355470	−	0.205231i
$549$		0			0
$550$	63.0145	−	109.144i	0.00488536	−	0.00846169i
$551$	6466.80			0.499991
$552$		0			0
$553$	−4800.16	−	5881.81i	−0.369120	−	0.452296i
$554$	−5504.01	+	3177.74i	−0.422099	+	0.243699i
$555$		0			0
$556$	9977.11	−	5760.28i	0.761014	−	0.439371i
$557$	16522.7	+	9539.40i	1.25689	+	0.725668i	0.972470	−	0.233030i	$-0.0748640\pi$
$557$	16522.7	+	9539.40i	1.25689	+	0.725668i	0.284425	+	0.958698i	$0.408197\pi$
$558$		0			0
$559$			14181.2i			1.07299i
$560$	−8231.01	+	1335.78i	−0.621114	+	0.100798i
$561$		0			0
$562$	3681.47	−	6376.49i	0.276323	−	0.478605i
$563$	−21574.7			−1.61503			−0.807516	−	0.589845i	$-0.799189\pi$
$563$	−21574.7			−1.61503			−0.807516	+	0.589845i	$0.799189\pi$
$564$		0			0
$565$			19499.1i			1.45192i
$566$	−1776.16			−0.131904
$567$		0			0
$568$	−11530.3			−0.851764
$569$			3053.95i			0.225006i	0.993651	+	0.112503i	$0.0358868\pi$
$569$			3053.95i			0.225006i	−0.993651	+	0.112503i	$0.964113\pi$
$570$		0			0
$571$	7012.51			0.513948			0.256974	−	0.966418i	$-0.417274\pi$
$571$	7012.51			0.513948			0.256974	+	0.966418i	$0.417274\pi$
$572$	990.456	−	1715.52i	0.0724005	−	0.125401i
$573$		0			0
$574$	7291.43	+	2767.14i	0.530206	+	0.201216i
$575$		−	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	$0.940151\pi$
$578$	−7680.69	+	4434.45i	−0.552724	+	0.319115i
$579$		0			0
$580$	−12252.2	+	7073.79i	−0.877144	+	0.506419i
$581$	11752.4	−	1907.25i	0.839195	−	0.136190i
$582$		0			0
$583$	696.518			0.0494800
$584$	−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	$-0.681308\pi$
$587$	6537.09	−	11322.6i	0.459650	−	0.796137i	0.998942	+	0.0459813i	$0.0146415\pi$
$588$		0			0
$589$	−4101.65	−	7104.27i	−0.286936	−	0.496988i
$590$	5599.65	+	3232.96i	0.390735	+	0.225591i
$591$		0			0
$592$	4764.71	+	8252.71i	0.330791	+	0.572947i
$593$	−555.269	−	961.755i	−0.0384523	−	0.0666013i	0.846159	−	0.532931i	$-0.178909\pi$
$593$	−555.269	−	961.755i	−0.0384523	−	0.0666013i	−0.884611	+	0.466330i	$0.845576\pi$
$594$		0			0
$595$	9318.94	−	24555.5i	0.642083	−	1.69189i
$596$	−5109.74	−	2950.11i	−0.351179	−	0.202754i
$597$		0			0
$598$			3270.94i			0.223677i
$599$		−	19490.2i		−	1.32946i	−0.747083	−	0.664731i	$-0.768546\pi$
$599$		−	19490.2i		−	1.32946i	0.747083	−	0.664731i	$-0.231454\pi$
$600$		0			0
$601$	−18365.6	−	10603.4i	−1.24650	−	0.719669i	−0.276093	−	0.961131i	$-0.589040\pi$
$601$	−18365.6	−	10603.4i	−1.24650	−	0.719669i	−0.970410	+	0.241462i	$0.922373\pi$
$602$	−592.716	−	3652.29i	−0.0401284	−	0.247269i
$603$		0			0
$604$	348.067	+	602.871i	0.0234481	+	0.0406133i
$605$	−8214.92	−	14228.7i	−0.552039	−	0.956160i
$606$		0			0
$607$	−5721.66	−	3303.40i	−0.382595	−	0.220891i	0.296352	−	0.955079i	$-0.404230\pi$
$607$	−5721.66	−	3303.40i	−0.382595	−	0.220891i	−0.678947	+	0.734188i	$0.737563\pi$
$608$	−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	$0.259894\pi$
