LMFDB - Embedded newform 189.4.i.a.143.1

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			143.1
Character	$\chi$	$=$	189.143
Dual form			189.4.i.a.152.22

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-5.38106i q^{2} -20.9559 q^{4} +(5.57991 - 9.66469i) q^{5} +(-8.46770 - 16.4711i) q^{7} +69.7163i q^{8} +O(q^{10})$	\(q-5.38106i q^{2} -20.9559 q^{4} +(5.57991 - 9.66469i) q^{5} +(-8.46770 - 16.4711i) q^{7} +69.7163i q^{8} +(-52.0063 - 30.0259i) q^{10} +(-18.1128 + 10.4574i) q^{11} +(-46.0055 + 26.5613i) q^{13} +(-88.6322 + 45.5652i) q^{14} +207.501 q^{16} +(44.2557 - 76.6531i) q^{17} +(-40.4504 + 23.3540i) q^{19} +(-116.932 + 202.532i) q^{20} +(56.2722 + 97.4663i) q^{22} +(68.0882 + 39.3108i) q^{23} +(0.229151 + 0.396901i) q^{25} +(142.928 + 247.559i) q^{26} +(177.448 + 345.167i) q^{28} +(17.2805 + 9.97690i) q^{29} +28.0527i q^{31} -558.845i q^{32} +(-412.475 - 238.143i) q^{34} +(-206.437 - 10.0697i) q^{35} +(-122.348 - 211.913i) q^{37} +(125.670 + 217.666i) q^{38} +(673.786 + 389.011i) q^{40} +(-16.9545 - 29.3660i) q^{41} +(87.5295 - 151.606i) q^{43} +(379.570 - 219.145i) q^{44} +(211.534 - 366.387i) q^{46} -146.930 q^{47} +(-199.596 + 278.945i) q^{49} +(2.13575 - 1.23308i) q^{50} +(964.085 - 556.615i) q^{52} +(-656.078 - 378.787i) q^{53} +233.406i q^{55} +(1148.31 - 590.336i) q^{56} +(53.6863 - 92.9874i) q^{58} +83.9249 q^{59} +92.1709i q^{61} +150.953 q^{62} -1347.18 q^{64} +592.839i q^{65} -897.056 q^{67} +(-927.416 + 1606.33i) q^{68} +(-54.1860 + 1110.85i) q^{70} +706.833i q^{71} +(-529.580 - 305.753i) q^{73} +(-1140.32 + 658.364i) q^{74} +(847.673 - 489.404i) q^{76} +(325.620 + 209.788i) q^{77} -266.121 q^{79} +(1157.84 - 2005.43i) q^{80} +(-158.020 + 91.2331i) q^{82} +(311.561 - 539.639i) q^{83} +(-493.886 - 855.436i) q^{85} +(-815.799 - 471.002i) q^{86} +(-729.054 - 1262.76i) q^{88} +(-355.240 - 615.294i) q^{89} +(827.055 + 532.850i) q^{91} +(-1426.85 - 823.791i) q^{92} +790.637i q^{94} +521.254i q^{95} +(-498.364 - 287.731i) q^{97} +(1501.02 + 1074.04i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$		−	5.38106i		−	1.90249i	−0.308431	−	0.951247i	$-0.599804\pi$
$2$		−	5.38106i		−	1.90249i	0.308431	−	0.951247i	$-0.400196\pi$
$3$		0			0
$3$		0			0
$4$	−20.9559			−2.61948
$5$	5.57991	−	9.66469i	0.499083	−	0.864436i	−0.500917	−	0.865495i	$-0.667004\pi$
$5$	5.57991	−	9.66469i	0.499083	−	0.864436i	0.999999	+	0.00105905i	$0.000337107\pi$
$6$		0			0
$7$	−8.46770	−	16.4711i	−0.457213	−	0.889357i
$7$	−8.46770	−	16.4711i	−0.457213	−	0.889357i
$8$			69.7163i			3.08105i
$9$		0			0
$10$	−52.0063	−	30.0259i	−1.64458	−	0.949501i
$11$	−18.1128	+	10.4574i	−0.496475	+	0.286640i	−0.727257	−	0.686366i	$-0.759205\pi$
$11$	−18.1128	+	10.4574i	−0.496475	+	0.286640i	0.230782	+	0.973006i	$0.425872\pi$
$12$		0			0
$13$	−46.0055	+	26.5613i	−0.981510	+	0.566675i	−0.902726	−	0.430216i	$-0.858437\pi$
$13$	−46.0055	+	26.5613i	−0.981510	+	0.566675i	−0.0787845	+	0.996892i	$0.525104\pi$
$14$	−88.6322	+	45.5652i	−1.69200	+	0.869844i
$15$		0			0
$16$	207.501			3.24220
$17$	44.2557	−	76.6531i	0.631387	−	1.09360i	−0.355881	−	0.934531i	$-0.615819\pi$
$17$	44.2557	−	76.6531i	0.631387	−	1.09360i	0.987268	−	0.159064i	$-0.0508475\pi$
$18$		0			0
$19$	−40.4504	+	23.3540i	−0.488419	+	0.281989i	−0.723918	−	0.689886i	$-0.757661\pi$
$19$	−40.4504	+	23.3540i	−0.488419	+	0.281989i	0.235499	+	0.971874i	$0.424327\pi$
$20$	−116.932	+	202.532i	−1.30734	+	2.26437i
$21$		0			0
$22$	56.2722	+	97.4663i	0.545330	+	0.944540i
$23$	68.0882	+	39.3108i	0.617277	+	0.356385i	0.775808	−	0.630969i	$-0.217342\pi$
$23$	68.0882	+	39.3108i	0.617277	+	0.356385i	−0.158531	+	0.987354i	$0.550676\pi$
$24$		0			0
$25$	0.229151	+	0.396901i	0.00183321	+	0.00317521i
$26$	142.928	+	247.559i	1.07810	+	1.86732i
$27$		0			0
$28$	177.448	+	345.167i	1.19766	+	2.32966i
$29$	17.2805	+	9.97690i	0.110652	+	0.0638849i	0.554305	−	0.832314i	$-0.312984\pi$
$29$	17.2805	+	9.97690i	0.110652	+	0.0638849i	−0.443653	+	0.896199i	$0.646318\pi$
$30$		0			0
$31$			28.0527i			0.162529i	0.996693	+	0.0812647i	$0.0258959\pi$
$31$			28.0527i			0.162529i	−0.996693	+	0.0812647i	$0.974104\pi$
$32$		−	558.845i		−	3.08721i
$33$		0			0
$34$	−412.475	−	238.143i	−2.08056	−	1.20121i
$35$	−206.437	−	10.0697i	−0.996980	−	0.0486314i
$36$		0			0
$37$	−122.348	−	211.913i	−0.543620	−	0.941577i	−0.998692	−	0.0511225i	$-0.983720\pi$
$37$	−122.348	−	211.913i	−0.543620	−	0.941577i	0.455073	−	0.890454i	$-0.349613\pi$
$38$	125.670	+	217.666i	0.536482	+	0.929214i
$39$		0			0
$40$	673.786	+	389.011i	2.66337	+	1.53770i
$41$	−16.9545	−	29.3660i	−0.0645816	−	0.111859i	0.831927	−	0.554885i	$-0.187238\pi$
$41$	−16.9545	−	29.3660i	−0.0645816	−	0.111859i	−0.896508	+	0.443027i	$0.853905\pi$
$42$		0			0
$43$	87.5295	−	151.606i	0.310421	−	0.537666i	−0.668032	−	0.744132i	$-0.732863\pi$
$43$	87.5295	−	151.606i	0.310421	−	0.537666i	0.978454	+	0.206467i	$0.0661965\pi$
$44$	379.570	−	219.145i	1.30051	−	0.750848i
$45$		0			0
$46$	211.534	−	366.387i	0.678021	−	1.17437i
$47$	−146.930			−0.455997			−0.227999	−	0.973661i	$-0.573218\pi$
$47$	−146.930			−0.455997			−0.227999	+	0.973661i	$0.573218\pi$
$48$		0			0
$49$	−199.596	+	278.945i	−0.581913	+	0.813251i
$50$	2.13575	−	1.23308i	0.00604082	−	0.00348767i
$51$		0			0
$52$	964.085	−	556.615i	2.57105	−	1.48440i
$53$	−656.078	−	378.787i	−1.70036	−	0.981705i	−0.945385	−	0.325955i	$-0.894314\pi$
$53$	−656.078	−	378.787i	−1.70036	−	0.981705i	−0.754978	−	0.655751i	$-0.772352\pi$
$54$		0			0
$55$			233.406i			0.572228i
$56$	1148.31	−	590.336i	2.74016	−	1.40870i
$57$		0			0
$58$	53.6863	−	92.9874i	0.121541	−	0.210515i
$59$	83.9249			0.185188			0.0925940	−	0.995704i	$-0.470484\pi$
$59$	83.9249			0.185188			0.0925940	+	0.995704i	$0.470484\pi$
$60$		0			0
$61$			92.1709i			0.193464i	0.995310	+	0.0967318i	$0.0308389\pi$
$61$			92.1709i			0.193464i	−0.995310	+	0.0967318i	$0.969161\pi$
$62$	150.953			0.309211
$63$		0			0
$64$	−1347.18			−2.63120
$65$			592.839i			1.13127i
$66$		0			0
$67$	−897.056			−1.63571			−0.817857	−	0.575422i	$-0.804838\pi$
$67$	−897.056			−1.63571			−0.817857	+	0.575422i	$0.804838\pi$
$68$	−927.416	+	1606.33i	−1.65391	+	2.86465i
$69$		0			0
$70$	−54.1860	+	1110.85i	−0.0925209	+	1.89675i
$71$			706.833i			1.18149i	0.806859	+	0.590744i	$0.201166\pi$
$71$			706.833i			1.18149i	−0.806859	+	0.590744i	$0.798834\pi$
$72$		0			0
$73$	−529.580	−	305.753i	−0.849078	−	0.490215i	0.0112618	−	0.999937i	$-0.496415\pi$
$73$	−529.580	−	305.753i	−0.849078	−	0.490215i	−0.860340	+	0.509721i	$0.829749\pi$
$74$	−1140.32	+	658.364i	−1.79134	+	1.03423i
$75$		0			0
$76$	847.673	−	489.404i	1.27940	−	0.738664i
$77$	325.620	+	209.788i	0.481920	+	0.310488i
$78$		0			0
$79$	−266.121			−0.378999			−0.189500	−	0.981881i	$-0.560687\pi$
$79$	−266.121			−0.378999			−0.189500	+	0.981881i	$0.560687\pi$
$80$	1157.84	−	2005.43i	1.61813	−	2.80268i
$81$		0			0
$82$	−158.020	+	91.2331i	−0.212810	+	0.122866i
$83$	311.561	−	539.639i	0.412027	−	0.713651i	−0.583084	−	0.812412i	$-0.698154\pi$
