LMFDB - Embedded newform 108.5.f.a.91.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [108,5,Mod(19,108)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(108, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 4]))

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("108.19");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 108 = 2^{2} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	108.f (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:	$11.1639560131$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 36)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			91.4
Character	$\chi$	$=$	108.91
Dual form			108.5.f.a.19.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.61656 + 1.70894i) q^{2} +(10.1591 - 12.3610i) q^{4} +(2.83091 - 4.90328i) q^{5} +(-45.1595 + 26.0728i) q^{7} +(-15.6169 + 62.0654i) q^{8} +O(q^{10})$	\(q+(-3.61656 + 1.70894i) q^{2} +(10.1591 - 12.3610i) q^{4} +(2.83091 - 4.90328i) q^{5} +(-45.1595 + 26.0728i) q^{7} +(-15.6169 + 62.0654i) q^{8} +(-1.85878 + 22.5709i) q^{10} +(92.3736 - 53.3319i) q^{11} +(61.0686 - 105.774i) q^{13} +(118.765 - 171.469i) q^{14} +(-49.5864 - 251.152i) q^{16} +122.675 q^{17} +593.624i q^{19} +(-31.8498 - 84.8055i) q^{20} +(-242.934 + 350.739i) q^{22} +(473.649 + 273.461i) q^{23} +(296.472 + 513.504i) q^{25} +(-40.0976 + 486.900i) q^{26} +(-136.493 + 823.090i) q^{28} +(367.933 + 637.279i) q^{29} +(-507.427 - 292.963i) q^{31} +(608.535 + 823.566i) q^{32} +(-443.662 + 209.644i) q^{34} +295.239i q^{35} +2289.29 q^{37} +(-1014.47 - 2146.88i) q^{38} +(260.114 + 252.275i) q^{40} +(-1434.13 + 2483.99i) q^{41} +(1943.81 - 1122.26i) q^{43} +(279.197 - 1683.63i) q^{44} +(-2180.31 - 179.555i) q^{46} +(-913.531 + 527.427i) q^{47} +(159.084 - 275.542i) q^{49} +(-1949.76 - 1350.47i) q^{50} +(-687.066 - 1829.43i) q^{52} +4752.60 q^{53} -603.911i q^{55} +(-912.971 - 3210.02i) q^{56} +(-2419.72 - 1675.99i) q^{58} +(-1864.25 - 1076.32i) q^{59} +(33.1660 + 57.4451i) q^{61} +(2335.80 + 192.360i) q^{62} +(-3608.23 - 1938.53i) q^{64} +(-345.759 - 598.872i) q^{65} +(-3554.82 - 2052.38i) q^{67} +(1246.26 - 1516.38i) q^{68} +(-504.545 - 1067.75i) q^{70} -5031.65i q^{71} +2705.16 q^{73} +(-8279.36 + 3912.25i) q^{74} +(7337.76 + 6030.67i) q^{76} +(-2781.03 + 4816.88i) q^{77} +(1196.02 - 690.524i) q^{79} +(-1371.84 - 467.852i) q^{80} +(941.652 - 11434.4i) q^{82} +(2605.31 - 1504.18i) q^{83} +(347.282 - 601.509i) q^{85} +(-5112.05 + 7380.57i) q^{86} +(1867.48 + 6566.08i) q^{88} -3186.35 q^{89} +6368.92i q^{91} +(8192.07 - 3076.64i) q^{92} +(2402.50 - 3468.64i) q^{94} +(2910.71 + 1680.50i) q^{95} +(2407.03 + 4169.10i) q^{97} +(-104.455 + 1268.38i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + q^{2} - q^{4} + 2 q^{5} - 122 q^{8}+O(q^{10}) $ 44 * q + q^2 - q^4 + 2 * q^5 - 122 * q^8	$ 44 q + q^{2} - q^{4} + 2 q^{5} - 122 q^{8} + 28 q^{10} - 2 q^{13} - 252 q^{14} - q^{16} + 56 q^{17} + 140 q^{20} - 33 q^{22} - 1752 q^{25} - 1096 q^{26} - 516 q^{28} - 526 q^{29} + 121 q^{32} + 385 q^{34} - 8 q^{37} - 1395 q^{38} - 2276 q^{40} + 2762 q^{41} - 6714 q^{44} + 3576 q^{46} + 3428 q^{49} - 6375 q^{50} + 1438 q^{52} + 10088 q^{53} + 7506 q^{56} - 4064 q^{58} - 2 q^{61} + 18324 q^{62} + 9026 q^{64} + 2014 q^{65} + 11405 q^{68} + 3666 q^{70} - 3416 q^{73} - 14620 q^{74} + 1581 q^{76} + 3942 q^{77} - 45520 q^{80} - 8486 q^{82} - 1252 q^{85} - 22113 q^{86} + 1995 q^{88} - 13048 q^{89} + 30294 q^{92} + 7524 q^{94} + 5638 q^{97} + 92938 q^{98}+O(q^{100}) $ 44 * q + q^2 - q^4 + 2 * q^5 - 122 * q^8 + 28 * q^10 - 2 * q^13 - 252 * q^14 - q^16 + 56 * q^17 + 140 * q^20 - 33 * q^22 - 1752 * q^25 - 1096 * q^26 - 516 * q^28 - 526 * q^29 + 121 * q^32 + 385 * q^34 - 8 * q^37 - 1395 * q^38 - 2276 * q^40 + 2762 * q^41 - 6714 * q^44 + 3576 * q^46 + 3428 * q^49 - 6375 * q^50 + 1438 * q^52 + 10088 * q^53 + 7506 * q^56 - 4064 * q^58 - 2 * q^61 + 18324 * q^62 + 9026 * q^64 + 2014 * q^65 + 11405 * q^68 + 3666 * q^70 - 3416 * q^73 - 14620 * q^74 + 1581 * q^76 + 3942 * q^77 - 45520 * q^80 - 8486 * q^82 - 1252 * q^85 - 22113 * q^86 + 1995 * q^88 - 13048 * q^89 + 30294 * q^92 + 7524 * q^94 + 5638 * q^97 + 92938 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/108\mathbb{Z}\right)^\times$.

$n$	$29$	$55$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$

Coefficient data

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

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

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

$2$	−3.61656	+	1.70894i	−0.904141	+	0.427234i
$2$	−3.61656	+	1.70894i	−0.904141	+	0.427234i
$3$		0			0
$3$		0			0
$4$	10.1591	−	12.3610i	0.634942	−	0.772560i
$5$	2.83091	−	4.90328i	0.113236	−	0.196131i	−0.803837	−	0.594850i	$-0.797212\pi$
$5$	2.83091	−	4.90328i	0.113236	−	0.196131i	0.917073	+	0.398718i	$0.130545\pi$
$6$		0			0
$7$	−45.1595	+	26.0728i	−0.921621	+	0.532098i	−0.884152	−	0.467199i	$-0.845263\pi$
$7$	−45.1595	+	26.0728i	−0.921621	+	0.532098i	−0.0374695	+	0.999298i	$0.511930\pi$
$8$	−15.6169	+	62.0654i	−0.244014	+	0.969772i
$9$		0			0
$10$	−1.85878	+	22.5709i	−0.0185878	+	0.225709i
$11$	92.3736	−	53.3319i	0.763418	−	0.440760i	−0.0671034	−	0.997746i	$-0.521376\pi$
$11$	92.3736	−	53.3319i	0.763418	−	0.440760i	0.830522	+	0.556986i	$0.188042\pi$
$12$		0			0
$13$	61.0686	−	105.774i	0.361352	−	0.625881i	−0.626831	−	0.779155i	$-0.715648\pi$
$13$	61.0686	−	105.774i	0.361352	−	0.625881i	0.988184	+	0.153274i	$0.0489818\pi$
$14$	118.765	−	171.469i	0.605945	−	0.874840i
$15$		0			0
$16$	−49.5864	−	251.152i	−0.193697	−	0.981061i
$17$	122.675			0.424481			0.212240	−	0.977217i	$-0.431924\pi$
$17$	122.675			0.424481			0.212240	+	0.977217i	$0.431924\pi$
$18$		0			0
$19$			593.624i			1.64439i	0.569207	+	0.822194i	$0.307250\pi$
$19$			593.624i			1.64439i	−0.569207	+	0.822194i	$0.692750\pi$
$20$	−31.8498	−	84.8055i	−0.0796244	−	0.212014i
$21$		0			0
$22$	−242.934	+	350.739i	−0.501930	+	0.724667i
$23$	473.649	+	273.461i	0.895366	+	0.516940i	0.875694	−	0.482867i	$-0.160404\pi$
$23$	473.649	+	273.461i	0.895366	+	0.516940i	0.0196720	+	0.999806i	$0.493738\pi$
$24$		0			0
$25$	296.472	+	513.504i	0.474355	+	0.821607i
$26$	−40.0976	+	486.900i	−0.0593160	+	0.720266i
$27$		0			0
$28$	−136.493	+	823.090i	−0.174099	+	1.04986i
$29$	367.933	+	637.279i	0.437495	+	0.757763i	0.997496	−	0.0707290i	$-0.0225326\pi$
$29$	367.933	+	637.279i	0.437495	+	0.757763i	−0.560001	+	0.828492i	$0.689199\pi$
$30$		0			0
$31$	−507.427	−	292.963i	−0.528020	−	0.304853i	0.212190	−	0.977228i	$-0.431941\pi$
$31$	−507.427	−	292.963i	−0.528020	−	0.304853i	−0.740210	+	0.672376i	$0.765274\pi$
$32$	608.535	+	823.566i	0.594272	+	0.804264i
$33$		0			0
$34$	−443.662	+	209.644i	−0.383791	+	0.181353i
$35$			295.239i			0.241012i
$36$		0			0
$37$	2289.29			1.67223			0.836117	−	0.548551i	$-0.184820\pi$
$37$	2289.29			1.67223			0.836117	+	0.548551i	$0.184820\pi$
$38$	−1014.47	−	2146.88i	−0.702539	−	1.48676i
$39$		0			0
$40$	260.114	+	252.275i	0.162571	+	0.157672i
$41$	−1434.13	+	2483.99i	−0.853142	+	1.47769i	0.0252152	+	0.999682i	$0.491973\pi$
$41$	−1434.13	+	2483.99i	−0.853142	+	1.47769i	−0.878358	+	0.478004i	$0.841360\pi$
$42$		0			0
$43$	1943.81	−	1122.26i	1.05128	−	0.606955i	0.128270	−	0.991739i	$-0.459057\pi$
$43$	1943.81	−	1122.26i	1.05128	−	0.606955i	0.923007	+	0.384784i	$0.125724\pi$
$44$	279.197	−	1683.63i	0.144213	−	0.869643i
$45$		0			0
$46$	−2180.31	−	179.555i	−1.03039	−	0.0848557i
$47$	−913.531	+	527.427i	−0.413550	+	0.238763i	−0.692314	−	0.721597i	$-0.743409\pi$
$47$	−913.531	+	527.427i	−0.413550	+	0.238763i	0.278764	+	0.960360i	$0.410075\pi$
$48$		0			0
$49$	159.084	−	275.542i	0.0662574	−	0.114761i
$50$	−1949.76	−	1350.47i	−0.779902	−	0.540188i
$51$		0			0
$52$	−687.066	−	1829.43i	−0.254092	−	0.676564i