$614$	4805.66			0.315864
$615$		0			0
$616$	−399.936	+	1053.83i	−0.0261589	+	0.0689288i
$617$	10903.4	−	6295.11i	0.711436	−	0.410748i	−0.100156	−	0.994972i	$-0.531934\pi$
$617$	10903.4	−	6295.11i	0.711436	−	0.410748i	0.811593	+	0.584224i	$0.198601\pi$
$618$		0			0
$619$	12536.5	−	7237.96i	0.814031	−	0.469981i	−0.0343227	−	0.999411i	$-0.510927\pi$
$619$	12536.5	−	7237.96i	0.814031	−	0.469981i	0.848354	+	0.529430i	$0.177594\pi$
$620$	15542.2	+	8973.29i	1.00676	+	0.581252i
$621$		0			0
$622$		−	1370.59i		−	0.0883531i
$623$	978.404	−	2578.10i	0.0629196	−	0.165793i
$624$		0			0
$625$	9256.66	−	16033.0i	0.592426	−	1.02611i
$626$	−473.890			−0.0302563
$627$		0			0
$628$			5459.54i			0.346910i
$629$	−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	$0.452162\pi$
$632$			6704.01i			0.421948i
$633$		0			0
$634$	−4743.68			−0.297154
$635$	−10258.7	+	17768.6i	−0.641110	+	1.11043i
$636$		0			0
$637$	−8522.65	−	25566.5i	−0.530110	−	1.59024i
$638$			689.624i			0.0427938i
$639$		0			0
$640$	15952.0	+	9209.91i	0.985249	+	0.568834i
$641$	−14622.2	+	8442.16i	−0.901004	+	0.520195i	−0.877526	−	0.479529i	$-0.840807\pi$
$641$	−14622.2	+	8442.16i	−0.901004	+	0.520195i	−0.0234785	+	0.999724i	$0.507474\pi$
$642$		0			0
$643$	−7268.42	+	4196.42i	−0.445783	+	0.257373i	−0.706048	−	0.708164i	$-0.749524\pi$
$643$	−7268.42	+	4196.42i	−0.445783	+	0.257373i	0.260265	+	0.965537i	$0.416190\pi$
$644$	755.931	+	4658.01i	0.0462544	+	0.285018i
$645$		0			0
$646$	4861.04			0.296061
$647$	−1835.83	+	3179.75i	−0.111552	+	0.193213i	−0.916396	−	0.400273i	$-0.868915\pi$
$647$	−1835.83	+	3179.75i	−0.111552	+	0.193213i	0.804844	+	0.593486i	$0.202249\pi$
$648$		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
$653$	5712.79	+	3298.28i	0.342357	+	0.197660i	0.661314	−	0.750109i	$-0.269999\pi$
$653$	5712.79	+	3298.28i	0.342357	+	0.197660i	−0.318957	+	0.947769i	$0.603333\pi$
$654$		0			0
$655$	17621.5	+	30521.3i	1.05119	+	1.82071i
$656$	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	0.973811	−	0.227358i	$-0.0730087\pi$
$659$	21380.3	+	12343.9i	1.26382	+	0.729666i	0.290008	+	0.957024i	$0.406342\pi$
$660$		0			0
$661$		−	443.450i		−	0.0260941i	−0.999915	−	0.0130471i	$-0.995847\pi$
$661$		−	443.450i		−	0.0260941i	0.999915	−	0.0130471i	$-0.00415313\pi$
$662$		−	11469.5i		−	0.673378i
$663$		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
$668$	13005.0	+	22525.4i	0.753262	+	1.30469i
$669$		0			0
$670$	−1157.07	−	668.036i	−0.0667188	−	0.0385201i
$671$	662.764	+	1147.94i	0.0381307	+	0.0660444i
$672$		0			0
$673$	−12123.6	+	20998.6i	−0.694397	+	1.20273i	0.275986	+	0.961162i	$0.410996\pi$
$673$	−12123.6	+	20998.6i	−0.694397	+	1.20273i	−0.970383	+	0.241570i	$0.922338\pi$
$674$	1726.58	−	996.840i	0.0986725	−	0.0569686i
$675$		0			0
$676$	13469.3	−	23329.5i	0.766345	−	1.32735i
$677$	25277.0			1.43497			0.717485	−	0.696574i	$-0.245293\pi$
