LMFDB - Embedded newform 108.5.f.a.19.19

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			19.19
Character	$\chi$	$=$	108.19
Dual form			108.5.f.a.91.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.28826 + 2.27757i) q^{2} +(5.62536 + 14.9785i) q^{4} +(2.83091 + 4.90328i) q^{5} +(45.1595 + 26.0728i) q^{7} +(-15.6169 + 62.0654i) q^{8} +O(q^{10})$	\(q+(3.28826 + 2.27757i) q^{2} +(5.62536 + 14.9785i) q^{4} +(2.83091 + 4.90328i) q^{5} +(45.1595 + 26.0728i) q^{7} +(-15.6169 + 62.0654i) q^{8} +(-1.85878 + 22.5709i) q^{10} +(-92.3736 - 53.3319i) q^{11} +(61.0686 + 105.774i) q^{13} +(89.1136 + 188.588i) q^{14} +(-192.711 + 168.519i) q^{16} +122.675 q^{17} +593.624i q^{19} +(-57.5188 + 69.9855i) q^{20} +(-182.282 - 385.757i) q^{22} +(-473.649 + 273.461i) q^{23} +(296.472 - 513.504i) q^{25} +(-40.0976 + 486.900i) q^{26} +(-136.493 + 823.090i) q^{28} +(367.933 - 637.279i) q^{29} +(507.427 - 292.963i) q^{31} +(-1017.50 + 115.223i) q^{32} +(403.388 + 279.401i) q^{34} +295.239i q^{35} +2289.29 q^{37} +(-1352.02 + 1951.99i) q^{38} +(-348.534 + 99.1276i) q^{40} +(-1434.13 - 2483.99i) q^{41} +(-1943.81 - 1122.26i) q^{43} +(279.197 - 1683.63i) q^{44} +(-2180.31 - 179.555i) q^{46} +(913.531 + 527.427i) q^{47} +(159.084 + 275.542i) q^{49} +(2144.42 - 1013.30i) q^{50} +(-1240.80 + 1509.73i) q^{52} +4752.60 q^{53} -603.911i q^{55} +(-2323.47 + 2395.66i) q^{56} +(2661.31 - 1257.55i) q^{58} +(1864.25 - 1076.32i) q^{59} +(33.1660 - 57.4451i) q^{61} +(2335.80 + 192.360i) q^{62} +(-3608.23 - 1938.53i) q^{64} +(-345.759 + 598.872i) q^{65} +(3554.82 - 2052.38i) q^{67} +(690.091 + 1837.49i) q^{68} +(-672.427 + 970.824i) q^{70} -5031.65i q^{71} +2705.16 q^{73} +(7527.78 + 5214.01i) q^{74} +(-8891.60 + 3339.35i) q^{76} +(-2781.03 - 4816.88i) q^{77} +(-1196.02 - 690.524i) q^{79} +(-1371.84 - 467.852i) q^{80} +(941.652 - 11434.4i) q^{82} +(-2605.31 - 1504.18i) q^{83} +(347.282 + 601.509i) q^{85} +(-3835.74 - 8117.45i) q^{86} +(4752.65 - 4900.33i) q^{88} -3186.35 q^{89} +6368.92i q^{91} +(-6760.48 - 5556.22i) q^{92} +(1802.68 + 3814.95i) q^{94} +(-2910.71 + 1680.50i) q^{95} +(2407.03 - 4169.10i) q^{97} +(-104.455 + 1268.38i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/108\mathbb{Z}\right)^\times$.

$n$	$29$	$55$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$

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 $

$2$	3.28826	+	2.27757i	0.822066	+	0.569392i
$2$	3.28826	+	2.27757i	0.822066	+	0.569392i
$3$		0			0
$3$		0			0
$4$	5.62536	+	14.9785i	0.351585	+	0.936156i
$5$	2.83091	+	4.90328i	0.113236	+	0.196131i	0.917073	−	0.398718i	$-0.130545\pi$
$5$	2.83091	+	4.90328i	0.113236	+	0.196131i	−0.803837	+	0.594850i	$0.797212\pi$
$6$		0			0
$7$	45.1595	+	26.0728i	0.921621	+	0.532098i	0.884152	−	0.467199i	$-0.154737\pi$
$7$	45.1595	+	26.0728i	0.921621	+	0.532098i	0.0374695	+	0.999298i	$0.488070\pi$
$8$	−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	$-0.478624\pi$
$11$	−92.3736	−	53.3319i	−0.763418	−	0.440760i	−0.830522	+	0.556986i	$0.811958\pi$
$12$		0			0
$13$	61.0686	+	105.774i	0.361352	+	0.625881i	0.988184	−	0.153274i	$-0.0489818\pi$
$13$	61.0686	+	105.774i	0.361352	+	0.625881i	−0.626831	+	0.779155i	$0.715648\pi$
$14$	89.1136	+	188.588i	0.454661	+	0.962184i
$15$		0			0
$16$	−192.711	+	168.519i	−0.752776	+	0.658277i
$17$	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	$0.692750\pi$
$20$	−57.5188	+	69.9855i	−0.143797	+	0.174964i
$21$		0			0
$22$	−182.282	−	385.757i	−0.376615	−	0.797018i
$23$	−473.649	+	273.461i	−0.895366	+	0.516940i	−0.875694	−	0.482867i	$-0.839596\pi$
$23$	−473.649	+	273.461i	−0.895366	+	0.516940i	−0.0196720	+	0.999806i	$0.506262\pi$
$24$		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	−0.560001	−	0.828492i	$-0.689199\pi$
$29$	367.933	−	637.279i	0.437495	−	0.757763i	0.997496	+	0.0707290i	$0.0225326\pi$
$30$		0			0
$31$	507.427	−	292.963i	0.528020	−	0.304853i	−0.212190	−	0.977228i	$-0.568059\pi$
$31$	507.427	−	292.963i	0.528020	−	0.304853i	0.740210	+	0.672376i	$0.234726\pi$
$32$	−1017.50	+	115.223i	−0.993649	+	0.112523i
$33$		0			0
$34$	403.388	+	279.401i	0.348951	+	0.241696i
$35$			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	$0.184820\pi$
$38$	−1352.02	+	1951.99i	−0.936302	+	1.35180i
$39$		0			0
$40$	−348.534	+	99.1276i	−0.217834	+	0.0619548i
$41$	−1434.13	−	2483.99i	−0.853142	−	1.47769i	−0.878358	−	0.478004i	$-0.841360\pi$
$41$	−1434.13	−	2483.99i	−0.853142	−	1.47769i	0.0252152	−	0.999682i	$-0.491973\pi$
$42$		0			0
$43$	−1943.81	−	1122.26i	−1.05128	−	0.606955i	−0.128270	−	0.991739i	$-0.540943\pi$
$43$	−1943.81	−	1122.26i	−1.05128	−	0.606955i	−0.923007	+	0.384784i	$0.874276\pi$
$44$	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	$-0.256591\pi$
$47$	913.531	+	527.427i	0.413550	+	0.238763i	−0.278764	+	0.960360i	$0.589925\pi$
$48$		0			0
$49$	159.084	+	275.542i	0.0662574	+	0.114761i
$50$	2144.42	−	1013.30i	0.857768	−	0.405321i
$51$		0			0
$52$	−1240.80	+	1509.73i	−0.458876	+	0.558333i
$53$	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
$56$	−2323.47	+	2395.66i	−0.740902	+	0.763923i
$57$		0			0
$58$	2661.31	−	1257.55i	0.791114	−	0.373825i
$59$	1864.25	−	1076.32i	0.535549	−	0.309200i	−0.207724	−	0.978188i	$-0.566606\pi$
$59$	1864.25	−	1076.32i	0.535549	−	0.309200i	0.743273	+	0.668988i	$0.233272\pi$
$60$		0			0