$53$	4752.60			1.69192			0.845960	−	0.533246i	$-0.179028\pi$
$53$	4752.60			1.69192			0.845960	+	0.533246i	$0.179028\pi$
$54$		0			0
$55$		−	603.911i		−	0.199640i
$56$	−912.971	−	3210.02i	−0.291126	−	1.02360i
$57$		0			0
$58$	−2419.72	−	1675.99i	−0.719299	−	0.498212i
$59$	−1864.25	−	1076.32i	−0.535549	−	0.309200i	0.207724	−	0.978188i	$-0.433394\pi$
$59$	−1864.25	−	1076.32i	−0.535549	−	0.309200i	−0.743273	+	0.668988i	$0.766728\pi$
$60$		0			0
$61$	33.1660	+	57.4451i	0.00891319	+	0.0154381i	0.870448	−	0.492261i	$-0.163829\pi$
$61$	33.1660	+	57.4451i	0.00891319	+	0.0154381i	−0.861534	+	0.507699i	$0.830496\pi$
$62$	2335.80	+	192.360i	0.607648	+	0.0500416i
$63$		0			0
$64$	−3608.23	−	1938.53i	−0.880915	−	0.473275i
$65$	−345.759	−	598.872i	−0.0818365	−	0.141745i
$66$		0			0
$67$	−3554.82	−	2052.38i	−0.791897	−	0.457202i	0.0487331	−	0.998812i	$-0.484482\pi$
$67$	−3554.82	−	2052.38i	−0.791897	−	0.457202i	−0.840630	+	0.541610i	$0.817815\pi$
$68$	1246.26	−	1516.38i	0.269521	−	0.327937i
$69$		0			0
$70$	−504.545	−	1067.75i	−0.102968	−	0.217908i
$71$		−	5031.65i		−	0.998145i	−0.866560	−	0.499072i	$-0.833674\pi$
$71$		−	5031.65i		−	0.998145i	0.866560	−	0.499072i	$-0.166326\pi$
$72$		0			0
$73$	2705.16			0.507631			0.253815	−	0.967253i	$-0.418314\pi$
$73$	2705.16			0.507631			0.253815	+	0.967253i	$0.418314\pi$
$74$	−8279.36	+	3912.25i	−1.51194	+	0.714435i
$75$		0			0
$76$	7337.76	+	6030.67i	1.27039	+	1.04409i
$77$	−2781.03	+	4816.88i	−0.469055	+	0.812427i
$78$		0			0
$79$	1196.02	−	690.524i	0.191639	−	0.110643i	−0.401110	−	0.916030i	$-0.631376\pi$
$79$	1196.02	−	690.524i	0.191639	−	0.110643i	0.592750	+	0.805387i	$0.298042\pi$
$80$	−1371.84	−	467.852i	−0.214350	−	0.0731019i
$81$		0			0
$82$	941.652	−	11434.4i	0.140043	−	1.70053i
$83$	2605.31	−	1504.18i	0.378184	−	0.218345i	−0.298844	−	0.954302i	$-0.596601\pi$
$83$	2605.31	−	1504.18i	0.378184	−	0.218345i	0.677028	+	0.735957i	$0.263268\pi$
$84$		0			0
$85$	347.282	−	601.509i	0.0480667	−	0.0832539i
$86$	−5112.05	+	7380.57i	−0.691191	+	0.997914i
$87$		0			0
$88$	1867.48	+	6566.08i	0.241152	+	0.847893i
$89$	−3186.35			−0.402267			−0.201133	−	0.979564i	$-0.564462\pi$
$89$	−3186.35			−0.402267			−0.201133	+	0.979564i	$0.564462\pi$
$90$		0			0
$91$			6368.92i			0.769100i
$92$	8192.07	−	3076.64i	0.967872	−	0.363497i
$93$		0			0
$94$	2402.50	−	3468.64i	0.271899	−	0.392558i
$95$	2910.71	+	1680.50i	0.322516	+	0.186205i
$96$		0			0
$97$	2407.03	+	4169.10i	0.255822	+	0.443097i	0.965118	−	0.261814i	$-0.0843206\pi$
$97$	2407.03	+	4169.10i	0.255822	+	0.443097i	−0.709296	+	0.704910i	$0.750987\pi$
$98$	−104.455	+	1268.38i	−0.0108762	+	0.132068i
$99$		0			0
$100$	9359.28	+	1552.05i	0.935928	+	0.155205i
$101$	−3510.47	−	6080.30i	−0.344130	−	0.596050i	0.641066	−	0.767486i	$-0.278493\pi$
$101$	−3510.47	−	6080.30i	−0.344130	−	0.596050i	−0.985195	+	0.171436i	$0.945159\pi$
$102$		0			0
$103$	1858.85	+	1073.21i	0.175214	+	0.101160i	0.585042	−	0.811003i	$-0.301078\pi$
$103$	1858.85	+	1073.21i	0.175214	+	0.101160i	−0.409828	+	0.912163i	$0.634411\pi$
$104$	5611.20	+	5442.10i	0.518787	+	0.503153i
$105$		0			0
$106$	−17188.1	+	8121.90i	−1.52973	+	0.722846i
$107$			13846.7i			1.20943i	0.796443	+	0.604713i	$0.206712\pi$
$107$			13846.7i			1.20943i	−0.796443	+	0.604713i	$0.793288\pi$
$108$		0			0
$109$	−19384.9			−1.63159			−0.815793	−	0.578344i	$-0.803699\pi$
$109$	−19384.9			−1.63159			−0.815793	+	0.578344i	$0.803699\pi$
$110$	1032.05	+	2184.08i	0.0852930	+	0.180503i
$111$		0			0
$112$	8787.53	+	10049.0i	0.700536	+	0.801102i
$113$	6817.20	−	11807.7i	0.533887	−	0.924719i	−0.465329	−	0.885138i	$-0.654064\pi$
$113$	6817.20	−	11807.7i	0.533887	−	0.924719i	0.999216	−	0.0395818i	$-0.0126026\pi$
$114$		0			0
$115$	2681.71	−	1548.29i	0.202776	−	0.117073i
$116$	11615.2	+	1926.16i	0.863201	+	0.143145i
$117$		0			0
$118$	8581.54	+	706.715i	0.616313	+	0.0507551i
$119$	−5539.93	+	3198.48i	−0.391211	+	0.225866i
$120$		0			0
$121$	−1631.91	+	2826.55i	−0.111462	+	0.193057i
$122$	−218.117	−	151.076i	−0.0146545	−	0.0101502i
$123$		0			0
$124$	−8776.30	+	3296.05i	−0.570779	+	0.214363i
$125$	6895.78			0.441330
$126$		0			0
$127$			15689.6i			0.972754i	0.873749	+	0.486377i	$0.161682\pi$
$127$			15689.6i			0.972754i	−0.873749	+	0.486377i	$0.838318\pi$
$128$	16362.2	+	844.606i	0.998670	+	0.0515506i
$129$		0			0
$130$	2273.89	+	1574.98i	0.134550	+	0.0931941i
$131$	7250.25	+	4185.93i	0.422484	+	0.243921i	0.696140	−	0.717907i	$-0.254899\pi$
$131$	7250.25	+	4185.93i	0.422484	+	0.243921i	−0.273656	+	0.961828i	$0.588233\pi$
$132$		0			0
$133$	−15477.5	−	26807.7i	−0.874977	−	1.51550i
$134$	16363.6	+	1347.59i	0.911319	+	0.0750497i
$135$		0			0
$136$	−1915.80	+	7613.87i	−0.103579	+	0.411650i
$137$	−14965.1	−	25920.4i	−0.797333	−	1.38102i	−0.921347	−	0.388741i	$-0.872910\pi$
$137$	−14965.1	−	25920.4i	−0.797333	−	1.38102i	0.124014	−	0.992280i	$-0.460423\pi$
$138$		0			0
$139$	−20651.8	−	11923.3i	−1.06888	−	0.617118i	−0.141005	−	0.990009i	$-0.545033\pi$
$139$	−20651.8	−	11923.3i	−1.06888	−	0.617118i	−0.927875	+	0.372891i	$0.878367\pi$
$140$	3649.44	+	2999.36i	0.186196	+	0.153028i
$141$		0			0
$142$	8598.76	+	18197.3i	0.426441	+	0.902464i
$143$		−	13027.6i		−	0.637078i
$144$		0			0
$145$	4166.34			0.198161
$146$	−9783.40	+	4622.95i	−0.458970	+	0.216877i
$147$		0			0
$148$	23257.0	−	28297.8i	1.06177	−	1.29190i
$149$	2636.98	−	4567.39i	0.118778	−	0.205729i	−0.800506	−	0.599325i	$-0.795436\pi$
$149$	2636.98	−	4567.39i	0.118778	−	0.205729i	0.919284	+	0.393596i	$0.128769\pi$
$150$		0			0
$151$	28946.1	−	16712.0i	1.26951	−	0.732951i	0.294614	−	0.955616i	$-0.404809\pi$
$151$	28946.1	−	16712.0i	1.26951	−	0.732951i	0.974895	+	0.222665i	$0.0714756\pi$
$152$	−36843.5	−	9270.55i	−1.59468	−	0.401253i
$153$		0			0
$154$	1826.02	−	22173.2i	0.0769954	−	0.934945i
$155$	−2872.96	+	1658.71i	−0.119582	+	0.0690408i
$156$		0			0
$157$	−8500.73	+	14723.7i	−0.344871	+	0.597334i	−0.985330	−	0.170658i	$-0.945411\pi$
$157$	−8500.73	+	14723.7i	−0.344871	+	0.597334i	0.640459	+	0.767992i	$0.278744\pi$
$158$	−3145.43	+	4541.25i	−0.125999	+	0.181912i
$159$		0			0
$160$	5760.88	−	652.373i	0.225034	−	0.0254833i
$161$	−28519.6			−1.10025
$162$		0			0
$163$			30843.8i			1.16089i	0.814298	+	0.580447i	$0.197122\pi$
$163$			30843.8i			1.16089i	−0.814298	+	0.580447i	$0.802878\pi$
$164$	16135.0	+	42962.3i	0.599904	+	1.59735i
$165$		0			0
$166$	−6851.74	+	9892.27i	−0.248648	+	0.358988i
$167$	−13682.1	−	7899.35i	−0.490591	−	0.283243i	0.234229	−	0.972181i	$-0.424743\pi$
$167$	−13682.1	−	7899.35i	−0.490591	−	0.283243i	−0.724819	+	0.688939i	$0.758077\pi$
$168$		0			0
$169$	6821.76	+	11815.6i	0.238849	+	0.413698i
$170$	−228.025	+	2768.88i	−0.00789015	+	0.0958090i
$171$		0			0
$172$	5875.12	−	35428.5i	0.198591	−	1.19756i
$173$	23531.4	+	40757.6i	0.786241	+	1.36181i	0.928255	+	0.371944i	$0.121309\pi$
$173$	23531.4	+	40757.6i	0.786241	+	1.36181i	−0.142015	+	0.989865i	$0.545358\pi$
$174$		0			0
$175$	−26777.0	−	15459.7i	−0.874352	−	0.504807i
$176$	−17974.9	−	20555.3i	−0.580284	−	0.663586i
$177$		0			0
$178$	11523.7	−	5445.28i	0.363706	−	0.171862i
$179$		−	2545.69i		−	0.0794511i	−0.999211	−	0.0397256i	$-0.987352\pi$
$179$		−	2545.69i		−	0.0794511i	0.999211	−	0.0397256i	$-0.0126484\pi$
$180$		0			0
$181$	5676.58			0.173272			0.0866362	−	0.996240i	$-0.472388\pi$
$181$	5676.58			0.173272			0.0866362	+	0.996240i	$0.472388\pi$
$182$	−10884.1	−	23033.6i	−0.328586	−	0.695375i
$183$		0			0
$184$	−24369.4	+	25126.6i	−0.719795	+	0.742160i
$185$	6480.77	−	11225.0i	0.189358	−	0.327977i
$186$		0			0
$187$	11331.9	−	6542.49i	0.324056	−	0.187094i
$188$	−2761.12	+	16650.3i	−0.0781214	+	0.471092i
$189$		0			0
$190$	−13398.6	−	1103.41i	−0.371153	−	0.0305655i
$191$	28127.2	−	16239.2i	0.771009	−	0.445142i	−0.0622257	−	0.998062i	$-0.519820\pi$