$677$	25277.0			1.43497			0.717485	+	0.696574i	$0.245293\pi$
$678$		0			0
$679$	2072.86	+	12772.8i	0.117156	+	0.721910i
$680$	−20085.4	+	11596.3i	−1.13270	+	0.653967i
$681$		0			0
$682$	757.604	−	437.403i	0.0425369	−	0.0245587i
$683$	−15251.8	−	8805.63i	−0.854457	−	0.493321i	0.00769531	−	0.999970i	$-0.497550\pi$
$683$	−15251.8	−	8805.63i	−0.854457	−	0.493321i	−0.862152	+	0.506650i	$0.830884\pi$
$684$		0			0
$685$			9694.97i			0.540768i
$686$	3263.54	+	6228.32i	0.181637	+	0.346645i
$687$		0			0
$688$	3257.44	−	5642.06i	0.180507	−	0.312647i
$689$	14705.5			0.813112
$690$		0			0
$691$		−	29169.4i		−	1.60587i	−0.596068	−	0.802934i	$-0.703271\pi$
$691$		−	29169.4i		−	1.60587i	0.596068	−	0.802934i	$-0.296729\pi$
$692$	529.917			0.0291104
$693$		0			0
$694$	3514.71			0.192243
$695$			21211.8i			1.15771i
$696$		0			0
$697$	−43250.9			−2.35042
$698$	−4112.41	+	7122.90i	−0.223004	+	0.386255i
$699$		0			0
$700$	1362.04	−	3588.99i	0.0735434	−	0.193787i
$701$		−	21991.9i		−	1.18491i	−0.805603	−	0.592456i	$-0.798159\pi$
$701$		−	21991.9i		−	1.18491i	0.805603	−	0.592456i	$-0.201841\pi$
$702$		0			0
$703$	8831.65	+	5098.95i	0.473815	+	0.273557i
$704$	−321.379	+	185.548i	−0.0172052	+	0.00993340i
$705$		0			0
$706$	5843.09	−	3373.51i	0.311484	−	0.179835i
$707$	3928.21	−	10350.9i	0.208961	−	0.550614i
$708$		0			0
$709$	17360.1			0.919566			0.459783	−	0.888031i	$-0.347927\pi$
$709$	17360.1			0.919566			0.459783	+	0.888031i	$0.347927\pi$
$710$	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
$716$	−1443.70	−	833.522i	−0.0753543	−	0.0435058i
$717$		0			0
$718$	4498.12	+	7790.97i	0.233800	+	0.404953i
$719$	−12003.3	−	20790.4i	−0.622599	−	1.07837i	−0.989000	−	0.147916i	$-0.952744\pi$
$719$	−12003.3	−	20790.4i	−0.622599	−	1.07837i	0.366401	−	0.930457i	$-0.380590\pi$
$720$		0			0
$721$	1538.91	+	9482.71i	0.0794898	+	0.489812i
$722$	5144.75	+	2970.32i	0.265191	+	0.153108i
$723$		0			0
$724$			28555.0i			1.46580i
$725$		−	5121.99i		−	0.262381i
$726$		0			0
$727$	16384.0	+	9459.32i	0.835831	+	0.482568i	0.855845	−	0.517232i	$-0.173038\pi$
$727$	16384.0	+	9459.32i	0.835831	+	0.482568i	−0.0200136	+	0.999800i	$0.506371\pi$
$728$	−8443.79	+	22249.4i	−0.429873	+	1.13272i
$729$		0			0
$730$	−5037.36	−	8724.96i	−0.255398	−	0.442363i
$731$	10259.9	+	17770.7i	0.519120	+	0.899143i
$732$		0			0
$733$	29766.7	+	17185.8i	1.49994	+	0.865993i	1.00000		6.42512e-5i	$-2.04518e-5\pi$
$733$	29766.7	+	17185.8i	1.49994	+	0.865993i	0.499944	+	0.866058i	$0.333354\pi$
$734$	−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	$0.982988\pi$
$740$	−22310.2			−1.10830
$741$		0			0
$742$	−3787.32	+	614.630i	−0.187381	+	0.0304094i
$743$	−32847.1	+	18964.3i	−1.62186	+	0.936382i	−0.635439	+	0.772151i	$0.719181\pi$
$743$	−32847.1	+	18964.3i	−1.62186	+	0.936382i	−0.986422	+	0.164231i	$0.947486\pi$
$744$		0			0