$61$	33.1660	−	57.4451i	0.00891319	−	0.0154381i	−0.861534	−	0.507699i	$-0.830496\pi$
$61$	33.1660	−	57.4451i	0.00891319	−	0.0154381i	0.870448	+	0.492261i	$0.163829\pi$
$62$	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	$-0.515518\pi$
$67$	3554.82	−	2052.38i	0.791897	−	0.457202i	0.840630	+	0.541610i	$0.182185\pi$
$68$	690.091	+	1837.49i	0.149241	+	0.397380i
$69$		0			0
$70$	−672.427	+	970.824i	−0.137230	+	0.198127i
$71$		−	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	$0.418314\pi$
$74$	7527.78	+	5214.01i	1.37469	+	0.952157i
$75$		0			0
$76$	−8891.60	+	3339.35i	−1.53940	+	0.578143i
$77$	−2781.03	−	4816.88i	−0.469055	−	0.812427i
$78$		0			0
$79$	−1196.02	−	690.524i	−0.191639	−	0.110643i	0.401110	−	0.916030i	$-0.368624\pi$
$79$	−1196.02	−	690.524i	−0.191639	−	0.110643i	−0.592750	+	0.805387i	$0.701958\pi$
$80$	−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	$-0.403399\pi$
$83$	−2605.31	−	1504.18i	−0.378184	−	0.218345i	−0.677028	+	0.735957i	$0.736732\pi$
$84$		0			0
$85$	347.282	+	601.509i	0.0480667	+	0.0832539i
$86$	−3835.74	−	8117.45i	−0.518624	−	1.09755i
$87$		0			0
$88$	4752.65	−	4900.33i	0.613721	−	0.632790i
$89$	−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
$92$	−6760.48	−	5556.22i	−0.798734	−	0.656454i
$93$		0			0
$94$	1802.68	+	3814.95i	0.204015	+	0.431751i
$95$	−2910.71	+	1680.50i	−0.322516	+	0.186205i
$96$		0			0
$97$	2407.03	−	4169.10i	0.255822	−	0.443097i	−0.709296	−	0.704910i	$-0.750987\pi$
$97$	2407.03	−	4169.10i	0.255822	−	0.443097i	0.965118	+	0.261814i	$0.0843206\pi$
$98$	−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	−0.985195	−	0.171436i	$-0.945159\pi$
$101$	−3510.47	+	6080.30i	−0.344130	+	0.596050i	0.641066	+	0.767486i	$0.278493\pi$
$102$		0			0
$103$	−1858.85	+	1073.21i	−0.175214	+	0.101160i	−0.585042	−	0.811003i	$-0.698922\pi$
$103$	−1858.85	+	1073.21i	−0.175214	+	0.101160i	0.409828	+	0.912163i	$0.365589\pi$
$104$	−7518.59	+	2138.39i	−0.695136	+	0.197706i
$105$		0			0
$106$	15627.8	+	10824.4i	1.39087	+	0.963366i
$107$			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	$0.803699\pi$
$110$	1375.45	−	1985.82i	0.113674	−	0.164117i
$111$		0			0
$112$	−13096.5	+	2585.71i	−1.04404	+	0.206132i
$113$	6817.20	+	11807.7i	0.533887	+	0.924719i	0.999216	+	0.0395818i	$0.0126026\pi$
$113$	6817.20	+	11807.7i	0.533887	+	0.924719i	−0.465329	+	0.885138i	$0.654064\pi$
$114$		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
$122$	239.894	−	113.357i	0.0161176	−	0.00761603i
$123$		0			0
$124$	7242.61	+	5952.47i	0.471034	+	0.387128i
$125$	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	$0.838318\pi$
$128$	−7449.66	−	14592.4i	−0.454691	−	0.890649i
$129$		0			0
$130$	−2500.92	+	1181.76i	−0.147983	+	0.0699266i
$131$	−7250.25	+	4185.93i	−0.422484	+	0.243921i	−0.696140	−	0.717907i	$-0.745101\pi$
$131$	−7250.25	+	4185.93i	−0.422484	+	0.243921i	0.273656	+	0.961828i	$0.411767\pi$
$132$		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	0.124014	+	0.992280i	$0.460423\pi$
$137$	−14965.1	+	25920.4i	−0.797333	+	1.38102i	−0.921347	+	0.388741i	$0.872910\pi$
$138$		0			0
$139$	20651.8	−	11923.3i	1.06888	−	0.617118i	0.141005	−	0.990009i	$-0.454967\pi$
$139$	20651.8	−	11923.3i	1.06888	−	0.617118i	0.927875	+	0.372891i	$0.121633\pi$
$140$	−4422.24	+	1660.83i	−0.225624	+	0.0847361i
$141$		0			0
$142$	11459.9	−	16545.4i	0.568336	−	0.820541i
$143$		−	13027.6i		−	0.637078i
$144$		0			0
$145$	4166.34			0.198161
$146$	8895.30	+	6161.20i	0.417306	+	0.289041i
$147$		0			0
$148$	12878.1	+	34290.1i	0.587933	+	1.56547i
$149$	2636.98	+	4567.39i	0.118778	+	0.205729i	0.919284	−	0.393596i	$-0.128769\pi$
$149$	2636.98	+	4567.39i	0.118778	+	0.205729i	−0.800506	+	0.599325i	$0.795436\pi$
$150$		0			0
$151$	−28946.1	−	16712.0i	−1.26951	−	0.732951i	−0.294614	−	0.955616i	$-0.595191\pi$
$151$	−28946.1	−	16712.0i	−1.26951	−	0.732951i	−0.974895	+	0.222665i	$0.928524\pi$
$152$	−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	0.640459	−	0.767992i	$-0.278744\pi$
$157$	−8500.73	−	14723.7i	−0.344871	−	0.597334i	−0.985330	+	0.170658i	$0.945411\pi$
$158$	−2360.12	−	4994.65i	−0.0945410	−	0.200074i
$159$		0			0
$160$	−3445.41	−	4662.88i	−0.134586	−	0.182144i
$161$	−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	$0.802878\pi$
$164$	29138.9	−	35454.5i	1.08339	−	1.31821i
$165$		0			0
$166$	−5141.09	−	10879.9i	−0.186569	−	0.394829i
$167$	13682.1	−	7899.35i	0.490591	−	0.283243i	−0.234229	−	0.972181i	$-0.575257\pi$
$167$	13682.1	−	7899.35i	0.490591	−	0.283243i	0.724819	+	0.688939i	$0.241923\pi$
$168$		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	−0.142015	−	0.989865i	$-0.545358\pi$
$173$	23531.4	−	40757.6i	0.786241	−	1.36181i	0.928255	−	0.371944i	$-0.121309\pi$
$174$		0			0
$175$	26777.0	−	15459.7i	0.874352	−	0.504807i
$176$	26788.8	−	5289.07i	0.864825	−	0.170747i
$177$		0			0
$178$	−10477.6	−	7257.14i	−0.330690	−	0.229047i
$179$		−	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	$0.472388\pi$
$182$	−14505.6	+	20942.7i	−0.437920	+	0.632251i
$183$		0			0
$184$	−9575.56	−	33667.8i	−0.282832	−	0.994441i
$185$	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	$-0.480180\pi$
$191$	−28127.2	−	16239.2i	−0.771009	−	0.445142i	−0.833234	+	0.552920i	$0.813513\pi$
$192$		0			0
$193$	−393.717	−	681.937i	−0.0105699	−	0.0183075i	0.860692	−	0.509126i	$-0.170031\pi$