$191$	28127.2	−	16239.2i	0.771009	−	0.445142i	0.833234	+	0.552920i	$0.186487\pi$
$192$		0			0
$193$	−393.717	+	681.937i	−0.0105699	+	0.0183075i	−0.871262	−	0.490818i	$-0.836698\pi$
$193$	−393.717	+	681.937i	−0.0105699	+	0.0183075i	0.860692	+	0.509126i	$0.170031\pi$
$194$	−15829.9	−	10964.3i	−0.420605	−	0.291326i
$195$		0			0
$196$	−1789.81	−	4765.68i	−0.0465903	−	0.124055i
$197$	−24825.9			−0.639694			−0.319847	−	0.947469i	$-0.603632\pi$
$197$	−24825.9			−0.639694			−0.319847	+	0.947469i	$0.603632\pi$
$198$		0			0
$199$		−	12008.5i		−	0.303237i	−0.988439	−	0.151619i	$-0.951551\pi$
$199$		−	12008.5i		−	0.303237i	0.988439	−	0.151619i	$-0.0484485\pi$
$200$	−36500.8	+	10381.3i	−0.912520	+	0.259533i
$201$		0			0
$202$	23086.7	+	15990.7i	0.565794	+	0.391889i
$203$	−33231.3	−	19186.1i	−0.806409	−	0.465580i
$204$		0			0
$205$	8119.80	+	14063.9i	0.193213	+	0.334656i
$206$	−8556.69	−	704.668i	−0.201638	−	0.0166054i
$207$		0			0
$208$	−29593.5	−	10092.5i	−0.684020	−	0.233278i
$209$	31659.1	+	54835.2i	0.724780	+	1.25536i
$210$		0			0
$211$	−25764.7	−	14875.2i	−0.578708	−	0.334117i	0.181912	−	0.983315i	$-0.441771\pi$
$211$	−25764.7	−	14875.2i	−0.578708	−	0.334117i	−0.760620	+	0.649198i	$0.775105\pi$
$212$	48282.1	−	58746.7i	1.07427	−	1.30711i
$213$		0			0
$214$	−23663.2	−	50077.6i	−0.516708	−	1.09349i
$215$		−	12708.1i		−	0.274917i
$216$		0			0
$217$	30553.5			0.648846
$218$	70106.6	−	33127.5i	1.47518	−	0.697069i
$219$		0			0
$220$	−7464.92	−	6135.18i	−0.154234	−	0.126760i
$221$	7491.58	−	12975.8i	0.153387	−	0.265674i
$222$		0			0
$223$	45854.8	−	26474.3i	0.922093	−	0.532371i	0.0377910	−	0.999286i	$-0.487968\pi$
$223$	45854.8	−	26474.3i	0.922093	−	0.532371i	0.884302	+	0.466915i	$0.154635\pi$
$224$	−48953.8	−	21325.6i	−0.975642	−	0.425016i
$225$		0			0
$226$	−4476.18	+	54353.6i	−0.0876376	+	1.06417i
$227$	−32593.5	+	18817.9i	−0.632528	+	0.365190i	−0.781730	−	0.623616i	$-0.785663\pi$
$227$	−32593.5	+	18817.9i	−0.632528	+	0.365190i	0.149203	+	0.988807i	$0.452329\pi$
$228$		0			0
$229$	28619.2	−	49569.9i	0.545741	−	0.945251i	−0.452819	−	0.891603i	$-0.649582\pi$
$229$	28619.2	−	49569.9i	0.545741	−	0.945251i	0.998560	−	0.0536486i	$-0.0170851\pi$
$230$	−7052.66	+	10182.4i	−0.133321	+	0.192483i
$231$		0			0
$232$	−45298.9	+	12883.6i	−0.841612	+	0.239366i
$233$	36468.7			0.671751			0.335876	−	0.941906i	$-0.390968\pi$
$233$	36468.7			0.671751			0.335876	+	0.941906i	$0.390968\pi$
$234$		0			0
$235$			5972.39i			0.108147i
$236$	−32243.4	+	12109.4i	−0.578918	+	0.217420i
$237$		0			0
$238$	14569.5	−	21034.9i	0.257212	−	0.371353i
$239$	45342.6	+	26178.6i	0.793799	+	0.458300i	0.841298	−	0.540571i	$-0.181792\pi$
$239$	45342.6	+	26178.6i	0.793799	+	0.458300i	−0.0474993	+	0.998871i	$0.515125\pi$
$240$		0			0
$241$	6755.56	+	11701.0i	0.116313	+	0.201460i	0.918304	−	0.395877i	$-0.129559\pi$
$241$	6755.56	+	11701.0i	0.116313	+	0.201460i	−0.801991	+	0.597336i	$0.796226\pi$
$242$	1071.51	−	13011.2i	0.0182964	−	0.222171i
$243$		0			0
$244$	1047.01	+	173.627i	0.0175862	+	0.00291633i
$245$	−900.705	−	1560.07i	−0.0150055	−	0.0259903i
$246$		0			0
$247$	62789.9	+	36251.8i	1.02919	+	0.594204i
$248$	26107.3	−	26918.5i	0.424482	−	0.437671i
$249$		0			0
$250$	−24939.0	+	11784.4i	−0.399024	+	0.188551i
$251$			111309.i			1.76678i	0.468635	+	0.883392i	$0.344746\pi$
$251$			111309.i			1.76678i	−0.468635	+	0.883392i	$0.655254\pi$
$252$		0			0
$253$	58336.8			0.911385
$254$	−26812.4	−	56742.3i	−0.415594	−	0.879507i
$255$		0			0
$256$	−60618.4	+	24907.4i	−0.924963	+	0.380057i
$257$	−36956.5	+	64010.6i	−0.559532	+	0.969138i	0.438003	+	0.898973i	$0.355686\pi$
$257$	−36956.5	+	64010.6i	−0.559532	+	0.969138i	−0.997535	+	0.0701645i	$0.977648\pi$
$258$		0			0
$259$	−103383.	+	59688.2i	−1.54117	+	0.889793i
$260$	−10915.2	−	1810.08i	−0.161468	−	0.0267763i
$261$		0			0
$262$	−33374.5	−	2748.48i	−0.486197	−	0.0400397i
$263$	6380.84	−	3683.98i	0.0922500	−	0.0532606i	−0.453165	−	0.891426i	$-0.649705\pi$
$263$	6380.84	−	3683.98i	0.0922500	−	0.0532606i	0.545415	+	0.838166i	$0.316372\pi$
$264$		0			0
$265$	13454.2	−	23303.3i	0.191587	−	0.331838i
$266$	101788.	+	70502.0i	1.43858	+	0.996410i
$267$		0			0
$268$	−61483.1	+	23090.8i	−0.856024	+	0.321491i
$269$	38604.8			0.533502			0.266751	−	0.963765i	$-0.414050\pi$
$269$	38604.8			0.533502			0.266751	+	0.963765i	$0.414050\pi$
$270$		0			0
$271$		−	12540.3i		−	0.170753i	−0.996349	−	0.0853767i	$-0.972791\pi$
$271$		−	12540.3i		−	0.170753i	0.996349	−	0.0853767i	$-0.0272094\pi$
$272$	−6083.01	−	30810.0i	−0.0822206	−	0.416442i
$273$		0			0
$274$	98418.7	+	68168.3i	1.31092	+	0.907990i
$275$	54772.4	+	31622.8i	0.724263	+	0.418153i
$276$		0			0
$277$	46052.4	+	79765.0i	0.600195	+	1.03957i	0.992791	+	0.119857i	$0.0382436\pi$
$277$	46052.4	+	79765.0i	0.600195	+	1.03957i	−0.392596	+	0.919711i	$0.628423\pi$
$278$	95064.9	+	7828.87i	1.23007	+	0.101300i
$279$		0			0
$280$	−18324.1	−	4610.71i	−0.233726	−	0.0588101i
$281$	11148.0	+	19308.8i	0.141183	+	0.244537i	0.927942	−	0.372723i	$-0.121576\pi$
$281$	11148.0	+	19308.8i	0.141183	+	0.244537i	−0.786759	+	0.617260i	$0.788243\pi$
$282$		0			0
$283$	21648.6	+	12498.8i	0.270307	+	0.156062i	0.629027	−	0.777383i	$-0.283453\pi$
$283$	21648.6	+	12498.8i	0.270307	+	0.156062i	−0.358720	+	0.933445i	$0.616787\pi$
$284$	−62196.0	−	51116.9i	−0.771126	−	0.633764i
$285$		0			0
$286$	22263.4	+	47115.2i	0.272182	+	0.576009i
$287$		−	149568.i		−	1.81582i
$288$		0			0
$289$	−68471.9			−0.819816
$290$	−15067.8	+	7120.01i	−0.179166	+	0.0846612i
$291$		0			0
$292$	27482.0	−	33438.4i	0.322316	−	0.392175i
$293$	−11748.6	+	20349.1i	−0.136852	+	0.237034i	−0.926303	−	0.376779i	$-0.877032\pi$
$293$	−11748.6	+	20349.1i	−0.136852	+	0.237034i	0.789452	+	0.613813i	$0.210365\pi$
$294$		0			0
$295$	−10555.0	+	6093.95i	−0.121287	+	0.0700253i
$296$	−35751.5	+	142086.i	−0.408048	+	1.62169i
$297$		0			0
$298$	−1731.44	+	21024.7i	−0.0194974	+	0.236754i
$299$	57850.1	−	33399.7i	0.647085	−	0.373595i
$300$		0			0
$301$	−58521.0	+	101361.i	−0.645920	+	1.11877i
$302$	−76125.6	+	109907.i	−0.834673	+	1.20507i
$303$		0			0
$304$	149090.	−	29435.7i	1.61325	−	0.318513i
$305$	375.559			0.00403719
$306$		0			0
$307$		−	32060.0i		−	0.340163i	−0.985430	−	0.170082i	$-0.945597\pi$
$307$		−	32060.0i		−	0.340163i	0.985430	−	0.170082i	$-0.0544031\pi$
$308$	31288.6	+	83311.2i	0.329826	+	0.878217i
$309$		0			0
$310$	7555.63	−	10908.5i	0.0786226	−	0.113512i
$311$	−61441.4	−	35473.2i	−0.635244	−	0.366758i	0.147536	−	0.989057i	$-0.452866\pi$
$311$	−61441.4	−	35473.2i	−0.635244	−	0.366758i	−0.782780	+	0.622298i	$0.786199\pi$
$312$		0			0
$313$	−59259.6	−	102641.i	−0.604882	−	1.04769i	−0.992070	−	0.125685i	$-0.959887\pi$
$313$	−59259.6	−	102641.i	−0.604882	−	1.04769i	0.387189	−	0.922001i	$-0.373446\pi$
$314$	5581.58	−	67776.4i	0.0566106	−	0.687415i
$315$		0			0
$316$	3614.95	−	21799.1i	0.0362016	−	0.218305i
$317$	−67390.6	−	116724.i	−0.670626	−	1.16156i	−0.977727	−	0.209882i	$-0.932692\pi$
$317$	−67390.6	−	116724.i	−0.670626	−	1.16156i	0.307100	−	0.951677i	$-0.400641\pi$
$318$		0			0
$319$	67974.6	+	39245.2i	0.667983	+	0.385660i
$320$	−19719.7	+	12204.3i	−0.192576	+	0.119183i
$321$		0			0
$322$	103143.	−	48738.2i	0.994782	−	0.470065i
$323$			72822.8i			0.698011i
$324$		0			0
$325$	72420.4			0.685637
$326$	−52710.0	−	111548.i	−0.495973	−	1.04961i
$327$		0			0
$328$	−131773.	−	127802.i	−1.22484	−	1.18793i
$329$	27503.0	−	47636.7i	0.254091	−	0.440098i
$330$		0			0
$331$	−133143.	+	76870.2i	−1.21524	+	0.701620i	−0.963896	−	0.266278i	$-0.914206\pi$
$331$	−133143.	+	76870.2i	−1.21524	+	0.701620i	−0.251345	+	0.967898i	$0.580873\pi$
$332$	7874.49	−	47485.2i	0.0714408	−	0.430806i
$333$		0			0
$334$	62981.6	+	5186.72i	0.564574	+	0.0464943i
$335$	−20126.8	+	11620.2i	−0.179343	+	0.103544i
$336$		0			0