$745$	9408.10	−	5431.77i	0.462666	−	0.267120i
$746$	13098.9	+	7562.68i	0.642877	+	0.371165i
$747$		0			0
$748$		−	2866.34i		−	0.140112i
$749$	−12968.5	−	4921.62i	−0.632654	−	0.240096i
$750$		0			0
$751$	7380.95	−	12784.2i	0.358635	−	0.621173i	−0.629098	−	0.777326i	$-0.716576\pi$
$751$	7380.95	−	12784.2i	0.358635	−	0.621173i	0.987733	+	0.156152i	$0.0499091\pi$
$752$	−5561.23			−0.269677
$753$		0			0
$754$			14559.9i			0.703238i
$755$	−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	$0.210415\pi$
$758$		−	5211.54i		−	0.249725i
$759$		0			0
$760$	7880.01			0.376103
$761$	12619.0	−	21856.7i	0.601099	−	1.04113i	−0.391556	−	0.920154i	$-0.628063\pi$
$761$	12619.0	−	21856.7i	0.601099	−	1.04113i	0.992655	−	0.120980i	$-0.0386037\pi$
$762$		0			0
$763$	−3359.95	+	545.274i	−0.159421	+	0.0258719i
$764$			18258.2i			0.864605i
$765$		0			0
$766$	11857.3	+	6845.81i	0.559297	+	0.322910i
$767$	−31864.9	+	18397.2i	−1.50010	+	0.866081i
$768$		0			0
$769$	2558.83	−	1477.34i	0.119992	−	0.0692775i	−0.438803	−	0.898583i	$-0.644597\pi$
$769$	2558.83	−	1477.34i	0.119992	−	0.0692775i	0.558795	+	0.829306i	$0.311264\pi$
$770$	−601.687	−	737.269i	−0.0281601	−	0.0345056i
$771$		0			0
$772$	823.113			0.0383737
$773$	15778.4	−	27329.0i	0.734165	−	1.27161i	−0.220924	−	0.975291i	$-0.570907\pi$
$773$	15778.4	−	27329.0i	0.734165	−	1.27161i	0.955089	−	0.296319i	$-0.0957593\pi$
$774$		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
$779$	12726.3	+	7347.55i	0.585325	+	0.337937i
$780$		0			0
$781$	1311.88	+	2272.24i	0.0601059	+	0.104106i
$782$	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
$787$		−	10085.3i		−	0.456801i	−0.973567	−	0.228401i	$-0.926650\pi$
$787$		−	10085.3i		−	0.456801i	0.973567	−	0.228401i	$-0.0733496\pi$
$788$			4003.80i			0.181002i
$789$		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
$794$	−3653.47	−	6327.99i	−0.163296	−	0.282836i
$795$		0			0
$796$	700.983	+	404.713i	0.0312132	+	0.0180209i
$797$	−17563.1	−	30420.2i	−0.780573	−	1.35199i	−0.931609	−	0.363463i	$-0.881594\pi$
$797$	−17563.1	−	30420.2i	−0.780573	−	1.35199i	0.151036	−	0.988528i	$-0.451739\pi$
$798$		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
$803$	2715.42			0.119334
$804$		0			0
$805$	−8123.27	−	3082.83i	−0.355662	−	0.134976i
$806$	15995.2	−	9234.82i	0.699015	−	0.403577i
$807$		0			0
$808$	−8466.58	+	4888.18i	−0.368630	+	0.212829i
$809$	17101.2	+	9873.35i	0.743195	+	0.429084i	0.823230	−	0.567708i	$-0.192170\pi$
$809$	17101.2	+	9873.35i	0.743195	+	0.429084i	−0.0800351	+	0.996792i	$0.525503\pi$
$810$		0			0
$811$		−	32458.3i		−	1.40538i	−0.711494	−	0.702692i	$-0.751981\pi$
$811$		−	32458.3i		−	1.40538i	0.711494	−	0.702692i	$-0.248019\pi$
$812$	3364.87	+	20734.2i	0.145423	+	0.896092i
$813$		0			0
$814$	−543.756	+	941.814i	−0.0234136	+	0.0405535i
$815$	−1147.82			−0.0493330
$816$		0			0
$817$		−	6971.91i		−	0.298551i