$83$	311.561	−	539.639i	0.412027	−	0.713651i	0.995111	+	0.0987602i	$0.0314877\pi$
$84$		0			0
$85$	−493.886	−	855.436i	−0.630229	−	1.09159i
$86$	−815.799	−	471.002i	−1.02291	−	0.590575i
$87$		0			0
$88$	−729.054	−	1262.76i	−0.883152	−	1.52966i
$89$	−355.240	−	615.294i	−0.423094	−	0.732821i	0.573146	−	0.819453i	$-0.305723\pi$
$89$	−355.240	−	615.294i	−0.423094	−	0.732821i	−0.996240	+	0.0866325i	$0.972389\pi$
$90$		0			0
$91$	827.055	+	532.850i	0.952736	+	0.613822i
$92$	−1426.85	−	823.791i	−1.61695	−	0.933545i
$93$		0			0
$94$			790.637i			0.867532i
$95$			521.254i			0.562943i
$96$		0			0
$97$	−498.364	−	287.731i	−0.521662	−	0.301182i	0.215952	−	0.976404i	$-0.430714\pi$
$97$	−498.364	−	287.731i	−0.521662	−	0.301182i	−0.737614	+	0.675222i	$0.764048\pi$
$98$	1501.02	+	1074.04i	1.54720	+	1.10709i
$99$		0			0
$100$	−4.80206	−	8.31740i	−0.00480206	−	0.00831740i
$101$	179.810	+	311.441i	0.177147	+	0.306827i	0.940902	−	0.338679i	$-0.109980\pi$
$101$	179.810	+	311.441i	0.177147	+	0.306827i	−0.763755	+	0.645506i	$0.776647\pi$
$102$		0			0
$103$	−251.479	−	145.192i	−0.240573	−	0.138895i	0.374867	−	0.927078i	$-0.377688\pi$
$103$	−251.479	−	145.192i	−0.240573	−	0.138895i	−0.615440	+	0.788184i	$0.711022\pi$
$104$	−1851.75	−	3207.33i	−1.74596	−	3.02409i
$105$		0			0
$106$	−2038.28	+	3530.40i	−1.86769	+	3.23493i
$107$	431.398	−	249.068i	0.389765	−	0.225031i	−0.292293	−	0.956329i	$-0.594418\pi$
$107$	431.398	−	249.068i	0.389765	−	0.225031i	0.682058	+	0.731298i	$0.261085\pi$
$108$		0			0
$109$	890.674	−	1542.69i	0.782671	−	1.35563i	−0.147710	−	0.989031i	$-0.547190\pi$
$109$	890.674	−	1542.69i	0.782671	−	1.35563i	0.930381	−	0.366595i	$-0.119477\pi$
$110$	1255.98			1.08866
$111$		0			0
$112$	−1757.06	−	3417.77i	−1.48238	−	2.88348i
$113$	929.808	−	536.825i	0.774062	−	0.446905i	−0.0602596	−	0.998183i	$-0.519193\pi$
$113$	929.808	−	536.825i	0.774062	−	0.446905i	0.834322	+	0.551278i	$0.185860\pi$
$114$		0			0
$115$	759.853	−	438.701i	0.616145	−	0.355731i
$116$	−362.127	−	209.074i	−0.289851	−	0.167345i
$117$		0			0
$118$		−	451.605i		−	0.352319i
$119$	−1637.31	−	79.8657i	−1.26128	−	0.0615234i
$120$		0			0
$121$	−446.784	+	773.852i	−0.335675	+	0.581407i
$122$	495.978			0.368063
$123$		0			0
$124$		−	587.868i		−	0.425743i
$125$	1400.09			1.00182
$126$		0			0
$127$	−533.256			−0.372589			−0.186295	−	0.982494i	$-0.559648\pi$
$127$	−533.256			−0.372589			−0.186295	+	0.982494i	$0.559648\pi$
$128$			2778.48i			1.91863i
$129$		0			0
$130$	3190.10			2.15224
$131$	747.776	−	1295.19i	0.498729	−	0.863824i	−0.501270	−	0.865291i	$-0.667134\pi$
$131$	747.776	−	1295.19i	0.498729	−	0.863824i	0.999999	+	0.00146681i	$0.000466899\pi$
$132$		0			0
$133$	727.189	+	468.509i	0.474100	+	0.305450i
$134$			4827.11i			3.11193i
$135$		0			0
$136$	5343.97	+	3085.34i	3.36942	+	1.94534i
$137$	531.501	−	306.862i	0.331454	−	0.191365i	−0.325032	−	0.945703i	$-0.605375\pi$
$137$	531.501	−	306.862i	0.331454	−	0.191365i	0.656486	+	0.754338i	$0.272042\pi$
$138$		0			0
$139$	−1143.72	+	660.327i	−0.697907	+	0.402937i	−0.806567	−	0.591142i	$-0.798677\pi$
$139$	−1143.72	+	660.327i	−0.697907	+	0.402937i	0.108660	+	0.994079i	$0.465344\pi$
$140$	4326.07	+	211.020i	2.61157	+	0.127389i
$141$		0			0
$142$	3803.51			2.24777
$143$	555.527	−	962.200i	0.324863	−	0.562680i
$144$		0			0
$145$	192.847	−	111.340i	0.110449	−	0.0637677i
$146$	−1645.28	+	2849.71i	−0.932631	+	1.61536i
$147$		0			0
$148$	2563.91	+	4440.82i	1.42400	+	2.46644i
$149$	−2704.57	−	1561.48i	−1.48703	−	0.858535i	−0.487135	−	0.873327i	$-0.661958\pi$
$149$	−2704.57	−	1561.48i	−1.48703	−	0.858535i	−0.999891	+	0.0147920i	$0.995291\pi$
$150$		0			0
$151$	1420.88	+	2461.03i	0.765758	+	1.32633i	0.939845	+	0.341602i	$0.110969\pi$
$151$	1420.88	+	2461.03i	0.765758	+	1.32633i	−0.174087	+	0.984730i	$0.555697\pi$
$152$	−1628.16	−	2820.05i	−0.868822	−	1.50484i
$153$		0			0
$154$	1128.88	−	1752.18i	0.590701	−	0.916849i
$155$	271.121	+	156.532i	0.140496	+	0.0811156i
$156$		0			0
$157$		−	3516.25i		−	1.78744i	−0.448628	−	0.893718i	$-0.648087\pi$
$157$		−	3516.25i		−	1.78744i	0.448628	−	0.893718i	$-0.351913\pi$
$158$			1432.01i			0.721044i
$159$		0			0
$160$	−5401.07	−	3118.31i	−2.66870	−	1.54077i
$161$	70.9419	−	1454.36i	0.0347267	−	0.711924i
$162$		0			0
$163$	−842.172	−	1458.68i	−0.404687	−	0.700939i	0.589598	−	0.807697i	$-0.299286\pi$
$163$	−842.172	−	1458.68i	−0.404687	−	0.700939i	−0.994285	+	0.106758i	$0.965953\pi$
$164$	355.295	+	615.390i	0.169170	+	0.293011i
$165$		0			0
$166$	−2903.83	−	1676.53i	−1.35772	−	0.783878i
$167$	17.5745	+	30.4399i	0.00814343	+	0.0141048i	0.870068	−	0.492931i	$-0.164075\pi$
$167$	17.5745	+	30.4399i	0.00814343	+	0.0141048i	−0.861925	+	0.507036i	$0.830741\pi$
$168$		0			0
$169$	312.505	−	541.274i	0.142242	−	0.246370i
$170$	−4603.15	+	2657.63i	−2.07674	+	1.19901i
$171$		0			0
$172$	−1834.26	+	3177.02i	−0.813143	+	1.40841i
$173$	4006.89			1.76091			0.880457	−	0.474126i	$-0.157236\pi$
$173$	4006.89			1.76091			0.880457	+	0.474126i	$0.157236\pi$
$174$		0			0
$175$	4.59703	−	7.13522i	0.00198573	−	0.00308212i
$176$	−3758.43	+	2169.93i	−1.60967	+	0.929344i
$177$		0			0
$178$	−3310.94	+	1911.57i	−1.39419	+	0.804934i
$179$	−779.715	−	450.169i	−0.325579	−	0.187973i	0.328298	−	0.944574i	$-0.393525\pi$
$179$	−779.715	−	450.169i	−0.325579	−	0.187973i	−0.653877	+	0.756601i	$0.726858\pi$
$180$		0			0
$181$		−	245.907i		−	0.100984i	−0.998724	−	0.0504921i	$-0.983921\pi$
$181$		−	245.907i		−	0.100984i	0.998724	−	0.0504921i	$-0.0160790\pi$
$182$	2867.30	−	4450.44i	1.16779	−	1.81257i
$183$		0			0
$184$	−2740.60	+	4746.86i	−1.09804	+	1.90186i
$185$	−2730.77			−1.08524
$186$		0			0
$187$			1851.21i			0.723923i
$188$	3079.03			1.19448
$189$		0			0
$190$	2804.90			1.07099
$191$		−	2720.33i		−	1.03055i	−0.857023	−	0.515277i	$-0.827689\pi$
$191$		−	2720.33i		−	1.03055i	0.857023	−	0.515277i	$-0.172311\pi$
$192$		0			0
$193$	555.522			0.207188			0.103594	−	0.994620i	$-0.466966\pi$
$193$	555.522			0.207188			0.103594	+	0.994620i	$0.466966\pi$
$194$	−1548.30	+	2681.73i	−0.572996	+	0.992459i
$195$		0			0
$196$	4182.71	−	5845.53i	1.52431	−	2.13030i
$197$		−	514.407i		−	0.186041i	−0.995664	−	0.0930203i	$-0.970348\pi$
$197$		−	514.407i		−	0.186041i	0.995664	−	0.0930203i	$-0.0296521\pi$
$198$		0			0
$199$	2295.03	+	1325.04i	0.817540	+	0.472007i	0.849567	−	0.527480i	$-0.176863\pi$
$199$	2295.03	+	1325.04i	0.817540	+	0.472007i	−0.0320276	+	0.999487i	$0.510196\pi$
$200$	−27.6705	+	15.9756i	−0.00978299	+	0.00564821i
$201$		0			0
$202$	1675.88	−	967.571i	0.583736	−	0.337020i
$203$	18.0047	−	369.111i	0.00622505	−	0.127618i
$204$		0			0
$205$	−378.418			−0.128926
$206$	−781.285	+	1353.23i	−0.264246	+	0.457688i
$207$		0			0
$208$	−9546.19	+	5511.49i	−3.18225	+	1.83728i
$209$	488.447	−	846.016i	0.161658	−	0.280001i
$210$		0			0
$211$	−2125.08	−	3680.75i	−0.693348	−	1.20091i	−0.970734	−	0.240156i	$-0.922801\pi$
$211$	−2125.08	−	3680.75i	−0.693348	−	1.20091i	0.277386	−	0.960759i	$-0.410532\pi$
$212$	13748.7	+	7937.80i	4.45407	+	2.57156i
