LMFDB - Embedded newform 189.3.k.a.10.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [189,3,Mod(10,189)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([2, 1]))

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

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

chi := DirichletCharacter("189.10");

S:= CuspForms(chi, 3);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.14987699641$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			10.11
Character	$\chi$	$=$	189.10
Dual form			189.3.k.a.19.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.12025 - 1.94033i) q^{2} +(-0.509909 - 0.883189i) q^{4} -1.93444i q^{5} +(3.87064 - 5.83251i) q^{7} +6.67708 q^{8} +O(q^{10})$	\(q+(1.12025 - 1.94033i) q^{2} +(-0.509909 - 0.883189i) q^{4} -1.93444i q^{5} +(3.87064 - 5.83251i) q^{7} +6.67708 q^{8} +(-3.75345 - 2.16706i) q^{10} +0.372337 q^{11} +(-5.01827 - 2.89730i) q^{13} +(-6.98089 - 14.0442i) q^{14} +(9.51962 - 16.4885i) q^{16} +(-9.96576 - 5.75374i) q^{17} +(18.2323 - 10.5264i) q^{19} +(-1.70848 + 0.986391i) q^{20} +(0.417109 - 0.722455i) q^{22} -27.2835 q^{23} +21.2579 q^{25} +(-11.2434 + 6.49139i) q^{26} +(-7.12488 - 0.444454i) q^{28} +(20.1404 + 34.8842i) q^{29} +(-42.2746 + 24.4073i) q^{31} +(-7.97450 - 13.8122i) q^{32} +(-22.3282 + 12.8912i) q^{34} +(-11.2827 - 7.48753i) q^{35} +(14.7691 + 25.5809i) q^{37} -47.1687i q^{38} -12.9164i q^{40} +(19.6397 + 11.3390i) q^{41} +(10.7407 + 18.6035i) q^{43} +(-0.189858 - 0.328844i) q^{44} +(-30.5642 + 52.9388i) q^{46} +(46.1622 + 26.6518i) q^{47} +(-19.0363 - 45.1511i) q^{49} +(23.8141 - 41.2473i) q^{50} +5.90944i q^{52} +(-43.7300 + 75.7426i) q^{53} -0.720265i q^{55} +(25.8446 - 38.9441i) q^{56} +90.2490 q^{58} +(7.99438 - 4.61556i) q^{59} +(-61.0848 - 35.2673i) q^{61} +109.369i q^{62} +40.4233 q^{64} +(-5.60467 + 9.70757i) q^{65} +(37.7720 + 65.4230i) q^{67} +11.7355i q^{68} +(-27.1676 + 13.5041i) q^{70} +97.4729 q^{71} +(-75.3269 - 43.4900i) q^{73} +66.1804 q^{74} +(-18.5936 - 10.7350i) q^{76} +(1.44118 - 2.17166i) q^{77} +(23.5997 - 40.8759i) q^{79} +(-31.8960 - 18.4152i) q^{80} +(44.0025 - 25.4049i) q^{82} +(-81.1770 + 46.8676i) q^{83} +(-11.1303 + 19.2782i) q^{85} +48.1291 q^{86} +2.48612 q^{88} +(25.6803 - 14.8266i) q^{89} +(-36.3225 + 18.0547i) q^{91} +(13.9121 + 24.0965i) q^{92} +(103.426 - 59.7132i) q^{94} +(-20.3627 - 35.2693i) q^{95} +(-122.538 + 70.7471i) q^{97} +(-108.933 - 13.6437i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - q^{2} - 23 q^{4} + 16 q^{8}+O(q^{10}) $ 28 * q - q^2 - 23 * q^4 + 16 * q^8	$ 28 q - q^{2} - 23 q^{4} + 16 q^{8} - 6 q^{10} + 14 q^{11} + 15 q^{13} + 11 q^{14} - 27 q^{16} + 33 q^{17} - 6 q^{19} - 108 q^{20} - 10 q^{22} + 68 q^{23} - 62 q^{25} - 54 q^{26} - 16 q^{28} - 70 q^{29} + 45 q^{31} - 153 q^{32} + 12 q^{34} - 18 q^{35} + 9 q^{37} + 234 q^{41} + 30 q^{43} - 51 q^{44} - 22 q^{46} + 111 q^{47} + 34 q^{49} - 241 q^{50} - 148 q^{53} + 412 q^{56} - 34 q^{58} - 42 q^{59} + 120 q^{61} - 48 q^{64} - 114 q^{65} - 34 q^{67} + 264 q^{70} + 350 q^{71} - 6 q^{73} + 718 q^{74} + 72 q^{76} + 32 q^{77} - 82 q^{79} + 609 q^{80} - 18 q^{82} - 738 q^{83} + 3 q^{85} + 34 q^{86} - 50 q^{88} - 21 q^{89} + 39 q^{91} - 288 q^{92} - 3 q^{94} - 507 q^{95} - 57 q^{97} - 811 q^{98}+O(q^{100}) $ 28 * q - q^2 - 23 * q^4 + 16 * q^8 - 6 * q^10 + 14 * q^11 + 15 * q^13 + 11 * q^14 - 27 * q^16 + 33 * q^17 - 6 * q^19 - 108 * q^20 - 10 * q^22 + 68 * q^23 - 62 * q^25 - 54 * q^26 - 16 * q^28 - 70 * q^29 + 45 * q^31 - 153 * q^32 + 12 * q^34 - 18 * q^35 + 9 * q^37 + 234 * q^41 + 30 * q^43 - 51 * q^44 - 22 * q^46 + 111 * q^47 + 34 * q^49 - 241 * q^50 - 148 * q^53 + 412 * q^56 - 34 * q^58 - 42 * q^59 + 120 * q^61 - 48 * q^64 - 114 * q^65 - 34 * q^67 + 264 * q^70 + 350 * q^71 - 6 * q^73 + 718 * q^74 + 72 * q^76 + 32 * q^77 - 82 * q^79 + 609 * q^80 - 18 * q^82 - 738 * q^83 + 3 * q^85 + 34 * q^86 - 50 * q^88 - 21 * q^89 + 39 * q^91 - 288 * q^92 - 3 * q^94 - 507 * q^95 - 57 * q^97 - 811 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	1.12025	−	1.94033i	0.560124	−	0.970163i	−0.437361	−	0.899286i	$-0.644087\pi$
$2$	1.12025	−	1.94033i	0.560124	−	0.970163i	0.997485	−	0.0708770i	$-0.0225798\pi$
$3$		0			0
$3$		0			0
$4$	−0.509909	−	0.883189i	−0.127477	−	0.220797i
$5$		−	1.93444i		−	0.386889i	−0.981111	−	0.193444i	$-0.938034\pi$
$5$		−	1.93444i		−	0.386889i	0.981111	−	0.193444i	$-0.0619659\pi$
$6$		0			0
$7$	3.87064	−	5.83251i	0.552948	−	0.833216i
$7$	3.87064	−	5.83251i	0.552948	−	0.833216i
$8$	6.67708			0.834635
$9$		0			0
$10$	−3.75345	−	2.16706i	−0.375345	−	0.216706i
$11$	0.372337			0.0338488			0.0169244	−	0.999857i	$-0.494613\pi$
$11$	0.372337			0.0338488			0.0169244	+	0.999857i	$0.494613\pi$
$12$		0			0
$13$	−5.01827	−	2.89730i	−0.386021	−	0.222869i	0.294414	−	0.955678i	$-0.404876\pi$
$13$	−5.01827	−	2.89730i	−0.386021	−	0.222869i	−0.680435	+	0.732809i	$0.738209\pi$
$14$	−6.98089	−	14.0442i	−0.498635	−	1.00315i
$15$		0			0
$16$	9.51962	−	16.4885i	0.594976	−	1.03053i
$17$	−9.96576	−	5.75374i	−0.586221	−	0.338455i	0.177381	−	0.984142i	$-0.443238\pi$
$17$	−9.96576	−	5.75374i	−0.586221	−	0.338455i	−0.763602	+	0.645687i	$0.776571\pi$
$18$		0			0
$19$	18.2323	−	10.5264i	0.959593	−	0.554021i	0.0635451	−	0.997979i	$-0.479759\pi$
$19$	18.2323	−	10.5264i	0.959593	−	0.554021i	0.896048	+	0.443958i	$0.146426\pi$
$20$	−1.70848	+	0.986391i	−0.0854239	+	0.0493195i
$21$		0			0
$22$	0.417109	−	0.722455i	0.0189595	−	0.0328389i
$23$	−27.2835			−1.18624			−0.593119	−	0.805115i	$-0.702104\pi$
$23$	−27.2835			−1.18624			−0.593119	+	0.805115i	$0.702104\pi$
$24$		0			0
$25$	21.2579			0.850317
$26$	−11.2434	+	6.49139i	−0.432439	+	0.249669i
$27$		0			0
$28$	−7.12488	−	0.444454i	−0.254460	−	0.0158734i
$29$	20.1404	+	34.8842i	0.694497	+	1.20290i	0.970350	+	0.241704i	$0.0777063\pi$
$29$	20.1404	+	34.8842i	0.694497	+	1.20290i	−0.275853	+	0.961200i	$0.588960\pi$
$30$		0			0
$31$	−42.2746	+	24.4073i	−1.36370	+	0.787331i	−0.990114	−	0.140265i	$-0.955205\pi$
$31$	−42.2746	+	24.4073i	−1.36370	+	0.787331i	−0.373584	+	0.927596i	$0.621871\pi$
$32$	−7.97450	−	13.8122i	−0.249203	−	0.431633i
$33$		0			0
$34$	−22.3282	+	12.8912i	−0.656713	+	0.379154i
$35$	−11.2827	−	7.48753i	−0.322362	−	0.213929i
$36$		0			0
$37$	14.7691	+	25.5809i	0.399166	+	0.691376i	0.993623	−	0.112751i	$-0.0359663\pi$
$37$	14.7691	+	25.5809i	0.399166	+	0.691376i	−0.594457	+	0.804127i	$0.702633\pi$
$38$		−	47.1687i		−	1.24128i
$39$		0			0
$40$		−	12.9164i		−	0.322911i
$41$	19.6397	+	11.3390i	0.479016	+	0.276560i	0.720006	−	0.693968i	$-0.244139\pi$
$41$	19.6397	+	11.3390i	0.479016	+	0.276560i	−0.240990	+	0.970528i	$0.577472\pi$
$42$		0			0
$43$	10.7407	+	18.6035i	0.249785	+	0.432639i	0.963466	−	0.267831i	$-0.0863069\pi$
$43$	10.7407	+	18.6035i	0.249785	+	0.432639i	−0.713681	+	0.700470i	$0.752974\pi$
$44$	−0.189858	−	0.328844i	−0.00431495	−	0.00747372i
$45$		0			0
$46$	−30.5642	+	52.9388i	−0.664440	+	1.15084i
$47$	46.1622	+	26.6518i	0.982175	+	0.567059i	0.902926	−	0.429796i	$-0.141414\pi$
$47$	46.1622	+	26.6518i	0.982175	+	0.567059i	0.0792489	+	0.996855i	$0.474748\pi$
$48$		0			0
$49$	−19.0363	−	45.1511i	−0.388496	−	0.921450i
$50$	23.8141	−	41.2473i	0.476283	−	0.824946i
$51$		0			0
$52$			5.90944i			0.113643i
$53$	−43.7300	+	75.7426i	−0.825094	+	1.42911i	0.0767530	+	0.997050i	$0.475545\pi$
$53$	−43.7300	+	75.7426i	−0.825094	+	1.42911i	−0.901847	+	0.432055i	$0.857789\pi$
$54$		0			0
$55$		−	0.720265i		−	0.0130957i
$56$	25.8446	−	38.9441i	0.461510	−	0.695431i
$57$		0			0
$58$	90.2490			1.55602