$337$	11471.8	−	19869.8i	0.101012	−	0.174958i	−0.811090	−	0.584922i	$-0.801125\pi$
$337$	11471.8	−	19869.8i	0.101012	−	0.174958i	0.912102	+	0.409964i	$0.134459\pi$
$338$	−44863.5	−	31074.1i	−0.392699	−	0.271997i
$339$		0			0
$340$	−3907.17	−	10403.5i	−0.0337990	−	0.0899958i
$341$	−62497.2			−0.537467
$342$		0			0
$343$		−	108611.i		−	0.923175i
$344$	39297.3	+	138170.i	0.332082	+	1.16760i
$345$		0			0
$346$	−154755.	−	107189.i	−1.29268	−	0.895358i
$347$	6260.87	+	3614.72i	0.0519967	+	0.0300203i	0.525773	−	0.850625i	$-0.323776\pi$
$347$	6260.87	+	3614.72i	0.0519967	+	0.0300203i	−0.473776	+	0.880645i	$0.657109\pi$
$348$		0			0
$349$	−55282.6	−	95752.3i	−0.453877	−	0.786137i	0.544746	−	0.838601i	$-0.316626\pi$
$349$	−55282.6	−	95752.3i	−0.453877	−	0.786137i	−0.998623	+	0.0524636i	$0.983293\pi$
$350$	123260.	+	10150.9i	1.00621	+	0.0828641i
$351$		0			0
$352$	100135.	+	43621.5i	0.808165	+	0.352059i
$353$	−30801.7	−	53350.1i	−0.247187	−	0.428140i	0.715557	−	0.698554i	$-0.246173\pi$
$353$	−30801.7	−	53350.1i	−0.247187	−	0.428140i	−0.962744	+	0.270414i	$0.912840\pi$
$354$		0			0
$355$	−24671.6	−	14244.1i	−0.195767	−	0.113026i
$356$	−32370.4	+	39386.4i	−0.255416	+	0.310775i
$357$		0			0
$358$	4350.43	+	9206.66i	0.0339442	+	0.0718350i
$359$		−	84462.7i		−	0.655354i	−0.944790	−	0.327677i	$-0.893734\pi$
$359$		−	84462.7i		−	0.655354i	0.944790	−	0.327677i	$-0.106266\pi$
$360$		0			0
$361$	−222069.			−1.70401
$362$	−20529.7	+	9700.91i	−0.156663	+	0.0740279i
$363$		0			0
$364$	78725.9	+	64702.3i	0.594176	+	0.488334i
$365$	7658.07	−	13264.2i	0.0574823	−	0.0995622i
$366$		0			0
$367$	161018.	−	92963.9i	1.19548	−	0.690212i	0.235937	−	0.971768i	$-0.424184\pi$
$367$	161018.	−	92963.9i	1.19548	−	0.690212i	0.959545	+	0.281556i	$0.0908507\pi$
$368$	45193.7	−	132518.i	0.333720	−	0.978538i
$369$		0			0
$370$	−4255.27	+	51671.2i	−0.0310831	+	0.377438i
$371$	−214625.	+	123914.i	−1.55931	+	0.900268i
$372$		0			0
$373$	42545.6	−	73691.2i	0.305800	−	0.529661i	−0.671639	−	0.740878i	$-0.734409\pi$
$373$	42545.6	−	73691.2i	0.305800	−	0.529661i	0.977439	+	0.211217i	$0.0677428\pi$
$374$	−29801.9	+	43026.9i	−0.213060	+	0.307607i
$375$		0			0
$376$	−18468.5	−	64935.4i	−0.130634	−	0.459310i
$377$	89876.5			0.632359
$378$		0			0
$379$		−	146982.i		−	1.02326i	−0.859206	−	0.511630i	$-0.829042\pi$
$379$		−	146982.i		−	1.02326i	0.859206	−	0.511630i	$-0.170958\pi$
$380$	50342.6	−	18906.8i	0.348633	−	0.130934i
$381$		0			0
$382$	−73971.9	+	106798.i	−0.506921	+	0.731872i
$383$	−161253.	−	93099.7i	−1.09929	−	0.634674i	−0.163254	−	0.986584i	$-0.552199\pi$
$383$	−161253.	−	93099.7i	−1.09929	−	0.634674i	−0.936034	+	0.351910i	$0.885532\pi$
$384$		0			0
$385$	15745.7	+	27272.3i	0.106228	+	0.183993i
$386$	258.515	−	3139.11i	0.00173504	−	0.0210684i
$387$		0			0
$388$	75987.2	+	12601.0i	0.504751	+	0.0837030i
$389$	−128002.	−	221706.i	−0.845897	−	1.46514i	−0.884840	−	0.465894i	$-0.845733\pi$
$389$	−128002.	−	221706.i	−0.845897	−	1.46514i	0.0389437	−	0.999241i	$-0.487601\pi$
$390$		0			0
$391$	58104.8	+	33546.8i	0.380066	+	0.219431i
$392$	14617.2	+	14176.7i	0.0951245	+	0.0922579i
$393$		0			0
$394$	89784.4	−	42425.9i	0.578374	−	0.273299i
$395$		−	7819.24i		−	0.0501153i
$396$		0			0
$397$	−260735.			−1.65432			−0.827159	−	0.561968i	$-0.810044\pi$
$397$	−260735.			−1.65432			−0.827159	+	0.561968i	$0.810044\pi$
$398$	20521.7	+	43429.5i	0.129553	+	0.274169i
$399$		0			0
$400$	114267.	−	99922.3i	0.714166	−	0.624514i
$401$	26507.0	−	45911.4i	0.164843	−	0.285517i	−0.771756	−	0.635918i	$-0.780621\pi$
$401$	26507.0	−	45911.4i	0.164843	−	0.285517i	0.936600	+	0.350401i	$0.113955\pi$
$402$		0			0
$403$	−61975.7	+	35781.7i	−0.381603	+	0.220318i
$404$	−110821.	−	18377.6i	−0.678986	−	0.112597i
$405$		0			0
$406$	152971.	+	12597.6i	0.928019	+	0.0764251i
$407$	211470.	−	122092.i	1.27661	−	0.737053i
$408$		0			0
$409$	−73697.8	+	127648.i	−0.440563	+	0.763078i	−0.997731	−	0.0673220i	$-0.978555\pi$
$409$	−73697.8	+	127648.i	−0.440563	+	0.763078i	0.557168	+	0.830400i	$0.311888\pi$
$410$	−53400.1	−	36986.8i	−0.317668	−	0.220028i
$411$		0			0
$412$	32150.1	−	12074.4i	0.189403	−	0.0711328i
$413$	112251.			0.658099
$414$		0			0
$415$		−	17032.8i		−	0.0988983i
$416$	124274.	−	14073.0i	0.718115	−	0.0813206i
$417$		0			0
$418$	−208207.	−	144212.i	−1.19163	−	0.825368i
$419$	201431.	+	116296.i	1.14736	+	0.662426i	0.948242	−	0.317550i	$-0.102860\pi$
$419$	201431.	+	116296.i	1.14736	+	0.662426i	0.199115	+	0.979976i	$0.436193\pi$
$420$		0			0
$421$	34900.8	+	60449.9i	0.196911	+	0.341060i	0.947525	−	0.319680i	$-0.103576\pi$
$421$	34900.8	+	60449.9i	0.196911	+	0.341060i	−0.750614	+	0.660741i	$0.770242\pi$
$422$	118600.	+	9767.08i	0.665980	+	0.0548454i
$423$		0			0
$424$	−74220.8	+	294972.i	−0.412852	+	1.64078i
$425$	36369.7	+	62994.1i	0.201355	+	0.348756i
$426$		0			0
$427$	−2995.51	−	1729.46i	−0.0164292	−	0.00948539i
$428$	171159.	+	140670.i	0.934354	+	0.767916i
$429$		0			0
$430$	21717.3	+	45959.5i	0.117454	+	0.248564i
$431$			147873.i			0.796037i	0.917377	+	0.398019i	$0.130302\pi$
$431$			147873.i			0.796037i	−0.917377	+	0.398019i	$0.869698\pi$
$432$		0			0
$433$	294850.			1.57262			0.786312	−	0.617830i	$-0.211988\pi$
$433$	294850.			1.57262			0.786312	+	0.617830i	$0.211988\pi$
$434$	−110499.	+	52214.0i	−0.586649	+	0.277209i
$435$		0			0
$436$	−196932.	+	239615.i	−1.03596	+	1.26050i
$437$	−162333.	+	281169.i	−0.850050	+	1.47233i
$438$		0			0
$439$	−62468.0	+	36065.9i	−0.324137	+	0.187140i	−0.653235	−	0.757155i	$-0.726589\pi$
$439$	−62468.0	+	36065.9i	−0.324137	+	0.187140i	0.329098	+	0.944296i	$0.393255\pi$
$440$	37482.0	+	9431.20i	0.193605	+	0.0487149i
$441$		0			0
$442$	−4918.98	+	59730.5i	−0.0251785	+	0.305739i
$443$	−165331.	+	95453.7i	−0.842453	+	0.486391i	−0.858097	−	0.513487i	$-0.828353\pi$
$443$	−165331.	+	95453.7i	−0.842453	+	0.486391i	0.0156440	+	0.999878i	$0.495020\pi$
$444$		0			0
$445$	−9020.28	+	15623.6i	−0.0455512	+	0.0788970i
$446$	−120594.	+	174109.i	−0.606255	+	0.875288i
$447$		0			0
$448$	213489.	−	6533.50i	1.06370	−	0.0325529i
$449$	−192859.			−0.956639			−0.478319	−	0.878186i	$-0.658754\pi$
$449$	−192859.			−0.956639			−0.478319	+	0.878186i	$0.658754\pi$
$450$		0			0
$451$			305940.i			1.50412i
$452$	−76698.5	−	204223.i	−0.375414	−	0.999603i
$453$		0			0
$454$	85718.0	−	123756.i	0.415873	−	0.600421i
$455$	31228.6	+	18029.8i	0.150844	+	0.0870901i
$456$		0			0
$457$	2962.66	+	5131.48i	0.0141857	+	0.0245703i	0.873031	−	0.487665i	$-0.162151\pi$
$457$	2962.66	+	5131.48i	0.0141857	+	0.0245703i	−0.858845	+	0.512235i	$0.828818\pi$
$458$	−18791.4	+	228181.i	−0.0895834	+	1.08780i
$459$		0			0
$460$	8105.41	−	48877.7i	0.0383053	−	0.230991i
$461$	63341.9	+	109711.i	0.298050	+	0.516238i	0.975690	−	0.219156i	$-0.0703304\pi$
$461$	63341.9	+	109711.i	0.298050	+	0.516238i	−0.677640	+	0.735394i	$0.736997\pi$
$462$		0			0
$463$	204011.	+	117786.i	0.951682	+	0.549454i	0.893603	−	0.448858i	$-0.148169\pi$
$463$	204011.	+	117786.i	0.951682	+	0.549454i	0.0580790	+	0.998312i	$0.481502\pi$
$464$	141809.	−	124007.i	0.658671	−	0.575985i
$465$		0			0
$466$	−131891.	+	62322.7i	−0.607358	+	0.286995i
$467$			97776.2i			0.448332i	0.974551	+	0.224166i	$0.0719658\pi$
$467$			97776.2i			0.448332i	−0.974551	+	0.224166i	$0.928034\pi$
$468$		0			0
$469$	214045.			0.973105
$470$	−10206.4	−	21599.5i	−0.0462039	−	0.0977798i
$471$		0			0
$472$	95916.2	−	98896.5i	0.430534	−	0.443912i
$473$	119705.	−	207334.i	0.535043	−	0.926721i
$474$		0			0
$475$	−304829.	+	175993.i	−1.35104	+	0.780024i
$476$	−16744.3	+	100972.i	−0.0739015	+	0.445645i
$477$		0			0
$478$	−208722.	−	17188.8i	−0.913508	−	0.0752300i
$479$	349162.	−	201589.i	1.52179	−	0.878608i	0.522126	−	0.852869i	$-0.325139\pi$
$479$	349162.	−	201589.i	1.52179	−	0.878608i	0.999669	−	0.0257398i	$-0.00819415\pi$