$213$		0			0
$214$	−1340.25	−	2321.38i	−0.428120	−	0.741525i
$215$	−976.814	−	1691.89i	−0.309852	−	0.536679i
$216$		0			0
$217$	462.059	−	237.542i	0.144547	−	0.0743105i
$218$	−8301.33	−	4792.78i	−2.57907	−	1.48903i
$219$		0			0
$220$		−	4891.23i		−	1.49894i
$221$			4701.96i			1.43117i
$222$		0			0
$223$	5738.30	+	3313.01i	1.72316	+	0.994868i	0.912172	+	0.409808i	$0.134404\pi$
$223$	5738.30	+	3313.01i	1.72316	+	0.994868i	0.810990	+	0.585060i	$0.198929\pi$
$224$	−9204.82	+	4732.14i	−2.74564	+	1.41151i
$225$		0			0
$226$	−2888.69	−	5003.36i	−0.850234	−	1.47265i
$227$	2172.30	+	3762.53i	0.635156	+	1.10012i	0.986482	+	0.163870i	$0.0523976\pi$
$227$	2172.30	+	3762.53i	0.635156	+	1.10012i	−0.351326	+	0.936253i	$0.614269\pi$
$228$		0			0
$229$	5258.68	+	3036.10i	1.51748	+	0.876118i	0.999789	+	0.0205512i	$0.00654209\pi$
$229$	5258.68	+	3036.10i	1.51748	+	0.876118i	0.517692	+	0.855567i	$0.326791\pi$
$230$	−2360.68	−	4088.82i	−0.676777	−	1.17221i
$231$		0			0
$232$	−695.552	+	1204.73i	−0.196833	+	0.340925i
$233$	−1383.45	+	798.736i	−0.388983	+	0.224579i	−0.681719	−	0.731614i	$-0.738767\pi$
$233$	−1383.45	+	798.736i	−0.388983	+	0.224579i	0.292737	+	0.956193i	$0.405434\pi$
$234$		0			0
$235$	−819.854	+	1420.03i	−0.227580	+	0.394181i
$236$	−1758.72			−0.485097
$237$		0			0
$238$	−429.763	+	8810.46i	−0.117048	+	2.39957i
$239$	−1923.70	+	1110.65i	−0.520643	+	0.300593i	−0.737198	−	0.675677i	$-0.763851\pi$
$239$	−1923.70	+	1110.65i	−0.520643	+	0.300593i	0.216555	+	0.976270i	$0.430518\pi$
$240$		0			0
$241$	−3133.07	+	1808.88i	−0.837424	+	0.483487i	−0.856388	−	0.516333i	$-0.827297\pi$
$241$	−3133.07	+	1808.88i	−0.837424	+	0.483487i	0.0189641	+	0.999820i	$0.493963\pi$
$242$	4164.15	+	2404.17i	1.10612	+	0.638620i
$243$		0			0
$244$		−	1931.52i		−	0.506774i
$245$	1582.19	+	3485.52i	0.412581	+	0.908906i
$246$		0			0
$247$	1240.63	−	2148.83i	0.319592	−	0.553550i
$248$	−1955.73			−0.500762
$249$		0			0
$250$		−	7533.99i		−	1.90597i
$251$	2133.73			0.536572			0.268286	−	0.963339i	$-0.413543\pi$
$251$	2133.73			0.536572			0.268286	+	0.963339i	$0.413543\pi$
$252$		0			0
$253$	−1644.36			−0.408617
$254$			2869.49i			0.708849i
$255$		0			0
$256$	4173.76			1.01898
$257$	1940.38	−	3360.84i	0.470963	−	0.815733i	−0.528485	−	0.848943i	$-0.677240\pi$
$257$	1940.38	−	3360.84i	0.470963	−	0.815733i	0.999448	+	0.0332100i	$0.0105730\pi$
$258$		0			0
$259$	−2454.44	+	3809.63i	−0.588848	+	0.913973i
$260$		−	12423.4i		−	2.96334i
$261$		0			0
$262$	−6969.48	−	4023.83i	−1.64342	−	0.948829i
$263$	848.811	−	490.061i	0.199011	−	0.114899i	−0.397183	−	0.917739i	$-0.630012\pi$
$263$	848.811	−	490.061i	0.199011	−	0.114899i	0.596194	+	0.802840i	$0.296679\pi$
$264$		0			0
$265$	−7321.72	+	4227.19i	−1.69724	+	0.979904i
$266$	2521.07	−	3913.05i	0.581117	−	0.901972i
$267$		0			0
$268$	18798.6			4.28472
$269$	531.834	−	921.163i	0.120544	−	0.208789i	−0.799438	−	0.600749i	$-0.794869\pi$
$269$	531.834	−	921.163i	0.120544	−	0.208789i	0.919983	+	0.391959i	$0.128203\pi$
$270$		0			0
$271$	6310.12	−	3643.15i	1.41444	−	0.816626i	0.418635	−	0.908154i	$-0.362509\pi$
$271$	6310.12	−	3643.15i	1.41444	−	0.816626i	0.995802	+	0.0915283i	$0.0291752\pi$
$272$	9183.10	−	15905.6i	2.04709	−	3.54566i
$273$		0			0
$274$	−1651.25	−	2860.04i	−0.364071	−	0.630589i
$275$	−8.30115	−	4.79267i	−0.00182028	−	0.00105094i
$276$		0			0
$277$	−3151.92	−	5459.29i	−0.683685	−	1.18418i	−0.973848	−	0.227200i	$-0.927043\pi$
$277$	−3151.92	−	5459.29i	−0.683685	−	1.18418i	0.290163	−	0.956977i	$-0.406291\pi$
$278$	3553.26	+	6154.43i	0.766585	+	1.32776i
$279$		0			0
$280$	702.025	−	14392.0i	0.149836	−	3.07175i
$281$	−2554.99	−	1475.12i	−0.542412	−	0.313162i	0.203644	−	0.979045i	$-0.434721\pi$
$281$	−2554.99	−	1475.12i	−0.542412	−	0.313162i	−0.746056	+	0.665883i	$0.768055\pi$
$282$		0			0
$283$			5012.69i			1.05291i	0.850203	+	0.526455i	$0.176479\pi$
$283$			5012.69i			1.05291i	−0.850203	+	0.526455i	$0.823521\pi$
$284$		−	14812.3i		−	3.09489i
$285$		0			0
$286$	−5177.66	−	2989.32i	−1.07049	−	0.618050i
$287$	−340.126	+	527.922i	−0.0699547	+	0.108579i
$288$		0			0
$289$	−1460.64	−	2529.90i	−0.297300	−	0.514939i
$290$	−599.130	−	1037.72i	−0.121318	−	0.210128i
$291$		0			0
$292$	11097.8	+	6407.32i	2.22414	+	1.28411i
$293$	978.283	+	1694.44i	0.195058	+	0.337850i	0.946919	−	0.321471i	$-0.104177\pi$
$293$	978.283	+	1694.44i	0.195058	+	0.337850i	−0.751862	+	0.659321i	$0.770844\pi$
$294$		0			0
$295$	468.294	−	811.108i	0.0924241	−	0.160083i
$296$	14773.8	−	8529.66i	2.90105	−	1.67492i
$297$		0			0
$298$	−8402.44	+	14553.5i	−1.63336	+	2.82906i
$299$	−4176.58			−0.807819
$300$		0			0
$301$	−3238.29	−	157.959i	−0.620106	−	0.0302479i
$302$	13243.0	−	7645.84i	2.52334	−	1.45685i
$303$		0			0
$304$	−8393.49	+	4845.99i	−1.58355	+	0.914264i
$305$	890.804	+	514.306i	0.167237	+	0.0965543i
$306$		0			0
$307$			868.942i			0.161541i	0.996733	+	0.0807706i	$0.0257381\pi$
$307$			868.942i			0.161541i	−0.996733	+	0.0807706i	$0.974262\pi$
$308$	−6823.64	−	4396.29i	−1.26238	−	0.813318i
$309$		0			0
$310$	842.306	−	1458.92i	0.154322	−	0.267293i
$311$	−3562.19			−0.649495			−0.324748	−	0.945801i	$-0.605279\pi$
$311$	−3562.19			−0.649495			−0.324748	+	0.945801i	$0.605279\pi$
$312$		0			0
$313$		−	3304.34i		−	0.596717i	−0.954454	−	0.298359i	$-0.903561\pi$
$313$		−	3304.34i		−	0.596717i	0.954454	−	0.298359i	$-0.0964392\pi$
$314$	−18921.2			−3.40059
$315$		0			0
$316$	5576.79			0.992782
$317$		−	577.403i		−	0.102303i	−0.998691	−	0.0511517i	$-0.983711\pi$
$317$		−	577.403i		−	0.102303i	0.998691	−	0.0511517i	$-0.0162892\pi$
$318$		0			0
$319$	−417.331			−0.0732479
$320$	−7517.13	+	13020.0i	−1.31319	+	2.27451i
$321$		0			0
$322$	−7826.02	−	381.743i	−1.35443	−	0.0660674i
$323$			4134.20i			0.712177i
$324$		0			0
$325$	−21.0844	−	12.1731i	−0.00359863	−	0.00207767i
$326$	−7849.28	+	4531.78i	−1.33353	+	0.769915i
$327$		0			0
$328$	2047.29	−	1182.00i	0.344642	−	0.198979i
$329$	1244.16	+	2420.10i	0.208488	+	0.405545i
$330$		0			0
$331$	−1031.68			−0.171319			−0.0856593	−	0.996324i	$-0.527300\pi$
$331$	−1031.68			−0.171319			−0.0856593	+	0.996324i	$0.527300\pi$
$332$	−6529.02	+	11308.6i	−1.07930	+	1.86940i
$333$		0			0
$334$	163.799	−	94.5694i	0.0268344	−	0.0154928i
$335$	−5005.49	+	8669.77i	−0.816356	+	1.41397i
$336$		0			0
$337$	602.886	+	1044.23i	0.0974519	+	0.168792i	0.910629	−	0.413224i	$-0.135597\pi$
$337$	602.886	+	1044.23i	0.0974519	+	0.168792i	−0.813177	+	0.582016i	$0.802264\pi$
$338$	−2912.63	−	1681.61i	−0.468717	−	0.270614i
$339$		0			0
$340$	10349.8	+	17926.4i	1.65087	+	2.85940i
$341$	−293.359	−	508.113i	−0.0465874	−	0.0806917i
$342$		0			0
$343$	6284.66	+	925.550i	0.989329	+	0.145700i
$344$	10569.4	+	6102.23i	1.65658	+	0.956425i
$345$		0			0
$346$		−	21561.3i		−	3.35013i
$347$			8189.26i			1.26692i	0.773774	+	0.633462i	$0.218367\pi$
$347$			8189.26i			1.26692i	−0.773774	+	0.633462i	$0.781633\pi$
$348$		0			0
$349$	−5904.90	−	3409.20i	−0.905679	−	0.522894i	−0.0266409	−	0.999645i	$-0.508481\pi$