$193$	−393.717	−	681.937i	−0.0105699	−	0.0183075i	−0.871262	+	0.490818i	$0.836698\pi$
$194$	17410.3	−	8226.92i	0.462598	−	0.218592i
$195$		0			0
$196$	−3232.29	+	3932.86i	−0.0841393	+	0.102376i
$197$	−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	$-0.0484485\pi$
$200$	27240.9	+	26420.0i	0.681022	+	0.660499i
$201$		0			0
$202$	−25391.6	+	11998.3i	−0.622283	+	0.294048i
$203$	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	$-0.558229\pi$
$211$	25764.7	−	14875.2i	0.578708	−	0.334117i	0.760620	+	0.649198i	$0.224895\pi$
$212$	26735.1	+	71186.9i	0.594854	+	1.58390i
$213$		0			0
$214$	−31536.9	+	45531.7i	−0.688638	+	0.994228i
$215$		−	12708.1i		−	0.274917i
$216$		0			0
$217$	30553.5			0.648846
$218$	−63742.6	−	44150.4i	−1.34127	−	0.929012i
$219$		0			0
$220$	9045.68	−	3397.22i	0.186894	−	0.0701905i
$221$	7491.58	+	12975.8i	0.153387	+	0.265674i
$222$		0			0
$223$	−45854.8	−	26474.3i	−0.922093	−	0.532371i	−0.0377910	−	0.999286i	$-0.512032\pi$
$223$	−45854.8	−	26474.3i	−0.922093	−	0.532371i	−0.884302	+	0.466915i	$0.845365\pi$
$224$	−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	$-0.214337\pi$
$227$	32593.5	+	18817.9i	0.632528	+	0.365190i	−0.149203	+	0.988807i	$0.547671\pi$
$228$		0			0
$229$	28619.2	+	49569.9i	0.545741	+	0.945251i	0.998560	+	0.0536486i	$0.0170851\pi$
$229$	28619.2	+	49569.9i	0.545741	+	0.945251i	−0.452819	+	0.891603i	$0.649582\pi$
$230$	−5291.85	−	11199.0i	−0.100035	−	0.211701i
$231$		0			0
$232$	33807.0	+	32788.2i	0.628102	+	0.609174i
$233$	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
$236$	26608.8	+	21868.9i	0.477750	+	0.392648i
$237$		0			0
$238$	10932.0	+	23135.0i	0.192995	+	0.408429i
$239$	−45342.6	+	26178.6i	−0.793799	+	0.458300i	−0.841298	−	0.540571i	$-0.818208\pi$
$239$	−45342.6	+	26178.6i	−0.793799	+	0.458300i	0.0474993	+	0.998871i	$0.484875\pi$
$240$		0			0
$241$	6755.56	−	11701.0i	0.116313	−	0.201460i	−0.801991	−	0.597336i	$-0.796226\pi$
$241$	6755.56	−	11701.0i	0.116313	−	0.201460i	0.918304	+	0.395877i	$0.129559\pi$
$242$	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
$248$	10258.5	+	36068.9i	0.166793	+	0.586447i
$249$		0			0
$250$	22675.1	+	15705.6i	0.362802	+	0.251290i
$251$			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
$254$	−35734.0	+	51591.4i	−0.553879	+	0.799668i
$255$		0			0
$256$	8738.74	−	64950.8i	0.133343	−	0.991070i
$257$	−36956.5	−	64010.6i	−0.559532	−	0.969138i	−0.997535	−	0.0701645i	$-0.977648\pi$
$257$	−36956.5	−	64010.6i	−0.559532	−	0.969138i	0.438003	−	0.898973i	$-0.355686\pi$
$258$		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	$-0.350295\pi$
$263$	−6380.84	−	3683.98i	−0.0922500	−	0.0532606i	−0.545415	+	0.838166i	$0.683628\pi$
$264$		0			0
$265$	13454.2	+	23303.3i	0.191587	+	0.331838i
$266$	−111950.	+	52900.0i	−1.58220	+	0.747639i
$267$		0			0
$268$	50738.7	+	41700.5i	0.706431	+	0.580593i
$269$	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	$-0.0272094\pi$
$272$	−23640.8	+	20673.1i	−0.319539	+	0.279426i
$273$		0			0
$274$	−108245.	+	51148.9i	−1.44180	+	0.681295i
$275$	−54772.4	+	31622.8i	−0.724263	+	0.418153i
$276$		0			0
$277$	46052.4	−	79765.0i	0.600195	−	1.03957i	−0.392596	−	0.919711i	$-0.628423\pi$
$277$	46052.4	−	79765.0i	0.600195	−	1.03957i	0.992791	−	0.119857i	$-0.0382436\pi$
$278$	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	−0.786759	−	0.617260i	$-0.788243\pi$
$281$	11148.0	−	19308.8i	0.141183	−	0.244537i	0.927942	+	0.372723i	$0.121576\pi$
$282$		0			0
$283$	−21648.6	+	12498.8i	−0.270307	+	0.156062i	−0.629027	−	0.777383i	$-0.716547\pi$
$283$	−21648.6	+	12498.8i	−0.270307	+	0.156062i	0.358720	+	0.933445i	$0.383213\pi$
$284$	75366.5	−	28304.8i	0.934419	−	0.350933i
$285$		0			0
$286$	29671.3	−	42838.2i	0.362747	−	0.523720i
$287$		−	149568.i		−	1.81582i
$288$		0			0
$289$	−68471.9			−0.819816
$290$	13700.0	+	9489.12i	0.162902	+	0.112831i
$291$		0			0
$292$	15217.5	+	40519.3i	0.178475	+	0.475222i
$293$	−11748.6	−	20349.1i	−0.136852	−	0.237034i	0.789452	−	0.613813i	$-0.210365\pi$
$293$	−11748.6	−	20349.1i	−0.136852	−	0.237034i	−0.926303	+	0.376779i	$0.877032\pi$
$294$		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
$302$	−57119.6	−	120880.i	−0.626283	−	1.32538i
$303$		0			0
$304$	−100037.	−	114398.i	−1.08246	−	1.23786i
$305$	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	$-0.0544031\pi$
$308$	56505.3	−	68752.3i	0.595646	−	0.724746i
$309$		0			0
$310$	5669.24	+	11997.6i	0.0589931	+	0.124845i
$311$	61441.4	−	35473.2i	0.635244	−	0.366758i	−0.147536	−	0.989057i	$-0.547134\pi$
$311$	61441.4	−	35473.2i	0.635244	−	0.366758i	0.782780	+	0.622298i	$0.213801\pi$
$312$		0			0
$313$	−59259.6	+	102641.i	−0.604882	+	1.04769i	0.387189	+	0.922001i	$0.373446\pi$
$313$	−59259.6	+	102641.i	−0.604882	+	1.04769i	−0.992070	+	0.125685i	$0.959887\pi$
$314$	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	0.307100	+	0.951677i	$0.400641\pi$
$317$	−67390.6	+	116724.i	−0.670626	+	1.16156i	−0.977727	+	0.209882i	$0.932692\pi$
$318$		0			0
$319$	−67974.6	+	39245.2i	−0.667983	+	0.385660i
$320$	−709.388	−	23180.0i	−0.00692762	−	0.226367i
$321$		0			0
$322$	−93780.0	−	64955.4i	−0.904479	−	0.626474i
$323$			72822.8i			0.698011i
$324$		0			0
$325$	72420.4			0.685637
$326$	−70248.8	+	101422.i	−0.661003	+	0.954331i
$327$		0			0
$328$	176567.	−	50217.8i	1.64120	−	0.466778i