$480$		0			0
$481$	139803.	−	242147.i	0.604266	−	1.04662i
$482$	−44428.1	−	30772.5i	−0.191233	−	0.132455i
$483$		0			0
$484$	18360.2	+	48887.1i	0.0783766	+	0.208691i
$485$	27256.3			0.115873
$486$		0			0
$487$		−	195207.i		−	0.823071i	−0.911394	−	0.411536i	$-0.864993\pi$
$487$		−	195207.i		−	0.823071i	0.911394	−	0.411536i	$-0.135007\pi$
$488$	−4083.30	+	1161.35i	−0.0171464	+	0.00487665i
$489$		0			0
$490$	5923.51	+	4102.83i	0.0246710	+	0.0170880i
$491$	65937.1	+	38068.8i	0.273506	+	0.157909i	0.630480	−	0.776206i	$-0.282858\pi$
$491$	65937.1	+	38068.8i	0.273506	+	0.157909i	−0.356974	+	0.934114i	$0.616191\pi$
$492$		0			0
$493$	45136.2	+	78178.1i	0.185708	+	0.321656i
$494$	−289036.	−	23802.9i	−1.18440	−	0.0975386i
$495$		0			0
$496$	−48416.8	+	141968.i	−0.196803	+	0.577069i
$497$	131189.	+	227226.i	0.531111	+	0.919912i
$498$		0			0
$499$	−12618.3	−	7285.17i	−0.0506757	−	0.0292576i	0.474448	−	0.880283i	$-0.342648\pi$
$499$	−12618.3	−	7285.17i	−0.0506757	−	0.0292576i	−0.525124	+	0.851026i	$0.675981\pi$
$500$	70054.7	−	85238.4i	0.280219	−	0.340953i
$501$		0			0
$502$	−190220.	−	402557.i	−0.754830	−	1.59742i
$503$		−	280154.i		−	1.10729i	−0.832753	−	0.553645i	$-0.813236\pi$
$503$		−	280154.i		−	1.10729i	0.832753	−	0.553645i	$-0.186764\pi$
$504$		0			0
$505$	−39751.2			−0.155872
$506$	−210979.	+	99693.9i	−0.824020	+	0.389375i
$507$		0			0
$508$	193938.	+	159391.i	0.751511	+	0.617643i
$509$	101505.	−	175811.i	0.391787	−	0.678595i	−0.600899	−	0.799325i	$-0.705190\pi$
$509$	101505.	−	175811.i	0.391787	−	0.678595i	0.992685	+	0.120731i	$0.0385238\pi$
$510$		0			0
$511$	−122164.	+	70531.3i	−0.467843	+	0.270110i
$512$	176665.	−	193672.i	0.673924	−	0.738801i
$513$		0			0
$514$	24265.7	−	294655.i	0.0918472	−	1.11529i
$515$	10524.5	−	6076.30i	0.0396813	−	0.0229100i
$516$		0			0
$517$	−56257.4	+	97440.7i	−0.210474	+	0.364552i
$518$	271888.	−	392541.i	1.01328	−	1.46294i
$519$		0			0
$520$	42568.9	−	12107.2i	0.157429	−	0.0447750i
$521$	30822.1			0.113550			0.0567749	−	0.998387i	$-0.481918\pi$
$521$	30822.1			0.113550			0.0567749	+	0.998387i	$0.481918\pi$
$522$		0			0
$523$		−	94412.3i		−	0.345164i	−0.984995	−	0.172582i	$-0.944789\pi$
$523$		−	94412.3i		−	0.345164i	0.984995	−	0.172582i	$-0.0552109\pi$
$524$	125398.	−	47094.8i	0.456697	−	0.171518i
$525$		0			0
$526$	−16781.0	+	24227.8i	−0.0606523	+	0.0875674i
$527$	−62248.6	−	35939.3i	−0.224134	−	0.129404i
$528$		0			0
$529$	9641.45	+	16699.5i	0.0344533	+	0.0596749i
$530$	−8834.03	+	107270.i	−0.0314490	+	0.381881i
$531$		0			0
$532$	−488606.	−	81025.8i	−1.72638	−	0.286286i
$533$	175161.	+	303387.i	0.616570	+	1.06793i
$534$		0			0
$535$	67894.3	+	39198.8i	0.237206	+	0.136951i
$536$	182897.	−	188580.i	0.636615	−	0.656396i
$537$		0			0
$538$	−139617.	+	65973.1i	−0.482361	+	0.227930i
$539$		−	33937.0i		−	0.116814i
$540$		0			0
$541$	166561.			0.569087			0.284544	−	0.958663i	$-0.408158\pi$
$541$	166561.			0.569087			0.284544	+	0.958663i	$0.408158\pi$
$542$	21430.6	+	45352.8i	0.0729517	+	0.154385i
$543$		0			0
$544$	74651.9	+	101031.i	0.252257	+	0.341395i
$545$	−54876.8	+	95049.4i	−0.184755	+	0.320005i
$546$		0			0
$547$	256245.	−	147943.i	0.856410	−	0.494448i	−0.00639865	−	0.999980i	$-0.502037\pi$
$547$	256245.	−	147943.i	0.856410	−	0.494448i	0.862808	+	0.505531i	$0.168703\pi$
$548$	−472433.	−	78343.7i	−1.57318	−	0.260881i
$549$		0			0
$550$	−252129.	−	20763.6i	−0.833485	−	0.0686399i
$551$	−378304.	+	218414.i	−1.24606	+	0.719411i
$552$		0			0
$553$	−36007.8	+	62367.3i	−0.117746	+	0.203942i
$554$	−302865.	−	209775.i	−0.986800	−	0.683492i
$555$		0			0
$556$	−357187.	+	134146.i	−1.15544	+	0.433939i
$557$	30600.2			0.0986312			0.0493156	−	0.998783i	$-0.484296\pi$
$557$	30600.2			0.0986312			0.0493156	+	0.998783i	$0.484296\pi$
$558$		0			0
$559$		−	274139.i		−	0.877298i
$560$	74149.8	−	14639.8i	0.236447	−	0.0466832i
$561$		0			0
$562$	−73314.9	−	50780.5i	−0.232124	−	0.160777i
$563$	−210267.	−	121398.i	−0.663369	−	0.382996i	0.130191	−	0.991489i	$-0.458441\pi$
$563$	−210267.	−	121398.i	−0.663369	−	0.382996i	−0.793559	+	0.608493i	$0.791774\pi$
$564$		0			0
$565$	−38597.8	−	66853.3i	−0.120911	−	0.209424i
$566$	−99653.3	−	8206.73i	−0.311070	−	0.0256175i
$567$		0			0
$568$	312291.	+	78578.6i	0.967973	+	0.243561i
$569$	148459.	+	257138.i	0.458545	+	0.794223i	0.998884	−	0.0472242i	$-0.0150375\pi$
$569$	148459.	+	257138.i	0.458545	+	0.794223i	−0.540339	+	0.841447i	$0.681704\pi$
$570$		0			0
$571$	−228446.	−	131893.i	−0.700665	−	0.404529i	0.106930	−	0.994267i	$-0.465898\pi$
$571$	−228446.	−	131893.i	−0.700665	−	0.404529i	−0.807595	+	0.589737i	$0.799231\pi$
$572$	−161034.	−	132349.i	−0.492181	−	0.404508i
$573$		0			0
$574$	255601.	+	540921.i	0.775781	+	1.64176i
$575$			324294.i			0.980852i
$576$		0			0
$577$	350367.			1.05238			0.526188	−	0.850368i	$-0.323621\pi$
$577$	350367.			1.05238			0.526188	+	0.850368i	$0.323621\pi$
$578$	247633.	−	117014.i	0.741229	−	0.350253i
$579$		0			0
$580$	42326.2	−	51499.9i	0.125821	−	0.153091i
$581$	−78436.3	+	135856.i	−0.232362	+	0.402463i
$582$		0			0
$583$	439015.	−	253466.i	1.29164	−	0.745730i
$584$	−42246.2	+	167897.i	−0.123869	+	0.492286i
$585$		0			0
$586$	7714.12	−	93671.5i	0.0224642	−	0.272780i
$587$	−5965.76	+	3444.33i	−0.0173137	+	0.00999606i	−0.508632	−	0.860984i	$-0.669849\pi$
$587$	−5965.76	+	3444.33i	−0.0173137	+	0.00999606i	0.491318	+	0.870980i	$0.336515\pi$
$588$		0			0
$589$	173910.	−	301221.i	0.501296	−	0.868270i
$590$	27758.8	−	40077.0i	0.0797437	−	0.115131i
$591$		0			0
$592$	−113517.	−	574959.i	−0.323906	−	1.64056i
$593$	−544416.			−1.54818			−0.774090	−	0.633076i	$-0.781792\pi$
$593$	−544416.			−1.54818			−0.774090	+	0.633076i	$0.781792\pi$
$594$		0			0
$595$			36218.4i			0.102305i
$596$	−29668.0	−	78996.0i	−0.0835209	−	0.222389i
$597$		0			0
$598$	−152140.	+	219654.i	−0.425444	+	0.614239i
$599$	−122771.	−	70881.9i	−0.342170	−	0.197552i	0.319061	−	0.947734i	$-0.396633\pi$
$599$	−122771.	−	70881.9i	−0.342170	−	0.197552i	−0.661231	+	0.750182i	$0.729966\pi$
$600$		0			0
$601$	265380.	+	459652.i	0.734715	+	1.27256i	0.954848	+	0.297094i	$0.0960176\pi$
$601$	265380.	+	459652.i	0.734715	+	1.27256i	−0.220133	+	0.975470i	$0.570649\pi$
$602$	38424.9	−	466588.i	0.106028	−	1.28748i
$603$		0			0
$604$	87488.8	−	527580.i	0.239816	−	1.44615i
$605$	9239.58	+	16003.4i	0.0252430	+	0.0437222i
$606$		0			0
$607$	−35215.7	−	20331.8i	−0.0955782	−	0.0551821i	0.451449	−	0.892297i	$-0.350907\pi$
$607$	−35215.7	−	20331.8i	−0.0955782	−	0.0551821i	−0.547027	+	0.837115i	$0.684241\pi$
$608$	−488889.	+	361241.i	−1.32252	+	0.977214i
$609$		0			0
$610$	−1358.23	+	641.807i	−0.00365019	+	0.00172482i
$611$			128837.i			0.345110i
$612$		0			0
$613$	−498556.			−1.32676			−0.663382	−	0.748281i	$-0.730879\pi$
$613$	−498556.			−1.32676			−0.663382	+	0.748281i	$0.730879\pi$
$614$	54788.5	+	115947.i	0.145329	+	0.307555i
$615$		0			0
$616$	−255531.	−	247830.i	−0.673413	−	0.653120i
$617$	−45030.4	+	77995.0i	−0.118287	+	0.204879i	−0.919089	−	0.394050i	$-0.871074\pi$
$617$	−45030.4	+	77995.0i	−0.118287	+	0.204879i	0.800802	+	0.598929i	$0.204407\pi$
$618$		0			0
$619$	149379.	−	86244.1i	0.389860	−	0.225086i	−0.292240	−	0.956345i	$-0.594400\pi$
$619$	149379.	−	86244.1i	0.389860	−	0.225086i	0.682099	+	0.731259i	$0.261067\pi$
$620$	−8683.45	+	52363.5i	−0.0225896	+	0.136221i
$621$		0			0
$622$	282828.	+	23291.7i	0.731042	+	0.0602034i
$623$	143894.	−	83077.2i	0.370738	−	0.214045i
$624$		0			0
$625$	−165774.	+	287128.i	−0.424380	+	0.735049i
$626$	389723.	+	269936.i	0.994505	+	0.688830i
$627$		0			0
$628$	95639.3	+	254656.i	0.242503	+	0.645706i
$629$	280838.			0.709831
$630$		0			0
$631$			210621.i			0.528985i	0.964388	+	0.264492i	$0.0852044\pi$
$631$			210621.i			0.528985i	−0.964388	+	0.264492i	$0.914796\pi$