$818$	5365.13			0.229324
$819$		0			0
$820$	−32148.9			−1.36913
$821$			35660.5i			1.51591i	0.652307	+	0.757955i	$0.273801\pi$
$821$			35660.5i			1.51591i	−0.652307	+	0.757955i	$0.726199\pi$
$822$		0			0
$823$	950.762			0.0402691			0.0201346	−	0.999797i	$-0.493591\pi$
$823$	950.762			0.0402691			0.0201346	+	0.999797i	$0.493591\pi$
$824$	4241.61	−	7346.69i	0.179325	−	0.310599i
$825$		0			0
$826$	7437.71	−	6069.93i	0.313306	−	0.255690i
$827$		−	18206.6i		−	0.765545i	−0.923843	−	0.382772i	$-0.874969\pi$
$827$		−	18206.6i		−	0.765545i	0.923843	−	0.382772i	$-0.125031\pi$
$828$		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	$0.988210\pi$
$830$	7687.11	−	4438.15i	0.321474	−	0.185603i
$831$		0			0
$832$	−6785.23	+	3917.45i	−0.282735	+	0.163237i
$833$	−29177.0	−	25871.9i	−1.21359	−	1.07612i
$834$		0			0
$835$	−47890.0			−1.98479
$836$	−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	$-0.923365\pi$
$839$	−6782.34	+	11747.4i	−0.279085	+	0.483390i	0.692072	+	0.721828i	$0.256698\pi$
$840$		0			0
$841$	1819.14	+	3150.84i	0.0745884	+	0.129191i
$842$	−9069.68	−	5236.38i	−0.371213	−	0.214320i
$843$		0			0
$844$	−15974.0	−	27667.9i	−0.651480	−	1.12840i
$845$	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
$850$		−	3850.16i		−	0.155364i
$851$			9929.25i			0.399965i
$852$		0			0
$853$	−658.326	−	380.085i	−0.0264252	−	0.0152566i	0.486729	−	0.873553i	$-0.338190\pi$
$853$	−658.326	−	380.085i	−0.0264252	−	0.0152566i	−0.513154	+	0.858296i	$0.671523\pi$
$854$	−4616.76	−	5657.09i	−0.184991	−	0.226676i
$855$		0			0
$856$	6124.35	+	10607.7i	0.244540	+	0.423555i
$857$	13159.3	+	22792.6i	0.524519	+	0.908494i	0.999592	+	0.0285474i	$0.00908817\pi$
$857$	13159.3	+	22792.6i	0.524519	+	0.908494i	−0.475073	+	0.879946i	$0.657579\pi$
$858$		0			0
$859$	−15865.8	−	9160.13i	−0.630192	−	0.363841i	0.150635	−	0.988589i	$-0.451868\pi$
$859$	−15865.8	−	9160.13i	−0.630192	−	0.363841i	−0.780826	+	0.624748i	$0.785202\pi$
$860$	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	−0.713000	−	0.701164i	$-0.752664\pi$
$863$	−11719.7	+	6766.36i	−0.462274	+	0.266894i	0.250726	+	0.968058i	$0.419331\pi$
$864$		0			0
$865$	−487.844	+	844.971i	−0.0191760	+	0.0332137i
$866$	−16607.8			−0.651680
$867$		0			0
$868$	20643.8	−	16847.5i	0.807256	−	0.658803i
$869$	1321.13	−	762.757i	0.0515724	−	0.0297753i
$870$		0			0
$871$	6584.33	−	3801.47i	0.256144	−	0.147885i
$872$	2603.11	+	1502.90i	0.101092	+	0.0583655i
$873$		0			0
$874$		−	1608.10i		−	0.0622365i
$875$	−13789.4	−	16896.6i	−0.532761	−	0.652812i
$876$		0			0
$877$	−7203.70	+	12477.2i	−0.277368	+	0.480415i	−0.970730	−	0.240174i	$-0.922795\pi$
$877$	−7203.70	+	12477.2i	−0.277368	+	0.480415i	0.693362	+	0.720589i	$0.256129\pi$
$878$	−6145.42			−0.236216
$879$		0			0
$880$		−	1675.57i		−	0.0641859i
$881$	−10256.6			−0.392229			−0.196115	−	0.980581i	$-0.562832\pi$