$329$	27503.0	+	47636.7i	0.254091	+	0.440098i
$330$		0			0
$331$	133143.	+	76870.2i	1.21524	+	0.701620i	0.963896	−	0.266278i	$-0.0857939\pi$
$331$	133143.	+	76870.2i	1.21524	+	0.701620i	0.251345	+	0.967898i	$0.419127\pi$
$332$	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	0.912102	−	0.409964i	$-0.134459\pi$
$337$	11471.8	+	19869.8i	0.101012	+	0.174958i	−0.811090	+	0.584922i	$0.801125\pi$
$338$	49342.7	−	23315.9i	0.431906	−	0.204089i
$339$		0			0
$340$	−7056.12	+	8585.46i	−0.0610391	+	0.0742687i
$341$	−62497.2			−0.537467
$342$		0			0
$343$		−	108611.i		−	0.923175i
$344$	100010.	−	103117.i	0.845134	−	0.871393i
$345$		0			0
$346$	170206.	−	80427.3i	1.42174	−	0.671817i
$347$	−6260.87	+	3614.72i	−0.0519967	+	0.0300203i	−0.525773	−	0.850625i	$-0.676224\pi$
$347$	−6260.87	+	3614.72i	−0.0519967	+	0.0300203i	0.473776	+	0.880645i	$0.342891\pi$
$348$		0			0
$349$	−55282.6	+	95752.3i	−0.453877	+	0.786137i	−0.998623	−	0.0524636i	$-0.983293\pi$
$349$	−55282.6	+	95752.3i	−0.453877	+	0.786137i	0.544746	+	0.838601i	$0.316626\pi$
$350$	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	−0.962744	−	0.270414i	$-0.912840\pi$
$353$	−30801.7	+	53350.1i	−0.247187	+	0.428140i	0.715557	+	0.698554i	$0.246173\pi$
$354$		0			0
$355$	24671.6	−	14244.1i	0.195767	−	0.113026i
$356$	−17924.4	−	47726.8i	−0.141431	−	0.376584i
$357$		0			0
$358$	5797.99	−	8370.91i	0.0452388	−	0.0653141i
$359$		−	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
$362$	18666.1	+	12928.8i	0.142441	+	0.0986600i
$363$		0			0
$364$	−95396.8	+	35827.5i	−0.719998	+	0.270404i
$365$	7658.07	+	13264.2i	0.0574823	+	0.0995622i
$366$		0			0
$367$	−161018.	−	92963.9i	−1.19548	−	0.690212i	−0.235937	−	0.971768i	$-0.575816\pi$
$367$	−161018.	−	92963.9i	−1.19548	−	0.690212i	−0.959545	+	0.281556i	$0.909149\pi$
$368$	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	0.977439	−	0.211217i	$-0.0677428\pi$
$373$	42545.6	+	73691.2i	0.305800	+	0.529661i	−0.671639	+	0.740878i	$0.734409\pi$
$374$	−22361.4	−	47322.7i	−0.159866	−	0.338319i
$375$		0			0
$376$	−47001.5	+	48461.9i	−0.332457	+	0.342787i
$377$	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	$-0.170958\pi$
$380$	−41545.1	−	34144.6i	−0.287708	−	0.236458i
$381$		0			0
$382$	−55503.6	−	117460.i	−0.380360	−	0.804942i
$383$	161253.	−	93099.7i	1.09929	−	0.634674i	0.163254	−	0.986584i	$-0.447801\pi$
$383$	161253.	−	93099.7i	1.09929	−	0.634674i	0.936034	+	0.351910i	$0.114468\pi$
$384$		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	0.0389437	+	0.999241i	$0.487601\pi$
$389$	−128002.	+	221706.i	−0.845897	+	1.46514i	−0.884840	+	0.465894i	$0.845733\pi$
$390$		0			0
$391$	−58104.8	+	33546.8i	−0.380066	+	0.219431i
$392$	−19586.0	+	5570.52i	−0.127460	+	0.0362513i
$393$		0			0
$394$	−81634.1	−	56542.7i	−0.525871	−	0.364237i
$395$		−	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	$0.810044\pi$
$398$	27350.2	−	39487.1i	0.172661	−	0.249281i
$399$		0			0
$400$	29401.9	+	148919.i	0.183762	+	0.930743i
$401$	26507.0	+	45911.4i	0.164843	+	0.285517i	0.936600	−	0.350401i	$-0.113955\pi$
$401$	26507.0	+	45911.4i	0.164843	+	0.285517i	−0.771756	+	0.635918i	$0.780621\pi$
$402$		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	0.557168	−	0.830400i	$-0.311888\pi$
$409$	−73697.8	−	127648.i	−0.440563	−	0.763078i	−0.997731	+	0.0673220i	$0.978555\pi$
$410$	58731.5	−	27752.4i	0.349385	−	0.165095i
$411$		0			0
$412$	−26531.7	−	21805.6i	−0.156304	−	0.128462i
$413$	112251.			0.658099
$414$		0			0
$415$		−	17032.8i		−	0.0988983i
$416$	−74324.7	−	100588.i	−0.429483	−	0.581246i
$417$		0			0
$418$	228995.	−	108207.i	1.31061	−	0.619302i
$419$	−201431.	+	116296.i	−1.14736	+	0.662426i	−0.948242	−	0.317550i	$-0.897140\pi$
$419$	−201431.	+	116296.i	−1.14736	+	0.662426i	−0.199115	+	0.979976i	$0.563807\pi$
$420$		0			0
$421$	34900.8	−	60449.9i	0.196911	−	0.341060i	−0.750614	−	0.660741i	$-0.770242\pi$
$421$	34900.8	−	60449.9i	0.196911	−	0.341060i	0.947525	+	0.319680i	$0.103576\pi$
$422$	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
$428$	−207403.	+	77892.8i	−1.13221	+	0.425216i
$429$		0			0
$430$	28943.5	−	41787.5i	0.156536	−	0.226000i
$431$			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	$0.211988\pi$
$434$	100468.	+	69587.7i	0.533395	+	0.369448i
$435$		0			0
$436$	−109047.	−	290356.i	−0.573641	−	1.52742i
$437$	−162333.	−	281169.i	−0.850050	−	1.47233i
$438$		0			0
$439$	62468.0	+	36065.9i	0.324137	+	0.187140i	0.653235	−	0.757155i	$-0.273411\pi$
$439$	62468.0	+	36065.9i	0.324137	+	0.187140i	−0.329098	+	0.944296i	$0.606745\pi$
$440$	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	$-0.171647\pi$
$443$	165331.	+	95453.7i	0.842453	+	0.486391i	−0.0156440	+	0.999878i	$0.504980\pi$
$444$		0			0
$445$	−9020.28	−	15623.6i	−0.0455512	−	0.0788970i
$446$	−90485.7	−	191492.i	−0.454894	−	0.962677i
$447$		0			0
$448$	−112402.	−	181620.i	−0.560041	−	0.904914i
$449$	−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
$452$	−138513.	+	168534.i	−0.677975	+	0.824919i
$453$		0			0
$454$	64317.1	+	136112.i	0.312043	+	0.660367i
$455$	−31228.6	+	18029.8i	−0.150844	+	0.0870901i
$456$		0			0
$457$	2962.66	−	5131.48i	0.0141857	−	0.0245703i	−0.858845	−	0.512235i	$-0.828818\pi$
$457$	2962.66	−	5131.48i	0.0141857	−	0.0245703i	0.873031	+	0.487665i	$0.162151\pi$
$458$	−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	−0.677640	−	0.735394i	$-0.736997\pi$