$59$	7.99438	−	4.61556i	0.135498	−	0.0782298i	−0.430719	−	0.902486i	$-0.641740\pi$
$59$	7.99438	−	4.61556i	0.135498	−	0.0782298i	0.566217	+	0.824256i	$0.308407\pi$
$60$		0			0
$61$	−61.0848	−	35.2673i	−1.00139	−	0.578153i	−0.0927306	−	0.995691i	$-0.529560\pi$
$61$	−61.0848	−	35.2673i	−1.00139	−	0.578153i	−0.908659	+	0.417539i	$0.862893\pi$
$62$			109.369i			1.76401i
$63$		0			0
$64$	40.4233			0.631614
$65$	−5.60467	+	9.70757i	−0.0862256	+	0.149347i
$66$		0			0
$67$	37.7720	+	65.4230i	0.563761	+	0.976463i	0.997164	+	0.0752625i	$0.0239795\pi$
$67$	37.7720	+	65.4230i	0.563761	+	0.976463i	−0.433403	+	0.901200i	$0.642687\pi$
$68$			11.7355i			0.172581i
$69$		0			0
$70$	−27.1676	+	13.5041i	−0.388109	+	0.192916i
$71$	97.4729			1.37286			0.686429	−	0.727197i	$-0.259177\pi$
$71$	97.4729			1.37286			0.686429	+	0.727197i	$0.259177\pi$
$72$		0			0
$73$	−75.3269	−	43.4900i	−1.03188	−	0.595754i	−0.114354	−	0.993440i	$-0.536480\pi$
$73$	−75.3269	−	43.4900i	−1.03188	−	0.595754i	−0.917521	+	0.397687i	$0.869813\pi$
$74$	66.1804			0.894330
$75$		0			0
$76$	−18.5936	−	10.7350i	−0.244653	−	0.141250i
$77$	1.44118	−	2.17166i	0.0187166	−	0.0282033i
$78$		0			0
$79$	23.5997	−	40.8759i	0.298730	−	0.517416i	−0.677115	−	0.735877i	$-0.736770\pi$
$79$	23.5997	−	40.8759i	0.298730	−	0.517416i	0.975846	+	0.218461i	$0.0701036\pi$
$80$	−31.8960	−	18.4152i	−0.398700	−	0.230190i
$81$		0			0
$82$	44.0025	−	25.4049i	0.536616	−	0.309816i
$83$	−81.1770	+	46.8676i	−0.978036	+	0.564669i	−0.901677	−	0.432411i	$-0.857663\pi$
$83$	−81.1770	+	46.8676i	−0.978036	+	0.564669i	−0.0763594	+	0.997080i	$0.524330\pi$
$84$		0			0
$85$	−11.1303	+	19.2782i	−0.130944	+	0.226802i
$86$	48.1291			0.559641
$87$		0			0
$88$	2.48612			0.0282514
$89$	25.6803	−	14.8266i	0.288543	−	0.166590i	−0.348742	−	0.937219i	$-0.613391\pi$
$89$	25.6803	−	14.8266i	0.288543	−	0.166590i	0.637285	+	0.770628i	$0.280058\pi$
$90$		0			0
$91$	−36.3225	+	18.0547i	−0.399148	+	0.198403i
$92$	13.9121	+	24.0965i	0.151218	+	0.261918i
$93$		0			0
$94$	103.426	−	59.7132i	1.10028	−	0.635246i
$95$	−20.3627	−	35.2693i	−0.214345	−	0.371256i
$96$		0			0
$97$	−122.538	+	70.7471i	−1.26327	+	0.729351i	−0.973706	−	0.227806i	$-0.926845\pi$
$97$	−122.538	+	70.7471i	−1.26327	+	0.729351i	−0.289567	+	0.957158i	$0.593511\pi$
$98$	−108.933	−	13.6437i	−1.11156	−	0.139222i
$99$		0			0
$100$	−10.8396	−	18.7748i	−0.108396	−	0.187748i
$101$		−	46.9206i		−	0.464561i	−0.972649	−	0.232280i	$-0.925381\pi$
$101$		−	46.9206i		−	0.464561i	0.972649	−	0.232280i	$-0.0746187\pi$
$102$		0			0
$103$			131.547i			1.27715i	0.769559	+	0.638576i	$0.220476\pi$
$103$			131.547i			1.27715i	−0.769559	+	0.638576i	$0.779524\pi$
$104$	−33.5074	−	19.3455i	−0.322187	−	0.186015i
$105$		0			0
$106$	97.9768	+	169.701i	0.924310	+	1.60095i
$107$	−69.9586	−	121.172i	−0.653819	−	1.13245i	−0.982188	−	0.187899i	$-0.939832\pi$
$107$	−69.9586	−	121.172i	−0.653819	−	1.13245i	0.328369	−	0.944549i	$-0.393501\pi$
$108$		0			0
$109$	55.5420	−	96.2016i	0.509560	−	0.882583i	−0.490379	−	0.871509i	$-0.663142\pi$
$109$	55.5420	−	96.2016i	0.509560	−	0.882583i	0.999939	−	0.0110739i	$-0.00352500\pi$
$110$	−1.39755	−	0.806875i	−0.0127050	−	0.00733522i
$111$		0			0
$112$	−59.3221	−	119.344i	−0.529662	−	1.06557i
$113$	−50.7636	+	87.9252i	−0.449236	+	0.778099i	−0.998336	−	0.0576571i	$-0.981637\pi$
$113$	−50.7636	+	87.9252i	−0.449236	+	0.778099i	0.549101	+	0.835756i	$0.314970\pi$
$114$		0			0
$115$			52.7783i			0.458942i
$116$	20.5396	−	35.5756i	0.177065	−	0.306686i
$117$		0			0
$118$		−	20.6823i		−	0.175273i
$119$	−72.1326	+	35.8548i	−0.606156	+	0.301301i
$120$		0			0
$121$	−120.861			−0.998854
$122$	−136.860	+	79.0162i	−1.12180	+	0.647674i
$123$		0			0
$124$	43.1125	+	24.8910i	0.347681	+	0.200734i
$125$		−	89.4834i		−	0.715867i
$126$		0			0
$127$	−49.1014			−0.386625			−0.193312	−	0.981137i	$-0.561923\pi$
$127$	−49.1014			−0.386625			−0.193312	+	0.981137i	$0.561923\pi$
$128$	77.1821	−	133.683i	0.602985	−	1.04440i
$129$		0			0
$130$	12.5572	+	21.7498i	0.0965941	+	0.167306i
$131$		−	124.241i		−	0.948403i	−0.880416	−	0.474202i	$-0.842737\pi$
$131$		−	124.241i		−	0.948403i	0.880416	−	0.474202i	$-0.157263\pi$
$132$		0			0
$133$	9.17517	−	147.084i	0.0689863	−	1.10589i
$134$	169.256			1.26310
$135$		0			0
$136$	−66.5422	−	38.4182i	−0.489281	−	0.282487i
$137$	−4.63071			−0.0338008			−0.0169004	−	0.999857i	$-0.505380\pi$
$137$	−4.63071			−0.0338008			−0.0169004	+	0.999857i	$0.505380\pi$
$138$		0			0
$139$	−37.7043	−	21.7686i	−0.271254	−	0.156608i	0.358204	−	0.933644i	$-0.383389\pi$
$139$	−37.7043	−	21.7686i	−0.271254	−	0.156608i	−0.629457	+	0.777035i	$0.716723\pi$
$140$	−0.859772	+	13.7827i	−0.00614123	+	0.0984477i
$141$		0			0
$142$	109.194	−	189.129i	0.768970	−	1.33190i
$143$	−1.86849	−	1.07877i	−0.0130664	−	0.00754386i
$144$		0			0
$145$	67.4815	−	38.9605i	0.465390	−	0.268693i
$146$	−168.770	+	97.4391i	−1.15596	+	0.667391i
$147$		0			0
$148$	15.0618	−	26.0879i	0.101769	−	0.176269i
$149$	26.2607			0.176246			0.0881232	−	0.996110i	$-0.471913\pi$
$149$	26.2607			0.176246			0.0881232	+	0.996110i	$0.471913\pi$
$150$		0			0
$151$	119.873			0.793861			0.396931	−	0.917849i	$-0.370075\pi$
$151$	119.873			0.793861			0.396931	+	0.917849i	$0.370075\pi$
$152$	121.738	−	70.2857i	0.800910	−	0.462406i
$153$		0			0
$154$	−2.59924	−	5.22916i	−0.0168782	−	0.0339556i
$155$	47.2145	+	81.7779i	0.304610	+	0.527599i
$156$		0			0
$157$	169.702	−	97.9773i	1.08090	−	0.624059i	0.149763	−	0.988722i	$-0.452149\pi$
$157$	169.702	−	97.9773i	1.08090	−	0.624059i	0.931140	+	0.364663i	$0.118816\pi$
$158$	−52.8750	−	91.5822i	−0.334652	−	0.579634i
$159$		0			0
$160$	−26.7190	+	15.4262i	−0.166994	+	0.0964139i
$161$	−105.604	+	159.131i	−0.655928	+	0.988392i
$162$		0			0
$163$	41.8418	+	72.4721i	0.256698	+	0.444614i	0.965355	−	0.260939i	$-0.0840321\pi$
$163$	41.8418	+	72.4721i	0.256698	+	0.444614i	−0.708657	+	0.705553i	$0.750699\pi$
$164$		−	23.1274i		−	0.141020i
$165$		0			0
$166$			210.013i			1.26514i
$167$	215.835	+	124.612i	1.29242	+	0.746181i	0.979083	−	0.203460i	$-0.0652188\pi$
$167$	215.835	+	124.612i	1.29242	+	0.746181i	0.313340	+	0.949641i	$0.398552\pi$
$168$		0			0
$169$	−67.7113	−	117.279i	−0.400659	−	0.693961i
$170$	24.9373	+	43.1927i	0.146690	+	0.254075i
$171$		0			0
$172$	10.9536	−	18.9722i	0.0636837	−	0.110303i
$173$	−241.148	−	139.227i	−1.39392	−	0.804779i	−0.400171	−	0.916440i	$-0.631049\pi$
$173$	−241.148	−	139.227i	−1.39392	−	0.804779i	−0.993746	+	0.111661i	$0.964383\pi$
$174$		0			0
$175$	82.2818	−	123.987i	0.470181	−	0.708497i
$176$	3.54451	−	6.13926i	0.0201392	−	0.0348822i
$177$		0			0
$178$		−	66.4376i		−	0.373245i
$179$	128.758	−	223.015i	0.719317	−	1.24589i	−0.241954	−	0.970288i	$-0.577788\pi$
$179$	128.758	−	223.015i	0.719317	−	1.24589i	0.961271	−	0.275605i	$-0.0888782\pi$
$180$		0			0
$181$			29.2542i			0.161625i	0.996729	+	0.0808126i	$0.0257515\pi$
$181$			29.2542i			0.161625i	−0.996729	+	0.0808126i	$0.974248\pi$
$182$	−5.65812	+	90.7032i	−0.0310886	+	0.498369i
$183$		0			0
$184$	−182.174			−0.990076
$185$	49.4848	−	28.5701i	0.267486	−	0.154433i
$186$		0			0
$187$	−3.71062	−	2.14233i	−0.0198429	−	0.0114563i
$188$		−	54.3599i		−	0.289149i
$189$		0			0
$190$	−91.2452			−0.480238
$191$	−30.3852	+	52.6287i	−0.159085	+	0.275543i	−0.934539	−	0.355861i	$-0.884188\pi$
$191$	−30.3852	+	52.6287i	−0.159085	+	0.275543i	0.775454	+	0.631404i	$0.217521\pi$
$192$		0			0
$193$	−12.4384	−	21.5439i	−0.0644474	−	0.111626i	0.832001	−	0.554774i	$-0.187195\pi$
$193$	−12.4384	−	21.5439i	−0.0644474	−	0.111626i	−0.896449	+	0.443147i	$0.853862\pi$