$881$	−10256.6			−0.392229			−0.196115	+	0.980581i	$0.562832\pi$
$882$		0			0
$883$	−41832.5			−1.59431			−0.797155	−	0.603774i	$-0.793663\pi$
$883$	−41832.5			−1.59431			−0.797155	+	0.603774i	$0.793663\pi$
$884$		−	60516.6i		−	2.30248i
$885$		0			0
$886$	−8094.90			−0.306945
$887$	−3961.65	+	6861.78i	−0.149965	+	0.259747i	−0.931214	−	0.364472i	$-0.881250\pi$
$887$	−3961.65	+	6861.78i	−0.149965	+	0.259747i	0.781249	+	0.624219i	$0.214583\pi$
$888$		0			0
$889$	19260.9	+	23601.1i	0.726648	+	0.890388i
$890$		−	2055.78i		−	0.0774270i
$891$		0			0
$892$	16062.9	+	9273.92i	0.602944	+	0.348110i
$893$	−5154.03	+	2975.68i	−0.193139	+	0.111509i
$894$		0			0
$895$	2658.16	−	1534.69i	0.0992765	−	0.0573173i
$896$	21188.2	−	17291.7i	0.790009	−	0.644728i
$897$		0			0
$898$	17622.2			0.654854
$899$	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
$905$	−45531.9	−	26287.9i	−1.67241	−	0.965567i
$906$		0			0
$907$	−11092.5	−	19212.7i	−0.406085	−	0.703359i	0.588362	−	0.808597i	$-0.299773\pi$
$907$	−11092.5	−	19212.7i	−0.406085	−	0.703359i	−0.994447	+	0.105238i	$0.966440\pi$
$908$	−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	0.954593	−	0.297913i	$-0.0962904\pi$
$911$	32277.9	+	18635.6i	1.17389	+	0.677746i	0.219297	+	0.975658i	$0.429624\pi$
$912$		0			0
$913$			2392.42i			0.0867223i
$914$		−	17260.6i		−	0.624651i
$915$		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	$0.909361\pi$
$920$	3836.21	+	6644.51i	0.137474	+	0.238112i
$921$		0			0
$922$	−9858.77	−	5691.96i	−0.352149	−	0.203313i
$923$	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
$929$	−14754.4			−0.521073			−0.260537	−	0.965464i	$-0.583899\pi$
$929$	−14754.4			−0.521073			−0.260537	+	0.965464i	$0.583899\pi$
$930$		0			0
$931$	4190.00	+	12569.3i	0.147499	+	0.442473i
$932$	18735.5	−	10816.9i	0.658478	−	0.380173i
$933$		0			0
$934$	−11446.2	+	6608.49i	−0.400998	+	0.231516i
$935$	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	$-0.0892076\pi$
$938$	−1536.88	+	1254.25i	−0.0534976	+	0.0436595i
$939$		0			0
$940$	6509.97	−	11275.6i	0.225885	−	0.391244i
$941$	−45967.7			−1.59246			−0.796229	−	0.604996i	$-0.793175\pi$
$941$	−45967.7			−1.59246			−0.796229	+	0.604996i	$0.793175\pi$
$942$		0			0
$943$			14308.0i			0.494095i
$944$	16903.5			0.582798
$945$		0			0
$946$	743.490			0.0255528
$947$		−	41679.5i		−	1.43020i	−0.699021	−	0.715101i	$-0.746381\pi$
$947$		−	41679.5i		−	1.43020i	0.699021	−	0.715101i	$-0.253619\pi$
$948$		0			0
$949$	57330.3			1.96103
$950$	−654.074	+	1132.89i	−0.0223379	+	0.0386903i
$951$		0			0
$952$	5516.14	+	33990.2i	0.187793	+	1.15717i
$953$			8368.68i			0.284458i	0.989834	+	0.142229i	$0.0454269\pi$
$953$			8368.68i			0.284458i	−0.989834	+	0.142229i	$0.954573\pi$
$954$		0			0
$955$	−29113.3	−	16808.6i	−0.986477	−	0.569543i
$956$	−2632.99	+	1520.16i	−0.0890763	+	0.0514282i
$957$		0			0
$958$	6257.95	−	3613.03i	0.211049	−	0.121849i