$461$	63341.9	−	109711.i	0.298050	−	0.516238i	0.975690	+	0.219156i	$0.0703304\pi$
$462$		0			0
$463$	−204011.	+	117786.i	−0.951682	+	0.549454i	−0.893603	−	0.448858i	$-0.851831\pi$
$463$	−204011.	+	117786.i	−0.951682	+	0.549454i	−0.0580790	+	0.998312i	$0.518498\pi$
$464$	36488.9	+	184814.i	0.169483	+	0.858418i
$465$		0			0
$466$	119919.	+	83060.0i	0.552224	+	0.382490i
$467$			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
$470$	−13602.5	+	19638.8i	−0.0615778	+	0.0889036i
$471$		0			0
$472$	37688.8	+	132514.i	0.169172	+	0.594810i
$473$	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	−0.999669	−	0.0257398i	$-0.991806\pi$
$479$	−349162.	−	201589.i	−1.52179	−	0.878608i	−0.522126	−	0.852869i	$-0.674861\pi$
$480$		0			0
$481$	139803.	+	242147.i	0.604266	+	1.04662i
$482$	48863.8	−	23089.6i	0.210326	−	0.0993855i
$483$		0			0
$484$	33157.4	−	40344.0i	0.141543	−	0.172222i
$485$	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	$-0.135007\pi$
$488$	3047.41	+	2955.57i	0.0127965	+	0.0124109i
$489$		0			0
$490$	−6514.92	+	3078.49i	−0.0271342	+	0.0128217i
$491$	−65937.1	+	38068.8i	−0.273506	+	0.157909i	−0.630480	−	0.776206i	$-0.717142\pi$
$491$	−65937.1	+	38068.8i	−0.273506	+	0.157909i	0.356974	+	0.934114i	$0.383809\pi$
$492$		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	$-0.657352\pi$
$499$	12618.3	−	7285.17i	0.0506757	−	0.0292576i	0.525124	+	0.851026i	$0.324019\pi$
$500$	38791.2	+	103288.i	0.155165	+	0.413153i
$501$		0			0
$502$	−253514.	+	366014.i	−1.00599	+	1.45241i
$503$		−	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
$506$	191827.	+	132866.i	0.749219	+	0.518935i
$507$		0			0
$508$	−235006.	+	88259.4i	−0.910650	+	0.342006i
$509$	101505.	+	175811.i	0.391787	+	0.678595i	0.992685	−	0.120731i	$-0.0385238\pi$
$509$	101505.	+	175811.i	0.391787	+	0.678595i	−0.600899	+	0.799325i	$0.705190\pi$
$510$		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
$518$	204007.	+	431732.i	0.760300	+	1.60900i
$519$		0			0
$520$	−31769.6	−	30812.2i	−0.117491	−	0.113950i
$521$	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	$-0.0552109\pi$
$524$	−103484.	−	85050.4i	−0.376887	−	0.309752i
$525$		0			0
$526$	−12591.4	−	26646.7i	−0.0455095	−	0.0963101i
$527$	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
$536$	71866.5	+	252683.i	0.250148	+	0.879523i
$537$		0			0
$538$	126943.	+	87925.0i	0.438574	+	0.303772i
$539$		−	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	$0.408158\pi$
$542$	28561.4	−	41235.8i	0.0972257	−	0.140371i
$543$		0			0
$544$	−124821.	+	14135.0i	−0.421785	+	0.0477637i
$545$	−54876.8	−	95049.4i	−0.184755	−	0.320005i
$546$		0			0
$547$	−256245.	−	147943.i	−0.856410	−	0.494448i	0.00639865	−	0.999980i	$-0.497963\pi$
$547$	−256245.	−	147943.i	−0.856410	−	0.494448i	−0.862808	+	0.505531i	$0.831297\pi$
$548$	−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
$554$	333103.	−	157401.i	1.08532	−	0.512847i
$555$		0			0
$556$	294768.	+	242260.i	0.953521	+	0.783669i
$557$	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
$560$	−49753.4	−	56895.7i	−0.158652	−	0.181428i
$561$		0			0
$562$	80634.7	−	38102.3i	0.255299	−	0.120637i
$563$	210267.	−	121398.i	0.663369	−	0.382996i	−0.130191	−	0.991489i	$-0.541559\pi$
$563$	210267.	−	121398.i	0.663369	−	0.382996i	0.793559	+	0.608493i	$0.208226\pi$
$564$		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	−0.540339	−	0.841447i	$-0.681704\pi$
$569$	148459.	−	257138.i	0.458545	−	0.794223i	0.998884	+	0.0472242i	$0.0150375\pi$
$570$		0			0
$571$	228446.	−	131893.i	0.700665	−	0.404529i	−0.106930	−	0.994267i	$-0.534102\pi$
$571$	228446.	−	131893.i	0.700665	−	0.404529i	0.807595	+	0.589737i	$0.200769\pi$
$572$	195134.	−	73285.1i	0.596405	−	0.223987i
$573$		0			0
$574$	340650.	−	491818.i	1.03392	−	1.49273i
$575$			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	$0.323621\pi$
$578$	−225154.	−	155949.i	−0.673943	−	0.466797i
$579$		0			0
$580$	23437.2	+	62405.5i	0.0696705	+	0.185510i
$581$	−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	$-0.330151\pi$
$587$	5965.76	+	3444.33i	0.0173137	+	0.00999606i	−0.491318	+	0.870980i	$0.663485\pi$
$588$		0			0
$589$	173910.	+	301221.i	0.501296	+	0.868270i
$590$	20828.3	+	44078.3i	0.0598344	+	0.126625i
$591$		0			0
$592$	−441170.	+	385788.i	−1.25882	+	1.10079i
$593$	−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
$596$	−53578.6	+	65191.2i	−0.150834	+	0.183526i
$597$		0			0
$598$	−114156.	−	241585.i	−0.319225	−	0.675565i
$599$	122771.	−	70881.9i	0.342170	−	0.197552i	−0.319061	−	0.947734i	$-0.603367\pi$
$599$	122771.	−	70881.9i	0.342170	−	0.197552i	0.661231	+	0.750182i	$0.270034\pi$
$600$		0			0
$601$	265380.	−	459652.i	0.734715	−	1.27256i	−0.220133	−	0.975470i	$-0.570649\pi$
$601$	265380.	−	459652.i	0.734715	−	1.27256i	0.954848	−	0.297094i	$-0.0960176\pi$
$602$	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	$-0.649093\pi$
$607$	35215.7	−	20331.8i	0.0955782	−	0.0551821i	0.547027	+	0.837115i	$0.315759\pi$
$608$	−68399.3	−	604011.i	−0.185031	−	1.63395i
$609$		0			0
$610$	1234.94	+	855.362i	0.00331883	+	0.00229874i
$611$			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	$0.730879\pi$
$614$	73018.9	−	105422.i	0.193686	−	0.279636i
$615$		0			0
$616$	342393.	−	97381.0i	0.902325	−	0.256633i