$632$	24179.5	+	85015.4i	0.0605359	+	0.212845i
$633$		0			0
$634$	443196.	+	306973.i	1.10260	+	0.763699i
$635$	76930.2	+	44415.7i	0.190787	+	0.110151i
$636$		0			0
$637$	−19430.1	−	33653.9i	−0.0478846	−	0.0829385i
$638$	−312902.	−	25768.4i	−0.768718	−	0.0633061i
$639$		0			0
$640$	50461.3	−	77837.5i	0.123196	−	0.190033i
$641$	−232262.	−	402289.i	−0.565278	−	0.979089i	−0.997024	−	0.0770943i	$-0.975436\pi$
$641$	−232262.	−	402289.i	−0.565278	−	0.979089i	0.431746	−	0.901995i	$-0.357898\pi$
$642$		0			0
$643$	−361978.	−	208988.i	−0.875509	−	0.505476i	−0.00633423	−	0.999980i	$-0.502016\pi$
$643$	−361978.	−	208988.i	−0.875509	−	0.505476i	−0.869175	+	0.494504i	$0.835350\pi$
$644$	−289733.	+	352530.i	−0.698596	+	0.850010i
$645$		0			0
$646$	−124450.	−	263368.i	−0.298214	−	0.631101i
$647$		−	825841.i		−	1.97282i	−0.164299	−	0.986411i	$-0.552536\pi$
$647$		−	825841.i		−	1.97282i	0.164299	−	0.986411i	$-0.447464\pi$
$648$		0			0
$649$	−229610.			−0.545131
$650$	−261913.	+	123762.i	−0.619913	+	0.292928i
$651$		0			0
$652$	381258.	+	313344.i	0.896859	+	0.737100i
$653$	164273.	−	284529.i	0.385247	−	0.667267i	−0.606557	−	0.795040i	$-0.707450\pi$
$653$	164273.	−	284529.i	0.385247	−	0.667267i	0.991803	+	0.127773i	$0.0407830\pi$
$654$		0			0
$655$	41049.6	−	23700.0i	0.0956811	−	0.0552415i
$656$	694972.	+	237013.i	1.61495	+	0.550762i
$657$		0			0
$658$	−18058.5	+	219282.i	−0.0417090	+	0.506467i
$659$	144939.	−	83680.3i	0.333744	−	0.192687i	−0.323758	−	0.946140i	$-0.604946\pi$
$659$	144939.	−	83680.3i	0.333744	−	0.192687i	0.657502	+	0.753453i	$0.271613\pi$
$660$		0			0
$661$	152616.	−	264339.i	0.349300	−	0.605005i	−0.636826	−	0.771008i	$-0.719753\pi$
$661$	152616.	−	264339.i	0.349300	−	0.605005i	0.986125	+	0.166003i	$0.0530862\pi$
$662$	350154.	−	505539.i	0.798994	−	1.15356i
$663$		0			0
$664$	52670.6	+	185190.i	0.119463	+	0.420032i
$665$	−175261.			−0.396317
$666$		0			0
$667$			402461.i			0.904633i
$668$	−236641.	+	88873.4i	−0.530318	+	0.199168i
$669$		0			0
$670$	52931.6	−	76420.5i	0.117914	−	0.170240i
$671$	6127.32	+	3537.61i	0.0136090	+	0.00785715i
$672$		0			0
$673$	−403032.	−	698073.i	−0.889836	−	1.54124i	−0.840069	−	0.542480i	$-0.817485\pi$
$673$	−403032.	−	698073.i	−0.889836	−	1.54124i	−0.0497671	−	0.998761i	$-0.515848\pi$
$674$	−7532.41	+	91465.0i	−0.0165811	+	0.201342i
$675$		0			0
$676$	215355.	+	35712.5i	0.471262	+	0.0781496i
$677$	−183117.	−	317169.i	−0.399533	−	0.692011i	0.594136	−	0.804365i	$-0.297494\pi$
$677$	−183117.	−	317169.i	−0.399533	−	0.692011i	−0.993668	+	0.112354i	$0.964161\pi$
$678$		0			0
$679$	−217400.	−	125516.i	−0.471542	−	0.272245i
$680$	31909.5	+	30947.9i	0.0690084	+	0.0669288i
$681$		0			0
$682$	226025.	−	106804.i	0.485946	−	0.229624i
$683$			398332.i			0.853894i	0.904277	+	0.426947i	$0.140411\pi$
$683$			398332.i			0.853894i	−0.904277	+	0.426947i	$0.859589\pi$
$684$		0			0
$685$	−169460.			−0.361148
$686$	185609.	+	392797.i	0.394412	+	0.834680i
$687$		0			0
$688$	−378244.	−	432543.i	−0.799089	−	0.913802i
$689$	290235.	−	502701.i	0.611379	−	1.05894i
$690$		0			0
$691$	−304679.	+	175906.i	−0.638096	+	0.368405i	−0.783881	−	0.620912i	$-0.786763\pi$
$691$	−304679.	+	175906.i	−0.638096	+	0.368405i	0.145785	+	0.989316i	$0.453429\pi$
$692$	742860.	+	123189.i	1.55130	+	0.257252i
$693$		0			0
$694$	−28820.2	−	2373.42i	−0.0598381	−	0.00492784i
$695$	−116927.	+	67507.8i	−0.242072	+	0.139760i
$696$		0			0
$697$	−175932.	+	304723.i	−0.362143	+	0.627249i
$698$	363568.	+	251820.i	0.746233	+	0.516868i
$699$		0			0
$700$	−463127.	+	173933.i	−0.945156	+	0.354965i
$701$	620142.			1.26199			0.630994	−	0.775788i	$-0.282647\pi$
$701$	620142.			1.26199			0.630994	+	0.775788i	$0.282647\pi$
$702$		0			0
$703$			1.35898e6i			2.74980i
$704$	−436691.	+	13364.3i	−0.881107	+	0.0269650i
$705$		0			0
$706$	202568.	+	140306.i	0.406408	+	0.281493i
$707$	317061.	+	183055.i	0.634314	+	0.366222i
$708$		0			0
$709$	−157448.	−	272708.i	−0.313217	−	0.542508i	0.665840	−	0.746095i	$-0.268073\pi$
$709$	−157448.	−	272708.i	−0.313217	−	0.542508i	−0.979057	+	0.203587i	$0.934740\pi$
$710$	113569.	+	9352.70i	0.225290	+	0.0185533i
$711$		0			0
$712$	49760.9	−	197762.i	0.0981585	−	0.390107i
$713$	−160228.	−	277523.i	−0.315181	−	0.545909i
$714$		0			0
$715$	−63878.0	−	36880.0i	−0.124951	−	0.0721404i
$716$	−31467.2	−	25861.9i	−0.0613807	−	0.0504469i
$717$		0			0
$718$	144341.	+	305465.i	0.279990	+	0.592533i
$719$			361941.i			0.700132i	0.936725	+	0.350066i	$0.113841\pi$
$719$			361941.i			0.700132i	−0.936725	+	0.350066i	$0.886159\pi$
$720$		0			0
$721$	−111926.			−0.215308
$722$	803126.	−	379501.i	1.54067	−	0.728013i
$723$		0			0
$724$	57668.8	−	70167.9i	0.110018	−	0.133863i
$725$	−218164.	+	377870.i	−0.415056	+	0.718897i
$726$		0			0
$727$	267542.	−	154465.i	0.506200	−	0.292255i	−0.225070	−	0.974343i	$-0.572261\pi$
$727$	267542.	−	154465.i	0.506200	−	0.292255i	0.731270	+	0.682088i	$0.238928\pi$
$728$	−395289.	−	99462.6i	−0.745852	−	0.187671i
$729$		0			0
$730$	−5028.29	+	61057.9i	−0.00943572	+	0.114577i
$731$	238457.	−	137673.i	0.446247	−	0.257641i
$732$		0			0
$733$	−441272.	+	764305.i	−0.821293	+	1.42252i	0.0834259	+	0.996514i	$0.473414\pi$
$733$	−441272.	+	764305.i	−0.821293	+	1.42252i	−0.904719	+	0.426008i	$0.859920\pi$
$734$	−423464.	+	611380.i	−0.786002	+	1.13480i
$735$		0			0
$736$	63018.1	+	556492.i	0.116335	+	1.02731i
$737$	−437829.			−0.806065
$738$		0			0
$739$			396910.i			0.726781i	0.931637	+	0.363390i	$0.118381\pi$
$739$			396910.i			0.726781i	−0.931637	+	0.363390i	$0.881619\pi$
$740$	−72913.3	−	194144.i	−0.133151	−	0.354537i
$741$		0			0
$742$	564444.	−	814923.i	1.02521	−	1.48016i
$743$	831366.	+	479989.i	1.50596	+	0.869469i	0.999976	+	0.00692819i	$0.00220533\pi$
$743$	831366.	+	479989.i	1.50596	+	0.869469i	0.505988	+	0.862541i	$0.331128\pi$
$744$		0			0
$745$	−14930.1	−	25859.7i	−0.0268999	−	0.0465920i
$746$	−27935.5	+	339217.i	−0.0501971	+	0.609536i
$747$		0			0
$748$	34250.5	−	206539.i	0.0612158	−	0.369147i
$749$	−361023.	−	625310.i	−0.643534	−	1.11463i
$750$		0			0
$751$	−572212.	−	330367.i	−1.01456	−	0.585756i	−0.102036	−	0.994781i	$-0.532536\pi$
$751$	−572212.	−	330367.i	−1.01456	−	0.585756i	−0.912523	+	0.409025i	$0.865869\pi$
$752$	177763.	+	203282.i	0.314344	+	0.359470i
$753$		0			0
$754$	−325044.	+	153593.i	−0.571742	+	0.270165i
$755$		−	189241.i		−	0.331987i
$756$		0			0
$757$	326842.			0.570356			0.285178	−	0.958475i	$-0.407947\pi$
$757$	326842.			0.570356			0.285178	+	0.958475i	$0.407947\pi$
$758$	251183.	+	531570.i	0.437171	+	0.925171i
$759$		0			0
$760$	−149757.	+	154410.i	−0.259274	+	0.267330i
$761$	164813.	−	285464.i	0.284591	−	0.492927i	−0.687919	−	0.725788i	$-0.741475\pi$
$761$	164813.	−	285464.i	0.284591	−	0.492927i	0.972510	+	0.232861i	$0.0748088\pi$
$762$		0			0
$763$	875410.	−	505418.i	1.50370	−	0.868164i
$764$	85013.7	−	512654.i	0.145647	−	0.878290i
$765$		0			0
$766$	742285.	+	61129.3i	1.26507	+	0.104182i
$767$	−227694.	+	131459.i	−0.387044	+	0.223460i
$768$		0			0
$769$	299738.	−	519162.i	0.506862	−	0.877910i	−0.493107	−	0.869969i	$-0.664139\pi$
$769$	299738.	−	519162.i	0.506862	−	0.877910i	0.999968	−	0.00794129i	$-0.00252782\pi$
$770$	−103552.	−	71723.7i	−0.174653	−	0.120971i
$771$		0			0
$772$	4429.60	+	11794.6i	0.00743241	+	0.0197901i
$773$	58555.0			0.0979952			0.0489976	−	0.998799i	$-0.484397\pi$
$773$	58555.0			0.0979952			0.0489976	+	0.998799i	$0.484397\pi$
$774$		0			0
$775$		−	347422.i		−	0.578433i
$776$	−296347.	+	84285.0i	−0.492127	+	0.139967i
$777$		0			0
$778$	841808.	+	583066.i	1.39077	+	0.963294i
$779$	−1.47456e6	−	851336.i	−2.42989	−	1.40290i
$780$		0			0
$781$	−268347.	−	464791.i	−0.439942	−	0.762002i
$782$	−267469.	−	22026.9i	−0.437381	−	0.0360196i
$783$		0			0
$784$	−77091.2	−	26291.1i	−0.125422	−	0.0427737i