$194$			317.017i			1.63411i
$195$		0			0
$196$	−30.1701	+	39.8356i	−0.153929	+	0.203243i
$197$	−174.320			−0.884873			−0.442437	−	0.896800i	$-0.645886\pi$
$197$	−174.320			−0.884873			−0.442437	+	0.896800i	$0.645886\pi$
$198$		0			0
$199$	250.227	+	144.468i	1.25742	+	0.725972i	0.972572	−	0.232600i	$-0.0747234\pi$
$199$	250.227	+	144.468i	1.25742	+	0.725972i	0.284848	+	0.958573i	$0.408057\pi$
$200$	141.941			0.709705
$201$		0			0
$202$	−91.0413	−	52.5627i	−0.450699	−	0.260211i
$203$	281.419	+	17.5551i	1.38630	+	0.0864782i
$204$		0			0
$205$	21.9346	−	37.9918i	0.106998	−	0.185326i
$206$	255.243	+	147.365i	1.23905	+	0.715363i
$207$		0			0
$208$	−95.5441	+	55.1624i	−0.459347	+	0.265204i
$209$	6.78854	−	3.91937i	0.0324811	−	0.0187530i
$210$		0			0
$211$	−149.601	+	259.116i	−0.709009	+	1.22804i	0.256217	+	0.966619i	$0.417524\pi$
$211$	−149.601	+	259.116i	−0.709009	+	1.22804i	−0.965225	+	0.261419i	$0.915809\pi$
$212$	89.1933			0.420723
$213$		0			0
$214$	−313.484			−1.46488
$215$	35.9874	−	20.7773i	0.167383	−	0.0966388i
$216$		0			0
$217$	−21.2742	+	341.039i	−0.0980379	+	1.57161i
$218$	−124.442	−	215.539i	−0.570833	−	0.988712i
$219$		0			0
$220$	−0.636130	+	0.367270i	−0.00289150	+	0.00166941i
$221$	33.3406	+	57.7477i	0.150863	+	0.261302i
$222$		0			0
$223$	−14.0772	+	8.12745i	−0.0631263	+	0.0364460i	−0.531231	−	0.847227i	$-0.678270\pi$
$223$	−14.0772	+	8.12745i	−0.0631263	+	0.0364460i	0.468105	+	0.883673i	$0.344937\pi$
$224$	−111.426	−	6.95085i	−0.497439	−	0.0310306i
$225$		0			0
$226$	113.736	+	196.996i	0.503255	+	0.871664i
$227$			30.5448i			0.134559i	0.997734	+	0.0672793i	$0.0214319\pi$
$227$			30.5448i			0.134559i	−0.997734	+	0.0672793i	$0.978568\pi$
$228$		0			0
$229$		−	182.597i		−	0.797368i	−0.917088	−	0.398684i	$-0.869467\pi$
$229$		−	182.597i		−	0.797368i	0.917088	−	0.398684i	$-0.130533\pi$
$230$	102.407	+	59.1248i	0.445249	+	0.257064i
$231$		0			0
$232$	134.479	+	232.925i	0.579652	+	1.00399i
$233$	−174.898	−	302.932i	−0.750635	−	1.30014i	−0.947515	−	0.319710i	$-0.896414\pi$
$233$	−174.898	−	302.932i	−0.750635	−	1.30014i	0.196880	−	0.980428i	$-0.436919\pi$
$234$		0			0
$235$	51.5563	−	89.2982i	0.219389	−	0.379992i
$236$	−8.15281	−	4.70703i	−0.0345458	−	0.0199450i
$237$		0			0
$238$	−11.2364	+	180.127i	−0.0472119	+	0.756836i
$239$	−49.6154	+	85.9365i	−0.207596	+	0.359567i	−0.950957	−	0.309324i	$-0.899897\pi$
$239$	−49.6154	+	85.9365i	−0.207596	+	0.359567i	0.743361	+	0.668891i	$0.233231\pi$
$240$		0			0
$241$			280.989i			1.16593i	0.812498	+	0.582964i	$0.198107\pi$
$241$			280.989i			1.16593i	−0.812498	+	0.582964i	$0.801893\pi$
$242$	−135.395	+	234.510i	−0.559482	+	0.969051i
$243$		0			0
$244$			71.9325i			0.294805i
$245$	−87.3422	+	36.8247i	−0.356499	+	0.150305i
$246$		0			0
$247$	−121.993			−0.493897
$248$	−282.271	+	162.969i	−1.13819	+	0.657135i
$249$		0			0
$250$	−173.627	−	100.244i	−0.694507	−	0.400974i
$251$			16.5983i			0.0661286i	0.999453	+	0.0330643i	$0.0105266\pi$
$251$			16.5983i			0.0661286i	−0.999453	+	0.0330643i	$0.989473\pi$
$252$		0			0
$253$	−10.1586			−0.0401527
$254$	−55.0057	+	95.2726i	−0.216558	+	0.375089i
$255$		0			0
$256$	−92.0795	−	159.486i	−0.359686	−	0.622994i
$257$			85.2012i			0.331522i	0.986166	+	0.165761i	$0.0530080\pi$
$257$			85.2012i			0.331522i	−0.986166	+	0.165761i	$0.946992\pi$
$258$		0			0
$259$	206.367	+	12.8733i	0.796783	+	0.0497038i
$260$	11.4315			0.0439672
$261$		0			0
$262$	−241.068	−	139.180i	−0.920105	−	0.531223i
$263$	356.654			1.35610			0.678050	−	0.735016i	$-0.262825\pi$
$263$	356.654			1.35610			0.678050	+	0.735016i	$0.262825\pi$
$264$		0			0
$265$	146.520	+	84.5932i	0.552905	+	0.319220i
$266$	−275.112	−	182.573i	−1.03426	−	0.686365i
$267$		0			0
$268$	38.5206	−	66.7196i	0.143733	−	0.248954i
$269$	333.500	+	192.546i	1.23978	+	0.715785i	0.969048	−	0.246871i	$-0.0794025\pi$
$269$	333.500	+	192.546i	1.23978	+	0.715785i	0.270727	+	0.962656i	$0.412736\pi$
$270$		0			0
$271$	53.9536	−	31.1502i	0.199091	−	0.114945i	−0.397140	−	0.917758i	$-0.629997\pi$
$271$	53.9536	−	31.1502i	0.199091	−	0.114945i	0.596231	+	0.802813i	$0.296664\pi$
$272$	−189.741	+	109.547i	−0.697576	+	0.402746i
$273$		0			0
$274$	−5.18755	+	8.98509i	−0.0189327	+	0.0327923i
$275$	7.91511			0.0287822
$276$		0			0
$277$	85.0115			0.306901			0.153450	−	0.988156i	$-0.450961\pi$
$277$	85.0115			0.306901			0.153450	+	0.988156i	$0.450961\pi$
$278$	−84.4762	+	48.7724i	−0.303871	+	0.175440i
$279$		0			0
$280$	−75.3352	−	49.9949i	−0.269054	−	0.178553i
$281$	−73.8831	−	127.969i	−0.262929	−	0.455407i	0.704090	−	0.710111i	$-0.251355\pi$
$281$	−73.8831	−	127.969i	−0.262929	−	0.455407i	−0.967019	+	0.254704i	$0.918022\pi$
$282$		0			0
$283$	303.815	−	175.408i	1.07355	−	0.619815i	0.144402	−	0.989519i	$-0.453874\pi$
$283$	303.815	−	175.408i	1.07355	−	0.619815i	0.929150	+	0.369704i	$0.120541\pi$
$284$	−49.7023	−	86.0869i	−0.175008	−	0.303123i
$285$		0			0
$286$	−4.18634	+	2.41698i	−0.0146375	+	0.00845099i
$287$	142.153	−	70.6594i	0.495305	−	0.246200i
$288$		0			0
$289$	−78.2890	−	135.601i	−0.270896	−	0.469206i
$290$		−	174.582i		−	0.602005i
$291$		0			0
$292$			88.7038i			0.303780i
$293$	−42.7689	−	24.6927i	−0.145969	−	0.0842753i	0.425237	−	0.905082i	$-0.360191\pi$
$293$	−42.7689	−	24.6927i	−0.145969	−	0.0842753i	−0.571206	+	0.820807i	$0.693524\pi$
$294$		0			0
$295$	−8.92853	−	15.4647i	−0.0302662	−	0.0524226i
$296$	98.6148	+	170.806i	0.333158	+	0.577047i
$297$		0			0
$298$	29.4185	−	50.9544i	0.0987198	−	0.170988i
$299$	136.916	+	79.0484i	0.457913	+	0.264376i
$300$		0			0
$301$	150.079	+	9.36199i	0.498600	+	0.0311030i
$302$	134.288	−	232.593i	0.444661	−	0.770175i
$303$		0			0
$304$		−	400.829i		−	1.31852i
$305$	−68.2226	+	118.165i	−0.223681	+	0.387426i
$306$		0			0
$307$		−	432.680i		−	1.40938i	−0.709515	−	0.704691i	$-0.751086\pi$
$307$		−	432.680i		−	1.40938i	0.709515	−	0.704691i	$-0.248914\pi$
$308$	−2.65286	−	0.165487i	−0.00861317	−	0.000537295i
$309$		0			0
$310$	211.568			0.682476
$311$	144.790	−	83.5947i	0.465563	−	0.268793i	−0.248817	−	0.968550i	$-0.580042\pi$
$311$	144.790	−	83.5947i	0.465563	−	0.268793i	0.714381	+	0.699757i	$0.246709\pi$
$312$		0			0
$313$	−223.941	−	129.293i	−0.715467	−	0.413075i	0.0976148	−	0.995224i	$-0.468879\pi$
$313$	−223.941	−	129.293i	−0.715467	−	0.413075i	−0.813082	+	0.582149i	$0.802212\pi$
$314$		−	439.035i		−	1.39820i
$315$		0			0
$316$	−48.1348			−0.152325
$317$	−101.257	+	175.382i	−0.319422	+	0.553255i	−0.980368	−	0.197179i	$-0.936822\pi$
$317$	−101.257	+	175.382i	−0.319422	+	0.553255i	0.660946	+	0.750434i	$0.270155\pi$
$318$		0			0
$319$	7.49902	+	12.9887i	0.0235079	+	0.0407169i
$320$		−	78.1966i		−	0.244364i
$321$		0			0
$322$	190.463	+	383.173i	0.591500	+	1.18998i
$323$	−242.265			−0.750045
$324$		0			0
$325$	−106.678	−	61.5906i	−0.328240	−	0.189510i
$326$	187.493			0.575131
$327$		0			0
$328$	131.136	+	75.7112i	0.399804	+	0.230827i
$329$	334.124	−	166.082i	1.01557	−	0.504809i
$330$		0			0
$331$	−17.0781	+	29.5802i	−0.0515956	+	0.0893662i	−0.890670	−	0.454651i	$-0.849764\pi$
$331$	−17.0781	+	29.5802i	−0.0515956	+	0.0893662i	0.839074	+	0.544017i	$0.183097\pi$
$332$	82.7858	+	47.7964i	0.249355	+	0.143965i
$333$		0			0
$334$	483.576	−	279.193i	1.44783	−	0.835907i
$335$	126.557	−	73.0678i	0.377783	−	0.218113i
$336$		0			0
$337$	205.854	−	356.550i	0.610844	−	1.05801i	−0.380255	−	0.924882i	$-0.624164\pi$
$337$	205.854	−	356.550i	0.610844	−	1.05801i	0.991099	−	0.133130i	$-0.0425029\pi$
$338$	−303.414			−0.897673
$339$		0			0
$340$	22.7017			0.0667698