$617$	−45030.4	−	77995.0i	−0.118287	−	0.204879i	0.800802	−	0.598929i	$-0.204407\pi$
$617$	−45030.4	−	77995.0i	−0.118287	−	0.204879i	−0.919089	+	0.394050i	$0.871074\pi$
$618$		0			0
$619$	−149379.	−	86244.1i	−0.389860	−	0.225086i	0.292240	−	0.956345i	$-0.405600\pi$
$619$	−149379.	−	86244.1i	−0.389860	−	0.225086i	−0.682099	+	0.731259i	$0.738933\pi$
$620$	−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
$626$	−428633.	+	202542.i	−1.09380	+	0.516852i
$627$		0			0
$628$	172719.	−	210154.i	0.437946	−	0.532867i
$629$	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	$0.914796\pi$
$632$	61535.7	−	63447.8i	0.154061	−	0.158848i
$633$		0			0
$634$	−487445.	+	230332.i	−1.21268	+	0.573029i
$635$	−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	0.431746	+	0.901995i	$0.357898\pi$
$641$	−232262.	+	402289.i	−0.565278	+	0.979089i	−0.997024	+	0.0770943i	$0.975436\pi$
$642$		0			0
$643$	361978.	−	208988.i	0.875509	−	0.505476i	0.00633423	−	0.999980i	$-0.497984\pi$
$643$	361978.	−	208988.i	0.875509	−	0.505476i	0.869175	+	0.494504i	$0.164650\pi$
$644$	−160433.	−	427181.i	−0.386832	−	1.03001i
$645$		0			0
$646$	−165859.	+	239461.i	−0.397442	+	0.573811i
$647$		−	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
$650$	238138.	+	164943.i	0.563639	+	0.390397i
$651$		0			0
$652$	−461993.	+	173507.i	−1.08678	+	0.408153i
$653$	164273.	+	284529.i	0.385247	+	0.667267i	0.991803	−	0.127773i	$-0.0407830\pi$
$653$	164273.	+	284529.i	0.385247	+	0.667267i	−0.606557	+	0.795040i	$0.707450\pi$
$654$		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	$-0.395054\pi$
$659$	−144939.	−	83680.3i	−0.333744	−	0.192687i	−0.657502	+	0.753453i	$0.728387\pi$
$660$		0			0
$661$	152616.	+	264339.i	0.349300	+	0.605005i	0.986125	−	0.166003i	$-0.0530862\pi$
$661$	152616.	+	264339.i	0.349300	+	0.605005i	−0.636826	+	0.771008i	$0.719753\pi$
$662$	262732.	+	556012.i	0.599512	+	1.26873i
$663$		0			0
$664$	134044.	−	138209.i	0.304027	−	0.313473i
$665$	−175261.			−0.396317
$666$		0			0
$667$			402461.i			0.904633i
$668$	195287.	+	160500.i	0.437644	+	0.359685i
$669$		0			0
$670$	39716.3	+	84050.4i	0.0884748	+	0.187236i
$671$	−6127.32	+	3537.61i	−0.0136090	+	0.00785715i
$672$		0			0
$673$	−403032.	+	698073.i	−0.889836	+	1.54124i	−0.0497671	+	0.998761i	$0.515848\pi$
$673$	−403032.	+	698073.i	−0.889836	+	1.54124i	−0.840069	+	0.542480i	$0.817485\pi$
$674$	−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	−0.993668	−	0.112354i	$-0.964161\pi$
$677$	−183117.	+	317169.i	−0.399533	+	0.692011i	0.594136	+	0.804365i	$0.297494\pi$
$678$		0			0
$679$	217400.	−	125516.i	0.471542	−	0.272245i
$680$	−42756.4	+	12160.5i	−0.0924662	+	0.0262986i
$681$		0			0
$682$	−205507.	−	142342.i	−0.441833	−	0.306029i
$683$			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
$686$	247368.	−	357140.i	0.525649	−	0.758911i
$687$		0			0
$688$	563715.	−	111298.i	1.19092	−	0.235130i
$689$	290235.	+	502701.i	0.611379	+	1.05894i
$690$		0			0
$691$	304679.	+	175906.i	0.638096	+	0.368405i	0.783881	−	0.620912i	$-0.213237\pi$
$691$	304679.	+	175906.i	0.638096	+	0.368405i	−0.145785	+	0.989316i	$0.546571\pi$
$692$	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
$698$	−399866.	+	188949.i	−0.820737	+	0.387823i
$699$		0			0
$700$	382194.	+	314113.i	0.779987	+	0.641047i
$701$	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
$704$	229919.	+	371503.i	0.463906	+	0.749579i
$705$		0			0
$706$	−222793.	+	105276.i	−0.446984	+	0.211213i
$707$	−317061.	+	183055.i	−0.634314	+	0.366222i
$708$		0			0
$709$	−157448.	+	272708.i	−0.313217	+	0.542508i	−0.979057	−	0.203587i	$-0.934740\pi$
$709$	−157448.	+	272708.i	−0.313217	+	0.542508i	0.665840	+	0.746095i	$0.268073\pi$
$710$	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
$716$	38130.7	−	14320.4i	0.0743786	−	0.0279338i
$717$		0			0
$718$	192370.	−	277736.i	0.373154	−	0.538745i
$719$			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
$722$	−730221.	−	505777.i	−1.40081	−	0.970252i
$723$		0			0
$724$	31932.8	+	85026.6i	0.0609200	+	0.162210i
$725$	−218164.	−	377870.i	−0.415056	−	0.718897i
$726$		0			0
$727$	−267542.	−	154465.i	−0.506200	−	0.292255i	0.225070	−	0.974343i	$-0.427739\pi$
$727$	−267542.	−	154465.i	−0.506200	−	0.292255i	−0.731270	+	0.682088i	$0.761072\pi$
$728$	−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	−0.904719	−	0.426008i	$-0.859920\pi$
$733$	−441272.	−	764305.i	−0.821293	−	1.42252i	0.0834259	−	0.996514i	$-0.473414\pi$
$734$	−317739.	−	672420.i	−0.589764	−	1.24810i
$735$		0			0
$736$	450427.	−	332821.i	0.831512	−	0.614406i
$737$	−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	$0.881619\pi$
$740$	−131677.	+	160217.i	−0.240462	+	0.292580i
$741$		0			0
$742$	423522.	+	896284.i	0.769250	+	1.62794i
$743$	−831366.	+	479989.i	−1.50596	+	0.869469i	−0.505988	+	0.862541i	$0.668872\pi$
$743$	−831366.	+	479989.i	−1.50596	+	0.869469i	−0.999976	+	0.00692819i	$0.997795\pi$
$744$		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	$-0.467464\pi$
$751$	572212.	−	330367.i	1.01456	−	0.585756i	0.912523	+	0.409025i	$0.134131\pi$
$752$	−264929.	+	52306.4i	−0.468482	+	0.0924952i
$753$		0			0
$754$	295538.	+	204700.i	0.519841	+	0.360060i
$755$		−	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	$0.407947\pi$
$758$	334762.	−	483316.i	0.582636	−	0.841187i
$759$		0			0
$760$	−58844.6	−	206898.i	−0.101878	−	0.358203i