$349$	−5904.90	−	3409.20i	−0.905679	−	0.522894i	−0.879038	+	0.476751i	$0.841814\pi$
$350$	−38.3951	−	24.7369i	−0.00586372	−	0.00377784i
$351$		0			0
$352$	5844.10	+	10122.3i	0.884919	+	1.53272i
$353$	−2141.82	−	3709.74i	−0.322940	−	0.559348i	0.658154	−	0.752884i	$-0.271338\pi$
$353$	−2141.82	−	3709.74i	−0.322940	−	0.559348i	−0.981093	+	0.193536i	$0.938004\pi$
$354$		0			0
$355$	6831.33	+	3944.07i	1.02132	+	0.589660i
$356$	7444.36	+	12894.0i	1.10829	+	1.91961i
$357$		0			0
$358$	−2422.39	+	4195.70i	−0.357618	+	0.619412i
$359$	2426.70	−	1401.06i	0.356759	−	0.205975i	−0.310899	−	0.950443i	$-0.600630\pi$
$359$	2426.70	−	1401.06i	0.356759	−	0.205975i	0.667658	+	0.744468i	$0.267297\pi$
$360$		0			0
$361$	−2338.68	+	4050.71i	−0.340965	+	0.590568i
$362$	−1323.24			−0.192122
$363$		0			0
$364$	−17331.6	−	11166.3i	−2.49567	−	1.60790i
$365$	−5910.02	+	3412.15i	−0.847520	+	0.489316i
$366$		0			0
$367$	2944.63	−	1700.08i	0.418824	−	0.241808i	−0.275750	−	0.961229i	$-0.588926\pi$
$367$	2944.63	−	1700.08i	0.418824	−	0.241808i	0.694574	+	0.719421i	$0.255593\pi$
$368$	14128.4	+	8157.02i	2.00134	+	1.15547i
$369$		0			0
$370$			14694.4i			2.06467i
$371$	−683.575	+	14013.8i	−0.0956589	+	1.96108i
$372$		0			0
$373$	3251.77	−	5632.23i	0.451395	−	0.781839i	−0.547078	−	0.837082i	$-0.684260\pi$
$373$	3251.77	−	5632.23i	0.451395	−	0.781839i	0.998473	+	0.0552425i	$0.0175932\pi$
$374$	9961.46			1.37726
$375$		0			0
$376$		−	10243.4i		−	1.40495i
$377$	−1060.00			−0.144808
$378$		0			0
$379$	−5033.39			−0.682184			−0.341092	−	0.940030i	$-0.610797\pi$
$379$	−5033.39			−0.682184			−0.341092	+	0.940030i	$0.610797\pi$
$380$		−	10923.3i		−	1.47462i
$381$		0			0
$382$	−14638.3			−1.96062
$383$	−739.780	+	1281.34i	−0.0986971	+	0.170948i	−0.911146	−	0.412085i	$-0.864801\pi$
$383$	−739.780	+	1281.34i	−0.0986971	+	0.170948i	0.812449	+	0.583033i	$0.198134\pi$
$384$		0			0
$385$	3844.47	−	1976.42i	0.508915	−	0.261630i
$386$		−	2989.30i		−	0.394174i
$387$		0			0
$388$	10443.6	+	6029.64i	1.36648	+	0.788940i
$389$	8261.81	−	4769.96i	1.07684	−	0.621713i	0.146797	−	0.989167i	$-0.453104\pi$
$389$	8261.81	−	4769.96i	1.07684	−	0.621713i	0.930042	+	0.367453i	$0.119770\pi$
$390$		0			0
$391$	6026.59	−	3479.45i	0.779482	−	0.450034i
$392$	−19447.0	−	13915.1i	−2.50567	−	1.79290i
$393$		0			0
$394$	−2768.06			−0.353941
$395$	−1484.93	+	2571.98i	−0.189152	+	0.327621i
$396$		0			0
$397$	−5619.88	+	3244.64i	−0.710463	+	0.410186i	−0.811232	−	0.584724i	$-0.801203\pi$
$397$	−5619.88	+	3244.64i	−0.710463	+	0.410186i	0.100770	+	0.994910i	$0.467869\pi$
$398$	7130.11	−	12349.7i	0.897990	−	1.55536i
$399$		0			0
$400$	47.5491	+	82.3574i	0.00594363	+	0.0102947i
$401$	−12583.0	−	7264.79i	−1.56699	−	0.904705i	−0.996517	−	0.0833912i	$-0.973425\pi$
$401$	−12583.0	−	7264.79i	−1.56699	−	0.904705i	−0.570477	−	0.821313i	$-0.693242\pi$
$402$		0			0
$403$	−745.116	−	1290.58i	−0.0921014	−	0.159524i
$404$	−3768.08	−	6526.51i	−0.464032	−	0.803727i
$405$		0			0
$406$	−1986.21	−	96.8846i	−0.242793	−	0.0118431i
$407$	4432.14	+	2558.90i	0.539787	+	0.311646i
$408$		0			0
$409$			15061.3i			1.82087i	0.413656	+	0.910433i	$0.364252\pi$
$409$			15061.3i			1.82087i	−0.413656	+	0.910433i	$0.635748\pi$
$410$			2036.29i			0.245281i
$411$		0			0
$412$	5269.96	+	3042.61i	0.630175	+	0.363832i
$413$	−710.651	−	1382.34i	−0.0846703	−	0.164698i
$414$		0			0
$415$	−3476.96	−	6022.28i	−0.411271	−	0.712342i
$416$	14843.7	+	25710.0i	1.74945	+	3.03013i
$417$		0			0
$418$	−4552.46	−	2628.37i	−0.532699	−	0.307554i
$419$	6285.98	+	10887.6i	0.732912	+	1.26944i	0.955633	+	0.294558i	$0.0951726\pi$
$419$	6285.98	+	10887.6i	0.732912	+	1.26944i	−0.222722	+	0.974882i	$0.571494\pi$
$420$		0			0
$421$	−1122.71	+	1944.60i	−0.129971	+	0.225116i	−0.923665	−	0.383201i	$-0.874822\pi$
$421$	−1122.71	+	1944.60i	−0.129971	+	0.225116i	0.793694	+	0.608317i	$0.208155\pi$
$422$	−19806.3	+	11435.2i	−2.28473	+	1.31909i
$423$		0			0
$424$	26407.6	−	45739.3i	3.02469	−	5.23891i
$425$	40.5650			0.00462986
$426$		0			0
$427$	1518.16	−	780.476i	0.172058	−	0.0884540i
$428$	−9040.31	+	5219.43i	−1.02098	+	0.589464i
$429$		0			0
$430$	−9104.18	+	5256.30i	−1.02103	+	0.589491i
$431$	6698.97	+	3867.65i	0.748673	+	0.432246i	0.825214	−	0.564820i	$-0.191054\pi$
$431$	6698.97	+	3867.65i	0.748673	+	0.432246i	−0.0765415	+	0.997066i	$0.524388\pi$
$432$		0			0
$433$		−	12830.5i		−	1.42400i	−0.702179	−	0.712000i	$-0.747790\pi$
$433$		−	12830.5i		−	1.42400i	0.702179	−	0.712000i	$-0.252210\pi$
$434$	−1278.23	−	2486.37i	−0.141375	−	0.274999i
$435$		0			0
$436$	−18664.8	+	32328.5i	−2.05019	+	3.55104i
$437$	−3672.26			−0.401987
$438$		0			0
$439$		−	754.434i		−	0.0820208i	−0.999159	−	0.0410104i	$-0.986942\pi$
$439$		−	754.434i		−	0.0820208i	0.999159	−	0.0410104i	$-0.0130577\pi$
$440$	−16272.2			−1.76306
$441$		0			0
$442$	25301.5			2.72278
$443$			489.361i			0.0524836i	0.999656	+	0.0262418i	$0.00835399\pi$
$443$			489.361i			0.0524836i	−0.999656	+	0.0262418i	$0.991646\pi$
$444$		0			0
$445$	−7928.84			−0.844636
$446$	17827.5	−	30878.2i	1.89273	−	3.27830i
$447$		0			0
$448$	11407.5	+	22189.5i	1.20302	+	2.34008i
$449$		−	10214.2i		−	1.07358i	−0.843714	−	0.536792i	$-0.819636\pi$
$449$		−	10214.2i		−	1.07358i	0.843714	−	0.536792i	$-0.180364\pi$
$450$		0			0
$451$	614.187	+	354.601i	0.0641262	+	0.0370233i
$452$	−19484.9	+	11249.6i	−2.02764	+	1.17066i
$453$		0			0
$454$	20246.4	−	11689.3i	2.09298	−	1.20838i
$455$	9764.72	−	5019.98i	1.00610	−	0.517232i
$456$		0			0
$457$	−2698.79			−0.276245			−0.138123	−	0.990415i	$-0.544107\pi$
$457$	−2698.79			−0.276245			−0.138123	+	0.990415i	$0.544107\pi$
$458$	16337.4	−	28297.3i	1.66681	−	2.88700i
$459$		0			0
$460$	−15923.4	+	9193.36i	−1.61398	+	0.931832i
$461$	7226.87	−	12517.3i	0.730128	−	1.26462i	−0.226700	−	0.973965i	$-0.572794\pi$
$461$	7226.87	−	12517.3i	0.730128	−	1.26462i	0.956828	−	0.290654i	$-0.0938728\pi$
$462$		0			0
$463$	−2870.33	−	4971.56i	−0.288111	−	0.499024i	0.685247	−	0.728310i	$-0.259694\pi$
$463$	−2870.33	−	4971.56i	−0.288111	−	0.499024i	−0.973359	+	0.229287i	$0.926361\pi$
$464$	3585.72	+	2070.22i	0.358756	+	0.207128i
$465$		0			0
$466$	4298.05	+	7444.44i	0.427260	+	0.740037i
$467$	−6803.45	−	11783.9i	−0.674146	−	1.16766i	−0.976718	−	0.214529i	$-0.931178\pi$
$467$	−6803.45	−	11783.9i	−0.674146	−	1.16766i	0.302571	−	0.953127i	$-0.402155\pi$
$468$		0			0
$469$	7596.00	+	14775.5i	0.747869	+	1.45473i
$470$	7641.27	+	4411.69i	0.749926	+	0.432970i
$471$		0			0
$472$			5850.93i			0.570574i
$473$			3661.34i			0.355917i
$474$		0			0
$475$	−18.5385	−	10.7032i	−0.00179075	−	0.00103389i
$476$	34311.2	+	1673.65i	3.30389	+	0.161159i
$477$		0			0
$478$	5976.46	+	10351.5i	0.571877	+	0.990519i
$479$	328.624	+	569.193i	0.0313470	+	0.0542945i	0.881273	−	0.472607i	$-0.156687\pi$
$479$	328.624	+	569.193i	0.0313470	+	0.0542945i	−0.849926	+	0.526902i	$0.823354\pi$
$480$		0			0
$481$	11257.4	+	6499.45i	1.06714	+	0.616112i
$482$	9733.71	+	16859.3i	0.919830	+	1.59319i
$483$		0			0
$484$	9362.73	−	16216.7i	0.879295	−	1.52298i