$341$	−15.7404	+	9.08773i	−0.0461595	+	0.0266502i
$342$		0			0
$343$	−337.027	−	63.7340i	−0.982585	−	0.185813i
$344$	71.7168	+	124.217i	0.208479	+	0.361096i
$345$		0			0
$346$	−540.290	+	311.937i	−1.56153	+	0.901551i
$347$	−298.744	−	517.439i	−0.860933	−	1.49118i	−0.871029	−	0.491231i	$-0.836547\pi$
$347$	−298.744	−	517.439i	−0.860933	−	1.49118i	0.0100965	−	0.999949i	$-0.496786\pi$
$348$		0			0
$349$	72.8266	−	42.0465i	0.208672	−	0.120477i	−0.392022	−	0.919956i	$-0.628224\pi$
$349$	72.8266	−	42.0465i	0.208672	−	0.120477i	0.600694	+	0.799479i	$0.294891\pi$
$350$	−148.399	−	298.550i	−0.423998	−	0.852999i
$351$		0			0
$352$	−2.96920	−	5.14281i	−0.00843523	−	0.0146102i
$353$		−	458.436i		−	1.29869i	−0.760496	−	0.649343i	$-0.775044\pi$
$353$		−	458.436i		−	1.29869i	0.760496	−	0.649343i	$-0.224956\pi$
$354$		0			0
$355$		−	188.556i		−	0.531143i
$356$	−26.1893	−	15.1204i	−0.0735654	−	0.0424730i
$357$		0			0
$358$	−288.481	−	499.664i	−0.805813	−	1.39571i
$359$	−6.42758	−	11.1329i	−0.0179041	−	0.0310109i	0.856935	−	0.515425i	$-0.172366\pi$
$359$	−6.42758	−	11.1329i	−0.0179041	−	0.0310109i	−0.874839	+	0.484414i	$0.839033\pi$
$360$		0			0
$361$	41.1103	−	71.2051i	0.113879	−	0.197244i
$362$	56.7626	+	32.7719i	0.156803	+	0.0905302i
$363$		0			0
$364$	34.4669	+	22.8733i	0.0946892	+	0.0628388i
$365$	−84.1290	+	145.716i	−0.230490	+	0.399221i
$366$		0			0
$367$			618.348i			1.68487i	0.538796	+	0.842436i	$0.318879\pi$
$367$			618.348i			1.68487i	−0.538796	+	0.842436i	$0.681121\pi$
$368$	−259.728	+	449.863i	−0.705784	+	1.22245i
$369$		0			0
$370$		−	128.022i		−	0.346006i
$371$	272.506	+	548.228i	0.734518	+	1.47770i
$372$		0			0
$373$	0.579265			0.00155299			0.000776495	−	1.00000i	$-0.499753\pi$
$373$	0.579265			0.00155299			0.000776495		1.00000i	$0.499753\pi$
$374$	−8.31363	+	4.79988i	−0.0222290	+	0.0128339i
$375$		0			0
$376$	308.229	+	177.956i	0.819758	+	0.473287i
$377$		−	233.411i		−	0.619128i
$378$		0			0
$379$	18.5015			0.0488165			0.0244083	−	0.999702i	$-0.492230\pi$
$379$	18.5015			0.0488165			0.0244083	+	0.999702i	$0.492230\pi$
$380$	−20.7663	+	35.9683i	−0.0546481	+	0.0946533i
$381$		0			0
$382$	68.0779	+	117.914i	0.178214	+	0.308676i
$383$			56.6187i			0.147829i	0.997265	+	0.0739147i	$0.0235493\pi$
$383$			56.6187i			0.147829i	−0.997265	+	0.0739147i	$0.976451\pi$
$384$		0			0
$385$	−4.20095	−	2.78788i	−0.0109116	−	0.00724126i
$386$	−55.7361			−0.144394
$387$		0			0
$388$	124.966	+	72.1492i	0.322077	+	0.185951i
$389$	−413.566			−1.06315			−0.531575	−	0.847011i	$-0.678400\pi$
$389$	−413.566			−1.06315			−0.531575	+	0.847011i	$0.678400\pi$
$390$		0			0
$391$	271.901	+	156.982i	0.695398	+	0.401488i
$392$	−127.107	−	301.477i	−0.324253	−	0.769075i
$393$		0			0
$394$	−195.282	+	338.238i	−0.495639	+	0.858471i
$395$	−79.0721	−	45.6523i	−0.200182	−	0.115575i
$396$		0			0
$397$	−540.503	+	312.059i	−1.36147	+	0.786044i	−0.989819	−	0.142330i	$-0.954541\pi$
$397$	−540.503	+	312.059i	−1.36147	+	0.786044i	−0.371648	+	0.928374i	$0.621207\pi$
$398$	560.632	−	323.681i	1.40862	−	0.813269i
$399$		0			0
$400$	202.367	−	350.511i	0.505919	−	0.876277i
$401$	−126.874			−0.316395			−0.158198	−	0.987407i	$-0.550568\pi$
$401$	−126.874			−0.316395			−0.158198	+	0.987407i	$0.550568\pi$
$402$		0			0
$403$	282.861			0.701888
$404$	−41.4398	+	23.9253i	−0.102574	+	0.0592209i
$405$		0			0
$406$	349.321	−	526.378i	0.860397	−	1.29650i
$407$	5.49910	+	9.52472i	0.0135113	+	0.0234023i
$408$		0			0
$409$	−374.582	+	216.265i	−0.915848	+	0.528765i	−0.882308	−	0.470672i	$-0.844011\pi$
$409$	−374.582	+	216.265i	−0.915848	+	0.528765i	−0.0335397	+	0.999437i	$0.510678\pi$
$410$	−49.1443	−	85.1205i	−0.119864	−	0.207611i
$411$		0			0
$412$	116.181	−	67.0769i	0.281992	−	0.162808i
$413$	4.02308	−	64.4924i	0.00974110	−	0.156156i
$414$		0			0
$415$	90.6626	+	157.032i	0.218464	+	0.378391i
$416$			92.4181i			0.222159i
$417$		0			0
$418$		−	17.5626i		−	0.0420159i
$419$	−150.801	−	87.0648i	−0.359906	−	0.207792i	0.309134	−	0.951019i	$-0.399961\pi$
$419$	−150.801	−	87.0648i	−0.359906	−	0.207792i	−0.669040	+	0.743227i	$0.733294\pi$
$420$		0			0
$421$	−175.470	−	303.923i	−0.416793	−	0.721907i	0.578822	−	0.815454i	$-0.303513\pi$
$421$	−175.470	−	303.923i	−0.416793	−	0.721907i	−0.995615	+	0.0935470i	$0.970179\pi$
$422$	335.180	+	580.549i	0.794265	+	1.37571i
$423$		0			0
$424$	−291.989	+	505.739i	−0.688653	+	1.19278i
$425$	−211.852	−	122.313i	−0.498474	−	0.287794i
$426$		0			0
$427$	−442.134	+	219.770i	−1.03544	+	0.514685i
$428$	−71.3451	+	123.573i	−0.166694	+	0.288723i
$429$		0			0
$430$		−	93.1031i		−	0.216519i
$431$	−367.837	+	637.113i	−0.853451	+	1.47822i	0.0246236	+	0.999697i	$0.492161\pi$
$431$	−367.837	+	637.113i	−0.853451	+	1.47822i	−0.878075	+	0.478524i	$0.841172\pi$
$432$		0			0
$433$			134.778i			0.311266i	0.987815	+	0.155633i	$0.0497417\pi$
$433$			134.778i			0.311266i	−0.987815	+	0.155633i	$0.950258\pi$
$434$	637.894	+	423.327i	1.46980	+	0.975408i
$435$		0			0
$436$	−113.285			−0.259829
$437$	−497.439	+	287.197i	−1.13831	+	0.657201i
$438$		0			0
$439$	5.06360	+	2.92347i	0.0115344	+	0.00665939i	0.505756	−	0.862677i	$-0.331214\pi$
$439$	5.06360	+	2.92347i	0.0115344	+	0.00665939i	−0.494222	+	0.869336i	$0.664547\pi$
$440$		−	4.80927i		−	0.0109302i
$441$		0			0
$442$	149.399			0.338007
$443$	−80.1590	+	138.839i	−0.180946	+	0.313407i	−0.942203	−	0.335043i	$-0.891249\pi$
$443$	−80.1590	+	138.839i	−0.180946	+	0.313407i	0.761257	+	0.648450i	$0.224583\pi$
$444$		0			0
$445$	−28.6811	−	49.6772i	−0.0644520	−	0.111634i
$446$			36.4190i			0.0816570i
$447$		0			0
$448$	156.464	−	235.769i	0.349250	−	0.526271i
$449$	−46.7901			−0.104209			−0.0521047	−	0.998642i	$-0.516593\pi$
$449$	−46.7901			−0.104209			−0.0521047	+	0.998642i	$0.516593\pi$
$450$		0			0
$451$	7.31257	+	4.22191i	0.0162141	+	0.00936122i
$452$	103.539			0.229069
$453$		0			0
$454$	59.2669	+	34.2177i	0.130544	+	0.0753695i
$455$	34.9258	+	70.2638i	0.0767601	+	0.154426i
$456$		0			0
$457$	−277.170	+	480.073i	−0.606499	+	1.05049i	0.385314	+	0.922786i	$0.374093\pi$
$457$	−277.170	+	480.073i	−0.606499	+	1.05049i	−0.991813	+	0.127702i	$0.959240\pi$
$458$	−354.298	−	204.554i	−0.773577	−	0.446625i
$459$		0			0
$460$	46.6132	−	26.9122i	0.101333	−	0.0585047i
$461$	−117.654	+	67.9273i	−0.255214	+	0.147348i	−0.622149	−	0.782899i	$-0.713740\pi$
$461$	−117.654	+	67.9273i	−0.255214	+	0.147348i	0.366935	+	0.930246i	$0.380407\pi$
$462$		0			0
$463$	0.952160	−	1.64919i	0.00205650	−	0.00356196i	−0.864995	−	0.501780i	$-0.832679\pi$
$463$	0.952160	−	1.64919i	0.00205650	−	0.00356196i	0.867052	+	0.498218i	$0.166012\pi$
$464$	766.916			1.65284
$465$		0			0
$466$	−783.716			−1.68179
$467$	89.3271	−	51.5730i	0.191278	−	0.110435i	−0.401302	−	0.915946i	$-0.631442\pi$
$467$	89.3271	−	51.5730i	0.191278	−	0.110435i	0.592581	+	0.805511i	$0.298109\pi$
$468$		0			0
$469$	527.782	+	32.9234i	1.12533	+	0.0701991i
$470$	−115.512	−	200.072i	−0.245770	−	0.425686i
$471$		0			0
$472$	53.3791	−	30.8184i	0.113091	−	0.0652933i
$473$	3.99917	+	6.92677i	0.00845491	+	0.0146443i
$474$		0			0
$475$	387.580	−	223.769i	0.815958	−	0.471094i
$476$	68.4476	+	45.4240i	0.143797	+	0.0954286i
$477$		0			0
$478$	111.163	+	192.540i	0.232559	+	0.402804i
$479$		−	191.432i		−	0.399649i	−0.979832	−	0.199825i	$-0.935963\pi$
$479$		−	191.432i		−	0.399649i	0.979832	−	0.199825i	$-0.0640372\pi$
$480$		0			0
$481$		−	171.163i		−	0.355848i
$482$	545.209	+	314.777i	1.13114	+	0.653064i
$483$		0			0
$484$	61.6283	+	106.743i	0.127331	+	0.220544i
$485$	136.856	+	237.042i	0.282178	+	0.488746i
$486$		0			0