$959$	13457.9	+	5107.36i	0.453159	+	0.171976i
$960$		0			0
$961$	−15309.3			−0.513891
$962$	−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	0.991052	−	0.133477i	$-0.0426142\pi$
$967$	11424.7	+	19788.2i	0.379932	+	0.658061i	−0.611120	+	0.791538i	$0.709281\pi$
$968$	18655.1	+	10770.5i	0.619417	+	0.357621i
$969$		0			0
$970$	4823.51	+	8354.56i	0.159663	+	0.276545i
$971$	−3871.68	−	6705.94i	−0.127959	−	0.221631i	0.794927	−	0.606705i	$-0.207509\pi$
$971$	−3871.68	−	6705.94i	−0.127959	−	0.221631i	−0.922886	+	0.385074i	$0.874176\pi$
$972$		0			0
$973$	29444.8	+	11174.5i	0.970152	+	0.368178i
$974$	−3114.83	−	1798.35i	−0.102470	−	0.0591609i
$975$		0			0
$976$		−	12856.7i		−	0.421653i
$977$		−	12127.3i		−	0.397119i	−0.980089	−	0.198560i	$-0.936374\pi$
$977$		−	12127.3i		−	0.397119i	0.980089	−	0.198560i	$-0.0636263\pi$
$978$		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
$983$	−17612.4	−	30505.6i	−0.571465	−	0.989806i	−0.996416	−	0.0845894i	$-0.973042\pi$
$983$	−17612.4	−	30505.6i	−0.571465	−	0.989806i	0.424951	−	0.905216i	$-0.360291\pi$
$984$		0			0
$985$	−6384.21	−	3685.92i	−0.206515	−	0.119232i
$986$	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	$0.142864\pi$
$992$	−36270.0			−1.16086
$993$		0			0
$994$	−9138.45	−	11197.7i	−0.291604	−	0.357313i
$995$	−1290.66	+	745.161i	−0.0411222	+	0.0237419i
$996$		0			0
$997$	−2467.95	+	1424.87i	−0.0783961	+	0.0452620i	−0.538686	−	0.842507i	$-0.681079\pi$
$997$	−2467.95	+	1424.87i	−0.0783961	+	0.0452620i	0.460290	+	0.887769i	$0.347746\pi$
$998$	−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.i.a.143.9		44
3.2	odd	2		63.4.i.a.38.14	yes	44
7.5	odd	6		189.4.s.a.89.9		44
9.4	even	3		63.4.s.a.59.14	yes	44
9.5	odd	6		189.4.s.a.17.9		44
21.5	even	6		63.4.s.a.47.14	yes	44
63.5	even	6	inner	189.4.i.a.152.14		44
63.40	odd	6		63.4.i.a.5.9	✓	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.4.i.a.5.9	✓	44	63.40	odd	6
63.4.i.a.38.14	yes	44	3.2	odd	2
63.4.s.a.47.14	yes	44	21.5	even	6
63.4.s.a.59.14	yes	44	9.4	even	3
189.4.i.a.143.9		44	1.1	even	1	trivial
189.4.i.a.152.14		44	63.5	even	6	inner
189.4.s.a.17.9		44	9.5	odd	6
189.4.s.a.89.9		44	7.5	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.i (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-1.10690i q^{2} +6.77476 q^{4} +(-6.23688 + 10.8026i) q^{5} +(11.7098 + 14.3485i) q^{7} -16.3542i q^{8} +O(q^{10})\)	\(q-1.10690i q^{2} +6.77476 q^{4} +(-6.23688 + 10.8026i) q^{5} +(11.7098 + 14.3485i) q^{7} -16.3542i q^{8} +(11.9574 + 6.90363i) q^{10} +(-3.22287 + 1.86072i) q^{11} +(-68.0440 + 39.2852i) q^{13} +(15.8824 - 12.9617i) q^{14} +36.0955 q^{16} +(-56.8448 + 98.4582i) q^{17} +(33.4526 - 19.3138i) q^{19} +(-42.2534 + 73.1851i) q^{20} +(2.05964 + 3.56741i) q^{22} +(32.5713 + 18.8050i) q^{23} +(-15.2974 - 26.4959i) q^{25} +(43.4849 + 75.3181i) q^{26} +(79.3314 + 