$485$	−5561.66	+	3211.02i	−0.520705	+	0.300629i
$486$		0			0
$487$	−7324.80	+	12686.9i	−0.681557	+	1.18049i	0.292949	+	0.956128i	$0.405363\pi$
$487$	−7324.80	+	12686.9i	−0.681557	+	1.18049i	−0.974506	+	0.224363i	$0.927970\pi$
$488$	−6425.81			−0.596072
$489$		0			0
$490$	18755.8	−	8513.86i	1.72919	−	0.784933i
$491$	−11501.8	+	6640.54i	−1.05716	+	0.610353i	−0.924646	−	0.380827i	$-0.875639\pi$
$491$	−11501.8	+	6640.54i	−1.05716	+	0.610353i	−0.132517	+	0.991181i	$0.542306\pi$
$492$		0			0
$493$	1529.52	−	883.069i	0.139729	−	0.0806723i
$494$	−11563.0	−	6675.90i	−1.05312	−	0.608022i
$495$		0			0
$496$			5820.96i			0.526953i
$497$	11642.3	−	5985.25i	1.05077	−	0.540192i
$498$		0			0
$499$	7277.87	−	12605.6i	0.652910	−	1.13087i	−0.329503	−	0.944154i	$-0.606881\pi$
$499$	7277.87	−	12605.6i	0.652910	−	1.13087i	0.982413	−	0.186719i	$-0.0597853\pi$
$500$	−29340.1			−2.62426
$501$		0			0
$502$		−	11481.7i		−	1.02083i
$503$	9247.39			0.819723			0.409862	−	0.912148i	$-0.365577\pi$
$503$	9247.39			0.819723			0.409862	+	0.912148i	$0.365577\pi$
$504$		0			0
$505$	4013.30			0.353643
$506$			8848.41i			0.777391i
$507$		0			0
$508$	11174.8			0.975991
$509$	6496.47	−	11252.2i	0.565719	−	0.979853i	−0.431264	−	0.902226i	$-0.641932\pi$
$509$	6496.47	−	11252.2i	0.565719	−	0.979853i	0.996982	−	0.0776275i	$-0.0247345\pi$
$510$		0			0
$511$	−551.775	+	11311.8i	−0.0477673	+	0.979266i
$512$		−	231.437i		−	0.0199769i
$513$		0			0
$514$	−18084.9	−	10441.3i	−1.55193	−	0.896005i
$515$	−2806.46	+	1620.31i	−0.240131	+	0.138640i
$516$		0			0
$517$	2661.31	−	1536.51i	0.226391	−	0.130707i
$518$	20499.9	+	13207.5i	1.73883	+	1.12028i
$519$		0			0
$520$	−41330.5			−3.48551
$521$	−2666.59	+	4618.68i	−0.224233	+	0.388384i	−0.956089	−	0.293076i	$-0.905321\pi$
$521$	−2666.59	+	4618.68i	−0.224233	+	0.388384i	0.731856	+	0.681460i	$0.238654\pi$
$522$		0			0
$523$	−3169.82	+	1830.10i	−0.265022	+	0.153011i	−0.626623	−	0.779322i	$-0.715564\pi$
$523$	−3169.82	+	1830.10i	−0.265022	+	0.153011i	0.361601	+	0.932333i	$0.382230\pi$
$524$	−15670.3	+	27141.7i	−1.30641	+	2.26277i
$525$		0			0
$526$	−2637.05	−	4567.50i	−0.218595	−	0.378617i
$527$	2150.33	+	1241.49i	0.177741	+	0.102619i
$528$		0			0
$529$	−2992.83	−	5183.73i	−0.245979	−	0.426048i
$530$	22746.8	+	39398.6i	1.86426	+	3.22899i
$531$		0			0
$532$	−15238.9	−	9818.00i	−1.24190	−	0.800121i
$533$	1560.00	+	900.665i	0.126775	+	0.0731935i
$534$		0			0
$535$		−	5559.11i		−	0.449236i
$536$		−	62539.4i		−	5.03972i
$537$		0			0
$538$	−4956.84	−	2861.83i	−0.397220	−	0.229335i
$539$	698.197	−	7139.75i	0.0557949	−	0.570558i
$540$		0			0
$541$	−3530.92	−	6115.74i	−0.280603	−	0.486019i	0.690930	−	0.722921i	$-0.257201\pi$
$541$	−3530.92	−	6115.74i	−0.280603	−	0.486019i	−0.971533	+	0.236903i	$0.923868\pi$
$542$	−19604.0	−	33955.2i	−1.55363	−	2.69096i
$543$		0			0
$544$	−42837.3	−	24732.1i	−3.37616	−	1.94923i
$545$	−9939.77	−	17216.2i	−0.781235	−	1.35314i
$546$		0			0
$547$	−5097.66	+	8829.41i	−0.398465	+	0.690161i	−0.993537	−	0.113511i	$-0.963790\pi$
$547$	−5097.66	+	8829.41i	−0.398465	+	0.690161i	0.595072	+	0.803672i	$0.297124\pi$
$548$	−11138.1	+	6430.56i	−0.868238	+	0.501277i
$549$		0			0
$550$	−25.7897	+	44.6690i	−0.00199941	+	0.00346308i
$551$	−932.004			−0.0720593
$552$		0			0
$553$	2253.43	+	4383.31i	0.173283	+	0.337066i
$554$	−29376.8	+	16960.7i	−2.25289	+	1.30071i
$555$		0			0
$556$	23967.6	−	13837.7i	1.82815	−	1.05549i
$557$	16089.2	+	9289.11i	1.22392	+	0.706629i	0.965751	−	0.259471i	$-0.0835484\pi$
$557$	16089.2	+	9289.11i	1.22392	+	0.706629i	0.258166	+	0.966100i	$0.416882\pi$
$558$		0			0
$559$			9299.59i			0.703633i
$560$	−42835.9	−	2089.48i	−3.23241	−	0.157673i
$561$		0			0
$562$	−7937.73	+	13748.5i	−0.595788	+	1.03193i
$563$	11255.2			0.842538			0.421269	−	0.906936i	$-0.361585\pi$
$563$	11255.2			0.842538			0.421269	+	0.906936i	$0.361585\pi$
$564$		0			0
$565$		−	11981.8i		−	0.892170i
$566$	26973.6			2.00315
$567$		0			0
$568$	−49277.8			−3.64023
$569$		−	21344.6i		−	1.57261i	−0.617841	−	0.786303i	$-0.711993\pi$
$569$		−	21344.6i		−	1.57261i	0.617841	−	0.786303i	$-0.288007\pi$
$570$		0			0
$571$	22418.7			1.64307			0.821537	−	0.570155i	$-0.193117\pi$
$571$	22418.7			1.64307			0.821537	+	0.570155i	$0.193117\pi$
$572$	−11641.5	+	20163.7i	−0.850974	+	1.47393i
$573$		0			0
$574$	2840.78	+	1830.24i	0.206571	+	0.133088i
$575$			36.0324i			0.00261331i
$576$		0			0
$577$	5328.83	+	3076.60i	0.384475	+	0.221977i	0.679764	−	0.733431i	$-0.262082\pi$
$577$	5328.83	+	3076.60i	0.384475	+	0.221977i	−0.295288	+	0.955408i	$0.595416\pi$
$578$	−13613.5	+	7859.77i	−0.979668	+	0.565612i
$579$		0			0
$580$	−4041.28	+	2333.23i	−0.289319	+	0.167038i
$581$	−11526.7	−	562.256i	−0.823075	−	0.0401485i
$582$		0			0
$583$	15844.6			1.12558
$584$	21316.0	−	36920.4i	1.51038	−	2.61605i
$585$		0			0
$586$	9117.87	−	5264.20i	0.642757	−	0.371096i
$587$	−465.944	+	807.038i	−0.0327624	+	0.0567462i	−0.881942	−	0.471358i	$-0.843764\pi$
$587$	−465.944	+	807.038i	−0.0327624	+	0.0567462i	0.849179	+	0.528105i	$0.177097\pi$
$588$		0			0
$589$	−655.144	−	1134.74i	−0.0458314	−	0.0793824i
$590$	−4364.63	−	2519.92i	−0.304557	−	0.175836i
$591$		0			0
$592$	−25387.4	−	43972.2i	−1.76252	−	3.05278i
$593$	−9100.59	−	15762.7i	−0.630213	−	1.09156i	−0.987508	−	0.157570i	$-0.949634\pi$
$593$	−9100.59	−	15762.7i	−0.630213	−	1.09156i	0.357294	−	0.933992i	$-0.383699\pi$
$594$		0			0
$595$	−9907.91	+	15378.4i	−0.682663	+	1.05959i
$596$	56676.5	+	32722.2i	3.89524	+	2.24892i
$597$		0			0
$598$			22474.4i			1.53687i
$599$		−	6910.09i		−	0.471350i	−0.971832	−	0.235675i	$-0.924270\pi$
$599$		−	6910.09i		−	0.471350i	0.971832	−	0.235675i	$-0.0757301\pi$
$600$		0			0
$601$	4408.10	+	2545.02i	0.299185	+	0.172734i	0.642077	−	0.766640i	$-0.278073\pi$
$601$	4408.10	+	2545.02i	0.299185	+	0.172734i	−0.342892	+	0.939375i	$0.611406\pi$
$602$	−849.990	+	17425.4i	−0.0575465	+	1.17975i
$603$		0			0
$604$	−29775.7	−	51573.1i	−2.00589	−	3.47430i
$605$	4986.03	+	8636.05i	0.335059	+	0.580340i
$606$		0			0
$607$	1216.35	+	702.257i	0.0813343	+	0.0469584i	0.540116	−	0.841591i	$-0.318381\pi$
$607$	1216.35	+	702.257i	0.0813343	+	0.0469584i	−0.458781	+	0.888549i	$0.651714\pi$
$608$	13051.3	+	22605.5i	0.870560	+	1.50785i
$609$		0			0
$610$	2767.51	−	4793.47i	0.183694	−	0.318167i
$611$	6759.57	−	3902.64i	0.447566	−	0.258402i
$612$		0			0
$613$	3445.72	−	5968.16i	0.227033	−	0.393233i	−0.729894	−	0.683560i	$-0.760431\pi$
$613$	3445.72	−	5968.16i	0.227033	−	0.393233i	0.956928	+	0.290327i	$0.0937641\pi$
$614$	4675.83			0.307331
$615$		0			0
$616$	−14625.6	+	22701.0i	−0.956630	+	1.48482i
$617$	13688.9	−	7903.27i	0.893181	−	0.515678i	0.0181995	−	0.999834i	$-0.494207\pi$
$617$	13688.9	−	7903.27i	0.893181	−	0.515678i	0.874982	+	0.484156i	$0.160873\pi$
$618$		0			0
$619$	21238.9	−	12262.3i	1.37910	−	0.796223i	0.387047	−	0.922060i	$-0.373495\pi$
$619$	21238.9	−	12262.3i	1.37910	−	0.796223i	0.992051	+	0.125837i	$0.0401618\pi$
$620$	−5681.56	−	3280.25i	−0.368027	−	0.212481i
$621$		0			0
$622$			19168.4i			1.23566i