$487$	−224.406	+	388.683i	−0.460794	+	0.798118i	−0.999001	−	0.0446948i	$-0.985768\pi$
$487$	−224.406	+	388.683i	−0.460794	+	0.798118i	0.538207	+	0.842813i	$0.319102\pi$
$488$	−407.868	−	235.483i	−0.835795	−	0.482547i
$489$		0			0
$490$	−26.3930	+	210.725i	−0.0538633	+	0.430051i
$491$	40.8828	−	70.8111i	0.0832644	−	0.144218i	−0.821386	−	0.570373i	$-0.806799\pi$
$491$	40.8828	−	70.8111i	0.0832644	−	0.144218i	0.904650	+	0.426155i	$0.140132\pi$
$492$		0			0
$493$		−	463.530i		−	0.940224i
$494$	−136.662	+	236.705i	−0.276644	+	0.479161i
$495$		0			0
$496$			929.392i			1.87377i
$497$	377.282	−	568.511i	0.759119	−	1.14389i
$498$		0			0
$499$	−27.5430			−0.0551964			−0.0275982	−	0.999619i	$-0.508786\pi$
$499$	−27.5430			−0.0551964			−0.0275982	+	0.999619i	$0.508786\pi$
$500$	−79.0307	+	45.6284i	−0.158061	+	0.0912568i
$501$		0			0
$502$	32.2061	+	18.5942i	0.0641556	+	0.0370402i
$503$			49.4903i			0.0983902i	0.998789	+	0.0491951i	$0.0156656\pi$
$503$			49.4903i			0.0983902i	−0.998789	+	0.0491951i	$0.984334\pi$
$504$		0			0
$505$	−90.7653			−0.179733
$506$	−11.3802	+	19.7111i	−0.0224905	+	0.0389547i
$507$		0			0
$508$	25.0372	+	43.3658i	0.0492859	+	0.0853657i
$509$		−	125.689i		−	0.246934i	−0.992349	−	0.123467i	$-0.960599\pi$
$509$		−	125.689i		−	0.246934i	0.992349	−	0.123467i	$-0.0394013\pi$
$510$		0			0
$511$	−545.219	+	271.011i	−1.06696	+	0.530354i
$512$	204.849			0.400097
$513$		0			0
$514$	165.318	+	95.4464i	0.321630	+	0.185693i
$515$	254.470			0.494116
$516$		0			0
$517$	17.1879	+	9.92344i	0.0332454	+	0.0191943i
$518$	256.160	−	385.998i	0.494518	−	0.745169i
$519$		0			0
$520$	−37.4228	+	64.8182i	−0.0719670	+	0.124650i
$521$	606.831	+	350.354i	1.16474	+	0.672464i	0.952436	−	0.304739i	$-0.0985692\pi$
$521$	606.831	+	350.354i	1.16474	+	0.672464i	0.212306	+	0.977203i	$0.431903\pi$
$522$		0			0
$523$	−302.754	+	174.795i	−0.578879	+	0.334216i	−0.760688	−	0.649118i	$-0.775138\pi$
$523$	−302.754	+	174.795i	−0.578879	+	0.334216i	0.181809	+	0.983334i	$0.441805\pi$
$524$	−109.728	+	63.3515i	−0.209405	+	0.120900i
$525$		0			0
$526$	399.541	−	692.026i	0.759584	−	1.31564i
$527$	561.732			1.06591
$528$		0			0
$529$	215.388			0.407160
$530$	328.277	−	189.531i	0.619390	−	0.357605i
$531$		0			0
$532$	−134.581	+	66.8959i	−0.252972	+	0.125744i
$533$	−65.7048	−	113.804i	−0.123273	−	0.213516i
$534$		0			0
$535$	−234.400	+	135.331i	−0.438131	+	0.252955i
$536$	252.207	+	436.835i	0.470535	+	0.814990i
$537$		0			0
$538$	747.204	−	431.399i	1.38886	−	0.801856i
$539$	−7.08792	−	16.8114i	−0.0131501	−	0.0311900i
$540$		0			0
$541$	−350.723	−	607.469i	−0.648286	−	1.12286i	−0.983532	−	0.180734i	$-0.942153\pi$
$541$	−350.723	−	607.469i	−0.648286	−	1.12286i	0.335246	−	0.942131i	$-0.391180\pi$
$542$		−	139.584i		−	0.257534i
$543$		0			0
$544$			183.533i			0.337376i
$545$	−186.096	−	107.443i	−0.341461	−	0.197143i
$546$		0			0
$547$	−202.629	−	350.964i	−0.370437	−	0.641616i	0.619195	−	0.785237i	$-0.287459\pi$
$547$	−202.629	−	350.964i	−0.370437	−	0.641616i	−0.989633	+	0.143620i	$0.954126\pi$
$548$	2.36124	+	4.08979i	0.00430884	+	0.00746313i
$549$		0			0
$550$	8.86688	−	15.3579i	0.0161216	−	0.0279234i
$551$	734.410	+	424.012i	1.33287	+	0.769532i
$552$		0			0
$553$	−147.063	−	295.861i	−0.265937	−	0.535011i
$554$	95.2339	−	164.950i	0.171902	−	0.297744i
$555$		0			0
$556$			44.4000i			0.0798560i
$557$	51.7943	−	89.7104i	0.0929880	−	0.161060i	−0.815779	−	0.578364i	$-0.803692\pi$
$557$	51.7943	−	89.7104i	0.0929880	−	0.161060i	0.908767	+	0.417304i	$0.137025\pi$
$558$		0			0
$559$		−	124.477i		−	0.222677i
$560$	−230.865	+	114.755i	−0.412258	+	0.204920i
$561$		0			0
$562$	−331.069			−0.589092
$563$	−113.286	+	65.4059i	−0.201219	+	0.116174i	−0.597224	−	0.802074i	$-0.703730\pi$
$563$	−113.286	+	65.4059i	−0.201219	+	0.116174i	0.396005	+	0.918248i	$0.370396\pi$
$564$		0			0
$565$	170.086	+	98.1994i	0.301038	+	0.173804i
$566$		−	786.000i		−	1.38869i
$567$		0			0
$568$	650.834			1.14584
$569$	−317.790	+	550.428i	−0.558506	+	0.967361i	0.439115	+	0.898431i	$0.355292\pi$
$569$	−317.790	+	550.428i	−0.558506	+	0.967361i	−0.997621	+	0.0689303i	$0.978041\pi$
$570$		0			0
$571$	−86.0297	−	149.008i	−0.150665	−	0.260959i	0.780807	−	0.624772i	$-0.214808\pi$
$571$	−86.0297	−	149.008i	−0.150665	−	0.260959i	−0.931472	+	0.363813i	$0.881475\pi$
$572$			2.20030i			0.00384668i
$573$		0			0
$574$	22.1438	−	354.978i	0.0385780	−	0.618429i
$575$	−579.990			−1.00868
$576$		0			0
$577$	27.4829	+	15.8672i	0.0476306	+	0.0274996i	0.523626	−	0.851948i	$-0.324579\pi$
$577$	27.4829	+	15.8672i	0.0476306	+	0.0274996i	−0.475996	+	0.879448i	$0.657912\pi$
$578$	−350.812			−0.606942
$579$		0			0
$580$	−68.8189	−	39.7326i	−0.118653	−	0.0685045i
$581$	−40.8514	+	654.873i	−0.0703122	+	1.12715i
$582$		0			0
$583$	−16.2823	+	28.2017i	−0.0279285	+	0.0483735i
$584$	−502.964	−	290.386i	−0.861240	−	0.497237i
$585$		0			0
$586$	−95.8236	+	55.3238i	−0.163521	+	0.0944092i
$587$	−780.765	+	450.775i	−1.33009	+	0.767929i	−0.985314	−	0.170754i	$-0.945380\pi$
$587$	−780.765	+	450.775i	−1.33009	+	0.767929i	−0.344779	+	0.938684i	$0.612046\pi$
$588$		0			0
$589$	−513.842	+	890.000i	−0.872396	+	1.51104i
$590$	−40.0087			−0.0678113
$591$		0			0
$592$	562.387			0.949978
$593$	92.1847	−	53.2228i	0.155455	−	0.0897518i	−0.420255	−	0.907406i	$-0.638059\pi$
$593$	92.1847	−	53.2228i	0.155455	−	0.0897518i	0.575709	+	0.817654i	$0.304726\pi$
$594$		0			0
$595$	69.3590	+	139.536i	0.116570	+	0.234515i
$596$	−13.3906	−	23.1932i	−0.0224674	−	0.0389147i
$597$		0			0
$598$	306.759	−	177.108i	0.512976	−	0.296167i
$599$	−407.540	−	705.880i	−0.680367	−	1.17843i	−0.974869	−	0.222780i	$-0.928487\pi$
$599$	−407.540	−	705.880i	−0.680367	−	1.17843i	0.294501	−	0.955651i	$-0.404846\pi$
$600$		0			0
$601$	222.029	−	128.189i	0.369433	−	0.213292i	−0.303778	−	0.952743i	$-0.598248\pi$
$601$	222.029	−	128.189i	0.369433	−	0.213292i	0.673211	+	0.739451i	$0.264915\pi$
$602$	186.290	−	280.714i	0.309453	−	0.466302i
$603$		0			0
$604$	−61.1244	−	105.871i	−0.101199	−	0.175282i
$605$			233.800i			0.386445i
$606$		0			0
$607$		−	323.825i		−	0.533485i	−0.963768	−	0.266742i	$-0.914053\pi$
$607$		−	323.825i		−	0.533485i	0.963768	−	0.266742i	$-0.0859473\pi$
$608$	−290.786	−	167.886i	−0.478267	−	0.276128i
$609$		0			0
$610$	152.852	+	264.748i	0.250578	+	0.434014i
$611$	−154.436	−	267.492i	−0.252760	−	0.437793i
$612$		0			0
$613$	310.620	−	538.010i	0.506721	−	0.877667i	−0.493248	−	0.869888i	$-0.664191\pi$
$613$	310.620	−	538.010i	0.506721	−	0.877667i	0.999970	−	0.00777855i	$-0.00247602\pi$
$614$	−839.540	−	484.709i	−1.36733	−	0.789428i
$615$		0			0
$616$	9.62289	−	14.5003i	0.0156216	−	0.0235395i
$617$	−372.353	+	644.935i	−0.603490	+	1.04527i	0.388799	+	0.921323i	$0.372890\pi$
$617$	−372.353	+	644.935i	−0.603490	+	1.04527i	−0.992288	+	0.123952i	$0.960443\pi$
$618$		0			0
$619$		−	183.637i		−	0.296668i	−0.988937	−	0.148334i	$-0.952609\pi$
$619$		−	183.637i		−	0.296668i	0.988937	−	0.148334i	$-0.0473910\pi$
$620$	48.1502	−	83.3986i	0.0776616	−	0.134514i
$621$		0			0
$622$		−	374.587i		−	0.602230i
$623$	12.9233	−	207.169i	0.0207437	−	0.332535i
$624$		0			0
$625$	358.348			0.573356
$626$	−501.739	+	289.679i	−0.801501	+	0.462747i
$627$		0			0
$628$	−173.065	−	99.9191i	−0.275581	−	0.159107i
$629$		−	339.911i		−	0.540399i
$630$		0			0
$631$	325.873			0.516439			0.258220	−	0.966086i	$-0.416864\pi$
$631$	325.873			0.516439			0.258220	+	0.966086i	$0.416864\pi$
$632$	157.577	−	272.932i	0.249331	−	0.431854i
$633$		0			0
$634$	226.865	+	392.942i	0.357831	+	0.619782i
$635$			94.9838i			0.149581i