$785$	48129.6	+	83362.8i	0.0781039	+	0.135280i
$786$		0			0
$787$	553254.	+	319421.i	0.893254	+	0.515720i	0.875005	−	0.484113i	$-0.160858\pi$
$787$	553254.	+	319421.i	0.893254	+	0.515720i	0.0182482	+	0.999833i	$0.494191\pi$
$788$	−252208.	+	306872.i	−0.406169	+	0.494202i
$789$		0			0
$790$	13362.6	+	28278.8i	0.0214110	+	0.0453113i
$791$			710975.i			1.13632i
$792$		0			0
$793$	8101.59			0.0128832
$794$	942966.	−	445580.i	1.49574	−	0.706781i
$795$		0			0
$796$	−148436.	−	121995.i	−0.234269	−	0.192538i
$797$	−587628.	+	1.01780e6i	−0.925095	+	1.60231i	−0.133686	+	0.991024i	$0.542681\pi$
$797$	−587628.	+	1.01780e6i	−0.925095	+	1.60231i	−0.791409	+	0.611287i	$0.790652\pi$
$798$		0			0
$799$	−112067.	+	64702.1i	−0.175544	+	0.101350i
$800$	−242492.	+	556649.i	−0.378893	+	0.869765i
$801$		0			0
$802$	−17404.5	+	211340.i	−0.0270591	+	0.328574i
$803$	249886.	−	144272.i	0.387535	−	0.223743i
$804$		0			0
$805$	−80736.4	+	139840.i	−0.124588	+	0.215793i
$806$	162991.	−	235319.i	0.250895	−	0.362233i
$807$		0			0
$808$	432199.	−	122923.i	0.662005	−	0.188283i
$809$	215543.			0.329334			0.164667	−	0.986349i	$-0.447345\pi$
$809$	215543.			0.329334			0.164667	+	0.986349i	$0.447345\pi$
$810$		0			0
$811$		−	1.05773e6i		−	1.60817i	−0.594512	−	0.804087i	$-0.702655\pi$
$811$		−	1.05773e6i		−	1.60817i	0.594512	−	0.804087i	$-0.297345\pi$
$812$	−574758.	+	215858.i	−0.871712	+	0.327382i
$813$		0			0
$814$	−556146.	+	802942.i	−0.839345	+	1.21181i
$815$	151236.	+	87315.9i	0.227687	+	0.131455i
$816$		0			0
$817$	666201.	+	1.15389e6i	0.998070	+	1.72871i
$818$	48390.0	−	587594.i	0.0723185	−	0.878153i
$819$		0			0
$820$	256333.	+	42507.8i	0.381221	+	0.0632180i
$821$	−37925.7	−	65689.3i	−0.0562662	−	0.0974559i	0.836520	−	0.547936i	$-0.184586\pi$
$821$	−37925.7	−	65689.3i	−0.0562662	−	0.0974559i	−0.892787	+	0.450480i	$0.851253\pi$
$822$		0			0
$823$	−569508.	−	328806.i	−0.840815	−	0.485445i	0.0167265	−	0.999860i	$-0.494676\pi$
$823$	−569508.	−	328806.i	−0.840815	−	0.485445i	−0.857541	+	0.514416i	$0.828009\pi$
$824$	−95638.4	+	98610.1i	−0.140857	+	0.145234i
$825$		0			0
$826$	−405964.	+	191830.i	−0.595014	+	0.281162i
$827$		−	669017.i		−	0.978196i	−0.872229	−	0.489098i	$-0.837326\pi$
$827$		−	669017.i		−	0.978196i	0.872229	−	0.489098i	$-0.162674\pi$
$828$		0			0
$829$	−637042.			−0.926955			−0.463478	−	0.886109i	$-0.653399\pi$
$829$	−637042.			−0.926955			−0.463478	+	0.886109i	$0.653399\pi$
$830$	29107.9	+	61600.1i	0.0422527	+	0.0894180i
$831$		0			0
$832$	−425395.	+	263273.i	−0.614534	+	0.380328i
$833$	19515.6	−	33802.1i	0.0281250	−	0.0487139i
$834$		0			0
$835$	−77465.4	+	44724.7i	−0.111105	+	0.0641467i
$836$	999443.	+	165738.i	1.43003	+	0.237143i
$837$		0			0
$838$	−927231.	−	76360.1i	−1.32038	−	0.108737i
$839$	−872716.	+	503863.i	−1.23979	+	0.715795i	−0.969052	−	0.246858i	$-0.920602\pi$
$839$	−872716.	+	503863.i	−1.23979	+	0.715795i	−0.270741	+	0.962652i	$0.587269\pi$
$840$		0			0
$841$	82891.1	−	143572.i	0.117197	−	0.202991i
$842$	−229526.	−	158978.i	−0.323748	−	0.224240i
$843$		0			0
$844$	−445617.	+	167357.i	−0.625572	+	0.234941i
$845$	77247.2			0.108186
$846$		0			0
$847$		−	170194.i		−	0.237234i
$848$	−235664.	−	1.19362e6i	−0.327720	−	1.65988i
$849$		0			0
$850$	−239186.	−	165669.i	−0.331054	−	0.229299i
$851$	1.08432e6	+	626031.i	1.49726	+	0.864444i
$852$		0			0
$853$	96790.1	+	167645.i	0.133025	+	0.230406i	0.924841	−	0.380353i	$-0.124198\pi$
$853$	96790.1	+	167645.i	0.133025	+	0.230406i	−0.791816	+	0.610759i	$0.790864\pi$
$854$	13789.0	+	1135.56i	0.0189068	+	0.00155703i
$855$		0			0
$856$	−859402.	−	216242.i	−1.17287	−	0.295116i
$857$	461864.	+	799972.i	0.628858	+	1.08921i	0.987781	+	0.155847i	$0.0498107\pi$
$857$	461864.	+	799972.i	0.628858	+	1.08921i	−0.358923	+	0.933367i	$0.616856\pi$
$858$		0			0
$859$	628431.	+	362825.i	0.851670	+	0.491712i	0.861214	−	0.508243i	$-0.169705\pi$
$859$	628431.	+	362825.i	0.851670	+	0.491712i	−0.00954418	+	0.999954i	$0.503038\pi$
$860$	−157084.	−	129102.i	−0.212390	−	0.174557i
$861$		0			0
$862$	−252705.	−	534791.i	−0.340094	−	0.719730i
$863$		−	444700.i		−	0.597097i	−0.954394	−	0.298549i	$-0.903497\pi$
$863$		−	444700.i		−	0.597097i	0.954394	−	0.298549i	$-0.0965025\pi$
$864$		0			0
$865$	266461.			0.356124
$866$	−1.06634e6	+	503879.i	−1.42187	+	0.671878i
$867$		0			0
$868$	310396.	−	377671.i	0.411980	−	0.501272i
$869$	73653.9	−	127572.i	0.0975341	−	0.168934i
$870$		0			0
$871$	−434176.	+	250672.i	−0.572308	+	0.330422i
$872$	302731.	−	1.20313e6i	0.398129	−	1.58227i
$873$		0			0
$874$	106588.	−	1.29428e6i	0.139536	−	1.69436i
$875$	−311409.	+	179792.i	−0.406739	+	0.234831i
$876$		0			0
$877$	288301.	−	499353.i	0.374841	−	0.649244i	−0.615462	−	0.788167i	$-0.711031\pi$
$877$	288301.	−	499353.i	0.374841	−	0.649244i	0.990303	+	0.138922i	$0.0443638\pi$
$878$	164285.	−	237188.i	0.213113	−	0.307684i
$879$		0			0
$880$	−151673.	+	29945.8i	−0.195859	+	0.0386696i
$881$	1.16458e6			1.50044			0.750219	−	0.661190i	$-0.229948\pi$
$881$	1.16458e6			1.50044			0.750219	+	0.661190i	$0.229948\pi$
$882$		0			0
$883$		−	12142.2i		−	0.0155731i	−0.999970	−	0.00778655i	$-0.997521\pi$
$883$		−	12142.2i		−	0.0155731i	0.999970	−	0.00778655i	$-0.00247856\pi$
$884$	−84285.7	−	224425.i	−0.107857	−	0.287189i
$885$		0			0
$886$	434805.	−	627754.i	0.553894	−	0.799691i
$887$	−1.12130e6	−	647385.i	−1.42520	−	0.822840i	−0.428464	−	0.903559i	$-0.640945\pi$
$887$	−1.12130e6	−	647385.i	−1.42520	−	0.822840i	−0.996737	+	0.0807193i	$0.974278\pi$
$888$		0			0
$889$	−409071.	−	708532.i	−0.517601	−	0.896511i
$890$	5922.72	−	71918.8i	0.00747723	−	0.0907951i
$891$		0			0
$892$	138595.	−	835763.i	0.174188	−	1.05040i
$893$	−313094.	−	542294.i	−0.392619	−	0.680036i
$894$		0			0
$895$	−12482.2	−	7206.63i	−0.0155828	−	0.00899676i
$896$	−760930.	+	388467.i	−0.947826	+	0.483881i
$897$		0			0
$898$	697488.	−	329584.i	0.864937	−	0.408709i
$899$		−	431164.i		−	0.533485i
$900$		0			0
$901$	583026.			0.718188
$902$	−522832.	−	1.10645e6i	−0.642613	−	1.35994i
$903$		0			0
$904$	626389.	+	607512.i	0.766491	+	0.743393i
$905$	16069.9	−	27833.8i	0.0196207	−	0.0339841i
$906$		0			0
$907$	593065.	−	342406.i	0.720921	−	0.416224i	−0.0941708	−	0.995556i	$-0.530020\pi$
$907$	593065.	−	342406.i	0.720921	−	0.416224i	0.815091	+	0.579332i	$0.196687\pi$
$908$	−98513.1	+	594059.i	−0.119487	+	0.720540i
$909$		0			0
$910$	−143752.	−	11838.4i	−0.173593	−	0.0142958i
$911$	621519.	−	358834.i	0.748890	−	0.432372i	−0.0764028	−	0.997077i	$-0.524343\pi$
$911$	621519.	−	358834.i	0.748890	−	0.432372i	0.825293	+	0.564705i	$0.191010\pi$
$912$		0			0
$913$	160441.	−	277893.i	0.192475	−	0.333377i
$914$	−19484.0	−	13495.3i	−0.0233231	−	0.0161544i
$915$		0			0
$916$	−321987.	−	857345.i	−0.383749	−	1.02180i
$917$	−436556.			−0.519160
$918$		0			0
$919$		−	441444.i		−	0.522691i	−0.965245	−	0.261345i	$-0.915834\pi$
$919$		−	441444.i		−	0.522691i	0.965245	−	0.261345i	$-0.0841661\pi$
$920$	54215.1	+	190621.i	0.0640538	+	0.225214i
$921$		0			0
$922$	−416570.	−	288531.i	−0.490034	−	0.339415i
$923$	−532217.	−	307275.i	−0.624720	−	0.360682i
$924$		0			0
$925$	678710.	+	1.17556e6i	0.793232	+	1.37392i
$926$	−939108.	−	77338.2i	−1.09520	−	0.0901929i
$927$		0			0
$928$	−300941.	+	690823.i	−0.349451	+	0.802179i
$929$	633285.	+	1.09688e6i	0.733783	+	1.27095i	0.955255	+	0.295783i	$0.0955804\pi$
$929$	633285.	+	1.09688e6i	0.733783	+	1.27095i	−0.221472	+	0.975167i	$0.571086\pi$
$930$		0			0
$931$	163568.	+	94436.2i	0.188712	+	0.108953i
$932$	370488.	−	450788.i	0.426523	−	0.518968i
$933$		0			0
$934$	−167093.	−	353614.i	−0.191543	−	0.405355i
$935$		−	74084.8i		−	0.0847434i
$936$		0			0
$937$	377258.			0.429694			0.214847	−	0.976648i	$-0.431075\pi$
$937$	377258.			0.429694			0.214847	+	0.976648i	$0.431075\pi$