$623$	−7126.52	+	11061.3i	−0.458295	+	0.711337i
$624$		0			0
$625$	7783.75	−	13481.9i	0.498160	−	0.862839i
$626$	−17780.9			−1.13525
$627$		0			0
$628$			73686.1i			4.68216i
$629$	−21658.4			−1.37294
$630$		0			0
$631$	−21001.1			−1.32494			−0.662471	−	0.749087i	$-0.730492\pi$
$631$	−21001.1			−1.32494			−0.662471	+	0.749087i	$0.730492\pi$
$632$		−	18553.0i		−	1.16772i
$633$		0			0
$634$	−3107.04			−0.194632
$635$	−2975.52	+	5153.76i	−0.185953	+	0.322080i
$636$		0			0
$637$	1773.38	−	18134.5i	0.110304	−	1.12797i
$638$			2245.69i			0.139354i
$639$		0			0
$640$	26853.1	+	15503.7i	1.65854	+	0.957556i
$641$	−2840.87	+	1640.18i	−0.175051	+	0.101066i	−0.584965	−	0.811058i	$-0.698892\pi$
$641$	−2840.87	+	1640.18i	−0.175051	+	0.101066i	0.409914	+	0.912124i	$0.365559\pi$
$642$		0			0
$643$	−19195.0	+	11082.2i	−1.17726	+	0.679690i	−0.955378	−	0.295385i	$-0.904552\pi$
$643$	−19195.0	+	11082.2i	−1.17726	+	0.679690i	−0.221879	+	0.975074i	$0.571219\pi$
$644$	−1486.65	+	30477.4i	−0.0909660	+	1.86487i
$645$		0			0
$646$	22246.4			1.35491
$647$	−11897.6	+	20607.3i	−0.722944	+	1.25217i	0.236871	+	0.971541i	$0.423878\pi$
$647$	−11897.6	+	20607.3i	−0.722944	+	1.25217i	−0.959815	+	0.280634i	$0.909455\pi$
$648$		0			0
$649$	−1520.12	+	877.640i	−0.0919412	+	0.0530823i
$650$	−65.5042	+	113.457i	−0.00395275	+	0.00684636i
$651$		0			0
$652$	17648.4	+	30568.0i	1.06007	+	1.83610i
$653$	−6319.94	−	3648.82i	−0.378742	−	0.218667i	0.298529	−	0.954401i	$-0.403504\pi$
$653$	−6319.94	−	3648.82i	−0.378742	−	0.218667i	−0.677271	+	0.735734i	$0.736837\pi$
$654$		0			0
$655$	−8345.05	−	14454.1i	−0.497814	−	0.862239i
$656$	−3518.07	−	6093.47i	−0.209386	−	0.362668i
$657$		0			0
$658$	13022.7	−	6694.88i	0.771546	−	0.396647i
$659$	−16759.1	−	9675.89i	−0.990657	−	0.571956i	−0.0851863	−	0.996365i	$-0.527149\pi$
$659$	−16759.1	−	9675.89i	−0.990657	−	0.571956i	−0.905471	+	0.424409i	$0.860482\pi$
$660$		0			0
$661$		−	19625.8i		−	1.15485i	−0.816443	−	0.577426i	$-0.804057\pi$
$661$		−	19625.8i		−	1.15485i	0.816443	−	0.577426i	$-0.195943\pi$
$662$			5551.56i			0.325933i
$663$		0			0
$664$	37621.6	+	21720.8i	2.19880	+	1.26948i
$665$	8585.64	−	4413.82i	0.500657	−	0.257385i
$666$		0			0
$667$	784.399	+	1358.62i	0.0455353	+	0.0788695i
$668$	−368.288	−	637.894i	−0.0213316	−	0.0369474i
$669$		0			0
$670$	46652.6	+	26934.9i	2.69007	+	1.55311i
$671$	−963.872	−	1669.48i	−0.0554544	−	0.0960498i
$672$		0			0
$673$	−5545.58	+	9605.22i	−0.317632	+	0.550155i	−0.979993	−	0.199030i	$-0.936221\pi$
$673$	−5545.58	+	9605.22i	−0.317632	+	0.550155i	0.662361	+	0.749184i	$0.269554\pi$
$674$	5619.07	−	3244.17i	0.321125	−	0.185402i
$675$		0			0
$676$	−6548.81	+	11342.9i	−0.372599	+	0.645361i
$677$	19031.2			1.08040			0.540199	−	0.841537i	$-0.318349\pi$
$677$	19031.2			1.08040			0.540199	+	0.841537i	$0.318349\pi$
$678$		0			0
$679$	−519.251	+	10645.0i	−0.0293476	+	0.601648i
$680$	59637.8	−	34431.9i	3.36324	−	1.94177i
$681$		0			0
$682$	−2734.19	+	1578.59i	−0.153515	+	0.0886322i
$683$	−20397.8	−	11776.7i	−1.14275	−	0.659768i	−0.195641	−	0.980676i	$-0.562679\pi$
$683$	−20397.8	−	11776.7i	−1.14275	−	0.659768i	−0.947110	+	0.320908i	$0.896012\pi$
$684$		0			0
$685$		−	6849.06i		−	0.382028i
$686$	4980.44	−	33818.2i	0.277193	−	1.88219i
$687$		0			0
$688$	18162.4	−	31458.3i	1.00645	−	1.74322i
$689$	40244.3			2.22523
$690$		0			0
$691$		−	12997.3i		−	0.715541i	−0.933810	−	0.357771i	$-0.883537\pi$
$691$		−	12997.3i		−	0.715541i	0.933810	−	0.357771i	$-0.116463\pi$
$692$	−83967.8			−4.61268
$693$		0			0
$694$	44066.9			2.41031
$695$			14738.3i			0.804395i
$696$		0			0
$697$	−3001.33			−0.163104
$698$	−18345.1	+	31774.7i	−0.994803	+	1.72305i
$699$		0			0
$700$	−96.3347	+	149.525i	−0.00520158	+	0.00807357i
$701$		−	11465.8i		−	0.617773i	−0.951099	−	0.308887i	$-0.900044\pi$
$701$		−	11465.8i		−	0.617773i	0.951099	−	0.308887i	$-0.0999563\pi$
$702$		0			0
$703$	9898.07	+	5714.65i	0.531028	+	0.306589i
$704$	24401.2	−	14088.0i	1.30633	−	0.754208i
$705$		0			0
$706$	−19962.4	+	11525.3i	−1.06416	+	0.614390i
$707$	3607.20	−	5598.87i	0.191885	−	0.297832i
$708$		0			0
$709$	−26714.8			−1.41509			−0.707543	−	0.706670i	$-0.750197\pi$
$709$	−26714.8			−1.41509			−0.707543	+	0.706670i	$0.750197\pi$
$710$	21223.3	−	36759.8i	1.12182	−	1.94306i
$711$		0			0
$712$	42896.0	−	24766.0i	2.25786	−	1.30358i
$713$	−1102.77	+	1910.06i	−0.0579231	+	0.100326i
$714$		0			0
$715$	−6199.58	−	10738.0i	−0.324267	−	0.561647i
$716$	16339.6	+	9433.67i	0.852848	+	0.492392i
$717$		0			0
$718$	−7539.18	−	13058.3i	−0.391866	−	0.678732i
$719$	12300.2	+	21304.6i	0.637999	+	1.10505i	0.985871	+	0.167505i	$0.0535711\pi$
$719$	12300.2	+	21304.6i	0.637999	+	1.10505i	−0.347872	+	0.937542i	$0.613096\pi$
$720$		0			0
$721$	−262.019	+	5371.58i	−0.0135341	+	0.277459i
$722$	21797.1	+	12584.6i	1.12355	+	0.648683i
$723$		0			0
$724$			5153.19i			0.264526i
$725$			9.14487i			0.000468458i
$726$		0			0
$727$	9597.32	+	5541.01i	0.489608	+	0.282675i	0.724412	−	0.689368i	$-0.242112\pi$
$727$	9597.32	+	5541.01i	0.489608	+	0.282675i	−0.234804	+	0.972043i	$0.575445\pi$
$728$	−37148.3	+	57659.2i	−1.89122	+	2.93543i
$729$		0			0
$730$	18361.0	+	31802.2i	0.930920	+	1.61240i
$731$	−7747.36	−	13418.8i	−0.391992	−	0.678951i
$732$		0			0
$733$	−18488.0	−	10674.0i	−0.931608	−	0.537864i	−0.0442885	−	0.999019i	$-0.514102\pi$
$733$	−18488.0	−	10674.0i	−0.931608	−	0.537864i	−0.887320	+	0.461154i	$0.847435\pi$
$734$	−9148.25	−	15845.2i	−0.460038	−	0.796810i
$735$		0			0
$736$	21968.6	−	38050.8i	1.10024	−	1.90567i
$737$	16248.2	−	9380.91i	0.812090	−	0.468861i
$738$		0			0
$739$	4254.96	−	7369.80i	0.211801	−	0.366850i	−0.740477	−	0.672082i	$-0.765400\pi$
$739$	4254.96	−	7369.80i	0.211801	−	0.366850i	0.952278	+	0.305231i	$0.0987337\pi$
$740$	57225.6			2.84278
$741$		0			0
$742$	75409.1	+	3678.36i	3.73094	+	0.181990i
$743$	3827.12	−	2209.59i	0.188968	−	0.109101i	−0.402531	−	0.915406i	$-0.631870\pi$
$743$	3827.12	−	2209.59i	0.188968	−	0.109101i	0.591499	+	0.806305i	$0.298536\pi$
$744$		0			0
$745$	−30182.5	+	17425.9i	−1.48430	+	0.856959i
$746$	−30307.4	−	17498.0i	−1.48744	−	0.858776i
$747$		0			0
$748$		−	38793.6i		−	1.89630i
$749$	−7755.38	−	4996.58i	−0.378338	−	0.243753i
$750$		0			0
$751$	−7824.79	+	13552.9i	−0.380201	+	0.658527i	−0.991091	−	0.133188i	$-0.957478\pi$
$751$	−7824.79	+	13552.9i	−0.380201	+	0.658527i	0.610890	+	0.791716i	$0.290812\pi$
$752$	−30488.0			−1.47844
$753$		0			0
$754$			5703.91i			0.275496i
$755$	31713.5			1.52871
$756$		0			0
$757$	−2004.92			−0.0962616			−0.0481308	−	0.998841i	$-0.515326\pi$
$757$	−2004.92			−0.0962616			−0.0481308	+	0.998841i	$0.515326\pi$
$758$			27085.0i			1.29785i
$759$		0			0
$760$	−36339.9			−1.73446
$761$	−16344.8	+	28310.0i	−0.778579	+	1.34854i	0.154183	+	0.988042i	$0.450726\pi$
$761$	−16344.8	+	28310.0i	−0.778579	+	1.34854i	−0.932761	+	0.360495i	$0.882608\pi$
$762$		0			0
$763$	−32951.9	−	1607.35i	−1.56348	−	0.0762647i
$764$			57006.8i			2.69952i
$765$		0			0
$766$	6894.95	+	3980.80i	0.325228	+	0.187771i