$636$		0			0
$637$	−35.2868	+	281.734i	−0.0553953	+	0.442283i
$638$	33.6030			0.0526693
$639$		0			0
$640$	−258.603	−	149.304i	−0.404067	−	0.233288i
$641$	178.662			0.278725			0.139362	−	0.990241i	$-0.455495\pi$
$641$	178.662			0.278725			0.139362	+	0.990241i	$0.455495\pi$
$642$		0			0
$643$	60.1837	+	34.7471i	0.0935983	+	0.0540390i	0.546069	−	0.837740i	$-0.316124\pi$
$643$	60.1837	+	34.7471i	0.0935983	+	0.0540390i	−0.452470	+	0.891780i	$0.649457\pi$
$644$	194.391	+	12.1263i	0.301850	+	0.0188296i
$645$		0			0
$646$	−271.396	+	470.072i	−0.420118	+	0.727666i
$647$	712.875	+	411.579i	1.10182	+	0.636134i	0.936697	−	0.350140i	$-0.113866\pi$
$647$	712.875	+	411.579i	1.10182	+	0.636134i	0.165119	+	0.986274i	$0.447199\pi$
$648$		0			0
$649$	2.97660	−	1.71854i	0.00458644	−	0.00264798i
$650$	−239.012	+	137.993i	−0.367710	+	0.212298i
$651$		0			0
$652$	42.6710	−	73.9084i	0.0654463	−	0.113356i
$653$	−782.435			−1.19822			−0.599108	−	0.800668i	$-0.704478\pi$
$653$	−782.435			−1.19822			−0.599108	+	0.800668i	$0.704478\pi$
$654$		0			0
$655$	−240.337			−0.366926
$656$	373.924	−	215.885i	0.570006	−	0.329093i
$657$		0			0
$658$	52.0480	−	834.362i	0.0791004	−	1.26803i
$659$	−90.6800	−	157.062i	−0.137602	−	0.238334i	0.788986	−	0.614411i	$-0.210606\pi$
$659$	−90.6800	−	157.062i	−0.137602	−	0.238334i	−0.926589	+	0.376077i	$0.877273\pi$
$660$		0			0
$661$	−167.119	+	96.4862i	−0.252827	+	0.145970i	−0.621058	−	0.783764i	$-0.713297\pi$
$661$	−167.119	+	96.4862i	−0.252827	+	0.145970i	0.368231	+	0.929734i	$0.379964\pi$
$662$	38.2635	+	66.2743i	0.0577999	+	0.100112i
$663$		0			0
$664$	−542.025	+	312.939i	−0.816303	+	0.471293i
$665$	−284.525	−	17.7489i	−0.427857	−	0.0266900i
$666$		0			0
$667$	−549.500	−	951.762i	−0.823839	−	1.42693i
$668$		−	254.164i		−	0.380484i
$669$		0			0
$670$		−	327.416i		−	0.488681i
$671$	−22.7441	−	13.1313i	−0.0338958	−	0.0195698i
$672$		0			0
$673$	−41.9447	−	72.6503i	−0.0623249	−	0.107950i	0.833179	−	0.553003i	$-0.186518\pi$
$673$	−41.9447	−	72.6503i	−0.0623249	−	0.107950i	−0.895504	+	0.445053i	$0.853185\pi$
$674$	−461.215	−	798.849i	−0.684296	−	1.18524i
$675$		0			0
$676$	−69.0532	+	119.604i	−0.102150	+	0.176929i
$677$	179.443	+	103.601i	0.265056	+	0.153030i	0.626639	−	0.779310i	$-0.284430\pi$
$677$	179.443	+	103.601i	0.265056	+	0.153030i	−0.361583	+	0.932340i	$0.617764\pi$
$678$		0			0
$679$	−61.6656	+	988.538i	−0.0908182	+	1.45587i
$680$	−74.3178	+	128.722i	−0.109291	+	0.189297i
$681$		0			0
$682$			40.7220i			0.0597097i
$683$	639.939	−	1108.41i	0.936953	−	1.62285i	0.165841	−	0.986153i	$-0.446966\pi$
$683$	639.939	−	1108.41i	0.936953	−	1.62285i	0.771113	−	0.636698i	$-0.219700\pi$
$684$		0			0
$685$			8.95786i			0.0130772i
$686$	−501.218	+	582.544i	−0.730639	+	0.849189i
$687$		0			0
$688$	408.991			0.594464
$689$	438.898	−	253.398i	0.637007	−	0.367776i
$690$		0			0
$691$	1052.86	+	607.869i	1.52368	+	0.879695i	0.999607	+	0.0280193i	$0.00892000\pi$
$691$	1052.86	+	607.869i	1.52368	+	0.879695i	0.524069	+	0.851676i	$0.324413\pi$
$692$			283.972i			0.410364i
$693$		0			0
$694$	−1338.67			−1.92892
$695$	−42.1101	+	72.9368i	−0.0605900	+	0.104945i
$696$		0			0
$697$	−130.483	−	226.003i	−0.187206	−	0.324251i
$698$		−	188.410i		−	0.269928i
$699$		0			0
$700$	−151.460	−	9.44818i	−0.216372	−	0.0134974i
$701$	1171.72			1.67149			0.835747	−	0.549114i	$-0.185035\pi$
$701$	1171.72			1.67149			0.835747	+	0.549114i	$0.185035\pi$
$702$		0			0
$703$	538.550	+	310.932i	0.766074	+	0.442293i
$704$	15.0511			0.0213794
$705$		0			0
$706$	−889.515	−	513.562i	−1.25994	−	0.727425i
$707$	−273.665	−	181.613i	−0.387079	−	0.256878i
$708$		0			0
$709$	55.8366	−	96.7119i	0.0787540	−	0.136406i	−0.823959	−	0.566650i	$-0.808239\pi$
$709$	55.8366	−	96.7119i	0.0787540	−	0.136406i	0.902713	+	0.430244i	$0.141572\pi$
$710$	−365.860	−	211.229i	−0.515295	−	0.297506i
$711$		0			0
$712$	171.470	−	98.9981i	0.240828	−	0.139042i
$713$	1153.40	−	665.915i	1.61767	−	0.933962i
$714$		0			0
$715$	−2.08682	+	3.61448i	−0.00291863	+	0.00505522i
$716$	−262.619			−0.366786
$717$		0			0
$718$	−28.8019			−0.0401141
$719$	−1204.35	+	695.331i	−1.67503	+	0.967081i	−0.710283	+	0.703917i	$0.751433\pi$
$719$	−1204.35	+	695.331i	−1.67503	+	0.967081i	−0.964751	+	0.263164i	$0.915234\pi$
$720$		0			0
$721$	767.247	+	509.170i	1.06414	+	0.706199i
$722$	−92.1074	−	159.535i	−0.127573	−	0.220962i
$723$		0			0
$724$	25.8370	−	14.9170i	0.0356864	−	0.0206036i
$725$	428.143	+	741.566i	0.590543	+	1.02285i
$726$		0			0
$727$	−570.198	+	329.204i	−0.784317	+	0.452826i	−0.837958	−	0.545735i	$-0.816251\pi$
$727$	−570.198	+	329.204i	−0.784317	+	0.452826i	0.0536411	+	0.998560i	$0.482917\pi$
$728$	−242.528	+	120.553i	−0.333143	+	0.165595i
$729$		0			0
$730$	188.491	+	326.475i	0.258206	+	0.447226i
$731$		−	247.197i		−	0.338163i
$732$		0			0
$733$		−	372.006i		−	0.507512i	−0.967268	−	0.253756i	$-0.918334\pi$
$733$		−	372.006i		−	0.507512i	0.967268	−	0.253756i	$-0.0816659\pi$
$734$	1199.80	+	692.703i	1.63460	+	0.943737i
$735$		0			0
$736$	217.572	+	376.846i	0.295614	+	0.512019i
$737$	14.0639	+	24.3594i	0.0190826	+	0.0330521i
$738$		0			0
$739$	470.172	−	814.362i	0.636227	−	1.10198i	−0.350026	−	0.936740i	$-0.613827\pi$
$739$	470.172	−	814.362i	0.636227	−	1.10198i	0.986254	−	0.165238i	$-0.0528393\pi$
$740$	−50.4655	−	29.1363i	−0.0681967	−	0.0393734i
$741$		0			0
$742$	1369.01	+	85.4000i	1.84503	+	0.115094i
$743$	103.438	−	179.161i	0.139217	−	0.241131i	−0.787983	−	0.615697i	$-0.788875\pi$
$743$	103.438	−	179.161i	0.139217	−	0.241131i	0.927201	+	0.374565i	$0.122208\pi$
$744$		0			0
$745$		−	50.7999i		−	0.0681878i
$746$	0.648921	−	1.12396i	0.000869867	−	0.00150665i
$747$		0			0
$748$			4.36957i			0.00584167i
$749$	−977.521	−	60.9784i	−1.30510	−	0.0814130i
$750$		0			0
$751$	1448.31			1.92850			0.964252	−	0.264986i	$-0.0853675\pi$
$751$	1448.31			1.92850			0.964252	+	0.264986i	$0.0853675\pi$
$752$	878.894	−	507.430i	1.16874	−	0.674773i
$753$		0			0
$754$	−452.894	−	261.478i	−0.600655	−	0.346788i
$755$		−	231.888i		−	0.307136i
$756$		0			0
$757$	−296.987			−0.392321			−0.196161	−	0.980572i	$-0.562847\pi$
$757$	−296.987			−0.392321			−0.196161	+	0.980572i	$0.562847\pi$
$758$	20.7262	−	35.8989i	0.0273433	−	0.0473600i
$759$		0			0
$760$	−135.964	−	235.496i	−0.178900	−	0.309863i
$761$			294.080i			0.386439i	0.981156	+	0.193220i	$0.0618930\pi$
$761$			294.080i			0.386439i	−0.981156	+	0.193220i	$0.938107\pi$
$762$		0			0
$763$	−346.113	−	696.311i	−0.453622	−	0.912596i
$764$	61.9748			0.0811188
$765$		0			0
$766$	109.859	+	63.4270i	0.143419	+	0.0828028i
$767$	−53.4906			−0.0697401
$768$		0			0
$769$	−91.6783	−	52.9305i	−0.119218	−	0.0688303i	0.439205	−	0.898387i	$-0.355260\pi$
$769$	−91.6783	−	52.9305i	−0.119218	−	0.0688303i	−0.558423	+	0.829556i	$0.688593\pi$
$770$	−10.1155	+	5.02809i	−0.0131370	+	0.00652999i
$771$		0			0
$772$	−12.6849	+	21.9708i	−0.0164312	+	0.0284596i
$773$	1070.93	+	618.299i	1.38541	+	0.799869i	0.992794	−	0.119832i	$-0.0382355\pi$
$773$	1070.93	+	618.299i	1.38541	+	0.799869i	0.392620	+	0.919701i	$0.371569\pi$
$774$		0			0
$775$	−898.671	+	518.848i	−1.15958	+	0.669481i
$776$	−818.193	+	472.384i	−1.05437	+	0.608742i
$777$		0			0
$778$	−463.296	+	802.452i	−0.595496	+	1.03143i
$779$	477.434			0.612880
$780$		0			0
$781$	36.2927			0.0464696
$782$	609.192	−	351.717i	0.779018	−	0.449766i
$783$		0			0
$784$	−925.690	−	115.941i	−1.18073	−	0.147884i
$785$	−189.532	−	328.278i	−0.241442	−	0.418189i
$786$		0			0
$787$	728.889	−	420.825i	0.926162	−	0.534720i	0.0405663	−	0.999177i	$-0.487084\pi$