$761$	164813.	+	285464.i	0.284591	+	0.492927i	0.972510	−	0.232861i	$-0.0748088\pi$
$761$	164813.	+	285464.i	0.284591	+	0.492927i	−0.687919	+	0.725788i	$0.741475\pi$
$762$		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	0.999968	+	0.00794129i	$0.00252782\pi$
$769$	299738.	+	519162.i	0.506862	+	0.877910i	−0.493107	+	0.869969i	$0.664139\pi$
$770$	113890.	−	53816.7i	0.192091	−	0.0907686i
$771$		0			0
$772$	7999.60	−	9733.43i	0.0134225	−	0.0163317i
$773$	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
$776$	221166.	+	214501.i	0.367279	+	0.356211i
$777$		0			0
$778$	−925854.	+	437494.i	−1.52962	+	0.722792i
$779$	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	$-0.839142\pi$
$787$	−553254.	+	319421.i	−0.893254	+	0.515720i	−0.0182482	+	0.999833i	$0.505809\pi$
$788$	−139655.	−	371855.i	−0.224907	−	0.598854i
$789$		0			0
$790$	17808.9	−	25711.7i	0.0285353	−	0.0411981i
$791$			710975.i			1.13632i
$792$		0			0
$793$	8101.59			0.0128832
$794$	−857367.	−	593843.i	−1.35996	−	0.941955i
$795$		0			0
$796$	179869.	−	67552.1i	0.283877	−	0.106614i
$797$	−587628.	−	1.01780e6i	−0.925095	−	1.60231i	−0.791409	−	0.611287i	$-0.790652\pi$
$797$	−587628.	−	1.01780e6i	−0.925095	−	1.60231i	−0.133686	−	0.991024i	$-0.542681\pi$
$798$		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
$806$	122297.	+	258814.i	0.188255	+	0.398398i
$807$		0			0
$808$	−322554.	−	312834.i	−0.494060	−	0.479171i
$809$	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	$-0.297345\pi$
$812$	474317.	+	389826.i	0.719377	+	0.591233i
$813$		0			0
$814$	−417295.	−	883108.i	−0.629788	−	1.33280i
$815$	−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	−0.892787	−	0.450480i	$-0.851253\pi$
$821$	−37925.7	+	65689.3i	−0.0562662	+	0.0974559i	0.836520	+	0.547936i	$0.184586\pi$
$822$		0			0
$823$	569508.	−	328806.i	0.840815	−	0.485445i	−0.0167265	−	0.999860i	$-0.505324\pi$
$823$	569508.	−	328806.i	0.840815	−	0.485445i	0.857541	+	0.514416i	$0.171991\pi$
$824$	−37579.6	−	132130.i	−0.0553475	−	0.194602i
$825$		0			0
$826$	369112.	+	255660.i	0.541000	+	0.374716i
$827$		−	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	$0.653399\pi$
$830$	38793.3	−	56008.2i	0.0563119	−	0.0813010i
$831$		0			0
$832$	−15303.0	−	500039.i	−0.0221070	−	0.722367i
$833$	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	$-0.0793980\pi$
$839$	872716.	+	503863.i	1.23979	+	0.715795i	0.270741	+	0.962652i	$0.412731\pi$
$840$		0			0
$841$	82891.1	+	143572.i	0.117197	+	0.202991i
$842$	252442.	−	119286.i	0.356071	−	0.168254i
$843$		0			0
$844$	367744.	+	302237.i	0.516251	+	0.424290i
$845$	77247.2			0.108186
$846$		0			0
$847$		−	170194.i		−	0.237234i
$848$	−915877.	+	800904.i	−1.27364	+	1.11375i
$849$		0			0
$850$	263067.	−	124307.i	0.364106	−	0.172051i
$851$	−1.08432e6	+	626031.i	−1.49726	+	0.864444i
$852$		0			0
$853$	96790.1	−	167645.i	0.133025	−	0.230406i	−0.791816	−	0.610759i	$-0.790864\pi$
$853$	96790.1	−	167645.i	0.133025	−	0.230406i	0.924841	+	0.380353i	$0.124198\pi$
$854$	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	−0.358923	−	0.933367i	$-0.616856\pi$
$857$	461864.	−	799972.i	0.628858	−	1.08921i	0.987781	−	0.155847i	$-0.0498107\pi$
$858$		0			0
$859$	−628431.	+	362825.i	−0.851670	+	0.491712i	−0.861214	−	0.508243i	$-0.830295\pi$
$859$	−628431.	+	362825.i	−0.851670	+	0.491712i	0.00954418	+	0.999954i	$0.496962\pi$
$860$	190348.	−	71487.4i	0.257366	−	0.0966569i
$861$		0			0
$862$	−336790.	+	486244.i	−0.453257	+	0.654395i
$863$		−	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
$866$	969543.	+	671540.i	1.29280	+	0.895439i
$867$		0			0
$868$	171875.	+	457646.i	0.228125	+	0.607421i
$869$	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	0.990303	−	0.138922i	$-0.0443638\pi$
$877$	288301.	+	499353.i	0.374841	+	0.649244i	−0.615462	+	0.788167i	$0.711031\pi$
$878$	123269.	+	260869.i	0.159906	+	0.338403i
$879$		0			0
$880$	101770.	+	116380.i	0.131419	+	0.150284i
$881$	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	$-0.00247856\pi$
$884$	−152215.	+	185206.i	−0.194784	+	0.237001i
$885$		0			0
$886$	326248.	+	690429.i	0.415605	+	0.879532i
$887$	1.12130e6	−	647385.i	1.42520	−	0.822840i	0.428464	−	0.903559i	$-0.359055\pi$
$887$	1.12130e6	−	647385.i	1.42520	−	0.822840i	0.996737	+	0.0807193i	$0.0257217\pi$
$888$		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
$896$	44042.5	−	853218.i	0.0548600	−	1.06278i
$897$		0			0
$898$	−634173.	−	439250.i	−0.786420	−	0.544703i
$899$		−	431164.i		−	0.533485i
$900$		0			0
$901$	583026.			0.718188
$902$	−696800.	+	1.00601e6i	−0.856436	+	1.23649i
$903$		0			0
$904$	−839316.	+	238712.i	−1.02704	+	0.292104i
$905$	16069.9	+	27833.8i	0.0196207	+	0.0339841i
$906$		0			0
$907$	−593065.	−	342406.i	−0.720921	−	0.416224i	0.0941708	−	0.995556i	$-0.469980\pi$
$907$	−593065.	−	342406.i	−0.720921	−	0.416224i	−0.815091	+	0.579332i	$0.803313\pi$
$908$	−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	$-0.475657\pi$
$911$	−621519.	−	358834.i	−0.748890	−	0.432372i	−0.825293	+	0.564705i	$0.808990\pi$
$912$		0			0
$913$	160441.	+	277893.i	0.192475	+	0.333377i
$914$	21429.3	−	10126.0i	0.0256517	−	0.0121212i
$915$		0			0
$916$	−581489.	+	707521.i	−0.693028	+	0.843235i
$917$	−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	$-0.0841661\pi$
$920$	137975.	−	142262.i	0.163014	−	0.168079i