$767$	−3861.01	+	2229.15i	−0.181764	+	0.104941i
$768$		0			0
$769$	−25569.0	+	14762.2i	−1.19901	+	0.692250i	−0.960335	−	0.278849i	$-0.910047\pi$
$769$	−25569.0	+	14762.2i	−1.19901	+	0.692250i	−0.238677	+	0.971099i	$0.576714\pi$
$770$	−10635.2	−	20687.3i	−0.497749	−	0.968207i
$771$		0			0
$772$	−11641.4			−0.542726
$773$	−17060.8	+	29550.1i	−0.793834	+	1.37496i	0.129743	+	0.991548i	$0.458585\pi$
$773$	−17060.8	+	29550.1i	−0.793834	+	1.37496i	−0.923577	+	0.383413i	$0.874749\pi$
$774$		0			0
$775$	−11.1341	+	6.42830i	−0.000516065	+	0.000297950i
$776$	20059.5	−	34744.1i	0.927957	−	1.60727i
$777$		0			0
$778$	−25667.4	−	44457.3i	−1.18281	−	2.04868i
$779$	1371.63	+	791.911i	0.0630857	+	0.0364225i
$780$		0			0
$781$	−7391.67	−	12802.7i	−0.338662	−	0.586579i
$782$	−18723.2	−	32429.5i	−0.856187	−	1.48296i
$783$		0			0
$784$	−41416.4	+	57881.4i	−1.88668	+	2.63672i
$785$	−33983.5	−	19620.4i	−1.54513	−	0.892079i
$786$		0			0
$787$			2283.16i			0.103413i	0.998662	+	0.0517064i	$0.0164660\pi$
$787$			2283.16i			0.103413i	−0.998662	+	0.0517064i	$0.983534\pi$
$788$			10779.8i			0.487330i
$789$		0			0
$790$	13840.0	+	7990.52i	0.623297	+	0.359861i
$791$	−16715.5	−	10769.3i	−0.751369	−	0.484087i
$792$		0			0
$793$	−2448.18	−	4240.37i	−0.109631	−	0.189887i
$794$	17459.6	+	30240.9i	0.780376	+	1.35165i
$795$		0			0
$796$	−48094.3	−	27767.3i	−2.14153	−	1.23641i
$797$	7941.56	+	13755.2i	0.352954	+	0.611335i	0.986766	−	0.162153i	$-0.0518438\pi$
$797$	7941.56	+	13755.2i	0.352954	+	0.611335i	−0.633811	+	0.773488i	$0.718510\pi$
$798$		0			0
$799$	−6502.47	+	11262.6i	−0.287911	+	0.498677i
$800$	221.807	−	128.060i	0.00980256	−	0.00565951i
$801$		0			0
$802$	−39092.3	+	67709.9i	−1.72119	+	2.98120i
$803$	12789.6			0.562061
$804$		0			0
$805$	−13660.1	−	8800.84i	−0.598082	−	0.385328i
$806$	−6944.68	+	4009.51i	−0.303494	+	0.175222i
$807$		0			0
$808$	−21712.5	+	12535.7i	−0.945350	+	0.545798i
$809$	14181.4	+	8187.64i	0.616306	+	0.355824i	0.775429	−	0.631434i	$-0.217533\pi$
$809$	14181.4	+	8187.64i	0.616306	+	0.355824i	−0.159123	+	0.987259i	$0.550867\pi$
$810$		0			0
$811$		−	31487.1i		−	1.36333i	−0.731664	−	0.681665i	$-0.761256\pi$
$811$		−	31487.1i		−	1.36333i	0.731664	−	0.681665i	$-0.238744\pi$
$812$	−377.305	+	7735.03i	−0.0163064	+	0.334293i
$813$		0			0
$814$	13769.6	−	23849.7i	0.592905	−	1.02694i
$815$	−18797.0			−0.807889
$816$		0			0
$817$			8176.67i			0.350141i
$818$	81045.9			3.46419
$819$		0			0
$820$	7930.07			0.337720
$821$			34836.7i			1.48089i	0.672117	+	0.740445i	$0.265385\pi$
$821$			34836.7i			1.48089i	−0.672117	+	0.740445i	$0.734615\pi$
$822$		0			0
$823$	5838.20			0.247274			0.123637	−	0.992327i	$-0.460544\pi$
$823$	5838.20			0.247274			0.123637	+	0.992327i	$0.460544\pi$
$824$	10122.2	−	17532.2i	0.427942	−	0.741217i
$825$		0			0
$826$	−7438.45	+	3824.06i	−0.313337	+	0.161085i
$827$		−	21130.4i		−	0.888483i	−0.895907	−	0.444241i	$-0.853473\pi$
$827$		−	21130.4i		−	0.888483i	0.895907	−	0.444241i	$-0.146527\pi$
$828$		0			0
$829$	7567.18	+	4368.91i	0.317031	+	0.183038i	0.650069	−	0.759876i	$-0.274740\pi$
$829$	7567.18	+	4368.91i	0.317031	+	0.183038i	−0.333037	+	0.942914i	$0.608073\pi$
$830$	−32406.3	+	18709.8i	−1.35523	+	0.782440i
$831$		0			0
$832$	61977.5	−	35782.7i	2.58255	−	1.49104i
$833$	12548.8	+	27644.6i	0.521955	+	1.14985i
$834$		0			0
$835$	392.256			0.0162570
$836$	−10235.8	+	17729.0i	−0.423461	+	0.733456i
$837$		0			0
$838$	58587.0	−	33825.2i	2.41510	−	1.39436i
$839$	−15401.3	+	26675.8i	−0.633744	+	1.09768i	0.353036	+	0.935610i	$0.385149\pi$
$839$	−15401.3	+	26675.8i	−0.633744	+	1.09768i	−0.986780	+	0.162067i	$0.948184\pi$
$840$		0			0
$841$	−11995.4	−	20776.7i	−0.491837	−	0.851887i
$842$	10464.0	+	6041.39i	0.428282	+	0.247269i
$843$		0			0
$844$	44532.9	+	77133.2i	1.81621	+	3.14577i
$845$	−3487.50	−	6040.53i	−0.141981	−	0.245918i
$846$		0			0
$847$	16529.4	+	806.285i	0.670553	+	0.0327087i
$848$	−136137.	−	78598.6i	−5.51292	−	3.18289i
$849$		0			0
$850$		−	218.283i		−	0.00880828i
$851$		−	19238.4i		−	0.774952i
$852$		0			0
$853$	31952.4	+	18447.7i	1.28257	+	0.740491i	0.977317	−	0.211782i	$-0.0679266\pi$
$853$	31952.4	+	18447.7i	1.28257	+	0.740491i	0.305250	+	0.952272i	$0.401260\pi$
$854$	−4199.79	−	8169.31i	−0.168283	−	0.327340i
$855$		0			0
$856$	17364.1	+	30075.5i	0.693332	+	1.20089i
$857$	16576.7	+	28711.6i	0.660733	+	1.14442i	0.980423	+	0.196901i	$0.0630878\pi$
$857$	16576.7	+	28711.6i	0.660733	+	1.14442i	−0.319690	+	0.947522i	$0.603579\pi$
$858$		0			0
$859$	−3221.36	−	1859.85i	−0.127953	−	0.0738736i	0.434657	−	0.900596i	$-0.356869\pi$
$859$	−3221.36	−	1859.85i	−0.127953	−	0.0738736i	−0.562610	+	0.826722i	$0.690203\pi$
$860$	20470.0	+	35455.0i	0.811651	+	1.40582i
$861$		0			0
$862$	20812.1	−	36047.6i	0.822346	−	1.42434i
$863$	−7627.67	+	4403.84i	−0.300868	+	0.173706i	−0.642833	−	0.766007i	$-0.722241\pi$
$863$	−7627.67	+	4403.84i	−0.300868	+	0.173706i	0.341965	+	0.939713i	$0.388908\pi$
$864$		0			0
$865$	22358.1	−	38725.4i	0.878842	−	1.52220i
$866$	−69041.5			−2.70915
$867$		0			0
$868$	−9682.85	+	4977.89i	−0.378637	+	0.194655i
$869$	4820.20	−	2782.95i	0.188164	−	0.108636i
$870$		0			0
$871$	41269.5	−	23827.0i	1.60547	−	0.926918i
$872$	107551.	+	62094.5i	4.17676	+	2.41145i
$873$		0			0
$874$			19760.7i			0.764777i
$875$	−11855.6	−	23061.1i	−0.458047	−	0.890980i
$876$		0			0
$877$	−18519.5	+	32076.7i	−0.713067	+	1.23507i	0.250634	+	0.968082i	$0.419361\pi$
$877$	−18519.5	+	32076.7i	−0.713067	+	1.23507i	−0.963701	+	0.266986i	$0.913972\pi$
$878$	−4059.66			−0.156044
$879$		0			0
$880$			48432.1i			1.85528i
$881$	−40772.5			−1.55921			−0.779603	−	0.626274i	$-0.784579\pi$
$881$	−40772.5			−1.55921			−0.779603	+	0.626274i	$0.784579\pi$
$882$		0			0
$883$	18142.6			0.691447			0.345723	−	0.938336i	$-0.387634\pi$
$883$	18142.6			0.691447			0.345723	+	0.938336i	$0.387634\pi$
$884$		−	98533.5i		−	3.74891i
$885$		0			0
$886$	2633.28			0.0998498
$887$	18911.6	−	32755.8i	0.715884	−	1.23995i	−0.246733	−	0.969083i	$-0.579357\pi$
$887$	18911.6	−	32755.8i	0.715884	−	1.23995i	0.962618	−	0.270864i	$-0.0873095\pi$
$888$		0			0
$889$	4515.45	+	8783.33i	0.170353	+	0.331365i
$890$			42665.6i			1.60691i
$891$		0			0
$892$	−120251.	−	69426.9i	−4.51379	−	2.60604i
$893$	5943.36	−	3431.40i	0.222718	−	0.128586i
$894$		0			0
$895$	−8701.48	+	5023.80i	−0.324981	+	0.187628i
$896$	45764.7	−	23527.3i	1.70635	−	0.877224i
$897$		0			0
$898$	−54963.5			−2.04249
$899$	−279.879	+	484.764i	−0.0103832	+	0.0179842i
$900$		0			0
$901$	−58070.4	+	33527.0i	−2.14718	+	1.23967i
$902$	1908.13	−	3304.98i	0.0704366	−	0.122000i
$903$		0			0
$904$	37425.4	+	64822.8i	1.37694	+	2.38493i
$905$	−2376.62	−	1372.14i	−0.0872944	−	0.0503994i
$906$		0			0
$907$	5291.43	+	9165.03i	0.193715	+	0.335524i	0.946478	−	0.322767i	$-0.104613\pi$
$907$	5291.43	+	9165.03i	0.193715	+	0.335524i	−0.752764	+	0.658291i	$0.771280\pi$
$908$	−45522.4	−	78847.0i	−1.66378	−	2.88175i
$909$		0			0
$910$	−27012.8	−	52544.6i	−0.984030	−	1.91411i