$787$	728.889	−	420.825i	0.926162	−	0.534720i	0.885596	+	0.464457i	$0.153750\pi$
$788$	88.8874	+	153.957i	0.112801	+	0.195377i
$789$		0			0
$790$	−177.161	+	102.284i	−0.224254	+	0.129473i
$791$	316.337	+	636.406i	0.399920	+	0.804559i
$792$		0			0
$793$	204.360	+	353.962i	0.257705	+	0.446358i
$794$			1398.33i			1.76113i
$795$		0			0
$796$		−	294.663i		−	0.370180i
$797$	138.377	+	79.8921i	0.173622	+	0.100241i	0.584293	−	0.811543i	$-0.301372\pi$
$797$	138.377	+	79.8921i	0.173622	+	0.100241i	−0.410670	+	0.911784i	$0.634705\pi$
$798$		0			0
$799$	−306.695	−	531.211i	−0.383848	−	0.664844i
$800$	−169.521	−	293.620i	−0.211902	−	0.367025i
$801$		0			0
$802$	−142.131	+	246.178i	−0.177220	+	0.306955i
$803$	−28.0470	−	16.1929i	−0.0349277	−	0.0201655i
$804$		0			0
$805$	307.830	+	204.286i	0.382398	+	0.253771i
$806$	316.874	−	548.842i	0.393144	−	0.680946i
$807$		0			0
$808$		−	313.293i		−	0.387739i
$809$	17.7511	−	30.7458i	0.0219420	−	0.0380046i	−0.854846	−	0.518882i	$-0.826348\pi$
$809$	17.7511	−	30.7458i	0.0219420	−	0.0380046i	0.876788	+	0.480877i	$0.159682\pi$
$810$		0			0
$811$		−	264.939i		−	0.326682i	−0.986570	−	0.163341i	$-0.947773\pi$
$811$		−	264.939i		−	0.326682i	0.986570	−	0.163341i	$-0.0522271\pi$
$812$	−127.994	−	257.497i	−0.157628	−	0.317115i
$813$		0			0
$814$	24.6414			0.0302720
$815$	140.193	−	80.9406i	0.172016	−	0.0993136i
$816$		0			0
$817$	391.656	+	226.123i	0.479383	+	0.276772i
$818$			969.081i			1.18470i
$819$		0			0
$820$	−44.7386			−0.0545592
$821$	753.781	−	1305.59i	0.918126	−	1.59024i	0.115866	−	0.993265i	$-0.463036\pi$
$821$	753.781	−	1305.59i	0.918126	−	1.59024i	0.802260	−	0.596975i	$-0.203631\pi$
$822$		0			0
$823$	−617.420	−	1069.40i	−0.750207	−	1.29940i	−0.947722	−	0.319097i	$-0.896621\pi$
$823$	−617.420	−	1069.40i	−0.750207	−	1.29940i	0.197515	−	0.980300i	$-0.436713\pi$
$824$			878.348i			1.06596i
$825$		0			0
$826$	−120.629	−	80.0535i	−0.146040	−	0.0969171i
$827$	−642.770			−0.777231			−0.388616	−	0.921400i	$-0.627047\pi$
$827$	−642.770			−0.777231			−0.388616	+	0.921400i	$0.627047\pi$
$828$		0			0
$829$	831.340	+	479.974i	1.00282	+	0.578980i	0.909082	−	0.416617i	$-0.136784\pi$
$829$	831.340	+	479.974i	1.00282	+	0.578980i	0.0937403	+	0.995597i	$0.470118\pi$
$830$	406.258			0.489468
$831$		0			0
$832$	−202.855	−	117.119i	−0.243816	−	0.140767i
$833$	−70.0759	+	559.495i	−0.0841248	+	0.671662i
$834$		0			0
$835$	241.055	−	417.520i	0.288689	−	0.500024i
$836$	−6.92308	−	3.99704i	−0.00828120	−	0.00478115i
$837$		0			0
$838$	−337.868	+	195.068i	−0.403184	+	0.232778i
$839$	−409.757	+	236.574i	−0.488388	+	0.281971i	−0.723905	−	0.689899i	$-0.757655\pi$
$839$	−409.757	+	236.574i	−0.488388	+	0.281971i	0.235518	+	0.971870i	$0.424321\pi$
$840$		0			0
$841$	−390.772	+	676.837i	−0.464652	+	0.804800i
$842$	−786.279			−0.933823
$843$		0			0
$844$	305.131			0.361530
$845$	−226.870	+	130.984i	−0.268486	+	0.155010i
$846$		0			0
$847$	−467.811	+	704.925i	−0.552315	+	0.832261i
$848$	832.586	+	1442.08i	0.981823	+	1.70057i
$849$		0			0
$850$	−474.652	+	274.041i	−0.558414	+	0.322401i
$851$	−402.954	−	697.936i	−0.473506	−	0.820136i
$852$		0			0
$853$	−1068.57	+	616.937i	−1.25271	+	0.723255i	−0.971648	−	0.236433i	$-0.924022\pi$
$853$	−1068.57	+	616.937i	−1.25271	+	0.723255i	−0.281067	+	0.959688i	$0.590688\pi$
$854$	−68.8733	+	1104.08i	−0.0806479	+	1.29284i
$855$		0			0
$856$	−467.120	−	809.075i	−0.545701	−	0.945181i
$857$		−	397.309i		−	0.463605i	−0.972763	−	0.231802i	$-0.925538\pi$
$857$		−	397.309i		−	0.463605i	0.972763	−	0.231802i	$-0.0744622\pi$
$858$		0			0
$859$			546.401i			0.636090i	0.948076	+	0.318045i	$0.103026\pi$
$859$			546.401i			0.636090i	−0.948076	+	0.318045i	$0.896974\pi$
$860$	−36.7006	−	21.1891i	−0.0426752	−	0.0246385i
$861$		0			0
$862$	824.138	+	1427.45i	0.956076	+	1.65597i
$863$	7.86960	+	13.6305i	0.00911888	+	0.0157944i	0.870549	−	0.492082i	$-0.163764\pi$
$863$	7.86960	+	13.6305i	0.00911888	+	0.0157944i	−0.861430	+	0.507876i	$0.830431\pi$
$864$		0			0
$865$	−269.326	+	466.487i	−0.311360	+	0.539291i
$866$	261.513	+	150.985i	0.301978	+	0.174347i
$867$		0			0
$868$	312.050	−	155.110i	0.359504	−	0.178698i
$869$	8.78704	−	15.2196i	0.0101117	−	0.0175139i
$870$		0			0
$871$		−	437.747i		−	0.502580i
$872$	370.858	−	642.346i	0.425296	−	0.736635i
$873$		0			0
$874$			1286.93i			1.47246i
$875$	−521.912	−	346.358i	−0.596471	−	0.395837i
$876$		0			0
$877$	−173.468			−0.197797			−0.0988984	−	0.995098i	$-0.531532\pi$
$877$	−173.468			−0.197797			−0.0988984	+	0.995098i	$0.531532\pi$
$878$	11.3450	−	6.55002i	0.0129214	−	0.00746017i
$879$		0			0
$880$	−11.8761	−	6.85665i	−0.0134955	−	0.00779164i
$881$			1381.76i			1.56840i	0.620507	+	0.784201i	$0.286927\pi$
$881$			1381.76i			1.56840i	−0.620507	+	0.784201i	$0.713073\pi$
$882$		0			0
$883$	1346.90			1.52537			0.762685	−	0.646771i	$-0.223881\pi$
$883$	1346.90			1.52537			0.762685	+	0.646771i	$0.223881\pi$
$884$	34.0014	−	58.8921i	0.0384631	−	0.0666200i
$885$		0			0
$886$	179.596	+	311.069i	0.202704	+	0.351094i
$887$			615.089i			0.693449i	0.937967	+	0.346724i	$0.112706\pi$
$887$			615.089i			0.693449i	−0.937967	+	0.346724i	$0.887294\pi$
$888$		0			0
$889$	−190.054	+	286.384i	−0.213784	+	0.322142i
$890$	−128.520			−0.144404
$891$		0			0
$892$	14.3561	+	8.28852i	0.0160943	+	0.00929206i
$893$	1122.19			1.25665
$894$		0			0
$895$	−431.410	−	249.074i	−0.482022	−	0.278295i
$896$	−480.965	−	967.605i	−0.536792	−	1.07992i
$897$		0			0
$898$	−52.4164	+	90.7880i	−0.0583702	+	0.101100i
$899$	−1702.86	−	983.145i	−1.89417	−	1.09360i
$900$		0			0
$901$	871.606	−	503.222i	0.967376	−	0.558515i
$902$	16.3838	−	9.45917i	0.0181638	−	0.0104869i
$903$		0			0
$904$	−338.953	+	587.084i	−0.374948	+	0.649429i
$905$	56.5906			0.0625310
$906$		0			0
$907$	−498.782			−0.549925			−0.274962	−	0.961455i	$-0.588665\pi$
$907$	−498.782			−0.549925			−0.274962	+	0.961455i	$0.588665\pi$
$908$	26.9768	−	15.5751i	0.0297102	−	0.0171532i
$909$		0			0
$910$	175.460	+	10.9453i	0.192813	+	0.0120278i
$911$	−462.758	−	801.521i	−0.507967	−	0.879825i	−0.999957	−	0.00922428i	$-0.997064\pi$
$911$	−462.758	−	801.521i	−0.507967	−	0.879825i	0.491990	−	0.870601i	$-0.336270\pi$
$912$		0			0
$913$	−30.2252	+	17.4505i	−0.0331053	+	0.0191134i
$914$	620.998	+	1075.60i	0.679429	+	1.17681i
$915$		0			0
$916$	−161.268	+	93.1080i	−0.176057	+	0.101646i
$917$	−724.636	−	480.891i	−0.790224	−	0.524418i
$918$		0			0
$919$	544.947	+	943.877i	0.592979	+	1.02707i	0.993829	+	0.110925i	$0.0353815\pi$
$919$	544.947	+	943.877i	0.592979	+	1.02707i	−0.400850	+	0.916144i	$0.631285\pi$
$920$			352.405i			0.383049i
$921$		0			0
$922$			304.382i			0.330132i
$923$	−489.146	−	282.408i	−0.529952	−	0.305968i
$924$		0			0
$925$	313.961	+	543.797i	0.339418	+	0.587889i
$926$	−2.13331	−	3.69500i	−0.00230379	−	0.00399028i
$927$		0			0
$928$	321.219	−	556.368i	0.346142	−	0.599535i
$929$	465.713	+	268.879i	0.501306	+	0.289429i	0.729253	−	0.684245i	$-0.239868\pi$
$929$	465.713	+	268.879i	0.501306	+	0.289429i	−0.227947	+	0.973674i	$0.573201\pi$
$930$		0			0
$931$	−822.353	−	622.822i	−0.883301	−	0.668982i
$932$	−178.364	+	308.936i	−0.191378	+	0.331476i
$933$		0			0
$934$		−	231.098i		−	0.247428i
$935$	−4.14421	+	7.17799i	−0.00443231	+	0.00767699i
$936$		0			0
$937$		−	647.389i		−	0.690917i	−0.938434	−	0.345459i	$-0.887723\pi$
$937$		−	647.389i		−	0.690917i	0.938434	−	0.345459i	$-0.112277\pi$
$938$	655.129	−	987.187i	0.698431	−	1.05244i
$939$		0			0
$940$	−105.156			−0.111868
$941$	113.565	−	65.5667i	0.120685	−	0.0696777i	−0.438442	−	0.898759i	$-0.644470\pi$