$921$		0			0
$922$	458160.	−	216495.i	0.538959	−	0.254674i
$923$	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	−0.221472	−	0.975167i	$-0.571086\pi$
$929$	633285.	−	1.09688e6i	0.733783	−	1.27095i	0.955255	−	0.295783i	$-0.0955804\pi$
$930$		0			0
$931$	−163568.	+	94436.2i	−0.188712	+	0.108953i
$932$	205150.	+	546246.i	0.236178	+	0.628864i
$933$		0			0
$934$	−222692.	+	321514.i	−0.255277	+	0.368558i
$935$		−	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	$0.431075\pi$
$938$	703837.	+	487503.i	0.799957	+	0.554079i
$939$		0			0
$940$	−89457.5	+	33596.9i	−0.101242	+	0.0380227i
$941$	−645770.	−	1.11851e6i	−0.729288	−	1.26316i	−0.957185	−	0.289478i	$-0.906518\pi$
$941$	−645770.	−	1.11851e6i	−0.729288	−	1.26316i	0.227897	−	0.973685i	$-0.426815\pi$
$942$		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	$-0.561602\pi$
$947$	−1.02088e6	−	589403.i	−1.13834	−	0.657222i	−0.946019	+	0.324110i	$0.894935\pi$
$948$		0			0
$949$	165200.	+	286136.i	0.183434	+	0.317716i
$950$	601521.	+	1.27298e6i	0.666506	+	1.41050i
$951$		0			0
$952$	−285031.	+	293888.i	−0.314499	+	0.324271i
$953$	−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
$956$	−647184.	−	531900.i	−0.708128	−	0.581988i
$957$		0			0
$958$	−689005.	−	1.45812e6i	−0.750743	−	1.58877i
$959$	−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	$-0.674738\pi$
$967$	−41063.4	+	23708.0i	−0.0439139	+	0.0253537i	0.477882	+	0.878424i	$0.341405\pi$
$968$	200916.	−	57143.3i	0.214420	−	0.0609838i
$969$		0			0
$970$	89626.0	+	62078.1i	0.0952556	+	0.0659774i
$971$		−	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
$974$	444597.	−	641892.i	0.468650	−	0.676619i
$975$		0			0
$976$	3289.16	+	16659.4i	0.00345291	+	0.0174888i
$977$	−143356.	−	248299.i	−0.150185	−	0.260128i	0.781111	−	0.624393i	$-0.214654\pi$
$977$	−143356.	−	248299.i	−0.150185	−	0.260128i	−0.931295	+	0.364265i	$0.881320\pi$
$978$		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	$-0.235839\pi$
$983$	504643.	+	291356.i	0.522249	+	0.301521i	−0.215605	+	0.976481i	$0.569172\pi$
$984$		0			0
$985$	−70279.8	−	121728.i	−0.0724366	−	0.125464i
$986$	326476.	−	154270.i	0.335813	−	0.158682i
$987$		0			0
$988$	−896213.	−	736569.i	−0.918116	−	0.754570i
$989$	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	$0.845054\pi$
$992$	−482550.	+	356557.i	−0.490364	+	0.362331i
$993$		0			0
$994$	948909.	−	448388.i	0.960399	−	0.453818i
$995$	58881.0	−	33995.0i	0.0594742	−	0.0343375i
$996$		0			0
$997$	697626.	−	1.20832e6i	0.701830	−	1.21561i	−0.265993	−	0.963975i	$-0.585700\pi$
$997$	697626.	−	1.20832e6i	0.701830	−	1.21561i	0.967823	−	0.251631i	$-0.0809668\pi$
$998$	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.19.19		44
3.2	odd	2		36.5.f.a.7.4	✓	44
4.3	odd	2	inner	108.5.f.a.19.4		44
9.2	odd	6		324.5.d.f.163.12		22
9.4	even	3	inner	108.5.f.a.91.4		44
9.5	odd	6		36.5.f.a.31.19	yes	44
9.7	even	3		324.5.d.e.163.11		22
12.11	even	2		36.5.f.a.7.19	yes	44
36.7	odd	6		324.5.d.e.163.12		22
36.11	even	6		324.5.d.f.163.11		22
36.23	even	6		36.5.f.a.31.4	yes	44
36.31	odd	6	inner	108.5.f.a.91.19		44

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

\(f(q)\)	\(=\)	\(q+(3.28826 + 2.27757i) q^{2} +(5.62536 + 14.9785i) q^{4} +(2.83091 + 4.90328i) q^{5} +(45.1595 + 26.0728i) q^{7} +(-15.6169 + 62.0654i) q^{8} +O(q^{10})\)	\(q+(3.28826 + 2.27757i) q^{2} +(5.62536 + 14.9785i) q^{4} +(2.83091 + 4.90328i) q^{5} +(45.1595 + 26.0728i) q^{7} +(-15.6169 + 62.0654i) q^{8} +(-1.85878 + 22.5709i) q^{10} +(-92.3736 - 53.3319i) q^{11} +(61.0686 + 105.774i) q^{13} +(89.1136 + 188.588i) q^{14} +(-192.711 + 168.519i) q^{16} +122.675 q^{17} +593.624i q^{19} +(-57.5188 + 69.9855i) q^{20} +(-182.282 - 385.757i) q^{22} +(-473.649 + 273.461i) q^{23} +(296.472 - 513.504i) q^{25} +(-40.0976 + 486.900i) q^{26} +(-136.493 + 823.090i) q^{28} +(367.933 - 637.279i) q^{29} +(507.427 - 292.963i) q^{31} +(-1017.50 + 115.223i) q^{32} +(403.388 + 279.401i) q^{34} +295.239i q^{35} +2289.29 q^{37} +(-1352.02 + 1951.99i) q^{38} +(-348.534 + 99.1276i) q^{40} +(-1434.13 - 2483.99i) q^{41} +(-1943.81 - 1122.26i) q^{43} +(279.197 - 1683.63i) q^{44} +(-2180.31 - 179.555i) q^{46} +(913.531 + 527.427i) q^{47} +(159.084 + 275.542i) q^{49} +(2144.42 - 1013.30i) q^{50} +(-1240.80 + 1509.73i) q^{52} +4752.60 q^{53} -603.911i q^{55} +(-2323.47 + 2395.66i) q^{56} +(2661.31 - 1257.55i) q^{58} +(1864.25 - 1076.32i) q^{59} +(33.1660 - 57.4451i) q^{61} +(2335.80 + 192.360i) q^{62} +(-3608.23 - 1938.53i) q^{64} +(-345.759 + 598.872i) q^{65} +(3554.82 - 2052.38i) q^{67} +(690.091 + 1837.49i) q^{68} +(-672.427 + 970.824i) q^{70} -5031.65i q^{71} +2705.16 q^{73} +(7527.78 + 5214.01i) q^{74} +(-8891.60 + 3339.35i) q^{76} +(-2781.03 - 4816.88i) q^{77} +(-1196.02 - 690.524i) q^{79} +(-1371.84 - 467.852i) q^{80} +(941.652 - 11434.4i) q^{82} +(-2605.31 - 1504.18i) q^{83} +(347.282 + 601.509i) q^{85} +(-3835.74 - 8117.45i) q^{86} +(4752.65 - 4900.33i) q^{88} -3186.35 q^{89} +6368.92i q^{91} +(-6760.48 - 5556.22i) q^{92} +(1802.68 + 3814.95i) q^{94} +(-2910.71 + 1680.50i) q^{95} +(2407.03 - 4169.10i) q^{97} +(-104.455 + 1268.38i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + q^{2} - q^{4} + 2 q^{5} - 122 q^{8}+O(q^{10}) \) 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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