$911$	6711.96	+	3875.15i	0.244102	+	0.140932i	0.617061	−	0.786916i	$-0.288323\pi$
$911$	6711.96	+	3875.15i	0.244102	+	0.140932i	−0.372959	+	0.927848i	$0.621657\pi$
$912$		0			0
$913$			13032.5i			0.472413i
$914$			14522.4i			0.525555i
$915$		0			0
$916$	−110200.	−	63624.0i	−3.97501	−	2.29498i
$917$	−27665.1	−	1349.47i	−0.996274	−	0.0485969i
$918$		0			0
$919$	19531.7	+	33829.9i	0.701080	+	1.21431i	0.968088	+	0.250611i	$0.0806316\pi$
$919$	19531.7	+	33829.9i	0.701080	+	1.21431i	−0.267008	+	0.963694i	$0.586035\pi$
$920$	30584.6	+	52974.1i	1.09603	+	1.89837i
$921$		0			0
$922$	−67356.4	−	38888.3i	−2.40593	−	1.38906i
$923$	−18774.4	−	32518.2i	−0.669520	−	1.15964i
$924$		0			0
$925$	56.0725	−	97.1203i	0.00199314	−	0.00345221i
$926$	−26752.3	+	15445.4i	−0.949389	+	0.548130i
$927$		0			0
$928$	5575.54	−	9657.13i	0.197227	−	0.341606i
$929$	1716.74			0.0606292			0.0303146	−	0.999540i	$-0.490349\pi$
$929$	1716.74			0.0606292			0.0303146	+	0.999540i	$0.490349\pi$
$930$		0			0
$931$	1559.25	−	15944.8i	0.0548896	−	0.561300i
$932$	28991.4	−	16738.2i	1.01893	−	0.588281i
$933$		0			0
$934$	−63410.1	+	36609.8i	−2.22146	+	1.28256i
$935$	17891.3	+	10329.6i	0.625785	+	0.361297i
$936$		0			0
$937$		−	26395.9i		−	0.920296i	−0.887842	−	0.460148i	$-0.847796\pi$
$937$		−	26395.9i		−	0.920296i	0.887842	−	0.460148i	$-0.152204\pi$
$938$	79508.0	−	40874.6i	2.76762	−	1.42282i
$939$		0			0
$940$	17180.7	−	29757.9i	0.596143	−	1.03255i
$941$	−20858.8			−0.722611			−0.361306	−	0.932447i	$-0.617669\pi$
$941$	−20858.8			−0.722611			−0.361306	+	0.932447i	$0.617669\pi$
$942$		0			0
$943$		−	2665.97i		−	0.0920637i
$944$	17414.5			0.600417
$945$		0			0
$946$	19701.9			0.677129
$947$		−	15415.7i		−	0.528978i	−0.964389	−	0.264489i	$-0.914797\pi$
$947$		−	15415.7i		−	0.528978i	0.964389	−	0.264489i	$-0.0852032\pi$
$948$		0			0
$949$	32484.8			1.11117
$950$	−57.5947	+	99.7569i	−0.00196697	+	0.00340688i
$951$		0			0
$952$	5567.94	−	114147.i	0.189557	−	3.88606i
$953$		−	7952.81i		−	0.270322i	−0.990824	−	0.135161i	$-0.956845\pi$
$953$		−	7952.81i		−	0.270322i	0.990824	−	0.135161i	$-0.0431552\pi$
$954$		0			0
$955$	−26291.1	−	15179.2i	−0.890849	−	0.514332i
$956$	40312.7	−	23274.6i	1.36381	−	0.787398i
$957$		0			0
$958$	3062.86	−	1768.34i	0.103295	−	0.0596374i
$959$	−9554.96	−	6156.00i	−0.321737	−	0.207287i
$960$		0			0
$961$	29004.0			0.973584
$962$	34974.0	−	60576.7i	1.17215	−	2.03022i
$963$		0			0
$964$	65656.2	−	37906.6i	2.19362	−	1.26648i
$965$	3099.76	−	5368.95i	0.103404	−	0.179101i
$966$		0			0
$967$	16044.1	+	27789.3i	0.533552	+	0.924139i	0.999232	+	0.0391858i	$0.0124764\pi$
$967$	16044.1	+	27789.3i	0.533552	+	0.924139i	−0.465680	+	0.884953i	$0.654190\pi$
$968$	−53950.1	−	31148.1i	−1.79134	−	1.03423i
$969$		0			0
$970$	17278.7	+	29927.6i	0.571945	+	0.990638i
$971$	15951.3	+	27628.5i	0.527191	+	0.913121i	0.999498	+	0.0316872i	$0.0100880\pi$
$971$	15951.3	+	27628.5i	0.527191	+	0.913121i	−0.472307	+	0.881434i	$0.656579\pi$
$972$		0			0
$973$	20561.0	+	13246.9i	0.677447	+	0.436461i
$974$	68269.1	+	39415.2i	2.24588	+	1.29666i
$975$		0			0
$976$			19125.6i			0.627248i
$977$			42815.5i			1.40204i	0.713143	+	0.701018i	$0.247271\pi$
$977$			42815.5i			1.40204i	−0.713143	+	0.701018i	$0.752729\pi$
$978$		0			0
$979$	12868.8	+	7429.81i	0.420111	+	0.242551i
$980$	−33156.1	−	73042.1i	−1.08075	−	2.38086i
$981$		0			0
$982$	35733.2	+	61891.7i	1.16119	+	2.01125i
$983$	191.121	+	331.032i	0.00620124	+	0.0107409i	0.869109	−	0.494620i	$-0.164693\pi$
$983$	191.121	+	331.032i	0.00620124	+	0.0107409i	−0.862908	+	0.505361i	$0.831359\pi$
$984$		0			0
$985$	−4971.59	−	2870.35i	−0.160820	−	0.0928496i
$986$	−4751.85	−	8230.45i	−0.153479	−	0.265833i
$987$		0			0
$988$	−25998.4	+	45030.6i	−0.837165	+	1.45001i
$989$	11919.5	−	6881.70i	0.383232	−	0.221259i
$990$		0			0
$991$	427.302	−	740.109i	0.0136970	−	0.0237238i	−0.859096	−	0.511815i	$-0.828973\pi$
$991$	427.302	−	740.109i	0.0136970	−	0.0237238i	0.872793	+	0.488091i	$0.162307\pi$
$992$	15677.1			0.501763
$993$		0			0
$994$	−32207.0	−	62648.2i	−1.02771	−	1.99907i
$995$	25612.1	−	14787.2i	0.816040	−	0.471141i
$996$		0			0
$997$	7666.88	−	4426.48i	0.243543	−	0.140610i	−0.373261	−	0.927726i	$-0.621760\pi$
$997$	7666.88	−	4426.48i	0.243543	−	0.140610i	0.616804	+	0.787117i	$0.288427\pi$
$998$	−67831.7	−	39162.7i	−2.15148	−	1.24216i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.4.i.a.143.1		44
3.2	odd	2		63.4.i.a.38.22	yes	44
7.5	odd	6		189.4.s.a.89.1		44
9.4	even	3		63.4.s.a.59.22	yes	44
9.5	odd	6		189.4.s.a.17.1		44
21.5	even	6		63.4.s.a.47.22	yes	44
63.5	even	6	inner	189.4.i.a.152.22		44
63.40	odd	6		63.4.i.a.5.1	✓	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.4.i.a.5.1	✓	44	63.40	odd	6
63.4.i.a.38.22	yes	44	3.2	odd	2
63.4.s.a.47.22	yes	44	21.5	even	6
63.4.s.a.59.22	yes	44	9.4	even	3
189.4.i.a.143.1		44	1.1	even	1	trivial
189.4.i.a.152.22		44	63.5	even	6	inner
189.4.s.a.17.1		44	9.5	odd	6
189.4.s.a.89.1		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)

\(f(q)\)	\(=\)	\(q-5.38106i q^{2} -20.9559 q^{4} +(5.57991 - 9.66469i) q^{5} +(-8.46770 - 16.4711i) q^{7} +69.7163i q^{8} +O(q^{10})\)	\(q-5.38106i q^{2} -20.9559 q^{4} +(5.57991 - 9.66469i) q^{5} +(-8.46770 - 16.4711i) q^{7} +69.7163i q^{8} +(-52.0063 - 30.0259i) q^{10} +(-18.1128 + 10.4574i) q^{11} +(-46.0055 + 26.5613i) q^{13} +(-88.6322 + 45.5652i) q^{14} +207.501 q^{16} +(44.2557 - 76.6531i) q^{17} +(-40.4504 + 23.3540i) q^{19} +(-116.932 + 202.532i) q^{20} +(56.2722 + 97.4663i) q^{22} +(68.0882 + 39.3108i) q^{23} +(0.229151 + 0.396901i) q^{25} +(142.928 + 247.559i) q^{26} +(177.448 + 345.167i) q^{28} +(17.2805 + 9.97690i) q^{29} +28.0527i q^{31} -558.845i q^{32} +(-412.475 - 238.143i) q^{34} +(-206.437 - 10.0697i) q^{35} +(-122.348 - 211.913i) q^{37} +(125.670 + 217.666i) q^{38} +(673.786 + 389.011i) q^{40} +(-16.9545 - 29.3660i) q^{41} +(87.5295 - 151.606i) q^{43} +(379.570 - 219.145i) q^{44} +(211.534 - 366.387i) q^{46} -146.930 q^{47} +(-199.596 + 278.945i) q^{49} +(2.13575 - 1.23308i) q^{50} +(964.085 - 556.615i) q^{52} +(-656.078 - 378.787i) q^{53} +233.406i q^{55} +(1148.31 - 590.336i) q^{56} +(53.6863 - 92.9874i) q^{58} +83.9249 q^{59} +92.1709i q^{61} +150.953 q^{62} -1347.18 q^{64} +592.839i q^{65} -897.056 q^{67} +(-927.416 + 1606.33i) q^{68} +(-54.1860 + 1110.85i) q^{70} +706.833i q^{71} +(-529.580 - 305.753i) q^{73} +(-1140.32 + 658.364i) q^{74} +(847.673 - 489.404i) q^{76} +(325.620 + 209.788i) q^{77} -266.121 q^{79} +(1157.84 - 2005.43i) q^{80} +(-158.020 + 91.2331i) q^{82} +(311.561 - 539.639i) q^{83} +(-493.886 - 855.436i) q^{85} +(-815.799 - 471.002i) q^{86} +(-729.054 - 1262.76i) q^{88} +(-355.240 - 615.294i) q^{89} +(827.055 + 532.850i) q^{91} +(-1426.85 - 823.791i) q^{92} +790.637i q^{94} +521.254i q^{95} +(-498.364 - 287.731i) q^{97} +(1501.02 + 1074.04i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - 162 q^{4} + 3 q^{5} + 5 q^{7}+O(q^{10}) \) 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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