$941$	113.565	−	65.5667i	0.120685	−	0.0696777i	0.559127	+	0.829082i	$0.311136\pi$
$942$		0			0
$943$	−535.838	−	309.366i	−0.568227	−	0.328066i
$944$		−	175.753i		−	0.186179i
$945$		0			0
$946$	17.9202			0.0189432
$947$	209.492	−	362.851i	0.221217	−	0.383159i	−0.733961	−	0.679192i	$-0.762331\pi$
$947$	209.492	−	362.851i	0.221217	−	0.383159i	0.955178	+	0.296033i	$0.0956639\pi$
$948$		0			0
$949$	252.007	+	436.489i	0.265550	+	0.459947i
$950$		−	1002.71i		−	1.05548i
$951$		0			0
$952$	−481.635	+	239.405i	−0.505919	+	0.251476i
$953$	1131.25			1.18704			0.593520	−	0.804819i	$-0.297738\pi$
$953$	1131.25			1.18704			0.593520	+	0.804819i	$0.297738\pi$
$954$		0			0
$955$	101.807	+	58.7785i	0.106604	+	0.0615481i
$956$	101.197			0.105855
$957$		0			0
$958$	−371.440	−	214.451i	−0.387725	−	0.223853i
$959$	−17.9238	+	27.0087i	−0.0186901	+	0.0281634i
$960$		0			0
$961$	710.930	−	1231.37i	0.739781	−	1.28134i
$962$	−332.111	−	191.745i	−0.345230	−	0.199319i
$963$		0			0
$964$	248.166	−	143.279i	0.257433	−	0.148629i
$965$	−41.6754	+	24.0613i	−0.0431869	+	0.0249340i
$966$		0			0
$967$	−115.840	+	200.640i	−0.119793	+	0.207488i	−0.919686	−	0.392656i	$-0.871556\pi$
$967$	−115.840	+	200.640i	−0.119793	+	0.207488i	0.799893	+	0.600143i	$0.204890\pi$
$968$	−807.001			−0.833679
$969$		0			0
$970$	613.251			0.632218
$971$	−402.557	+	232.416i	−0.414579	+	0.239358i	−0.692755	−	0.721173i	$-0.743603\pi$
$971$	−402.557	+	232.416i	−0.414579	+	0.239358i	0.278176	+	0.960530i	$0.410270\pi$
$972$		0			0
$973$	−272.905	+	135.652i	−0.280478	+	0.139416i
$974$	502.782	+	870.843i	0.516203	+	0.894089i
$975$		0			0
$976$	−1163.01	+	671.463i	−1.19161	+	0.687974i
$977$	−889.489	−	1540.64i	−0.910429	−	1.57691i	−0.813459	−	0.581622i	$-0.802418\pi$
$977$	−889.489	−	1540.64i	−0.910429	−	1.57691i	−0.0969695	−	0.995287i	$-0.530915\pi$
$978$		0			0
$979$	9.56174	−	5.52047i	0.00976684	−	0.00563889i
$980$	77.0597	+	58.3624i	0.0786324	+	0.0595535i
$981$		0			0
$982$	−91.5977	−	158.652i	−0.0932767	−	0.161560i
$983$		−	229.966i		−	0.233943i	−0.993135	−	0.116972i	$-0.962681\pi$
$983$		−	229.966i		−	0.233943i	0.993135	−	0.116972i	$-0.0373186\pi$
$984$		0			0
$985$			337.212i			0.342347i
$986$	−899.400	−	519.269i	−0.912170	−	0.526642i
$987$		0			0
$988$	62.2052	+	107.743i	0.0629607	+	0.109051i
$989$	−293.045	−	507.568i	−0.296304	−	0.513213i
$990$		0			0
$991$	−561.974	+	973.368i	−0.567078	+	0.982208i	0.429775	+	0.902936i	$0.358593\pi$
$991$	−561.974	+	973.368i	−0.567078	+	0.982208i	−0.996853	+	0.0792720i	$0.974740\pi$
$992$	674.238	+	389.272i	0.679676	+	0.392411i
$993$		0			0
$994$	−680.448	−	1368.92i	−0.684555	−	1.37719i
$995$	279.466	−	484.050i	0.280870	−	0.486482i
$996$		0			0
$997$		−	639.933i		−	0.641858i	−0.947103	−	0.320929i	$-0.896005\pi$
$997$		−	639.933i		−	0.641858i	0.947103	−	0.320929i	$-0.103995\pi$
$998$	−30.8550	+	53.4424i	−0.0309168	+	0.0535495i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.3.k.a.10.11		28
3.2	odd	2		63.3.k.a.31.4	✓	28
7.5	odd	6		189.3.t.a.145.4		28
9.2	odd	6		63.3.t.a.52.11	yes	28
9.7	even	3		189.3.t.a.73.4		28
21.2	odd	6		441.3.t.a.166.11		28
21.5	even	6		63.3.t.a.40.11	yes	28
21.11	odd	6		441.3.l.a.391.4		28
21.17	even	6		441.3.l.b.391.4		28
21.20	even	2		441.3.k.b.31.4		28
63.2	odd	6		441.3.k.b.313.4		28
63.11	odd	6		441.3.l.b.97.4		28
63.20	even	6		441.3.t.a.178.11		28
63.38	even	6		441.3.l.a.97.4		28
63.47	even	6		63.3.k.a.61.4	yes	28
63.61	odd	6	inner	189.3.k.a.19.11		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.3.k.a.31.4	✓	28	3.2	odd	2
63.3.k.a.61.4	yes	28	63.47	even	6
63.3.t.a.40.11	yes	28	21.5	even	6
63.3.t.a.52.11	yes	28	9.2	odd	6
189.3.k.a.10.11		28	1.1	even	1	trivial
189.3.k.a.19.11		28	63.61	odd	6	inner
189.3.t.a.73.4		28	9.7	even	3
189.3.t.a.145.4		28	7.5	odd	6
441.3.k.b.31.4		28	21.20	even	2
441.3.k.b.313.4		28	63.2	odd	6
441.3.l.a.97.4		28	63.38	even	6
441.3.l.a.391.4		28	21.11	odd	6
441.3.l.b.97.4		28	63.11	odd	6
441.3.l.b.391.4		28	21.17	even	6
441.3.t.a.166.11		28	21.2	odd	6
441.3.t.a.178.11		28	63.20	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(1.12025 - 1.94033i) q^{2} +(-0.509909 - 0.883189i) q^{4} -1.93444i q^{5} +(3.87064 - 5.83251i) q^{7} +6.67708 q^{8} +O(q^{10})\)	\(q+(1.12025 - 1.94033i) q^{2} +(-0.509909 - 0.883189i) q^{4} -1.93444i q^{5} +(3.87064 - 5.83251i) q^{7} +6.67708 q^{8} +(-3.75345 - 2.16706i) q^{10} +0.372337 q^{11} +(-5.01827 - 2.89730i) q^{13} +(-6.98089 - 14.0442i) q^{14} +(9.51962 - 16.4885i) q^{16} +(-9.96576 - 5.75374i) q^{17} +(18.2323 - 10.5264i) q^{19} +(-1.70848 + 0.986391i) q^{20} +(0.417109 - 0.722455i) q^{22} -27.2835 q^{23} +21.2579 q^{25} +(-11.2434 + 6.49139i) q^{26} +(-7.12488 - 0.444454i) q^{28} +(20.1404 + 34.8842i) q^{29} +(-42.2746 + 24.4073i) q^{31} +(-7.97450 - 13.8122i) q^{32} +(-22.3282 + 12.8912i) q^{34} +(-11.2827 - 7.48753i) q^{35} +(14.7691 + 25.5809i) q^{37} -47.1687i q^{38} -12.9164i q^{40} +(19.6397 + 11.3390i) q^{41} +(10.7407 + 18.6035i) q^{43} +(-0.189858 - 0.328844i) q^{44} +(-30.5642 + 52.9388i) q^{46} +(46.1622 + 26.6518i) q^{47} +(-19.0363 - 45.1511i) q^{49} +(23.8141 - 41.2473i) q^{50} +5.90944i q^{52} +(-43.7300 + 75.7426i) q^{53} -0.720265i q^{55} +(25.8446 - 38.9441i) q^{56} +90.2490 q^{58} +(7.99438 - 4.61556i) q^{59} +(-61.0848 - 35.2673i) q^{61} +109.369i q^{62} +40.4233 q^{64} +(-5.60467 + 9.70757i) q^{65} +(37.7720 + 65.4230i) q^{67} +11.7355i q^{68} +(-27.1676 + 13.5041i) q^{70} +97.4729 q^{71} +(-75.3269 - 43.4900i) q^{73} +66.1804 q^{74} +(-18.5936 - 10.7350i) q^{76} +(1.44118 - 2.17166i) q^{77} +(23.5997 - 40.8759i) q^{79} +(-31.8960 - 18.4152i) q^{80} +(44.0025 - 25.4049i) q^{82} +(-81.1770 + 46.8676i) q^{83} +(-11.1303 + 19.2782i) q^{85} +48.1291 q^{86} +2.48612 q^{88} +(25.6803 - 14.8266i) q^{89} +(-36.3225 + 18.0547i) q^{91} +(13.9121 + 24.0965i) q^{92} +(103.426 - 59.7132i) q^{94} +(-20.3627 - 35.2693i) q^{95} +(-122.538 + 70.7471i) q^{97} +(-108.933 - 13.6437i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - q^{2} - 23 q^{4} + 16 q^{8}+O(q^{10}) \) 28 * q - q^2 - 23 * q^4 + 16 * q^8	\( 28 q - q^{2} - 23 q^{4} + 16 q^{8} - 6 q^{10} + 14 q^{11} + 15 q^{13} + 11 q^{14} - 27 q^{16} + 33 q^{17} - 6 q^{19} - 108 q^{20} - 10 q^{22} + 68 q^{23} - 62 q^{25} - 54 q^{26} - 16 q^{28} - 70 q^{29} + 45 q^{31} - 153 q^{32} + 12 q^{34} - 18 q^{35} + 9 q^{37} + 234 q^{41} + 30 q^{43} - 51 q^{44} - 22 q^{46} + 111 q^{47} + 34 q^{49} - 241 q^{50} - 148 q^{53} + 412 q^{56} - 34 q^{58} - 42 q^{59} + 120 q^{61} - 48 q^{64} - 114 q^{65} - 34 q^{67} + 264 q^{70} + 350 q^{71} - 6 q^{73} + 718 q^{74} + 72 q^{76} + 32 q^{77} - 82 q^{79} + 609 q^{80} - 18 q^{82} - 738 q^{83} + 3 q^{85} + 34 q^{86} - 50 q^{88} - 21 q^{89} + 39 q^{91} - 288 q^{92} - 3 q^{94} - 507 q^{95} - 57 q^{97} - 811 q^{98}+O(q^{100}) \) 28 * q - q^2 - 23 * q^4 + 16 * q^8 - 6 * q^10 + 14 * q^11 + 15 * q^13 + 11 * q^14 - 27 * q^16 + 33 * q^17 - 6 * q^19 - 108 * q^20 - 10 * q^22 + 68 * q^23 - 62 * q^25 - 54 * q^26 - 16 * q^28 - 70 * q^29 + 45 * q^31 - 153 * q^32 + 12 * q^34 - 18 * q^35 + 9 * q^37 + 234 * q^41 + 30 * q^43 - 51 * q^44 - 22 * q^46 + 111 * q^47 + 34 * q^49 - 241 * q^50 - 148 * q^53 + 412 * q^56 - 34 * q^58 - 42 * q^59 + 120 * q^61 - 48 * q^64 - 114 * q^65 - 34 * q^67 + 264 * q^70 + 350 * q^71 - 6 * q^73 + 718 * q^74 + 72 * q^76 + 32 * q^77 - 82 * q^79 + 609 * q^80 - 18 * q^82 - 738 * q^83 + 3 * q^85 + 34 * q^86 - 50 * q^88 - 21 * q^89 + 39 * q^91 - 288 * q^92 - 3 * q^94 - 507 * q^95 - 57 * q^97 - 811 * q^98

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