97.2077i) q^{28} +(144.984 + 83.7067i) q^{29} -212.368i q^{31} -170.788i q^{32} +(108.984 + 62.9218i) q^{34} +(-228.034 + 37.0068i) q^{35} +(132.003 + 228.635i) q^{37} +(-21.3786 - 37.0288i) q^{38} +(176.668 + 101.999i) q^{40} +(190.215 + 329.461i) q^{41} +(90.2450 - 156.309i) q^{43} +(-21.8342 + 12.6060i) q^{44} +(20.8154 - 36.0533i) q^{46} -154.070 q^{47} +(-68.7592 + 336.037i) q^{49} +(-29.3284 + 16.9328i) q^{50} +(-460.982 + 266.148i) q^{52} +(-162.088 - 93.5816i) q^{53} -46.4205i q^{55} +(234.659 - 191.506i) q^{56} +(92.6553 - 160.484i) q^{58} +468.298 q^{59} -356.186i q^{61} -235.071 q^{62} +99.7183 q^{64} -980.069i q^{65} -96.7659 q^{67} +(-385.110 + 667.031i) q^{68} +(40.9629 + 252.412i) q^{70} -705.036i q^{71} +(-631.911 - 364.834i) q^{73} +(253.077 - 146.114i) q^{74} +(226.633 - 130.847i) q^{76} +(-64.4379 - 24.4546i) q^{77} -409.925 q^{79} +(-225.124 + 389.926i) q^{80} +(364.682 - 210.549i) q^{82} +(321.436 - 556.744i) q^{83} +(-709.069 - 1228.14i) q^{85} +(-173.019 - 99.8925i) q^{86} +(30.4307 + 52.7076i) q^{88} +(-74.4458 - 128.944i) q^{89} +(-1360.47 - 516.306i) q^{91} +(220.663 + 127.400i) q^{92} +170.540i q^{94} +481.833i q^{95} +(605.085 + 349.346i) q^{97} +(371.961 + 76.1098i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - 162 q^{4} + 3 q^{5} + 5 q^{7}+O(q^{10}) \) 44 * q - 162 * q^4 + 3 * q^5 + 5 * q^7	\( 44 q - 162 q^{4} + 3 q^{5} + 5 q^{7} - 6 q^{10} - 9 q^{11} - 36 q^{13} - 54 q^{14} + 526 q^{16} + 72 q^{17} - 6 q^{19} - 24 q^{20} + 14 q^{22} + 285 q^{23} - 349 q^{25} + 96 q^{26} - 156 q^{28} + 132 q^{29} + 24 q^{34} - 765 q^{35} + 82 q^{37} + 873 q^{38} + 420 q^{40} - 618 q^{41} + 82 q^{43} - 603 q^{44} + 266 q^{46} + 402 q^{47} - 79 q^{49} + 1845 q^{50} + 189 q^{52} - 564 q^{53} - 66 q^{56} + 269 q^{58} - 1494 q^{59} + 2904 q^{62} - 1144 q^{64} - 590 q^{67} - 3504 q^{68} - 105 q^{70} - 6 q^{73} - 1515 q^{74} - 144 q^{76} + 4443 q^{77} + 1102 q^{79} + 4239 q^{80} + 18 q^{82} - 1830 q^{83} - 237 q^{85} - 1209 q^{86} - 623 q^{88} - 4266 q^{89} - 1140 q^{91} - 7896 q^{92} - 792 q^{97} - 5667 q^{98}+O(q^{100}) \) 44 * q - 162 * q^4 + 3 * q^5 + 5 * q^7 - 6 * q^10 - 9 * q^11 - 36 * q^13 - 54 * q^14 + 526 * q^16 + 72 * q^17 - 6 * q^19 - 24 * q^20 + 14 * q^22 + 285 * q^23 - 349 * q^25 + 96 * q^26 - 156 * q^28 + 132 * q^29 + 24 * q^34 - 765 * q^35 + 82 * q^37 + 873 * q^38 + 420 * q^40 - 618 * q^41 + 82 * q^43 - 603 * q^44 + 266 * q^46 + 402 * q^47 - 79 * q^49 + 1845 * q^50 + 189 * q^52 - 564 * q^53 - 66 * q^56 + 269 * q^58 - 1494 * q^59 + 2904 * q^62 - 1144 * q^64 - 590 * q^67 - 3504 * q^68 - 105 * q^70 - 6 * q^73 - 1515 * q^74 - 144 * q^76 + 4443 * q^77 + 1102 * q^79 + 4239 * q^80 + 18 * q^82 - 1830 * q^83 - 237 * q^85 - 1209 * q^86 - 623 * q^88 - 4266 * q^89 - 1140 * q^91 - 7896 * q^92 - 792 * q^97 - 5667 * q^98

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