$938$	−774108.	+	365790.i	−0.879825	+	0.415744i
$939$		0			0
$940$	73824.5	+	60674.0i	0.0835497	+	0.0686668i
$941$	−645770.	+	1.11851e6i	−0.729288	+	1.26316i	0.227897	+	0.973685i	$0.426815\pi$
$941$	−645770.	+	1.11851e6i	−0.729288	+	1.26316i	−0.957185	+	0.289478i	$0.906518\pi$
$942$		0			0
$943$	−1.35855e6	+	784359.i	−1.52775	+	0.882046i
$944$	−177879.	+	521580.i	−0.199610	+	0.585298i
$945$		0			0
$946$	−78598.0	+	954405.i	−0.0878273	+	1.06647i
$947$	1.02088e6	−	589403.i	1.13834	−	0.657222i	0.192322	−	0.981332i	$-0.438398\pi$
$947$	1.02088e6	−	589403.i	1.13834	−	0.657222i	0.946019	+	0.324110i	$0.105065\pi$
$948$		0			0
$949$	165200.	−	286136.i	0.183434	−	0.317716i
$950$	801672.	−	1.15742e6i	0.888279	−	1.28246i
$951$		0			0
$952$	−111999.	−	393788.i	−0.123577	−	0.434499i
$953$	−613396.			−0.675391			−0.337695	−	0.941255i	$-0.609647\pi$
$953$	−613396.			−0.675391			−0.337695	+	0.941255i	$0.609647\pi$
$954$		0			0
$955$		−	183887.i		−	0.201625i
$956$	784231.	−	294528.i	0.858081	−	0.322263i
$957$		0			0
$958$	−918265.	+	1.32575e6i	−1.00055	+	1.44455i
$959$	1.35163e6	+	780367.i	1.46968	+	0.848519i
$960$		0			0
$961$	−290105.	−	502477.i	−0.314130	−	0.544089i
$962$	−91795.0	+	1.11465e6i	−0.0991903	+	1.20445i
$963$		0			0
$964$	213265.	+	35365.9i	0.229491	+	0.0380567i
$965$	2229.15	+	3861.01i	0.00239379	+	0.00414616i
$966$		0			0
$967$	41063.4	+	23708.0i	0.0439139	+	0.0253537i	0.521796	−	0.853070i	$-0.325262\pi$
$967$	41063.4	+	23708.0i	0.0439139	+	0.0253537i	−0.477882	+	0.878424i	$0.658595\pi$
$968$	−149946.	−	145427.i	−0.160023	−	0.155201i
$969$		0			0
$970$	−98574.2	+	46579.3i	−0.104766	+	0.0495051i
$971$		−	746340.i		−	0.791586i	−0.918340	−	0.395793i	$-0.870470\pi$
$971$		−	746340.i		−	0.791586i	0.918340	−	0.395793i	$-0.129530\pi$
$972$		0			0
$973$	1.24350e6			1.31347
$974$	333596.	+	705978.i	0.351644	+	0.744172i
$975$		0			0
$976$	12782.9	−	11178.2i	0.0134193	−	0.0117347i
$977$	−143356.	+	248299.i	−0.150185	+	0.260128i	−0.931295	−	0.364265i	$-0.881320\pi$
$977$	−143356.	+	248299.i	−0.150185	+	0.260128i	0.781111	+	0.624393i	$0.214654\pi$
$978$		0			0
$979$	−294335.	+	169934.i	−0.307098	+	0.177303i
$980$	−28434.2	−	4715.26i	−0.0296067	−	0.00490969i
$981$		0			0
$982$	−303523.	−	24996.0i	−0.314752	−	0.0259208i
$983$	−504643.	+	291356.i	−0.522249	+	0.301521i	−0.737854	−	0.674960i	$-0.764161\pi$
$983$	−504643.	+	291356.i	−0.522249	+	0.301521i	0.215605	+	0.976481i	$0.430828\pi$
$984$		0			0
$985$	−70279.8	+	121728.i	−0.0724366	+	0.125464i
$986$	−296839.	−	205601.i	−0.305329	−	0.211481i
$987$		0			0
$988$	1.08599e6	−	407859.i	1.11253	−	0.417826i
$989$	1.22758e6			1.25504
$990$		0			0
$991$			918794.i			0.935558i	0.883845	+	0.467779i	$0.154946\pi$
$991$			918794.i			0.935558i	−0.883845	+	0.467779i	$0.845054\pi$
$992$	−67512.3	−	596178.i	−0.0686056	−	0.605833i
$993$		0			0
$994$	−862770.	−	597585.i	−0.873217	−	0.604821i
$995$	−58881.0	−	33995.0i	−0.0594742	−	0.0343375i
$996$		0			0
$997$	697626.	+	1.20832e6i	0.701830	+	1.21561i	0.967823	+	0.251631i	$0.0809668\pi$
$997$	697626.	+	1.20832e6i	0.701830	+	1.21561i	−0.265993	+	0.963975i	$0.585700\pi$
$998$	58084.7	+	4783.45i	0.0583178	+	0.00480264i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	108.5.f.a.91.4		44
3.2	odd	2		36.5.f.a.31.19	yes	44
4.3	odd	2	inner	108.5.f.a.91.19		44
9.2	odd	6		36.5.f.a.7.4	✓	44
9.4	even	3		324.5.d.e.163.11		22
9.5	odd	6		324.5.d.f.163.12		22
9.7	even	3	inner	108.5.f.a.19.19		44
12.11	even	2		36.5.f.a.31.4	yes	44
36.7	odd	6	inner	108.5.f.a.19.4		44
36.11	even	6		36.5.f.a.7.19	yes	44
36.23	even	6		324.5.d.f.163.11		22
36.31	odd	6		324.5.d.e.163.12		22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
36.5.f.a.7.4	✓	44	9.2	odd	6
36.5.f.a.7.19	yes	44	36.11	even	6
36.5.f.a.31.4	yes	44	12.11	even	2
36.5.f.a.31.19	yes	44	3.2	odd	2
108.5.f.a.19.4		44	36.7	odd	6	inner
108.5.f.a.19.19		44	9.7	even	3	inner
108.5.f.a.91.4		44	1.1	even	1	trivial
108.5.f.a.91.19		44	4.3	odd	2	inner
324.5.d.e.163.11		22	9.4	even	3
324.5.d.e.163.12		22	36.31	odd	6
324.5.d.f.163.11		22	36.23	even	6
324.5.d.f.163.12		22	9.5	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 108 = 2^{2} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	108.f (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-3.61656 + 1.70894i) q^{2} +(10.1591 - 12.3610i) q^{4} +(2.83091 - 4.90328i) q^{5} +(-45.1595 + 26.0728i) q^{7} +(-15.6169 + 62.0654i) q^{8} +O(q^{10})\)	\(q+(-3.61656 + 1.70894i) q^{2} +(10.1591 - 12.3610i) q^{4} +(2.83091 - 4.90328i) q^{5} +(-45.1595 + 26.0728i) q^{7} +(-15.6169 + 62.0654i) q^{8} +(-1.85878 + 22.5709i) q^{10} +(92.3736 - 53.3319i) q^{11} +(61.0686 - 105.774i) q^{13} +(118.765 - 171.469i) q^{14} +(-49.5864 - 251.152i) q^{16} +122.675 q^{17} +593.624i q^{19} +(-31.8498 - 84.8055i) q^{20} +(-242.934 + 350.739i) q^{22} +(473.649 + 273.461i) q^{23} +(296.472 + 513.504i) q^{25} +(-40.0976 + 486.900i) q^{26} +(-136.493 + 823.090i) q^{28} +(367.933 + 637.279i) q^{29} +(-507.427 - 292.963i) q^{31} +(608.535 + 823.566i) q^{32} +(-443.662 + 209.644i) q^{34} +295.239i q^{35} +2289.29 q^{37} +(-1014.47 - 2146.88i) q^{38} +(260.114 + 252.275i) q^{40} +(-1434.13 + 2483.99i) q^{41} +(1943.81 - 1122.26i) q^{43} +(279.197 - 1683.63i) q^{44} +(-2180.31 - 179.555i) q^{46} +(-913.531 + 527.427i) q^{47} +(159.084 - 275.542i) q^{49} +(-1949.76 - 1350.47i) q^{50} +(-687.066 - 1829.43i) q^{52} +4752.60 q^{53} -603.911i q^{55} +(-912.971 - 3210.02i) q^{56} +(-2419.72 - 1675.99i) q^{58} +(-1864.25 - 1076.32i) q^{59} +(33.1660 + 57.4451i) q^{61} +(2335.80 + 192.360i) q^{62} +(-3608.23 - 1938.53i) q^{64} +(-345.759 - 598.872i) q^{65} +(-3554.82 - 2052.38i) q^{67} +(1246.26 - 1516.38i) q^{68} +(-504.545 - 1067.75i) q^{70} -5031.65i q^{71} +2705.16 q^{73} +(-8279.36 + 3912.25i) q^{74} +(7337.76 + 6030.67i) q^{76} +(-2781.03 + 4816.88i) q^{77} +(1196.02 - 690.524i) q^{79} +(-1371.84 - 467.852i) q^{80} +(941.652 - 11434.4i) q^{82} +(2605.31 - 1504.18i) q^{83} +(347.282 - 601.509i) q^{85} +(-5112.05 + 7380.57i) q^{86} +(1867.48 + 6566.08i) q^{88} -3186.35 q^{89} +6368.92i q^{91} +(8192.07 - 3076.64i) q^{92} +(2402.50 - 3468.64i) q^{94} +(2910.71 + 1680.50i) q^{95} +(2407.03 + 4169.10i) q^{97} +(-104.455 + 1268.38i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + q^{2} - q^{4} + 2 q^{5} - 122 q^{8}+O(q^{10}) \) 44 * q + q^2 - q^4 + 2 * q^5 - 122 * q^8	\( 44 q + q^{2} - q^{4} + 2 q^{5} - 122 q^{8} + 28 q^{10} - 2 q^{13} - 252 q^{14} - q^{16} + 56 q^{17} + 140 q^{20} - 33 q^{22} - 1752 q^{25} - 1096 q^{26} - 516 q^{28} - 526 q^{29} + 121 q^{32} + 385 q^{34} - 8 q^{37} - 1395 q^{38} - 2276 q^{40} + 2762 q^{41} - 6714 q^{44} + 3576 q^{46} + 3428 q^{49} - 6375 q^{50} + 1438 q^{52} + 10088 q^{53} + 7506 q^{56} - 4064 q^{58} - 2 q^{61} + 18324 q^{62} + 9026 q^{64} + 2014 q^{65} + 11405 q^{68} + 3666 q^{70} - 3416 q^{73} - 14620 q^{74} + 1581 q^{76} + 3942 q^{77} - 45520 q^{80} - 8486 q^{82} - 1252 q^{85} - 22113 q^{86} + 1995 q^{88} - 13048 q^{89} + 30294 q^{92} + 7524 q^{94} + 5638 q^{97} + 92938 q^{98}+O(q^{100}) \) 44 * q + q^2 - q^4 + 2 * q^5 - 122 * q^8 + 28 * q^10 - 2 * q^13 - 252 * q^14 - q^16 + 56 * q^17 + 140 * q^20 - 33 * q^22 - 1752 * q^25 - 1096 * q^26 - 516 * q^28 - 526 * q^29 + 121 * q^32 + 385 * q^34 - 8 * q^37 - 1395 * q^38 - 2276 * q^40 + 2762 * q^41 - 6714 * q^44 + 3576 * q^46 + 3428 * q^49 - 6375 * q^50 + 1438 * q^52 + 10088 * q^53 + 7506 * q^56 - 4064 * q^58 - 2 * q^61 + 18324 * q^62 + 9026 * q^64 + 2014 * q^65 + 11405 * q^68 + 3666 * q^70 - 3416 * q^73 - 14620 * q^74 + 1581 * q^76 + 3942 * q^77 - 45520 * q^80 - 8486 * q^82 - 1252 * q^85 - 22113 * q^86 + 1995 * q^88 - 13048 * q^89 + 30294 * q^92 + 7524 * q^94 + 5638 * q^97 + 92938 * q^98

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